On the feasibility of a KBN-K mate within 50 moves using a particular method Prove that it is possible, from any starting KBN-K position, to accomplish the mate by manoeuvering to arrive at key positions from a well-known method or strategy whilst the losing king actively tries to avoid reaching the key positions that would lead to mate within 50 moves. In terms of the players' goals, the winning player's goal is to reach the key positions and still have moves to mate within 50 moves, and the losing player's goal is to avoid getting mated within 50 moves.
Given a starting KBN-K position, there exist paths through the tree of variations satisfying the winning player's goal with optimal play by the losing player. Is this satisfied for ALL legal KBNK positions using that particular stratagem only? How would one go about attempting to prove this using KBN-K tablebases?
Is this satisfied for ALL legal KBNK positions using that particular stratagem only?

Absolutely not! Please don't try to prove something that's impossible. Consider this position.
[startflipped &quot;&quot;]
[FEN &quot;3kB3/4N3/8/8/8/8/8/3K4 b - - 0 1&quot;]