This is an old project I worked on in highschool in sophomore and junior year. I'm very interested in formal methods and type theory, but when I started working on the project I didn't know that there were a lot of systems out there already built what I was planning to do. The project was basically a HOL SMT solver. The project as a whole went through many versions, but it actually started as a first order logic solver that searched for set theory proofs. The following posts document the later portion of the project, where I switched to designing a type theory solver instead.

Proof Engine structures

Proof engine operations

Higher order unification

Proof engine solver algorithm