0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.36 % Computer : n025.cluster.edu 0.13/0.36 % Model : x86_64 x86_64 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.36 % Memory : 8042.1875MB 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.36 % CPULimit : 960 0.13/0.36 % DateTime : Thu Jul 2 14:19:24 EDT 2020 0.13/0.36 % CPUTime : 67.41/65.24 ============================== Prover9 =============================== 67.41/65.24 Prover9 (32) version 2009-11A, November 2009. 67.41/65.24 Process 6769 was started by sandbox2 on n025.cluster.edu, 67.41/65.24 Thu Jul 2 14:20:17 2020 67.41/65.24 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_6269_n025.cluster.edu". 67.41/65.24 ============================== end of head =========================== 67.41/65.24 67.41/65.24 ============================== INPUT ================================= 67.41/65.24 67.41/65.24 % Reading from file /tmp/Prover9_6269_n025.cluster.edu 67.41/65.24 67.41/65.24 set(prolog_style_variables). 67.41/65.24 set(auto2). 67.41/65.24 % set(auto2) -> set(auto). 67.41/65.24 % set(auto) -> set(auto_inference). 67.41/65.24 % set(auto) -> set(auto_setup). 67.41/65.24 % set(auto_setup) -> set(predicate_elim). 67.41/65.24 % set(auto_setup) -> assign(eq_defs, unfold). 67.41/65.24 % set(auto) -> set(auto_limits). 67.41/65.24 % set(auto_limits) -> assign(max_weight, "100.000"). 67.41/65.24 % set(auto_limits) -> assign(sos_limit, 20000). 67.41/65.24 % set(auto) -> set(auto_denials). 67.41/65.24 % set(auto) -> set(auto_process). 67.41/65.24 % set(auto2) -> assign(new_constants, 1). 67.41/65.24 % set(auto2) -> assign(fold_denial_max, 3). 67.41/65.24 % set(auto2) -> assign(max_weight, "200.000"). 67.41/65.24 % set(auto2) -> assign(max_hours, 1). 67.41/65.24 % assign(max_hours, 1) -> assign(max_seconds, 3600). 67.41/65.24 % set(auto2) -> assign(max_seconds, 0). 67.41/65.24 % set(auto2) -> assign(max_minutes, 5). 67.41/65.24 % assign(max_minutes, 5) -> assign(max_seconds, 300). 67.41/65.24 % set(auto2) -> set(sort_initial_sos). 67.41/65.24 % set(auto2) -> assign(sos_limit, -1). 67.41/65.24 % set(auto2) -> assign(lrs_ticks, 3000). 67.41/65.24 % set(auto2) -> assign(max_megs, 400). 67.41/65.24 % set(auto2) -> assign(stats, some). 67.41/65.24 % set(auto2) -> clear(echo_input). 67.41/65.24 % set(auto2) -> set(quiet). 67.41/65.24 % set(auto2) -> clear(print_initial_clauses). 67.41/65.24 % set(auto2) -> clear(print_given). 67.41/65.24 assign(lrs_ticks,-1). 67.41/65.24 assign(sos_limit,10000). 67.41/65.24 assign(order,kbo). 67.41/65.24 set(lex_order_vars). 67.41/65.24 clear(print_given). 67.41/65.24 67.41/65.24 % formulas(sos). % not echoed (34332 formulas) 67.41/65.24 67.41/65.24 ============================== end of input ========================== 67.41/65.24 67.41/65.24 % From the command line: assign(max_seconds, 960). 67.41/65.24 67.41/65.24 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 67.41/65.24 67.41/65.24 % Formulas that are not ordinary clauses: 67.41/65.24 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 2 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 3 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 4 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 5 (all A all B ((all C ((exists D (r2_hidden(C,D) & r2_hidden(D,A))) <-> r2_hidden(C,B))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 6 (all A all B all C (C = k2_tarski(A,B) <-> (all D (D = A | D = B <-> r2_hidden(D,C))))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 7 (all A all B k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 8 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 9 (all A all B all C (p1_s1_tarski(A,C) & p1_s1_tarski(A,B) -> B = C)) -> (exists A all B ((exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))) <-> r2_hidden(B,A))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 10 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 11 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 12 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 13 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 14 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 15 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 16 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 17 (all A all B (r2_tarski(A,B) <-> (exists C ((all D -((all E -(r2_hidden(E,A) & r2_hidden(k4_tarski(E,D),C))) & r2_hidden(D,B))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),C) & r2_hidden(k4_tarski(D,E),C) -> (G = E <-> F = D))) & (all D -((all E -(r2_hidden(k4_tarski(D,E),C) & r2_hidden(E,B))) & r2_hidden(D,A))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 18 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 19 (all A all B (k1_tarski(A) = B <-> (all C (r2_hidden(C,B) <-> A = C)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 20 (all A all B -((all C -((all D -(r2_hidden(D,C) & r2_hidden(D,B))) & r2_hidden(C,B))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 21 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 22 (all A all B (r1_tarski(A,B) <-> (all C (r2_hidden(C,A) -> r2_hidden(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 23 (all A exists B (r2_hidden(A,B) & (all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & (all E (r1_tarski(E,C) -> r2_hidden(E,D))))))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & (all C -(r1_tarski(C,B) & -r2_tarski(C,B) & -r2_hidden(C,B))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 24 (all A all B all C -(r2_hidden(C,k2_xboole_0(A,B)) & -(r2_hidden(C,B) & -r2_hidden(C,A)) & r1_xboole_0(A,B) & -(r2_hidden(C,A) & -r2_hidden(C,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 25 (all A all B (r1_tarski(B,A) & r1_tarski(A,B) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 26 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 27 (all A (k1_xboole_0 = A <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 28 (all A all B all C ((all D (-r2_hidden(D,B) & r2_hidden(D,A) <-> r2_hidden(D,C))) <-> k4_xboole_0(A,B) = C)) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 29 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 30 (all A all B all C ((all D ((r2_hidden(D,B) <-> r2_hidden(D,C)) <-> -r2_hidden(D,A))) -> k5_xboole_0(B,C) = A)) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 31 (all A all B all C (-(r2_hidden(A,B) <-> r2_hidden(A,C)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 32 (all A all B all C (C = k3_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,A) & r2_hidden(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 33 (all A all B (r1_xboole_0(A,B) <-> k3_xboole_0(A,B) = k1_xboole_0)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 34 (all A all B all C ((all D (r2_hidden(D,A) | r2_hidden(D,B) <-> r2_hidden(D,C))) <-> C = k2_xboole_0(A,B))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 35 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 36 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 37 (exists A all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 38 (all A all B (r3_xboole_0(A,B) <-> r1_tarski(B,A) | r1_tarski(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 39 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 40 (all A all B k5_xboole_0(B,A) = k5_xboole_0(A,B)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 41 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 42 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f1_s2_xboole_0))) -> f2_s2_xboole_0 = f1_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 43 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 44 (all A all B (r2_xboole_0(A,B) <-> B != A & r1_tarski(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 45 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 46 (all A all B (-(-r1_xboole_0(A,B) & (all C -r2_hidden(C,k3_xboole_0(A,B)))) & -(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 47 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 48 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (p1_s3_xboole_0(C) <-> r2_hidden(C,B))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 49 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 50 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 51 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 52 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 53 (all A all B k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) = k5_xboole_0(A,B)) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 54 (all A all B k2_xboole_0(B,A) = k2_xboole_0(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 55 (all A all B (-((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)) & -((all C -(r2_hidden(C,A) & r2_hidden(C,B))) & -r1_xboole_0(A,B)))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 56 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 57 (all A (v1_xboole_0(A) <-> A = k1_xboole_0)) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 58 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 59 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 60 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 61 (all A all B -(v1_xboole_0(B) & B != A & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 62 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 63 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 64 (all A k2_xboole_0(A,k1_xboole_0) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 65 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 66 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 67 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 68 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 69 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 70 (all A all B all C k4_xboole_0(A,k5_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 71 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C))) # label(t5_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 72 (all A all B r1_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t89_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 73 (all A (r1_tarski(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 74 (all A all B k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 75 (all A all B all C (r1_tarski(k2_xboole_0(A,B),C) -> r1_tarski(A,C))) # label(t11_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 76 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)))) # label(t26_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 77 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) & r1_tarski(k4_xboole_0(B,A),C) -> r1_tarski(k5_xboole_0(A,B),C))) # label(t97_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 78 (all A all B all C k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C))) # label(t42_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 79 (all A all B all C k4_xboole_0(k5_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C)))) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 80 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k2_xboole_0(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 81 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(k4_xboole_0(A,B),C))) # label(t43_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 82 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 83 (all A all B k4_xboole_0(A,k3_xboole_0(A,B)) = k4_xboole_0(A,B)) # label(t47_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 84 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 85 (all A all B r1_tarski(k4_xboole_0(A,B),k5_xboole_0(A,B))) # label(t96_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 86 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 87 (all A all B all C (r1_tarski(A,k4_xboole_0(B,C)) -> r1_xboole_0(A,C) & r1_tarski(A,B))) # label(t106_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 88 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)))) # label(t9_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 89 (all A all B all C all D (r1_xboole_0(D,B) & r1_xboole_0(C,A) & k2_xboole_0(A,B) = k2_xboole_0(C,D) -> B = C)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 90 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 91 (all A all B all C (r1_tarski(C,B) & r1_tarski(A,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 92 (all A all B all C ((all D (r1_tarski(D,B) & r1_tarski(D,C) -> r1_tarski(D,A))) & r1_tarski(A,C) & r1_tarski(A,B) -> k3_xboole_0(B,C) = A)) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 93 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 94 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(A,C) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 95 (all A all B k2_xboole_0(A,B) = k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 96 (all A all B all C r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C))) # label(t31_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 97 (all A all B r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B)) # label(t90_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 98 (all A all B all C (r1_xboole_0(B,C) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 99 (all A all B k1_xboole_0 = k4_xboole_0(A,k2_xboole_0(A,B))) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 100 (all A all B all C (r1_tarski(A,B) -> r1_xboole_0(A,k4_xboole_0(C,B)))) # label(t85_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 101 (all A all B all C k3_xboole_0(k5_xboole_0(A,C),B) = k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 102 (all A all B all C (r1_tarski(B,C) & r2_xboole_0(A,B) -> r2_xboole_0(A,C))) # label(t58_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 103 (all A all B all C (r2_xboole_0(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t56_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 104 (all A all B all C (r1_tarski(A,k5_xboole_0(B,C)) <-> r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 105 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 106 (all A all B all C (r1_xboole_0(A,k4_xboole_0(B,C)) -> r1_xboole_0(B,k4_xboole_0(A,C)))) # label(t81_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 107 (all A all B all C (-(-r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) & r1_xboole_0(A,B)) & -(r1_xboole_0(A,k2_xboole_0(B,C)) & -(r1_xboole_0(A,C) & r1_xboole_0(A,B))))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 108 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(k3_xboole_0(C,A),k3_xboole_0(C,B)))) # label(t76_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 109 (all A all B k5_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B))) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 110 (all A all B all C r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C))) # label(t29_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 111 (all A all B k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t95_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 112 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 113 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 114 (all A all B (r1_xboole_0(A,B) <-> k4_xboole_0(A,B) = A)) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 115 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t80_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 116 (all A all B -(r1_tarski(A,B) & r2_xboole_0(B,A))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 117 (all A all B all C -(-r1_xboole_0(A,B) & r1_tarski(A,C) & r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 118 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k4_xboole_0(k4_xboole_0(A,B),C)) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 119 (all A all B all C (-v1_xboole_0(C) -> -(r1_xboole_0(A,B) & r1_tarski(C,B) & r1_tarski(C,A)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 120 (all A all B all C (r1_tarski(A,B) -> k3_xboole_0(k2_xboole_0(A,C),B) = k2_xboole_0(A,k3_xboole_0(C,B)))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 121 (all A all B k3_xboole_0(A,B) = k4_xboole_0(A,k4_xboole_0(A,B))) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 122 (all A all B all C all D (r1_xboole_0(A,D) & r1_xboole_0(C,D) & r1_xboole_0(B,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 123 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(A,C))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 124 (all A all B k2_xboole_0(A,B) = k5_xboole_0(A,k4_xboole_0(B,A))) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 125 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 126 (all A all B all C (r1_tarski(C,B) & (all D (r1_tarski(C,D) & r1_tarski(A,D) -> r1_tarski(B,D))) & r1_tarski(A,B) -> B = k2_xboole_0(A,C))) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 127 (all A all B -(r2_xboole_0(A,B) & k1_xboole_0 = k4_xboole_0(B,A))) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 128 (all A all B (k4_xboole_0(A,B) = k4_xboole_0(B,A) -> B = A)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 129 (all A all B k2_xboole_0(A,k2_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 130 (all A all B (r1_xboole_0(A,B) -> A = k4_xboole_0(k2_xboole_0(A,B),B))) # label(t88_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 131 (all A all B all C (r1_tarski(A,B) & r1_tarski(B,C) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 132 (all A all B all C (r1_tarski(A,B) & r1_tarski(A,C) -> r1_tarski(A,k3_xboole_0(B,C)))) # label(t19_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 133 (all A all B all C k3_xboole_0(k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(B,C)),k2_xboole_0(C,A)) = k2_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(B,C)),k3_xboole_0(C,A))) # label(t25_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 134 (all A all B k4_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 135 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),B))) # label(t109_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 136 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 137 (all A all B (k2_xboole_0(A,B) = k1_xboole_0 -> k1_xboole_0 = A)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 138 (all A (k1_xboole_0 != A -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 139 (all A all B all C k5_xboole_0(k5_xboole_0(A,B),C) = k5_xboole_0(A,k5_xboole_0(B,C))) # label(t91_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 140 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 141 (all A all B all C (r1_tarski(A,B) -> r1_tarski(A,k2_xboole_0(C,B)))) # label(t10_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 142 (all A all B all C all D (r1_tarski(A,B) & r1_xboole_0(B,D) & r1_tarski(C,D) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 143 (all A all B all C all D k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D)) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 144 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 145 (all A (-(A != k1_xboole_0 & r1_xboole_0(A,A)) & -(-r1_xboole_0(A,A) & k1_xboole_0 = A))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 146 (all A all B A = k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 147 (all A all B all C -(r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)) & -r1_xboole_0(A,B))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 148 (all A all B all C (r1_tarski(A,C) & r1_tarski(A,B) & r1_xboole_0(B,C) -> A = k1_xboole_0)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 149 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> A = k1_xboole_0)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 150 (all A all B all C (r1_xboole_0(A,B) -> k2_xboole_0(k4_xboole_0(C,A),B) = k4_xboole_0(k2_xboole_0(C,B),A))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 151 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) -> r1_tarski(A,k2_xboole_0(B,C)))) # label(t44_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 152 (all A all B all C -(r1_xboole_0(A,B) & -r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 153 (all A all B k2_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t94_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 154 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)))) # label(t34_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 155 (all A all B all C k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C)) = k2_xboole_0(A,k3_xboole_0(B,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 156 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,B) = B)) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 157 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) = k4_xboole_0(A,k4_xboole_0(B,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 158 (all A all B all C (r1_tarski(A,k3_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t18_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 159 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,k4_xboole_0(B,A)) = B)) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 160 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k3_xboole_0(B,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 161 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C))) # label(t4_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 162 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k4_xboole_0(A,C),B)) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 163 (all A all B r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B))) # label(t103_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 164 (all A all B r1_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t82_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 165 (all A all B (-v1_xboole_0(B) -> -(r1_xboole_0(B,A) & r1_tarski(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 166 (all A all B -(r1_xboole_0(k3_xboole_0(A,B),B) & -r1_xboole_0(A,B))) # label(t75_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 167 (all A all B (k1_xboole_0 = k4_xboole_0(A,B) <-> r1_tarski(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 168 (all A all B k4_xboole_0(A,B) = k5_xboole_0(A,k3_xboole_0(A,B))) # label(t100_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 169 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 170 (all A all B all C (r1_tarski(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 171 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 172 (all A all B all C k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C))) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 173 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),B))) # label(t108_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 174 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 175 (all A all B all C k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t23_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 176 (all A all B (-(-r2_xboole_0(A,B) & B != A & -r2_xboole_0(B,A)) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 177 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 178 (all A all B all C (r1_xboole_0(C,B) & k2_xboole_0(A,B) = k2_xboole_0(C,B) & r1_xboole_0(A,B) -> C = A)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 179 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),C)) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 180 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 181 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)))) # label(t33_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 182 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 183 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 184 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,C,A,D)) # label(t110_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 185 (all A all B all C all D all E ((all F (-(B != F & D != F & F != A & C != F) <-> r2_hidden(F,E))) <-> E = k2_enumset1(A,B,C,D))) # label(d2_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 186 (all A all B all C all D all E k6_enumset1(A,A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t86_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 187 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 188 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 189 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,D,C,B)) # label(t107_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 190 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G))) # label(t59_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 191 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 192 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 193 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,C,B,A)) # label(t125_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 194 (all A all B all C all D all E all F all G k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_tarski(F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t60_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 195 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,C,D,B)) # label(t105_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 196 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_enumset1(F,G,H))) # label(t66_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 197 (all A all B all C all D (k1_enumset1(A,B,C) = D <-> (all E (-(E != B & A != E & C != E) <-> r2_hidden(E,D))))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 198 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 199 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_tarski(A),k5_enumset1(B,C,D,E,F,G,H))) # label(t62_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 200 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(C,B,A)) # label(t102_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 201 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 202 (all A k5_enumset1(A,A,A,A,A,A,A) = k1_tarski(A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 203 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,B,D,C)) # label(t103_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.24 204 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,B,A,D)) # label(t116_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 205 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 206 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 207 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 208 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F))) # label(t51_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 209 (all A all B k3_enumset1(A,A,A,A,B) = k2_tarski(A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 210 (all A k1_enumset1(A,A,A) = k1_tarski(A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 211 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 212 (all A all B all C all D k2_enumset1(A,C,B,D) = k2_enumset1(A,B,C,D)) # label(t104_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 213 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,D,B,A)) # label(t119_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 214 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 215 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E))) # label(t47_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 216 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 217 (all A all B all C all D k2_enumset1(C,D,A,B) = k2_enumset1(A,B,C,D)) # label(t118_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 218 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 219 (all A all B all C all D k2_enumset1(A,B,C,D) = k4_enumset1(A,A,A,B,C,D)) # label(t79_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 220 (all A k1_tarski(A) = k4_enumset1(A,A,A,A,A,A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 221 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 222 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 223 (all A all B all C k1_enumset1(A,B,C) = k4_enumset1(A,A,A,A,B,C)) # label(t84_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 224 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 225 (all A all B all C all D all E all F all G all H k2_xboole_0(k1_enumset1(A,B,C),k3_enumset1(D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t64_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 226 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k5_enumset1(A,A,B,C,D,E,F)) # label(t74_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 227 (all A all B all C all D all E all F all G all H all I (I = k6_enumset1(A,B,C,D,E,F,G,H) <-> (all J (r2_hidden(J,I) <-> -(J != G & H != J & F != J & J != A & C != J & J != D & E != J & B != J))))) # label(d6_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 228 (all A all B all C k5_enumset1(A,A,A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t89_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 229 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 230 (all A all B all C all D all E all F k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t54_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 231 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D))) # label(t45_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 232 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,B,D,A)) # label(t117_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 233 (all A all B all C all D all E all F k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F)) = k4_enumset1(A,B,C,D,E,F)) # label(t55_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 234 (all A all B all C k1_enumset1(B,A,C) = k1_enumset1(A,B,C)) # label(t99_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 235 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_tarski(A,B),k1_enumset1(C,D,E))) # label(t48_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 236 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 237 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 238 (all A all B all C all D all E all F (k3_enumset1(A,B,C,D,E) = F <-> (all G (-(G != D & G != A & G != C & G != E & B != G) <-> r2_hidden(G,F))))) # label(d3_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 239 (all A all B all C all D all E k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) = k3_enumset1(A,B,C,D,E)) # label(t49_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 240 (all A all B all C all D all E all F all G k2_xboole_0(k1_enumset1(A,B,C),k2_enumset1(D,E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t58_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 241 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 242 (all A all B k2_tarski(A,B) = k4_enumset1(A,A,A,A,A,B)) # label(t88_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 243 (all A all B k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B)) # label(t41_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 244 (all A all B all C all D all E all F all G all H k2_xboole_0(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t65_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 245 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 246 (all A all B all C all D all E all F all G all H (H = k5_enumset1(A,B,C,D,E,F,G) <-> (all I (r2_hidden(I,H) <-> -(A != I & I != B & C != I & I != D & F != I & I != G & I != E))))) # label(d5_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 247 (all A all B all C all D all E all F all G (G = k4_enumset1(A,B,C,D,E,F) <-> (all H (-(H != A & H != F & H != B & H != C & D != H & E != H) <-> r2_hidden(H,G))))) # label(d4_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 248 (all A all B all C all D all E all F all G all H k2_xboole_0(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t63_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 249 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 250 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 251 (all A k2_enumset1(A,A,A,A) = k1_tarski(A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 252 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 253 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,D,A,C)) # label(t112_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 254 (all A k6_enumset1(A,A,A,A,A,A,A,A) = k1_tarski(A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 255 (all A all B all C all D k2_enumset1(B,A,D,C) = k2_enumset1(A,B,C,D)) # label(t109_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 256 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 257 (all A k3_enumset1(A,A,A,A,A) = k1_tarski(A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 258 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 259 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 260 (all A all B all C all D k2_enumset1(B,D,C,A) = k2_enumset1(A,B,C,D)) # label(t113_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 261 (all A k1_tarski(A) = k2_tarski(A,A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 262 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,A,C,D)) # label(t108_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 263 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F))) # label(t52_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 264 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 265 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 266 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 267 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 268 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 269 (all A all B k1_enumset1(A,A,B) = k2_tarski(A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 270 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 271 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 272 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 273 (all A all B all C k1_enumset1(A,B,C) = k2_enumset1(A,A,B,C)) # label(t71_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 274 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 275 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D))) # label(t46_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 276 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 277 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(B,C,A)) # label(t100_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 278 (all A all B all C k2_xboole_0(k2_tarski(A,B),k1_tarski(C)) = k1_enumset1(A,B,C)) # label(t43_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 279 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 280 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 281 (all A all B k2_enumset1(A,A,A,B) = k2_tarski(A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 282 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 283 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 284 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k2_tarski(G,H))) # label(t67_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 285 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 286 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 287 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 288 (all A all B all C all D all E all F k6_enumset1(A,A,A,B,C,D,E,F) = k4_enumset1(A,B,C,D,E,F)) # label(t81_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 289 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 290 (all A all B all C all D k6_enumset1(A,A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t90_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 291 (all A all B all C k6_enumset1(A,A,A,A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t93_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 292 (all A all B all C all D k2_enumset1(B,C,D,A) = k2_enumset1(A,B,C,D)) # label(t111_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 293 (all A all B k6_enumset1(A,A,A,A,A,A,A,B) = k2_tarski(A,B)) # label(t95_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 294 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 295 (all A all B all C all D k2_enumset1(A,B,C,D) = k3_enumset1(A,A,B,C,D)) # label(t72_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 296 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 297 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 298 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 299 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k5_enumset1(A,A,A,B,C,D,E)) # label(t80_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 300 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 301 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,B,C,A)) # label(t123_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 302 (all A all B all C k1_enumset1(A,B,C) = k2_xboole_0(k1_tarski(A),k2_tarski(B,C))) # label(t42_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 303 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_tarski(A),k4_enumset1(B,C,D,E,F,G))) # label(t56_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 304 (all A all B all C all D all E all F all G k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t61_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 305 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k6_enumset1(A,A,B,C,D,E,F,G)) # label(t75_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 306 (all A all B k2_tarski(A,B) = k5_enumset1(A,A,A,A,A,A,B)) # label(t92_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 307 (all A all B all C k1_enumset1(A,B,C) = k3_enumset1(A,A,A,B,C)) # label(t78_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 308 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 309 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D))) # label(t44_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 310 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F))) # label(t53_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 311 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(A,C,B)) # label(t98_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 312 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 313 (all A all B all C all D all E k4_enumset1(A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t73_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 314 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_tarski(A,B),k3_enumset1(C,D,E,F,G))) # label(t57_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 315 (all A all B all C all D k2_enumset1(A,B,C,D) = k5_enumset1(A,A,A,A,B,C,D)) # label(t85_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 316 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 317 (all A all B all C all D all E all F all G all H k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k1_tarski(H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t68_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 318 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_tarski(E))) # label(t50_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 319 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 320 (all A all B -(k1_xboole_0 != A & k1_tarski(B) != A & k4_xboole_0(A,k1_tarski(B)) = k1_xboole_0)) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 321 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 322 (all A all B (r2_hidden(A,B) -> k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 323 (all A all B all C (r1_tarski(A,B) -> r2_hidden(C,A) | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))))) # label(t40_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 324 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 325 (all A all B all C -(-(k1_tarski(A) = C & B = k1_xboole_0) & -(B = k1_tarski(A) & k1_xboole_0 = C) & -(B = k1_tarski(A) & C = k1_tarski(A)) & k2_xboole_0(B,C) = k1_tarski(A))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 326 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0 -> A = B)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 327 (all A all B all C (r1_tarski(k2_tarski(A,B),C) <-> r2_hidden(B,C) & r2_hidden(A,C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 328 (all A all B all C -(-r1_xboole_0(k2_tarski(A,C),B) & -r2_hidden(A,B) & -r2_hidden(C,B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 329 (all A all B r1_tarski(k1_zfmisc_1(k4_xboole_0(A,B)),k2_xboole_0(k1_tarski(k1_xboole_0),k4_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t84_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 330 (all A all B all C (k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 331 (all A all B all C all D (r1_xboole_0(A,B) | r1_xboole_0(C,D) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 332 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)),k1_zfmisc_1(k2_xboole_0(A,B)))) # label(t81_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 333 (all A all B all C (k2_zfmisc_1(k4_xboole_0(A,B),C) = k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k4_xboole_0(A,B)))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 334 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 335 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 336 (all A all B (k1_zfmisc_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 337 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 338 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> k1_tarski(C) = k2_tarski(A,B))) # label(t27_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 339 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 340 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t118_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 341 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t95_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 342 (all A all B (k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B) -> A = B)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 343 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 344 (all A all B all C all D k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) = k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D)))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 345 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 346 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & (all G all H (r2_hidden(k4_tarski(G,H),D) <-> r2_hidden(k4_tarski(G,H),A))) & r1_tarski(D,k2_zfmisc_1(E,F)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 347 (all A all B (B != A -> r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t17_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 348 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> k2_zfmisc_1(A,B) = k1_xboole_0 | r1_tarski(A,C) & r1_tarski(B,D))) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 349 (all A all B (r1_tarski(A,k2_zfmisc_1(A,B)) | r1_tarski(A,k2_zfmisc_1(B,A)) -> A = k1_xboole_0)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 350 (all A all B k2_tarski(A,B) = k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B)))) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 351 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 352 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 353 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 354 (all A all B all C (k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k3_xboole_0(A,B),C))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 355 (all A A = k3_tarski(k1_tarski(A))) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 356 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> k1_xboole_0 = A)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 357 (all A all B (k3_xboole_0(A,k1_tarski(B)) = k1_tarski(B) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 358 (all A all B all C all D (k4_tarski(C,D) = k4_tarski(A,B) -> A = C & B = D)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 359 (all A all B k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B)) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 360 (all A exists B ((all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & (all C -(-r2_tarski(C,B) & r1_tarski(C,B) & -r2_hidden(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 361 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t79_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 362 (all A all B all C (k1_xboole_0 = k4_xboole_0(k2_tarski(A,B),C) <-> r2_hidden(B,C) & r2_hidden(A,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 363 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C))) # label(t124_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 364 (all A all B all C all D -(A != D & A != C & k2_tarski(A,B) = k2_tarski(C,D))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 365 (all A A = k3_tarski(k1_zfmisc_1(A))) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 366 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 367 (all A all B k2_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k2_xboole_0(A,B))) # label(t96_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 368 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> A = C)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 369 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(k1_tarski(C) != A & A != k1_tarski(B) & A != k1_xboole_0 & k2_tarski(B,C) != A))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 370 (all A all B (-r2_hidden(A,B) -> k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t141_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 371 (all A all B (A != B -> k5_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B))) # label(t29_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 372 (all A all B all C all D (A != B -> r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) & r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 373 (all A all B all C all D -(A != C & A != D & r1_tarski(k2_tarski(A,B),k2_tarski(C,D)))) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 374 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(C,B))) -> r1_tarski(k3_tarski(A),B))) # label(t94_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 375 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 376 (all A all B k1_xboole_0 = k4_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 377 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & r2_hidden(F,C) & k4_tarski(E,F) = D)) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 378 (all A all B (k1_xboole_0 = A | k1_xboole_0 = B <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 379 (all A all B k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t14_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 380 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 381 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 382 (all A all B all C k2_zfmisc_1(k2_zfmisc_1(A,B),C) = k3_zfmisc_1(A,B,C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 383 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 384 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(B,D) & r2_hidden(A,C))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 385 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 386 (all A all B all C (r2_hidden(A,B) -> k3_xboole_0(k2_tarski(A,C),B) = k1_tarski(A) | C != A & r2_hidden(C,B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 387 (all A all B all C all D ((all E all F (r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)) <-> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)))) -> k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B))) # label(t108_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 388 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> r1_xboole_0(C,D) | C = D)) -> k3_tarski(k3_xboole_0(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 389 (all A all B all C (-r2_hidden(A,C) & -r2_hidden(B,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 390 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 391 (all A all B all C all D (r1_tarski(A,k2_zfmisc_1(B,C)) & (all E all F (r2_hidden(k4_tarski(E,F),A) -> r2_hidden(k4_tarski(E,F),D))) -> r1_tarski(A,D))) # label(t109_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 392 (all A all B -(A = B & r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 393 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 394 (all A all B (-r2_hidden(A,B) -> r1_xboole_0(k1_tarski(A),B))) # label(t56_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 395 (all A all B all C (-(A != k2_tarski(B,C) & A != k1_tarski(C) & k1_tarski(B) != A & A != k1_xboole_0) <-> k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0)) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 396 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 397 (all A all B (k1_tarski(A) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 398 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 399 (all A all B all C all D all E -(r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))) & (all F all G -(r2_hidden(F,k3_xboole_0(B,D)) & r2_hidden(G,k3_xboole_0(C,E)) & A = k4_tarski(F,G))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 400 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 401 (all A all B r1_tarski(k3_tarski(k3_xboole_0(A,B)),k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t97_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 402 (all A all B all C all D (B = D & r2_hidden(A,C) <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))))) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 403 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 404 (all A all B r1_tarski(k2_zfmisc_1(A,B),k1_zfmisc_1(k1_zfmisc_1(k2_xboole_0(A,B))))) # label(t105_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 405 (all A all B all C (k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) -> r2_hidden(A,C))) # label(t63_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 406 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 407 (all A all B all C (k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),C) <-> (B = A | r2_hidden(B,C)) & -r2_hidden(A,C))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 408 (all A all B all C (k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) = k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) & k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k4_tarski(A,C),k4_tarski(B,C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 409 (all A all B (k1_tarski(A) = k4_xboole_0(k1_tarski(A),B) <-> -r2_hidden(A,B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 410 (all A all B -(k1_tarski(B) != A & (all C -(r2_hidden(C,A) & C != B)) & k1_xboole_0 != A)) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 411 (all A all B (B != A -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 412 (all A all B all C k2_xboole_0(k2_tarski(A,B),C) != k1_xboole_0) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 413 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 414 (all A all B (k1_zfmisc_1(A) = B <-> (all C (r2_hidden(C,B) <-> r1_tarski(C,A))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 415 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) -> r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)))) # label(t107_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 416 (all A all B ((all C (r2_hidden(C,A) -> r1_xboole_0(C,B))) -> r1_xboole_0(k3_tarski(A),B))) # label(t98_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 417 (all A all B (k2_zfmisc_1(B,A) = k2_zfmisc_1(A,B) -> B = A | B = k1_xboole_0 | A = k1_xboole_0)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 418 (all A all B all C all D k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 419 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 420 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 421 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 422 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> r2_hidden(B,D) & C = A)) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 423 (all A all B (k1_xboole_0 != A -> k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0 & k2_zfmisc_1(A,k1_tarski(B)) != k1_xboole_0)) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 424 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(k4_xboole_0(A,B)),k1_zfmisc_1(k4_xboole_0(B,A))),k1_zfmisc_1(k5_xboole_0(A,B)))) # label(t86_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 425 (all A all B all C -(A != B & r1_tarski(k1_tarski(A),k2_tarski(B,C)) & A != C)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 426 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> k3_xboole_0(k2_tarski(A,C),B) = k2_tarski(A,C))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 427 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 428 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))) <-> D = B & A = C)) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 429 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 430 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> k2_xboole_0(k2_tarski(A,C),B) = B)) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 431 (all A all B all C -((r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C))) & A != k1_xboole_0 & -r1_tarski(B,C))) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 432 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 433 (all A all B (k1_tarski(A) = k4_xboole_0(k1_tarski(A),B) | k4_xboole_0(k1_tarski(A),B) = k1_xboole_0)) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 434 (all A all B all C -(k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_xboole_0 & k4_xboole_0(k2_tarski(A,B),C) != k2_tarski(A,B))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 435 (all A all B all C (k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) = k2_zfmisc_1(C,k2_tarski(A,B)) & k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)) = k2_zfmisc_1(k2_tarski(A,B),C))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 436 (all A all B all C -((all D all E k4_tarski(D,E) != A) & r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 437 (all A all B all C -(r1_xboole_0(k2_tarski(A,B),C) & r2_hidden(A,C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 438 (all A all B (r1_tarski(A,k1_tarski(B)) <-> A = k1_tarski(B) | k1_xboole_0 = A)) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 439 (all A all B (r1_xboole_0(k1_tarski(A),B) | k1_tarski(A) = k3_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 440 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k1_tarski(A),B))) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 441 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 442 (all A all B -(r1_xboole_0(k1_tarski(A),B) & r2_hidden(A,B))) # label(t54_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 443 (all A all B (r2_hidden(A,B) <-> r1_tarski(k1_tarski(A),B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 444 (all A all B all C (r2_hidden(A,B) & A != C <-> r2_hidden(A,k4_xboole_0(B,k1_tarski(C))))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 445 (all A all B k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 446 (all A k2_tarski(k1_xboole_0,k1_tarski(A)) = k1_zfmisc_1(k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 447 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> B = C)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 448 (all A all B (r2_hidden(A,B) -> k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 449 (all A all B all C (r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C) -> r2_hidden(A,C))) # label(t47_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 450 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k4_tarski(E,F) = D & r2_hidden(F,B))))) <-> C = k2_zfmisc_1(A,B))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 451 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) <-> A != B)) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 452 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 453 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 454 (all A all B k1_tarski(A) = k3_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 455 (all A all B all C all D k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 456 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(D,E)) & r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 457 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & B != C & k1_xboole_0 != B & C != k1_xboole_0)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 458 (all A all B k1_zfmisc_1(k3_xboole_0(A,B)) = k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 459 (all A all B (r1_tarski(k2_xboole_0(k1_tarski(A),B),B) -> r2_hidden(A,B))) # label(t45_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 460 (all A all B all C -(r2_hidden(B,C) & k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) & A != B)) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 461 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 462 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) & (all C -(r2_hidden(C,A) & (all D all E k4_tarski(D,E) != C))) & (all C -(r2_hidden(C,B) & (all D all E C != k4_tarski(D,E)))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 463 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 464 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 465 (all A all B all C all D (k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) -> B = D & C = A | k1_xboole_0 = B | k1_xboole_0 = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 466 (all A all B (k4_xboole_0(A,k1_tarski(B)) = A <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 467 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 468 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 469 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k2_subset_1(A)))) # label(t28_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 470 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (-r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 471 (all A (k1_xboole_0 != A -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 472 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),C) -> r1_tarski(k3_subset_1(A,C),B)))))) # label(t36_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 473 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_xboole_0(D,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 474 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k6_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),C))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 475 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 476 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 477 (all A all B all C all D (-v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 478 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 479 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> -r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t51_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 480 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -r2_hidden(E,D) & r2_hidden(E,C)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 481 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r1_subset_1(A,A))) # label(irreflexivity_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 482 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 483 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 484 (all A k3_subset_1(A,k1_subset_1(A)) = k2_subset_1(A)) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 485 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (k1_xboole_0 != A -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 486 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 487 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 488 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k5_subset_1(A,B,k3_subset_1(A,C)))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 489 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) -> r1_subset_1(B,A)))) # label(symmetry_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 490 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)) & (all B (m1_subset_1(B,f1_s3_subset_1) -> (r2_hidden(B,A) <-> p1_s3_subset_1(B)))))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 491 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 492 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 493 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,k3_subset_1(A,C)) & r2_hidden(B,C)))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 494 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 495 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k7_subset_1(A,B,C)) = k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 496 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 497 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,D) & r2_hidden(E,C)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 498 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),B) <-> k2_subset_1(A) = B))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 499 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r2_subset_1(A,A))) # label(irreflexivity_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 500 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 501 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k2_xboole_0(B,C) = k4_subset_1(A,B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 502 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,B),k3_subset_1(A,k5_subset_1(A,B,C))))))) # label(t42_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 503 (all A A = k2_subset_1(A)) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 504 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -(r2_hidden(E,C) <-> r2_hidden(E,D))))) -> B = k7_subset_1(A,C,D)))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 505 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,A) -> (k1_xboole_0 != A -> m1_subset_1(k6_enumset1(B,C,D,E,F,G,H,I),k1_zfmisc_1(A))))))))))))))))))) # label(t62_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 506 (all A all B ((-v1_xboole_0(A) -> (r2_hidden(B,A) <-> m1_subset_1(B,A))) & (v1_xboole_0(A) -> (m1_subset_1(B,A) <-> v1_xboole_0(B))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 507 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 508 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 509 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 510 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (A != k1_xboole_0 -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 511 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_xboole_0(A,B) <-> r1_subset_1(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 512 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,C,B) = k4_subset_1(A,B,C))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 513 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k5_subset_1(A,B,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 514 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> B = A))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.25 515 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 516 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 517 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 518 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 519 (all A k1_subset_1(A) = k1_xboole_0) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 520 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 521 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) <-> r1_tarski(B,C)))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 522 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 523 (all A (-$T -> (all B (m1_subset_1(B,A) -> B = k8_subset_1(A))))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 524 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A))))))))) # label(t57_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 525 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) & B != k1_xboole_0))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 526 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 527 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> ((all C (m1_subset_1(C,A) -> r2_hidden(C,B))) -> A = B))) # label(t49_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 528 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) & r1_xboole_0(B,C) -> B = k3_subset_1(A,C)))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 529 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 530 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 531 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 532 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 533 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 534 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) & r1_tarski(B,C) -> k1_xboole_0 = B))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 535 (all A (m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)) & v1_xboole_0(k1_subset_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 536 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 537 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,k3_subset_1(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 538 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k7_subset_1(A,C,B))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 539 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 540 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 541 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 542 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (k1_xboole_0 != A -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 543 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f3_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (p1_s4_subset_1(A) <-> r2_hidden(A,f2_s4_subset_1)))) -> f3_s4_subset_1 = f2_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 544 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 545 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 546 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 547 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 548 (all A all B (r2_hidden(A,B) -> m1_subset_1(k1_tarski(A),k1_zfmisc_1(B)))) # label(t63_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 549 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) -> r2_subset_1(B,A)))) # label(symmetry_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 550 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 551 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,k3_subset_1(A,B)) = k2_subset_1(A))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 552 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 553 (exists A ((all B (p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1) <-> r2_hidden(B,A))) & m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 554 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 555 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 556 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,D) | r2_hidden(E,C) <-> r2_hidden(E,B)))) -> B = k4_subset_1(A,C,D)))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 557 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_xboole_0(A,B) = k3_subset_1(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 558 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 559 (all A all B (m1_subset_1(B,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 560 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k4_subset_1(A,B,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 561 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 562 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) -> r1_tarski(C,k3_subset_1(A,B))))))) # label(t35_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 563 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 564 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) <-> r1_xboole_0(B,k3_subset_1(A,C))))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 565 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 566 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k3_xboole_0(B,C) = k5_subset_1(A,B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 567 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 568 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,B) = B)) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 569 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,k4_subset_1(A,B,C)),k3_subset_1(A,B)))))) # label(t41_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 570 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 571 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 572 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) <-> r1_xboole_0(B,C)))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 573 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 574 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (B = k1_subset_1(A) <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 575 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 576 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 577 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> r1_xboole_0(B,k3_subset_1(A,B)))) # label(t26_subset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 578 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)))) # label(fc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 579 (all A all B k2_setfam_1(A,B) = k2_setfam_1(B,A)) # label(commutativity_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 580 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 581 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k5_setfam_1(A,B) = k3_tarski(B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 582 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> A = k1_xboole_0 | r1_tarski(B,k1_setfam_1(A)))) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 583 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 584 (all A all B (k1_xboole_0 != B -> k4_xboole_0(A,k3_tarski(B)) = k1_setfam_1(k4_setfam_1(k1_tarski(A),B)))) # label(t37_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 585 (all A all B all C (r1_setfam_1(B,C) & r1_setfam_1(A,B) -> r1_setfam_1(A,C))) # label(t23_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 586 (all A (r1_setfam_1(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 587 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 588 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 589 (all A all B (k1_xboole_0 != B -> k1_setfam_1(k2_setfam_1(k1_tarski(A),B)) = k2_xboole_0(A,k1_setfam_1(B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 590 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 591 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 592 (all A all B (r1_setfam_1(A,B) <-> (all C -((all D -(r2_hidden(D,B) & r1_tarski(C,D))) & r2_hidden(C,A))))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 593 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(B,C) -> r1_tarski(k8_setfam_1(A,C),k8_setfam_1(A,B))))))) # label(t59_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 594 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 595 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 596 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 597 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 598 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 599 (all A all B k3_xboole_0(A,B) = k1_setfam_1(k2_tarski(A,B))) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 600 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 601 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 602 (all A all B r1_tarski(k1_setfam_1(k4_setfam_1(A,B)),k4_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t41_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 603 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 604 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 605 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,C) = k7_setfam_1(A,B) -> C = B))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 606 (all A all B (r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),A))) # label(t4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 607 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 608 (all A all B all C (r1_tarski(k3_tarski(A),B) & r2_hidden(C,A) -> r1_tarski(C,B))) # label(t56_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 609 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 610 (all A all B all C ((all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) & r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 611 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 612 (all A (v1_setfam_1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 613 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 614 (all A all B (-r1_xboole_0(A,B) -> k1_setfam_1(k3_setfam_1(A,B)) = k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t34_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 615 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 616 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 617 (all A all B (r2_setfam_1(A,B) <-> (all C -(r2_hidden(C,B) & (all D -(r1_tarski(D,C) & r2_hidden(D,A))))))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 618 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 619 (all A (r2_hidden(k1_xboole_0,A) -> k1_xboole_0 = k1_setfam_1(A))) # label(t5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 620 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | k1_xboole_0 = A)) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 621 (all A all B all C ((all D ((exists E exists F (r2_hidden(F,B) & r2_hidden(E,A) & k4_xboole_0(E,F) = D)) <-> r2_hidden(D,C))) <-> k4_setfam_1(A,B) = C)) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 622 (all A all B (r1_setfam_1(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t18_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 623 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 624 (all A (-v2_setfam_1(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 625 (all A all B all C (r1_xboole_0(A,C) & r2_hidden(A,B) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 626 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 627 (all A all B ((A = k1_xboole_0 -> (k1_xboole_0 = B <-> k1_setfam_1(A) = B)) & (k1_xboole_0 != A -> ((all C (r2_hidden(C,B) <-> (all D (r2_hidden(D,A) -> r2_hidden(C,D))))) <-> k1_setfam_1(A) = B)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 628 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & k1_xboole_0 = k7_setfam_1(A,B)))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 629 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 630 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 631 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)))) # label(fc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 632 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),k7_setfam_1(A,C)) -> r1_tarski(B,C)))))) # label(t51_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 633 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(r2_hidden(D,C) & -r1_tarski(D,B) & -r1_tarski(D,A))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 634 (all A all B -(k1_xboole_0 != A & -r1_tarski(k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)),k1_setfam_1(k2_setfam_1(A,B))) & B != k1_xboole_0)) # label(t40_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 635 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 636 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(B,k7_setfam_1(A,C)) <-> r1_tarski(k7_setfam_1(A,B),C)))))) # label(t52_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 637 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k1_setfam_1(B) = k6_setfam_1(A,B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 638 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> (r2_hidden(B,k8_setfam_1(A,C)) <-> (all D (r2_hidden(D,C) -> r2_hidden(B,D))))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 639 (all A all B all C ((all D ((exists E exists F (D = k3_xboole_0(E,F) & r2_hidden(F,B) & r2_hidden(E,A))) <-> r2_hidden(D,C))) <-> C = k3_setfam_1(A,B))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 640 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 641 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 = B -> A = k8_setfam_1(A,B)) & (k1_xboole_0 != B -> k8_setfam_1(A,B) = k6_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 642 (all A all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 643 (all A all B (r1_setfam_1(B,k1_tarski(A)) -> (all C (r2_hidden(C,B) -> r1_tarski(C,A))))) # label(t24_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 644 (all A all B all C (k2_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (k2_xboole_0(E,F) = D & r2_hidden(F,B) & r2_hidden(E,A))))))) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 645 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,k7_setfam_1(A,B)) = B)) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 646 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 647 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 648 (all A all B k3_tarski(k3_setfam_1(k1_tarski(A),B)) = k3_xboole_0(A,k3_tarski(B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 649 (all A all B (v1_setfam_1(B) & v1_setfam_1(A) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 650 (all A all B k3_setfam_1(A,B) = k3_setfam_1(B,A)) # label(commutativity_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 651 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 652 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B)) = k5_setfam_1(A,k7_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 653 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 654 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(k3_subset_1(A,C),k7_setfam_1(A,B)) <-> r2_hidden(C,B)))))) # label(t49_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 655 (all A all B -(k1_xboole_0 != A & k1_xboole_0 != B & k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) != k1_setfam_1(k2_xboole_0(A,B)))) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 656 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_tarski(A) = B -> k7_setfam_1(A,B) = k1_tarski(k1_xboole_0)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 657 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 658 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 659 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> k4_subset_1(k1_zfmisc_1(A),k7_setfam_1(A,B),k7_setfam_1(A,C)) = k7_setfam_1(A,k4_subset_1(k1_zfmisc_1(A),B,C)))))) # label(t54_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 660 (all A all B (B != k1_xboole_0 -> k3_tarski(k4_setfam_1(k1_tarski(A),B)) = k4_xboole_0(A,k1_setfam_1(B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 661 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,B) = C <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(k3_subset_1(A,D),B) <-> r2_hidden(D,C))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 662 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 663 (all A all B (r2_setfam_1(B,A) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | A = k1_xboole_0)) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 664 (all A (-r2_hidden(k1_xboole_0,A) <-> v1_setfam_1(A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 665 (all A A = k1_setfam_1(k1_tarski(A))) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 666 (all A all B k3_tarski(k3_setfam_1(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t39_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 667 (all A (v2_setfam_1(A) <-> (all B (-v1_xboole_0(B) -> -r2_hidden(B,A))))) # label(d11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 668 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k6_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 669 (all A all B all C (r1_tarski(A,C) & r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),C))) # label(t8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 670 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 671 (all A all B (m1_subset_1(A,B) -> r2_hidden(A,B) | v1_xboole_0(B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 672 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(C)) & r2_hidden(A,B) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 673 (all A all B (m1_subset_1(A,k1_zfmisc_1(B)) <-> r1_tarski(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 674 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 675 (all A all B all C -(v1_xboole_0(C) & m1_subset_1(B,k1_zfmisc_1(C)) & r2_hidden(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 676 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 677 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 678 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 679 (all A (v1_relat_1(A) -> r1_tarski(k2_relat_1(A),k3_relat_1(A)) & r1_tarski(k1_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 680 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v3_relat_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 681 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 682 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k5_relat_1(B,k6_relat_1(A)))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 683 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))))))) # label(t14_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 684 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 685 (all A all B (v1_relat_1(B) -> -(k9_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & A != k1_xboole_0))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 686 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 687 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k7_relat_1(C,B))) <-> r2_hidden(A,B) & r2_hidden(A,k1_relat_1(C))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 688 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 689 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 690 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 691 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C))))))))) # label(t49_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 692 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 693 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 694 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E ((exists F (r2_hidden(k4_tarski(D,F),A) & r2_hidden(k4_tarski(F,E),B))) <-> r2_hidden(k4_tarski(D,E),C))) <-> k5_relat_1(A,B) = C))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 695 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k2_relat_1(B)) & (all C -r2_hidden(C,k1_relat_1(B)))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 696 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k3_relat_1(A),k3_relat_1(B))))))) # label(t34_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 697 (all A all B all C all D all E (v1_relat_1(E) -> (E = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) -> k1_relat_1(E) = k2_tarski(A,C) & k2_tarski(B,D) = k2_relat_1(E)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 698 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k2_relat_1(A),k2_relat_1(B)),k2_relat_1(k4_xboole_0(A,B))))))) # label(t28_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 699 (all A (v1_relat_1(A) -> (k1_relat_1(A) = k1_xboole_0 <-> k1_xboole_0 = k2_relat_1(A)))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 700 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_relat_1(A),k3_relat_1(B))))))) # label(t31_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 701 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 702 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 703 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(C,B) & r1_tarski(k1_relat_1(C),A) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 704 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B))))))))) # label(t48_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 705 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 706 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k1_relat_1(B),A),k9_relat_1(k4_relat_1(B),k9_relat_1(B,A))))) # label(t163_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 707 (all A (v1_relat_1(A) -> k10_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 708 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 709 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k2_relat_1(k7_relat_1(B,A)))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 710 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 711 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 712 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 713 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 714 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 715 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t100_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 716 (all A all B all C (v1_relat_1(C) -> r1_tarski(k10_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t176_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 717 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(B,k10_relat_1(C,A)) = k10_relat_1(k5_relat_1(B,C),A))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 718 (all A (v1_relat_1(A) -> (v2_relat_1(A) <-> -r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(d9_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 719 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(B,A)) & v1_xboole_0(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 720 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> k2_relat_1(A) = B)))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 721 (all A (v1_relat_1(A) -> k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 722 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(B)) = k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 723 (all A all B (v1_relat_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k7_relat_1(B,A)))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 724 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 725 (all A all B (v1_relat_1(B) -> k3_xboole_0(k2_relat_1(B),A) = k2_relat_1(k8_relat_1(A,B)))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 726 (all A all B (v1_relat_1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k4_tarski(C,C),B))) -> r1_tarski(k6_relat_1(A),B)))) # label(t73_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 727 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 728 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 729 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)))))) # label(t44_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 730 (all A (v1_relat_1(A) -> (all B all C ((all D ((exists E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B))) <-> r2_hidden(D,C))) <-> C = k10_relat_1(A,B))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 731 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k5_relat_1(A,B) = k1_xboole_0))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 732 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)) & v1_xboole_0(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 733 (all A all B all C (v1_relat_1(C) -> k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 734 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t89_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 735 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t157_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 736 (all A all B all C all D v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t5_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 737 (all A (v1_xboole_0(A) -> v1_relat_1(k1_relat_1(A)) & v1_xboole_0(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 738 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A))))))) # label(t105_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 739 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k2_relat_1(k8_relat_1(A,B)) = A))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 740 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t99_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 741 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)),k5_relat_1(A,k4_xboole_0(B,C))))))))) # label(t53_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 742 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 743 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 744 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k5_relat_1(k6_relat_1(A),B)))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 745 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 746 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 747 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 748 (all A (v1_relat_1(A) -> A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t80_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 749 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k4_xboole_0(A,B),C) = k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 750 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)))) # label(t124_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 751 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 752 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 753 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 754 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(B,C) & r2_hidden(k4_tarski(A,B),D) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 755 (all A (v1_relat_1(A) -> A = k7_relat_1(A,k1_relat_1(A)))) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 756 (all A (v1_relat_1(A) <-> (all B -(r2_hidden(B,A) & (all C all D k4_tarski(C,D) != B))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 757 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k2_relat_1(B),A),k10_relat_1(k4_relat_1(B),k10_relat_1(B,A))))) # label(t183_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 758 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k5_relat_1(B,k6_relat_1(A))))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 759 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k4_xboole_0(A,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 760 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 761 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,D) = k7_relat_1(A,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 762 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t156_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 763 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k8_relat_1(A,C),B) = k8_relat_1(A,k7_relat_1(C,B)))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 764 (all A k1_xboole_0 = k10_relat_1(k1_xboole_0,A)) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 765 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k7_relat_1(B,A)))) # label(t97_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 766 (all A all B (v1_relat_1(B) -> v1_relat_1(k4_xboole_0(B,A)))) # label(t10_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 767 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 768 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k1_relat_1(C) = k1_tarski(A) & k2_relat_1(C) = k1_tarski(B)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 769 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 770 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,C))))) # label(t131_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 771 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 772 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 773 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 774 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k8_relat_1(B,C))) <-> r2_hidden(A,k2_relat_1(C)) & r2_hidden(A,B)))) # label(t115_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 775 (all A (v1_relat_1(A) -> k3_relat_1(A) = k3_relat_1(k4_relat_1(A)))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 776 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(k4_tarski(D,A),C) & r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B))) <-> r2_hidden(A,k9_relat_1(C,B))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 777 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 778 