Thanks for attaching those - it looks like your system is overheating.
It looks like your CPU is gradually being underclocked to try and reduce the temperature of the system (1), but this doesn't work and the system goes in to hibernation mode to try and stop the laptop from overheating further (2):
1) "The speed of processor 0 in group 0 is being limited by system firmware."
2) "The system was hibernated due to a critical thermal event."
Can you check that the air vents around the laptop are free of dust/debris and that the fans are working when it is on?
It may be useful to monitor the temperature of your CPU using a temperature monitoring tool like this:
http://openhardwaremonitor.org/
It may be that the overheating is incorrectly detected - on the other hand, it may confirm that you need to give the laptop a bit of an overhaul to see why the CPU overheats (clogged exhaust ports, cooler fan not working, heatsink unseated, etc...). Is the laptop still within warranty?
edit: I did a bit more googling and it looks like this model laptop is very susceptible to overheating. Other users have had success by getting an air duster and vacuum to clean out the ventilation ports, then updating the BIOS from the HP support site.