%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET987+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art05.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 15:43:26 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    :    9 (   6 unt;   0 def)
%            Number of atoms       :   14 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   11 (   6   ~;   3   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t65_zfmisc_1,plain,
    ! [A,B] :
      ( ( ~ $equal(set_difference(A,singleton(B)),A)
        | ~ in(B,A) )
      & ( $equal(set_difference(A,singleton(B)),A)
        | in(B,A) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET987+1.tptp',unknown),
    [] ).

cnf(155324640,plain,
    ( $equal(set_difference(A,singleton(B)),A)
    | in(B,A) ),
    inference(rewrite,[status(thm)],[t65_zfmisc_1]),
    [] ).

fof(t141_zfmisc_1,plain,
    ( ~ in(a,b)
    & ~ $equal(set_difference(set_union2(b,singleton(a)),singleton(a)),b) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET987+1.tptp',unknown),
    [] ).

cnf(155311072,plain,
    ~ in(a,b),
    inference(rewrite,[status(thm)],[t141_zfmisc_1]),
    [] ).

cnf(165810696,plain,
    $equal(set_difference(b,singleton(a)),b),
    inference(resolution,[status(thm)],[155324640,155311072]),
    [] ).

cnf(155303592,plain,
    ~ $equal(set_difference(set_union2(b,singleton(a)),singleton(a)),b),
    inference(rewrite,[status(thm)],[t141_zfmisc_1]),
    [] ).

fof(t40_xboole_1,plain,
    ! [A,B] : $equal(set_difference(set_union2(A,B),B),set_difference(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET987+1.tptp',unknown),
    [] ).

cnf(155315056,plain,
    $equal(set_difference(set_union2(A,B),B),set_difference(A,B)),
    inference(rewrite,[status(thm)],[t40_xboole_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[165810696,155303592,155315056,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t65_zfmisc_1,plain,(((~$equal(set_difference(A,singleton(B)),A)|~in(B,A))&($equal(set_difference(A,singleton(B)),A)|in(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET987+1.tptp',unknown),[]).
% 
% cnf(155324640,plain,($equal(set_difference(A,singleton(B)),A)|in(B,A)),inference(rewrite,[status(thm)],[t65_zfmisc_1]),[]).
% 
% fof(t141_zfmisc_1,plain,((~in(a,b)&~$equal(set_difference(set_union2(b,singleton(a)),singleton(a)),b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET987+1.tptp',unknown),[]).
% 
% cnf(155311072,plain,(~in(a,b)),inference(rewrite,[status(thm)],[t141_zfmisc_1]),[]).
% 
% cnf(165810696,plain,($equal(set_difference(b,singleton(a)),b)),inference(resolution,[status(thm)],[155324640,155311072]),[]).
% 
% cnf(155303592,plain,(~$equal(set_difference(set_union2(b,singleton(a)),singleton(a)),b)),inference(rewrite,[status(thm)],[t141_zfmisc_1]),[]).
% 
% fof(t40_xboole_1,plain,($equal(set_difference(set_union2(A,B),B),set_difference(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET987+1.tptp',unknown),[]).
% 
% cnf(155315056,plain,($equal(set_difference(set_union2(A,B),B),set_difference(A,B))),inference(rewrite,[status(thm)],[t40_xboole_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[165810696,155303592,155315056,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------