## TPTP Problem File: KRS136+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KRS136+1 : TPTP v8.1.0. Released v3.1.0.
% Domain   : Knowledge Representation (Semantic Web)
% Problem  : Some set theory
% Version  : Especial.
% English  : The abstract syntax form of the conclusions is:
%            EquivalentClasses(restriction( first:p,minCardinality(1)))
%            ObjectProperty(first:p). This is trivially true given that
%            first:p is an individualvaluedPropertyID.

% Refs     : [Bec03] Bechhofer (2003), Email to G. Sutcliffe
%          : [TR+04] Tsarkov et al. (2004), Using Vampire to Reason with OW
% Source   : [Bec03]
% Names    : positive_I5.26-Manifest009 [Bec03]

% Status   : Theorem
% Rating   : 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v3.1.0
% Syntax   : Number of formulae    :    3 (   0 unt;   0 def)
%            Number of atoms       :    8 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :    9 (   4   ~;   0   |;   3   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   0 prp; 1-1 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    4 (   4   !;   0   ?)
% SPC      : FOF_THM_EPR_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) ) ).

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

%------------------------------------------------------------------------------
```