%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET064-7 : 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 15:26:43 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(equality1,plain,
! [B,A] :
( $equal(B,A)
| member(not_subclass_element(A,B),A)
| member(not_subclass_element(B,A),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET064-7.tptp',unknown),
[] ).
cnf(146615464,plain,
( $equal(B,A)
| member(not_subclass_element(A,B),A)
| member(not_subclass_element(B,A),B) ),
inference(rewrite,[status(thm)],[equality1]),
[] ).
fof(prove_null_class_is_unique_1,plain,
~ $equal(null_class,z),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET064-7.tptp',unknown),
[] ).
cnf(146676424,plain,
~ $equal(null_class,z),
inference(rewrite,[status(thm)],[prove_null_class_is_unique_1]),
[] ).
cnf(158181664,plain,
( member(not_subclass_element(z,null_class),z)
| member(not_subclass_element(null_class,z),null_class) ),
inference(resolution,[status(thm)],[146615464,146676424]),
[] ).
fof(existence_of_null_class,plain,
! [A] : ~ member(A,null_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET064-7.tptp',unknown),
[] ).
cnf(146652328,plain,
~ member(A,null_class),
inference(rewrite,[status(thm)],[existence_of_null_class]),
[] ).
cnf(158191472,plain,
member(not_subclass_element(z,null_class),z),
inference(resolution,[status(thm)],[158181664,146652328]),
[] ).
fof(prove_null_class_is_unique_2,plain,
~ member(not_subclass_element(z,null_class),z),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET064-7.tptp',unknown),
[] ).
cnf(146681832,plain,
~ member(not_subclass_element(z,null_class),z),
inference(rewrite,[status(thm)],[prove_null_class_is_unique_2]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[158191472,146681832]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(equality1,plain,($equal(B,A)|member(not_subclass_element(A,B),A)|member(not_subclass_element(B,A),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET064-7.tptp',unknown),[]).
%
% cnf(146615464,plain,($equal(B,A)|member(not_subclass_element(A,B),A)|member(not_subclass_element(B,A),B)),inference(rewrite,[status(thm)],[equality1]),[]).
%
% fof(prove_null_class_is_unique_1,plain,(~$equal(null_class,z)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET064-7.tptp',unknown),[]).
%
% cnf(146676424,plain,(~$equal(null_class,z)),inference(rewrite,[status(thm)],[prove_null_class_is_unique_1]),[]).
%
% cnf(158181664,plain,(member(not_subclass_element(z,null_class),z)|member(not_subclass_element(null_class,z),null_class)),inference(resolution,[status(thm)],[146615464,146676424]),[]).
%
% fof(existence_of_null_class,plain,(~member(A,null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET064-7.tptp',unknown),[]).
%
% cnf(146652328,plain,(~member(A,null_class)),inference(rewrite,[status(thm)],[existence_of_null_class]),[]).
%
% cnf(158191472,plain,(member(not_subclass_element(z,null_class),z)),inference(resolution,[status(thm)],[158181664,146652328]),[]).
%
% fof(prove_null_class_is_unique_2,plain,(~member(not_subclass_element(z,null_class),z)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET064-7.tptp',unknown),[]).
%
% cnf(146681832,plain,(~member(not_subclass_element(z,null_class),z)),inference(rewrite,[status(thm)],[prove_null_class_is_unique_2]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[158191472,146681832]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------