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LogicNLI-reimpl

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unigram 1

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

Lucy is wise.

entailment

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

wise(lucy)

% SZS status Unsatisfiable for 561103516648413142836480 % SZS output start Proof for 561103516648413142836480 5. ! [X0] : ((~generous(X0) <~> wise(X0)) <=> kind(X0)) [input p4] 9. ! [X0] : ((~strong(X0) & ~generous(X0)) <=> (~humble(X0) & ~tall(X0))) [input p8] 10. ! [X0] : ((~funny(X0) | strong(X0)) <=> (humble(X0) <~> generous(X0))) [input p9] 12. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (~calm(X0) | patient(X0))) [input p11] 13. ! [X0] : ((~strong(X0) & ~creative(X0)) <=> (~curious(X0) <~> old(X0))) [input p12] 15. ! [X0] : ((~patient(X0) | ~curious(X0)) => (rich(X0) & ~humble(X0))) [input p14] 16. ! [X0] : ((~humble(X0) <~> curious(X0)) <=> (~tall(X0) & old(X0))) [input p15] 19. ~quiet(lucy) & kind(lucy) [input p18] 22. patient(lucy) | generous(lucy) [input p21] 24. ~wise(lucy) [input hypothesis] 27. kind(lucy) [pure predicate removal 19] 33. ! [X0] : ((rich(X0) & ~humble(X0)) | (patient(X0) & curious(X0))) [ennf transformation 15] 48. ! [X0] : ((((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | ~kind(X0)) & (kind(X0) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))))) [nnf transformation 5] 50. ! [X0] : (((~strong(X0) & ~generous(X0)) | (humble(X0) | tall(X0))) & ((~humble(X0) & ~tall(X0)) | (strong(X0) | generous(X0)))) [nnf transformation 9] 51. ! [X0] : (((~strong(X0) & ~generous(X0)) | humble(X0) | tall(X0)) & ((~humble(X0) & ~tall(X0)) | strong(X0) | generous(X0))) [flattening 50] 52. ! [X0] : (((~funny(X0) | strong(X0)) | ((humble(X0) | ~generous(X0)) & (generous(X0) | ~humble(X0)))) & (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | (funny(X0) & ~strong(X0)))) [nnf transformation 10] 53. ! [X0] : ((~funny(X0) | strong(X0) | ((humble(X0) | ~generous(X0)) & (generous(X0) | ~humble(X0)))) & (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | (funny(X0) & ~strong(X0)))) [flattening 52] 58. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (calm(X0) & ~patient(X0))) & ((~calm(X0) | patient(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 12] 59. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (calm(X0) & ~patient(X0))) & (~calm(X0) | patient(X0) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [flattening 58] 60. ! [X0] : (((~strong(X0) & ~creative(X0)) | ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | (strong(X0) | creative(X0)))) [nnf transformation 13] 61. ! [X0] : (((~strong(X0) & ~creative(X0)) | ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | strong(X0) | creative(X0))) [flattening 60] 66. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | (tall(X0) | ~old(X0))) & ((~tall(X0) & old(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [nnf transformation 16] 67. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | tall(X0) | ~old(X0)) & ((~tall(X0) & old(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [flattening 66] 91. ~generous(X0) | wise(X0) | ~kind(X0) [cnf transformation 48] 99. ~humble(X0) | strong(X0) | generous(X0) [cnf transformation 51] 103. humble(X0) | generous(X0) | funny(X0) [cnf transformation 53] 118. ~funny(X0) | humble(X0) | ~patient(X0) [cnf transformation 59] 120. ~humble(X0) | funny(X0) | ~patient(X0) [cnf transformation 59] 127. ~curious(X0) | ~strong(X0) | ~old(X0) [cnf transformation 61] 134. ~humble(X0) | curious(X0) [cnf transformation 33] 135. ~humble(X0) | patient(X0) [cnf transformation 33] 139. old(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 67] 147. kind(lucy) [cnf transformation 27] 151. patient(lucy) | generous(lucy) [cnf transformation 22] 153. ~wise(lucy) [cnf transformation 24] 314. ~humble(X0) | old(X0) [subsumption resolution 139,134] 333. 38 <=> generous(lucy) [avatar definition] 334. ~generous(lucy) <- (~38) [avatar component clause 333] 335. generous(lucy) <- (38) [avatar component clause 333] 337. 39 <=> patient(lucy) [avatar definition] 339. patient(lucy) <- (39) [avatar component clause 337] 340. 38 | 39 [avatar split clause 151,337,333] 370. wise(lucy) | ~kind(lucy) <- (38) [resolution 91,335] 380. ~kind(lucy) <- (38) [subsumption resolution 370,153] 381. $false <- (38) [subsumption resolution 380,147] 382. ~38 [avatar contradiction clause 381] 474. generous(X3) | funny(X3) | patient(X3) [resolution 103,135] 525. funny(X0) | ~patient(X0) | generous(X0) | funny(X0) [resolution 120,103] 529. funny(X0) | ~patient(X0) | generous(X0) [duplicate literal removal 525] 530. generous(X0) | funny(X0) [subsumption resolution 529,474] 631. funny(lucy) <- (~38) [resolution 530,334] 708. humble(lucy) | ~patient(lucy) <- (~38) [resolution 631,118] 714. 65 <=> humble(lucy) [avatar definition] 716. humble(lucy) <- (65) [avatar component clause 714] 718. humble(lucy) <- (~38, 39) [subsumption resolution 708,339] 719. 65 | 38 | ~39 [avatar split clause 718,337,333,714] 880. strong(lucy) | generous(lucy) <- (65) [resolution 716,99] 885. curious(lucy) <- (65) [resolution 716,134] 888. old(lucy) <- (65) [resolution 716,314] 889. strong(lucy) <- (~38, 65) [subsumption resolution 880,334] 994. ~strong(lucy) | ~old(lucy) <- (65) [resolution 885,127] 996. ~old(lucy) <- (~38, 65) [subsumption resolution 994,889] 997. $false <- (~38, 65) [subsumption resolution 996,888] 998. 38 | ~65 [avatar contradiction clause 997] 1000. $false [avatar sat refutation 340,382,719,998] % SZS output end Proof for 561103516648413142836480 % ------------------------------ % 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]: 5500 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

