Consider the following premises. For all x_9, x_9 will play a game or x_9 is not rich. For all x_9, x_9 is rich if and only if x_9 will play a game. There is at least one x_9 for which x_9 will not play a game. Can we infer the following from them? There is at least one x_9 for which x_9 is not rich.
 From the fact that for all x_9, x_9 is rich if and only if x_9 will play a game we can infer that for all x_9, if x_9 plays a game, then x_9 is rich. From the fact that for all x_9, x_9 will play a game or x_9 is not rich we can infer that for all x_9, if x_9 were rich, then x_9 is playing a game. From the fact that for all x_9, if x_9 were rich, then x_9 is playing a game, and that for all x_9, if x_9 plays a game, then x_9 is rich we can infer that for all x_9, x_9 is rich if and only if x_9 will play a game. Finally, from the fact that for all x_9, x_9 is rich if and only if x_9 will play a game, and that there is at least one x_9 for which x_9 will not play a game we can infer that there is at least one x_9 for which x_9 is not rich. Therefore, the answer is yes.