Consider the following premises. For all x_7, x_7 will not drive a car or x_7 is a carpenter. For all x_7, x_7 will drive a car. For all x_7, x_7 is a carpenter if and only if x_7 will make tea. There is at least one x_7 for which if x_7 were a scientist, then x_7 is making tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will make tea.
 From the fact that for all x_7, x_7 is a carpenter if and only if x_7 will make tea we can infer that for all x_7, if x_7 were a carpenter, then x_7 is making tea via universal biconditional elimination. From the fact that for all x_7, x_7 will drive a car we can infer that for all x_7, x_7 will drive a car or x_7 is a scientist via universal addition. From the fact that for all x_7, x_7 will drive a car or x_7 is a scientist, and that for all x_7, x_7 will not drive a car or x_7 is a carpenter we can infer that for all x_7, x_7 is a scientist or x_7 is a carpenter via universal resolution. Finally, from the fact that there is at least one x_7 for which if x_7 were a scientist, then x_7 is making tea, that for all x_7, if x_7 were a carpenter, then x_7 is making tea, and that for all x_7, x_7 is a scientist or x_7 is a carpenter we can infer that there is at least one x_7 for which x_7 will make tea via existential disjunction elimination. Therefore, the answer is yes.