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Implying that such people deprive themselves of God's grace and mercy (which is the twofold significance of the term rahmah in this context) by rejecting all belief in His existence: in other words, belief in God - or one's readiness to believe in Him - is, in and by itself, already an outcome of His grace and mercy, just as suffering in the hereafter is an outcome of one's being "bent on denying the truth".
lit., My mercy.
The emphasis is on "they" (ulaika). It is only the people who ignore or reject Allah's Signs and reject a Hereafter, that will find themselves in despair and suffering. Allah's Mercy is open to all, but if any reject His Mercy, they must suffer.