%--------------------------------------------------------------------------
% File     : GEO113+1 : TPTP v9.0.0. Released v2.4.0.
% Domain   : Geometry (Oriented curves)
% Problem  : Basic property of orderings on linear structures 3
% Version  : [EHK99] axioms.
% English  : If c is open and Q is between P and R wrt. c, then P is not
%            between Q and R wrt. c

% Refs     : [KE99]  Kulik & Eschenbach (1999), A Geometry of Oriented Curv
%          : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source   : [KE99]
% Names    : Theorem 3.8 (3) [KE99]
%          : T6 [EHK99]

% Status   : Theorem
% Rating   : 1.00 v2.7.0, 0.83 v2.5.0, 1.00 v2.4.0
% Syntax   : Number of formulae    :   18 (   1 unt;   0 def)
%            Number of atoms       :   76 (  11 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :   64 (   6   ~;   9   |;  26   &)
%                                         (  10 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   0 prp; 1-4 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   62 (  52   !;  10   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Include simple curve axioms
include('Axioms/GEO004+0.ax').
%----Include axioms of betweenness for simple curves
include('Axioms/GEO004+1.ax').
%--------------------------------------------------------------------------
fof(theorem_3_8_3,conjecture,
    ! [C,P,Q,R] :
      ( ( open(C)
        & between_c(C,P,Q,R) )
     => ~ between_c(C,Q,P,R) ) ).

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