%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET167-6 : 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 15:29:34 EDT 2009
% Result : Unsatisfiable 2.4s
% Output : Refutation 2.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 35 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 4 sgn 13 !; 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/SET167-6.tptp',unknown),
[] ).
cnf(172452864,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/SET167-6.tptp',unknown),
[] ).
cnf(172483992,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
cnf(184719072,plain,
( ~ member(B,A)
| member(B,universal_class) ),
inference(resolution,[status(thm)],[172452864,172483992]),
[] ).
fof(prove_members_of_union2_1,plain,
member(x,y),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),
[] ).
cnf(173642984,plain,
member(x,y),
inference(rewrite,[status(thm)],[prove_members_of_union2_1]),
[] ).
cnf(187737368,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[184719072,173642984]),
[] ).
fof(intersection1,plain,
! [A,B,C] :
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),
[] ).
cnf(172644056,plain,
( ~ member(A,intersection(B,C))
| member(A,B) ),
inference(rewrite,[status(thm)],[intersection1]),
[] ).
fof(complement1,plain,
! [A,B] :
( ~ member(A,complement(B))
| ~ member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),
[] ).
cnf(172663176,plain,
( ~ member(A,complement(B))
| ~ member(A,B) ),
inference(rewrite,[status(thm)],[complement1]),
[] ).
cnf(187485240,plain,
~ member(x,complement(y)),
inference(resolution,[status(thm)],[172663176,173642984]),
[] ).
cnf(196397064,plain,
~ member(x,intersection(complement(y),A)),
inference(resolution,[status(thm)],[172644056,187485240]),
[] ).
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/SET167-6.tptp',unknown),
[] ).
cnf(172674440,plain,
( ~ member(A,universal_class)
| member(A,complement(B))
| member(A,B) ),
inference(rewrite,[status(thm)],[complement2]),
[] ).
fof(prove_members_of_union2_2,plain,
~ member(x,union(y,z)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),
[] ).
cnf(173646824,plain,
~ member(x,union(y,z)),
inference(rewrite,[status(thm)],[prove_members_of_union2_2]),
[] ).
fof(union,plain,
! [A,B] : $equal(complement(intersection(complement(A),complement(B))),union(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),
[] ).
cnf(172683880,plain,
$equal(complement(intersection(complement(A),complement(B))),union(A,B)),
inference(rewrite,[status(thm)],[union]),
[] ).
cnf(186795840,plain,
~ member(x,complement(intersection(complement(y),complement(z)))),
inference(paramodulation,[status(thm)],[173646824,172683880,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[187737368,196397064,172674440,186795840]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 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/SET167-6.tptp',unknown),[]).
%
% cnf(172452864,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/SET167-6.tptp',unknown),[]).
%
% cnf(172483992,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% cnf(184719072,plain,(~member(B,A)|member(B,universal_class)),inference(resolution,[status(thm)],[172452864,172483992]),[]).
%
% fof(prove_members_of_union2_1,plain,(member(x,y)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),[]).
%
% cnf(173642984,plain,(member(x,y)),inference(rewrite,[status(thm)],[prove_members_of_union2_1]),[]).
%
% cnf(187737368,plain,(member(x,universal_class)),inference(resolution,[status(thm)],[184719072,173642984]),[]).
%
% fof(intersection1,plain,(~member(A,intersection(B,C))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),[]).
%
% cnf(172644056,plain,(~member(A,intersection(B,C))|member(A,B)),inference(rewrite,[status(thm)],[intersection1]),[]).
%
% fof(complement1,plain,(~member(A,complement(B))|~member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),[]).
%
% cnf(172663176,plain,(~member(A,complement(B))|~member(A,B)),inference(rewrite,[status(thm)],[complement1]),[]).
%
% cnf(187485240,plain,(~member(x,complement(y))),inference(resolution,[status(thm)],[172663176,173642984]),[]).
%
% cnf(196397064,plain,(~member(x,intersection(complement(y),A))),inference(resolution,[status(thm)],[172644056,187485240]),[]).
%
% fof(complement2,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),[]).
%
% cnf(172674440,plain,(~member(A,universal_class)|member(A,complement(B))|member(A,B)),inference(rewrite,[status(thm)],[complement2]),[]).
%
% fof(prove_members_of_union2_2,plain,(~member(x,union(y,z))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),[]).
%
% cnf(173646824,plain,(~member(x,union(y,z))),inference(rewrite,[status(thm)],[prove_members_of_union2_2]),[]).
%
% fof(union,plain,($equal(complement(intersection(complement(A),complement(B))),union(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET167-6.tptp',unknown),[]).
%
% cnf(172683880,plain,($equal(complement(intersection(complement(A),complement(B))),union(A,B))),inference(rewrite,[status(thm)],[union]),[]).
%
% cnf(186795840,plain,(~member(x,complement(intersection(complement(y),complement(z))))),inference(paramodulation,[status(thm)],[173646824,172683880,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[187737368,196397064,172674440,186795840]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------