%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET880+1 : TPTP v3.4.2. Released v3.2.0.
% 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 15:40:27 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 (   4 unt;   0 def)
%            Number of atoms       :   35 (   0 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :   42 (  17   ~;  18   |;   7   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   11 (   0 sgn   5   !;   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/SET880+1.tptp',unknown),
    [] ).

cnf(141105600,plain,
    ( ~ $equal(set_difference(singleton(A),B),empty_set)
    | in(A,B) ),
    inference(rewrite,[status(thm)],[l36_zfmisc_1]),
    [] ).

fof(t21_zfmisc_1,plain,
    ( $equal(set_difference(singleton(a),singleton(b)),empty_set)
    & ~ $equal(b,a) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET880+1.tptp',unknown),
    [] ).

cnf(141179880,plain,
    $equal(set_difference(singleton(a),singleton(b)),empty_set),
    inference(rewrite,[status(thm)],[t21_zfmisc_1]),
    [] ).

cnf(151645424,plain,
    in(a,singleton(b)),
    inference(resolution,[status(thm)],[141105600,141179880]),
    [] ).

fof(d1_tarski,plain,
    ! [C,B,A] :
      ( ( in(C,B)
        | ~ $equal(A,C)
        | ~ $equal(singleton(A),B) )
      & ( ~ in(C,B)
        | $equal(A,C)
        | ~ $equal(singleton(A),B) )
      & ( $equal(c(A,B,C),A)
        | ~ $equal(c(A,B,C),A)
        | $equal(singleton(A),B) )
      & ( ~ in(c(A,B,C),B)
        | ~ $equal(c(A,B,C),A)
        | $equal(singleton(A),B) )
      & ( $equal(c(A,B,C),A)
        | in(c(A,B,C),B)
        | $equal(singleton(A),B) )
      & ( ~ in(c(A,B,C),B)
        | in(c(A,B,C),B)
        | $equal(singleton(A),B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET880+1.tptp',unknown),
    [] ).

cnf(141076744,plain,
    ( ~ in(C,B)
    | $equal(A,C)
    | ~ $equal(singleton(A),B) ),
    inference(rewrite,[status(thm)],[d1_tarski]),
    [] ).

cnf(141172464,plain,
    ~ $equal(b,a),
    inference(rewrite,[status(thm)],[t21_zfmisc_1]),
    [] ).

cnf(151633440,plain,
    ( ~ in(a,A)
    | ~ $equal(singleton(b),A) ),
    inference(resolution,[status(thm)],[141076744,141172464]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__equality_resolution,[status(thm)],[151645424,151633440]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 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/SET880+1.tptp',unknown),[]).
% 
% cnf(141105600,plain,(~$equal(set_difference(singleton(A),B),empty_set)|in(A,B)),inference(rewrite,[status(thm)],[l36_zfmisc_1]),[]).
% 
% fof(t21_zfmisc_1,plain,(($equal(set_difference(singleton(a),singleton(b)),empty_set)&~$equal(b,a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET880+1.tptp',unknown),[]).
% 
% cnf(141179880,plain,($equal(set_difference(singleton(a),singleton(b)),empty_set)),inference(rewrite,[status(thm)],[t21_zfmisc_1]),[]).
% 
% cnf(151645424,plain,(in(a,singleton(b))),inference(resolution,[status(thm)],[141105600,141179880]),[]).
% 
% fof(d1_tarski,plain,(((in(C,B)|~$equal(A,C)|~$equal(singleton(A),B))&(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B))&($equal(c(A,B,C),A)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&($equal(c(A,B,C),A)|in(c(A,B,C),B)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|in(c(A,B,C),B)|$equal(singleton(A),B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET880+1.tptp',unknown),[]).
% 
% cnf(141076744,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
% 
% cnf(141172464,plain,(~$equal(b,a)),inference(rewrite,[status(thm)],[t21_zfmisc_1]),[]).
% 
% cnf(151633440,plain,(~in(a,A)|~$equal(singleton(b),A)),inference(resolution,[status(thm)],[141076744,141172464]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__equality_resolution,[status(thm)],[151645424,151633440]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------