%------------------------------------------------------------------------------
% File     : SWB028+2 : TPTP v8.2.0. 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 v8.2.0, 0.19 v8.1.0, 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 unt;   0 def)
%            Number of atoms       :   42 (   2 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   31 (   0   ~;   0   |;  17   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   0 prp; 1-3 aty)
%            Number of functors    :   10 (  10 usr;  10 con; 0-0 aty)
%            Number of variables   :   28 (  26   !;   2   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%------------------------------------------------------------------------------
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) ) ).

%------------------------------------------------------------------------------