Consider the following premises. For all x_1, if x_1 plays a game, then x_1 is a writer. For all x_1, if x_1 were a writer, then x_1 is playing a game. There is at least one x_1 for which x_1 will not play a game. Can we infer the following from them? There is at least one x_1 for which x_1 is not a writer.
 From the fact that for all x_1, if x_1 were a writer, then x_1 is playing a game, and that for all x_1, if x_1 plays a game, then x_1 is a writer we can infer that for all x_1, x_1 is a writer if and only if x_1 will play a game. Finally, from the fact that for all x_1, x_1 is a writer if and only if x_1 will play a game, and that there is at least one x_1 for which x_1 will not play a game we can infer that there is at least one x_1 for which x_1 is not a writer. Therefore, the answer is yes.