TSTP Solution File: SET125-6 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET125-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 15:28:58 EDT 2009
% Result : Unsatisfiable 7.5s
% Output : Refutation 7.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 17 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 6 sgn 15 !; 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/SET125-6.tptp',unknown),
[] ).
cnf(145548344,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/SET/SET125-6.tptp',unknown),
[] ).
cnf(145578704,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
cnf(157493344,plain,
( ~ member(B,A)
| member(B,universal_class) ),
inference(resolution,[status(thm)],[145548344,145578704]),
[] ).
fof(prove_set_builder_alternate_defn3_1,plain,
member(x,z),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),
[] ).
cnf(146510216,plain,
member(x,z),
inference(rewrite,[status(thm)],[prove_set_builder_alternate_defn3_1]),
[] ).
cnf(176312608,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[157493344,146510216]),
[] ).
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/SET125-6.tptp',unknown),
[] ).
cnf(145761696,plain,
( ~ member(A,universal_class)
| member(A,complement(B))
| member(A,B) ),
inference(rewrite,[status(thm)],[complement2]),
[] ).
fof(intersection2,plain,
! [A,B,C] :
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),
[] ).
cnf(145740568,plain,
( ~ member(A,intersection(B,C))
| member(A,C) ),
inference(rewrite,[status(thm)],[intersection2]),
[] ).
fof(complement1,plain,
! [A,B] :
( ~ member(A,complement(B))
| ~ member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),
[] ).
cnf(145750656,plain,
( ~ member(A,complement(B))
| ~ member(A,B) ),
inference(rewrite,[status(thm)],[complement1]),
[] ).
cnf(157914232,plain,
~ member(x,complement(z)),
inference(resolution,[status(thm)],[145750656,146510216]),
[] ).
cnf(172000320,plain,
~ member(x,intersection(A,complement(z))),
inference(resolution,[status(thm)],[145740568,157914232]),
[] ).
cnf(201231776,plain,
member(x,complement(intersection(A,complement(z)))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[176312608,145761696,172000320]),
[] ).
fof(union,plain,
! [A,B] : $equal(complement(intersection(complement(A),complement(B))),union(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),
[] ).
cnf(145766824,plain,
$equal(complement(intersection(complement(A),complement(B))),union(A,B)),
inference(rewrite,[status(thm)],[union]),
[] ).
cnf(304285448,plain,
member(x,union(A,z)),
inference(paramodulation,[status(thm)],[201231776,145766824,theory(equality)]),
[] ).
fof(prove_set_builder_alternate_defn3_2,plain,
~ member(x,set_builder(y,z)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),
[] ).
cnf(146514200,plain,
~ member(x,set_builder(y,z)),
inference(rewrite,[status(thm)],[prove_set_builder_alternate_defn3_2]),
[] ).
fof(definition_of_set_builder,plain,
! [A,B] : $equal(union(singleton(A),B),set_builder(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),
[] ).
cnf(146506328,plain,
$equal(union(singleton(A),B),set_builder(A,B)),
inference(rewrite,[status(thm)],[definition_of_set_builder]),
[] ).
cnf(160108712,plain,
~ member(x,union(singleton(y),z)),
inference(paramodulation,[status(thm)],[146514200,146506328,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[304285448,160108712]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 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/SET125-6.tptp',unknown),[]).
%
% cnf(145548344,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/SET/SET125-6.tptp',unknown),[]).
%
% cnf(145578704,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% cnf(157493344,plain,(~member(B,A)|member(B,universal_class)),inference(resolution,[status(thm)],[145548344,145578704]),[]).
%
% fof(prove_set_builder_alternate_defn3_1,plain,(member(x,z)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),[]).
%
% cnf(146510216,plain,(member(x,z)),inference(rewrite,[status(thm)],[prove_set_builder_alternate_defn3_1]),[]).
%
% cnf(176312608,plain,(member(x,universal_class)),inference(resolution,[status(thm)],[157493344,146510216]),[]).
%
% fof(complement2,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),[]).
%
% cnf(145761696,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),inference(rewrite,[status(thm)],[complement2]),[]).
%
% fof(intersection2,plain,(~member(A,intersection(B,C))|member(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),[]).
%
% cnf(145740568,plain,(~member(A,intersection(B,C))|member(A,C)),inference(rewrite,[status(thm)],[intersection2]),[]).
%
% fof(complement1,plain,(~member(A,complement(B))|~member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),[]).
%
% cnf(145750656,plain,(~member(A,complement(B))|~member(A,B)),inference(rewrite,[status(thm)],[complement1]),[]).
%
% cnf(157914232,plain,(~member(x,complement(z))),inference(resolution,[status(thm)],[145750656,146510216]),[]).
%
% cnf(172000320,plain,(~member(x,intersection(A,complement(z)))),inference(resolution,[status(thm)],[145740568,157914232]),[]).
%
% cnf(201231776,plain,(member(x,complement(intersection(A,complement(z))))),inference(forward_subsumption_resolution__resolution,[status(thm)],[176312608,145761696,172000320]),[]).
%
% fof(union,plain,($equal(complement(intersection(complement(A),complement(B))),union(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),[]).
%
% cnf(145766824,plain,($equal(complement(intersection(complement(A),complement(B))),union(A,B))),inference(rewrite,[status(thm)],[union]),[]).
%
% cnf(304285448,plain,(member(x,union(A,z))),inference(paramodulation,[status(thm)],[201231776,145766824,theory(equality)]),[]).
%
% fof(prove_set_builder_alternate_defn3_2,plain,(~member(x,set_builder(y,z))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),[]).
%
% cnf(146514200,plain,(~member(x,set_builder(y,z))),inference(rewrite,[status(thm)],[prove_set_builder_alternate_defn3_2]),[]).
%
% fof(definition_of_set_builder,plain,($equal(union(singleton(A),B),set_builder(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET125-6.tptp',unknown),[]).
%
% cnf(146506328,plain,($equal(union(singleton(A),B),set_builder(A,B))),inference(rewrite,[status(thm)],[definition_of_set_builder]),[]).
%
% cnf(160108712,plain,(~member(x,union(singleton(y),z))),inference(paramodulation,[status(thm)],[146514200,146506328,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[304285448,160108712]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------