Consider the following premises. For all x_16, x_16 is excited if and only if x_16 will play squash. For all x_16, x_16 will take a plane or x_16 is a writer. There is at least one x_16 for which x_16 will not play squash. For all x_16, x_16 will take a plane if and only if x_16 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_16, x_16 is not a writer.
 From the fact that for all x_16, x_16 is excited if and only if x_16 will play squash, and that there is at least one x_16 for which x_16 will not play squash we can infer that there is at least one x_16 for which x_16 is not excited via existential biconditional elimination. From the fact that for all x_16, x_16 will take a plane if and only if x_16 is excited, and that there is at least one x_16 for which x_16 is not excited we can infer that there is at least one x_16 for which x_16 will not take a plane via existential biconditional elimination. Finally, from the fact that for all x_16, x_16 will take a plane or x_16 is a writer, and that there is at least one x_16 for which x_16 will not take a plane we can infer that there is at least one x_16 for which x_16 is a writer via existential disjunctive syllogism, which contradicts that For all x_16, x_16 is not a writer. Therefore, the answer is no.