Consider the following premises. Susan is a politician and Linda is climbing a mountain. If Susan were a politician, then it is windy. It is not windy. Can we infer the following from them? It is late.
 From the fact that Susan is a politician and Linda is climbing a mountain we can infer that Susan is a politician. From the fact that if Susan were a politician, then it is windy, and that it is not windy we can infer that Susan is not a politician. From the fact that Susan is a politician we can infer that Susan is a politician or it is late. Finally, from the fact that Susan is a politician or it is late, and that Susan is not a politician we can infer that it is late. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.