## TPTP Problem File: SWB039+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWB039+1 : TPTP v7.5.0. Released v5.2.0.
% Domain   : Semantic Web
% Problem  : Class Intersection Extensional
% Version  : [Sch11] axioms.
% English  : If a class is an equivalent class to the intersection of other
%            classes, then the former class defines the intersection of the
%            other classes. This test checks that class intersection is
%            realized as an iff-condition.

% Refs     : [Sch11] Schneider, M. (2011), Email to G. Sutcliffe
% Source   : [Sch11]
% Names    : rdfbased-sem-bool-intersection-ext [Sch11]

% Status   : Theorem
% Rating   : 0.94 v7.4.0, 0.90 v7.1.0, 0.87 v7.0.0, 0.93 v6.4.0, 0.92 v6.2.0, 0.88 v6.1.0, 0.90 v6.0.0, 0.96 v5.5.0, 1.00 v5.2.0
% Syntax   : Number of formulae    :  560 ( 196 unit)
%            Number of atoms       : 1783 (  90 equality)
%            Maximal formula depth :   27 (   5 average)
%            Number of connectives : 1359 ( 136   ~;  35   |; 767   &)
%                                         ( 126 <=>; 295  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :   13 (   1 propositional; 0-3 arity)
%            Number of functors    :  160 ( 159 constant; 0-2 arity)
%            Number of variables   :  978 (   0 sgn; 911   !;  67   ?)
%            Maximal term depth    :    2 (   1 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
%----Include OWL 2 Full axioms
include('Axioms/SWB001+0.ax').
%------------------------------------------------------------------------------
fof(conclusion_rdfbased_sem_bool_intersection_ext,conjecture,(
? [X1,X0] :
( iext(uri_rdf_first,X0,uri_ex_x)
& iext(uri_rdf_rest,X0,X1)
& iext(uri_rdf_first,X1,uri_ex_y)
& iext(uri_rdf_rest,X1,uri_rdf_nil)
& iext(uri_owl_intersectionOf,uri_ex_c,X0) ) )).

fof(premise_rdfbased_sem_bool_intersection_ext,axiom,(
? [X0,X1,X2] :
( iext(uri_rdf_first,X0,uri_ex_y)
& iext(uri_rdf_rest,X0,uri_rdf_nil)
& iext(uri_owl_intersectionOf,X1,X2)
& iext(uri_rdf_first,X2,uri_ex_x)
& iext(uri_rdf_rest,X2,X0)
& iext(uri_owl_equivalentClass,uri_ex_c,X1) ) )).

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