TSTP Solution File: GRP565-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP565-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n028.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 01:15:22 EDT 2023
% Result : Unsatisfiable 0.83s 1.18s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP565-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 01:55:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.83/1.18 % SZS status Unsatisfiable
% 0.83/1.18 % SZS output start Proof
% 0.83/1.18 original problem:
% 0.83/1.18 axioms:
% 0.83/1.18 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity(), C))), double_divide(identity(), identity())) = B
% 0.83/1.18 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 0.83/1.18 inverse(A) = double_divide(A, identity())
% 0.83/1.18 identity() = double_divide(A, inverse(A))
% 0.83/1.18 goal:
% 0.83/1.18 multiply(inverse(a1()), a1()) != identity()
% 0.83/1.18 To show the unsatisfiability of the original goal,
% 0.83/1.18 it suffices to show that multiply(inverse(a1()), a1()) = identity() (skolemized goal) is valid under the axioms.
% 0.83/1.18 Here is an equational proof:
% 0.83/1.18 0: double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), double_divide(identity(), X2))), double_divide(identity(), identity())) = X1.
% 0.83/1.18 Proof: Axiom.
% 0.83/1.18
% 0.83/1.18 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.83/1.18 Proof: Axiom.
% 0.83/1.18
% 0.83/1.18 2: inverse(X0) = double_divide(X0, identity()).
% 0.83/1.18 Proof: Axiom.
% 0.83/1.18
% 0.83/1.18 3: identity() = double_divide(X0, inverse(X0)).
% 0.83/1.18 Proof: Axiom.
% 0.83/1.18
% 0.83/1.18 4: double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), double_divide(identity(), X2))), inverse(identity())) = X1.
% 0.83/1.18 Proof: Rewrite equation 0,
% 0.83/1.18 lhs with equations [2]
% 0.83/1.18 rhs with equations [].
% 0.83/1.18
% 0.83/1.18 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.83/1.18 Proof: Rewrite equation 1,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 7: X1 = double_divide(double_divide(X3, double_divide(double_divide(X1, inverse(X3)), double_divide(identity(), identity()))), inverse(identity())).
% 0.83/1.18 Proof: A critical pair between equations 4 and 2.
% 0.83/1.18
% 0.83/1.18 8: X1 = double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X0, inverse(identity()))), identity())), inverse(identity())).
% 0.83/1.18 Proof: A critical pair between equations 4 and 3.
% 0.83/1.18
% 0.83/1.18 13: X1 = double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X0, double_divide(identity(), identity()))), identity())), double_divide(identity(), identity())).
% 0.83/1.18 Proof: Rewrite equation 8,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2,2].
% 0.83/1.18
% 0.83/1.18 14: X1 = double_divide(double_divide(X3, double_divide(double_divide(X1, double_divide(X3, identity())), double_divide(identity(), identity()))), double_divide(identity(), identity())).
% 0.83/1.18 Proof: Rewrite equation 7,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2,2].
% 0.83/1.18
% 0.83/1.18 15: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.83/1.18 Proof: Rewrite equation 3,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 16: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.83/1.18 Proof: Rewrite equation 5,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 19: X4 = double_divide(double_divide(X4, double_divide(identity(), double_divide(identity(), identity()))), double_divide(identity(), identity())).
% 0.83/1.18 Proof: A critical pair between equations 14 and 15.
% 0.83/1.18
% 0.83/1.18 20: X4 = double_divide(double_divide(double_divide(X5, double_divide(X4, double_divide(identity(), identity()))), X5), double_divide(identity(), identity())).
% 0.83/1.18 Proof: A critical pair between equations 14 and 13.
% 0.83/1.18
% 0.83/1.18 35: X4 = double_divide(double_divide(double_divide(X5, double_divide(X4, inverse(identity()))), X5), inverse(identity())).
% 0.83/1.18 Proof: Rewrite equation 20,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2,2].
% 0.83/1.18
% 0.83/1.18 36: X4 = double_divide(double_divide(X4, double_divide(identity(), inverse(identity()))), inverse(identity())).
% 0.83/1.18 Proof: Rewrite equation 19,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2,2].
% 0.83/1.18
% 0.83/1.18 39: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.83/1.18 Proof: Rewrite equation 16,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 40: identity() = double_divide(X0, inverse(X0)).
% 0.83/1.18 Proof: Rewrite equation 15,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 49: X4 = double_divide(double_divide(X4, identity()), inverse(identity())).
% 0.83/1.18 Proof: A critical pair between equations 36 and 40.
% 0.83/1.18
% 0.83/1.18 52: identity() = double_divide(double_divide(double_divide(X5, identity()), X5), inverse(identity())).
% 0.83/1.18 Proof: A critical pair between equations 35 and 40.
% 0.83/1.18
% 0.83/1.18 65: identity() = double_divide(double_divide(double_divide(X5, identity()), X5), double_divide(identity(), identity())).
% 0.83/1.18 Proof: Rewrite equation 52,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 67: X4 = double_divide(double_divide(X4, identity()), double_divide(identity(), identity())).
% 0.83/1.18 Proof: Rewrite equation 49,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 71: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.83/1.18 Proof: Rewrite equation 40,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 72: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.83/1.18 Proof: Rewrite equation 39,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 84: identity() = double_divide(identity(), identity()).
% 0.83/1.18 Proof: A critical pair between equations 65 and 67.
% 0.83/1.18
% 0.83/1.18 101: identity() = inverse(identity()).
% 0.83/1.18 Proof: Rewrite equation 84,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 109: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.83/1.18 Proof: Rewrite equation 72,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 110: identity() = double_divide(X0, inverse(X0)).
% 0.83/1.18 Proof: Rewrite equation 71,
% 0.83/1.18 lhs with equations []
% 0.83/1.18 rhs with equations [2].
% 0.83/1.18
% 0.83/1.18 117: multiply(inverse(a1()), a1()) = identity().
% 0.83/1.18 Proof: Rewrite lhs with equations [109,110,101]
% 0.83/1.18 rhs with equations [].
% 0.83/1.18
% 0.83/1.18 % SZS output end Proof
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