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Running out of time

I know the general rule is that when one player runs out of time, he'll lose the game if a helpmate is possible(This is generally why he loses when the opponent still has a Bishop/Knight and draws when the opponent has only the king)

However, there are certain positions where helpmate isn't possible at all, for instance:

FEN: 4k3/8/8/p2p2p1/P2P2P1/8/8/4K3 w - - 0 1

How does lichess treat this?

I know the general rule is that when one player runs out of time, he'll lose the game if a helpmate is possible(This is generally why he loses when the opponent still has a Bishop/Knight and draws when the opponent has only the king) However, there are certain positions where helpmate isn't possible at all, for instance: FEN: 4k3/8/8/p2p2p1/P2P2P1/8/8/4K3 w - - 0 1 How does lichess treat this?
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