The Man In The Secluded House

Riddle: A man was murdered one stormy night. He lived in a house in the middle of nowhere. Only he, his wife and offspring knew the location of this house. His wife had died years ago, and his two only son lived with him. One of the sons reported the murder and gave investigators directions to the house so that they could investigate. The only evidence found was a diary with the last page reading "I killed my father." The two sons were questioned and denied doing it. They were given a lie detector test and both tested truthful. But if they were all secluded, who killed the man?