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% File     : Toma---0.4
% Problem  : COL060-3 : TPTP v8.1.2. Bugfixed v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n009.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 18:31:10 EDT 2023

% Result   : Unsatisfiable 0.19s 0.51s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : COL060-3 : TPTP v8.1.2. Bugfixed v1.2.0.
% 0.03/0.13  % Command    : toma --casc %s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun Aug 27 05:16:20 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.19/0.51  % SZS status Unsatisfiable
% 0.19/0.51  % SZS output start Proof
% 0.19/0.51  original problem:
% 0.19/0.51  axioms:
% 0.19/0.51  apply(apply(apply(b(), X), Y), Z) = apply(X, apply(Y, Z))
% 0.19/0.51  apply(apply(t(), X), Y) = apply(Y, X)
% 0.19/0.51  goal:
% 0.19/0.51  apply(apply(apply(apply(apply(b(), apply(apply(b(), apply(t(), b())), b())), t()), x()), y()), z()) != apply(y(), apply(x(), z()))
% 0.19/0.51  To show the unsatisfiability of the original goal,
% 0.19/0.51  it suffices to show that apply(apply(apply(apply(apply(b(), apply(apply(b(), apply(t(), b())), b())), t()), x()), y()), z()) = apply(y(), apply(x(), z())) (skolemized goal) is valid under the axioms.
% 0.19/0.51  Here is an equational proof:
% 0.19/0.51  0: apply(apply(apply(b(), X0), X1), X2) = apply(X0, apply(X1, X2)).
% 0.19/0.51  Proof: Axiom.
% 0.19/0.51  
% 0.19/0.51  1: apply(apply(t(), X0), X1) = apply(X1, X0).
% 0.19/0.51  Proof: Axiom.
% 0.19/0.51  
% 0.19/0.51  3: apply(X0, apply(X4, X2)) = apply(apply(apply(t(), X4), apply(b(), X0)), X2).
% 0.19/0.51  Proof: A critical pair between equations 0 and 1.
% 0.19/0.51  
% 0.19/0.51  4: apply(apply(apply(apply(apply(b(), apply(apply(b(), apply(t(), b())), b())), t()), x()), y()), z()) = apply(y(), apply(x(), z())).
% 0.19/0.51  Proof: Rewrite lhs with equations [1,1,3,3,3,3]
% 0.19/0.51                 rhs with equations [].
% 0.19/0.51  
% 0.19/0.51  % SZS output end Proof
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