TSTP Solution File: GRP600-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP600-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n024.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 : Thu Aug 31 01:15:28 EDT 2023
% Result : Unsatisfiable 1.39s 1.78s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP600-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n024.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 : Mon Aug 28 20:59:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.39/1.78 % SZS status Unsatisfiable
% 1.39/1.78 % SZS output start Proof
% 1.39/1.78 original problem:
% 1.39/1.78 axioms:
% 1.39/1.78 double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(inverse(C), B))))) = C
% 1.39/1.78 multiply(A, B) = inverse(double_divide(B, A))
% 1.39/1.78 goal:
% 1.39/1.78 multiply(a(), b()) != multiply(b(), a())
% 1.39/1.78 To show the unsatisfiability of the original goal,
% 1.39/1.78 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 1.39/1.78 Here is an equational proof:
% 1.39/1.78 0: double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(double_divide(inverse(X2), X1))))) = X2.
% 1.39/1.78 Proof: Axiom.
% 1.39/1.78
% 1.39/1.78 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.39/1.78 Proof: Axiom.
% 1.39/1.78
% 1.39/1.78 2: X2 = double_divide(double_divide(double_divide(inverse(X2), X4), inverse(double_divide(inverse(X5), X4))), inverse(X5)).
% 1.39/1.78 Proof: A critical pair between equations 0 and 0.
% 1.39/1.78
% 1.39/1.78 3: X2 = double_divide(X5, inverse(double_divide(double_divide(X3, X4), inverse(double_divide(inverse(X2), inverse(double_divide(X3, inverse(double_divide(inverse(X5), X4))))))))).
% 1.39/1.78 Proof: A critical pair between equations 0 and 0.
% 1.39/1.78
% 1.39/1.78 5: X2 = double_divide(X9, inverse(double_divide(double_divide(double_divide(X7, X8), inverse(double_divide(X7, inverse(double_divide(inverse(inverse(X2)), X8))))), inverse(X9)))).
% 1.39/1.78 Proof: A critical pair between equations 3 and 3.
% 1.39/1.78
% 1.39/1.78 6: X2 = double_divide(X5, inverse(double_divide(double_divide(double_divide(inverse(X5), X7), inverse(double_divide(inverse(X8), X7))), inverse(double_divide(inverse(X2), inverse(X8)))))).
% 1.39/1.78 Proof: A critical pair between equations 3 and 0.
% 1.39/1.78
% 1.39/1.78 15: X2 = double_divide(X9, inverse(double_divide(inverse(X2), inverse(X9)))).
% 1.39/1.78 Proof: Rewrite equation 5,
% 1.39/1.78 lhs with equations []
% 1.39/1.78 rhs with equations [0].
% 1.39/1.78
% 1.39/1.78 17: X2 = double_divide(double_divide(inverse(X11), inverse(inverse(X2))), inverse(X11)).
% 1.39/1.78 Proof: A critical pair between equations 15 and 15.
% 1.39/1.78
% 1.39/1.78 29: double_divide(inverse(X5), inverse(inverse(X13))) = double_divide(X13, inverse(X5)).
% 1.39/1.78 Proof: A critical pair between equations 2 and 17.
% 1.39/1.78
% 1.39/1.78 39: X2 = double_divide(double_divide(inverse(X8), inverse(inverse(X13))), inverse(double_divide(X13, inverse(double_divide(inverse(X2), inverse(X8)))))).
% 1.39/1.78 Proof: A critical pair between equations 6 and 17.
% 1.39/1.78
% 1.39/1.78 56: inverse(inverse(X15)) = X15.
% 1.39/1.78 Proof: A critical pair between equations 39 and 15.
% 1.39/1.78
% 1.39/1.78 94: double_divide(inverse(X5), X13) = double_divide(X13, inverse(X5)).
% 1.39/1.78 Proof: Rewrite equation 29,
% 1.39/1.78 lhs with equations [56]
% 1.39/1.78 rhs with equations [].
% 1.39/1.78
% 1.39/1.78 98: double_divide(inverse(inverse(X16)), X13) = double_divide(X13, X16).
% 1.39/1.78 Proof: A critical pair between equations 94 and 56.
% 1.39/1.78
% 1.39/1.78 114: double_divide(X16, X13) = double_divide(X13, X16).
% 1.39/1.78 Proof: Rewrite equation 98,
% 1.39/1.78 lhs with equations [56]
% 1.39/1.78 rhs with equations [].
% 1.39/1.78
% 1.39/1.78 118: multiply(a(), b()) = multiply(b(), a()).
% 1.39/1.78 Proof: Rewrite lhs with equations [1,114]
% 1.39/1.78 rhs with equations [1].
% 1.39/1.78
% 1.39/1.78 % SZS output end Proof
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