TPTP Axioms File: SWB003+0.ax


%------------------------------------------------------------------------------
% File     : SWB003+0 : TPTP v7.5.0. Released v5.2.0.
% Domain   : Semantic Web
% Axioms   : RDFS
% Version  : [Sch03] axioms : Especial.
% English  :

% Refs     : [Sch03] Schneider, M. (2011), Email to G. Sutcliffe
% Source   : [Sch03]
% Names    : axioms-rdfs-standard [Sch03]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   80 (  62 unit)
%            Number of atoms       :  108 (   0 equality)
%            Maximal formula depth :    9 (   2 average)
%            Number of connectives :   28 (   0   ~;   0   |;   8   &)
%                                         (   5 <=>;  15  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    6 (   0 propositional; 1-3 arity)
%            Number of functors    :   33 (  33 constant; 0-0 arity)
%            Number of variables   :   37 (   0 sgn;  37   !;   0   ?)
%            Maximal term depth    :    1 (   1 average)
% SPC      : FOF_SAT_EPR

% Comments :
%------------------------------------------------------------------------------
%----I(s p o) = true -> I(p) in IP
%----Note: the "iext" predicate seems to represent a true triple,
%----not quite the IEXT mapping [CHECK!]
fof(simple_iext_property,axiom,(
    ! [S,P,O] :
      ( iext(P,S,O)
     => ip(P) ) )).

%----Set IR
%----The set IR is the set of all resources.

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

%----Set LV
%----The set LV of all data values is a subset of IR.
fof(simple_lv,axiom,(
    ! [X] :
      ( lv(X)
     => ir(X) ) )).

%----Axiomatic Triples for the Collection Vocabulary (Lists): rdf:first
fof(rdf_collection_first_type,axiom,(
    iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property) )).

%----Axiomatic Triples for the Collection Vocabulary (Lists): rdf:nil
fof(rdf_collection_nil_type,axiom,(
    iext(uri_rdf_type,uri_rdf_nil,uri_rdf_List) )).

%----Axiomatic Triples for the Collection Vocabulary (Lists): rdf:rest
fof(rdf_collection_rest_type,axiom,(
    iext(uri_rdf_type,uri_rdf_rest,uri_rdf_Property) )).

%----Axiomatic Triples for the Container Vocabulary: rdf:_n
fof(rdf_container_n_type_001,axiom,(
    iext(uri_rdf_type,uri_rdf__1,uri_rdf_Property) )).

%----Axiomatic Triples for the Container Vocabulary: rdf:_n
fof(rdf_container_n_type_002,axiom,(
    iext(uri_rdf_type,uri_rdf__2,uri_rdf_Property) )).

%----Axiomatic Triples for the Container Vocabulary: rdf:_n
fof(rdf_container_n_type_003,axiom,(
    iext(uri_rdf_type,uri_rdf__3,uri_rdf_Property) )).

%----Axiomatic Triples for the Reification Vocabulary: rdf:object
fof(rdf_reification_object_type,axiom,(
    iext(uri_rdf_type,uri_rdf_object,uri_rdf_Property) )).

%----Axiomatic Triples for rdf:value--
fof(rdf_reification_predicate_type,axiom,(
    iext(uri_rdf_type,uri_rdf_value,uri_rdf_Property) )).

%----Axiomatic Triples for the Reification Vocabulary: rdf:subject
fof(rdf_reification_subject_type,axiom,(
    iext(uri_rdf_type,uri_rdf_subject,uri_rdf_Property) )).

%----IP and rdf:Property
fof(rdf_type_ip,axiom,(
    ! [P] :
      ( iext(uri_rdf_type,P,uri_rdf_Property)
    <=> ip(P) ) )).

%----Axiomatic Triple for rdf:type
fof(rdf_type_type,axiom,(
    iext(uri_rdf_type,uri_rdf_type,uri_rdf_Property) )).

