TSTP Solution File: GRP487-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP487-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n018.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 1.80s 2.09s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP487-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n018.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 : Tue Aug 29 00:16:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.80/2.09 % SZS status Unsatisfiable
% 1.80/2.09 % SZS output start Proof
% 1.80/2.09 original problem:
% 1.80/2.09 axioms:
% 1.80/2.09 double_divide(A, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(A, identity()), double_divide(B, C))), B), identity())) = C
% 1.80/2.09 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 1.80/2.09 inverse(A) = double_divide(A, identity())
% 1.80/2.09 identity() = double_divide(A, inverse(A))
% 1.80/2.09 goal:
% 1.80/2.09 multiply(inverse(a1()), a1()) != identity()
% 1.80/2.09 To show the unsatisfiability of the original goal,
% 1.80/2.09 it suffices to show that multiply(inverse(a1()), a1()) = identity() (skolemized goal) is valid under the axioms.
% 1.80/2.09 Here is an equational proof:
% 1.80/2.09 0: double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), double_divide(X1, X2))), X1), identity())) = X2.
% 1.80/2.09 Proof: Axiom.
% 1.80/2.09
% 1.80/2.09 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.80/2.09 Proof: Axiom.
% 1.80/2.09
% 1.80/2.09 2: inverse(X0) = double_divide(X0, identity()).
% 1.80/2.09 Proof: Axiom.
% 1.80/2.09
% 1.80/2.09 3: identity() = double_divide(X0, inverse(X0)).
% 1.80/2.09 Proof: Axiom.
% 1.80/2.09
% 1.80/2.09 4: double_divide(X0, inverse(double_divide(double_divide(identity(), double_divide(inverse(X0), double_divide(X1, X2))), X1))) = X2.
% 1.80/2.09 Proof: Rewrite equation 0,
% 1.80/2.09 lhs with equations [2,2]
% 1.80/2.09 rhs with equations [].
% 1.80/2.09
% 1.80/2.09 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.80/2.09 Proof: Rewrite equation 1,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 6: identity() = double_divide(X0, inverse(double_divide(double_divide(identity(), double_divide(inverse(X0), inverse(X3))), X3))).
% 1.80/2.09 Proof: A critical pair between equations 4 and 2.
% 1.80/2.09
% 1.80/2.09 7: X2 = double_divide(X0, inverse(inverse(double_divide(identity(), double_divide(inverse(X0), double_divide(identity(), X2)))))).
% 1.80/2.09 Proof: A critical pair between equations 4 and 2.
% 1.80/2.09
% 1.80/2.09 8: inverse(X3) = double_divide(X0, inverse(double_divide(double_divide(identity(), double_divide(inverse(X0), identity())), X3))).
% 1.80/2.09 Proof: A critical pair between equations 4 and 3.
% 1.80/2.09
% 1.80/2.09 10: double_divide(X3, identity()) = double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), identity())), X3), identity())).
% 1.80/2.09 Proof: Rewrite equation 8,
% 1.80/2.09 lhs with equations [2]
% 1.80/2.09 rhs with equations [2,2].
% 1.80/2.09
% 1.80/2.09 11: X2 = double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), double_divide(identity(), X2))), identity()), identity())).
% 1.80/2.09 Proof: Rewrite equation 7,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2,2,2].
% 1.80/2.09
% 1.80/2.09 12: identity() = double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), double_divide(X3, identity()))), X3), identity())).
% 1.80/2.09 Proof: Rewrite equation 6,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2,2,2].
% 1.80/2.09
% 1.80/2.09 13: identity() = double_divide(X0, double_divide(X0, identity())).
% 1.80/2.09 Proof: Rewrite equation 3,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 14: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.80/2.09 Proof: Rewrite equation 5,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 17: identity() = double_divide(X0, double_divide(double_divide(double_divide(identity(), identity()), double_divide(X0, identity())), identity())).
% 1.80/2.09 Proof: A critical pair between equations 12 and 13.
% 1.80/2.09
% 1.80/2.09 22: double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), identity())), identity()), identity()) = double_divide(X0, double_divide(identity(), identity())).
% 1.80/2.09 Proof: A critical pair between equations 10 and 13.
% 1.80/2.09
% 1.80/2.09 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())).
% 1.80/2.09 Proof: A critical pair between equations 10 and 11.
% 1.80/2.09
% 1.80/2.09 31: inverse(X3) = double_divide(double_divide(identity(), double_divide(inverse(identity()), double_divide(identity(), X5))), inverse(double_divide(X5, X3))).
