## TPTP Problem File: SWB028+2.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWB028+2 : TPTP v7.5.0. Released v5.2.0.
% Domain   : Semantic Web
% Problem  : Inferred Property Characteristics III
% Version  : [Sch11] axioms : Reduced > Incomplete.
% English  :

% Refs     : [Sch11] Schneider, M. (2011), Email to G. Sutcliffe
% Source   : [Sch11]
% Names    : 028_Inferred_Property_Characteristics_III [Sch11]

% Status   : Theorem
% Rating   : 0.22 v7.4.0, 0.17 v7.3.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.20 v6.0.0, 0.17 v5.5.0, 0.22 v5.4.0, 0.25 v5.3.0, 0.26 v5.2.0
% Syntax   : Number of formulae    :   11 (   2 unit)
%            Number of atoms       :   42 (   2 equality)
%            Maximal formula depth :    9 (   6 average)
%            Number of connectives :   31 (   0   ~;   0   |;  17   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    5 (   0 propositional; 1-3 arity)
%            Number of functors    :   10 (  10 constant; 0-0 arity)
%            Number of variables   :   28 (   0 sgn;  26   !;   2   ?)
%            Maximal term depth    :    1 (   1 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
fof(owl_class_inversefunctionalproperty_type,axiom,(
ic(uri_owl_InverseFunctionalProperty) )).

fof(owl_prop_inverseof_ext,axiom,(
! [X,Y] :
( iext(uri_owl_inverseOf,X,Y)
=> ( ip(X)
& ip(Y) ) ) )).

fof(owl_prop_equivalentclass_ext,axiom,(
! [X,Y] :
( iext(uri_owl_equivalentClass,X,Y)
=> ( ic(X)
& ic(Y) ) ) )).

fof(owl_char_functional,axiom,(
! [P] :
( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X,Y1,Y2] :
( ( iext(P,X,Y1)
& iext(P,X,Y2) )
=> Y1 = Y2 ) ) ) )).

fof(owl_char_inversefunctional,axiom,(
! [P] :
( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1,X2,Y] :
( ( iext(P,X1,Y)
& iext(P,X2,Y) )
=> X1 = X2 ) ) ) )).

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_eqdis_equivalentclass,axiom,(
! [C1,C2] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X] :
( icext(C1,X)
<=> icext(C2,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_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_028_Inferred_Property_Characteristics_III,conjecture,(
iext(uri_rdfs_subClassOf,uri_ex_InversesOfFunctionalProperties,uri_owl_InverseFunctionalProperty) )).

fof(testcase_premise_fullish_028_Inferred_Property_Characteristics_III,axiom,(
? [BNODE_z] :
( iext(uri_owl_equivalentClass,uri_ex_InversesOfFunctionalProperties,BNODE_z)
& iext(uri_rdf_type,BNODE_z,uri_owl_Restriction)
& iext(uri_owl_onProperty,BNODE_z,uri_owl_inverseOf)
& iext(uri_owl_someValuesFrom,BNODE_z,uri_owl_FunctionalProperty) ) )).

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