Firebird 3.0

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create table work_days (worker_id int, date_from date, date_to date);


EXECUTE BLOCK
AS
BEGIN
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(1, '2019-10-01', '2020-04-30');
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(1, '2020-05-01', '2020-07-19');
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(1, '2020-10-01', '9999-01-01');
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(2, '2019-10-01', '2020-04-30');
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(2, '2020-05-01', '2020-07-31');
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(2, '2020-11-01', '9999-01-01');
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(3, '2018-03-12', '2018-08-20');
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(3, '2019-10-01', '2020-04-15');
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(3, '2020-07-01', '2020-07-31');
insert into WORK_DAYS(WORKER_ID, DATE_FROM, DATE_TO) VALUES(3, '2020-11-01', '9999-01-01');
END
10 rows affected

with wd as (
      select worker_id, date_from as dte, 1 as inc
      from work_days wd
      union all
      select worker_id, DATEADD(1 day to date_to), -1 as inc
      from work_days wd
     ),
     wd_cnt as (
      select wd.dte, sum(sum(inc)) over (order by dte) as num_on_date,
             lead(wd.dte) over (order by wd.dte) as next_dte
      from wd
      group by wd.dte
     )
select dte, DATEADD(-1 day to next_dte)
from wd_cnt
where num_on_date = (select count(distinct worker_id) from work_days);


DTE
DATEADD


2019-10-01
2020-04-15

2020-07-01
2020-07-19

2020-11-01
9999-01-01
DTE	DATEADD
2019-10-01	2020-04-15
2020-07-01	2020-07-19
2020-11-01	9999-01-01