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 will cook if and only if x_9 is an astronaut. For all x_9, if x_9 drives a car, then x_9 is a janitor. There is at least one x_9 for which if x_9 were a janitor, then x_9 is an astronaut.
There is at least one x_9 for which if x_9 drives a car, then x_9 is an astronaut can be inferred via the existential transitivity rule. For all x_9, if x_9 cooks, then x_9 is an astronaut can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 were an astronaut, then x_9 is cooking can be inferred via the universal biconditional elimination rule.