Consider the following premises. For all x_2, x_2 will sleep or x_2 will not cook. There is at least one x_2 for which x_2 will cook. Can we infer the following from them? For all x_2, x_2 will not sleep.
 From the fact that for all x_2, x_2 will sleep or x_2 will not cook we can infer that for all x_2, if x_2 cooks, then x_2 is sleeping. Finally, from the fact that for all x_2, if x_2 cooks, then x_2 is sleeping, and that there is at least one x_2 for which x_2 will cook we can infer that there is at least one x_2 for which x_2 will sleep, which contradicts that For all x_2, x_2 will not sleep. Therefore, the answer is no.