Consider the following premises. For all x_10, x_10 is curious if and only if x_10 will drink water. For all x_10, x_10 will drink water. For all x_10, if x_10 climbs a mountain, then x_10 is curious. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which neither x_10 is curious nor x_10 is a police officer.
 From the fact that for all x_10, x_10 is curious if and only if x_10 will drink water we can infer that for all x_10, if x_10 drinks water, then x_10 is curious via universal biconditional elimination. From the fact that for all x_10, x_10 will drink water we can infer that for all x_10, x_10 will drink water or x_10 will climb a mountain via universal addition. From the fact that for all x_10, if x_10 drinks water, then x_10 is curious, that for all x_10, if x_10 climbs a mountain, then x_10 is curious, and that for all x_10, x_10 will drink water or x_10 will climb a mountain we can infer that for all x_10, x_10 is curious via universal disjunction elimination. Finally, from the fact that for all x_10, x_10 is curious we can infer that for all x_10, x_10 is curious or x_10 is a police officer via universal addition, which contradicts that There is at least one x_10 for which neither x_10 is curious nor x_10 is a police officer. Therefore, the answer is no.