Consider the following premises. For all x_6, if x_6 drives a car, then x_6 is a writer. For all x_6, if x_6 goes running, then x_6 is a bartender. There is at least one x_6 for which if x_6 were a writer, then x_6 is sleeping. For all x_6, if x_6 sleeps, then x_6 is running. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, the fact that x_6 drives a car does not imply that x_6 is a bartender.
That contradicts the premises. Therefore the answer is no.