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 y_1 for which if y_1 drinks water, then y_1 is an astronaut. For all y_1, y_1 will not sleep. For all y_1, if y_1 were an astronaut, then y_1 is drinking water. For all y_1, y_1 will sleep if and only if y_1 is an astronaut.
There is at least one y_1 for which y_1 will drink water if and only if y_1 is an astronaut can be inferred via the existential biconditional introduction rule. There is at least one y_1 for which y_1 is an astronaut if and only if y_1 will drink water can be inferred via the existential biconditional introduction rule. For all y_1, if y_1 sleeps, then y_1 is an astronaut can be inferred via the universal biconditional elimination rule. For all y_1, if y_1 were an astronaut, then y_1 is sleeping can be inferred via the universal biconditional elimination rule. For all y_1, y_1 is not an astronaut can be inferred via the universal biconditional elimination rule.