TSTP Solution File: GRP496-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP496-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n001.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 01:15:09 EDT 2023
% Result : Unsatisfiable 0.13s 0.66s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.29 % Problem : GRP496-1 : TPTP v8.1.2. Released v2.6.0.
% 0.08/0.31 % Command : toma --casc %s
% 0.09/0.51 % Computer : n001.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8042.1875MB
% 0.09/0.51 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Mon Aug 28 23:44:21 EDT 2023
% 0.09/0.52 % CPUTime :
% 0.13/0.66 % SZS status Unsatisfiable
% 0.13/0.66 % SZS output start Proof
% 0.13/0.66 original problem:
% 0.13/0.66 axioms:
% 0.13/0.66 double_divide(double_divide(identity(), double_divide(A, double_divide(B, identity()))), double_divide(double_divide(B, double_divide(C, A)), identity())) = C
% 0.13/0.66 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 0.13/0.66 inverse(A) = double_divide(A, identity())
% 0.13/0.66 identity() = double_divide(A, inverse(A))
% 0.13/0.66 goal:
% 0.13/0.66 multiply(inverse(a1()), a1()) != identity()
% 0.13/0.66 To show the unsatisfiability of the original goal,
% 0.13/0.66 it suffices to show that multiply(inverse(a1()), a1()) = identity() (skolemized goal) is valid under the axioms.
% 0.13/0.66 Here is an equational proof:
% 0.13/0.66 0: double_divide(double_divide(identity(), double_divide(X0, double_divide(X1, identity()))), double_divide(double_divide(X1, double_divide(X2, X0)), identity())) = X2.
% 0.13/0.66 Proof: Axiom.
% 0.13/0.66
% 0.13/0.66 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.13/0.66 Proof: Axiom.
% 0.13/0.66
% 0.13/0.66 2: inverse(X0) = double_divide(X0, identity()).
% 0.13/0.66 Proof: Axiom.
% 0.13/0.66
% 0.13/0.66 3: identity() = double_divide(X0, inverse(X0)).
% 0.13/0.66 Proof: Axiom.
% 0.13/0.66
% 0.13/0.66 4: double_divide(double_divide(identity(), double_divide(X0, inverse(X1))), inverse(double_divide(X1, double_divide(X2, X0)))) = X2.
% 0.13/0.66 Proof: Rewrite equation 0,
% 0.13/0.66 lhs with equations [2,2]
% 0.13/0.66 rhs with equations [].
% 0.13/0.66
% 0.13/0.66 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.13/0.66 Proof: Rewrite equation 1,
% 0.13/0.66 lhs with equations []
% 0.13/0.66 rhs with equations [2].
% 0.13/0.66
% 0.13/0.66 6: inverse(identity()) = identity().
% 0.13/0.66 Proof: A critical pair between equations 4 and 3.
% 0.13/0.66
% 0.13/0.66 17: double_divide(identity(), identity()) = identity().
% 0.13/0.66 Proof: Rewrite equation 6,
% 0.13/0.66 lhs with equations [2]
% 0.13/0.66 rhs with equations [].
% 0.13/0.66
% 0.13/0.66 18: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.13/0.66 Proof: Rewrite equation 3,
% 0.13/0.66 lhs with equations []
% 0.13/0.66 rhs with equations [2].
% 0.13/0.66
% 0.13/0.66 19: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.13/0.66 Proof: Rewrite equation 5,
% 0.13/0.66 lhs with equations []
% 0.13/0.66 rhs with equations [2].
% 0.13/0.66
% 0.13/0.66 21: multiply(inverse(a1()), a1()) = identity().
% 0.13/0.66 Proof: Rewrite lhs with equations [2,19,18,17]
% 0.13/0.66 rhs with equations [].
% 0.13/0.66
% 0.13/0.66 % SZS output end Proof
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