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_9, x_9 is a doctor or x_9 will cook. For all x_9, x_9 is not a doctor. For all x_9, if x_9 cooks, then x_9 is taking a plane. There is at least one x_9 for which x_9 is excited if and only if x_9 will take a plane.
For all x_9, x_9 will cook can be inferred via the universal disjunctive syllogism rule. There is at least one x_9 for which if x_9 were excited, then x_9 is taking a plane can be inferred via the existential biconditional elimination rule. There is at least one x_9 for which if x_9 takes a plane, then x_9 is excited can be inferred via the existential biconditional elimination rule.