TSTP Solution File: GRP582-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP582-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n002.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 1.33s 1.66s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP582-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 21:05:20 EDT 2023
% 0.19/0.35 % CPUTime :
% 1.33/1.66 % SZS status Unsatisfiable
% 1.33/1.66 % SZS output start Proof
% 1.33/1.66 original problem:
% 1.33/1.66 axioms:
% 1.33/1.66 double_divide(double_divide(A, double_divide(double_divide(identity(), B), double_divide(C, double_divide(B, A)))), double_divide(identity(), identity())) = C
% 1.33/1.66 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 1.33/1.66 inverse(A) = double_divide(A, identity())
% 1.33/1.66 identity() = double_divide(A, inverse(A))
% 1.33/1.66 goal:
% 1.33/1.66 multiply(identity(), a2()) != a2()
% 1.33/1.66 To show the unsatisfiability of the original goal,
% 1.33/1.66 it suffices to show that multiply(identity(), a2()) = a2() (skolemized goal) is valid under the axioms.
% 1.33/1.66 Here is an equational proof:
% 1.33/1.66 0: double_divide(double_divide(X0, double_divide(double_divide(identity(), X1), double_divide(X2, double_divide(X1, X0)))), double_divide(identity(), identity())) = X2.
% 1.33/1.66 Proof: Axiom.
% 1.33/1.66
% 1.33/1.66 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.33/1.66 Proof: Axiom.
% 1.33/1.66
% 1.33/1.66 2: inverse(X0) = double_divide(X0, identity()).
% 1.33/1.66 Proof: Axiom.
% 1.33/1.66
% 1.33/1.66 3: identity() = double_divide(X0, inverse(X0)).
% 1.33/1.66 Proof: Axiom.
% 1.33/1.66
% 1.33/1.66 4: double_divide(double_divide(X0, double_divide(double_divide(identity(), X1), double_divide(X2, double_divide(X1, X0)))), inverse(identity())) = X2.
% 1.33/1.66 Proof: Rewrite equation 0,
% 1.33/1.66 lhs with equations [2]
% 1.33/1.66 rhs with equations [].
% 1.33/1.66
% 1.33/1.66 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.33/1.66 Proof: Rewrite equation 1,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 6: X2 = double_divide(double_divide(identity(), double_divide(double_divide(identity(), X3), double_divide(X2, inverse(X3)))), inverse(identity())).
% 1.33/1.66 Proof: A critical pair between equations 4 and 2.
% 1.33/1.66
% 1.33/1.66 8: X2 = double_divide(double_divide(inverse(X3), double_divide(double_divide(identity(), X3), double_divide(X2, identity()))), inverse(identity())).
% 1.33/1.66 Proof: A critical pair between equations 4 and 3.
% 1.33/1.66
% 1.33/1.66 9: X2 = double_divide(double_divide(X0, double_divide(identity(), double_divide(X2, double_divide(inverse(identity()), X0)))), inverse(identity())).
% 1.33/1.66 Proof: A critical pair between equations 4 and 3.
% 1.33/1.66
% 1.33/1.66 12: X2 = double_divide(double_divide(X0, double_divide(identity(), double_divide(X2, double_divide(double_divide(identity(), identity()), X0)))), double_divide(identity(), identity())).
% 1.33/1.66 Proof: Rewrite equation 9,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2].
% 1.33/1.66
% 1.33/1.66 13: X2 = double_divide(double_divide(double_divide(X3, identity()), double_divide(double_divide(identity(), X3), double_divide(X2, identity()))), double_divide(identity(), identity())).
% 1.33/1.66 Proof: Rewrite equation 8,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2].
% 1.33/1.66
% 1.33/1.66 15: X2 = double_divide(double_divide(identity(), double_divide(double_divide(identity(), X3), double_divide(X2, double_divide(X3, identity())))), double_divide(identity(), identity())).
% 1.33/1.66 Proof: Rewrite equation 6,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2].
% 1.33/1.66
% 1.33/1.66 16: identity() = double_divide(X0, double_divide(X0, identity())).
% 1.33/1.66 Proof: Rewrite equation 3,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 17: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.33/1.66 Proof: Rewrite equation 5,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 19: double_divide(identity(), identity()) = double_divide(double_divide(identity(), double_divide(identity(), identity())), double_divide(identity(), identity())).
% 1.33/1.66 Proof: A critical pair between equations 12 and 16.
% 1.33/1.66
% 1.33/1.66 20: double_divide(identity(), X3) = double_divide(double_divide(double_divide(X3, identity()), identity()), double_divide(identity(), identity())).
% 1.33/1.66 Proof: A critical pair between equations 13 and 16.
% 1.33/1.66
% 1.33/1.66 38: double_divide(identity(), X3) = double_divide(inverse(inverse(X3)), inverse(identity())).
% 1.33/1.66 Proof: Rewrite equation 20,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2,2].
% 1.33/1.66
% 1.33/1.66 39: inverse(identity()) = double_divide(double_divide(identity(), inverse(identity())), inverse(identity())).
% 1.33/1.66 Proof: Rewrite equation 19,
% 1.33/1.66 lhs with equations [2]
% 1.33/1.66 rhs with equations [2,2].
% 1.33/1.66
% 1.33/1.66 41: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.33/1.66 Proof: Rewrite equation 17,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 42: identity() = double_divide(X0, inverse(X0)).
% 1.33/1.66 Proof: Rewrite equation 16,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 43: X2 = double_divide(double_divide(identity(), double_divide(double_divide(identity(), X3), double_divide(X2, inverse(X3)))), inverse(identity())).
% 1.33/1.66 Proof: Rewrite equation 15,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2].
