Proof:
Given: No mathematician has squared the circle.

Therefore: No one who has squared the circle is a mathematician.
Therefore: All who have squared the circle are nonmathematicians.
Therefore: Some nonmathematician has squared the circle.
Therefore: It is possible to square a circle. [QED]

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Theorem: It is possible to square the circle.

Proof:

Given: No mathematician has squared the circle.

Therefore: No one who has squared the circle is a mathematician.

Therefore: All who have squared the circle are nonmathematicians.

Therefore: Some nonmathematician has squared the circle.

Therefore: It is possible to square a circle. [QED]

:-)

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