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,A) & C = D)) <-> B = k6_relat_1(A)))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 779 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 780 (all A (v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A))) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 781 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 782 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(B,k2_relat_1(B))))) # label(t170_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 783 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 784 (all A all B (v1_relat_1(B) -> (k7_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 785 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 786 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),A))) # label(t116_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.26 787 (all A (v1_relat_1(A) -> k1_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k2_relat_1(A) = k1_relat_1(k4_relat_1(A)))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 788 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C)))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 789 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k4_xboole_0(A,B)))))) # label(t41_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 790 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 791 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t27_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 792 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)))))) # label(t45_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 793 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 794 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 795 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k7_relat_1(C,A)),k5_relat_1(B,C)))))) # label(t93_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 796 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> k1_xboole_0 = B))))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 797 (all A all B (v1_relat_1(B) -> k8_relat_1(A,k8_relat_1(A,B)) = k8_relat_1(A,B))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 798 (all A all B (v1_relat_1(B) -> (r1_tarski(A,B) -> v1_relat_1(A)))) # label(t3_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 799 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)))))) # label(t122_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 800 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 801 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k1_relat_1(B)))) # label(t167_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 802 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t118_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 803 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),A))) # label(t87_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 804 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 805 (all A (v1_relat_1(A) -> r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t21_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 806 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,B))))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 807 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 808 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 809 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 810 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),B) <-> r2_hidden(k4_tarski(D,E),C))) <-> k8_relat_1(A,B) = C))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 811 (all A all B (v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 812 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k5_relat_1(k4_relat_1(B),k4_relat_1(A)) = k4_relat_1(k5_relat_1(A,B)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 813 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 814 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = A <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A)))))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 815 (all A (v1_relat_1(A) -> k8_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 816 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,D) = k7_relat_1(A,D) & k7_relat_1(A,C) = k7_relat_1(B,C) -> k7_relat_1(B,k2_xboole_0(C,D)) = k7_relat_1(A,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 817 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k2_relat_1(C)) & r2_hidden(A,k1_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 818 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)))))) # label(t121_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 819 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(k4_xboole_0(A,B))))))) # label(t15_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 820 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 821 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) <-> (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B)))))))) # label(d3_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 822 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_relat_1(A),k2_relat_1(B)) & r1_tarski(k1_relat_1(A),k1_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 823 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B))))) # label(t104_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 824 (exists A (v3_relat_1(A) & v1_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 825 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 826 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(k7_relat_1(C,A),B),k9_relat_1(C,B)))) # label(t161_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 827 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(B,k1_relat_1(B))))) # label(t147_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 828 (all A all B (v1_relat_1(B) -> (k9_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 829 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t108_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 830 (exists A (v1_relat_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(B,f1_s1_relat_1) & p1_s1_relat_1(B,C) & r2_hidden(C,f2_s1_relat_1))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 831 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> k1_relat_1(k7_relat_1(B,A)) = A))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 832 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(B,k6_relat_1(A)),B) & r1_tarski(k5_relat_1(k6_relat_1(A),B),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 833 (all A (v1_relat_1(A) -> k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 834 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 835 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k2_relat_1(B)))) # label(t144_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 836 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k2_relat_1(B)) -> k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A))))))) # label(t47_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 837 (all A (v1_relat_1(A) -> A = k8_relat_1(k2_relat_1(A),A))) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 838 (all A all B (v1_relat_1(B) -> -(k10_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k2_relat_1(B)) & A != k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 839 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 840 (all A (v1_relat_1(A) -> (r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0)) <-> v3_relat_1(A)))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 841 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_xboole_0 = A))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 842 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 843 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 844 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k3_relat_1(C) = k2_tarski(A,B)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 845 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k1_relat_1(B) = A & k5_relat_1(B,D) = k6_relat_1(A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & r1_tarski(k2_relat_1(C),A) -> D = C))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 846 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k8_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(B,k8_relat_1(A,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 847 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 848 (all A (v1_relat_1(A) -> k4_relat_1(k4_relat_1(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 849 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 850 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 851 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k5_relat_1(A,B)) = k10_relat_1(A,k1_relat_1(B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 852 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k5_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 853 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> (C = k7_relat_1(A,B) <-> (all D all E (r2_hidden(D,B) & r2_hidden(k4_tarski(D,E),A) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 854 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 855 (all A all B (v1_relat_1(B) -> r1_tarski(k8_relat_1(A,B),B))) # label(t117_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 856 (all A (A = k1_relat_1(k6_relat_1(A)) & A = k2_relat_1(k6_relat_1(A)))) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 857 (all A all B (v1_relat_1(B) -> r1_tarski(k7_relat_1(B,A),B))) # label(t88_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 858 (all A all B (v1_relat_1(B) -> k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 859 (all A (v1_relat_1(A) -> (all B ((all C ((exists D r2_hidden(k4_tarski(C,D),A)) <-> r2_hidden(C,B))) <-> k1_relat_1(A) = B)))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 860 (all A all B (v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(t9_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 861 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 862 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 863 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 864 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t154_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 865 (all A all B (v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 866 (all A all B (v1_relat_1(B) -> -(-v3_relat_1(k7_relat_1(B,A)) & v3_relat_1(B)))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 867 (all A all B (v1_relat_1(B) -> k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 868 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 869 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k2_xboole_0(A,B)))) # label(t175_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 870 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 871 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 872 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)),k9_relat_1(C,k4_xboole_0(A,B))))) # label(t155_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 873 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(D,C),A))) <-> B = k4_relat_1(A)))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 874 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k8_relat_1(A,B) = B))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 875 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k10_relat_1(C,B)) <-> (exists D (r2_hidden(D,k2_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(A,D),C)))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 876 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k1_relat_1(B)) & (all C -r2_hidden(C,k2_relat_1(B)))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 877 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,A),B)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 878 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(k2_xboole_0(A,B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 879 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 880 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 881 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 882 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(A,k3_xboole_0(B,C)),k3_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C))))))))) # label(t52_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 883 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 884 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 885 (all A (v1_relat_1(A) -> k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) = A)) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 886 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(k4_tarski(E,D),A) & r2_hidden(E,B))))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 887 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) | k1_xboole_0 = k1_relat_1(A) -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 888 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 889 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(B),A) <-> k1_xboole_0 = k10_relat_1(B,A)))) # label(t173_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 890 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 891 (all A (v1_xboole_0(A) -> v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 892 (all A (v1_xboole_0(A) -> v1_xboole_0(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 893 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 894 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k7_relat_1(B,A),C),k5_relat_1(B,C)))))) # label(t92_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 895 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 896 (all A (v1_relat_1(A) -> (all B (r1_xboole_0(B,k1_relat_1(A)) -> k7_relat_1(A,B) = k1_xboole_0)))) # label(t187_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 897 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D)) <-> r2_hidden(A,C) & r2_hidden(k4_tarski(A,B),D)))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 898 (all A (v1_relat_1(A) -> k1_xboole_0 = k9_relat_1(A,k1_xboole_0))) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 899 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 900 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(C,A))))))) # label(t179_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 901 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t178_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 902 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t134_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 903 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)),k10_relat_1(C,k4_xboole_0(A,B))))) # label(t177_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 904 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C))))))) # label(t132_relat_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 905 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 906 (all A all B k5_relat_1(k6_relat_1(B),k6_relat_1(A)) = k6_relat_1(k3_xboole_0(A,B))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 907 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 908 (all A (v2_relat_1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 909 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 910 (exists A ((all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))) & v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = f1_s4_funct_1)) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 911 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 912 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 913 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> v2_funct_1(k8_relat_1(A,B))))) # label(t99_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 914 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,k1_funct_1(B,A)) = k1_funct_1(k5_relat_1(B,C),A)))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 915 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) <-> k1_xboole_0 != k10_relat_1(B,k1_tarski(A))))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 916 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 917 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A)))) # label(t152_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 918 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 919 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 920 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k10_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 921 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A) & k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 922 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 923 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 924 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B all C (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) -> C = B))))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 925 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C) & k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 926 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 927 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k1_relat_1(k2_funct_1(A)) = k2_relat_1(A) & k1_relat_1(A) = k2_relat_1(k2_funct_1(A))))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 928 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 929 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 930 (all A (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 931 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A)) & v2_funct_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 932 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 933 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k3_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 934 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(B,A) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 935 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 936 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 937 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(B,k2_relat_1(C)) & k10_relat_1(C,B) = k10_relat_1(C,A) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 938 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 939 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 940 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 941 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_relat_1(A)) & k5_relat_1(C,A) = k5_relat_1(B,A) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) & k1_relat_1(B) = k1_relat_1(C) -> C = B)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 942 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k10_relat_1(B,k9_relat_1(B,A)))))) # label(t146_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 943 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 944 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k2_relat_1(B) & k1_relat_1(B) = k2_relat_1(A) & v2_funct_1(A) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (C = k1_funct_1(B,D) <-> k1_funct_1(A,C) = D))) -> B = k2_funct_1(A)))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 945 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A))) & k2_relat_1(k5_relat_1(A,k2_funct_1(A))) = k1_relat_1(A)))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 946 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k4_relat_1(A) = k2_funct_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 947 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k5_relat_1(k6_relat_1(A),C),B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 948 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k9_relat_1(B,k10_relat_1(B,A))))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 949 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 950 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> A = k2_funct_1(k2_funct_1(A))))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 951 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 952 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(A,k9_relat_1(C,B)) = k9_relat_1(k8_relat_1(A,C),B))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 953 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 954 (all A all B -((all C (v1_funct_1(C) & v1_relat_1(C) -> -(r1_tarski(k2_relat_1(C),A) & k1_relat_1(C) = B))) & -(B != k1_xboole_0 & A = k1_xboole_0))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 955 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 956 (all A (v2_funct_1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 957 (all A k6_relat_1(A) = k2_funct_1(k6_relat_1(A))) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 958 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> v2_funct_1(k7_relat_1(B,A))))) # label(t84_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 959 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k4_xboole_0(A,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 960 (all A (v1_funct_1(A) <-> (all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 961 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k6_relat_1(A) <-> k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 962 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 963 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k9_relat_1(A,k4_xboole_0(B,C)) = k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 964 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 965 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(B) & k1_relat_1(B) = A & B = k5_relat_1(C,B) & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(C) -> C = k6_relat_1(A)))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 966 (all A all B all C (v1_relat_1(C) -> r1_tarski(k3_xboole_0(A,k10_relat_1(C,B)),k10_relat_1(C,k3_xboole_0(k9_relat_1(C,A),B))))) # label(t151_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 967 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -(r2_hidden(B,k1_relat_1(A)) & v1_xboole_0(k1_funct_1(A,B)))) <-> v2_relat_1(A)))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 968 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 969 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 970 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 971 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 972 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 973 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((r2_hidden(B,k1_relat_1(A)) -> (k1_funct_1(A,B) = C <-> r2_hidden(k4_tarski(B,C),A))) & (-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> C = k1_funct_1(A,B))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 974 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) <-> r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 975 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 976 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 977 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k5_relat_1(k6_relat_1(A),B)))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 978 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 979 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 980 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 981 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A) & k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 982 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 983 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k9_relat_1(B,k10_relat_1(B,A)) = k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 984 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) & k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 985 (all A ((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) & (all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) -> v1_relat_1(A) & v1_funct_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 986 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A)))) <-> r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 987 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k7_relat_1(C,A) = B <-> k3_xboole_0(k1_relat_1(C),A) = k1_relat_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D)))))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 988 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k2_relat_1(B) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(A) & v2_funct_1(B)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 989 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 990 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 991 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 992 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 993 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 994 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 995 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k1_relat_1(D) & k1_relat_1(C) = A & k5_relat_1(B,C) = k5_relat_1(B,D) -> C = D))))) & r1_tarski(k2_relat_1(B),A) -> k2_relat_1(B) = A))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 996 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 997 (all A all B (r2_hidden(B,A) -> k1_funct_1(k6_relat_1(A),B) = B)) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 998 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))),k3_xboole_0(k9_relat_1(C,A),B)))) # label(t149_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 999 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1000 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1001 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(B) & k1_relat_1(C) = A -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1002 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1003 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k3_xboole_0(k9_relat_1(C,A),B) = k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1004 (all A (k1_xboole_0 != A -> (all B exists C (v1_relat_1(C) & v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & A = k1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1005 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1006 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) & v2_funct_1(B) -> A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) & k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) = A))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1007 (all A all B all C (p1_s1_funct_1(A,C) & p1_s1_funct_1(A,B) -> B = C)) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C))))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1008 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1009 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B)))) <-> v3_relat_1(A)))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1010 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1011 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_tarski(k1_funct_1(B,A)) = k9_relat_1(B,k1_tarski(A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1012 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> k2_funct_1(k5_relat_1(A,B)) = k5_relat_1(k2_funct_1(B),k2_funct_1(A))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1013 (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) & (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> B = C)) -> (exists A (f1_s2_funct_1 = k1_relat_1(A) & v1_relat_1(A) & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1014 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1015 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_tarski(A) -> k1_tarski(k1_funct_1(B,A)) = k2_relat_1(B)))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1016 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1017 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k2_relat_1(A) = k1_relat_1(k5_relat_1(k2_funct_1(A),A))))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1018 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C))) <-> v2_funct_1(A)))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1019 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1020 (all A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1021 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1022 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1023 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(k2_funct_1(B),A) = k9_relat_1(B,A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1024 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)))))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1025 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1026 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1027 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1028 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1029 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1030 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1031 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1032 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k3_xboole_0(A,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1033 (exists A (v1_funct_1(A) & v1_relat_1(A) & v2_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1034 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1035 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1036 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1037 (exists A (f1_s3_funct_1 = k1_relat_1(A) & v1_funct_1(A) & v1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> k1_funct_1(A,B) = f2_s3_funct_1(B))))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1038 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_relat_1(B) & k2_relat_1(C) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(B) -> B = C))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1039 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1040 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & k1_relat_1(B) = k2_relat_1(A) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1041 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1042 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k6_relat_1(k2_relat_1(A)) = k5_relat_1(B,A) & k1_relat_1(A) = k2_relat_1(B) & v2_funct_1(A) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1043 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1044 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(B,k1_funct_1(C,A)) = k1_funct_1(k5_relat_1(C,B),A)))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1045 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1046 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1047 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) <-> r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1048 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.27 1049 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(C)) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(k5_relat_1(B,C),k9_relat_1(C,A)))))))) # label(t160_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1050 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1051 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1052 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1053 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k2_funct_1(A) <-> (all C all D ((r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C) -> k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A))) & (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C)))) & k1_relat_1(B) = k2_relat_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1054 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1055 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1056 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(B,A) = k9_relat_1(k2_funct_1(B),A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1057 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1058 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1059 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (C = k9_relat_1(A,B) <-> (all D ((exists E (D = k1_funct_1(A,E) & r2_hidden(E,B) & r2_hidden(E,k1_relat_1(A)))) <-> r2_hidden(D,C))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1060 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(k8_relat_1(A,B)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t89_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1061 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & v1_funct_1(B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1062 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1063 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1064 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1065 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1066 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1067 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (B = k8_relat_1(A,C) <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(k1_funct_1(C,D),A) & r2_hidden(D,k1_relat_1(C))))))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1068 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & B = k1_funct_1(C,A) <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1069 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1070 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1071 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B -(r2_hidden(B,k2_relat_1(A)) & (all C k10_relat_1(A,k1_tarski(B)) != k1_tarski(C)))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1072 (all A all B (v1_relat_1(B) -> ((all C -(k1_xboole_0 = k10_relat_1(B,k1_tarski(C)) & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1073 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k5_relat_1(A,B) = A & k2_relat_1(A) = k1_relat_1(B) -> k6_relat_1(k1_relat_1(B)) = B))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1074 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B)) = k9_relat_1(C,k2_tarski(A,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1075 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) & r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1076 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1077 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1078 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1079 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & k1_relat_1(A) = k1_relat_1(B) -> B = A))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1080 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1081 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1082 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1083 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1084 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k9_relat_1(k6_relat_1(A),B) = B)) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1085 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1086 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k8_relat_1(A,B)) & v1_relat_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1087 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1088 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1089 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1090 (all A all B all C (v1_relat_1(C) -> k10_relat_1(k7_relat_1(C,A),B) = k3_xboole_0(A,k10_relat_1(C,B)))) # label(t139_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1091 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1092 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C)))) <-> B = k2_relat_1(A))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1093 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1094 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1095 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k1_relat_1(C) & k2_relat_1(B) = A & k1_relat_1(D) = A & k5_relat_1(B,D) = k5_relat_1(B,C) -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1096 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & v2_funct_1(C) & r1_tarski(A,k1_relat_1(C)) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1097 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A)) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1098 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1099 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(C,B) = k1_funct_1(k8_relat_1(A,C),B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1100 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(r2_hidden(D,k1_relat_1(B)) & C = k1_funct_1(B,D))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1101 $T # label(t5_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1102 $T # label(t22_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1103 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(C,B) & r1_tarski(A,B) -> v1_relat_1(k2_xboole_0(A,C)) & v1_funct_1(k2_xboole_0(A,C))))))))) # label(t32_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1104 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) & v2_funct_1(B) -> v2_funct_1(A)))))) # label(t26_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1105 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k7_relat_1(A,k1_tarski(B)) = k1_tarski(k4_tarski(B,k1_funct_1(A,B))))))) # label(t89_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1106 $T # label(t86_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1107 $T # label(t62_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1108 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> v1_funct_1(k2_xboole_0(A,B)) & v1_relat_1(k2_xboole_0(A,B))))))) # label(t31_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1109 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r1_tarski(A,B) -> k8_relat_1(k2_relat_1(A),B) = A))))) # label(t79_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1110 $T # label(t76_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1111 $T # label(t56_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1112 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k3_xboole_0(A,B) -> v2_funct_1(C) | -v2_funct_1(A) & -v2_funct_1(B)))))))) # label(t30_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1113 $T # label(t45_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1114 $T # label(t2_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1115 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k7_relat_1(C,B)) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B)))) # label(t52_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1116 $T # label(t55_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1117 $T # label(t71_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1118 $T # label(t3_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1119 $T # label(t43_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1120 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(C,D),A) -> B = C))))) # label(t25_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1121 $T # label(t65_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1122 $T # label(t44_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1123 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k8_relat_1(B,C)) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,A),B)))) # label(t67_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1124 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k4_xboole_0(B,A)) & v1_relat_1(k4_xboole_0(B,A)))) # label(t38_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1125 $T # label(t51_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1126 $T # label(t59_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1127 $T # label(t84_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1128 $T # label(t57_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1129 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k3_xboole_0(B,A)) & v1_funct_1(k3_xboole_0(B,A)))) # label(t27_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1130 $T # label(t21_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1131 $T # label(t83_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1132 $T # label(t81_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1133 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> r1_tarski(k5_relat_1(C,k7_relat_1(B,A)),k5_relat_1(C,B)) & r1_tarski(k5_relat_1(k7_relat_1(B,A),D),k5_relat_1(B,D)))))))) # label(t54_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1134 $T # label(t63_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1135 $T # label(t73_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1136 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(B)) & r1_tarski(B,C) -> k7_relat_1(C,A) = k7_relat_1(B,A)))))) # label(t88_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1137 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(D,C)) -> r2_hidden(k4_tarski(k1_funct_1(D,A),B),C) & r2_hidden(k4_tarski(A,k1_funct_1(D,A)),D)))))) # label(t12_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1138 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,k1_funct_1(C,A)),C) & r2_hidden(k1_funct_1(C,A),B) <-> r2_hidden(A,k10_relat_1(C,B))))) # label(t87_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1139 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> -(k2_xboole_0(C,D) = B & k1_funct_1(C,A) != k1_funct_1(B,A) & r2_hidden(A,k1_relat_1(B)) & k1_funct_1(D,A) != k1_funct_1(B,A)))))))) # label(t36_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1140 $T # label(t41_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1141 $T # label(t7_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1142 $T # label(t10_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1143 (all A (v1_relat_1(A) & v1_funct_1(A) -> (A = k1_xboole_0 -> k2_funct_1(A) = k1_xboole_0))) # label(t49_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1144 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> k7_relat_1(B,k1_relat_1(A)) = A))))) # label(t64_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1145 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k1_funct_1(C,A) = B))) # label(t16_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1146 $T # label(t80_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1147 $T # label(t14_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1148 $T # label(t61_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1149 $T # label(t78_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1150 $T # label(t82_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1151 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k3_xboole_0(B,C) = A -> r1_tarski(k2_relat_1(A),k3_xboole_0(k2_relat_1(B),k2_relat_1(C))) & r1_tarski(k1_relat_1(A),k3_xboole_0(k1_relat_1(B),k1_relat_1(C)))))))))) # label(t28_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1152 $T # label(t58_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1153 $T # label(t39_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1154 $T # label(t20_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1155 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> r1_tarski(k5_relat_1(C,k8_relat_1(A,B)),k5_relat_1(C,B)) & r1_tarski(k5_relat_1(k8_relat_1(A,B),D),k5_relat_1(B,D)))))))) # label(t69_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1156 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(t6_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1157 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(A) & C = k2_xboole_0(A,B) & r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) & v2_funct_1(B) -> v2_funct_1(C)))))))) # label(t37_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1158 $T # label(t68_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1159 (all A all B (v1_funct_1(k1_tarski(k4_tarski(A,B))) & v1_relat_1(k1_tarski(k4_tarski(A,B))))) # label(t15_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1160 $T # label(t70_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1161 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C)) & r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B))))))))) # label(t13_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1162 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) & r1_tarski(k1_relat_1(A),k1_relat_1(B)) <-> r1_tarski(A,B)))))) # label(t8_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1163 $T # label(t66_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1164 $T # label(t53_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1165 $T # label(t60_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1166 (all A all B all C all D (v1_funct_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) & v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) <-> (A = C -> B = D))) # label(t19_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1167 $T # label(t75_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1168 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k2_xboole_0(D,B) = C & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k1_funct_1(C,A)))))))) # label(t35_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1169 $T # label(t40_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1170 $T # label(t24_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1171 $T # label(t85_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1172 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_tarski(A) = k1_relat_1(B) -> B = k1_tarski(k4_tarski(A,k1_funct_1(B,A)))))) # label(t18_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1173 $T # label(t48_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1174 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(B)) & C = k2_xboole_0(B,D) -> k1_funct_1(C,A) = k1_funct_1(B,A)))))))) # label(t34_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1175 $T # label(t74_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1176 $T # label(t72_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1177 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B all C (r2_hidden(k4_tarski(C,B),k2_funct_1(A)) <-> r2_hidden(k4_tarski(B,C),A)))))) # label(t47_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1178 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) & k1_relat_1(A) = k1_relat_1(B) -> A = B))))) # label(t9_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1179 $T # label(t42_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1180 (all A (v1_relat_1(A) & v1_funct_1(A) -> (A = k1_xboole_0 -> v2_funct_1(A)))) # label(t46_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1181 $T # label(t50_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1182 $T # label(t17_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1183 $T # label(t77_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1184 $T # label(t1_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1185 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k3_xboole_0(C,D) = B & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k1_funct_1(D,A) & k1_funct_1(C,A) = k1_funct_1(B,A)))))))) # label(t29_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1186 $T # label(t11_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1187 $T # label(t23_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1188 $T # label(t4_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1189 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k2_xboole_0(B,C) -> k2_xboole_0(k2_relat_1(B),k2_relat_1(C)) = k2_relat_1(A) & k1_relat_1(A) = k2_xboole_0(k1_relat_1(B),k1_relat_1(C))))))))) # label(t33_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1190 (all A (v1_relat_1(A) -> (v4_relat_2(A) <-> r4_relat_2(A,k3_relat_1(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1191 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) -> v5_relat_2(k4_xboole_0(A,B))))))) # label(t38_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1192 (all A (v1_relat_1(A) -> (r8_relat_2(A,k3_relat_1(A)) <-> v8_relat_2(A)))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1193 (all A (v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)))) # label(t23_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1194 (all A (v1_relat_1(A) -> (r1_tarski(k3_xboole_0(A,k4_relat_1(A)),k6_relat_1(k1_relat_1(A))) <-> v4_relat_2(A)))) # label(t39_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1195 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1196 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1197 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(k4_tarski(D,C),A) & r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) -> D = C)) <-> r4_relat_2(A,B))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1198 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v3_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1199 (all A all B (v1_relat_1(B) -> (r5_relat_2(B,A) -> r4_relat_2(k2_xboole_0(B,k6_relat_1(A)),A)))) # label(t20_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1200 (all A (v1_relat_1(A) -> (r7_relat_2(A,k3_relat_1(A)) <-> v7_relat_2(A)))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1201 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(D,B) & -r2_hidden(k4_tarski(C,D),A) & -r2_hidden(k4_tarski(D,C),A))) <-> r7_relat_2(A,B))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1202 (all A (v1_relat_1(A) -> (v2_relat_2(A) & v8_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1203 (all A (v1_relat_1(A) -> (v8_relat_2(A) -> v8_relat_2(k4_relat_1(A))))) # label(t42_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1204 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v2_relat_2(A) & v4_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1205 (all A (v1_relat_1(A) -> (r5_relat_2(A,k3_relat_1(A)) <-> v5_relat_2(A)))) # label(d13_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1206 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1207 (all A (v1_relat_1(A) -> (r1_tarski(k5_relat_1(A,A),A) <-> v8_relat_2(A)))) # label(t44_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1208 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A)))))) # label(t45_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1209 (all A (v1_relat_1(A) -> (all B (r2_relat_2(A,B) <-> (all C -(r2_hidden(C,B) & r2_hidden(k4_tarski(C,C),A))))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1210 (all A (v1_relat_1(A) -> (r1_relat_2(A,k3_relat_1(A)) <-> v1_relat_2(A)))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1211 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1212 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1213 (all A (v1_relat_1(A) -> (k2_xboole_0(A,k4_relat_1(A)) = k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) <-> v7_relat_2(A)))) # label(t47_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1214 (all A (v1_relat_1(A) -> (r6_relat_2(A,k3_relat_1(A)) <-> v6_relat_2(A)))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1215 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1216 (all A (v1_relat_1(A) -> (v4_relat_2(A) -> v4_relat_2(k4_relat_1(A))))) # label(t40_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1217 (all A (v1_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)))) # label(t24_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1218 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v4_relat_2(A) -> v4_relat_2(k3_xboole_0(A,B)) & v4_relat_2(k4_xboole_0(A,B))))))) # label(t41_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1219 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1220 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B))) <-> r5_relat_2(A,B))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1221 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v1_relat_2(A) & v6_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1222 (all A (v1_relat_1(A) -> (all B ((all C all D all E (r2_hidden(E,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,E),A) -> r2_hidden(k4_tarski(C,E),A))) <-> r8_relat_2(A,B))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1223 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(A) -> v2_relat_2(k4_xboole_0(A,B))))))) # label(t33_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1224 (all A (v1_relat_1(A) -> (v3_relat_2(A) <-> k4_relat_1(A) = A))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1225 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1226 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(A) & v8_relat_2(B) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1227 (all A (v1_relat_1(A) -> (v3_relat_2(A) -> v3_relat_2(k4_relat_1(A))))) # label(t34_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1228 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v1_relat_2(A) & v1_relat_2(B) -> v1_relat_2(k2_xboole_0(A,B)) & v1_relat_2(k3_xboole_0(A,B))))))) # label(t31_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1229 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(A) & v3_relat_2(B) -> v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k4_xboole_0(A,B)) & v3_relat_2(k2_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1230 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1231 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1232 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1233 (all A (v1_relat_1(A) -> (v2_relat_2(A) -> v2_relat_2(k4_relat_1(A))))) # label(t28_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1234 (all A (v1_relat_1(A) -> (r1_tarski(k6_relat_1(k3_relat_1(A)),A) <-> v1_relat_2(A)))) # label(t17_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1235 (all A all B (v1_relat_1(B) -> (r4_relat_2(B,A) <-> r5_relat_2(k4_xboole_0(B,k6_relat_1(A)),A)))) # label(t19_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1236 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1237 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v5_relat_2(k4_relat_1(A))))) # label(t36_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1238 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1239 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r1_xboole_0(k6_relat_1(k3_relat_1(A)),A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1240 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r2_relat_2(A,k3_relat_1(A))))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1241 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1242 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1243 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> v1_relat_2(k4_relat_1(A))))) # label(t27_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1244 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) & v5_relat_2(B) -> v5_relat_2(k3_xboole_0(A,B))))))) # label(t37_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1245 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1246 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) -> r2_hidden(k4_tarski(C,C),A))) <-> r1_relat_2(A,B))))) # label(d1_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1247 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(B) & v2_relat_2(A) -> v2_relat_2(k2_xboole_0(A,B)) & v2_relat_2(k3_xboole_0(A,B))))))) # label(t32_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1248 (all A (v1_relat_1(A) -> (r3_relat_2(A,k3_relat_1(A)) <-> v3_relat_2(A)))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1249 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k2_relat_1(k4_relat_1(A)) = k2_relat_1(A) & k1_relat_1(A) = k1_relat_1(k4_relat_1(A))))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1250 (all A (v1_relat_1(A) -> (all B ((all C all D -(-r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) & C != D & -r2_hidden(k4_tarski(D,C),A) & r2_hidden(D,B))) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1251 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1252 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1253 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1254 (all A all B (v1_funct_1(A) & v3_ordinal1(B) & v1_relat_1(A) & v5_ordinal1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1255 (all A all B all C all D all E all F -(r2_hidden(C,D) & r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(F,A) & r2_hidden(E,F))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1256 (all A A != k1_ordinal1(A)) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1257 (all A (v3_ordinal1(A) -> (all B ((exists C ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = f3_s5_ordinal1(k2_ordinal1(C,D))))) & f3_s5_ordinal1(C) = B & v5_ordinal1(C) & v1_relat_1(C) & v1_funct_1(C) & k1_relat_1(C) = A)) <-> B = f2_s5_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f2_s5_ordinal1(A)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1258 (exists A (v1_funct_1(A) & (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) -> (C = k2_ordinal1(A,B) & r2_hidden(B,f1_s4_ordinal1) -> k1_funct_1(A,B) = f2_s4_ordinal1(C)))))) & v1_relat_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s4_ordinal1)) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1259 (all A all B -(r1_tarski(B,A) & r2_hidden(A,B))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1260 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r1_ordinal1(B,A) | r1_ordinal1(A,B))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1261 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(B != A & -r2_hidden(B,A) & -r2_hidden(A,B)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1262 (all A all B (r2_hidden(A,B) | A = B <-> r2_hidden(A,k1_ordinal1(B)))) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1263 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_tarski(A,B) <-> r1_ordinal1(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1264 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1265 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1266 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1267 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1268 (exists A (v3_ordinal1(A) & p1_s1_ordinal1(A))) -> (exists A (p1_s1_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & v3_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1269 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1270 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1271 (all A -((all B (r2_hidden(B,A) -> v3_ordinal1(B))) & (all B (v3_ordinal1(B) -> -r1_tarski(A,B))))) # label(t36_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1272 (exists A (-v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1273 (all A all B (m1_ordinal1(B,A) -> (all C (v3_ordinal1(C) -> m1_ordinal1(k2_ordinal1(B,C),A))))) # label(t48_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1274 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1275 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1276 (all A all B all C -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,A))) # label(t3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1277 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1278 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v5_ordinal1(A) <-> v3_ordinal1(k1_relat_1(A))))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1279 f1_s3_ordinal1 = k1_relat_1(f3_s3_ordinal1) & k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f3_s3_ordinal1,A) = B -> k1_funct_1(f3_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (B = k2_ordinal1(f4_s3_ordinal1,A) & r2_hidden(A,f1_s3_ordinal1) -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) -> f4_s3_ordinal1 = f3_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1280 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1281 (exists A (v1_ordinal1(A) & v2_ordinal1(A) & v1_xboole_0(A) & v3_ordinal1(A) & v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1282 (all A (v3_ordinal1(A) -> v2_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1283 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1284 (all A (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1285 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1286 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(B,A) & B != A & -r2_xboole_0(A,B)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1287 (all A (v3_ordinal1(A) -> v1_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1288 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1289 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_xboole_0(A,B) -> r2_hidden(A,B)))))) # label(t21_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1290 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1291 (all A ((all B all C -(r2_hidden(C,A) & -r2_hidden(B,C) & C != B & -r2_hidden(C,B) & r2_hidden(B,A))) <-> v2_ordinal1(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1292 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1293 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r3_xboole_0(B,C))) <-> v6_ordinal1(A))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1294 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> A = B)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1295 (all A -(all B (r2_hidden(B,A) <-> v3_ordinal1(B)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1296 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s2_ordinal1(B)))) -> p1_s2_ordinal1(A)))) -> (all A (v3_ordinal1(A) -> p1_s2_ordinal1(A))) # label(s2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1297 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(E,A) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(C,D))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1298 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1299 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1300 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1301 (all A all B (v1_relat_1(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_funct_1(A) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1302 (all A (v4_ordinal1(A) <-> A = k3_tarski(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1303 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v1_ordinal1(A) & v3_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1304 (all A all B (v3_ordinal1(B) -> -(r1_tarski(A,B) & (all C (v3_ordinal1(C) -> -((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D)))) & r2_hidden(C,A)))) & k1_xboole_0 != A))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1305 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1306 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1307 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r2_hidden(B,A) | r1_ordinal1(A,B))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1308 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r1_tarski(A,B) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1309 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1310 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1311 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1312 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1313 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1314 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1315 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,k1_ordinal1(B)) <-> r1_ordinal1(A,B)))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1316 (all A all B (r1_tarski(A,B) -> (all C (m1_ordinal1(C,A) -> m1_ordinal1(C,B))))) # label(t47_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1317 (all A exists B (v3_ordinal1(B) & -r2_hidden(B,A) & (all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1318 (all A all B (m1_ordinal1(B,A) -> v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1319 (all A all B (v5_ordinal1(B) & v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) <-> m1_ordinal1(B,A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1320 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1321 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r1_ordinal1(k1_ordinal1(A),B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1322 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1323 (all A (v2_ordinal1(A) & v1_ordinal1(A) <-> v3_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1324 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v2_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1325 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1326 (all A ((all B (r2_hidden(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)) & v1_relat_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1327 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A))) <-> v1_ordinal1(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1328 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) <-> (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A))))))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1329 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(C,A) & r2_hidden(A,B) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1330 (all A all B all C all D -(r2_hidden(B,C) & r2_hidden(D,A) & r2_hidden(A,B) & r2_hidden(C,D))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1331 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1332 (all A (v3_ordinal1(A) -> -(-v4_ordinal1(A) & (all B (v3_ordinal1(B) -> k1_ordinal1(B) != A))) & -((exists B (v3_ordinal1(B) & A = k1_ordinal1(B))) & v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.28 1333 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k3_tarski(A)))) # label(t35_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1334 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B) & r1_tarski(B,A))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1335 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B))) & r2_hidden(B,k3_relat_1(A))))))) # label(t57_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1336 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D)),A) & k1_funct_1(B,C) != k1_funct_1(B,D) | D = C)) & r1_tarski(k2_relat_1(B),k3_relat_1(A)) & k3_relat_1(A) = k1_relat_1(B) & v2_wellord1(A) -> (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(C,k1_funct_1(B,C)),A)))))))) # label(t43_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1337 (all A all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k2_wellord1(B,A)),k3_relat_1(B)) & r1_tarski(k3_relat_1(k2_wellord1(B,A)),A))) # label(t20_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1338 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> ((all C (r2_hidden(C,A) -> (all D (r2_hidden(k4_tarski(D,C),B) -> r2_hidden(D,A))))) <-> -((all C -(r2_hidden(C,k3_relat_1(B)) & A = k1_wellord1(B,C))) & A != k3_relat_1(B)))))) # label(t36_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1339 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> -(-r4_wellord1(A,B) & v2_wellord1(A) & v2_wellord1(B) & (all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(A,k2_wellord1(B,k1_wellord1(B,C))))) & (all C -(r4_wellord1(k2_wellord1(A,k1_wellord1(A,C)),B) & r2_hidden(C,k3_relat_1(A))))))))) # label(t63_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1340 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r3_wellord1(A,B,D) & r3_wellord1(B,C,E) -> r3_wellord1(A,C,k5_relat_1(D,E))))))))))))) # label(t51_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1341 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> v2_wellord1(k2_wellord1(B,A))))) # label(t32_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1342 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) & r4_wellord1(A,B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k3_wellord1(A,B) <-> r3_wellord1(A,B,C))))))))) # label(d9_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1343 (all A all B (v1_relat_1(B) -> (v8_relat_2(B) -> v8_relat_2(k2_wellord1(B,A))))) # label(t24_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1344 (all A all B all C (v1_relat_1(C) -> k2_wellord1(C,k3_xboole_0(A,B)) = k2_wellord1(k2_wellord1(C,A),B))) # label(t26_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1345 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) <-> (all D all E (r2_hidden(E,k3_relat_1(A)) & r2_hidden(D,k3_relat_1(A)) & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) <-> r2_hidden(k4_tarski(D,E),A))) & v2_funct_1(C) & k2_relat_1(C) = k3_relat_1(B) & k3_relat_1(A) = k1_relat_1(C)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1346 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) <-> (exists C (r3_wellord1(A,B,C) & v1_relat_1(C) & v1_funct_1(C)))))))) # label(d8_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1347 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1348 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> (all C -((all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B))) & r2_hidden(D,C))) & r1_tarski(C,A) & C != k1_xboole_0))))) # label(t9_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1349 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) & r1_relat_2(A,B) & r1_wellord1(A,B) & r6_relat_2(A,B) & r8_relat_2(A,B) <-> r2_wellord1(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1350 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> (all D all E (r2_hidden(k4_tarski(D,E),A) -> D = E | r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & k1_funct_1(C,D) != k1_funct_1(C,E)))))))))) # label(t45_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1351 (all A all B all C (v1_relat_1(C) -> -(r2_hidden(B,k3_relat_1(C)) & A != B & r4_wellord1(k2_wellord1(C,k1_wellord1(C,A)),k2_wellord1(C,k1_wellord1(C,B))) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C)))) # label(t58_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1352 (all A all B (v1_relat_1(B) -> (v6_relat_2(B) -> v6_relat_2(k2_wellord1(B,A))))) # label(t23_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1353 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k2_wellord1(k2_wellord1(C,B),A) = k2_wellord1(C,A)))) # label(t29_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1354 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1355 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r3_wellord1(A,B,C) & r3_wellord1(A,B,D) -> C = D)))))))))) # label(t55_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1356 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1357 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,k3_relat_1(B)) & r3_wellord1(B,C,D) & v2_wellord1(B) -> r4_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A))) & r3_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)),k7_relat_1(D,A))))))))) # label(t59_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1358 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -((all C -((all D (r2_hidden(D,B) -> r2_hidden(k4_tarski(C,D),A))) & r2_hidden(C,B))) & r1_tarski(B,k3_relat_1(A)) & B != k1_xboole_0))))) # label(t10_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1359 (all A all B all C all D (v1_relat_1(D) -> (all E (v1_relat_1(E) -> (v2_wellord1(D) & r4_wellord1(k2_wellord1(D,k1_wellord1(D,A)),k2_wellord1(E,k1_wellord1(E,C))) & r4_wellord1(D,k2_wellord1(E,k1_wellord1(E,B))) & r2_hidden(A,k3_relat_1(D)) & r2_hidden(B,k3_relat_1(E)) & r2_hidden(C,k3_relat_1(E)) & v2_wellord1(E) -> r1_tarski(k1_wellord1(E,C),k1_wellord1(E,B)) & r2_hidden(k4_tarski(C,B),E)))))) # label(t62_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1360 (all A (v1_relat_1(A) -> (all B ((all C -(C != k1_xboole_0 & r1_tarski(C,B) & (all D -(r2_hidden(D,C) & r1_xboole_0(k1_wellord1(A,D),C))))) <-> r1_wellord1(A,B))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1361 (all A all B (v1_relat_1(B) -> r1_tarski(k2_wellord1(B,A),B) & r1_tarski(k2_wellord1(B,A),k2_zfmisc_1(A,A)))) # label(t15_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1362 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1363 (all A (v1_relat_1(A) -> (v4_relat_2(A) & v6_relat_2(A) & v1_wellord1(A) & v8_relat_2(A) & v1_relat_2(A) <-> v2_wellord1(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1364 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) -> (B = A | r2_hidden(A,k1_wellord1(C,B)) <-> r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)))))) # label(t38_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1365 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k1_wellord1(C,A)) & r2_hidden(A,k3_relat_1(C)) -> k1_wellord1(C,B) = k1_wellord1(k2_wellord1(C,k1_wellord1(C,A)),B)))) # label(t35_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1366 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_zfmisc_1(B,B)) & r2_hidden(A,C) <-> r2_hidden(A,k2_wellord1(C,B))))) # label(t16_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1367 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1368 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C)) & v2_wellord1(C) -> (r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)) <-> r2_hidden(k4_tarski(A,B),C))))) # label(t37_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1369 (all A all B (v1_relat_1(B) -> r2_hidden(A,k3_relat_1(B)) | k1_xboole_0 = k1_wellord1(B,A))) # label(t2_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1370 (all A (v1_relat_1(A) -> (all B all C (k1_wellord1(A,B) = C <-> (all D (r2_hidden(D,C) <-> B != D & r2_hidden(k4_tarski(D,B),A))))))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1371 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1372 (all A (v1_relat_1(A) -> k2_wellord1(A,k3_relat_1(A)) = A)) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1373 (all A (v1_relat_1(A) -> (r1_wellord1(A,k3_relat_1(A)) <-> v1_wellord1(A)))) # label(t5_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1374 (all A all B (v1_relat_1(B) -> (v1_relat_2(B) -> v1_relat_2(k2_wellord1(B,A))))) # label(t22_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1375 (all A all B (v1_relat_1(A) -> v1_relat_1(k2_wellord1(A,B)))) # label(dt_k2_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1376 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> A = k3_relat_1(k2_wellord1(B,A))))) # label(t39_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1377 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) -> r4_wellord1(B,A)))))) # label(t50_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1378 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) -> r3_xboole_0(k1_wellord1(C,A),k1_wellord1(C,B))))) # label(t33_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1379 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B ((all C (r2_hidden(C,k3_relat_1(A)) & r1_tarski(k1_wellord1(A,C),B) -> r2_hidden(C,B))) -> r1_tarski(k3_relat_1(A),B)))))) # label(t41_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1380 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) & v2_wellord1(A) -> (all D -((all E -(r2_hidden(E,k3_relat_1(B)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,D)),k2_wellord1(B,k1_wellord1(B,E))))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t61_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1381 (all A all B all C (v1_relat_1(C) -> r1_tarski(k1_wellord1(k2_wellord1(C,A),B),k1_wellord1(C,B)))) # label(t21_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1382 (all A all B (v1_relat_1(B) -> k2_wellord1(k2_wellord1(B,A),A) = k2_wellord1(B,A))) # label(t28_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1383 (all A (v1_relat_1(A) -> ((all B -(k1_xboole_0 != B & (all C -(r2_hidden(C,B) & r1_xboole_0(k1_wellord1(A,C),B))) & r1_tarski(B,k3_relat_1(A)))) <-> v1_wellord1(A)))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1384 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> r2_wellord1(A,k3_relat_1(A))))) # label(t8_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1385 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> k3_relat_1(k2_wellord1(B,k1_wellord1(B,A))) = k1_wellord1(B,A)))) # label(t40_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1386 (all A all B (v1_relat_1(B) -> k8_relat_1(A,k7_relat_1(B,A)) = k2_wellord1(B,A))) # label(t18_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1387 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1388 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1389 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> (v1_wellord1(A) -> v1_wellord1(B)) & (v4_relat_2(A) -> v4_relat_2(B)) & (v6_relat_2(A) -> v6_relat_2(B)) & (v1_relat_2(A) -> v1_relat_2(B)) & (v8_relat_2(A) -> v8_relat_2(B))))))))) # label(t53_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1390 (all A all B all C (v1_relat_1(C) -> (r2_hidden(B,k3_relat_1(C)) & v2_wellord1(C) & r2_hidden(A,k3_relat_1(C)) & (all D (r2_hidden(D,k1_wellord1(C,A)) -> r2_hidden(k4_tarski(D,B),C) & B != D)) -> r2_hidden(k4_tarski(A,B),C)))) # label(t42_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1391 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k3_relat_1(B)) & (all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(k2_wellord1(B,k1_wellord1(B,C)),k2_wellord1(B,A)))) & v2_wellord1(B) & -r4_wellord1(B,k2_wellord1(B,A))))) # label(t64_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1392 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -((all C -(r2_hidden(k4_tarski(B,C),A) & (all D -(r2_hidden(D,k3_relat_1(A)) & r2_hidden(k4_tarski(B,D),A) & -r2_hidden(k4_tarski(C,D),A) & D != B)) & r2_hidden(C,k3_relat_1(A)))) & (exists C (-r2_hidden(k4_tarski(C,B),A) & r2_hidden(C,k3_relat_1(A)))) & r2_hidden(B,k3_relat_1(A)))) | k1_xboole_0 = k3_relat_1(A)))) # label(t12_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1393 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1394 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(k2_wellord1(C,B))) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(A,B)))) # label(t19_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1395 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) -> r3_wellord1(B,A,k2_funct_1(C))))))))) # label(t49_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1396 (all A (v1_relat_1(A) -> -(v2_wellord1(A) & k3_relat_1(A) != k1_xboole_0 & (all B -(r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A)))))))) # label(t11_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1397 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k3_wellord1(A,B)) & v1_funct_1(k3_wellord1(A,B)))) # label(dt_k3_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1398 (all A (v1_relat_1(A) -> (all B k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B))))) # label(d6_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1399 (all A all B (v1_relat_1(B) -> (v1_wellord1(B) -> v1_wellord1(k2_wellord1(B,A))))) # label(t31_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1400 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r4_wellord1(A,B) & r4_wellord1(B,C) -> r4_wellord1(A,C)))))))) # label(t52_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1401 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1402 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> (all D -((all E -(k9_relat_1(C,k1_wellord1(A,D)) = k1_wellord1(B,E) & r2_hidden(E,k3_relat_1(B)))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t60_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1403 (all A all B all C (v1_relat_1(C) -> k2_wellord1(k2_wellord1(C,B),A) = k2_wellord1(k2_wellord1(C,A),B))) # label(t27_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1404 (all A (v1_relat_1(A) -> r3_wellord1(A,A,k6_relat_1(k3_relat_1(A))))) # label(t47_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1405 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1406 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> v2_wellord1(B)))))))) # label(t54_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1407 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1408 (all A all B (v1_relat_1(B) -> k7_relat_1(k8_relat_1(A,B),A) = k2_wellord1(B,A))) # label(t17_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1409 (all A all B (v1_relat_1(B) -> r1_tarski(k1_wellord1(B,A),k3_relat_1(B)))) # label(t13_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1410 (all A all B (v1_relat_1(B) -> (v4_relat_2(B) -> v4_relat_2(k2_wellord1(B,A))))) # label(t25_wellord1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1411 (all A all B all C all D (r2_hidden(C,A) & r2_hidden(D,B) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1412 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1413 (all A all B all C all D (m1_relset_1(D,A,B) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B))) # label(dt_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1414 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k4_relset_1(B,A,C)))) & r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t50_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1415 (all A all B all C (m2_relset_1(C,B,A) -> ((all D -((all E -r2_hidden(k4_tarski(D,E),C)) & r2_hidden(D,B))) <-> k4_relset_1(B,A,C) = B))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1416 (all A all B all C all D (m1_relset_1(C,A,B) -> m2_relset_1(k8_relset_1(A,B,C,D),A,B))) # label(dt_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1417 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1418 (all A all B all C (m1_relset_1(C,A,B) -> m2_relset_1(k6_relset_1(A,B,C),B,A))) # label(dt_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1419 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k1_relset_1(A,B,C,D),A,B))) # label(dt_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1420 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1421 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1422 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> v1_relat_1(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1423 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1424 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(k2_relat_1(D),B) -> m2_relset_1(D,C,B)))) # label(t14_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1425 (all A all B all C (m1_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k2_relat_1(C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1426 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k11_relset_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1427 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> C = k1_xboole_0))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1428 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> ((exists E (r2_hidden(k4_tarski(D,E),C) & m1_subset_1(E,B))) <-> r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1429 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(A,B) -> m2_relset_1(D,C,B)))) # label(t16_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1430 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1431 (exists A ((all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (r2_hidden(k4_tarski(B,C),A) <-> p1_s2_relset_1(B,C)))))) & m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1432 (all A all B all C (m2_relset_1(C,B,A) -> k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) & k4_relset_1(B,A,C) = k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1433 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> C = k2_relset_1(A,B,C,C))) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1434 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(A,B) -> m2_relset_1(D,B,C)))) # label(t15_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1435 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> k9_relset_1(A,B,C,D) = D))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1436 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> B = k4_relset_1(B,A,C) & r1_tarski(B,k5_relset_1(B,A,C))))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1437 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(k6_relat_1(C),D) -> r1_tarski(C,k4_relset_1(A,B,D)) & r1_tarski(C,k5_relset_1(A,B,D))))) # label(t30_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1438 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(C,D) & r1_tarski(A,B) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1439 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C)))) & r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1440 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1441 (all A all B (m2_relset_1(B,A,A) -> k5_relat_1(B,k6_relat_1(A)) = B & B = k5_relat_1(k6_relat_1(A),B))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1442 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,D) = k3_xboole_0(C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1443 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k10_relset_1(A,B,C,A) & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1444 (all A all B all C (m2_relset_1(C,A,B) <-> m1_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1445 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1446 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> ((exists H (r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E) & m1_subset_1(H,B))) <-> r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1447 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A)))) # label(t10_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1448 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1449 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)) & k5_relset_1(B,A,k6_relset_1(A,B,C)) = k4_relset_1(A,B,C))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1450 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1451 (all A all B all C all D (m2_relset_1(D,A,B) -> -(r2_hidden(C,D) & (all E all F -(r2_hidden(E,A) & C = k4_tarski(E,F) & r2_hidden(F,B)))))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1452 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> ((exists F (r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D) & m1_subset_1(F,C))) <-> r2_hidden(E,k10_relset_1(C,A,D,B))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1453 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1454 (all A all B all C (r1_tarski(C,k2_zfmisc_1(A,B)) <-> m1_relset_1(C,A,B))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1455 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1456 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1457 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)))) # label(dt_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1458 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1459 (all A all B all C (m2_relset_1(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C)))) <-> B = k5_relset_1(A,B,C)))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1460 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> k5_relset_1(A,B,C) = B & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1461 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(k1_relat_1(D),B) -> m2_relset_1(D,B,C)))) # label(t13_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1462 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> D = k8_relset_1(B,A,D,C)))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1463 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_xboole_0(C,D) = k1_relset_1(A,B,C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1464 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,D) = k2_relset_1(A,B,D,C))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1465 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1466 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1467 (all A all B all C all D (m2_relset_1(D,B,C) -> (r1_tarski(A,D) -> m2_relset_1(A,B,C)))) # label(t4_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1468 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> m2_relset_1(k2_relset_1(A,B,C,D),A,B))) # label(dt_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1469 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> (r2_hidden(E,k11_relset_1(A,C,D,B)) <-> (exists F (r2_hidden(k4_tarski(E,F),D) & m1_subset_1(F,C) & r2_hidden(F,B)))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1470 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1471 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1472 (all A all B all C (m1_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k1_relat_1(C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1473 (all A all B all C (m2_relset_1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1474 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1475 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k3_relat_1(C),k2_xboole_0(A,B)))) # label(t19_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1476 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,k6_relset_1(A,B,C)) = C)) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1477 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1) & r2_hidden(C,f2_s1_relset_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1478 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k4_xboole_0(C,D) = k3_relset_1(A,B,C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1479 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1480 (all A all B all C all D (m2_relset_1(D,A,C) -> m2_relset_1(k8_relset_1(A,C,D,B),B,C))) # label(t33_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1481 (all A all B all C (m2_relset_1(C,A,B) -> (m2_relset_1(C,k1_xboole_0,B) -> C = k1_xboole_0))) # label(t26_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1482 (all A all B all C all D (m1_relset_1(D,A,B) -> k9_relset_1(A,B,C,D) = k8_relat_1(C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1483 (all A all B all C all D (m1_relset_1(C,A,B) -> k8_relset_1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1484 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1485 (all A all B all C all D (m1_relset_1(C,A,B) -> k11_relset_1(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1486 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1487 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1488 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> m2_relset_1(B,A,k2_relat_1(B))))) # label(t9_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1489 (all A all B all C all D (m1_relset_1(C,A,B) -> k9_relat_1(C,D) = k10_relset_1(A,B,C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1490 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,C) = k4_relat_1(C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1491 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1492 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1493 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,D,C) = k1_relset_1(A,B,C,D))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1494 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1495 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> ((exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(E,D),C))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1496 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1497 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> k5_relat_1(E,F) = k7_relset_1(A,B,C,D,E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1498 (all A all B all C all D (m2_relset_1(D,C,A) -> m2_relset_1(k9_relset_1(C,A,B,D),C,B))) # label(t35_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1499 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1500 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(C,A),k4_partfun1(C,B)))) # label(t127_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1501 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1502 (all A all B all C (k4_partfun1(A,B) = C <-> (all D ((exists E (r1_tarski(k2_relat_1(E),B) & v1_funct_1(E) & D = E & r1_tarski(k1_relat_1(E),A) & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1503 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1504 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1505 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(C,k6_relat_1(B)))) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1506 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1507 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,C)))) # label(t125_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1508 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k3_partfun1(C,A,B),C))) # label(t147_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1509 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (D = k5_partfun1(A,B,C) <-> (all E ((exists F (m2_relset_1(F,A,B) & r1_partfun1(C,F) & v1_partfun1(F,A,B) & E = F & v1_funct_1(F))) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1510 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1511 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1512 