Android Stockfish 10 cannot solve this puzzle
Something with moving the knight to d6, sacrificing it, and then promoting each corresponding pawn to a knight, and repeating the process, then checkmating with the knight? Just not sure of exact moves.
There are numerous examples of chess engines not being able to calculate certain endgame positions or studies.
Excluding under promotions, it's interesting that some chess engines can solve certain problems that other engines can't solve.
I think both Komodo and Houdini are much better than Stockfish at solving endgame studies that don't involve under promotion. Not positive though, been too long since I read an article about it.
The OP position is a fabulous mate-in-16 composed by Jan Hartong. Stockfish can't solve it because of the excessive length of the problem. It's not because the solution involves underpromotions, e.g. if you shortened the problem by playing the first 4 moves of the solution for Stockfish, it solves the resulting mate-in-12 position in seconds, even though plenty of underpromotion moves remain.
See this blog of mine for two exceptional forced-mate problems that Stockfish can't solve despite being relatively short (one is a mate-in-7).
I don't think any regular chess engine can solve any problem with an under promotion.
Here's some chess composition software: Chess Composition Software