TSTP Solution File: SET924+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET924+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 15:41:46 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 3 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 24 ( 10 ~; 10 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t67_zfmisc_1,plain,
( ( ~ in(a,b)
| $equal(set_difference(singleton(a),b),singleton(a)) )
& ( ~ $equal(set_difference(singleton(a),b),singleton(a))
| $equal(set_difference(singleton(a),b),singleton(a)) )
& ( ~ in(a,b)
| in(a,b) )
& ( ~ $equal(set_difference(singleton(a),b),singleton(a))
| in(a,b) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET924+1.tptp',unknown),
[] ).
cnf(141328456,plain,
( ~ in(a,b)
| $equal(set_difference(singleton(a),b),singleton(a)) ),
inference(rewrite,[status(thm)],[t67_zfmisc_1]),
[] ).
cnf(141318424,plain,
( ~ $equal(set_difference(singleton(a),b),singleton(a))
| in(a,b) ),
inference(rewrite,[status(thm)],[t67_zfmisc_1]),
[] ).
fof(l34_zfmisc_1,plain,
! [A,B] :
( ( ~ $equal(set_difference(singleton(A),B),singleton(A))
| ~ in(A,B) )
& ( $equal(set_difference(singleton(A),B),singleton(A))
| in(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET924+1.tptp',unknown),
[] ).
cnf(141334912,plain,
( $equal(set_difference(singleton(A),B),singleton(A))
| in(A,B) ),
inference(rewrite,[status(thm)],[l34_zfmisc_1]),
[] ).
cnf(151777160,plain,
in(a,b),
inference(resolution,[status(thm)],[141318424,141334912]),
[] ).
cnf(151791216,plain,
$equal(set_difference(singleton(a),b),singleton(a)),
inference(resolution,[status(thm)],[141328456,151777160]),
[] ).
cnf(141340616,plain,
( ~ $equal(set_difference(singleton(A),B),singleton(A))
| ~ in(A,B) ),
inference(rewrite,[status(thm)],[l34_zfmisc_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[151791216,141340616,151777160]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t67_zfmisc_1,plain,(((~in(a,b)|$equal(set_difference(singleton(a),b),singleton(a)))&(~$equal(set_difference(singleton(a),b),singleton(a))|$equal(set_difference(singleton(a),b),singleton(a)))&(~in(a,b)|in(a,b))&(~$equal(set_difference(singleton(a),b),singleton(a))|in(a,b)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET924+1.tptp',unknown),[]).
%
% cnf(141328456,plain,(~in(a,b)|$equal(set_difference(singleton(a),b),singleton(a))),inference(rewrite,[status(thm)],[t67_zfmisc_1]),[]).
%
% cnf(141318424,plain,(~$equal(set_difference(singleton(a),b),singleton(a))|in(a,b)),inference(rewrite,[status(thm)],[t67_zfmisc_1]),[]).
%
% fof(l34_zfmisc_1,plain,(((~$equal(set_difference(singleton(A),B),singleton(A))|~in(A,B))&($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET924+1.tptp',unknown),[]).
%
% cnf(141334912,plain,($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)),inference(rewrite,[status(thm)],[l34_zfmisc_1]),[]).
%
% cnf(151777160,plain,(in(a,b)),inference(resolution,[status(thm)],[141318424,141334912]),[]).
%
% cnf(151791216,plain,($equal(set_difference(singleton(a),b),singleton(a))),inference(resolution,[status(thm)],[141328456,151777160]),[]).
%
% cnf(141340616,plain,(~$equal(set_difference(singleton(A),B),singleton(A))|~in(A,B)),inference(rewrite,[status(thm)],[l34_zfmisc_1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[151791216,141340616,151777160]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------