## TPTP Axioms File: LCL014^0.ax

```%------------------------------------------------------------------------------
% File     : LCL014^0 : TPTP v7.5.0. Released v4.1.0.
% Domain   : Logical Calculi
% Axioms   : Region Connection Calculus
% 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    : RCC.ax [Ben10a]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   22 (   1 unit;  11 type;   9 defn)
%            Number of atoms       :  118 (   9 equality;  46 variable)
%            Maximal formula depth :   10 (   6 average)
%            Number of connectives :   64 (   6   ~;   0   |;  10   &;  46   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&;   0  !!;   0  ??)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11   :)
%            Number of variables   :   25 (   0 sgn;   4   !;   3   ?;  18   ^)
%                                         (  25   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      :

%------------------------------------------------------------------------------
thf(reg_type,type,(
reg: \$tType )).

thf(c_type,type,(
c: reg > reg > \$o )).

thf(dc_type,type,(
dc: reg > reg > \$o )).

thf(p_type,type,(
p: reg > reg > \$o )).

thf(eq_type,type,(
eq: reg > reg > \$o )).

thf(o_type,type,(
o: reg > reg > \$o )).

thf(po_type,type,(
po: reg > reg > \$o )).

thf(ec_type,type,(
ec: reg > reg > \$o )).

thf(pp_type,type,(
pp: reg > reg > \$o )).

thf(tpp_type,type,(
tpp: reg > reg > \$o )).

thf(ntpp_type,type,(
ntpp: reg > reg > \$o )).

thf(c_reflexive,axiom,(
! [X: reg] :
( c @ X @ X ) )).

thf(c_symmetric,axiom,(
! [X: reg,Y: reg] :
( ( c @ X @ Y )
=> ( c @ Y @ X ) ) )).

thf(dc,definition,
( dc
= ( ^ [X: reg,Y: reg] :
~ ( c @ X @ Y ) ) )).

thf(p,definition,
( p
= ( ^ [X: reg,Y: reg] :
! [Z: reg] :
( ( c @ Z @ X )
=> ( c @ Z @ Y ) ) ) )).

thf(eq,definition,
( eq
= ( ^ [X: reg,Y: reg] :
( ( p @ X @ Y )
& ( p @ Y @ X ) ) ) )).

thf(o,definition,
( o
= ( ^ [X: reg,Y: reg] :
? [Z: reg] :
( ( p @ Z @ X )
& ( p @ Z @ Y ) ) ) )).

thf(po,definition,
( po
= ( ^ [X: reg,Y: reg] :
( ( o @ X @ Y )
& ~ ( p @ X @ Y )
& ~ ( p @ Y @ X ) ) ) )).

thf(ec,definition,
( ec
= ( ^ [X: reg,Y: reg] :
( ( c @ X @ Y )
& ~ ( o @ X @ Y ) ) ) )).

thf(pp,definition,
( pp
= ( ^ [X: reg,Y: reg] :
( ( p @ X @ Y )
& ~ ( p @ Y @ X ) ) ) )).

thf(tpp,definition,
( tpp
= ( ^ [X: reg,Y: reg] :
( ( pp @ X @ Y )
& ? [Z: reg] :
( ( ec @ Z @ X )
& ( ec @ Z @ Y ) ) ) ) )).

thf(ntpp,definition,
( ntpp
= ( ^ [X: reg,Y: reg] :
( ( pp @ X @ Y )
& ~ ( ? [Z: reg] :
( ( ec @ Z @ X )
& ( ec @ Z @ Y ) ) ) ) ) )).

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