An old challenge

[Spenner]

Can you put in an unanswerable statement though?

Or how about a more detailed question like this:

"The door on the left is A, then B, then C. Only answers with A and B are a theorum of this system, and therefore they are the only answerable results of this formal system. Is door A the desired awesome door? If yes, then A = true"

I mighta worded that bad I'm horrible with mathspeak : < but anyhow, there's no need to include the notion of the third door. It doesn't answer if it's not an answerable part of the question, therefore it's implied to be C