Consider the following premises. For all x_5, if x_5 were sad, then x_5 is playing a game. For all x_5, x_5 is not sad. For all x_5, if x_5 plays a game, then x_5 is sad. For all x_5, if x_5 were a mechanic, then x_5 is playing a game. Can we infer the following from them? For all x_5, x_5 is not a mechanic.
 From the fact that for all x_5, if x_5 were sad, then x_5 is playing a game, and that for all x_5, if x_5 plays a game, then x_5 is sad we can infer that for all x_5, x_5 is sad if and only if x_5 will play a game. From the fact that for all x_5, x_5 is sad if and only if x_5 will play a game, and that for all x_5, x_5 is not sad we can infer that for all x_5, x_5 will not play a game. Finally, from the fact that for all x_5, if x_5 were a mechanic, then x_5 is playing a game, and that for all x_5, x_5 will not play a game we can infer that for all x_5, x_5 is not a mechanic. Therefore, the answer is yes.