% 1.33/1.66
% 1.33/1.66 45: X2 = double_divide(double_divide(inverse(X3), double_divide(double_divide(identity(), X3), inverse(X2))), inverse(identity())).
% 1.33/1.66 Proof: Rewrite equation 13,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2,2].
% 1.33/1.66
% 1.33/1.66 58: X2 = double_divide(double_divide(inverse(identity()), double_divide(inverse(identity()), inverse(X2))), inverse(identity())).
% 1.33/1.66 Proof: A critical pair between equations 45 and 2.
% 1.33/1.66
% 1.33/1.66 67: X2 = double_divide(double_divide(double_divide(identity(), identity()), double_divide(double_divide(identity(), identity()), double_divide(X2, identity()))), double_divide(identity(), identity())).
% 1.33/1.66 Proof: Rewrite equation 58,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2,2,2].
% 1.33/1.66
% 1.33/1.66 73: X2 = double_divide(double_divide(double_divide(X3, identity()), double_divide(double_divide(identity(), X3), double_divide(X2, identity()))), double_divide(identity(), identity())).
% 1.33/1.66 Proof: Rewrite equation 45,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2,2].
% 1.33/1.66
% 1.33/1.66 75: X2 = double_divide(double_divide(identity(), double_divide(double_divide(identity(), X3), double_divide(X2, double_divide(X3, identity())))), double_divide(identity(), identity())).
% 1.33/1.66 Proof: Rewrite equation 43,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2].
% 1.33/1.66
% 1.33/1.66 76: identity() = double_divide(X0, double_divide(X0, identity())).
% 1.33/1.66 Proof: Rewrite equation 42,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 77: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.33/1.66 Proof: Rewrite equation 41,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 79: double_divide(identity(), identity()) = identity().
% 1.33/1.66 Proof: Rewrite equation 39,
% 1.33/1.66 lhs with equations [2]
% 1.33/1.66 rhs with equations [2,76,2,76].
% 1.33/1.66
% 1.33/1.66 80: double_divide(identity(), X3) = double_divide(double_divide(double_divide(X3, identity()), identity()), identity()).
% 1.33/1.66 Proof: Rewrite equation 38,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2,2,79].
% 1.33/1.66
% 1.33/1.66 114: double_divide(identity(), X3) = inverse(inverse(inverse(X3))).
% 1.33/1.66 Proof: Rewrite equation 80,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2,2].
% 1.33/1.66
% 1.33/1.66 115: inverse(identity()) = identity().
% 1.33/1.66 Proof: Rewrite equation 79,
% 1.33/1.66 lhs with equations [2]
% 1.33/1.66 rhs with equations [].
% 1.33/1.66
% 1.33/1.66 117: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.33/1.66 Proof: Rewrite equation 77,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 119: X2 = inverse(inverse(inverse(inverse(double_divide(inverse(inverse(inverse(X3))), double_divide(X2, inverse(X3))))))).
% 1.33/1.66 Proof: Rewrite equation 75,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [114,2,114,2,115,2].
% 1.33/1.66
% 1.33/1.66 121: X2 = inverse(double_divide(inverse(X3), double_divide(inverse(inverse(inverse(X3))), inverse(X2)))).
% 1.33/1.66 Proof: Rewrite equation 73,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,114,2,2,115,2].
% 1.33/1.66
% 1.33/1.66 124: X2 = inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X2)))))))).
% 1.33/1.66 Proof: Rewrite equation 67,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,115,2,115,2,114,114,2,115,2].
% 1.33/1.66
% 1.33/1.66 136: inverse(inverse(inverse(inverse(inverse(X5))))) = inverse(inverse(inverse(X5))).
% 1.33/1.66 Proof: A critical pair between equations 119 and 121.
% 1.33/1.66
% 1.33/1.66 141: double_divide(double_divide(double_divide(double_divide(double_divide(X5, identity()), identity()), identity()), identity()), identity()) = double_divide(double_divide(double_divide(X5, identity()), identity()), identity()).
% 1.33/1.66 Proof: Rewrite equation 136,
% 1.33/1.66 lhs with equations [2,2,2,2,2]
% 1.33/1.66 rhs with equations [2,2,2].
% 1.33/1.66
% 1.33/1.66 150: X2 = double_divide(double_divide(double_divide(double_divide(X2, identity()), identity()), identity()), identity()).
% 1.33/1.66 Proof: Rewrite equation 124,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2,2,2,2,141,2,2,141,2].
% 1.33/1.66
% 1.33/1.66 156: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.33/1.66 Proof: Rewrite equation 117,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 177: double_divide(double_divide(double_divide(X6, identity()), identity()), identity()) = double_divide(X6, identity()).
% 1.33/1.66 Proof: A critical pair between equations 141 and 150.
% 1.33/1.66
% 1.33/1.66 187: inverse(inverse(inverse(X6))) = inverse(X6).
% 1.33/1.66 Proof: Rewrite equation 177,
% 1.33/1.66 lhs with equations [2,2,2]
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 196: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.33/1.66 Proof: Rewrite equation 156,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2].
% 1.33/1.66
% 1.33/1.66 200: X2 = inverse(inverse(X2)).
% 1.33/1.66 Proof: Rewrite equation 150,
% 1.33/1.66 lhs with equations []
% 1.33/1.66 rhs with equations [2,2,2,187,2].
% 1.33/1.66
% 1.33/1.66 202: multiply(identity(), a2()) = a2().
% 1.33/1.66 Proof: Rewrite lhs with equations [196,2,200]
% 1.33/1.66 rhs with equations [].
% 1.33/1.66
% 1.33/1.66 % SZS output end Proof
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