Consider the following premises. For all x_13, if x_13 were a writer, then x_13 is reading a book. For all x_13, if x_13 reads a book, then x_13 is making tea. For all x_13, if x_13 were a janitor, then x_13 is a writer. For all x_13, x_13 will not make tea. For all x_13, if x_13 were a writer, then x_13 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 is not a janitor.
 From the fact that for all x_13, if x_13 were a janitor, then x_13 is a writer, and that for all x_13, if x_13 were a writer, then x_13 is a janitor we can infer that for all x_13, x_13 is a janitor if and only if x_13 is a writer via universal biconditional introduction. From the fact that for all x_13, if x_13 reads a book, then x_13 is making tea, and that for all x_13, x_13 will not make tea we can infer that for all x_13, x_13 will not read a book via universal modus tollens. From the fact that for all x_13, if x_13 were a writer, then x_13 is reading a book, and that for all x_13, x_13 will not read a book we can infer that for all x_13, x_13 is not a writer via universal modus tollens. From the fact that for all x_13, x_13 is a janitor if and only if x_13 is a writer we can infer that for all x_13, if x_13 were a janitor, then x_13 is a writer via universal biconditional elimination. Finally, from the fact that for all x_13, if x_13 were a janitor, then x_13 is a writer, and that for all x_13, x_13 is not a writer we can infer that for all x_13, x_13 is not a janitor via universal modus tollens. Therefore, the answer is yes.