Consider the following premises. There is at least one x_15 for which x_15 will cook if and only if x_15 is sad. For all x_15, if x_15 were a scientist, then x_15 is rich. For all x_15, x_15 is a scientist. For all x_15, x_15 is sad or x_15 is not rich. Can we infer the following from them? There is at least one x_15 for which x_15 will cook.
 From the fact that for all x_15, x_15 is sad or x_15 is not rich we can infer that for all x_15, if x_15 were rich, then x_15 is sad. From the fact that for all x_15, if x_15 were a scientist, then x_15 is rich, and that for all x_15, if x_15 were rich, then x_15 is sad we can infer that for all x_15, if x_15 were a scientist, then x_15 is sad. From the fact that for all x_15, if x_15 were a scientist, then x_15 is sad, and that for all x_15, x_15 is a scientist we can infer that for all x_15, x_15 is sad. From the fact that there is at least one x_15 for which x_15 will cook if and only if x_15 is sad we can infer that there is at least one x_15 for which if x_15 were sad, then x_15 is cooking. Finally, from the fact that there is at least one x_15 for which if x_15 were sad, then x_15 is cooking, and that for all x_15, x_15 is sad we can infer that there is at least one x_15 for which x_15 will cook. Therefore, the answer is yes.