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: Joseph is running if and only if David is not cooking. If David cooks, then Jessica is a doctor. Jessica is not a doctor.
David is not cooking can be inferred via the modus tollens rule. If Joseph goes running, then David is not cooking can be inferred via the biconditional elimination rule. If David doesn't cook, then Joseph is running can be inferred via the biconditional elimination rule.