%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET479-6 : 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 15:31:07 EDT 2009
% Result : Unsatisfiable 4.7s
% Output : Refutation 4.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 5 sgn 8 !; 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/SET479-6.tptp',unknown),
[] ).
cnf(162352072,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(definition_of_domain_relation1,plain,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),
[] ).
cnf(163394056,plain,
subclass(domain_relation,cross_product(universal_class,universal_class)),
inference(rewrite,[status(thm)],[definition_of_domain_relation1]),
[] ).
cnf(179095672,plain,
( ~ member(A,domain_relation)
| member(A,cross_product(universal_class,universal_class)) ),
inference(resolution,[status(thm)],[162352072,163394056]),
[] ).
fof(cartesian_product2,plain,
! [A,B,C,D] :
( ~ member(ordered_pair(A,B),cross_product(C,D))
| member(B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),
[] ).
cnf(162484320,plain,
( ~ member(ordered_pair(A,B),cross_product(C,D))
| member(B,D) ),
inference(rewrite,[status(thm)],[cartesian_product2]),
[] ).
fof(prove_replacement_property1_2,plain,
~ member(domain_of(x),universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),
[] ).
cnf(163530856,plain,
~ member(domain_of(x),universal_class),
inference(rewrite,[status(thm)],[prove_replacement_property1_2]),
[] ).
cnf(178546344,plain,
~ member(ordered_pair(A,domain_of(x)),cross_product(B,universal_class)),
inference(resolution,[status(thm)],[162484320,163530856]),
[] ).
cnf(239366416,plain,
~ member(ordered_pair(A,domain_of(x)),domain_relation),
inference(resolution,[status(thm)],[179095672,178546344]),
[] ).
fof(definition_of_domain_relation3,plain,
! [A] :
( ~ member(A,universal_class)
| member(ordered_pair(A,domain_of(A)),domain_relation) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),
[] ).
cnf(163409552,plain,
( ~ member(A,universal_class)
| member(ordered_pair(A,domain_of(A)),domain_relation) ),
inference(rewrite,[status(thm)],[definition_of_domain_relation3]),
[] ).
fof(prove_replacement_property1_1,plain,
member(x,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),
[] ).
cnf(163527168,plain,
member(x,universal_class),
inference(rewrite,[status(thm)],[prove_replacement_property1_1]),
[] ).
cnf(175130560,plain,
member(ordered_pair(x,domain_of(x)),domain_relation),
inference(resolution,[status(thm)],[163409552,163527168]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[239366416,175130560]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 4 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/SET479-6.tptp',unknown),[]).
%
% cnf(162352072,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(definition_of_domain_relation1,plain,(subclass(domain_relation,cross_product(universal_class,universal_class))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),[]).
%
% cnf(163394056,plain,(subclass(domain_relation,cross_product(universal_class,universal_class))),inference(rewrite,[status(thm)],[definition_of_domain_relation1]),[]).
%
% cnf(179095672,plain,(~member(A,domain_relation)|member(A,cross_product(universal_class,universal_class))),inference(resolution,[status(thm)],[162352072,163394056]),[]).
%
% fof(cartesian_product2,plain,(~member(ordered_pair(A,B),cross_product(C,D))|member(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),[]).
%
% cnf(162484320,plain,(~member(ordered_pair(A,B),cross_product(C,D))|member(B,D)),inference(rewrite,[status(thm)],[cartesian_product2]),[]).
%
% fof(prove_replacement_property1_2,plain,(~member(domain_of(x),universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),[]).
%
% cnf(163530856,plain,(~member(domain_of(x),universal_class)),inference(rewrite,[status(thm)],[prove_replacement_property1_2]),[]).
%
% cnf(178546344,plain,(~member(ordered_pair(A,domain_of(x)),cross_product(B,universal_class))),inference(resolution,[status(thm)],[162484320,163530856]),[]).
%
% cnf(239366416,plain,(~member(ordered_pair(A,domain_of(x)),domain_relation)),inference(resolution,[status(thm)],[179095672,178546344]),[]).
%
% fof(definition_of_domain_relation3,plain,(~member(A,universal_class)|member(ordered_pair(A,domain_of(A)),domain_relation)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),[]).
%
% cnf(163409552,plain,(~member(A,universal_class)|member(ordered_pair(A,domain_of(A)),domain_relation)),inference(rewrite,[status(thm)],[definition_of_domain_relation3]),[]).
%
% fof(prove_replacement_property1_1,plain,(member(x,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET479-6.tptp',unknown),[]).
%
% cnf(163527168,plain,(member(x,universal_class)),inference(rewrite,[status(thm)],[prove_replacement_property1_1]),[]).
%
% cnf(175130560,plain,(member(ordered_pair(x,domain_of(x)),domain_relation)),inference(resolution,[status(thm)],[163409552,163527168]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[239366416,175130560]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------