Nathaniel and Gareth Train died in a gunfight with heavily armed police at their Wieambilla property in the western Darling Downs region on Monday night.

The pair, along with Gareth’s wife Stacey, ambushed and shot dead constables Matthew Arnold, 26, and Rachel McCrow, 29, before killing 58-year-old neighbour Alan Dare when he came to help.

Queensland Police Commissioner Katarina Carroll said investigators would look at the killers’ possible extremist links after a series of posts under the name of Gareth Train were uncovered on conspiracy theory forums.

The posts include references to anti-vaccine sentiments and claims high-profile shootings were hoaxes or false-flag operations.

“It’s very difficult at the moment for us to reason with what has happened, there are no obvious reasons,” Carroll told ABC’s 7.30 program on Tuesday night.

“But within the next few days and the next few weeks, I have no doubt that we will come back … (with) some insight into what we believe took place.”

Carroll said every possible motivation for the killings was being looked at, including whether it was a premeditated attack on the officers.

“Some of the stuff that’s online from these people, we will investigate what they have been doing not only in recent weeks but in recent years, who they’ve been interacting with … their online presence, every aspect of this will be thorough,” she said.

The police commissioner described the deadly shooting as “senseless and callous”.

Carroll said NSW police had asked local officers to check on Nathaniel Train at the isolated Wieambilla property.

“That person had been missing for up to about 12 months, but people had been in contact with him,” she told reporters.

“However, that contact was lost in recent days, and they just wanted to check on that missing person.”

A series of posts under the name of Gareth Train appear on conspiracy theory forums and include references to anti-vaccine sentiments and claims high-profile shootings were hoaxes or false-flag operations.

One post refers to “black op police” and urges people to prepare themselves.

“Has reading anything from the 1901 constitution or quoting common law to the black op police with the guns helped anyone in Victoria and their rights,” a post from a user named Gareth Train said.

NSW Police last week launched a public appeal to find Nathaniel Train, 46, a former school principal who was last seen at his Dubbo home on December 16, 2021.

He cut contact with his family in early October and was reported missing on December 4 this year after going to live with his brother and sister-in-law at their Wieambilla home.

Both Nathaniel and Stacey Train previously worked in the Queensland education system before the 46-year-old moved interstate.

He worked as executive principal at Walgett Community College Primary School, but the NSW Department of Education said he hadn’t been employed in the state’s education system since August 2021 and he officially left employment in March.

While at the school in northern NSW, he sent 16 emails over two weeks about problems there and the need for assistance, the state’s parliament heard in May.

Nathaniel Train then seemed to disappear, cutting off contact with loved ones before returning to Queensland.

Stacey Train held a senior teaching post at Tara Shire State College before she resigned in December 2021.