expected

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  - Possibly true: ∀x. x =!= 0 \/ (∃n. n * x >= 1)
    Checked 100 possibilities without finding a counterexample.
  - Certainly true: ∀f. any([∀x. f(x) =!= not x, ∀x. f(x) =!= x, ∀x. f(x) =!= false, ∀x. f(x) =!= true])
    No counterexamples exist; all possible values were checked.
  - Certainly false: all([true, true, true, false, true])
  - Certainly true: ∃k. hasFactors(2 ^ k + 1)
    Found example:
      k = 3