Consider the following premises. For all x_12, x_12 will not play squash. There is at least one x_12 for which x_12 will play squash or x_12 will work. For all x_12, x_12 will work if and only if x_12 will cook. Can we infer the following from them? There is at least one x_12 for which x_12 will cook.
 From the fact that for all x_12, x_12 will work if and only if x_12 will cook we can infer that for all x_12, if x_12 works, then x_12 is cooking. From the fact that there is at least one x_12 for which x_12 will play squash or x_12 will work, and that for all x_12, x_12 will not play squash we can infer that there is at least one x_12 for which x_12 will work. Finally, from the fact that for all x_12, if x_12 works, then x_12 is cooking, and that there is at least one x_12 for which x_12 will work we can infer that there is at least one x_12 for which x_12 will cook. Therefore, the answer is yes.