%------------------------------------------------------------------------------
% File     : GEO006+5 : TPTP v9.0.0. Released v3.3.0.
% Domain   : Geometry (Constructive)
% Axioms   : Rules of construction
% Version  : [vPl95] axioms.
% English  :

% Refs     : [vPl95] von Plato (1995), The Axioms of Constructive Geometry
% Source   : [ILTP]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    4 (   0 unt;   0 def)
%            Number of atoms       :   14 (   0 equ)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :   10 (   0   ~;   0   |;   6   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   0 prp; 1-2 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 2-2 aty)
%            Number of variables   :    8 (   8   !;   0   ?)
% SPC      : 

% Comments : Requires GEO006+[0-4]
%------------------------------------------------------------------------------
%----Connecting line of points A and B
fof(con1,axiom,
    ! [A,B] :
      ( ( point(A)
        & point(B)
        & distinct_points(A,B) )
     => line(line_connecting(A,B)) ) ).

%----Intersection point of lines L and M
fof(int1,axiom,
    ! [L,M] :
      ( ( line(L)
        & line(M)
        & convergent_lines(L,M) )
     => point(intersection_point(L,M)) ) ).

%----Parallel lines
fof(par1,axiom,
    ! [L,A] :
      ( ( line(L)
        & point(A) )
     => line(parallel_through_point(L,A)) ) ).

%----Orthogonal lines
fof(orth1,axiom,
    ! [L,A] :
      ( ( line(L)
        & point(A) )
     => line(orthogonal_through_point(L,A)) ) ).

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