Consider the following premises. For all x_5, x_5 is not a police officer. For all x_5, if x_5 were happy, then x_5 is a police officer. For all x_5, if x_5 listens to a song, then x_5 is cooking. For all x_5, x_5 will cook if and only if x_5 is happy. Can we infer the following from them? For all x_5, x_5 will not listen to a song.
 From the fact that for all x_5, if x_5 were happy, then x_5 is a police officer, and that for all x_5, x_5 is not a police officer we can infer that for all x_5, x_5 is not happy. From the fact that for all x_5, x_5 will cook if and only if x_5 is happy, and that for all x_5, x_5 is not happy we can infer that for all x_5, x_5 will not cook. Finally, from the fact that for all x_5, if x_5 listens to a song, then x_5 is cooking, and that for all x_5, x_5 will not cook we can infer that for all x_5, x_5 will not listen to a song. Therefore, the answer is yes.