%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET926+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 15:41:51 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   10 (   5 unt;   0 def)
%            Number of atoms       :   19 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   19 (  10   ~;   6   |;   3   &)
%                                         (   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   :    8 (   0 sgn   4   !;   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/SET926+1.tptp',unknown),
    [] ).

cnf(149325376,plain,
    ( $equal(set_difference(singleton(A),B),empty_set)
    | ~ in(A,B) ),
    inference(rewrite,[status(thm)],[l36_zfmisc_1]),
    [] ).

fof(t69_zfmisc_1,plain,
    ( ~ $equal(set_difference(singleton(a),b),empty_set)
    & ~ $equal(set_difference(singleton(a),b),singleton(a)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET926+1.tptp',unknown),
    [] ).

cnf(149407720,plain,
    ~ $equal(set_difference(singleton(a),b),empty_set),
    inference(rewrite,[status(thm)],[t69_zfmisc_1]),
    [] ).

cnf(159842864,plain,
    ~ in(a,b),
    inference(resolution,[status(thm)],[149325376,149407720]),
    [] ).

cnf(149396072,plain,
    ~ $equal(set_difference(singleton(a),b),singleton(a)),
    inference(rewrite,[status(thm)],[t69_zfmisc_1]),
    [] ).

fof(l34_zfmisc_1,plain,
    ! [A,B] :
      ( ( ~ $equal(set_difference(singleton(A),B),singleton(A))
        | ~ in(A,B) )
      & ( $equal(set_difference(singleton(A),B),singleton(A))
        | in(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET926+1.tptp',unknown),
    [] ).

cnf(149313152,plain,
    ( $equal(set_difference(singleton(A),B),singleton(A))
    | in(A,B) ),
    inference(rewrite,[status(thm)],[l34_zfmisc_1]),
    [] ).

cnf(159899712,plain,
    in(a,b),
    inference(resolution,[status(thm)],[149396072,149313152]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[159842864,159899712]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 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/SET926+1.tptp',unknown),[]).
% 
% cnf(149325376,plain,($equal(set_difference(singleton(A),B),empty_set)|~in(A,B)),inference(rewrite,[status(thm)],[l36_zfmisc_1]),[]).
% 
% fof(t69_zfmisc_1,plain,((~$equal(set_difference(singleton(a),b),empty_set)&~$equal(set_difference(singleton(a),b),singleton(a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET926+1.tptp',unknown),[]).
% 
% cnf(149407720,plain,(~$equal(set_difference(singleton(a),b),empty_set)),inference(rewrite,[status(thm)],[t69_zfmisc_1]),[]).
% 
% cnf(159842864,plain,(~in(a,b)),inference(resolution,[status(thm)],[149325376,149407720]),[]).
% 
% cnf(149396072,plain,(~$equal(set_difference(singleton(a),b),singleton(a))),inference(rewrite,[status(thm)],[t69_zfmisc_1]),[]).
% 
% fof(l34_zfmisc_1,plain,(((~$equal(set_difference(singleton(A),B),singleton(A))|~in(A,B))&($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET926+1.tptp',unknown),[]).
% 
% cnf(149313152,plain,($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)),inference(rewrite,[status(thm)],[l34_zfmisc_1]),[]).
% 
% cnf(159899712,plain,(in(a,b)),inference(resolution,[status(thm)],[149396072,149313152]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[159842864,159899712]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------