TSTP Solution File: GRP491-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP491-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n008.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 0.75s 1.13s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP491-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.14 % Command : toma --casc %s
% 0.12/0.34 % Computer : n008.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 21:48:02 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.75/1.13 % SZS status Unsatisfiable
% 0.75/1.13 % SZS output start Proof
% 0.75/1.13 original problem:
% 0.75/1.13 axioms:
% 0.75/1.13 double_divide(double_divide(identity(), A), double_divide(identity(), double_divide(double_divide(double_divide(A, B), identity()), double_divide(C, B)))) = C
% 0.75/1.13 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 0.75/1.13 inverse(A) = double_divide(A, identity())
% 0.75/1.13 identity() = double_divide(A, inverse(A))
% 0.75/1.13 goal:
% 0.75/1.13 multiply(identity(), a2()) != a2()
% 0.75/1.13 To show the unsatisfiability of the original goal,
% 0.75/1.13 it suffices to show that multiply(identity(), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.75/1.13 Here is an equational proof:
% 0.75/1.13 0: double_divide(double_divide(identity(), X0), double_divide(identity(), double_divide(double_divide(double_divide(X0, X1), identity()), double_divide(X2, X1)))) = X2.
% 0.75/1.13 Proof: Axiom.
% 0.75/1.13
% 0.75/1.13 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.75/1.13 Proof: Axiom.
% 0.75/1.13
% 0.75/1.13 2: inverse(X0) = double_divide(X0, identity()).
% 0.75/1.13 Proof: Axiom.
% 0.75/1.13
% 0.75/1.13 3: identity() = double_divide(X0, inverse(X0)).
% 0.75/1.13 Proof: Axiom.
% 0.75/1.13
% 0.75/1.13 4: double_divide(double_divide(identity(), X0), double_divide(identity(), double_divide(inverse(double_divide(X0, X1)), double_divide(X2, X1)))) = X2.
% 0.75/1.13 Proof: Rewrite equation 0,
% 0.75/1.13 lhs with equations [2]
% 0.75/1.13 rhs with equations [].
% 0.75/1.13
% 0.75/1.13 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.75/1.13 Proof: Rewrite equation 1,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 7: X2 = double_divide(double_divide(identity(), X3), double_divide(identity(), double_divide(inverse(inverse(X3)), double_divide(X2, identity())))).
% 0.75/1.13 Proof: A critical pair between equations 4 and 2.
% 0.75/1.13
% 0.75/1.13 10: X2 = double_divide(double_divide(identity(), X3), double_divide(identity(), double_divide(inverse(identity()), double_divide(X2, inverse(X3))))).
% 0.75/1.13 Proof: A critical pair between equations 4 and 3.
% 0.75/1.13
% 0.75/1.13 17: X2 = double_divide(double_divide(identity(), X3), double_divide(identity(), double_divide(double_divide(identity(), identity()), double_divide(X2, double_divide(X3, identity()))))).
% 0.75/1.13 Proof: Rewrite equation 10,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2].
% 0.75/1.13
% 0.75/1.13 20: X2 = double_divide(double_divide(identity(), X3), double_divide(identity(), double_divide(double_divide(double_divide(X3, identity()), identity()), double_divide(X2, identity())))).
% 0.75/1.13 Proof: Rewrite equation 7,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2].
% 0.75/1.13
% 0.75/1.13 21: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.75/1.13 Proof: Rewrite equation 3,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 22: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.75/1.13 Proof: Rewrite equation 5,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 25: X4 = double_divide(double_divide(identity(), X4), double_divide(identity(), double_divide(double_divide(identity(), identity()), identity()))).
% 0.75/1.13 Proof: A critical pair between equations 17 and 21.
% 0.75/1.13
% 0.75/1.13 27: double_divide(double_divide(X3, identity()), identity()) = double_divide(double_divide(identity(), X3), double_divide(identity(), identity())).
% 0.75/1.13 Proof: A critical pair between equations 20 and 21.
% 0.75/1.13
% 0.75/1.13 45: X4 = double_divide(double_divide(identity(), X4), double_divide(identity(), inverse(inverse(identity())))).
% 0.75/1.13 Proof: Rewrite equation 25,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2].
% 0.75/1.13
% 0.75/1.13 48: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.75/1.13 Proof: Rewrite equation 22,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 49: identity() = double_divide(X0, inverse(X0)).
