Consider the following premises. For all x_8, x_8 will cook or x_8 will not play tennis. There is at least one x_8 for which if x_8 cooks, then x_8 is playing tennis. For all x_8, x_8 will not play a game. For all x_8, x_8 will play a game if and only if x_8 will cook. Can we infer the following from them? There is at least one x_8 for which x_8 will not play tennis.
 From the fact that for all x_8, x_8 will cook or x_8 will not play tennis we can infer that for all x_8, if x_8 plays tennis, then x_8 is cooking. From the fact that for all x_8, x_8 will play a game if and only if x_8 will cook, and that for all x_8, x_8 will not play a game we can infer that for all x_8, x_8 will not cook. From the fact that there is at least one x_8 for which if x_8 cooks, then x_8 is playing tennis, and that for all x_8, if x_8 plays tennis, then x_8 is cooking we can infer that there is at least one x_8 for which x_8 will cook if and only if x_8 will play tennis. Finally, from the fact that there is at least one x_8 for which x_8 will cook if and only if x_8 will play tennis, and that for all x_8, x_8 will not cook we can infer that there is at least one x_8 for which x_8 will not play tennis. Therefore, the answer is yes.