Looking for solutions with predicted variations for these...

[acase]

Here is another one from the EPD and the Chest database that is supposed to be a mate in 35 but ShashChess obliterates any delusions of mate in 35 and sees a mate in 12!

[pgn][Event "Mate in 35"]
[Site "British chess magazine"]
[Date "1946"]
[Round "?"]
[White "Theimer, Ernst Theodore"]
[Black "?"]
[Result "1-0"]
[Time "07:03:43"]
[TimeControl "0"]
[SetUp "1"]
[FEN "8/p5p1/3p2Pp/2p2K1R/4P1Nb/p2P3r/P3p1p1/4Nbrk w - - 0 1"]
[Termination "normal"]
[PlyCount "23"]
[WhiteType "program"]
[BlackType "program"]

1. e5 {+M12/87 37 ShashChess33.1-x86-64-bmi2} dxe5 2. Nxe5 Kh2 3. Kg4 Rg3+
4. Kxh4 Rh3+ 5. Kg4 Rxh5 6. N5f3+ Kh1 7. Kxh5 c4 8. Nd2 cxd3 9. Kh4 a5 10.
Ne4 Kh2 11. Nf3+ Kh1 12. Nf2# 1-0
[/pgn]

Here is a link to the problem:
https://www.yacpdb.org/#search/OHA1cDEz ... LzEvMA==/1

[acase]

Another one from the EPD and the Chest database, this one is listed as a mate in 51 in the Chest database and it is listed as a mate in 49 on yacpdb, however The Huntsman sees a mate in 40:

[pgn][Event "Mate in 40"]
[Site "Columbus, Ohio"]
[Date "2023.07.13"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[Time "14:16:20"]
[TimeControl "0"]
[SetUp "1"]
[FEN "7K/8/5Q2/8/6B1/3P3p/p5p1/6kq w - - 0 1"]
[Termination "normal"]
[PlyCount "79"]
[WhiteType "program"]
[BlackType "program"]

1. Qd4+ {+M40/82 1728} Kf1 2. Qf4+ Kg1 3. Qe3+ Kh2 4. Qe5+ Kg1 5. Bh5 Kf1
6. Qf4+ Kg1 7. Qe3+ Kh2 8. Qe5+ Kg1 9. Kg7 Kf2 10. Qe2+ Kg3 11. Qe3+ Kh2
12. Qe5+ Kg1 13. Kf6 Kf2 14. Qf4+ Kg1 15. Qe3+ Kh2 16. Qe5+ Kg1 17. Kf5 Kf2
18. Qe2+ Kg1 19. Qe3+ Kh2 20. Qe5+ Kg1 21. Ke4 Qh2 22. Qa1+ Kf2 23. Qb2+
Kg3 24. Qe5+ Kh4 25. Qf6+ Kxh5 26. Kf5 Qf4+ 27. Kxf4 g1=Q 28. Qh8+ Kg6 29.
Qg8+ Kf6 30. Qxg1 Ke6 31. Qa1 Ke7 32. Qxa2 Kd6 33. Kf5 Kc7 34. Ke5 Kc6 35.
Qa8+ Kc5 36. Qd5+ Kb4 37. Kd4 h2 38. Qb7+ Ka3 39. Kc3 h1=Q 40. Qb3# 1-0
[/pgn]

Here is the yacpdb link:
https://www.yacpdb.org/#search/N0s4NVEy ... LzEvMS8w/1

[acase]

