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LogicNLI-reimpl

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unigram 1

If someone is either patient or not patient then someone is not calm or brave and vice versa. Everyone who is either calm or not wise is not kind or not old and vice versa. Everyone who is both creative and calm is not patient or patient. Everyone who is both not funny and not calm is both not funny and not curious and vice versa. Everyone who is not patient or humble is not creative and vice versa. Everyone who is both not happy and not old is either calm or not rich and vice versa. Everyone who is both quiet and rich is both strong and not funny and vice versa. Everyone who is both not curious and not tall is strong and vice versa. If mary is both not old and not tall then someone is both not funny and generous. Everyone who is both wise and old is either not creative or not rich and vice versa. Everyone who is both calm and not rich is not wise. Everyone who is either strong or kind is not calm or not happy and vice versa. If someone is both humble and not brave then lucy is brave or kind and vice versa. Everyone who is either strong or not kind is patient and vice versa. Everyone who is either not tall or not creative is happy and vice versa. Everyone who is happy or not rich is both not patient and not curious. Paul is patient or humble. Someone is tall or not strong. Someone is not humble or not rich. Susan is both not strong and not tall. Someone is either not humble or strong. Someone is either generous or strong. Someone is curious.

Paul is generous.

neutral

((?[X]:((patient(X)<~>~patient(X))))<=>(?[X]:((~calm(X)|brave(X)))))& (![X]:((calm(X)<~>~wise(X))<=>(~kind(X)|~old(X))))& (![X]:((creative(X)&calm(X))=>(~patient(X)|patient(X))))& (![X]:((~funny(X)&~calm(X))<=>(~funny(X)&~curious(X))))& (![X]:((~patient(X)|humble(X))<=>~creative(X)))& (![X]:((~happy(X)&~old(X))<=>(calm(X)<~>~rich(X))))& (![X]:((quiet(X)&rich(X))<=>(strong(X)&~funny(X))))& (![X]:((~curious(X)&~tall(X))<=>strong(X)))& (((~old(mary)&~tall(mary)))=>(?[X]:((~funny(X)&generous(X)))))& (![X]:((wise(X)&old(X))<=>(~creative(X)<~>~rich(X))))& (![X]:((calm(X)&~rich(X))=>~wise(X)))& (![X]:((strong(X)<~>kind(X))<=>(~calm(X)|~happy(X))))& ((?[X]:((humble(X)&~brave(X))))<=>((brave(lucy)|kind(lucy))))& (![X]:((strong(X)<~>~kind(X))<=>patient(X)))& (![X]:((~tall(X)<~>~creative(X))<=>happy(X)))& (![X]:((happy(X)|~rich(X))=>(~patient(X)&~curious(X))))& ((patient(paul)|humble(paul)))& (?[X]:((tall(X)|~strong(X))))& (?[X]:((~humble(X)|~rich(X))))& ((~strong(susan)&~tall(susan)))& (?[X]:((~humble(X)<~>strong(X))))& (?[X]:((generous(X)<~>strong(X))))& (?[X]:(curious(X)))

generous(paul)

Everyone who is rich or strong is not tall or not creative. Everyone who is strong is generous or not creative and vice versa. Everyone who is either not strong or patient is both humble and brave and vice versa. If susan is not kind or patient then someone is both not old and funny and vice versa. Everyone who is both humble and creative is either not quiet or not old. Everyone who is not patient or not creative is both rich and not humble. Everyone who is both rich and kind is quiet. Everyone who is both kind and tall is patient and vice versa. Everyone who is both not old and not calm is tall. If someone is not kind then someone is not funny or generous and vice versa. If someone is either not patient or not creative then john is not funny. If fred is creative then john is not tall or strong. Everyone who is either not generous or not kind is humble or not old. Everyone who is strong is either old or creative and vice versa. Everyone who is wise or not brave is wise or not old. Everyone who is either not brave or not happy is funny. Someone is not old. Alice is both patient and calm. Susan is quiet or strong. Someone is both funny and not patient. Someone is not quiet. Someone is not wise. Mary is either curious or kind. Someone is both rich and not calm.

Alice is not rich.

entailment

(![X]:((rich(X)|strong(X))=>(~tall(X)|~creative(X))))& (![X]:(strong(X)<=>(generous(X)|~creative(X))))& (![X]:((~strong(X)<~>patient(X))<=>(humble(X)&brave(X))))& (((~kind(susan)|patient(susan)))<=>(?[X]:((~old(X)&funny(X)))))& (![X]:((humble(X)&creative(X))=>(~quiet(X)<~>~old(X))))& (![X]:((~patient(X)|~creative(X))=>(rich(X)&~humble(X))))& (![X]:((rich(X)&kind(X))=>quiet(X)))& (![X]:((kind(X)&tall(X))<=>patient(X)))& (![X]:((~old(X)&~calm(X))=>tall(X)))& ((?[X]:(~kind(X)))<=>(?[X]:((~funny(X)|generous(X)))))& ((?[X]:((~patient(X)<~>~creative(X))))=>(~funny(john)))& ((creative(fred))=>((~tall(john)|strong(john))))& (![X]:((~generous(X)<~>~kind(X))=>(humble(X)|~old(X))))& (![X]:(strong(X)<=>(old(X)<~>creative(X))))& (![X]:((wise(X)|~brave(X))=>(wise(X)|~old(X))))& (![X]:((~brave(X)<~>~happy(X))=>funny(X)))& (?[X]:(~old(X)))& ((patient(alice)&calm(alice)))& ((quiet(susan)|strong(susan)))& (?[X]:((funny(X)&~patient(X))))& (?[X]:(~quiet(X)))& (?[X]:(~wise(X)))& ((curious(mary)<~>kind(mary)))& (?[X]:((rich(X)&~calm(X))))

~rich(alice)

% SZS status Unsatisfiable for 8968027115681088907435595 % SZS output start Proof for 8968027115681088907435595 1. ! [X0] : ((strong(X0) | rich(X0)) => (~creative(X0) | ~tall(X0))) [input p0] 2. ! [X0] : (strong(X0) <=> (~creative(X0) | generous(X0))) [input p1] 3. ! [X0] : ((~strong(X0) <~> patient(X0)) <=> (brave(X0) & humble(X0))) [input p2] 6. ! [X0] : ((~creative(X0) | ~patient(X0)) => (~humble(X0) & rich(X0))) [input p5] 8. ! [X0] : ((tall(X0) & kind(X0)) <=> patient(X0)) [input p7] 18. calm(alice) & patient(alice) [input p17] 25. rich(alice) [input hypothesis] 27. ! [X0] : ((~creative(X0) | ~tall(X0)) | (~strong(X0) & ~rich(X0))) [ennf transformation 1] 28. ! [X0] : (~creative(X0) | ~tall(X0) | (~strong(X0) & ~rich(X0))) [flattening 27] 31. ! [X0] : ((~humble(X0) & rich(X0)) | (creative(X0) & patient(X0))) [ennf transformation 6] 44. ! [X0] : ((strong(X0) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | ~strong(X0))) [nnf transformation 2] 45. ! [X0] : ((strong(X0) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | ~strong(X0))) [flattening 44] 46. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [nnf transformation 3] 47. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [flattening 46] 54. ! [X0] : (((tall(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | (~tall(X0) | ~kind(X0)))) [nnf transformation 8] 55. ! [X0] : (((tall(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | ~tall(X0) | ~kind(X0))) [flattening 54] 76. ~creative(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 28] 80. creative(X0) | strong(X0) [cnf transformation 45] 82. ~patient(X0) | ~strong(X0) | humble(X0) [cnf transformation 47] 97. ~humble(X0) | creative(X0) [cnf transformation 31] 101. ~patient(X0) | tall(X0) [cnf transformation 55] 120. patient(alice) [cnf transformation 18] 131. rich(alice) [cnf transformation 25] 230. tall(alice) [resolution 101,120] 238. ~tall(X1) | ~rich(X1) | strong(X1) [resolution 76,80] 257. ~strong(alice) | humble(alice) [resolution 82,120] 261. 22 <=> humble(alice) [avatar definition] 263. humble(alice) <- (22) [avatar component clause 261] 265. 23 <=> strong(alice) [avatar definition] 268. 22 | ~23 [avatar split clause 257,265,261] 380. ~rich(alice) | strong(alice) [resolution 238,230] 383. strong(alice) [subsumption resolution 380,131] 387. 23 [avatar split clause 383,265] 394. creative(alice) <- (22) [resolution 263,97] 427. ~tall(alice) | ~rich(alice) <- (22) [resolution 394,76] 432. ~rich(alice) <- (22) [subsumption resolution 427,230] 433. $false <- (22) [subsumption resolution 432,131] 434. ~22 [avatar contradiction clause 433] 435. $false [avatar sat refutation 268,387,434] % SZS output end Proof for 8968027115681088907435595 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.031 s % ------------------------------ % ------------------------------

Everyone who is both brave and happy is curious. If someone is both not calm and curious then paul is either funny or not calm. Everyone who is happy is not happy or not funny and vice versa. If lucy is either curious or not funny then paul is either not wise or not patient. Everyone who is not generous is quiet. Everyone who is patient or wise is both curious and rich. If lucy is quiet then susan is not creative or not strong. Everyone who is not calm is not patient or not generous. If someone is either curious or not generous then someone is not curious. If john is either rich or not calm then someone is either tall or not funny. Everyone who is either not rich or not patient is either not brave or not generous. If someone is funny then fred is both happy and not old and vice versa. If alice is not rich then alice is both humble and not old. Everyone who is either strong or not wise is both not patient and calm. If susan is either not wise or calm then paul is both strong and calm and vice versa. Someone is either patient or humble. Someone is brave. Alice is not wise. Susan is wise. Someone is both not rich and calm. Lucy is brave. Someone is both not wise and not generous.

Fred is not happy.

contradiction

(![X]:((brave(X)&happy(X))=>curious(X)))& ((?[X]:((~calm(X)&curious(X))))=>((funny(paul)<~>~calm(paul))))& (![X]:(happy(X)<=>(~happy(X)|~funny(X))))& (((curious(lucy)<~>~funny(lucy)))=>((~wise(paul)<~>~patient(paul))))& (![X]:(~generous(X)=>quiet(X)))& (![X]:((patient(X)|wise(X))=>(curious(X)&rich(X))))& ((quiet(lucy))=>((~creative(susan)|~strong(susan))))& (![X]:(~calm(X)=>(~patient(X)|~generous(X))))& ((?[X]:((curious(X)<~>~generous(X))))=>(?[X]:(~curious(X))))& (((rich(john)<~>~calm(john)))=>(?[X]:((tall(X)<~>~funny(X)))))& (![X]:((~rich(X)<~>~patient(X))=>(~brave(X)<~>~generous(X))))& ((?[X]:(funny(X)))<=>((happy(fred)&~old(fred))))& ((~rich(alice))=>((humble(alice)&~old(alice))))& (![X]:((strong(X)<~>~wise(X))=>(~patient(X)&calm(X))))& (((~wise(susan)<~>calm(susan)))<=>((strong(paul)&calm(paul))))& (?[X]:((patient(X)<~>humble(X))))& (?[X]:(brave(X)))& (~wise(alice))& (wise(susan))& (?[X]:((~rich(X)&calm(X))))& (brave(lucy))& (?[X]:((~wise(X)&~generous(X))))

~happy(fred)

% SZS status Unsatisfiable for 7628622512087120425238638 % SZS output start Proof for 7628622512087120425238638 3. ! [X0] : (happy(X0) <=> (~funny(X0) | ~happy(X0))) [input p2] 23. ~happy(fred) [input hypothesis] 40. ! [X0] : ((happy(X0) | (funny(X0) & happy(X0))) & ((~funny(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 3] 41. ! [X0] : ((happy(X0) | (funny(X0) & happy(X0))) & (~funny(X0) | ~happy(X0) | ~happy(X0))) [flattening 40] 72. happy(X0) | happy(X0) [cnf transformation 41] 118. ~happy(fred) [cnf transformation 23] 120. happy(X0) [duplicate literal removal 72] 224. $false [subsumption resolution 118,120] % SZS output end Proof for 7628622512087120425238638 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Everyone who is either not calm or wise is not old or curious and vice versa. Everyone who is both not old and tall is both old and kind and vice versa. If alice is not quiet or not funny then fred is either humble or patient. If john is either not curious or not generous then someone is both brave and wise and vice versa. Everyone who is either not quiet or not happy is patient and vice versa. If someone is not funny or not generous then fred is quiet. Everyone who is both kind and not quiet is happy. Everyone who is not generous or quiet is either not wise or not curious and vice versa. If someone is either not patient or strong then someone is not kind. If john is either patient or quiet then lucy is both funny and kind and vice versa. If fred is either not old or not happy then someone is either not calm or kind. Everyone who is both quiet and strong is not happy or quiet and vice versa. Everyone who is either not old or not funny is either strong or humble and vice versa. If paul is both not humble and not old then lucy is patient or not tall and vice versa. Everyone who is either kind or creative is either old or not tall and vice versa. Everyone who is not creative is either not creative or creative and vice versa. Alice is happy. Someone is either not curious or brave. Someone is either not generous or not calm. Mary is wise. John is both not kind and generous. Someone is not brave or wise. Someone is brave or not quiet. Alice is generous or patient.

John is not generous.

contradiction

(![X]:((~calm(X)<~>wise(X))<=>(~old(X)|curious(X))))& (![X]:((~old(X)&tall(X))<=>(old(X)&kind(X))))& (((~quiet(alice)|~funny(alice)))=>((humble(fred)<~>patient(fred))))& (((~curious(john)<~>~generous(john)))<=>(?[X]:((brave(X)&wise(X)))))& (![X]:((~quiet(X)<~>~happy(X))<=>patient(X)))& ((?[X]:((~funny(X)|~generous(X))))=>(quiet(fred)))& (![X]:((kind(X)&~quiet(X))=>happy(X)))& (![X]:((~generous(X)|quiet(X))<=>(~wise(X)<~>~curious(X))))& ((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:(~kind(X))))& (((patient(john)<~>quiet(john)))<=>((funny(lucy)&kind(lucy))))& (((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))& (![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))& (![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))& (((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))& (![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))& (![X]:(~creative(X)<=>(~creative(X)<~>creative(X))))& (happy(alice))& (?[X]:((~curious(X)<~>brave(X))))& (?[X]:((~generous(X)<~>~calm(X))))& (wise(mary))& ((~kind(john)&generous(john)))& (?[X]:((~brave(X)|wise(X))))& (?[X]:((brave(X)|~quiet(X))))& ((generous(alice)|patient(alice)))

~generous(john)

% SZS status Unsatisfiable for 8113939486004136649731386 % SZS output start Proof for 8113939486004136649731386 21. generous(john) & ~kind(john) [input p20] 25. ~generous(john) [input hypothesis] 153. generous(john) [cnf transformation 21] 157. ~generous(john) [cnf transformation 25] 192. 7 <=> generous(john) [avatar definition] 320. 7 [avatar split clause 153,192] 348. ~7 [avatar split clause 157,192] 349. $false [avatar sat refutation 320,348] % SZS output end Proof for 8113939486004136649731386 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Everyone who is kind is either kind or humble and vice versa. Everyone who is both quiet and generous is either creative or not brave. Everyone who is wise is not old or brave and vice versa. Everyone who is either not quiet or not kind is not calm and vice versa. If fred is both not humble and rich then someone is either not strong or not generous and vice versa. If lucy is either curious or rich then someone is not kind or not wise. If someone is both creative and quiet then fred is funny or rich and vice versa. Everyone who is either not creative or creative is not old. If someone is happy or quiet then someone is happy and vice versa. If alice is either quiet or tall then susan is not kind or rich. If john is humble then someone is not quiet. If paul is both not funny and tall then fred is not curious. If alice is either not happy or patient then someone is either not curious or tall and vice versa. Everyone who is not kind or not curious is either not happy or funny and vice versa. Everyone who is not tall or not brave is both not patient and tall and vice versa. Everyone who is brave or not tall is both not brave and not quiet and vice versa. Lucy is kind. Someone is either generous or not humble. Someone is both kind and rich. Susan is either not quiet or not creative. Someone is not rich or not humble. Someone is quiet. Someone is either kind or wise.

Paul is not humble.

entailment

(![X]:(kind(X)<=>(kind(X)<~>humble(X))))& (![X]:((quiet(X)&generous(X))=>(creative(X)<~>~brave(X))))& (![X]:(wise(X)<=>(~old(X)|brave(X))))& (![X]:((~quiet(X)<~>~kind(X))<=>~calm(X)))& (((~humble(fred)&rich(fred)))<=>(?[X]:((~strong(X)<~>~generous(X)))))& (((curious(lucy)<~>rich(lucy)))=>(?[X]:((~kind(X)|~wise(X)))))& ((?[X]:((creative(X)&quiet(X))))<=>((funny(fred)|rich(fred))))& (![X]:((~creative(X)<~>creative(X))=>~old(X)))& ((?[X]:((happy(X)|quiet(X))))<=>(?[X]:(happy(X))))& (((quiet(alice)<~>tall(alice)))=>((~kind(susan)|rich(susan))))& ((humble(john))=>(?[X]:(~quiet(X))))& (((~funny(paul)&tall(paul)))=>(~curious(fred)))& (((~happy(alice)<~>patient(alice)))<=>(?[X]:((~curious(X)<~>tall(X)))))& (![X]:((~kind(X)|~curious(X))<=>(~happy(X)<~>funny(X))))& (![X]:((~tall(X)|~brave(X))<=>(~patient(X)&tall(X))))& (![X]:((brave(X)|~tall(X))<=>(~brave(X)&~quiet(X))))& (kind(lucy))& (?[X]:((generous(X)<~>~humble(X))))& (?[X]:((kind(X)&rich(X))))& ((~quiet(susan)<~>~creative(susan)))& (?[X]:((~rich(X)|~humble(X))))& (?[X]:(quiet(X)))& (?[X]:((kind(X)<~>wise(X))))

~humble(paul)

% SZS status Unsatisfiable for 797818720452600317148945 % SZS output start Proof for 797818720452600317148945 1. ! [X0] : (kind(X0) <=> (kind(X0) <~> humble(X0))) [input p0] 24. humble(paul) [input hypothesis] 35. ! [X0] : ((kind(X0) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 1] 85. ~humble(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 35] 87. kind(X0) | kind(X0) | ~humble(X0) [cnf transformation 35] 150. humble(paul) [cnf transformation 24] 157. ~humble(X0) | ~kind(X0) [duplicate literal removal 85] 158. kind(X0) | ~humble(X0) [duplicate literal removal 87] 159. ~humble(X0) [subsumption resolution 157,158] 327. $false [subsumption resolution 150,159] % SZS output end Proof for 797818720452600317148945 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Everyone who is both not humble and not creative is not happy or not old and vice versa. Everyone who is either not calm or not wise is not strong. Everyone who is both not calm and strong is both not quiet and not rich. If john is both not funny and not happy then someone is tall or not funny. Everyone who is happy is both creative and curious. If fred is funny then susan is either not quiet or tall and vice versa. Everyone who is not creative or funny is kind. Everyone who is both quiet and not tall is either not patient or not old. If fred is curious then lucy is old or wise. If someone is not tall then alice is either not funny or not old and vice versa. If fred is either not generous or brave then someone is brave or not rich and vice versa. If someone is both quiet and not strong then someone is kind and vice versa. Everyone who is both not wise and patient is either not rich or strong and vice versa. Everyone who is both not patient and not tall is happy or humble and vice versa. Everyone who is rich or not wise is either quiet or not funny and vice versa. Everyone who is either not strong or generous is wise or not patient and vice versa. Someone is both not funny and humble. Someone is both not funny and not quiet. Fred is both not curious and calm. Someone is both not happy and tall. Someone is either quiet or kind. Susan is not curious or not strong. Alice is both not strong and funny. Mary is not rich.

Susan is not tall.

neutral

(![X]:((~humble(X)&~creative(X))<=>(~happy(X)|~old(X))))& (![X]:((~calm(X)<~>~wise(X))=>~strong(X)))& (![X]:((~calm(X)&strong(X))=>(~quiet(X)&~rich(X))))& (((~funny(john)&~happy(john)))=>(?[X]:((tall(X)|~funny(X)))))& (![X]:(happy(X)=>(creative(X)&curious(X))))& ((funny(fred))<=>((~quiet(susan)<~>tall(susan))))& (![X]:((~creative(X)|funny(X))=>kind(X)))& (![X]:((quiet(X)&~tall(X))=>(~patient(X)<~>~old(X))))& ((curious(fred))=>((old(lucy)|wise(lucy))))& ((?[X]:(~tall(X)))<=>((~funny(alice)<~>~old(alice))))& (((~generous(fred)<~>brave(fred)))<=>(?[X]:((brave(X)|~rich(X)))))& ((?[X]:((quiet(X)&~strong(X))))<=>(?[X]:(kind(X))))& (![X]:((~wise(X)&patient(X))<=>(~rich(X)<~>strong(X))))& (![X]:((~patient(X)&~tall(X))<=>(happy(X)|humble(X))))& (![X]:((rich(X)|~wise(X))<=>(quiet(X)<~>~funny(X))))& (![X]:((~strong(X)<~>generous(X))<=>(wise(X)|~patient(X))))& (?[X]:((~funny(X)&humble(X))))& (?[X]:((~funny(X)&~quiet(X))))& ((~curious(fred)&calm(fred)))& (?[X]:((~happy(X)&tall(X))))& (?[X]:((quiet(X)<~>kind(X))))& ((~curious(susan)|~strong(susan)))& ((~strong(alice)&funny(alice)))& (~rich(mary))

~tall(susan)

If someone is curious then someone is patient and vice versa. If alice is either tall or not tall then someone is kind or happy and vice versa. If paul is either not humble or not rich then someone is both not tall and not generous and vice versa. Everyone who is either not calm or brave is not tall. If someone is either not calm or not creative then someone is not curious or wise. Everyone who is either not patient or funny is tall or quiet and vice versa. Everyone who is curious is not creative or not quiet. Everyone who is either not rich or curious is not calm or not generous. Everyone who is not funny or funny is either not rich or not wise. If someone is not creative then lucy is both not quiet and not strong. Everyone who is not tall is not wise or tall and vice versa. Everyone who is either kind or not patient is both rich and happy and vice versa. Everyone who is either not kind or brave is humble and vice versa. If alice is not curious then someone is not rich and vice versa. Everyone who is both not wise and not happy is either not patient or not quiet. If lucy is not brave or not humble then someone is not generous or not calm. Someone is both generous and not quiet. Someone is not calm or curious. Someone is both funny and not humble. Someone is both not wise and kind. Someone is both generous and not strong. John is not kind or not patient. Someone is either not happy or not funny.

Lucy is calm.

neutral

((?[X]:(curious(X)))<=>(?[X]:(patient(X))))& (((tall(alice)<~>~tall(alice)))<=>(?[X]:((kind(X)|happy(X)))))& (((~humble(paul)<~>~rich(paul)))<=>(?[X]:((~tall(X)&~generous(X)))))& (![X]:((~calm(X)<~>brave(X))=>~tall(X)))& ((?[X]:((~calm(X)<~>~creative(X))))=>(?[X]:((~curious(X)|wise(X)))))& (![X]:((~patient(X)<~>funny(X))<=>(tall(X)|quiet(X))))& (![X]:(curious(X)=>(~creative(X)|~quiet(X))))& (![X]:((~rich(X)<~>curious(X))=>(~calm(X)|~generous(X))))& (![X]:((~funny(X)|funny(X))=>(~rich(X)<~>~wise(X))))& ((?[X]:(~creative(X)))=>((~quiet(lucy)&~strong(lucy))))& (![X]:(~tall(X)<=>(~wise(X)|tall(X))))& (![X]:((kind(X)<~>~patient(X))<=>(rich(X)&happy(X))))& (![X]:((~kind(X)<~>brave(X))<=>humble(X)))& ((~curious(alice))<=>(?[X]:(~rich(X))))& (![X]:((~wise(X)&~happy(X))=>(~patient(X)<~>~quiet(X))))& (((~brave(lucy)|~humble(lucy)))=>(?[X]:((~generous(X)|~calm(X)))))& (?[X]:((generous(X)&~quiet(X))))& (?[X]:((~calm(X)|curious(X))))& (?[X]:((funny(X)&~humble(X))))& (?[X]:((~wise(X)&kind(X))))& (?[X]:((generous(X)&~strong(X))))& ((~kind(john)|~patient(john)))& (?[X]:((~happy(X)<~>~funny(X))))

calm(lucy)

Everyone who is not generous is both not humble and not patient and vice versa. If someone is both not kind and humble then fred is either wise or rich and vice versa. Everyone who is both not old and not generous is both strong and kind. If someone is happy then lucy is kind and vice versa. Everyone who is generous or not creative is both curious and strong and vice versa. Everyone who is both not strong and quiet is both rich and funny. Everyone who is both not funny and not kind is both calm and kind and vice versa. Everyone who is both tall and not funny is not curious or tall and vice versa. If alice is not generous or not kind then someone is quiet or patient and vice versa. Everyone who is either not old or not funny is either calm or old and vice versa. Everyone who is either kind or wise is tall and vice versa. If someone is either not humble or not generous then mary is either creative or not old. If paul is both not patient and wise then mary is not happy. If someone is wise then someone is both not tall and kind and vice versa. Paul is either happy or not old. Alice is both not rich and creative. Someone is either old or rich. Paul is not generous or humble. Someone is either not strong or old. Susan is both not funny and not rich.

Paul is not generous.

neutral

(![X]:(~generous(X)<=>(~humble(X)&~patient(X))))& ((?[X]:((~kind(X)&humble(X))))<=>((wise(fred)<~>rich(fred))))& (![X]:((~old(X)&~generous(X))=>(strong(X)&kind(X))))& ((?[X]:(happy(X)))<=>(kind(lucy)))& (![X]:((generous(X)|~creative(X))<=>(curious(X)&strong(X))))& (![X]:((~strong(X)&quiet(X))=>(rich(X)&funny(X))))& (![X]:((~funny(X)&~kind(X))<=>(calm(X)&kind(X))))& (![X]:((tall(X)&~funny(X))<=>(~curious(X)|tall(X))))& (((~generous(alice)|~kind(alice)))<=>(?[X]:((quiet(X)|patient(X)))))& (![X]:((~old(X)<~>~funny(X))<=>(calm(X)<~>old(X))))& (![X]:((kind(X)<~>wise(X))<=>tall(X)))& ((?[X]:((~humble(X)<~>~generous(X))))=>((creative(mary)<~>~old(mary))))& (((~patient(paul)&wise(paul)))=>(~happy(mary)))& ((?[X]:(wise(X)))<=>(?[X]:((~tall(X)&kind(X)))))& ((happy(paul)<~>~old(paul)))& ((~rich(alice)&creative(alice)))& (?[X]:((old(X)<~>rich(X))))& ((~generous(paul)|humble(paul)))& (?[X]:((~strong(X)<~>old(X))))& ((~funny(susan)&~rich(susan)))

~generous(paul)

If mary is both rich and wise then someone is both tall and not patient and vice versa. If someone is calm then alice is not curious or strong and vice versa. If alice is both not funny and patient then fred is creative. If someone is either creative or not quiet then someone is either wise or not kind and vice versa. Everyone who is strong or curious is either kind or not kind and vice versa. Everyone who is both calm and creative is not happy. Everyone who is not tall is both kind and not curious. Everyone who is either humble or calm is rich or not rich. If someone is not patient or humble then someone is both not rich and not generous. If lucy is both quiet and creative then mary is either quiet or not kind. If fred is not patient or creative then someone is both old and funny and vice versa. If someone is either calm or not old then susan is funny or quiet. If someone is either creative or old then someone is not curious or quiet. If alice is either tall or humble then susan is tall and vice versa. Everyone who is either not wise or not humble is both not rich and not generous. If someone is curious then someone is both calm and not calm and vice versa. Someone is strong. Someone is both not happy and quiet. John is not calm. Someone is not tall or old. Someone is both not happy and not brave. Lucy is both not quiet and not patient. Someone is either old or strong. Susan is not calm.

Alice is not strong.

contradiction

(((rich(mary)&wise(mary)))<=>(?[X]:((tall(X)&~patient(X)))))& ((?[X]:(calm(X)))<=>((~curious(alice)|strong(alice))))& (((~funny(alice)&patient(alice)))=>(creative(fred)))& ((?[X]:((creative(X)<~>~quiet(X))))<=>(?[X]:((wise(X)<~>~kind(X)))))& (![X]:((strong(X)|curious(X))<=>(kind(X)<~>~kind(X))))& (![X]:((calm(X)&creative(X))=>~happy(X)))& (![X]:(~tall(X)=>(kind(X)&~curious(X))))& (![X]:((humble(X)<~>calm(X))=>(rich(X)|~rich(X))))& ((?[X]:((~patient(X)|humble(X))))=>(?[X]:((~rich(X)&~generous(X)))))& (((quiet(lucy)&creative(lucy)))=>((quiet(mary)<~>~kind(mary))))& (((~patient(fred)|creative(fred)))<=>(?[X]:((old(X)&funny(X)))))& ((?[X]:((calm(X)<~>~old(X))))=>((funny(susan)|quiet(susan))))& ((?[X]:((creative(X)<~>old(X))))=>(?[X]:((~curious(X)|quiet(X)))))& (((tall(alice)<~>humble(alice)))<=>(tall(susan)))& (![X]:((~wise(X)<~>~humble(X))=>(~rich(X)&~generous(X))))& ((?[X]:(curious(X)))<=>(?[X]:((calm(X)&~calm(X)))))& (?[X]:(strong(X)))& (?[X]:((~happy(X)&quiet(X))))& (~calm(john))& (?[X]:((~tall(X)|old(X))))& (?[X]:((~happy(X)&~brave(X))))& ((~quiet(lucy)&~patient(lucy)))& (?[X]:((old(X)<~>strong(X))))& (~calm(susan))

~strong(alice)

% SZS status Unsatisfiable for 4200048882192102546156739 % SZS output start Proof for 4200048882192102546156739 5. ! [X0] : ((curious(X0) | strong(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p4] 16. ? [X0] : curious(X0) <=> ? [X0] : (~calm(X0) & calm(X0)) [input p15] 25. ~strong(alice) [input hypothesis] 29. ? [X0] : curious(X0) <=> ? [X1] : (~calm(X1) & calm(X1)) [rectify 16] 63. ! [X0] : (((curious(X0) | strong(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | (~curious(X0) & ~strong(X0)))) [nnf transformation 5] 64. ! [X0] : ((curious(X0) | strong(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | (~curious(X0) & ~strong(X0)))) [flattening 63] 82. (? [X0] : curious(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X1] : (~calm(X1) & calm(X1)) | ! [X0] : ~curious(X0)) [nnf transformation 29] 83. (? [X0] : curious(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X2] : (~calm(X2) & calm(X2)) | ! [X3] : ~curious(X3)) [rectify 82] 84. ? [X0] : curious(X0) => curious(sK7) [choice axiom] 85. ? [X2] : (~calm(X2) & calm(X2)) => (~calm(sK8) & calm(sK8)) [choice axiom] 86. (curious(sK7) | ! [X1] : (calm(X1) | ~calm(X1))) & ((~calm(sK8) & calm(sK8)) | ! [X3] : ~curious(X3)) [skolemisation 83,85,84] 116. curious(X0) | strong(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 64] 117. curious(X0) | strong(X0) | kind(X0) | kind(X0) [cnf transformation 64] 141. calm(sK8) | ~curious(X3) [cnf transformation 86] 142. ~calm(sK8) | ~curious(X3) [cnf transformation 86] 153. ~strong(alice) [cnf transformation 25] 154. curious(X0) | strong(X0) | ~kind(X0) [duplicate literal removal 116] 155. curious(X0) | strong(X0) | kind(X0) [duplicate literal removal 117] 180. 6 <=> strong(alice) [avatar definition] 182. ~strong(alice) <- (~6) [avatar component clause 180] 246. strong(X0) | curious(X0) [subsumption resolution 154,155] 346. 43 <=> ! [X3] : ~curious(X3) [avatar definition] 347. ~curious(X3) <- (43) [avatar component clause 346] 349. 44 <=> calm(sK8) [avatar definition] 352. 43 | ~44 [avatar split clause 142,349,346] 353. 43 | 44 [avatar split clause 141,349,346] 374. ~6 [avatar split clause 153,180] 376. curious(alice) <- (~6) [resolution 246,182] 378. $false <- (~6, 43) [subsumption resolution 376,347] 379. 6 | ~43 [avatar contradiction clause 378] 382. $false [avatar sat refutation 352,353,374,379] % SZS output end Proof for 4200048882192102546156739 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Everyone who is both wise and funny is both strong and wise and vice versa. Everyone who is not rich is either not curious or quiet. If someone is calm then alice is both not calm and not quiet. Everyone who is not happy is not rich and vice versa. If mary is either strong or old then someone is not happy. If someone is funny then john is not brave or quiet and vice versa. Everyone who is not brave or not patient is not patient or calm and vice versa. If paul is not creative or not wise then john is rich and vice versa. Everyone who is not old or wise is kind and vice versa. Everyone who is not calm or curious is not funny. Everyone who is either not humble or funny is happy and vice versa. Everyone who is quiet or not brave is not humble or patient. Everyone who is not quiet or not brave is either brave or humble and vice versa. Everyone who is happy is both generous and kind and vice versa. Everyone who is both not generous and not calm is either not happy or not rich. If someone is both not calm and not happy then john is not curious. Someone is both not happy and old. Paul is brave or not curious. Someone is either patient or creative. Someone is either calm or happy. Someone is either not brave or not generous. Someone is kind. John is rich. Someone is not curious or not rich.

Mary is not kind.

neutral

(![X]:((wise(X)&funny(X))<=>(strong(X)&wise(X))))& (![X]:(~rich(X)=>(~curious(X)<~>quiet(X))))& ((?[X]:(calm(X)))=>((~calm(alice)&~quiet(alice))))& (![X]:(~happy(X)<=>~rich(X)))& (((strong(mary)<~>old(mary)))=>(?[X]:(~happy(X))))& ((?[X]:(funny(X)))<=>((~brave(john)|quiet(john))))& (![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))& (((~creative(paul)|~wise(paul)))<=>(rich(john)))& (![X]:((~old(X)|wise(X))<=>kind(X)))& (![X]:((~calm(X)|curious(X))=>~funny(X)))& (![X]:((~humble(X)<~>funny(X))<=>happy(X)))& (![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))& (![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))& (![X]:(happy(X)<=>(generous(X)&kind(X))))& (![X]:((~generous(X)&~calm(X))=>(~happy(X)<~>~rich(X))))& ((?[X]:((~calm(X)&~happy(X))))=>(~curious(john)))& (?[X]:((~happy(X)&old(X))))& ((brave(paul)|~curious(paul)))& (?[X]:((patient(X)<~>creative(X))))& (?[X]:((calm(X)<~>happy(X))))& (?[X]:((~brave(X)<~>~generous(X))))& (?[X]:(kind(X)))& (rich(john))& (?[X]:((~curious(X)|~rich(X))))

~kind(mary)

Everyone who is humble or generous is either happy or not creative. If susan is both not old and not rich then someone is both not humble and not strong and vice versa. If fred is either not humble or patient then someone is either calm or brave and vice versa. Everyone who is both not tall and funny is not humble or patient and vice versa. Everyone who is both not kind and patient is not kind or not happy and vice versa. Everyone who is not tall is both not humble and curious. Everyone who is not rich is old or happy and vice versa. If someone is not calm then lucy is not old or not tall and vice versa. If someone is either creative or patient then someone is not creative or not kind and vice versa. If mary is either quiet or not brave then fred is both not curious and not rich. If paul is creative or patient then fred is not rich and vice versa. Everyone who is strong or quiet is tall or quiet and vice versa. If someone is both not strong and not brave then someone is not strong and vice versa. If fred is not creative then fred is not humble or not kind and vice versa. Everyone who is not old or humble is not patient. Everyone who is both not brave and funny is not strong. Alice is both happy and not creative. Susan is both not rich and funny. Someone is old. Mary is old or curious. Someone is both not rich and not kind. Someone is not kind. Paul is either not old or curious. Someone is both not generous and not kind.

Paul is rich.

contradiction

(![X]:((humble(X)|generous(X))=>(happy(X)<~>~creative(X))))& (((~old(susan)&~rich(susan)))<=>(?[X]:((~humble(X)&~strong(X)))))& (((~humble(fred)<~>patient(fred)))<=>(?[X]:((calm(X)<~>brave(X)))))& (![X]:((~tall(X)&funny(X))<=>(~humble(X)|patient(X))))& (![X]:((~kind(X)&patient(X))<=>(~kind(X)|~happy(X))))& (![X]:(~tall(X)=>(~humble(X)&curious(X))))& (![X]:(~rich(X)<=>(old(X)|happy(X))))& ((?[X]:(~calm(X)))<=>((~old(lucy)|~tall(lucy))))& ((?[X]:((creative(X)<~>patient(X))))<=>(?[X]:((~creative(X)|~kind(X)))))& (((quiet(mary)<~>~brave(mary)))=>((~curious(fred)&~rich(fred))))& (((creative(paul)|patient(paul)))<=>(~rich(fred)))& (![X]:((strong(X)|quiet(X))<=>(tall(X)|quiet(X))))& ((?[X]:((~strong(X)&~brave(X))))<=>(?[X]:(~strong(X))))& ((~creative(fred))<=>((~humble(fred)|~kind(fred))))& (![X]:((~old(X)|humble(X))=>~patient(X)))& (![X]:((~brave(X)&funny(X))=>~strong(X)))& ((happy(alice)&~creative(alice)))& ((~rich(susan)&funny(susan)))& (?[X]:(old(X)))& ((old(mary)|curious(mary)))& (?[X]:((~rich(X)&~kind(X))))& (?[X]:(~kind(X)))& ((~old(paul)<~>curious(paul)))& (?[X]:((~generous(X)&~kind(X))))

rich(paul)

% SZS status Unsatisfiable for 2914120935386738501649246 % SZS output start Proof for 2914120935386738501649246 5. ! [X0] : ((patient(X0) & ~kind(X0)) <=> (~happy(X0) | ~kind(X0))) [input p4] 7. ! [X0] : (~rich(X0) <=> (happy(X0) | old(X0))) [input p6] 15. ! [X0] : ((humble(X0) | ~old(X0)) => ~patient(X0)) [input p14] 25. rich(paul) [input hypothesis] 33. ! [X0] : (~patient(X0) | (~humble(X0) & old(X0))) [ennf transformation 15] 48. ! [X0] : (((patient(X0) & ~kind(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~patient(X0) | kind(X0)))) [nnf transformation 5] 49. ! [X0] : (((patient(X0) & ~kind(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~patient(X0) | kind(X0))) [flattening 48] 50. ! [X0] : ((~rich(X0) | (~happy(X0) & ~old(X0))) & ((happy(X0) | old(X0)) | rich(X0))) [nnf transformation 7] 51. ! [X0] : ((~rich(X0) | (~happy(X0) & ~old(X0))) & (happy(X0) | old(X0) | rich(X0))) [flattening 50] 106. patient(X0) | happy(X0) [cnf transformation 49] 110. ~rich(X0) | ~old(X0) [cnf transformation 51] 111. ~rich(X0) | ~happy(X0) [cnf transformation 51] 138. ~patient(X0) | old(X0) [cnf transformation 33] 153. rich(paul) [cnf transformation 25] 284. 29 <=> patient(paul) [avatar definition] 285. ~patient(paul) <- (~29) [avatar component clause 284] 286. patient(paul) <- (29) [avatar component clause 284] 333. 39 <=> old(paul) [avatar definition] 353. happy(paul) <- (~29) [resolution 106,285] 360. ~old(paul) [resolution 110,153] 363. ~happy(paul) [resolution 111,153] 365. $false <- (~29) [subsumption resolution 363,353] 366. 29 [avatar contradiction clause 365] 371. old(paul) <- (29) [resolution 138,286] 378. 39 | ~29 [avatar split clause 371,284,333] 379. ~39 [avatar split clause 360,333] 380. $false [avatar sat refutation 366,378,379] % SZS output end Proof for 2914120935386738501649246 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Everyone who is both patient and not curious is not creative. If someone is tall or not old then paul is both brave and not tall and vice versa. Everyone who is either not wise or creative is both funny and not calm. If susan is both not humble and not funny then someone is either brave or not generous. Everyone who is quiet or brave is either wise or patient. If paul is not wise then alice is either tall or happy. If someone is both not old and not creative then someone is either not happy or not quiet and vice versa. If someone is both brave and humble then someone is both not kind and patient. Everyone who is both humble and not brave is not creative or not curious. Everyone who is not calm is curious and vice versa. Everyone who is curious or patient is either happy or brave. Everyone who is not generous is kind or not calm and vice versa. If paul is both not wise and not kind then someone is either curious or not rich. Everyone who is not brave or not humble is not strong. If john is funny or old then someone is either not patient or not funny. If alice is generous or strong then someone is either funny or brave and vice versa. Someone is either wise or not strong. Someone is not funny. Someone is not patient. Someone is brave or not creative. Someone is either calm or brave. Mary is both not rich and not funny. Susan is not curious. Paul is both not tall and not brave.

Susan is not patient.

entailment

(![X]:((patient(X)&~curious(X))=>~creative(X)))& ((?[X]:((tall(X)|~old(X))))<=>((brave(paul)&~tall(paul))))& (![X]:((~wise(X)<~>creative(X))=>(funny(X)&~calm(X))))& (((~humble(susan)&~funny(susan)))=>(?[X]:((brave(X)<~>~generous(X)))))& (![X]:((quiet(X)|brave(X))=>(wise(X)<~>patient(X))))& ((~wise(paul))=>((tall(alice)<~>happy(alice))))& ((?[X]:((~old(X)&~creative(X))))<=>(?[X]:((~happy(X)<~>~quiet(X)))))& ((?[X]:((brave(X)&humble(X))))=>(?[X]:((~kind(X)&patient(X)))))& (![X]:((humble(X)&~brave(X))=>(~creative(X)|~curious(X))))& (![X]:(~calm(X)<=>curious(X)))& (![X]:((curious(X)|patient(X))=>(happy(X)<~>brave(X))))& (![X]:(~generous(X)<=>(kind(X)|~calm(X))))& (((~wise(paul)&~kind(paul)))=>(?[X]:((curious(X)<~>~rich(X)))))& (![X]:((~brave(X)|~humble(X))=>~strong(X)))& (((funny(john)|old(john)))=>(?[X]:((~patient(X)<~>~funny(X)))))& (((generous(alice)|strong(alice)))<=>(?[X]:((funny(X)<~>brave(X)))))& (?[X]:((wise(X)<~>~strong(X))))& (?[X]:(~funny(X)))& (?[X]:(~patient(X)))& (?[X]:((brave(X)|~creative(X))))& (?[X]:((calm(X)<~>brave(X))))& ((~rich(mary)&~funny(mary)))& (~curious(susan))& ((~tall(paul)&~brave(paul)))

~patient(susan)

% SZS status Unsatisfiable for 1923680143406185467664779 % SZS output start Proof for 1923680143406185467664779 1. ! [X0] : ((~curious(X0) & patient(X0)) => ~creative(X0)) [input p0] 2. ? [X0] : (~old(X0) | tall(X0)) <=> (~tall(paul) & brave(paul)) [input p1] 3. ! [X0] : ((~wise(X0) <~> creative(X0)) => (~calm(X0) & funny(X0))) [input p2] 5. ! [X0] : ((brave(X0) | quiet(X0)) => (wise(X0) <~> patient(X0))) [input p4] 7. ? [X0] : (~creative(X0) & ~old(X0)) <=> ? [X0] : (~happy(X0) <~> ~quiet(X0)) [input p6] 10. ! [X0] : (~calm(X0) <=> curious(X0)) [input p9] 11. ! [X0] : ((patient(X0) | curious(X0)) => (happy(X0) <~> brave(X0))) [input p10] 23. ~curious(susan) [input p22] 24. ~brave(paul) & ~tall(paul) [input p23] 25. patient(susan) [input hypothesis] 26. ? [X0] : (~creative(X0) & ~old(X0)) <=> ? [X1] : (~happy(X1) <~> ~quiet(X1)) [rectify 7] 28. ! [X0] : (~creative(X0) | (curious(X0) | ~patient(X0))) [ennf transformation 1] 29. ! [X0] : (~creative(X0) | curious(X0) | ~patient(X0)) [flattening 28] 30. ! [X0] : ((~calm(X0) & funny(X0)) | (~wise(X0) <=> creative(X0))) [ennf transformation 3] 33. ! [X0] : ((wise(X0) <~> patient(X0)) | (~brave(X0) & ~quiet(X0))) [ennf transformation 5] 38. ! [X0] : ((happy(X0) <~> brave(X0)) | (~patient(X0) & ~curious(X0))) [ennf transformation 11] 43. (? [X0] : (~old(X0) | tall(X0)) | (tall(paul) | ~brave(paul))) & ((~tall(paul) & brave(paul)) | ! [X0] : (old(X0) & ~tall(X0))) [nnf transformation 2] 44. (? [X0] : (~old(X0) | tall(X0)) | tall(paul) | ~brave(paul)) & ((~tall(paul) & brave(paul)) | ! [X0] : (old(X0) & ~tall(X0))) [flattening 43] 45. (? [X0] : (~old(X0) | tall(X0)) | tall(paul) | ~brave(paul)) & ((~tall(paul) & brave(paul)) | ! [X1] : (old(X1) & ~tall(X1))) [rectify 44] 46. ? [X0] : (~old(X0) | tall(X0)) => (~old(sK0) | tall(sK0)) [choice axiom] 47. ((~old(sK0) | tall(sK0)) | tall(paul) | ~brave(paul)) & ((~tall(paul) & brave(paul)) | ! [X1] : (old(X1) & ~tall(X1))) [skolemisation 45,46] 48. ! [X0] : ((~calm(X0) & funny(X0)) | ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0)))) [nnf transformation 30] 52. ! [X0] : (((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | (~brave(X0) & ~quiet(X0))) [nnf transformation 33] 54. (? [X0] : (~creative(X0) & ~old(X0)) | ! [X1] : ((~happy(X1) | quiet(X1)) & (~quiet(X1) | happy(X1)))) & (? [X1] : ((quiet(X1) | happy(X1)) & (~quiet(X1) | ~happy(X1))) | ! [X0] : (creative(X0) | old(X0))) [nnf transformation 26] 55. (? [X0] : (~creative(X0) & ~old(X0)) | ! [X1] : ((~happy(X1) | quiet(X1)) & (~quiet(X1) | happy(X1)))) & (? [X2] : ((quiet(X2) | happy(X2)) & (~quiet(X2) | ~happy(X2))) | ! [X3] : (creative(X3) | old(X3))) [rectify 54] 56. ? [X0] : (~creative(X0) & ~old(X0)) => (~creative(sK2) & ~old(sK2)) [choice axiom] 57. ? [X2] : ((quiet(X2) | happy(X2)) & (~quiet(X2) | ~happy(X2))) => ((quiet(sK3) | happy(sK3)) & (~quiet(sK3) | ~happy(sK3))) [choice axiom] 58. ((~creative(sK2) & ~old(sK2)) | ! [X1] : ((~happy(X1) | quiet(X1)) & (~quiet(X1) | happy(X1)))) & (((quiet(sK3) | happy(sK3)) & (~quiet(sK3) | ~happy(sK3))) | ! [X3] : (creative(X3) | old(X3))) [skolemisation 55,57,56] 62. ! [X0] : ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0))) [nnf transformation 10] 63. ! [X0] : (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | (~patient(X0) & ~curious(X0))) [nnf transformation 38] 89. ~creative(X0) | curious(X0) | ~patient(X0) [cnf transformation 29] 91. brave(paul) | old(X1) [cnf transformation 47] 97. ~calm(X0) | creative(X0) | wise(X0) [cnf transformation 48] 103. ~quiet(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 52] 104. ~wise(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 52] 110. ~old(sK2) | ~happy(X1) | quiet(X1) [cnf transformation 58] 116. calm(X0) | curious(X0) [cnf transformation 62] 119. ~patient(X0) | happy(X0) | brave(X0) [cnf transformation 63] 148. ~curious(susan) [cnf transformation 23] 150. ~brave(paul) [cnf transformation 24] 151. patient(susan) [cnf transformation 25] 153. 1 <=> brave(paul) [avatar definition] 170. 5 <=> ! [X1] : old(X1) [avatar definition] 171. old(X1) <- (5) [avatar component clause 170] 177. 5 | 1 [avatar split clause 91,153,170] 212. 14 <=> ! [X1] : (~happy(X1) | quiet(X1)) [avatar definition] 213. ~happy(X1) | quiet(X1) <- (14) [avatar component clause 212] 224. 17 <=> old(sK2) [avatar definition] 226. ~old(sK2) <- (~17) [avatar component clause 224] 227. 14 | ~17 [avatar split clause 110,224,212] 346. ~1 [avatar split clause 150,153] 348. $false <- (5, ~17) [resolution 226,171] 349. ~5 | 17 [avatar contradiction clause 348] 411. wise(X0) | creative(X0) | curious(X0) [resolution 97,116] 467. happy(susan) | brave(susan) [resolution 119,151] 469. 60 <=> brave(susan) [avatar definition] 471. brave(susan) <- (60) [avatar component clause 469] 473. 61 <=> happy(susan) [avatar definition] 475. happy(susan) <- (61) [avatar component clause 473] 476. 60 | 61 [avatar split clause 467,473,469] 520. creative(X0) | curious(X0) | ~patient(X0) | ~brave(X0) [resolution 411,104] 531. ~brave(X0) | ~patient(X0) | curious(X0) [subsumption resolution 520,89] 576. ~patient(susan) | curious(susan) <- (60) [resolution 531,471] 578. curious(susan) <- (60) [subsumption resolution 576,151] 579. $false <- (60) [subsumption resolution 578,148] 580. ~60 [avatar contradiction clause 579] 585. quiet(susan) <- (14, 61) [resolution 475,213] 587. ~wise(susan) | ~patient(susan) <- (14, 61) [resolution 585,103] 590. ~wise(susan) <- (14, 61) [subsumption resolution 587,151] 607. creative(susan) | curious(susan) <- (14, 61) [resolution 590,411] 608. creative(susan) <- (14, 61) [subsumption resolution 607,148] 609. curious(susan) | ~patient(susan) <- (14, 61) [resolution 608,89] 610. ~patient(susan) <- (14, 61) [subsumption resolution 609,148] 611. $false <- (14, 61) [subsumption resolution 610,151] 612. ~14 | ~61 [avatar contradiction clause 611] 613. $false [avatar sat refutation 177,227,346,349,476,580,612] % SZS output end Proof for 1923680143406185467664779 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.029 s % ------------------------------ % ------------------------------

If someone is both strong and not creative then fred is both creative and wise. Everyone who is curious is not tall or not rich and vice versa. Everyone who is quiet or not strong is both not patient and not creative. Everyone who is both rich and not creative is both not happy and not quiet. If someone is both brave and happy then someone is both not brave and not rich and vice versa. Everyone who is not wise or funny is both funny and not creative. Everyone who is not wise is either old or not curious. If someone is funny or not quiet then alice is both calm and not brave. Everyone who is not quiet or brave is both calm and not creative. If mary is either not rich or not curious then someone is both rich and strong and vice versa. Everyone who is not kind or humble is old or not generous and vice versa. If someone is not calm then someone is not creative. Everyone who is not wise is both not curious and not calm and vice versa. If paul is creative or not brave then paul is not happy and vice versa. If someone is either old or patient then someone is happy. If lucy is not calm or not kind then someone is not old or brave and vice versa. Susan is not strong. Someone is wise or not generous. Someone is not creative. Someone is either not kind or not funny. Paul is not brave or not creative. Someone is both calm and not kind. Someone is both not happy and not funny.

Mary is not creative.

entailment

((?[X]:((strong(X)&~creative(X))))=>((creative(fred)&wise(fred))))& (![X]:(curious(X)<=>(~tall(X)|~rich(X))))& (![X]:((quiet(X)|~strong(X))=>(~patient(X)&~creative(X))))& (![X]:((rich(X)&~creative(X))=>(~happy(X)&~quiet(X))))& ((?[X]:((brave(X)&happy(X))))<=>(?[X]:((~brave(X)&~rich(X)))))& (![X]:((~wise(X)|funny(X))=>(funny(X)&~creative(X))))& (![X]:(~wise(X)=>(old(X)<~>~curious(X))))& ((?[X]:((funny(X)|~quiet(X))))=>((calm(alice)&~brave(alice))))& (![X]:((~quiet(X)|brave(X))=>(calm(X)&~creative(X))))& (((~rich(mary)<~>~curious(mary)))<=>(?[X]:((rich(X)&strong(X)))))& (![X]:((~kind(X)|humble(X))<=>(old(X)|~generous(X))))& ((?[X]:(~calm(X)))=>(?[X]:(~creative(X))))& (![X]:(~wise(X)<=>(~curious(X)&~calm(X))))& (((creative(paul)|~brave(paul)))<=>(~happy(paul)))& ((?[X]:((old(X)<~>patient(X))))=>(?[X]:(happy(X))))& (((~calm(lucy)|~kind(lucy)))<=>(?[X]:((~old(X)|brave(X)))))& (~strong(susan))& (?[X]:((wise(X)|~generous(X))))& (?[X]:(~creative(X)))& (?[X]:((~kind(X)<~>~funny(X))))& ((~brave(paul)|~creative(paul)))& (?[X]:((calm(X)&~kind(X))))& (?[X]:((~happy(X)&~funny(X))))

~creative(mary)

% SZS status Unsatisfiable for 6068760549523989124903604 % SZS output start Proof for 6068760549523989124903604 3. ! [X0] : ((~strong(X0) | quiet(X0)) => (~creative(X0) & ~patient(X0))) [input p2] 9. ! [X0] : ((brave(X0) | ~quiet(X0)) => (~creative(X0) & calm(X0))) [input p8] 24. creative(mary) [input hypothesis] 30. ! [X0] : ((~creative(X0) & ~patient(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 3] 36. ! [X0] : ((~creative(X0) & calm(X0)) | (~brave(X0) & quiet(X0))) [ennf transformation 9] 87. ~creative(X0) | ~quiet(X0) [cnf transformation 30] 107. ~creative(X0) | quiet(X0) [cnf transformation 36] 140. creative(mary) [cnf transformation 24] 199. ~creative(X0) [subsumption resolution 107,87] 296. $false [subsumption resolution 140,199] % SZS output end Proof for 6068760549523989124903604 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

If someone is both not humble and not curious then someone is both curious and happy. If someone is both strong and generous then someone is either brave or happy and vice versa. If someone is not happy then susan is both not wise and curious. Everyone who is kind is both not calm and calm and vice versa. Everyone who is both tall and brave is both wise and not tall and vice versa. Everyone who is creative is not calm or wise and vice versa. If someone is either not generous or generous then someone is both not curious and not patient. If someone is creative or not quiet then mary is funny and vice versa. Everyone who is either not brave or quiet is both calm and happy and vice versa. Everyone who is both not wise and funny is both not generous and not calm and vice versa. If someone is patient then mary is either strong or generous and vice versa. Everyone who is not funny is not rich. If someone is not tall or quiet then someone is either not wise or calm. Everyone who is not generous or funny is strong. Everyone who is both not rich and funny is both not calm and patient. If susan is both generous and not creative then mary is not rich or quiet. Lucy is either strong or not patient. John is not curious. Someone is tall or humble. Someone is either wise or creative. Lucy is either not brave or not calm. Fred is either not tall or not old. John is quiet or funny. Alice is not patient.

Lucy is not calm.

neutral

((?[X]:((~humble(X)&~curious(X))))=>(?[X]:((curious(X)&happy(X)))))& ((?[X]:((strong(X)&generous(X))))<=>(?[X]:((brave(X)<~>happy(X)))))& ((?[X]:(~happy(X)))=>((~wise(susan)&curious(susan))))& (![X]:(kind(X)<=>(~calm(X)&calm(X))))& (![X]:((tall(X)&brave(X))<=>(wise(X)&~tall(X))))& (![X]:(creative(X)<=>(~calm(X)|wise(X))))& ((?[X]:((~generous(X)<~>generous(X))))=>(?[X]:((~curious(X)&~patient(X)))))& ((?[X]:((creative(X)|~quiet(X))))<=>(funny(mary)))& (![X]:((~brave(X)<~>quiet(X))<=>(calm(X)&happy(X))))& (![X]:((~wise(X)&funny(X))<=>(~generous(X)&~calm(X))))& ((?[X]:(patient(X)))<=>((strong(mary)<~>generous(mary))))& (![X]:(~funny(X)=>~rich(X)))& ((?[X]:((~tall(X)|quiet(X))))=>(?[X]:((~wise(X)<~>calm(X)))))& (![X]:((~generous(X)|funny(X))=>strong(X)))& (![X]:((~rich(X)&funny(X))=>(~calm(X)&patient(X))))& (((generous(susan)&~creative(susan)))=>((~rich(mary)|quiet(mary))))& ((strong(lucy)<~>~patient(lucy)))& (~curious(john))& (?[X]:((tall(X)|humble(X))))& (?[X]:((wise(X)<~>creative(X))))& ((~brave(lucy)<~>~calm(lucy)))& ((~tall(fred)<~>~old(fred)))& ((quiet(john)|funny(john)))& (~patient(alice))

~calm(lucy)

Everyone who is both not old and not curious is either rich or not happy and vice versa. Everyone who is either patient or not old is patient and vice versa. If susan is not calm then someone is not old and vice versa. Everyone who is both not curious and rich is not quiet. If paul is funny or calm then mary is both not generous and tall and vice versa. If someone is either not creative or not humble then someone is not creative and vice versa. If john is kind then alice is happy or humble and vice versa. If john is quiet then susan is not quiet. Everyone who is both not creative and quiet is both not kind and wise and vice versa. If lucy is either not rich or not brave then someone is curious. Everyone who is either not happy or quiet is creative or not happy. If paul is both not quiet and old then someone is not wise or rich and vice versa. Everyone who is strong is both wise and curious. Everyone who is either not creative or not brave is quiet. If someone is brave then paul is either not curious or not quiet and vice versa. If someone is brave or not kind then someone is strong and vice versa. Someone is not brave. Lucy is both not happy and calm. Paul is either quiet or not curious. Someone is either kind or quiet. Someone is both kind and not curious.

John is brave.

contradiction

(![X]:((~old(X)&~curious(X))<=>(rich(X)<~>~happy(X))))& (![X]:((patient(X)<~>~old(X))<=>patient(X)))& ((~calm(susan))<=>(?[X]:(~old(X))))& (![X]:((~curious(X)&rich(X))=>~quiet(X)))& (((funny(paul)|calm(paul)))<=>((~generous(mary)&tall(mary))))& ((?[X]:((~creative(X)<~>~humble(X))))<=>(?[X]:(~creative(X))))& ((kind(john))<=>((happy(alice)|humble(alice))))& ((quiet(john))=>(~quiet(susan)))& (![X]:((~creative(X)&quiet(X))<=>(~kind(X)&wise(X))))& (((~rich(lucy)<~>~brave(lucy)))=>(?[X]:(curious(X))))& (![X]:((~happy(X)<~>quiet(X))=>(creative(X)|~happy(X))))& (((~quiet(paul)&old(paul)))<=>(?[X]:((~wise(X)|rich(X)))))& (![X]:(strong(X)=>(wise(X)&curious(X))))& (![X]:((~creative(X)<~>~brave(X))=>quiet(X)))& ((?[X]:(brave(X)))<=>((~curious(paul)<~>~quiet(paul))))& ((?[X]:((brave(X)|~kind(X))))<=>(?[X]:(strong(X))))& (?[X]:(~brave(X)))& ((~happy(lucy)&calm(lucy)))& ((quiet(paul)<~>~curious(paul)))& (?[X]:((kind(X)<~>quiet(X))))& (?[X]:((kind(X)&~curious(X))))

brave(john)

% SZS status Unsatisfiable for 6467285720145573546607445 % SZS output start Proof for 6467285720145573546607445 15. ? [X0] : brave(X0) <=> (~curious(paul) <~> ~quiet(paul)) [input p14] 19. quiet(paul) <~> ~curious(paul) [input p18] 22. brave(john) [input hypothesis] 61. (? [X0] : brave(X0) | ((~curious(paul) | quiet(paul)) & (~quiet(paul) | curious(paul)))) & (((quiet(paul) | curious(paul)) & (~quiet(paul) | ~curious(paul))) | ! [X0] : ~brave(X0)) [nnf transformation 15] 62. (? [X0] : brave(X0) | ((~curious(paul) | quiet(paul)) & (~quiet(paul) | curious(paul)))) & (((quiet(paul) | curious(paul)) & (~quiet(paul) | ~curious(paul))) | ! [X1] : ~brave(X1)) [rectify 61] 63. ? [X0] : brave(X0) => brave(sK5) [choice axiom] 64. (brave(sK5) | ((~curious(paul) | quiet(paul)) & (~quiet(paul) | curious(paul)))) & (((quiet(paul) | curious(paul)) & (~quiet(paul) | ~curious(paul))) | ! [X1] : ~brave(X1)) [skolemisation 62,63] 72. (curious(paul) | ~quiet(paul)) & (~curious(paul) | quiet(paul)) [nnf transformation 19] 121. ~quiet(paul) | ~curious(paul) | ~brave(X1) [cnf transformation 64] 122. quiet(paul) | curious(paul) | ~brave(X1) [cnf transformation 64] 131. ~curious(paul) | quiet(paul) [cnf transformation 72] 132. curious(paul) | ~quiet(paul) [cnf transformation 72] 137. brave(john) [cnf transformation 22] 231. 20 <=> quiet(paul) [avatar definition] 250. 24 <=> curious(paul) [avatar definition] 260. 26 <=> ! [X1] : ~brave(X1) [avatar definition] 261. ~brave(X1) <- (26) [avatar component clause 260] 262. 26 | 24 | 20 [avatar split clause 122,231,250,260] 263. 26 | ~24 | ~20 [avatar split clause 121,231,250,260] 285. ~20 | 24 [avatar split clause 132,250,231] 286. 20 | ~24 [avatar split clause 131,250,231] 304. $false <- (26) [resolution 261,137] 305. ~26 [avatar contradiction clause 304] 306. $false [avatar sat refutation 262,263,285,286,305] % SZS output end Proof for 6467285720145573546607445 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.030 s % ------------------------------ % ------------------------------

If susan is either humble or not curious then lucy is not rich or old and vice versa. If someone is not brave or not humble then someone is not creative or rich and vice versa. Everyone who is either not patient or humble is either old or curious and vice versa. If john is both not brave and not funny then alice is either funny or patient and vice versa. If someone is calm or wise then someone is not strong or calm. Everyone who is both not happy and creative is wise or brave and vice versa. Everyone who is either brave or not patient is either brave or wise. Everyone who is happy or not wise is both brave and not brave and vice versa. Everyone who is either funny or not kind is kind and vice versa. Everyone who is not generous or quiet is both strong and not tall. Everyone who is not rich or not tall is quiet or patient and vice versa. If john is not generous then paul is both quiet and old and vice versa. If someone is both funny and not humble then alice is both not quiet and tall and vice versa. If susan is both happy and brave then someone is either calm or happy. John is not happy. Paul is either not quiet or old. John is not calm or quiet. Someone is not curious or generous. Someone is either brave or strong. Susan is either not kind or quiet.

