Eevee screen space refraction aliasing

I understand that Eevee doesn’t do ‘real’ refraction. I’m just wondering if there’s anything I can do to get rid of the aliasing artefacts present in Eevee renders of glass objects such as this:

I’ve tried changing the render samples, the shadow settings, the subdivisions, and anything else I can think of. Should I just write this off as something Eevee can’t do?

Here’s the .blend if anyone wants to try:
2019-10-25_06-09-43_01.blend (146.2 KB)

That is a fundamental limitation of screenspace refraction. If you want better refractions, use cycles.