Here's a passage that was written in 1957, some years before Jack introduced his anti-life equation...
It was man's mind that all their schemes and systems were intended to despoil and destroy. Now choose to perish or to learn that the anti-mind is the anti-life.
Man's mind is his basic tool of survival. Life is given to him, survival is not. His body is given to him, its sustenance is not. His mind is given to him, its content is not. To remain alive, he must act, and before he can act he must know the nature and purpose of his action. He cannot obtain his food without a knowledge of food and of the way to obtain it. He cannot dig a ditch-or build a cyclotron-without a knowledge of his aim and of the means to achieve it. To remain alive, he must think.
But to think is an act of choice. The key to what you so recklessly call 'human nature,' the open secret you live with, yet dread to name, is the fact that man is a being of volitional consciousness. Reason does not work automatically; thinking is not a mechanical process; the connections of logic are not made by instinct. The function of your stomach, lungs or heart is automatic; the function of your mind is not. In any hour and issue of your life, you are free to think or to evade that effort. But you are not free to escape from your nature, from the fact that reason is your means of survival -- so that for you, who are a human being, the question 'to be or not to be' is the question 'to think or not to think.'
A is A -- and Man is Man. Rights are conditions of existence required by man's nature for his proper survival. If man is to live on earth, it is right for him to use his mind, it is right to act on his own free judgment, it is right to work for his values and to keep the product of his work. If life on earth is his purpose, he has a right to live as a rational being: nature forbids him the irrational. Any group, any gang, any nation that attempts to negate man's rights, is wrong, which means: is evil, which means: is anti-life.
Any of that sound familiar? Although the phrase "A is A" (or "A = A") is attributed first to Gottfried Leibniz, who was essentially summarizing the Law of Identity, it has been immortalized in comics through the character of Mr. A, Steve Ditko's famously objectivist character who debuted in 1967 still several years before Kirby's Fourth World. Indeed the character's name is derived from that very equation.
But, in reading that passage above, it's clear that "A = A" is not the anti-life equation. Quite the opposite, in fact. "A = A" is the affirmation of existence, the affirmation of life. Anti-life, as described above, is not having the ability to think for oneself and make choices for oneself. Anti-life is thoughtless existence, where one is not permitted to question others, where one accepts the reality one is told without giving any thought to whether that is right or wrong. Where rationality and common sense are irrelevant. Where up is down, good is bad, and lies are truth.
That aspect of anti-life is expanded upon in George Orwell's 1984. Although more famous for introducing "Big Brother" into the common vernacular, it also presented a government that was entitled to claim whatever they wanted, and the population at large was to accept it without question. The Ministry of Peace conducts perpetual war on whomever it choses, and the Ministry of Truth tells people that the country they're at war at now is the country they've always been at war with, regardless of who they actually used to be fighting. He introduced the term doublethink which is where people are able to hold two mutually exclusive and even contradictory ideas as being equally and simultaneously valid, such as black being the same as white.
Or where A is not the same as A.
A ≠ A
There is no mystical equation that, when recited, will cause people to become living zombies. There is no physical manifestation of anti-life. All the subsequent creators who've tackled Kirby's anti-life equation don't know what the hell they're talking about, and are throwing out overly complex metaphors to make them look more clever than they are. (Morrison especially.)
The equation is simple: A ≠ A.
But just telling someone that is nothing. The equation itself is meaningless. It's the thought behind the equation that's the key. Being able to get someone to actually believe that A does not equal A... THAT is the real anti-life equation. It's not telling someone A ≠ A, it's being able to prove it. You can't just say A ≠ A, you need to convince someone of it's truth. And when you do that, you've eliminated their own thoughts, and their own ability to reason, and supplanted them with your will. THAT is the anti-life equation.
Oh, and that passage I quoted above? That's from Ayn Rand, the very same philosopher who had such an influence on Steve Ditko; she had a pretty big impact on Jack Kirby, too.