Consider the following premises. For all x_10, x_10 will play a game or x_10 is excited. For all x_10, if x_10 were rich, then x_10 is not happy. There is at least one x_10 for which if x_10 plays a game, then x_10 is rich. For all x_10, x_10 is happy. Can we infer the following from them? There is at least one x_10 for which x_10 is excited.
 From the fact that for all x_10, if x_10 were rich, then x_10 is not happy, and that for all x_10, x_10 is happy we can infer that for all x_10, x_10 is not rich. From the fact that there is at least one x_10 for which if x_10 plays a game, then x_10 is rich, and that for all x_10, x_10 is not rich we can infer that there is at least one x_10 for which x_10 will not play a game. Finally, from the fact that for all x_10, x_10 will play a game or x_10 is excited, and that there is at least one x_10 for which x_10 will not play a game we can infer that there is at least one x_10 for which x_10 is excited. Therefore, the answer is yes.