Consider the following premises. For all x_5, if x_5 sleeps, then x_5 is a janitor. For all x_5, if x_5 reads a book, then x_5 is bored. For all x_5, x_5 will read a book. For all x_5, if x_5 were bored, then x_5 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is not a janitor.
 From the fact that for all x_5, if x_5 reads a book, then x_5 is bored, and that for all x_5, x_5 will read a book we can infer that for all x_5, x_5 is bored via universal modus ponens. From the fact that for all x_5, if x_5 were bored, then x_5 is sleeping, and that for all x_5, if x_5 sleeps, then x_5 is a janitor we can infer that for all x_5, if x_5 were bored, then x_5 is a janitor via universal transitivity. Finally, from the fact that for all x_5, if x_5 were bored, then x_5 is a janitor, and that for all x_5, x_5 is bored we can infer that for all x_5, x_5 is a janitor via universal modus ponens, which contradicts that There is at least one x_5 for which x_5 is not a janitor. Therefore, the answer is no.