Consider the following premises. For all x_4, if x_4 listens to a song, then x_4 is rich. For all x_4, x_4 will listen to a song or x_4 will not climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which the fact that x_4 climbs a mountain does not imply that x_4 is rich.
 From the fact that for all x_4, x_4 will listen to a song or x_4 will not climb a mountain we can infer that for all x_4, if x_4 climbs a mountain, then x_4 is listening to a song via universal rewriting. Finally, from the fact that for all x_4, if x_4 climbs a mountain, then x_4 is listening to a song, and that for all x_4, if x_4 listens to a song, then x_4 is rich we can infer that for all x_4, if x_4 climbs a mountain, then x_4 is rich via universal transitivity, which contradicts that There is at least one x_4 for which the fact that x_4 climbs a mountain does not imply that x_4 is rich. Therefore, the answer is no.