So this website claims this puzzle cannot be solved by a modern chess engine like Stockfish:

https://www.youtube.com/watch?v=8wCJalNkTEI

I let Stockfish 12 lose on my Mac Pro and after 43 minutes it found the solution:

43.23: +5.99/52 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Qe8 c4+ 6.Kc6 Ba3 7.Bd1+ Kh3 8.Qxe3 Nb4+ 9.Kb5 c2 10.g4+ Kg2 11.Qd2+ Kg3 12.Qc3+ Nd3 13.Bxc2 Bb2 14.Qxc4 Ne1 15.Qc7+ Kg2 16.Qc6+ Kf2 17.Bd1 Bd4 18.Qxh6 Be3 19.Qh4+ Kf1 20.Qg3 Bf2 21.Qf4 Nh7 22.g5 Kg1 23.Qe4 Kh2 24.Bf3 Kg1 25.Qg4+ Kh2 26.g6 Nf6

I gave it more time and after 26 hours 41 minutes it found mate in 32:

#32/74 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Qf6 Kxg3 6.Qe5+ Kf3 7.Bd1+ Kg2 8.Qd5+ Kg1 9.Qc4 c2 10.Qg4+ Kf2 11.Qe2+ Kg3 12.Qxe3+ Kg2 13.Bxc2 c4+ 14.Kd5 Bc5 15.Be4+ Kf1 16.Qf4+ Ke1 17.Kxc4 Nxe4 18.Qxe4+ Kd2 19.Qf4+ Ke2 20.Qxh6 Bf2 21.Qxa6 Ke3 22.Qf6 Bg3 23.Qd4+ Kf3 24.Kd3 Bf4 25.Qf6 Kg4 26.Ke4 Bc1 27.Qf5+ Kg3 28.Qf3+ Kh2 29.Qf2+ Kh3 30.Kf3 Bf4 31.Qg2+ Kh4 32.Qg4#

In the course of an additional 43 hours it found other variations of mate in 32. After 168 hours it has not found anything new, so I cancelled it.

So the question is - who is right? The web site claiming that the puzzle is flawed and there is no clear forced win for white, or Stockfish believing in a mate in 32? Either way, it is interesting but rare to see positions evaluate like this (from initially thinking black is clearly ahead, to switching its mind after 43 minutes of running on 16 cores and 20GB of RAM):

