EXPERT RESPONSE
Like it or not, the simplest way to solve this problem is with a table that will contain your list of strings to be tested against your table T1. The technique involves a LEFT OUTER JOIN, with an IS NULL test in the WHERE clause, to find those rows of the left table (your list of strings to be tested) that don't have a match in the right table (your table T1).
The wrinkle here is that you said you do not want the help of a second table, so the solution here is to achieve this without actually creating a table. We'll use an imaginary table.
There are two ways to do this. The first, which isn't actually Standard SQL, is to create the table "out of thin air" as it were.
SELECT dt.string
FROM ( SELECT 'aaaaa' AS string
UNION ALL
SELECT 'bbbbb'
UNION ALL
SELECT 'ccccc'
) AS dt
LEFT OUTER
JOIN T1
ON T1.x = dt.string
WHERE T1.x IS NULL
Here, "dt" is a table alias which stands for derived table, which is what we call a subquery used in the FROM clause.
In the subquery, we see several SELECT statements UNIONed together, but there is no FROM clause in them. Only some database systems support a SELECT statement which has no FROM clause (Microsoft SQL Server and MySQL do).
If your database system requires a FROM clause, then all you need to do is select the strings from any convenient table where it is easy to target a specific row. In Oracle, you have the built-in DUAL table which can be used, and probably was intended, for this purpose. It works in this context because it has only one row.
SELECT dt.string
FROM ( SELECT 'aaaaa' AS string
FROM dual
UNION ALL
SELECT 'bbbbb'
FROM dual
UNION ALL
SELECT 'ccccc'
FROM dual
) AS dt
LEFT OUTER
JOIN T1
ON T1.x = dt.string
WHERE T1.x IS NULL
Note that it does not matter what columns the DUAL table actually has, because we are selecting a constant instead of a column from it.
If you're not using Oracle but still need to use a FROM clause, you could instead use any table you wish, including the T1 table itself, provided that you retrieve only one row from it.
SELECT dt.string
FROM ( SELECT 'aaaaa' AS string
FROM T1
WHERE x = 'aaaaa'
UNION ALL
SELECT 'bbbbb'
FROM T1
WHERE x = 'aaaaa'
UNION ALL
SELECT 'ccccc'
FROM T1
WHERE x = 'aaaaa'
) AS dt
LEFT OUTER
JOIN T1
ON T1.x = dt.string
WHERE T1.x IS NULL
Neat, eh?
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