Susan is not wise.

contradiction

(((humble(susan)<~>~curious(susan)))<=>((~rich(lucy)|old(lucy))))& ((?[X]:((~brave(X)|~humble(X))))<=>(?[X]:((~creative(X)|rich(X)))))& (![X]:((~patient(X)<~>humble(X))<=>(old(X)<~>curious(X))))& (((~brave(john)&~funny(john)))<=>((funny(alice)<~>patient(alice))))& ((?[X]:((calm(X)|wise(X))))=>(?[X]:((~strong(X)|calm(X)))))& (![X]:((~happy(X)&creative(X))<=>(wise(X)|brave(X))))& (![X]:((brave(X)<~>~patient(X))=>(brave(X)<~>wise(X))))& (![X]:((happy(X)|~wise(X))<=>(brave(X)&~brave(X))))& (![X]:((funny(X)<~>~kind(X))<=>kind(X)))& (![X]:((~generous(X)|quiet(X))=>(strong(X)&~tall(X))))& (![X]:((~rich(X)|~tall(X))<=>(quiet(X)|patient(X))))& ((~generous(john))<=>((quiet(paul)&old(paul))))& ((?[X]:((funny(X)&~humble(X))))<=>((~quiet(alice)&tall(alice))))& (((happy(susan)&brave(susan)))=>(?[X]:((calm(X)<~>happy(X)))))& (~happy(john))& ((~quiet(paul)<~>old(paul)))& ((~calm(john)|quiet(john)))& (?[X]:((~curious(X)|generous(X))))& (?[X]:((brave(X)<~>strong(X))))& ((~kind(susan)<~>quiet(susan)))

~wise(susan)

% SZS status Unsatisfiable for 1974743911365613093208578 % SZS output start Proof for 1974743911365613093208578 8. ! [X0] : ((~wise(X0) | happy(X0)) <=> (~brave(X0) & brave(X0))) [input p7] 21. ~wise(susan) [input hypothesis] 45. ! [X0] : (((~wise(X0) | happy(X0)) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 8] 46. ! [X0] : ((~wise(X0) | happy(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [flattening 45] 103. brave(X0) | wise(X0) [cnf transformation 46] 105. ~brave(X0) | wise(X0) [cnf transformation 46] 137. ~wise(susan) [cnf transformation 21] 234. wise(X0) [subsumption resolution 103,105] 310. $false [subsumption resolution 137,234] % SZS output end Proof for 1974743911365613093208578 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

Everyone who is either not funny or quiet is both not brave and not funny. If someone is not patient or not old then someone is not old and vice versa. Everyone who is not old is brave. If someone is both wise and not happy then john is either humble or quiet. Everyone who is strong or wise is both not curious and rich. Everyone who is not curious is either not happy or not rich. Everyone who is either creative or not happy is not humble or kind. If someone is not brave then lucy is old. Everyone who is not strong or generous is both wise and curious and vice versa. If someone is not tall then john is happy or not calm and vice versa. Everyone who is not calm is wise and vice versa. Everyone who is not brave or not quiet is calm or not kind. Everyone who is both not humble and tall is not brave. If mary is both calm and not humble then someone is both patient and not calm and vice versa. Everyone who is not calm or wise is both tall and not creative and vice versa. If someone is funny or kind then fred is either not generous or not humble and vice versa. John is either not funny or wise. Mary is kind or not quiet. Someone is either old or not brave. Someone is curious or patient. Someone is not kind. John is both not funny and not happy. Someone is wise or old.

Lucy is patient.

neutral

(![X]:((~funny(X)<~>quiet(X))=>(~brave(X)&~funny(X))))& ((?[X]:((~patient(X)|~old(X))))<=>(?[X]:(~old(X))))& (![X]:(~old(X)=>brave(X)))& ((?[X]:((wise(X)&~happy(X))))=>((humble(john)<~>quiet(john))))& (![X]:((strong(X)|wise(X))=>(~curious(X)&rich(X))))& (![X]:(~curious(X)=>(~happy(X)<~>~rich(X))))& (![X]:((creative(X)<~>~happy(X))=>(~humble(X)|kind(X))))& ((?[X]:(~brave(X)))=>(old(lucy)))& (![X]:((~strong(X)|generous(X))<=>(wise(X)&curious(X))))& ((?[X]:(~tall(X)))<=>((happy(john)|~calm(john))))& (![X]:(~calm(X)<=>wise(X)))& (![X]:((~brave(X)|~quiet(X))=>(calm(X)|~kind(X))))& (![X]:((~humble(X)&tall(X))=>~brave(X)))& (((calm(mary)&~humble(mary)))<=>(?[X]:((patient(X)&~calm(X)))))& (![X]:((~calm(X)|wise(X))<=>(tall(X)&~creative(X))))& ((?[X]:((funny(X)|kind(X))))<=>((~generous(fred)<~>~humble(fred))))& ((~funny(john)<~>wise(john)))& ((kind(mary)|~quiet(mary)))& (?[X]:((old(X)<~>~brave(X))))& (?[X]:((curious(X)|patient(X))))& (?[X]:(~kind(X)))& ((~funny(john)&~happy(john)))& (?[X]:((wise(X)|old(X))))

patient(lucy)

Everyone who is not quiet or generous is either strong or not humble. Everyone who is both old and brave is funny or brave. Everyone who is not wise or quiet is both not tall and not patient. Everyone who is either kind or not kind is funny and vice versa. If john is generous or not brave then someone is not brave and vice versa. Everyone who is wise is both not funny and curious. Everyone who is either not wise or not happy is either not brave or not creative. Everyone who is not kind or creative is both funny and wise. Everyone who is both tall and not funny is not wise. Everyone who is both kind and curious is not curious or not wise. Everyone who is either funny or happy is either not curious or not generous. Everyone who is either calm or quiet is both creative and old and vice versa. If susan is either patient or wise then alice is not rich and vice versa. If susan is patient or generous then fred is funny. If someone is either curious or not old then someone is either not strong or strong and vice versa. Someone is not generous. Someone is either not kind or not happy. Alice is wise or not happy. Someone is not quiet. Someone is old or kind. John is funny or not tall.

John is not creative.

entailment

(![X]:((~quiet(X)|generous(X))=>(strong(X)<~>~humble(X))))& (![X]:((old(X)&brave(X))=>(funny(X)|brave(X))))& (![X]:((~wise(X)|quiet(X))=>(~tall(X)&~patient(X))))& (![X]:((kind(X)<~>~kind(X))<=>funny(X)))& (((generous(john)|~brave(john)))<=>(?[X]:(~brave(X))))& (![X]:(wise(X)=>(~funny(X)&curious(X))))& (![X]:((~wise(X)<~>~happy(X))=>(~brave(X)<~>~creative(X))))& (![X]:((~kind(X)|creative(X))=>(funny(X)&wise(X))))& (![X]:((tall(X)&~funny(X))=>~wise(X)))& (![X]:((kind(X)&curious(X))=>(~curious(X)|~wise(X))))& (![X]:((funny(X)<~>happy(X))=>(~curious(X)<~>~generous(X))))& (![X]:((calm(X)<~>quiet(X))<=>(creative(X)&old(X))))& (((patient(susan)<~>wise(susan)))<=>(~rich(alice)))& (((patient(susan)|generous(susan)))=>(funny(fred)))& ((?[X]:((curious(X)<~>~old(X))))<=>(?[X]:((~strong(X)<~>strong(X)))))& (?[X]:(~generous(X)))& (?[X]:((~kind(X)<~>~happy(X))))& ((wise(alice)|~happy(alice)))& (?[X]:(~quiet(X)))& (?[X]:((old(X)|kind(X))))& ((funny(john)|~tall(john)))

~creative(john)

% SZS status Unsatisfiable for 5226273394300146600211918 % SZS output start Proof for 5226273394300146600211918 4. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> funny(X0)) [input p3] 6. ! [X0] : (wise(X0) => (curious(X0) & ~funny(X0))) [input p5] 8. ! [X0] : ((creative(X0) | ~kind(X0)) => (wise(X0) & funny(X0))) [input p7] 22. creative(john) [input hypothesis] 31. ! [X0] : ((curious(X0) & ~funny(X0)) | ~wise(X0)) [ennf transformation 6] 33. ! [X0] : ((wise(X0) & funny(X0)) | (~creative(X0) & kind(X0))) [ennf transformation 8] 39. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~funny(X0)) & (funny(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 4] 71. funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 39] 72. funny(X0) | kind(X0) | kind(X0) [cnf transformation 39] 78. ~funny(X0) | ~wise(X0) [cnf transformation 31] 87. wise(X0) | ~creative(X0) [cnf transformation 33] 119. creative(john) [cnf transformation 22] 125. funny(X0) | ~kind(X0) [duplicate literal removal 71] 126. funny(X0) | kind(X0) [duplicate literal removal 72] 127. funny(X0) [subsumption resolution 125,126] 146. ~wise(X0) [subsumption resolution 78,127] 149. ~creative(X0) [subsumption resolution 87,146] 185. $false [subsumption resolution 119,149] % SZS output end Proof for 5226273394300146600211918 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 4989 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

Everyone who is brave is either not wise or not kind and vice versa. If someone is not brave or funny then someone is not brave. If mary is not strong or strong then john is calm or generous. Everyone who is both not happy and tall is either not humble or not old. If mary is not rich then someone is both not happy and old. Everyone who is generous is both strong and not patient. Everyone who is quiet or kind is happy or funny and vice versa. Everyone who is both generous and wise is not humble and vice versa. If someone is both not tall and not old then someone is brave or not generous and vice versa. If susan is kind then someone is both funny and patient and vice versa. Everyone who is not quiet is both creative and funny and vice versa. Everyone who is not kind or not humble is not generous or not curious. If john is not curious then someone is wise or not rich. If someone is kind then someone is both curious and not kind. Everyone who is kind or quiet is both strong and patient and vice versa. Everyone who is both kind and calm is quiet. Someone is either creative or not curious. Susan is either generous or not curious. Paul is both creative and wise. Someone is either funny or not happy. Someone is rich. Lucy is either quiet or humble. Lucy is not patient or humble.

Lucy is humble.

entailment

(![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))& ((?[X]:((~brave(X)|funny(X))))=>(?[X]:(~brave(X))))& (((~strong(mary)|strong(mary)))=>((calm(john)|generous(john))))& (![X]:((~happy(X)&tall(X))=>(~humble(X)<~>~old(X))))& ((~rich(mary))=>(?[X]:((~happy(X)&old(X)))))& (![X]:(generous(X)=>(strong(X)&~patient(X))))& (![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))& (![X]:((generous(X)&wise(X))<=>~humble(X)))& ((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))& ((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))& (![X]:(~quiet(X)<=>(creative(X)&funny(X))))& (![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))& ((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))& ((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))& (![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))& (![X]:((kind(X)&calm(X))=>quiet(X)))& (?[X]:((creative(X)<~>~curious(X))))& ((generous(susan)<~>~curious(susan)))& ((creative(paul)&wise(paul)))& (?[X]:((funny(X)<~>~happy(X))))& (?[X]:(rich(X)))& ((quiet(lucy)<~>humble(lucy)))& ((~patient(lucy)|humble(lucy)))

humble(lucy)

% SZS status Unsatisfiable for 1701857695690504564674912 % SZS output start Proof for 1701857695690504564674912 15. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p14] 22. quiet(lucy) <~> humble(lucy) [input p21] 23. humble(lucy) | ~patient(lucy) [input p22] 24. ~humble(lucy) [input hypothesis] 68. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 15] 69. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 68] 79. (~humble(lucy) | ~quiet(lucy)) & (humble(lucy) | quiet(lucy)) [nnf transformation 22] 120. ~quiet(X0) | patient(X0) [cnf transformation 69] 132. humble(lucy) | quiet(lucy) [cnf transformation 79] 134. humble(lucy) | ~patient(lucy) [cnf transformation 23] 135. ~humble(lucy) [cnf transformation 24] 282. 33 <=> quiet(lucy) [avatar definition] 283. quiet(lucy) <- (33) [avatar component clause 282] 286. 34 <=> humble(lucy) [avatar definition] 290. 33 | 34 [avatar split clause 132,286,282] 292. 35 <=> patient(lucy) [avatar definition] 294. ~patient(lucy) <- (~35) [avatar component clause 292] 295. ~35 | 34 [avatar split clause 134,286,292] 296. ~34 [avatar split clause 135,286] 304. patient(lucy) <- (33) [resolution 120,283] 307. $false <- (33, ~35) [subsumption resolution 304,294] 308. ~33 | 35 [avatar contradiction clause 307] 309. $false [avatar sat refutation 290,295,296,308] % SZS output end Proof for 1701857695690504564674912 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

If someone is creative then alice is either calm or not happy and vice versa. Everyone who is both calm and rich is either not wise or not brave and vice versa. Everyone who is either humble or not brave is both not curious and not creative and vice versa. If someone is either not tall or not curious then john is not old or rich and vice versa. Everyone who is either quiet or funny is funny or strong. Everyone who is both curious and not strong is quiet. If someone is either not calm or humble then susan is either brave or not generous. If susan is kind then someone is either not patient or happy and vice versa. If someone is either not wise or not patient then someone is either kind or not humble and vice versa. Everyone who is not calm is not strong. If someone is both not wise and quiet then lucy is generous. Everyone who is creative is either not funny or not strong and vice versa. If alice is both not happy and not calm then paul is kind and vice versa. Everyone who is tall is not humble or humble and vice versa. If someone is wise then susan is either rich or curious and vice versa. If paul is either funny or old then someone is either not quiet or not creative and vice versa. John is either calm or curious. Someone is old. Someone is either not curious or creative. John is either not curious or humble. Susan is either brave or happy. Someone is brave. Someone is not brave.

Paul is not kind.

neutral

((?[X]:(creative(X)))<=>((calm(alice)<~>~happy(alice))))& (![X]:((calm(X)&rich(X))<=>(~wise(X)<~>~brave(X))))& (![X]:((humble(X)<~>~brave(X))<=>(~curious(X)&~creative(X))))& ((?[X]:((~tall(X)<~>~curious(X))))<=>((~old(john)|rich(john))))& (![X]:((quiet(X)<~>funny(X))=>(funny(X)|strong(X))))& (![X]:((curious(X)&~strong(X))=>quiet(X)))& ((?[X]:((~calm(X)<~>humble(X))))=>((brave(susan)<~>~generous(susan))))& ((kind(susan))<=>(?[X]:((~patient(X)<~>happy(X)))))& ((?[X]:((~wise(X)<~>~patient(X))))<=>(?[X]:((kind(X)<~>~humble(X)))))& (![X]:(~calm(X)=>~strong(X)))& ((?[X]:((~wise(X)&quiet(X))))=>(generous(lucy)))& (![X]:(creative(X)<=>(~funny(X)<~>~strong(X))))& (((~happy(alice)&~calm(alice)))<=>(kind(paul)))& (![X]:(tall(X)<=>(~humble(X)|humble(X))))& ((?[X]:(wise(X)))<=>((rich(susan)<~>curious(susan))))& (((funny(paul)<~>old(paul)))<=>(?[X]:((~quiet(X)<~>~creative(X)))))& ((calm(john)<~>curious(john)))& (?[X]:(old(X)))& (?[X]:((~curious(X)<~>creative(X))))& ((~curious(john)<~>humble(john)))& ((brave(susan)<~>happy(susan)))& (?[X]:(brave(X)))& (?[X]:(~brave(X)))

~kind(paul)

Everyone who is not creative or not brave is both creative and old. Everyone who is calm or not creative is not generous and vice versa. Everyone who is either calm or happy is both not curious and old and vice versa. Everyone who is either not strong or creative is either creative or tall and vice versa. If someone is either not funny or not old then john is wise. Everyone who is not wise or calm is either brave or funny and vice versa. If someone is both generous and not tall then mary is either creative or not rich and vice versa. If someone is not quiet then mary is old or humble. Everyone who is not humble or not calm is either generous or not funny and vice versa. If alice is both wise and humble then someone is not old or not kind and vice versa. Everyone who is not old is either funny or quiet and vice versa. If susan is not kind or not calm then someone is strong. Everyone who is either not funny or not strong is humble or not generous. Everyone who is not wise is both rich and not quiet. Everyone who is calm or not tall is both curious and tall. Everyone who is either not wise or patient is strong. Mary is not brave or calm. Paul is generous or not brave. Someone is not brave or funny. Paul is tall. Paul is happy or funny. Someone is not brave.

John is funny.

neutral

(![X]:((~creative(X)|~brave(X))=>(creative(X)&old(X))))& (![X]:((calm(X)|~creative(X))<=>~generous(X)))& (![X]:((calm(X)<~>happy(X))<=>(~curious(X)&old(X))))& (![X]:((~strong(X)<~>creative(X))<=>(creative(X)<~>tall(X))))& ((?[X]:((~funny(X)<~>~old(X))))=>(wise(john)))& (![X]:((~wise(X)|calm(X))<=>(brave(X)<~>funny(X))))& ((?[X]:((generous(X)&~tall(X))))<=>((creative(mary)<~>~rich(mary))))& ((?[X]:(~quiet(X)))=>((old(mary)|humble(mary))))& (![X]:((~humble(X)|~calm(X))<=>(generous(X)<~>~funny(X))))& (((wise(alice)&humble(alice)))<=>(?[X]:((~old(X)|~kind(X)))))& (![X]:(~old(X)<=>(funny(X)<~>quiet(X))))& (((~kind(susan)|~calm(susan)))=>(?[X]:(strong(X))))& (![X]:((~funny(X)<~>~strong(X))=>(humble(X)|~generous(X))))& (![X]:(~wise(X)=>(rich(X)&~quiet(X))))& (![X]:((calm(X)|~tall(X))=>(curious(X)&tall(X))))& (![X]:((~wise(X)<~>patient(X))=>strong(X)))& ((~brave(mary)|calm(mary)))& ((generous(paul)|~brave(paul)))& (?[X]:((~brave(X)|funny(X))))& (tall(paul))& ((happy(paul)|funny(paul)))& (?[X]:(~brave(X)))

funny(john)

If someone is old or curious then someone is both patient and calm. If alice is both not curious and wise then fred is not strong and vice versa. If fred is quiet or patient then someone is not curious or old. If alice is not curious then someone is both tall and not strong. Everyone who is both not tall and old is both not kind and curious and vice versa. Everyone who is both strong and curious is not rich or not humble and vice versa. Everyone who is rich or calm is either not kind or funny. Everyone who is either humble or tall is both generous and wise and vice versa. Everyone who is both not curious and not funny is rich or funny and vice versa. Everyone who is generous or old is both not old and not creative and vice versa. Everyone who is both brave and tall is not quiet and vice versa. Everyone who is either not quiet or not tall is not curious. Everyone who is funny or happy is not calm or strong. Everyone who is either rich or calm is old and vice versa. If someone is kind then paul is either generous or not old and vice versa. If someone is both not funny and creative then mary is not happy or not kind. Lucy is both not quiet and not old. Someone is both generous and not kind. John is not rich. John is both not rich and strong. Someone is not calm or not rich. Fred is either not patient or humble. John is either not rich or brave.

Paul is not brave.

neutral

((?[X]:((old(X)|curious(X))))=>(?[X]:((patient(X)&calm(X)))))& (((~curious(alice)&wise(alice)))<=>(~strong(fred)))& (((quiet(fred)|patient(fred)))=>(?[X]:((~curious(X)|old(X)))))& ((~curious(alice))=>(?[X]:((tall(X)&~strong(X)))))& (![X]:((~tall(X)&old(X))<=>(~kind(X)&curious(X))))& (![X]:((strong(X)&curious(X))<=>(~rich(X)|~humble(X))))& (![X]:((rich(X)|calm(X))=>(~kind(X)<~>funny(X))))& (![X]:((humble(X)<~>tall(X))<=>(generous(X)&wise(X))))& (![X]:((~curious(X)&~funny(X))<=>(rich(X)|funny(X))))& (![X]:((generous(X)|old(X))<=>(~old(X)&~creative(X))))& (![X]:((brave(X)&tall(X))<=>~quiet(X)))& (![X]:((~quiet(X)<~>~tall(X))=>~curious(X)))& (![X]:((funny(X)|happy(X))=>(~calm(X)|strong(X))))& (![X]:((rich(X)<~>calm(X))<=>old(X)))& ((?[X]:(kind(X)))<=>((generous(paul)<~>~old(paul))))& ((?[X]:((~funny(X)&creative(X))))=>((~happy(mary)|~kind(mary))))& ((~quiet(lucy)&~old(lucy)))& (?[X]:((generous(X)&~kind(X))))& (~rich(john))& ((~rich(john)&strong(john)))& (?[X]:((~calm(X)|~rich(X))))& ((~patient(fred)<~>humble(fred)))& ((~rich(john)<~>brave(john)))

~brave(paul)

If someone is patient or not kind then someone is old. If susan is both rich and not old then someone is both happy and creative. Everyone who is not brave or not humble is both tall and not wise. Everyone who is humble or not humble is creative or not happy and vice versa. If someone is funny then someone is either rich or not rich. Everyone who is either strong or not curious is either creative or strong. Everyone who is calm or not old is either brave or not brave. Everyone who is not patient or not rich is not generous or curious. Everyone who is either not happy or humble is quiet or happy and vice versa. If someone is both creative and not creative then john is old. If someone is both humble and funny then someone is either not rich or not kind and vice versa. Everyone who is either not quiet or quiet is rich and vice versa. Everyone who is creative is tall and vice versa. Everyone who is either not old or brave is both not funny and funny and vice versa. Everyone who is funny or strong is both not happy and not brave. Everyone who is both strong and rich is both strong and brave and vice versa. Someone is both humble and not brave. Someone is creative or not funny. Paul is humble or creative. Someone is not wise or brave. Someone is kind or not happy. John is not creative or not strong. Someone is either tall or generous. Someone is not happy or not old.

John is old.

neutral

((?[X]:((patient(X)|~kind(X))))=>(?[X]:(old(X))))& (((rich(susan)&~old(susan)))=>(?[X]:((happy(X)&creative(X)))))& (![X]:((~brave(X)|~humble(X))=>(tall(X)&~wise(X))))& (![X]:((humble(X)|~humble(X))<=>(creative(X)|~happy(X))))& ((?[X]:(funny(X)))=>(?[X]:((rich(X)<~>~rich(X)))))& (![X]:((strong(X)<~>~curious(X))=>(creative(X)<~>strong(X))))& (![X]:((calm(X)|~old(X))=>(brave(X)<~>~brave(X))))& (![X]:((~patient(X)|~rich(X))=>(~generous(X)|curious(X))))& (![X]:((~happy(X)<~>humble(X))<=>(quiet(X)|happy(X))))& ((?[X]:((creative(X)&~creative(X))))=>(old(john)))& ((?[X]:((humble(X)&funny(X))))<=>(?[X]:((~rich(X)<~>~kind(X)))))& (![X]:((~quiet(X)<~>quiet(X))<=>rich(X)))& (![X]:(creative(X)<=>tall(X)))& (![X]:((~old(X)<~>brave(X))<=>(~funny(X)&funny(X))))& (![X]:((funny(X)|strong(X))=>(~happy(X)&~brave(X))))& (![X]:((strong(X)&rich(X))<=>(strong(X)&brave(X))))& (?[X]:((humble(X)&~brave(X))))& (?[X]:((creative(X)|~funny(X))))& ((humble(paul)|creative(paul)))& (?[X]:((~wise(X)|brave(X))))& (?[X]:((kind(X)|~happy(X))))& ((~creative(john)|~strong(john)))& (?[X]:((tall(X)<~>generous(X))))& (?[X]:((~happy(X)|~old(X))))

old(john)

If someone is kind or quiet then someone is happy. Everyone who is both not tall and not generous is either curious or not curious and vice versa. If susan is tall then someone is humble. Everyone who is not strong is tall or not strong. Everyone who is not patient is funny or quiet. Everyone who is old or not happy is creative or calm. If someone is either not brave or quiet then mary is both curious and humble and vice versa. Everyone who is either calm or kind is not generous or not kind and vice versa. Everyone who is not calm or happy is either strong or quiet and vice versa. Everyone who is either tall or strong is strong or not brave and vice versa. Everyone who is patient is either not brave or not strong and vice versa. Everyone who is both not calm and calm is funny and vice versa. Everyone who is old is both not funny and patient and vice versa. If fred is both not creative and calm then mary is kind and vice versa. If someone is not old or not strong then lucy is old. Everyone who is both not creative and generous is strong. Someone is both brave and calm. Someone is either not kind or curious. Alice is either brave or not tall. Fred is not rich or not strong. John is both creative and happy. Someone is both not kind and not curious. Someone is creative.

Mary is rich.

neutral

((?[X]:((kind(X)|quiet(X))))=>(?[X]:(happy(X))))& (![X]:((~tall(X)&~generous(X))<=>(curious(X)<~>~curious(X))))& ((tall(susan))=>(?[X]:(humble(X))))& (![X]:(~strong(X)=>(tall(X)|~strong(X))))& (![X]:(~patient(X)=>(funny(X)|quiet(X))))& (![X]:((old(X)|~happy(X))=>(creative(X)|calm(X))))& ((?[X]:((~brave(X)<~>quiet(X))))<=>((curious(mary)&humble(mary))))& (![X]:((calm(X)<~>kind(X))<=>(~generous(X)|~kind(X))))& (![X]:((~calm(X)|happy(X))<=>(strong(X)<~>quiet(X))))& (![X]:((tall(X)<~>strong(X))<=>(strong(X)|~brave(X))))& (![X]:(patient(X)<=>(~brave(X)<~>~strong(X))))& (![X]:((~calm(X)&calm(X))<=>funny(X)))& (![X]:(old(X)<=>(~funny(X)&patient(X))))& (((~creative(fred)&calm(fred)))<=>(kind(mary)))& ((?[X]:((~old(X)|~strong(X))))=>(old(lucy)))& (![X]:((~creative(X)&generous(X))=>strong(X)))& (?[X]:((brave(X)&calm(X))))& (?[X]:((~kind(X)<~>curious(X))))& ((brave(alice)<~>~tall(alice)))& ((~rich(fred)|~strong(fred)))& ((creative(john)&happy(john)))& (?[X]:((~kind(X)&~curious(X))))& (?[X]:(creative(X)))

rich(mary)

If someone is old or not rich then someone is not patient and vice versa. Everyone who is both not generous and tall is both not funny and humble and vice versa. Everyone who is either not old or patient is not generous and vice versa. Everyone who is both not brave and not patient is either not patient or not wise and vice versa. Everyone who is either calm or funny is both not kind and not happy and vice versa. Everyone who is either not funny or happy is generous or rich and vice versa. If paul is patient or not happy then someone is either quiet or not rich. If someone is both not kind and generous then fred is humble or not quiet. Everyone who is either not tall or happy is quiet and vice versa. Everyone who is both not quiet and not generous is both not generous and funny. Everyone who is both wise and tall is either curious or generous. If someone is either generous or funny then someone is both kind and not strong and vice versa. If someone is both not strong and old then paul is both not generous and curious. Everyone who is not quiet is either patient or calm. Everyone who is funny is brave and vice versa. Everyone who is not humble or happy is either not patient or not wise. John is either curious or not kind. John is both wise and not curious. Someone is both happy and tall. Someone is not old. Someone is both not generous and not rich. Someone is curious. Someone is not rich or quiet. Someone is not curious.

Paul is calm.

neutral

((?[X]:((old(X)|~rich(X))))<=>(?[X]:(~patient(X))))& (![X]:((~generous(X)&tall(X))<=>(~funny(X)&humble(X))))& (![X]:((~old(X)<~>patient(X))<=>~generous(X)))& (![X]:((~brave(X)&~patient(X))<=>(~patient(X)<~>~wise(X))))& (![X]:((calm(X)<~>funny(X))<=>(~kind(X)&~happy(X))))& (![X]:((~funny(X)<~>happy(X))<=>(generous(X)|rich(X))))& (((patient(paul)|~happy(paul)))=>(?[X]:((quiet(X)<~>~rich(X)))))& ((?[X]:((~kind(X)&generous(X))))=>((humble(fred)|~quiet(fred))))& (![X]:((~tall(X)<~>happy(X))<=>quiet(X)))& (![X]:((~quiet(X)&~generous(X))=>(~generous(X)&funny(X))))& (![X]:((wise(X)&tall(X))=>(curious(X)<~>generous(X))))& ((?[X]:((generous(X)<~>funny(X))))<=>(?[X]:((kind(X)&~strong(X)))))& ((?[X]:((~strong(X)&old(X))))=>((~generous(paul)&curious(paul))))& (![X]:(~quiet(X)=>(patient(X)<~>calm(X))))& (![X]:(funny(X)<=>brave(X)))& (![X]:((~humble(X)|happy(X))=>(~patient(X)<~>~wise(X))))& ((curious(john)<~>~kind(john)))& ((wise(john)&~curious(john)))& (?[X]:((happy(X)&tall(X))))& (?[X]:(~old(X)))& (?[X]:((~generous(X)&~rich(X))))& (?[X]:(curious(X)))& (?[X]:((~rich(X)|quiet(X))))& (?[X]:(~curious(X)))

calm(paul)

Everyone who is either not quiet or kind is both creative and funny. If lucy is both not generous and patient then someone is kind or not old. If lucy is creative or not quiet then someone is wise or brave. Everyone who is either not humble or rich is not generous or not funny. If susan is calm then someone is either not creative or not tall. Everyone who is both happy and wise is not curious or not rich. If someone is either not creative or humble then someone is both not kind and rich and vice versa. Everyone who is not old is both not quiet and humble. Everyone who is both humble and not happy is not happy. If someone is curious then mary is curious or creative and vice versa. If someone is patient then someone is not kind or old. Everyone who is not patient is not rich or humble and vice versa. Everyone who is either quiet or not creative is patient or rich. Everyone who is either not brave or not happy is strong or not wise. If someone is not happy then someone is both kind and quiet and vice versa. Everyone who is strong is both not curious and tall. Fred is either humble or not old. Lucy is either not strong or patient. Fred is not brave or patient. Mary is not rich or not calm. Someone is not patient or not kind. Someone is not patient or not tall. Someone is either rich or brave. Paul is both calm and strong.

Paul is calm.

entailment

(![X]:((~quiet(X)<~>kind(X))=>(creative(X)&funny(X))))& (((~generous(lucy)&patient(lucy)))=>(?[X]:((kind(X)|~old(X)))))& (((creative(lucy)|~quiet(lucy)))=>(?[X]:((wise(X)|brave(X)))))& (![X]:((~humble(X)<~>rich(X))=>(~generous(X)|~funny(X))))& ((calm(susan))=>(?[X]:((~creative(X)<~>~tall(X)))))& (![X]:((happy(X)&wise(X))=>(~curious(X)|~rich(X))))& ((?[X]:((~creative(X)<~>humble(X))))<=>(?[X]:((~kind(X)&rich(X)))))& (![X]:(~old(X)=>(~quiet(X)&humble(X))))& (![X]:((humble(X)&~happy(X))=>~happy(X)))& ((?[X]:(curious(X)))<=>((curious(mary)|creative(mary))))& ((?[X]:(patient(X)))=>(?[X]:((~kind(X)|old(X)))))& (![X]:(~patient(X)<=>(~rich(X)|humble(X))))& (![X]:((quiet(X)<~>~creative(X))=>(patient(X)|rich(X))))& (![X]:((~brave(X)<~>~happy(X))=>(strong(X)|~wise(X))))& ((?[X]:(~happy(X)))<=>(?[X]:((kind(X)&quiet(X)))))& (![X]:(strong(X)=>(~curious(X)&tall(X))))& ((humble(fred)<~>~old(fred)))& ((~strong(lucy)<~>patient(lucy)))& ((~brave(fred)|patient(fred)))& ((~rich(mary)|~calm(mary)))& (?[X]:((~patient(X)|~kind(X))))& (?[X]:((~patient(X)|~tall(X))))& (?[X]:((rich(X)<~>brave(X))))& ((calm(paul)&strong(paul)))

calm(paul)

% SZS status Unsatisfiable for 7497727590349227656594655 % SZS output start Proof for 7497727590349227656594655 24. strong(paul) & calm(paul) [input p23] 25. ~calm(paul) [input hypothesis] 134. calm(paul) [cnf transformation 24] 136. ~calm(paul) [cnf transformation 25] 324. $false [subsumption resolution 136,134] % SZS output end Proof for 7497727590349227656594655 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------

Everyone who is either not curious or not creative is old or curious. If someone is either strong or not quiet then alice is both creative and not patient and vice versa. Everyone who is creative is generous. If fred is either not kind or strong then someone is either happy or old and vice versa. Everyone who is kind or humble is either curious or strong and vice versa. Everyone who is either not creative or funny is brave or not humble and vice versa. If alice is both kind and not calm then lucy is not kind or not funny. Everyone who is either not old or rich is not happy or not patient and vice versa. If lucy is both kind and funny then someone is not calm or not old and vice versa. If lucy is tall then someone is not strong and vice versa. If someone is not old then fred is both wise and curious and vice versa. If alice is old or wise then mary is not rich and vice versa. If someone is both funny and kind then someone is humble or patient. Everyone who is both not funny and strong is rich or strong and vice versa. Everyone who is both kind and creative is not calm or not happy. If john is either generous or humble then someone is not curious or not calm and vice versa. Someone is either tall or not calm. Someone is rich or not creative. Susan is either happy or not curious. Someone is not calm. Someone is either wise or not calm. Someone is both not wise and not rich. Someone is humble or calm. Lucy is not strong.

Susan is strong.

neutral

(![X]:((~curious(X)<~>~creative(X))=>(old(X)|curious(X))))& ((?[X]:((strong(X)<~>~quiet(X))))<=>((creative(alice)&~patient(alice))))& (![X]:(creative(X)=>generous(X)))& (((~kind(fred)<~>strong(fred)))<=>(?[X]:((happy(X)<~>old(X)))))& (![X]:((kind(X)|humble(X))<=>(curious(X)<~>strong(X))))& (![X]:((~creative(X)<~>funny(X))<=>(brave(X)|~humble(X))))& (((kind(alice)&~calm(alice)))=>((~kind(lucy)|~funny(lucy))))& (![X]:((~old(X)<~>rich(X))<=>(~happy(X)|~patient(X))))& (((kind(lucy)&funny(lucy)))<=>(?[X]:((~calm(X)|~old(X)))))& ((tall(lucy))<=>(?[X]:(~strong(X))))& ((?[X]:(~old(X)))<=>((wise(fred)&curious(fred))))& (((old(alice)|wise(alice)))<=>(~rich(mary)))& ((?[X]:((funny(X)&kind(X))))=>(?[X]:((humble(X)|patient(X)))))& (![X]:((~funny(X)&strong(X))<=>(rich(X)|strong(X))))& (![X]:((kind(X)&creative(X))=>(~calm(X)|~happy(X))))& (((generous(john)<~>humble(john)))<=>(?[X]:((~curious(X)|~calm(X)))))& (?[X]:((tall(X)<~>~calm(X))))& (?[X]:((rich(X)|~creative(X))))& ((happy(susan)<~>~curious(susan)))& (?[X]:(~calm(X)))& (?[X]:((wise(X)<~>~calm(X))))& (?[X]:((~wise(X)&~rich(X))))& (?[X]:((humble(X)|calm(X))))& (~strong(lucy))

strong(susan)

Everyone who is either not calm or not curious is either funny or creative and vice versa. If lucy is kind or not generous then someone is both wise and not brave and vice versa. Everyone who is not curious is funny and vice versa. Everyone who is both generous and kind is both not wise and not old and vice versa. If mary is either tall or quiet then someone is both not old and not quiet. Everyone who is either curious or not curious is not old or kind and vice versa. Everyone who is not brave or curious is not curious and vice versa. If someone is curious or humble then john is creative. If someone is either not kind or not happy then alice is both funny and not humble and vice versa. Everyone who is both generous and not generous is generous. Everyone who is both brave and not patient is either wise or not quiet. Everyone who is either tall or patient is both not quiet and not creative. Everyone who is either not funny or not kind is curious or not patient and vice versa. If someone is either creative or brave then someone is wise or kind. Everyone who is both creative and strong is patient or old and vice versa. If someone is quiet or not strong then fred is both quiet and not strong and vice versa. Someone is not calm or tall. Paul is either curious or not rich. Someone is both calm and not brave. Paul is not tall or creative. Alice is both not calm and kind. Someone is either tall or not strong. Someone is either not creative or kind.

Alice is not strong.

contradiction

(![X]:((~calm(X)<~>~curious(X))<=>(funny(X)<~>creative(X))))& (((kind(lucy)|~generous(lucy)))<=>(?[X]:((wise(X)&~brave(X)))))& (![X]:(~curious(X)<=>funny(X)))& (![X]:((generous(X)&kind(X))<=>(~wise(X)&~old(X))))& (((tall(mary)<~>quiet(mary)))=>(?[X]:((~old(X)&~quiet(X)))))& (![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))& (![X]:((~brave(X)|curious(X))<=>~curious(X)))& ((?[X]:((curious(X)|humble(X))))=>(creative(john)))& ((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))& (![X]:((generous(X)&~generous(X))=>generous(X)))& (![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))& (![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))& (![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))& ((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))& (![X]:((creative(X)&strong(X))<=>(patient(X)|old(X))))& ((?[X]:((quiet(X)|~strong(X))))<=>((quiet(fred)&~strong(fred))))& (?[X]:((~calm(X)|tall(X))))& ((curious(paul)<~>~rich(paul)))& (?[X]:((calm(X)&~brave(X))))& ((~tall(paul)|creative(paul)))& ((~calm(alice)&kind(alice)))& (?[X]:((tall(X)<~>~strong(X))))& (?[X]:((~creative(X)<~>kind(X))))

~strong(alice)

% SZS status Unsatisfiable for 9189583969832499308612483 % SZS output start Proof for 9189583969832499308612483 3. ! [X0] : (~curious(X0) <=> funny(X0)) [input p2] 7. ! [X0] : ((curious(X0) | ~brave(X0)) <=> ~curious(X0)) [input p6] 13. ! [X0] : ((~funny(X0) <~> ~kind(X0)) <=> (~patient(X0) | curious(X0))) [input p12] 15. ! [X0] : ((strong(X0) & creative(X0)) <=> (old(X0) | patient(X0))) [input p14] 21. kind(alice) & ~calm(alice) [input p20] 24. ~strong(alice) [input hypothesis] 40. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 3] 48. ! [X0] : (((curious(X0) | ~brave(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [nnf transformation 7] 49. ! [X0] : ((curious(X0) | ~brave(X0) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [flattening 48] 57. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [nnf transformation 13] 58. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [flattening 57] 63. ! [X0] : (((strong(X0) & creative(X0)) | (~old(X0) & ~patient(X0))) & ((old(X0) | patient(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 15] 64. ! [X0] : (((strong(X0) & creative(X0)) | (~old(X0) & ~patient(X0))) & (old(X0) | patient(X0) | ~strong(X0) | ~creative(X0))) [flattening 63] 94. funny(X0) | curious(X0) [cnf transformation 40] 111. ~curious(X0) | ~curious(X0) [cnf transformation 49] 131. ~kind(X0) | ~funny(X0) | patient(X0) [cnf transformation 58] 139. ~patient(X0) | strong(X0) [cnf transformation 64] 153. kind(alice) [cnf transformation 21] 158. ~strong(alice) [cnf transformation 24] 160. ~curious(X0) [duplicate literal removal 111] 218. 12 <=> funny(alice) [avatar definition] 219. funny(alice) <- (12) [avatar component clause 218] 220. ~funny(alice) <- (~12) [avatar component clause 218] 383. ~funny(alice) | patient(alice) [resolution 131,153] 385. patient(alice) <- (12) [subsumption resolution 383,219] 401. strong(alice) <- (12) [resolution 385,139] 417. $false <- (12) [subsumption resolution 401,158] 418. ~12 [avatar contradiction clause 417] 425. curious(alice) <- (~12) [resolution 220,94] 426. $false <- (~12) [subsumption resolution 425,160] 427. 12 [avatar contradiction clause 426] 428. $false [avatar sat refutation 418,427] % SZS output end Proof for 9189583969832499308612483 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

If someone is quiet then fred is either creative or generous. Everyone who is not kind or not old is wise and vice versa. Everyone who is kind is funny or not rich. If paul is not funny or calm then paul is not generous or humble and vice versa. Everyone who is both happy and not curious is not happy or curious. Everyone who is not curious is both not generous and not humble. If someone is either patient or funny then someone is either brave or wise and vice versa. Everyone who is not creative is not patient. If someone is not old then someone is both not brave and not tall. Everyone who is both calm and not old is either brave or not tall. Everyone who is both not generous and not rich is either not creative or rich and vice versa. Everyone who is both not quiet and kind is creative or not generous. If someone is old or not tall then alice is both patient and calm and vice versa. Everyone who is either tall or calm is not tall or not rich and vice versa. Everyone who is humble or not funny is either not tall or not kind and vice versa. If someone is both creative and generous then someone is either calm or rich and vice versa. Fred is either not wise or wise. Someone is both curious and rich. Someone is not funny. Paul is brave. Paul is either kind or not funny. Fred is either happy or creative. John is either funny or tall. Alice is funny.

Fred is wise.

neutral

((?[X]:(quiet(X)))=>((creative(fred)<~>generous(fred))))& (![X]:((~kind(X)|~old(X))<=>wise(X)))& (![X]:(kind(X)=>(funny(X)|~rich(X))))& (((~funny(paul)|calm(paul)))<=>((~generous(paul)|humble(paul))))& (![X]:((happy(X)&~curious(X))=>(~happy(X)|curious(X))))& (![X]:(~curious(X)=>(~generous(X)&~humble(X))))& ((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))& (![X]:(~creative(X)=>~patient(X)))& ((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))& (![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))& (![X]:((~generous(X)&~rich(X))<=>(~creative(X)<~>rich(X))))& (![X]:((~quiet(X)&kind(X))=>(creative(X)|~generous(X))))& ((?[X]:((old(X)|~tall(X))))<=>((patient(alice)&calm(alice))))& (![X]:((tall(X)<~>calm(X))<=>(~tall(X)|~rich(X))))& (![X]:((humble(X)|~funny(X))<=>(~tall(X)<~>~kind(X))))& ((?[X]:((creative(X)&generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))& ((~wise(fred)<~>wise(fred)))& (?[X]:((curious(X)&rich(X))))& (?[X]:(~funny(X)))& (brave(paul))& ((kind(paul)<~>~funny(paul)))& ((happy(fred)<~>creative(fred)))& ((funny(john)<~>tall(john)))& (funny(alice))

wise(fred)

Everyone who is funny is either not wise or calm and vice versa. Everyone who is both happy and brave is either not brave or not curious and vice versa. If susan is either not generous or not rich then alice is both not kind and humble and vice versa. If someone is either creative or not patient then john is generous and vice versa. If someone is not quiet then paul is both quiet and not rich and vice versa. If someone is tall then someone is both not wise and generous and vice versa. If someone is either not wise or not humble then someone is wise. If someone is not wise then someone is not rich or humble and vice versa. Everyone who is patient is either brave or not patient and vice versa. If paul is funny then fred is strong and vice versa. Everyone who is either not humble or not rich is not strong or not humble and vice versa. Everyone who is rich or not old is both tall and old. Everyone who is both patient and calm is humble or not happy. If someone is not creative then susan is not rich or happy. Everyone who is either patient or not wise is rich. If someone is both not curious and not kind then someone is patient and vice versa. Someone is not kind. Someone is both not wise and not creative. John is either tall or generous. Someone is quiet or not kind. Paul is either wise or funny. Lucy is both not creative and not generous. Alice is not funny. Someone is not humble.

Alice is brave.

entailment

(![X]:(funny(X)<=>(~wise(X)<~>calm(X))))& (![X]:((happy(X)&brave(X))<=>(~brave(X)<~>~curious(X))))& (((~generous(susan)<~>~rich(susan)))<=>((~kind(alice)&humble(alice))))& ((?[X]:((creative(X)<~>~patient(X))))<=>(generous(john)))& ((?[X]:(~quiet(X)))<=>((quiet(paul)&~rich(paul))))& ((?[X]:(tall(X)))<=>(?[X]:((~wise(X)&generous(X)))))& ((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))& ((?[X]:(~wise(X)))<=>(?[X]:((~rich(X)|humble(X)))))& (![X]:(patient(X)<=>(brave(X)<~>~patient(X))))& ((funny(paul))<=>(strong(fred)))& (![X]:((~humble(X)<~>~rich(X))<=>(~strong(X)|~humble(X))))& (![X]:((rich(X)|~old(X))=>(tall(X)&old(X))))& (![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))& ((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))& (![X]:((patient(X)<~>~wise(X))=>rich(X)))& ((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))& (?[X]:(~kind(X)))& (?[X]:((~wise(X)&~creative(X))))& ((tall(john)<~>generous(john)))& (?[X]:((quiet(X)|~kind(X))))& ((wise(paul)<~>funny(paul)))& ((~creative(lucy)&~generous(lucy)))& (~funny(alice))& (?[X]:(~humble(X)))

brave(alice)

% SZS status Unsatisfiable for 5961892176560407980450497 % SZS output start Proof for 5961892176560407980450497 9. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~patient(X0))) [input p8] 25. ~brave(alice) [input hypothesis] 66. ! [X0] : ((patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 9] 117. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 66] 120. patient(X0) | brave(X0) | patient(X0) [cnf transformation 66] 149. ~brave(alice) [cnf transformation 25] 152. ~patient(X0) | brave(X0) [duplicate literal removal 117] 153. patient(X0) | brave(X0) [duplicate literal removal 120] 276. brave(X0) [subsumption resolution 152,153] 338. $false [subsumption resolution 149,276] % SZS output end Proof for 5961892176560407980450497 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

If someone is both creative and generous then someone is not kind or not creative. Everyone who is not old or not strong is both kind and old and vice versa. Everyone who is quiet or not curious is both brave and not wise. Everyone who is both happy and kind is calm and vice versa. Everyone who is not generous or calm is either not happy or not old and vice versa. Everyone who is both happy and not kind is both humble and not calm. Everyone who is quiet is not humble or humble. If someone is not generous or not patient then someone is happy or curious and vice versa. If alice is both not kind and not funny then fred is funny or strong and vice versa. If someone is either kind or not kind then someone is both not patient and generous. Everyone who is not funny is calm or not calm and vice versa. Everyone who is either not old or brave is either not happy or not humble. If fred is both not wise and not patient then someone is quiet. If john is either creative or not strong then susan is happy or not curious. Everyone who is either kind or calm is either patient or kind and vice versa. Everyone who is tall is not funny. Susan is either not brave or rich. Someone is both wise and not creative. Alice is both happy and not calm. Lucy is either not quiet or not generous. Alice is creative. Someone is not curious.

Alice is not generous.

contradiction

((?[X]:((creative(X)&generous(X))))=>(?[X]:((~kind(X)|~creative(X)))))& (![X]:((~old(X)|~strong(X))<=>(kind(X)&old(X))))& (![X]:((quiet(X)|~curious(X))=>(brave(X)&~wise(X))))& (![X]:((happy(X)&kind(X))<=>calm(X)))& (![X]:((~generous(X)|calm(X))<=>(~happy(X)<~>~old(X))))& (![X]:((happy(X)&~kind(X))=>(humble(X)&~calm(X))))& (![X]:(quiet(X)=>(~humble(X)|humble(X))))& ((?[X]:((~generous(X)|~patient(X))))<=>(?[X]:((happy(X)|curious(X)))))& (((~kind(alice)&~funny(alice)))<=>((funny(fred)|strong(fred))))& ((?[X]:((kind(X)<~>~kind(X))))=>(?[X]:((~patient(X)&generous(X)))))& (![X]:(~funny(X)<=>(calm(X)|~calm(X))))& (![X]:((~old(X)<~>brave(X))=>(~happy(X)<~>~humble(X))))& (((~wise(fred)&~patient(fred)))=>(?[X]:(quiet(X))))& (((creative(john)<~>~strong(john)))=>((happy(susan)|~curious(susan))))& (![X]:((kind(X)<~>calm(X))<=>(patient(X)<~>kind(X))))& (![X]:(tall(X)=>~funny(X)))& ((~brave(susan)<~>rich(susan)))& (?[X]:((wise(X)&~creative(X))))& ((happy(alice)&~calm(alice)))& ((~quiet(lucy)<~>~generous(lucy)))& (creative(alice))& (?[X]:(~curious(X)))

~generous(alice)

% SZS status Unsatisfiable for 4386282711082501853716136 % SZS output start Proof for 4386282711082501853716136 2. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (old(X0) & kind(X0))) [input p1] 5. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~happy(X0) <~> ~old(X0))) [input p4] 19. ~calm(alice) & happy(alice) [input p18] 23. ~generous(alice) [input hypothesis] 43. ! [X0] : (((~strong(X0) | ~old(X0)) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | (strong(X0) & old(X0)))) [nnf transformation 2] 44. ! [X0] : ((~strong(X0) | ~old(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | (strong(X0) & old(X0)))) [flattening 43] 47. ! [X0] : (((calm(X0) | ~generous(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) & (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (~calm(X0) & generous(X0)))) [nnf transformation 5] 48. ! [X0] : ((calm(X0) | ~generous(X0) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) & (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (~calm(X0) & generous(X0)))) [flattening 47] 76. old(X0) | old(X0) [cnf transformation 44] 86. ~old(X0) | ~happy(X0) | generous(X0) [cnf transformation 48] 130. happy(alice) [cnf transformation 19] 136. ~generous(alice) [cnf transformation 23] 145. old(X0) [duplicate literal removal 76] 163. ~happy(X0) | generous(X0) [subsumption resolution 86,145] 302. generous(alice) [resolution 163,130] 305. $false [subsumption resolution 302,136] % SZS output end Proof for 4386282711082501853716136 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

If someone is either old or not brave then someone is both tall and rich and vice versa. If someone is either wise or not strong then paul is both happy and not curious. If someone is happy then someone is patient or happy. If someone is both old and creative then someone is both kind and not generous and vice versa. If someone is either not humble or curious then susan is rich. If mary is not calm then someone is not happy and vice versa. If mary is both funny and happy then lucy is both old and wise and vice versa. If fred is both not creative and not funny then someone is both curious and not kind. Everyone who is either not wise or funny is happy or rich and vice versa. If john is creative or not funny then someone is both not tall and funny. Everyone who is not curious or not kind is rich or happy and vice versa. Everyone who is either not old or not kind is either calm or not patient and vice versa. Everyone who is not generous or not humble is rich. If lucy is either not tall or wise then lucy is either not rich or quiet. Everyone who is curious is not curious or creative and vice versa. If alice is either not strong or curious then someone is either kind or wise. Lucy is either not curious or kind. Mary is not brave. Alice is both tall and not brave. Susan is either not quiet or not happy. Someone is either not kind or old. Paul is kind. Lucy is strong.

Lucy is not funny.

contradiction

((?[X]:((old(X)<~>~brave(X))))<=>(?[X]:((tall(X)&rich(X)))))& ((?[X]:((wise(X)<~>~strong(X))))=>((happy(paul)&~curious(paul))))& ((?[X]:(happy(X)))=>(?[X]:((patient(X)|happy(X)))))& ((?[X]:((old(X)&creative(X))))<=>(?[X]:((kind(X)&~generous(X)))))& ((?[X]:((~humble(X)<~>curious(X))))=>(rich(susan)))& ((~calm(mary))<=>(?[X]:(~happy(X))))& (((funny(mary)&happy(mary)))<=>((old(lucy)&wise(lucy))))& (((~creative(fred)&~funny(fred)))=>(?[X]:((curious(X)&~kind(X)))))& (![X]:((~wise(X)<~>funny(X))<=>(happy(X)|rich(X))))& (((creative(john)|~funny(john)))=>(?[X]:((~tall(X)&funny(X)))))& (![X]:((~curious(X)|~kind(X))<=>(rich(X)|happy(X))))& (![X]:((~old(X)<~>~kind(X))<=>(calm(X)<~>~patient(X))))& (![X]:((~generous(X)|~humble(X))=>rich(X)))& (((~tall(lucy)<~>wise(lucy)))=>((~rich(lucy)<~>quiet(lucy))))& (![X]:(curious(X)<=>(~curious(X)|creative(X))))& (((~strong(alice)<~>curious(alice)))=>(?[X]:((kind(X)<~>wise(X)))))& ((~curious(lucy)<~>kind(lucy)))& (~brave(mary))& ((tall(alice)&~brave(alice)))& ((~quiet(susan)<~>~happy(susan)))& (?[X]:((~kind(X)<~>old(X))))& (kind(paul))& (strong(lucy))

~funny(lucy)

% SZS status Unsatisfiable for 1012832541534290596709467 % SZS output start Proof for 1012832541534290596709467 2. ? [X0] : (wise(X0) <~> ~strong(X0)) => (~curious(paul) & happy(paul)) [input p1] 9. ! [X0] : ((~wise(X0) <~> funny(X0)) <=> (rich(X0) | happy(X0))) [input p8] 11. ! [X0] : ((~kind(X0) | ~curious(X0)) <=> (happy(X0) | rich(X0))) [input p10] 15. ! [X0] : (curious(X0) <=> (creative(X0) | ~curious(X0))) [input p14] 17. ~curious(lucy) <~> kind(lucy) [input p16] 22. kind(paul) [input p21] 23. strong(lucy) [input p22] 24. ~funny(lucy) [input hypothesis] 28. (~curious(paul) & happy(paul)) | ! [X0] : (wise(X0) <=> ~strong(X0)) [ennf transformation 2] 42. (~curious(paul) & happy(paul)) | ! [X0] : ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))) [nnf transformation 28] 60. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [nnf transformation 9] 61. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [flattening 60] 64. ! [X0] : (((~kind(X0) | ~curious(X0)) | (~happy(X0) & ~rich(X0))) & ((happy(X0) | rich(X0)) | (kind(X0) & curious(X0)))) [nnf transformation 11] 65. ! [X0] : ((~kind(X0) | ~curious(X0) | (~happy(X0) & ~rich(X0))) & (happy(X0) | rich(X0) | (kind(X0) & curious(X0)))) [flattening 64] 68. ! [X0] : ((curious(X0) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | ~curious(X0))) [nnf transformation 15] 69. ! [X0] : ((curious(X0) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ~curious(X0))) [flattening 68] 73. (~kind(lucy) | curious(lucy)) & (kind(lucy) | ~curious(lucy)) [nnf transformation 17] 84. happy(paul) | ~strong(X0) | ~wise(X0) [cnf transformation 42] 103. funny(X0) | happy(X0) | rich(X0) | wise(X0) [cnf transformation 61] 115. ~kind(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 65] 116. ~kind(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 65] 132. curious(X0) | curious(X0) [cnf transformation 69] 138. kind(lucy) | ~curious(lucy) [cnf transformation 73] 147. kind(paul) [cnf transformation 22] 148. strong(lucy) [cnf transformation 23] 149. ~funny(lucy) [cnf transformation 24] 151. curious(X0) [duplicate literal removal 132] 192. 10 <=> ! [X0] : (~strong(X0) | ~wise(X0)) [avatar definition] 193. ~strong(X0) | ~wise(X0) <- (10) [avatar component clause 192] 196. 11 <=> happy(paul) [avatar definition] 200. 10 | 11 [avatar split clause 84,196,192] 269. 28 <=> wise(lucy) [avatar definition] 327. 40 <=> rich(lucy) [avatar definition] 355. kind(lucy) [subsumption resolution 138,151] 384. ~wise(lucy) <- (10) [resolution 193,148] 424. ~curious(lucy) | ~rich(lucy) [resolution 115,355] 427. ~curious(paul) | ~happy(paul) [resolution 116,147] 428. ~curious(lucy) | ~happy(lucy) [resolution 116,355] 430. happy(lucy) | rich(lucy) | wise(lucy) [resolution 103,149] 441. ~happy(lucy) [subsumption resolution 428,151] 444. ~happy(paul) [subsumption resolution 427,151] 445. ~11 [avatar split clause 444,196] 467. ~28 | ~10 [avatar split clause 384,192,269] 470. rich(lucy) | wise(lucy) [subsumption resolution 430,441] 471. 28 | 40 [avatar split clause 470,327,269] 472. ~rich(lucy) [subsumption resolution 424,151] 473. ~40 [avatar split clause 472,327] 474. $false [avatar sat refutation 200,445,467,471,473] % SZS output end Proof for 1012832541534290596709467 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

If someone is curious then someone is not curious and vice versa. If someone is either not patient or not brave then someone is either not funny or old and vice versa. Everyone who is both not calm and humble is calm or not brave and vice versa. If someone is either old or tall then someone is both not creative and brave. Everyone who is wise or tall is both not generous and not humble. If lucy is not generous then someone is both humble and rich and vice versa. Everyone who is not humble is not strong. Everyone who is not humble or not tall is not brave or not happy. If someone is strong or not funny then someone is patient. Everyone who is both old and generous is both generous and kind and vice versa. Everyone who is either patient or not rich is not generous. Everyone who is strong or generous is not curious and vice versa. Everyone who is both strong and not wise is either not brave or not curious. Everyone who is either creative or humble is curious and vice versa. If john is old or kind then someone is calm and vice versa. Everyone who is both not happy and not strong is not rich. Someone is not generous or calm. Susan is not creative or not wise. Alice is either brave or not wise. Susan is either brave or not funny. Fred is happy. Someone is either not generous or old. Susan is either not curious or kind.

