TPTP Problem File: GEO256+1.p
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% File : GEO256+1 : TPTP v8.2.0. Bugfixed v6.4.0.
% Domain : Geometry (Constructive)
% Problem : Property of order and betweeness
% Version : [vPl98] axioms : Especial.
% English :
% Refs : [vPl98] von Plato (1998), A Constructive Theory of Ordered Aff
% : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% Source : [ILTP]
% Names : Theorem 6.2.ii [vPl98]
% Status : Theorem
% Rating : 0.00 v6.4.0
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 94 ( 17 ~; 25 |; 28 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 12 usr; 0 prp; 1-4 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 76 ( 76 !; 0 ?)
% SPC : FOF_THM_RFO_NEQ
% Comments : Definitions unfolded, hence Especial.
% Bugfixes : v6.4.0 - Bugfix in GEO007+1.ax
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include('Axioms/GEO007+0.ax').
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fof(con,conjecture,
! [L,A,B,C,D] :
( ( distinct_points(A,C)
& distinct_points(B,C)
& ~ apart_point_and_line(C,L)
& left_apart_point(D,L) )
=> ( before_on_line(L,A,B)
=> ( before_on_line(L,A,C)
| before_on_line(L,C,B) ) ) ) ).
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