Let’s explore the "˜vacuous truth’ angle ... I’ve never heard that term before but I surmise I get what it means.
So let’s say no antibiotics have ever been used against X.
Is it true to say "X is more resistant to some antibiotics that have been used against it than it was before they were used"?
No, it really can’t be true. The statement is not conditional. It makes a positive claim that this species *is* more resistant to antibiotics that *have* been used against it.
So if no antibiotics have ever been used against X, then (E) is full-fledged false.
I think your EDIT comment is a good angle ... we could have used some antibiotics on X yesterday, and we would not necessarily yet see X be more resistant to it.
You should also consider that the first sentence says
IF an antibiotic doesn’t eliminate completely "”> bacteria develops more resistance
We know that all antibiotics on the market TODAY can’t eliminate X completely, but (E) does not specify whether the antibiotics in question are ones on the market today. So (E) could also be falsified by considering antibiotics NOT on the market that DO eliminate X completely, in which case the conditional would not apply to those antibiotics.
Hope this helps.