Consider the following premises. For all x_11, if x_11 reads a book, then x_11 is playing a game. If it is cloudy, then Thomas is a writer. If Thomas plays a game, then it is cloudy. For all x_11, if x_11 were a writer, then x_11 is reading a book. Can we infer the following from them? If is not true that Thomas is a writer if and only if Thomas is playing a game.
 From the fact that for all x_11, if x_11 were a writer, then x_11 is reading a book, and that for all x_11, if x_11 reads a book, then x_11 is playing a game we can infer that for all x_11, if x_11 were a writer, then x_11 is playing a game. From the fact that for all x_11, if x_11 were a writer, then x_11 is playing a game we can infer that if Thomas were a writer, then Thomas is playing a game. From the fact that if Thomas plays a game, then it is cloudy, and that if it is cloudy, then Thomas is a writer we can infer that if Thomas plays a game, then Thomas is a writer. Finally, from the fact that if Thomas were a writer, then Thomas is playing a game, and that if Thomas plays a game, then Thomas is a writer we can infer that Thomas is a writer if and only if Thomas is playing a game, which contradicts that If is not true that Thomas is a writer if and only if Thomas is playing a game. Therefore, the answer is no.