John is kind.

contradiction

((?[X]:(curious(X)))<=>(?[X]:(~curious(X))))& ((?[X]:((~patient(X)<~>~brave(X))))<=>(?[X]:((~funny(X)<~>old(X)))))& (![X]:((~calm(X)&humble(X))<=>(calm(X)|~brave(X))))& ((?[X]:((old(X)<~>tall(X))))=>(?[X]:((~creative(X)&brave(X)))))& (![X]:((wise(X)|tall(X))=>(~generous(X)&~humble(X))))& ((~generous(lucy))<=>(?[X]:((humble(X)&rich(X)))))& (![X]:(~humble(X)=>~strong(X)))& (![X]:((~humble(X)|~tall(X))=>(~brave(X)|~happy(X))))& ((?[X]:((strong(X)|~funny(X))))=>(?[X]:(patient(X))))& (![X]:((old(X)&generous(X))<=>(generous(X)&kind(X))))& (![X]:((patient(X)<~>~rich(X))=>~generous(X)))& (![X]:((strong(X)|generous(X))<=>~curious(X)))& (![X]:((strong(X)&~wise(X))=>(~brave(X)<~>~curious(X))))& (![X]:((creative(X)<~>humble(X))<=>curious(X)))& (((old(john)|kind(john)))<=>(?[X]:(calm(X))))& (![X]:((~happy(X)&~strong(X))=>~rich(X)))& (?[X]:((~generous(X)|calm(X))))& ((~creative(susan)|~wise(susan)))& ((brave(alice)<~>~wise(alice)))& ((brave(susan)<~>~funny(susan)))& (happy(fred))& (?[X]:((~generous(X)<~>old(X))))& ((~curious(susan)<~>kind(susan)))

kind(john)

% SZS status Unsatisfiable for 2238777355607420785563599 % SZS output start Proof for 2238777355607420785563599 3. ! [X0] : ((humble(X0) & ~calm(X0)) <=> (~brave(X0) | calm(X0))) [input p2] 15. (kind(john) | old(john)) <=> ? [X0] : calm(X0) [input p14] 24. kind(john) [input hypothesis] 50. ! [X0] : (((humble(X0) & ~calm(X0)) | (brave(X0) & ~calm(X0))) & ((~brave(X0) | calm(X0)) | (~humble(X0) | calm(X0)))) [nnf transformation 3] 51. ! [X0] : (((humble(X0) & ~calm(X0)) | (brave(X0) & ~calm(X0))) & (~brave(X0) | calm(X0) | ~humble(X0) | calm(X0))) [flattening 50] 70. ((kind(john) | old(john)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (~kind(john) & ~old(john))) [nnf transformation 15] 71. (kind(john) | old(john) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (~kind(john) & ~old(john))) [flattening 70] 72. (kind(john) | old(john) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | (~kind(john) & ~old(john))) [rectify 71] 73. ? [X1] : calm(X1) => calm(sK7) [choice axiom] 74. (kind(john) | old(john) | ! [X0] : ~calm(X0)) & (calm(sK7) | (~kind(john) & ~old(john))) [skolemisation 72,73] 94. ~calm(X0) | ~calm(X0) [cnf transformation 51] 130. calm(sK7) | ~kind(john) [cnf transformation 74] 144. kind(john) [cnf transformation 24] 146. ~calm(X0) [duplicate literal removal 94] 250. ~kind(john) [subsumption resolution 130,146] 302. $false [subsumption resolution 144,250] % SZS output end Proof for 2238777355607420785563599 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Everyone who is strong is either not humble or not quiet. Everyone who is both quiet and not humble is kind and vice versa. Everyone who is either not funny or not creative is both not generous and tall and vice versa. If mary is curious then someone is quiet and vice versa. Everyone who is not rich is not humble and vice versa. If john is patient then lucy is either brave or not rich. Everyone who is both patient and wise is patient or not patient and vice versa. Everyone who is curious or happy is wise and vice versa. Everyone who is both not funny and humble is brave or curious and vice versa. Everyone who is funny is either not wise or not strong and vice versa. If paul is strong then someone is not wise or wise. If fred is not funny then susan is both not wise and curious and vice versa. Everyone who is wise is not old. Everyone who is either brave or patient is either old or not kind. If alice is either curious or brave then someone is both not curious and generous and vice versa. Everyone who is quiet is either brave or not patient. Someone is not happy or not wise. Someone is not funny or brave. Someone is either curious or rich. Lucy is happy. Someone is both tall and brave. John is not funny. Someone is not calm or curious.

Susan is not generous.

neutral

(![X]:(strong(X)=>(~humble(X)<~>~quiet(X))))& (![X]:((quiet(X)&~humble(X))<=>kind(X)))& (![X]:((~funny(X)<~>~creative(X))<=>(~generous(X)&tall(X))))& ((curious(mary))<=>(?[X]:(quiet(X))))& (![X]:(~rich(X)<=>~humble(X)))& ((patient(john))=>((brave(lucy)<~>~rich(lucy))))& (![X]:((patient(X)&wise(X))<=>(patient(X)|~patient(X))))& (![X]:((curious(X)|happy(X))<=>wise(X)))& (![X]:((~funny(X)&humble(X))<=>(brave(X)|curious(X))))& (![X]:(funny(X)<=>(~wise(X)<~>~strong(X))))& ((strong(paul))=>(?[X]:((~wise(X)|wise(X)))))& ((~funny(fred))<=>((~wise(susan)&curious(susan))))& (![X]:(wise(X)=>~old(X)))& (![X]:((brave(X)<~>patient(X))=>(old(X)<~>~kind(X))))& (((curious(alice)<~>brave(alice)))<=>(?[X]:((~curious(X)&generous(X)))))& (![X]:(quiet(X)=>(brave(X)<~>~patient(X))))& (?[X]:((~happy(X)|~wise(X))))& (?[X]:((~funny(X)|brave(X))))& (?[X]:((curious(X)<~>rich(X))))& (happy(lucy))& (?[X]:((tall(X)&brave(X))))& (~funny(john))& (?[X]:((~calm(X)|curious(X))))

~generous(susan)

Everyone who is happy or brave is tall or not creative and vice versa. Everyone who is either not patient or funny is tall or generous. If someone is either not creative or not quiet then someone is both generous and not brave. If paul is either calm or tall then someone is not happy or old. Everyone who is either curious or humble is both not calm and not funny and vice versa. Everyone who is either not kind or not humble is not happy or not patient. Everyone who is both calm and not calm is creative or not happy and vice versa. Everyone who is both not creative and brave is both not strong and not quiet. Everyone who is either not quiet or generous is old. If someone is either old or generous then someone is either not calm or wise. Everyone who is both not patient and strong is not humble or curious and vice versa. If susan is creative or not curious then someone is happy or curious. Everyone who is not happy is either not old or happy. Everyone who is not curious or not kind is either not kind or generous and vice versa. Everyone who is either not funny or not tall is not kind or not quiet. Everyone who is not patient is either not creative or strong. Alice is both patient and not brave. Someone is not old. Alice is not calm. Paul is not humble or not generous. John is either quiet or wise.

John is not calm.

entailment

(![X]:((happy(X)|brave(X))<=>(tall(X)|~creative(X))))& (![X]:((~patient(X)<~>funny(X))=>(tall(X)|generous(X))))& ((?[X]:((~creative(X)<~>~quiet(X))))=>(?[X]:((generous(X)&~brave(X)))))& (((calm(paul)<~>tall(paul)))=>(?[X]:((~happy(X)|old(X)))))& (![X]:((curious(X)<~>humble(X))<=>(~calm(X)&~funny(X))))& (![X]:((~kind(X)<~>~humble(X))=>(~happy(X)|~patient(X))))& (![X]:((calm(X)&~calm(X))<=>(creative(X)|~happy(X))))& (![X]:((~creative(X)&brave(X))=>(~strong(X)&~quiet(X))))& (![X]:((~quiet(X)<~>generous(X))=>old(X)))& ((?[X]:((old(X)<~>generous(X))))=>(?[X]:((~calm(X)<~>wise(X)))))& (![X]:((~patient(X)&strong(X))<=>(~humble(X)|curious(X))))& (((creative(susan)|~curious(susan)))=>(?[X]:((happy(X)|curious(X)))))& (![X]:(~happy(X)=>(~old(X)<~>happy(X))))& (![X]:((~curious(X)|~kind(X))<=>(~kind(X)<~>generous(X))))& (![X]:((~funny(X)<~>~tall(X))=>(~kind(X)|~quiet(X))))& (![X]:(~patient(X)=>(~creative(X)<~>strong(X))))& ((patient(alice)&~brave(alice)))& (?[X]:(~old(X)))& (~calm(alice))& ((~humble(paul)|~generous(paul)))& ((quiet(john)<~>wise(john)))

~calm(john)

% SZS status Unsatisfiable for 7875960783566261374589635 % SZS output start Proof for 7875960783566261374589635 5. ! [X0] : ((curious(X0) <~> humble(X0)) <=> (~funny(X0) & ~calm(X0))) [input p4] 7. ! [X0] : ((~calm(X0) & calm(X0)) <=> (~happy(X0) | creative(X0))) [input p6] 11. ! [X0] : ((strong(X0) & ~patient(X0)) <=> (curious(X0) | ~humble(X0))) [input p10] 16. ! [X0] : (~patient(X0) => (~creative(X0) <~> strong(X0))) [input p15] 22. calm(john) [input hypothesis] 39. ! [X0] : ((~creative(X0) <~> strong(X0)) | patient(X0)) [ennf transformation 16] 50. ! [X0] : ((((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | (funny(X0) | calm(X0))) & ((~funny(X0) & ~calm(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0))))) [nnf transformation 5] 51. ! [X0] : ((((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | funny(X0) | calm(X0)) & ((~funny(X0) & ~calm(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0))))) [flattening 50] 53. ! [X0] : (((~calm(X0) & calm(X0)) | (happy(X0) & ~creative(X0))) & ((~happy(X0) | creative(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 7] 54. ! [X0] : (((~calm(X0) & calm(X0)) | (happy(X0) & ~creative(X0))) & (~happy(X0) | creative(X0) | calm(X0) | ~calm(X0))) [flattening 53] 60. ! [X0] : (((strong(X0) & ~patient(X0)) | (~curious(X0) & humble(X0))) & ((curious(X0) | ~humble(X0)) | (~strong(X0) | patient(X0)))) [nnf transformation 11] 61. ! [X0] : (((strong(X0) & ~patient(X0)) | (~curious(X0) & humble(X0))) & (curious(X0) | ~humble(X0) | ~strong(X0) | patient(X0))) [flattening 60] 68. ! [X0] : (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | patient(X0)) [nnf transformation 39] 85. ~humble(X0) | curious(X0) | ~calm(X0) [cnf transformation 51] 93. calm(X0) | ~creative(X0) [cnf transformation 54] 95. ~calm(X0) | ~creative(X0) [cnf transformation 54] 106. ~patient(X0) | humble(X0) [cnf transformation 61] 107. ~curious(X0) | ~patient(X0) [cnf transformation 61] 108. strong(X0) | humble(X0) [cnf transformation 61] 109. ~curious(X0) | strong(X0) [cnf transformation 61] 123. ~strong(X0) | creative(X0) | patient(X0) [cnf transformation 68] 131. calm(john) [cnf transformation 22] 172. ~creative(X0) [subsumption resolution 93,95] 193. ~strong(X0) | patient(X0) [subsumption resolution 123,172] 221. patient(X0) | humble(X0) [resolution 193,108] 222. humble(X0) [subsumption resolution 221,106] 229. ~calm(X0) | curious(X0) [resolution 85,222] 230. curious(john) [resolution 229,131] 233. strong(john) [resolution 230,109] 234. ~patient(john) [resolution 230,107] 405. patient(john) [resolution 233,193] 407. $false [subsumption resolution 405,234] % SZS output end Proof for 7875960783566261374589635 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Everyone who is not humble or not brave is not wise or patient and vice versa. Everyone who is tall is both rich and creative. Everyone who is not rich or creative is both curious and not calm. If paul is brave then someone is happy or not generous. If someone is not tall then someone is either quiet or not calm. If paul is either curious or not brave then lucy is either rich or not quiet and vice versa. If someone is not calm or generous then paul is both not strong and funny. If mary is either not brave or not curious then paul is not brave or not rich. Everyone who is happy or not rich is both not humble and generous and vice versa. Everyone who is not happy is both not wise and patient and vice versa. If fred is happy then alice is both quiet and kind. Everyone who is either not patient or not curious is either rich or not curious and vice versa. If fred is old then someone is not patient. If someone is not rich or not generous then john is either not happy or happy. If fred is not old or tall then fred is both wise and not quiet. Everyone who is both patient and kind is either brave or strong and vice versa. Someone is humble or kind. Mary is either not rich or not quiet. Someone is not creative. Someone is curious or not rich. Someone is calm. John is either humble or curious. Paul is both not strong and not rich. John is either happy or not generous.

Fred is humble.

contradiction

(![X]:((~humble(X)|~brave(X))<=>(~wise(X)|patient(X))))& (![X]:(tall(X)=>(rich(X)&creative(X))))& (![X]:((~rich(X)|creative(X))=>(curious(X)&~calm(X))))& ((brave(paul))=>(?[X]:((happy(X)|~generous(X)))))& ((?[X]:(~tall(X)))=>(?[X]:((quiet(X)<~>~calm(X)))))& (((curious(paul)<~>~brave(paul)))<=>((rich(lucy)<~>~quiet(lucy))))& ((?[X]:((~calm(X)|generous(X))))=>((~strong(paul)&funny(paul))))& (((~brave(mary)<~>~curious(mary)))=>((~brave(paul)|~rich(paul))))& (![X]:((happy(X)|~rich(X))<=>(~humble(X)&generous(X))))& (![X]:(~happy(X)<=>(~wise(X)&patient(X))))& ((happy(fred))=>((quiet(alice)&kind(alice))))& (![X]:((~patient(X)<~>~curious(X))<=>(rich(X)<~>~curious(X))))& ((old(fred))=>(?[X]:(~patient(X))))& ((?[X]:((~rich(X)|~generous(X))))=>((~happy(john)<~>happy(john))))& (((~old(fred)|tall(fred)))=>((wise(fred)&~quiet(fred))))& (![X]:((patient(X)&kind(X))<=>(brave(X)<~>strong(X))))& (?[X]:((humble(X)|kind(X))))& ((~rich(mary)<~>~quiet(mary)))& (?[X]:(~creative(X)))& (?[X]:((curious(X)|~rich(X))))& (?[X]:(calm(X)))& ((humble(john)<~>curious(john)))& ((~strong(paul)&~rich(paul)))& ((happy(john)<~>~generous(john)))

humble(fred)

% SZS status Unsatisfiable for 19143516303203230976535 % SZS output start Proof for 19143516303203230976535 3. ! [X0] : ((creative(X0) | ~rich(X0)) => (~calm(X0) & curious(X0))) [input p2] 9. ! [X0] : ((~rich(X0) | happy(X0)) <=> (generous(X0) & ~humble(X0))) [input p8] 10. ! [X0] : (~happy(X0) <=> (patient(X0) & ~wise(X0))) [input p9] 12. ! [X0] : ((~patient(X0) <~> ~curious(X0)) <=> (rich(X0) <~> ~curious(X0))) [input p11] 25. humble(fred) [input hypothesis] 29. ! [X0] : ((~calm(X0) & curious(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 3] 49. ! [X0] : (((~rich(X0) | happy(X0)) | (~generous(X0) | humble(X0))) & ((generous(X0) & ~humble(X0)) | (rich(X0) & ~happy(X0)))) [nnf transformation 9] 50. ! [X0] : ((~rich(X0) | happy(X0) | ~generous(X0) | humble(X0)) & ((generous(X0) & ~humble(X0)) | (rich(X0) & ~happy(X0)))) [flattening 49] 51. ! [X0] : ((~happy(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | happy(X0))) [nnf transformation 10] 52. ! [X0] : ((~happy(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | happy(X0))) [flattening 51] 53. ! [X0] : ((((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0))))) [nnf transformation 12] 76. curious(X0) | rich(X0) [cnf transformation 29] 95. ~happy(X0) | ~humble(X0) [cnf transformation 50] 96. ~humble(X0) | rich(X0) [cnf transformation 50] 101. happy(X0) | patient(X0) [cnf transformation 52] 108. curious(X0) | ~rich(X0) | ~patient(X0) | curious(X0) [cnf transformation 53] 109. ~curious(X0) | ~patient(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 53] 140. humble(fred) [cnf transformation 25] 142. curious(X0) | ~rich(X0) | ~patient(X0) [duplicate literal removal 108] 143. ~curious(X0) | ~patient(X0) | ~rich(X0) [duplicate literal removal 109] 218. 16 <=> happy(fred) [avatar definition] 219. happy(fred) <- (16) [avatar component clause 218] 220. ~happy(fred) <- (~16) [avatar component clause 218] 231. ~patient(X0) | curious(X0) [subsumption resolution 142,76] 305. rich(fred) [resolution 96,140] 309. patient(fred) <- (~16) [resolution 101,220] 312. curious(fred) <- (~16) [resolution 309,231] 348. ~patient(fred) | ~rich(fred) <- (~16) [resolution 143,312] 351. ~rich(fred) <- (~16) [subsumption resolution 348,309] 352. $false <- (~16) [subsumption resolution 351,305] 353. 16 [avatar contradiction clause 352] 377. ~humble(fred) <- (16) [resolution 219,95] 380. $false <- (16) [subsumption resolution 377,140] 381. ~16 [avatar contradiction clause 380] 382. $false [avatar sat refutation 353,381] % SZS output end Proof for 19143516303203230976535 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Everyone who is calm or not old is kind or brave. Everyone who is both not strong and brave is either not creative or not patient and vice versa. If someone is creative or curious then alice is both quiet and not strong and vice versa. Everyone who is both not calm and happy is old or not patient and vice versa. Everyone who is either humble or not quiet is patient and vice versa. If someone is tall then someone is not rich or rich and vice versa. If mary is either old or curious then someone is kind or not old. If someone is both not strong and creative then mary is not patient or not humble. Everyone who is funny is both creative and strong. If someone is both not quiet and not generous then someone is not generous and vice versa. Everyone who is both happy and quiet is wise or funny and vice versa. If susan is calm then alice is not tall or tall and vice versa. Everyone who is both tall and rich is brave. Everyone who is either kind or not funny is either not wise or wise. Everyone who is not brave is humble and vice versa. If fred is humble or curious then paul is either not patient or not old. Someone is both not kind and not curious. Someone is not quiet. Someone is wise or happy. Someone is both tall and brave. Someone is calm. Susan is both not curious and not kind. Lucy is either happy or not quiet.

Lucy is patient.

neutral

(![X]:((calm(X)|~old(X))=>(kind(X)|brave(X))))& (![X]:((~strong(X)&brave(X))<=>(~creative(X)<~>~patient(X))))& ((?[X]:((creative(X)|curious(X))))<=>((quiet(alice)&~strong(alice))))& (![X]:((~calm(X)&happy(X))<=>(old(X)|~patient(X))))& (![X]:((humble(X)<~>~quiet(X))<=>patient(X)))& ((?[X]:(tall(X)))<=>(?[X]:((~rich(X)|rich(X)))))& (((old(mary)<~>curious(mary)))=>(?[X]:((kind(X)|~old(X)))))& ((?[X]:((~strong(X)&creative(X))))=>((~patient(mary)|~humble(mary))))& (![X]:(funny(X)=>(creative(X)&strong(X))))& ((?[X]:((~quiet(X)&~generous(X))))<=>(?[X]:(~generous(X))))& (![X]:((happy(X)&quiet(X))<=>(wise(X)|funny(X))))& ((calm(susan))<=>((~tall(alice)|tall(alice))))& (![X]:((tall(X)&rich(X))=>brave(X)))& (![X]:((kind(X)<~>~funny(X))=>(~wise(X)<~>wise(X))))& (![X]:(~brave(X)<=>humble(X)))& (((humble(fred)|curious(fred)))=>((~patient(paul)<~>~old(paul))))& (?[X]:((~kind(X)&~curious(X))))& (?[X]:(~quiet(X)))& (?[X]:((wise(X)|happy(X))))& (?[X]:((tall(X)&brave(X))))& (?[X]:(calm(X)))& ((~curious(susan)&~kind(susan)))& ((happy(lucy)<~>~quiet(lucy)))

patient(lucy)

Everyone who is not patient is either creative or not curious. Everyone who is both not happy and not patient is either quiet or happy. Everyone who is not creative is both not generous and not wise and vice versa. If someone is both not curious and funny then lucy is not quiet and vice versa. Everyone who is curious is generous or not quiet and vice versa. If someone is both not brave and kind then someone is not brave or not quiet and vice versa. If john is quiet then mary is either kind or not quiet. Everyone who is brave or not funny is not funny or not kind. Everyone who is not humble or not kind is either not quiet or not kind. Everyone who is not kind is not funny or rich. If someone is either not wise or old then someone is calm. Everyone who is not strong is not creative or not patient. Everyone who is humble is either not happy or not humble. Everyone who is either rich or wise is not rich or quiet. If mary is not humble then someone is creative or not strong and vice versa. Everyone who is both strong and old is not strong or kind. Mary is either old or not generous. Lucy is either not humble or not wise. Paul is either not curious or strong. Paul is both happy and not generous. Someone is funny or not generous. Someone is not rich or not funny. Someone is funny or not kind. Someone is either not wise or rich.

Mary is not kind.

neutral

(![X]:(~patient(X)=>(creative(X)<~>~curious(X))))& (![X]:((~happy(X)&~patient(X))=>(quiet(X)<~>happy(X))))& (![X]:(~creative(X)<=>(~generous(X)&~wise(X))))& ((?[X]:((~curious(X)&funny(X))))<=>(~quiet(lucy)))& (![X]:(curious(X)<=>(generous(X)|~quiet(X))))& ((?[X]:((~brave(X)&kind(X))))<=>(?[X]:((~brave(X)|~quiet(X)))))& ((quiet(john))=>((kind(mary)<~>~quiet(mary))))& (![X]:((brave(X)|~funny(X))=>(~funny(X)|~kind(X))))& (![X]:((~humble(X)|~kind(X))=>(~quiet(X)<~>~kind(X))))& (![X]:(~kind(X)=>(~funny(X)|rich(X))))& ((?[X]:((~wise(X)<~>old(X))))=>(?[X]:(calm(X))))& (![X]:(~strong(X)=>(~creative(X)|~patient(X))))& (![X]:(humble(X)=>(~happy(X)<~>~humble(X))))& (![X]:((rich(X)<~>wise(X))=>(~rich(X)|quiet(X))))& ((~humble(mary))<=>(?[X]:((creative(X)|~strong(X)))))& (![X]:((strong(X)&old(X))=>(~strong(X)|kind(X))))& ((old(mary)<~>~generous(mary)))& ((~humble(lucy)<~>~wise(lucy)))& ((~curious(paul)<~>strong(paul)))& ((happy(paul)&~generous(paul)))& (?[X]:((funny(X)|~generous(X))))& (?[X]:((~rich(X)|~funny(X))))& (?[X]:((funny(X)|~kind(X))))& (?[X]:((~wise(X)<~>rich(X))))

~kind(mary)

Everyone who is not humble is humble or happy. Everyone who is both creative and not kind is both strong and not calm and vice versa. Everyone who is strong is patient or calm. If susan is both not old and not rich then mary is both not wise and not happy and vice versa. If someone is not happy or not humble then someone is calm or not humble and vice versa. Everyone who is not patient or calm is both wise and creative. Everyone who is not calm is both generous and not rich. Everyone who is both not brave and calm is both brave and not humble. If someone is both brave and not kind then john is wise or not tall. Everyone who is kind is rich and vice versa. If fred is either not happy or tall then someone is both funny and happy. Everyone who is calm or not old is calm and vice versa. If susan is both not brave and patient then john is not wise. Everyone who is either wise or not calm is not tall or not old. If someone is either patient or not strong then someone is either not funny or not brave and vice versa. Everyone who is calm or not rich is kind or not generous. Someone is kind or not humble. Someone is brave or not calm. Lucy is curious. Someone is both not tall and happy. Fred is calm. Someone is either happy or not patient. Susan is either not kind or quiet.

John is kind.

entailment

(![X]:(~humble(X)=>(humble(X)|happy(X))))& (![X]:((creative(X)&~kind(X))<=>(strong(X)&~calm(X))))& (![X]:(strong(X)=>(patient(X)|calm(X))))& (((~old(susan)&~rich(susan)))<=>((~wise(mary)&~happy(mary))))& ((?[X]:((~happy(X)|~humble(X))))<=>(?[X]:((calm(X)|~humble(X)))))& (![X]:((~patient(X)|calm(X))=>(wise(X)&creative(X))))& (![X]:(~calm(X)=>(generous(X)&~rich(X))))& (![X]:((~brave(X)&calm(X))=>(brave(X)&~humble(X))))& ((?[X]:((brave(X)&~kind(X))))=>((wise(john)|~tall(john))))& (![X]:(kind(X)<=>rich(X)))& (((~happy(fred)<~>tall(fred)))=>(?[X]:((funny(X)&happy(X)))))& (![X]:((calm(X)|~old(X))<=>calm(X)))& (((~brave(susan)&patient(susan)))=>(~wise(john)))& (![X]:((wise(X)<~>~calm(X))=>(~tall(X)|~old(X))))& ((?[X]:((patient(X)<~>~strong(X))))<=>(?[X]:((~funny(X)<~>~brave(X)))))& (![X]:((calm(X)|~rich(X))=>(kind(X)|~generous(X))))& (?[X]:((kind(X)|~humble(X))))& (?[X]:((brave(X)|~calm(X))))& (curious(lucy))& (?[X]:((~tall(X)&happy(X))))& (calm(fred))& (?[X]:((happy(X)<~>~patient(X))))& ((~kind(susan)<~>quiet(susan)))

kind(john)

% SZS status Unsatisfiable for 6920771965652146994595 % SZS output start Proof for 6920771965652146994595 2. ! [X0] : ((~kind(X0) & creative(X0)) <=> (~calm(X0) & strong(X0))) [input p1] 6. ! [X0] : ((calm(X0) | ~patient(X0)) => (creative(X0) & wise(X0))) [input p5] 7. ! [X0] : (~calm(X0) => (~rich(X0) & generous(X0))) [input p6] 10. ! [X0] : (kind(X0) <=> rich(X0)) [input p9] 16. ! [X0] : ((~rich(X0) | calm(X0)) => (~generous(X0) | kind(X0))) [input p15] 24. ~kind(john) [input hypothesis] 32. ! [X0] : ((creative(X0) & wise(X0)) | (~calm(X0) & patient(X0))) [ennf transformation 6] 33. ! [X0] : ((~rich(X0) & generous(X0)) | calm(X0)) [ennf transformation 7] 43. ! [X0] : ((~generous(X0) | kind(X0)) | (rich(X0) & ~calm(X0))) [ennf transformation 16] 44. ! [X0] : (~generous(X0) | kind(X0) | (rich(X0) & ~calm(X0))) [flattening 43] 45. ! [X0] : (((~kind(X0) & creative(X0)) | (calm(X0) | ~strong(X0))) & ((~calm(X0) & strong(X0)) | (kind(X0) | ~creative(X0)))) [nnf transformation 2] 46. ! [X0] : (((~kind(X0) & creative(X0)) | calm(X0) | ~strong(X0)) & ((~calm(X0) & strong(X0)) | kind(X0) | ~creative(X0))) [flattening 45] 54. ! [X0] : ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0))) [nnf transformation 10] 78. ~calm(X0) | kind(X0) | ~creative(X0) [cnf transformation 46] 93. ~calm(X0) | creative(X0) [cnf transformation 32] 94. generous(X0) | calm(X0) [cnf transformation 33] 95. ~rich(X0) | calm(X0) [cnf transformation 33] 99. ~kind(X0) | rich(X0) [cnf transformation 54] 120. ~generous(X0) | kind(X0) | rich(X0) [cnf transformation 44] 130. ~kind(john) [cnf transformation 24] 261. ~generous(X0) | rich(X0) [subsumption resolution 120,99] 308. rich(X0) | calm(X0) [resolution 261,94] 309. calm(X0) [subsumption resolution 308,95] 339. ~creative(X0) | kind(X0) [resolution 309,78] 341. creative(X2) [resolution 309,93] 366. kind(X0) [resolution 339,341] 369. $false [resolution 366,130] % SZS output end Proof for 6920771965652146994595 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

If someone is kind then lucy is not old and vice versa. If someone is both wise and kind then someone is both old and not rich and vice versa. Everyone who is both creative and not curious is not strong or wise. If lucy is either not humble or not tall then john is either not creative or not rich and vice versa. Everyone who is not wise or not funny is either generous or patient and vice versa. If someone is quiet or not calm then someone is either happy or not wise. Everyone who is either humble or not strong is not funny or quiet. If someone is either not tall or old then someone is not calm or not humble. Everyone who is not quiet or not generous is not creative or wise and vice versa. Everyone who is either generous or wise is either happy or strong. Everyone who is quiet or kind is generous. Everyone who is not wise or not calm is not quiet. Everyone who is either quiet or patient is quiet or tall. Everyone who is curious or happy is not happy or quiet. If lucy is not patient or wise then someone is both brave and generous and vice versa. If paul is either generous or not creative then someone is not curious and vice versa. Mary is not funny. Alice is not quiet. Fred is happy or curious. Someone is both creative and generous. Susan is rich. Someone is either patient or old. Someone is strong or not generous. Mary is not happy or strong.

Fred is curious.

entailment

((?[X]:(kind(X)))<=>(~old(lucy)))& ((?[X]:((wise(X)&kind(X))))<=>(?[X]:((old(X)&~rich(X)))))& (![X]:((creative(X)&~curious(X))=>(~strong(X)|wise(X))))& (((~humble(lucy)<~>~tall(lucy)))<=>((~creative(john)<~>~rich(john))))& (![X]:((~wise(X)|~funny(X))<=>(generous(X)<~>patient(X))))& ((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((happy(X)<~>~wise(X)))))& (![X]:((humble(X)<~>~strong(X))=>(~funny(X)|quiet(X))))& ((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((~calm(X)|~humble(X)))))& (![X]:((~quiet(X)|~generous(X))<=>(~creative(X)|wise(X))))& (![X]:((generous(X)<~>wise(X))=>(happy(X)<~>strong(X))))& (![X]:((quiet(X)|kind(X))=>generous(X)))& (![X]:((~wise(X)|~calm(X))=>~quiet(X)))& (![X]:((quiet(X)<~>patient(X))=>(quiet(X)|tall(X))))& (![X]:((curious(X)|happy(X))=>(~happy(X)|quiet(X))))& (((~patient(lucy)|wise(lucy)))<=>(?[X]:((brave(X)&generous(X)))))& (((generous(paul)<~>~creative(paul)))<=>(?[X]:(~curious(X))))& (~funny(mary))& (~quiet(alice))& ((happy(fred)|curious(fred)))& (?[X]:((creative(X)&generous(X))))& (rich(susan))& (?[X]:((patient(X)<~>old(X))))& (?[X]:((strong(X)|~generous(X))))& ((~happy(mary)|strong(mary)))

curious(fred)

% SZS status Unsatisfiable for 1483762946380957315318181 % SZS output start Proof for 1483762946380957315318181 9. ! [X0] : ((~generous(X0) | ~quiet(X0)) <=> (wise(X0) | ~creative(X0))) [input p8] 11. ! [X0] : ((kind(X0) | quiet(X0)) => generous(X0)) [input p10] 12. ! [X0] : ((~calm(X0) | ~wise(X0)) => ~quiet(X0)) [input p11] 14. ! [X0] : ((happy(X0) | curious(X0)) => (quiet(X0) | ~happy(X0))) [input p13] 19. curious(fred) | happy(fred) [input p18] 25. ~curious(fred) [input hypothesis] 36. ! [X0] : (generous(X0) | (~kind(X0) & ~quiet(X0))) [ennf transformation 11] 37. ! [X0] : (~quiet(X0) | (calm(X0) & wise(X0))) [ennf transformation 12] 40. ! [X0] : ((quiet(X0) | ~happy(X0)) | (~happy(X0) & ~curious(X0))) [ennf transformation 14] 41. ! [X0] : (quiet(X0) | ~happy(X0) | (~happy(X0) & ~curious(X0))) [flattening 40] 63. ! [X0] : (((~generous(X0) | ~quiet(X0)) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | (generous(X0) & quiet(X0)))) [nnf transformation 9] 64. ! [X0] : ((~generous(X0) | ~quiet(X0) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | (generous(X0) & quiet(X0)))) [flattening 63] 115. ~quiet(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 64] 120. ~quiet(X0) | generous(X0) [cnf transformation 36] 122. ~quiet(X0) | wise(X0) [cnf transformation 37] 127. quiet(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 41] 139. curious(fred) | happy(fred) [cnf transformation 19] 147. ~curious(fred) [cnf transformation 25] 148. ~happy(X0) | quiet(X0) [duplicate literal removal 127] 291. 31 <=> happy(fred) [avatar definition] 293. happy(fred) <- (31) [avatar component clause 291] 295. 32 <=> curious(fred) [avatar definition] 298. 31 | 32 [avatar split clause 139,295,291] 327. ~32 [avatar split clause 147,295] 329. quiet(fred) <- (31) [resolution 148,293] 331. wise(fred) <- (31) [resolution 329,122] 332. generous(fred) <- (31) [resolution 329,120] 362. ~generous(fred) | ~wise(fred) <- (31) [resolution 115,329] 363. ~wise(fred) <- (31) [subsumption resolution 362,332] 364. $false <- (31) [subsumption resolution 363,331] 365. ~31 [avatar contradiction clause 364] 366. $false [avatar sat refutation 298,327,365] % SZS output end Proof for 1483762946380957315318181 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Everyone who is generous or rich is both not wise and not calm. If someone is not happy or not generous then paul is either humble or not curious and vice versa. If alice is either funny or not patient then lucy is rich and vice versa. Everyone who is either creative or not curious is kind. If someone is either creative or calm then john is both patient and not funny and vice versa. Everyone who is not calm or not humble is not happy or generous and vice versa. Everyone who is both generous and not brave is not patient or not quiet and vice versa. Everyone who is not quiet is not curious or patient and vice versa. Everyone who is both not generous and brave is either not funny or not calm. If john is either not calm or strong then john is tall and vice versa. Everyone who is both wise and not rich is either not creative or rich. Everyone who is not wise is funny and vice versa. If someone is both not happy and not tall then someone is both not curious and wise. Everyone who is funny is not wise and vice versa. If someone is both not tall and quiet then someone is strong and vice versa. If someone is not brave or not funny then fred is not tall and vice versa. Mary is both not happy and funny. Lucy is either not tall or patient. Paul is either not humble or curious. Someone is happy or not quiet. Mary is rich. Someone is both curious and not wise. John is both tall and quiet.

Mary is creative.

contradiction

(![X]:((generous(X)|rich(X))=>(~wise(X)&~calm(X))))& ((?[X]:((~happy(X)|~generous(X))))<=>((humble(paul)<~>~curious(paul))))& (((funny(alice)<~>~patient(alice)))<=>(rich(lucy)))& (![X]:((creative(X)<~>~curious(X))=>kind(X)))& ((?[X]:((creative(X)<~>calm(X))))<=>((patient(john)&~funny(john))))& (![X]:((~calm(X)|~humble(X))<=>(~happy(X)|generous(X))))& (![X]:((generous(X)&~brave(X))<=>(~patient(X)|~quiet(X))))& (![X]:(~quiet(X)<=>(~curious(X)|patient(X))))& (![X]:((~generous(X)&brave(X))=>(~funny(X)<~>~calm(X))))& (((~calm(john)<~>strong(john)))<=>(tall(john)))& (![X]:((wise(X)&~rich(X))=>(~creative(X)<~>rich(X))))& (![X]:(~wise(X)<=>funny(X)))& ((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~curious(X)&wise(X)))))& (![X]:(funny(X)<=>~wise(X)))& ((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:(strong(X))))& ((?[X]:((~brave(X)|~funny(X))))<=>(~tall(fred)))& ((~happy(mary)&funny(mary)))& ((~tall(lucy)<~>patient(lucy)))& ((~humble(paul)<~>curious(paul)))& (?[X]:((happy(X)|~quiet(X))))& (rich(mary))& (?[X]:((curious(X)&~wise(X))))& ((tall(john)&quiet(john)))

creative(mary)

% SZS status Unsatisfiable for 299744695652001325923463 % SZS output start Proof for 299744695652001325923463 1. ! [X0] : ((rich(X0) | generous(X0)) => (~calm(X0) & ~wise(X0))) [input p0] 5. ? [X0] : (creative(X0) <~> calm(X0)) <=> (~funny(john) & patient(john)) [input p4] 8. ! [X0] : (~quiet(X0) <=> (patient(X0) | ~curious(X0))) [input p7] 21. rich(mary) [input p20] 23. quiet(john) & tall(john) [input p22] 24. creative(mary) [input hypothesis] 28. ! [X0] : ((~calm(X0) & ~wise(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 1] 39. (? [X0] : ((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (funny(john) | ~patient(john))) & ((~funny(john) & patient(john)) | ! [X0] : ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) [nnf transformation 5] 40. (? [X0] : ((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | funny(john) | ~patient(john)) & ((~funny(john) & patient(john)) | ! [X0] : ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) [flattening 39] 41. (? [X0] : ((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | funny(john) | ~patient(john)) & ((~funny(john) & patient(john)) | ! [X1] : ((creative(X1) | ~calm(X1)) & (calm(X1) | ~creative(X1)))) [rectify 40] 42. ? [X0] : ((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) => ((~calm(sK1) | ~creative(sK1)) & (calm(sK1) | creative(sK1))) [choice axiom] 43. (((~calm(sK1) | ~creative(sK1)) & (calm(sK1) | creative(sK1))) | funny(john) | ~patient(john)) & ((~funny(john) & patient(john)) | ! [X1] : ((creative(X1) | ~calm(X1)) & (calm(X1) | ~creative(X1)))) [skolemisation 41,42] 48. ! [X0] : ((~quiet(X0) | (~patient(X0) & curious(X0))) & ((patient(X0) | ~curious(X0)) | quiet(X0))) [nnf transformation 8] 49. ! [X0] : ((~quiet(X0) | (~patient(X0) & curious(X0))) & (patient(X0) | ~curious(X0) | quiet(X0))) [flattening 48] 76. ~calm(X0) | ~rich(X0) [cnf transformation 28] 87. patient(john) | calm(X1) | ~creative(X1) [cnf transformation 43] 104. ~quiet(X0) | ~patient(X0) [cnf transformation 49] 132. rich(mary) [cnf transformation 21] 136. quiet(john) [cnf transformation 23] 137. creative(mary) [cnf transformation 24] 184. 10 <=> patient(john) [avatar definition] 206. 15 <=> ! [X1] : (calm(X1) | ~creative(X1)) [avatar definition] 207. ~creative(X1) | calm(X1) <- (15) [avatar component clause 206] 210. 15 | 10 [avatar split clause 87,184,206] 311. ~patient(john) [resolution 104,136] 317. ~10 [avatar split clause 311,184] 341. calm(mary) <- (15) [resolution 207,137] 351. ~rich(mary) <- (15) [resolution 341,76] 353. $false <- (15) [subsumption resolution 351,132] 354. ~15 [avatar contradiction clause 353] 357. $false [avatar sat refutation 210,317,354] % SZS output end Proof for 299744695652001325923463 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

If lucy is not rich then someone is both quiet and generous and vice versa. If fred is either tall or not wise then alice is both old and not generous and vice versa. Everyone who is not patient is not creative. Everyone who is either not quiet or quiet is generous and vice versa. If someone is either not wise or happy then fred is not curious or old. If someone is not happy then someone is strong. Everyone who is either quiet or not happy is brave or not tall. Everyone who is not happy is either curious or not rich. If someone is both quiet and humble then susan is kind or funny. Everyone who is either funny or strong is either not old or not wise and vice versa. If fred is not curious then paul is both not wise and not quiet. If someone is both not kind and creative then someone is either not calm or not curious and vice versa. If alice is brave or not generous then alice is either not funny or not strong. If fred is both happy and strong then someone is both calm and not generous and vice versa. If someone is tall then susan is either brave or not tall. If mary is not calm or creative then someone is happy or quiet and vice versa. Paul is not creative or not calm. Someone is kind. Someone is not wise or not creative. Alice is both calm and kind. Paul is both not patient and wise. Someone is tall. Someone is not calm. Lucy is quiet or happy.

Fred is not curious.

contradiction

((~rich(lucy))<=>(?[X]:((quiet(X)&generous(X)))))& (((tall(fred)<~>~wise(fred)))<=>((old(alice)&~generous(alice))))& (![X]:(~patient(X)=>~creative(X)))& (![X]:((~quiet(X)<~>quiet(X))<=>generous(X)))& ((?[X]:((~wise(X)<~>happy(X))))=>((~curious(fred)|old(fred))))& ((?[X]:(~happy(X)))=>(?[X]:(strong(X))))& (![X]:((quiet(X)<~>~happy(X))=>(brave(X)|~tall(X))))& (![X]:(~happy(X)=>(curious(X)<~>~rich(X))))& ((?[X]:((quiet(X)&humble(X))))=>((kind(susan)|funny(susan))))& (![X]:((funny(X)<~>strong(X))<=>(~old(X)<~>~wise(X))))& ((~curious(fred))=>((~wise(paul)&~quiet(paul))))& ((?[X]:((~kind(X)&creative(X))))<=>(?[X]:((~calm(X)<~>~curious(X)))))& (((brave(alice)|~generous(alice)))=>((~funny(alice)<~>~strong(alice))))& (((happy(fred)&strong(fred)))<=>(?[X]:((calm(X)&~generous(X)))))& ((?[X]:(tall(X)))=>((brave(susan)<~>~tall(susan))))& (((~calm(mary)|creative(mary)))<=>(?[X]:((happy(X)|quiet(X)))))& ((~creative(paul)|~calm(paul)))& (?[X]:(kind(X)))& (?[X]:((~wise(X)|~creative(X))))& ((calm(alice)&kind(alice)))& ((~patient(paul)&wise(paul)))& (?[X]:(tall(X)))& (?[X]:(~calm(X)))& ((quiet(lucy)|happy(lucy)))

~curious(fred)

% SZS status Unsatisfiable for 9066198627986126663945854 % SZS output start Proof for 9066198627986126663945854 11. ~curious(fred) => (~quiet(paul) & ~wise(paul)) [input p10] 21. wise(paul) & ~patient(paul) [input p20] 25. ~curious(fred) [input hypothesis] 36. (~quiet(paul) & ~wise(paul)) | curious(fred) [ennf transformation 11] 107. ~wise(paul) | curious(fred) [cnf transformation 36] 135. wise(paul) [cnf transformation 21] 139. ~curious(fred) [cnf transformation 25] 187. 10 <=> curious(fred) [avatar definition] 213. 16 <=> wise(paul) [avatar definition] 216. 10 | ~16 [avatar split clause 107,213,187] 334. 16 [avatar split clause 135,213] 344. ~10 [avatar split clause 139,187] 345. $false [avatar sat refutation 216,334,344] % SZS output end Proof for 9066198627986126663945854 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Everyone who is quiet or curious is both brave and not patient. Everyone who is not happy is either not strong or not funny and vice versa. Everyone who is kind or not rich is not strong and vice versa. Everyone who is both curious and not curious is quiet or not funny. If someone is not patient then mary is not patient and vice versa. If john is strong then mary is generous or creative and vice versa. If lucy is tall then paul is both not patient and brave and vice versa. If someone is not creative then paul is both not curious and wise. Everyone who is wise or not curious is both not rich and generous and vice versa. If someone is either not kind or not patient then someone is either not funny or not calm and vice versa. If fred is not tall or not humble then someone is creative or quiet and vice versa. If lucy is not kind or happy then someone is both funny and brave and vice versa. Everyone who is not happy is kind and vice versa. If john is calm or not tall then someone is either not curious or not creative and vice versa. Everyone who is either not wise or wise is not tall and vice versa. If john is both not curious and not humble then john is tall or humble and vice versa. Someone is either not patient or not curious. Someone is not calm. Lucy is kind. Fred is either not kind or not quiet. Lucy is either creative or patient. Someone is humble. Fred is both generous and quiet.

Mary is rich.

contradiction

(![X]:((quiet(X)|curious(X))=>(brave(X)&~patient(X))))& (![X]:(~happy(X)<=>(~strong(X)<~>~funny(X))))& (![X]:((kind(X)|~rich(X))<=>~strong(X)))& (![X]:((curious(X)&~curious(X))=>(quiet(X)|~funny(X))))& ((?[X]:(~patient(X)))<=>(~patient(mary)))& ((strong(john))<=>((generous(mary)|creative(mary))))& ((tall(lucy))<=>((~patient(paul)&brave(paul))))& ((?[X]:(~creative(X)))=>((~curious(paul)&wise(paul))))& (![X]:((wise(X)|~curious(X))<=>(~rich(X)&generous(X))))& ((?[X]:((~kind(X)<~>~patient(X))))<=>(?[X]:((~funny(X)<~>~calm(X)))))& (((~tall(fred)|~humble(fred)))<=>(?[X]:((creative(X)|quiet(X)))))& (((~kind(lucy)|happy(lucy)))<=>(?[X]:((funny(X)&brave(X)))))& (![X]:(~happy(X)<=>kind(X)))& (((calm(john)|~tall(john)))<=>(?[X]:((~curious(X)<~>~creative(X)))))& (![X]:((~wise(X)<~>wise(X))<=>~tall(X)))& (((~curious(john)&~humble(john)))<=>((tall(john)|humble(john))))& (?[X]:((~patient(X)<~>~curious(X))))& (?[X]:(~calm(X)))& (kind(lucy))& ((~kind(fred)<~>~quiet(fred)))& ((creative(lucy)<~>patient(lucy)))& (?[X]:(humble(X)))& ((generous(fred)&quiet(fred)))

rich(mary)

% SZS status Unsatisfiable for 7890532133196430497818876 % SZS output start Proof for 7890532133196430497818876 1. ! [X0] : ((curious(X0) | quiet(X0)) => (~patient(X0) & brave(X0))) [input p0] 2. ! [X0] : (~happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p1] 3. ! [X0] : ((~rich(X0) | kind(X0)) <=> ~strong(X0)) [input p2] 9. ! [X0] : ((~curious(X0) | wise(X0)) <=> (generous(X0) & ~rich(X0))) [input p8] 12. (happy(lucy) | ~kind(lucy)) <=> ? [X0] : (brave(X0) & funny(X0)) [input p11] 13. ! [X0] : (~happy(X0) <=> kind(X0)) [input p12] 19. kind(lucy) [input p18] 24. rich(mary) [input hypothesis] 26. ! [X0] : ((~patient(X0) & brave(X0)) | (~curious(X0) & ~quiet(X0))) [ennf transformation 1] 30. ! [X0] : ((~happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | happy(X0))) [nnf transformation 2] 31. ! [X0] : (((~rich(X0) | kind(X0)) | strong(X0)) & (~strong(X0) | (rich(X0) & ~kind(X0)))) [nnf transformation 3] 32. ! [X0] : ((~rich(X0) | kind(X0) | strong(X0)) & (~strong(X0) | (rich(X0) & ~kind(X0)))) [flattening 31] 41. ! [X0] : (((~curious(X0) | wise(X0)) | (~generous(X0) | rich(X0))) & ((generous(X0) & ~rich(X0)) | (curious(X0) & ~wise(X0)))) [nnf transformation 9] 42. ! [X0] : ((~curious(X0) | wise(X0) | ~generous(X0) | rich(X0)) & ((generous(X0) & ~rich(X0)) | (curious(X0) & ~wise(X0)))) [flattening 41] 53. ((happy(lucy) | ~kind(lucy)) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X0] : (brave(X0) & funny(X0)) | (~happy(lucy) & kind(lucy))) [nnf transformation 12] 54. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X0] : (brave(X0) & funny(X0)) | (~happy(lucy) & kind(lucy))) [flattening 53] 55. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X1] : (brave(X1) & funny(X1)) | (~happy(lucy) & kind(lucy))) [rectify 54] 56. ? [X1] : (brave(X1) & funny(X1)) => (brave(sK4) & funny(sK4)) [choice axiom] 57. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & ((brave(sK4) & funny(sK4)) | (~happy(lucy) & kind(lucy))) [skolemisation 55,56] 58. ! [X0] : ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))) [nnf transformation 13] 77. ~curious(X0) | brave(X0) [cnf transformation 26] 81. funny(X0) | strong(X0) | happy(X0) [cnf transformation 30] 83. ~strong(X0) | ~happy(X0) | funny(X0) [cnf transformation 30] 84. ~kind(X0) | ~strong(X0) [cnf transformation 32] 86. ~rich(X0) | kind(X0) | strong(X0) [cnf transformation 32] 99. ~rich(X0) | curious(X0) [cnf transformation 42] 119. happy(lucy) | ~kind(lucy) | ~brave(X0) | ~funny(X0) [cnf transformation 57] 120. kind(X0) | happy(X0) [cnf transformation 58] 121. ~kind(X0) | ~happy(X0) [cnf transformation 58] 140. kind(lucy) [cnf transformation 19] 148. rich(mary) [cnf transformation 24] 272. 27 <=> ! [X0] : (~brave(X0) | ~funny(X0)) [avatar definition] 273. ~funny(X0) | ~brave(X0) <- (27) [avatar component clause 272] 275. 28 <=> kind(lucy) [avatar definition] 276. kind(lucy) <- (28) [avatar component clause 275] 279. 29 <=> happy(lucy) [avatar definition] 282. 27 | ~28 | 29 [avatar split clause 119,279,275,272] 335. 28 [avatar split clause 140,275] 376. curious(mary) [resolution 99,148] 379. brave(mary) [resolution 376,77] 381. ~strong(X0) | happy(X0) [resolution 120,84] 383. ~happy(lucy) <- (28) [resolution 121,276] 400. strong(X1) | happy(X1) | ~brave(X1) <- (27) [resolution 81,273] 402. ~brave(X1) | happy(X1) <- (27) [subsumption resolution 400,381] 415. kind(mary) | strong(mary) [resolution 86,148] 417. 46 <=> strong(mary) [avatar definition] 419. strong(mary) <- (46) [avatar component clause 417] 421. 47 <=> kind(mary) [avatar definition] 423. kind(mary) <- (47) [avatar component clause 421] 424. 46 | 47 [avatar split clause 415,421,417] 425. ~happy(mary) | funny(mary) <- (46) [resolution 419,83] 428. 48 <=> funny(mary) [avatar definition] 430. funny(mary) <- (48) [avatar component clause 428] 432. 49 <=> happy(mary) [avatar definition] 434. ~happy(mary) <- (~49) [avatar component clause 432] 435. 48 | ~49 | ~46 [avatar split clause 425,417,432,428] 455. ~happy(mary) <- (47) [resolution 423,121] 457. happy(mary) <- (27) [resolution 402,379] 463. $false <- (27, ~49) [subsumption resolution 457,434] 464. ~27 | 49 [avatar contradiction clause 463] 467. ~29 | ~28 [avatar split clause 383,275,279] 468. ~49 | ~47 [avatar split clause 455,421,432] 495. ~brave(mary) <- (27, 48) [resolution 430,273] 498. $false <- (27, 48) [subsumption resolution 495,379] 499. ~27 | ~48 [avatar contradiction clause 498] 500. $false [avatar sat refutation 282,335,424,435,464,467,468,499] % SZS output end Proof for 7890532133196430497818876 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

Everyone who is calm or not generous is both quiet and brave and vice versa. If someone is either not generous or calm then mary is generous. Everyone who is not humble or not kind is funny. If fred is either tall or not patient then alice is both not happy and strong. If someone is both not generous and not old then someone is either not brave or brave and vice versa. If someone is both patient and tall then someone is both creative and kind and vice versa. Everyone who is not humble or funny is both not humble and not funny. Everyone who is either tall or not creative is not rich and vice versa. If mary is either not curious or curious then someone is either not funny or funny. If alice is quiet then paul is not patient or not rich. Everyone who is quiet or not quiet is either funny or quiet. If someone is either old or humble then fred is calm or rich and vice versa. Everyone who is quiet is creative and vice versa. Everyone who is both not curious and funny is either tall or not curious and vice versa. If alice is old or happy then john is humble and vice versa. Everyone who is quiet or creative is brave or kind. Susan is not strong. Paul is either wise or rich. Someone is both wise and tall. Lucy is creative or not tall. John is both wise and not curious.

Fred is tall.

neutral

(![X]:((calm(X)|~generous(X))<=>(quiet(X)&brave(X))))& ((?[X]:((~generous(X)<~>calm(X))))=>(generous(mary)))& (![X]:((~humble(X)|~kind(X))=>funny(X)))& (((tall(fred)<~>~patient(fred)))=>((~happy(alice)&strong(alice))))& ((?[X]:((~generous(X)&~old(X))))<=>(?[X]:((~brave(X)<~>brave(X)))))& ((?[X]:((patient(X)&tall(X))))<=>(?[X]:((creative(X)&kind(X)))))& (![X]:((~humble(X)|funny(X))=>(~humble(X)&~funny(X))))& (![X]:((tall(X)<~>~creative(X))<=>~rich(X)))& (((~curious(mary)<~>curious(mary)))=>(?[X]:((~funny(X)<~>funny(X)))))& ((quiet(alice))=>((~patient(paul)|~rich(paul))))& (![X]:((quiet(X)|~quiet(X))=>(funny(X)<~>quiet(X))))& ((?[X]:((old(X)<~>humble(X))))<=>((calm(fred)|rich(fred))))& (![X]:(quiet(X)<=>creative(X)))& (![X]:((~curious(X)&funny(X))<=>(tall(X)<~>~curious(X))))& (((old(alice)|happy(alice)))<=>(humble(john)))& (![X]:((quiet(X)|creative(X))=>(brave(X)|kind(X))))& (~strong(susan))& ((wise(paul)<~>rich(paul)))& (?[X]:((wise(X)&tall(X))))& ((creative(lucy)|~tall(lucy)))& ((wise(john)&~curious(john)))

tall(fred)

If lucy is either not old or wise then susan is generous. Everyone who is either not creative or not curious is calm and vice versa. If someone is tall or not old then paul is both not happy and not patient. Everyone who is both funny and curious is either not happy or creative and vice versa. Everyone who is both kind and not happy is either rich or not creative and vice versa. If someone is not happy or not creative then alice is not old or creative. Everyone who is either generous or not brave is not humble and vice versa. If someone is either not creative or kind then fred is both not happy and strong. If someone is strong or creative then someone is humble and vice versa. Everyone who is both generous and wise is both creative and not old and vice versa. Everyone who is not happy is not generous and vice versa. Everyone who is not quiet is happy and vice versa. Everyone who is either not curious or creative is either humble or quiet and vice versa. Everyone who is both not curious and curious is not happy or funny. If paul is brave or rich then susan is both not generous and not funny and vice versa. Everyone who is either brave or not tall is both calm and curious. Someone is not curious or funny. Someone is either not wise or rich. Someone is curious or happy. Someone is brave or not happy. Someone is not happy. Someone is not wise or brave. Someone is not brave or tall. Someone is not kind.

Paul is not happy.

entailment

(((~old(lucy)<~>wise(lucy)))=>(generous(susan)))& (![X]:((~creative(X)<~>~curious(X))<=>calm(X)))& ((?[X]:((tall(X)|~old(X))))=>((~happy(paul)&~patient(paul))))& (![X]:((funny(X)&curious(X))<=>(~happy(X)<~>creative(X))))& (![X]:((kind(X)&~happy(X))<=>(rich(X)<~>~creative(X))))& ((?[X]:((~happy(X)|~creative(X))))=>((~old(alice)|creative(alice))))& (![X]:((generous(X)<~>~brave(X))<=>~humble(X)))& ((?[X]:((~creative(X)<~>kind(X))))=>((~happy(fred)&strong(fred))))& ((?[X]:((strong(X)|creative(X))))<=>(?[X]:(humble(X))))& (![X]:((generous(X)&wise(X))<=>(creative(X)&~old(X))))& (![X]:(~happy(X)<=>~generous(X)))& (![X]:(~quiet(X)<=>happy(X)))& (![X]:((~curious(X)<~>creative(X))<=>(humble(X)<~>quiet(X))))& (![X]:((~curious(X)&curious(X))=>(~happy(X)|funny(X))))& (((brave(paul)|rich(paul)))<=>((~generous(susan)&~funny(susan))))& (![X]:((brave(X)<~>~tall(X))=>(calm(X)&curious(X))))& (?[X]:((~curious(X)|funny(X))))& (?[X]:((~wise(X)<~>rich(X))))& (?[X]:((curious(X)|happy(X))))& (?[X]:((brave(X)|~happy(X))))& (?[X]:(~happy(X)))& (?[X]:((~wise(X)|brave(X))))& (?[X]:((~brave(X)|tall(X))))& (?[X]:(~kind(X)))

~happy(paul)

% SZS status Unsatisfiable for 3597430228050107919515635 % SZS output start Proof for 3597430228050107919515635 2. ! [X0] : ((~creative(X0) <~> ~curious(X0)) <=> calm(X0)) [input p1] 3. ? [X0] : (~old(X0) | tall(X0)) => (~patient(paul) & ~happy(paul)) [input p2] 4. ! [X0] : ((curious(X0) & funny(X0)) <=> (~happy(X0) <~> creative(X0))) [input p3] 7. ! [X0] : ((generous(X0) <~> ~brave(X0)) <=> ~humble(X0)) [input p6] 11. ! [X0] : (~happy(X0) <=> ~generous(X0)) [input p10] 12. ! [X0] : (~quiet(X0) <=> happy(X0)) [input p11] 13. ! [X0] : ((~curious(X0) <~> creative(X0)) <=> (humble(X0) <~> quiet(X0))) [input p12] 16. ! [X0] : ((brave(X0) <~> ~tall(X0)) => (curious(X0) & calm(X0))) [input p15] 23. ? [X0] : (tall(X0) | ~brave(X0)) [input p22] 25. happy(paul) [input hypothesis] 27. ! [X0] : (calm(X0) => (~creative(X0) <~> ~curious(X0))) [unused predicate definition removal 2] 28. ? [X0] : (~old(X0) | tall(X0)) => ~happy(paul) [pure predicate removal 3] 30. ! [X0] : ((~creative(X0) <~> ~curious(X0)) | ~calm(X0)) [ennf transformation 27] 31. ~happy(paul) | ! [X0] : (old(X0) & ~tall(X0)) [ennf transformation 28] 37. ! [X0] : ((curious(X0) & calm(X0)) | (brave(X0) <=> ~tall(X0))) [ennf transformation 16] 39. ! [X0] : (((curious(X0) | creative(X0)) & (~curious(X0) | ~creative(X0))) | ~calm(X0)) [nnf transformation 30] 40. ! [X0] : (((curious(X0) & funny(X0)) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) & (((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | (~curious(X0) | ~funny(X0)))) [nnf transformation 4] 41. ! [X0] : (((curious(X0) & funny(X0)) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) & (((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | ~curious(X0) | ~funny(X0))) [flattening 40] 44. ! [X0] : ((((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | humble(X0)) & (~humble(X0) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))))) [nnf transformation 7] 53. ! [X0] : ((~happy(X0) | generous(X0)) & (~generous(X0) | happy(X0))) [nnf transformation 11] 54. ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))) [nnf transformation 12] 55. ! [X0] : ((((~creative(X0) | curious(X0)) & (creative(X0) | ~curious(X0))) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ((~curious(X0) | ~creative(X0)) & (creative(X0) | curious(X0))))) [nnf transformation 13] 58. ! [X0] : ((curious(X0) & calm(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) [nnf transformation 37] 72. ? [X0] : (tall(X0) | ~brave(X0)) => (tall(sK8) | ~brave(sK8)) [choice axiom] 73. tall(sK8) | ~brave(sK8) [skolemisation 23,72] 78. ~calm(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 39] 80. ~happy(paul) | ~tall(X0) [cnf transformation 31] 86. happy(X0) | creative(X0) | curious(X0) [cnf transformation 41] 97. ~humble(X0) | generous(X0) | brave(X0) [cnf transformation 44] 99. ~generous(X0) | brave(X0) | humble(X0) [cnf transformation 44] 111. ~generous(X0) | happy(X0) [cnf transformation 53] 112. ~happy(X0) | generous(X0) [cnf transformation 53] 113. quiet(X0) | happy(X0) [cnf transformation 54] 114. ~quiet(X0) | ~happy(X0) [cnf transformation 54] 119. ~humble(X0) | ~curious(X0) | quiet(X0) | creative(X0) [cnf transformation 55] 120. ~quiet(X0) | ~curious(X0) | humble(X0) | creative(X0) [cnf transformation 55] 130. brave(X0) | calm(X0) | tall(X0) [cnf transformation 58] 132. brave(X0) | curious(X0) | tall(X0) [cnf transformation 58] 140. tall(sK8) | ~brave(sK8) [cnf transformation 73] 142. happy(paul) [cnf transformation 25] 161. 5 <=> happy(paul) [avatar definition] 166. 6 <=> ! [X0] : ~tall(X0) [avatar definition] 167. ~tall(X0) <- (6) [avatar component clause 166] 168. 6 | ~5 [avatar split clause 80,161,166] 291. 34 <=> brave(sK8) [avatar definition] 293. ~brave(sK8) <- (~34) [avatar component clause 291] 295. 35 <=> tall(sK8) [avatar definition] 297. tall(sK8) <- (35) [avatar component clause 295] 298. ~34 | 35 [avatar split clause 140,295,291] 299. 5 [avatar split clause 142,161] 606. ~curious(X1) | humble(X1) | creative(X1) | happy(X1) [resolution 120,113] 608. humble(X1) | creative(X1) | happy(X1) [subsumption resolution 606,86] 685. $false <- (6, 35) [subsumption resolution 297,167] 686. ~6 | ~35 [avatar contradiction clause 685] 719. curious(sK8) | tall(sK8) <- (~34) [resolution 293,132] 720. calm(sK8) | tall(sK8) <- (~34) [resolution 293,130] 721. curious(sK8) <- (6, ~34) [subsumption resolution 719,167] 722. calm(sK8) <- (6, ~34) [subsumption resolution 720,167] 766. 74 <=> creative(sK8) [avatar definition] 768. ~creative(sK8) <- (~74) [avatar component clause 766] 770. 75 <=> quiet(sK8) [avatar definition] 772. quiet(sK8) <- (75) [avatar component clause 770] 774. 76 <=> humble(sK8) [avatar definition] 776. humble(sK8) <- (76) [avatar component clause 774] 779. ~creative(sK8) | ~curious(sK8) <- (6, ~34) [resolution 722,78] 846. creative(X2) | happy(X2) | generous(X2) | brave(X2) [resolution 608,97] 850. brave(X2) | generous(X2) | creative(X2) [subsumption resolution 846,112] 1207. generous(sK8) | creative(sK8) <- (~34) [resolution 850,293] 1209. generous(sK8) <- (~34, ~74) [subsumption resolution 1207,768] 1261. brave(sK8) | humble(sK8) <- (~34, ~74) [resolution 1209,99] 1264. humble(sK8) <- (~34, ~74) [subsumption resolution 1261,293] 1265. 76 | 34 | 74 [avatar split clause 1264,766,291,774] 1267. 98 <=> generous(sK8) [avatar definition] 1269. generous(sK8) <- (98) [avatar component clause 1267] 1271. 74 | 98 | 34 [avatar split clause 1207,291,1267,766] 1272. ~creative(sK8) <- (6, ~34) [subsumption resolution 779,721] 1273. ~74 | ~6 | 34 [avatar split clause 1272,291,166,766] 1278. ~happy(sK8) <- (75) [resolution 772,114] 1281. ~curious(sK8) | quiet(sK8) | creative(sK8) <- (76) [resolution 776,119] 1287. happy(sK8) <- (98) [resolution 1269,111] 1289. $false <- (75, 98) [subsumption resolution 1287,1278] 1290. ~75 | ~98 [avatar contradiction clause 1289] 1291. quiet(sK8) | creative(sK8) <- (6, ~34, 76) [subsumption resolution 1281,721] 1292. quiet(sK8) <- (6, ~34, ~74, 76) [subsumption resolution 1291,768] 1293. 75 | ~6 | 34 | 74 | ~76 [avatar split clause 1292,774,766,291,166,770] 1294. $false [avatar sat refutation 168,298,299,686,1265,1271,1273,1290,1293] % SZS output end Proof for 3597430228050107919515635 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5628 % Time elapsed: 0.043 s % ------------------------------ % ------------------------------

Everyone who is either patient or brave is either funny or tall and vice versa. Everyone who is both patient and strong is both not brave and rich. If lucy is quiet then someone is not strong and vice versa. Everyone who is funny or kind is not patient or not quiet and vice versa. If someone is either humble or rich then someone is not curious or rich. Everyone who is not calm is not tall and vice versa. If someone is either patient or generous then someone is both wise and humble and vice versa. If alice is not wise then someone is curious or not kind and vice versa. Everyone who is either quiet or not humble is not patient. Everyone who is both not old and happy is either curious or not happy and vice versa. Everyone who is both wise and not old is happy. If someone is not wise or strong then john is either tall or not wise and vice versa. Everyone who is not curious is brave or curious and vice versa. If fred is either funny or calm then someone is either not calm or brave and vice versa. Everyone who is not strong is not curious or not quiet. Someone is both not strong and not kind. Paul is not wise or old. Someone is quiet. Susan is not happy or not strong. Someone is both not humble and not quiet. Lucy is not curious or not happy. Someone is rich. Fred is kind or patient.

