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 : n022.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 06:42:47 EDT 2020 0.11/0.33 % CPUTime : 0.17/0.49 % SZS status Theorem 0.17/0.49 1.86/0.62 % SZS output start Proof 1.86/0.62 Take the following subset of the input axioms: 2.62/0.69 fof(ax1, axiom, ![U, V]: (instrumentality(U, V) <= furniture(U, V))). 2.62/0.69 fof(ax18, axiom, ![U, V]: (object(U, V) => nonliving(U, V))). 2.62/0.69 fof(ax2, axiom, ![U, V]: (furniture(U, V) <= seat(U, V))). 2.62/0.69 fof(ax20, axiom, ![U, V]: (object(U, V) <= artifact(U, V))). 2.62/0.69 fof(ax21, axiom, ![U, V]: (instrumentality(U, V) => artifact(U, V))). 2.62/0.69 fof(ax3, axiom, ![U, V]: (seat(U, V) <= frontseat(U, V))). 2.62/0.69 fof(ax40, axiom, ![U, V]: (living(U, V) <= organism(U, V))). 2.62/0.69 fof(ax47, axiom, ![U, V]: (human_person(U, V) => organism(U, V))). 2.62/0.69 fof(ax48, axiom, ![U, V]: (human_person(U, V) <= man(U, V))). 2.62/0.69 fof(ax49, axiom, ![U, V]: (fellow(U, V) => man(U, V))). 2.62/0.69 fof(ax50, axiom, ![U, V]: (~nonliving(U, V) <= animate(U, V))). 2.62/0.69 fof(ax51, axiom, ![U, V]: (existent(U, V) => ~nonexistent(U, V))). 2.62/0.69 fof(ax52, axiom, ![U, V]: (nonhuman(U, V) => ~human(U, V))). 2.62/0.69 fof(ax53, axiom, ![U, V]: (~living(U, V) <= nonliving(U, V))). 2.62/0.69 fof(ax54, axiom, ![U, V]: (~multiple(U, V) <= singleton(U, V))). 2.62/0.69 fof(ax55, axiom, ![U, V]: (~general(U, V) <= specific(U, V))). 2.62/0.69 fof(ax56, axiom, ![U, V]: (~male(U, V) <= unisex(U, V))). 2.62/0.69 fof(ax57, axiom, ![U, V]: (~old(U, V) <= young(U, V))). 2.62/0.69 fof(ax59, axiom, ![U, V, X, W]: (W=X <= be(U, V, W, X))). 2.62/0.69 fof(ax60, axiom, ![U, V]: (two(U, V) <=> ?[W]: (member(U, W, V) & ?[X]: (member(U, X, V) & (![Y]: (member(U, Y, V) => (W=Y | X=Y)) & X!=W))))). 2.62/0.69 fof(ax61, axiom, ![U]: ~?[V]: member(U, V, V)). 2.62/0.69 fof(co1, conjecture, ~?[U]: (actual_world(U) & ?[V, X, W, Y, Z]: (of(U, V, W) & (city(U, W) & (street(U, W) & (lonely(U, W) & (chevy(U, X) & (dirty(U, X) & (event(U, Y) & (agent(U, Y, X) & (![X1]: (?[X2, X3]: (frontseat(U, X3) & (state(U, X2) & (be(U, X2, X1, X3) & in(U, X3, X3)))) <= member(U, X1, Z)) & (![X4]: (member(U, X4, Z) => (young(U, X4) & fellow(U, X4))) & (group(U, Z) & (two(U, Z) & (in(U, Y, W) & (down(U, Y, W) & (barrel(U, Y) & (present(U, Y) & (old(U, X) & (white(U, X) & (placename(U, V) & hollywood_placename(U, V)))))))))))))))))))))). 2.62/0.69 2.62/0.69 Now clausify the problem and encode Horn clauses using encoding 3 of 2.62/0.69 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 2.62/0.69 We repeatedly replace C & s=t => u=v by the two clauses: 2.62/0.69 fresh(y, y, x1...xn) = u 2.62/0.69 C => fresh(s, t, x1...xn) = v 2.62/0.69 where fresh is a fresh function symbol and x1..xn are the free 2.62/0.69 variables of u and v. 2.62/0.69 A predicate p(X) is encoded as p(X)=true (this is sound, because the 2.62/0.69 input problem has no model of domain size 1). 2.62/0.69 2.62/0.69 The encoding turns the above axioms into the following unit equations and goals: 2.62/0.69 2.62/0.69 Axiom 1 (ax1): fresh57(X, X, Y, Z) = true2. 2.62/0.69 Axiom 2 (ax18): fresh49(X, X, Y, Z) = true2. 2.62/0.69 Axiom 3 (ax2): fresh47(X, X, Y, Z) = true2. 2.62/0.69 Axiom 4 (ax20): fresh46(X, X, Y, Z) = true2. 2.62/0.69 Axiom 5 (ax21): fresh45(X, X, Y, Z) = true2. 2.62/0.69 Axiom 6 (ax3): fresh36(X, X, Y, Z) = true2. 2.62/0.69 Axiom 7 (ax40): fresh24(X, X, Y, Z) = true2. 