TSTP Solution File: GRP528-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP528-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n008.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 01:15:15 EDT 2023
% Result : Unsatisfiable 1.37s 1.68s
% Output : CNFRefutation 1.37s
% 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 : GRP528-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 01:03:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 1.37/1.68 % SZS status Unsatisfiable
% 1.37/1.68 % SZS output start Proof
% 1.37/1.68 original problem:
% 1.37/1.68 axioms:
% 1.37/1.68 divide(A, divide(divide(A, B), divide(C, B))) = C
% 1.37/1.68 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 1.37/1.68 inverse(A) = divide(divide(B, B), A)
% 1.37/1.68 goal:
% 1.37/1.68 multiply(a(), b()) != multiply(b(), a())
% 1.37/1.68 To show the unsatisfiability of the original goal,
% 1.37/1.68 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 1.37/1.68 Here is an equational proof:
% 1.37/1.68 0: divide(X0, divide(divide(X0, X1), divide(X2, X1))) = X2.
% 1.37/1.68 Proof: Axiom.
% 1.37/1.68
% 1.37/1.68 1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 1.37/1.68 Proof: Axiom.
% 1.37/1.68
% 1.37/1.68 2: inverse(X0) = divide(divide(X1, X1), X0).
% 1.37/1.68 Proof: Axiom.
% 1.37/1.68
% 1.37/1.68 3: multiply(X0, X1) = divide(X0, inverse(X1)).
% 1.37/1.68 Proof: Rewrite equation 1,
% 1.37/1.68 lhs with equations []
% 1.37/1.68 rhs with equations [2].
% 1.37/1.68
% 1.37/1.68 4: X2 = divide(X3, inverse(divide(X2, X3))).
% 1.37/1.68 Proof: A critical pair between equations 0 and 2.
% 1.37/1.68
% 1.37/1.68 7: inverse(X0) = divide(inverse(divide(X2, X2)), X0).
% 1.37/1.68 Proof: A critical pair between equations 2 and 2.
% 1.37/1.68
% 1.37/1.68 8: divide(divide(X0, divide(X5, X4)), X4) = divide(X0, X5).
% 1.37/1.69 Proof: A critical pair between equations 0 and 0.
% 1.37/1.69
% 1.37/1.69 13: X2 = inverse(divide(divide(divide(X3, X3), X1), divide(X2, X1))).
% 1.37/1.69 Proof: A critical pair between equations 0 and 2.
% 1.37/1.69
% 1.37/1.69 15: X2 = divide(X3, divide(X5, divide(X2, divide(divide(X3, X4), divide(X5, X4))))).
% 1.37/1.69 Proof: A critical pair between equations 0 and 0.
% 1.37/1.69
% 1.37/1.69 16: X2 = inverse(divide(inverse(X1), divide(X2, X1))).
% 1.37/1.69 Proof: Rewrite equation 13,
% 1.37/1.69 lhs with equations []
% 1.37/1.69 rhs with equations [2].
% 1.37/1.69
% 1.37/1.69 17: X6 = divide(X6, divide(X8, X8)).
% 1.37/1.69 Proof: A critical pair between equations 15 and 0.
% 1.37/1.69
% 1.37/1.69 18: divide(divide(X5, X7), X5) = inverse(X7).
% 1.37/1.69 Proof: A critical pair between equations 8 and 2.
% 1.37/1.69
% 1.37/1.69 20: X2 = inverse(inverse(divide(X2, divide(X3, X3)))).
% 1.37/1.69 Proof: A critical pair between equations 16 and 7.
% 1.37/1.69
% 1.37/1.69 22: X4 = divide(inverse(divide(X5, X4)), inverse(X5)).
% 1.37/1.69 Proof: A critical pair between equations 4 and 4.
% 1.37/1.69
% 1.37/1.69 30: X4 = multiply(inverse(divide(X5, X4)), X5).
