| {"id": "story_380", "NL_sentence": "People in this club who perform in school talent shows often attend and are very engaged with school events. People in this club either perform in school talent shows often or are inactive and disinterested community members. People in this club who chaperone high school dances are not students who attend the school. All people in this club who are inactive and disinterested members of their community chaperone high school dances. All young children and teenagers in this club who wish to further their academic careers and educational opportunities are students who attend the school. Bonnie is in this club and she either both attends and is very engaged with school events and is a student who attends the school or is not someone who both attends and is very engaged with school events and is not a student who attends the school.", "FOL_sentence": "∀x (InThisClub(x) ∧ PerformOftenIn(x, schoolTalentShow) → Attend(x, schoolEvent) ∧ VeryEngagedWith(x, schoolEvent)) ∧ ∀x (InThisClub(x) → PerformOftenIn(x, schoolTalentShow) ⊕ (InActive(x) ∧ Disinterested(x) ∧ MemberOf(x, community))) ∧ ∀x (InThisClub(x) ∧ Chaperone(x, highSchoolDance) → ¬(Student(x) ∧ AttendSchool(x))) ∧ ∀x (InThisClub(x) ∧ (InActive(x) ∧ Disinterested(x) ∧ MemberOf(x, community)) → Chaperone(x, highSchoolDance)) ∧ ∀x (InThisClub(x) ∧ (YoungChild(x) ∨ Teenager(x)) ∧ WishToFurther(x, academicCareer) ∧ WishToFurther(x, educationalOpportunity) → (Student(x) ∧ AttendSchool(x))) ∧ InThisClub(bonnie) ∧ ((Attend(bonnie, schoolEvent) ∧ VeryEngagedWith(bonnie, schoolEvent) ∧ Student(bonnie) ∧ AttendSchool(bonnie)) ⊕ (¬(Attend(bonnie, schoolEvent) ∧ VeryEngagedWith(bonnie, schoolEvent)) ∧ ¬(Student(bonnie) ∧ AttendSchool(bonnie)))", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "either_or", "correction_explanation": "1. Spelling: Corrected 'Studen' to 'Student' and 'bonne' to 'bonnie'. 2. Linkage: 'highSchoolDances' changed to 'highSchoolDance' in Premise 4. 3. Missing Parenthesis & Operators: Fixed the missing opening parenthesis for the implication in Premise 5. Changed 'YoungChildren' to 'YoungChild' and XOR '⊕' to inclusive OR '∨' in Premise 5 to match 'young children and teenagers'. Added missing 'educationalOpportunity' to WishToFurther to fully capture the NL. 4. Premise 6: Removed hallucinated outer parentheses added by the previous reviewer and properly bounded the variables to 'bonnie'.", "FOL_sentence_old": "∀x (InThisClub(x) ∧ PerformOftenIn(x, schoolTalentShow) → Attend(x, schoolEvent) ∧ VeryEngagedWith(x, schoolEvent))\n∀x (InThisClub(x) → PerformOftenIn(x, schoolTalentShow) ⊕ (InActive(x) ∧ Disinterested(x) ∧ MemberOf(x, community)))\n∀x (InThisClub(x) ∧ Chaperone(x, highSchoolDance) → ¬(Studen(x) ∧ AttendSchool(x)))\n∀x (InThisClub(x) ∧ (InActive(x) ∧ Disinterested(x) ∧ MemberOf(x, community)) → Chaperone(x, highSchoolDances))\n∀x (InThisClub(x) ∧ (YoungChildren(x) ⊕ Teenager(x)) ∧ WishToFurther(x, academicCareer)) → Studen(x) ∧ AttendSchool(x))\nInThisClub(bonnie) ∧ ¬((Attend(x, schoolEvent) ∧ VeryEngagedWith(bonnie, schoolEvent)) ⊕ (Studen(bonne) ∧ AttendSchool(bonnie)))"} | |
| {"id": "concl_380_1", "NL_sentence": "Bonnie performs in school talent shows often.", "FOL_sentence": "PerformOftenIn(bonnie, schoolTalentShow)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "1. Predicate Match: Corrected 'Perform' to 'PerformOftenIn' to match the premises. 2. Removed Extraneous Conjunction: The original included 'InThisClub(bonnie)' which is not stated in the conclusion NL. The conclusion only asserts the performance.", "FOL_sentence_old": "InThisClub(bonnie) ∧ (Perform(bonnie, schoolTalentShow))", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_380_2", "NL_sentence": "If Bonnie is either both a young child or teenager who wishes to further her academic career and educational opportunities and chaperones high school dances or neither is a young child nor teenager who wishes to further her academic career and educational opportunities, then Bonnie is either a student who attends the school or is an inactive and disinterested member of the community.", "FOL_sentence": "(((YoungChild(bonnie) ∨ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer) ∧ WishToFurther(bonnie, educationalOpportunity) ∧ Chaperone(bonnie, highSchoolDance)) ⊕ (¬(YoungChild(bonnie) ∨ Teenager(bonnie)) ∧ ¬WishToFurther(bonnie, academicCareer) ∧ ¬WishToFurther(bonnie, educationalOpportunity))) → ((Student(bonnie) ∧ AttendSchool(bonnie)) ⊕ (InActive(bonnie) ∧ Disinterested(bonnie) ∧ MemberOf(bonnie, community)))", "label": "True", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "either_or", "correction_explanation": "1. Syntax & Unbalanced Parentheses: Completely rebuilt the formula to fix severe syntax errors and unmatched parentheses. 2. Variable Scope: Replaced the unbound 'x' with 'bonnie' in 'Student'. 3. Predicate Consistency: Corrected 'Studen' to 'Student' and 'YoungChildren' to 'YoungChild'. 4. Consequent Match: Rewrote the consequent to accurately reflect 'either a student... or an inactive... member' instead of the hallucinated repetition of the antecedent found in the old FOL. Added 'educationalOpportunity' to fully map the NL.", "FOL_sentence_old": "¬((YoungChildren(bonnie) ⊕ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer)) ⊕ Chaperone(bonnie, highSchoolDance)) → (Studen(x) ∧ AttendSchool(x)) ⊕ (YoungChildren(bonnie) ⊕ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer))", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "concl_380_3", "NL_sentence": "If Bonnie either chaperones high school dances or, if she does not, she performs in school talent shows often, then Bonnie is both a young child or teenager who wishes to further her academic career and educational opportunities and an inactive and disinterested member of the community.", "FOL_sentence": "(Chaperone(bonnie, highSchoolDance) ⊕ PerformOftenIn(bonnie, schoolTalentShow)) → ((YoungChild(bonnie) ∨ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer) ∧ WishToFurther(bonnie, educationalOpportunity) ∧ InActive(bonnie) ∧ Disinterested(bonnie) ∧ MemberOf(bonnie, community))", "label": "False", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "either_or", "correction_explanation": "Predicate Match: Corrected 'Perform' to 'PerformOftenIn' to properly link with the premises. Missing Entities: Added 'WishToFurther(bonnie, educationalOpportunity)' to strictly align with the NL.", "FOL_sentence_old": "(Chaperone(bonnie, highSchoolDance) ⊕ Perform(bonnie, schoolTalentShow)) → (YoungChildren(bonnie) ⊕ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer)) ∧ (InActive(bonnie) ∧ Disinterested(bonnie) ∧ MemberOf(bonnie, community))", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "False"} | |
| {"id": "story_426", "NL_sentence": "All employees who schedule a meeting with their customers will go to the company building today. Everyone who has lunch in the company building schedules meetings with their customers. Employees have lunch either in the company building or at home. If an employee has lunch at home, they are working remotely from home. All employees who are in other countries work remotely from home. No managers work remotely from home. James will appear in the company today if and only if he is a manager.", "FOL_sentence": "∀x ((Employee(x) ∧ Schedule(x, meeting, customers)) → AppearIn(x, company)) ∧ ∀x (HasLunch(x, company) → Schedule(x, meeting, customers)) ∧ ∀x (Employee(x) → (HasLunch(x, company) ⊕ HasLunch(x, home))) ∧ ∀x ((Employee(x) ∧ HasLunch(x, home)) → Work(x, home)) ∧ ∀x ((Employee(x) ∧ (¬In(x, homeCountry))) → Work(x, home)) ∧ ∀x (Manager(x) → ¬Work(x, home)) ∧ ¬(Manager(james) ⊕ AppearIn(james, company))", "corrected": "yes", "ambiguity": true, "correction_explanation": "1. 'Everyone who has lunch in the company' is relativized to 'everyone that is an employee', but this restriction is not present in NL", "ambiguity_explanation": "either_or", "FOL_sentence_old": "∀x ((Employee(x) ∧ Schedule(x, meeting, customers)) → AppearIn(x, company))\n∀x ((Employee(x) ∧ HasLunch(x, company)) → Schedule(x, meeting, customers))\n∀x (Employee(x) → (HasLunch(x, company) ⊕ HasLunch(x, home)))\n∀x ((Employee(x) ∧ HasLunch(x, home)) → Work(x, home))\n∀x ((Employee(x) ∧ (¬In(x, homeCountry))) → Work(x, home))\n∀x (Manager(x) → ¬Work(x, home))\n¬(Manager(james) ⊕ AppearIn(james, company))"} | |
| {"id": "concl_426_4", "NL_sentence": "James has lunch in the company.", "FOL_sentence": "HasLunch(james, company)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "HasLunch(james, company)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_426_5", "NL_sentence": "James does not have lunch in the company.", "FOL_sentence": "¬HasLunch(james, company)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "¬HasLunch(james, company)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_426_6", "NL_sentence": "If James is either a manager or in other countries, then James does not either have lunch at home or work remotely from home. If James either has lunch at home or works remotely from home, then he is neither a manager nor does he work in other countries.", "FOL_sentence": "((Manager(james) ∨ ¬In(james, homeCountry)) → ¬(HasLunch(james, home) ∨ Work(james, home))) ∧ ((HasLunch(james, home) ∨ Work(james, home)) → ¬(Manager(james) ∨ ¬In(james, homeCountry)))", "label": "Uncertain", "ambiguity": true, "ambiguity_explanation": "either_or", "corrected": "yes", "correction_explanation": "Translation Failure: The original FOL 'Manager(james) → ¬Work(james, home)' completely ignored the vast majority of the NL sentence. The NL contains two complex conditionals that act as contrapositives involving 'in other countries' and 'lunch at home'. The FOL has been rewritten to exhaustively translate the English sentence exactly as written. Because the premises do not establish whether James is an employee or his current location, we cannot logically evaluate this complex implication. The label is therefore corrected from True to Uncertain. (2) There is a problem also with other countries that is not really the opposite of homeCountry.", "FOL_sentence_old": "Manager(james) → ¬Work(james, home)", "label_old": "True", "label_old_z3": "True", "label_z3": "Uncertain"} | |
| {"id": "story_198", "NL_sentence": "When the Monkeypox virus occurs in a being, it may get Monkeypox. Monkeypox virus can occur in certain animals. Humans are mammals. Mammals are animals. Symptoms of Monkeypox include fever, headache, muscle pains, and tiredness. People feel tired when they get the flu.", "FOL_sentence": "∃x (OccurIn(monkeypoxVirus, x) ∧ Get(x, monkeypoxVirus)) ∧ ∃x (Animal(x) ∧ OccurIn(monkeypoxVirus, x)) ∧ ∀x (Human(x) → Mammal(x)) ∧ ∀x (Mammal(x) → Animal(x)) ∧ ∀x ((Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tiredness(x)) → SymptomOf(x, monkeypoxVirus)) ∧ ∀x (Human(x) ∧ Get(x, flu) → Feel(x, tired))", "corrected": "yes", "correction_explanation": "1. Translation Failure (Premise 5): The original FOL weakly asserted via an existential quantifier ('∃x') that there is at least one symptom that is one of those conditions. The NL 'Symptoms ... include ...' requires a universal implication to denote that all instances of these conditions are symptoms. Corrected to '∀x ((Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tired(x)) → SymptomOf(x, monkeypoxVirus))'. 2. Typo (Premise 5): Corrected 'SymptonOf' to 'SymptomOf'.", "FOL_sentence_old": "∃x (OccurIn(monkeypoxVirus, x) ∧ Get(x, monkeypoxVirus))\n∃x (Animal(x) ∧ OccurIn(monkeypoxVirus, x))\n∀x (Human(x) → Mammal(x))\n∀x (Mammal(x) → Animal(x))\n∃x (SymptonOf(x, monkeypoxVirus) ∧ (Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tired(x)))\n∀x (Human(x) ∧ Get(x, flu) → Feel(x, tired))"} | |
| {"id": "concl_198_7", "NL_sentence": "There is an animal.", "FOL_sentence": "∃x (Animal(x))", "label": "True", "corrected": "no", "FOL_sentence_old": "∃x (Animal(x))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_198_8", "NL_sentence": "No one gets the flu.", "FOL_sentence": "∀x (Human(x) → ¬Get(x, flu))", "label": "Uncertain", "corrected": "no", "correction_explanation": "There is no referement to humans (in the story it is talked about animals also), but usually 'no one' refer to human beings, so the original formalization can be considered acceptable", "FOL_sentence_old": "∀x (Human(x) → ¬Get(x, flu))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_198_9", "NL_sentence": "Symptoms of Monkeypox include coughing.", "FOL_sentence": "∃x (SymptomOf(x, monkeypoxVirus) ∧ Coughing(x))", "label": "Uncertain", "corrected": "yes", "correction_explanation": "1. Typo: Corrected 'SymptonOf' to 'SymptomOf'.", "FOL_sentence_old": "∃x (SymptonOf(x, monkeypoxVirus) ∧ Coughing(x))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_0", "NL_sentence": "There are six types of wild turkeys: Eastern wild turkey, Osceola wild turkey, Gould's wild turkey, Merriam's wild turkey, Rio Grande wild turkey, and Ocellated wild turkey. Tom is not an Eastern wild turkey. Tom is not an Osceola wild turkey. Tom is not a Gould's wild turkey. Tom is neither a Merriam's wild turkey nor a Rio Grande wild turkey. Tom is a wild turkey.", "FOL_sentence": "∀x (WildTurkey(x) ↔ (EasternWildTurkey(x) ∨ OsceolaWildTurkey(x) ∨ GouldsWildTurkey(x) ∨ MerriamsWildTurkey(x) ∨ RiograndeWildTurkey(x) ∨ OcellatedWildTurkey(x))) ∧ ¬(EasternWildTurkey(tom)) ∧ ¬(OsceolaWildTurkey(tom)) ∧ ¬(GouldsWildTurkey(tom)) ∧ ¬(MerriamsWildTurkey(tom) ∨ RiograndeWildTurkey(tom)) ∧ WildTurkey(tom)", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "option_partition", "correction_explanation": "Now inserted a bi-implication instead of a simple implication, since if x is an eastern wild turkey, then it is also a wild turkey.", "FOL_sentence_old": "∀x (WildTurkey(x) → (EasternWildTurkey(x) ∨ OsceolaWildTurkey(x) ∨ GouldsWildTurkey(x) ∨ MerriamsWildTurkey(x) ∨ RiograndeWildTurkey(x) ∨ OcellatedWildTurkey(x)))\n¬(EasternWildTurkey(tom))\n¬(OsceolaWildTurkey(tom))\n¬(GouldsWildTurkey(tom))\n¬(MerriamsWildTurkey(tom) ∨ RiograndeWildTurkey(tom))\nWildTurkey(tom)"} | |
| {"id": "concl_0_10", "NL_sentence": "Tom is an Ocellated wild turkey.", "FOL_sentence": "OcellatedWildTurkey(tom)", "label": "True", "corrected": "no", "FOL_sentence_old": "OcellatedWildTurkey(tom)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_0_11", "NL_sentence": "Tom is an Eastern wild turkey.", "FOL_sentence": "EasternWildTurkey(tom)", "label": "False", "corrected": "no", "FOL_sentence_old": "EasternWildTurkey(tom)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_0_12", "NL_sentence": "Joey is a wild turkey.", "FOL_sentence": "WildTurkey(joey)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "WildTurkey(joey)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_20", "NL_sentence": "A Japanese game company created the game the Legend of Zelda. All games on the Top 10 list are made by Japanese game companies. If a game sells more than one million copies, then it will be included in the Top 10 list. The Legend of Zelda sold more than one million copies.", "FOL_sentence": "Game(theLegendofZelda) ∧ ∃x (Japanese(x) ∧ VideoGameCompany(x) ∧ Created(x, theLegendofZelda)) ∧ ∀x ∀y ((Game(x) ∧ InTop10(x) ∧ Created(y,x)) → (Japanese(y) ∧ VideoGameCompany(y))) ∧ ∀x ((Game(x) ∧ ∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(x, y))) → InTop10(x)) ∧ ∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(theLegendofZelda,y))", "corrected": "yes", "correction_explanation": "1. Translation Failure (Premise 2): The NL says 'Japanese game companies', but the old FOL only asserted 'Japanese(y)'. Corrected the consequent to '(Japanese(y) ∧ VideoGameCompany(y))'. 2. Syntax Error (Premise 3): Removed an unmatched closing parenthesis. 3. Broken Predicate Link (Premise 2 & 3): Standardized 'Top10' to 'InTop10' to resolve the logical chain. 4. Silent Edits Reverted: Removed hallucinated outer parentheses around Premise 1 and restored original spacing in Premises 2, 3, and 4.", "FOL_sentence_old": "Game(theLegendofZelda) ∧ ∃x (Japanese(x) ∧ VideoGameCompany(x) ∧ Created(x, theLegendofZelda))\n∀x ∀y ((Game(x) ∧ InTop10(x) ∧ Created(y,x)) → Japanese(y))\n∀x ((Game(x) ∧ ∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(x, y))) → Top10(x)))\n∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(theLegendofZelda,y))"} | |
| {"id": "concl_20_13", "NL_sentence": "The Legend of Zelda is on the Top 10 list.", "FOL_sentence": "InTop10(theLegendofZelda)", "label": "True", "corrected": "yes", "correction_explanation": "Standardized the predicate 'Top10' to 'InTop10' to correctly link with the adjusted premises.", "FOL_sentence_old": "Top10(theLegendofZelda)", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "concl_20_14", "NL_sentence": "FIFA 22 is made by a Japanese video game company.", "FOL_sentence": "∃x(Created(x, fifa22) ∧ Japanese(x) ∧ VideoGameCompany(x))", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "∃x(Created(x, fifa22) ∧ Japanese(x) ∧ VideoGameCompany(x))", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_20_15", "NL_sentence": "The Legend of Zelda is not on the Top 10 list.", "FOL_sentence": "¬InTop10(theLegendofZelda)", "label": "False", "corrected": "yes", "correction_explanation": "Standardized the predicate 'Top10' to 'InTop10' to correctly link with the adjusted premises.", "FOL_sentence_old": "¬Top10(theLegendofZelda)", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "False"} | |
| {"id": "story_282", "NL_sentence": "All squares are four-sided. All four-sided things are shapes.", "FOL_sentence": "∀x (Square(x) → FourSided(x)) ∧ ∀x (FourSided(x) → Shape(x))", "corrected": "no", "FOL_sentence_old": "∀x (Square(x) → FourSided(x))\n∀x (FourSided(x) → Shape(x))"} | |
| {"id": "concl_282_16", "NL_sentence": "All squares are shapes.", "FOL_sentence": "∀x (Square(x) → Shape(x))", "label": "True", "corrected": "no", "FOL_sentence_old": "∀x (Square(x) → Shape(x))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "story_471", "NL_sentence": "All rabbits that can be spotted near the campus are cute. Some turtles can be spotted near the campus. The only animals that can be spotted near the campus are rabbits and squirrels. If something is skittish, then it is not calm. All the squirrels that can be spotted near the campus are skittish. Rockie can be spotted near the campus, and it is calm.", "FOL_sentence": "∀x (Rabbit(x) ∧ CanBeSpottedNear(x, campus) → Cute(x)) ∧ ∃x (Turtle(x) ∧ CanBeSpottedNear(x, campus)) ∧ ∀x (CanBeSpottedNear(x, campus) → (Rabbit(x) ∨ Squirrel(x))) ∧ ∀x (Skittish(x) → ¬Calm(x)) ∧ ∀x (Squirrel(x) ∧ CanBeSpottedNear(x, campus) → Skittish(x)) ∧ CanBeSpottedNear(rockie, campus) ∧ Calm(rockie)", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "some_plural", "correction_explanation": "1. Translation Failure (Premise 3): Corrected the exclusive OR '⊕' to an inclusive OR '∨'. The NL states 'are rabbits and squirrels', which translates logically to the union of those two sets, not strictly an XOR relationship. 2. Silent Edits Reverted (Premises 1, 5, 6): Removed hallucinated inner and outer parentheses that were added by the previous reviewer without documentation.", "FOL_sentence_old": "∀x (Rabbit(x) ∧ CanBeSpottedNear(x, campus) → Cute(x))\n∃x (Turtle(x) ∧ CanBeSpottedNear(x, campus))\n∀x (CanBeSpottedNear(x, campus) → (Rabbit(x) ⊕ Squirrel(x)))\n∀x (Skittish(x) → ¬Calm(x))\n∀x (Squirrel(x) ∧ CanBeSpottedNear(x, campus) → Skittish(x))\nCanBeSpottedNear(rockie, campus) ∧ Calm(rockie) "} | |
| {"id": "concl_471_17", "NL_sentence": "Rockie is a turtle.", "FOL_sentence": "Turtle(rockie)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Turtle(rockie)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_471_18", "NL_sentence": "Rockie is not a turtle.", "FOL_sentence": "¬Turtle(rockie)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "¬Turtle(rockie)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_471_19", "NL_sentence": "Rockie is a turtle or cute.", "FOL_sentence": "Turtle(rockie) ∨ Cute(rockie)", "label": "True", "corrected": "no", "FOL_sentence_old": "Turtle(rockie) ∨ Cute(rockie)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_471_20", "NL_sentence": "If Rockie is not both a turtle and a squirrel, then Rockie is either cute or skittish.", "FOL_sentence": "¬(Turtle(rockie) ∧ Squirrel(rockie)) → (Cute(rockie) ⊕ Skittish(rockie))", "label": "True", "ambiguity": true, "ambiguity_explanation": "either_or", "corrected": "yes", "correction_explanation": "Added parentheses because of operator precedences", "FOL_sentence_old": "¬(Turtle(rockie) ∧ Squirrel(rockie)) → Cute(rockie) ⊕ Skittish(rockie)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_471_21", "NL_sentence": "If Rockie is cute and calm, then Rockie is a skittish turtle.", "FOL_sentence": "(Cute(rockie) ∧ Calm(rockie)) → (Turtle(rockie) ∧ Skittish(rockie))", "label": "False", "corrected": "no", "correction_explanation": "Added parentheses (even if not necessary): it is not considered a correction.", "FOL_sentence_old": "Cute(rockie) ∧ Calm(rockie) → Turtle(rockie) ∧ Skittish(rockie)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_184", "NL_sentence": "\"Stranger Things\" is a popular Netflix show. If a Netflix show is popular, Karen will binge-watch it. If and only if Karen binge-watches a Netflix show, she will download it. Karen does not download \"Black Mirror\". \"Black Mirror\" is a Netflix show. If Karen binge-watches a Netflix show, she will share it with Lisa.", "FOL_sentence": "NetflixShow(strangerThings) ∧ Popular(strangerThings) ∧ ∀x ((NetflixShow(x) ∧ Popular(x)) → BingeWatch(karen, x)) ∧ ∀x (NetflixShow(x) → (BingeWatch(karen, x) ↔ Download(karen, x))) ∧ ¬Download(karen, blackMirror) ∧ NetflixShow(blackMirror) ∧ ∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) → ShareWith(karen, x, lisa))", "corrected": "yes", "correction_explanation": "Karen may download things that are not Netflix shows, but the original FOL incorrectly restricted the biconditional to only Netflix shows. The NL states 'If and only if Karen binge-watches a Netflix show, she will download it', which means the biconditional should be between 'BingeWatch(karen, x)' and 'Download(karen, x)' without restricting 'x' to being a Netflix show in the antecedent. Corrected to '∀x (NetflixShow(x) → (BingeWatch(karen, x) ↔ Download(karen, x)))' to accurately reflect the NL.", "FOL_sentence_old": "NetflixShow(strangerThings) ∧ Popular(strangerThings)\n∀x ((NetflixShow(x) ∧ Popular(x)) → BingeWatch(karen, x))\n∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) ↔ Download(karen, x))\n¬Download(karen, blackMirror)\nNetflixShow(blackMirror)\n∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) → ShareWith(karen, x, lisa))"} | |
| {"id": "concl_184_22", "NL_sentence": "Karen will share \"Stranger Things\" with Lisa.", "FOL_sentence": "ShareWith(karen, strangerThings, lisa)", "label": "True", "corrected": "no", "FOL_sentence_old": "ShareWith(karen, strangerThings, lisa)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_184_23", "NL_sentence": "\"Black Mirror\" is popular.", "FOL_sentence": "Popular(blackMirror)", "label": "False", "corrected": "no", "FOL_sentence_old": "Popular(blackMirror)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_184_24", "NL_sentence": "Karen will share \"Black Mirror\" with Lisa.", "FOL_sentence": "ShareWith(karen, blackMirror, lisa)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "ShareWith(karen, blackMirror, lisa)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_232", "NL_sentence": "Beijing is the capital of the People's Republic of China. Beijing is the capital city of the world's most populous nation. Beijing is located in Northern China. Beijing hosted the 2008 Summer Olympics and 2008 Summer Paralympics Games. Beijing has hosted the Summer and Winter Olympics and the Summer and Winter Paralympics. Many of Beijing's 91 universities consistently rank among the best universities in the world.", "FOL_sentence": "CapitalOf(beijing, peoplesRepublicOfChina) ∧ ∃x (WorldsMostPopulousNation(x) ∧ CapitalOf(beijing, x)) ∧ LocatedIn(beijing, northernChina) ∧ Hosted(beijing, summerOlympics2008) ∧ Hosted(beijing, summerParalympicGames2008) ∧ Hosted(beijing, summerOlympics) ∧ Hosted(beijing, winterOlympics) ∧ Hosted(beijing, summerParalympicGames) ∧ Hosted(beijing, winterParalympicGames) ∧ ∃x (University(x) ∧ InBeijing(x) ∧ ConsistentlyRankAmongTheBestIn(x, theWorld))", "corrected": "yes", "correction_explanation": "1. Translation Failure (Premise 2): The original '∃x (CapitalOf(beijing, x) → ...)' is a weak existential implication that evaluates to true if there is literally anything Beijing is NOT the capital of. Corrected to an existential conjunction '∃x (WorldsMostPopulousNation(x) ∧ CapitalOf(beijing, x))' to accurately capture the definite description. 2. Invalid Syntax (Premise 4): FOL constants cannot start with numbers. Renamed '2008SummerOlympics' and '2008SummerParalympicGames' to 'summerOlympics2008' and 'summerParalympicGames2008'. 3. Silent Edits Reverted (Premises 4 and 5): Removed hallucinated outer parentheses added by the previous reviewer.", "FOL_sentence_old": "CapitalOf(beijing, peoplesRepublicOfChina)\n∃x (CapitalOf(beijing, x) → WorldsMostPopulousNation(x))\nLocatedIn(beijing, northernChina)\nHosted(beijing, 2008SummerOlympics) ∧ Hosted(beijing, 2008SummerParalympicGames)\nHosted(beijing, summerOlympics) ∧ Hosted(beijing, winterOlympics) ∧ Hosted(beijing, summerParalympicGames) ∧ Hosted(beijing, winterParalympicGames)\n∃x (University(x) ∧ InBeijing(x) ∧ ConsistentlyRankAmongTheBestIn(x, theWorld))"} | |
| {"id": "concl_232_25", "NL_sentence": "Beijing hosted both the 2008 Summer Olympics and the Winter Olympics.", "FOL_sentence": "Hosted(beijing, summerOlympics2008) ∧ Hosted(beijing, winterOlympics)", "label": "True", "corrected": "yes", "correction_explanation": "Translation Failure: The old FOL used 'summerOlympics' which refers to the generic games from Premise 5, but the NL specifically calls out the '2008 Summer Olympics'. Updated to use 'summerOlympics2008' to accurately reflect the text and correctly link to Premise 4.", "FOL_sentence_old": "Hosted(beijing, summerOlympics) ∧ Hosted(beijing, winterOlympics)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_232_26", "NL_sentence": "Beijing is located in southern China.", "FOL_sentence": "LocatedIn(beijing, southernChina)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "LocatedIn(beijing, southernChina)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_232_27", "NL_sentence": "Beijing is the second largest Chinese city.", "FOL_sentence": "SecondLargestChineseCity(beijing)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "SecondLargestChineseCity(beijing)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_452", "NL_sentence": "All aliens are extraterrestrials. If someone is from Mars, then they are an alien. No extraterrestrials are human. All highly intelligent beings from Earth are humans. Marvin is a highly intelligent being. Marvin is either from Earth and from Mars, or he is from neither. If Marvin is not from Earth, then Marvin is an extraterrestrial.", "FOL_sentence": "∀x (Alien(x) → Extraterrestrial(x)) ∧ ∀x (From(x, mars) → Alien(x)) ∧ ∀x (Extraterrestrial(x) → ¬Human(x)) ∧ ∀x (HighlyIntelligentBeing(x) ∧ From(x, earth) → Human(x)) ∧ HighlyIntelligentBeing(marvin) ∧ ¬(From(marvin, earth) ⊕ From(marvin, mars)) ∧ (¬From(marvin, earth) → Extraterrestrial(marvin))", "ambiguity": true, "ambiguity_explanation": "either_or", "corrected": "no", "correction_explanation": "No semantic corrections required. The original FOL accurately translated the NL sentences. The negated XOR '¬(A ⊕ B)' perfectly captures the 'both or neither' phrasing of the NL. Minor additions of grouping parentheses for readability do not constitute a formal correction.", "FOL_sentence_old": "∀x (Alien(x) → Extraterrestrial(x))\n∀x (From(x, mars) → Alien(x))\n∀x (Extraterrestrial(x) → ¬Human(x))\n∀x (HighlyIntelligentBeing(x) ∧ From(x, earth) → Human(x))\nHighlyIntelligentBeing(marvin)\n¬(From(marvin, earth) ⊕ From(marvin, mars))\n¬From(marvin, earth) → Extraterrestrial(marvin)"} | |
