Well, for various reasons that I don't really want to get into right now, I believe in typing with dichotomies, not individual functions. You are I>E, N>S, T>F and P>J. That's all there is to it.
Now, this is just from my experience, but I find that INTPs can be surprisingly empathetic. They just can't reliably display the correct expressions to go with how they are feeling, so other people assume they have no emotions, hence the robot stereotypes. In reality, the mostly logically rigid types are IXTJs. You can go to r/INTJ and experience it yourself. INTPs are known for their relatively flat affect and general social awkwardness, but they aren't blunt and abrasive in the same way that XXTJs are.
What you describe as "obvious" is a sort of automatic logical framework that you subconsciously construct when you try to understand something in your own way. It connects to everything else you already know and after processing it, you get a "yeah, that makes sense" or "no that's not quite right" out of it. Thats how I think "Ti" works for INTPs. It's not "Te", where you can easily explain it while referencing outside sources like data and specific facts. It's more subjective because the output is based on what you already understand. If you are missing crucial pieces of information, you get the wrong output. That's why cross-checking is so important: logical theorizing without data leads to pseudoscience and conspiracy theories.
In case you don't recognize some of these, I'll list em L to R, up to down.
Kumiko Oumae- Hibike Euphonium, Shouma Takakura- Mawaru Penguindrum, Ashitaka- Princess Mononoke
Aerith Gainsborough- Final Fantasy VII, Dale Cooper- Twin Peaks, Nia Teppelin- Tengen Toppa Gurren Lagann
Shinra Kishitani- Durarara, Raoden- Elantris, Xion- Kingdom Hearts
Chart made with befunky
They’re called zebra mildliners. Go live your brightest life ✨:
Zebra Mildliner Highlighter Pen Set, 20 Pastel Color Set (Japan Import) https://www.amazon.com/dp/B072QXQHFC/ref=cm_sw_r_cp_api_glt_fabc_FV373NAE44HH1ZEGB47Z?_encoding=UTF8&psc=1