id	sid	eid	entity	type
ejpam-5125	1	1	european journal	ORG
ejpam-5125	2	1	17	CARDINAL
ejpam-5125	2	2	2	CARDINAL
ejpam-5125	2	3	2024	DATE
ejpam-5125	2	4	819	CARDINAL
ejpam-5125	2	5	1307-5543	DATE
ejpam-5125	3	1	new york	GPE
ejpam-5125	3	2	bandaru1	GPE
ejpam-5125	3	3	1	CARDINAL
ejpam-5125	3	4	vit-ap university	ORG
ejpam-5125	3	5	pradesh-522237	DATE
ejpam-5125	3	6	india 2	ORG
ejpam-5125	3	7	telangana-502329	DATE
ejpam-5125	3	8	india	GPE
ejpam-5125	8	1	2020	DATE
ejpam-5125	8	2	06d99	CARDINAL
ejpam-5125	9	1	1.	CARDINAL
ejpam-5125	9	2	garret birkhoff	PERSON
ejpam-5125	9	3	mid-1930	DATE
ejpam-5125	9	4	1	CARDINAL
ejpam-5125	11	1	two	CARDINAL
ejpam-5125	12	1	3	CARDINAL
ejpam-5125	12	2	4	CARDINAL
ejpam-5125	13	1	the year 1948	DATE
ejpam-5125	16	1	three	CARDINAL
ejpam-5125	19	1	one	CARDINAL
ejpam-5125	19	2	birkhoff theorem ∗corresponding	ORG
ejpam-5125	21	1	r. bandaru	PERSON
ejpam-5125	21	2	s. ajjarapu	PERSON
ejpam-5125	22	1	819	CARDINAL
ejpam-5125	22	2	2024	CARDINAL
ejpam-5125	23	1	r. bandaru	PERSON
ejpam-5125	23	2	s. ajjarapu	PERSON
ejpam-5125	24	1	j. pure	PERSON
ejpam-5125	24	2	17	CARDINAL
ejpam-5125	24	3	2	CARDINAL
ejpam-5125	24	4	2024	CARDINAL
ejpam-5125	24	5	819-834 820	QUANTITY
ejpam-5125	25	1	george boole	PERSON
ejpam-5125	25	2	first	ORDINAL
ejpam-5125	25	3	the nineteenth century	DATE
ejpam-5125	25	4	boolean algebras	ORG
ejpam-5125	25	5	2	CARDINAL
ejpam-5125	26	1	boolean algebras	ORG
ejpam-5125	33	1	algebras	ORG
ejpam-5125	34	1	j. a. kalman	PERSON
ejpam-5125	34	2	5	CARDINAL
ejpam-5125	34	3	m. swamy	PERSON
ejpam-5125	34	4	g. c. rao	PERSON
ejpam-5125	34	5	8	CARDINAL
ejpam-5125	35	1	adls	ORG
ejpam-5125	36	1	6	CARDINAL
ejpam-5125	39	1	adl	PERSON
ejpam-5125	39	2	∨	ORG
ejpam-5125	41	1	2	CARDINAL
ejpam-5125	42	1	3	CARDINAL
ejpam-5125	43	1	4	CARDINAL
ejpam-5125	44	1	2	CARDINAL
ejpam-5125	45	1	1	CARDINAL
ejpam-5125	46	1	v,∨,∧	NORP
ejpam-5125	46	2	1	CARDINAL
ejpam-5125	46	3	p2 ∧ p3	PRODUCT
ejpam-5125	47	1	p1 ∨	ORG
ejpam-5125	47	2	p1 ∨ p3	PRODUCT
ejpam-5125	48	1	p1 ∧ p2	PRODUCT
ejpam-5125	48	2	p1 ∨ p3	ORG
ejpam-5125	48	3	p2 ∨ p3	PRODUCT
ejpam-5125	49	1	p1 ∨	PRODUCT
ejpam-5125	51	1	r. bandaru	PERSON
ejpam-5125	51	2	s. ajjarapu	PERSON
ejpam-5125	52	1	j. pure	PERSON
ejpam-5125	52	2	17	CARDINAL
ejpam-5125	52	3	2	CARDINAL
ejpam-5125	52	4	2024	CARDINAL
ejpam-5125	52	5	819	CARDINAL
ejpam-5125	52	6	p1 ∧ p2	PRODUCT
ejpam-5125	53	1	1	CARDINAL
ejpam-5125	56	1	p1 ∧ p2 = p1 or	PRODUCT
ejpam-5125	57	1	1	CARDINAL
ejpam-5125	57	2	1	CARDINAL
ejpam-5125	58	1	1	CARDINAL
ejpam-5125	60	1	∨	ORG
ejpam-5125	61	1	v,∨,∧	NORP
ejpam-5125	61	2	y0	GPE
ejpam-5125	62	1	2	CARDINAL
ejpam-5125	62	2	0	CARDINAL
ejpam-5125	62	3	1	DATE
ejpam-5125	62	4	2	DATE
ejpam-5125	62	5	3	DATE
ejpam-5125	62	6	4	CARDINAL
ejpam-5125	62	7	4	CARDINAL
ejpam-5125	62	8	0	CARDINAL
ejpam-5125	62	9	0	CARDINAL
ejpam-5125	62	10	2	CARDINAL
ejpam-5125	62	11	2 2	CARDINAL
ejpam-5125	62	12	2 3	DATE
ejpam-5125	62	13	∨ ∧ 1	ORG
ejpam-5125	63	1	0 ∧	MONEY
ejpam-5125	63	2	0	CARDINAL
ejpam-5125	64	1	1	CARDINAL
ejpam-5125	64	2	2	CARDINAL
ejpam-5125	65	1	0	CARDINAL