| {"id": "concl_452_28", "NL_sentence": "Marvin is an alien.", "FOL_sentence": "Alien(marvin)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Alien(marvin)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_452_29", "NL_sentence": "Marvin is neither a human nor from Mars.", "FOL_sentence": "¬Human(marvin) ∧ ¬From(marvin, mars)", "label": "True", "corrected": "no", "FOL_sentence_old": "¬Human(marvin) ∧ ¬From(marvin, mars)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_452_30", "NL_sentence": "If Marvin is not from Mars, then Marvin is a human.", "FOL_sentence": "¬From(marvin, mars) → Human(marvin)", "label": "False", "corrected": "no", "note": "In the only consistent case (Case B), ¬From(marvin, mars) is true but Human(marvin) is false, making the implication false. Label False is correct.", "FOL_sentence_old": "¬From(marvin, mars) → Human(marvin)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_340", "NL_sentence": "Everyone at the mixer is a Grand Slam champion or an Oscar-nominated actor. Every Grand Slam champion at the mixer is a professional tennis player. All Oscar-nominated actors at the mixer are celebrities. All professional tennis players at the mixer are athletes. If a person at the mixer is a celebrity, then they are well paid. If a person at the mixer is an athlete, then they are famous. All well-paid people at the mixer live in tax havens. Djokovic is at the mixer: if Djokovic is a famous athlete, then Djokovic is well-paid.", "FOL_sentence": "∀x (At(x, mixer) → (GrandSlamChampion(x) ∨ (OscarNominated(x) ∧ Actor(x)))) ∧ ∀x (At(x, mixer) → (GrandSlamChampion(x) → (Professional(x) ∧ TennisPlayer(x)))) ∧ ∀x (At(x, mixer) → ((OscarNominated(x) ∧ Actor(x)) → Celebrity(x))) ∧ ∀x ((At(x, mixer) ∧ Professional(x) ∧ TennisPlayer(x)) → Athlete(x)) ∧ ∀x ((At(x, mixer) ∧ Celebrity(x)) → WellPaid(x)) ∧ ∀x ((At(x, mixer) ∧ Athlete(x)) → Famous(x)) ∧ ∀x ((At(x, mixer) ∧ WellPaid(x)) → ∃y (TaxHaven(y) ∧ LiveIn(x, y))) ∧ At(djokovic, mixer) ∧ ((Famous(djokovic) ∧ Athlete(djokovic)) → WellPaid(djokovic))", "corrected": "yes", "correction_explanation": "Corrections applied: (1) Premises 2 and 3: The original FOL statements contained fatal syntax errors (missing closing parentheses) and a major semantic error (using a conjunction '∧' instead of an implication '→' for a universal claim, which asserted that everyone at the mixer actually *is* a champion/actor rather than setting a condition). Corrected the structure to '∀x (At(x, mixer) → (Condition(x) → Result(x)))' to accurately reflect the NL. (2) Since GrandSlam(x) was alwasy used with also Champion(x), we found no need to separate the predicate symbols, even because there is not a clear meaning behind GrandSlam(x) if not 'x is a Grand Slam champion'. They are unified in the unique predicate symbol GrandSlamChampion(x). (3) TaxHaven should not be considered a constant but a predicate.", "FOL_sentence_old": "∀x (At(x, mixer) → (GrandSlam(x) ∧ Champion(x)) ∨ (OscarNominated(x) ∧ Actor(x)))\n∀x (At(x, mixer) ∧ (GrandSlam(x) ∧ Champion(x) → Professional(x) ∧ TennisPlayer(x))\n∀x (At(x, mixer) ∧ (OscarNominated(x) ∧ Actor(x) → Celebrity(x))\n∀x (At(x, mixer) ∧ Professional(x) ∧ TennisPlayer(x) → Athlete(x))\n∀x (At(x, mixer) ∧ Celebrity(x) → WellPaid(x))\n∀x (At(x, mixer) ∧ Athlete(x) → Famous(x))\n∀x (At(x, mixer) ∧ WellPaid(x) → LiveIn(x, taxHaven))\nAt(djokovic, mixer) ∧ (Famous(djokovic) ∧ Athlete(djokovic) → WellPaid(djokovic))"} | |
| {"id": "concl_340_31", "NL_sentence": "Djokovic is a Grand Slam champion.", "FOL_sentence": "GrandSlamChampion(djokovic)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "Note: label_31 was missing from the original input (label_32 was written twice); label inferred from context as 'Uncertain' based on the value appearing in the field wrongly assigned to conclusion_31. Unified the predicate symbols as written in story_340.", "FOL_sentence_old": "GrandSlam(djokovic) ∧ Champion(djokovic)", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_340_32", "NL_sentence": "Djokovic lives in a tax haven.", "FOL_sentence": "∃x (TaxHaven(x) ∧ LiveIn(djokovic, x))", "label": "True", "corrected": "yes", "correction_explanation": "TaxHaven is a predicate now", "FOL_sentence_old": "LiveIn(djokovic, taxHaven)", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "concl_340_33", "NL_sentence": "Djokovic does not live in a tax haven.", "FOL_sentence": "¬ (∃x (TaxHaven(x) ∧ LiveIn(djokovic, x)))", "label": "False", "corrected": "yes", "correction": "TaxHaven is a predicate now", "FOL_sentence_old": "¬LiveIn(djokovic, taxHaven)", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "False"} | |
| {"id": "story_96", "NL_sentence": "Diamond Mine is a professional wrestling stable formed in WWE. Roderick Strong leads Diamond Mine. Diamond Mine includes the Creed Brothers and Ivy Nile. Imperium has a feud with Diamond Mine.", "FOL_sentence": "ProfessionalWrestlingStable(diamondMine) ∧ In(diamondMine, wWE) ∧ Leads(roderickStrong, diamondMine) ∧ Includes(diamondMine, creedBrothers) ∧ Includes(diamondMine, ivyNile) ∧ Feuds(imperium, diamondMine)", "corrected": "no", "FOL_sentence_old": "ProfessionalWrestlingStable(diamondMine) ∧ In(diamondMine, wWE)\nLeads(roderickStrong, diamondMine)\nIncludes(diamondMine, creedBrothers) ∧ Includes(diamondMine, ivyNile)\nFeuds(imperium, diamondMine)"} | |
| {"id": "concl_96_34", "NL_sentence": "Roderick Strong leads a professional wrestling stable.", "FOL_sentence": "∃x (Leads(roderickStrong, x) ∧ ProfessionalWrestlingStable(x))", "label": "True", "corrected": "yes", "correction_explanation": "The constant 'roderickstrong' was written in all lowercase in the original FOL, inconsistently with the camelCase convention used in the premises ('roderickStrong'). Normalised to 'roderickStrong' for consistency.", "FOL_sentence_old": "∃x (Leads(roderickstrong, x) ∧ ProfessionalWrestlingStable(x))", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "concl_96_35", "NL_sentence": "Roderick Strong leads the Creed Brothers.", "FOL_sentence": "Leads(roderickStrong, creedBrothers)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "Same casing issue as conclusion 34: 'roderickstrong' → 'roderickStrong' and 'creedbrothers' → 'creedBrothers', to align with camelCase convention used in the premises.", "FOL_sentence_old": "Leads(roderickstrong, creedbrothers)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_96_36", "NL_sentence": "Imperium doesn't have a feud with a professional wrestling stable that includes Ivy Nile.", "FOL_sentence": "∀x ((ProfessionalWrestlingStable(x) ∧ Includes(x, ivyNile)) → ¬Feuds(imperium, x))", "label": "False", "corrected": "yes", "correction_explanation": "Casing issue: 'ivynile' → 'ivyNile' to align with camelCase convention used in the premises.", "FOL_sentence_old": "∀x ((ProfessionalWrestlingStable(x) ∧ Includes(x, ivynile)) → ¬Feuds(imperium, x))", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "story_219", "NL_sentence": "Symphony No. 9 is a music piece. Composers write music pieces. Beethoven wrote Symphony No. 9. Vienna Music Society premiered Symphony No. 9. Vienna Music Society is an orchestra. Beethoven leads the Vienna Music Society. Orchestras are led by conductors.", "FOL_sentence": "MusicPiece(symphony9) ∧ ∀x(Composer(x) → ∃y(MusicPiece(y) ∧ Write(x, y))) ∧ Write(beethoven, symphony9) ∧ Premiered(viennaMusicSociety, symphony9) ∧ Orchestra(viennaMusicSociety) ∧ Lead(beethoven, viennaMusicSociety) ∧ ∀x (Orchestra(x) → ∃y (Conductor(y) ∧ Lead(y, x)))", "ambiguity": true, "ambiguity_explanation": "Composers write music pieces can be interpreted as: it can mean that all the composers write some music pieces, that only composers write music pieces, .... Here it is translated in the first way", "corrected": "yes", "correction_explanation": "Corrections applied: (1) Premise 3: The original 'Writtenby(symphony9, beethoven)' uses an inconsistent predicate. To properly resolve against Premise 2's 'Write(y, x)', it must be rewritten as 'Write(beethoven, symphony9)'. (2) Premise 7: The original FOL contained a critical scoping error '... (∃y Conductor(y) ∧ Lead(y, x))' leaving 'y' free in the second conjunct. Corrected to '... ∃y (Conductor(y) ∧ Lead(y, x))' to bind both predicates.", "FOL_sentence_old": "MusicPiece(symphony9)\n∀x (MusicPiece(x) → ∃y (Composer(y) ∧ Write(y, x)))\nWrittenby(symphony9, beethoven)\nPremiered(viennaMusicSociety, symphony9)\nOrchestra(viennaMusicSociety)\nLead(beethoven, viennaMusicSociety)\n∀x (Orchestra(x) → (∃y Conductor(y) ∧ Lead(y, x)))"} | |
| {"id": "concl_219_37", "NL_sentence": "Beethoven is a composer.", "FOL_sentence": "Composer(beethoven)", "corrected": "no", "correction_explanation": "Label correction: The original label 'True' is invalid in strict formal logic. While Premise 2 states every music piece has some composer who wrote it, and Premise 3 states Beethoven wrote it, there is no rule stating that ONLY composers write music pieces or that a piece has a unique writer. Thus, 'Composer(beethoven)' cannot be definitively proven. Changed label to Uncertain.", "FOL_sentence_old": "Composer(beethoven)", "label_old": "True", "label_new": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_219_38", "NL_sentence": "Some orchestras premiered music pieces.", "FOL_sentence": "∃x ∃y (Orchestra(x) ∧ MusicPiece(y) ∧ Premiered(x, y))", "label": "True", "corrected": "no", "ambiguity": true, "ambiguity_explanation": "some_plural", "FOL_sentence_old": "∃x ∃y (Orchestra(x) ∧ MusicPiece(y) ∧ Premiered(x, y))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_219_39", "NL_sentence": "Beethoven is not a conductor.", "FOL_sentence": "¬Conductor(beethoven)", "corrected": "no", "correction_explanation": "Label correction: The original label 'False' implies we can prove Beethoven IS a conductor. However, just because he leads the orchestra (P6) and a conductor leads the orchestra (P7), without an equality axiom or a rule stating ONLY conductors lead orchestras, we cannot definitively prove he is a conductor, nor can we prove he is not. Changed label to Uncertain.", "FOL_sentence_old": "¬Conductor(beethoven)", "label_old": "False", "label_new": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_350", "NL_sentence": "All of Zaha Hadid's design styles that Max adores have interesting geometries. No brutalist buildings that Max adores have interesting geometries. Every style that Max adores is either Zaha Hadid's design style or Kelly Wearstler's design style. All of Kelly Wearstler's design styles that Max adores are evocative. All of Kelly Wearstler's design styles that Max adores are dreamy. If a design by Max that he adores has interesting geometries, then the design is a brutalist building and evocative.", "FOL_sentence": "∀x (Adore(max, x) ∧ ZahaHadid(x) ∧ DesignStyle(x) → InterestingGeometry(x)) ∧ ∀x (Adore(max, x) ∧ BrutalistBuilding(x) → ¬InterestingGeometry(x)) ∧ ∀x (Adore(max, x) → ((ZahaHadid(x) ∧ DesignStyle(x)) ⊕ (KellyWearstler(x) ∧ DesignStyle(x)))) ∧ ∀x (Adore(max, x) ∧ KellyWearstler(x) ∧ DesignStyle(x) → Evocative(x)) ∧ ∀x (Adore(max, x) ∧ KellyWearstler(x) ∧ DesignStyle(x) → Dreamy(x)) ∧ ∀x (Adore(max, x) ∧ Design(x) ∧ ByMax(x) ∧ InterestingGeometry(x) → BrutalistBuilding(x) ∧ Evocative(x))", "corrected": "yes", "correction_explanation": "Two corrections made: (1) Premise 3: unclosed parenthesis in the original fixed. (2) Premise 6: the original uses '∃x (Adore(max, x) ∧ Design(x) ∧ ByMax(x) ∧ InterestingGeometry(x) → BrutalistBuilding(x) ∧ Evocative(x))'. This is a well-known FOL scoping pitfall: '∃x (P → Q)' is not the intended reading for a conditional generalisation — and in fact '∃x (P ∧ Q → R)' is logically equivalent to '∃x (¬(P ∧ Q) ∨ R)', which is almost trivially true and does not capture the intended universal conditional. The NL reads as a general rule ('if a design... then...'), so the correct quantifier is ∀, giving '∀x (Adore(max, x) ∧ Design(x) ∧ ByMax(x) ∧ InterestingGeometry(x) → BrutalistBuilding(x) ∧ Evocative(x))'.", "ambiguity": true, "ambiguity_explanation": "either_or", "FOL_sentence_old": "∀x (Adore(max, x) ∧ ZahaHadid(x) ∧ DesignStyle(x) → InterestingGeometry(x))\n∀x (Adore(max, x) ∧ BrutalistBuilding(x) → ¬InterestingGeometry(x))\n∀x (Adore(max, x) → ((ZahaHadid(x) ∧ DesignStyle(x)) ⊕ (KellyWearstler(x) ∧ DesignStyle(x)))\n∀x (Adore(max, x) ∧ KellyWearstler(x) ∧ DesignStyle(x) → Evocative(x))\n∀x (Adore(max, x) ∧ KellyWearstler(x) ∧ DesignStyle(x) → Dreamy(x))\n∃x (Adore(max, x) ∧ Design(x) ∧ ByMax(x) ∧ InterestingGeometry(x) → BrutalistBuilding(x) ∧ Evocative(x))"} | |
| {"id": "concl_350_40", "NL_sentence": "A design by Max is a brutalist building.", "FOL_sentence": "∃x (Design(x) ∧ ByMax(x) ∧ BrutalistBuilding(x))", "ambiguity": true, "ambiguity_explanation": "existential_universal", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "∃x (Design(x) ∧ ByMax(x) ∧ BrutalistBuilding(x))", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_350_41", "NL_sentence": "A design by Max is evocative and dreamy.", "FOL_sentence": "∃x (Design(x) ∧ ByMax(x) ∧ Evocative(x) ∧ Dreamy(x))", "ambiguity": true, "ambiguity_explanation": "existential_universal", "corrected": "yes", "correction_explanation": "Label correction: FOR THE ORIGINAL INTERPRETATION: The original label 'True' commits an existential fallacy. The premises are exclusively universal conditionals (∀x). They establish rules about properties, but never assert that any design actually exists in the domain. Furthermore, there is no rule linking a design ByMax to the Dreamy property (which requires KellyWearstler). Because we cannot prove the existence of such an entity, the label must be Uncertain. IF THE INTERPRETATION IS UNIVERSAL: then however, any premise talks about designs by Max that he adores, so it can be True, since nothing informed us about the objects x that satisfy only the properties Design(x) ∧ ByMax(x)", "FOL_sentence_old": "∃x (Design(x) ∧ ByMax(x) ∧ Evocative(x) ∧ Dreamy(x))", "label_old": "True", "label_new": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_350_42", "NL_sentence": "A design by Max is either evocative or dreamy.", "FOL_sentence": "∃x (Design(x) ∧ ByMax(x) ∧ (Evocative(x) ⊕ Dreamy(x)))", "ambiguity": true, "ambiguity_explanation": "existential_universal, either_or", "corrected": "yes", "correction_explanation": "Label correction: The original label 'False' is logically invalid. To prove this existential statement False, the solver must prove that NO design by Max is either evocative or dreamy. Because the premises do not explicitly forbid Max from having a design that is solely evocative (e.g., via Premise 6), and because we don't even know if he has designs at all, the solver cannot definitively prove this False. The label must be Uncertain. Same as before, even considering the other interpretation", "FOL_sentence_old": "∃x (Design(x) ∧ ByMax(x) ∧ (Evocative(x) ⊕ Dreamy(x)))", "label_old": "False", "label_new": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "story_385", "NL_sentence": "If someone is ranked highly by the Women's Tennis Association, then they are one of the most active players in major tennis. Everyone who lost to Iga Świątek at Roland Garros 2022 is ranked highly by the Women's Tennis Association. All female tennis players at Roland Garros 2022 lost to Iga Świątek. All tennis players at Roland Garros 2022 are either female or male. All male tennis players at Roland Garros in 2022 lost to Rafael Nadal. If Coco Gauff is ranked highly by the Women's Tennis Association or lost to Rafael Nadal, then Coco Gauff is not a male tennis player at Roland Garros 2022. Coco Gauff is at Roland Garros 2022.", "FOL_sentence": "∀x (RankedHighlyBy(x, womensTennisAssociation) → MostActivePlayerIn(x, majorTennis)) ∧ ∀x (LostTo(x, świątek, rolandGarros2022) → RankedHighlyBy(x, womensTennisAssociation)) ∧ ∀x ((FemaleTennisPlayer(x) ∧ At(x, rolandGarros2022)) → LostTo(x, świątek, rolandGarros2022)) ∧ ∀x ((TennisPlayer(x) ∧ At(x, rolandGarros2022)) → (FemaleTennisPlayer(x) ⊕ MaleTennisPlayer(x))) ∧ ∀x ((MaleTennisPlayer(x) ∧ At(x, rolandGarros2022)) → LostTo(x, nadal, rolandGarros2022)) ∧ ((RankedHighlyBy(cocoGauff, womensTennisAssociation) ∨ LostTo(cocoGauff, nadal, rolandGarros2022)) → ¬(MaleTennisPlayer(cocoGauff) ∧ At(cocoGauff, rolandGarros2022))) ∧ TennisPlayer(cocoGauff) ∧ At(cocoGauff, rolandGarros2022)", "ambiguity": true, "ambiguity_explanation": "either_or", "corrected": "yes", "correction_explanation": "Critical corrections applied: (1) Predicate Unification: The original FOL mixed 'Female(x) ∧ TennisPlayer(x)' with 'FemaleTennisPlayer(x)'. Standardized to 'FemaleTennisPlayer(x)' and 'MaleTennisPlayer(x)' throughout to repair the broken logical chain. (2) Translation Failure: Premise 5 incorrectly translated 'Rafael Nadal' as 'świątek'. Corrected to 'nadal'. (3) Syntax/Translation: Premise 6 was completely broken, using wrong constants ('świątek' instead of 'nadal') and wrong unary predicates ('AtRolandGarros2022(x)'). Standardized to match the established premises, and added strict grouping parentheses to the antecedent to ensure standard parser precedence. (4) the property 'x losts to y at z' were translated as LostTo(x, y) ∧ At(x, z), that is not the correct formalization. Now it is fixed extending LostTo as a ternary binary.", "FOL_sentence_old": "∀x (RankedHighlyBy(x, womensTennisAssociation) → MostActivePlayerIn(x, majorTennis))\n∀x (LostTo(x, świątek) ∧ At(x, rolandGarros2022) → RankedHighlyBy(x, womensTennisAssociation))\n∀x (FemaleTennisPlayer(x) ∧ At(x, rolandGarros2022) → LostTo(x, świątek) ∧ At(x, rolandGarros2022))\n∀x (TennisPlayer(x) ∧ At(x, rolandGarros2022) → (Female(x) ∧ TennisPlayer(x)) ⊕ (Male(x) ∧ TennisPlayer(x))) \n∀x (Male(x) ∧ TennisPlayer(x) ∧ At(x, rolandGarros2022) → LostTo(x, świątek) ∧ At(x, rolandGarros2022))\nRankedHighlyBy(cocoGauff, womensTennisAssociation) ∨ (LostTo(cocoGauff, świątek) ∧ LostAt(cocoGauff, rolandGarros2022)) → ¬(Male(cocoGauff) ∧ TennisPlayer(cocoGauff) ∧ AtRolandGarros2022(cocoGauff))\nTennisPlayer(cocoGauff) ∧ At(cocoGauff, rolandGarros2022)"} | |
| {"id": "concl_385_43", "NL_sentence": "Coco Gauff is among the most active major tennis players.", "FOL_sentence": "MostActivePlayerIn(cocoGauff, majorTennis)", "corrected": "no", "correction_explanation": "The original NL sentence was 'Coco Gauff is among the most active Grand-Slam players.'. Most active player is mentioned only about 'major tennis' in the story and never in Grand-Slams competition. With the provided ontology is not formalizable correctly. We corrected the original NL_sentence.", "FOL_sentence_old": "MostActivePlayerIn(cocoGauff, majorTennis)", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "concl_385_44", "NL_sentence": "Coco Gauff has lost to Rafael Nadal.", "FOL_sentence": "∃x LostTo(cocoGauff, nadal, x)", "corrected": "yes", "correction_explanation": "Translation correction: (1) The original FOL translated 'Rafael Nadal' as 'świątek'. Corrected to 'nadal'. (2) The original FOL inappropriately appended '∧ At(cocoGauff, rolandGarros2022)', which is a premise, not part of the conclusion's statement. Removed. (3) Used LostTo ternary.", "FOL_sentence_old": "LostTo(cocoGauff, świątek) ∧ At(cocoGauff, rolandGarros2022)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_385_45", "NL_sentence": "Coco Gauff is not both a player who lost to Iga Świątek at Roland Garros 2022 and one of the most active players in major tennis.", "FOL_sentence": "¬LostTo(cocoGauff, świątek, rolandGarros2022) ∨ ¬MostActivePlayerIn(cocoGauff, majorTennis)", "corrected": "yes", "correction_explanation": "ontology_correction", "FOL_sentence_old": "¬(LostTo(cocoGauff, świątek) ∧ At(cocoGauff, rolandGarros2022)) ∨ ¬MostActivePlayerIn(cocoGauff, majorTennis)", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "story_256", "NL_sentence": "All cats are mammals. Some pets are not mammals.", "FOL_sentence": "∀x (Cat(x) → Mammal(x)) ∧ ∃x (Pet(x) ∧ ¬Mammal(x))", "corrected": "no", "ambiguity": true, "ambiguity_explanation": "some_plural", "FOL_sentence_old": "∀x (Cat(x) → Mammal(x))\n∃x (Pet(x) ∧ ¬Mammal(x))"} | |
| {"id": "concl_256_46", "NL_sentence": "No pets are cats.", "FOL_sentence": "∀x (Pet(x) → ¬Cat(x))", "corrected": "no", "FOL_sentence_old": "∀x (Pet(x) → ¬Cat(x))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_159", "NL_sentence": "There are four seasons in a year: Spring, Summer, Fall, and Winter. All students who want to have a long vacation have summer as their favorite season. Emma's favorite season is summer. Mia's favorite season is not the same as Emma's. James wants to have a long vacation.", "FOL_sentence": "Season(spring) ∧ Season(summer) ∧ Season(fall) ∧ Season(winter) ∧ ∀x (Season(x) → (x = spring ∨ x = summer ∨ x = fall ∨ x = winter)) ∧ ∀x (Student(x) ∧ Want(x, longVacation) → Favorite(x, summer)) ∧ Favorite(emma, summer) ∧ ∀x ∀y (Season(x) ∧ Season(y) ∧ Favorite(mia, x) ∧ Favorite(emma, y) → ¬(x=y)) ∧ Want(james, longVacation)", "corrected": "yes", "correction_explanation": " 1. Spring, Summer, Fall, and Winter are all seasons (∧ adopted) and the only ones 2. Translation Failure (Premise 2): Added the missing 'Student(x)' predicate to match the NL text 'All students who...'. 4. Broken Linkage (Premise 2 & 5): Corrected casing mismatch from 'longvacation' to 'longVacation'.", "FOL_sentence_old": "Season(spring) ∨ Season(summer) ∨ Season(fall) ∨ Season(winter) ∧ (Season(spring) → ¬Season(summer) ∧ ¬Season(fall) ∧ ¬Season(winter)) ∧ (Season(summer) → ¬Season(spring) ∧ ¬Season(fall) ∧ ¬Season(winter)) ∧ (Season(fall) → ¬Season(spring) ∧ ¬Season(summer) ∧ ¬Season(winter)) ∧ (Season(winter) → ¬Season(spring) ∧ ¬Season(summer) ∧ ¬Season(fall))\n∀x (Want(x, longvacation) → Favorite(x, summer))\nFavorite(emma, summer)\n∀x ∀y (Season(x) ∧ Season(y) ∧ Favorite(mia, x) ∧ Favorite(emma, y) → ¬(x=y))\nWant(james, longVacation)"} | |
| {"id": "concl_159_47", "NL_sentence": "James's favorite season is summer.", "FOL_sentence": "Favorite(james, summer)", "label": "Uncertain", "corrected": "no", "correction_explanation": "Label corrected from True to Uncertain. Premise 2 restricts the rule to 'All students', but there is no premise explicitly stating that James is a student. Deducing this conclusion without the Student(james) constraint is a logical fallacy.", "FOL_sentence_old": "Favorite(james, summer)", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_159_48", "NL_sentence": "Mia's favorite season is spring.", "FOL_sentence": "Favorite(mia, spring)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Favorite(mia, spring)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_343", "NL_sentence": "No digital media are analog. Every printed text is analog media. All streaming services are digital media. If an object is a hardcover book, then it is printed text. If 1984 is a streaming service, then 1984 is a hardcover book.", "FOL_sentence": "∀x (DigitalMedia(x) → ¬AnalogMedia(x)) ∧ ∀x (PrintedText(x) → AnalogMedia(x)) ∧ ∀x (StreamingService(x) → DigitalMedia(x)) ∧ ∀x (HardcoverBook(x) → PrintedText(x)) ∧ (StreamingService(y1984) → HardcoverBook(y1984))", "corrected": "yes", "correction_explanation": "ontology : Only changed '1984' with 'y1984' to avoid conflict with z3-parser", "FOL_sentence_old": "∀x (DigitalMedia(x) → ¬AnalogMedia(x))\n∀x (PrintedText(x) → AnalogMedia(x))\n∀x (StreamingService(x) → DigitalMedia(x))\n∀x (HardcoverBook(x) → PrintedText(x))\nStreamingService(1984) → HardcoverBook(1984)"} | |
| {"id": "concl_343_49", "NL_sentence": "1984 is printed text.", "FOL_sentence": "PrintedText(y1984)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "ontology", "FOL_sentence_old": "PrintedText(1984)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_343_50", "NL_sentence": "1984 is a streaming service.", "FOL_sentence": "StreamingService(y1984)", "label": "False", "corrected": "yes", "correction_explanation": "ontology", "FOL_sentence_old": "StreamingService(1984)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_343_51", "NL_sentence": "1984 is not a streaming service.", "FOL_sentence": "¬StreamingService(y1984)", "label": "True", "corrected": "yes", "correction_explanation": "ontology", "FOL_sentence_old": "¬StreamingService(1984)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "story_213", "NL_sentence": "All Romance languages are Indo-European languages. Romance languages are a language family. All languages within a language family are related to each other. French and Spanish are both Romance languages. German is related to Spanish. Basque is not related to any other language.", "FOL_sentence": "∀x (RomanceLanguage(x) → IndoEuropeanLanguage(x)) ∧ ∀x (RomanceLanguage(x) → MemberOf(x, romanceFamily)) ∧ ∀x ∀y ∀z ((MemberOf(x, z) ∧ MemberOf(y, z)) → (Related(x, y) ∧ Related(y, x))) ∧ RomanceLanguage(french) ∧ RomanceLanguage(spanish) ∧ Related(german, spanish) ∧ ∀x (x ≠ basque → ¬Related(basque, x))", "corrected": "yes", "correction_explanation": "1. Broken Linkage (Premise 2): Replaced the generic constant 'languageFamily' with the specific 'romanceFamily'. Using a generic constant would incorrectly assign all language families in the domain to a single object. 2. Translation Failure & Broken Linkage (Premise 6): The original translation introduced an undefined 'Language(x)' predicate. Since 'Language' is never linked to 'RomanceLanguage', it breaks the logical chain (we cannot prove French or Spanish are 'Languages' to trigger the rule). Furthermore, it ignored the word 'other'. Corrected to '∀x (x ≠ basque → ¬Related(basque, x))' to accurately capture 'any other' without hallucinating disconnected predicates.", "FOL_sentence_old": "∀x (RomanceLanguage(x) → IndoEuropeanLanguage(x))\n∀x (RomanceLanguage(x) → MemberOf(x, languageFamily))\n∀x ∀y ∀z ((MemberOf(x, z) ∧ MemberOf(y, z)) → (Related(x, y) ∧ Related(y, x)))\nRomanceLanguage(french) ∧ RomanceLanguage(spanish)\nRelated(german, spanish)\n∀x (Language(x) → ¬Related(basque, x))"} | |
| {"id": "concl_213_52", "NL_sentence": "Basque is a Romance language.", "FOL_sentence": "RomanceLanguage(basque)", "label": "False", "corrected": "no", "NLI_requires_more_info": "(french ≠ basque)", "note": "The label 'False' is correct: if Basque were a Romance language, it would be a member of romanceFamily (premise 2), and hence related to French and Spanish (premise 3). But premise 6 states Basque is not related to any language, yielding a contradiction. Therefore RomanceLanguage(basque) is refutable.", "FOL_sentence_old": "RomanceLanguage(basque)", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "concl_213_53", "NL_sentence": "German is a Romance language.", "FOL_sentence": "RomanceLanguage(german)", "label": "Uncertain", "corrected": "no", "note": "The label 'Uncertain' is correct: the premises establish that German is related to Spanish, but relatedness is not sufficient to establish Romance language membership — the Related predicate is introduced for German only via premise 5 as a bare fact, not derived from family membership. Nothing in the premises rules out German being a Romance language, nor does anything entail it. The conclusion is therefore neither provable nor refutable.", "FOL_sentence_old": "RomanceLanguage(german)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_213_54", "NL_sentence": "French is an Indo-European language.", "FOL_sentence": "IndoEuropeanLanguage(french)", "label": "True", "corrected": "no", "note": "The label 'True' is directly derivable: premise 4 establishes RomanceLanguage(french), and premise 1 states ∀x (RomanceLanguage(x) → IndoEuropeanLanguage(x)), so IndoEuropeanLanguage(french) follows by universal instantiation and modus ponens.", "FOL_sentence_old": "IndoEuropeanLanguage(french)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "story_79", "NL_sentence": "Robert Lewandowski is a striker. Strikers are soccer players. Robert Lewandowski left Bayern Munchen. If a player leaves a team they no longer play for that team.", "FOL_sentence": "Striker(robertLewandowski) ∧ ∀x (Striker(x) → SoccerPlayer(x)) ∧ Left(robertLewandowski, bayernMunchen) ∧ ∀x ∀y (Player(x) ∧ Team(y) ∧ Left(x, y) → ¬PlaysFor(x, y))", "corrected": "yes", "correction_explanation": "Translation Failure (Premise 4): The original FOL '∀x ∀y (Left(x, y) → ¬PlaysFor(x, y))' ignored the explicit domain constraints 'player' and 'team' from the NL text ('If a player leaves a team...'). Corrected to '∀x ∀y (Player(x) ∧ Team(y) ∧ Left(x, y) → ¬PlaysFor(x, y))' to maintain absolute semantic fidelity to the natural language, even if it changes downstream entailment.", "FOL_sentence_old": "Striker(robertLewandowski)\n∀x (Striker(x) → SoccerPlayer(x))\nLeft(robertLewandowski, bayernMunchen)\n∀x ∀y (Left(x, y) → ¬PlaysFor(x, y))"} | |
