Consider the following premises. For all x_16, x_16 will drive a car. For all x_16, x_16 is fast if and only if x_16 is a mechanic. There is at least one x_16 for which if x_16 drives a car, then x_16 is fast. For all x_16, if x_16 were a mechanic, then x_16 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_16, x_16 will not climb a mountain.
 From the fact that for all x_16, x_16 is fast if and only if x_16 is a mechanic we can infer that for all x_16, if x_16 were fast, then x_16 is a mechanic via universal biconditional elimination. From the fact that for all x_16, if x_16 were fast, then x_16 is a mechanic, and that for all x_16, if x_16 were a mechanic, then x_16 is climbing a mountain we can infer that for all x_16, if x_16 were fast, then x_16 is climbing a mountain via universal transitivity. From the fact that there is at least one x_16 for which if x_16 drives a car, then x_16 is fast, and that for all x_16, x_16 will drive a car we can infer that there is at least one x_16 for which x_16 is fast via existential modus ponens. Finally, from the fact that for all x_16, if x_16 were fast, then x_16 is climbing a mountain, and that there is at least one x_16 for which x_16 is fast we can infer that there is at least one x_16 for which x_16 will climb a mountain via existential modus ponens, which contradicts that For all x_16, x_16 will not climb a mountain. Therefore, the answer is no.