Consider:
All teachers are human.
Some calligraphers are not teachers.
It does not follow that some humans are not calligraphers. All humans might be calligraphers, with the particular non-teacher calligraphers being other individuals.
As a countermodel, take every teacher to be human and every human to be a calligrapher, while some non-teachers are calligraphers as well. Both premises are true and the proposed conclusion false. The mere words “universal” and “negative” do not prove validity.
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The Fourth Figure: Productive Conditions, Moods and Proofs
Consider:
All teachers are human.
Some calligraphers are not teachers.
It does not follow that some humans are not calligraphers. All humans might be calligraphers, with the particular non-teacher calligraphers being other individuals.
As a countermodel, take every teacher to be human and every human to be a calligrapher, while some non-teachers are calligraphers as well. Both premises are true and the proposed conclusion false. The mere words “universal” and “negative” do not prove validity.