%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL023-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art05.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 11:31:44 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   10 (  10 unt;   0 def)
%            Number of atoms       :   10 (   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    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   21 (   0 sgn   7   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_fixed_point,plain,
    ! [A] : ~ $equal(apply(combinator,A),A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL023-1.tptp',unknown),
    [] ).

cnf(166759320,plain,
    ~ $equal(apply(combinator,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/COL023-1.tptp',unknown),
    [] ).

cnf(166750416,plain,
    $equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
    inference(rewrite,[status(thm)],[b_definition]),
    [] ).

cnf(174558576,plain,
    ~ $equal(apply(apply(apply(b,combinator),A),B),apply(A,B)),
    inference(paramodulation,[status(thm)],[166759320,166750416,theory(equality)]),
    [] ).

cnf(174662128,plain,
    ~ $equal(apply(apply(apply(apply(b,apply(b,combinator)),B),C),A),apply(apply(B,C),A)),
    inference(paramodulation,[status(thm)],[174558576,166750416,theory(equality)]),
    [] ).

fof(n_definition,plain,
    ! [A,B,C] : $equal(apply(apply(apply(n,A),B),C),apply(apply(apply(A,C),B),C)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL023-1.tptp',unknown),
    [] ).

cnf(166754600,plain,
    $equal(apply(apply(apply(n,A),B),C),apply(apply(apply(A,C),B),C)),
    inference(rewrite,[status(thm)],[n_definition]),
    [] ).

cnf(176266648,plain,
    ~ $equal(apply(apply(apply(n,apply(b,apply(b,combinator))),B),A),apply(apply(A,B),A)),
    inference(paramodulation,[status(thm)],[174662128,166754600,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(equality_resolution,[status(thm)],[176266648]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_fixed_point,plain,(~$equal(apply(combinator,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL023-1.tptp',unknown),[]).
% 
% cnf(166759320,plain,(~$equal(apply(combinator,A),A)),inference(rewrite,[status(thm)],[prove_fixed_point]),[]).
% 
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL023-1.tptp',unknown),[]).
% 
% cnf(166750416,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
% 
% cnf(174558576,plain,(~$equal(apply(apply(apply(b,combinator),A),B),apply(A,B))),inference(paramodulation,[status(thm)],[166759320,166750416,theory(equality)]),[]).
% 
% cnf(174662128,plain,(~$equal(apply(apply(apply(apply(b,apply(b,combinator)),B),C),A),apply(apply(B,C),A))),inference(paramodulation,[status(thm)],[174558576,166750416,theory(equality)]),[]).
% 
% fof(n_definition,plain,($equal(apply(apply(apply(n,A),B),C),apply(apply(apply(A,C),B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL023-1.tptp',unknown),[]).
% 
% cnf(166754600,plain,($equal(apply(apply(apply(n,A),B),C),apply(apply(apply(A,C),B),C))),inference(rewrite,[status(thm)],[n_definition]),[]).
% 
% cnf(176266648,plain,(~$equal(apply(apply(apply(n,apply(b,apply(b,combinator))),B),A),apply(apply(A,B),A))),inference(paramodulation,[status(thm)],[174662128,166754600,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(equality_resolution,[status(thm)],[176266648]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------