TSTP Solution File: GRP520-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP520-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n025.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 2.10s 2.43s
% Output : CNFRefutation 2.10s
% 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 : GRP520-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.10/0.33 % Computer : n025.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Tue Aug 29 02:44:09 EDT 2023
% 0.10/0.34 % CPUTime :
% 2.10/2.43 % SZS status Unsatisfiable
% 2.10/2.43 % SZS output start Proof
% 2.10/2.43 original problem:
% 2.10/2.43 axioms:
% 2.10/2.43 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C
% 2.10/2.43 goal:
% 2.10/2.43 multiply(a(), b()) != multiply(b(), a())
% 2.10/2.43 To show the unsatisfiability of the original goal,
% 2.10/2.43 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 2.10/2.43 Here is an equational proof:
% 2.10/2.43 0: multiply(X0, multiply(multiply(inverse(multiply(X0, X1)), X2), X1)) = X2.
% 2.10/2.43 Proof: Axiom.
% 2.10/2.43
% 2.10/2.43 1: X2 = multiply(X3, multiply(multiply(inverse(X5), X2), multiply(multiply(inverse(multiply(X3, X4)), X5), X4))).
% 2.10/2.43 Proof: A critical pair between equations 0 and 0.
% 2.10/2.43
% 2.10/2.43 2: multiply(multiply(inverse(multiply(inverse(multiply(X0, X1)), X4)), X5), X4) = multiply(X0, multiply(X5, X1)).
% 2.10/2.43 Proof: A critical pair between equations 0 and 0.
% 2.10/2.43
% 2.10/2.43 3: X2 = multiply(multiply(inverse(X8), X2), X8).
% 2.10/2.43 Proof: A critical pair between equations 1 and 0.
% 2.10/2.43
% 2.10/2.43 4: X9 = multiply(inverse(multiply(X6, X7)), multiply(X6, multiply(X9, X7))).
% 2.10/2.43 Proof: A critical pair between equations 0 and 2.
% 2.10/2.43
% 2.10/2.43 7: multiply(X0, multiply(X5, X1)) = multiply(multiply(inverse(X8), X5), multiply(multiply(inverse(multiply(inverse(multiply(X0, X1)), X7)), X8), X7)).
% 2.10/2.43 Proof: A critical pair between equations 2 and 0.
% 2.10/2.43
% 2.10/2.43 8: X2 = multiply(X6, multiply(multiply(inverse(X5), X2), multiply(multiply(inverse(X8), X5), multiply(multiply(inverse(multiply(X6, X7)), X8), X7)))).
% 2.10/2.43 Proof: A critical pair between equations 1 and 0.
% 2.10/2.43
% 2.10/2.43 11: multiply(multiply(inverse(multiply(inverse(multiply(X6, X7)), X8)), X9), multiply(X5, X8)) = multiply(multiply(inverse(multiply(inverse(multiply(X6, multiply(X9, X7))), X4)), X5), X4).
% 2.10/2.43 Proof: A critical pair between equations 2 and 2.
% 2.10/2.43
% 2.10/2.43 12: multiply(X6, multiply(X5, multiply(multiply(inverse(X7), X8), multiply(multiply(inverse(multiply(X6, X9)), X7), X9)))) = multiply(multiply(inverse(multiply(inverse(X8), X4)), X5), X4).
% 2.10/2.43 Proof: A critical pair between equations 2 and 1.
% 2.10/2.43
% 2.10/2.43 13: multiply(X0, multiply(X5, X1)) = multiply(multiply(inverse(X8), X5), multiply(multiply(inverse(X7), X8), multiply(multiply(inverse(multiply(inverse(multiply(X0, X1)), X9)), X7), X9))).
% 2.10/2.43 Proof: A critical pair between equations 2 and 1.
% 2.10/2.43
% 2.10/2.43 16: multiply(X0, multiply(X5, X1)) = multiply(multiply(inverse(X8), X5), multiply(multiply(inverse(X7), X8), multiply(X0, multiply(X7, X1)))).
% 2.10/2.43 Proof: Rewrite equation 13,
% 2.10/2.43 lhs with equations []
% 2.10/2.43 rhs with equations [2].
% 2.10/2.43
% 2.10/2.43 17: multiply(multiply(inverse(multiply(inverse(multiply(X6, X7)), X8)), X9), multiply(X5, X8)) = multiply(X6, multiply(X5, multiply(X9, X7))).
% 2.10/2.43 Proof: Rewrite equation 11,
% 2.10/2.43 lhs with equations []
% 2.10/2.43 rhs with equations [2].
