%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET102-7 : 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 15:28:36 EDT 2009
% Result : Unsatisfiable 24.7s
% Output : Refutation 24.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 33 ( 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 : 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 : 34 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(unordered_pairs_in_universal,plain,
! [A,B] : member(unordered_pair(A,B),universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),
[] ).
cnf(146490440,plain,
member(unordered_pair(A,B),universal_class),
inference(rewrite,[status(thm)],[unordered_pairs_in_universal]),
[] ).
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/SET102-7.tptp',unknown),
[] ).
cnf(146398616,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/SET102-7.tptp',unknown),
[] ).
cnf(146428976,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
cnf(156067696,plain,
( ~ member(B,A)
| member(B,universal_class) ),
inference(resolution,[status(thm)],[146398616,146428976]),
[] ).
fof(complement1,plain,
! [A,B] :
( ~ member(A,complement(B))
| ~ member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),
[] ).
cnf(146597600,plain,
( ~ member(A,complement(B))
| ~ member(A,B) ),
inference(rewrite,[status(thm)],[complement1]),
[] ).
fof(unordered_pair3,plain,
! [A,B] :
( ~ member(A,universal_class)
| member(A,unordered_pair(B,A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),
[] ).
cnf(146486816,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(B,A)) ),
inference(rewrite,[status(thm)],[unordered_pair3]),
[] ).
cnf(205972800,plain,
~ member(A,complement(unordered_pair(B,A))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156067696,146597600,146486816]),
[] ).
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/SET102-7.tptp',unknown),
[] ).
cnf(146510264,plain,
$equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B)),
inference(rewrite,[status(thm)],[ordered_pair]),
[] ).
cnf(465776568,plain,
~ member(unordered_pair(A,singleton(B)),complement(ordered_pair(A,B))),
inference(paramodulation,[status(thm)],[205972800,146510264,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/SET102-7.tptp',unknown),
[] ).
cnf(146608640,plain,
( ~ member(A,universal_class)
| member(A,complement(B))
| member(A,B) ),
inference(rewrite,[status(thm)],[complement2]),
[] ).
fof(prove_unordered_pair_member_of_ordered_pair_1,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),
[] ).
cnf(147793120,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(rewrite,[status(thm)],[prove_unordered_pair_member_of_ordered_pair_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[146490440,465776568,146608640,147793120]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 22 seconds
% START OF PROOF SEQUENCE
% fof(unordered_pairs_in_universal,plain,(member(unordered_pair(A,B),universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),[]).
%
% cnf(146490440,plain,(member(unordered_pair(A,B),universal_class)),inference(rewrite,[status(thm)],[unordered_pairs_in_universal]),[]).
%
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),[]).
%
% cnf(146398616,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/SET102-7.tptp',unknown),[]).
%
% cnf(146428976,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% cnf(156067696,plain,(~member(B,A)|member(B,universal_class)),inference(resolution,[status(thm)],[146398616,146428976]),[]).
%
% fof(complement1,plain,(~member(A,complement(B))|~member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),[]).
%
% cnf(146597600,plain,(~member(A,complement(B))|~member(A,B)),inference(rewrite,[status(thm)],[complement1]),[]).
%
% fof(unordered_pair3,plain,(~member(A,universal_class)|member(A,unordered_pair(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),[]).
%
% cnf(146486816,plain,(~member(A,universal_class)|member(A,unordered_pair(B,A))),inference(rewrite,[status(thm)],[unordered_pair3]),[]).
%
% cnf(205972800,plain,(~member(A,complement(unordered_pair(B,A)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[156067696,146597600,146486816]),[]).
%
% 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/SET102-7.tptp',unknown),[]).
%
% cnf(146510264,plain,($equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B))),inference(rewrite,[status(thm)],[ordered_pair]),[]).
%
% cnf(465776568,plain,(~member(unordered_pair(A,singleton(B)),complement(ordered_pair(A,B)))),inference(paramodulation,[status(thm)],[205972800,146510264,theory(equality)]),[]).
%
% fof(complement2,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),[]).
%
% cnf(146608640,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),inference(rewrite,[status(thm)],[complement2]),[]).
%
% fof(prove_unordered_pair_member_of_ordered_pair_1,plain,(~member(unordered_pair(x,singleton(y)),ordered_pair(x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET102-7.tptp',unknown),[]).
%
% cnf(147793120,plain,(~member(unordered_pair(x,singleton(y)),ordered_pair(x,y))),inference(rewrite,[status(thm)],[prove_unordered_pair_member_of_ordered_pair_1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[146490440,465776568,146608640,147793120]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------