Consider the following premises. For all x_3, if x_3 climbs a mountain, then x_3 is playing tennis. For all x_3, x_3 will climb a mountain and x_3 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 will not play tennis.
 From the fact that for all x_3, x_3 will climb a mountain and x_3 is a police officer we can infer that for all x_3, x_3 will climb a mountain via universal simplification. Finally, from the fact that for all x_3, if x_3 climbs a mountain, then x_3 is playing tennis, and that for all x_3, x_3 will climb a mountain we can infer that for all x_3, x_3 will play tennis via universal modus ponens, which contradicts that There is at least one x_3 for which x_3 will not play tennis. Therefore, the answer is no.