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