Consider the following premises. For all x_6, x_6 will play a game or x_6 will write a letter. For all x_6, x_6 will not play a game. For all x_6, if x_6 were a bartender, then x_6 is driving a car. For all x_6, x_6 will read a book or x_6 is a bartender. For all x_6, if x_6 reads a book, then x_6 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not play a game.
That is one of the premises. Therefore, the answer is yes.