Program to solve positions Are there any programs out there that take a completely won position and compute the minimum checkmate depth (say if it is around 50 moves)?
You need to use mate search function of a chess engine.

Some engines have this function, for example, Houdini 4: http://www.cruxis.com/chess/manual/index.html?game_play.htm

You can activate it using UCI parameters, or more easily, using a Fritz GUI on Windows as it has a mate search button, which makes life easier.