If the co-reference system works perfectly, the system should find a social network involving four people: {John, Tim, Mary, Mark}, and the ties: moth-erOf (Mary, John), and brotherOf (Mark, Tim).
if the co-reference system mistakenly links "John" to "his" in the second clause and links "Tim" to "his" in the first clause, then we will still have a network with four people, but the ties will be: motherOf (Mary, Tim), and brotherOf (Mark, John), which are completely wrong.