Consider the following premises. For all x_15, if x_15 were a musician, then x_15 is a janitor. There is at least one x_15 for which x_15 is a janitor if and only if x_15 is a carpenter. For all x_15, x_15 is not a carpenter. For all x_15, x_15 is a musician if and only if x_15 will take a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 will take a plane.
 From the fact that there is at least one x_15 for which x_15 is a janitor if and only if x_15 is a carpenter, and that for all x_15, x_15 is not a carpenter we can infer that there is at least one x_15 for which x_15 is not a janitor via existential biconditional elimination. From the fact that for all x_15, if x_15 were a musician, then x_15 is a janitor, and that there is at least one x_15 for which x_15 is not a janitor we can infer that there is at least one x_15 for which x_15 is not a musician via existential modus tollens. Finally, from the fact that for all x_15, x_15 is a musician if and only if x_15 will take a plane, and that there is at least one x_15 for which x_15 is not a musician we can infer that there is at least one x_15 for which x_15 will not take a plane via existential biconditional elimination, which contradicts that For all x_15, x_15 will take a plane. Therefore, the answer is no.