Consider the following premises. There is at least one x_11 for which if x_11 were a mechanic, then x_11 is poor. For all x_11, x_11 will sleep or x_11 is a mechanic. For all x_11, if x_11 were poor, then x_11 is making tea. For all x_11, x_11 will not sleep or x_11 is a poet. For all x_11, x_11 will make tea or x_11 is not a poet. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 will make tea.
 From the fact that for all x_11, x_11 will sleep or x_11 is a mechanic, and that for all x_11, x_11 will not sleep or x_11 is a poet we can infer that for all x_11, x_11 is a mechanic or x_11 is a poet via universal resolution. From the fact that for all x_11, x_11 will make tea or x_11 is not a poet we can infer that for all x_11, if x_11 were a poet, then x_11 is making tea via universal rewriting. From the fact that there is at least one x_11 for which if x_11 were a mechanic, then x_11 is poor, and that for all x_11, if x_11 were poor, then x_11 is making tea we can infer that there is at least one x_11 for which if x_11 were a mechanic, then x_11 is making tea via existential transitivity. Finally, from the fact that there is at least one x_11 for which if x_11 were a mechanic, then x_11 is making tea, that for all x_11, if x_11 were a poet, then x_11 is making tea, and that for all x_11, x_11 is a mechanic or x_11 is a poet we can infer that there is at least one x_11 for which x_11 will make tea via existential disjunction elimination. Therefore, the answer is yes.