Consider the following premises. For all y_4, y_4 will write a letter or y_4 will not sleep. For all y_4, y_4 will sleep or y_4 will not write a letter. For all y_4, y_4 will not write a letter. Can we infer the following from them? For all y_4, y_4 will sleep or y_4 will not write a letter.
That is one of the premises. Therefore, the answer is yes.