Consider the following premises. For all x_17, x_17 will drink water if and only if x_17 will drive a car. For all x_17, if x_17 were excited, then x_17 is fast. For all x_17, x_17 is not fast. There is at least one x_17 for which if x_17 plays tennis, then x_17 is driving a car. For all x_17, if x_17 drinks water, then x_17 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_17, x_17 will play tennis.
 From the fact that for all x_17, x_17 will drink water if and only if x_17 will drive a car we can infer that for all x_17, if x_17 drives a car, then x_17 is drinking water via universal biconditional elimination. From the fact that for all x_17, if x_17 drives a car, then x_17 is drinking water, and that for all x_17, if x_17 drinks water, then x_17 is excited we can infer that for all x_17, if x_17 drives a car, then x_17 is excited via universal transitivity. From the fact that there is at least one x_17 for which if x_17 plays tennis, then x_17 is driving a car, and that for all x_17, if x_17 drives a car, then x_17 is excited we can infer that there is at least one x_17 for which if x_17 plays tennis, then x_17 is excited via existential transitivity. From the fact that for all x_17, if x_17 were excited, then x_17 is fast, and that for all x_17, x_17 is not fast we can infer that for all x_17, x_17 is not excited via universal modus tollens. Finally, from the fact that there is at least one x_17 for which if x_17 plays tennis, then x_17 is excited, and that for all x_17, x_17 is not excited we can infer that there is at least one x_17 for which x_17 will not play tennis via existential modus tollens, which contradicts that For all x_17, x_17 will play tennis. Therefore, the answer is no.