hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
True arithmetic
In mathematical logic, true arithmetic is the set of all true first-order statements about the arithmetic of natural numbers. This is the theory associated with the standard model of the Peano axioms in the language of the first-order Peano axioms.
True arithmetic is occasionally called Skolem arithmetic, though this term usually refers to the different theory of natural numbers with multiplication.

Theory (mathematical logic)
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, giving rise to a formal system that combines the language with deduction rules. An element  of a deductively closed theory  is then called a theorem of the theory. In many deductive systems there is usually a subset  that is called "the set of axioms" of the theory , in which case the deductive system is also called an "axiomatic system". By definition, every axiom is automatically a theorem. A first-order theory is a set of first-order sentences (theorems) recursively obtained by the inference rules of the system applied to the set of axioms.
Abdullahi Ali Ahmed Waafow
Abdullahi Ali Ahmed Waafow (died 27 July 2022) was a Somali general and politician who served in the 8th Transitional Federal Parliament of Somalia in the 2000s. A member of the Bimaal clan, Waafow later became the mayor (district commissioner) of the southern city of Merca in the Lower Shabelle region, a position he would hold until his assassination.

On 27 July 2022, Waafow was killed when an al-Shabaab suicide bomber ran up to him and detonated while Waafow was giving a speech outside an administrative office in Merca. Around twenty other people were also killed, mainly Waafow's advisors and security personnel. Waafow was targeted by al-Shabaab due to his support for AMISOM peacekeepers in Lower Shabelle.

Merca
Merca (Somali: Marka; Arabic: مركة)  is the capital city of the Lower Shebelle province of Somalia, a historic port city in the region. It is located approximately 109 km (68 mi) to the southwest of the nation's capital Mogadishu. Merca is the traditional home territory of the Bimal clan and was the center of the Bimal revolt.
Beau James
Beau James is a 1957 American drama film directed by Melville Shavelson and starring Bob Hope, Vera Miles, Paul Douglas and Alexis Smith. It is based on a 1944 non-fiction book of the same name by Gene Fowler. The film features Hope in a rare dramatic role as Jimmy Walker, the colorful but controversial Mayor of New York City from 1926 to 1932.

Melville Shavelson
Melville Shavelson (April 1, 1917 – August 8, 2007) was an American film director, producer, screenwriter, and author.  He was President of the Writers Guild of America, West (WGAw) from 1969 to 1971, 1979 to 1981, and 1985 to 1987.
Wolf Wetzel
Wolf Wetzel (born 1956) is a German author, journalist and publicist. He is the author of several books and publishes in various media, including Der Freitag, junge Welt, and NachDenkSeiten. He wrote at Rubikon from its foundation in 2017 until his departure in 2018. Wetzel has also been a deputy board member of Business Crime Control since 2011.

Manova News
Manova News, formerly branded Rubikon, is a German online blog described to be following the Querfront strategy as well as spreading conspiracy ideologies. The motto of the blog is "Magazine for Freedom and Peace, Environment and Human Rights".

Owner, publisher and deputy editor-in-chief is the German Jens Wernicke. Editor-in-chief is Roland Rottenfußer.
Formula-G
Formula-G or Turkish Solar Car Grand Prix is a solar car championship. The last race was done in Ankara, Turkey in 2007. The first and second positions in this year was held by the teams of Istanbul Technical University. The third place was held by Sakarya University. The 2005 and 2006 races were both held in Istanbul Park, Turkey, the former being held on 30 August.

Istanbul Park
Istanbul Park (Turkish: İstanbul Park), also known as the TOSFED İstanbul Park, is a motor sports race track in the Tuzla district of Istanbul, Turkey. Designed by Hermann Tilke, it opened on 19–21 August 2005. It has been called "the best race track in the world" by former Formula One Chief Executive Bernie Ecclestone, who held the managing rights of the circuit between 2007 and 2011. The circuit was then managed by the Turkish company Intercity since October 2012 to March 2024. After Intercity, the operator was firstly changed as Can Bilim Eğitim Kurumları A.Ş. in April 2024 for 30 years, however its tender rights was cancelled in December 2024 by the administrative court. In June 2025, it was announced that the operating rights of this circuit was given to Turkish Automobile Sports Federation for at least 10 years, and the name was changed as TOSFED İstanbul Park.
Örebro County
Örebro County (Swedish: Örebro län) is a county or län in central Sweden. It borders the counties of Västra Götaland, Värmland, Dalarna, Västmanland, Södermanland and Östergötland. It is frequently culturally divided into the hilly northern region of Bergslagen, where mining and metallurgic industry have been important since the Middle Ages, and the southern Mälardalen of lakes and farms.

