TSTP Solution File: GRP616-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP616-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n008.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 01:15:31 EDT 2023
% Result : Unsatisfiable 12.79s 13.06s
% Output : CNFRefutation 12.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP616-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.13/0.36 % Computer : n008.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Tue Aug 29 01:03:47 EDT 2023
% 0.13/0.36 % CPUTime :
% 12.79/13.06 % SZS status Unsatisfiable
% 12.79/13.06 % SZS output start Proof
% 12.79/13.06 original problem:
% 12.79/13.06 axioms:
% 12.79/13.06 double_divide(inverse(double_divide(inverse(double_divide(A, inverse(B))), C)), double_divide(A, C)) = B
% 12.79/13.06 multiply(A, B) = inverse(double_divide(B, A))
% 12.79/13.06 goal:
% 12.79/13.06 multiply(a(), b()) != multiply(b(), a())
% 12.79/13.06 To show the unsatisfiability of the original goal,
% 12.79/13.06 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 12.79/13.06 Here is an equational proof:
% 12.79/13.06 0: double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(X1))), X2)), double_divide(X0, X2)) = X1.
% 12.79/13.06 Proof: Axiom.
% 12.79/13.06
% 12.79/13.06 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 12.79/13.06 Proof: Axiom.
% 12.79/13.06
% 12.79/13.06 2: X1 = double_divide(inverse(X4), double_divide(inverse(double_divide(X3, inverse(X4))), double_divide(X3, inverse(X1)))).
% 12.79/13.06 Proof: A critical pair between equations 0 and 0.
% 12.79/13.06
% 12.79/13.06 3: X1 = double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X3, inverse(X4))), X5)), inverse(X1))), double_divide(X3, X5))), X4).
% 12.79/13.06 Proof: A critical pair between equations 0 and 0.
% 12.79/13.06
% 12.79/13.06 4: X1 = double_divide(inverse(X7), double_divide(X0, double_divide(inverse(double_divide(X6, inverse(double_divide(X0, inverse(X1))))), double_divide(X6, inverse(X7))))).
% 12.79/13.06 Proof: A critical pair between equations 0 and 2.
% 12.79/13.06
% 12.79/13.06 5: X1 = double_divide(inverse(double_divide(inverse(X9), double_divide(inverse(double_divide(inverse(double_divide(X6, inverse(inverse(X1)))), X8)), double_divide(X6, X8)))), X9).
% 12.79/13.06 Proof: A critical pair between equations 3 and 3.
% 12.79/13.06
% 12.79/13.06 15: X1 = double_divide(inverse(double_divide(inverse(X9), inverse(X1))), X9).
% 12.79/13.06 Proof: Rewrite equation 5,
% 12.79/13.06 lhs with equations []
% 12.79/13.06 rhs with equations [0].
% 12.79/13.06
% 12.79/13.06 17: X1 = double_divide(inverse(X11), double_divide(inverse(inverse(X1)), inverse(X11))).
% 12.79/13.06 Proof: A critical pair between equations 15 and 15.
% 12.79/13.06
% 12.79/13.06 29: double_divide(inverse(inverse(X13)), inverse(X4)) = double_divide(inverse(X4), X13).
% 12.79/13.06 Proof: A critical pair between equations 2 and 17.
% 12.79/13.06
% 12.79/13.06 32: X1 = double_divide(inverse(double_divide(inverse(inverse(X13)), inverse(double_divide(X0, inverse(X1))))), double_divide(X0, X13)).
% 12.79/13.06 Proof: A critical pair between equations 4 and 17.
% 12.79/13.06
% 12.79/13.06 53: X1 = double_divide(inverse(inverse(X9)), inverse(double_divide(inverse(X9), inverse(X1)))).
% 12.79/13.06 Proof: Rewrite equation 15,
% 12.79/13.06 lhs with equations []
% 12.79/13.06 rhs with equations [29].
% 12.79/13.06
% 12.79/13.06 62: X12 = double_divide(inverse(double_divide(inverse(X12), inverse(X13))), X13).
% 12.79/13.06 Proof: A critical pair between equations 17 and 53.
% 12.79/13.06
% 12.79/13.06 71: X1 = double_divide(inverse(double_divide(inverse(inverse(inverse(X1))), inverse(X16))), X16).
% 12.79/13.06 Proof: A critical pair between equations 2 and 32.
% 12.79/13.06
% 12.79/13.06 72: X1 = inverse(inverse(X1)).
% 12.79/13.06 Proof: Rewrite equation 71,
% 12.79/13.06 lhs with equations []
% 12.79/13.06 rhs with equations [62].
% 12.79/13.06
% 12.79/13.06 104: double_divide(X13, inverse(X4)) = double_divide(inverse(X4), X13).
% 12.79/13.06 Proof: Rewrite equation 29,
% 12.79/13.06 lhs with equations [72]
% 12.79/13.06 rhs with equations [].
% 12.79/13.06
% 12.79/13.06 107: double_divide(X13, inverse(inverse(X14))) = double_divide(X14, X13).
% 12.79/13.06 Proof: A critical pair between equations 104 and 72.
% 12.79/13.06
% 12.79/13.06 128: double_divide(X13, X14) = double_divide(X14, X13).
% 12.79/13.06 Proof: Rewrite equation 107,
% 12.79/13.06 lhs with equations [72]
% 12.79/13.06 rhs with equations [].
% 12.79/13.06
% 12.79/13.06 132: multiply(a(), b()) = multiply(b(), a()).
% 12.79/13.06 Proof: Rewrite lhs with equations [1,128]
% 12.79/13.06 rhs with equations [1].
% 12.79/13.06
% 12.79/13.06 % SZS output end Proof
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