Consider the following premises. It is late or John is not writing a letter. It is not late. If it is late, then John is writing a letter. Can we infer the following from them? John is writing a letter.
 From the fact that it is late or John is not writing a letter we can infer that if John writes a letter, then it is late. From the fact that if John writes a letter, then it is late, and that if it is late, then John is writing a letter we can infer that John is writing a letter if and only if it is late. Finally, from the fact that John is writing a letter if and only if it is late, and that it is not late we can infer that John is not writing a letter, which contradicts that John is writing a letter. Therefore, the answer is no.