I have two toilets in the house that appear to be running all of the time but there is no sign of water entering the toilet bowls except during flushing. Both toilets are insulated but one, the one downstairs is sweating quite badly. I suspect that if I could stop the running then the sweating might also stop. I've checked the flaps and they seem fine and, as I said there is no sign of water entering the bowl. I've also checked the overflow and the water level in the tank is about an inch below the top. Both toilets are reasonably new 2 and four years respectively and were installed by plumbers.

Suggestions/solutions appreciated.