OS X could not be installed on your computer. OSX can't be installed on the disk Macintosh HD because a recovery system can't be created.

You need to disable the encryption by turning off FileVault.

I think all you have to do is turn off FileVault. You cannot actually decrypt the drive if you have set up the encrypted filesystem. But I don't think that is necessary. Besides you must repartition the drive which means you will lose everything on the drive, so you would need a current and reliable backup before doing that.

Just turn off FileVault for now and see if that solves your problem.

I'm stumped. I don't know what you may have done with your computer that put you in this state. I can suggest the extreme solution: backup your entire Home folder onto an external drive. Boot from your Recovery HD and reinstall OS X from scratch:

Install or Reinstall Lion/Mountain Lion from Scratch

Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

Erase the hard drive:

1. Select Disk Utility from the main menu and click on the Continue button.

2. After DU loads select your startup volume (usually Macintosh HD) from the

left side list. Click on the Erase tab in the DU main window.

3. Set the format type to Mac OS Extended (Journaled.) Optionally, click on

the Security button and set the ZeroData option to one-pass. Click on

the Erase button and wait until the process has completed.

4. Quit DU and return to the main menu.

Reinstall Lion/Mountain Lion: Select Reinstall Lion/Mountain Lion and click on the Install button.

Note: You will need an active Internet connection. I suggest using Ethernet if possible

because it is three times faster than wireless.