%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET923+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 15:41:43 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   12 (   6 unt;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   28 (  13   ~;  10   |;   5   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   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   :    9 (   0 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t37_xboole_1,plain,
    ! [A,B] :
      ( ( ~ $equal(empty_set,set_difference(A,B))
        | subset(A,B) )
      & ( $equal(empty_set,set_difference(A,B))
        | ~ subset(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET923+1.tptp',unknown),
    [] ).

cnf(164611232,plain,
    ( ~ $equal(empty_set,set_difference(A,B))
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[t37_xboole_1]),
    [] ).

fof(t66_zfmisc_1,plain,
    ( $equal(set_difference(a,singleton(b)),empty_set)
    & ~ $equal(empty_set,a)
    & ~ $equal(singleton(b),a) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET923+1.tptp',unknown),
    [] ).

cnf(164694704,plain,
    $equal(set_difference(a,singleton(b)),empty_set),
    inference(rewrite,[status(thm)],[t66_zfmisc_1]),
    [] ).

cnf(178410968,plain,
    subset(a,singleton(b)),
    inference(paramodulation,[status(thm)],[164611232,164694704,theory(equality)]),
    [] ).

fof(l4_zfmisc_1,plain,
    ! [A,B] :
      ( ( ~ subset(A,singleton(B))
        | $equal(empty_set,A)
        | $equal(singleton(B),A) )
      & ( ~ $equal(singleton(B),A)
        | subset(A,singleton(B)) )
      & ( ~ $equal(empty_set,A)
        | subset(A,singleton(B)) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET923+1.tptp',unknown),
    [] ).

cnf(164581688,plain,
    ( ~ subset(A,singleton(B))
    | $equal(empty_set,A)
    | $equal(singleton(B),A) ),
    inference(rewrite,[status(thm)],[l4_zfmisc_1]),
    [] ).

cnf(164687512,plain,
    ~ $equal(empty_set,a),
    inference(rewrite,[status(thm)],[t66_zfmisc_1]),
    [] ).

cnf(177764152,plain,
    ( ~ subset(a,singleton(A))
    | $equal(singleton(A),a) ),
    inference(resolution,[status(thm)],[164581688,164687512]),
    [] ).

cnf(164675992,plain,
    ~ $equal(singleton(b),a),
    inference(rewrite,[status(thm)],[t66_zfmisc_1]),
    [] ).

cnf(177777000,plain,
    ~ subset(a,singleton(b)),
    inference(resolution,[status(thm)],[177764152,164675992]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[178410968,177777000]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t37_xboole_1,plain,(((~$equal(empty_set,set_difference(A,B))|subset(A,B))&($equal(empty_set,set_difference(A,B))|~subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET923+1.tptp',unknown),[]).
% 
% cnf(164611232,plain,(~$equal(empty_set,set_difference(A,B))|subset(A,B)),inference(rewrite,[status(thm)],[t37_xboole_1]),[]).
% 
% fof(t66_zfmisc_1,plain,(($equal(set_difference(a,singleton(b)),empty_set)&~$equal(empty_set,a)&~$equal(singleton(b),a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET923+1.tptp',unknown),[]).
% 
% cnf(164694704,plain,($equal(set_difference(a,singleton(b)),empty_set)),inference(rewrite,[status(thm)],[t66_zfmisc_1]),[]).
% 
% cnf(178410968,plain,(subset(a,singleton(b))),inference(paramodulation,[status(thm)],[164611232,164694704,theory(equality)]),[]).
% 
% fof(l4_zfmisc_1,plain,(((~subset(A,singleton(B))|$equal(empty_set,A)|$equal(singleton(B),A))&(~$equal(singleton(B),A)|subset(A,singleton(B)))&(~$equal(empty_set,A)|subset(A,singleton(B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET923+1.tptp',unknown),[]).
% 
% cnf(164581688,plain,(~subset(A,singleton(B))|$equal(empty_set,A)|$equal(singleton(B),A)),inference(rewrite,[status(thm)],[l4_zfmisc_1]),[]).
% 
% cnf(164687512,plain,(~$equal(empty_set,a)),inference(rewrite,[status(thm)],[t66_zfmisc_1]),[]).
% 
% cnf(177764152,plain,(~subset(a,singleton(A))|$equal(singleton(A),a)),inference(resolution,[status(thm)],[164581688,164687512]),[]).
% 
% cnf(164675992,plain,(~$equal(singleton(b),a)),inference(rewrite,[status(thm)],[t66_zfmisc_1]),[]).
% 
% cnf(177777000,plain,(~subset(a,singleton(b))),inference(resolution,[status(thm)],[177764152,164675992]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[178410968,177777000]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------