0.09/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.11 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.10/0.31 % Computer : n018.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.31 % CPULimit : 960 0.16/0.31 % WCLimit : 120 0.16/0.31 % DateTime : Thu Jul 2 06:53:52 EDT 2020 0.16/0.31 % CPUTime : 0.16/0.47 % SZS status Theorem 0.16/0.47 1.48/0.59 % SZS output start Proof 1.48/0.59 Take the following subset of the input axioms: 2.12/0.66 fof(ax1, axiom, ![U, V]: (furniture(U, V) => instrumentality(U, V))). 2.12/0.66 fof(ax16, axiom, ![U, V]: (object(U, V) => unisex(U, V))). 2.12/0.66 fof(ax2, axiom, ![U, V]: (seat(U, V) => furniture(U, V))). 2.12/0.66 fof(ax20, axiom, ![U, V]: (object(U, V) <= artifact(U, V))). 2.12/0.66 fof(ax21, axiom, ![U, V]: (artifact(U, V) <= instrumentality(U, V))). 2.12/0.66 fof(ax3, axiom, ![U, V]: (seat(U, V) <= frontseat(U, V))). 2.12/0.66 fof(ax37, axiom, ![U, V]: (male(U, V) <= man(U, V))). 2.12/0.66 fof(ax49, axiom, ![U, V]: (man(U, V) <= fellow(U, V))). 2.12/0.66 fof(ax50, axiom, ![U, V]: (~nonliving(U, V) <= animate(U, V))). 2.12/0.66 fof(ax51, axiom, ![U, V]: (~nonexistent(U, V) <= existent(U, V))). 2.12/0.66 fof(ax52, axiom, ![U, V]: (nonhuman(U, V) => ~human(U, V))). 2.12/0.66 fof(ax53, axiom, ![U, V]: (~living(U, V) <= nonliving(U, V))). 2.12/0.66 fof(ax54, axiom, ![U, V]: (singleton(U, V) => ~multiple(U, V))). 2.12/0.66 fof(ax55, axiom, ![U, V]: (~general(U, V) <= specific(U, V))). 2.12/0.66 fof(ax56, axiom, ![U, V]: (unisex(U, V) => ~male(U, V))). 2.12/0.66 fof(ax57, axiom, ![U, V]: (~old(U, V) <= young(U, V))). 2.12/0.66 fof(ax59, axiom, ![U, V, X, W]: (X=W <= be(U, V, W, X))). 2.12/0.66 fof(ax60, axiom, ![U, V]: (?[W]: (member(U, W, V) & ?[X]: (member(U, X, V) & (W!=X & ![Y]: ((W=Y | Y=X) <= member(U, Y, V))))) <=> two(U, V))). 2.12/0.66 fof(ax61, axiom, ![U]: ~?[V]: member(U, V, V)). 2.12/0.66 fof(co1, conjecture, ~?[U]: (?[V, X, W, Y, Z]: (chevy(U, X) & (white(U, X) & (dirty(U, X) & (agent(U, Y, X) & (present(U, Y) & (barrel(U, Y) & (in(U, Y, X) & (![X1]: (?[X2, X3]: (frontseat(U, X3) & (state(U, X2) & (in(U, X3, X3) & be(U, X2, X1, X3)))) <= member(U, X1, Z)) & (group(U, Z) & (![X4]: ((fellow(U, X4) & young(U, X4)) <= member(U, X4, Z)) & (two(U, Z) & (down(U, Y, V) & (event(U, Y) & (old(U, X) & (placename(U, W) & (hollywood_placename(U, W) & (city(U, X) & (of(U, W, X) & (lonely(U, V) & street(U, V)))))))))))))))))))) & actual_world(U))). 2.12/0.66 2.12/0.66 Now clausify the problem and encode Horn clauses using encoding 3 of 2.12/0.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 2.12/0.66 We repeatedly replace C & s=t => u=v by the two clauses: 2.12/0.66 fresh(y, y, x1...xn) = u 2.12/0.66 C => fresh(s, t, x1...xn) = v 2.12/0.66 where fresh is a fresh function symbol and x1..xn are the free 2.12/0.66 variables of u and v. 2.12/0.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the 2.12/0.66 input problem has no model of domain size 1). 2.12/0.66 2.12/0.66 The encoding turns the above axioms into the following unit equations and goals: 2.12/0.66 2.12/0.66 Axiom 1 (ax1): fresh57(X, X, Y, Z) = true2. 2.12/0.66 Axiom 2 (ax16): fresh51(X, X, Y, Z) = true2. 2.12/0.66 Axiom 3 (ax2): fresh47(X, X, Y, Z) = true2. 2.12/0.66 Axiom 4 (ax20): fresh46(X, X, Y, Z) = true2. 2.12/0.66 Axiom 5 (ax21): fresh45(X, X, Y, Z) = true2. 2.12/0.66 Axiom 6 (ax3): fresh36(X, X, Y, Z) = true2. 2.12/0.66 Axiom 7 (ax37): fresh28(X, X, Y, Z) = true2. 2.12/0.66 Axiom 8 (ax49): fresh15(X, X, Y, Z) = true2. 2.12/0.66 Axiom 9 (ax59): fresh(X, X, Y, Z) = Y. 2.12/0.66 Axiom 10 (ax60_6): fresh11(X, X, Y, Z) = true2. 2.12/0.66 Axiom 11 (co1_21): fresh5(X, X, Y) = true2. 2.12/0.66 Axiom 12 (co1_22): fresh4(X, X, Y) = true2. 2.12/0.66 Axiom 13 (co1_23): fresh3(X, X, Y) = true2. 2.12/0.66 Axiom 14 (ax1): fresh57(furniture(X, Y), true2, X, Y) = instrumentality(X, Y). 2.12/0.66 Axiom 15 (ax37): fresh28(man(X, Y), true2, X, Y) = male(X, Y). 2.12/0.66 Axiom 16 (ax21): fresh45(instrumentality(X, Y), true2, X, Y) = artifact(X, Y). 2.12/0.66 Axiom 17 (ax16): fresh51(object(X, Y), true2, X, Y) = unisex(X, Y). 2.12/0.66 Axiom 18 (ax60_6): fresh11(two(X, Y), true2, X, Y) = member(X, sK9_ax60_X(X, Y), Y). 2.12/0.66 Axiom 19 (ax20): fresh46(artifact(X, Y), true2, X, Y) = object(X, Y). 2.12/0.66 Axiom 20 (ax59): fresh(be(X, Y, Z, W), true2, Z, W) = W. 2.12/0.66 Axiom 21 (ax2): fresh47(seat(X, Y), true2, X, Y) = furniture(X, Y). 