What is the meaning of -을지?

Used to convey a doubt, or an indirect question about the future:

Used to connect a dependent clause conveying such a doubt or question to the main clause conveying judgment or a fact.

I wonder...; an intimate-style suffix introducing a doubt that one does not necessarily expect to be answered; mainly used when talking to oneself.

In the polite level, conveys a careful, indirect question; used to add further politeness than -는지 (-neunji).

Source: wiktionary.org