0.00: -1.65/3 1.Ne5 Ne4+ 2.Kd5 Nf6+ 3.Kc4 0.00: +2.17/4 1.Nf6+ Kg7 2.Nh5+ Kg6 0.00: 0.00/5 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.Bd1+ Kg6 5.Bc2+ 0.00: 0.00/6 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.Bd1+ Kg6 5.Bc2+ 0.00: -2.22/7 1.Nxe3 Ba5 2.Kc6 Ne6 3.Kd5 Nd4 0.00: -1.97/8 1.Nxe3 Ba5 2.Kd5 Kg6 3.Be2 0.00: -3.12/9 1.Nxe3 Ba5 2.Kc6 Nb8+ 3.Kxc5 Nxd7+ 4.Kc6 Ne5+ 5.Kc5 Kg6 6.Bc2+ Kf6 7.Nd5+ Ke6 0.00: -2.67/10 1.Nxe3 Ba5 2.Kd5 Kg7 3.Ba4 Kf6 4.Kc4 0.00: -3.09/11 1.Nxe3 Ba5 2.Kd5 Nf7 3.Kc4 Nb8 4.Bc2+ Kg7 5.d8=R Nxd8 6.Kxc5 Nbc6 7.Nf5+ Kf6 8.Nxh6 0.00: -3.40/12 1.Bb3 Ba5 2.Nxe3 Kg7 3.Kd5 Nf7 4.Kc4 Nb8 5.d8=B Nxd8 6.Kb5 0.00: -3.28/13 1.Nxe3 Ba5 2.Kd5 Bd8 3.Kc4 Nf7 4.Bh5 Nd6+ 5.Kd5 Nb7 6.Kc6 Na5+ 7.Kb5 Nb8 8.Kxc5 0.00: -3.18/14 1.Nxe3 Ba5 2.Kc6 Bd8 3.Kb5 Nb8 4.Kxc5 Nf7 5.Bc2+ Kg7 6.g4 Nxd7+ 7.Kb4 Bg5 8.Nd5 Nf6 9.Nxc3 Nxg4 0.00: -3.14/15 1.Nxe3 Ba5 2.Kc6 Nb8+ 3.Kb5 Bd8 4.Kxc5 Kg6 5.Bc2+ Kf6 6.Kc4 Nf3 7.Kxc3 Kg5 8.Nf5 Nxd7 9.Kc4 Bc7 0.00: -3.34/16 1.Nxe3 Ba5 2.Be2 Nb8 3.Bd3+ Kh8 4.Bc2 Na6 5.Kc6 Bd8 6.Kb5 Nb8 7.Kxc5 Nxd7+ 8.Kc4 Nf3 9.Nf5 Bf6 10.Nxh6 0.00: -3.33/17 1.Nxe3 Ba5 2.Be2 Nb8 3.Bd3+ Kh8 4.Bc2 Na6 5.Kc6 Bd8 6.Kb5 Nb8 7.Kc4 Nxd7 8.Kxc3 Ne5 9.Nf5 Ngf3 10.Bd1 Bf6 11.Nxh6 Nf7+ 12.Kc4 N3e5+ 13.Kxc5 0.23: -4.17/29 1.Kd5 Nf7 2.Nxe3 Ba5 3.Ba4 Bd8 4.Kc4 Ne5+ 5.Kxc3 Nb8 6.Bc2+ Kg7 7.Nf5+ Kf6 8.Nxh6 Ba5+ 9.Kb3 Nbxd7 10.Nf5 Nb6 11.Ne3 Bd2 12.Nf1 Be1 13.Ne3 Kg5 14.Ng2 Bd2 15.Bd1 Nd5 16.Be2 Nc3 17.Ba6 Kg4 18.Nh4 Ne4 19.Bc8+ Kxg3 20.Nf5+ Kf4 21.Ng7 c4+ 22.Kc2 Ng4 23.Bxg4 Kxg4 3.05: -5.05/37 1.Nxe3 Ba5 2.Kd5 Nf7 3.Ba4 Bd8 4.Kc4 Ne5+ 5.Kxc3 Nb8 6.Bc2+ Kg7 7.Nf5+ Kf6 8.Nxh6 Nbxd7 9.Kd2 Nb6 10.Ke3 Nd5+ 11.Ke2 Nc3+ 12.Ke3 Kg5 13.Nf5 Ng4+ 14.Kd2 Ba5 15.Nh4 c4 16.Ng2 Nb5+ 17.Kd1 Na3 18.Ba4 Nf2+ 19.Ke2 Ne4 20.Kf3 Nc5 21.Be8 Nc2 22.g4 c3 23.Nf4 Nb4 24.Ke2 Kxf4 25.g5 3.53: -5.21/38 1.Nxe3 Ba5 2.Kd5 Nf7 3.Ba4 Bd8 4.Kc4 Kg6 5.Kb5 Nb8 6.Kxc5 Ne5 7.Kb4 Nbxd7 8.Nd5 Kg5 9.Nxc3 Be7+ 10.Kb5 Ng4 11.Nd5 Bf6 12.Kc6 Nf8 13.Bd1 Nf2 14.Bc2 Ne6 15.Kd7 Nd4 16.Bb1 Ne2 17.Bc2 Ng4 18.Nf4 Nxf4 19.Be4 Ne2 20.Bb7 Nxg3 21.Ba8 6.08: -5.53/39 1.Nxe3 Ba5 2.Kd5 Nf7 3.Ba4 Bd8 4.Kc4 Kg6 5.Kb5 Nb8 