TSTP Solution File: GRP497-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP497-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n027.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 01:15:10 EDT 2023
% Result : Unsatisfiable 0.59s 0.84s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP497-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.14/0.34 % Computer : n027.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 01:47:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.59/0.84 % SZS status Unsatisfiable
% 0.59/0.84 % SZS output start Proof
% 0.59/0.84 original problem:
% 0.59/0.84 axioms:
% 0.59/0.84 double_divide(double_divide(identity(), double_divide(A, double_divide(B, identity()))), double_divide(double_divide(B, double_divide(C, A)), identity())) = C
% 0.59/0.84 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 0.59/0.84 inverse(A) = double_divide(A, identity())
% 0.59/0.84 identity() = double_divide(A, inverse(A))
% 0.59/0.84 goal:
% 0.59/0.84 multiply(identity(), a2()) != a2()
% 0.59/0.84 To show the unsatisfiability of the original goal,
% 0.59/0.84 it suffices to show that multiply(identity(), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.59/0.84 Here is an equational proof:
% 0.59/0.84 0: double_divide(double_divide(identity(), double_divide(X0, double_divide(X1, identity()))), double_divide(double_divide(X1, double_divide(X2, X0)), identity())) = X2.
% 0.59/0.84 Proof: Axiom.
% 0.59/0.84
% 0.59/0.84 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.59/0.84 Proof: Axiom.
% 0.59/0.84
% 0.59/0.84 2: inverse(X0) = double_divide(X0, identity()).
% 0.59/0.84 Proof: Axiom.
% 0.59/0.84
% 0.59/0.84 3: identity() = double_divide(X0, inverse(X0)).
% 0.59/0.84 Proof: Axiom.
% 0.59/0.84
% 0.59/0.84 4: double_divide(double_divide(identity(), double_divide(X0, inverse(X1))), inverse(double_divide(X1, double_divide(X2, X0)))) = X2.
% 0.59/0.84 Proof: Rewrite equation 0,
% 0.59/0.84 lhs with equations [2,2]
% 0.59/0.84 rhs with equations [].
% 0.59/0.84
% 0.59/0.84 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.59/0.84 Proof: Rewrite equation 1,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2].
% 0.59/0.84
% 0.59/0.84 6: inverse(identity()) = identity().
% 0.59/0.84 Proof: A critical pair between equations 4 and 3.
% 0.59/0.84
% 0.59/0.84 7: X2 = double_divide(double_divide(identity(), identity()), inverse(double_divide(X3, double_divide(X2, X3)))).
% 0.59/0.84 Proof: A critical pair between equations 4 and 3.
% 0.59/0.84
% 0.59/0.84 8: X3 = double_divide(double_divide(identity(), double_divide(identity(), inverse(X1))), inverse(double_divide(X1, inverse(X3)))).
% 0.59/0.84 Proof: A critical pair between equations 4 and 2.
% 0.59/0.84
% 0.59/0.84 9: X3 = double_divide(double_divide(identity(), double_divide(inverse(X3), inverse(X1))), inverse(double_divide(X1, identity()))).
% 0.59/0.84 Proof: A critical pair between equations 4 and 3.
% 0.59/0.84
% 0.59/0.84 11: double_divide(identity(), double_divide(X3, inverse(X4))) = double_divide(double_divide(identity(), double_divide(inverse(double_divide(X4, double_divide(X5, X3))), inverse(X1))), inverse(double_divide(X1, X5))).
% 0.59/0.84 Proof: A critical pair between equations 4 and 4.
% 0.59/0.84
% 0.59/0.84 12: double_divide(identity(), double_divide(X3, double_divide(X4, identity()))) = double_divide(double_divide(identity(), double_divide(double_divide(double_divide(X4, double_divide(X5, X3)), identity()), double_divide(X1, identity()))), double_divide(double_divide(X1, X5), identity())).
% 0.59/0.84 Proof: Rewrite equation 11,
% 0.59/0.84 lhs with equations [2]
% 0.59/0.84 rhs with equations [2,2,2].
