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: For all z_2, z_2 will sleep or z_2 will listen to a song. For all z_2, z_2 is a nurse if and only if z_2 will sleep. There is at least one z_2 for which z_2 is not a nurse.
For all z_2, if z_2 were a nurse, then z_2 is sleeping can be inferred via the universal biconditional elimination rule. For all z_2, if z_2 sleeps, then z_2 is a nurse can be inferred via the universal biconditional elimination rule. There is at least one z_2 for which z_2 will not sleep can be inferred via the existential biconditional elimination rule.