You could always argue against having the existence of tautologies though, however successful you may be!

I don’t think a counterargument that proves both x and ~x is a paradox but a contradiction. And I don’t think such lousy counterarguments prove anything about the argument they are attempting to defeat (i.e. that they are invincible) they are just lousy.

As for making an argument which claims itself to be useless, what you have is a paradox not an invincible idea.

Let me propose X to be an invincible argument. Let’s say that Y is a counter-argument to X, but that in making that counter argument, Y also proves X. You are left simply with Y -> X and Y -> ~X.

You are then left with the choice of renouncing Y, renouncing one of the rules Y -> X or Y -> ~X, or joining the dialetheists over coffee and not coffee.

Cheers,
-MP