Consider the following premises. There is at least one x_6 for which x_6 is a writer if and only if x_6 is a doctor. For all x_6, if x_6 were a politician, then x_6 is a nurse. For all x_6, if x_6 were a nurse, then x_6 is a writer. For all x_6, x_6 is a doctor or x_6 is a politician. Can we infer the following from them? For all x_6, x_6 is not a writer.
 From the fact that for all x_6, if x_6 were a politician, then x_6 is a nurse, and that for all x_6, if x_6 were a nurse, then x_6 is a writer we can infer that for all x_6, if x_6 were a politician, then x_6 is a writer. From the fact that there is at least one x_6 for which x_6 is a writer if and only if x_6 is a doctor we can infer that there is at least one x_6 for which if x_6 were a doctor, then x_6 is a writer. Finally, from the fact that there is at least one x_6 for which if x_6 were a doctor, then x_6 is a writer, that for all x_6, if x_6 were a politician, then x_6 is a writer, and that for all x_6, x_6 is a doctor or x_6 is a politician we can infer that there is at least one x_6 for which x_6 is a writer, which contradicts that For all x_6, x_6 is not a writer. Therefore, the answer is no.