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: If Joseph sleeps, then Karen is not taking a plane. If Michael drives a car, then Karen is taking a plane. Karen is a nurse or Michael is driving a car. For all x, x is a nurse if and only if x will take a plane.
For all x, if x were a nurse, then x is taking a plane can be inferred via the universal biconditional elimination rule. For all x, if x takes a plane, then x is a nurse can be inferred via the universal biconditional elimination rule.