Consider the following premises. For all x_8, x_8 is a carpenter if and only if x_8 is curious. For all x_8, if x_8 were fast, then x_8 is a politician. For all x_8, x_8 is curious or x_8 is fast. For all x_8, if x_8 were a politician, then x_8 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is a carpenter.
 From the fact that for all x_8, x_8 is a carpenter if and only if x_8 is curious we can infer that for all x_8, if x_8 were curious, then x_8 is a carpenter via universal biconditional elimination. From the fact that for all x_8, if x_8 were fast, then x_8 is a politician, and that for all x_8, if x_8 were a politician, then x_8 is a carpenter we can infer that for all x_8, if x_8 were fast, then x_8 is a carpenter via universal transitivity. Finally, from the fact that for all x_8, if x_8 were curious, then x_8 is a carpenter, that for all x_8, if x_8 were fast, then x_8 is a carpenter, and that for all x_8, x_8 is curious or x_8 is fast we can infer that for all x_8, x_8 is a carpenter via universal disjunction elimination. Therefore, the answer is yes.