Consider the following premises. For all x_2, x_2 will read a book or x_2 will not go running. There is at least one x_2 for which if x_2 reads a book, then x_2 is running. Can we infer the following from them? There is at least one x_2 for which x_2 will go running if and only if x_2 will read a book.
 From the fact that for all x_2, x_2 will read a book or x_2 will not go running we can infer that for all x_2, if x_2 goes running, then x_2 is reading a book. Finally, from the fact that for all x_2, if x_2 goes running, then x_2 is reading a book, and that there is at least one x_2 for which if x_2 reads a book, then x_2 is running we can infer that there is at least one x_2 for which x_2 will go running if and only if x_2 will read a book. Therefore, the answer is yes.