RAQQA, Syria -- The heart of Raqqa is shattered, laid waste by three years of ISIS rule and a siege that's lasted four months.

On the front line, U.S.-backed Syrian militiamen decided to put on a show for the camera. ISIS gunmen are hiding in the ruins of a nearby apartment building, they said, but it looked more like boredom than real fighting. Progress here is grindingly slow.

They know exactly where ISIS is -- in a tiny sector of the city -- but they can't flush them out.

The ruins of Raqqa CBS News

Around 250 fighters are thought to be dug in, some of them in a stadium, others around Naim Square, which ISIS once decorated with severed heads.

But amongst the fighters are civilians being used as human shields. "They have women and children with them," commander Zaaem Ahmadi told CBS News. He used to be an electrician in Raqqa, and claims to have killed dozens of ISIS extremists. He took us to see a long-dead corpse.

One of the many stray cats in Raqqa CBS News

The only signs of life in most neighborhoods, apart from the fighters, are stray cats. They're struggling to survive, like everyone else in this beleaguered city.

U.S.-backed forces continue to say that they are just days away from victory in Raqqa, but they've already opened up a new front further to the south, where ISIS is being squeezed into a shrinking area in the desert. So the fighting will continue.