Here's the mate in 31 for this one

8/6B1/4B3/8/1B2p3/4p3/4p1pp/2k1Kbrr w - - 0 1

[pgn][Event "Mate in 31"] [Site "Columbus, Ohio"] [Date "2024.01.26"] [Round "?"] [White "?"] [Black "?"] [Result "1-0"] [Time "07:37:51"] [TimeControl "0"] [SetUp "1"] [FEN "8/6B1/4B3/8/1B2p3/4p3/4p1pp/2k1Kbrr w - - 0 1"] [Termination "normal"] [PlyCount "61"] [WhiteType "program"] [BlackType "program"] 1. Ba3+ (1. Ba2 Kc2 2. Ba3 Kd3 3. Bb1+ Kc4 4. Bc2 Kb5 5. Bb3 Ka5 6. Bc3+ Kb5 7. Bab4 Kc6 8. Bc4 Kc7 9. Ba5+ Kb7 10. Bd4 Kc8 11. Bd5 Kb8 12. Bdb6 Kc8 13. Bc7 Kd7 14. Bb7 Ke6 15. Bc6 Kf7 16. Bd6 Ke6 17. Bc5 Kf7 18. Bd7 Kg6 19. Bc3 Kf7 20. Bd6 Kg6 21. Be6 Kh6 22. Bf4+ Kg6 23. Bce5 Kh7 24. Bd5 Kg6 25. Bg8 Kh5 26. Bf7+ Kh4 27. Bg6 Kg4 28. Bd6 Kh3 29. Bg5 Kg4 30. Bdf4 Kf3 31. Bh5#) 1. .. Kc2 (1. .. Kb1 2. Bf6 Kc2 3. Ba2 Kd3 4. Bb1+ Kc4 5. Bc2 Kb5 6. Bb3 Kb6 7. Bd8+ Kb5 8. Bae7 Ka6 9. Bc4+ Ka7 10. Bc5+ Kb7 11. Bdb6 Kb8 12. Bd5 Kc8 13. Ba3 Kb8 14. Bd6+ Kc8 15. Bbc7 Kd7 16. Bb7 Ke6 17. Bc6 Kf7 18. Bd7 Kf6 19. Bd8+ Kf7 20. Bh4 Kg8 21. Be6+ Kg7 22. Bde7 Kh6 23. Bef6 Kg6 24. Bhg5 Kh7 25. Bb3 Kg6 26. Bg8 Kf5 27. Bf7 Kg4 28. Bg6 Kf3 29. Be5 Kg4 30. Bgf6 Kf3 31. Bh5#) 2. Ba2 Kd3 3. Bb1+ Kc4 4. Bc2 Kb5 5. Bb3 Ka5 (5. .. Kc6 6. Bc4 Kb6 7. Bb4 Kb7 8. Bd4 Kc6 9. Bbc5 Kb7 10. Bb6 Kc6 11. Ba6 Kd5 12. Bb5 Ke6 13. Bdc5 Kd5 14. Ba7 Ke6 15. Bc6 Ke5 16. Bb8+ Ke6 17. Bc7 Kf7 18. Bd7 Kg6 19. Bd8 Kh6 20. Be6 Kg7 21. Bce7 Kg6 22. Bg5 Kg7 23. Bde7 Kg6 24. Bef6 Kh7 25. Bb3 Kg6 26. Bg8 Kf5 27. Bf7 Kg4 28. Bg6 Kh3 29. Bf4 Kg4 30. B4e5 Kf3 31. Bh5#) (5. .. Kb6 6. Bb4 Kb5 7. Bgf8 Kc6 8. Bc4 Kb6 9. Bfd6 Kc6 10. Bbc5 Kb7 11. Bb5 Kc8 12. Ba6+ Kd8 13. Bb6+ Kd7 14. Bb4 Kc6 15. B4c5 Kd5 16. Bb5 Ke6 17. Bc6 Ke5 18. Ba5 Ke6 19. Bc3 Kf7 20. Bd7 Kg6 21. Be6 Kh6 22. Bf8+ Kh7 23. Ba1 Kg6 24. Bg8 Kf5 25. Bf7 Kg5 26. Bfg7 Kg4 27. Bgf6 Kf4 28. Bg6 Kf3 29. Bae5 Kg4 30. Bd6 Kf3 31. Bh5#) 6. Bc3+ Kb5 7. Bab4 Kc6 8. Bc4 Kb6 9. Bd4+ Kb7 10. Ba5 Kc8 11. Bd5 Kb8 12. Bc5 Kc8 13. Bab6 Kb8 (13. .. Kd7 14. Bb7 Ke6 15. Bc7 Kf7 16. Bc6 Ke6 17. B5d6 Kf7 18. Bd7 Kf6 19. Bd8+ Kf7 20. Bh4 Kg8 21. Be6+ Kg7 22. Bde7 Kh7 23. Bef6 Kg6 24. Bhg5 Kh7 25. Bd5 Kg6 26. Bg8 Kf5 27. Bf7 Kg4 28. Bg6 Kh3 29. Be5 Kg4 30. Be7 Kf3 31. Bh5#) 14. Bd6+ Kc8 15. Bbc7 Kd7 16. Bb7 Ke6 17. Bc6 Kf7 18. Bd7 Kf6 19. Bd8+ Kf7 20. Bh4 Kg6 21. Be6 Kg7 22. Bde7 Kh6 23. Bef6 Kg6 24. Bhg5 Kh7 25. Bc4 Kg6 26. Bg8 Kf5 27. Bf7 Kg4 28. Bg6 Kf3 29. Be5 Kg4 30. Be7 Kf3 31. Bh5# 1-0 [/pgn]

[acase]

Here is the solution to this mate in 42 from you requested from the ChestUCI database:

here is the FEN:
8/p5p1/1pP3p1/p5p1/k3p3/4p3/K7/8 w - - 0 1

And here is the PGN:

[pgn][Event "Mate in 42"] [Site "Columbus, Ohio"] [Date "2024.01.27"] [Round "?"] [White "?"] [Black "?"] [Result "*"] [Time "16:34:11"] [TimeControl "0"] [SetUp "1"] [FEN "8/p5p1/1pP3p1/p5p1/k3p3/4p3/K7/8 w - - 0 1"] [Termination "normal"] [PlyCount "83"] [WhiteType "human"] [BlackType "human"] [Comment "bm #42;"] 1. c7 e2 2. c8=Q e1=Q 3. Qc4+ Qb4 4. Qc6+ Qb5 5. Qxe4+ Qb4 6. Qd3 g4 7. Qd7+ Qb5 8. Qxg4+ Qb4 9. Qd7+ Qb5 10. Qd4+ Qb4 11. Qd3 g5 12. Qd7+ Qb5 13. Qd4+ Qb4 14. Qd3 g4 15. Qd7+ Qb5 16. Qxg4+ Qb4 17. Qd7+ Qb5 18. Qd4+ Qb4 19. Qd3 g6 20. Qd7+ Qb5 21. Qd4+ Qb4 22. Qd3 g5 23. Qd7+ Qb5 24. Qd4+ Qb4 25. Qd3 g4 26. Qd7+ Qb5 27. Qxg4+ Qb4 28. Qd7+ Qb5 29. Qd4+ Qb4 30. Qd3 a6 31. Qd7+ Qb5 32. Qd4+ Qb4 33. Qd3 Qb2+ 34. Kxb2 Kb4 35. Qc3+ Kb5 36. Qc7 Kb4 37. Kc2 a4 38. Qc6 a5 39. Kd3 Ka3 40. Kc3 Ka2 41. Qg2+ Ka1 42. Qb2# * [/pgn]