Consider the following premises. There is at least one y for which if y works, then y is playing a game. For all y, if y plays a game, then y is reading a book. For all y, y will cook if and only if y will 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 works does not imply that y is cooking.
That contradicts the premises. Therefore the answer is no.