Consider the following premises. For all x_5, x_5 will climb a mountain or x_5 is a janitor. For all x_5, x_5 will not sleep. For all x_5, x_5 will cook. For all x_5, if x_5 climbs a mountain, then x_5 is sleeping. Can we infer the following from them? There is at least one x_5 for which either x_5 is a janitor or x_5 will cook are not true.
 From the fact that for all x_5, if x_5 climbs a mountain, then x_5 is sleeping, and that for all x_5, x_5 will not sleep we can infer that for all x_5, x_5 will not climb a mountain. From the fact that for all x_5, x_5 will climb a mountain or x_5 is a janitor, and that for all x_5, x_5 will not climb a mountain we can infer that for all x_5, x_5 is a janitor. Finally, from the fact that for all x_5, x_5 is a janitor, and that for all x_5, x_5 will cook we can infer that for all x_5, x_5 is a janitor and x_5 will cook, which contradicts that There is at least one x_5 for which either x_5 is a janitor or x_5 will cook are not true. Therefore, the answer is no.