Consider the following premises. For all x_8, x_8 is not a doctor or x_8 is poor. For all x_8, if x_8 were a lawyer, then x_8 is a soldier. For all x_8, x_8 is a writer or x_8 is a doctor. For all x_8, if x_8 were poor, then x_8 is a soldier. For all x_8, x_8 is not a writer or x_8 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which neither x_8 is a soldier nor x_8 is a poet.
 From the fact that for all x_8, x_8 is a writer or x_8 is a doctor, and that for all x_8, x_8 is not a writer or x_8 is a lawyer we can infer that for all x_8, x_8 is a doctor or x_8 is a lawyer via universal resolution. From the fact that for all x_8, x_8 is a doctor or x_8 is a lawyer, and that for all x_8, x_8 is not a doctor or x_8 is poor we can infer that for all x_8, x_8 is a lawyer or x_8 is poor via universal resolution. From the fact that for all x_8, if x_8 were a lawyer, then x_8 is a soldier, that for all x_8, if x_8 were poor, then x_8 is a soldier, and that for all x_8, x_8 is a lawyer or x_8 is poor we can infer that for all x_8, x_8 is a soldier via universal disjunction elimination. Finally, from the fact that for all x_8, x_8 is a soldier we can infer that for all x_8, x_8 is a soldier or x_8 is a poet via universal addition, which contradicts that There is at least one x_8 for which neither x_8 is a soldier nor x_8 is a poet. Therefore, the answer is no.