ejpam-5125	65	2	0	CARDINAL
ejpam-5125	65	3	1	CARDINAL
ejpam-5125	65	4	0	CARDINAL
ejpam-5125	65	5	2	CARDINAL
ejpam-5125	65	6	2	CARDINAL
ejpam-5125	66	1	2	CARDINAL
ejpam-5125	66	2	0	CARDINAL
ejpam-5125	67	1	2	CARDINAL
ejpam-5125	67	2	0	CARDINAL
ejpam-5125	68	1	3	CARDINAL
ejpam-5125	69	1	0	CARDINAL
ejpam-5125	69	2	1	CARDINAL
ejpam-5125	69	3	x0	ORG
ejpam-5125	71	1	1	CARDINAL
ejpam-5125	72	1	2	CARDINAL
ejpam-5125	74	1	v,∨,∧	NORP
ejpam-5125	74	2	0	DATE
ejpam-5125	76	1	r. bandaru	PERSON
ejpam-5125	76	2	s. ajjarapu	PERSON
ejpam-5125	77	1	j. pure	PERSON
ejpam-5125	77	2	17	CARDINAL
ejpam-5125	77	3	2	CARDINAL
ejpam-5125	77	4	2024	CARDINAL
ejpam-5125	77	5	819	CARDINAL
ejpam-5125	77	6	1	CARDINAL
ejpam-5125	78	1	1	CARDINAL
ejpam-5125	79	1	2	CARDINAL
ejpam-5125	80	1	l4	ORG
ejpam-5125	80	2	p1 ∧ p2	PRODUCT
ejpam-5125	81	1	p2 ∧ p1	PRODUCT
ejpam-5125	82	1	l6	ORG
ejpam-5125	82	2	p1 ∧	ORG
ejpam-5125	84	1	1	CARDINAL
ejpam-5125	84	2	2	CARDINAL
ejpam-5125	85	1	p1 ∧ p2)∨	PRODUCT
ejpam-5125	87	1	p1∨p2)∧p1 = p1	PERSON
ejpam-5125	88	1	l6	ORG
ejpam-5125	90	1	2	CARDINAL
ejpam-5125	90	2	p1 ∨	PRODUCT
ejpam-5125	93	1	p2 ∨	PRODUCT
ejpam-5125	93	2	p2 ∧ p1	PRODUCT
ejpam-5125	94	1	3	CARDINAL
ejpam-5125	97	1	1	CARDINAL
ejpam-5125	98	1	p2 ≤ p1	PRODUCT
ejpam-5125	99	1	p1 ∨	PRODUCT
ejpam-5125	99	2	p2 ∨	PRODUCT
ejpam-5125	99	3	2	CARDINAL
ejpam-5125	102	1	p1 ∨	ORG
ejpam-5125	102	2	p1 ∧ p2	PRODUCT
ejpam-5125	102	3	p1 ∨ p3	ORG
ejpam-5125	102	4	p2 ∨ p3	PRODUCT
ejpam-5125	103	1	p3 ∧ p3 = p3 implies p1 ≤ p3	PRODUCT
ejpam-5125	104	1	4	CARDINAL
ejpam-5125	104	2	p1 ∧ p2 = p1	PRODUCT
ejpam-5125	104	3	p1 ∨	ORG
ejpam-5125	106	1	p1 ∧ p2 = p1.	PRODUCT
ejpam-5125	107	1	p1 ∨	ORG
ejpam-5125	107	2	p1 ∧ p2)∨	PRODUCT
ejpam-5125	108	1	p1 ∨	PRODUCT
ejpam-5125	108	2	p1 ∧ p2 = p1 ∧	PRODUCT
ejpam-5125	109	1	5	CARDINAL
ejpam-5125	109	2	p1 ∨	PRODUCT
ejpam-5125	109	3	p1 ∧ p2 = p2	PRODUCT
ejpam-5125	113	1	p1 ∨	PRODUCT
ejpam-5125	113	2	p1 ∧ p2	PRODUCT
ejpam-5125	114	1	6	CARDINAL
ejpam-5125	115	1	1	CARDINAL
ejpam-5125	115	2	∨	CARDINAL
ejpam-5125	116	1	2	CARDINAL
ejpam-5125	116	2	p1 ∨	ORG
ejpam-5125	117	1	3	CARDINAL
ejpam-5125	118	1	4	CARDINAL
ejpam-5125	118	2	p1 ∧ p2	PRODUCT
ejpam-5125	119	1	5	CARDINAL
ejpam-5125	119	2	p1 ∧ p2	PRODUCT
ejpam-5125	120	1	6	CARDINAL
ejpam-5125	120	2	p1 ∧ p2	PRODUCT
ejpam-5125	122	1	1	CARDINAL
ejpam-5125	123	1	1	CARDINAL
ejpam-5125	123	2	p1 ∨	PRODUCT
ejpam-5125	124	1	5	CARDINAL
ejpam-5125	124	2	∨	CARDINAL
ejpam-5125	125	1	2	CARDINAL
ejpam-5125	126	1	1	CARDINAL
ejpam-5125	127	1	5	CARDINAL
ejpam-5125	128	1	r. bandaru	PERSON
ejpam-5125	128	2	s. ajjarapu	PERSON
ejpam-5125	129	1	j. pure	PERSON
ejpam-5125	129	2	17	CARDINAL
ejpam-5125	129	3	2	CARDINAL
ejpam-5125	129	4	2024	CARDINAL
ejpam-5125	129	5	819	CARDINAL
ejpam-5125	129	6	7	CARDINAL
ejpam-5125	131	1	i4	ORG
ejpam-5125	131	2	1	CARDINAL
ejpam-5125	132	1	1 ∨	QUANTITY
ejpam-5125	132	2	1	CARDINAL
ejpam-5125	135	1	p1 ∧ 1 = p1 ∧ (	PRODUCT
ejpam-5125	135	2	1 ∧	QUANTITY
ejpam-5125	135	3	p1 ∨ 1	LAW
ejpam-5125	136	1	1 ∨	QUANTITY
ejpam-5125	136	2	1 ∨	CARDINAL
ejpam-5125	136	3	1	CARDINAL
ejpam-5125	136	4	1	CARDINAL
