18K seems high. I did some tests for Universal once and we pulled 10K from some 70mm IMAX ride prints. 8K was solid, 10K was very borderline.
This was using 32bit renderman, and it was constantly OOM'ing because we were really pushing it.
I seem to recall that we rendered out at 7k, even though the optical resolution was meant to be 12k.
As I've not seen anyone else mention it, I feel the need to point out that Digital IMAX (which is the vast majority of screens and showings) maxes out at 4K.
Tim webber says it was rendered at 4k. Which contradicts what I remember. If he meant 4k textures that would make sense. 4k textures might have been why renderman kept on OOMing though and we had to tile the render even more.
Also I don't know how they printed it back out to film. It might have been sent to hollywood to laser/print out.