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_2, if y_2 works, then y_2 is drinking water. For all y_2, y_2 will not work. There is at least one y_2 for which if y_2 drinks water, then y_2 is working. For all y_2, y_2 will drink water if and only if y_2 will go running.
There is at least one y_2 for which y_2 will not drink water can be inferred via the existential modus tollens rule. There is at least one y_2 for which y_2 will drink water if and only if y_2 will work can be inferred via the existential biconditional introduction rule. There is at least one y_2 for which y_2 will work if and only if y_2 will drink water can be inferred via the existential biconditional introduction rule. For all y_2, if y_2 drinks water, then y_2 is running can be inferred via the universal biconditional elimination rule. For all y_2, if y_2 goes running, then y_2 is drinking water can be inferred via the universal biconditional elimination rule.