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

Lucy is not brave.

contradiction

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

~brave(lucy)

% SZS status Unsatisfiable for 3119560741802424425139677 % SZS output start Proof for 3119560741802424425139677 12. ! [X0] : ((~rich(X0) | happy(X0)) => ~wise(X0)) [input p11] 15. ! [X0] : ((~tall(X0) & happy(X0)) <=> (tall(X0) | ~brave(X0))) [input p14] 16. ? [X0] : ~wise(X0) => (old(lucy) & ~generous(lucy)) [input p15] 19. ~old(lucy) [input p18] 23. ~brave(lucy) [input hypothesis] 28. ! [X0] : (~wise(X0) | (rich(X0) & ~happy(X0))) [ennf transformation 12] 31. (old(lucy) & ~generous(lucy)) | ! [X0] : wise(X0) [ennf transformation 16] 62. ! [X0] : (((~tall(X0) & happy(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 15] 63. ! [X0] : (((~tall(X0) & happy(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | tall(X0) | ~happy(X0))) [flattening 62] 118. ~wise(X0) | ~happy(X0) [cnf transformation 28] 128. brave(X0) | happy(X0) [cnf transformation 63] 133. old(lucy) | wise(X0) [cnf transformation 31] 137. ~old(lucy) [cnf transformation 19] 143. ~brave(lucy) [cnf transformation 23] 265. 25 <=> ! [X0] : wise(X0) [avatar definition] 266. wise(X0) <- (25) [avatar component clause 265] 268. 26 <=> old(lucy) [avatar definition] 271. 25 | 26 [avatar split clause 133,268,265] 288. ~26 [avatar split clause 137,268] 322. ~happy(X0) <- (25) [resolution 118,266] 324. happy(lucy) [resolution 128,143] 326. $false <- (25) [subsumption resolution 324,322] 327. ~25 [avatar contradiction clause 326] 330. $false [avatar sat refutation 271,288,327] % SZS output end Proof for 3119560741802424425139677 % ------------------------------ % 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 tall is both rich and wise and vice versa. If someone is either not creative or not quiet then paul is patient. If lucy is both humble and old then someone is not curious or curious. If someone is not happy or curious then someone is either not strong or calm and vice versa. If paul is curious then someone is either tall or funny. If susan is not quiet then fred is either not brave or not calm. Everyone who is calm or rich is humble and vice versa. Everyone who is not brave or calm is both not happy and funny. Everyone who is both not generous and funny is happy or brave and vice versa. If fred is not creative or quiet then someone is patient and vice versa. Everyone who is generous is either not patient or rich and vice versa. Everyone who is happy is not funny or not brave. Everyone who is not humble is both not calm and happy and vice versa. Everyone who is either not funny or curious is both not patient and strong and vice versa. Everyone who is not brave is creative. If someone is not rich then someone is both funny and not rich. John is brave or rich. Mary is either not calm or old. Mary is either strong or not calm. John is tall or old. Paul is either generous or humble. Paul is not quiet. Someone is not patient or not humble.

