Consider the following premises. For all x_5, if x_5 works, then x_5 is cooking. For all x_5, x_5 will not write a letter. For all x_5, if x_5 cooks, then x_5 is working. For all x_5, if x_5 cooks, then x_5 is writing a letter. Can we infer the following from them? For all x_5, x_5 will not work.
 From the fact that for all x_5, if x_5 cooks, then x_5 is working, and that for all x_5, if x_5 works, then x_5 is cooking we can infer that for all x_5, x_5 will cook if and only if x_5 will work. From the fact that for all x_5, if x_5 cooks, then x_5 is writing a letter, and that for all x_5, x_5 will not write a letter we can infer that for all x_5, x_5 will not cook. Finally, from the fact that for all x_5, x_5 will cook if and only if x_5 will work, and that for all x_5, x_5 will not cook we can infer that for all x_5, x_5 will not work. Therefore, the answer is yes.