% 0.59/0.84
% 0.59/0.84 14: X3 = double_divide(double_divide(identity(), double_divide(double_divide(X3, identity()), double_divide(X1, identity()))), double_divide(double_divide(X1, identity()), identity())).
% 0.59/0.84 Proof: Rewrite equation 9,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2,2,2].
% 0.59/0.84
% 0.59/0.84 15: X3 = double_divide(double_divide(identity(), double_divide(identity(), double_divide(X1, identity()))), double_divide(double_divide(X1, double_divide(X3, identity())), identity())).
% 0.59/0.84 Proof: Rewrite equation 8,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2,2,2].
% 0.59/0.84
% 0.59/0.84 16: X2 = double_divide(double_divide(identity(), identity()), double_divide(double_divide(X3, double_divide(X2, X3)), identity())).
% 0.59/0.84 Proof: Rewrite equation 7,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2].
% 0.59/0.84
% 0.59/0.84 17: double_divide(identity(), identity()) = identity().
% 0.59/0.84 Proof: Rewrite equation 6,
% 0.59/0.84 lhs with equations [2]
% 0.59/0.84 rhs with equations [].
% 0.59/0.84
% 0.59/0.84 18: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.59/0.84 Proof: Rewrite equation 3,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2].
% 0.59/0.84
% 0.59/0.84 19: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.59/0.84 Proof: Rewrite equation 5,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2].
% 0.59/0.84
% 0.59/0.84 20: double_divide(double_divide(identity(), double_divide(X0, double_divide(X1, identity()))), double_divide(double_divide(X1, double_divide(X2, X0)), identity())) = X2.
% 0.59/0.84 Proof: Rewrite equation 4,
% 0.59/0.84 lhs with equations [2,2]
% 0.59/0.84 rhs with equations [].
% 0.59/0.84
% 0.59/0.84 21: X2 = double_divide(identity(), double_divide(double_divide(X3, double_divide(X2, X3)), identity())).
% 0.59/0.84 Proof: A critical pair between equations 16 and 17.
% 0.59/0.84
% 0.59/0.84 22: double_divide(identity(), double_divide(X3, double_divide(X4, identity()))) = double_divide(X4, double_divide(identity(), X3)).
% 0.59/0.84 Proof: A critical pair between equations 12 and 14.
% 0.59/0.84
% 0.59/0.84 24: X4 = double_divide(double_divide(identity(), double_divide(identity(), double_divide(X4, identity()))), double_divide(identity(), identity())).
% 0.59/0.84 Proof: A critical pair between equations 15 and 18.
% 0.59/0.84
% 0.59/0.84 28: X3 = double_divide(double_divide(identity(), double_divide(double_divide(X3, identity()), identity())), double_divide(double_divide(identity(), identity()), identity())).
% 0.59/0.84 Proof: A critical pair between equations 14 and 17.
% 0.59/0.84
% 0.59/0.84 31: X2 = double_divide(double_divide(identity(), double_divide(X0, identity())), double_divide(double_divide(identity(), double_divide(X2, X0)), identity())).
% 0.59/0.84 Proof: A critical pair between equations 20 and 17.
% 0.59/0.84
% 0.59/0.84 34: X2 = double_divide(double_divide(identity(), inverse(X0)), inverse(double_divide(identity(), double_divide(X2, X0)))).
% 0.59/0.84 Proof: Rewrite equation 31,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2,2].
% 0.59/0.84
% 0.59/0.84 37: X3 = double_divide(double_divide(identity(), inverse(inverse(X3))), inverse(inverse(identity()))).
% 0.59/0.84 Proof: Rewrite equation 28,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2,2,2,2].
% 0.59/0.84
% 0.59/0.84 41: X4 = double_divide(double_divide(identity(), double_divide(identity(), inverse(X4))), inverse(identity())).
% 0.59/0.84 Proof: Rewrite equation 24,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2,2].
% 0.59/0.84
% 0.59/0.84 43: X2 = double_divide(identity(), inverse(double_divide(X3, double_divide(X2, X3)))).
% 0.59/0.84 Proof: Rewrite equation 21,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2].
% 0.59/0.84
% 0.59/0.84 45: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.59/0.84 Proof: Rewrite equation 19,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2].
