id	sid	tid	token	lemma	pos
ejpam-5859	1	1	european	european	PROPN
ejpam-5859	1	2	journal	journal	PROPN
ejpam-5859	1	3	of	of	ADP
ejpam-5859	1	4	pure	pure	ADJ
ejpam-5859	1	5	and	and	CCONJ
ejpam-5859	1	6	applied	applied	ADJ
ejpam-5859	1	7	mathematics	mathematic	NOUN
ejpam-5859	1	8	2025	2025	NUM
ejpam-5859	1	9	,	,	PUNCT
ejpam-5859	1	10	vol	vol	NOUN
ejpam-5859	1	11	.	.	PROPN
ejpam-5859	1	12	18	18	NUM
ejpam-5859	1	13	,	,	PUNCT
ejpam-5859	1	14	issue	issue	NOUN
ejpam-5859	1	15	2	2	NUM
ejpam-5859	1	16	,	,	PUNCT
ejpam-5859	1	17	article	article	NOUN
ejpam-5859	1	18	number	number	NOUN
ejpam-5859	1	19	5859	5859	NUM
ejpam-5859	1	20	issn	issn	PROPN
ejpam-5859	1	21	1307	1307	NUM
ejpam-5859	1	22	-	-	SYM
ejpam-5859	1	23	5543	5543	NUM
ejpam-5859	1	24	–	–	PUNCT
ejpam-5859	1	25	ejpam.com	ejpam.com	X
ejpam-5859	1	26	published	publish	VERB
ejpam-5859	1	27	by	by	ADP
ejpam-5859	1	28	new	new	PROPN
ejpam-5859	1	29	york	york	PROPN
ejpam-5859	1	30	business	business	PROPN
ejpam-5859	1	31	global	global	ADJ
ejpam-5859	1	32	on	on	ADP
ejpam-5859	1	33	filters	filter	NOUN
ejpam-5859	1	34	of	of	ADP
ejpam-5859	1	35	implicative	implicative	NOUN
ejpam-5859	1	36	negatively	negatively	ADV
ejpam-5859	1	37	partially	partially	ADV
ejpam-5859	1	38	ordered	order	VERB
ejpam-5859	1	39	ternary	ternary	ADJ
ejpam-5859	1	40	semigroups	semigroup	NOUN
ejpam-5859	1	41	kansada	kansada	PROPN
ejpam-5859	1	42	nakwan1	nakwan1	PROPN
ejpam-5859	1	43	,	,	PUNCT
ejpam-5859	1	44	panuwat	panuwat	VERB
ejpam-5859	1	45	luangchaisri1	luangchaisri1	NOUN
ejpam-5859	1	46	,	,	PUNCT
ejpam-5859	1	47	thawhat	thawhat	PROPN
ejpam-5859	1	48	changphas1,∗	changphas1,∗	NOUN
ejpam-5859	1	49	1	1	NUM
ejpam-5859	1	50	department	department	NOUN
ejpam-5859	1	51	of	of	ADP
ejpam-5859	1	52	mathematics	mathematic	NOUN
ejpam-5859	1	53	,	,	PUNCT
ejpam-5859	1	54	faculty	faculty	NOUN
ejpam-5859	1	55	of	of	ADP
ejpam-5859	1	56	science	science	NOUN
ejpam-5859	1	57	,	,	PUNCT
ejpam-5859	1	58	khon	khon	PROPN
ejpam-5859	1	59	kaen	kaen	PROPN
ejpam-5859	1	60	university	university	PROPN
ejpam-5859	1	61	,	,	PUNCT
ejpam-5859	1	62	khon	khon	PROPN
ejpam-5859	1	63	kaen	kaen	PROPN
ejpam-5859	1	64	40002	40002	NUM
ejpam-5859	1	65	,	,	PUNCT
ejpam-5859	1	66	thailand	thailand	PROPN
ejpam-5859	1	67	abstract	abstract	NOUN
ejpam-5859	1	68	.	.	PUNCT
ejpam-5859	2	1	in	in	ADP
ejpam-5859	2	2	this	this	DET
ejpam-5859	2	3	paper	paper	NOUN
ejpam-5859	2	4	,	,	PUNCT
ejpam-5859	2	5	we	we	PRON
ejpam-5859	2	6	study	study	VERB
ejpam-5859	2	7	a	a	DET
ejpam-5859	2	8	special	special	ADJ
ejpam-5859	2	9	set	set	NOUN
ejpam-5859	2	10	in	in	ADP
ejpam-5859	2	11	an	an	DET
ejpam-5859	2	12	implicative	implicative	NOUN
ejpam-5859	2	13	n.p.o.(negatively	n.p.o.(negatively	ADV
ejpam-5859	2	14	partially	partially	ADV
ejpam-5859	2	15	ordered	order	VERB
ejpam-5859	2	16	)	)	PUNCT
ejpam-5859	2	17	ternary	ternary	ADJ
ejpam-5859	2	18	semigroup	semigroup	NOUN
ejpam-5859	2	19	,	,	PUNCT
ejpam-5859	2	20	and	and	CCONJ
ejpam-5859	2	21	prove	prove	VERB
ejpam-5859	2	22	that	that	SCONJ
ejpam-5859	2	23	a	a	DET
ejpam-5859	2	24	filter	filter	NOUN
ejpam-5859	2	25	can	can	AUX
ejpam-5859	2	26	be	be	AUX
ejpam-5859	2	27	represented	represent	VERB
ejpam-5859	2	28	by	by	ADP
ejpam-5859	2	29	the	the	DET
ejpam-5859	2	30	union	union	NOUN
ejpam-5859	2	31	of	of	ADP
ejpam-5859	2	32	such	such	ADJ
ejpam-5859	2	33	sets	set	NOUN
ejpam-5859	2	34	.	.	PUNCT
ejpam-5859	3	1	indeed	indeed	ADV
ejpam-5859	3	2	,	,	PUNCT
ejpam-5859	3	3	let	let	VERB
ejpam-5859	3	4	(	(	PUNCT
ejpam-5859	3	5	t	t	NOUN
ejpam-5859	3	6	,	,	PUNCT
ejpam-5859	3	7	[	[	PUNCT
ejpam-5859	3	8	]	]	X
ejpam-5859	3	9	,	,	PUNCT
ejpam-5859	3	10	≤	≤	NUM
ejpam-5859	3	11	,	,	PUNCT
ejpam-5859	3	12	[	[	PUNCT
ejpam-5859	3	13	]	]	X
ejpam-5859	3	14	∗	∗	NOUN
ejpam-5859	3	15	)	)	PUNCT
ejpam-5859	3	16	be	be	VERB
ejpam-5859	3	17	an	an	DET
ejpam-5859	3	18	implicative	implicative	ADJ
ejpam-5859	3	19	n.p.o	n.p.o	NOUN
ejpam-5859	3	20	.	.	PUNCT
ejpam-5859	4	1	ternary	ternary	PROPN
ejpam-5859	4	2	semigroup	semigroup	PROPN
ejpam-5859	4	3	.	.	PUNCT
ejpam-5859	5	1	for	for	ADP
ejpam-5859	5	2	any	any	DET
ejpam-5859	5	3	a	a	PRON
ejpam-5859	5	4	,	,	PUNCT
ejpam-5859	5	5	b	b	PROPN
ejpam-5859	5	6	∈	∈	PROPN
ejpam-5859	5	7	t	t	NOUN
ejpam-5859	5	8	,	,	PUNCT
ejpam-5859	5	9	we	we	PRON
ejpam-5859	5	10	define	define	VERB
ejpam-5859	5	11	s(a	s(a	PROPN
ejpam-5859	5	12	,	,	PUNCT
ejpam-5859	5	13	b	b	NOUN
ejpam-5859	5	14	)	)	PUNCT
ejpam-5859	5	15	:	:	PUNCT
ejpam-5859	6	1	=	=	PUNCT
ejpam-5859	6	2	{	{	PUNCT
ejpam-5859	6	3	c	c	NOUN
ejpam-5859	6	4	∈	∈	PROPN
ejpam-5859	6	5	t	t	NOUN
ejpam-5859	6	6	:	:	PUNCT
ejpam-5859	7	1	[	[	X
ejpam-5859	7	2	aa[bbc]∗]∗	aa[bbc]∗]∗	NOUN
ejpam-5859	7	3	=	=	NOUN
ejpam-5859	7	4	1	1	NUM
ejpam-5859	7	5	}	}	PUNCT
ejpam-5859	7	6	.	.	PUNCT
ejpam-5859	8	1	we	we	PRON
ejpam-5859	8	2	have	have	VERB
ejpam-5859	8	3	the	the	DET
ejpam-5859	8	4	following	following	NOUN
ejpam-5859	8	5	:	:	PUNCT
ejpam-5859	8	6	(	(	PUNCT
ejpam-5859	8	7	1	1	X
ejpam-5859	8	8	)	)	PUNCT
ejpam-5859	8	9	a	a	DET
ejpam-5859	8	10	non	non	ADJ
ejpam-5859	8	11	-	-	ADJ
ejpam-5859	8	12	empty	empty	ADJ
ejpam-5859	8	13	subset	subset	NOUN
ejpam-5859	8	14	f	f	PROPN
ejpam-5859	8	15	of	of	ADP
ejpam-5859	8	16	t	t	PROPN
ejpam-5859	8	17	is	be	AUX
ejpam-5859	8	18	a	a	DET
ejpam-5859	8	19	filter	filter	NOUN
ejpam-5859	8	20	if	if	SCONJ
ejpam-5859	8	21	and	and	CCONJ
ejpam-5859	8	22	only	only	ADV
ejpam-5859	8	23	if	if	SCONJ
ejpam-5859	8	24	it	it	PRON
ejpam-5859	8	25	satisfies	satisfy	VERB
ejpam-5859	8	26	the	the	DET
ejpam-5859	8	27	following	follow	VERB
ejpam-5859	8	28	conditions	condition	NOUN
ejpam-5859	8	29	:	:	PUNCT
ejpam-5859	8	30	(	(	PUNCT
ejpam-5859	8	31	f3	f3	ADJ
ejpam-5859	8	32	)	)	PUNCT
ejpam-5859	8	33	1	1	NUM
ejpam-5859	8	34	∈	∈	PROPN
ejpam-5859	8	35	f	f	NOUN
ejpam-5859	8	36	;	;	PUNCT
ejpam-5859	8	37	(	(	PUNCT
ejpam-5859	8	38	f4	f4	NOUN
ejpam-5859	8	39	)	)	PUNCT
ejpam-5859	8	40	for	for	ADP
ejpam-5859	8	41	any	any	DET
ejpam-5859	8	42	a	a	DET
ejpam-5859	8	43	,	,	PUNCT
ejpam-5859	8	44	b	b	NOUN
ejpam-5859	8	45	,	,	PUNCT
ejpam-5859	8	46	c	c	PROPN
ejpam-5859	8	47	∈	∈	PROPN
ejpam-5859	8	48	t	t	NOUN
ejpam-5859	8	49	,	,	PUNCT
ejpam-5859	8	50	if	if	SCONJ
ejpam-5859	8	51	[	[	X
ejpam-5859	8	52	abc]∗	abc]∗	PROPN
ejpam-5859	8	53	∈	∈	PROPN
ejpam-5859	8	54	f	f	PROPN
ejpam-5859	8	55	and	and	CCONJ
ejpam-5859	8	56	a	a	DET
ejpam-5859	8	57	,	,	PUNCT
ejpam-5859	8	58	b	b	PROPN
ejpam-5859	8	59	∈	∈	PROPN
ejpam-5859	8	60	f	f	X
ejpam-5859	8	61	,	,	PUNCT
ejpam-5859	8	62	then	then	ADV
ejpam-5859	8	63	c	c	PROPN
ejpam-5859	8	64	∈	∈	PROPN
ejpam-5859	8	65	f	f	X
ejpam-5859	8	66	.	.	PUNCT
ejpam-5859	9	1	(	(	PUNCT
ejpam-5859	9	2	2	2	X
ejpam-5859	9	3	)	)	PUNCT
ejpam-5859	9	4	if	if	SCONJ
ejpam-5859	9	5	t	t	PROPN
ejpam-5859	9	6	is	be	AUX
ejpam-5859	9	7	commutative	commutative	ADJ
ejpam-5859	9	8	and	and	CCONJ
ejpam-5859	9	9	f	f	PROPN
ejpam-5859	9	10	is	be	AUX
ejpam-5859	9	11	a	a	DET
ejpam-5859	9	12	filter	filter	NOUN
ejpam-5859	9	13	of	of	ADP
ejpam-5859	9	14	t	t	PROPN
ejpam-5859	9	15	,	,	PUNCT
ejpam-5859	9	16	then	then	ADV
ejpam-5859	9	17	f	f	PROPN
ejpam-5859	9	18	=	=	PUNCT
ejpam-5859	10	1	⋃	⋃	NOUN
ejpam-5859	10	2	a	a	PRON
ejpam-5859	10	3	,	,	PUNCT
ejpam-5859	10	4	b∈f	b∈f	ADJ
ejpam-5859	10	5	s(a	s(a	PROPN
ejpam-5859	10	6	,	,	PUNCT
ejpam-5859	10	7	b	b	NOUN
ejpam-5859	10	8	)	)	PUNCT
ejpam-5859	10	9	.	.	PUNCT
ejpam-5859	11	1	2020	2020	NUM
ejpam-5859	11	2	mathematics	mathematic	NOUN
ejpam-5859	11	3	subject	subject	NOUN
ejpam-5859	11	4	classifications	classification	NOUN
ejpam-5859	11	5	:	:	PUNCT
ejpam-5859	11	6	20m12	20m12	NUM
ejpam-5859	11	7	,	,	PUNCT
ejpam-5859	11	8	06f99	06f99	NUM
ejpam-5859	11	9	,	,	PUNCT
ejpam-5859	11	10	06a06	06a06	NOUN
ejpam-5859	11	11	,	,	PUNCT
ejpam-5859	11	12	06a12	06a12	NUM
ejpam-5859	11	13	key	key	ADJ
ejpam-5859	11	14	words	word	NOUN
ejpam-5859	11	15	and	and	CCONJ
ejpam-5859	11	16	phrases	phrase	NOUN
ejpam-5859	11	17	:	:	PUNCT
ejpam-5859	11	18	implicative	implicative	ADJ
ejpam-5859	11	19	negatively	negatively	ADV
ejpam-5859	11	20	partially	partially	ADV
ejpam-5859	11	21	ordered	order	VERB
ejpam-5859	11	22	ternary	ternary	ADJ
ejpam-5859	11	23	semigroup	semigroup	NOUN
ejpam-5859	11	24	(	(	PUNCT
ejpam-5859	11	25	inpots	inpot	NOUN
ejpam-5859	11	26	)	)	PUNCT
ejpam-5859	11	27	,	,	PUNCT
ejpam-5859	11	28	filter	filter	NOUN
ejpam-5859	11	29	,	,	PUNCT
ejpam-5859	11	30	left	leave	VERB
ejpam-5859	11	31	self	self	NOUN
ejpam-5859	11	32	-	-	PUNCT
ejpam-5859	11	33	distributive	distributive	ADJ
ejpam-5859	11	34	1	1	NUM
ejpam-5859	11	35	.	.	PUNCT
ejpam-5859	12	1	introduction	introduction	NOUN
ejpam-5859	12	2	implicative	implicative	NOUN
ejpam-5859	12	3	negatively	negatively	ADV
ejpam-5859	12	4	partially	partially	ADV
ejpam-5859	12	5	ordered	order	VERB
ejpam-5859	12	6	semigroups	semigroup	NOUN
ejpam-5859	12	7	and	and	CCONJ
ejpam-5859	12	8	filters	filter	NOUN
ejpam-5859	12	9	were	be	AUX
ejpam-5859	12	10	introduced	introduce	VERB
ejpam-5859	12	11	and	and	CCONJ
ejpam-5859	12	12	studied	study	VERB
ejpam-5859	12	13	in	in	ADP
ejpam-5859	12	14	[	[	X
ejpam-5859	12	15	3	3	NUM
ejpam-5859	12	16	]	]	PUNCT
ejpam-5859	12	17	by	by	ADP
ejpam-5859	12	18	chan	chan	PROPN
ejpam-5859	12	19	and	and	CCONJ
ejpam-5859	12	20	shum	shum	NOUN
ejpam-5859	12	21	.	.	PUNCT
ejpam-5859	13	1	the	the	DET
ejpam-5859	13	2	implicative	implicative	NOUN
ejpam-5859	13	3	negatively	negatively	ADV
ejpam-5859	13	4	partially	partially	ADV
ejpam-5859	13	5	ordered	order	VERB
ejpam-5859	13	6	semigroup	semigroup	PROPN
ejpam-5859	13	7	is	be	AUX
ejpam-5859	13	8	a	a	DET
ejpam-5859	13	9	generalization	generalization	NOUN
ejpam-5859	13	10	of	of	ADP
ejpam-5859	13	11	the	the	DET
ejpam-5859	13	12	implicative	implicative	ADJ
ejpam-5859	13	13	semilattice	semilattice	NOUN
ejpam-5859	13	14	(	(	PUNCT
ejpam-5859	13	15	cf	cf	NOUN
ejpam-5859	13	16	.	.	PUNCT
ejpam-5859	14	1	[	[	X
ejpam-5859	14	2	2	2	NUM
ejpam-5859	14	3	]	]	PUNCT
ejpam-5859	14	4	,	,	PUNCT
ejpam-5859	14	5	[	[	X
ejpam-5859	14	6	8	8	NUM
ejpam-5859	14	7	]	]	NUM
ejpam-5859	14	8	)	)	PUNCT
ejpam-5859	14	9	,	,	PUNCT
ejpam-5859	14	10	it	it	PRON
ejpam-5859	14	11	is	be	AUX
ejpam-5859	14	12	closed	close	VERB
ejpam-5859	14	13	to	to	ADP
ejpam-5859	14	14	implications	implication	NOUN
ejpam-5859	14	15	in	in	ADP
ejpam-5859	14	16	mathematical	mathematical	ADJ
ejpam-5859	14	17	logic	logic	NOUN
ejpam-5859	14	18	(	(	PUNCT
ejpam-5859	14	19	cf	cf	NOUN
ejpam-5859	14	20	.	.	PUNCT
ejpam-5859	15	1	[	[	X
ejpam-5859	15	2	1	1	NUM
ejpam-5859	15	3	]	]	PUNCT
ejpam-5859	15	4	,	,	PUNCT
ejpam-5859	15	5	[	[	X
ejpam-5859	15	6	4	4	NUM
ejpam-5859	15	7	]	]	NUM
ejpam-5859	15	8	)	)	PUNCT
ejpam-5859	15	9	.	.	PUNCT
ejpam-5859	16	1	as	as	SCONJ
ejpam-5859	16	2	demonstrated	demonstrate	VERB
ejpam-5859	16	3	in	in	ADP
ejpam-5859	16	4	[	[	X
ejpam-5859	16	5	8	8	NUM
ejpam-5859	16	6	]	]	PUNCT
ejpam-5859	16	7	,	,	PUNCT
ejpam-5859	16	8	filters	filter	NOUN
ejpam-5859	16	9	play	play	VERB
ejpam-5859	16	10	a	a	DET
ejpam-5859	16	11	crucial	crucial	ADJ
ejpam-5859	16	12	role	role	NOUN
ejpam-5859	16	13	in	in	ADP
ejpam-5859	16	14	implicative	implicative	ADJ
ejpam-5859	16	15	semilattice	semilattice	NOUN
ejpam-5859	16	16	theory	theory	NOUN
ejpam-5859	16	17	.	.	PUNCT
ejpam-5859	17	1	quotient	quotient	VERB
ejpam-5859	17	2	structures	structure	NOUN
ejpam-5859	17	3	of	of	ADP
ejpam-5859	17	4	implicative	implicative	ADJ
ejpam-5859	17	5	negatively	negatively	ADV
ejpam-5859	17	6	partially	partially	ADV
ejpam-5859	17	7	∗corresponding	∗corresponde	VERB
ejpam-5859	17	8	author	author	NOUN
ejpam-5859	17	9	.	.	PUNCT
ejpam-5859	18	1	doi	doi	NOUN
ejpam-5859	18	2	:	:	PUNCT
ejpam-5859	18	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5859	https://doi.org/10.29020/nybg.ejpam.v18i2.5859	PRON
ejpam-5859	18	4	email	email	NOUN
ejpam-5859	18	5	addresses	address	VERB
ejpam-5859	18	6	:	:	PUNCT
ejpam-5859	18	7	kansada.n@kkumail.com	kansada.n@kkumail.com	PROPN
ejpam-5859	18	8	(	(	PUNCT
ejpam-5859	18	9	k.	k.	PROPN
ejpam-5859	18	10	nakwan	nakwan	PROPN
ejpam-5859	18	11	)	)	PUNCT
ejpam-5859	18	12	,	,	PUNCT
ejpam-5859	18	13	panulu@kku.ac.th	panulu@kku.ac.th	NOUN
ejpam-5859	18	14	(	(	PUNCT
ejpam-5859	18	15	p.	p.	NOUN
ejpam-5859	18	16	luangchaisri	luangchaisri	PROPN
ejpam-5859	18	17	)	)	PUNCT
ejpam-5859	18	18	,	,	PUNCT
ejpam-5859	18	19	thacha@kku.ac.th	thacha@kku.ac.th	NOUN
ejpam-5859	18	20	(	(	PUNCT
ejpam-5859	18	21	t.	t.	NOUN
ejpam-5859	18	22	changphas	changphas	PROPN
ejpam-5859	18	23	)	)	PUNCT
ejpam-5859	18	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5859	19	1	1	1	NUM
ejpam-5859	19	2	copyright	copyright	NOUN
ejpam-5859	19	3	:	:	PUNCT
ejpam-5859	19	4	©	©	PROPN
ejpam-5859	19	5	2025	2025	NUM
ejpam-5859	19	6	the	the	DET
ejpam-5859	19	7	author(s	author(s	NOUN
ejpam-5859	19	8	)	)	PUNCT
ejpam-5859	19	9	.	.	PUNCT
ejpam-5859	20	1	(	(	PUNCT
ejpam-5859	20	2	cc	cc	NOUN
ejpam-5859	20	3	by	by	ADP
ejpam-5859	20	4	-	-	PUNCT
ejpam-5859	20	5	nc	nc	PROPN
ejpam-5859	20	6	4.0	4.0	NUM
ejpam-5859	20	7	)	)	PUNCT
ejpam-5859	20	8	k.	k.	PROPN
ejpam-5859	20	9	nakwan	nakwan	PROPN
ejpam-5859	20	10	,	,	PUNCT
ejpam-5859	20	11	p.	p.	PROPN
ejpam-5859	20	12	luangchaisri	luangchaisri	VERB
ejpam-5859	20	13	,	,	PUNCT
ejpam-5859	20	14	t.	t.	PROPN
ejpam-5859	20	15	changphas	changphas	PROPN
ejpam-5859	20	16	/	/	SYM
ejpam-5859	20	17	eur	eur	PROPN
ejpam-5859	20	18	.	.	PUNCT
ejpam-5859	21	1	j.	j.	PROPN
ejpam-5859	21	2	pure	pure	PROPN
ejpam-5859	21	3	appl	appl	PROPN
ejpam-5859	21	4	.	.	PROPN
ejpam-5859	21	5	math	math	PROPN
ejpam-5859	21	6	,	,	PUNCT
ejpam-5859	21	7	18	18	NUM
ejpam-5859	21	8	(	(	PUNCT
ejpam-5859	21	9	2	2	NUM
ejpam-5859	21	10	)	)	PUNCT
ejpam-5859	21	11	(	(	PUNCT
ejpam-5859	21	12	2025	2025	NUM
ejpam-5859	21	13	)	)	PUNCT
ejpam-5859	21	14	,	,	PUNCT
ejpam-5859	21	15	5859	5859	NUM
ejpam-5859	21	16	2	2	NUM
ejpam-5859	21	17	of	of	ADP
ejpam-5859	21	18	8	8	NUM
ejpam-5859	21	19	ordered	order	VERB
ejpam-5859	21	20	semigroups	semigroup	NOUN
ejpam-5859	21	21	through	through	ADP
ejpam-5859	21	22	filters	filter	NOUN
ejpam-5859	21	23	were	be	AUX
ejpam-5859	21	24	constructed	construct	VERB
ejpam-5859	21	25	in	in	ADP
ejpam-5859	21	26	[	[	X
ejpam-5859	21	27	3	3	NUM
ejpam-5859	21	28	]	]	PUNCT
ejpam-5859	21	29	.	.	PUNCT
ejpam-5859	22	1	additionally	additionally	ADV
ejpam-5859	22	2	,	,	PUNCT
ejpam-5859	22	3	in	in	ADP
ejpam-5859	22	4	[	[	PUNCT
ejpam-5859	22	5	6	6	NUM
ejpam-5859	22	6	]	]	PUNCT
ejpam-5859	22	7	,	,	PUNCT
ejpam-5859	22	8	filters	filter	VERB
ejpam-5859	22	9	within	within	ADP
ejpam-5859	22	10	commutative	commutative	ADJ
ejpam-5859	22	11	implicative	implicative	NOUN
ejpam-5859	22	12	negatively	negatively	ADV
ejpam-5859	22	13	partially	partially	ADV
ejpam-5859	22	14	ordered	order	VERB
ejpam-5859	22	15	semigroups	semigroup	NOUN
ejpam-5859	22	16	were	be	AUX
ejpam-5859	22	17	examined	examine	VERB
ejpam-5859	22	18	.	.	PUNCT
ejpam-5859	23	1	in	in	ADP
ejpam-5859	23	2	[	[	X
ejpam-5859	23	3	5	5	NUM
ejpam-5859	23	4	]	]	PUNCT
ejpam-5859	23	5	,	,	PUNCT
ejpam-5859	23	6	the	the	DET
ejpam-5859	23	7	author	author	NOUN
ejpam-5859	23	8	introduced	introduce	VERB
ejpam-5859	23	9	a	a	DET
ejpam-5859	23	10	set	set	NOUN
ejpam-5859	23	11	in	in	ADP
ejpam-5859	23	12	an	an	DET
ejpam-5859	23	13	implicative	implicative	ADJ
ejpam-5859	23	14	negatively	negatively	ADV
ejpam-5859	23	15	partially	partially	ADV
ejpam-5859	23	16	ordered	order	VERB
ejpam-5859	23	17	semigroup	semigroup	NOUN
ejpam-5859	23	18	,	,	PUNCT
ejpam-5859	23	19	and	and	CCONJ
ejpam-5859	23	20	gave	give	VERB
ejpam-5859	23	21	an	an	DET
ejpam-5859	23	22	equivalent	equivalent	ADJ
ejpam-5859	23	23	condition	condition	NOUN
ejpam-5859	23	24	of	of	ADP
ejpam-5859	23	25	a	a	DET
ejpam-5859	23	26	filter	filter	NOUN
ejpam-5859	23	27	.	.	PUNCT
ejpam-5859	24	1	moreover	moreover	ADV
ejpam-5859	24	2	,	,	PUNCT