| {"id": "concl_79_55", "NL_sentence": "Robert Lewandowski is a soccer player.", "FOL_sentence": "SoccerPlayer(robertLewandowski)", "label": "True", "corrected": "no", "FOL_sentence_old": "SoccerPlayer(robertLewandowski)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_79_56", "NL_sentence": "Robert Lewandowski plays for Bayern Munchen.", "FOL_sentence": "PlaysFor(robertLewandowski, bayernMunchen)", "label": "Uncertain", "corrected": "no", "correction_explanation": "Label corrected from False to Uncertain. With Premise 4 strictly translated to require Player(x) and Team(y), we cannot logically deduce that Lewandowski does not play for Bayern Munchen. There is no premise stating that Bayern Munchen is a 'Team' (Team(bayernMunchen)), nor one stating Lewandowski is a 'Player' (we only know 'SoccerPlayer'). Without these exact predicates established, the implication fails to trigger.", "FOL_sentence_old": "PlaysFor(robertLewandowski, bayernMunchen)", "label_old": "False", "label_old_z3": "False", "label_z3": "Uncertain"} | |
| {"id": "concl_79_57", "NL_sentence": "Robert Lewandowski is a star.", "FOL_sentence": "Star(robertLewandowski)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "Translation Failure: The NL simply says 'is a star', but the original FOL hallucinated the more specific predicate 'SoccerStar'. Corrected the FOL to the strictly literal 'Star(robertLewandowski)'. The label remains Uncertain.", "FOL_sentence_old": "SoccerStar(robertLewandowski)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_2", "NL_sentence": "Billings is a city in the state of Montana in U.S. The state of Montana includes the cities of Butte, Helena, and Missoula. White Sulphur Springs and Butte are cities in the same state in U.S. The city of St Pierre is not in the state of Montana. Any city in Butte is not in St Pierre. A city can only be in one state in U.S. except for Bristol, Texarkana, Texhoma and Union City.", "FOL_sentence": "City(billings) ∧ In(billings, montana) ∧ State(montana) ∧ City(butte) ∧ In(butte, montana) ∧ City(helena) ∧ In(helena, montana) ∧ City(missoula) ∧ In(missoula, montana) ∧ ∃x (City(whiteSulphurSprings) ∧ In(whiteSulphurSprings, x) ∧ City(butte) ∧ In(butte, x) ∧ State(x)) ∧ City(stPierre) ∧ ¬(In(stPierre, montana)) ∧ ∀x ((City(x) ∧ City(butte) ∧ In(x, butte)) → ¬(In(x, stPierre))) ∧ ∀x ∀y ((City(x) ∧ State(y) ∧ In(x, y) ∧ ¬(x=bristol) ∧ ¬(x=texarkana) ∧ ¬(x=texhoma) ∧ ¬(x=unionCity)) → ¬∃z (¬(z=y) ∧ State(z) ∧ In(x, z)))", "corrected": "yes", "correction_explanation": "1. Broken Linkage (Premises 4 & 5): Replaced the mismatched constant 'pierre' with 'stPierre' to correctly link with the conclusions. 2. Scope & Syntax Error (Premise 6): The original FOL '∀x ∃y ((City...' contained an unbalanced parenthesis and mis-scoped 'y' as an existential variable, leaving it unbound in the consequent. Corrected the quantifier to '∀y' and removed the rogue parenthesis. 3. Invalid Swaps Reverted: Restored 'City(butte)' in Premise 5, which the previous reviewer invalidly removed as a logically equivalent swap.", "FOL_sentence_old": "City(billings) ∧ In(billings, montana)\nCity(butte) ∧ In(butte, montana) ∧ City(helena) ∧ In(helena, montana) ∧ City(missoula) ∧ In(missoula, montana)\n∃x (City(whitesulphursprings) ∧ In(whitesulphursprings, x) ∧ City(butte) ∧ In(butte, x))\nCity(pierre) ∧ ¬(In(pierre, montana))\n∀x ((City(x) ∧ City(butte) ∧ In(x, butte)) → ¬(In(x, pierre)))\n∀x ∃y ((City(x) ∧ (In(x, y) ∧ ¬(x=bristol) ∧ ¬(x=texarkana) ∧ ¬(x=texhoma) ∧ ¬(x=unionCity)) → ¬∃z (¬(z=y) ∧ In(x, z)))"} | |
| {"id": "concl_2_58", "NL_sentence": "Butte and St Pierre are in the same state.", "FOL_sentence": "∃x (State(x) ∧ In(butte, x) ∧ In(stPierre, x))", "label": "False", "corrected": "yes", "NLI_requires_more_info": "¬(butte=bristol) ∧ ¬(butte=texarkana) ∧ ¬(butte=texhoma) ∧ ¬(butte=unionCity) ∧ ¬(stPierre=bristol) ∧ ¬(stPierre=texarkana) ∧ ¬(stPierre=texhoma) ∧ ¬(stPierre=unionCity)", "FOL_sentence_old": "∃x (In(butte, x) ∧ In(stPierre, x))", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "False"} | |
| {"id": "concl_2_59", "NL_sentence": "St Pierre and Bismarck are in the same state.", "FOL_sentence": "∃x (In(stPierre, x) ∧ In(bismarck, x) ∧ State(x))", "label": "Uncertain", "corrected": "yes", "correction_explanation": "Broken Linkage: The original FOL used 'pierre', but the conclusions (and updated premises) standardise on 'stPierre'. Corrected to 'stPierre' to fix the broken logical chain. Modified also the ontology State. (2) Removed also the fact that these two are cities (not explicitely said in NL)", "FOL_sentence_old": "∃x (City(pierre) ∧ In(pierre, x) ∧ City(bismarck) ∧ In(bismarck, x))", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_2_60", "NL_sentence": "Montana is home to the city of Missoula.", "FOL_sentence": "City(missoula) ∧ In(missoula, montana)", "label": "True", "corrected": "no", "FOL_sentence_old": "City(missoula) ∧ In(missoula, montana)", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "story_192", "NL_sentence": "International students in the US have either an F1 visa or a J1 visa. An international student in the US with an F1 visa needs to apply for CPT or OPT if the student wants to work in the US. Mike is an international student. Mike needs to apply for CPT if he wants to work in the US.", "FOL_sentence": "∀x (InternationalStudent(x) ∧ In(x, unitedStates) → F1Visa(x) ⊕ J1Visa(x)) ∧ ∀x (InternationalStudent(x) ∧ In(x, unitedStates) ∧ F1Visa(x) ∧ WantToWorkIn(x, unitedStates) → Apply(x, cpt) ∨ Apply(x, opt)) ∧ InternationalStudent(mike) ∧ WantToWorkIn(mike, unitedStates) → Apply(mike, cpt)", "ambiguity": true, "ambiguity_commentary": "either_or", "corrected": "yes", "correction_explanation": "1. Scope Error (Premise 4): The original FOL 'WantToWorkIn(x, unitedStates) → Apply(mike, cpt)' used a free, unbound variable 'x' in the antecedent while referring to the constant 'mike' in the consequent. Corrected to 'WantToWorkIn(mike, unitedStates)' to accurately match the NL text.", "FOL_sentence_old": "∀x (InternationalStudent(x) ∧ In(x, unitedStates) → F1Visa(x) ⊕ J1Visa(x))\n∀x (InternationalStudent(x) ∧ In(x, unitedStates) ∧ F1Visa(x) ∧ WantToWorkIn(x, unitedStates) → Apply(x, cpt) ∨ Apply(x, opt))\nInternationalStudent(mike)\nWantToWorkIn(x, unitedStates) → Apply(mike, cpt)"} | |
| {"id": "concl_192_61", "NL_sentence": "Mike has an F1 visa.", "FOL_sentence": "F1Visa(mike)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "F1Visa(mike)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_192_62", "NL_sentence": "Mike has a J1 visa.", "FOL_sentence": "J1Visa(mike)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "J1Visa(mike)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_442", "NL_sentence": "All Brown Swiss cattle are cows. Some pets are Brown Swiss cattle. All cows are domesticated animals. Alligators are not domesticated animals. Ted is an alligator.", "FOL_sentence": "∀x (BrownSwissCattle(x) → Cow(x)) ∧ ∃x (Pet(x) ∧ BrownSwissCattle(x)) ∧ ∀x (Cow(x) → DomesticatedAnimal(x)) ∧ ∀x (Alligator(x) → ¬DomesticatedAnimal(x)) ∧ Alligator(ted)", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "some_plural", "correction_explanation": "Typo Correction: The original FOL misspelled 'Alligator' as 'Aligator' in Premises 4 and 5. Corrected to 'Alligator' to maintain strict semantic alignment with the standard spelling in the Natural Language text.", "FOL_sentence_old": "∀x (BrownSwissCattle(x) → Cow(x))\n∃x (Pet(x) ∧ BrownSwissCattle(x))\n∀x (Cow(x) → DomesticatedAnimal(x))\n∀x (Aligator(x) → ¬DomesticatedAnimal(x))\nAligator(ted)"} | |
| {"id": "concl_442_63", "NL_sentence": "Ted is a pet.", "FOL_sentence": "Pet(ted)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Pet(ted)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_442_64", "NL_sentence": "Ted is a pet and Brown Swiss cattle.", "FOL_sentence": "Pet(ted) ∧ BrownSwissCattle(ted)", "label": "False", "corrected": "no", "FOL_sentence_old": "Pet(ted) ∧ BrownSwissCattle(ted)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_442_65", "NL_sentence": "If Ted is a Brown Swiss cattle, then Ted is not a pet.", "FOL_sentence": "BrownSwissCattle(ted) → ¬Pet(ted)", "label": "True", "corrected": "no", "FOL_sentence_old": "BrownSwissCattle(ted) → ¬Pet(ted)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "story_234", "NL_sentence": "Yale University is a private Ivy League research university. Yale University moved to New Haven in 1716. Yale University's endowment was valued at $42.3 billion. A list of residential colleges at Yale: Benjamin Franklin College, Berkeley College, Branford College, Davenport College, Ezra Stiles College, Grace Hopper College, Jonathan Edwards College, Morse College, Pauli Murray College, Pierson College, Saybrook College, Silliman College, Timothy Dwight College, and Trumbull College.", "FOL_sentence": "PrivateIvyLeagueResearchUniversity(yaleUniversity) ∧ MovedTo(yaleUniversity, newHaven) ∧ MovedIn(yaleUniversity, year1716) ∧ ValuedAt(yaleUniversitysEndowment, usd42point3billion) ∧ ResidentialCollege(benjaminFranklinCollege) ∧ At(benjaminFranklinCollege, yaleUniversity) ∧ ResidentialCollege(berkeleyCollege) ∧ At(berkeleyCollege, yaleUniversity) ∧ ResidentialCollege(branfordCollege) ∧ At(branfordCollege, yaleUniversity) ∧ ResidentialCollege(davenportCollege) ∧ At(davenportCollege, yaleUniversity) ∧ ResidentialCollege(ezraStilesCollege) ∧ At(ezraStilesCollege, yaleUniversity) ∧ ResidentialCollege(graceHopperCollege) ∧ At(graceHopperCollege, yaleUniversity) ∧ ResidentialCollege(jonathanEdwardsCollege) ∧ At(jonathanEdwardsCollege, yaleUniversity) ∧ ResidentialCollege(morseCollege) ∧ At(morseCollege, yaleUniversity) ∧ ResidentialCollege(pauliMurrayCollege) ∧ At(pauliMurrayCollege, yaleUniversity) ∧ ResidentialCollege(piersonCollege) ∧ At(piersonCollege, yaleUniversity) ∧ ResidentialCollege(saybrookCollege) ∧ At(saybrookCollege, yaleUniversity) ∧ ResidentialCollege(sillimanCollege) ∧ At(sillimanCollege, yaleUniversity) ∧ ResidentialCollege(timothyDwightCollege) ∧ At(timothyDwightCollege, yaleUniversity) ∧ ResidentialCollege(trumbullCollege) ∧ At(trumbullCollege, yaleUniversity)", "corrected": "yes", "correction_explanation": "1. Translation Failure / Category Error (Premise 4): The original FOL used a universal conditional that failed to assert the existence of the colleges, making Conclusion 68 unprovable. It also treated specific college entities as unary properties instead of constants. Replaced with a single conjunction of ground facts (e.g., 'ResidentialCollege(piersonCollege) ∧ At(piersonCollege, yale)') to properly ground the facts. 2. Typo (Premise 4): Corrected 'BerkleyCollege' to 'BerkeleyCollege' to match the NL. 4. Syntax Error (Premise 3): The constant '42point3billion' starts with a digit, which violates standard FOL syntax rules (for z3-parser). Renamed to 'usd42point3billion'. 5. Unified 'yale' and 'yaleUniversity'", "FOL_sentence_old": "PrivateIvyLeagueResearchUniversity(yaleUniversity)\nMovedTo(yaleUniversity, newHaven) ∧ MovedIn(yaleUniversity, year1716)\nValuedAt(yaleUniversitysEndowment, 42point3billion)\n∀x (ResidentialCollege(x) → At(x, yale) ∧ (BenjaminFranklinCollege(x) ⊕ BerkleyCollege(x) ⊕ BranfordCollege(x) ⊕ DavenportCollege(x) ⊕ EzraStilesCollege(x) ⊕ GraceHopperCollege(x) ⊕ JonathanEdwardsCollege(x) ⊕ MorseCollege(x) ⊕ PauliMurrayCollege(x) ⊕ PiersonCollege(x) ⊕ SaybrookCollege(x) ⊕ SillimanCollege(x) ⊕ TimothyDwightCollege(x) ⊕ TrumbullCollege(x)))"} | |
| {"id": "concl_234_66", "NL_sentence": "A private Ivy League research university moved to New Haven.", "FOL_sentence": "∃x (PrivateIvyLeagueResearchUniversity(x) ∧ MovedTo(x, newHaven))", "label": "True", "corrected": "no", "FOL_sentence_old": "∃x (PrivateIvyLeagueResearchUniversity(x) ∧ MovedTo(x, newHaven))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_234_67", "NL_sentence": "Yale University has the largest university endowment of any educational institution.", "FOL_sentence": "LargestUniversityEndowmentOf(yaleUniversity, anyEducationalInstitution)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "Broken Linkage: The original FOL uses 'yale' instead of 'yaleUniversity' as the constant. Unified to 'yaleUniversity' to match the premises.", "FOL_sentence_old": "LargestUniversityEndowmentOf(yale, anyEducationalInstitution)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_234_68", "NL_sentence": "Pierson College is a residential college at Yale.", "FOL_sentence": "ResidentialCollege(piersonCollege) ∧ At(piersonCollege, yaleUniversity)", "label": "True", "corrected": "yes", "correction_explanation": "Identified 'yale' and 'yaleUniversity'", "FOL_sentence_old": "ResidentialCollege(piersonCollege) ∧ At(piersonCollege, yale)", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "story_120", "NL_sentence": "Badults is a British Sitcom series starring members of Pappy's. Badults was piloted in July 2013 on BBC Three. The working title 'The Secret Dude Society' was used for Badults. Andrew Collins was the script editor for Badults.", "FOL_sentence": "∃x (BritishSitcom(badults) ∧ Series(badults) ∧ MemberOf(x, pappys) ∧ Star(x, badults)) ∧ PilotedIn(badults, july2013) ∧ PilotedOn(badults, bBCThree) ∧ WorkingTitle(theSecretDudeSociety, badults) ∧ UsedFor(theSecretDudeSociety, badults) ∧ ScriptEditorFor(andrewCollins, badults)", "corrected": "yes", "corerection_explanation": "ontology_correction", "FOL_sentence_old": "∃x (BritishSitcom(badults) ∧ Series(badults) ∧ MemberOf(x, pappys) ∧ Starring(badults, x))\nPilotedIn(badults, july2013) ∧ PilotedOn(badults, bBCThree)\nWorkingTitle(theSecretDudeSociety, badults) ∧ UsedFor(theSecretDudeSociety, badults)\nScriptEditorFor(andrewCollins, badults)"} | |
| {"id": "concl_120_69", "NL_sentence": "Andrew Collins was the script editor for a series with the working title 'The Secret Dude Society'.", "FOL_sentence": "∃x (ScriptEditorFor(andrewCollins, x) ∧ Series(x) ∧ WorkingTitle(theSecretDudeSociety, x))", "label": "True", "corrected": "no", "FOL_sentence_old": "∃x (ScriptEditorFor(andrewCollins, x) ∧ Series(x) ∧ WorkingTitle(theSecretDudeSociety, x))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_120_70", "NL_sentence": "No members of Pappy's have starred in a show piloting on BBC Two or BBC Three.", "FOL_sentence": "∀x ∀y (MemberOf(x, pappys) ∧ Star(x, y) → ¬(PilotedOn(y, bBCTwo) ∨ PilotedOn(y, bBCThree)))", "label": "False", "corrected": "no", "FOL_sentence_old": "∀x ∀y (MemberOf(x, pappys) ∧ Starring(y, x) → ¬(PilotedOn(y, bBCTwo) ∨ PilotedOn(y, bBCThree)))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_322", "NL_sentence": "All growth stocks are bought to earn profits from rapid price appreciation. If a stock is bought to earn profits from rapid price appreciation, then it is not suitable for a retirement fund. Some stocks are growth stocks. All mature stocks are suitable for a retirement fund. KO is a mature stock.", "FOL_sentence": "∀x ((Stock(x) ∧ Growth(x)) → BoughtToEarnProfitFrom(x, rapidPriceAppreciation)) ∧ ∀x ((Stock(x) ∧ BoughtToEarnProfitFrom(x, rapidPriceAppreciation)) → ¬SuitableFor(x, retirementFund)) ∧ ∃x (Stock(x) ∧ Growth(x)) ∧ ∀x ((Stock(x) ∧ Mature(x)) → SuitableFor(x, retirementFund)) ∧ Stock(kO) ∧ Mature(kO)", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "some_plural", "correction_explanation": "1. Compositional Semantics / Translation Failure: Based on the insight that 'growth stock' and 'mature stock' intrinsically imply being a 'stock', the monolithic predicates 'GrowthStock(x)' and 'MatureStock(x)' have been decomposed into 'Stock(x) ∧ Growth(x)' and 'Stock(x) ∧ Mature(x)'. This ensures the domain constraint 'Stock' is universally active across all premises. 2. Translation Failure (Premise 2): Added the 'Stock(x)' constraint to match 'If a stock is bought...'. 3. Broken Linkage (Premise 2): Fixed the ternary 'BoughtToEarnProfitFrom' by removing the hallucinated 'earnProfit' argument to match Premise 1.", "FOL_sentence_old": "∀x (GrowthStock(x) → BoughtToEarnProfitFrom(x, rapidPriceAppreciation))\n∀x (BoughtToEarnProfitFrom(x, earnProfit, rapidPriceAppreciation) → ¬SuitableFor(x, retirementFund)) \n∃x (Stock(x) ∧ GrowthStock(x))\n∀x (MatureStock(x) → SuitableFor(x, retirementFund))\nMatureStock(kO)"} | |
| {"id": "concl_322_71", "NL_sentence": "KO is a stock.", "FOL_sentence": "Stock(kO)", "label": "True", "corrected": "no", "correction_explanation": "With the compositional decomposition of 'MatureStock(kO)' into 'Stock(kO) ∧ Mature(kO)' in Premise 5, it is now explicitly established that KO is a stock. The label is therefore corrected from Uncertain to True.", "FOL_sentence_old": "Stock(kO)", "label_old": "Uncertain", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_322_72", "NL_sentence": "KO is a stock and a growth stock.", "FOL_sentence": "Stock(kO) ∧ Growth(kO)", "label": "False", "corrected": "yes", "correction_explanation": "1. Translation Failure: The original FOL '¬GrowthStock(kO)' directly contradicted the positive phrasing of the NL. Corrected to 'Stock(kO) ∧ Growth(kO)' to strictly map the text. 2. Logic Check: The label 'False' is logically sound because assuming KO is a Growth stock triggers a contradiction: Premise 1 forces BoughtToEarnProfitFrom to be true, which (combined with Stock(kO)) forces ¬SuitableFor via Premise 2, directly contradicting the SuitableFor conclusion derived from Premises 4 and 5.", "FOL_sentence_old": "¬GrowthStock(kO)", "label_old": "False", "label_old_z3": "True", "label_z3": "False"} | |
| {"id": "concl_322_73", "NL_sentence": "If KO is a growth stock or bought to earn profits from rapid price appreciation, then KO is neither a stock nor is its price volatile.", "FOL_sentence": "((Stock(kO) ∧ Growth(kO)) ∨ BoughtToEarnProfitFrom(kO, rapidPriceAppreciation)) → (¬Stock(kO) ∧ ¬VolatilePrice(kO))", "label": "True", "corrected": "yes", "correction_explanation": "1. Translation Failure: Applied the 'Stock ∧ Growth' decomposition. 2. Broken Linkage: Fixed the ternary 'BoughtToEarnProfitFrom' predicate to binary. 3. Translation Failure: Replaced '¬BoughtToEarnProfitFrom' in the consequent with '¬VolatilePrice(kO)' to accurately capture 'nor is its price volatile'. 4. Scope: Added required grouping parentheses around the antecedent. 5. Entailment Logic Evaluation: With the new compositional semantics, Stock(kO) is definitively True, making the consequent definitively False. Because KO is a Stock and is SuitableFor a retirement fund, BoughtToEarnProfitFrom MUST be definitively False (otherwise Premise 2 would trigger a contradiction). By extension, Growth(kO) must also be False. Thus, both sides of the antecedent's disjunction are definitively False, making the material implication vacuously True.", "FOL_sentence_old": "GrowthStock(kO) ∨ BoughtToEarnProfitFrom(kO, earnProfit, rapidPriceAppreciation) → ¬Stock(kO) ∧ ¬BoughtToEarnProfitFrom(kO, rapidPriceAppreciation)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "story_83", "NL_sentence": "All vehicle registration plates in Istanbul begin with the number 34. Plates that do not begin with the number 34 are not from Istanbul. Joe's vehicle registration plate is from Istanbul. Tom's license plate begins with the number 35. If a license plate begins with the number 35, then it does not begin with the number 34.", "FOL_sentence": "∀x (VehicleRegistrationPlateIn(x, istanbul) → BeginWith(x, num34)) ∧ ∀x (¬BeginWith(x, num34) → ¬VehicleRegistrationPlateIn(x, istanbul)) ∧ ∃x (Owns(joe, x) ∧ VehicleRegistrationPlateIn(x, istanbul)) ∧ ∃x ∃y (Owns(tom, x) ∧ VehicleRegistrationPlateIn(x, y) ∧ BeginWith(x, num35)) ∧ ∀x (BeginWith(x, num35) → ¬BeginWith(x, num34))", "corrected": "yes", "correction_explanation": "Broken Linkage (Premise 2): The original FOL used 'FromIstanbul(x)', which disconnected it from the 'VehicleRegistrationPlateIn(x, istanbul)' predicate used in Premise 1, Premise 3, and Conclusion 75. Unified the predicate to 'VehicleRegistrationPlateIn(x, istanbul)' to allow the logical chain to resolve. Note: The previous reviewer correctly identified this fix in their explanation but failed to actually apply it to the FOL string in their output. It has now been applied.", "FOL_sentence_old": "∀x (VehicleRegistrationPlateIn(x, istanbul) → BeginWith(x, num34))\n∀x (¬BeginWith(x, num34) → ¬FromIstanbul(x))\n∃x (Owns(joe, x) ∧ VehicleRegistrationPlateIn(x, istanbul))\n∃x (Owns(tom, x) ∧ BeginWith(x, num35))\n∀x (BeginWith(x, num35) → ¬BeginWith(x, num34))"} | |
| {"id": "concl_83_74", "NL_sentence": "Joe's license plate begins with the number 34.", "FOL_sentence": "∃x (Owns(joe, x) ∧ BeginWith(x, num34) ∧ ∃y VehicleRegistrationPlateIn(x, y))", "label": "True", "corrected": "yes", "correction_explanation": "There is no referement to x that is a license plate in the original FOL_sentence: given the provided ontology, we can express this information saying that x is a vehicle registration plate in some place", "FOL_sentence_old": "∃x (Owns(joe, x) ∧ BeginWith(x, num34))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_83_75", "NL_sentence": "Tom's license plate is from Istanbul.", "FOL_sentence": "∃x (Owns(tom, x) ∧ VehicleRegistrationPlateIn(x, istanbul))", "label": "False", "corrected": "no", "NLI_requires_more_info": "∀x ∀y ∀z ∀u ((Owns(tom, x) ∧ VehicleRegistrationPlateIn(x, y) ∧ Owns(tom, z) ∧ VehicleRegistrationPlateIn(z, u)) → (x=z ∧ y=u))", "FOL_sentence_old": "∃x (Owns(tom, x) ∧ VehicleRegistrationPlateIn(x, istanbul))", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "story_368", "NL_sentence": "If people at Mary's school work in student jobs on campus, then they need to earn money to help pay for their college tuition. If people at Mary's school order takeout frequently in college, then they work in student jobs on campus. People at Mary's school order takeout frequently in college or enjoy the dining hall meals and recipes. If people at Mary's school enjoy the dining hall meals and recipes, then they are not picky eaters. If people at Mary's school enjoy the dining hall meals and recipes, then they spend a lot of their time eating and catching up with friends in the campus dining halls. Hannah is at Mary's school. Hannah works in student jobs on campus and if she needs to earn money to help pay for her college tuition, then she is neither picky nor needs to earn money to help pay for her college tuition.", "FOL_sentence": "∀x ((At(x, marysSchool) ∧ WorkIn(x, studentJob, campus)) → NeedToEarnMoneyToHelpPayFor(x, collegeTuition)) ∧ ∀x ((At(x, marysSchool) ∧ OrderFrequently(x, takeout)) → WorkIn(x, studentJob, campus)) ∧ ∀x (At(x, marysSchool) → (OrderFrequently(x, takeout) ∨ Enjoy(x, diningHallMeal))) ∧ ∀x ((At(x, marysSchool) ∧ Enjoy(x, diningHallMeal)) → ¬PickyEater(x)) ∧ ∀x ((At(x, marysSchool) ∧ Enjoy(x, diningHallMeal)) → (Spend(x, aLotOfTime, eating, diningHall) ∧ Spend(x, aLotOfTime, catchingUpWithFriends, diningHall))) ∧ At(hannah, marysSchool) ∧ WorkIn(hannah, studentJob, campus) ∧ (NeedToEarnMoneyToHelpPayFor(hannah, collegeTuition) → (¬PickyEater(hannah) ∧ ¬NeedToEarnMoneyToHelpPayFor(hannah, collegeTuition)))", "corrected": "yes", "correction_explanation": "1. Scope & Syntax Error (Premise 3): The original lacked an implication '→', asserting that all entities in the universe are at Mary's school. Corrected to '∀x (At(...) → (Order(...) ∨ Enjoy(...)))'. 2. Translation Failure (Premise 7): The NL says 'Hannah works... AND if she needs...', meaning the 'WorkIn' fact is independent of the conditional. The original FOL erroneously folded it into the antecedent. Corrected to 'WorkIn(...) ∧ (Need(...) → ...)'. Applied De Morgan's to the consequent to accurately match the 'neither... nor...' phrasing.", "FOL_sentence_old": "∀x (At(x, marysSchool) ∧ WorkIn(x, studentJob, campus) → NeedToEarnMoneyToHelpPayFor(x, collegeTuition))\n∀x (At(x, marysSchool) ∧ OrderFrequently(x, takeout) → WorkIn(x, studentJob, campus))\n∀x (At(x, marysSchool) ∧ (OrderFrequently(x, takeout) ∨ Enjoy(x, diningHallMeal)))\n∀x (At(x, marysSchool) ∧ Enjoy(x, diningHallMeal) → ¬PickyEater(x))\n∀x (At(x, marysSchool) ∧ Enjoy(x, diningHallMeal) → Spend(x, aLotOfTime, eating) ∧ Spend(x, aLotOfTime, catchingUpWithFriends, diningHall))\nAt(hannah, marysSchool)\n(WorkIn(hannah, studentJob, campus) ∧ NeedToEarnMoneyToHelpPayFor(hannah, collegeTuition) → ¬(PickyEater(hannah) ∨ NeedToEarnMoneyToHelpPayFor(hannah, collegeTuition))"} | |
| {"id": "concl_368_76", "NL_sentence": "Hannah needs to earn money to help pay for her college tuition.", "FOL_sentence": "NeedToEarnMoneyToHelpPayFor(hannah, collegeTuition)", "label": "True", "corrected": "no", "correction_explanation": "Label corrected from Uncertain to True. The premises contain a logical contradiction: Premise 6 (At) and Premise 7 (WorkIn) trigger Premise 1, which proves NeedToEarnMoney. However, Premise 7 states NeedToEarnMoney → ¬NeedToEarnMoney. This yields NeedToEarnMoney ∧ ¬NeedToEarnMoney. Under the Principle of Explosion in classical logic, contradictory premises allow any statement to be proven True.", "FOL_sentence_old": "NeedToEarnMoneyToHelpPayFor(hannah, collegeTuition)", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "concl_368_77", "NL_sentence": "Hannah is at Mary's school and she is not a picky eater and spends a lot of her time eating and catching up with friends in the campus dining halls.", "FOL_sentence": "At(hannah, marysSchool) ∧ ¬PickyEater(hannah) ∧ Spend(hannah, aLotOfTime, eating, diningHall) ∧ Spend(hannah, aLotOfTime, catchingUpWithFriends, diningHall)", "label": "True", "corrected": "yes", "correction_explanation": "The premises contain a logical contradiction", "FOL_sentence_old": "¬(PickyEater(hannah) ∧ Spend(hannah, aLotOfTime, eating, diningHall) ∧ Spend(hannah, aLotOfTime, catchingUpWithFriends, diningHall))", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "concl_368_78", "NL_sentence": "Hannah is at Mary's school and she either is not a picky eater or, if she is, then she spends a lot of her time eating and catching up with friends in the campus dining halls.", "FOL_sentence": "At(hannah, marysSchool) ∧ (¬PickyEater(hannah) ∨ PickyEater(hannah)) ∧ (PickyEater(hannah) → (Spend(hannah, aLotOfTime, eating) ∧ Spend(hannah, aLotOfTime, catchingUpWithFriends, diningHall)))", "label": "True", "corrected": "yes", "FOL_sentence_old": "PickyEater(hannah) ⊕ (Spend(hannah, aLotOfTime, eating) ∧ Spend(hannah, aLotOfTime, catchingUpWithFriends, diningHall))", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "story_319", "NL_sentence": "No baked sweets are spicy. All cupcakes are baked sweets. All mala hotpots are spicy. All products from Baked by Melissa are cupcakes. Dried Thai chilies are spicy or mala hotpots or not baked sweets.", "FOL_sentence": "∀x (BakedSweet(x) → ¬Spicy(x)) ∧ ∀x (Cupcake(x) → BakedSweet(x)) ∧ ∀x (MalaHotpot(x) → Spicy(x)) ∧ ∀x (Product(x) ∧ From(x, bakedByMelissa) → Cupcake(x)) ∧ (Spicy(driedThaiChili) ∨ MalaHotpot(driedThaiChili)∨ ¬BakedSweet(driedThaiChili))", "corrected": "no", "FOL_sentence_old": "∀x (BakedSweet(x) → ¬Spicy(x))\n∀x (Cupcake(x) → BakedSweet(x))\n∀x (MalaHotpot(x) → Spicy(x))\n∀x (Product(x) ∧ From(x, bakedByMelissa) → Cupcake(x))\nSpicy(driedThaiChili) ∨ MalaHotpot(driedThaiChili)∨ ¬BakedSweet(driedThaiChili)"} | |
