%------------------------------------------------------------------------------
% File     : KRS145+1 : TPTP v8.2.0. 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-Manifest004 [Bec03]

% Status   : Theorem
% Rating   : 0.11 v8.2.0, 0.08 v8.1.0, 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.1.0, 0.10 v6.0.0, 0.13 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.22 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.00 v3.3.0, 0.11 v3.2.0, 0.22 v3.1.0
% Syntax   : Number of formulae    :   11 (   0 unt;   0 def)
%            Number of atoms       :   49 (  15 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :   44 (   6   ~;   4   |;  21   &)
%                                         (   2 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   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   :   32 (  28   !;   4   ?)
% 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,Y1,Y2] :
            ( ( rp(X,Y0)
              & rp(X,Y1)
              & rp(X,Y2) )
           => ( Y0 = Y1
              | Y0 = Y2
              | Y1 = Y2 ) )
        & ? [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,Y1] :
              ( rp(X,Y0)
              & rp(X,Y1)
              & Y0 != Y1 )
          & ! [Y0,Y1,Y2] :
              ( ( rp(X,Y0)
                & rp(X,Y1)
                & rp(X,Y2) )
             => ( Y0 = Y1
                | Y0 = Y2
                | Y1 = Y2 ) ) ) ) ) ).

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