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If someone says they have "big black ants" it's almost always Camponotus pennsylvanicus. These carpenter ants are the largest and most common wood-damaging ants in North America. The main nest is in the dead wood of a living or standing dead tree. Workers take some of the larvae with them to create satellite colonies in other trees, or in the water-damaged wood of a house or other human-built structure.
The adults are unable to eat solid food, so they feed solid food to the larvae who regurgitate liquid that the adults can consume. In this case (and in at least one other case I've dealt with) the food source was live crickets being kept to feed zoo animals. The carpenter ant workers use their powerful mandibles to chop up the helpless microlivestock into small bits.
The long-term fix for a carpenter ant problem is a carpenter. Remove all the water-damaged (fungus-infected) wood and replace it with dry wood, and the ants won't be able to live there.