## TPTP Problem File: GEG014^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : GEG014^1 : TPTP v8.1.2. Released v4.1.0.
% Domain   : Geography
% Problem  : Two unequal regions in France
% Version  : [RCC92] axioms.
% English  :

% 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 73 [Ben10b]

% Status   : Theorem
% Rating   : 0.46 v8.1.0, 0.55 v7.5.0, 0.57 v7.4.0, 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, 0.14 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0, 0.80 v5.0.0, 0.60 v4.1.0
% Syntax   : Number of formulae    :   98 (  41 unt;  49 typ;  40 def)
%            Number of atoms       :  172 (  45 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  238 (  11   ~;   4   |;  20   &; 193   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Number of types       :    4 (   2 usr)
%            Number of type conns  :  195 ( 195   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   58 (  56 usr;  14 con; 0-3 aty)
%            Number of variables   :  118 (  74   ^  33   !;  11   ?; 118   :)
% SPC      : TH0_THM_EQU_NAR

%------------------------------------------------------------------------------
%----Include Region Connection Calculus axioms
include('Axioms/LCL013^0.ax').
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(a,type,
a: \$i > \$i > \$o ).

thf(fool,type,
fool: \$i > \$i > \$o ).

thf(t_axiom_for_fool,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: \$i > \$o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ) ).

thf(k_axiom_for_fool,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: \$i > \$o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ fool @ ( mbox @ fool @ A ) ) ) ) ) ).

thf(i_axiom_for_fool_a,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: \$i > \$o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ a @ Phi ) ) ) ) ).

thf(ax1,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X: \$i] : ( tpp @ catalunya @ spain ) ) ) ).

thf(ax2,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [X: \$i] : ( ec @ spain @ france ) ) ) ).

thf(ax3,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X: \$i] : ( ntpp @ paris @ france ) ) ) ).

thf(con,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X: \$i] :
? [Z: reg,Y: reg] :
( ~ ( eq @ Z @ Y )
& ( o @ Z @ france )
& ( o @ Z @ france ) ) ) ) ).

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