The mother, who cannot be named for legal reasons, and one of the twins took the case to court after the other brother was named as the father on the child's birth certificate.
The pair launched the legal action as they wanted to be legally recognised as having parental responsibility for the baby, known as child P.
A family court judge declined to remove the name of the alleged "father" on the birth certificate, prompting the woman and the other twin to take the case to the Court of Appeal in London.
But a panel of judges there have now ruled it is "not possible" to know for sure who the father is.
The court heard that DNA testing could not distinguish which of the men was the father, although scientists may potentially be able to do so in the future.
But Sir Andrew McFarlane, sitting with Lady Justice King and Lord Justice Stuart-Smith, did say that the twin on the birth register would no longer have parental responsibility until the court hears further arguments.
In a judgment handed down earlier this month, he said: "Currently, the truth of P's paternity is that their father is one or other of these two identical twins, but it is not possible to say which.
"It is possible, indeed likely, that by the time P reaches maturity, it may be possible for science to identify one father and exclude the other twin, but, for the coming time, that cannot be done without very significant cost, and so her 'truth' is binary and not a single man."
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Judge Madeleine Reardon previously found that "both brothers had had sex" with the woman "within four days of each other in the month when P was conceived", and that it was "equally likely that each of the brothers is P's father".
Sir Andrew said that the first twin "was not entitled" to be registered as the father and that any parental responsibility he had "shall cease" as a result.
However, the judge added that he was "wholly unpersuaded" to declare that the man was not the father either.
Sir Andrew said: "The failure to prove a fact means that that fact is not proved; it does not mean that the contrary is proved.
"There is a distinction between something being not proven, and making a positive declaration that the fact asserted is not true."
The case continues.
Denis Donaldson, 55, was killed at a remote cottage in County Donegal in April 2006, months after admitting his role as a police and MI5 agent for two decades.
Antoin Duffy, who is in his 40s and of no fixed address, has been charged with the murder of Mr Donaldson at Cloghercor, Doochary.
He has also been charged with the attempted murder of a second man in County Donegal in November 2007.
Duffy appeared before the Special Criminal Court in Dublin on Monday afternoon.
Earlier he was arrested by Irish police after arriving at Casement Aerodrome in Baldonnel, on the western outskirts of the city, following his extradition from Scotland on a European Arrest Warrant.
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Duffy is also charged with the possession of a shotgun and ammunition.
He was remanded in custody before the next court appearance on 13 April, where he is to appear in person.
He was also granted legal aid by the court.
He was killed in a plane crash on his way to begin his Premier League career in January 2019.
Cardiff paid Nantes a club-record fee for Sala, 28, but he never played after the light aircraft came down in the English Channel.
The Welsh club sued Nantes for more than £100m over alleged negligence connected to the crash, which also killed pilot David Ibbotson.
Sky Sports News reported that Cardiff contended Nantes were responsible because they enlisted agent Willie McKay, whose son, Mark McKay, was Sala's representative, to arrange the flight. Nantes denied that claim.
However, the court has now decided Nantes was not at fault, and Cardiff did not suffer any reputational harm.
It called Cardiff's claim "extravagant" and instead said Nantes had suffered reputational damage.
Cardiff was ordered to pay €300,000 in damages and €180,000 (£416,000 in total) in legal costs.
The club have been involved in a legal battle over the case for years. They were previously told to pay the £15m transfer fee after their claim that the deal had not been finalised was also rejected.
In 2021, the person who arranged the flight, David Henderson, was found guilty of endangering the safety of an aircraft and jailed for 18 months.
He had asked Mr Ibbotson to fly the Piper Malibu plane because he was away on holiday, despite him not having a commercial licence or a qualification to fly at night.
Mr Ibbotson's rating to fly that type of aircraft had also expired.
Cardiff City said in a statement on Monday: "We deeply regret that the court did not recognise Nantes' liability in this tragedy.
