Consider the following premises. For all x_4, if x_4 takes a plane, then x_4 is cooking. For all x_4, x_4 is not a taxi driver. There is at least one x_4 for which if x_4 cooks, then x_4 is a taxi driver. For all x_4, if x_4 were a taxi driver, then x_4 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 will take a plane.
 From the fact that for all x_4, if x_4 takes a plane, then x_4 is cooking, and that there is at least one x_4 for which if x_4 cooks, then x_4 is a taxi driver we can infer that there is at least one x_4 for which if x_4 takes a plane, then x_4 is a taxi driver via existential transitivity. From the fact that for all x_4, if x_4 were a taxi driver, then x_4 is taking a plane, and that there is at least one x_4 for which if x_4 takes a plane, then x_4 is a taxi driver we can infer that there is at least one x_4 for which x_4 is a taxi driver if and only if x_4 will take a plane via existential biconditional introduction. Finally, from the fact that there is at least one x_4 for which x_4 is a taxi driver if and only if x_4 will take a plane, and that for all x_4, x_4 is not a taxi driver we can infer that there is at least one x_4 for which x_4 will not take a plane via existential biconditional elimination, which contradicts that For all x_4, x_4 will take a plane. Therefore, the answer is no.