TPTP Problem File: GEO214+2.p
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%------------------------------------------------------------------------------
% File : GEO214+2 : TPTP v9.0.0. Released v3.3.0.
% Domain : Geometry (Constructive)
% Problem : Corollary to non-orthogonal lines and a third line
% Version : [vPl95] axioms : Reduced > Especial.
% English : If the line L is not orthogonal to M, then M is orthogonal to
% L.
% Refs : [vPl95] von Plato (1995), The Axioms of Constructive Geometry
% : [Li97] Li (1997), Replacing the Axioms for Connecting Lines a
% : [Li98] Li (1998), A Shorter and Intuitive Axiom to Replace th
% : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% Source : [ILTP]
% Names :
% Status : Theorem
% Rating : 0.00 v5.5.0, 0.04 v5.3.0, 0.13 v5.2.0, 0.14 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v3.7.0, 0.00 v3.3.0
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 43 ( 7 ~; 16 |; 5 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 5 usr; 0 prp; 2-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 2-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% SPC : FOF_THM_RFO_NEQ
% Comments : Definitions unfolded, hence Especial.
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include('Axioms/GEO008+0.ax').
include('Axioms/GEO006+2.ax').
include('Axioms/GEO006+3.ax').
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fof(con,conjecture,
! [L,M] :
( unorthogonal_lines(L,M)
=> unorthogonal_lines(M,L) ) ).
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