TSTP Solution File: GRP573-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP573-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n019.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 01:15:24 EDT 2023
% Result : Unsatisfiable 1.30s 1.53s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP573-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.36 % Computer : n019.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Aug 28 23:30:28 EDT 2023
% 0.13/0.36 % CPUTime :
% 1.30/1.53 % SZS status Unsatisfiable
% 1.30/1.53 % SZS output start Proof
% 1.30/1.53 original problem:
% 1.30/1.53 axioms:
% 1.30/1.53 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity()))), double_divide(identity(), identity())) = B
% 1.30/1.53 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 1.30/1.53 inverse(A) = double_divide(A, identity())
% 1.30/1.53 identity() = double_divide(A, inverse(A))
% 1.30/1.53 goal:
% 1.30/1.53 multiply(inverse(a1()), a1()) != identity()
% 1.30/1.53 To show the unsatisfiability of the original goal,
% 1.30/1.53 it suffices to show that multiply(inverse(a1()), a1()) = identity() (skolemized goal) is valid under the axioms.
% 1.30/1.53 Here is an equational proof:
% 1.30/1.53 0: double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), double_divide(X2, identity()))), double_divide(identity(), identity())) = X1.
% 1.30/1.53 Proof: Axiom.
% 1.30/1.53
% 1.30/1.53 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.30/1.53 Proof: Axiom.
% 1.30/1.53
% 1.30/1.53 2: inverse(X0) = double_divide(X0, identity()).
% 1.30/1.53 Proof: Axiom.
% 1.30/1.53
% 1.30/1.53 3: identity() = double_divide(X0, inverse(X0)).
% 1.30/1.53 Proof: Axiom.
% 1.30/1.53
% 1.30/1.53 4: double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), inverse(X2))), inverse(identity())) = X1.
% 1.30/1.53 Proof: Rewrite equation 0,
% 1.30/1.53 lhs with equations [2,2]
% 1.30/1.53 rhs with equations [].
% 1.30/1.53
% 1.30/1.53 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.30/1.53 Proof: Rewrite equation 1,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 6: X1 = double_divide(double_divide(identity(), double_divide(double_divide(X1, inverse(X3)), inverse(X3))), inverse(identity())).
% 1.30/1.53 Proof: A critical pair between equations 4 and 2.
% 1.30/1.53
% 1.30/1.53 7: X1 = double_divide(double_divide(inverse(X3), double_divide(double_divide(X1, identity()), inverse(X3))), inverse(identity())).
% 1.30/1.53 Proof: A critical pair between equations 4 and 3.
% 1.30/1.53
% 1.30/1.53 10: X1 = double_divide(double_divide(double_divide(X3, identity()), double_divide(double_divide(X1, identity()), double_divide(X3, identity()))), double_divide(identity(), identity())).
% 1.30/1.53 Proof: Rewrite equation 7,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2,2,2].
% 1.30/1.53
% 1.30/1.53 11: X1 = double_divide(double_divide(identity(), double_divide(double_divide(X1, double_divide(X3, identity())), double_divide(X3, identity()))), double_divide(identity(), identity())).
% 1.30/1.53 Proof: Rewrite equation 6,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2,2,2].
% 1.30/1.53
% 1.30/1.53 12: identity() = double_divide(X0, double_divide(X0, identity())).
% 1.30/1.53 Proof: Rewrite equation 3,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 13: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.30/1.53 Proof: Rewrite equation 5,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 14: double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), double_divide(X2, identity()))), double_divide(identity(), identity())) = X1.
% 1.30/1.53 Proof: Rewrite equation 4,
% 1.30/1.53 lhs with equations [2,2]
% 1.30/1.53 rhs with equations [].
% 1.30/1.53
% 1.30/1.53 15: X1 = double_divide(double_divide(double_divide(double_divide(X1, identity()), identity()), identity()), double_divide(identity(), identity())).
% 1.30/1.53 Proof: A critical pair between equations 10 and 12.
% 1.30/1.53
% 1.30/1.53 16: X4 = double_divide(double_divide(identity(), double_divide(identity(), double_divide(X4, identity()))), double_divide(identity(), identity())).
% 1.30/1.53 Proof: A critical pair between equations 11 and 12.
% 1.30/1.53
% 1.30/1.53 18: double_divide(double_divide(X4, identity()), double_divide(double_divide(X5, identity()), double_divide(X4, identity()))) = double_divide(double_divide(identity(), double_divide(X5, double_divide(identity(), identity()))), double_divide(identity(), identity())).
% 1.30/1.53 Proof: A critical pair between equations 11 and 10.
% 1.30/1.53
% 1.30/1.53 20: double_divide(X4, double_divide(double_divide(X5, double_divide(X6, X4)), double_divide(X6, identity()))) = double_divide(double_divide(identity(), double_divide(X5, double_divide(identity(), identity()))), double_divide(identity(), identity())).
% 1.30/1.53 Proof: A critical pair between equations 11 and 14.
% 1.30/1.53
% 1.30/1.53 33: X4 = double_divide(double_divide(identity(), double_divide(identity(), inverse(X4))), inverse(identity())).
% 1.30/1.53 Proof: Rewrite equation 16,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2,2].
% 1.30/1.53
% 1.30/1.53 34: X1 = double_divide(inverse(inverse(inverse(X1))), inverse(identity())).
% 1.30/1.53 Proof: Rewrite equation 15,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2,2,2,2].
% 1.30/1.53
% 1.30/1.53 36: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.30/1.53 Proof: Rewrite equation 13,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 37: identity() = double_divide(X0, inverse(X0)).
