Consider the following premises. For all x_8, x_8 will listen to a song or x_8 is rich. For all x_8, if x_8 listens to a song, then x_8 is playing a game. For all x_8, x_8 will climb a mountain and x_8 will drink water. For all x_8, if x_8 were rich, then x_8 is playing a game. Can we infer the following from them? There is at least one x_8 for which either x_8 will play a game or x_8 will climb a mountain are not true.
 From the fact that for all x_8, if x_8 listens to a song, then x_8 is playing a game, that for all x_8, if x_8 were rich, then x_8 is playing a game, and that for all x_8, x_8 will listen to a song or x_8 is rich we can infer that for all x_8, x_8 will play a game. From the fact that for all x_8, x_8 will climb a mountain and x_8 will drink water we can infer that for all x_8, x_8 will climb a mountain. Finally, from the fact that for all x_8, x_8 will play a game, and that for all x_8, x_8 will climb a mountain we can infer that for all x_8, x_8 will play a game and x_8 will climb a mountain, which contradicts that There is at least one x_8 for which either x_8 will play a game or x_8 will climb a mountain are not true. Therefore, the answer is no.