This is still one of the hardest position for Engines to solve

[Chessqueen]

[d]3k4/8/7p/2p1p1pP/1pPpPpP1/1P1P1P2/N7/2K5 w - - 0 1

Crystal 150121:
NNUE evaluation using nn-62ef826d1a6d.nnue enabled
1/1 00:00 225 113k +2.75 Kd2 Ke7
2/2 00:00 585 293k +2.58 Kd2 Ke7
3/3 00:00 816 408k +4.11 Kd2 Ke7 Nc1
4/4 00:00 1k 601k +4.09 Kd2 Ke7 Nc1 Kf6 Ne2
5/5 00:00 2k 927k +3.87 Kd2 Ke7 Nc1 Kf6 Ne2
6/6 00:00 3k 1,327k +3.50 Kd2 Ke7 Nc1 Kf6 Ke2 Ke6
7/7 00:00 3k 1,720k +3.48 Kd2 Ke7 Nc1 Kf6 Ne2 Kf7 Kc1
8/11 00:00 6k 2,799k +3.74 Kd2 Ke7 Nc1 Kf6 Ne2 Kf7 Kc1 Kf6
9/34 00:00 15k 4,896k +3.88 Kd2 Ke7 Nc1 Kf6 Ne2 Kf7 Kd1 Ke6 Kc1 Kf6 Ng1 Ke7 Kd1 Ke6
10/22 00:00 31k 7,811k +3.64 Kd2 Ke7 Nc1 Kf6 Ne2 Kf7 Ng1 Kf6 Kd1 Ke6 Ke2 Kd6 Kd2 Ke7
11/44 00:00 117k 10,592k +3.60 Kd2 Ke7 Nc1 Kf6 Kd1 Ke6 Ne2 Ke7 Kd2 Kf6 Kc2 Ke6 Kb2 Kf7 Ka2 Kf6
12/62 00:00 799k 11,092k +2.91 Kd1 Kd7 Nc1 Ke6 Ne2 Ke7 Ke1 Kd6 Ng1 Ke7 Nh3 Ke6 Kf1 Ke7 Kg2 Ke6 Nf2 Kd7 Nd1 Ke6
13/66 00:00 1,670k 12,104k +2.79 Kd2 Ke7 Kc2 Kf7 Kb1 Ke6 Kb2 Ke7 Nc1 Kd7 Kb1 Ke7 Ka1 Kd7 Ne2 Ke6 Kb1 Kf7 Ka2 Kf6 Ng1 Ke6 Kb2 Ke7
14/30 00:00 1,893k 12,210k +2.62 Kd1 Ke7 Nc1 Ke6 Ne2 Ke7 Kc1 Kf6 Ng1 Ke6 Kb2 Kf6 Ka1 Kf7 Nh3 Ke6 Kb1 Kf7 Kb2 Ke7 Nf2 Ke6 Kc1 Ke7
15/59 00:00 2,181k 12,119k +2.57 Kd2 Ke7 Kc2 Ke6 Nc1 Ke7 Kb1 Kd7 Kb2 Ke7 Ne2 Ke6 Ng1 Ke7 Nh3 Kf7 Nf2 Ke6 Ka2 Kd6 Kb1 Ke6 Kb2 Kd6 Nh3 Ke7 Kc2 Kf6 Kc1 Kf7
16/66 00:00 4,827k 14,073k +1.39 Kd2 Ke7 Kc2 Kf7 Kb1 Ke6 Kc1 Ke7 Kd2 Kf7 Kc2 Ke7 Nc1 Kf7 Kb2 Ke7 Kb1 Kd7 Ne2 Ke6 Kc2 Ke7 Ng1 Kf7 Kd2 Kf6 Nh3 Ke7
17/51 00:00 9,557k 15,668k +1.33 Kd2 Ke7 Kc1 Kd7 Kc2 Ke6 Nc1 Kd7 Ne2 Ke7 Kd2 Kd6 Ng1 Ke6 Ke1 Ke7 Nh3 Ke6 Nf2 Kf7 Nd1 Ke7 Nb2 Ke6
18/54 00:00 13,779k 16,078k +1.28 Kd2 Ke7 Nc1 Kf6 Ne2 Ke7 Ng1 Ke6 Nh3 Kf7 Nf2 Ke6 Nd1 Kd7 Nb2 Kd6 Kd1 Kd7 Ke1 Kd6 Kd2 Ke6 Na4 Kd6 Kc2 Kc6 Kb1 Kd6 Nb6 Ke6 Nd5 Kf7 Kb2 Ke6 Kc2 Kf7 Kd2 Ke6 Ke2 Kf7 Nc7 Ke7 Kd1 Kd7 Nb5 Ke6 Ke2 Kd7 Na7 Kd6 Kd1 Kd7
19/62 00:01 23,616k 17,051k 0.00 Kd1 Kd7 Nc1 Ke7 Kc2 Kf6 Kb1 Ke7
20/28 00:01 24,114k 17,066k 0.00 Kd1 Kd7 Nc1 Ke7 Kc2 Kf6 Kb1 Ke7
21/28 00:01 25,346k 17,137k 0.00 Kd1 Kd7 Nc1 Ke7 Kc2 Kf6 Kb1 Ke7
22/28 00:01 28,328k 17,294k 0.00 Kd1 Kd7 Nc1 Ke7 Kc2 Kf6 Kb1 Ke7
