%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET910+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art06.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 15:41:18 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    6 (   3 unt;   0 def)
%            Number of atoms       :    9 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   4   ~;   2   |;   1   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    4 (   0 sgn   2   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t51_zfmisc_1,plain,
    ( $equal(set_intersection2(a,singleton(b)),singleton(b))
    & ~ in(b,a) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET910+1.tptp',unknown),
    [] ).

cnf(164593344,plain,
    $equal(set_intersection2(a,singleton(b)),singleton(b)),
    inference(rewrite,[status(thm)],[t51_zfmisc_1]),
    [] ).

fof(l30_zfmisc_1,plain,
    ! [A,B] :
      ( ~ $equal(set_intersection2(A,singleton(B)),singleton(B))
      | in(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET910+1.tptp',unknown),
    [] ).

cnf(164599680,plain,
    ( ~ $equal(set_intersection2(A,singleton(B)),singleton(B))
    | in(B,A) ),
    inference(rewrite,[status(thm)],[l30_zfmisc_1]),
    [] ).

cnf(164581792,plain,
    ~ in(b,a),
    inference(rewrite,[status(thm)],[t51_zfmisc_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[164593344,164599680,164581792]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t51_zfmisc_1,plain,(($equal(set_intersection2(a,singleton(b)),singleton(b))&~in(b,a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET910+1.tptp',unknown),[]).
% 
% cnf(164593344,plain,($equal(set_intersection2(a,singleton(b)),singleton(b))),inference(rewrite,[status(thm)],[t51_zfmisc_1]),[]).
% 
% fof(l30_zfmisc_1,plain,(~$equal(set_intersection2(A,singleton(B)),singleton(B))|in(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET910+1.tptp',unknown),[]).
% 
% cnf(164599680,plain,(~$equal(set_intersection2(A,singleton(B)),singleton(B))|in(B,A)),inference(rewrite,[status(thm)],[l30_zfmisc_1]),[]).
% 
% cnf(164581792,plain,(~in(b,a)),inference(rewrite,[status(thm)],[t51_zfmisc_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[164593344,164599680,164581792]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------