TSTP Solution File: SET061-7 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET061-7 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 15:26:16 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 : 21 ( 10 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 3 sgn 12 !; 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/SET061-7.tptp',unknown),
[] ).
cnf(148997880,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(prove_existence_of_null_class_1,plain,
member(z,null_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),
[] ).
cnf(150005024,plain,
member(z,null_class),
inference(rewrite,[status(thm)],[prove_existence_of_null_class_1]),
[] ).
cnf(158681176,plain,
( ~ subclass(null_class,A)
| member(z,A) ),
inference(resolution,[status(thm)],[148997880,150005024]),
[] ).
fof(class_elements_are_sets,plain,
! [A] : subclass(A,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),
[] ).
cnf(149027952,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
cnf(158695856,plain,
member(z,universal_class),
inference(resolution,[status(thm)],[158681176,149027952]),
[] ).
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/SET061-7.tptp',unknown),
[] ).
cnf(149201960,plain,
( ~ member(A,universal_class)
| member(A,complement(B))
| member(A,B) ),
inference(rewrite,[status(thm)],[complement2]),
[] ).
fof(complement1,plain,
! [A,B] :
( ~ member(A,complement(B))
| ~ member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),
[] ).
cnf(149191016,plain,
( ~ member(A,complement(B))
| ~ member(A,B) ),
inference(rewrite,[status(thm)],[complement1]),
[] ).
cnf(158660448,plain,
~ member(z,complement(null_class)),
inference(resolution,[status(thm)],[149191016,150005024]),
[] ).
cnf(164081720,plain,
member(z,complement(complement(null_class))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[158695856,149201960,158660448]),
[] ).
fof(intersection1,plain,
! [A,B,C] :
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),
[] ).
cnf(149176400,plain,
( ~ member(A,intersection(B,C))
| member(A,B) ),
inference(rewrite,[status(thm)],[intersection1]),
[] ).
cnf(163990360,plain,
~ member(z,intersection(complement(null_class),A)),
inference(resolution,[status(thm)],[149176400,158660448]),
[] ).
fof(regularity2,plain,
! [A] :
( $equal(null_class,A)
| $equal(intersection(A,regular(A)),null_class) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),
[] ).
cnf(149560376,plain,
( $equal(null_class,A)
| $equal(intersection(A,regular(A)),null_class) ),
inference(rewrite,[status(thm)],[regularity2]),
[] ).
cnf(175257464,plain,
$equal(null_class,complement(null_class)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[150005024,163990360,149560376,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164081720,175257464,158660448,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 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/SET061-7.tptp',unknown),[]).
%
% cnf(148997880,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(prove_existence_of_null_class_1,plain,(member(z,null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),[]).
%
% cnf(150005024,plain,(member(z,null_class)),inference(rewrite,[status(thm)],[prove_existence_of_null_class_1]),[]).
%
% cnf(158681176,plain,(~subclass(null_class,A)|member(z,A)),inference(resolution,[status(thm)],[148997880,150005024]),[]).
%
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),[]).
%
% cnf(149027952,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% cnf(158695856,plain,(member(z,universal_class)),inference(resolution,[status(thm)],[158681176,149027952]),[]).
%
% fof(complement2,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),[]).
%
% cnf(149201960,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),inference(rewrite,[status(thm)],[complement2]),[]).
%
% fof(complement1,plain,(~member(A,complement(B))|~member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),[]).
%
% cnf(149191016,plain,(~member(A,complement(B))|~member(A,B)),inference(rewrite,[status(thm)],[complement1]),[]).
%
% cnf(158660448,plain,(~member(z,complement(null_class))),inference(resolution,[status(thm)],[149191016,150005024]),[]).
%
% cnf(164081720,plain,(member(z,complement(complement(null_class)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[158695856,149201960,158660448]),[]).
%
% fof(intersection1,plain,(~member(A,intersection(B,C))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),[]).
%
% cnf(149176400,plain,(~member(A,intersection(B,C))|member(A,B)),inference(rewrite,[status(thm)],[intersection1]),[]).
%
% cnf(163990360,plain,(~member(z,intersection(complement(null_class),A))),inference(resolution,[status(thm)],[149176400,158660448]),[]).
%
% fof(regularity2,plain,($equal(null_class,A)|$equal(intersection(A,regular(A)),null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-7.tptp',unknown),[]).
%
% cnf(149560376,plain,($equal(null_class,A)|$equal(intersection(A,regular(A)),null_class)),inference(rewrite,[status(thm)],[regularity2]),[]).
%
% cnf(175257464,plain,($equal(null_class,complement(null_class))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[150005024,163990360,149560376,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164081720,175257464,158660448,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------