| {"id": "concl_319_79", "NL_sentence": "Dried Thai chilies are products of Baked by Melissa.", "FOL_sentence": "Product(driedThaiChili) ∧ From(driedThaiChili, bakedByMelissa)", "label": "False", "corrected": "no", "FOL_sentence_old": "Product(driedThaiChili) ∧ From(driedThaiChili, bakedByMelissa)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_319_80", "NL_sentence": "Dried Thai chilies are not products of Baked by Melissa.", "FOL_sentence": "¬(Product(driedThaiChili) ∧ From(driedThaiChili, bakedByMelissa))", "label": "True", "corrected": "no", "FOL_sentence_old": "¬(Product(driedThaiChili) ∧ From(driedThaiChili, bakedByMelissa))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_319_81", "NL_sentence": "Dried Thai chilies are a mala hotpot.", "FOL_sentence": "MalaHotpot(driedThaiChili)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "MalaHotpot(driedThaiChili)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_319_82", "NL_sentence": "Dried Thai chilies are neither products of Baked by Melissa nor baked sweets.", "FOL_sentence": "¬(Product(driedThaiChili) ∧ From(driedThaiChili, bakedByMelissa)) ∧ ¬BakedSweet(driedThaiChili)", "label": "True", "corrected": "no", "FOL_sentence_old": "¬(Product(driedThaiChili) ∧ From(driedThaiChili, bakedByMelissa)) ∧ ¬BakedSweet(driedThaiChili)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_319_83", "NL_sentence": "Dried Thai chilies are cupcakes and products of Baked by Melissa.", "FOL_sentence": "Cupcake(driedThaiChili) ∧ Product(driedThaiChili) ∧ From(driedThaiChili, bakedByMelissa)", "label": "False", "corrected": "no", "FOL_sentence_old": "Cupcake(driedThaiChili) ∧ Product(driedThaiChili) ∧ From(driedThaiChili, bakedByMelissa)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_306", "NL_sentence": "If a restaurant is listed in Yelp's recommendations, then the restaurant has not received many negative reviews. All restaurants with a rating greater than four are listed in Yelp's recommendations. Some restaurants that do not provide take-out service receive many negative reviews. All restaurants that are popular among local residents have ratings greater than four. The Hamden Plaza Subway store has a rating greater than four, or it is popular among local residents.", "FOL_sentence": "∀x (ListedIn(x, yelpRecommendation) → ¬ReceiveManyNegativeReviews(x)) ∧ ∀x (∃y (HaveRating(x, y) ∧ GreaterThan(y, four)) → ListedIn(x, yelpRecommendation)) ∧ ∃x (¬Provide(x, takeOutService) ∧ ReceiveManyNegativeReviews(x)) ∧ ∀x (PopularAmong(x, localResidents) → ∃y (HaveRating(x, y) ∧ GreaterThan(y, four))) ∧ (∃y (HaveRating(hamdenPlazaSubway, y) ∧ GreaterThan(y, four)) ∨ PopularAmong(hamdenPlazaSubway, localResidents))", "corrected": "yes", "correction_explanation": "(1) Since FOL is not suitable to express ambiguous quantity as 'many' that should be treated as 'at least one' with an existential, it is replaced the formulation '∃y (NegativeReview(y) ∧ Receive(x, y))' with 'ReceiveManyNegativeReviews(x)'. Furthermore, the original formulation '∀x ∃y (ListedIn(x, yelpRecommendation) → NegativeReview(y) ∧ ¬Receive(x, y))' is malformed since there can be a restaurant listed in the yelp reccomandation even when it has negative reviews if we consider as y a negative review that is not received by that specific restaurant.(2) Adjusted the intepretation of 'some' as at least two different entities (two-witness interpretation). (2) Premise 2: the original '∀x ∀y (HaveRating(x, y) ∧ GreaterThan(y, 4) → ListedIn(x, yelpRecommendation))' universally quantifies over y, but a more correct reading is existential (even because it is not specified that there is only on rating). (3) Premise 3: the original '∃x ∃y (¬Provide(x, takeOutService) → NegativeReview(y) ∧ Receive(x, y))' uses a conditional inside existential quantifiers, giving 'there exist x and y such that if x doesn't provide takeout then y is a negative review received by x' — nearly vacuously true, beacuse satisfies even if there are no restaurants than don't provide take-out service with negative reviews (because for holding, we only need to have a restaurant x that provide takeOutService).(4) Premise 5: the original uses ⊕ (exclusive disjunction) but the NL says 'has a rating greater than four, or it is popular among local residents' — a simple inclusive disjunction with no exclusivity implied. Also, the original wraps the left disjunct as '∀x (HaveRating(hamdenPlazaSubway, x) ∧ GreaterThan(x, 4) ⊕ ...)' using universal quantification, which is incorrect — the rating is an existential property. Corrected to inclusive ∨ with existential: '(∃y (HaveRating(hamdenPlazaSubway, y) ∧ GreaterThan(y, 4)) ∨ PopularAmong(hamdenPlazaSubway, localResidents))'.\n Replaced '4' with 'four' to not create conflict with z3-parser", "FOL_sentence_old": "∀x ∃y (ListedIn(x, yelpRecommendation) → NegativeReview(y) ∧ ¬Receive(x, y))\n∀x ∀y (HaveRating(x, y) ∧ GreaterThan(y, 4) → ListedIn(x, yelpRecommendation))\n∃x ∃y (¬Provide(x, takeOutService) → NegativeReview(y) ∧ Receive(x, y))\n∀x ∀y (PopularAmong(x, localResidents) → HaveRating(x, y) ∧ GreaterThan(y, 4))\n∀x (HaveRating(hamdenPlazaSubway, x) ∧ GreaterThan(x, 4) ⊕ PopularAmong(hamdenPlazaSubway, localResidents))"} | |
| {"id": "concl_306_84", "NL_sentence": "If the Hamden Plaza Subway store provides take-out service and receives many negative reviews, then its rating is greater than 4 and it does not provide take-out service.", "FOL_sentence": "(Provide(hamdenPlazaSubway, takeOutService) ∧ ReceiveManyNegativeReviews(hamdenPlazaSubway)) → (∃y (HaveRating(hamdenPlazaSubway, y) ∧ GreaterThan(y, four)) ∧ ¬Provide(hamdenPlazaSubway, takeOutService))", "label": "True", "corrected": "yes", "correction_explanation": "Three issues in the original FOL: (1) Unclosed parenthesis: the original '∃x ((TakeOutService(...) ∧ ... → ...)' has a misplaced opening parenthesis after ∃x, incorrectly scoping the entire conditional under the existential quantifier. The existential should only scope over the negative review variable x, not over the whole implication. Corrected by restructuring as a top-level conditional with ∃x scoped only over the NegativeReview conjunct. (2) The original consequent uses 'PopularAmong(hamdenPlazaSubway, localResidents)' but the NL says 'its rating is greater than 4' — these are entirely different properties. Corrected to 'RatingGreaterThan(hamdenPlazaSubway, 4)' to match the NL. (3) The original antecedent uses 'TakeOutService(hamdenPlazaSubway)' as a unary predicate (the store IS a takeout service) while the NL and consequent use 'Provide(hamdenPlazaSubway, takeOutService)' as a binary predicate (the store PROVIDES takeout service). Unified to use 'Provide(hamdenPlazaSubway, takeOutService)' in the antecedent for consistency with the consequent and the NL.", "FOL_sentence_old": "∃x ((TakeOutService(hamdenPlazaSubway) ∧ NegativeReview(x) ∧ Receive(hamdenPlazaSubway, x) → PopularAmong(hamdenPlazaSubway, localResidents) ∧ ¬Provide(hamdenPlazaSubway, takeOutService))", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "concl_306_85", "NL_sentence": "The Hamden Plaza Subway store provides take-out service or does not receive many negative reviews.", "FOL_sentence": "Provide(hamdenPlazaSubway, takeOutService) ∨ ¬ReceiveManyNegativeReviews(hamdenPlazaSubway)", "label": "True", "corrected": "yes", "correction_explanation": "ontology : two issues in the original: (1) The original wraps the entire disjunction under '∃x (...)', making it 'there exists a review x such that (Provide ∨ (NegativeReview(x) ∧ ¬Receive(...)))'. The existential is misplaced — 'Provide(hamdenPlazaSubway, takeOutService)' does not depend on x, and the second disjunct should express 'does not receive many negative reviews' as a negated existential rather than a positive existential with ¬Receive. Corrected to a top-level disjunction: 'Provide(hamdenPlazaSubway, takeOutService) ∨ ¬∃x (NegativeReview(x) ∧ Receive(hamdenPlazaSubway, x))'. (2) The label 'True' is derivable: premise 5 (corrected) gives either HaveRating > 4 or PopularAmong, both of which via premises 4→2 or directly via premise 2 yield ListedIn(hamdenPlazaSubway, yelpRecommendation), which by corrected premise 1 gives ¬∃y (NegativeReview(y) ∧ Receive(hamdenPlazaSubway, y)) — satisfying the second disjunct of the conclusion.", "FOL_sentence_old": "∃x (Provide(hamdenPlazaSubway, takeOutService) ∨ (NegativeReview(x) ∧ ¬Receive(hamdenPlazaSubway, x)))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_306_86", "NL_sentence": "The Hamden Plaza store does not provide take-out service.", "FOL_sentence": "¬Provide(hamdenPlazaSubway, takeOutService)", "label": "Uncertain", "corrected": "no", "note": "The label 'Uncertain' is correct: nothing in the premises establishes whether or not Hamden Plaza Subway provides take-out service. Premise 3 asserts that SOME restaurants without take-out service receive negative reviews, but this does not constrain Hamden Plaza Subway specifically. The conclusion is neither provable nor refutable.", "FOL_sentence_old": "¬Provide(hamdenPlazaSubway, takeOutService)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_245", "NL_sentence": "In superhero movies, the good guys always win. The Surprising Adventures of Sir Digby Chicken Caesar is a superhero movie. Good guys fight bad guys and vice versa. Sir Digby fights his nemesis. If a superhero movie is named after a character, that character is a good guy. The Surprising Adventures of Sir Digby Chicken Caesar is named after Sir Digby. If somebody wins a fight, the person they are fighting does not win. If a superhero movie is named after a character, that character is in the movie.", "FOL_sentence": "∀x ∀y (SuperheroMovie(x) ∧ In(y, x) ∧ GoodGuy(y) → Wins(y)) ∧ SuperheroMovie(theSurprisingAdventuresOfSirDigbyChickenCaesar) ∧ ∀x ∀y ((GoodGuy(x) ∧ BadGuy(y)) → (Fight(x, y) ∧ Fight(y, x))) ∧ Fight(sirDigby, sirDigbysNemesis) ∧ ∀x ∀y (SuperheroMovie(x) ∧ NamedAfter(x, y) → GoodGuy(y)) ∧ NamedAfter(theSurprisingAdventuresOfSirDigbyChickenCaesar, sirDigby) ∧ ∀x ∀y (Fight(x, y) ∧ Wins(x) → ¬Wins(y)) ∧ ∀x ∀y (SuperheroMovie(x) ∧ NamedAfter(x, y) → In(y, x))", "corrected": "yes", "correction_explanation": "(1) The original translation for Premise 3 is '∀x ∀y (GoodGuy(x) ∧ Fight(x, y) ↔ BadGuy(y) ∧ Fight(y, x))', that holds also when there are a good guy and a bad guy that don't fight each other (both the parts of the bi-implication are false); it is replaced with '∀x ∀y ((GoodGuy(x) ∧ BadGuy(y)) → (Fight(x, y) ∧ Fight(y, x)))', intended as ALL good guys fight bad guys (usually this is the menaning retained by this construct. (The conclusion labels are not affected by this formalization choice, even if some information that may be conceived by the author (like that if a good guy is fighting with another guy, then the latter is a bad guy) can lack with this formalization. [NOTE: if a different formalization doesn't affect the conclusion, this means that this formalization is not tested by the FOLIO approach!] (2) Premise 7: the original uses two different predicate names — 'Fights(x, y)' in the antecedent and 'Wins(y)' in the consequent, while premise 1 uses 'Wins(y)' and premise 4 uses 'Fight(x, y)' (without the trailing 's'). The predicate 'Fights' is a typo/inconsistency; corrected to 'Fight(x, y)' to unify with the predicate used in premises 3 and 4. (3) Premise 7: the original uses 'Win(x)' in the antecedent but 'Wins(y)' in the consequent — two different predicate names for the same concept. Unified to 'Wins' throughout for consistency with premise 1. (4) Constant casing: the original uses 'theSurprisingAdventuresofSirDigbyChickenCaesar' (lowercase 'of') in some places; normalised to 'theSurprisingAdventuresOfSirDigbyChickenCaesar' (camelCase 'Of') consistently throughout.", "FOL_sentence_old": "∀x ∀y (SuperheroMovie(x) ∧ In(y, x) ∧ GoodGuy(y) → Wins(y))\nSuperheroMovie(theSurprisingAdventuresofSirDigbyChickenCaesar)\n∀x ∀y (GoodGuy(x) ∧ Fight(x, y) ⟷ BadGuy(y) ∧ Fight(y, x))\nFight(sirDigby, sirDigbysNemesis)\n∀x ∀y (SuperheroMovie(x) ∧ NamedAfter(x, y) → GoodGuy(y))\nNamedAfter(theSurprisingAdventuresofSirDigbyChickenCaesar, sirDigby)\n∀x ∀y (Fights(x, y) ∧ Win(x) → ¬Wins(y))\n∀x ∀y (SuperheroMovie(x) ∧ NamedAfter(x, y) → In(y, x))"} | |
| {"id": "concl_245_87", "NL_sentence": "Sir Digby's nemesis does not win.", "FOL_sentence": "¬Wins(sirDigbysNemesis)", "label": "True", "corrected": "yes", "correction_explanation": "The original uses '¬Win(sirDigbysNemesis)' with the predicate 'Win' (without trailing 's'), inconsistent with 'Wins' used in premises 1 and 7. Corrected to '¬Wins(sirDigbysNemesis)' for consistency.", "FOL_sentence_old": "¬Win(sirDigbysNemesis)", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "story_58", "NL_sentence": "Books contain tons of knowledge. When a person reads a book, that person gains knowledge. If a person gains knowledge, they become smarter. Harry read the book 'Walden' by Henry Thoreau.", "FOL_sentence": "∀x (Book(x) → Contains(x, knowledge)) ∧ ∀x ∀y (Book(x) ∧ ReadBook(y, x) → Gains(y, knowledge)) ∧ ∀x (Gains(x, knowledge) → Smarter(x)) ∧ ReadBook(harry, walden) ∧ Book(walden)", "corrected": "yes", "correction_explanation": "Added Book(x) in the seecond premises. One consideration: premise 4 in the original reads 'ReadBook(harry, walden) ∧ Book(walden)' — while 'Book(walden)' is not explicitly stated as a separate premise in the NL ('Harry read the book Walden' implies walden is a book), it is a reasonable and necessary grounding fact for the chain of reasoning to work (premise 1 requires Book(x) to fire). The original FOL correctly includes it as a conjunct in premise 4, so it is retained. However, note that premise 2 uses 'ReadBook(x, y)' without requiring Book(y) in the antecedent — meaning any ReadBook fact triggers Gains(x, knowledge) regardless of whether y is a book. This is a minor semantic looseness inherited from the original but not corrected as it does not affect the conclusions.", "FOL_sentence_old": "∀x (Book(x) → Contains(x, knowledge))\n∀x ∀y (ReadBook(x, y) → Gains(x, knowledge))\n∀x (Gains(x, knowledge) → Smarter(x))\nReadBook(harry, walden) ∧ Book(walden)"} | |
| {"id": "concl_58_88", "NL_sentence": "Walden contains knowledge.", "FOL_sentence": "Contains(walden, knowledge)", "label": "True", "corrected": "yes", "correction_explanation": "Significant NL/FOL mismatch in the original.", "note": "The original FOL 'Gains(harry, knowledge)' would also be True (derivable from premise 4 via premise 2), but it corresponds to conclusion 89's content rather than conclusion 88's NL. The two conclusions appear to have had their FOL formulas swapped or mislabelled in the original dataset.", "FOL_sentence_old": "Gains(harry, knowledge)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_58_89", "NL_sentence": "Harry is smarter than before.", "FOL_sentence": "Smarter(harry)", "label": "True", "corrected": "no", "FOL_sentence_old": "Smarter(harry)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_58_90", "NL_sentence": "A smarter person has gained knowledge.", "FOL_sentence": "∀x (Smarter(x) → Gains(x, knowledge))", "label": "Uncertain", "corrected": "yes", "correction_explanation": "The original FOL uses 'GainKnowledge(x)' as a unary predicate, which is inconsistent with the binary predicate 'Gains(x, knowledge)' used throughout the premises. The NL 'has gained knowledge' corresponds directly to 'Gains(x, knowledge)'; corrected to '∀x (Smarter(x) → Gains(x, knowledge))' for consistency.", "ambiguity": true, "ambiguity_explanation": "existential_universal", "note": "The label 'Uncertain' is correct: the premises only establish Smarter as a consequence of Gains (premise 3: Gains → Smarter), not the converse.", "FOL_sentence_old": "∀x (Smarter(x) → GainKnowledge(x))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_191", "NL_sentence": "A natural language processing task can be categorized as either a language generation task or a language understanding task. If the output of a natural language processing task is a text sequence, then it is a language generation task. Machine translation is a natural language processing task. The output of machine translation is a text sequence.", "FOL_sentence": "∀x (NaturalLanguageProcessingTask(x) ↔ LanguageGenerationTask(x) ⊕ LanguageUnderstandingTask(x)) ∧ ∀x (NaturalLanguageProcessingTask(x) ∧ OutputSequence(x, text) → LanguageGenerationTask(x)) ∧ NaturalLanguageProcessingTask(machineTranslation) ∧ OutputSequence(machineTranslation, text)", "corrected": "yes", "correction_explanation": "Ontology. One correction made: premise 2 in the original uses 'NaturalLanguageProcessingTasks(x)' (plural, with trailing 's') as the predicate name, inconsistent with 'NaturalLanguageProcessingTask(x)' (singular) used in premises 1, 3 and the conclusions. This is a typo that would make premise 2 refer to a completely different predicate, disconnecting the reasoning chain. Corrected to 'NaturalLanguageProcessingTask(x)' throughout.", "FOL_sentence_old": "∀x (NaturalLanguageProcessingTask(x) → LanguageGenerationTask(x) ⊕ LanguageUnderstandingTask(x))\n∀x (NaturalLanguageProcessingTasks(x) ∧ OutputSequence(x, text) → LanguageGenerationTask(x))\nNaturalLanguageProcessingTask(machineTranslation)\nOutputSequence(machineTranslation, text)"} | |
| {"id": "concl_191_91", "NL_sentence": "Machine translation is a language generation task.", "FOL_sentence": "LanguageGenerationTask(machineTranslation)", "label": "True", "corrected": "no", "FOL_sentence_old": "LanguageGenerationTask(machineTranslation)", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "concl_191_92", "NL_sentence": "Machine translation is a language understanding task.", "FOL_sentence": "LanguageUnderstandingTask(machineTranslation)", "label": "False", "corrected": "no", "note": "The label 'False' is correct under the exclusive disjunction (⊕) reading of premise 1.", "FOL_sentence_old": "LanguageUnderstandingTask(machineTranslation)", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "story_166", "NL_sentence": "Pets are allowed in some managed buildings. A deposit is required to rent an apartment in a managed building. The security deposit can be either equal to the monthly rent at a managed building or more. Fluffy is Tom's cat. Cats are pets. The Olive Garden is a managed building. The monthly rent at the Olive Garden is $2000. $2000 is more than $1500. Tom will rent an apartment in a managed building if he is allowed to move in with Fluffy, and the security deposit is no more than $1500. If a managed building allows pets, then people are allowed to move in with a pet.", "FOL_sentence": "∃x (ManagedBuilding(x) ∧ AllowPet(x)) ∧ ∀x ∀y (ManagedBuilding(x) ∧ RentApartmentIn(y, x) → DepositRequired(y)) ∧ ∀x ∀y ∀z ((SecurityDeposit(x, z) ∧ ManagedBuilding(z) ∧ MonthlyRentAt(y, z)) → (MoreThan(x, y) ⊕ Equal(x, y))) ∧ Cat(fluffy) ∧ BelongTo(fluffy, tom) ∧ ∀x (Cat(x) → Pet(x)) ∧ ManagedBuilding(oliveGarden) ∧ MonthlyRentAt(uSD2000, oliveGarden) ∧ MoreThan(uSD2000, uSD1500) ∧ ∀x ∀y (ManagedBuilding(x) ∧ AllowedToMoveInWith(tom, x, fluffy) ∧ SecurityDeposit(y, x) ∧ ¬MoreThan(y, uSD1500) → RentApartmentIn(tom, x)) ∧ ∀x ∀y ∀z (ManagedBuilding(x) ∧ AllowPet(x) ∧ Pet(z) → AllowedToMoveInWith(y, x, z))", "corrected": "yes", "correction_explanation": "(1) It is used the two-witness choice to indicate 'some buildings': this makes the instance uniform to the other similar instances that used this grammatical construct (in the original dataset, the construct is treated inconsistently, one time with the two-witness choice, and another time with the single one). This doesn't affect the conclusions labels, so it is not considered as a correction. (2) Fixed the unclosed parenthesis in the original. (3) Premise 3 also implicitly treats SecurityDeposit as a unary predicate (one argument), but conclusion 95 uses it as a binary predicate 'SecurityDeposit(x, oliveGarden)'. This inconsistency is resolved by considering it as a binary predicate also in the premises.", "ambiguity": true, "ambiguity_explanation": "either_or, 'Tom will rent an apartment in a managed building if he is allowed to move in with Fluffy, and the security deposit is no more than $1500.' should be treated as an implication of sufficient conditions or we mean that if he is not allowed to move in with Fluffy then he will not rent the house? This affect the concl_166_93", "FOL_sentence_old": "∃x (ManagedBuilding(x) ∧ AllowPet(x))\n∀x ∀y (ManagedBuilding(x) ∧ RentApartmentIn(y, x) → DepositRequired(y))\n∀x ∀y ∀z (SecurityDeposit(x) ∧ ManagedBuilding(z) ∧ MonthlyRentAt(y, z) → (MoreThan(x, y) ⊕ Equal(x, y))\nCat(fluffy) ∧ BelongTo(fluffy, tom)\n∀x (Cat(x) → Pet(x))\nManagedBuilding(oliveGarden)\nMonthlyRentAt(uSD2000, oliveGarden)\nMoreThan(uSD2000, uSD1500)\n∀x ∀y (ManagedBuilding(x) ∧ AllowedToMoveInWith(tom, x, fluffy) ∧ SecurityDeposit(y) ∧ ¬MoreThan(y, uSD1500) → RentApartmentIn(tom, x))\n∀x ∀y ∀z (ManagedBuilding(x) ∧ AllowPet(x) ∧ Pet(z) → AllowedToMoveInWith(y, x, z))"} | |
| {"id": "concl_166_93", "NL_sentence": "Tom will rent an apartment in The Olive Garden.", "FOL_sentence": "RentApartmentIn(tom, oliveGarden)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "RentApartmentIn(tom, oliveGarden)", "label_old": "False", "label_mismatch_explanation": "see correction_explanation of story_166 that explains the label mismatch", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_166_94", "NL_sentence": "Tom is allowed to move into an apartment in The Olive Garden with Fluffy.", "FOL_sentence": "AllowedToMoveInWith(tom, oliveGarden, fluffy)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "AllowedToMoveInWith(tom, oliveGarden, fluffy)", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_166_95", "NL_sentence": "The security deposit at the Olive Garden is either $2000 or more.", "FOL_sentence": "∀x (SecurityDeposit(x, oliveGarden) → (MoreThan(x, uSD2000) ⊕ Equal(x, uSD2000)))", "label": "True", "corrected": "no", "ambiguity": true, "ambiguity_explanation": "either_or", "correction_explanation": "The binary form is more precise and appropriate for conclusion 95 (it specifies the deposit AT Olive Garden), and is arguably the better modelling choice throughout.", "FOL_sentence_old": "∀x (SecurityDeposit(x, oliveGarden) → MoreThan(x, uSD2000) ⊕ Equal(x, uSD2000))", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "story_352", "NL_sentence": "All business organizations are legal entities. All companies are business organizations. All private companies are companies. All legal entities are created under law. All legal entities have legal obligations. If the Harvard Weekly Book Club is created under law, then it is not a private company.", "FOL_sentence": "∀x (BusinessOrganization(x) → LegalEntity(x)) ∧ ∀x (Company(x) → BusinessOrganization(x)) ∧ ∀x (PrivateCompany(x) → Company(x)) ∧ ∀x (LegalEntity(x) → CreatedUnderLaw(x)) ∧ ∀x (LegalEntity(x) → LegalObligation(x)) ∧ (CreatedUnderLaw(harvardWeeklyBookClub) → ¬PrivateCompany(harvardWeeklyBookClub))", "corrected": "no", "FOL_sentence_old": "∀x (BusinessOrganization(x) → LegalEntity(x))\n∀x (Company(x) → BusinessOrganization(x))\n∀x (PrivateCompany(x) → Company(x))\n∀x (LegalEntity(x) → CreatedUnderLaw(x))\n∀x (LegalEntity(x) → LegalObligation(x))\nCreatedUnderLaw(harvardWeeklyBookClub) → ¬PrivateCompany(harvardWeeklyBookClub)"} | |
| {"id": "concl_352_96", "NL_sentence": "The Harvard Weekly Book Club has legal obligations.", "FOL_sentence": "LegalObligation(harvardWeeklyBookClub)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "LegalObligation(harvardWeeklyBookClub)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_352_97", "NL_sentence": "The Harvard Weekly Book Club has legal obligations and is a private company.", "FOL_sentence": "LegalObligation(harvardWeeklyBookClub) ∧ PrivateCompany(harvardWeeklyBookClub)", "label": "False", "corrected": "no", "note": "The label 'False' is correct: as established in the story note, PrivateCompany(harvardWeeklyBookClub) is refutable via the contradiction chain (PrivateCompany → ... → CreatedUnderLaw → ¬PrivateCompany). Since the second conjunct is False, the conjunction is False regardless of the truth value of LegalObligation(harvardWeeklyBookClub).", "FOL_sentence_old": "LegalObligation(harvardWeeklyBookClub) ∧ PrivateCompany(harvardWeeklyBookClub)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_352_98", "NL_sentence": "If the Harvard Weekly Book Club is a private company, then it either has legal obligations or is created under law.", "FOL_sentence": "PrivateCompany(harvardWeeklyBookClub) → (LegalObligation(harvardWeeklyBookClub) ⊕ CreatedUnderLaw(harvardWeeklyBookClub))", "label": "True", "corrected": "no", "correction_explanation": "The original FOL omits the outer parentheses around the full implication, which could cause precedence ambiguity with the ⊕ operator potentially binding more tightly than →. Added explicit parentheses to scope the implication unambiguously", "ambiguity": true, "ambiguity_explanation": "either_or", "FOL_sentence_old": "PrivateCompany(harvardWeeklyBookClub) → LegalObligation(harvardWeeklyBookClub) ⊕ CreatedUnderLaw(harvardWeeklyBookClub)", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "story_472", "NL_sentence": "Animals are either invertebrates or vertebrates. All animals with backbones reproduce by male-and-female mating. All vertebrate animals have a backbone. All bees do not reproduce by male-and-female mating. All queen bees are bees. Harry is a bee.", "FOL_sentence": "∀x (Animal(x) → Invertebrate(x) ⊕ Vertebrate(x)) ∧ ∀x (Animal(x) ∧ HasBackbone(x) → ReproduceBy(x, maleAndFemaleMating)) ∧ ∀x (Animal(x) ∧ Vertebrate(x) → HasBackbone(x)) ∧ ∀x (Bee(x) → ¬ReproduceBy(x, maleAndFemaleMating)) ∧ ∀x (QueenBee(x) → Bee(x)) ∧ Bee(harry) ∧ ∀x (Bee(x) → Animal(x))", "corrected": "yes", "correction_explanation": "Renamed only constants and predicate symbols (no correction, but suggestion). Added the formula '∀x (Bee(x) → Animal(x))' because needed for the conclusions 100 and 101 to work with the label given by the authors.", "ambiguity": true, "ambiguity_explanation": "either_or", "FOL_sentence_old": "∀x (Animal(x) → Invertebrate(x) ⊕ Vertebrate(x))\n∀x (Animal(x) ∧ With(x, backbone) → ReproduceBy(x, male-and-femaleMating))\n∀x (Animal(x) ∧ Vertebrate(x) → With(x, backbone))\n∀x (Bee(x) → ¬ReproduceBy(x, male-and-femaleMating))\n∀x (QueenBee(x) → Bee(x))\nBee(harry)"} | |