2.62/0.69 Axiom 8 (ax47): fresh17(X, X, Y, Z) = true2. 2.62/0.69 Axiom 9 (ax48): fresh16(X, X, Y, Z) = true2. 2.62/0.69 Axiom 10 (ax49): fresh15(X, X, Y, Z) = true2. 2.62/0.69 Axiom 11 (ax59): fresh(X, X, Y, Z) = Z. 2.62/0.69 Axiom 12 (ax60_4): fresh11(X, X, Y, Z) = true2. 2.62/0.69 Axiom 13 (co1_19): fresh7(X, X, Y) = true2. 2.62/0.69 Axiom 14 (co1_21): fresh5(X, X, Y) = true2. 2.62/0.69 Axiom 15 (co1_24): fresh2(X, X, Y) = true2. 2.62/0.69 Axiom 16 (ax2): fresh47(seat(X, Y), true2, X, Y) = furniture(X, Y). 2.62/0.69 Axiom 17 (ax18): fresh49(object(X, Y), true2, X, Y) = nonliving(X, Y). 2.62/0.69 Axiom 18 (ax60_4): fresh11(two(X, Y), true2, X, Y) = member(X, sK9_ax60_X(X, Y), Y). 2.62/0.69 Axiom 19 (ax47): fresh17(human_person(X, Y), true2, X, Y) = organism(X, Y). 2.62/0.69 Axiom 20 (ax3): fresh36(frontseat(X, Y), true2, X, Y) = seat(X, Y). 2.62/0.69 Axiom 21 (ax1): fresh57(furniture(X, Y), true2, X, Y) = instrumentality(X, Y). 2.62/0.69 Axiom 22 (ax20): fresh46(artifact(X, Y), true2, X, Y) = object(X, Y). 2.62/0.69 Axiom 23 (ax59): fresh(be(X, Y, Z, W), true2, Z, W) = Z. 2.62/0.69 Axiom 24 (ax40): fresh24(organism(X, Y), true2, X, Y) = living(X, Y). 2.62/0.69 Axiom 25 (ax49): fresh15(fellow(X, Y), true2, X, Y) = man(X, Y). 2.62/0.69 Axiom 26 (ax21): fresh45(instrumentality(X, Y), true2, X, Y) = artifact(X, Y). 2.62/0.69 Axiom 27 (ax48): fresh16(man(X, Y), true2, X, Y) = human_person(X, Y). 2.62/0.69 Axiom 28 (co1_3): two(sK8_co1_U, sK3_co1_Z) = true2. 2.62/0.69 Axiom 29 (co1_19): fresh7(member(sK8_co1_U, X, sK3_co1_Z), true2, X) = frontseat(sK8_co1_U, sK2_co1_X3(X)). 2.62/0.69 Axiom 30 (co1_21): fresh5(member(sK8_co1_U, X, sK3_co1_Z), true2, X) = be(sK8_co1_U, sK1_co1_X2(X), X, sK2_co1_X3(X)). 2.62/0.69 Axiom 31 (co1_24): fresh2(member(sK8_co1_U, X, sK3_co1_Z), true2, X) = fellow(sK8_co1_U, X). 2.62/0.69 2.62/0.69 Lemma 32: member(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK3_co1_Z) = true2. 2.62/0.69 Proof: 2.62/0.69 member(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK3_co1_Z) 2.62/0.69 = { by axiom 18 (ax60_4) } 2.62/0.69 fresh11(two(sK8_co1_U, sK3_co1_Z), true2, sK8_co1_U, sK3_co1_Z) 2.62/0.69 = { by axiom 28 (co1_3) } 2.62/0.69 fresh11(true2, true2, sK8_co1_U, sK3_co1_Z) 2.62/0.69 = { by axiom 12 (ax60_4) } 3.22/0.76 true2 3.22/0.76 3.22/0.76 Goal 1 (ax53): tuple(nonliving(X, Y), living(X, Y)) = tuple(true2, true2). 3.22/0.76 The goal is true when: 3.22/0.76 X = sK8_co1_U 3.22/0.76 Y = sK9_ax60_X(sK8_co1_U, sK3_co1_Z) 3.22/0.76 3.22/0.76 Proof: 3.22/0.76 tuple(nonliving(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 23 (ax59) } 3.22/0.76 tuple(nonliving(sK8_co1_U, fresh(be(sK8_co1_U, sK1_co1_X2(sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z)))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 30 (co1_21) } 3.22/0.76 tuple(nonliving(sK8_co1_U, fresh(fresh5(member(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK3_co1_Z), true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z)))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by lemma 32 } 3.22/0.76 tuple(nonliving(sK8_co1_U, fresh(fresh5(true2, true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z)))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 14 (co1_21) } 3.22/0.76 tuple(nonliving(sK8_co1_U, fresh(true2, true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z)))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 11 (ax59) } 