ejpam-5125	137	1	1	CARDINAL
ejpam-5125	137	2	p1 ∧ p3	PRODUCT
ejpam-5125	137	3	p2 ∧ p3	PRODUCT
ejpam-5125	141	1	p1 ∨	ORG
ejpam-5125	141	2	p1 ∧ p3	PRODUCT
ejpam-5125	141	3	p2 ∧ p3	PRODUCT
ejpam-5125	142	1	p1 ∧ p3	PRODUCT
ejpam-5125	142	2	∧ p3.	PRODUCT
ejpam-5125	143	1	l6	ORG
ejpam-5125	144	1	p1 ∨	PRODUCT
ejpam-5125	144	2	p1 ∧ p3	PRODUCT
ejpam-5125	144	3	p2 ∧ p3	PRODUCT
ejpam-5125	146	1	p1 ∨	ORG
ejpam-5125	147	1	p1 ∧ p3	PRODUCT
ejpam-5125	147	2	p2 ∧ p3	PRODUCT
ejpam-5125	148	1	p1 ∨	ORG
ejpam-5125	149	1	p1 ∧ p3	PRODUCT
ejpam-5125	150	1	p1 ∨	ORG
ejpam-5125	151	1	p3 ∨	PRODUCT
ejpam-5125	152	1	p1 ∨	PRODUCT
ejpam-5125	152	2	p1 ∨	ORG
ejpam-5125	153	1	p1 ∨	PRODUCT
ejpam-5125	155	1	p1 ∨	PRODUCT
ejpam-5125	155	2	p1 ∧ p3	PRODUCT
ejpam-5125	156	1	p1 ∧ p3	PRODUCT
ejpam-5125	156	2	p3 ∨	ORG
ejpam-5125	156	3	p1 ∧ p3	PRODUCT
ejpam-5125	158	1	p1 ∨	PRODUCT
ejpam-5125	158	2	p3 ∨	PRODUCT
ejpam-5125	159	1	p3 ∨	ORG
ejpam-5125	159	2	p1 ∨	PRODUCT
ejpam-5125	159	3	p3 ∨	PRODUCT
ejpam-5125	161	1	p1 ∨	PRODUCT
ejpam-5125	161	2	p3 ∨	ORG
ejpam-5125	161	3	p1 ∨	ORG
ejpam-5125	162	1	p3 ∨	PRODUCT
ejpam-5125	164	1	p1 ∨	PRODUCT
ejpam-5125	164	2	p3 ∨	ORG
ejpam-5125	164	3	p1 ∨	PRODUCT
ejpam-5125	166	1	p1 ∨	PRODUCT
ejpam-5125	166	2	p3 ∨	ORG
ejpam-5125	167	1	p1 ∧ p3	PRODUCT
ejpam-5125	168	1	p1 ∧ p3	PRODUCT
ejpam-5125	168	2	p2 ∧ p3	PRODUCT
ejpam-5125	169	1	2	CARDINAL
ejpam-5125	169	2	1	CARDINAL
ejpam-5125	169	3	p1 ∧ p2	PRODUCT
ejpam-5125	170	1	2	CARDINAL
ejpam-5125	171	1	3	CARDINAL
ejpam-5125	171	2	p2 ∧ p1	PRODUCT
ejpam-5125	172	1	4	CARDINAL
ejpam-5125	173	1	5	CARDINAL
ejpam-5125	174	1	6	CARDINAL
ejpam-5125	175	1	7	CARDINAL
ejpam-5125	176	1	∈	ORG
ejpam-5125	177	1	9	CARDINAL
ejpam-5125	177	2	p1 ∧ p2	PRODUCT
ejpam-5125	178	1	r. bandaru	PERSON
ejpam-5125	178	2	s. ajjarapu	PERSON
ejpam-5125	179	1	j. pure	PERSON
ejpam-5125	179	2	17	CARDINAL
ejpam-5125	179	3	2	CARDINAL
ejpam-5125	179	4	2024	CARDINAL
ejpam-5125	179	5	819	CARDINAL
ejpam-5125	181	1	1	CARDINAL
ejpam-5125	181	2	2	CARDINAL
ejpam-5125	181	3	1	CARDINAL
ejpam-5125	182	1	p1 ∧	ORG
ejpam-5125	182	2	p1 ∨ p1	ORG
ejpam-5125	182	3	p1 ∧ p2	PRODUCT
ejpam-5125	183	1	2	CARDINAL
ejpam-5125	183	2	1	CARDINAL
ejpam-5125	183	3	2	CARDINAL
ejpam-5125	184	1	p1 ∧ p2	PRODUCT
ejpam-5125	184	2	p1 ∨ p1	ORG
ejpam-5125	185	1	3	CARDINAL
ejpam-5125	185	2	4	CARDINAL
ejpam-5125	186	1	3	CARDINAL
ejpam-5125	187	1	p2 ∧	PRODUCT
ejpam-5125	187	2	p2 ∨	PERSON
ejpam-5125	187	3	p2 ∧ p1	PRODUCT
ejpam-5125	187	4	4	CARDINAL
ejpam-5125	187	5	3	CARDINAL
ejpam-5125	187	6	4	CARDINAL
ejpam-5125	188	1	p2 ∧ p1	PRODUCT
ejpam-5125	188	2	p2 ∨	PERSON
ejpam-5125	190	1	1	CARDINAL
ejpam-5125	190	2	5	CARDINAL
ejpam-5125	190	3	1	CARDINAL
ejpam-5125	191	1	p2 ∧ p1 =	PRODUCT
ejpam-5125	192	1	p1 ∧ p2	PRODUCT
ejpam-5125	192	2	p1 ∧ p2	PRODUCT
ejpam-5125	192	3	p1 ∧ p2	PRODUCT
ejpam-5125	192	4	p2 ∧ p1	PRODUCT
ejpam-5125	193	1	p2 ∧ p1	PRODUCT
ejpam-5125	194	1	p2 ∧ p1	PRODUCT
ejpam-5125	196	1	5	CARDINAL
ejpam-5125	196	2	1	CARDINAL
ejpam-5125	196	3	5	CARDINAL
ejpam-5125	197	1	p1 ∧ p2	PRODUCT
ejpam-5125	197	2	p2 ∧ p1	PRODUCT
