Consider the following premises. For all x_8, if x_8 plays tennis, then x_8 is happy. For all x_8, x_8 is happy if and only if x_8 will play a game. For all x_8, if x_8 plays a game, then x_8 is playing tennis. There is at least one x_8 for which x_8 will not play a game. Can we infer the following from them? If we can, name the inference rule being used: 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 is happy if and only if x_8 will play a game we can infer that for all x_8, if x_8 were happy, then x_8 is playing a game via universal biconditional elimination. From the fact that for all x_8, if x_8 plays tennis, then x_8 is happy, and that for all x_8, if x_8 were happy, then x_8 is playing a game we can infer that for all x_8, if x_8 plays tennis, then x_8 is playing a game via universal transitivity. From the fact that for all x_8, if x_8 plays a game, then x_8 is playing tennis, and that for all x_8, if x_8 plays tennis, then x_8 is playing a game we can infer that for all x_8, x_8 will play a game if and only if x_8 will play tennis via universal biconditional introduction. Finally, from the fact that for all x_8, x_8 will play a game if and only if x_8 will play tennis, and that there is at least one x_8 for which x_8 will not play a game we can infer that there is at least one x_8 for which x_8 will not play tennis via existential biconditional elimination. Therefore, the answer is yes.