Initially, Adam came to the Arachne Nest to kill Nollura and use that to provoke Ureyn into a fight. Still, as it turned out, Gareyna had changed several details in her story quite significantly.
Either way, Adam's goal remained unchanged. He still needed to challenge Ureyn to a fight to obtain the Connected Heart.
He didn't kill Nollura, but there was no longer any need to. Now that she was with him, he had two options. Adam could either use Nollura's help or use the Black Cut emblem that Norax had given her earlier.
Step. Step. Step.
Thus, Adam and Nollura left the nest, heading straight for one of the many gray mills. On the way there, Adam had a lot to learn about the upcoming String Duel, but now he was on the home stretch before finally getting a worthy fight.
The cave remained empty, except for a few black spiders who could finally breathe a sigh of relief. Although Adam and Nollura's fight was short, the simple spiders had to endure stress several times.