Paul is brave.

entailment

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

brave(paul)

% SZS status Unsatisfiable for 1603575108927248786880970 % SZS output start Proof for 1603575108927248786880970 8. ! [X0] : ((calm(X0) | ~brave(X0)) => (funny(X0) & ~happy(X0))) [input p7] 9. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (brave(X0) | happy(X0))) [input p8] 12. ! [X0] : (happy(X0) => (~brave(X0) | ~funny(X0))) [input p11] 13. ! [X0] : (~humble(X0) <=> (happy(X0) & ~calm(X0))) [input p12] 21. generous(paul) <~> humble(paul) [input p20] 24. ~brave(paul) [input hypothesis] 32. ! [X0] : ((funny(X0) & ~happy(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 8] 33. ! [X0] : ((~brave(X0) | ~funny(X0)) | ~happy(X0)) [ennf transformation 12] 34. ! [X0] : (~brave(X0) | ~funny(X0) | ~happy(X0)) [flattening 33] 53. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | (~funny(X0) | generous(X0)))) [nnf transformation 9] 54. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ~funny(X0) | generous(X0))) [flattening 53] 61. ! [X0] : ((~humble(X0) | (~happy(X0) | calm(X0))) & ((happy(X0) & ~calm(X0)) | humble(X0))) [nnf transformation 13] 62. ! [X0] : ((~humble(X0) | ~happy(X0) | calm(X0)) & ((happy(X0) & ~calm(X0)) | humble(X0))) [flattening 61] 70. (~humble(paul) | ~generous(paul)) & (humble(paul) | generous(paul)) [nnf transformation 21] 92. ~happy(X0) | brave(X0) [cnf transformation 32] 94. brave(X0) | funny(X0) [cnf transformation 32] 96. brave(X0) | happy(X0) | ~funny(X0) | generous(X0) [cnf transformation 54] 100. funny(X0) | ~brave(X0) [cnf transformation 54] 108. ~brave(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 34] 110. happy(X0) | humble(X0) [cnf transformation 62] 128. ~humble(paul) | ~generous(paul) [cnf transformation 70] 131. ~brave(paul) [cnf transformation 24] 206. funny(X0) [subsumption resolution 100,94] 207. brave(X0) | happy(X0) | generous(X0) [subsumption resolution 96,206] 208. generous(X0) | brave(X0) [subsumption resolution 207,92] 227. ~brave(X0) | ~happy(X0) [subsumption resolution 108,206] 228. ~happy(X0) [subsumption resolution 227,92] 229. humble(X0) [subsumption resolution 110,228] 275. ~generous(paul) [subsumption resolution 128,229] 283. brave(paul) [resolution 208,275] 286. $false [subsumption resolution 283,131] % SZS output end Proof for 1603575108927248786880970 % ------------------------------ % 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 not kind or generous then mary is old or not wise and vice versa. Everyone who is both humble and curious is not funny or patient. If paul is not tall then someone is creative. If fred is both generous and not curious then fred is both strong and patient and vice versa. If john is both curious and not humble then paul is wise. Everyone who is both not strong and not creative is either wise or not generous. Everyone who is not quiet is strong. If susan is both not brave and not quiet then someone is creative or wise. Everyone who is either not patient or humble is both curious and not old and vice versa. If john is both quiet and creative then mary is happy or not rich and vice versa. Everyone who is both not funny and happy is either rich or not tall. Everyone who is both not rich and not creative is not humble. Everyone who is both brave and not happy is both not kind and rich and vice versa. If someone is both not creative and not quiet then john is both rich and not patient. Everyone who is both not humble and quiet is either not happy or not old and vice versa. Everyone who is old is either not wise or kind and vice versa. John is not quiet. Someone is either not creative or generous. Mary is either not happy or quiet. Mary is either strong or not kind. Someone is not rich or not kind. Someone is not quiet. Paul is either quiet or brave. Someone is both creative and not brave.