% 1.37/1.69 Proof: Rewrite equation 22,
% 1.37/1.69 lhs with equations []
% 1.37/1.69 rhs with equations [3].
% 1.37/1.69
% 1.37/1.69 31: X2 = inverse(inverse(X2)).
% 1.37/1.69 Proof: Rewrite equation 20,
% 1.37/1.69 lhs with equations []
% 1.37/1.69 rhs with equations [17].
% 1.37/1.69
% 1.37/1.69 32: X2 = multiply(X3, divide(X2, X3)).
% 1.37/1.69 Proof: Rewrite equation 4,
% 1.37/1.69 lhs with equations []
% 1.37/1.69 rhs with equations [3].
% 1.37/1.69
% 1.37/1.69 42: X10 = divide(X0, divide(X0, X10)).
% 1.37/1.69 Proof: A critical pair between equations 0 and 17.
% 1.37/1.69
% 1.37/1.69 47: divide(X7, X6) = multiply(X7, inverse(X6)).
% 1.37/1.69 Proof: A critical pair between equations 30 and 16.
% 1.37/1.69
% 1.37/1.69 51: X10 = multiply(X0, inverse(multiply(X0, inverse(X10)))).
% 1.37/1.69 Proof: Rewrite equation 42,
% 1.37/1.69 lhs with equations []
% 1.37/1.69 rhs with equations [47,47].
% 1.37/1.69
% 1.37/1.69 58: X2 = multiply(X3, multiply(X2, inverse(X3))).
% 1.37/1.69 Proof: Rewrite equation 32,
% 1.37/1.69 lhs with equations []
% 1.37/1.69 rhs with equations [47].
% 1.37/1.69
% 1.37/1.69 61: multiply(multiply(X5, inverse(X7)), inverse(X5)) = inverse(X7).
% 1.37/1.69 Proof: Rewrite equation 18,
% 1.37/1.69 lhs with equations [47,47]
% 1.37/1.69 rhs with equations [].
% 1.37/1.69
% 1.37/1.69 78: X11 = multiply(multiply(X11, inverse(X12)), X12).
% 1.37/1.69 Proof: A critical pair between equations 58 and 51.
% 1.37/1.69
% 1.37/1.69 88: X11 = multiply(divide(X11, X12), X12).
% 1.37/1.69 Proof: Rewrite equation 78,
% 1.37/1.69 lhs with equations []
% 1.37/1.69 rhs with equations [47].
% 1.37/1.69
% 1.37/1.69 91: divide(divide(X5, X7), X5) = inverse(X7).
% 1.37/1.69 Proof: Rewrite equation 61,
% 1.37/1.69 lhs with equations [47,47]
% 1.37/1.69 rhs with equations [].
% 1.37/1.69
% 1.37/1.69 123: divide(divide(X5, inverse(X8)), X5) = X8.
% 1.37/1.69 Proof: A critical pair between equations 91 and 31.
% 1.37/1.69
% 1.37/1.69 135: multiply(multiply(X5, X8), inverse(X5)) = X8.
% 1.37/1.69 Proof: Rewrite equation 123,
% 1.37/1.69 lhs with equations [47,31,47]
% 1.37/1.69 rhs with equations [].
% 1.37/1.69
% 1.37/1.69 149: X11 = multiply(multiply(X11, inverse(X12)), X12).
% 1.37/1.69 Proof: Rewrite equation 88,
% 1.37/1.69 lhs with equations []
% 1.37/1.69 rhs with equations [47].
% 1.37/1.69
% 1.37/1.69 179: multiply(X13, X14) = multiply(X14, X13).
% 1.37/1.69 Proof: A critical pair between equations 149 and 135.
% 1.37/1.69
% 1.37/1.69 245: multiply(a(), b()) = multiply(b(), a()).
% 1.37/1.69 Proof: Rewrite lhs with equations []
% 1.37/1.69 rhs with equations [179].
% 1.37/1.69
% 1.37/1.69 % SZS output end Proof
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