John is not generous.

neutral

(![X]:((patient(X)<~>brave(X))<=>(funny(X)<~>tall(X))))& (![X]:((patient(X)&strong(X))=>(~brave(X)&rich(X))))& ((quiet(lucy))<=>(?[X]:(~strong(X))))& (![X]:((funny(X)|kind(X))<=>(~patient(X)|~quiet(X))))& ((?[X]:((humble(X)<~>rich(X))))=>(?[X]:((~curious(X)|rich(X)))))& (![X]:(~calm(X)<=>~tall(X)))& ((?[X]:((patient(X)<~>generous(X))))<=>(?[X]:((wise(X)&humble(X)))))& ((~wise(alice))<=>(?[X]:((curious(X)|~kind(X)))))& (![X]:((quiet(X)<~>~humble(X))=>~patient(X)))& (![X]:((~old(X)&happy(X))<=>(curious(X)<~>~happy(X))))& (![X]:((wise(X)&~old(X))=>happy(X)))& ((?[X]:((~wise(X)|strong(X))))<=>((tall(john)<~>~wise(john))))& (![X]:(~curious(X)<=>(brave(X)|curious(X))))& (((funny(fred)<~>calm(fred)))<=>(?[X]:((~calm(X)<~>brave(X)))))& (![X]:(~strong(X)=>(~curious(X)|~quiet(X))))& (?[X]:((~strong(X)&~kind(X))))& ((~wise(paul)|old(paul)))& (?[X]:(quiet(X)))& ((~happy(susan)|~strong(susan)))& (?[X]:((~humble(X)&~quiet(X))))& ((~curious(lucy)|~happy(lucy)))& (?[X]:(rich(X)))& ((kind(fred)|patient(fred)))

~generous(john)

Everyone who is either not tall or funny is rich or curious and vice versa. Everyone who is both not calm and not generous is both not kind and not tall. If someone is not generous then someone is calm or rich and vice versa. Everyone who is either not wise or not patient is either not wise or not calm and vice versa. Everyone who is happy or not strong is not tall or not happy and vice versa. Everyone who is both not old and not patient is creative or generous. If john is not patient then someone is kind or not strong. Everyone who is creative is not curious. Everyone who is both not brave and not happy is not wise or wise and vice versa. Everyone who is not happy or not old is not wise or not patient. Everyone who is either not strong or not humble is creative and vice versa. Everyone who is not curious is both not tall and not humble and vice versa. Everyone who is brave or not tall is both not generous and calm and vice versa. Everyone who is either humble or not tall is either wise or creative. If alice is either kind or creative then susan is humble and vice versa. Everyone who is not calm is either patient or not strong and vice versa. Someone is either not quiet or not happy. Someone is not calm or not happy. Someone is happy or not wise. Fred is generous. Someone is patient or not humble. John is either humble or not humble. Someone is happy or generous. Someone is either generous or not tall.

Alice is tall.

entailment

(![X]:((~tall(X)<~>funny(X))<=>(rich(X)|curious(X))))& (![X]:((~calm(X)&~generous(X))=>(~kind(X)&~tall(X))))& ((?[X]:(~generous(X)))<=>(?[X]:((calm(X)|rich(X)))))& (![X]:((~wise(X)<~>~patient(X))<=>(~wise(X)<~>~calm(X))))& (![X]:((happy(X)|~strong(X))<=>(~tall(X)|~happy(X))))& (![X]:((~old(X)&~patient(X))=>(creative(X)|generous(X))))& ((~patient(john))=>(?[X]:((kind(X)|~strong(X)))))& (![X]:(creative(X)=>~curious(X)))& (![X]:((~brave(X)&~happy(X))<=>(~wise(X)|wise(X))))& (![X]:((~happy(X)|~old(X))=>(~wise(X)|~patient(X))))& (![X]:((~strong(X)<~>~humble(X))<=>creative(X)))& (![X]:(~curious(X)<=>(~tall(X)&~humble(X))))& (![X]:((brave(X)|~tall(X))<=>(~generous(X)&calm(X))))& (![X]:((humble(X)<~>~tall(X))=>(wise(X)<~>creative(X))))& (((kind(alice)<~>creative(alice)))<=>(humble(susan)))& (![X]:(~calm(X)<=>(patient(X)<~>~strong(X))))& (?[X]:((~quiet(X)<~>~happy(X))))& (?[X]:((~calm(X)|~happy(X))))& (?[X]:((happy(X)|~wise(X))))& (generous(fred))& (?[X]:((patient(X)|~humble(X))))& ((humble(john)<~>~humble(john)))& (?[X]:((happy(X)|generous(X))))& (?[X]:((generous(X)<~>~tall(X))))

tall(alice)

% SZS status Unsatisfiable for 3965711501142324810453695 % SZS output start Proof for 3965711501142324810453695 4. ! [X0] : ((~wise(X0) <~> ~patient(X0)) <=> (~wise(X0) <~> ~calm(X0))) [input p3] 8. ! [X0] : (creative(X0) => ~curious(X0)) [input p7] 9. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> (wise(X0) | ~wise(X0))) [input p8] 10. ! [X0] : ((~old(X0) | ~happy(X0)) => (~patient(X0) | ~wise(X0))) [input p9] 11. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> creative(X0)) [input p10] 12. ! [X0] : (~curious(X0) <=> (~humble(X0) & ~tall(X0))) [input p11] 13. ! [X0] : ((~tall(X0) | brave(X0)) <=> (calm(X0) & ~generous(X0))) [input p12] 14. ! [X0] : ((humble(X0) <~> ~tall(X0)) => (wise(X0) <~> creative(X0))) [input p13] 16. ! [X0] : (~calm(X0) <=> (patient(X0) <~> ~strong(X0))) [input p15] 25. ~tall(alice) [input hypothesis] 27. ! [X0] : (~happy(X0) => (~patient(X0) | ~wise(X0))) [pure predicate removal 10] 32. ! [X0] : (~curious(X0) | ~creative(X0)) [ennf transformation 8] 33. ! [X0] : ((~patient(X0) | ~wise(X0)) | happy(X0)) [ennf transformation 27] 34. ! [X0] : (~patient(X0) | ~wise(X0) | happy(X0)) [flattening 33] 35. ! [X0] : ((wise(X0) <~> creative(X0)) | (humble(X0) <=> ~tall(X0))) [ennf transformation 14] 43. ! [X0] : ((((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))))) [nnf transformation 4] 48. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | (happy(X0) | brave(X0)))) [nnf transformation 9] 49. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | happy(X0) | brave(X0))) [flattening 48] 50. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~creative(X0)) & (creative(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 11] 51. ! [X0] : ((~curious(X0) | (humble(X0) | tall(X0))) & ((~humble(X0) & ~tall(X0)) | curious(X0))) [nnf transformation 12] 52. ! [X0] : ((~curious(X0) | humble(X0) | tall(X0)) & ((~humble(X0) & ~tall(X0)) | curious(X0))) [flattening 51] 53. ! [X0] : (((~tall(X0) | brave(X0)) | (~calm(X0) | generous(X0))) & ((calm(X0) & ~generous(X0)) | (tall(X0) & ~brave(X0)))) [nnf transformation 13] 54. ! [X0] : ((~tall(X0) | brave(X0) | ~calm(X0) | generous(X0)) & ((calm(X0) & ~generous(X0)) | (tall(X0) & ~brave(X0)))) [flattening 53] 55. ! [X0] : (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0)))) [nnf transformation 35] 57. ! [X0] : ((~calm(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) & (((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | calm(X0))) [nnf transformation 16] 85. ~calm(X0) | ~wise(X0) | ~wise(X0) | patient(X0) [cnf transformation 43] 86. calm(X0) | wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 43] 89. ~patient(X0) | ~wise(X0) | ~wise(X0) | calm(X0) [cnf transformation 43] 90. patient(X0) | wise(X0) | ~calm(X0) | wise(X0) [cnf transformation 43] 97. ~creative(X0) | ~curious(X0) [cnf transformation 32] 101. ~happy(X0) | wise(X0) [cnf transformation 49] 102. ~happy(X0) | ~wise(X0) [cnf transformation 49] 103. ~patient(X0) | ~wise(X0) | happy(X0) [cnf transformation 34] 104. ~humble(X0) | creative(X0) | strong(X0) [cnf transformation 50] 107. ~creative(X0) | strong(X0) | humble(X0) [cnf transformation 50] 109. ~humble(X0) | curious(X0) [cnf transformation 52] 114. calm(X0) | tall(X0) [cnf transformation 54] 117. humble(X0) | wise(X0) | creative(X0) | tall(X0) [cnf transformation 55] 124. ~strong(X0) | patient(X0) | calm(X0) [cnf transformation 57] 126. ~calm(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 57] 139. ~tall(alice) [cnf transformation 25] 142. ~calm(X0) | ~wise(X0) | patient(X0) [duplicate literal removal 85] 143. calm(X0) | wise(X0) | ~patient(X0) [duplicate literal removal 86] 144. ~patient(X0) | ~wise(X0) | calm(X0) [duplicate literal removal 89] 145. ~calm(X0) | wise(X0) | patient(X0) [duplicate literal removal 90] 170. ~patient(X0) | calm(X0) [subsumption resolution 143,144] 171. ~calm(X0) | patient(X0) [subsumption resolution 142,145] 185. ~happy(X0) [subsumption resolution 101,102] 187. ~patient(X0) | ~wise(X0) [subsumption resolution 103,185] 199. 12 <=> creative(alice) [avatar definition] 200. creative(alice) <- (12) [avatar component clause 199] 201. ~creative(alice) <- (~12) [avatar component clause 199] 206. ~strong(X0) | ~patient(X0) [subsumption resolution 126,170] 207. ~strong(X0) | patient(X0) [subsumption resolution 124,171] 208. ~strong(X0) [subsumption resolution 207,206] 228. patient(X0) | tall(X0) [resolution 171,114] 233. ~wise(X0) | tall(X0) [resolution 228,187] 261. wise(X2) | creative(X2) | tall(X2) | creative(X2) | strong(X2) [resolution 117,104] 263. wise(X2) | creative(X2) | tall(X2) | strong(X2) [duplicate literal removal 261] 285. wise(X2) | creative(X2) | tall(X2) [subsumption resolution 263,208] 286. creative(X2) | tall(X2) [subsumption resolution 285,233] 377. tall(alice) <- (~12) [resolution 286,201] 382. $false <- (~12) [subsumption resolution 377,139] 383. 12 [avatar contradiction clause 382] 395. strong(alice) | humble(alice) <- (12) [resolution 200,107] 396. ~curious(alice) <- (12) [resolution 200,97] 397. humble(alice) <- (12) [subsumption resolution 395,208] 425. curious(alice) <- (12) [resolution 397,109] 426. $false <- (12) [subsumption resolution 425,396] 427. ~12 [avatar contradiction clause 426] 428. $false [avatar sat refutation 383,427] % SZS output end Proof for 3965711501142324810453695 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

If someone is both not rich and not calm then someone is either kind or not brave and vice versa. If susan is not wise or not happy then someone is old. Everyone who is both not wise and quiet is happy or quiet. Everyone who is either happy or wise is curious and vice versa. Everyone who is both humble and not patient is not kind and vice versa. Everyone who is curious is either not curious or not humble and vice versa. Everyone who is not calm or not tall is either quiet or not old. If someone is both strong and not creative then someone is both patient and wise. If someone is calm then someone is either not creative or calm. If someone is not rich then someone is brave. Everyone who is curious is both generous and not humble. If someone is not kind then alice is generous or not patient and vice versa. Everyone who is either not wise or brave is not calm. Everyone who is funny or not quiet is not brave and vice versa. Everyone who is quiet is happy or creative and vice versa. If someone is either curious or not funny then mary is rich or brave. Alice is generous or not wise. Fred is both not rich and not creative. Someone is either tall or kind. Fred is either patient or not patient. Someone is both tall and not old. Someone is patient. Susan is both quiet and not creative. Someone is wise or strong.

Fred is not kind.

contradiction

((?[X]:((~rich(X)&~calm(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))& (((~wise(susan)|~happy(susan)))=>(?[X]:(old(X))))& (![X]:((~wise(X)&quiet(X))=>(happy(X)|quiet(X))))& (![X]:((happy(X)<~>wise(X))<=>curious(X)))& (![X]:((humble(X)&~patient(X))<=>~kind(X)))& (![X]:(curious(X)<=>(~curious(X)<~>~humble(X))))& (![X]:((~calm(X)|~tall(X))=>(quiet(X)<~>~old(X))))& ((?[X]:((strong(X)&~creative(X))))=>(?[X]:((patient(X)&wise(X)))))& ((?[X]:(calm(X)))=>(?[X]:((~creative(X)<~>calm(X)))))& ((?[X]:(~rich(X)))=>(?[X]:(brave(X))))& (![X]:(curious(X)=>(generous(X)&~humble(X))))& ((?[X]:(~kind(X)))<=>((generous(alice)|~patient(alice))))& (![X]:((~wise(X)<~>brave(X))=>~calm(X)))& (![X]:((funny(X)|~quiet(X))<=>~brave(X)))& (![X]:(quiet(X)<=>(happy(X)|creative(X))))& ((?[X]:((curious(X)<~>~funny(X))))=>((rich(mary)|brave(mary))))& ((generous(alice)|~wise(alice)))& ((~rich(fred)&~creative(fred)))& (?[X]:((tall(X)<~>kind(X))))& ((patient(fred)<~>~patient(fred)))& (?[X]:((tall(X)&~old(X))))& (?[X]:(patient(X)))& ((quiet(susan)&~creative(susan)))& (?[X]:((wise(X)|strong(X))))

~kind(fred)

% SZS status Unsatisfiable for 208531890625050949113638 % SZS output start Proof for 208531890625050949113638 5. ! [X0] : ((~patient(X0) & humble(X0)) <=> ~kind(X0)) [input p4] 6. ! [X0] : (curious(X0) <=> (~curious(X0) <~> ~humble(X0))) [input p5] 25. ~kind(fred) [input hypothesis] 49. ! [X0] : (((~patient(X0) & humble(X0)) | kind(X0)) & (~kind(X0) | (patient(X0) | ~humble(X0)))) [nnf transformation 5] 50. ! [X0] : (((~patient(X0) & humble(X0)) | kind(X0)) & (~kind(X0) | patient(X0) | ~humble(X0))) [flattening 49] 51. ! [X0] : ((curious(X0) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) & (((humble(X0) | curious(X0)) & (~humble(X0) | ~curious(X0))) | ~curious(X0))) [nnf transformation 6] 98. humble(X0) | kind(X0) [cnf transformation 50] 100. ~humble(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 51] 102. curious(X0) | ~humble(X0) | curious(X0) [cnf transformation 51] 141. ~kind(fred) [cnf transformation 25] 142. ~humble(X0) | ~curious(X0) [duplicate literal removal 100] 143. curious(X0) | ~humble(X0) [duplicate literal removal 102] 189. ~humble(X0) [subsumption resolution 142,143] 239. 22 <=> ! [X1] : kind(X1) [avatar definition] 240. kind(X1) <- (22) [avatar component clause 239] 284. kind(X0) [resolution 98,189] 285. 22 [avatar split clause 284,239] 286. $false <- (22) [resolution 240,141] 293. ~22 [avatar contradiction clause 286] 294. $false [avatar sat refutation 285,293] % SZS output end Proof for 208531890625050949113638 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

Everyone who is tall is not wise or curious. Everyone who is not generous or not wise is either not humble or not strong and vice versa. If lucy is curious or old then lucy is strong or not calm. If someone is either not calm or curious then fred is either wise or not calm. If someone is both not quiet and happy then susan is tall or not curious. If someone is not generous or not kind then paul is either not patient or old. Everyone who is not patient is both humble and wise. Everyone who is either not humble or humble is both creative and not rich and vice versa. If lucy is old then lucy is not kind or calm. Everyone who is either not creative or not funny is not old and vice versa. If alice is either not strong or not brave then susan is either not quiet or not rich. Everyone who is both not old and not brave is funny or happy and vice versa. Everyone who is either kind or not generous is either humble or generous. If fred is either humble or old then lucy is either rich or generous. Everyone who is both happy and kind is strong. Everyone who is curious is both not kind and funny and vice versa. Fred is generous. Someone is both not humble and not happy. Fred is not wise or patient. Someone is either not patient or patient. Someone is both calm and not quiet. Mary is both quiet and not curious. Someone is not tall. Lucy is either not strong or not funny.

Susan is not funny.

entailment

(![X]:(tall(X)=>(~wise(X)|curious(X))))& (![X]:((~generous(X)|~wise(X))<=>(~humble(X)<~>~strong(X))))& (((curious(lucy)|old(lucy)))=>((strong(lucy)|~calm(lucy))))& ((?[X]:((~calm(X)<~>curious(X))))=>((wise(fred)<~>~calm(fred))))& ((?[X]:((~quiet(X)&happy(X))))=>((tall(susan)|~curious(susan))))& ((?[X]:((~generous(X)|~kind(X))))=>((~patient(paul)<~>old(paul))))& (![X]:(~patient(X)=>(humble(X)&wise(X))))& (![X]:((~humble(X)<~>humble(X))<=>(creative(X)&~rich(X))))& ((old(lucy))=>((~kind(lucy)|calm(lucy))))& (![X]:((~creative(X)<~>~funny(X))<=>~old(X)))& (((~strong(alice)<~>~brave(alice)))=>((~quiet(susan)<~>~rich(susan))))& (![X]:((~old(X)&~brave(X))<=>(funny(X)|happy(X))))& (![X]:((kind(X)<~>~generous(X))=>(humble(X)<~>generous(X))))& (((humble(fred)<~>old(fred)))=>((rich(lucy)<~>generous(lucy))))& (![X]:((happy(X)&kind(X))=>strong(X)))& (![X]:(curious(X)<=>(~kind(X)&funny(X))))& (generous(fred))& (?[X]:((~humble(X)&~happy(X))))& ((~wise(fred)|patient(fred)))& (?[X]:((~patient(X)<~>patient(X))))& (?[X]:((calm(X)&~quiet(X))))& ((quiet(mary)&~curious(mary)))& (?[X]:(~tall(X)))& ((~strong(lucy)<~>~funny(lucy)))

~funny(susan)

% SZS status Unsatisfiable for 776227881907978143838078 % SZS output start Proof for 776227881907978143838078 8. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~rich(X0) & creative(X0))) [input p7] 10. ! [X0] : ((~creative(X0) <~> ~funny(X0)) <=> ~old(X0)) [input p9] 12. ! [X0] : ((~brave(X0) & ~old(X0)) <=> (happy(X0) | funny(X0))) [input p11] 25. funny(susan) [input hypothesis] 46. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (rich(X0) | ~creative(X0))) & ((~rich(X0) & creative(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 8] 47. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | rich(X0) | ~creative(X0)) & ((~rich(X0) & creative(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 46] 48. ! [X0] : ((((funny(X0) | creative(X0)) & (~funny(X0) | ~creative(X0))) | old(X0)) & (~old(X0) | ((~creative(X0) | funny(X0)) & (~funny(X0) | creative(X0))))) [nnf transformation 10] 50. ! [X0] : (((~brave(X0) & ~old(X0)) | (~happy(X0) & ~funny(X0))) & ((happy(X0) | funny(X0)) | (brave(X0) | old(X0)))) [nnf transformation 12] 51. ! [X0] : (((~brave(X0) & ~old(X0)) | (~happy(X0) & ~funny(X0))) & (happy(X0) | funny(X0) | brave(X0) | old(X0))) [flattening 50] 86. creative(X0) | humble(X0) | humble(X0) [cnf transformation 47] 87. creative(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47] 94. ~old(X0) | ~creative(X0) | funny(X0) [cnf transformation 48] 95. ~funny(X0) | ~creative(X0) | old(X0) [cnf transformation 48] 102. ~old(X0) | ~funny(X0) [cnf transformation 51] 131. funny(susan) [cnf transformation 25] 134. creative(X0) | humble(X0) [duplicate literal removal 86] 135. ~humble(X0) | creative(X0) [duplicate literal removal 87] 205. creative(X0) [subsumption resolution 134,135] 211. ~funny(X0) | old(X0) [subsumption resolution 95,205] 212. ~old(X0) | funny(X0) [subsumption resolution 94,205] 229. ~old(X0) [subsumption resolution 102,212] 252. old(susan) [resolution 211,131] 253. $false [subsumption resolution 252,229] % SZS output end Proof for 776227881907978143838078 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.021 s % ------------------------------ % ------------------------------

Everyone who is either not generous or strong is both not generous and not rich and vice versa. If lucy is either curious or not calm then mary is not tall or creative and vice versa. Everyone who is not creative is either not happy or happy and vice versa. If fred is not generous then alice is not curious or not strong and vice versa. Everyone who is humble is quiet and vice versa. If someone is not old or not generous then someone is not rich. Everyone who is both not funny and humble is both not creative and not calm and vice versa. Everyone who is not funny or not kind is either not curious or funny and vice versa. If someone is both patient and not tall then someone is both not generous and not strong and vice versa. If someone is not creative or not humble then susan is both not strong and brave. Everyone who is kind is rich or tall. Everyone who is both not wise and rich is wise. Everyone who is both not curious and generous is rich and vice versa. Everyone who is both old and not rich is not humble and vice versa. If john is both not strong and not quiet then john is not rich or not brave. If mary is either not strong or funny then mary is wise or patient and vice versa. Susan is both not rich and humble. Someone is either not funny or not happy. John is not calm. Someone is both generous and brave. Someone is both not humble and generous. Someone is not patient or calm. Someone is not curious or not brave.

Mary is not old.

neutral

(![X]:((~generous(X)<~>strong(X))<=>(~generous(X)&~rich(X))))& (((curious(lucy)<~>~calm(lucy)))<=>((~tall(mary)|creative(mary))))& (![X]:(~creative(X)<=>(~happy(X)<~>happy(X))))& ((~generous(fred))<=>((~curious(alice)|~strong(alice))))& (![X]:(humble(X)<=>quiet(X)))& ((?[X]:((~old(X)|~generous(X))))=>(?[X]:(~rich(X))))& (![X]:((~funny(X)&humble(X))<=>(~creative(X)&~calm(X))))& (![X]:((~funny(X)|~kind(X))<=>(~curious(X)<~>funny(X))))& ((?[X]:((patient(X)&~tall(X))))<=>(?[X]:((~generous(X)&~strong(X)))))& ((?[X]:((~creative(X)|~humble(X))))=>((~strong(susan)&brave(susan))))& (![X]:(kind(X)=>(rich(X)|tall(X))))& (![X]:((~wise(X)&rich(X))=>wise(X)))& (![X]:((~curious(X)&generous(X))<=>rich(X)))& (![X]:((old(X)&~rich(X))<=>~humble(X)))& (((~strong(john)&~quiet(john)))=>((~rich(john)|~brave(john))))& (((~strong(mary)<~>funny(mary)))<=>((wise(mary)|patient(mary))))& ((~rich(susan)&humble(susan)))& (?[X]:((~funny(X)<~>~happy(X))))& (~calm(john))& (?[X]:((generous(X)&brave(X))))& (?[X]:((~humble(X)&generous(X))))& (?[X]:((~patient(X)|calm(X))))& (?[X]:((~curious(X)|~brave(X))))

~old(mary)

If fred is both not rich and patient then john is not curious or not wise. If someone is either humble or wise then alice is happy. Everyone who is not happy is both not wise and not brave and vice versa. Everyone who is either not calm or rich is not patient or quiet and vice versa. If someone is either not calm or brave then paul is patient and vice versa. If someone is generous then someone is not humble. Everyone who is either brave or funny is either not patient or not rich. If john is not wise then someone is curious or tall. Everyone who is both wise and happy is wise or not strong and vice versa. If susan is not quiet then someone is not tall or not kind. Everyone who is both not wise and quiet is both rich and patient. Everyone who is either curious or not creative is both not funny and curious. Everyone who is either wise or not funny is not tall or not happy and vice versa. Everyone who is both not old and wise is old or not calm and vice versa. Everyone who is either wise or not curious is both patient and not quiet. Everyone who is not calm or calm is both tall and not calm. Lucy is generous or not funny. Someone is brave. Fred is not quiet. Alice is creative. Someone is not rich. Someone is either old or not generous. Someone is not curious or brave.

Lucy is not wise.

contradiction

(((~rich(fred)&patient(fred)))=>((~curious(john)|~wise(john))))& ((?[X]:((humble(X)<~>wise(X))))=>(happy(alice)))& (![X]:(~happy(X)<=>(~wise(X)&~brave(X))))& (![X]:((~calm(X)<~>rich(X))<=>(~patient(X)|quiet(X))))& ((?[X]:((~calm(X)<~>brave(X))))<=>(patient(paul)))& ((?[X]:(generous(X)))=>(?[X]:(~humble(X))))& (![X]:((brave(X)<~>funny(X))=>(~patient(X)<~>~rich(X))))& ((~wise(john))=>(?[X]:((curious(X)|tall(X)))))& (![X]:((wise(X)&happy(X))<=>(wise(X)|~strong(X))))& ((~quiet(susan))=>(?[X]:((~tall(X)|~kind(X)))))& (![X]:((~wise(X)&quiet(X))=>(rich(X)&patient(X))))& (![X]:((curious(X)<~>~creative(X))=>(~funny(X)&curious(X))))& (![X]:((wise(X)<~>~funny(X))<=>(~tall(X)|~happy(X))))& (![X]:((~old(X)&wise(X))<=>(old(X)|~calm(X))))& (![X]:((wise(X)<~>~curious(X))=>(patient(X)&~quiet(X))))& (![X]:((~calm(X)|calm(X))=>(tall(X)&~calm(X))))& ((generous(lucy)|~funny(lucy)))& (?[X]:(brave(X)))& (~quiet(fred))& (creative(alice))& (?[X]:(~rich(X)))& (?[X]:((old(X)<~>~generous(X))))& (?[X]:((~curious(X)|brave(X))))

~wise(lucy)

% SZS status Unsatisfiable for 2733384180586941687527033 % SZS output start Proof for 2733384180586941687527033 14. ! [X0] : ((wise(X0) & ~old(X0)) <=> (~calm(X0) | old(X0))) [input p13] 16. ! [X0] : ((calm(X0) | ~calm(X0)) => (~calm(X0) & tall(X0))) [input p15] 24. ~wise(lucy) [input hypothesis] 37. ! [X0] : ((~calm(X0) & tall(X0)) | (~calm(X0) & calm(X0))) [ennf transformation 16] 58. ! [X0] : (((wise(X0) & ~old(X0)) | (calm(X0) & ~old(X0))) & ((~calm(X0) | old(X0)) | (~wise(X0) | old(X0)))) [nnf transformation 14] 59. ! [X0] : (((wise(X0) & ~old(X0)) | (calm(X0) & ~old(X0))) & (~calm(X0) | old(X0) | ~wise(X0) | old(X0))) [flattening 58] 113. calm(X0) | wise(X0) [cnf transformation 59] 121. ~calm(X0) | ~calm(X0) [cnf transformation 37] 130. ~wise(lucy) [cnf transformation 24] 131. ~calm(X0) [duplicate literal removal 121] 228. wise(X0) [resolution 113,131] 229. $false [resolution 228,130] % SZS output end Proof for 2733384180586941687527033 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.020 s % ------------------------------ % ------------------------------

If mary is creative or kind then susan is happy. Everyone who is both curious and patient is not rich or not old. If someone is both not brave and creative then someone is old or not patient and vice versa. Everyone who is both humble and not brave is humble. If someone is either calm or not humble then alice is both humble and not humble and vice versa. If someone is either not generous or curious then someone is generous. If paul is not generous then someone is generous or not generous. If lucy is calm or not funny then john is either not calm or rich. Everyone who is generous is not generous. If someone is both old and kind then fred is not happy or not curious and vice versa. Everyone who is both not old and funny is either brave or happy. If someone is patient or not funny then someone is either not kind or patient. Everyone who is both old and humble is not quiet and vice versa. Everyone who is both happy and rich is either strong or kind and vice versa. Everyone who is both brave and not patient is wise. If someone is either rich or wise then someone is both quiet and old. Someone is not brave or creative. Someone is either not wise or not kind. Lucy is either calm or not funny. Fred is either tall or not old. Someone is both kind and not happy. Alice is not strong. Someone is not brave or quiet.

Alice is not generous.

entailment

(((creative(mary)|kind(mary)))=>(happy(susan)))& (![X]:((curious(X)&patient(X))=>(~rich(X)|~old(X))))& ((?[X]:((~brave(X)&creative(X))))<=>(?[X]:((old(X)|~patient(X)))))& (![X]:((humble(X)&~brave(X))=>humble(X)))& ((?[X]:((calm(X)<~>~humble(X))))<=>((humble(alice)&~humble(alice))))& ((?[X]:((~generous(X)<~>curious(X))))=>(?[X]:(generous(X))))& ((~generous(paul))=>(?[X]:((generous(X)|~generous(X)))))& (((calm(lucy)|~funny(lucy)))=>((~calm(john)<~>rich(john))))& (![X]:(generous(X)=>~generous(X)))& ((?[X]:((old(X)&kind(X))))<=>((~happy(fred)|~curious(fred))))& (![X]:((~old(X)&funny(X))=>(brave(X)<~>happy(X))))& ((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~kind(X)<~>patient(X)))))& (![X]:((old(X)&humble(X))<=>~quiet(X)))& (![X]:((happy(X)&rich(X))<=>(strong(X)<~>kind(X))))& (![X]:((brave(X)&~patient(X))=>wise(X)))& ((?[X]:((rich(X)<~>wise(X))))=>(?[X]:((quiet(X)&old(X)))))& (?[X]:((~brave(X)|creative(X))))& (?[X]:((~wise(X)<~>~kind(X))))& ((calm(lucy)<~>~funny(lucy)))& ((tall(fred)<~>~old(fred)))& (?[X]:((kind(X)&~happy(X))))& (~strong(alice))& (?[X]:((~brave(X)|quiet(X))))

~generous(alice)

% SZS status Unsatisfiable for 7240128117883397602833566 % SZS output start Proof for 7240128117883397602833566 9. ! [X0] : (generous(X0) => ~generous(X0)) [input p8] 24. generous(alice) [input hypothesis] 38. ! [X0] : (~generous(X0) | ~generous(X0)) [ennf transformation 9] 113. ~generous(X0) | ~generous(X0) [cnf transformation 38] 148. generous(alice) [cnf transformation 24] 149. ~generous(X0) [duplicate literal removal 113] 340. $false [subsumption resolution 148,149] % SZS output end Proof for 7240128117883397602833566 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

If mary is not curious or not funny then paul is generous or not curious and vice versa. Everyone who is either not generous or curious is both not humble and not funny. If someone is both happy and not calm then someone is calm or rich and vice versa. Everyone who is either not brave or not happy is not old or not strong and vice versa. Everyone who is both not wise and patient is either creative or not tall and vice versa. If someone is not kind then john is both creative and kind. If paul is not tall or not strong then fred is happy. Everyone who is both not calm and not kind is either calm or quiet and vice versa. Everyone who is either old or not tall is creative or humble and vice versa. Everyone who is both wise and not kind is both wise and quiet. Everyone who is not strong or calm is both not tall and tall. If alice is not rich then someone is both not rich and not calm. If someone is rich or strong then paul is not wise or not calm and vice versa. If john is not tall then someone is not happy. If someone is humble then someone is quiet or not creative and vice versa. Everyone who is not calm or calm is not creative or curious. Someone is not kind. Someone is rich or not tall. Someone is either not curious or patient. Alice is brave or strong. Alice is both quiet and not old. Someone is either old or not happy. Someone is generous or not brave.

Fred is strong.

entailment

(((~curious(mary)|~funny(mary)))<=>((generous(paul)|~curious(paul))))& (![X]:((~generous(X)<~>curious(X))=>(~humble(X)&~funny(X))))& ((?[X]:((happy(X)&~calm(X))))<=>(?[X]:((calm(X)|rich(X)))))& (![X]:((~brave(X)<~>~happy(X))<=>(~old(X)|~strong(X))))& (![X]:((~wise(X)&patient(X))<=>(creative(X)<~>~tall(X))))& ((?[X]:(~kind(X)))=>((creative(john)&kind(john))))& (((~tall(paul)|~strong(paul)))=>(happy(fred)))& (![X]:((~calm(X)&~kind(X))<=>(calm(X)<~>quiet(X))))& (![X]:((old(X)<~>~tall(X))<=>(creative(X)|humble(X))))& (![X]:((wise(X)&~kind(X))=>(wise(X)&quiet(X))))& (![X]:((~strong(X)|calm(X))=>(~tall(X)&tall(X))))& ((~rich(alice))=>(?[X]:((~rich(X)&~calm(X)))))& ((?[X]:((rich(X)|strong(X))))<=>((~wise(paul)|~calm(paul))))& ((~tall(john))=>(?[X]:(~happy(X))))& ((?[X]:(humble(X)))<=>(?[X]:((quiet(X)|~creative(X)))))& (![X]:((~calm(X)|calm(X))=>(~creative(X)|curious(X))))& (?[X]:(~kind(X)))& (?[X]:((rich(X)|~tall(X))))& (?[X]:((~curious(X)<~>patient(X))))& ((brave(alice)|strong(alice)))& ((quiet(alice)&~old(alice)))& (?[X]:((old(X)<~>~happy(X))))& (?[X]:((generous(X)|~brave(X))))

strong(fred)

% SZS status Unsatisfiable for 8141429856583674437230303 % SZS output start Proof for 8141429856583674437230303 11. ! [X0] : ((calm(X0) | ~strong(X0)) => (tall(X0) & ~tall(X0))) [input p10] 24. ~strong(fred) [input hypothesis] 32. ! [X0] : ((tall(X0) & ~tall(X0)) | (~calm(X0) & strong(X0))) [ennf transformation 11] 122. ~tall(X0) | strong(X0) [cnf transformation 32] 124. tall(X0) | strong(X0) [cnf transformation 32] 148. ~strong(fred) [cnf transformation 24] 231. strong(X0) [subsumption resolution 122,124] 329. $false [subsumption resolution 148,231] % SZS output end Proof for 8141429856583674437230303 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.021 s % ------------------------------ % ------------------------------

If susan is patient then someone is both rich and wise. If susan is either calm or quiet then someone is either not happy or quiet and vice versa. Everyone who is funny or not funny is either not patient or not brave. Everyone who is both not rich and not curious is either not happy or generous and vice versa. If someone is generous or not humble then someone is either humble or calm. If someone is not old or not tall then someone is both not funny and not brave and vice versa. If john is either not old or not generous then someone is both old and not calm and vice versa. Everyone who is either not brave or kind is both brave and not happy. If lucy is either not brave or not curious then mary is not curious. If someone is either calm or tall then fred is both not curious and not calm and vice versa. Everyone who is both tall and not wise is kind and vice versa. If someone is both happy and not rich then someone is funny or happy. Everyone who is both not patient and strong is curious or not tall and vice versa. Everyone who is both not tall and not strong is either brave or not curious and vice versa. Everyone who is calm is tall or calm. If someone is rich then john is calm or not humble and vice versa. Someone is not tall or creative. Lucy is not wise. Alice is funny or not curious. Someone is kind or not happy. Someone is not patient or not generous. Someone is either not curious or rich. John is happy. Alice is either happy or old.

Mary is old.

entailment

((patient(susan))=>(?[X]:((rich(X)&wise(X)))))& (((calm(susan)<~>quiet(susan)))<=>(?[X]:((~happy(X)<~>quiet(X)))))& (![X]:((funny(X)|~funny(X))=>(~patient(X)<~>~brave(X))))& (![X]:((~rich(X)&~curious(X))<=>(~happy(X)<~>generous(X))))& ((?[X]:((generous(X)|~humble(X))))=>(?[X]:((humble(X)<~>calm(X)))))& ((?[X]:((~old(X)|~tall(X))))<=>(?[X]:((~funny(X)&~brave(X)))))& (((~old(john)<~>~generous(john)))<=>(?[X]:((old(X)&~calm(X)))))& (![X]:((~brave(X)<~>kind(X))=>(brave(X)&~happy(X))))& (((~brave(lucy)<~>~curious(lucy)))=>(~curious(mary)))& ((?[X]:((calm(X)<~>tall(X))))<=>((~curious(fred)&~calm(fred))))& (![X]:((tall(X)&~wise(X))<=>kind(X)))& ((?[X]:((happy(X)&~rich(X))))=>(?[X]:((funny(X)|happy(X)))))& (![X]:((~patient(X)&strong(X))<=>(curious(X)|~tall(X))))& (![X]:((~tall(X)&~strong(X))<=>(brave(X)<~>~curious(X))))& (![X]:(calm(X)=>(tall(X)|calm(X))))& ((?[X]:(rich(X)))<=>((calm(john)|~humble(john))))& (?[X]:((~tall(X)|creative(X))))& (~wise(lucy))& ((funny(alice)|~curious(alice)))& (?[X]:((kind(X)|~happy(X))))& (?[X]:((~patient(X)|~generous(X))))& (?[X]:((~curious(X)<~>rich(X))))& (happy(john))& ((happy(alice)<~>old(alice)))

old(mary)

% SZS status Unsatisfiable for 3664189645073135533453203 % SZS output start Proof for 3664189645073135533453203 3. ! [X0] : ((~funny(X0) | funny(X0)) => (~patient(X0) <~> ~brave(X0))) [input p2] 6. ? [X0] : (~tall(X0) | ~old(X0)) <=> ? [X0] : (~brave(X0) & ~funny(X0)) [input p5] 8. ! [X0] : ((~brave(X0) <~> kind(X0)) => (~happy(X0) & brave(X0))) [input p7] 11. ! [X0] : ((~wise(X0) & tall(X0)) <=> kind(X0)) [input p10] 13. ! [X0] : ((strong(X0) & ~patient(X0)) <=> (~tall(X0) | curious(X0))) [input p12] 14. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (brave(X0) <~> ~curious(X0))) [input p13] 25. ~old(mary) [input hypothesis] 27. ? [X0] : (~tall(X0) | ~old(X0)) <=> ? [X1] : (~brave(X1) & ~funny(X1)) [rectify 6] 31. ! [X0] : ((~patient(X0) <~> ~brave(X0)) | (funny(X0) & ~funny(X0))) [ennf transformation 3] 33. ! [X0] : ((~happy(X0) & brave(X0)) | (~brave(X0) <=> kind(X0))) [ennf transformation 8] 44. ! [X0] : (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (funny(X0) & ~funny(X0))) [nnf transformation 31] 51. (? [X0] : (~tall(X0) | ~old(X0)) | ! [X1] : (brave(X1) | funny(X1))) & (? [X1] : (~brave(X1) & ~funny(X1)) | ! [X0] : (tall(X0) & old(X0))) [nnf transformation 27] 52. (? [X0] : (~tall(X0) | ~old(X0)) | ! [X1] : (brave(X1) | funny(X1))) & (? [X2] : (~brave(X2) & ~funny(X2)) | ! [X3] : (tall(X3) & old(X3))) [rectify 51] 53. ? [X0] : (~tall(X0) | ~old(X0)) => (~tall(sK3) | ~old(sK3)) [choice axiom] 54. ? [X2] : (~brave(X2) & ~funny(X2)) => (~brave(sK4) & ~funny(sK4)) [choice axiom] 55. ((~tall(sK3) | ~old(sK3)) | ! [X1] : (brave(X1) | funny(X1))) & ((~brave(sK4) & ~funny(sK4)) | ! [X3] : (tall(X3) & old(X3))) [skolemisation 52,54,53] 60. ! [X0] : ((~happy(X0) & brave(X0)) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0)))) [nnf transformation 33] 67. ! [X0] : (((~wise(X0) & tall(X0)) | ~kind(X0)) & (kind(X0) | (wise(X0) | ~tall(X0)))) [nnf transformation 11] 68. ! [X0] : (((~wise(X0) & tall(X0)) | ~kind(X0)) & (kind(X0) | wise(X0) | ~tall(X0))) [flattening 67] 72. ! [X0] : (((strong(X0) & ~patient(X0)) | (tall(X0) & ~curious(X0))) & ((~tall(X0) | curious(X0)) | (~strong(X0) | patient(X0)))) [nnf transformation 13] 73. ! [X0] : (((strong(X0) & ~patient(X0)) | (tall(X0) & ~curious(X0))) & (~tall(X0) | curious(X0) | ~strong(X0) | patient(X0))) [flattening 72] 74. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) & (((curious(X0) | ~brave(X0)) & (~curious(X0) | brave(X0))) | (strong(X0) | tall(X0)))) [nnf transformation 14] 75. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) & (((curious(X0) | ~brave(X0)) & (~curious(X0) | brave(X0))) | strong(X0) | tall(X0))) [flattening 74] 101. brave(X0) | patient(X0) | ~funny(X0) [cnf transformation 44] 102. brave(X0) | patient(X0) | funny(X0) [cnf transformation 44] 115. ~brave(sK4) | old(X3) [cnf transformation 55] 124. brave(X0) | kind(X0) | brave(X0) [cnf transformation 60] 137. ~kind(X0) | tall(X0) [cnf transformation 68] 141. ~curious(X0) | ~patient(X0) [cnf transformation 73] 148. ~tall(X0) | brave(X0) | curious(X0) [cnf transformation 75] 164. ~old(mary) [cnf transformation 25] 165. kind(X0) | brave(X0) [duplicate literal removal 124] 210. brave(X0) | patient(X0) [subsumption resolution 101,102] 246. 18 <=> brave(sK4) [avatar definition] 248. ~brave(sK4) <- (~18) [avatar component clause 246] 251. 19 <=> ! [X3] : old(X3) [avatar definition] 252. old(X3) <- (19) [avatar component clause 251] 253. 19 | ~18 [avatar split clause 115,246,251] 406. tall(X1) | brave(X1) [resolution 165,137] 485. $false <- (19) [resolution 252,164] 488. ~19 [avatar contradiction clause 485] 501. brave(X1) | curious(X1) | brave(X1) [resolution 148,406] 502. curious(X1) | brave(X1) [duplicate literal removal 501] 629. brave(X3) | ~patient(X3) [resolution 502,141] 635. brave(X3) [subsumption resolution 629,210] 638. $false <- (~18) [resolution 635,248] 639. 18 [avatar contradiction clause 638] 640. $false [avatar sat refutation 253,488,639] % SZS output end Proof for 3664189645073135533453203 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

If someone is either not strong or not patient then mary is rich or not strong. If someone is both not funny and rich then someone is quiet. Everyone who is strong or old is quiet and vice versa. Everyone who is either generous or not patient is both not patient and not generous. If someone is both not happy and rich then paul is either not old or not curious and vice versa. Everyone who is both kind and humble is either not tall or humble. Everyone who is both not humble and tall is not patient or not strong and vice versa. If john is not curious or not rich then paul is both curious and strong. If alice is wise then alice is both humble and not quiet and vice versa. Everyone who is strong is not patient and vice versa. Everyone who is both not brave and old is strong or not brave. If someone is not curious or kind then someone is both not rich and not old and vice versa. If someone is both old and not calm then someone is not rich or tall. Everyone who is either not patient or brave is not humble or not calm and vice versa. Everyone who is both not tall and tall is either calm or not happy. If someone is both not strong and kind then alice is both quiet and old and vice versa. Someone is both happy and patient. Alice is rich or happy. Lucy is happy. Lucy is generous. Someone is tall. Someone is either calm or funny. Paul is not curious or not happy. Someone is not happy or not rich.

Mary is tall.

entailment

((?[X]:((~strong(X)<~>~patient(X))))=>((rich(mary)|~strong(mary))))& ((?[X]:((~funny(X)&rich(X))))=>(?[X]:(quiet(X))))& (![X]:((strong(X)|old(X))<=>quiet(X)))& (![X]:((generous(X)<~>~patient(X))=>(~patient(X)&~generous(X))))& ((?[X]:((~happy(X)&rich(X))))<=>((~old(paul)<~>~curious(paul))))& (![X]:((kind(X)&humble(X))=>(~tall(X)<~>humble(X))))& (![X]:((~humble(X)&tall(X))<=>(~patient(X)|~strong(X))))& (((~curious(john)|~rich(john)))=>((curious(paul)&strong(paul))))& ((wise(alice))<=>((humble(alice)&~quiet(alice))))& (![X]:(strong(X)<=>~patient(X)))& (![X]:((~brave(X)&old(X))=>(strong(X)|~brave(X))))& ((?[X]:((~curious(X)|kind(X))))<=>(?[X]:((~rich(X)&~old(X)))))& ((?[X]:((old(X)&~calm(X))))=>(?[X]:((~rich(X)|tall(X)))))& (![X]:((~patient(X)<~>brave(X))<=>(~humble(X)|~calm(X))))& (![X]:((~tall(X)&tall(X))=>(calm(X)<~>~happy(X))))& ((?[X]:((~strong(X)&kind(X))))<=>((quiet(alice)&old(alice))))& (?[X]:((happy(X)&patient(X))))& ((rich(alice)|happy(alice)))& (happy(lucy))& (generous(lucy))& (?[X]:(tall(X)))& (?[X]:((calm(X)<~>funny(X))))& ((~curious(paul)|~happy(paul)))& (?[X]:((~happy(X)|~rich(X))))

tall(mary)

% SZS status Unsatisfiable for 6101687725989938090516212 % SZS output start Proof for 6101687725989938090516212 7. ! [X0] : ((tall(X0) & ~humble(X0)) <=> (~strong(X0) | ~patient(X0))) [input p6] 10. ! [X0] : (strong(X0) <=> ~patient(X0)) [input p9] 25. ~tall(mary) [input hypothesis] 53. ! [X0] : (((tall(X0) & ~humble(X0)) | (strong(X0) & patient(X0))) & ((~strong(X0) | ~patient(X0)) | (~tall(X0) | humble(X0)))) [nnf transformation 7] 54. ! [X0] : (((tall(X0) & ~humble(X0)) | (strong(X0) & patient(X0))) & (~strong(X0) | ~patient(X0) | ~tall(X0) | humble(X0))) [flattening 53] 57. ! [X0] : ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0))) [nnf transformation 10] 104. tall(X0) | patient(X0) [cnf transformation 54] 105. tall(X0) | strong(X0) [cnf transformation 54] 113. ~patient(X0) | ~strong(X0) [cnf transformation 57] 144. ~tall(mary) [cnf transformation 25] 156. 3 <=> strong(mary) [avatar definition] 157. strong(mary) <- (3) [avatar component clause 156] 328. patient(mary) [resolution 104,144] 329. strong(mary) [resolution 105,144] 332. 3 [avatar split clause 329,156] 342. ~strong(mary) [resolution 113,328] 344. $false <- (3) [subsumption resolution 342,157] 345. ~3 [avatar contradiction clause 344] 346. $false [avatar sat refutation 332,345] % SZS output end Proof for 6101687725989938090516212 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Everyone who is generous or creative is either old or not curious. If alice is both not brave and funny then someone is either not rich or brave and vice versa. Everyone who is both old and not kind is quiet or wise. Everyone who is humble or curious is both not calm and old and vice versa. If fred is either happy or not patient then fred is either brave or not strong. Everyone who is either old or not generous is either strong or old. If mary is not strong or not quiet then john is not patient. Everyone who is both not patient and patient is old or calm and vice versa. If someone is generous then lucy is either happy or tall and vice versa. Everyone who is either old or not happy is both quiet and not old. Everyone who is either old or not old is both funny and not happy. Everyone who is either curious or old is brave and vice versa. Everyone who is either not quiet or not humble is not rich. If john is both not quiet and brave then someone is either not wise or quiet and vice versa. If someone is both not wise and not strong then fred is both not old and not kind. Everyone who is quiet is both not curious and not patient. Lucy is kind. Fred is either wise or quiet. Mary is not kind. Paul is quiet or not humble. Someone is both strong and not generous. Susan is quiet or not patient. Mary is patient or not brave.

Fred is not strong.

entailment

(![X]:((generous(X)|creative(X))=>(old(X)<~>~curious(X))))& (((~brave(alice)&funny(alice)))<=>(?[X]:((~rich(X)<~>brave(X)))))& (![X]:((old(X)&~kind(X))=>(quiet(X)|wise(X))))& (![X]:((humble(X)|curious(X))<=>(~calm(X)&old(X))))& (((happy(fred)<~>~patient(fred)))=>((brave(fred)<~>~strong(fred))))& (![X]:((old(X)<~>~generous(X))=>(strong(X)<~>old(X))))& (((~strong(mary)|~quiet(mary)))=>(~patient(john)))& (![X]:((~patient(X)&patient(X))<=>(old(X)|calm(X))))& ((?[X]:(generous(X)))<=>((happy(lucy)<~>tall(lucy))))& (![X]:((old(X)<~>~happy(X))=>(quiet(X)&~old(X))))& (![X]:((old(X)<~>~old(X))=>(funny(X)&~happy(X))))& (![X]:((curious(X)<~>old(X))<=>brave(X)))& (![X]:((~quiet(X)<~>~humble(X))=>~rich(X)))& (((~quiet(john)&brave(john)))<=>(?[X]:((~wise(X)<~>quiet(X)))))& ((?[X]:((~wise(X)&~strong(X))))=>((~old(fred)&~kind(fred))))& (![X]:(quiet(X)=>(~curious(X)&~patient(X))))& (kind(lucy))& ((wise(fred)<~>quiet(fred)))& (~kind(mary))& ((quiet(paul)|~humble(paul)))& (?[X]:((strong(X)&~generous(X))))& ((quiet(susan)|~patient(susan)))& ((patient(mary)|~brave(mary)))

~strong(fred)

% SZS status Unsatisfiable for 6784901556308390475787380 % SZS output start Proof for 6784901556308390475787380 5. (happy(fred) <~> ~patient(fred)) => (brave(fred) <~> ~strong(fred)) [input p4] 8. ! [X0] : ((patient(X0) & ~patient(X0)) <=> (calm(X0) | old(X0))) [input p7] 10. ! [X0] : ((old(X0) <~> ~happy(X0)) => (~old(X0) & quiet(X0))) [input p9] 11. ! [X0] : ((old(X0) <~> ~old(X0)) => (~happy(X0) & funny(X0))) [input p10] 12. ! [X0] : ((curious(X0) <~> old(X0)) <=> brave(X0)) [input p11] 16. ! [X0] : (quiet(X0) => (~patient(X0) & ~curious(X0))) [input p15] 24. strong(fred) [input hypothesis] 29. (brave(fred) <~> ~strong(fred)) | (happy(fred) <=> ~patient(fred)) [ennf transformation 5] 32. ! [X0] : ((~old(X0) & quiet(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 10] 33. ! [X0] : ((~happy(X0) & funny(X0)) | (old(X0) <=> ~old(X0))) [ennf transformation 11] 36. ! [X0] : ((~patient(X0) & ~curious(X0)) | ~quiet(X0)) [ennf transformation 16] 45. ((strong(fred) | ~brave(fred)) & (~strong(fred) | brave(fred))) | ((happy(fred) | patient(fred)) & (~patient(fred) | ~happy(fred))) [nnf transformation 29] 47. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | (~patient(X0) | patient(X0)))) [nnf transformation 8] 48. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | ~patient(X0) | patient(X0))) [flattening 47] 53. ! [X0] : ((~old(X0) & quiet(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 32] 54. ! [X0] : ((~happy(X0) & funny(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 33] 55. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | ~brave(X0)) & (brave(X0) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 12] 80. ~strong(fred) | brave(fred) | happy(fred) | patient(fred) [cnf transformation 45] 90. ~patient(X0) | ~old(X0) [cnf transformation 48] 92. ~old(X0) | patient(X0) [cnf transformation 48] 99. quiet(X0) | old(X0) | happy(X0) [cnf transformation 53] 105. ~happy(X0) | old(X0) | old(X0) [cnf transformation 54] 108. old(X0) | curious(X0) | ~brave(X0) [cnf transformation 55] 120. ~quiet(X0) | ~curious(X0) [cnf transformation 36] 121. ~patient(X0) | ~quiet(X0) [cnf transformation 36] 131. strong(fred) [cnf transformation 24] 135. ~happy(X0) | old(X0) [duplicate literal removal 105] 168. 7 <=> patient(fred) [avatar definition] 170. patient(fred) <- (7) [avatar component clause 168] 172. 8 <=> happy(fred) [avatar definition] 174. happy(fred) <- (8) [avatar component clause 172] 176. 9 <=> brave(fred) [avatar definition] 177. brave(fred) <- (9) [avatar component clause 176] 180. 10 <=> strong(fred) [avatar definition] 185. 7 | 8 | 9 | ~10 [avatar split clause 80,180,176,172,168] 202. ~old(X0) [subsumption resolution 90,92] 222. happy(X0) | quiet(X0) [subsumption resolution 99,202] 223. ~happy(X0) [subsumption resolution 135,202] 225. ~brave(X0) | curious(X0) [subsumption resolution 108,202] 291. 10 [avatar split clause 131,180] 292. ~quiet(fred) <- (7) [resolution 121,170] 293. quiet(X0) [resolution 222,223] 295. ~curious(X0) [resolution 293,120] 302. $false <- (7) [subsumption resolution 292,293] 303. ~7 [avatar contradiction clause 302] 305. curious(fred) <- (9) [resolution 177,225] 306. $false <- (9) [subsumption resolution 305,295] 307. ~9 [avatar contradiction clause 306] 308. $false <- (8) [subsumption resolution 174,223] 309. ~8 [avatar contradiction clause 308] 310. $false [avatar sat refutation 185,291,303,307,309] % SZS output end Proof for 6784901556308390475787380 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

If someone is both not calm and not curious then someone is not humble or not quiet and vice versa. Everyone who is funny is either strong or not brave. Everyone who is wise or not creative is strong. Everyone who is happy is both not funny and not curious and vice versa. If someone is either kind or not rich then someone is both not quiet and tall and vice versa. If someone is not tall or not quiet then someone is quiet. If someone is both not generous and funny then someone is either strong or creative. Everyone who is both quiet and not curious is not old and vice versa. Everyone who is happy is either humble or not generous and vice versa. Everyone who is not creative or generous is both not quiet and not calm. Everyone who is not creative or creative is not wise or tall. Everyone who is funny is not calm or humble and vice versa. Everyone who is kind or not rich is either quiet or happy. Everyone who is not tall or creative is humble. If someone is creative or old then lucy is both curious and wise and vice versa. Susan is either wise or not tall. Lucy is not generous or funny. Someone is quiet or humble. Fred is not rich. Someone is either not wise or not humble. Someone is either strong or not old. Susan is not humble.

Susan is generous.

entailment

((?[X]:((~calm(X)&~curious(X))))<=>(?[X]:((~humble(X)|~quiet(X)))))& (![X]:(funny(X)=>(strong(X)<~>~brave(X))))& (![X]:((wise(X)|~creative(X))=>strong(X)))& (![X]:(happy(X)<=>(~funny(X)&~curious(X))))& ((?[X]:((kind(X)<~>~rich(X))))<=>(?[X]:((~quiet(X)&tall(X)))))& ((?[X]:((~tall(X)|~quiet(X))))=>(?[X]:(quiet(X))))& ((?[X]:((~generous(X)&funny(X))))=>(?[X]:((strong(X)<~>creative(X)))))& (![X]:((quiet(X)&~curious(X))<=>~old(X)))& (![X]:(happy(X)<=>(humble(X)<~>~generous(X))))& (![X]:((~creative(X)|generous(X))=>(~quiet(X)&~calm(X))))& (![X]:((~creative(X)|creative(X))=>(~wise(X)|tall(X))))& (![X]:(funny(X)<=>(~calm(X)|humble(X))))& (![X]:((kind(X)|~rich(X))=>(quiet(X)<~>happy(X))))& (![X]:((~tall(X)|creative(X))=>humble(X)))& ((?[X]:((creative(X)|old(X))))<=>((curious(lucy)&wise(lucy))))& ((wise(susan)<~>~tall(susan)))& ((~generous(lucy)|funny(lucy)))& (?[X]:((quiet(X)|humble(X))))& (~rich(fred))& (?[X]:((~wise(X)<~>~humble(X))))& (?[X]:((strong(X)<~>~old(X))))& (~humble(susan))

generous(susan)

% SZS status Unsatisfiable for 65424798629462957193755 % SZS output start Proof for 65424798629462957193755 4. ! [X0] : (happy(X0) <=> (~curious(X0) & ~funny(X0))) [input p3] 9. ! [X0] : (happy(X0) <=> (humble(X0) <~> ~generous(X0))) [input p8] 10. ! [X0] : ((generous(X0) | ~creative(X0)) => (~calm(X0) & ~quiet(X0))) [input p9] 12. ! [X0] : (funny(X0) <=> (humble(X0) | ~calm(X0))) [input p11] 14. ! [X0] : ((creative(X0) | ~tall(X0)) => humble(X0)) [input p13] 22. ~humble(susan) [input p21] 23. ~generous(susan) [input hypothesis] 32. ! [X0] : ((~calm(X0) & ~quiet(X0)) | (~generous(X0) & creative(X0))) [ennf transformation 10] 36. ! [X0] : (humble(X0) | (~creative(X0) & tall(X0))) [ennf transformation 14] 43. ! [X0] : ((happy(X0) | (curious(X0) | funny(X0))) & ((~curious(X0) & ~funny(X0)) | ~happy(X0))) [nnf transformation 4] 44. ! [X0] : ((happy(X0) | curious(X0) | funny(X0)) & ((~curious(X0) & ~funny(X0)) | ~happy(X0))) [flattening 43] 59. ! [X0] : ((happy(X0) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0)))) & (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | ~happy(X0))) [nnf transformation 9] 60. ! [X0] : ((funny(X0) | (~humble(X0) & calm(X0))) & ((humble(X0) | ~calm(X0)) | ~funny(X0))) [nnf transformation 12] 61. ! [X0] : ((funny(X0) | (~humble(X0) & calm(X0))) & (humble(X0) | ~calm(X0) | ~funny(X0))) [flattening 60] 86. ~happy(X0) | ~funny(X0) [cnf transformation 44] 105. generous(X0) | humble(X0) | happy(X0) [cnf transformation 59] 108. ~calm(X0) | creative(X0) [cnf transformation 32] 113. funny(X0) | calm(X0) [cnf transformation 61] 120. ~creative(X0) | humble(X0) [cnf transformation 36] 135. ~humble(susan) [cnf transformation 22] 136. ~generous(susan) [cnf transformation 23] 328. 37 <=> funny(susan) [avatar definition] 330. ~funny(susan) <- (~37) [avatar component clause 328] 362. humble(susan) | happy(susan) [resolution 105,136] 370. happy(susan) [subsumption resolution 362,135] 403. ~funny(susan) [resolution 370,86] 515. calm(susan) <- (~37) [resolution 330,113] 564. creative(susan) <- (~37) [resolution 515,108] 579. humble(susan) <- (~37) [resolution 564,120] 580. $false <- (~37) [subsumption resolution 579,135] 581. 37 [avatar contradiction clause 580] 582. ~37 [avatar split clause 403,328] 583. $false [avatar sat refutation 581,582] % SZS output end Proof for 65424798629462957193755 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

If fred is both brave and tall then fred is not generous or not tall. Everyone who is not wise is brave or not patient. Everyone who is wise is rich or creative. Everyone who is either not rich or not calm is creative and vice versa. Everyone who is not calm is both not humble and not rich. Everyone who is either tall or not humble is both not curious and patient and vice versa. Everyone who is either creative or not rich is curious. If mary is creative or not old then someone is either tall or not old. If someone is both creative and not calm then someone is both quiet and not quiet and vice versa. If someone is either not curious or not old then mary is not brave or not curious. Everyone who is patient or quiet is both not kind and not strong and vice versa. If fred is generous then fred is not tall or creative and vice versa. Everyone who is either not calm or not strong is either kind or not rich and vice versa. If someone is both not kind and old then someone is not humble and vice versa. Everyone who is either not quiet or not calm is both not strong and quiet and vice versa. Everyone who is both patient and not humble is strong or not strong. Someone is not tall or not kind. Lucy is either not rich or funny. Paul is funny or not calm. John is not quiet. Susan is not old.

