Add comments to example 2
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# Perform the proofs under the assumption that n is a nonnegative integer input constant
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input: n -> integer.
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assume: n >= 0.
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# p/1 is an auxiliary predicate, so replace all occurrences of p/1 with its completed definition
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output: q/1.
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axiom: forall N1, N2, N3 (N1 > N2 and N3 > 0 -> N1 * N3 > N2 * N3).
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# Induction principle instantiated for p.
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# This axiom is necessary because we use Vampire without higher-order reasoning
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axiom: (p(0) and forall N (N >= 0 and p(N) -> p(N + 1))) -> (forall N p(N)).
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assume: n >= 0.
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assert: exists N (forall X (q(X) <-> X = N) and N >= 0 and N * N <= n and (N + 1) * (N + 1) > n).
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