2.12/0.66 Axiom 22 (ax3): fresh36(frontseat(X, Y), true2, X, Y) = seat(X, Y). 2.12/0.66 Axiom 23 (ax49): fresh15(fellow(X, Y), true2, X, Y) = man(X, Y). 2.12/0.66 Axiom 24 (co1_3): two(sK8_co1_U, sK3_co1_Z) = true2. 2.12/0.66 Axiom 25 (co1_21): fresh5(member(sK8_co1_U, X, sK3_co1_Z), true2, X) = frontseat(sK8_co1_U, sK2_co1_X3(X)). 2.12/0.67 Axiom 26 (co1_22): fresh4(member(sK8_co1_U, X, sK3_co1_Z), true2, X) = be(sK8_co1_U, sK1_co1_X2(X), X, sK2_co1_X3(X)). 2.12/0.67 Axiom 27 (co1_23): fresh3(member(sK8_co1_U, X, sK3_co1_Z), true2, X) = fellow(sK8_co1_U, X). 2.12/0.67 2.12/0.67 Lemma 28: member(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK3_co1_Z) = true2. 2.12/0.67 Proof: 2.12/0.67 member(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z), sK3_co1_Z) 2.12/0.67 = { by axiom 18 (ax60_6) } 2.12/0.67 fresh11(two(sK8_co1_U, sK3_co1_Z), true2, sK8_co1_U, sK3_co1_Z) 2.12/0.67 = { by axiom 24 (co1_3) } 2.12/0.67 fresh11(true2, true2, sK8_co1_U, sK3_co1_Z) 2.12/0.67 = { by axiom 10 (ax60_6) } 2.46/0.70 true2 2.46/0.70 2.46/0.70 Goal 1 (ax56): tuple(unisex(X, Y), male(X, Y)) = tuple(true2, true2). 2.46/0.70 The goal is true when: 2.46/0.70 X = sK8_co1_U 2.46/0.70 Y = sK9_ax60_X(sK8_co1_U, sK3_co1_Z) 2.46/0.70 2.46/0.70 Proof: 2.46/0.70 tuple(unisex(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z)), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 9 (ax59) } 2.46/0.71 tuple(unisex(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)))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 12 (co1_22) } 2.46/0.71 tuple(unisex(sK8_co1_U, fresh(fresh4(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)))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by lemma 28 } 2.46/0.71 tuple(unisex(sK8_co1_U, fresh(fresh4(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)))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 26 (co1_22) } 2.46/0.71 tuple(unisex(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)))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 20 (ax59) } 2.46/0.71 tuple(unisex(sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 17 (ax16) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 19 (ax20) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 16 (ax21) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 14 (ax1) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 21 (ax2) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 22 (ax3) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 25 (co1_21) } 2.46/0.71 tuple(fresh51(fresh46(fresh45(fresh57(fresh47(fresh36(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, 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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by lemma 28 } 2.46/0.71 tuple(fresh51(fresh46(fresh45(fresh57(fresh47(fresh36(fresh5(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 11 (co1_21) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 6 (ax3) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 3 (ax2) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 1 (ax1) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 5 (ax21) } 2.46/0.71 tuple(fresh51(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))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 4 (ax20) } 2.46/0.71 tuple(fresh51(true2, true2, sK8_co1_U, sK2_co1_X3(sK9_ax60_X(sK8_co1_U, sK3_co1_Z))), male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 2 (ax16) } 2.46/0.71 tuple(true2, male(sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 15 (ax37) } 2.46/0.71 tuple(true2, fresh28(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))) 2.46/0.71 = { by axiom 23 (ax49) } 2.46/0.71 tuple(true2, fresh28(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))) 2.46/0.71 = { by axiom 27 (co1_23) } 2.46/0.71 tuple(true2, fresh28(fresh15(fresh3(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))) 2.46/0.71 = { by lemma 28 } 2.46/0.71 tuple(true2, fresh28(fresh15(fresh3(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))) 2.46/0.71 = { by axiom 13 (co1_23) } 2.46/0.71 tuple(true2, fresh28(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))) 2.46/0.71 = { by axiom 8 (ax49) } 2.46/0.71 tuple(true2, fresh28(true2, true2, sK8_co1_U, sK9_ax60_X(sK8_co1_U, sK3_co1_Z))) 2.46/0.71 = { by axiom 7 (ax37) } 2.46/0.71 tuple(true2, true2) 2.46/0.71 % SZS output end Proof 2.46/0.71 2.46/0.71 RESULT: Theorem (the conjecture is true). 2.46/0.71 EOF