% 0.59/0.84
% 0.59/0.84 46: identity() = double_divide(X0, inverse(X0)).
% 0.59/0.84 Proof: Rewrite equation 18,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2].
% 0.59/0.84
% 0.59/0.84 47: inverse(identity()) = identity().
% 0.59/0.84 Proof: Rewrite equation 17,
% 0.59/0.84 lhs with equations [2]
% 0.59/0.84 rhs with equations [].
% 0.59/0.84
% 0.59/0.84 52: double_divide(identity(), double_divide(X3, inverse(X4))) = double_divide(X4, double_divide(identity(), X3)).
% 0.59/0.84 Proof: Rewrite equation 22,
% 0.59/0.84 lhs with equations [2]
% 0.59/0.84 rhs with equations [].
% 0.59/0.84
% 0.59/0.84 57: X2 = double_divide(identity(), inverse(double_divide(identity(), double_divide(X2, identity())))).
% 0.59/0.84 Proof: A critical pair between equations 34 and 46.
% 0.59/0.84
% 0.59/0.84 58: X3 = double_divide(double_divide(identity(), inverse(inverse(X3))), inverse(identity())).
% 0.59/0.84 Proof: A critical pair between equations 37 and 47.
% 0.59/0.84
% 0.59/0.84 60: X4 = double_divide(double_divide(identity(), double_divide(identity(), inverse(X4))), identity()).
% 0.59/0.84 Proof: A critical pair between equations 41 and 47.
% 0.59/0.84
% 0.59/0.84 62: double_divide(identity(), double_divide(identity(), inverse(X4))) = double_divide(X4, inverse(identity())).
% 0.59/0.84 Proof: A critical pair between equations 52 and 2.
% 0.59/0.84
% 0.59/0.84 63: double_divide(identity(), double_divide(inverse(identity()), inverse(X4))) = double_divide(X4, identity()).
% 0.59/0.84 Proof: A critical pair between equations 52 and 46.
% 0.59/0.84
% 0.59/0.84 65: double_divide(identity(), double_divide(identity(), double_divide(X4, identity()))) = double_divide(X4, identity()).
% 0.59/0.84 Proof: Rewrite equation 63,
% 0.59/0.84 lhs with equations [47,2]
% 0.59/0.84 rhs with equations [].
% 0.59/0.84
% 0.59/0.84 67: X4 = double_divide(double_divide(X4, identity()), identity()).
% 0.59/0.84 Proof: Rewrite equation 60,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2,65].
% 0.59/0.84
% 0.59/0.84 69: X3 = double_divide(double_divide(identity(), X3), identity()).
% 0.59/0.84 Proof: Rewrite equation 58,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2,2,67,47].
% 0.59/0.84
% 0.59/0.84 70: X2 = double_divide(identity(), double_divide(X2, identity())).
% 0.59/0.84 Proof: Rewrite equation 57,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2,69].
% 0.59/0.84
% 0.59/0.84 75: double_divide(identity(), identity()) = identity().
% 0.59/0.84 Proof: Rewrite equation 47,
% 0.59/0.84 lhs with equations [2]
% 0.59/0.84 rhs with equations [].
% 0.59/0.84
% 0.59/0.84 77: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.59/0.84 Proof: Rewrite equation 45,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2].
% 0.59/0.84
% 0.59/0.84 79: X2 = double_divide(X3, double_divide(X2, X3)).
% 0.59/0.84 Proof: Rewrite equation 43,
% 0.59/0.84 lhs with equations []
% 0.59/0.84 rhs with equations [2,70].
% 0.59/0.84
% 0.59/0.84 82: double_divide(identity(), X4) = double_divide(X4, identity()).
% 0.59/0.84 Proof: Rewrite equation 62,
% 0.59/0.84 lhs with equations [2,79]
% 0.59/0.84 rhs with equations [2,75].
% 0.59/0.84
% 0.59/0.84 84: multiply(identity(), a2()) = a2().
% 0.59/0.84 Proof: Rewrite lhs with equations [77,82,69]
% 0.59/0.84 rhs with equations [].
% 0.59/0.84
% 0.59/0.84 % SZS output end Proof
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