Consider the following premises. There is at least one x_8 for which x_8 will cook if and only if x_8 will read a book. For all x_8, x_8 is a writer if and only if x_8 will cook. Can we infer the following from them? There is at least one x_8 for which if x_8 were a writer, then x_8 is reading a book.
 From the fact that there is at least one x_8 for which x_8 will cook if and only if x_8 will read a book we can infer that there is at least one x_8 for which if x_8 cooks, then x_8 is reading a book. From the fact that for all x_8, x_8 is a writer if and only if x_8 will cook we can infer that for all x_8, if x_8 were a writer, then x_8 is cooking. Finally, from the fact that for all x_8, if x_8 were a writer, then x_8 is cooking, and that there is at least one x_8 for which if x_8 cooks, then x_8 is reading a book we can infer that there is at least one x_8 for which if x_8 were a writer, then x_8 is reading a book. Therefore, the answer is yes.