An old conjecture of Erdos-Turán on additive bases

There is a 1941 conjecture of Erdos and Turán on what is now called additive basis that we restate:

Conjecture 0.1(Erdos and Turán). Suppose that $0=\delta_0<\delta_1<\delta_2<\delta_3\cdots$ is an increasing sequence of integers and

Suppose that

If $b_i>0$ for all $i$, then $\{b_n\}$ is unbounded.

Our main purpose is to show that the sequence $\{b_n\}$ cannot be bounded by $7$. There is a surprisingly simple, though computationally very intensive, algorithm that establishes this.