TSTP Solution File: GRP524-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP524-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n003.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 01:15:14 EDT 2023
% Result : Unsatisfiable 0.77s 1.19s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP524-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.03/0.13 % Command : toma --casc %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 21:03:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.77/1.19 % SZS status Unsatisfiable
% 0.77/1.19 % SZS output start Proof
% 0.77/1.19 original problem:
% 0.77/1.19 axioms:
% 0.77/1.19 divide(A, divide(B, divide(C, divide(A, B)))) = C
% 0.77/1.19 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.77/1.19 inverse(A) = divide(divide(B, B), A)
% 0.77/1.19 goal:
% 0.77/1.19 multiply(a(), b()) != multiply(b(), a())
% 0.77/1.19 To show the unsatisfiability of the original goal,
% 0.77/1.19 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 0.77/1.19 Here is an equational proof:
% 0.77/1.19 0: divide(X0, divide(X1, divide(X2, divide(X0, X1)))) = X2.
% 0.77/1.19 Proof: Axiom.
% 0.77/1.19
% 0.77/1.19 1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.77/1.19 Proof: Axiom.
% 0.77/1.19
% 0.77/1.19 2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.77/1.19 Proof: Axiom.
% 0.77/1.19
% 0.77/1.19 3: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.77/1.19 Proof: Rewrite equation 1,
% 0.77/1.19 lhs with equations []
% 0.77/1.19 rhs with equations [2].
% 0.77/1.19
% 0.77/1.19 6: inverse(X0) = divide(inverse(divide(X2, X2)), X0).
% 0.77/1.19 Proof: A critical pair between equations 2 and 2.
% 0.77/1.19
% 0.77/1.19 7: X3 = divide(X4, divide(divide(X5, divide(X3, X4)), X5)).
% 0.77/1.19 Proof: A critical pair between equations 0 and 0.
% 0.77/1.19
% 0.77/1.19 12: X2 = inverse(divide(X1, divide(X2, divide(divide(X3, X3), X1)))).
% 0.77/1.19 Proof: A critical pair between equations 0 and 2.
% 0.77/1.19
% 0.77/1.19 13: X2 = divide(X3, divide(divide(X4, divide(X5, divide(X3, X4))), divide(X2, X5))).
% 0.77/1.19 Proof: A critical pair between equations 0 and 0.
% 0.77/1.19
% 0.77/1.19 14: X2 = inverse(divide(X1, divide(X2, inverse(X1)))).
% 0.77/1.19 Proof: Rewrite equation 12,
% 0.77/1.19 lhs with equations []
% 0.77/1.19 rhs with equations [2].
% 0.77/1.19
% 0.77/1.19 16: divide(inverse(X6), divide(X8, X6)) = inverse(X8).
% 0.77/1.19 Proof: A critical pair between equations 14 and 7.
% 0.77/1.19
% 0.77/1.19 22: X7 = divide(divide(X8, divide(X6, X7)), divide(X8, X6)).
% 0.77/1.19 Proof: A critical pair between equations 7 and 0.
% 0.77/1.19
% 0.77/1.19 24: divide(X7, divide(X8, divide(X8, X7))) = divide(X9, X9).
% 0.77/1.19 Proof: A critical pair between equations 0 and 13.
% 0.77/1.19
% 0.77/1.19 25: divide(divide(X0, X6), divide(X8, X6)) = divide(X0, X8).
% 0.77/1.19 Proof: A critical pair between equations 0 and 7.
% 0.77/1.19
% 0.77/1.19 38: X11 = divide(X11, divide(X12, X12)).
% 0.77/1.19 Proof: A critical pair between equations 0 and 24.
% 0.77/1.19
% 0.77/1.19 39: X9 = divide(X3, divide(X3, X9)).
% 0.77/1.19 Proof: A critical pair between equations 13 and 22.
% 0.77/1.19
% 0.77/1.19 44: divide(X9, X8) = inverse(divide(X8, X9)).
% 0.77/1.19 Proof: A critical pair between equations 25 and 2.
% 0.77/1.19
% 0.77/1.19 49: multiply(X0, X1) = divide(X0, divide(divide(X1, X1), X1)).
% 0.77/1.19 Proof: Rewrite equation 3,
% 0.77/1.19 lhs with equations []
% 0.77/1.19 rhs with equations [2].
% 0.77/1.19
% 0.77/1.19 57: inverse(X0) = divide(divide(X2, X2), X0).
% 0.77/1.19 Proof: Rewrite equation 6,
% 0.77/1.19 lhs with equations []
% 0.77/1.19 rhs with equations [44].
% 0.77/1.19
% 0.77/1.19 67: divide(divide(X10, X11), X10) = inverse(X11).
% 0.77/1.19 Proof: A critical pair between equations 44 and 39.
% 0.77/1.19
% 0.77/1.19 72: inverse(X13) = divide(inverse(divide(X14, X14)), X13).
% 0.77/1.19 Proof: A critical pair between equations 16 and 38.
% 0.77/1.19
% 0.77/1.19 73: divide(X11, divide(X10, X10)) = inverse(inverse(X11)).
% 0.77/1.19 Proof: A critical pair between equations 44 and 57.
% 0.77/1.19
% 0.77/1.19 74: divide(X11, X10) = divide(inverse(X10), inverse(X11)).
% 0.77/1.19 Proof: A critical pair between equations 39 and 16.
% 0.77/1.19
% 0.77/1.19 78: divide(X11, X10) = divide(divide(divide(X10, X10), X10), inverse(X11)).
% 0.77/1.19 Proof: Rewrite equation 74,
% 0.77/1.19 lhs with equations []
% 0.77/1.19 rhs with equations [67].
% 0.77/1.19
% 0.77/1.19 79: X11 = inverse(inverse(X11)).
% 0.77/1.19 Proof: Rewrite equation 73,
% 0.77/1.19 lhs with equations [38]
% 0.77/1.19 rhs with equations [].
% 0.77/1.19
% 0.77/1.19 80: inverse(X13) = divide(divide(X14, X14), X13).
% 0.77/1.19 Proof: Rewrite equation 72,
% 0.77/1.19 lhs with equations []
% 0.77/1.19 rhs with equations [44].
% 0.77/1.19
% 0.77/1.19 99: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.77/1.19 Proof: Rewrite equation 49,
% 0.77/1.19 lhs with equations []
% 0.77/1.19 rhs with equations [57].
% 0.77/1.19
% 0.77/1.19 107: divide(X11, X10) = divide(inverse(X10), inverse(X11)).
% 0.77/1.19 Proof: Rewrite equation 78,
% 0.77/1.19 lhs with equations []
% 0.77/1.19 rhs with equations [80].
% 0.77/1.19
% 0.77/1.19 108: multiply(a(), b()) = multiply(b(), a()).
% 0.77/1.19 Proof: Rewrite lhs with equations [99]
% 0.77/1.19 rhs with equations [99,107,79].
% 0.77/1.19
% 0.77/1.19 % SZS output end Proof
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