Västmanland
Västmanland (Swedish pronunciation: [ˈvɛ̂sːtmanˌland] or [ˈvɛ̌sːt-] ⓘ) is a historical Swedish province, or landskap, in middle Sweden. It borders Södermanland, Närke, Värmland, Dalarna and Uppland.

Västmanland means "West Man Land" or, less literally, "The Land of the Western Men", where the "western men" (västermännen) were the people living west of Uppland, the core province of early Sweden.
King Ezana's Stele
King Ezana's Stele is a 4th century obelisk in the ancient city of Axum, in the Tigray Region of Ethiopia. The monument stands in the middle of the Northern Stelae Park, which contains hundreds of smaller and less decorated stelae. This stele is probably the last one erected and the largest of those that remain unbroken. King Ezana of Axum's Stele stands 21 m (69 ft) tall, smaller than the collapsed 33 m (108 ft) Great Stele and the better-known 24 m (79 ft) "Obelisk of Axum" (reassembled and unveiled on 4 September 2008). It is decorated with a false door at its base and apertures resembling windows on all sides.

Axum
Axum, also spelled Aksum (/ˈɑːksuːm/ ⓘ), is a town in the Tigray Region of Ethiopia with a population of 66,900 residents (as of 2015). It is the site of the historic capital of the Aksumite Empire.

Axum is located in the Central Zone of the Tigray Region, near the base of the Adwa mountains. It has an elevation of 2,131 metres (6,991 feet) and is surrounded by La'ilay Maychew, a separately administered woreda of the Tigray region.

In 1980, UNESCO added Axum's archaeological sites to its list of World Heritage Sites due to their historic value. Prior to the beginning of the Tigray War in 2020, Axum was a leading tourist destination for foreign visitors.
Kemmental
Kemmental is a municipality in the district of Kreuzlingen in the canton of Thurgau in Switzerland.

The municipality was formed on 1 January 1996 through the merger of Alterswilen, Hugelshofen, Altishausen, Dotnacht, Ellighausen, Lippoldswilen, Neuwilen and Siegershausen.

Altishausen
Altishausen is a village and former municipality in the canton of Thurgau, Switzerland.

It was first recorded in year 1159 as Altinshusin.

The municipality had 120 inhabitants in 1850, which increased to 155 in 1950. After a decline to 111 in 1970 it rose to 161 in 1990.

In 1996 the municipality was merged with the other, neighboring municipalities Alterswilen, Dotnacht, Ellighausen, Hugelshofen, Lippoldswilen, Neuwilen and Siegershausen to form a new and larger municipality Kemmental.
Bobby Cummines
Robert Cummines OBE, FRSA (born 23 November 1951) is an English former business crime leader, protection racketeer, armed robber, and criminal enforcer who was chief executive of Unlock, The National Association of Reformed Offenders from April 1999 until March 2012. Despite being described as a gangster in media, Cummines has refused the label, saying he never considered himself one, instead stating he was a "businessman whose business was crime."

Unlock (charity)
Unlock National Association of Ex-Offenders, commonly referred to as Unlock, is an independent United Kingdom-based charity, established in 2000 to campaign for the equality of reformed offenders. Unlock describes its vision as "A fair and inclusive society where people with criminal records can move on positively in their lives".
Sanjay Bangar
Sanjay Bapusaheb Bangar  (born 11 October 1972) is an Indian cricket commentator and the head of cricket development of the IPL franchise Punjab Kings. He is a former Indian international cricketer. He played as an all-rounder and represented the India national cricket team in Tests and ODIs.

Kolkata Knight Riders
The Kolkata Knight Riders, also known as KKR, are  a professional Twenty20 cricket team based in Kolkata, West Bengal, that competes in the Indian Premier League (IPL). The franchise is owned by actor Shah Rukh Khan, actress Juhi Chawla, and her spouse Jay Mehta. Their home ground is Eden Gardens.

The franchise, which has gained immense popularity due to its association with celebrity owners, qualified for the IPL playoffs for the first time in 2011. They became the IPL champions in 2012, by defeating Chennai Super Kings in the final. They repeated the feat in 2014, defeating Kings XI Punjab. In 2024, they won the title for the third time by beating Sunrisers Hyderabad. The Knight Riders hold the record for the longest winning streak by any IPL team (14).

