Consider the following premises. There is at least one x_8 for which if x_8 were a nurse, then x_8 is driving a car. For all x_8, if x_8 were a writer, then x_8 is a nurse. For all x_8, x_8 is a nurse. For all x_8, if x_8 drives a car, then x_8 is a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not drive a car.
 From the fact that for all x_8, if x_8 drives a car, then x_8 is a writer, and that for all x_8, if x_8 were a writer, then x_8 is a nurse we can infer that for all x_8, if x_8 drives a car, then x_8 is a nurse via universal transitivity. From the fact that for all x_8, if x_8 drives a car, then x_8 is a nurse, and that there is at least one x_8 for which if x_8 were a nurse, then x_8 is driving a car we can infer that there is at least one x_8 for which x_8 will drive a car if and only if x_8 is a nurse via existential biconditional introduction. From the fact that there is at least one x_8 for which x_8 will drive a car if and only if x_8 is a nurse we can infer that there is at least one x_8 for which if x_8 were a nurse, then x_8 is driving a car via existential biconditional elimination. Finally, from the fact that there is at least one x_8 for which if x_8 were a nurse, then x_8 is driving a car, and that for all x_8, x_8 is a nurse we can infer that there is at least one x_8 for which x_8 will drive a car via existential modus ponens, which contradicts that For all x_8, x_8 will not drive a car. Therefore, the answer is no.