TSTP Solution File: GRP548-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP548-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n019.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 0.74s 1.06s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP548-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.12 % Command : toma --casc %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 01:42:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.74/1.06 % SZS status Unsatisfiable
% 0.74/1.06 % SZS output start Proof
% 0.74/1.06 original problem:
% 0.74/1.06 axioms:
% 0.74/1.06 divide(divide(identity(), divide(A, B)), divide(divide(B, C), A)) = C
% 0.74/1.06 multiply(A, B) = divide(A, divide(identity(), B))
% 0.74/1.06 inverse(A) = divide(identity(), A)
% 0.74/1.06 identity() = divide(A, A)
% 0.74/1.06 goal:
% 0.74/1.06 multiply(a(), b()) != multiply(b(), a())
% 0.74/1.06 To show the unsatisfiability of the original goal,
% 0.74/1.06 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 0.74/1.06 Here is an equational proof:
% 0.74/1.06 0: divide(divide(identity(), divide(X0, X1)), divide(divide(X1, X2), X0)) = X2.
% 0.74/1.06 Proof: Axiom.
% 0.74/1.06
% 0.74/1.06 1: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.74/1.06 Proof: Axiom.
% 0.74/1.06
% 0.74/1.06 2: inverse(X0) = divide(identity(), X0).
% 0.74/1.06 Proof: Axiom.
% 0.74/1.06
% 0.74/1.06 3: identity() = divide(X0, X0).
% 0.74/1.06 Proof: Axiom.
% 0.74/1.06
% 0.74/1.06 4: divide(inverse(divide(X0, X1)), divide(divide(X1, X2), X0)) = X2.
% 0.74/1.06 Proof: Rewrite equation 0,
% 0.74/1.06 lhs with equations [2]
% 0.74/1.06 rhs with equations [].
% 0.74/1.06
% 0.74/1.06 5: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.74/1.06 Proof: Rewrite equation 1,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2].
% 0.74/1.06
% 0.74/1.06 6: inverse(identity()) = identity().
% 0.74/1.06 Proof: A critical pair between equations 2 and 3.
% 0.74/1.06
% 0.74/1.06 7: X3 = divide(inverse(divide(X0, X3)), divide(identity(), X0)).
% 0.74/1.06 Proof: A critical pair between equations 4 and 3.
% 0.74/1.06
% 0.74/1.06 8: X2 = divide(inverse(divide(divide(X1, X2), X1)), identity()).
% 0.74/1.06 Proof: A critical pair between equations 4 and 3.
% 0.74/1.06
% 0.74/1.06 9: X2 = divide(inverse(identity()), divide(divide(X3, X2), X3)).
% 0.74/1.06 Proof: A critical pair between equations 4 and 3.
% 0.74/1.06
% 0.74/1.06 10: X3 = divide(inverse(divide(X0, identity())), divide(inverse(X3), X0)).
% 0.74/1.06 Proof: A critical pair between equations 4 and 2.
% 0.74/1.06
% 0.74/1.06 11: X2 = divide(inverse(inverse(X3)), divide(divide(X3, X2), identity())).
% 0.74/1.06 Proof: A critical pair between equations 4 and 2.
% 0.74/1.06
% 0.74/1.06 15: X2 = divide(divide(identity(), divide(identity(), X3)), divide(divide(X3, X2), identity())).
% 0.74/1.06 Proof: Rewrite equation 11,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2,2].
% 0.74/1.06
% 0.74/1.06 16: X3 = divide(divide(identity(), divide(X0, identity())), divide(divide(identity(), X3), X0)).
% 0.74/1.06 Proof: Rewrite equation 10,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2,2].
% 0.74/1.06
% 0.74/1.06 17: X2 = divide(identity(), divide(divide(X3, X2), X3)).
% 0.74/1.06 Proof: Rewrite equation 9,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [6].
% 0.74/1.06
% 0.74/1.06 18: X2 = divide(X2, identity()).
% 0.74/1.06 Proof: Rewrite equation 8,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2,17].
% 0.74/1.06
% 0.74/1.06 19: X3 = divide(divide(identity(), divide(X0, X3)), divide(identity(), X0)).
% 0.74/1.06 Proof: Rewrite equation 7,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2].
% 0.74/1.06
% 0.74/1.06 20: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.74/1.06 Proof: Rewrite equation 5,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2].
% 0.74/1.06
% 0.74/1.06 25: X3 = divide(divide(identity(), divide(identity(), X3)), identity()).
% 0.74/1.06 Proof: A critical pair between equations 19 and 18.
% 0.74/1.06
% 0.74/1.06 32: X3 = divide(X5, divide(divide(identity(), X3), divide(identity(), X5))).
% 0.74/1.06 Proof: A critical pair between equations 16 and 17.
% 0.74/1.06
% 0.74/1.06 37: X3 = divide(X5, divide(inverse(X3), inverse(X5))).
% 0.74/1.06 Proof: Rewrite equation 32,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2,2].
% 0.74/1.06
% 0.74/1.06 42: X3 = inverse(inverse(X3)).
% 0.74/1.06 Proof: Rewrite equation 25,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2,2,18].
% 0.74/1.06
% 0.74/1.06 45: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.74/1.06 Proof: Rewrite equation 20,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2].
% 0.74/1.06
% 0.74/1.06 48: X2 = divide(X3, divide(X3, X2)).
% 0.74/1.06 Proof: Rewrite equation 15,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2,2,42,18].
% 0.74/1.06
% 0.74/1.06 67: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.74/1.06 Proof: Rewrite equation 45,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2].
% 0.74/1.06
% 0.74/1.06 69: X3 = divide(X5, divide(divide(identity(), X3), divide(identity(), X5))).
% 0.74/1.06 Proof: Rewrite equation 37,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2,2].
% 0.74/1.06
% 0.74/1.06 77: divide(divide(identity(), X7), divide(identity(), X6)) = divide(X6, X7).
% 0.74/1.06 Proof: A critical pair between equations 48 and 69.
% 0.74/1.06
% 0.74/1.06 92: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.74/1.06 Proof: Rewrite equation 67,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2].
% 0.74/1.06
% 0.74/1.06 96: divide(inverse(X7), inverse(X6)) = divide(X6, X7).
% 0.74/1.06 Proof: Rewrite equation 77,
% 0.74/1.06 lhs with equations [2,2]
% 0.74/1.06 rhs with equations [].
% 0.74/1.06
% 0.74/1.06 114: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.74/1.06 Proof: Rewrite equation 92,
% 0.74/1.06 lhs with equations []
% 0.74/1.06 rhs with equations [2].
% 0.74/1.06
% 0.74/1.06 120: divide(divide(identity(), X7), divide(identity(), X6)) = divide(X6, X7).
% 0.74/1.06 Proof: Rewrite equation 96,
% 0.74/1.06 lhs with equations [2,2]
% 0.74/1.06 rhs with equations [].
% 0.74/1.06
% 0.74/1.06 121: multiply(a(), b()) = multiply(b(), a()).
% 0.74/1.06 Proof: Rewrite lhs with equations [114]
% 0.74/1.06 rhs with equations [114,120,48].
% 0.74/1.06
% 0.74/1.06 % SZS output end Proof
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