ejpam-5859	24	3	it	it	PRON
ejpam-5859	24	4	is	be	AUX
ejpam-5859	24	5	obtained	obtain	VERB
ejpam-5859	24	6	that	that	SCONJ
ejpam-5859	24	7	a	a	DET
ejpam-5859	24	8	filter	filter	NOUN
ejpam-5859	24	9	is	be	AUX
ejpam-5859	24	10	the	the	DET
ejpam-5859	24	11	union	union	NOUN
ejpam-5859	24	12	of	of	ADP
ejpam-5859	24	13	that	that	DET
ejpam-5859	24	14	special	special	ADJ
ejpam-5859	24	15	sets	set	NOUN
ejpam-5859	24	16	.	.	PUNCT
ejpam-5859	25	1	in	in	ADP
ejpam-5859	25	2	this	this	DET
ejpam-5859	25	3	paper	paper	NOUN
ejpam-5859	25	4	,	,	PUNCT
ejpam-5859	25	5	we	we	PRON
ejpam-5859	25	6	follow	follow	VERB
ejpam-5859	25	7	these	these	DET
ejpam-5859	25	8	concepts	concept	NOUN
ejpam-5859	25	9	to	to	PART
ejpam-5859	25	10	derive	derive	VERB
ejpam-5859	25	11	a	a	DET
ejpam-5859	25	12	special	special	ADJ
ejpam-5859	25	13	set	set	NOUN
ejpam-5859	25	14	in	in	ADP
ejpam-5859	25	15	an	an	DET
ejpam-5859	25	16	implicative	implicative	ADJ
ejpam-5859	25	17	negatively	negatively	ADV
ejpam-5859	25	18	partially	partially	ADV
ejpam-5859	25	19	ordered	order	VERB
ejpam-5859	25	20	ternary	ternary	ADJ
ejpam-5859	25	21	semigroup	semigroup	NOUN
ejpam-5859	25	22	,	,	PUNCT
ejpam-5859	25	23	and	and	CCONJ
ejpam-5859	25	24	prove	prove	VERB
ejpam-5859	25	25	that	that	SCONJ
ejpam-5859	25	26	a	a	DET
ejpam-5859	25	27	filter	filter	NOUN
ejpam-5859	25	28	can	can	AUX
ejpam-5859	25	29	be	be	AUX
ejpam-5859	25	30	represented	represent	VERB
ejpam-5859	25	31	by	by	ADP
ejpam-5859	25	32	the	the	DET
ejpam-5859	25	33	union	union	NOUN
ejpam-5859	25	34	of	of	ADP
ejpam-5859	25	35	such	such	ADJ
ejpam-5859	25	36	sets	set	NOUN
ejpam-5859	25	37	.	.	PUNCT
ejpam-5859	26	1	also	also	ADV
ejpam-5859	26	2	,	,	PUNCT
ejpam-5859	26	3	some	some	DET
ejpam-5859	26	4	important	important	ADJ
ejpam-5859	26	5	results	result	NOUN
ejpam-5859	26	6	are	be	AUX
ejpam-5859	26	7	investigated	investigate	VERB
ejpam-5859	26	8	.	.	PUNCT
ejpam-5859	27	1	2	2	X
ejpam-5859	27	2	.	.	X
ejpam-5859	27	3	preliminaries	preliminary	NOUN
ejpam-5859	27	4	we	we	PRON
ejpam-5859	27	5	collects	collect	VERB
ejpam-5859	27	6	results	result	NOUN
ejpam-5859	27	7	obtained	obtain	VERB
ejpam-5859	27	8	in	in	ADP
ejpam-5859	27	9	negatively	negatively	ADV
ejpam-5859	27	10	partially	partially	ADV
ejpam-5859	27	11	ordered	order	VERB
ejpam-5859	27	12	ternary	ternary	ADJ
ejpam-5859	27	13	semigroups	semigroup	NOUN
ejpam-5859	27	14	.	.	PUNCT
ejpam-5859	28	1	definition	definition	NOUN
ejpam-5859	28	2	1	1	NUM
ejpam-5859	28	3	.	.	PUNCT
ejpam-5859	29	1	[	[	X
ejpam-5859	29	2	7	7	X
ejpam-5859	29	3	]	]	X
ejpam-5859	29	4	a	a	DET
ejpam-5859	29	5	system	system	NOUN
ejpam-5859	29	6	(	(	PUNCT
ejpam-5859	29	7	t	t	PROPN
ejpam-5859	29	8	,	,	PUNCT
ejpam-5859	29	9	[	[	PUNCT
ejpam-5859	29	10	]	]	X
ejpam-5859	29	11	,	,	PUNCT
ejpam-5859	29	12	≤	≤	NUM
ejpam-5859	29	13	)	)	PUNCT
ejpam-5859	29	14	is	be	AUX
ejpam-5859	29	15	called	call	VERB
ejpam-5859	29	16	a	a	DET
ejpam-5859	29	17	npots	npot	NOUN
ejpam-5859	29	18	(	(	PUNCT
ejpam-5859	29	19	negatively	negatively	ADV
ejpam-5859	29	20	partially	partially	ADV
ejpam-5859	29	21	ordered	order	VERB
ejpam-5859	29	22	ternary	ternary	ADJ
ejpam-5859	29	23	semigroup	semigroup	NOUN
ejpam-5859	29	24	)	)	PUNCT
ejpam-5859	29	25	if	if	SCONJ
ejpam-5859	29	26	(	(	PUNCT
ejpam-5859	29	27	1	1	NUM
ejpam-5859	29	28	)	)	PUNCT
ejpam-5859	29	29	(	(	PUNCT
ejpam-5859	29	30	t	t	PROPN
ejpam-5859	29	31	,	,	PUNCT
ejpam-5859	29	32	[	[	X
ejpam-5859	29	33	]	]	X
ejpam-5859	29	34	)	)	PUNCT
ejpam-5859	29	35	is	be	AUX
ejpam-5859	29	36	a	a	DET
ejpam-5859	29	37	ternary	ternary	ADJ
ejpam-5859	29	38	semigroup	semigroup	NOUN
ejpam-5859	29	39	;	;	PUNCT
ejpam-5859	29	40	(	(	PUNCT
ejpam-5859	29	41	2	2	X
ejpam-5859	29	42	)	)	PUNCT
ejpam-5859	29	43	a	a	DET
ejpam-5859	29	44	partially	partially	ADV
ejpam-5859	29	45	order	order	VERB
ejpam-5859	29	46	≤	≤	NOUN
ejpam-5859	29	47	on	on	ADP
ejpam-5859	29	48	t	t	PROPN
ejpam-5859	29	49	is	be	AUX
ejpam-5859	29	50	compatible	compatible	ADJ
ejpam-5859	29	51	with	with	ADP
ejpam-5859	29	52	[	[	PUNCT
ejpam-5859	29	53	]	]	X
ejpam-5859	29	54	;	;	PUNCT
ejpam-5859	29	55	(	(	PUNCT
ejpam-5859	29	56	3	3	X
ejpam-5859	29	57	)	)	PUNCT
ejpam-5859	29	58	∀a	∀a	NOUN
ejpam-5859	29	59	,	,	PUNCT
ejpam-5859	29	60	b	b	X
ejpam-5859	29	61	,	,	PUNCT
ejpam-5859	29	62	c	c	PROPN
ejpam-5859	29	63	∈	∈	PROPN
ejpam-5859	29	64	t	t	PROPN
ejpam-5859	29	65	,	,	PUNCT
ejpam-5859	29	66	[	[	X
ejpam-5859	29	67	abc	abc	X
ejpam-5859	29	68	]	]	X
ejpam-5859	29	69	≤	≤	X
ejpam-5859	29	70	a	a	DET
ejpam-5859	29	71	,	,	PUNCT
ejpam-5859	29	72	[	[	X
ejpam-5859	29	73	abc	abc	X
ejpam-5859	29	74	]	]	X
ejpam-5859	29	75	≤	≤	PROPN
ejpam-5859	29	76	b	b	NUM
ejpam-5859	29	77	,	,	PUNCT
ejpam-5859	29	78	[	[	X
ejpam-5859	29	79	abc	abc	X
ejpam-5859	29	80	]	]	X
ejpam-5859	29	81	≤	≤	ADJ
ejpam-5859	29	82	c.	c.	NOUN
ejpam-5859	29	83	definition	definition	NOUN
ejpam-5859	29	84	2	2	NUM
ejpam-5859	29	85	.	.	PUNCT
ejpam-5859	30	1	[	[	X
ejpam-5859	30	2	7	7	X
ejpam-5859	30	3	]	]	X
ejpam-5859	30	4	a	a	DET
ejpam-5859	30	5	npots	npot	NOUN
ejpam-5859	30	6	(	(	PUNCT
ejpam-5859	30	7	t	t	PROPN
ejpam-5859	30	8	,	,	PUNCT
ejpam-5859	30	9	[	[	PUNCT
ejpam-5859	30	10	]	]	X
ejpam-5859	30	11	,	,	PUNCT
ejpam-5859	30	12	≤	≤	NUM
ejpam-5859	30	13	)	)	PUNCT
ejpam-5859	30	14	is	be	AUX
ejpam-5859	30	15	called	call	VERB
ejpam-5859	30	16	an	an	DET
ejpam-5859	30	17	inpots	inpot	NOUN
ejpam-5859	30	18	(	(	PUNCT
ejpam-5859	30	19	implicative	implicative	ADJ
ejpam-5859	30	20	negatively	negatively	ADV
ejpam-5859	30	21	partially	partially	ADV
ejpam-5859	30	22	ordered	order	VERB
ejpam-5859	30	23	ternary	ternary	ADJ
ejpam-5859	30	24	semigroup	semigroup	NOUN
ejpam-5859	30	25	)	)	PUNCT
ejpam-5859	30	26	if	if	SCONJ
ejpam-5859	30	27	there	there	PRON
ejpam-5859	30	28	is	be	VERB
ejpam-5859	30	29	an	an	DET
ejpam-5859	30	30	additional	additional	ADJ
ejpam-5859	30	31	ternary	ternary	ADJ
ejpam-5859	30	32	multiplication	multiplication	NOUN
ejpam-5859	30	33	[	[	PUNCT
ejpam-5859	30	34	]	]	X
ejpam-5859	30	35	∗	∗	NOUN
ejpam-5859	30	36	on	on	ADP
ejpam-5859	30	37	t	t	PROPN
ejpam-5859	30	38	such	such	ADJ
ejpam-5859	30	39	that	that	PRON
ejpam-5859	30	40	for	for	ADP
ejpam-5859	30	41	all	all	DET
ejpam-5859	30	42	a	a	DET
ejpam-5859	30	43	,	,	PUNCT
ejpam-5859	30	44	b	b	NOUN
ejpam-5859	30	45	,	,	PUNCT
ejpam-5859	30	46	c	c	X
ejpam-5859	30	47	,	,	PUNCT
ejpam-5859	30	48	u	u	PROPN
ejpam-5859	30	49	∈	∈	PROPN
ejpam-5859	30	50	t	t	PROPN
ejpam-5859	30	51	,	,	PUNCT
ejpam-5859	30	52	u	u	NOUN
ejpam-5859	30	53	≤	≤	X
ejpam-5859	31	1	[	[	X
ejpam-5859	31	2	cbc]∗	cbc]∗	PROPN
ejpam-5859	31	3	⇔	⇔	PROPN
ejpam-5859	31	4	[	[	X
ejpam-5859	31	5	uab	uab	X
ejpam-5859	31	6	]	]	PUNCT
ejpam-5859	31	7	≤	≤	PROPN
ejpam-5859	31	8	c.	c.	NOUN
ejpam-5859	31	9	here	here	ADV
ejpam-5859	31	10	,	,	PUNCT
ejpam-5859	31	11	[	[	PUNCT
ejpam-5859	31	12	]	]	X
ejpam-5859	31	13	∗	∗	NOUN
ejpam-5859	31	14	is	be	AUX
ejpam-5859	31	15	a	a	DET
ejpam-5859	31	16	ternary	ternary	ADJ
ejpam-5859	31	17	implication	implication	NOUN
ejpam-5859	31	18	.	.	PUNCT
ejpam-5859	32	1	a	a	DET
ejpam-5859	32	2	multiplicative	multiplicative	ADJ
ejpam-5859	32	3	identity	identity	NOUN
ejpam-5859	32	4	of	of	ADP
ejpam-5859	32	5	a	a	DET
ejpam-5859	32	6	ternary	ternary	ADJ
ejpam-5859	32	7	semigroup	semigroup	NOUN
ejpam-5859	32	8	(	(	PUNCT
ejpam-5859	32	9	t	t	PROPN
ejpam-5859	32	10	,	,	PUNCT
ejpam-5859	32	11	[	[	X
ejpam-5859	32	12	]	]	X
ejpam-5859	32	13	)	)	PUNCT
ejpam-5859	32	14	is	be	AUX
ejpam-5859	32	15	an	an	DET
ejpam-5859	32	16	element	element	NOUN
ejpam-5859	32	17	1	1	NUM
ejpam-5859	32	18	of	of	ADP
ejpam-5859	32	19	t	t	NOUN
ejpam-5859	32	20	satisfying	satisfy	VERB
ejpam-5859	32	21	the	the	DET
ejpam-5859	32	22	condition	condition	NOUN
ejpam-5859	32	23	[	[	X
ejpam-5859	32	24	1a1	1a1	NUM
ejpam-5859	32	25	]	]	X
ejpam-5859	32	26	=	=	PUNCT
ejpam-5859	33	1	[	[	X
ejpam-5859	33	2	11a	11a	NOUN
ejpam-5859	33	3	]	]	X
ejpam-5859	33	4	=	=	SYM
ejpam-5859	33	5	[	[	X
ejpam-5859	33	6	a11	a11	X
ejpam-5859	33	7	]	]	X
ejpam-5859	33	8	=	=	PUNCT
ejpam-5859	33	9	a	a	PRON
ejpam-5859	33	10	for	for	ADP
ejpam-5859	33	11	any	any	DET
ejpam-5859	33	12	a	a	DET
ejpam-5859	33	13	∈	∈	PROPN
ejpam-5859	33	14	t	t	NOUN
ejpam-5859	33	15	.	.	PUNCT
ejpam-5859	34	1	example	example	NOUN
ejpam-5859	35	1	1	1	NUM
ejpam-5859	35	2	.	.	X
ejpam-5859	35	3	consider	consider	VERB
ejpam-5859	35	4	the	the	DET
ejpam-5859	35	5	inpots	inpot	NOUN
ejpam-5859	35	6	(	(	PUNCT
ejpam-5859	35	7	t	t	NOUN
ejpam-5859	35	8	,	,	PUNCT
ejpam-5859	35	9	[	[	PUNCT
ejpam-5859	35	10	]	]	X
ejpam-5859	35	11	,	,	PUNCT
ejpam-5859	35	12	≤	≤	NUM
ejpam-5859	35	13	,	,	PUNCT
ejpam-5859	35	14	[	[	PUNCT
ejpam-5859	35	15	]	]	X
ejpam-5859	35	16	∗	∗	NOUN
ejpam-5859	35	17	)	)	PUNCT
ejpam-5859	35	18	defined	define	VERB
ejpam-5859	35	19	as	as	SCONJ
ejpam-5859	35	20	follows	follow	VERB
ejpam-5859	35	21	:	:	PUNCT
ejpam-5859	35	22	[	[	PUNCT
ejpam-5859	35	23	]	]	X
ejpam-5859	35	24	1	1	NUM
ejpam-5859	35	25	a	a	DET
ejpam-5859	35	26	0	0	NUM
ejpam-5859	35	27	11	11	NUM
ejpam-5859	35	28	1	1	NUM
ejpam-5859	35	29	0	0	NUM
ejpam-5859	35	30	0	0	NUM
ejpam-5859	35	31	1a	1a	X
ejpam-5859	35	32	0	0	NUM
ejpam-5859	35	33	0	0	NUM
ejpam-5859	35	34	0	0	NUM
ejpam-5859	35	35	10	10	NUM
ejpam-5859	35	36	0	0	NUM
ejpam-5859	35	37	0	0	NUM
ejpam-5859	35	38	0	0	NUM
ejpam-5859	36	1	[	[	PUNCT
ejpam-5859	36	2	]	]	X
ejpam-5859	36	3	1	1	NUM
ejpam-5859	36	4	a	a	DET
ejpam-5859	36	5	0	0	NUM
ejpam-5859	36	6	aa	aa	NOUN
ejpam-5859	36	7	0	0	NUM
ejpam-5859	36	8	0	0	SYM
ejpam-5859	36	9	0	0	NUM
ejpam-5859	36	10	a1	a1	NOUN
ejpam-5859	36	11	0	0	NUM
ejpam-5859	36	12	0	0	NUM
ejpam-5859	36	13	0	0	NUM
ejpam-5859	36	14	a0	a0	NOUN
ejpam-5859	36	15	0	0	NUM
ejpam-5859	36	16	0	0	NUM
ejpam-5859	36	17	0	0	NUM
ejpam-5859	37	1	[	[	PUNCT
ejpam-5859	37	2	]	]	X
ejpam-5859	37	3	1	1	NUM
ejpam-5859	37	4	a	a	PRON
ejpam-5859	37	5	0	0	NUM
ejpam-5859	37	6	00	00	NUM
ejpam-5859	37	7	0	0	NUM
ejpam-5859	37	8	0	0	NUM
ejpam-5859	37	9	0	0	NUM
ejpam-5859	37	10	01	01	NUM
ejpam-5859	37	11	0	0	NUM
ejpam-5859	37	12	0	0	NUM
ejpam-5859	37	13	0	0	NUM
ejpam-5859	37	14	0a	0a	NOUN
ejpam-5859	37	15	0	0	NUM
ejpam-5859	37	16	0	0	NUM
ejpam-5859	37	17	0	0	NUM
ejpam-5859	38	1	[	[	PUNCT
ejpam-5859	38	2	]	]	X
ejpam-5859	38	3	∗	∗	NOUN
ejpam-5859	38	4	1	1	NUM
ejpam-5859	38	5	a	a	DET
ejpam-5859	38	6	0	0	NUM
ejpam-5859	38	7	11	11	NUM
ejpam-5859	38	8	1	1	NUM
ejpam-5859	38	9	a	a	DET
ejpam-5859	38	10	a	a	DET
ejpam-5859	38	11	1a	1a	NUM
ejpam-5859	38	12	1	1	NUM
ejpam-5859	38	13	1	1	NUM
ejpam-5859	38	14	1	1	NUM
ejpam-5859	38	15	10	10	NUM
ejpam-5859	38	16	1	1	NUM
ejpam-5859	38	17	1	1	NUM
ejpam-5859	38	18	1	1	NUM
ejpam-5859	38	19	[	[	PUNCT
ejpam-5859	38	20	]	]	X
ejpam-5859	38	21	∗	∗	NOUN
ejpam-5859	38	22	1	1	NUM
ejpam-5859	38	23	a	a	DET
ejpam-5859	38	24	0	0	NUM
ejpam-5859	38	25	aa	aa	NOUN
ejpam-5859	38	26	1	1	NUM
ejpam-5859	38	27	1	1	NUM
ejpam-5859	38	28	1	1	NUM
ejpam-5859	38	29	a1	a1	NOUN
ejpam-5859	38	30	1	1	NUM
ejpam-5859	38	31	1	1	NUM
ejpam-5859	38	32	1	1	NUM
ejpam-5859	38	33	a0	a0	NOUN
ejpam-5859	38	34	1	1	NUM
ejpam-5859	38	35	1	1	NUM
ejpam-5859	38	36	1	1	NUM
ejpam-5859	38	37	[	[	PUNCT
ejpam-5859	38	38	]	]	X
ejpam-5859	38	39	∗	∗	NOUN
ejpam-5859	38	40	1	1	NUM
ejpam-5859	38	41	a	a	PRON
ejpam-5859	38	42	0	0	NUM
ejpam-5859	38	43	00	00	NUM
ejpam-5859	38	44	1	1	NUM
ejpam-5859	38	45	1	1	NUM
ejpam-5859	38	46	1	1	NUM
ejpam-5859	38	47	01	01	NUM
ejpam-5859	38	48	1	1	NUM
ejpam-5859	38	49	1	1	NUM
ejpam-5859	38	50	1	1	NUM
ejpam-5859	38	51	0a	0a	NUM
ejpam-5859	38	52	1	1	NUM
ejpam-5859	38	53	1	1	NUM
ejpam-5859	38	54	1	1	NUM
ejpam-5859	38	55	k.	k.	NOUN
ejpam-5859	38	56	nakwan	nakwan	PROPN
ejpam-5859	38	57	,	,	PUNCT
ejpam-5859	38	58	p.	p.	PROPN
ejpam-5859	38	59	luangchaisri	luangchaisri	VERB
ejpam-5859	38	60	,	,	PUNCT
ejpam-5859	38	61	t.	t.	PROPN
ejpam-5859	38	62	changphas	changphas	PROPN
ejpam-5859	38	63	/	/	SYM
ejpam-5859	38	64	eur	eur	PROPN
ejpam-5859	38	65	.	.	PUNCT
ejpam-5859	39	1	j.	j.	PROPN
ejpam-5859	39	2	pure	pure	PROPN
ejpam-5859	39	3	appl	appl	PROPN
ejpam-5859	39	4	.	.	PROPN
ejpam-5859	39	5	math	math	PROPN
ejpam-5859	39	6	,	,	PUNCT
ejpam-5859	39	7	18	18	NUM
ejpam-5859	39	8	(	(	PUNCT
ejpam-5859	39	9	2	2	NUM
ejpam-5859	39	10	)	)	PUNCT
ejpam-5859	39	11	(	(	PUNCT
ejpam-5859	39	12	2025	2025	NUM
ejpam-5859	39	13	)	)	PUNCT
ejpam-5859	39	14	,	,	PUNCT
ejpam-5859	39	15	5859	5859	NUM
ejpam-5859	39	16	3	3	NUM
ejpam-5859	39	17	of	of	ADP
ejpam-5859	39	18	8	8	NUM
ejpam-5859	39	19	and	and	CCONJ
ejpam-5859	39	20	≤=	≤=	PROPN
ejpam-5859	39	21	{	{	PUNCT
ejpam-5859	39	22	(	(	PUNCT
ejpam-5859	39	23	0	0	NUM
ejpam-5859	39	24	,	,	PUNCT
ejpam-5859	39	25	0	0	NUM
ejpam-5859	39	26	)	)	PUNCT
ejpam-5859	39	27	,	,	PUNCT
ejpam-5859	39	28	(	(	PUNCT
ejpam-5859	39	29	1	1	NUM
ejpam-5859	39	30	,	,	PUNCT
ejpam-5859	39	31	1	1	NUM
ejpam-5859	39	32	)	)	PUNCT
ejpam-5859	39	33	,	,	PUNCT
ejpam-5859	39	34	(	(	PUNCT
ejpam-5859	39	35	a	a	X
ejpam-5859	39	36	,	,	PUNCT
ejpam-5859	39	37	a	a	NOUN
ejpam-5859	39	38	)	)	PUNCT
ejpam-5859	39	39	,	,	PUNCT
ejpam-5859	39	40	(	(	PUNCT
ejpam-5859	39	41	a	a	DET
ejpam-5859	39	42	,	,	PUNCT
ejpam-5859	39	43	1	1	NUM
ejpam-5859	39	44	)	)	PUNCT
ejpam-5859	39	45	,	,	PUNCT
ejpam-5859	39	46	(	(	PUNCT
ejpam-5859	39	47	0	0	NUM
ejpam-5859	39	48	,	,	PUNCT
ejpam-5859	39	49	a	a	PRON
ejpam-5859	39	50	)	)	PUNCT
ejpam-5859	39	51	,	,	PUNCT
ejpam-5859	39	52	(	(	PUNCT
ejpam-5859	39	53	0	0	NUM
ejpam-5859	39	54	,	,	PUNCT
ejpam-5859	39	55	1	1	NUM
ejpam-5859	39	56	)	)	PUNCT
ejpam-5859	39	57	}	}	PUNCT
ejpam-5859	39	58	.	.	PUNCT
ejpam-5859	40	1	we	we	PRON
ejpam-5859	40	2	place	place	VERB
ejpam-5859	40	3	x1x2	x1x2	PUNCT
ejpam-5859	41	1	in	in	ADP
ejpam-5859	41	2	the	the	DET
ejpam-5859	41	3	first	first	ADJ
ejpam-5859	41	4	column	column	NOUN
ejpam-5859	41	5	and	and	CCONJ
ejpam-5859	41	6	x3	x3	VERB
ejpam-5859	41	7	in	in	ADP
ejpam-5859	41	8	the	the	DET
ejpam-5859	41	9	first	first	ADJ
ejpam-5859	41	10	row	row	NOUN
ejpam-5859	41	11	to	to	PART
ejpam-5859	41	12	express	express	VERB
ejpam-5859	41	13	the	the	DET
ejpam-5859	41	14	calculation	calculation	NOUN
ejpam-5859	41	15	[	[	X
ejpam-5859	41	16	x1x2x3	x1x2x3	X
ejpam-5859	41	17	]	]	X
ejpam-5859	41	18	using	use	VERB
ejpam-5859	41	19	a	a	DET
ejpam-5859	41	20	multiplication	multiplication	NOUN
ejpam-5859	41	21	table	table	NOUN
ejpam-5859	41	22	.	.	PUNCT
ejpam-5859	42	1	observed	observe	VERB
ejpam-5859	42	2	that	that	SCONJ
ejpam-5859	42	3	the	the	DET
ejpam-5859	42	4	greatest	great	ADJ
ejpam-5859	42	5	element	element	NOUN
ejpam-5859	42	6	1	1	NUM
ejpam-5859	42	7	is	be	AUX
ejpam-5859	42	8	not	not	PART
ejpam-5859	42	9	identity	identity	NOUN
ejpam-5859	42	10	since	since	SCONJ
ejpam-5859	42	11	[	[	X
ejpam-5859	42	12	1a1	1a1	NUM
ejpam-5859	42	13	]	]	X
ejpam-5859	42	14	=	=	SYM
ejpam-5859	42	15	0	0	NUM
ejpam-5859	42	16	̸=	̸=	PROPN
ejpam-5859	42	17	a.	a.	NOUN
ejpam-5859	42	18	the	the	DET
ejpam-5859	42	19	following	following	NOUN
ejpam-5859	42	20	shows	show	VERB
ejpam-5859	42	21	that	that	SCONJ
ejpam-5859	42	22	not	not	PART
ejpam-5859	42	23	every	every	DET
ejpam-5859	42	24	npots	npot	NOUN
ejpam-5859	42	25	with	with	ADP
ejpam-5859	42	26	identity	identity	NOUN
ejpam-5859	42	27	admits	admit	VERB
ejpam-5859	42	28	the	the	DET
ejpam-5859	42	29	inpots	inpot	NOUN
ejpam-5859	42	30	.	.	PUNCT
ejpam-5859	43	1	example	example	NOUN
ejpam-5859	44	1	2	2	NUM
ejpam-5859	44	2	.	.	PUNCT
ejpam-5859	44	3	let	let	VERB
ejpam-5859	44	4	us	we	PRON
ejpam-5859	44	5	consider	consider	VERB
ejpam-5859	44	6	a	a	DET
ejpam-5859	44	7	npots	npot	NOUN
ejpam-5859	44	8	(	(	PUNCT
ejpam-5859	44	9	t	t	PROPN
ejpam-5859	44	10	,	,	PUNCT
ejpam-5859	44	11	[	[	PUNCT
ejpam-5859	44	12	]	]	X
ejpam-5859	44	13	,	,	PUNCT
ejpam-5859	44	14	≤	≤	NUM
ejpam-5859	44	15	)	)	PUNCT
ejpam-5859	44	16	defined	define	VERB
ejpam-5859	44	17	as	as	SCONJ
ejpam-5859	44	18	follows	follow	VERB
