TPTP Problem File: GEO105+1.p
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% File : GEO105+1 : TPTP v9.0.0. Released v2.4.0.
% Domain : Geometry (Oriented curves)
% Problem : If subcurves meet at an endpoint then there's a meeting
% Version : [EHK99] axioms.
% English : If two sub-curves of an open curve meet at a point and this
% point is an endpoint for another sub-curve then this sub-curve
% meets one of the former sub-curves at this point.
% Refs : [KE99] Kulik & Eschenbach (1999), A Geometry of Oriented Curv
% : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source : [KE99]
% Names : Proposition 2.23 [KE99]
% Status : Theorem
% Rating : 1.00 v2.7.0, 0.83 v2.5.0, 1.00 v2.4.0
% Syntax : Number of formulae : 17 ( 1 unt; 0 def)
% Number of atoms : 75 ( 10 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 62 ( 4 ~; 10 |; 26 &)
% ( 9 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 0 prp; 1-3 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 58 ( 49 !; 9 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
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%----Include simple curve axioms
include('Axioms/GEO004+0.ax').
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fof(proposition_2_23,conjecture,
! [C,C1,C2,C3,P] :
( ( part_of(C1,C)
& part_of(C2,C)
& part_of(C3,C)
& meet(P,C1,C2)
& end_point(P,C3)
& open(C) )
=> ( meet(P,C1,C3)
| meet(P,C2,C3) ) ) ).
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