@Bornok is right that the best approach is to use a "choice filter". These are generally used in the context of cascading selects but in fact any true/false expression can be used to filter values in a list. You shouldn't need the extra calculates introduced, though.
You can see the technique described at Reducing multiple choices dependent on previous selection - #11 by Matthew_Reeve and you can see what it looks like with the negation in your form in this example.
The interesting part that is a little tricky to come up with is that name refers to the name column in the choices sheet. It's also possible to filter on label using label instead.