Consider the following premises. For all x_4, x_4 will work if and only if x_4 is a cashier. There is at least one x_4 for which if x_4 works, then x_4 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, the fact that x_4 were a cashier does not imply that x_4 is a janitor.
That contradicts the premises. Therefore the answer is no.