OpenLLM-France/wikimedia huggingface dataset:
# Mario Adventure/Story

After Mario defeated Bowser in Super Mario Bros. 3, he and his brother Luigi began to escort Peach back to the Mushroom Kingdom. They were having a nice, safe journey until a Bob-omb fell from the sky! Luigi looked up and to his surprise saw an enemy he had never saw before! It looked like a Lakitu, but it was black with odd eyes. He claimed to be Warkitu, a mutant Lakitu. Mario got into his usual stance to take down this "Warkitu". However, Warkitu started to throw more Bob-ombs on the ground. Peach ran behind Luigi for safety while Mario tried to dodge the bombs, but Mario was hit and knocked out cold...
When he finally came to, he found himself in an odd world. Fortunately, Toad found him just in time to explain what was going on. Toad told that Bowser had stolen a powerful crystal that magnify the natural forces of the world. Everything had mutated. Some of Mario's enemies had become more powerful! However, Mario's abilities also became more powerful! Toad explained that the crystal's power worked for both good and evil. Mario obtained a nearby Fire Flower that changed his clothes to an unfamiliar orange. Mario found himself jumping higher than before, and his fireballs moved in a straight line! When they came in contact with an object, they didn't disperse, they continued going! Mario smiled and knew that with these new powers, he must set out on another adventure in this strange new land to restore peace and find out what happened to Peach and Luigi!
Mario traveled to the usual place that lead to Bowser's world, but the entrance was gone! Not knowing what to do, he asked Toad what could done. Toad explained that the only way to reach Bowser's Castle is by warping there. So Mario journeyed to the Warp Zone. On his arrival, he saw there were giant locks blocking the path to the warp pipe to Bowser's world. He asked a local who had put them there. The local explained that Bowser placed the locks there and hid the magic keys to them in the seven worlds that can be visited from the Warp Zone. Mario thought, no sweat, he would just go find the magic keys and unlock the locks. However, little did he know, Bowser had hidden the keys very well and guarded many areas to throw Mario off. And to make it worse, each of his kids had re-stolen the wands, which would be needed if Mario were to activate the magic needed for the keys to work. A very complex situation laid before Mario. He knew he had to do it. So packing a bag for collecting coins, Mario set off on his adventure...
# Messier Index/M95

Messier 95 (also known as M95 or NGC 3351) is a w:barred spiral galaxy about 33 million w:light-years away in the w:constellation Leo. It was discovered by w:Pierre Méchain in w:1781, and catalogued by w:Charles Messier four days later.

## Nucleus

The center of the galaxy contains a ring-shaped circumnuclear star-forming region with a diameter of approximately 2000 ly (600 pc).

## Galaxy group information

M95 is one of several galaxies within the w:M96 Group, a w:group of galaxies in the w:constellation Leo. The group also includes the w:Messier objects M96 and M105.

## External links

* SEDS: Spiral Galaxy M95
* Astronomy Picture of the Day: M95 on 3/14/07

## References

* 1 2 3 4 5 6 7 8 9 "NASA/IPAC Extragalactic Database". Results for NGC 3351. Retrieved 2007-10-03.
* ↑ Jensen, Joseph B.; Tonry, John L.; Barris, Brian J.; Thompson, Rodger I.; Liu, Michael C.; Rieke, Marcia J.; Ajhar, Edward A.; Blakeslee, John P. (2003). "Measuring Distances and Probing the Unresolved Stellar Populations of Galaxies Using Infrared Surface Brightness Fluctuations". Astrophysical Journal. 583 (2): 712–726. doi:10.1086/345430. {{cite journal}}: Unknown parameter |month= ignored (help)CS1 maint: multiple names: authors list (link)
* ↑ L. Colina, M. L. Garcia Vargas, J. M. Mas-Hesse, A. Alberdi, A. Krabbe (1997). "Nuclear Star-forming Structures and the Starburst–Active Galactic Nucleus Connection in Barred Spirals NGC 3351 and NGC 4303". The Astrophysical Journal Letters. 484: L41–L45. doi:10.1086/310766.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* ↑ R. B. Tully (1988). Nearby Galaxies Catalog. Cambridge: Cambridge University Press. ISBN 0-521-35299-1.
* ↑ P. Fouque, E. Gourgoulhon, P. Chamaraux, G. Paturel (1992). "Groups of galaxies within 80 Mpc. II - The catalogue of groups and group members". Astronomy and Astrophysics Supplement. 93: 211–233.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* ↑ A. Garcia (1993). "General study of group membership. II - Determination of nearby groups". Astronomy and Astrophysics Supplement. 100: 47–90.
* ↑ G. Giuricin, C. Marinoni, L. Ceriani, A. Pisani (2000). "Nearby Optical Galaxies: Selection of the Sample and Identification of Groups". Astrophysical Journal. 543: 178–194. doi:10.1086/317070.{{cite journal}}: CS1 maint: multiple names: authors list (link)
# Messier Index/M9

