TSTP Solution File: SET083-7 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET083-7 : TPTP v3.4.2. Bugfixed v2.1.0.
% 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 15:27:50 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 17 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 20 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_singleton_identified_by_element1_2,plain,
member(x,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),
[] ).
cnf(176532248,plain,
member(x,universal_class),
inference(rewrite,[status(thm)],[prove_singleton_identified_by_element1_2]),
[] ).
fof(set_in_its_singleton,plain,
! [A] :
( ~ member(A,universal_class)
| member(A,singleton(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),
[] ).
cnf(176501872,plain,
( ~ member(A,universal_class)
| member(A,singleton(A)) ),
inference(rewrite,[status(thm)],[set_in_its_singleton]),
[] ).
fof(subclass_members,plain,
! [A,B,C] :
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),
[] ).
cnf(175326736,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(equal_implies_subclass1,plain,
! [B,A] :
( ~ $equal(B,A)
| subclass(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),
[] ).
cnf(175368920,plain,
( ~ $equal(B,A)
| subclass(A,B) ),
inference(rewrite,[status(thm)],[equal_implies_subclass1]),
[] ).
cnf(197780640,plain,
( ~ member(C,A)
| member(C,B)
| ~ $equal(B,A) ),
inference(resolution,[status(thm)],[175326736,175368920]),
[] ).
fof(prove_singleton_identified_by_element1_1,plain,
$equal(singleton(y),singleton(x)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),
[] ).
cnf(176528184,plain,
$equal(singleton(y),singleton(x)),
inference(rewrite,[status(thm)],[prove_singleton_identified_by_element1_1]),
[] ).
cnf(199188160,plain,
( ~ member(A,singleton(x))
| member(A,singleton(y)) ),
inference(resolution,[status(thm)],[197780640,176528184]),
[] ).
fof(only_member_in_singleton,plain,
! [A,B] :
( ~ member(A,singleton(B))
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),
[] ).
cnf(176519880,plain,
( ~ member(A,singleton(B))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[only_member_in_singleton]),
[] ).
fof(prove_singleton_identified_by_element1_3,plain,
~ $equal(y,x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),
[] ).
cnf(176540032,plain,
~ $equal(y,x),
inference(rewrite,[status(thm)],[prove_singleton_identified_by_element1_3]),
[] ).
cnf(193231904,plain,
~ member(x,singleton(y)),
inference(resolution,[status(thm)],[176519880,176540032]),
[] ).
cnf(200455144,plain,
~ member(x,singleton(x)),
inference(resolution,[status(thm)],[199188160,193231904]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[176532248,176501872,200455144]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_singleton_identified_by_element1_2,plain,(member(x,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),[]).
%
% cnf(176532248,plain,(member(x,universal_class)),inference(rewrite,[status(thm)],[prove_singleton_identified_by_element1_2]),[]).
%
% fof(set_in_its_singleton,plain,(~member(A,universal_class)|member(A,singleton(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),[]).
%
% cnf(176501872,plain,(~member(A,universal_class)|member(A,singleton(A))),inference(rewrite,[status(thm)],[set_in_its_singleton]),[]).
%
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),[]).
%
% cnf(175326736,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(equal_implies_subclass1,plain,(~$equal(B,A)|subclass(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),[]).
%
% cnf(175368920,plain,(~$equal(B,A)|subclass(A,B)),inference(rewrite,[status(thm)],[equal_implies_subclass1]),[]).
%
% cnf(197780640,plain,(~member(C,A)|member(C,B)|~$equal(B,A)),inference(resolution,[status(thm)],[175326736,175368920]),[]).
%
% fof(prove_singleton_identified_by_element1_1,plain,($equal(singleton(y),singleton(x))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),[]).
%
% cnf(176528184,plain,($equal(singleton(y),singleton(x))),inference(rewrite,[status(thm)],[prove_singleton_identified_by_element1_1]),[]).
%
% cnf(199188160,plain,(~member(A,singleton(x))|member(A,singleton(y))),inference(resolution,[status(thm)],[197780640,176528184]),[]).
%
% fof(only_member_in_singleton,plain,(~member(A,singleton(B))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),[]).
%
% cnf(176519880,plain,(~member(A,singleton(B))|$equal(B,A)),inference(rewrite,[status(thm)],[only_member_in_singleton]),[]).
%
% fof(prove_singleton_identified_by_element1_3,plain,(~$equal(y,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET083-7.tptp',unknown),[]).
%
% cnf(176540032,plain,(~$equal(y,x)),inference(rewrite,[status(thm)],[prove_singleton_identified_by_element1_3]),[]).
%
% cnf(193231904,plain,(~member(x,singleton(y))),inference(resolution,[status(thm)],[176519880,176540032]),[]).
%
% cnf(200455144,plain,(~member(x,singleton(x))),inference(resolution,[status(thm)],[199188160,193231904]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[176532248,176501872,200455144]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------