ejpam-5125	198	1	5	CARDINAL
ejpam-5125	198	2	3	CARDINAL
ejpam-5125	198	3	5	CARDINAL
ejpam-5125	199	1	p2 ∧ p1	PRODUCT
ejpam-5125	199	2	p1 ∧ p2	PRODUCT
ejpam-5125	200	1	3	CARDINAL
ejpam-5125	200	2	5	CARDINAL
ejpam-5125	200	3	3	CARDINAL
ejpam-5125	201	1	p1 ∧ p2 =	PRODUCT
ejpam-5125	202	1	p2 ∧ p1	PRODUCT
ejpam-5125	202	2	p2 ∧ p1	PRODUCT
ejpam-5125	203	1	p2 ∧ p1	PRODUCT
ejpam-5125	203	2	p2 ∧ p1	PRODUCT
ejpam-5125	204	1	p1 ∧	ORG
ejpam-5125	204	2	p2 ∧ p1	PRODUCT
ejpam-5125	205	1	p2 ∧ p1	PRODUCT
ejpam-5125	205	2	p1 ∧ p2	PRODUCT
ejpam-5125	206	1	p1 ∧ p2	PRODUCT
ejpam-5125	208	1	p1 ∧ p2	PRODUCT
ejpam-5125	210	1	6	CARDINAL
ejpam-5125	210	2	3	CARDINAL
ejpam-5125	210	3	6	CARDINAL
ejpam-5125	211	1	p1 ∧	ORG
ejpam-5125	212	1	3	CARDINAL
ejpam-5125	212	2	6	CARDINAL
ejpam-5125	212	3	3	CARDINAL
ejpam-5125	213	1	p2 ∨	PRODUCT
ejpam-5125	213	2	p1 ∨	PRODUCT
ejpam-5125	214	1	p1 ∨	ORG
ejpam-5125	214	2	p1 ∨	ORG
ejpam-5125	214	3	p2 ∨ p1	PRODUCT
ejpam-5125	215	1	p2 ∧	PRODUCT
ejpam-5125	217	1	5	CARDINAL
ejpam-5125	217	2	7	CARDINAL
ejpam-5125	217	3	9	CARDINAL
ejpam-5125	218	1	5	CARDINAL
ejpam-5125	218	2	7	CARDINAL
ejpam-5125	218	3	5	CARDINAL
ejpam-5125	219	1	p1 ∧ p2 = p2 ∧ p1 ≤ p1	PRODUCT
ejpam-5125	220	1	7	CARDINAL
ejpam-5125	221	1	7	CARDINAL
ejpam-5125	221	2	7	CARDINAL
ejpam-5125	222	1	p1 ∧ p2 ≤ p1	PRODUCT
ejpam-5125	224	1	8) ⇒	MONEY
ejpam-5125	224	2	9	CARDINAL
ejpam-5125	225	1	∈	ORG
ejpam-5125	226	1	p1 ∧ p2	PRODUCT
ejpam-5125	226	2	p1 ∨ p1	ORG
ejpam-5125	226	3	p1 ∧ p2	PRODUCT
ejpam-5125	227	1	p1 ∧ p2	PRODUCT
ejpam-5125	227	2	p1 ∧ p2	PRODUCT
ejpam-5125	228	1	r. bandaru	PERSON
ejpam-5125	228	2	s. ajjarapu	PERSON
ejpam-5125	229	1	j. pure	PERSON
ejpam-5125	229	2	17	CARDINAL
ejpam-5125	229	3	2	CARDINAL
ejpam-5125	229	4	2024	CARDINAL
ejpam-5125	229	5	819	CARDINAL
ejpam-5125	230	1	9	CARDINAL
ejpam-5125	230	2	9	CARDINAL
ejpam-5125	231	1	p1 ∧ p2	PRODUCT
ejpam-5125	231	2	p1 ∧ p2 ≤ p1	PRODUCT
ejpam-5125	231	3	5	CARDINAL
ejpam-5125	231	4	1	CARDINAL
ejpam-5125	231	5	5	CARDINAL
ejpam-5125	232	1	5	CARDINAL
ejpam-5125	232	2	7	CARDINAL
ejpam-5125	232	3	9	CARDINAL
ejpam-5125	233	1	3	CARDINAL
ejpam-5125	233	2	p1 ∨	ORG
ejpam-5125	233	3	p2 ∧ p3	PRODUCT
ejpam-5125	234	1	p1 ∨	ORG
ejpam-5125	234	2	p3 ∨ p1	ORG
ejpam-5125	235	1	p1 ∧ p2 = p2 ∧ p1.	PRODUCT
ejpam-5125	237	1	p1 ∨	ORG
ejpam-5125	237	2	p2 ∧ p3	PRODUCT
ejpam-5125	239	1	p1 ∨	ORG
ejpam-5125	239	2	p3 ∨ p1	ORG
ejpam-5125	240	1	p2 ∧ p1 =	PRODUCT
ejpam-5125	240	2	p1 ∧ p2	PRODUCT
ejpam-5125	240	3	p1 ∧ p2	PRODUCT
ejpam-5125	241	1	p1 ∧ p2	PRODUCT
ejpam-5125	241	2	p2 ∧ p1	PRODUCT
ejpam-5125	241	3	p2 ∧ p1	PRODUCT
ejpam-5125	241	4	p2 ∧ p1	PRODUCT
ejpam-5125	243	1	2	CARDINAL
ejpam-5125	244	1	8	CARDINAL
ejpam-5125	245	1	p1 ∨	ORG
ejpam-5125	245	2	p2 ∧ p3	PRODUCT
ejpam-5125	245	3	p3 ∧ p2	PRODUCT
ejpam-5125	247	1	p1 ≤ p1 ∨	PRODUCT
ejpam-5125	247	2	p1 ≤ p1 ∨ p3	PRODUCT
ejpam-5125	247	3	p1 ∨	PRODUCT
ejpam-5125	247	4	p1 ∨ p3	PRODUCT
ejpam-5125	248	1	p1 ∨ p3	ORG
ejpam-5125	249	1	p1 ∨	ORG
ejpam-5125	249	2	p2 ∧ p3	PRODUCT
ejpam-5125	249	3	p1 ∨	ORG
ejpam-5125	249	4	p1 ∨ p3	PRODUCT
ejpam-5125	249	5	p1 ∨ p3	ORG