ejpam-5859	44	19	:	:	PUNCT
ejpam-5859	44	20	[	[	PUNCT
ejpam-5859	44	21	]	]	X
ejpam-5859	44	22	1	1	NUM
ejpam-5859	44	23	2	2	NUM
ejpam-5859	44	24	3	3	NUM
ejpam-5859	44	25	4	4	NUM
ejpam-5859	44	26	6	6	NUM
ejpam-5859	44	27	11	11	NUM
ejpam-5859	44	28	1	1	NUM
ejpam-5859	44	29	2	2	NUM
ejpam-5859	44	30	3	3	NUM
ejpam-5859	44	31	4	4	NUM
ejpam-5859	44	32	6	6	NUM
ejpam-5859	44	33	12	12	NUM
ejpam-5859	44	34	2	2	NUM
ejpam-5859	44	35	2	2	NUM
ejpam-5859	44	36	6	6	NUM
ejpam-5859	44	37	4	4	NUM
ejpam-5859	44	38	6	6	NUM
ejpam-5859	44	39	13	13	NUM
ejpam-5859	44	40	3	3	NUM
ejpam-5859	44	41	3	3	NUM
ejpam-5859	44	42	3	3	NUM
ejpam-5859	44	43	6	6	NUM
ejpam-5859	44	44	6	6	NUM
ejpam-5859	44	45	14	14	NUM
ejpam-5859	44	46	4	4	NUM
ejpam-5859	44	47	4	4	NUM
ejpam-5859	44	48	6	6	NUM
ejpam-5859	44	49	4	4	NUM
ejpam-5859	44	50	6	6	NUM
ejpam-5859	44	51	16	16	NUM
ejpam-5859	44	52	6	6	NUM
ejpam-5859	44	53	6	6	NUM
ejpam-5859	44	54	6	6	NUM
ejpam-5859	44	55	6	6	NUM
ejpam-5859	44	56	6	6	NUM
ejpam-5859	44	57	[	[	PUNCT
ejpam-5859	44	58	]	]	SYM
ejpam-5859	44	59	1	1	NUM
ejpam-5859	44	60	2	2	NUM
ejpam-5859	44	61	3	3	NUM
ejpam-5859	44	62	4	4	NUM
ejpam-5859	44	63	6	6	NUM
ejpam-5859	44	64	21	21	NUM
ejpam-5859	44	65	2	2	NUM
ejpam-5859	44	66	2	2	NUM
ejpam-5859	44	67	6	6	NUM
ejpam-5859	44	68	4	4	NUM
ejpam-5859	44	69	6	6	NUM
ejpam-5859	44	70	22	22	NUM
ejpam-5859	44	71	2	2	NUM
ejpam-5859	44	72	2	2	NUM
ejpam-5859	44	73	6	6	NUM
ejpam-5859	44	74	4	4	NUM
ejpam-5859	44	75	6	6	NUM
ejpam-5859	44	76	23	23	NUM
ejpam-5859	44	77	6	6	NUM
ejpam-5859	44	78	6	6	NUM
ejpam-5859	44	79	6	6	NUM
ejpam-5859	44	80	6	6	NUM
ejpam-5859	44	81	6	6	NUM
ejpam-5859	44	82	24	24	NUM
ejpam-5859	44	83	4	4	NUM
ejpam-5859	44	84	4	4	NUM
ejpam-5859	44	85	6	6	NUM
ejpam-5859	44	86	4	4	NUM
ejpam-5859	44	87	6	6	NUM
ejpam-5859	44	88	26	26	NUM
ejpam-5859	44	89	6	6	NUM
ejpam-5859	44	90	6	6	NUM
ejpam-5859	44	91	6	6	NUM
ejpam-5859	44	92	6	6	NUM
ejpam-5859	44	93	6	6	NUM
ejpam-5859	44	94	[	[	PUNCT
ejpam-5859	44	95	]	]	SYM
ejpam-5859	44	96	1	1	NUM
ejpam-5859	44	97	2	2	NUM
ejpam-5859	44	98	3	3	NUM
ejpam-5859	44	99	4	4	NUM
ejpam-5859	44	100	6	6	NUM
ejpam-5859	44	101	31	31	NUM
ejpam-5859	44	102	3	3	NUM
ejpam-5859	44	103	6	6	NUM
ejpam-5859	44	104	3	3	NUM
ejpam-5859	44	105	6	6	NUM
ejpam-5859	44	106	6	6	NUM
ejpam-5859	44	107	32	32	NUM
ejpam-5859	44	108	6	6	NUM
ejpam-5859	44	109	6	6	NUM
ejpam-5859	44	110	6	6	NUM
ejpam-5859	44	111	6	6	NUM
ejpam-5859	44	112	6	6	NUM
ejpam-5859	44	113	33	33	NUM
ejpam-5859	44	114	3	3	NUM
ejpam-5859	44	115	6	6	NUM
ejpam-5859	44	116	3	3	NUM
ejpam-5859	44	117	6	6	NUM
ejpam-5859	44	118	6	6	NUM
ejpam-5859	44	119	34	34	NUM
ejpam-5859	44	120	6	6	NUM
ejpam-5859	44	121	6	6	NUM
ejpam-5859	44	122	6	6	NUM
ejpam-5859	44	123	6	6	NUM
ejpam-5859	44	124	6	6	NUM
ejpam-5859	44	125	36	36	NUM
ejpam-5859	44	126	6	6	NUM
ejpam-5859	44	127	6	6	NUM
ejpam-5859	44	128	6	6	NUM
ejpam-5859	44	129	6	6	NUM
ejpam-5859	44	130	6	6	NUM
ejpam-5859	44	131	[	[	PUNCT
ejpam-5859	44	132	]	]	SYM
ejpam-5859	44	133	1	1	NUM
ejpam-5859	44	134	2	2	NUM
ejpam-5859	44	135	3	3	NUM
ejpam-5859	44	136	4	4	NUM
ejpam-5859	44	137	6	6	NUM
ejpam-5859	44	138	41	41	NUM
ejpam-5859	44	139	4	4	NUM
ejpam-5859	44	140	4	4	NUM
ejpam-5859	44	141	6	6	NUM
ejpam-5859	44	142	4	4	NUM
ejpam-5859	44	143	6	6	NUM
ejpam-5859	44	144	42	42	NUM
ejpam-5859	44	145	4	4	NUM
ejpam-5859	44	146	4	4	NUM
ejpam-5859	44	147	6	6	NUM
ejpam-5859	44	148	4	4	NUM
ejpam-5859	44	149	6	6	NUM
ejpam-5859	44	150	43	43	NUM
ejpam-5859	44	151	6	6	NUM
ejpam-5859	44	152	6	6	NUM
ejpam-5859	44	153	6	6	NUM
ejpam-5859	44	154	6	6	NUM
ejpam-5859	44	155	6	6	NUM
ejpam-5859	44	156	44	44	NUM
ejpam-5859	44	157	4	4	NUM
ejpam-5859	44	158	4	4	NUM
ejpam-5859	44	159	6	6	NUM
ejpam-5859	44	160	4	4	NUM
ejpam-5859	44	161	6	6	NUM
ejpam-5859	44	162	46	46	NUM
ejpam-5859	44	163	6	6	NUM
ejpam-5859	44	164	6	6	NUM
ejpam-5859	44	165	6	6	NUM
ejpam-5859	44	166	6	6	NUM
ejpam-5859	44	167	6	6	NUM
ejpam-5859	44	168	[	[	PUNCT
ejpam-5859	44	169	]	]	SYM
ejpam-5859	44	170	1	1	NUM
ejpam-5859	44	171	2	2	NUM
ejpam-5859	44	172	3	3	NUM
ejpam-5859	44	173	4	4	NUM
ejpam-5859	44	174	6	6	NUM
ejpam-5859	44	175	61	61	NUM
ejpam-5859	44	176	6	6	NUM
ejpam-5859	44	177	6	6	NUM
ejpam-5859	44	178	6	6	NUM
ejpam-5859	44	179	6	6	NUM
ejpam-5859	44	180	6	6	NUM
ejpam-5859	44	181	62	62	NUM
ejpam-5859	44	182	6	6	NUM
ejpam-5859	44	183	6	6	NUM
ejpam-5859	44	184	6	6	NUM
ejpam-5859	44	185	6	6	NUM
ejpam-5859	44	186	6	6	NUM
ejpam-5859	44	187	63	63	NUM
ejpam-5859	44	188	6	6	NUM
ejpam-5859	44	189	6	6	NUM
ejpam-5859	44	190	6	6	NUM
ejpam-5859	44	191	6	6	NUM
ejpam-5859	44	192	6	6	NUM
ejpam-5859	44	193	64	64	NUM
ejpam-5859	44	194	6	6	NUM
ejpam-5859	44	195	6	6	NUM
ejpam-5859	44	196	6	6	NUM
ejpam-5859	44	197	6	6	NUM
ejpam-5859	44	198	6	6	NUM
ejpam-5859	44	199	66	66	NUM
ejpam-5859	44	200	6	6	NUM
ejpam-5859	44	201	6	6	NUM
ejpam-5859	44	202	6	6	NUM
ejpam-5859	44	203	6	6	NUM
ejpam-5859	44	204	6	6	NUM
ejpam-5859	44	205	and	and	CCONJ
ejpam-5859	44	206	≤	≤	NUM
ejpam-5859	44	207	=	=	SYM
ejpam-5859	44	208	{	{	PUNCT
ejpam-5859	44	209	(	(	PUNCT
ejpam-5859	44	210	1	1	NUM
ejpam-5859	44	211	,	,	PUNCT
ejpam-5859	44	212	1	1	NUM
ejpam-5859	44	213	)	)	PUNCT
ejpam-5859	44	214	,	,	PUNCT
ejpam-5859	44	215	(	(	PUNCT
ejpam-5859	44	216	2	2	NUM
ejpam-5859	44	217	,	,	PUNCT
ejpam-5859	44	218	2	2	NUM
ejpam-5859	44	219	)	)	PUNCT
ejpam-5859	44	220	,	,	PUNCT
ejpam-5859	44	221	(	(	PUNCT
ejpam-5859	44	222	3	3	NUM
ejpam-5859	44	223	,	,	PUNCT
ejpam-5859	44	224	3	3	NUM
ejpam-5859	44	225	)	)	PUNCT
ejpam-5859	44	226	,	,	PUNCT
ejpam-5859	44	227	(	(	PUNCT
ejpam-5859	44	228	4	4	NUM
ejpam-5859	44	229	,	,	PUNCT
ejpam-5859	44	230	4	4	NUM
ejpam-5859	44	231	)	)	PUNCT
ejpam-5859	44	232	,	,	PUNCT
ejpam-5859	44	233	(	(	PUNCT
ejpam-5859	44	234	6	6	NUM
ejpam-5859	44	235	,	,	PUNCT
ejpam-5859	44	236	6	6	NUM
ejpam-5859	44	237	)	)	PUNCT
ejpam-5859	44	238	,	,	PUNCT
ejpam-5859	44	239	(	(	PUNCT
ejpam-5859	44	240	3	3	NUM
ejpam-5859	44	241	,	,	PUNCT
ejpam-5859	44	242	1	1	NUM
ejpam-5859	44	243	)	)	PUNCT
ejpam-5859	44	244	,	,	PUNCT
ejpam-5859	44	245	(	(	PUNCT
ejpam-5859	44	246	2	2	NUM
ejpam-5859	44	247	,	,	PUNCT
ejpam-5859	44	248	1	1	NUM
ejpam-5859	44	249	)	)	PUNCT
ejpam-5859	44	250	,	,	PUNCT
ejpam-5859	44	251	(	(	PUNCT
ejpam-5859	44	252	4	4	NUM
ejpam-5859	44	253	,	,	PUNCT
ejpam-5859	44	254	a	a	NOUN
ejpam-5859	44	255	)	)	PUNCT
ejpam-5859	44	256	,	,	PUNCT
ejpam-5859	44	257	(	(	PUNCT
ejpam-5859	44	258	4	4	NUM
ejpam-5859	44	259	,	,	PUNCT
ejpam-5859	44	260	1	1	NUM
ejpam-5859	44	261	)	)	PUNCT
ejpam-5859	44	262	,	,	PUNCT
ejpam-5859	44	263	(	(	PUNCT
ejpam-5859	44	264	6	6	NUM
ejpam-5859	44	265	,	,	PUNCT
ejpam-5859	44	266	4	4	NUM
ejpam-5859	44	267	)	)	PUNCT
ejpam-5859	44	268	,	,	PUNCT
ejpam-5859	44	269	(	(	PUNCT
ejpam-5859	44	270	6	6	NUM
ejpam-5859	44	271	,	,	PUNCT
ejpam-5859	44	272	2	2	NUM
ejpam-5859	44	273	)	)	PUNCT
ejpam-5859	44	274	,	,	PUNCT
ejpam-5859	44	275	(	(	PUNCT
ejpam-5859	44	276	6	6	NUM
ejpam-5859	44	277	,	,	PUNCT
ejpam-5859	44	278	3	3	NUM
ejpam-5859	44	279	)	)	PUNCT
ejpam-5859	44	280	,	,	PUNCT
ejpam-5859	44	281	(	(	PUNCT
ejpam-5859	44	282	6	6	NUM
ejpam-5859	44	283	,	,	PUNCT
ejpam-5859	44	284	1	1	NUM
ejpam-5859	44	285	)	)	PUNCT
ejpam-5859	44	286	}	}	PUNCT
ejpam-5859	44	287	.	.	PUNCT
ejpam-5859	45	1	the	the	DET
ejpam-5859	45	2	element	element	NOUN
ejpam-5859	45	3	1	1	NUM
ejpam-5859	45	4	is	be	AUX
ejpam-5859	45	5	the	the	DET
ejpam-5859	45	6	greatest	great	ADJ
ejpam-5859	45	7	element	element	NOUN
ejpam-5859	45	8	.	.	PUNCT
ejpam-5859	46	1	suppose	suppose	VERB
ejpam-5859	46	2	t	t	PROPN
ejpam-5859	46	3	is	be	AUX
ejpam-5859	46	4	an	an	DET
ejpam-5859	46	5	inpots	inpot	NOUN
ejpam-5859	46	6	with	with	ADP
ejpam-5859	46	7	ternary	ternary	ADJ
ejpam-5859	46	8	implication	implication	NOUN
ejpam-5859	46	9	[	[	PUNCT
ejpam-5859	46	10	]	]	X
ejpam-5859	46	11	∗.	∗.	X
ejpam-5859	46	12	clearly	clearly	ADV
ejpam-5859	46	13	,	,	PUNCT
ejpam-5859	46	14	[	[	X
ejpam-5859	46	15	322	322	NUM
ejpam-5859	46	16	]	]	X
ejpam-5859	46	17	=	=	PUNCT
ejpam-5859	46	18	6	6	NUM
ejpam-5859	46	19	≤	≤	NUM
ejpam-5859	46	20	4	4	NUM
ejpam-5859	46	21	and	and	CCONJ
ejpam-5859	46	22	[	[	X
ejpam-5859	46	23	422	422	NUM
ejpam-5859	46	24	]	]	X
ejpam-5859	46	25	=	=	SYM
ejpam-5859	46	26	2	2	NUM
ejpam-5859	46	27	≤	≤	NUM
ejpam-5859	46	28	2	2	NUM
ejpam-5859	46	29	.	.	PUNCT
ejpam-5859	47	1	then	then	ADV
ejpam-5859	47	2	3	3	NUM
ejpam-5859	47	3	≤	≤	NOUN
ejpam-5859	48	1	[	[	X
ejpam-5859	48	2	224]∗	224]∗	NUM
ejpam-5859	48	3	and	and	CCONJ
ejpam-5859	48	4	4	4	NUM
ejpam-5859	48	5	≤	≤	NOUN
ejpam-5859	49	1	[	[	X
ejpam-5859	49	2	224]∗	224]∗	NUM
ejpam-5859	49	3	,	,	PUNCT
ejpam-5859	49	4	so	so	SCONJ
ejpam-5859	49	5	[	[	X
ejpam-5859	49	6	224]∗	224]∗	NUM
ejpam-5859	49	7	=	=	SYM
ejpam-5859	49	8	1	1	NUM
ejpam-5859	49	9	.	.	PUNCT
ejpam-5859	50	1	as	as	ADP
ejpam-5859	50	2	1	1	NUM
ejpam-5859	50	3	≤	≤	NOUN
ejpam-5859	50	4	[	[	X
ejpam-5859	50	5	224]∗	224]∗	NUM
ejpam-5859	50	6	,	,	PUNCT
ejpam-5859	50	7	we	we	PRON
ejpam-5859	50	8	have	have	VERB
ejpam-5859	50	9	2	2	NUM
ejpam-5859	50	10	=	=	SYM
ejpam-5859	51	1	[	[	X
ejpam-5859	51	2	122	122	NUM
ejpam-5859	51	3	]	]	PUNCT
ejpam-5859	51	4	≤	≤	NUM
ejpam-5859	51	5	4	4	NUM
ejpam-5859	51	6	.	.	PUNCT
ejpam-5859	52	1	this	this	PRON
ejpam-5859	52	2	is	be	AUX
ejpam-5859	52	3	a	a	DET
ejpam-5859	52	4	contradiction	contradiction	NOUN
ejpam-5859	52	5	.	.	PUNCT
ejpam-5859	53	1	hence	hence	ADV
ejpam-5859	53	2	,	,	PUNCT
ejpam-5859	53	3	t	t	PROPN
ejpam-5859	53	4	is	be	AUX
ejpam-5859	53	5	not	not	PART
ejpam-5859	53	6	an	an	DET
ejpam-5859	53	7	inpots	inpot	NOUN
ejpam-5859	53	8	.	.	PUNCT
ejpam-5859	54	1	definition	definition	NOUN
ejpam-5859	54	2	3	3	NUM
ejpam-5859	54	3	.	.	PUNCT
ejpam-5859	55	1	[	[	X
ejpam-5859	55	2	9	9	NUM
ejpam-5859	55	3	]	]	PUNCT
ejpam-5859	55	4	an	an	DET
ejpam-5859	55	5	inpots	inpot	NOUN
ejpam-5859	55	6	(	(	PUNCT
ejpam-5859	55	7	t	t	NOUN
ejpam-5859	55	8	,	,	PUNCT
ejpam-5859	55	9	[	[	PUNCT
ejpam-5859	55	10	]	]	X
ejpam-5859	55	11	,	,	PUNCT
ejpam-5859	55	12	≤	≤	NUM
ejpam-5859	55	13	,	,	PUNCT
ejpam-5859	55	14	[	[	PUNCT
ejpam-5859	55	15	]	]	X
ejpam-5859	55	16	∗	∗	NOUN
ejpam-5859	55	17	)	)	PUNCT
ejpam-5859	55	18	is	be	AUX
ejpam-5859	55	19	called	call	VERB
ejpam-5859	55	20	commutative	commutative	ADJ
ejpam-5859	55	21	if	if	SCONJ
ejpam-5859	55	22	[	[	X
ejpam-5859	55	23	a1a2a3	a1a2a3	X
ejpam-5859	55	24	]	]	X
ejpam-5859	55	25	=	=	SYM
ejpam-5859	56	1	[	[	X
ejpam-5859	56	2	aα(1)aα(2)aα(3	aα(1)aα(2)aα(3	NOUN
ejpam-5859	56	3	)	)	PUNCT
ejpam-5859	56	4	]	]	PUNCT
ejpam-5859	56	5	for	for	ADP
ejpam-5859	56	6	any	any	DET
ejpam-5859	56	7	permutation	permutation	NOUN
ejpam-5859	56	8	α	α	PRON
ejpam-5859	56	9	∈	∈	PROPN
ejpam-5859	56	10	s3	s3	PROPN
ejpam-5859	56	11	.	.	PUNCT
ejpam-5859	57	1	k.	k.	PROPN
ejpam-5859	57	2	nakwan	nakwan	PROPN
ejpam-5859	57	3	,	,	PUNCT
ejpam-5859	57	4	p.	p.	PROPN
ejpam-5859	57	5	luangchaisri	luangchaisri	VERB
ejpam-5859	57	6	,	,	PUNCT
ejpam-5859	57	7	t.	t.	PROPN
ejpam-5859	57	8	changphas	changphas	PROPN
ejpam-5859	57	9	/	/	SYM
ejpam-5859	57	10	eur	eur	PROPN
ejpam-5859	57	11	.	.	PUNCT
ejpam-5859	58	1	j.	j.	PROPN
ejpam-5859	58	2	pure	pure	PROPN
ejpam-5859	58	3	appl	appl	PROPN
ejpam-5859	58	4	.	.	PROPN
ejpam-5859	58	5	math	math	PROPN
ejpam-5859	58	6	,	,	PUNCT
ejpam-5859	58	7	18	18	NUM
ejpam-5859	58	8	(	(	PUNCT
ejpam-5859	58	9	2	2	NUM
ejpam-5859	58	10	)	)	PUNCT
ejpam-5859	58	11	(	(	PUNCT
ejpam-5859	58	12	2025	2025	NUM
ejpam-5859	58	13	)	)	PUNCT
ejpam-5859	58	14	,	,	PUNCT
ejpam-5859	58	15	5859	5859	NUM
ejpam-5859	58	16	4	4	NUM
ejpam-5859	58	17	of	of	ADP
ejpam-5859	58	18	8	8	NUM
ejpam-5859	58	19	the	the	DET
ejpam-5859	58	20	example	example	NOUN
ejpam-5859	58	21	shows	show	VERB
ejpam-5859	58	22	an	an	DET
ejpam-5859	58	23	infinite	infinite	ADJ
ejpam-5859	58	24	commutative	commutative	ADJ
ejpam-5859	58	25	inpots	inpot	NOUN
ejpam-5859	58	26	.	.	PUNCT
ejpam-5859	59	1	example	example	NOUN
ejpam-5859	60	1	3	3	NUM
ejpam-5859	60	2	.	.	PUNCT
ejpam-5859	61	1	[	[	X
ejpam-5859	61	2	7	7	X
ejpam-5859	61	3	]	]	X
ejpam-5859	61	4	let	let	VERB
ejpam-5859	61	5	z+	z+	NUM
ejpam-5859	61	6	be	be	AUX
ejpam-5859	61	7	a	a	DET
ejpam-5859	61	8	ts	ts	ADJ
ejpam-5859	61	9	such	such	ADJ
ejpam-5859	61	10	that	that	SCONJ
ejpam-5859	61	11	[	[	X
ejpam-5859	61	12	abc	abc	X
ejpam-5859	61	13	]	]	X
ejpam-5859	61	14	=	=	PUNCT
ejpam-5859	61	15	abc	abc	PROPN
ejpam-5859	61	16	for	for	ADP
ejpam-5859	61	17	all	all	DET
ejpam-5859	61	18	a	a	DET
ejpam-5859	61	19	,	,	PUNCT
ejpam-5859	61	20	b	b	NOUN
ejpam-5859	61	21	,	,	PUNCT
ejpam-5859	61	22	c	c	PROPN
ejpam-5859	61	23	∈	∈	PROPN
ejpam-5859	61	24	z+	z+	X
ejpam-5859	61	25	.	.	X
ejpam-5859	62	1	consider	consider	VERB
ejpam-5859	62	2	≤=	≤=	PROPN
ejpam-5859	62	3	{	{	PUNCT
ejpam-5859	62	4	(	(	PUNCT
ejpam-5859	62	5	a	a	PRON
ejpam-5859	62	6	,	,	PUNCT
ejpam-5859	62	7	b	b	NOUN
ejpam-5859	62	8	)	)	PUNCT
ejpam-5859	62	9	∈	∈	PROPN
ejpam-5859	62	10	z+	z+	NUM
ejpam-5859	62	11	×	×	PROPN
ejpam-5859	62	12	z+	z+	NUM
ejpam-5859	62	13	:	:	PUNCT
ejpam-5859	62	14	b	b	X
ejpam-5859	62	15	|	|	ADV
ejpam-5859	62	16	a	a	PRON
ejpam-5859	62	17	}	}	PUNCT
ejpam-5859	62	18	.	.	PUNCT
ejpam-5859	63	1	here	here	ADV
ejpam-5859	63	2	,	,	PUNCT
ejpam-5859	63	3	b	b	NOUN
ejpam-5859	63	4	|	|	ADV
ejpam-5859	63	5	a	a	DET
ejpam-5859	63	6	means	means	NOUN
ejpam-5859	63	7	b	b	NOUN
ejpam-5859	63	8	divides	divide	NOUN
ejpam-5859	63	9	a.	a.	NOUN
ejpam-5859	63	10	then	then	ADV
ejpam-5859	63	11	(	(	PUNCT
ejpam-5859	63	12	z+	z+	X
ejpam-5859	63	13	,	,	PUNCT
ejpam-5859	63	14	[	[	PUNCT
ejpam-5859	63	15	]	]	X
ejpam-5859	63	16	,	,	PUNCT
ejpam-5859	63	17	≤	≤	NUM
ejpam-5859	63	18	)	)	PUNCT
ejpam-5859	63	19	is	be	AUX
ejpam-5859	63	20	a	a	DET
ejpam-5859	63	21	commutative	commutative	ADJ
ejpam-5859	63	22	npots	npot	NOUN
ejpam-5859	63	23	;	;	PUNCT
ejpam-5859	63	24	1	1	NUM
ejpam-5859	63	25	is	be	AUX
ejpam-5859	63	26	the	the	DET
ejpam-5859	63	27	greatest	great	ADJ
ejpam-5859	63	28	element	element	NOUN
ejpam-5859	63	29	.	.	PUNCT
ejpam-5859	64	1	define	define	VERB
ejpam-5859	64	2	[	[	X
ejpam-5859	64	3	abc]∗	abc]∗	X
ejpam-5859	64	4	=	=	SYM
ejpam-5859	64	5	c	c	NOUN
ejpam-5859	64	6	gcd(ab	gcd(ab	NOUN
ejpam-5859	64	7	,	,	PUNCT
ejpam-5859	64	8	c	c	NOUN
ejpam-5859	64	9	)	)	PUNCT
ejpam-5859	64	10	for	for	ADP
ejpam-5859	64	11	all	all	DET
ejpam-5859	64	12	a	a	DET
ejpam-5859	64	13	,	,	PUNCT
ejpam-5859	64	14	b	b	NOUN
ejpam-5859	64	15	,	,	PUNCT
ejpam-5859	64	16	c	c	PROPN
ejpam-5859	64	17	∈	∈	PROPN
ejpam-5859	64	18	z+	z+	PUNCT
ejpam-5859	64	19	.	.	PUNCT
ejpam-5859	65	1	then	then	ADV
ejpam-5859	65	2	(	(	PUNCT
ejpam-5859	65	3	z+	z+	X
ejpam-5859	65	4	,	,	PUNCT
ejpam-5859	65	5	[	[	PUNCT
ejpam-5859	65	6	]	]	X
ejpam-5859	65	7	,	,	PUNCT
ejpam-5859	65	8	≤	≤	NUM
ejpam-5859	65	9	,	,	PUNCT
ejpam-5859	65	10	[	[	PUNCT
ejpam-5859	65	11	]	]	X
ejpam-5859	65	12	∗	∗	NOUN
ejpam-5859	65	13	)	)	PUNCT
ejpam-5859	65	14	is	be	AUX
ejpam-5859	65	15	a	a	DET
ejpam-5859	65	16	commutative	commutative	ADJ
ejpam-5859	65	17	inpots	inpot	NOUN
ejpam-5859	65	18	.	.	PUNCT
ejpam-5859	66	1	theorem	theorem	NOUN
ejpam-5859	66	2	1	1	NUM
ejpam-5859	66	3	.	.	PUNCT
ejpam-5859	67	1	[	[	X
ejpam-5859	67	2	7	7	X
ejpam-5859	67	3	]	]	X
ejpam-5859	67	4	let	let	NOUN
ejpam-5859	67	5	(	(	PUNCT
ejpam-5859	67	6	t	t	NOUN
ejpam-5859	67	7	,	,	PUNCT
ejpam-5859	67	8	[	[	PUNCT
ejpam-5859	67	9	]	]	X
ejpam-5859	67	10	,	,	PUNCT
ejpam-5859	67	11	≤	≤	NUM
ejpam-5859	67	12	,	,	PUNCT
ejpam-5859	67	13	[	[	PUNCT
ejpam-5859	67	14	]	]	X
ejpam-5859	67	15	∗	∗	NOUN
ejpam-5859	67	16	)	)	PUNCT
ejpam-5859	67	17	be	be	VERB
ejpam-5859	67	18	an	an	DET
ejpam-5859	67	19	inpots	inpot	NOUN
ejpam-5859	67	20	.	.	PUNCT
ejpam-5859	68	1	then	then	ADV
ejpam-5859	68	2	,	,	PUNCT
ejpam-5859	68	3	for	for	ADP
ejpam-5859	68	4	a	a	DET
ejpam-5859	68	5	,	,	PUNCT
ejpam-5859	68	6	b	b	PROPN
ejpam-5859	68	7	∈	∈	PROPN
ejpam-5859	68	8	t	t	NOUN
