TSTP Solution File: COL062-2 by Toma---0.4
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% File : Toma---0.4
% Problem : COL062-2 : TPTP v8.1.2. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n015.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 : Wed Aug 30 18:31:11 EDT 2023
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COL062-2 : TPTP v8.1.2. Bugfixed v1.2.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.35 % Computer : n015.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 : Sun Aug 27 05:21:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 original problem:
% 0.19/0.52 axioms:
% 0.19/0.52 apply(apply(apply(b(), X), Y), Z) = apply(X, apply(Y, Z))
% 0.19/0.52 apply(apply(t(), X), Y) = apply(Y, X)
% 0.19/0.52 goal:
% 0.19/0.52 apply(apply(apply(apply(apply(b(), apply(t(), apply(apply(b(), b()), t()))), apply(apply(b(), b()), t())), x()), y()), z()) != apply(apply(x(), z()), y())
% 0.19/0.52 To show the unsatisfiability of the original goal,
% 0.19/0.52 it suffices to show that apply(apply(apply(apply(apply(b(), apply(t(), apply(apply(b(), b()), t()))), apply(apply(b(), b()), t())), x()), y()), z()) = apply(apply(x(), z()), y()) (skolemized goal) is valid under the axioms.
% 0.19/0.52 Here is an equational proof:
% 0.19/0.52 0: apply(apply(apply(b(), X0), X1), X2) = apply(X0, apply(X1, X2)).
% 0.19/0.52 Proof: Axiom.
% 0.19/0.52
% 0.19/0.52 1: apply(apply(t(), X0), X1) = apply(X1, X0).
% 0.19/0.52 Proof: Axiom.
% 0.19/0.52
% 0.19/0.52 3: apply(X0, apply(X4, X2)) = apply(apply(apply(t(), X4), apply(b(), X0)), X2).
% 0.19/0.52 Proof: A critical pair between equations 0 and 1.
% 0.19/0.52
% 0.19/0.52 4: apply(apply(apply(apply(apply(b(), apply(t(), apply(apply(b(), b()), t()))), apply(apply(b(), b()), t())), x()), y()), z()) = apply(apply(x(), z()), y()).
% 0.19/0.52 Proof: Rewrite lhs with equations [1,1,1,3,3,3,3,3]
% 0.19/0.52 rhs with equations [1].
% 0.19/0.52
% 0.19/0.52 % SZS output end Proof
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