## TPTP Problem File: SWB105+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWB105+1 : TPTP v7.5.0. Released v5.2.0.
% Domain   : Semantic Web
% Problem  : Universal Existential Restriction Duality
% Version  : [Sch11] axioms.
% English  : Universal and existential restrictions are dual: The universal
%            restriction on property p to the complement of class c is
%            equivalent to the complement of the existential restriction on p
%            to c.

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

% Status   : Theorem
% Rating   : 0.86 v7.5.0, 0.91 v7.4.0, 0.87 v7.3.0, 0.86 v7.1.0, 0.83 v7.0.0, 0.90 v6.4.0, 0.88 v6.3.0, 0.83 v6.2.0, 0.80 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.4.0, 0.93 v5.3.0, 0.96 v5.2.0
% Syntax   : Number of formulae    :  560 ( 197 unit)
%            Number of atoms       : 1779 (  90 equality)
%            Maximal formula depth :   27 (   5 average)
%            Number of connectives : 1355 ( 136   ~;  35   |; 763   &)
%                                         ( 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   :  973 (   0 sgn; 911   !;  62   ?)
%            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_sameall,conjecture,(
iext(uri_owl_equivalentClass,uri_ex_z1,uri_ex_nz2) )).

fof(premise_rdfbased_sem_restrict_term_sameall,axiom,
( iext(uri_owl_complementOf,uri_ex_nz2,uri_ex_z2)
& iext(uri_owl_complementOf,uri_ex_nc,uri_ex_c)
& iext(uri_owl_someValuesFrom,uri_ex_z2,uri_ex_c)
& iext(uri_owl_onProperty,uri_ex_z2,uri_ex_p)
& iext(uri_owl_allValuesFrom,uri_ex_z1,uri_ex_nc)
& iext(uri_owl_onProperty,uri_ex_z1,uri_ex_p) )).

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