%----Axiomatic Triple for rdf:type
fof(rdf_value_type,axiom,(
    iext(uri_rdf_type,uri_rdf_type,uri_rdf_Property) )).

fof(rdfs_annotation_comment_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdfs_comment,uri_rdfs_Resource) )).

fof(rdfs_annotation_comment_range,axiom,(
    iext(uri_rdfs_range,uri_rdfs_comment,uri_rdfs_Literal) )).

fof(rdfs_annotation_isdefinedby_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdfs_isDefinedBy,uri_rdfs_Resource) )).

fof(rdfs_annotation_isdefinedby_range,axiom,(
    iext(uri_rdfs_range,uri_rdfs_isDefinedBy,uri_rdfs_Resource) )).

fof(rdfs_annotation_isdefinedby_sub,axiom,(
    iext(uri_rdfs_subPropertyOf,uri_rdfs_isDefinedBy,uri_rdfs_seeAlso) )).

fof(rdfs_annotation_label_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdfs_label,uri_rdfs_Resource) )).

fof(rdfs_annotation_label_range,axiom,(
    iext(uri_rdfs_range,uri_rdfs_label,uri_rdfs_Literal) )).

fof(rdfs_annotation_seealso_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdfs_seeAlso,uri_rdfs_Resource) )).

fof(rdfs_annotation_seealso_range,axiom,(
    iext(uri_rdfs_range,uri_rdfs_seeAlso,uri_rdfs_Resource) )).

%----Definition of ICEXT
fof(rdfs_cext_def,axiom,(
    ! [X,C] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ) )).

%----IC and rdfs:Resource
fof(rdfs_class_instsub_resource,axiom,(
    ! [C] :
      ( ic(C)
     => iext(uri_rdfs_subClassOf,C,uri_rdfs_Resource) ) )).

%----IC and rdfs:Resource
fof(rdfs_collection_first_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdf_first,uri_rdf_List) )).

%----IC and rdfs:Resource
fof(rdfs_collection_first_range,axiom,(
    iext(uri_rdfs_range,uri_rdf_first,uri_rdfs_Resource) )).

fof(rdfs_collection_rest_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdf_rest,uri_rdf_List) )).

fof(rdfs_collection_rest_range,axiom,(
    iext(uri_rdfs_range,uri_rdf_rest,uri_rdf_List) )).

fof(rdfs_container_alt_sub,axiom,(
    iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container) )).

fof(rdfs_container_bag_sub,axiom,(
    iext(uri_rdfs_subClassOf,uri_rdf_Bag,uri_rdfs_Container) )).

%----rdfs:ContainerMembershipProperty
fof(rdfs_container_containermembershipproperty_instsub_member,axiom,(
    ! [P] :
      ( icext(uri_rdfs_ContainerMembershipProperty,P)
     => iext(uri_rdfs_subPropertyOf,P,uri_rdfs_member) ) )).

fof(rdfs_container_containermembershipproperty_sub,axiom,(
    iext(uri_rdfs_subClassOf,uri_rdfs_ContainerMembershipProperty,uri_rdf_Property) )).

fof(rdfs_container_member_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdfs_member,uri_rdfs_Resource) )).

fof(rdfs_container_member_range,axiom,(
    iext(uri_rdfs_range,uri_rdfs_member,uri_rdfs_Resource) )).

fof(rdfs_container_n_domain_001,axiom,(
    iext(uri_rdfs_domain,uri_rdf__1,uri_rdfs_Resource) )).

fof(rdfs_container_n_domain_002,axiom,(
    iext(uri_rdfs_domain,uri_rdf__2,uri_rdfs_Resource) )).

fof(rdfs_container_n_domain_003,axiom,(
    iext(uri_rdfs_domain,uri_rdf__3,uri_rdfs_Resource) )).

fof(rdfs_container_n_range_001,axiom,(
    iext(uri_rdfs_range,uri_rdf__1,uri_rdfs_Resource) )).