% 0.75/1.13 Proof: Rewrite equation 21,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 53: X2 = double_divide(double_divide(identity(), X3), double_divide(identity(), double_divide(inverse(identity()), double_divide(X2, inverse(X3))))).
% 0.75/1.13 Proof: Rewrite equation 17,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2].
% 0.75/1.13
% 0.75/1.13 57: inverse(inverse(X3)) = double_divide(double_divide(identity(), X3), inverse(identity())).
% 0.75/1.13 Proof: Rewrite equation 27,
% 0.75/1.13 lhs with equations [2,2]
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 78: double_divide(double_divide(X3, identity()), identity()) = double_divide(double_divide(identity(), X3), double_divide(identity(), identity())).
% 0.75/1.13 Proof: Rewrite equation 57,
% 0.75/1.13 lhs with equations [2,2]
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 82: X2 = double_divide(double_divide(identity(), X3), double_divide(identity(), double_divide(double_divide(identity(), identity()), double_divide(X2, double_divide(X3, identity()))))).
% 0.75/1.13 Proof: Rewrite equation 53,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2].
% 0.75/1.13
% 0.75/1.13 86: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.75/1.13 Proof: Rewrite equation 49,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 87: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.75/1.13 Proof: Rewrite equation 48,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 89: X4 = double_divide(double_divide(identity(), X4), double_divide(identity(), double_divide(double_divide(identity(), identity()), identity()))).
% 0.75/1.13 Proof: Rewrite equation 45,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2].
% 0.75/1.13
% 0.75/1.13 97: identity() = double_divide(double_divide(X4, identity()), double_divide(double_divide(identity(), X4), double_divide(identity(), identity()))).
% 0.75/1.13 Proof: A critical pair between equations 86 and 78.
% 0.75/1.13
% 0.75/1.13 118: identity() = double_divide(inverse(X4), double_divide(double_divide(identity(), X4), inverse(identity()))).
% 0.75/1.13 Proof: Rewrite equation 97,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2].
% 0.75/1.13
% 0.75/1.13 126: X4 = double_divide(double_divide(identity(), X4), double_divide(identity(), inverse(inverse(identity())))).
% 0.75/1.13 Proof: Rewrite equation 89,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2].
% 0.75/1.13
% 0.75/1.13 128: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.75/1.13 Proof: Rewrite equation 87,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 133: X2 = double_divide(double_divide(identity(), X3), double_divide(identity(), double_divide(inverse(identity()), double_divide(X2, inverse(X3))))).
% 0.75/1.13 Proof: Rewrite equation 82,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2].
% 0.75/1.13
% 0.75/1.13 143: inverse(inverse(X3)) = double_divide(double_divide(identity(), X3), inverse(identity())).
% 0.75/1.13 Proof: Rewrite equation 78,
% 0.75/1.13 lhs with equations [2,2]
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 148: identity() = double_divide(inverse(identity()), double_divide(inverse(identity()), inverse(identity()))).
% 0.75/1.13 Proof: A critical pair between equations 118 and 2.
% 0.75/1.13
% 0.75/1.13 151: double_divide(identity(), identity()) = double_divide(double_divide(identity(), identity()), double_divide(identity(), identity())).
% 0.75/1.13 Proof: A critical pair between equations 133 and 118.
% 0.75/1.13
% 0.75/1.13 161: identity() = double_divide(identity(), identity()).
% 0.75/1.13 Proof: Rewrite equation 148,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,2,2,151,151].
% 0.75/1.13
% 0.75/1.13 163: double_divide(double_divide(X3, identity()), identity()) = double_divide(double_divide(identity(), X3), identity()).
% 0.75/1.13 Proof: Rewrite equation 143,
% 0.75/1.13 lhs with equations [2,2]
% 0.75/1.13 rhs with equations [2,161].
% 0.75/1.13
% 0.75/1.13 172: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.75/1.13 Proof: Rewrite equation 128,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2].
% 0.75/1.13
% 0.75/1.13 174: X4 = double_divide(double_divide(identity(), X4), identity()).
% 0.75/1.13 Proof: Rewrite equation 126,
% 0.75/1.13 lhs with equations []
% 0.75/1.13 rhs with equations [2,161,2,161,161].
% 0.75/1.13
% 0.75/1.13 179: multiply(identity(), a2()) = a2().
% 0.75/1.13 Proof: Rewrite lhs with equations [172,163,174]
% 0.75/1.13 rhs with equations [].
% 0.75/1.13
% 0.75/1.13 % SZS output end Proof
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