Convert the following set of sentences into symbolic form and then construct a proof for the final

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Convert the following set of sentences into symbolic form and then construct a proof for the final sentence based on the first two sentences::

Anyone who studies both artificial intelligence and botany is cool. There is at least one person who studies botany but is not cool. Therefore, there must be at least one person who does not study artificial intelligence.

Use A(x) and B(x) respectively for x studying artificial intelligence and botany. Use C(x) for x being cool.

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