Consider the following premises. For all x_10, x_10 will go running or x_10 is a musician. For all x_10, x_10 will cook or x_10 will sleep. For all x_10, x_10 will not go running. For all x_10, if x_10 cooks, then x_10 is not a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will sleep or x_10 will listen to a song.
 From the fact that for all x_10, x_10 will go running or x_10 is a musician, and that for all x_10, x_10 will not go running we can infer that for all x_10, x_10 is a musician via universal disjunctive syllogism. From the fact that for all x_10, if x_10 cooks, then x_10 is not a musician, and that for all x_10, x_10 is a musician we can infer that for all x_10, x_10 will not cook via universal modus tollens. From the fact that for all x_10, x_10 will cook or x_10 will sleep, and that for all x_10, x_10 will not cook we can infer that for all x_10, x_10 will sleep via universal disjunctive syllogism. Finally, from the fact that for all x_10, x_10 will sleep we can infer that for all x_10, x_10 will sleep or x_10 will listen to a song via universal addition. Therefore, the answer is yes.