CREATE TABLE scheduled_availability (
  employeeID int(11) NOT NULL default '0',
  start datetime default NULL,
  end datetime default NULL
) TYPE=MyISAM;

CREATE TABLE appointments (
  employeeeID int(11) NOT NULL default '0',
  start datetime default NULL,
  end datetime default NULL
) TYPE=MyISAM;

CREATE TABLE times (
  start datetime default NULL,
  end datetime default NULL
) TYPE=MyISAM;


INSERT INTO times VALUES ('2005-08-16 16:35:40','2005-08-16 17:35:40');
INSERT INTO times VALUES ('2005-08-16 17:35:40','2005-08-16 18:35:40');
INSERT INTO times VALUES ('2005-08-16 18:35:40','2005-08-16 19:35:40');
INSERT INTO times VALUES ('2005-08-16 19:35:40','2005-08-16 20:35:40');
INSERT INTO times VALUES ('2005-08-16 20:35:40','2005-08-16 21:35:40');
INSERT INTO times VALUES ('2005-08-16 21:35:40','2005-08-16 22:35:40');
INSERT INTO times VALUES ('2005-08-16 22:35:40','2005-08-16 23:35:40');

INSERT INTO appointments VALUES (1,'2005-08-16 16:35:40','2005-08-16 17:35:40');

mysql> select times.start, times.end from times, appointments where appointments.start != times.start and appointments.end != times.end;
+---------------------+---------------------+
| start               | end                 |
+---------------------+---------------------+
| 2005-08-16 17:35:40 | 2005-08-16 18:35:40 |
| 2005-08-16 18:35:40 | 2005-08-16 19:35:40 |
| 2005-08-16 19:35:40 | 2005-08-16 20:35:40 |
| 2005-08-16 20:35:40 | 2005-08-16 21:35:40 |
| 2005-08-16 21:35:40 | 2005-08-16 22:35:40 |
| 2005-08-16 22:35:40 | 2005-08-16 23:35:40 |
+---------------------+---------------------+
6 rows in set (0.00 sec)