| {"id": "concl_472_99", "NL_sentence": "Harry is a queen bee.", "FOL_sentence": "QueenBee(harry)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "QueenBee(harry)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_472_100", "NL_sentence": "Harry is an invertebrate or a queen bee.", "FOL_sentence": "Invertebrate(harry) ∨ QueenBee(harry)", "label": "True", "corrected": "no", "correction_explanation": "The label 'True' is only derivable if Bee(x) → Animal(x) is assumed as a background axiom (not stated in the premises). If this assumption is made, then Invertebrate(harry) follows and the disjunction is True. Without it, the label should arguably be 'Uncertain'. This missing axiom is a gap in the premise set and we added it in the premises.", "FOL_sentence_old": "Invertebrate(harry) ∨ QueenBee(harry)", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "concl_472_101", "NL_sentence": "If Harry is either both a vertebrate and an animal with a backbone, or neither a vertebrate nor an animal with a backbone, then Harry is neither an invertebrate nor a queen bee.", "FOL_sentence": "((Vertebrate(harry) ∧ HasBackbone(harry)) ∨ (¬Vertebrate(harry) ∧ ¬HasBackbone(harry))) → (¬Invertebrate(harry) ∧ ¬QueenBee(harry))", "label": "False", "corrected": "yes", "correction_explanation": "Three issues in the original: (1) The original FOL '¬(Invertebrate(harry) ⊕ With(harry, backbone))' uses Invertebrate instead of Vertebrate in the antecedent — a predicate substitution error inconsistent with the NL which refers to 'vertebrate'. Corrected to '¬(Vertebrate(harry) ⊕ HasBackbone(harry))'. (2) The predicate 'With(harry, backbone)' corrected to 'HasBackbone(harry)' as per the premise corrections. (3) Added outer parentheses for unambiguous scoping of the full conditional.", "note": "The label 'False' requires analysis: the antecedent ¬(Vertebrate(harry) ⊕ HasBackbone(harry)) is true when Harry is either both a vertebrate and has a backbone, or neither. As established in conclusion 100 (assuming Animal(harry)), Harry is an invertebrate — meaning ¬Vertebrate(harry) and, since HasBackbone implies being reproduced by male-female, then it can't be. This means Vertebrate and HasBackbone are both false, satisfying the 'neither' case, making the antecedent true. The consequent requires ¬Invertebrate(harry) ∧ ¬QueenBee(harry). But Invertebrate(harry) holds (from the Animal(harry) assumption chain), making ¬Invertebrate(harry) false, and thus the consequent false. A true antecedent with a false consequent makes the conditional False — consistent with the label.", "FOL_sentence_old": "¬(Invertebrate(harry) ⊕ With(harry, backbone)) → ¬Invertebrate(harry) ∧ ¬QueenBee(harry)", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "story_379", "NL_sentence": "People who are born in a multiple birth with siblings spend a lot of time hanging out with and playing with their siblings. If people have siblings who were born together, then they were born in a multiple birth. If people complain often about annoying siblings, then they have siblings who were born together. If people live at home, then they do not live with strangers. If people spend a lot of time hanging out with and playing with their siblings, then they often live at home. Luke either is a baby born in a multiple birth and lives with strangers, or is not a baby born in a multiple birth and does not live with strangers.", "FOL_sentence": "∀x (BornIn(x, multipleBirth) → SpendTimePlayingWith(x, siblings)) ∧ ∀x (∃y (Sibling(x, y) ∧ BornTogether(x, y)) → BornIn(x, multipleBirth)) ∧ ∀x (ComplainAboutOften(x, annoyingSiblings) → ∃y (Sibling(x, y) ∧ BornTogether(x, y))) ∧ ∀x (LiveAt(x, home) → ¬LiveWith(x, strangers)) ∧ ∀x (SpendTimePlayingWith(x, siblings) → LiveAt(x, home)) ∧ ¬(BornIn(luke, multipleBirth) ⊕ LiveWith(luke, strangers))", "corrected": "yes", "correction_explanation": "Four corrections made: (1) Premise 1: the original uses 'SpendTimePlayingWith(x, sibling)' (singular 'sibling') while premise 5 uses 'SpendTimeplayingWith(x, sibling)' (lowercase 'p' in 'playing'). Both refer to the same relation; unified to 'SpendTimePlayingWith(x, siblings)' with consistent camelCase and plural 'siblings' to match the NL 'their siblings'. (2) Premise 5: 'SpendTimeplayingWith' (lowercase 'p') corrected to 'SpendTimePlayingWith' (uppercase 'P') for camelCase consistency. (3) BornTogether has now arity 2 and not 1.", "FOL_sentence_old": "∀x (BornIn(x, multipleBirth) → SpendTimePlayingWith(x, sibling))\n∀x (∃y (Sibling(x, y) ∧ BornTogether(y)) → BornIn(x, multipleBirth))\n∀x (ComplainAboutOften(x, annoyingSiblings) → ∃y (Sibling(x, y) ∧ BornTogether(y)))\n∀x (LiveAt(x, home) → ¬LiveWith(x, strangers))\n∀x (SpendTimeplayingWith(x, sibling) → LiveAt(x, home))\n¬(BornIn(luke, multipleBirth) ⊕ LiveWith(luke, strangers))"} | |
| {"id": "concl_379_102", "NL_sentence": "Luke spends a lot of time hanging out and playing with his siblings.", "FOL_sentence": "SpendTimePlayingWith(luke, siblings)", "label": "Uncertain", "corrected": "yes", "FOL_sentence_old": "SpendTime(luke, playingWith, siblings)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_379_103", "NL_sentence": "Luke complains often about annoying siblings.", "FOL_sentence": "ComplainAboutOften(luke, annoyingSiblings)", "label": "False", "corrected": "no", "note": "The label 'False' is correct via the following chain: if ComplainAboutOften(luke, annoyingSiblings) held, then by premise 3, ∃y (Sibling(luke, y) ∧ BornTogether(y)), and by premise 2, BornIn(luke, multipleBirth). By premise 1, SpendTimePlayingWith(luke, siblings). By premise 5, LiveAt(luke, home). By premise 4, ¬LiveWith(luke, strangers). But premise 6 (XNOR) with BornIn(luke, multipleBirth) = true requires LiveWith(luke, strangers) = true — contradiction. Therefore ComplainAboutOften(luke, annoyingSiblings) is refutable.", "FOL_sentence_old": "ComplainAboutOften(luke, annoyingSiblings)", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "concl_379_104", "NL_sentence": "Luke is neither born in a multiple birth nor complains often about annoying siblings.", "FOL_sentence": "¬BornIn(luke, multipleBirth) ∧ ¬ComplainAboutOften(luke, annoyingSiblings)", "label": "True", "corrected": "yes", "correction_explanation": "Two issues in the original: (1) The original FOL uses '¬(BornIn(luke, multipleBirth) ∨ ComplainAbout(luke, often, annoyingSiblings))' — equivalent by De Morgan to '¬BornIn ∧ ¬ComplainAbout', which correctly represents 'neither... nor...'. However, the predicate name 'ComplainAbout(luke, often, annoyingSiblings)' is a ternary decomposition inconsistent with the binary 'ComplainAboutOften(x, annoyingSiblings)' used in premise 3 and conclusion 103. Corrected to use the binary predicate.", "FOL_sentence_old": "¬(BornIn(luke, multipleBirth) ∨ ComplainAbout(luke, often, annoyingSiblings) )", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "story_197", "NL_sentence": "It costs $205 to take the GRE test, which is cheaper than $300. ETS provides financial aid to those GRE applicants who prove economic hardship. Those living in single-parent families or having few resources available to them can prove economic hardship. Tom lives in a single-parent family. Tom's dad has been out of work, and Tom has few resources available to him. Tom is applying to take the GRE test.", "FOL_sentence": "Cost(gre, uSD205) ∧ Cheaper(uSD205, uSD300) ∧ ∀x (ApplicantOf(x, gre) ∧ Prove(x, economicHardship) → ProvideTo(ets, financialAid, x)) ∧ ∀x (LivingIn(x, singleParentFamily) ∨ AvailableTo(fewResources, x) → Prove(x, economicHardship)) ∧ LivingIn(tom, singleParentFamily) ∧ OutOfWork(tomsDad) ∧ AvailableTo(fewResources, tom) ∧ ApplicantOf(tom, gre)", "corrected": "yes", "correction_explanation": "Some corrections made: (1) Constant naming: the original uses bare numerals '205' and '300' as FOL constants: changed to 'uSD205' and 'uSD300' with a prefix to comply with FOL syntax. Similarly 'gRE' uses an inconsistent capitalisation pattern; normalised to 'gre' throughout. (2) Premise 2: the original uses 'ProvideTo(ets, financialAid, x)' as a ternary predicate, while conclusion 105 uses 'ProvidesFinancialAidTo(eTS, tom)' as a binary predicate — two different predicates for the same relation. Unified to 'ProvideTo(ets, financialAid, x)' in the premises (ternary form retained as it encodes both the provider, the aid type, and the recipient), and conclusion 105 corrected accordingly.", "FOL_sentence_old": "Cost(gRE, 205) ∧ Cheaper(205, 300)\n∀x (ApplicantOf(x, gre) ∧ Prove(x, economicHardship) → ProvideTo(ets, financialAid, x))\n∀x (LivingIn(x, singleParentFamily) ∨ AvailableTo(fewResources, x) → Prove(x, economicHardship))\nLivingIn(tom, singleParentFamily)\nOutOfWork(tomsDad) ∧ AvailableTo(fewResources, tom)\nApplicantOf(tom, gre)"} | |
| {"id": "concl_197_105", "NL_sentence": "ETS provides financial aid to Tom.", "FOL_sentence": "ProvideTo(ets, financialAid, tom)", "label": "True", "corrected": "yes", "correction_explanation": "The original FOL uses 'ProvidesFinancialAidTo(eTS, tom)' — a binary predicate inconsistent with 'ProvideTo(ets, financialAid, x)' used in premise 2. Corrected to 'ProvideTo(ets, financialAid, tom)' for consistency. Also 'eTS' → 'ets' for consistent casing.", "FOL_sentence_old": "ProvidesFinancialAidTo(eTS, tom)", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "concl_197_106", "NL_sentence": "It costs below US $300 to take the GRE test.", "FOL_sentence": "∃x (Cost(gre, x) ∧ Cheaper(x, uSD300))", "label": "True", "corrected": "yes", "correction_explanation": "Two issues in the original: (1) The original uses a free variable 'x' in 'Cost(gRE, x) ∧ Cheaper(x, 300)' without any quantifier — x is unbound, making the formula not a well-formed closed FOL sentence. Corrected to an existential: '∃x (Cost(gre, x) ∧ Cheaper(x, uSD300))'.", "FOL_sentence_old": "Cost(gRE, x) ∧ Cheaper(x, 300)", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "concl_197_107", "NL_sentence": "No one taking the GRE test has financial aid provided to them by something.", "FOL_sentence": "¬∃x ∃y (ApplicantOf(x, gre) ∧ ProvideTo(y, financialAid, x))", "label": "False", "corrected": "yes", "correction_explanation": "Three issues in the original: (1) The original uses 'Applicant(x, gRE)' — a different predicate name from 'ApplicantOf(x, gre)' used in premises 2 and 6. Corrected to 'ApplicantOf(x, gre)'. (2) The original uses 'ProvidesFinancialAidTo(y, x)' — binary predicate inconsistent with the ternary 'ProvideTo(ets, financialAid, x)' in premise 2. Corrected to 'ProvideTo(y, financialAid, x)' to match the premise structure while keeping y as a variable for the provider. (3) 'gRE' → 'gre' for casing consistency.", "note": "The label 'False' is correct: as established in conclusion 105, ProvideTo(ets, financialAid, tom) is derivable, and ApplicantOf(tom, gre) is a premise. Therefore ∃x ∃y (ApplicantOf(x, gre) ∧ ProvideTo(y, financialAid, x)) holds (with x = tom, y = ets), directly refuting the universal negation.", "FOL_sentence_old": "¬(∃x ∃y (Applicant(x, gRE) ∧ ProvidesFinancialAidTo(y, x)))", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "story_361", "NL_sentence": "If people spill a lot of food on their clothing, then they are not notably tidy. All clumsy foodies who go out frequently to find new food restaurants to try are people who spill a lot of food on their clothing. If people are cleanly, then they are notably tidy. If people value order and spotlessness, then they are cleanly. All people whose families prioritize order and spotlessness themselves value order and spotlessness. Peter is either a person who spills a lot of food on his clothing and is cleanly, or a person who does not spill a lot of food on his clothing and is not cleanly.", "FOL_sentence": "∀x (SpillOn(x, aLotOfFood, clothing) → ¬NotablyTidy(x)) ∧ ∀x (ClumsyFoodie(x) ∧ GoOutFrequentlyToFindToTry(x, newFoodRestaurant) → SpillOn(x, aLotOfFood, clothing)) ∧ ∀x (Cleanly(x) → NotablyTidy(x)) ∧ ∀x (Value(x, order) ∧ Value(x, spotlessness) → Cleanly(x)) ∧ ∀x (∃y (FamilyOf(y, x) ∧ Prioritize(y, order) ∧ Prioritize(y, spotlessness)) → Value(x, order) ∧ Value(x, spotlessness)) ∧ ¬(SpillOn(peter, aLotOfFood, clothing) ⊕ Cleanly(peter))", "corrected": "yes", "correction_explanation": "Four corrections made: (1) Premise 1: the original uses 'Spill(x, aLotOfFood, clothing)' as the predicate, while premise 2 uses 'SpillOn(x, aLotOfFood, clothing)'. These must refer to the same relation; unified to 'SpillOn(x, aLotOfFood, clothing)' throughout for consistency. (2) Premise 5: the original has an unclosed parenthesis. (3) Premise 6: the original uses 'Spill(peter, aLotOfFood, clothing)' — again unified to 'SpillOn(peter, aLotOfFood, clothing)'.", "FOL_sentence_old": "∀x (Spill(x, aLotOfFood, clothing) → ¬NotablyTidy(x))\n∀x (ClumsyFoodie(x) ∧ GoOutFrequentlyToFindToTry(x, newFoodRestaurant) → SpillOn(x, aLotOfFood, clothing))\n∀x (Cleanly(x) → NotablyTidy(x))\n∀x (Value(x, order) ∧ Value(x, spotlessness) → Cleanly(x))\n∀x ((∃y (FamilyOf(y, x) ∧ Prioritize(y, order) ∧ Prioritize(y, spotlessness)) → Value(x, order) ∧ Value(x, spotlessness)) \n¬(Spill(peter, aLotOfFood, clothing) ⊕ Cleanly(peter))"} | |
| {"id": "concl_361_108", "NL_sentence": "Peter is notably tidy.", "FOL_sentence": "NotablyTidy(peter)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "NotablyTidy(peter)", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_361_109", "NL_sentence": "Peter is either a clumsy foodie who goes out frequently to find new food restaurants to try or he is someone whose family prioritizes order and spotlessness.", "FOL_sentence": "(ClumsyFoodie(peter) ∧ GoOutFrequentlyToFindToTry(peter, newFoodRestaurant)) ⊕ (∃y (FamilyOf(y, peter) ∧ Prioritize(y, order) ∧ Prioritize(y, spotlessness)))", "label": "False", "corrected": "yes", "ambiguity": true, "amniguity_explanation": "either_or", "correction_explanation": "The original formalization lacked the information 'who goes out frequently to find new food restaurants to try'. It is also used ⊕ to express the either ... or, even if it doesn't change the label of the reason why the label 'false' is right.", "note": "The label 'False' is correct under the following reasoning: as established in conclusion 108's note, case (b) holds — ¬SpillOn(peter) ∧ ¬Cleanly(peter). If ClumsyFoodie(peter) ∧ GoOutFrequentlyToFindToTry(peter, newFoodRestaurant) held, premise 2 would give SpillOn(peter, aLotOfFood, clothing), contradicting ¬SpillOn(peter). So ClumsyFoodie(peter) is refutable. Similarly, if ∃y (FamilyOf(y, peter) ∧ Prioritize(y, order) ∧ Prioritize(y, spotlessness)) held, premise 5 would give Value(peter, order) ∧ Value(peter, spotlessness), then premise 4 would give Cleanly(peter), contradicting ¬Cleanly(peter). Therefore both disjuncts are refutable, making the disjunction False.", "FOL_sentence_old": "ClumsyFoodie(peter) ∨ (∃y (FamilyOf(y, peter) ∧ Prioritize(y, order) ∧ Prioritize(y, spotlessness)))", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "False"} | |
| {"id": "concl_361_110", "NL_sentence": "Peter is either both a clumsy foodie who goes out frequently to find new food restaurants to try and is someone whose family prioritizes order and spotlessness, or he neither is a clumsy foodie who goes out frequently to find new food restaurants to try nor does his family prioritize order and spotlessness.", "FOL_sentence": "¬((ClumsyFoodie(peter) ∧ GoOutFrequentlyToFindToTry(peter, newFoodRestaurant)) ⊕ (∃y (FamilyOf(y, peter) ∧ Prioritize(y, order) ∧ Prioritize(y, spotlessness))))", "label": "True", "corrected": "yes", "correction_explanation": "The original formalization lacked the information 'who goes out frequently to find new food restaurants to try'.", "note": "The label 'True' is correct: the NL expresses the XNOR pattern ('both... or neither...'), correctly encoded as ¬(P ⊕ Q). As established in conclusion 109, both ClumsyFoodie(peter) and ∃y (FamilyOf(y, peter) ∧ Prioritize(y, order) ∧ Prioritize(y, spotlessness)) are refutable — meaning both P and Q are false. Under XNOR, P = false and Q = false satisfies ¬(P ⊕ Q) since neither holds (the 'neither' case of 'both or neither'). The conclusion is therefore True.", "FOL_sentence_old": "¬(ClumsyFoodie(peter) ⊕ (∃y (FamilyOf(y, peter) ∧ Prioritize(y, order) ∧ Prioritize(y, spotlessness))))", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "story_262", "NL_sentence": "All fir trees are evergreens. Some objects of worship are fir trees.", "FOL_sentence": "∀x (FirTree(x) → Evergreen(x)) ∧ ∃x (ObjectOfWorship(x) ∧ FirTree(x))", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "some_plural", "FOL_sentence_old": "∀x (FirTree(x) → Evergreen(x))\n∃x ∃y (ObjectOfWorship(x) ∧ ObjectOfWorship(y) ∧ FirTree(x) ∧ FirTree(y) ∧ ¬(x=y))"} | |
| {"id": "concl_262_111", "NL_sentence": "Some evergreens are not objects of worship.", "FOL_sentence": "∃x ∃y (Evergreen(x) ∧ Evergreen(y) ∧ ¬ObjectOfWorship(x) ∧ ¬ObjectOfWorship(y) ∧ ¬(x=y))", "label": "Uncertain", "corrected": "no", "ambiguity": true, "ambiguity_explanation": "some_plural", "FOL_sentence_old": "∃x ∃y (Evergreen(x) ∧ Evergreen(y) ∧ ¬ObjectOfWorship(x) ∧ ¬ObjectOfWorship(y) ∧ ¬(x=y))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_124", "NL_sentence": "The Picuris Mountains are a mountain range in New Mexico or Texas. Juan de Onate visited the Picuris Mountains. The Harding Pegmatite Mine, located in the Picuris Mountains, was donated. There are no mountain ranges in Texas that have mines that have been donated.", "FOL_sentence": "MountainRange(thePicurisMountains) ∧ (In(thePicurisMountains, newMexico) ∨ In(thePicurisMountains, texas)) ∧ Visited(juanDeOnate, thePicurisMountains) ∧ In(hardingPegmatiteMine, thePicurisMountains) ∧ Mine(hardingPegmatiteMine) ∧ Donated(hardingPegmatiteMine) ∧ ∀x ∀y (Mine(x) ∧ Donated(x) ∧ In(x, y) ∧ MountainRange(y) → ¬In(y, texas))", "corrected": "yes", "correction_explanation": "Or translated as inclusive or (∨)", "FOL_sentence_old": "MountainRange(thePicurisMountains) ∧ (In(thePicurisMountains, newMexico) ⊕ In(thePicurisMountains, texas))\nVisited(juanDeOnate, thePicurisMountains)\nIn(hardingPegmatiteMine, thePicurisMountains) ∧ Mine(hardingPegmatiteMine) ∧ Donated(hardingPegmatiteMine)\n∀x ∀y (Mine(x) ∧ Donated(x) ∧ In(x, y) ∧ MountainRange(y) → ¬In(y, texas))"} | |
| {"id": "concl_124_112", "NL_sentence": "Juan de Onate visited a mountain range in New Mexico.", "FOL_sentence": "∃x (Visited(juanDeOnate, x) ∧ MountainRange(x) ∧ In(x, newMexico))", "label": "True", "corrected": "no", "FOL_sentence_old": "∃x (Visited(juanDeOnate, x) ∧ MountainRange(x) ∧ In(x, newMexico))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_124_113", "NL_sentence": "Juan de Onate visited a mountain range in Texas.", "FOL_sentence": "∃x (Visited(juanDeOnate, x) ∧ MountainRange(x) ∧ In(x, texas))", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "∃x (Visited(juanDeOnate, x) ∧ MountainRange(x) ∧ In(x, texas))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_124_114", "NL_sentence": "The Harding Pegmatite Mine is not located in a mountain range in New Mexico.", "FOL_sentence": "∀x (In(hardingPegmatiteMine, x) → ¬(MountainRange(x) ∧ In(x, newMexico)))", "label": "False", "corrected": "no", "FOL_sentence_old": "∀x (In(hardingPegmatiteMine, x) → ¬(MountainRange(x) ∧ In(x, newMexico)))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_183", "NL_sentence": "If a man is taller than another man, the taller one can block the other's shooting. Michael is a man who is taller than everyone else in his class. If person x is taller than person y, and person y is taller than person z, then x is taller than z. Peter is a man who is taller than Michael. Michael can block any shooting from a person as long as the person does not jump when shooting. Michael cannot block Windy's shooting. Every shooter who can jump when shooting is a great shooter.", "FOL_sentence": "∀x ∀y (Man(x) ∧ Man(y) ∧ Taller(x, y) → CanBlock(x, y)) ∧ Man(michael) ∧ SameClass(michael, michael) ∧ ∀x (Man(x) ∧ SameClass(x, michael) ∧ ¬(x = michael) → Taller(michael, x)) ∧ ∀x ∀y ∀z (Taller(x, y) ∧ Taller(y, z) → Taller(x, z)) ∧ Man(peter) ∧ Taller(peter, michael) ∧ ∀x (¬JumpWhenShooting(x) → CanBlock(michael, x)) ∧ ¬CanBlock(michael, windy) ∧ ∀x (JumpWhenShooting(x) → GreatShooter(x))", "corrected": "yes", "correction_explanation": "Two corrections made: (1) Premise 2: the original does not assert Man(michael) or SameClass(michael, michael) — Michael's own class membership and being a man are implied by the NL but never stated. Added but not needed for the conclusions.", "FOL_sentence_old": "∀x ∀y (Man(x) ∧ Man(y) ∧ Taller(x, y) → CanBlock(x, y))\n∀x (Man(x) ∧ SameClass(x, michael) ∧ ¬(x=michael) → Taller(michael, x))\n∀x ∀y ∀z ((Taller(x, y) ∧ Taller(y, z)) → Taller(x, z))\nMan(peter) ∧ Taller(peter, michael)\n∀x (¬JumpWhenShooting(x) → CanBlock(michael, x))\n¬CanBlock(michael, windy)\n∀x (JumpWhenShooting(x) → GreatShooter(x))"} | |
| {"id": "concl_183_115", "NL_sentence": "Peter is shorter than a man in Michael's class.", "FOL_sentence": "∃x (Man(x) ∧ SameClass(x, michael) ∧ Taller(x, peter))", "label": "False", "NLI_requires_more_info": "∀x ∀y (Taller(x, y) → ¬Taller(y, x)) ", "corrected": "yes", "correction_explanation": "F := 'A shorter than B' is not really equivalent to G := 'B not taller than A' since G holds also when A and B have the same size, but F not. So, it should be better to formalize it in the proposed way", "FOL_sentence_old": "∃x (Man(x) ∧ SameClass(x, michael) ∧ ¬Taller(peter, x))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_183_116", "NL_sentence": "Windy is a great shooter.", "FOL_sentence": "GreatShooter(windy)", "label": "True", "corrected": "no", "FOL_sentence_old": "GreatShooter(windy)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_183_117", "NL_sentence": "Peter can block Windy's shooting.", "FOL_sentence": "CanBlock(peter, windy)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "CanBlock(peter, windy)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_151", "NL_sentence": "Barutin Cove is a cove named after the Bulgarian settlement of Barutin. Barutin Cove is on the southwest coast of Snow Island. Snow Island, Greenwich Island, and Deception Island are located in the South Shetland Islands. Antarctica is located on the South Shetland Islands. If place A is located in place B and place B is located in place C, then place A is located in place C.", "FOL_sentence": "Cove(barutinCove) ∧ NamedAfter(barutinCove, barutinSettlement) ∧ LocatedIn(barutinSettlement, bulgaria) ∧ LocatedIn(barutinCove, snowIsland) ∧ LocatedIn(snowIsland, southShetlandIslands) ∧ LocatedIn(greenwichIsland, southShetlandIslands) ∧ LocatedIn(deceptionIsland, southShetlandIslands) ∧ LocatedIn(antarctica, southShetlandIslands) ∧ ∀x ∀y ∀z (LocatedIn(x, y) ∧ LocatedIn(y, z) → LocatedIn(x, z))", "corrected": "yes", "correction_explanation": "Two corrections made: (1) Premise 4: the original states 'Antarctica is located on the South Shetland Islands' — 'LocatedIn(southShetlandIslands, antarctica)'. However, this is geographically inverted: the South Shetland Islands are located IN Antarctica, not the other way around. The NL premise is factually incorrect as stated. The FOL faithfully represents the NL as written ('LocatedIn(southShetlandIslands, antarctica)'), which is the correct direction for the logical chain to work (Barutin Cove → Snow Island → South Shetland Islands → Antarctica). Retained as-is since the FOL correctly mirrors the NL, but flagged as a real-world factual inversion — in reality it is the South Shetland Islands that are located in Antarctica, which is what the FOL encodes and what is needed for the conclusions to be derivable. The NL should have read 'The South Shetland Islands are located in Antarctica' rather than 'Antarctica is located on the South Shetland Islands'. (2) Premise 1: the original FOL includes 'LocatedIn(barutinSettlement, bulgaria)' which is not stated in the NL premise — the NL only says 'named after the Bulgarian settlement of Barutin', implying the settlement is Bulgarian but not explicitly asserting LocatedIn(barutinSettlement, bulgaria) as a FOL fact. However this grounding is necessary for conclusion 119 to be True; it is retained as a reasonable inference from 'Bulgarian settlement' and flagged.", "FOL_sentence_old": "Cove(barutinCove) ∧ NamedAfter(barutinCove, barutinSettlement) ∧ LocatedIn(barutinSettlement, bulgaria)\nLocatedIn(barutinCove, snowIsland)\nLocatedIn(snowIsland, southShetlandIslands) ∧ LocatedIn(greenwichIsland, southShetlandIslands) ∧ LocatedIn(deceptionIsland, southShetlandIslands)\nLocatedIn(southShetlandIslands, antarctica)\n∀x ∀y ∀z ((LocatedIn(x, y) ∧ LocatedIn(y, z)) → LocatedIn(x, z))"} | |
| {"id": "concl_151_118", "NL_sentence": "Barutin Cove is named after all islands in Antarctica.", "FOL_sentence": "∀x (LocatedIn(x, antarctica) → NamedAfter(barutinCove, x))", "label": "Uncertain", "corrected": "no", "correction_explanation": "The formalization can be considered correct. However, it lacks any referement to the concept of 'island'. If required, it should be put both in the story and in the conclusions.", "FOL_sentence_old": "∀x (LocatedIn(x, antarctica) → NamedAfter(barutinCove, x))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_151_119", "NL_sentence": "There is at least one cove in Antarctica named after a place in Bulgaria.", "FOL_sentence": "∃x ∃y (Cove(x) ∧ LocatedIn(x, antarctica) ∧ NamedAfter(x, y) ∧ LocatedIn(y, bulgaria))", "label": "Uncertain", "corrected": "yes", "correction_explanation": "The original FOL uses 'NameAfter(x, y)' — missing the 'd' suffix, making it inconsistent with 'NamedAfter' used throughout the premises and conclusion 118. Corrected to 'NamedAfter(x, y)'.", "FOL_sentence_old": "∃x ∃y (Cove(x) ∧ LocatedIn(x, antarctica) ∧ NameAfter(x, y) ∧ LocatedIn(y, bulgaria))", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_151_120", "NL_sentence": "Barutin Cove is not located in Antarctica.", "FOL_sentence": "¬LocatedIn(barutinCove, antarctica)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "¬LocatedIn(barutinCove, antarctica)", "label_old": "False", "label_old_z3": "False", "label_z3": "Uncertain"} | |
| {"id": "story_295", "NL_sentence": "Some affection is love. Some love is positive.", "FOL_sentence": "∃x (Affection(x) ∧ Love(x)) ∧ ∃x (Love(x) ∧ Positive(x))", "corrected": "no", "FOL_sentence_old": "∃x (Affection(x) ∧ Love(x))\n∃x (Love(x) ∧ Positive(x))"} | |
| {"id": "concl_295_121", "NL_sentence": "Some affection is positive.", "FOL_sentence": "∃x (Affection(x) ∧ Positive(x))", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "∃x (Affection(x) ∧ Positive(x))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_315", "NL_sentence": "If something can transport multiple passengers, then it is not a one-seater. All Tesla Model 3 can transport multiple passengers. All single-seat electric cars are one-seaters. All Solo EV cars are single-seat electric cars. If John's car is not a Tesla Model 3, then John's car is not a Tesla Model 3 or a single-seat electric car.", "FOL_sentence": "∀x (∃y ∃z (Passenger(y) ∧ Passenger(z) ∧ Transport(x, y) ∧ Transport(x, z) ∧ ¬(y=z)) → ¬OneSeater(x)) ∧ ∀x (TeslaModel3(x) → ∃y ∃z (Passenger(y) ∧ Passenger(z) ∧ Transport(x, y) ∧ Transport(x, z) ∧ ¬(y=z))) ∧ ∀x (SingleSeat(x) ∧ ElectricCar(x) → OneSeater(x)) ∧ ∀x (SoloEV(x) ∧ Car(x) → SingleSeat(x) ∧ ElectricCar(x)) ∧ (¬TeslaModel3(johnsCar) → ¬TeslaModel3(johnsCar) ∧ ¬(SingleSeat(johnsCar) ∧ ElectricCar(johnsCar))) ∧ Car(johnsCar)", "corrected": "yes", "correction_explanation": "Four corrections made: (1) Premises 1 and 2: the original has 'Transport(x, y) ∧ Transport(x, y)' — the second conjunct is a duplicate of the first (both use y), meaning the two-passenger condition is never actually enforced. (2) Premise 2: the original has an unclosed parenthesis after the existential block; corrected by adding the missing closing parenthesis. (3) Premise 5: the original uses a free variable 'x' in 'SingleSeat(x) ∧ ElectricCar(johnsCar)' (4) Added the contextual information that John's car is a car.", "FOL_sentence_old": "∀x (∃y ∃z (Passenger(y) ∧ Passenger(z) ∧ Transport(x, y) ∧ Transport(x, y) ∧ ¬(y=z)) → ¬OneSeater(x))\n∀x (TeslaModel3(x) → (∃y ∃z (Passenger(y) ∧ Passenger(z) ∧ Transport(x, y) ∧ Transport(x, y) ∧ ¬(y=z)))\n∀x (SingleSeat(x) ∧ ElectricCar(x) → OneSeater(x))\n∀x (SoloEV(x) ∧ Car(x) → SingleSeat(x) ∧ ElectricCar(x))\n¬TeslaModel3(johnsCar) → ¬(TeslaModel3(johnsCar) ∨ (SingleSeat(x) ∧ ElectricCar(johnsCar)))"} | |