Fred is curious.

entailment

(((brave(fred)&tall(fred)))=>((~generous(fred)|~tall(fred))))& (![X]:(~wise(X)=>(brave(X)|~patient(X))))& (![X]:(wise(X)=>(rich(X)|creative(X))))& (![X]:((~rich(X)<~>~calm(X))<=>creative(X)))& (![X]:(~calm(X)=>(~humble(X)&~rich(X))))& (![X]:((tall(X)<~>~humble(X))<=>(~curious(X)&patient(X))))& (![X]:((creative(X)<~>~rich(X))=>curious(X)))& (((creative(mary)|~old(mary)))=>(?[X]:((tall(X)<~>~old(X)))))& ((?[X]:((creative(X)&~calm(X))))<=>(?[X]:((quiet(X)&~quiet(X)))))& ((?[X]:((~curious(X)<~>~old(X))))=>((~brave(mary)|~curious(mary))))& (![X]:((patient(X)|quiet(X))<=>(~kind(X)&~strong(X))))& ((generous(fred))<=>((~tall(fred)|creative(fred))))& (![X]:((~calm(X)<~>~strong(X))<=>(kind(X)<~>~rich(X))))& ((?[X]:((~kind(X)&old(X))))<=>(?[X]:(~humble(X))))& (![X]:((~quiet(X)<~>~calm(X))<=>(~strong(X)&quiet(X))))& (![X]:((patient(X)&~humble(X))=>(strong(X)|~strong(X))))& (?[X]:((~tall(X)|~kind(X))))& ((~rich(lucy)<~>funny(lucy)))& ((funny(paul)|~calm(paul)))& (~quiet(john))& (~old(susan))

curious(fred)

% SZS status Unsatisfiable for 8949041198240046212635434 % SZS output start Proof for 8949041198240046212635434 5. ! [X0] : (~calm(X0) => (~rich(X0) & ~humble(X0))) [input p4] 7. ! [X0] : ((creative(X0) <~> ~rich(X0)) => curious(X0)) [input p6] 9. ? [X0] : (~calm(X0) & creative(X0)) <=> ? [X0] : (~quiet(X0) & quiet(X0)) [input p8] 11. ! [X0] : ((quiet(X0) | patient(X0)) <=> (~strong(X0) & ~kind(X0))) [input p10] 15. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (quiet(X0) & ~strong(X0))) [input p14] 22. ~curious(fred) [input hypothesis] 23. ? [X0] : (~calm(X0) & creative(X0)) <=> ? [X1] : (~quiet(X1) & quiet(X1)) [rectify 9] 31. ! [X0] : ((~rich(X0) & ~humble(X0)) | calm(X0)) [ennf transformation 5] 32. ! [X0] : (curious(X0) | (creative(X0) <=> ~rich(X0))) [ennf transformation 7] 41. ! [X0] : (curious(X0) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 32] 45. (? [X0] : (~calm(X0) & creative(X0)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X1] : (~quiet(X1) & quiet(X1)) | ! [X0] : (calm(X0) | ~creative(X0))) [nnf transformation 23] 46. (? [X0] : (~calm(X0) & creative(X0)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X2] : (~quiet(X2) & quiet(X2)) | ! [X3] : (calm(X3) | ~creative(X3))) [rectify 45] 47. ? [X0] : (~calm(X0) & creative(X0)) => (~calm(sK1) & creative(sK1)) [choice axiom] 48. ? [X2] : (~quiet(X2) & quiet(X2)) => (~quiet(sK2) & quiet(sK2)) [choice axiom] 49. ((~calm(sK1) & creative(sK1)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & ((~quiet(sK2) & quiet(sK2)) | ! [X3] : (calm(X3) | ~creative(X3))) [skolemisation 46,48,47] 51. ! [X0] : (((quiet(X0) | patient(X0)) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | (~quiet(X0) & ~patient(X0)))) [nnf transformation 11] 52. ! [X0] : ((quiet(X0) | patient(X0) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | (~quiet(X0) & ~patient(X0)))) [flattening 51] 61. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 15] 62. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [flattening 61] 74. ~rich(X0) | calm(X0) [cnf transformation 31] 82. curious(X0) | creative(X0) | rich(X0) [cnf transformation 41] 87. quiet(sK2) | calm(X3) | ~creative(X3) [cnf transformation 49] 88. ~quiet(sK2) | calm(X3) | ~creative(X3) [cnf transformation 49] 96. ~strong(X0) | ~quiet(X0) [cnf transformation 52] 114. quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 62] 116. ~calm(X0) | ~quiet(X0) | ~quiet(X0) | strong(X0) [cnf transformation 62] 125. ~curious(fred) [cnf transformation 22] 126. quiet(X0) | ~calm(X0) [duplicate literal removal 114] 127. ~calm(X0) | ~quiet(X0) | strong(X0) [duplicate literal removal 116] 163. 8 <=> ! [X3] : (calm(X3) | ~creative(X3)) [avatar definition] 164. calm(X3) | ~creative(X3) <- (8) [avatar component clause 163] 166. 9 <=> quiet(sK2) [avatar definition] 169. 8 | ~9 [avatar split clause 88,166,163] 170. 8 | 9 [avatar split clause 87,166,163] 219. ~quiet(X0) | ~calm(X0) [subsumption resolution 127,96] 220. ~calm(X0) [subsumption resolution 126,219] 240. ~creative(X3) <- (8) [subsumption resolution 164,220] 277. creative(fred) | rich(fred) [resolution 82,125] 280. rich(fred) <- (8) [subsumption resolution 277,240] 284. calm(fred) <- (8) [resolution 280,74] 288. $false <- (8) [subsumption resolution 284,220] 289. ~8 [avatar contradiction clause 288] 290. $false [avatar sat refutation 169,170,289] % SZS output end Proof for 8949041198240046212635434 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

If fred is wise or not rich then someone is both humble and not wise and vice versa. If fred is not generous then fred is not kind or calm. If someone is funny or rich then someone is not quiet and vice versa. Everyone who is funny is happy or not creative. If someone is not calm then someone is tall and vice versa. Everyone who is not humble or not tall is both humble and not happy and vice versa. If someone is funny then lucy is both tall and not calm. If susan is both not quiet and creative then someone is happy or not quiet and vice versa. If someone is not calm then john is both creative and brave. Everyone who is quiet or not happy is not humble or not curious. Everyone who is creative or not old is both not humble and wise. Everyone who is both not funny and brave is patient or not kind and vice versa. If someone is not generous then someone is either rich or not calm. Lucy is generous. Susan is either tall or not wise. Someone is not rich or not kind. Someone is either not happy or not kind. Someone is not creative. Someone is not funny or not curious.

John is generous.

entailment

(((wise(fred)|~rich(fred)))<=>(?[X]:((humble(X)&~wise(X)))))& ((~generous(fred))=>((~kind(fred)|calm(fred))))& ((?[X]:((funny(X)|rich(X))))<=>(?[X]:(~quiet(X))))& (![X]:(funny(X)=>(happy(X)|~creative(X))))& ((?[X]:(~calm(X)))<=>(?[X]:(tall(X))))& (![X]:((~humble(X)|~tall(X))<=>(humble(X)&~happy(X))))& ((?[X]:(funny(X)))=>((tall(lucy)&~calm(lucy))))& (((~quiet(susan)&creative(susan)))<=>(?[X]:((happy(X)|~quiet(X)))))& ((?[X]:(~calm(X)))=>((creative(john)&brave(john))))& (![X]:((quiet(X)|~happy(X))=>(~humble(X)|~curious(X))))& (![X]:((creative(X)|~old(X))=>(~humble(X)&wise(X))))& (![X]:((~funny(X)&brave(X))<=>(patient(X)|~kind(X))))& ((?[X]:(~generous(X)))=>(?[X]:((rich(X)<~>~calm(X)))))& (generous(lucy))& ((tall(susan)<~>~wise(susan)))& (?[X]:((~rich(X)|~kind(X))))& (?[X]:((~happy(X)<~>~kind(X))))& (?[X]:(~creative(X)))& (?[X]:((~funny(X)|~curious(X))))

generous(john)

% SZS status Unsatisfiable for 5705311646366374099728075 % SZS output start Proof for 5705311646366374099728075 3. ? [X0] : (rich(X0) | funny(X0)) <=> ? [X0] : ~quiet(X0) [input p2] 6. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~happy(X0) & humble(X0))) [input p5] 8. (creative(susan) & ~quiet(susan)) <=> ? [X0] : (~quiet(X0) | happy(X0)) [input p7] 9. ? [X0] : ~calm(X0) => (brave(john) & creative(john)) [input p8] 11. ! [X0] : ((~old(X0) | creative(X0)) => (wise(X0) & ~humble(X0))) [input p10] 13. ? [X0] : ~generous(X0) => ? [X0] : (rich(X0) <~> ~calm(X0)) [input p12] 20. ~generous(john) [input hypothesis] 21. ? [X0] : (rich(X0) | funny(X0)) <=> ? [X1] : ~quiet(X1) [rectify 3] 23. ? [X0] : ~generous(X0) => ? [X1] : (rich(X1) <~> ~calm(X1)) [rectify 13] 24. ! [X0] : (creative(X0) => (wise(X0) & ~humble(X0))) [pure predicate removal 11] 32. (brave(john) & creative(john)) | ! [X0] : calm(X0) [ennf transformation 9] 33. ! [X0] : ((wise(X0) & ~humble(X0)) | ~creative(X0)) [ennf transformation 24] 34. ? [X1] : (rich(X1) <~> ~calm(X1)) | ! [X0] : generous(X0) [ennf transformation 23] 40. (? [X0] : (rich(X0) | funny(X0)) | ! [X1] : quiet(X1)) & (? [X1] : ~quiet(X1) | ! [X0] : (~rich(X0) & ~funny(X0))) [nnf transformation 21] 41. (? [X0] : (rich(X0) | funny(X0)) | ! [X1] : quiet(X1)) & (? [X2] : ~quiet(X2) | ! [X3] : (~rich(X3) & ~funny(X3))) [rectify 40] 42. ? [X0] : (rich(X0) | funny(X0)) => (rich(sK1) | funny(sK1)) [choice axiom] 43. ? [X2] : ~quiet(X2) => ~quiet(sK2) [choice axiom] 44. ((rich(sK1) | funny(sK1)) | ! [X1] : quiet(X1)) & (~quiet(sK2) | ! [X3] : (~rich(X3) & ~funny(X3))) [skolemisation 41,43,42] 50. ! [X0] : (((~tall(X0) | ~humble(X0)) | (happy(X0) | ~humble(X0))) & ((~happy(X0) & humble(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 6] 51. ! [X0] : ((~tall(X0) | ~humble(X0) | happy(X0) | ~humble(X0)) & ((~happy(X0) & humble(X0)) | (tall(X0) & humble(X0)))) [flattening 50] 52. ((creative(susan) & ~quiet(susan)) | ! [X0] : (quiet(X0) & ~happy(X0))) & (? [X0] : (~quiet(X0) | happy(X0)) | (~creative(susan) | quiet(susan))) [nnf transformation 8] 53. ((creative(susan) & ~quiet(susan)) | ! [X0] : (quiet(X0) & ~happy(X0))) & (? [X0] : (~quiet(X0) | happy(X0)) | ~creative(susan) | quiet(susan)) [flattening 52] 54. ((creative(susan) & ~quiet(susan)) | ! [X0] : (quiet(X0) & ~happy(X0))) & (? [X1] : (~quiet(X1) | happy(X1)) | ~creative(susan) | quiet(susan)) [rectify 53] 55. ? [X1] : (~quiet(X1) | happy(X1)) => (~quiet(sK5) | happy(sK5)) [choice axiom] 56. ((creative(susan) & ~quiet(susan)) | ! [X0] : (quiet(X0) & ~happy(X0))) & ((~quiet(sK5) | happy(sK5)) | ~creative(susan) | quiet(susan)) [skolemisation 54,55] 59. ? [X1] : ((calm(X1) | ~rich(X1)) & (~calm(X1) | rich(X1))) | ! [X0] : generous(X0) [nnf transformation 34] 60. ? [X0] : ((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | ! [X1] : generous(X1) [rectify 59] 61. ? [X0] : ((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) => ((calm(sK6) | ~rich(sK6)) & (~calm(sK6) | rich(sK6))) [choice axiom] 62. ((calm(sK6) | ~rich(sK6)) & (~calm(sK6) | rich(sK6))) | ! [X1] : generous(X1) [skolemisation 60,61] 78. ~quiet(sK2) | ~rich(X3) [cnf transformation 44] 83. humble(X0) | humble(X0) [cnf transformation 51] 94. creative(susan) | quiet(X0) [cnf transformation 56] 95. creative(john) | calm(X0) [cnf transformation 32] 97. ~humble(X0) | ~creative(X0) [cnf transformation 33] 104. ~calm(sK6) | rich(sK6) | generous(X1) [cnf transformation 62] 113. ~generous(john) [cnf transformation 20] 114. humble(X0) [duplicate literal removal 83] 154. 9 <=> ! [X1] : quiet(X1) [avatar definition] 155. quiet(X1) <- (9) [avatar component clause 154] 166. 12 <=> ! [X3] : ~rich(X3) [avatar definition] 167. ~rich(X3) <- (12) [avatar component clause 166] 169. 13 <=> quiet(sK2) [avatar definition] 171. ~quiet(sK2) <- (~13) [avatar component clause 169] 172. 12 | ~13 [avatar split clause 78,169,166] 186. 17 <=> ! [X3] : calm(X3) [avatar definition] 187. calm(X3) <- (17) [avatar component clause 186] 204. 21 <=> creative(susan) [avatar definition] 206. creative(susan) <- (21) [avatar component clause 204] 207. 9 | 21 [avatar split clause 94,204,154] 233. 27 <=> creative(john) [avatar definition] 235. creative(john) <- (27) [avatar component clause 233] 236. 17 | 27 [avatar split clause 95,233,186] 237. ~creative(X0) [subsumption resolution 97,114] 239. 28 <=> ! [X1] : generous(X1) [avatar definition] 240. generous(X1) <- (28) [avatar component clause 239] 242. 29 <=> rich(sK6) [avatar definition] 243. rich(sK6) <- (29) [avatar component clause 242] 246. 30 <=> calm(sK6) [avatar definition] 247. ~calm(sK6) <- (~30) [avatar component clause 246] 250. 28 | 29 | ~30 [avatar split clause 104,246,242,239] 280. $false <- (21) [subsumption resolution 206,237] 281. ~21 [avatar contradiction clause 280] 284. $false <- (9, ~13) [resolution 171,155] 285. ~9 | 13 [avatar contradiction clause 284] 290. $false <- (17, ~30) [resolution 247,187] 291. ~17 | 30 [avatar contradiction clause 290] 292. $false <- (27) [subsumption resolution 235,237] 293. ~27 [avatar contradiction clause 292] 296. $false <- (28) [resolution 240,113] 297. ~28 [avatar contradiction clause 296] 298. $false <- (12, 29) [subsumption resolution 243,167] 299. ~12 | ~29 [avatar contradiction clause 298] 300. $false [avatar sat refutation 172,207,236,250,281,285,291,293,297,299] % SZS output end Proof for 5705311646366374099728075 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

If mary is both not curious and kind then someone is both quiet and not tall and vice versa. Everyone who is both not tall and not curious is both not brave and curious and vice versa. Everyone who is either brave or generous is both brave and curious and vice versa. Everyone who is either not rich or strong is either strong or brave and vice versa. If someone is not old or generous then someone is both not kind and calm and vice versa. If someone is both not creative and patient then someone is creative. If someone is not patient then someone is both brave and wise. If someone is both tall and not wise then susan is tall or funny and vice versa. Everyone who is both not kind and funny is both not calm and curious. Everyone who is either not quiet or rich is both funny and not happy. If fred is both humble and generous then lucy is both creative and not wise. Everyone who is quiet or not quiet is tall. If alice is generous then someone is happy. Everyone who is both not creative and wise is old. Everyone who is either not generous or not tall is wise or not humble. If someone is either not patient or tall then someone is either creative or funny. Someone is not creative or funny. Susan is happy or generous. Mary is wise. Someone is not funny. Someone is not quiet. Someone is wise or creative. Susan is generous or not humble.

Mary is not patient.

neutral

(((~curious(mary)&kind(mary)))<=>(?[X]:((quiet(X)&~tall(X)))))& (![X]:((~tall(X)&~curious(X))<=>(~brave(X)&curious(X))))& (![X]:((brave(X)<~>generous(X))<=>(brave(X)&curious(X))))& (![X]:((~rich(X)<~>strong(X))<=>(strong(X)<~>brave(X))))& ((?[X]:((~old(X)|generous(X))))<=>(?[X]:((~kind(X)&calm(X)))))& ((?[X]:((~creative(X)&patient(X))))=>(?[X]:(creative(X))))& ((?[X]:(~patient(X)))=>(?[X]:((brave(X)&wise(X)))))& ((?[X]:((tall(X)&~wise(X))))<=>((tall(susan)|funny(susan))))& (![X]:((~kind(X)&funny(X))=>(~calm(X)&curious(X))))& (![X]:((~quiet(X)<~>rich(X))=>(funny(X)&~happy(X))))& (((humble(fred)&generous(fred)))=>((creative(lucy)&~wise(lucy))))& (![X]:((quiet(X)|~quiet(X))=>tall(X)))& ((generous(alice))=>(?[X]:(happy(X))))& (![X]:((~creative(X)&wise(X))=>old(X)))& (![X]:((~generous(X)<~>~tall(X))=>(wise(X)|~humble(X))))& ((?[X]:((~patient(X)<~>tall(X))))=>(?[X]:((creative(X)<~>funny(X)))))& (?[X]:((~creative(X)|funny(X))))& ((happy(susan)|generous(susan)))& (wise(mary))& (?[X]:(~funny(X)))& (?[X]:(~quiet(X)))& (?[X]:((wise(X)|creative(X))))& ((generous(susan)|~humble(susan)))

~patient(mary)

Everyone who is kind or not wise is not quiet. Everyone who is quiet is rich and vice versa. Everyone who is either not humble or humble is both wise and not quiet and vice versa. If paul is both kind and patient then someone is curious or not quiet. Everyone who is not humble is not funny or not brave and vice versa. If alice is either patient or calm then someone is not funny or old and vice versa. If paul is either not tall or not patient then someone is either kind or brave. Everyone who is rich is both not old and not quiet and vice versa. Everyone who is kind is not calm or not rich. If paul is old then john is tall and vice versa. Everyone who is humble is both rich and not happy. If someone is either calm or kind then someone is not quiet or not happy and vice versa. If fred is either tall or not kind then someone is both not quiet and not creative. Everyone who is not tall or kind is not generous and vice versa. If someone is not creative then someone is wise and vice versa. Everyone who is both not creative and creative is rich. Someone is brave. Lucy is either happy or creative. Someone is both not strong and curious. Alice is kind or strong. Someone is not brave. Someone is both kind and strong.

Lucy is not rich.

entailment

(![X]:((kind(X)|~wise(X))=>~quiet(X)))& (![X]:(quiet(X)<=>rich(X)))& (![X]:((~humble(X)<~>humble(X))<=>(wise(X)&~quiet(X))))& (((kind(paul)&patient(paul)))=>(?[X]:((curious(X)|~quiet(X)))))& (![X]:(~humble(X)<=>(~funny(X)|~brave(X))))& (((patient(alice)<~>calm(alice)))<=>(?[X]:((~funny(X)|old(X)))))& (((~tall(paul)<~>~patient(paul)))=>(?[X]:((kind(X)<~>brave(X)))))& (![X]:(rich(X)<=>(~old(X)&~quiet(X))))& (![X]:(kind(X)=>(~calm(X)|~rich(X))))& ((old(paul))<=>(tall(john)))& (![X]:(humble(X)=>(rich(X)&~happy(X))))& ((?[X]:((calm(X)<~>kind(X))))<=>(?[X]:((~quiet(X)|~happy(X)))))& (((tall(fred)<~>~kind(fred)))=>(?[X]:((~quiet(X)&~creative(X)))))& (![X]:((~tall(X)|kind(X))<=>~generous(X)))& ((?[X]:(~creative(X)))<=>(?[X]:(wise(X))))& (![X]:((~creative(X)&creative(X))=>rich(X)))& (?[X]:(brave(X)))& ((happy(lucy)<~>creative(lucy)))& (?[X]:((~strong(X)&curious(X))))& ((kind(alice)|strong(alice)))& (?[X]:(~brave(X)))& (?[X]:((kind(X)&strong(X))))

~rich(lucy)

% SZS status Unsatisfiable for 7287402733067043342769241 % SZS output start Proof for 7287402733067043342769241 2. ! [X0] : (quiet(X0) <=> rich(X0)) [input p1] 3. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~quiet(X0) & wise(X0))) [input p2] 23. rich(lucy) [input hypothesis] 36. ! [X0] : ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))) [nnf transformation 2] 37. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 3] 38. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 37] 76. ~rich(X0) | quiet(X0) [cnf transformation 36] 79. ~quiet(X0) | humble(X0) | humble(X0) [cnf transformation 38] 80. ~quiet(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 38] 125. rich(lucy) [cnf transformation 23] 128. ~quiet(X0) | humble(X0) [duplicate literal removal 79] 129. ~quiet(X0) | ~humble(X0) [duplicate literal removal 80] 130. ~quiet(X0) [subsumption resolution 128,129] 242. quiet(lucy) [resolution 76,125] 243. $false [subsumption resolution 242,130] % SZS output end Proof for 7287402733067043342769241 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.027 s % ------------------------------ % ------------------------------

Everyone who is both brave and not old is calm. Everyone who is not humble is not tall or not creative. Everyone who is tall or strong is strong or not happy and vice versa. Everyone who is funny or strong is both not generous and creative and vice versa. If john is funny then someone is both not tall and not creative and vice versa. Everyone who is happy is both generous and wise and vice versa. If someone is either tall or patient then fred is not calm. Everyone who is not happy is not curious or brave. If someone is not kind then mary is either happy or generous. Everyone who is patient is humble or strong. Everyone who is brave or not kind is either happy or humble and vice versa. Everyone who is patient or humble is both not brave and not wise. Everyone who is either not generous or generous is humble or not happy and vice versa. Everyone who is both funny and not funny is both old and not rich. If someone is not strong or not old then john is both not creative and not brave and vice versa. Everyone who is both not quiet and not curious is both calm and not brave and vice versa. Lucy is not creative. Alice is both humble and patient. Someone is either kind or not strong. Susan is both calm and humble. Lucy is not strong or not generous. Susan is humble or not strong. Fred is not funny.

Mary is tall.

entailment

(![X]:((brave(X)&~old(X))=>calm(X)))& (![X]:(~humble(X)=>(~tall(X)|~creative(X))))& (![X]:((tall(X)|strong(X))<=>(strong(X)|~happy(X))))& (![X]:((funny(X)|strong(X))<=>(~generous(X)&creative(X))))& ((funny(john))<=>(?[X]:((~tall(X)&~creative(X)))))& (![X]:(happy(X)<=>(generous(X)&wise(X))))& ((?[X]:((tall(X)<~>patient(X))))=>(~calm(fred)))& (![X]:(~happy(X)=>(~curious(X)|brave(X))))& ((?[X]:(~kind(X)))=>((happy(mary)<~>generous(mary))))& (![X]:(patient(X)=>(humble(X)|strong(X))))& (![X]:((brave(X)|~kind(X))<=>(happy(X)<~>humble(X))))& (![X]:((patient(X)|humble(X))=>(~brave(X)&~wise(X))))& (![X]:((~generous(X)<~>generous(X))<=>(humble(X)|~happy(X))))& (![X]:((funny(X)&~funny(X))=>(old(X)&~rich(X))))& ((?[X]:((~strong(X)|~old(X))))<=>((~creative(john)&~brave(john))))& (![X]:((~quiet(X)&~curious(X))<=>(calm(X)&~brave(X))))& (~creative(lucy))& ((humble(alice)&patient(alice)))& (?[X]:((kind(X)<~>~strong(X))))& ((calm(susan)&humble(susan)))& ((~strong(lucy)|~generous(lucy)))& ((humble(susan)|~strong(susan)))& (~funny(fred))

tall(mary)

% SZS status Unsatisfiable for 338222576103068584955105 % SZS output start Proof for 338222576103068584955105 3. ! [X0] : ((strong(X0) | tall(X0)) <=> (~happy(X0) | strong(X0))) [input p2] 4. ! [X0] : ((strong(X0) | funny(X0)) <=> (creative(X0) & ~generous(X0))) [input p3] 6. ! [X0] : (happy(X0) <=> (wise(X0) & generous(X0))) [input p5] 9. ? [X0] : ~kind(X0) => (happy(mary) <~> generous(mary)) [input p8] 11. ! [X0] : ((~kind(X0) | brave(X0)) <=> (happy(X0) <~> humble(X0))) [input p10] 12. ! [X0] : ((humble(X0) | patient(X0)) => (~wise(X0) & ~brave(X0))) [input p11] 18. patient(alice) & humble(alice) [input p17] 24. ~tall(mary) [input hypothesis] 33. (happy(mary) <~> generous(mary)) | ! [X0] : kind(X0) [ennf transformation 9] 36. ! [X0] : ((~wise(X0) & ~brave(X0)) | (~humble(X0) & ~patient(X0))) [ennf transformation 12] 39. ! [X0] : (((strong(X0) | tall(X0)) | (happy(X0) & ~strong(X0))) & ((~happy(X0) | strong(X0)) | (~strong(X0) & ~tall(X0)))) [nnf transformation 3] 40. ! [X0] : ((strong(X0) | tall(X0) | (happy(X0) & ~strong(X0))) & (~happy(X0) | strong(X0) | (~strong(X0) & ~tall(X0)))) [flattening 39] 41. ! [X0] : (((strong(X0) | funny(X0)) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | (~strong(X0) & ~funny(X0)))) [nnf transformation 4] 42. ! [X0] : ((strong(X0) | funny(X0) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | (~strong(X0) & ~funny(X0)))) [flattening 41] 47. ! [X0] : ((happy(X0) | (~wise(X0) | ~generous(X0))) & ((wise(X0) & generous(X0)) | ~happy(X0))) [nnf transformation 6] 48. ! [X0] : ((happy(X0) | ~wise(X0) | ~generous(X0)) & ((wise(X0) & generous(X0)) | ~happy(X0))) [flattening 47] 50. ((~generous(mary) | ~happy(mary)) & (generous(mary) | happy(mary))) | ! [X0] : kind(X0) [nnf transformation 33] 51. ! [X0] : (((~kind(X0) | brave(X0)) | ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0)))) & (((~humble(X0) | ~happy(X0)) & (humble(X0) | happy(X0))) | (kind(X0) & ~brave(X0)))) [nnf transformation 11] 52. ! [X0] : ((~kind(X0) | brave(X0) | ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0)))) & (((~humble(X0) | ~happy(X0)) & (humble(X0) | happy(X0))) | (kind(X0) & ~brave(X0)))) [flattening 51] 70. happy(X0) | tall(X0) | strong(X0) [cnf transformation 40] 72. ~generous(X0) | ~strong(X0) [cnf transformation 42] 79. ~happy(X0) | generous(X0) [cnf transformation 48] 80. ~happy(X0) | wise(X0) [cnf transformation 48] 85. generous(mary) | happy(mary) | kind(X0) [cnf transformation 50] 86. ~generous(mary) | ~happy(mary) | kind(X0) [cnf transformation 50] 93. ~kind(X0) | brave(X0) | happy(X0) | ~humble(X0) [cnf transformation 52] 95. ~humble(X0) | ~brave(X0) [cnf transformation 36] 96. ~patient(X0) | ~wise(X0) [cnf transformation 36] 115. humble(alice) [cnf transformation 18] 116. patient(alice) [cnf transformation 18] 124. ~tall(mary) [cnf transformation 24] 157. ~happy(mary) | kind(X0) [subsumption resolution 86,79] 159. 8 <=> ! [X0] : kind(X0) [avatar definition] 160. kind(X0) <- (8) [avatar component clause 159] 162. 9 <=> happy(mary) [avatar definition] 164. ~happy(mary) <- (~9) [avatar component clause 162] 165. 8 | ~9 [avatar split clause 157,162,159] 166. generous(mary) | kind(X0) [subsumption resolution 85,79] 168. 10 <=> generous(mary) [avatar definition] 170. generous(mary) <- (10) [avatar component clause 168] 171. 8 | 10 [avatar split clause 166,168,159] 213. ~strong(mary) <- (10) [resolution 72,170] 227. ~wise(alice) [resolution 96,116] 235. tall(mary) | strong(mary) <- (~9) [resolution 70,164] 241. strong(mary) <- (~9) [subsumption resolution 235,124] 242. $false <- (~9, 10) [subsumption resolution 241,213] 243. 9 | ~10 [avatar contradiction clause 242] 280. brave(X1) | happy(X1) | ~humble(X1) <- (8) [resolution 93,160] 283. ~humble(X1) | happy(X1) <- (8) [subsumption resolution 280,95] 284. happy(alice) <- (8) [resolution 283,115] 294. wise(alice) <- (8) [resolution 284,80] 297. $false <- (8) [subsumption resolution 294,227] 298. ~8 [avatar contradiction clause 297] 299. $false [avatar sat refutation 165,171,243,298] % SZS output end Proof for 338222576103068584955105 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

If fred is either not strong or brave then mary is both kind and happy. Everyone who is either not calm or strong is not calm. If someone is wise then someone is either not curious or funny. Everyone who is curious or generous is both not strong and humble and vice versa. Everyone who is creative or old is happy or kind. Everyone who is curious is both brave and not calm. If someone is not calm then someone is either patient or tall. Everyone who is not curious is both creative and not wise. Everyone who is not wise is quiet or not patient. Everyone who is both not wise and not old is strong and vice versa. Everyone who is either not creative or not brave is either not strong or strong and vice versa. Everyone who is patient or calm is both creative and not tall and vice versa. Everyone who is both not wise and not kind is rich or not creative. Everyone who is not calm or not tall is happy and vice versa. If alice is both not kind and not tall then alice is not brave. If paul is not happy or not tall then someone is both not quiet and rich. Lucy is not calm or not funny. Someone is rich. Someone is either not quiet or not kind. Someone is both not brave and strong. John is kind or wise. Alice is brave. Someone is either not rich or quiet.

John is wise.

neutral

(((~strong(fred)<~>brave(fred)))=>((kind(mary)&happy(mary))))& (![X]:((~calm(X)<~>strong(X))=>~calm(X)))& ((?[X]:(wise(X)))=>(?[X]:((~curious(X)<~>funny(X)))))& (![X]:((curious(X)|generous(X))<=>(~strong(X)&humble(X))))& (![X]:((creative(X)|old(X))=>(happy(X)|kind(X))))& (![X]:(curious(X)=>(brave(X)&~calm(X))))& ((?[X]:(~calm(X)))=>(?[X]:((patient(X)<~>tall(X)))))& (![X]:(~curious(X)=>(creative(X)&~wise(X))))& (![X]:(~wise(X)=>(quiet(X)|~patient(X))))& (![X]:((~wise(X)&~old(X))<=>strong(X)))& (![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))& (![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))& (![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))& (![X]:((~calm(X)|~tall(X))<=>happy(X)))& (((~kind(alice)&~tall(alice)))=>(~brave(alice)))& (((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))& ((~calm(lucy)|~funny(lucy)))& (?[X]:(rich(X)))& (?[X]:((~quiet(X)<~>~kind(X))))& (?[X]:((~brave(X)&strong(X))))& ((kind(john)|wise(john)))& (brave(alice))& (?[X]:((~rich(X)<~>quiet(X))))

wise(john)

If someone is either strong or calm then someone is both not patient and generous. Everyone who is either calm or old is not generous or patient. Everyone who is not patient or not curious is not kind or not humble. Everyone who is either not humble or not generous is both not creative and wise and vice versa. Everyone who is not old or not strong is either creative or old. Everyone who is not strong or not quiet is not humble and vice versa. Everyone who is not generous or not happy is not old. If someone is either not humble or quiet then paul is not generous. Everyone who is quiet is either strong or not funny. Everyone who is wise or rich is humble or funny. Everyone who is either not creative or not quiet is both not old and brave. If john is calm then someone is either not humble or not strong. If mary is quiet or not strong then paul is both not generous and rich and vice versa. Everyone who is either not funny or strong is not happy or humble and vice versa. Everyone who is either not calm or not creative is not curious and vice versa. If someone is both not brave and not humble then susan is not calm and vice versa. John is not humble. Someone is not happy or wise. Mary is not humble or rich. Someone is tall. Susan is either not generous or not strong. Someone is not brave. Someone is not calm. Someone is both not generous and calm.

Paul is not quiet.

neutral

((?[X]:((strong(X)<~>calm(X))))=>(?[X]:((~patient(X)&generous(X)))))& (![X]:((calm(X)<~>old(X))=>(~generous(X)|patient(X))))& (![X]:((~patient(X)|~curious(X))=>(~kind(X)|~humble(X))))& (![X]:((~humble(X)<~>~generous(X))<=>(~creative(X)&wise(X))))& (![X]:((~old(X)|~strong(X))=>(creative(X)<~>old(X))))& (![X]:((~strong(X)|~quiet(X))<=>~humble(X)))& (![X]:((~generous(X)|~happy(X))=>~old(X)))& ((?[X]:((~humble(X)<~>quiet(X))))=>(~generous(paul)))& (![X]:(quiet(X)=>(strong(X)<~>~funny(X))))& (![X]:((wise(X)|rich(X))=>(humble(X)|funny(X))))& (![X]:((~creative(X)<~>~quiet(X))=>(~old(X)&brave(X))))& ((calm(john))=>(?[X]:((~humble(X)<~>~strong(X)))))& (((quiet(mary)|~strong(mary)))<=>((~generous(paul)&rich(paul))))& (![X]:((~funny(X)<~>strong(X))<=>(~happy(X)|humble(X))))& (![X]:((~calm(X)<~>~creative(X))<=>~curious(X)))& ((?[X]:((~brave(X)&~humble(X))))<=>(~calm(susan)))& (~humble(john))& (?[X]:((~happy(X)|wise(X))))& ((~humble(mary)|rich(mary)))& (?[X]:(tall(X)))& ((~generous(susan)<~>~strong(susan)))& (?[X]:(~brave(X)))& (?[X]:(~calm(X)))& (?[X]:((~generous(X)&calm(X))))

~quiet(paul)

Everyone who is not brave or humble is brave. Everyone who is old is either patient or strong. If alice is both not curious and curious then john is generous or rich. If someone is either funny or not patient then paul is curious and vice versa. If paul is not creative or curious then someone is not rich or kind. If fred is not brave or not wise then someone is not curious. Everyone who is either curious or tall is either not rich or patient. Everyone who is either not kind or kind is strong or not creative. If john is either quiet or patient then someone is generous or not calm. If mary is either rich or not quiet then mary is either curious or not tall and vice versa. If someone is both not quiet and not calm then someone is not patient or calm and vice versa. If someone is both curious and not rich then lucy is both not brave and not wise and vice versa. Everyone who is both patient and old is both not old and happy and vice versa. If alice is wise then john is rich or not curious and vice versa. Everyone who is not happy is brave or strong. If someone is either wise or patient then someone is both generous and not rich. Susan is calm. Someone is funny or not tall. Susan is either strong or not patient. Someone is either not brave or not funny. Lucy is both wise and kind. Someone is strong or wise. Someone is not wise or old.

Mary is not brave.

contradiction

(![X]:((~brave(X)|humble(X))=>brave(X)))& (![X]:(old(X)=>(patient(X)<~>strong(X))))& (((~curious(alice)&curious(alice)))=>((generous(john)|rich(john))))& ((?[X]:((funny(X)<~>~patient(X))))<=>(curious(paul)))& (((~creative(paul)|curious(paul)))=>(?[X]:((~rich(X)|kind(X)))))& (((~brave(fred)|~wise(fred)))=>(?[X]:(~curious(X))))& (![X]:((curious(X)<~>tall(X))=>(~rich(X)<~>patient(X))))& (![X]:((~kind(X)<~>kind(X))=>(strong(X)|~creative(X))))& (((quiet(john)<~>patient(john)))=>(?[X]:((generous(X)|~calm(X)))))& (((rich(mary)<~>~quiet(mary)))<=>((curious(mary)<~>~tall(mary))))& ((?[X]:((~quiet(X)&~calm(X))))<=>(?[X]:((~patient(X)|calm(X)))))& ((?[X]:((curious(X)&~rich(X))))<=>((~brave(lucy)&~wise(lucy))))& (![X]:((patient(X)&old(X))<=>(~old(X)&happy(X))))& ((wise(alice))<=>((rich(john)|~curious(john))))& (![X]:(~happy(X)=>(brave(X)|strong(X))))& ((?[X]:((wise(X)<~>patient(X))))=>(?[X]:((generous(X)&~rich(X)))))& (calm(susan))& (?[X]:((funny(X)|~tall(X))))& ((strong(susan)<~>~patient(susan)))& (?[X]:((~brave(X)<~>~funny(X))))& ((wise(lucy)&kind(lucy)))& (?[X]:((strong(X)|wise(X))))& (?[X]:((~wise(X)|old(X))))

~brave(mary)

% SZS status Unsatisfiable for 7834076326458468412802131 % SZS output start Proof for 7834076326458468412802131 1. ! [X0] : ((humble(X0) | ~brave(X0)) => brave(X0)) [input p0] 24. ~brave(mary) [input hypothesis] 30. ! [X0] : (~brave(X0) => brave(X0)) [pure predicate removal 1] 31. ! [X0] : (brave(X0) | brave(X0)) [ennf transformation 30] 81. brave(X0) | brave(X0) [cnf transformation 31] 135. ~brave(mary) [cnf transformation 24] 140. brave(X0) [duplicate literal removal 81] 317. $false [subsumption resolution 135,140] % SZS output end Proof for 7834076326458468412802131 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

If someone is either patient or brave then alice is funny or not tall. Everyone who is either not rich or not creative is both not humble and not calm and vice versa. Everyone who is both not tall and brave is generous or not tall and vice versa. Everyone who is both not creative and not humble is either patient or brave and vice versa. If john is generous then someone is either patient or rich and vice versa. Everyone who is not strong or not tall is either not brave or not tall and vice versa. Everyone who is both rich and not kind is generous or not generous and vice versa. Everyone who is generous or strong is not old and vice versa. Everyone who is either rich or not wise is humble and vice versa. If paul is both not tall and not curious then susan is calm or not patient and vice versa. If someone is either rich or old then someone is both not rich and wise. If paul is both kind and old then john is both old and not generous. Everyone who is generous or not funny is curious and vice versa. If mary is either rich or not humble then mary is not funny and vice versa. Everyone who is either funny or quiet is old and vice versa. Someone is both funny and brave. Lucy is both not humble and not quiet. John is either quiet or not humble. Someone is funny or patient. Someone is old or curious. Someone is not wise or not generous.

Susan is not patient.

contradiction

((?[X]:((patient(X)<~>brave(X))))=>((funny(alice)|~tall(alice))))& (![X]:((~rich(X)<~>~creative(X))<=>(~humble(X)&~calm(X))))& (![X]:((~tall(X)&brave(X))<=>(generous(X)|~tall(X))))& (![X]:((~creative(X)&~humble(X))<=>(patient(X)<~>brave(X))))& ((generous(john))<=>(?[X]:((patient(X)<~>rich(X)))))& (![X]:((~strong(X)|~tall(X))<=>(~brave(X)<~>~tall(X))))& (![X]:((rich(X)&~kind(X))<=>(generous(X)|~generous(X))))& (![X]:((generous(X)|strong(X))<=>~old(X)))& (![X]:((rich(X)<~>~wise(X))<=>humble(X)))& (((~tall(paul)&~curious(paul)))<=>((calm(susan)|~patient(susan))))& ((?[X]:((rich(X)<~>old(X))))=>(?[X]:((~rich(X)&wise(X)))))& (((kind(paul)&old(paul)))=>((old(john)&~generous(john))))& (![X]:((generous(X)|~funny(X))<=>curious(X)))& (((rich(mary)<~>~humble(mary)))<=>(~funny(mary)))& (![X]:((funny(X)<~>quiet(X))<=>old(X)))& (?[X]:((funny(X)&brave(X))))& ((~humble(lucy)&~quiet(lucy)))& ((quiet(john)<~>~humble(john)))& (?[X]:((funny(X)|patient(X))))& (?[X]:((old(X)|curious(X))))& (?[X]:((~wise(X)|~generous(X))))

~patient(susan)

% SZS status Unsatisfiable for 7235698036064304731835455 % SZS output start Proof for 7235698036064304731835455 5. generous(john) <=> ? [X0] : (patient(X0) <~> rich(X0)) [input p4] 7. ! [X0] : ((~kind(X0) & rich(X0)) <=> (~generous(X0) | generous(X0))) [input p6] 8. ! [X0] : ((strong(X0) | generous(X0)) <=> ~old(X0)) [input p7] 11. ? [X0] : (rich(X0) <~> old(X0)) => ? [X0] : (wise(X0) & ~rich(X0)) [input p10] 22. ~patient(susan) [input hypothesis] 23. ? [X0] : (rich(X0) <~> old(X0)) => ? [X1] : (wise(X1) & ~rich(X1)) [rectify 11] 26. ? [X1] : (wise(X1) & ~rich(X1)) | ! [X0] : (rich(X0) <=> old(X0)) [ennf transformation 23] 36. (generous(john) | ! [X0] : ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0)))) & (? [X0] : ((~rich(X0) | ~patient(X0)) & (rich(X0) | patient(X0))) | ~generous(john)) [nnf transformation 5] 37. (generous(john) | ! [X0] : ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0)))) & (? [X1] : ((~rich(X1) | ~patient(X1)) & (rich(X1) | patient(X1))) | ~generous(john)) [rectify 36] 38. ? [X1] : ((~rich(X1) | ~patient(X1)) & (rich(X1) | patient(X1))) => ((~rich(sK0) | ~patient(sK0)) & (rich(sK0) | patient(sK0))) [choice axiom] 39. (generous(john) | ! [X0] : ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0)))) & (((~rich(sK0) | ~patient(sK0)) & (rich(sK0) | patient(sK0))) | ~generous(john)) [skolemisation 37,38] 42. ! [X0] : (((~kind(X0) & rich(X0)) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 7] 43. ! [X0] : (((~kind(X0) & rich(X0)) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | kind(X0) | ~rich(X0))) [flattening 42] 44. ! [X0] : (((strong(X0) | generous(X0)) | old(X0)) & (~old(X0) | (~strong(X0) & ~generous(X0)))) [nnf transformation 8] 45. ! [X0] : ((strong(X0) | generous(X0) | old(X0)) & (~old(X0) | (~strong(X0) & ~generous(X0)))) [flattening 44] 49. ? [X1] : (wise(X1) & ~rich(X1)) | ! [X0] : ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))) [nnf transformation 26] 50. ? [X0] : (wise(X0) & ~rich(X0)) | ! [X1] : ((rich(X1) | ~old(X1)) & (old(X1) | ~rich(X1))) [rectify 49] 51. ? [X0] : (wise(X0) & ~rich(X0)) => (wise(sK1) & ~rich(sK1)) [choice axiom] 52. (wise(sK1) & ~rich(sK1)) | ! [X1] : ((rich(X1) | ~old(X1)) & (old(X1) | ~rich(X1))) [skolemisation 50,51] 88. generous(john) | patient(X0) | ~rich(X0) [cnf transformation 39] 96. rich(X0) | ~generous(X0) [cnf transformation 43] 97. generous(X0) | rich(X0) [cnf transformation 43] 100. ~old(X0) | ~generous(X0) [cnf transformation 45] 112. ~rich(sK1) | old(X1) | ~rich(X1) [cnf transformation 52] 138. ~patient(susan) [cnf transformation 22] 158. 5 <=> ! [X0] : (patient(X0) | ~rich(X0)) [avatar definition] 159. patient(X0) | ~rich(X0) <- (5) [avatar component clause 158] 161. 6 <=> generous(john) [avatar definition] 163. generous(john) <- (6) [avatar component clause 161] 164. 5 | 6 [avatar split clause 88,161,158] 181. rich(X0) [subsumption resolution 96,97] 185. 10 <=> patient(susan) [avatar definition] 186. ~patient(susan) <- (~10) [avatar component clause 185] 207. 14 <=> ! [X1] : old(X1) [avatar definition] 208. old(X1) <- (14) [avatar component clause 207] 214. old(X1) | ~rich(X1) [subsumption resolution 112,181] 215. old(X1) [subsumption resolution 214,181] 216. 14 [avatar split clause 215,207] 266. ~10 [avatar split clause 138,185] 267. patient(X0) <- (5) [subsumption resolution 159,181] 268. $false <- (5, ~10) [resolution 267,186] 269. ~5 | 10 [avatar contradiction clause 268] 279. ~generous(X0) <- (14) [resolution 100,208] 281. $false <- (6, 14) [resolution 279,163] 283. ~6 | ~14 [avatar contradiction clause 281] 284. $false [avatar sat refutation 164,216,266,269,283] % SZS output end Proof for 7235698036064304731835455 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.019 s % ------------------------------ % ------------------------------

Everyone who is kind or not wise is not quiet. Everyone who is quiet is rich and vice versa. Everyone who is either not humble or humble is both wise and not quiet and vice versa. If paul is both kind and patient then someone is curious or not quiet. Everyone who is not humble is not funny or not brave and vice versa. If alice is either patient or calm then someone is not funny or old and vice versa. If paul is either not tall or not patient then someone is either kind or brave. Everyone who is rich is both not old and not quiet and vice versa. Everyone who is kind is not calm or not rich. If paul is old then john is tall and vice versa. Everyone who is humble is both rich and not happy. If someone is either calm or kind then someone is not quiet or not happy and vice versa. If fred is either tall or not kind then someone is both not quiet and not creative. Everyone who is not tall or kind is not generous and vice versa. If someone is not creative then someone is wise and vice versa. Everyone who is both not creative and creative is rich. Someone is brave. Lucy is either happy or creative. Someone is both not strong and curious. Alice is kind or strong. Someone is not brave. Someone is both kind and strong.

Paul is not funny.

neutral

(![X]:((kind(X)|~wise(X))=>~quiet(X)))& (![X]:(quiet(X)<=>rich(X)))& (![X]:((~humble(X)<~>humble(X))<=>(wise(X)&~quiet(X))))& (((kind(paul)&patient(paul)))=>(?[X]:((curious(X)|~quiet(X)))))& (![X]:(~humble(X)<=>(~funny(X)|~brave(X))))& (((patient(alice)<~>calm(alice)))<=>(?[X]:((~funny(X)|old(X)))))& (((~tall(paul)<~>~patient(paul)))=>(?[X]:((kind(X)<~>brave(X)))))& (![X]:(rich(X)<=>(~old(X)&~quiet(X))))& (![X]:(kind(X)=>(~calm(X)|~rich(X))))& ((old(paul))<=>(tall(john)))& (![X]:(humble(X)=>(rich(X)&~happy(X))))& ((?[X]:((calm(X)<~>kind(X))))<=>(?[X]:((~quiet(X)|~happy(X)))))& (((tall(fred)<~>~kind(fred)))=>(?[X]:((~quiet(X)&~creative(X)))))& (![X]:((~tall(X)|kind(X))<=>~generous(X)))& ((?[X]:(~creative(X)))<=>(?[X]:(wise(X))))& (![X]:((~creative(X)&creative(X))=>rich(X)))& (?[X]:(brave(X)))& ((happy(lucy)<~>creative(lucy)))& (?[X]:((~strong(X)&curious(X))))& ((kind(alice)|strong(alice)))& (?[X]:(~brave(X)))& (?[X]:((kind(X)&strong(X))))

~funny(paul)

If alice is curious or generous then someone is humble or not wise and vice versa. Everyone who is strong or not humble is both humble and calm. If someone is both generous and funny then someone is either funny or quiet and vice versa. Everyone who is both not funny and not quiet is calm and vice versa. If lucy is not rich or strong then paul is either not creative or kind and vice versa. If someone is either not tall or rich then someone is patient or kind and vice versa. Everyone who is creative or not funny is both patient and not old and vice versa. Everyone who is curious or funny is either rich or quiet. If someone is either rich or not happy then john is not patient. Everyone who is either brave or patient is both quiet and not old. Everyone who is generous or not strong is either old or strong. If someone is not curious or not quiet then fred is rich. Everyone who is not brave or generous is either tall or curious and vice versa. If fred is not brave or calm then someone is not funny. Everyone who is funny is either brave or patient. If susan is either tall or curious then someone is either strong or not funny and vice versa. Mary is creative or not creative. Someone is not quiet or wise. Mary is generous. Someone is either not humble or kind. Alice is both tall and not old. Alice is both not wise and not old.

Mary is not quiet.

entailment

(((curious(alice)|generous(alice)))<=>(?[X]:((humble(X)|~wise(X)))))& (![X]:((strong(X)|~humble(X))=>(humble(X)&calm(X))))& ((?[X]:((generous(X)&funny(X))))<=>(?[X]:((funny(X)<~>quiet(X)))))& (![X]:((~funny(X)&~quiet(X))<=>calm(X)))& (((~rich(lucy)|strong(lucy)))<=>((~creative(paul)<~>kind(paul))))& ((?[X]:((~tall(X)<~>rich(X))))<=>(?[X]:((patient(X)|kind(X)))))& (![X]:((creative(X)|~funny(X))<=>(patient(X)&~old(X))))& (![X]:((curious(X)|funny(X))=>(rich(X)<~>quiet(X))))& ((?[X]:((rich(X)<~>~happy(X))))=>(~patient(john)))& (![X]:((brave(X)<~>patient(X))=>(quiet(X)&~old(X))))& (![X]:((generous(X)|~strong(X))=>(old(X)<~>strong(X))))& ((?[X]:((~curious(X)|~quiet(X))))=>(rich(fred)))& (![X]:((~brave(X)|generous(X))<=>(tall(X)<~>curious(X))))& (((~brave(fred)|calm(fred)))=>(?[X]:(~funny(X))))& (![X]:(funny(X)=>(brave(X)<~>patient(X))))& (((tall(susan)<~>curious(susan)))<=>(?[X]:((strong(X)<~>~funny(X)))))& ((creative(mary)|~creative(mary)))& (?[X]:((~quiet(X)|wise(X))))& (generous(mary))& (?[X]:((~humble(X)<~>kind(X))))& ((tall(alice)&~old(alice)))& ((~wise(alice)&~old(alice)))

~quiet(mary)

% SZS status Unsatisfiable for 5846778076535272110947587 % SZS output start Proof for 5846778076535272110947587 2. ! [X0] : ((~humble(X0) | strong(X0)) => (calm(X0) & humble(X0))) [input p1] 3. ? [X0] : (funny(X0) & generous(X0)) <=> ? [X0] : (funny(X0) <~> quiet(X0)) [input p2] 4. ! [X0] : ((~quiet(X0) & ~funny(X0)) <=> calm(X0)) [input p3] 7. ! [X0] : ((~funny(X0) | creative(X0)) <=> (~old(X0) & patient(X0))) [input p6] 10. ! [X0] : ((brave(X0) <~> patient(X0)) => (~old(X0) & quiet(X0))) [input p9] 11. ! [X0] : ((~strong(X0) | generous(X0)) => (old(X0) <~> strong(X0))) [input p10] 15. ! [X0] : (funny(X0) => (brave(X0) <~> patient(X0))) [input p14] 16. (tall(susan) <~> curious(susan)) <=> ? [X0] : (strong(X0) <~> ~funny(X0)) [input p15] 19. generous(mary) [input p18] 23. quiet(mary) [input hypothesis] 24. ? [X0] : (funny(X0) & generous(X0)) <=> ? [X1] : (funny(X1) <~> quiet(X1)) [rectify 3] 26. ! [X0] : ((calm(X0) & humble(X0)) | (humble(X0) & ~strong(X0))) [ennf transformation 2] 29. ! [X0] : ((~old(X0) & quiet(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 10] 30. ! [X0] : ((old(X0) <~> strong(X0)) | (strong(X0) & ~generous(X0))) [ennf transformation 11] 33. ! [X0] : ((brave(X0) <~> patient(X0)) | ~funny(X0)) [ennf transformation 15] 39. (? [X0] : (funny(X0) & generous(X0)) | ! [X1] : ((funny(X1) | ~quiet(X1)) & (quiet(X1) | ~funny(X1)))) & (? [X1] : ((~quiet(X1) | ~funny(X1)) & (quiet(X1) | funny(X1))) | ! [X0] : (~funny(X0) | ~generous(X0))) [nnf transformation 24] 40. (? [X0] : (funny(X0) & generous(X0)) | ! [X1] : ((funny(X1) | ~quiet(X1)) & (quiet(X1) | ~funny(X1)))) & (? [X2] : ((~quiet(X2) | ~funny(X2)) & (quiet(X2) | funny(X2))) | ! [X3] : (~funny(X3) | ~generous(X3))) [rectify 39] 41. ? [X0] : (funny(X0) & generous(X0)) => (funny(sK1) & generous(sK1)) [choice axiom] 42. ? [X2] : ((~quiet(X2) | ~funny(X2)) & (quiet(X2) | funny(X2))) => ((~quiet(sK2) | ~funny(sK2)) & (quiet(sK2) | funny(sK2))) [choice axiom] 43. ((funny(sK1) & generous(sK1)) | ! [X1] : ((funny(X1) | ~quiet(X1)) & (quiet(X1) | ~funny(X1)))) & (((~quiet(sK2) | ~funny(sK2)) & (quiet(sK2) | funny(sK2))) | ! [X3] : (~funny(X3) | ~generous(X3))) [skolemisation 40,42,41] 44. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) | funny(X0)))) [nnf transformation 4] 45. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | quiet(X0) | funny(X0))) [flattening 44] 53. ! [X0] : (((~funny(X0) | creative(X0)) | (old(X0) | ~patient(X0))) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [nnf transformation 7] 54. ! [X0] : ((~funny(X0) | creative(X0) | old(X0) | ~patient(X0)) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [flattening 53] 57. ! [X0] : ((~old(X0) & quiet(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 29] 58. ! [X0] : (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (strong(X0) & ~generous(X0))) [nnf transformation 30] 63. ! [X0] : (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~funny(X0)) [nnf transformation 33] 64. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (? [X0] : ((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [nnf transformation 16] 65. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (? [X1] : ((funny(X1) | ~strong(X1)) & (~funny(X1) | strong(X1))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [rectify 64] 66. ? [X1] : ((funny(X1) | ~strong(X1)) & (~funny(X1) | strong(X1))) => ((funny(sK6) | ~strong(sK6)) & (~funny(sK6) | strong(sK6))) [choice axiom] 67. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (((funny(sK6) | ~strong(sK6)) & (~funny(sK6) | strong(sK6))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [skolemisation 65,66] 79. ~strong(X0) | calm(X0) [cnf transformation 26] 81. quiet(sK2) | funny(sK2) | ~funny(X3) | ~generous(X3) [cnf transformation 43] 82. ~quiet(sK2) | ~funny(sK2) | ~funny(X3) | ~generous(X3) [cnf transformation 43] 83. generous(sK1) | quiet(X1) | ~funny(X1) [cnf transformation 43] 84. generous(sK1) | funny(X1) | ~quiet(X1) [cnf transformation 43] 86. funny(sK1) | funny(X1) | ~quiet(X1) [cnf transformation 43] 88. ~funny(X0) | ~calm(X0) [cnf transformation 45] 103. patient(X0) | funny(X0) [cnf transformation 54] 105. ~old(X0) | funny(X0) [cnf transformation 54] 113. ~brave(X0) | patient(X0) | quiet(X0) [cnf transformation 57] 115. ~brave(X0) | patient(X0) | ~old(X0) [cnf transformation 57] 116. ~old(X0) | brave(X0) | ~patient(X0) [cnf transformation 57] 118. strong(X0) | old(X0) | strong(X0) [cnf transformation 58] 131. patient(X0) | brave(X0) | ~funny(X0) [cnf transformation 63] 132. ~brave(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 63] 133. ~funny(sK6) | strong(sK6) | curious(susan) | ~tall(susan) [cnf transformation 67] 134. ~funny(sK6) | strong(sK6) | tall(susan) | ~curious(susan) [cnf transformation 67] 135. funny(sK6) | ~strong(sK6) | curious(susan) | ~tall(susan) [cnf transformation 67] 136. funny(sK6) | ~strong(sK6) | tall(susan) | ~curious(susan) [cnf transformation 67] 137. curious(susan) | tall(susan) | ~funny(X0) | ~strong(X0) [cnf transformation 67] 139. ~curious(susan) | ~tall(susan) | ~funny(X0) | ~strong(X0) [cnf transformation 67] 143. generous(mary) [cnf transformation 19] 150. quiet(mary) [cnf transformation 23] 151. old(X0) | strong(X0) [duplicate literal removal 118] 180. 7 <=> ! [X1] : (funny(X1) | ~quiet(X1)) [avatar definition] 181. ~quiet(X1) | funny(X1) <- (7) [avatar component clause 180] 183. 8 <=> funny(sK1) [avatar definition] 185. funny(sK1) <- (8) [avatar component clause 183] 186. 7 | 8 [avatar split clause 86,183,180] 188. 9 <=> ! [X1] : (quiet(X1) | ~funny(X1)) [avatar definition] 189. ~funny(X1) | quiet(X1) <- (9) [avatar component clause 188] 192. 10 <=> generous(sK1) [avatar definition] 194. generous(sK1) <- (10) [avatar component clause 192] 195. 7 | 10 [avatar split clause 84,192,180] 196. 9 | 10 [avatar split clause 83,192,188] 198. 11 <=> ! [X3] : (~funny(X3) | ~generous(X3)) [avatar definition] 199. ~funny(X3) | ~generous(X3) <- (11) [avatar component clause 198] 201. 12 <=> funny(sK2) [avatar definition] 202. funny(sK2) <- (12) [avatar component clause 201] 203. ~funny(sK2) <- (~12) [avatar component clause 201] 205. 13 <=> quiet(sK2) [avatar definition] 206. quiet(sK2) <- (13) [avatar component clause 205] 207. ~quiet(sK2) <- (~13) [avatar component clause 205] 208. 11 | ~12 | ~13 [avatar split clause 82,205,201,198] 209. 11 | 12 | 13 [avatar split clause 81,205,201,198] 304. brave(X0) | patient(X0) [subsumption resolution 131,103] 306. 35 <=> ! [X0] : (strong(X0) | funny(X0)) [avatar definition] 307. funny(X0) | strong(X0) <- (35) [avatar component clause 306] 309. 36 <=> tall(susan) [avatar definition] 313. 37 <=> curious(susan) [avatar definition] 318. 38 <=> ! [X0] : (~funny(X0) | ~strong(X0)) [avatar definition] 319. ~funny(X0) | ~strong(X0) <- (38) [avatar component clause 318] 320. 38 | ~36 | ~37 [avatar split clause 139,313,309,318] 322. 38 | 36 | 37 [avatar split clause 137,313,309,318] 324. 39 <=> strong(sK6) [avatar definition] 325. strong(sK6) <- (39) [avatar component clause 324] 328. 40 <=> funny(sK6) [avatar definition] 329. ~funny(sK6) <- (~40) [avatar component clause 328] 330. funny(sK6) <- (40) [avatar component clause 328] 331. ~37 | 36 | ~39 | 40 [avatar split clause 136,328,324,309,313] 332. ~36 | 37 | ~39 | 40 [avatar split clause 135,328,324,313,309] 333. ~37 | 36 | 39 | ~40 [avatar split clause 134,328,324,309,313] 334. ~36 | 37 | 39 | ~40 [avatar split clause 133,328,324,313,309] 351. strong(X0) | funny(X0) [resolution 151,105] 353. 35 [avatar split clause 351,306] 354. funny(mary) <- (7) [resolution 181,150] 360. ~generous(mary) <- (7, 11) [resolution 199,354] 361. $false <- (7, 11) [subsumption resolution 360,143] 362. ~7 | ~11 [avatar contradiction clause 361] 363. ~generous(sK1) <- (8, 11) [resolution 185,199] 366. $false <- (8, 10, 11) [subsumption resolution 363,194] 367. ~8 | ~10 | ~11 [avatar contradiction clause 366] 368. quiet(sK2) <- (9, 12) [resolution 202,189] 370. $false <- (9, 12, ~13) [subsumption resolution 368,207] 371. ~9 | ~12 | 13 [avatar contradiction clause 370] 375. strong(sK6) <- (35, ~40) [resolution 307,329] 379. 39 | ~35 | 40 [avatar split clause 375,328,306,324] 380. calm(sK6) <- (39) [resolution 325,79] 384. ~strong(sK1) <- (8, 38) [resolution 319,185] 454. patient(X0) | quiet(X0) | patient(X0) [resolution 113,304] 455. patient(X0) | quiet(X0) [duplicate literal removal 454] 478. patient(X0) | ~old(X0) | patient(X0) [resolution 115,304] 479. ~old(X0) | patient(X0) [duplicate literal removal 478] 481. brave(X0) | ~patient(X0) | strong(X0) [resolution 116,151] 482. brave(X0) | strong(X0) [subsumption resolution 481,304] 576. patient(X0) | strong(X0) [resolution 479,151] 579. strong(X2) | ~patient(X2) | ~funny(X2) [resolution 482,132] 582. ~patient(X2) | ~funny(X2) <- (38) [subsumption resolution 579,319] 714. ~funny(X0) | strong(X0) <- (38) [resolution 582,576] 715. ~funny(X1) | quiet(X1) <- (38) [resolution 582,455] 719. strong(X0) <- (35, 38) [subsumption resolution 714,307] 720. 9 | ~38 [avatar split clause 715,318,188] 732. $false <- (8, 35, 38) [resolution 719,384] 733. ~8 | ~35 | ~38 [avatar contradiction clause 732] 741. funny(sK2) <- (7, 13) [resolution 181,206] 744. $false <- (7, ~12, 13) [subsumption resolution 741,203] 745. ~7 | 12 | ~13 [avatar contradiction clause 744] 781. ~calm(sK6) <- (40) [resolution 330,88] 782. $false <- (39, 40) [subsumption resolution 781,380] 783. ~39 | ~40 [avatar contradiction clause 782] 784. $false [avatar sat refutation 186,195,196,208,209,320,322,331,332,333,334,353,362,367,371,379,720,733,745,783] % SZS output end Proof for 5846778076535272110947587 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.031 s % ------------------------------ % ------------------------------

If alice is patient then alice is either creative or not tall and vice versa. Everyone who is calm is either kind or not rich. If alice is not calm then someone is either not wise or patient. If lucy is calm or not old then lucy is either not calm or not wise. If someone is either not humble or humble then mary is both calm and not quiet and vice versa. Everyone who is generous or not funny is both brave and kind and vice versa. If lucy is both happy and not brave then someone is not rich or not calm and vice versa. If someone is either not old or not brave then someone is not brave. Everyone who is old is not rich and vice versa. If susan is both not happy and curious then alice is not calm or wise and vice versa. Everyone who is both generous and not happy is old or not funny and vice versa. If fred is old or not strong then someone is happy or kind and vice versa. If someone is brave or not creative then lucy is either tall or funny and vice versa. If alice is quiet or not patient then someone is both tall and strong and vice versa. Everyone who is both not curious and not kind is calm. If john is both wise and not patient then paul is either not creative or not kind and vice versa. John is both not calm and not brave. Mary is both not patient and kind. Someone is not happy or not generous. Fred is both strong and humble. Someone is brave. Alice is rich or not wise. Someone is either not strong or not calm. Someone is both old and not tall.

