If something is inconceivable, it is too strange or too far from ordinary life to be thought real or possible. You cannot really picture it happening. People use it of futures they cannot imagine, and also — a little loosely — of things they simply find shocking: “It is inconceivable that they would lie.” Though actually, that second use is often drama more than strict meaning; “I find it hard to believe” is weaker, and careful speakers keep inconceivable for ideas the mind truly cannot hold as possible. It is a fairly formal, rather heavy adjective. It is about what the mind can accept, not about whether a rule allows the thing.