Who propounded "All doesn't exist" in the Buddha's time?

[SN 12.15](https://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.015.than.html) says, > 'Everything exists': That is one extreme. 'Everything doesn't exist': That is a second extreme. Avoiding these two extremes, the Tathagata teaches the Dhamma via the middle We know that by the Buddha's time, the early Upanishads propounded some sort of "everything is existence" or "everything is the Self" doctrine. But who propounded the latter doctrine ("Everything doesn't exist") in the Buddha's time? Certainly not Carvakas or Lokayatas, who were simply materialists. So who exactly was propounding this during the Buddha's time?