ejpam-5125	249	6	p3 ∧ p2	PRODUCT
ejpam-5125	250	1	4	CARDINAL
ejpam-5125	254	1	p1 ∨	ORG
ejpam-5125	254	2	p2 ∨ p3	PRODUCT
ejpam-5125	255	1	p1 ∨	PERSON
ejpam-5125	255	2	p3 ∧ p1	ORG
ejpam-5125	256	1	p2 ∨ p3	PRODUCT
ejpam-5125	257	1	p3 ∧ p1	ORG
ejpam-5125	257	2	p2 ∨ p3	PRODUCT
ejpam-5125	258	1	∨	CARDINAL
ejpam-5125	258	2	p2 ∨ p3	PRODUCT
ejpam-5125	260	1	p2 ∨ p3	PRODUCT
ejpam-5125	262	1	p2 ∨ p3	PRODUCT
ejpam-5125	263	1	∨	CARDINAL
ejpam-5125	263	2	p2 ∨ p3	PRODUCT
ejpam-5125	264	1	p2 ∨ p3	PRODUCT
ejpam-5125	264	2	p3 ∧	ORG
ejpam-5125	264	3	p2 ∨ p3	PRODUCT
ejpam-5125	265	1	p1 ∨	ORG
ejpam-5125	265	2	p2 ∨ p3	PRODUCT
ejpam-5125	265	3	p1 ∨	ORG
ejpam-5125	266	1	p1 ∧ p3	PRODUCT
ejpam-5125	266	2	p2 ∨ p3	PRODUCT
ejpam-5125	266	3	∧ p3	PRODUCT
ejpam-5125	267	1	p1 ∨	ORG
ejpam-5125	268	1	p1 ∧ p3	PRODUCT
ejpam-5125	269	1	p1 ∨	ORG
ejpam-5125	269	2	∨	CARDINAL
ejpam-5125	269	3	∨	ORG
ejpam-5125	270	1	p1 ∨	PRODUCT
ejpam-5125	270	2	∨	CARDINAL
ejpam-5125	270	3	p1 ∨	ORG
ejpam-5125	270	4	p2 ∨	PRODUCT
ejpam-5125	272	1	r. bandaru	PERSON
ejpam-5125	272	2	s. ajjarapu	PERSON
ejpam-5125	273	1	j. pure	PERSON
ejpam-5125	273	2	17	CARDINAL
ejpam-5125	273	3	2	CARDINAL
ejpam-5125	273	4	2024	CARDINAL
ejpam-5125	273	5	819	CARDINAL
ejpam-5125	273	6	4	CARDINAL
ejpam-5125	274	1	0	CARDINAL
ejpam-5125	274	2	1	DATE
ejpam-5125	274	3	2	DATE
ejpam-5125	274	4	3	DATE
ejpam-5125	274	5	4	DATE
ejpam-5125	274	6	5	CARDINAL
ejpam-5125	274	7	4	CARDINAL
ejpam-5125	274	8	0	CARDINAL
ejpam-5125	274	9	∨ ∧ 1	ORG
ejpam-5125	275	1	0 ∧	MONEY
ejpam-5125	275	2	2	CARDINAL
ejpam-5125	275	3	0	CARDINAL
ejpam-5125	276	1	4	CARDINAL
ejpam-5125	277	1	3	CARDINAL
ejpam-5125	277	2	0	CARDINAL
ejpam-5125	277	3	2	CARDINAL
ejpam-5125	277	4	4	CARDINAL
ejpam-5125	277	5	2	CARDINAL
ejpam-5125	278	1	v,∨,∧	NORP
ejpam-5125	278	2	1	CARDINAL
ejpam-5125	278	3	p1 ∧	ORG
ejpam-5125	278	4	p2 ∧ p3	PRODUCT
ejpam-5125	279	1	p1 ∧ p2	PRODUCT
ejpam-5125	280	1	5	CARDINAL
ejpam-5125	281	1	0	CARDINAL
ejpam-5125	281	2	1	DATE
ejpam-5125	281	3	2	DATE
ejpam-5125	281	4	3	DATE
ejpam-5125	281	5	4	CARDINAL
ejpam-5125	281	6	4	CARDINAL
ejpam-5125	281	7	0	CARDINAL
ejpam-5125	281	8	0	CARDINAL
ejpam-5125	281	9	2	CARDINAL
ejpam-5125	281	10	2 2	CARDINAL
ejpam-5125	281	11	2 3	DATE
ejpam-5125	281	12	∨ ∧ 1	ORG
ejpam-5125	282	1	9	CARDINAL
ejpam-5125	283	1	p1 ∨	ORG
ejpam-5125	283	2	p2 ∨	PRODUCT
ejpam-5125	283	3	p3 ∨	ORG
ejpam-5125	285	1	p1 ≤ p1 ∨	PRODUCT
ejpam-5125	285	2	p1 ≤ p1 ∨ p3	PRODUCT
ejpam-5125	285	3	p1 ∨ p3	PRODUCT
ejpam-5125	286	1	p1 ∨ p3	ORG
ejpam-5125	287	1	p1 ∨ p2 ∨ p1	ORG
ejpam-5125	287	2	p1 ∨ p3 ∨ p1	ORG
ejpam-5125	288	1	p1 ∨	ORG
ejpam-5125	288	2	p3 ∨	ORG
ejpam-5125	289	1	10	CARDINAL
ejpam-5125	290	1	p1 ∨	PRODUCT
ejpam-5125	290	2	1	CARDINAL
ejpam-5125	290	3	p2 ∨	PRODUCT
ejpam-5125	290	4	1	CARDINAL
ejpam-5125	290	5	5	CARDINAL
ejpam-5125	291	1	v,∨,∧	NORP
ejpam-5125	291	2	1	CARDINAL
ejpam-5125	292	1	1	CARDINAL
ejpam-5125	292	2	v,∨,∧	NORP
ejpam-5125	292	3	1	CARDINAL
ejpam-5125	293	1	2	CARDINAL
ejpam-5125	294	1	3	CARDINAL
ejpam-5125	294	2	p1 ∧ p2	PRODUCT
ejpam-5125	295	1	4	CARDINAL
ejpam-5125	296	1	5	CARDINAL
