Consider the following premises. For all x_4, if x_4 plays a game, then x_4 is a bartender. For all x_4, if x_4 were a bartender, then x_4 is playing a game. For all x_4, if x_4 plays a game, then x_4 is a bartender. Can we infer the following from them? There is at least one x_4 for which the fact that x_4 were a bartender does not imply that x_4 is playing a game.
 From the fact that for all x_4, if x_4 were a bartender, then x_4 is playing a game, and that for all x_4, if x_4 plays a game, then x_4 is a bartender we can infer that for all x_4, x_4 is a bartender if and only if x_4 will play a game. From the fact that for all x_4, x_4 is a bartender if and only if x_4 will play a game we can infer that for all x_4, if x_4 were a bartender, then x_4 is playing a game. From the fact that for all x_4, if x_4 were a bartender, then x_4 is playing a game, and that for all x_4, if x_4 plays a game, then x_4 is a bartender we can infer that for all x_4, x_4 is a bartender if and only if x_4 will play a game. Finally, from the fact that for all x_4, x_4 is a bartender if and only if x_4 will play a game we can infer that for all x_4, if x_4 were a bartender, then x_4 is playing a game, which contradicts that There is at least one x_4 for which the fact that x_4 were a bartender does not imply that x_4 is playing a game. Therefore, the answer is no.