Consider the following premises. For all x_6, x_6 will play a game. For all x_6, x_6 will not read a book. For all x_6, if x_6 plays a game, then x_6 is a bartender. For all x_6, x_6 will read a book or x_6 is a mechanic. Can we infer the following from them? There is at least one x_6 for which either x_6 is a mechanic or x_6 is a bartender are not true.
 From the fact that for all x_6, x_6 will read a book or x_6 is a mechanic, and that for all x_6, x_6 will not read a book we can infer that for all x_6, x_6 is a mechanic. From the fact that for all x_6, if x_6 plays a game, then x_6 is a bartender, and that for all x_6, x_6 will play a game we can infer that for all x_6, x_6 is a bartender. Finally, from the fact that for all x_6, x_6 is a mechanic, and that for all x_6, x_6 is a bartender we can infer that for all x_6, x_6 is a mechanic and x_6 is a bartender, which contradicts that There is at least one x_6 for which either x_6 is a mechanic or x_6 is a bartender are not true. Therefore, the answer is no.