0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.11/0.32 % Computer : n007.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Thu Jul 2 07:06:39 EDT 2020 0.11/0.32 % CPUTime : 9.62/1.62 % SZS status Theorem 9.62/1.62 9.62/1.62 % SZS output start Proof 9.62/1.62 Take the following subset of the input axioms: 9.62/1.63 fof(cl5_nebula_init_0046, conjecture, ![D, E]: ((leq(n0, D) & (leq(n0, E) & (leq(E, n4) & leq(D, n135299)))) => (a_select3(q_init, D, E)=init <= gt(pv10, D))) <= (leq(pv10, n135299) & (![A]: ((leq(A, pred(pv10)) & leq(n0, A)) => ![B]: ((leq(n0, B) & leq(B, n4)) => init=a_select3(q_init, A, B))) & (![C]: (a_select3(center_init, C, n0)=init <= (leq(C, n4) & leq(n0, C))) & leq(n0, pv10))))). 9.62/1.63 fof(leq_gt_pred, axiom, ![X, Y]: (gt(Y, X) <=> leq(X, pred(Y)))). 9.62/1.63 9.62/1.63 Now clausify the problem and encode Horn clauses using encoding 3 of 9.62/1.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 9.62/1.63 We repeatedly replace C & s=t => u=v by the two clauses: 9.62/1.63 fresh(y, y, x1...xn) = u 9.62/1.63 C => fresh(s, t, x1...xn) = v 9.62/1.63 where fresh is a fresh function symbol and x1..xn are the free 9.62/1.63 variables of u and v. 9.62/1.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the 9.62/1.63 input problem has no model of domain size 1). 9.62/1.63 9.62/1.63 The encoding turns the above axioms into the following unit equations and goals: 9.62/1.63 9.62/1.63 Axiom 1 (cl5_nebula_init_0046_8): fresh46(X, X, Y, Z) = a_select3(q_init, Y, Z). 9.62/1.63 Axiom 2 (cl5_nebula_init_0046_8): fresh43(X, X, Y, Z) = init. 9.62/1.63 Axiom 3 (cl5_nebula_init_0046_8): fresh45(X, X, Y, Z) = fresh46(leq(Z, n4), true3, Y, Z). 9.62/1.63 Axiom 4 (cl5_nebula_init_0046_8): fresh44(X, X, Y, Z) = fresh45(leq(n0, Y), true3, Y, Z). 9.62/1.63 Axiom 5 (leq_gt_pred_1): fresh34(X, X, Y, Z) = true3. 9.62/1.63 Axiom 6 (leq_gt_pred_1): fresh34(gt(X, Y), true3, Y, X) = leq(Y, pred(X)). 9.62/1.63 Axiom 7 (cl5_nebula_init_0046_1): leq(n0, sK2_cl5_nebula_init_0046_E) = true3. 9.62/1.63 Axiom 8 (cl5_nebula_init_0046_2): leq(n0, sK1_cl5_nebula_init_0046_D) = true3. 9.62/1.63 Axiom 9 (cl5_nebula_init_0046_4): leq(sK2_cl5_nebula_init_0046_E, n4) = true3. 9.62/1.63 Axiom 10 (cl5_nebula_init_0046_6): gt(pv10, sK1_cl5_nebula_init_0046_D) = true3. 9.62/1.63 Axiom 11 (cl5_nebula_init_0046_8): fresh44(leq(n0, X), true3, Y, X) = fresh43(leq(Y, pred(pv10)), true3, Y, X). 9.62/1.63 9.62/1.63 Goal 1 (cl5_nebula_init_0046_7): a_select3(q_init, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) = init. 9.62/1.63 Proof: 9.62/1.63 a_select3(q_init, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 1 (cl5_nebula_init_0046_8) } 9.62/1.63 fresh46(true3, true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 9 (cl5_nebula_init_0046_4) } 9.62/1.63 fresh46(leq(sK2_cl5_nebula_init_0046_E, n4), true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 3 (cl5_nebula_init_0046_8) } 9.62/1.63 fresh45(true3, true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 8 (cl5_nebula_init_0046_2) } 9.62/1.63 fresh45(leq(n0, sK1_cl5_nebula_init_0046_D), true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 4 (cl5_nebula_init_0046_8) } 9.62/1.63 fresh44(true3, true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 7 (cl5_nebula_init_0046_1) } 9.62/1.63 fresh44(leq(n0, sK2_cl5_nebula_init_0046_E), true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 11 (cl5_nebula_init_0046_8) } 9.62/1.63 fresh43(leq(sK1_cl5_nebula_init_0046_D, pred(pv10)), true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 6 (leq_gt_pred_1) } 9.62/1.63 fresh43(fresh34(gt(pv10, sK1_cl5_nebula_init_0046_D), true3, sK1_cl5_nebula_init_0046_D, pv10), true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 10 (cl5_nebula_init_0046_6) } 9.62/1.63 fresh43(fresh34(true3, true3, sK1_cl5_nebula_init_0046_D, pv10), true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 5 (leq_gt_pred_1) } 9.62/1.63 fresh43(true3, true3, sK1_cl5_nebula_init_0046_D, sK2_cl5_nebula_init_0046_E) 9.62/1.63 = { by axiom 2 (cl5_nebula_init_0046_8) } 9.62/1.63 init 9.62/1.63 % SZS output end Proof 9.62/1.63 9.62/1.63 RESULT: Theorem (the conjecture is true). 9.62/1.64 EOF