If you wish to see a particularly deep game of chess between mankind and an artificial super intelligence, then the 1969 movie "Colossus: the Forbin Project" is a must-watch. Not for blinding special effects, but because of the masterful script that makes this movie into a masterpiece.
But personally, I feel any superintelligence would not be all that blunt about its intentions to foist its solution onto the human population. Much more likely, the smart programming will discover mankind's desire to have free will way before humans discovered its presence, and would know that secrecy and gentle coercion work way better.
