This query evaluates all combinations of id1, id2 and id3 (the cross join) and finds which combinations are not present in table a.
select b.id1, c.id2, d.id3 from
TableB b cross join TableC c cross join TableD d WHERE NOT EXIST
(select 1 FROM TableA a WHERE a.id1=b.id1 AND a.id2=c.id2 AND a.id3=d.id3)
EDIT: With an RIGHT JOIN
SELECT allPerms.id1, allPerms.id2, allPerms.id3 FROM a RIGHT JOIN (select b.id1, c.id2, d.id3 from
TableB b cross join TableC c cross join TableD) allPerms
ON a.id1=allPerms.id1 AND a.id2=allPerms.id2 AND a.id3=allPerms.id3
WHERE a.id1 IS NULL
The two are pretty much the same. Since we are not actually fetching values from the joined table, some people prefer the first approach, since it captures the intent and spirit of the query. The second version is more "implementation oriented". A good optimizer will produce an efficient plan for both, but on some lesser RDBMSs, the second version will run faster.
With a predefined set for table D - id3 has values (2,5,6)
select b.id1, c.id2 from
TableB b cross join TableC c WHERE NOT EXIST
(select 1 FROM TableA a WHERE a.id1=b.id1 AND a.id2=c.id2 AND a.id3 IN (2,5,6))
But, this doesn't give you the id3 that is missing in the table A row. For that, I think the simplest is to emulate the table via a union, e.g.
select b.id1, c.id2, d.id3 from
TableB b, TableC c, (select 2 id3 union select 5 union select 6) d
WHERE NOT EXIST
(select 1 FROM TableA a WHERE a.id1=b.id1 AND a.id2=c.id2 AND a.id3=d.id3)
(This is still using cross join - it's implied if tables are separated by commas.)