## TPTP Problem File: SWB010+2.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWB010+2 : TPTP v7.5.0. Released v5.2.0.
% Domain   : Semantic Web
% Problem  : Negative Property Assertions
% Version  : [Sch11] axioms : Reduced > Incomplete.
% English  :

% Refs     : [Sch11] Schneider, M. (2011), Email to G. Sutcliffe
% Source   : [Sch11]
% Names    : 010_Negative_Property_Assertions [Sch11]

% Status   : Theorem
% Rating   : 0.33 v7.5.0, 0.34 v7.4.0, 0.30 v7.3.0, 0.28 v7.2.0, 0.24 v7.1.0, 0.22 v7.0.0, 0.17 v6.4.0, 0.23 v6.3.0, 0.17 v6.2.0, 0.28 v6.1.0, 0.23 v6.0.0, 0.26 v5.5.0, 0.22 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0
% Syntax   : Number of formulae    :   10 (   1 unit)
%            Number of atoms       :   44 (   1 equality)
%            Maximal formula depth :   12 (   7 average)
%            Number of connectives :   36 (   2   ~;   0   |;  22   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    6 (   0 propositional; 1-3 arity)
%            Number of functors    :   17 (  17 constant; 0-0 arity)
%            Number of variables   :   28 (   0 sgn;  22   !;   6   ?)
%            Maximal term depth    :    1 (   1 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
fof(simple_ir,axiom,(
! [X] : ir(X) )).

fof(rdfs_cext_def,axiom,(
! [X,C] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) )).

fof(owl_prop_sourceindividual_ext,axiom,(
! [X,Y] :
( iext(uri_owl_sourceIndividual,X,Y)
=> ( icext(uri_owl_NegativePropertyAssertion,X)
& ir(Y) ) ) )).

fof(owl_prop_onproperty_ext,axiom,(
! [X,Y] :
( iext(uri_owl_onProperty,X,Y)
=> ( icext(uri_owl_Restriction,X)
& ip(Y) ) ) )).

fof(owl_bool_complementof_class,axiom,(
! [Z,C] :
( iext(uri_owl_complementOf,Z,C)
=> ( ic(Z)
& ic(C)
& ! [X] :
( icext(Z,X)
<=> ~ icext(C,X) ) ) ) )).

fof(owl_enum_class_001,axiom,(
! [Z,S1,A1] :
( ( iext(uri_rdf_first,S1,A1)
& iext(uri_rdf_rest,S1,uri_rdf_nil) )
=> ( iext(uri_owl_oneOf,Z,S1)
<=> ( ic(Z)
& ! [X] :
( icext(Z,X)
<=> X = A1 ) ) ) ) )).

fof(owl_restrict_allvaluesfrom,axiom,(
! [Z,P,C] :
( ( iext(uri_owl_allValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
=> ! [X] :
( icext(Z,X)
<=> ! [Y] :
( iext(P,X,Y)
=> icext(C,Y) ) ) ) )).

fof(owl_npa_object_fi,axiom,(
! [P,A1,A2] :
( ( ir(A1)
& ip(P)
& ir(A2)
& ~ iext(P,A1,A2) )
=> ? [Z] :
( iext(uri_owl_sourceIndividual,Z,A1)
& iext(uri_owl_assertionProperty,Z,P)
& iext(uri_owl_targetIndividual,Z,A2) ) ) )).

fof(testcase_conclusion_fullish_010_Negative_Property_Assertions,conjecture,(
? [BNODE_z] :
( iext(uri_rdf_type,BNODE_z,uri_owl_NegativePropertyAssertion)
& iext(uri_owl_sourceIndividual,BNODE_z,uri_ex_s)
& iext(uri_owl_assertionProperty,BNODE_z,uri_ex_p)
& iext(uri_owl_targetIndividual,BNODE_z,uri_ex_o) ) )).

fof(testcase_premise_fullish_010_Negative_Property_Assertions,axiom,(
? [BNODE_x1,BNODE_x2,BNODE_x3,BNODE_x4] :
( iext(uri_rdf_type,uri_ex_p,uri_owl_ObjectProperty)
& iext(uri_rdf_type,uri_ex_s,BNODE_x1)
& iext(uri_owl_onProperty,BNODE_x1,uri_ex_p)
& iext(uri_owl_allValuesFrom,BNODE_x1,BNODE_x2)
& iext(uri_owl_complementOf,BNODE_x2,BNODE_x3)
& iext(uri_owl_oneOf,BNODE_x3,BNODE_x4)
& iext(uri_rdf_first,BNODE_x4,uri_ex_o)
& iext(uri_rdf_rest,BNODE_x4,uri_rdf_nil) ) )).

%------------------------------------------------------------------------------
```