TSTP Solution File: GRP493-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP493-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n004.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 0.65s 0.90s
% Output : CNFRefutation 0.65s
% 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 : GRP493-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n004.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 : Tue Aug 29 02:28:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.65/0.90 % SZS status Unsatisfiable
% 0.65/0.90 % SZS output start Proof
% 0.65/0.90 original problem:
% 0.65/0.90 axioms:
% 0.65/0.90 double_divide(double_divide(identity(), A), double_divide(double_divide(double_divide(B, C), double_divide(identity(), identity())), double_divide(A, C))) = B
% 0.65/0.90 multiply(A, B) = double_divide(double_divide(B, A), identity())
% 0.65/0.90 inverse(A) = double_divide(A, identity())
% 0.65/0.90 identity() = double_divide(A, inverse(A))
% 0.65/0.90 goal:
% 0.65/0.90 multiply(inverse(a1()), a1()) != identity()
% 0.65/0.90 To show the unsatisfiability of the original goal,
% 0.65/0.90 it suffices to show that multiply(inverse(a1()), a1()) = identity() (skolemized goal) is valid under the axioms.
% 0.65/0.90 Here is an equational proof:
% 0.65/0.90 0: double_divide(double_divide(identity(), X0), double_divide(double_divide(double_divide(X1, X2), double_divide(identity(), identity())), double_divide(X0, X2))) = X1.
% 0.65/0.90 Proof: Axiom.
% 0.65/0.90
% 0.65/0.90 1: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.65/0.90 Proof: Axiom.
% 0.65/0.90
% 0.65/0.90 2: inverse(X0) = double_divide(X0, identity()).
% 0.65/0.90 Proof: Axiom.
% 0.65/0.90
% 0.65/0.90 3: identity() = double_divide(X0, inverse(X0)).
% 0.65/0.90 Proof: Axiom.
% 0.65/0.90
% 0.65/0.90 4: double_divide(double_divide(identity(), X0), double_divide(double_divide(double_divide(X1, X2), inverse(identity())), double_divide(X0, X2))) = X1.
% 0.65/0.90 Proof: Rewrite equation 0,
% 0.65/0.90 lhs with equations [2]
% 0.65/0.90 rhs with equations [].
% 0.65/0.90
% 0.65/0.90 5: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.65/0.90 Proof: Rewrite equation 1,
% 0.65/0.90 lhs with equations []
% 0.65/0.90 rhs with equations [2].
% 0.65/0.90
% 0.65/0.90 10: X3 = double_divide(double_divide(identity(), X0), double_divide(double_divide(identity(), inverse(identity())), double_divide(X0, inverse(X3)))).
% 0.65/0.90 Proof: A critical pair between equations 4 and 3.
% 0.65/0.90
% 0.65/0.90 17: X3 = double_divide(double_divide(identity(), X0), double_divide(double_divide(identity(), double_divide(identity(), identity())), double_divide(X0, double_divide(X3, identity())))).
% 0.65/0.90 Proof: Rewrite equation 10,
% 0.65/0.90 lhs with equations []
% 0.65/0.90 rhs with equations [2,2].
% 0.65/0.90
% 0.65/0.90 21: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.65/0.90 Proof: Rewrite equation 3,
% 0.65/0.90 lhs with equations []
% 0.65/0.90 rhs with equations [2].
% 0.65/0.90
% 0.65/0.90 22: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.65/0.90 Proof: Rewrite equation 5,
% 0.65/0.90 lhs with equations []
% 0.65/0.90 rhs with equations [2].
% 0.65/0.90
% 0.65/0.90 24: X4 = double_divide(double_divide(identity(), X4), double_divide(double_divide(identity(), double_divide(identity(), identity())), identity())).
% 0.65/0.90 Proof: A critical pair between equations 17 and 21.
% 0.65/0.90
% 0.65/0.90 47: X4 = double_divide(double_divide(identity(), X4), inverse(double_divide(identity(), inverse(identity())))).
% 0.65/0.90 Proof: Rewrite equation 24,
% 0.65/0.90 lhs with equations []
% 0.65/0.90 rhs with equations [2,2].
% 0.65/0.90
% 0.65/0.90 49: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 0.65/0.90 Proof: Rewrite equation 22,
% 0.65/0.90 lhs with equations []
% 0.65/0.90 rhs with equations [2].
% 0.65/0.90
% 0.65/0.90 50: identity() = double_divide(X0, inverse(X0)).
% 0.65/0.90 Proof: Rewrite equation 21,
% 0.65/0.90 lhs with equations []
% 0.65/0.90 rhs with equations [2].
% 0.65/0.90
% 0.65/0.90 57: inverse(identity()) = identity().
% 0.65/0.90 Proof: A critical pair between equations 47 and 50.
% 0.65/0.90
% 0.65/0.90 73: double_divide(identity(), identity()) = identity().
% 0.65/0.90 Proof: Rewrite equation 57,
% 0.65/0.90 lhs with equations [2]
% 0.65/0.90 rhs with equations [].
% 0.65/0.90
% 0.65/0.90 79: identity() = double_divide(X0, double_divide(X0, identity())).
% 0.65/0.90 Proof: Rewrite equation 50,
% 0.65/0.90 lhs with equations []
% 0.65/0.90 rhs with equations [2].
% 0.65/0.90
% 0.65/0.90 80: multiply(X0, X1) = double_divide(double_divide(X1, X0), identity()).
% 0.65/0.90 Proof: Rewrite equation 49,
% 0.65/0.90 lhs with equations []
% 0.65/0.90 rhs with equations [2].
% 0.65/0.90
% 0.65/0.90 90: multiply(inverse(a1()), a1()) = identity().
% 0.65/0.90 Proof: Rewrite lhs with equations [2,80,79,73]
% 0.65/0.90 rhs with equations [].
% 0.65/0.90
% 0.65/0.90 % SZS output end Proof
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