Is there anything that common house ants won't burrow through?

The best treatment is to remove the things that attract the ants. If that is your cat's food dish I suspect that eventually, no matter how many cracks you seal up, that the ants will figure out how to come around the end of the slab and over to what they find attractive as a food source.

So maybe you want to start a regimen with your cat. Put down its food for say half an hour at each feeding and then take it up. Cats can learn to eat on a schedule. But at the same time they will also remind you of the schedule each and every day.

Ants leave trace information down to tell other ants their route to food source. They are very very smart bugs. Basically if you remove a food source they will still keep going to the same spot for a few days and then eventually branch out around the spot until they figure out their is no food.

So typically with a cat or small kids it is really really hard to get rid of them. I did a little studying last summer after an ant problem and the conclusion I had is that almost any ant coming into my house was coming in a door. All houses are different so I won't try to over-generalize but the doors are certainly a weak point on most. No matter how tight you think your doors are, an ant can probably get through.

So what I did was bomb 1-2 feet in front of each door with bug spray 3 times a day for about 3 days. I literally had an ant grave yard in front of two of the doors. Ants gone after three days.

With your specific case I would also say that you need to move the cat food entirely to a new place until you are positive ants are gone. They are like little robots. They are trying that spot not the cat food. Once there is no food in that spot they will use their little robot heads to try near spots (so move cat food out of room for sure). After a few days they will either find new food in your house or give up and get food somewhere else.

Dawn and vinegar. They will not cross over a line of dawn. I witnessed this two days ago as I am battling a group that wants to live and eat my house.

As they approached from the woods, the dawn was the only barrier they refused to cross. I bought a anti-ant powder and watched them cross without care.

I cleaned my floor with vinegar and the ones inside had no idea where to go.

Final suggestion in my current and on going research to battle these things, I read (have not yet confirmed) that steel wool is a great thing to push into cracks and crevices.

Good luck!

I second what treeNinja has proposed about the dawn and vinegar.

I also would like to add that cinnamon does a great job as well (is dry, can be easily remediated once the ants are gone).

Having two cats myself, I can say that cinnamon will not likely be an issue for your furry friends. I have one that is indifferent to the use of cinnamon and one that has slowly learned to leave it alone (she was initially drawn to its strong odor and tried to lick it up, but quickly learned it doesn't taste like it smells :)

BTW, this would be a comment but my reputation isn't sufficient for adding those at this time.

Super glue. Have wall mount faucet. Ants found slight gap in fitting on each side where faucet front and back screw together. Filled with loctite super glue. It has worked so far.