Consider the following premises. Thomas is not cooking. For all x_3, if x_3 cooks, then x_3 is a cashier. For all x_3, if x_3 were a cashier, then x_3 is cooking. Can we infer the following from them? Thomas is a cashier.
 From the fact that for all x_3, if x_3 cooks, then x_3 is a cashier, and that for all x_3, if x_3 were a cashier, then x_3 is cooking we can infer that for all x_3, x_3 will cook if and only if x_3 is a cashier. From the fact that for all x_3, x_3 will cook if and only if x_3 is a cashier we can infer that Thomas is cooking if and only if Thomas is a cashier. Finally, from the fact that Thomas is cooking if and only if Thomas is a cashier, and that Thomas is not cooking we can infer that Thomas is not a cashier, which contradicts that Thomas is a cashier. Therefore, the answer is no.