Consider the following premises. For all x_8, if x_8 drinks water, then x_8 is not sleeping. For all x_8, if x_8 climbs a mountain, then x_8 is drinking water. For all x_8, x_8 will sleep and x_8 will play squash. For all x_8, if x_8 drinks water, then x_8 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not climb a mountain.
 From the fact that for all x_8, x_8 will sleep and x_8 will play squash we can infer that for all x_8, x_8 will sleep via universal simplification. From the fact that for all x_8, if x_8 drinks water, then x_8 is climbing a mountain, and that for all x_8, if x_8 climbs a mountain, then x_8 is drinking water we can infer that for all x_8, x_8 will drink water if and only if x_8 will climb a mountain via universal biconditional introduction. From the fact that for all x_8, if x_8 drinks water, then x_8 is not sleeping, and that for all x_8, x_8 will sleep we can infer that for all x_8, x_8 will not drink water via universal modus tollens. Finally, from the fact that for all x_8, x_8 will drink water if and only if x_8 will climb a mountain, and that for all x_8, x_8 will not drink water we can infer that for all x_8, x_8 will not climb a mountain via universal biconditional elimination. Therefore, the answer is yes.