ejpam-5125	297	1	6	CARDINAL
ejpam-5125	298	1	p2 ∨	FAC
ejpam-5125	299	1	r. bandaru	PERSON
ejpam-5125	299	2	s. ajjarapu	PERSON
ejpam-5125	300	1	j. pure	PERSON
ejpam-5125	300	2	17	CARDINAL
ejpam-5125	300	3	2	CARDINAL
ejpam-5125	300	4	2024	CARDINAL
ejpam-5125	300	5	819	CARDINAL
ejpam-5125	301	1	1	CARDINAL
ejpam-5125	301	2	2	CARDINAL
ejpam-5125	301	3	v,∨,∧	NORP
ejpam-5125	301	4	1	CARDINAL
ejpam-5125	302	1	2	CARDINAL
ejpam-5125	303	1	2	CARDINAL
ejpam-5125	303	2	3	CARDINAL
ejpam-5125	303	3	4	CARDINAL
ejpam-5125	303	4	5	CARDINAL
ejpam-5125	303	5	2	CARDINAL
ejpam-5125	303	6	5	CARDINAL
ejpam-5125	303	7	6	DATE
ejpam-5125	303	8	p2 ∨	FAC
ejpam-5125	304	1	p2 ∨	PRODUCT
ejpam-5125	305	1	6	CARDINAL
ejpam-5125	307	1	p2 ∨ p1	PRODUCT
ejpam-5125	307	2	p1 ∨	ORG
ejpam-5125	308	1	p1 ∨	PRODUCT
ejpam-5125	310	1	6	CARDINAL
ejpam-5125	311	1	v,∨,∧	NORP
ejpam-5125	311	2	1	CARDINAL
ejpam-5125	311	3	2	CARDINAL
ejpam-5125	311	4	2	DATE
ejpam-5125	311	5	0	DATE
ejpam-5125	312	1	p2 ∧ p3	PRODUCT
ejpam-5125	313	1	p1 ∨	ORG
ejpam-5125	313	2	p1 ∨ p3	PRODUCT
ejpam-5125	313	3	p1 ∧ p2	PRODUCT
ejpam-5125	313	4	p1 ∨ p3	ORG
ejpam-5125	314	1	p2 ∨ p3	PRODUCT
ejpam-5125	314	2	p1 ∧ p3	PRODUCT
ejpam-5125	314	3	p2 ∧ p3	PRODUCT
ejpam-5125	314	4	p1 ∨	PRODUCT
ejpam-5125	314	5	p1 ∧ p2	PRODUCT
ejpam-5125	314	6	1	CARDINAL
ejpam-5125	314	7	1	CARDINAL
ejpam-5125	316	1	3	CARDINAL
ejpam-5125	317	1	∈	ORG
ejpam-5125	317	2	0	CARDINAL
ejpam-5125	318	1	∈	ORG
ejpam-5125	318	2	a ≤ p1 | p1 ∈ v	QUANTITY
ejpam-5125	319	1	3	CARDINAL
ejpam-5125	320	1	4	CARDINAL
ejpam-5125	321	1	∈	ORG
ejpam-5125	321	2	⇒ p1 ∧	ORG
ejpam-5125	321	3	∈	ORG
ejpam-5125	327	1	∈	ORG
ejpam-5125	327	2	s. r. bandaru	PERSON
ejpam-5125	327	3	s. ajjarapu	PERSON
ejpam-5125	328	1	j. pure	PERSON
ejpam-5125	328	2	17	CARDINAL
ejpam-5125	328	3	2	CARDINAL
ejpam-5125	328	4	2024	CARDINAL
ejpam-5125	328	5	819-834 828	QUANTITY
ejpam-5125	330	1	n ∨	ORG
ejpam-5125	331	1	∈	ORG
ejpam-5125	332	1	1 ≤ i ≤	QUANTITY
ejpam-5125	333	1	⊆	CARDINAL
ejpam-5125	333	2	⊆	CARDINAL
ejpam-5125	334	1	first	ORDINAL
ejpam-5125	334	2	∈	ORG
ejpam-5125	335	1	∈	ORG
ejpam-5125	338	1	∈	ORG
ejpam-5125	339	1	⊆	CARDINAL
ejpam-5125	340	1	∈	ORG
ejpam-5125	341	1	∈ s.	PERSON
ejpam-5125	342	1	⊆	CARDINAL
ejpam-5125	343	1	∈	ORG
ejpam-5125	343	2	m. let s	PERSON
ejpam-5125	343	3	∈	ORG
ejpam-5125	343	4	t1 ∨	ORG
ejpam-5125	343	5	t2 ∨ l	ORG
ejpam-5125	344	1	t1 ∨	ORG
ejpam-5125	344	2	t2 ∨	ORG
ejpam-5125	345	1	t1 ∨	ORG
ejpam-5125	345	2	t2 ∨ l ∨ s	ORG
ejpam-5125	346	1	∨	PERSON
ejpam-5125	346	2	s∨ l ∈	ORG
ejpam-5125	347	1	∈	ORG
ejpam-5125	348	1	∨	GPE
ejpam-5125	348	2	t ∧	ORG
ejpam-5125	348	3	∨	GPE
ejpam-5125	349	1	s ∧ u ∈	ORG
ejpam-5125	350	1	s.	PERSON
ejpam-5125	350	2	⊆	CARDINAL
ejpam-5125	352	1	∈	ORG
ejpam-5125	352	2	⊆	CARDINAL
ejpam-5125	352	3	1 ≤	QUANTITY
ejpam-5125	354	1	⊆	CARDINAL
ejpam-5125	355	1	s.	PERSON
ejpam-5125	356	1	r. bandaru	PERSON
ejpam-5125	356	2	s. ajjarapu	PERSON
ejpam-5125	357	1	j. pure	PERSON
ejpam-5125	357	2	17	CARDINAL
ejpam-5125	357	3	2	CARDINAL
ejpam-5125	357	4	2024	CARDINAL
ejpam-5125	357	5	819	CARDINAL
ejpam-5125	357	6	5	CARDINAL
