OS X El Capitan with Safari 9.1.3 ???

Check your current version of El Capitan using "About This Mac" in the  menu (top-left of screen). It should show Version 10.11.6

Click on the version number to see the build. It should be 15G1611

If it's older, such as 15G1011, it's because you installed the defective version of El Capitan that was released 2017-09-25

Your screen shot shows an El Capitan install on 2017-10-06, so you probably have the bad version. That version will not do security updates, or the Safari 11 update. See if you still have the installer in you Applications folder. It is named "Install OS X El Capitan". Do a "Get Info" (⌘i) on it. The bad one is Version 1.7.55, created 2017-08-08.

The good one is version 1.7.50, created 2016-05-18

Look in the Purchased tab of the App Store app for the correct version of "OS X El Capitan", dated before 2017-09-25, and download and install it, You can then use the Updates section of the App Store to bring it up to date and install Safari 11. It make take more than one update. The install will not delete any of your files.

If you don't have a good version in you Purchased section, you may be stuck. The Apple link in

https://support.apple.com/HT206886

gets the bad (2017-09-25) version.

This post may also be useful.

VikingOSXOct 11, 2017 9:29 AM in response to Ap_Mac_Mwnci

Level 7 (27,397 points)

Mac OS X

Oct 11, 2017 9:29 AM Re: Updated from Mavericks to El Capitan: What version of Safari should now be installed?in response to Ap_Mac_Mwnci

There are seven security updates through July 2017, since El Capitan 10.11.6 was released. There are just two requirements to receive them in the Updates tab of the Mac App Store:

1. OS X 10.11.6 is installed
2. The Mac App Store System Preference is configured with these checked:
   1. Automatically check for updates
   2. Install system data files and security updates

These settings allowed me to be automatically notified in the Mac App Store Updates tab when these security updates were released. Safari 11 was in Security Update 2017-003 released in July.

If you review your installation history ( menu : About This Mac : System Report... button : Software : Installations, you will see what Security updates have been installed. Mine appears:

You can obtain the missing Security Updates for El Capitan 10.11.6 directly from Apple's Download site, and by specifying “Security Update 2016-001.” Make absolutely certain that you choose those for El Capitan, and install all of them in numeric order.

If you can't get it from the App Store Purchased tab, the USB version should work. Check its "Install OS X El Capitan". It it's not Version 1.7.55 then it's OK to use, Copy it from the USB stick to your Applications folder, then run it from there. After the install, do updates until there are no more. That should get you Safari 11.

You can try the 10.11.6 combo update. The worst that can happen is it refuses to install. Check the El Capitan build number after, then do the App Store updates.

First look for the earlier El Capitan 10.11.6 in the Purchases section of the App Store. After downloading, but before installing, you can check the version in the Applications folder. It should be 1.7.50, not 1.7.55.

It is hard to tell what version of OS X you will get using the Recovery Partition. It might revert to the version that originally came with the computer. Option-Command-R seems the right key combination, but it could get you the bad version.

https://support.apple.com/HT204904

Open the Mac App store and look in the Purchased tab. See if there was an update to Safari, recently. If there was re-install.

Also, by chance do you run any antivirus, cleaning or any other third party "maintenance" apps?

You can do an non-intrusive re-install of Mac OS from the recovery partition. Non-intrusive means that it will not affect your data files, apps or settings it will only fill in missing parts of Mac OS. Safari is considered part of Mac OS. However even though this is non-instrusive it is wise to have a backup of your complete system, I.e. Time Machine, a bootable clone etc. Once you have a backup that you have tested then do the re-install.

To do the re-install reboot the computer in the Recovery Partition (Command + R) and install Mac OS.