"So there might exist a line that, unexpectedly, leads to a win for Black and we cannot rule out this possibility"
correct - although the 'we' there is inappropriate ... better would have been 'cannot be objectively ruled out'
plus - the other 'material' surrounding the key and quoted phrase is superfluous.
Depends what we mean by objectively. You see, I tend to think of that as being somewhat synonymous with "pragmatically". "Deductively" might have been clearer.
As for the chess problem I had in mind - the moves didn't copy properly.
And whoever can always just quickly put it in an engine and claim 'the eye'. Or has seen it before.
I'll find another example.
No, I hadn't seen it before but white's avenue of approach was absolutely obvious, since otherwise, black appeared to be winning. And I'm an afar better chess player than you, so you shouldn't imagine that if it's hard for you then it's hard for me.