Disk install currently stuck on "Install Progress: 34%" for a day now after prologue

When you insert a disc the installation data comes directly from the disc itself, the PS4 will usually start to download the latest update automatically and at the same time that the game is installing but it will not apply the update until the installation is complete.

I would suggest deleting the game from the XMB and starting the installation again from the beginning. Also I would not play the game until the installation is 100% complete and the latest update is installed. It shouldn't matter as games are designed to be partly playable before the installation is complete but it will minimise the chance of something going wrong during the installation.

If it stops installing again there may be an error on the disc and you should return it to EB games and explain that it will not install. If the game was second hand there may be physical damage to the disc so worth having a look for that too.

I had the same problem. I was able to solve it by lowering the air temperature in the room by about 10°C and placing the console on a cold marble plate to cool it.

You should also try placing the PlayStation 3 on the other side; for example, I always place it vertically, so I placed it down horizontally.