Mary is not kind.

contradiction

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

~kind(mary)

% SZS status Unsatisfiable for 106118526864623008453750 % SZS output start Proof for 106118526864623008453750 7. ! [X0] : (~quiet(X0) => strong(X0)) [input p6] 10. (creative(john) & quiet(john)) <=> (~rich(mary) | happy(mary)) [input p9] 17. ~quiet(john) [input p16] 19. ~happy(mary) <~> quiet(mary) [input p18] 20. strong(mary) <~> ~kind(mary) [input p19] 25. ~kind(mary) [input hypothesis] 33. ! [X0] : (strong(X0) | quiet(X0)) [ennf transformation 7] 55. ((creative(john) & quiet(john)) | (rich(mary) & ~happy(mary))) & ((~rich(mary) | happy(mary)) | (~creative(john) | ~quiet(john))) [nnf transformation 10] 56. ((creative(john) & quiet(john)) | (rich(mary) & ~happy(mary))) & (~rich(mary) | happy(mary) | ~creative(john) | ~quiet(john)) [flattening 55] 66. (~quiet(mary) | happy(mary)) & (quiet(mary) | ~happy(mary)) [nnf transformation 19] 67. (kind(mary) | ~strong(mary)) & (~kind(mary) | strong(mary)) [nnf transformation 20] 88. quiet(X0) | strong(X0) [cnf transformation 33] 97. quiet(john) | ~happy(mary) [cnf transformation 56] 120. ~quiet(john) [cnf transformation 17] 124. ~quiet(mary) | happy(mary) [cnf transformation 66] 126. kind(mary) | ~strong(mary) [cnf transformation 67] 133. ~kind(mary) [cnf transformation 25] 229. 22 <=> happy(mary) [avatar definition] 234. 23 <=> quiet(john) [avatar definition] 238. ~22 | 23 [avatar split clause 97,234,229] 253. ~23 [avatar split clause 120,234] 265. 29 <=> quiet(mary) [avatar definition] 267. ~quiet(mary) <- (~29) [avatar component clause 265] 268. 22 | ~29 [avatar split clause 124,265,229] 271. 30 <=> strong(mary) [avatar definition] 273. ~strong(mary) <- (~30) [avatar component clause 271] 275. 31 <=> kind(mary) [avatar definition] 278. ~30 | 31 [avatar split clause 126,275,271] 299. ~31 [avatar split clause 133,275] 302. strong(mary) <- (~29) [resolution 88,267] 303. $false <- (~29, ~30) [subsumption resolution 302,273] 304. 29 | 30 [avatar contradiction clause 303] 305. $false [avatar sat refutation 238,253,268,278,299,304] % SZS output end Proof for 106118526864623008453750 % ------------------------------ % 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 john is patient then susan is either not rich or strong and vice versa. If lucy is either funny or not patient then john is either not calm or not old and vice versa. Everyone who is both not patient and not tall is both not curious and not quiet. Everyone who is old or kind is both rich and strong. Everyone who is humble or generous is either quiet or not patient and vice versa. Everyone who is both calm and not tall is either happy or funny. If lucy is both not strong and happy then someone is not calm. If mary is not patient or humble then lucy is either not generous or not creative and vice versa. Everyone who is either funny or tall is not wise and vice versa. If someone is quiet or not happy then someone is not strong. Everyone who is either not wise or patient is funny or curious and vice versa. If john is not wise or quiet then someone is either kind or funny. Everyone who is either creative or old is both curious and not old and vice versa. Everyone who is either happy or not calm is either creative or kind and vice versa. Everyone who is both tall and not curious is rich and vice versa. Everyone who is curious is both old and not wise and vice versa. John is both not calm and brave. Someone is either not creative or curious. Someone is both humble and not quiet. Someone is either generous or not funny. Paul is either not brave or humble. Paul is either wise or not kind. Paul is both brave and strong.

