Yes, you are correct about the motions/stays. My mistake on that one.
However, the full court does not vote on each and every writ of certiorari submitted to them. By not being selected for consideration (conference & discuss list), the cert is “automatically denied.”
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In that case, you should be able to find one case on the Supreme Court's docket in which certiorari was denied and the docket does not say "circulated for conference." Look-- you won't find one.