Consider the following premises. For all x_5, if x_5 reads a book, then x_5 is a taxi driver. For all x_5, x_5 will sleep or x_5 will write a letter. There is at least one x_5 for which if x_5 writes a letter, then x_5 is an astronaut. For all x_5, if x_5 were a taxi driver, then x_5 is an astronaut. For all x_5, if x_5 sleeps, then x_5 is reading a book. 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 for all x_5, if x_5 sleeps, then x_5 is reading a book, and that for all x_5, if x_5 reads a book, then x_5 is a taxi driver we can infer that for all x_5, if x_5 sleeps, then x_5 is a taxi driver via universal transitivity. From the fact that for all x_5, if x_5 sleeps, then x_5 is a taxi driver, and that for all x_5, if x_5 were a taxi driver, then x_5 is an astronaut we can infer that for all x_5, if x_5 sleeps, then x_5 is an astronaut via universal transitivity. Finally, from the fact that for all x_5, if x_5 sleeps, then x_5 is an astronaut, that there is at least one x_5 for which if x_5 writes a letter, then x_5 is an astronaut, and that for all x_5, x_5 will sleep or x_5 will write a letter we can infer that there is at least one x_5 for which x_5 is an astronaut via existential disjunction elimination, which contradicts that For all x_5, x_5 is not an astronaut. Therefore, the answer is no.