Consider the following premises. For all x_15, if x_15 reads a book, then x_15 is an artist. For all x_15, x_15 will sleep or x_15 will not play a game. There is at least one x_15 for which x_15 is an artist if and only if x_15 will play a game. For all x_15, if x_15 sleeps, then x_15 is reading a book. Can we infer the following from them? There is at least one x_15 for which x_15 will play a game if and only if x_15 is an artist.
 From the fact that for all x_15, x_15 will sleep or x_15 will not play a game we can infer that for all x_15, if x_15 plays a game, then x_15 is sleeping. From the fact that for all x_15, if x_15 plays a game, then x_15 is sleeping, and that for all x_15, if x_15 sleeps, then x_15 is reading a book we can infer that for all x_15, if x_15 plays a game, then x_15 is reading a book. From the fact that there is at least one x_15 for which x_15 is an artist if and only if x_15 will play a game we can infer that there is at least one x_15 for which if x_15 were an artist, then x_15 is playing a game. From the fact that for all x_15, if x_15 plays a game, then x_15 is reading a book, and that for all x_15, if x_15 reads a book, then x_15 is an artist we can infer that for all x_15, if x_15 plays a game, then x_15 is an artist. Finally, from the fact that for all x_15, if x_15 plays a game, then x_15 is an artist, and that there is at least one x_15 for which if x_15 were an artist, then x_15 is playing a game we can infer that there is at least one x_15 for which x_15 will play a game if and only if x_15 is an artist. Therefore, the answer is yes.