A colleague used a phrase (fitting the context incredibly well), which everybody reacted to as quite unusual. Then, we had a discussion whether it's grammatically correct. In fact, we're not certain if it's proper English and it boils down (according to me) to whether can may be used in infinite tense.
The context (not relevant for the grammatical correctness but possibly nice to know) is that a person can't perform an action. It's a reference to Terminator 3, where someone angrily throws out Drop dead! and Arnie replies I'm unable to comply., in a phlegmatic manner. In our case, the person communicates that they can't do something, which is an inability to being able to do it.
I'm unable to can.
Obviously, there are more natural ways to express it. We're not looking for those alternatives. We'd like to know if the correct pattern of I'm unable to jump or I'm unable to answer may be applied on I'm unable to can. It's an auxiliary verb and it just sounds clunky. On the other hand, I'm unable to be feels fine.