%------------------------------------------------------------------------------
% File     : KRS158+1 : TPTP v9.0.0. Released v3.1.0.
% Domain   : Knowledge Representation (Semantic Web)
% Problem  : DL Test: k_lin 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-Manifest665 [Bec03]

% Status   : Theorem
% Rating   : 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.04 v5.4.0, 0.09 v5.3.0, 0.22 v5.2.0, 0.00 v3.2.0, 0.11 v3.1.0
% Syntax   : Number of formulae    :   31 (  11 unt;   0 def)
%            Number of atoms       :   71 (   0 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :   47 (   7   ~;   0   |;  21   &)
%                                         (  17 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   22 (  22 usr;   0 prp; 1-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   31 (  21   !;  10   ?)
% 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)
    <=> ? [Y0] : ra_Px3(X,Y0) ) ).

%----Equality cC10
fof(axiom_3,axiom,
    ! [X] :
      ( cC10(X)
    <=> ? [Y] :
          ( rR1(X,Y)
          & cC2xcomp(Y) ) ) ).

%----Equality cC10xcomp
fof(axiom_4,axiom,
    ! [X] :
      ( cC10xcomp(X)
    <=> ~ ? [Y] : ra_Px3(X,Y) ) ).

%----Equality cC12
fof(axiom_5,axiom,
    ! [X] :
      ( cC12(X)
    <=> ( cC10xcomp(X)
        & cC2xcomp(X) ) ) ).

%----Equality cC14
fof(axiom_6,axiom,
    ! [X] :
      ( cC14(X)
    <=> ? [Y] :
          ( rR1(X,Y)
          & cC12(Y) ) ) ).

%----Equality cC16
fof(axiom_7,axiom,
    ! [X] :
      ( cC16(X)
    <=> ( cC14(X)
        & cC8(X) ) ) ).

%----Equality cC18
fof(axiom_8,axiom,
    ! [X] :
      ( cC18(X)
    <=> ( cTOP(X)
        & cC16(X) ) ) ).

%----Equality cC2
fof(axiom_9,axiom,
    ! [X] :
      ( cC2(X)
    <=> ~ ? [Y] : ra_Px1(X,Y) ) ).

%----Equality cC2xcomp
fof(axiom_10,axiom,
    ! [X] :
      ( cC2xcomp(X)
    <=> ? [Y0] : ra_Px1(X,Y0) ) ).

%----Equality cC4
fof(axiom_11,axiom,
    ! [X] :
      ( cC4(X)
    <=> ? [Y0] : ra_Px6(X,Y0) ) ).

%----Equality cC4
fof(axiom_12,axiom,
    ! [X] :
      ( cC4(X)
    <=> ? [Y] :
          ( rR1(X,Y)
          & cC2xcomp(Y) ) ) ).

%----Equality cC4xcomp
fof(axiom_13,axiom,
    ! [X] :
      ( cC4xcomp(X)
    <=> ~ ? [Y] : ra_Px6(X,Y) ) ).

%----Equality cC6
fof(axiom_14,axiom,
    ! [X] :
      ( cC6(X)
    <=> ( cC4xcomp(X)
        & cC2xcomp(X) ) ) ).

%----Equality cC8
fof(axiom_15,axiom,
    ! [X] :
      ( cC8(X)
    <=> ? [Y] :
          ( rR1(X,Y)
          & cC6(Y) ) ) ).

%----Equality cTEST
fof(axiom_16,axiom,
    ! [X] :
      ( cTEST(X)
    <=> ( cTOP(X)
        & cC18(X) ) ) ).

%----iV16560
fof(axiom_17,axiom,
    cowlThing(iV16560) ).

%----iV16560
fof(axiom_18,axiom,
    cTEST(iV16560) ).

%----iV16560
fof(axiom_19,axiom,
    cTOP(iV16560) ).

fof(axiom_20,axiom,
    rR1(iV16560,iV16562) ).

fof(axiom_21,axiom,
    rR1(iV16560,iV16561) ).

%----iV16561
fof(axiom_22,axiom,
    cowlThing(iV16561) ).

%----iV16561
fof(axiom_23,axiom,
    ! [X] :
      ( rR1(iV16561,X)
     => cC2(X) ) ).

%----iV16561
fof(axiom_24,axiom,
    cC4xcomp(iV16561) ).

%----iV16561
fof(axiom_25,axiom,
    cC2xcomp(iV16561) ).

%----iV16562
fof(axiom_26,axiom,
    cowlThing(iV16562) ).

%----iV16562
fof(axiom_27,axiom,
    ! [X] :
      ( rR1(iV16562,X)
     => cC2(X) ) ).

%----iV16562
fof(axiom_28,axiom,
    cC10xcomp(iV16562) ).

%----iV16562
fof(axiom_29,axiom,
    cC2xcomp(iV16562) ).

%----Thing and Nothing
%----String and Integer disjoint
%----iV16560
%----iV16560
%----iV16560
%----iV16560
%----iV16560
%----iV16561
%----iV16561
%----iV16562
%----iV16562
fof(the_axiom,conjecture,
    ( ! [X] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & cC18(iV16560)
    & cC14(iV16560)
    & cC8(iV16560)
    & cC16(iV16560)
    & cowlThing(iV16560)
    & cC6(iV16561)
    & cowlThing(iV16561)
    & cC12(iV16562)
    & cowlThing(iV16562) ) ).

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