TFA isn't about AI; it's about taking the same arguments mathematicians are already writing down semi-formally with a hand-wavy argument that it could be made completely formal, and instead/also writing them down formally.
In cases where the Hilbert machine applies, the mathematician writing down the semi-formal argument already has to state the new axioms, justify them, and reason about how they apply, and the proposal would just take that "reason about how they apply" step and write it in a computer-verifiable way.
In cases where the Hilbert machine applies, the mathematician writing down the semi-formal argument already has to state the new axioms, justify them, and reason about how they apply, and the proposal would just take that "reason about how they apply" step and write it in a computer-verifiable way.