Leonard (2010)

The story is both a mystery in terms of plot and identity. Two unknown characters escape from an extreme situation and somehow find themselves together in a room which they both have the specific key to unlock it. When questioning each others identity, both the men have the same name (Leonard) as well as the same appearance. As they both fight each other is desperation, everything seems fixed as both the key to the room and note on the table have these two Leonard's killing each other, for whatever secret they are holding.