TSTP Solution File: GRP512-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP512-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n014.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 1.65s 2.07s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP512-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.12/0.35 % Computer : n014.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Aug 28 19:59:15 EDT 2023
% 0.12/0.35 % CPUTime :
% 1.65/2.07 % SZS status Unsatisfiable
% 1.65/2.07 % SZS output start Proof
% 1.65/2.07 original problem:
% 1.65/2.07 axioms:
% 1.65/2.07 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) = B
% 1.65/2.07 goal:
% 1.65/2.07 multiply(a(), b()) != multiply(b(), a())
% 1.65/2.07 To show the unsatisfiability of the original goal,
% 1.65/2.07 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 1.65/2.07 Here is an equational proof:
% 1.65/2.07 0: multiply(multiply(multiply(X0, X1), X2), inverse(multiply(X0, X2))) = X1.
% 1.65/2.07 Proof: Axiom.
% 1.65/2.07
% 1.65/2.07 1: X5 = multiply(X4, inverse(multiply(multiply(X3, X4), inverse(multiply(X3, X5))))).
% 1.65/2.07 Proof: A critical pair between equations 0 and 0.
% 1.65/2.07
% 1.65/2.07 2: X1 = multiply(multiply(multiply(multiply(multiply(X3, X4), X5), X1), inverse(multiply(X3, X5))), inverse(X4)).
% 1.65/2.07 Proof: A critical pair between equations 0 and 0.
% 1.65/2.07
% 1.65/2.07 9: X5 = multiply(inverse(multiply(X6, X8)), inverse(multiply(X7, inverse(multiply(multiply(multiply(X6, X7), X8), X5))))).
% 1.65/2.07 Proof: A critical pair between equations 1 and 0.
% 1.65/2.07
% 1.65/2.07 12: inverse(X7) = multiply(multiply(X9, inverse(multiply(multiply(multiply(X6, X7), X8), inverse(multiply(X6, X8))))), inverse(X9)).
% 1.65/2.07 Proof: A critical pair between equations 2 and 2.
% 1.65/2.07
% 1.65/2.07 13: inverse(multiply(multiply(X7, X6), inverse(multiply(X7, X8)))) = multiply(X4, inverse(multiply(multiply(X6, X4), inverse(X8)))).
% 1.65/2.07 Proof: A critical pair between equations 1 and 1.
% 1.65/2.07
% 1.65/2.07 16: inverse(X7) = multiply(multiply(X9, inverse(X7)), inverse(X9)).
% 1.65/2.07 Proof: Rewrite equation 12,
% 1.65/2.07 lhs with equations []
% 1.65/2.07 rhs with equations [0].
% 1.65/2.07
% 1.65/2.07 18: inverse(X10) = multiply(inverse(X11), inverse(multiply(X10, inverse(X11)))).
% 1.65/2.07 Proof: A critical pair between equations 16 and 16.
% 1.65/2.07
% 1.65/2.07 23: inverse(multiply(X10, X12)) = multiply(X11, inverse(multiply(multiply(X10, X11), X12))).
% 1.65/2.07 Proof: A critical pair between equations 16 and 0.
% 1.65/2.07
% 1.65/2.07 24: X11 = multiply(X10, multiply(X12, inverse(multiply(multiply(X10, X12), inverse(X11))))).
% 1.65/2.07 Proof: A critical pair between equations 1 and 13.
% 1.65/2.07
% 1.65/2.07 26: inverse(multiply(multiply(X6, X9), X11)) = multiply(inverse(multiply(X6, X9)), inverse(X11)).
% 1.65/2.07 Proof: A critical pair between equations 9 and 1.
% 1.65/2.07
% 1.65/2.07 34: X11 = multiply(X10, multiply(X12, multiply(inverse(multiply(X10, X12)), inverse(inverse(X11))))).
% 1.65/2.07 Proof: Rewrite equation 24,
% 1.65/2.07 lhs with equations []
% 1.65/2.07 rhs with equations [26].
% 1.65/2.07
% 1.65/2.07 35: inverse(multiply(X10, X12)) = multiply(X11, multiply(inverse(multiply(X10, X11)), inverse(X12))).
% 1.65/2.07 Proof: Rewrite equation 23,
% 1.65/2.07 lhs with equations []
% 1.65/2.07 rhs with equations [26].
% 1.65/2.07
% 1.65/2.07 38: inverse(X10) = multiply(inverse(X11), multiply(X11, multiply(inverse(multiply(X10, X11)), inverse(inverse(X11))))).
% 1.65/2.07 Proof: Rewrite equation 18,
% 1.65/2.07 lhs with equations []
% 1.65/2.07 rhs with equations [35].
% 1.65/2.07
% 1.65/2.07 40: X5 = multiply(X4, multiply(inverse(multiply(X3, X4)), inverse(inverse(multiply(X3, X5))))).
% 1.65/2.07 Proof: Rewrite equation 1,
% 1.65/2.07 lhs with equations []
% 1.65/2.07 rhs with equations [26].
% 1.65/2.07
% 1.65/2.07 50: X13 = inverse(inverse(X13)).
% 1.65/2.07 Proof: A critical pair between equations 34 and 38.
% 1.65/2.07
% 1.65/2.07 53: inverse(multiply(X14, inverse(multiply(X14, X15)))) = X15.
% 1.65/2.07 Proof: A critical pair between equations 35 and 40.
% 1.65/2.07
% 1.65/2.07 61: multiply(inverse(multiply(X12, inverse(X13))), inverse(inverse(X12))) = inverse(inverse(X13)).
% 1.65/2.07 Proof: A critical pair between equations 26 and 16.
% 1.65/2.07
% 1.65/2.07 62: multiply(inverse(multiply(X12, inverse(X13))), X12) = X13.
% 1.65/2.07 Proof: Rewrite equation 61,
% 1.65/2.07 lhs with equations [50]
% 1.65/2.07 rhs with equations [50].
% 1.65/2.07
% 1.65/2.07 82: multiply(X16, X17) = multiply(X17, X16).
% 1.65/2.07 Proof: A critical pair between equations 62 and 53.
% 1.65/2.07
% 1.65/2.07 103: multiply(a(), b()) = multiply(b(), a()).
% 1.65/2.07 Proof: Rewrite lhs with equations []
% 1.65/2.07 rhs with equations [82].
% 1.65/2.07
% 1.65/2.07 % SZS output end Proof
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