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 drive a car. For all x_9, x_9 is a poet. For all x_9, if x_9 sleeps, then x_9 is not driving a car. There is at least one x_9 for which x_9 will work if and only if x_9 will sleep.
For all x_9, x_9 will not sleep can be inferred via the universal modus tollens rule. For all x_9, x_9 will drive a car and x_9 is a poet can be inferred via the universal conjunction rule. For all x_9, x_9 is a poet and x_9 will drive a car can be inferred via the universal conjunction rule. There is at least one x_9 for which if x_9 works, then x_9 is sleeping can be inferred via the existential biconditional elimination rule. There is at least one x_9 for which if x_9 sleeps, then x_9 is working can be inferred via the existential biconditional elimination rule.