Given:
A semiprime number is defined as the product of two primes
$a$, $b$, $c$, $d$, $e$ and $f$ are all distinct semiprimes
Can a proof be constructed showing that the following equation cannot be satisfied:
$$a + b = c + d$$
Moreover, can this be expanded to sums of more than two semiprimes, for example:
$$a + b + c = d + e + f$$
Both equations can be satisfied. $$ 4 + 21 = 10 + 15 $$
and
$$ 9 + 10 + 21 = 4 + 14 + 22 $$
Hence no such proof is possible.