Consider the following premises. For all y, y will play a game if and only if y will listen to a song. There is at least one y for which if y plays a game, then y is listening to a song. For all y, y will listen to a song or y will not read a book. Can we infer the following from them? If we can, name the inference rule being used: For all y, the fact that y reads a book does not imply that y is playing a game.
That contradicts the premises. Therefore the answer is no.