The best replacement for exist is exists.

The best alternatives to exist are rated as following:
★★★★★  exists
★  not in
★  subsist
★  access denied
★  stella
★  is unavailable
★  marklogic
★  basex
  shimano stella
  certate
  sedna
  god does not exist
  is empty
  do they
  depend
  persist
  xindice

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Speaking about exist, one probably shouldn't forget about evil.

Other search terms related to exist and their ratings are:
★★★★★ evil
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exist
exists
not in