Alright, first of all. Let's stop inventing nonsense out of the air. And blatant lying have no place here either. Remember that *any controversial unsourced material* will be challenged and removed as per WP:Verifiability. Now, that everyone knows that, we can hopefully start a sensible and reasonable discussion on Seoul again. I will start with pointing out some very basic mistakes here:
The reference everyone seems to quote  has no mention of this invented system called "Seoul Subway Line 1-9". Strictly speaking, it lists lines owned by Seoul City's government. 
That reference also says that Line 7 extension to Incheon is to open by late 2012, which it did. Since it is outdated, the true number is 327km.
Gyeongchun has no grade crossings (Terra is still remembering the now passed away Gyeongchun line from the 80s) and will never have KTX service (which he is again confusing with Wongju-Ganneung Line, a separate line under construction exclusively for HSR)
Gyeongbu Line for the metro service of Line 1 operate on a separate track, hence no track sharing. 
Gyeongin - Are you kidding me? Freight and intercity trains? Where is that nonsense coming from? This is an exclusive metro line with no other traffic whatsoever. This line is metro exclusive. How old are you? I mean like you seem to remember Seoul from the 80s or something.

Now, I have addressed the issues above assuming that track sharing is not allowed, which is an invented original research as raised by BsBsBs. Looking back at the sources..neither APTA nor USDT make any mention of that. The 2011 UITP source does mention something similar to it in a footnote saying that "networks that are functionally separate from the rest of the rail system" are basically metros from what I understand. Now remember they say "functionally" - not "track sharing". That's because the Korean government's legal law defines Line 1's Gyeongbu section for example, as a metro because it has a dedicated track on its own that follow the same path as the intercity trains next to it. In other words, it is functionally separate from the rest of the railway system and hence meets UITP's definition, which is very Eurocentric by the way. Seoul Metro and SMRT are members of UITP, so clearly track sharing is absent from their definitions. But functionally separate is present. And this is exactly how things should be done. And this 10 minute rule is completely absent anywhere in UITP/APTA or USDT and was voted out by consensus by multiple users (except IJBall). Legally, Incheon Subway is part of the metro system, so there's no doubt in including that as I have mentioned before with the legal sources. From what I know, Korail will be completely updating their website on April 1st, with the new updated data for their subways. So we will have direct numbers for all of Korail's metros pretty soon. The issue of sorting metros by systems and not by operators, is something that is not agreed with here. It would require a name change on this article. This will need external consensus and is something we will deal at a later time.