Consider the following premises. For all x_8, x_8 is a carpenter or x_8 will play squash. For all x_8, x_8 is not a carpenter. For all x_8, if x_8 plays tennis, then x_8 is listening to a song. For all x_8, x_8 will sleep or x_8 will play tennis. For all x_8, if x_8 sleeps, then x_8 is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will play squash and x_8 will listen to a song.
 From the fact that for all x_8, if x_8 sleeps, then x_8 is listening to a song, that for all x_8, if x_8 plays tennis, then x_8 is listening to a song, and that for all x_8, x_8 will sleep or x_8 will play tennis we can infer that for all x_8, x_8 will listen to a song via universal disjunction elimination. From the fact that for all x_8, x_8 is a carpenter or x_8 will play squash, and that for all x_8, x_8 is not a carpenter we can infer that for all x_8, x_8 will play squash via universal disjunctive syllogism. Finally, from the fact that for all x_8, x_8 will play squash, and that for all x_8, x_8 will listen to a song we can infer that for all x_8, x_8 will play squash and x_8 will listen to a song via universal conjunction. Therefore, the answer is yes.