fof(rdfs_container_n_range_002,axiom,(
    iext(uri_rdfs_range,uri_rdf__2,uri_rdfs_Resource) )).

fof(rdfs_container_n_range_003,axiom,(
    iext(uri_rdfs_range,uri_rdf__3,uri_rdfs_Resource) )).

fof(rdfs_container_n_type_001,axiom,(
    iext(uri_rdf_type,uri_rdf__1,uri_rdfs_ContainerMembershipProperty) )).

fof(rdfs_container_n_type_002,axiom,(
    iext(uri_rdf_type,uri_rdf__2,uri_rdfs_ContainerMembershipProperty) )).

fof(rdfs_container_n_type_003,axiom,(
    iext(uri_rdf_type,uri_rdf__3,uri_rdfs_ContainerMembershipProperty) )).

fof(rdfs_container_seq_sub,axiom,(
    iext(uri_rdfs_subClassOf,uri_rdfs_Seq,uri_rdfs_Container) )).

fof(rdfs_dat_xmlliteral_sub,axiom,(
    iext(uri_rdfs_subClassOf,uri_rdf_XMLLiteral,uri_rdfs_Literal) )).

%----type of rdf:XMLLiteral
fof(rdfs_dat_xmlliteral_type,axiom,(
    iext(uri_rdf_type,uri_rdf_XMLLiteral,uri_rdfs_Datatype) )).

%----rdfs:Datatype and rdfs:Literal
fof(rdfs_datatype_instsub_literal,axiom,(
    ! [D] :
      ( icext(uri_rdfs_Datatype,D)
     => iext(uri_rdfs_subClassOf,D,uri_rdfs_Literal) ) )).

%----rdfs:Datatype is a sub class of rdfs:Class
fof(rdfs_datatype_sub,axiom,(
    iext(uri_rdfs_subClassOf,uri_rdfs_Datatype,uri_rdfs_Class) )).

%----domain of rdfs:domain
fof(rdfs_domain_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdfs_domain,uri_rdf_Property) )).

%----Semantic Condition for rdfs:domain
fof(rdfs_domain_main,axiom,(
    ! [P,C,X,Y] :
      ( ( iext(uri_rdfs_domain,P,C)
        & iext(P,X,Y) )
     => icext(C,X) ) )).

%----range of rdfs:domain
fof(rdfs_domain_range,axiom,(
    iext(uri_rdfs_range,uri_rdfs_domain,uri_rdfs_Class) )).

%----Definition of set IC based on class extensions of rdfs:Class
fof(rdfs_ic_def,axiom,(
    ! [X] :
      ( ic(X)
    <=> icext(uri_rdfs_Class,X) ) )).

%----Definition of set IR based on class extensions of rdfs:Resource
fof(rdfs_ir_def,axiom,(
    ! [X] :
      ( ir(X)
    <=> icext(uri_rdfs_Resource,X) ) )).

%----Definition of set LV based on class extensions of rdfs:Literal
fof(rdfs_lv_def,axiom,(
    ! [X] :
      ( lv(X)
    <=> icext(uri_rdfs_Literal,X) ) )).

%----type of rdf:Property (derivable RDFS-valid triple)
fof(rdfs_property_type,axiom,(
    iext(uri_rdf_type,uri_rdf_Property,uri_rdfs_Class) )).

%----domain of rdfs:range
fof(rdfs_range_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdfs_range,uri_rdf_Property) )).

%----Semantic Condition for rdfs:range
fof(rdfs_range_main,axiom,(
    ! [P,C,X,Y] :
      ( ( iext(uri_rdfs_range,P,C)
        & iext(P,X,Y) )
     => icext(C,Y) ) )).

