%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET917+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art03.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 15:41:34 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   12 (   7 unt;   0 def)
%            Number of atoms       :   17 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   11 (   6   ~;   4   |;   1   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 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   :   12 (   0 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l32_zfmisc_1,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | $equal(set_intersection2(B,singleton(A)),singleton(A)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET917+1.tptp',unknown),
    [] ).

cnf(154658184,plain,
    ( ~ in(A,B)
    | $equal(set_intersection2(B,singleton(A)),singleton(A)) ),
    inference(rewrite,[status(thm)],[l32_zfmisc_1]),
    [] ).

fof(l28_zfmisc_1,plain,
    ! [A,B] :
      ( in(A,B)
      | disjoint(singleton(A),B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET917+1.tptp',unknown),
    [] ).

cnf(154638480,plain,
    ( in(A,B)
    | disjoint(singleton(A),B) ),
    inference(rewrite,[status(thm)],[l28_zfmisc_1]),
    [] ).

fof(t58_zfmisc_1,plain,
    ( ~ disjoint(singleton(a),b)
    & ~ $equal(set_intersection2(singleton(a),b),singleton(a)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET917+1.tptp',unknown),
    [] ).

cnf(154744600,plain,
    ~ disjoint(singleton(a),b),
    inference(rewrite,[status(thm)],[t58_zfmisc_1]),
    [] ).

cnf(165180688,plain,
    in(a,b),
    inference(resolution,[status(thm)],[154638480,154744600]),
    [] ).

cnf(165223040,plain,
    $equal(set_intersection2(b,singleton(a)),singleton(a)),
    inference(resolution,[status(thm)],[154658184,165180688]),
    [] ).

cnf(154733096,plain,
    ~ $equal(set_intersection2(singleton(a),b),singleton(a)),
    inference(rewrite,[status(thm)],[t58_zfmisc_1]),
    [] ).

fof(commutativity_k3_xboole_0,plain,
    ! [B,A] : $equal(set_intersection2(B,A),set_intersection2(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET917+1.tptp',unknown),
    [] ).

cnf(154628040,plain,
    $equal(set_intersection2(B,A),set_intersection2(A,B)),
    inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[165223040,154733096,154628040,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l32_zfmisc_1,plain,(~in(A,B)|$equal(set_intersection2(B,singleton(A)),singleton(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET917+1.tptp',unknown),[]).
% 
% cnf(154658184,plain,(~in(A,B)|$equal(set_intersection2(B,singleton(A)),singleton(A))),inference(rewrite,[status(thm)],[l32_zfmisc_1]),[]).
% 
% fof(l28_zfmisc_1,plain,(in(A,B)|disjoint(singleton(A),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET917+1.tptp',unknown),[]).
% 
% cnf(154638480,plain,(in(A,B)|disjoint(singleton(A),B)),inference(rewrite,[status(thm)],[l28_zfmisc_1]),[]).
% 
% fof(t58_zfmisc_1,plain,((~disjoint(singleton(a),b)&~$equal(set_intersection2(singleton(a),b),singleton(a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET917+1.tptp',unknown),[]).
% 
% cnf(154744600,plain,(~disjoint(singleton(a),b)),inference(rewrite,[status(thm)],[t58_zfmisc_1]),[]).
% 
% cnf(165180688,plain,(in(a,b)),inference(resolution,[status(thm)],[154638480,154744600]),[]).
% 
% cnf(165223040,plain,($equal(set_intersection2(b,singleton(a)),singleton(a))),inference(resolution,[status(thm)],[154658184,165180688]),[]).
% 
% cnf(154733096,plain,(~$equal(set_intersection2(singleton(a),b),singleton(a))),inference(rewrite,[status(thm)],[t58_zfmisc_1]),[]).
% 
% fof(commutativity_k3_xboole_0,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET917+1.tptp',unknown),[]).
% 
% cnf(154628040,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[165223040,154733096,154628040,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------