Teacher.available_at_or_around_or_partially start_time: Time.now, end_time: Time.now.+(2.hours)

SELECT     "teachers".*
INNER JOIN "teacher_availability_periods"
ON         "teacher_availability_periods"."teacher_id" = "teachers"."id"
WHERE (((
  "teacher_availability_periods"."starts_at_sfsow" <= 446340)
  AND (
      "teacher_availability_periods"."ends_at_sfsow" >= 453540)
                OR         ( (
                                                 "teacher_availability_periods"."starts_at_sfsow" <= 442740)
                           AND        (
                                                 "teacher_availability_periods"."ends_at_sfsow" >= 446340)
                           OR         (
                                                 "teacher_availability_periods"."starts_at_sfsow" <= 453540)
                           AND        (
                                                 "teacher_availability_periods"."ends_at_sfsow" >= 457140)))
     OR         (
                           "teacher_availability_periods"."starts_at_sfsow" >= 446340)
     AND        (
                           "teacher_availability_periods"."ends_at_sfsow" <= 453540))