Consider the following premises. For all x_11, x_11 will sleep if and only if x_11 is an artist. For all x_11, x_11 will write a letter if and only if x_11 is an artist. For all x_11, x_11 will write a letter or x_11 will sleep. Can we infer the following from them? For all x_11, x_11 is an artist or x_11 will play a game.
 From the fact that for all x_11, x_11 will write a letter if and only if x_11 is an artist we can infer that for all x_11, if x_11 writes a letter, then x_11 is an artist. From the fact that for all x_11, x_11 will sleep if and only if x_11 is an artist we can infer that for all x_11, if x_11 sleeps, then x_11 is an artist. From the fact that for all x_11, if x_11 writes a letter, then x_11 is an artist, that for all x_11, if x_11 sleeps, then x_11 is an artist, and that for all x_11, x_11 will write a letter or x_11 will sleep we can infer that for all x_11, x_11 is an artist. Finally, from the fact that for all x_11, x_11 is an artist we can infer that for all x_11, x_11 is an artist or x_11 will play a game. Therefore, the answer is yes.