23/101 00:03 54,606k 16,771k 0.00 Kd1 Ke7 Nc1 Ke6 Ne2 Ke7
24/14 00:03 59,920k 16,912k 0.00 Kd1 Ke7 Nc1 Ke6 Ne2 Ke7
25/14+ 00:03 63,655k 17,020k +0.03 Kd1
25/52+ 00:03 63,795k 17,021k +0.08 Kd1
25/52+ 00:03 63,919k 17,018k +0.14 Kd1
25/68+ 00:03 64,746k 17,034k +0.23 Kd1
25/68+ 00:03 66,590k 17,066k +0.35 Kd1
25/68+ 00:03 67,171k 17,066k +1.03 Kd1
25/69+ 00:03 67,431k 17,058k +1.47 Kd1
25/87+ 00:04 68,329k 17,044k +2.03 Kd1
25/87+ 00:04 68,339k 17,042k +2.75 Kd1
25/87+ 00:04 68,364k 17,040k +3.68 Kd1
25/87+ 00:04 70,015k 16,912k +4.87 Kd2
25/87+ 00:04 70,028k 16,911k +6.37 Kd2
25/99 00:06 112,321k 16,685k +3.82 Kd2 Ke7 Nc1 Kd7 Kd1 Ke6 Ke1 Kf7 Kd2 Ke7 Ne2 Kd7 Ng1 Ke6 Ke1 Ke7 Kf1 Ke6 Nh3 Kf6 Nf2 Ke6 Ke2 Kd7 Ke1 Kd6 Nh3 Ke7 Kd2 Kf7 Nf2 Ke7 Nd1 Kd6 Ke2 Ke7 Ke1 Ke6 Nb2 Kd7
26/36+ 00:06 112,338k 16,682k +3.86 Kd2
26/36+ 00:06 112,351k 16,679k +3.90 Kd2
26/46+ 00:06 112,391k 16,675k +3.96 Kd2
26/46+ 00:06 112,416k 16,671k +4.05 Kd2
26/46+ 00:06 112,440k 16,670k +4.17 Kd2
26/71+ 00:06 112,529k 16,659k +4.86 Kd2
26/71+ 00:06 112,579k 16,656k +5.29 Kd2
26/71+ 00:06 112,649k 16,647k +5.85 Kd2
26/71+ 00:06 112,664k 16,647k +6.87 Kd2
26/71+ 00:06 112,793k 16,629k +7.80 Kd2
26/79- 00:07 117,917k 16,177k +3.77 Kd2 Ke7
26/96- 00:08 131,229k 15,245k +2.24 Kd2 Ke7
26/96- 00:13 216,538k 16,536k +0.34 Kd2 Ke7
26/96 00:13 218,833k 16,558k 0.00 Kd2 Ke7 Nc1 Kf7 Ne2 Ke6 Kc2 Ke7 Ng1 Kf7 Kc1 Ke7
27/16 00:13 227,584k 16,637k 0.00 Kd2 Ke7 Nc1 Kf7 Ne2 Ke6 Kc2 Ke7 Ng1 Kf7 Kc1 Ke7
28/16 00:14 233,807k 16,696k 0.00 Kd2 Ke7 Nc1 Kf7 Ne2 Ke6 Kc2 Ke7 Ng1 Kf7 Kc1 Ke7
29/16 00:15 264,172k 16,911k 0.00 Kd2 Ke7 Nc1 Kf7 Ne2 Ke6 Kc2 Ke7 Ng1 Kf7 Kc1 Ke7
30/16 00:18 318,023k 17,139k 0.00 Kd2 Ke7 Nc1 Kf7 Ne2 Ke6 Kc2 Ke7 Ng1 Kf7 Kc1 Ke7
31/20+ 00:20 349,330k 17,262k +0.46 Kb1
31/60+ 00:20 349,368k 17,262k +0.68 Kb1
31/60+ 00:20 349,396k 17,262k +1.47 Kb1
31/60+ 00:20 349,449k 17,261k +1.64 Kb1
31/64+ 00:20 349,499k 17,260k +1.89 Kb1
31/64+ 00:20 349,670k 17,258k +2.22 Kb1
31/64+ 00:20 349,700k 17,258k +2.65 Kb1
31/64+ 00:20 349,881k 17,256k +3.21 Kb1
