## TPTP Problem File: SWB103+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWB103+1 : TPTP v7.5.0. Released v5.2.0.
% Domain   : Semantic Web
% Problem  : Exact-QCR As Min-QCR Max-QCR Intersection
% Version  : [Sch11] axioms.
% English  : The intersection of a min- and a max-QCR for the same
%            cardinality, property and class is equivalent to an exact-QCR for
%            the same cardinality, property and class.

% Refs     : [Sch11] Schneider, M. (2011), Email to G. Sutcliffe
% Source   : [Sch11]
% Names    : rdfbased-sem-restrict-term-minmaxexact [Sch11]

% Status   : Theorem
% Rating   : 0.97 v7.1.0, 0.91 v7.0.0, 0.93 v6.4.0, 0.92 v6.2.0, 1.00 v5.2.0
% Syntax   : Number of formulae    :  560 ( 197 unit)
%            Number of atoms       : 1787 (  90 equality)
%            Maximal formula depth :   27 (   5 average)
%            Number of connectives : 1363 ( 136   ~;  35   |; 771   &)
%                                         ( 126 <=>; 295  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :   13 (   1 propositional; 0-3 arity)
%            Number of functors    :  163 ( 162 constant; 0-2 arity)
%            Number of variables   :  975 (   0 sgn; 911   !;  64   ?)
%            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_restrict_term_minmaxexact,conjecture,(
iext(uri_owl_equivalentClass,uri_ex_z4,uri_ex_z1) )).

fof(premise_rdfbased_sem_restrict_term_minmaxexact,axiom,(
? [X0,X1] :
( iext(uri_owl_minQualifiedCardinality,uri_ex_z2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z2,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_z2,uri_ex_c)
& iext(uri_rdf_first,X0,uri_ex_z3)
& iext(uri_rdf_rest,X0,uri_rdf_nil)
& iext(uri_owl_maxQualifiedCardinality,uri_ex_z3,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z3,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_z3,uri_ex_c)
& iext(uri_rdf_first,X1,uri_ex_z2)
& iext(uri_rdf_rest,X1,X0)
& iext(uri_owl_qualifiedCardinality,uri_ex_z1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z1,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_z1,uri_ex_c)
& iext(uri_owl_intersectionOf,uri_ex_z4,X1) ) )).

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