TSTP Solution File: SET062-6 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET062-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 15:26:25 EDT 2009
% Result : Unsatisfiable 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(regularity2,plain,
! [A] :
( $equal(null_class,A)
| $equal(intersection(A,regular(A)),null_class) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
[] ).
cnf(155555200,plain,
( $equal(null_class,A)
| $equal(intersection(A,regular(A)),null_class) ),
inference(rewrite,[status(thm)],[regularity2]),
[] ).
fof(equal_implies_subclass2,plain,
! [B,A] :
( ~ $equal(B,A)
| subclass(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
[] ).
cnf(155048640,plain,
( ~ $equal(B,A)
| subclass(B,A) ),
inference(rewrite,[status(thm)],[equal_implies_subclass2]),
[] ).
fof(prove_null_class_is_subclass_1,plain,
~ subclass(null_class,x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
[] ).
cnf(154981504,plain,
~ subclass(null_class,x),
inference(rewrite,[status(thm)],[prove_null_class_is_subclass_1]),
[] ).
cnf(164655272,plain,
~ $equal(null_class,x),
inference(resolution,[status(thm)],[155048640,154981504]),
[] ).
cnf(164803712,plain,
$equal(intersection(x,regular(x)),null_class),
inference(resolution,[status(thm)],[155555200,164655272]),
[] ).
fof(not_subclass_members1,plain,
! [A,B] :
( member(not_subclass_element(A,B),A)
| subclass(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
[] ).
cnf(155001648,plain,
( member(not_subclass_element(A,B),A)
| subclass(A,B) ),
inference(rewrite,[status(thm)],[not_subclass_members1]),
[] ).
cnf(164668656,plain,
member(not_subclass_element(null_class,x),null_class),
inference(resolution,[status(thm)],[155001648,154981504]),
[] ).
cnf(166012976,plain,
member(not_subclass_element(null_class,x),intersection(x,regular(x))),
inference(paramodulation,[status(thm)],[164803712,164668656,theory(equality)]),
[] ).
fof(intersection1,plain,
! [A,B,C] :
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
[] ).
cnf(155175312,plain,
( ~ member(A,intersection(B,C))
| member(A,B) ),
inference(rewrite,[status(thm)],[intersection1]),
[] ).
cnf(178322376,plain,
member(not_subclass_element(null_class,x),x),
inference(resolution,[status(thm)],[166012976,155175312]),
[] ).
fof(not_subclass_members2,plain,
! [A,B] :
( ~ member(not_subclass_element(A,B),B)
| subclass(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),
[] ).
cnf(155013768,plain,
( ~ member(not_subclass_element(A,B),B)
| subclass(A,B) ),
inference(rewrite,[status(thm)],[not_subclass_members2]),
[] ).
cnf(172294744,plain,
~ member(not_subclass_element(null_class,x),x),
inference(resolution,[status(thm)],[155013768,154981504]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[178322376,172294744]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(regularity2,plain,($equal(null_class,A)|$equal(intersection(A,regular(A)),null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
%
% cnf(155555200,plain,($equal(null_class,A)|$equal(intersection(A,regular(A)),null_class)),inference(rewrite,[status(thm)],[regularity2]),[]).
%
% fof(equal_implies_subclass2,plain,(~$equal(B,A)|subclass(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
%
% cnf(155048640,plain,(~$equal(B,A)|subclass(B,A)),inference(rewrite,[status(thm)],[equal_implies_subclass2]),[]).
%
% fof(prove_null_class_is_subclass_1,plain,(~subclass(null_class,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
%
% cnf(154981504,plain,(~subclass(null_class,x)),inference(rewrite,[status(thm)],[prove_null_class_is_subclass_1]),[]).
%
% cnf(164655272,plain,(~$equal(null_class,x)),inference(resolution,[status(thm)],[155048640,154981504]),[]).
%
% cnf(164803712,plain,($equal(intersection(x,regular(x)),null_class)),inference(resolution,[status(thm)],[155555200,164655272]),[]).
%
% fof(not_subclass_members1,plain,(member(not_subclass_element(A,B),A)|subclass(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
%
% cnf(155001648,plain,(member(not_subclass_element(A,B),A)|subclass(A,B)),inference(rewrite,[status(thm)],[not_subclass_members1]),[]).
%
% cnf(164668656,plain,(member(not_subclass_element(null_class,x),null_class)),inference(resolution,[status(thm)],[155001648,154981504]),[]).
%
% cnf(166012976,plain,(member(not_subclass_element(null_class,x),intersection(x,regular(x)))),inference(paramodulation,[status(thm)],[164803712,164668656,theory(equality)]),[]).
%
% fof(intersection1,plain,(~member(A,intersection(B,C))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
%
% cnf(155175312,plain,(~member(A,intersection(B,C))|member(A,B)),inference(rewrite,[status(thm)],[intersection1]),[]).
%
% cnf(178322376,plain,(member(not_subclass_element(null_class,x),x)),inference(resolution,[status(thm)],[166012976,155175312]),[]).
%
% fof(not_subclass_members2,plain,(~member(not_subclass_element(A,B),B)|subclass(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET062-6.tptp',unknown),[]).
%
% cnf(155013768,plain,(~member(not_subclass_element(A,B),B)|subclass(A,B)),inference(rewrite,[status(thm)],[not_subclass_members2]),[]).
%
% cnf(172294744,plain,(~member(not_subclass_element(null_class,x),x)),inference(resolution,[status(thm)],[155013768,154981504]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[178322376,172294744]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------