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: There is at least one z for which z is an astronaut if and only if z is a scientist. For all z, if z listens to a song, then z is a scientist. For all z, z will listen to a song or z is not a scientist.
For all z, if z were a scientist, then z is listening to a song can be inferred via the universal rewriting rule. There is at least one z for which if z were an astronaut, then z is a scientist can be inferred via the existential biconditional elimination rule. There is at least one z for which if z were a scientist, then z is an astronaut can be inferred via the existential biconditional elimination rule.