TSTP Solution File: GRP514-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP514-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n018.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 01:15:12 EDT 2023
% Result : Unsatisfiable 1.49s 1.92s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP514-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 21:41:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.49/1.92 % SZS status Unsatisfiable
% 1.49/1.92 % SZS output start Proof
% 1.49/1.92 original problem:
% 1.49/1.92 axioms:
% 1.49/1.92 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B
% 1.49/1.92 goal:
% 1.49/1.92 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 1.49/1.92 To show the unsatisfiability of the original goal,
% 1.49/1.92 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 1.49/1.92 Here is an equational proof:
% 1.49/1.92 0: multiply(X0, multiply(multiply(X1, X2), inverse(multiply(X0, X2)))) = X1.
% 1.49/1.92 Proof: Axiom.
% 1.49/1.92
% 1.49/1.92 1: X1 = multiply(X3, multiply(multiply(X1, multiply(multiply(X4, X5), inverse(multiply(X3, X5)))), inverse(X4))).
% 1.49/1.92 Proof: A critical pair between equations 0 and 0.
% 1.49/1.92
% 1.49/1.92 2: X3 = multiply(X0, multiply(X4, inverse(multiply(X0, multiply(multiply(X4, X5), inverse(multiply(X3, X5))))))).
% 1.49/1.92 Proof: A critical pair between equations 0 and 0.
% 1.49/1.92
% 1.49/1.92 3: X6 = multiply(X6, multiply(X7, inverse(X7))).
% 1.49/1.92 Proof: A critical pair between equations 2 and 0.
% 1.49/1.92
% 1.49/1.92 5: X3 = multiply(X0, multiply(X6, inverse(multiply(X0, multiply(X7, inverse(multiply(X3, multiply(multiply(X7, X8), inverse(multiply(X6, X8)))))))))).
% 1.49/1.92 Proof: A critical pair between equations 2 and 0.
% 1.49/1.92
% 1.49/1.92 7: X1 = multiply(X3, multiply(multiply(X1, multiply(X7, inverse(multiply(X3, multiply(multiply(X7, X8), inverse(multiply(X6, X8))))))), inverse(X6))).
% 1.49/1.92 Proof: A critical pair between equations 1 and 0.
% 1.49/1.92
% 1.49/1.92 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))).
% 1.49/1.92 Proof: A critical pair between equations 1 and 1.
% 1.49/1.92
% 1.49/1.92 15: X8 = multiply(X4, multiply(X8, inverse(X4))).
% 1.49/1.92 Proof: A critical pair between equations 1 and 3.
% 1.49/1.92
% 1.49/1.92 18: X1 = multiply(X9, multiply(multiply(X1, multiply(X7, inverse(X9))), inverse(X7))).
% 1.49/1.92 Proof: A critical pair between equations 7 and 3.
% 1.49/1.92
% 1.49/1.92 19: X9 = multiply(X0, multiply(X7, inverse(multiply(X0, multiply(X7, inverse(X9)))))).
% 1.49/1.92 Proof: A critical pair between equations 5 and 3.
% 1.49/1.92
% 1.49/1.92 20: X1 = multiply(X8, multiply(multiply(X1, multiply(multiply(X4, multiply(X10, inverse(X8))), inverse(X10))), inverse(X4))).
% 1.49/1.92 Proof: A critical pair between equations 14 and 3.
% 1.49/1.92
% 1.49/1.92 27: multiply(X10, X12) = multiply(X10, multiply(multiply(X11, X12), inverse(X11))).
% 1.49/1.92 Proof: A critical pair between equations 19 and 0.
% 1.49/1.92
% 1.49/1.92 28: X10 = multiply(multiply(X10, X12), multiply(X11, inverse(multiply(X11, X12)))).
% 1.49/1.92 Proof: A critical pair between equations 18 and 0.
% 1.49/1.92
% 1.49/1.92 35: X1 = multiply(multiply(X11, X13), multiply(multiply(X1, multiply(X12, inverse(multiply(X12, X13)))), inverse(X11))).
% 1.49/1.92 Proof: A critical pair between equations 20 and 0.
% 1.49/1.92
% 1.49/1.92 47: X1 = multiply(multiply(X1, multiply(X12, inverse(multiply(X12, X15)))), X15).
% 1.49/1.92 Proof: A critical pair between equations 35 and 28.
% 1.49/1.92
% 1.49/1.92 60: X16 = multiply(multiply(X17, inverse(X17)), X16).
% 1.49/1.92 Proof: A critical pair between equations 18 and 47.
% 1.49/1.92
% 1.49/1.92 66: multiply(X16, multiply(X17, inverse(multiply(X17, inverse(X4))))) = multiply(X4, X16).
% 1.49/1.92 Proof: A critical pair between equations 15 and 47.
% 1.49/1.92
% 1.49/1.92 67: multiply(X10, multiply(X17, inverse(multiply(X17, inverse(X16))))) = multiply(X10, X16).
% 1.49/1.92 Proof: A critical pair between equations 27 and 47.
% 1.49/1.92
% 1.49/1.92 83: multiply(X16, X4) = multiply(X4, X16).
% 1.49/1.92 Proof: Rewrite equation 66,
% 1.49/1.92 lhs with equations [67]
% 1.49/1.92 rhs with equations [].
% 1.49/1.92
% 1.49/1.92 84: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 1.49/1.92 Proof: Rewrite lhs with equations [83,60]
% 1.49/1.92 rhs with equations [].
% 1.49/1.92
% 1.49/1.92 % SZS output end Proof
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