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1513 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1514 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1515 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1516 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1517 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1518 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1519 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1520 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_partfun1(k1_xboole_0,A))) # label(t141_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1521 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (r2_hidden(B,f1_s1_partfun1) -> (-p1_s1_partfun1(B) -> f3_s1_partfun1(B) = k1_funct_1(A,B)) & (p1_s1_partfun1(B) -> k1_funct_1(A,B) = f2_s1_partfun1(B)))) & f1_s1_partfun1 = k1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1522 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1523 (all A all B all C (m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A <-> v1_partfun1(C,A,B)))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1524 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1525 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k3_partfun1(C,A,B) = C)) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1526 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1527 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1528 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1529 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1530 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1531 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D))))) # label(t84_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1532 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1533 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B)))) & r1_partfun1(C,D) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1534 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,D) = k1_funct_1(A,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1535 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) -> k1_funct_1(k3_partfun1(D,B,C),A) = k1_funct_1(D,A)))) # label(t80_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1536 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1537 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1538 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> k2_partfun1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1539 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1540 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1541 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1542 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k3_partfun1(D,B,k3_xboole_0(A,C)) = k9_relset_1(B,C,A,k3_partfun1(D,B,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1543 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & k1_tarski(A) = k1_relat_1(D) -> v1_funct_1(D) & m2_relset_1(D,B,C)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1544 (all A all B all C all D all E all F (r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))))) # label(t1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1545 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1546 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1547 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1548 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),C,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1549 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & (all B all C (p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) & r2_hidden(B,f1_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1550 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.29 1551 (all A exists B (v4_relat_2(B) & v1_relat_1(B) & m1_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_2(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1552 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1553 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r2_hidden(C,k9_relat_1(D,A)) & (all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & C = k1_funct_1(D,E))))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1554 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1555 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (r1_tarski(B,C) & r1_tarski(A,C) & v1_relat_1(C) & v1_funct_1(C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1556 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1557 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1558 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1559 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1560 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1561 (all A (v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1562 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1563 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1564 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1565 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(C,A),B) & r1_tarski(A,k1_relat_1(C)) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1566 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(C,k4_relset_1(A,B,D)) -> r2_hidden(k1_funct_1(D,C),B)))) # label(t27_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1567 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0 & k2_relat_1(B) = k1_xboole_0)) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1568 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1569 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> D = C)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1570 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1571 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1572 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1573 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(C,A,B) & v1_partfun1(D,A,B) & r1_partfun1(C,D) -> D = C))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1574 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1575 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1576 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1577 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k3_partfun1(C,A,B),C))) # label(t76_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1578 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1579 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (A != k1_xboole_0 -> k1_xboole_0 = k5_partfun1(A,k1_xboole_0,B)))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1580 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1581 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1582 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,E) = k1_funct_1(C,D) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1583 (all A all B (m2_relset_1(k1_xboole_0,A,B) & v1_funct_1(k1_xboole_0))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1584 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1585 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1586 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1587 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1588 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1589 (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> r2_hidden(B,f2_s2_partfun1))) & (all A all B all C (p1_s2_partfun1(A,B) & p1_s2_partfun1(A,C) & r2_hidden(A,f1_s2_partfun1) -> B = C)) -> (exists A (v1_funct_1(A) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B (r2_hidden(B,f1_s2_partfun1) & (exists C p1_s2_partfun1(B,C)) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1590 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1591 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1592 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k5_partfun1(A,B,C) = k1_tarski(C) <-> v1_partfun1(C,A,B)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1593 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> m2_relset_1(k2_partfun1(A,B,C,D),A,B) & v1_funct_1(k2_partfun1(A,B,C,D)))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1594 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1595 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r1_partfun1(C,D) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (B = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1596 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),A,B))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1597 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> B = k1_funct_1(D,C)))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1598 (all A (v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1599 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> B = k1_xboole_0)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1600 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1601 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1602 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1603 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1604 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> v2_funct_1(C))) # label(t70_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1605 (all A all B (v1_funct_1(B) & v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1606 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1607 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & (all C (v1_funct_1(C) & v1_relat_1(C) -> k2_xboole_0(A,B) != C))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1608 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1609 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(k6_relat_1(A),C))) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1610 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1611 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1612 (all A all B exists C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_relat_1(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1613 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1614 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1615 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1616 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1617 (exists A (v1_xboole_0(A) & v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1618 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (k4_relset_1(A,B,D) = k4_relset_1(A,B,C) & (all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E)))) -> C = D))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1619 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1620 (all A all B all C (v1_funct_1(A) & v1_relat_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1621 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1622 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1623 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t116_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1624 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1625 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (v1_partfun1(E,A,B) & r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1626 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1627 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))))) # label(t69_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1628 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k3_partfun1(k5_relat_1(D,E),C,B) = k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B))))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1629 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & k1_funct_1(D,E) = C))) & r2_hidden(C,k2_relat_1(D))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1630 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1631 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1632 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k1_xboole_0 = B & v1_partfun1(C,A,B) -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1633 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1634 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(A) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1635 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1636 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_xboole_0,B) -> C = D)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1637 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1638 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1639 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (k2_xboole_0(A,B) = C & v1_relat_1(C) & v1_funct_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1640 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,C) & r1_tarski(B,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1641 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> A = k1_xboole_0)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1642 (all A all B r1_tarski(k4_partfun1(k1_xboole_0,A),k4_partfun1(B,A))) # label(t126_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1643 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1644 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1645 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1646 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k7_relat_1(k8_relat_1(C,A),B) = k3_partfun1(A,B,C)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1647 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> k3_partfun1(C,A,B) = C))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1648 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1649 (all A all B all C (p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) & (all A all B all C all D (p1_s4_partfun1(A,B,D) & p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> D = C)) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1) & v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) <-> r2_hidden(C,f2_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(B,f1_s4_partfun1))))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1650 (all A (v3_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1651 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1652 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1653 (all A all B all C (r2_hidden(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t120_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1654 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1655 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) <-> r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1656 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1657 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A) & v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1658 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k9_relat_1(C,A) = k2_relat_1(C))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1659 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1660 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1661 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1662 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1663 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1664 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1665 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v2_funct_1(B))) # label(t59_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1666 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) & k1_relat_1(A) = k1_relat_1(B) -> A = B))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1667 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1668 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1669 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k7_relat_1(B,A),B))) # label(t144_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1670 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) -> k5_relat_1(E,F) = k1_partfun1(A,B,C,D,E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1671 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> k2_partfun1(A,B,k3_partfun1(D,A,B),C) = k3_partfun1(D,k3_xboole_0(A,C),B))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1672 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1673 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1674 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1675 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1676 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1677 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1678 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1679 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k9_relset_1(A,B,C,D),A,C) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1680 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> k4_relset_1(A,k1_xboole_0,B) = k1_xboole_0 & k1_xboole_0 = k2_relat_1(B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1681 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (k4_relset_1(A,k1_tarski(B),D) = k4_relset_1(A,k1_tarski(B),C) -> D = C))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1682 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) -> v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1683 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1684 (all A all B (v1_funct_1(B) & v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1685 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1686 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1687 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k2_funct_1(k3_partfun1(C,A,B)) = k3_partfun1(k2_funct_1(C),B,A)))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1688 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.41/65.30 1689 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> E = D))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1690 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1691 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(A,C) -> m2_relset_1(D,C,B) & v1_funct_1(D)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1692 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1693 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1694 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(A,k1_relat_1(C)) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1695 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1696 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1697 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1698 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_tarski(k1_xboole_0) = k5_partfun1(k1_xboole_0,A,B))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1699 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_partfun1(C,E) & r1_tarski(D,C) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1700 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1701 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(C,D) -> m2_relset_1(C,A,B) & v1_funct_1(C)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1702 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1703 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1704 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)) & r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1705 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1706 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1707 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1708 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1709 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) <-> p1_s3_partfun1(B) & r2_hidden(B,f1_s3_partfun1))) & (all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> k1_funct_1(A,B) = f3_s3_partfun1(B))))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1710 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1711 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_tarski(B,D) & r1_tarski(A,C) -> m2_relset_1(E,C,D) & v1_funct_1(E)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1712 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1713 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1714 (all A all B all C k4_tarski(k4_tarski(A,B),C) = k3_mcart_1(A,B,C)) # label(d3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1715 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> C = F & B = E & A = D | k1_xboole_0 = B | C = k1_xboole_0 | k1_xboole_0 = A)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1716 (all A all B all C all D k2_enumset1(k4_tarski(A,C),k4_tarski(A,D),k4_tarski(B,C),k4_tarski(B,D)) = k2_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D))) # label(t25_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1717 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1718 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(C,D,A,B)) & -r1_tarski(A,k4_zfmisc_1(A,B,C,D)) & -r1_tarski(A,k4_zfmisc_1(B,C,D,A)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C))) -> k1_xboole_0 = A)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1719 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> E != k10_mcart_1(A,B,C,D,E) & k9_mcart_1(A,B,C,D,E) != E & E != k8_mcart_1(A,B,C,D,E) & E != k11_mcart_1(A,B,C,D,E))) & A != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1720 (all A all B all C all D all E all F all G all H (r2_hidden(C,G) & r2_hidden(D,H) & r2_hidden(B,F) & r2_hidden(A,E) <-> r2_hidden(k4_mcart_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1721 (all A all B all C all D all E all F -(E != k1_xboole_0 & k1_xboole_0 != F & B != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != D & (exists G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) & (exists H (m1_subset_1(H,k3_zfmisc_1(D,E,F)) & -(k6_mcart_1(D,E,F,H) = k6_mcart_1(A,B,C,G) & k7_mcart_1(A,B,C,G) = k7_mcart_1(D,E,F,H) & k5_mcart_1(A,B,C,G) = k5_mcart_1(D,E,F,H)) & H = G)))) & A != k1_xboole_0)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1722 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1723 (all A all B all C all D all E ((all F (r2_hidden(F,A) <-> (exists G exists H exists I exists J (r2_hidden(J,E) & F = k4_mcart_1(G,H,I,J) & r2_hidden(I,D) & r2_hidden(G,B) & r2_hidden(H,C))))) -> k4_zfmisc_1(B,C,D,E) = A)) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1724 (all A all B all C all D k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D)) = k1_tarski(k4_mcart_1(A,B,C,D))) # label(t65_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1725 (all A all B all C all D all E all F all G all H (k4_mcart_1(E,F,G,H) = k4_mcart_1(A,B,C,D) -> A = E & F = B & C = G & H = D)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1726 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(E,F,G,H) = k4_zfmisc_1(A,B,C,D) -> A = k1_xboole_0 | B = k1_xboole_0 | C = k1_xboole_0 | D = k1_xboole_0 | A = E & F = B & H = D & G = C)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1727 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k1_tarski(D))) # label(t41_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1728 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) -> m1_subset_1(k13_mcart_1(A,B,C,D,E,F),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))) # label(dt_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1729 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k7_mcart_1(A,B,C,D),C))) # label(dt_k7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1730 (all A all B all C k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C)) = k1_tarski(k3_mcart_1(A,B,C))) # label(t39_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1731 (all A all B all C all D all E all F all G all H -(k1_xboole_0 != B & D != k1_xboole_0 & A != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != F & G != k1_xboole_0 & (exists I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) & (exists J (m1_subset_1(J,k4_zfmisc_1(E,F,G,H)) & -(k11_mcart_1(A,B,C,D,I) = k11_mcart_1(E,F,G,H,J) & k9_mcart_1(A,B,C,D,I) = k9_mcart_1(E,F,G,H,J) & k10_mcart_1(A,B,C,D,I) = k10_mcart_1(E,F,G,H,J) & k8_mcart_1(A,B,C,D,I) = k8_mcart_1(E,F,G,H,J)) & J = I)))) & H != k1_xboole_0 & E != k1_xboole_0)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1732 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(A != k1_xboole_0 & k1_xboole_0 != B & C != k1_xboole_0 & (exists E exists F exists G (-(E = k5_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) = G & k6_mcart_1(A,B,C,D) = F) & D = k3_mcart_1(E,F,G)))))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1733 (all A all B all C all D ((all E ((exists F exists G exists H (r2_hidden(F,B) & r2_hidden(G,C) & r2_hidden(H,D) & E = k3_mcart_1(F,G,H))) <-> r2_hidden(E,A))) -> A = k3_zfmisc_1(B,C,D))) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1734 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k10_mcart_1(A,B,C,D,I),G) & r2_hidden(k8_mcart_1(A,B,C,D,I),E) & r2_hidden(k11_mcart_1(A,B,C,D,I),H)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1735 (all A k2_mcart_1(k2_mcart_1(A)) = k20_mcart_1(A)) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1736 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k3_mcart_1(A,B,C),D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1737 (all A all B all C (-(-r1_tarski(A,k3_zfmisc_1(A,B,C)) & -r1_tarski(A,k3_zfmisc_1(B,C,A)) & -r1_tarski(A,k3_zfmisc_1(C,A,B))) -> k1_xboole_0 = A)) # label(t49_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1738 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k11_mcart_1(A,B,C,D,E),D))) # label(dt_k11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1739 (all A all B all C all D all E all F all G all H (m1_subset_1(E,k1_zfmisc_1(A)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(G,k1_zfmisc_1(C)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = k4_zfmisc_1(E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1740 (all A all B all C all D -(D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> (F = k9_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> F = H))))))) & B != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != A)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1741 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D)) # label(t53_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1742 (all A k17_mcart_1(A) = k1_mcart_1(k1_mcart_1(A))) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1743 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> F = D))))))) -> B = k1_xboole_0 | k1_xboole_0 = A | k5_mcart_1(A,B,C,E) = D | k1_xboole_0 = C))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1744 (all A all B all C all D k3_mcart_1(k4_tarski(A,B),C,D) = k4_mcart_1(A,B,C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1745 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),C)) -> k1_mcart_1(A) = B & r2_hidden(k2_mcart_1(A),C))) # label(t12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.30 1746 (all A all B all C all D all E all F all G all H (m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(E,k1_zfmisc_1(A)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(F,k1_zfmisc_1(B)) -> m1_subset_1(k14_mcart_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))) # label(dt_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1747 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C))) # label(t10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1748 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1749 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k2_tarski(C,D))) -> k1_mcart_1(A) = B & (C = k2_mcart_1(A) | k2_mcart_1(A) = D))) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1750 (all A all B all C -(-(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> (k7_mcart_1(A,B,C,D) = E <-> (all F all G all H (k3_mcart_1(F,G,H) = D -> H = E))))))) & k1_xboole_0 != A & k1_xboole_0 != B & k1_xboole_0 != C)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1751 (all A all B all C all D -(D != k1_xboole_0 & k1_xboole_0 != B & A != k1_xboole_0 & C != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,A) -> (k8_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> F = G))))))))) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1752 (all A all B all C all D all E all F k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1753 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D -(k4_tarski(C,D) = B & (r2_hidden(C,A) | r2_hidden(D,A)))))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1754 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k7_mcart_1(A,B,C,D) != D & D != k6_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) != D)) & C != k1_xboole_0 & k1_xboole_0 != A)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1755 (all A all B all C all D (A != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != B & k1_xboole_0 != D <-> k1_xboole_0 != k4_zfmisc_1(A,B,C,D))) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1756 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> E = H))))))))) -> k1_xboole_0 = D | k9_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = B | C = k1_xboole_0 | k1_xboole_0 = A))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1757 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(B) = k1_relat_1(A) <-> B = k15_mcart_1(A)))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1758 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> B = k1_mcart_1(A) & C = k2_mcart_1(A))) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1759 (all A all B all C -(k1_xboole_0 != A & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,B) -> ((all F all G all H (D = k3_mcart_1(F,G,H) -> G = E)) <-> k6_mcart_1(A,B,C,D) = E))))) & k1_xboole_0 != C & k1_xboole_0 != B)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1760 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> F = C & B = E & A = D | k1_xboole_0 = k3_zfmisc_1(A,B,C))) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1761 (all A -((all B -((all C all D all E -(B = k3_mcart_1(C,D,E) & (r2_hidden(C,A) | r2_hidden(D,A)))) & r2_hidden(B,A))) & A != k1_xboole_0)) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1762 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D),k3_mcart_1(A,B,E),k3_mcart_1(A,C,E)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,E))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1763 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> (all G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) -> (r2_hidden(G,k3_zfmisc_1(D,E,F)) -> r2_hidden(k7_mcart_1(A,B,C,G),F) & r2_hidden(k6_mcart_1(A,B,C,G),E) & r2_hidden(k5_mcart_1(A,B,C,G),D)))))))))) # label(t76_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1764 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> (D = k2_mcart_1(A) | k2_mcart_1(A) = C) & r2_hidden(k1_mcart_1(A),B))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1765 (all A all B all C all D all E all F (k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) = A & E = k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) & D = k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) & k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) = B)) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1766 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1767 (all A all B all C all D -(k1_xboole_0 != B & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> E = k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)))) & k1_xboole_0 != A & k1_xboole_0 != C & D != k1_xboole_0)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1768 (all A all B all C -(C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D = k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1769 (all A all B all C all D all E all F all G all H (-r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) -> -r1_xboole_0(B,F) & -r1_xboole_0(A,E) & -r1_xboole_0(C,G) & -r1_xboole_0(D,H))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1770 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B ((all C all D (k4_tarski(C,D) = A -> D = B)) <-> k2_mcart_1(A) = B)))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1771 (all A all B all C all D all E all F (r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F)) <-> r2_hidden(C,F) & r2_hidden(B,E) & r2_hidden(A,D))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1772 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> J = E))))))))) -> A = k1_xboole_0 | k1_xboole_0 = C | D = k1_xboole_0 | E = k11_mcart_1(A,B,C,D,F) | B = k1_xboole_0))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1773 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k8_mcart_1(A,B,C,D,E),A))) # label(dt_k8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1774 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,k1_tarski(C))) -> k2_mcart_1(A) = C & r2_hidden(k1_mcart_1(A),B))) # label(t13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1775 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D),k3_mcart_1(A,C,E),k3_mcart_1(B,C,E)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k2_tarski(D,E))) # label(t44_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1776 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> G = E))))))))) -> B = k1_xboole_0 | k8_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | k1_xboole_0 = A | C = k1_xboole_0))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1777 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k16_mcart_1(A) = B <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k2_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B)))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1778 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k10_mcart_1(A,B,C,D,E),C))) # label(dt_k10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1779 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> G = D))))))) -> A = k1_xboole_0 | C = k1_xboole_0 | k6_mcart_1(A,B,C,E) = D | B = k1_xboole_0))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1780 (all A all B (B = k2_mcart_1(k4_tarski(A,B)) & k1_mcart_1(k4_tarski(A,B)) = A)) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1781 (all A -(k1_xboole_0 != A & (all B -((all C all D all E all F all G (r2_hidden(E,F) & r2_hidden(G,B) & r2_hidden(F,G) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))))) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1782 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(B,C,E),k3_mcart_1(A,D,E),k3_mcart_1(B,D,E)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k1_tarski(E))) # label(t43_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1783 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D (r2_hidden(D,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))))) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1784 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> D = H))))))) -> k1_xboole_0 = C | A = k1_xboole_0 | k7_mcart_1(A,B,C,E) = D | B = k1_xboole_0))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1785 (all A all B -(k1_xboole_0 != A & B != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k2_mcart_1(C) & k1_mcart_1(C) != C)))) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1786 (all A all B (k2_zfmisc_1(A,B) != k1_xboole_0 -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k1_mcart_1(C) & k2_mcart_1(C) != C)))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1787 (all A all B all C all D all E all F (m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(A)) -> k3_zfmisc_1(D,E,F) = k13_mcart_1(A,B,C,D,E,F))) # label(redefinition_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1788 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> k2_mcart_1(A) = D & (k1_mcart_1(A) = B | k1_mcart_1(A) = C))) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1789 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k16_mcart_1(A)) & v1_funct_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1790 (all A all B all C all D -((exists E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) & (exists F exists G exists H exists I (-(k8_mcart_1(A,B,C,D,E) = F & k10_mcart_1(A,B,C,D,E) = H & k11_mcart_1(A,B,C,D,E) = I & k9_mcart_1(A,B,C,D,E) = G) & E = k4_mcart_1(F,G,H,I))))) & D != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != A & B != k1_xboole_0)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1791 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1792 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k5_mcart_1(A,B,C,D),A))) # label(dt_k5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1793 (all A all B all C all D all E all F (r1_tarski(C,D) & r1_tarski(E,F) & r1_tarski(A,B) -> r1_tarski(k3_zfmisc_1(A,C,E),k3_zfmisc_1(B,D,F)))) # label(t77_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1794 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> (k10_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> I = F))))))) & k1_xboole_0 != D & k1_xboole_0 != A & B != k1_xboole_0 & k1_xboole_0 != C)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1795 (all A all B all C (k3_zfmisc_1(A,B,C) != k1_xboole_0 <-> A != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1796 (all A -((all B -((all C all D all E all F -((r2_hidden(D,A) | r2_hidden(C,A)) & k4_mcart_1(C,D,E,F) = B)) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1797 (all A all B all C -(k1_xboole_0 != C & k1_xboole_0 != A & k1_xboole_0 != B & (exists D ((exists E exists F exists G (-(k6_mcart_1(A,B,C,D) = F & k5_mcart_1(A,B,C,D) = E & G = k7_mcart_1(A,B,C,D)) & k3_mcart_1(E,F,G) = D)) & m1_subset_1(D,k3_zfmisc_1(A,B,C)))))) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1798 (all A ((exists B exists C A = k4_tarski(B,C)) -> k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A)) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1799 (all A all B all C all D all E all F all G all H (r1_tarski(E,F) & r1_tarski(G,H) & r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1800 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(E,F,G,H) = k4_zfmisc_1(A,B,C,D) -> k1_xboole_0 = k4_zfmisc_1(A,B,C,D) | G = C & F = B & E = A & D = H)) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1801 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -((exists F exists G exists H exists I (k4_mcart_1(F,G,H,I) = E & -(k10_mcart_1(A,B,C,D,E) = H & k9_mcart_1(A,B,C,D,E) = G & k8_mcart_1(A,B,C,D,E) = F & k11_mcart_1(A,B,C,D,E) = I))) & B != k1_xboole_0 & A != k1_xboole_0 & C != k1_xboole_0 & D != k1_xboole_0))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1802 (all A k19_mcart_1(A) = k1_mcart_1(k2_mcart_1(A))) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1803 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k4_tarski(k4_tarski(A,B),C),D)) # label(t31_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1804 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1805 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k6_mcart_1(A,B,C,D),B))) # label(dt_k6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1806 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1807 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> k2_mcart_1(A) != A & k1_mcart_1(A) != A)) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1808 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1809 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k2_zfmisc_1(C,D) = k12_mcart_1(A,B,C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1810 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1811 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k9_mcart_1(A,B,C,D,E),B))) # label(dt_k9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1812 (all A all B all C -(A != k1_xboole_0 & B != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,A) -> ((all F all G all H (k3_mcart_1(F,G,H) = D -> E = F)) <-> k5_mcart_1(A,B,C,D) = E))))) & k1_xboole_0 != C)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1813 (all A -((all B -(r2_hidden(B,A) & r1_xboole_0(B,A))) & A != k1_xboole_0)) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1814 (all A all B (k4_zfmisc_1(B,B,B,B) = k4_zfmisc_1(A,A,A,A) -> B = A)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1815 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(E,B) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))))))) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1816 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> B = E & C = F & D = A)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1817 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_mcart_1(A)) & v1_relat_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1818 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != B & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k2_mcart_1(E) = k11_mcart_1(A,B,C,D,E) & k2_mcart_1(k1_mcart_1(E)) = k10_mcart_1(A,B,C,D,E) & k1_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k8_mcart_1(A,B,C,D,E) & k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k9_mcart_1(A,B,C,D,E))) & D != k1_xboole_0)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1819 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> (k11_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = J))))))) & k1_xboole_0 != B & A != k1_xboole_0 & k1_xboole_0 != D & C != k1_xboole_0)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1820 (all A all B -(k1_xboole_0 != A & k1_xboole_0 != B & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k4_tarski(k1_mcart_1(C),k2_mcart_1(C)) = C)))) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1821 (all A ((exists B exists C k4_tarski(B,C) = A) -> A != k1_mcart_1(A) & k2_mcart_1(A) != A)) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1822 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> E = I))))))))) -> k1_xboole_0 = A | k1_xboole_0 = C | E = k10_mcart_1(A,B,C,D,F) | k1_xboole_0 = D | B = k1_xboole_0))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1823 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t23_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1824 (all A all B all C (r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C) -> (all D all E k4_tarski(D,E) != A) | r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1825 (all A all B all C all D all E all F (-r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) -> -r1_xboole_0(B,E) & -r1_xboole_0(C,F) & -r1_xboole_0(A,D))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1826 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1827 (all A all B all C all D all E -((all F all G all H all I -(r2_hidden(F,B) & r2_hidden(H,D) & r2_hidden(I,E) & k4_mcart_1(F,G,H,I) = A & r2_hidden(G,C))) & r2_hidden(A,k4_zfmisc_1(B,C,D,E)))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1828 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k3_zfmisc_1(k2_zfmisc_1(A,B),C,D)) # label(t54_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1829 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1830 (all A all B all C -(C != k1_xboole_0 & k1_xboole_0 != A & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k1_mcart_1(k1_mcart_1(D)) = k5_mcart_1(A,B,C,D) & k2_mcart_1(k1_mcart_1(D)) = k6_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) = k2_mcart_1(D))) & k1_xboole_0 != B)) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1831 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1832 (all A -(k1_xboole_0 != A & (all B -((all C all D all E all F (r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))))) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1833 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1834 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1835 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1836 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (D = k2_mcart_1(A) | k2_mcart_1(A) = E) & (C = k1_mcart_1(A) | B = k1_mcart_1(A)))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1837 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B ((all C all D (A = k4_tarski(C,D) -> C = B)) <-> k1_mcart_1(A) = B)))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1838 (all A all B (k3_zfmisc_1(B,B,B) = k3_zfmisc_1(A,A,A) -> B = A)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1839 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> (k1_mcart_1(A) = B | k1_mcart_1(A) = C) & r2_hidden(k2_mcart_1(A),D))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1840 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1841 (all A all B all C all D k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1842 (all A all B all C all D -(r2_hidden(A,k3_zfmisc_1(B,C,D)) & (all E all F all G -(r2_hidden(E,B) & r2_hidden(F,C) & k3_mcart_1(E,F,G) = A & r2_hidden(G,D))))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1843 (all A (-v1_xboole_0(A) -> -((all B (v1_funct_1(B) & v1_relat_1(B) -> -(A = k1_relat_1(B) & (all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C)))))) & (all B -(k1_xboole_0 = B & r2_hidden(B,A)))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1844 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1845 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1846 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1847 (all A -((all B all C -(r2_hidden(B,f2_s2_wellord2) & p1_s2_wellord2(A,B,C) & r2_hidden(C,f3_s2_wellord2))) & r2_hidden(A,f1_s2_wellord2))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (exists B (k1_relat_1(A) = f1_s2_wellord2 & v1_relat_1(B) & (all C (r2_hidden(C,f1_s2_wellord2) -> p1_s2_wellord2(C,k1_funct_1(A,C),k1_funct_1(B,C)))) & f1_s2_wellord2 = k1_relat_1(B) & v1_funct_1(B))))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1848 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1849 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_wellord1(k1_wellord2(A),k1_wellord2(B)) -> B = A))))) # label(t11_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1850 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1851 (all A all B (r2_wellord2(A,B) <-> r2_tarski(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1852 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1853 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1854 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1855 (all A -(r2_hidden(A,f1_s1_wellord2) & (all B -(r2_hidden(B,f2_s1_wellord2) & p1_s1_wellord2(A,B))))) -> (exists A (r1_tarski(k2_relat_1(A),f2_s1_wellord2) & v1_relat_1(A) & v1_funct_1(A) & (all B (r2_hidden(B,f1_s1_wellord2) -> p1_s1_wellord2(B,k1_funct_1(A,B)))) & k1_relat_1(A) = f1_s1_wellord2)) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1856 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B (v3_ordinal1(B) -> (r4_wellord1(A,k1_wellord2(B)) <-> B = k2_wellord2(A))))))) # label(d2_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1857 (all A (v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_wellord1(A,k1_wellord2(B)) & r4_wellord1(A,k1_wellord2(C)) -> C = B))))))) # label(t12_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1858 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1859 (all A all B all C (r2_wellord2(A,B) & r2_wellord2(B,C) -> r2_wellord2(A,C))) # label(t22_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1860 (all A (v1_relat_1(A) -> -((all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & v2_wellord1(A)))) # label(t14_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1861 (all A all B (r1_tarski(A,B) -> k2_wellord1(k1_wellord2(B),A) = k1_wellord2(A))) # label(t8_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1862 (all A (v1_relat_1(A) -> -((all B -((all C (v3_ordinal1(C) -> -r4_wellord1(k2_wellord1(A,k1_wellord1(A,B)),k1_wellord2(C)))) & r2_hidden(B,k3_relat_1(A)))) & (all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & v2_wellord1(A)))) # label(t13_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1863 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,B) -> r1_ordinal1(k2_wellord2(k1_wellord2(A)),B)))) # label(t17_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1864 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1865 (all A exists B (r2_wellord1(B,A) & v1_relat_1(B))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1866 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1867 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1868 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) -> (r1_wellord2(A,B) <-> k2_wellord2(B) = A))))) # label(d3_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1869 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1870 (all A all B (r2_wellord2(A,B) <-> (exists C (A = k1_relat_1(C) & k2_relat_1(C) = B & v1_funct_1(C) & v2_funct_1(C) & v1_relat_1(C))))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1871 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> v2_wellord1(k2_wellord1(B,A)) & k3_relat_1(k2_wellord1(B,A)) = A))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1872 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1873 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1874 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1875 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> k1_wellord1(k1_wellord2(B),A) = A))))) # label(t10_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1876 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> v2_wellord1(k1_wellord2(B)))))) # label(t9_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1877 (all A all B (v1_relat_1(B) -> (A = k3_relat_1(B) & (all C all D (r2_hidden(C,A) & r2_hidden(D,A) -> (r2_hidden(k4_tarski(C,D),B) <-> r1_tarski(C,D)))) <-> k1_wellord2(A) = B))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1878 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1879 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1880 (all A (-v1_xboole_0(A) -> -((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r1_xboole_0(B,C) | B = C)) & (all B exists C (r2_hidden(C,A) & (all D k3_xboole_0(B,C) != k1_tarski(D)))) & (all B -(r2_hidden(B,A) & B = k1_xboole_0))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1881 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1882 (all A exists B (v1_relat_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1883 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1884 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1885 (all A all B all C (v1_funct_1(k9_funct_2(A,B,C)) & m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1886 (all A all B all C (v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> C = D)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1887 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1888 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F -(r2_hidden(F,A) & r2_hidden(F,C) & k1_funct_1(D,F) = E)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1889 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (k5_partfun1(A,B,D) = k5_partfun1(A,B,C) & (all E B != k1_tarski(E)) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1890 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1891 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1892 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1893 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_partfun1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1894 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1895 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1896 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)))) # label(t159_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1897 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B) = f3_s13_funct_2(B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_1(A))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1898 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1899 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> A = k2_relat_1(D) & v2_funct_1(C) | B = k1_xboole_0))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1900 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (r1_partfun1(C,E) & r1_partfun1(D,E) -> r1_partfun1(C,D) | k1_xboole_0 = B & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1901 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1902 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> k1_xboole_0 = B & A != k1_xboole_0 | m2_relset_1(D,A,C) & v1_funct_1(D) & v1_funct_2(D,A,C)))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1903 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> -(r2_hidden(C,B) & (all E -(k1_funct_1(D,E) = C & r2_hidden(E,A))) & k2_relat_1(D) = B))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1904 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> -r1_partfun1(C,D))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1905 (all A all B (v3_funct_2(B,A,A) & v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,A,A) & v1_funct_1(C) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> k6_funct_2(A,B) = C))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1906 (all A all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> -((k1_xboole_0 = C -> k1_xboole_0 = B) & (k1_xboole_0 = B -> k1_xboole_0 = A) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D)))))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1907 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1908 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(B,A,A) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1909 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1910 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,C) & v1_funct_1(E) & v1_funct_2(E,B,C) -> (k2_relat_1(E) = C & B = k2_relat_1(D) -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | B = k1_xboole_0 | C = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1911 (all A -(r2_hidden(A,f1_s1_funct_2) & (all B -(r2_hidden(B,f2_s1_funct_2) & p1_s1_funct_2(A,B))))) -> (exists A ((all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1912 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1913 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & v1_funct_2(B,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_1(B) -> k4_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1914 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k2_relat_1(D) = B | k1_xboole_0 = C))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1915 (all A all B all C (C = k1_funct_2(A,B) <-> (all D ((exists E (r1_tarski(k2_relat_1(E),B) & D = E & v1_funct_1(E) & k1_relat_1(E) = A & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1916 (all A all B all C all D all E (v1_funct_1(D) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & -v1_xboole_0(B) -> v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1917 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1918 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1919 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> B = k2_relat_1(C)))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1920 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1921 (all A all B all C (v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> (v2_funct_1(C) <-> (all D all E (k1_funct_1(C,D) = k1_funct_1(C,E) & r2_hidden(E,A) & r2_hidden(D,A) -> D = E)))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1922 (all A all B all C all D all E all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (r2_hidden(E,B) & r2_hidden(D,A) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | k1_xboole_0 = C))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1923 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(C,A) -> r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1924 (all A all B all C (v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (r1_tarski(B,A) -> B = k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) & k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1925 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (B != k1_xboole_0 -> (all E (r2_hidden(k1_funct_1(D,E),C) & r2_hidden(E,A) <-> r2_hidden(E,k10_relat_1(D,C))))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1926 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1927 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(C,A) -> k1_xboole_0 = B | k1_funct_1(E,k1_funct_1(D,C)) = k1_funct_1(k5_relat_1(D,E),C)))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1928 f3_s11_funct_2 != f4_s11_funct_2 -> (exists A (v1_funct_1(A) & f5_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) & f6_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(B != f4_s11_funct_2 & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & f3_s11_funct_2 != B))))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1929 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1930 (all A all B exists C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_relat_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1931 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1932 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.31 1933 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (p1_s7_funct_2(A,B,C) & m1_subset_1(C,f3_s7_funct_2))))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & (all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1934 (all A all B all C (v3_funct_2(B,A,A) & v1_funct_2(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) & m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> k5_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1935 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1936 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k4_funct_2(A,B,C) = B & k2_relat_1(B) = A -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1937 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1938 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A) & v1_funct_1(B)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1939 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (B = k2_relat_1(C) & v2_funct_1(C) -> k6_partfun1(A) = k5_relat_1(C,k2_funct_1(C)) & k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C) | B = k1_xboole_0))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1940 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (exists E (r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(D,E) != k1_funct_1(C,E))))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1941 (all A all B all C all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> A != k1_xboole_0 & B = k1_xboole_0 | v2_funct_1(D) | k1_xboole_0 != B & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1942 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v1_partfun1(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1943 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D -(r2_hidden(D,B) & (all E -(r2_hidden(E,A) & k1_funct_1(C,E) = D)))) -> k2_relat_1(C) = B | k1_xboole_0 = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1944 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1945 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1946 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1947 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1948 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(-((all D all E (m2_relset_1(E,D,A) & v1_funct_1(E) & v1_funct_2(E,D,A) -> (all F (v1_funct_1(F) & v1_funct_2(F,D,A) & m2_relset_1(F,D,A) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> F = E))))) <-> v2_funct_1(C)) & B != k1_xboole_0 & A != k1_xboole_0))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1949 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1950 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (-(B = k1_xboole_0 & C != k1_xboole_0 & A != k1_xboole_0) -> v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_1(k1_partfun1(A,B,B,C,D,E))))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1951 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1952 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1953 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1954 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1955 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1956 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1957 (all A all B all C (m1_relset_1(C,A,B) -> (v2_funct_2(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & v2_funct_1(C) -> v3_funct_2(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1958 (all A all B (r2_hidden(B,f2_s6_funct_2) & r2_hidden(A,f1_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & (all B all C (r2_hidden(B,f1_s6_funct_2) & r2_hidden(C,f2_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_1(A))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1959 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1960 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1961 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(D) = B & v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> C = k1_xboole_0 & B != k1_xboole_0 | v2_funct_1(E) & v2_funct_1(D)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1962 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1963 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_1(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & v1_funct_2(B,A,A) -> v1_funct_1(B) & v2_funct_1(B) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1964 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1965 (all A (r2_hidden(A,f1_s9_funct_2) -> (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)) & (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2) & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> k1_funct_1(A,B) = f4_s9_funct_2(B)) & (p1_s9_funct_2(B) -> k1_funct_1(A,B) = f3_s9_funct_2(B)))))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1966 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1967 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1968 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) -> (r2_hidden(C,A) -> k1_funct_1(D,C) = B))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1969 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1970 (all A all B (-v1_xboole_0(B) -> -v1_xboole_0(k1_funct_2(A,B)))) # label(fc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1971 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1972 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1973 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,C) & E = k1_funct_1(D,F) & r2_hidden(F,A))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1974 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> r2_hidden(D,k5_partfun1(A,B,C)) | k1_xboole_0 = B & A != k1_xboole_0))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1975 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | k1_xboole_0 = B))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1976 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1977 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1978 (all A all B all C all D all E (v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(D) & -v1_xboole_0(B) -> k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1979 (all A all B all C all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) & v1_funct_2(D,k1_tarski(A),B) -> (k1_xboole_0 != B -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1980 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1981 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & (all E all F ((k1_funct_1(C,F) = E & r2_hidden(F,A) -> r2_hidden(E,B) & F = k1_funct_1(D,E)) & (F = k1_funct_1(D,E) & r2_hidden(E,B) -> E = k1_funct_1(C,F) & r2_hidden(F,A)))) & k2_relat_1(C) = B -> k2_funct_1(C) = D | k1_xboole_0 = B | k1_xboole_0 = A))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1982 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1983 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1984 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> B = k1_xboole_0 & A != k1_xboole_0 | v1_partfun1(C,A,B)))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1985 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1986 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) -> (B != k1_xboole_0 -> k2_relat_1(C) = k1_tarski(k1_funct_1(C,A))))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1987 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1988 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1989 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_2(C,A,B) & v2_funct_1(C) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1990 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1991 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1992 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v3_funct_2(C,A,B) & v1_funct_2(C,A,B) -> v2_funct_2(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1993 (exists A (f4_s10_funct_2 = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & (all B (m1_subset_1(B,f1_s10_funct_2) -> (B != f3_s10_funct_2 -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1994 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1995 (all A all B (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(B,A,A) -> k6_funct_2(A,B) = k2_funct_1(B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1996 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,D) = k2_funct_2(A,B,C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1997 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1998 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (k2_relat_1(B) = A & v2_funct_1(B) -> m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 1999 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2000 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2001 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> ((all C all D (k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(D,A) & r2_hidden(C,A) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2002 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2003 (all A all B -(r2_hidden(A,f1_s5_funct_2) & r2_hidden(B,f2_s5_funct_2) & (all C -(p1_s5_funct_2(A,B,C) & r2_hidden(C,f3_s5_funct_2))))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s5_funct_2) & r2_hidden(C,f2_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2004 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2005 (all A all B all C (m2_relset_1(C,A,B) -> (k1_xboole_0 = B -> (k1_xboole_0 = C <-> v1_funct_2(C,A,B)) | A = k1_xboole_0) & ((k1_xboole_0 = B -> k1_xboole_0 = A) -> (A = k4_relset_1(A,B,C) <-> v1_funct_2(C,A,B))))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2006 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r2_hidden(C,A) -> B = k1_xboole_0 | r2_hidden(k1_funct_1(D,C),B)))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2007 (all A all B all C all D (m1_subset_1(D,A) & v1_funct_1(C) & -v1_xboole_0(A) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> k1_funct_1(C,D) = k8_funct_2(A,B,C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2008 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2009 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (v2_funct_1(B) & k4_funct_2(A,C,B) = B -> k6_partfun1(A) = C))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2010 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2011 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2012 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2013 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2014 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))))) -> D = E))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2015 (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & (all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> f4_s8_funct_2(B,C) = k1_funct_1(A,k4_tarski(B,C)))))))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2016 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2017 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B = k2_relat_1(C) & v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2018 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2019 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) -> v1_funct_1(k6_funct_2(A,B)) & v1_funct_2(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2020 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2021 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2022 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> E = D))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2023 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2024 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (v2_funct_2(C,A,B) <-> B = k2_relat_1(C)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2025 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2026 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,B)))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2027 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A ((all B (r2_hidden(B,f1_s2_funct_2) -> k1_funct_1(A,B) = f3_s2_funct_2(B))) & m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_1(A))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2028 (all A all B (v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k5_funct_2(A,B,k6_funct_2(A,B)) = k6_partfun1(A) & k6_partfun1(A) = k5_funct_2(A,k6_funct_2(A,B),B))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2029 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k2_relat_1(B) = A & A = k2_relat_1(C) -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2030 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2031 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E k1_tarski(E) != B) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2032 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2033 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> -(r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2034 (all A all B all C (m2_relset_1(C,A,B) -> k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C)) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2035 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_partfun1(C,D) -> D = C | k1_xboole_0 = B & k1_xboole_0 != A))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2036 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) -> (all C all D (r2_hidden(D,A) & r2_hidden(C,A) & k1_funct_1(B,D) = k1_funct_1(B,C) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2037 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2038 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2039 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_1(D) & v1_funct_2(D,A,C) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2040 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s4_funct_2) -> f3_s4_funct_2(B) = k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B))) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2041 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2042 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A ((all B (m1_subset_1(B,f1_s12_funct_2) -> f3_s12_funct_2(B) = k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B))) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & v1_funct_1(A))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2043 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) -> v1_funct_2(k4_funct_2(A,B,C),A,A) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_1(k4_funct_2(A,B,C)))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2044 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2045 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> A = k4_relset_1(A,A,B) & r1_tarski(k2_relat_1(B),A))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2046 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (p1_s14_funct_2(A,B) & m1_subset_1(B,f2_s14_funct_2))))) -> (exists A (m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2047 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((all D -(r2_hidden(D,B) & k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D)))) <-> k2_relat_1(C) = B))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2048 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (k1_xboole_0 != B -> ((all D (k1_xboole_0 != D -> (all E (m2_relset_1(E,B,D) & v1_funct_2(E,B,D) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,F) = k1_partfun1(A,B,B,D,C,E) -> F = E))))))) <-> k2_relat_1(C) = B)))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2049 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2050 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2051 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2052 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2053 (all A all B r1_tarski(k1_funct_2(A,B),k4_partfun1(A,B))) # label(t141_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2054 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2055 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2056 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2057 (all A all B all C (v1_funct_1(B) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v3_funct_2(B,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) -> m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)) & v1_funct_2(k5_funct_2(A,B,C),A,A) & v3_funct_2(k5_funct_2(A,B,C),A,A))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2058 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2059 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2060 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2061 (all A all B all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2062 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k2_funct_2(A,B,C,A) = k2_relat_1(C)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2063 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_2(B,k1_relat_1(B),A) & v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2064 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2065 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (A = k4_relset_1(A,B,C) -> v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2066 (all A all B k1_funct_2(A,B) = k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B))) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2067 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A)) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2068 (all A (k1_xboole_0 != A -> k1_xboole_0 = k1_funct_2(A,k1_xboole_0))) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2069 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> k3_funct_2(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2070 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & k2_relat_1(C) = B & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> A = k1_xboole_0 | k2_funct_1(C) = D | B = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2071 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2072 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2073 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (exists C (v1_funct_1(C) & m2_relset_1(C,A,A) & r1_partfun1(B,C) & v1_funct_2(C,A,A))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2074 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) -> k2_funct_2(k1_xboole_0,A,C,B) = k1_xboole_0)) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2075 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(E = k1_funct_1(D,F) & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2076 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2077 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2078 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2079 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2080 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2081 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2082 (all A all B (m2_relset_1(B,A,A) -> B = k7_relset_1(A,A,A,A,k6_partfun1(A),B) & k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B)) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2083 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(B != k1_xboole_0 & (exists D (m2_relset_1(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & v1_funct_2(D,B,A) & v1_funct_1(D))) & -v2_funct_1(C)))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2084 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(C,A) -> k1_xboole_0 != A & k1_xboole_0 = B | m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) & v1_funct_2(k2_partfun1(A,B,D,C),C,B)))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2085 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (C = k5_funct_2(A,B,C) -> B = k6_partfun1(A)))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2086 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2087 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (r2_hidden(C,A) & r2_hidden(k1_funct_1(E,C),D) -> k1_funct_1(k9_relset_1(A,B,D,E),C) = k1_funct_1(E,C) | B = k1_xboole_0))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2088 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2089 (all A all B all C (v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2090 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2091 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2092 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (p1_s3_funct_2(A,B) & m1_subset_1(B,f2_s3_funct_2))))) -> (exists A (m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_1(A) & (all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2093 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) & v1_funct_1(D) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2094 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (v2_funct_1(D) & r2_hidden(C,A) -> B = k1_xboole_0 | C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C))))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2095 (all A all B all C all D (v1_funct_2(C,A,B) & m1_subset_1(D,A) & -v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,A,B) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2096 (all A all B all C (np__1 = k1_funct_1(k4_funct_3(B,C),A) -> r2_hidden(A,B))) # label(t42_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2097 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(D) = k2_zfmisc_1(A,B) & k2_zfmisc_1(A,B) = k1_relat_1(C) & (all E all F (r2_hidden(E,A) & r2_hidden(F,B) -> k1_funct_1(C,k4_tarski(E,F)) = k1_funct_1(D,k4_tarski(E,F)))) -> D = C))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2098 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t12_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2099 (all A all B all C all D all E (-v1_xboole_0(B) & m1_relset_1(E,A,C) & v1_funct_1(D) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,A,C) & v1_funct_2(D,A,B) & -v1_xboole_0(C) -> v1_funct_1(k14_funct_3(A,B,C,D,E)) & m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_2(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)))) # label(dt_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2100 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k7_relat_1(k6_relat_1(A),B) = k6_funct_3(A,B))) # label(t53_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2101 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k15_funct_3(A,B)))))) # label(t88_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2102 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> k4_tarski(k8_funct_2(A,B,D,F),k8_funct_2(A,C,E,F)) = k8_funct_2(A,k2_zfmisc_1(B,C),k14_funct_3(A,B,C,D,E),F))))))))))))) # label(t79_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2103 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k10_relat_1(C,A),k2_relat_1(B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,k2_relat_1(k5_relat_1(B,C)))))))) # label(t5_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2104 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k7_funct_3(A,B) <-> k1_relat_1(C) = k2_zfmisc_1(A,B) & (all D all E (r2_hidden(E,B) & r2_hidden(D,A) -> D = k1_funct_1(C,k4_tarski(D,E))))))) # label(d5_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2105 (all A all B (v1_funct_2(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & m2_relset_1(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & v1_funct_1(k5_funct_3(A,B)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2106 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,A,C) & v1_funct_1(E) & v1_funct_2(E,A,C) -> (all F (v1_funct_2(F,B,D) & v1_funct_1(F) & m2_relset_1(F,B,D) -> k13_funct_3(k5_relat_1(k9_funct_3(A,B),E),k5_relat_1(k10_funct_3(A,B),F)) = k16_funct_3(A,B,C,D,E,F))))))))) # label(t98_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2107 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2108 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & -(v1_funct_1(k13_funct_3(D,E)) & v1_funct_2(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)) & m2_relset_1(k13_funct_3(D,E),A,k2_zfmisc_1(B,C))) & (C = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2109 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k2_zfmisc_1(k9_relat_1(C,A),k9_relat_1(D,B)) = k9_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)))))) # label(t93_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2110 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k6_funct_3(A,B) = k6_relat_1(B))) # label(redefinition_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2111 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(B) = k1_relat_1(A) & k1_relat_1(D) = k1_relat_1(C) & k13_funct_3(A,B) = k13_funct_3(D,C) -> A = D & B = C))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2112 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k4_funct_3(A,B) = C <-> k1_relat_1(C) = B & (all D (r2_hidden(D,B) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = np__1) & (-r2_hidden(D,A) -> np__0 = k1_funct_1(C,D))))))) # label(d3_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2113 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v2_funct_1(A) -> r1_tarski(k9_relat_1(k1_funct_3(A),B),k10_relat_1(k3_funct_3(A),B)))))) # label(t36_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2114 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k5_relat_1(k3_funct_3(B),k3_funct_3(A)) = k3_funct_3(k5_relat_1(A,B))))))) # label(t38_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2115 (all A (v1_funct_1(k12_funct_3(A)) & v1_funct_2(k12_funct_3(A),A,k2_zfmisc_1(A,A)) & m2_relset_1(k12_funct_3(A),A,k2_zfmisc_1(A,A)))) # label(dt_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2116 (all A all B r1_tarski(k2_relat_1(k8_funct_3(A,B)),B)) # label(t61_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2117 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k3_tarski(k10_relat_1(k3_funct_3(B),A)) = k9_relat_1(B,k3_tarski(A))))) # label(t32_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2118 (all A all B (m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_1(k10_funct_3(A,B)) & v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B))) # label(dt_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2119 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_xboole_0 = k1_funct_1(k1_funct_3(A),k1_xboole_0))) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2120 (all A all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_2(F,C,D) & v1_funct_1(F) & m2_relset_1(F,C,D) -> v1_funct_2(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & v1_funct_1(k15_funct_3(E,F)) & m2_relset_1(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))) # label(t95_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2121 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2122 (all A r1_tarski(k2_relat_1(k11_funct_3(A)),k2_zfmisc_1(A,A))) # label(t66_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2123 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_zfmisc_1(k2_relat_1(A)) = k1_relat_1(B) & (all C (r1_tarski(C,k2_relat_1(A)) -> k10_relat_1(A,C) = k1_funct_1(B,C))) <-> k3_funct_3(A) = B))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2124 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2125 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2126 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> v1_funct_1(k1_funct_3(C)) & v1_funct_2(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & m2_relset_1(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t22_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2127 (all A all B k7_funct_3(A,B) = k9_funct_3(A,B)) # label(redefinition_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2128 (all A all B k4_funct_3(A,B) = k5_funct_3(A,B)) # label(redefinition_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2129 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k4_tarski(C,C))) <-> B = k11_funct_3(A)))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2130 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k3_funct_3(B),A))))) # label(t30_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2131 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k5_relat_1(k15_funct_3(B,D),k15_funct_3(A,C)) = k15_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)))))))))) # label(t92_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2132 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) & v1_funct_1(D) & v1_funct_2(D,A,C) -> r1_tarski(k10_relat_1(k1_funct_3(D),B),k1_zfmisc_1(A)))))) # label(t14_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2133 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_relat_1(A) = k2_funct_2(k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A)),k1_relat_1(A),k9_funct_3(k1_relat_1(A),k2_relat_1(A)),A))) # label(t100_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2134 (all A all B (r1_tarski(A,B) -> k6_relat_1(A) = k7_relat_1(k6_relat_1(B),A))) # label(t1_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2135 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & k1_relat_1(B) = A -> k1_relat_1(k13_funct_3(B,C)) = A))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2136 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) & v2_funct_1(A) -> k10_relat_1(k3_funct_3(A),B) = k9_relat_1(k1_funct_3(A),B))))) # label(t37_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.32 2137 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k8_funct_3(A,B) = C <-> (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k1_funct_1(C,k4_tarski(D,E)) = E)) & k1_relat_1(C) = k2_zfmisc_1(A,B)))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2138 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2139 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k1_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t18_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2140 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_funct_3(A,B)) & v1_relat_1(k15_funct_3(A,B)))) # label(dt_k15_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2141 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> r1_tarski(k2_relat_1(k13_funct_3(D,E)),k2_zfmisc_1(B,C)))))) # label(t80_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2142 (all A all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k10_relat_1(k13_funct_3(C,D),k2_zfmisc_1(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(D,B)))))))) # label(t77_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2143 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)))) <-> k13_funct_3(A,B) = C))))))) # label(d8_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2144 (all A all B k6_relat_1(k2_zfmisc_1(A,B)) = k15_funct_3(k6_relat_1(A),k6_relat_1(B))) # label(t90_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2145 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2146 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2147 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2148 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(k4_tarski(C,D),k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))) -> k4_tarski(k1_funct_1(A,C),k1_funct_1(B,D)) = k1_funct_1(k15_funct_3(A,B),k4_tarski(C,D)))))))) # label(t86_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2149 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_3(A)) & v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & m2_relset_1(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t21_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2150 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2151 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k13_funct_3(A,B)) & v1_funct_1(k13_funct_3(A,B)))) # label(dt_k13_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2152 (all A all B all C (r2_hidden(A,k4_xboole_0(B,C)) -> np__0 = k1_funct_1(k4_funct_3(C,B),A))) # label(t43_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2153 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) & v1_funct_2(D,A,C) & v1_funct_1(D) -> (r1_tarski(B,k1_zfmisc_1(A)) -> k2_funct_2(A,C,D,k3_tarski(B)) = k3_tarski(k9_relat_1(k1_funct_3(D),B))))))) # label(t17_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2154 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,B) & k1_relat_1(D) = B & k1_relat_1(C) = B -> k4_tarski(k1_funct_1(C,A),k1_funct_1(D,A)) = k1_funct_1(k13_funct_3(C,D),A)))))) # label(t69_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2155 (all A all B (v1_funct_1(k4_funct_3(A,B)) & v1_relat_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2156 (all A (v1_relat_1(k11_funct_3(A)) & v1_funct_1(k11_funct_3(A)))) # label(dt_k11_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2157 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(k13_funct_3(B,C),A),k2_zfmisc_1(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t76_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2158 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2159 (all A all B (v1_funct_2(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & m2_relset_1(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & v1_funct_1(k9_funct_3(A,B)))) # label(dt_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2160 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> k5_relat_1(k12_funct_3(A),k16_funct_3(A,A,B,C,D,E)) = k13_funct_3(D,E))))) # label(t99_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2161 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_funct_1(k6_funct_3(A,B)) & m2_relset_1(k6_funct_3(A,B),B,A) & v1_funct_2(k6_funct_3(A,B),B,A))) # label(dt_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2162 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2163 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(k5_relat_1(B,C))) -> r1_tarski(k9_relat_1(B,A),k1_relat_1(C))))))) # label(t2_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2164 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k1_funct_3(B))) -> k1_funct_1(k1_funct_3(B),A) = k9_relat_1(B,A)))) # label(t8_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2165 (all A all B k6_relat_1(k2_zfmisc_1(A,B)) = k13_funct_3(k9_funct_3(A,B),k10_funct_3(A,B))) # label(t73_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2166 (all A all B -(r2_hidden(A,f1_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(B,f2_s1_funct_3))) & (all A all B all C all D (p1_s1_funct_3(A,B,C) & r2_hidden(B,f2_s1_funct_3) & r2_hidden(A,f1_s1_funct_3) & p1_s1_funct_3(A,B,D) -> C = D)) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = k2_zfmisc_1(f1_s1_funct_3,f2_s1_funct_3) & (all B all C (r2_hidden(C,f2_s1_funct_3) & r2_hidden(B,f1_s1_funct_3) -> p1_s1_funct_3(B,C,k1_funct_1(A,k4_tarski(B,C))))))) # label(s1_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2167 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k3_funct_3(A)) & v1_funct_1(k3_funct_3(A)))) # label(dt_k3_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2168 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2169 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k10_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)) = k2_zfmisc_1(k10_relat_1(C,A),k10_relat_1(D,B)))))) # label(t94_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2170 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,A,C) & m2_relset_1(F,A,C) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,A,C) & v1_funct_2(G,A,C) -> (k13_funct_3(D,F) = k13_funct_3(E,G) -> k1_xboole_0 != A & C = k1_xboole_0 | F = G & D = E | B = k1_xboole_0 & A != k1_xboole_0))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2171 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k1_funct_3(B),A))))) # label(t19_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2172 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,C) -> r2_hidden(k1_funct_1(k6_funct_3(B,C),A),B)))) # label(t56_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2173 