%------------------------------------------------------------------------------
% File     : GEO006+3 : TPTP v9.0.0. Released v3.3.0.
% Domain   : Geometry (Constructive)
% Axioms   : Orthogonality
% Version  : [vPl95] axioms.
% English  :

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

% Status   : Satisfiable
% Syntax   : Number of formulae    :    5 (   2 unt;   0 def)
%            Number of atoms       :   15 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   12 (   2   ~;   5   |;   3   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   13 (  13   !;   0   ?)
% SPC      : 

% Comments : Requires GEO006+0, GEO006+2
%------------------------------------------------------------------------------
%----Compatibility of convergence and unorthogonality
fof(occu1,axiom,
    ! [L,M] :
      ( convergent_lines(L,M)
      | unorthogonal_lines(L,M) ) ).

%----Apartness axiom for the conjunction of convergence and unorthogonality
fof(oac1,axiom,
    ! [L,M,N] :
      ( ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) )
     => ( ( convergent_lines(L,N)
          & unorthogonal_lines(L,N) )
        | ( convergent_lines(M,N)
          & unorthogonal_lines(M,N) ) ) ) ).

%----Axioms for the orthogonal construction
fof(ooc1,axiom,
    ! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) ).

fof(ooc2,axiom,
    ! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)) ).

%----Constructive uniqueness axiom for orthogonals
fof(ouo1,axiom,
    ! [A,L,M,N] :
      ( distinct_lines(L,M)
     => ( apart_point_and_line(A,L)
        | apart_point_and_line(A,M)
        | unorthogonal_lines(L,N)
        | unorthogonal_lines(M,N) ) ) ).

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