%------------------------------------------------------------------------------
% File     : KRS160+1 : TPTP v9.0.0. Released v3.1.0.
% Domain   : Knowledge Representation (Semantic Web)
% Problem  : DL Test: k_ph ABox test from DL98 systems comparison
% 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_description-logic-Manifest667 [Bec03]

% Status   : Theorem
% Rating   : 0.00 v6.0.0, 0.25 v5.5.0, 0.00 v5.4.0, 0.04 v5.3.0, 0.13 v5.2.0, 0.00 v3.2.0, 0.11 v3.1.0
% Syntax   : Number of formulae    :   23 (   8 unt;   0 def)
%            Number of atoms       :   49 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   33 (   7   ~;   0   |;  12   &)
%                                         (  13 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   18 (  18 usr;   0 prp; 1-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   24 (  16   !;   8   ?)
% SPC      : FOF_THM_RFO_NEQ

% 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.
%------------------------------------------------------------------------------
%----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 cC10
fof(axiom_2,axiom,
    ! [X] :
      ( cC10(X)
    <=> ( cC4(X)
        & cC2(X) ) ) ).

%----Equality cC12
fof(axiom_3,axiom,
    ! [X] :
      ( cC12(X)
    <=> ? [Y] :
          ( rR1(X,Y)
          & cC10(Y) ) ) ).

%----Equality cC2
fof(axiom_4,axiom,
    ! [X] :
      ( cC2(X)
    <=> ~ ? [Y] : ra_Px1(X,Y) ) ).

%----Equality cC2xcomp
fof(axiom_5,axiom,
    ! [X] :
      ( cC2xcomp(X)
    <=> ? [Y0] : ra_Px1(X,Y0) ) ).

%----Equality cC6
fof(axiom_6,axiom,
    ! [X] :
      ( cC6(X)
    <=> ( cC2xcomp(X)
        & cC4(X) ) ) ).

%----Equality cC6
fof(axiom_7,axiom,
    ! [X] :
      ( cC6(X)
    <=> ~ ? [Y] : ra_Px4(X,Y) ) ).

%----Equality cC6xcomp
fof(axiom_8,axiom,
    ! [X] :
      ( cC6xcomp(X)
    <=> ? [Y0] : ra_Px4(X,Y0) ) ).

%----Equality cC8
fof(axiom_9,axiom,
    ! [X] :
      ( cC8(X)
    <=> ? [Y0] : ra_Px2(X,Y0) ) ).

%----Equality cC8
fof(axiom_10,axiom,
    ! [X] :
      ( cC8(X)
    <=> ? [Y] :
          ( rR1(X,Y)
          & cC6(Y) ) ) ).

%----Equality cC8xcomp
fof(axiom_11,axiom,
    ! [X] :
      ( cC8xcomp(X)
    <=> ~ ? [Y] : ra_Px2(X,Y) ) ).

%----Equality cTEST
fof(axiom_12,axiom,
    ! [X] :
      ( cTEST(X)
    <=> ( cC8xcomp(X)
        & cC12(X) ) ) ).

%----iV21080
fof(axiom_13,axiom,
    cTEST(iV21080) ).

%----iV21080
fof(axiom_14,axiom,
    cC8xcomp(iV21080) ).

%----iV21080
fof(axiom_15,axiom,
    cowlThing(iV21080) ).

%----iV21080
fof(axiom_16,axiom,
    ! [X] :
      ( rR1(iV21080,X)
     => cC6xcomp(X) ) ).

fof(axiom_17,axiom,
    rR1(iV21080,iV21081) ).

%----iV21081
fof(axiom_18,axiom,
    cC4(iV21081) ).

%----iV21081
fof(axiom_19,axiom,
    cC6xcomp(iV21081) ).

%----iV21081
fof(axiom_20,axiom,
    cC2(iV21081) ).

%----iV21081
fof(axiom_21,axiom,
    cowlThing(iV21081) ).

%----Thing and Nothing
%----String and Integer disjoint
%----iV21080
%----iV21080
%----iV21081
%----iV21081
fof(the_axiom,conjecture,
    ( ! [X] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & cowlThing(iV21080)
    & cC12(iV21080)
    & cC10(iV21081)
    & cowlThing(iV21081) ) ).

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