We present a Horn-clause-based framework for analysing security protocols that use platform configuration registers (PCRs), which are registers for maintaining state inside the Trusted Platform Module (TPM). In our model, the PCR state space is unbounded, and our experience shows that a naïve analysis using ProVerif or SPASS does not terminate. To address this, we extract a set of instances of the Horn clauses of our model, for which ProVerif does terminate on our examples. We prove the soundness of this extraction process: no attacks are lost, that is, any query derivable in the more general set of clauses is also derivable from the extracted instances. The effectiveness of our framework is demonstrated in two case studies: a simplified version of Microsoft Bitlocker, and a digital envelope protocol that allows a user to choose whether to perform a decryption, or to verifiably renounce the ability to perform the decryption.