Consider the following premises. There is at least one y_4 for which y_4 will sleep or y_4 is not a poet. For all y_4, y_4 is a poet if and only if y_4 will sleep. Can we infer the following from them? For all y_4, if is not true that y_4 is a poet if and only if y_4 will sleep.
That contradicts the premises. Therefore the answer is no.