31/64+ 00:20 350,475k 17,252k +3.94 Kb1
31/64+ 00:20 350,510k 17,251k +4.87 Kb1
31/64+ 00:20 350,744k 17,249k +6.05 Kb1
31/70+ 00:20 351,674k 17,246k +7.55 Kb1
31/101 00:27 488,679k 17,575k 0.00 Kb1 Ke7 Nc1 Kf7 Kc2 Ke7
32/16 00:33 588,967k 17,664k 0.00 Kb1 Ke7 Nc1 Kf7 Kc2 Ke7
33/16 00:36 640,867k 17,701k 0.00 Kb1 Ke7 Nc1 Kf7 Kc2 Ke7
34/16 00:40 710,719k 17,753k 0.00 Kb1 Ke7 Nc1 Kf7 Kc2 Ke7
35/16 00:47 845,954k 17,876k 0.00 Kb1 Ke7 Nc1 Kf7 Kc2 Ke7
36/16 00:53 958,667k 17,902k 0.00 Kb1 Ke7 Nc1 Kf7 Kc2 Ke7
37/40+ 01:00 1,092,101k 17,920k +0.14 Kb1
37/40+ 01:00 1,092,138k 17,919k +0.23 Kb1
37/40+ 01:00 1,092,305k 17,918k +0.35 Kb1
37/40+ 01:00 1,092,473k 17,916k +1.41 Kb1
37/58+ 01:01 1,092,974k 17,912k +1.65 Kb1
37/58+ 01:01 1,093,249k 17,910k +1.98 Kb1
37/58+ 01:01 1,093,521k 17,907k +2.41 Kb1
37/58+ 01:01 1,094,624k 17,898k +2.98 Kb1
37/58+ 01:01 1,096,787k 17,881k +3.70 Kb1
37/104+ 01:01 1,098,669k 17,860k +4.63 Kb1
37/104+ 01:01 1,099,885k 17,854k +5.81 Kb1
37/104+ 01:02 1,106,952k 17,803k +7.31 Kb1
37/118+ 08:01 5,538,501k 11,505k +9.21 Kb1
37/122+ 09:35 6,270,509k 10,892k +11.61 Kb1
37/130 12:05 7,562,840k 10,427k +12.63 Kb1 Kd7 Nc1 Ke6 Ka2 Kf7 Ne2 Ke7 Kb2 Ke6 Kc1 Kf7 Kb1 Kf6 Ng1 Ke6 Nh3 Ke7 Kc1 Ke6 Kd2 Ke7 Nf2 Ke6 Nd1 Kd7 Nb2 Kd6 Na4 Kc6 Ke2 Kd6 Nb6 Ke6 Ke1 Ke7 Kd2 Ke6 Kc2 Ke7 Nd5+ Kf7 Nc7 Ke7 Kd1 Kd7 Nb5 Ke6 Na3 Kd7 Nc2 Ke6 Ne1 Kd7 Ng2 Ke7 Ke2 Ke6 Kf1 Kf6 Ke1 Ke6 Nh4 Kf7 Nf5 Kg8 Kd2 Kh8 Nxh6
38/96+ 12:10 7,623,015k 10,430k +12.67 Kb1
38/104+ 12:11 7,627,904k 10,427k +12.72 Kb1
38/104+ 12:11 7,627,944k 10,427k +12.78 Kb1
38/118- 15:33 9,111,101k 9,761k +12.59 Kb1 Kd7
38/118- 16:11 9,563,267k 9,848k +12.47 Kb1 Kd7
38/118+ 16:28 9,767,244k 9,884k +12.60 Kb1
38/121 17:26 10,315,180k 9,857k +12.62 Kb1 Kd7 Nc1 Ke7 Kc2 Ke6 Kd2 Kf6 Ke1 Ke7 Ne2 Kd6 Ng1 Ke6 Kf1 Ke7 Nh3 Ke6 Ke2 Ke7 Kd2 Ke6 Kd1 Ke7 Kc2 Ke6 Kb1 Ke7 Ka1 Ke6 Ng1 Ke7 Kb2 Kf7 Nh3 Ke6 Ka1 Ke7 Ng1 Ke6 Ka2 Kf6 Nh3 Ke7 Nf2 Ke6 Kb1 Ke7 Nd1 Kd7 Nb2 Kc6 Na4 Kd6 Kc2 Kc6 Kd1 Kd6 Nb6 Ke6 Kc2 Ke7 Nc8+ Kd7 Na7 Kd6 Kd2 Kd7 Nb5 Ke7 Na3 Kd7 Nc2 Ke7 Ne1 Kd7 Ng2 Ke7 Ke2 Kf7 Nh4 Ke6 Ke1 gxh4 Kf1 Kf6 Kg2 Ke6 Kh3 Kf7 Kxh4 Kg8 g5 Kg7



