layered cluster subgraph question

In this tweet I posted a GraphvizFiddle link on "3SAT-3COL reduction applied to unsatisfiable 2SAT formula ➫ small non 3-colorable graph without K4-{e} as subgraph". Below picture is a screenshot of the generated "dot" tool layout.

I had to put "x", "~x", "y" and "~y" boolean literals into a single cluster subgraph because I found no way to enforce a cluster containing "x" and "~x" and another cluster containing "y", "~y" to be layed out at same rank. "rank=same" works well for nodes. My question is, whether somehow it is possible to have "rank=same" work for clusters as well? If not, is there a workaround to achieve that goal?

You can play with the graph and layout directly with this GraphvizFiddle link (modify & click "Draw"):
3SAT-3COL

Hermann <GraphvizFiddle/> <Viz.js_form10/>

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