TSTP Solution File: GRP581-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP581-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n011.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 01:15:25 EDT 2023
% Result : Unsatisfiable 0.62s 0.89s
% Output : CNFRefutation 0.62s
% 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 : GRP581-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % Command : toma --casc %s
% 0.14/0.35 % Computer : n011.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 19:44:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.62/0.89 % SZS status Unsatisfiable
% 0.62/0.89 % SZS output start Proof
% 0.62/0.89 original problem:
% 0.62/0.89 axioms:
% 0.62/0.89 double_divide(double_divide(A, double_divide(double_divide(identity(), B), double_divide(C, double_divide(B, A)))), double_divide(identity(), identity())) = C
% 0.62/0.89 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 0.62/0.89 inverse(A) = double_divide(A, identity())
% 0.62/0.89 identity() = double_divide(A, inverse(A))
% 0.62/0.89 goal:
% 0.62/0.89 multiply(inverse(a1()), a1()) != identity()
% 0.62/0.89 To show the unsatisfiability of the original goal,
% 0.62/0.89 it suffices to show that multiply(inverse(a1()), a1()) = identity() (skolemized goal) is valid under the axioms.
% 0.62/0.89 Here is an equational proof:
% 0.62/0.89 0: double_divide(double_divide(X0, double_divide(double_divide(identity(), X1), double_divide(X2, double_divide(X1, X0)))), double_divide(identity(), identity())) = X2.
% 0.62/0.89 Proof: Axiom.
% 0.62/0.89
% 0.62/0.89 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.62/0.89 Proof: Axiom.
% 0.62/0.89
% 0.62/0.89 2: inverse(X0) = double_divide(X0, identity()).
% 0.62/0.89 Proof: Axiom.
% 0.62/0.89
% 0.62/0.89 3: identity() = double_divide(X0, inverse(X0)).
% 0.62/0.89 Proof: Axiom.
% 0.62/0.89
% 0.62/0.89 4: double_divide(double_divide(X0, double_divide(double_divide(identity(), X1), double_divide(X2, double_divide(X1, X0)))), inverse(identity())) = X2.
% 0.62/0.89 Proof: Rewrite equation 0,
% 0.62/0.89 lhs with equations [2]
% 0.62/0.89 rhs with equations [].
% 0.62/0.89
% 0.62/0.89 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.62/0.89 Proof: Rewrite equation 1,
% 0.62/0.89 lhs with equations []
% 0.62/0.89 rhs with equations [2].
% 0.62/0.89
% 0.62/0.89 9: X2 = double_divide(double_divide(X0, double_divide(identity(), double_divide(X2, double_divide(inverse(identity()), X0)))), inverse(identity())).
% 0.62/0.89 Proof: A critical pair between equations 4 and 3.
% 0.62/0.89
% 0.62/0.89 12: X2 = double_divide(double_divide(X0, double_divide(identity(), double_divide(X2, double_divide(double_divide(identity(), identity()), X0)))), double_divide(identity(), identity())).
% 0.62/0.89 Proof: Rewrite equation 9,
% 0.62/0.89 lhs with equations []
% 0.62/0.89 rhs with equations [2,2].
% 0.62/0.89
% 0.62/0.89 16: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.62/0.89 Proof: Rewrite equation 3,
% 0.62/0.89 lhs with equations []
% 0.62/0.89 rhs with equations [2].
% 0.62/0.89
% 0.62/0.89 17: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.62/0.89 Proof: Rewrite equation 5,
% 0.62/0.89 lhs with equations []
% 0.62/0.89 rhs with equations [2].
% 0.62/0.89
% 0.62/0.89 19: double_divide(identity(), identity()) = double_divide(double_divide(identity(), double_divide(identity(), identity())), double_divide(identity(), identity())).
% 0.62/0.89 Proof: A critical pair between equations 12 and 16.
% 0.62/0.89
% 0.62/0.89 39: inverse(identity()) = double_divide(double_divide(identity(), inverse(identity())), inverse(identity())).
% 0.62/0.89 Proof: Rewrite equation 19,
% 0.62/0.89 lhs with equations [2]
% 0.62/0.89 rhs with equations [2,2].
% 0.62/0.89
% 0.62/0.89 41: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.62/0.89 Proof: Rewrite equation 17,
% 0.62/0.89 lhs with equations []
% 0.62/0.89 rhs with equations [2].
% 0.62/0.89
% 0.62/0.89 42: identity() = double_divide(X0, inverse(X0)).
% 0.62/0.89 Proof: Rewrite equation 16,
% 0.62/0.89 lhs with equations []
% 0.62/0.89 rhs with equations [2].
% 0.62/0.89
% 0.62/0.89 76: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.62/0.89 Proof: Rewrite equation 42,
% 0.62/0.89 lhs with equations []
% 0.62/0.89 rhs with equations [2].
% 0.62/0.89
% 0.62/0.89 77: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.62/0.89 Proof: Rewrite equation 41,
% 0.62/0.89 lhs with equations []
% 0.62/0.89 rhs with equations [2].
% 0.62/0.89
% 0.62/0.89 79: double_divide(identity(), identity()) = identity().
% 0.62/0.89 Proof: Rewrite equation 39,
% 0.62/0.89 lhs with equations [2]
% 0.62/0.89 rhs with equations [2,76,2,76].
% 0.62/0.89
% 0.62/0.89 89: multiply(inverse(a1()), a1()) = identity().
% 0.62/0.89 Proof: Rewrite lhs with equations [2,77,76,79]
% 0.62/0.89 rhs with equations [].
% 0.62/0.89
% 0.62/0.89 % SZS output end Proof
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