Consider the following premises. For all x_8, x_8 will read a book if and only if x_8 is a lawyer. There is at least one x_8 for which if x_8 listens to a song, then x_8 is not reading a book. For all x_8, x_8 will drink water or x_8 is a lawyer. For all x_8, if x_8 drinks water, then x_8 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will not listen to a song.
 From the fact that for all x_8, x_8 will read a book if and only if x_8 is a lawyer we can infer that for all x_8, if x_8 were a lawyer, then x_8 is reading a book via universal biconditional elimination. From the fact that for all x_8, if x_8 drinks water, then x_8 is reading a book, that for all x_8, if x_8 were a lawyer, then x_8 is reading a book, and that for all x_8, x_8 will drink water or x_8 is a lawyer we can infer that for all x_8, x_8 will read a book via universal disjunction elimination. Finally, from the fact that there is at least one x_8 for which if x_8 listens to a song, then x_8 is not reading a book, and that for all x_8, x_8 will read a book we can infer that there is at least one x_8 for which x_8 will not listen to a song via existential modus tollens. Therefore, the answer is yes.