%------------------------------------------------------------------------------
% File     : GEO196+1 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Geometry (Constructive)
% Problem  : Symmetry of incidence
% Version  : [vPl95] axioms : Especial.
% English  : If the lines X and Y are convergent, U and V are convergent,
%            and the intersection point of X and Y is incident with U and V,
%            then the intersection point of U and V is incident with X and Y.

% Refs     : [vPl95] von Plato (1995), The Axioms of Constructive Geometry
%          : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% Source   : [ILTP]
% Names    : Theorem 4.11 [vPl95]

% Status   : Theorem
% Rating   : 0.00 v7.3.0, 0.14 v7.2.0, 0.17 v7.1.0, 0.00 v6.1.0, 0.12 v6.0.0, 0.50 v5.5.0, 0.25 v5.4.0, 0.26 v5.3.0, 0.35 v5.2.0, 0.29 v5.0.0, 0.25 v4.1.0, 0.28 v4.0.1, 0.32 v4.0.0, 0.35 v3.7.0, 0.29 v3.5.0, 0.25 v3.4.0, 0.00 v3.3.0
% Syntax   : Number of formulae    :   15 (   3 unt;   0 def)
%            Number of atoms       :   41 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   37 (  11   ~;   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   :   37 (  37   !;   0   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments : Definitions unfolded, hence Especial.
%------------------------------------------------------------------------------
include('Axioms/GEO006+0.ax').
%------------------------------------------------------------------------------
fof(con,conjecture,
    ! [X,Y,U,V] :
      ( ( convergent_lines(X,Y)
        & convergent_lines(U,V)
        & ~ apart_point_and_line(intersection_point(X,Y),U)
        & ~ apart_point_and_line(intersection_point(X,Y),V) )
     => ( ~ apart_point_and_line(intersection_point(U,V),X)
        & ~ apart_point_and_line(intersection_point(U,V),Y) ) ) ).

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