TSTP Solution File: NUM180-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : NUM180-1 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 14:51:07 EDT 2009
% Result : Unsatisfiable 6.1s
% Output : Refutation 6.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 14 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/NUM/NUM180-1.tptp',unknown),
[] ).
cnf(144249928,plain,
( member(not_subclass_element(A,B),A)
| subclass(A,B) ),
inference(rewrite,[status(thm)],[not_subclass_members1]),
[] ).
fof(prove_limit_ordinals_are_ordinals_1,plain,
~ subclass(limit_ordinals,ordinal_numbers),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM180-1.tptp',unknown),
[] ).
cnf(146103440,plain,
~ subclass(limit_ordinals,ordinal_numbers),
inference(rewrite,[status(thm)],[prove_limit_ordinals_are_ordinals_1]),
[] ).
cnf(155854864,plain,
member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals),
inference(resolution,[status(thm)],[144249928,146103440]),
[] ).
fof(limit_ordinals,plain,
$equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM180-1.tptp',unknown),
[] ).
cnf(145917768,plain,
$equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals),
inference(rewrite,[status(thm)],[limit_ordinals]),
[] ).
cnf(166467992,plain,
member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers)),
inference(paramodulation,[status(thm)],[155854864,145917768,theory(equality)]),
[] ).
fof(intersection2,plain,
! [A,B,C] :
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM180-1.tptp',unknown),
[] ).
cnf(144459416,plain,
( ~ member(A,intersection(B,C))
| member(A,C) ),
inference(rewrite,[status(thm)],[intersection2]),
[] ).
cnf(254368120,plain,
member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers),
inference(resolution,[status(thm)],[166467992,144459416]),
[] ).
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/NUM/NUM180-1.tptp',unknown),
[] ).
cnf(144263104,plain,
( ~ member(not_subclass_element(A,B),B)
| subclass(A,B) ),
inference(rewrite,[status(thm)],[not_subclass_members2]),
[] ).
cnf(155897784,plain,
~ member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers),
inference(resolution,[status(thm)],[144263104,146103440]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[254368120,155897784]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 5 seconds
% START OF PROOF SEQUENCE
% fof(not_subclass_members1,plain,(member(not_subclass_element(A,B),A)|subclass(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM180-1.tptp',unknown),[]).
%
% cnf(144249928,plain,(member(not_subclass_element(A,B),A)|subclass(A,B)),inference(rewrite,[status(thm)],[not_subclass_members1]),[]).
%
% fof(prove_limit_ordinals_are_ordinals_1,plain,(~subclass(limit_ordinals,ordinal_numbers)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM180-1.tptp',unknown),[]).
%
% cnf(146103440,plain,(~subclass(limit_ordinals,ordinal_numbers)),inference(rewrite,[status(thm)],[prove_limit_ordinals_are_ordinals_1]),[]).
%
% cnf(155854864,plain,(member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals)),inference(resolution,[status(thm)],[144249928,146103440]),[]).
%
% fof(limit_ordinals,plain,($equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM180-1.tptp',unknown),[]).
%
% cnf(145917768,plain,($equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals)),inference(rewrite,[status(thm)],[limit_ordinals]),[]).
%
% cnf(166467992,plain,(member(not_subclass_element(limit_ordinals,ordinal_numbers),intersection(complement(kind_1_ordinals),ordinal_numbers))),inference(paramodulation,[status(thm)],[155854864,145917768,theory(equality)]),[]).
%
% fof(intersection2,plain,(~member(A,intersection(B,C))|member(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM180-1.tptp',unknown),[]).
%
% cnf(144459416,plain,(~member(A,intersection(B,C))|member(A,C)),inference(rewrite,[status(thm)],[intersection2]),[]).
%
% cnf(254368120,plain,(member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers)),inference(resolution,[status(thm)],[166467992,144459416]),[]).
%
% fof(not_subclass_members2,plain,(~member(not_subclass_element(A,B),B)|subclass(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM180-1.tptp',unknown),[]).
%
% cnf(144263104,plain,(~member(not_subclass_element(A,B),B)|subclass(A,B)),inference(rewrite,[status(thm)],[not_subclass_members2]),[]).
%
% cnf(155897784,plain,(~member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers)),inference(resolution,[status(thm)],[144263104,146103440]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[254368120,155897784]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------