TSTP Solution File: GRP516-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP516-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n032.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 01:15:13 EDT 2023
% Result : Unsatisfiable 1.42s 1.78s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP516-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.10/0.11 % Command : toma --casc %s
% 0.10/0.30 % Computer : n032.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 : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Aug 28 21:26:31 EDT 2023
% 0.10/0.30 % CPUTime :
% 1.42/1.78 % SZS status Unsatisfiable
% 1.42/1.78 % SZS output start Proof
% 1.42/1.78 original problem:
% 1.42/1.78 axioms:
% 1.42/1.78 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B
% 1.42/1.78 goal:
% 1.42/1.78 multiply(a(), b()) != multiply(b(), a())
% 1.42/1.78 To show the unsatisfiability of the original goal,
% 1.42/1.78 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 1.42/1.78 Here is an equational proof:
% 1.42/1.78 0: multiply(X0, multiply(multiply(X1, X2), inverse(multiply(X0, X2)))) = X1.
% 1.42/1.78 Proof: Axiom.
% 1.42/1.78
% 1.42/1.78 1: X1 = multiply(X3, multiply(multiply(X1, multiply(multiply(X4, X5), inverse(multiply(X3, X5)))), inverse(X4))).
% 1.42/1.78 Proof: A critical pair between equations 0 and 0.
% 1.42/1.78
% 1.42/1.78 2: X3 = multiply(X0, multiply(X4, inverse(multiply(X0, multiply(multiply(X4, X5), inverse(multiply(X3, X5))))))).
% 1.42/1.78 Proof: A critical pair between equations 0 and 0.
% 1.42/1.78
% 1.42/1.78 3: X6 = multiply(X6, multiply(X7, inverse(X7))).
% 1.42/1.78 Proof: A critical pair between equations 2 and 0.
% 1.42/1.78
% 1.42/1.78 5: X3 = multiply(X0, multiply(X6, inverse(multiply(X0, multiply(X7, inverse(multiply(X3, multiply(multiply(X7, X8), inverse(multiply(X6, X8)))))))))).
% 1.42/1.78 Proof: A critical pair between equations 2 and 0.
% 1.42/1.78
% 1.42/1.78 7: X1 = multiply(X3, multiply(multiply(X1, multiply(X7, inverse(multiply(X3, multiply(multiply(X7, X8), inverse(multiply(X6, X8))))))), inverse(X6))).
% 1.42/1.78 Proof: A critical pair between equations 1 and 0.
% 1.42/1.78
% 1.42/1.78 14: X1 = multiply(X6, multiply(multiply(X1, multiply(multiply(X4, multiply(multiply(X7, multiply(multiply(X8, X9), inverse(multiply(X6, X9)))), inverse(X8))), inverse(X7))), inverse(X4))).
% 1.42/1.78 Proof: A critical pair between equations 1 and 1.
% 1.42/1.78
% 1.42/1.78 15: X8 = multiply(X4, multiply(X8, inverse(X4))).
% 1.42/1.78 Proof: A critical pair between equations 1 and 3.
% 1.42/1.78
% 1.42/1.78 18: X1 = multiply(X9, multiply(multiply(X1, multiply(X7, inverse(X9))), inverse(X7))).
% 1.42/1.78 Proof: A critical pair between equations 7 and 3.
% 1.42/1.78
% 1.42/1.78 19: X9 = multiply(X0, multiply(X7, inverse(multiply(X0, multiply(X7, inverse(X9)))))).
% 1.42/1.78 Proof: A critical pair between equations 5 and 3.
% 1.42/1.78
% 1.42/1.78 20: X1 = multiply(X8, multiply(multiply(X1, multiply(multiply(X4, multiply(X10, inverse(X8))), inverse(X10))), inverse(X4))).
% 1.42/1.78 Proof: A critical pair between equations 14 and 3.
% 1.42/1.78
% 1.42/1.78 27: multiply(X10, X12) = multiply(X10, multiply(multiply(X11, X12), inverse(X11))).
% 1.42/1.78 Proof: A critical pair between equations 19 and 0.
% 1.42/1.78
% 1.42/1.78 28: X10 = multiply(multiply(X10, X12), multiply(X11, inverse(multiply(X11, X12)))).
% 1.42/1.78 Proof: A critical pair between equations 18 and 0.
% 1.42/1.78
% 1.42/1.78 35: X1 = multiply(multiply(X11, X13), multiply(multiply(X1, multiply(X12, inverse(multiply(X12, X13)))), inverse(X11))).
% 1.42/1.78 Proof: A critical pair between equations 20 and 0.
% 1.42/1.78
% 1.42/1.78 47: X1 = multiply(multiply(X1, multiply(X12, inverse(multiply(X12, X15)))), X15).
% 1.42/1.78 Proof: A critical pair between equations 35 and 28.
% 1.42/1.78
% 1.42/1.78 66: multiply(X16, multiply(X17, inverse(multiply(X17, inverse(X4))))) = multiply(X4, X16).
% 1.42/1.78 Proof: A critical pair between equations 15 and 47.
% 1.42/1.78
% 1.42/1.78 67: multiply(X10, multiply(X17, inverse(multiply(X17, inverse(X16))))) = multiply(X10, X16).
% 1.42/1.78 Proof: A critical pair between equations 27 and 47.
% 1.42/1.78
% 1.42/1.78 83: multiply(X16, X4) = multiply(X4, X16).
% 1.42/1.78 Proof: Rewrite equation 66,
% 1.42/1.78 lhs with equations [67]
% 1.42/1.78 rhs with equations [].
% 1.42/1.78
% 1.42/1.78 84: multiply(a(), b()) = multiply(b(), a()).
% 1.42/1.78 Proof: Rewrite lhs with equations []
% 1.42/1.78 rhs with equations [83].
% 1.42/1.78
% 1.42/1.78 % SZS output end Proof
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