Consider the following premises. For all x_7, x_7 will cook. For all x_7, x_7 will drink water if and only if x_7 will work. For all x_7, x_7 will drink water. Can we infer the following from them? There is at least one x_7 for which either x_7 will cook or x_7 will work are not true.
 From the fact that for all x_7, x_7 will drink water if and only if x_7 will work we can infer that for all x_7, if x_7 drinks water, then x_7 is working. From the fact that for all x_7, if x_7 drinks water, then x_7 is working, and that for all x_7, x_7 will drink water we can infer that for all x_7, x_7 will work. Finally, from the fact that for all x_7, x_7 will cook, and that for all x_7, x_7 will work we can infer that for all x_7, x_7 will cook and x_7 will work, which contradicts that There is at least one x_7 for which either x_7 will cook or x_7 will work are not true. Therefore, the answer is no.