Lucy is not rich.

contradiction

((patient(alice))<=>((creative(alice)<~>~tall(alice))))& (![X]:(calm(X)=>(kind(X)<~>~rich(X))))& ((~calm(alice))=>(?[X]:((~wise(X)<~>patient(X)))))& (((calm(lucy)|~old(lucy)))=>((~calm(lucy)<~>~wise(lucy))))& ((?[X]:((~humble(X)<~>humble(X))))<=>((calm(mary)&~quiet(mary))))& (![X]:((generous(X)|~funny(X))<=>(brave(X)&kind(X))))& (((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))& ((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))& (![X]:(old(X)<=>~rich(X)))& (((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))& (![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))& (((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))& ((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))& (((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))& (![X]:((~curious(X)&~kind(X))=>calm(X)))& (((wise(john)&~patient(john)))<=>((~creative(paul)<~>~kind(paul))))& ((~calm(john)&~brave(john)))& ((~patient(mary)&kind(mary)))& (?[X]:((~happy(X)|~generous(X))))& ((strong(fred)&humble(fred)))& (?[X]:(brave(X)))& ((rich(alice)|~wise(alice)))& (?[X]:((~strong(X)<~>~calm(X))))& (?[X]:((old(X)&~tall(X))))

~rich(lucy)

% SZS status Unsatisfiable for 6591653130908651102759696 % SZS output start Proof for 6591653130908651102759696 6. ! [X0] : ((~funny(X0) | generous(X0)) <=> (kind(X0) & brave(X0))) [input p5] 7. (~brave(lucy) & happy(lucy)) <=> ? [X0] : (~calm(X0) | ~rich(X0)) [input p6] 9. ! [X0] : (old(X0) <=> ~rich(X0)) [input p8] 11. ! [X0] : ((~happy(X0) & generous(X0)) <=> (~funny(X0) | old(X0))) [input p10] 17. ~brave(john) & ~calm(john) [input p16] 25. ~rich(lucy) [input hypothesis] 44. ! [X0] : (((~funny(X0) | generous(X0)) | (~kind(X0) | ~brave(X0))) & ((kind(X0) & brave(X0)) | (funny(X0) & ~generous(X0)))) [nnf transformation 6] 45. ! [X0] : ((~funny(X0) | generous(X0) | ~kind(X0) | ~brave(X0)) & ((kind(X0) & brave(X0)) | (funny(X0) & ~generous(X0)))) [flattening 44] 46. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & (? [X0] : (~calm(X0) | ~rich(X0)) | (brave(lucy) | ~happy(lucy))) [nnf transformation 7] 47. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & (? [X0] : (~calm(X0) | ~rich(X0)) | brave(lucy) | ~happy(lucy)) [flattening 46] 48. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & (? [X1] : (~calm(X1) | ~rich(X1)) | brave(lucy) | ~happy(lucy)) [rectify 47] 49. ? [X1] : (~calm(X1) | ~rich(X1)) => (~calm(sK2) | ~rich(sK2)) [choice axiom] 50. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & ((~calm(sK2) | ~rich(sK2)) | brave(lucy) | ~happy(lucy)) [skolemisation 48,49] 55. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 9] 58. ! [X0] : (((~happy(X0) & generous(X0)) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | (happy(X0) | ~generous(X0)))) [nnf transformation 11] 59. ! [X0] : (((~happy(X0) & generous(X0)) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | happy(X0) | ~generous(X0))) [flattening 58] 103. ~generous(X0) | brave(X0) [cnf transformation 45] 112. ~brave(lucy) | calm(X0) [cnf transformation 50] 116. old(X0) | rich(X0) [cnf transformation 55] 123. ~old(X0) | generous(X0) [cnf transformation 59] 149. ~calm(john) [cnf transformation 17] 162. ~rich(lucy) [cnf transformation 25] 199. 7 <=> old(lucy) [avatar definition] 200. ~old(lucy) <- (~7) [avatar component clause 199] 201. old(lucy) <- (7) [avatar component clause 199] 232. 14 <=> ! [X0] : calm(X0) [avatar definition] 233. calm(X0) <- (14) [avatar component clause 232] 235. 15 <=> brave(lucy) [avatar definition] 237. ~brave(lucy) <- (~15) [avatar component clause 235] 238. 14 | ~15 [avatar split clause 112,235,232] 412. $false <- (14) [resolution 233,149] 413. ~14 [avatar contradiction clause 412] 428. generous(lucy) <- (7) [resolution 123,201] 432. brave(lucy) <- (7) [resolution 428,103] 433. $false <- (7, ~15) [subsumption resolution 432,237] 434. ~7 | 15 [avatar contradiction clause 433] 435. rich(lucy) <- (~7) [resolution 200,116] 436. $false <- (~7) [subsumption resolution 435,162] 437. 7 [avatar contradiction clause 436] 438. $false [avatar sat refutation 238,413,434,437] % SZS output end Proof for 6591653130908651102759696 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

If someone is not humble then lucy is patient or not brave. If someone is not quiet then someone is both not humble and kind. If someone is not quiet then lucy is not curious. Everyone who is both happy and not calm is either calm or old. Everyone who is both not brave and not happy is both happy and quiet and vice versa. Everyone who is not kind or not humble is curious or not generous. Everyone who is both patient and not happy is either not calm or calm. If lucy is both not funny and not rich then someone is humble. If paul is either not old or old then alice is not tall or not quiet and vice versa. If someone is old or not patient then fred is brave or tall. If someone is both old and not calm then lucy is not kind. Everyone who is both old and not funny is either creative or kind and vice versa. If lucy is not creative then john is kind. Everyone who is either patient or not generous is not humble. If john is strong then lucy is patient or not strong. Everyone who is calm is rich and vice versa. Someone is not funny or strong. Someone is not happy or humble. Lucy is both curious and generous. Fred is wise. Alice is kind. Someone is either not calm or quiet. Someone is not humble.

Lucy is not happy.

entailment

((?[X]:(~humble(X)))=>((patient(lucy)|~brave(lucy))))& ((?[X]:(~quiet(X)))=>(?[X]:((~humble(X)&kind(X)))))& ((?[X]:(~quiet(X)))=>(~curious(lucy)))& (![X]:((happy(X)&~calm(X))=>(calm(X)<~>old(X))))& (![X]:((~brave(X)&~happy(X))<=>(happy(X)&quiet(X))))& (![X]:((~kind(X)|~humble(X))=>(curious(X)|~generous(X))))& (![X]:((patient(X)&~happy(X))=>(~calm(X)<~>calm(X))))& (((~funny(lucy)&~rich(lucy)))=>(?[X]:(humble(X))))& (((~old(paul)<~>old(paul)))<=>((~tall(alice)|~quiet(alice))))& ((?[X]:((old(X)|~patient(X))))=>((brave(fred)|tall(fred))))& ((?[X]:((old(X)&~calm(X))))=>(~kind(lucy)))& (![X]:((old(X)&~funny(X))<=>(creative(X)<~>kind(X))))& ((~creative(lucy))=>(kind(john)))& (![X]:((patient(X)<~>~generous(X))=>~humble(X)))& ((strong(john))=>((patient(lucy)|~strong(lucy))))& (![X]:(calm(X)<=>rich(X)))& (?[X]:((~funny(X)|strong(X))))& (?[X]:((~happy(X)|humble(X))))& ((curious(lucy)&generous(lucy)))& (wise(fred))& (kind(alice))& (?[X]:((~calm(X)<~>quiet(X))))& (?[X]:(~humble(X)))

~happy(lucy)

% SZS status Unsatisfiable for 4606728967949655109285815 % SZS output start Proof for 4606728967949655109285815 3. ? [X0] : ~quiet(X0) => ~curious(lucy) [input p2] 5. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> (quiet(X0) & happy(X0))) [input p4] 19. generous(lucy) & curious(lucy) [input p18] 24. happy(lucy) [input hypothesis] 30. ~curious(lucy) | ! [X0] : quiet(X0) [ennf transformation 3] 50. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | (happy(X0) | brave(X0)))) [nnf transformation 5] 51. ! [X0] : (((~happy(X0) & ~brave(X0)) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | happy(X0) | brave(X0))) [flattening 50] 73. ~curious(lucy) | quiet(X0) [cnf transformation 30] 79. ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 51] 108. curious(lucy) [cnf transformation 19] 114. happy(lucy) [cnf transformation 24] 118. ~happy(X0) | ~quiet(X0) [duplicate literal removal 79] 133. 4 <=> ! [X1] : quiet(X1) [avatar definition] 134. quiet(X1) <- (4) [avatar component clause 133] 146. 7 <=> curious(lucy) [avatar definition] 149. 4 | ~7 [avatar split clause 73,146,133] 237. 7 [avatar split clause 108,146] 253. ~quiet(lucy) [resolution 118,114] 255. $false <- (4) [subsumption resolution 253,134] 256. ~4 [avatar contradiction clause 255] 258. $false [avatar sat refutation 149,237,256] % SZS output end Proof for 4606728967949655109285815 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.028 s % ------------------------------ % ------------------------------

If someone is old then paul is both not tall and not quiet and vice versa. If lucy is curious then mary is either generous or patient. Everyone who is not patient is old. Everyone who is kind or strong is both not creative and calm and vice versa. If alice is not happy or not tall then paul is both not patient and creative. If mary is patient then fred is both creative and wise and vice versa. Everyone who is brave is tall. Everyone who is strong or tall is both generous and not old and vice versa. Everyone who is either not generous or tall is not happy. Everyone who is both not old and happy is not calm and vice versa. Everyone who is either quiet or wise is both not generous and strong and vice versa. If someone is creative then alice is both generous and strong. If lucy is not curious or quiet then someone is either creative or old. If someone is not generous then fred is not old. Everyone who is happy or generous is strong or brave. Everyone who is both not calm and quiet is both strong and old and vice versa. Someone is either not generous or kind. John is either humble or quiet. John is not rich. Alice is either not happy or not generous. Someone is not tall or not curious.

Paul is generous.

contradiction

((?[X]:(old(X)))<=>((~tall(paul)&~quiet(paul))))& ((curious(lucy))=>((generous(mary)<~>patient(mary))))& (![X]:(~patient(X)=>old(X)))& (![X]:((kind(X)|strong(X))<=>(~creative(X)&calm(X))))& (((~happy(alice)|~tall(alice)))=>((~patient(paul)&creative(paul))))& ((patient(mary))<=>((creative(fred)&wise(fred))))& (![X]:(brave(X)=>tall(X)))& (![X]:((strong(X)|tall(X))<=>(generous(X)&~old(X))))& (![X]:((~generous(X)<~>tall(X))=>~happy(X)))& (![X]:((~old(X)&happy(X))<=>~calm(X)))& (![X]:((quiet(X)<~>wise(X))<=>(~generous(X)&strong(X))))& ((?[X]:(creative(X)))=>((generous(alice)&strong(alice))))& (((~curious(lucy)|quiet(lucy)))=>(?[X]:((creative(X)<~>old(X)))))& ((?[X]:(~generous(X)))=>(~old(fred)))& (![X]:((happy(X)|generous(X))=>(strong(X)|brave(X))))& (![X]:((~calm(X)&quiet(X))<=>(strong(X)&old(X))))& (?[X]:((~generous(X)<~>kind(X))))& ((humble(john)<~>quiet(john)))& (~rich(john))& ((~happy(alice)<~>~generous(alice)))& (?[X]:((~tall(X)|~curious(X))))

generous(paul)

% SZS status Unsatisfiable for 3497470447122446725872676 % SZS output start Proof for 3497470447122446725872676 1. ? [X0] : old(X0) <=> (~quiet(paul) & ~tall(paul)) [input p0] 3. ! [X0] : (~patient(X0) => old(X0)) [input p2] 4. ! [X0] : ((strong(X0) | kind(X0)) <=> (calm(X0) & ~creative(X0))) [input p3] 5. (~tall(alice) | ~happy(alice)) => (creative(paul) & ~patient(paul)) [input p4] 7. ! [X0] : (brave(X0) => tall(X0)) [input p6] 8. ! [X0] : ((tall(X0) | strong(X0)) <=> (~old(X0) & generous(X0))) [input p7] 9. ! [X0] : ((~generous(X0) <~> tall(X0)) => ~happy(X0)) [input p8] 15. ! [X0] : ((generous(X0) | happy(X0)) => (brave(X0) | strong(X0))) [input p14] 20. ~happy(alice) <~> ~generous(alice) [input p19] 22. generous(paul) [input hypothesis] 25. ! [X0] : (old(X0) | patient(X0)) [ennf transformation 3] 26. (creative(paul) & ~patient(paul)) | (tall(alice) & happy(alice)) [ennf transformation 5] 27. ! [X0] : (tall(X0) | ~brave(X0)) [ennf transformation 7] 28. ! [X0] : (~happy(X0) | (~generous(X0) <=> tall(X0))) [ennf transformation 9] 32. ! [X0] : ((brave(X0) | strong(X0)) | (~generous(X0) & ~happy(X0))) [ennf transformation 15] 33. ! [X0] : (brave(X0) | strong(X0) | (~generous(X0) & ~happy(X0))) [flattening 32] 34. (? [X0] : old(X0) | (quiet(paul) | tall(paul))) & ((~quiet(paul) & ~tall(paul)) | ! [X0] : ~old(X0)) [nnf transformation 1] 35. (? [X0] : old(X0) | quiet(paul) | tall(paul)) & ((~quiet(paul) & ~tall(paul)) | ! [X0] : ~old(X0)) [flattening 34] 36. (? [X0] : old(X0) | quiet(paul) | tall(paul)) & ((~quiet(paul) & ~tall(paul)) | ! [X1] : ~old(X1)) [rectify 35] 37. ? [X0] : old(X0) => old(sK0) [choice axiom] 38. (old(sK0) | quiet(paul) | tall(paul)) & ((~quiet(paul) & ~tall(paul)) | ! [X1] : ~old(X1)) [skolemisation 36,37] 40. ! [X0] : (((strong(X0) | kind(X0)) | (~calm(X0) | creative(X0))) & ((calm(X0) & ~creative(X0)) | (~strong(X0) & ~kind(X0)))) [nnf transformation 4] 41. ! [X0] : ((strong(X0) | kind(X0) | ~calm(X0) | creative(X0)) & ((calm(X0) & ~creative(X0)) | (~strong(X0) & ~kind(X0)))) [flattening 40] 44. ! [X0] : (((tall(X0) | strong(X0)) | (old(X0) | ~generous(X0))) & ((~old(X0) & generous(X0)) | (~tall(X0) & ~strong(X0)))) [nnf transformation 8] 45. ! [X0] : ((tall(X0) | strong(X0) | old(X0) | ~generous(X0)) & ((~old(X0) & generous(X0)) | (~tall(X0) & ~strong(X0)))) [flattening 44] 46. ! [X0] : (~happy(X0) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) [nnf transformation 28] 60. (generous(alice) | happy(alice)) & (~generous(alice) | ~happy(alice)) [nnf transformation 20] 63. ~tall(paul) | ~old(X1) [cnf transformation 38] 68. patient(X0) | old(X0) [cnf transformation 25] 70. ~creative(X0) | ~strong(X0) [cnf transformation 41] 74. ~patient(paul) | happy(alice) [cnf transformation 26] 76. creative(paul) | happy(alice) [cnf transformation 26] 81. ~brave(X0) | tall(X0) [cnf transformation 27] 83. ~tall(X0) | generous(X0) [cnf transformation 45] 87. ~happy(X0) | tall(X0) | generous(X0) [cnf transformation 46] 88. ~happy(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 46] 106. ~generous(X0) | strong(X0) | brave(X0) [cnf transformation 33] 115. ~generous(alice) | ~happy(alice) [cnf transformation 60] 118. generous(paul) [cnf transformation 22] 120. 1 <=> tall(paul) [avatar definition] 133. 4 <=> ! [X1] : ~old(X1) [avatar definition] 134. ~old(X1) <- (4) [avatar component clause 133] 136. 4 | ~1 [avatar split clause 63,120,133] 156. 9 <=> creative(paul) [avatar definition] 158. creative(paul) <- (9) [avatar component clause 156] 161. 10 <=> happy(alice) [avatar definition] 164. 10 | 9 [avatar split clause 76,156,161] 166. 11 <=> patient(paul) [avatar definition] 168. ~patient(paul) <- (~11) [avatar component clause 166] 170. 10 | ~11 [avatar split clause 74,166,161] 182. ~happy(X0) | ~tall(X0) [subsumption resolution 88,83] 183. ~happy(X0) | generous(X0) [subsumption resolution 87,182] 244. ~happy(alice) [subsumption resolution 115,183] 245. ~10 [avatar split clause 244,161] 258. old(paul) <- (~11) [resolution 68,168] 260. ~strong(paul) <- (9) [resolution 70,158] 296. strong(paul) | brave(paul) [resolution 106,118] 299. brave(paul) <- (9) [subsumption resolution 296,260] 314. tall(paul) <- (9) [resolution 299,81] 317. 1 | ~9 [avatar split clause 314,156,120] 322. $false <- (4, ~11) [resolution 134,258] 323. ~4 | 11 [avatar contradiction clause 322] 325. $false [avatar sat refutation 136,164,170,245,317,323] % SZS output end Proof for 3497470447122446725872676 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Everyone who is creative is not strong or happy. Everyone who is either not generous or brave is both brave and not brave. Everyone who is both patient and not brave is not calm or wise and vice versa. If lucy is strong then john is both not patient and not old. If someone is both not strong and rich then john is both not humble and not strong. Everyone who is both not old and brave is both not generous and not creative and vice versa. If paul is wise or not kind then susan is creative. Everyone who is not creative is both calm and not quiet. If someone is quiet or old then susan is both curious and funny and vice versa. If lucy is both brave and rich then someone is not wise or not humble. Everyone who is both not kind and wise is both kind and old and vice versa. Everyone who is not patient or not curious is not patient or strong and vice versa. Everyone who is either old or happy is not quiet and vice versa. Everyone who is both not kind and calm is strong and vice versa. If someone is both not kind and not old then someone is both strong and happy. If someone is either creative or not curious then someone is not strong or not generous and vice versa. Lucy is not brave or tall. Mary is both not generous and not creative. Someone is not strong. Mary is not strong. Alice is both brave and patient. Someone is either not tall or creative. Lucy is not generous. Someone is both kind and calm.

Mary is not kind.

contradiction

(![X]:(creative(X)=>(~strong(X)|happy(X))))& (![X]:((~generous(X)<~>brave(X))=>(brave(X)&~brave(X))))& (![X]:((patient(X)&~brave(X))<=>(~calm(X)|wise(X))))& ((strong(lucy))=>((~patient(john)&~old(john))))& ((?[X]:((~strong(X)&rich(X))))=>((~humble(john)&~strong(john))))& (![X]:((~old(X)&brave(X))<=>(~generous(X)&~creative(X))))& (((wise(paul)|~kind(paul)))=>(creative(susan)))& (![X]:(~creative(X)=>(calm(X)&~quiet(X))))& ((?[X]:((quiet(X)|old(X))))<=>((curious(susan)&funny(susan))))& (((brave(lucy)&rich(lucy)))=>(?[X]:((~wise(X)|~humble(X)))))& (![X]:((~kind(X)&wise(X))<=>(kind(X)&old(X))))& (![X]:((~patient(X)|~curious(X))<=>(~patient(X)|strong(X))))& (![X]:((old(X)<~>happy(X))<=>~quiet(X)))& (![X]:((~kind(X)&calm(X))<=>strong(X)))& ((?[X]:((~kind(X)&~old(X))))=>(?[X]:((strong(X)&happy(X)))))& ((?[X]:((creative(X)<~>~curious(X))))<=>(?[X]:((~strong(X)|~generous(X)))))& ((~brave(lucy)|tall(lucy)))& ((~generous(mary)&~creative(mary)))& (?[X]:(~strong(X)))& (~strong(mary))& ((brave(alice)&patient(alice)))& (?[X]:((~tall(X)<~>creative(X))))& (~generous(lucy))& (?[X]:((kind(X)&calm(X))))

~kind(mary)

% SZS status Unsatisfiable for 3885597990878945094759401 % SZS output start Proof for 3885597990878945094759401 8. ! [X0] : (~creative(X0) => (~quiet(X0) & calm(X0))) [input p7] 14. ! [X0] : ((calm(X0) & ~kind(X0)) <=> strong(X0)) [input p13] 18. ~creative(mary) & ~generous(mary) [input p17] 20. ~strong(mary) [input p19] 25. ~kind(mary) [input hypothesis] 36. ! [X0] : ((~quiet(X0) & calm(X0)) | creative(X0)) [ennf transformation 8] 53. ! [X0] : (((calm(X0) & ~kind(X0)) | ~strong(X0)) & (strong(X0) | (~calm(X0) | kind(X0)))) [nnf transformation 14] 54. ! [X0] : (((calm(X0) & ~kind(X0)) | ~strong(X0)) & (strong(X0) | ~calm(X0) | kind(X0))) [flattening 53] 88. calm(X0) | creative(X0) [cnf transformation 36] 107. ~calm(X0) | strong(X0) | kind(X0) [cnf transformation 54] 120. ~creative(mary) [cnf transformation 18] 122. ~strong(mary) [cnf transformation 20] 130. ~kind(mary) [cnf transformation 25] 340. kind(X1) | strong(X1) | creative(X1) [resolution 107,88] 444. strong(mary) | creative(mary) [resolution 340,130] 448. creative(mary) [subsumption resolution 444,122] 449. $false [subsumption resolution 448,120] % SZS output end Proof for 3885597990878945094759401 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.028 s % ------------------------------ % ------------------------------

If someone is not old then susan is strong or tall and vice versa. If someone is quiet then fred is not kind. Everyone who is generous is not brave and vice versa. Everyone who is both curious and not funny is both rich and creative and vice versa. If someone is not kind or patient then someone is either strong or not strong. If lucy is both not kind and not patient then mary is not old and vice versa. Everyone who is generous is both patient and calm and vice versa. Everyone who is either not generous or creative is tall. If fred is not creative then alice is both not quiet and curious. Everyone who is both quiet and funny is not creative or funny. If alice is wise or not patient then someone is either not wise or quiet. Everyone who is either not funny or quiet is both not rich and tall. If susan is creative or not funny then paul is either not quiet or not patient. If someone is either not quiet or calm then alice is both not curious and kind and vice versa. If susan is not wise or calm then someone is funny. Everyone who is both quiet and not brave is either old or curious and vice versa. Someone is not generous. Someone is not rich or patient. Susan is both not funny and happy. Paul is not humble. Someone is not creative or calm. Someone is not rich or not strong. Someone is either not curious or not humble. Someone is not old.

Susan is happy.

entailment

((?[X]:(~old(X)))<=>((strong(susan)|tall(susan))))& ((?[X]:(quiet(X)))=>(~kind(fred)))& (![X]:(generous(X)<=>~brave(X)))& (![X]:((curious(X)&~funny(X))<=>(rich(X)&creative(X))))& ((?[X]:((~kind(X)|patient(X))))=>(?[X]:((strong(X)<~>~strong(X)))))& (((~kind(lucy)&~patient(lucy)))<=>(~old(mary)))& (![X]:(generous(X)<=>(patient(X)&calm(X))))& (![X]:((~generous(X)<~>creative(X))=>tall(X)))& ((~creative(fred))=>((~quiet(alice)&curious(alice))))& (![X]:((quiet(X)&funny(X))=>(~creative(X)|funny(X))))& (((wise(alice)|~patient(alice)))=>(?[X]:((~wise(X)<~>quiet(X)))))& (![X]:((~funny(X)<~>quiet(X))=>(~rich(X)&tall(X))))& (((creative(susan)|~funny(susan)))=>((~quiet(paul)<~>~patient(paul))))& ((?[X]:((~quiet(X)<~>calm(X))))<=>((~curious(alice)&kind(alice))))& (((~wise(susan)|calm(susan)))=>(?[X]:(funny(X))))& (![X]:((quiet(X)&~brave(X))<=>(old(X)<~>curious(X))))& (?[X]:(~generous(X)))& (?[X]:((~rich(X)|patient(X))))& ((~funny(susan)&happy(susan)))& (~humble(paul))& (?[X]:((~creative(X)|calm(X))))& (?[X]:((~rich(X)|~strong(X))))& (?[X]:((~curious(X)<~>~humble(X))))& (?[X]:(~old(X)))

happy(susan)

% SZS status Unsatisfiable for 2705665492454404202392208 % SZS output start Proof for 2705665492454404202392208 19. happy(susan) & ~funny(susan) [input p18] 25. ~happy(susan) [input hypothesis] 135. happy(susan) [cnf transformation 19] 142. ~happy(susan) [cnf transformation 25] 314. $false [subsumption resolution 142,135] % SZS output end Proof for 2705665492454404202392208 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Everyone who is either not creative or not generous is not happy. Everyone who is not tall or not generous is both not old and not patient. Everyone who is rich or creative is old or not patient and vice versa. Everyone who is either not old or kind is not creative or not humble and vice versa. If someone is not strong then someone is not old or not creative and vice versa. If someone is either not rich or funny then someone is not wise or not brave and vice versa. Everyone who is not creative is either not rich or quiet. Everyone who is not curious or quiet is curious or not brave. Everyone who is either not strong or kind is humble or brave and vice versa. Everyone who is calm is brave and vice versa. If lucy is both kind and not funny then someone is either not wise or not strong. Everyone who is both calm and brave is either strong or not humble and vice versa. If paul is curious then someone is either not tall or not creative. If lucy is not tall then mary is both not funny and not curious and vice versa. Everyone who is both creative and curious is either not old or not quiet and vice versa. If someone is either not tall or not brave then someone is not old or funny. Paul is not funny. Mary is not humble. Someone is quiet or not curious. Someone is not old or brave. Someone is both old and not kind. John is not strong. John is calm or kind. Someone is either calm or not creative.

John is not old.

entailment

(![X]:((~creative(X)<~>~generous(X))=>~happy(X)))& (![X]:((~tall(X)|~generous(X))=>(~old(X)&~patient(X))))& (![X]:((rich(X)|creative(X))<=>(old(X)|~patient(X))))& (![X]:((~old(X)<~>kind(X))<=>(~creative(X)|~humble(X))))& ((?[X]:(~strong(X)))<=>(?[X]:((~old(X)|~creative(X)))))& ((?[X]:((~rich(X)<~>funny(X))))<=>(?[X]:((~wise(X)|~brave(X)))))& (![X]:(~creative(X)=>(~rich(X)<~>quiet(X))))& (![X]:((~curious(X)|quiet(X))=>(curious(X)|~brave(X))))& (![X]:((~strong(X)<~>kind(X))<=>(humble(X)|brave(X))))& (![X]:(calm(X)<=>brave(X)))& (((kind(lucy)&~funny(lucy)))=>(?[X]:((~wise(X)<~>~strong(X)))))& (![X]:((calm(X)&brave(X))<=>(strong(X)<~>~humble(X))))& ((curious(paul))=>(?[X]:((~tall(X)<~>~creative(X)))))& ((~tall(lucy))<=>((~funny(mary)&~curious(mary))))& (![X]:((creative(X)&curious(X))<=>(~old(X)<~>~quiet(X))))& ((?[X]:((~tall(X)<~>~brave(X))))=>(?[X]:((~old(X)|funny(X)))))& (~funny(paul))& (~humble(mary))& (?[X]:((quiet(X)|~curious(X))))& (?[X]:((~old(X)|brave(X))))& (?[X]:((old(X)&~kind(X))))& (~strong(john))& ((calm(john)|kind(john)))& (?[X]:((calm(X)<~>~creative(X))))

~old(john)

% SZS status Unsatisfiable for 1900440083253168431258429 % SZS output start Proof for 1900440083253168431258429 4. ! [X0] : ((~old(X0) <~> kind(X0)) <=> (~humble(X0) | ~creative(X0))) [input p3] 9. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (brave(X0) | humble(X0))) [input p8] 10. ! [X0] : (calm(X0) <=> brave(X0)) [input p9] 12. ! [X0] : ((brave(X0) & calm(X0)) <=> (strong(X0) <~> ~humble(X0))) [input p11] 22. ~strong(john) [input p21] 23. kind(john) | calm(john) [input p22] 25. old(john) [input hypothesis] 41. ! [X0] : ((((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (humble(X0) & creative(X0))) & ((~humble(X0) | ~creative(X0)) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))))) [nnf transformation 4] 42. ! [X0] : ((((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (humble(X0) & creative(X0))) & (~humble(X0) | ~creative(X0) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))))) [flattening 41] 54. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 9] 55. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [flattening 54] 56. ! [X0] : ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0))) [nnf transformation 10] 60. ! [X0] : (((brave(X0) & calm(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~brave(X0) | ~calm(X0)))) [nnf transformation 12] 61. ! [X0] : (((brave(X0) & calm(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | ~brave(X0) | ~calm(X0))) [flattening 60] 91. ~old(X0) | kind(X0) | humble(X0) [cnf transformation 42] 111. ~humble(X0) | strong(X0) | ~kind(X0) [cnf transformation 55] 112. ~brave(X0) | strong(X0) | ~kind(X0) [cnf transformation 55] 113. ~calm(X0) | brave(X0) [cnf transformation 56] 117. ~humble(X0) | strong(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 61] 122. brave(X0) | strong(X0) | humble(X0) [cnf transformation 61] 142. ~strong(john) [cnf transformation 22] 143. kind(john) | calm(john) [cnf transformation 23] 146. old(john) [cnf transformation 25] 225. ~calm(X0) | strong(X0) | ~humble(X0) [subsumption resolution 117,113] 290. 33 <=> calm(john) [avatar definition] 292. calm(john) <- (33) [avatar component clause 290] 294. 34 <=> kind(john) [avatar definition] 296. kind(john) <- (34) [avatar component clause 294] 297. 33 | 34 [avatar split clause 143,294,290] 353. kind(john) | humble(john) [resolution 91,146] 356. 44 <=> humble(john) [avatar definition] 358. humble(john) <- (44) [avatar component clause 356] 359. 44 | 34 [avatar split clause 353,294,356] 397. strong(X0) | humble(X0) | strong(X0) | ~kind(X0) [resolution 122,112] 401. strong(X0) | humble(X0) | ~kind(X0) [duplicate literal removal 397] 402. ~kind(X0) | strong(X0) [subsumption resolution 401,111] 434. strong(john) | ~humble(john) <- (33) [resolution 225,292] 437. ~humble(john) <- (33) [subsumption resolution 434,142] 438. $false <- (33, 44) [subsumption resolution 437,358] 439. ~33 | ~44 [avatar contradiction clause 438] 478. strong(john) <- (34) [resolution 402,296] 479. $false <- (34) [subsumption resolution 478,142] 480. ~34 [avatar contradiction clause 479] 481. $false [avatar sat refutation 297,359,439,480] % SZS output end Proof for 1900440083253168431258429 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.026 s % ------------------------------ % ------------------------------

If someone is both not kind and not strong then mary is either strong or not patient. Everyone who is either not humble or not funny is both calm and not creative. Everyone who is either calm or tall is either generous or calm and vice versa. Everyone who is either not old or patient is funny. Everyone who is not patient is not strong and vice versa. If fred is not humble then someone is both patient and rich and vice versa. Everyone who is either quiet or funny is either brave or not patient. Everyone who is either quiet or not tall is calm and vice versa. Everyone who is either happy or not kind is not calm or quiet and vice versa. If fred is both calm and not rich then lucy is both tall and humble and vice versa. If alice is not happy then susan is calm and vice versa. Everyone who is both not generous and not kind is humble or rich and vice versa. If someone is not patient then someone is not kind or not brave and vice versa. Everyone who is either not creative or not kind is either quiet or generous and vice versa. Everyone who is patient or strong is both brave and not strong. Everyone who is both not wise and not tall is funny or not rich and vice versa. Mary is generous or not kind. Lucy is both old and not patient. Someone is either calm or not curious. Fred is either not kind or brave. Paul is not calm or old. Alice is either not old or patient. Lucy is not kind.

Susan is not strong.

entailment

((?[X]:((~kind(X)&~strong(X))))=>((strong(mary)<~>~patient(mary))))& (![X]:((~humble(X)<~>~funny(X))=>(calm(X)&~creative(X))))& (![X]:((calm(X)<~>tall(X))<=>(generous(X)<~>calm(X))))& (![X]:((~old(X)<~>patient(X))=>funny(X)))& (![X]:(~patient(X)<=>~strong(X)))& ((~humble(fred))<=>(?[X]:((patient(X)&rich(X)))))& (![X]:((quiet(X)<~>funny(X))=>(brave(X)<~>~patient(X))))& (![X]:((quiet(X)<~>~tall(X))<=>calm(X)))& (![X]:((happy(X)<~>~kind(X))<=>(~calm(X)|quiet(X))))& (((calm(fred)&~rich(fred)))<=>((tall(lucy)&humble(lucy))))& ((~happy(alice))<=>(calm(susan)))& (![X]:((~generous(X)&~kind(X))<=>(humble(X)|rich(X))))& ((?[X]:(~patient(X)))<=>(?[X]:((~kind(X)|~brave(X)))))& (![X]:((~creative(X)<~>~kind(X))<=>(quiet(X)<~>generous(X))))& (![X]:((patient(X)|strong(X))=>(brave(X)&~strong(X))))& (![X]:((~wise(X)&~tall(X))<=>(funny(X)|~rich(X))))& ((generous(mary)|~kind(mary)))& ((old(lucy)&~patient(lucy)))& (?[X]:((calm(X)<~>~curious(X))))& ((~kind(fred)<~>brave(fred)))& ((~calm(paul)|old(paul)))& ((~old(alice)<~>patient(alice)))& (~kind(lucy))

~strong(susan)

% SZS status Unsatisfiable for 1328935273697599041447340 % SZS output start Proof for 1328935273697599041447340 15. ! [X0] : ((strong(X0) | patient(X0)) => (~strong(X0) & brave(X0))) [input p14] 24. strong(susan) [input hypothesis] 30. ! [X0] : ((~strong(X0) & brave(X0)) | (~strong(X0) & ~patient(X0))) [ennf transformation 15] 122. ~strong(X0) | ~strong(X0) [cnf transformation 30] 139. strong(susan) [cnf transformation 24] 140. ~strong(X0) [duplicate literal removal 122] 280. $false [subsumption resolution 139,140] % SZS output end Proof for 1328935273697599041447340 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

If john is both calm and not strong then someone is either not curious or tall and vice versa. Everyone who is either creative or not quiet is quiet or not quiet. If someone is tall then john is wise. If someone is happy then someone is not generous. If alice is not humble then someone is either not rich or strong. If someone is not wise then alice is either not creative or creative and vice versa. Everyone who is both not creative and calm is both rich and not generous. Everyone who is either humble or generous is both not creative and quiet. Everyone who is either funny or not calm is wise and vice versa. If fred is both not funny and not old then lucy is either quiet or calm and vice versa. If susan is either rich or not brave then lucy is either wise or generous and vice versa. If lucy is either creative or not humble then someone is not wise. Everyone who is not humble is both humble and not old and vice versa. Everyone who is humble is both not funny and not happy and vice versa. Everyone who is either not humble or not curious is either not humble or brave. Everyone who is not generous is both not humble and humble. Susan is not rich or patient. Fred is creative. Paul is either kind or not calm. Someone is tall. Alice is creative or not rich. Lucy is not brave. Someone is wise.

Alice is old.

entailment

(((calm(john)&~strong(john)))<=>(?[X]:((~curious(X)<~>tall(X)))))& (![X]:((creative(X)<~>~quiet(X))=>(quiet(X)|~quiet(X))))& ((?[X]:(tall(X)))=>(wise(john)))& ((?[X]:(happy(X)))=>(?[X]:(~generous(X))))& ((~humble(alice))=>(?[X]:((~rich(X)<~>strong(X)))))& ((?[X]:(~wise(X)))<=>((~creative(alice)<~>creative(alice))))& (![X]:((~creative(X)&calm(X))=>(rich(X)&~generous(X))))& (![X]:((humble(X)<~>generous(X))=>(~creative(X)&quiet(X))))& (![X]:((funny(X)<~>~calm(X))<=>wise(X)))& (((~funny(fred)&~old(fred)))<=>((quiet(lucy)<~>calm(lucy))))& (((rich(susan)<~>~brave(susan)))<=>((wise(lucy)<~>generous(lucy))))& (((creative(lucy)<~>~humble(lucy)))=>(?[X]:(~wise(X))))& (![X]:(~humble(X)<=>(humble(X)&~old(X))))& (![X]:(humble(X)<=>(~funny(X)&~happy(X))))& (![X]:((~humble(X)<~>~curious(X))=>(~humble(X)<~>brave(X))))& (![X]:(~generous(X)=>(~humble(X)&humble(X))))& ((~rich(susan)|patient(susan)))& (creative(fred))& ((kind(paul)<~>~calm(paul)))& (?[X]:(tall(X)))& ((creative(alice)|~rich(alice)))& (~brave(lucy))& (?[X]:(wise(X)))

old(alice)

% SZS status Unsatisfiable for 6154877614201189319533957 % SZS output start Proof for 6154877614201189319533957 13. ! [X0] : (~humble(X0) <=> (~old(X0) & humble(X0))) [input p12] 24. ~old(alice) [input hypothesis] 62. ! [X0] : ((~humble(X0) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | humble(X0))) [nnf transformation 13] 63. ! [X0] : ((~humble(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | humble(X0))) [flattening 62] 114. humble(X0) | humble(X0) [cnf transformation 63] 116. ~humble(X0) | old(X0) | ~humble(X0) [cnf transformation 63] 133. ~old(alice) [cnf transformation 24] 136. humble(X0) [duplicate literal removal 114] 137. ~humble(X0) | old(X0) [duplicate literal removal 116] 292. old(X0) [resolution 137,136] 293. $false [resolution 292,133] % SZS output end Proof for 6154877614201189319533957 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.018 s % ------------------------------ % ------------------------------

If lucy is wise then mary is funny. Everyone who is not rich is not old and vice versa. If someone is not generous then someone is either not generous or not strong and vice versa. Everyone who is not wise is not generous and vice versa. If lucy is both funny and not funny then alice is not kind or not tall. If someone is both not quiet and generous then someone is both generous and not humble. Everyone who is either funny or not humble is funny or humble. Everyone who is happy or not curious is tall and vice versa. If paul is both generous and wise then someone is not humble. Everyone who is not generous or tall is both not funny and not strong. If lucy is old or creative then john is not patient or patient. If someone is either wise or not kind then someone is not funny or old and vice versa. If fred is both happy and not quiet then mary is both funny and not creative. Everyone who is either quiet or calm is both happy and humble and vice versa. If fred is old or creative then paul is either patient or not humble. Everyone who is both kind and rich is not funny and vice versa. John is both humble and not tall. Mary is humble or not happy. Someone is not happy. Someone is rich or not kind. Mary is either creative or rich. Mary is not curious or kind. Someone is either tall or not kind.

John is curious.

entailment

((wise(lucy))=>(funny(mary)))& (![X]:(~rich(X)<=>~old(X)))& ((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)<~>~strong(X)))))& (![X]:(~wise(X)<=>~generous(X)))& (((funny(lucy)&~funny(lucy)))=>((~kind(alice)|~tall(alice))))& ((?[X]:((~quiet(X)&generous(X))))=>(?[X]:((generous(X)&~humble(X)))))& (![X]:((funny(X)<~>~humble(X))=>(funny(X)|humble(X))))& (![X]:((happy(X)|~curious(X))<=>tall(X)))& (((generous(paul)&wise(paul)))=>(?[X]:(~humble(X))))& (![X]:((~generous(X)|tall(X))=>(~funny(X)&~strong(X))))& (((old(lucy)|creative(lucy)))=>((~patient(john)|patient(john))))& ((?[X]:((wise(X)<~>~kind(X))))<=>(?[X]:((~funny(X)|old(X)))))& (((happy(fred)&~quiet(fred)))=>((funny(mary)&~creative(mary))))& (![X]:((quiet(X)<~>calm(X))<=>(happy(X)&humble(X))))& (((old(fred)|creative(fred)))=>((patient(paul)<~>~humble(paul))))& (![X]:((kind(X)&rich(X))<=>~funny(X)))& ((humble(john)&~tall(john)))& ((humble(mary)|~happy(mary)))& (?[X]:(~happy(X)))& (?[X]:((rich(X)|~kind(X))))& ((creative(mary)<~>rich(mary)))& ((~curious(mary)|kind(mary)))& (?[X]:((tall(X)<~>~kind(X))))

curious(john)

% SZS status Unsatisfiable for 334393501879826195830834 % SZS output start Proof for 334393501879826195830834 8. ! [X0] : ((~curious(X0) | happy(X0)) <=> tall(X0)) [input p7] 17. ~tall(john) & humble(john) [input p16] 24. ~curious(john) [input hypothesis] 53. ! [X0] : (((~curious(X0) | happy(X0)) | ~tall(X0)) & (tall(X0) | (curious(X0) & ~happy(X0)))) [nnf transformation 8] 54. ! [X0] : ((~curious(X0) | happy(X0) | ~tall(X0)) & (tall(X0) | (curious(X0) & ~happy(X0)))) [flattening 53] 90. curious(X0) | tall(X0) [cnf transformation 54] 121. ~tall(john) [cnf transformation 17] 130. ~curious(john) [cnf transformation 24] 315. tall(john) [resolution 90,130] 317. $false [subsumption resolution 315,121] % SZS output end Proof for 334393501879826195830834 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Everyone who is not patient or not calm is either generous or tall and vice versa. Everyone who is either not wise or generous is either not old or funny. Everyone who is not wise is not brave or happy and vice versa. Everyone who is both wise and not kind is strong or not brave. Everyone who is either not creative or quiet is humble or not patient. Everyone who is not old is both not brave and old and vice versa. Everyone who is either patient or tall is both curious and not rich and vice versa. Everyone who is both calm and patient is either not calm or patient. Everyone who is both not brave and rich is both old and not patient and vice versa. Everyone who is either not happy or kind is calm. Everyone who is wise or generous is not strong or curious and vice versa. Everyone who is either not old or old is not strong. If alice is either not humble or tall then someone is not funny or strong and vice versa. If mary is not curious then fred is either not funny or not patient. Everyone who is both not funny and not tall is brave or quiet and vice versa. If alice is not calm or not wise then alice is both not creative and kind and vice versa. Someone is creative or not brave. John is generous. Susan is tall or patient. Someone is either not strong or generous. Someone is quiet. Someone is either quiet or funny. Someone is both not quiet and patient.

John is not creative.

neutral

(![X]:((~patient(X)|~calm(X))<=>(generous(X)<~>tall(X))))& (![X]:((~wise(X)<~>generous(X))=>(~old(X)<~>funny(X))))& (![X]:(~wise(X)<=>(~brave(X)|happy(X))))& (![X]:((wise(X)&~kind(X))=>(strong(X)|~brave(X))))& (![X]:((~creative(X)<~>quiet(X))=>(humble(X)|~patient(X))))& (![X]:(~old(X)<=>(~brave(X)&old(X))))& (![X]:((patient(X)<~>tall(X))<=>(curious(X)&~rich(X))))& (![X]:((calm(X)&patient(X))=>(~calm(X)<~>patient(X))))& (![X]:((~brave(X)&rich(X))<=>(old(X)&~patient(X))))& (![X]:((~happy(X)<~>kind(X))=>calm(X)))& (![X]:((wise(X)|generous(X))<=>(~strong(X)|curious(X))))& (![X]:((~old(X)<~>old(X))=>~strong(X)))& (((~humble(alice)<~>tall(alice)))<=>(?[X]:((~funny(X)|strong(X)))))& ((~curious(mary))=>((~funny(fred)<~>~patient(fred))))& (![X]:((~funny(X)&~tall(X))<=>(brave(X)|quiet(X))))& (((~calm(alice)|~wise(alice)))<=>((~creative(alice)&kind(alice))))& (?[X]:((creative(X)|~brave(X))))& (generous(john))& ((tall(susan)|patient(susan)))& (?[X]:((~strong(X)<~>generous(X))))& (?[X]:(quiet(X)))& (?[X]:((quiet(X)<~>funny(X))))& (?[X]:((~quiet(X)&patient(X))))

~creative(john)

Everyone who is both wise and not creative is both calm and not patient. Everyone who is not kind or calm is kind or rich. Everyone who is not old or not creative is either not humble or not tall and vice versa. Everyone who is not calm or kind is not kind or not strong and vice versa. If fred is old or not brave then lucy is not funny or not brave. Everyone who is both funny and not happy is either generous or curious. Everyone who is not funny or not tall is not humble or quiet and vice versa. Everyone who is humble is both not calm and not quiet. Everyone who is both not curious and not rich is wise or humble. Everyone who is not happy is brave and vice versa. If someone is humble or not curious then someone is humble or strong. Everyone who is both patient and not quiet is either not creative or rich. If lucy is calm then fred is quiet or not wise and vice versa. If alice is either calm or creative then someone is humble and vice versa. If paul is either patient or old then someone is old or not kind and vice versa. Everyone who is either rich or not strong is patient and vice versa. Someone is either not humble or not patient. John is funny. Lucy is either rich or not brave. John is both humble and not happy. Mary is not patient or patient. Mary is either patient or not rich. Susan is either not brave or not kind. Someone is not wise or not humble.

Mary is not strong.

contradiction

(![X]:((wise(X)&~creative(X))=>(calm(X)&~patient(X))))& (![X]:((~kind(X)|calm(X))=>(kind(X)|rich(X))))& (![X]:((~old(X)|~creative(X))<=>(~humble(X)<~>~tall(X))))& (![X]:((~calm(X)|kind(X))<=>(~kind(X)|~strong(X))))& (((old(fred)|~brave(fred)))=>((~funny(lucy)|~brave(lucy))))& (![X]:((funny(X)&~happy(X))=>(generous(X)<~>curious(X))))& (![X]:((~funny(X)|~tall(X))<=>(~humble(X)|quiet(X))))& (![X]:(humble(X)=>(~calm(X)&~quiet(X))))& (![X]:((~curious(X)&~rich(X))=>(wise(X)|humble(X))))& (![X]:(~happy(X)<=>brave(X)))& ((?[X]:((humble(X)|~curious(X))))=>(?[X]:((humble(X)|strong(X)))))& (![X]:((patient(X)&~quiet(X))=>(~creative(X)<~>rich(X))))& ((calm(lucy))<=>((quiet(fred)|~wise(fred))))& (((calm(alice)<~>creative(alice)))<=>(?[X]:(humble(X))))& (((patient(paul)<~>old(paul)))<=>(?[X]:((old(X)|~kind(X)))))& (![X]:((rich(X)<~>~strong(X))<=>patient(X)))& (?[X]:((~humble(X)<~>~patient(X))))& (funny(john))& ((rich(lucy)<~>~brave(lucy)))& ((humble(john)&~happy(john)))& ((~patient(mary)|patient(mary)))& ((patient(mary)<~>~rich(mary)))& ((~brave(susan)<~>~kind(susan)))& (?[X]:((~wise(X)|~humble(X))))

~strong(mary)

% SZS status Unsatisfiable for 8461109554551766184725714 % SZS output start Proof for 8461109554551766184725714 16. ! [X0] : ((rich(X0) <~> ~strong(X0)) <=> patient(X0)) [input p15] 22. patient(mary) <~> ~rich(mary) [input p21] 25. ~strong(mary) [input hypothesis] 63. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | ~patient(X0)) & (patient(X0) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [nnf transformation 16] 68. (rich(mary) | ~patient(mary)) & (~rich(mary) | patient(mary)) [nnf transformation 22] 117. strong(X0) | rich(X0) | patient(X0) [cnf transformation 63] 119. ~rich(X0) | strong(X0) | ~patient(X0) [cnf transformation 63] 128. ~rich(mary) | patient(mary) [cnf transformation 68] 129. rich(mary) | ~patient(mary) [cnf transformation 68] 133. ~strong(mary) [cnf transformation 25] 247. 24 <=> patient(mary) [avatar definition] 248. patient(mary) <- (24) [avatar component clause 247] 249. ~patient(mary) <- (~24) [avatar component clause 247] 251. 25 <=> rich(mary) [avatar definition] 252. ~rich(mary) <- (~25) [avatar component clause 251] 253. rich(mary) <- (25) [avatar component clause 251] 254. ~24 | 25 [avatar split clause 129,251,247] 255. 24 | ~25 [avatar split clause 128,251,247] 395. rich(mary) | patient(mary) [resolution 117,133] 399. patient(mary) <- (~25) [subsumption resolution 395,252] 400. $false <- (~24, ~25) [subsumption resolution 399,249] 401. 24 | 25 [avatar contradiction clause 400] 427. strong(mary) | ~patient(mary) <- (25) [resolution 119,253] 428. ~patient(mary) <- (25) [subsumption resolution 427,133] 429. $false <- (24, 25) [subsumption resolution 428,248] 430. ~24 | ~25 [avatar contradiction clause 429] 431. $false [avatar sat refutation 254,255,401,430] % SZS output end Proof for 8461109554551766184725714 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Everyone who is both old and generous is either tall or not quiet. If mary is both funny and not calm then someone is calm or not patient. If lucy is either brave or creative then someone is humble. If lucy is both not kind and happy then paul is not kind and vice versa. If mary is calm then someone is brave and vice versa. Everyone who is not creative or humble is funny. Everyone who is either not happy or kind is brave or kind and vice versa. Everyone who is not funny or not strong is both funny and quiet and vice versa. Everyone who is not happy or happy is either humble or not quiet. Everyone who is not kind is either not creative or patient. If lucy is not funny then alice is not creative or not tall and vice versa. If fred is not humble then lucy is happy. If mary is kind then someone is both tall and calm. Everyone who is both rich and curious is either not calm or not brave and vice versa. If someone is both not rich and not quiet then paul is curious and vice versa. Someone is not old. Susan is either not humble or not kind. Fred is either generous or not tall. Susan is either not brave or curious. Lucy is wise. Fred is either kind or not calm. Lucy is either not happy or not brave. Someone is either tall or happy.

Lucy is creative.

neutral

(![X]:((old(X)&generous(X))=>(tall(X)<~>~quiet(X))))& (((funny(mary)&~calm(mary)))=>(?[X]:((calm(X)|~patient(X)))))& (((brave(lucy)<~>creative(lucy)))=>(?[X]:(humble(X))))& (((~kind(lucy)&happy(lucy)))<=>(~kind(paul)))& ((calm(mary))<=>(?[X]:(brave(X))))& (![X]:((~creative(X)|humble(X))=>funny(X)))& (![X]:((~happy(X)<~>kind(X))<=>(brave(X)|kind(X))))& (![X]:((~funny(X)|~strong(X))<=>(funny(X)&quiet(X))))& (![X]:((~happy(X)|happy(X))=>(humble(X)<~>~quiet(X))))& (![X]:(~kind(X)=>(~creative(X)<~>patient(X))))& ((~funny(lucy))<=>((~creative(alice)|~tall(alice))))& ((~humble(fred))=>(happy(lucy)))& ((kind(mary))=>(?[X]:((tall(X)&calm(X)))))& (![X]:((rich(X)&curious(X))<=>(~calm(X)<~>~brave(X))))& ((?[X]:((~rich(X)&~quiet(X))))<=>(curious(paul)))& (?[X]:(~old(X)))& ((~humble(susan)<~>~kind(susan)))& ((generous(fred)<~>~tall(fred)))& ((~brave(susan)<~>curious(susan)))& (wise(lucy))& ((kind(fred)<~>~calm(fred)))& ((~happy(lucy)<~>~brave(lucy)))& (?[X]:((tall(X)<~>happy(X))))

creative(lucy)

Everyone who is patient is old or not creative and vice versa. If lucy is either not quiet or not humble then someone is both not calm and old. Everyone who is not creative is either not kind or not strong. Everyone who is not tall or kind is not humble or not patient. Everyone who is either funny or curious is not brave. If paul is both not quiet and not funny then lucy is tall. Everyone who is both funny and happy is both rich and calm and vice versa. Everyone who is not curious or not creative is old or not quiet. If john is both brave and not humble then alice is either patient or funny. Everyone who is both not brave and not generous is either not curious or not quiet and vice versa. If someone is creative then mary is either strong or not kind and vice versa. If lucy is calm then paul is either rich or calm. If someone is not old or not quiet then someone is not calm or not kind and vice versa. If someone is either kind or not old then alice is old. Everyone who is both not brave and calm is both not strong and wise and vice versa. If susan is either funny or not generous then someone is both not curious and not strong. Someone is creative. Someone is not generous or old. Someone is both kind and quiet. Paul is either not rich or not brave. Someone is funny. Fred is not kind or generous. Alice is both happy and not old. Someone is either not old or not happy.

Alice is old.

contradiction

(![X]:(patient(X)<=>(old(X)|~creative(X))))& (((~quiet(lucy)<~>~humble(lucy)))=>(?[X]:((~calm(X)&old(X)))))& (![X]:(~creative(X)=>(~kind(X)<~>~strong(X))))& (![X]:((~tall(X)|kind(X))=>(~humble(X)|~patient(X))))& (![X]:((funny(X)<~>curious(X))=>~brave(X)))& (((~quiet(paul)&~funny(paul)))=>(tall(lucy)))& (![X]:((funny(X)&happy(X))<=>(rich(X)&calm(X))))& (![X]:((~curious(X)|~creative(X))=>(old(X)|~quiet(X))))& (((brave(john)&~humble(john)))=>((patient(alice)<~>funny(alice))))& (![X]:((~brave(X)&~generous(X))<=>(~curious(X)<~>~quiet(X))))& ((?[X]:(creative(X)))<=>((strong(mary)<~>~kind(mary))))& ((calm(lucy))=>((rich(paul)<~>calm(paul))))& ((?[X]:((~old(X)|~quiet(X))))<=>(?[X]:((~calm(X)|~kind(X)))))& ((?[X]:((kind(X)<~>~old(X))))=>(old(alice)))& (![X]:((~brave(X)&calm(X))<=>(~strong(X)&wise(X))))& (((funny(susan)<~>~generous(susan)))=>(?[X]:((~curious(X)&~strong(X)))))& (?[X]:(creative(X)))& (?[X]:((~generous(X)|old(X))))& (?[X]:((kind(X)&quiet(X))))& ((~rich(paul)<~>~brave(paul)))& (?[X]:(funny(X)))& ((~kind(fred)|generous(fred)))& ((happy(alice)&~old(alice)))& (?[X]:((~old(X)<~>~happy(X))))

old(alice)

% SZS status Unsatisfiable for 1922030132493812296257944 % SZS output start Proof for 1922030132493812296257944 23. ~old(alice) & happy(alice) [input p22] 25. old(alice) [input hypothesis] 136. ~old(alice) [cnf transformation 23] 139. old(alice) [cnf transformation 25] 247. 25 <=> old(alice) [avatar definition] 299. ~25 [avatar split clause 136,247] 310. 25 [avatar split clause 139,247] 311. $false [avatar sat refutation 299,310] % SZS output end Proof for 1922030132493812296257944 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

Everyone who is either brave or not happy is both generous and not generous and vice versa. If john is both quiet and calm then alice is both curious and humble. Everyone who is either not quiet or not calm is either rich or strong and vice versa. Everyone who is not strong or not generous is not quiet and vice versa. Everyone who is not patient or brave is happy or funny. Everyone who is not rich or brave is either not calm or humble. If someone is funny or not generous then susan is both brave and not wise. If lucy is calm or not patient then someone is humble. If someone is both rich and old then john is either not quiet or curious. Everyone who is both quiet and not brave is either not rich or not happy and vice versa. Everyone who is both not rich and strong is not rich or not brave and vice versa. If someone is happy then paul is either not creative or happy. Everyone who is creative or happy is not generous. If someone is not tall then fred is both not funny and quiet and vice versa. Everyone who is not generous or patient is not strong or quiet and vice versa. Everyone who is both humble and not curious is either not curious or not brave. Fred is not quiet or wise. Someone is both brave and not curious. Someone is not funny or wise. Someone is strong or not quiet. Paul is not kind or humble. John is either not kind or calm. Alice is patient or not humble.

