Problem TBG-2. Ternary Boolean group associativity. We have the following (gL)-basis for Boolean groups in terms of a ternary operation (Thm. TBG-1).

\{ \begin{matrix}p(x, x, x) = x \\ p(x, y, p(z, u, v)) = p(y, z, p(u, v, x)) \end{matrix} \} .

Can the associative law be replaced with an equation with fewer variables?