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 x, x will play a game or x is a nurse. For all x, if x plays a game, then x is listening to a song. For all x, if x were a nurse, then x is listening to a song. For all x, if x listens to a song, then x is a nurse.
For all x, if x plays a game, then x is a nurse can be inferred via the universal transitivity rule. For all x, x will listen to a song can be inferred via the universal disjunction elimination rule. For all x, x is a nurse if and only if x will listen to a song can be inferred via the universal biconditional introduction rule. For all x, x will listen to a song if and only if x is a nurse can be inferred via the universal biconditional introduction rule.