The Short Version
'Oh my, he has an annihilation already, it's frighteningly similar to mine too.'
From the traces of residual energy left by Arthur's last attack, Cattleya was able to deduce what he utilized in that attack.
The bloodline ability of the devilian royal family; Annihilation.
The Annihilation possessed by each of the members of the royal family was subtly different. Creusery's annihilation gave him the ability to burn almost anything, corporeal and incorporeal.
Cattleya's annihilation was just pure unrestrained destruction. Arthur's 'extreme Nothingness' was an application of his annihilation.
'But it's not awakened completely huh? Well that's all I can tell'
She stood up once again and deactivated her bloodline ability, alongside the authority that she used, one that did not fit her personality.
The low-rank authority of wisdom. That was what enabled her to read the traces of energy and deduce the abilities that Arthur might have used.