Consider the following premises. For all x_17, if x_17 drinks water, then x_17 is climbing a mountain. For all x_17, x_17 will climb a mountain or x_17 will play squash. For all x_17, if x_17 climbs a mountain, then x_17 is drinking water. For all x_17, if x_17 drinks water, then x_17 is writing a letter. There is at least one x_17 for which x_17 will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_17, x_17 will not play squash.
 From the fact that for all x_17, if x_17 drinks water, then x_17 is climbing a mountain, and that for all x_17, if x_17 climbs a mountain, then x_17 is drinking water we can infer that for all x_17, x_17 will drink water if and only if x_17 will climb a mountain via universal biconditional introduction. From the fact that for all x_17, if x_17 drinks water, then x_17 is writing a letter, and that there is at least one x_17 for which x_17 will not write a letter we can infer that there is at least one x_17 for which x_17 will not drink water via existential modus tollens. From the fact that for all x_17, x_17 will drink water if and only if x_17 will climb a mountain, and that there is at least one x_17 for which x_17 will not drink water we can infer that there is at least one x_17 for which x_17 will not climb a mountain via existential biconditional elimination. Finally, from the fact that for all x_17, x_17 will climb a mountain or x_17 will play squash, and that there is at least one x_17 for which x_17 will not climb a mountain we can infer that there is at least one x_17 for which x_17 will play squash via existential disjunctive syllogism, which contradicts that For all x_17, x_17 will not play squash. Therefore, the answer is no.