%------------------------------------------------------------------------------
% File     : GEO213+3 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Geometry (Constructive)
% Problem  : Corollary to non-orthogonal lines and a third line
% Version  : [vPl95] axioms.
% English  : If line L is not orthogonal to line M, then a third line N
%            is distinct from L or not orthogonal to M.

% Refs     : [vPl95] von Plato (1995), The Axioms of Constructive Geometry
%          : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
%          : [Rat07] Raths (2007), Email to Geoff Sutcliffe
% Source   : [Rat07]
% Names    : Corollary 8.4 [vPl95]

% Status   : CounterSatisfiable
% Rating   : 0.33 v8.2.0, 0.00 v7.4.0, 0.33 v7.3.0, 0.00 v7.0.0, 0.33 v6.4.0, 0.00 v6.2.0, 0.22 v6.1.0, 0.10 v6.0.0, 0.00 v5.5.0, 0.29 v5.4.0, 0.73 v5.3.0, 0.77 v5.2.0, 0.62 v5.0.0, 0.56 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :   36 (   7 unt;   0 def)
%            Number of atoms       :   96 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   88 (  28   ~;  20   |;  13   &)
%                                         (   5 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  13 usr;   0 prp; 1-2 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 2-2 aty)
%            Number of variables   :   84 (  84   !;   0   ?)
% SPC      : FOF_CSA_RFO_NEQ

% Comments : Intuitively this is a theorem, so the encoding must be bugged.
%------------------------------------------------------------------------------
include('Axioms/GEO006+0.ax').
include('Axioms/GEO006+1.ax').
include('Axioms/GEO006+2.ax').
include('Axioms/GEO006+3.ax').
include('Axioms/GEO006+4.ax').
include('Axioms/GEO006+5.ax').
include('Axioms/GEO006+6.ax').
%------------------------------------------------------------------------------
fof(con,conjecture,
    ! [L,M,N] :
      ( not_orthogonal_lines(L,M)
     => ( distinct_lines(L,N)
        | not_orthogonal_lines(M,N) ) ) ).

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