TSTP Solution File: GRP540-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP540-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n006.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 01:15:17 EDT 2023
% Result : Unsatisfiable 0.50s 0.93s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP540-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n006.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 02:16:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.50/0.93 % SZS status Unsatisfiable
% 0.50/0.93 % SZS output start Proof
% 0.50/0.93 original problem:
% 0.50/0.93 axioms:
% 0.50/0.93 divide(divide(A, B), divide(divide(A, C), B)) = C
% 0.50/0.93 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.50/0.93 inverse(A) = divide(divide(B, B), A)
% 0.50/0.93 identity() = divide(A, A)
% 0.50/0.93 goal:
% 0.50/0.93 multiply(a(), b()) != multiply(b(), a())
% 0.50/0.93 To show the unsatisfiability of the original goal,
% 0.50/0.93 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 0.50/0.93 Here is an equational proof:
% 0.50/0.93 0: divide(divide(X0, X1), divide(divide(X0, X2), X1)) = X2.
% 0.50/0.93 Proof: Axiom.
% 0.50/0.93
% 0.50/0.93 1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.50/0.93 Proof: Axiom.
% 0.50/0.93
% 0.50/0.93 2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.50/0.93 Proof: Axiom.
% 0.50/0.93
% 0.50/0.93 3: identity() = divide(X0, X0).
% 0.50/0.93 Proof: Axiom.
% 0.50/0.93
% 0.50/0.93 4: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.50/0.93 Proof: Rewrite equation 1,
% 0.50/0.93 lhs with equations []
% 0.50/0.93 rhs with equations [3].
% 0.50/0.93
% 0.50/0.93 5: inverse(X0) = divide(identity(), X0).
% 0.50/0.93 Proof: Rewrite equation 2,
% 0.50/0.93 lhs with equations []
% 0.50/0.93 rhs with equations [3].
% 0.50/0.93
% 0.50/0.93 11: X3 = divide(divide(X3, X1), divide(identity(), X1)).
% 0.50/0.93 Proof: A critical pair between equations 0 and 3.
% 0.50/0.93
% 0.50/0.93 16: X4 = divide(divide(X3, divide(divide(X3, X5), X4)), X5).
% 0.50/0.93 Proof: A critical pair between equations 0 and 0.
% 0.50/0.93
% 0.50/0.93 20: X3 = divide(divide(X3, X1), inverse(X1)).
% 0.50/0.93 Proof: Rewrite equation 11,
% 0.50/0.93 lhs with equations []
% 0.50/0.93 rhs with equations [5].
% 0.50/0.93
% 0.50/0.93 21: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.50/0.93 Proof: Rewrite equation 4,
% 0.50/0.93 lhs with equations []
% 0.50/0.93 rhs with equations [5].
% 0.50/0.93
% 0.50/0.93 33: X4 = divide(divide(X6, divide(identity(), X4)), X6).
% 0.50/0.93 Proof: A critical pair between equations 16 and 3.
% 0.50/0.93
% 0.50/0.93 35: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.50/0.93 Proof: Rewrite equation 21,
% 0.50/0.93 lhs with equations []
% 0.50/0.93 rhs with equations [5].
% 0.50/0.93
% 0.50/0.93 36: X3 = divide(divide(X3, X1), divide(identity(), X1)).
% 0.50/0.93 Proof: Rewrite equation 20,
% 0.50/0.93 lhs with equations []
% 0.50/0.93 rhs with equations [5].
% 0.50/0.93
% 0.50/0.93 49: divide(X7, divide(identity(), X8)) = divide(X8, divide(identity(), X7)).
% 0.50/0.93 Proof: A critical pair between equations 36 and 33.
% 0.50/0.93
% 0.50/0.93 58: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.50/0.93 Proof: Rewrite equation 35,
% 0.50/0.93 lhs with equations []
% 0.50/0.93 rhs with equations [5].
% 0.50/0.93
% 0.50/0.93 59: divide(X7, inverse(X8)) = divide(X8, inverse(X7)).
% 0.50/0.93 Proof: Rewrite equation 49,
% 0.50/0.93 lhs with equations [5]
% 0.50/0.93 rhs with equations [5].
% 0.50/0.93
% 0.50/0.93 74: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.50/0.93 Proof: Rewrite equation 58,
% 0.50/0.93 lhs with equations []
% 0.50/0.93 rhs with equations [5].
% 0.50/0.93
% 0.50/0.93 80: divide(X7, divide(identity(), X8)) = divide(X8, divide(identity(), X7)).
% 0.50/0.93 Proof: Rewrite equation 59,
% 0.50/0.93 lhs with equations [5]
% 0.50/0.93 rhs with equations [5].
% 0.50/0.93
% 0.50/0.93 81: multiply(a(), b()) = multiply(b(), a()).
% 0.50/0.93 Proof: Rewrite lhs with equations [74]
% 0.50/0.93 rhs with equations [74,80].
% 0.50/0.93
% 0.50/0.93 % SZS output end Proof
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