Consider the following premises. There is at least one x_12 for which x_12 will not climb a mountain. For all x_12, if x_12 takes a plane, then x_12 is a taxi driver. For all x_12, x_12 will climb a mountain if and only if x_12 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will not take a plane.
 From the fact that for all x_12, x_12 will climb a mountain if and only if x_12 is a taxi driver we can infer that for all x_12, if x_12 were a taxi driver, then x_12 is climbing a mountain via universal biconditional elimination. From the fact that for all x_12, if x_12 were a taxi driver, then x_12 is climbing a mountain, and that there is at least one x_12 for which x_12 will not climb a mountain we can infer that there is at least one x_12 for which x_12 is not a taxi driver via existential modus tollens. Finally, from the fact that for all x_12, if x_12 takes a plane, then x_12 is a taxi driver, and that there is at least one x_12 for which x_12 is not a taxi driver we can infer that there is at least one x_12 for which x_12 will not take a plane via existential modus tollens. Therefore, the answer is yes.