TSTP Solution File: GRP488-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP488-1 : 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 01:15:08 EDT 2023
% Result : Unsatisfiable 1.77s 2.18s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP488-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 20:54:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 1.77/2.18 % SZS status Unsatisfiable
% 1.77/2.18 % SZS output start Proof
% 1.77/2.18 original problem:
% 1.77/2.18 axioms:
% 1.77/2.18 double_divide(A, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(A, identity()), double_divide(B, C))), B), identity())) = C
% 1.77/2.18 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 1.77/2.18 inverse(A) = double_divide(A, identity())
% 1.77/2.18 identity() = double_divide(A, inverse(A))
% 1.77/2.18 goal:
% 1.77/2.18 multiply(identity(), a2()) != a2()
% 1.77/2.18 To show the unsatisfiability of the original goal,
% 1.77/2.18 it suffices to show that multiply(identity(), a2()) = a2() (skolemized goal) is valid under the axioms.
% 1.77/2.18 Here is an equational proof:
% 1.77/2.18 0: double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), double_divide(X1, X2))), X1), identity())) = X2.
% 1.77/2.18 Proof: Axiom.
% 1.77/2.18
% 1.77/2.18 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.77/2.18 Proof: Axiom.
% 1.77/2.18
% 1.77/2.18 2: inverse(X0) = double_divide(X0, identity()).
% 1.77/2.18 Proof: Axiom.
% 1.77/2.18
% 1.77/2.18 3: identity() = double_divide(X0, inverse(X0)).
% 1.77/2.18 Proof: Axiom.
% 1.77/2.18
% 1.77/2.18 4: double_divide(X0, inverse(double_divide(double_divide(identity(), double_divide(inverse(X0), double_divide(X1, X2))), X1))) = X2.
% 1.77/2.18 Proof: Rewrite equation 0,
% 1.77/2.18 lhs with equations [2,2]
% 1.77/2.18 rhs with equations [].
% 1.77/2.18
% 1.77/2.18 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.77/2.18 Proof: Rewrite equation 1,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 6: identity() = double_divide(X0, inverse(double_divide(double_divide(identity(), double_divide(inverse(X0), inverse(X3))), X3))).
% 1.77/2.18 Proof: A critical pair between equations 4 and 2.
% 1.77/2.18
% 1.77/2.18 7: X2 = double_divide(X0, inverse(inverse(double_divide(identity(), double_divide(inverse(X0), double_divide(identity(), X2)))))).
% 1.77/2.18 Proof: A critical pair between equations 4 and 2.
% 1.77/2.18
% 1.77/2.18 8: inverse(X3) = double_divide(X0, inverse(double_divide(double_divide(identity(), double_divide(inverse(X0), identity())), X3))).
% 1.77/2.18 Proof: A critical pair between equations 4 and 3.
% 1.77/2.18
% 1.77/2.18 9: inverse(double_divide(double_divide(identity(), double_divide(inverse(X3), double_divide(X4, X5))), X4)) = double_divide(X0, inverse(double_divide(double_divide(identity(), double_divide(inverse(X0), X5)), X3))).
% 1.77/2.18 Proof: A critical pair between equations 4 and 4.
% 1.77/2.18
% 1.77/2.18 10: double_divide(X3, identity()) = double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), identity())), X3), identity())).
% 1.77/2.18 Proof: Rewrite equation 8,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,2].
% 1.77/2.18
% 1.77/2.18 11: X2 = double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), double_divide(identity(), X2))), identity()), identity())).
% 1.77/2.18 Proof: Rewrite equation 7,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2,2,2].
% 1.77/2.18
% 1.77/2.18 12: identity() = double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), double_divide(X3, identity()))), X3), identity())).
% 1.77/2.18 Proof: Rewrite equation 6,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2,2,2].
% 1.77/2.18
% 1.77/2.18 13: identity() = double_divide(X0, double_divide(X0, identity())).
% 1.77/2.18 Proof: Rewrite equation 3,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 14: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.77/2.18 Proof: Rewrite equation 5,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 16: double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X3, identity()), double_divide(X4, X5))), X4), identity()) = double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), X5)), X3), identity())).
% 1.77/2.18 Proof: Rewrite equation 9,
% 1.77/2.18 lhs with equations [2,2]
% 1.77/2.18 rhs with equations [2,2].
% 1.77/2.18
% 1.77/2.18 17: identity() = double_divide(X0, double_divide(double_divide(double_divide(identity(), identity()), double_divide(X0, identity())), identity())).
% 1.77/2.18 Proof: A critical pair between equations 12 and 13.
% 1.77/2.18
% 1.77/2.18 20: double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X7, identity()), double_divide(X4, double_divide(X7, identity())))), X4), identity()) = identity().
% 1.77/2.18 Proof: A critical pair between equations 16 and 12.
% 1.77/2.18
% 1.77/2.18 24: double_divide(X3, identity()) = double_divide(double_divide(identity(), double_divide(double_divide(identity(), identity()), identity())), double_divide(double_divide(double_divide(identity(), identity()), X3), identity())).
