## TPTP Problem File: GEG002^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : GEG002^1 : TPTP v7.2.0. Released v4.1.0.
% Domain   : Geography
% Problem  : Catalunya and Paris, and Spain and Paris, are disconnected
% Version  : [RCC92] axioms.
% English  : The assumptions express that Catalunya is a border region of
%            Spain, Spain and France are two different countries sharing a
%            common border, and Paris is a proper part of France. The
%            conjecture is that Catalunya and Paris are disconnected as well
%            as Spain and Paris.

% Refs     : [RCC92] Randell et al. (1992), A Spatial Logic Based on Region
%          : [Ben10a] Benzmueller (2010), Email to Geoff Sutcliffe
%          : [Ben10b] Benzmueller (2010), Simple Type Theory as a Framework
% Source   : [Ben10a]
% Names    : Problem 61 [Ben10b]

% Status   : Theorem
% Rating   : 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0
% Syntax   : Number of formulae    :   30 (   0 unit;  15 type;   9 defn)
%            Number of atoms       :  102 (   9 equality;  46 variable)
%            Maximal formula depth :   10 (   5 average)
%            Number of connectives :   75 (   6   ~;   0   |;  11   &;  56   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15   :;   0   =)
%            Number of variables   :   25 (   0 sgn;   4   !;   3   ?;  18   ^)
%                                         (  25   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

%------------------------------------------------------------------------------
%----Include Region Connection Calculus axioms
include('Axioms/LCL014^0.ax').
%------------------------------------------------------------------------------
thf(catalunya,type,(
catalunya: reg )).

thf(france,type,(
france: reg )).

thf(spain,type,(
spain: reg )).

thf(paris,type,(
paris: reg )).

thf(ax1,axiom,
( tpp @ catalunya @ spain )).

thf(ax2,axiom,
( ec @ spain @ france )).

thf(ax3,axiom,
( ntpp @ paris @ france )).

thf(con,conjecture,
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) )).

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