% 1.30/1.53 Proof: Rewrite equation 12,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 39: X1 = double_divide(double_divide(inverse(X3), double_divide(inverse(X1), inverse(X3))), inverse(identity())).
% 1.30/1.53 Proof: Rewrite equation 10,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2,2,2,2].
% 1.30/1.53
% 1.30/1.53 42: double_divide(X4, double_divide(double_divide(X5, double_divide(X6, X4)), inverse(X6))) = double_divide(double_divide(identity(), double_divide(X5, inverse(identity()))), inverse(identity())).
% 1.30/1.53 Proof: Rewrite equation 20,
% 1.30/1.53 lhs with equations [2]
% 1.30/1.53 rhs with equations [2,2].
% 1.30/1.53
% 1.30/1.53 44: double_divide(inverse(X4), double_divide(inverse(X5), inverse(X4))) = double_divide(double_divide(identity(), double_divide(X5, inverse(identity()))), inverse(identity())).
% 1.30/1.53 Proof: Rewrite equation 18,
% 1.30/1.53 lhs with equations [2,2,2]
% 1.30/1.53 rhs with equations [2,2].
% 1.30/1.53
% 1.30/1.53 45: identity() = double_divide(double_divide(identity(), identity()), inverse(identity())).
% 1.30/1.53 Proof: A critical pair between equations 33 and 37.
% 1.30/1.53
% 1.30/1.53 47: double_divide(inverse(X4), double_divide(inverse(identity()), inverse(X4))) = identity().
% 1.30/1.53 Proof: A critical pair between equations 44 and 33.
% 1.30/1.53
% 1.30/1.53 49: inverse(inverse(X4)) = double_divide(double_divide(inverse(identity()), X4), inverse(identity())).
% 1.30/1.53 Proof: A critical pair between equations 39 and 34.
% 1.30/1.53
% 1.30/1.53 50: double_divide(X4, double_divide(double_divide(identity(), double_divide(X6, X4)), inverse(X6))) = identity().
% 1.30/1.53 Proof: A critical pair between equations 42 and 33.
% 1.30/1.53
% 1.30/1.53 61: double_divide(X4, double_divide(double_divide(identity(), double_divide(X6, X4)), double_divide(X6, identity()))) = identity().
% 1.30/1.53 Proof: Rewrite equation 50,
% 1.30/1.53 lhs with equations [2]
% 1.30/1.53 rhs with equations [].
% 1.30/1.53
% 1.30/1.53 62: double_divide(double_divide(X4, identity()), identity()) = double_divide(double_divide(double_divide(identity(), identity()), X4), double_divide(identity(), identity())).
% 1.30/1.53 Proof: Rewrite equation 49,
% 1.30/1.53 lhs with equations [2,2]
% 1.30/1.53 rhs with equations [2,2].
% 1.30/1.53
% 1.30/1.53 63: double_divide(double_divide(X4, identity()), double_divide(double_divide(identity(), identity()), double_divide(X4, identity()))) = identity().
% 1.30/1.53 Proof: Rewrite equation 47,
% 1.30/1.53 lhs with equations [2,2,2]
% 1.30/1.53 rhs with equations [].
% 1.30/1.53
% 1.30/1.53 65: identity() = double_divide(double_divide(identity(), identity()), double_divide(identity(), identity())).
% 1.30/1.53 Proof: Rewrite equation 45,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 69: identity() = double_divide(X0, double_divide(X0, identity())).
% 1.30/1.53 Proof: Rewrite equation 37,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 70: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.30/1.53 Proof: Rewrite equation 36,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 84: identity() = double_divide(identity(), double_divide(identity(), double_divide(identity(), identity()))).
% 1.30/1.53 Proof: A critical pair between equations 61 and 69.
% 1.30/1.53
% 1.30/1.53 85: identity() = double_divide(double_divide(double_divide(identity(), identity()), identity()), identity()).
% 1.30/1.53 Proof: A critical pair between equations 63 and 69.
% 1.30/1.53
% 1.30/1.53 86: double_divide(double_divide(double_divide(identity(), identity()), identity()), identity()) = double_divide(identity(), double_divide(identity(), identity())).
% 1.30/1.53 Proof: A critical pair between equations 62 and 65.
% 1.30/1.53
% 1.30/1.53 104: inverse(inverse(inverse(identity()))) = double_divide(identity(), inverse(identity())).
% 1.30/1.53 Proof: Rewrite equation 86,
% 1.30/1.53 lhs with equations [2,2,2]
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 105: identity() = inverse(inverse(inverse(identity()))).
% 1.30/1.53 Proof: Rewrite equation 85,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2,2,2].
% 1.30/1.53
% 1.30/1.53 106: identity() = inverse(identity()).
% 1.30/1.53 Proof: Rewrite equation 84,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2,104,105,2].
% 1.30/1.53
% 1.30/1.53 117: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.30/1.53 Proof: Rewrite equation 70,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 118: identity() = double_divide(X0, inverse(X0)).
% 1.30/1.53 Proof: Rewrite equation 69,
% 1.30/1.53 lhs with equations []
% 1.30/1.53 rhs with equations [2].
% 1.30/1.53
% 1.30/1.53 132: multiply(inverse(a1()), a1()) = identity().
% 1.30/1.53 Proof: Rewrite lhs with equations [117,118,106]
% 1.30/1.53 rhs with equations [].
% 1.30/1.53
% 1.30/1.53 % SZS output end Proof
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