Consider the following premises. For all y_2, y_2 will not sleep. For all y_2, if y_2 were a bartender, then y_2 is sleeping. For all y_2, y_2 will listen to a song if and only if y_2 is a bartender. Can we infer the following from them? For all y_2, y_2 will not listen to a song.
 From the fact that for all y_2, if y_2 were a bartender, then y_2 is sleeping, and that for all y_2, y_2 will not sleep we can infer that for all y_2, y_2 is not a bartender. Finally, from the fact that for all y_2, y_2 will listen to a song if and only if y_2 is a bartender, and that for all y_2, y_2 is not a bartender we can infer that for all y_2, y_2 will not listen to a song. Therefore, the answer is yes.