Consider the following premises. For all x_1, x_1 will go running if and only if x_1 will cook. There is at least one x_1 for which if x_1 goes running, then x_1 is reading a book. For all x_1, x_1 will not read a book. Can we infer the following from them? For all x_1, x_1 will cook.
 From the fact that there is at least one x_1 for which if x_1 goes running, then x_1 is reading a book, and that for all x_1, x_1 will not read a book we can infer that there is at least one x_1 for which x_1 will not go running. Finally, from the fact that for all x_1, x_1 will go running if and only if x_1 will cook, and that there is at least one x_1 for which x_1 will not go running we can infer that there is at least one x_1 for which x_1 will not cook, which contradicts that For all x_1, x_1 will cook. Therefore, the answer is no.