Optimal strong Mal’cev conditions for omitting type 1 in locally finite varieties

We show that the class of locally finite varieties omitting type 1 has the following properties. This class is: definable by an idempotent, linear, strong Mal’cev condition in a language with one 4-ary function symbol; not definable by an idempotent, linear, strong Mal’cev condition in a language with only one function symbol of arity strictly less than 4; definable by an idempotent, linear, strong Mal’cev condition in a language with two 3-ary function symbols; not definable by an idempotent, linear, strong Mal’cev condition in a language with function symbols of arity less than 4 unless at least two of the symbols have arity 3.