OK, interviewers can be idiots. Well too often, it sounds like. It does not mean that we should explain every case of idiocy. As to this particular case, I'm not quite sure the question was idiotic. Perhaps they told you a bit more. Perhaps you were expected to ask for clarification; and they wanted to see if you are capable of asking question to pull information. Not a fair interviewer's behavior, but…
The rest of it is off-topic. I think, as your whole question is off-topic, I can allow myself a bit of off-topic answer. If someone removed this whole thread as off-topic, it would be fair enough though.
How would I behave in this situation? I would ask a question: what do they consider as a "proof", what are the assumptions. I would try to find out the flaw in there definition, but there is a (remote) possibility that you are expected to talk about formalization of the proof and Computer Algebra Systems (CAS). Are you familiar with such things? Very few developers are, in fact. Anyway, you are supposed to take a pretty active role at the interview, at least active enough to freely discuss the questions asked, figure out all the detail you need to give an answer. Think about it: how it happens at work? When you receive some requirements for some work, you need to discuss anything which may concern you. Same goes about interview test questions or assignments.
Anyway, if you really sure that some of your interviewers is an idiot (it does not even matter if this is true or not), I would advice to relax and enjoy the situation. You would not be able to work with those people anyway, so you would have nothing to loose. Relax and use the rest of the interview for collecting some experience, ask more questions, with confidence.