| {"id": "concl_315_122", "NL_sentence": "John's car is a Tesla Model 3.", "FOL_sentence": "TeslaModel3(johnsCar) ∧ Car(johnsCar)", "label": "Uncertain", "corrected": "yes", "note": "The label 'Uncertain' is correct: nothing in the premises positively asserts TeslaModel3(johnsCar), nor is it refutable. The premises only establish conditional relationships. Under the open-world assumption, John's car could or could not be a Tesla Model 3. Note however that if TeslaModel3(johnsCar) were false, then by the corrected premise 5, ¬(SingleSeat(johnsCar) ∧ ElectricCar(johnsCar)) would hold, and by premise 4, ¬(SoloEV(johnsCar) ∧ Car(johnsCar)) would follow. The truth value of TeslaModel3(johnsCar) itself remains undetermined.", "FOL_sentence_old": "TeslaModel3(johnsCar)", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "concl_315_123", "NL_sentence": "John's car is a Solo EV.", "FOL_sentence": "SoloEV(johnsCar) ∧ Car(johnsCar)", "label": "False", "corrected": "yes", "correction_explanation": "If we translate it as in the original 'SoloEV(johnsCar) ∧ Car(johnsCar)', then it was not derivable from the premises since in the previous translation there was nothing that implied Car(johnsCar), hence the label should be 'Uncertain'. Now it is fixed in this regard.", "note": "The label 'False' is correct via the following reasoning: suppose SoloEV(johnsCar) ∧ Car(johnsCar) held. By premise 4, SingleSeat(johnsCar) ∧ ElectricCar(johnsCar) would follow, making johnsCar a one-seater (premise 3). But premise 2 gives TeslaModel3(x) → transports multiple passengers, and premise 1 gives multiple passengers → ¬OneSeater. If johnsCar were also a Tesla Model 3, it would be both a one-seater and not a one-seater — contradiction. If johnsCar is not a Tesla Model 3, corrected premise 5 gives ¬(SingleSeat(johnsCar) ∧ ElectricCar(johnsCar)) — contradicting what we derived from SoloEV. In both cases a contradiction arises, so SoloEV(johnsCar) ∧ Car(johnsCar) is refutable.", "FOL_sentence_old": "SoloEV(johnsCar) ∧ Car(johnsCar)", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "False"} | |
| {"id": "concl_315_124", "NL_sentence": "John's car is not a Solo EV.", "FOL_sentence": "¬SoloEV(johnsCar) ∧ Car(johnsCar)", "label": "True", "corrected": "no", "correction_explanation": "Not considered as an error, but only as a suggestion for a better translation. Giving the fact that 'John's car is a aìcar', these formulations are equivalent.", "FOL_sentence_old": "¬(SoloEV(johnsCar) ∧ Car(johnsCar))", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "story_467", "NL_sentence": "All of Peter's pets that are mammals are also animals. All monkeys are mammals. Peter's pets are all either monkeys or birds. Peter's birds can fly. All animals that are Peter's pets can breathe. If Peter's pet can fly, then it has wings. Rock is Peter's pet. Rock can fly, or Rock is a bird, or Rock cannot breathe.", "FOL_sentence": "∀x (PetersPet(x) ∧ Mammal(x) → Animal(x)) ∧ ∀x (Monkey(x) → Mammal(x)) ∧ ∀x (PetersPet(x) → Monkey(x) ⊕ Bird(x)) ∧ ∀x (PetersPet(x) ∧ Bird(x) → CanFly(x)) ∧ ∀x (PetersPet(x) ∧ Animal(x) → Breathe(x)) ∧ ∀x (PetersPet(x) ∧ CanFly(x) → ∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z))) ∧ PetersPet(rock) ∧ (CanFly(rock) ∨ Bird(rock) ∨ ¬Breathe(rock))", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "either_or", "correction_explanation": "Four corrections made: (1) Premise 4: the original reads '∀x (Bird(x) → CanFly(x))' — this universally asserts ALL birds can fly, not just Peter's birds. (2) Premise 7: the original uses 'PeterSPet(rock)' — capital S mid-word and missing apostrophe handling, inconsistent with 'PetersPet' used in all other premises. Corrected to 'PetersPet(rock)'.", "FOL_sentence_old": "∀x (PetersPet(x) ∧ Mammal(x) → Animal(x))\n∀x (Monkey(x) → Mammal(x))\n∀x (PetersPet(x) → Monkey(x) ⊕ Bird(x))\n∀x (Bird(x) → CanFly(x))\n∀x (PetersPet(x) ∧ Animal(x) → Breathe(x))\n∀x (PetersPet(x) ∧ CanFly(x) → ∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(x, y) ∧ Have(x, z)))\nPeterSPet(rock)\nCanFly(rock) ∨ Bird(rock) ∨ ¬Breathe(rock)"} | |
| {"id": "concl_467_125", "NL_sentence": "Rock is a monkey.", "FOL_sentence": "Monkey(rock)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Monkey(rock)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_467_126", "NL_sentence": "Rock has wings.", "FOL_sentence": "∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(rock, y) ∧ Have(rock, z))", "label": "True", "corrected": "no", "note": "The label 'True' is derivable regardless of whether Rock is a monkey or a bird, as shown in conclusion 125's analysis: (Case 1) Rock is a monkey → Breathe(rock) → ¬Breathe(rock) false in premise 8 → CanFly(rock) must hold (since Bird(rock) is false) → PetersPet(rock) ∧ CanFly(rock) + premise 6 → Rock has wings. (Case 2) Rock is a bird → corrected premise 4 → CanFly(rock) → PetersPet(rock) ∧ CanFly(rock) + premise 6 → Rock has wings. In both exhaustive cases (from ⊕ in premise 3) Rock has wings — the conclusion is True.", "FOL_sentence_old": "∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(rock, y) ∧ Have(rock, z))", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "concl_467_127", "NL_sentence": "Rock does not have wings.", "FOL_sentence": "¬∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(rock, y) ∧ Have(rock, z))", "label": "False", "corrected": "no", "FOL_sentence_old": "¬(∃y ∃z (¬(y=z) ∧ Wing(y) ∧ Wing(z) ∧ Have(rock, y) ∧ Have(rock, z)))", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "story_330", "NL_sentence": "All people who make wedding plans are people who are engaged. All people who invite others to come to their ceremony make wedding plans. Anyone who has a well-attended wedding invites others to come to their ceremony. Some people that have well-attended weddings have larger families. If John is engaged, then John does not invite friends to their ceremony and make wedding plans. If John has a larger family, then either John has a well-attended wedding or invites friends to their ceremony.", "FOL_sentence": "∀x (Make(x, weddingPlan) → Engaged(x)) ∧ ∀x ((∃y InviteToComeTo(x, y, wedding)) → Make(x, weddingPlan)) ∧ ∀x (Have(x, wellAttendedWedding) → ∃y InviteToComeTo(x, y, wedding)) ∧ ∃x (Have(x, wellAttendedWedding) ∧ Have(x, largerFamily)) ∧ (Engaged(john) → (¬(∃y InviteToComeTo(john, y, wedding)) ∧ ¬Make(john, weddingPlan))) ∧ (Have(john, largerFamily) → (Have(john, wellAttendedWedding) ⊕ (∃y (InviteToComeTo(john, y, wedding)))))", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "either_or", "correction_explanation": "Several corrections made: (1) Premise 5: the original has two major errors. First, '¬(y=x)' and '¬(z=x)' use a free variable 'x' instead of 'john' — corrected to '¬(y=john)' and '¬(z=john)'. Second, the original uses a mixed predicate 'Invite(john, z, comeTo, wedding)' (4-ary) inconsistent with 'InviteToComeTo(john, z, wedding)' (3-ary) used in all other premises; unified to 'InviteToComeTo'. Third, the NL reads 'John does not invite friends to their ceremony AND make wedding plans' — interpreted as two separate negative consequences: John neither invites others nor makes wedding plans. Corrected consequent to '¬∃y ∃z (...InviteToComeTo...) ∧ ¬Make(john, weddingPlan)'. (2) Premise 6: the original uses free variable 'x' in the invite consequent ('¬(y=x)', 'Invite(x, y, comeTo, wedding)') instead of 'john'; corrected to use 'john' throughout. Also unified 4-ary 'Invite(x, y, comeTo, wedding)' to 3-ary 'InviteToComeTo(john, y, wedding)'. (3) The ⊕ in premise 6 correctly captures 'either... or...' for the two disjuncts regarding John's well-attended wedding vs inviting friends — these are plausibly exclusive (though see ambiguity note). (4) Premises 2 and 3 encode 'inviting others' as requiring at least two distinct invitees (y ≠ z, both ≠ x) — this is a specific modelling choice for 'multiple' that is retained as-is.", "FOL_sentence_old": "∀x (Make(x, weddingPlan) → Engaged(x))\n ∀x (∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ InviteToComeTo(x, y, wedding) ∧ InviteToComeTo(x, z, wedding)) → Make(x, weddingPlan))\n ∀x (Have(x, wellAttendedWedding) → ∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ InviteToComeTo(x, y, wedding) ∧ InviteToComeTo(x, z, wedding)))\n ∃x (Have(x, wellAttendedWedding) ∧ Have(x, largerFamily))\n Engaged(john) → ¬(∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ InviteToComeTo(john, y, wedding) ∧ Invite(john, z, comeTo, wedding))) ∧ Make(john, weddingPlan)\n Have(john, largerFamily) → Have(john, wellAttendedWedding) ⊕ ∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ Invite(x, y, comeTo, wedding) ∧ InviteToComeTo(x, z, wedding))"} | |
| {"id": "concl_330_128", "NL_sentence": "John has a larger family.", "FOL_sentence": "Have(john, largerFamily)", "label": "False", "corrected": "yes", "correction_explanation": "The original FOL uses 'Have(john, largeFamily)' — 'largeFamily' (missing 'r') instead of 'largerFamily' used consistently in the premises. Corrected to 'Have(john, largerFamily)'.", "note": "The label 'False' is justified via the following chain: suppose Have(john, largerFamily). By corrected premise 6 (⊕): Have(john, wellAttendedWedding) ⊕ ∃y∃z(...InviteToComeTo(john,...)...). Case A: Have(john, wellAttendedWedding) holds. By premise 3, john invites others → by premise 2, Make(john, weddingPlan) → by premise 1, Engaged(john). By corrected premise 5: Engaged(john) → ¬∃y∃z(...InviteToComeTo...) ∧ ¬Make(john, weddingPlan). But we derived Make(john, weddingPlan) — contradiction. Case B: ∃y∃z(...InviteToComeTo(john,...)...) holds. By premise 2 → Make(john, weddingPlan) → Engaged(john) → ¬∃y∃z(...InviteToComeTo...) — contradiction. Both cases yield contradictions, so Have(john, largerFamily) is refutable.", "FOL_sentence_old": "Have(john, largeFamily)", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "concl_330_129", "NL_sentence": "John does not have a larger family.", "FOL_sentence": "¬Have(john, largerFamily)", "label": "True", "corrected": "no", "FOL_sentence_old": "¬Have(john, largerFamily)", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "concl_330_130", "NL_sentence": "John is engaged.", "FOL_sentence": "Engaged(john)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Engaged(john)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_330_131", "NL_sentence": "John neither has a larger family nor does he invite others to his wedding.", "FOL_sentence": "¬Have(john, largerFamily) ∧ ¬∃y(InviteToComeTo(john, y, wedding))", "label": "True", "ambiguity": true, "ambiguity_explanation": "others reference to what?", "corrected": "no", "note": "The label 'True' is correct for both conjuncts: (1) ¬Have(john, largerFamily) is established via conclusion 129. (2) ¬∃y∃z(...InviteToComeTo(john,...)...): suppose john did invite others. By premise 2 → Make(john, weddingPlan) → by premise 1 → Engaged(john) → by corrected premise 5 → ¬∃y∃z(...InviteToComeTo(john,...)) — contradiction. Therefore john does not invite others. Both conjuncts are True.", "FOL_sentence_old": "¬Have(john, largerFamily) ∧ ¬(∃y ∃z (¬(y=john) ∧ ¬(z=john) ∧ ¬(y=z) ∧ InviteToComeTo(john, y, wedding) ∧ InviteToComeTo(john, z, wedding)))", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "story_26", "NL_sentence": "Some mammals have teeth. Platypuses have no teeth. Platypuses are mammals. Humans have teeth.", "FOL_sentence": "∃x(Mammal(x) ∧ Have(x, teeth)) ∧ ¬Have(platypus, teeth) ∧ Mammal(platypus) ∧ Have(humans, teeth)", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "some_plural", "FOL_sentence_old": "∃x ∃y (Mammal(x) ∧ Mammal(y) ∧ (¬(x=y)) ∧ Have(x, teeth) ∧ Have(y, teeth))\n¬Have(platypus, teeth)\nMammal(platypus)\nHave(humans, teeth)"} | |
| {"id": "concl_26_132", "NL_sentence": "Platypuses are mammals with no teeth.", "FOL_sentence": "Mammal(platypus) ∧ ¬Have(platypus, teeth)", "label": "True", "corrected": "no", "FOL_sentence_old": "Mammal(platypus) ∧ (¬Have(platypus, teeth))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_26_133", "NL_sentence": "Platypuses are reptiles.", "FOL_sentence": "Reptile(platypus)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Reptile(platypus)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_26_134", "NL_sentence": "Humans are mammals.", "FOL_sentence": "Mammal(humans)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Mammal(humans)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_203", "NL_sentence": "Plungers suck. Vacuums suck. Vampires suck. Space is a vacuum. A duster is a household appliance that doesn't suck.", "FOL_sentence": "∀x (Plunger(x) → Suck(x)) ∧ ∀x (Vacuum(x) → Suck(x)) ∧ ∀x (Vampire(x) → Suck(x)) ∧ Vacuum(space) ∧ HouseholdAppliance(duster) ∧ ¬Suck(duster)", "corrected": "no", "FOL_sentence_old": "∀x (Plunger(x) → Suck(x))\n∀x (Vacuum(x) → Suck(x))\n∀x (Vampire(x) → Suck(x))\nVacuum(space)\nHouseholdAppliance(duster) ∧ ¬Suck(duster)"} | |
| {"id": "concl_203_135", "NL_sentence": "Space sucks.", "FOL_sentence": "Suck(space)", "label": "True", "corrected": "no", "FOL_sentence_old": "Suck(space)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_203_136", "NL_sentence": "Space is a vampire.", "FOL_sentence": "Vampire(space)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Vampire(space)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_203_137", "NL_sentence": "If something is a household appliance, it sucks.", "FOL_sentence": "∀x (HouseholdAppliance(x) → Suck(x))", "label": "False", "corrected": "yes", "correction_explanation": "The original FOL uses 'HouseHoldApp(x)' — an abbreviated and inconsistently cased predicate name, different from 'HouseholdAppliance' used in premise 5. Corrected to 'HouseholdAppliance(x)' for consistency.", "FOL_sentence_old": "∀x (HouseHoldApp(x) → Suck(x))", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "story_131", "NL_sentence": "Machine Learning algorithms can be categorized as supervised learning, unsupervised learning, and reinforcement learning. Unsupervised learning algorithms do not require labeled data. The state-of-the-art text summarization model is trained with machine learning algorithms. Reinforcement learning is not used to train the state-of-the-art text summarization model. The Machine Learning algorithm for training text summarization models requires labeled data.", "FOL_sentence": "∀x (MachineLearningAlgorithm(x) ↔ (SupervisedLearningAlgorithm(x) ∨ UnsupervisedLearningAlgorithm(x) ∨ ReinforcementLearningAlgorithm(x))) ∧ ∀x (UnsupervisedLearningAlgorithm(x) → ¬Require(x, labeledData)) ∧ (∃x (MachineLearningAlgorithm(x) ∧ TrainedWith(stateOfTheArtTextSummarizationModel, x)) ∧ ∀x (TrainedWith(stateOfTheArtTextSummarizationModel, x) → MachineLearningAlgorithm(x))) ∧ ∀x (ReinforcementLearningAlgorithm(x) → ¬TrainedWith(stateOfTheArtTextSummarizationModel, x)) ∧ ∀x ((MachineLearningAlgorithm(x) ∧ TrainedWith(stateOfTheArtTextSummarizationModel, x)) → Require(x, labeledData))", "corrected": "yes", "correction_explanation": "Two corrections made: (1) Premise 3: the original reads '∀x (TrainedWith(stateOfTheArtTextSummarizationModel, x) → MachineLearningAlgorithm(x))' — this says that anything the model is trained WITH is a machine learning algorithm. While this is a reasonable interpretation, the NL says 'the model IS TRAINED WITH machine learning algorithms', asserting the existence of at least one such algorithm: '∃x (MachineLearningAlgorithm(x) ∧ TrainedWith(stateOfTheArtTextSummarizationModel, x))'. The universal conditional form of the original would not allow deriving that any ML algorithm is actually used — it only constrains what could be used. The existential form is required to derive conclusions 138 and 139. Added the existential form. (2) Premise 1: the original uses ∨ (inclusive disjunction) for the three-way categorisation. The NL lists the three categories with 'and' as an enumeration of possibilities, not an exclusive partition. The inclusive ∨ is retained as the standard reading — an algorithm could theoretically belong to multiple categories, though in practice they are treated as mutually exclusive (this doesn't affect the conclusions). Flagged as ambiguous.", "ambiguity": true, "ambiguity_explanation": "option_partition", "FOL_sentence_old": "∀x (MachineLearningAlgorithm(x) → SupervisedLearningAlgorithm(x) ∨ UnsupervisedLearningAlgorithm(x) ∨ ReinforcementLearningAlgorithm(x))\n∀x (UnsupervisedLearningAlgorithm(x) → ¬Require(x, labeledData))\n∀x (TrainedWith(stateOfTheArtTextSummarizationModel, x) → MachineLearningAlgorithm(x))\n∀x (ReinforcementLearningAlgorithm(x) → ¬TrainedWith(stateOfTheArtTextSummarizationModel, x))\n∀x ((MachineLearningAlgorithm(x) ∧ TrainedWith(stateOfTheArtTextSummarizationModel, x)) → Require(x, labeledData))"} | |
| {"id": "concl_131_138", "NL_sentence": "Supervised learning is used to train the state-of-the-art text summarization model.", "FOL_sentence": "∃x (SupervisedLearningAlgorithm(x) ∧ TrainedWith(stateOfTheArtTextSummarizationModel, x))", "label": "True", "corrected": "no", "note": "Now the label 'True' is corrected (because we change the premises formalization and add the existential info about the algorithm for the state of the art models) but with the previous formalization the label should be 'Uncertain'", "FOL_sentence_old": "∃x (SupervisedLearningAlgorithm(x) ∧ TrainedWith(stateOfTheArtTextSummarizationModel, x))", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "concl_131_139", "NL_sentence": "Unsupervised learning is used to train the state-of-the-art text summarization model.", "FOL_sentence": "∃x (UnsupervisedLearningAlgorithm(x) ∧ TrainedWith(stateOfTheArtTextSummarizationModel, x))", "label": "False", "corrected": "no", "FOL_sentence_old": "∃x (UnsupervisedLearningAlgorithm(x) ∧ TrainedWith(stateOfTheArtTextSummarizationModel, x))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_460", "NL_sentence": "If a film is appropriate for people of all ages, then children can watch it without guidance from parents. If a film contains excessive erotic and violent content, children cannot watch it without guidance from their parents. If a film is rated General Audience, then it is appropriate for people of all ages. All family-friendly animated films are rated General Audience. All movies in the Frozen series are family-friendly animated films. 'Hachi: A Dog's Tale' is a film. 'Hachi: A Dog's Tale' is either a family-friendly animated film or is appropriate for people of all ages.", "FOL_sentence": "∀x (Film(x) ∧ AppropriateFor(x, peopleOfAllAges) → CanWatchWithout(children, x, guidanceFromParents)) ∧ ∀x (Film(x) ∧ Contain(x, excessiveEroticViolentContent) → ¬CanWatchWithout(children, x, guidanceFromParents)) ∧ ∀x (Film(x) ∧ Rated(x, generalAudience) → AppropriateFor(x, peopleOfAllAges)) ∧ ∀x (Film(x) ∧ FamilyFriendly(x) ∧ Animated(x) → Rated(x, generalAudience)) ∧ ∀x (Film(x) ∧ InFrozenSeries(x) → FamilyFriendly(x) ∧ Animated(x)) ∧ Film(hachiADogsTale) ∧ ((FamilyFriendly(hachiADogsTale) ∧ Animated(hachiADogsTale)) ⊕ AppropriateFor(hachiADogsTale, peopleOfAllAges))", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "either_or", "correction_explanation": "Several corrections made: (1) Premise 1: the original uses 'Rated(x, adultsOnly)' as the antecedent condition, but the NL says 'appropriate for people of all ages' — not 'rated adults only'. The original FOL has the wrong antecedent condition entirely. Corrected to 'AppropriateFor(x, peopleOfAllAges)' to match the NL. (2) Premise 5: the original uses 'InfrozenSeries' (lowercase 'f') — corrected to 'InFrozenSeries' for camelCase consistency. (3) Premise 7: the original reads '(FamilyFriendly(hachiADogsTale) ∧ Animated(hachiADogsTale)) ⊕ Rated(hachiADogsTale, adultsOnly)'. The NL says 'either a family-friendly animated film or is appropriate for people of all ages' — the second disjunct should be 'AppropriateFor(hachiADogsTale, peopleOfAllAges)', not 'Rated(hachiADogsTale, adultsOnly)'. The original uses the wrong predicate in the second disjunct. Corrected accordingly. (4) Constant naming: 'hachiAdogsTale' normalised to 'hachiADogsTale' for camelCase consistency. (5) Since they always appear altoghether (and to avoid any possible misinterpretations, erotic and violent content are clashed in the unique symbol excessiveEroticViolentContent", "FOL_sentence_old": "∀x (Film(x) ∧ Rated(x, adultsOnly) → CanWatchWithout(children, x, guidanceFromParents))\n∀x (Film(x) ∧ Contain(x, excessiveEroticContent) ∧ Contain(x, excessiveViolentContent) → ¬CanWatchWithout(children, x, guidanceFromParents))\n∀x (Film(x) ∧ Rated(x, generalAudience) → AppropriateFor(x, peopleOfAllAges))\n∀x (Film(x) ∧ FamilyFriendly(x) ∧ Animated(x) → Rated(x, generalAudience))\n∀x (Film(x) ∧ InfrozenSeries(x) → FamilyFriendly(x) ∧ Animated(x))\nFilm(hachiAdogsTale)\n(FamilyFriendly(hachiAdogsTale) ∧ Animated(hachiAdogsTale)) ⊕ Rated(hachiAdogsTale, adultsOnly)"} | |
| {"id": "concl_460_140", "NL_sentence": "'Hachi: A Dog's Tale' is rated General Audience.", "FOL_sentence": "Rated(hachiADogsTale, generalAudience)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "The original FOL uses a free variable 'x' ('Rated(x, generalAudience)') instead of the constant 'hachiADogsTale'. Corrected to 'Rated(hachiADogsTale, generalAudience)'.", "note": "The label 'Uncertain' requires analysis under the corrected premise 7 (⊕ between FamilyFriendly∧Animated and AppropriateFor). If hachiADogsTale is FamilyFriendly ∧ Animated (first disjunct of ⊕): premise 4 → Rated(hachiADogsTale, generalAudience) — True. If hachiADogsTale is AppropriateFor(..., peopleOfAllAges) only (second disjunct of ⊕): no chain reaches Rated(generalAudience) since premise 3 goes from Rated → Appropriate (not the converse). In this case Rated(generalAudience) is not entailed. Since ⊕ allows either case, the conclusion is Uncertain.", "FOL_sentence_old": "Rated(x, generalAudience)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_460_141", "NL_sentence": "'Hachi: A Dog's Tale' contains excessive erotic and violent content or is in the 'Frozen' series or both.", "FOL_sentence": "Contain(hachiADogsTale, excessiveEroticViolentContent) ∨ InFrozenSeries(hachiADogsTale)", "label": "False", "corrected": "yes", "correction_explanation": "Three major errors in the original: (1) Both occurrences of 'x' are free variables — neither is bound to 'hachiADogsTale'. Corrected to use 'hachiADogsTale' throughout. (2) The second disjunct 'InfrozenSeries(excessiveViolentContent)' uses 'excessiveViolentContent' as the argument to InFrozenSeries — a category error; 'excessiveViolentContent' is a content type constant, not a film. Corrected to 'InFrozenSeries(hachiADogsTale)'. (3) 'InfrozenSeries' → 'InFrozenSeries' for camelCase consistency.", "FOL_sentence_old": "(Contain(x, excessiveEroticContent) ∧ Contain(x, excessiveViolentContent)) ∨ InfrozenSeries(excessiveViolentContent)", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "concl_460_142", "NL_sentence": "'Hachi: A Dog's Tale' either contains excessive erotic and violent content and is a film in the 'Frozen' series, or it neither contains excessive erotic and violent content nor is a film in the 'Frozen' series.", "FOL_sentence": "(Contain(hachiADogsTale, excessiveEroticViolentContent) ∧ InFrozenSeries(hachiADogsTale)) ⊕ ¬(Contain(hachiADogsTale, excessiveEroticViolentContent) ∧ InFrozenSeries(hachiADogsTale))", "label": "True", "corrected": "yes", "correction_explanation": "Same errors as conclusion 141: (1) free variable 'x' replaced with 'hachiADogsTale' throughout. (2) 'InfrozenSeries(excessiveViolentContent)' — category error corrected to 'InFrozenSeries(hachiADogsTale)'. (3) Casing: 'InfrozenSeries' → 'InFrozenSeries'.", "note": "The label 'True' is correct, but actually the sentence is a tautology (excluded-middle principle). It doesn't test the correct formalization of the premises.", "ambiguity": true, "ambiguity_commentary": "either_or", "FOL_sentence_old": "¬((Contain(x, excessiveEroticContent) ∧ Contain(x, excessiveViolentContent)) ⊕ InfrozenSeries(excessiveViolentContent))", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "story_46", "NL_sentence": "Breeding back is a form of artificial selection by the deliberate selective breeding of domestic animals. Heck cattle were bred back in the 1920s to resemble the aurochs. Heck cattle are animals. Aurochs are animals. Some animals to be bred back resemble extinct animals.", "FOL_sentence": "∀x (BreedingBack(x) → ArtificialSelection(x) ∧ DeliberateSelectiveBreedingOfDomesticAnimals(x)) ∧ ∃x ∃y ∃z ∃w (HeckCattle(x) ∧ BreedingBack(x) ∧ HeckCattle(y) ∧ BreedingBack(y) ∧ ¬(x=y) ∧ Auroch(z) ∧ Resemble(x, z) ∧ Auroch(w) ∧ Resemble(y, w) ∧ ¬(w=z)) ∧ ∀x (HeckCattle(x) → Animal(x)) ∧ ∀x (Auroch(x) → Animal(x)) ∧ ∃x ∃y ∃w ∃z (Animal(x) ∧ Animal(y) ∧ ¬(x=y) ∧ BreedingBack(x) ∧ BreedingBack(y) ∧ Dead(w) ∧ Resemble(x, w) ∧ ¬(w=z) ∧ Dead(z) ∧ Resemble(y, z))", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "some_plural", "correction_explanation": "Two corrections made: (1) Premise 5: the original FOL is severely malformed: '∃x ∃y (Animal(x) ∧ Animal(y) ∧ ¬(x=y) ∧ BreedingBack(x) ∧ BreedingBack(y) ∧ (∃w(Dead(w) ∧ Resemble(x, w)) ∧ (¬(w=z)) ∧ (∃z(Dead(z) ∧ Resemble(y, z))))'. Multiple errors: (a) The variable 'z' appears free in '¬(w=z)' — z is introduced in the inner ∃z but the inequality ¬(w=z) appears before z is quantified, making it a scope error. (b) The variable 'w' leaks outside its ∃w scope in the ¬(w=z) conjunct. (2) Premise 1: original correctly uses conjunction in the consequent; parentheses clarified. (3) Premises (2) with the two-witness pattern to be consistent with the conclusion_143", "note": "The predicate 'Dead' is used to represent 'extinct' in premise 5 and conclusion 144. This is a modelling simplification — 'extinct' applies to species while 'dead' applies to individuals.", "FOL_sentence_old": "∀x (BreedingBack(x) → (ArtificialSelection(x) ∧ DeliberateSelectiveBreedingOfDomesticAnimals(x)))\n∃x ∃y (HeckCattle(x) ∧ BreedingBack(x) ∧ Auroch(y) ∧ Resemble(x, y))\n∀x (HeckCattle(x) → Animal(x))\n∀x (Auroch(x) → Animal(x))\n∃x ∃y (Animal(x) ∧ Animal(y) ∧ (¬(x=y)) ∧ BreedingBack(x) ∧ BreedingBack(y) ∧ (∃w(Dead(w) ∧ Resemble(x, w)) ∧ (¬(w=z)) ∧ (∃z(Dead(z) ∧ Resemble(y, z))))"} | |
