TPTP Problem File: GEO098+1.p
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% File : GEO098+1 : TPTP v8.2.0. Released v2.4.0.
% Domain : Geometry (Oriented curves)
% Problem : For closed curves, there are two complementary sub-curves
% Version : [EHK99] axioms.
% English :
% Refs : [KE99] Kulik & Eschenbach (1999), A Geometry of Oriented Curv
% : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source : [KE99]
% Names : Theorem 2.16 [KE99]
% Status : Unknown
% Rating : 1.00 v2.4.0
% Syntax : Number of formulae : 17 ( 1 unt; 0 def)
% Number of atoms : 74 ( 12 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 62 ( 5 ~; 9 |; 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 ( 47 !; 11 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments : Infinox says this has no finite (counter-) models.
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%----Include simple curve axioms
include('Axioms/GEO004+0.ax').
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fof(theorem_2_16,conjecture,
! [C,P,Q] :
( ( closed(C)
& incident_c(P,C)
& incident_c(Q,C)
& P != Q )
=> ? [C1,C2] :
( meet(P,C1,C2)
& meet(Q,C1,C2)
& C = sum(C1,C2) ) ) ).
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