JPA Criteria based query that INTERSECTS three queries at once

I want to find all "a" that have "b" = 500 and "b" = 501 and "c" = 2 installed.

In SQL I would do it like this:

select a from table1 where id in (select info_id from table2 where b = '500')
intersect
select a from table1 where id in (select info_id from table2 where b = '501')
intersect
select a from table1 where id in (select info_id from table2 where id in (select ecu_id from table3        where c = '2'));

So I would create three SQL queries and then take the intersection of those 3.
But I now have to use JPA criteria based queries, no native SQL or JPQL.

We could do three distinct JPA criteria based queries:

one that returns a list of "a" where "b" = 500,

one that returns a list of "a" where "b" = 501 and

one that returns a list of "a" where "c" = 2.

And then filter for all "a" that appear in all three returned lists. But that would take too long, our database contains many million "a" entries...

So this is one solution in SQL:
http://tpcg.io/mV3rZ2Of

This is very long as a JPA Criteria Query, so I only show how I translated the last Exists condition, which was the hardest part:

Subquery<Table3> subQuery = searchQuery.subquery(Table3.class);
Root<Table3> fromTable3SubQuery = subQuery.from(Table3.class);
List<Predicate> subRestrictions = new ArrayList<>();

Subquery<Table2> subQueryForInExpression = searchQuery.subquery(Table2.class);
Root<Table2> fromTable2SubQuery = subQueryForInExpression.from(Table2.class);
subQueryForInExpression.select(fromTable2SubQuery.get(ID)).where(criteriaBuilder.equal(fromTable2SubQuery.get(info_id), root.get(ID)));

subRestrictions.add(criteriaBuilder.equal(fromTable3SubQuery.get(c), '2'));
subRestrictions.add(criteriaBuilder.in(fromTable3SubQuery.get(ecu_id)).value(subQueryForInExpression));

restrictions.add(criteriaBuilder.exists(subQuery.select(
                    fromTable3SubQuery.get(c)).where(
                            subRestrictions.toArray(new Predicate[0]))));

-> This represents only the last Existspart, which is asking for the c = '2' connection. The others are similar, but without the subQueryForInExpression parts...