Consider the following premises. For all x_11, x_11 is not a cashier or x_11 is a bartender. For all x_11, x_11 is a cashier or x_11 is a lawyer. For all x_11, x_11 is rich if and only if x_11 is a lawyer. For all x_11, x_11 is not rich. Can we infer the following from them? There is at least one z for which z is a bartender.
 From the fact that for all x_11, x_11 is a cashier or x_11 is a lawyer, and that for all x_11, x_11 is not a cashier or x_11 is a bartender we can infer that for all x_11, x_11 is a lawyer or x_11 is a bartender. From the fact that for all x_11, x_11 is rich if and only if x_11 is a lawyer, and that for all x_11, x_11 is not rich we can infer that for all x_11, x_11 is not a lawyer. From the fact that for all x_11, x_11 is a lawyer or x_11 is a bartender, and that for all x_11, x_11 is not a lawyer we can infer that for all x_11, x_11 is a bartender. From the fact that for all x_11, x_11 is a bartender we can infer that Patricia is a bartender. Finally, from the fact that Patricia is a bartender we can infer that there is at least one z for which z is a bartender. Therefore, the answer is yes.