Consider the following premises. For all x_1, if x_1 plays squash, then x_1 is cooking. For all x_1, x_1 will not work. For all x_1, x_1 will work if and only if x_1 will cook. Can we infer the following from them? For all x_1, x_1 will not play squash.
 From the fact that for all x_1, x_1 will work if and only if x_1 will cook, and that for all x_1, x_1 will not work we can infer that for all x_1, x_1 will not cook. Finally, from the fact that for all x_1, if x_1 plays squash, then x_1 is cooking, and that for all x_1, x_1 will not cook we can infer that for all x_1, x_1 will not play squash. Therefore, the answer is yes.