New simple proof system

I took basic logic and made it as familiar and easy to learn as possible. Proofs look just like proofs in elementary school algebra--a series of steps where each step has a formula on the left and a justification on the right. Formulas are manipulated using rewrite rules (commutativity, etc.) rather than the typical deduction rules. This isn't any sort of limitation. It can implement both intuitionistic and classical logic using only rewrite rules (currently it uses intuitionistic).

I wrote up the result as a sort of game. The first real proof is problem 8, which is just a few steps. Some of the later problems are ferociously difficult (but possible)--no one I've shown it to has gotten close to solving them, so if anyone manages to solve problem 25, 35, 36, or 37, please let me know.

It's completely free.