Consider the following premises. For all x_12, if x_12 were excited, then x_12 is a police officer. There is at least one x_12 for which if x_12 were sad, then x_12 is not playing squash. For all x_12, if x_12 climbs a mountain, then x_12 is excited. For all x_12, if x_12 drinks water, then x_12 is excited. For all x_12, if x_12 were a police officer, then x_12 is playing squash. For all x_12, x_12 will drink water or x_12 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, x_12 is sad.
 From the fact that for all x_12, if x_12 drinks water, then x_12 is excited, that for all x_12, if x_12 climbs a mountain, then x_12 is excited, and that for all x_12, x_12 will drink water or x_12 will climb a mountain we can infer that for all x_12, x_12 is excited via universal disjunction elimination. From the fact that for all x_12, if x_12 were excited, then x_12 is a police officer, and that for all x_12, if x_12 were a police officer, then x_12 is playing squash we can infer that for all x_12, if x_12 were excited, then x_12 is playing squash via universal transitivity. From the fact that for all x_12, if x_12 were excited, then x_12 is playing squash, and that for all x_12, x_12 is excited we can infer that for all x_12, x_12 will play squash via universal modus ponens. Finally, from the fact that there is at least one x_12 for which if x_12 were sad, then x_12 is not playing squash, and that for all x_12, x_12 will play squash we can infer that there is at least one x_12 for which x_12 is not sad via existential modus tollens, which contradicts that For all x_12, x_12 is sad. Therefore, the answer is no.