Unfortunately it's not possible, because TLS negotiates a symmetric key which is then used to encrypt and authenticate the rest of the session. If you post the transcript of a TLS session in an attempt to "prove" that you retrieved a specific document, a third party can verify that you did in fact negotiate a symmetric key with the correct server; but since it's a symmetric key, anyone with knowledge of the key can arbitrarily modify the transcript of the session [well, the part of the session where the HTTP request and response happen]. This obviously includes the original prover, and so a TLS transcript proves nothing at all.