How to eliminate extra "NOT EXISTS"-query here?

Hi, I'm testing if some dataset contains an array of elements and want to
return all “not containing the specified array”, including entries in master
table not being referenced.

I have the following schema:

drop table if exists stuff;
drop table if exists test;
CREATE TABLE test(
id varchar primary key
);

create table stuff(
id serial primary key,
test_id varchar NOT NULL REFERENCES test(id),
v varchar not null,
unique (test_id, v)
);

INSERT INTO test(id) values ('a');
INSERT INTO test(id) values ('b');
INSERT INTO test(id) values ('c');
INSERT INTO test(id) values ('d');

INSERT INTO stuff(test_id, v)
values ('a', 'x')
;

INSERT INTO stuff(test_id, v)
values ('b', 'x')
, ('b', 'y')
;

INSERT INTO stuff(test_id, v)
values ('c', 'x')
, ('c', 'y')
, ('c', 'z')
;

select * from test t
WHERE NOT ARRAY['x']::varchar[] <@ (select array_agg(s.v) from stuff s WHERE s.
test_id= t.id)
;

select * from test t
WHERE NOT ARRAY['x', 'y']::varchar[] <@ (select array_agg(s.v) from stuff s
WHERE s.test_id = t.id)
;

select * from test t
WHERE NOT ARRAY['x', 'y', 'z']::varchar[] <@ (select array_agg(s.v) from stuff
s WHERE s.test_id = t.id)
;

select * from test t
WHERE NOT ARRAY ['x', 'y', 'z', 't']::varchar[] <@ (select array_agg(s.v) from
stuffs WHERE s.test_id = t.id)
;

-- This works, but I'd rather not do the extra EXISTS
select * from test t
WHERE (NOT ARRAY ['x', 'y', 'z', 't']::varchar[] <@ (select array_agg(s.v) from
stuffs WHERE s.test_id = t.id)
OR NOT EXISTS (
select * from stuff s where s.test_id = t.id
)
)
;

So, I want to return all entries in test not having any of ARRAY ['x', 'y',
'z', 't'] referenced in the table stuff, and I'd like to have test.id="d"
returned as well, but in order to do that I need to execute the “or not
exists”-query. Is it possible to avoid that?

--
Andreas Joseph Krogh
CTO / Partner - Visena AS
Mobile: +47 909 56 963
andreas(at)visena(dot)com <mailto:andreas(at)visena(dot)com>
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