| {"id": "concl_46_143", "NL_sentence": "Some Heck cattle are artificially selected.", "FOL_sentence": "∃x ∃y (HeckCattle(x) ∧ ArtificialSelection(x) ∧ ¬(x=y) ∧ HeckCattle(y) ∧ ArtificialSelection(y))", "label": "True", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "some_plural", "correction_explanation": "The original FOL uses the two-witness pattern '∃x ∃y (HeckCattle(x) ∧ ArtificialSelection(x) ∧ ¬(x=y) ∧ HeckCattle(y) ∧ ArtificialSelection(y))' — but not in Premise 2 (hence with the translations provided, no entailment in the FOL version'. Now, we used the two-witness pattern also in the premises.", "note": "Directly derivable: premise 2 gives ∃x (HeckCattle(x) ∧ BreedingBack(x) ∧ ...); call this individual h. BreedingBack(h) + premise 1 → ArtificialSelection(h). HeckCattle(h) ∧ ArtificialSelection(h) → existential introduction yields the conclusion.", "FOL_sentence_old": "∃x ∃y(HeckCattle(x) ∧ ArtificialSelection(x) ∧ (¬(x=y)) ∧ HeckCattle(y) ∧ ArtificialSelection(y))", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "concl_46_144", "NL_sentence": "Aurochs are extinct.", "FOL_sentence": "∀x (Auroch(x) → Dead(x))", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "∀x (Auroch(x) → Dead(x))", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "story_483", "NL_sentence": "Everyone who can register to vote in the United States can participate in the 2024 United States presidential election. If someone has United States citizenship, then they can register to vote in the United States. A person either has United States citizenship or Taiwanese citizenship. No Russian Federation officials hold Taiwanese citizenship. Vladimir neither holds Taiwanese citizenship nor is he a manager at Gazprom. Ekaterina can register to vote in the United States, or she is a Russian Federation official.", "FOL_sentence": "∀x (CanRegisterToVoteIn(x, unitedStates) → CanParticipateIn(x, y2024UnitedStatesElection)) ∧ ∀x (Have(x, unitedStatesCitizenship) → CanRegisterToVoteIn(x, unitedStates)) ∧ ∀x (Have(x, unitedStatesCitizenship) ⊕ Have(x, taiwaneseCitizenship)) ∧ ∀x (RussianFederationOfficial(x) → ¬Have(x, taiwaneseCitizenship)) ∧ (¬Have(vladimir, taiwaneseCitizenship) ∧ ¬ManagerAt(vladimir, gazprom)) ∧ (CanRegisterToVoteIn(ekaterina, unitedStates) ∨ RussianFederationOfficial(ekaterina))", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "either_or", "correction_explanation": "Five suggestions made (but they are not to be considered as corrections): (1) Add an 'y' to the constant '2024UnitedStatesElection' that began with a digit consistently throughout all premises and conclusions. (2) Premise 3: the original uses inclusive ∨ for 'either has United States citizenship or Taiwanese citizenship'. We use exclusive. (3) Premise 4: the original splits the Russian Federation official condition into two separate predicates 'Russian(x) ∧ FederationOfficial(x)', which is an awkward decomposition. Unified to a single predicate 'RussianFederationOfficial(x)' consistent with the NL 'Russian Federation officials'. Applied consistently to premise 6 as well. (4) Premise 6: the original has the disjuncts in reverse order relative to the NL ('Russian ∧ FederationOfficial ∨ CanRegisterToVote') — reordered to match NL order: 'CanRegisterToVoteIn(ekaterina, unitedStates) ∨ RussianFederationOfficial(ekaterina)'. Logically equivalent but more readable. (5) Conclusions 145 and 146: 'Russian(x) ∧ FederationOfficial(x)' unified to 'RussianFederationOfficial(x)' for consistency.", "FOL_sentence_old": "∀x (CanRegisterToVoteIn(x, unitedStates) → CanParticipateIn(x, 2024UnitedStatesElection))\n∀x (Have(x, unitedStatesCitizenship) → CanRegisterToVoteIn(x, unitedStates))\n∀x (Have(x, unitedStatesCitizenship) ∨ Have(x, taiwaneseCitizenship))\n∀x (Russian(x) ∧ FederationOfficial(x) → ¬Have(x, taiwaneseCitizenship))\n¬Have(vladimir, taiwaneseCitizenship) ∧ ¬ManagerAt(vladimir, gazprom)\n(Russian(ekaterina) ∧ FederationOfficial(ekaterina)) ∨ CanRegisterToVoteIn(ekaterina, unitedStates)"} | |
| {"id": "concl_483_145", "NL_sentence": "Vladimir is a Russian Federation official.", "FOL_sentence": "RussianFederationOfficial(vladimir)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "ontology : 'Russian(vladimir) ∧ FederationOfficial(vladimir)' unified to 'RussianFederationOfficial(vladimir)' for consistency with the unified predicate. -> needed because the intended meaning is that Vladimir is an ufficial of the Russian Federation (not that he is russian and he is also a federation official)", "FOL_sentence_old": "Russian(vladimir) ∧ FederationOfficial(vladimir)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_483_146", "NL_sentence": "Vladimir is not a Russian Federation official.", "FOL_sentence": "¬RussianFederationOfficial(vladimir)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "ontology : '¬(Russian(vladimir) ∧ FederationOfficial(vladimir))' unified to '¬RussianFederationOfficial(vladimir)'.", "FOL_sentence_old": "¬(Russian(vladimir) ∧ FederationOfficial(vladimir))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_483_147", "NL_sentence": "Ekaterina can participate in the 2024 United States presidential election or is a manager at Gazprom.", "FOL_sentence": "CanParticipateIn(ekaterina, y2024UnitedStatesElection) ∨ ManagerAt(ekaterina, gazprom)", "label": "True", "corrected": "yes", "correction_explanation": "ontology : Constant '2024UnitedStatesElection' → 'y2024UnitedStatesElection' for FOL naming compliance.", "FOL_sentence_old": "CanParticipateIn(ekaterina, 2024UnitedStatesElection) ∨ ManagerAt(ekaterina, gazprom)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_483_148", "NL_sentence": "Ekaterina can participate in the 2024 United States presidential election or Vladimir is a manager at Gazprom.", "FOL_sentence": "CanParticipateIn(ekaterina, y2024UnitedStatesElection) ∨ ManagerAt(vladimir, gazprom)", "label": "True", "corrected": "yes", "correction_explanation": "The original FOL uses ⊕ (exclusive disjunction) but the NL says 'or' without any indication of exclusivity. As shown in conclusion 147's derivation, CanParticipateIn(ekaterina, y2024UnitedStatesElection) is provable in both cases — meaning the first disjunct is always True. If the first disjunct is always True, then under ⊕ the conclusion would require ManagerAt(vladimir, gazprom) to be False for ⊕ to hold. Premise 5 establishes ¬ManagerAt(vladimir, gazprom), so under ⊕: True ⊕ False = True. Under ∨: True ∨ False = True. Both give True, but ⊕ is not warranted by the NL. Corrected to ∨.", "FOL_sentence_old": "CanParticipateIn(ekaterina, 2024UnitedStatesElection) ⊕ ManagerAt(vladimir, gazprom)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_483_149", "NL_sentence": "It is not true that Ekaterina can register to vote in the United States and Vladimir can participate in the 2024 United States presidential election.", "FOL_sentence": "¬(CanRegisterToVoteIn(ekaterina, unitedStates) ∧ CanParticipateIn(vladimir, y2024UnitedStatesElection))", "label": "False", "corrected": "yes", "correction_explanation": "Two corrections: (1) The original FOL omits the negation '¬' entirely — it reads 'CanRegisterToVoteIn(ekaterina, unitedStates) ∧ CanParticipateIn(vladimir, y2024UnitedStatesElection)', which is a positive conjunction. But the NL says 'It is NOT true that...', requiring the negation.", "FOL_sentence_old": "CanRegisterToVoteIn(ekaterina, unitedStates) ∧ CanParticipateIn(vladimir, 2024UnitedStatesElection)", "label_old": "False", "label_old_z3": "True", "label_z3": "False"} | |
| {"id": "story_80", "NL_sentence": "New Vessel Press is a publishing house specializing in translating foreign literature into English. All of New Vessel Press's published books are in English. Neapolitan Chronicles is a book published by New Vessel Press. Neapolitan Chronicles was translated from Italian. Palace of Flies is a book published by New Vessel Press.", "FOL_sentence": "PublishingHouse(newVesselPress) ∧ SpecializesInTranslatingIntoEnglish(newVesselPress, foreignLiterature) ∧ ∀x (Book(x) ∧ PublishedBy(x, newVesselPress) → In(x, english)) ∧ Book(neapolitanChronicles) ∧ PublishedBy(neapolitanChronicles, newVesselPress) ∧ TranslatedFrom(neapolitanChronicles, italian) ∧ Book(palaceOfFlies) ∧ PublishedBy(palaceOfFlies, newVesselPress)", "corrected": "no", "FOL_sentence_old": "PublishingHouse(newVesselPress) ∧ SpecializesInTranslatingIntoEnglish(newVesselPress, foreignLiterature)\n∀x ((Book(x) ∧ PublishedBy(x, newVesselPress)) → In(x, english))\nBook(neapolitanChronicles) ∧ PublishedBy(neapolitanChronicles, newVesselPress)\nTranslatedFrom(neapolitanChronicles, italian)\nBook(palaceOfFlies) ∧ PublishedBy(palaceOfFlies, newVesselPress)"} | |
| {"id": "concl_80_150", "NL_sentence": "Neapolitan Chronicles is an English book.", "FOL_sentence": "Book(neapolitanChronicles) ∧ In(neapolitanChronicles, english)", "label": "True", "corrected": "no", "FOL_sentence_old": "Book(neapolitanChronicles) ∧ In(neapolitanChronicles, english)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_80_151", "NL_sentence": "Harry Potter was published by New Vessel Press.", "FOL_sentence": "PublishedBy(harryPotter, newVesselPress)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "PublishedBy(harryPotter, newVesselPress)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_80_152", "NL_sentence": "Palace of Flies was translated from Italian.", "FOL_sentence": "TranslatedFrom(palaceOfFlies, italian)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "TranslatedFrom(palaceOfFlies, italian)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_363", "NL_sentence": "All hydrocarbons are organic compounds. All alkanes are hydrocarbons. All organic compounds are chemical compounds. All organic compounds contain carbon. No chemical compounds contain only one element. The mixture either both is a chemical compound and contains only one element, or neither.", "FOL_sentence": "∀x (Hydrocarbon(x) → OrganicCompound(x)) ∧ ∀x (Alkane(x) → Hydrocarbon(x)) ∧ ∀x (OrganicCompound(x) → ChemicalCompound(x)) ∧ ∀x (OrganicCompound(x) → Contain(x, carbon)) ∧ ∀x (ChemicalCompound(x) → (¬∃y (Contain(x, y) ∧ ∀z (Contain(x, z) → z = y)))) ∧ ¬(ChemicalCompound(mixture) ⊕ ∃y (Contain(mixture, y) ∧ ∀z (Contain(mixture, z) → z = y)))", "corrected": "yes", "correction_explanation": "Multiple corrections made: (1) Predicate naming inconsistency: the original uses both 'Orgranic(x) ∧ Compound(x)' (typo 'Orgranic', and splits organic compound into two predicates) and 'Chemical(x) ∧ Compound(x)' (same split). Unified to single predicates 'OrganicCompound(x)' and 'ChemicalCompound(x)' throughout, matching the NL 'organic compounds' and 'chemical compounds' as single concepts. (2) Premise 1: 'Orgranic' typo corrected to 'OrganicCompound'. (3) The fact that 'a compound contains only one element' was expressed as ∀y ∀z (¬(Contain(x, y) ∧ Contain(x, z) ∧ (y=z))). But this is satisfiable also if the compound doesn't contain any element. (4) Premise 6: the original has a free variable 'x' in the second disjunct of the ⊕ ('∀y ∀z (Contain(x, y) ∧ Contain(x, z) ∧ y=z)') — x is unbound. Corrected to use 'mixture' consistently. Also the 'only one element' condition is reformulated consistently as '∀y ∀z (Contain(mixture, y) ∧ Contain(mixture, z) → y = z)' — meaning all elements contained are the same.", "FOL_sentence_old": "∀x (Hydrocarbon(x) → Orgranic(x) ∧ Compound(x))\n∀x (Alkane(x) → Hydrocarbon(x))\n∀x (Orgranic(x) ∧ Compound(x) → Chemical(x) ∧ Compound(x))\n∀x (Orgranic(x) ∧ Compound(x) → Contain(x, carbon))\n∀x (Chemical(x) ∧ Compound(x) → ∀y ∀z (¬(Contain(x, y) ∧ Contain(x, z) ∧ (y=z))))\n¬((Chemical(mixture) ∧ Compound(mixture)) ⊕ (∀y ∀z (Contain(x, y) ∧ Contain(x, z) ∧ y=z)))"} | |
| {"id": "concl_363_153", "NL_sentence": "The mixture contains carbon.", "FOL_sentence": "Contain(mixture, carbon)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Contain(mixture, carbon)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_363_154", "NL_sentence": "The mixture is an alkane and contains carbon.", "FOL_sentence": "Alkane(mixture) ∧ Contain(mixture, carbon)", "label": "False", "corrected": "no", "FOL_sentence_old": "Alkane(mixture) ∧ Contain(mixture, carbon)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_258", "NL_sentence": "All humans are mortal. All Greeks are humans.", "FOL_sentence": "∀x (Human(x) → Mortal(x)) ∧ ∀x (Greek(x) → Human(x))", "corrected": "no", "FOL_sentence_old": "∀x (Human(x) → Mortal(x))\n∀x (Greek(x) → Human(x))"} | |
| {"id": "concl_258_156", "NL_sentence": "Some Greeks are mortal.", "FOL_sentence": "∃x (Greek(x) ∧ Mortal(x))", "label": "Uncertain", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "some_plural", "note": "The label 'Uncertain' is correct even under the corrected formulation: the premises establish that IF any Greek exists, they are mortal (Greek → Human → Mortal by universal chain). However, the premises never assert the existence of any Greek", "FOL_sentence_old": "∃x ∃y (Greek(x) ∧ Greek(y) ∧ Mortal(x) ∧ Mortal(y) ∧ ¬(x=y))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_435", "NL_sentence": "None of the students who currently work in the library are from the computer science department. All of the students with part-time jobs offered by the university currently work in the library. All of the students who are taking the database course are from the computer science department. All of the students taking a class with Professor David are taking the database course. All students working in the lab are taking a class with Professor David. James is a student working in the lab. James doesn't work in the lab or have a part-time job offered by the university.", "FOL_sentence": "∀x (Student(x) ∧ WorkIn(x, library) → ¬From(x, computerScienceDepartment)) ∧ ∀x (Student(x) ∧ ∃y (PartTimeJob(y) ∧ Have(x, y) ∧ OfferedBy(y, university)) → WorkIn(x, library)) ∧ ∀x (Student(x) ∧ Take(x, databaseCourse) → From(x, computerScienceDepartment)) ∧ ∀x (Student(x) ∧ InstructedBy(x, professorDavid) → Take(x, databaseCourse)) ∧ ∀x (Student(x) ∧ WorkIn(x, lab) → InstructedBy(x, professorDavid)) ∧ (Student(james) ∧ WorkIn(james, lab)) ∧ (¬WorkIn(james, lab) ∧ ¬∃y (PartTimeJob(y) ∧ Have(james, y) ∧ OfferedBy(y, university)))", "corrected": "yes", "correction_explanation": "Four corrections made: (1) Premise 2: the original '∀x (Student(x) ∧ Have(x, partTimeJob) ∧ OfferedBy(y, university) → WorkIn(x, library))' has a free variable 'y' in 'OfferedBy(y, university)' — y is unbound, making the formula ill-formed. (2) Premise 7: the original reads '¬∃x (PartTimeJob(x) ∧ Have(james, x) ∧ OfferedBy(x, computerScienceDepartment)) ∧ ¬WorkIn(james, lab)'. Two errors: (a) 'OfferedBy(x, computerScienceDepartment)' uses 'computerScienceDepartment' as the offerer, but the NL says 'offered by the university' — corrected to 'university'. (b) a remark more than an error: the premise should not to be considered ambiguous and should be treated as 'James neither works in lab, nor have a part-time job...' (notice the verb 'have' in the premises that goes with 'doesn't'). The problem with this formulation (that is the same given originally by the authors) is that the premises are contradictories, hence any conclusion must be True (and we set it so).", "FOL_sentence_old": "∀x (Student(x) ∧ WorkIn(x, library) → (¬From(x, computerScienceDepartment)))\n∀x (Student(x) ∧ Have(x, partTimeJob) ∧ OfferedBy(y, university) → WorkIn(x, library))\n∀x ((Student(x) ∧ Take(x, databaseCourse)) → From(x, computerScienceDepartment))\n∀x ((Student(x) ∧ InstructedBy(x, professorDavid)) → Take(x, databaseCourse))\n∀x ((Student(x) ∧ WorkIn(x, lab)) → InstructedBy(x, professorDavid))\nStudent(james) ∧ WorkIn(james, lab)\n¬∃x (PartTimeJob(x) ∧ Have(james, x) ∧ OfferedBy(x, computerScienceDepartment)) ∧ ¬WorkIn(james, lab)"} | |
| {"id": "concl_435_157", "NL_sentence": "James has a part-time job offered by the university.", "FOL_sentence": "∃y (PartTimeJob(y) ∧ Have(james, y) ∧ OfferedBy(y, university))", "label": "True", "corrected": "no", "FOL_sentence_old": "∃y (PartTimeJob(y) ∧ Have(james, y) ∧ OfferedBy(y, university))", "label_old": "False", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_435_158", "NL_sentence": "James does not have a part-time job offered by the university.", "FOL_sentence": "¬∃y (PartTimeJob(y) ∧ Have(james, y) ∧ OfferedBy(y, university))", "label": "True", "corrected": "no", "FOL_sentence_old": "¬∃y(PartTimeJob(y) ∧ Have(james, y) ∧ OfferedBy(y, university))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_435_159", "NL_sentence": "James either takes the database course or has a part-time job offered by the university.", "FOL_sentence": "Take(james, databaseCourse) ⊕ (∃y (PartTimeJob(y) ∧ Have(james, y) ∧ OfferedBy(y, university)))", "label": "True", "corrected": "yes", "ambiguity": true, "ambiguity_explanation": "either_or", "correction_explanation": "The original FOL has an unclosed parenthesis — added missing closing parenthesis around the full ⊕ expression.", "FOL_sentence_old": "Take(james, databaseCourse) ⊕ (∃y (PartTimeJob(y) ∧ Have(james, y) ∧ OfferedBy(y, university))", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "concl_435_160", "NL_sentence": "James takes the database course.", "FOL_sentence": "Take(james, databaseCourse)", "label": "True", "corrected": "no", "note": "The label 'Uncertain' appears inconsistent with the derivation chain shown in conclusion 159's note: WorkIn(james, lab) (premise 6) + premise 5 → InstructedBy(james, professorDavid) + premise 4 → Take(james, databaseCourse). This chain is valid and Take(james, databaseCourse) should be True, not Uncertain. The label appears to be a dataset error. However, there is a subtle issue: premise 4 requires 'Student(james) ∧ InstructedBy(james, professorDavid)' — Student(james) is established by premise 6, so the chain is complete. The label 'Uncertain' is retained as given but flagged as a likely dataset inconsistency — the correct label should be 'True' given the valid derivation chain.", "FOL_sentence_old": "Take(james, databaseCourse)", "label_old": "Uncertain", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "story_217", "NL_sentence": "If George likes music, he wants to compose. If George has access to a program, he can compose. If George can compose and wants to compose, he will compose.", "FOL_sentence": "(LikeMusic(george) → WantToCompose(george)) ∧ (AccessToProgram(george) → CanCompose(george)) ∧ (WantToCompose(george) ∧ CanCompose(george) → WillCompose(george))", "corrected": "yes", "correction_explanation": "ontology", "FOL_sentence_old": "LikeMusic(george) → WantToCompose(george)\nAccesstoProgram(george) → CanCompose(george)\n(WantToCompose(george) ∧ CanCompose(george)) → WillCompose(george)"} | |
| {"id": "concl_217_161", "NL_sentence": "If George likes music and has access to a program, he will compose.", "FOL_sentence": "(LikeMusic(george) ∧ AccessToProgram(george)) → WillCompose(george)", "label": "True", "corrected": "yes", "FOL_sentence_old": "(LikeMusic(george) ∧ AccesstoProgram(george)) → WillCompose(george)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_217_162", "NL_sentence": "If George will not compose, George cannot compose.", "FOL_sentence": "¬WillCompose(george) → ¬CanCompose(george)", "label": "Uncertain", "corrected": "yes", "FOL_sentence_old": "¬WantToCompose(george) → ¬WillCompose(george)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "story_292", "NL_sentence": "A hawk never swims. Some birds are hawks.", "FOL_sentence": "∀x (Hawk(x) → ¬Swim(x)) ∧ ∃x (Bird(x) ∧ Hawk(x))", "corrected": "no", "ambiguity": true, "ambiguity_explanation": "some_plural", "FOL_sentence_old": "∀x (Hawk(x) → ¬Swim(x))\n∃x ∃y (Bird(x) ∧ Bird(y) ∧ Hawk(x) ∧ Hawk(y) ∧ ¬(x=y))"} | |
| {"id": "concl_292_163", "NL_sentence": "All birds swim.", "FOL_sentence": "∀x (Bird(x) → Swim(x))", "label": "False", "corrected": "no", "FOL_sentence_old": "∀x (Bird(x) → Swim(x))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_318", "NL_sentence": "Some show airing at 8 pm on Monday gives out roses on TV. If a show gives out roses on TV, then the show is an episode of The Bachelor. The Bachelor portrays the lives of real people. All shows portraying the lives of real people are reality TV shows. Breaking Bad is a show. Breaking Bad is not a reality TV show.", "FOL_sentence": "∃x (Show(x) ∧ AiringAt(x, eightPMMonday) ∧ GivesOutOnTV(x, rose)) ∧ ∀x (Show(x) ∧ GivesOutOnTV(x, rose) → TheBachelor(x)) ∧ ∀x (TheBachelor(x) → Portray(x, livesOfRealPeople)) ∧ ∀x (Portray(x, livesOfRealPeople) → RealityTVShow(x)) ∧ Show(breakingBad) ∧ ¬RealityTVShow(breakingBad)", "corrected": "yes", "correction_explanation": "Several corrections made: (1) Premise 1: the original uses 'GivenOutOn(x, rose, tV)' (passive, 3-ary with capitalised 'tV') while premise 2 uses 'GivenOutOnAt(rose, tV, x)' (different argument order and predicate name) and conclusions use 'GivenOutOn(y, tv)' (2-ary). The predicate is used with inconsistent names, arities and argument orders across premises and conclusions. Unified to a consistent 3-ary predicate 'GivesOutOn(x, rose, tv)' where x is the show, matching the NL 'a show gives out roses on TV'. (2) Premise 1: 'AiringAtOn(x, 8PMMonday)' — the constant '8PMMonday' begins with a digit; replaced with 'eightPMMonday'. (3) Premise 4: the original uses 'liveOfRealPeople' (missing 's') while premise 3 uses 'lifeOfRealPeople' — both are inconsistent with each other and with the NL 'lives of real people'. Unified to 'livesOfRealPeople' throughout.", "FOL_sentence_old": "∃x (Show(x) ∧ AiringAtOn(x, 8PMMonday) ∧ GivenOutOn(x, rose, tV))\n∀x (Show(x) ∧ GivenOutOnAt(rose, tV, x) → TheBachelor(x))\n∀x (TheBachelor(x) → Portray(x, lifeOfRealPeople))\n∀x (Portray(x, liveOfRealPeople) → RealityTVShow(x))\nShow(breakingBad)\n¬RealityTVShow(breakingBad)"} | |
| {"id": "concl_318_164", "NL_sentence": "Breaking Bad is on Monday at 8 pm.", "FOL_sentence": "AiringAt(breakingBad, eightPMMonday)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "The original FOL reads '∀x (MondayAt8PM(x) ∧ On(breakingBad, x))' — a universal statement asserting that everything that is a Monday-8PM slot has Breaking Bad on it, which is a much stronger and stranger claim than the NL; furthermore, there is a symbol mismatch. The NL simply says 'Breaking Bad is on Monday at 8 pm', which is a ground atom. Corrected to 'AiringAt(breakingBad, eightPMMonday)' using the predicate from the corrected premises.", "FOL_sentence_old": "∀x (MondayAt8PM(x) ∧ On(breakingBad, x))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_318_165", "NL_sentence": "Breaking Bad is a TV show in which roses are given out on Monday at 8 pm.", "FOL_sentence": "Show(breakingBad) ∧ GivesOutOnTV(breakingBad, rose) ∧ AiringAt(breakingBad, eightPMMonday)", "label": "False", "corrected": "yes", "correction_explanation": "The original FOL reads '∀x ∀y (MondayAt8PM(x) ∧ Rose(y) ∧ GivenOutOn(y, tv) ∧ On(tv, x) ∧ From(y, breakingBad))' — a universal statement with multiple undefined predicates and a category error (From(y, breakingBad) treats y as a rose coming from Breaking Bad). Rewritten to use consistent predicate vocabulary: 'Show(breakingBad) ∧ GivesOutOn(breakingBad, rose, tv) ∧ AiringAt(breakingBad, eightPMMonday)'.", "FOL_sentence_old": "∀x ∀y (MondayAt8PM(x) ∧ Rose(y) ∧ GivenOutOn(y, tv) ∧ On(tv, x) ∧ From(y, breakingBad))", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "concl_318_166", "NL_sentence": "If roses are given out during Breaking Bad, then it is on Monday at 8 pm.", "FOL_sentence": "GivesOutOnTV(breakingBad, rose) → AiringAt(breakingBad, eightPMMonday)", "label": "True", "corrected": "yes", "correction_explanation": "The original FOL reads '∀x ∀y ((Rose(y) ∧ GivenOutOn(y, tv) ∧ On(tv, x) ∧ From(y, breakingBad)) → MondayAt8PM(x))' — using undefined predicates and a universally quantified structure. Simplified to a ground conditional using consistent predicate vocabulary: 'GivesOutOn(breakingBad, rose, tv) → AiringAt(breakingBad, eightPMMonday)'.", "note": "The label 'True' is by ex falso.", "FOL_sentence_old": "∀x ∀y ((Rose(y) ∧ GivenOutOn(y, tv) ∧ On(tv, x) ∧ From(y, breakingBad)) → MondayAt8PM(x))", "label_old": "True", "label_old_z3": "Uncertain", "label_z3": "True"} | |
| {"id": "story_107", "NL_sentence": "Heinrich Schmidt was a German politician. Heinrich Schmidt was also a member of the Prussian State Parliament and the Nazi Reichstag.", "FOL_sentence": "German(heinrichSchmidt) ∧ Politician(heinrichSchmidt) ∧ Member(heinrichSchmidt, prussianStateParliament) ∧ Member(heinrichSchmidt, naziReichstag)", "corrected": "no", "FOL_sentence_old": "German(heinrichSchmidt) ∧ Politician(heinrichSchmidt)\nMember(heinrichSchmidt, prussianStateParliament) ∧ Member(heinrichSchmidt, naziReichstag)"} | |
| {"id": "concl_107_167", "NL_sentence": "Heinrich Schmidt was German or Russian or both.", "FOL_sentence": "German(heinrichSchmidt) ∨ Russian(heinrichSchmidt)", "label": "True", "corrected": "no", "FOL_sentence_old": "German(heinrichSchmidt) ∨ Russian(heinrichSchmidt)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_107_168", "NL_sentence": "Some German politician was part of both the Prussian State Parliament and the Nazi Reichstag.", "FOL_sentence": "∃x (German(x) ∧ Politician(x) ∧ Member(x, prussianStateParliament) ∧ Member(x, naziReichstag))", "label": "True", "corrected": "no", "FOL_sentence_old": "∃x (German(x) ∧ Politician(x) ∧ Member(x, prussianStateParliament) ∧ Member(x, naziReichstag))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_107_169", "NL_sentence": "No politicians are part of the Nazi Reichstag.", "FOL_sentence": "∀x (Politician(x) → ¬Member(x, naziReichstag))", "label": "False", "corrected": "no", "FOL_sentence_old": "∀x (Politician(x) → ¬Member(x, naziReichstag))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_386", "NL_sentence": "If something is a deadly disease, then it comes with a low survival rate. Severe cancers are deadly diseases. Bile duct cancer is a severe form of cancer. All Cholangiocarcinoma is bile duct cancer. Mild flu comes with a low survival rate. Colorectal cancer is not both a bile duct cancer and with a low survival rate.", "FOL_sentence": "∀x (DeadlyDisease(x) → ComeWith(x, lowSurvivalRate)) ∧ ∀x (SevereCancer(x) → DeadlyDisease(x)) ∧ ∀x (BileDuctCancer(x) → SevereCancer(x)) ∧ ∀x (Cholangiocarcinoma(x) → BileDuctCancer(x)) ∧ ∀x (MildFlu(x) → ComeWith(x, lowSurvivalRate)) ∧ ¬(BileDuctCancer(colorectalCancer) ∧ ComeWith(colorectalCancer, lowSurvivalRate))", "corrected": "yes", "correction_explanation": "Three corrections made: (1) Predicate naming: the original uses 'DeadlyDiseases(x)' (plural) in premises 1 and 2 — corrected to singular 'DeadlyDisease(x)' to match standard predicate naming conventions and the NL 'a deadly disease'. (2) Premise 5: the original reads '∀x (MildFlu(x) → ¬ComeWith(x, lowSurvivalRate))' — this says mild flu does NOT come with a low survival rate, which is the correct biological reading (mild flu has high survival). However, the NL premise states 'Mild flu comes with a low survival rate', which is the opposite.", "FOL_sentence_old": "∀x (DeadlyDiseases(x) → ComeWith(x, lowSurvivalRate))\n∀x (SevereCancer(x) → DeadlyDiseases(x))\n∀x (BileDuctCancer(x) → SevereCancer(x))\n∀x (Cholangiocarcinoma(x) → BileDuctCancer(x))\n∀x (MildFlu(x) → ¬ComeWith(x, lowSurvivalRate)) \n¬(BileDuctCancer(colorectalCancer) ∧ ComeWith(colorectalCancer, lowSurvivalRate))"} | |
| {"id": "concl_386_170", "NL_sentence": "Colorectal cancer is a kind of severe cancer.", "FOL_sentence": "SevereCancer(colorectalCancer)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "SevereCancer(colorectalCancer)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_386_171", "NL_sentence": "If colorectal cancer is a kind of bile duct cancer or a form of Cholangiocarcinoma, then colorectal cancer is a kind of bile duct cancer and a kind of mild flu.", "FOL_sentence": "(BileDuctCancer(colorectalCancer) ∨ Cholangiocarcinoma(colorectalCancer)) → (BileDuctCancer(colorectalCancer) ∧ MildFlu(colorectalCancer))", "label": "True", "corrected": "no", "note": "The label 'True' is correct via ex falso.", "FOL_sentence_old": "¬(BileDuctCancer(colorectalCancer) ∨ Cholangiocarcinoma(colorectalCancer)) ∨ (BileDuctCancer(colorectalCancer) ∧ MildFlu(colorectalCancer))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_386_172", "NL_sentence": "Colorectal cancer is a form of Cholangiocarcinoma and it is a kind of mild flu or a kind of bile duct cancer, or all of the above.", "FOL_sentence": "Cholangiocarcinoma(colorectalCancer) ∧ (MildFlu(colorectalCancer) ∨ BileDuctCancer(colorectalCancer))", "label": "False", "corrected": "no", "FOL_sentence_old": "Cholangiocarcinoma(colorectalCancer) ∧ (MildFlu(colorectalCancer) ∨ BileDuctCancer(colorectalCancer))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_355", "NL_sentence": "All people who eat salads regularly are very conscious about their health and eating habits. All people who grew up in health-conscious childhood homes eat salads regularly. All people who fulfill their daily nutritional intakes grew up in health-conscious childhood homes. All people who disregard their physical well-being are not very conscious about their health and eating habits. If people visit the gym at least once a day, then they always fulfill their daily nutritional intakes. Taylor either grew up in a health-conscious childhood home and disregards her physical well-being, or she did neither.", "FOL_sentence": "∀x (RegularlyEat(x, salad) → ConsciousAbout(x, health) ∧ ConsciousAbout(x, eatingHabit)) ∧ ∀x (GrewUpIn(x, healthConsciousChildhoodHome) → RegularlyEat(x, salad)) ∧ ∀x (Fulfill(x, dailyNutritionalIntake) → GrewUpIn(x, healthConsciousChildhoodHome)) ∧ ∀x (Disregard(x, physicalWellbeing) → ¬(ConsciousAbout(x, health) ∧ ConsciousAbout(x, eatingHabit))) ∧ ∀x (VisitDaily(x, gym) → Fulfill(x, dailyNutritionalIntake)) ∧ ¬(GrewUpIn(taylor, healthConsciousChildhoodHome) ⊕ Disregard(taylor, physicalWellbeing))", "corrected": "yes", "correction_explanation": "Five corrections made: (1) Constant naming: the original uses 'health-consciousChildhoodHome' with a hyphen — hyphens are not suggested as FOL constant identifiers as they can be parsed as subtraction operators. Corrected to 'healthConsciousChildhoodHome' (camelCase) throughout all premises and conclusions. (2) Premise 1: the original uses 'ConsciousAbout(x, eatinggHabit)' — double 'g' typo, causing a mismatch. Corrected to 'ConsciousAbout(x, eatingHabit)'. (3) Premise 6: the original uses 'GrowUpIn' (present tense) instead of 'GrewUpIn' (past tense) used in premises 2 and 3. Unified to 'GrewUpIn' throughout", "FOL_sentence_old": "∀x (RegularlyEat(x, salad) → ConsciousAbout(x, health) ∧ ConsciousAbout(x, eatinggHabit))\n∀x (GrewUpIn(x, health-consciousChildhoodHome) → RegularlyEat(x, salad))\n∀x (Fulfill(x, dailyNutritionalIntake) → GrewUpIn(x, health-consciousChildhoodHome))\n∀x (Disregard(x, physicalWellbeing) → ¬(ConsciousAbout(x, health) ∧ ConsciousAbout(x, eatingHabit)))\n∀x (VisitDaily(x, gym) → Fulfill(x, dailyNutritionalIntake))\n¬(GrowUpIn(taylor, health-consciousChildhoodHome) ⊕ Disregard(taylor, physicalWellbeing))"} | |
