TSTP Solution File: GRP481-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP481-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n013.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 01:15:07 EDT 2023
% Result : Unsatisfiable 0.74s 1.08s
% Output : CNFRefutation 0.74s
% 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 : GRP481-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 20:42:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.74/1.08 % SZS status Unsatisfiable
% 0.74/1.08 % SZS output start Proof
% 0.74/1.08 original problem:
% 0.74/1.08 axioms:
% 0.74/1.08 double_divide(double_divide(double_divide(A, double_divide(B, identity())), double_divide(double_divide(C, double_divide(D, double_divide(D, identity()))), double_divide(A, identity()))), B) = C
% 0.74/1.08 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 0.74/1.08 inverse(A) = double_divide(A, identity())
% 0.74/1.08 identity() = double_divide(A, inverse(A))
% 0.74/1.08 goal:
% 0.74/1.08 multiply(inverse(a1()), a1()) != identity()
% 0.74/1.08 To show the unsatisfiability of the original goal,
% 0.74/1.08 it suffices to show that multiply(inverse(a1()), a1()) = identity() (skolemized goal) is valid under the axioms.
% 0.74/1.08 Here is an equational proof:
% 0.74/1.08 0: double_divide(double_divide(double_divide(X0, double_divide(X1, identity())), double_divide(double_divide(X2, double_divide(X3, double_divide(X3, identity()))), double_divide(X0, identity()))), X1) = X2.
% 0.74/1.08 Proof: Axiom.
% 0.74/1.08
% 0.74/1.08 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.74/1.08 Proof: Axiom.
% 0.74/1.08
% 0.74/1.08 2: inverse(X0) = double_divide(X0, identity()).
% 0.74/1.08 Proof: Axiom.
% 0.74/1.08
% 0.74/1.08 3: identity() = double_divide(X0, inverse(X0)).
% 0.74/1.08 Proof: Axiom.
% 0.74/1.08
% 0.74/1.08 4: double_divide(double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(X2), inverse(X0))), X1) = X2.
% 0.74/1.08 Proof: Rewrite equation 0,
% 0.74/1.08 lhs with equations [2,2,3,2,2]
% 0.74/1.08 rhs with equations [].
% 0.74/1.08
% 0.74/1.08 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.74/1.08 Proof: Rewrite equation 1,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 6: X2 = double_divide(double_divide(double_divide(inverse(X2), inverse(X1)), identity()), X1).
% 0.74/1.08 Proof: A critical pair between equations 4 and 3.
% 0.74/1.08
% 0.74/1.08 7: X2 = double_divide(double_divide(identity(), double_divide(inverse(X2), inverse(X3))), X3).
% 0.74/1.08 Proof: A critical pair between equations 4 and 3.
% 0.74/1.08
% 0.74/1.08 8: X2 = inverse(double_divide(double_divide(X0, inverse(identity())), double_divide(inverse(X2), inverse(X0)))).
% 0.74/1.08 Proof: A critical pair between equations 4 and 2.
% 0.74/1.08
% 0.74/1.08 11: X2 = double_divide(double_divide(double_divide(X0, double_divide(identity(), identity())), double_divide(double_divide(X2, identity()), double_divide(X0, identity()))), identity()).
% 0.74/1.08 Proof: Rewrite equation 8,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2,2,2,2].
% 0.74/1.08
% 0.74/1.08 12: X2 = double_divide(double_divide(identity(), double_divide(double_divide(X2, identity()), double_divide(X3, identity()))), X3).
% 0.74/1.08 Proof: Rewrite equation 7,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2,2].
% 0.74/1.08
% 0.74/1.08 13: X2 = double_divide(double_divide(double_divide(double_divide(X2, identity()), double_divide(X1, identity())), identity()), X1).
% 0.74/1.08 Proof: Rewrite equation 6,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2,2].
% 0.74/1.08
% 0.74/1.08 14: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.74/1.08 Proof: Rewrite equation 3,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 15: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.74/1.08 Proof: Rewrite equation 5,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 17: X2 = double_divide(double_divide(identity(), identity()), double_divide(X2, identity())).
% 0.74/1.08 Proof: A critical pair between equations 12 and 14.
% 0.74/1.08
% 0.74/1.08 19: identity() = double_divide(double_divide(double_divide(double_divide(X3, identity()), double_divide(identity(), identity())), identity()), X3).
% 0.74/1.08 Proof: A critical pair between equations 14 and 13.
% 0.74/1.08
% 0.74/1.08 20: double_divide(double_divide(X4, identity()), double_divide(double_divide(X3, identity()), identity())) = double_divide(double_divide(identity(), X4), X3).
% 0.74/1.08 Proof: A critical pair between equations 12 and 13.
% 0.74/1.08
% 0.74/1.08 21: double_divide(double_divide(X3, identity()), double_divide(double_divide(X1, identity()), identity())) = double_divide(double_divide(X3, identity()), X1).
% 0.74/1.08 Proof: A critical pair between equations 13 and 13.
% 0.74/1.08
% 0.74/1.08 23: double_divide(double_divide(X3, identity()), double_divide(double_divide(X0, identity()), identity())) = double_divide(double_divide(double_divide(X0, double_divide(identity(), identity())), X3), identity()).
% 0.74/1.08 Proof: A critical pair between equations 11 and 13.
% 0.74/1.08
% 0.74/1.08 25: double_divide(identity(), double_divide(double_divide(X4, identity()), double_divide(identity(), identity()))) = double_divide(double_divide(identity(), double_divide(X4, double_divide(X3, identity()))), X3).
% 0.74/1.08 Proof: A critical pair between equations 12 and 12.