Messier 9 or M9 (also designated NGC 6333) is a w:globular cluster in the w:constellation of w:Ophiuchus. It was discovered by w:Charles Messier in w:1764.
M9 is one of the nearer globular clusters to the center of the w:Milky Way Galaxy with a distance of around 5,500 w:light-years. Its distance from w:Earth is 25,800 light-years.
The total w:luminosity of this cluster is around 120,000 times that of the w:Sun, the w:absolute magnitude being -8.04. The brightest individual w:stars in M9 are of w:apparent magnitude 13.5, making them visible in moderately sized w:telescopes. There have been 13 w:variable stars found in M9.
Nearby, at about 80' to the northeast of M9 is the dimmer globular cluster w:NGC 6356, while at about 80' to the southeast is the globular w:NGC 6342.

## External links

* Messier 9, SEDS Messier pages
* M9, Galactic Globular Clusters Database page

## References

* 1 2 3 4 "SIMBAD Astronomical Database". Results for NGC 6333. Retrieved 2006-11-15.
# Messier Index/M97

The Owl Nebula (also known as w:Messier Object 97 or NGC 3587) is a w:planetary nebula in the w:constellation w:Ursa Major. It was discovered by w:Pierre Méchain in 1781.
M97 is regarded as one of the more complex of the planetaries. The 16th magnitude central w:star has about 0.7 w:solar mass and the nebula itself about 0.15 solar mass. The nebula formed roughly 6,000 years ago.
The nebula gets it name due to the appearance of owl-like "eyes" when view through a large (>200 mm) telescope under dark sky conditions with the aid of a so-called "nebula filter." The "eyes" are also easily visible through photographs taken of the nebula.

## External links

* The Owl Nebula @ SEDS Messier pages
* NightSkyInfo.com - M97, the Owl Nebula
* M97, imaged with a semiprofessional amateur-telescope
# Messier Index/M91

Messier 91 (also known as NGC 4548) is a barred spiral galaxy about 63 million light-years away in the constellation Coma Berenices. It was most probably discovered by Charles Messier in 1781 and independently rediscovered by William Herschel on April 8, 1784. M91 is a member of the Virgo Cluster of galaxies.

## External links

* SEDS Messier: Spiral Galaxy M91

## References

* 1 2 3 4 5 6 7 8 9 "NASA/IPAC Extragalactic Database". Results for NGC 4548. Retrieved 2006-12-13.
* ↑ J. L. Tonry, A. Dressler, J. P. Blakeslee, E. A. Ajhar, A. B. Fletcher, G. A. Luppino, M. R. Metzger, C. B. Moore (2001). "The SBF Survey of Galaxy Distances. IV. SBF Magnitudes, Colors, and Distances". Astrophysical Journal. 546 (2): 681–693. doi:10.1086/318301.{{cite journal}}: CS1 maint: multiple names: authors list (link)
# Messier Index/M92

Messier 92 (also known as M92 or NGC 6341) is a w:globular cluster in the constellation Hercules. It was discovered by w:Johann Elert Bode in w:1777 and independently rediscovered by w:Charles Messier on w:March 18, w:1781. M92 is at a distance of about 26,000 w:light-years away from w:Earth.
M92 is one of the brighter globular clusters in the northern hemisphere, but it is often overlooked by amateur astronomers because of its proximity to the even more spectacular w:Messier 13.

## External links

* Messier 92 @ SEDS Messier pages
* Messier 92, Galactic Globular Clusters Database page

## References

* 1 2 3 4 "SIMBAD Astronomical Database". Results for NGC 6341. Retrieved 2006-11-17.
# Messier Index/M93

Messier 93 (also known as M 93 or NGC 2447) is an w:open cluster in the w:constellation w:Puppis. It was discovered by w:Charles Messier in w:1781.
M93 is at a distance of about 3,600 w:light years from w:Earth and has a spatial radius of some 10 to 12 light years. Its age is estimated at some 100 million w:years.

## External links

* Open Cluster M93 @ SEDS Messier pages
# Messier Index/M96

Messier 96 (also known as NGC 3368) is an w:intermediate spiral galaxy about 31 million w:light-years away in the w:constellation Leo. It was discovered by w:Pierre Méchain in w:1781.

