Consider the following premises. For all x_14, if x_14 drives a car, then x_14 is reading a book. For all x_14, x_14 will play a game or x_14 will drive a car. For all x_14, x_14 will work or x_14 is a poet. For all x_14, x_14 will read a book or x_14 will not play a game. For all x_14, x_14 is a politician or x_14 will not work. For all x_14, if x_14 were a poet, then x_14 is a politician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which either x_14 is a politician or x_14 will read a book are not true.
 From the fact that for all x_14, x_14 is a politician or x_14 will not work we can infer that for all x_14, if x_14 works, then x_14 is a politician via universal rewriting. From the fact that for all x_14, x_14 will read a book or x_14 will not play a game we can infer that for all x_14, if x_14 plays a game, then x_14 is reading a book via universal rewriting. From the fact that for all x_14, if x_14 works, then x_14 is a politician, that for all x_14, if x_14 were a poet, then x_14 is a politician, and that for all x_14, x_14 will work or x_14 is a poet we can infer that for all x_14, x_14 is a politician via universal disjunction elimination. From the fact that for all x_14, if x_14 plays a game, then x_14 is reading a book, that for all x_14, if x_14 drives a car, then x_14 is reading a book, and that for all x_14, x_14 will play a game or x_14 will drive a car we can infer that for all x_14, x_14 will read a book via universal disjunction elimination. Finally, from the fact that for all x_14, x_14 is a politician, and that for all x_14, x_14 will read a book we can infer that for all x_14, x_14 is a politician and x_14 will read a book via universal conjunction, which contradicts that There is at least one x_14 for which either x_14 is a politician or x_14 will read a book are not true. Therefore, the answer is no.