%----range of rdfs:range
fof(rdfs_range_range,axiom,(
    iext(uri_rdfs_range,uri_rdfs_range,uri_rdfs_Class) )).

fof(rdfs_reification_object_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdf_object,uri_rdfs_Statement) )).

fof(rdfs_reification_object_range,axiom,(
    iext(uri_rdfs_range,uri_rdf_predicate,uri_rdfs_Resource) )).

fof(rdfs_reification_predicate_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdf_predicate,uri_rdfs_Statement) )).

fof(rdfs_reification_predicate_range,axiom,(
    iext(uri_rdfs_range,uri_rdf_predicate,uri_rdfs_Resource) )).

fof(rdfs_reification_subject_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdf_subject,uri_rdfs_Statement) )).

fof(rdfs_reification_subject_range,axiom,(
    iext(uri_rdfs_range,uri_rdf_subject,uri_rdfs_Resource) )).

%----domain of rdfs:subClassOf
fof(rdfs_subclassof_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdfs_subClassOf,uri_rdfs_Class) )).

%----Main Semantic Conditions for rdfs:subClassOf
fof(rdfs_subclassof_main,axiom,(
    ! [C,D] :
      ( iext(uri_rdfs_subClassOf,C,D)
     => ( ic(C)
        & ic(D)
        & ! [X] :
            ( icext(C,X)
           => icext(D,X) ) ) ) )).

%----range of rdfs:subClassOf
fof(rdfs_subclassof_range,axiom,(
    iext(uri_rdfs_range,uri_rdfs_subClassOf,uri_rdfs_Class) )).

%----Reflexivity of rdfs:subClassOf on IC
fof(rdfs_subclassof_reflex,axiom,(
    ! [C] :
      ( ic(C)
     => iext(uri_rdfs_subClassOf,C,C) ) )).

%----Transitivity of rdfs:subClassOf on IC
fof(rdfs_subclassof_trans,axiom,(
    ! [C,D,E] :
      ( ( iext(uri_rdfs_subClassOf,C,D)
        & iext(uri_rdfs_subClassOf,D,E) )
     => iext(uri_rdfs_subClassOf,C,E) ) )).

%----domain of rdfs:subPropertyOf
fof(rdfs_subpropertyof_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdfs_subPropertyOf,uri_rdf_Property) )).

%----Main Semantic Condition for rdfs:subPropertyOf
fof(rdfs_subpropertyof_main,axiom,(
    ! [P,Q] :
      ( iext(uri_rdfs_subPropertyOf,P,Q)
     => ( ip(P)
        & ip(Q)
        & ! [X,Y] :
            ( iext(P,X,Y)
           => iext(Q,X,Y) ) ) ) )).

%----range of rdfs:subPropertyOf
fof(rdfs_subpropertyof_range,axiom,(
    iext(uri_rdfs_range,uri_rdfs_subPropertyOf,uri_rdf_Property) )).

%----Reflexivity of rdfs:subPropertyOf on IP
fof(rdfs_subpropertyof_reflex,axiom,(
    ! [P] :
      ( ip(P)
     => iext(uri_rdfs_subPropertyOf,P,P) ) )).

%----Transitivity of rdfs:subPropertyOf on IP
fof(rdfs_subpropertyof_trans,axiom,(
    ! [P,Q,R] :
      ( ( iext(uri_rdfs_subPropertyOf,P,Q)
        & iext(uri_rdfs_subPropertyOf,Q,R) )
     => iext(uri_rdfs_subPropertyOf,P,R) ) )).

%----domain of rdf:type
fof(rdfs_type_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdf_type,uri_rdfs_Resource) )).

%----range of rdf:type
fof(rdfs_type_range,axiom,(
    iext(uri_rdfs_range,uri_rdf_type,uri_rdfs_Class) )).

fof(rdfs_value_domain,axiom,(
    iext(uri_rdfs_domain,uri_rdf_value,uri_rdfs_Resource) )).

fof(rdfs_value_range,axiom,(
    iext(uri_rdfs_range,uri_rdf_value,uri_rdfs_Resource) )).

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