Susan is not creative.

neutral

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

~creative(susan)

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

Susan is not rich.

contradiction

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

~rich(susan)

% SZS status Unsatisfiable for 810922110461461302744432 % SZS output start Proof for 810922110461461302744432 5. ! [X0] : ((humble(X0) <~> rich(X0)) => (patient(X0) & curious(X0))) [input p4] 10. ! [X0] : ((patient(X0) <~> rich(X0)) => ~curious(X0)) [input p9] 13. ! [X0] : ((kind(X0) & tall(X0)) <=> ~humble(X0)) [input p12] 15. ! [X0] : (~tall(X0) <=> kind(X0)) [input p14] 25. ~rich(susan) [input hypothesis] 37. ! [X0] : ((patient(X0) & curious(X0)) | (humble(X0) <=> rich(X0))) [ennf transformation 5] 39. ! [X0] : (~curious(X0) | (patient(X0) <=> rich(X0))) [ennf transformation 10] 55. ! [X0] : ((patient(X0) & curious(X0)) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) [nnf transformation 37] 68. ! [X0] : (~curious(X0) | ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0)))) [nnf transformation 39] 76. ! [X0] : (((kind(X0) & tall(X0)) | humble(X0)) & (~humble(X0) | (~kind(X0) | ~tall(X0)))) [nnf transformation 13] 77. ! [X0] : (((kind(X0) & tall(X0)) | humble(X0)) & (~humble(X0) | ~kind(X0) | ~tall(X0))) [flattening 76] 78. ! [X0] : ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0))) [nnf transformation 15] 102. ~humble(X0) | rich(X0) | curious(X0) [cnf transformation 55] 104. ~humble(X0) | rich(X0) | patient(X0) [cnf transformation 55] 123. ~patient(X0) | rich(X0) | ~curious(X0) [cnf transformation 68] 131. humble(X0) | tall(X0) [cnf transformation 77] 132. kind(X0) | humble(X0) [cnf transformation 77] 134. ~kind(X0) | ~tall(X0) [cnf transformation 78] 149. ~rich(susan) [cnf transformation 25] 162. 4 <=> rich(susan) [avatar definition] 163. ~rich(susan) <- (~4) [avatar component clause 162] 281. 30 <=> ! [X1] : humble(X1) [avatar definition] 282. humble(X1) <- (30) [avatar component clause 281] 347. ~4 [avatar split clause 149,162] 359. ~tall(X1) | humble(X1) [resolution 134,132] 360. humble(X1) [subsumption resolution 359,131] 361. 30 [avatar split clause 360,281] 379. rich(X0) | curious(X0) <- (30) [resolution 102,282] 391. patient(X0) | rich(X0) <- (30) [resolution 104,282] 449. rich(X0) | rich(X0) | ~curious(X0) <- (30) [resolution 391,123] 450. rich(X0) | ~curious(X0) <- (30) [duplicate literal removal 449] 451. rich(X0) <- (30) [subsumption resolution 450,379] 466. $false <- (~4, 30) [resolution 451,163] 471. 4 | ~30 [avatar contradiction clause 466] 472. $false [avatar sat refutation 347,361,471] % SZS output end Proof for 810922110461461302744432 % ------------------------------ % 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: 0.033 s % ------------------------------ % ------------------------------

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

Alice is old.

entailment

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

old(alice)

