Consider the following premises. For all x_3, x_3 is happy if and only if x_3 will play a game. For all x_3, x_3 is not a carpenter. For all x_3, x_3 is a carpenter or x_3 will not play a game. Can we infer the following from them? For all x_3, x_3 is not happy.
 From the fact that for all x_3, x_3 is a carpenter or x_3 will not play a game we can infer that for all x_3, if x_3 plays a game, then x_3 is a carpenter. From the fact that for all x_3, if x_3 plays a game, then x_3 is a carpenter, and that for all x_3, x_3 is not a carpenter we can infer that for all x_3, x_3 will not play a game. Finally, from the fact that for all x_3, x_3 is happy if and only if x_3 will play a game, and that for all x_3, x_3 will not play a game we can infer that for all x_3, x_3 is not happy. Therefore, the answer is yes.