These scholars also used the following Hadith to support their opinion: Aadee ibn Hatem (RA) said:
"I said: ‘O Prophet of Allah, I send my (hunting) dog and mention the Name of Allah.’ The Prophet (SAW) told me: ‘If you send your dog mentioning the Name of Allah and he killed, you eat; but if he eats from it, do not eat. He has caught it for himself.’ I said: ‘I send my dog, and then I find another dog with him, and I do not know which one caught for me.’ The Prophet (SAW) said: ‘Do not eat, because you only invoked the Name on your dog, and not on the other.’" (Reported by Al-Bukhari and Muslim, among other similar Hadith)
If the invocation is dropped deliberately, the Dhabeehah is considered to be "dead," and it is Haram to eat. But if one forgot to mention it, then his slaughter is lawful and the Dhabeehah is Halal.
SECOND: That invocation is not a requirement, and that if one has not made it (on purpose or just forgot to do so), the slaughter would be lawful, and the Dhabeehah Halal. This is basically the Shafi’ee School’s opinion, but is also one of the opinions reported on behalf of Malik and Ahmad.
THIRD: That it is a condition for the lawfulness of the Dhabeehah, and that if the Muslim does not invoke the Name of Allah (SWT), his Dhabeehah is not Halal. This opinion does not differentiate between those who forget to make the invocation form those who deliberately omit it: the Dhabeehah in either case is not Halal. This opinion was adopted by Abdullah ibn Umar, Dawood Ad-dhahiri and Ibn Sereen.
Forgetfulness, however, is a valid excuse for not applying or associating consequences of actions to the doer. Rulings and conditions cannot be applied to the person who did or did not do something because of forgetting. The same concept also applies to cases in which the person is under duress, or has done something wrong by mistake.
In conclusion, the correct ruling regarding the requirement of invoking the Name of Allah (SWT) over slaughtered animals is that the invocation is obligatory (Waajib) for the slaughter to be Halal, and that if one deliberately omits it, his Dhabeehah is Haram to eat. ALL THIS RELATES TO CASES IN WHICH THE PERSON PERFORMING THE SLAUGHTERING IS A MUSLIM.