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The Battle of Floor 0507 was a skirmish between the Twelfth Doctor and the residents of Floor 0507 against the Cybermen invading from Floor 1056 on a Mondasian colony ship. Initially ruled by the Saxon Master, the Cybermen turned on him when the Doctor rewrote their definition of humanity, leading to the group fleeing to the upper floor while the Cybermen prepared to conquer the entire ship.
The Cybermen held a significant advantage as they were further away from a black hole, meaning years for them was mere days for the Doctor and the others on the solar farm, allowing them more preparation time.
The skirmish was eventually ended when the Doctor, having had Nardole evacuate the majority of the residents to floor 0502, used his sonic screwdriver to ignite the floor, destroying all Cybermen present at the cost of forcing him to regenerate. (TV: The Doctor Falls)
History
Origins
Due to the colony ship being sucked into the orbit of a black hole, 20 members of the 50 member crew on board went to floor 1056 to reverse the thrusters. However, the time dilation meant they aged much faster, several generations soon being spawned. At some point, the Saxon Master crashed his TARDIS here and took control, eventually steering the residents down a path to convert themselves into cybernetic humanoids, and eventually a complete Cyberman. The patients would venture to the higher floors and capture the other residents for conversion. (TV: World Enough and Time) A group went to floor 0507, but were repelled by the residents, being shot down daily. (TV: The Doctor Falls)
Eventually, the Twelfth Doctor, Bill, Nardole and Missy landed on the ship, finding the sole survivor on floor 0000, Jorj, who was spared due to not being completely human. He shot Bill due to her being a human, the patients coming and taking her away. Bill was later kept under the Master's watch at the hospital (under the guise of "Razor") until he had her converted into the first true Cyberman. The Doctor, Nardole and Missy followed after knocking Jorj out and figuring out the time dilation between the numerous floors. However, the Doctor was too late to save Bill and Missy joined the Master, siding against the Doctor as they gloated about the "genesis of the Cybermen". (TV: World Enough and Time)
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The pair then captured the Doctor, knocking him out and taking him to the top of the hospital where they gloated about their victory. However, the Doctor revealed that he had changed the definition of humanity in the Cyber network, turning the army against the Master. After fending the initial group off with his Laser screwdriver, the Master was knocked out by Missy using her Sonic umbrella, who then freed the Doctor from his restraints. Nardole then arrived in a shuttlecraft, the group proceeding to use it to evacuate. However, the Doctor was electrocuted by a Cyberman, Bill (as a Cyberman) having to save him using her laser beam. She then forced the two Masters to take her and the Doctor with them. The shuttlecraft eventually crashed on floor 0507. (TV: The Doctor Falls)
Preparing for war
Over the next two weeks, Nardole took command of the village, having the residents prepare for the upcoming attack from the Cybermen, fortifying the town with sandbags. Missy and the Master took to locating the lifts on the level, eventually finding and revealing one to the Doctor and Bill. However, Missy accidentally called the lift to their level, forcing the four to fight off a highly advanced Cyberman, as years had passed for floor 1056.
Realising the Cybermen now knew where they were and would now have years to prepare an invasion while they would have only a day, the Doctor returned to the village to rally the residents for the battle, the Cybermen sending a warning in the form of an alarm in an effort to frighten them. Understanding they would need a way out, the Doctor had Bill blast a hold in the wall to an underground passage leading to the lifts while the Masters schemed to flee to the Master's TARDIS on floor 1056.
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Nardole used a computer to hack into the fuel lines beneath the floor, enabling him to detonate them on command. The Doctor decided they would use such a tactic to make the Cybermen believe they had superior weapons so they would not attack beyond the first wave, at least for a while.
Shortly before the Cybermen arrived, the two Masters revealed their plan to leave to the Doctor. Infuriated, the Doctor pursued them, proceeding to criticise the pair for their indifference and that he was staying to fight because it was "kind" and "right". Although the Master refused to listen and left, Missy was moved by the Doctor's speech, considering siding with him. However, she sided with the Master, thanking the Doctor for trying to make her good. (TV: The Doctor Falls)
The battle
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The initial wave of Cybermen arrived, marching towards the town. However, they were met by Alit, who tossed an apple at them. Nardole, using his computer, ignited the fuel line beneath the platoon, blowing them up. The Master and Missy manoeuvred through the forest to the lift, witnessing the explosions in the distance, avoiding the Cybermen. Nardole proceeded to do destroy several of the Cybermen, the house remaining safe, the Cybermen soon retreating. Understanding they had little time before the Cybermen returned with their entire army, the Doctor downloaded Nardole's software into his sonic screwdriver and (after a long argument) convinced Nardole to go with the evacuating children to protect them. Bill also opted to stay with the Doctor, wishing to die defending the children rather than continue living as a Cyberman.
In the forest, the Master and Missy successfully reached the lift. However, having changed her mind, Missy tricked her predecessor and stabbed him in the back, asserting she wanted to stand with the Doctor. This wound would force the Master's regeneration into Missy, though she made it precise so that he would have enough time to return to his TARDIS first. Helping the dying Master into the lift, she prepared to return to the main site of the battle. However, the Master struck her down with his laser screwdriver, professing he would refuse to let her help the Doctor. Laughing at their "perfect ending", the Master descended in the lift as Missy appeared to die.
By morning, Bill and the Doctor knew the rest of the Cyber-Army were imminent, sharing one last goodbye with Bill before she left. Alone, the Doctor reiterated the words his wife River Song once told him: "without hope, without witness, without reward." The second wave arrived, the Doctor and Bill each charging into opposite ends of the forest, fighting off various types of Cybermen. As the Doctor destroyed numerous models of them, he shouted out the numerous occasions he had beaten them. Eventually, he was surrounded and struck down by one Cyberman's laser beam. Wearily declaring he was still the Doctor, the Cyberman rebuked him and fired again. As his body attempted to regenerate, the Doctor ignited the entire floor, destroying all of the Cybermen and mortally wounding himself in the process. (TV: The Doctor Falls)
Aftermath
Safe on floor 0502, Nardole stood outside the lift, wondering if the Doctor and Bill would return. The children convinced him to move on and focus on living with them. Nardole stated to the children that the Doctor's actions had only destroyed "most" of the Cybermen, but would buy them several years for Nardole to come up with a new plan.
Below them on floor 0507, the Doctor had become motionless after the explosion which had destroyed all the Cybermen but Bill. Bill was then confronted by the oil creature in the form of Heather, which had tracked Bill down due to leaving itself as residue in Bill's tears. It turned her into a creature like itself, and together they took the Doctor back to the TARDIS. Heather invited Bill along to explore the universe with her, and after bidding the Doctor farewell Bill and Heather left.
After Bill and Heather's departure, the Doctor awakened and began to regenerate. (TV: The Doctor Falls) He eventually finished the process, regenerating into the Thirteenth Doctor. (TV: Twice Upon a Time)