Consider the following premises. For all x_4, if x_4 climbs a mountain, then x_4 is driving a car. For all x_4, if x_4 were a musician, then x_4 is driving a car. For all x_4, x_4 will not play tennis or x_4 is a musician. For all x_4, x_4 is a carpenter or x_4 will play tennis. For all x_4, x_4 is not a carpenter or x_4 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 will not drive a car.
 From the fact that for all x_4, x_4 is a carpenter or x_4 will play tennis, and that for all x_4, x_4 is not a carpenter or x_4 will climb a mountain we can infer that for all x_4, x_4 will play tennis or x_4 will climb a mountain via universal resolution. From the fact that for all x_4, x_4 will play tennis or x_4 will climb a mountain, and that for all x_4, x_4 will not play tennis or x_4 is a musician we can infer that for all x_4, x_4 will climb a mountain or x_4 is a musician via universal resolution. Finally, from the fact that for all x_4, if x_4 climbs a mountain, then x_4 is driving a car, that for all x_4, if x_4 were a musician, then x_4 is driving a car, and that for all x_4, x_4 will climb a mountain or x_4 is a musician we can infer that for all x_4, x_4 will drive a car via universal disjunction elimination, which contradicts that There is at least one x_4 for which x_4 will not drive a car. Therefore, the answer is no.