User blog comment:DontDrinkH20/"Interesting numbers" and the 3 Classes of Googolisms/@comment-27513631-20180813194237/@comment-27513631-20180813215113

Oh right - I misread and thought that clause only applied to \(\land\) and \(\lor\), and was just \(\max\) for \(+\) and \(\cdot\).

In that case, \(\exists x(x=S(S(0))\land S(a)=(x\cdot x)\cdot x)\) is a complexity-6 formula defining 7. We save one complexity by swapping the universal for an existential, and it costs nothing to replace \(a\) with \(S(a)\), as the other side of the equality still has a higher complexity.