Example MFL-8. Simple basis does not work with Moufang-1.

\{ \begin{matrix}1 · x = x \\ x′ · x = 1 \\ Moufang-1 \end{matrix} \} ⇏ \{Moufang-2\}.

The clauses

1 · x = x x′ · x = 1 (x · (y · z)) · x = (x · y) · (z · x) ((A · B) · C) · B ≠ A · (B · (C · B))

have the following model (found by MACE 1.2.0 on gyro at 0.78 seconds).

. | 0 1 2            '   0 1 2
--+------            ---------
0 | 1 0 1                0 1 0
1 | 0 1 2
2 | 1 2 1            A: 0,  B: 2,  C: 1