What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Patricia is a police officer. William is taking a plane if and only if Joseph is an astronaut. Joseph is not an astronaut.
Patricia is a police officer and Joseph is not an astronaut. Joseph is not an astronaut and Patricia is a police officer. If William takes a plane, then Joseph is an astronaut. If Joseph were an astronaut, then William is taking a plane. William is not taking a plane.