Consider the following premises. For all x_2, x_2 will read a book or x_2 is not an astronaut. For all x_2, x_2 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 will not read a book.
 From the fact that for all x_2, x_2 will read a book or x_2 is not an astronaut we can infer that for all x_2, if x_2 were an astronaut, then x_2 is reading a book via universal rewriting. Finally, from the fact that for all x_2, if x_2 were an astronaut, then x_2 is reading a book, and that for all x_2, x_2 is an astronaut we can infer that for all x_2, x_2 will read a book via universal modus ponens, which contradicts that There is at least one x_2 for which x_2 will not read a book. Therefore, the answer is no.