ejpam-5125	358	1	p2 ∧ p1 = p1	PRODUCT
ejpam-5125	359	1	11	CARDINAL
ejpam-5125	361	1	p1 ∧ p2 ∈	PRODUCT
ejpam-5125	361	2	p2 ∧ p1 ∈	PRODUCT
ejpam-5125	362	1	6	CARDINAL
ejpam-5125	363	1	p1 ∧ p2	PRODUCT
ejpam-5125	363	2	p2 ∧ p1	PRODUCT
ejpam-5125	363	3	8	CARDINAL
ejpam-5125	364	1	∧q	CARDINAL
ejpam-5125	365	1	∩q	ORDINAL
ejpam-5125	365	2	p1 ∨	ORG
ejpam-5125	366	1	7	DATE
ejpam-5125	369	1	∈	ORG
ejpam-5125	371	1	p1 ∨	ORG
ejpam-5125	372	1	si ∈ s	ORG
ejpam-5125	372	2	1 ≤	QUANTITY
ejpam-5125	372	3	s. proof	PERSON
ejpam-5125	374	1	i=1 tj	PERSON
ejpam-5125	376	1	p1 ∨	ORG
ejpam-5125	379	1	p1 ∧	ORG
ejpam-5125	380	1	n ∧ i=1 si	ORG
ejpam-5125	381	1	p1 ∧	ORG
ejpam-5125	382	1	p3 ∨	ORG
ejpam-5125	382	2	∧ n ∧ i=1 si	PRODUCT
ejpam-5125	382	3	p1 ∧	ORG
ejpam-5125	383	1	p2 ∧	PRODUCT
ejpam-5125	384	1	u ∨	ORG
ejpam-5125	384	2	∈	ORG
ejpam-5125	384	3	∈	ORG
ejpam-5125	385	1	u ∨	PERSON
ejpam-5125	385	2	p1 ∨	ORG
ejpam-5125	386	1	u ∨ p1	ORG
ejpam-5125	388	1	s.	PERSON
ejpam-5125	390	1	8	CARDINAL
ejpam-5125	394	1	r. bandaru	PERSON
ejpam-5125	394	2	s. ajjarapu	PERSON
ejpam-5125	395	1	j. pure	PERSON
ejpam-5125	395	2	17	CARDINAL
ejpam-5125	395	3	2	CARDINAL
ejpam-5125	395	4	2024	CARDINAL
ejpam-5125	395	5	819	CARDINAL
ejpam-5125	395	6	12	CARDINAL
ejpam-5125	398	1	p2 ∨	PRODUCT
ejpam-5125	399	1	2	CARDINAL
ejpam-5125	399	2	p1 ∨	ORG
ejpam-5125	401	1	3	CARDINAL
ejpam-5125	401	2	p1 ∧ p2	PRODUCT
ejpam-5125	402	1	p2 ∧ p1	PRODUCT
ejpam-5125	404	1	10	CARDINAL
ejpam-5125	407	1	1	CARDINAL
ejpam-5125	407	2	⊆	CARDINAL
ejpam-5125	408	1	2	CARDINAL
ejpam-5125	409	1	3	CARDINAL
ejpam-5125	410	1	4	CARDINAL
ejpam-5125	411	1	⊆	CARDINAL
ejpam-5125	412	1	11	CARDINAL
ejpam-5125	413	1	p1 ∧ p2 |	PRODUCT
ejpam-5125	414	1	12	CARDINAL
ejpam-5125	415	1	u(v	ORG
ejpam-5125	420	1	∈	ORG
ejpam-5125	421	1	first	ORDINAL
ejpam-5125	421	2	u(v	GPE
ejpam-5125	426	1	u(v	GPE
ejpam-5125	429	1	∈	ORG
ejpam-5125	437	1	one-one	CARDINAL
ejpam-5125	439	1	r. bandaru	PERSON
ejpam-5125	439	2	s. ajjarapu	PERSON
ejpam-5125	440	1	j. pure	PERSON
ejpam-5125	440	2	17	CARDINAL
ejpam-5125	440	3	2	CARDINAL
ejpam-5125	440	4	2024	CARDINAL
ejpam-5125	440	5	819-834 831	QUANTITY
ejpam-5125	442	1	∈	ORG
ejpam-5125	446	1	4	CARDINAL
ejpam-5125	446	2	nonzero congruences	ORG
ejpam-5125	446	3	non-zero	PRODUCT
ejpam-5125	449	1	9	DATE
ejpam-5125	450	1	∈	ORG
ejpam-5125	450	2	u ≤ a⇒ u = a. lemma 13	FAC
ejpam-5125	452	1	∈	ORG
ejpam-5125	452	2	1	CARDINAL
ejpam-5125	453	1	2	CARDINAL
ejpam-5125	454	1	3	CARDINAL
ejpam-5125	456	1	10	CARDINAL
ejpam-5125	457	1	14	CARDINAL
ejpam-5125	458	1	∈	ORG
ejpam-5125	465	1	p1 ∨	ORG
ejpam-5125	465	2	p1 ∨ p3	PRODUCT
ejpam-5125	465	3	p1 ∧ p3	PRODUCT
ejpam-5125	467	1	p2 ∧ s	PRODUCT
ejpam-5125	467	2	∨ a. r. bandaru	PERSON
ejpam-5125	467	3	s. ajjarapu	PERSON
ejpam-5125	468	1	j. pure	PERSON
ejpam-5125	468	2	17	CARDINAL
ejpam-5125	468	3	2	CARDINAL
ejpam-5125	468	4	2024	CARDINAL
ejpam-5125	468	5	819-834 832	QUANTITY
ejpam-5125	468	6	p1 ∨ p3	PRODUCT
ejpam-5125	468	7	p2 ∨	ORG
ejpam-5125	468	8	s),∈	ORG
ejpam-5125	469	1	p1 ∧ p3	PRODUCT
ejpam-5125	469	2	p2 ∧ s	PRODUCT
