Consider the following premises. For all x_12, if x_12 plays a game, then x_12 is climbing a mountain. For all x_12, x_12 will play a game or x_12 is poor. For all x_12, if x_12 were a police officer, then x_12 is cooking. For all x_12, x_12 is a police officer. There is at least one x_12 for which if x_12 were poor, then x_12 is climbing a mountain. Can we infer the following from them? For all x_12, either x_12 will cook or x_12 will climb a mountain are not true.
 From the fact that for all x_12, if x_12 plays a game, then x_12 is climbing a mountain, that there is at least one x_12 for which if x_12 were poor, then x_12 is climbing a mountain, and that for all x_12, x_12 will play a game or x_12 is poor we can infer that there is at least one x_12 for which x_12 will climb a mountain. From the fact that for all x_12, if x_12 were a police officer, then x_12 is cooking, and that for all x_12, x_12 is a police officer we can infer that for all x_12, x_12 will cook. Finally, from the fact that for all x_12, x_12 will cook, and that there is at least one x_12 for which x_12 will climb a mountain we can infer that there is at least one x_12 for which x_12 will cook and x_12 will climb a mountain, which contradicts that For all x_12, either x_12 will cook or x_12 will climb a mountain are not true. Therefore, the answer is no.