Is it obligatory for one who vowed to pray four nights to pray the entire night, or is it sufficient to pray part of it?

A conditional vow [dependent] on an undesirable condition is disliked. If the condition occurs, fulfilling it becomes obligatory by consensus. If the person making the vow had a specific intention, then oaths and vows are referred back to the intention. If they intended a specific time, its performance becomes binding upon them. If they vowed to perform night prayers (qiyam al-layl) and left it unrestricted, then performing all of them becomes binding upon them. It is permissible to make up for missed night prayers on another night according to some scholars, as Ibn Rajab mentioned from Al-Awza'i.