How to fix IntelliJ IDEA's SDK after it got “c

问题:

Due to a separate issue in intellij (adding python module corrupts scala/java project), I need to revive/fix the scala/java SDK.

As can be seen in first screenshot even basic java classes e.g.

IllegalArgumentException

can not be found

But the SDK is already present/not missing (as shown in second screenshot). I have already done

File | Invalidate caches.

That did not help.

So .. how to reset / clean INtellij SDK's after it got confused/corrupted?

I am using 13.1.5 ultimate.