PS. For those interested, my own "presuppositional" proof, parodying Sye's proof by his principle "the impossibility of the contrary" (which turns out to be the key to Sye's proof) is:
My claim: Sye's mind is addled and his thinking unreliable because he was hit on the head by a rock.
Prove this is false, Sye.
Try to, and I will say - "But your "proof" presupposes your mind is not addled and you can recognise a proof when you see it. So it fails."
Ask me to prove my claim and I will say: "But prove to me your mind is not addled, then, Sye". Which you won't be able to, for the above reason. I might then add, with a flourish - "So you see, my claim is proved by the impossibility of the contrary".
And of course I have a good explanation for why your brain is addled, Sye - you were hit on the head by a rock.
Have I proved to Sye that he was hit on the head by a rock? Of course not. Still I might tie Sye up in knots like this: each time he tries to offer an argument that his reasoning is reliable and justified, and/or that he wasn't hit on the head by a rock, I say, "Oh dear, Sye, you are trying to use logic - and you can't do so with justification till you have proved you were not hit on the head by that rock! My proof works!! I win!!" Repeat ad nauseum until he gives up. Then claim victory.
This, in effect, is Sye's core argumentative strategy. The first thing you need to know, before engaging with him, is that he will constantly run this argument over and over and over. But he has many other strategies too, to give him credit. Yes of course it's ultimately all bullshit, but boy he can really construct a complex edifice out of it!
Incidentally, we presented Sye with not one but three atheist-friendly accounts of logic, none of which did Sye refute, or even attempt to refute. Yet he keeps claiming there are none. Some chutzpah.