Consider the following premises. There is at least one x_3 for which x_3 is a writer if and only if x_3 will play squash. For all x_3, x_3 will play a game if and only if x_3 will play squash. For all x_3, x_3 is not a writer. Can we infer the following from them? For all x_3, x_3 is not a writer.
That is one of the premises. Therefore, the answer is yes.