Consider the following premises. There is at least one x_10 for which x_10 will play squash if and only if x_10 will play a game. For all x_10, x_10 will sleep. For all x_10, x_10 will sleep if and only if x_10 will play a game. Can we infer the following from them? There is at least one x_10 for which x_10 will play a game.
 From the fact that there is at least one x_10 for which x_10 will play squash if and only if x_10 will play a game we can infer that there is at least one x_10 for which if x_10 plays squash, then x_10 is playing a game. From the fact that for all x_10, x_10 will sleep we can infer that for all x_10, x_10 will sleep or x_10 will play squash. From the fact that for all x_10, x_10 will sleep if and only if x_10 will play a game we can infer that for all x_10, if x_10 sleeps, then x_10 is playing a game. Finally, from the fact that for all x_10, if x_10 sleeps, then x_10 is playing a game, that there is at least one x_10 for which if x_10 plays squash, then x_10 is playing a game, and that for all x_10, x_10 will sleep or x_10 will play squash we can infer that there is at least one x_10 for which x_10 will play a game. Therefore, the answer is yes.