Now it did unexpected shutdown while being plugged into the power adapter.
I don't know what could be suspicious but I have copied few lines before and after the event here:
30/06/2016 20:52:07.477 com.apple.AddressBook.InternetAccountsBridge[598]: dnssd_clientstub ConnectToServer: connect() failed path:/var/run/mDNSResponder Socket:4 Err:-1 Errno:1 Operation not permitted
30/06/2016 20:53:59.912 apsd[75]: BUG in libdispatch: 15F34 - 1718 - 0x0
30/06/2016 20:55:21.154 nbagent[601]: XPC Activity invoked with state=0
30/06/2016 20:55:21.154 nbagent[601]: XPC Activity invoked with state=2
30/06/2016 20:56:06.000 syslogd[42]: ASL Sender Statistics
30/06/2016 20:58:30.953 Safari[246]: KeychainGetICDPStatus: keychain: -25300
30/06/2016 20:58:30.953 Safari[246]: KeychainGetICDPStatus: status: off
30/06/2016 21:00:49.435 Console[592]: Marker - 30 Jun 2016, 21:00:49
30/06/2016 21:00:50.705 Console[592]: Marker - 30 Jun 2016, 21:00:50
30/06/2016 21:00:54.153 Console[592]: Marker - 30 Jun 2016, 21:00:54
30/06/2016 21:01:07.603 CalendarAgent[248]: [com.apple.calendar.store.log.caldav.coredav] [Refusing to parse response to PROPPATCH because of content-type: [text/plain; charset="utf-8"].]
30/06/2016 21:01:07.842 CalendarAgent[248]: [com.apple.calendar.store.log.caldav.coredav] [Refusing to parse response to PROPPATCH because of content-type: [text/plain; charset="utf-8"].]
30/06/2016 21:01:09.142 CalendarAgent[248]: [com.apple.calendar.store.log.caldav.coredav] [Refusing to parse response to PROPPATCH because of content-type: [text/plain; charset="utf-8"].]
30/06/2016 21:01:09.386 CalendarAgent[248]: [com.apple.calendar.store.log.caldav.coredav] [Refusing to parse response to PROPPATCH because of content-type: [text/plain; charset="utf-8"].]
30/06/2016 21:01:53.000 bootlog[0]: BOOT_TIME 1467277313 0
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.AccountPolicyHelper" claims selected messages.
Those messages may not appear in standard system log files or in the ASL database.
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.Accounts" claims selected messages.
Those messages may not appear in standard system log files or in the ASL database.
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.Accounts" claims selected messages.
Those messages may not appear in standard system log files or in the ASL database.
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.authd" sharing output destination "/var/log/asl" with ASL Module "com.apple.asl".
Output parameters from ASL Module "com.apple.asl" override any specified in ASL Module "com.apple.authd".
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.authd" sharing output destination "/var/log/system.log" with ASL Module "com.apple.asl".
Output parameters from ASL Module "com.apple.asl" override any specified in ASL Module "com.apple.authd".
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.authd" claims selected messages.
Those messages may not appear in standard system log files or in the ASL database.
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.authkit.osx.asl" sharing output destination "/var/log/Accounts" with ASL Module "com.apple.Accounts".
Output parameters from ASL Module "com.apple.Accounts" override any specified in ASL Module "com.apple.authkit.osx.asl".
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.authkit.osx.asl" claims selected messages.
Those messages may not appear in standard system log files or in the ASL database.
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.authkit.osx.asl" claims selected messages.
Those messages may not appear in standard system log files or in the ASL database.
30/06/2016 21:01:54.000 syslogd[41]: Configuration Notice:
ASL Module "com.apple.awdd" claims selected messages.
Those messages may not appear in standard system log files or in the ASL database.