Word for indecipherable, confused, non understandable, convoluted beyond hope of untanglement

As @user888379 pointed out, intractable is the word I was looking for. I have looked up the definition of this word and I now see that it does not carry along as much information as I had originally thought it did and that I must have ascribed more meaning to this word than it deserved based on the limited context in which I had seen it used.

edit - it turns out that while intractable doesn't really mean what I had originally thought it meant, the term intractable conflict is one in common use and tends to more closely follow the meaning that I had described in the original post.

See:

1. https://www.beyondintractability.org/essay/meaning_intractability

2. https://centerforinterculturaldialogue.files.wordpress.com/2014/06/key-concept-intractable-conflict.pdf

These conflicts are often likened to untying the Gordian Knot. The knot has become a metaphor for intractable and difficult to solve problems, especially with regard to statecraft and conflict. It comes from the legend quoted below from the Wikipedia article:

The Phrygians were without a king, but an oracle at Telmissus (the ancient capital of Lycia) decreed that the next man to enter the city driving an ox-cart should become their king. A peasant farmer named Gordias drove into town on an ox-cart and was immediately declared king. Out of gratitude, his son Midas dedicated the ox-cart to the Phrygian god Sabazios (whom the Greeks identified with Zeus) and tied it to a post with an intricate knot of cornel bark (Cornus mas). The knot was later described by Roman historian Quintus Curtius Rufus as comprising "several knots all so tightly entangled that it was impossible to see how they were fastened".

The ox-cart still stood in the palace of the former kings of Phrygia at Gordium in the fourth century BC when Alexander arrived, at which point Phrygia had been reduced to a satrapy, or province, of the Persian Empire. An oracle had declared that any man who could unravel its elaborate knots was destined to become ruler of all of Asia. Alexander wanted to untie the knot but struggled to do so without success. He then reasoned that it would make no difference how the knot was loosed, so he drew his sword and sliced it in half with a single stroke. In an alternative version of the story, Alexander loosed the knot by pulling the linchpin from the yoke.

I'm aware this is not the single word you've requested, but it's a helpful metaphor nonetheless.