Consider the following premises. For all x_28, x_28 is not a cashier. It is overcast if and only if Mary is a cashier. Barbara is a poet or Jessica is running. For all x_23, if x_23 were a poet, then x_23 is a carpenter. If Jessica goes running, then Barbara is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Barbara is a carpenter and it is not overcast.
 From the fact that for all x_28, x_28 is not a cashier we can infer that Mary is not a cashier via universal instantiation. From the fact that for all x_23, if x_23 were a poet, then x_23 is a carpenter we can infer that if Barbara were a poet, then Barbara is a carpenter via universal instantiation. From the fact that if Barbara were a poet, then Barbara is a carpenter, that if Jessica goes running, then Barbara is a carpenter, and that Barbara is a poet or Jessica is running we can infer that Barbara is a carpenter via disjunction elimination. From the fact that it is overcast if and only if Mary is a cashier, and that Mary is not a cashier we can infer that it is not overcast via biconditional elimination. Finally, from the fact that Barbara is a carpenter, and that it is not overcast we can infer that Barbara is a carpenter and it is not overcast via conjunction. Therefore, the answer is yes.