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