unsolved

P is solvable if, at some point in time, a proof will be provided that solution to P can be found.

P is unsolvable if, at some point in time, a proof will be provided that P does not have solution.

Problem P is "fatal" if no proof could ever be provided whether P is solvable or unsolvable.  It is impossible to tell about problem if it is "fatal". That's why it is fatal ;)