% 1.80/2.09 Proof: Rewrite equation 25,
% 1.80/2.09 lhs with equations [2]
% 1.80/2.09 rhs with equations [2,2].
% 1.80/2.09
% 1.80/2.09 34: inverse(inverse(double_divide(identity(), inverse(inverse(X0))))) = double_divide(X0, inverse(identity())).
% 1.80/2.09 Proof: Rewrite equation 22,
% 1.80/2.09 lhs with equations [2,2,2,2]
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 38: identity() = double_divide(X0, inverse(double_divide(inverse(identity()), inverse(X0)))).
% 1.80/2.09 Proof: Rewrite equation 17,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2,2,2].
% 1.80/2.09
% 1.80/2.09 40: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.80/2.09 Proof: Rewrite equation 14,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 41: identity() = double_divide(X0, inverse(X0)).
% 1.80/2.09 Proof: Rewrite equation 13,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 43: inverse(X3) = double_divide(X0, inverse(double_divide(double_divide(identity(), inverse(inverse(X0))), X3))).
% 1.80/2.09 Proof: Rewrite equation 10,
% 1.80/2.09 lhs with equations [2]
% 1.80/2.09 rhs with equations [2,2,2].
% 1.80/2.09
% 1.80/2.09 47: identity() = double_divide(inverse(identity()), inverse(identity())).
% 1.80/2.09 Proof: A critical pair between equations 38 and 41.
% 1.80/2.09
% 1.80/2.09 49: inverse(double_divide(inverse(identity()), double_divide(identity(), identity()))) = identity().
% 1.80/2.09 Proof: A critical pair between equations 31 and 41.
% 1.80/2.09
% 1.80/2.09 56: inverse(identity()) = double_divide(X0, inverse(inverse(double_divide(identity(), inverse(inverse(X0)))))).
% 1.80/2.09 Proof: A critical pair between equations 43 and 2.
% 1.80/2.09
% 1.80/2.09 59: double_divide(identity(), identity()) = double_divide(X0, double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), identity())), identity()), identity())).
% 1.80/2.09 Proof: Rewrite equation 56,
% 1.80/2.09 lhs with equations [2]
% 1.80/2.09 rhs with equations [2,2,2,2].
% 1.80/2.09
% 1.80/2.09 65: double_divide(double_divide(double_divide(identity(), identity()), double_divide(identity(), identity())), identity()) = identity().
% 1.80/2.09 Proof: Rewrite equation 49,
% 1.80/2.09 lhs with equations [2,2]
% 1.80/2.09 rhs with equations [].
% 1.80/2.09
% 1.80/2.09 66: identity() = double_divide(double_divide(identity(), identity()), double_divide(identity(), identity())).
% 1.80/2.09 Proof: Rewrite equation 47,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2,2].
% 1.80/2.09
% 1.80/2.09 72: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 1.80/2.09 Proof: Rewrite equation 40,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 82: double_divide(double_divide(double_divide(identity(), double_divide(double_divide(X0, identity()), identity())), identity()), identity()) = double_divide(X0, double_divide(identity(), identity())).
% 1.80/2.09 Proof: Rewrite equation 34,
% 1.80/2.09 lhs with equations [2,2,2,2]
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 85: identity() = double_divide(identity(), identity()).
% 1.80/2.09 Proof: A critical pair between equations 65 and 66.
% 1.80/2.09
% 1.80/2.09 88: double_divide(identity(), identity()) = double_divide(X1, double_divide(X1, double_divide(identity(), identity()))).
% 1.80/2.09 Proof: A critical pair between equations 59 and 82.
% 1.80/2.09
% 1.80/2.09 101: identity() = double_divide(X1, inverse(X1)).
% 1.80/2.09 Proof: Rewrite equation 88,
% 1.80/2.09 lhs with equations [85]
% 1.80/2.09 rhs with equations [85,2].
% 1.80/2.09
% 1.80/2.09 102: identity() = inverse(identity()).
% 1.80/2.09 Proof: Rewrite equation 85,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 113: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.80/2.09 Proof: Rewrite equation 72,
% 1.80/2.09 lhs with equations []
% 1.80/2.09 rhs with equations [2].
% 1.80/2.09
% 1.80/2.09 121: multiply(inverse(a1()), a1()) = identity().
% 1.80/2.09 Proof: Rewrite lhs with equations [113,101,102]
% 1.80/2.09 rhs with equations [].
% 1.80/2.09
% 1.80/2.09 % SZS output end Proof
%------------------------------------------------------------------------------