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Hadith 1990

أَخْبَرَنَا أَبُو الْوَلِيدِ، حَدَّثَنَا شُعْبَةُ، عَنْ سَلَمَةَ بْنِ كُهَيْلٍ، قَالَ: سَمِعْتُ حُجَيَّةَ بْنَ عَدِيٍّ، قَالَ: سَمِعْتُ عَلِيًّا وَسَأَلَهُ رَجُلٌ، فَقَالَ: يَا أَمِيرَ الْمُؤْمِنِينَ، الْبَقَرَةُ ? قَالَ: عَنْ سَبْعَةٍ، قُلْتُ: الْقَرْنُ ؟ قَالَ: لَا يَضُرُّكَ . قَالَ: قُلْتُ: الْعَرَجُ ؟ قَالَ: إِذَا بَلَغَتْ الْمَنْسَكَ . ثُمَّ قَالَ: "أَمَرَنَا رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ أَنْ نَسْتَشْرِفَ الْعَيْنَ وَالْأُذُنَ".
Hujayyah bin ‘Adi said: I heard a man ask Sayyiduna ‘Ali (may Allah be pleased with him): O Commander of the Faithful! For how many people is a cow (sufficient)? He replied: For seven people. I asked: What is the ruling about (a cow with) a horn? He replied: There is no harm. I asked: And (what about) lameness? He replied: If it can reach the place of sacrifice, then there is no problem (i.e., if it can walk, there is no harm). Then he said: The Messenger of Allah (peace and blessings be upon him) commanded us to “examine the eyes and ears well.”
Hadith Reference سنن دارمي / من كتاب الاضاحي / 1990
Hadith Grading تحقیق (حسین سلیم أسد الدارانی): إسناده حسن، [مكتبه الشامله نمبر: 1994]
Hadith Takhrij اس روایت کی سند حسن ہے لیکن دوسری سند سے حدیث صحیح ہے۔ دیکھئے: [ترمذي 1498] ، [نسائي 4388، الطرف الأخير فقط] ، [أبويعلی 333] ، [ابن حبان 5920]
Brief Explanation
(Commentary on Hadith 1989)

The last sentence of this hadith is mentioned in al-Nasa’i and al-Tirmidhi, while the first part is not mentioned there. The apparent meaning of this narration is that, according to Sayyiduna Ali radi Allahu anhu, defects of the ear and eye are among the impediments to sacrifice, and the breaking of the horn or lameness were not ordered by the Messenger of Allah sallallahu alayhi wa sallam to be checked (for exclusion) (and Allah knows best).

However, a broken horn and lameness are also defects that should not be present in a sacrificial animal, as is explicitly mentioned in the next hadith.

Yes, if an animal is naturally without horns, then there is no harm in that.