%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL002-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art03.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:30:33 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   12 (  12 unt;   0 def)
%            Number of atoms       :   12 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   26 (   0 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_fixed_point,plain,
    ! [A] : ~ $equal(apply(fixed_pt,A),A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-1.tptp',unknown),
    [] ).

cnf(170925128,plain,
    ~ $equal(apply(fixed_pt,A),A),
    inference(rewrite,[status(thm)],[prove_fixed_point]),
    [] ).

fof(b_definition,plain,
    ! [A,B,C] : $equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-1.tptp',unknown),
    [] ).

cnf(170908416,plain,
    $equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
    inference(rewrite,[status(thm)],[b_definition]),
    [] ).

cnf(178732408,plain,
    ~ $equal(apply(apply(apply(b,fixed_pt),A),B),apply(A,B)),
    inference(paramodulation,[status(thm)],[170925128,170908416,theory(equality)]),
    [] ).

fof(c_definition,plain,
    ! [A,B,C] : $equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-1.tptp',unknown),
    [] ).

cnf(170912456,plain,
    $equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B)),
    inference(rewrite,[status(thm)],[c_definition]),
    [] ).

cnf(178921192,plain,
    ~ $equal(apply(apply(apply(c,apply(b,fixed_pt)),B),A),apply(A,B)),
    inference(paramodulation,[status(thm)],[178732408,170912456,theory(equality)]),
    [] ).

fof(s_definition,plain,
    ! [A,B,C] : $equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-1.tptp',unknown),
    [] ).

cnf(170904168,plain,
    $equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C))),
    inference(rewrite,[status(thm)],[s_definition]),
    [] ).

cnf(179581192,plain,
    ~ $equal(apply(apply(apply(s,apply(c,apply(b,fixed_pt))),B),A),apply(apply(B,A),A)),
    inference(paramodulation,[status(thm)],[178921192,170904168,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(equality_resolution,[status(thm)],[179581192]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_fixed_point,plain,(~$equal(apply(fixed_pt,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-1.tptp',unknown),[]).
% 
% cnf(170925128,plain,(~$equal(apply(fixed_pt,A),A)),inference(rewrite,[status(thm)],[prove_fixed_point]),[]).
% 
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-1.tptp',unknown),[]).
% 
% cnf(170908416,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
% 
% cnf(178732408,plain,(~$equal(apply(apply(apply(b,fixed_pt),A),B),apply(A,B))),inference(paramodulation,[status(thm)],[170925128,170908416,theory(equality)]),[]).
% 
% fof(c_definition,plain,($equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-1.tptp',unknown),[]).
% 
% cnf(170912456,plain,($equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B))),inference(rewrite,[status(thm)],[c_definition]),[]).
% 
% cnf(178921192,plain,(~$equal(apply(apply(apply(c,apply(b,fixed_pt)),B),A),apply(A,B))),inference(paramodulation,[status(thm)],[178732408,170912456,theory(equality)]),[]).
% 
% fof(s_definition,plain,($equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-1.tptp',unknown),[]).
% 
% cnf(170904168,plain,($equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C)))),inference(rewrite,[status(thm)],[s_definition]),[]).
% 
% cnf(179581192,plain,(~$equal(apply(apply(apply(s,apply(c,apply(b,fixed_pt))),B),A),apply(apply(B,A),A))),inference(paramodulation,[status(thm)],[178921192,170904168,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(equality_resolution,[status(thm)],[179581192]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------