% SZS status Unsatisfiable for 612539241582155404583121 % SZS output start Proof for 612539241582155404583121 2. ? [X0] : (~calm(X0) & ~quiet(X0)) <=> (calm(fred) | ~old(fred)) [input p1] 3. ! [X0] : ((kind(X0) & ~creative(X0)) <=> (rich(X0) | ~calm(X0))) [input p2] 4. (~calm(alice) & old(alice)) <=> ? [X0] : (happy(X0) | quiet(X0)) [input p3] 5. ! [X0] : (kind(X0) => (generous(X0) & quiet(X0))) [input p4] 23. ~old(alice) [input hypothesis] 29. ! [X0] : ((generous(X0) & quiet(X0)) | ~kind(X0)) [ennf transformation 5] 38. (? [X0] : (~calm(X0) & ~quiet(X0)) | (~calm(fred) & old(fred))) & ((calm(fred) | ~old(fred)) | ! [X0] : (calm(X0) | quiet(X0))) [nnf transformation 2] 39. (? [X0] : (~calm(X0) & ~quiet(X0)) | (~calm(fred) & old(fred))) & (calm(fred) | ~old(fred) | ! [X0] : (calm(X0) | quiet(X0))) [flattening 38] 40. (? [X0] : (~calm(X0) & ~quiet(X0)) | (~calm(fred) & old(fred))) & (calm(fred) | ~old(fred) | ! [X1] : (calm(X1) | quiet(X1))) [rectify 39] 41. ? [X0] : (~calm(X0) & ~quiet(X0)) => (~calm(sK0) & ~quiet(sK0)) [choice axiom] 42. ((~calm(sK0) & ~quiet(sK0)) | (~calm(fred) & old(fred))) & (calm(fred) | ~old(fred) | ! [X1] : (calm(X1) | quiet(X1))) [skolemisation 40,41] 43. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~kind(X0) | creative(X0)))) [nnf transformation 3] 44. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~kind(X0) | creative(X0))) [flattening 43] 45. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | (calm(alice) | ~old(alice))) [nnf transformation 4] 46. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | calm(alice) | ~old(alice)) [flattening 45] 47. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X1] : (happy(X1) | quiet(X1)) | calm(alice) | ~old(alice)) [rectify 46] 48. ? [X1] : (happy(X1) | quiet(X1)) => (happy(sK1) | quiet(sK1)) [choice axiom] 49. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & ((happy(sK1) | quiet(sK1)) | calm(alice) | ~old(alice)) [skolemisation 47,48] 76. ~calm(sK0) | ~calm(fred) [cnf transformation 42] 80. kind(X0) | calm(X0) [cnf transformation 44] 83. old(alice) | ~quiet(X0) [cnf transformation 49] 87. ~kind(X0) | quiet(X0) [cnf transformation 29] 128. ~old(alice) [cnf transformation 23] 130. 1 <=> calm(fred) [avatar definition] 132. ~calm(fred) <- (~1) [avatar component clause 130] 134. 2 <=> calm(sK0) [avatar definition] 136. ~calm(sK0) <- (~2) [avatar component clause 134] 137. ~1 | ~2 [avatar split clause 76,134,130] 162. 8 <=> ! [X0] : ~quiet(X0) [avatar definition] 163. ~quiet(X0) <- (8) [avatar component clause 162] 166. 9 <=> old(alice) [avatar definition] 170. 8 | 9 [avatar split clause 83,166,162] 194. 15 <=> ! [X0] : calm(X0) [avatar definition] 195. calm(X0) <- (15) [avatar component clause 194] 286. ~9 [avatar split clause 128,166] 295. quiet(X0) | calm(X0) [resolution 87,80] 296. calm(X0) <- (8) [subsumption resolution 295,163] 297. 15 | ~8 [avatar split clause 296,162,194] 298. $false <- (~1, 15) [resolution 195,132] 299. $false <- (~2, 15) [resolution 195,136] 302. 2 | ~15 [avatar contradiction clause 299] 303. 1 | ~15 [avatar contradiction clause 298] 304. $false [avatar sat refutation 137,170,286,297,302,303] % SZS output end Proof for 612539241582155404583121 % ------------------------------ % 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 not strong or tall is both kind and old and vice versa. If paul is either not old or humble then someone is not strong. Everyone who is not patient or not tall is either not kind or calm and vice versa. If someone is either not old or kind then someone is both wise and not wise. Everyone who is either not strong or not creative is either not curious or rich. If someone is both patient and tall then paul is not humble or not curious. If john is either wise or not generous then someone is kind or curious. If someone is both not wise and not happy then someone is tall and vice versa. Everyone who is both happy and not creative is either not happy or rich. Everyone who is either rich or humble is both happy and rich and vice versa. Everyone who is old or creative is both not calm and not strong. Everyone who is either strong or not generous is either not old or kind and vice versa. Everyone who is funny is both not wise and happy and vice versa. If john is either not quiet or not kind then lucy is either wise or not humble and vice versa. If someone is happy then fred is humble and vice versa. Someone is creative or strong. Someone is either wise or happy. Someone is both not brave and not curious.