## M96 Group

M96 is the brightest galaxy within the w:M96 Group, a w:group of galaxies in the w:constellation Leo also includes the w:Messier objects M95 and M105, as well as at least nine other galaxies.

## External links

* NOAO: M96
* SEDS: Spiral Galaxy M96

## References

* 1 2 3 4 5 6 7 8 9 "NASA/IPAC Extragalactic Database". Results for NGC 3368. Retrieved 2006-10-24.
* ↑ Jensen, Joseph B.; Tonry, John L.; Barris, Brian J.; Thompson, Rodger I.; Liu, Michael C.; Rieke, Marcia J.; Ajhar, Edward A.; Blakeslee, John P. (2003). "Measuring Distances and Probing the Unresolved Stellar Populations of Galaxies Using Infrared Surface Brightness Fluctuations". Astrophysical Journal. 583 (2): 712–726. doi:10.1086/345430. {{cite journal}}: Unknown parameter |month= ignored (help)CS1 maint: multiple names: authors list (link)
* ↑ R. B. Tully (1988). Nearby Galaxies Catalog. Cambridge: Cambridge University Press. ISBN 0-521-35299-1.
* ↑ P. Fouque, E. Gourgoulhon, P. Chamaraux, G. Paturel (1992). "Groups of galaxies within 80 Mpc. II - The catalogue of groups and group members". Astronomy and Astrophysics Supplement. 93: 211–233.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* ↑ A. Garcia (1993). "General study of group membership. II - Determination of nearby groups". Astronomy and Astrophysics Supplement. 100: 47–90.
* ↑ G. Giuricin, C. Marinoni, L. Ceriani, A. Pisani (2000). "Nearby Optical Galaxies: Selection of the Sample and Identification of Groups". Astrophysical Journal. 543: 178–194. doi:10.1086/317070.{{cite journal}}: CS1 maint: multiple names: authors list (link)
# Messier Index/M98

Messier 98 (also known as M98 or NGC 4192) is an intermediate w:spiral galaxy about 60 million w:light-years away in the w:constellation w:Coma Berenices. It was discovered by w:Pierre Méchain in w:1781.

## Virgo Cluster membership

Messier 98 is a member of the w:Virgo Cluster, which is a large, relatively nearby w:cluster of galaxies.

## External links

* Spiral Galaxy M98 @ SEDS Messier pages

## References

* 1 2 3 4 5 6 7 "NASA/IPAC Extragalactic Database". Results for Messier 98. Retrieved 2006-11-18.
* ↑ B. Binggeli, A. Sandage, G. A. Tammann (1985). "Studies of the Virgo Cluster. II - A catalog of 2096 galaxies in the Virgo Cluster area". Astronomical Journal. 90: 1681–1759. doi:10.1086/113874.{{cite journal}}: CS1 maint: multiple names: authors list (link)
# Muggles' Guide to Harry Potter/Characters/Poliakoff
## Overview

Poliakoff is one of the Durmstrang students who hopes to become a Champion in the Triwizard Tournament, occurring in Harry's fourth year.

## Role in the Books
### Goblet of Fire

As the Durmstrang contingent return to their ship in the Lake after their first dinner at Hogwarts, headmaster Karkaroff inquires solicitously if Krum has gotten enough to eat, or wants some mulled wine. Poliakoff suggests he would like some wine, and Karkaroff snaps at him, saying he did not offer any to him, and accuses him of having "dribbled food all down the front of his robes".

## Strengths

Poliakoff has been chosen to be part of the Durmstrang contingent and a potential Triwizard champion (although realistically he never has much of a chance); presumably, therefore, he is strong enough to take part, were he chosen.
He is also a little bit of an opportunist, asking for some wine.

## Weaknesses

Karkaroff's accusation about Poliakoff dribbling food may suggest something about him - such as clumsiness - but we must take into account Karkaroff's priorities here, and not read too much into it.

## Relationships with Other Characters

Karkaroff appears to dislike him, but then Karkaroff doesn't much like anyone.

## Analysis

Poliakoff is such a minor character that one wonders why he was introduced at all. His function seems to be more one of showing Karkaroff's character. Karkaroff has decided that Viktor Krum is to be the Durmstrang Champion in the Triwizard Tournament; while the remaining students are present to provide a semblance of choice, Karkaroff does not expect anything of them and so treats them as useless. It is quite possible that this is also intended to show the basic difference between Durmstrang and Hogwarts as school environments.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
* Why do you think Poliakoff brazenly asks for some mulled wine, when it was only offered to Krum?
* Do you think he, along with the other Durmstrang students, were merely brought along for show, as the choice for champion had seemingly been made already?
# Muggles' Guide to Harry Potter/Characters/Piers Polkiss
## Overview

Piers Polkiss is a friend of Dudley Dursley.

