Consider the following premises. For all x_2, x_2 will cook or x_2 will not play squash. There is at least one x_2 for which x_2 will not cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will play squash.
 From the fact that for all x_2, x_2 will cook or x_2 will not play squash we can infer that for all x_2, if x_2 plays squash, then x_2 is cooking via universal rewriting. Finally, from the fact that for all x_2, if x_2 plays squash, then x_2 is cooking, and that there is at least one x_2 for which x_2 will not cook we can infer that there is at least one x_2 for which x_2 will not play squash via existential modus tollens, which contradicts that For all x_2, x_2 will play squash. Therefore, the answer is no.