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 x for which if x were a police officer, then x is cooking. For all x, x will sleep or x will play a game. For all x, x will cook if and only if x will play a game. For all x, x will not sleep or x is a police officer.
For all x, x will play a game or x is a police officer can be inferred via the universal resolution rule. For all x, if x cooks, then x is playing a game can be inferred via the universal biconditional elimination rule. For all x, if x plays a game, then x is cooking can be inferred via the universal biconditional elimination rule.