SELECT
  t.start,
  t.end
FROM appointment_times t
  JOIN scheduled_availability s ON
	AND t.start >= s.start
	AND t.end <= s.end
  LEFT JOIN appointments a ON
	a.EmployeeID = s.EmployeeID
	AND t.start <= a.end
	AND t.end >= a.start
WHERE a.EmployeeID IS NULL
;