Consider the following premises. For all x_11, if x_11 were a writer, then x_11 is playing a game. For all x_11, if x_11 plays a game, then x_11 is a writer. There is at least one x_11 for which if x_11 were a writer, then x_11 is a janitor. For all x_11, x_11 will not play a game. For all x_11, x_11 is a janitor if and only if x_11 is a writer. Can we infer the following from them? For all x_11, x_11 is a janitor.
 From the fact that for all x_11, if x_11 were a writer, then x_11 is playing a game, and that for all x_11, if x_11 plays a game, then x_11 is a writer we can infer that for all x_11, x_11 is a writer if and only if x_11 will play a game. From the fact that for all x_11, x_11 is a janitor if and only if x_11 is a writer we can infer that for all x_11, if x_11 were a janitor, then x_11 is a writer. From the fact that for all x_11, x_11 is a writer if and only if x_11 will play a game, and that for all x_11, x_11 will not play a game we can infer that for all x_11, x_11 is not a writer. From the fact that there is at least one x_11 for which if x_11 were a writer, then x_11 is a janitor, and that for all x_11, if x_11 were a janitor, then x_11 is a writer we can infer that there is at least one x_11 for which x_11 is a writer if and only if x_11 is a janitor. Finally, from the fact that there is at least one x_11 for which x_11 is a writer if and only if x_11 is a janitor, and that for all x_11, x_11 is not a writer we can infer that there is at least one x_11 for which x_11 is not a janitor, which contradicts that For all x_11, x_11 is a janitor. Therefore, the answer is no.