Consider the following premises. For all x_7, x_7 will sleep. There is at least one x_7 for which if x_7 sleeps, then x_7 is listening to a song. For all x_7, x_7 will drive a car or x_7 will not listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not drive a car.
 From the fact that for all x_7, x_7 will drive a car or x_7 will not listen to a song we can infer that for all x_7, if x_7 listens to a song, then x_7 is driving a car via universal rewriting. From the fact that there is at least one x_7 for which if x_7 sleeps, then x_7 is listening to a song, and that for all x_7, if x_7 listens to a song, then x_7 is driving a car we can infer that there is at least one x_7 for which if x_7 sleeps, then x_7 is driving a car via existential transitivity. Finally, from the fact that there is at least one x_7 for which if x_7 sleeps, then x_7 is driving a car, and that for all x_7, x_7 will sleep we can infer that there is at least one x_7 for which x_7 will drive a car via existential modus ponens, which contradicts that For all x_7, x_7 will not drive a car. Therefore, the answer is no.