RSA-based authentication and key-agreement protocol
What you are looking for is authenticated key agreement with perfect forward secrecy based on certificates.

First, to address @Paulo's comment, TLS/SSL does provide this functionality with any of the Diffie-Hellman based suites. However it is more complicated than you require, as it generates several different shared secrets used for different purposes. SSH and IPSec have similar protocols.

The landmark key exchange protocol with the required properties is called the station-to-station protocol. I recommend the discussion of it (and the whole chapter for context) in the Handbook of Applied Cryptography (ch 12, pg 519). 

STS does require an encryption function which you specified you wanted to avoid. A modern key exchange that does not have an encryption function is MQV and its variants. Since you also wanted a rigorous security proof, likely more has been written about MQV and its variant's security than any other protocol (although the history is somewhat sordid). The drawback for you is that it requires the public keys (in the certificates) are discrete log-based not RSA (STS can work with RSA public keys since the long-term secret is only used for signatures). It may also be patent encumbered.

To conclude, I don't have a perfect protocol that both works with RSA and avoids using encryption or MACs but looking into these two protocols should give you a head start on finding something you can work with.