Consider the following premises. There is at least one x_9 for which x_9 will sleep if and only if x_9 will cook. For all x_9, x_9 is rich if and only if x_9 will cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, the fact that x_9 sleeps does not imply that x_9 is rich.
That contradicts the premises. Therefore the answer is no.