To resolve the ongoing feud between Prochek and Olbram in the Kingdom Come: Deliverance 2 side quest, "Battle of the Frogs and Mice," follow these steps:
To begin the "Battle of the Frogs and Mice" side quest, you must first complete either the "Mice" or "Frogs" quests assigned by Prochek or Olbram. Once you've completed one of these, the new quest will become available. Start by speaking with Prochek in Tachov or Olbram in Zhelejov. After initiating the quest, head to the designated pasture to proceed.
In this quest, you have the option to side with either Prochek or Olbram. To align with Prochek, visit him in Tachov and choose the dialogue option, "Let's get those Zhelejovites!" To support Olbram, go to Zhelejov and select, "Let's go and see those Tachovites!"
During their negotiations at the pasture, avoid attempting to reconcile them as it will only trigger the fight prematurely. Instead, if you can pass the dialogue check during the negotiations, a member of the opposing side will flee, making the subsequent fight easier. Winning the fight for either side will earn you some groschen.
If you prefer a peaceful resolution, you can end the feud. Before heading to the pasture, ask Prochek or Olbram if they are willing to end the feud. Then, travel to Troskowitz and speak with Bailiff Thrush. Choose the dialogue option, "You'd finally have some peace."
Passing this dialogue check allows you to access the scribe's room and read the Troskowitz Chronicle. If persuasion fails, you can sneak in to read it, but remember to save your game beforehand.
Once inside, speak to the scribe and select the dialogue option, "Fecit, ordinem in regione ope clavi ferrei."
Next, go to the pasture and locate three oak trees aligned next to each other. Examine the middle tree to find a nail. Your options with the nail are:
Your choice here doesn't significantly impact the outcome, so select according to your preference or remain neutral. After deciding, speak with Bailiff Thrush again, and he will agree to end the feud. Then, converse with Prochek or Olbram to bring them to the pasture, successfully resolving the conflict.
Afterwards, speak with Bailiff Thrush once more to receive the "Master Studies I" book.
By following these steps, you'll effectively end the feud in the "Battle of the Frogs and Mice" side quest in Kingdom Come: Deliverance 2.