Logged on User Contained in Set

The following relevance returns, “Error: Singular expression refers to non-unique object” when more than one user is logged on. How can I change this to work when multiple users are logged on?

name of logged on users as lowercase is not contained by set of ("name1";"name1";"name3";"name4")

Here is the relevance that seems to work when multiple users are logged on.

not exists ((names of it) of (logged on users)) whose (it as lowercase is contained by set of ("name1";"name2";"name3";"name4"))
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A slightly tighter variation:

q: not exists logged on user whose (name of it is contained by set of ("name1";"name1";"name3";"name4"))
A: True
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I like of like this method:

not exists (it is contained by set of ("user1";"user2")) whose(it) of (it as lowercase) of names of logged on users

I like to keep the flow from right to left as much as possible while keeping the relevance as plural as possible.

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