A good way to tell when soup has gone bad is to simply smell the soup.
When you smell the soup is should smell good and not sour or give any unpleasant odors.
If you smell the soup and the soup smells sour or unpleasant then it's bad and should be thrown out.
You could also taste the soup by tasting a small amount of the soup and if it tastes bad then throw it out because it's no longer good.
Or if you notice any mold growth in the soup or the soup smells rancid, sour or makes you want to vomit then don't taste it to check it.
The soup when good should never smell sour, rancid or have any mold growth in it when it's good.
If you've left the soup in the refrigerator longer than 4 days then likely is bad and should be discarded for safety reasons.
If you want to keep soup longer than 4 days you should place the soup in freezer safe containers or freezer bags and freeze the soup.
When frozen the soup can last up to a year but it's best to eat the frozen soup within 6 months for freshness.