Consider the following premises. If Joseph plays tennis, then Michael is a mechanic. If Susan cooks, then Joseph is playing tennis. If it is windy, then Thomas is working. Susan is cooking or it is windy. If Michael were a mechanic, then Thomas is working. Can we infer the following from them? If we can, name the inference rule being used: Thomas is not working.
 From the fact that if Susan cooks, then Joseph is playing tennis, and that if Joseph plays tennis, then Michael is a mechanic we can infer that if Susan cooks, then Michael is a mechanic via transitivity. From the fact that if Susan cooks, then Michael is a mechanic, and that if Michael were a mechanic, then Thomas is working we can infer that if Susan cooks, then Thomas is working via transitivity. Finally, from the fact that if Susan cooks, then Thomas is working, that if it is windy, then Thomas is working, and that Susan is cooking or it is windy we can infer that Thomas is working via disjunction elimination, which contradicts that Thomas is not working. Therefore, the answer is no.