0.08/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.10 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.10/0.30 % Computer : n018.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 960 0.10/0.30 % WCLimit : 120 0.10/0.30 % DateTime : Thu Jul 2 06:44:07 EDT 2020 0.10/0.31 % CPUTime : 0.16/0.46 % SZS status Theorem 0.16/0.46 1.84/0.58 % SZS output start Proof 1.84/0.58 Take the following subset of the input axioms: 1.84/0.63 fof(ax1, axiom, ![U, V]: (furniture(U, V) => instrumentality(U, V))). 1.84/0.63 fof(ax18, axiom, ![U, V]: (nonliving(U, V) <= object(U, V))). 1.84/0.63 fof(ax2, axiom, ![U, V]: (furniture(U, V) <= seat(U, V))). 1.84/0.63 fof(ax20, axiom, ![U, V]: (artifact(U, V) => object(U, V))). 1.84/0.63 fof(ax21, axiom, ![U, V]: (artifact(U, V) <= instrumentality(U, V))). 1.84/0.63 fof(ax3, axiom, ![U, V]: (seat(U, V) <= frontseat(U, V))). 1.84/0.63 fof(ax40, axiom, ![U, V]: (living(U, V) <= organism(U, V))). 1.84/0.63 fof(ax47, axiom, ![U, V]: (human_person(U, V) => organism(U, V))). 1.84/0.63 fof(ax48, axiom, ![U, V]: (human_person(U, V) <= man(U, V))). 1.84/0.63 fof(ax49, axiom, ![U, V]: (man(U, V) <= fellow(U, V))). 1.84/0.63 fof(ax50, axiom, ![U, V]: (~nonliving(U, V) <= animate(U, V))). 1.84/0.63 fof(ax51, axiom, ![U, V]: (~nonexistent(U, V) <= existent(U, V))). 1.84/0.63 fof(ax52, axiom, ![U, V]: (nonhuman(U, V) => ~human(U, V))). 1.84/0.63 fof(ax53, axiom, ![U, V]: (nonliving(U, V) => ~living(U, V))). 1.84/0.63 fof(ax54, axiom, ![U, V]: (~multiple(U, V) <= singleton(U, V))). 1.84/0.63 fof(ax55, axiom, ![U, V]: (specific(U, V) => ~general(U, V))). 1.84/0.63 fof(ax56, axiom, ![U, V]: (~male(U, V) <= unisex(U, V))). 1.84/0.63 fof(ax57, axiom, ![U, V]: (young(U, V) => ~old(U, V))). 1.84/0.63 fof(ax59, axiom, ![U, V, X, W]: (X=W <= be(U, V, W, X))). 1.84/0.63 fof(ax60, axiom, ![U, V]: (two(U, V) <=> ?[W]: (?[X]: (![Y]: (member(U, Y, V) => (Y=W | Y=X)) & (X!=W & member(U, X, V))) & member(U, W, V)))). 1.84/0.63 fof(ax61, axiom, ![U]: ~?[V]: member(U, V, V)). 1.84/0.63 fof(co1, conjecture, ~?[U]: (?[V, X, W, Y, Z, X1]: (of(U, W, V) & (city(U, V) & (old(U, X) & (lonely(U, Y) & (agent(U, Z, X) & (present(U, Z) & (down(U, Z, Y) & (![X2]: (member(U, X2, X1) => ?[X3, X4]: (in(U, X4, X4) & (be(U, X3, X2, X4) & (state(U, X3) & frontseat(U, X4))))) & (group(U, X1) & (![X5]: ((young(U, X5) & fellow(U, X5)) <= member(U, X5, X1)) & (two(U, X1) & (in(U, Z, V) & (barrel(U, Z) & (event(U, Z) & (street(U, Y) & (dirty(U, X) & (white(U, X) & (chevy(U, X) & (placename(U, W) & hollywood_placename(U, W)))))))))))))))))))) & actual_world(U))). 1.84/0.63 1.84/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of 1.84/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 1.84/0.63 We repeatedly replace C & s=t => u=v by the two clauses: 1.84/0.63 fresh(y, y, x1...xn) = u 1.84/0.63 C => fresh(s, t, x1...xn) = v 1.84/0.63 where fresh is a fresh function symbol and x1..xn are the free 1.84/0.63 variables of u and v. 1.84/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the 1.84/0.63 input problem has no model of domain size 1). 1.84/0.63 1.84/0.63 The encoding turns the above axioms into the following unit equations and goals: 1.84/0.63 1.84/0.63 Axiom 1 (ax1): fresh57(X, X, Y, Z) = true2. 1.84/0.63 Axiom 2 (ax18): fresh49(X, X, Y, Z) = true2. 1.84/0.63 Axiom 3 (ax2): fresh47(X, X, Y, Z) = true2. 1.84/0.63 Axiom 4 (ax20): fresh46(X, X, Y, Z) = true2. 1.84/0.63 Axiom 5 (ax21): fresh45(X, X, Y, Z) = true2. 1.84/0.63 Axiom 6 (ax3): fresh36(X, X, Y, Z) = true2. 