What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all x_5, if x_5 cooks, then x_5 is a police officer. For all x_5, if x_5 were a writer, then x_5 is cooking. For all x_5, x_5 is a writer if and only if x_5 is excited. For all x_5, x_5 is not a police officer.
For all x_5, x_5 will not cook can be inferred via the universal modus tollens rule. For all x_5, if x_5 were a writer, then x_5 is a police officer can be inferred via the universal transitivity rule. For all x_5, if x_5 were a writer, then x_5 is excited can be inferred via the universal biconditional elimination rule. For all x_5, if x_5 were excited, then x_5 is a writer can be inferred via the universal biconditional elimination rule.