Consider the following premises. For all x_6, x_6 will work if and only if x_6 is poor. For all x_6, if x_6 drinks water, then x_6 is not listening to a song. For all x_6, x_6 will listen to a song. For all x_6, if x_6 works, then x_6 is drinking water. Can we infer the following from them? For all x_6, x_6 is not poor.
 From the fact that for all x_6, if x_6 drinks water, then x_6 is not listening to a song, and that for all x_6, x_6 will listen to a song we can infer that for all x_6, x_6 will not drink water. From the fact that for all x_6, if x_6 works, then x_6 is drinking water, and that for all x_6, x_6 will not drink water we can infer that for all x_6, x_6 will not work. Finally, from the fact that for all x_6, x_6 will work if and only if x_6 is poor, and that for all x_6, x_6 will not work we can infer that for all x_6, x_6 is not poor. Therefore, the answer is yes.