% 2.10/2.43
% 2.10/2.43 18: multiply(X0, multiply(X5, X1)) = multiply(multiply(inverse(X8), X5), multiply(X0, multiply(X8, X1))).
% 2.10/2.43 Proof: Rewrite equation 7,
% 2.10/2.43 lhs with equations []
% 2.10/2.43 rhs with equations [2].
% 2.10/2.43
% 2.10/2.43 19: multiply(X10, multiply(X12, X11)) = multiply(X12, multiply(X10, X11)).
% 2.10/2.43 Proof: A critical pair between equations 3 and 4.
% 2.10/2.43
% 2.10/2.43 20: multiply(X6, multiply(inverse(multiply(X6, X7)), multiply(X11, X7))) = X11.
% 2.10/2.43 Proof: A critical pair between equations 17 and 3.
% 2.10/2.43
% 2.10/2.43 21: multiply(multiply(inverse(multiply(inverse(X12), X4)), X10), X4) = multiply(X10, X12).
% 2.10/2.43 Proof: A critical pair between equations 12 and 1.
% 2.10/2.43
% 2.10/2.43 22: X2 = multiply(multiply(inverse(X11), X5), multiply(multiply(inverse(X5), X2), X11)).
% 2.10/2.43 Proof: A critical pair between equations 8 and 0.
% 2.10/2.43
% 2.10/2.43 24: multiply(inverse(X10), X11) = multiply(inverse(multiply(X6, X10)), multiply(X6, X11)).
% 2.10/2.43 Proof: A critical pair between equations 4 and 3.
% 2.10/2.43
% 2.10/2.43 29: multiply(X9, multiply(X10, X1)) = multiply(multiply(inverse(X7), X9), multiply(X10, multiply(X7, X1))).
% 2.10/2.43 Proof: A critical pair between equations 16 and 18.
% 2.10/2.43
% 2.10/2.43 31: multiply(inverse(X10), X11) = multiply(X6, multiply(inverse(multiply(X6, X10)), X11)).
% 2.10/2.43 Proof: Rewrite equation 24,
% 2.10/2.43 lhs with equations []
% 2.10/2.43 rhs with equations [19].
% 2.10/2.43
% 2.10/2.43 32: multiply(inverse(X7), multiply(X11, X7)) = X11.
% 2.10/2.43 Proof: Rewrite equation 20,
% 2.10/2.43 lhs with equations [31]
% 2.10/2.43 rhs with equations [].
% 2.10/2.43
% 2.10/2.43 36: multiply(X0, multiply(X5, X1)) = multiply(X5, multiply(X0, X1)).
% 2.10/2.43 Proof: Rewrite equation 18,
% 2.10/2.43 lhs with equations []
% 2.10/2.43 rhs with equations [29].
% 2.10/2.43
% 2.10/2.43 38: multiply(X0, multiply(X5, X1)) = multiply(X8, multiply(multiply(inverse(X8), X5), multiply(X0, X1))).
% 2.10/2.43 Proof: Rewrite equation 16,
% 2.10/2.43 lhs with equations []
% 2.10/2.43 rhs with equations [29,36].
% 2.10/2.43
% 2.10/2.43 42: X13 = multiply(multiply(inverse(X12), X12), X13).
% 2.10/2.43 Proof: A critical pair between equations 22 and 3.
% 2.10/2.43
% 2.10/2.43 46: multiply(inverse(X10), X12) = inverse(multiply(inverse(X12), X10)).
% 2.10/2.43 Proof: A critical pair between equations 31 and 32.
% 2.10/2.43
% 2.10/2.43 47: multiply(X0, multiply(X10, X1)) = multiply(multiply(X0, X1), X10).
% 2.10/2.43 Proof: A critical pair between equations 38 and 3.
% 2.10/2.43
% 2.10/2.43 57: multiply(X4, multiply(multiply(inverse(X4), X12), X10)) = multiply(X10, X12).
% 2.10/2.43 Proof: Rewrite equation 21,
% 2.10/2.43 lhs with equations [46,47,36]
% 2.10/2.43 rhs with equations [].
% 2.10/2.43
% 2.10/2.43 63: multiply(X15, X14) = multiply(X14, X15).
% 2.10/2.43 Proof: A critical pair between equations 57 and 42.
% 2.10/2.43
% 2.10/2.43 81: multiply(a(), b()) = multiply(b(), a()).
% 2.10/2.43 Proof: Rewrite lhs with equations []
% 2.10/2.43 rhs with equations [63].
% 2.10/2.43
% 2.10/2.43 % SZS output end Proof
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