Consider the following premises. For all x_8, if x_8 were a janitor, then x_8 is excited. For all x_8, if x_8 reads a book, then x_8 is excited. For all x_8, if x_8 were fast, then x_8 is not excited. For all x_8, x_8 is fast or x_8 will listen to a song. For all x_8, x_8 is a janitor or x_8 will read a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will listen to a song.
 From the fact that for all x_8, if x_8 were a janitor, then x_8 is excited, that for all x_8, if x_8 reads a book, then x_8 is excited, and that for all x_8, x_8 is a janitor or x_8 will read a book we can infer that for all x_8, x_8 is excited via universal disjunction elimination. From the fact that for all x_8, if x_8 were fast, then x_8 is not excited, and that for all x_8, x_8 is excited we can infer that for all x_8, x_8 is not fast via universal modus tollens. Finally, from the fact that for all x_8, x_8 is fast or x_8 will listen to a song, and that for all x_8, x_8 is not fast we can infer that for all x_8, x_8 will listen to a song via universal disjunctive syllogism. Therefore, the answer is yes.