%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : COL012-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.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 11:31:19 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    5 (   5 unt;   0 def)
%            Number of atoms       :    5 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn   3   !;   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/COL012-1.tptp',unknown),
    [] ).

cnf(173092456,plain,
    ~ $equal(apply(combinator,A),A),
    inference(rewrite,[status(thm)],[prove_fixed_point]),
    [] ).

fof(u_definition,plain,
    ! [B,A] : $equal(apply(B,apply(apply(A,A),B)),apply(apply(u,A),B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL012-1.tptp',unknown),
    [] ).

cnf(173087640,plain,
    $equal(apply(B,apply(apply(A,A),B)),apply(apply(u,A),B)),
    inference(rewrite,[status(thm)],[u_definition]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[173092456,173087640]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_fixed_point,plain,(~$equal(apply(combinator,A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL012-1.tptp',unknown),[]).
% 
% cnf(173092456,plain,(~$equal(apply(combinator,A),A)),inference(rewrite,[status(thm)],[prove_fixed_point]),[]).
% 
% fof(u_definition,plain,($equal(apply(B,apply(apply(A,A),B)),apply(apply(u,A),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL012-1.tptp',unknown),[]).
% 
% cnf(173087640,plain,($equal(apply(B,apply(apply(A,A),B)),apply(apply(u,A),B))),inference(rewrite,[status(thm)],[u_definition]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[173092456,173087640]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------