I recently learnt that だれも means "everyone" with an affirmative verb and "no-one" with a negative verb. So, the literal translation of the Japanese "No-one is here" would be "Everyone is not here". Then how would one go about saying "Not everyone is here?"
`Not everyone is here.' is translated into
Here 「すべて～ではない」is a partial negation.
`Everyne is not here' is translated into
Here「すべて～ない」is a total negation.
If you are familiar with formal language representations :-),
In contract to the expresson 「すべての人がここにいない」(total negation),
"Not everything is X" is the same logically as "Some things (exist which) are not X", so in the general case you can do something like
Unfortunately, for the "is here" case, where our verb is いる, that would give us something like いない人もいる, which is at best confusing, so we might want to look for a rephrase.
Depending on how you want the emphasis you can also negate the clause "everything is X" directly by inserting a noun like わけ: