Gerard Baden-Clay’s lawyers will argue at a High Court appeal next month there is no proof he intended to kill his wife.

The Queensland Director of Public Prosecutions is appealing to overturn a decision by Queensland’s Court of Appeal last year to downgrade Baden-Clay’s murder conviction to manslaughter.

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Allison Baden-Clay’s body was found on a creek bank in April 2012, 10 days after her husband reported her missing from their Brisbane home.

In written submissions filed to the High Court on Monday, Baden-Clay’s defence team argued there was no direct evidence that he caused Allison’s death or did so with the intention of murdering her.

The submission said the case against Baden-Clay depended entirely on circumstantial evidence and the prosecution had not exhausted the possibility Baden-Clay accidentally killed his wife.

“The scratches to the face say something about the relationship between the deceased and (Baden-Clay) but nothing about intention,” the submission said.

“They do not show who initiated violence.”

In written submissions lodged earlier this month, the DPP argued there was evidence for the jury to conclude Baden-Clay had motive to get “rid of his wife”.

The DPP also argued the Court of Appeal took a “piecemeal” approach to the circumstantial evidence instead of considering the case as a whole.