TSTP Solution File: NUM183-1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : NUM183-1 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 14:51:09 EDT 2009
% Result : Unsatisfiable 26.1s
% Output : Refutation 26.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 17 ~; 13 |; 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_ordinals_are_kind_1_or_limit_1,plain,
member(x,ordinal_numbers),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),
[] ).
cnf(157556488,plain,
member(x,ordinal_numbers),
inference(rewrite,[status(thm)],[prove_ordinals_are_kind_1_or_limit_1]),
[] ).
fof(intersection3,plain,
! [A,B,C] :
( ~ member(A,B)
| ~ member(A,C)
| member(A,intersection(B,C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),
[] ).
cnf(155907864,plain,
( ~ member(A,B)
| ~ member(A,C)
| member(A,intersection(B,C)) ),
inference(rewrite,[status(thm)],[intersection3]),
[] ).
fof(prove_ordinals_are_kind_1_or_limit_3,plain,
~ member(x,limit_ordinals),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),
[] ).
cnf(157575144,plain,
~ member(x,limit_ordinals),
inference(rewrite,[status(thm)],[prove_ordinals_are_kind_1_or_limit_3]),
[] ).
fof(limit_ordinals,plain,
$equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),
[] ).
cnf(157374296,plain,
$equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals),
inference(rewrite,[status(thm)],[limit_ordinals]),
[] ).
cnf(176851376,plain,
~ member(x,intersection(complement(kind_1_ordinals),ordinal_numbers)),
inference(paramodulation,[status(thm)],[157575144,157374296,theory(equality)]),
[] ).
cnf(303928360,plain,
~ member(x,complement(kind_1_ordinals)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[157556488,155907864,176851376]),
[] ).
fof(subclass_members,plain,
! [A,B,C] :
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),
[] ).
cnf(155680640,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(class_elements_are_sets,plain,
! [A] : subclass(A,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),
[] ).
cnf(155717968,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
cnf(171720920,plain,
( ~ member(B,A)
| member(B,universal_class) ),
inference(resolution,[status(thm)],[155680640,155717968]),
[] ).
cnf(186950872,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[171720920,157556488]),
[] ).
fof(complement2,plain,
! [A,B] :
( ~ member(A,universal_class)
| member(A,complement(B))
| member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),
[] ).
cnf(155930624,plain,
( ~ member(A,universal_class)
| member(A,complement(B))
| member(A,B) ),
inference(rewrite,[status(thm)],[complement2]),
[] ).
fof(prove_ordinals_are_kind_1_or_limit_2,plain,
~ member(x,kind_1_ordinals),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),
[] ).
cnf(157565152,plain,
~ member(x,kind_1_ordinals),
inference(rewrite,[status(thm)],[prove_ordinals_are_kind_1_or_limit_2]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[303928360,186950872,155930624,157565152]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 25 seconds
% START OF PROOF SEQUENCE
% fof(prove_ordinals_are_kind_1_or_limit_1,plain,(member(x,ordinal_numbers)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),[]).
%
% cnf(157556488,plain,(member(x,ordinal_numbers)),inference(rewrite,[status(thm)],[prove_ordinals_are_kind_1_or_limit_1]),[]).
%
% fof(intersection3,plain,(~member(A,B)|~member(A,C)|member(A,intersection(B,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),[]).
%
% cnf(155907864,plain,(~member(A,B)|~member(A,C)|member(A,intersection(B,C))),inference(rewrite,[status(thm)],[intersection3]),[]).
%
% fof(prove_ordinals_are_kind_1_or_limit_3,plain,(~member(x,limit_ordinals)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),[]).
%
% cnf(157575144,plain,(~member(x,limit_ordinals)),inference(rewrite,[status(thm)],[prove_ordinals_are_kind_1_or_limit_3]),[]).
%
% fof(limit_ordinals,plain,($equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),[]).
%
% cnf(157374296,plain,($equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals)),inference(rewrite,[status(thm)],[limit_ordinals]),[]).
%
% cnf(176851376,plain,(~member(x,intersection(complement(kind_1_ordinals),ordinal_numbers))),inference(paramodulation,[status(thm)],[157575144,157374296,theory(equality)]),[]).
%
% cnf(303928360,plain,(~member(x,complement(kind_1_ordinals))),inference(forward_subsumption_resolution__resolution,[status(thm)],[157556488,155907864,176851376]),[]).
%
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),[]).
%
% cnf(155680640,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),[]).
%
% cnf(155717968,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% cnf(171720920,plain,(~member(B,A)|member(B,universal_class)),inference(resolution,[status(thm)],[155680640,155717968]),[]).
%
% cnf(186950872,plain,(member(x,universal_class)),inference(resolution,[status(thm)],[171720920,157556488]),[]).
%
% fof(complement2,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),[]).
%
% cnf(155930624,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),inference(rewrite,[status(thm)],[complement2]),[]).
%
% fof(prove_ordinals_are_kind_1_or_limit_2,plain,(~member(x,kind_1_ordinals)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM183-1.tptp',unknown),[]).
%
% cnf(157565152,plain,(~member(x,kind_1_ordinals)),inference(rewrite,[status(thm)],[prove_ordinals_are_kind_1_or_limit_2]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[303928360,186950872,155930624,157565152]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------