TSTP Solution File: GRP542-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP542-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n016.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 0.45s 0.78s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP542-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 01:55:30 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.45/0.78 % SZS status Unsatisfiable
% 0.45/0.78 % SZS output start Proof
% 0.45/0.78 original problem:
% 0.45/0.78 axioms:
% 0.45/0.78 divide(divide(identity(), divide(divide(divide(A, B), C), A)), C) = B
% 0.45/0.78 multiply(A, B) = divide(A, divide(identity(), B))
% 0.45/0.78 inverse(A) = divide(identity(), A)
% 0.45/0.78 identity() = divide(A, A)
% 0.45/0.78 goal:
% 0.45/0.78 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 0.45/0.78 To show the unsatisfiability of the original goal,
% 0.45/0.78 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.45/0.78 Here is an equational proof:
% 0.45/0.78 0: divide(divide(identity(), divide(divide(divide(X0, X1), X2), X0)), X2) = X1.
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 1: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 2: inverse(X0) = divide(identity(), X0).
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 3: identity() = divide(X0, X0).
% 0.45/0.78 Proof: Axiom.
% 0.45/0.78
% 0.45/0.78 4: divide(inverse(divide(divide(divide(X0, X1), X2), X0)), X2) = X1.
% 0.45/0.78 Proof: Rewrite equation 0,
% 0.45/0.78 lhs with equations [2]
% 0.45/0.78 rhs with equations [].
% 0.45/0.78
% 0.45/0.78 5: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.45/0.78 Proof: Rewrite equation 1,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2].
% 0.45/0.78
% 0.45/0.78 7: X3 = divide(inverse(divide(divide(identity(), X2), X3)), X2).
% 0.45/0.78 Proof: A critical pair between equations 4 and 3.
% 0.45/0.78
% 0.45/0.78 8: X1 = divide(inverse(divide(identity(), X0)), divide(X0, X1)).
% 0.45/0.78 Proof: A critical pair between equations 4 and 3.
% 0.45/0.78
% 0.45/0.78 9: X3 = divide(inverse(divide(divide(inverse(X3), X2), identity())), X2).
% 0.45/0.78 Proof: A critical pair between equations 4 and 2.
% 0.45/0.78
% 0.45/0.78 10: X5 = divide(inverse(divide(divide(X4, X2), inverse(divide(divide(divide(X3, X4), X5), X3)))), X2).
% 0.45/0.78 Proof: A critical pair between equations 4 and 4.
% 0.45/0.78
% 0.45/0.78 11: X5 = divide(divide(identity(), divide(divide(X4, X2), divide(identity(), divide(divide(divide(X3, X4), X5), X3)))), X2).
% 0.45/0.78 Proof: Rewrite equation 10,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2,2].
% 0.45/0.78
% 0.45/0.78 12: X3 = divide(divide(identity(), divide(divide(divide(identity(), X3), X2), identity())), X2).
% 0.45/0.78 Proof: Rewrite equation 9,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2,2].
% 0.45/0.78
% 0.45/0.78 13: X1 = divide(divide(identity(), divide(identity(), X0)), divide(X0, X1)).
% 0.45/0.78 Proof: Rewrite equation 8,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2].
% 0.45/0.78
% 0.45/0.78 14: X3 = divide(divide(identity(), divide(divide(identity(), X2), X3)), X2).
% 0.45/0.78 Proof: Rewrite equation 7,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2].
% 0.45/0.78
% 0.45/0.78 15: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.45/0.78 Proof: Rewrite equation 5,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2].
% 0.45/0.78
% 0.45/0.78 18: X1 = divide(divide(identity(), identity()), divide(identity(), X1)).
% 0.45/0.78 Proof: A critical pair between equations 13 and 3.
% 0.45/0.78
% 0.45/0.78 19: X5 = divide(identity(), divide(divide(divide(X3, identity()), X5), X3)).
% 0.45/0.78 Proof: A critical pair between equations 11 and 14.
% 0.45/0.78
% 0.45/0.78 21: divide(X4, X5) = divide(divide(identity(), X5), divide(identity(), X4)).
% 0.45/0.78 Proof: A critical pair between equations 14 and 13.
% 0.45/0.78
% 0.45/0.78 24: divide(identity(), X4) = divide(divide(identity(), divide(X5, identity())), divide(X4, X5)).
% 0.45/0.78 Proof: A critical pair between equations 12 and 13.
% 0.45/0.78
% 0.45/0.78 32: inverse(X4) = divide(inverse(divide(X5, identity())), divide(X4, X5)).
% 0.45/0.78 Proof: Rewrite equation 24,
% 0.45/0.78 lhs with equations [2]
% 0.45/0.78 rhs with equations [2].
% 0.45/0.78
% 0.45/0.78 35: X5 = inverse(divide(inverse(X3), inverse(divide(divide(X3, identity()), X5)))).
% 0.45/0.78 Proof: Rewrite equation 19,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [21,2,2,2].
% 0.45/0.78
% 0.45/0.78 36: X1 = divide(inverse(identity()), inverse(X1)).
% 0.45/0.78 Proof: Rewrite equation 18,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2,2].
% 0.45/0.78
% 0.45/0.78 39: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.45/0.78 Proof: Rewrite equation 15,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2].
% 0.45/0.78
% 0.45/0.78 41: X1 = divide(inverse(inverse(X0)), divide(X0, X1)).
% 0.45/0.78 Proof: Rewrite equation 13,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2,2].
% 0.45/0.78
% 0.45/0.78 45: divide(X4, X5) = divide(inverse(X5), inverse(X4)).
% 0.45/0.78 Proof: Rewrite equation 21,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2,2].
% 0.45/0.78
% 0.45/0.78 47: divide(X6, identity()) = X6.
% 0.45/0.78 Proof: A critical pair between equations 45 and 36.
% 0.45/0.78
% 0.45/0.78 55: X5 = inverse(divide(divide(identity(), identity()), X5)).
% 0.45/0.78 Proof: A critical pair between equations 35 and 36.
% 0.45/0.78
% 0.45/0.78 60: X5 = divide(identity(), divide(identity(), X5)).
% 0.45/0.78 Proof: Rewrite equation 55,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [47,2].
% 0.45/0.78
% 0.45/0.78 63: X1 = divide(X0, divide(X0, X1)).
% 0.45/0.78 Proof: Rewrite equation 41,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2,2,60].
% 0.45/0.78
% 0.45/0.78 64: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.45/0.78 Proof: Rewrite equation 39,
% 0.45/0.78 lhs with equations []
% 0.45/0.78 rhs with equations [2].
% 0.45/0.78
% 0.45/0.78 68: divide(identity(), X4) = divide(divide(identity(), X5), divide(X4, X5)).
% 0.45/0.78 Proof: Rewrite equation 32,
% 0.45/0.78 lhs with equations [2]
% 0.45/0.78 rhs with equations [47,2].
% 0.45/0.78
% 0.45/0.78 71: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 0.45/0.78 Proof: Rewrite lhs with equations [2,64,68,3,64,63]
% 0.45/0.78 rhs with equations [].
% 0.45/0.78
% 0.45/0.78 % SZS output end Proof
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