Aye the free MBAM is the on demand scanner that does not offer real time protection and needs to be run manually which is fine.
From your Speccy report;
Running: Malwarebytes Service
Running: McAfee Module Core Service
Stopped: McAfee Home Network
Stopped: McAfee Proxy Service
Scheduler
McAfee Remediation (Prepare)
Updates Not Installed
12/21/2017 Definition Update for Windows Defender Antivirus - KB2267602 (Definition 1.259.639.0)
Installation Status: Canceled
Install this update to revise the definition files that are used
to detect viruses, spyware, and other potentially unwanted software.
Once you have installed this item, it cannot be removed.
12/12/2017 9NBLGGH4R9NZ-EyeoGmbH.AdblockPlus
Installation Status: Failed
9NBLGGH4R9NZ-1152921504626640508
MBAMService.exe
Process ID: 3712
User: SYSTEM
Domain: NT AUTHORITY
Path: C:\Program Files\Malwarebytes\Anti-Malware\MBAMService.exe
Memory Usage: 38 MB
Peak Memory Usage: 49 MB
mbamtray.exe
Process ID: 9632
User: mine
Domain: DESKTOP-S01DA7B
Path: C:\Program Files\Malwarebytes\Anti-Malware\mbamtray.exe
Memory Usage: 27 MB
Peak Memory Usage: 31 MB
mbamtray.exe
Process ID: 3632
User: boodieness
Domain: DESKTOP-S01DA7B
Path: C:\Program Files\Malwarebytes\Anti-Malware\mbamtray.exe
Memory Usage: 26 MB
Peak Memory Usage: 31 MB
Memory Compression
Process ID: 1532
User: SYSTEM
Domain: NT AUTHORITY
Memory Usage: 312 MB
Peak Memory Usage: 589 MB
ModuleCoreService.exe
Process ID: 1936
User: SYSTEM
Domain: NT AUTHORITY
Path: C:\Program Files\Common Files\McAfee\ModuleCore\ModuleCoreService.exe
Memory Usage: 28 MB
Peak Memory Usage: 36 MB
ModuleCoreService.exe
Process ID: 15168
User: mine
Domain: DESKTOP-S01DA7B
Path: C:\Program Files\Common Files\McAfee\ModuleCore\ModuleCoreService.exe
Memory Usage: 11 MB
Peak Memory Usage: 24 MB
ModuleCoreService.exe
Process ID: 7804
User: boodieness
Domain: DESKTOP-S01DA7B
Path: C:\Program Files\Common Files\McAfee\ModuleCore\ModuleCoreService.exe
Memory Usage: 10 MB
Peak Memory Usage: 13 MB
The above may not be the cause of the computer shutting down but is most likely what is using up so much memory.
Physical Memory
Memory Usage: 61 %
Total Physical: 8.00 GB
Available Physical: 3.09 GB
Total Virtual: 9.25 GB
Available Virtual: 2.93 GB
How to remove McAfee products from a PC running Windows