Consider the following premises. For all x_13, x_13 will not read a book. There is at least one x_13 for which x_13 will read a book or x_13 will sleep. For all x_13, if x_13 sleeps, then x_13 is a janitor. For all x_13, if x_13 listens to a song, then x_13 is not a janitor. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 will listen to a song.
 From the fact that there is at least one x_13 for which x_13 will read a book or x_13 will sleep, and that for all x_13, x_13 will not read a book we can infer that there is at least one x_13 for which x_13 will sleep via existential disjunctive syllogism. From the fact that for all x_13, if x_13 sleeps, then x_13 is a janitor, and that there is at least one x_13 for which x_13 will sleep we can infer that there is at least one x_13 for which x_13 is a janitor via existential modus ponens. Finally, from the fact that for all x_13, if x_13 listens to a song, then x_13 is not a janitor, and that there is at least one x_13 for which x_13 is a janitor we can infer that there is at least one x_13 for which x_13 will not listen to a song via existential modus tollens, which contradicts that For all x_13, x_13 will listen to a song. Therefore, the answer is no.