Position legality issue, pls. help

I wonder if there is an outright proof that this position is illegal:

It is illegal, there isn't a single move white could have done to get into that position, unless black was in check after his move. The only place the rook giving check could have come from is b4, where it would still have been giving check. A discovered check by moving the bishop from b4 to a5 wouldn't have been legal because check would have been given by the b6 rook after black's last turn

What I see in this position is that both sides have four promoted pieces ( black has one pawn in addition ). This for me does not exclude the possibility that the position may be legal.

I know that to establish the legality of a position is a science in its own right that is why I ask for the opinion of experts in the field whether there is some hidden feature of this position which makes it unreachable through a series of legal moves from the conventional starting position.

Why couldn't white have played Bc5?

It took a while to create a proof game (and it most certainly is not the most efficient way to get here), but the position is legal:

Legal AND Black wins....Yes white could have played Bb4 to C5, revealing the rooks check.  Black WINS this game after his only legal move Nd6xc4 revealing a checkmate on the white king.

You sir, are awesome! *bows in awe*

Thanks a lot. I really admire how you can come up with such a complicated game in this short amount of time.

In fact this is a 'self-solving puzzle' ( which means that there is only one legal move by each side in each position up to mate ) with the restriction that there should be three consecutive knight moves by one side. I posted this puzzle in the thread http://www.chess.com/forum/view/more-puzzles/self-solving-puzzles . I could engine test the solution itself but was not absolutely sure if the starting position was legal. Your post gave me real confidence in my problem.

1. ... Ndxc4+ is actually not mate because white has 2. Bxd8+.

For some reason I don't think this position is legal :). But I'm in trouble as to exactly why...

Of course it's legal... after all of the pieces were captured, both white and black demoted their kings into white pawns.

... oh, yeah, and black had to promote his a pawn to something and then demote it back to a pawn somewhere else.

I stand corrected! Though black still wins there are a few more forced moves until mate it is achieved. I took care to not make a mistake this time. Black wins after ...Nxc4+ Bxd8+ Na5+ Bxb3+ Nxb3 mate.

brilliant puzzle