Consider the following premises. For all x_2, x_2 will listen to a song. There is at least one x_2 for which x_2 will sleep if and only if x_2 is poor. For all x_2, if x_2 were poor, then x_2 is not listening to a song. Can we infer the following from them? There is at least one x_2 for which x_2 will not sleep.
 From the fact that for all x_2, if x_2 were poor, then x_2 is not listening to a song, and that for all x_2, x_2 will listen to a song we can infer that for all x_2, x_2 is not poor. Finally, from the fact that there is at least one x_2 for which x_2 will sleep if and only if x_2 is poor, and that for all x_2, x_2 is not poor we can infer that there is at least one x_2 for which x_2 will not sleep. Therefore, the answer is yes.