Paul is strong.

entailment

(![X]:((brave(X)<~>~happy(X))<=>(generous(X)&~generous(X))))& (((quiet(john)&calm(john)))=>((curious(alice)&humble(alice))))& (![X]:((~quiet(X)<~>~calm(X))<=>(rich(X)<~>strong(X))))& (![X]:((~strong(X)|~generous(X))<=>~quiet(X)))& (![X]:((~patient(X)|brave(X))=>(happy(X)|funny(X))))& (![X]:((~rich(X)|brave(X))=>(~calm(X)<~>humble(X))))& ((?[X]:((funny(X)|~generous(X))))=>((brave(susan)&~wise(susan))))& (((calm(lucy)|~patient(lucy)))=>(?[X]:(humble(X))))& ((?[X]:((rich(X)&old(X))))=>((~quiet(john)<~>curious(john))))& (![X]:((quiet(X)&~brave(X))<=>(~rich(X)<~>~happy(X))))& (![X]:((~rich(X)&strong(X))<=>(~rich(X)|~brave(X))))& ((?[X]:(happy(X)))=>((~creative(paul)<~>happy(paul))))& (![X]:((creative(X)|happy(X))=>~generous(X)))& ((?[X]:(~tall(X)))<=>((~funny(fred)&quiet(fred))))& (![X]:((~generous(X)|patient(X))<=>(~strong(X)|quiet(X))))& (![X]:((humble(X)&~curious(X))=>(~curious(X)<~>~brave(X))))& ((~quiet(fred)|wise(fred)))& (?[X]:((brave(X)&~curious(X))))& (?[X]:((~funny(X)|wise(X))))& (?[X]:((strong(X)|~quiet(X))))& ((~kind(paul)|humble(paul)))& ((~kind(john)<~>calm(john)))& ((patient(alice)|~humble(alice)))

strong(paul)

% SZS status Unsatisfiable for 782776943396434992230092 % SZS output start Proof for 782776943396434992230092 1. ! [X0] : ((brave(X0) <~> ~happy(X0)) <=> (~generous(X0) & generous(X0))) [input p0] 10. ! [X0] : ((~brave(X0) & quiet(X0)) <=> (~rich(X0) <~> ~happy(X0))) [input p9] 11. ! [X0] : ((strong(X0) & ~rich(X0)) <=> (~brave(X0) | ~rich(X0))) [input p10] 24. ~strong(paul) [input hypothesis] 37. ! [X0] : ((((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0))))) [nnf transformation 1] 38. ! [X0] : ((((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0))))) [flattening 37] 45. ! [X0] : (((~brave(X0) & quiet(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (brave(X0) | ~quiet(X0)))) [nnf transformation 10] 46. ! [X0] : (((~brave(X0) & quiet(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | brave(X0) | ~quiet(X0))) [flattening 45] 47. ! [X0] : (((strong(X0) & ~rich(X0)) | (brave(X0) & rich(X0))) & ((~brave(X0) | ~rich(X0)) | (~strong(X0) | rich(X0)))) [nnf transformation 11] 48. ! [X0] : (((strong(X0) & ~rich(X0)) | (brave(X0) & rich(X0))) & (~brave(X0) | ~rich(X0) | ~strong(X0) | rich(X0))) [flattening 47] 65. generous(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 38] 66. generous(X0) | brave(X0) | happy(X0) [cnf transformation 38] 67. ~generous(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 38] 68. ~generous(X0) | brave(X0) | happy(X0) [cnf transformation 38] 101. ~brave(X0) | ~rich(X0) | happy(X0) [cnf transformation 46] 104. ~rich(X0) | brave(X0) [cnf transformation 48] 105. strong(X0) | rich(X0) [cnf transformation 48] 129. ~strong(paul) [cnf transformation 24] 131. happy(X0) | brave(X0) [subsumption resolution 66,68] 132. ~happy(X0) | ~brave(X0) [subsumption resolution 65,67] 184. ~rich(X0) | happy(X0) [subsumption resolution 101,131] 194. 14 <=> happy(paul) [avatar definition] 195. happy(paul) <- (14) [avatar component clause 194] 253. rich(paul) [resolution 105,129] 254. brave(paul) [resolution 253,104] 269. happy(paul) [resolution 184,253] 272. 14 [avatar split clause 269,194] 275. ~brave(paul) <- (14) [resolution 195,132] 277. $false <- (14) [subsumption resolution 275,254] 278. ~14 [avatar contradiction clause 277] 279. $false [avatar sat refutation 272,278] % SZS output end Proof for 782776943396434992230092 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

Everyone who is wise or generous is humble or curious. If mary is both wise and not happy then someone is not old. Everyone who is both not creative and happy is either humble or creative and vice versa. If someone is either not rich or not quiet then someone is not rich and vice versa. Everyone who is curious or not patient is both not generous and not happy and vice versa. If paul is both not rich and rich then alice is either kind or not quiet and vice versa. If someone is rich then susan is either generous or not quiet and vice versa. Everyone who is quiet or happy is both not brave and kind and vice versa. Everyone who is both not old and not rich is calm or tall. If someone is not calm or rich then alice is both happy and rich and vice versa. If someone is both curious and brave then alice is both not quiet and not strong. If susan is both wise and not curious then lucy is either not patient or quiet and vice versa. Everyone who is tall or not calm is patient and vice versa. Everyone who is not brave is happy. Everyone who is rich or not strong is either old or quiet. If mary is not creative then fred is brave or patient and vice versa. Alice is curious or kind. Lucy is either wise or not humble. Susan is quiet or not happy. John is both not humble and patient. Fred is not old or not kind. Alice is either not rich or not generous. Someone is quiet.

Alice is humble.

entailment

(![X]:((wise(X)|generous(X))=>(humble(X)|curious(X))))& (((wise(mary)&~happy(mary)))=>(?[X]:(~old(X))))& (![X]:((~creative(X)&happy(X))<=>(humble(X)<~>creative(X))))& ((?[X]:((~rich(X)<~>~quiet(X))))<=>(?[X]:(~rich(X))))& (![X]:((curious(X)|~patient(X))<=>(~generous(X)&~happy(X))))& (((~rich(paul)&rich(paul)))<=>((kind(alice)<~>~quiet(alice))))& ((?[X]:(rich(X)))<=>((generous(susan)<~>~quiet(susan))))& (![X]:((quiet(X)|happy(X))<=>(~brave(X)&kind(X))))& (![X]:((~old(X)&~rich(X))=>(calm(X)|tall(X))))& ((?[X]:((~calm(X)|rich(X))))<=>((happy(alice)&rich(alice))))& ((?[X]:((curious(X)&brave(X))))=>((~quiet(alice)&~strong(alice))))& (((wise(susan)&~curious(susan)))<=>((~patient(lucy)<~>quiet(lucy))))& (![X]:((tall(X)|~calm(X))<=>patient(X)))& (![X]:(~brave(X)=>happy(X)))& (![X]:((rich(X)|~strong(X))=>(old(X)<~>quiet(X))))& ((~creative(mary))<=>((brave(fred)|patient(fred))))& ((curious(alice)|kind(alice)))& ((wise(lucy)<~>~humble(lucy)))& ((quiet(susan)|~happy(susan)))& ((~humble(john)&patient(john)))& ((~old(fred)|~kind(fred)))& ((~rich(alice)<~>~generous(alice)))& (?[X]:(quiet(X)))

humble(alice)

% SZS status Unsatisfiable for 3618382864533128244411661 % SZS output start Proof for 3618382864533128244411661 1. ! [X0] : ((generous(X0) | wise(X0)) => (curious(X0) | humble(X0))) [input p0] 3. ! [X0] : ((happy(X0) & ~creative(X0)) <=> (humble(X0) <~> creative(X0))) [input p2] 5. ! [X0] : ((~patient(X0) | curious(X0)) <=> (~happy(X0) & ~generous(X0))) [input p4] 10. ? [X0] : (rich(X0) | ~calm(X0)) <=> (rich(alice) & happy(alice)) [input p9] 22. ~rich(alice) <~> ~generous(alice) [input p21] 24. ~humble(alice) [input hypothesis] 26. ! [X0] : ((curious(X0) | humble(X0)) | (~generous(X0) & ~wise(X0))) [ennf transformation 1] 27. ! [X0] : (curious(X0) | humble(X0) | (~generous(X0) & ~wise(X0))) [flattening 26] 37. ! [X0] : (((happy(X0) & ~creative(X0)) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) & (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~happy(X0) | creative(X0)))) [nnf transformation 3] 38. ! [X0] : (((happy(X0) & ~creative(X0)) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) & (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | ~happy(X0) | creative(X0))) [flattening 37] 44. ! [X0] : (((~patient(X0) | curious(X0)) | (happy(X0) | generous(X0))) & ((~happy(X0) & ~generous(X0)) | (patient(X0) & ~curious(X0)))) [nnf transformation 5] 45. ! [X0] : ((~patient(X0) | curious(X0) | happy(X0) | generous(X0)) & ((~happy(X0) & ~generous(X0)) | (patient(X0) & ~curious(X0)))) [flattening 44] 54. (? [X0] : (rich(X0) | ~calm(X0)) | (~rich(alice) | ~happy(alice))) & ((rich(alice) & happy(alice)) | ! [X0] : (~rich(X0) & calm(X0))) [nnf transformation 10] 55. (? [X0] : (rich(X0) | ~calm(X0)) | ~rich(alice) | ~happy(alice)) & ((rich(alice) & happy(alice)) | ! [X0] : (~rich(X0) & calm(X0))) [flattening 54] 56. (? [X0] : (rich(X0) | ~calm(X0)) | ~rich(alice) | ~happy(alice)) & ((rich(alice) & happy(alice)) | ! [X1] : (~rich(X1) & calm(X1))) [rectify 55] 57. ? [X0] : (rich(X0) | ~calm(X0)) => (rich(sK4) | ~calm(sK4)) [choice axiom] 58. ((rich(sK4) | ~calm(sK4)) | ~rich(alice) | ~happy(alice)) & ((rich(alice) & happy(alice)) | ! [X1] : (~rich(X1) & calm(X1))) [skolemisation 56,57] 67. (generous(alice) | rich(alice)) & (~generous(alice) | ~rich(alice)) [nnf transformation 22] 71. ~generous(X0) | humble(X0) | curious(X0) [cnf transformation 27] 73. creative(X0) | humble(X0) | ~happy(X0) | creative(X0) [cnf transformation 38] 76. ~creative(X0) | humble(X0) | ~creative(X0) [cnf transformation 38] 83. ~curious(X0) | ~generous(X0) [cnf transformation 45] 105. happy(alice) | ~rich(X1) [cnf transformation 58] 136. generous(alice) | rich(alice) [cnf transformation 67] 138. ~humble(alice) [cnf transformation 24] 139. creative(X0) | humble(X0) | ~happy(X0) [duplicate literal removal 73] 140. ~creative(X0) | humble(X0) [duplicate literal removal 76] 154. ~happy(X0) | humble(X0) [subsumption resolution 139,140] 211. 16 <=> ! [X1] : ~rich(X1) [avatar definition] 212. ~rich(X1) <- (16) [avatar component clause 211] 216. 17 <=> happy(alice) [avatar definition] 217. happy(alice) <- (17) [avatar component clause 216] 220. 18 <=> rich(alice) [avatar definition] 221. rich(alice) <- (18) [avatar component clause 220] 237. 16 | 17 [avatar split clause 105,216,211] 286. 31 <=> curious(alice) [avatar definition] 288. curious(alice) <- (31) [avatar component clause 286] 315. 37 <=> generous(alice) [avatar definition] 317. generous(alice) <- (37) [avatar component clause 315] 318. 18 | 37 [avatar split clause 136,315,220] 330. humble(alice) <- (17) [resolution 154,217] 331. $false <- (17) [subsumption resolution 330,138] 332. ~17 [avatar contradiction clause 331] 334. $false <- (16, 18) [resolution 212,221] 335. ~16 | ~18 [avatar contradiction clause 334] 342. humble(alice) | curious(alice) <- (37) [resolution 71,317] 348. curious(alice) <- (37) [subsumption resolution 342,138] 351. 31 | ~37 [avatar split clause 348,315,286] 352. ~generous(alice) <- (31) [resolution 288,83] 353. $false <- (31, 37) [subsumption resolution 352,317] 354. ~31 | ~37 [avatar contradiction clause 353] 355. $false [avatar sat refutation 237,318,332,335,351,354] % SZS output end Proof for 3618382864533128244411661 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.016 s % ------------------------------ % ------------------------------

Everyone who is either curious or patient is strong or not humble and vice versa. Everyone who is calm or not old is both brave and rich. Everyone who is happy or generous is both not wise and calm. If fred is both not wise and funny then lucy is both not curious and strong. If someone is not old then someone is both not strong and humble. Everyone who is kind or not strong is creative or old and vice versa. Everyone who is either not quiet or not patient is either old or calm. If lucy is both strong and brave then someone is not strong or brave and vice versa. If john is either not generous or not old then someone is both brave and happy and vice versa. If someone is either not old or calm then someone is humble or rich. If lucy is not rich or kind then someone is both kind and humble. If someone is either happy or not happy then someone is both quiet and not strong and vice versa. If john is not humble or not brave then someone is either not patient or not rich and vice versa. If alice is both curious and not brave then someone is either patient or not patient. Everyone who is either not brave or generous is curious or not strong and vice versa. Everyone who is either humble or not curious is quiet and vice versa. Someone is both not creative and humble. Lucy is both generous and kind. Someone is not patient or strong. Someone is not calm. Someone is either strong or not humble. Someone is not happy or not brave. Someone is either brave or humble. Someone is either humble or not generous.

Lucy is curious.

entailment

(![X]:((curious(X)<~>patient(X))<=>(strong(X)|~humble(X))))& (![X]:((calm(X)|~old(X))=>(brave(X)&rich(X))))& (![X]:((happy(X)|generous(X))=>(~wise(X)&calm(X))))& (((~wise(fred)&funny(fred)))=>((~curious(lucy)&strong(lucy))))& ((?[X]:(~old(X)))=>(?[X]:((~strong(X)&humble(X)))))& (![X]:((kind(X)|~strong(X))<=>(creative(X)|old(X))))& (![X]:((~quiet(X)<~>~patient(X))=>(old(X)<~>calm(X))))& (((strong(lucy)&brave(lucy)))<=>(?[X]:((~strong(X)|brave(X)))))& (((~generous(john)<~>~old(john)))<=>(?[X]:((brave(X)&happy(X)))))& ((?[X]:((~old(X)<~>calm(X))))=>(?[X]:((humble(X)|rich(X)))))& (((~rich(lucy)|kind(lucy)))=>(?[X]:((kind(X)&humble(X)))))& ((?[X]:((happy(X)<~>~happy(X))))<=>(?[X]:((quiet(X)&~strong(X)))))& (((~humble(john)|~brave(john)))<=>(?[X]:((~patient(X)<~>~rich(X)))))& (((curious(alice)&~brave(alice)))=>(?[X]:((patient(X)<~>~patient(X)))))& (![X]:((~brave(X)<~>generous(X))<=>(curious(X)|~strong(X))))& (![X]:((humble(X)<~>~curious(X))<=>quiet(X)))& (?[X]:((~creative(X)&humble(X))))& ((generous(lucy)&kind(lucy)))& (?[X]:((~patient(X)|strong(X))))& (?[X]:(~calm(X)))& (?[X]:((strong(X)<~>~humble(X))))& (?[X]:((~happy(X)|~brave(X))))& (?[X]:((brave(X)<~>humble(X))))& (?[X]:((humble(X)<~>~generous(X))))

curious(lucy)

% SZS status Unsatisfiable for 8919019634482485059953364 % SZS output start Proof for 8919019634482485059953364 8. (brave(lucy) & strong(lucy)) <=> ? [X0] : (brave(X0) | ~strong(X0)) [input p7] 12. ? [X0] : (happy(X0) <~> ~happy(X0)) <=> ? [X0] : (~strong(X0) & quiet(X0)) [input p11] 15. ! [X0] : ((~brave(X0) <~> generous(X0)) <=> (~strong(X0) | curious(X0))) [input p14] 18. kind(lucy) & generous(lucy) [input p17] 25. ~curious(lucy) [input hypothesis] 28. ? [X0] : (happy(X0) <~> ~happy(X0)) <=> ? [X1] : (~strong(X1) & quiet(X1)) [rectify 12] 47. ((brave(lucy) & strong(lucy)) | ! [X0] : (~brave(X0) & strong(X0))) & (? [X0] : (brave(X0) | ~strong(X0)) | (~brave(lucy) | ~strong(lucy))) [nnf transformation 8] 48. ((brave(lucy) & strong(lucy)) | ! [X0] : (~brave(X0) & strong(X0))) & (? [X0] : (brave(X0) | ~strong(X0)) | ~brave(lucy) | ~strong(lucy)) [flattening 47] 49. ((brave(lucy) & strong(lucy)) | ! [X0] : (~brave(X0) & strong(X0))) & (? [X1] : (brave(X1) | ~strong(X1)) | ~brave(lucy) | ~strong(lucy)) [rectify 48] 50. ? [X1] : (brave(X1) | ~strong(X1)) => (brave(sK1) | ~strong(sK1)) [choice axiom] 51. ((brave(lucy) & strong(lucy)) | ! [X0] : (~brave(X0) & strong(X0))) & ((brave(sK1) | ~strong(sK1)) | ~brave(lucy) | ~strong(lucy)) [skolemisation 49,50] 62. (? [X0] : ((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | ! [X1] : (strong(X1) | ~quiet(X1))) & (? [X1] : (~strong(X1) & quiet(X1)) | ! [X0] : ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 28] 63. (? [X0] : ((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | ! [X1] : (strong(X1) | ~quiet(X1))) & (? [X2] : (~strong(X2) & quiet(X2)) | ! [X3] : ((happy(X3) | happy(X3)) & (~happy(X3) | ~happy(X3)))) [rectify 62] 64. ? [X0] : ((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) => ((happy(sK5) | ~happy(sK5)) & (~happy(sK5) | happy(sK5))) [choice axiom] 65. ? [X2] : (~strong(X2) & quiet(X2)) => (~strong(sK6) & quiet(sK6)) [choice axiom] 66. (((happy(sK5) | ~happy(sK5)) & (~happy(sK5) | happy(sK5))) | ! [X1] : (strong(X1) | ~quiet(X1))) & ((~strong(sK6) & quiet(sK6)) | ! [X3] : ((happy(X3) | happy(X3)) & (~happy(X3) | ~happy(X3)))) [skolemisation 63,65,64] 75. ! [X0] : ((((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | (strong(X0) & ~curious(X0))) & ((~strong(X0) | curious(X0)) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0))))) [nnf transformation 15] 76. ! [X0] : ((((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | (strong(X0) & ~curious(X0))) & (~strong(X0) | curious(X0) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0))))) [flattening 75] 118. strong(lucy) | strong(X0) [cnf transformation 51] 120. brave(lucy) | strong(X0) [cnf transformation 51] 136. ~strong(sK6) | ~happy(X3) | ~happy(X3) [cnf transformation 66] 137. ~strong(sK6) | happy(X3) | happy(X3) [cnf transformation 66] 149. ~generous(X0) | curious(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 76] 160. generous(lucy) [cnf transformation 18] 171. ~curious(lucy) [cnf transformation 25] 174. ~strong(sK6) | ~happy(X3) [duplicate literal removal 136] 175. ~strong(sK6) | happy(X3) [duplicate literal removal 137] 193. 5 <=> brave(lucy) [avatar definition] 195. brave(lucy) <- (5) [avatar component clause 193] 198. 6 <=> ! [X0] : strong(X0) [avatar definition] 199. strong(X0) <- (6) [avatar component clause 198] 200. 6 | 5 [avatar split clause 120,193,198] 202. 7 <=> strong(lucy) [avatar definition] 204. strong(lucy) <- (7) [avatar component clause 202] 206. 6 | 7 [avatar split clause 118,202,198] 278. 23 <=> ! [X3] : happy(X3) [avatar definition] 279. happy(X3) <- (23) [avatar component clause 278] 281. 24 <=> strong(sK6) [avatar definition] 283. ~strong(sK6) <- (~24) [avatar component clause 281] 284. 23 | ~24 [avatar split clause 175,281,278] 286. 25 <=> ! [X3] : ~happy(X3) [avatar definition] 287. ~happy(X3) <- (25) [avatar component clause 286] 288. 25 | ~24 [avatar split clause 174,281,286] 372. $false <- (23, 25) [subsumption resolution 279,287] 373. ~23 | ~25 [avatar contradiction clause 372] 376. $false <- (6, ~24) [subsumption resolution 283,199] 377. ~6 | 24 [avatar contradiction clause 376] 655. curious(lucy) | ~brave(lucy) | ~strong(lucy) [resolution 149,160] 656. ~brave(lucy) | ~strong(lucy) [subsumption resolution 655,171] 657. ~strong(lucy) <- (5) [subsumption resolution 656,195] 658. $false <- (5, 7) [subsumption resolution 657,204] 659. ~5 | ~7 [avatar contradiction clause 658] 660. $false [avatar sat refutation 200,206,284,288,373,377,659] % SZS output end Proof for 8919019634482485059953364 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Everyone who is not tall or not calm is rich. Everyone who is calm is brave and vice versa. If someone is both not rich and not brave then john is not calm or quiet. If paul is not generous then paul is not calm and vice versa. If john is curious then someone is rich. If someone is strong or brave then mary is either not strong or not curious and vice versa. If paul is quiet then someone is either not strong or not rich. If someone is either curious or not old then paul is either brave or generous and vice versa. If fred is not old or happy then mary is curious or strong and vice versa. If someone is rich then john is both not funny and not curious. Everyone who is either not curious or happy is brave or old and vice versa. If fred is creative or strong then john is either not patient or brave. Everyone who is kind or not humble is both quiet and not brave and vice versa. If someone is either strong or not curious then someone is either not tall or not humble and vice versa. Everyone who is generous is either old or not happy and vice versa. Paul is humble. Mary is brave or wise. John is humble or happy. Someone is not happy. Someone is either not generous or not happy. Mary is both strong and not tall.

Paul is brave.

contradiction

(![X]:((~tall(X)|~calm(X))=>rich(X)))& (![X]:(calm(X)<=>brave(X)))& ((?[X]:((~rich(X)&~brave(X))))=>((~calm(john)|quiet(john))))& ((~generous(paul))<=>(~calm(paul)))& ((curious(john))=>(?[X]:(rich(X))))& ((?[X]:((strong(X)|brave(X))))<=>((~strong(mary)<~>~curious(mary))))& ((quiet(paul))=>(?[X]:((~strong(X)<~>~rich(X)))))& ((?[X]:((curious(X)<~>~old(X))))<=>((brave(paul)<~>generous(paul))))& (((~old(fred)|happy(fred)))<=>((curious(mary)|strong(mary))))& ((?[X]:(rich(X)))=>((~funny(john)&~curious(john))))& (![X]:((~curious(X)<~>happy(X))<=>(brave(X)|old(X))))& (((creative(fred)|strong(fred)))=>((~patient(john)<~>brave(john))))& (![X]:((kind(X)|~humble(X))<=>(quiet(X)&~brave(X))))& ((?[X]:((strong(X)<~>~curious(X))))<=>(?[X]:((~tall(X)<~>~humble(X)))))& (![X]:(generous(X)<=>(old(X)<~>~happy(X))))& (humble(paul))& ((brave(mary)|wise(mary)))& ((humble(john)|happy(john)))& (?[X]:(~happy(X)))& (?[X]:((~generous(X)<~>~happy(X))))& ((strong(mary)&~tall(mary)))

brave(paul)

% SZS status Unsatisfiable for 48392012847811344738040 % SZS output start Proof for 48392012847811344738040 2. ! [X0] : (calm(X0) <=> brave(X0)) [input p1] 4. ~generous(paul) <=> ~calm(paul) [input p3] 8. ? [X0] : (curious(X0) <~> ~old(X0)) <=> (brave(paul) <~> generous(paul)) [input p7] 11. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (old(X0) | brave(X0))) [input p10] 15. ! [X0] : (generous(X0) <=> (old(X0) <~> ~happy(X0))) [input p14] 22. brave(paul) [input hypothesis] 34. ! [X0] : ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0))) [nnf transformation 2] 35. (~generous(paul) | calm(paul)) & (~calm(paul) | generous(paul)) [nnf transformation 4] 45. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) [nnf transformation 8] 46. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [rectify 45] 47. ? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) => ((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) [choice axiom] 48. (((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [skolemisation 46,47] 51. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 11] 52. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 51] 61. ! [X0] : ((generous(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | ~generous(X0))) [nnf transformation 15] 70. ~brave(X0) | calm(X0) [cnf transformation 34] 72. ~calm(paul) | generous(paul) [cnf transformation 35] 85. ~generous(paul) | ~brave(paul) | ~old(X1) | ~curious(X1) [cnf transformation 48] 86. ~generous(paul) | ~brave(paul) | curious(X1) | old(X1) [cnf transformation 48] 98. ~curious(X0) | happy(X0) | ~brave(X0) [cnf transformation 52] 100. ~happy(X0) | curious(X0) | ~brave(X0) [cnf transformation 52] 117. ~happy(X0) | old(X0) | ~generous(X0) [cnf transformation 61] 118. ~old(X0) | happy(X0) | ~generous(X0) [cnf transformation 61] 128. brave(paul) [cnf transformation 22] 142. 4 <=> calm(paul) [avatar definition] 146. 5 <=> generous(paul) [avatar definition] 147. generous(paul) <- (5) [avatar component clause 146] 150. 5 | ~4 [avatar split clause 72,142,146] 203. 17 <=> brave(paul) [avatar definition] 205. brave(paul) <- (17) [avatar component clause 203] 219. 20 <=> ! [X1] : (curious(X1) | old(X1)) [avatar definition] 220. old(X1) | curious(X1) <- (20) [avatar component clause 219] 221. 20 | ~17 | ~5 [avatar split clause 86,146,203,219] 223. 21 <=> ! [X1] : (~old(X1) | ~curious(X1)) [avatar definition] 224. ~old(X1) | ~curious(X1) <- (21) [avatar component clause 223] 225. 21 | ~17 | ~5 [avatar split clause 85,146,203,223] 314. 17 [avatar split clause 128,203] 315. calm(paul) <- (17) [resolution 70,205] 318. 4 | ~17 [avatar split clause 315,203,142] 345. ~generous(X0) | happy(X0) | curious(X0) <- (20) [resolution 118,220] 373. happy(paul) | curious(paul) <- (5, 20) [resolution 345,147] 377. 45 <=> curious(paul) [avatar definition] 379. curious(paul) <- (45) [avatar component clause 377] 381. 46 <=> happy(paul) [avatar definition] 383. happy(paul) <- (46) [avatar component clause 381] 384. 45 | 46 | ~5 | ~20 [avatar split clause 373,219,146,381,377] 409. happy(paul) | ~brave(paul) <- (45) [resolution 379,98] 410. happy(paul) <- (17, 45) [subsumption resolution 409,205] 411. 46 | ~17 | ~45 [avatar split clause 410,377,203,381] 414. old(paul) | ~generous(paul) <- (46) [resolution 383,117] 416. curious(paul) | ~brave(paul) <- (46) [resolution 383,100] 417. old(paul) <- (5, 46) [subsumption resolution 414,147] 434. ~curious(paul) <- (5, 21, 46) [resolution 417,224] 437. ~45 | ~5 | ~21 | ~46 [avatar split clause 434,381,223,146,377] 438. curious(paul) <- (17, 46) [subsumption resolution 416,205] 439. 45 | ~17 | ~46 [avatar split clause 438,381,203,377] 442. $false [avatar sat refutation 150,221,225,314,318,384,411,437,439] % SZS output end Proof for 48392012847811344738040 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

If someone is either not happy or not funny then paul is not quiet or not generous and vice versa. Everyone who is quiet is calm or not kind and vice versa. If someone is both kind and not curious then john is wise and vice versa. Everyone who is calm is tall or not brave. If fred is both tall and not happy then john is creative and vice versa. If john is humble then alice is both not funny and not wise and vice versa. Everyone who is tall or brave is both not quiet and not kind. If susan is generous or not wise then someone is both not wise and happy and vice versa. If someone is both strong and generous then paul is not happy. Everyone who is either not wise or not generous is not funny or quiet. Everyone who is not wise is not rich or not tall. If mary is both not old and not humble then lucy is curious. Everyone who is either not old or wise is not strong or humble and vice versa. Everyone who is not patient is both strong and not curious. If someone is not creative then lucy is both strong and not rich and vice versa. Everyone who is either strong or not creative is calm. Someone is either quiet or funny. Mary is either not funny or strong. Someone is wise. Someone is generous or not funny. Mary is not quiet. Alice is either wise or not calm. Mary is not happy.

Susan is not patient.

neutral

((?[X]:((~happy(X)<~>~funny(X))))<=>((~quiet(paul)|~generous(paul))))& (![X]:(quiet(X)<=>(calm(X)|~kind(X))))& ((?[X]:((kind(X)&~curious(X))))<=>(wise(john)))& (![X]:(calm(X)=>(tall(X)|~brave(X))))& (((tall(fred)&~happy(fred)))<=>(creative(john)))& ((humble(john))<=>((~funny(alice)&~wise(alice))))& (![X]:((tall(X)|brave(X))=>(~quiet(X)&~kind(X))))& (((generous(susan)|~wise(susan)))<=>(?[X]:((~wise(X)&happy(X)))))& ((?[X]:((strong(X)&generous(X))))=>(~happy(paul)))& (![X]:((~wise(X)<~>~generous(X))=>(~funny(X)|quiet(X))))& (![X]:(~wise(X)=>(~rich(X)|~tall(X))))& (((~old(mary)&~humble(mary)))=>(curious(lucy)))& (![X]:((~old(X)<~>wise(X))<=>(~strong(X)|humble(X))))& (![X]:(~patient(X)=>(strong(X)&~curious(X))))& ((?[X]:(~creative(X)))<=>((strong(lucy)&~rich(lucy))))& (![X]:((strong(X)<~>~creative(X))=>calm(X)))& (?[X]:((quiet(X)<~>funny(X))))& ((~funny(mary)<~>strong(mary)))& (?[X]:(wise(X)))& (?[X]:((generous(X)|~funny(X))))& (~quiet(mary))& ((wise(alice)<~>~calm(alice)))& (~happy(mary))

~patient(susan)

Everyone who is not old is curious. Everyone who is either not old or calm is both not brave and not generous and vice versa. Everyone who is strong is either not kind or patient and vice versa. If paul is not patient or not calm then fred is both not patient and not kind. Everyone who is not tall or brave is both not calm and not rich. Everyone who is either not generous or old is not humble. Everyone who is not curious is strong or not rich and vice versa. Everyone who is old or not quiet is not calm or tall. Everyone who is either not curious or not creative is either calm or not kind and vice versa. Everyone who is both patient and not wise is both old and not kind and vice versa. If someone is not happy or not patient then lucy is both quiet and not generous. Everyone who is both not kind and not creative is humble or not kind and vice versa. Everyone who is either wise or not funny is not old. Everyone who is either not creative or funny is either not rich or not calm. Everyone who is not calm is not humble or humble. Everyone who is curious is happy or not strong and vice versa. Someone is curious or not wise. John is calm or wise. Someone is not curious or strong. Alice is both strong and rich. Mary is not humble.

Paul is old.

entailment

(![X]:(~old(X)=>curious(X)))& (![X]:((~old(X)<~>calm(X))<=>(~brave(X)&~generous(X))))& (![X]:(strong(X)<=>(~kind(X)<~>patient(X))))& (((~patient(paul)|~calm(paul)))=>((~patient(fred)&~kind(fred))))& (![X]:((~tall(X)|brave(X))=>(~calm(X)&~rich(X))))& (![X]:((~generous(X)<~>old(X))=>~humble(X)))& (![X]:(~curious(X)<=>(strong(X)|~rich(X))))& (![X]:((old(X)|~quiet(X))=>(~calm(X)|tall(X))))& (![X]:((~curious(X)<~>~creative(X))<=>(calm(X)<~>~kind(X))))& (![X]:((patient(X)&~wise(X))<=>(old(X)&~kind(X))))& ((?[X]:((~happy(X)|~patient(X))))=>((quiet(lucy)&~generous(lucy))))& (![X]:((~kind(X)&~creative(X))<=>(humble(X)|~kind(X))))& (![X]:((wise(X)<~>~funny(X))=>~old(X)))& (![X]:((~creative(X)<~>funny(X))=>(~rich(X)<~>~calm(X))))& (![X]:(~calm(X)=>(~humble(X)|humble(X))))& (![X]:(curious(X)<=>(happy(X)|~strong(X))))& (?[X]:((curious(X)|~wise(X))))& ((calm(john)|wise(john)))& (?[X]:((~curious(X)|strong(X))))& ((strong(alice)&rich(alice)))& (~humble(mary))

old(paul)

% SZS status Unsatisfiable for 3627243852124307784402223 % SZS output start Proof for 3627243852124307784402223 1. ! [X0] : (~old(X0) => curious(X0)) [input p0] 3. ! [X0] : (strong(X0) <=> (~kind(X0) <~> patient(X0))) [input p2] 4. (~calm(paul) | ~patient(paul)) => (~kind(fred) & ~patient(fred)) [input p3] 7. ! [X0] : (~curious(X0) <=> (~rich(X0) | strong(X0))) [input p6] 9. ! [X0] : ((~curious(X0) <~> ~creative(X0)) <=> (calm(X0) <~> ~kind(X0))) [input p8] 10. ! [X0] : ((~wise(X0) & patient(X0)) <=> (~kind(X0) & old(X0))) [input p9] 12. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (~kind(X0) | humble(X0))) [input p11] 22. ~old(paul) [input hypothesis] 27. ! [X0] : (curious(X0) | old(X0)) [ennf transformation 1] 28. (~kind(fred) & ~patient(fred)) | (calm(paul) & patient(paul)) [ennf transformation 4] 38. ! [X0] : ((strong(X0) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | ~strong(X0))) [nnf transformation 3] 40. ! [X0] : ((~curious(X0) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | curious(X0))) [nnf transformation 7] 41. ! [X0] : ((~curious(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | curious(X0))) [flattening 40] 42. ! [X0] : ((((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0))))) [nnf transformation 9] 43. ! [X0] : (((~wise(X0) & patient(X0)) | (kind(X0) | ~old(X0))) & ((~kind(X0) & old(X0)) | (wise(X0) | ~patient(X0)))) [nnf transformation 10] 44. ! [X0] : (((~wise(X0) & patient(X0)) | kind(X0) | ~old(X0)) & ((~kind(X0) & old(X0)) | wise(X0) | ~patient(X0))) [flattening 43] 45. ! [X0] : (((~creative(X0) & ~kind(X0)) | (kind(X0) & ~humble(X0))) & ((~kind(X0) | humble(X0)) | (creative(X0) | kind(X0)))) [nnf transformation 12] 46. ! [X0] : (((~creative(X0) & ~kind(X0)) | (kind(X0) & ~humble(X0))) & (~kind(X0) | humble(X0) | creative(X0) | kind(X0))) [flattening 45] 55. curious(X0) | old(X0) [cnf transformation 27] 64. patient(X0) | strong(X0) | kind(X0) [cnf transformation 38] 65. ~patient(X0) | ~kind(X0) | strong(X0) [cnf transformation 38] 66. ~patient(fred) | patient(paul) [cnf transformation 28] 67. ~patient(fred) | calm(paul) [cnf transformation 28] 68. ~kind(fred) | patient(paul) [cnf transformation 28] 69. ~kind(fred) | calm(paul) [cnf transformation 28] 75. ~strong(X0) | ~curious(X0) [cnf transformation 41] 80. ~calm(X0) | kind(X0) | ~curious(X0) | creative(X0) [cnf transformation 42] 87. ~old(X0) | kind(X0) | patient(X0) [cnf transformation 44] 95. ~creative(X0) | kind(X0) [cnf transformation 46] 112. ~old(paul) [cnf transformation 22] 114. 1 <=> calm(paul) [avatar definition] 116. calm(paul) <- (1) [avatar component clause 114] 118. 2 <=> kind(fred) [avatar definition] 120. ~kind(fred) <- (~2) [avatar component clause 118] 121. 1 | ~2 [avatar split clause 69,118,114] 123. 3 <=> patient(paul) [avatar definition] 125. patient(paul) <- (3) [avatar component clause 123] 126. 3 | ~2 [avatar split clause 68,118,123] 128. 4 <=> patient(fred) [avatar definition] 130. ~patient(fred) <- (~4) [avatar component clause 128] 131. 1 | ~4 [avatar split clause 67,128,114] 132. 3 | ~4 [avatar split clause 66,128,123] 172. strong(fred) | kind(fred) <- (~4) [resolution 64,130] 175. strong(fred) <- (~2, ~4) [subsumption resolution 172,120] 176. ~curious(fred) <- (~2, ~4) [resolution 175,75] 179. old(fred) <- (~2, ~4) [resolution 176,55] 186. kind(fred) | patient(fred) <- (~2, ~4) [resolution 87,179] 205. patient(fred) <- (~2, ~4) [subsumption resolution 186,120] 206. $false <- (~2, ~4) [subsumption resolution 205,130] 207. 2 | 4 [avatar contradiction clause 206] 218. ~kind(paul) | strong(paul) <- (3) [resolution 125,65] 221. 17 <=> kind(paul) [avatar definition] 232. 19 <=> strong(paul) [avatar definition] 234. strong(paul) <- (19) [avatar component clause 232] 235. 19 | ~17 | ~3 [avatar split clause 218,123,221,232] 338. kind(paul) | ~curious(paul) | creative(paul) <- (1) [resolution 80,116] 348. kind(paul) | ~curious(paul) <- (1) [subsumption resolution 338,95] 350. 38 <=> curious(paul) [avatar definition] 352. ~curious(paul) <- (~38) [avatar component clause 350] 353. ~38 | 17 | ~1 [avatar split clause 348,114,221,350] 356. ~curious(paul) <- (19) [resolution 234,75] 357. ~38 | ~19 [avatar split clause 356,232,350] 362. old(paul) <- (~38) [resolution 352,55] 363. $false <- (~38) [subsumption resolution 362,112] 364. 38 [avatar contradiction clause 363] 365. $false [avatar sat refutation 121,126,131,132,207,235,353,357,364] % SZS output end Proof for 3627243852124307784402223 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Everyone who is both not funny and not strong is either kind or not kind. If john is either not generous or patient then someone is not generous and vice versa. If someone is calm or not humble then paul is not old or wise. If someone is strong or not rich then lucy is both humble and creative. If paul is either creative or not brave then fred is either not old or not curious. If someone is not rich then fred is either calm or quiet and vice versa. If lucy is not calm then susan is both not funny and humble. If paul is not quiet then someone is funny or brave and vice versa. Everyone who is not humble is brave or not old and vice versa. Everyone who is either quiet or calm is brave or not funny. Everyone who is either not strong or old is not kind. Everyone who is either old or humble is either not curious or calm and vice versa. Everyone who is both quiet and not wise is quiet and vice versa. If paul is both funny and kind then paul is either brave or not funny and vice versa. If paul is not happy then someone is kind or strong and vice versa. Everyone who is either happy or not old is not curious or not patient and vice versa. Paul is both calm and not strong. Someone is funny. Someone is either rich or creative. Lucy is brave. Someone is either rich or funny. Lucy is not quiet. Someone is both not generous and creative. Lucy is not patient.

Paul is quiet.

contradiction

(![X]:((~funny(X)&~strong(X))=>(kind(X)<~>~kind(X))))& (((~generous(john)<~>patient(john)))<=>(?[X]:(~generous(X))))& ((?[X]:((calm(X)|~humble(X))))=>((~old(paul)|wise(paul))))& ((?[X]:((strong(X)|~rich(X))))=>((humble(lucy)&creative(lucy))))& (((creative(paul)<~>~brave(paul)))=>((~old(fred)<~>~curious(fred))))& ((?[X]:(~rich(X)))<=>((calm(fred)<~>quiet(fred))))& ((~calm(lucy))=>((~funny(susan)&humble(susan))))& ((~quiet(paul))<=>(?[X]:((funny(X)|brave(X)))))& (![X]:(~humble(X)<=>(brave(X)|~old(X))))& (![X]:((quiet(X)<~>calm(X))=>(brave(X)|~funny(X))))& (![X]:((~strong(X)<~>old(X))=>~kind(X)))& (![X]:((old(X)<~>humble(X))<=>(~curious(X)<~>calm(X))))& (![X]:((quiet(X)&~wise(X))<=>quiet(X)))& (((funny(paul)&kind(paul)))<=>((brave(paul)<~>~funny(paul))))& ((~happy(paul))<=>(?[X]:((kind(X)|strong(X)))))& (![X]:((happy(X)<~>~old(X))<=>(~curious(X)|~patient(X))))& ((calm(paul)&~strong(paul)))& (?[X]:(funny(X)))& (?[X]:((rich(X)<~>creative(X))))& (brave(lucy))& (?[X]:((rich(X)<~>funny(X))))& (~quiet(lucy))& (?[X]:((~generous(X)&creative(X))))& (~patient(lucy))

quiet(paul)

% SZS status Unsatisfiable for 7183864348897050798205763 % SZS output start Proof for 7183864348897050798205763 8. ~quiet(paul) <=> ? [X0] : (brave(X0) | funny(X0)) [input p7] 14. (kind(paul) & funny(paul)) <=> (brave(paul) <~> ~funny(paul)) [input p13] 25. quiet(paul) [input hypothesis] 46. (~quiet(paul) | ! [X0] : (~brave(X0) & ~funny(X0))) & (? [X0] : (brave(X0) | funny(X0)) | quiet(paul)) [nnf transformation 8] 47. (~quiet(paul) | ! [X0] : (~brave(X0) & ~funny(X0))) & (? [X1] : (brave(X1) | funny(X1)) | quiet(paul)) [rectify 46] 48. ? [X1] : (brave(X1) | funny(X1)) => (brave(sK2) | funny(sK2)) [choice axiom] 49. (~quiet(paul) | ! [X0] : (~brave(X0) & ~funny(X0))) & ((brave(sK2) | funny(sK2)) | quiet(paul)) [skolemisation 47,48] 57. ((kind(paul) & funny(paul)) | ((brave(paul) | funny(paul)) & (~funny(paul) | ~brave(paul)))) & (((funny(paul) | ~brave(paul)) & (~funny(paul) | brave(paul))) | (~kind(paul) | ~funny(paul))) [nnf transformation 14] 58. ((kind(paul) & funny(paul)) | ((brave(paul) | funny(paul)) & (~funny(paul) | ~brave(paul)))) & (((funny(paul) | ~brave(paul)) & (~funny(paul) | brave(paul))) | ~kind(paul) | ~funny(paul)) [flattening 57] 98. ~quiet(paul) | ~funny(X0) [cnf transformation 49] 99. ~quiet(paul) | ~brave(X0) [cnf transformation 49] 121. funny(paul) | brave(paul) | funny(paul) [cnf transformation 58] 145. quiet(paul) [cnf transformation 25] 147. funny(paul) | brave(paul) [duplicate literal removal 121] 202. 13 <=> brave(paul) [avatar definition] 204. brave(paul) <- (13) [avatar component clause 202] 252. 23 <=> ! [X0] : ~brave(X0) [avatar definition] 253. ~brave(X0) <- (23) [avatar component clause 252] 255. 24 <=> quiet(paul) [avatar definition] 258. 23 | ~24 [avatar split clause 99,255,252] 260. 25 <=> ! [X0] : ~funny(X0) [avatar definition] 261. ~funny(X0) <- (25) [avatar component clause 260] 262. 25 | ~24 [avatar split clause 98,255,260] 277. 28 <=> funny(paul) [avatar definition] 279. funny(paul) <- (28) [avatar component clause 277] 286. 13 | 28 [avatar split clause 147,277,202] 326. 24 [avatar split clause 145,255] 327. $false <- (13, 23) [subsumption resolution 204,253] 328. ~13 | ~23 [avatar contradiction clause 327] 329. $false <- (25, 28) [subsumption resolution 279,261] 330. ~25 | ~28 [avatar contradiction clause 329] 331. $false [avatar sat refutation 258,262,286,326,328,330] % SZS output end Proof for 7183864348897050798205763 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.018 s % ------------------------------ % ------------------------------

If mary is both funny and tall then lucy is both not humble and not calm and vice versa. If susan is brave or not humble then john is both kind and not humble and vice versa. If someone is both not quiet and not funny then someone is not funny or rich. Everyone who is not creative is both not brave and strong. If someone is funny then someone is not curious or not brave. Everyone who is not patient or not old is not strong or not curious and vice versa. If someone is happy or rich then john is either not rich or not humble. Everyone who is both calm and not tall is humble or tall. Everyone who is either not old or curious is not rich or humble and vice versa. If someone is not brave or generous then mary is both not kind and happy. Everyone who is both kind and not kind is not calm or not generous and vice versa. If someone is brave or old then someone is calm or not humble and vice versa. Everyone who is either not quiet or not kind is quiet and vice versa. If mary is both not humble and curious then someone is creative or not generous and vice versa. Everyone who is both not kind and not tall is both not humble and not happy and vice versa. Someone is either generous or not happy. Alice is tall or calm. Someone is creative. Someone is tall or generous. Lucy is either not patient or brave.

John is not tall.

contradiction

(((funny(mary)&tall(mary)))<=>((~humble(lucy)&~calm(lucy))))& (((brave(susan)|~humble(susan)))<=>((kind(john)&~humble(john))))& ((?[X]:((~quiet(X)&~funny(X))))=>(?[X]:((~funny(X)|rich(X)))))& (![X]:(~creative(X)=>(~brave(X)&strong(X))))& ((?[X]:(funny(X)))=>(?[X]:((~curious(X)|~brave(X)))))& (![X]:((~patient(X)|~old(X))<=>(~strong(X)|~curious(X))))& ((?[X]:((happy(X)|rich(X))))=>((~rich(john)<~>~humble(john))))& (![X]:((calm(X)&~tall(X))=>(humble(X)|tall(X))))& (![X]:((~old(X)<~>curious(X))<=>(~rich(X)|humble(X))))& ((?[X]:((~brave(X)|generous(X))))=>((~kind(mary)&happy(mary))))& (![X]:((kind(X)&~kind(X))<=>(~calm(X)|~generous(X))))& ((?[X]:((brave(X)|old(X))))<=>(?[X]:((calm(X)|~humble(X)))))& (![X]:((~quiet(X)<~>~kind(X))<=>quiet(X)))& (((~humble(mary)&curious(mary)))<=>(?[X]:((creative(X)|~generous(X)))))& (![X]:((~kind(X)&~tall(X))<=>(~humble(X)&~happy(X))))& (?[X]:((generous(X)<~>~happy(X))))& ((tall(alice)|calm(alice)))& (?[X]:(creative(X)))& (?[X]:((tall(X)|generous(X))))& ((~patient(lucy)<~>brave(lucy)))

~tall(john)

% SZS status Unsatisfiable for 8008793062093701026773791 % SZS output start Proof for 8008793062093701026773791 8. ! [X0] : ((~tall(X0) & calm(X0)) => (tall(X0) | humble(X0))) [input p7] 11. ! [X0] : ((~kind(X0) & kind(X0)) <=> (~generous(X0) | ~calm(X0))) [input p10] 13. ! [X0] : ((~quiet(X0) <~> ~kind(X0)) <=> quiet(X0)) [input p12] 15. ! [X0] : ((~tall(X0) & ~kind(X0)) <=> (~happy(X0) & ~humble(X0))) [input p14] 21. ~tall(john) [input hypothesis] 29. ! [X0] : ((tall(X0) | humble(X0)) | (tall(X0) | ~calm(X0))) [ennf transformation 8] 30. ! [X0] : (tall(X0) | humble(X0) | tall(X0) | ~calm(X0)) [flattening 29] 47. ! [X0] : (((~kind(X0) & kind(X0)) | (generous(X0) & calm(X0))) & ((~generous(X0) | ~calm(X0)) | (kind(X0) | ~kind(X0)))) [nnf transformation 11] 48. ! [X0] : (((~kind(X0) & kind(X0)) | (generous(X0) & calm(X0))) & (~generous(X0) | ~calm(X0) | kind(X0) | ~kind(X0))) [flattening 47] 54. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | ~quiet(X0)) & (quiet(X0) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [nnf transformation 13] 60. ! [X0] : (((~tall(X0) & ~kind(X0)) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | (tall(X0) | kind(X0)))) [nnf transformation 15] 61. ! [X0] : (((~tall(X0) & ~kind(X0)) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | tall(X0) | kind(X0))) [flattening 60] 91. tall(X0) | humble(X0) | tall(X0) | ~calm(X0) [cnf transformation 30] 103. kind(X0) | calm(X0) [cnf transformation 48] 105. ~kind(X0) | calm(X0) [cnf transformation 48] 111. quiet(X0) | ~kind(X0) | quiet(X0) [cnf transformation 54] 113. ~kind(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 54] 120. ~humble(X0) | tall(X0) | kind(X0) [cnf transformation 61] 131. ~tall(john) [cnf transformation 21] 132. quiet(X0) | ~kind(X0) [duplicate literal removal 111] 133. ~quiet(X0) | ~kind(X0) [duplicate literal removal 113] 134. ~calm(X0) | humble(X0) | tall(X0) [duplicate literal removal 91] 233. calm(X0) [subsumption resolution 103,105] 248. ~kind(X0) [subsumption resolution 132,133] 269. ~humble(X0) | tall(X0) [subsumption resolution 120,248] 327. humble(X0) | tall(X0) [resolution 134,233] 328. tall(X0) [subsumption resolution 327,269] 357. $false [resolution 328,131] % SZS output end Proof for 8008793062093701026773791 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Everyone who is both old and not curious is either not creative or not kind. Everyone who is both strong and not humble is either not strong or tall. Everyone who is not kind is both not curious and not humble. Everyone who is calm or not kind is either not tall or calm and vice versa. Everyone who is not generous is both not wise and not funny. Everyone who is both patient and kind is either kind or tall and vice versa. Everyone who is curious or not quiet is quiet or not humble and vice versa. Everyone who is both calm and not tall is not happy or not rich and vice versa. If mary is either not rich or kind then lucy is wise or not rich and vice versa. If lucy is not happy or funny then lucy is not kind or not funny and vice versa. Everyone who is quiet is both not happy and not brave and vice versa. Everyone who is brave is both not generous and humble. Everyone who is both kind and humble is wise or quiet and vice versa. Everyone who is either funny or rich is not creative and vice versa. Everyone who is not patient is either old or kind and vice versa. Someone is either kind or not generous. John is both not wise and happy. Someone is either calm or not happy. Someone is rich or not creative. Someone is both generous and not calm. Someone is curious or wise.

Mary is brave.

contradiction

(![X]:((old(X)&~curious(X))=>(~creative(X)<~>~kind(X))))& (![X]:((strong(X)&~humble(X))=>(~strong(X)<~>tall(X))))& (![X]:(~kind(X)=>(~curious(X)&~humble(X))))& (![X]:((calm(X)|~kind(X))<=>(~tall(X)<~>calm(X))))& (![X]:(~generous(X)=>(~wise(X)&~funny(X))))& (![X]:((patient(X)&kind(X))<=>(kind(X)<~>tall(X))))& (![X]:((curious(X)|~quiet(X))<=>(quiet(X)|~humble(X))))& (![X]:((calm(X)&~tall(X))<=>(~happy(X)|~rich(X))))& (((~rich(mary)<~>kind(mary)))<=>((wise(lucy)|~rich(lucy))))& (((~happy(lucy)|funny(lucy)))<=>((~kind(lucy)|~funny(lucy))))& (![X]:(quiet(X)<=>(~happy(X)&~brave(X))))& (![X]:(brave(X)=>(~generous(X)&humble(X))))& (![X]:((kind(X)&humble(X))<=>(wise(X)|quiet(X))))& (![X]:((funny(X)<~>rich(X))<=>~creative(X)))& (![X]:(~patient(X)<=>(old(X)<~>kind(X))))& (?[X]:((kind(X)<~>~generous(X))))& ((~wise(john)&happy(john)))& (?[X]:((calm(X)<~>~happy(X))))& (?[X]:((rich(X)|~creative(X))))& (?[X]:((generous(X)&~calm(X))))& (?[X]:((curious(X)|wise(X))))

brave(mary)

% SZS status Unsatisfiable for 2111394053033039716704250 % SZS output start Proof for 2111394053033039716704250 7. ! [X0] : ((~quiet(X0) | curious(X0)) <=> (~humble(X0) | quiet(X0))) [input p6] 11. ! [X0] : (quiet(X0) <=> (~brave(X0) & ~happy(X0))) [input p10] 12. ! [X0] : (brave(X0) => (humble(X0) & ~generous(X0))) [input p11] 22. brave(mary) [input hypothesis] 29. ! [X0] : ((humble(X0) & ~generous(X0)) | ~brave(X0)) [ennf transformation 12] 36. ! [X0] : (((~quiet(X0) | curious(X0)) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | (quiet(X0) & ~curious(X0)))) [nnf transformation 7] 37. ! [X0] : ((~quiet(X0) | curious(X0) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | (quiet(X0) & ~curious(X0)))) [flattening 36] 44. ! [X0] : ((quiet(X0) | (brave(X0) | happy(X0))) & ((~brave(X0) & ~happy(X0)) | ~quiet(X0))) [nnf transformation 11] 45. ! [X0] : ((quiet(X0) | brave(X0) | happy(X0)) & ((~brave(X0) & ~happy(X0)) | ~quiet(X0))) [flattening 44] 83. ~humble(X0) | quiet(X0) | quiet(X0) [cnf transformation 37] 102. ~brave(X0) | ~quiet(X0) [cnf transformation 45] 105. ~brave(X0) | humble(X0) [cnf transformation 29] 129. brave(mary) [cnf transformation 22] 132. ~humble(X0) | quiet(X0) [duplicate literal removal 83] 215. ~quiet(mary) [resolution 102,129] 217. humble(mary) [resolution 105,129] 222. quiet(mary) [resolution 132,217] 223. $false [subsumption resolution 222,215] % SZS output end Proof for 2111394053033039716704250 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Everyone who is funny or not curious is either curious or not quiet and vice versa. Everyone who is both generous and happy is not brave. Everyone who is funny or happy is both calm and not rich and vice versa. Everyone who is both not curious and brave is either quiet or curious and vice versa. If someone is both not rich and not brave then someone is either curious or not quiet and vice versa. If alice is either creative or wise then susan is creative and vice versa. If someone is both humble and creative then alice is not wise or not tall and vice versa. If susan is not happy then susan is either brave or wise. Everyone who is either curious or patient is either not generous or quiet. If someone is both not happy and generous then someone is creative or not curious and vice versa. If someone is not brave or not kind then someone is not old. Everyone who is not rich is both tall and not funny and vice versa. If mary is either not rich or rich then alice is either curious or not patient and vice versa. If someone is both patient and wise then john is not brave and vice versa. If someone is both kind and not patient then lucy is both not tall and tall and vice versa. If someone is not old then someone is not kind or not humble. Susan is patient or generous. Someone is either not happy or not wise. Someone is both calm and tall. Someone is either old or not brave. Alice is both humble and not brave. Someone is both not kind and not wise.

Alice is curious.

contradiction

(![X]:((funny(X)|~curious(X))<=>(curious(X)<~>~quiet(X))))& (![X]:((generous(X)&happy(X))=>~brave(X)))& (![X]:((funny(X)|happy(X))<=>(calm(X)&~rich(X))))& (![X]:((~curious(X)&brave(X))<=>(quiet(X)<~>curious(X))))& ((?[X]:((~rich(X)&~brave(X))))<=>(?[X]:((curious(X)<~>~quiet(X)))))& (((creative(alice)<~>wise(alice)))<=>(creative(susan)))& ((?[X]:((humble(X)&creative(X))))<=>((~wise(alice)|~tall(alice))))& ((~happy(susan))=>((brave(susan)<~>wise(susan))))& (![X]:((curious(X)<~>patient(X))=>(~generous(X)<~>quiet(X))))& ((?[X]:((~happy(X)&generous(X))))<=>(?[X]:((creative(X)|~curious(X)))))& ((?[X]:((~brave(X)|~kind(X))))=>(?[X]:(~old(X))))& (![X]:(~rich(X)<=>(tall(X)&~funny(X))))& (((~rich(mary)<~>rich(mary)))<=>((curious(alice)<~>~patient(alice))))& ((?[X]:((patient(X)&wise(X))))<=>(~brave(john)))& ((?[X]:((kind(X)&~patient(X))))<=>((~tall(lucy)&tall(lucy))))& ((?[X]:(~old(X)))=>(?[X]:((~kind(X)|~humble(X)))))& ((patient(susan)|generous(susan)))& (?[X]:((~happy(X)<~>~wise(X))))& (?[X]:((calm(X)&tall(X))))& (?[X]:((old(X)<~>~brave(X))))& ((humble(alice)&~brave(alice)))& (?[X]:((~kind(X)&~wise(X))))

curious(alice)

% SZS status Unsatisfiable for 7975439818033128333501983 % SZS output start Proof for 7975439818033128333501983 1. ! [X0] : ((~curious(X0) | funny(X0)) <=> (curious(X0) <~> ~quiet(X0))) [input p0] 3. ! [X0] : ((happy(X0) | funny(X0)) <=> (~rich(X0) & calm(X0))) [input p2] 4. ! [X0] : ((brave(X0) & ~curious(X0)) <=> (quiet(X0) <~> curious(X0))) [input p3] 12. ! [X0] : (~rich(X0) <=> (~funny(X0) & tall(X0))) [input p11] 23. curious(alice) [input hypothesis] 34. ! [X0] : (((~curious(X0) | funny(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (curious(X0) & ~funny(X0)))) [nnf transformation 1] 35. ! [X0] : ((~curious(X0) | funny(X0) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (curious(X0) & ~funny(X0)))) [flattening 34] 36. ! [X0] : (((happy(X0) | funny(X0)) | (rich(X0) | ~calm(X0))) & ((~rich(X0) & calm(X0)) | (~happy(X0) & ~funny(X0)))) [nnf transformation 3] 37. ! [X0] : ((happy(X0) | funny(X0) | rich(X0) | ~calm(X0)) & ((~rich(X0) & calm(X0)) | (~happy(X0) & ~funny(X0)))) [flattening 36] 38. ! [X0] : (((brave(X0) & ~curious(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (~brave(X0) | curious(X0)))) [nnf transformation 4] 39. ! [X0] : (((brave(X0) & ~curious(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ~brave(X0) | curious(X0))) [flattening 38] 61. ! [X0] : ((~rich(X0) | (funny(X0) | ~tall(X0))) & ((~funny(X0) & tall(X0)) | rich(X0))) [nnf transformation 12] 62. ! [X0] : ((~rich(X0) | funny(X0) | ~tall(X0)) & ((~funny(X0) & tall(X0)) | rich(X0))) [flattening 61] 90. ~curious(X0) | funny(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 35] 95. ~rich(X0) | ~funny(X0) [cnf transformation 37] 101. ~curious(X0) | quiet(X0) | ~curious(X0) [cnf transformation 39] 133. ~funny(X0) | rich(X0) [cnf transformation 62] 162. curious(alice) [cnf transformation 23] 168. ~curious(X0) | quiet(X0) [duplicate literal removal 101] 170. ~quiet(X0) | funny(X0) | ~curious(X0) [duplicate literal removal 90] 289. ~funny(X0) [subsumption resolution 133,95] 295. 26 <=> curious(alice) [avatar definition] 296. curious(alice) <- (26) [avatar component clause 295] 374. 26 [avatar split clause 162,295] 379. quiet(alice) <- (26) [resolution 168,296] 392. funny(alice) | ~curious(alice) <- (26) [resolution 170,379] 394. ~curious(alice) <- (26) [subsumption resolution 392,289] 395. $false <- (26) [subsumption resolution 394,296] 396. ~26 [avatar contradiction clause 395] 400. $false [avatar sat refutation 374,396] % SZS output end Proof for 7975439818033128333501983 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

If mary is both not brave and happy then john is both humble and not calm and vice versa. Everyone who is not tall is not creative and vice versa. If alice is either humble or not generous then susan is not strong and vice versa. Everyone who is not creative is both not humble and generous. If someone is both not wise and not old then john is either wise or humble. Everyone who is both humble and curious is either not wise or tall and vice versa. Everyone who is both not wise and patient is either creative or not tall. Everyone who is both not brave and wise is not funny and vice versa. If lucy is either brave or not funny then someone is both not kind and kind. If susan is either not humble or old then someone is either not calm or not tall and vice versa. If paul is both quiet and not rich then someone is strong or not brave. Everyone who is both happy and not old is either not humble or not brave and vice versa. Everyone who is either generous or not rich is either not brave or not funny and vice versa. Everyone who is generous is not quiet. Everyone who is both kind and not kind is quiet and vice versa. Everyone who is not humble is either calm or not old. Mary is kind. Someone is not generous. Someone is either not strong or kind. Mary is not creative. Mary is patient or not humble. Fred is either wise or not generous. Alice is not curious. John is both not brave and not wise.

