%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET925+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.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 15:41:48 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    9 (   3 unt;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   24 (  10   ~;  10   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn   2   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l36_zfmisc_1,plain,
    ! [A,B] :
      ( ( ~ $equal(set_difference(singleton(A),B),empty_set)
        | in(A,B) )
      & ( $equal(set_difference(singleton(A),B),empty_set)
        | ~ in(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET925+1.tptp',unknown),
    [] ).

cnf(172063864,plain,
    ( $equal(set_difference(singleton(A),B),empty_set)
    | ~ in(A,B) ),
    inference(rewrite,[status(thm)],[l36_zfmisc_1]),
    [] ).

fof(t68_zfmisc_1,plain,
    ( ( in(a,b)
      | $equal(set_difference(singleton(a),b),empty_set) )
    & ( ~ $equal(set_difference(singleton(a),b),empty_set)
      | $equal(set_difference(singleton(a),b),empty_set) )
    & ( in(a,b)
      | ~ in(a,b) )
    & ( ~ $equal(set_difference(singleton(a),b),empty_set)
      | ~ in(a,b) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET925+1.tptp',unknown),
    [] ).

cnf(172057464,plain,
    ( in(a,b)
    | $equal(set_difference(singleton(a),b),empty_set) ),
    inference(rewrite,[status(thm)],[t68_zfmisc_1]),
    [] ).

cnf(182513432,plain,
    $equal(set_difference(singleton(a),b),empty_set),
    inference(resolution,[status(thm)],[172063864,172057464]),
    [] ).

cnf(172046464,plain,
    ( ~ $equal(set_difference(singleton(a),b),empty_set)
    | ~ in(a,b) ),
    inference(rewrite,[status(thm)],[t68_zfmisc_1]),
    [] ).

cnf(172069464,plain,
    ( ~ $equal(set_difference(singleton(A),B),empty_set)
    | in(A,B) ),
    inference(rewrite,[status(thm)],[l36_zfmisc_1]),
    [] ).

cnf(182569688,plain,
    in(a,b),
    inference(resolution,[status(thm)],[172069464,182513432]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[182513432,172046464,182569688]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l36_zfmisc_1,plain,(((~$equal(set_difference(singleton(A),B),empty_set)|in(A,B))&($equal(set_difference(singleton(A),B),empty_set)|~in(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET925+1.tptp',unknown),[]).
% 
% cnf(172063864,plain,($equal(set_difference(singleton(A),B),empty_set)|~in(A,B)),inference(rewrite,[status(thm)],[l36_zfmisc_1]),[]).
% 
% fof(t68_zfmisc_1,plain,(((in(a,b)|$equal(set_difference(singleton(a),b),empty_set))&(~$equal(set_difference(singleton(a),b),empty_set)|$equal(set_difference(singleton(a),b),empty_set))&(in(a,b)|~in(a,b))&(~$equal(set_difference(singleton(a),b),empty_set)|~in(a,b)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET925+1.tptp',unknown),[]).
% 
% cnf(172057464,plain,(in(a,b)|$equal(set_difference(singleton(a),b),empty_set)),inference(rewrite,[status(thm)],[t68_zfmisc_1]),[]).
% 
% cnf(182513432,plain,($equal(set_difference(singleton(a),b),empty_set)),inference(resolution,[status(thm)],[172063864,172057464]),[]).
% 
% cnf(172046464,plain,(~$equal(set_difference(singleton(a),b),empty_set)|~in(a,b)),inference(rewrite,[status(thm)],[t68_zfmisc_1]),[]).
% 
% cnf(172069464,plain,(~$equal(set_difference(singleton(A),B),empty_set)|in(A,B)),inference(rewrite,[status(thm)],[l36_zfmisc_1]),[]).
% 
% cnf(182569688,plain,(in(a,b)),inference(resolution,[status(thm)],[172069464,182513432]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[182513432,172046464,182569688]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------