- Certainly true: (∃n. 2 * n == 0) /\ (∃n. 2 * n == 0)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Possibly true: (∃n. 2 * n == 0) /\ (∀n. n >= 0)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Certainly false: (∃n. 2 * n == 0) /\ (∀n. n > 0)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Possibly false: (∃n. 2 * n == 0) /\ (∃n. 2 * n == 1)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Possibly true: (∀n. n >= 0) /\ (∃n. 2 * n == 0)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Possibly true: (∀n. n >= 0) /\ (∀n. n >= 0)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Certainly false: (∀n. n >= 0) /\ (∀n. n > 0)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Possibly false: (∀n. n >= 0) /\ (∃n. 2 * n == 1)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Certainly false: (∀n. n > 0) /\ (∃n. 2 * n == 0)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Certainly false: (∀n. n > 0) /\ (∀n. n >= 0)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Certainly false: (∀n. n > 0) /\ (∀n. n > 0)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Certainly false: (∀n. n > 0) /\ (∃n. 2 * n == 1)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Possibly false: (∃n. 2 * n == 1) /\ (∃n. 2 * n == 0)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Possibly false: (∃n. 2 * n == 1) /\ (∀n. n >= 0)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Certainly false: (∃n. 2 * n == 1) /\ (∀n. n > 0)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Possibly false: (∃n. 2 * n == 1) /\ (∃n. 2 * n == 1)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Certainly true: (∃n. 2 * n == 0) \/ (∃n. 2 * n == 0)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Certainly true: (∃n. 2 * n == 0) \/ (∀n. n >= 0)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Certainly true: (∃n. 2 * n == 0) \/ (∀n. n > 0)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Certainly true: (∃n. 2 * n == 0) \/ (∃n. 2 * n == 1)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Certainly true: (∀n. n >= 0) \/ (∃n. 2 * n == 0)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Possibly true: (∀n. n >= 0) \/ (∀n. n >= 0)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Possibly true: (∀n. n >= 0) \/ (∀n. n > 0)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Possibly true: (∀n. n >= 0) \/ (∃n. 2 * n == 1)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Certainly true: (∀n. n > 0) \/ (∃n. 2 * n == 0)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Possibly true: (∀n. n > 0) \/ (∀n. n >= 0)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Certainly false: (∀n. n > 0) \/ (∀n. n > 0)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Possibly false: (∀n. n > 0) \/ (∃n. 2 * n == 1)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Certainly true: (∃n. 2 * n == 1) \/ (∃n. 2 * n == 0)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Possibly true: (∃n. 2 * n == 1) \/ (∀n. n >= 0)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Possibly false: (∃n. 2 * n == 1) \/ (∀n. n > 0)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Possibly false: (∃n. 2 * n == 1) \/ (∃n. 2 * n == 1)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Certainly true: (∃n. 2 * n == 0) -> (∃n. 2 * n == 0)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Possibly true: (∃n. 2 * n == 0) -> (∀n. n >= 0)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Certainly false: (∃n. 2 * n == 0) -> (∀n. n > 0)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Possibly false: (∃n. 2 * n == 0) -> (∃n. 2 * n == 1)
    - Left side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Certainly true: (∀n. n >= 0) -> (∃n. 2 * n == 0)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Possibly true: (∀n. n >= 0) -> (∀n. n >= 0)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Possibly false: (∀n. n >= 0) -> (∀n. n > 0)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Possibly false: (∀n. n >= 0) -> (∃n. 2 * n == 1)
    - Left side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Certainly true: (∀n. n > 0) -> (∃n. 2 * n == 0)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Certainly true: (∀n. n > 0) -> (∀n. n >= 0)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Certainly true: (∀n. n > 0) -> (∀n. n > 0)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Certainly true: (∀n. n > 0) -> (∃n. 2 * n == 1)
    - Left side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Certainly true: (∃n. 2 * n == 1) -> (∃n. 2 * n == 0)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Certainly true: ∃n. 2 * n == 0
        Found example:
          n = 0
  - Possibly true: (∃n. 2 * n == 1) -> (∀n. n >= 0)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Possibly true: ∀n. n >= 0
        Checked 100 possibilities without finding a counterexample.
  - Possibly true: (∃n. 2 * n == 1) -> (∀n. n > 0)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Certainly false: ∀n. n > 0
        Found counterexample:
          n = 0
  - Possibly true: (∃n. 2 * n == 1) -> (∃n. 2 * n == 1)
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
  - Possibly true: (∃n. 2 * n == 1) -> (∃n. 2 * n == 1) /\ (5 == 5 \/ (∀n. n < 5))
    - Left side:
        Possibly false: ∃n. 2 * n == 1
        No example was found; checked 100 possibilities.
    - Right side:
        Possibly false: (∃n. 2 * n == 1) /\ (5 == 5 \/ (∀n. n < 5))
        - Left side:
            Possibly false: ∃n. 2 * n == 1
            No example was found; checked 100 possibilities.
        - Right side:
            Certainly true: 5 == 5 \/ (∀n. n < 5)
            - Left side:
                Certainly true: 5 == 5
            - Right side:
                Certainly false: ∀n. n < 5
                Found counterexample:
                  n = 5