Consider the following premises. For all x_7, x_7 will read a book and x_7 is a nurse. For all x_7, if x_7 drinks water, then x_7 is not reading a book. There is at least one x_7 for which if x_7 were a lawyer, then x_7 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 is not a lawyer.
 From the fact that for all x_7, x_7 will read a book and x_7 is a nurse we can infer that for all x_7, x_7 will read a book via universal simplification. From the fact that for all x_7, if x_7 drinks water, then x_7 is not reading a book, and that for all x_7, x_7 will read a book we can infer that for all x_7, x_7 will not drink water via universal modus tollens. Finally, from the fact that there is at least one x_7 for which if x_7 were a lawyer, then x_7 is drinking water, and that for all x_7, x_7 will not drink water we can infer that there is at least one x_7 for which x_7 is not a lawyer via existential modus tollens. Therefore, the answer is yes.