Consider the following premises. For all x_8, x_8 is a politician. For all x_8, if x_8 were a politician, then x_8 is climbing a mountain. For all x_8, x_8 will climb a mountain or x_8 will not drive a car. For all x_8, if x_8 climbs a mountain, then x_8 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is not a doctor.
 From the fact that for all x_8, x_8 will climb a mountain or x_8 will not drive a car we can infer that for all x_8, if x_8 drives a car, then x_8 is climbing a mountain via universal rewriting. From the fact that for all x_8, x_8 is a politician we can infer that for all x_8, x_8 is a politician or x_8 will drive a car via universal addition. From the fact that for all x_8, if x_8 were a politician, then x_8 is climbing a mountain, that for all x_8, if x_8 drives a car, then x_8 is climbing a mountain, and that for all x_8, x_8 is a politician or x_8 will drive a car we can infer that for all x_8, x_8 will climb a mountain via universal disjunction elimination. Finally, from the fact that for all x_8, if x_8 climbs a mountain, then x_8 is a doctor, and that for all x_8, x_8 will climb a mountain we can infer that for all x_8, x_8 is a doctor via universal modus ponens, which contradicts that There is at least one x_8 for which x_8 is not a doctor. Therefore, the answer is no.