Consider the following premises. For all x_14, if x_14 were a janitor, then x_14 is driving a car. There is at least one x_14 for which x_14 is fast or x_14 will climb a mountain. For all x_14, x_14 will drive a car if and only if x_14 is a politician. For all x_14, if x_14 climbs a mountain, then x_14 is driving a car. For all x_14, if x_14 were fast, then x_14 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 is not a politician.
 From the fact that for all x_14, if x_14 were fast, then x_14 is a janitor, and that for all x_14, if x_14 were a janitor, then x_14 is driving a car we can infer that for all x_14, if x_14 were fast, then x_14 is driving a car via universal transitivity. From the fact that for all x_14, if x_14 were fast, then x_14 is driving a car, that for all x_14, if x_14 climbs a mountain, then x_14 is driving a car, and that there is at least one x_14 for which x_14 is fast or x_14 will climb a mountain we can infer that there is at least one x_14 for which x_14 will drive a car via existential disjunction elimination. From the fact that for all x_14, x_14 will drive a car if and only if x_14 is a politician we can infer that for all x_14, if x_14 drives a car, then x_14 is a politician via universal biconditional elimination. Finally, from the fact that for all x_14, if x_14 drives a car, then x_14 is a politician, and that there is at least one x_14 for which x_14 will drive a car we can infer that there is at least one x_14 for which x_14 is a politician via existential modus ponens, which contradicts that For all x_14, x_14 is not a politician. Therefore, the answer is no.