$p-MC(Σ₁[2]) ≤fpt p-Clique$ (Flum–Grohe, Lemma 6.14). For an instance $(A, ∃x̄ ψ)$, list the $q$ atoms of $ψ$ and their two variables ($2q$ rows); for every truth valuation $c$ of the atoms under which $ψ$ holds, the vertices $(c, e, r)$ — a candidate value $e$ for the variable of row $r$ — are joined when their rows differ, rows of one variable carry one value, and the two rows of an atom carry values that give the atom the truth value $c$ assigns it. A $2q$-clique is exactly a satisfying assignment. The candidates are the entries of the word inside the universe and the first $|x| + 2q$ elements (isolated elements are interchangeable), so the graph has at most $2^q · 4|x| · 2q$ vertices; the new parameter is $2q ≤ 2|φ|$.