Susan is not rich.

neutral

(((~brave(mary)&happy(mary)))<=>((humble(john)&~calm(john))))& (![X]:(~tall(X)<=>~creative(X)))& (((humble(alice)<~>~generous(alice)))<=>(~strong(susan)))& (![X]:(~creative(X)=>(~humble(X)&generous(X))))& ((?[X]:((~wise(X)&~old(X))))=>((wise(john)<~>humble(john))))& (![X]:((humble(X)&curious(X))<=>(~wise(X)<~>tall(X))))& (![X]:((~wise(X)&patient(X))=>(creative(X)<~>~tall(X))))& (![X]:((~brave(X)&wise(X))<=>~funny(X)))& (((brave(lucy)<~>~funny(lucy)))=>(?[X]:((~kind(X)&kind(X)))))& (((~humble(susan)<~>old(susan)))<=>(?[X]:((~calm(X)<~>~tall(X)))))& (((quiet(paul)&~rich(paul)))=>(?[X]:((strong(X)|~brave(X)))))& (![X]:((happy(X)&~old(X))<=>(~humble(X)<~>~brave(X))))& (![X]:((generous(X)<~>~rich(X))<=>(~brave(X)<~>~funny(X))))& (![X]:(generous(X)=>~quiet(X)))& (![X]:((kind(X)&~kind(X))<=>quiet(X)))& (![X]:(~humble(X)=>(calm(X)<~>~old(X))))& (kind(mary))& (?[X]:(~generous(X)))& (?[X]:((~strong(X)<~>kind(X))))& (~creative(mary))& ((patient(mary)|~humble(mary)))& ((wise(fred)<~>~generous(fred)))& (~curious(alice))& ((~brave(john)&~wise(john)))

~rich(susan)

Everyone who is funny or not happy is either not happy or not curious. If someone is either rich or not brave then someone is curious or strong. Everyone who is not humble is both not humble and happy and vice versa. If someone is either not humble or curious then susan is both not curious and humble. Everyone who is strong is tall and vice versa. Everyone who is not humble or calm is either brave or quiet and vice versa. If someone is rich or not creative then someone is not calm. If paul is tall or not generous then john is both not tall and wise. Everyone who is creative is not funny or not humble and vice versa. Everyone who is quiet or strong is tall or rich and vice versa. If someone is both quiet and strong then someone is quiet or funny and vice versa. Everyone who is creative or not funny is either quiet or rich and vice versa. Everyone who is both not funny and tall is not kind or not happy and vice versa. If someone is either not happy or not brave then someone is not wise and vice versa. If mary is wise or not rich then mary is either not creative or generous and vice versa. Someone is kind or not generous. Susan is either not calm or not tall. Someone is either not calm or not brave. Fred is either creative or not happy.

Fred is not strong.

contradiction

(![X]:((funny(X)|~happy(X))=>(~happy(X)<~>~curious(X))))& ((?[X]:((rich(X)<~>~brave(X))))=>(?[X]:((curious(X)|strong(X)))))& (![X]:(~humble(X)<=>(~humble(X)&happy(X))))& ((?[X]:((~humble(X)<~>curious(X))))=>((~curious(susan)&humble(susan))))& (![X]:(strong(X)<=>tall(X)))& (![X]:((~humble(X)|calm(X))<=>(brave(X)<~>quiet(X))))& ((?[X]:((rich(X)|~creative(X))))=>(?[X]:(~calm(X))))& (((tall(paul)|~generous(paul)))=>((~tall(john)&wise(john))))& (![X]:(creative(X)<=>(~funny(X)|~humble(X))))& (![X]:((quiet(X)|strong(X))<=>(tall(X)|rich(X))))& ((?[X]:((quiet(X)&strong(X))))<=>(?[X]:((quiet(X)|funny(X)))))& (![X]:((creative(X)|~funny(X))<=>(quiet(X)<~>rich(X))))& (![X]:((~funny(X)&tall(X))<=>(~kind(X)|~happy(X))))& ((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:(~wise(X))))& (((wise(mary)|~rich(mary)))<=>((~creative(mary)<~>generous(mary))))& (?[X]:((kind(X)|~generous(X))))& ((~calm(susan)<~>~tall(susan)))& (?[X]:((~calm(X)<~>~brave(X))))& ((creative(fred)<~>~happy(fred)))

~strong(fred)

% SZS status Unsatisfiable for 6548197517352304684414070 % SZS output start Proof for 6548197517352304684414070 5. ! [X0] : (strong(X0) <=> tall(X0)) [input p4] 9. ! [X0] : (creative(X0) <=> (~humble(X0) | ~funny(X0))) [input p8] 10. ! [X0] : ((strong(X0) | quiet(X0)) <=> (rich(X0) | tall(X0))) [input p9] 12. ! [X0] : ((~funny(X0) | creative(X0)) <=> (quiet(X0) <~> rich(X0))) [input p11] 13. ! [X0] : ((tall(X0) & ~funny(X0)) <=> (~happy(X0) | ~kind(X0))) [input p12] 19. creative(fred) <~> ~happy(fred) [input p18] 20. ~strong(fred) [input hypothesis] 38. ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))) [nnf transformation 5] 44. ! [X0] : ((creative(X0) | (humble(X0) & funny(X0))) & ((~humble(X0) | ~funny(X0)) | ~creative(X0))) [nnf transformation 9] 45. ! [X0] : ((creative(X0) | (humble(X0) & funny(X0))) & (~humble(X0) | ~funny(X0) | ~creative(X0))) [flattening 44] 46. ! [X0] : (((strong(X0) | quiet(X0)) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | (~strong(X0) & ~quiet(X0)))) [nnf transformation 10] 47. ! [X0] : ((strong(X0) | quiet(X0) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | (~strong(X0) & ~quiet(X0)))) [flattening 46] 53. ! [X0] : (((~funny(X0) | creative(X0)) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | (funny(X0) & ~creative(X0)))) [nnf transformation 12] 54. ! [X0] : ((~funny(X0) | creative(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | (funny(X0) & ~creative(X0)))) [flattening 53] 55. ! [X0] : (((tall(X0) & ~funny(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~tall(X0) | funny(X0)))) [nnf transformation 13] 56. ! [X0] : (((tall(X0) & ~funny(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~tall(X0) | funny(X0))) [flattening 55] 70. (happy(fred) | ~creative(fred)) & (~happy(fred) | creative(fred)) [nnf transformation 19] 85. ~tall(X0) | strong(X0) [cnf transformation 38] 99. creative(X0) | funny(X0) [cnf transformation 45] 101. ~quiet(X0) | tall(X0) | rich(X0) [cnf transformation 47] 104. ~rich(X0) | quiet(X0) | strong(X0) [cnf transformation 47] 110. ~creative(X0) | quiet(X0) | rich(X0) [cnf transformation 54] 112. ~creative(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 54] 118. ~funny(X0) | happy(X0) [cnf transformation 56] 136. ~happy(fred) | creative(fred) [cnf transformation 70] 138. ~strong(fred) [cnf transformation 20] 315. 39 <=> creative(fred) [avatar definition] 316. creative(fred) <- (39) [avatar component clause 315] 317. ~creative(fred) <- (~39) [avatar component clause 315] 319. 40 <=> happy(fred) [avatar definition] 320. ~happy(fred) <- (~40) [avatar component clause 319] 323. 39 | ~40 [avatar split clause 136,319,315] 327. funny(fred) <- (~39) [resolution 99,317] 340. happy(fred) <- (~39) [resolution 118,327] 341. $false <- (~39, ~40) [subsumption resolution 340,320] 342. 39 | 40 [avatar contradiction clause 341] 432. quiet(fred) | rich(fred) <- (39) [resolution 110,316] 434. 53 <=> rich(fred) [avatar definition] 435. ~rich(fred) <- (~53) [avatar component clause 434] 436. rich(fred) <- (53) [avatar component clause 434] 438. 54 <=> quiet(fred) [avatar definition] 440. quiet(fred) <- (54) [avatar component clause 438] 441. 53 | 54 | ~39 [avatar split clause 432,315,438,434] 447. quiet(fred) | strong(fred) <- (53) [resolution 436,104] 448. quiet(fred) <- (53) [subsumption resolution 447,138] 449. 54 | ~53 [avatar split clause 448,434,438] 452. ~quiet(fred) | ~rich(fred) <- (39) [resolution 112,316] 453. ~rich(fred) <- (39, 54) [subsumption resolution 452,440] 456. ~53 | ~39 | ~54 [avatar split clause 453,438,315,434] 473. tall(fred) | rich(fred) <- (54) [resolution 440,101] 476. tall(fred) <- (~53, 54) [subsumption resolution 473,435] 565. strong(fred) <- (~53, 54) [resolution 476,85] 566. $false <- (~53, 54) [subsumption resolution 565,138] 567. 53 | ~54 [avatar contradiction clause 566] 568. $false [avatar sat refutation 323,342,441,449,456,567] % SZS output end Proof for 6548197517352304684414070 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

If susan is not strong then someone is quiet. Everyone who is rich or old is not funny and vice versa. If john is not old then mary is either not wise or wise. If fred is both generous and calm then someone is rich and vice versa. If someone is either not creative or kind then someone is both patient and not wise and vice versa. Everyone who is not old or brave is generous or rich. If lucy is not generous or not funny then fred is either not patient or rich. Everyone who is not brave or not quiet is either quiet or not old and vice versa. Everyone who is quiet or calm is not wise. Everyone who is either not happy or humble is either patient or humble. If someone is not creative then susan is either creative or not rich and vice versa. If mary is not happy then someone is strong or not old and vice versa. Everyone who is either patient or not kind is not strong or not wise. Everyone who is both kind and not humble is not rich or strong and vice versa. If someone is humble then someone is either not tall or not calm and vice versa. If someone is either not quiet or tall then paul is both not humble and not curious. Alice is not funny or not wise. Alice is kind. Alice is both wise and not generous. John is not quiet or wise. Someone is not creative or rich. Someone is both not happy and not old. Susan is quiet or not funny.

Lucy is not funny.

neutral

((~strong(susan))=>(?[X]:(quiet(X))))& (![X]:((rich(X)|old(X))<=>~funny(X)))& ((~old(john))=>((~wise(mary)<~>wise(mary))))& (((generous(fred)&calm(fred)))<=>(?[X]:(rich(X))))& ((?[X]:((~creative(X)<~>kind(X))))<=>(?[X]:((patient(X)&~wise(X)))))& (![X]:((~old(X)|brave(X))=>(generous(X)|rich(X))))& (((~generous(lucy)|~funny(lucy)))=>((~patient(fred)<~>rich(fred))))& (![X]:((~brave(X)|~quiet(X))<=>(quiet(X)<~>~old(X))))& (![X]:((quiet(X)|calm(X))=>~wise(X)))& (![X]:((~happy(X)<~>humble(X))=>(patient(X)<~>humble(X))))& ((?[X]:(~creative(X)))<=>((creative(susan)<~>~rich(susan))))& ((~happy(mary))<=>(?[X]:((strong(X)|~old(X)))))& (![X]:((patient(X)<~>~kind(X))=>(~strong(X)|~wise(X))))& (![X]:((kind(X)&~humble(X))<=>(~rich(X)|strong(X))))& ((?[X]:(humble(X)))<=>(?[X]:((~tall(X)<~>~calm(X)))))& ((?[X]:((~quiet(X)<~>tall(X))))=>((~humble(paul)&~curious(paul))))& ((~funny(alice)|~wise(alice)))& (kind(alice))& ((wise(alice)&~generous(alice)))& ((~quiet(john)|wise(john)))& (?[X]:((~creative(X)|rich(X))))& (?[X]:((~happy(X)&~old(X))))& ((quiet(susan)|~funny(susan)))

~funny(lucy)

If someone is both strong and generous then paul is both not tall and not wise. Everyone who is either not creative or patient is both old and not strong. Everyone who is either not kind or not old is both not happy and funny. If someone is not patient or not calm then someone is either not curious or quiet and vice versa. If someone is both happy and not quiet then susan is not brave or generous. If someone is not happy then alice is not quiet. Everyone who is both tall and creative is both quiet and not tall and vice versa. If paul is not wise then john is both strong and not wise. Everyone who is both creative and not creative is either not kind or old and vice versa. If susan is not old then someone is creative and vice versa. If someone is both creative and strong then someone is either wise or not kind. Everyone who is not happy is either brave or calm. If someone is generous or kind then someone is either curious or humble. If someone is either strong or not old then mary is generous or humble and vice versa. Everyone who is curious is not kind and vice versa. Everyone who is not creative or not happy is both not rich and calm and vice versa. Someone is either rich or creative. Fred is not old. Someone is both not quiet and not generous. Someone is either quiet or kind. Lucy is not humble or not patient. Fred is quiet. Someone is both wise and not kind. Paul is either rich or not happy.

Lucy is not funny.

contradiction

((?[X]:((strong(X)&generous(X))))=>((~tall(paul)&~wise(paul))))& (![X]:((~creative(X)<~>patient(X))=>(old(X)&~strong(X))))& (![X]:((~kind(X)<~>~old(X))=>(~happy(X)&funny(X))))& ((?[X]:((~patient(X)|~calm(X))))<=>(?[X]:((~curious(X)<~>quiet(X)))))& ((?[X]:((happy(X)&~quiet(X))))=>((~brave(susan)|generous(susan))))& ((?[X]:(~happy(X)))=>(~quiet(alice)))& (![X]:((tall(X)&creative(X))<=>(quiet(X)&~tall(X))))& ((~wise(paul))=>((strong(john)&~wise(john))))& (![X]:((creative(X)&~creative(X))<=>(~kind(X)<~>old(X))))& ((~old(susan))<=>(?[X]:(creative(X))))& ((?[X]:((creative(X)&strong(X))))=>(?[X]:((wise(X)<~>~kind(X)))))& (![X]:(~happy(X)=>(brave(X)<~>calm(X))))& ((?[X]:((generous(X)|kind(X))))=>(?[X]:((curious(X)<~>humble(X)))))& ((?[X]:((strong(X)<~>~old(X))))<=>((generous(mary)|humble(mary))))& (![X]:(curious(X)<=>~kind(X)))& (![X]:((~creative(X)|~happy(X))<=>(~rich(X)&calm(X))))& (?[X]:((rich(X)<~>creative(X))))& (~old(fred))& (?[X]:((~quiet(X)&~generous(X))))& (?[X]:((quiet(X)<~>kind(X))))& ((~humble(lucy)|~patient(lucy)))& (quiet(fred))& (?[X]:((wise(X)&~kind(X))))& ((rich(paul)<~>~happy(paul)))

~funny(lucy)

% SZS status Unsatisfiable for 1973305770866612328928125 % SZS output start Proof for 1973305770866612328928125 3. ! [X0] : ((~kind(X0) <~> ~old(X0)) => (funny(X0) & ~happy(X0))) [input p2] 9. ! [X0] : ((~creative(X0) & creative(X0)) <=> (~kind(X0) <~> old(X0))) [input p8] 25. ~funny(lucy) [input hypothesis] 31. ! [X0] : ((funny(X0) & ~happy(X0)) | (~kind(X0) <=> ~old(X0))) [ennf transformation 3] 40. ! [X0] : ((funny(X0) & ~happy(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0)))) [nnf transformation 31] 48. ! [X0] : (((~creative(X0) & creative(X0)) | ((~kind(X0) | ~old(X0)) & (old(X0) | kind(X0)))) & (((~old(X0) | kind(X0)) & (old(X0) | ~kind(X0))) | (creative(X0) | ~creative(X0)))) [nnf transformation 9] 49. ! [X0] : (((~creative(X0) & creative(X0)) | ((~kind(X0) | ~old(X0)) & (old(X0) | kind(X0)))) & (((~old(X0) | kind(X0)) & (old(X0) | ~kind(X0))) | creative(X0) | ~creative(X0))) [flattening 48] 90. ~old(X0) | funny(X0) | kind(X0) [cnf transformation 40] 91. ~kind(X0) | funny(X0) | old(X0) [cnf transformation 40] 108. creative(X0) | old(X0) | kind(X0) [cnf transformation 49] 109. creative(X0) | ~kind(X0) | ~old(X0) [cnf transformation 49] 110. ~creative(X0) | old(X0) | kind(X0) [cnf transformation 49] 111. ~kind(X0) | ~creative(X0) | ~old(X0) [cnf transformation 49] 148. ~funny(lucy) [cnf transformation 25] 228. ~kind(X0) | ~old(X0) [subsumption resolution 109,111] 229. kind(X0) | old(X0) [subsumption resolution 108,110] 436. funny(X0) | old(X0) | old(X0) [resolution 91,229] 437. funny(X0) | old(X0) [duplicate literal removal 436] 488. old(lucy) [resolution 437,148] 545. 58 <=> kind(lucy) [avatar definition] 547. kind(lucy) <- (58) [avatar component clause 545] 558. funny(lucy) | kind(lucy) [resolution 488,90] 562. ~old(lucy) <- (58) [resolution 547,228] 565. $false <- (58) [subsumption resolution 562,488] 566. ~58 [avatar contradiction clause 565] 567. kind(lucy) [subsumption resolution 558,148] 568. 58 [avatar split clause 567,545] 569. $false [avatar sat refutation 566,568] % SZS output end Proof for 1973305770866612328928125 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

If someone is either kind or patient then john is strong. If mary is both not humble and brave then john is both strong and not quiet. Everyone who is not calm is tall. Everyone who is quiet or curious is both not kind and not humble. Everyone who is not tall is both not creative and not brave and vice versa. Everyone who is both happy and patient is both old and brave. Everyone who is both not patient and brave is not rich or not brave and vice versa. Everyone who is not brave or not wise is both not happy and strong. Everyone who is creative is both not generous and not curious and vice versa. Everyone who is not rich is brave and vice versa. Everyone who is strong or not creative is not calm or not wise. If someone is not curious or humble then someone is both calm and not creative and vice versa. If someone is wise then john is either patient or not patient. If susan is not strong then someone is both funny and patient and vice versa. If mary is not funny then john is humble or quiet. If someone is humble or patient then someone is not strong or funny and vice versa. Alice is either creative or happy. Mary is both not kind and not patient. John is either funny or rich. John is strong or humble. Someone is either happy or wise. Someone is either wise or funny. Someone is either creative or not old. Someone is either not funny or not strong.

Mary is not humble.

neutral

((?[X]:((kind(X)<~>patient(X))))=>(strong(john)))& (((~humble(mary)&brave(mary)))=>((strong(john)&~quiet(john))))& (![X]:(~calm(X)=>tall(X)))& (![X]:((quiet(X)|curious(X))=>(~kind(X)&~humble(X))))& (![X]:(~tall(X)<=>(~creative(X)&~brave(X))))& (![X]:((happy(X)&patient(X))=>(old(X)&brave(X))))& (![X]:((~patient(X)&brave(X))<=>(~rich(X)|~brave(X))))& (![X]:((~brave(X)|~wise(X))=>(~happy(X)&strong(X))))& (![X]:(creative(X)<=>(~generous(X)&~curious(X))))& (![X]:(~rich(X)<=>brave(X)))& (![X]:((strong(X)|~creative(X))=>(~calm(X)|~wise(X))))& ((?[X]:((~curious(X)|humble(X))))<=>(?[X]:((calm(X)&~creative(X)))))& ((?[X]:(wise(X)))=>((patient(john)<~>~patient(john))))& ((~strong(susan))<=>(?[X]:((funny(X)&patient(X)))))& ((~funny(mary))=>((humble(john)|quiet(john))))& ((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~strong(X)|funny(X)))))& ((creative(alice)<~>happy(alice)))& ((~kind(mary)&~patient(mary)))& ((funny(john)<~>rich(john)))& ((strong(john)|humble(john)))& (?[X]:((happy(X)<~>wise(X))))& (?[X]:((wise(X)<~>funny(X))))& (?[X]:((creative(X)<~>~old(X))))& (?[X]:((~funny(X)<~>~strong(X))))

~humble(mary)

If alice is generous then someone is patient or brave. If mary is both creative and old then paul is not strong or not humble. If someone is either curious or not old then someone is both strong and not patient. If mary is either old or not tall then someone is brave. Everyone who is not generous or old is not happy. If someone is both quiet and not rich then someone is either patient or happy. Everyone who is not rich or not happy is not rich and vice versa. If someone is either generous or not calm then john is not rich or strong. If someone is either tall or not calm then paul is not happy or quiet and vice versa. Everyone who is not strong or wise is either wise or not strong and vice versa. Everyone who is not kind is either not quiet or not patient and vice versa. Everyone who is not rich is generous or not wise and vice versa. If someone is both strong and not rich then someone is both calm and not quiet. Everyone who is both not patient and funny is creative or funny and vice versa. Everyone who is not generous is not wise or kind. Everyone who is not creative is not funny or not rich and vice versa. Someone is not wise. John is not happy or tall. Mary is quiet. Paul is creative or not calm. Someone is both not tall and not wise. Someone is either wise or tall. Someone is strong or not strong. Mary is not curious or old.

Alice is not creative.

entailment

((generous(alice))=>(?[X]:((patient(X)|brave(X)))))& (((creative(mary)&old(mary)))=>((~strong(paul)|~humble(paul))))& ((?[X]:((curious(X)<~>~old(X))))=>(?[X]:((strong(X)&~patient(X)))))& (((old(mary)<~>~tall(mary)))=>(?[X]:(brave(X))))& (![X]:((~generous(X)|old(X))=>~happy(X)))& ((?[X]:((quiet(X)&~rich(X))))=>(?[X]:((patient(X)<~>happy(X)))))& (![X]:((~rich(X)|~happy(X))<=>~rich(X)))& ((?[X]:((generous(X)<~>~calm(X))))=>((~rich(john)|strong(john))))& ((?[X]:((tall(X)<~>~calm(X))))<=>((~happy(paul)|quiet(paul))))& (![X]:((~strong(X)|wise(X))<=>(wise(X)<~>~strong(X))))& (![X]:(~kind(X)<=>(~quiet(X)<~>~patient(X))))& (![X]:(~rich(X)<=>(generous(X)|~wise(X))))& ((?[X]:((strong(X)&~rich(X))))=>(?[X]:((calm(X)&~quiet(X)))))& (![X]:((~patient(X)&funny(X))<=>(creative(X)|funny(X))))& (![X]:(~generous(X)=>(~wise(X)|kind(X))))& (![X]:(~creative(X)<=>(~funny(X)|~rich(X))))& (?[X]:(~wise(X)))& ((~happy(john)|tall(john)))& (quiet(mary))& ((creative(paul)|~calm(paul)))& (?[X]:((~tall(X)&~wise(X))))& (?[X]:((wise(X)<~>tall(X))))& (?[X]:((strong(X)|~strong(X))))& ((~curious(mary)|old(mary)))

~creative(alice)

% SZS status Unsatisfiable for 961326168729201777998056 % SZS output start Proof for 961326168729201777998056 5. ! [X0] : ((old(X0) | ~generous(X0)) => ~happy(X0)) [input p4] 7. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> ~rich(X0)) [input p6] 12. ! [X0] : (~rich(X0) <=> (~wise(X0) | generous(X0))) [input p11] 16. ! [X0] : (~creative(X0) <=> (~rich(X0) | ~funny(X0))) [input p15] 25. creative(alice) [input hypothesis] 34. ! [X0] : (~happy(X0) | (~old(X0) & generous(X0))) [ennf transformation 5] 50. ! [X0] : (((~happy(X0) | ~rich(X0)) | rich(X0)) & (~rich(X0) | (happy(X0) & rich(X0)))) [nnf transformation 7] 51. ! [X0] : ((~happy(X0) | ~rich(X0) | rich(X0)) & (~rich(X0) | (happy(X0) & rich(X0)))) [flattening 50] 61. ! [X0] : ((~rich(X0) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | rich(X0))) [nnf transformation 12] 62. ! [X0] : ((~rich(X0) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | rich(X0))) [flattening 61] 68. ! [X0] : ((~creative(X0) | (rich(X0) & funny(X0))) & ((~rich(X0) | ~funny(X0)) | creative(X0))) [nnf transformation 16] 69. ! [X0] : ((~creative(X0) | (rich(X0) & funny(X0))) & (~rich(X0) | ~funny(X0) | creative(X0))) [flattening 68] 83. ~happy(X0) | generous(X0) [cnf transformation 34] 88. ~rich(X0) | happy(X0) [cnf transformation 51] 107. ~rich(X0) | ~generous(X0) [cnf transformation 62] 119. ~creative(X0) | rich(X0) [cnf transformation 69] 130. creative(alice) [cnf transformation 25] 262. rich(alice) [resolution 119,130] 266. ~generous(alice) [resolution 262,107] 267. happy(alice) [resolution 262,88] 293. generous(alice) [resolution 267,83] 294. $false [subsumption resolution 293,266] % SZS output end Proof for 961326168729201777998056 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.030 s % ------------------------------ % ------------------------------

Everyone who is either wise or not patient is both not rich and generous and vice versa. If someone is either happy or strong then mary is both not humble and not strong. Everyone who is humble is either patient or not brave and vice versa. Everyone who is not curious or not patient is not tall or brave. If someone is either not brave or not creative then someone is humble or not rich and vice versa. Everyone who is curious or funny is both generous and not rich. Everyone who is either not tall or not wise is old or patient and vice versa. Everyone who is both not brave and kind is both not generous and happy. Everyone who is not tall is both not happy and not generous. If someone is happy then mary is both tall and not creative and vice versa. Everyone who is not funny or strong is humble. If someone is both tall and happy then someone is both not curious and not kind. If fred is either not brave or not curious then alice is either creative or patient. Everyone who is both not calm and not brave is not curious or strong. If mary is not happy then someone is not happy and vice versa. If someone is old then lucy is both not happy and not wise and vice versa. Mary is either brave or old. Fred is both not funny and tall. Fred is both not happy and humble. Someone is not old. Alice is not tall. Someone is quiet. Someone is not rich or old. Someone is either not kind or kind.

Lucy is strong.

contradiction

(![X]:((wise(X)<~>~patient(X))<=>(~rich(X)&generous(X))))& ((?[X]:((happy(X)<~>strong(X))))=>((~humble(mary)&~strong(mary))))& (![X]:(humble(X)<=>(patient(X)<~>~brave(X))))& (![X]:((~curious(X)|~patient(X))=>(~tall(X)|brave(X))))& ((?[X]:((~brave(X)<~>~creative(X))))<=>(?[X]:((humble(X)|~rich(X)))))& (![X]:((curious(X)|funny(X))=>(generous(X)&~rich(X))))& (![X]:((~tall(X)<~>~wise(X))<=>(old(X)|patient(X))))& (![X]:((~brave(X)&kind(X))=>(~generous(X)&happy(X))))& (![X]:(~tall(X)=>(~happy(X)&~generous(X))))& ((?[X]:(happy(X)))<=>((tall(mary)&~creative(mary))))& (![X]:((~funny(X)|strong(X))=>humble(X)))& ((?[X]:((tall(X)&happy(X))))=>(?[X]:((~curious(X)&~kind(X)))))& (((~brave(fred)<~>~curious(fred)))=>((creative(alice)<~>patient(alice))))& (![X]:((~calm(X)&~brave(X))=>(~curious(X)|strong(X))))& ((~happy(mary))<=>(?[X]:(~happy(X))))& ((?[X]:(old(X)))<=>((~happy(lucy)&~wise(lucy))))& ((brave(mary)<~>old(mary)))& ((~funny(fred)&tall(fred)))& ((~happy(fred)&humble(fred)))& (?[X]:(~old(X)))& (~tall(alice))& (?[X]:(quiet(X)))& (?[X]:((~rich(X)|old(X))))& (?[X]:((~kind(X)<~>kind(X))))

strong(lucy)

% SZS status Unsatisfiable for 6774794915209951352643359 % SZS output start Proof for 6774794915209951352643359 1. ! [X0] : ((wise(X0) <~> ~patient(X0)) <=> (generous(X0) & ~rich(X0))) [input p0] 2. ? [X0] : (happy(X0) <~> strong(X0)) => (~strong(mary) & ~humble(mary)) [input p1] 3. ! [X0] : (humble(X0) <=> (patient(X0) <~> ~brave(X0))) [input p2] 4. ! [X0] : ((~patient(X0) | ~curious(X0)) => (brave(X0) | ~tall(X0))) [input p3] 6. ! [X0] : ((funny(X0) | curious(X0)) => (~rich(X0) & generous(X0))) [input p5] 7. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (patient(X0) | old(X0))) [input p6] 9. ! [X0] : (~tall(X0) => (~generous(X0) & ~happy(X0))) [input p8] 11. ! [X0] : ((strong(X0) | ~funny(X0)) => humble(X0)) [input p10] 16. ? [X0] : old(X0) <=> (~wise(lucy) & ~happy(lucy)) [input p15] 17. brave(mary) <~> old(mary) [input p16] 21. ~tall(alice) [input p20] 25. strong(lucy) [input hypothesis] 30. (~strong(mary) & ~humble(mary)) | ! [X0] : (happy(X0) <=> strong(X0)) [ennf transformation 2] 31. ! [X0] : ((brave(X0) | ~tall(X0)) | (patient(X0) & curious(X0))) [ennf transformation 4] 32. ! [X0] : (brave(X0) | ~tall(X0) | (patient(X0) & curious(X0))) [flattening 31] 33. ! [X0] : ((~rich(X0) & generous(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 6] 36. ! [X0] : ((~generous(X0) & ~happy(X0)) | tall(X0)) [ennf transformation 9] 37. ! [X0] : (humble(X0) | (~strong(X0) & funny(X0))) [ennf transformation 11] 40. ! [X0] : ((((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~generous(X0) | rich(X0))) & ((generous(X0) & ~rich(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0))))) [nnf transformation 1] 41. ! [X0] : ((((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | ~generous(X0) | rich(X0)) & ((generous(X0) & ~rich(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0))))) [flattening 40] 42. (~strong(mary) & ~humble(mary)) | ! [X0] : ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0))) [nnf transformation 30] 43. ! [X0] : ((humble(X0) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0)))) & (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ~humble(X0))) [nnf transformation 3] 49. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | (~patient(X0) & ~old(X0))) & ((patient(X0) | old(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 7] 50. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | (~patient(X0) & ~old(X0))) & (patient(X0) | old(X0) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [flattening 49] 64. (? [X0] : old(X0) | (wise(lucy) | happy(lucy))) & ((~wise(lucy) & ~happy(lucy)) | ! [X0] : ~old(X0)) [nnf transformation 16] 65. (? [X0] : old(X0) | wise(lucy) | happy(lucy)) & ((~wise(lucy) & ~happy(lucy)) | ! [X0] : ~old(X0)) [flattening 64] 66. (? [X0] : old(X0) | wise(lucy) | happy(lucy)) & ((~wise(lucy) & ~happy(lucy)) | ! [X1] : ~old(X1)) [rectify 65] 67. ? [X0] : old(X0) => old(sK5) [choice axiom] 68. (old(sK5) | wise(lucy) | happy(lucy)) & ((~wise(lucy) & ~happy(lucy)) | ! [X1] : ~old(X1)) [skolemisation 66,67] 69. (~old(mary) | ~brave(mary)) & (old(mary) | brave(mary)) [nnf transformation 17] 79. ~patient(X0) | generous(X0) | ~wise(X0) [cnf transformation 41] 80. generous(X0) | wise(X0) | patient(X0) [cnf transformation 41] 81. ~generous(X0) | wise(X0) | ~patient(X0) | rich(X0) [cnf transformation 41] 82. ~generous(X0) | ~wise(X0) | patient(X0) | rich(X0) [cnf transformation 41] 84. ~humble(mary) | happy(X0) | ~strong(X0) [cnf transformation 42] 89. ~brave(X0) | humble(X0) | ~patient(X0) [cnf transformation 43] 92. ~tall(X0) | brave(X0) | patient(X0) [cnf transformation 32] 100. ~funny(X0) | generous(X0) [cnf transformation 33] 102. ~funny(X0) | ~rich(X0) [cnf transformation 33] 103. ~wise(X0) | old(X0) | patient(X0) | tall(X0) [cnf transformation 50] 104. ~tall(X0) | old(X0) | patient(X0) | wise(X0) [cnf transformation 50] 106. ~tall(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 50] 108. ~patient(X0) | tall(X0) | wise(X0) [cnf transformation 50] 112. ~generous(X0) | tall(X0) [cnf transformation 36] 116. funny(X0) | humble(X0) [cnf transformation 37] 126. ~happy(lucy) | ~old(X1) [cnf transformation 68] 130. ~old(mary) | ~brave(mary) [cnf transformation 69] 136. ~tall(alice) [cnf transformation 21] 140. strong(lucy) [cnf transformation 25] 142. 1 <=> ! [X0] : (happy(X0) | ~strong(X0)) [avatar definition] 143. ~strong(X0) | happy(X0) <- (1) [avatar component clause 142] 154. 4 <=> humble(mary) [avatar definition] 156. ~humble(mary) <- (~4) [avatar component clause 154] 157. 1 | ~4 [avatar split clause 84,154,142] 194. 13 <=> tall(mary) [avatar definition] 195. tall(mary) <- (13) [avatar component clause 194] 236. 22 <=> patient(alice) [avatar definition] 237. patient(alice) <- (22) [avatar component clause 236] 238. ~patient(alice) <- (~22) [avatar component clause 236] 257. 26 <=> happy(lucy) [avatar definition] 270. 29 <=> ! [X1] : ~old(X1) [avatar definition] 271. ~old(X1) <- (29) [avatar component clause 270] 273. 29 | ~26 [avatar split clause 126,257,270] 275. 30 <=> brave(mary) [avatar definition] 276. brave(mary) <- (30) [avatar component clause 275] 279. 31 <=> old(mary) [avatar definition] 281. ~old(mary) <- (~31) [avatar component clause 279] 282. ~30 | ~31 [avatar split clause 130,279,275] 295. ~rich(X0) | humble(X0) [resolution 116,102] 296. humble(X1) | generous(X1) [resolution 116,100] 298. generous(mary) <- (~4) [resolution 296,156] 299. tall(mary) <- (~4) [resolution 298,112] 300. wise(X0) | patient(X0) | tall(X0) [resolution 80,112] 301. tall(X0) | wise(X0) [subsumption resolution 300,108] 302. wise(alice) [resolution 301,136] 329. humble(mary) | ~patient(mary) <- (30) [resolution 89,276] 332. ~patient(mary) <- (~4, 30) [subsumption resolution 329,156] 368. brave(mary) | patient(mary) <- (13) [resolution 92,195] 389. wise(mary) | ~patient(mary) | rich(mary) <- (~4) [resolution 81,298] 398. generous(alice) | ~wise(alice) <- (22) [resolution 237,79] 399. generous(alice) <- (22) [subsumption resolution 398,302] 401. ~wise(mary) | patient(mary) | rich(mary) <- (~4) [resolution 82,298] 404. ~wise(mary) | rich(mary) <- (~4, 30) [subsumption resolution 401,332] 406. 43 <=> rich(mary) [avatar definition] 408. rich(mary) <- (43) [avatar component clause 406] 410. 44 <=> wise(mary) [avatar definition] 413. 43 | ~44 | 4 | ~30 [avatar split clause 404,275,154,410,406] 426. tall(alice) <- (22) [resolution 399,112] 427. $false <- (22) [subsumption resolution 426,136] 428. ~22 [avatar contradiction clause 427] 429. old(alice) | patient(alice) | tall(alice) [resolution 103,302] 430. old(alice) | tall(alice) <- (~22) [subsumption resolution 429,238] 431. old(alice) <- (~22) [subsumption resolution 430,136] 435. old(X0) | patient(X0) | wise(X0) | wise(X0) [resolution 104,301] 439. old(X0) | patient(X0) | wise(X0) [duplicate literal removal 435] 509. 54 <=> patient(mary) [avatar definition] 513. 54 | 30 | ~13 [avatar split clause 368,194,275,509] 519. 13 | 4 [avatar split clause 299,154,194] 520. 43 | ~54 | 44 | 4 [avatar split clause 389,154,410,509,406] 542. ~wise(mary) | ~patient(mary) <- (13) [resolution 195,106] 545. humble(mary) | ~patient(mary) <- (30) [resolution 276,89] 552. patient(mary) | wise(mary) <- (~31) [resolution 281,439] 556. happy(lucy) <- (1) [resolution 143,140] 559. 26 | ~1 [avatar split clause 556,142,257] 562. $false <- (~22, 29) [resolution 271,431] 564. 22 | ~29 [avatar contradiction clause 562] 567. ~54 | 4 | ~30 [avatar split clause 545,275,154,509] 568. ~54 | ~44 | ~13 [avatar split clause 542,194,410,509] 569. 44 | 54 | 31 [avatar split clause 552,279,509,410] 604. humble(mary) <- (43) [resolution 408,295] 606. $false <- (~4, 43) [subsumption resolution 604,156] 607. 4 | ~43 [avatar contradiction clause 606] 608. $false [avatar sat refutation 157,273,282,413,428,513,519,520,559,564,567,568,569,607] % SZS output end Proof for 6774794915209951352643359 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.029 s % ------------------------------ % ------------------------------

Everyone who is either brave or not brave is both not calm and strong. Everyone who is either funny or rich is both funny and not humble and vice versa. If john is not old or creative then alice is either not kind or not quiet. Everyone who is either not strong or not old is funny or quiet. Everyone who is both generous and not quiet is either patient or brave. If someone is either not tall or wise then paul is brave. If someone is either tall or not quiet then susan is both calm and not kind. Everyone who is not happy or not creative is brave or creative and vice versa. If paul is both humble and old then paul is either not calm or funny. Everyone who is either old or quiet is either calm or humble. Everyone who is both tall and not humble is not happy or not creative and vice versa. Everyone who is not strong or not curious is rich and vice versa. If lucy is either creative or brave then someone is either not calm or not patient and vice versa. If someone is funny or creative then someone is kind and vice versa. If someone is not humble then someone is both generous and not creative and vice versa. Everyone who is both calm and not funny is both old and quiet and vice versa. Someone is not funny or patient. Someone is either humble or funny. Someone is not quiet or not humble. Someone is not old. Paul is both happy and tall. Someone is rich or strong.

Alice is old.

contradiction

(![X]:((brave(X)<~>~brave(X))=>(~calm(X)&strong(X))))& (![X]:((funny(X)<~>rich(X))<=>(funny(X)&~humble(X))))& (((~old(john)|creative(john)))=>((~kind(alice)<~>~quiet(alice))))& (![X]:((~strong(X)<~>~old(X))=>(funny(X)|quiet(X))))& (![X]:((generous(X)&~quiet(X))=>(patient(X)<~>brave(X))))& ((?[X]:((~tall(X)<~>wise(X))))=>(brave(paul)))& ((?[X]:((tall(X)<~>~quiet(X))))=>((calm(susan)&~kind(susan))))& (![X]:((~happy(X)|~creative(X))<=>(brave(X)|creative(X))))& (((humble(paul)&old(paul)))=>((~calm(paul)<~>funny(paul))))& (![X]:((old(X)<~>quiet(X))=>(calm(X)<~>humble(X))))& (![X]:((tall(X)&~humble(X))<=>(~happy(X)|~creative(X))))& (![X]:((~strong(X)|~curious(X))<=>rich(X)))& (((creative(lucy)<~>brave(lucy)))<=>(?[X]:((~calm(X)<~>~patient(X)))))& ((?[X]:((funny(X)|creative(X))))<=>(?[X]:(kind(X))))& ((?[X]:(~humble(X)))<=>(?[X]:((generous(X)&~creative(X)))))& (![X]:((calm(X)&~funny(X))<=>(old(X)&quiet(X))))& (?[X]:((~funny(X)|patient(X))))& (?[X]:((humble(X)<~>funny(X))))& (?[X]:((~quiet(X)|~humble(X))))& (?[X]:(~old(X)))& ((happy(paul)&tall(paul)))& (?[X]:((rich(X)|strong(X))))

old(alice)

% SZS status Unsatisfiable for 3948840294915334740734191 % SZS output start Proof for 3948840294915334740734191 1. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (strong(X0) & ~calm(X0))) [input p0] 7. ? [X0] : (tall(X0) <~> ~quiet(X0)) => (~kind(susan) & calm(susan)) [input p6] 8. ! [X0] : ((~creative(X0) | ~happy(X0)) <=> (creative(X0) | brave(X0))) [input p7] 10. ! [X0] : ((old(X0) <~> quiet(X0)) => (calm(X0) <~> humble(X0))) [input p9] 11. ! [X0] : ((~humble(X0) & tall(X0)) <=> (~creative(X0) | ~happy(X0))) [input p10] 23. old(alice) [input hypothesis] 26. ! [X0] : ((strong(X0) & ~calm(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 1] 33. (~kind(susan) & calm(susan)) | ! [X0] : (tall(X0) <=> ~quiet(X0)) [ennf transformation 7] 36. ! [X0] : ((calm(X0) <~> humble(X0)) | (old(X0) <=> quiet(X0))) [ennf transformation 10] 37. ! [X0] : ((strong(X0) & ~calm(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 26] 44. (~kind(susan) & calm(susan)) | ! [X0] : ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0))) [nnf transformation 33] 45. ! [X0] : (((~creative(X0) | ~happy(X0)) | (~creative(X0) & ~brave(X0))) & ((creative(X0) | brave(X0)) | (creative(X0) & happy(X0)))) [nnf transformation 8] 46. ! [X0] : ((~creative(X0) | ~happy(X0) | (~creative(X0) & ~brave(X0))) & (creative(X0) | brave(X0) | (creative(X0) & happy(X0)))) [flattening 45] 48. ! [X0] : (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ((old(X0) | ~quiet(X0)) & (quiet(X0) | ~old(X0)))) [nnf transformation 36] 49. ! [X0] : (((~humble(X0) & tall(X0)) | (creative(X0) & happy(X0))) & ((~creative(X0) | ~happy(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 11] 50. ! [X0] : (((~humble(X0) & tall(X0)) | (creative(X0) & happy(X0))) & (~creative(X0) | ~happy(X0) | humble(X0) | ~tall(X0))) [flattening 49] 80. ~calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 37] 81. ~calm(X0) | brave(X0) | brave(X0) [cnf transformation 37] 100. calm(susan) | ~quiet(X0) | ~tall(X0) [cnf transformation 44] 107. ~creative(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 46] 110. humble(X0) | calm(X0) | quiet(X0) | ~old(X0) [cnf transformation 48] 115. happy(X0) | tall(X0) [cnf transformation 50] 116. tall(X0) | creative(X0) [cnf transformation 50] 117. ~humble(X0) | happy(X0) [cnf transformation 50] 118. ~humble(X0) | creative(X0) [cnf transformation 50] 148. old(alice) [cnf transformation 23] 150. ~happy(X0) | ~creative(X0) [duplicate literal removal 107] 153. ~calm(X0) | ~brave(X0) [duplicate literal removal 80] 154. ~calm(X0) | brave(X0) [duplicate literal removal 81] 158. ~calm(X0) [subsumption resolution 153,154] 168. 3 <=> quiet(alice) [avatar definition] 169. ~quiet(alice) <- (~3) [avatar component clause 168] 170. quiet(alice) <- (3) [avatar component clause 168] 201. 10 <=> ! [X0] : (~quiet(X0) | ~tall(X0)) [avatar definition] 202. ~tall(X0) | ~quiet(X0) <- (10) [avatar component clause 201] 206. ~quiet(X0) | ~tall(X0) [subsumption resolution 100,158] 207. 10 [avatar split clause 206,201] 223. ~old(X0) | quiet(X0) | humble(X0) [subsumption resolution 110,158] 334. ~creative(X0) | tall(X0) [resolution 150,115] 338. tall(X0) [subsumption resolution 334,116] 345. ~quiet(X0) <- (10) [resolution 202,338] 362. quiet(alice) | humble(alice) [resolution 223,148] 365. humble(alice) <- (~3) [subsumption resolution 362,169] 378. creative(alice) <- (~3) [resolution 365,118] 379. happy(alice) <- (~3) [resolution 365,117] 390. ~creative(alice) <- (~3) [resolution 379,150] 391. $false <- (~3) [subsumption resolution 390,378] 392. 3 [avatar contradiction clause 391] 394. $false <- (3, 10) [subsumption resolution 170,345] 395. ~3 | ~10 [avatar contradiction clause 394] 396. $false [avatar sat refutation 207,392,395] % SZS output end Proof for 3948840294915334740734191 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.020 s % ------------------------------ % ------------------------------

Everyone who is either humble or not happy is both wise and not kind and vice versa. Everyone who is not strong is not funny or humble and vice versa. Everyone who is not happy is either curious or humble. Everyone who is either not funny or not kind is either brave or humble. Everyone who is brave is either not patient or not tall. If alice is not happy or not old then someone is both quiet and not brave and vice versa. Everyone who is funny is not humble or not calm and vice versa. Everyone who is not kind is either calm or not creative. Everyone who is both generous and not brave is both happy and brave and vice versa. Everyone who is calm or kind is both not brave and calm. If someone is not wise then someone is either humble or not quiet and vice versa. Everyone who is rich is not old and vice versa. If john is either not wise or not happy then alice is both not calm and patient. If susan is not creative or generous then someone is either old or strong and vice versa. If someone is either wise or not brave then susan is both strong and creative and vice versa. Everyone who is not old or funny is not calm or not old. Someone is both rich and not strong. Mary is either not calm or not brave. Fred is both not curious and not tall. Paul is either strong or old. Someone is both not tall and not funny. Someone is either old or not kind.

Paul is wise.

entailment

(![X]:((humble(X)<~>~happy(X))<=>(wise(X)&~kind(X))))& (![X]:(~strong(X)<=>(~funny(X)|humble(X))))& (![X]:(~happy(X)=>(curious(X)<~>humble(X))))& (![X]:((~funny(X)<~>~kind(X))=>(brave(X)<~>humble(X))))& (![X]:(brave(X)=>(~patient(X)<~>~tall(X))))& (((~happy(alice)|~old(alice)))<=>(?[X]:((quiet(X)&~brave(X)))))& (![X]:(funny(X)<=>(~humble(X)|~calm(X))))& (![X]:(~kind(X)=>(calm(X)<~>~creative(X))))& (![X]:((generous(X)&~brave(X))<=>(happy(X)&brave(X))))& (![X]:((calm(X)|kind(X))=>(~brave(X)&calm(X))))& ((?[X]:(~wise(X)))<=>(?[X]:((humble(X)<~>~quiet(X)))))& (![X]:(rich(X)<=>~old(X)))& (((~wise(john)<~>~happy(john)))=>((~calm(alice)&patient(alice))))& (((~creative(susan)|generous(susan)))<=>(?[X]:((old(X)<~>strong(X)))))& ((?[X]:((wise(X)<~>~brave(X))))<=>((strong(susan)&creative(susan))))& (![X]:((~old(X)|funny(X))=>(~calm(X)|~old(X))))& (?[X]:((rich(X)&~strong(X))))& ((~calm(mary)<~>~brave(mary)))& ((~curious(fred)&~tall(fred)))& ((strong(paul)<~>old(paul)))& (?[X]:((~tall(X)&~funny(X))))& (?[X]:((old(X)<~>~kind(X))))

wise(paul)

% SZS status Unsatisfiable for 405534713895619577432510 % SZS output start Proof for 405534713895619577432510 1. ! [X0] : ((humble(X0) <~> ~happy(X0)) <=> (~kind(X0) & wise(X0))) [input p0] 4. ! [X0] : ((~funny(X0) <~> ~kind(X0)) => (brave(X0) <~> humble(X0))) [input p3] 7. ! [X0] : (funny(X0) <=> (~calm(X0) | ~humble(X0))) [input p6] 8. ! [X0] : (~kind(X0) => (calm(X0) <~> ~creative(X0))) [input p7] 9. ! [X0] : ((~brave(X0) & generous(X0)) <=> (brave(X0) & happy(X0))) [input p8] 10. ! [X0] : ((kind(X0) | calm(X0)) => (calm(X0) & ~brave(X0))) [input p9] 11. ? [X0] : ~wise(X0) <=> ? [X0] : (humble(X0) <~> ~quiet(X0)) [input p10] 14. (generous(susan) | ~creative(susan)) <=> ? [X0] : (old(X0) <~> strong(X0)) [input p13] 15. ? [X0] : (wise(X0) <~> ~brave(X0)) <=> (creative(susan) & strong(susan)) [input p14] 20. strong(paul) <~> old(paul) [input p19] 23. ~wise(paul) [input hypothesis] 24. ? [X0] : ~wise(X0) <=> ? [X1] : (humble(X1) <~> ~quiet(X1)) [rectify 11] 27. ! [X0] : ((brave(X0) <~> humble(X0)) | (~funny(X0) <=> ~kind(X0))) [ennf transformation 4] 29. ! [X0] : ((calm(X0) <~> ~creative(X0)) | kind(X0)) [ennf transformation 8] 30. ! [X0] : ((calm(X0) & ~brave(X0)) | (~kind(X0) & ~calm(X0))) [ennf transformation 10] 35. ! [X0] : ((((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | (kind(X0) | ~wise(X0))) & ((~kind(X0) & wise(X0)) | ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0))))) [nnf transformation 1] 36. ! [X0] : ((((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | kind(X0) | ~wise(X0)) & ((~kind(X0) & wise(X0)) | ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0))))) [flattening 35] 40. ! [X0] : (((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) [nnf transformation 27] 47. ! [X0] : ((funny(X0) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | ~funny(X0))) [nnf transformation 7] 48. ! [X0] : ((funny(X0) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | ~funny(X0))) [flattening 47] 49. ! [X0] : (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | kind(X0)) [nnf transformation 29] 50. ! [X0] : (((~brave(X0) & generous(X0)) | (~brave(X0) | ~happy(X0))) & ((brave(X0) & happy(X0)) | (brave(X0) | ~generous(X0)))) [nnf transformation 9] 51. ! [X0] : (((~brave(X0) & generous(X0)) | ~brave(X0) | ~happy(X0)) & ((brave(X0) & happy(X0)) | brave(X0) | ~generous(X0))) [flattening 50] 52. (? [X0] : ~wise(X0) | ! [X1] : ((humble(X1) | quiet(X1)) & (~quiet(X1) | ~humble(X1)))) & (? [X1] : ((quiet(X1) | ~humble(X1)) & (~quiet(X1) | humble(X1))) | ! [X0] : wise(X0)) [nnf transformation 24] 53. (? [X0] : ~wise(X0) | ! [X1] : ((humble(X1) | quiet(X1)) & (~quiet(X1) | ~humble(X1)))) & (? [X2] : ((quiet(X2) | ~humble(X2)) & (~quiet(X2) | humble(X2))) | ! [X3] : wise(X3)) [rectify 52] 54. ? [X0] : ~wise(X0) => ~wise(sK1) [choice axiom] 55. ? [X2] : ((quiet(X2) | ~humble(X2)) & (~quiet(X2) | humble(X2))) => ((quiet(sK2) | ~humble(sK2)) & (~quiet(sK2) | humble(sK2))) [choice axiom] 56. (~wise(sK1) | ! [X1] : ((humble(X1) | quiet(X1)) & (~quiet(X1) | ~humble(X1)))) & (((quiet(sK2) | ~humble(sK2)) & (~quiet(sK2) | humble(sK2))) | ! [X3] : wise(X3)) [skolemisation 53,55,54] 58. ((generous(susan) | ~creative(susan)) | ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (~generous(susan) & creative(susan))) [nnf transformation 14] 59. (generous(susan) | ~creative(susan) | ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (~generous(susan) & creative(susan))) [flattening 58] 60. (generous(susan) | ~creative(susan) | ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (? [X1] : ((~strong(X1) | ~old(X1)) & (strong(X1) | old(X1))) | (~generous(susan) & creative(susan))) [rectify 59] 61. ? [X1] : ((~strong(X1) | ~old(X1)) & (strong(X1) | old(X1))) => ((~strong(sK3) | ~old(sK3)) & (strong(sK3) | old(sK3))) [choice axiom] 62. (generous(susan) | ~creative(susan) | ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (((~strong(sK3) | ~old(sK3)) & (strong(sK3) | old(sK3))) | (~generous(susan) & creative(susan))) [skolemisation 60,61] 63. (? [X0] : ((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (~creative(susan) | ~strong(susan))) & ((creative(susan) & strong(susan)) | ! [X0] : ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) [nnf transformation 15] 64. (? [X0] : ((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ~creative(susan) | ~strong(susan)) & ((creative(susan) & strong(susan)) | ! [X0] : ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) [flattening 63] 65. (? [X0] : ((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ~creative(susan) | ~strong(susan)) & ((creative(susan) & strong(susan)) | ! [X1] : ((wise(X1) | brave(X1)) & (~brave(X1) | ~wise(X1)))) [rectify 64] 66. ? [X0] : ((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) => ((brave(sK4) | ~wise(sK4)) & (~brave(sK4) | wise(sK4))) [choice axiom] 67. (((brave(sK4) | ~wise(sK4)) & (~brave(sK4) | wise(sK4))) | ~creative(susan) | ~strong(susan)) & ((creative(susan) & strong(susan)) | ! [X1] : ((wise(X1) | brave(X1)) & (~brave(X1) | ~wise(X1)))) [skolemisation 65,66] 71. (~old(paul) | ~strong(paul)) & (old(paul) | strong(paul)) [nnf transformation 20] 78. wise(X0) | humble(X0) | happy(X0) [cnf transformation 36] 91. ~brave(X0) | ~humble(X0) | ~funny(X0) | kind(X0) [cnf transformation 40] 101. calm(X0) | funny(X0) [cnf transformation 48] 102. ~creative(X0) | calm(X0) | kind(X0) [cnf transformation 49] 105. brave(X0) | brave(X0) | ~generous(X0) [cnf transformation 51] 107. ~brave(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 51] 108. ~calm(X0) | ~brave(X0) [cnf transformation 30] 109. ~brave(X0) | ~kind(X0) [cnf transformation 30] 112. ~quiet(sK2) | humble(sK2) | wise(X3) [cnf transformation 56] 113. quiet(sK2) | ~humble(sK2) | wise(X3) [cnf transformation 56] 114. ~wise(sK1) | ~quiet(X1) | ~humble(X1) [cnf transformation 56] 115. ~wise(sK1) | humble(X1) | quiet(X1) [cnf transformation 56] 125. generous(susan) | ~creative(susan) | strong(X0) | ~old(X0) [cnf transformation 62] 126. generous(susan) | ~creative(susan) | old(X0) | ~strong(X0) [cnf transformation 62] 130. creative(susan) | wise(X1) | brave(X1) [cnf transformation 67] 141. old(paul) | strong(paul) [cnf transformation 71] 142. ~old(paul) | ~strong(paul) [cnf transformation 71] 147. ~wise(paul) [cnf transformation 23] 148. ~generous(X0) | brave(X0) [duplicate literal removal 105] 149. ~brave(X0) | ~happy(X0) [duplicate literal removal 107] 175. 6 <=> ! [X1] : (humble(X1) | quiet(X1)) [avatar definition] 176. quiet(X1) | humble(X1) <- (6) [avatar component clause 175] 178. 7 <=> wise(sK1) [avatar definition] 180. ~wise(sK1) <- (~7) [avatar component clause 178] 181. 6 | ~7 [avatar split clause 115,178,175] 183. 8 <=> ! [X1] : (~quiet(X1) | ~humble(X1)) [avatar definition] 184. ~quiet(X1) | ~humble(X1) <- (8) [avatar component clause 183] 185. 8 | ~7 [avatar split clause 114,178,183] 187. 9 <=> ! [X3] : wise(X3) [avatar definition] 188. wise(X3) <- (9) [avatar component clause 187] 190. 10 <=> humble(sK2) [avatar definition] 191. humble(sK2) <- (10) [avatar component clause 190] 194. 11 <=> quiet(sK2) [avatar definition] 195. ~quiet(sK2) <- (~11) [avatar component clause 194] 196. quiet(sK2) <- (11) [avatar component clause 194] 197. 9 | ~10 | 11 [avatar split clause 113,194,190,187] 198. 9 | 10 | ~11 [avatar split clause 112,194,190,187] 220. 16 <=> ! [X0] : (old(X0) | ~strong(X0)) [avatar definition] 221. ~strong(X0) | old(X0) <- (16) [avatar component clause 220] 223. 17 <=> creative(susan) [avatar definition] 224. creative(susan) <- (17) [avatar component clause 223] 227. 18 <=> generous(susan) [avatar definition] 229. generous(susan) <- (18) [avatar component clause 227] 230. 16 | ~17 | 18 [avatar split clause 126,227,223,220] 232. 19 <=> ! [X0] : (strong(X0) | ~old(X0)) [avatar definition] 233. ~old(X0) | strong(X0) <- (19) [avatar component clause 232] 234. 19 | ~17 | 18 [avatar split clause 125,227,223,232] 262. 25 <=> ! [X1] : (wise(X1) | brave(X1)) [avatar definition] 263. brave(X1) | wise(X1) <- (25) [avatar component clause 262] 264. 25 | 17 [avatar split clause 130,223,262] 281. 29 <=> strong(paul) [avatar definition] 282. strong(paul) <- (29) [avatar component clause 281] 283. ~strong(paul) <- (~29) [avatar component clause 281] 285. 30 <=> old(paul) [avatar definition] 286. old(paul) <- (30) [avatar component clause 285] 287. ~old(paul) <- (~30) [avatar component clause 285] 288. ~29 | ~30 [avatar split clause 142,285,281] 289. 29 | 30 [avatar split clause 141,285,281] 306. ~brave(X0) | funny(X0) [resolution 108,101] 310. old(paul) <- (16, 29) [resolution 221,282] 311. $false <- (16, 29, ~30) [subsumption resolution 310,287] 312. ~16 | ~29 | 30 [avatar contradiction clause 311] 313. brave(susan) <- (18) [resolution 229,148] 317. ~kind(susan) <- (18) [resolution 313,109] 320. humble(sK1) | happy(sK1) <- (~7) [resolution 78,180] 325. 33 <=> happy(sK1) [avatar definition] 327. happy(sK1) <- (33) [avatar component clause 325] 329. 34 <=> humble(sK1) [avatar definition] 331. humble(sK1) <- (34) [avatar component clause 329] 332. 33 | 34 | 7 [avatar split clause 320,178,329,325] 389. calm(susan) | kind(susan) <- (17) [resolution 102,224] 390. calm(susan) <- (17, 18) [subsumption resolution 389,317] 409. ~brave(susan) <- (17, 18) [resolution 390,108] 411. $false <- (17, 18) [subsumption resolution 409,313] 412. ~17 | ~18 [avatar contradiction clause 411] 423. strong(paul) <- (19, 30) [resolution 286,233] 424. $false <- (19, ~29, 30) [subsumption resolution 423,283] 425. ~19 | 29 | ~30 [avatar contradiction clause 424] 435. ~happy(X1) | wise(X1) <- (25) [resolution 263,149] 436. ~kind(X2) | wise(X2) <- (25) [resolution 263,109] 473. ~humble(X0) | ~funny(X0) | kind(X0) | wise(X0) <- (25) [resolution 91,263] 475. ~funny(X0) | ~humble(X0) | wise(X0) <- (25) [subsumption resolution 473,436] 498. funny(X0) | wise(X0) <- (25) [resolution 306,263] 596. wise(X0) | ~humble(X0) | wise(X0) <- (25) [resolution 498,475] 599. ~humble(X0) | wise(X0) <- (25) [duplicate literal removal 596] 726. wise(sK1) <- (25, 34) [resolution 599,331] 736. $false <- (~7, 25, 34) [subsumption resolution 726,180] 737. 7 | ~25 | ~34 [avatar contradiction clause 736] 760. wise(sK1) <- (25, 33) [resolution 327,435] 763. $false <- (~7, 25, 33) [subsumption resolution 760,180] 764. 7 | ~25 | ~33 [avatar contradiction clause 763] 769. humble(sK2) <- (6, ~11) [resolution 176,195] 772. 10 | ~6 | 11 [avatar split clause 769,194,175,190] 776. $false <- (9) [resolution 188,147] 777. ~9 [avatar contradiction clause 776] 782. ~humble(sK2) <- (8, 11) [resolution 184,196] 785. $false <- (8, 10, 11) [subsumption resolution 782,191] 786. ~8 | ~10 | ~11 [avatar contradiction clause 785] 787. $false [avatar sat refutation 181,185,197,198,230,234,264,288,289,312,332,412,425,737,764,772,777,786] % SZS output end Proof for 405534713895619577432510 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------