%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL002-5 : TPTP v3.4.2. Bugfixed v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art09.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 11:30:38 EDT 2009

% Result   : Unsatisfiable 0.6s
% Output   : Refutation 0.6s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (  14 unt;   0 def)
%            Number of atoms       :   14 (   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    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   20 (   0 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(weak_fixed_point,plain,
    ! [A] : $equal(apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A)))),weak_fixed_point(A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-5.tptp',unknown),
    [] ).

cnf(170919688,plain,
    $equal(apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A)))),weak_fixed_point(A)),
    inference(rewrite,[status(thm)],[weak_fixed_point]),
    [] ).

fof(prove_weak_fixed_point,plain,
    ~ $equal(apply(fixed_pt,weak_fixed_point(fixed_pt)),weak_fixed_point(fixed_pt)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-5.tptp',unknown),
    [] ).

cnf(170924216,plain,
    ~ $equal(apply(fixed_pt,weak_fixed_point(fixed_pt)),weak_fixed_point(fixed_pt)),
    inference(rewrite,[status(thm)],[prove_weak_fixed_point]),
    [] ).

cnf(178751984,plain,
    ~ $equal(apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))),weak_fixed_point(fixed_pt)),
    inference(paramodulation,[status(thm)],[170924216,170919688,theory(equality)]),
    [] ).

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/COL002-5.tptp',unknown),
    [] ).

cnf(170903040,plain,
    $equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
    inference(rewrite,[status(thm)],[b_definition]),
    [] ).

cnf(178800744,plain,
    ~ $equal(apply(apply(apply(b,fixed_pt),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),apply(s,apply(c,apply(b,fixed_pt)))),weak_fixed_point(fixed_pt)),
    inference(paramodulation,[status(thm)],[178751984,170903040,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/COL002-5.tptp',unknown),
    [] ).

cnf(170907112,plain,
    $equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B)),
    inference(rewrite,[status(thm)],[c_definition]),
    [] ).

cnf(180291472,plain,
    ~ $equal(apply(apply(apply(c,apply(b,fixed_pt)),apply(s,apply(c,apply(b,fixed_pt)))),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),weak_fixed_point(fixed_pt)),
    inference(paramodulation,[status(thm)],[178800744,170907112,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/COL002-5.tptp',unknown),
    [] ).

cnf(170898760,plain,
    $equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C))),
    inference(rewrite,[status(thm)],[s_definition]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[170919688,180291472,170898760,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(weak_fixed_point,plain,($equal(apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A)))),weak_fixed_point(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-5.tptp',unknown),[]).
% 
% cnf(170919688,plain,($equal(apply(apply(apply(s,apply(c,apply(b,A))),apply(s,apply(c,apply(b,A)))),apply(s,apply(c,apply(b,A)))),weak_fixed_point(A))),inference(rewrite,[status(thm)],[weak_fixed_point]),[]).
% 
% fof(prove_weak_fixed_point,plain,(~$equal(apply(fixed_pt,weak_fixed_point(fixed_pt)),weak_fixed_point(fixed_pt))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-5.tptp',unknown),[]).
% 
% cnf(170924216,plain,(~$equal(apply(fixed_pt,weak_fixed_point(fixed_pt)),weak_fixed_point(fixed_pt))),inference(rewrite,[status(thm)],[prove_weak_fixed_point]),[]).
% 
% cnf(178751984,plain,(~$equal(apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))),weak_fixed_point(fixed_pt))),inference(paramodulation,[status(thm)],[170924216,170919688,theory(equality)]),[]).
% 
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-5.tptp',unknown),[]).
% 
% cnf(170903040,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
% 
% cnf(178800744,plain,(~$equal(apply(apply(apply(b,fixed_pt),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),apply(s,apply(c,apply(b,fixed_pt)))),weak_fixed_point(fixed_pt))),inference(paramodulation,[status(thm)],[178751984,170903040,theory(equality)]),[]).
% 
% fof(c_definition,plain,($equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-5.tptp',unknown),[]).
% 
% cnf(170907112,plain,($equal(apply(apply(apply(c,A),B),C),apply(apply(A,C),B))),inference(rewrite,[status(thm)],[c_definition]),[]).
% 
% cnf(180291472,plain,(~$equal(apply(apply(apply(c,apply(b,fixed_pt)),apply(s,apply(c,apply(b,fixed_pt)))),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),weak_fixed_point(fixed_pt))),inference(paramodulation,[status(thm)],[178800744,170907112,theory(equality)]),[]).
% 
% fof(s_definition,plain,($equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL002-5.tptp',unknown),[]).
% 
% cnf(170898760,plain,($equal(apply(apply(apply(s,A),B),C),apply(apply(A,C),apply(B,C)))),inference(rewrite,[status(thm)],[s_definition]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[170919688,180291472,170898760,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------