%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET978+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art08.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 15:43:14 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   15 (   6 unt;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   34 (  17   ~;  13   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   24 (   8 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t127_zfmisc_1,plain,
    ! [A,B,C,D] :
      ( ( ~ disjoint(A,B)
        | disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) )
      & ( ~ disjoint(C,D)
        | disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET978+1.tptp',unknown),
    [] ).

cnf(169441464,plain,
    ( ~ disjoint(A,B)
    | disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    inference(rewrite,[status(thm)],[t127_zfmisc_1]),
    [] ).

fof(symmetry_r1_xboole_0,plain,
    ! [A,B] :
      ( ~ disjoint(A,B)
      | disjoint(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET978+1.tptp',unknown),
    [] ).

cnf(169420856,plain,
    ( ~ disjoint(A,B)
    | disjoint(B,A) ),
    inference(rewrite,[status(thm)],[symmetry_r1_xboole_0]),
    [] ).

fof(t17_zfmisc_1,plain,
    ! [B,A] :
      ( $equal(B,A)
      | disjoint(singleton(A),singleton(B)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET978+1.tptp',unknown),
    [] ).

cnf(169588400,plain,
    ( $equal(B,A)
    | disjoint(singleton(A),singleton(B)) ),
    inference(rewrite,[status(thm)],[t17_zfmisc_1]),
    [] ).

fof(t131_zfmisc_1,plain,
    ( ( ~ $equal(b,a)
      | ~ disjoint(cartesian_product2(c,singleton(a)),cartesian_product2(d,singleton(b))) )
    & ( ~ disjoint(cartesian_product2(singleton(a),c),cartesian_product2(singleton(b),d))
      | ~ disjoint(cartesian_product2(c,singleton(a)),cartesian_product2(d,singleton(b))) )
    & ( ~ $equal(b,a)
      | ~ $equal(b,a) )
    & ( ~ disjoint(cartesian_product2(singleton(a),c),cartesian_product2(singleton(b),d))
      | ~ $equal(b,a) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET978+1.tptp',unknown),
    [] ).

cnf(169569848,plain,
    ~ $equal(b,a),
    inference(rewrite,[status(thm)],[t131_zfmisc_1]),
    [] ).

cnf(182654152,plain,
    disjoint(singleton(a),singleton(b)),
    inference(resolution,[status(thm)],[169588400,169569848]),
    [] ).

cnf(182663776,plain,
    disjoint(singleton(b),singleton(a)),
    inference(resolution,[status(thm)],[169420856,182654152]),
    [] ).

cnf(182748888,plain,
    disjoint(cartesian_product2(singleton(b),A),cartesian_product2(singleton(a),B)),
    inference(resolution,[status(thm)],[169441464,182663776]),
    [] ).

cnf(169437384,plain,
    ( ~ disjoint(C,D)
    | disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    inference(rewrite,[status(thm)],[t127_zfmisc_1]),
    [] ).

cnf(182683744,plain,
    disjoint(cartesian_product2(A,singleton(a)),cartesian_product2(B,singleton(b))),
    inference(resolution,[status(thm)],[169437384,182654152]),
    [] ).

cnf(169574760,plain,
    ( ~ disjoint(cartesian_product2(singleton(a),c),cartesian_product2(singleton(b),d))
    | ~ disjoint(cartesian_product2(c,singleton(a)),cartesian_product2(d,singleton(b))) ),
    inference(rewrite,[status(thm)],[t131_zfmisc_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[182748888,182683744,169574760,169420856]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t127_zfmisc_1,plain,(((~disjoint(A,B)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D)))&(~disjoint(C,D)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET978+1.tptp',unknown),[]).
% 
% cnf(169441464,plain,(~disjoint(A,B)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D))),inference(rewrite,[status(thm)],[t127_zfmisc_1]),[]).
% 
% fof(symmetry_r1_xboole_0,plain,(~disjoint(A,B)|disjoint(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET978+1.tptp',unknown),[]).
% 
% cnf(169420856,plain,(~disjoint(A,B)|disjoint(B,A)),inference(rewrite,[status(thm)],[symmetry_r1_xboole_0]),[]).
% 
% fof(t17_zfmisc_1,plain,($equal(B,A)|disjoint(singleton(A),singleton(B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET978+1.tptp',unknown),[]).
% 
% cnf(169588400,plain,($equal(B,A)|disjoint(singleton(A),singleton(B))),inference(rewrite,[status(thm)],[t17_zfmisc_1]),[]).
% 
% fof(t131_zfmisc_1,plain,(((~$equal(b,a)|~disjoint(cartesian_product2(c,singleton(a)),cartesian_product2(d,singleton(b))))&(~disjoint(cartesian_product2(singleton(a),c),cartesian_product2(singleton(b),d))|~disjoint(cartesian_product2(c,singleton(a)),cartesian_product2(d,singleton(b))))&(~$equal(b,a)|~$equal(b,a))&(~disjoint(cartesian_product2(singleton(a),c),cartesian_product2(singleton(b),d))|~$equal(b,a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET978+1.tptp',unknown),[]).
% 
% cnf(169569848,plain,(~$equal(b,a)),inference(rewrite,[status(thm)],[t131_zfmisc_1]),[]).
% 
% cnf(182654152,plain,(disjoint(singleton(a),singleton(b))),inference(resolution,[status(thm)],[169588400,169569848]),[]).
% 
% cnf(182663776,plain,(disjoint(singleton(b),singleton(a))),inference(resolution,[status(thm)],[169420856,182654152]),[]).
% 
% cnf(182748888,plain,(disjoint(cartesian_product2(singleton(b),A),cartesian_product2(singleton(a),B))),inference(resolution,[status(thm)],[169441464,182663776]),[]).
% 
% cnf(169437384,plain,(~disjoint(C,D)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D))),inference(rewrite,[status(thm)],[t127_zfmisc_1]),[]).
% 
% cnf(182683744,plain,(disjoint(cartesian_product2(A,singleton(a)),cartesian_product2(B,singleton(b)))),inference(resolution,[status(thm)],[169437384,182654152]),[]).
% 
% cnf(169574760,plain,(~disjoint(cartesian_product2(singleton(a),c),cartesian_product2(singleton(b),d))|~disjoint(cartesian_product2(c,singleton(a)),cartesian_product2(d,singleton(b)))),inference(rewrite,[status(thm)],[t131_zfmisc_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[182748888,182683744,169574760,169420856]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------