% 0.74/1.08
% 0.74/1.08 31: double_divide(identity(), double_divide(inverse(X4), inverse(identity()))) = double_divide(double_divide(identity(), double_divide(X4, inverse(X3))), X3).
% 0.74/1.08 Proof: Rewrite equation 25,
% 0.74/1.08 lhs with equations [2,2]
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 34: double_divide(inverse(X3), inverse(inverse(X1))) = double_divide(inverse(X3), X1).
% 0.74/1.08 Proof: Rewrite equation 21,
% 0.74/1.08 lhs with equations [2,2,2]
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 35: identity() = double_divide(inverse(double_divide(inverse(X3), inverse(identity()))), X3).
% 0.74/1.08 Proof: Rewrite equation 19,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2,2,2].
% 0.74/1.08
% 0.74/1.08 37: X2 = double_divide(inverse(identity()), inverse(X2)).
% 0.74/1.08 Proof: Rewrite equation 17,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2,2].
% 0.74/1.08
% 0.74/1.08 39: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.74/1.08 Proof: Rewrite equation 15,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 40: identity() = double_divide(X0, inverse(X0)).
% 0.74/1.08 Proof: Rewrite equation 14,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 46: double_divide(inverse(X3), X0) = inverse(double_divide(double_divide(X0, inverse(identity())), X3)).
% 0.74/1.08 Proof: Rewrite equation 23,
% 0.74/1.08 lhs with equations [2,2,2,34]
% 0.74/1.08 rhs with equations [2,2].
% 0.74/1.08
% 0.74/1.08 47: double_divide(inverse(X4), X3) = double_divide(double_divide(identity(), X4), X3).
% 0.74/1.08 Proof: Rewrite equation 20,
% 0.74/1.08 lhs with equations [2,2,2,34]
% 0.74/1.08 rhs with equations [].
% 0.74/1.08
% 0.74/1.08 48: inverse(identity()) = identity().
% 0.74/1.08 Proof: A critical pair between equations 37 and 40.
% 0.74/1.08
% 0.74/1.08 49: double_divide(inverse(X3), X3) = identity().
% 0.74/1.08 Proof: A critical pair between equations 34 and 40.
% 0.74/1.08
% 0.74/1.08 51: double_divide(inverse(identity()), X1) = inverse(X1).
% 0.74/1.08 Proof: A critical pair between equations 34 and 37.
% 0.74/1.08
% 0.74/1.08 53: double_divide(inverse(X3), identity()) = inverse(double_divide(identity(), X3)).
% 0.74/1.08 Proof: A critical pair between equations 46 and 40.
% 0.74/1.08
% 0.74/1.08 55: identity() = inverse(inverse(double_divide(inverse(identity()), inverse(identity())))).
% 0.74/1.08 Proof: A critical pair between equations 35 and 2.
% 0.74/1.08
% 0.74/1.08 63: identity() = double_divide(identity(), identity()).
% 0.74/1.08 Proof: Rewrite equation 55,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [48,48,53,48,53,48].
% 0.74/1.08
% 0.74/1.08 65: double_divide(double_divide(X3, identity()), X3) = identity().
% 0.74/1.08 Proof: Rewrite equation 49,
% 0.74/1.08 lhs with equations [2]
% 0.74/1.08 rhs with equations [].
% 0.74/1.08
% 0.74/1.08 66: double_divide(double_divide(X4, identity()), X3) = double_divide(double_divide(identity(), X4), X3).
% 0.74/1.08 Proof: Rewrite equation 47,
% 0.74/1.08 lhs with equations [2]
% 0.74/1.08 rhs with equations [].
% 0.74/1.08
% 0.74/1.08 72: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.74/1.08 Proof: Rewrite equation 40,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 73: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.74/1.08 Proof: Rewrite equation 39,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 75: X2 = double_divide(identity(), double_divide(X2, identity())).
% 0.74/1.08 Proof: Rewrite equation 37,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2,63,2].
% 0.74/1.08
% 0.74/1.08 80: double_divide(identity(), X1) = double_divide(X1, identity()).
% 0.74/1.08 Proof: Rewrite equation 51,
% 0.74/1.08 lhs with equations [2,63]
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 81: double_divide(identity(), X4) = double_divide(double_divide(identity(), double_divide(X4, double_divide(X3, identity()))), X3).
% 0.74/1.08 Proof: Rewrite equation 31,
% 0.74/1.08 lhs with equations [2,2,63,80,75]
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 82: double_divide(double_divide(identity(), X5), X5) = identity().
% 0.74/1.08 Proof: A critical pair between equations 66 and 65.
% 0.74/1.08
% 0.74/1.08 88: double_divide(identity(), identity()) = double_divide(double_divide(identity(), X5), X5).
% 0.74/1.08 Proof: A critical pair between equations 81 and 75.
% 0.74/1.08
% 0.74/1.08 98: inverse(identity()) = identity().
% 0.74/1.08 Proof: Rewrite equation 88,
% 0.74/1.08 lhs with equations [2]
% 0.74/1.08 rhs with equations [82].
% 0.74/1.08
% 0.74/1.08 104: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.74/1.08 Proof: Rewrite equation 73,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 105: identity() = double_divide(X0, inverse(X0)).
% 0.74/1.08 Proof: Rewrite equation 72,
% 0.74/1.08 lhs with equations []
% 0.74/1.08 rhs with equations [2].
% 0.74/1.08
% 0.74/1.08 111: multiply(inverse(a1()), a1()) = identity().
% 0.74/1.08 Proof: Rewrite lhs with equations [104,105,98]
% 0.74/1.08 rhs with equations [].
% 0.74/1.08
% 0.74/1.08 % SZS output end Proof
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