docker.service não iniciando no Linux Mint 18.3

No meu notebook rodando x64 Linux Mint 18.3 Cinnamon, tentei instalar o Docker:

sudo apt-key adv --keyserver hkp://p80.pool.sks-keyservers.net:80 \
  --recv-keys 58118E89F3A912897C070ADBF76221572C52609D

sudo apt-add-repository 'deb https://apt.dockerproject.org/repo 
ubuntu-xenial main'

sudo apt update

sudo apt install linux-image-generic linux-image-extra-virtual

sudo apt install docker-engine

Somente durante a última etapa, o processo falha. Eu acho que na verdade está instalando o software, mas meu sistema não pode executar o serviço Docker:

Job for docker.service failed because the control process exited with 
error code. See "systemctl status docker.service" and "journalctl -xe" 
for details.
invoke-rc.d: initscript docker, action "start" failed.
● docker.service - Docker Application Container Engine
Loaded: loaded (/lib/systemd/system/docker.service; enabled; vendor 
preset: enabled)
Active: activating (auto-restart) (Result: exit-code) since Di 2018-
02-
27 10:45:35 CET; 17ms ago
Docs: https://docs.docker.com
Process: 9906 ExecStart=/usr/bin/dockerd -H fd:// (code=exited, 
status=1/FAILURE)
Main PID: 9906 (code=exited, status=1/FAILURE)

Feb 27 10:45:35 silberpfeil systemd[1]: Failed to start Docker 
Application Container Engine.
Feb 27 10:45:35 silberpfeil systemd[1]: docker.service: Unit entered 
failed state.
Feb 27 10:45:35 silberpfeil systemd[1]: docker.service: Failed with 
result 'exit-code'.

"Silberpfeil" é o nome do meu sistema. Nesse protocolo de erro, há uma dica que diz que devo procurar esse erro em

• "systemctl status docker.service"
• "journalctl -xe"

O primeiro retorna:

● docker.service - Docker Application Container Engine
Loaded: loaded (/lib/systemd/system/docker.service; enabled; vendor 
preset: enabled)
Active: inactive (dead) (Result: exit-code) since Di 2018-02-27 
10:45:38 CET; 9min ago
Docs: https://docs.docker.com
Process: 10011 ExecStart=/usr/bin/dockerd -H fd:// (code=exited, 
status=1/FAILURE)
Main PID: 10011 (code=exited, status=1/FAILURE)

Feb 27 10:45:38 silberpfeil systemd[1]: Failed to start Docker 
Application Container Engine.
Feb 27 10:45:38 silberpfeil systemd[1]: docker.service: Unit entered 
failed state.
Feb 27 10:45:38 silberpfeil systemd[1]: docker.service: Failed with 
result 'exit-code'.
Feb 27 10:45:38 silberpfeil systemd[1]: docker.service: Service hold-
off time over, scheduling restart.
Feb 27 10:45:38 silberpfeil systemd[1]: Stopped Docker Application 
Container Engine.
Feb 27 10:45:38 silberpfeil systemd[1]: docker.service: Start request 
repeated too quickly.
Feb 27 10:45:38 silberpfeil systemd[1]: Failed to start Docker 
Application Container Engine.

O segundo diz coisas demais para postá-las aqui. Tanto quanto você não precisa dele para ajudar. Olhando para ele, pude ver algo dizendo Docker olhando com grep:

Feb 27 10:45:37 silberpfeil dockerd[10011]: time="2018-02-
27T10:45:37.123564185+01:00" level=info msg="libcontainerd: new 
containerd process, pid: 10033"
Feb 27 10:45:38 silberpfeil dockerd[10011]: time="2018-02-
27T10:45:38.129863280+01:00" level=warning msg="failed to rename 
/var/lib/docker/tmp for background deletion: %!s(<nil>). Deleting 
synchronously"
Feb 27 10:45:38 silberpfeil dockerd[10011]: time="2018-02-
27T10:45:38.140660647+01:00" level=error msg="[graphdriver] prior 
storage driver aufs failed: driver not supported"
Feb 27 10:45:38 silberpfeil dockerd[10011]: Error starting daemon: 
error initializing graphdriver: driver not supported
Feb 27 10:45:38 silberpfeil systemd[1]: docker.service: Main process 
exited, code=exited, status=1/FAILURE
-- Subject: Unit docker.service has failed
-- Unit docker.service has failed.
Feb 27 10:45:38 silberpfeil systemd[1]: docker.service: Unit entered 
failed state.
Feb 27 10:45:38 silberpfeil systemd[1]: docker.service: Failed with 
result 'exit-code'.
Feb 27 10:45:38 silberpfeil systemd[1]: docker.service: Service hold-
off time over, scheduling restart.
-- Subject: Unit docker.service has finished shutting down
-- Unit docker.service has finished shutting down.
-- Subject: Unit docker.socket has finished shutting down
-- Unit docker.socket has finished shutting down.
-- Subject: Unit docker.socket has begun shutting down
-- Unit docker.socket has begun shutting down.
-- Subject: Unit docker.socket has begun start-up
-- Unit docker.socket has begun starting up.
-- Subject: Unit docker.socket has finished start-up
-- Unit docker.socket has finished starting up.
Feb 27 10:45:38 silberpfeil systemd[1]: docker.service: Start request 
repeated too quickly.
-- Subject: Unit docker.service has failed
-- Unit docker.service has failed.
Feb 27 10:45:38 silberpfeil systemd[1]: docker.socket: Unit entered 
failed state.

Alguém consegue encontrar algo?