Consider the following premises. For all x_10, if x_10 were a poet, then x_10 is cooking. For all x_10, x_10 will climb a mountain or x_10 is a bartender. For all x_10, x_10 is a poet if and only if x_10 will drink water. For all x_10, x_10 will not climb a mountain or x_10 will drink water. For all x_10, if x_10 were a bartender, then x_10 is cooking. Can we infer the following from them? There is at least one x_10 for which x_10 will not cook.
 From the fact that for all x_10, x_10 will climb a mountain or x_10 is a bartender, and that for all x_10, x_10 will not climb a mountain or x_10 will drink water we can infer that for all x_10, x_10 is a bartender or x_10 will drink water. From the fact that for all x_10, x_10 is a poet if and only if x_10 will drink water we can infer that for all x_10, if x_10 drinks water, then x_10 is a poet. From the fact that for all x_10, if x_10 drinks water, then x_10 is a poet, and that for all x_10, if x_10 were a poet, then x_10 is cooking we can infer that for all x_10, if x_10 drinks water, then x_10 is cooking. Finally, from the fact that for all x_10, if x_10 were a bartender, then x_10 is cooking, that for all x_10, if x_10 drinks water, then x_10 is cooking, and that for all x_10, x_10 is a bartender or x_10 will drink water we can infer that for all x_10, x_10 will cook, which contradicts that There is at least one x_10 for which x_10 will not cook. Therefore, the answer is no.