Consider the following premises. For all y, if y were fast, then y is sad. There is at least one y for which if y were sad, then y is playing a game. For all y, y will play a game if and only if y is fast. Can we infer the following from them? If we can, name the inference rule being used: For all y, if is not true that y is fast if and only if y will play a game.
That contradicts the premises. Therefore the answer is no.