Here are instructions for verifying a Chainpoint proof without needing a trusted third-party.
Each Chainpoint proof contains a set of operations. To verify the proof, step through the operations and check if the resulting value matches the Merkle root of a Bitcoin block header. So long as you have a copy of the Bitcoin blockchain or access to a block explorer, you can verify a Chainpoint proof.
We'll use this open-source library to parse and step through the operations of Chainpoint proof. It works offline.
https://github.com/chainpoint/chainpoint-parse