## TPTP Axioms File: GEO006+5.ax

```%------------------------------------------------------------------------------
% File     : GEO006+5 : TPTP v7.5.0. 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 unit)
%            Number of atoms       :   14 (   0 equality)
%            Maximal formula depth :    6 (   6 average)
%            Number of connectives :   10 (   0 ~  ;   0  |;   6  &)
%                                         (   0 <=>;   4 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    4 (   0 propositional; 1-2 arity)
%            Number of functors    :    4 (   0 constant; 2-2 arity)
%            Number of variables   :    8 (   0 singleton;   8 !;   0 ?)
%            Maximal term depth    :    2 (   1 average)
% SPC      :

%------------------------------------------------------------------------------
%----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)) ) )).

%------------------------------------------------------------------------------
```