Is white really winning here?

[Pafifi]

[pgn]
[FEN "7k/8/7K/p1P1p1p1/P4n2/3rN1p1/5r2/3R2B1 w - - 0 1"]
1. Rxd3 Nxd3 2. Bxf2 Nxc5 3. Bg1 Kg8
[/pgn]
A friend of mine designed a puzzle that was said to be very difficult. I used Stockfish and Sting SF to analyze for a long time only to get a draw. Can White really win? The given moves are hints that are not necessarily right.

[peter]

[pgn]
[FEN "7k/8/7K/p1P1p1p1/P4n2/3rN1p1/5r2/3R2B1 w - - 0 1"]
1. Rxd3 Nxd3 2. Bxf2 Nxc5 3. Bg1 Kg8
[/pgn]
A friend of mine designed a puzzle that was said to be very difficult. I used Stockfish and Sting SF to analyze for a long time only to get a draw. Can White really win? The given moves are hints that are not necessarily right.

Maybe I haven't found the special point till now, but after the given moves I don't find a winning line. If Black fails with 3...Nxa4 (?) instead of ...Kg8, there is one, made with with MateFinder here:

7k/8/7K/p1P1p1p1/P4n2/3rN1p1/5r2/3R2B1 w - - 0 1

1. Rxd3 Nxd3 2. Bxf2 Nxc5 3. Bg1 Nxa4 (?)

4. Nd1 Kg8 5. Kg6 e4 6. Bd4 g2 7. Bg1 Kh8
8. Be3 g4 9. Ba7 g3 10. Be3 Kg8 11. Bd4 Kf8 12. Kf6 Ke8 13. Ke6 Kd8 14. Kd6 Ke8
15. Kc6 g1=Q 16. Bxg1 g2 17. Kb5 e3 18. Bxe3

At the end it's #34.
Output after 3...Nxa4(?):

[d]7k/8/7K/p3p1p1/n7/4N1p1/8/6B1 w - - 0 1
Analysis by MateFinder 040120 64:

4.Nd1 Kg8 5.Kg6 e4 6.Bd4 e3 7.Bxe3 Kh8 8.Bg1 Kg8 9.Kf6 Kh7 10.Ke5 Kg6 11.Kd5 Kh5 12.Kc4 Kg4 13.Kb5 Nb2 14.Nxb2 Kf3 15.Nd1 Kg2 16.Bb6 Kf1 17.Ne3+ Ke2 18.Ka4 Kf3 19.Kxa5 Ke2 20.Nc4 Kf3 21.Kb5 Ke2 22.Kc5 Ke1 23.Kd5 g2 24.Kc6 Ke2 25.Kb5 g4 26.Kb4 g3 27.Kc3 Kf3 28.Bg1 Kf4 29.Kb4 Kg5
+- (64.83) Depth: 51/57 00:01:19 3634MN

If Black doesnt blunder with 3...Nxa4(?), I don't see White win.
Any ideas anybody?

Maybe your friend should just start the puzzle from position after 3 moves?

[mmt]

SF11 with 6-men EGTB is sure it's a draw.

[Pafifi]

My foolish friend admitted his mistake. This one shall be winning.
[d]7k/8/7K/p1P1p1p1/B7/3nN1p1/5r2/6B1 w - - 0 1

[mmt]

Interesting, Matefinder doesn't find a mate at depth 33 for this position either but SF11 does at depth 38.