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 Robert doesn't listen to a song, then it is late. For all z, z will listen to a song if and only if z is a nurse. Robert is not a nurse.
For all z, if z listens to a song, then z is a nurse can be inferred via the universal biconditional elimination rule. For all z, if z were a nurse, then z is listening to a song can be inferred via the universal biconditional elimination rule.