ejpam-5859	68	9	,	,	PUNCT
ejpam-5859	68	10	(	(	PUNCT
ejpam-5859	68	11	1	1	X
ejpam-5859	68	12	)	)	PUNCT
ejpam-5859	68	13	a	a	DET
ejpam-5859	68	14	≤	≤	NOUN
ejpam-5859	68	15	[	[	X
ejpam-5859	68	16	aaa]∗	aaa]∗	NOUN
ejpam-5859	68	17	;	;	PUNCT
ejpam-5859	68	18	(	(	PUNCT
ejpam-5859	68	19	2	2	X
ejpam-5859	68	20	)	)	PUNCT
ejpam-5859	69	1	[	[	X
ejpam-5859	69	2	aaa]∗	aaa]∗	NOUN
ejpam-5859	69	3	=	=	PUNCT
ejpam-5859	70	1	[	[	X
ejpam-5859	70	2	bbb]∗	bbb]∗	NOUN
ejpam-5859	70	3	;	;	PUNCT
ejpam-5859	70	4	(	(	PUNCT
ejpam-5859	70	5	3	3	X
ejpam-5859	70	6	)	)	PUNCT
ejpam-5859	70	7	[	[	X
ejpam-5859	70	8	aaa]∗	aaa]∗	PROPN
ejpam-5859	70	9	is	be	AUX
ejpam-5859	70	10	the	the	DET
ejpam-5859	70	11	greatest	great	ADJ
ejpam-5859	70	12	element	element	NOUN
ejpam-5859	70	13	of	of	ADP
ejpam-5859	70	14	t	t	PROPN
ejpam-5859	70	15	;	;	PUNCT
ejpam-5859	70	16	then	then	ADV
ejpam-5859	70	17	an	an	DET
ejpam-5859	70	18	inpots	inpot	NOUN
ejpam-5859	70	19	always	always	ADV
ejpam-5859	70	20	contains	contain	VERB
ejpam-5859	70	21	the	the	DET
ejpam-5859	70	22	greatest	great	ADJ
ejpam-5859	70	23	element	element	NOUN
ejpam-5859	70	24	.	.	PUNCT
ejpam-5859	71	1	let	let	VERB
ejpam-5859	71	2	1	1	NUM
ejpam-5859	71	3	be	be	AUX
ejpam-5859	71	4	the	the	DET
ejpam-5859	71	5	greatest	great	ADJ
ejpam-5859	71	6	element	element	NOUN
ejpam-5859	71	7	of	of	ADP
ejpam-5859	71	8	a	a	DET
ejpam-5859	71	9	npots	npot	NOUN
ejpam-5859	71	10	(	(	PUNCT
ejpam-5859	71	11	t	t	PROPN
ejpam-5859	71	12	,	,	PUNCT
ejpam-5859	71	13	[	[	PUNCT
ejpam-5859	71	14	]	]	X
ejpam-5859	71	15	,	,	PUNCT
ejpam-5859	71	16	≤	≤	NUM
ejpam-5859	71	17	)	)	PUNCT
ejpam-5859	71	18	if	if	SCONJ
ejpam-5859	71	19	exists	exist	VERB
ejpam-5859	71	20	.	.	PUNCT
ejpam-5859	72	1	assume	assume	VERB
ejpam-5859	72	2	1	1	NUM
ejpam-5859	72	3	is	be	AUX
ejpam-5859	72	4	the	the	DET
ejpam-5859	72	5	multiplicative	multiplicative	ADJ
ejpam-5859	72	6	identity	identity	NOUN
ejpam-5859	72	7	.	.	PUNCT
ejpam-5859	73	1	then	then	ADV
ejpam-5859	73	2	,	,	PUNCT
ejpam-5859	73	3	for	for	ADP
ejpam-5859	73	4	any	any	DET
ejpam-5859	73	5	u	u	NOUN
ejpam-5859	73	6	,	,	PUNCT
ejpam-5859	73	7	v	v	NOUN
ejpam-5859	73	8	,	,	PUNCT
ejpam-5859	73	9	w	w	PROPN
ejpam-5859	73	10	∈	∈	PROPN
ejpam-5859	73	11	t	t	NOUN
ejpam-5859	73	12	,	,	PUNCT
ejpam-5859	73	13	[	[	X
ejpam-5859	73	14	uvw	uvw	X
ejpam-5859	73	15	]	]	X
ejpam-5859	73	16	=	=	SYM
ejpam-5859	73	17	1	1	NUM
ejpam-5859	73	18	⇔	⇔	X
ejpam-5859	73	19	u	u	NOUN
ejpam-5859	73	20	=	=	PROPN
ejpam-5859	73	21	1	1	NUM
ejpam-5859	73	22	,	,	PUNCT
ejpam-5859	73	23	v	v	NOUN
ejpam-5859	73	24	=	=	SYM
ejpam-5859	73	25	1	1	NUM
ejpam-5859	73	26	,	,	PUNCT
ejpam-5859	73	27	w	w	NOUN
ejpam-5859	73	28	=	=	NOUN
ejpam-5859	73	29	1	1	X
ejpam-5859	73	30	.	.	PUNCT
ejpam-5859	74	1	throughout	throughout	ADP
ejpam-5859	74	2	this	this	DET
ejpam-5859	74	3	paper	paper	NOUN
ejpam-5859	74	4	,	,	PUNCT
ejpam-5859	74	5	we	we	PRON
ejpam-5859	74	6	assume	assume	VERB
ejpam-5859	74	7	1	1	NUM
ejpam-5859	74	8	is	be	AUX
ejpam-5859	74	9	both	both	CCONJ
ejpam-5859	74	10	the	the	DET
ejpam-5859	74	11	multiplicative	multiplicative	ADJ
ejpam-5859	74	12	identity	identity	NOUN
ejpam-5859	74	13	and	and	CCONJ
ejpam-5859	74	14	the	the	DET
ejpam-5859	74	15	greatest	great	ADJ
ejpam-5859	74	16	element	element	NOUN
ejpam-5859	74	17	of	of	ADP
ejpam-5859	74	18	an	an	DET
ejpam-5859	74	19	inpots	inpot	NOUN
ejpam-5859	74	20	.	.	PUNCT
ejpam-5859	75	1	theorem	theorem	NOUN
ejpam-5859	75	2	2	2	NUM
ejpam-5859	75	3	.	.	PUNCT
ejpam-5859	76	1	[	[	X
ejpam-5859	76	2	7	7	X
ejpam-5859	76	3	]	]	X
ejpam-5859	76	4	let	let	NOUN
ejpam-5859	76	5	(	(	PUNCT
ejpam-5859	76	6	t	t	NOUN
ejpam-5859	76	7	,	,	PUNCT
ejpam-5859	76	8	[	[	PUNCT
ejpam-5859	76	9	]	]	X
ejpam-5859	76	10	,	,	PUNCT
ejpam-5859	76	11	≤	≤	NUM
ejpam-5859	76	12	,	,	PUNCT
ejpam-5859	76	13	[	[	PUNCT
ejpam-5859	76	14	]	]	X
ejpam-5859	76	15	∗	∗	NOUN
ejpam-5859	76	16	)	)	PUNCT
ejpam-5859	76	17	be	be	VERB
ejpam-5859	76	18	an	an	DET
ejpam-5859	76	19	inpots	inpot	NOUN
ejpam-5859	76	20	.	.	PUNCT
ejpam-5859	77	1	then	then	ADV
ejpam-5859	77	2	,	,	PUNCT
ejpam-5859	77	3	for	for	SCONJ
ejpam-5859	77	4	a	a	DET
ejpam-5859	77	5	,	,	PUNCT
ejpam-5859	77	6	b	b	NOUN
ejpam-5859	77	7	,	,	PUNCT
ejpam-5859	77	8	c	c	X
ejpam-5859	77	9	,	,	PUNCT
ejpam-5859	77	10	u	u	NOUN
ejpam-5859	77	11	,	,	PUNCT
ejpam-5859	77	12	v	v	PROPN
ejpam-5859	77	13	∈	∈	PROPN
ejpam-5859	77	14	t	t	NOUN
ejpam-5859	77	15	,	,	PUNCT
ejpam-5859	77	16	(	(	PUNCT
ejpam-5859	77	17	1	1	X
ejpam-5859	77	18	)	)	PUNCT
ejpam-5859	77	19	a	a	DET
ejpam-5859	77	20	≤	≤	NUM
ejpam-5859	77	21	1	1	NUM
ejpam-5859	77	22	,	,	PUNCT
ejpam-5859	77	23	[	[	X
ejpam-5859	77	24	aaa]∗	aaa]∗	ADP
ejpam-5859	77	25	=	=	SYM
ejpam-5859	77	26	1	1	NUM
ejpam-5859	77	27	,	,	PUNCT
ejpam-5859	77	28	a	a	PRON
ejpam-5859	77	29	=	=	X
ejpam-5859	77	30	[	[	X
ejpam-5859	77	31	11a]∗	11a]∗	NUM
ejpam-5859	77	32	;	;	PUNCT
ejpam-5859	77	33	(	(	PUNCT
ejpam-5859	77	34	2	2	X
ejpam-5859	77	35	)	)	PUNCT
ejpam-5859	77	36	a	a	DET
ejpam-5859	77	37	≤	≤	NOUN
ejpam-5859	77	38	[	[	X
ejpam-5859	77	39	bc[abc]]∗	bc[abc]]∗	NOUN
ejpam-5859	77	40	;	;	PUNCT
ejpam-5859	77	41	(	(	PUNCT
ejpam-5859	77	42	3	3	X
ejpam-5859	77	43	)	)	PUNCT
ejpam-5859	77	44	a	a	DET
ejpam-5859	77	45	≤	≤	NOUN
ejpam-5859	77	46	[	[	X
ejpam-5859	77	47	aa[aaa]]∗	aa[aaa]]∗	NOUN
ejpam-5859	77	48	;	;	PUNCT
ejpam-5859	77	49	(	(	PUNCT
ejpam-5859	77	50	4	4	X
ejpam-5859	77	51	)	)	PUNCT
ejpam-5859	77	52	a	a	DET
ejpam-5859	77	53	≤	≤	NOUN
ejpam-5859	77	54	[	[	X
ejpam-5859	77	55	bca]∗	bca]∗	NOUN
ejpam-5859	77	56	;	;	PUNCT
ejpam-5859	77	57	(	(	PUNCT
ejpam-5859	77	58	5	5	X
ejpam-5859	77	59	)	)	PUNCT
ejpam-5859	77	60	if	if	SCONJ
ejpam-5859	77	61	a	a	DET
ejpam-5859	77	62	≤	≤	NUM
ejpam-5859	77	63	b	b	NOUN
ejpam-5859	77	64	,	,	PUNCT
ejpam-5859	77	65	then	then	ADV
ejpam-5859	77	66	[	[	X
ejpam-5859	77	67	buv]∗	buv]∗	NOUN
ejpam-5859	77	68	≤	≤	X
ejpam-5859	77	69	[	[	PUNCT
ejpam-5859	77	70	auv]∗	auv]∗	NOUN
ejpam-5859	77	71	and	and	CCONJ
ejpam-5859	77	72	[	[	X
ejpam-5859	77	73	uva]∗	uva]∗	NOUN
ejpam-5859	77	74	≤	≤	NOUN
ejpam-5859	78	1	[	[	X
ejpam-5859	78	2	uvb]∗	uvb]∗	X
ejpam-5859	78	3	;	;	PUNCT
ejpam-5859	78	4	(	(	PUNCT
ejpam-5859	78	5	6	6	X
ejpam-5859	78	6	)	)	PUNCT
ejpam-5859	78	7	a	a	DET
ejpam-5859	78	8	≤	≤	PROPN
ejpam-5859	78	9	b	b	X
ejpam-5859	78	10	⇔	⇔	X
ejpam-5859	78	11	[	[	X
ejpam-5859	78	12	a1b]∗	a1b]∗	X
ejpam-5859	78	13	=	=	SYM
ejpam-5859	78	14	1	1	NUM
ejpam-5859	78	15	⇔	⇔	X
ejpam-5859	78	16	[	[	X
ejpam-5859	78	17	1ab]∗	1ab]∗	NOUN
ejpam-5859	78	18	=	=	SYM
ejpam-5859	78	19	1	1	NUM
ejpam-5859	78	20	;	;	PUNCT
ejpam-5859	78	21	(	(	PUNCT
ejpam-5859	78	22	7	7	X
ejpam-5859	78	23	)	)	PUNCT
ejpam-5859	79	1	[	[	X
ejpam-5859	79	2	ab[cuv]∗]∗	ab[cuv]∗]∗	X
ejpam-5859	79	3	=	=	PUNCT
ejpam-5859	80	1	[	[	X
ejpam-5859	80	2	[	[	X
ejpam-5859	80	3	abc]uv]∗	abc]uv]∗	X
ejpam-5859	80	4	=	=	PUNCT
ejpam-5859	81	1	[	[	X
ejpam-5859	81	2	a[bcu]v]∗.	a[bcu]v]∗.	PROPN
ejpam-5859	81	3	3	3	X
ejpam-5859	81	4	.	.	PUNCT
ejpam-5859	81	5	filters	filter	NOUN
ejpam-5859	81	6	of	of	ADP
ejpam-5859	81	7	implicative	implicative	NOUN
ejpam-5859	81	8	negatively	negatively	ADV
ejpam-5859	81	9	partially	partially	ADV
ejpam-5859	81	10	ordered	order	VERB
ejpam-5859	81	11	ternary	ternary	ADJ
ejpam-5859	81	12	semigroups	semigroup	NOUN
ejpam-5859	81	13	we	we	PRON
ejpam-5859	81	14	begin	begin	VERB
ejpam-5859	81	15	with	with	ADP
ejpam-5859	81	16	filters	filter	NOUN
ejpam-5859	81	17	of	of	ADP
ejpam-5859	81	18	an	an	DET
ejpam-5859	81	19	inpots	inpot	NOUN
ejpam-5859	81	20	.	.	PUNCT
ejpam-5859	82	1	definition	definition	NOUN
ejpam-5859	82	2	4	4	NUM
ejpam-5859	82	3	.	.	PUNCT
ejpam-5859	83	1	[	[	X
ejpam-5859	83	2	7	7	X
ejpam-5859	83	3	]	]	X
ejpam-5859	83	4	let	let	NOUN
ejpam-5859	83	5	(	(	PUNCT
ejpam-5859	83	6	t	t	NOUN
ejpam-5859	83	7	,	,	PUNCT
ejpam-5859	83	8	[	[	PUNCT
ejpam-5859	83	9	]	]	X
ejpam-5859	83	10	,	,	PUNCT
ejpam-5859	83	11	≤	≤	NUM
ejpam-5859	83	12	,	,	PUNCT
ejpam-5859	83	13	[	[	PUNCT
ejpam-5859	83	14	]	]	X
ejpam-5859	83	15	∗	∗	NOUN
ejpam-5859	83	16	)	)	PUNCT
ejpam-5859	83	17	be	be	VERB
ejpam-5859	83	18	an	an	DET
ejpam-5859	83	19	inpots	inpot	NOUN
ejpam-5859	83	20	.	.	PUNCT
ejpam-5859	84	1	then	then	ADV
ejpam-5859	84	2	∅	∅	NOUN
ejpam-5859	84	3	=	=	NOUN
ejpam-5859	84	4	̸	̸	NUM
ejpam-5859	84	5	f	f	NOUN
ejpam-5859	85	1	⊆	⊆	NUM
ejpam-5859	85	2	t	t	PROPN
ejpam-5859	85	3	is	be	AUX
ejpam-5859	85	4	called	call	VERB
ejpam-5859	85	5	a	a	DET
ejpam-5859	85	6	filter	filter	NOUN
ejpam-5859	85	7	of	of	ADP
ejpam-5859	85	8	t	t	PROPN
ejpam-5859	85	9	if	if	SCONJ
ejpam-5859	85	10	k.	k.	PROPN
ejpam-5859	85	11	nakwan	nakwan	PROPN
ejpam-5859	85	12	,	,	PUNCT
ejpam-5859	85	13	p.	p.	PROPN
ejpam-5859	85	14	luangchaisri	luangchaisri	VERB
ejpam-5859	85	15	,	,	PUNCT
ejpam-5859	85	16	t.	t.	PROPN
ejpam-5859	85	17	changphas	changphas	PROPN
ejpam-5859	85	18	/	/	SYM
ejpam-5859	85	19	eur	eur	PROPN
ejpam-5859	85	20	.	.	PUNCT
ejpam-5859	86	1	j.	j.	PROPN
ejpam-5859	86	2	pure	pure	PROPN
ejpam-5859	86	3	appl	appl	PROPN
ejpam-5859	86	4	.	.	PROPN
ejpam-5859	86	5	math	math	PROPN
ejpam-5859	86	6	,	,	PUNCT
ejpam-5859	86	7	18	18	NUM
ejpam-5859	86	8	(	(	PUNCT
ejpam-5859	86	9	2	2	NUM
ejpam-5859	86	10	)	)	PUNCT
ejpam-5859	86	11	(	(	PUNCT
ejpam-5859	86	12	2025	2025	NUM
ejpam-5859	86	13	)	)	PUNCT
ejpam-5859	86	14	,	,	PUNCT
ejpam-5859	86	15	5859	5859	NUM
ejpam-5859	86	16	5	5	NUM
ejpam-5859	86	17	of	of	ADP
ejpam-5859	86	18	8	8	NUM
ejpam-5859	86	19	(	(	PUNCT
ejpam-5859	86	20	f1	f1	NOUN
ejpam-5859	86	21	)	)	PUNCT
ejpam-5859	87	1	[	[	X
ejpam-5859	87	2	abc	abc	X
ejpam-5859	87	3	]	]	X
ejpam-5859	87	4	∈	∈	PROPN
ejpam-5859	87	5	f	f	PROPN
ejpam-5859	87	6	for	for	ADP
ejpam-5859	87	7	any	any	DET
ejpam-5859	87	8	a	a	DET
ejpam-5859	87	9	,	,	PUNCT
ejpam-5859	87	10	b	b	NOUN
ejpam-5859	87	11	,	,	PUNCT
ejpam-5859	87	12	c	c	PROPN
ejpam-5859	87	13	∈	∈	PROPN
ejpam-5859	87	14	f	f	X
ejpam-5859	87	15	;	;	PUNCT
ejpam-5859	87	16	(	(	PUNCT
ejpam-5859	87	17	f2	f2	PROPN
ejpam-5859	87	18	)	)	PUNCT
ejpam-5859	87	19	for	for	ADP
ejpam-5859	87	20	any	any	DET
ejpam-5859	87	21	x	x	NOUN
ejpam-5859	87	22	,	,	PUNCT
ejpam-5859	87	23	y	y	PROPN
ejpam-5859	87	24	∈	∈	PROPN
ejpam-5859	87	25	t	t	PROPN
ejpam-5859	87	26	,	,	PUNCT
ejpam-5859	87	27	a	a	DET
ejpam-5859	87	28	≤	≤	PROPN
ejpam-5859	87	29	b	b	NOUN
ejpam-5859	87	30	and	and	CCONJ
ejpam-5859	87	31	a	a	DET
ejpam-5859	87	32	∈	∈	NOUN
ejpam-5859	87	33	f	f	X
ejpam-5859	87	34	imply	imply	VERB
ejpam-5859	87	35	b	b	PROPN
ejpam-5859	87	36	∈	∈	PROPN
ejpam-5859	87	37	f	f	X
ejpam-5859	87	38	.	.	PUNCT
ejpam-5859	88	1	proposition	proposition	NOUN
ejpam-5859	88	2	1	1	NUM
ejpam-5859	88	3	.	.	PUNCT
ejpam-5859	89	1	let	let	VERB
ejpam-5859	89	2	(	(	PUNCT
ejpam-5859	89	3	t	t	NOUN
ejpam-5859	89	4	,	,	PUNCT
ejpam-5859	89	5	[	[	PUNCT
ejpam-5859	89	6	]	]	X
ejpam-5859	89	7	,	,	PUNCT
ejpam-5859	89	8	≤	≤	NUM
ejpam-5859	89	9	,	,	PUNCT
ejpam-5859	89	10	[	[	PUNCT
ejpam-5859	89	11	]	]	X
ejpam-5859	89	12	∗	∗	NOUN
ejpam-5859	89	13	)	)	PUNCT
ejpam-5859	89	14	be	be	VERB
ejpam-5859	89	15	an	an	DET
ejpam-5859	89	16	inpots	inpot	NOUN
ejpam-5859	89	17	.	.	PUNCT
ejpam-5859	90	1	then	then	ADV
ejpam-5859	90	2	∅	∅	NOUN
ejpam-5859	90	3	=	=	NOUN
ejpam-5859	90	4	̸	̸	NUM
ejpam-5859	90	5	f	f	NOUN
ejpam-5859	91	1	⊆	⊆	NUM
ejpam-5859	91	2	t	t	PROPN
ejpam-5859	91	3	is	be	AUX
ejpam-5859	91	4	a	a	DET
ejpam-5859	91	5	filter	filter	NOUN
ejpam-5859	91	6	if	if	SCONJ
ejpam-5859	91	7	and	and	CCONJ
ejpam-5859	91	8	only	only	ADV
ejpam-5859	91	9	if	if	SCONJ
ejpam-5859	91	10	it	it	PRON
ejpam-5859	91	11	holds	hold	VERB
ejpam-5859	91	12	the	the	DET
ejpam-5859	91	13	conditions	condition	NOUN
ejpam-5859	91	14	:	:	PUNCT
ejpam-5859	91	15	(	(	PUNCT
ejpam-5859	91	16	f3	f3	ADJ
ejpam-5859	91	17	)	)	PUNCT
ejpam-5859	91	18	1	1	NUM
ejpam-5859	91	19	∈	∈	PROPN
ejpam-5859	91	20	f	f	NOUN
ejpam-5859	91	21	;	;	PUNCT
ejpam-5859	91	22	(	(	PUNCT
ejpam-5859	91	23	f4	f4	NOUN
ejpam-5859	91	24	)	)	PUNCT
ejpam-5859	91	25	for	for	ADP
ejpam-5859	91	26	any	any	DET
ejpam-5859	91	27	a	a	DET
ejpam-5859	91	28	,	,	PUNCT
ejpam-5859	91	29	b	b	NOUN
ejpam-5859	91	30	,	,	PUNCT
ejpam-5859	91	31	c	c	PROPN
ejpam-5859	91	32	∈	∈	PROPN
ejpam-5859	91	33	t	t	NOUN
ejpam-5859	91	34	,	,	PUNCT
ejpam-5859	91	35	if	if	SCONJ
ejpam-5859	91	36	[	[	X
ejpam-5859	91	37	abc]∗	abc]∗	PROPN
ejpam-5859	91	38	∈	∈	PROPN
ejpam-5859	91	39	f	f	PROPN
ejpam-5859	91	40	and	and	CCONJ
ejpam-5859	91	41	a	a	DET
ejpam-5859	91	42	,	,	PUNCT
ejpam-5859	91	43	b	b	PROPN
ejpam-5859	91	44	∈	∈	PROPN
ejpam-5859	91	45	f	f	X
ejpam-5859	91	46	,	,	PUNCT
ejpam-5859	91	47	then	then	ADV
ejpam-5859	91	48	c	c	PROPN
ejpam-5859	91	49	∈	∈	PROPN
ejpam-5859	91	50	f	f	X
ejpam-5859	91	51	.	.	PUNCT
ejpam-5859	92	1	proof	proof	NOUN
ejpam-5859	92	2	.	.	PUNCT
ejpam-5859	93	1	assume	assume	VERB
ejpam-5859	93	2	that	that	SCONJ
ejpam-5859	93	3	f	f	PROPN
ejpam-5859	93	4	is	be	AUX
ejpam-5859	93	5	a	a	DET
ejpam-5859	93	6	filter	filter	NOUN
ejpam-5859	93	7	of	of	ADP
ejpam-5859	93	8	t	t	PROPN
ejpam-5859	93	9	.	.	PUNCT
ejpam-5859	94	1	since	since	SCONJ
ejpam-5859	94	2	1	1	NUM
ejpam-5859	94	3	is	be	AUX
ejpam-5859	94	4	the	the	DET
ejpam-5859	94	5	greatest	great	ADJ
ejpam-5859	94	6	element	element	NOUN
ejpam-5859	94	7	of	of	ADP
ejpam-5859	94	8	t	t	PROPN
ejpam-5859	94	9	,	,	PUNCT
ejpam-5859	94	10	1	1	NUM
ejpam-5859	94	11	∈	∈	PROPN
ejpam-5859	94	12	f	f	NOUN
ejpam-5859	94	13	.	.	PUNCT
ejpam-5859	95	1	it	it	PRON
ejpam-5859	95	2	is	be	AUX
ejpam-5859	95	3	observed	observe	VERB
ejpam-5859	95	4	that	that	SCONJ
ejpam-5859	95	5	for	for	ADP
ejpam-5859	95	6	any	any	DET
ejpam-5859	95	7	a	a	DET
ejpam-5859	95	8	,	,	PUNCT
ejpam-5859	95	9	b	b	NOUN
ejpam-5859	95	10	,	,	PUNCT
ejpam-5859	95	11	c	c	PROPN
ejpam-5859	95	12	∈	∈	PROPN
ejpam-5859	95	13	t	t	PROPN
ejpam-5859	95	14	,	,	PUNCT
ejpam-5859	95	15	from	from	ADP
ejpam-5859	95	16	[	[	X
ejpam-5859	95	17	abc]∗	abc]∗	X
ejpam-5859	95	18	≤	≤	X
ejpam-5859	95	19	[	[	X
ejpam-5859	95	20	abc]∗	abc]∗	PROPN
ejpam-5859	95	21	,	,	PUNCT
ejpam-5859	95	22	we	we	PRON
ejpam-5859	95	23	have	have	VERB
ejpam-5859	95	24	[	[	X
ejpam-5859	95	25	[	[	X
ejpam-5859	95	26	abc]∗ab	abc]∗ab	ADJ
ejpam-5859	95	27	]	]	X
ejpam-5859	95	28	≤	≤	ADJ
ejpam-5859	95	29	c.	c.	NOUN
ejpam-5859	95	30	(	(	PUNCT
ejpam-5859	95	31	2.1	2.1	NUM
ejpam-5859	95	32	)	)	PUNCT
ejpam-5859	95	33	let	let	VERB
ejpam-5859	95	34	a	a	DET
ejpam-5859	95	35	,	,	PUNCT
ejpam-5859	95	36	b	b	NOUN
ejpam-5859	95	37	,	,	PUNCT
ejpam-5859	95	38	c	c	PROPN
ejpam-5859	95	39	∈	∈	PROPN
ejpam-5859	95	40	t	t	PROPN
ejpam-5859	95	41	be	be	AUX
ejpam-5859	95	42	such	such	ADJ
ejpam-5859	96	1	that	that	SCONJ
ejpam-5859	96	2	[	[	X
ejpam-5859	96	3	abc]∗	abc]∗	PROPN
ejpam-5859	96	4	∈	∈	PROPN
ejpam-5859	96	5	f	f	PROPN
ejpam-5859	96	6	and	and	CCONJ
ejpam-5859	96	7	a	a	DET
ejpam-5859	96	8	,	,	PUNCT
ejpam-5859	96	9	b	b	PROPN
ejpam-5859	96	10	∈	∈	PROPN
ejpam-5859	96	11	f	f	X
ejpam-5859	96	12	.	.	PUNCT
ejpam-5859	97	1	by	by	ADP
ejpam-5859	97	2	assumption	assumption	NOUN
ejpam-5859	97	3	,	,	PUNCT
ejpam-5859	97	4	we	we	PRON
ejpam-5859	97	5	have	have	VERB
ejpam-5859	97	6	[	[	X
ejpam-5859	97	7	[	[	X
ejpam-5859	97	8	abc]∗ab	abc]∗ab	ADJ
ejpam-5859	97	9	]	]	X
ejpam-5859	97	10	∈	∈	PROPN
ejpam-5859	97	11	f	f	X
ejpam-5859	97	12	.	.	PUNCT
ejpam-5859	98	1	using	use	VERB
ejpam-5859	98	2	(	(	PUNCT
ejpam-5859	98	3	2.1	2.1	NUM
ejpam-5859	98	4	)	)	PUNCT
ejpam-5859	98	5	,	,	PUNCT
ejpam-5859	98	6	we	we	PRON
ejpam-5859	98	7	get	get	VERB
ejpam-5859	98	8	[	[	X
ejpam-5859	98	9	[	[	X
ejpam-5859	98	10	abc]∗ab	abc]∗ab	ADJ
ejpam-5859	98	11	]	]	X
ejpam-5859	98	12	≤	≤	ADJ
ejpam-5859	98	13	c.	c.	NOUN
ejpam-5859	98	14	this	this	PRON
ejpam-5859	98	15	implies	imply	VERB
ejpam-5859	98	16	that	that	SCONJ
ejpam-5859	98	17	c	c	PROPN
ejpam-5859	98	18	∈	∈	PROPN
ejpam-5859	98	19	f	f	X
ejpam-5859	98	20	.	.	PUNCT
ejpam-5859	99	1	hence	hence	ADV
ejpam-5859	99	2	,	,	PUNCT