John is not strong.

contradiction

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

~strong(john)

% SZS status Unsatisfiable for 2001963167851411522956787 % SZS output start Proof for 2001963167851411522956787 1. ! [X0] : ((tall(X0) | ~strong(X0)) <=> (old(X0) & kind(X0))) [input p0] 4. ? [X0] : (~old(X0) <~> kind(X0)) => ? [X0] : (~wise(X0) & wise(X0)) [input p3] 19. ~strong(john) [input hypothesis] 20. ? [X0] : (~old(X0) <~> kind(X0)) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 4] 24. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~old(X0) <=> kind(X0)) [ennf transformation 20] 32. ! [X0] : (((tall(X0) | ~strong(X0)) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | (~tall(X0) & strong(X0)))) [nnf transformation 1] 33. ! [X0] : ((tall(X0) | ~strong(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | (~tall(X0) & strong(X0)))) [flattening 32] 39. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))) [nnf transformation 24] 40. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : ((~old(X1) | ~kind(X1)) & (kind(X1) | old(X1))) [rectify 39] 41. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK1) & wise(sK1)) [choice axiom] 42. (~wise(sK1) & wise(sK1)) | ! [X1] : ((~old(X1) | ~kind(X1)) & (kind(X1) | old(X1))) [skolemisation 40,41] 68. kind(X0) | strong(X0) [cnf transformation 33] 70. old(X0) | strong(X0) [cnf transformation 33] 82. wise(sK1) | ~old(X1) | ~kind(X1) [cnf transformation 42] 84. ~wise(sK1) | ~old(X1) | ~kind(X1) [cnf transformation 42] 129. ~strong(john) [cnf transformation 19] 150. 4 <=> ! [X1] : (~old(X1) | ~kind(X1)) [avatar definition] 151. ~old(X1) | ~kind(X1) <- (4) [avatar component clause 150] 153. 5 <=> wise(sK1) [avatar definition] 156. 4 | ~5 [avatar split clause 84,153,150] 161. 4 | 5 [avatar split clause 82,153,150] 277. ~kind(X0) | strong(X0) <- (4) [resolution 151,70] 278. strong(X0) <- (4) [subsumption resolution 277,68] 282. $false <- (4) [resolution 278,129] 287. ~4 [avatar contradiction clause 282] 288. $false [avatar sat refutation 156,161,287] % SZS output end Proof for 2001963167851411522956787 % ------------------------------ % 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 either not creative or humble is strong. Everyone who is both not wise and not curious is wise or kind. Everyone who is not patient or not happy is kind or not brave and vice versa. If lucy is not rich or generous then someone is old or not wise and vice versa. Everyone who is funny is calm or old. Everyone who is either calm or not funny is both not calm and strong. If john is not calm then john is both humble and not funny and vice versa. If someone is creative then someone is creative or quiet and vice versa. Everyone who is both kind and not quiet is both not curious and not quiet. Everyone who is not kind is either generous or not patient. If paul is not funny or brave then someone is tall and vice versa. Everyone who is funny is either not quiet or not rich. Everyone who is not quiet is not happy and vice versa. Everyone who is not patient or not quiet is not quiet or not rich. If someone is curious then john is not humble. Everyone who is not wise is not curious or not tall. Lucy is either patient or brave. Someone is either not old or curious. Lucy is not wise or funny. Someone is happy or not old. Someone is both not strong and humble. Someone is not funny or strong. Someone is both not wise and not kind. Someone is not wise or not kind.

John is calm.

entailment

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

calm(john)

