what mathematical theorem is this

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Reading Gödel, Escher, Bach by Douglas R. Hofstadter, at p. 552, Achilles asks the Crab to play this piece:

∀a:∃b:∃c:<~∃d:∃e:<(SSd * SSe) = b ν (SSd * SSe) = c> ^ (a+a)=(b+c)>

And it seems that the Crab wasn't capable of playing this.

What is this composition stating?

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It's not a theorem (yet); it's the Goldbach conjecture. In English, it reads, "For all $a$, there exist $b$ and $c$ such that neither $b$ nor $c$ are expressible as the product of two numbers $d+2$ and $e+2$ (i.e., $b$ and $c$ are either $0$, $1$, or primes) and $b+c = 2a$." (All numbers $a$ through $e$ are assumed to be non-negative integers in $\mathsf{TNT}$.)

Or, more concisely, "Every even number $\geq 4$ is the sum of two primes." The wording allows us to ignore the cases where $2a = 0$ or $2$, since they are the sum of qualifying $b$ and $c$ (either $0+0$ or $1+1$).

That's why Achilles indirectly calls the situation a "Prime teas." :-)

(Incidentally, in the original hardback from Basic Books, this particular passage is at the bottom of p. $557$.)