%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : COL064-6 : 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 18:31:14 EDT 2023

% Result   : Unsatisfiable 0.92s 1.12s
% Output   : CNFRefutation 0.92s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : COL064-6 : TPTP v8.1.2. Bugfixed v1.2.0.
% 0.06/0.13  % Command    : toma --casc %s
% 0.13/0.34  % Computer : n009.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   : Sun Aug 27 05:01:35 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.92/1.12  % SZS status Unsatisfiable
% 0.92/1.12  % SZS output start Proof
% 0.92/1.12  original problem:
% 0.92/1.12  axioms:
% 0.92/1.12  apply(apply(apply(b(), X), Y), Z) = apply(X, apply(Y, Z))
% 0.92/1.12  apply(apply(t(), X), Y) = apply(Y, X)
% 0.92/1.12  goal:
% 0.92/1.12  apply(apply(apply(apply(apply(b(), apply(apply(b(), apply(apply(b(), apply(t(), apply(apply(b(), b()), t()))), b())), b())), t()), x()), y()), z()) != apply(apply(z(), x()), y())
% 0.92/1.12  To show the unsatisfiability of the original goal,
% 0.92/1.12  it suffices to show that apply(apply(apply(apply(apply(b(), apply(apply(b(), apply(apply(b(), apply(t(), apply(apply(b(), b()), t()))), b())), b())), t()), x()), y()), z()) = apply(apply(z(), x()), y()) (skolemized goal) is valid under the axioms.
% 0.92/1.12  Here is an equational proof:
% 0.92/1.12  0: apply(apply(apply(b(), X0), X1), X2) = apply(X0, apply(X1, X2)).
% 0.92/1.12  Proof: Axiom.
% 0.92/1.12  
% 0.92/1.12  1: apply(apply(t(), X0), X1) = apply(X1, X0).
% 0.92/1.12  Proof: Axiom.
% 0.92/1.12  
% 0.92/1.12  2: apply(apply(t(), X5), apply(apply(b(), X3), X4)) = apply(X3, apply(X4, X5)).
% 0.92/1.12  Proof: A critical pair between equations 1 and 0.
% 0.92/1.12  
% 0.92/1.12  3: apply(X0, apply(X4, X2)) = apply(apply(apply(t(), X4), apply(b(), X0)), X2).
% 0.92/1.12  Proof: A critical pair between equations 0 and 1.
% 0.92/1.12  
% 0.92/1.12  4: apply(apply(t(), X7), apply(apply(b(), X3), X6)) = apply(X3, apply(apply(t(), X7), X6)).
% 0.92/1.12  Proof: A critical pair between equations 2 and 1.
% 0.92/1.12  
% 0.92/1.12  18: apply(apply(apply(apply(apply(b(), apply(apply(b(), apply(apply(b(), apply(t(), apply(apply(b(), b()), t()))), b())), b())), t()), x()), y()), z()) = apply(apply(z(), x()), y()).
% 0.92/1.12  Proof: Rewrite lhs with equations [1,1,1,3,3,3,3,0,0,4]
% 0.92/1.12                 rhs with equations [1,1].
% 0.92/1.12  
% 0.92/1.12  % SZS output end Proof
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