Consider the following premises. For all x_12, x_12 is a mechanic or x_12 is a janitor. For all x_12, if x_12 were a mechanic, then x_12 is a poet. For all x_12, x_12 is not a taxi driver. For all x_12, x_12 is a taxi driver or x_12 is a soldier. There is at least one x_12 for which if x_12 were a janitor, then x_12 is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, either x_12 is a poet or x_12 is a soldier are not true.
 From the fact that for all x_12, if x_12 were a mechanic, then x_12 is a poet, that there is at least one x_12 for which if x_12 were a janitor, then x_12 is a poet, and that for all x_12, x_12 is a mechanic or x_12 is a janitor we can infer that there is at least one x_12 for which x_12 is a poet via existential disjunction elimination. From the fact that for all x_12, x_12 is a taxi driver or x_12 is a soldier, and that for all x_12, x_12 is not a taxi driver we can infer that for all x_12, x_12 is a soldier via universal disjunctive syllogism. Finally, from the fact that there is at least one x_12 for which x_12 is a poet, and that for all x_12, x_12 is a soldier we can infer that some poets are soldiers via existential conjunction, which contradicts that For all x_12, either x_12 is a poet or x_12 is a soldier are not true. Therefore, the answer is no.