Consider the following premises. For all x_6, if x_6 drinks water, then x_6 is cooking. For all x_6, x_6 will drink water or x_6 will not listen to a song. For all x_6, x_6 will not cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not listen to a song.
 From the fact that for all x_6, x_6 will drink water or x_6 will not listen to a song we can infer that for all x_6, if x_6 listens to a song, then x_6 is drinking water via universal rewriting. From the fact that for all x_6, if x_6 listens to a song, then x_6 is drinking water, and that for all x_6, if x_6 drinks water, then x_6 is cooking we can infer that for all x_6, if x_6 listens to a song, then x_6 is cooking via universal transitivity. Finally, from the fact that for all x_6, if x_6 listens to a song, then x_6 is cooking, and that for all x_6, x_6 will not cook we can infer that for all x_6, x_6 will not listen to a song via universal modus tollens. Therefore, the answer is yes.