TPTP Problem File: GEO095+1.p
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%--------------------------------------------------------------------------
% File : GEO095+1 : TPTP v8.2.0. Released v2.4.0.
% Domain : Geometry (Oriented curves)
% Problem : Endpoints of open sum are endpoints of curves
% Version : [EHK99] axioms.
% English : If two curves meet and their sum is open, then the endpoints of
% the two curves that are not the meeting-point are also the
% endpoints of the sum of these curves.
% Refs : [KE99] Kulik & Eschenbach (1999), A Geometry of Oriented Curv
% : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source : [KE99]
% Names : Proposition 2.14 (4) [KE99]
% Status : Unknown
% Rating : 1.00 v2.4.0
% Syntax : Number of formulae : 17 ( 1 unt; 0 def)
% Number of atoms : 76 ( 13 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 66 ( 7 ~; 9 |; 28 &)
% ( 9 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 :
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%----Include simple curve axioms
include('Axioms/GEO004+0.ax').
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fof(proposition_2_14_4,conjecture,
! [C1,C2,P] :
( ( meet(P,C1,C2)
& open(sum(C1,C2)) )
=> ? [Q,R] :
( P != Q
& Q != R
& P != R
& end_point(Q,sum(C1,C2))
& end_point(Q,C1)
& end_point(R,sum(C1,C2))
& end_point(R,C2) ) ) ).
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