Consider the following premises. For all x_14, if x_14 were a mechanic, then x_14 is sleeping. For all x_14, x_14 will sleep if and only if x_14 will play a game. There is at least one x_14 for which if x_14 were a mechanic, then x_14 is playing a game. For all x_14, if x_14 plays a game, then x_14 is a mechanic. Can we infer the following from them? For all x_14, if is not true that x_14 will play a game if and only if x_14 is a mechanic.
That contradicts the premises. Therefore the answer is no.