Consider the following premises. For all x_6, if x_6 drinks water, then x_6 is climbing a mountain. For all x_6, if x_6 plays a game, then x_6 is cooking. For all x_6, x_6 is not a nurse or x_6 will play a game. For all x_6, if x_6 cooks, then x_6 is climbing a mountain. For all x_6, x_6 is a nurse or x_6 will drink water. Can we infer the following from them? There is at least one x_6 for which x_6 will not climb a mountain.
 From the fact that for all x_6, x_6 is a nurse or x_6 will drink water, and that for all x_6, x_6 is not a nurse or x_6 will play a game we can infer that for all x_6, x_6 will drink water or x_6 will play a game. From the fact that for all x_6, if x_6 plays a game, then x_6 is cooking, and that for all x_6, if x_6 cooks, then x_6 is climbing a mountain we can infer that for all x_6, if x_6 plays a game, then x_6 is climbing a mountain. Finally, from the fact that for all x_6, if x_6 drinks water, then x_6 is climbing a mountain, that for all x_6, if x_6 plays a game, then x_6 is climbing a mountain, and that for all x_6, x_6 will drink water or x_6 will play a game we can infer that for all x_6, x_6 will climb a mountain, which contradicts that There is at least one x_6 for which x_6 will not climb a mountain. Therefore, the answer is no.