Consider the following premises. For all x_13, x_13 is not a bartender or x_13 will cook. For all x_13, x_13 will not listen to a song. There is at least one x_13 for which x_13 will listen to a song. Can we infer the following from them? There is at least one x_13 for which x_13 is bored or x_13 will cook.
 From the fact that there is at least one x_13 for which x_13 will listen to a song we can infer that there is at least one x_13 for which x_13 will listen to a song or x_13 is a bartender. From the fact that there is at least one x_13 for which x_13 will listen to a song or x_13 is a bartender, and that for all x_13, x_13 will not listen to a song we can infer that there is at least one x_13 for which x_13 is a bartender. From the fact that there is at least one x_13 for which x_13 is a bartender we can infer that there is at least one x_13 for which x_13 is a bartender or x_13 is bored. Finally, from the fact that there is at least one x_13 for which x_13 is a bartender or x_13 is bored, and that for all x_13, x_13 is not a bartender or x_13 will cook we can infer that there is at least one x_13 for which x_13 is bored or x_13 will cook. Therefore, the answer is yes.