Consider the following premises. There is at least one x_1 for which x_1 is bored if and only if x_1 will sleep. For all x_1, x_1 will sleep if and only if x_1 is bored. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, if is not true that x_1 is bored if and only if x_1 will sleep.
That contradicts the premises. Therefore the answer is no.