Is it obligatory to repeat ablution for someone who performed it and inadvertently forgot the intention?

If what is meant is to abandon uttering the intention (niyyah) verbally, then this does not cause harm; because verbalizing it is not legislated according to many scholars, and it is not a condition for the validity of the intention, whose place is the heart. Even if one vocalizes something contrary to what is in their heart, what matters is what they intended with their heart.

However, if what is meant is forgetting the heartfelt intention, then this is very unlikely and resembles obsessive whispering (waswasah). For intention is the heart's resolve to act, and it is inconceivable that a person performs the acts of ablution except with an intention, as every action has an intention.

But if it is assumed that a person did not intend ablution or intended mere cooling, then that does not suffice for the obligatory ablution; for intention is a condition for the validity of ablution, and therefore, that ablution and the prayer performed with it must be repeated.