Consider the following premises. For all x_4, x_4 will not go running. For all x_4, x_4 will listen to a song if and only if x_4 will go running. There is at least one x_4 for which x_4 will listen to a song if and only if x_4 is a bartender. Can we infer the following from them? There is at least one x_4 for which x_4 is not a bartender.
 From the fact that for all x_4, x_4 will listen to a song if and only if x_4 will go running, and that for all x_4, x_4 will not go running we can infer that for all x_4, x_4 will not listen to a song. Finally, from the fact that there is at least one x_4 for which x_4 will listen to a song if and only if x_4 is a bartender, and that for all x_4, x_4 will not listen to a song we can infer that there is at least one x_4 for which x_4 is not a bartender. Therefore, the answer is yes.