%------------------------------------------------------------------------------
% File     : KRS078+1 : TPTP v9.0.0. Released v3.1.0.
% Domain   : Knowledge Representation (Semantic Web)
% Problem  : DL Test: t12.1
% 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    : inconsistent_description-logic-Manifest015 [Bec03]

% Status   : Unsatisfiable
% Rating   : 0.00 v3.1.0
% Syntax   : Number of formulae    :   18 (   1 unt;   0 def)
%            Number of atoms       :   57 (  14 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :   43 (   4   ~;   0   |;  21   &)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   11 (  10 usr;   0 prp; 1-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   43 (  40   !;   3   ?)
% SPC      : FOF_UNS_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(cUnsatisfiable_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cUnsatisfiable(A) )
     => cUnsatisfiable(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(cp_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cp(A) )
     => cp(B) ) ).

fof(cq_substitution_1,axiom,
    ! [A,B] :
      ( ( A = B
        & cq(A) )
     => cq(B) ) ).

fof(rinvR_substitution_1,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rinvR(A,C) )
     => rinvR(B,C) ) ).

fof(rinvR_substitution_2,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rinvR(C,A) )
     => rinvR(C,B) ) ).

fof(rr_substitution_1,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rr(A,C) )
     => rr(B,C) ) ).

fof(rr_substitution_2,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rr(C,A) )
     => rr(C,B) ) ).

fof(rs_substitution_1,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rs(A,C) )
     => rs(B,C) ) ).

fof(rs_substitution_2,axiom,
    ! [A,B,C] :
      ( ( A = B
        & rs(C,A) )
     => rs(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 cUnsatisfiable
fof(axiom_2,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y] :
            ( rr(X,Y)
            & ? [Z] :
                ( rinvR(Y,Z)
                & ! [W] :
                    ( rs(Z,W)
                   => cp(W) ) )
            & ! [Z0,Z1] :
                ( ( rinvR(Y,Z0)
                  & rinvR(Y,Z1) )
               => Z0 = Z1 ) )
        & ? [Y] :
            ( rs(X,Y)
            & ~ cq(Y)
            & ~ cp(Y) ) ) ) ).

%----Inverse: rinvR
fof(axiom_3,axiom,
    ! [X,Y] :
      ( rinvR(X,Y)
    <=> rr(Y,X) ) ).

%----i2003_11_14_17_19_13721
fof(axiom_4,axiom,
    cUnsatisfiable(i2003_11_14_17_19_13721) ).

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