% 1.77/2.18 Proof: A critical pair between equations 10 and 10.
% 1.77/2.18
% 1.77/2.18 25: double_divide(X3, identity()) = double_divide(double_divide(identity(), double_divide(double_divide(identity(), identity()), double_divide(identity(), X5))), double_divide(double_divide(X5, X3), identity())).
% 1.77/2.18 Proof: A critical pair between equations 10 and 11.
% 1.77/2.18
% 1.77/2.18 26: double_divide(X3, identity()) = double_divide(double_divide(identity(), double_divide(double_divide(identity(), identity()), double_divide(identity(), identity()))), double_divide(double_divide(identity(), X3), identity())).
% 1.77/2.18 Proof: A critical pair between equations 10 and 12.
% 1.77/2.18
% 1.77/2.18 27: double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), identity())), X3), identity())) = double_divide(double_divide(double_divide(identity(), identity()), double_divide(X3, identity())), identity()).
% 1.77/2.18 Proof: A critical pair between equations 16 and 13.
% 1.77/2.18
% 1.77/2.18 30: inverse(X3) = double_divide(double_divide(identity(), double_divide(inverse(identity()), inverse(identity()))), inverse(double_divide(identity(), X3))).
% 1.77/2.18 Proof: Rewrite equation 26,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,2,2].
% 1.77/2.18
% 1.77/2.18 31: inverse(X3) = double_divide(double_divide(identity(), double_divide(inverse(identity()), double_divide(identity(), X5))), inverse(double_divide(X5, X3))).
% 1.77/2.18 Proof: Rewrite equation 25,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,2].
% 1.77/2.18
% 1.77/2.18 32: inverse(X3) = double_divide(double_divide(identity(), inverse(inverse(identity()))), inverse(double_divide(inverse(identity()), X3))).
% 1.77/2.18 Proof: Rewrite equation 24,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,2,2,2].
% 1.77/2.18
% 1.77/2.18 36: inverse(double_divide(double_divide(identity(), double_divide(inverse(X7), double_divide(X4, inverse(X7)))), X4)) = identity().
% 1.77/2.18 Proof: Rewrite equation 20,
% 1.77/2.18 lhs with equations [2,2,2]
% 1.77/2.18 rhs with equations [].
% 1.77/2.18
% 1.77/2.18 38: identity() = double_divide(X0, inverse(double_divide(inverse(identity()), inverse(X0)))).
% 1.77/2.18 Proof: Rewrite equation 17,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2,2,2].
% 1.77/2.18
% 1.77/2.18 40: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.77/2.18 Proof: Rewrite equation 14,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 41: identity() = double_divide(X0, inverse(X0)).
% 1.77/2.18 Proof: Rewrite equation 13,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 42: X2 = double_divide(X0, inverse(inverse(double_divide(identity(), double_divide(inverse(X0), double_divide(identity(), X2)))))).
% 1.77/2.18 Proof: Rewrite equation 11,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2,2,2].
% 1.77/2.18
% 1.77/2.18 43: inverse(X3) = double_divide(X0, inverse(double_divide(double_divide(identity(), inverse(inverse(X0))), X3))).
% 1.77/2.18 Proof: Rewrite equation 10,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,2,2].
% 1.77/2.18
% 1.77/2.18 44: inverse(X3) = inverse(double_divide(inverse(identity()), inverse(X3))).
% 1.77/2.18 Proof: Rewrite equation 27,
% 1.77/2.18 lhs with equations [2,2,2,43]
% 1.77/2.18 rhs with equations [2,2,2].
% 1.77/2.18
% 1.77/2.18 46: inverse(inverse(identity())) = inverse(identity()).
% 1.77/2.18 Proof: A critical pair between equations 44 and 41.
% 1.77/2.18
% 1.77/2.18 47: identity() = double_divide(inverse(identity()), inverse(identity())).
% 1.77/2.18 Proof: A critical pair between equations 38 and 41.
% 1.77/2.18
% 1.77/2.18 49: inverse(double_divide(inverse(identity()), double_divide(identity(), identity()))) = identity().
% 1.77/2.18 Proof: A critical pair between equations 31 and 41.
% 1.77/2.18
% 1.77/2.18 51: identity() = inverse(double_divide(double_divide(identity(), double_divide(inverse(X8), identity())), X8)).
% 1.77/2.18 Proof: A critical pair between equations 36 and 41.
% 1.77/2.18
% 1.77/2.18 53: inverse(inverse(X4)) = double_divide(double_divide(identity(), inverse(inverse(identity()))), inverse(X4)).
% 1.77/2.18 Proof: A critical pair between equations 32 and 44.
% 1.77/2.18
% 1.77/2.18 63: identity() = double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X8, identity()), identity())), X8), identity()).
% 1.77/2.18 Proof: Rewrite equation 51,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2,2].
% 1.77/2.18
% 1.77/2.18 65: double_divide(double_divide(double_divide(identity(), identity()), double_divide(identity(), identity())), identity()) = identity().
