According to this post by u/dangi12012-1, Behting Study Cracked by Stockfish at depth 70!, Stockfish 12 NNUE evaluated 0.00 after 25 minutes with a powerful 16-core AMD Ryzen 3950X and 58 GB hash.
The post has the full info but here is the final PV:
info depth 72 seldepth 23 multipv 1 score cp 0 nodes 459232159581 nps 102464614 hashfull 426 tbhits 0 time 4481861 pv d5c6 g2g1q f5h4 g1a7 h4f3 a7a6 c6c5 c4c3 d2c3 a6a7 c5d6 a7a3 d6e6 a3c3 e6d5 c3c8 d5e4 c8h3 e4d5 h3g3 d5e4
After 1. Kc6 g1=Q, Stockfish 14 on Lichess analysis board considers it a draw, but then reconsiders and puts it at -2.5. After dxc3 this is a 7-piece tablebase draw but Lichess analysis doesn't have that.
[Title "Stockfish 12 NNUE at depth 72"]
[FEN "8/8/7p/3KNN1k/2p4p/8/3P2p1/8 w - - 0 1"]
1. Kc6 g1=Q 2. Nxh4 Qa7 3. Nhf3 Qa6+ 4. Kc5 c3 5. dxc3 Qa7+ 6. Kd6 Qa3+ 7. Ke6 Qxc3 8. Kd5 Qc8 9. Ke4 Qh3 10. Kd5 Qg3 11. Ke4
For what it's worth, I tried it out on my own relatively modest laptop with i7-7700HQ, 8 cores, 16 GB hash and Stockfish 15 NNUE for about 40 minutes and it still gave -4.65 eval, after 18 billion nodes instead of 459 billion. Probably would've benefited a lot from a 7-piece tablebase, or even just the 6-piece one.
info depth 69 seldepth 130 multipv 1 score cp -456 nodes 18878194760 nps 8098927 hashfull 691 tbhits 0 time 2330950 pv f5g7 h5g5 e5f3 g5g4 d5e4 h4h3 g7f5 g2g1q f3g1 h3h2 f5h6 g4h5 g1f3 h2h1q h6f5 h5g4 f5e3 g4g3 e3f5 g3f2 f5d4 h1h7 e4d5 h7c7 f3e5 c7a5 d5e4 a5a2 e5g4 f2e1 d4f3 e1e2 g4e5 a2a6 e4d5 a6b5 d5d4 e2f2 d4e4 b5b7 e4d4 f2g3 d4c4 g3f4 c4c5 b7a6 c5d5 a6a5 d5d6 a5d8 d6c5 f4e4 d2d3 e4f4 c5c6 d8f6 c6d5 f6b6 d3d4 b6b3 d5d6 b3a3 d6e6 a3a6 e6d5 a6b6 f3h4 b6d8 d5e6 d8d4 e5g6 f4e4 e6e7 d4a7 e7f6 a7f2 f6e6 f2e3 e6e7 e3e2 e7f7 e2f1 f7e7 e4d5 h4g2 f1a1 g2f4 d5e4 f4e6 a1a7 e7f6 a7f2 f6e7 e4f5 g6f8 f2e3 e7d6 e3d3 d6c6 d3d2 e6c5 d2h6 c5e6 f5e5 c6c7 h6e3 c7c6 e3f3 c6d7 f3f7 d7c6 f7e8 c6c7
The current PGN viewer at move 11 doesn't recognize in a valid PGN that Nd4 can only refer to one knight, so move 11 has to be written out.
[title "Stockfish 15 NNUE at depth 69"]
[fen "8/8/7p/3KNN1k/2p4p/8/3P2p1/8 w - - 0 1"]
1. Ng7+ Kg5 2. Nf3+ Kg4 3. Ke4 h3 4. Nf5 g1=Q 5. Nxg1 h2 6. Nxh6+ Kh5 7. Nf3 h1=Q 8. Nf5 Kg4 9. Ne3+ Kg3 10. Nf5+ Kf2 11. Nf5d4 Qh7+ 12. Kd5 Qc7 13. Ne5 Qa5+ 14. Ke4 Qa2 15. Ng4+ Ke1 16. Nf3+ Ke2 17. Nge5 Qa6 18. Kd5 Qb5+ 19. Kd4 Kf2 20. Ke4 Qb7+ 21. Kd4 Kg3 22. Kxc4 Kf4 23. Kc5 Qa6 24. Kd5 Qa5+ 25. Kd6 Qd8+ 26. Kc5 Ke4 27. d3+ Kf4 28. Kc6 Qf6+ 29. Kd5 Qb6 30. d4 Qb3+ 31. Kd6 Qa3+ 32. Ke6 Qa6+ 33. Kd5 Qb6 34. Nh4 Qd8+ 35. Ke6 Qxd4
Now, do you count engines using tablebases as solving the study? Stockfish with just the 5-man tablebase (a couple hundred megabytes of relevant files) is able to compute a draw in a few minutes. The eval quickly neutralizes from -4 to 0.0 around depth 45 and stays there for increased depth (tested up to 72).
info depth 45 seldepth 54 multipv 1 score cp 0 nodes 2418702985 nps 8967492 hashfull 60 tbhits 3503813 time 269719 pv d5c6 g2g1q f5h4 g1a1 h4f3 a1a8 c6c5 a8a3 c5c4 a3d6 d2d4 d6a6 c4c5 a6e6 d4d5 e6c8 c5d4 c8c7 d5d6 c7d6 d4e4 d6c5 e4d3 c5f2 d3e4 f2e2 e4f4 e2c2 f4g3 c2a4 g3h2 a4f4 h2g2 f4e3 g2g3 e3b3
I also left Crystal, a Stockfish derivative designed to solve chess problems, on overnight, but it computes depth much slower than stockfish and didn't solve the study.
info depth 57 seldepth 118 multipv 1 score cp -245 nodes 9016985399 nps 9322203 hashfull 519 tbhits 0 time 967259 pv f5g7 h5g5 e5f3 g5g4 g7f5 h4h3 d5e4 g2g1q f3g1 h3h2 f5h6 g4h5 g1f3 h2h1q h6f5 h5g4 f5e3 g4g3 e3f5 g3g2 e4e3 h1c1 f5d4 c1a3 e3f4 a3b4 f4e3 b4b8 f3h4 g2g3 h4f5 g3h3 d4f3 h3g2 f5d4 b8e8 e3f4 e8h5 f4e3 h5d5 f3e1 g2g3 e1f3 d5c5 e3e4 c5h5 d4f5 g3f2 f5d4 h5h1 e4d5 f2g3 d5c4 h1f1 c4d5 g3f4 f3e5 f1g2 d4f3 g2g8 d5d4 g8b3 d4c5 b3a3 c5d5 a3a2 d5d4 a2b2 d4d5 b2b6 d2d3 b6d8 d5e6 d8a5 e6d6 a5b4 d6e6 b4c5 d3d4 c5b6 e6d5 b6b3 d5d6 b3b8 d6c5 b8a7 c5d6 a7a6 d6d5 a6b6 f3h4 b6a5 d5e6 f4e4 e6e7 a5c7 e7e6 c7d8 e5g6 d8b6 e6f7 b6d4 f7e7 d4f2 e7e6 f2f1 e6e7 e4d5 h4g2 f1f2 g2f4 d5e4 f4e6 f2a7 e7f6