%--------------------------------------------------------------------------
% File     : GEO106+1 : TPTP v8.2.0. Released v2.4.0.
% Domain   : Geometry (Oriented curves)
% Problem  : Two common endpoints means identical or sum to whole
% Version  : [EHK99] axioms.
% English  : If two sub-curves have two common endpoints then they are
%            identical or their sum is the whole curve.

% Refs     : [KE99]  Kulik & Eschenbach (1999), A Geometry of Oriented Curv
%          : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source   : [KE99]
% Names    : Theorem 2.24 [KE99]

% Status   : Unknown
% Rating   : 1.00 v2.4.0
% Syntax   : Number of formulae    :   17 (   1 unt;   0 def)
%            Number of atoms       :   77 (  13 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :   65 (   5   ~;  10   |;  28   &)
%                                         (   9 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   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 (  47   !;  11   ?)
% SPC      : FOF_UNK_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Include simple curve axioms
include('Axioms/GEO004+0.ax').
%--------------------------------------------------------------------------
fof(theorem_2_24,conjecture,
    ! [C,C1,C2] :
      ( ( ? [P,Q] :
            ( end_point(P,C1)
            & end_point(Q,C1)
            & end_point(P,C2)
            & end_point(Q,C2)
            & P != Q )
        & closed(C)
        & part_of(C1,C)
        & part_of(C2,C) )
     => ( C1 = C2
        | C = sum(C1,C2) ) ) ).

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