I have found a different solution myself in between:

SELECT s.*
  FROM set_ids s
  JOIN set_ids oth
       ON s.set_id <> oth.set_id
 WHERE NOT EXISTS
           (SELECT element_id
              FROM sets
             WHERE set_id = oth.set_id
            EXCEPT
            SELECT element_id
              FROM sets
             WHERE set_id = s.set_id)