1.84/0.63 Axiom 7 (ax40): fresh24(X, X, Y, Z) = true2. 1.84/0.63 Axiom 8 (ax47): fresh17(X, X, Y, Z) = true2. 1.84/0.63 Axiom 9 (ax48): fresh16(X, X, Y, Z) = true2. 1.84/0.63 Axiom 10 (ax49): fresh15(X, X, Y, Z) = true2. 1.84/0.63 Axiom 11 (ax59): fresh(X, X, Y, Z) = Y. 1.84/0.63 Axiom 12 (ax60_4): fresh11(X, X, Y, Z) = true2. 1.84/0.63 Axiom 13 (co1_19): fresh7(X, X, Y) = true2. 1.84/0.63 Axiom 14 (co1_21): fresh5(X, X, Y) = true2. 1.84/0.63 Axiom 15 (co1_24): fresh2(X, X, Y) = true2. 1.84/0.63 Axiom 16 (ax40): fresh24(organism(X, Y), true2, X, Y) = living(X, Y). 1.84/0.63 Axiom 17 (ax21): fresh45(instrumentality(X, Y), true2, X, Y) = artifact(X, Y). 1.84/0.63 Axiom 18 (ax2): fresh47(seat(X, Y), true2, X, Y) = furniture(X, Y). 1.84/0.63 Axiom 19 (ax3): fresh36(frontseat(X, Y), true2, X, Y) = seat(X, Y). 1.84/0.63 Axiom 20 (ax49): fresh15(fellow(X, Y), true2, X, Y) = man(X, Y). 1.84/0.63 Axiom 21 (ax20): fresh46(artifact(X, Y), true2, X, Y) = object(X, Y). 1.84/0.63 Axiom 22 (ax18): fresh49(object(X, Y), true2, X, Y) = nonliving(X, Y). 1.84/0.63 Axiom 23 (ax48): fresh16(man(X, Y), true2, X, Y) = human_person(X, Y). 1.84/0.63 Axiom 24 (ax60_4): fresh11(two(X, Y), true2, X, Y) = member(X, sK10_ax60_X(X, Y), Y). 1.84/0.63 Axiom 25 (ax47): fresh17(human_person(X, Y), true2, X, Y) = organism(X, Y). 1.84/0.63 Axiom 26 (ax1): fresh57(furniture(X, Y), true2, X, Y) = instrumentality(X, Y). 1.84/0.63 Axiom 27 (ax59): fresh(be(X, Y, Z, W), true2, Z, W) = W. 1.84/0.63 Axiom 28 (co1_7): two(sK9_co1_U, sK3_co1_X1) = true2. 1.84/0.63 Axiom 29 (co1_19): fresh7(member(sK9_co1_U, X, sK3_co1_X1), true2, X) = frontseat(sK9_co1_U, sK2_co1_X4(X)). 1.84/0.63 Axiom 30 (co1_21): fresh5(member(sK9_co1_U, X, sK3_co1_X1), true2, X) = be(sK9_co1_U, sK1_co1_X3(X), X, sK2_co1_X4(X)). 1.84/0.63 Axiom 31 (co1_24): fresh2(member(sK9_co1_U, X, sK3_co1_X1), true2, X) = fellow(sK9_co1_U, X). 1.84/0.63 1.84/0.63 Lemma 32: member(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK3_co1_X1) = true2. 1.84/0.63 Proof: 1.84/0.63 member(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK3_co1_X1) 1.84/0.63 = { by axiom 24 (ax60_4) } 1.84/0.63 fresh11(two(sK9_co1_U, sK3_co1_X1), true2, sK9_co1_U, sK3_co1_X1) 1.84/0.63 = { by axiom 28 (co1_7) } 1.84/0.63 fresh11(true2, true2, sK9_co1_U, sK3_co1_X1) 1.84/0.63 = { by axiom 12 (ax60_4) } 2.53/0.68 true2 2.53/0.68 2.53/0.68 Goal 1 (ax53): tuple(living(X, Y), nonliving(X, Y)) = tuple(true2, true2). 2.53/0.68 The goal is true when: 2.53/0.68 X = sK9_co1_U 2.53/0.68 Y = sK10_ax60_X(sK9_co1_U, sK3_co1_X1) 2.53/0.68 2.53/0.68 Proof: 2.53/0.68 tuple(living(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 16 (ax40) } 2.53/0.68 tuple(fresh24(organism(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 25 (ax47) } 2.53/0.68 tuple(fresh24(fresh17(human_person(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 23 (ax48) } 2.53/0.68 tuple(fresh24(fresh17(fresh16(man(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 20 (ax49) } 2.53/0.68 tuple(fresh24(fresh17(fresh16(fresh15(fellow(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 31 (co1_24) } 2.53/0.68 tuple(fresh24(fresh17(fresh16(fresh15(fresh2(member(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK3_co1_X1), true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by lemma 32 } 2.53/0.68 tuple(fresh24(fresh17(fresh16(fresh15(fresh2(true2, true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 15 (co1_24) } 2.53/0.68 tuple(fresh24(fresh17(fresh16(fresh15(true2, true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 