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 y_3, if y_3 plays a game, then y_3 is drinking water. There is at least one y_3 for which if y_3 drinks water, then y_3 is playing a game. For all y_3, y_3 will not play a game. For all y_3, if y_3 plays a game, then y_3 is drinking water.
There is at least one y_3 for which y_3 will not drink water can be inferred via the existential modus tollens rule. There is at least one y_3 for which y_3 will drink water if and only if y_3 will play a game can be inferred via the existential biconditional introduction rule. There is at least one y_3 for which y_3 will drink water if and only if y_3 will play a game can be inferred via the existential biconditional introduction rule. There is at least one y_3 for which y_3 will play a game if and only if y_3 will drink water can be inferred via the existential biconditional introduction rule. There is at least one y_3 for which y_3 will play a game if and only if y_3 will drink water can be inferred via the existential biconditional introduction rule.