Consider the following premises. If Richard were a poet, then Michael is an artist. If it is cloudy, then Patricia is fast. Richard is a poet or it is cloudy. If Patricia were fast, then Michael is an artist. Can we infer the following from them? If we can, name the inference rule being used: Michael is not an artist.
 From the fact that if it is cloudy, then Patricia is fast, and that if Patricia were fast, then Michael is an artist we can infer that if it is cloudy, then Michael is an artist via transitivity. Finally, from the fact that if Richard were a poet, then Michael is an artist, that if it is cloudy, then Michael is an artist, and that Richard is a poet or it is cloudy we can infer that Michael is an artist via disjunction elimination, which contradicts that Michael is not an artist. Therefore, the answer is no.