In my Japanese class back at university the teacher told us that the opposite of 知っています is not 知っていません but 知りません. It’s just one of those things to remember.
I overheard a Japanese conversation between a foreigner and someone whom I consider to be a totally fluent speaker of Japanese. The first guy said 「知ってないと思うよ」 to which the second guy said 「うん、知ってない」. This shocked me but I thought that it could be Japanese which is used in conversation only. However, my 習字 teacher insists that it isn’t even used in conversation. So I’m a little confused – still, I’ll stick with 知りません・知らない which I hear all the time.