Black to move and Mate
[d]2r3k1/5rp1/p3p2p/1pq2p2/4nQN1/3R2P1/PP2PP1P/5RK1 b - - 0 1

[Dann Corbit]

For the first problem, the right engines solve it fairly quickly.
For the second problem, I assume there must be an esoteric mate of some kind with a move other than Ng5. The "problem" here is that Ng5 wins very easily so all the engines I tried are drawn to it like a magnet. LC0, for instance, found an advantage of +8 full pawns instantly, and after a reasonable time had a queen advantage (still rapidly rising, so it is not a stalemate):
[d]2r3k1/5rp1/p3p2p/1pq2p2/4nQN1/3R2P1/PP2PP1P/5RK1 b - - acd 19/47; acn 26767k; ce 969; bm Ng5; pv Ng5 Nxh6+ gxh6 Kg2 e5 Qd2 Qc2 Rd1 Qxd2 R3xd2 Ne4 Rd8+ Rf8 R8d7 Rc2 Kf1 Rxb2 Ra7 Nd2+ Ke1 Rd8 Rxa6 Rd4 Ra7 Nc4 a4 Rxd1+ Kxd1 Ra2 Ra8+ Kf7 Ra7+ Ke8 Ra8+ Kd7 Ra7+ Kc8 Ra6 Rxa4 Rxh6 Kc7 Kc2;

I do not see any defect in the engines that instantly find a winning move, even if there is a faster win. Finding the shortest mate is the job of a mate finder, not a chess playing engine.

Now, here I will agree that the mate finding engines might need some work due to the following:
There are no SMP dedicated mate finders (other than chess engines with a mate finding mode, but that is not the same thing)
There are no mate finders that know how to use a GPU, and a depth first proof number search run on a GPU would make a devastating mate finder.

I suppose that the reason we have no mate finders with either of those capabilities is that nobody cares enough to write one.

[Chessqueen]

For the first problem, the right engines solve it fairly quickly.
For the second problem, I assume there must be an esoteric mate of some kind with a move other than Ng5. The "problem" here is that Ng5 wins very easily so all the engines I tried are drawn to it like a magnet. LC0, for instance, found an advantage of +8 full pawns instantly, and after a reasonable time had a queen advantage (still rapidly rising, so it is not a stalemate):
[d]2r3k1/5rp1/p3p2p/1pq2p2/4nQN1/3R2P1/PP2PP1P/5RK1 b - - acd 19/47; acn 26767k; ce 969; bm Ng5; pv Ng5 Nxh6+ gxh6 Kg2 e5 Qd2 Qc2 Rd1 Qxd2 R3xd2 Ne4 Rd8+ Rf8 R8d7 Rc2 Kf1 Rxb2 Ra7 Nd2+ Ke1 Rd8 Rxa6 Rd4 Ra7 Nc4 a4 Rxd1+ Kxd1 Ra2 Ra8+ Kf7 Ra7+ Ke8 Ra8+ Kd7 Ra7+ Kc8 Ra6 Rxa4 Rxh6 Kc7 Kc2;

I do not see any defect in the engines that instantly find a winning move, even if there is a faster win. Finding the shortest mate is the job of a mate finder, not a chess playing engine.

