Consider the following premises. For all x_2, if x_2 listens to a song, then x_2 is playing squash. For all x_2, if x_2 plays squash, then x_2 is a bartender. For all x_2, if x_2 were a bartender, then x_2 is listening to a song. Can we infer the following from them? There is at least one x_2 for which the fact that x_2 were a bartender does not imply that x_2 is playing squash.
 From the fact that for all x_2, if x_2 were a bartender, then x_2 is listening to a song, and that for all x_2, if x_2 listens to a song, then x_2 is playing squash we can infer that for all x_2, if x_2 were a bartender, then x_2 is playing squash. From the fact that for all x_2, if x_2 plays squash, then x_2 is a bartender, and that for all x_2, if x_2 were a bartender, then x_2 is playing squash we can infer that for all x_2, x_2 will play squash if and only if x_2 is a bartender. Finally, from the fact that for all x_2, x_2 will play squash if and only if x_2 is a bartender we can infer that for all x_2, if x_2 were a bartender, then x_2 is playing squash, which contradicts that There is at least one x_2 for which the fact that x_2 were a bartender does not imply that x_2 is playing squash. Therefore, the answer is no.