Now thinking about it in terms of mathematical logic, the DoJ and Supreme Court‘s interpretations is wrong:

It’s actually a law of logic (https://en.wikipedia.org/wiki/De_Morgan's_laws) that says that:

not (A and B and C)

is equal to

(not A) or (not B) or (not C)

—

In this case:

The defendant is eligible for relief if he does not (A and B and C)

Which is the same as

The defendant is a eligible for relief if he does (not A) or (not B) or (not C)

—

Which is not what the DoJ is saying. The DoJ is saying that

not (A and B and C)

is equal to

(not A) and (not B) and (not C)