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2174 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t27_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2175 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2176 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_3(B))) -> k10_relat_1(B,A) = k1_funct_1(k3_funct_3(B),A)))) # label(t24_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2177 (all A all B all C all D all E all F (m1_relset_1(E,A,C) & m1_relset_1(F,B,D) & v1_funct_2(E,A,C) & v1_funct_1(F) & v1_funct_2(F,B,D) & v1_funct_1(E) -> m2_relset_1(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_1(k16_funct_3(A,B,C,D,E,F)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2178 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2179 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k2_tarski(np__0,np__1)) & v1_funct_2(B,A,k2_tarski(np__0,np__1)) -> k4_funct_3(k3_funct_2(A,k2_tarski(np__0,np__1),B,k1_tarski(np__1)),A) = B)) # label(t49_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2180 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(k3_funct_3(B),A) = k10_relat_1(k1_funct_3(B),A)))) # label(t34_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2181 (all A all B all C (-v1_xboole_0(B) & v1_funct_2(C,A,B) & v1_funct_1(C) & m1_relset_1(C,A,B) -> k2_funct_3(A,B,C) = k1_funct_3(C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2182 (all A all B (v1_funct_1(k8_funct_3(A,B)) & v1_relat_1(k8_funct_3(A,B)))) # label(dt_k8_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2183 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k13_funct_3(k5_relat_1(C,A),k5_relat_1(C,B)) = k5_relat_1(C,k13_funct_3(A,B)))))))) # label(t75_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2184 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2185 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k13_funct_3(k5_relat_1(k9_funct_3(k1_relat_1(A),k1_relat_1(B)),A),k5_relat_1(k10_funct_3(k1_relat_1(A),k1_relat_1(B)),B)) = k15_funct_3(A,B))))) # label(t87_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2186 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k3_funct_3(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t25_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2187 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2188 (all A all B (k1_xboole_0 != A -> k2_relat_1(k7_funct_3(B,A)) = B)) # label(t60_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2189 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k3_xboole_0(k1_relat_1(B),k1_relat_1(C))) -> k4_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) = k1_funct_1(k13_funct_3(B,C),A)))))) # label(t68_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2190 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k1_funct_3(A) <-> (all C (r1_tarski(C,k1_relat_1(A)) -> k9_relat_1(A,C) = k1_funct_1(B,C))) & k1_zfmisc_1(k1_relat_1(A)) = k1_relat_1(B)))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2191 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(k1_funct_3(A),k1_funct_3(B)) = k1_funct_3(k5_relat_1(A,B)))))) # label(t20_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2192 (all A all B all C (k4_funct_3(C,B) = k4_funct_3(A,B) & r1_tarski(C,B) & r1_tarski(A,B) -> C = A)) # label(t47_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2193 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k10_relat_1(k1_funct_3(B),A)))) # label(t33_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2194 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k1_funct_3(B),A)),k9_relat_1(B,k3_tarski(A))))) # label(t15_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2195 (all A all B (v1_relat_1(k7_funct_3(A,B)) & v1_funct_1(k7_funct_3(A,B)))) # label(dt_k7_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2196 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2197 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2198 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) -> r1_tarski(k10_relat_1(k3_funct_3(A),B),k9_relat_1(k1_funct_3(A),B)))))) # label(t35_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2199 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(D) = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A) & r1_tarski(k2_relat_1(D),B) -> D = k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B)) & k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) = C))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2200 (all A all B k8_funct_3(A,B) = k10_funct_3(A,B)) # label(redefinition_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2201 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k10_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t28_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2202 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k13_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)) = k5_relat_1(k13_funct_3(B,D),k15_funct_3(A,C)))))))))) # label(t91_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2203 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> D = k7_funct_2(A,k2_zfmisc_1(B,C),B,k14_funct_3(A,B,C,D,E),k9_funct_3(B,C)) & E = k7_funct_2(A,k2_zfmisc_1(B,C),C,k14_funct_3(A,B,C,D,E),k10_funct_3(B,C)))))))))) # label(t82_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2204 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2205 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k13_funct_3(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t71_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2206 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k3_tarski(k9_relat_1(k1_funct_3(B),A)) = k9_relat_1(B,k3_tarski(A))))) # label(t16_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2207 (all A k11_funct_3(A) = k12_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2208 (all A all B all C all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> -(-(E = k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) & k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C)) = D) & (k1_xboole_0 = C -> A = k1_xboole_0) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2209 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_2(F,C,D) & v1_funct_1(F) & m2_relset_1(F,C,D) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,C) -> k1_funct_1(k16_funct_3(A,C,B,D,E,F),k4_tarski(G,H)) = k4_tarski(k8_funct_2(A,B,E,G),k8_funct_2(C,D,F,H)))))))))))))))))) # label(t96_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2210 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,C) & v1_funct_2(F,A,C) -> (all G (m2_relset_1(G,A,C) & v1_funct_1(G) & v1_funct_2(G,A,C) -> (k14_funct_3(A,B,C,E,G) = k14_funct_3(A,B,C,D,F) -> E = D & F = G))))))))))))) # label(t84_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2211 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k3_funct_3(A)) & m2_relset_1(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_2(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t39_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2212 (exists A ((all B all C (r2_hidden(B,f1_s2_funct_3) & r2_hidden(C,f2_s2_funct_3) -> k1_funct_1(A,k4_tarski(B,C)) = f3_s2_funct_3(B,C))) & k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3) = k1_relat_1(A) & v1_relat_1(A) & v1_funct_1(A))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2213 (all A all B r1_tarski(k2_relat_1(k7_funct_3(A,B)),A)) # label(t59_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2214 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k10_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t13_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2215 (all A all B all C all D all E (v1_funct_1(D) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & m1_relset_1(D,A,B) & -v1_xboole_0(C) & v1_funct_1(E) & v1_funct_2(D,A,B) & -v1_xboole_0(B) -> k13_funct_3(D,E) = k14_funct_3(A,B,C,D,E))) # label(redefinition_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2216 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k3_funct_3(B),A)),k9_relat_1(B,k3_tarski(A))))) # label(t31_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2217 (all A all B (k1_xboole_0 != A -> k2_relat_1(k8_funct_3(A,B)) = B)) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2218 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k1_funct_3(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t10_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2219 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k3_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t29_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2220 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & k1_relat_1(B) = A -> k5_relat_1(k12_funct_3(A),k15_funct_3(B,C)) = k13_funct_3(B,C)))))) # label(t89_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2221 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(B,A),k1_relat_1(C)) & r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k1_relat_1(k5_relat_1(B,C)))))))) # label(t3_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2222 (all A all B r1_tarski(k2_relat_1(k4_funct_3(A,B)),k2_tarski(np__0,np__1))) # label(t48_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2223 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> -((D = k1_xboole_0 -> C = k1_xboole_0) & (k1_xboole_0 = B -> k1_xboole_0 = A) & k16_funct_3(A,C,B,D,E,F) != k13_funct_3(k5_relat_1(k9_funct_3(A,C),E),k5_relat_1(k10_funct_3(A,C),F))))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2224 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2225 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2226 (all A all B all C all D all E all F (v1_funct_2(E,A,C) & v1_funct_1(F) & v1_funct_2(F,B,D) & m1_relset_1(E,A,C) & m1_relset_1(F,B,D) & v1_funct_1(E) -> k15_funct_3(E,F) = k16_funct_3(A,B,C,D,E,F))) # label(redefinition_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2227 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k1_funct_3(A)) & v1_funct_1(k1_funct_3(A)))) # label(dt_k1_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2228 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k15_funct_3(A,B) = C <-> (all D all E (r2_hidden(D,k1_relat_1(A)) & r2_hidden(E,k1_relat_1(B)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)) = k1_funct_1(C,k4_tarski(D,E)))) & k1_relat_1(C) = k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2229 (all A all B all C (-v1_xboole_0(B) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> v1_funct_1(k2_funct_3(A,B,C)) & m2_relset_1(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_2(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(dt_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2230 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) & r1_tarski(A,k2_relat_1(k5_relat_1(B,C))) -> r1_tarski(k10_relat_1(C,A),k2_relat_1(B))))))) # label(t4_funct_3) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2231 (all A ((exists B (A = B & p1_s10_domain_1(B) & p2_s10_domain_1(B) & m1_subset_1(B,f1_s10_domain_1))) <-> r2_hidden(A,a_0_3_domain_1))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2232 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_1_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(E,D) & r2_hidden(E,C) & E = A))))) # label(fraenkel_a_3_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2233 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_2_2_domain_1(B,C)) <-> (exists D (m1_subset_1(D,B) & A = D & -r2_hidden(D,C)))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2234 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_5_domain_1(A,B,C))))))) # label(t62_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2235 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & A = C & p2_s5_domain_1(C))) <-> r2_hidden(A,a_1_4_domain_1(B))))) # label(fraenkel_a_1_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2236 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k15_domain_1(A,B,C,D) = k18_mcart_1(D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2237 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_5_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & E = A & (-r2_hidden(E,C) <-> r2_hidden(E,D))))))) # label(fraenkel_a_3_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2238 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F ((exists G (m1_subset_1(G,B) & (exists H ((exists I ((exists J (m1_subset_1(J,E) & F = k4_mcart_1(G,H,I,J))) & m1_subset_1(I,D))) & m1_subset_1(H,C))))) <-> r2_hidden(F,A))) -> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2239 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) -> ((exists E exists F exists G (A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(G,D) & m1_subset_1(E,B) & p1_s3_domain_1(E,F,G) & m1_subset_1(F,C))) <-> r2_hidden(A,a_3_8_domain_1(B,C,D))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2240 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E ((r2_hidden(E,C) | r2_hidden(E,D)) & m1_subset_1(E,B) & A = E)) <-> r2_hidden(A,a_3_2_domain_1(B,C,D))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2241 (all A ((exists B (p1_s10_domain_1(B) & A = B & m1_subset_1(B,f1_s10_domain_1))) <-> r2_hidden(A,a_0_4_domain_1))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2242 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_4_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t61_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2243 (all A all B all C all D (-v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) & -v1_xboole_0(B) -> m1_subset_1(k14_domain_1(A,B,C,D),A))) # label(dt_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2244 (all A (-v1_xboole_0(A) -> m1_subset_1(a_1_2_domain_1(A),k1_zfmisc_1(A)))) # label(s1_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2245 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2246 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = a_8_0_domain_1(A,B,C,D,E,F,G,H))))))))))))))))) # label(t55_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2247 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2248 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_6_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & (-r2_hidden(E,D) <-> r2_hidden(E,C)) & E = A))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2249 (all A (r2_hidden(A,a_0_1_domain_1) <-> (exists B (A = f3_s8_domain_1(B) & p1_s8_domain_1(B) & m1_subset_1(B,f1_s8_domain_1))))) # label(fraenkel_a_0_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2250 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2251 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) -> m1_subset_1(k15_domain_1(A,B,C,D),B))) # label(dt_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2252 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (r2_hidden(E,C) & -r2_hidden(E,D) & m1_subset_1(E,B) & E = A)) <-> r2_hidden(A,a_3_3_domain_1(B,C,D))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2253 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (k6_mcart_1(B,C,D,E) = A <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> A = G)))))))))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2254 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> m1_subset_1(a_3_8_domain_1(A,B,C),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))))))) # label(s3_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2255 (all A all B (-v1_xboole_0(B) -> ((exists C (A = C & m1_subset_1(C,B) & p1_s5_domain_1(C))) <-> r2_hidden(A,a_1_3_domain_1(B))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2256 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (r2_hidden(A,k3_zfmisc_1(B,C,D)) <-> (exists E ((exists F (m1_subset_1(F,C) & (exists G (m1_subset_1(G,D) & k3_mcart_1(E,F,G) = A)))) & m1_subset_1(E,B)))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2257 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2258 (all A all B all C all D all E all F all G (m1_subset_1(E,k1_zfmisc_1(B)) & -v1_xboole_0(D) & -v1_xboole_0(B) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(D)) & -v1_xboole_0(C) -> ((exists H exists I exists J (m1_subset_1(H,B) & r2_hidden(J,G) & r2_hidden(I,F) & A = k4_domain_1(B,C,D,H,I,J) & m1_subset_1(I,C) & m1_subset_1(J,D) & r2_hidden(H,E))) <-> r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G))))) # label(fraenkel_a_6_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2259 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2260 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2261 (all A all B all C all D all E all F all G all H (m1_subset_1(E,A) & m1_subset_1(G,A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(F,A) & m1_subset_1(H,A) & m1_subset_1(D,A) -> k5_enumset1(B,C,D,E,F,G,H) = k12_domain_1(A,B,C,D,E,F,G,H))) # label(redefinition_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2262 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2263 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k14_domain_1(A,B,C,D) = k17_mcart_1(D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2264 (all A (r2_hidden(A,a_0_0_domain_1) <-> (exists B (m1_subset_1(B,f1_s7_domain_1) & p1_s7_domain_1(B) & A = B)))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2265 (all A all B all C all D all E all F all G all H all I (m1_subset_1(G,A) & m1_subset_1(I,A) & m1_subset_1(E,A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(H,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k13_domain_1(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(A)))) # label(dt_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2266 (all A all B all C all D all E all F (m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(B,A) -> m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)))) # label(dt_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2267 (all A all B all C all D all E (-v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(E) -> (r2_hidden(A,a_4_2_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(G,C) & p1_s4_domain_1(F,G,H,I) & m1_subset_1(I,E) & m1_subset_1(F,B) & A = k5_domain_1(B,C,D,E,F,G,H,I) & m1_subset_1(H,D)))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2268 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> ((exists D exists E (m1_subset_1(E,C) & A = k1_domain_1(B,C,D,E) & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_0_domain_1(B,C))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2269 (all A all B (-v1_xboole_0(B) -> ((exists C (A = C & p1_s6_domain_1(C) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_5_domain_1(B))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2270 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> k2_tarski(B,C) = k7_domain_1(A,B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2271 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> k1_mcart_1(C) = k2_domain_1(A,B,C))) # label(redefinition_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2272 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E (r2_hidden(E,A) <-> (exists F ((exists G (m1_subset_1(G,C) & (exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))))) & m1_subset_1(F,B))))) -> A = k3_zfmisc_1(B,C,D)))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2273 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2274 (all A all B all C all D all E all F all G (m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(B,A) & -v1_xboole_0(A) & m1_subset_1(G,A) & m1_subset_1(F,A) -> k4_enumset1(B,C,D,E,F,G) = k11_domain_1(A,B,C,D,E,F,G))) # label(redefinition_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2275 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2276 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> m1_subset_1(a_2_3_domain_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))))))) # label(s2_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2277 (all A all B all C (m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k2_domain_1(A,B,C),A))) # label(dt_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2278 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2279 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> k3_zfmisc_1(A,B,C) = a_3_0_domain_1(A,B,C))))))) # label(t50_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2280 (all A all B all C all D all E all F all G all H (m1_subset_1(G,A) & m1_subset_1(H,A) & -v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)))) # label(dt_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2281 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2282 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_1_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & -$T & A = C))))) # label(fraenkel_a_1_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2283 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_2_domain_1(A,B,C) = k4_subset_1(A,B,C))))))) # label(t59_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2284 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H ((exists I (k4_mcart_1(F,G,H,I) = A & m1_subset_1(I,E))) & m1_subset_1(H,D))))))) <-> r2_hidden(A,k4_zfmisc_1(B,C,D,E))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2285 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k6_domain_1(A,B) = k1_tarski(B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2286 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2287 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(F,C) & m1_subset_1(E,B) & m1_subset_1(D,A) & -v1_xboole_0(C) -> k4_domain_1(A,B,C,D,E,F) = k3_mcart_1(D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2288 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_6_domain_1(A,B,C))))))) # label(t63_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2289 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2290 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> a_4_1_domain_1(A,B,C,D) = k12_mcart_1(A,B,C,D))))))))) # label(t53_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2291 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> (k5_mcart_1(A,B,C,E) = k5_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = k6_mcart_1(A,B,C,E) & k7_mcart_1(A,B,C,E) = k7_mcart_1(A,B,C,D) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2292 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2293 (all A all B all C all D all E all F all G all H all I (m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(G,A) & m1_subset_1(I,A) & m1_subset_1(H,A) -> k13_domain_1(A,B,C,D,E,F,G,H,I) = k6_enumset1(B,C,D,E,F,G,H,I))) # label(redefinition_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2294 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k7_domain_1(A,C,B) = k7_domain_1(A,B,C))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2295 (all A all B all C all D (-v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k19_mcart_1(D) = k16_domain_1(A,B,C,D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2296 (all A all B all C all D (m1_subset_1(D,A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> k1_enumset1(B,C,D) = k8_domain_1(A,B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2297 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2298 (all A all B all C all D all E all F all G (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & -v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) -> m1_subset_1(k11_domain_1(A,B,C,D,E,F,G),k1_zfmisc_1(A)))) # label(dt_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2299 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> H = A))))))))) <-> A = k9_mcart_1(B,C,D,E,F)))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2300 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2301 (all A all B all C all D all E (m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k2_enumset1(B,C,D,E) = k9_domain_1(A,B,C,D,E))) # label(redefinition_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2302 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_7_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2303 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2304 (all A ((exists B exists C (m1_subset_1(C,f2_s9_domain_1) & m1_subset_1(B,f1_s9_domain_1) & p1_s9_domain_1(B,C) & f4_s9_domain_1(B,C) = A)) <-> r2_hidden(A,a_0_2_domain_1))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2305 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2306 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_3_domain_1(B,C)) <-> (exists D exists E (m1_subset_1(E,C) & p1_s2_domain_1(D,E) & k1_domain_1(B,C,D,E) = A & m1_subset_1(D,B)))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2307 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2308 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2309 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(B,A) -> k3_enumset1(B,C,D,E,F) = k10_domain_1(A,B,C,D,E,F))) # label(redefinition_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2310 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> a_6_0_domain_1(A,B,C,D,E,F) = k13_mcart_1(A,B,C,D,E,F))))))))))))) # label(t54_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2311 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(A) -> k3_domain_1(A,B,C) = k2_mcart_1(C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2312 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2313 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2314 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,C) -> A != k4_tarski(D,E)))))))))) # label(t9_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2315 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & p1_s1_domain_1(C) & A = C))))) # label(fraenkel_a_1_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.33 2316 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_4_domain_1(B,C,D)) <-> (exists E ((-r2_hidden(E,C) & r2_hidden(E,D) | r2_hidden(E,C) & -r2_hidden(E,D)) & m1_subset_1(E,B) & E = A))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2317 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2318 (all A all B all C all D all E all F (m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(D,A) & -v1_xboole_0(C) & -v1_xboole_0(A) & -v1_xboole_0(B) -> m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)))) # label(dt_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2319 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> a_2_2_domain_1(A,B) = k3_subset_1(A,B))))) # label(t57_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2320 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k17_domain_1(A,B,C,D),C))) # label(dt_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2321 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2322 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_1_domain_1(A,B,C) = k5_subset_1(A,B,C))))))) # label(t58_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2323 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2324 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_3_domain_1(A,B,C) = k6_subset_1(A,B,C))))))) # label(t60_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2325 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2326 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (A = k10_mcart_1(B,C,D,E,F) <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> I = A)))))))))))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2327 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & p2_s6_domain_1(C) & C = A)) <-> r2_hidden(A,a_1_6_domain_1(B))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2328 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> a_4_0_domain_1(A,B,C,D) = k4_zfmisc_1(A,B,C,D))))))))) # label(t51_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2329 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k11_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> A = J)))))))))))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2330 (all A all B all C (m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2331 (all A (r2_hidden(A,a_0_5_domain_1) <-> (exists B (B = A & m1_subset_1(B,f1_s10_domain_1) & p2_s10_domain_1(B))))) # label(fraenkel_a_0_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2332 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> G = A))))))))) <-> A = k8_mcart_1(B,C,D,E,F)))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2333 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)))) # label(dt_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2334 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2335 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2336 (all A all B all C all D (m1_subset_1(D,A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2337 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k2_zfmisc_1(A,B) = a_2_0_domain_1(A,B))))) # label(t49_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2338 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2339 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) -> (r2_hidden(A,a_3_0_domain_1(B,C,D)) <-> (exists E exists F exists G (A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(G,D)))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2340 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(A) -> m1_subset_1(k16_domain_1(A,B,C,D),B))) # label(dt_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2341 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_2_1_domain_1(B,C)) <-> (exists D (m1_subset_1(D,B) & D = A & r2_hidden(D,C)))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2342 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> m1_subset_1(a_4_2_domain_1(A,B,C,D),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))))))))) # label(s4_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2343 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s5_domain_1(B) -> p2_s5_domain_1(B)))) -> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A))))) # label(s5_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2344 (all A all B all C all D all E all F all G all H (-v1_xboole_0(D) & m1_subset_1(F,B) & m1_subset_1(H,D) & m1_subset_1(E,A) & -v1_xboole_0(B) & -v1_xboole_0(A) & -v1_xboole_0(C) & m1_subset_1(G,C) -> k5_domain_1(A,B,C,D,E,F,G,H) = k4_mcart_1(E,F,G,H))) # label(redefinition_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2345 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2346 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(E) & -v1_xboole_0(C) -> ((exists F exists G exists H exists I (m1_subset_1(F,B) & m1_subset_1(H,D) & k5_domain_1(B,C,D,E,F,G,H,I) = A & m1_subset_1(I,E) & m1_subset_1(G,C))) <-> r2_hidden(A,a_4_0_domain_1(B,C,D,E))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2347 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F (r2_hidden(F,A) <-> (exists G (m1_subset_1(G,B) & (exists H (m1_subset_1(H,C) & (exists I ((exists J (m1_subset_1(J,E) & F = k4_mcart_1(G,H,I,J))) & m1_subset_1(I,D))))))))) <-> A = k4_zfmisc_1(B,C,D,E)))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2348 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E ((exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H (E = k3_mcart_1(F,G,H) & m1_subset_1(H,D))))))) <-> r2_hidden(E,A))) <-> k3_zfmisc_1(B,C,D) = A))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2349 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2350 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2351 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2352 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(E) & m1_subset_1(H,k1_zfmisc_1(D)) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(I,k1_zfmisc_1(E)) & m1_subset_1(F,k1_zfmisc_1(B)) -> ((exists J exists K exists L exists M (r2_hidden(K,G) & m1_subset_1(L,D) & m1_subset_1(M,E) & r2_hidden(L,H) & r2_hidden(M,I) & r2_hidden(J,F) & A = k5_domain_1(B,C,D,E,J,K,L,M) & m1_subset_1(K,C) & m1_subset_1(J,B))) <-> r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2353 (all A (-v1_xboole_0(A) -> k1_subset_1(A) = a_1_1_domain_1(A))) # label(t56_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2354 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,B) & -v1_xboole_0(A) & m1_subset_1(C,A) -> k4_tarski(C,D) = k1_domain_1(A,B,C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2355 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & A = C))))) # label(fraenkel_a_1_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2356 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> a_2_1_domain_1(A,B) = B)))) # label(t52_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2357 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (A = k7_mcart_1(B,C,D,E) <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (k4_domain_1(B,C,D,F,G,H) = E -> H = A)))))))))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2358 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p2_s6_domain_1(B) <-> p1_s6_domain_1(B)))) -> a_1_5_domain_1(A) = a_1_6_domain_1(A)))) # label(s6_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2359 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E (-(r2_hidden(E,D) <-> r2_hidden(E,C)) & m1_subset_1(E,B) & A = E)) <-> r2_hidden(A,a_3_7_domain_1(B,C,D))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2360 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,B) & -v1_xboole_0(A) & -v1_xboole_0(B) -> m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2361 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> (k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k10_mcart_1(A,B,C,D,E) = k10_mcart_1(A,B,C,D,F) & k9_mcart_1(A,B,C,D,F) = k9_mcart_1(A,B,C,D,E) & k8_mcart_1(A,B,C,D,F) = k8_mcart_1(A,B,C,D,E) -> F = E))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2362 (all A all B all C all D all E (m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(E,k1_zfmisc_1(C)) -> ((exists F exists G (m1_subset_1(F,B) & k1_domain_1(B,C,F,G) = A & r2_hidden(F,D) & r2_hidden(G,E) & m1_subset_1(G,C))) <-> r2_hidden(A,a_4_1_domain_1(B,C,D,E))))) # label(fraenkel_a_4_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2363 (all A all B all C all D all E all F all G all H (m1_subset_1(F,B) & m1_subset_1(G,C) & m1_subset_1(H,D) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & m1_subset_1(E,A) & -v1_xboole_0(A) -> m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)))) # label(dt_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2364 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (k4_domain_1(B,C,D,F,G,H) = E -> F = A))))))) <-> A = k5_mcart_1(B,C,D,E)))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2365 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2366 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> (all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> (k2_mcart_1(D) = k2_mcart_1(C) & k1_mcart_1(D) = k1_mcart_1(C) -> C = D))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2367 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2368 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r1_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t16_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2369 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2370 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> D = k2_binop_1(A,A,A,C,D,B))) <-> r2_binop_1(A,B,C)))))))) # label(d17_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2371 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2372 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2373 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r6_binop_1(A,B,C) <-> r5_binop_1(A,B,C) & r4_binop_1(A,B,C)))))) # label(d11_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2374 (all A all B all C all D all E all F (-v1_xboole_0(B) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & v1_funct_1(D) & -v1_xboole_0(A) & m1_subset_1(E,A) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> m1_subset_1(k2_binop_1(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2375 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2376 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2377 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r3_binop_1(A,C,B) & r3_binop_1(A,D,B) -> C = D))))))) # label(t18_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2378 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & -v1_xboole_0(A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) -> k1_binop_1(D,E,F) = k2_binop_1(A,B,C,D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2379 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2380 (all A (m1_relset_1(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> (v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_funct_1(A) -> v1_xboole_0(A) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_binop_1(A,k1_xboole_0) & v2_binop_1(A,k1_xboole_0) & v1_funct_1(A)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2381 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k2_binop_1(A,B,C,E,F,G) = k2_binop_1(A,B,C,D,F,G))))) -> E = D))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2382 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r7_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_funct_1(B,k1_binop_1(C,D,E)) = k1_binop_1(C,k1_funct_1(B,D),k1_funct_1(B,E))))))))))) # label(d12_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2383 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_binop_1(A,D,B) & r1_binop_1(A,C,B) -> D = C))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2384 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r7_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k8_funct_2(A,A,B,k2_binop_1(A,A,A,C,D,E)) = k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E))))))))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2385 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),F) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,F)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2386 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C))))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2387 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),k2_binop_1(A,A,A,B,D,F)) = k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,E,F))))))))))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2388 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2389 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> ((exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A))) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> k3_binop_1(A,B) = C)))))) # label(d8_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2390 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E) = k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E))))))))))))) # label(d14_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2391 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(B,k1_binop_1(C,D,E),F) = k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F))))))))))))) # label(d10_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2392 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (v1_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_binop_1(B,C,D) = k1_binop_1(B,D,C)))))))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2393 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r4_binop_1(A,C,B))))))))) # label(t26_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2394 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> C = k2_binop_1(A,A,A,B,C,C)))))))) # label(d15_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2395 (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & (all B (m1_subset_1(B,f1_s2_binop_1) -> (all C (m1_subset_1(C,f1_s2_binop_1) -> k2_binop_1(f1_s2_binop_1,f1_s2_binop_1,f1_s2_binop_1,A,B,C) = f2_s2_binop_1(B,C))))) & v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1))) # label(s2_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2396 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v1_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,B,C,D) = k2_binop_1(A,A,A,B,D,C)))))))))) # label(d13_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2397 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r3_binop_1(A,B,C) <-> r1_binop_1(A,B,C) & r2_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2398 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F))))))))))))) # label(d9_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2399 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_binop_1(B,C,k1_binop_1(B,D,E)) = k1_binop_1(B,k1_binop_1(B,C,D),E)))))))))) # label(d3_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2400 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2401 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,C,B,D) = D)) <-> r1_binop_1(A,B,C)))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2402 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> C = k1_binop_1(B,C,C)))))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2403 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D) & k1_binop_1(B,D,C) = D))))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2404 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D))) <-> r3_binop_1(A,C,B))))))) # label(t12_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2405 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,D,F)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2406 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2407 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2408 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> k1_binop_1(B,D,C) = D)))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2409 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r2_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(C,D,B)))))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2410 (all A all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r1_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> k1_binop_1(C,B,D) = D))))))) # label(d5_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2411 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2412 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2413 (all A (m1_subset_1(A,f1_s1_binop_1) -> (all B (m1_subset_1(B,f1_s1_binop_1) -> (exists C (m1_subset_1(C,f1_s1_binop_1) & p1_s1_binop_1(A,B,C))))))) -> (exists A ((all B (m1_subset_1(B,f1_s1_binop_1) -> (all C (m1_subset_1(C,f1_s1_binop_1) -> p1_s1_binop_1(B,C,k2_binop_1(f1_s1_binop_1,f1_s1_binop_1,f1_s1_binop_1,A,B,C)))))) & v1_funct_2(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1))) # label(s1_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2414 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r4_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2415 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2416 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),F) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,F)))))))) <-> r5_binop_1(A,B,C)))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2417 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2418 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2419 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) = k1_binop_1(B,k1_binop_1(C,D,E),F) & k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F)))))))) <-> r6_binop_1(A,B,C)))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2420 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2421 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2422 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(A,k7_relat_1(B,C))))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2423 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k1_relat_1(k3_funcop_1(A,B,C)) = k3_xboole_0(k1_relat_1(B),k1_relat_1(C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2424 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F)) = k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F)))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2425 (all A all B (-v1_xboole_0(B) -> v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2426 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A) = k5_funcop_1(A,B,C))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2427 (exists A (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2428 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2429 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2430 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k4_funcop_1(k5_relat_1(C,A),B,D) = k5_relat_1(k4_funcop_1(C,B,D),A)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2431 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D) = k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D))))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2432 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k2_funcop_1(k10_relat_1(A,B),C) = k5_relat_1(A,k2_funcop_1(B,C))))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2433 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k13_funct_3(k7_relat_1(A,C),B) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2434 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) & v1_funct_2(E,B,A) & m1_relset_1(D,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k6_funcop_1(A,B,C,D,E)))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2435 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B k7_relat_1(k1_funcop_1(A),B) = k1_funcop_1(k7_relat_1(A,B))))) # label(t7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2436 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2437 (all A k12_funct_3(A) = k13_funct_3(k6_partfun1(A),k6_partfun1(A))) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2438 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,B) -> v1_funct_1(k4_funcop_1(C,D,E)) & v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2439 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k4_funcop_1(D,A,E),C) = k7_relat_1(k4_funcop_1(D,B,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2440 (all A (v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2441 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funcop_1(k1_funcop_1(A)) = A)) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2442 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E) = k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E))))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2443 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> m2_relset_1(k5_funcop_1(C,E,D),A,B) & v1_funct_2(k5_funcop_1(C,E,D),A,B) & v1_funct_1(k5_funcop_1(C,E,D)))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2444 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B) & v1_funct_1(k3_funcop_1(C,D,E)))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2445 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> k2_funcop_1(k1_relat_1(A),B) = A)))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2446 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k4_funcop_1(C,k5_relat_1(B,A),D) = k5_relat_1(B,k4_funcop_1(C,A,D))))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2447 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> B = k1_funct_1(A,C))) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2448 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2449 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,B) & v1_funct_2(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2450 (all A all B all C (r2_hidden(B,C) -> A = k10_relat_1(k2_funcop_1(A,B),C))) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2451 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2452 (all A all B k2_zfmisc_1(A,k1_tarski(B)) = k2_funcop_1(A,B)) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2453 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2454 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(A) & v1_funct_1(B) -> v1_relat_1(k4_funcop_1(A,B,C)) & v1_funct_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2455 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) = k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F))))))))))))))) # label(t78_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2456 (all A (k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k1_xboole_0 = k2_relat_1(k2_funcop_1(k1_xboole_0,A)))) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2457 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2458 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2459 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2460 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_1(C) & -v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & v1_funct_2(E,B,A) -> k5_funcop_1(C,D,E) = k8_funcop_1(A,B,C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2461 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> k6_funcop_1(B,A,C,D,D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2462 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2463 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_funcop_1(A)) & v1_funct_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.34 2464 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2465 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2466 (all A all B A = k10_relat_1(k2_funcop_1(A,B),k1_tarski(B))) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2467 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2468 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2469 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k2_funcop_1(B,k1_funct_1(A,C)) = k5_relat_1(k2_funcop_1(B,C),A))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2470 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(C) -> D = k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)))) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2471 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,A) -> v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)) & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2472 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & v1_funct_1(D) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)) = k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2473 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_funct_1(k5_funcop_1(B,D,A),C) = k1_binop_1(B,D,k1_funct_1(A,C)))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2474 (all A all B all C all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2475 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,B),D) = k7_relat_1(k3_funcop_1(E,C,A),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2476 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2477 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2478 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_funct_1(D,E) = k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)))) -> D = k3_funcop_1(C,A,B)))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2479 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2480 (all A all B all C (r2_hidden(B,A) -> C = k1_funct_1(k2_funcop_1(A,C),B))) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2481 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2482 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2483 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F) = k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F))))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2484 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C)) = k4_funcop_1(B,A,C)))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2485 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & v1_funct_1(D) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k7_funcop_1(A,B,C,D,E)))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2486 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2487 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_funcop_1(C,D,k5_relat_1(B,A)) = k5_relat_1(B,k5_funcop_1(C,D,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2488 (all A all B all C all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> v1_funct_1(k10_funcop_1(A,B,C,D)) & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2489 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2490 (all A all B all C k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2491 (all A all B all C all D all E (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(D,B,A) & v1_funct_1(E) & m1_relset_1(E,B,A) & -v1_xboole_0(B) & -v1_xboole_0(A) & v1_funct_2(D,B,A) & v1_funct_2(E,B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) -> k6_funcop_1(A,B,C,D,E) = k3_funcop_1(C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2492 (all A all B (r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) & A = k1_relat_1(k2_funcop_1(A,B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2493 (all A all B all C (-r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = k1_xboole_0)) # label(t22_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2494 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2495 (all A all B (v1_funcop_1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2496 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)) = k4_relat_1(k9_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2497 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (v3_binop_1(C,B) -> D = k6_funcop_1(B,A,C,D,D)))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2498 (all A all B all C k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C))) = k2_funcop_1(A,k4_tarski(C,B))) # label(t26_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2499 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_funcop_1(B,C,A) = k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2500 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2501 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2502 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2503 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2504 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,A,B) & v1_funct_1(F) & v1_funct_2(F,A,B) -> ((all G (m1_subset_1(G,A) -> k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)) = k8_funct_2(A,B,F,G))) -> k6_funcop_1(B,A,C,D,E) = F))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2505 (all A all B (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2506 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2507 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2508 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2509 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)) = k5_relat_1(C,k3_funcop_1(D,A,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2510 (all A all B (v1_funct_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2511 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2512 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(A) & k1_relat_1(B) = k1_xboole_0 -> A = B))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2513 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k5_funcop_1(C,D,B),A) = k5_funcop_1(k5_relat_1(C,A),D,B)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2514 (all A all B all C (r2_hidden(C,B) -> m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2515 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,B) & v1_funct_2(E,B,B) -> k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2516 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(k3_funcop_1(C,A,B),D))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2517 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(r2_hidden(C,k1_relat_1(A)) & k1_xboole_0 != B & k1_xboole_0 = k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)))))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2518 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(A) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2519 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2520 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) & v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k5_funcop_1(A,B,C)) & v1_relat_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2521 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k1_funct_1(B,C) = k4_tarski(E,D))) & -(k1_funct_1(B,C) != k1_funct_1(A,C) & (all D all E k4_tarski(D,E) != k1_funct_1(A,C))))) & k1_relat_1(B) = k1_relat_1(A) <-> B = k1_funcop_1(A)))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2522 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_funct_1(A) -> v1_relat_1(k3_funcop_1(A,B,C)) & v1_funct_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2523 (all A all B all C all D (m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k1_funcop_1(D) = k10_funcop_1(A,B,C,D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2524 (all A (v1_relat_1(A) -> (all B all C (k2_zfmisc_1(B,C) = A -> k1_relat_1(A) = B & k2_relat_1(A) = C | C = k1_xboole_0 | B = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2525 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C))))))) # label(t70_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2526 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(A) -> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2527 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2528 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (m1_subset_1(E,A) -> k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))) = k1_funct_1(k1_funcop_1(D),E))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2529 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & v1_funct_1(E) & m2_relset_1(E,A,B) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,E,D) = k6_funcop_1(B,A,C,D,E)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2530 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D))) -> k1_binop_1(B,k1_funct_1(A,C),D) = k1_funct_1(k4_funcop_1(B,A,D),C))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2531 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,A) & v1_funct_1(E) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2532 (all A all B (v1_xboole_0(B) -> v1_xboole_0(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2533 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,B) -> (v1_binop_1(C,B) -> k7_funcop_1(B,A,C,D,E) = k8_funcop_1(B,A,C,E,D)))))))))))) # label(t79_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2534 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_1(D) & v1_funct_2(D,A,A) -> k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2535 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k4_funcop_1(C,k7_relat_1(A,B),D) = k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D))))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2536 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) = k8_funct_2(B,A,D,G))) -> D = k7_funcop_1(A,B,C,E,F)))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2537 (all A all B (A != k1_xboole_0 -> k1_tarski(B) = k2_relat_1(k2_funcop_1(A,B)))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2538 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & v1_funct_2(D,B,A) & v1_funct_1(D) & -v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,B,A) -> k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2539 (all A all B all C all D all E all F (k4_funct_4(A,B,C,D) = k4_funct_4(A,B,E,F) -> B = A | C = E & F = D)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2540 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(A) & v1_relat_1(B) -> v1_funct_1(k3_funct_4(A,B)) & v1_relat_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2541 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_partfun1(A,B) & r1_tarski(k2_relat_1(D),k1_relat_1(B)) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2542 (all A all B all C all D all E all F all G (m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(D,E),F) -> m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_1(k3_funct_4(G,H)))))) # label(t62_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2543 (all A (v1_relat_1(A) & v1_funct_1(A) -> A = k1_funct_4(k1_xboole_0,A))) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2544 (all A all B all C k2_funcop_1(k2_tarski(A,B),C) = k4_funct_4(A,B,C,C)) # label(t68_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2545 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2546 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(A),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2547 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D all E all F all G (r2_hidden(k4_tarski(F,G),k1_relat_1(B)) & r2_hidden(k4_tarski(D,E),k1_relat_1(A)) -> k1_funct_1(C,k4_tarski(k4_tarski(D,F),k4_tarski(E,G))) = k4_tarski(k1_funct_1(A,k4_tarski(D,E)),k1_funct_1(B,k4_tarski(F,G))))) & (all D ((exists E exists F exists G exists H (r2_hidden(k4_tarski(E,F),k1_relat_1(A)) & r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & k4_tarski(k4_tarski(E,G),k4_tarski(F,H)) = D)) <-> r2_hidden(D,k1_relat_1(C)))) <-> C = k3_funct_4(A,B)))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2548 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k2_zfmisc_1(B,A) = k1_relat_1(k2_funct_4(C))))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2549 (all A (v1_relat_1(A) & v1_funct_1(A) -> (exists B exists C r1_tarski(k1_relat_1(k2_funct_4(A)),k2_zfmisc_1(B,C))))) # label(t45_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2550 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k1_relat_1(C))),B)))))))) # label(t27_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2551 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(k1_relat_1(B),C) & r1_tarski(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = A)))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2552 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (D = k1_funct_1(E,B) & k1_relat_1(E) = k2_tarski(A,B) & k1_funct_1(E,A) = C -> k4_funct_4(A,B,C,D) = E))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2553 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (k1_relat_1(E) = k2_zfmisc_1(A,B) & k2_zfmisc_1(C,D) = k1_relat_1(F) -> k1_relat_1(k3_funct_4(E,F)) = k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D))))))) # label(t61_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2554 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (k1_xboole_0 != C -> D = k2_funct_4(k2_funct_4(D))))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2555 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t18_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2556 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(B,A) = k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2557 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2558 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_4(A)) & v1_relat_1(k2_funct_4(A)))) # label(dt_k2_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2559 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> B = k1_funct_4(A,B) & B = k1_funct_4(B,A)))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2560 (all A all B (v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(B) & v1_relat_1(A) -> A = k1_funct_4(A,A))) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2561 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2562 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> v1_funct_1(k1_funct_4(C,D)) & m2_relset_1(k1_funct_4(C,D),A,B))))) # label(t41_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2563 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(C,k1_relat_1(B)) -> k7_relat_1(A,C) = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2564 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k7_relat_1(A,k2_xboole_0(B,C)) = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C))))) # label(t83_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2565 (all A all B all C all D all E all F all G (m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) -> (all H (m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_2(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> -(-(v1_funct_1(k3_funct_4(G,H)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F))) & F != k1_xboole_0 & k1_xboole_0 != C))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2566 (all A -((all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))) & (all B all C -r1_tarski(A,k2_zfmisc_1(B,C))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2567 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_funct_4(k2_funct_4(A)),A))) # label(t52_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2568 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(C) -> k1_funct_4(A,C) = k1_funct_4(k1_funct_4(A,B),C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2569 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_funct_4(A,B) = k2_xboole_0(A,B) <-> r1_partfun1(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2570 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_funct_4(k2_funct_4(C)) = C))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2571 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (-r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2572 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2573 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C))) <-> r2_hidden(k4_tarski(A,B),k1_relat_1(C))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2574 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> r1_tarski(k1_relat_1(k2_funct_4(C)),k2_zfmisc_1(B,A))))) # label(t46_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2575 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (k1_xboole_0 != C -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D))))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2576 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> D = k1_funct_4(C,D))))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2577 (all A all B all C all D (B != A -> k2_tarski(C,D) = k2_relat_1(k4_funct_4(A,B,C,D)))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2578 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_relat_1(k2_funct_4(C)) = k2_relat_1(C)))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2579 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2580 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k1_funct_4(A,k1_xboole_0))) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2581 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B A = k1_funct_4(A,k7_relat_1(A,B))))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2582 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(A,k1_funct_4(B,A)))))) # label(t26_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2583 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> D = k2_funct_4(k2_funct_4(D)))))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2584 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2585 (all A all B all C all D (v1_funct_1(k4_funct_4(A,B,C,D)) & v1_relat_1(k4_funct_4(A,B,C,D)))) # label(fc1_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2586 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),E) & m2_relset_1(G,k2_zfmisc_1(A,B),E) -> (all H (m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_2(H,k2_zfmisc_1(C,D),F) & v1_funct_1(H) -> v1_funct_1(k3_funct_4(G,H)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)))))))))) # label(t64_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2587 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2588 (all A all B all C all D (A != B -> C = k1_funct_1(k4_funct_4(A,B,C,D),A) & D = k1_funct_1(k4_funct_4(A,B,C,D),B))) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2589 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))) # label(t49_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2590 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> A = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)))))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2591 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2592 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)) = B)))) # label(t24_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2593 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r1_xboole_0(C,D) & r1_tarski(k1_relat_1(A),C) & r1_tarski(k1_relat_1(B),D) -> B = k7_relat_1(k1_funct_4(A,B),D) & k7_relat_1(k1_funct_4(A,B),C) = A)))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2594 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2595 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(E),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(F),k2_zfmisc_1(C,D)) -> r1_tarski(k1_relat_1(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))))) # label(t60_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2596 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r1_tarski(k2_funcop_1(k1_tarski(A),k1_funct_1(B,A)),B)))) # label(t8_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2597 (all A all B all C all D (A != C -> k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2598 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(A)) = A))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2599 (all A all B (v1_funct_2(B,A,A) & v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> C = k1_funct_4(B,C))))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2600 (all A all B all C all D (r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) & k2_tarski(A,B) = k1_relat_1(k4_funct_4(A,B,C,D)))) # label(t65_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2601 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k2_xboole_0(A,B) = k1_funct_4(A,B)))))) # label(t32_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2602 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2603 (all A all B (r1_tarski(k6_partfun1(A),k6_partfun1(B)) <-> r1_tarski(A,B))) # label(t4_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2604 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2605 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2606 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_partfun1(B,C) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2607 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2608 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> r1_tarski(A,k1_funct_4(A,B))))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2609 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F))) -> k1_funct_1(k3_funct_4(E,F),k4_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k4_tarski(k1_funct_1(E,k4_tarski(A,C)),k1_funct_1(F,k4_tarski(B,D)))))))) # label(t58_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2610 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B))))))) # label(t10_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2611 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(k2_funct_4(C))) -> k1_funct_1(k2_funct_4(C),k4_tarski(A,B)) = k1_funct_1(C,k4_tarski(B,A))))) # label(t44_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2612 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & v1_funct_1(k5_funct_4(A,B,C,D,E)) & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2613 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,k1_funct_4(B,C)))))))) # label(t15_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2614 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (r2_hidden(k4_tarski(B,D),k1_relat_1(F)) & r2_hidden(k4_tarski(A,C),k1_relat_1(E)) <-> r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F)))))))) # label(t57_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.35 2615 (all A all B k2_funcop_1(k1_tarski(A),B) = k1_tarski(k4_tarski(A,B))) # label(t70_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2616 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(B,C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2617 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2618 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = B))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2619 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2620 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> r1_tarski(A,C))) # label(t6_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2621 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2622 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2623 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k7_relat_1(k1_funct_4(A,B),C) = k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C))))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2624 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> D = k1_funct_4(C,D)))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2625 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> k4_funct_4(B,C,D,E) = k5_funct_4(A,B,C,D,E))) # label(redefinition_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2626 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k2_funct_4(A) <-> (all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k1_funct_1(A,k4_tarski(C,D)) = k1_funct_1(B,k4_tarski(D,C)))) & (all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (k4_tarski(E,D) = C & r2_hidden(k4_tarski(D,E),k1_relat_1(A))))))))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2627 (all A all B k1_funct_4(k6_partfun1(A),k6_partfun1(B)) = k6_partfun1(k2_xboole_0(A,B))) # label(t23_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2628 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_funcop_1(A,C),k2_funcop_1(B,C)))) # label(t5_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2629 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k1_funct_4(B,C))) <-> r2_hidden(A,k1_relat_1(C)) | r2_hidden(A,k1_relat_1(B))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2630 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> k1_xboole_0 = A | D = B)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2631 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_funct_4(A,B) = C <-> k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) & (all D (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(A,D) = k1_funct_1(C,D)) & (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))))))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.36 2632 (all A all B all C all D k4_funct_4(A,B,C,D) = k1_funct_4(k2_funcop_1(k1_tarski(A),C),k2_funcop_1(k1_tarski(B),D))) # label(d4_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.38 2633 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_funct_4(A,B) = k1_funct_4(B,A) <-> r1_partfun1(A,B)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 67.51/65.38 2634 (all A all B (v3_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.38 2635 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r2_hidden(C,A)))) -> r1_ordinal1(k7_ordinal2(B),A))))) # label(t28_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.38 2636 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & f4_s16_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s16_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f6_s16_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_ordinal2(C) = B & v1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & v5_ordinal1(C))) <-> B = f3_s16_ordinal2(A)))))) & v4_ordinal1(f2_s16_ordinal2) & f2_s16_ordinal2 = k1_relat_1(f1_s16_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> f3_s16_ordinal2(A) = k1_funct_1(f1_s16_ordinal2,A)))) & f2_s16_ordinal2 != k1_xboole_0 -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.38 2637 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_relat_1(C) & v1_funct_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & k1_ordinal2(C) = A & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(f1_s13_ordinal2) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & v1_ordinal2(C))) & B != A & (exists C (f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_xboole_0 = D | k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D))))) & B = k1_ordinal2(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & v1_relat_1(C)))))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 67.51/65.38 2638 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v1_funct_1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s13_ordinal2(C,k1_funct_1(B,C))))) & A = k1_ordinal2(B) & v1_ordinal2(B) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> C = k1_xboole_0 | f4_s13_ordinal2(C,k2_ordinal1(B,C)) = k1_funct_1(B,C)))) & k1_relat_1(B) = k1_ordinal1(f1_s13_ordinal2) & v5_ordinal1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 67.51/65.38 2639 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.38 2640 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.51/65.38 2641 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (v3_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k1_funct_1(A,B) & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> k1_xboole_0 = B | r1_ordinal2(C,k2_ordinal1(A,B)))))))))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2642 (all A (v3_ordinal1(A) -> (all B (B = f1_s8_ordinal2(A) <-> (exists C (v1_funct_1(C) & B = k1_ordinal2(C) & v1_relat_1(C) & v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | f4_s8_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s8_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f2_s8_ordinal2 & k1_relat_1(C) = k1_ordinal1(A))))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2643 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2644 (all A (v3_ordinal1(A) -> A = k2_ordinal2(A))) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2645 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2646 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2647 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k16_ordinal2(A,k1_ordinal1(B)) = k15_ordinal2(A,k16_ordinal2(A,B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2648 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2649 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2650 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f6_s4_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A)) = f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A))))) & k1_relat_1(f6_s4_ordinal2) = f1_s4_ordinal2 & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) | k1_xboole_0 = A))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) -> f5_s4_ordinal2 = f6_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2651 (all A all B -((exists C (v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & v1_funct_1(C) & v1_relat_1(C) & B = k1_ordinal2(C) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2)) & A != B & (exists C (k1_ordinal2(C) = A & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_xboole_0 = D | f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & v5_ordinal1(C) & v1_relat_1(C) & v1_funct_1(C))))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 67.59/65.41 2652 (exists A exists B (v1_funct_1(B) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> C = k1_xboole_0 | f4_s7_ordinal2(C,k2_ordinal1(B,C)) = k1_funct_1(B,C)))) & v5_ordinal1(B) & k1_ordinal2(B) = A & k1_relat_1(B) = k1_ordinal1(f1_s7_ordinal2) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & v1_relat_1(B))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2653 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> A = k1_xboole_0 | r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A))))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2654 (all A (v4_ordinal2(A) <-> r2_hidden(A,k5_ordinal2))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2655 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2656 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2657 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,C))))))))) # label(t58_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2658 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2659 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2660 (all A (v3_ordinal1(A) -> (all B all C (r2_hidden(A,B) & r1_tarski(B,C) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2661 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2662 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2663 (exists A (v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> f2_s2_ordinal2(B) = k1_funct_1(A,B)))) & k1_relat_1(A) = f1_s2_ordinal2 & v1_funct_1(A) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2664 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2665 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2666 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2667 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2668 (all A all B (k2_ordinal2(A) = B <-> (all C (v3_ordinal1(C) & r2_hidden(C,A) <-> r2_hidden(C,B))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2669 (all A (v3_ordinal1(A) -> (all B (f4_s9_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s9_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f1_s9_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f3_s9_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & v5_ordinal1(C) & v1_relat_1(C))))))) -> (all A (v3_ordinal1(A) -> f4_s9_ordinal2(k1_ordinal1(A)) = f2_s9_ordinal2(A,f4_s9_ordinal2(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2670 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2671 (all A all B (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) & v3_ordinal1(B) & v1_ordinal2(A) -> v1_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)) & v2_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2672 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k4_ordinal2) = A & k4_ordinal2 = k16_ordinal2(k4_ordinal2,A))) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2673 k1_relat_1(f1_s10_ordinal2) = f2_s10_ordinal2 & v4_ordinal1(f2_s10_ordinal2) & k1_xboole_0 != f2_s10_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (all B (B = f3_s10_ordinal2(A) <-> (exists C (v1_funct_1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f4_s10_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s10_ordinal2(D,k1_funct_1(C,D))))) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f3_s10_ordinal2(f2_s10_ordinal2) = f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2674 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2675 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2676 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t49_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2677 (all A all B (B = k3_ordinal2(A) <-> (all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (v3_ordinal1(D) & C = D & v4_ordinal1(D))))))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2678 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k1_xboole_0) = A)) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2679 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k1_ordinal1(k14_ordinal2(A,B)) = k14_ordinal2(A,k1_ordinal1(B)))))) # label(t45_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2680 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(C,A),k15_ordinal2(C,B))))))))) # label(t59_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2681 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v5_ordinal1(C) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s14_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_relat_1(C) & v1_ordinal2(C))) <-> f1_s14_ordinal2(A) = B))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2682 (all A (v3_ordinal1(A) -> (exists B ((exists C (v4_ordinal1(B) & A = k14_ordinal2(B,C) & v3_ordinal1(C) & v4_ordinal2(C))) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2683 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(A,C),k14_ordinal2(B,C))))))))) # label(t51_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2684 (all A all B (r1_tarski(A,B) -> r1_ordinal1(k7_ordinal2(A),k7_ordinal2(B)))) # label(t30_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2685 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2686 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2687 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k15_ordinal2(A,B),B) = k15_ordinal2(k1_ordinal1(A),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2688 (exists A ((r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s11_ordinal2) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s11_ordinal2) & v4_ordinal1(B) -> k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B)) | k1_xboole_0 = B))) & k1_relat_1(A) = f1_s11_ordinal2 & v5_ordinal1(A) & v1_ordinal2(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s11_ordinal2(B,k1_funct_1(A,B))))) & v1_funct_1(A) & v1_relat_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2689 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2690 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (r1_ordinal2(B,A) <-> B = k12_ordinal2(A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2691 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2692 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2693 (all A all B (v3_ordinal1(B) -> (B = k7_ordinal2(A) <-> (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) & r1_tarski(k2_ordinal2(A),B)))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2694 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2695 (all A all B (r1_tarski(A,B) -> r1_tarski(k2_ordinal2(A),k2_ordinal2(B)))) # label(t11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2696 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C))))))) <-> v2_ordinal2(A)))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2697 (exists A (v1_relat_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s5_ordinal2 & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s5_ordinal2) -> k1_funct_1(A,B) = f4_s5_ordinal2(B,k2_ordinal1(A,B)) | k1_xboole_0 = B))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s5_ordinal2(B,k1_funct_1(A,B))))) & v1_funct_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2698 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> k2_ordinal2(B) = k1_xboole_0 | r1_ordinal1(A,k6_ordinal2(B)))))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2699 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B))))))) # label(t1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2700 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_funct_1(D) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) = k1_funct_1(D,E) | k1_xboole_0 = E))) & k1_relat_1(D) = k1_ordinal1(A) & v5_ordinal1(D) & v1_relat_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k1_funct_1(D,k1_ordinal1(E)) = k14_ordinal2(k1_funct_1(D,E),B)))) & k1_xboole_0 = k1_funct_1(D,k1_xboole_0) & k1_ordinal2(D) = C & v1_ordinal2(D))) <-> k15_ordinal2(A,B) = C))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2701 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> (k10_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & B = k9_ordinal2(C) & v1_relat_1(C) & v1_ordinal2(C) & k1_relat_1(A) = k1_relat_1(C) & v5_ordinal1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.42 2702 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2703 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> (r1_ordinal2(A,B) <-> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(r2_hidden(A,D) & r2_hidden(C,A) & (all E (v3_ordinal1(E) -> -(r2_hidden(E,k1_relat_1(B)) & (all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(C,k1_funct_1(B,F)) & r2_hidden(k1_funct_1(B,F),D)))))))))))))) & (k1_xboole_0 = A -> (r1_ordinal2(A,B) <-> (exists C ((all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r2_hidden(D,k1_relat_1(B)) -> k1_xboole_0 = k1_funct_1(B,D)))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2704 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_ordinal2(A),k3_ordinal2(B)))) # label(t14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2705 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2706 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2707 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2708 (exists A (v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) & v1_relat_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2709 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2710 p1_s1_ordinal2(k1_xboole_0) & (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) -> p1_s1_ordinal2(A) | A = k1_xboole_0))) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2711 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2712 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2713 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2714 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(A,k7_ordinal2(B)))))) # label(t27_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2715 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2716 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2717 (exists A (v4_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A) & v3_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2718 (all A (v3_ordinal1(A) -> (exists B (r2_hidden(A,B) & v3_ordinal1(B) & v4_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2719 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2720 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k1_setfam_1(A)))) # label(t17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2721 (all A (v3_ordinal1(A) -> (r2_hidden(A,f3_s6_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A)))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> f4_s6_ordinal2 = k1_funct_1(f1_s6_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A)) = f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A))))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C ((all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_relat_1(C) = k1_ordinal1(A) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> k1_funct_1(f1_s6_ordinal2,A) = f2_s6_ordinal2(A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2722 (all A all B (v3_ordinal1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2723 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2724 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2725 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & k8_ordinal2(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k1_relat_1(A) = k1_relat_1(C) & v1_relat_1(C))) <-> k11_ordinal2(A) = B))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2726 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r1_ordinal1(k6_ordinal2(B),A))))) # label(t22_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2727 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2728 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k14_ordinal2(A,k4_ordinal2))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2729 (all A all B (v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) & v5_ordinal1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)) & v1_ordinal2(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2730 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t50_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2731 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2732 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2733 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(k6_ordinal2(B),B))))) # label(t25_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2734 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> f2_s3_ordinal2(B) = k1_funct_1(A,B)))) & f1_s3_ordinal2 = k1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2735 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f3_s15_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & v1_relat_1(C) & f1_s15_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s15_ordinal2(D,k1_funct_1(C,D))))) & B = k1_ordinal2(C) & v5_ordinal1(C))) <-> B = f4_s15_ordinal2(A)))))) -> (all A (v3_ordinal1(A) -> f4_s15_ordinal2(k1_ordinal1(A)) = f2_s15_ordinal2(A,f4_s15_ordinal2(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2736 (all A (k5_ordinal2 = A <-> (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v3_ordinal1(A) & v4_ordinal1(A) & r2_hidden(k1_xboole_0,A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.59/65.47 2737 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v5_ordinal1(C) & v1_relat_1(C) & v1_funct_1(C) & v1_ordinal2(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & A = k1_relat_1(C) -> k14_ordinal2(B,A) = k8_ordinal2(C)))) | A = k1_xboole_0))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2738 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2739 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k9_ordinal2(A)))) # label(dt_k9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2740 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)) & k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2741 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (r1_tarski(k2_relat_1(A),B) & v3_ordinal1(B))) <-> v1_ordinal2(A)))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2742 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2743 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k15_ordinal2(A,B)))) # label(dt_k15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2744 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2745 k1_relat_1(f1_s12_ordinal2) = f3_s12_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f3_s12_ordinal2) & v4_ordinal1(A) -> k1_xboole_0 = A | f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A)) = f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A))))) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_xboole_0) = f4_s12_ordinal2) & (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f2_s12_ordinal2(A) = B <-> (exists C (v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f6_s12_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_ordinal2(C) = B & v5_ordinal1(C) & v1_funct_1(C) & k1_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & v1_relat_1(C)))))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> k1_funct_1(f1_s12_ordinal2,A) = f2_s12_ordinal2(A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2746 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k14_ordinal2(A,B) <-> (exists D (A = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k1_ordinal1(k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_xboole_0 = E | k8_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & v1_ordinal2(D) & v1_relat_1(D) & v1_funct_1(D) & k1_relat_1(D) = k1_ordinal1(B) & C = k1_ordinal2(D) & v5_ordinal1(D)))))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2747 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k3_tarski(k8_ordinal2(C)) = k15_ordinal2(A,B)))) | k1_xboole_0 = A))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2748 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2749 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k16_ordinal2(A,B) = C <-> (exists D (C = k1_ordinal2(D) & k1_ordinal1(B) = k1_relat_1(D) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k15_ordinal2(A,k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & v1_funct_1(D) & v1_relat_1(D) & v5_ordinal1(D) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_xboole_0 = E | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & v1_ordinal2(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2750 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k4_ordinal2) = A & k15_ordinal2(k4_ordinal2,A) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2751 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2752 (all A (v3_ordinal1(A) -> (r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2753 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2754 (all A (v3_ordinal1(A) -> (all B -((all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))) & r2_hidden(A,k7_ordinal2(B)))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2755 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2756 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) -> k16_ordinal2(B,A) = k12_ordinal2(C)))) | A = k1_xboole_0))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2757 (all A all B (r1_tarski(k1_ordinal1(A),B) -> r1_tarski(A,B))) # label(t2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2758 $T # label(t46_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2759 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(k5_ordinal3(A,C),k5_ordinal3(B,C)) | -r2_hidden(C,A) & -r1_ordinal1(C,A)))))))) # label(t66_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2760 $T # label(t64_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2761 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(k14_ordinal2(A,B),C) -> r2_hidden(B,k5_ordinal3(C,A))))))))) # label(t74_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2762 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(k14_ordinal2(A,B),k14_ordinal2(A,C)) -> r1_ordinal1(B,C)))))))) # label(t26_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2763 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != