Consider the following premises. For all x_5, x_5 will sleep. For all x_5, x_5 is not a politician or x_5 is an astronaut. For all x_5, x_5 is a politician or x_5 will take a plane. There is at least one x_5 for which if x_5 takes a plane, then x_5 is not sleeping. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is not an astronaut.
 From the fact that there is at least one x_5 for which if x_5 takes a plane, then x_5 is not sleeping, and that for all x_5, x_5 will sleep we can infer that there is at least one x_5 for which x_5 will not take a plane via existential modus tollens. From the fact that for all x_5, x_5 is a politician or x_5 will take a plane, and that for all x_5, x_5 is not a politician or x_5 is an astronaut we can infer that for all x_5, x_5 will take a plane or x_5 is an astronaut via universal resolution. Finally, from the fact that for all x_5, x_5 will take a plane or x_5 is an astronaut, and that there is at least one x_5 for which x_5 will not take a plane we can infer that there is at least one x_5 for which x_5 is an astronaut via existential disjunctive syllogism, which contradicts that For all x_5, x_5 is not an astronaut. Therefore, the answer is no.