How to properly set up an SPF record?

Question

Domain Name System

Hello everyone, help with the correct setting of SPF records for the domain.
Given: VPS with a dedicated IP hosting several sites that use sending emails to users.
What needs to be done: configure SPF so that its check ends as PASS.
What has been done:
Chose the main domain xxx.xx . Its DNS is
xxx.xx. --- A --- 111.11.1.100
mail --- A --- 111.11.1.100
xxx.xx. --- MX --- mail.xxx.xx.
100.1.11.111.in-addr.arpa --- PTR --- xxx.xx
DNS of the second domain yyy.yy (from which outgoing mail is not checked):
yyy.yy. --- A --- 111.11.1.100
@ --- MX --- ALT1.ASPMX.L.GOOGLE.COM. (and other GApps MX)
@ --- MX --- xxx.xx.
100.1.11.111.in-addr.arpa --- PTR --- xxx.xx
yyy.yy. --- TXT --- v=spf1 a mx ip4:111.11.1.100 include:_spf.google.com ~all Failed email
headers:
Return-Path: < [email protected] >
Received: from xxx. xx (xxx.xx. [111.11.1.100])
by mx.google.com with ESMTP id ****
for ***;
Mon, 01 Dec 2014 05:08:32 -0800 (PST)
Received-SPF: none (google.com: [email protected] does not designate permitted sender hosts) client-ip=111.11.1.100;
Authentication-Results: mx.google.com;
spf=none (google.com: [email protected] does not designate permitted sender hosts) [email protected]
Received: by xxx.xx (Postfix, from userid 999)
What am I doing wrong and how can I do it right?

Answer 1

The letter was sent on behalf of xxx.xx, which has no spf entry at all.