And this one:
[d]6k1/8/r2BK2P/6N1/8/8/8/8 w - - bm #46;
is annotated as ECE3.1020
Online tablebase files show the mate is correct, but I do not have the full path.
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Have you got by any chance 6-man Nalimov EGTB downloaded? If that (I guess that KBNPkr and KQBNkr are enough), Chest 5.2 has an option in SearchMode called EgtbAnalysis that should work. However, I do not know if it only shows a single path or all of them, like a tree of mainlines... since the winning Ke5 has two optimal black moves in the sense of longer distances to get checkmated (..., Rb6 and ..., Kh8), and more equal optimal moves later by both sides.
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Says Rf4, Rg4, and Rh4 are mate in 36
Ke7 Kf8, and Kf7 are mate in 38
all other moves draw or lose.
Oops, wrong position, that was for this one:
4K3/8/3r4/1Pk5/2P1R3/8/8/8 w - -
For this position (6k1/8/r2BK2P/6N1/8/8/8/8 w - -), the same site says:
Ke5 is mate in 46, Ke7 is mate in 48, Kd7 is mate in 52 and all other moves draw.
Taking ideas is not a vice, it is a virtue. We have another word for this. It is called learning.
But sharing ideas is an even greater virtue. We have another word for this. It is called teaching.