If you have just installed Linux Mint 17 and doesn’t boot on Sony VAIO Pro 13 (or any other modern HW) it means that you have hard-coded path to EFI image in your UEFI firmware Check what’s the hard-coded path in your case and simply copy your EFI image there
mint ~ # apt-get install efibootmgr -y
mint ~ # mkdir /mnt/1 ; mount /dev/sda1 /mnt/1
mint ~ # efibootmgr --verbose
BootCurrent: 0006
Timeout: 0 seconds
BootOrder: 0006,0005
Boot0005* Windows Boot Manager HD(1,800,100000,01234567-1234-1234-1234-0123456789ab)File(\EFI\Boot\bootx64.efi)
Boot0006* UEFI: SanDisk Extreme 0001 ACPI(a0341d0,0)PCI(1d,0)USB(1,0)USB(1,0)HD(1,40,f4201,56789abc-5678-5678-9012-601012345678)..BO
In my case the path is \EFI\Boot\bootx64.efi
EFI firmware will search removable media for a FAT32 filesystem containing the file \EFI\Boot\bootx64.efi (for both 32bit and 64bit systems)
Some EFI systems may also need a startup script, in which case put the following in /EFI/BOOT/startup.nsh: BOOTX64
mint ~ # mkdir /mnt/1/EFI/Boot
mint ~ # cp -p /mnt/1/EFI/ubuntu/grubx64.efi /mnt/1/EFI/Boot/bootx64.efi
mint ~ # umount /dev/sda1
mint ~ # sync
mint ~ # reboot