TSTP Solution File: GRP552-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP552-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n018.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 01:15:19 EDT 2023
% Result : Unsatisfiable 0.48s 0.75s
% Output : CNFRefutation 0.48s
% 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 : GRP552-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n018.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 : Mon Aug 28 22:03:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.48/0.75 % SZS status Unsatisfiable
% 0.48/0.75 % SZS output start Proof
% 0.48/0.75 original problem:
% 0.48/0.75 axioms:
% 0.48/0.75 divide(divide(identity(), A), divide(divide(divide(B, A), C), B)) = C
% 0.48/0.75 multiply(A, B) = divide(A, divide(identity(), B))
% 0.48/0.75 inverse(A) = divide(identity(), A)
% 0.48/0.75 identity() = divide(A, A)
% 0.48/0.75 goal:
% 0.48/0.75 multiply(a(), b()) != multiply(b(), a())
% 0.48/0.75 To show the unsatisfiability of the original goal,
% 0.48/0.75 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 0.48/0.75 Here is an equational proof:
% 0.48/0.75 0: divide(divide(identity(), X0), divide(divide(divide(X1, X0), X2), X1)) = X2.
% 0.48/0.75 Proof: Axiom.
% 0.48/0.75
% 0.48/0.75 1: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.48/0.75 Proof: Axiom.
% 0.48/0.75
% 0.48/0.75 2: inverse(X0) = divide(identity(), X0).
% 0.48/0.75 Proof: Axiom.
% 0.48/0.75
% 0.48/0.75 3: identity() = divide(X0, X0).
% 0.48/0.75 Proof: Axiom.
% 0.48/0.75
% 0.48/0.75 4: divide(inverse(X0), divide(divide(divide(X1, X0), X2), X1)) = X2.
% 0.48/0.75 Proof: Rewrite equation 0,
% 0.48/0.75 lhs with equations [2]
% 0.48/0.75 rhs with equations [].
% 0.48/0.75
% 0.48/0.75 5: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.48/0.75 Proof: Rewrite equation 1,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2].
% 0.48/0.75
% 0.48/0.75 7: X2 = divide(inverse(X3), divide(divide(identity(), X2), X3)).
% 0.48/0.75 Proof: A critical pair between equations 4 and 3.
% 0.48/0.75
% 0.48/0.75 8: divide(X1, X0) = divide(inverse(X0), divide(identity(), X1)).
% 0.48/0.75 Proof: A critical pair between equations 4 and 3.
% 0.48/0.75
% 0.48/0.75 9: X2 = divide(inverse(X3), divide(divide(inverse(X3), X2), identity())).
% 0.48/0.75 Proof: A critical pair between equations 4 and 2.
% 0.48/0.75
% 0.48/0.75 12: X2 = divide(divide(identity(), X3), divide(divide(divide(identity(), X3), X2), identity())).
% 0.48/0.75 Proof: Rewrite equation 9,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2,2].
% 0.48/0.75
% 0.48/0.75 13: X2 = divide(divide(identity(), X3), divide(divide(identity(), X2), X3)).
% 0.48/0.75 Proof: Rewrite equation 7,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2].
% 0.48/0.75
% 0.48/0.75 14: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.48/0.75 Proof: Rewrite equation 5,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2].
% 0.48/0.75
% 0.48/0.75 16: divide(X1, X0) = divide(divide(identity(), X0), divide(identity(), X1)).
% 0.48/0.75 Proof: Rewrite equation 8,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2].
% 0.48/0.75
% 0.48/0.75 22: divide(identity(), X3) = divide(divide(identity(), X3), divide(identity(), identity())).
% 0.48/0.75 Proof: A critical pair between equations 12 and 3.
% 0.48/0.75
% 0.48/0.75 24: X4 = divide(divide(identity(), divide(identity(), X5)), divide(X5, X4)).
% 0.48/0.75 Proof: A critical pair between equations 13 and 16.
% 0.48/0.75
% 0.48/0.75 33: X4 = divide(inverse(inverse(X5)), divide(X5, X4)).
% 0.48/0.75 Proof: Rewrite equation 24,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2,2].
% 0.48/0.75
% 0.48/0.75 35: inverse(X3) = divide(inverse(X3), inverse(identity())).
% 0.48/0.75 Proof: Rewrite equation 22,
% 0.48/0.75 lhs with equations [2]
% 0.48/0.75 rhs with equations [2,2].
% 0.48/0.75
% 0.48/0.75 40: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.48/0.75 Proof: Rewrite equation 14,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2].
% 0.48/0.75
% 0.48/0.75 44: divide(X1, X0) = divide(inverse(X0), inverse(X1)).
% 0.48/0.75 Proof: Rewrite equation 16,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2,2].
% 0.48/0.75
% 0.48/0.75 45: inverse(identity()) = identity().
% 0.48/0.75 Proof: A critical pair between equations 35 and 3.
% 0.48/0.75
% 0.48/0.75 53: X6 = divide(inverse(inverse(identity())), inverse(X6)).
% 0.48/0.75 Proof: A critical pair between equations 33 and 2.
% 0.48/0.75
% 0.48/0.75 58: X6 = divide(identity(), divide(identity(), X6)).
% 0.48/0.75 Proof: Rewrite equation 53,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [45,45,2].
% 0.48/0.75
% 0.48/0.75 62: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.48/0.75 Proof: Rewrite equation 40,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2].
% 0.48/0.75
% 0.48/0.75 64: X4 = divide(X5, divide(X5, X4)).
% 0.48/0.75 Proof: Rewrite equation 33,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2,2,58].
% 0.48/0.75
% 0.48/0.75 68: divide(X1, X0) = divide(divide(identity(), X0), divide(identity(), X1)).
% 0.48/0.75 Proof: Rewrite equation 44,
% 0.48/0.75 lhs with equations []
% 0.48/0.75 rhs with equations [2,2].
% 0.48/0.75
% 0.48/0.75 69: multiply(a(), b()) = multiply(b(), a()).
% 0.48/0.75 Proof: Rewrite lhs with equations [62]
% 0.48/0.75 rhs with equations [62,68,64].
% 0.48/0.75
% 0.48/0.75 % SZS output end Proof
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