Consider the following premises. There is at least one x_12 for which x_12 will climb a mountain or x_12 is an astronaut. For all x_12, x_12 will climb a mountain if and only if x_12 is a scientist. For all x_12, if x_12 plays squash, then x_12 is not a scientist. For all x_12, if x_12 were an astronaut, then x_12 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, x_12 will play squash.
 From the fact that for all x_12, x_12 will climb a mountain if and only if x_12 is a scientist we can infer that for all x_12, if x_12 climbs a mountain, then x_12 is a scientist via universal biconditional elimination. From the fact that for all x_12, if x_12 climbs a mountain, then x_12 is a scientist, that for all x_12, if x_12 were an astronaut, then x_12 is a scientist, and that there is at least one x_12 for which x_12 will climb a mountain or x_12 is an astronaut we can infer that there is at least one x_12 for which x_12 is a scientist via existential disjunction elimination. Finally, from the fact that for all x_12, if x_12 plays squash, then x_12 is not a scientist, and that there is at least one x_12 for which x_12 is a scientist we can infer that there is at least one x_12 for which x_12 will not play squash via existential modus tollens, which contradicts that For all x_12, x_12 will play squash. Therefore, the answer is no.