%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET911+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 15:41:21 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 4 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 4 ( 0 sgn 2 !; 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/SET911+1.tptp',unknown),
[] ).
cnf(167399680,plain,
( ~ in(A,B)
| $equal(set_intersection2(B,singleton(A)),singleton(A)) ),
inference(rewrite,[status(thm)],[l32_zfmisc_1]),
[] ).
fof(t52_zfmisc_1,plain,
( in(a,b)
& ~ $equal(set_intersection2(b,singleton(a)),singleton(a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET911+1.tptp',unknown),
[] ).
cnf(167380112,plain,
in(a,b),
inference(rewrite,[status(thm)],[t52_zfmisc_1]),
[] ).
cnf(177830800,plain,
$equal(set_intersection2(b,singleton(a)),singleton(a)),
inference(resolution,[status(thm)],[167399680,167380112]),
[] ).
cnf(167367000,plain,
~ $equal(set_intersection2(b,singleton(a)),singleton(a)),
inference(rewrite,[status(thm)],[t52_zfmisc_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[177830800,167367000]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l32_zfmisc_1,plain,(~in(A,B)|$equal(set_intersection2(B,singleton(A)),singleton(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET911+1.tptp',unknown),[]).
%
% cnf(167399680,plain,(~in(A,B)|$equal(set_intersection2(B,singleton(A)),singleton(A))),inference(rewrite,[status(thm)],[l32_zfmisc_1]),[]).
%
% fof(t52_zfmisc_1,plain,((in(a,b)&~$equal(set_intersection2(b,singleton(a)),singleton(a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET911+1.tptp',unknown),[]).
%
% cnf(167380112,plain,(in(a,b)),inference(rewrite,[status(thm)],[t52_zfmisc_1]),[]).
%
% cnf(177830800,plain,($equal(set_intersection2(b,singleton(a)),singleton(a))),inference(resolution,[status(thm)],[167399680,167380112]),[]).
%
% cnf(167367000,plain,(~$equal(set_intersection2(b,singleton(a)),singleton(a))),inference(rewrite,[status(thm)],[t52_zfmisc_1]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[177830800,167367000]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------