% 1.77/2.18 Proof: Rewrite equation 49,
% 1.77/2.18 lhs with equations [2,2]
% 1.77/2.18 rhs with equations [].
% 1.77/2.18
% 1.77/2.18 66: identity() = double_divide(double_divide(identity(), identity()), double_divide(identity(), identity())).
% 1.77/2.18 Proof: Rewrite equation 47,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2,2].
% 1.77/2.18
% 1.77/2.18 67: double_divide(double_divide(identity(), identity()), identity()) = double_divide(identity(), identity()).
% 1.77/2.18 Proof: Rewrite equation 46,
% 1.77/2.18 lhs with equations [2,2]
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 68: double_divide(X3, identity()) = double_divide(double_divide(double_divide(identity(), identity()), double_divide(X3, identity())), identity()).
% 1.77/2.18 Proof: Rewrite equation 44,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,2,2].
% 1.77/2.18
% 1.77/2.18 70: X2 = double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), double_divide(identity(), X2))), identity()), identity())).
% 1.77/2.18 Proof: Rewrite equation 42,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2,2,2].
% 1.77/2.18
% 1.77/2.18 71: identity() = double_divide(X0, double_divide(X0, identity())).
% 1.77/2.18 Proof: Rewrite equation 41,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 72: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.77/2.18 Proof: Rewrite equation 40,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 80: double_divide(X3, identity()) = double_divide(double_divide(identity(), identity()), double_divide(double_divide(identity(), X3), identity())).
% 1.77/2.18 Proof: Rewrite equation 30,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,2,66,2].
% 1.77/2.18
% 1.77/2.18 83: double_divide(double_divide(X4, identity()), identity()) = double_divide(identity(), double_divide(X4, identity())).
% 1.77/2.18 Proof: Rewrite equation 53,
% 1.77/2.18 lhs with equations [2,2]
% 1.77/2.18 rhs with equations [2,2,67,71,2].
% 1.77/2.18
% 1.77/2.18 85: identity() = double_divide(identity(), identity()).
% 1.77/2.18 Proof: A critical pair between equations 65 and 66.
% 1.77/2.18
% 1.77/2.18 90: double_divide(double_divide(identity(), X4), identity()) = double_divide(double_divide(X4, identity()), identity()).
% 1.77/2.18 Proof: A critical pair between equations 68 and 80.
% 1.77/2.18
% 1.77/2.18 102: identity() = inverse(identity()).
% 1.77/2.18 Proof: Rewrite equation 85,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 103: inverse(inverse(X4)) = double_divide(identity(), inverse(X4)).
% 1.77/2.18 Proof: Rewrite equation 83,
% 1.77/2.18 lhs with equations [2,2]
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 106: inverse(X3) = inverse(inverse(double_divide(identity(), X3))).
% 1.77/2.18 Proof: Rewrite equation 80,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,102,2,103].
% 1.77/2.18
% 1.77/2.18 113: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.77/2.18 Proof: Rewrite equation 72,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 114: X2 = double_divide(X0, inverse(double_divide(inverse(X0), double_divide(identity(), X2)))).
% 1.77/2.18 Proof: Rewrite equation 70,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2,2,2,106].
% 1.77/2.18
% 1.77/2.18 116: inverse(X3) = inverse(inverse(inverse(X3))).
% 1.77/2.18 Proof: Rewrite equation 68,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,102,2,103,2].
% 1.77/2.18
% 1.77/2.18 118: identity() = inverse(double_divide(inverse(X8), X8)).
% 1.77/2.18 Proof: Rewrite equation 63,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2,2,103,116,2].
% 1.77/2.18
% 1.77/2.18 119: inverse(double_divide(identity(), X4)) = inverse(inverse(X4)).
% 1.77/2.18 Proof: Rewrite equation 90,
% 1.77/2.18 lhs with equations [2]
% 1.77/2.18 rhs with equations [2,2].
% 1.77/2.18
% 1.77/2.18 121: X2 = double_divide(double_divide(identity(), X2), identity()).
% 1.77/2.18 Proof: A critical pair between equations 114 and 118.
% 1.77/2.18
% 1.77/2.18 143: X4 = double_divide(double_divide(X4, identity()), identity()).
% 1.77/2.18 Proof: Rewrite equation 119,
% 1.77/2.18 lhs with equations [2,121]
% 1.77/2.18 rhs with equations [2,2].
% 1.77/2.18
% 1.77/2.18 146: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.77/2.18 Proof: Rewrite equation 113,
% 1.77/2.18 lhs with equations []
% 1.77/2.18 rhs with equations [2].
% 1.77/2.18
% 1.77/2.18 159: multiply(identity(), a2()) = a2().
% 1.77/2.18 Proof: Rewrite lhs with equations [146,143]
% 1.77/2.18 rhs with equations [].
% 1.77/2.18
% 1.77/2.18 % SZS output end Proof
%------------------------------------------------------------------------------