## TPTP Problem File: SWB040+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWB040+1 : TPTP v7.5.0. Released v5.2.0.
% Domain   : Semantic Web
% Problem  : Class Modus Tollens
% Version  : [Sch11] axioms.
% English  : If a class is subsumed by another class, then the complement of
%            the latter class is subsumed by the complement of the former
%            class.

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

% Status   : Theorem
% Rating   : 0.56 v7.4.0, 0.53 v7.3.0, 0.55 v7.2.0, 0.52 v7.1.0, 0.43 v7.0.0, 0.47 v6.4.0, 0.50 v6.2.0, 0.64 v6.1.0, 0.80 v6.0.0, 0.87 v5.5.0, 0.89 v5.3.0, 0.93 v5.2.0
% Syntax   : Number of formulae    :  560 ( 197 unit)
%            Number of atoms       : 1776 (  90 equality)
%            Maximal formula depth :   27 (   5 average)
%            Number of connectives : 1352 ( 136   ~;  35   |; 760   &)
%                                         ( 126 <=>; 295  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :   13 (   1 propositional; 0-3 arity)
%            Number of functors    :  161 ( 160 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_bool_tollens,conjecture,(
iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1) )).

fof(premise_rdfbased_sem_bool_tollens,axiom,
( iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
& iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
& iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2) )).

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