Consider the following premises. There is at least one y_3 for which y_3 is a cashier or y_3 is not a writer. For all y_3, if y_3 were a cashier, then y_3 is taking a plane. For all y_3, y_3 is a writer if and only if y_3 will take a plane. Can we infer the following from them? If we can, name the inference rule being used: For all y_3, if is not true that y_3 will take a plane if and only if y_3 is a writer.
That contradicts the premises. Therefore the answer is no.