Consider the following premises. For all x_1, if x_1 plays a game, then x_1 is a bartender. For all x_1, if x_1 were a bartender, then x_1 is playing a game. There is at least one x_1 for which x_1 is not a bartender. Can we infer the following from them? For all x_1, x_1 will play a game.
 From the fact that for all x_1, if x_1 plays a game, then x_1 is a bartender, and that for all x_1, if x_1 were a bartender, then x_1 is playing a game we can infer that for all x_1, x_1 will play a game if and only if x_1 is a bartender. Finally, from the fact that for all x_1, x_1 will play a game if and only if x_1 is a bartender, and that there is at least one x_1 for which x_1 is not a bartender we can infer that there is at least one x_1 for which x_1 will not play a game, which contradicts that For all x_1, x_1 will play a game. Therefore, the answer is no.