ejpam-5125	472	1	p1 ≤ a.	ORG
ejpam-5125	476	1	p1 ∨	ORG
ejpam-5125	477	1	φ	PERSON
ejpam-5125	478	1	15	CARDINAL
ejpam-5125	479	1	∈	ORG
ejpam-5125	479	2	p1∧a	ORG
ejpam-5125	482	1	p1 ∧	PRODUCT
ejpam-5125	486	1	p1 ∧	ORG
ejpam-5125	486	2	p3 ∧	PRODUCT
ejpam-5125	486	3	t ∧ a. hence	ORG
ejpam-5125	486	4	p1 ∧ p3	PRODUCT
ejpam-5125	487	1	∧ p3 ∧	PRODUCT
ejpam-5125	487	2	p1 ∧	ORG
ejpam-5125	487	3	p2 ∧	PRODUCT
ejpam-5125	487	4	p2 ∧ t	PRODUCT
ejpam-5125	487	5	p1 ∨ p3	PRODUCT
ejpam-5125	487	6	p1 ∧	ORG
ejpam-5125	487	7	p3 ∧	ORG
ejpam-5125	487	8	p2 ∧	PRODUCT
ejpam-5125	487	9	p2 ∨	PERSON
ejpam-5125	487	10	p1 ∧ p3	PRODUCT
ejpam-5125	487	11	p2 ∧ t	PRODUCT
ejpam-5125	487	12	p1 ∨ p3	PRODUCT
ejpam-5125	487	13	p2 ∨	PRODUCT
ejpam-5125	492	1	p1∧a	ORG
ejpam-5125	493	1	13	CARDINAL
ejpam-5125	495	1	two	CARDINAL
ejpam-5125	498	1	non-zero	PRODUCT
ejpam-5125	499	1	select p1	PERSON
ejpam-5125	499	2	∈	ORG
ejpam-5125	509	1	θp1∨a ̸= ∆v	PERSON
ejpam-5125	510	1	θp1∨a	PERSON
ejpam-5125	512	1	r. bandaru	PERSON
ejpam-5125	512	2	s. ajjarapu	PERSON
ejpam-5125	513	1	j. pure	PERSON
ejpam-5125	513	2	17	CARDINAL
ejpam-5125	513	3	2	CARDINAL
ejpam-5125	513	4	2024	CARDINAL
ejpam-5125	513	5	819-834 833	QUANTITY
ejpam-5125	515	1	three	CARDINAL
ejpam-5125	516	1	two	CARDINAL
ejpam-5125	516	2	φ ∩	ORG
ejpam-5125	517	1	two	CARDINAL
ejpam-5125	518	1	11	CARDINAL
ejpam-5125	519	1	two	CARDINAL
ejpam-5125	520	1	13	CARDINAL
ejpam-5125	521	1	two	CARDINAL
ejpam-5125	522	1	14	DATE
ejpam-5125	524	1	1	CARDINAL
ejpam-5125	525	1	2	CARDINAL
ejpam-5125	525	2	∈	ORG
ejpam-5125	526	1	3	CARDINAL
ejpam-5125	526	2	two	CARDINAL
ejpam-5125	529	1	1	CARDINAL
ejpam-5125	529	2	2	CARDINAL
ejpam-5125	529	3	15	CARDINAL
ejpam-5125	530	1	2	CARDINAL
ejpam-5125	531	1	η	PERSON
ejpam-5125	531	2	p1 ∧ p3	PRODUCT
ejpam-5125	531	3	p2 ∧ p3	PRODUCT
ejpam-5125	531	4	2	CARDINAL
ejpam-5125	532	1	13	CARDINAL
ejpam-5125	532	2	3	CARDINAL
ejpam-5125	533	1	3	CARDINAL
ejpam-5125	533	2	1	CARDINAL
ejpam-5125	534	1	5	CARDINAL
ejpam-5125	540	1	834	CARDINAL
ejpam-5125	542	1	1	CARDINAL
ejpam-5125	544	1	american mathematical society	ORG
ejpam-5125	544	2	new york	GPE
ejpam-5125	544	3	1940	DATE
ejpam-5125	545	1	2	CARDINAL
ejpam-5125	547	1	dover	GPE
ejpam-5125	547	2	new york	GPE
ejpam-5125	547	3	1958	DATE
ejpam-5125	548	1	3	CARDINAL
ejpam-5125	549	1	birkhoff systems	ORG
ejpam-5125	550	1	algebraic hyperstructures	PERSON
ejpam-5125	550	2	2(4):1–12	CARDINAL
ejpam-5125	550	3	2021	DATE
ejpam-5125	551	1	4	CARDINAL
ejpam-5125	551	2	j harding	PERSON
ejpam-5125	553	1	i. order	PERSON
ejpam-5125	553	2	34:45–68	CARDINAL
ejpam-5125	553	3	2017	DATE
ejpam-5125	554	1	5	CARDINAL
ejpam-5125	556	1	fundamenta mathematicae	PERSON
ejpam-5125	556	2	71:161–163	CARDINAL
ejpam-5125	556	3	1971	DATE
ejpam-5125	557	1	6	CARDINAL
ejpam-5125	559	1	mathematiche annalen	PERSON
ejpam-5125	559	2	139:275–286, 1960	DATE
ejpam-5125	562	1	mathematiche annalen	PERSON
ejpam-5125	562	2	151:332–345	DATE
ejpam-5125	562	3	1963	DATE
ejpam-5125	563	1	8	CARDINAL
ejpam-5125	563	2	g c rao	PERSON
ejpam-5125	565	1	australian	NORP
ejpam-5125	566	1	31:77–91, 1981	DATE