TSTP Solution File: SET411-6 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET411-6 : 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 15:31:03 EDT 2009
% Result : Unsatisfiable 2.4s
% Output : Refutation 2.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 4 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(intersection2,plain,
! [A,B,C] :
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),
[] ).
cnf(166000512,plain,
( ~ member(A,intersection(B,C))
| member(A,C) ),
inference(rewrite,[status(thm)],[intersection2]),
[] ).
fof(compose_can_define_singleton,plain,
$equal(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),
[] ).
cnf(166897512,plain,
$equal(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation),
inference(rewrite,[status(thm)],[compose_can_define_singleton]),
[] ).
cnf(204221328,plain,
( ~ member(A,singleton_relation)
| member(A,element_relation) ),
inference(paramodulation,[status(thm)],[166000512,166897512,theory(equality)]),
[] ).
fof(prove_compose_condition_for_singleton_membership1_1,plain,
member(ordered_pair(x,y),singleton_relation),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),
[] ).
cnf(166983392,plain,
member(ordered_pair(x,y),singleton_relation),
inference(rewrite,[status(thm)],[prove_compose_condition_for_singleton_membership1_1]),
[] ).
cnf(234271280,plain,
member(ordered_pair(x,y),element_relation),
inference(resolution,[status(thm)],[204221328,166983392]),
[] ).
fof(element_relation2,plain,
! [A,B] :
( ~ member(ordered_pair(A,B),element_relation)
| member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),
[] ).
cnf(165972736,plain,
( ~ member(ordered_pair(A,B),element_relation)
| member(A,B) ),
inference(rewrite,[status(thm)],[element_relation2]),
[] ).
fof(class_elements_are_sets,plain,
! [A] : subclass(A,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),
[] ).
cnf(165832032,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
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/SET411-6.tptp',unknown),
[] ).
cnf(165801000,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(prove_compose_condition_for_singleton_membership1_2,plain,
~ member(x,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),
[] ).
cnf(166988080,plain,
~ member(x,universal_class),
inference(rewrite,[status(thm)],[prove_compose_condition_for_singleton_membership1_2]),
[] ).
cnf(178601632,plain,
~ member(x,A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165832032,165801000,166988080]),
[] ).
cnf(178716032,plain,
~ member(ordered_pair(x,A),element_relation),
inference(resolution,[status(thm)],[165972736,178601632]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[234271280,178716032]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(intersection2,plain,(~member(A,intersection(B,C))|member(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),[]).
%
% cnf(166000512,plain,(~member(A,intersection(B,C))|member(A,C)),inference(rewrite,[status(thm)],[intersection2]),[]).
%
% fof(compose_can_define_singleton,plain,($equal(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),[]).
%
% cnf(166897512,plain,($equal(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation)),inference(rewrite,[status(thm)],[compose_can_define_singleton]),[]).
%
% cnf(204221328,plain,(~member(A,singleton_relation)|member(A,element_relation)),inference(paramodulation,[status(thm)],[166000512,166897512,theory(equality)]),[]).
%
% fof(prove_compose_condition_for_singleton_membership1_1,plain,(member(ordered_pair(x,y),singleton_relation)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),[]).
%
% cnf(166983392,plain,(member(ordered_pair(x,y),singleton_relation)),inference(rewrite,[status(thm)],[prove_compose_condition_for_singleton_membership1_1]),[]).
%
% cnf(234271280,plain,(member(ordered_pair(x,y),element_relation)),inference(resolution,[status(thm)],[204221328,166983392]),[]).
%
% fof(element_relation2,plain,(~member(ordered_pair(A,B),element_relation)|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),[]).
%
% cnf(165972736,plain,(~member(ordered_pair(A,B),element_relation)|member(A,B)),inference(rewrite,[status(thm)],[element_relation2]),[]).
%
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),[]).
%
% cnf(165832032,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),[]).
%
% cnf(165801000,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(prove_compose_condition_for_singleton_membership1_2,plain,(~member(x,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET411-6.tptp',unknown),[]).
%
% cnf(166988080,plain,(~member(x,universal_class)),inference(rewrite,[status(thm)],[prove_compose_condition_for_singleton_membership1_2]),[]).
%
% cnf(178601632,plain,(~member(x,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165832032,165801000,166988080]),[]).
%
% cnf(178716032,plain,(~member(ordered_pair(x,A),element_relation)),inference(resolution,[status(thm)],[165972736,178601632]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[234271280,178716032]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------