%------------------------------------------------------------------------------
% File     : KRS167+1 : TPTP v9.0.0. Released v3.1.0.
% Domain   : Knowledge Representation (Semantic Web)
% Problem  : Two classes with the same complete description are equivalent
% Version  : Especial.
% English  :

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

% Status   : Theorem
% Rating   : 0.09 v9.0.0, 0.08 v8.2.0, 0.06 v8.1.0, 0.03 v7.2.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.00 v6.1.0, 0.03 v6.0.0, 0.04 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.19 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    :   13 (   0 unt;   0 def)
%            Number of atoms       :   44 (  10 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   35 (   4   ~;   0   |;  16   &)
%                                         (   5 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   0 prp; 1-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   31 (  29   !;   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(cc1_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cc1(A) )
     => cc1(B) ) ).

fof(cc2_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cc2(A) )
     => cc2(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) ) ).

%----Equality cc1
fof(axiom_2,axiom,
    ! [X] :
      ( cc1(X)
    <=> ( ? [Y0] : rp(X,Y0)
        & ! [Y0,Y1] :
            ( ( rp(X,Y0)
              & rp(X,Y1) )
           => Y0 = Y1 ) ) ) ).

%----Equality cc2
fof(axiom_3,axiom,
    ! [X] :
      ( cc2(X)
    <=> ( ? [Y0] : rp(X,Y0)
        & ! [Y0,Y1] :
            ( ( rp(X,Y0)
              & rp(X,Y1) )
           => Y0 = Y1 ) ) ) ).

%----Thing and Nothing
%----String and Integer disjoint
%----Equality cc1
fof(the_axiom,conjecture,
    ( ! [X] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & ! [X] :
        ( cc1(X)
      <=> cc2(X) ) ) ).

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