[drdeca]

My understanding is that with usual SSL, it seems that one cannot make a proof based on your interaction with the server that you could use to convince a skeptic at some undetermined later time, However, others here have mentioned the tlsnotary idea which, if you are interacting with the person you want to prove it to live while you get the info from the server, then you can. And, if the server supports the TLS-N extension, then you can instead make a proof that should convince arbitrary people later.