ejpam-5859	99	3	f	f	PROPN
ejpam-5859	99	4	satisfies	satisfie	NOUN
ejpam-5859	99	5	(	(	PUNCT
ejpam-5859	99	6	f3	f3	ADJ
ejpam-5859	99	7	)	)	PUNCT
ejpam-5859	99	8	and	and	CCONJ
ejpam-5859	99	9	(	(	PUNCT
ejpam-5859	99	10	f4	f4	NOUN
ejpam-5859	99	11	)	)	PUNCT
ejpam-5859	99	12	.	.	PUNCT
ejpam-5859	100	1	conversely	conversely	ADV
ejpam-5859	100	2	,	,	PUNCT
ejpam-5859	100	3	assume	assume	VERB
ejpam-5859	100	4	that	that	SCONJ
ejpam-5859	100	5	f	f	PROPN
ejpam-5859	100	6	satisfies	satisfie	NOUN
ejpam-5859	100	7	(	(	PUNCT
ejpam-5859	100	8	f3	f3	ADJ
ejpam-5859	100	9	)	)	PUNCT
ejpam-5859	100	10	and	and	CCONJ
ejpam-5859	100	11	(	(	PUNCT
ejpam-5859	100	12	f4	f4	PROPN
ejpam-5859	100	13	)	)	PUNCT
ejpam-5859	100	14	.	.	PUNCT
ejpam-5859	101	1	if	if	SCONJ
ejpam-5859	101	2	a	a	PRON
ejpam-5859	101	3	,	,	PUNCT
ejpam-5859	101	4	b	b	PROPN
ejpam-5859	101	5	∈	∈	PROPN
ejpam-5859	101	6	t	t	NOUN
ejpam-5859	101	7	such	such	ADJ
ejpam-5859	101	8	that	that	SCONJ
ejpam-5859	101	9	a	a	DET
ejpam-5859	101	10	≤	≤	PROPN
ejpam-5859	101	11	b	b	NOUN
ejpam-5859	101	12	and	and	CCONJ
ejpam-5859	101	13	a	a	DET
ejpam-5859	101	14	∈	∈	PROPN
ejpam-5859	101	15	f	f	NOUN
ejpam-5859	101	16	,	,	PUNCT
ejpam-5859	101	17	then	then	ADV
ejpam-5859	101	18	by	by	ADP
ejpam-5859	101	19	theorem	theorem	NOUN
ejpam-5859	101	20	2	2	NUM
ejpam-5859	101	21	(	(	PUNCT
ejpam-5859	101	22	6	6	NUM
ejpam-5859	101	23	)	)	PUNCT
ejpam-5859	101	24	we	we	PRON
ejpam-5859	101	25	have	have	VERB
ejpam-5859	101	26	[	[	X
ejpam-5859	101	27	1ab]∗	1ab]∗	NUM
ejpam-5859	101	28	=	=	SYM
ejpam-5859	101	29	1	1	NUM
ejpam-5859	101	30	∈	∈	PROPN
ejpam-5859	101	31	f	f	NOUN
ejpam-5859	101	32	.	.	PUNCT
ejpam-5859	102	1	by	by	ADP
ejpam-5859	102	2	(	(	PUNCT
ejpam-5859	102	3	f4	f4	PROPN
ejpam-5859	102	4	)	)	PUNCT
ejpam-5859	102	5	,	,	PUNCT
ejpam-5859	102	6	b	b	X
ejpam-5859	102	7	∈	∈	PROPN
ejpam-5859	102	8	f	f	X
ejpam-5859	102	9	.	.	PUNCT
ejpam-5859	103	1	thus	thus	ADV
ejpam-5859	103	2	,	,	PUNCT
ejpam-5859	103	3	f	f	PROPN
ejpam-5859	103	4	satisfies	satisfie	NOUN
ejpam-5859	103	5	(	(	PUNCT
ejpam-5859	103	6	f2	f2	PROPN
ejpam-5859	103	7	)	)	PUNCT
ejpam-5859	103	8	.	.	PUNCT
ejpam-5859	104	1	let	let	VERB
ejpam-5859	104	2	a	a	DET
ejpam-5859	104	3	,	,	PUNCT
ejpam-5859	104	4	b	b	NOUN
ejpam-5859	104	5	,	,	PUNCT
ejpam-5859	104	6	c	c	PROPN
ejpam-5859	104	7	∈	∈	PROPN
ejpam-5859	104	8	f	f	X
ejpam-5859	104	9	.	.	PUNCT
ejpam-5859	105	1	by	by	ADP
ejpam-5859	105	2	theorem	theorem	NOUN
ejpam-5859	105	3	2	2	NUM
ejpam-5859	105	4	(	(	PUNCT
ejpam-5859	105	5	2	2	NUM
ejpam-5859	105	6	)	)	PUNCT
ejpam-5859	105	7	,	,	PUNCT
ejpam-5859	105	8	a	a	DET
ejpam-5859	105	9	≤	≤	X
ejpam-5859	105	10	[	[	X
ejpam-5859	105	11	bc[abc]]∗	bc[abc]]∗	NOUN
ejpam-5859	105	12	,	,	PUNCT
ejpam-5859	105	13	and	and	CCONJ
ejpam-5859	105	14	so	so	ADV
ejpam-5859	105	15	by	by	ADP
ejpam-5859	105	16	(	(	PUNCT
ejpam-5859	105	17	f2	f2	PROPN
ejpam-5859	105	18	)	)	PUNCT
ejpam-5859	105	19	we	we	PRON
ejpam-5859	105	20	get	get	VERB
ejpam-5859	105	21	[	[	X
ejpam-5859	105	22	bc[abc]]∗	bc[abc]]∗	NOUN
ejpam-5859	105	23	∈	∈	ADJ
ejpam-5859	105	24	f	f	X
ejpam-5859	105	25	.	.	PUNCT
ejpam-5859	106	1	from	from	ADP
ejpam-5859	106	2	(	(	PUNCT
ejpam-5859	106	3	f4	f4	PROPN
ejpam-5859	106	4	)	)	PUNCT
ejpam-5859	106	5	,	,	PUNCT
ejpam-5859	106	6	[	[	X
ejpam-5859	106	7	abc	abc	X
ejpam-5859	106	8	]	]	X
ejpam-5859	106	9	∈	∈	PROPN
ejpam-5859	106	10	f	f	X
ejpam-5859	106	11	.	.	PUNCT
ejpam-5859	107	1	hence	hence	ADV
ejpam-5859	107	2	,	,	PUNCT
ejpam-5859	107	3	f	f	PROPN
ejpam-5859	107	4	satisfies	satisfie	NOUN
ejpam-5859	107	5	(	(	PUNCT
ejpam-5859	107	6	f1	f1	NOUN
ejpam-5859	107	7	)	)	PUNCT
ejpam-5859	107	8	.	.	PUNCT
ejpam-5859	108	1	consequently	consequently	ADV
ejpam-5859	108	2	,	,	PUNCT
ejpam-5859	108	3	f	f	PROPN
ejpam-5859	108	4	is	be	AUX
ejpam-5859	108	5	a	a	DET
ejpam-5859	108	6	filter	filter	NOUN
ejpam-5859	108	7	of	of	ADP
ejpam-5859	108	8	t	t	PROPN
ejpam-5859	108	9	.	.	PUNCT
ejpam-5859	109	1	definition	definition	NOUN
ejpam-5859	109	2	5	5	NUM
ejpam-5859	109	3	.	.	PUNCT
ejpam-5859	110	1	let	let	AUX
ejpam-5859	110	2	(	(	PUNCT
ejpam-5859	110	3	t	t	NOUN
ejpam-5859	110	4	,	,	PUNCT
ejpam-5859	110	5	[	[	PUNCT
ejpam-5859	110	6	]	]	X
ejpam-5859	110	7	,	,	PUNCT
ejpam-5859	110	8	≤	≤	NUM
ejpam-5859	110	9	,	,	PUNCT
ejpam-5859	110	10	[	[	PUNCT
ejpam-5859	110	11	]	]	X
ejpam-5859	110	12	∗	∗	NOUN
ejpam-5859	110	13	)	)	PUNCT
ejpam-5859	110	14	be	be	VERB
ejpam-5859	110	15	an	an	DET
ejpam-5859	110	16	inpots	inpot	NOUN
ejpam-5859	110	17	.	.	PUNCT
ejpam-5859	111	1	for	for	ADP
ejpam-5859	111	2	any	any	DET
ejpam-5859	111	3	a	a	PRON
ejpam-5859	111	4	,	,	PUNCT
ejpam-5859	111	5	b	b	PROPN
ejpam-5859	111	6	∈	∈	PROPN
ejpam-5859	111	7	t	t	NOUN
ejpam-5859	111	8	,	,	PUNCT
ejpam-5859	111	9	define	define	VERB
ejpam-5859	111	10	s(a	s(a	PROPN
ejpam-5859	111	11	,	,	PUNCT
ejpam-5859	111	12	b	b	NOUN
ejpam-5859	111	13	)	)	PUNCT
ejpam-5859	111	14	:	:	PUNCT
ejpam-5859	112	1	=	=	PUNCT
ejpam-5859	112	2	{	{	PUNCT
ejpam-5859	112	3	c	c	NOUN
ejpam-5859	112	4	∈	∈	PROPN
ejpam-5859	112	5	t	t	NOUN
ejpam-5859	112	6	:	:	PUNCT
ejpam-5859	113	1	[	[	X
ejpam-5859	113	2	aa[bbc]∗]∗	aa[bbc]∗]∗	NOUN
ejpam-5859	113	3	=	=	NOUN
ejpam-5859	113	4	1	1	NUM
ejpam-5859	113	5	}	}	PUNCT
ejpam-5859	113	6	.	.	PUNCT
ejpam-5859	114	1	observe	observe	VERB
ejpam-5859	114	2	that	that	SCONJ
ejpam-5859	114	3	1	1	NUM
ejpam-5859	114	4	,	,	PUNCT
ejpam-5859	114	5	b	b	X
ejpam-5859	114	6	∈	∈	PROPN
ejpam-5859	114	7	s(a	s(a	PROPN
ejpam-5859	114	8	,	,	PUNCT
ejpam-5859	114	9	b	b	NOUN
ejpam-5859	114	10	)	)	PUNCT
ejpam-5859	114	11	for	for	ADP
ejpam-5859	114	12	any	any	DET
ejpam-5859	114	13	a	a	PRON
ejpam-5859	114	14	,	,	PUNCT
ejpam-5859	114	15	b	b	PROPN
ejpam-5859	114	16	∈	∈	PROPN
ejpam-5859	114	17	t	t	NOUN
ejpam-5859	114	18	.	.	PUNCT
ejpam-5859	115	1	proposition	proposition	NOUN
ejpam-5859	115	2	2	2	NUM
ejpam-5859	115	3	.	.	X
ejpam-5859	116	1	for	for	ADP
ejpam-5859	116	2	a	a	DET
ejpam-5859	116	3	commutative	commutative	ADJ
ejpam-5859	116	4	inpots	inpot	NOUN
ejpam-5859	116	5	(	(	PUNCT
ejpam-5859	116	6	t	t	NOUN
ejpam-5859	116	7	,	,	PUNCT
ejpam-5859	116	8	[	[	PUNCT
ejpam-5859	116	9	]	]	X
ejpam-5859	116	10	,	,	PUNCT
ejpam-5859	116	11	≤	≤	NUM
ejpam-5859	116	12	,	,	PUNCT
ejpam-5859	116	13	[	[	PUNCT
ejpam-5859	116	14	]	]	X
ejpam-5859	116	15	∗	∗	NOUN
ejpam-5859	116	16	)	)	PUNCT
ejpam-5859	116	17	,	,	PUNCT
ejpam-5859	116	18	a	a	DET
ejpam-5859	116	19	∈	∈	PROPN
ejpam-5859	116	20	s(a	s(a	PROPN
ejpam-5859	116	21	,	,	PUNCT
ejpam-5859	116	22	b	b	NOUN
ejpam-5859	116	23	)	)	PUNCT
ejpam-5859	116	24	for	for	ADP
ejpam-5859	116	25	all	all	DET
ejpam-5859	116	26	a	a	PRON
ejpam-5859	116	27	,	,	PUNCT
ejpam-5859	116	28	b	b	PROPN
ejpam-5859	116	29	∈	∈	PROPN
ejpam-5859	116	30	t	t	NOUN
ejpam-5859	116	31	.	.	PUNCT
ejpam-5859	117	1	proof	proof	NOUN
ejpam-5859	117	2	.	.	PUNCT
ejpam-5859	118	1	let	let	VERB
ejpam-5859	118	2	a	a	DET
ejpam-5859	118	3	,	,	PUNCT
ejpam-5859	118	4	b	b	PROPN
ejpam-5859	118	5	∈	∈	PROPN
ejpam-5859	118	6	t	t	NOUN
ejpam-5859	118	7	.	.	PUNCT
ejpam-5859	119	1	by	by	ADP
ejpam-5859	119	2	theorem	theorem	NOUN
ejpam-5859	119	3	2	2	NUM
ejpam-5859	119	4	(	(	PUNCT
ejpam-5859	119	5	7	7	NUM
ejpam-5859	119	6	)	)	PUNCT
ejpam-5859	119	7	,	,	PUNCT
ejpam-5859	120	1	[	[	X
ejpam-5859	120	2	aa[bba]∗]∗	aa[bba]∗]∗	X
ejpam-5859	120	3	=	=	PUNCT
ejpam-5859	120	4	[	[	X
ejpam-5859	120	5	a[abb]a]∗	a[abb]a]∗	X
ejpam-5859	120	6	=	=	SYM
ejpam-5859	121	1	[	[	X
ejpam-5859	121	2	a[bba]a]∗	a[bba]a]∗	X
ejpam-5859	121	3	=	=	SYM
ejpam-5859	122	1	[	[	X
ejpam-5859	122	2	ab[baa]∗]∗	ab[baa]∗]∗	X
ejpam-5859	122	3	=	=	PUNCT
ejpam-5859	123	1	[	[	X
ejpam-5859	123	2	[	[	X
ejpam-5859	123	3	abb]aa]∗	abb]aa]∗	NOUN
ejpam-5859	123	4	=	=	PUNCT
ejpam-5859	124	1	[	[	X
ejpam-5859	124	2	[	[	X
ejpam-5859	124	3	bba]aa]∗	bba]aa]∗	X
ejpam-5859	124	4	=	=	PUNCT
ejpam-5859	125	1	[	[	X
ejpam-5859	125	2	bb[aaa]∗]∗	bb[aaa]∗]∗	X
ejpam-5859	125	3	=	=	PUNCT
ejpam-5859	126	1	[	[	X
ejpam-5859	126	2	bb1]∗.	bb1]∗.	NOUN
ejpam-5859	126	3	from	from	ADP
ejpam-5859	126	4	theorem	theorem	ADJ
ejpam-5859	126	5	2	2	NUM
ejpam-5859	126	6	(	(	PUNCT
ejpam-5859	126	7	4	4	NUM
ejpam-5859	126	8	)	)	PUNCT
ejpam-5859	126	9	,	,	PUNCT
ejpam-5859	126	10	1	1	NUM
ejpam-5859	126	11	≤	≤	NOUN
ejpam-5859	127	1	[	[	X
ejpam-5859	127	2	bb1]∗	bb1]∗	PROPN
ejpam-5859	127	3	≤	≤	NUM
ejpam-5859	127	4	1	1	NUM
ejpam-5859	127	5	.	.	PUNCT
ejpam-5859	128	1	this	this	PRON
ejpam-5859	128	2	implies	imply	VERB
ejpam-5859	128	3	that	that	SCONJ
ejpam-5859	128	4	[	[	X
ejpam-5859	128	5	aa[bba]∗]∗	aa[bba]∗]∗	PROPN
ejpam-5859	128	6	=	=	SYM
ejpam-5859	128	7	1	1	NUM
ejpam-5859	128	8	,	,	PUNCT
ejpam-5859	128	9	and	and	CCONJ
ejpam-5859	128	10	so	so	ADV
ejpam-5859	128	11	a	a	DET
ejpam-5859	128	12	∈	∈	PROPN
ejpam-5859	128	13	s(a	s(a	PROPN
ejpam-5859	128	14	,	,	PUNCT
ejpam-5859	128	15	b	b	NOUN
ejpam-5859	128	16	)	)	PUNCT
ejpam-5859	128	17	.	.	PUNCT
ejpam-5859	129	1	k.	k.	PROPN
ejpam-5859	129	2	nakwan	nakwan	PROPN
ejpam-5859	129	3	,	,	PUNCT
ejpam-5859	129	4	p.	p.	PROPN
ejpam-5859	129	5	luangchaisri	luangchaisri	VERB
ejpam-5859	129	6	,	,	PUNCT
ejpam-5859	129	7	t.	t.	PROPN
ejpam-5859	129	8	changphas	changphas	PROPN
ejpam-5859	129	9	/	/	SYM
ejpam-5859	129	10	eur	eur	PROPN
ejpam-5859	129	11	.	.	PUNCT
ejpam-5859	130	1	j.	j.	PROPN
ejpam-5859	130	2	pure	pure	PROPN
ejpam-5859	130	3	appl	appl	PROPN
ejpam-5859	130	4	.	.	PROPN
ejpam-5859	130	5	math	math	PROPN
ejpam-5859	130	6	,	,	PUNCT
ejpam-5859	130	7	18	18	NUM
ejpam-5859	130	8	(	(	PUNCT
ejpam-5859	130	9	2	2	NUM
ejpam-5859	130	10	)	)	PUNCT
ejpam-5859	130	11	(	(	PUNCT
ejpam-5859	130	12	2025	2025	NUM
ejpam-5859	130	13	)	)	PUNCT
ejpam-5859	130	14	,	,	PUNCT
ejpam-5859	130	15	5859	5859	NUM
ejpam-5859	130	16	6	6	NUM
ejpam-5859	130	17	of	of	ADP
ejpam-5859	130	18	8	8	NUM
ejpam-5859	130	19	proposition	proposition	NOUN
ejpam-5859	130	20	3	3	NUM
ejpam-5859	130	21	.	.	PUNCT
ejpam-5859	131	1	let	let	VERB
ejpam-5859	131	2	(	(	PUNCT
ejpam-5859	131	3	t	t	NOUN
ejpam-5859	131	4	,	,	PUNCT
ejpam-5859	131	5	[	[	PUNCT
ejpam-5859	131	6	]	]	X
ejpam-5859	131	7	,	,	PUNCT
ejpam-5859	131	8	≤	≤	NUM
ejpam-5859	131	9	,	,	PUNCT
ejpam-5859	131	10	[	[	PUNCT
ejpam-5859	131	11	]	]	X
ejpam-5859	131	12	∗	∗	NOUN
ejpam-5859	131	13	)	)	PUNCT
ejpam-5859	131	14	be	be	VERB
ejpam-5859	131	15	an	an	DET
ejpam-5859	131	16	inpots	inpot	NOUN
ejpam-5859	131	17	,	,	PUNCT
ejpam-5859	131	18	and	and	CCONJ
ejpam-5859	131	19	b	b	X
ejpam-5859	131	20	∈	∈	PROPN
ejpam-5859	131	21	t	t	NOUN
ejpam-5859	131	22	.	.	PUNCT
ejpam-5859	132	1	if	if	SCONJ
ejpam-5859	132	2	[	[	X
ejpam-5859	132	3	buv]∗	buv]∗	X
ejpam-5859	132	4	=	=	NOUN
ejpam-5859	132	5	1	1	NUM
ejpam-5859	132	6	for	for	ADP
ejpam-5859	132	7	all	all	DET
ejpam-5859	132	8	u	u	NOUN
ejpam-5859	132	9	,	,	PUNCT
ejpam-5859	132	10	v	v	PROPN
ejpam-5859	132	11	∈	∈	PROPN
ejpam-5859	132	12	t	t	NOUN
ejpam-5859	132	13	,	,	PUNCT
ejpam-5859	132	14	then	then	ADV
ejpam-5859	132	15	s(a	s(a	PROPN
ejpam-5859	132	16	,	,	PUNCT
ejpam-5859	132	17	b	b	NOUN
ejpam-5859	132	18	)	)	PUNCT
ejpam-5859	132	19	=	=	SYM
ejpam-5859	132	20	t	t	NOUN
ejpam-5859	132	21	=	=	PUNCT
ejpam-5859	132	22	s(b	s(b	NOUN
ejpam-5859	132	23	,	,	PUNCT
ejpam-5859	132	24	a	a	PRON
ejpam-5859	132	25	)	)	PUNCT
ejpam-5859	132	26	for	for	ADP
ejpam-5859	132	27	all	all	DET
ejpam-5859	132	28	a	a	DET
ejpam-5859	132	29	∈	∈	PROPN
ejpam-5859	132	30	t	t	NOUN
ejpam-5859	132	31	.	.	PUNCT
ejpam-5859	133	1	proof	proof	NOUN
ejpam-5859	133	2	.	.	PUNCT
ejpam-5859	134	1	assume	assume	VERB
ejpam-5859	134	2	that	that	SCONJ
ejpam-5859	135	1	[	[	X
ejpam-5859	135	2	buv]∗	buv]∗	X
ejpam-5859	135	3	=	=	NOUN
ejpam-5859	135	4	1	1	NUM
ejpam-5859	135	5	for	for	ADP
ejpam-5859	135	6	all	all	DET
ejpam-5859	135	7	u	u	NOUN
ejpam-5859	135	8	,	,	PUNCT
ejpam-5859	135	9	v	v	PROPN
ejpam-5859	135	10	∈	∈	PROPN
ejpam-5859	135	11	t	t	NOUN
ejpam-5859	135	12	and	and	CCONJ
ejpam-5859	135	13	a	a	DET
ejpam-5859	135	14	∈	∈	PROPN
ejpam-5859	135	15	t	t	NOUN
ejpam-5859	135	16	.	.	PUNCT
ejpam-5859	136	1	clearly	clearly	ADV
ejpam-5859	136	2	,	,	PUNCT
ejpam-5859	136	3	s(a	s(a	PROPN
ejpam-5859	136	4	,	,	PUNCT
ejpam-5859	136	5	b	b	NOUN
ejpam-5859	136	6	)	)	PUNCT
ejpam-5859	136	7	⊆	⊆	NUM
ejpam-5859	136	8	t	t	NOUN
ejpam-5859	136	9	and	and	CCONJ
ejpam-5859	136	10	s(b	s(b	NOUN
ejpam-5859	136	11	,	,	PUNCT
ejpam-5859	136	12	a	a	PRON
ejpam-5859	136	13	)	)	PUNCT
ejpam-5859	136	14	⊆	⊆	NUM
ejpam-5859	136	15	t	t	NOUN
ejpam-5859	136	16	.	.	PUNCT
ejpam-5859	137	1	by	by	ADP
ejpam-5859	137	2	assumption	assumption	NOUN
ejpam-5859	137	3	,	,	PUNCT
ejpam-5859	137	4	we	we	PRON
ejpam-5859	137	5	have	have	VERB
ejpam-5859	137	6	[	[	X
ejpam-5859	137	7	aa[bba]∗]∗	aa[bba]∗]∗	X
ejpam-5859	137	8	=	=	PUNCT
ejpam-5859	138	1	[	[	X
ejpam-5859	138	2	aa1]∗.	aa1]∗.	PROPN
ejpam-5859	138	3	since	since	SCONJ
ejpam-5859	138	4	1	1	NUM
ejpam-5859	138	5	≤	≤	NOUN
ejpam-5859	138	6	[	[	X
ejpam-5859	138	7	aa1]∗	aa1]∗	PROPN
ejpam-5859	138	8	≤	≤	NUM
ejpam-5859	138	9	1	1	NUM
ejpam-5859	138	10	,	,	PUNCT
ejpam-5859	138	11	we	we	PRON
ejpam-5859	138	12	have	have	VERB
ejpam-5859	138	13	[	[	PUNCT
ejpam-5859	138	14	aa[bba]∗]∗	aa[bba]∗]∗	PROPN
ejpam-5859	138	15	=	=	SYM
ejpam-5859	138	16	1	1	NUM
ejpam-5859	138	17	,	,	PUNCT
ejpam-5859	138	18	and	and	CCONJ
ejpam-5859	138	19	then	then	ADV
ejpam-5859	138	20	a	a	DET
ejpam-5859	138	21	∈	∈	PROPN
ejpam-5859	138	22	s(a	s(a	PROPN
ejpam-5859	138	23	,	,	PUNCT
ejpam-5859	138	24	b	b	NOUN
ejpam-5859	138	25	)	)	PUNCT
ejpam-5859	138	26	.	.	PUNCT
ejpam-5859	139	1	thus	thus	ADV
ejpam-5859	139	2	,	,	PUNCT
ejpam-5859	139	3	t	t	PROPN
ejpam-5859	139	4	⊆	⊆	NUM
ejpam-5859	139	5	s(a	s(a	PROPN
ejpam-5859	139	6	,	,	PUNCT
ejpam-5859	139	7	b	b	NOUN
ejpam-5859	139	8	)	)	PUNCT
ejpam-5859	139	9	.	.	PUNCT
ejpam-5859	140	1	by	by	ADP
ejpam-5859	140	2	assumption	assumption	NOUN
ejpam-5859	140	3	,	,	PUNCT
ejpam-5859	140	4	[	[	X
ejpam-5859	140	5	bb[aaa]∗]∗	bb[aaa]∗]∗	X
ejpam-5859	140	6	=	=	PUNCT
ejpam-5859	141	1	[	[	X
ejpam-5859	141	2	bb1]∗	bb1]∗	X
ejpam-5859	141	3	=	=	SYM
ejpam-5859	141	4	1	1	X
ejpam-5859	141	5	.	.	PUNCT
ejpam-5859	142	1	this	this	PRON
ejpam-5859	142	2	shows	show	VERB
ejpam-5859	142	3	that	that	SCONJ
ejpam-5859	142	4	a	a	DET
ejpam-5859	142	5	∈	∈	PROPN
ejpam-5859	142	6	s(b	s(b	NOUN
ejpam-5859	142	7	,	,	PUNCT
ejpam-5859	142	8	a	a	PRON
ejpam-5859	142	9	)	)	PUNCT
ejpam-5859	142	10	,	,	PUNCT
ejpam-5859	142	11	and	and	CCONJ
ejpam-5859	142	12	so	so	ADV
ejpam-5859	142	13	t	t	PROPN
ejpam-5859	142	14	⊆	⊆	NUM
ejpam-5859	142	15	s(b	s(b	NOUN
ejpam-5859	142	16	,	,	PUNCT
ejpam-5859	142	17	a	a	PRON
ejpam-5859	142	18	)	)	PUNCT
ejpam-5859	142	19	.	.	PUNCT
ejpam-5859	142	20	example	example	NOUN
ejpam-5859	143	1	4	4	X
ejpam-5859	143	2	.	.	PUNCT
ejpam-5859	143	3	let	let	VERB
ejpam-5859	143	4	us	we	PRON
ejpam-5859	143	5	consider	consider	VERB
ejpam-5859	143	6	the	the	DET
ejpam-5859	143	7	inpots	inpot	NOUN
ejpam-5859	143	8	(	(	PUNCT
ejpam-5859	143	9	t	t	NOUN
ejpam-5859	143	10	,	,	PUNCT
ejpam-5859	143	11	[	[	PUNCT
ejpam-5859	143	12	]	]	X
ejpam-5859	143	13	,	,	PUNCT
ejpam-5859	143	14	≤	≤	NUM
ejpam-5859	143	15	,	,	PUNCT
ejpam-5859	143	16	[	[	PUNCT
ejpam-5859	143	17	]	]	X
ejpam-5859	143	18	∗	∗	NOUN
ejpam-5859	143	19	)	)	PUNCT
ejpam-5859	143	20	defined	define	VERB
ejpam-5859	143	21	as	as	SCONJ
ejpam-5859	143	22	follows	follow	VERB
ejpam-5859	143	23	:	:	PUNCT
ejpam-5859	143	24	[	[	PUNCT
ejpam-5859	143	25	]	]	X
ejpam-5859	143	26	1	1	NUM
ejpam-5859	143	27	2	2	NUM
ejpam-5859	143	28	3	3	NUM
ejpam-5859	143	29	4	4	NUM
ejpam-5859	143	30	5	5	NUM
ejpam-5859	143	31	7	7	NUM
ejpam-5859	143	32	11	11	NUM
ejpam-5859	143	33	1	1	NUM
ejpam-5859	143	34	2	2	NUM
ejpam-5859	143	35	3	3	NUM
ejpam-5859	143	36	4	4	NUM
ejpam-5859	143	37	5	5	NUM
ejpam-5859	143	38	7	7	NUM
ejpam-5859	143	39	12	12	NUM
ejpam-5859	143	40	2	2	NUM
ejpam-5859	143	41	3	3	NUM
ejpam-5859	143	42	3	3	NUM
