%------------------------------------------------------------------------------
% File     : KRS172+1 : TPTP v8.2.0. Released v3.1.0.
% Domain   : Knowledge Representation (Semantic Web)
% Problem  : The same property extension means equivalentProperty
% Version  : Especial.
% English  : If p and q have the same property extension then p
%            equivalentProperty q.

% Refs     : [Bec03] Bechhofer (2003), Email to G. Sutcliffe
%          : [TR+04] Tsarkov et al. (2004), Using Vampire to Reason with OW
% Source   : [Bec03]
% Names    : positive_equivalentProperty-Manifest004 [Bec03]

% Status   : Theorem
% Rating   : 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v4.1.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.12 v3.7.0, 0.00 v3.2.0, 0.11 v3.1.0
% Syntax   : Number of formulae    :   19 (   1 unt;   0 def)
%            Number of atoms       :   52 (  11 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   37 (   4   ~;   0   |;  15   &)
%                                         (   5 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   0 prp; 1-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   40 (  40   !;   0   ?)
% SPC      : FOF_THM_EPR_SEQ

% Comments : Sean Bechhofer says there are some errors in the encoding of
%            datatypes, so this problem may not be perfect. At least it's
%            still representative of the type of reasoning required for OWL.
%------------------------------------------------------------------------------
fof(cd_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cd(A) )
     => cd(B) ) ).

fof(cowlNothing_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cowlNothing(A) )
     => cowlNothing(B) ) ).

fof(cowlThing_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cowlThing(A) )
     => cowlThing(B) ) ).

fof(rp_substitution_1,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rp(A,C) )
     => rp(B,C) ) ).

fof(rp_substitution_2,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rp(C,A) )
     => rp(C,B) ) ).

fof(rq_substitution_1,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rq(A,C) )
     => rq(B,C) ) ).

fof(rq_substitution_2,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rq(C,A) )
     => rq(C,B) ) ).

fof(xsd_integer_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & xsd_integer(A) )
     => xsd_integer(B) ) ).

fof(xsd_string_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & xsd_string(A) )
     => xsd_string(B) ) ).

%----Thing and Nothing
fof(axiom_0,axiom,
    ! [X] :
      ( cowlThing(X)
      & ~ cowlNothing(X) ) ).

%----String and Integer disjoint
fof(axiom_1,axiom,
    ! [X] :
      ( xsd_string(X)
    <=> ~ xsd_integer(X) ) ).

%----Equality cd
fof(axiom_2,axiom,
    ! [X] :
      ( cd(X)
    <=> rq(X,iv) ) ).

%----Equality cd
fof(axiom_3,axiom,
    ! [X] :
      ( cd(X)
    <=> rp(X,iv) ) ).

%----Functional: rp
fof(axiom_4,axiom,
    ! [X,Y,Z] :
      ( ( rp(X,Y)
        & rp(X,Z) )
     => Y = Z ) ).

%----Domain: rp
fof(axiom_5,axiom,
    ! [X,Y] :
      ( rp(X,Y)
     => cd(X) ) ).

%----Functional: rq
fof(axiom_6,axiom,
    ! [X,Y,Z] :
      ( ( rq(X,Y)
        & rq(X,Z) )
     => Y = Z ) ).

%----Domain: rq
fof(axiom_7,axiom,
    ! [X,Y] :
      ( rq(X,Y)
     => cd(X) ) ).

%----iv
fof(axiom_8,axiom,
    cowlThing(iv) ).

%----Thing and Nothing
%----String and Integer disjoint
fof(the_axiom,conjecture,
    ( ! [X] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & ! [X,Y] :
        ( rq(X,Y)
      <=> rp(X,Y) ) ) ).

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