Consider the following premises. For all x_13, if x_13 cooks, then x_13 is a cashier. There is at least one x_13 for which x_13 will play a game if and only if x_13 is a cashier. For all x_13, x_13 is curious if and only if x_13 is a cashier. For all x_13, x_13 is not curious. For all x_13, if x_13 were curious, then x_13 is cooking. Can we infer the following from them? For all x_13, x_13 is curious if and only if x_13 is a cashier.
That is one of the premises. Therefore, the answer is yes.