ejpam-5859	143	43	5	5	NUM
ejpam-5859	143	44	7	7	NUM
ejpam-5859	143	45	7	7	NUM
ejpam-5859	143	46	13	13	NUM
ejpam-5859	143	47	3	3	NUM
ejpam-5859	143	48	3	3	NUM
ejpam-5859	143	49	3	3	NUM
ejpam-5859	143	50	7	7	NUM
ejpam-5859	143	51	7	7	NUM
ejpam-5859	143	52	7	7	NUM
ejpam-5859	143	53	14	14	NUM
ejpam-5859	143	54	4	4	NUM
ejpam-5859	143	55	5	5	NUM
ejpam-5859	143	56	7	7	NUM
ejpam-5859	143	57	4	4	NUM
ejpam-5859	143	58	5	5	NUM
ejpam-5859	143	59	7	7	NUM
ejpam-5859	143	60	15	15	NUM
ejpam-5859	143	61	5	5	NUM
ejpam-5859	143	62	7	7	NUM
ejpam-5859	143	63	7	7	NUM
ejpam-5859	143	64	5	5	NUM
ejpam-5859	143	65	7	7	NUM
ejpam-5859	143	66	7	7	NUM
ejpam-5859	143	67	17	17	NUM
ejpam-5859	143	68	7	7	NUM
ejpam-5859	143	69	7	7	NUM
ejpam-5859	143	70	7	7	NUM
ejpam-5859	143	71	7	7	NUM
ejpam-5859	143	72	7	7	NUM
ejpam-5859	143	73	7	7	NUM
ejpam-5859	143	74	[	[	PUNCT
ejpam-5859	143	75	]	]	SYM
ejpam-5859	143	76	1	1	NUM
ejpam-5859	143	77	2	2	NUM
ejpam-5859	143	78	3	3	NUM
ejpam-5859	143	79	4	4	NUM
ejpam-5859	143	80	5	5	NUM
ejpam-5859	143	81	7	7	NUM
ejpam-5859	143	82	21	21	NUM
ejpam-5859	143	83	2	2	NUM
ejpam-5859	143	84	3	3	NUM
ejpam-5859	143	85	3	3	NUM
ejpam-5859	143	86	5	5	NUM
ejpam-5859	143	87	7	7	NUM
ejpam-5859	143	88	7	7	NUM
ejpam-5859	143	89	22	22	NUM
ejpam-5859	143	90	3	3	NUM
ejpam-5859	143	91	3	3	NUM
ejpam-5859	143	92	3	3	NUM
ejpam-5859	143	93	7	7	NUM
ejpam-5859	143	94	7	7	NUM
ejpam-5859	143	95	7	7	NUM
ejpam-5859	143	96	23	23	NUM
ejpam-5859	143	97	3	3	NUM
ejpam-5859	143	98	3	3	NUM
ejpam-5859	143	99	3	3	NUM
ejpam-5859	143	100	7	7	NUM
ejpam-5859	143	101	7	7	NUM
ejpam-5859	143	102	7	7	NUM
ejpam-5859	143	103	24	24	NUM
ejpam-5859	143	104	5	5	NUM
ejpam-5859	143	105	7	7	NUM
ejpam-5859	143	106	7	7	NUM
ejpam-5859	143	107	5	5	NUM
ejpam-5859	143	108	7	7	NUM
ejpam-5859	143	109	7	7	NUM
ejpam-5859	143	110	25	25	NUM
ejpam-5859	143	111	7	7	NUM
ejpam-5859	143	112	7	7	NUM
ejpam-5859	143	113	7	7	NUM
ejpam-5859	143	114	7	7	NUM
ejpam-5859	143	115	7	7	NUM
ejpam-5859	143	116	7	7	NUM
ejpam-5859	143	117	27	27	NUM
ejpam-5859	143	118	7	7	NUM
ejpam-5859	143	119	7	7	NUM
ejpam-5859	143	120	7	7	NUM
ejpam-5859	143	121	7	7	NUM
ejpam-5859	143	122	7	7	NUM
ejpam-5859	143	123	7	7	NUM
ejpam-5859	143	124	[	[	PUNCT
ejpam-5859	143	125	]	]	SYM
ejpam-5859	143	126	1	1	NUM
ejpam-5859	143	127	2	2	NUM
ejpam-5859	143	128	3	3	NUM
ejpam-5859	143	129	4	4	NUM
ejpam-5859	143	130	5	5	NUM
ejpam-5859	143	131	7	7	NUM
ejpam-5859	143	132	31	31	NUM
ejpam-5859	143	133	3	3	NUM
ejpam-5859	143	134	3	3	NUM
ejpam-5859	143	135	3	3	NUM
ejpam-5859	143	136	7	7	NUM
ejpam-5859	143	137	7	7	NUM
ejpam-5859	143	138	7	7	NUM
ejpam-5859	143	139	3a	3a	NUM
ejpam-5859	143	140	3	3	NUM
ejpam-5859	143	141	3	3	NUM
ejpam-5859	143	142	3	3	NUM
ejpam-5859	143	143	7	7	NUM
ejpam-5859	143	144	7	7	NUM
ejpam-5859	143	145	7	7	NUM
ejpam-5859	143	146	33	33	NUM
ejpam-5859	143	147	3	3	NUM
ejpam-5859	143	148	3	3	NUM
ejpam-5859	143	149	3	3	NUM
ejpam-5859	143	150	7	7	NUM
ejpam-5859	143	151	7	7	NUM
ejpam-5859	143	152	7	7	NUM
ejpam-5859	143	153	34	34	NUM
ejpam-5859	143	154	7	7	NUM
ejpam-5859	143	155	7	7	NUM
ejpam-5859	143	156	7	7	NUM
ejpam-5859	143	157	7	7	NUM
ejpam-5859	143	158	7	7	NUM
ejpam-5859	143	159	7	7	NUM
ejpam-5859	143	160	35	35	NUM
ejpam-5859	143	161	7	7	NUM
ejpam-5859	143	162	7	7	NUM
ejpam-5859	143	163	7	7	NUM
ejpam-5859	143	164	7	7	NUM
ejpam-5859	143	165	7	7	NUM
ejpam-5859	143	166	7	7	NUM
ejpam-5859	143	167	37	37	NUM
ejpam-5859	143	168	7	7	NUM
ejpam-5859	143	169	7	7	NUM
ejpam-5859	143	170	7	7	NUM
ejpam-5859	143	171	7	7	NUM
ejpam-5859	143	172	7	7	NUM
ejpam-5859	143	173	7	7	NUM
ejpam-5859	143	174	[	[	PUNCT
ejpam-5859	143	175	]	]	SYM
ejpam-5859	143	176	1	1	NUM
ejpam-5859	143	177	2	2	NUM
ejpam-5859	143	178	3	3	NUM
ejpam-5859	143	179	4	4	NUM
ejpam-5859	143	180	5	5	NUM
ejpam-5859	143	181	7	7	NUM
ejpam-5859	143	182	41	41	NUM
ejpam-5859	143	183	4	4	NUM
ejpam-5859	143	184	5	5	NUM
ejpam-5859	143	185	7	7	NUM
ejpam-5859	143	186	4	4	NUM
ejpam-5859	143	187	5	5	NUM
ejpam-5859	143	188	7	7	NUM
ejpam-5859	143	189	42	42	NUM
ejpam-5859	143	190	5	5	NUM
ejpam-5859	143	191	7	7	NUM
ejpam-5859	143	192	7	7	NUM
ejpam-5859	143	193	5	5	NUM
ejpam-5859	143	194	7	7	NUM
ejpam-5859	143	195	7	7	NUM
ejpam-5859	143	196	43	43	NUM
ejpam-5859	143	197	7	7	NUM
ejpam-5859	143	198	7	7	NUM
ejpam-5859	143	199	7	7	NUM
ejpam-5859	143	200	7	7	NUM
ejpam-5859	143	201	7	7	NUM
ejpam-5859	143	202	7	7	NUM
ejpam-5859	143	203	44	44	NUM
ejpam-5859	143	204	4	4	NUM
ejpam-5859	143	205	5	5	NUM
ejpam-5859	143	206	7	7	NUM
ejpam-5859	143	207	4	4	NUM
ejpam-5859	143	208	5	5	NUM
ejpam-5859	143	209	7	7	NUM
ejpam-5859	143	210	45	45	NUM
ejpam-5859	143	211	5	5	NUM
ejpam-5859	143	212	7	7	NUM
ejpam-5859	143	213	7	7	NUM
ejpam-5859	143	214	5	5	NUM
ejpam-5859	143	215	7	7	NUM
ejpam-5859	143	216	7	7	NUM
ejpam-5859	143	217	47	47	NUM
ejpam-5859	143	218	7	7	NUM
ejpam-5859	143	219	7	7	NUM
ejpam-5859	143	220	7	7	NUM
ejpam-5859	143	221	7	7	NUM
ejpam-5859	143	222	7	7	NUM
ejpam-5859	143	223	7	7	NUM
ejpam-5859	143	224	[	[	PUNCT
ejpam-5859	143	225	]	]	SYM
ejpam-5859	143	226	1	1	NUM
ejpam-5859	143	227	2	2	NUM
ejpam-5859	143	228	3	3	NUM
ejpam-5859	143	229	4	4	NUM
ejpam-5859	143	230	5	5	NUM
ejpam-5859	143	231	7	7	NUM
ejpam-5859	143	232	51	51	NUM
ejpam-5859	143	233	5	5	NUM
ejpam-5859	143	234	7	7	NUM
ejpam-5859	143	235	7	7	NUM
ejpam-5859	143	236	5	5	NUM
ejpam-5859	143	237	7	7	NUM
ejpam-5859	143	238	7	7	NUM
ejpam-5859	143	239	52	52	NUM
ejpam-5859	143	240	7	7	NUM
ejpam-5859	143	241	7	7	NUM
ejpam-5859	143	242	7	7	NUM
ejpam-5859	143	243	7	7	NUM
ejpam-5859	143	244	7	7	NUM
ejpam-5859	143	245	7	7	NUM
ejpam-5859	143	246	53	53	NUM
ejpam-5859	143	247	7	7	NUM
ejpam-5859	143	248	7	7	NUM
ejpam-5859	143	249	7	7	NUM
ejpam-5859	143	250	7	7	NUM
ejpam-5859	143	251	7	7	NUM
ejpam-5859	143	252	7	7	NUM
ejpam-5859	143	253	54	54	NUM
ejpam-5859	143	254	5	5	NUM
ejpam-5859	143	255	7	7	NUM
ejpam-5859	143	256	7	7	NUM
ejpam-5859	143	257	5	5	NUM
ejpam-5859	143	258	7	7	NUM
ejpam-5859	143	259	7	7	NUM
ejpam-5859	143	260	55	55	NUM
ejpam-5859	143	261	7	7	NUM
ejpam-5859	143	262	7	7	NUM
ejpam-5859	143	263	7	7	NUM
ejpam-5859	143	264	7	7	NUM
ejpam-5859	143	265	7	7	NUM
ejpam-5859	143	266	7	7	NUM
ejpam-5859	143	267	57	57	NUM
ejpam-5859	143	268	7	7	NUM
ejpam-5859	143	269	7	7	NUM
ejpam-5859	143	270	7	7	NUM
ejpam-5859	143	271	7	7	NUM
ejpam-5859	143	272	7	7	NUM
ejpam-5859	143	273	7	7	NUM
ejpam-5859	143	274	[	[	PUNCT
ejpam-5859	143	275	]	]	SYM
ejpam-5859	143	276	1	1	NUM
ejpam-5859	143	277	2	2	NUM
ejpam-5859	143	278	3	3	NUM
ejpam-5859	143	279	4	4	NUM
ejpam-5859	143	280	5	5	NUM
ejpam-5859	143	281	7	7	NUM
ejpam-5859	143	282	71	71	NUM
ejpam-5859	143	283	7	7	NUM
ejpam-5859	143	284	7	7	NUM
ejpam-5859	143	285	7	7	NUM
ejpam-5859	143	286	7	7	NUM
ejpam-5859	143	287	7	7	NUM
ejpam-5859	143	288	7	7	NUM
ejpam-5859	143	289	72	72	NUM
ejpam-5859	143	290	7	7	NUM
ejpam-5859	143	291	7	7	NUM
ejpam-5859	143	292	7	7	NUM
ejpam-5859	143	293	7	7	NUM
ejpam-5859	143	294	7	7	NUM
ejpam-5859	143	295	7	7	NUM
ejpam-5859	143	296	73	73	NUM
ejpam-5859	143	297	7	7	NUM
ejpam-5859	143	298	7	7	NUM
ejpam-5859	143	299	7	7	NUM
ejpam-5859	143	300	7	7	NUM
ejpam-5859	143	301	7	7	NUM
ejpam-5859	143	302	7	7	NUM
ejpam-5859	143	303	74	74	NUM
ejpam-5859	143	304	7	7	NUM
ejpam-5859	143	305	7	7	NUM
ejpam-5859	143	306	7	7	NUM
ejpam-5859	143	307	7	7	NUM
ejpam-5859	143	308	7	7	NUM
ejpam-5859	143	309	7	7	NUM
ejpam-5859	143	310	75	75	NUM
ejpam-5859	143	311	7	7	NUM
ejpam-5859	143	312	7	7	NUM
ejpam-5859	143	313	7	7	NUM
ejpam-5859	143	314	7	7	NUM
ejpam-5859	143	315	7	7	NUM
ejpam-5859	143	316	7	7	NUM
ejpam-5859	143	317	77	77	NUM
ejpam-5859	143	318	7	7	NUM
ejpam-5859	143	319	7	7	NUM
ejpam-5859	143	320	7	7	NUM
ejpam-5859	143	321	7	7	NUM
ejpam-5859	143	322	7	7	NUM
ejpam-5859	143	323	7	7	NUM
ejpam-5859	143	324	[	[	PUNCT
ejpam-5859	143	325	]	]	X
ejpam-5859	143	326	∗	∗	NOUN
ejpam-5859	143	327	1	1	NUM
ejpam-5859	143	328	2	2	NUM
ejpam-5859	143	329	3	3	NUM
ejpam-5859	143	330	4	4	NUM
ejpam-5859	143	331	5	5	NUM
ejpam-5859	143	332	7	7	NUM
ejpam-5859	143	333	11	11	NUM
ejpam-5859	143	334	1	1	NUM
ejpam-5859	143	335	2	2	NUM
ejpam-5859	143	336	3	3	NUM
ejpam-5859	143	337	4	4	NUM
ejpam-5859	143	338	5	5	NUM
ejpam-5859	143	339	7	7	NUM
ejpam-5859	143	340	12	12	NUM
ejpam-5859	143	341	1	1	NUM
ejpam-5859	143	342	1	1	NUM
ejpam-5859	143	343	2	2	NUM
ejpam-5859	143	344	4	4	NUM
ejpam-5859	143	345	4	4	NUM
ejpam-5859	143	346	5	5	NUM
ejpam-5859	143	347	13	13	NUM
ejpam-5859	143	348	1	1	NUM
ejpam-5859	143	349	1	1	NUM
ejpam-5859	143	350	1	1	NUM
ejpam-5859	143	351	4	4	NUM
ejpam-5859	143	352	4	4	NUM
ejpam-5859	143	353	4	4	NUM
ejpam-5859	143	354	14	14	NUM
ejpam-5859	143	355	1	1	NUM
ejpam-5859	143	356	2	2	NUM
ejpam-5859	143	357	3	3	NUM
ejpam-5859	143	358	1	1	NUM
ejpam-5859	143	359	2	2	NUM
ejpam-5859	143	360	3	3	NUM
ejpam-5859	143	361	15	15	NUM
ejpam-5859	143	362	1	1	NUM
ejpam-5859	143	363	1	1	NUM
ejpam-5859	143	364	2	2	NUM
ejpam-5859	143	365	1	1	NUM
ejpam-5859	143	366	1	1	NUM
ejpam-5859	143	367	2	2	NUM
ejpam-5859	143	368	17	17	NUM
ejpam-5859	143	369	1	1	NUM
ejpam-5859	143	370	1	1	NUM
ejpam-5859	143	371	1	1	NUM
ejpam-5859	143	372	1	1	NUM
ejpam-5859	143	373	1	1	NUM
ejpam-5859	143	374	1	1	NUM
ejpam-5859	143	375	[	[	PUNCT
ejpam-5859	143	376	]	]	X
ejpam-5859	143	377	∗	∗	NOUN
ejpam-5859	143	378	1	1	NUM
ejpam-5859	143	379	2	2	NUM
ejpam-5859	143	380	3	3	NUM
ejpam-5859	143	381	4	4	NUM
ejpam-5859	143	382	5	5	NUM
ejpam-5859	143	383	7	7	NUM
ejpam-5859	143	384	21	21	NUM
ejpam-5859	143	385	1	1	NUM
ejpam-5859	143	386	1	1	NUM
ejpam-5859	143	387	2	2	NUM
ejpam-5859	143	388	4	4	NUM
ejpam-5859	143	389	4	4	NUM
ejpam-5859	143	390	5	5	NUM
ejpam-5859	143	391	22	22	NUM
ejpam-5859	143	392	1	1	NUM
ejpam-5859	143	393	1	1	NUM
ejpam-5859	143	394	1	1	NUM
ejpam-5859	143	395	4	4	NUM
ejpam-5859	143	396	4	4	NUM
ejpam-5859	143	397	4	4	NUM
ejpam-5859	143	398	23	23	NUM
ejpam-5859	143	399	1	1	NUM
ejpam-5859	143	400	1	1	NUM
ejpam-5859	143	401	1	1	NUM
ejpam-5859	143	402	4	4	NUM
ejpam-5859	143	403	4	4	NUM
ejpam-5859	143	404	4	4	NUM
ejpam-5859	143	405	24	24	NUM
ejpam-5859	143	406	1	1	NUM
ejpam-5859	143	407	1	1	NUM
ejpam-5859	143	408	3	3	NUM
ejpam-5859	143	409	1	1	NUM
ejpam-5859	143	410	1	1	NUM
ejpam-5859	143	411	2	2	NUM
ejpam-5859	143	412	25	25	NUM
ejpam-5859	143	413	1	1	NUM
ejpam-5859	143	414	1	1	NUM
ejpam-5859	143	415	1	1	NUM
ejpam-5859	143	416	1	1	NUM
ejpam-5859	143	417	1	1	NUM
ejpam-5859	143	418	1	1	NUM
ejpam-5859	143	419	27	27	NUM
ejpam-5859	143	420	1	1	NUM
ejpam-5859	143	421	1	1	NUM
ejpam-5859	143	422	1	1	NUM
ejpam-5859	143	423	1	1	NUM
ejpam-5859	143	424	1	1	NUM
ejpam-5859	143	425	1	1	NUM
ejpam-5859	143	426	k.	k.	NOUN
ejpam-5859	143	427	nakwan	nakwan	PROPN
ejpam-5859	143	428	,	,	PUNCT
ejpam-5859	143	429	p.	p.	PROPN
ejpam-5859	143	430	luangchaisri	luangchaisri	VERB
ejpam-5859	143	431	,	,	PUNCT
ejpam-5859	143	432	t.	t.	PROPN
ejpam-5859	143	433	changphas	changphas	PROPN
ejpam-5859	143	434	/	/	SYM
ejpam-5859	143	435	eur	eur	PROPN
ejpam-5859	143	436	.	.	PUNCT
ejpam-5859	144	1	j.	j.	PROPN
ejpam-5859	144	2	pure	pure	PROPN
ejpam-5859	144	3	appl	appl	PROPN
ejpam-5859	144	4	.	.	PROPN
ejpam-5859	144	5	math	math	PROPN
ejpam-5859	144	6	,	,	PUNCT
ejpam-5859	144	7	18	18	NUM
ejpam-5859	144	8	(	(	PUNCT
ejpam-5859	144	9	2	2	NUM
ejpam-5859	144	10	)	)	PUNCT
ejpam-5859	144	11	(	(	PUNCT
ejpam-5859	144	12	2025	2025	NUM
ejpam-5859	144	13	)	)	PUNCT
ejpam-5859	144	14	,	,	PUNCT
ejpam-5859	144	15	5859	5859	NUM
ejpam-5859	144	16	7	7	NUM
ejpam-5859	144	17	of	of	ADP
ejpam-5859	144	18	8	8	NUM
ejpam-5859	144	19	[	[	PUNCT
ejpam-5859	144	20	]	]	X
ejpam-5859	144	21	∗	∗	NOUN
ejpam-5859	144	22	1	1	NUM
ejpam-5859	144	23	2	2	NUM
ejpam-5859	144	24	3	3	NUM
ejpam-5859	144	25	4	4	NUM
ejpam-5859	144	26	5	5	NUM
ejpam-5859	144	27	7	7	NUM
ejpam-5859	144	28	31	31	NUM
ejpam-5859	144	29	1	1	NUM
ejpam-5859	144	30	1	1	NUM
ejpam-5859	144	31	1	1	NUM
ejpam-5859	144	32	4	4	NUM
ejpam-5859	144	33	4	4	NUM
ejpam-5859	144	34	4	4	NUM
ejpam-5859	144	35	3a	3a	NUM
ejpam-5859	144	36	1	1	NUM
ejpam-5859	144	37	1	1	NUM
ejpam-5859	144	38	1	1	NUM
ejpam-5859	144	39	4	4	NUM
ejpam-5859	144	40	4	4	NUM
ejpam-5859	144	41	4	4	NUM
ejpam-5859	144	42	33	33	NUM
ejpam-5859	144	43	1	1	NUM
ejpam-5859	144	44	1	1	NUM
ejpam-5859	144	45	1	1	NUM
ejpam-5859	144	46	4	4	NUM
ejpam-5859	144	47	4	4	NUM
ejpam-5859	144	48	4	4	NUM
ejpam-5859	144	49	34	34	NUM
ejpam-5859	144	50	1	1	NUM
ejpam-5859	144	51	1	1	NUM
ejpam-5859	144	52	1	1	NUM
ejpam-5859	144	53	1	1	NUM
ejpam-5859	144	54	1	1	NUM
ejpam-5859	144	55	1	1	NUM
ejpam-5859	144	56	35	35	NUM
ejpam-5859	144	57	1	1	NUM
ejpam-5859	144	58	1	1	NUM
ejpam-5859	144	59	1	1	NUM
ejpam-5859	144	60	1	1	NUM
ejpam-5859	144	61	1	1	NUM
ejpam-5859	144	62	1	1	NUM
ejpam-5859	144	63	37	37	NUM
ejpam-5859	144	64	1	1	NUM
ejpam-5859	144	65	1	1	NUM
ejpam-5859	144	66	1	1	NUM
ejpam-5859	144	67	1	1	NUM
ejpam-5859	144	68	1	1	NUM
ejpam-5859	144	69	1	1	NUM
ejpam-5859	144	70	[	[	PUNCT
ejpam-5859	144	71	]	]	X
ejpam-5859	144	72	∗	∗	NOUN
ejpam-5859	144	73	1	1	NUM
ejpam-5859	144	74	2	2	NUM
ejpam-5859	144	75	3	3	NUM
ejpam-5859	144	76	4	4	NUM
ejpam-5859	144	77	5	5	NUM
ejpam-5859	144	78	7	7	NUM
ejpam-5859	144	79	41	41	NUM
ejpam-5859	144	80	1	1	NUM
ejpam-5859	144	81	2	2	NUM
ejpam-5859	144	82	3	3	NUM
ejpam-5859	144	83	1	1	NUM
ejpam-5859	144	84	2	2	NUM
ejpam-5859	144	85	3	3	NUM
ejpam-5859	144	86	42	42	NUM
ejpam-5859	144	87	1	1	NUM
ejpam-5859	144	88	1	1	NUM
ejpam-5859	144	89	2	2	NUM
ejpam-5859	144	90	1	1	NUM
ejpam-5859	144	91	1	1	NUM
ejpam-5859	144	92	2	2	NUM
ejpam-5859	144	93	43	43	NUM
ejpam-5859	144	94	1	1	NUM
ejpam-5859	144	95	1	1	NUM
ejpam-5859	144	96	1	1	NUM
ejpam-5859	144	97	1	1	NUM
ejpam-5859	144	98	1	1	NUM
ejpam-5859	144	99	1	1	NUM
ejpam-5859	144	100	44	44	NUM
ejpam-5859	144	101	1	1	NUM
ejpam-5859	144	102	2	2	NUM
ejpam-5859	144	103	3	3	NUM
ejpam-5859	144	104	1	1	NUM
ejpam-5859	144	105	2	2	NUM
ejpam-5859	144	106	3	3	NUM
ejpam-5859	144	107	45	45	NUM
ejpam-5859	144	108	1	1	NUM
ejpam-5859	144	109	1	1	NUM
ejpam-5859	144	110	2	2	NUM
ejpam-5859	144	111	1	1	NUM
ejpam-5859	144	112	1	1	NUM
ejpam-5859	144	113	2	2	NUM
ejpam-5859	144	114	47	47	NUM
ejpam-5859	144	115	1	1	NUM
ejpam-5859	144	116	1	1	NUM
ejpam-5859	144	117	1	1	NUM
ejpam-5859	144	118	1	1	NUM
ejpam-5859	144	119	1	1	NUM
ejpam-5859	144	120	1	1	NUM
ejpam-5859	144	121	[	[	PUNCT
ejpam-5859	144	122	]	]	X
ejpam-5859	144	123	∗	∗	NOUN
ejpam-5859	144	124	1	1	NUM
ejpam-5859	144	125	2	2	NUM
ejpam-5859	144	126	3	3	NUM
ejpam-5859	144	127	4	4	NUM
ejpam-5859	144	128	5	5	NUM
ejpam-5859	144	129	7	7	NUM
ejpam-5859	144	130	51	51	NUM
ejpam-5859	144	131	1	1	NUM
ejpam-5859	144	132	1	1	NUM
ejpam-5859	144	133	2	2	NUM
ejpam-5859	144	134	1	1	NUM
ejpam-5859	144	135	1	1	NUM
ejpam-5859	144	136	2	2	NUM
ejpam-5859	144	137	52	52	NUM
ejpam-5859	144	138	1	1	NUM
ejpam-5859	144	139	1	1	NUM
ejpam-5859	144	140	1	1	NUM
ejpam-5859	144	141	1	1	NUM
ejpam-5859	144	142	1	1	NUM
ejpam-5859	144	143	1	1	NUM
ejpam-5859	144	144	53	53	NUM
ejpam-5859	144	145	1	1	NUM
ejpam-5859	144	146	1	1	NUM
ejpam-5859	144	147	1	1	NUM
ejpam-5859	144	148	1	1	NUM
ejpam-5859	144	149	1	1	NUM
ejpam-5859	144	150	1	1	NUM
ejpam-5859	144	151	54	54	NUM
ejpam-5859	144	152	1	1	NUM
ejpam-5859	144	153	1	1	NUM
ejpam-5859	144	154	2	2	NUM
ejpam-5859	144	155	1	1	NUM
ejpam-5859	144	156	1	1	NUM
ejpam-5859	144	157	2	2	NUM
ejpam-5859	144	158	55	55	NUM
ejpam-5859	144	159	1	1	NUM
ejpam-5859	144	160	1	1	NUM
ejpam-5859	144	161	1	1	NUM
ejpam-5859	144	162	1	1	NUM
ejpam-5859	144	163	1	1	NUM
ejpam-5859	144	164	1	1	NUM
ejpam-5859	144	165	57	57	NUM
ejpam-5859	144	166	1	1	NUM
ejpam-5859	144	167	1	1	NUM
ejpam-5859	144	168	1	1	NUM
ejpam-5859	144	169	1	1	NUM
ejpam-5859	144	170	1	1	NUM
ejpam-5859	144	171	1	1	NUM
ejpam-5859	144	172	[	[	PUNCT
ejpam-5859	144	173	]	]	X
ejpam-5859	144	174	∗	∗	NOUN
ejpam-5859	144	175	1	1	NUM