6.Kxc5 Ne5 7.Kd4 Nbxd7 8.Kxc3 Ba5+ 9.Kb2 Nf6 10.Bc2+ Kg5 11.Nf5 Nfg4 12.Nd6 Ne3 13.Ne4+ Kf5 14.Bb1 N5g4 15.Bd3 Ke5 16.Ng5 Kd4 17.Ba6 hxg5 18.Kc1 Nf6 19.Bc8 Ne4 20.Be6 Nxg3 21.Ba2 Ne2+ 22.Kb2 Bb4 23.Kb1 g4 24.Be6 14.13: -6.01/40 1.Nxe3 Ba5 2.Kd5 Nf7 3.Ba4 Bd8 4.Kc4 Kg6 5.Kb5 Nb8 6.Kxc5 Ne5 7.Kb4 Nbxd7 8.Nd5 Kg5 9.Bd1 Nf6 10.Nxc3 Bb6 11.Kb5 Bd4 12.Ne2 Bf2 13.Ka6 Nf3 14.Nf4 Kg4 15.Ne2 Be3 16.Kb5 Kh3 17.Kc4 Ne5+ 18.Kb3 Kg2 19.Bc2 Kf2 20.Nc3 Kxg3 21.Bf5 h5 22.Kc2 Bb6 23.Kd1 h4 24.Bc8 Kf2 25.Na4 Bd4 26.Kc2 Kf3 27.Bb7+ Kf4 36.18: -6.73/52 1.Nxe3 Ba5 43.23: +5.99/52 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Qe8 c4+ 6.Kc6 Ba3 7.Bd1+ Kh3 8.Qxe3 Nb4+ 9.Kb5 c2 10.g4+ Kg2 11.Qd2+ Kg3 12.Qc3+ Nd3 13.Bxc2 Bb2 14.Qxc4 Ne1 15.Qc7+ Kg2 16.Qc6+ Kf2 17.Bd1 Bd4 18.Qxh6 Be3 19.Qh4+ Kf1 20.Qg3 Bf2 21.Qf4 Nh7 22.g5 Kg1 23.Qe4 Kh2 24.Bf3 Kg1 25.Qg4+ Kh2 26.g6 Nf6 55.26: +27.52/53 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Bd1+ Kh3 6.Qc8+ Kh2 7.Qxa6 c4+ 8.Kc6 c2 9.Qa2 Bd2 10.Qxc2 c3 11.Qf5 Nh3 12.Qf1 Ng5 13.Qe2+ Kg1 14.Kd5 Nh3 15.Qf3 Kh2 16.Kd4 Kg1 17.Be2 Ng5 18.Qf1+ Kh2 19.Bd1 Ne6+ 20.Kd5 Ng5 21.Ke5 Bc1 22.Bc2 Bd2 23.Qe2+ Kg1 24.Bf5 c2 25.Bxc2 Nh3 26.Kd4 Nf2 27.Bd3 Kg2 28.Be4+ Kg1 29.Qf3 Kf1 30.Bd3+ Kg1 31.g4 Bc3+ 32.Kxe3 Nh1 33.Qh3 1:20.58: +43.01/54 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Bd1+ Kh3 6.Qc8+ Kg2 7.Qxa6 c4+ 8.Ke5 c2 9.Qa2 Bc3+ 10.Kd5 Kf2 11.Qxc2+ Bd2 12.Qf5+ Kg2 13.Qg4 c3 14.Qe2+ Kg1 15.Bc2 Nh3 16.Qf3 Nf2 17.Ke5 Bc1 18.Kd4 Bd2 19.Bb3 c2 20.Bxc2 Kh2 21.Bf5 Bc1 22.Bd3 Kg1 23.Be2 Bb2+ 24.Kc4 Bc3 25.g4 Be5 26.Qxe3 Bc7 27.Qc1+ Kh2 28.Qxh6+ Kg1 29.Qe3 Bb8 30.Qc1+ Kh2 31.Qh6+ Nh3 1:40.09: +62.77/56 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Bd1+ Kh3 6.Qc8+ Kh2 7.Qxa6 c4+ 8.Kd5 c2 9.Qa2 Bd2 10.Qxc2 Kg2 11.Ke5 Nf7+ 12.Ke4 Ng5+ 13.Kf5 c3 14.Qb1 Kg1 15.Qd3 Nh3 16.Qe2 Nf2 17.Bc2 h5 18.Ke5 Kh1 19.Bf5 Kg1 20.Kf4 c2 21.Bxc2 Nh3+ 22.Ke4 Ng5+ 23.Kf5 Nf7 24.Kf4 h4 25.gxh4 Nd8 26.Qg4+ Kf2 27.Qf3+ Ke1 28.Bd3 e2+ 29.Kg3 1:47.30: +73.12/57 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Bd1+ Kh3 6.Qc8+ Kh2 7.Qxa6 c4+ 8.Kd5 c2 9.Qa2 Kg2 10.Ke5 Nf7+ 11.Ke4 