k1_relat_1(A) -> k14_ordinal2(B,k8_ordinal2(A)) = k8_ordinal2(k1_ordinal3(B,A))))))) # label(t51_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2764 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(A),k1_ordinal1(B)) <-> r2_hidden(A,B)))))) # label(t5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2765 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v1_ordinal1(k2_xboole_0(A,B)) & v3_ordinal1(k2_xboole_0(A,B)) & v2_ordinal1(k2_xboole_0(A,B)))) # label(fc1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2766 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> B = k14_ordinal2(A,k5_ordinal3(B,A))))))) # label(t60_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2767 (all A (v3_ordinal1(A) -> (A != k1_xboole_0 -> r2_hidden(k1_xboole_0,A)))) # label(t10_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2768 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(k15_ordinal2(k6_ordinal3(A,B),B),A))))) # label(t77_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2769 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(k15_ordinal2(A,B),k15_ordinal2(C,B)) -> r2_hidden(A,C)))))))) # label(t37_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2770 $T # label(t3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2771 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> v4_ordinal1(k14_ordinal2(B,A)) | k1_xboole_0 = A))))) # label(t32_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2772 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (k3_ordinal3(A,B) = C <-> (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k15_ordinal2(A,k1_funct_1(B,D)) = k1_funct_1(C,D)))) & k1_relat_1(B) = k1_relat_1(C)))))))) # label(d4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2773 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k15_ordinal2(k6_ordinal3(A,B),B),k7_ordinal3(A,B)) = A)))) # label(t78_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2774 (all A v3_ordinal1(k3_tarski(k2_ordinal2(A)))) # label(t7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2775 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> -(C != k1_xboole_0 & B = k14_ordinal2(A,C)))) & r2_hidden(A,B)))))) # label(t31_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2776 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> C = k1_xboole_0 | r2_hidden(A,k15_ordinal2(C,B)) & r2_hidden(A,k15_ordinal2(B,C))))))))) # label(t35_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2777 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k7_ordinal3(A,B)))) # label(dt_k7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2778 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k6_ordinal3(A,B)))) # label(dt_k6_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2779 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k5_ordinal3(k5_ordinal3(A,B),C) = k5_ordinal3(A,k14_ordinal2(B,C)))))))) # label(t70_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2780 $T # label(t4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2781 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(k15_ordinal2(A,B),k15_ordinal2(C,B)) -> k1_xboole_0 = B | r1_ordinal1(A,C)))))))) # label(t38_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2782 (all A (v3_ordinal1(A) -> k6_ordinal2(k1_tarski(A)) = A)) # label(t12_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2783 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k15_ordinal2(C,B) = k15_ordinal2(A,B) -> k1_xboole_0 = B | A = C))))))) # label(t36_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2784 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k5_ordinal3(k14_ordinal2(A,B),A) = B)))) # label(t65_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2785 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(A,k14_ordinal2(C,B)) & r2_hidden(A,k14_ordinal2(B,C))))))))) # label(t28_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2786 (all A (v3_ordinal1(A) -> k1_xboole_0 = k6_ordinal3(k1_xboole_0,A) & k7_ordinal3(k1_xboole_0,A) = k1_xboole_0 & A = k7_ordinal3(A,k1_xboole_0))) # label(t83_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2787 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r2_hidden(D,C) & A = k14_ordinal2(k15_ordinal2(B,C),D) -> D = k7_ordinal3(A,C) & k6_ordinal3(A,C) = B))))))))) # label(t79_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2788 $T # label(t45_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2789 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k4_ordinal2,A) & v4_ordinal1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,B) -> k1_funct_1(C,D) = k15_ordinal2(D,A)))) & k1_relat_1(C) = B -> k8_ordinal2(C) = k15_ordinal2(B,A)))) | k1_xboole_0 = B))))) # label(t57_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2790 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k14_ordinal2(k14_ordinal2(A,B),C) = k14_ordinal2(A,k14_ordinal2(B,C)))))))) # label(t33_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2791 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 = k14_ordinal2(A,B) -> A = k1_xboole_0 & B = k1_xboole_0))))) # label(t29_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2792 (all A (v3_ordinal1(A) -> k5_ordinal3(A,A) = k1_xboole_0)) # label(t67_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2793 (all A (v3_ordinal1(A) -> k1_xboole_0 = k5_ordinal3(k1_xboole_0,A) & k5_ordinal3(A,k1_xboole_0) = A)) # label(t69_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2794 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k5_ordinal3(C,B),k5_ordinal3(C,A))))))))) # label(t71_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2795 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r1_ordinal1(A,B) & r1_ordinal1(C,D) -> r1_ordinal1(k14_ordinal2(A,C),k14_ordinal2(B,D))))))))))) # label(t21_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2796 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k5_ordinal3(A,C),k5_ordinal3(B,C))))))))) # label(t72_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2797 (all A all B (v1_relat_1(B) & v3_ordinal1(A) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> v1_relat_1(k4_ordinal3(A,B)) & v1_funct_1(k4_ordinal3(A,B)) & v5_ordinal1(k4_ordinal3(A,B)) & v1_ordinal2(k4_ordinal3(A,B)))) # label(dt_k4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2798 (all A (v1_ordinal2(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(k8_ordinal2(A)) -> k1_xboole_0 = B | k8_ordinal2(k4_ordinal3(B,A)) = k15_ordinal2(k8_ordinal2(A),B) | k1_relat_1(A) = k1_xboole_0))))) # label(t52_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2799 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r1_ordinal1(A,B) & r1_ordinal1(C,D) -> r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,D))))))))))) # label(t23_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2800 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(r1_ordinal1(A,B) & (all C (v3_ordinal1(C) -> k14_ordinal2(A,C) != B))))))) # label(t30_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2801 (all A (v3_ordinal1(A) -> k2_ordinal2(k1_tarski(A)) = k1_tarski(A))) # label(t9_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2802 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r2_hidden(A,B) -> -(r1_ordinal1(C,D) & D != k1_xboole_0) & -r2_hidden(C,D) | r2_hidden(k15_ordinal2(A,C),k15_ordinal2(B,D))))))))))) # label(t22_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2803 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> B = k2_xboole_0(A,B) | A = k2_xboole_0(A,B))))) # label(t15_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2804 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k5_ordinal3(k15_ordinal2(A,B),k15_ordinal2(C,B)) = k15_ordinal2(k5_ordinal3(A,C),B))))))) # label(t76_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2805 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k7_ordinal3(k15_ordinal2(A,B),B) = k1_xboole_0)))) # label(t82_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2806 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(A,k14_ordinal2(B,k5_ordinal3(A,B))))))) # label(t75_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2807 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k15_ordinal2(A,k15_ordinal2(B,C)) = k15_ordinal2(k15_ordinal2(A,B),C))))))) # label(t58_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2808 (all A (v3_ordinal1(A) -> -(A != k4_ordinal2 & k1_xboole_0 != A & r1_ordinal1(A,k4_ordinal2)))) # label(t19_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2809 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (k1_ordinal3(A,B) = C <-> (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k14_ordinal2(A,k1_funct_1(B,D)) = k1_funct_1(C,D)))) & k1_relat_1(B) = k1_relat_1(C)))))))) # label(d2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2810 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> A = k3_xboole_0(A,B) | B = k3_xboole_0(A,B))))) # label(t16_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2811 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) & v1_relat_1(A) -> (all B (v1_ordinal2(B) & v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (all C (v3_ordinal1(C) -> ((all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (k1_funct_1(A,D) = E & r2_hidden(D,k1_relat_1(A)) -> k15_ordinal2(E,C) = k1_funct_1(B,D)))))) & k1_relat_1(B) = k1_relat_1(A) & v4_ordinal1(k8_ordinal2(A)) -> k1_xboole_0 = k1_relat_1(A) | k1_xboole_0 = C | k15_ordinal2(k8_ordinal2(A),C) = k8_ordinal2(B)))))))) # label(t50_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2812 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,k15_ordinal2(B,C)) -> r2_hidden(k6_ordinal3(A,C),B) & r2_hidden(k7_ordinal3(A,C),C)))))))) # label(t80_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2813 $T # label(t61_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2814 (all A (v3_ordinal1(A) -> (r2_hidden(A,k4_ordinal2) -> k1_xboole_0 = A))) # label(t17_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2815 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> -(-r2_hidden(A,B) & r2_hidden(A,k14_ordinal2(B,C)) & (all D (v3_ordinal1(D) -> -(r2_hidden(D,C) & k14_ordinal2(B,D) = A)))))))))) # label(t42_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2816 $T # label(t59_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2817 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(k1_xboole_0 != A & (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(r2_hidden(D,A) & B = k14_ordinal2(k15_ordinal2(C,A),D))))))))))) # label(t55_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2818 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k5_ordinal3(A,B)))) # label(dt_k5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2819 $T # label(t63_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2820 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> k5_ordinal3(B,A) != k1_xboole_0 & r2_hidden(k1_xboole_0,k5_ordinal3(B,A))))))) # label(t68_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2821 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (A != k1_xboole_0 -> k6_ordinal3(k15_ordinal2(B,A),A) = B))))) # label(t81_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2822 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> v3_ordinal1(k1_setfam_1(B)))))) # label(t13_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2823 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(k15_ordinal2(A,B) = k1_xboole_0 & A != k1_xboole_0 & k1_xboole_0 != B))))) # label(t34_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2824 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> v3_ordinal1(k3_tarski(B)))))) # label(t6_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2825 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k15_ordinal2(k14_ordinal2(A,B),C) = k14_ordinal2(k15_ordinal2(A,C),k15_ordinal2(B,C)))))))) # label(t54_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2826 (all A (v3_ordinal1(A) -> k1_xboole_0 = k6_ordinal2(A))) # label(t11_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2827 (all A r1_tarski(A,k1_ordinal1(A))) # label(t1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2828 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(B,k14_ordinal2(A,B)) & r1_ordinal1(A,k14_ordinal2(A,B)))))) # label(t27_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2829 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(k14_ordinal2(A,B),k14_ordinal2(A,C)) -> r2_hidden(B,C)))))))) # label(t25_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2830 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v1_ordinal1(k3_xboole_0(A,B)) & v3_ordinal1(k3_xboole_0(A,B)) & v2_ordinal1(k3_xboole_0(A,B)))) # label(fc2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2831 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (A != k1_xboole_0 -> k14_ordinal2(B,k3_tarski(A)) = k3_tarski(k14_ordinal2(B,A))))))) # label(t53_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2832 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (C = k2_ordinal3(A,B) <-> (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k14_ordinal2(k1_funct_1(B,D),A) = k1_funct_1(C,D)))) & k1_relat_1(B) = k1_relat_1(C)))))))) # label(d3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2833 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v3_ordinal1(A) & v1_ordinal2(B) & v5_ordinal1(B) -> v1_funct_1(k1_ordinal3(A,B)) & v1_ordinal2(k1_ordinal3(A,B)) & v5_ordinal1(k1_ordinal3(A,B)) & v1_relat_1(k1_ordinal3(A,B)))) # label(dt_k1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2834 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> k2_ordinal2(B) = B)))) # label(t8_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2835 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> (all C (v1_ordinal2(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_relat_1(C) -> (C = k4_ordinal3(A,B) <-> (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k15_ordinal2(k1_funct_1(B,D),A) = k1_funct_1(C,D)))) & k1_relat_1(B) = k1_relat_1(C)))))))) # label(d5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2836 $T # label(t43_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2837 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k14_ordinal2(A,C) = k14_ordinal2(A,B) -> C = B))))))) # label(t24_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2838 $T # label(t40_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2839 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r2_hidden(C,D) -> -r2_hidden(A,B) & -r1_ordinal1(A,B) | r2_hidden(k14_ordinal2(A,C),k14_ordinal2(B,D))))))))))) # label(t20_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2840 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> (all C (v3_ordinal1(C) -> (k1_relat_1(B) = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (E = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(B,D) = k14_ordinal2(C,E)))))) -> k1_xboole_0 = k1_relat_1(A) | k8_ordinal2(B) = k14_ordinal2(C,k8_ordinal2(A))))))))) # label(t47_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2841 (all A (v3_ordinal1(A) -> k7_ordinal3(A,k4_ordinal2) = k1_xboole_0 & A = k6_ordinal3(A,k4_ordinal2))) # label(t84_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2842 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != A -> r1_ordinal1(B,k15_ordinal2(B,A)) & r1_ordinal1(B,k15_ordinal2(A,B))))))) # label(t39_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2843 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (B = k1_xboole_0 -> (k6_ordinal3(A,B) = C <-> k1_xboole_0 = C)) & (k1_xboole_0 != B -> ((exists D (r2_hidden(D,B) & A = k14_ordinal2(k15_ordinal2(C,B),D) & v3_ordinal1(D))) <-> k6_ordinal3(A,B) = C)))))))) # label(d7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2844 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (-r1_ordinal1(B,A) -> (C = k1_xboole_0 <-> C = k5_ordinal3(A,B))) & (r1_ordinal1(B,A) -> (C = k5_ordinal3(A,B) <-> k14_ordinal2(B,C) = A)))))))) # label(d6_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2845 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> v4_ordinal1(k15_ordinal2(A,B))))))) # label(t48_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2846 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (r2_hidden(E,A) & k14_ordinal2(k15_ordinal2(D,A),E) = k14_ordinal2(k15_ordinal2(B,A),C) & r2_hidden(C,A) -> E = C & B = D))))))))))) # label(t56_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2847 $T # label(t62_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2848 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k7_ordinal3(A,B) = k5_ordinal3(A,k15_ordinal2(k6_ordinal3(A,B),B)))))) # label(d8_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2849 $T # label(d1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2850 $T # label(t14_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2851 $T # label(t44_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2852 (all A all B (v1_relat_1(B) & v3_ordinal1(A) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> v1_funct_1(k3_ordinal3(A,B)) & v1_ordinal2(k3_ordinal3(A,B)) & v5_ordinal1(k3_ordinal3(A,B)) & v1_relat_1(k3_ordinal3(A,B)))) # label(dt_k3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2853 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> -(v4_ordinal1(B) & r2_hidden(A,k15_ordinal2(B,C)) & (all D (v3_ordinal1(D) -> -(r2_hidden(D,B) & r2_hidden(A,k15_ordinal2(D,C)))))))))))) # label(t49_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2854 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k4_ordinal2 = k15_ordinal2(A,B) -> k4_ordinal2 = A & B = k4_ordinal2))))) # label(t41_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2855 (all A all B (v5_ordinal1(B) & v1_relat_1(B) & v3_ordinal1(A) & v1_ordinal2(B) & v1_funct_1(B) -> v1_relat_1(k2_ordinal3(A,B)) & v1_ordinal2(k2_ordinal3(A,B)) & v1_funct_1(k2_ordinal3(A,B)) & v5_ordinal1(k2_ordinal3(A,B)))) # label(dt_k2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2856 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,k14_ordinal2(C,A)) -> k1_xboole_0 = A | r2_hidden(k5_ordinal3(B,C),A)))))))) # label(t73_ordinal3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2857 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> r2_arytm_3(k3_arytm_3(A,B),k2_arytm_3(A,B)))))) # label(t17_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2858 $T # label(t67_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2859 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (A != k1_xboole_0 -> k5_arytm_3(k2_arytm_3(B,A),k2_arytm_3(C,A)) = k5_arytm_3(B,C)))))))) # label(t33_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2860 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (k12_arytm_3 = A <-> k10_arytm_3(A,B) = B))))) # label(t92_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2861 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -((r3_arytm_3(B,C) & -r3_arytm_3(B,A) | r3_arytm_3(A,B) & -r3_arytm_3(C,B)) & r3_arytm_3(C,A)))))))) # label(t76_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2862 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> k11_arytm_3(A,k10_arytm_3(B,C)) = k10_arytm_3(k11_arytm_3(A,B),k11_arytm_3(A,C)))))))) # label(t63_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2863 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal2(k14_ordinal2(A,B)) -> r2_hidden(B,k5_ordinal2) & r2_hidden(A,k5_ordinal2)))))) # label(t1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2864 (all A (m1_subset_1(A,k6_arytm_3) -> k11_arytm_3(A,k13_arytm_3) = A)) # label(t59_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2865 (all A all B (m1_subset_1(A,k6_arytm_3) & m1_subset_1(B,k6_arytm_3) -> r3_arytm_3(B,A) | r3_arytm_3(A,B))) # label(connectedness_r3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2866 (all A all B (v4_ordinal2(A) & v3_ordinal1(B) & v3_ordinal1(A) & v4_ordinal2(B) -> m1_subset_1(k5_arytm_3(A,B),k5_ordinal2))) # label(dt_k5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2867 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> ((exists C (B = k10_arytm_3(A,C) & m1_subset_1(C,k6_arytm_3))) <-> r3_arytm_3(A,B)))))) # label(d12_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2868 (all A (m1_subset_1(A,k6_arytm_3) -> m1_subset_1(k8_arytm_3(A),k5_ordinal2))) # label(dt_k8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2869 (all A (v3_ordinal1(A) & v1_xboole_0(A) -> v4_ordinal2(A) & v3_ordinal1(A) & v1_ordinal1(A) & v2_ordinal1(A))) # label(cc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2870 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (k5_arytm_3(B,A) = k4_ordinal2 -> k5_arytm_3(A,B) = k9_arytm_3(A,B)) & (k1_xboole_0 = B -> k9_arytm_3(A,B) = k1_xboole_0) & -(B != k1_xboole_0 & k4_tarski(k5_arytm_3(A,B),k5_arytm_3(B,A)) != k9_arytm_3(A,B) & k4_ordinal2 != k5_arytm_3(B,A)))))) # label(d9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2871 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) -> k3_arytm_3(B,A) = k3_arytm_3(A,B))) # label(commutativity_k3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2872 (all A (r2_hidden(A,a_0_1_arytm_3) <-> (exists B (m1_subset_1(B,k5_ordinal2) & A = k4_tarski(B,k4_ordinal2))))) # label(fraenkel_a_0_1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2873 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -(r3_arytm_3(B,C) & r3_arytm_3(A,B) & A = C & B != C))))))) # label(t97_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2874 (all A all B (v3_ordinal1(A) & v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) -> k14_ordinal2(A,B) = k1_arytm_3(A,B))) # label(redefinition_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2875 (all A (v3_ordinal1(A) -> (all B (m1_subset_1(B,A) -> v2_ordinal1(B) & v3_ordinal1(B) & v1_ordinal1(B))))) # label(cc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2876 (all A all B (v4_ordinal2(A) & v3_ordinal1(B) & v3_ordinal1(A) & v4_ordinal2(B) -> v1_ordinal1(k5_ordinal3(A,B)) & v2_ordinal1(k5_ordinal3(A,B)) & v4_ordinal2(k5_ordinal3(A,B)) & v3_ordinal1(k5_ordinal3(A,B)))) # label(fc4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2877 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -(B != k12_arytm_3 & A != k12_arytm_3 & k12_arytm_3 = k11_arytm_3(A,B)))))) # label(t86_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2878 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> k11_arytm_3(k11_arytm_3(A,B),C) = k11_arytm_3(A,k11_arytm_3(B,C)))))))) # label(t58_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2879 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -((all C (m1_subset_1(C,k6_arytm_3) -> -(r2_hidden(C,k5_ordinal2) & r3_arytm_3(B,k11_arytm_3(C,A))))) & k12_arytm_3 != A))))) # label(t103_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2880 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (r2_hidden(A,k5_ordinal2) & r2_hidden(k10_arytm_3(A,B),k5_ordinal2) -> r2_hidden(B,k5_ordinal2)))))) # label(t78_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2881 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (A != k1_xboole_0 -> k4_ordinal2 = k5_arytm_3(A,A)))) # label(t32_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2882 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -(all C (m1_subset_1(C,k6_arytm_3) -> A != k10_arytm_3(B,C) & B != k10_arytm_3(A,C))))))) # label(t100_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2883 (all A (v3_ordinal1(A) -> (r2_hidden(A,k6_arytm_3) -> r2_hidden(A,k5_ordinal2)))) # label(t37_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2884 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k6_ordinal3(A,B)) & v4_ordinal2(k6_ordinal3(A,B)) & v1_ordinal1(k6_ordinal3(A,B)) & v2_ordinal1(k6_ordinal3(A,B)))) # label(fc6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2885 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal2(k15_ordinal2(A,B)) -> v1_xboole_0(k15_ordinal2(A,B)) | r2_hidden(B,k5_ordinal2) & r2_hidden(A,k5_ordinal2)))))) # label(t2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2886 (all A ((exists B exists C (m1_subset_1(B,k5_ordinal2) & k4_tarski(B,C) = A & k1_xboole_0 != C & r1_arytm_3(B,C) & m1_subset_1(C,k5_ordinal2))) <-> r2_hidden(A,a_0_0_arytm_3))) # label(fraenkel_a_0_0_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2887 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -((all C (m1_subset_1(C,k6_arytm_3) -> k11_arytm_3(A,C) != B)) & k12_arytm_3 != A))))) # label(t61_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2888 (all A (m1_subset_1(A,k6_arytm_3) -> (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A)))) # label(cc4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2889 (all A (m1_subset_1(A,k5_ordinal2) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r2_hidden(k4_tarski(A,B),k6_arytm_3) <-> k4_ordinal2 != B & r1_arytm_3(A,B) & B != k1_xboole_0))))) # label(t39_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2890 (all A (m1_subset_1(A,k5_ordinal2) -> v2_ordinal1(A) & v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A))) # label(cc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2891 (all A all B (v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) & v4_ordinal2(A) -> k4_arytm_3(A,B) = k4_arytm_3(B,A))) # label(commutativity_k4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2892 (all A (v3_ordinal1(A) -> r1_arytm_3(k4_ordinal2,A))) # label(t6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2893 (all A all B (v4_ordinal2(B) & v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) -> m1_subset_1(k4_arytm_3(A,B),k5_ordinal2))) # label(dt_k4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2894 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (r2_hidden(k1_xboole_0,A) -> r2_hidden(k7_ordinal3(B,A),A)))))) # label(t10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2895 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) & v4_ordinal2(A) & v4_ordinal2(B) -> m1_subset_1(k9_arytm_3(A,B),k6_arytm_3))) # label(dt_k9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2896 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (all D (v3_ordinal1(D) & v4_ordinal2(D) -> -(B != k1_xboole_0 & -(k2_arytm_3(C,A) = k2_arytm_3(B,D) <-> k9_arytm_3(C,B) = k9_arytm_3(D,A)) & A != k1_xboole_0))))))))) # label(t51_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.54 2897 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> k4_ordinal2 = k5_arytm_3(k4_ordinal2,A) & k5_arytm_3(A,k4_ordinal2) = A)) # label(t29_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2898 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(-r3_arytm_3(B,D) & k11_arytm_3(C,D) = k11_arytm_3(A,B) & -r3_arytm_3(A,C)))))))))) # label(t91_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2899 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> -((all C (v3_ordinal1(C) & v4_ordinal2(C) -> (all D (v4_ordinal2(D) & v3_ordinal1(D) -> (all E (v4_ordinal2(E) & v3_ordinal1(E) -> -(B = k2_arytm_3(C,E) & k2_arytm_3(C,D) = A & r1_arytm_3(D,E)))))))) & -(k1_xboole_0 = B & k1_xboole_0 = A)))))) # label(t8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2900 (all A -r2_hidden(k4_tarski(k12_arytm_3,A),k6_arytm_3)) # label(t68_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2901 (all A (m1_subset_1(A,k6_arytm_3) -> A = k10_arytm_3(A,k12_arytm_3))) # label(t56_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2902 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (r1_arytm_3(A,B) -> k5_arytm_3(A,B) = A))))) # label(t28_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2903 (all A (-v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_arytm_3)) -> -((all B (m1_subset_1(B,k6_arytm_3) -> -((all C (m1_subset_1(C,k6_arytm_3) -> (r2_hidden(C,A) -> r3_arytm_3(C,B)))) & r2_hidden(B,A)))) & r2_hidden(A,k6_arytm_3)))) # label(t99_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2904 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (all D (v4_ordinal2(D) & v3_ordinal1(D) -> -(A != k1_xboole_0 & k10_arytm_3(k9_arytm_3(C,B),k9_arytm_3(D,A)) != k9_arytm_3(k1_arytm_3(k2_arytm_3(C,A),k2_arytm_3(B,D)),k2_arytm_3(B,A)) & B != k1_xboole_0))))))))) # label(t52_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2905 (all A (m1_subset_1(A,k6_arytm_3) -> -((all B (m1_subset_1(B,k6_arytm_3) -> k13_arytm_3 != k11_arytm_3(A,B))) & A != k12_arytm_3))) # label(t60_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2906 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r2_hidden(A,k5_ordinal2) -> (B = k7_arytm_3(A) <-> B = A)) & (-r2_hidden(A,k5_ordinal2) -> ((exists C (A = k4_tarski(B,C) & v4_ordinal2(C) & v3_ordinal1(C))) <-> B = k7_arytm_3(A))))))) # label(d7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2907 (all A all B (m1_subset_1(B,k6_arytm_3) & m1_subset_1(A,k6_arytm_3) -> k11_arytm_3(B,A) = k11_arytm_3(A,B))) # label(commutativity_k11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2908 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) & v4_ordinal2(B) & v4_ordinal2(A) -> k1_arytm_3(A,B) = k1_arytm_3(B,A))) # label(commutativity_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2909 (all A (m1_subset_1(A,k6_arytm_3) -> (r2_hidden(A,k5_ordinal2) <-> k4_ordinal2 = k8_arytm_3(A)))) # label(t44_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2910 (all A all B (v3_ordinal1(B) & v4_ordinal2(B) & v4_ordinal2(A) & v3_ordinal1(A) -> v2_ordinal1(k14_ordinal2(A,B)) & v1_ordinal1(k14_ordinal2(A,B)) & v3_ordinal1(k14_ordinal2(A,B)) & v4_ordinal2(k14_ordinal2(A,B)))) # label(fc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2911 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (r2_arytm_3(B,A) & r2_arytm_3(A,B) -> A = B))))) # label(t13_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2912 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -((all D (m1_subset_1(D,k6_arytm_3) -> (all E (m1_subset_1(E,k6_arytm_3) -> -(r3_arytm_3(D,B) & r3_arytm_3(E,C) & E != C & A = k10_arytm_3(D,E)))))) & k12_arytm_3 != C & -r3_arytm_3(k10_arytm_3(B,C),A)))))))) # label(t98_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2913 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (m1_subset_1(C,k5_ordinal2) -> (C = k4_arytm_3(A,B) <-> (all D (v3_ordinal1(D) & v4_ordinal2(D) -> (r2_arytm_3(D,B) & r2_arytm_3(D,A) -> r2_arytm_3(D,C)))) & r2_arytm_3(C,B) & r2_arytm_3(C,A)))))))) # label(d4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2914 (all A all B (v3_ordinal1(B) & v4_ordinal2(B) & v3_ordinal1(A) & v4_ordinal2(A) -> v3_ordinal1(k1_arytm_3(A,B)))) # label(dt_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2915 (all A all B (m1_subset_1(A,k6_arytm_3) & m1_subset_1(B,k6_arytm_3) -> m1_subset_1(k11_arytm_3(A,B),k6_arytm_3))) # label(dt_k11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2916 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (k1_xboole_0 != A -> k9_arytm_3(k1_arytm_3(B,C),A) = k10_arytm_3(k9_arytm_3(B,A),k9_arytm_3(C,A))))))))) # label(t53_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2917 (all A (m1_subset_1(A,k6_arytm_3) -> (A = k12_arytm_3 <-> r2_hidden(a_1_0_arytm_3(A),k6_arytm_3)))) # label(t81_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2918 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (k1_xboole_0 != A -> k1_xboole_0 != k6_ordinal3(A,k4_arytm_3(B,A)) & k1_xboole_0 != k4_arytm_3(B,A)))))) # label(t23_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2919 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(A,B) & r3_arytm_3(B,C) -> r3_arytm_3(A,C)))))))) # label(t74_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2920 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (r2_arytm_3(A,B) & r2_arytm_3(A,k1_arytm_3(B,C)) -> r2_arytm_3(A,C)))))))) # label(t16_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2921 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (k12_arytm_3 = k10_arytm_3(A,B) -> A = k12_arytm_3))))) # label(t70_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2922 (all A all B -v3_ordinal1(k4_tarski(A,B))) # label(t36_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2923 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> -(A != k1_xboole_0 & k1_xboole_0 = k5_arytm_3(A,B)))))) # label(t30_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2924 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v3_ordinal1(C) & B = k15_ordinal2(A,C))) <-> r2_arytm_3(A,B)))))) # label(d2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2925 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -(r3_arytm_3(A,k10_arytm_3(B,C)) & (all D (m1_subset_1(D,k6_arytm_3) -> (all E (m1_subset_1(E,k6_arytm_3) -> -(A = k10_arytm_3(D,E) & r3_arytm_3(D,B) & r3_arytm_3(E,C))))))))))))) # label(t95_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2926 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> k11_arytm_3(A,B) = k9_arytm_3(k2_arytm_3(k7_arytm_3(A),k7_arytm_3(B)),k2_arytm_3(k8_arytm_3(A),k8_arytm_3(B))))))) # label(d11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2927 (all A all B (m1_subset_1(B,k6_arytm_3) & m1_subset_1(A,k6_arytm_3) -> m1_subset_1(k10_arytm_3(A,B),k6_arytm_3))) # label(dt_k10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2928 (all A (m1_subset_1(A,k6_arytm_3) -> r1_arytm_3(k7_arytm_3(A),k8_arytm_3(A)))) # label(t40_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2929 (all A (v3_ordinal1(A) -> (r1_arytm_3(k1_xboole_0,A) -> k4_ordinal2 = A))) # label(t7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2930 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (v3_ordinal1(B) & m1_subset_1(B,k6_arytm_3) -> -(-r3_arytm_3(k10_arytm_3(B,k13_arytm_3),A) & r2_hidden(A,k5_ordinal2) & -r3_arytm_3(A,B)))))) # label(t79_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2931 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (B = k15_ordinal2(C,E) & A = k15_ordinal2(C,D) -> k4_ordinal2 = C))))))) <-> r1_arytm_3(A,B)))))) # label(d1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2932 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> r3_arytm_3(A,k10_arytm_3(A,B)))))) # label(t85_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2933 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (r1_arytm_3(A,B) <-> k4_ordinal2 = k4_arytm_3(A,B)))))) # label(t25_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2934 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> k14_ordinal2(A,B) = k14_ordinal2(B,A))))) # label(t3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2935 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> -v1_xboole_0(k1_ordinal1(A)) & v4_ordinal2(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)))) # label(fc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2936 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> (k10_arytm_3(C,D) = k10_arytm_3(A,B) & r3_arytm_3(A,C) -> r3_arytm_3(D,B)))))))))) # label(t93_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2937 $T # label(dt_k6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2938 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (r3_arytm_3(B,A) & r3_arytm_3(A,B) -> B = A))))) # label(t73_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2939 (all A (m1_subset_1(A,k6_arytm_3) -> k8_arytm_3(A) != k1_xboole_0)) # label(t41_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2940 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k5_ordinal2) -> (-r2_hidden(A,k5_ordinal2) -> (k8_arytm_3(A) = B <-> (exists C (v4_ordinal2(C) & A = k4_tarski(C,B) & v3_ordinal1(C))))) & (r2_hidden(A,k5_ordinal2) -> (B = k8_arytm_3(A) <-> B = k4_ordinal2)))))) # label(d8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2941 (all A (m1_subset_1(A,k6_arytm_3) -> (exists B (m1_subset_1(B,k6_arytm_3) & A = k10_arytm_3(B,B))))) # label(t66_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2942 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (p1_s1_arytm_3(A) -> p1_s1_arytm_3(k1_ordinal1(A))))) & p1_s1_arytm_3(k1_xboole_0) -> (all A (v4_ordinal2(A) & v3_ordinal1(A) -> p1_s1_arytm_3(A))) # label(s1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2943 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> k4_arytm_3(k2_arytm_3(A,B),k2_arytm_3(C,B)) = k2_arytm_3(k4_arytm_3(A,C),B))))))) # label(t22_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2944 (all A (m1_subset_1(A,k6_arytm_3) -> (r3_arytm_3(A,k12_arytm_3) -> k12_arytm_3 = A))) # label(t72_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2945 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (k4_arytm_3(A,B) = k1_xboole_0 -> A = k1_xboole_0))))) # label(t20_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2946 (all A all B (v3_ordinal1(B) & v4_ordinal2(A) & v3_ordinal1(A) & v4_ordinal2(B) -> m1_subset_1(k3_arytm_3(A,B),k5_ordinal2))) # label(dt_k3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2947 f1_s2_arytm_3 = k12_arytm_3 & p1_s2_arytm_3(f1_s2_arytm_3) & -p1_s2_arytm_3(f3_s2_arytm_3) & r2_hidden(f3_s2_arytm_3,k5_ordinal2) & k13_arytm_3 = f2_s2_arytm_3 -> (exists A (-p1_s2_arytm_3(k10_arytm_3(A,f2_s2_arytm_3)) & p1_s2_arytm_3(A) & r2_hidden(A,k5_ordinal2) & m1_subset_1(A,k6_arytm_3))) # label(s2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2948 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (m1_subset_1(C,k5_ordinal2) -> ((all D (v3_ordinal1(D) & v4_ordinal2(D) -> (r2_arytm_3(A,D) & r2_arytm_3(B,D) -> r2_arytm_3(C,D)))) & r2_arytm_3(A,C) & r2_arytm_3(B,C) <-> C = k3_arytm_3(A,B)))))))) # label(d3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2949 (exists A (v2_ordinal1(A) & m1_subset_1(A,k6_arytm_3) & v1_ordinal1(A) & v3_ordinal1(A) & -v1_xboole_0(A))) # label(rc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2950 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> A = k2_arytm_3(k5_arytm_3(A,B),k4_arytm_3(A,B)))))) # label(t26_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2951 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -((all D (m1_subset_1(D,k6_arytm_3) -> -(r3_arytm_3(D,C) & A = k11_arytm_3(B,D)))) & r3_arytm_3(A,k11_arytm_3(B,C))))))))) # label(t87_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2952 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (k11_arytm_3(A,B) = k11_arytm_3(A,C) -> A = k12_arytm_3 | B = C))))))) # label(t62_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2953 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> A = k3_arytm_3(A,A) & A = k4_arytm_3(A,A))) # label(t21_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2954 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -(-r3_arytm_3(B,A) & (all C (m1_subset_1(C,k6_arytm_3) -> -(-r3_arytm_3(C,A) & -r3_arytm_3(B,C))))))))) # label(t101_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2955 (all A (m1_subset_1(A,k6_arytm_3) -> A = k9_arytm_3(k7_arytm_3(A),k8_arytm_3(A)))) # label(t45_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2956 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(A) & v3_ordinal1(B) -> v1_ordinal1(k15_ordinal2(A,B)) & v4_ordinal2(k15_ordinal2(A,B)) & v2_ordinal1(k15_ordinal2(A,B)) & v3_ordinal1(k15_ordinal2(A,B)))) # label(fc5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2957 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(A,B) -> r3_arytm_3(k11_arytm_3(A,C),k11_arytm_3(B,C))))))))) # label(t90_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2958 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (A != k1_xboole_0 -> k9_arytm_3(A,A) = k4_ordinal2))) # label(t47_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2959 (all A (m1_subset_1(A,k5_ordinal2) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r1_arytm_3(A,B) -> k8_arytm_3(k9_arytm_3(A,B)) = B & A = k7_arytm_3(k9_arytm_3(A,B)) | k1_xboole_0 = B))))) # label(t49_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2960 (all A (m1_subset_1(A,k6_arytm_3) -> r3_arytm_3(k12_arytm_3,A))) # label(t71_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2961 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (-r3_arytm_3(B,A) <-> r3_arytm_3(A,B) & B != A))))) # label(t75_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2962 (all A all B (v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) & v3_ordinal1(A) -> k2_arytm_3(A,B) = k2_arytm_3(B,A))) # label(commutativity_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2963 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(A) & v3_ordinal1(B) -> v1_ordinal1(k7_ordinal3(A,B)) & v2_ordinal1(k7_ordinal3(A,B)) & v4_ordinal2(k7_ordinal3(A,B)) & v3_ordinal1(k7_ordinal3(A,B)))) # label(fc7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2964 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -((all D (m1_subset_1(D,k6_arytm_3) -> -(-r3_arytm_3(D,A) & r3_arytm_3(D,C) & r3_arytm_3(D,B)))) & -r3_arytm_3(C,A) & -r3_arytm_3(B,A)))))))) # label(t96_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2965 (all A (m1_subset_1(A,k6_arytm_3) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & m1_subset_1(B,k6_arytm_3) -> k1_arytm_3(A,B) = k10_arytm_3(A,B))))) # label(t64_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2966 (all A (m1_subset_1(A,k6_arytm_3) -> (-r2_hidden(A,k5_ordinal2) -> k4_tarski(k7_arytm_3(A),k8_arytm_3(A)) = A & k4_ordinal2 != k8_arytm_3(A)))) # label(t42_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2967 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> k15_ordinal2(B,A) = k15_ordinal2(A,B))))) # label(t4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2968 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> k10_arytm_3(A,B) = k9_arytm_3(k1_arytm_3(k2_arytm_3(k7_arytm_3(A),k8_arytm_3(B)),k2_arytm_3(k7_arytm_3(B),k8_arytm_3(A))),k2_arytm_3(k8_arytm_3(A),k8_arytm_3(B))))))) # label(d10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2969 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (-(k1_xboole_0 = A & B = k1_xboole_0) -> r1_arytm_3(k5_arytm_3(A,B),k5_arytm_3(B,A))))))) # label(t27_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2970 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_arytm_3(A,B) -> r1_arytm_3(B,A)))) # label(symmetry_r1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2971 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -(-r3_arytm_3(B,A) & -r3_arytm_3(C,B) & r3_arytm_3(C,A)))))))) # label(t77_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2972 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> r2_arytm_3(A,k1_xboole_0) & r2_arytm_3(k4_ordinal2,A))) # label(t14_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2973 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (all D (v3_ordinal1(D) & v4_ordinal2(D) -> k9_arytm_3(k2_arytm_3(B,D),k2_arytm_3(C,A)) = k11_arytm_3(k9_arytm_3(B,C),k9_arytm_3(D,A)))))))))) # label(t55_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2974 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -((all D (m1_subset_1(D,k6_arytm_3) -> -(B = k10_arytm_3(A,D) & r3_arytm_3(D,C)))) & r3_arytm_3(A,B) & r3_arytm_3(B,k10_arytm_3(A,C))))))))) # label(t94_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2975 (all A (m1_subset_1(A,k1_zfmisc_1(k6_arytm_3)) -> -((all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(C,B) & r2_hidden(B,A) -> r2_hidden(C,A)))))) & (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(r2_hidden(B,A) & r2_hidden(C,A) & B != C & B != D & r2_hidden(D,A) & C != D))))))) & (exists B (m1_subset_1(B,k6_arytm_3) & r2_hidden(B,A) & B != k12_arytm_3))))) # label(t82_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2976 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> k10_arytm_3(k10_arytm_3(A,B),C) = k10_arytm_3(A,k10_arytm_3(B,C)))))))) # label(t57_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2977 $T # label(t84_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2978 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (-(A = k1_xboole_0 & B = k1_xboole_0) -> r1_arytm_3(k6_ordinal3(A,k4_arytm_3(A,B)),k6_ordinal3(B,k4_arytm_3(A,B)))))))) # label(t24_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2979 (all A (m1_subset_1(A,k6_arytm_3) -> m1_subset_1(k7_arytm_3(A),k5_ordinal2))) # label(dt_k7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2980 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (k1_xboole_0 != A -> r2_arytm_3(k6_ordinal3(k2_arytm_3(B,A),k3_arytm_3(B,A)),B)))))) # label(t18_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2981 (all A all B (m1_subset_1(A,k6_arytm_3) & m1_subset_1(B,k6_arytm_3) -> k10_arytm_3(A,B) = k10_arytm_3(B,A))) # label(commutativity_k10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2982 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> k4_arytm_3(A,k1_xboole_0) = A & k3_arytm_3(A,k1_xboole_0) = k1_xboole_0)) # label(t19_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2983 (all A (m1_subset_1(A,k6_arytm_3) -> -((all B (m1_subset_1(B,k6_arytm_3) -> -(-r3_arytm_3(A,B) & -r2_hidden(B,k5_ordinal2)))) & k12_arytm_3 != A))) # label(t80_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2984 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(k11_arytm_3(B,A),k11_arytm_3(C,A)) -> r3_arytm_3(B,C) | k12_arytm_3 = A))))))) # label(t88_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2985 $T # label(t12_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2986 (exists A (v4_ordinal2(A) & m1_subset_1(A,k6_arytm_3) & v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(rc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2987 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (k1_xboole_0 != A -> k7_arytm_3(k9_arytm_3(B,A)) = k5_arytm_3(B,A) & k5_arytm_3(A,B) = k8_arytm_3(k9_arytm_3(B,A))))))) # label(t48_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2988 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> k9_arytm_3(k1_xboole_0,A) = k1_xboole_0 & B = k9_arytm_3(B,k4_ordinal2))))) # label(t46_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2989 (all A all B -r2_hidden(k4_tarski(A,B),k5_ordinal2)) # label(t38_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2990 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (r2_arytm_3(A,B) & r2_hidden(k1_xboole_0,B) -> r1_ordinal1(A,B)))))) # label(t15_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2991 (all A (m1_subset_1(A,k6_arytm_3) -> k12_arytm_3 = k11_arytm_3(A,k12_arytm_3))) # label(t54_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2992 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k2_arytm_3(A,B)))) # label(dt_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2993 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) & v3_ordinal1(A) & v3_ordinal1(B) -> k2_arytm_3(A,B) = k15_ordinal2(A,B))) # label(redefinition_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2994 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (r2_arytm_3(B,A) <-> k2_arytm_3(B,k6_ordinal3(A,B)) = A))))) # label(t11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2995 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> k5_arytm_3(A,B) = k6_ordinal3(A,k4_arytm_3(A,B)))))) # label(d5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2996 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (k1_xboole_0 != A -> k4_ordinal2 = k5_arytm_3(A,k1_xboole_0)) & k5_arytm_3(k1_xboole_0,A) = k1_xboole_0)) # label(t31_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2997 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(k10_arytm_3(A,B),k10_arytm_3(C,B)) <-> r3_arytm_3(A,C)))))))) # label(t83_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2998 (all A (m1_subset_1(A,k6_arytm_3) -> -(-r2_hidden(A,k5_ordinal2) & (all B (m1_subset_1(B,k5_ordinal2) -> (all C (m1_subset_1(C,k5_ordinal2) -> -(k1_xboole_0 != C & r1_arytm_3(B,C) & k4_ordinal2 != C & A = k4_tarski(B,C))))))))) # label(t35_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 2999 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (A != k1_xboole_0 -> k9_arytm_3(k2_arytm_3(B,A),k2_arytm_3(C,A)) = k9_arytm_3(B,C)))))))) # label(t50_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3000 (all A all B (m1_subset_1(B,k6_arytm_3) -> (r2_hidden(A,a_1_0_arytm_3(B)) <-> (exists C (m1_subset_1(C,k6_arytm_3) & -r3_arytm_3(B,C) & C = A))))) # label(fraenkel_a_1_0_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3001 (all A (m1_subset_1(A,k6_arytm_3) -> -(all B (m1_subset_1(B,k6_arytm_3) -> r3_arytm_3(B,A))))) # label(t102_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3002 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> ((exists C (B = k2_arytm_3(A,C) & v4_ordinal2(C) & v3_ordinal1(C))) <-> r2_arytm_3(A,B)))))) # label(t9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3003 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r2_arytm_3(A,A))) # label(reflexivity_r2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3004 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & v4_ordinal2(A) & -v1_xboole_0(A))) # label(rc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3005 (all A (m1_subset_1(A,k6_arytm_3) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & m1_subset_1(B,k6_arytm_3) -> k11_arytm_3(A,B) = k2_arytm_3(A,B))))) # label(t65_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3006 (all A (m1_subset_1(A,k6_arytm_3) -> -(k1_xboole_0 != k7_arytm_3(A) & A = k1_xboole_0) & -(A != k1_xboole_0 & k1_xboole_0 = k7_arytm_3(A)))) # label(t43_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3007 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(-r3_arytm_3(A,C) & k10_arytm_3(C,D) = k10_arytm_3(A,B) & -r3_arytm_3(B,D)))))))))) # label(t89_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3008 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (k10_arytm_3(A,B) = k10_arytm_3(C,B) -> A = C))))))) # label(t69_arytm_3) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3009 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(r2_hidden(A,k6_arytm_3) & r2_hidden(B,k6_arytm_3) & (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(C = A & D = B & k11_arytm_3(C,D) = k8_arytm_2(A,B))))))))))) # label(t22_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3010 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(all C (m1_subset_1(C,k2_arytm_2) -> A != k7_arytm_2(B,C) & k7_arytm_2(A,C) != B)))))) # label(t11_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3011 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) -> k7_arytm_2(B,A) = k7_arytm_2(A,B))) # label(commutativity_k7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3012 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A = k12_arytm_3 -> k7_arytm_2(A,B) = B) & -(k12_arytm_3 != B & k12_arytm_3 != A & k4_arytm_2(k5_arytm_2(k3_arytm_2(A),k3_arytm_2(B))) != k7_arytm_2(A,B)) & (B = k12_arytm_3 -> A = k7_arytm_2(A,B)))))) # label(d8_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3013 (all A all B (m1_subset_1(B,k2_arytm_2) & m1_subset_1(A,k2_arytm_2) -> m1_subset_1(k7_arytm_2(A,B),k2_arytm_2))) # label(dt_k7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3014 (all A all B (m1_subset_1(A,k1_arytm_2) & m1_subset_1(B,k1_arytm_2) -> k6_arytm_2(A,B) = k6_arytm_2(B,A))) # label(commutativity_k6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3015 (all A all B (m1_subset_1(B,k6_arytm_3) -> (r2_hidden(A,a_1_0_arytm_2(B)) <-> (exists C (-r3_arytm_3(B,C) & m1_subset_1(C,k6_arytm_3) & A = C))))) # label(fraenkel_a_1_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3016 (all A (m1_subset_1(A,k2_arytm_2) -> m2_subset_1(k3_arytm_2(A),k1_zfmisc_1(k6_arytm_3),k1_arytm_2))) # label(dt_k3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3017 (all A ((exists B (m1_subset_1(B,k6_arytm_3) & a_1_0_arytm_2(B) = A & B != k12_arytm_3)) <-> r2_hidden(A,a_0_1_arytm_2))) # label(fraenkel_a_0_1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3018 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(r1_arytm_2(A,B) & (all C (m1_subset_1(C,k2_arytm_2) -> B != k7_arytm_2(A,C)))))))) # label(t10_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3019 (all A (m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (all B (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> a_2_0_arytm_2(A,B) = k5_arytm_2(A,B))))) # label(d6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3020 (all A (m1_subset_1(A,k2_arytm_2) -> (r2_hidden(A,k5_ordinal2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r2_hidden(B,k5_ordinal2) & r1_arytm_2(B,A) & A != B <-> r2_hidden(B,A))))))) # label(t19_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3021 (all A all B (m1_subset_1(B,k1_arytm_2) & m1_subset_1(A,k1_arytm_2) -> k5_arytm_2(B,A) = k5_arytm_2(A,B))) # label(commutativity_k5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3022 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> k8_arytm_2(A,k8_arytm_2(B,C)) = k8_arytm_2(k8_arytm_2(A,B),C))))))) # label(t13_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3023 (all A -r2_hidden(k4_tarski(k12_arytm_3,A),k2_arytm_2)) # label(t3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3024 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) -> r1_arytm_2(A,B) | r1_arytm_2(B,A))) # label(connectedness_r1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3025 (all A (m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (all B (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> a_2_1_arytm_2(A,B) = k6_arytm_2(A,B))))) # label(d7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3026 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A = k12_arytm_3 -> k12_arytm_3 = k8_arytm_2(A,B)))))) # label(t4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3027 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (k7_arytm_2(A,B) = k7_arytm_2(A,C) -> B = C))))))) # label(t12_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3028 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> k8_arytm_2(A,B) = k4_arytm_2(k6_arytm_2(k3_arytm_2(A),k3_arytm_2(B))))))) # label(d9_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3029 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r2_hidden(A,k6_arytm_3) & r2_hidden(B,k6_arytm_3) -> (r1_arytm_2(A,B) <-> (exists C ((exists D (r3_arytm_3(C,D) & m1_subset_1(D,k6_arytm_3) & A = C & D = B)) & m1_subset_1(C,k6_arytm_3))))) & (r2_hidden(A,k6_arytm_3) -> r2_hidden(B,k6_arytm_3) | (r1_arytm_2(A,B) <-> r2_hidden(A,B))) & (r2_hidden(B,k6_arytm_3) -> r2_hidden(A,k6_arytm_3) | (-r2_hidden(B,A) <-> r1_arytm_2(A,B))) & -(-(-r2_hidden(B,k6_arytm_3) & r2_hidden(A,k6_arytm_3)) & -(r1_arytm_2(A,B) <-> r1_tarski(A,B)) & -(r2_hidden(B,k6_arytm_3) & -r2_hidden(A,k6_arytm_3)) & -(r2_hidden(A,k6_arytm_3) & r2_hidden(B,k6_arytm_3))))))) # label(d5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3030 $T # label(dt_k2_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3031 (all A (m1_subset_1(A,k1_zfmisc_1(k2_arytm_2)) -> ((all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r2_hidden(B,A) & k13_arytm_3 = C -> r2_hidden(k7_arytm_2(B,C),A)))))) & r2_hidden(k12_arytm_3,A) -> r1_tarski(k5_ordinal2,A)))) # label(t18_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3032 (all A all B (m1_subset_1(B,k1_arytm_2) & m1_subset_1(A,k1_arytm_2) -> m2_subset_1(k6_arytm_2(A,B),k1_zfmisc_1(k6_arytm_3),k1_arytm_2))) # label(dt_k6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3033 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r2_hidden(B,k5_ordinal2) & r2_hidden(A,k5_ordinal2) -> r2_hidden(k7_arytm_2(B,A),k5_ordinal2)))))) # label(t17_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3034 (all A (m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> ((exists C (m1_subset_1(C,k6_arytm_3) & (all D (m1_subset_1(D,k6_arytm_3) -> (-r3_arytm_3(C,D) <-> r2_hidden(D,A)))))) -> (k4_arytm_2(A) = B <-> (exists C (B = C & m1_subset_1(C,k6_arytm_3) & (all D (m1_subset_1(D,k6_arytm_3) -> (-r3_arytm_3(C,D) <-> r2_hidden(D,A)))))))) & ((all C (m1_subset_1(C,k6_arytm_3) -> -(all D (m1_subset_1(D,k6_arytm_3) -> (r2_hidden(D,A) <-> -r3_arytm_3(C,D)))))) -> (k4_arytm_2(A) = B <-> A = B)))))) # label(d4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3035 (all A (m1_subset_1(A,k1_arytm_2) -> m1_subset_1(k4_arytm_2(A),k2_arytm_2))) # label(dt_k4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3036 (all A ((exists B (A = B & (all C (m1_subset_1(C,k6_arytm_3) -> (r2_hidden(C,B) -> (all D (m1_subset_1(D,k6_arytm_3) -> (r3_arytm_3(D,C) -> r2_hidden(D,B)))) & (exists D (m1_subset_1(D,k6_arytm_3) & -r3_arytm_3(D,C) & r2_hidden(D,B)))))) & m1_subset_1(B,k1_zfmisc_1(k6_arytm_3)))) <-> r2_hidden(A,a_0_0_arytm_2))) # label(fraenkel_a_0_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3037 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> k7_arytm_2(k7_arytm_2(A,B),C) = k7_arytm_2(A,k7_arytm_2(B,C)))))))) # label(t7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3038 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (k7_arytm_2(B,C) = A -> r1_arytm_2(C,A)))))))) # label(t20_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3039 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) -> k8_arytm_2(A,B) = k8_arytm_2(B,A))) # label(commutativity_k8_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3040 (all A all B all C (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) & m2_subset_1(C,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> ((exists D exists E (m1_subset_1(E,k6_arytm_3) & r2_hidden(D,B) & A = k11_arytm_3(D,E) & m1_subset_1(D,k6_arytm_3) & r2_hidden(E,C))) <-> r2_hidden(A,a_2_1_arytm_2(B,C))))) # label(fraenkel_a_2_1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3041 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k7_arytm_2(A,B) = k12_arytm_3 -> A = k12_arytm_3))))) # label(t6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3042 (all A all B all C (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) & m2_subset_1(C,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (r2_hidden(A,a_2_0_arytm_2(B,C)) <-> (exists D exists E (m1_subset_1(D,k6_arytm_3) & k10_arytm_3(D,E) = A & r2_hidden(E,C) & r2_hidden(D,B) & m1_subset_1(E,k6_arytm_3)))))) # label(fraenkel_a_2_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3043 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k13_arytm_3 = A -> k8_arytm_2(A,B) = B))))) # label(t16_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3044 (all A (m1_subset_1(A,k1_zfmisc_1(k2_arytm_2)) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_arytm_2)) -> -((all C (m1_subset_1(C,k2_arytm_2) -> (exists D (m1_subset_1(D,k2_arytm_2) & (exists E (-(r1_arytm_2(D,C) & r1_arytm_2(C,E)) & r2_hidden(D,A) & m1_subset_1(E,k2_arytm_2) & r2_hidden(E,B))))))) & (exists C (r2_hidden(C,B) & m1_subset_1(C,k2_arytm_2))) & (exists C (m1_subset_1(C,k2_arytm_2) & r2_hidden(C,A))) & (all C (m1_subset_1(C,k2_arytm_2) -> (all D (m1_subset_1(D,k2_arytm_2) -> (r2_hidden(C,A) & r2_hidden(D,B) -> r1_arytm_2(C,D))))))))))) # label(t9_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3045 (all A (m1_subset_1(A,k2_arytm_2) -> -(A != k12_arytm_3 & (all B (m1_subset_1(B,k2_arytm_2) -> k13_arytm_3 != k8_arytm_2(A,B)))))) # label(t15_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3046 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) -> m1_subset_1(k8_arytm_2(A,B),k2_arytm_2))) # label(dt_k8_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3047 (all A all B (m1_subset_1(B,k1_arytm_2) & m1_subset_1(A,k1_arytm_2) -> m2_subset_1(k5_arytm_2(A,B),k1_zfmisc_1(k6_arytm_3),k1_arytm_2))) # label(dt_k5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3048 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> k7_arytm_2(k8_arytm_2(A,B),k8_arytm_2(A,C)) = k8_arytm_2(A,k7_arytm_2(B,C)))))))) # label(t14_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3049 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (r2_hidden(A,k6_arytm_3) -> (k3_arytm_2(A) = B <-> (exists C (a_1_0_arytm_2(C) = B & m1_subset_1(C,k6_arytm_3) & C = A)))) & (-r2_hidden(A,k6_arytm_3) -> (k3_arytm_2(A) = B <-> A = B)))))) # label(d3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3050 $T # label(t5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3051 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> k2_arytm_1(k1_arytm_1(B,A),C) = k2_arytm_1(B,k7_arytm_2(A,C))))))))) # label(t24_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3052 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(B,A) -> (k1_arytm_1(A,B) = C <-> A = k7_arytm_2(C,B))) & (-r1_arytm_2(B,A) -> (C = k1_xboole_0 <-> C = k1_arytm_1(A,B))))))))) # label(d1_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3053 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(B,A) -> B = A))))) # label(t4_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3054 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(B,A) -> k4_tarski(k1_xboole_0,k8_arytm_2(C,k1_arytm_1(A,B))) = k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A)) | k1_xboole_0 = C | k1_arytm_1(A,B) = k1_xboole_0))))))) # label(t28_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3055 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> r1_arytm_2(k1_arytm_1(A,B),A))))) # label(t11_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3056 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> r1_arytm_2(k8_arytm_2(A,C),k8_arytm_2(B,C))))))))) # label(t8_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3057 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> k7_arytm_2(C,k1_arytm_1(B,A)) = k2_arytm_1(k7_arytm_2(C,B),A)))))))) # label(t20_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3058 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(A,B) & k1_xboole_0 = k1_arytm_1(B,A) -> A = B))))) # label(t10_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3059 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (-r1_arytm_2(A,B) -> k2_arytm_1(C,k1_arytm_1(A,B)) = k2_arytm_1(k7_arytm_2(C,B),A)))))))) # label(t21_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3060 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(A,C) -> k7_arytm_2(B,k1_arytm_1(C,A)) = k7_arytm_2(k1_arytm_1(B,A),C)))))))) # label(t12_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3061 (all A (m1_subset_1(A,k2_arytm_2) -> k2_arytm_1(A,A) = k1_xboole_0)) # label(t18_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3062 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A)) = k8_arytm_2(C,k1_arytm_1(B,A))))))))) # label(t26_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3063 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(k7_arytm_2(A,C),k7_arytm_2(B,C)) <-> r1_arytm_2(A,B)))))))) # label(t7_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3064 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (B = k7_arytm_2(A,B) -> A = k1_xboole_0))))) # label(t1_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3065 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> -(C != k1_xboole_0 & -r1_arytm_2(A,B) & k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A)) != k4_tarski(k1_xboole_0,k8_arytm_2(C,k1_arytm_1(A,B)))))))))) # label(t27_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3066 (all A all B (m1_subset_1(B,k2_arytm_2) & m1_subset_1(A,k2_arytm_2) -> m1_subset_1(k1_arytm_1(A,B),k2_arytm_2))) # label(dt_k1_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3067 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (-r1_arytm_2(B,A) -> k2_arytm_1(A,B) = k4_tarski(k1_xboole_0,k1_arytm_1(B,A))) & (r1_arytm_2(B,A) -> k2_arytm_1(A,B) = k1_arytm_1(A,B)))))) # label(d2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3068 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,C) & r1_arytm_2(A,B) -> k7_arytm_2(k1_arytm_1(B,A),C) = k7_arytm_2(k1_arytm_1(C,A),B)))))))) # label(t15_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3069 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> r1_arytm_2(k1_arytm_1(A,C),k1_arytm_1(B,C))))))))) # label(t17_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3070 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (B = k1_xboole_0 & r1_arytm_2(A,B) -> A = k1_xboole_0))))) # label(t5_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3071 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> r1_arytm_2(k1_arytm_1(C,B),k1_arytm_1(C,A))))))))) # label(t16_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3072 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> -(-r1_arytm_2(A,C) & k2_arytm_1(B,k1_arytm_1(A,C)) != k2_arytm_1(C,k1_arytm_1(A,B)) & -r1_arytm_2(A,B)))))))) # label(t23_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3073 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(C,A) -> k7_arytm_2(k1_arytm_1(B,A),C) = k1_arytm_1(B,k1_arytm_1(A,C))))))))) # label(t14_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3074 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A = k1_xboole_0 -> k2_arytm_1(A,B) = k4_tarski(k1_xboole_0,B) | k1_xboole_0 = B))))) # label(t19_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3075 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> k1_arytm_1(k7_arytm_2(C,B),A) = k7_arytm_2(C,k1_arytm_1(B,A))))))))) # label(t13_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3076 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(C,B) & r1_arytm_2(A,B) -> k2_arytm_1(k1_arytm_1(B,C),A) = k2_arytm_1(k1_arytm_1(B,A),C)))))))) # label(t25_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3077 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(-r1_arytm_2(A,B) & k1_arytm_1(A,B) = k1_xboole_0))))) # label(t9_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3078 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(B,C) -> r1_arytm_2(A,C)))))))) # label(t3_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.55 3079 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(A != k1_xboole_0 & k1_xboole_0 = k8_arytm_2(A,B) & B != k1_xboole_0))))) # label(t2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3080 $T # label(dt_k2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3081 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> r1_arytm_2(A,C) | k7_arytm_2(k1_arytm_1(B,A),C) = k2_arytm_1(B,k1_arytm_1(A,C))))))))) # label(t22_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3082 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A = k1_xboole_0 -> r1_arytm_2(A,B)))))) # label(t6_arytm_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3083 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3084 (all A all B all C all D all E all F all G all H v1_finset_1(k6_enumset1(A,B,C,D,E,F,G,H))) # label(fc8_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3085 (all A all B (v1_funct_1(A) & v1_finset_1(B) & v1_relat_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3086 (all A all B (v1_finset_1(k2_zfmisc_1(A,B)) -> v1_finset_1(B) | k1_xboole_0 = A)) # label(t23_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3087 (all A ((all B (r2_hidden(B,A) -> v1_finset_1(B))) & v1_finset_1(A) <-> v1_finset_1(k3_tarski(A)))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3088 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3089 (all A all B all C all D all E all F v1_finset_1(k4_enumset1(A,B,C,D,E,F))) # label(fc6_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3090 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (p1_s1_finset_1(B) -> f2_s1_finset_1(B) = k1_funct_1(A,B)) & (-p1_s1_finset_1(B) -> k1_funct_1(A,B) = f3_s1_finset_1(B))))) & k1_relat_1(A) = f1_s1_finset_1)) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3091 (all A all B (v1_finset_1(A) -> v1_finset_1(k4_xboole_0(A,B)))) # label(t16_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3092 (all A (v1_finset_1(A) <-> v1_finset_1(k1_zfmisc_1(A)))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3093 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(k1_relat_1(A)) <-> v1_finset_1(A)))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3094 (all A (-v1_xboole_0(A) -> (exists B (v1_finset_1(B) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3095 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3096 (all A (v1_finset_1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3097 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(t19_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3098 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3099 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,A) -> r1_tarski(B,C))))) & v6_ordinal1(A) & k1_xboole_0 != A & v1_finset_1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3100 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k2_relat_1(A))))) # label(t26_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3101 (all A all B (v1_finset_1(B) & r1_tarski(A,B) -> v1_finset_1(A))) # label(t13_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3102 (all A -(v1_finset_1(A) & (all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & v6_ordinal1(A) & A != k1_xboole_0)) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3103 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3104 (all A all B (r1_tarski(B,f1_s2_finset_1) & p1_s2_finset_1(B) & r2_hidden(A,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & p1_s2_finset_1(k1_xboole_0) & v1_finset_1(f1_s2_finset_1) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3105 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3106 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k5_xboole_0(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3107 (all A all B all C all D (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3108 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3109 (all A (-v1_xboole_0(A) -> (exists B (v1_finset_1(B) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3110 (all A all B all C all D v1_finset_1(k2_enumset1(A,B,C,D))) # label(fc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3111 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_finset_1(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3112 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3113 (all A all B all C all D all E all F all G v1_finset_1(k5_enumset1(A,B,C,D,E,F,G))) # label(fc7_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3114 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_xboole_0(A,B)))) # label(t14_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3115 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k5_xboole_0(A,B)))) # label(t28_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3116 (all A exists B (v1_xboole_0(B) & v2_ordinal1(B) & v3_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3117 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_xboole_0(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3118 (all A all B (v1_finset_1(A) -> v1_finset_1(k4_xboole_0(A,B)))) # label(fc12_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3119 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(D) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3120 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3121 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> A = k1_xboole_0 | v1_finset_1(B))) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3122 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3123 (all A all B all C (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3124 (all A all B all C (v1_finset_1(C) & v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3125 (all A all B (v1_finset_1(A) -> v1_finset_1(k3_xboole_0(A,B)))) # label(fc11_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3126 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3127 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3128 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3129 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v1_finset_1(A) -> v1_finset_1(k9_relat_1(B,A))))) # label(t17_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3130 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3131 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & (all C -((all D (r1_tarski(C,D) & r2_hidden(D,B) -> C = D)) & r2_hidden(C,B)))))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3132 (exists A (v1_finset_1(A) & -v1_xboole_0(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3133 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v1_finset_1(k10_relat_1(B,A)) & r1_tarski(A,k2_relat_1(B)) -> v1_finset_1(A)))) # label(t27_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3134 (all A all B (v1_finset_1(B) -> v1_finset_1(k3_xboole_0(A,B)))) # label(fc10_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3135 (all A all B all C all D all E v1_finset_1(k3_enumset1(A,B,C,D,E))) # label(fc5_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3136 (all A ((exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & r2_hidden(k1_relat_1(B),k5_ordinal2))) <-> v1_finset_1(A))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3137 (all A all B (v1_finset_1(A) -> v1_finset_1(k3_xboole_0(A,B)))) # label(t15_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3138 (all A all B (v1_finset_1(k2_tarski(A,B)) & -v1_xboole_0(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3139 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3140 (exists A (v1_finsub_1(A) & v3_finsub_1(A) & -v1_xboole_0(A) & v4_finsub_1(A) & v2_finsub_1(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3141 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3142 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & v4_finsub_1(A) & m1_subset_1(C,A) -> m1_subset_1(k2_finsub_1(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3143 (all A (v1_finsub_1(A) & v3_finsub_1(A) <-> v4_finsub_1(A))) # label(d4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3144 (all A (v3_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_xboole_0(B,C),A))))) # label(d3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3145 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k4_finsub_1(A,B,C) = k4_finsub_1(A,C,B))) # label(commutativity_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3146 (all A (v1_finsub_1(k5_finsub_1(A)) & -v1_xboole_0(k5_finsub_1(A)) & v3_finsub_1(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)))) # label(fc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3147 $T # label(t29_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3148 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) & v4_finsub_1(A) -> B = k3_finsub_1(A,B,B))) # label(idempotence_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3149 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t17_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3150 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k3_finsub_1(A,B,C),A))) # label(dt_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3151 $T # label(t4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3152 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & -v1_xboole_0(A) & m1_subset_1(C,A) -> k3_xboole_0(B,C) = k3_finsub_1(A,B,C))) # label(redefinition_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3153 $T # label(t12_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3154 (all A all B all C (v4_finsub_1(A) & -v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k1_finsub_1(A,B,C),A))) # label(dt_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3155 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_xboole_0(B,C) = k2_finsub_1(A,B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3156 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_finsub_1(A),k5_finsub_1(B)))) # label(t23_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3157 (all A (v1_finset_1(A) -> k5_finsub_1(A) = k1_zfmisc_1(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3158 (all A (v4_finsub_1(A) & -v1_xboole_0(A) -> r2_hidden(k1_xboole_0,A))) # label(t18_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3159 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k3_xboole_0(B,C),A) & r2_hidden(k5_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t16_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3160 (all A (v4_finsub_1(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)) & -v1_xboole_0(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3161 $T # label(t7_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3162 $T # label(t5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3163 (all A all B all C (m1_subset_1(C,A) & v4_finsub_1(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k3_finsub_1(A,B,C) = k3_finsub_1(A,C,B))) # label(commutativity_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3164 $T # label(t2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3165 (all A v4_finsub_1(k5_finsub_1(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3166 (all A (v4_finsub_1(A) -> v1_finsub_1(A) & v3_finsub_1(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3167 $T # label(t31_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3168 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k1_finsub_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3169 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(B,k1_zfmisc_1(A)))) # label(t32_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3170 $T # label(t9_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3171 (all A (v4_finsub_1(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v4_finsub_1(B) -> -v1_xboole_0(k3_xboole_0(A,B)) & v4_finsub_1(k3_xboole_0(A,B)))))) # label(t21_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3172 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) -> m1_subset_1(k4_finsub_1(A,B,C),A))) # label(dt_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3173 (all A r1_tarski(k5_finsub_1(A),k1_zfmisc_1(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3174 $T # label(t6_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3175 $T # label(t1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3176 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(t30_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3177 (all A (v4_finsub_1(A) <-> (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k4_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3178 (all A all B r1_tarski(k2_xboole_0(k5_finsub_1(A),k5_finsub_1(B)),k5_finsub_1(k2_xboole_0(A,B)))) # label(t25_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3179 (all A (v1_finsub_1(A) & v3_finsub_1(A) -> v4_finsub_1(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3180 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_finset_1(A) -> m1_subset_1(B,k5_finsub_1(A))))) # label(t34_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3181 (all A (v2_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k3_xboole_0(B,C),A))))) # label(d2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3182 $T # label(t22_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3183 (all A all B all C (v4_finsub_1(C) & -v1_xboole_0(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k5_xboole_0(A,B),C)))) # label(t14_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3184 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k4_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t15_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3185 (all A all B (v4_finsub_1(B) -> ((all C (r1_tarski(C,A) & v1_finset_1(C) <-> r2_hidden(C,B))) <-> k5_finsub_1(A) = B))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3186 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k5_xboole_0(B,C) = k4_finsub_1(A,B,C))) # label(redefinition_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3187 $T # label(t11_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3188 $T # label(t3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3189 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> k1_finsub_1(A,C,B) = k1_finsub_1(A,B,C))) # label(commutativity_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3190 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> B = k1_finsub_1(A,B,B))) # label(idempotence_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3191 (all A all B all C (-v1_xboole_0(C) & v4_finsub_1(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k3_xboole_0(A,B),C)))) # label(t13_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3192 (all A all B k3_xboole_0(k5_finsub_1(A),k5_finsub_1(B)) = k5_finsub_1(k3_xboole_0(A,B))) # label(t24_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3193 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k2_xboole_0(B,C),A))) <-> v1_finsub_1(A))) # label(d1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3194 $T # label(t33_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3195 $T # label(t19_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3196 (all A v4_finsub_1(k1_zfmisc_1(A))) # label(t20_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3197 $T # label(t8_finsub_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3198 (all A k1_xboole_0 = k3_binop_1(k5_finsub_1(A),k9_setwiseo(A))) # label(t55_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3199 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_2(E,B,A) & v1_funct_1(E) & m2_relset_1(E,B,A) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> D = k1_xboole_0 | (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> (r2_hidden(G,D) -> F = k8_funct_2(B,A,E,G)))) -> F = k7_setwiseo(B,A,C,D,E))))))))))))))) # label(t33_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3200 (all A all B all C -(r1_tarski(A,k2_xboole_0(B,k1_tarski(C))) & -r2_hidden(C,A) & -r1_tarski(A,B))) # label(t5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3201 (all A r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A))) # label(t52_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3202 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))))) # label(t18_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3203 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (v1_binop_1(C,A) & v3_binop_1(C,A) & v2_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(F,D) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,F),k7_setwiseo(B,A,C,D,E)) = k7_setwiseo(B,A,C,D,E))))))))))))))) # label(t31_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3204 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k4_xboole_0(k9_relat_1(C,B),A) = k9_relat_1(C,k4_xboole_0(B,k10_relat_1(C,A))))) # label(t11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3205 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> m1_subset_1(k6_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3206 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,A) & v1_funct_2(C,B,A) -> (all D (m1_subset_1(D,B) -> k2_funct_2(B,A,C,k1_tarski(D)) = k1_tarski(k8_funct_2(B,A,C,D)))))))))) # label(t13_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3207 $T # label(t66_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3208 $T # label(t20_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3209 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)))) # label(dt_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3210 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> r2_hidden(k8_funct_2(A,B,E,F),D)))) -> r1_tarski(k2_funct_2(A,B,E,C),D)))))))))) # label(t15_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3211 $T # label(t48_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3212 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(k5_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3213 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) & v1_funct_2(E,A,B) -> (v3_binop_1(C,B) & v1_binop_1(C,B) & v2_binop_1(C,B) -> (all F (m1_subset_1(F,B) -> (k2_funct_2(A,B,E,D) = k2_setwiseo(B,F) -> F = k7_setwiseo(A,B,C,D,E))))))))))))))) # label(t34_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3214 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) & m1_subset_1(D,k5_finsub_1(A)) & v1_funct_2(C,A,B) & -v1_xboole_0(A) -> m1_subset_1(k8_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3215 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> k8_funct_2(A,k5_finsub_1(B),C,D) = k10_setwiseo(A,B,k2_setwiseo(A,D),C))))))) # label(t56_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3216 (all A v3_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t49_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3217 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k4_xboole_0(B,C) = k6_setwiseo(A,B,C))) # label(redefinition_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3218 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k2_tarski(B,C) = k3_setwiseo(A,B,C))) # label(redefinition_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3219 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F))))))))))))))) # label(t29_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3220 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v1_setwiseo(C,A) & v2_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F))))))))))))))) # label(t41_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3221 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) & r2_hidden(C,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) -> B = C))))))))) # label(t69_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3222 (all A all B all C all D (m1_subset_1(C,k5_finsub_1(A)) & m1_relset_1(D,A,k5_finsub_1(B)) & -v1_xboole_0(A) & v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) -> m1_subset_1(k10_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3223 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (v1_funct_2(D,k2_zfmisc_1(B,B),B) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v1_setwiseo(D,B) & v3_binop_1(D,B) & v2_binop_1(D,B) & v1_binop_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,k5_finsub_1(C)) & m2_relset_1(E,A,k5_finsub_1(C)) -> (all F (v1_funct_2(F,k5_finsub_1(C),B) & m2_relset_1(F,k5_finsub_1(C),B) & v1_funct_1(F) -> ((all G (m1_subset_1(G,k5_finsub_1(C)) -> (all H (m1_subset_1(H,k5_finsub_1(C)) -> k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)) = k2_binop_1(B,B,B,D,k8_funct_2(k5_finsub_1(C),B,F,G),k8_funct_2(k5_finsub_1(C),B,F,H)))))) & k8_funct_2(k5_finsub_1(C),B,F,k1_setwiseo(C)) = k3_binop_1(B,D) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)) = k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)))))))))))))))) # label(t65_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3224 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_1(F) -> k10_setwiseo(B,C,k8_setwiseo(A,B,E,D),F) = k10_setwiseo(A,C,D,k7_funct_2(A,B,k5_finsub_1(C),E,F)))))))))))) # label(t63_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3225 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k3_tarski(k8_setwiseo(A,k5_finsub_1(B),C,D)) = k10_setwiseo(A,B,D,C))))))) # label(t61_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3226 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> k10_setwiseo(A,A,B,k11_setwiseo(A)) = B)))) # label(t71_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3227 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (v2_binop_1(C,B) & v1_setwiseo(C,B) & v3_binop_1(C,B) & v1_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(D,D),D) & v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(D,D),D) -> (v1_setwiseo(E,D) & v2_binop_1(E,D) & v1_binop_1(E,D) & v3_binop_1(E,D) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (all G (v1_funct_1(G) & m2_relset_1(G,B,D) & v1_funct_2(G,B,D) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) = k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)))))) & k8_funct_2(B,D,G,k3_binop_1(B,C)) = k3_binop_1(D,E) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)) = k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F))))))))))))))))))))) # label(t45_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3228 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v1_setwiseo(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) = k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D)))))))))))))) # label(t42_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3229 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (r2_hidden(E,k10_setwiseo(A,B,D,C)) <-> (exists F (r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)) & m1_subset_1(F,A) & r2_hidden(F,D))))))))))) # label(t70_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3230 (all A exists B (v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k5_finsub_1(A)))) # label(rc1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3231 (all A v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A))) # label(t53_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3232 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (v3_binop_1(D,A) & v2_binop_1(D,A) & v1_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (k1_xboole_0 != E -> (all F (v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,k5_finsub_1(C),A) & v1_funct_2(G,k5_finsub_1(C),A) -> ((all H (m1_subset_1(H,k5_finsub_1(C)) -> (all I (m1_subset_1(I,k5_finsub_1(C)) -> k8_funct_2(k5_finsub_1(C),A,G,k5_setwiseo(C,H,I)) = k2_binop_1(A,A,A,D,k8_funct_2(k5_finsub_1(C),A,G,H),k8_funct_2(k5_finsub_1(C),A,G,I)))))) -> k7_setwiseo(B,A,D,E,k7_funct_2(B,k5_finsub_1(C),A,F,G)) = k8_funct_2(k5_finsub_1(C),A,G,k10_setwiseo(B,C,E,F))))))))))))))))) # label(t64_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3233 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v2_binop_1(C,A) & v1_binop_1(C,A) & v1_setwiseo(C,A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> k7_setwiseo(B,A,C,k1_setwiseo(B),D) = k3_binop_1(A,C)))))))))) # label(t40_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3234 (all A (-v1_xboole_0(A) -> (exists B (v1_finset_1(B) & -v1_xboole_0(B) & m1_subset_1(B,k5_finsub_1(A)))))) # label(rc2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3235 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v1_setwiseo(B,A) -> (all C (m1_subset_1(C,A) -> C = k2_binop_1(A,A,A,B,k3_binop_1(A,B),C) & k2_binop_1(A,A,A,B,C,k3_binop_1(A,B)) = C))))))) # label(t23_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3236 (all A all B (v1_funct_2(B,A,k5_finsub_1(A)) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_1(B) -> (k11_setwiseo(A) = B <-> (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k1_tarski(C)))))) # label(d6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3237 (all A v2_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t51_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3238 (all A (m1_subset_1(A,f1_s3_setwiseo) -> p1_s3_setwiseo(k2_setwiseo(f1_s3_setwiseo,A)))) & (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (all B (m1_subset_1(B,k5_finsub_1(f1_s3_setwiseo)) -> (p1_s3_setwiseo(A) & p1_s3_setwiseo(B) -> A = k1_xboole_0 | p1_s3_setwiseo(k5_setwiseo(f1_s3_setwiseo,A,B)) | B = k1_xboole_0))))) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (k1_xboole_0 != A -> p1_s3_setwiseo(A)))) # label(s3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.56 3239 (all A all B all C (r2_hidden(A,B) | A = C <-> r2_hidden(A,k2_xboole_0(B,k1_tarski(C))))) # label(t6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3240 $T # label(t47_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3241 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_setwiseo(D,A) & v2_binop_1(D,A) & v1_binop_1(D,A) & v3_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m2_relset_1(F,B,C) & v1_funct_2(F,B,C) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,C,A) & v1_funct_2(G,C,A) -> k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)) = k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G)))))))))))))))) # label(t44_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3242 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)) = k10_setwiseo(A,B,k3_setwiseo(A,D,E),C))))))))) # label(t57_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3243 $T # label(t46_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3244 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_2(E,A,B) & v1_funct_1(E) & m2_relset_1(E,A,B) -> (v1_binop_1(C,B) & v2_binop_1(C,B) -> D = k1_xboole_0 & -v1_setwiseo(C,B) | (all F (m1_subset_1(F,B) -> ((exists G (m2_relset_1(G,k5_finsub_1(A),B) & v1_funct_1(G) & v1_funct_2(G,k5_finsub_1(A),B) & k8_funct_2(k5_finsub_1(A),B,G,D) = F & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> k1_funct_1(G,k1_xboole_0) = H))) & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> (all I (m1_subset_1(I,A) -> (r2_hidden(I,k6_setwiseo(A,D,H)) -> k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) = k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I)))))) | k1_xboole_0 = H))) & (all H (m1_subset_1(H,A) -> k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H))))) <-> F = k7_setwiseo(A,B,C,D,E))))))))))))))) # label(d3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3245 (all A (-v1_xboole_0(A) -> (all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) & m2_relset_1(D,A,k5_finsub_1(B)) -> (all E (m2_relset_1(E,k5_finsub_1(B),k5_finsub_1(C)) & v1_funct_1(E) & v1_funct_2(E,k5_finsub_1(B),k5_finsub_1(C)) -> ((all F (m1_subset_1(F,k5_finsub_1(B)) -> (all G (m1_subset_1(G,k5_finsub_1(B)) -> k5_setwiseo(C,k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,F),k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,G)) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k5_setwiseo(B,F,G)))))) & k1_setwiseo(C) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k1_setwiseo(B)) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k10_setwiseo(A,B,F,D)) = k10_setwiseo(A,C,F,k7_funct_2(A,k5_finsub_1(B),k5_finsub_1(C),D,E))))))))))) # label(t72_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3246 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,B,A) & m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,B) -> r2_hidden(D,k3_funct_2(B,A,C,k1_tarski(k8_funct_2(B,A,C,D)))))))))))) # label(t12_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3247 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k3_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3248 (all A all B all C r1_tarski(k1_tarski(A),k1_enumset1(A,B,C))) # label(t3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3249 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(E,A,B) & m1_relset_1(E,A,B) & -v1_xboole_0(B) & -v1_xboole_0(A) & v1_funct_1(E) & m1_subset_1(D,k5_finsub_1(A)) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> m1_subset_1(k7_setwiseo(A,B,C,D,E),B))) # label(dt_k7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3250 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r1_tarski(C,B) -> m1_subset_1(C,k5_finsub_1(A)))))) # label(t16_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3251 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v2_binop_1(C,A) & v3_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> -(k1_xboole_0 != F & k1_xboole_0 != E & k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) != k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D))))))))))))))) # label(t30_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3252 $T # label(t1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3253 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (C = B <-> r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C))))))) # label(t68_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3254 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) -> k10_setwiseo(A,B,k1_setwiseo(A),C) = k1_xboole_0)))) # label(t59_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3255 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k3_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F))))))))))))))) # label(t27_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3256 (all A v1_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t50_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3257 (all A all B (m2_relset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) -> (B = k9_setwiseo(A) <-> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k2_binop_1(k5_finsub_1(A),k5_finsub_1(A),k5_finsub_1(A),B,C,D) = k5_setwiseo(A,C,D)))))))) # label(d4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3258 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,B,A) & m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (k1_xboole_0 = k2_funct_2(B,A,C,D) -> D = k1_xboole_0))))))))) # label(t19_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3259 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v1_setwiseo(B,A) <-> (exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A)))))))) # label(d2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3260 (all A (v1_funct_1(k11_setwiseo(A)) & v1_funct_2(k11_setwiseo(A),A,k5_finsub_1(A)) & m2_relset_1(k11_setwiseo(A),A,k5_finsub_1(A)))) # label(dt_k11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3261 (all A (v1_funct_1(k9_setwiseo(A)) & v1_funct_2(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & m2_relset_1(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)))) # label(dt_k9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3262 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k5_setwiseo(A,C,B) = k5_setwiseo(A,B,C))) # label(commutativity_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3263 $T # label(t10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.57 3264 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (r6_binop_1(A,D,C) & v1_binop_1(C,A) & v3_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (v1_funct_1(F) & v1_funct_2(F,B,A) & m2_relset_1(F,B,A) -> (all G (m1_subset_1(G,A) -> k7_setwiseo(B,A,C,E,k7_funcop_1(A,B,D,F,G)) = k2_binop_1(A,A,A,D,k7_setwiseo(B,A,C,E,F),G))))))))))))))))) # label(t37_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3265 $T # label(t17_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3266 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (v1_binop_1(C,B) & v2_binop_1(C,B) & v1_setwiseo(C,B) & v3_binop_1(C,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k8_setwiseo(A,B,D,F) = k8_setwiseo(A,B,E,G) -> k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E))))))))))))))))) # label(t43_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3267 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k5_setwiseo(A,B,B) = B)) # label(idempotence_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3268 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k3_setwiseo(A,B,C) = k3_setwiseo(A,C,B))) # label(commutativity_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3269 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m2_relset_1(D,A,k5_finsub_1(B)) & v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) -> k7_setwiseo(A,k5_finsub_1(B),k9_setwiseo(B),C,D) = k10_setwiseo(A,B,C,D))))))) # label(d5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3270 (all A r3_binop_1(k5_finsub_1(A),k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)),k9_setwiseo(A))) # label(t54_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3271 (all A all B all C r1_tarski(k2_tarski(A,B),k1_enumset1(A,B,C))) # label(t4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3272 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k1_tarski(B) = k2_setwiseo(A,B))) # label(redefinition_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3273 (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> (all B (m1_subset_1(B,f1_s4_setwiseo) -> (p1_s4_setwiseo(A) -> p1_s4_setwiseo(k5_setwiseo(f1_s4_setwiseo,A,k2_setwiseo(f1_s4_setwiseo,B)))))))) & p1_s4_setwiseo(k1_setwiseo(f1_s4_setwiseo)) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> p1_s4_setwiseo(A))) # label(s4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3274 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> -v1_setwiseo(C,B) & k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> ((exists G (v1_funct_2(G,k5_finsub_1(A),B) & k8_funct_2(k5_finsub_1(A),B,G,D) = F & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> H = k1_xboole_0 | (all I (m1_subset_1(I,A) -> (r2_hidden(I,D) -> k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) = k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))))))))) & v1_funct_1(G) & m2_relset_1(G,k5_finsub_1(A),B) & (all H (m1_subset_1(H,A) -> k8_funct_2(A,B,E,H) = k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)))) & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> k1_funct_1(G,k1_xboole_0) = H))))) <-> F = k7_setwiseo(A,B,C,D,E))))))))))))))) # label(t25_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3275 (all A (v1_xboole_0(k1_setwiseo(A)) & m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)))) # label(dt_k1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3276 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k5_setwiseo(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3277 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v1_setwiseo(B,A) <-> r3_binop_1(A,k3_binop_1(A,B),B)))))) # label(t22_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3278 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v1_binop_1(C,A) & v3_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> k7_setwiseo(B,A,C,k4_setwiseo(B,E,F,G),D) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)),k8_funct_2(B,A,D,G))))))))))))))))) # label(t28_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3279 $T # label(t7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3280 (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> (all B (m1_subset_1(B,f1_s2_setwiseo) -> (p1_s2_setwiseo(A) -> r2_hidden(B,A) | p1_s2_setwiseo(k5_setwiseo(f1_s2_setwiseo,A,k2_setwiseo(f1_s2_setwiseo,B)))))))) & p1_s2_setwiseo(k1_setwiseo(f1_s2_setwiseo)) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> p1_s2_setwiseo(A))) # label(s2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3281 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k4_setwiseo(A,B,C,D) = k1_enumset1(B,C,D))) # label(redefinition_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3282 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r2_hidden(C,B) -> m1_subset_1(C,A))))))) # label(t14_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3283 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (v1_binop_1(C,B) & v3_binop_1(C,B) & v2_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(D,D),D) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(D,D),D) -> (v3_binop_1(E,D) & v2_binop_1(E,D) & v1_binop_1(E,D) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (all G (v1_funct_2(G,B,D) & m2_relset_1(G,B,D) & v1_funct_1(G) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) = k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)))))) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> (H != k1_xboole_0 -> k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)))))))))))))))))))))) # label(t39_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3284 (all A all B all C (r1_tarski(k2_xboole_0(A,k1_tarski(B)),C) <-> r1_tarski(A,C) & r2_hidden(B,C))) # label(t8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3285 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k10_setwiseo(A,B,k5_setwiseo(A,D,E),C) = k5_setwiseo(B,k10_setwiseo(A,B,D,C),k10_setwiseo(A,B,E,C)))))))))) # label(t62_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3286 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) & v1_funct_2(E,A,B) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k2_funct_2(A,B,E,G) = k2_funct_2(A,B,D,F) -> k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E) | k1_xboole_0 = F)))))))))))))))) # label(t35_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3287 (all A all B all C all D (m1_subset_1(D,A) & -v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k4_setwiseo(A,B,C,D),k5_finsub_1(A)))) # label(dt_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3288 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,A,k5_finsub_1(A)) & m2_relset_1(B,A,k5_finsub_1(A)) -> (B = k11_setwiseo(A) <-> (all C (m1_subset_1(C,A) -> k2_setwiseo(A,C) = k8_funct_2(A,k5_finsub_1(A),B,C)))))))) # label(t67_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3289 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & r6_binop_1(A,D,C) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (k1_xboole_0 != E -> (all F (v1_funct_1(F) & v1_funct_2(F,B,A) & m2_relset_1(F,B,A) -> (all G (m1_subset_1(G,A) -> k2_binop_1(A,A,A,D,G,k7_setwiseo(B,A,C,E,F)) = k7_setwiseo(B,A,C,E,k8_funcop_1(A,B,D,G,F)))))))))))))))))) # label(t36_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3290 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & -v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) -> k9_relat_1(C,D) = k8_setwiseo(A,B,C,D))) # label(redefinition_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3291 $T # label(t24_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3292 $T # label(t2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3293 $T # label(t9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3294 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k10_setwiseo(A,B,k5_setwiseo(A,E,k2_setwiseo(A,D)),C) = k5_setwiseo(B,k10_setwiseo(A,B,E,C),k8_funct_2(A,k5_finsub_1(B),C,D)))))))))) # label(t60_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3295 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_binop_1(D,A) & v3_binop_1(D,A) & v2_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> (all G (v1_funct_2(G,C,A) & m2_relset_1(G,C,A) & v1_funct_1(G) -> k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)))))))))))))))))) # label(t38_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3296 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k5_setwiseo(B,k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)),k8_funct_2(A,k5_finsub_1(B),C,F)) = k10_setwiseo(A,B,k4_setwiseo(A,D,E,F),C))))))))))) # label(t58_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3297 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_2(D,B,A) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> (r1_tarski(E,F) -> k7_setwiseo(B,A,C,F,D) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) | k1_xboole_0 = E)))))))))))))) # label(t32_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3298 (exists A (m2_relset_1(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)) & v1_funct_2(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)) & v1_funct_1(A) & (all B (m1_subset_1(B,f1_s1_setwiseo) -> (all C (m1_subset_1(C,f1_s1_setwiseo) -> (r2_hidden(C,k8_funct_2(f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo),A,B)) <-> p1_s1_setwiseo(C,B) & r2_hidden(C,f2_s1_setwiseo)))))))) # label(s1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3299 (all A k1_setwiseo(A) = k1_xboole_0) # label(d1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3300 $T # label(t21_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3301 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> k8_funct_2(B,A,D,E) = k7_setwiseo(B,A,C,k2_setwiseo(B,E),D)))))))))))) # label(t26_setwiseo) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3302 (all A (r2_hidden(A,a_0_16_fraenkel) <-> (exists B (k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) = A & r2_hidden(B,f3_s9_fraenkel) & p1_s9_fraenkel(B) & m1_subset_1(B,f1_s9_fraenkel))))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3303 (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> (p1_s8_fraenkel(A,B) <-> p2_s8_fraenkel(A,B)))))) & (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> f3_s8_fraenkel(B,A) = f3_s8_fraenkel(A,B))))) -> a_0_15_fraenkel = a_0_14_fraenkel # label(s8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3304 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> m1_fraenkel(k2_setwiseo(k1_zfmisc_1(k2_zfmisc_1(A,B)),C),A,B))) # label(t10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3305 (all A (r2_hidden(A,a_0_3_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & m1_subset_1(B,f1_s2_fraenkel) & p2_s2_fraenkel(B,C) & A = f3_s2_fraenkel(B,C))))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3306 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) -> v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3307 (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p1_s9_fraenkel(A) <-> p2_s9_fraenkel(A))))) & k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) -> a_0_16_fraenkel = a_0_17_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3308 v1_finset_1(f4_s25_fraenkel) & (all A (m2_fraenkel(A,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (all B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (k7_relat_1(A,f3_s25_fraenkel) = k7_relat_1(B,f3_s25_fraenkel) -> f5_s25_fraenkel(A) = f5_s25_fraenkel(B)))))) & v1_finset_1(f3_s25_fraenkel) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3309 (exists A (m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)) & (all B (m1_subset_1(B,f1_s24_fraenkel) -> (r2_hidden(B,A) <-> (exists C (p1_s24_fraenkel(B,C) & B = f4_s24_fraenkel(C) & m1_subset_1(C,f2_s24_fraenkel) & r2_hidden(C,f3_s24_fraenkel)))))))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3310 (all A ((all B (r2_hidden(B,A) -> v1_funct_1(B) & v1_relat_1(B))) <-> v1_fraenkel(A))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3311 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f4_s7_fraenkel(A,B) = f3_s7_fraenkel(A,B))))) -> a_0_12_fraenkel = a_0_13_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3312 (all A (r2_hidden(A,a_0_0_fraenkel) <-> (exists B (A = f2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel) & p1_s1_fraenkel(B))))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.58 3313 (all A (m1_subset_1(A,f1_s6_fraenkel) -> (p1_s6_fraenkel(A) -> f3_s6_fraenkel(A) = f2_s6_fraenkel(A)))) -> a_0_11_fraenkel = a_0_10_fraenkel # label(s6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3314 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3315 (all A all B r1_tarski(k1_funct_2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B)))) # label(t5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3316 (all A (r2_hidden(A,a_0_2_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s2_fraenkel) & p1_s2_fraenkel(B,C) & m1_subset_1(C,f2_s2_fraenkel) & f3_s2_fraenkel(B,C) = A)))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3317 (all A (m1_subset_1(A,f1_s2_fraenkel) -> (all B (m1_subset_1(B,f2_s2_fraenkel) -> (p1_s2_fraenkel(A,B) -> p2_s2_fraenkel(A,B)))))) -> r1_tarski(a_0_2_fraenkel,a_0_3_fraenkel) # label(s2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3318 v1_finset_1(f4_s22_fraenkel) & v1_finset_1(f3_s22_fraenkel) -> v1_finset_1(a_0_39_fraenkel) # label(s22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3319 (all A ((exists B (p1_s14_fraenkel(B) & p2_s14_fraenkel(B) & A = f2_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))) <-> r2_hidden(A,a_0_26_fraenkel))) # label(fraenkel_a_0_26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3320 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> k1_funct_2(C,D) = k1_xboole_0 | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> (exists F (m2_fraenkel(F,B,A,k1_fraenkel(B,A)) & k7_relat_1(F,C) = E)))))))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3321 (all A (r2_hidden(A,a_0_10_fraenkel) <-> (exists B (p1_s6_fraenkel(B) & A = f2_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel))))) # label(fraenkel_a_0_10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3322 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)))) # label(fc2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3323 (all A (m1_subset_1(A,f1_s12_fraenkel) -> (all B (m1_subset_1(B,f2_s12_fraenkel) -> (p1_s12_fraenkel(A,B) -> p2_s12_fraenkel(f3_s12_fraenkel(A,B))))))) -> (all A (r2_hidden(A,a_0_20_fraenkel) -> p2_s12_fraenkel(A))) # label(s12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3324 (all A ((exists B (f2_s14_fraenkel(B) = A & r2_hidden(B,a_0_25_fraenkel) & p1_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))) <-> r2_hidden(A,a_0_24_fraenkel))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3325 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -((all C (m1_subset_1(C,f1_s16_fraenkel) -> -(f3_s16_fraenkel(C,B) = f3_s16_fraenkel(A,B) & p2_s16_fraenkel(C,B)))) & p1_s16_fraenkel(A,B)))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3326 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3327 (all A (r2_hidden(A,a_0_29_fraenkel) <-> (exists B exists C (f3_s15_fraenkel(B,C) = A & p1_s15_fraenkel(B,C) & m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & m1_subset_1(C,f2_s15_fraenkel))))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3328 (all A (m1_subset_1(A,f1_s27_fraenkel) -> -((all B (m1_subset_1(B,f2_s27_fraenkel) -> -p1_s27_fraenkel(A,B))) & r2_hidden(A,f3_s27_fraenkel)))) -> (exists A (m2_fraenkel(A,f1_s27_fraenkel,f2_s27_fraenkel,k1_fraenkel(f1_s27_fraenkel,f2_s27_fraenkel)) & (all B (m1_subset_1(B,f1_s27_fraenkel) -> (r2_hidden(B,f3_s27_fraenkel) -> p1_s27_fraenkel(B,k8_funct_2(f1_s27_fraenkel,f2_s27_fraenkel,A,B))))))) # label(s27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3329 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> k1_funct_2(C,D) = k1_xboole_0 | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> v1_funct_1(E) & m2_relset_1(E,B,A))))))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3330 (all A (m1_subset_1(A,f1_s23_fraenkel) -> (all B (m1_subset_1(B,f1_s23_fraenkel) -> (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(A,B) & p1_s23_fraenkel(B,C) -> p1_s23_fraenkel(A,C)))))))) & (all A (m1_subset_1(A,f1_s23_fraenkel) -> p1_s23_fraenkel(A,A))) -> (all A (m1_subset_1(A,f1_s23_fraenkel) -> -(r2_hidden(A,f2_s23_fraenkel) & (all B (m1_subset_1(B,f1_s23_fraenkel) -> -(r2_hidden(B,f2_s23_fraenkel) & (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(C,B) & r2_hidden(C,f2_s23_fraenkel) -> p1_s23_fraenkel(B,C)))) & p1_s23_fraenkel(B,A))))))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3331 (all A ((exists B exists C (p1_s11_fraenkel(B,C) & m1_subset_1(B,f1_s11_fraenkel) & m1_subset_1(C,f2_s11_fraenkel) & A = f3_s11_fraenkel(B,C))) <-> r2_hidden(A,a_0_19_fraenkel))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3332 (all A (r2_hidden(A,a_0_19_fraenkel) -> p2_s11_fraenkel(A))) -> (all A (m1_subset_1(A,f1_s11_fraenkel) -> (all B (m1_subset_1(B,f2_s11_fraenkel) -> (p1_s11_fraenkel(A,B) -> p2_s11_fraenkel(f3_s11_fraenkel(A,B))))))) # label(s11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3333 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p2_s19_fraenkel(A,B) <-> p1_s19_fraenkel(A,B) & f4_s19_fraenkel = B))))) -> a_0_35_fraenkel = a_0_34_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3334 (all A (r2_hidden(A,a_0_40_fraenkel) <-> (exists B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) & A = f5_s25_fraenkel(B) & r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel))))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3335 (all A ((exists B (p2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel) & A = f2_s1_fraenkel(B))) <-> r2_hidden(A,a_0_1_fraenkel))) # label(fraenkel_a_0_1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3336 (all A (r2_hidden(A,a_0_25_fraenkel) <-> (exists B (m1_subset_1(B,f1_s14_fraenkel) & B = A & p2_s14_fraenkel(B))))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3337 (all A (r2_hidden(A,a_0_28_fraenkel) <-> (exists B (m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & A = B)))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3338 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f3_s5_fraenkel(A) = f2_s5_fraenkel(A))) -> a_0_8_fraenkel = a_0_9_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3339 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3340 (all A (r2_hidden(A,a_0_14_fraenkel) <-> (exists B exists C (f3_s8_fraenkel(B,C) = A & m1_subset_1(C,f2_s8_fraenkel) & p1_s8_fraenkel(B,C) & m1_subset_1(B,f1_s8_fraenkel))))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3341 (all A (r2_hidden(A,a_0_17_fraenkel) <-> (exists B (p2_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel) & A = k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f5_s9_fraenkel,B) & m1_subset_1(B,f1_s9_fraenkel))))) # label(fraenkel_a_0_17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3342 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3343 (all A (r2_hidden(A,a_0_18_fraenkel) <-> (exists B (p1_s10_fraenkel(B) & B = A & m1_subset_1(B,f1_s10_fraenkel))))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3344 (all A ((exists B (A = f3_s20_fraenkel(B,f4_s20_fraenkel) & p1_s20_fraenkel(B,f4_s20_fraenkel) & m1_subset_1(B,f1_s20_fraenkel))) <-> r2_hidden(A,a_0_37_fraenkel))) # label(fraenkel_a_0_37_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3345 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3346 (all A (r2_hidden(A,a_0_33_fraenkel) <-> (exists B (-r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel) & f3_s18_fraenkel(B) = A & p1_s18_fraenkel(B) & m1_subset_1(B,f1_s18_fraenkel))))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3347 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3348 (all A ((exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & A = f3_s8_fraenkel(C,B) & m1_subset_1(C,f2_s8_fraenkel) & p2_s8_fraenkel(B,C))) <-> r2_hidden(A,a_0_15_fraenkel))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3349 (all A ((exists B (p2_s3_fraenkel(B) & f2_s3_fraenkel(B) = A & m1_subset_1(B,f1_s3_fraenkel))) <-> r2_hidden(A,a_0_5_fraenkel))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3350 (all A all B all C (-v1_xboole_0(C) & v1_fraenkel(C) -> ((all D (m1_subset_1(D,C) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D))) <-> m1_fraenkel(C,A,B)))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3351 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3352 (all A all B (-v1_xboole_0(B) -> m1_fraenkel(k1_fraenkel(A,B),A,B))) # label(dt_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3353 (all A (r2_hidden(A,a_0_7_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & m1_subset_1(C,f2_s4_fraenkel) & p2_s4_fraenkel(B,C) & A = f3_s4_fraenkel(B,C))))) # label(fraenkel_a_0_7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3354 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3355 (all A ((exists B exists C (f5_s22_fraenkel(B,C) = A & m1_subset_1(C,f2_s22_fraenkel) & m1_subset_1(B,f1_s22_fraenkel) & r2_hidden(C,f4_s22_fraenkel) & r2_hidden(B,f3_s22_fraenkel))) <-> r2_hidden(A,a_0_39_fraenkel))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3356 (all A ((exists B exists C (m1_subset_1(C,f2_s4_fraenkel) & f3_s4_fraenkel(B,C) = A & p1_s4_fraenkel(B,C) & m1_subset_1(B,f1_s4_fraenkel))) <-> r2_hidden(A,a_0_6_fraenkel))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3357 (all A ((exists B (m1_subset_1(B,f1_s5_fraenkel) & p1_s5_fraenkel(B) & f3_s5_fraenkel(B) = A)) <-> r2_hidden(A,a_0_9_fraenkel))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3358 (all A ((exists B exists C (m1_subset_1(C,f2_s16_fraenkel) & p2_s16_fraenkel(B,C) & f3_s16_fraenkel(B,C) = A & m1_subset_1(B,f1_s16_fraenkel))) <-> r2_hidden(A,a_0_31_fraenkel))) # label(fraenkel_a_0_31_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3359 (all A ((exists B exists C (m1_subset_1(B,f1_s13_fraenkel) & p1_s13_fraenkel(B,C) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & m1_subset_1(C,f2_s13_fraenkel) & f4_s13_fraenkel(B,C) = A)) <-> r2_hidden(A,a_0_23_fraenkel))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3360 (all A ((exists B (p1_s5_fraenkel(B) & A = f2_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))) <-> r2_hidden(A,a_0_8_fraenkel))) # label(fraenkel_a_0_8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3361 (all A ((exists B exists C (p1_s16_fraenkel(B,C) & f3_s16_fraenkel(B,C) = A & m1_subset_1(C,f2_s16_fraenkel) & m1_subset_1(B,f1_s16_fraenkel))) <-> r2_hidden(A,a_0_30_fraenkel))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3362 (all A ((exists B exists C (p1_s15_fraenkel(B,C) & m1_subset_1(C,f2_s15_fraenkel) & r2_hidden(B,a_0_28_fraenkel) & f3_s15_fraenkel(B,C) = A & m1_subset_1(B,f1_s15_fraenkel))) <-> r2_hidden(A,a_0_27_fraenkel))) # label(fraenkel_a_0_27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3363 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3364 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (all D (m1_subset_1(D,C) <-> m2_fraenkel(D,A,B,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3365 (all A (r2_hidden(A,a_0_22_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s13_fraenkel) & p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C) & m1_subset_1(B,f1_s13_fraenkel))))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3366 (all A (r2_hidden(A,a_0_4_fraenkel) <-> (exists B (f2_s3_fraenkel(B) = A & m1_subset_1(B,f1_s3_fraenkel) & p1_s3_fraenkel(B))))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3367 (all A ((exists B exists C (m1_subset_1(B,f1_s20_fraenkel) & C = f4_s20_fraenkel & m1_subset_1(C,f2_s20_fraenkel) & f3_s20_fraenkel(B,C) = A & p1_s20_fraenkel(B,C))) <-> r2_hidden(A,a_0_36_fraenkel))) # label(fraenkel_a_0_36_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3368 (all A all B all C (m1_fraenkel(C,A,B) -> v1_fraenkel(C) & -v1_xboole_0(C))) # label(dt_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3369 (all A (-v1_xboole_0(A) -> (all B m1_fraenkel(k1_funct_2(B,A),B,A)))) # label(t11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3370 (all A (m1_subset_1(A,f1_s1_fraenkel) -> (p1_s1_fraenkel(A) -> p2_s1_fraenkel(A)))) -> r1_tarski(a_0_0_fraenkel,a_0_1_fraenkel) # label(s1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3371 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3372 (all A ((exists B exists C (m1_subset_1(B,f1_s12_fraenkel) & m1_subset_1(C,f2_s12_fraenkel) & p1_s12_fraenkel(B,C) & A = f3_s12_fraenkel(B,C))) <-> r2_hidden(A,a_0_20_fraenkel))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3373 (all A (r2_hidden(A,a_0_35_fraenkel) <-> (exists B (m1_subset_1(B,f1_s19_fraenkel) & p1_s19_fraenkel(B,f4_s19_fraenkel) & A = f3_s19_fraenkel(B,f4_s19_fraenkel))))) # label(fraenkel_a_0_35_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3374 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p1_s3_fraenkel(A) <-> p2_s3_fraenkel(A)))) -> a_0_4_fraenkel = a_0_5_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3375 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3376 (all A (-v1_xboole_0(A) -> (all B all C all D (m2_fraenkel(D,B,A,k1_fraenkel(B,A)) -> k7_relat_1(D,C) = k7_relat_1(D,k3_xboole_0(B,C)))))) # label(t15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3377 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (exists D m2_fraenkel(D,A,B,C)))) # label(existence_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3378 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (k7_relat_1(D,E) = k7_relat_1(C,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,C,F) = k8_funct_2(A,B,D,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3379 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3380 (all A ((exists B exists C (m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C) & m1_subset_1(B,f1_s7_fraenkel) & f3_s7_fraenkel(B,C) = A)) <-> r2_hidden(A,a_0_12_fraenkel))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3381 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3382 (all A ((exists B exists C (A = f4_s7_fraenkel(B,C) & m1_subset_1(B,f1_s7_fraenkel) & m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C))) <-> r2_hidden(A,a_0_13_fraenkel))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3383 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k1_funct_2(A,B)))) # label(t16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3384 (all A (v1_fraenkel(A) -> (all B (m1_subset_1(B,A) -> v1_relat_1(B) & v1_funct_1(B))))) # label(cc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3385 (all A ((exists B (p1_s17_fraenkel(B) & m1_subset_1(B,f1_s17_fraenkel) & A = f3_s17_fraenkel(B) & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel))) <-> r2_hidden(A,a_0_32_fraenkel))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3386 (all A (r2_hidden(A,a_0_34_fraenkel) <-> (exists B exists C (p2_s19_fraenkel(B,C) & m1_subset_1(B,f1_s19_fraenkel) & m1_subset_1(C,f2_s19_fraenkel) & A = f3_s19_fraenkel(B,C))))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3387 (all A (m1_subset_1(A,f1_s26_fraenkel) -> -((all B (m1_subset_1(B,f2_s26_fraenkel) -> -p1_s26_fraenkel(A,B))) & r2_hidden(A,f3_s26_fraenkel)))) -> (exists A (v1_funct_2(A,f1_s26_fraenkel,f2_s26_fraenkel) & (all B (m1_subset_1(B,f1_s26_fraenkel) -> (r2_hidden(B,f3_s26_fraenkel) -> p1_s26_fraenkel(B,k8_funct_2(f1_s26_fraenkel,f2_s26_fraenkel,A,B))))) & m2_relset_1(A,f1_s26_fraenkel,f2_s26_fraenkel) & v1_funct_1(A))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3388 (all A (r2_hidden(A,a_0_38_fraenkel) <-> (exists B (r2_hidden(B,f2_s21_fraenkel) & A = f3_s21_fraenkel(B) & m1_subset_1(B,f1_s21_fraenkel))))) # label(fraenkel_a_0_38_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3389 (all A (m1_subset_1(A,f1_s4_fraenkel) -> (all B (m1_subset_1(B,f2_s4_fraenkel) -> (p2_s4_fraenkel(A,B) <-> p1_s4_fraenkel(A,B)))))) -> a_0_6_fraenkel = a_0_7_fraenkel # label(s4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3390 (all A all B (-v1_xboole_0(B) -> k1_fraenkel(A,B) = k1_funct_2(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3391 (all A (r2_hidden(A,a_0_21_fraenkel) <-> (exists B (m1_subset_1(B,f3_s13_fraenkel) & p2_s13_fraenkel(B) & r2_hidden(B,a_0_22_fraenkel) & A = B)))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3392 (all A ((exists B (A = f3_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel) & p1_s6_fraenkel(B))) <-> r2_hidden(A,a_0_11_fraenkel))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3393 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3394 (all A (r2_hidden(A,a_0_0_numbers) <-> (exists B (B = A & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)) & k1_funct_1(B,k13_arytm_3) = np__0)))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3395 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3396 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3397 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3398 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k4_arytm_0(A),k1_numbers))) # label(dt_k4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3399 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_arytm_0(k2_arytm_0(A,B),C) = k2_arytm_0(A,k2_arytm_0(B,C)))))))) # label(t15_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3400 (all A -(k12_arytm_3 = A & r2_hidden(k4_tarski(k12_arytm_3,A),k1_numbers))) # label(t3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3401 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k1_arytm_0(A,B) = k1_arytm_0(B,A))) # label(commutativity_k1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3402 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (k2_arytm_0(A,B) = k13_arytm_3 & k2_arytm_0(A,C) = k13_arytm_3 -> C = B | A = np__0))))))) # label(t20_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3403 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B = np__0 -> A = k1_arytm_0(A,B)))))) # label(t13_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3404 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> -r2_hidden(k5_funct_4(k1_numbers,np__0,k13_arytm_3,A,B),k1_numbers))))) # label(t10_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3405 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k3_arytm_0(k1_arytm_0(A,B)) = k1_arytm_0(k3_arytm_0(A),k3_arytm_0(B)))))) # label(t27_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3406 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> ((exists D ((exists E (B = E & C = k7_arytm_2(D,E) & D = A & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2))) <-> C = k1_arytm_0(A,B))) & (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (k1_arytm_0(A,B) = C <-> (exists D (m1_subset_1(D,k2_arytm_2) & (exists E (m1_subset_1(E,k2_arytm_2) & k4_tarski(np__0,E) = B & D = A & C = k2_arytm_1(D,E))))))) & -(-(C = k1_arytm_0(A,B) <-> (exists D ((exists E (C = k4_tarski(np__0,k7_arytm_2(D,E)) & m1_subset_1(E,k2_arytm_2) & k4_tarski(np__0,D) = A & k4_tarski(np__0,E) = B)) & m1_subset_1(D,k2_arytm_2)))) & -(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2)) & -(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_arytm_2)) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2))) & (r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2) -> ((exists D ((exists E (m1_subset_1(E,k2_arytm_2) & k4_tarski(np__0,D) = A & k2_arytm_1(E,D) = C & B = E)) & m1_subset_1(D,k2_arytm_2))) <-> k1_arytm_0(A,B) = C)))))))) # label(d2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3407 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k1_arytm_0(k2_arytm_0(A,B),k2_arytm_0(A,C)) = k2_arytm_0(A,k1_arytm_0(B,C)))))))) # label(t16_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3408 (all A (m1_subset_1(A,k1_numbers) -> k3_arytm_0(k3_arytm_0(A)) = A)) # label(involutiveness_k3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3409 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (k13_arytm_3 = B -> k2_arytm_0(A,B) = A))))) # label(t21_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3410 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k2_arytm_1(A,B) = k12_arytm_3 -> B = A))))) # label(t6_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3411 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k3_arytm_0(k2_arytm_0(A,B)) = k2_arytm_0(k3_arytm_0(A),B))))) # label(t17_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3412 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k1_arytm_0(k1_arytm_0(A,B),C) = k1_arytm_0(A,k1_arytm_0(B,C)))))))) # label(t25_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3413 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 != B -> k5_arytm_0(A,B) = k5_funct_4(k1_numbers,np__0,k13_arytm_3,A,B)) & (np__0 = B -> k5_arytm_0(A,B) = A))))) # label(d7_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3414 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 = B -> np__0 = k2_arytm_0(A,B)))))) # label(t14_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3415 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k1_arytm_0(A,B),k1_numbers))) # label(dt_k1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3416 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B != np__0 -> A = k2_arytm_0(k2_arytm_0(A,B),k4_arytm_0(B))))))) # label(t22_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3417 (all A all B k4_tarski(A,B) != k13_arytm_3) # label(t7_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3418 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (k8_arytm_2(A,C) = k8_arytm_2(A,B) -> A = k12_arytm_3 | C = B))))))) # label(t8_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3419 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (A != np__0 -> (k4_arytm_0(A) = B <-> k2_arytm_0(A,B) = k13_arytm_3)) & (np__0 = A -> (B = np__0 <-> B = k4_arytm_0(A))))))) # label(d5_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3420 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> (k5_arytm_0(A,B) = k5_arytm_0(C,D) -> B = D & A = C))))))))) # label(t12_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3421 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k4_arytm_0(k2_arytm_0(A,B)) = k2_arytm_0(k4_arytm_0(A),k4_arytm_0(B)))))) # label(t24_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3422 $T # label(d6_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3423 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 = k1_arytm_0(k2_arytm_0(A,A),k2_arytm_0(B,B)) -> np__0 = A))))) # label(t19_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3424 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k2_arytm_0(A,B),k1_numbers))) # label(dt_k2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3425 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k3_arytm_0(A),k1_numbers))) # label(dt_k3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3426 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> r2_hidden(k2_arytm_1(A,B),k1_numbers))))) # label(t4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3427 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k5_arytm_0(A,B),k2_numbers))) # label(dt_k5_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3428 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> ((exists D ((exists E (D = A & m1_subset_1(E,k2_arytm_2) & k8_arytm_2(D,E) = C & B = E)) & m1_subset_1(D,k2_arytm_2))) <-> C = k2_arytm_0(A,B))) & (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> A = np__0 | (C = k2_arytm_0(A,B) <-> (exists D ((exists E (k4_tarski(np__0,k8_arytm_2(D,E)) = C & B = k4_tarski(np__0,E) & D = A & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2))))) & (r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (k2_arytm_0(A,B) = C <-> (exists D ((exists E (m1_subset_1(E,k2_arytm_2) & k8_arytm_2(E,D) = C & B = k4_tarski(np__0,E) & k4_tarski(np__0,D) = A)) & m1_subset_1(D,k2_arytm_2))))) & -(-(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2)) & -(B != np__0 & r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(k2_arytm_0(A,B) = C <-> np__0 = C) & -(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & np__0 != A & r2_hidden(A,k2_arytm_2))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> B = np__0 | (C = k2_arytm_0(A,B) <-> (exists D (m1_subset_1(D,k2_arytm_2) & (exists E (E = B & m1_subset_1(E,k2_arytm_2) & k4_tarski(np__0,D) = A & k4_tarski(np__0,k8_arytm_2(E,D)) = C)))))))))))) # label(d3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3429 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> -(A != np__0 & B != np__0 & k2_arytm_0(A,B) = np__0))))) # label(t23_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3430 (all A (m1_subset_1(A,k1_numbers) -> r2_hidden(k2_arytm_0(A,A),k2_arytm_2))) # label(t18_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3431 (all A (m1_subset_1(A,k2_arytm_2) -> (A != k12_arytm_3 -> r2_hidden(k4_tarski(k12_arytm_3,A),k1_numbers)))) # label(t2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3432 $T # label(d1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3433 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (r2_hidden(k5_arytm_0(A,B),k1_numbers) -> np__0 = B))))) # label(t26_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3434 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (k1_arytm_0(A,B) = np__0 <-> k3_arytm_0(A) = B))))) # label(d4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3435 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k2_arytm_0(A,B) = k2_arytm_0(B,A))) # label(commutativity_k2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3436 $T # label(t9_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3437 (all A (m1_subset_1(A,k1_numbers) -> A = k4_arytm_0(k4_arytm_0(A)))) # label(involutiveness_k4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3438 (all A (m1_subset_1(A,k2_numbers) -> (exists B ((exists C (A = k5_arytm_0(B,C) & m1_subset_1(C,k1_numbers))) & m1_subset_1(B,k1_numbers))))) # label(t11_arytm_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3439 (all A (v1_xcmplx_0(A) -> (v1_xboole_0(A) <-> A = np__0))) # label(d3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3440 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3441 (all A (v4_ordinal2(A) -> v1_xcmplx_0(A))) # label(cc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3442 (exists A (-v1_xboole_0(A) & v1_xcmplx_0(A))) # label(rc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3443 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k3_xcmplx_0(A,k5_xcmplx_0(B)))))) # label(d9_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3444 $T # label(dt_k3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3445 $T # label(dt_k6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3446 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B))))) # label(d8_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3447 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3448 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3449 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)))) # label(dt_k5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3450 (all A (r2_hidden(A,k2_numbers) <-> v1_xcmplx_0(A))) # label(d2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3451 (all A (v1_xcmplx_0(A) & -v1_xboole_0(A) -> -v1_xboole_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3452 (all A (v1_xcmplx_0(A) -> A = k4_xcmplx_0(k4_xcmplx_0(A)))) # label(involutiveness_k4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3453 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = A -> (np__0 = B <-> B = k5_xcmplx_0(A))) & (np__0 != A -> (k3_xcmplx_0(A,B) = np__1 <-> B = k5_xcmplx_0(A))))))) # label(d7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3454 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A))) # label(commutativity_k3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3455 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = k2_xcmplx_0(A,B) <-> B = k4_xcmplx_0(A)))))) # label(d6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3456 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)))) # label(dt_k4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3457 (all A (m1_subset_1(A,k1_numbers) -> v1_xcmplx_0(A))) # label(cc1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3458 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3459 (all A all B (v1_xcmplx_0(A) & -v1_xboole_0(B) & v1_xcmplx_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc8_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3460 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C ((exists D ((exists E ((exists F (m1_subset_1(F,k1_numbers) & (exists G (A = k5_arytm_0(D,E) & k5_arytm_0(k1_arytm_0(D,F),k1_arytm_0(E,G)) = C & k5_arytm_0(F,G) = B & m1_subset_1(G,k1_numbers))))) & m1_subset_1(E,k1_numbers))) & m1_subset_1(D,k1_numbers))) <-> C = k2_xcmplx_0(A,B))))))) # label(d4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3461 $T # label(dt_k1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3462 (all A (v1_xcmplx_0(A) -> A = k5_xcmplx_0(k5_xcmplx_0(A)))) # label(involutiveness_k5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3463 $T # label(dt_k7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3464 (exists A v1_xcmplx_0(A)) # label(rc1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3465 $T # label(dt_k2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3466 (all A (-v1_xboole_0(A) & v1_xcmplx_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & -v1_xboole_0(k5_xcmplx_0(A)))) # label(fc7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3467 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A))) # label(commutativity_k2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3468 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (C = k3_xcmplx_0(A,B) <-> (exists D ((exists E ((exists F ((exists G (k5_arytm_0(F,G) = B & C = k5_arytm_0(k1_arytm_0(k2_arytm_0(D,F),k3_arytm_0(k2_arytm_0(E,G))),k1_arytm_0(k2_arytm_0(D,G),k2_arytm_0(E,F))) & k5_arytm_0(D,E) = A & m1_subset_1(G,k1_numbers))) & m1_subset_1(F,k1_numbers))) & m1_subset_1(E,k1_numbers))) & m1_subset_1(D,k1_numbers))))))))) # label(d5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3469 (all A all B (-v1_xboole_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(A) & -v1_xboole_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v1_xboole_0(k7_xcmplx_0(A,B)))) # label(fc9_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3470 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(np__0,A))) # label(t5_arithm) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3471 (all A (v1_xcmplx_0(A) -> np__0 = k3_xcmplx_0(A,np__0))) # label(t2_arithm) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3472 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(A,np__0) = A)) # label(t1_arithm) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3473 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(np__1,A) = A)) # label(t3_arithm) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3474 (all A (v1_xcmplx_0(A) -> A = k6_xcmplx_0(A,np__0))) # label(t4_arithm) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3475 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,np__1) = A)) # label(t6_arithm) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3476 (exists A (-v1_xboole_0(A) & v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v2_xreal_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3477 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) <-> v2_xreal_0(A)))) # label(d3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3478 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k7_xcmplx_0(B,A)) & -v2_xreal_0(k7_xcmplx_0(B,A)) & v1_xcmplx_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3479 (all A all B (-v2_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) -> v3_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3480 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3481 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3482 (all A all B (-v2_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) & -v2_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3483 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,A))) # label(reflexivity_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3484 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3485 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3486 (exists A (v1_xcmplx_0(A) & -v2_xreal_0(A) & v1_xboole_0(A) & -v3_xreal_0(A) & v1_xreal_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3487 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3488 (all A all B (-v2_xreal_0(A) & v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v2_xreal_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3489 (all A all B (-v3_xreal_0(A) & v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3490 (all A all B (-v2_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3491 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3492 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3493 (all A (v1_xreal_0(A) -> v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3494 (all A (-v1_xboole_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3495 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3496 (exists A (-v3_xreal_0(A) & v2_xreal_0(A) & -v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3497 (all A (v2_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(A) & -v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3498 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v2_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc25_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3499 (all A all B (v1_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) & -v2_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3500 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.59 3501 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3502 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3503 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (A = C & m1_subset_1(D,k2_arytm_2) & r1_arytm_2(C,D) & B = D)))))) & (r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (k4_tarski(np__0,C) = A & r1_arytm_2(D,C) & B = k4_tarski(np__0,D) & m1_subset_1(D,k2_arytm_2))))))) & -(-(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r1_xreal_0(A,B) <-> r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2)) & -(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3504 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) & -v2_xreal_0(B) & -v3_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3505 (all A all B (-v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3506 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3507 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(B) -> -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3508 (all A (v1_xreal_0(A) -> (v3_xreal_0(A) <-> -r1_xreal_0(np__0,A)))) # label(d4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3509 (all A all B (v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3510 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3511 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & v3_xreal_0(A) & -v2_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3512 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3513 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3514 (all A all B (-v3_xreal_0(A) & v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3515 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3516 (all A (v3_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) & v1_xcmplx_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3517 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3518 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(B,A) | r1_xreal_0(A,B))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3519 (all A all B (-v3_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3520 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3521 (all A all B (-v2_xreal_0(B) & v1_xreal_0(A) & -v2_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3522 (all A (v1_xboole_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3523 (all A (-v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3524 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & v3_xreal_0(B) -> v3_xreal_0(A)))))) # label(t2_real) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3525 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(v3_xreal_0(B) & r1_xreal_0(A,B) & -v3_xreal_0(A)))))) # label(t3_real) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3526 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,B) & -v3_xreal_0(B) & -v2_xreal_0(A)))))) # label(t8_real) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3527 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-v3_xreal_0(B) & -r1_xreal_0(A,B) & -v2_xreal_0(A)))))) # label(t7_real) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3528 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> v2_xreal_0(B) | v3_xreal_0(A) | v1_xboole_0(A)))))) # label(t6_real) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3529 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> v3_xreal_0(A) | v2_xreal_0(B) | v1_xboole_0(B)))))) # label(t5_real) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3530 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & v2_xreal_0(A) -> v2_xreal_0(B)))))) # label(t1_real) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3531 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-v2_xreal_0(B) & v2_xreal_0(A) & r1_xreal_0(A,B)))))) # label(t4_real) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3532 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> B = k3_xcmplx_0(k3_xcmplx_0(B,k7_xcmplx_0(np__1,A)),A)))))) # label(t110_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3533 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D))))))))) # label(t64_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3534 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,np__2) = k2_xcmplx_0(k7_xcmplx_0(A,np__4),k7_xcmplx_0(A,np__4)))) # label(t72_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3535 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_xcmplx_0(B) = k4_xcmplx_0(A) -> B = A))))) # label(t134_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3536 (all A (v1_xcmplx_0(A) -> -(A != k4_xcmplx_0(np__1) & np__1 != A & np__0 != A & k7_xcmplx_0(np__1,A) = A))) # label(t200_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3537 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k4_xcmplx_0(A),B) = k4_xcmplx_0(k3_xcmplx_0(A,B)))))) # label(t175_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3538 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k6_xcmplx_0(A,B),C) = k4_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(B,A),C)))))))) # label(t186_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3539 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k6_xcmplx_0(A,B),A) = k4_xcmplx_0(B))))) # label(t232_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3540 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(A,B),C),D),B) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,k7_xcmplx_0(D,C)),B),k3_xcmplx_0(k7_xcmplx_0(D,C),A)))))))))) # label(t236_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3541 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k7_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(A,C),B),D))))))))) # label(t84_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3542 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> B = k7_xcmplx_0(A,k7_xcmplx_0(A,B))))))) # label(t52_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3543 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k7_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)))))))))) # label(t85_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3544 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k2_xcmplx_0(A,A),A) = k3_xcmplx_0(np__3,A))) # label(t12_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3545 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k3_xcmplx_0(B,C) = k7_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(A,C))))))))) # label(t94_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3546 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C)))))))) # label(t168_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3547 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,np__2) = k7_xcmplx_0(k2_xcmplx_0(A,A),np__4))) # label(t73_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3548 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k6_xcmplx_0(C,D) = k2_xcmplx_0(A,B) -> k6_xcmplx_0(C,B) = k2_xcmplx_0(A,D)))))))))) # label(t35_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3549 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) = k3_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),D))))))))) # label(t44_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3550 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(np__1,A) = k7_xcmplx_0(np__1,B) -> A = B))))) # label(t59_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3551 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k3_xcmplx_0(C,A) = k3_xcmplx_0(D,B) -> k7_xcmplx_0(C,B) = k7_xcmplx_0(D,A) | A = np__0 | np__0 = B))))))))) # label(t95_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3552 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k2_xcmplx_0(A,C),B) = k2_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)))))))) # label(t63_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3553 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k4_xcmplx_0(A),B) = k4_xcmplx_0(k6_xcmplx_0(A,B)))))) # label(t162_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3554 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k7_xcmplx_0(B,C) = k7_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))))))))) # label(t55_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3555 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k7_xcmplx_0(B,k7_xcmplx_0(A,A)) = B))))) # label(t51_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3556 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(k6_xcmplx_0(A,C),B))))))) # label(t21_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3557 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(A != np__0 & np__0 != B & np__0 = k3_xcmplx_0(A,k5_xcmplx_0(B))))))) # label(t208_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3558 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,k3_xcmplx_0(np__2,A)) = k4_xcmplx_0(A))) # label(t187_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3559 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k7_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)) = k7_xcmplx_0(B,C)))))))) # label(t92_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3560 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k3_xcmplx_0(A,B))))) # label(t177_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3561 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(A,B) = k2_xcmplx_0(k2_xcmplx_0(A,C),k6_xcmplx_0(B,C)))))))) # label(t28_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3562 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k2_xcmplx_0(A,B) -> B = np__0))))) # label(t3_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3563 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k7_xcmplx_0(B,A) = k7_xcmplx_0(C,A) -> np__0 = A | B = C))))))) # label(t53_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3564 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(k7_xcmplx_0(C,B),A))))))) # label(t81_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3565 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k6_xcmplx_0(k2_xcmplx_0(A,B),B))))) # label(t26_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3566 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(A),B)))))) # label(t191_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3567 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(C,B) = k6_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C)))))))) # label(t23_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3568 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k7_xcmplx_0(D,B) = k7_xcmplx_0(C,A) -> k7_xcmplx_0(C,A) = k7_xcmplx_0(k6_xcmplx_0(C,D),k6_xcmplx_0(A,B)) | A = B | np__0 = B | np__0 = A))))))))) # label(t124_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3569 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k6_xcmplx_0(A,B),B) = A)))) # label(t27_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3570 (all A (v1_xcmplx_0(A) -> A = k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(np__1)))) # label(t181_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3571 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) = k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D))))))))) # label(t9_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3572 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k6_xcmplx_0(A,B) = k6_xcmplx_0(C,B) -> C = A))))))) # label(t19_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3573 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(B != np__0 & A != np__0 & np__0 = k3_xcmplx_0(A,B)))))) # label(t6_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3574 $T # label(t212_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3575 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),C),B))))))) # label(t146_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3576 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,B) = k6_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)))))))) # label(t22_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3577 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k4_xcmplx_0(A),B) = k6_xcmplx_0(k4_xcmplx_0(B),A))))) # label(t144_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3578 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B)) = k2_xcmplx_0(A,B))))) # label(t164_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3579 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)),A) = k6_xcmplx_0(B,C)))))))) # label(t130_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3580 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C)) = k6_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t173_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3581 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),C),A) = k6_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t158_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3582 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) = k3_xcmplx_0(A,k2_xcmplx_0(B,C)))))))) # label(t8_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3583 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)))))))))) # label(t10_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3584 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k3_xcmplx_0(k3_xcmplx_0(B,A),k5_xcmplx_0(A)) = B))))) # label(t204_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3585 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> -(k6_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) != k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) & np__0 != A & np__0 != B))))))))) # label(t131_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3586 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,B) = k6_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t151_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3587 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k7_xcmplx_0(A,k4_xcmplx_0(B))) = k7_xcmplx_0(A,B))))) # label(t190_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3588 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(B) = k6_xcmplx_0(k6_xcmplx_0(A,A),B))))) # label(t230_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3589 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(A,k3_xcmplx_0(B,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),C))))))) # label(t79_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3590 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(np__4,A) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A))) # label(t13_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3591 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) = k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)))))))))) # label(t47_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3592 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(B,A) = k7_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)))))) # label(t216_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3593 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(np__2,A) = k2_xcmplx_0(A,A))) # label(t11_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3594 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(A,B),C) = k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)))))))) # label(t172_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3595 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k3_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(A,C)) = k7_xcmplx_0(B,C)))))))) # label(t99_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3596 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)))))) # label(t192_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3597 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(np__1,B),C),A))))))) # label(t102_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3598 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> -(A != np__0 & k2_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) != k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) & B != np__0))))))))) # label(t117_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3599 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(A,k7_xcmplx_0(B,C)))))))) # label(t83_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3600 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_xcmplx_0(k3_xcmplx_0(A,k5_xcmplx_0(B))) = k3_xcmplx_0(k5_xcmplx_0(A),B))))) # label(t206_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3601 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(B,C) != A))))))) # label(t234_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3602 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,np__3),k7_xcmplx_0(A,np__3)),k7_xcmplx_0(A,np__3)) = A)) # label(t69_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3603 (all A (v1_xcmplx_0(A) -> (np__0 != A -> k4_xcmplx_0(np__1) = k7_xcmplx_0(A,k4_xcmplx_0(A))))) # label(t199_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3604 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(A,C),k6_xcmplx_0(C,B)) = k2_xcmplx_0(A,B))))))) # label(t31_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3605 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k4_xcmplx_0(A),B))))) # label(t188_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3606 (all A (v1_xcmplx_0(A) -> (np__0 != A -> k3_xcmplx_0(A,k7_xcmplx_0(np__1,A)) = np__1))) # label(t107_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3607 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k7_xcmplx_0(A,B) -> A = B))))) # label(t58_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3608 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k2_xcmplx_0(k2_xcmplx_0(A,B),k4_xcmplx_0(B)))))) # label(t137_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3609 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,k6_xcmplx_0(B,C)) = k2_xcmplx_0(A,k6_xcmplx_0(C,B)))))))) # label(t38_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3610 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(B,k3_xcmplx_0(C,A)) = k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(B,C)))))))) # label(t104_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3611 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != A & k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)) = np__0 & np__0 != B))))) # label(t112_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3612 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) = k3_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D))))))))) # label(t42_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3613 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k3_xcmplx_0(A,k5_xcmplx_0(B)) -> A = B))))) # label(t210_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3614 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)))))))))) # label(t77_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3615 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_xcmplx_0(k3_xcmplx_0(A,B)) = k7_xcmplx_0(k5_xcmplx_0(A),B))))) # label(t223_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3616 (all A (v1_xcmplx_0(A) -> k5_xcmplx_0(A) = k7_xcmplx_0(np__1,A))) # label(t217_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3617 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) = A)))) # label(t138_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3618 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,np__4),k7_xcmplx_0(A,np__4)),k7_xcmplx_0(A,np__4)),k7_xcmplx_0(A,np__4)) = A)) # label(t71_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3619 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k4_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C)))))))) # label(t169_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3620 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k2_xcmplx_0(A,B) = k2_xcmplx_0(C,B) -> A = C))))))) # label(t2_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3621 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(k7_xcmplx_0(A,C),B))))))) # label(t48_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3622 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(A,np__0))) # label(t49_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3623 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(np__1,k7_xcmplx_0(np__1,A)))) # label(t56_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3624 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k5_xcmplx_0(k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B))))))) # label(t207_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3625 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(np__1)))) # label(t195_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3626 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = k6_xcmplx_0(A,B) -> B = A))))) # label(t15_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3627 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k3_xcmplx_0(A,k7_xcmplx_0(np__1,B)))))) # label(t100_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3628 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k2_xcmplx_0(A,k4_xcmplx_0(B)) = np__0 -> B = A))))) # label(t136_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3629 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(k6_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) != k3_xcmplx_0(k6_xcmplx_0(B,A),k5_xcmplx_0(k3_xcmplx_0(A,B))) & np__0 != A & np__0 != B))))) # label(t214_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3630 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k6_xcmplx_0(A,B),k2_xcmplx_0(C,D)) = k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)))))))))) # label(t46_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3631 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t1_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3632 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k3_xcmplx_0(A,k7_xcmplx_0(k7_xcmplx_0(B,A),C)) = k7_xcmplx_0(B,C)))))))) # label(t98_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3633 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k4_xcmplx_0(A),k3_xcmplx_0(np__2,A)) = A)) # label(t184_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3634 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k6_xcmplx_0(C,D) = k6_xcmplx_0(A,B) -> k2_xcmplx_0(A,D) = k2_xcmplx_0(B,C)))))))))) # label(t34_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3635 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & k7_xcmplx_0(A,B) = np__0 & np__0 != A))))) # label(t50_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3636 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,k7_xcmplx_0(A,np__2)) = k7_xcmplx_0(A,np__2))) # label(t122_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3637 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (all E (v1_xcmplx_0(E) -> k3_xcmplx_0(k7_xcmplx_0(E,C),k7_xcmplx_0(A,k3_xcmplx_0(B,D))) = k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),k7_xcmplx_0(D,E))))))))))))) # label(t235_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3638 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,C) = k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),B))))))) # label(t228_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3639 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(A,np__0))) # label(t62_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3640 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,k5_xcmplx_0(B)) = k3_xcmplx_0(A,B))))) # label(t221_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3641 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k4_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C)))))))) # label(t170_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3642 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(C,B),A))))))) # label(t76_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3643 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> B = k3_xcmplx_0(B,k3_xcmplx_0(k7_xcmplx_0(np__1,A),A))))))) # label(t109_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3644 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),B),A) = k6_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t160_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3645 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) = k3_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(C,D)))))))))) # label(t45_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3646 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (all E (v1_xcmplx_0(E) -> k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),k7_xcmplx_0(D,E))) = k3_xcmplx_0(k7_xcmplx_0(E,C),k7_xcmplx_0(A,k3_xcmplx_0(B,D))))))))))))) # label(t87_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3647 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(B,A) = k5_xcmplx_0(k7_xcmplx_0(A,B)))))) # label(t215_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3648 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,k4_xcmplx_0(np__1)) = k4_xcmplx_0(A))) # label(t194_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3649 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k3_xcmplx_0(A,k2_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))) = k2_xcmplx_0(B,C)))))))) # label(t115_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3650 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,B) = k2_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(C,B)))))))) # label(t39_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3651 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(k2_xcmplx_0(A,A),np__2))) # label(t65_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3652 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C))))))) # label(t226_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3653 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(np__1,B)) = k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)))))) # label(t103_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3654 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(A,C),B))))))) # label(t29_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3655 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t189_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3656 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k6_xcmplx_0(A,C),B) = k6_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)))))))) # label(t121_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3657 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(k4_xcmplx_0(A),B) = k7_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t193_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3658 (all A (v1_xcmplx_0(A) -> -(np__0 != A & k4_xcmplx_0(np__1) != A & np__1 != A & A = k5_xcmplx_0(A)))) # label(t225_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3659 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k6_xcmplx_0(B,A),k4_xcmplx_0(C)) = k3_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t185_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3660 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(np__2,B)),k7_xcmplx_0(A,k3_xcmplx_0(np__2,B))) = k7_xcmplx_0(A,B))))) # label(t119_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3661 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k6_xcmplx_0(A,B) = k6_xcmplx_0(C,D) -> k6_xcmplx_0(A,C) = k6_xcmplx_0(B,D)))))))))) # label(t24_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3662 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) = k3_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)))))))))) # label(t41_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3663 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(np__1,A)) = B))))) # label(t108_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3664 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = np__0 & A != np__0))))) # label(t209_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3665 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),A),B))))) # label(t139_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3666 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(k2_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) != k3_xcmplx_0(k2_xcmplx_0(A,B),k5_xcmplx_0(k3_xcmplx_0(A,B))) & B != np__0 & A != np__0))))) # label(t213_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3667 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k3_xcmplx_0(B,C) = k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(C,A))))))))) # label(t91_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3668 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k7_xcmplx_0(B,C)))))))) # label(t75_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3669 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k6_xcmplx_0(A,B)) = k6_xcmplx_0(B,A))))) # label(t143_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3670 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k7_xcmplx_0(A,np__2),k7_xcmplx_0(A,np__2)) = A)) # label(t66_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3671 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)) = k6_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t171_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3672 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(k4_xcmplx_0(np__1),A) = k4_xcmplx_0(A))) # label(t180_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3673 (all A (v1_xcmplx_0(A) -> k4_xcmplx_0(k5_xcmplx_0(A)) = k5_xcmplx_0(k4_xcmplx_0(A)))) # label(t224_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3674 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k7_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(A,C)),A) = k2_xcmplx_0(k7_xcmplx_0(B,A),C)))))))) # label(t114_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3675 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(B) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),A))))) # label(t233_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3676 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)),A) = k2_xcmplx_0(B,C)))))))) # label(t116_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3677 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k3_xcmplx_0(C,A) = k3_xcmplx_0(B,A) -> B = C | A = np__0))))))) # label(t5_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3678 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k6_xcmplx_0(A,B) = k6_xcmplx_0(A,C) -> C = B))))))) # label(t20_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3679 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k7_xcmplx_0(A,k7_xcmplx_0(np__1,B)))))) # label(t101_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3680 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k6_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),D))))))))) # label(t125_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3681 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(A,B) = k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)))))) # label(t163_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3682 (all A (v1_xcmplx_0(A) -> (k4_xcmplx_0(A) = np__0 -> np__0 = A))) # label(t135_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3683 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_xcmplx_0(B,A) = k4_xcmplx_0(A) -> np__0 = A | B = k4_xcmplx_0(np__1)))))) # label(t182_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3684 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,k6_xcmplx_0(B,B)) = A)))) # label(t25_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3685 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k6_xcmplx_0(A,B) = k2_xcmplx_0(A,k4_xcmplx_0(C)) -> C = B))))))) # label(t154_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3686 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)))))) # label(t205_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3687 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k6_xcmplx_0(A,B) = k2_xcmplx_0(C,k4_xcmplx_0(B)) -> A = C))))))) # label(t153_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3688 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),B),A) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t165_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3689 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k3_xcmplx_0(A,k2_xcmplx_0(B,k7_xcmplx_0(C,A))) = k2_xcmplx_0(k3_xcmplx_0(A,B),C)))))))) # label(t237_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3690 (all A (v1_xcmplx_0(A) -> (np__0 != A -> k7_xcmplx_0(k4_xcmplx_0(A),A) = k4_xcmplx_0(np__1)))) # label(t198_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3691 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k5_xcmplx_0(B) = k5_xcmplx_0(A) -> A = B))))) # label(t202_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3692 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(np__1,B),k7_xcmplx_0(A,C)))))))) # label(t105_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3693 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(A),B)) = k3_xcmplx_0(A,B))))) # label(t179_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3694 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k7_xcmplx_0(C,A) = k7_xcmplx_0(D,B) -> A = np__0 | A = k4_xcmplx_0(B) | B = np__0 | k7_xcmplx_0(C,A) = k7_xcmplx_0(k2_xcmplx_0(C,D),k2_xcmplx_0(A,B))))))))))) # label(t201_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3695 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t167_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3696 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k4_xcmplx_0(B),A) = k4_xcmplx_0(k2_xcmplx_0(A,B)))))) # label(t161_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3697 (all A (v1_xcmplx_0(A) -> (np__0 != A -> np__1 = k7_xcmplx_0(A,A)))) # label(t60_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3698 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k5_xcmplx_0(B) = k7_xcmplx_0(np__1,A) -> A = B))))) # label(t220_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3699 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),A),B) = k6_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t159_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3700 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)))))))))) # label(t126_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3701 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> k2_xcmplx_0(A,B) = k3_xcmplx_0(A,k2_xcmplx_0(np__1,k7_xcmplx_0(B,A)))))))) # label(t118_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3702 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C))))))) # label(t227_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3703 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),C),A))))))) # label(t156_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3704 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(A != np__0 & B != np__0 & np__1 != k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(B,A))))))) # label(t113_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3705 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,A) = np__0)) # label(t14_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3706 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k3_xcmplx_0(A,k4_xcmplx_0(B))) = k3_xcmplx_0(A,B))))) # label(t178_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3707 (all A (v1_xcmplx_0(A) -> -(np__1 = k3_xcmplx_0(A,A) & k4_xcmplx_0(np__1) != A & np__1 != A))) # label(t183_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3708 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(np__1,C),k7_xcmplx_0(A,B)))))))) # label(t106_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3709 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A),np__4) = A)) # label(t70_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3710 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k3_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(C,B)))))))))) # label(t86_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3711 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k7_xcmplx_0(k3_xcmplx_0(B,A),A)))))) # label(t90_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3712 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k3_xcmplx_0(A,C),B) = k7_xcmplx_0(A,k7_xcmplx_0(B,C)))))))) # label(t78_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3713 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B))) = k2_xcmplx_0(A,B))))) # label(t142_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3714 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k6_xcmplx_0(A,C))))))) # label(t229_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3715 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> k6_xcmplx_0(A,B) = k3_xcmplx_0(A,k6_xcmplx_0(np__1,k7_xcmplx_0(B,A)))))))) # label(t132_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3716 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(A,k7_xcmplx_0(C,B)))))))) # label(t80_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3717 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k3_xcmplx_0(C,A) = k7_xcmplx_0(D,B) -> k3_xcmplx_0(C,B) = k7_xcmplx_0(D,A) | B = np__0 | A = np__0))))))))) # label(t97_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3718 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(k6_xcmplx_0(B,k3_xcmplx_0(C,A)),A) = k6_xcmplx_0(k7_xcmplx_0(B,A),C)))))))) # label(t127_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3719 (all A (v1_xcmplx_0(A) -> A = k5_xcmplx_0(k7_xcmplx_0(np__1,A)))) # label(t219_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3720 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k6_xcmplx_0(A,B) = A -> np__0 = B))))) # label(t16_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3721 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,B) = k6_xcmplx_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)))))))) # label(t32_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3722 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) = A -> np__1 = B | A = np__0))))) # label(t61_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3723 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k7_xcmplx_0(k2_xcmplx_0(A,B),np__2) -> B = A))))) # label(t67_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3724 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) = k3_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),D))))))))) # label(t43_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3725 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(B,k3_xcmplx_0(A,C)) = k3_xcmplx_0(k5_xcmplx_0(A),k7_xcmplx_0(B,C)))))))) # label(t222_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3726 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> B = k6_xcmplx_0(A,k6_xcmplx_0(A,B)))))) # label(t18_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3727 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(A,k2_xcmplx_0(B,C)))))))) # label(t36_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3728 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_xcmplx_0(np__1) = k7_xcmplx_0(A,B) -> k4_xcmplx_0(A) = B & A = k4_xcmplx_0(B)))))) # label(t196_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3729 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,k6_xcmplx_0(k4_xcmplx_0(B),C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t157_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3730 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(A,k6_xcmplx_0(B,C)))))))) # label(t37_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3731 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),C),A) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t147_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3732 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> k7_xcmplx_0(B,k3_xcmplx_0(A,k7_xcmplx_0(np__1,A))) = B))))) # label(t111_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3733 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) = k4_xcmplx_0(A) -> B = k4_xcmplx_0(np__1) | np__0 = A))))) # label(t197_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3734 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k3_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(C,A)),A) = k7_xcmplx_0(B,C)))))))) # label(t93_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3735 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),B),A) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t148_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3736 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k3_xcmplx_0(A,k6_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))) = k6_xcmplx_0(B,C)))))))) # label(t129_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3737 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) != np__0 -> B = k7_xcmplx_0(A,k7_xcmplx_0(A,B))))))) # label(t54_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3738 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),np__3))) # label(t68_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3739 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k3_xcmplx_0(B,k7_xcmplx_0(A,A))))))) # label(t89_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3740 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(A,B)))))) # label(t140_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3741 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)))))))))) # label(t123_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3742 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,k4_xcmplx_0(B)) = k3_xcmplx_0(k4_xcmplx_0(A),B))))) # label(t176_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3743 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k7_xcmplx_0(D,A) = k7_xcmplx_0(C,B) -> k3_xcmplx_0(D,B) = k3_xcmplx_0(C,A) | A = np__0 | np__0 = B))))))))) # label(t96_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3744 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)) = k2_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t141_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3745 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),A),B) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t166_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3746 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k4_xcmplx_0(B),k6_xcmplx_0(k4_xcmplx_0(A),B)) = A)))) # label(t145_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3747 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k6_xcmplx_0(B,k7_xcmplx_0(C,A)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),C),A)))))))) # label(t128_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3748 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k6_xcmplx_0(B,C)) = k6_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C)))))))) # label(t149_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3749 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(A,k3_xcmplx_0(B,C)) = k3_xcmplx_0(k3_xcmplx_0(A,B),C))))))) # label(t4_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3750 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(np__0,A) = k4_xcmplx_0(A))) # label(t150_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3751 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k3_xcmplx_0(A,B) -> k7_xcmplx_0(np__1,B) = A))))) # label(t74_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3752 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k3_xcmplx_0(B,A) -> np__1 = B | A = np__0))))) # label(t7_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3753 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,B),C),C),A) = B))))))) # label(t133_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3754 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(A,k6_xcmplx_0(B,B)) = A)))) # label(t17_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3755 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(np__1,k5_xcmplx_0(A)) = A)) # label(t218_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3756 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k2_xcmplx_0(A,B) = k2_xcmplx_0(C,D) -> k6_xcmplx_0(D,B) = k6_xcmplx_0(A,C)))))))))) # label(t33_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3757 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(np__3,B)),k7_xcmplx_0(A,k3_xcmplx_0(np__3,B))),k7_xcmplx_0(A,k3_xcmplx_0(np__3,B))))))) # label(t120_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.60 3758 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(np__1,k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A))))) # label(t57_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3759 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) = A)))) # label(t152_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3760 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(C,B),A) = k2_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t30_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3761 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(C,k7_xcmplx_0(A,B)) = k7_xcmplx_0(A,k7_xcmplx_0(B,C)))))))) # label(t82_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3762 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k4_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C)))))))) # label(t174_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3763 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k3_xcmplx_0(k7_xcmplx_0(B,A),A) = B))))) # label(t88_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3764 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),A),B) = k6_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t155_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3765 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(B) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),A),B))))) # label(t231_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3766 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k3_xcmplx_0(A,B) -> A = k5_xcmplx_0(B)))))) # label(t211_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3767 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(A,k6_xcmplx_0(B,C)) = k6_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)))))))) # label(t40_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3768 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__0) & r1_xreal_0(np__0,A) -> r1_xreal_0(k3_xcmplx_0(A,B),np__0)))))) # label(t133_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3769 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(k2_xcmplx_0(A,B),np__0) & -r1_xreal_0(B,np__0)))))) # label(t36_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3770 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,B) & r1_xreal_0(np__0,A) & r1_xreal_0(k2_xcmplx_0(A,C),B)))))))) # label(t42_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3771 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__0) & r1_xreal_0(B,C) -> r1_xreal_0(B,k6_xcmplx_0(C,A))))))))) # label(t54_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3772 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,k7_xcmplx_0(A,B)) & -(-r1_xreal_0(np__0,B) & -r1_xreal_0(A,np__0)) & -(-r1_xreal_0(B,np__0) & -r1_xreal_0(np__0,A))))))) # label(t145_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3773 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(A,B),np__0) & -r1_xreal_0(B,np__0)))))) # label(t141_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3774 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,A) & -r1_xreal_0(np__0,k5_xcmplx_0(A)) & -r1_xreal_0(k5_xcmplx_0(B),np__0)))))) # label(t127_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3775 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> r1_xreal_0(np__0,k2_xcmplx_0(A,B))))))) # label(t35_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3776 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__0) & -r1_xreal_0(np__0,A) & r1_xreal_0(np__0,k7_xcmplx_0(B,A))))))) # label(t144_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3777 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> -r1_xreal_0(A,B) & -r1_xreal_0(B,k4_xcmplx_0(A)) | r1_xreal_0(np__0,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)))))))) # label(t96_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3778 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B)) & r1_xreal_0(k3_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(np__0,B)))))))))) # label(t114_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3779 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,k6_xcmplx_0(B,A)) & -r1_xreal_0(A,np__0)))))) # label(t46_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3780 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0) & r1_xreal_0(np__0,k7_xcmplx_0(A,B))))))) # label(t143_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3781 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(np__0,B)))))))))) # label(t109_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3782 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(A,B) & r1_xreal_0(C,D) -> r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C))))))))))) # label(t15_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3783 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) & -r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__0) & -r1_xreal_0(C,B)))))))) # label(t78_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3784 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(A,np__0) -> r1_xreal_0(k7_xcmplx_0(A,B),np__0)))))) # label(t140_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3785 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) & -r1_xreal_0(B,np__0)))))))))) # label(t111_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3786 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & -r1_xreal_0(np__1,C) & -r1_xreal_0(A,k7_xcmplx_0(B,C))))) -> r1_xreal_0(A,B)))))) # label(t211_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3787 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,np__0) & r1_xreal_0(k4_xcmplx_0(np__1),B) & -r1_xreal_0(A,k4_xcmplx_0(np__1)) & r1_xreal_0(A,np__0) & r1_xreal_0(np__1,k3_xcmplx_0(A,B))))))) # label(t168_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3788 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(C,np__1) -> r1_xreal_0(A,k3_xcmplx_0(B,C))))) -> r1_xreal_0(A,B)))))) # label(t169_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3789 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,B) & r1_xreal_0(A,np__0) & r1_xreal_0(np__1,k7_xcmplx_0(A,B))))))) # label(t192_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3790 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,k3_xcmplx_0(A,B)) & -r1_xreal_0(B,np__1) & -r1_xreal_0(np__0,A)))))) # label(t160_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3791 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(B,np__0) & -r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B)) & r1_xreal_0(k7_xcmplx_0(C,A),k3_xcmplx_0(D,B)) & -r1_xreal_0(np__0,A)))))))))) # label(t118_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3792 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(A,B) -> r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t188_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3793 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,k7_xcmplx_0(np__1,np__2)) -> r1_xreal_0(np__0,k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,A)))))) # label(t220_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3794 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)) & -r1_xreal_0(np__0,A) & -r1_xreal_0(C,B)))))))) # label(t71_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3795 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(np__0,A) -> r1_xreal_0(B,k2_xcmplx_0(A,C))))))))) # label(t40_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3796 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) -> r1_xreal_0(k2_xcmplx_0(A,B),B)))))) # label(t34_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3797 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D)) <-> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(D,B))))))))))) # label(t23_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3798 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & r1_xreal_0(B,A) & -r1_xreal_0(np__0,k5_xcmplx_0(A))))))) # label(t94_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3799 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)),np__0) -> r1_xreal_0(B,A) & r1_xreal_0(k4_xcmplx_0(A),B)))))) # label(t95_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3800 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,k3_xcmplx_0(B,A)) & r1_xreal_0(k7_xcmplx_0(C,A),B) & -r1_xreal_0(A,np__0)))))))) # label(t83_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3801 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) | r1_xreal_0(np__0,A) | r1_xreal_0(np__0,B)))))))))) # label(t105_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3802 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(np__0,A) -> r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))))))))) # label(t74_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3803 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__1) & r1_xreal_0(np__0,B) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,A) -> r1_xreal_0(k3_xcmplx_0(A,B),np__1)))))) # label(t162_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3804 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__1,B) & -r1_xreal_0(np__0,A) & r1_xreal_0(k3_xcmplx_0(A,B),A)))))) # label(t158_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3805 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(k4_xcmplx_0(np__1),A) & r1_xreal_0(B,np__0) & r1_xreal_0(k4_xcmplx_0(np__1),B) -> r1_xreal_0(k3_xcmplx_0(A,B),np__1)))))) # label(t167_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3806 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t129_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3807 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) & r1_xreal_0(A,B) & -r1_xreal_0(k5_xcmplx_0(A),np__0)))))) # label(t93_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3808 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k3_xcmplx_0(A,B),np__1) & r1_xreal_0(np__1,B) & -r1_xreal_0(A,np__1)))))) # label(t163_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3809 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(A != B & r1_xreal_0(k6_xcmplx_0(B,A),np__0) & r1_xreal_0(k6_xcmplx_0(A,B),np__0)))))) # label(t57_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3810 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(A,np__0) | r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) | r1_xreal_0(B,np__0)))))))))) # label(t104_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3811 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__0) & r1_xreal_0(C,B) -> r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) | r1_xreal_0(np__0,B)))))))) # label(t123_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3812 (all A (v1_xreal_0(A) -> -(r1_xreal_0(A,k7_xcmplx_0(A,np__3)) & -r1_xreal_0(A,np__0)))) # label(t223_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3813 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,C) & r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) & -r1_xreal_0(np__0,B)))))))) # label(t103_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3814 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(C,k6_xcmplx_0(B,A)) & r1_xreal_0(np__0,A) & -r1_xreal_0(C,B)))))))) # label(t53_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3815 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(k6_xcmplx_0(B,A),B)))))) # label(t45_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3816 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(A,np__2),np__0)))) # label(t217_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3817 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(C,np__0) & r1_xreal_0(B,A) & r1_xreal_0(A,np__0) & r1_xreal_0(D,C) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D))))))))))) # label(t69_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3818 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,C) & r1_xreal_0(np__0,B) -> r1_xreal_0(A,np__0) | r1_xreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(B,A))))))))) # label(t120_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3819 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,B) & r1_xreal_0(np__0,C) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C))))))))) # label(t66_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3820 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k3_xcmplx_0(B,A),C) -> r1_xreal_0(A,np__0) | r1_xreal_0(B,k7_xcmplx_0(C,A))))))))) # label(t79_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3821 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__1,k7_xcmplx_0(B,A)) & -r1_xreal_0(A,B) & -r1_xreal_0(A,np__0)))))) # label(t193_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3822 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(A,np__0) | r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A))))))) # label(t87_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3823 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,k4_xcmplx_0(A)) & r1_xreal_0(k2_xcmplx_0(B,A),np__0)))))) # label(t64_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3824 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,k4_xcmplx_0(np__1)) & r1_xreal_0(k3_xcmplx_0(A,B),np__1) & -r1_xreal_0(k4_xcmplx_0(np__1),A)))))) # label(t166_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3825 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(A,B) & r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t190_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3826 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(B,A) & r1_xreal_0(C,D) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D))))))))))) # label(t16_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3827 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,k3_xcmplx_0(A,B)) & -r1_xreal_0(np__1,B) & -r1_xreal_0(A,np__0)))))) # label(t159_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3828 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(B,np__0) -> r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t130_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3829 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__0) -> k3_xcmplx_0(A,B) = np__0))))) # label(t128_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3830 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,k7_xcmplx_0(np__1,np__2)) -> r1_xreal_0(k6_xcmplx_0(k3_xcmplx_0(np__2,A),np__1),np__0)))) # label(t219_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3831 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) <-> r1_xreal_0(A,B)))))))) # label(t8_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3832 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k5_xcmplx_0(A),np__0) & -r1_xreal_0(A,np__0)) & -(r1_xreal_0(A,np__0) & -r1_xreal_0(k5_xcmplx_0(A),np__0)))) # label(t124_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3833 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) & r1_xreal_0(np__0,A) -> r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t187_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3834 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),C),k3_xcmplx_0(A,D)),B) & -r1_xreal_0(D,B) & r1_xreal_0(B,C) & -r1_xreal_0(np__1,A) & -r1_xreal_0(A,np__0)))))))))) # label(t179_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3835 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,k4_xcmplx_0(A)) & r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))))))) # label(t199_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3836 (all A (v1_xreal_0(A) -> -(r1_xreal_0(np__0,k5_xcmplx_0(A)) & -r1_xreal_0(np__0,A)) & -(r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,k5_xcmplx_0(A))))) # label(t125_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3837 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(D,C) & r1_xreal_0(np__0,A) & r1_xreal_0(A,np__1) & r1_xreal_0(B,C) -> r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,D)),C)))))))))) # label(t176_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3838 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) & r1_xreal_0(A,B) & -r1_xreal_0(D,C)))))))))) # label(t17_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3839 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(B,A) & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) & r1_xreal_0(C,D)))))))))) # label(t10_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3840 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(np__1,k7_xcmplx_0(A,B)) & -r1_xreal_0(B,A)))))) # label(t191_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3841 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(A,B) & r1_xreal_0(np__0,A) & r1_xreal_0(np__0,C) & r1_xreal_0(C,D) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D))))))))))) # label(t68_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3842 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,B) & r1_xreal_0(B,C) -> r1_xreal_0(A,C)))))))) # label(t2_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3843 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(C,k7_xcmplx_0(B,A)) & -r1_xreal_0(k3_xcmplx_0(C,A),B)))))))) # label(t85_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3844 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k6_xcmplx_0(np__1,A),np__0) & -r1_xreal_0(np__1,A)))) # label(t151_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3845 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(B,k4_xcmplx_0(A)) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t197_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3846 (all A (v1_xreal_0(A) -> (r1_xreal_0(k7_xcmplx_0(np__1,np__2),A) -> r1_xreal_0(k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,A)),np__0)))) # label(t222_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3847 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k3_xcmplx_0(A,B),np__0) & -r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__0)))))) # label(t131_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3848 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(B,np__0) & r1_xreal_0(k3_xcmplx_0(C,B),k7_xcmplx_0(D,A)) & -r1_xreal_0(np__0,A) & -r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A))))))))))) # label(t116_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3849 (all A (v1_xreal_0(A) -> (r1_xreal_0(k7_xcmplx_0(np__1,np__2),A) -> r1_xreal_0(np__0,k6_xcmplx_0(k3_xcmplx_0(np__2,A),np__1))))) # label(t221_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3850 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & -r1_xreal_0(A,np__0) & -r1_xreal_0(B,A)))))) # label(t90_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3851 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) -> r1_xreal_0(k5_xcmplx_0(A),np__0) | r1_xreal_0(B,A)))))) # label(t91_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3852 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & -r1_xreal_0(np__0,B) & r1_xreal_0(k3_xcmplx_0(C,B),k7_xcmplx_0(D,A)) & -r1_xreal_0(A,np__0)))))))))) # label(t117_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3853 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k4_xcmplx_0(A),np__0) & r1_xreal_0(np__0,A)) & -(r1_xreal_0(k4_xcmplx_0(A),np__0) & -r1_xreal_0(np__0,A)))) # label(t60_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3854 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(k4_xcmplx_0(A),B) & -r1_xreal_0(np__0,A)))))) # label(t201_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3855 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(B,C) & -r1_xreal_0(A,np__0) & r1_xreal_0(k2_xcmplx_0(A,C),B)))))))) # label(t41_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3856 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(C,np__0) -> r1_xreal_0(k6_xcmplx_0(A,C),B)))) -> r1_xreal_0(A,B)))))) # label(t59_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3857 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(np__0,k2_xcmplx_0(A,B))))))) # label(t62_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3858 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,B) <-> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C))))))))) # label(t11_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3859 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(k6_xcmplx_0(A,B),np__0)))))) # label(t49_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3860 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k3_xcmplx_0(B,A),C) -> r1_xreal_0(k7_xcmplx_0(C,A),B) | r1_xreal_0(np__0,A)))))))) # label(t80_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3861 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(k3_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B)) & -r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__0)))))))))) # label(t115_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3862 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) | r1_xreal_0(np__0,B) | r1_xreal_0(A,np__0)))))))))) # label(t106_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3863 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__1) & r1_xreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C))) & r1_xreal_0(np__0,A) -> A = np__0 | r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),C)))))))) # label(t181_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3864 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,B) & r1_xreal_0(np__0,A) & r1_xreal_0(np__0,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A))) & -r1_xreal_0(B,k4_xcmplx_0(A))))))) # label(t97_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3865 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__1) & r1_xreal_0(B,C) -> r1_xreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)))))))))) # label(t173_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3866 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(B)) & r1_xreal_0(A,np__0) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t198_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3867 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,k2_xcmplx_0(A,B)) & -r1_xreal_0(k4_xcmplx_0(B),A)))))) # label(t63_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3868 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & -r1_xreal_0(np__1,C) & -r1_xreal_0(k3_xcmplx_0(A,C),B)))) -> r1_xreal_0(A,B)))))) # label(t170_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3869 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(C,B) & r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,D))) & -r1_xreal_0(np__1,A) & -r1_xreal_0(A,np__0) & r1_xreal_0(D,C)))))))))) # label(t180_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3870 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,k4_xcmplx_0(np__1)) & r1_xreal_0(k2_xcmplx_0(np__1,A),np__0)))) # label(t150_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3871 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t195_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3872 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k4_xcmplx_0(A),B) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) & -r1_xreal_0(A,np__0)))))) # label(t207_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3873 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(B)) -> r1_xreal_0(k2_xcmplx_0(A,B),np__0)))))) # label(t61_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3874 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,k3_xcmplx_0(A,B)) & -(-r1_xreal_0(B,np__0) & -r1_xreal_0(np__0,A)) & -(-r1_xreal_0(np__0,B) & -r1_xreal_0(A,np__0))))))) # label(t135_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3875 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,k6_xcmplx_0(B,C)) -> r1_xreal_0(C,k6_xcmplx_0(B,A))))))))) # label(t13_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3876 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,k3_xcmplx_0(C,A)) -> r1_xreal_0(k7_xcmplx_0(B,A),C) | r1_xreal_0(A,np__0)))))))) # label(t81_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3877 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(np__0,C) -> r1_xreal_0(k2_xcmplx_0(A,C),B)))) -> r1_xreal_0(A,B)))))) # label(t44_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3878 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,A) & r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t189_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3879 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) <-> r1_xreal_0(A,B)))))) # label(t26_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3880 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__1,B) & r1_xreal_0(A,np__0) -> r1_xreal_0(k3_xcmplx_0(A,B),A)))))) # label(t156_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3881 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,A) -> r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),C)))))))) # label(t174_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3882 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(B,A) & -r1_xreal_0(C,D) & -r1_xreal_0(np__0,C) & r1_xreal_0(k3_xcmplx_0(B,D),k3_xcmplx_0(A,C)) & -r1_xreal_0(np__0,A)))))))))) # label(t72_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3883 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(B,np__0) -> r1_xreal_0(k7_xcmplx_0(A,B),np__0)))))) # label(t139_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3884 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(np__1,k7_xcmplx_0(B,A)) | r1_xreal_0(A,np__0)))))) # label(t183_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3885 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) = np__0 & np__0 != A & r1_xreal_0(np__0,C) & r1_xreal_0(np__0,B) & C != np__0 & r1_xreal_0(np__0,D) & r1_xreal_0(np__0,A)))))))))) # label(t73_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3886 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(B,A)) & -r1_xreal_0(A,np__0) & -r1_xreal_0(C,B)))))))) # label(t70_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3887 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(np__0,k6_xcmplx_0(B,A))))))) # label(t50_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3888 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) -> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,D))))))))))) # label(t18_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3889 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(np__0,A) & -(np__0 = C & np__0 = A) & r1_xreal_0(np__0,C) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,B) & -(C = np__0 & np__0 = B) & -(np__1 = A & B = np__0) & k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(k6_xcmplx_0(np__1,A),C)) = np__0))))))) # label(t172_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3890 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) & -r1_xreal_0(k4_xcmplx_0(B),A)))))) # label(t208_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3891 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(B,k7_xcmplx_0(C,A)) & -r1_xreal_0(C,k3_xcmplx_0(B,A)) & -r1_xreal_0(np__0,A)))))))) # label(t84_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3892 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(np__0,C) -> r1_xreal_0(A,k6_xcmplx_0(B,C))))) -> r1_xreal_0(A,B)))))) # label(t58_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3893 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k6_xcmplx_0(A,B),C) -> r1_xreal_0(k6_xcmplx_0(A,C),B)))))))) # label(t14_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3894 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(A,np__1) & r1_xreal_0(B,D) & r1_xreal_0(B,C) & r1_xreal_0(np__0,A) -> r1_xreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),C),k3_xcmplx_0(A,D)))))))))))) # label(t175_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3895 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,k4_xcmplx_0(A)) -> r1_xreal_0(A,np__0) | r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))))))) # label(t203_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3896 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__0) & r1_xreal_0(A,B) -> r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t186_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3897 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & -r1_xreal_0(B,np__0) & r1_xreal_0(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(A,np__0)))))))))) # label(t113_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3898 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) & -r1_xreal_0(B,k4_xcmplx_0(A))))))) # label(t209_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3899 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(A,k4_xcmplx_0(B)) & -r1_xreal_0(A,np__0)))))) # label(t200_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3900 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,k2_xcmplx_0(B,C)) <-> r1_xreal_0(k6_xcmplx_0(A,B),C)))))))) # label(t22_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3901 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__0) & np__0 = k2_xcmplx_0(A,B) & r1_xreal_0(A,np__0) -> np__0 = A))))) # label(t30_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3902 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(np__1)) & r1_xreal_0(B,k4_xcmplx_0(np__1)) -> r1_xreal_0(np__1,k3_xcmplx_0(A,B))))))) # label(t165_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3903 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(B,np__1) & r1_xreal_0(np__1,k3_xcmplx_0(A,B)) & -r1_xreal_0(np__1,A) & r1_xreal_0(np__0,B)))))) # label(t164_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3904 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(np__0,A) | r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) | r1_xreal_0(B,np__0)))))))))) # label(t107_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3905 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) -> r1_xreal_0(k6_xcmplx_0(D,B),k6_xcmplx_0(C,A))))))))))) # label(t19_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3906 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(B,C) & r1_xreal_0(C,k2_xcmplx_0(B,A)) & -r1_xreal_0(np__0,A)))))))) # label(t39_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3907 (all A (v1_xreal_0(A) -> -r1_xreal_0(A,k6_xcmplx_0(A,np__1)))) # label(t148_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3908 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(k7_xcmplx_0(A,B),np__1)))))) # label(t185_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3909 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__1) & r1_xreal_0(k3_xcmplx_0(A,B),A)))))) # label(t157_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3910 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0) & -r1_xreal_0(C,A) & r1_xreal_0(B,D) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B))))))))))) # label(t99_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3911 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(A,np__3),np__0)))) # label(t224_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3912 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,B) & -r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & r1_xreal_0(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B))))))))))) # label(t112_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3913 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) & r1_xreal_0(A,B) -> B = A))))) # label(t1_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3914 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(B)) -> r1_xreal_0(B,k4_xcmplx_0(A))))))) # label(t27_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3915 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) -> r1_xreal_0(k6_xcmplx_0(D,C),k6_xcmplx_0(B,A))))))))))) # label(t20_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3916 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__1,A) -> r1_xreal_0(k5_xcmplx_0(A),np__1)))) # label(t213_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3917 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) -> r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) | r1_xreal_0(np__0,A)))))) # label(t88_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3918 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,k6_xcmplx_0(A,B)) & -r1_xreal_0(B,A)))))) # label(t51_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3919 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,B) & r1_xreal_0(A,np__0) & r1_xreal_0(C,k2_xcmplx_0(B,A))))))))) # label(t38_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3920 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(C,np__1) -> r1_xreal_0(k7_xcmplx_0(A,C),B)))) -> r1_xreal_0(A,B)))))) # label(t212_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3921 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,k2_xcmplx_0(A,B)) & -r1_xreal_0(np__0,A)))))) # label(t32_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3922 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> r1_xreal_0(np__0,k7_xcmplx_0(A,B))))))) # label(t138_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3923 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__1) & r1_xreal_0(A,np__0) -> r1_xreal_0(A,k3_xcmplx_0(A,B))))))) # label(t154_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3924 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k2_xcmplx_0(B,A),B)))))) # label(t31_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3925 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,B),k2_xcmplx_0(C,D)) -> r1_xreal_0(k6_xcmplx_0(A,D),k2_xcmplx_0(C,B))))))))))) # label(t25_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3926 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) & k2_xcmplx_0(A,B) = np__0 -> np__0 = A))))) # label(t29_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3927 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> k7_xcmplx_0(B,C) != A)) & B != np__0))))) # label(t227_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3928 (all A (v1_xreal_0(A) -> -(all B (v1_xreal_0(B) -> r1_xreal_0(A,B))))) # label(t4_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3929 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0) & r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A))))))) # label(t126_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3930 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(B)) -> r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) | r1_xreal_0(A,np__0)))))) # label(t204_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3931 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,k6_xcmplx_0(C,B)) <-> r1_xreal_0(k2_xcmplx_0(A,B),C)))))))) # label(t21_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3932 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k4_xcmplx_0(np__1),A) & r1_xreal_0(k5_xcmplx_0(A),k4_xcmplx_0(np__1))))) # label(t216_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3933 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(B,np__0) & -r1_xreal_0(D,B) & -r1_xreal_0(A,np__0) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & r1_xreal_0(A,C)))))))))) # label(t100_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3934 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(A,k4_xcmplx_0(B)) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t210_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3935 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__0) & r1_xreal_0(A,np__0) -> r1_xreal_0(np__0,k7_xcmplx_0(A,B))))))) # label(t137_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3936 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(A,np__1) & r1_xreal_0(B,np__1) & k3_xcmplx_0(A,B) = np__1 & r1_xreal_0(np__0,A) -> A = np__1))))) # label(t152_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3937 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(C,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) | r1_xreal_0(np__0,B)))))))) # label(t121_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3938 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k2_xcmplx_0(A,B),k6_xcmplx_0(C,D)) -> r1_xreal_0(k2_xcmplx_0(A,D),k6_xcmplx_0(C,B))))))))))) # label(t24_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3939 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(k7_xcmplx_0(B,A),C) & -r1_xreal_0(np__0,A) & -r1_xreal_0(k3_xcmplx_0(C,A),B)))))))) # label(t86_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3940 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,A) & -r1_xreal_0(B,C)))) & -r1_xreal_0(B,A)))))) # label(t7_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3941 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(np__1,k7_xcmplx_0(B,A)) & -r1_xreal_0(B,A)))))) # label(t194_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3942 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(B,np__1) -> r1_xreal_0(k3_xcmplx_0(A,B),A)))))) # label(t155_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3943 (all A (v1_xreal_0(A) -> r1_xreal_0(np__0,k3_xcmplx_0(A,A)))) # label(t65_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3944 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k3_xcmplx_0(A,B),np__0) & -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__0)) & -(-r1_xreal_0(np__0,B) & -r1_xreal_0(np__0,A))))))) # label(t136_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3945 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,C) & r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) & -r1_xreal_0(np__0,B)))))))) # label(t101_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3946 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__0) & r1_xreal_0(B,C) -> r1_xreal_0(k2_xcmplx_0(B,A),C)))))))) # label(t37_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3947 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(C,np__0) & r1_xreal_0(A,B) -> r1_xreal_0(k3_xcmplx_0(B,C),k3_xcmplx_0(A,C))))))))) # label(t67_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3948 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(np__0,B) & -r1_xreal_0(C,A) & -r1_xreal_0(D,B) & r1_xreal_0(np__0,A) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B))))))))))) # label(t98_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3949 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(k4_xcmplx_0(B),A)))))) # label(t28_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3950 (all A (v1_xreal_0(A) -> -(r1_xreal_0(A,k7_xcmplx_0(A,np__4)) & -r1_xreal_0(A,np__0)))) # label(t225_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3951 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,B) & r1_xreal_0(A,np__0) & r1_xreal_0(k6_xcmplx_0(C,A),B)))))))) # label(t55_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3952 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) | r1_xreal_0(np__0,A)))))) # label(t205_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3953 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(B,np__0) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(A,np__0)))))))))) # label(t108_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3954 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(A,np__0) -> r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) | r1_xreal_0(B,np__0)))))))) # label(t122_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3955 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k2_xcmplx_0(B,np__1),A) & r1_xreal_0(A,B)))))) # label(t147_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3956 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(C,np__0) -> r1_xreal_0(A,k2_xcmplx_0(B,C))))) -> r1_xreal_0(A,B)))))) # label(t43_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3957 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (exists C (-r1_xreal_0(C,B) & -r1_xreal_0(C,A) & v1_xreal_0(C))))))) # label(t5_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3958 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & r1_xreal_0(B,k6_xcmplx_0(A,np__1))))))) # label(t149_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3959 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,B) & r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) & -r1_xreal_0(B,np__0) & -r1_xreal_0(np__0,A)))))))) # label(t102_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3960 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k6_xcmplx_0(C,A),B) & r1_xreal_0(B,C)))))))) # label(t56_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3961 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),B) & r1_xreal_0(np__0,A) & r1_xreal_0(A,np__1) -> A = np__0 | r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)))))))))) # label(t182_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3962 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,B) & r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(A,np__0)))))))))) # label(t110_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3963 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(C,D) & r1_xreal_0(A,B) -> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D))))))))))) # label(t9_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3964 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) & -r1_xreal_0(np__0,A) & -r1_xreal_0(A,B)))))) # label(t89_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3965 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(B,k2_xcmplx_0(A,B))))))) # label(t33_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3966 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) -> r1_xreal_0(np__0,A) | r1_xreal_0(np__1,k7_xcmplx_0(B,A))))))) # label(t184_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3967 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(B),A) -> r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) | r1_xreal_0(np__0,A)))))) # label(t206_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3968 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) & -r1_xreal_0(C,B)))))))) # label(t77_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3969 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,k3_xcmplx_0(C,B)) & -r1_xreal_0(C,np__0) & -r1_xreal_0(np__1,C)))) -> r1_xreal_0(A,np__0)))))) # label(t171_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3970 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(k4_xcmplx_0(B),A)))))) # label(t202_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3971 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) -> r1_xreal_0(np__0,k5_xcmplx_0(A)) | r1_xreal_0(A,B)))))) # label(t92_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3972 (all A (v1_xreal_0(A) -> -(all B (v1_xreal_0(B) -> r1_xreal_0(B,A))))) # label(t3_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3973 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k6_xcmplx_0(B,A),B)))))) # label(t48_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3974 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__1,B) & r1_xreal_0(np__1,A) -> r1_xreal_0(np__1,k3_xcmplx_0(A,B))))))) # label(t161_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3975 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A)) & -r1_xreal_0(C,B)))))))) # label(t76_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3976 (all A (v1_xreal_0(A) -> -(r1_xreal_0(np__1,k5_xcmplx_0(A)) & -r1_xreal_0(A,np__1)))) # label(t214_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3977 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k6_xcmplx_0(B,A),np__0) & -r1_xreal_0(B,A)))))) # label(t52_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3978 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(B),A) & r1_xreal_0(np__0,A) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t196_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3979 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,k3_xcmplx_0(C,A)) -> r1_xreal_0(C,k7_xcmplx_0(B,A)) | r1_xreal_0(np__0,A)))))))) # label(t82_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3980 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,k4_xcmplx_0(np__1)) -> r1_xreal_0(k4_xcmplx_0(np__1),k5_xcmplx_0(A))))) # label(t215_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3981 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k6_xcmplx_0(C,B),k6_xcmplx_0(C,A)) <-> r1_xreal_0(A,B)))))))) # label(t12_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3982 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k7_xcmplx_0(A,np__4),np__0) & -r1_xreal_0(A,np__0)))) # label(t226_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3983 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__0) & r1_xreal_0(B,C) -> r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A))))))))) # label(t75_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3984 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),C),k3_xcmplx_0(A,D)),B) & -r1_xreal_0(C,B) & -r1_xreal_0(D,B) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,A)))))))))) # label(t177_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3985 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k3_xcmplx_0(A,B),np__0) & -r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,B)))))) # label(t132_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3986 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B)) & -r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(C,A),k3_xcmplx_0(D,B)) & -r1_xreal_0(np__0,B)))))))))) # label(t119_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3987 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k7_xcmplx_0(A,B),np__0) & -(-r1_xreal_0(B,np__0) & -r1_xreal_0(A,np__0)) & -(-r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,B))))))) # label(t146_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3988 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__1,B) -> r1_xreal_0(A,k3_xcmplx_0(A,B))))))) # label(t153_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3989 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(A,B),np__0) & -r1_xreal_0(np__0,B)))))) # label(t142_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3990 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (exists C (v1_xreal_0(C) & -r1_xreal_0(A,C) & -r1_xreal_0(B,C))))))) # label(t6_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3991 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(A,np__1) & -r1_xreal_0(C,D) & r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,D))) & -r1_xreal_0(C,B)))))))))) # label(t178_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3992 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) -> r1_xreal_0(B,k6_xcmplx_0(B,A))))))) # label(t47_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3993 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,B) & r1_xreal_0(np__0,k3_xcmplx_0(A,B)) & -r1_xreal_0(A,np__0)))))) # label(t134_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3994 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(A,k7_xcmplx_0(A,np__2))))) # label(t218_xreal_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3995 $T # label(t24_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3996 (all A all B (v4_ordinal2(B) -> (r2_hidden(A,a_1_0_axioms(B)) <-> (exists C (-r1_xreal_0(B,C) & C = A & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_0_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3997 $T # label(t9_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3998 $T # label(t11_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.61 3999 $T # label(t17_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4000 $T # label(t1_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4001 $T # label(t15_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4002 $T # label(t27_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4003 $T # label(t12_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4004 $T # label(t10_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4005 (all A (v1_xreal_0(A) -> -(A != np__0 & (all B (v1_xreal_0(B) -> k3_xcmplx_0(A,B) != np__1))))) # label(t20_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4006 $T # label(t3_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4007 $T # label(t21_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4008 $T # label(t22_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4009 $T # label(t2_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4010 $T # label(t6_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4011 (all A (v4_ordinal2(A) -> a_1_0_axioms(A) = A)) # label(t30_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4012 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (r2_hidden(np__0,A) & (all B (v1_xreal_0(B) -> (r2_hidden(B,A) -> r2_hidden(k2_xcmplx_0(B,np__1),A)))) -> r1_tarski(k5_numbers,A)))) # label(t29_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4013 $T # label(t14_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4014 $T # label(t25_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4015 $T # label(t7_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4016 $T # label(t13_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4017 $T # label(t23_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4018 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> -((all C (v1_xreal_0(C) -> (exists D (v1_xreal_0(D) & (exists E (v1_xreal_0(E) & r2_hidden(D,A) & r2_hidden(E,B) & -(r1_xreal_0(D,C) & r1_xreal_0(C,E)))))))) & (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r2_hidden(C,A) & r2_hidden(D,B) -> r1_xreal_0(C,D))))))))))) # label(t26_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4019 $T # label(t4_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4020 (all A (v1_xreal_0(A) -> (exists B (np__0 = k2_xcmplx_0(A,B) & v1_xreal_0(B))))) # label(t19_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4021 $T # label(t18_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4022 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(B,k5_numbers) & r2_hidden(A,k5_numbers) -> r2_hidden(k2_xcmplx_0(A,B),k5_numbers)))))) # label(t28_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4023 $T # label(t16_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4024 $T # label(t5_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4025 $T # label(t8_axioms) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4026 $T # label(t29_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4027 $T # label(d1_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4028 (all A (m1_subset_1(A,k1_numbers) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc1_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4029 (all A (m1_subset_1(A,k1_numbers) -> k1_real_1(A) = k4_xcmplx_0(A))) # label(redefinition_k1_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4030 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k3_real_1(A,B),k1_numbers))) # label(dt_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4031 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(C,D) & r1_xreal_0(A,B) -> r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C))) & -((r1_xreal_0(A,B) & -r1_xreal_0(D,C) | -r1_xreal_0(B,A) & r1_xreal_0(C,D)) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D))))))))))) # label(t92_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4032 $T # label(t16_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4033 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k7_xcmplx_0(A,B) = k6_real_1(A,B))) # label(redefinition_k6_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4034 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k4_real_1(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4035 $T # label(t32_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4036 $T # label(t11_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4037 $T # label(t44_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4038 $T # label(t57_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4039 $T # label(t91_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4040 $T # label(t10_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4041 $T # label(t3_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4042 $T # label(t45_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4043 $T # label(t39_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4044 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (-r1_xreal_0(A,np__0) -> -(r1_xreal_0(C,B) & -r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A))) & -(-r1_xreal_0(C,B) & r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A)))))))))) # label(t73_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4045 $T # label(t72_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4046 $T # label(t50_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4047 $T # label(t86_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4048 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k6_real_1(A,B),k1_numbers))) # label(dt_k6_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4049 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) <-> -(r1_xreal_0(B,A) & A != B)))))) # label(d5_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4050 $T # label(t6_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4051 $T # label(t81_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4052 $T # label(t55_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4053 $T # label(t58_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4054 $T # label(t34_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4055 $T # label(t85_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4056 $T # label(t37_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4057 $T # label(t22_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4058 $T # label(t77_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4059 $T # label(t64_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4060 $T # label(t41_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4061 $T # label(t7_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4062 $T # label(t84_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4063 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k4_real_1(B,A) = k4_real_1(A,B))) # label(commutativity_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4064 $T # label(t76_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4065 $T # label(t68_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4066 $T # label(t9_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4067 $T # label(t24_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4068 $T # label(t90_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4069 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k4_real_1(A,B),k1_numbers))) # label(dt_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4070 $T # label(t87_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4071 $T # label(t12_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4072 $T # label(t47_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4073 $T # label(t78_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4074 $T # label(t80_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4075 $T # label(t89_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4076 (all A (m1_subset_1(A,k1_numbers) -> k1_real_1(k1_real_1(A)) = A)) # label(involutiveness_k1_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4077 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k1_real_1(A),k1_numbers))) # label(dt_k1_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4078 $T # label(t30_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4079 $T # label(t79_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4080 $T # label(t14_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4081 $T # label(t20_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4082 $T # label(t33_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4083 (all A (v1_xreal_0(A) -> k6_xcmplx_0(A,np__0) = A)) # label(t25_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4084 $T # label(t23_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4085 $T # label(t28_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4086 $T # label(d2_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4087 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k3_real_1(A,B) = k3_real_1(B,A))) # label(commutativity_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4088 $T # label(t61_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4089 $T # label(t35_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4090 $T # label(t36_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4091 $T # label(t19_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4092 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (-r1_xreal_0(np__0,A) -> -(-r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) & r1_xreal_0(C,B)) & -(-r1_xreal_0(C,B) & r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)))))))))) # label(t74_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4093 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k2_real_1(A),k1_numbers))) # label(dt_k2_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4094 $T # label(t1_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4095 $T # label(t42_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4096 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k5_real_1(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k5_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4097 (all A (m1_subset_1(A,k1_numbers) -> A = k2_real_1(k2_real_1(A)))) # label(involutiveness_k2_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4098 $T # label(d3_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4099 $T # label(t82_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4100 $T # label(t51_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4101 (all A (m1_subset_1(A,k1_numbers) -> k2_real_1(A) = k5_xcmplx_0(A))) # label(redefinition_k2_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4102 $T # label(t17_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4103 $T # label(t27_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4104 $T # label(t43_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4105 $T # label(t67_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4106 (exists A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & (all B (m1_subset_1(B,k1_numbers) -> (p1_s1_real_1(B) <-> r2_hidden(B,A)))))) # label(s1_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4107 $T # label(t66_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4108 $T # label(t54_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4109 $T # label(t63_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4110 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k5_real_1(A,B),k1_numbers))) # label(dt_k5_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4111 $T # label(t4_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4112 $T # label(t59_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4113 $T # label(t15_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4114 $T # label(t60_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4115 $T # label(t52_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4116 $T # label(t46_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4117 $T # label(t83_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4118 $T # label(t65_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4119 $T # label(t75_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4120 $T # label(t40_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4121 $T # label(t8_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4122 $T # label(t18_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4123 $T # label(t13_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4124 $T # label(t21_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4125 $T # label(t69_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4126 $T # label(t48_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4127 $T # label(t88_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4128 $T # label(t38_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4129 $T # label(d4_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4130 $T # label(t71_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4131 $T # label(t70_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4132 $T # label(t62_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4133 $T # label(t5_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4134 $T # label(t2_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4135 $T # label(t49_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4136 $T # label(t31_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4137 $T # label(t53_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4138 $T # label(t56_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4139 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k3_real_1(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4140 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> k7_xcmplx_0(k8_square_1(A),k8_square_1(B)) = k8_square_1(k7_xcmplx_0(A,B))))))) # label(t99_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4141 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k7_square_1(A),k1_numbers))) # label(dt_k7_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4142 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) != np__0 -> k7_xcmplx_0(np__1,k6_xcmplx_0(A,B)) = k7_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B)))))))) # label(t71_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4143 (all A (v1_xcmplx_0(A) -> k5_square_1(A) = k5_square_1(k4_xcmplx_0(A)))) # label(t61_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4144 (all A (m1_subset_1(A,k2_numbers) -> k6_square_1(A) = k5_square_1(A))) # label(redefinition_k6_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4145 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> k1_square_1(A,B) = A) & (-r1_xreal_0(A,B) -> B = k1_square_1(A,B)))))) # label(d1_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4146 $T # label(t13_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4147 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k3_square_1(A,B),k1_numbers))) # label(dt_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4148 $T # label(dt_k5_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4149 $T # label(t80_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4150 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,C) & r1_xreal_0(A,B) <-> r1_xreal_0(A,k1_square_1(B,C))))))))) # label(t39_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4151 $T # label(t24_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4152 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k2_xcmplx_0(A,B) = k2_xcmplx_0(k1_square_1(A,B),k2_square_1(A,B)))))) # label(t53_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4153 $T # label(t27_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4154 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k3_square_1(A,A) = A)) # label(idempotence_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4155 (all A (v1_xcmplx_0(A) -> k5_square_1(k6_xcmplx_0(A,np__1)) = k2_xcmplx_0(k6_xcmplx_0(k5_square_1(A),k3_xcmplx_0(np__2,A)),np__1))) # label(t66_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4156 $T # label(t3_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4157 $T # label(t4_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4158 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k2_square_1(A,B)))) # label(dt_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4159 $T # label(t62_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4160 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> k2_square_1(B,A) = k2_square_1(A,B))) # label(commutativity_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4161 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> A = k2_square_1(A,k1_square_1(A,B)))))) # label(t54_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4162 $T # label(t33_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4163 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> r1_xreal_0(k1_square_1(A,B),A))))) # label(t35_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4164 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k2_square_1(A,C),B) <-> r1_xreal_0(C,B) & r1_xreal_0(A,B)))))))) # label(t50_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4165 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k2_xcmplx_0(k5_square_1(A),k3_xcmplx_0(k3_xcmplx_0(np__2,A),B)),k5_square_1(B)) = k5_square_1(k2_xcmplx_0(A,B)))))) # label(t63_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4166 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) -> k7_xcmplx_0(A,k8_square_1(A)) = k8_square_1(A)))) # label(t103_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4167 $T # label(t7_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4168 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k5_square_1(A)) & v1_xreal_0(k5_square_1(A)))) # label(fc2_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4169 $T # label(t88_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4170 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> A = k8_square_1(k5_square_1(A))))) # label(t89_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4171 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-(r1_xreal_0(A,np__0) & r1_xreal_0(B,np__0)) & -(r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A)) & r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t25_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4172 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> A = k1_square_1(A,A))) # label(idempotence_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4173 $T # label(t10_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4174 $T # label(t31_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4175 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> A = B | k7_xcmplx_0(k6_xcmplx_0(k8_square_1(A),k8_square_1(B)),k6_xcmplx_0(A,B)) = k7_xcmplx_0(np__1,k2_xcmplx_0(k8_square_1(A),k8_square_1(B)))))))) # label(t105_square_1) # label(axiom) # label(non_clause). [assumption]. 67.74/65.62 4176 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k1_square_1(A,B)))) # label(dt_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4177 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,np__0) -> k4_xcmplx_0(A) = k8_square_1(k5_square_1(A))))) # label(t90_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4178 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k4_square_1(A,B),k1_numbers))) # label(dt_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4179 $T # label(t98_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4180 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k1_square_1(k2_square_1(A,B),k2_square_1(A,C)) = k2_square_1(A,k1_square_1(B,C)))))))) # label(t57_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4181 $T # label(t6_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4182 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> k7_xcmplx_0(np__1,k2_xcmplx_0(k8_square_1(B),k8_square_1(A))) = k7_xcmplx_0(k6_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A)) | r1_xreal_0(B,A)))))) # label(t106_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4183 $T # label(t22_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4184 $T # label(t91_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4185 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k2_xcmplx_0(k5_square_1(A),k3_xcmplx_0(np__2,A)),np__1) = k5_square_1(k2_xcmplx_0(A,np__1)))) # label(t65_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4186 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k1_square_1(A,k1_square_1(B,C)) = k1_square_1(k1_square_1(A,B),C))))))) # label(t40_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4187 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k9_square_1(A),k1_numbers))) # label(dt_k9_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4188 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k2_square_1(k1_square_1(A,B),k1_square_1(A,C)) = k1_square_1(A,k2_square_1(B,C)))))))) # label(t56_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4189 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k1_square_1(A,B) = k3_square_1(A,B))) # label(redefinition_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4190 $T # label(t9_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4191 $T # label(t23_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4192 $T # label(t81_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4193 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) -> k7_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B))) = k7_xcmplx_0(np__1,k2_xcmplx_0(A,B))))))) # label(t70_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4194 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> k1_square_1(B,A) = k1_square_1(A,B))) # label(commutativity_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4195 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) & k8_square_1(B) = k8_square_1(A) -> A = B))))) # label(t96_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4196 $T # label(t19_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4197 (all A (v1_xreal_0(A) -> (np__0 = k8_square_1(A) & r1_xreal_0(np__0,A) -> np__0 = A))) # label(t92_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4198 (all A (m1_subset_1(A,k1_numbers) -> k9_square_1(A) = k8_square_1(A))) # label(redefinition_k9_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4199 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k5_square_1(A),k5_square_1(B)) = k5_square_1(k3_xcmplx_0(A,B)))))) # label(t68_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4200 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k2_square_1(k2_square_1(A,B),C) = k2_square_1(A,k2_square_1(B,C)))))))) # label(t51_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4201 $T # label(t32_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4202 (all A (v1_xreal_0(A) -> -(r1_xreal_0(np__1,k7_xcmplx_0(np__1,A)) & -r1_xreal_0(A,np__1)))) # label(t2_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4203 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(k8_square_1(A),k8_square_1(B))))))) # label(t94_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4204 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) -> k7_xcmplx_0(np__1,k8_square_1(A)) = k7_xcmplx_0(k8_square_1(A),A)))) # label(t102_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4205 $T # label(t37_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4206 $T # label(t43_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4207 $T # label(t20_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4208 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> A = k2_square_1(A,A))) # label(idempotence_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4209 (all A (v1_xreal_0(A) -> -(r1_xreal_0(A,k5_square_1(A)) & -r1_xreal_0(A,np__0) & -r1_xreal_0(np__1,A)))) # label(t75_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4210 $T # label(t41_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4211 $T # label(t34_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4212 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> A = k4_square_1(A,A))) # label(idempotence_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4213 $T # label(t1_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4214 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k1_square_1(A,k2_square_1(A,B)) = A)))) # label(t55_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4215 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k5_square_1(B),k5_square_1(A)) & r1_xreal_0(np__0,A) & -r1_xreal_0(B,A)))))) # label(t78_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4216 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k4_square_1(A,B) = k2_square_1(A,B))) # label(redefinition_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4217 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k6_xcmplx_0(k5_square_1(A),k3_xcmplx_0(k3_xcmplx_0(np__2,A),B)),k5_square_1(B)) = k5_square_1(k6_xcmplx_0(A,B)))))) # label(t64_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4218 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_square_1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k5_square_1(A),k5_square_1(B)))))) # label(t69_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4219 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> A = k2_square_1(A,B) | k2_square_1(A,B) = B)))) # label(t49_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4220 $T # label(t18_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4221 (all A (v1_xreal_0(A) -> v1_xreal_0(k8_square_1(A)))) # label(dt_k8_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4222 $T # label(t5_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4223 $T # label(t87_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4224 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k4_square_1(A,B) = k4_square_1(B,A))) # label(commutativity_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4225 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) = k3_xcmplx_0(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)))))) # label(t67_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4226 $T # label(t30_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4227 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) -> k8_square_1(k7_xcmplx_0(np__1,A)) = k7_xcmplx_0(np__1,k8_square_1(A))))) # label(t101_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4228 $T # label(t8_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4229 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(B,A) | k7_xcmplx_0(k2_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A)) = k7_xcmplx_0(np__1,k6_xcmplx_0(k8_square_1(B),k8_square_1(A)))))))) # label(t108_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4230 $T # label(t79_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4231 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (p2_s1_square_1(B) & p1_s1_square_1(A) -> r1_xreal_0(A,B)))))) -> (exists A (v1_xreal_0(A) & (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (p1_s1_square_1(B) & p2_s1_square_1(C) -> r1_xreal_0(A,C) & r1_xreal_0(B,A)))))))) # label(s1_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4232 $T # label(t16_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4233 $T # label(t26_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4234 $T # label(t42_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4235 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> k3_xcmplx_0(k8_square_1(A),k8_square_1(B)) = k8_square_1(k3_xcmplx_0(A,B))))))) # label(t97_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4236 (all A (m1_subset_1(A,k2_numbers) -> v1_xcmplx_0(A))) # label(cc1_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4237 $T # label(t47_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4238 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (-r1_xreal_0(B,A) -> B = k2_square_1(A,B)) & (r1_xreal_0(B,A) -> k2_square_1(A,B) = A))))) # label(d2_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4239 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k6_square_1(A),k2_numbers))) # label(dt_k6_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4240 $T # label(t12_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4241 $T # label(t52_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4242 $T # label(t45_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4243 $T # label(t14_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4244 (all A (v1_xcmplx_0(A) -> k5_square_1(A) = k3_xcmplx_0(A,A))) # label(d3_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4245 $T # label(t21_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4246 $T # label(t17_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4247 $T # label(t29_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4248 (all A (v1_xcmplx_0(A) -> (np__0 = k5_square_1(A) -> A = np__0))) # label(t73_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4249 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k3_square_1(B,A) = k3_square_1(A,B))) # label(commutativity_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4250 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> B = k1_square_1(A,B) | A = k1_square_1(A,B))))) # label(t38_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4251 (all A (m1_subset_1(A,k1_numbers) -> k7_square_1(A) = k5_square_1(A))) # label(redefinition_k7_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4252 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> k7_xcmplx_0(k2_xcmplx_0(k8_square_1(A),k8_square_1(B)),k6_xcmplx_0(A,B)) = k7_xcmplx_0(np__1,k6_xcmplx_0(k8_square_1(A),k8_square_1(B)))))))) # label(t107_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4253 $T # label(t44_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4254 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__1) & r1_xreal_0(k5_square_1(A),A)))) # label(t76_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4255 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k8_square_1(B),k8_square_1(A)) & r1_xreal_0(np__0,A) & -r1_xreal_0(B,A)))))) # label(t95_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4256 $T # label(t15_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4257 $T # label(t100_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4258 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(k5_square_1(A),k5_square_1(B))))))) # label(t77_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4259 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> (all B (v1_xreal_0(B) -> (k8_square_1(A) = B <-> r1_xreal_0(np__0,B) & k5_square_1(B) = A)))))) # label(d4_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4260 $T # label(t48_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4261 $T # label(t28_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4262 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k8_square_1(A),np__0)))) # label(t93_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4263 (all A (v1_xreal_0(A) -> r1_xreal_0(np__0,k5_square_1(A)))) # label(t72_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4264 $T # label(t11_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4265 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> r1_xreal_0(A,k2_square_1(A,B)))))) # label(t46_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4266 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> k6_xcmplx_0(A,B) = k3_xcmplx_0(k6_xcmplx_0(k8_square_1(A),k8_square_1(B)),k2_xcmplx_0(k8_square_1(A),k8_square_1(B)))))))) # label(t104_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4267 $T # label(t58_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4268 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k5_square_1(A)))) # label(fc1_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4269 $T # label(t36_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4270 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k5_square_1(A),np__0) & np__0 != A))) # label(t74_square_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4271 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(A,B) <-> B = k3_xcmplx_0(A,k3_nat_1(B,A))))))) # label(t49_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4272 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (-((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(A = k2_xcmplx_0(k3_xcmplx_0(B,C),D) & -r1_xreal_0(B,D)))) & -(np__0 = B & C = np__0)) <-> C = k3_nat_1(A,B)))))))) # label(d1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4273 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k2_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4274 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(r1_xreal_0(k2_xcmplx_0(B,A),B) & np__0 != A))))) # label(t41_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4275 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (r2_hidden(np__0,A) & (all B (m1_subset_1(B,k1_numbers) -> (r2_hidden(B,A) -> r2_hidden(k3_real_1(B,np__1),A)))) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r2_hidden(B,A)))))) # label(t2_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4276 $T # label(t12_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4277 $T # label(t25_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4278 (exists A (v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & -v1_xboole_0(A))) # label(rc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4279 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (k4_nat_1(A,B) = np__0 -> k3_nat_1(k2_xcmplx_0(A,C),B) = k1_nat_1(k3_nat_1(A,B),k3_nat_1(C,B))))))))) # label(t69_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4280 $T # label(t14_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4281 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4282 $T # label(t45_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4283 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (-r1_xreal_0(A,B) -> p1_s4_nat_1(B)))) -> p1_s4_nat_1(A)))) -> (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> p1_s4_nat_1(A))) # label(s4_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4284 $T # label(t32_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4285 $T # label(t6_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4286 $T # label(t7_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4287 $T # label(t17_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4288 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(r1_xreal_0(A,B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k2_xcmplx_0(A,C) != B))))))) # label(t28_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4289 $T # label(t33_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4290 (all A (v4_ordinal2(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v4_ordinal2(A))) # label(cc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4291 (all A all B (v4_ordinal2(B) & -v1_xboole_0(B) & v4_ordinal2(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)))) # label(fc4_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4292 (all A (v4_ordinal2(A) -> (-r1_xreal_0(np__1,A) -> np__0 = A))) # label(t39_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4293 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> k4_nat_1(k2_xcmplx_0(k4_nat_1(A,C),B),C) = k4_nat_1(k2_xcmplx_0(A,B),C))))))) # label(t74_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4294 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(B,A) -> r1_xreal_0(A,np__0) | r1_xreal_0(B,A)))))) # label(t54_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4295 $T # label(t10_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4296 (all A (v4_ordinal2(A) -> -(A != np__0 & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k1_nat_1(B,np__1) != A))))) # label(t22_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4297 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(k2_xcmplx_0(A,B),A) <-> r1_xreal_0(np__1,B)))))) # label(t59_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4298 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> np__0 = k4_nat_1(k3_xcmplx_0(A,B),A))))) # label(t63_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4299 $T # label(t24_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4300 $T # label(t31_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4301 (all A (v4_ordinal2(A) -> r1_xreal_0(np__0,A))) # label(t18_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4302 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(A,B) & r1_nat_1(B,A) -> B = A))))) # label(t52_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4303 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(p1_s7_nat_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r1_xreal_0(A,B) & p1_s7_nat_1(B)))) & A != np__0))) & (exists A (p1_s7_nat_1(A) & m2_subset_1(A,k1_numbers,k5_numbers))) -> p1_s7_nat_1(np__0) # label(s7_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4304 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k5_nat_1(B,A) = k5_nat_1(A,B))) # label(commutativity_k5_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4305 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (-(-(np__0 = A & f1_s3_nat_1 = B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(p1_s3_nat_1(C,D) & B = f2_s3_nat_1(A,D) & A = k1_nat_1(C,np__1))))))) <-> p1_s3_nat_1(A,B)))))) -> (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & p1_s3_nat_1(A,B))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (p1_s3_nat_1(A,C) & p1_s3_nat_1(A,B) -> B = C))))))) # label(s3_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4306 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> m2_subset_1(k6_xcmplx_0(B,A),k1_numbers,k5_numbers)))))) # label(t61_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4307 $T # label(t3_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4308 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k2_xcmplx_0(A,B) = k1_nat_1(A,B))) # label(redefinition_k1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4309 $T # label(t11_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4310 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> m2_subset_1(k4_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k4_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4311 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(A,np__0) -> k2_xcmplx_0(k3_xcmplx_0(A,k3_nat_1(B,A)),k4_nat_1(B,A)) = B))))) # label(t47_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4312 $T # label(t16_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4313 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (-r1_xreal_0(A,np__0) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (exists C ((exists D (B = k1_nat_1(k2_nat_1(A,C),D) & -r1_xreal_0(A,D) & m2_subset_1(D,k1_numbers,k5_numbers))) & m2_subset_1(C,k1_numbers,k5_numbers)))))))) # label(t42_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4314 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (np__0 != B -> k3_nat_1(k2_nat_1(A,B),B) = A))))) # label(t72_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4315 $T # label(t30_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4316 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k1_nat_1(B,A) = k1_nat_1(A,B))) # label(commutativity_k1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4317 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> k4_nat_1(k2_xcmplx_0(A,k4_nat_1(B,C)),C) = k4_nat_1(k2_xcmplx_0(A,B),C))))))) # label(t75_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4318 (exists A (-v1_xboole_0(A) & v3_ordinal1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)))) # label(rc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4319 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> m2_subset_1(k3_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k3_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4320 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_nat_1(f1_s8_nat_1(A),f1_s8_nat_1(k1_nat_1(A,np__1))) = f1_s8_nat_1(k1_nat_1(A,np__2)))) & -r1_xreal_0(f3_s8_nat_1,np__0) & -r1_xreal_0(f2_s8_nat_1,f3_s8_nat_1) & f2_s8_nat_1 = f1_s8_nat_1(np__0) & f1_s8_nat_1(np__1) = f3_s8_nat_1 -> (exists A (m2_subset_1(A,k1_numbers,k5_numbers) & f1_s8_nat_1(A) = k6_nat_1(f2_s8_nat_1,f3_s8_nat_1) & np__0 = f1_s8_nat_1(k1_nat_1(A,np__1)))) # label(s8_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4321 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k2_nat_1(B,A) = k2_nat_1(A,B))) # label(commutativity_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4322 (all A (m1_subset_1(A,k5_numbers) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v4_ordinal2(A))) # label(cc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4323 $T # label(t48_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4324 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(r1_xreal_0(B,k2_xcmplx_0(A,np__1)) & B != A & B != k2_xcmplx_0(A,np__1) & r1_xreal_0(A,B)))))) # label(t27_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.62 4325 (exists A (p1_s5_nat_1(A) & m2_subset_1(A,k1_numbers,k5_numbers))) -> (exists A ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (p1_s5_nat_1(B) -> r1_xreal_0(A,B)))) & m2_subset_1(A,k1_numbers,k5_numbers) & p1_s5_nat_1(A))) # label(s5_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4326 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,B) & r1_nat_1(B,C) -> r1_nat_1(A,C)))))))) # label(t51_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4327 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> r1_nat_1(A,A))) # label(reflexivity_r1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4328 (exists A (m1_subset_1(A,k5_numbers) & v2_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A) & v3_ordinal1(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A))) # label(rc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4329 (all A (v4_ordinal2(A) -> np__0 = k4_nat_1(A,A))) # label(t77_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4330 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(A,k4_nat_1(B,A))))))) # label(t46_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4331 (all A (v4_ordinal2(A) -> -r1_xreal_0(k2_xcmplx_0(A,np__1),np__0))) # label(t21_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4332 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(A,np__1) -> k4_nat_1(np__1,A) = np__1))))) # label(t64_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4333 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(A,B) -> r1_xreal_0(A,k2_xcmplx_0(B,C))))))))) # label(t37_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4334 (all A all B (v4_ordinal2(B) & -v1_xboole_0(B) & v4_ordinal2(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4335 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> k4_nat_1(k2_xcmplx_0(k3_xcmplx_0(B,C),A),B) = k4_nat_1(A,B))))))) # label(t73_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4336 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(A,B) -> B = k4_nat_1(B,A)))))) # label(t76_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4337 $T # label(t5_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4338 $T # label(t15_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4339 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,C) & r1_nat_1(A,B) -> r1_nat_1(A,k4_nat_1(B,C))))))))) # label(t58_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4340 (all A (m1_subset_1(A,k5_numbers) -> v1_xreal_0(A) & v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A) & v1_xcmplx_0(A) & -v3_xreal_0(A))) # label(cc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4341 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(B,A) -> m2_subset_1(k6_xcmplx_0(B,np__1),k1_numbers,k5_numbers)))))) # label(t60_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4342 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> (k2_xcmplx_0(k3_xcmplx_0(B,D),F) = A & A = k2_xcmplx_0(k3_xcmplx_0(B,C),E) -> r1_xreal_0(B,F) | F = E & C = D | r1_xreal_0(B,E)))))))))))))) # label(t43_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4343 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) <-> -r1_xreal_0(k2_xcmplx_0(B,np__1),A)))))) # label(t38_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4344 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(A,B) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C))))))))) # label(t20_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4345 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k6_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k6_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4346 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k6_nat_1(A,B) = k6_nat_1(B,A))) # label(commutativity_k6_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4347 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (p1_s1_nat_1(A) -> p1_s1_nat_1(k1_nat_1(A,np__1))))) & p1_s1_nat_1(np__0) -> (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> p1_s1_nat_1(A))) # label(s1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4348 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k3_xcmplx_0(A,B) = np__1 -> B = np__1 & A = np__1))))) # label(t40_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4349 (all A (v4_ordinal2(A) -> -(A != np__0 & r1_xreal_0(A,np__0)))) # label(t19_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4350 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k6_nat_1(A,B) = C <-> r1_nat_1(C,B) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_nat_1(D,B) & r1_nat_1(D,A) -> r1_nat_1(D,C)))) & r1_nat_1(C,A)))))))) # label(d5_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4351 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(-r1_xreal_0(np__2,A) & np__0 != A & A != np__1))) # label(t71_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4352 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_nat_1(A,C) & r1_nat_1(B,C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_nat_1(A,D) & r1_nat_1(B,D) -> r1_nat_1(C,D)))) <-> C = k5_nat_1(A,B)))))))) # label(d4_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4353 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> v4_ordinal2(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4354 (all A (v4_ordinal2(A) -> k4_nat_1(A,np__2) = np__1 | k4_nat_1(A,np__2) = np__0)) # label(t62_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4355 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_xreal_0(A,k2_xcmplx_0(A,B)))))) # label(t29_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4356 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k5_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k5_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4357 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r1_xreal_0(k1_nat_1(B,np__1),A) & r1_xreal_0(B,A) & A != B))))) # label(t70_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4358 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (np__0 = k4_nat_1(A,C) -> k4_nat_1(B,C) = k4_nat_1(k2_xcmplx_0(A,B),C)))))))) # label(t67_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4359 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(-r1_xreal_0(A,B) & A != k2_xcmplx_0(B,np__1) & r1_xreal_0(A,k2_xcmplx_0(B,np__1))))))) # label(t26_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4360 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,C) & r1_nat_1(A,B) -> r1_nat_1(A,k2_xcmplx_0(B,C))))))))) # label(t55_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4361 (all A (v4_ordinal2(A) -> r1_nat_1(A,np__0) & r1_nat_1(np__1,A))) # label(t53_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4362 $T # label(t50_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4363 $T # label(t8_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4364 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k6_nat_1(A,A) = A)) # label(idempotence_k6_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4365 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & B = k3_xcmplx_0(A,C))) <-> r1_nat_1(A,B)))))) # label(d3_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4366 (all A (v4_ordinal2(A) -> k4_nat_1(np__0,A) = np__0)) # label(t78_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4367 $T # label(t4_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4368 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k5_nat_1(A,A) = A)) # label(idempotence_k5_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4369 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (A != np__0 -> B = k3_nat_1(k3_xcmplx_0(A,B),A)))))) # label(t68_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4370 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,B) -> r1_nat_1(A,k3_xcmplx_0(B,C))))))))) # label(t56_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4371 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (np__0 = k4_nat_1(A,C) & k6_xcmplx_0(A,k3_xcmplx_0(D,C)) = B -> k4_nat_1(B,C) = np__0))))))))) # label(t65_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4372 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,B) & r1_nat_1(A,k2_xcmplx_0(B,C)) -> r1_nat_1(A,C)))))))) # label(t57_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4373 $T # label(t9_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4374 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4375 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k2_nat_1(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4376 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_xcmplx_0(A,B) = np__0 -> np__0 = B & np__0 = A))))) # label(t23_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4377 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (k4_nat_1(A,C) = np__0 -> B = k4_nat_1(k2_xcmplx_0(A,B),C) | r1_xreal_0(C,B) | C = np__0))))))) # label(t66_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4378 $T # label(t34_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4379 $T # label(t13_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4380 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k4_nat_1(A,B) = C <-> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(-r1_xreal_0(B,C) & k2_xcmplx_0(k3_xcmplx_0(B,D),C) = A))) & -(C = np__0 & B = np__0))))))))) # label(d2_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4381 $T # label(t44_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4382 $T # label(t35_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4383 p1_s2_nat_1(np__0) & (all A (v4_ordinal2(A) -> (p1_s2_nat_1(A) -> p1_s2_nat_1(k2_xcmplx_0(A,np__1))))) -> (all A (v4_ordinal2(A) -> p1_s2_nat_1(A))) # label(s2_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4384 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (p1_s6_nat_1(A) -> r1_xreal_0(A,f1_s6_nat_1)))) & (exists A (m2_subset_1(A,k1_numbers,k5_numbers) & p1_s6_nat_1(A))) -> (exists A ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (p1_s6_nat_1(B) -> r1_xreal_0(B,A)))) & p1_s6_nat_1(A) & m2_subset_1(A,k1_numbers,k5_numbers))) # label(s6_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4385 $T # label(t1_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4386 $T # label(t36_nat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4387 (all A (v1_xreal_0(A) -> r1_xreal_0(k1_int_1(A),k2_int_1(A)))) # label(t61_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4388 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(A,np__1),k1_int_1(A)) & -r1_xreal_0(A,k6_xcmplx_0(k1_int_1(A),np__1)))) # label(t50_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4389 (all A all B (v1_int_1(A) & v1_int_1(B) -> r2_int_1(A,A))) # label(reflexivity_r2_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4390 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4391 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc9_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4392 (all A (v1_xreal_0(A) -> m1_subset_1(k4_int_1(A),k1_numbers))) # label(dt_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4393 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4394 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4395 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4396 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4397 (all A (v1_xreal_0(A) -> A = k2_xcmplx_0(k1_int_1(A),k4_int_1(A)))) # label(t68_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4398 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> ((exists D (k6_xcmplx_0(A,B) = k3_xcmplx_0(C,D) & v1_int_1(D))) <-> r1_int_1(A,B,C)))))))) # label(d3_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4399 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4400 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))) # label(t20_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4401 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)))) # label(fc7_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4402 (all A (v1_int_1(A) -> k6_int_1(A,A) = np__0)) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4403 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),A))) # label(t52_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4404 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4405 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4406 (all A (v1_xreal_0(A) -> k3_int_1(A) = k4_int_1(A))) # label(redefinition_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4407 (all A ((all B (-(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B != k1_real_1(C) & C != B)) <-> r2_hidden(B,A))) <-> k4_numbers = A)) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4408 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4409 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4410 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(A,k6_xcmplx_0(B,np__1))))))) # label(t79_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4411 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E),C)))))))))))) # label(t39_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4412 (all A (v1_int_1(A) -> (p1_s4_int_1(A) -> p1_s4_int_1(k6_xcmplx_0(A,np__1)) & p1_s4_int_1(k2_xcmplx_0(A,np__1))))) & p1_s4_int_1(f1_s4_int_1) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4413 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4414 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4415 (all A (v1_xreal_0(A) -> k1_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t63_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4416 (all A (v1_int_1(A) -> v1_int_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4417 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (k2_xcmplx_0(B,A) = C -> r1_xreal_0(B,C)))))))) # label(t19_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4418 (exists A (m1_subset_1(A,k1_numbers) & v1_xreal_0(A) & v1_int_1(A) & v1_xcmplx_0(A))) # label(rc1_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4419 (all A (v1_int_1(A) -> v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4420 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4421 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,k1_int_1(A)) & v1_int_1(A)) & -(-v1_int_1(A) & r1_xreal_0(A,k1_int_1(A))))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4422 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k6_int_1(A,B)))) # label(dt_k6_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4423 (all A (v1_xreal_0(A) -> (k4_int_1(A) = np__0 <-> v1_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4424 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (r1_xreal_0(A,B) -> r2_hidden(k6_xcmplx_0(B,A),k5_numbers)))))) # label(t18_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4425 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k1_int_1(A),B) = k1_int_1(k2_xcmplx_0(A,B)))))) # label(t51_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4426 (all A (v1_int_1(A) -> (p1_s3_int_1(A) & r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(k6_xcmplx_0(A,np__1))))) & p1_s3_int_1(f1_s3_int_1) -> (all A (v1_int_1(A) -> (r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(A)))) # label(s3_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4427 (all A (v1_xreal_0(A) -> k1_int_1(k4_int_1(A)) = np__0)) # label(t70_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4428 (all A (v1_int_1(A) -> (-r1_xreal_0(np__0,A) -> r1_xreal_0(A,k1_real_1(np__1))))) # label(t21_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4429 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (A = np__1 & k1_real_1(np__1) = B | k1_real_1(np__1) = A & np__1 = B <-> k3_xcmplx_0(A,B) = k1_real_1(np__1)))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4430 (all A (v1_int_1(A) -> (p1_s5_int_1(A) -> r1_xreal_0(f1_s5_int_1,A)))) & (exists A (p1_s5_int_1(A) & v1_int_1(A))) -> (exists A (v1_int_1(A) & p1_s5_int_1(A) & (all B (v1_int_1(B) -> (p1_s5_int_1(B) -> r1_xreal_0(A,B)))))) # label(s5_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4431 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc1_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4432 (all A (v1_int_1(A) -> (p1_s6_int_1(A) -> r1_xreal_0(A,f1_s6_int_1)))) & (exists A (v1_int_1(A) & p1_s6_int_1(A))) -> (exists A (v1_int_1(A) & p1_s6_int_1(A) & (all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4433 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4434 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,A,B))))) # label(t32_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4435 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (np__0 != B -> k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B)) = k6_int_1(A,B)) & (np__0 = B -> np__0 = k6_int_1(A,B)))))) # label(d8_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4436 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4437 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4438 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(k2_xcmplx_0(A,np__1),B) & r1_xreal_0(A,B) <-> k2_int_1(A) = B))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4439 (all A (v1_xreal_0(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> A != k1_real_1(B) & B != A)) & v1_int_1(A)))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4440 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4441 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,B,np__1))))) # label(t34_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4442 (all A (v1_xreal_0(A) -> (np__0 != A -> np__1 = k1_int_1(k7_xcmplx_0(A,A))))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4443 (all A (v1_xreal_0(A) -> k2_int_1(A) = k2_int_1(k2_int_1(A)))) # label(t64_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4444 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k2_int_1(A),k1_int_1(A)) & v1_int_1(A)) & -(r1_xreal_0(k2_int_1(A),k1_int_1(A)) & -v1_int_1(A)))) # label(t60_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4445 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_int_1(A),k6_xcmplx_0(A,np__1)) & -r1_xreal_0(k2_xcmplx_0(k2_int_1(A),np__1),A))) # label(t57_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4446 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4447 (all A (m1_subset_1(A,k5_numbers) -> v1_int_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4448 (all A (v1_xreal_0(A) -> k6_xcmplx_0(A,k1_int_1(A)) = k3_int_1(A))) # label(d6_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4449 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k2_int_1(A)) & r1_xreal_0(np__0,k1_int_1(A)) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers)))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4450 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),C)))))))))))) # label(t37_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4451 (all A (v1_int_1(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(A,k1_int_1(B))))))) # label(t81_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4452 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4453 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4454 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4455 (all A (r2_hidden(A,k4_numbers) <-> v1_int_1(A))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4456 (all A (m1_subset_1(A,k5_numbers) -> -v3_xreal_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v1_int_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v2_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4457 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4458 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k3_int_1(A)) & v1_xreal_0(k3_int_1(A)))) # label(fc10_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4459 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4460 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k2_int_1(A),B) = k2_int_1(k2_xcmplx_0(A,B)))))) # label(t58_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4461 (exists A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) & (all B (v1_int_1(B) -> (p1_s1_int_1(B) <-> r2_hidden(B,A)))))) # label(s1_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4462 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4463 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (A = B | A = k4_xcmplx_0(B) -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4464 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4465 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4466 (all A (v1_xreal_0(A) -> -r1_xreal_0(np__1,k4_int_1(A)) & r1_xreal_0(np__0,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4467 (all A (v1_int_1(A) -> k5_int_1(A,np__0) = np__0)) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4468 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4469 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(k2_xcmplx_0(A,C),B,C) <-> r1_int_1(A,B,C)))))))) # label(t42_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4470 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(C = k6_xcmplx_0(B,A) & r1_xreal_0(np__1,C)))) & -r1_xreal_0(B,A)))))) # label(t78_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4471 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k2_int_1(A),A) & v1_int_1(A)) & -(r1_xreal_0(k2_int_1(A),A) & -v1_int_1(A)))) # label(t55_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4472 (all A (v1_xreal_0(A) -> (v1_int_1(A) -> v1_int_1(k6_xcmplx_0(A,np__1)) & v1_int_1(k2_xcmplx_0(A,np__1))))) # label(t17_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4473 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_xreal_0(np__0,k5_int_1(A,B)))))) # label(t82_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4474 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,C) & r1_xreal_0(A,B) -> C = B | r1_xreal_0(k2_xcmplx_0(A,np__1),B) | r1_xreal_0(k2_xcmplx_0(A,np__1),C)))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4475 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4476 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (r2_int_1(A,B) <-> (exists C (k3_xcmplx_0(A,C) = B & v1_int_1(C)))))))) # label(d9_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4477 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(k6_xcmplx_0(A,C),B,C) <-> r1_int_1(A,B,C)))))))) # label(t43_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4478 (all A (v1_int_1(A) -> r1_int_1(A,np__0,A) & r1_int_1(np__0,A,A))) # label(t33_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4479 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4480 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4481 (all A (v1_int_1(A) -> (p1_s2_int_1(A) & r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) & p1_s2_int_1(f1_s2_int_1) -> (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(A)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4482 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (k3_xcmplx_0(A,B) = C & r1_int_1(D,E,C) -> r1_int_1(D,E,A)))))))))))) # label(t41_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4483 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4484 (all A (v1_xreal_0(A) -> k2_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t65_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4485 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4486 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(D,E,C) & r1_int_1(A,B,C) -> r1_int_1(k6_xcmplx_0(A,D),k6_xcmplx_0(B,E),C)))))))))))) # label(t38_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4487 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4488 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k2_int_1(A) = k1_int_1(A)))) # label(t59_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4489 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4490 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4491 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,k6_xcmplx_0(A,np__1)) & r1_xreal_0(B,A) <-> B = k1_int_1(A)))))) # label(d4_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4492 (all A (v1_int_1(A) -> (r1_xreal_0(np__0,A) -> r2_hidden(A,k5_numbers)))) # label(t16_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4493 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> k5_int_1(A,B) = k1_int_1(k7_xcmplx_0(A,B)))))) # label(d7_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4494 (all A (v1_xreal_0(A) -> k1_int_1(k2_int_1(A)) = k2_int_1(A))) # label(t62_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4495 (all A (v1_int_1(A) -> (np__0 != A -> k5_int_1(A,A) = np__1))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4496 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(A,k6_xcmplx_0(C,B),D) <-> r1_int_1(k2_xcmplx_0(A,B),C,D)))))))))) # label(t40_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4497 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(B,D,C) & r1_int_1(A,B,C) -> r1_int_1(A,D,C)))))))))) # label(t36_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4498 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k1_real_1(np__1) = A & k1_real_1(np__1) = B | A = np__1 & B = np__1 <-> k3_xcmplx_0(A,B) = np__1))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4499 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) -> r1_int_1(B,A,C)))))))) # label(t35_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4500 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc4_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4501 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4502 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4503 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> A = k1_int_1(A)))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4504 (all A (v1_xreal_0(A) -> (A = k2_int_1(A) <-> v1_int_1(A)))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4505 (all A (v1_xreal_0(A) -> (k2_int_1(A) = k1_int_1(A) <-> k2_int_1(A) != k2_xcmplx_0(k1_int_1(A),np__1)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4506 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k4_int_1(A),np__0) & v1_int_1(A)) & -(-v1_int_1(A) & r1_xreal_0(k4_int_1(A),np__0)))) # label(t72_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4507 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(C,A) & r1_xreal_0(B,A) -> r1_xreal_0(B,k6_xcmplx_0(A,np__1)) | r1_xreal_0(C,k6_xcmplx_0(A,np__1)) | C = B))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4508 $T # label(t35_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4509 $T # label(t20_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4510 (all A all B (v1_rat_1(A) & m1_subset_1(B,k5_numbers) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_rat_1(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc12_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4511 (all A (v1_rat_1(A) -> r1_xreal_0(k2_real_1(k1_rat_1(A)),np__1))) # label(t34_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4512 (all A all B (v1_rat_1(B) & m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_rat_1(k3_xcmplx_0(A,B)))) # label(fc15_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4513 (all A (v1_rat_1(A) -> -(-r1_xreal_0(k4_xcmplx_0(k2_rat_1(A)),k1_rat_1(A)) & r1_xreal_0(k1_real_1(np__1),A)) & -(-r1_xreal_0(k1_real_1(np__1),A) & r1_xreal_0(k4_xcmplx_0(k2_rat_1(A)),k1_rat_1(A))))) # label(t66_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4514 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> -(np__0 != B & (all D (v1_int_1(D) -> -(B = k3_xcmplx_0(k1_rat_1(C),D) & k3_xcmplx_0(k2_rat_1(C),D) = A))) & C = k7_xcmplx_0(A,B)))))))) # label(t61_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4515 (exists A (m1_subset_1(A,k1_numbers) & v1_rat_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(rc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4516 (all A all B (m1_subset_1(A,k5_numbers) & v1_rat_1(B) -> v1_rat_1(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc13_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4517 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k2_rat_1(A) = k2_rat_1(B) & k1_rat_1(B) = k1_rat_1(A) -> B = A))))) # label(t84_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4518 $T # label(t74_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4519 $T # label(t19_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4520 $T # label(t4_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4521 (all A (v1_rat_1(A) -> (A = k1_real_1(np__1) <-> k4_xcmplx_0(k2_rat_1(A)) = k1_rat_1(A)))) # label(t49_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4522 $T # label(t54_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4523 (all A (v1_int_1(A) -> (all B (v1_rat_1(B) -> (np__0 != A -> B = k7_xcmplx_0(k3_xcmplx_0(k2_rat_1(B),A),k3_xcmplx_0(k1_rat_1(B),A))))))) # label(t50_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4524 (all A all B (v1_rat_1(B) & m1_subset_1(A,k5_numbers) -> v1_rat_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc14_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4525 (all A (v1_rat_1(A) -> -(r1_xreal_0(k1_rat_1(A),np__1) & -v1_int_1(A)) & -(-r1_xreal_0(k1_rat_1(A),np__1) & v1_int_1(A)))) # label(t45_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4526 $T # label(t11_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4527 (all A (v1_rat_1(A) -> (A != np__0 -> k7_xcmplx_0(k2_rat_1(A),A) = k1_rat_1(A)))) # label(t38_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4528 $T # label(t83_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4529 (all A (v1_rat_1(A) -> (r1_xreal_0(A,k1_real_1(np__1)) <-> r1_xreal_0(k2_rat_1(A),k1_real_1(k1_rat_1(A)))))) # label(t65_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4530 $T # label(t13_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4531 $T # label(t5_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4532 (all A (v1_rat_1(A) -> r1_xreal_0(np__1,k1_rat_1(A)))) # label(t29_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4533 (all A (v1_rat_1(A) -> (r1_xreal_0(np__0,A) -> k1_rat_1(A) != np__1 & k2_rat_1(A) != A | m2_subset_1(A,k1_numbers,k5_numbers)))) # label(t44_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4534 (all A (v1_rat_1(A) -> -(-r1_xreal_0(np__0,k2_rat_1(A)) & r1_xreal_0(np__0,A)) & -(r1_xreal_0(np__0,k2_rat_1(A)) & -r1_xreal_0(np__0,A)))) # label(t76_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4535 (all A (v1_rat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (v1_int_1(C) & k7_xcmplx_0(C,B) = A)) & B != np__0 & (all C (v1_int_1(C) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k7_xcmplx_0(C,D) = A -> np__0 = D | r1_xreal_0(B,D)))))) <-> B = k1_rat_1(A)))))) # label(d3_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4536 $T # label(t39_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4537 $T # label(t79_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4538 $T # label(t9_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4539 (all A (v1_rat_1(A) -> (k2_rat_1(A) = k1_real_1(k1_rat_1(A)) <-> A = k1_real_1(np__1)))) # label(t48_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4540 $T # label(t53_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4541 (all A (v1_rat_1(A) <-> r2_hidden(A,k3_numbers))) # label(d2_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4542 $T # label(t17_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4543 $T # label(t33_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4544 $T # label(t82_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4545 $T # label(t14_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4546 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k7_xcmplx_0(np__1,A) = B -> k1_rat_1(A) = k2_rat_1(B) & k2_rat_1(A) = k1_rat_1(B) | r1_xreal_0(A,np__0)) & (k1_rat_1(B) = k2_rat_1(A) & k1_rat_1(A) = k2_rat_1(B) -> -r1_xreal_0(A,np__0) & k7_xcmplx_0(np__1,A) = B))))) # label(t88_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4547 $T # label(t75_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4548 (all A all B (v1_rat_1(A) & m1_subset_1(B,k5_numbers) -> v1_rat_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc11_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4549 $T # label(t69_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4550 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,A) & (all C (v1_rat_1(C) -> -(-r1_xreal_0(C,A) & -r1_xreal_0(B,C))))))))) # label(t22_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4551 (all A (v1_xreal_0(A) -> (all B (v1_rat_1(B) -> (r1_xreal_0(A,B) <-> r1_xreal_0(k3_xcmplx_0(A,k1_rat_1(B)),k2_rat_1(B))))))) # label(t81_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4552 (all A (v1_rat_1(A) -> (k2_rat_1(A) = np__0 <-> np__0 = A))) # label(t36_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4553 $T # label(t70_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4554 $T # label(t2_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4555 (all A ((all B ((exists C ((exists D (v1_int_1(D) & k7_xcmplx_0(C,D) = B)) & v1_int_1(C))) <-> r2_hidden(B,A))) <-> A = k3_numbers)) # label(d1_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4556 (all A (v1_rat_1(A) -> k2_rat_1(A) = k3_xcmplx_0(k1_rat_1(A),A))) # label(d4_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4557 (all A (v1_rat_1(A) -> (exists B (v1_int_1(B) & (exists C (k7_xcmplx_0(B,C) = A & np__0 != C & m2_subset_1(C,k1_numbers,k5_numbers))))))) # label(t24_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4558 (all A (v1_rat_1(A) -> -r1_xreal_0(k1_rat_1(A),np__0))) # label(t27_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4559 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -((exists E ((exists F (m2_subset_1(F,k1_numbers,k5_numbers) & B = k3_xcmplx_0(E,D) & k2_nat_1(F,D) = A)) & v1_int_1(E))) & -r1_xreal_0(D,np__1)))) & C = k7_xcmplx_0(B,A) -> A = np__0 | k1_rat_1(C) = A & k2_rat_1(C) = B))))))) # label(t63_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4560 $T # label(t68_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4561 $T # label(t55_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4562 (all A (v1_rat_1(A) -> -(-v1_int_1(A) & r1_xreal_0(np__1,k2_real_1(k1_rat_1(A)))) & -(v1_int_1(A) & -r1_xreal_0(np__1,k2_real_1(k1_rat_1(A)))))) # label(t46_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4563 (all A (v1_int_1(A) -> v1_rat_1(A))) # label(t7_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4564 (all A (v1_xreal_0(A) -> (all B (v1_rat_1(B) -> -(-r1_xreal_0(k2_rat_1(B),k3_xcmplx_0(A,k1_rat_1(B))) & r1_xreal_0(B,A)) & -(-r1_xreal_0(B,A) & r1_xreal_0(k2_rat_1(B),k3_xcmplx_0(A,k1_rat_1(B)))))))) # label(t80_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4565 (all A (v1_rat_1(A) -> v1_rat_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc16_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4566 (all A (v1_int_1(A) -> v1_rat_1(A) & v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4567 (all A (v1_rat_1(A) -> (A = np__1 <-> k1_rat_1(A) = k2_rat_1(A)))) # label(t47_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4568 $T # label(t57_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4569 (all A (v1_rat_1(A) -> (k2_rat_1(A) = A | k1_rat_1(A) = np__1 -> v1_int_1(A)))) # label(t41_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4570 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v1_rat_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc3_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4571 (all A (v1_rat_1(A) -> -(r1_xreal_0(np__1,A) & -r1_xreal_0(k1_rat_1(A),k2_rat_1(A))) & -(r1_xreal_0(k1_rat_1(A),k2_rat_1(A)) & -r1_xreal_0(np__1,A)))) # label(t72_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4572 (all A (v1_rat_1(A) -> k1_rat_1(A) = k1_rat_1(k4_xcmplx_0(A)) & k2_rat_1(k4_xcmplx_0(A)) = k4_xcmplx_0(k2_rat_1(A)))) # label(t87_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4573 (all A ((exists B (v1_int_1(B) & (exists C (A = k7_xcmplx_0(B,C) & v1_int_1(C))))) -> v1_rat_1(A))) # label(t6_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4574 (all A (v1_rat_1(A) -> v1_int_1(k2_rat_1(A)))) # label(dt_k2_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4575 $T # label(t18_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4576 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_rat_1(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4577 (all A all B (v1_int_1(B) & v1_rat_1(A) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc5_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4578 $T # label(t56_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4579 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> -(-r1_xreal_0(B,A) & r1_xreal_0(k3_xcmplx_0(k2_rat_1(B),k1_rat_1(A)),k3_xcmplx_0(k2_rat_1(A),k1_rat_1(B)))) & -(-r1_xreal_0(k3_xcmplx_0(k2_rat_1(B),k1_rat_1(A)),k3_xcmplx_0(k2_rat_1(A),k1_rat_1(B))) & r1_xreal_0(B,A)))))) # label(t86_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4580 (all A (v1_rat_1(A) -> -(-r1_xreal_0(k1_real_1(np__1),A) & r1_xreal_0(k1_real_1(k1_rat_1(A)),k2_rat_1(A))) & -(-r1_xreal_0(k1_real_1(k1_rat_1(A)),k2_rat_1(A)) & r1_xreal_0(k1_real_1(np__1),A)))) # label(t64_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4581 (all A (v1_rat_1(A) -> (r1_xreal_0(A,np__1) <-> r1_xreal_0(k2_rat_1(A),k1_rat_1(A))))) # label(t73_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4582 (all A all B (v1_rat_1(B) & v1_int_1(A) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_rat_1(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc9_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4583 (all A (v1_rat_1(A) -> (k1_rat_1(A) = np__1 <-> A = k2_rat_1(A)))) # label(t42_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4584 (all A (v1_rat_1(A) -> m2_subset_1(k1_rat_1(A),k1_numbers,k5_numbers))) # label(dt_k1_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4585 $T # label(t12_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4586 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> v1_rat_1(k7_xcmplx_0(A,B)))))) # label(t16_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4587 $T # label(t23_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4588 (all A (v1_rat_1(A) -> A = k7_xcmplx_0(k2_rat_1(A),k1_rat_1(A)) & k3_xcmplx_0(k2_real_1(k1_rat_1(A)),k2_rat_1(A)) = A & A = k3_xcmplx_0(k2_rat_1(A),k2_real_1(k1_rat_1(A))))) # label(t37_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4589 (all A (v1_rat_1(A) -> v1_rat_1(k5_xcmplx_0(A)))) # label(t21_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4590 (all A all B (v1_int_1(B) & v1_rat_1(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_rat_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc6_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4591 $T # label(t10_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4592 (all A (v1_rat_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4593 (all A -(v1_rat_1(A) & (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> -(np__0 != C & k7_xcmplx_0(B,C) = A))))))) # label(t3_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4594 (all A all B (v1_rat_1(A) & m1_subset_1(B,k5_numbers) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_rat_1(k2_xcmplx_0(A,B)))) # label(fc10_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4595 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v1_rat_1(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc17_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4596 $T # label(t51_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4597 $T # label(t26_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4598 $T # label(t58_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4599 $T # label(t43_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4600 (all A (v1_rat_1(A) -> v1_rat_1(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)))) # label(fc18_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4601 (all A all B (v1_rat_1(B) & v1_int_1(A) -> v1_rat_1(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4602 (all A (v1_rat_1(A) -> (exists B (v1_int_1(B) & (exists C ((all D (v1_int_1(D) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (k7_xcmplx_0(D,E) = A -> E = np__0 | r1_xreal_0(C,E)))))) & k7_xcmplx_0(B,C) = A & np__0 != C & m2_subset_1(C,k1_numbers,k5_numbers))))))) # label(t25_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4603 (exists A v1_rat_1(A)) # label(rc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4604 $T # label(t52_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4605 (all A (v1_rat_1(A) -> -r1_xreal_0(k2_real_1(k1_rat_1(A)),np__0))) # label(t30_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4606 $T # label(t78_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4607 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_rat_1(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4608 $T # label(t71_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4609 (all A (v1_rat_1(A) -> (v1_int_1(A) -> k1_rat_1(A) = np__1 & A = k2_rat_1(A)))) # label(t40_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4610 $T # label(t28_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4611 $T # label(t85_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4612 $T # label(t31_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4613 (all A (v1_rat_1(A) -> (r1_xreal_0(k1_rat_1(A),k4_xcmplx_0(k2_rat_1(A))) <-> r1_xreal_0(A,k1_real_1(np__1))))) # label(t67_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4614 (all A all B (v1_int_1(A) & v1_rat_1(B) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc8_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4615 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> -(np__0 != A & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(A = k2_nat_1(k1_rat_1(C),D) & B = k3_xcmplx_0(k2_rat_1(C),D)))) & k7_xcmplx_0(B,A) = C))))))) # label(t60_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4616 (all A (v1_rat_1(A) -> (r1_xreal_0(k2_rat_1(A),np__0) <-> r1_xreal_0(A,np__0)))) # label(t77_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4617 (all A (v1_rat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r1_xreal_0(B,np__1) & (exists C ((exists D (k2_nat_1(D,B) = k1_rat_1(A) & k3_xcmplx_0(C,B) = k2_rat_1(A) & m2_subset_1(D,k1_numbers,k5_numbers))) & v1_int_1(C)))))))) # label(t62_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4618 $T # label(t15_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4619 (all A all B (v1_rat_1(A) & v1_int_1(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_rat_1(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc4_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4620 $T # label(t32_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4621 $T # label(t59_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.63 4622 (all A -((all B (v1_int_1(B) -> (all C (v1_int_1(C) -> -(C != np__0 & A = k7_xcmplx_0(B,C)))))) & r2_hidden(A,k3_numbers))) # label(t1_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4623 $T # label(t8_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4624 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k7_xcmplx_0(np__1,A) = B -> r1_xreal_0(np__0,A) | k4_xcmplx_0(k2_rat_1(A)) = k1_rat_1(B) & k2_rat_1(B) = k1_real_1(k1_rat_1(A))) & (k1_rat_1(B) = k4_xcmplx_0(k2_rat_1(A)) & k2_rat_1(B) = k1_real_1(k1_rat_1(A)) -> -r1_xreal_0(np__0,A) & B = k7_xcmplx_0(np__1,A)))))) # label(t89_rat_1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4625 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k16_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4626 (all A (v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k11_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C))))) <-> A = k35_binop_2))) # label(d11_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4627 (all A (m1_subset_1(A,k2_numbers) -> A = k1_binop_2(k1_binop_2(A)))) # label(involutiveness_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4628 (all A (m1_subset_1(A,k4_numbers) -> m1_subset_1(k19_binop_2(A),k4_numbers))) # label(dt_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4629 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k2_xcmplx_0(A,B) = k9_binop_2(A,B))) # label(redefinition_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4630 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k6_xcmplx_0(A,B) = k21_binop_2(A,B))) # label(redefinition_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4631 (all A (m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_1(A) & v1_funct_2(A,k2_numbers,k2_numbers) -> (k25_binop_2 = A <-> (all B (m1_subset_1(B,k2_numbers) -> k8_funct_2(k2_numbers,k2_numbers,A,B) = k1_binop_2(B)))))) # label(d1_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4632 (all A (v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) -> (A = k48_binop_2 <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k24_binop_2(B,C) = k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C)))))))) # label(d24_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4633 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k18_binop_2(A,B),k3_numbers))) # label(dt_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4634 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k1_binop_2(A),k2_numbers))) # label(dt_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4635 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k5_binop_2(B,C))))) <-> k29_binop_2 = A))) # label(d5_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4636 (all A (v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k21_binop_2(B,C))))) <-> k45_binop_2 = A))) # label(d21_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4637 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k5_binop_2(A,B) = k5_binop_2(B,A))) # label(commutativity_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4638 (all A (m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (k27_binop_2 = A <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k3_binop_2(B,C)))))))) # label(d3_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4639 (all A (m1_subset_1(A,k1_numbers) -> k4_xcmplx_0(A) = k7_binop_2(A))) # label(redefinition_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4640 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k17_binop_2(A,B),k3_numbers))) # label(dt_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4641 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k14_binop_2(A),k3_numbers))) # label(dt_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4642 (all A (v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (A = k28_binop_2 <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k4_binop_2(B,C)))))))) # label(d4_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4643 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k9_binop_2(B,A) = k9_binop_2(A,B))) # label(commutativity_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4644 (all A (v1_funct_1(A) & m2_relset_1(A,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_2(A,f1_s1_binop_2,f2_s1_binop_2) -> (all B (v1_funct_2(B,f1_s1_binop_2,f2_s1_binop_2) & m2_relset_1(B,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_1(B) -> ((all C (m1_subset_1(C,f1_s1_binop_2) -> k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,B,C) = f3_s1_binop_2(C))) & (all C (m1_subset_1(C,f1_s1_binop_2) -> f3_s1_binop_2(C) = k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,A,C))) -> B = A))))) # label(s1_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4645 (all A (m1_subset_1(A,k3_numbers) -> k13_binop_2(k13_binop_2(A)) = A)) # label(involutiveness_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4646 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k12_binop_2(A,B),k1_numbers))) # label(dt_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4647 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k15_binop_2(B,C))))) <-> A = k39_binop_2))) # label(d15_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4648 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4649 (all A (m1_subset_1(A,k4_numbers) -> k19_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4650 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> m1_subset_1(k16_binop_2(A,B),k3_numbers))) # label(dt_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4651 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k10_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4652 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k3_xcmplx_0(A,B) = k22_binop_2(A,B))) # label(redefinition_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4653 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k20_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4654 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) -> (all B (v1_funct_2(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) -> ((all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,B,C,D) = f2_s2_binop_2(C,D))))) & (all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,A,C,D) = f2_s2_binop_2(C,D))))) -> B = A))))) # label(s2_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4655 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k15_binop_2(A,B) = k15_binop_2(B,A))) # label(commutativity_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4656 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k15_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4657 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k23_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4658 (all A (m1_subset_1(A,k3_numbers) -> v1_xreal_0(A) & v1_rat_1(A) & v1_xcmplx_0(A))) # label(cc1_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4659 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k7_binop_2(A),k1_numbers))) # label(dt_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4660 (all A (m1_subset_1(A,k2_numbers) -> A = k2_binop_2(k2_binop_2(A)))) # label(involutiveness_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4661 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k3_binop_2(A,B),k2_numbers))) # label(dt_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4662 (all A (v1_funct_2(A,k3_numbers,k3_numbers) & v1_funct_1(A) & m2_relset_1(A,k3_numbers,k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> k13_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B))) <-> k37_binop_2 = A))) # label(d13_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4663 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k2_binop_2(A),k2_numbers))) # label(dt_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4664 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k22_binop_2(B,A) = k22_binop_2(A,B))) # label(commutativity_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4665 (all A (m1_subset_1(A,k1_numbers) -> k8_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4666 (all A (v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k6_binop_2(B,C))))) <-> A = k30_binop_2))) # label(d6_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4667 (all A (v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> (A = k44_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k20_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C)))))))) # label(d20_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4668 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k11_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4669 (all A (m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k23_binop_2(B,C) = k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C))))) <-> A = k47_binop_2))) # label(d23_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4670 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k4_binop_2(A,B),k2_numbers))) # label(dt_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4671 (all A (m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_1(A) & v1_funct_2(A,k1_numbers,k1_numbers) -> ((all B (m1_subset_1(B,k1_numbers) -> k7_binop_2(B) = k8_funct_2(k1_numbers,k1_numbers,A,B))) <-> k31_binop_2 = A))) # label(d7_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4672 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k24_binop_2(B,A) = k24_binop_2(A,B))) # label(commutativity_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4673 (all A (m2_relset_1(A,k3_numbers,k3_numbers) & v1_funct_2(A,k3_numbers,k3_numbers) & v1_funct_1(A) -> (k38_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> k14_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B)))))) # label(d14_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4674 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k9_binop_2(A,B),k1_numbers))) # label(dt_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4675 (all A (v1_funct_1(A) & v1_funct_2(A,k4_numbers,k4_numbers) & m2_relset_1(A,k4_numbers,k4_numbers) -> ((all B (m1_subset_1(B,k4_numbers) -> k8_funct_2(k4_numbers,k4_numbers,A,B) = k19_binop_2(B))) <-> k43_binop_2 = A))) # label(d19_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4676 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k18_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4677 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k8_binop_2(A),k1_numbers))) # label(dt_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4678 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> (k41_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k17_binop_2(B,C)))))))) # label(d17_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4679 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k11_binop_2(A,B),k1_numbers))) # label(dt_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4680 (all A (v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> (A = k33_binop_2 <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C)))))))) # label(d9_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4681 (all A (v1_funct_1(A) & v1_funct_2(A,k2_numbers,k2_numbers) & m2_relset_1(A,k2_numbers,k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> k2_binop_2(B) = k8_funct_2(k2_numbers,k2_numbers,A,B))) <-> k26_binop_2 = A))) # label(d2_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4682 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> m1_subset_1(k20_binop_2(A,B),k4_numbers))) # label(dt_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4683 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k3_binop_2(A,B) = k3_binop_2(B,A))) # label(commutativity_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4684 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k6_xcmplx_0(A,B) = k4_binop_2(A,B))) # label(redefinition_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4685 (all A (m1_subset_1(A,k1_numbers) -> k7_binop_2(k7_binop_2(A)) = A)) # label(involutiveness_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4686 (all A (v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> (A = k34_binop_2 <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k10_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C)))))))) # label(d10_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4687 (all A (m1_subset_1(A,k2_numbers) -> k1_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4688 (all A (m1_subset_1(A,k3_numbers) -> A = k14_binop_2(k14_binop_2(A)))) # label(involutiveness_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4689 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k5_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4690 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k24_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4691 (all A (m1_subset_1(A,k2_numbers) -> k2_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4692 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> (k40_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k16_binop_2(B,C)))))))) # label(d16_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4693 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k13_binop_2(A),k3_numbers))) # label(dt_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4694 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k2_xcmplx_0(A,B) = k3_binop_2(A,B))) # label(redefinition_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4695 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k17_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4696 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> m1_subset_1(k22_binop_2(A,B),k4_numbers))) # label(dt_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4697 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k20_binop_2(A,B) = k20_binop_2(B,A))) # label(commutativity_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4698 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k18_binop_2(B,C))))) <-> A = k42_binop_2))) # label(d18_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4699 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k10_binop_2(A,B),k1_numbers))) # label(dt_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4700 (all A (m1_subset_1(A,k3_numbers) -> k13_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4701 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k7_xcmplx_0(A,B) = k12_binop_2(A,B))) # label(redefinition_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4702 (all A (m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> (A = k46_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k22_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C)))))))) # label(d22_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4703 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k24_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4704 (all A (m1_subset_1(A,k4_numbers) -> k19_binop_2(k19_binop_2(A)) = A)) # label(involutiveness_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4705 (all A (m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k12_binop_2(B,C))))) <-> A = k36_binop_2))) # label(d12_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4706 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> m1_subset_1(k21_binop_2(A,B),k4_numbers))) # label(dt_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4707 (all A (m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_2(A,k1_numbers,k1_numbers) & v1_funct_1(A) -> (k32_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> k8_binop_2(B) = k8_funct_2(k1_numbers,k1_numbers,A,B)))))) # label(d8_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4708 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k17_binop_2(A,B) = k17_binop_2(B,A))) # label(commutativity_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4709 (all A (m1_subset_1(A,k1_numbers) -> k8_binop_2(k8_binop_2(A)) = A)) # label(involutiveness_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4710 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k15_binop_2(A,B),k3_numbers))) # label(dt_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4711 (all A (m1_subset_1(A,k3_numbers) -> k14_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4712 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k11_binop_2(B,A) = k11_binop_2(A,B))) # label(commutativity_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4713 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k6_binop_2(A,B),k2_numbers))) # label(dt_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4714 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k5_binop_2(A,B),k2_numbers))) # label(dt_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4715 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k6_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4716 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k23_binop_2(A,B) = k23_binop_2(B,A))) # label(commutativity_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4717 (all A all B (v1_int_1(A) & v1_int_1(B) -> v4_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4718 (all A all B (v5_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4719 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4720 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4721 (all A (v1_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B))))) # label(cc16_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4722 (all A all B (v1_membered(B) & v1_membered(A) -> v1_membered(k5_xboole_0(A,B)))) # label(fc42_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4723 (all A all B (v5_membered(A) & v5_membered(B) -> v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4724 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4725 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4726 (all A all B all C (v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4727 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v3_membered(B) & v1_membered(B) & v4_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4728 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> A = k2_numbers))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4729 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4730 (all A all B (v4_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4731 (exists A (v5_membered(A) & -v1_xboole_0(A) & v2_membered(A) & v4_membered(A) & v3_membered(A) & v1_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4732 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4733 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d9_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4734 (exists A ((all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))) & v1_membered(A))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4735 (exists A (v5_membered(A) & (all B (v4_ordinal2(B) -> (p1_s5_membered(B) <-> r2_hidden(B,A)))))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4736 (all A (v1_xreal_0(A) -> v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4737 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4738 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> A = B))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4739 (all A (v3_membered(A) -> (all B (v3_membered(B) -> ((all C (v1_rat_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> A = B))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4740 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d6_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4741 (all A (-v1_xboole_0(A) & v1_membered(A) -> (exists B (v1_xcmplx_0(B) & r2_hidden(B,A))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4742 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4743 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4744 (all A (v5_membered(A) -> ((all B (v4_ordinal2(B) -> r2_hidden(B,A))) -> A = k5_numbers))) # label(t15_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4745 (all A all B (r2_hidden(B,A) & v1_membered(B) -> v1_membered(k1_setfam_1(A)))) # label(t26_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4746 (all A (v5_membered(A) <-> (all B (r2_hidden(B,A) -> v4_ordinal2(B))))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4747 (all A (v3_membered(A) -> ((all B (v1_rat_1(B) -> r2_hidden(B,A))) -> A = k3_numbers))) # label(t13_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4748 (all A all B (v4_membered(B) & v4_membered(A) -> v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4749 (all A all B (v5_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4750 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4751 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_rat_1(B) & v1_xcmplx_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4752 (all A (v4_membered(A) -> ((all B (v1_int_1(B) -> r2_hidden(B,A))) -> A = k4_numbers))) # label(t14_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4753 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4754 (all A (v2_membered(A) & -v1_xboole_0(A) -> (exists B (v1_xreal_0(B) & r2_hidden(B,A))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4755 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4756 (all A ((all B (r2_hidden(B,A) -> v5_membered(B))) -> v5_membered(k3_tarski(A)))) # label(t25_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4757 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4758 (all A all B (r2_hidden(B,A) & v2_membered(B) -> v2_membered(k1_setfam_1(A)))) # label(t27_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4759 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4760 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v1_membered(A) & v2_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4761 (exists A (v2_membered(A) & (all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4762 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4763 (all A all B (v3_membered(A) -> v3_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4764 (all A all B all C (v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4765 (exists A (v3_membered(A) & (all B (v1_rat_1(B) -> (p1_s3_membered(B) <-> r2_hidden(B,A)))))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4766 (all A (v1_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B))))) # label(cc10_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4767 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v3_membered(B) & v2_membered(B) & v1_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4768 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4769 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4770 (all A ((all B (r2_hidden(B,A) -> v2_membered(B))) -> v2_membered(k3_tarski(A)))) # label(t22_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4771 (all A all B (v4_membered(B) & r2_hidden(B,A) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4772 (all A all B (v4_membered(A) -> v3_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4773 (all A (v1_xboole_0(A) -> v5_membered(A) & v4_membered(A) & v2_membered(A) & v1_membered(A) & v3_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4774 (all A all B (v2_membered(B) & v2_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4775 (all A all B (v3_membered(A) & v3_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4776 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4777 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4778 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v3_membered(B) & v5_membered(B) & v4_membered(B) & v2_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4779 (all A (v1_int_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4780 (all A ((all B (r2_hidden(B,A) -> v4_membered(B))) -> v4_membered(k3_tarski(A)))) # label(t24_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4781 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4782 (all A (v2_membered(A) <-> (all B (r2_hidden(B,A) -> v1_xreal_0(B))))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4783 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v4_ordinal2(B) & v1_rat_1(B) & v1_xcmplx_0(B) & v1_int_1(B) & v1_xreal_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4784 (all A all B all C (v4_ordinal2(A) & v4_ordinal2(B) & v4_ordinal2(C) -> v4_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4785 (all A (v2_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B))))) # label(cc17_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4786 (all A all B (r2_hidden(B,A) & v3_membered(B) -> v3_membered(k1_setfam_1(A)))) # label(t28_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4787 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4788 (all A (v2_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4789 (all A all B (v5_membered(A) -> v5_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4790 (all A all B (r2_hidden(B,A) & v5_membered(B) -> v5_membered(k1_setfam_1(A)))) # label(t30_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4791 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v2_membered(A) & v4_membered(A) & v1_membered(A) & v3_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4792 (all A (-v1_xboole_0(A) & v5_membered(A) -> (exists B (v4_ordinal2(B) & r2_hidden(B,A))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4793 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v2_membered(A) & v3_membered(A) & v1_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4794 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4795 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_int_1(B) & v1_rat_1(B) & v1_xcmplx_0(B) & v1_xreal_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4796 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4797 (all A ((all B (r2_hidden(B,A) -> v1_membered(B))) -> v1_membered(k3_tarski(A)))) # label(t21_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4798 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4799 (all A (v1_rat_1(A) -> v3_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4800 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d8_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4801 (all A (-v1_xboole_0(A) & v3_membered(A) -> (exists B (r2_hidden(B,A) & v1_rat_1(B))))) # label(t8_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4802 (all A all B (v1_membered(B) & v1_membered(A) -> v1_membered(k2_xboole_0(A,B)))) # label(fc22_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4803 (all A all B (v2_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4804 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4805 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4806 (all A ((all B (r2_hidden(B,A) -> v3_membered(B))) -> v3_membered(k3_tarski(A)))) # label(t23_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4807 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4808 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4809 (all A all B (v2_membered(B) & v2_membered(A) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4810 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4811 (exists A ((all B (v1_int_1(B) -> (r2_hidden(B,A) <-> p1_s4_membered(B)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4812 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4813 (all A all B (v4_membered(B) & v4_membered(A) -> v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4814 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (A = B <-> (all C (v1_int_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4815 (all A all B all C (v1_int_1(A) & v1_int_1(B) & v1_int_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4816 (all A (-v1_xboole_0(A) & v4_membered(A) -> (exists B (r2_hidden(B,A) & v1_int_1(B))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4817 (all A (v4_membered(A) <-> (all B (r2_hidden(B,A) -> v1_int_1(B))))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4818 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_tarski(A,B) <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4819 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4820 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (B = A <-> (all C (v1_xcmplx_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4821 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v3_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4822 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_rat_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4823 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4824 (all A all B (v3_membered(B) & v3_membered(A) -> v3_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4825 (all A (v2_membered(A) -> ((all B (v1_xreal_0(B) -> r2_hidden(B,A))) -> A = k1_numbers))) # label(t12_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4826 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> v1_membered(A) & v2_membered(A))) # label(cc6_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4827 (all A all B (v5_membered(A) & v5_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4828 (all A (v4_ordinal2(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4829 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4830 (all A all B (v2_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4831 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4832 (all A all B all C (v1_rat_1(B) & v1_rat_1(C) & v1_rat_1(A) -> v3_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4833 $T # label(t92_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4834 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> k17_complex1(A) = A))) # label(t129_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4835 $T # label(t58_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4836 $T # label(t74_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4837 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k8_complex1(k15_complex1(A),k15_complex1(B)) = k15_complex1(k2_xcmplx_0(A,B)))))) # label(t118_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4838 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> (np__0 = k3_complex1(B) & np__0 = k3_complex1(A) -> k3_complex1(k13_complex1(A,B)) = k6_real_1(k4_complex1(A),k4_complex1(B)) & np__0 = k4_complex1(k13_complex1(A,B)) | np__0 = k4_complex1(B)))))) # label(t110_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4839 $T # label(t1_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4840 $T # label(t41_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4841 (all A (v1_xcmplx_0(A) -> v1_xreal_0(k1_complex1(A)) & v1_xcmplx_0(k1_complex1(A)))) # label(fc1_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4842 $T # label(t89_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4843 $T # label(t105_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4844 $T # label(t60_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4845 $T # label(t108_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4846 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> r1_xreal_0(k17_complex1(k5_real_1(k17_complex1(A),k17_complex1(B))),k17_complex1(k6_xcmplx_0(A,B))))))) # label(t150_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4847 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k11_complex1(A,B),k2_numbers))) # label(dt_k11_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4848 (all A (m1_subset_1(A,k2_numbers) -> k5_xcmplx_0(A) = k12_complex1(A))) # label(redefinition_k12_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4849 $T # label(t97_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4850 $T # label(t77_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4851 $T # label(t95_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4852 $T # label(t39_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4853 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k3_complex1(k11_complex1(A,B)) = k5_real_1(k3_complex1(A),k3_complex1(B)) & k5_real_1(k4_complex1(A),k4_complex1(B)) = k4_complex1(k11_complex1(A,B)))))) # label(t48_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4854 $T # label(t21_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4855 (all A (m1_subset_1(A,k2_numbers) -> np__0 = k3_complex1(k11_complex1(A,k15_complex1(A))) & k4_complex1(k11_complex1(A,k15_complex1(A))) = k4_real_1(np__2,k4_complex1(A)))) # label(t128_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4856 (all A (v1_xcmplx_0(A) -> k17_complex1(A) = k17_complex1(k4_xcmplx_0(A)))) # label(t138_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4857 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(k3_complex1(A),k3_xcmplx_0(k4_complex1(A),k7_complex1)) = k14_complex1(A))) # label(d15_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4858 $T # label(t20_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4859 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> B = k4_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) & A = k3_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))))))) # label(t28_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4860 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (np__0 = k2_xcmplx_0(k5_square_1(A),k5_square_1(B)) <-> np__0 = A & np__0 = B))))) # label(t2_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4861 $T # label(d1_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4862 $T # label(dt_k1_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4863 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k16_complex1(A)) & v1_xreal_0(k16_complex1(A)))) # label(fc4_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4864 $T # label(t6_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.64 4865 (all A (v1_xreal_0(A) -> k5_square_1(A) = k7_square_1(k17_complex1(A)))) # label(t161_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4866 (all A (v1_xcmplx_0(A) -> (k15_complex1(A) = np__0 -> np__0 = A))) # label(t114_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4867 (all A (v1_xcmplx_0(A) -> (k3_complex1(A) = np__0 -> k17_complex1(A) = k17_complex1(k4_complex1(A))))) # label(t137_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4868 $T # label(t43_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4869 $T # label(t94_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4870 (all A (m1_subset_1(A,k2_numbers) -> (np__0 = k3_complex1(A) -> np__0 = k3_complex1(k12_complex1(A)) & k1_real_1(k2_real_1(k4_complex1(A))) = k4_complex1(k12_complex1(A)) | np__0 = k4_complex1(A)))) # label(t80_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4871 $T # label(t3_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4872 (all A (v1_xcmplx_0(A) -> k17_complex1(A) = k17_complex1(k17_complex1(A)))) # label(projectivity_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4873 $T # label(t33_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4874 (all A (v1_xcmplx_0(A) -> m1_subset_1(k17_complex1(A),k1_numbers))) # label(dt_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4875 $T # label(t49_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4876 $T # label(t103_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4877 $T # label(t101_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4878 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k8_complex1(B,A) = k8_complex1(A,B))) # label(commutativity_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4879 $T # label(t52_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4880 $T # label(t67_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4881 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> (k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) = k2_xcmplx_0(C,k3_xcmplx_0(D,k7_complex1)) -> C = A & D = B))))))))) # label(t163_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4882 $T # label(t106_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4883 (all A (m1_subset_1(A,k2_numbers) -> k10_complex1(A) = k4_xcmplx_0(A))) # label(redefinition_k10_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4884 (all A (v1_xcmplx_0(A) -> k17_complex1(k3_xcmplx_0(A,k15_complex1(A))) = k17_complex1(k3_xcmplx_0(A,A)))) # label(t155_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4885 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k2_square_1(A,B) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),k17_complex1(k6_xcmplx_0(A,B))),np__2))))) # label(t160_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4886 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k2_xcmplx_0(k5_real_1(k3_complex1(A),k3_complex1(B)),k3_xcmplx_0(k5_real_1(k4_complex1(A),k4_complex1(B)),k7_complex1)) = k11_complex1(A,B))))) # label(d12_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4887 (all A (v1_xcmplx_0(A) -> k15_complex1(A) = k14_complex1(A))) # label(redefinition_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4888 $T # label(t65_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4889 $T # label(t73_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4890 $T # label(t11_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4891 $T # label(t53_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4892 $T # label(t36_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4893 (all A (v1_xcmplx_0(A) -> (all B ((r2_hidden(A,k1_numbers) -> (B = A <-> k1_complex1(A) = B)) & (-r2_hidden(A,k1_numbers) -> ((exists C (C = A & v1_funct_1(C) & m2_relset_1(C,np__2,k1_numbers) & B = k1_funct_1(C,np__0) & v1_funct_2(C,np__2,k1_numbers))) <-> B = k1_complex1(A))))))) # label(d2_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4894 (all A (v1_xcmplx_0(A) -> k16_complex1(A) = k17_complex1(A))) # label(redefinition_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4895 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_complex1(B) = k3_complex1(A) & k4_complex1(B) = k4_complex1(A) -> B = A))))) # label(t9_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4896 (all A (m1_subset_1(A,k2_numbers) -> (k3_complex1(A) = np__0 -> k10_complex1(A) = k15_complex1(A)))) # label(t125_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4897 (all A (v1_xreal_0(A) -> k17_complex1(A) = A | k17_complex1(A) = k4_xcmplx_0(A))) # label(t157_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4898 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k10_complex1(A),k2_numbers))) # label(dt_k10_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4899 $T # label(t83_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4900 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),k3_real_1(k17_complex1(A),k17_complex1(B))))))) # label(t143_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4901 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k11_complex1(k15_complex1(A),k15_complex1(B)) = k15_complex1(k11_complex1(A,B)))))) # label(t120_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4902 $T # label(t91_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4903 $T # label(t102_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4904 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k9_complex1(k15_complex1(A),k15_complex1(B)) = k15_complex1(k9_complex1(A,B)))))) # label(t121_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4905 (all A (m1_subset_1(A,k2_numbers) -> k4_real_1(np__2,k4_real_1(k3_complex1(A),k4_complex1(A))) = k4_complex1(k9_complex1(A,A)) & k5_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = k3_complex1(k9_complex1(A,A)))) # label(t32_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4906 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = B <-> np__0 = k17_complex1(k6_xcmplx_0(A,B))))))) # label(t147_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4907 (all A (v1_xcmplx_0(A) -> (all B ((-r2_hidden(A,k1_numbers) -> ((exists C (C = A & k1_funct_1(C,np__1) = B & v1_funct_2(C,np__2,k1_numbers) & v1_funct_1(C) & m2_relset_1(C,np__2,k1_numbers))) <-> k2_complex1(A) = B)) & (r2_hidden(A,k1_numbers) -> (B = np__0 <-> B = k2_complex1(A))))))) # label(d3_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4908 $T # label(t75_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4909 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k2_xcmplx_0(k6_real_1(k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B)))),k3_xcmplx_0(k6_real_1(k5_real_1(k4_real_1(k3_complex1(B),k4_complex1(A)),k4_real_1(k3_complex1(A),k4_complex1(B))),k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B)))),k7_complex1)) = k13_complex1(A,B))))) # label(d14_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4910 $T # label(t59_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4911 (all A (m1_subset_1(A,k2_numbers) -> k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = k3_complex1(k9_complex1(A,k15_complex1(A))) & k4_complex1(k9_complex1(A,k15_complex1(A))) = np__0)) # label(t126_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4912 (all A (v1_xcmplx_0(A) -> -(r1_xreal_0(k17_complex1(A),np__0) & np__0 != A) & -(A = np__0 & -r1_xreal_0(k17_complex1(A),np__0)))) # label(t133_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4913 (all A (v1_xcmplx_0(A) -> k1_complex1(A) = k3_complex1(A))) # label(redefinition_k3_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4914 $T # label(t8_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4915 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> r1_xreal_0(k5_real_1(k17_complex1(A),k17_complex1(B)),k17_complex1(k6_xcmplx_0(A,B))))))) # label(t145_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4916 (all A (v1_xcmplx_0(A) -> k18_complex1(A) = k16_complex1(A))) # label(redefinition_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4917 (all A (m1_subset_1(A,k1_numbers) -> k4_complex1(k3_xcmplx_0(A,k7_complex1)) = A)) # label(t26_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4918 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k8_complex1(A,B) = k2_xcmplx_0(k3_real_1(k3_complex1(A),k3_complex1(B)),k3_xcmplx_0(k3_real_1(k4_complex1(A),k4_complex1(B)),k7_complex1)))))) # label(d9_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4919 (all A (v1_xcmplx_0(A) -> k18_complex1(A) = k18_complex1(k18_complex1(A)))) # label(projectivity_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4920 (all A (m1_subset_1(A,k2_numbers) -> k15_complex1(k10_complex1(A)) = k10_complex1(k15_complex1(A)))) # label(t119_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4921 (all A (v1_xcmplx_0(A) -> m1_subset_1(k18_complex1(A),k1_numbers))) # label(dt_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4922 (all A (v1_xcmplx_0(A) -> k3_complex1(A) = k3_complex1(k15_complex1(A)) & k4_complex1(k15_complex1(A)) = k1_real_1(k4_complex1(A)))) # label(t112_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4923 $T # label(t63_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4924 $T # label(t66_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4925 $T # label(t45_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4926 $T # label(t111_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4927 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k12_complex1(A),k2_numbers))) # label(dt_k12_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4928 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_complex1(A) = np__0 & np__0 = k3_complex1(B) -> np__0 = k4_complex1(k3_xcmplx_0(A,B)) & k1_real_1(k4_real_1(k4_complex1(A),k4_complex1(B))) = k3_complex1(k3_xcmplx_0(A,B))))))) # label(t31_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4929 (all A (v1_xcmplx_0(A) -> k16_complex1(k16_complex1(A)) = k16_complex1(A))) # label(projectivity_k16_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4930 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k17_complex1(k6_xcmplx_0(A,B)) = k17_complex1(k6_xcmplx_0(B,A)))))) # label(t146_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4931 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = B <-> k4_complex1(A) = k4_complex1(B) & k3_complex1(B) = k3_complex1(A)))))) # label(d5_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4932 (all A (v1_xcmplx_0(A) -> k14_complex1(k14_complex1(A)) = A)) # label(involutiveness_k14_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4933 $T # label(t117_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4934 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k1_square_1(A,B) = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),k17_complex1(k6_xcmplx_0(A,B))),np__2))))) # label(t159_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4935 $T # label(t61_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4936 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k9_complex1(A,B) = k2_xcmplx_0(k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_xcmplx_0(k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))),k7_complex1)))))) # label(d10_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4937 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> r1_xreal_0(k17_complex1(k6_xcmplx_0(B,C)),k3_real_1(k17_complex1(k6_xcmplx_0(B,A)),k17_complex1(k6_xcmplx_0(A,C)))))))))) # label(t149_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4938 (all A (v1_xcmplx_0(A) -> A = k15_complex1(k15_complex1(A)))) # label(involutiveness_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4939 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),np__0) & B != A) & -(B = A & -r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),np__0)))))) # label(t148_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4940 (all A (v1_xreal_0(A) -> k8_square_1(k5_square_1(A)) = k17_complex1(A))) # label(t158_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4941 $T # label(t76_complex1) # label(axiom) # label(non_clause). [assumption]. 67.83/65.65 4942 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k6_real_1(k5_real_1(k4_real_1(k3_complex1(B),k4_complex1(A)),k4_real_1(k3_complex1(A),k4_complex1(B))),k3_real_1(k7_square_1(k3_complex1(B)),k7_sq