Consider the following premises. For all x_6, if x_6 were a politician, then x_6 is a police officer. There is at least one x_6 for which if x_6 were a writer, then x_6 is a soldier. For all x_6, if x_6 were excited, then x_6 is a police officer. For all x_6, x_6 is a politician or x_6 is excited. For all x_6, x_6 is a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, either x_6 is a police officer or x_6 is a soldier are not true.
 From the fact that there is at least one x_6 for which if x_6 were a writer, then x_6 is a soldier, and that for all x_6, x_6 is a writer we can infer that there is at least one x_6 for which x_6 is a soldier via existential modus ponens. From the fact that for all x_6, if x_6 were a politician, then x_6 is a police officer, that for all x_6, if x_6 were excited, then x_6 is a police officer, and that for all x_6, x_6 is a politician or x_6 is excited we can infer that for all x_6, x_6 is a police officer via universal disjunction elimination. Finally, from the fact that for all x_6, x_6 is a police officer, and that there is at least one x_6 for which x_6 is a soldier we can infer that there is at least one x_6 for which x_6 is a police officer and x_6 is a soldier via existential conjunction, which contradicts that For all x_6, either x_6 is a police officer or x_6 is a soldier are not true. Therefore, the answer is no.