%------------------------------------------------------------------------------
% File     : KRS143+1 : TPTP v9.0.0. Released v3.1.0.
% Domain   : Knowledge Representation (Semantic Web)
% Problem  : An owl:cardinality constraint is simply shorthand
% Version  : Especial.
% English  : An owl:cardinality constraint is simply shorthand for a pair of
%            owl:minCardinality and owl:maxCardinality constraints.

% Refs     : [Bec03] Bechhofer (2003), Email to G. Sutcliffe
%          : [TR+04] Tsarkov et al. (2004), Using Vampire to Reason with OW
% Source   : [Bec03]
% Names    : positive_cardinality-Manifest002 [Bec03]

% Status   : Theorem
% Rating   : 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.1.0, 0.03 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.00 v4.1.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.00 v3.2.0, 0.11 v3.1.0
% Syntax   : Number of formulae    :   12 (   0 unt;   0 def)
%            Number of atoms       :   40 (   9 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :   32 (   4   ~;   0   |;  14   &)
%                                         (   2 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   0 prp; 1-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   29 (  27   !;   2   ?)
% SPC      : FOF_THM_RFO_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(cc_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cc(A) )
     => cc(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(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) ) ).

%----Super cc
fof(axiom_2,axiom,
    ! [X] :
      ( cc(X)
     => ? [Y0] : rp(X,Y0) ) ).

%----Super cc
fof(axiom_3,axiom,
    ! [X] :
      ( cc(X)
     => ! [Y0,Y1] :
          ( ( rp(X,Y0)
            & rp(X,Y1) )
         => Y0 = Y1 ) ) ).

%----Thing and Nothing
%----String and Integer disjoint
%----Super cc
fof(the_axiom,conjecture,
    ( ! [X] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & ! [X] :
        ( cc(X)
       => ( ? [Y0] : rp(X,Y0)
          & ! [Y0,Y1] :
              ( ( rp(X,Y0)
                & rp(X,Y1) )
             => Y0 = Y1 ) ) ) ) ).

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