Consider the following premises. For all x_4, if x_4 were a mechanic, then x_4 is working. For all x_4, if x_4 works, then x_4 is sleeping. For all x_4, if x_4 sleeps, then x_4 is a mechanic. Can we infer the following from them? The fact that Thomas sleeps does not imply that Thomas is working.
That contradicts the premises. Therefore the answer is no.