The incidence structure: the universe gets one new element per tuple (in the order the word lists them), unary symbols $P_i$ hold the new elements of the tuples of $R_i$, binary symbols $E_l$ connect entry $l$ of a tuple to its element. Each atom $R_i y_0 … y_{k-1}$ becomes $E_0 y_0 z ∧ … ∧ E_{k-1} y_{k-1} z ∧ P_i z$ for a fresh $z$, bound in front with the other quantifiers. The map is computed by one IMP+ program in cubic time; the new formula is at most six times as large.