%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET954+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 15:42:31 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   10 (   5 unt;   0 def)
%            Number of atoms       :   21 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   21 (  10   ~;   8   |;   3   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   16 (   4 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l55_zfmisc_1,plain,
    ! [B,D,A,C] :
      ( ( in(B,D)
        | ~ in(ordered_pair(A,B),cartesian_product2(C,D)) )
      & ( in(A,C)
        | ~ in(ordered_pair(A,B),cartesian_product2(C,D)) )
      & ( in(ordered_pair(A,B),cartesian_product2(C,D))
        | ~ in(A,C)
        | ~ in(B,D) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET954+1.tptp',unknown),
    [] ).

cnf(141930440,plain,
    ( in(A,C)
    | ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
    inference(rewrite,[status(thm)],[l55_zfmisc_1]),
    [] ).

fof(t107_zfmisc_1,plain,
    ( in(ordered_pair(a,b),cartesian_product2(c,d))
    & ~ in(ordered_pair(b,a),cartesian_product2(d,c)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET954+1.tptp',unknown),
    [] ).

cnf(142029568,plain,
    in(ordered_pair(a,b),cartesian_product2(c,d)),
    inference(rewrite,[status(thm)],[t107_zfmisc_1]),
    [] ).

cnf(152492920,plain,
    in(a,c),
    inference(resolution,[status(thm)],[141930440,142029568]),
    [] ).

cnf(141934480,plain,
    ( in(B,D)
    | ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
    inference(rewrite,[status(thm)],[l55_zfmisc_1]),
    [] ).

cnf(152502472,plain,
    in(b,d),
    inference(resolution,[status(thm)],[141934480,142029568]),
    [] ).

cnf(141924560,plain,
    ( in(ordered_pair(A,B),cartesian_product2(C,D))
    | ~ in(A,C)
    | ~ in(B,D) ),
    inference(rewrite,[status(thm)],[l55_zfmisc_1]),
    [] ).

cnf(142021984,plain,
    ~ in(ordered_pair(b,a),cartesian_product2(d,c)),
    inference(rewrite,[status(thm)],[t107_zfmisc_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[152492920,152502472,141924560,142021984]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l55_zfmisc_1,plain,(((in(B,D)|~in(ordered_pair(A,B),cartesian_product2(C,D)))&(in(A,C)|~in(ordered_pair(A,B),cartesian_product2(C,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|~in(A,C)|~in(B,D)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET954+1.tptp',unknown),[]).
% 
% cnf(141930440,plain,(in(A,C)|~in(ordered_pair(A,B),cartesian_product2(C,D))),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
% 
% fof(t107_zfmisc_1,plain,((in(ordered_pair(a,b),cartesian_product2(c,d))&~in(ordered_pair(b,a),cartesian_product2(d,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET954+1.tptp',unknown),[]).
% 
% cnf(142029568,plain,(in(ordered_pair(a,b),cartesian_product2(c,d))),inference(rewrite,[status(thm)],[t107_zfmisc_1]),[]).
% 
% cnf(152492920,plain,(in(a,c)),inference(resolution,[status(thm)],[141930440,142029568]),[]).
% 
% cnf(141934480,plain,(in(B,D)|~in(ordered_pair(A,B),cartesian_product2(C,D))),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
% 
% cnf(152502472,plain,(in(b,d)),inference(resolution,[status(thm)],[141934480,142029568]),[]).
% 
% cnf(141924560,plain,(in(ordered_pair(A,B),cartesian_product2(C,D))|~in(A,C)|~in(B,D)),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
% 
% cnf(142021984,plain,(~in(ordered_pair(b,a),cartesian_product2(d,c))),inference(rewrite,[status(thm)],[t107_zfmisc_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[152492920,152502472,141924560,142021984]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------