ejpam-5859	144	176	2	2	NUM
ejpam-5859	144	177	3	3	NUM
ejpam-5859	144	178	4	4	NUM
ejpam-5859	144	179	5	5	NUM
ejpam-5859	144	180	7	7	NUM
ejpam-5859	144	181	71	71	NUM
ejpam-5859	144	182	1	1	NUM
ejpam-5859	144	183	1	1	NUM
ejpam-5859	144	184	1	1	NUM
ejpam-5859	144	185	1	1	NUM
ejpam-5859	144	186	1	1	NUM
ejpam-5859	144	187	1	1	NUM
ejpam-5859	144	188	72	72	NUM
ejpam-5859	144	189	1	1	NUM
ejpam-5859	144	190	1	1	NUM
ejpam-5859	144	191	1	1	NUM
ejpam-5859	144	192	1	1	NUM
ejpam-5859	144	193	1	1	NUM
ejpam-5859	144	194	1	1	NUM
ejpam-5859	144	195	73	73	NUM
ejpam-5859	144	196	1	1	NUM
ejpam-5859	144	197	1	1	NUM
ejpam-5859	144	198	1	1	NUM
ejpam-5859	144	199	1	1	NUM
ejpam-5859	144	200	1	1	NUM
ejpam-5859	144	201	1	1	NUM
ejpam-5859	144	202	74	74	NUM
ejpam-5859	144	203	1	1	NUM
ejpam-5859	144	204	1	1	NUM
ejpam-5859	144	205	1	1	NUM
ejpam-5859	144	206	1	1	NUM
ejpam-5859	144	207	1	1	NUM
ejpam-5859	144	208	1	1	NUM
ejpam-5859	144	209	75	75	NUM
ejpam-5859	144	210	1	1	NUM
ejpam-5859	144	211	1	1	NUM
ejpam-5859	144	212	1	1	NUM
ejpam-5859	144	213	1	1	NUM
ejpam-5859	144	214	1	1	NUM
ejpam-5859	144	215	1	1	NUM
ejpam-5859	144	216	77	77	NUM
ejpam-5859	144	217	1	1	NUM
ejpam-5859	144	218	1	1	NUM
ejpam-5859	144	219	1	1	NUM
ejpam-5859	144	220	1	1	NUM
ejpam-5859	144	221	1	1	NUM
ejpam-5859	144	222	1	1	NUM
ejpam-5859	144	223	and	and	CCONJ
ejpam-5859	144	224	≤	≤	NUM
ejpam-5859	144	225	=	=	SYM
ejpam-5859	144	226	{	{	PUNCT
ejpam-5859	144	227	(	(	PUNCT
ejpam-5859	144	228	1	1	NUM
ejpam-5859	144	229	,	,	PUNCT
ejpam-5859	144	230	1	1	NUM
ejpam-5859	144	231	)	)	PUNCT
ejpam-5859	144	232	,	,	PUNCT
ejpam-5859	144	233	(	(	PUNCT
ejpam-5859	144	234	2	2	NUM
ejpam-5859	144	235	,	,	PUNCT
ejpam-5859	144	236	2	2	NUM
ejpam-5859	144	237	)	)	PUNCT
ejpam-5859	144	238	,	,	PUNCT
ejpam-5859	144	239	(	(	PUNCT
ejpam-5859	144	240	3	3	NUM
ejpam-5859	144	241	,	,	PUNCT
ejpam-5859	144	242	3	3	NUM
ejpam-5859	144	243	)	)	PUNCT
ejpam-5859	144	244	,	,	PUNCT
ejpam-5859	144	245	(	(	PUNCT
ejpam-5859	144	246	4	4	NUM
ejpam-5859	144	247	,	,	PUNCT
ejpam-5859	144	248	4	4	NUM
ejpam-5859	144	249	)	)	PUNCT
ejpam-5859	144	250	,	,	PUNCT
ejpam-5859	144	251	(	(	PUNCT
ejpam-5859	144	252	5	5	NUM
ejpam-5859	144	253	,	,	PUNCT
ejpam-5859	144	254	5	5	NUM
ejpam-5859	144	255	)	)	PUNCT
ejpam-5859	144	256	,	,	PUNCT
ejpam-5859	144	257	(	(	PUNCT
ejpam-5859	144	258	7	7	NUM
ejpam-5859	144	259	,	,	PUNCT
ejpam-5859	144	260	7	7	NUM
ejpam-5859	144	261	)	)	PUNCT
ejpam-5859	144	262	,	,	PUNCT
ejpam-5859	144	263	(	(	PUNCT
ejpam-5859	144	264	3	3	NUM
ejpam-5859	144	265	,	,	PUNCT
ejpam-5859	144	266	1	1	NUM
ejpam-5859	144	267	)	)	PUNCT
ejpam-5859	144	268	,	,	PUNCT
ejpam-5859	144	269	(	(	PUNCT
ejpam-5859	144	270	3	3	NUM
ejpam-5859	144	271	,	,	PUNCT
ejpam-5859	144	272	2	2	NUM
ejpam-5859	144	273	)	)	PUNCT
ejpam-5859	144	274	,	,	PUNCT
ejpam-5859	144	275	(	(	PUNCT
ejpam-5859	144	276	2	2	NUM
ejpam-5859	144	277	,	,	PUNCT
ejpam-5859	144	278	1	1	NUM
ejpam-5859	144	279	)	)	PUNCT
ejpam-5859	144	280	,	,	PUNCT
ejpam-5859	144	281	(	(	PUNCT
ejpam-5859	144	282	4	4	NUM
ejpam-5859	144	283	,	,	PUNCT
ejpam-5859	144	284	1	1	NUM
ejpam-5859	144	285	)	)	PUNCT
ejpam-5859	144	286	,	,	PUNCT
ejpam-5859	144	287	(	(	PUNCT
ejpam-5859	144	288	5	5	NUM
ejpam-5859	144	289	,	,	PUNCT
ejpam-5859	144	290	4	4	NUM
ejpam-5859	144	291	)	)	PUNCT
ejpam-5859	144	292	,	,	PUNCT
ejpam-5859	144	293	(	(	PUNCT
ejpam-5859	144	294	5	5	NUM
ejpam-5859	144	295	,	,	PUNCT
ejpam-5859	144	296	1	1	NUM
ejpam-5859	144	297	)	)	PUNCT
ejpam-5859	144	298	,	,	PUNCT
ejpam-5859	144	299	(	(	PUNCT
ejpam-5859	144	300	5	5	NUM
ejpam-5859	144	301	,	,	PUNCT
ejpam-5859	144	302	2)(7	2)(7	NUM
ejpam-5859	144	303	,	,	PUNCT
ejpam-5859	144	304	1	1	NUM
ejpam-5859	144	305	)	)	PUNCT
ejpam-5859	144	306	,	,	PUNCT
ejpam-5859	144	307	(	(	PUNCT
ejpam-5859	144	308	7	7	NUM
ejpam-5859	144	309	,	,	PUNCT
ejpam-5859	144	310	2	2	NUM
ejpam-5859	144	311	)	)	PUNCT
ejpam-5859	144	312	,	,	PUNCT
ejpam-5859	144	313	(	(	PUNCT
ejpam-5859	144	314	7	7	NUM
ejpam-5859	144	315	,	,	PUNCT
ejpam-5859	144	316	3	3	NUM
ejpam-5859	144	317	)	)	PUNCT
ejpam-5859	144	318	,	,	PUNCT
ejpam-5859	144	319	(	(	PUNCT
ejpam-5859	144	320	7	7	NUM
ejpam-5859	144	321	,	,	PUNCT
ejpam-5859	144	322	4	4	NUM
ejpam-5859	144	323	)	)	PUNCT
ejpam-5859	144	324	,	,	PUNCT
ejpam-5859	144	325	(	(	PUNCT
ejpam-5859	144	326	7	7	NUM
ejpam-5859	144	327	,	,	PUNCT
ejpam-5859	144	328	5	5	NUM
ejpam-5859	144	329	)	)	PUNCT
ejpam-5859	144	330	}	}	PUNCT
ejpam-5859	144	331	.	.	PUNCT
ejpam-5859	145	1	by	by	ADP
ejpam-5859	145	2	proposition	proposition	NOUN
ejpam-5859	145	3	3	3	NUM
ejpam-5859	145	4	,	,	PUNCT
ejpam-5859	145	5	we	we	PRON
ejpam-5859	145	6	have	have	VERB
ejpam-5859	145	7	s(a	s(a	PROPN
ejpam-5859	145	8	,	,	PUNCT
ejpam-5859	145	9	7	7	NUM
ejpam-5859	145	10	)	)	PUNCT
ejpam-5859	145	11	=	=	SYM
ejpam-5859	146	1	s(7	s(7	ADJ
ejpam-5859	146	2	,	,	PUNCT
ejpam-5859	146	3	a	a	PRON
ejpam-5859	146	4	)	)	PUNCT
ejpam-5859	146	5	=	=	SYM
ejpam-5859	146	6	t	t	NOUN
ejpam-5859	146	7	for	for	ADP
ejpam-5859	146	8	all	all	DET
ejpam-5859	146	9	a	a	DET
ejpam-5859	146	10	∈	∈	PROPN
ejpam-5859	146	11	t	t	NOUN
ejpam-5859	146	12	.	.	PUNCT
ejpam-5859	147	1	furthermore	furthermore	ADV
ejpam-5859	147	2	,	,	PUNCT
ejpam-5859	147	3	we	we	PRON
ejpam-5859	147	4	have	have	VERB
ejpam-5859	147	5	s(1	s(1	PROPN
ejpam-5859	147	6	,	,	PUNCT
ejpam-5859	147	7	1	1	NUM
ejpam-5859	147	8	)	)	PUNCT
ejpam-5859	147	9	=	=	PRON
ejpam-5859	147	10	{	{	PUNCT
ejpam-5859	147	11	1	1	NUM
ejpam-5859	147	12	}	}	PUNCT
ejpam-5859	148	1	,	,	PUNCT
ejpam-5859	148	2	s(1	s(1	PROPN
ejpam-5859	148	3	,	,	PUNCT
ejpam-5859	148	4	2	2	NUM
ejpam-5859	148	5	)	)	PUNCT
ejpam-5859	148	6	=	=	SYM
ejpam-5859	148	7	s(2	s(2	NOUN
ejpam-5859	148	8	,	,	PUNCT
ejpam-5859	148	9	1	1	NUM
ejpam-5859	148	10	)	)	PUNCT
ejpam-5859	148	11	=	=	SYM
ejpam-5859	149	1	s(1	s(1	PROPN
ejpam-5859	149	2	,	,	PUNCT
ejpam-5859	149	3	3	3	NUM
ejpam-5859	149	4	)	)	PUNCT
ejpam-5859	149	5	=	=	VERB
ejpam-5859	149	6	s(3	s(3	NOUN
ejpam-5859	149	7	,	,	PUNCT
ejpam-5859	149	8	1	1	X
ejpam-5859	149	9	)	)	PUNCT
ejpam-5859	149	10	=	=	SYM
ejpam-5859	149	11	s(2	s(2	NOUN
ejpam-5859	149	12	,	,	PUNCT
ejpam-5859	149	13	3	3	NUM
ejpam-5859	149	14	)	)	PUNCT
ejpam-5859	149	15	=	=	VERB
ejpam-5859	149	16	s(3	s(3	NOUN
ejpam-5859	149	17	,	,	PUNCT
ejpam-5859	149	18	2	2	NUM
ejpam-5859	149	19	)	)	PUNCT
ejpam-5859	149	20	=	=	SYM
ejpam-5859	149	21	s(2	s(2	NOUN
ejpam-5859	149	22	,	,	PUNCT
ejpam-5859	149	23	2	2	NUM
ejpam-5859	149	24	)	)	PUNCT
ejpam-5859	149	25	=	=	VERB
ejpam-5859	149	26	s(3	s(3	NOUN
ejpam-5859	149	27	,	,	PUNCT
ejpam-5859	149	28	3	3	X
ejpam-5859	149	29	)	)	PUNCT
ejpam-5859	149	30	=	=	NOUN
ejpam-5859	149	31	{	{	PUNCT
ejpam-5859	149	32	1	1	NUM
ejpam-5859	149	33	,	,	PUNCT
ejpam-5859	149	34	2	2	NUM
ejpam-5859	149	35	,	,	PUNCT
ejpam-5859	149	36	3	3	NUM
ejpam-5859	149	37	}	}	PUNCT
ejpam-5859	149	38	,	,	PUNCT
ejpam-5859	149	39	s(1	s(1	PROPN
ejpam-5859	149	40	,	,	PUNCT
ejpam-5859	149	41	4	4	NUM
ejpam-5859	149	42	)	)	PUNCT
ejpam-5859	149	43	=	=	SYM
ejpam-5859	149	44	s(4	s(4	NOUN
ejpam-5859	149	45	,	,	PUNCT
ejpam-5859	149	46	1	1	NUM
ejpam-5859	149	47	)	)	PUNCT
ejpam-5859	149	48	=	=	SYM
ejpam-5859	149	49	s(4	s(4	NOUN
ejpam-5859	149	50	,	,	PUNCT
ejpam-5859	149	51	4	4	NUM
ejpam-5859	149	52	)	)	PUNCT
ejpam-5859	149	53	=	=	PRON
ejpam-5859	149	54	{	{	PUNCT
ejpam-5859	149	55	1	1	NUM
ejpam-5859	149	56	,	,	PUNCT
ejpam-5859	149	57	4	4	NUM
ejpam-5859	149	58	}	}	PUNCT
ejpam-5859	149	59	,	,	PUNCT
ejpam-5859	149	60	and	and	CCONJ
ejpam-5859	149	61	s(2	s(2	NOUN
ejpam-5859	149	62	,	,	PUNCT
ejpam-5859	149	63	4	4	NUM
ejpam-5859	149	64	)	)	PUNCT
ejpam-5859	149	65	=	=	SYM
ejpam-5859	149	66	s(4	s(4	NOUN
ejpam-5859	149	67	,	,	PUNCT
ejpam-5859	149	68	2	2	NUM
ejpam-5859	149	69	)	)	PUNCT
ejpam-5859	149	70	=	=	VERB
ejpam-5859	149	71	s(3	s(3	NOUN
ejpam-5859	149	72	,	,	PUNCT
ejpam-5859	149	73	4	4	NUM
ejpam-5859	149	74	)	)	PUNCT
ejpam-5859	149	75	=	=	SYM
ejpam-5859	149	76	s(4	s(4	NOUN
ejpam-5859	149	77	,	,	PUNCT
ejpam-5859	149	78	3	3	NUM
ejpam-5859	149	79	)	)	PUNCT
ejpam-5859	149	80	=	=	SYM
ejpam-5859	150	1	s(1	s(1	PROPN
ejpam-5859	150	2	,	,	PUNCT
ejpam-5859	150	3	5	5	NUM
ejpam-5859	150	4	)	)	PUNCT
ejpam-5859	150	5	=	=	SYM
ejpam-5859	150	6	s(2	s(2	NOUN
ejpam-5859	150	7	,	,	PUNCT
ejpam-5859	150	8	5	5	NUM
ejpam-5859	150	9	)	)	PUNCT
ejpam-5859	150	10	=	=	SYM
ejpam-5859	150	11	s(3	s(3	NOUN
ejpam-5859	150	12	,	,	PUNCT
ejpam-5859	150	13	5	5	NUM
ejpam-5859	150	14	)	)	PUNCT
ejpam-5859	150	15	=	=	SYM
ejpam-5859	150	16	s(4	s(4	NOUN
ejpam-5859	150	17	,	,	PUNCT
ejpam-5859	150	18	5	5	NUM
ejpam-5859	150	19	)	)	PUNCT
ejpam-5859	150	20	=	=	SYM
ejpam-5859	151	1	s(5	s(5	PROPN
ejpam-5859	151	2	,	,	PUNCT
ejpam-5859	151	3	5	5	NUM
ejpam-5859	151	4	)	)	PUNCT
ejpam-5859	151	5	=	=	SYM
ejpam-5859	152	1	s(5	s(5	PROPN
ejpam-5859	152	2	,	,	PUNCT
ejpam-5859	152	3	1	1	NUM
ejpam-5859	152	4	)	)	PUNCT
ejpam-5859	152	5	=	=	SYM
ejpam-5859	153	1	s(5	s(5	PROPN
ejpam-5859	153	2	,	,	PUNCT
ejpam-5859	153	3	2	2	NUM
ejpam-5859	153	4	)	)	PUNCT
ejpam-5859	153	5	=	=	SYM
ejpam-5859	154	1	s(5	s(5	PROPN
ejpam-5859	154	2	,	,	PUNCT
ejpam-5859	154	3	3	3	NUM
ejpam-5859	154	4	)	)	PUNCT
ejpam-5859	154	5	=	=	SYM
ejpam-5859	155	1	s(5	s(5	PROPN
ejpam-5859	155	2	,	,	PUNCT
ejpam-5859	155	3	4	4	NUM
ejpam-5859	155	4	)	)	PUNCT
ejpam-5859	155	5	=	=	SYM
ejpam-5859	155	6	t	t	PROPN
ejpam-5859	155	7	.	.	PUNCT
ejpam-5859	156	1	we	we	PRON
ejpam-5859	156	2	observe	observe	VERB
ejpam-5859	156	3	that	that	SCONJ
ejpam-5859	156	4	for	for	ADP
ejpam-5859	156	5	any	any	DET
ejpam-5859	156	6	a	a	NOUN
ejpam-5859	156	7	,	,	PUNCT
ejpam-5859	156	8	b	b	PROPN
ejpam-5859	156	9	∈	∈	PROPN
ejpam-5859	156	10	t	t	NOUN
ejpam-5859	156	11	,	,	PUNCT
ejpam-5859	156	12	s(a	s(a	PROPN
ejpam-5859	156	13	,	,	PUNCT
ejpam-5859	156	14	b	b	NOUN
ejpam-5859	156	15	)	)	PUNCT
ejpam-5859	156	16	is	be	AUX
ejpam-5859	156	17	a	a	DET
ejpam-5859	156	18	filter	filter	NOUN
ejpam-5859	156	19	of	of	ADP
ejpam-5859	156	20	t	t	PROPN
ejpam-5859	156	21	.	.	PUNCT
ejpam-5859	157	1	theorem	theorem	NOUN
ejpam-5859	157	2	3	3	X
ejpam-5859	157	3	.	.	PUNCT
ejpam-5859	158	1	let	let	AUX
ejpam-5859	158	2	(	(	PUNCT
ejpam-5859	158	3	t	t	NOUN
ejpam-5859	158	4	,	,	PUNCT
ejpam-5859	158	5	[	[	PUNCT
ejpam-5859	158	6	]	]	X
ejpam-5859	158	7	,	,	PUNCT
ejpam-5859	158	8	≤	≤	NUM
ejpam-5859	158	9	,	,	PUNCT
ejpam-5859	158	10	[	[	PUNCT
ejpam-5859	158	11	]	]	X
ejpam-5859	158	12	∗	∗	NOUN
ejpam-5859	158	13	)	)	PUNCT
ejpam-5859	158	14	be	be	VERB
ejpam-5859	158	15	a	a	DET
ejpam-5859	158	16	commutative	commutative	ADJ
ejpam-5859	158	17	inpots	inpot	NOUN
ejpam-5859	158	18	.	.	PUNCT
ejpam-5859	159	1	if	if	SCONJ
ejpam-5859	159	2	f	f	PROPN
ejpam-5859	159	3	is	be	AUX
ejpam-5859	159	4	a	a	DET
ejpam-5859	159	5	filter	filter	NOUN
ejpam-5859	159	6	,	,	PUNCT
ejpam-5859	159	7	then	then	ADV
ejpam-5859	159	8	s(a	s(a	PROPN
ejpam-5859	159	9	,	,	PUNCT
ejpam-5859	159	10	b	b	NOUN
ejpam-5859	159	11	)	)	PUNCT
ejpam-5859	159	12	⊆	⊆	NUM
ejpam-5859	159	13	f	f	NOUN
ejpam-5859	159	14	for	for	ADP
ejpam-5859	159	15	all	all	DET
ejpam-5859	159	16	a	a	PRON
ejpam-5859	159	17	,	,	PUNCT
ejpam-5859	159	18	b	b	X
ejpam-5859	159	19	∈	∈	PROPN
ejpam-5859	159	20	f	f	X
ejpam-5859	159	21	.	.	PUNCT
ejpam-5859	160	1	proof	proof	NOUN
ejpam-5859	160	2	.	.	PUNCT
ejpam-5859	161	1	let	let	VERB
ejpam-5859	161	2	f	f	PRON
ejpam-5859	161	3	be	be	AUX
ejpam-5859	161	4	a	a	DET
ejpam-5859	161	5	filter	filter	NOUN
ejpam-5859	161	6	of	of	ADP
ejpam-5859	161	7	t	t	PROPN
ejpam-5859	161	8	and	and	CCONJ
ejpam-5859	161	9	let	let	VERB
ejpam-5859	161	10	a	a	DET
ejpam-5859	161	11	,	,	PUNCT
ejpam-5859	161	12	b	b	PROPN
ejpam-5859	161	13	∈	∈	PROPN
ejpam-5859	161	14	f	f	X
ejpam-5859	161	15	.	.	PUNCT
ejpam-5859	162	1	if	if	SCONJ
ejpam-5859	162	2	c	c	PROPN
ejpam-5859	162	3	∈	∈	PROPN
ejpam-5859	162	4	s(a	s(a	PROPN
ejpam-5859	162	5	,	,	PUNCT
ejpam-5859	162	6	b	b	NOUN
ejpam-5859	162	7	)	)	PUNCT
ejpam-5859	162	8	,	,	PUNCT
ejpam-5859	162	9	then	then	ADV
ejpam-5859	162	10	[	[	X
ejpam-5859	162	11	aa[bbc]∗]∗	aa[bbc]∗]∗	NOUN
ejpam-5859	162	12	=	=	SYM
ejpam-5859	162	13	1	1	NUM
ejpam-5859	162	14	∈	∈	NOUN
ejpam-5859	162	15	f	f	NOUN
ejpam-5859	162	16	,	,	PUNCT
ejpam-5859	162	17	and	and	CCONJ
ejpam-5859	162	18	by	by	ADP
ejpam-5859	162	19	(	(	PUNCT
ejpam-5859	162	20	f4	f4	NUM
ejpam-5859	162	21	)	)	PUNCT
ejpam-5859	162	22	we	we	PRON
ejpam-5859	162	23	have	have	VERB
ejpam-5859	162	24	c	c	NOUN
ejpam-5859	162	25	∈	∈	PROPN
ejpam-5859	162	26	f	f	PROPN
ejpam-5859	162	27	.	.	PUNCT
ejpam-5859	163	1	theorem	theorem	ADJ
ejpam-5859	163	2	4	4	NUM
ejpam-5859	163	3	.	.	PUNCT
ejpam-5859	164	1	let	let	AUX
ejpam-5859	164	2	(	(	PUNCT
ejpam-5859	164	3	t	t	NOUN
ejpam-5859	164	4	,	,	PUNCT
ejpam-5859	164	5	[	[	PUNCT
ejpam-5859	164	6	]	]	X
ejpam-5859	164	7	,	,	PUNCT
ejpam-5859	164	8	≤	≤	NUM
ejpam-5859	164	9	,	,	PUNCT
ejpam-5859	164	10	[	[	PUNCT
ejpam-5859	164	11	]	]	X
ejpam-5859	164	12	∗	∗	NOUN
ejpam-5859	164	13	)	)	PUNCT
ejpam-5859	164	14	be	be	VERB
ejpam-5859	164	15	a	a	DET
ejpam-5859	164	16	commutative	commutative	ADJ
ejpam-5859	164	17	inpots	inpot	NOUN
ejpam-5859	164	18	.	.	PUNCT
ejpam-5859	165	1	if	if	SCONJ
ejpam-5859	165	2	f	f	PROPN
ejpam-5859	165	3	is	be	AUX
ejpam-5859	165	4	a	a	DET
ejpam-5859	165	5	filter	filter	NOUN
ejpam-5859	165	6	of	of	ADP
ejpam-5859	165	7	t	t	PROPN
ejpam-5859	165	8	,	,	PUNCT
ejpam-5859	165	9	then	then	ADV
ejpam-5859	165	10	f	f	PROPN
ejpam-5859	165	11	=	=	PUNCT
ejpam-5859	166	1	⋃	⋃	NOUN
ejpam-5859	166	2	a	a	PRON
ejpam-5859	166	3	,	,	PUNCT
ejpam-5859	166	4	b∈f	b∈f	ADJ
ejpam-5859	166	5	s(a	s(a	PROPN
ejpam-5859	166	6	,	,	PUNCT
ejpam-5859	166	7	b	b	NOUN
ejpam-5859	166	8	)	)	PUNCT
ejpam-5859	166	9	.	.	PUNCT
ejpam-5859	167	1	proof	proof	NOUN
ejpam-5859	167	2	.	.	PUNCT
ejpam-5859	168	1	let	let	VERB
ejpam-5859	168	2	f	f	PRON
ejpam-5859	168	3	be	be	AUX
ejpam-5859	168	4	a	a	DET
ejpam-5859	168	5	filter	filter	NOUN
ejpam-5859	168	6	of	of	ADP
ejpam-5859	168	7	t	t	PROPN
ejpam-5859	168	8	.	.	PUNCT
ejpam-5859	169	1	by	by	ADP
ejpam-5859	169	2	proposition	proposition	NOUN
ejpam-5859	169	3	2	2	NUM
ejpam-5859	169	4	,	,	PUNCT
ejpam-5859	169	5	c	c	PROPN
ejpam-5859	169	6	∈	∈	PROPN
ejpam-5859	169	7	s(c	s(c	NOUN
ejpam-5859	169	8	,	,	PUNCT
ejpam-5859	169	9	1	1	NUM
ejpam-5859	169	10	)	)	PUNCT
ejpam-5859	169	11	for	for	ADP
ejpam-5859	169	12	any	any	DET
ejpam-5859	169	13	c	c	PROPN
ejpam-5859	169	14	∈	∈	PROPN
ejpam-5859	169	15	f	f	PROPN
ejpam-5859	169	16	.	.	PUNCT
ejpam-5859	170	1	then	then	ADV
ejpam-5859	170	2	f	f	PROPN
ejpam-5859	170	3	⊆	⊆	NUM
ejpam-5859	170	4	⋃	⋃	PUNCT
ejpam-5859	170	5	c∈f	c∈f	NOUN
ejpam-5859	170	6	s(c	s(c	NOUN
ejpam-5859	170	7	,	,	PUNCT
ejpam-5859	170	8	1	1	NUM
ejpam-5859	170	9	)	)	PUNCT
ejpam-5859	170	10	⊆	⊆	NUM
ejpam-5859	170	11	⋃	⋃	NOUN
ejpam-5859	170	12	a	a	PRON
ejpam-5859	170	13	,	,	PUNCT
ejpam-5859	170	14	b∈f	b∈f	ADJ
ejpam-5859	170	15	s(a	s(a	PROPN
ejpam-5859	170	16	,	,	PUNCT
ejpam-5859	170	17	b	b	NOUN
ejpam-5859	170	18	)	)	PUNCT
ejpam-5859	170	19	.	.	PUNCT
ejpam-5859	171	1	for	for	ADP
ejpam-5859	171	2	the	the	DET
ejpam-5859	171	3	reverse	reverse	ADJ
ejpam-5859	171	4	inclusion	inclusion	NOUN
ejpam-5859	171	5	,	,	PUNCT
ejpam-5859	171	6	let	let	VERB
ejpam-5859	171	7	c′	c′	NOUN
ejpam-5859	171	8	∈	∈	PROPN
ejpam-5859	171	9	⋃	⋃	NOUN
ejpam-5859	171	10	a	a	PRON
ejpam-5859	171	11	,	,	PUNCT
ejpam-5859	171	12	b∈f	b∈f	ADJ
ejpam-5859	171	13	s(a	s(a	PROPN
ejpam-5859	171	14	,	,	PUNCT
ejpam-5859	171	15	b	b	NOUN
ejpam-5859	171	16	)	)	PUNCT
ejpam-5859	171	17	.	.	PUNCT
ejpam-5859	172	1	then	then	ADV
ejpam-5859	172	2	there	there	PRON
ejpam-5859	172	3	exist	exist	VERB
ejpam-5859	172	4	x	x	NOUN
ejpam-5859	172	5	,	,	PUNCT
ejpam-5859	172	6	y	y	PROPN
ejpam-5859	172	7	∈	∈	PROPN
ejpam-5859	172	8	f	f	PROPN
ejpam-5859	172	9	such	such	ADJ
ejpam-5859	172	10	that	that	DET
ejpam-5859	172	11	c′	c′	PROPN
