SQLite

CREATE TABLE t1(x);
CREATE TABLE t2(y);
INSERT INTO t1 VALUES(111);
INSERT INTO t1 VALUES(222);
INSERT INTO t2 VALUES(333);
INSERT INTO t2 VALUES(444);

SELECT 'noindex', * FROM t1, t2
 WHERE (x=111 AND y!=444) OR x=222;

CREATE INDEX t1x ON t1(x);

SELECT 'w/index', * FROM t1, t2
 WHERE (x=111 AND y!=444) OR x=222;

This is problem is observed in SQLite versions 3.6.18 through 3.6.21. Versions 3.6.17 and earlier appear to work.

drh added on 2009-12-16 15:18:45:
Problem introduced on 2009-08-13 by check-in [19f799b32f9d]

drh added on 2009-12-16 16:40:47:
Another interesting test case. This one gives an assertion fault.

CREATE TABLE t1(v,w);
CREATE TABLE t2(x,y);
CREATE TABLE t3(z);
INSERT INTO t1 VALUES(111,222);
INSERT INTO t1 VALUES(333,444);
INSERT INTO t2 VALUES(222,333);
INSERT INTO t2 VALUES(444,555);
INSERT INTO t3 VALUES(888);
INSERT INTO t3 VALUES(999);

CREATE INDEX t1v ON t1(v);
CREATE INDEX t2x ON t2(x);

SELECT * FROM t1, t2, t3
 WHERE (v=111 AND x=w AND z!=999) OR (v=333 AND x=444);

drh added on 2009-12-16 22:11:58:
Fixed by check-in [2c2de252666662f5459904fc33a9f2956cbff23c]