Consider the following premises. There is at least one x_12 for which x_12 is not a lawyer or x_12 will climb a mountain. For all x_12, x_12 is a lawyer or x_12 will go running. For all x_12, if x_12 climbs a mountain, then x_12 is driving a car. For all x_12, x_12 will drive a car or x_12 will not go running. For all x_12, if x_12 drives a car, then x_12 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, x_12 will not drive a car.
 From the fact that for all x_12, if x_12 climbs a mountain, then x_12 is driving a car, and that for all x_12, if x_12 drives a car, then x_12 is climbing a mountain we can infer that for all x_12, x_12 will climb a mountain if and only if x_12 will drive a car via universal biconditional introduction. From the fact that for all x_12, x_12 is a lawyer or x_12 will go running, and that there is at least one x_12 for which x_12 is not a lawyer or x_12 will climb a mountain we can infer that there is at least one x_12 for which x_12 will go running or x_12 will climb a mountain via existential resolution. From the fact that for all x_12, x_12 will climb a mountain if and only if x_12 will drive a car we can infer that for all x_12, if x_12 climbs a mountain, then x_12 is driving a car via universal biconditional elimination. From the fact that for all x_12, x_12 will drive a car or x_12 will not go running we can infer that for all x_12, if x_12 goes running, then x_12 is driving a car via universal rewriting. Finally, from the fact that for all x_12, if x_12 goes running, then x_12 is driving a car, that for all x_12, if x_12 climbs a mountain, then x_12 is driving a car, and that there is at least one x_12 for which x_12 will go running or x_12 will climb a mountain we can infer that there is at least one x_12 for which x_12 will drive a car via existential disjunction elimination, which contradicts that For all x_12, x_12 will not drive a car. Therefore, the answer is no.