Break an authentication protocol based on a pre-shared symmetric key, with message numbers
(re-post of my comment as an answer)

The only party that generates encryptions of messages $m$ such that $m$:


contains 3 parts
begins with a "2"


is Alice. Each time she generates such a chipertext, the last component is $P_A$. If $E$ is a strong enough encryption (non malleable), then Trudy will not be able to generate by herself a an encryption  $E(m)$ of a massage in the formt $m=\langle 2,R,P_T \rangle $ that Bob would accept (except with negligible probability).