Apple MacBook Pro 2013 with 512Gb SSD cannot install OS X
Usually you shouldn't be urged to restore the backup twice. Probably something went wrong in the first and/or the second run.

To quickly resolve your problem boot to Internet Recovery Mode or an external drive/thumb drive containing a Recovery HD or full OS X, erase/reformat your internal drive and restore the 10.10.3 backup. If you boot to IRM or a second drive you may manipulate the internal disk without any restrictions.  

Just erasing a volume is not recommended because it might not recover any faulty or wrong partition table. So better repartition the drive.


Boot to Internet Recovery Mode by pressing altcmdR. The prerequisites for an Internet Recovery are listed here: Recovery/Internet Recovery.
In a few words you need the latest firmware update installed, either ethernet or WLAN (WPA/WPA2) and a router with DHCP activated for a successful internet recovery.
On a 50 Mbps-line it takes about 4 min (presenting a small animated globe) to boot into the Recovery Netboot image which is loaded from an Apple server.  

(Alternatively you may boot to an external drive containing a Recovery HD or a full OS X system or an OS X thumb drive.)
open Terminal and enter:

    diskutil cs list

copy the UUID of the Logical Volume Group (it's the first one listed) and enter:

    diskutil cs delete UUID


The content of the main volume will be lost doing that. A backup is required.
Quit Terminal and open "Disk Utility" and partition your internal disk: GUID partition scheme (use the "Options..." button at the bottom of the main pane for this), one partition, journaled HFS+.  
Close "Disk Utility".  
Attach your Time Machine backup drive.  
Open "Restore from Time Machine Backup" and restore your main drive if you have booted from a Recovery drive.
If you've booted from a full OS X external drive just open Time Machine and restore your internal drive.