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_11, x_11 will sleep if and only if x_11 will play a game. For all x_11, x_11 will play a game if and only if x_11 will sleep.
For all x_11, if x_11 sleeps, then x_11 is playing a game can be inferred via the universal biconditional elimination rule. For all x_11, if x_11 plays a game, then x_11 is sleeping can be inferred via the universal biconditional elimination rule. For all x_11, if x_11 plays a game, then x_11 is sleeping can be inferred via the universal biconditional elimination rule. For all x_11, if x_11 sleeps, then x_11 is playing a game can be inferred via the universal biconditional elimination rule.