The team's all-time leading run-scorer is Gautam Gambhir, while their leading wicket-taker is Sunil Narine. The official motto of the team is Korbo, Lorbo, Jeetbo (Perform, Fight, Win) and the official colours are purple and gold.
Rotating furnace
A rotating furnace is a device for making solid objects which have concave surfaces that are segments of axially symmetrical paraboloids. Usually, the objects are made of glass. The furnace makes use of the fact, already known to Newton, that the centrifugal-force-induced shape of the top surface of a spinning liquid is a concave paraboloid, identical to the shape of a reflecting telescope's primary focusing mirror.

Paraboloids can be used in various ways, including (after being silvered) as primary mirrors in reflecting telescopes and solar cookers.

Solar cooker
A solar cooker is a device which uses the energy of direct sunlight to heat, cook or pasteurize drink and other food materials. Many solar cookers currently in use are relatively inexpensive, low-tech devices, although some are as powerful or as expensive as traditional stoves, and advanced, large scale solar cookers can cook for hundreds of people. Because these cookers use no fuel and cost nothing to operate, many nonprofit organizations are promoting their use worldwide in order to help reduce fuel costs and air pollution, and to help slow down deforestation and desertification.
Kamianka, Chernivtsi Oblast
Kamianka (Ukrainian: Камянка; Romanian: Petriceni or Camenca) is a village in Chernivtsi Raion, Chernivtsi Oblast, Ukraine. It hosts the administration of Kamianka rural hromada, one of the hromadas of Ukraine.

Until 18 July 2020, Kamianka belonged to Hlyboka Raion. The raion was abolished in July 2020 as part of the administrative reform of Ukraine, which reduced the number of raions of Chernivtsi Oblast to three. The area of Hlyboka Raion was merged into Chernivtsi Raion.

Chernivtsi Raion
Chernivtsi Raion (Ukrainian: Чернівецький район) is a raion (district) of Chernivtsi Oblast, Ukraine. It was created on 18 July 2020 as part of the reform of administrative divisions of Ukraine. Most of its territory is located in the historical region of Bukovina, while the southeastern parts are in Bessarabia, and the Hertsa region. The center of the raion is the city of Chernivtsi. Four abolished raions, Hertsa, Hlyboka, Storozhynets, and Zastavna Raions, part of abolished Kitsman and Novoselytsia Raions, as well as the city of Chernivtsi, which was previously incorporated as a city of oblast significance, were merged into Chernivtsi Raion. Population: 648,643 (2022 estimate).
2017–18 Scottish League Two
The 2017–18 Scottish League Two (known as Ladbrokes League Two for sponsorship reasons) was the 24th season in the current format of 10 teams in the fourth-tier of Scottish football. The last placed team entered a play-off with a team nominated by the Scottish Football Association from outside the SPFL determining which team enters League Two in the 2018–19 season. The fixtures were published on 23 June 2017.

Ten teams contested the league: Annan Athletic, Berwick Rangers, Clyde, Cowdenbeath, Edinburgh City, Elgin City, Montrose, Peterhead, Stenhousemuir and Stirling Albion.

Stenhousemuir F.C.
Stenhousemuir Football Club is a Scottish football club located in Stenhousemuir, Falkirk. They are a member of the Scottish Professional Football League and currently play in Scottish League One after achieving automatic promotion from Scottish League Two in 2024.

Through much of its history, the team has competed in the lower leagues of Scottish football.

In September 2009, Stenhousemuir Football Club, Ltd. was re-registered as a Community Interest Company.
Ireland's Fittest Family
Ireland's Fittest Family is an Irish TV series where families from across Ireland compete in different adventure races and fitness competitions in an effort to win 15,000 euro.

Since 2014 there have been eleven seasons of the programme and five celebrity specials.

Nina Carberry
Nina Carberry (born 21 July 1984) is an Irish Fine Gael politician who has been a Member of the European Parliament (MEP) for Midlands–North-West since the 2024 European Parliament election. She is a former champion amateur National Hunt jockey with seven Cheltenham Festival wins to her name.
George Ashlin
George Coppinger Ashlin (28 May 1837 – 10 December 1921) was an Irish architect, particularly noted for his work on churches and cathedrals, and who became President of the Royal Institute of the Architects of Ireland.

