I spent more than an hour to solve this problem. I didn't find it on the web for some reason. Is it only me who had this problem? Anyway the solution was quite easy but still strange in my opinion. I just should have gone to project settings -> Modules -> expand project's main folder and find a warning there, stating that kotlin library was not found in the module dependencies list:

It was the only place I saw any warnings. Intellij Idea CE didn't say anything: there wasn't any popup about this problem. All of the project settings' menu items too. I mean if you just open Project settings, you won't see this warning, say, in Project menu item, or Libraries, where I would expect such a warning, and in other menu items too, including "Modules". You have to expand these Modules to find this warning.

I think that Jetbrains could do better, considering that Kotlin is their native language. I don't know, maybe Ultimate version notifies about this problem immediately when you just open the project but with CE you will have to spend some time to find it out if you didn't face the problem before.