THE parents of missing Madeleine McCann have accused the Supreme Court judges who ruled against them in their court fight with ex-police chief Goncalo Amaral of "contradictions".

Gerry and Kate McCann have said they strongly disagree with the judges' ruling that the lifting of their status as formal suspects does not mean they are innocent of any involvement.

3 Gerry and Kate McCann, parents of missing Madeleine, have accused judges of contradictions after ruling against them in the fight against a former detective Credit: PA:Press Association

3 Madeleine McCann was aged three when she disappeared almost 10 years ago while on holiday with her family in Portugal Credit: PA:Press Association

Their daughter disappeared in Portugal on May 3, 2007, while staying in a holiday villa with her family.

The Supreme Court issued the premise earlier this month after backing Amaral over his book The Truth of the Life - in which he claims the McCann's faked their daughter's abduction to cover up her death.

The couple’s fight back was laid out in a nine-page complaint revealed today and lodged with the Supreme Court last Friday in a bid to invalidate its ruling rejecting the McCanns’ libel appeal against Amaral and the makers of a TV documentary based on his book.

The document, drafted by the McCanns’ Portuguese lawyer Isabel Duarte and her colleague Ricardo Correia, says: “The appellants understand the archiving of the case took place because during the inquiry, sufficient evidence had been collected to show the ‘arguidos’ had not committed any crime.”

Accusing them of acting “frivolously” and contradicting themselves with their statements about the reasons for the 2008 probe archive, they added: “It cannot be stated that it is not acceptable that the archiving of the case is considered the equivalent to proof of innocence.”

Amaral was previously ordered to pay the McCann's €500,000 in a Lisbon court in April 2015. He successfully overturned this payment and a ban on selling his book in April last year.

RELATED STORIES CONSPIRACY COP Who is Goncalo Amaral? Ex-Madeleine McCann cop who claims parents killed her COVER UP CHALLENGE McCanns prepped for new court battle against detective who claimed they faked Maddie's kidnap THE HUNT GOES ON What happened to Madeleine McCann and when did she go missing? Exclusive 'wiping away the horror' Holiday flat where Maddie McCann went missing is closed to 'spooked' holidaymakers Exclusive 'DON'T SAY ANYTHING!' McCanns ban lawyer from answering questions after judges reveal they've NOT been cleared over Maddie Exclusive 'I'M LOOKING FOR MADDIE' Guide defends 'ghoulish' Maddie McCann tour around the apartment where tot went missing

Kate and Gerry, both 48, of Rothley, Leicestershire, have said they will sue if The Truth of the Lie is sold in Britain.

They said in a statement after learning of the Supreme Court ruling against them: “What we have been told by our lawyers is obviously extremely disappointing.

“It is eight years since we brought the action, and in that time the landscape has changed dramatically, namely there is now a joint Metropolitan Police and Policia Judiciaria investigation which is what we have always wanted.

“The police in both countries continue to work on the basis that there is no evidence Madeleine has come to physical harm.

“We will of course be discussing the implications of the Supreme Court ruling with our lawyers in due course.”

The decision by Lisbon’s Court of Appeal sparked the Supreme Court fight which was resolved on January 31.

The full 76-page ruling which sparked the new legal challenge by the McCanns was released just under a week later.

Judges made it clear in their decision their job was not to decide whether the McCanns bore any criminal responsibility over their daughter’s disappearance and it would be wrong for anyone to draw any inferences about the couple’s guilt or innocence from their ruling.

3 Former detective Goncalo Amaral, as Kate and Gerry McCann, the parents of missing Madeleine McCann, have said they were disappointed after Portugal's highest court threw out their libel case against him Credit: PA:Press Association

But they added: “It should not be said that the appellants were cleared via the ruling announcing the archiving of the criminal case.

“In truth, that ruling was not made in virtue of Portugal’s Public Prosecution Service having acquired the conviction that the appellants hadn’t committed a crime.

“The archiving of the case was determined by the fact that public prosecutors hadn’t managed to obtain sufficient evidence of the practice of crimes by the appellants.

“There is therefore a significant, and not merely a semantic difference, between the legally admissible foundations of the archive ruling.

“It doesn’t therefore seem acceptable that the ruling, based on the insufficiency of evidence, should be equated to proof of innocence.”

They added, highlighting the McCanns’ Tapas Nine friend Jane Tanner’s much-questioned sighting of the suspected ‘abductor’: “It’s true that the aforementioned criminal inquiry ended up being archived, namely because none of the apparent evidence that led to the appellants being made ‘arguidos’ was subsequently confirmed or consolidated.

“However even the archive ruling raises serious concerns relating to the truth of the allegation that Madeleine was kidnapped.”

Portuguese police chiefs said late last year they were “completely in tune” with British detectives still investigating Madeleine’s disappearance, appearing to end years of tension between the two forces whose theories on the youngster’s fate have differed wildly.

Portuguese prosecutors reopened their probe into Madeleine McCann’s disappearance in May 2014, and are now working in close coordination with Scotland Yard’s scaled-down Operation Grange probe into Madeleine’s fate.

Earlier this month the McCann's hit out at the “insensitive” way their daughter has been drawn into the controversial TV drama about the fake kidnap of Shannon Matthews.

And a tour guide defended his “ghoulish” business giving trips around the apartment where the youngster went missing – insisting he’s just trying to help find the missing toddler.

We pay for your stories! Do you have a story for The Sun Online news team? Email us at tips@the-sun.co.uk or call 0207 782 4368.