Consider the following premises. For all y_4, if y_4 listens to a song, then y_4 is sleeping. For all y_4, y_4 will not work. For all y_4, if y_4 sleeps, then y_4 is listening to a song. For all y_4, y_4 will sleep if and only if y_4 will work. Can we infer the following from them? If we can, name the inference rule being used: For all y_4, y_4 will not work.
That is one of the premises. Therefore, the answer is yes.