TSTP Solution File: TOP051-1 by Toma---0.4
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% File : Toma---0.4
% Problem : TOP051-1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 05:59:21 EDT 2023
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP051-1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 00:16:04 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 original problem:
% 0.19/0.46 axioms:
% 0.19/0.46 product(X, X) = X
% 0.19/0.46 product(product(X, Y), Y) = X
% 0.19/0.46 product(product(X, Y), Z) = product(product(X, Z), product(Y, Z))
% 0.19/0.46 product(a1(), a6()) = a2()
% 0.19/0.46 product(a2(), a7()) = a3()
% 0.19/0.46 product(a3(), a1()) = a4()
% 0.19/0.46 product(a4(), a10()) = a5()
% 0.19/0.46 product(a5(), a9()) = a6()
% 0.19/0.46 product(a6(), a2()) = a7()
% 0.19/0.46 product(a7(), a3()) = a8()
% 0.19/0.46 product(a8(), a6()) = a9()
% 0.19/0.46 product(a9(), a4()) = a10()
% 0.19/0.46 product(a10(), a5()) = a11()
% 0.19/0.46 goal:
% 0.19/0.46 tuple(a1(), a6(), a5(), a2(), a7(), a3(), a4(), a9(), a10(), a8()) != tuple(a2(), a7(), a6(), a3(), a8(), a4(), a5(), a10(), a11(), a9())
% 0.19/0.46 To show the unsatisfiability of the original goal,
% 0.19/0.46 it suffices to show that tuple(a1(), a6(), a5(), a2(), a7(), a3(), a4(), a9(), a10(), a8()) = tuple(a2(), a7(), a6(), a3(), a8(), a4(), a5(), a10(), a11(), a9()) (skolemized goal) is valid under the axioms.
% 0.19/0.46 Here is an equational proof:
% 0.19/0.46 0: product(X0, X0) = X0.
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 1: product(product(X0, X1), X1) = X0.
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 2: product(product(X0, X1), X2) = product(product(X0, X2), product(X1, X2)).
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 3: product(a1(), a6()) = a2().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 4: product(a2(), a7()) = a3().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 5: product(a3(), a1()) = a4().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 6: product(a4(), a10()) = a5().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 7: product(a5(), a9()) = a6().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 8: product(a6(), a2()) = a7().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 9: product(a7(), a3()) = a8().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 10: product(a8(), a6()) = a9().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 11: product(a9(), a4()) = a10().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 12: product(a10(), a5()) = a11().
% 0.19/0.46 Proof: Axiom.
% 0.19/0.46
% 0.19/0.46 13: product(product(a1(), a6()), product(a6(), product(a1(), a6()))) = a3().
% 0.19/0.46 Proof: Rewrite equation 4,
% 0.19/0.46 lhs with equations [3,8,3]
% 0.19/0.46 rhs with equations [].
% 0.19/0.46
% 0.19/0.46 14: product(product(a1(), product(a6(), a1())), product(product(a6(), a1()), product(a1(), product(a6(), a1())))) = a4().
% 0.19/0.46 Proof: Rewrite equation 5,
% 0.19/0.46 lhs with equations [13,2,2,0,2,2,0]
% 0.19/0.46 rhs with equations [].
% 0.19/0.46
% 0.19/0.46 15: product(product(product(a1(), product(a6(), a1())), product(product(a6(), a1()), product(a1(), product(a6(), a1())))), product(product(product(a6(), a1()), product(a1(), product(a6(), a1()))), product(product(a1(), product(a6(), a1())), product(product(a6(), a1()), product(a1(), product(a6(), a1())))))) = a5().
% 0.19/0.46 Proof: Rewrite equation 6,
% 0.19/0.46 lhs with equations [14,11,10,9,8,3,13,2,2,0,1,2,1,2,0,1,14]
% 0.19/0.46 rhs with equations [].
% 0.19/0.46
% 0.19/0.46 16: a1() = a6().
% 0.19/0.46 Proof: Rewrite equation 7,
% 0.19/0.46 lhs with equations [15,10,9,8,3,13,2,2,0,1,2,1,2,0,1,2,1,2,0,1,1,1]
% 0.19/0.46 rhs with equations [].
% 0.19/0.46
% 0.19/0.46 17: a1() = a7().
% 0.19/0.46 Proof: Rewrite equation 8,
% 0.19/0.46 lhs with equations [16,3,16,0,0]
% 0.19/0.46 rhs with equations [].
% 0.19/0.46
% 0.19/0.46 18: a1() = a8().
% 0.19/0.46 Proof: Rewrite equation 9,
% 0.19/0.46 lhs with equations [17,13,16,0,16,16,0,0,0,0]
% 0.19/0.46 rhs with equations [].
% 0.19/0.46
% 0.19/0.46 19: a1() = a9().
% 0.19/0.46 Proof: Rewrite equation 10,
% 0.19/0.46 lhs with equations [18,16,0]
% 0.19/0.46 rhs with equations [].
% 0.19/0.46
% 0.19/0.46 20: a1() = a10().
% 0.19/0.46 Proof: Rewrite equation 11,
% 0.19/0.46 lhs with equations [19,14,16,0,0,16,0,16,0,0,0,0,0]
% 0.19/0.46 rhs with equations [].
% 0.19/0.46
% 0.19/0.46 21: a1() = a11().
% 0.19/0.46 Proof: Rewrite equation 12,
% 0.19/0.46 lhs with equations [20,15,16,0,0,16,0,16,0,0,0,0,16,0,16,0,0,0,16,0,0,16,0,16,0,0,0,0,0,0,0]
% 0.19/0.46 rhs with equations [].
% 0.19/0.46
% 0.19/0.46 22: tuple(a1(), a6(), a5(), a2(), a7(), a3(), a4(), a9(), a10(), a8()) = tuple(a2(), a7(), a6(), a3(), a8(), a4(), a5(), a10(), a11(), a9()).
% 0.19/0.46 Proof: Rewrite lhs with equations [16,15,16,0,0,16,0,16,0,0,0,0,16,0,16,0,0,0,16,0,0,16,0,16,0,0,0,0,0,0,3,16,0,17,13,16,0,16,16,0,0,0,14,16,0,0,16,0,16,0,0,0,0,19,20,18]
% 0.19/0.46 rhs with equations [3,16,0,17,16,13,16,0,16,16,0,0,0,18,14,16,0,0,16,0,16,0,0,0,0,15,16,0,0,16,0,16,0,0,0,0,16,0,16,0,0,0,16,0,0,16,0,16,0,0,0,0,0,0,20,21,19].
% 0.19/0.46
% 0.19/0.46 % SZS output end Proof
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