ejpam-5859	172	12	∈	∈	PROPN
ejpam-5859	172	13	s(x	s(x	PROPN
ejpam-5859	172	14	,	,	PUNCT
ejpam-5859	172	15	y	y	NOUN
ejpam-5859	172	16	)	)	PUNCT
ejpam-5859	172	17	.	.	PUNCT
ejpam-5859	173	1	by	by	ADP
ejpam-5859	173	2	theorem	theorem	ADJ
ejpam-5859	173	3	3	3	NUM
ejpam-5859	173	4	,	,	PUNCT
ejpam-5859	173	5	c′	c′	NOUN
ejpam-5859	173	6	∈	∈	PROPN
ejpam-5859	173	7	f	f	X
ejpam-5859	173	8	.	.	PUNCT
ejpam-5859	174	1	this	this	PRON
ejpam-5859	174	2	shows	show	VERB
ejpam-5859	174	3	that	that	SCONJ
ejpam-5859	174	4	⋃	⋃	PROPN
ejpam-5859	174	5	a	a	PRON
ejpam-5859	174	6	,	,	PUNCT
ejpam-5859	174	7	b∈f	b∈f	ADJ
ejpam-5859	174	8	s(a	s(a	PROPN
ejpam-5859	174	9	,	,	PUNCT
ejpam-5859	174	10	b	b	NOUN
ejpam-5859	174	11	)	)	PUNCT
ejpam-5859	174	12	⊆	⊆	NUM
ejpam-5859	174	13	f	f	NOUN
ejpam-5859	174	14	.	.	PUNCT
ejpam-5859	175	1	k.	k.	PROPN
ejpam-5859	175	2	nakwan	nakwan	PROPN
ejpam-5859	175	3	,	,	PUNCT
ejpam-5859	175	4	p.	p.	PROPN
ejpam-5859	175	5	luangchaisri	luangchaisri	VERB
ejpam-5859	175	6	,	,	PUNCT
ejpam-5859	175	7	t.	t.	PROPN
ejpam-5859	175	8	changphas	changphas	PROPN
ejpam-5859	175	9	/	/	SYM
ejpam-5859	175	10	eur	eur	PROPN
ejpam-5859	175	11	.	.	PUNCT
ejpam-5859	176	1	j.	j.	PROPN
ejpam-5859	176	2	pure	pure	PROPN
ejpam-5859	176	3	appl	appl	PROPN
ejpam-5859	176	4	.	.	PROPN
ejpam-5859	176	5	math	math	PROPN
ejpam-5859	176	6	,	,	PUNCT
ejpam-5859	176	7	18	18	NUM
ejpam-5859	176	8	(	(	PUNCT
ejpam-5859	176	9	2	2	NUM
ejpam-5859	176	10	)	)	PUNCT
ejpam-5859	176	11	(	(	PUNCT
ejpam-5859	176	12	2025	2025	NUM
ejpam-5859	176	13	)	)	PUNCT
ejpam-5859	176	14	,	,	PUNCT
ejpam-5859	176	15	5859	5859	NUM
ejpam-5859	176	16	8	8	NUM
ejpam-5859	176	17	of	of	ADP
ejpam-5859	176	18	8	8	NUM
ejpam-5859	176	19	corollary	corollary	ADJ
ejpam-5859	176	20	1	1	NUM
ejpam-5859	176	21	.	.	PUNCT
ejpam-5859	177	1	let	let	AUX
ejpam-5859	177	2	(	(	PUNCT
ejpam-5859	177	3	t	t	NOUN
ejpam-5859	177	4	,	,	PUNCT
ejpam-5859	177	5	[	[	PUNCT
ejpam-5859	177	6	]	]	X
ejpam-5859	177	7	,	,	PUNCT
ejpam-5859	177	8	≤	≤	NUM
ejpam-5859	177	9	,	,	PUNCT
ejpam-5859	177	10	[	[	PUNCT
ejpam-5859	177	11	]	]	X
ejpam-5859	177	12	∗	∗	NOUN
ejpam-5859	177	13	)	)	PUNCT
ejpam-5859	177	14	be	be	VERB
ejpam-5859	177	15	a	a	DET
ejpam-5859	177	16	commutative	commutative	ADJ
ejpam-5859	177	17	inpots	inpot	NOUN
ejpam-5859	177	18	.	.	PUNCT
ejpam-5859	178	1	if	if	SCONJ
ejpam-5859	178	2	f	f	PROPN
ejpam-5859	178	3	is	be	AUX
ejpam-5859	178	4	a	a	DET
ejpam-5859	178	5	filter	filter	NOUN
ejpam-5859	178	6	of	of	ADP
ejpam-5859	178	7	t	t	PROPN
ejpam-5859	178	8	,	,	PUNCT
ejpam-5859	178	9	then	then	ADV
ejpam-5859	178	10	f	f	PROPN
ejpam-5859	178	11	=	=	PUNCT
ejpam-5859	178	12	⋃	⋃	NOUN
ejpam-5859	178	13	a∈f	a∈f	NOUN
ejpam-5859	178	14	s(a	s(a	PROPN
ejpam-5859	178	15	,	,	PUNCT
ejpam-5859	178	16	1	1	NUM
ejpam-5859	178	17	)	)	PUNCT
ejpam-5859	178	18	.	.	PUNCT
ejpam-5859	179	1	4	4	X
ejpam-5859	179	2	.	.	X
ejpam-5859	179	3	conclusions	conclusion	NOUN
ejpam-5859	179	4	in	in	ADP
ejpam-5859	179	5	this	this	DET
ejpam-5859	179	6	paper	paper	NOUN
ejpam-5859	179	7	,	,	PUNCT
ejpam-5859	179	8	we	we	PRON
ejpam-5859	179	9	introduce	introduce	VERB
ejpam-5859	179	10	the	the	DET
ejpam-5859	179	11	concept	concept	NOUN
ejpam-5859	179	12	of	of	ADP
ejpam-5859	179	13	filters	filter	NOUN
ejpam-5859	179	14	in	in	ADP
ejpam-5859	179	15	implicative	implicative	NOUN
ejpam-5859	179	16	negatively	negatively	ADV
ejpam-5859	179	17	partially	partially	ADV
ejpam-5859	179	18	ordered	order	VERB
ejpam-5859	179	19	ternary	ternary	ADJ
ejpam-5859	179	20	semigroups	semigroup	NOUN
ejpam-5859	179	21	(	(	PUNCT
ejpam-5859	179	22	definition	definition	NOUN
ejpam-5859	179	23	4	4	NUM
ejpam-5859	179	24	)	)	PUNCT
ejpam-5859	179	25	and	and	CCONJ
ejpam-5859	179	26	give	give	VERB
ejpam-5859	179	27	a	a	DET
ejpam-5859	179	28	characterization	characterization	NOUN
ejpam-5859	179	29	of	of	ADP
ejpam-5859	179	30	filters	filter	NOUN
ejpam-5859	179	31	(	(	PUNCT
ejpam-5859	179	32	proposition	proposition	NOUN
ejpam-5859	179	33	1	1	NUM
ejpam-5859	179	34	)	)	PUNCT
ejpam-5859	179	35	.	.	PUNCT
ejpam-5859	180	1	then	then	ADV
ejpam-5859	180	2	we	we	PRON
ejpam-5859	180	3	consider	consider	VERB
ejpam-5859	180	4	the	the	DET
ejpam-5859	180	5	set	set	NOUN
ejpam-5859	180	6	s(a	s(a	PROPN
ejpam-5859	180	7	,	,	PUNCT
ejpam-5859	180	8	b	b	NOUN
ejpam-5859	180	9	)	)	PUNCT
ejpam-5859	180	10	:	:	PUNCT
ejpam-5859	180	11	=	=	PUNCT
ejpam-5859	180	12	{	{	PUNCT
ejpam-5859	180	13	c	c	NOUN
ejpam-5859	180	14	∈	∈	PROPN
ejpam-5859	180	15	t	t	NOUN
ejpam-5859	180	16	:	:	PUNCT
ejpam-5859	181	1	[	[	X
ejpam-5859	181	2	aa[bbc]∗]∗	aa[bbc]∗]∗	NOUN
ejpam-5859	181	3	=	=	NOUN
ejpam-5859	181	4	1	1	NUM
ejpam-5859	181	5	}	}	PUNCT
ejpam-5859	181	6	where	where	SCONJ
ejpam-5859	181	7	a	a	DET
ejpam-5859	181	8	,	,	PUNCT
ejpam-5859	181	9	b	b	NOUN
ejpam-5859	181	10	are	be	AUX
ejpam-5859	181	11	elements	element	NOUN
ejpam-5859	181	12	of	of	ADP
ejpam-5859	181	13	an	an	DET
ejpam-5859	181	14	implicative	implicative	NOUN
ejpam-5859	181	15	negatively	negatively	ADV
ejpam-5859	181	16	partially	partially	ADV
ejpam-5859	181	17	ordered	order	VERB
ejpam-5859	181	18	ternary	ternary	ADJ
ejpam-5859	181	19	semigroup	semigroup	NOUN
ejpam-5859	181	20	(	(	PUNCT
ejpam-5859	181	21	t	t	PROPN
ejpam-5859	181	22	,	,	PUNCT
ejpam-5859	181	23	[	[	PUNCT
ejpam-5859	181	24	]	]	X
ejpam-5859	181	25	,	,	PUNCT
ejpam-5859	181	26	≤	≤	NUM
ejpam-5859	181	27	,	,	PUNCT
ejpam-5859	181	28	[	[	PUNCT
ejpam-5859	181	29	]	]	X
ejpam-5859	181	30	∗	∗	NOUN
ejpam-5859	181	31	)	)	PUNCT
ejpam-5859	181	32	.	.	PUNCT
ejpam-5859	182	1	the	the	DET
ejpam-5859	182	2	main	main	ADJ
ejpam-5859	182	3	result	result	NOUN
ejpam-5859	182	4	obtained	obtain	VERB
ejpam-5859	182	5	is	be	AUX
ejpam-5859	182	6	that	that	SCONJ
ejpam-5859	182	7	any	any	DET
ejpam-5859	182	8	filter	filter	NOUN
ejpam-5859	182	9	can	can	AUX
ejpam-5859	182	10	be	be	AUX
ejpam-5859	182	11	represented	represent	VERB
ejpam-5859	182	12	by	by	ADP
ejpam-5859	182	13	the	the	DET
ejpam-5859	182	14	union	union	NOUN
ejpam-5859	182	15	of	of	ADP
ejpam-5859	182	16	such	such	ADJ
ejpam-5859	182	17	sets	set	NOUN
ejpam-5859	182	18	(	(	PUNCT
ejpam-5859	182	19	theorem	theorem	NOUN
ejpam-5859	182	20	4	4	NUM
ejpam-5859	182	21	)	)	PUNCT
ejpam-5859	182	22	,	,	PUNCT
ejpam-5859	182	23	if	if	SCONJ
ejpam-5859	182	24	(	(	PUNCT
ejpam-5859	182	25	t	t	PROPN
ejpam-5859	182	26	,	,	PUNCT
ejpam-5859	182	27	[	[	PUNCT
ejpam-5859	182	28	]	]	X
ejpam-5859	182	29	,	,	PUNCT
ejpam-5859	182	30	≤	≤	NUM
ejpam-5859	182	31	,	,	PUNCT
ejpam-5859	182	32	[	[	PUNCT
ejpam-5859	182	33	]	]	X
ejpam-5859	182	34	∗	∗	NOUN
ejpam-5859	182	35	)	)	PUNCT
ejpam-5859	182	36	is	be	AUX
ejpam-5859	182	37	commutative	commutative	ADJ
ejpam-5859	182	38	.	.	PUNCT
ejpam-5859	183	1	acknowledgements	acknowledgement	VERB
ejpam-5859	183	2	the	the	DET
ejpam-5859	183	3	research	research	NOUN
ejpam-5859	183	4	on	on	ADP
ejpam-5859	183	5	”	"	PUNCT
ejpam-5859	183	6	on	on	ADP
ejpam-5859	183	7	filters	filter	NOUN
ejpam-5859	183	8	of	of	ADP
ejpam-5859	183	9	implicative	implicative	NOUN
ejpam-5859	183	10	negatively	negatively	ADV
ejpam-5859	183	11	partially	partially	ADV
ejpam-5859	183	12	ordered	order	VERB
ejpam-5859	183	13	ternary	ternary	ADJ
ejpam-5859	183	14	semigroups	semigroup	NOUN
ejpam-5859	183	15	”	"	PUNCT
ejpam-5859	183	16	by	by	ADP
ejpam-5859	183	17	khon	khon	PROPN
ejpam-5859	183	18	kaen	kaen	PROPN
ejpam-5859	183	19	university	university	PROPN
ejpam-5859	183	20	has	have	AUX
ejpam-5859	183	21	received	receive	VERB
ejpam-5859	183	22	funding	funding	NOUN
ejpam-5859	183	23	support	support	NOUN
ejpam-5859	183	24	from	from	ADP
ejpam-5859	183	25	the	the	DET
ejpam-5859	183	26	national	national	ADJ
ejpam-5859	183	27	science	science	NOUN
ejpam-5859	183	28	,	,	PUNCT
ejpam-5859	183	29	research	research	NOUN
ejpam-5859	183	30	and	and	CCONJ
ejpam-5859	183	31	innovation	innovation	NOUN
ejpam-5859	183	32	fund	fund	NOUN
ejpam-5859	183	33	(	(	PUNCT
ejpam-5859	183	34	nsrf	nsrf	NOUN
ejpam-5859	183	35	)	)	PUNCT
ejpam-5859	183	36	.	.	PUNCT
ejpam-5859	184	1	references	reference	NOUN
ejpam-5859	184	2	[	[	X
ejpam-5859	184	3	1	1	NUM
ejpam-5859	184	4	]	]	PUNCT
ejpam-5859	184	5	g.	g.	NOUN
ejpam-5859	184	6	birkhoff	birkhoff	PROPN
ejpam-5859	184	7	.	.	PUNCT
ejpam-5859	185	1	lattice	lattice	PROPN
ejpam-5859	185	2	theory	theory	PROPN
ejpam-5859	185	3	.	.	PUNCT
ejpam-5859	186	1	amer	amer	PROPN
ejpam-5859	186	2	.	.	PUNCT
ejpam-5859	186	3	math	math	PROPN
ejpam-5859	186	4	.	.	PUNCT
ejpam-5859	187	1	soc	soc	PROPN
ejpam-5859	187	2	.	.	PUNCT
ejpam-5859	188	1	coll	coll	PROPN
ejpam-5859	188	2	.	.	PUNCT
ejpam-5859	188	3	publ	publ	PROPN
ejpam-5859	188	4	.	.	PUNCT
ejpam-5859	189	1	vol	vol	NOUN
ejpam-5859	189	2	.	.	PUNCT
ejpam-5859	190	1	xxv	xxv	PROPN
ejpam-5859	190	2	,	,	PUNCT
ejpam-5859	190	3	providence	providence	NOUN
ejpam-5859	190	4	,	,	PUNCT
ejpam-5859	190	5	1967	1967	NUM
ejpam-5859	190	6	.	.	PUNCT
ejpam-5859	191	1	[	[	X
ejpam-5859	191	2	2	2	X
ejpam-5859	191	3	]	]	PUNCT
ejpam-5859	191	4	t.	t.	PROPN
ejpam-5859	191	5	s.	s.	PROPN
ejpam-5859	191	6	blyth	blyth	PROPN
ejpam-5859	191	7	.	.	PUNCT
ejpam-5859	192	1	pseudo	pseudo	NOUN
ejpam-5859	192	2	-	-	NOUN
ejpam-5859	192	3	residuals	residual	NOUN
ejpam-5859	192	4	in	in	ADP
ejpam-5859	192	5	semigroups	semigroup	NOUN
ejpam-5859	192	6	.	.	PUNCT
ejpam-5859	193	1	j.	j.	PROPN
ejpam-5859	193	2	london	london	PROPN
ejpam-5859	193	3	math	math	PROPN
ejpam-5859	193	4	.	.	PUNCT
ejpam-5859	194	1	soc	soc	PROPN
ejpam-5859	194	2	.	.	PUNCT
ejpam-5859	194	3	,	,	PUNCT
ejpam-5859	194	4	1(1):441–454	1(1):441–454	NUM
ejpam-5859	194	5	,	,	PUNCT
ejpam-5859	194	6	1965	1965	NUM
ejpam-5859	194	7	.	.	PUNCT
ejpam-5859	195	1	[	[	X
ejpam-5859	195	2	3	3	X
ejpam-5859	195	3	]	]	PUNCT
ejpam-5859	195	4	m.	m.	NOUN
ejpam-5859	195	5	w.	w.	PROPN
ejpam-5859	195	6	chan	chan	PROPN
ejpam-5859	195	7	and	and	CCONJ
ejpam-5859	195	8	k.	k.	PROPN
ejpam-5859	195	9	p.	p.	PROPN
ejpam-5859	195	10	shum	shum	PROPN
ejpam-5859	195	11	.	.	PUNCT
ejpam-5859	196	1	homomorphisms	homomorphism	NOUN
ejpam-5859	196	2	of	of	ADP
ejpam-5859	196	3	implicative	implicative	ADJ
ejpam-5859	196	4	semigroups	semigroup	NOUN
ejpam-5859	196	5	.	.	PUNCT
ejpam-5859	197	1	semigroup	semigroup	PROPN
ejpam-5859	197	2	forum	forum	PROPN
ejpam-5859	197	3	,	,	PUNCT
ejpam-5859	197	4	46:7–15	46:7–15	NUM
ejpam-5859	197	5	,	,	PUNCT
ejpam-5859	197	6	1993	1993	NUM
ejpam-5859	197	7	.	.	PUNCT
ejpam-5859	198	1	[	[	X
ejpam-5859	198	2	4	4	X
ejpam-5859	198	3	]	]	PUNCT
ejpam-5859	198	4	h.	h.	PROPN
ejpam-5859	198	5	b.	b.	PROPN
ejpam-5859	198	6	curry	curry	PROPN
ejpam-5859	198	7	.	.	PUNCT
ejpam-5859	199	1	foundations	foundation	NOUN
ejpam-5859	199	2	of	of	ADP
ejpam-5859	199	3	mathematical	mathematical	ADJ
ejpam-5859	199	4	logic	logic	NOUN
ejpam-5859	199	5	.	.	PUNCT
ejpam-5859	200	1	mcgrow	mcgrow	NOUN
ejpam-5859	200	2	-	-	PUNCT
ejpam-5859	200	3	hill	hill	PROPN
ejpam-5859	200	4	,	,	PUNCT
ejpam-5859	200	5	new	new	PROPN
ejpam-5859	200	6	york	york	PROPN
ejpam-5859	200	7	,	,	PUNCT
ejpam-5859	200	8	1963	1963	NUM
ejpam-5859	200	9	.	.	PUNCT
ejpam-5859	201	1	[	[	X
ejpam-5859	201	2	5	5	X
ejpam-5859	201	3	]	]	X
ejpam-5859	201	4	y.	y.	PROPN
ejpam-5859	201	5	b.	b.	PROPN
ejpam-5859	201	6	jun	jun	PROPN
ejpam-5859	201	7	.	.	PROPN
ejpam-5859	202	1	a	a	DET
ejpam-5859	202	2	note	note	NOUN
ejpam-5859	202	3	on	on	ADP
ejpam-5859	202	4	ordered	order	VERB
ejpam-5859	202	5	filters	filter	NOUN
ejpam-5859	202	6	of	of	ADP
ejpam-5859	202	7	implicative	implicative	ADJ
ejpam-5859	202	8	semigroups	semigroup	NOUN
ejpam-5859	202	9	.	.	PUNCT
ejpam-5859	203	1	bull	bull	NOUN
ejpam-5859	203	2	.	.	PUNCT
ejpam-5859	204	1	korean	korean	ADJ
ejpam-5859	204	2	math	math	PROPN
ejpam-5859	204	3	.	.	PUNCT
ejpam-5859	205	1	soc	soc	PROPN
ejpam-5859	205	2	.	.	PUNCT
ejpam-5859	205	3	,	,	PUNCT
ejpam-5859	206	1	34(2):185–191	34(2):185–191	PROPN
ejpam-5859	206	2	,	,	PUNCT
ejpam-5859	206	3	1997	1997	NUM
ejpam-5859	206	4	.	.	PUNCT
ejpam-5859	207	1	[	[	X
ejpam-5859	207	2	6	6	NUM
ejpam-5859	207	3	]	]	X
ejpam-5859	207	4	y.	y.	PROPN
ejpam-5859	207	5	b.	b.	PROPN
ejpam-5859	207	6	jun	jun	PROPN
ejpam-5859	207	7	,	,	PUNCT
ejpam-5859	207	8	j.	j.	PROPN
ejpam-5859	207	9	meng	meng	PROPN
ejpam-5859	207	10	,	,	PUNCT
ejpam-5859	207	11	and	and	CCONJ
ejpam-5859	207	12	x.	x.	PROPN
ejpam-5859	207	13	l.	l.	PROPN
ejpam-5859	207	14	xin	xin	PROPN
ejpam-5859	207	15	.	.	PUNCT
ejpam-5859	208	1	on	on	ADP
ejpam-5859	208	2	ordered	order	VERB
ejpam-5859	208	3	filters	filter	NOUN
ejpam-5859	208	4	of	of	ADP
ejpam-5859	208	5	implicative	implicative	ADJ
ejpam-5859	208	6	semigroups	semigroup	NOUN
ejpam-5859	208	7	.	.	PUNCT
ejpam-5859	209	1	semigroup	semigroup	PROPN
ejpam-5859	209	2	forum	forum	PROPN
ejpam-5859	209	3	,	,	PUNCT
ejpam-5859	209	4	54(1):75–82	54(1):75–82	NUM
ejpam-5859	209	5	,	,	PUNCT
ejpam-5859	209	6	1997	1997	NUM
ejpam-5859	209	7	.	.	PUNCT
ejpam-5859	210	1	[	[	X
ejpam-5859	210	2	7	7	X
ejpam-5859	210	3	]	]	PUNCT
ejpam-5859	210	4	k.	k.	PROPN
ejpam-5859	210	5	nakwan	nakwan	PROPN
ejpam-5859	210	6	,	,	PUNCT
ejpam-5859	210	7	p.	p.	PROPN
ejpam-5859	210	8	luangchaisri	luangchaisri	VERB
ejpam-5859	210	9	,	,	PUNCT
ejpam-5859	210	10	and	and	CCONJ
ejpam-5859	210	11	t.	t.	PROPN
ejpam-5859	210	12	changphas	changphas	PROPN
ejpam-5859	210	13	.	.	PUNCT
ejpam-5859	211	1	implicative	implicative	PROPN
ejpam-5859	211	2	negatively	negatively	ADV
ejpam-5859	211	3	partially	partially	ADV
ejpam-5859	211	4	ordered	order	VERB
ejpam-5859	211	5	ternary	ternary	ADJ
ejpam-5859	211	6	semigroups	semigroup	NOUN
ejpam-5859	211	7	.	.	PUNCT
ejpam-5859	212	1	eur	eur	PROPN
ejpam-5859	212	2	.	.	PUNCT
ejpam-5859	213	1	j.	j.	PROPN
ejpam-5859	213	2	pure	pure	PROPN
ejpam-5859	213	3	appl	appl	PROPN
ejpam-5859	213	4	.	.	PUNCT
ejpam-5859	213	5	math	math	PROPN
ejpam-5859	213	6	.	.	PUNCT
ejpam-5859	213	7	,	,	PUNCT
ejpam-5859	213	8	17(4):4180–4194	17(4):4180–4194	NUM
ejpam-5859	213	9	,	,	PUNCT
ejpam-5859	213	10	2024	2024	NUM
ejpam-5859	213	11	.	.	PUNCT
ejpam-5859	214	1	[	[	X
ejpam-5859	214	2	8	8	NUM
ejpam-5859	214	3	]	]	X
ejpam-5859	214	4	w.	w.	PROPN
ejpam-5859	214	5	c.	c.	PROPN
ejpam-5859	214	6	nemitz	nemitz	PROPN
ejpam-5859	214	7	.	.	PUNCT
ejpam-5859	215	1	implicative	implicative	ADJ
ejpam-5859	215	2	semi	semi	NOUN
ejpam-5859	215	3	-	-	NOUN
ejpam-5859	215	4	lattices	lattice	NOUN
ejpam-5859	215	5	.	.	PUNCT
ejpam-5859	216	1	trans	trans	PROPN
ejpam-5859	216	2	.	.	PUNCT
ejpam-5859	217	1	amer	amer	PROPN
ejpam-5859	217	2	.	.	PUNCT
ejpam-5859	217	3	math	math	PROPN
ejpam-5859	217	4	.	.	PUNCT
ejpam-5859	218	1	soc	soc	PROPN
ejpam-5859	218	2	.	.	PUNCT
ejpam-5859	218	3	,	,	PUNCT
ejpam-5859	218	4	117:128–142	117:128–142	NUM
ejpam-5859	218	5	,	,	PUNCT
ejpam-5859	218	6	1965	1965	NUM
ejpam-5859	218	7	.	.	PUNCT
ejpam-5859	219	1	[	[	X
ejpam-5859	219	2	9	9	NUM
ejpam-5859	219	3	]	]	X
ejpam-5859	219	4	y.	y.	NOUN
ejpam-5859	219	5	sarala	sarala	PROPN
ejpam-5859	219	6	,	,	PUNCT
ejpam-5859	219	7	a.	a.	PROPN
ejpam-5859	219	8	anjaneyulu	anjaneyulu	VERB
ejpam-5859	219	9	,	,	PUNCT
ejpam-5859	219	10	and	and	CCONJ
ejpam-5859	219	11	d.	d.	PROPN
ejpam-5859	219	12	madhusudhana	madhusudhana	PROPN
ejpam-5859	219	13	rao	rao	PROPN
ejpam-5859	219	14	.	.	PUNCT
ejpam-5859	220	1	ternary	ternary	ADJ
ejpam-5859	220	2	semigroups	semigroup	NOUN
ejpam-5859	220	3	.	.	PUNCT
ejpam-5859	221	1	international	international	ADJ
ejpam-5859	221	2	journal	journal	PROPN
ejpam-5859	221	3	of	of	ADP
ejpam-5859	221	4	mathematics	mathematics	PROPN
ejpam-5859	221	5	sciences	science	NOUN
ejpam-5859	221	6	,	,	PUNCT
ejpam-5859	221	7	technology	technology	NOUN
ejpam-5859	221	8	and	and	CCONJ
ejpam-5859	221	9	humanities	humanity	NOUN
ejpam-5859	221	10	,	,	PUNCT
ejpam-5859	221	11	76:848–859	76:848–859	NUM
ejpam-5859	221	12	,	,	PUNCT
ejpam-5859	221	13	2013	2013	NUM
ejpam-5859	221	14	.	.	PUNCT