Denial of the Antecedent

In other words, if they drink the borax solution they will die, but if they do not, the 'denial of the antecedent' infers they would live.

In this case they are drinking heartily and will carry the borax back to their nest where they will feed it to their larvae and their queen, and the antecedent will not be denied!

(i.e. no more ants in my kitchen)

Terro-ble, well maybe, but I don't like bugs in my coffee