%--------------------------------------------------------------------------
% File     : GEO004+1 : TPTP v9.0.0. Released v2.4.0.
% Domain   : Geometry (Oriented curves)
% Axioms   : Betweenness for simple curves
% Version  : [EHK99] axioms.
% English  :

% Refs     : [KE99]  Kulik & Eschenbach (1999), A Geometry of Oriented Curv
%          : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source   : [EHK99]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :    6 (   1 equ)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives :    6 (   1   ~;   0   |;   4   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (  11 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   0 prp; 2-4 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    5 (   4   !;   1   ?)
% SPC      : 

% Comments : Requires GEO004+0.ax
%--------------------------------------------------------------------------
fof(between_c_defn,axiom,
    ! [C,P,Q,R] :
      ( between_c(C,P,Q,R)
    <=> ( P != R
        & ? [Cpp] :
            ( part_of(Cpp,C)
            & end_point(P,Cpp)
            & end_point(R,Cpp)
            & inner_point(Q,Cpp) ) ) ) ).

%--------------------------------------------------------------------------