Consider the following premises. For all x_12, x_12 will play a game if and only if x_12 is a scientist. If Patricia cooks, then Barbara is a scientist. If Barbara plays a game, then Patricia is cooking. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Barbara is playing a game if and only if Barbara is a scientist.
That contradicts the premises. Therefore the answer is no.