So, I calculated the first five optimal moves w.r.t. the Stockfish's Evaluation Function:

1. Nxe3 Ba5

2. Kc6 Nb8+

3. Kb5 Bd8

4. Bg4 Kg7

5. Kxc5 Bf6

And the combined method persistently says that the Black is winning!

I fail to understand what you mean. Nxe3?? Is a losing blunder. The solution is Nf6+.

This controversial and strange-looking puzzle was created around 1970 by a Dutch game composer, Gijs Van Breukelen, and presented in a super tournament in which several grandmasters, notably Garry Kasparov and Mikhail Tal, had taken part. No one could solve the puzzle on the first try, but Tal did (?!). This puzzle is also known as Plaskett's Puzzle, named after Harold James Plaskett, a British chess grandmaster.

The strange thing about this puzzle is that the Black is the winner based on modern engines with -3.87 calculated by the Stockfish Chess Engine on depth 53 and -3.5 calculated by Stockfish on depth 54 (Cloud). Surprisingly, Tal's solution is one of the ways that win the game for the White. According to Tal's solution, the evaluation number of the Stockfish for the second move is reversed from -3 to +6! The local traps trick the Engines! Or can it be granted as a puzzle? Maybe it's just a position from a middle game.

Finally, I analyzed the position via a combined search technique; i.e., I combined the Stockfish and Lc0 in a way that the Lc0 was iteratively pruning the unfathomable bounds created by the Stockfish's Alpha-beta tree. So, the unpromising bounds were fathomed quickly. So, I calculated the first five optimal moves w.r.t. the Stockfish's Evaluation Function:

1. Nxe3 Ba5

2. Kc6 Nb8+

3. Kb5 Bd8

4. Bg4 Kg7

5. Kxc5 Bf6

And the combined method persistently says that the Black is winning!