Consider the following premises. For all x_12, x_12 is bored. There is at least one x_12 for which x_12 is happy or x_12 is not bored. For all x_12, if x_12 cooks, then x_12 is not happy. Can we infer the following from them? There is at least one x_12 for which x_12 will not cook.
 From the fact that there is at least one x_12 for which x_12 is happy or x_12 is not bored we can infer that there is at least one x_12 for which if x_12 were bored, then x_12 is happy. From the fact that there is at least one x_12 for which if x_12 were bored, then x_12 is happy, and that for all x_12, x_12 is bored we can infer that there is at least one x_12 for which x_12 is happy. Finally, from the fact that for all x_12, if x_12 cooks, then x_12 is not happy, and that there is at least one x_12 for which x_12 is happy we can infer that there is at least one x_12 for which x_12 will not cook. Therefore, the answer is yes.