Non-Specht variety generated by an involution semigroup of order five

The non-orthodox $0$-simple semigroup $A_2$ of order five admits a unary operation under which it is an involution semigroup. It is known that $A_2$ generates a Specht variety of semigroups. In contrast, it is shown that as an involution semigroup, $A_2$ generates a non-Specht variety. References: 44 entries.