About half of the problems in Compfiles have complete solutions. They are marked by the checkmarks in the list at https://dwrensha.github.io/compfiles/index.html .

As far as I know, based on published systems like LeanDojo [1] and Magnushammer [2], computers today can only solve a small handful of the very easiest of these problems (like maybe Imo1959P1).

[1] https://leandojo.org/

[2] https://arxiv.org/abs/2303.04488