Consider the following premises. For all x_5, x_5 will not cook. For all x_5, x_5 will drive a car. For all x_5, x_5 will cook if and only if x_5 will drive a car. Can we infer the following from them? There is at least one x_5 for which x_5 is not a poet.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.