Consider the following premises. For all x_9, if x_9 drinks water, then x_9 is climbing a mountain. For all x_9, x_9 will drink water or x_9 will work. For all x_9, if x_9 climbs a mountain, then x_9 is drinking water. For all x_9, x_9 will not climb a mountain. Can we infer the following from them? For all x_9, x_9 will work.
 From the fact that for all x_9, if x_9 climbs a mountain, then x_9 is drinking water, and that for all x_9, if x_9 drinks water, then x_9 is climbing a mountain we can infer that for all x_9, x_9 will climb a mountain if and only if x_9 will drink water. From the fact that for all x_9, x_9 will climb a mountain if and only if x_9 will drink water we can infer that for all x_9, if x_9 drinks water, then x_9 is climbing a mountain. From the fact that for all x_9, if x_9 drinks water, then x_9 is climbing a mountain, and that for all x_9, x_9 will not climb a mountain we can infer that for all x_9, x_9 will not drink water. Finally, from the fact that for all x_9, x_9 will drink water or x_9 will work, and that for all x_9, x_9 will not drink water we can infer that for all x_9, x_9 will work. Therefore, the answer is yes.