%--------------------------------------------------------------------------
% File     : GEO102+1 : TPTP v9.0.0. Released v2.4.0.
% Domain   : Geometry (Oriented curves)
% Problem  : Common endpoint of subcurves means inclusion
% Version  : [EHK99] axioms.
% English  : If two sub-curves of one curve have a common endpoint and
%            include a sub-curve starting at this endpoint, then one of the
%            two sub-curves is included in the other.

% Refs     : [KE99]  Kulik & Eschenbach (1999), A Geometry of Oriented Curv
%          : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source   : [KE99]
% Names    : Theorem 2.20 [KE99]

% Status   : Unknown
% Rating   : 1.00 v2.4.0
% Syntax   : Number of formulae    :   17 (   1 unt;   0 def)
%            Number of atoms       :   76 (  10 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :   63 (   4   ~;  10   |;  27   &)
%                                         (   9 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   0 prp; 1-3 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   58 (  46   !;  12   ?)
% SPC      : FOF_UNK_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Include simple curve axioms
include('Axioms/GEO004+0.ax').
%--------------------------------------------------------------------------
fof(theorem_2_20,conjecture,
    ! [C1,C2] :
      ( ( ? [C3,P] :
            ( part_of(C3,C1)
            & part_of(C3,C2)
            & end_point(P,C1)
            & end_point(P,C2)
            & end_point(P,C3) )
        & ? [C] :
            ( part_of(C1,C)
            & part_of(C2,C) ) )
     => ( part_of(C1,C2)
        | part_of(C2,C1) ) ) ).

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