TSTP Solution File: GRP564-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP564-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n029.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 01:15:22 EDT 2023
% Result : Unsatisfiable 1.25s 1.62s
% Output : CNFRefutation 1.25s
% 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 : GRP564-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.03/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 02:57:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 1.25/1.62 % SZS status Unsatisfiable
% 1.25/1.62 % SZS output start Proof
% 1.25/1.62 original problem:
% 1.25/1.62 axioms:
% 1.25/1.62 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B
% 1.25/1.62 multiply(A, B) = divide(A, inverse(B))
% 1.25/1.62 goal:
% 1.25/1.62 multiply(a(), b()) != multiply(b(), a())
% 1.25/1.62 To show the unsatisfiability of the original goal,
% 1.25/1.62 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 1.25/1.62 Here is an equational proof:
% 1.25/1.62 0: divide(divide(divide(X0, inverse(X1)), X2), divide(X0, X2)) = X1.
% 1.25/1.62 Proof: Axiom.
% 1.25/1.62
% 1.25/1.62 1: multiply(X0, X1) = divide(X0, inverse(X1)).
% 1.25/1.62 Proof: Axiom.
% 1.25/1.62
% 1.25/1.62 2: X1 = divide(X4, divide(divide(X3, inverse(X4)), divide(X3, inverse(X1)))).
% 1.25/1.62 Proof: A critical pair between equations 0 and 0.
% 1.25/1.62
% 1.25/1.62 3: X1 = divide(divide(divide(divide(divide(X3, inverse(X4)), X5), inverse(X1)), divide(X3, X5)), X4).
% 1.25/1.62 Proof: A critical pair between equations 0 and 0.
% 1.25/1.62
% 1.25/1.62 4: X1 = divide(divide(X9, divide(divide(divide(X6, inverse(inverse(X1))), X8), divide(X6, X8))), X9).
% 1.25/1.62 Proof: A critical pair between equations 3 and 3.
% 1.25/1.62
% 1.25/1.62 6: X1 = divide(X7, divide(X0, divide(divide(X6, inverse(divide(X0, inverse(X1)))), divide(X6, inverse(X7))))).
% 1.25/1.62 Proof: A critical pair between equations 0 and 2.
% 1.25/1.62
% 1.25/1.62 15: X1 = divide(divide(X9, inverse(X1)), X9).
% 1.25/1.62 Proof: Rewrite equation 4,
% 1.25/1.62 lhs with equations []
% 1.25/1.62 rhs with equations [0].
% 1.25/1.62
% 1.25/1.62 17: X1 = divide(X11, divide(inverse(X1), inverse(X11))).
% 1.25/1.62 Proof: A critical pair between equations 15 and 15.
% 1.25/1.62
% 1.25/1.62 29: divide(inverse(X13), inverse(X4)) = divide(X4, X13).
% 1.25/1.62 Proof: A critical pair between equations 2 and 17.
% 1.25/1.62
% 1.25/1.62 38: X1 = divide(divide(inverse(X13), inverse(divide(X0, inverse(X1)))), divide(X0, X13)).
% 1.25/1.62 Proof: A critical pair between equations 6 and 17.
% 1.25/1.62
% 1.25/1.62 54: X1 = divide(inverse(X9), inverse(divide(X9, inverse(X1)))).
% 1.25/1.62 Proof: Rewrite equation 15,
% 1.25/1.62 lhs with equations []
% 1.25/1.62 rhs with equations [29].
% 1.25/1.62
% 1.25/1.62 62: X12 = divide(divide(X12, inverse(X13)), X13).
% 1.25/1.62 Proof: A critical pair between equations 17 and 54.
% 1.25/1.62
% 1.25/1.62 71: X1 = divide(divide(inverse(inverse(X1)), inverse(X16)), X16).
% 1.25/1.62 Proof: A critical pair between equations 2 and 38.
% 1.25/1.62
% 1.25/1.62 72: X1 = inverse(inverse(X1)).
% 1.25/1.62 Proof: Rewrite equation 71,
% 1.25/1.62 lhs with equations []
% 1.25/1.62 rhs with equations [62].
% 1.25/1.62
% 1.25/1.62 81: multiply(a(), b()) = multiply(b(), a()).
% 1.25/1.62 Proof: Rewrite lhs with equations [1]
% 1.25/1.62 rhs with equations [1,29,72].
% 1.25/1.62
% 1.25/1.62 % SZS output end Proof
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