Consider the following premises. For all x_13, x_13 is not rich. For all x_13, x_13 is rich if and only if x_13 is happy. For all x_13, if x_13 were happy, then x_13 is bored. For all x_13, if x_13 were bored, then x_13 is happy. For all x_13, x_13 will cook if and only if x_13 is bored. Can we infer the following from them? There is at least one x_13 for which x_13 will cook.
 From the fact that for all x_13, if x_13 were happy, then x_13 is bored, and that for all x_13, if x_13 were bored, then x_13 is happy we can infer that for all x_13, x_13 is happy if and only if x_13 is bored. From the fact that for all x_13, x_13 is rich if and only if x_13 is happy we can infer that for all x_13, if x_13 were happy, then x_13 is rich. From the fact that for all x_13, if x_13 were happy, then x_13 is rich, and that for all x_13, x_13 is not rich we can infer that for all x_13, x_13 is not happy. From the fact that for all x_13, x_13 is happy if and only if x_13 is bored, and that for all x_13, x_13 is not happy we can infer that for all x_13, x_13 is not bored. Finally, from the fact that for all x_13, x_13 will cook if and only if x_13 is bored, and that for all x_13, x_13 is not bored we can infer that for all x_13, x_13 will not cook, which contradicts that There is at least one x_13 for which x_13 will cook. Therefore, the answer is no.