What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? There is at least one x for which if x were poor, then x is an astronaut. For all x, if x were an astronaut, then x is poor. For all x, if x were poor, then x is an astronaut.
For all x, x is an astronaut if and only if x is poor. For all x, x is poor if and only if x is an astronaut. There is at least one x for which x is poor if and only if x is an astronaut. There is at least one x for which x is an astronaut if and only if x is poor.