Bd2 12.Qxc2 Ng5+ 13.Ke5 c3 14.Qb1 Be1 15.Kf5 Kh2 16.Qb5 Bf2 17.Qe2 Nh3 18.Qf3 Ng1 19.Qh5+ Kg2 20.Qxh6 e2 21.Bxe2 Nxe2 22.Qc6+ Kf1 23.Ke4 Be1 24.Qc4 Kf2 25.Qf7+ Kg1 26.Qd5 Kf2 27.Qf5+ Kg1 28.Kd3 Nc1+ 29.Ke3 2:05.32: +152.40/59 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Qf6 Kxg3 6.Qe5+ Kf2 7.Qh2+ Ke1 8.Qh1+ Kf2 9.Bd1 c4+ 10.Kc6 Kg3 11.Kd5 Nc7+ 12.Kxc4 Ba5 13.Qe1+ Kf4 14.Qh4+ Ke5 15.Qd4+ Kf5 16.Bc2+ Ke6 17.Qxe3+ Kf6 18.Qf4+ Ke7 19.Qe5+ Nce6 20.Qxa5 Nf7 21.Kxc3 Nfg5 22.Bb3 Ne4+ 23.Kb4 N6c5 24.Qa7+ Kf6 25.Qf7+ Ke5 26.Qg7+ Nf6 27.Kxc5 Kf5 28.Qxh6 Ke5 2:31.21: +152.48/60 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Qf6 Kxg3 6.Qe5+ Kf2 7.Qh2+ Ke1 8.Qh1+ Kf2 9.Bd1 c4+ 10.Kc6 e2 11.Qh2+ Ke3 12.Qxe2+ Kd4 13.Qf2+ Ke5 14.Qb6 Ne6 15.Qxa6 Nd4+ 16.Kd7 c2 17.Bxc2 Nxc2 18.Qa4 Ne3 19.Qxb4 Ke4 20.Qd6 Ng4 21.Qe6+ Kf3 22.Ke8 Ne3 23.Qxh6 Ke4 2:33.04: +152.53/61 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Qf6 Ba3 6.Bd1+ Kxg3 7.Qf1 e2 8.Qe1+ Kh3 9.Qxe2 c4+ 10.Kd5 Nb4+ 11.Kxc4 c2 12.Bxc2 Nxc2 13.Qxc2 Bd6 14.Qf5+ Kh4 15.Qf6 Bg3 16.Qxh6+ Kg4 14:47.22: #38/62 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Qf6 Kxg3 6.Qe5+ Kf2 7.Qh2+ Ke1 8.Qh1+ Kf2 9.Qh4+ Ke2 10.Qg4+ Ke1 11.Ke5 c4 12.Bd1 Kf2 13.Kd5 Nc7+ 14.Kxc4 Bd6 15.Qe2+ Kg3 16.Qxe3+ Kg2 17.Qe2+ Kg1 18.Ba4 Nce6 19.Bc6 Nf4 20.Qe1+ Kh2 21.Qf2+ Kh3 22.Bd7+ Nge6 23.Bxe6+ Nxe6 24.Qe3+ Kg2 25.Qxe6 c2 26.Qe2+ Kg3 27.Qxc2 Bf4 28.Qb3+ Kg4 29.Kd4 h5 30.Ke4 Bd2 31.Qf3+ Kh4 32.Qf2+ Kg5 33.Qf5+ Kh6 34.Qf6+ Kh7 35.Qf7+ Kh8 36.Kf5 Bh6 37.Kg6 Bf8 38.Qxf8# 15:44.04: #34/63 1.Nf6+ Kg7 2.Nh5+ Kg6 3.Bc2+ Kxh5 4.d8=Q Kg4 5.Qf6 Kxg3 6.Qe5+ Kf2 7.Qf4+ Ke2 8.Qg4+ Kf2 9.Bd1 c4+ 10.Kd5 Nc7+ 11.Kxc4 Bd6 12.Qe2+ Kg3 13.Qxe3+ Kg2 14.Qe2+ Kg1 15.Ba4 Nce6 16.Bc6 Nf4 17.Qe1+ Kh2 18.Qf2+ Kh3 19.Bd7+ Nge6 20.Bxe6+ Nxe6 21.Qe3+ Kh4 22.Qxh6+ Kg3 23.Qxe6 Bb4 24.Kxb4 c2 25.Qg6+ Kf3 26.Qxc2 Kf4 27.Qc5 Kg4 28.Kc4 Kg3 29.Kd3 Kf4 30.Qh5 Kg3 31.Ke3 Kg2 32.Qg6+ Kf1 33.Qg8 Ke1 34.Qg1# ...

Oh. and it speaks volumes about the stability of my Mac Pro. Look at what it did while I was working normally on it during the week with hardly any noticeable slowdown: