Consider the following premises. Karen is playing squash or William is a poet. If William were a poet, then it is late. If it is late, then Mary is rich. It is late if and only if Karen is playing squash. Can we infer the following from them? If we can, name the inference rule being used: Mary is not rich.
 From the fact that it is late if and only if Karen is playing squash we can infer that if Karen plays squash, then it is late via biconditional elimination. From the fact that if Karen plays squash, then it is late, that if William were a poet, then it is late, and that Karen is playing squash or William is a poet we can infer that it is late via disjunction elimination. Finally, from the fact that if it is late, then Mary is rich, and that it is late we can infer that Mary is rich via modus ponens, which contradicts that Mary is not rich. Therefore, the answer is no.