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