%------------------------------------------------------------------------------
% File     : KRS174+1 : TPTP v8.2.0. Released v3.1.0.
% Domain   : Knowledge Representation (Semantic Web)
% Problem  : Sets with appropriate extensions are related by unionOf
% 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_unionOf-Manifest003 [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, 0.08 v3.7.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.00 v3.1.0
% Syntax   : Number of formulae    :   15 (   2 unt;   0 def)
%            Number of atoms       :   41 (  11 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   30 (   4   ~;   2   |;  11   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   0 prp; 1-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   22 (  22   !;   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(cA_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cA(A) )
     => cA(B) ) ).

fof(cA_and_B_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cA_and_B(A) )
     => cA_and_B(B) ) ).

fof(cB_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cB(A) )
     => cB(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(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) ) ).

%----Enumeration cA
fof(axiom_2,axiom,
    ! [X] :
      ( cA(X)
    <=> X = ia ) ).

%----Enumeration cA_and_B
fof(axiom_3,axiom,
    ! [X] :
      ( cA_and_B(X)
    <=> ( X = ib
        | X = ia ) ) ).

%----Enumeration cB
fof(axiom_4,axiom,
    ! [X] :
      ( cB(X)
    <=> X = ib ) ).

%----ia
fof(axiom_5,axiom,
    cowlThing(ia) ).

%----ib
fof(axiom_6,axiom,
    cowlThing(ib) ).

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

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