Consider the following premises. For all x_7, x_7 will not play a game. For all x_7, x_7 will cook if and only if x_7 will play a game. There is at least one x_7 for which x_7 will cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not write a letter.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.