## Role in the Books
### Philosopher's Stone

Piers accompanies the Dursleys on a trip to the zoo. He and Dudley are frightened when Harry unintentionally releases a large snake; it is Piers who later announces to the Dursleys that he thought he had seen Harry talking to the snake.

### Order of the Phoenix

Piers compliments Dudley on the way he had hit someone earlier, as Dudley says good night to his gang after an evening of mayhem. Dudley had told the Dursleys that he was having tea with Piers and the Polkiss family.

## Relationships with Other Characters

Piers is Dudley's best friend, and a member of his gang.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
# Muggles' Guide to Harry Potter/Characters/Professor Sinistra
## Overview

Professor Sinistra is the Astronomy professor at Hogwarts School of Witchcraft and Wizardry.

## Role in the Books
### Goblet of Fire

It is mentioned that Professor Sinistra is dancing with Professor Moody at the Yule Ball.

## Analysis

Astronomy in the Harry Potter world is very different from real astronomy. There are no physics present in the Harry Potter astronomy. Rather, the lesson focuses on nomenclature and its position in relationship to the other planets. The various stars outside of our Solar System, other galaxies, black holes, and other celestial objects play little importance. In short, Harry Potter's astronomy is descriptive.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
* How might Astronomy be important in learning about magic? Why is it considered separate from Divination?
* Think about what kind of personality Professor Sinistra might have, and describe it.
# Muggles' Guide to Harry Potter/Characters/Professor Tofty
## Overview

Professor Tofty is a member of the Wizarding Examinations Authority, the board of independent examiners who examine fifth year Hogwarts students taking their OWLs (Ordinary Wizarding Levels). He is described as the very oldest and baldest examiner in the group.

## Role in the Books
### Order of the Phoenix

Tofty arrives at Hogwarts as part of the group of examiners to test the fifth years (including Harry) on their OWL exams. It is mentioned that he looks older even than Griselda Marchbanks, who claims to have examined Professor Dumbledore's Transfiguration NEWT exam.
Professor Tofty examines Harry in the Charms and Defence Against the Dark Arts practical examinations. He supervises their Astronomy practical exam, during which the students see Hagrid sacked. He also supervises the History of Magic exam, and leads Harry out of the Great Hall when he has a nightmare during this exam.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
# Logic for Computer Scientists/Predicate Logic/Strategies for Resolution

5.8.1 Linear Resolution 5.8.2 Input and Unit Resolution 5.8.3 SLD-Resolution 5.8.4 A Prolog-like Implementation 5.8.5 Iterative Deepening
# Logic for Computer Scientists/Predicate Logic/Strategies for Resolution/Linear Resolution
## Linear Resolution

In contrast to the saturation-based procedure, which we gave for propositional resolution, we will discuss now a strategy which allows goal directed generation of resolvents. We will see later, namely in the case of Horn clauses, that this linear strategy, is the basis for the interpretation of logic programs.
Given a set of clauses $S$ and a clause $C_{0}$ in $S$. A linear deduction of top clause $C_{0}$ is a sequence $C_{0},C_{1},\cdots ,C_{n}$ , where $\forall 1\leq i\leq n$ $C_{i}$ is a resolvent of $C_{i-1}$ and $B$ with $B\in S\cup \{C_{j}\mid j<i\}$ . If $C_{n}=\square$ the sequence is called a linear refutation.

## Definition 25

The following is an example for a linear deduction. The clause set $S$ is given by:
${\begin{matrix}symptom(s)&(1)\\cause(c_{1})\lor cause(c_{2})\lor \lnot symptom(s)&(2)\\treatment(t_{0})\lor \lnot cause(c_{1})&(3)\\treatment(t_{1})\lor \lnot cause(c_{1})&(4)\\treatment(t_{0})\lor \lnot cause(c_{2})&(5)\\treatment(t_{2})\lor \lnot cause(c_{2})&(6)\\\end{matrix}}$
and together with the goal $\lnot treatment(x)$, we get the following refutation, where clauses from $S$ are given by the respective numbers: $\lnot treatment(X)$, (4),$\lnot cause(c_{1})$, (2), $cause(c_{2})\lor \lnot symptom(s)$, (1), $cause(c_{2})$, (6), $treatment(t_{2})$,$\square$
the same refutation can be given more naturally be the following picture: The following theorem states correctness and completeness of linear resolution. Note that completeness only states that there exists a linear refutation, there is no guaranty that every clause in the sequence really is necessary to derive the empty clause.

