Consider the following premises. For all x_11, if x_11 plays tennis, then x_11 is drinking water. For all x_11, if x_11 were a doctor, then x_11 is playing tennis. For all x_11, x_11 will cook if and only if x_11 will read a book. For all x_11, x_11 will drink water if and only if x_11 will read a book. For all x_11, x_11 will not cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is not a doctor.
 From the fact that for all x_11, x_11 will cook if and only if x_11 will read a book, and that for all x_11, x_11 will not cook we can infer that for all x_11, x_11 will not read a book via universal biconditional elimination. From the fact that for all x_11, x_11 will drink water if and only if x_11 will read a book, and that for all x_11, x_11 will not read a book we can infer that for all x_11, x_11 will not drink water via universal biconditional elimination. From the fact that for all x_11, if x_11 plays tennis, then x_11 is drinking water, and that for all x_11, x_11 will not drink water we can infer that for all x_11, x_11 will not play tennis via universal modus tollens. Finally, from the fact that for all x_11, if x_11 were a doctor, then x_11 is playing tennis, and that for all x_11, x_11 will not play tennis we can infer that for all x_11, x_11 is not a doctor via universal modus tollens. Therefore, the answer is yes.