drop table if exists t1;
create table t1 (a int, key (a));
insert into t1 values (NULL), (0), (1), (2), (3), (4), (5), (6), (7), (8), (9),
(10), (11), (12), (13), (14), (15), (16), (17), (18), (19);
explain select * from t1 where not(not(a));
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	20	Using where; Using index
select * from t1 where not(not(a));
a
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
explain select * from t1 where not(not(not(a > 10)));
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	11	Using where; Using index
select * from t1 where not(not(not(a > 10)));
a
0
1
2
3
4
5
6
7
8
9
10
explain select * from t1 where not(not(not(a < 5) and not(a > 10)));
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	6	Using where; Using index
select * from t1 where not(not(not(a < 5) and not(a > 10)));
a
5
6
7
8
9
10
explain select * from t1 where not(a = 10);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	19	Using where; Using index
select * from t1 where not(a = 10);
a
0
1
2
3
4
5
6
7
8
9
11
12
13
14
15
16
17
18
19
explain select * from t1 where not(a != 10);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	ref	a	a	5	const	1	Using index
select * from t1 where not(a != 1);
a
1
explain select * from t1 where not(a < 10);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	10	Using where; Using index
select * from t1 where not(a < 10);
a
10
11
12
13
14
15
16
17
18
19
explain select * from t1 where not(a >= 10);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	10	Using where; Using index
select * from t1 where not(a >= 10);
a
0
1
2
3
4
5
6
7
8
9
explain select * from t1 where not(a > 10);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	11	Using where; Using index
select * from t1 where not(a > 10);
a
0
1
2
3
4
5
6
7
8
9
10
explain select * from t1 where not(a <= 10);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	9	Using where; Using index
select * from t1 where not(a <= 10);
a
11
12
13
14
15
16
17
18
19
explain select * from t1 where not(a is null);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	20	Using where; Using index
select * from t1 where not(a is null);
a
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
explain select * from t1 where not(a is not null);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	ref	a	a	5	const	1	Using where; Using index
select * from t1 where not(a is not null);
a
NULL
explain select * from t1 where not(a < 5 or a > 15);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	11	Using where; Using index
select * from t1 where not(a < 5 or a > 15);
a
5
6
7
8
9
10
11
12
13
14
15
explain select * from t1 where not(a < 15 and a > 5);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	11	Using where; Using index
select * from t1 where not(a < 15 and a > 5);
a
0
1
2
3
4
5
15
16
17
18
19
explain select * from t1 where a = 2 or not(a < 10);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	11	Using where; Using index
select * from t1 where a = 2 or not(a < 10);
a
2
10
11
12
13
14
15
16
17
18
19
explain select * from t1 where a > 5 and not(a > 10);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	5	Using where; Using index
select * from t1 where a > 5 and not(a > 10);
a
6
7
8
9
10
explain select * from t1 where a > 5 xor a < 10;
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	index	NULL	a	5	NULL	21	Using where; Using index
select * from t1 where a > 5 xor a < 10;
a
0
1
2
3
4
5
10
11
12
13
14
15
16
17
18
19
explain select * from t1 where a = 2 or not(a < 5 or a > 15);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	12	Using where; Using index
select * from t1 where a = 2 or not(a < 5 or a > 15);
a
2
5
6
7
8
9
10
11
12
13
14
15
explain select * from t1 where a = 7 or not(a < 15 and a > 5);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	12	Using where; Using index
select * from t1 where a = 7 or not(a < 15 and a > 5);
a
0
1
2
3
4
5
7
15
