%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET084-7 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 15:27:55 EDT 2009
% Result : Unsatisfiable 0.8s
% Output : Refutation 0.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 10 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(existence_of_null_class,plain,
! [A] : ~ member(A,null_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),
[] ).
cnf(174374288,plain,
~ member(A,null_class),
inference(rewrite,[status(thm)],[existence_of_null_class]),
[] ).
fof(prove_singleton_identified_by_element2_2,plain,
member(y,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),
[] ).
cnf(174565376,plain,
member(y,universal_class),
inference(rewrite,[status(thm)],[prove_singleton_identified_by_element2_2]),
[] ).
fof(only_member_in_singleton,plain,
! [A,B] :
( ~ member(A,singleton(B))
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),
[] ).
cnf(174553008,plain,
( ~ member(A,singleton(B))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[only_member_in_singleton]),
[] ).
fof(prove_singleton_identified_by_element2_3,plain,
~ $equal(y,x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),
[] ).
cnf(174573160,plain,
~ $equal(y,x),
inference(rewrite,[status(thm)],[prove_singleton_identified_by_element2_3]),
[] ).
cnf(189310912,plain,
~ member(x,singleton(y)),
inference(resolution,[status(thm)],[174553008,174573160]),
[] ).
fof(set_in_its_singleton,plain,
! [A] :
( ~ member(A,universal_class)
| member(A,singleton(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),
[] ).
cnf(174535000,plain,
( ~ member(A,universal_class)
| member(A,singleton(A)) ),
inference(rewrite,[status(thm)],[set_in_its_singleton]),
[] ).
fof(prove_singleton_identified_by_element2_1,plain,
$equal(singleton(y),singleton(x)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),
[] ).
cnf(174561312,plain,
$equal(singleton(y),singleton(x)),
inference(rewrite,[status(thm)],[prove_singleton_identified_by_element2_1]),
[] ).
cnf(204938056,plain,
~ member(x,universal_class),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[189310912,174535000,174561312,theory(equality)]),
[] ).
fof(singleton_is_null_class,plain,
! [A] :
( member(A,universal_class)
| $equal(null_class,singleton(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),
[] ).
cnf(174557512,plain,
( member(A,universal_class)
| $equal(null_class,singleton(A)) ),
inference(rewrite,[status(thm)],[singleton_is_null_class]),
[] ).
cnf(205065208,plain,
$equal(null_class,singleton(x)),
inference(resolution,[status(thm)],[204938056,174557512]),
[] ).
cnf(205239864,plain,
$equal(singleton(y),null_class),
inference(paramodulation,[status(thm)],[205065208,174561312,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[174374288,174565376,205239864,174535000,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(existence_of_null_class,plain,(~member(A,null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),[]).
%
% cnf(174374288,plain,(~member(A,null_class)),inference(rewrite,[status(thm)],[existence_of_null_class]),[]).
%
% fof(prove_singleton_identified_by_element2_2,plain,(member(y,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),[]).
%
% cnf(174565376,plain,(member(y,universal_class)),inference(rewrite,[status(thm)],[prove_singleton_identified_by_element2_2]),[]).
%
% fof(only_member_in_singleton,plain,(~member(A,singleton(B))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),[]).
%
% cnf(174553008,plain,(~member(A,singleton(B))|$equal(B,A)),inference(rewrite,[status(thm)],[only_member_in_singleton]),[]).
%
% fof(prove_singleton_identified_by_element2_3,plain,(~$equal(y,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),[]).
%
% cnf(174573160,plain,(~$equal(y,x)),inference(rewrite,[status(thm)],[prove_singleton_identified_by_element2_3]),[]).
%
% cnf(189310912,plain,(~member(x,singleton(y))),inference(resolution,[status(thm)],[174553008,174573160]),[]).
%
% fof(set_in_its_singleton,plain,(~member(A,universal_class)|member(A,singleton(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),[]).
%
% cnf(174535000,plain,(~member(A,universal_class)|member(A,singleton(A))),inference(rewrite,[status(thm)],[set_in_its_singleton]),[]).
%
% fof(prove_singleton_identified_by_element2_1,plain,($equal(singleton(y),singleton(x))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),[]).
%
% cnf(174561312,plain,($equal(singleton(y),singleton(x))),inference(rewrite,[status(thm)],[prove_singleton_identified_by_element2_1]),[]).
%
% cnf(204938056,plain,(~member(x,universal_class)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[189310912,174535000,174561312,theory(equality)]),[]).
%
% fof(singleton_is_null_class,plain,(member(A,universal_class)|$equal(null_class,singleton(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET084-7.tptp',unknown),[]).
%
% cnf(174557512,plain,(member(A,universal_class)|$equal(null_class,singleton(A))),inference(rewrite,[status(thm)],[singleton_is_null_class]),[]).
%
% cnf(205065208,plain,($equal(null_class,singleton(x))),inference(resolution,[status(thm)],[204938056,174557512]),[]).
%
% cnf(205239864,plain,($equal(singleton(y),null_class)),inference(paramodulation,[status(thm)],[205065208,174561312,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[174374288,174565376,205239864,174535000,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------