Consider the following premises. For all x_13, x_13 will cook if and only if x_13 is a taxi driver. For all x_13, x_13 is a nurse or x_13 will play tennis. For all x_13, if x_13 takes a plane, then x_13 is a taxi driver. For all x_13, x_13 is not a nurse. There is at least one x_13 for which if x_13 plays tennis, then x_13 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 is not a taxi driver.
 From the fact that for all x_13, x_13 is a nurse or x_13 will play tennis, and that for all x_13, x_13 is not a nurse we can infer that for all x_13, x_13 will play tennis via universal disjunctive syllogism. From the fact that there is at least one x_13 for which if x_13 plays tennis, then x_13 is taking a plane, and that for all x_13, if x_13 takes a plane, then x_13 is a taxi driver we can infer that there is at least one x_13 for which if x_13 plays tennis, then x_13 is a taxi driver via existential transitivity. From the fact that for all x_13, x_13 will play tennis we can infer that for all x_13, x_13 will play tennis or x_13 will cook via universal addition. From the fact that for all x_13, x_13 will cook if and only if x_13 is a taxi driver we can infer that for all x_13, if x_13 cooks, then x_13 is a taxi driver via universal biconditional elimination. Finally, from the fact that there is at least one x_13 for which if x_13 plays tennis, then x_13 is a taxi driver, that for all x_13, if x_13 cooks, then x_13 is a taxi driver, and that for all x_13, x_13 will play tennis or x_13 will cook we can infer that there is at least one x_13 for which x_13 is a taxi driver via existential disjunction elimination, which contradicts that For all x_13, x_13 is not a taxi driver. Therefore, the answer is no.