Consider the following premises. For all x_7, x_7 will read a book or x_7 is a police officer. For all x_7, if x_7 were a janitor, then x_7 is an astronaut. There is at least one x_7 for which if x_7 were a police officer, then x_7 is an astronaut. For all x_7, x_7 will read a book if and only if x_7 is a janitor. Can we infer the following from them? There is at least one x_7 for which x_7 is an astronaut.
 From the fact that for all x_7, x_7 will read a book if and only if x_7 is a janitor we can infer that for all x_7, if x_7 reads a book, then x_7 is a janitor. From the fact that for all x_7, if x_7 reads a book, then x_7 is a janitor, and that for all x_7, if x_7 were a janitor, then x_7 is an astronaut we can infer that for all x_7, if x_7 reads a book, then x_7 is an astronaut. Finally, from the fact that for all x_7, if x_7 reads a book, then x_7 is an astronaut, that there is at least one x_7 for which if x_7 were a police officer, then x_7 is an astronaut, and that for all x_7, x_7 will read a book or x_7 is a police officer we can infer that there is at least one x_7 for which x_7 is an astronaut. Therefore, the answer is yes.