## Theorem 9

Linear resolution is complete and correct. Example:
# Logic for Computer Scientists/Preface

This is all about Computer science and technology of computers

## Preface

This logic course is intended for computer scientists and it assumes practically no previous knowledge except some basic mathematical notions like relations and orderings. The material presented here can, of course, be printed and used as an ordinary textbook. However, it should be pointed out; that this is not the intention of the author; the aim was to create an electronic, interactive script where logics can be experienced by interaction and experimentation. The reader who is interested in more traditional forms of a textbook is referred to the following sources:
* Uwe Schöning: Logik für Informatiker. BI-Wissenschaftsverlag, Mannheim, 1987. The chapter on propositional logics is based on the treatment in this book. Some definitions and proofs are given in the same way Schöning does.
* Chin-Liang Chang; Richard Char-Tung Lee: Symbolic Logic and Mechanical Theorem Proving. Academic Press, London, 1973. The chapter on predicate logics is based on this standard textbook on mechanical theorem proving.
* Melvin Fitting: First-Order Logic and Automated Theorem Proving. Springer-Verlag, Berlin, Heidelberg, New York, 1990. This is a modern computer science oriented treatment of analytic tableaux, which inspired the sections on tableaux of this course.
Further bibliographic information will be given at the end of each section. Up to Logic for Computer Scientists
# Logic for Computer Scientists/Predicate Logic/Strategies for Resolution/Input and Unit Resolution
## Definition 26

Given a set of clauses $S$. The inference rule input resolution is resolution, such that one parent clause is a clause from $S$. The inference rule unit resolution is resolution, such that at least one parent clause is a unit clause or a unit factor of a parent clause.
In an obvious way the notions of unit (input) derivations and refutations are defined.

## Theorem 10

For a set $S$ of clauses there exists a unit refutation iff there exists an input refutation. Unit resolution (and hence input resolution) is not complete for full first order logics!
For Horn clauses, however, it is a complete strategy and indeed, it is the basis for the SLD-resolution principle, which is the core of SLD-Resolution
# Logic for Computer Scientists/Predicate Logic/Strategies for Resolution/Iterative Deepending
## Iterative Deepening

Iterative deepening is a complete search strategy, which combines depth-first with breadth-first search.
* $depthbound=1$
* do while (not found) Search by limited depth-first search until $depthbound$. Set $depthbound=depthbound+1$
Number of expansions in a tree with branching factor $b$ until depth $d$ is
$1+b+b^{2}+\cdots +b^{d-1}+b^{d}$
The total number of expansions in iterative deepening search is
$(d+1)*1+d*b+(d-1)*b^{2}+\cdots +3*b^{d-2}+2*b^{d-1}+1*b^{d}$
Hence time complexity of iterative deepening is still $O(b^{d})$.
As exemplified by PTTP ("Prolog Technology Theorem Prover") Prolog can be viewed as an "almost complete" theorem prover, which has to be extended by only a few ingredients in order to handle the non-Horn case. By this technique the benefits of optimizing Prolog compilers are accessible to theorem proving. First we will briefly review the standard approach, and then we will describe the necessary modifications to obtain restart model elimination. The PTTP-approach transforms a given clause set into a Prolog program. The transformed Prolog program must execute the clauses according to some complete proof procedure. Model elimination turns out to be particularly useful for this, since it is, like Prolog, an input proof procedure. In particular, the transformation from the input clauses to Prolog works as follows:
* An input clause such as $C\gets A\land B$ is transformed into a Prolog clause (1) c :- a, b. Additionally, since in the model elimination calculus every literal in a clause can equally well serve as an entry point into the clause, all contrapositives are needed. In this case these are
This example also shows how negation is treated, namely by making it part of the predicate name.
* Prolog's unsound unification has to be replaced by a sound unification algorithm. This can either be done by directly building-in sound unification into the Prolog implementation, or by reprogramming sound unification in Prolog and calling this code instead of Prolog's unsound unification.
* A complete search strategy is needed. Usually depth bounded iterative deepening is used. The strategy can be compiled into the Prolog program by additional parameters, being used as "current depth" and "limit depth". The cost of an extension step can be uniformly 1 (depth bounded search), or can be proportional to the length of the input clause (inference bounded search).
* The model elimination reduction operation has to be implemented. This can be realized by memorizing the subgoals solved so far (the A-literals) as a list in an additional argument, and by Prolog code that checks a goal for a complementary member of that list. Of course, this check has to be carried out with sound unification. The Prolog clause (1) from above then looks like (1') c(Anc) :- a([-a|Anc]), b([-b|Anc]). where Anc is a Prolog list which contains the ancestor literals (called A-literals in); code for reduction steps then looks like