"We initiated these proceedings so that the full truth of this case could come to light, in respect of Emiliano Sala's memory.
"Today, we note with bitterness that the principles of transparency, integrity and safety in professional football have not prevailed in this decision."
Sala's body was recovered from the wreckage of the aircraft weeks after the crash, but Mr Ibbotson has never been found.
An inquest into Sala's death found he would have been unconscious at the time due to carbon monoxide poisoning, likely caused by a faulty exhaust system.
The works by French artists Pierre-Auguste Renoir, Henri Matisse and Paul Cezanne were taken in an operation lasting less than three minutes, police said.
The thieves targeted the Magnani-Rocca Foundation villa, south of the city of Parma, on the night of 22 March.
According to sources close to the investigation, the stolen masterpieces were Renoir's Les Poissons, Cezanne's Still Life With Cherries and Matisse's Odalisque On The Terrace.
The value of the three is worth "tens of millions euros", an investigator said.
However, Italian public broadcaster Rai reported the stolen works were worth €9m (£7.8m).
There has been no official confirmation on the combined value of the paintings.
The paintings were on the first floor of what is called the Villa of Masterpieces in the Sala dei Francesi - the Room of the French.
The thieves, wearing balaclavas, gained entry by forcing open a door and were described as an "organised group".
They were disturbed by the museum's alarm system and escaped before they could take more paintings, "which was their intention".
Investigators are assessing museum security footage.
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The Magnani-Rocca Foundation is a private museum which lies in the heart of the countryside 12 miles from Parma.
Established in 1977, the foundation hosts the collection of the art historian Luigi Magnani and also includes works by Durer, Rubens, Van Dyck, Goya and Monet.
It comes after a series of high-profile heists at major European museums, including last October when thieves stole jewels and other items worth £76m from the Louvre in Paris.
In a joint declaration, the UK, Germany, France and Italy said the proposed legislation would "significantly expand the possibilities for imposing the death penalty".
Calling the scheme, which Israel's Knesset began debating on Monday "de facto discriminatory", the statement said if it becomes law, "Israel risks undermining its commitments to democratic principles".
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The death penalty "is an inhumane and degrading form of punishment without any deterrent effect", adding that rejecting it "is a fundamental value that unites us", the four nations said.
Should it pass, the new law would be a triumph for Israel's far right, and especially minister of national security, Itamar Ben-Gvir, who has campaigned for tougher punishments for Palestinians convicted of nationalistic offences against Israelis.
Opponents of the idea, under which executions should be carried out within 90 days of sentencing, say it is racist, draconian and unlikely to deter attacks by Palestinian militants.
The legislation calls for the death penalty to go into effect within 30 days.
The bill's critics include Israelis and Palestinians, international rights groups and the UN, some of whom fear the death penalty could end up being applied solely to Palestinians convicted of murdering Jewish citizens of Israel.
Under the proposal, the sentence will be applied by a military court to anyone convicted of murdering an Israeli "as an act of terror".
Such courts try only West Bank Palestinians, who are not Israeli citizens. The bill says military courts can change the penalty to life imprisonment in "special circumstances".
Israel's courts, which try Israeli citizens, including Palestinian citizens of Israel, can choose between life imprisonment or the death penalty in cases of murder aiming to harm Israeli citizens and residents or "with the intent of rejecting the existence of the state of Israel".
Amichai Cohen, a senior fellow at the Israel Democracy Institute's Centre for Democratic Values and Institutions, said the distinction is discriminatory as it means, in effect, Jews "will not be indicted under this law".
In addition, the West Bank is not sovereign Israeli territory, so under international law, Israel's parliament should not be legislating over it, Mr Cohen said.
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Israel has the death penalty on its books, but the country hasn't put anyone to death since Nazi war criminal Adolf Eichmann in 1962.
The bill will not apply retroactively to any of the militants Israel currently holds who attacked the country on 7 October 2023.