Tralee
Tralee (/trəˈliː/ trə-LEE; Irish: Trá Lí, pronounced [t̪ˠɾˠaː(j) ˈl̠ʲiː]; formerly Tráigh Lí, meaning 'strand [of the River] Lee') is the county town of County Kerry in the south-west of Ireland. The town is on the northern side of the neck of the Dingle Peninsula, and is the largest town in County Kerry. The town's population was 26,079 as of the 2022 census, making it the 15th largest urban settlement in Ireland. Tralee is known for the Rose of Tralee International Festival, which has been held annually in August since 1959.
MFK Skalica
MFK Skalica is a Slovak football team, based in the town of Skalica. The club was founded in 1920. The club plays in the Fortuna Liga, the top tier of Slovak football, and hosts home games at the Mestský štadión Skalica.

The club colors since the foundation of ŠK Skalica have been and still are white and green.

Mestský štadión Skalica
The Municipal Stadium (Slovak: Mestský štadión) in Skalica, Slovakia, also colloquially known as Letňák, is a football stadium that serves as the home ground of MFK Skalica and has capacity of 2,494. Western stand has 858 seats, and Eastern Stand has 1,592 seats (including 278 in visitors sector). The stadium is also equipped with a 6-lane 400-meter athletic track.

The municipal stadium situated in Skalica is positioned to the south of the town center, approximately 3 km (2 miles) from the Slovak-Czech border.
Rajiformes
Rajiformes /ˈrædʒɪfɔːrmiːz/ is one of the four orders in the clade Batomorphi, often referred to as the superorder Batoidea, flattened cartilaginous fishes related to sharks. Rajiforms are distinguished by the presence of greatly enlarged pectoral fins, which reach as far forward as the sides of the head, with a generally flattened body. The undulatory pectoral fin motion diagnostic to this taxon is known as rajiform locomotion. The eyes and spiracles are located on the upper surface of the head and the gill slits are on the underside of the body. Most species give birth to live young, although some lay eggs enclosed in a horny capsule ("mermaid's purse").

Batomorph locomotion
Batomorphi is a division of cartilaginous fish consisting of skates, rays and other fish all characterized by dorsoventrally flattened bodies and large pectoral fins fused to the head. This distinctive morphology has resulted in several unique forms of locomotion. Most batomorphs exhibit median paired fin swimming, utilizing their enlarged pectoral fins. Batomorphs that exhibit median paired fin swimming fall somewhere along a spectrum of swimming modes from mobuliform to rajiform based on the number of waves present on their fin at once. Of the extant orders of Batomorphi this holds truest for the Myliobatiformes (rays) and the Rajiformes (skates). The two other orders: Rhinopristiformes and Torpediniformes exhibit a greater degree of body caudal fin swimming.
Sliabh Luachra
Sliabh Luachra (Irish pronunciation: [ʃl̠ʲiəw ˈl̪ˠuəxɾˠə]), sometimes anglicised Slieve Logher, is an upland region in Munster, Ireland. It is on the borders of counties Cork, Kerry and Limerick, and bounded to the south by the River Blackwater. It includes the Mullaghareirk Mountains.

Mullaghareirk Mountains
The Mullaghareirk Mountains (from Irish: Mullach an Radhairc, meaning 'the summit of the view') is a range of hills in Ireland on the borders of County Cork, County Kerry and County Limerick. The area is also known as Sliabh Luachra (sometimes anglicised 'Slieve Logher'). The highest point is Baraveha (Barr an Bheithe) at 451 metres (1,480 ft). It is bordered by the Blackwater valley to the south, Castleisland to the west, Athea to the north and the Deel valley to the east. Villages in the hills include Rockchapel, Ballydesmond, Brosna, Gneevgullia, Mountcollins, Newmarket, Meelin and Tournafulla. The Allaughaun River, a tributary of the River Feale, rises at the east end of the range.
Whatever Gets You thru the Night
"Whatever Gets You thru the Night" is a song written by John Lennon, released as a single in 1974 on Apple Records, catalogue number Apple 1874 in the United States and Apple R5998 in the United Kingdom. In the U.S. it peaked at No. 1 on all three record charts: Billboard Hot 100, Cashbox, and Record World, and at No. 36 in the UK. It was the lead single for Lennon's album Walls and Bridges; in the UK the single was released on the same day as the album. "Whatever Gets You thru the Night" was Lennon's only solo No. 1 single in the United States during his lifetime, making him the last member of the Beatles to finally reach the top of the charts. In Canada, the single spent two weeks at No. 2, and became the 30th biggest hit of 1974.

