%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SEU162+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art02.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 15:50:14 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   19 (   4 unt;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   41 (  18   ~;  19   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t83_xboole_1,plain,
    ! [A,B] :
      ( ( ~ disjoint(A,B)
        | $equal(set_difference(A,B),A) )
      & ( disjoint(A,B)
        | ~ $equal(set_difference(A,B),A) ) ),
    file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),
    [] ).

cnf(160360328,plain,
    ( ~ disjoint(A,B)
    | $equal(set_difference(A,B),A) ),
    inference(rewrite,[status(thm)],[t83_xboole_1]),
    [] ).

fof(symmetry_r1_xboole_0,plain,
    ! [A,B] :
      ( ~ disjoint(A,B)
      | disjoint(B,A) ),
    file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),
    [] ).

cnf(160264152,plain,
    ( ~ disjoint(A,B)
    | disjoint(B,A) ),
    inference(rewrite,[status(thm)],[symmetry_r1_xboole_0]),
    [] ).

fof(l28_zfmisc_1,plain,
    ! [A,B] :
      ( in(A,B)
      | disjoint(singleton(A),B) ),
    file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),
    [] ).

cnf(160258800,plain,
    ( in(A,B)
    | disjoint(singleton(A),B) ),
    inference(rewrite,[status(thm)],[l28_zfmisc_1]),
    [] ).

cnf(170782696,plain,
    ( disjoint(A,singleton(B))
    | in(B,A) ),
    inference(resolution,[status(thm)],[160264152,160258800]),
    [] ).

cnf(171027392,plain,
    ( $equal(set_difference(A,singleton(B)),A)
    | in(B,A) ),
    inference(resolution,[status(thm)],[160360328,170782696]),
    [] ).

fof(t65_zfmisc_1,plain,
    ( ( ~ in(b,a)
      | $equal(set_difference(a,singleton(b)),a) )
    & ( ~ $equal(set_difference(a,singleton(b)),a)
      | $equal(set_difference(a,singleton(b)),a) )
    & ( ~ in(b,a)
      | in(b,a) )
    & ( ~ $equal(set_difference(a,singleton(b)),a)
      | in(b,a) ) ),
    file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),
    [] ).

cnf(160349248,plain,
    ( ~ in(b,a)
    | $equal(set_difference(a,singleton(b)),a) ),
    inference(rewrite,[status(thm)],[t65_zfmisc_1]),
    [] ).

cnf(171961608,plain,
    $equal(set_difference(a,singleton(b)),a),
    inference(resolution,[status(thm)],[171027392,160349248]),
    [] ).

cnf(160343320,plain,
    ( ~ $equal(set_difference(a,singleton(b)),a)
    | in(b,a) ),
    inference(rewrite,[status(thm)],[t65_zfmisc_1]),
    [] ).

cnf(171953136,plain,
    in(b,a),
    inference(resolution,[status(thm)],[171027392,160343320]),
    [] ).

fof(l25_zfmisc_1,plain,
    ! [A,B] :
      ( ~ disjoint(singleton(A),B)
      | ~ in(A,B) ),
    file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),
    [] ).

cnf(160252296,plain,
    ( ~ disjoint(singleton(A),B)
    | ~ in(A,B) ),
    inference(rewrite,[status(thm)],[l25_zfmisc_1]),
    [] ).

cnf(172015560,plain,
    ~ disjoint(singleton(b),a),
    inference(resolution,[status(thm)],[171953136,160252296]),
    [] ).

cnf(160355544,plain,
    ( disjoint(A,B)
    | ~ $equal(set_difference(A,B),A) ),
    inference(rewrite,[status(thm)],[t83_xboole_1]),
    [] ).

cnf(170961032,plain,
    ( ~ $equal(set_difference(A,B),A)
    | disjoint(B,A) ),
    inference(resolution,[status(thm)],[160355544,160264152]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[171961608,172015560,170961032]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t83_xboole_1,plain,(((~disjoint(A,B)|$equal(set_difference(A,B),A))&(disjoint(A,B)|~$equal(set_difference(A,B),A)))),file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),[]).
% 
% cnf(160360328,plain,(~disjoint(A,B)|$equal(set_difference(A,B),A)),inference(rewrite,[status(thm)],[t83_xboole_1]),[]).
% 
% fof(symmetry_r1_xboole_0,plain,(~disjoint(A,B)|disjoint(B,A)),file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),[]).
% 
% cnf(160264152,plain,(~disjoint(A,B)|disjoint(B,A)),inference(rewrite,[status(thm)],[symmetry_r1_xboole_0]),[]).
% 
% fof(l28_zfmisc_1,plain,(in(A,B)|disjoint(singleton(A),B)),file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),[]).
% 
% cnf(160258800,plain,(in(A,B)|disjoint(singleton(A),B)),inference(rewrite,[status(thm)],[l28_zfmisc_1]),[]).
% 
% cnf(170782696,plain,(disjoint(A,singleton(B))|in(B,A)),inference(resolution,[status(thm)],[160264152,160258800]),[]).
% 
% cnf(171027392,plain,($equal(set_difference(A,singleton(B)),A)|in(B,A)),inference(resolution,[status(thm)],[160360328,170782696]),[]).
% 
% fof(t65_zfmisc_1,plain,(((~in(b,a)|$equal(set_difference(a,singleton(b)),a))&(~$equal(set_difference(a,singleton(b)),a)|$equal(set_difference(a,singleton(b)),a))&(~in(b,a)|in(b,a))&(~$equal(set_difference(a,singleton(b)),a)|in(b,a)))),file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),[]).
% 
% cnf(160349248,plain,(~in(b,a)|$equal(set_difference(a,singleton(b)),a)),inference(rewrite,[status(thm)],[t65_zfmisc_1]),[]).
% 
% cnf(171961608,plain,($equal(set_difference(a,singleton(b)),a)),inference(resolution,[status(thm)],[171027392,160349248]),[]).
% 
% cnf(160343320,plain,(~$equal(set_difference(a,singleton(b)),a)|in(b,a)),inference(rewrite,[status(thm)],[t65_zfmisc_1]),[]).
% 
% cnf(171953136,plain,(in(b,a)),inference(resolution,[status(thm)],[171027392,160343320]),[]).
% 
% fof(l25_zfmisc_1,plain,(~disjoint(singleton(A),B)|~in(A,B)),file('/tmp/SystemOnTPTP4201/SEU162+1.p',unknown),[]).
% 
% cnf(160252296,plain,(~disjoint(singleton(A),B)|~in(A,B)),inference(rewrite,[status(thm)],[l25_zfmisc_1]),[]).
% 
% cnf(172015560,plain,(~disjoint(singleton(b),a)),inference(resolution,[status(thm)],[171953136,160252296]),[]).
% 
% cnf(160355544,plain,(disjoint(A,B)|~$equal(set_difference(A,B),A)),inference(rewrite,[status(thm)],[t83_xboole_1]),[]).
% 
% cnf(170961032,plain,(~$equal(set_difference(A,B),A)|disjoint(B,A)),inference(resolution,[status(thm)],[160355544,160264152]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[171961608,172015560,170961032]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------