TSTP Solution File: SET101-6 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET101-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 15:28:30 EDT 2009
% Result : Unsatisfiable 3.2s
% Output : Refutation 3.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 25 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 8 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET101-6.tptp',unknown),
[] ).
cnf(164920704,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(class_elements_are_sets,plain,
! [A] : subclass(A,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(164950872,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
cnf(174110824,plain,
( ~ member(B,A)
| member(B,universal_class) ),
inference(resolution,[status(thm)],[164920704,164950872]),
[] ).
fof(complement1,plain,
! [A,B] :
( ~ member(A,complement(B))
| ~ member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(165121800,plain,
( ~ member(A,complement(B))
| ~ member(A,B) ),
inference(rewrite,[status(thm)],[complement1]),
[] ).
fof(unordered_pair2,plain,
! [A,B] :
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(165002016,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
inference(rewrite,[status(thm)],[unordered_pair2]),
[] ).
cnf(186397432,plain,
~ member(A,complement(unordered_pair(A,B))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174110824,165121800,165002016]),
[] ).
fof(ordered_pair,plain,
! [A,B] : $equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(165034976,plain,
$equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B)),
inference(rewrite,[status(thm)],[ordered_pair]),
[] ).
cnf(192261296,plain,
~ member(singleton(A),complement(ordered_pair(A,B))),
inference(paramodulation,[status(thm)],[186397432,165034976,theory(equality)]),
[] ).
fof(equal_implies_subclass2,plain,
! [B,A] :
( ~ $equal(B,A)
| subclass(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(164975976,plain,
( ~ $equal(B,A)
| subclass(B,A) ),
inference(rewrite,[status(thm)],[equal_implies_subclass2]),
[] ).
fof(singleton_set,plain,
! [A] : $equal(singleton(A),unordered_pair(A,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(165025352,plain,
$equal(singleton(A),unordered_pair(A,A)),
inference(rewrite,[status(thm)],[singleton_set]),
[] ).
cnf(175460728,plain,
subclass(singleton(A),unordered_pair(A,A)),
inference(resolution,[status(thm)],[164975976,165025352]),
[] ).
fof(subclass_implies_equal,plain,
! [A,B] :
( ~ subclass(A,B)
| ~ subclass(B,A)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(164982008,plain,
( ~ subclass(A,B)
| ~ subclass(B,A)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[subclass_implies_equal]),
[] ).
fof(equal_implies_subclass1,plain,
! [B,A] :
( ~ $equal(B,A)
| subclass(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(164966168,plain,
( ~ $equal(B,A)
| subclass(A,B) ),
inference(rewrite,[status(thm)],[equal_implies_subclass1]),
[] ).
cnf(175452640,plain,
subclass(unordered_pair(A,A),singleton(A)),
inference(resolution,[status(thm)],[164966168,165025352]),
[] ).
cnf(175499288,plain,
$equal(unordered_pair(A,A),singleton(A)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[175460728,164982008,175452640]),
[] ).
fof(unordered_pairs_in_universal,plain,
! [A,B] : member(unordered_pair(A,B),universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(165015280,plain,
member(unordered_pair(A,B),universal_class),
inference(rewrite,[status(thm)],[unordered_pairs_in_universal]),
[] ).
cnf(270928808,plain,
member(singleton(A),universal_class),
inference(paramodulation,[status(thm)],[175499288,165015280,theory(equality)]),
[] ).
fof(complement2,plain,
! [A,B] :
( ~ member(A,universal_class)
| member(A,complement(B))
| member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(165128688,plain,
( ~ member(A,universal_class)
| member(A,complement(B))
| member(A,B) ),
inference(rewrite,[status(thm)],[complement2]),
[] ).
fof(prove_singleton_member_of_ordered_pair_1,plain,
~ member(singleton(x),ordered_pair(x,y)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),
[] ).
cnf(165864976,plain,
~ member(singleton(x),ordered_pair(x,y)),
inference(rewrite,[status(thm)],[prove_singleton_member_of_ordered_pair_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[192261296,270928808,165128688,165864976]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(164920704,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(164950872,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% cnf(174110824,plain,(~member(B,A)|member(B,universal_class)),inference(resolution,[status(thm)],[164920704,164950872]),[]).
%
% fof(complement1,plain,(~member(A,complement(B))|~member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(165121800,plain,(~member(A,complement(B))|~member(A,B)),inference(rewrite,[status(thm)],[complement1]),[]).
%
% fof(unordered_pair2,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(165002016,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),inference(rewrite,[status(thm)],[unordered_pair2]),[]).
%
% cnf(186397432,plain,(~member(A,complement(unordered_pair(A,B)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[174110824,165121800,165002016]),[]).
%
% fof(ordered_pair,plain,($equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(165034976,plain,($equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B))),inference(rewrite,[status(thm)],[ordered_pair]),[]).
%
% cnf(192261296,plain,(~member(singleton(A),complement(ordered_pair(A,B)))),inference(paramodulation,[status(thm)],[186397432,165034976,theory(equality)]),[]).
%
% fof(equal_implies_subclass2,plain,(~$equal(B,A)|subclass(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(164975976,plain,(~$equal(B,A)|subclass(B,A)),inference(rewrite,[status(thm)],[equal_implies_subclass2]),[]).
%
% fof(singleton_set,plain,($equal(singleton(A),unordered_pair(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(165025352,plain,($equal(singleton(A),unordered_pair(A,A))),inference(rewrite,[status(thm)],[singleton_set]),[]).
%
% cnf(175460728,plain,(subclass(singleton(A),unordered_pair(A,A))),inference(resolution,[status(thm)],[164975976,165025352]),[]).
%
% fof(subclass_implies_equal,plain,(~subclass(A,B)|~subclass(B,A)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(164982008,plain,(~subclass(A,B)|~subclass(B,A)|$equal(B,A)),inference(rewrite,[status(thm)],[subclass_implies_equal]),[]).
%
% fof(equal_implies_subclass1,plain,(~$equal(B,A)|subclass(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(164966168,plain,(~$equal(B,A)|subclass(A,B)),inference(rewrite,[status(thm)],[equal_implies_subclass1]),[]).
%
% cnf(175452640,plain,(subclass(unordered_pair(A,A),singleton(A))),inference(resolution,[status(thm)],[164966168,165025352]),[]).
%
% cnf(175499288,plain,($equal(unordered_pair(A,A),singleton(A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[175460728,164982008,175452640]),[]).
%
% fof(unordered_pairs_in_universal,plain,(member(unordered_pair(A,B),universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(165015280,plain,(member(unordered_pair(A,B),universal_class)),inference(rewrite,[status(thm)],[unordered_pairs_in_universal]),[]).
%
% cnf(270928808,plain,(member(singleton(A),universal_class)),inference(paramodulation,[status(thm)],[175499288,165015280,theory(equality)]),[]).
%
% fof(complement2,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(165128688,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),inference(rewrite,[status(thm)],[complement2]),[]).
%
% fof(prove_singleton_member_of_ordered_pair_1,plain,(~member(singleton(x),ordered_pair(x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-6.tptp',unknown),[]).
%
% cnf(165864976,plain,(~member(singleton(x),ordered_pair(x,y))),inference(rewrite,[status(thm)],[prove_singleton_member_of_ordered_pair_1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[192261296,270928808,165128688,165864976]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------