TPTP Problem File: GEO135+1.p
View Solutions
- Solve Problem
%--------------------------------------------------------------------------
% File : GEO135+1 : TPTP v9.0.0. Released v2.4.0.
% Domain : Geometry (Oriented curves)
% Problem : Ordering can be determined by betweenness and incidence
% Version : [EHK99] axioms.
% English : The ordering of any pair of points R and S on an oriented line
% o can be determined on the basis of a given pair of points P and
% Q using betweenness and incidence only.
% Refs : [KE99] Kulik & Eschenbach (1999), A Geometry of Oriented Curv
% : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source : [KE99]
% Names : Corollary 4.18 [KE99]
% : T10 [EHK99]
% Status : Unknown
% Rating : 1.00 v2.4.0
% Syntax : Number of formulae : 28 ( 2 unt; 0 def)
% Number of atoms : 121 ( 18 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 104 ( 11 ~; 12 |; 42 &)
% ( 21 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 0 prp; 1-4 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 99 ( 85 !; 14 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments :
%--------------------------------------------------------------------------
%----Include simple curve axioms
include('Axioms/GEO004+0.ax').
%----Include axioms of betweenness for simple curves
include('Axioms/GEO004+1.ax').
%----Include oriented curve axioms
include('Axioms/GEO004+2.ax').
%--------------------------------------------------------------------------
fof(corollary_4_18,conjecture,
! [O,P,Q] :
( ordered_by(O,P,Q)
=> ! [R,S] :
( ordered_by(O,R,S)
<=> ( ( incident_o(S,O)
& ( between(O,R,P,Q)
| P = R )
& R != S
& ~ between(O,S,R,Q) )
| ( between(O,P,R,S)
& ~ between(O,Q,P,R) ) ) ) ) ).
%--------------------------------------------------------------------------