MySQL 5.7

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CREATE TABLE table1 (
  `ID` VARCHAR(100),
  `Val` VARCHAR(100),
  `Val2` VARCHAR(100)
);
INSERT INTO table1
  (`ID`, `Val`, `Val2`)
VALUES
  ('606541','3175031503131004','3175032612900004'),
  ('606542','3175031503131004','3175032612900004'),
  ('677315','3175031503131004','3175032612980004'),
  ('222222','1111111111111111','8888888888888888'),
  ('231233','1111111111111111','3175032612900004'),
  ('111111','9999992222211111','1111111111111111'),
  ('57','3173012102121018','3173015101870020'),
  ('59','3173012102121018','3173021107460002'),
  ('2','900','7000'),
  ('4','900','7001');
CREATE TEMPORARY TABLE IF NOT EXISTS table2 AS (
	SELECT Val
	FROM table1 
	GROUP BY Val
	HAVING COUNT(DISTINCT Val) = 1
	AND COUNT(*) > 1
)
CREATE TEMPORARY TABLE IF NOT EXISTS table3 AS (
	SELECT Val2
	FROM table1
	GROUP BY Val2
	HAVING COUNT(*) = 1
)
SELECT tb.* 
FROM table1 tb
INNER JOIN table2 tb2 ON tb.Val = tb2.Val
INNER JOIN table3 tb3 ON tb.Val2 = tb3.Val2


ID
Val
Val2


57
3173012102121018
3173015101870020

59
3173012102121018
3173021107460002

677315
3175031503131004
3175032612980004

2
900
7000

4
900
7001

222222
1111111111111111
8888888888888888


CREATE TEMPORARY TABLE IF NOT EXISTS newTable AS (
	SELECT tb.* 
	FROM table1 tb
	INNER JOIN table2 tb2 ON tb.Val = tb2.Val
	INNER JOIN table3 tb3 ON tb.Val2 = tb3.Val2
)
CREATE TEMPORARY TABLE IF NOT EXISTS table4 AS (
	SELECT Val
	FROM newTable 
	GROUP BY Val
	HAVING COUNT(DISTINCT Val) = 1
	AND COUNT(*) > 1
)
CREATE TEMPORARY TABLE IF NOT EXISTS table5 AS (
	SELECT Val2
	FROM newTable
	GROUP BY Val2
	HAVING COUNT(*) = 1
)
SELECT tb.* 
FROM newTable tb
INNER JOIN table4 tb4 ON tb.Val = tb4.Val
INNER JOIN table5 tb5 ON tb.Val2 = tb5.Val2


ID
Val
Val2


57
3173012102121018
3173015101870020

59
3173012102121018
3173021107460002

2
900
7000

4
900
7001

ID	Val	Val2
57	3173012102121018	3173015101870020
59	3173012102121018	3173021107460002
677315	3175031503131004	3175032612980004
2	900	7000
4	900	7001
222222	1111111111111111	8888888888888888