| {"id": "concl_355_173", "NL_sentence": "Taylor eats salads regularly.", "FOL_sentence": "RegularlyEat(taylor, salad)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "RegularlyEat(taylor, salad)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_355_174", "NL_sentence": "Taylor visits the gym at least once a day.", "FOL_sentence": "VisitDaily(taylor, gym)", "label": "False", "corrected": "no", "note": "The label 'False' is correct: suppose VisitDaily(taylor, gym). By premise 5 → Fulfill(taylor, dailyNutritionalIntake) → by premise 3 → GrewUpIn(taylor, healthConsciousChildhoodHome). But the 'neither' case of premise 6 gives ¬GrewUpIn(taylor, healthConsciousChildhoodHome) — contradiction. Therefore VisitDaily(taylor, gym) is refutable under the closed-world assumption.", "FOL_sentence_old": "VisitDaily(taylor, gym)", "label_old": "False", "label_old_z3": "Uncertain", "label_z3": "False"} | |
| {"id": "concl_355_175", "NL_sentence": "Taylor neither grew up in a health-conscious childhood home nor does she visit the gym at least once a day.", "FOL_sentence": "¬GrewUpIn(taylor, healthConsciousChildhoodHome) ∧ ¬VisitDaily(taylor, gym)", "label": "True", "corrected": "yes", "correction_explanation": "'GrowUpIn' → 'GrewUpIn' for tense consistency; added missing closing parenthesis.", "FOL_sentence_old": "¬GrowUpIn(taylor, health-consciousChildhoodHome) ∧ ¬VisitDaily(taylor, gym))", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "story_51", "NL_sentence": "The summer Olympic games is a sporting event. The last summer Olympic games was in Tokyo. The United States won the most medals in Tokyo.", "FOL_sentence": "SportingEvent(olympics) ∧ LastSummerOlympics(tokyoolympics) ∧ MostMedals(unitedStates, tokyoolympics)", "corrected": "yes", "correction_explanation": "ontology", "FOL_sentence_old": "SportingEvent(olympics)\nLastSummerOlympics(tokyo)\nMostMedals(unitedStates, tokyo)"} | |
| {"id": "concl_51_176", "NL_sentence": "The world championships is a sporting event.", "FOL_sentence": "SportingEvent(champs)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "SportingEvent(champs)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_51_177", "NL_sentence": "The last summer Olympic games were not in Tokyo.", "FOL_sentence": "¬LastSummerOlympics(tokyoolympics)", "label": "False", "corrected": "no", "FOL_sentence_old": "¬LastSummerOlympics(tokyo)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_51_178", "NL_sentence": "The United States won the most medals in the last summer Olympic games.", "FOL_sentence": "∃x (LastSummerOlympics(x) ∧ MostMedals(unitedStates, x))", "label": "True", "corrected": "no", "FOL_sentence_old": "∃x (LastSummerOlympics(x) ∧ MostMedals(unitedStates, x))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "story_259", "NL_sentence": "All horses have hooves. No humans have hooves.", "FOL_sentence": "∀x (Horse(x) → ∃y ∃z (¬(y=z) ∧ Hoof(y) ∧ Hoof(z) ∧ Have(x, y) ∧ Have(x, z))) ∧ ∀x (Human(x) → ¬∃y (Hoof(y) ∧ Have(x, y)))", "corrected": "yes", "correction_explanation": "Two corrections made: (1) Premise 1: the original encodes 'all horses have hooves' as having at least two distinct hooves — '∃y ∃z (¬(y=z) ∧ Hoof(y) ∧ Hoof(z) ∧ Have(x, y) ∧ Have(x, z))'. While horses biologically have four hooves, the NL 'have hooves' (plural) could reasonably be interpreted as at least two. This encoding is retained as a plausible formalisation of the plural NL. (2) Premise 2: the original '∀x (Human(x) → ¬(∃y ∃z (¬(y=z) ∧ Hoof(y) ∧ Hoof(z) ∧ Have(x, y) ∧ Have(x, z))))' says humans do not have two distinct hooves — but this would allow humans to have exactly one hoof, which is not the intended meaning. The NL 'no humans have hooves' means humans have NO hooves at all. Corrected to '∀x (Human(x) → ¬∃y (Hoof(y) ∧ Have(x, y)))' — no hoof whatsoever.", "FOL_sentence_old": "∀x (Horse(x) → ∃y ∃z (¬(y=z) ∧ Hoof(y) ∧ Hoof(z) ∧ Have(x, y) ∧ Have(x, z)))\n∀x (Human(x) → ¬(∃y ∃z (¬(y=z) ∧ Hoof(y) ∧ Hoof(z) ∧ Have(x, y) ∧ Have(x, z))))"} | |
| {"id": "concl_259_179", "NL_sentence": "Some humans are horses.", "FOL_sentence": "∃x (Human(x) ∧ Horse(x))", "label": "False", "corrected": "yes", "correction_explanation": "The original FOL uses the two-witness pattern '∃x (Human(x) ∧ Human(y) ∧ Horse(x) ∧ Horse(y) ∧ ¬(x=y))' — additionally, 'y' appears free (no ∃y quantifier is present). This is ill-formed (free variable y).", "ambiguity": true, "ambiguity_explanation": "some_plural", "FOL_sentence_old": "∃x (Human(x) ∧ Human(y) ∧ Horse(x) ∧ Horse(y) ∧ ¬(x=y))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_152", "NL_sentence": "Susan flies to LGA airport. The departure and arrival cannot be at the same airport. John flies from LGA airport.", "FOL_sentence": "FlyTo(susan, lgaAirport) ∧ ∀x ∀y ¬(FlyFrom(x, y) ∧ FlyTo(x, y)) ∧ FlyFrom(john, lgaAirport)", "corrected": "yes", "correction_explanation": "One correction made: premise 2 in the original reads '∀x ∀y (FlyFrom(x, y) ⊕ FlyTo(x, y))' — universally quantifying over both x (person) and y (airport). This asserts that for ALL persons x and ALL airports y, x either flies from y or flies to y (but not both). This is far too strong — it would mean every person either flies from or flies to every airport, which is nonsensical. The intended meaning of 'departure and arrival cannot be at the same airport' is that no person both departs from and arrives at the same airport, i.e. for any person x and airport y, they cannot both FlyFrom(x, y) AND FlyTo(x, y). The correct encoding is: '∀x ∀y ¬(FlyFrom(x, y) ∧ FlyTo(x, y))' — equivalently, FlyFrom(x, y) → ¬FlyTo(x, y) and vice versa.", "FOL_sentence_old": "FlyTo(susan, lgaAirport)\n∀x ∀y (FlyFrom(x, y) ⊕ FlyTo(x, y))\nFlyFrom(john, lgaAirport)"} | |
| {"id": "concl_152_180", "NL_sentence": "Susan flies from LGA airport.", "FOL_sentence": "FlyFrom(susan, lgaAirport)", "label": "False", "corrected": "no", "FOL_sentence_old": "FlyFrom(susan, lgaAirport)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_152_181", "NL_sentence": "John flies to LGA airport.", "FOL_sentence": "FlyTo(john, lgaAirport)", "label": "False", "corrected": "no", "FOL_sentence_old": "FlyTo(john, lgaAirport)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_441", "NL_sentence": "No one nice to animals is also mean to animals. Some grumpy people are mean to animals. All animal lovers are nice to animals. All pet owners love animals. Tom is a pet owner.", "FOL_sentence": "∀x (NiceTo(x, animal) → ¬MeanTo(x, animal)) ∧ ∃x (Grumpy(x) ∧ MeanTo(x, animal)) ∧ ∀x (AnimalLover(x) → NiceTo(x, animal)) ∧ ∀x (PetOwner(x) → AnimalLover(x)) ∧ PetOwner(tom)", "corrected": "no", "ambiguity": true, "ambiguity_explanation": "some_plural", "FOL_sentence_old": "∀x (NiceTo(x, animal) → ¬MeanTo(x, animal))\n∃x (Grumpy(x) ∧ MeanTo(x, animal))\n∀x (AnimalLover(x) → NiceTo(x, animal))\n∀x (PetOwner(x) → AnimalLover(x))\nPetOwner(tom)"} | |
| {"id": "concl_441_182", "NL_sentence": "Tom is a grumpy person.", "FOL_sentence": "Grumpy(tom)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Grumpy(tom)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_441_183", "NL_sentence": "Tom is not both a grumpy person and mean to animals.", "FOL_sentence": "¬(Grumpy(tom) ∧ MeanTo(tom, animal))", "label": "True", "corrected": "no", "FOL_sentence_old": "¬(Grumpy(tom) ∧ MeanTo(tom, animal))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_441_184", "NL_sentence": "If Tom is not both a grumpy person and mean to animals, then Tom is neither a grumpy person nor an animal lover.", "FOL_sentence": "(¬(Grumpy(tom) ∧ MeanTo(tom, animal)) → ¬Grumpy(tom) ∧ ¬AnimalLover(tom))", "label": "False", "corrected": "yes", "correction_explanation": "The original FOL has an unclosed parenthesis in the consequent — added missing opening parenthesis to wrap the full conditional correctly. ", "FOL_sentence_old": "¬(Grumpy(tom) ∧ MeanTo(tom, animal)) → ¬Grumpy(tom) ∧ ¬AnimalLover(tom))", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "False"} | |
| {"id": "story_64", "NL_sentence": "A podcast is not a novel. If a person is born in an American city, the person is American. If a book is a novel and it is written by a person, then the person is a novel writer. Dani Shapiro is an American writer. Family History is written by Dani Shapiro. Family History is a novel written in 2003. Dani Shapiro created a podcast called Family Secrets. Boston is an American city.", "FOL_sentence": "∀x (Podcast(x) → ¬Novel(x)) ∧ ∀x (∃y (BornIn(x, y) ∧ City(y) ∧ LocatedIn(y, america)) → American(x)) ∧ ∀x ∀y (Novel(x) ∧ WrittenBy(x, y) → WritesNovel(y)) ∧ American(daniShapiro) ∧ Writer(daniShapiro) ∧ WrittenBy(familyHistory, daniShapiro) ∧ Novel(familyHistory) ∧ WrittenIn(familyHistory, yr2003) ∧ Podcast(familySecrets) ∧ CreatedBy(familySecrets, daniShapiro) ∧ City(boston) ∧ LocatedIn(boston, america)", "corrected": "yes", "correction_explanation": "Several corrections made: (1) Constant naming: the original uses underscores in constant names ('dani_Shapiro', 'family_History', 'family_Secrets') — while underscores are technically valid in some FOL notations, the consistent convention throughout this dataset is camelCase. Normalised to 'daniShapiro', 'familyHistory', 'familySecrets'. (2) Premise 2: the original has an unclosed parenthesis — '∀x((∃y(BornIn(x, y) ∧ City(y) ∧ LocatedIn(y, america)) → American(x))' missing closing parenthesis; corrected. (3) Premise 8: the original uses 'City(boston) ∧ American(boston)' — but 'American(boston)' treats Boston as an entity that is American using the same predicate applied to persons (American(daniShapiro)). The NL says 'Boston is an American city', meaning Boston is a city located in America. Corrected to 'City(boston) ∧ LocatedIn(boston, america)' to use the location predicate consistent with premise 2, and removed the conflation of 'American' as applying to both cities and people.", "FOL_sentence_old": "∀x (Podcast(x) → ¬Novel(x))\n∀x((∃y(BornIn(x, y) ∧ City(y) ∧ LocatedIn(y,america)) → American(x))\n∀x ∀y ((Novel(x) ∧ WrittenBy(x, y)) → WritesNovel(y))\nAmerican(dani_Shapiro) ∧ Writer(dani_Shapiro)\nWrittenBy(family_History, dani_Shapiro)\nNovel(family_History) ∧ WrittenIn(family_History, yr2003)\nPodcast(family_Secrets) ∧ CreatedBy(family_Secrets, dani_Shapiro)\nCity(boston) ∧ American(boston)"} | |
| {"id": "concl_64_185", "NL_sentence": "Dani Shapiro is a novel writer.", "FOL_sentence": "WritesNovel(daniShapiro)", "label": "True", "corrected": "yes", "correction_explanation": "ontology", "FOL_sentence_old": "WritesNovel(dani_Shapiro)", "label_old": "True", "label_old_z3": "not_parsable", "label_z3": "True"} | |
| {"id": "concl_64_186", "NL_sentence": "Family Secrets is a novel.", "FOL_sentence": "Novel(familySecrets)", "label": "False", "corrected": "yes", "correction_explanation": "Two corrections: (1) Predicate name 'IsNovel' → 'Novel' to match premise usage. (2) Constant 'family_Secrets' → 'familySecrets' for camelCase consistency.", "FOL_sentence_old": "IsNovel(family_Secrets)", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "False"} | |
| {"id": "concl_64_187", "NL_sentence": "Dani Shapiro was born in Boston.", "FOL_sentence": "BornIn(daniShapiro, boston)", "label": "Uncertain", "corrected": "yes", "correction_explanation": "ontology", "FOL_sentence_old": "BornIn(dani_Shapiro, boston)", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "story_456", "NL_sentence": "Some professional basketball players are not American nationals. All professional basketball players can do jump shots. If someone can do jump shots, they leap straight into the air. If someone leaps straight into the air, they activate their leg muscles. Yuri does not activate his leg muscles.", "FOL_sentence": "∃x (Professional(x) ∧ BasketballPlayer(x) ∧ ¬AmericanNational(x)) ∧ ∀x (Professional(x) ∧ BasketballPlayer(x) → CanDo(x, jumpShot)) ∧ ∀x (CanDo(x, jumpShot) → LeapStraightIntoAir(x)) ∧ ∀x (LeapStraightIntoAir(x) → Activate(x, legMuscle)) ∧ ¬Activate(yuri, legMuscle)", "corrected": "no", "FOL_sentence_old": "∃x (Professional(x) ∧ BasketballPlayer(x) ∧ ¬AmericanNational(x))\n∀x (Professional(x) ∧ BasketballPlayer(x) → CanDo(x, jumpShot))\n∀x (CanDo(x, jumpShot) → LeapStraightIntoAir(x))\n∀x (LeapStraightIntoAir(x) → Activate(x, legMuscle))\n¬Activate(yuri, legMuscle)"} | |
| {"id": "concl_456_188", "NL_sentence": "Yuri is an American national.", "FOL_sentence": "AmericanNational(yuri)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "AmericanNational(yuri)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_456_189", "NL_sentence": "Yuri is not an American professional basketball player.", "FOL_sentence": "¬(AmericanNational(yuri) ∧ Professional(yuri) ∧ BasketballPlayer(yuri))", "label": "True", "corrected": "no", "FOL_sentence_old": "¬(AmericanNational(yuri) ∧ Professional(yuri) ∧ BasketballPlayer(yuri))", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "concl_456_190", "NL_sentence": "Yuri is an American professional basketball player.", "FOL_sentence": "AmericanNational(yuri) ∧ Professional(yuri) ∧ BasketballPlayer(yuri)", "label": "False", "corrected": "no", "FOL_sentence_old": "AmericanNational(yuri) ∧ Professional(yuri) ∧ BasketballPlayer(yuri)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_456_191", "NL_sentence": "If Yuri does not leap straight into the air, then Yuri is an American professional basketball player.", "FOL_sentence": "¬LeapStraightIntoAir(yuri) → (AmericanNational(yuri) ∧ Professional(yuri) ∧ BasketballPlayer(yuri))", "label": "False", "corrected": "no", "FOL_sentence_old": "¬LeapStraightIntoAir(yuri) → (AmericanNational(yuri) ∧ Professional(yuri) ∧ BasketballPlayer(yuri))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_456_192", "NL_sentence": "If Yuri is not an American professional basketball player, then Yuri is a professional basketball player.", "FOL_sentence": "¬(AmericanNational(yuri) ∧ Professional(yuri) ∧ BasketballPlayer(yuri)) → (Professional(yuri) ∧ BasketballPlayer(yuri))", "label": "False", "corrected": "no", "FOL_sentence_old": "¬(AmericanNational(yuri) ∧ Professional(yuri) ∧ BasketballPlayer(yuri)) → (Professional(yuri) ∧ BasketballPlayer(yuri))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_280", "NL_sentence": "Events are either happy or sad. At least one event is happy.", "FOL_sentence": "∀x (Event(x) → Happy(x) ⊕ Sad(x)) ∧ ∃x (Event(x) ∧ Happy(x))", "corrected": "no", "ambiguity": true, "ambiguity_commentary": "either_or", "FOL_sentence_old": "∀x (Event(x) → Happy(x) ⊕ Sad(x))\n∃x (Event(x) ∧ Happy(x)) "} | |
| {"id": "concl_280_193", "NL_sentence": "All events are sad.", "FOL_sentence": "∀x (Event(x) → Sad(x))", "label": "False", "corrected": "no", "FOL_sentence_old": "∀x (Event(x) → Sad(x))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "story_140", "NL_sentence": "The winner of the 1992 du Maurier Classic was Steinhauer. Steinhauer participated in the 1992 du Maurier Classic. One six-way tie was on the leaderboard, and one person in the six-way tie was from Belgium. Descampe is from Belgium and is on the leaderboard of the 1992 du Maurier Classic. All people on the leaderboard of the 1992 du Maurier Classic participated in the 1992 du Maurier Classic.", "FOL_sentence": "WinnerOf(steinhauer, duMaurierClassic, year1992) ∧ Participate(steinhauer, duMaurierClassic, year1992) ∧ ∃x ∃y (OnLeaderboardOf(x, duMaurierClassic) ∧ SixWayTie(x) ∧ In(y, x) ∧ From(y, belgium)) ∧ From(descampe, belgium) ∧ OnLeaderboardOf(descampe, duMaurierClassic) ∧ ∀x (OnLeaderboardOf(x, duMaurierClassic) → Participate(x, duMaurierClassic, year1992)) ∧ ∀x ∀y ∀z (OnLeaderboardOf(x, y) ∧ In(z, x) → OnLeaderboardOf(z, y))", "corrected": "yes", "correction_explanation": "Several corrections made: (1) Premise 2: the original uses 'Participate(duMaurierClassic, steinhauer, year1992)' with the event as the first argument and the person as the second — reversed from the NL 'Steinhauer participated in the 1992 du Maurier Classic' where the person is the subject. Corrected to 'Participate(steinhauer, duMaurierClassic, year1992)' for consistent person-first argument order. (2) Premise 3: the original has a misplaced closing parenthesis — '∃x ∃y (OnLeaderBoardOf(x, duMaurierClassic) ∧ SixWayTie(x)) ∧ In(y, sixWayTie) ∧ Belgium(y))' causes y to fall outside the ∃y scope. Corrected to '∃x ∃y (OnLeaderboardOf(x, duMaurierClassic) ∧ SixWayTie(x) ∧ In(y, x) ∧ From(y, belgium))' — y is now properly scoped, and 'In(y, sixWayTie)' is corrected to 'In(y, x)' since x is the six-way tie entity (not a separate constant 'sixWayTie'). Also 'Belgium(y)' corrected to 'From(y, belgium)' to match the predicate used in premise 4. (3) Predicate casing: 'OnLeaderBoardOf' (capital B) normalised to 'OnLeaderboardOf' throughout. (4) Premise 5: the original reads '∀x (LeaderBoard(maurier, x) → Participate(maurier, x))' — uses an undefined binary predicate 'LeaderBoard(maurier, x)' with 'maurier' as a new constant not introduced elsewhere, and 'Participate(maurier, x)' with the wrong argument order and wrong subject. Corrected to '∀x (OnLeaderboardOf(x, duMaurierClassic) → Participate(x, duMaurierClassic, year1992))' to match the NL 'all people on the leaderboard of the 1992 du Maurier Classic participated in the 1992 du Maurier Classic'. (5) Added (at the end of the premises) the implicitely assumed fact that any person in the tie in the leaderbord is in the leaderbord itself (not necessary for the conclusions).", "ambiguity": true, "ambiguity_explanation": "yes: premises 3 implicitly states that there is a unique six-way tie or only one person in it from Belgium? (No implications in the conclusions labels)", "FOL_sentence_old": "WinnerOf(steinhauer, duMaurierClassic, year1992)\nParticipate(duMaurierClassic, steinhauer, year1992)\n∃x ∃y (OnLeaderBoardOf(x, duMaurierClassic) ∧ SixWayTie(x)) ∧ In(y, sixWayTie) ∧ Belgium(y))\nFrom(descampe, belgium) ∧ OnLeaderBoardOf(descampe, duMaurierClassic)\n∀x (LeaderBoard(maurier, x) → Participate(maurier, x))"} | |
| {"id": "concl_140_194", "NL_sentence": "Steinhauer was not the winner of the 1992 du Maurier Classic.", "FOL_sentence": "¬WinnerOf(steinhauer, duMaurierClassic, year1992)", "label": "False", "corrected": "no", "FOL_sentence_old": "¬WinnerOf(steinhauer, duMaurierClassic, year1992)", "label_old": "False", "label_old_z3": "not_parsable", "label_z3": "False"} | |
| {"id": "concl_140_195", "NL_sentence": "Descampe is in the six-way tie in the leaderboard of the 1992 du Maurier Classic.", "FOL_sentence": "∃x (SixWayTie(x) ∧ OnLeaderboardOf(x, duMaurierClassic) ∧ In(descampe, x))", "label": "Uncertain", "corrected": "yes", "correction_explanation": "The original FOL 'SixWayTie(descampe)' treats 'SixWayTie' as a unary predicate applying directly to Descampe — asserting Descampe herself is a six-way tie, which is a category error. The NL says 'Descampe is IN the six-way tie', meaning Descampe is a participant in a six-way tie entity. Corrected to '∃x (SixWayTie(x) ∧ OnLeaderboardOf(x, duMaurierClassic) ∧ In(descampe, x))' — there exists a six-way tie x on the leaderboard such that Descampe is in it.", "FOL_sentence_old": "SixWayTie(descampe)", "label_old": "Uncertain", "label_old_z3": "not_parsable", "label_z3": "Uncertain"} | |
| {"id": "story_459", "NL_sentence": "Jane does not like any animals that bark. All dogs are animals that bark. Jane likes all animals that jump. If an animal has legs, then it jumps. If an animal is terricolous, then it has legs. KiKi is an animal. If KiKi neither jumps nor has legs, then KiKi is terricolous or has legs.", "FOL_sentence": "∀x (Animal(x) ∧ Bark(x) → ¬Like(jane, x)) ∧ ∀x (Dog(x) → Animal(x) ∧ Bark(x)) ∧ ∀x (Animal(x) ∧ Jump(x) → Like(jane, x)) ∧ ∀x (Animal(x) ∧ HasLegs(x) → Jump(x)) ∧ ∀x (Animal(x) ∧ Terricolous(x) → HasLegs(x)) ∧ Animal(kiki) ∧ (¬Jump(kiki) ∧ ¬HasLegs(kiki) → Terricolous(kiki) ∨ HasLegs(kiki))", "corrected": "yes", "correction_explanation": "Three corrections made: (1) Premises 4 and 5 and premise 7: the original encodes 'has legs' using the two-witness existential '∃y ∃z (¬(y=z) ∧ Leg(y) ∧ Leg(z) ∧ Have(x, y) ∧ Have(x, z))' — asserting at least two distinct leg objects. While most animals have more than one leg, the NL simply says 'has legs' as a property. This encoding is unnecessarily complex and creates asymmetric treatment compared to other predicates. More importantly, using this complex existential in premise 7's antecedent and consequent makes the formula hard to reason with. Simplified to a unary predicate 'HasLegs(x)' throughout for clarity and consistency. (2) Premise 7: the original antecedent uses '¬Jump(kiki) ∧ ¬(∃y ∃z (...))' which is the negation of the two-witness leg condition. Under the simplified HasLegs predicate, this becomes '¬Jump(kiki) ∧ ¬HasLegs(kiki)'. The consequent 'Terricolous(kiki) ∨ ∃y ∃z (...)' similarly simplified to 'Terricolous(kiki) ∨ HasLegs(kiki)'. (3) In premises 4 and 5, we should add the relativization to animals (add Animal(x) in the assumptions of the implications)", "FOL_sentence_old": "∀x (Animal(x) ∧ Bark(x) → ¬Like(jane, x))\n∀x (Dog(x) → Animal(x) ∧ Bark(x))\n∀x (Animal(x) ∧ Jump(x) → Like(jane, x))\n∀x (∃y ∃z (¬(y=z) ∧ Leg(y) ∧ Leg(z) ∧ Have(x, y) ∧ Have(x, z)) → Jump(x))\n∀x (Terricolous(x) → ∃y ∃z (¬(y=z) ∧ Leg(y) ∧ Leg(z) ∧ Have(x, y) ∧ Have(x, z)))\nAnimal(kiki)\n¬Jump(kiki) ∧ ¬(∃y ∃z (¬(y=z) ∧ Leg(y) ∧ Leg(z) ∧ Have(kiki, y) ∧ Have(kiki, z))) → Terricolous(kiki) ∨ ∃y ∃z (¬(y=z) ∧ Leg(y) ∧ Leg(z) ∧ Have(kiki, y) ∧ Have(kiki, z))"} | |
| {"id": "concl_459_196", "NL_sentence": "KiKi is terricolous.", "FOL_sentence": "Terricolous(kiki)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "Terricolous(kiki)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_459_197", "NL_sentence": "KiKi is a barking dog.", "FOL_sentence": "Bark(kiki) ∧ Dog(kiki)", "label": "False", "corrected": "no", "note": "The label 'False' was incorrect, since no information about the fact that Kiki is a dog (or it's barking) is mentioned in the premises.", "FOL_sentence_old": "Bark(kiki) ∧ Dog(kiki)", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_459_198", "NL_sentence": "KiKi does not bark and he is not a dog.", "FOL_sentence": "¬Bark(kiki) ∧ ¬Dog(kiki)", "label": "True", "corrected": "no", "note": "The label 'False' was incorrect, since no information about the fact that Kiki is a dog (or it's barking) is mentioned in the premises.", "FOL_sentence_old": "¬Bark(kiki) ∧ ¬Dog(kiki)", "label_old": "True", "label_old_z3": "True", "label_z3": "True"} | |
| {"id": "story_101", "NL_sentence": "Ailton Silva, born in 1995, is commonly known as Ailton. Ailton is a football player who was loaned out to Braga. Ailton Silva is a Brazilian footballer who plays for Náutico. Náutico is a football club along with Braga. Fluminense is a football club.", "FOL_sentence": "BornIn(ailtonSilva, year1995) ∧ CommonlyKnownAs(ailtonSilva, ailton) ∧ ailton = ailtonSilva ∧ FootballPlayer(ailton) ∧ LoanedTo(ailton, braga) ∧ Brazilian(ailtonSilva) ∧ FootballPlayer(ailtonSilva) ∧ PlayFor(ailtonSilva, nautico) ∧ FootballClub(nautico) ∧ FootballClub(braga) ∧ FootballClub(fluminense)", "corrected": "yes", "correction_explanation": "Three corrections made: (1) Premise 3: the original uses 'Footballplayer(ailtonSilva)' (lowercase 'p') inconsistent with 'FootballPlayer(ailton)' (uppercase 'P') in premise 2. Unified to 'FootballPlayer(ailtonSilva)'. (2) The story uses two distinct constants 'ailton' and 'ailtonSilva' for the same person — 'Ailton' is explicitly stated to be the common name for 'Ailton Silva' via CommonlyKnownAs(ailtonSilva, ailton). This means premises about 'ailton' (premises 2) and premises about 'ailtonSilva' (premises 1, 3) refer to the same individual but through different constants. For full logical interoperability, an identity axiom ailton = ailtonSilva or a bridging axiom would be needed. This is flagged as a modelling gap — without it, properties of 'ailton' (e.g. LoanedTo(ailton, braga)) cannot be directly transferred to 'ailtonSilva' via standard FOL.", "FOL_sentence_old": "BornIn(ailtonSilva, year1995) ∧ CommonlyKnownAs(ailtonSilva, ailton)\nFootballPlayer(ailton) ∧ LoanedTo(ailton, braga)\nBrazilian(ailtonSilva) ∧ Footballplayer(ailtonSilva) ∧ PlayFor(ailtonSilva, nautico)\nFootballClub(nautico) ∧ FootballClub(braga)\nFootballClub(fluminense)"} | |
| {"id": "concl_101_199", "NL_sentence": "No one playing for Nautico is Brazilian.", "FOL_sentence": "∀x (PlayFor(x, nautico) → ¬Brazilian(x))", "label": "False", "corrected": "no", "FOL_sentence_old": "∀x (PlayFor(x, nautico) → ¬Brazilian(x))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_101_200", "NL_sentence": "Ailton Silva does not play for a football club.", "FOL_sentence": "∀x (FootballClub(x) → ¬PlayFor(ailtonSilva, x))", "label": "False", "corrected": "no", "FOL_sentence_old": "∀x (FootballClub(x) → ¬PlayFor(ailtonSilva, x))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_101_201", "NL_sentence": "Ailton was not loaned out to a football club.", "FOL_sentence": "∀x (FootballClub(x) → ¬LoanedTo(ailton, x))", "label": "False", "corrected": "no", "FOL_sentence_old": "∀x (FootballClub(x) → ¬LoanedTo(ailton, x))", "label_old": "False", "label_old_z3": "False", "label_z3": "False"} | |
| {"id": "concl_101_202", "NL_sentence": "Ailton Silva played for Fluminense.", "FOL_sentence": "PlayFor(ailtonSilva, fluminense)", "label": "Uncertain", "corrected": "no", "FOL_sentence_old": "PlayFor(ailtonSilva, fluminense)", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "Uncertain"} | |
| {"id": "concl_101_203", "NL_sentence": "Ailton Silva was loaned out to a football club.", "FOL_sentence": "∃x (FootballClub(x) ∧ LoanedTo(ailtonSilva, x))", "label": "True", "corrected": "no", "note": "The label was 'Uncertain' (it reflects the two constants identity gap), but it should be True, since ailtonSilva = ailton.", "FOL_sentence_old": "∃x (FootballClub(x) ∧ LoanedTo(ailtonSilva, x))", "label_old": "Uncertain", "label_old_z3": "Uncertain", "label_z3": "True"} | |