TPTP Problem File: GEO148+1.p
View Solutions
- Solve Problem
%--------------------------------------------------------------------------
% File : GEO148+1 : TPTP v8.2.0. Released v2.4.0.
% Domain : Geometry (Oriented curves)
% Problem : No meeting if someone has already passed
% Version : [EHK99] axioms.
% English : A point can only be a meeting point of two moving objects if
% it is not the case that one object already passed through it
% when the other object was still moving towards it
% Refs : [KE99] Kulik & Eschenbach (1999), A Geometry of Oriented Curv
% : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source : [EHK99]
% Names : T14 [EHK99]
% Status : Theorem
% Rating : 0.19 v8.1.0, 0.14 v7.5.0, 0.19 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.25 v6.2.0, 0.28 v6.1.0, 0.23 v6.0.0, 0.22 v5.5.0, 0.26 v5.4.0, 0.32 v5.3.0, 0.41 v5.2.0, 0.25 v5.1.0, 0.29 v5.0.0, 0.38 v4.1.0, 0.39 v4.0.0, 0.38 v3.7.0, 0.35 v3.5.0, 0.37 v3.4.0, 0.32 v3.3.0, 0.29 v3.2.0, 0.27 v3.1.0, 0.33 v2.4.0
% Syntax : Number of formulae : 37 ( 3 unt; 0 def)
% Number of atoms : 136 ( 17 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 109 ( 10 ~; 10 |; 42 &)
% ( 24 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 0 prp; 1-4 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 123 ( 107 !; 16 ?)
% SPC : FOF_THM_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').
%----Include trajectory axioms
include('Axioms/GEO004+3.ax').
%--------------------------------------------------------------------------
fof(t14,conjecture,
! [P,X,Y] :
( connect(X,Y,P)
=> ! [Q1,Q2] :
( ( ordered_by(trajectory_of(Y),Q2,P)
& ordered_by(trajectory_of(X),P,Q1) )
=> ~ once(at_the_same_time(at(X,Q1),at(Y,Q2))) ) ) ).
%--------------------------------------------------------------------------