TPTP Problem File: GEG004^1.p

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```%------------------------------------------------------------------------------
% File     : GEG004^1 : TPTP v7.1.0. Released v4.1.0.
% Domain   : Geography
% Problem  : Is it commonly known that places are disconnected?
% Version  : [RCC92] axioms.
% English  : We here express that some spatial relations about Catalunya,
%            France, Spain, and Paris are commonly known (modality box_fool),
%            while others are known only to person Bob (modality box_bob). We
%            ask whether it is commonly known that Catalunya and Paris and
%            Spain and Paris are disconnected. (This is not the case).

% 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 63 [Ben10b]

% Status   : CounterSatisfiable
% Rating   : 0.67 v5.4.0, 1.00 v5.0.0, 0.67 v4.1.0
% Syntax   : Number of formulae    :   98 (   0 unit;  49 type;  40 defn)
%            Number of atoms       :  363 (  45 equality; 182 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :  234 (  10   ~;   4   |;  19   &; 191   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  195 ( 195   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   53 (  49   :;   0   =)
%            Number of variables   :  116 (   7 sgn;  33   !;   9   ?;  74   ^)
%                                         ( 116   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_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 @ fool
@ ^ [X: \$i] :
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ) ) )).

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