%--------------------------------------------------------------------------
% File     : GEO128+1 : TPTP v8.2.0. Released v2.4.0.
% Domain   : Geometry (Oriented curves)
% Problem  : Precedence of three points, of whoich two are ordered
% Version  : [EHK99] axioms.
% English  : If P precedes Q with respect to o, then any point R on o
%            precedes Q or is preceded by P.

% Refs     : [KE99]  Kulik & Eschenbach (1999), A Geometry of Oriented Curv
%          : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source   : [KE99]
% Names    : Theorem 4.13 [KE99]

% Status   : Unknown
% Rating   : 1.00 v2.4.0
% Syntax   : Number of formulae    :   28 (   2 unt;   0 def)
%            Number of atoms       :  116 (  16 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :   96 (   8   ~;  11   |;  38   &)
%                                         (  20 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   14 (  13 usr;   0 prp; 1-4 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :   98 (  84   !;  14   ?)
% SPC      : FOF_UNK_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Include simple curve axioms
include('Axioms/GEO004+0.ax').
%----Include axioms of betweenness for simple curves
include('Axioms/GEO004+1.ax').
%----Include oriented curve axioms
include('Axioms/GEO004+2.ax').
%--------------------------------------------------------------------------
fof(theorem_4_13,conjecture,
    ! [O,P,Q] :
      ( ordered_by(O,P,Q)
     => ! [R] :
          ( incident_o(R,O)
         => ( ordered_by(O,R,Q)
            | ordered_by(O,P,R) ) ) ) ).

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