Bobby Keys
Robert Henry Keys (December 18, 1943 – December 2, 2014) was an American saxophonist who performed as a member of several horn sections of the 1970s. He appears on albums by the Rolling Stones, Lynyrd Skynyrd, Harry Nilsson, Delaney & Bonnie and Friends, George Harrison, John Lennon, Ringo Starr, Eric Clapton, Joe Cocker, Joe Ely, and other prominent musicians. Keys played on hundreds of recordings, and was a touring musician from 1956 until his death in 2014.
Tabeirós – Terra de Montes
Tabeirós - Tierra de Montes is a comarca in the Galician province of Pontevedra in Spain, located in the southern part of the basin of the river Ulla. The overall population of this local region is 23,867 (2019). It consists of two distinct natural and historical units: to the north, in the lower valley, the lands of Tabeirós corresponding approximately to the municipality of La Estrada and to the south, the mountains of Tierra de Montes, famous for their gigs and isolated monasteries.

Province of Pontevedra
The province of Pontevedra (Spanish: Provincia de Pontevedra, Galician: Provincia de Pontevedra) is a province of Spain, located in the southwestern part of the autonomous community of Galicia. It is bordered by the provinces of A Coruña, Lugo, and Ourense, the country of Portugal and the Atlantic Ocean. There is a public institution named the Provincial Deputation of Pontevedra (provincial council), whose head office is in Pontevedra city, that provides direct services to citizens such as technical, financial and technological support to the councils of the 61 municipalities of the province of Pontevedra.

As of 2024, the population of the province is 947,869, of which 8% live in the capital, the city of Pontevedra, and 31% in Vigo.
John Jenkins (American football coach)
John Jenkins (born June 20, 1952) is an American football coach and former player.  He served as the head football coach the University of Houston from 1990 to 1992, compiling a record of 18–15.  A proponent of the run and shoot offense, Jenkins also coached professional football in the United States Football League (USFL), the Canadian Football League (CFL) and the Fall Experimental Football League (FXFL).  He served as the head coach of the CFL's Ottawa Renegades in 2006, the FXFL's Blacktips in 2014 and the Hudson Valley Fort for part of 2015.  During his career as a coach, Jenkins has mentored a number of notable quarterbacks such as Andre Ware, David Klingler, Jim Kelly, Eric Crouch, Kliff Kingsbury, Anthony Calvillo and Doug Flutie.

Ottawa Renegades
The Ottawa Renegades were a Canadian Football League franchise based in Ottawa, Ontario founded in 2002, six years after the storied Ottawa Rough Riders folded. After four seasons, the Renegades franchise was suspended indefinitely by the league due to financial instability, and its players were absorbed by the other teams in a dispersal draft.

After two years in limbo, the Renegades franchise was awarded to Jeff Hunt, best known as the owner of the Ottawa 67's, in March 2008. The new franchise was revived in 2014 and rebranded as the Ottawa Redblacks. For historical purposes, the CFL classifies the Redblacks, Renegades and Rough Riders as one discontinuous franchise.
Diazoalkane 1,3-dipolar cycloaddition
The Diazoalkane 1,3-dipolar cycloaddition is a 1,3-dipolar cycloaddition (an organic reaction) between a 1,3-dipole diazo  compound (notably diazomethane) and a dipolarophile. When the dipolarophile is an alkene, the reaction product is a pyrazoline.

The reaction product of a cycloaddition between diazomethane and trans-diethyl glutaconate is a 1-pyrazoline. This reaction is 100% regioselective because the diazo terminal nitrogen atom bonds exclusively to the alpha-carbon of the ester. The reaction is also a syn addition, and the configuration in the dipolarophile is preserved. The 1-pyrazoline is unstable and isomerizes to the 2-pyrazoline due to favorable conjugation with the ester group.

With diazo(phenyl)methane as the reactant the regioselectivity is reversed and the reaction is extended even further by simple air organic oxidation of the 2-pyrazoline to the pyrazole.

Another example of a diazo cycloaddition is a diazo-thioketone coupling.

Diazo
In organic chemistry, the diazo group is an organic moiety consisting of two linked nitrogen atoms at the terminal position.  Overall charge-neutral organic compounds containing the diazo group bound to a carbon atom are called diazo compounds or diazoalkanes and are described by the general structural formula R2C=N+=N−. The simplest example of a diazo compound is diazomethane, CH2N2.  Diazo compounds (R2C=N2) should not be confused with azo compounds (R−N=N−R) or with diazonium compounds (R−N+2).