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_2 for which if x_2 were a poet, then x_2 is drinking water. For all x_2, x_2 will sleep if and only if x_2 will drink water. For all x_2, if x_2 drinks water, then x_2 is a poet.
There is at least one x_2 for which x_2 is a poet if and only if x_2 will drink water can be inferred via the existential biconditional introduction rule. There is at least one x_2 for which x_2 will drink water if and only if x_2 is a poet can be inferred via the existential biconditional introduction rule. For all x_2, if x_2 sleeps, then x_2 is drinking water can be inferred via the universal biconditional elimination rule. For all x_2, if x_2 drinks water, then x_2 is sleeping can be inferred via the universal biconditional elimination rule.