10 (ax49) } 2.53/0.68 tuple(fresh24(fresh17(fresh16(true2, true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 9 (ax48) } 2.53/0.68 tuple(fresh24(fresh17(true2, true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 8 (ax47) } 2.53/0.68 tuple(fresh24(true2, true2, sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 7 (ax40) } 2.53/0.68 tuple(true2, nonliving(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1))) 2.53/0.68 = { by axiom 11 (ax59) } 2.53/0.68 tuple(true2, nonliving(sK9_co1_U, fresh(true2, true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))))) 2.53/0.68 = { by axiom 14 (co1_21) } 2.53/0.68 tuple(true2, nonliving(sK9_co1_U, fresh(fresh5(true2, true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))))) 2.53/0.68 = { by lemma 32 } 2.53/0.68 tuple(true2, nonliving(sK9_co1_U, fresh(fresh5(member(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK3_co1_X1), true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))))) 2.53/0.68 = { by axiom 30 (co1_21) } 2.53/0.68 tuple(true2, nonliving(sK9_co1_U, fresh(be(sK9_co1_U, sK1_co1_X3(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))))) 2.53/0.68 = { by axiom 27 (ax59) } 2.53/0.68 tuple(true2, nonliving(sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 22 (ax18) } 2.53/0.68 tuple(true2, fresh49(object(sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 21 (ax20) } 2.53/0.68 tuple(true2, fresh49(fresh46(artifact(sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 17 (ax21) } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(instrumentality(sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 26 (ax1) } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(fresh57(furniture(sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 18 (ax2) } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(fresh57(fresh47(seat(sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 19 (ax3) } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(fresh57(fresh47(fresh36(frontseat(sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 29 (co1_19) } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(fresh57(fresh47(fresh36(fresh7(member(sK9_co1_U, sK10_ax60_X(sK9_co1_U, sK3_co1_X1), sK3_co1_X1), true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by lemma 32 } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(fresh57(fresh47(fresh36(fresh7(true2, true2, sK10_ax60_X(sK9_co1_U, sK3_co1_X1)), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 13 (co1_19) } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(fresh57(fresh47(fresh36(true2, true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 6 (ax3) } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(fresh57(fresh47(true2, true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 3 (ax2) } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(fresh57(true2, true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 1 (ax1) } 2.53/0.68 tuple(true2, fresh49(fresh46(fresh45(true2, true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 5 (ax21) } 2.53/0.68 tuple(true2, fresh49(fresh46(true2, true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1))), true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 4 (ax20) } 2.53/0.68 tuple(true2, fresh49(true2, true2, sK9_co1_U, sK2_co1_X4(sK10_ax60_X(sK9_co1_U, sK3_co1_X1)))) 2.53/0.68 = { by axiom 2 (ax18) } 2.53/0.68 tuple(true2, true2) 2.53/0.68 % SZS output end Proof 2.53/0.68 2.53/0.68 RESULT: Theorem (the conjecture is true). 2.53/0.68 EOF