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