16
17
18
19
explain select * from t1 where NULL or not(a < 15 and a > 5);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	11	Using where; Using index
select * from t1 where NULL or not(a < 15 and a > 5);
a
0
1
2
3
4
5
15
16
17
18
19
explain select * from t1 where not(NULL and a > 5);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	6	Using where; Using index
select * from t1 where not(NULL and a > 5);
a
0
1
2
3
4
5
explain select * from t1 where not(NULL or a);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Impossible WHERE
select * from t1 where not(NULL or a);
a
explain select * from t1 where not(NULL and a);
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	ref	a	a	5	const	1	Using index
select * from t1 where not(NULL and a);
a
0
explain select * from t1 where not((a < 5 or a < 10) and (not(a > 16) or a > 17));
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	10	Using where; Using index
select * from t1 where not((a < 5 or a < 10) and (not(a > 16) or a > 17));
a
10
11
12
13
14
15
16
17
18
19
explain select * from t1 where not((a < 5 and a < 10) and (not(a > 16) or a > 17));
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	15	Using where; Using index
select * from t1 where not((a < 5 and a < 10) and (not(a > 16) or a > 17));
a
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
explain select * from t1 where ((a between 5 and 15) and (not(a like 10)));
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	t1	range	a	a	5	NULL	11	Using where; Using index
select * from t1 where ((a between 5 and 15) and (not(a like 10)));
a
5
6
7
8
9
11
12
13
14
15
# XOR (Note: XOR is negated by negating one of the operands)
# Should return 6,7
SELECT * FROM t1 WHERE ((a > 5) XOR (a > 7));
a
6
7
# Should return 0..5,8..19
SELECT * FROM t1 WHERE ((NOT (a > 5)) XOR (a > 7));
a
0
1
2
3
4
5
8
9
10
11
12
13
14
15
16
17
18
19
SELECT * FROM t1 WHERE ((a > 5) XOR (NOT (a > 7)));
a
0
1
2
3
4
5
8
9
10
11
12
13
14
15
16
17
18
19
SELECT * FROM t1 WHERE NOT ((a > 5) XOR (a > 7));
a
0
1
2
3
4
5
8
9
10
11
12
13
14
15
16
17
18
19
# Should return 6,7
SELECT * FROM t1 WHERE NOT ((NOT (a > 5)) XOR (a > 7));
a
6
7
SELECT * FROM t1 WHERE NOT ((a > 5) XOR (NOT (a > 7)));
a
6
7
# Should return 0..5,8..19
SELECT * FROM t1 WHERE NOT ((NOT (a > 5)) XOR (NOT (a > 7)));
a
0
1
2
3
4
5
8
9
10
11
12
13
14
15
16
17
18
19
# Should have empty result
SELECT * FROM t1 WHERE (NULL XOR (a > 7));
a
SELECT * FROM t1 WHERE NOT (NULL XOR (a > 7));
a
# Should be simplified to "...WHERE (a XOR a)
EXPLAIN EXTENDED SELECT * FROM t1 WHERE NOT ((NOT a) XOR (a));
id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
1	SIMPLE	t1	index	NULL	a	5	NULL	21	100.00	Using where; Using index
Warnings:
Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where `test`.`t1`.`a` xor `test`.`t1`.`a`
# Should be simplified to "...WHERE (a XOR a)
EXPLAIN EXTENDED SELECT * FROM t1 WHERE NOT (a XOR (NOT a));
id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
1	SIMPLE	t1	index	NULL	a	5	NULL	21	100.00	Using where; Using index
Warnings:
Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where `test`.`t1`.`a` xor `test`.`t1`.`a`
# End XOR
delete from t1 where a > 3;
select a, not(not(a)) from t1;
a	not(not(a))
NULL	NULL
0	0
1	1
2	1
3	1
explain extended select a, not(not(a)), not(a <= 2 and not(a)), not(a not like "1"), not (a not in (1,2)), not(a != 2) from t1 where not(not(a)) having not(not(a));
id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
1	SIMPLE	t1	range	a	a	5	NULL	4	100.00	Using where; Using index
Warnings:
Note	1003	select `test`.`t1`.`a` AS `a`,`test`.`t1`.`a` <> 0 AS `not(not(a))`,`test`.`t1`.`a` > 2 or `test`.`t1`.`a` <> 0 AS `not(a <= 2 and not(a))`,`test`.`t1`.`a` like '1' AS `not(a not like "1")`,`test`.`t1`.`a` in (1,2) AS `not (a not in (1,2))`,`test`.`t1`.`a` = 2 AS `not(a != 2)` from `test`.`t1` where `test`.`t1`.`a` <> 0 having `test`.`t1`.`a` <> 0
drop table t1;