Consider the following premises. There is at least one x_13 for which x_13 will listen to a song or x_13 will not cook. For all x_13, if x_13 were rich, then x_13 is cooking. For all x_13, x_13 will cook if and only if x_13 is a politician. For all x_13, x_13 is rich or x_13 is a politician. Can we infer the following from them? For all x_13, x_13 will not listen to a song.
 From the fact that for all x_13, x_13 will cook if and only if x_13 is a politician we can infer that for all x_13, if x_13 were a politician, then x_13 is cooking. From the fact that for all x_13, if x_13 were rich, then x_13 is cooking, that for all x_13, if x_13 were a politician, then x_13 is cooking, and that for all x_13, x_13 is rich or x_13 is a politician we can infer that for all x_13, x_13 will cook. From the fact that there is at least one x_13 for which x_13 will listen to a song or x_13 will not cook we can infer that there is at least one x_13 for which if x_13 cooks, then x_13 is listening to a song. Finally, from the fact that there is at least one x_13 for which if x_13 cooks, then x_13 is listening to a song, and that for all x_13, x_13 will cook we can infer that there is at least one x_13 for which x_13 will listen to a song, which contradicts that For all x_13, x_13 will not listen to a song. Therefore, the answer is no.