Consider the following premises. For all x_9, x_9 is a taxi driver or x_9 will go running. There is at least one x_9 for which x_9 is not a taxi driver or x_9 is an astronaut. For all x_9, x_9 is not poor. For all x_9, if x_9 goes running, then x_9 is not drinking water. For all x_9, x_9 is poor or x_9 will drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is an astronaut.
 From the fact that for all x_9, x_9 is poor or x_9 will drink water, and that for all x_9, x_9 is not poor we can infer that for all x_9, x_9 will drink water via universal disjunctive syllogism. From the fact that for all x_9, x_9 is a taxi driver or x_9 will go running, and that there is at least one x_9 for which x_9 is not a taxi driver or x_9 is an astronaut we can infer that there is at least one x_9 for which x_9 will go running or x_9 is an astronaut via existential resolution. From the fact that for all x_9, if x_9 goes running, then x_9 is not drinking water, and that for all x_9, x_9 will drink water we can infer that for all x_9, x_9 will not go running via universal modus tollens. Finally, from the fact that there is at least one x_9 for which x_9 will go running or x_9 is an astronaut, and that for all x_9, x_9 will not go running we can infer that there is at least one x_9 for which x_9 is an astronaut via existential disjunctive syllogism. Therefore, the answer is yes.