%------------------------------------------------------------------------------
% File     : GEO186+2 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Geometry (Constructive)
% Problem  : Lemma on symmetry and apartness
% Version  : [vPl95] axioms : Reduced > Especial.
% English  : If the lines U and V are convergent, then the point that is
%            incident with both lines is equal to the intersection point
%            of both lines.

% Refs     : [vPl95] von Plato (1995), The Axioms of Constructive Geometry
%          : [Li97]  Li (1997), Replacing the Axioms for Connecting Lines a
%          : [Li98]  Li (1998), A Shorter and Intuitive Axiom to Replace th
%          : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% Source   : [ILTP]
% Names    :

% Status   : Theorem
% Rating   : 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.12 v5.4.0, 0.09 v5.3.0, 0.17 v5.2.0, 0.14 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v4.0.0, 0.10 v3.7.0, 0.00 v3.3.0
% Syntax   : Number of formulae    :   13 (   3 unt;   0 def)
%            Number of atoms       :   39 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   32 (   6   ~;   9   |;   5   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   0 prp; 2-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 2-2 aty)
%            Number of variables   :   34 (  34   !;   0   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments :  Definitions unfolded, hence Especial.
%------------------------------------------------------------------------------
include('Axioms/GEO008+0.ax').
%------------------------------------------------------------------------------
fof(con,conjecture,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & convergent_lines(U,V)
        & ~ apart_point_and_line(X,U)
        & ~ apart_point_and_line(X,V) )
     => ~ distinct_points(X,intersection_point(U,V)) ) ).

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