TSTP Solution File: GRP494-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP494-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n003.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 0.53s 0.87s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP494-1 : TPTP v8.1.2. Released v2.6.0.
% 0.06/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n003.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 19:49:55 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.53/0.87 % SZS status Unsatisfiable
% 0.53/0.87 % SZS output start Proof
% 0.53/0.87 original problem:
% 0.53/0.87 axioms:
% 0.53/0.87 double_divide(double_divide(identity(), A), double_divide(double_divide(double_divide(B, C), double_divide(identity(), identity())), double_divide(A, C))) = B
% 0.53/0.87 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 0.53/0.87 inverse(A) = double_divide(A, identity())
% 0.53/0.87 identity() = double_divide(A, inverse(A))
% 0.53/0.87 goal:
% 0.53/0.87 multiply(identity(), a2()) != a2()
% 0.53/0.87 To show the unsatisfiability of the original goal,
% 0.53/0.87 it suffices to show that multiply(identity(), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.53/0.87 Here is an equational proof:
% 0.53/0.87 0: double_divide(double_divide(identity(), X0), double_divide(double_divide(double_divide(X1, X2), double_divide(identity(), identity())), double_divide(X0, X2))) = X1.
% 0.53/0.87 Proof: Axiom.
% 0.53/0.87
% 0.53/0.87 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.53/0.87 Proof: Axiom.
% 0.53/0.87
% 0.53/0.87 2: inverse(X0) = double_divide(X0, identity()).
% 0.53/0.87 Proof: Axiom.
% 0.53/0.87
% 0.53/0.87 3: identity() = double_divide(X0, inverse(X0)).
% 0.53/0.87 Proof: Axiom.
% 0.53/0.87
% 0.53/0.87 4: double_divide(double_divide(identity(), X0), double_divide(double_divide(double_divide(X1, X2), inverse(identity())), double_divide(X0, X2))) = X1.
% 0.53/0.87 Proof: Rewrite equation 0,
% 0.53/0.87 lhs with equations [2]
% 0.53/0.87 rhs with equations [].
% 0.53/0.87
% 0.53/0.87 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.53/0.87 Proof: Rewrite equation 1,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2].
% 0.53/0.87
% 0.53/0.87 7: X3 = double_divide(double_divide(identity(), X0), double_divide(double_divide(inverse(X3), inverse(identity())), double_divide(X0, identity()))).
% 0.53/0.87 Proof: A critical pair between equations 4 and 2.
% 0.53/0.87
% 0.53/0.87 10: X3 = double_divide(double_divide(identity(), X0), double_divide(double_divide(identity(), inverse(identity())), double_divide(X0, inverse(X3)))).
% 0.53/0.87 Proof: A critical pair between equations 4 and 3.
% 0.53/0.87
% 0.53/0.87 17: X3 = double_divide(double_divide(identity(), X0), double_divide(double_divide(identity(), double_divide(identity(), identity())), double_divide(X0, double_divide(X3, identity())))).
% 0.53/0.87 Proof: Rewrite equation 10,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2,2].
% 0.53/0.87
% 0.53/0.87 20: X3 = double_divide(double_divide(identity(), X0), double_divide(double_divide(double_divide(X3, identity()), double_divide(identity(), identity())), double_divide(X0, identity()))).
% 0.53/0.87 Proof: Rewrite equation 7,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2,2].
% 0.53/0.87
% 0.53/0.87 21: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.53/0.87 Proof: Rewrite equation 3,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2].
% 0.53/0.87
% 0.53/0.87 22: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.53/0.87 Proof: Rewrite equation 5,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2].
% 0.53/0.87
% 0.53/0.87 24: X4 = double_divide(double_divide(identity(), X4), double_divide(double_divide(identity(), double_divide(identity(), identity())), identity())).
% 0.53/0.87 Proof: A critical pair between equations 17 and 21.
% 0.53/0.87
% 0.53/0.87 26: X3 = double_divide(double_divide(identity(), double_divide(double_divide(X3, identity()), double_divide(identity(), identity()))), identity()).
% 0.53/0.87 Proof: A critical pair between equations 20 and 21.
% 0.53/0.87
% 0.53/0.87 45: X3 = inverse(double_divide(identity(), double_divide(inverse(X3), inverse(identity())))).
% 0.53/0.87 Proof: Rewrite equation 26,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2,2,2].
% 0.53/0.87
% 0.53/0.87 47: X4 = double_divide(double_divide(identity(), X4), inverse(double_divide(identity(), inverse(identity())))).
% 0.53/0.87 Proof: Rewrite equation 24,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2,2].
% 0.53/0.87
% 0.53/0.87 49: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.53/0.87 Proof: Rewrite equation 22,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2].
% 0.53/0.87
% 0.53/0.87 50: identity() = double_divide(X0, inverse(X0)).
% 0.53/0.87 Proof: Rewrite equation 21,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2].
% 0.53/0.87
% 0.53/0.87 57: inverse(identity()) = identity().
% 0.53/0.87 Proof: A critical pair between equations 47 and 50.
% 0.53/0.87
% 0.53/0.87 59: X4 = double_divide(double_divide(identity(), X4), inverse(identity())).
% 0.53/0.87 Proof: A critical pair between equations 47 and 50.
% 0.53/0.87
% 0.53/0.87 72: X4 = double_divide(double_divide(identity(), X4), identity()).
% 0.53/0.87 Proof: Rewrite equation 59,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [57].
% 0.53/0.87
% 0.53/0.87 73: double_divide(identity(), identity()) = identity().
% 0.53/0.87 Proof: Rewrite equation 57,
% 0.53/0.87 lhs with equations [2]
% 0.53/0.87 rhs with equations [].
% 0.53/0.87
% 0.53/0.87 80: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.53/0.87 Proof: Rewrite equation 49,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2].
% 0.53/0.87
% 0.53/0.87 83: X3 = double_divide(double_divide(X3, identity()), identity()).
% 0.53/0.87 Proof: Rewrite equation 45,
% 0.53/0.87 lhs with equations []
% 0.53/0.87 rhs with equations [2,2,73,2,72].
% 0.53/0.87
% 0.53/0.87 90: multiply(identity(), a2()) = a2().
% 0.53/0.87 Proof: Rewrite lhs with equations [80,83]
% 0.53/0.87 rhs with equations [].
% 0.53/0.87
% 0.53/0.87 % SZS output end Proof
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