Now, here I will agree that the mate finding engines might need some work due to the following:
There are no SMP dedicated mate finders (other than chess engines with a mate finding mode, but that is not the same thing)
There are no mate finders that know how to use a GPU, and a depth first proof number search run on a GPU would make a devastating mate finder.

I suppose that the reason we have no mate finders with either of those capabilities is that nobody cares enough to write one.

You are correct Mr. Corbit, the 1st problem Black Diamond and Crystal break though the pawn chain very easy after maneuvering the White knight and White King several times until the Black King is in the correct square, but it seems that it takes forever to show Mate in X moves, and I mean hours. So my question is which is the best engine to solve these type of position especially to find mate in the 1st problem, so we need a good Mate finder

For us human we know how to break trough and eventually win when we have an extra piece, but for engines it is NOT so easy

[pgn][Event "Computer chess game"]
[Site "MININT-UB2PIMJ"]
[Date "2021.04.26"]
[Round "?"]
[White "Chessqueen"]
[Black "Stockfish 13"]
[Result "1-0"]
[BlackElo "3475"]
[SetUp "1"]
[FEN "3k4/8/7p/2p1p1pP/1pPpPpP1/1P1P1P2/N7/2K5 w - - 0 1"]
[Time "08:21:52"]
[WhiteElo "2000"]
[TimeControl "600+1"]
[Termination "unterminated"]
[PlyCount "6"]
[WhiteType "human"]
[BlackType "program"]


1. Kb2 Ke7 2. Nc1 Kf8 3. Ne2 Ke7 4. Ng1 Ke8 5. Nh3 Kf8 6. Nf2 Ke7 7. Ka2
Ke6 8. Nd1 Ke7 9. Nb2 Ke6 10. Na4 Kd6 11. Kb2 Kc6 12. Ka2 Kd6 13. Nb6 Ke7
14. Nd5+ Ke6 15. Kb2 Kf7 16. Kc1 Ke6 17. Kd1 Kf7 18. Nc7 Ke7 19. Nb5 Ke6
20. Na3 Kd6 21. Nc2 Ke7 22. Ke2 Ke8 23. Ne1 Kf7 24. Kf2 Kg7 25. Ng2 Kf7 26.
Kg1 Kg7 27. Kh2 Kf6 28. Kh3 Kg7 29. Nh4 gxh4 30. Kxh4 Kf6 31. g5+ hxg5+ 32.
Kg4 Kg7 33. Kxg5 Kh7 34. Kf5 Kh6 35. Kxe5 Kxh5 36. Kxf4 Kh6 37. Kf5 Kg7
38. Ke5 Kg6 39. f4 Kh5 40. f5 Kh6 41. Ke6 Kg5 42. f6 Kf4 43. f7 Ke3
44. f8=Q Kxd3 45. Qf3+ Kc2 46. e5 d3 47. Kd7 d2 48. e6 d1=Q+
49. Qxd1+ Kxd1 {Black resigns} 1-0[/pgn]

[Dann Corbit]

If your chess engine/mate finder can resolve a mate in 2 in one thousandth of a second, it could solve a mate in 28 in 11 hours, assuming a branching factor of 1.4, and there is no zugzwang, and the move ordering is perfect, and the proportionality of the constant is 1.0

In other words, solutions to really deep mates (like the mate in 50 that you mentioned) are really special cases when they do happen and we should not expect problems like that to be solved in a "reasonable" time unless you mean several days or even several weeks.

I have many mates deeper than 100 in my database. In fact, this query:
select count(*) from Epd where dm >= 100
gives 7365 as the result.

Whereas this query:
select max(acs) from Epd where dm >= 0
gives 149004 as the result, which is 1.72 days.
Further, I have tried using chest319 to verify a mate in 13 as minimal and after one week it had not come to a conclusion and I gave up.

I remember in 1989 we used to joke about a computer announcing a mate in 20 as some fanciful future event (and except for special endgames, it was a fanciful future event).

The solutions engines and mate solvers give us today are really miraculous.
I suppose it boils down to this:
(Ecclesiastes 5:10)  A lover of silver will never be satisfied with silver, nor a lover of wealth with income. This too is futility.

So we humans always want more. No matter how much we have.

[Dann Corbit]

That would be pow(1.4,(28-2) moves x 2 plies/move)) = pow(1.4, 52) = 39,687,875.83 times as long = 39,687.9 seconds, or .46 days or 11 hours.