Consider the following premises. Elisabeth is a poet or Mary is not a scientist. It is late or Mary is a scientist. If it is late, then James is running. If James goes running, then Elisabeth is a poet. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is a poet.
 From the fact that Elisabeth is a poet or Mary is not a scientist we can infer that if Mary were a scientist, then Elisabeth is a poet via rewriting. From the fact that if it is late, then James is running, and that if James goes running, then Elisabeth is a poet we can infer that if it is late, then Elisabeth is a poet via transitivity. Finally, from the fact that if it is late, then Elisabeth is a poet, that if Mary were a scientist, then Elisabeth is a poet, and that it is late or Mary is a scientist we can infer that Elisabeth is a poet via disjunction elimination. Therefore, the answer is yes.