3.22/0.76 tuple(nonliving(sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 17 (ax18) } 3.22/0.76 tuple(fresh49(object(sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 22 (ax20) } 3.22/0.76 tuple(fresh49(fresh46(artifact(sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 26 (ax21) } 3.22/0.76 tuple(fresh49(fresh46(fresh45(instrumentality(sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 21 (ax1) } 3.22/0.76 tuple(fresh49(fresh46(fresh45(fresh57(furniture(sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 16 (ax2) } 3.22/0.76 tuple(fresh49(fresh46(fresh45(fresh57(fresh47(seat(sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 20 (ax3) } 3.22/0.76 tuple(fresh49(fresh46(fresh45(fresh57(fresh47(fresh36(frontseat(sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 29 (co1_19) } 3.22/0.76 tuple(fresh49(fresh46(fresh45(fresh57(fresh47(fresh36(fresh7(member(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK3_co1_Z), true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by lemma 32 } 3.22/0.76 tuple(fresh49(fresh46(fresh45(fresh57(fresh47(fresh36(fresh7(true2, true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 13 (co1_19) } 3.22/0.76 tuple(fresh49(fresh46(fresh45(fresh57(fresh47(fresh36(true2, true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 6 (ax3) } 3.22/0.76 tuple(fresh49(fresh46(fresh45(fresh57(fresh47(true2, true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 3 (ax2) } 3.22/0.76 tuple(fresh49(fresh46(fresh45(fresh57(true2, true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 1 (ax1) } 3.22/0.76 tuple(fresh49(fresh46(fresh45(true2, true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 5 (ax21) } 3.22/0.76 tuple(fresh49(fresh46(true2, true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 4 (ax20) } 3.22/0.76 tuple(fresh49(true2, true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 2 (ax18) } 3.22/0.76 tuple(true2, living(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 24 (ax40) } 3.22/0.76 tuple(true2, fresh24(organism(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 19 (ax47) } 3.22/0.76 tuple(true2, fresh24(fresh17(human_person(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 27 (ax48) } 3.22/0.76 tuple(true2, fresh24(fresh17(fresh16(man(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 25 (ax49) } 3.22/0.76 tuple(true2, fresh24(fresh17(fresh16(fresh15(fellow(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 31 (co1_24) } 3.22/0.76 tuple(true2, fresh24(fresh17(fresh16(fresh15(fresh2(member(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK3_co1_Z), true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by lemma 32 } 3.22/0.76 tuple(true2, fresh24(fresh17(fresh16(fresh15(fresh2(true2, true2, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 15 (co1_24) } 3.22/0.76 tuple(true2, fresh24(fresh17(fresh16(fresh15(true2, true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 10 (ax49) } 3.22/0.76 tuple(true2, fresh24(fresh17(fresh16(true2, true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 9 (ax48) } 3.22/0.76 tuple(true2, fresh24(fresh17(true2, true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 8 (ax47) } 3.22/0.76 tuple(true2, fresh24(true2, true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 3.22/0.76 = { by axiom 7 (ax40) } 3.22/0.76 tuple(true2, true2) 3.22/0.76 % SZS output end Proof 3.22/0.76 3.22/0.76 RESULT: Theorem (the conjecture is true). 3.22/0.76 EOF