TPTP Problem File: SWB013+2.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWB013+2 : TPTP v8.2.0. Released v5.2.0.
% Domain : Semantic Web
% Problem : Cliques
% Version : [Sch11] axioms : Reduced > Incomplete.
% English :
% Refs : [Sch11] Schneider, M. (2011), Email to G. Sutcliffe
% Source : [Sch11]
% Names : 013_Cliques [Sch11]
% Status : Theorem
% Rating : 0.28 v7.5.0, 0.31 v7.4.0, 0.27 v7.3.0, 0.17 v7.2.0, 0.21 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.21 v6.2.0, 0.32 v6.1.0, 0.40 v6.0.0, 0.48 v5.4.0, 0.50 v5.3.0, 0.52 v5.2.0
% Syntax : Number of formulae : 9 ( 1 unt; 0 def)
% Number of atoms : 59 ( 1 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 50 ( 0 ~; 0 |; 37 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 0 prp; 1-3 aty)
% Number of functors : 21 ( 21 usr; 21 con; 0-0 aty)
% Number of variables : 36 ( 30 !; 6 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
fof(rdfs_cext_def,axiom,
! [X,C] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ).
fof(owl_restrict_somevaluesfrom,axiom,
! [Z,P,C] :
( ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
=> ! [X] :
( icext(Z,X)
<=> ? [Y] :
( iext(P,X,Y)
& icext(C,Y) ) ) ) ).
fof(owl_rdfsext_subclassof,axiom,
! [C1,C2] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X] :
( icext(C1,X)
=> icext(C2,X) ) ) ) ).
fof(owl_rdfsext_subpropertyof,axiom,
! [P1,P2] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X,Y] :
( iext(P1,X,Y)
=> iext(P2,X,Y) ) ) ) ).
fof(owl_eqdis_sameas,axiom,
! [X,Y] :
( iext(uri_owl_sameAs,X,Y)
<=> X = Y ) ).
fof(owl_chain_003,axiom,
! [P,S1,P1,S2,P2,S3,P3] :
( ( iext(uri_rdf_first,S1,P1)
& iext(uri_rdf_rest,S1,S2)
& iext(uri_rdf_first,S2,P2)
& iext(uri_rdf_rest,S2,S3)
& iext(uri_rdf_first,S3,P3)
& iext(uri_rdf_rest,S3,uri_rdf_nil) )
=> ( iext(uri_owl_propertyChainAxiom,P,S1)
<=> ( ip(P)
& ip(P1)
& ip(P2)
& ip(P3)
& ! [Y0,Y1,Y2,Y3] :
( ( iext(P1,Y0,Y1)
& iext(P2,Y1,Y2)
& iext(P3,Y2,Y3) )
=> iext(P,Y0,Y3) ) ) ) ) ).
fof(owl_inv,axiom,
! [P1,P2] :
( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X,Y] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) ).
fof(testcase_conclusion_fullish_013_Cliques,conjecture,
iext(uri_foaf_knows,uri_ex_alice,uri_ex_bob) ).
fof(testcase_premise_fullish_013_Cliques,axiom,
? [BNODE_r,BNODE_i,BNODE_l1,BNODE_l2,BNODE_l3] :
( iext(uri_rdf_type,uri_ex_Clique,uri_owl_Class)
& iext(uri_rdfs_subPropertyOf,uri_ex_sameCliqueAs,uri_owl_sameAs)
& iext(uri_rdfs_range,uri_ex_sameCliqueAs,uri_ex_Clique)
& iext(uri_rdfs_subClassOf,uri_ex_Clique,BNODE_r)
& iext(uri_rdf_type,BNODE_r,uri_owl_Restriction)
& iext(uri_owl_onProperty,BNODE_r,uri_ex_sameCliqueAs)
& iext(uri_owl_someValuesFrom,BNODE_r,uri_ex_Clique)
& iext(uri_rdf_type,uri_foaf_knows,uri_owl_ObjectProperty)
& iext(uri_owl_propertyChainAxiom,uri_foaf_knows,BNODE_l1)
& iext(uri_rdf_first,BNODE_l1,uri_rdf_type)
& iext(uri_rdf_rest,BNODE_l1,BNODE_l2)
& iext(uri_rdf_first,BNODE_l2,uri_ex_sameCliqueAs)
& iext(uri_rdf_rest,BNODE_l2,BNODE_l3)
& iext(uri_rdf_first,BNODE_l3,BNODE_i)
& iext(uri_rdf_rest,BNODE_l3,uri_rdf_nil)
& iext(uri_owl_inverseOf,BNODE_i,uri_rdf_type)
& iext(uri_rdf_type,uri_ex_JoesGang,uri_ex_Clique)
& iext(uri_rdf_type,uri_ex_alice,uri_ex_JoesGang)
& iext(uri_rdf_type,uri_ex_bob,uri_ex_JoesGang) ) ).
%------------------------------------------------------------------------------