% SZS status Unsatisfiable for 1446369842531907213757660 % SZS output start Proof for 1446369842531907213757660 2. ! [X0] : ((~curious(X0) & ~wise(X0)) => (kind(X0) | wise(X0))) [input p1] 7. ~calm(john) <=> (~funny(john) & humble(john)) [input p6] 15. ? [X0] : curious(X0) => ~humble(john) [input p14] 23. ? [X0] : (~kind(X0) & ~wise(X0)) [input p22] 25. ~calm(john) [input hypothesis] 28. ! [X0] : ((kind(X0) | wise(X0)) | (curious(X0) | wise(X0))) [ennf transformation 2] 29. ! [X0] : (kind(X0) | wise(X0) | curious(X0) | wise(X0)) [flattening 28] 39. ~humble(john) | ! [X0] : ~curious(X0) [ennf transformation 15] 51. (~calm(john) | (funny(john) | ~humble(john))) & ((~funny(john) & humble(john)) | calm(john)) [nnf transformation 7] 52. (~calm(john) | funny(john) | ~humble(john)) & ((~funny(john) & humble(john)) | calm(john)) [flattening 51] 76. ? [X0] : (~kind(X0) & ~wise(X0)) => (~kind(sK8) & ~wise(sK8)) [choice axiom] 77. ~kind(sK8) & ~wise(sK8) [skolemisation 23,76] 82. kind(X0) | wise(X0) | curious(X0) | wise(X0) [cnf transformation 29] 96. humble(john) | calm(john) [cnf transformation 52] 115. ~humble(john) | ~curious(X0) [cnf transformation 39] 126. ~wise(sK8) [cnf transformation 77] 127. ~kind(sK8) [cnf transformation 77] 129. ~calm(john) [cnf transformation 25] 131. kind(X0) | wise(X0) | curious(X0) [duplicate literal removal 82] 160. 7 <=> humble(john) [avatar definition] 164. 8 <=> calm(john) [avatar definition] 169. 8 | 7 [avatar split clause 96,160,164] 210. 18 <=> ! [X0] : ~curious(X0) [avatar definition] 211. ~curious(X0) <- (18) [avatar component clause 210] 212. 18 | ~7 [avatar split clause 115,160,210] 269. ~8 [avatar split clause 129,164] 308. wise(sK8) | curious(sK8) [resolution 131,127] 311. curious(sK8) [subsumption resolution 308,126] 312. $false <- (18) [subsumption resolution 311,211] 313. ~18 [avatar contradiction clause 312] 316. $false [avatar sat refutation 169,212,269,313] % SZS output end Proof for 1446369842531907213757660 % ------------------------------ % 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 lucy is not calm or not happy then john is both funny and wise. If susan is both funny and curious then john is not brave or funny and vice versa. Everyone who is not generous is both funny and happy and vice versa. Everyone who is rich is not curious or not wise and vice versa. Everyone who is wise is both wise and not strong and vice versa. Everyone who is not calm is not calm or creative. If someone is not kind or rich then paul is funny. Everyone who is kind or not funny is humble. If someone is not calm then alice is both not happy and not generous and vice versa. If susan is rich or not generous then someone is either not wise or generous. Everyone who is happy or not curious is both not quiet and tall and vice versa. Everyone who is not happy is both not funny and old. If alice is not quiet then mary is either curious or patient and vice versa. Everyone who is either curious or generous is not happy or not strong and vice versa. If someone is not tall then lucy is both not kind and not generous and vice versa. Everyone who is strong is not quiet. Someone is either old or patient. Someone is both not patient and not brave. Lucy is not tall or tall. Someone is both generous and happy.

Alice is not funny.

neutral

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

~funny(alice)

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

Alice is happy.

contradiction

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

happy(alice)

% SZS status Unsatisfiable for 6220516012072502685339911 % SZS output start Proof for 6220516012072502685339911 18. ~happy(alice) & ~brave(alice) [input p17] 25. happy(alice) [input hypothesis] 143. ~happy(alice) [cnf transformation 18] 150. happy(alice) [cnf transformation 25] 317. 38 <=> happy(alice) [avatar definition] 334. ~38 [avatar split clause 143,317] 362. 38 [avatar split clause 150,317] 363. $false [avatar sat refutation 334,362] % SZS output end Proof for 6220516012072502685339911 % ------------------------------ % 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 happy or strong is either not calm or not brave and vice versa. Everyone who is not tall or creative is both not happy and not calm. Everyone who is either not creative or quiet is old or not generous. If someone is creative or patient then someone is both not humble and wise. Everyone who is not kind is either tall or rich and vice versa. If fred is both not funny and not generous then someone is both not wise and not humble and vice versa. Everyone who is both not brave and rich is not wise or not generous. If fred is not tall then someone is both not wise and tall and vice versa. If alice is happy then mary is generous or not generous. Everyone who is funny or brave is not brave or not humble. Everyone who is not brave is not calm or not funny. Everyone who is strong or not curious is both not humble and creative. If someone is not kind then someone is either curious or not rich and vice versa. If john is both not patient and brave then someone is both not kind and not old. Everyone who is either not kind or not patient is not funny or old and vice versa. Everyone who is patient or not happy is both calm and tall and vice versa. John is not brave or creative. Someone is not patient. Lucy is old. Someone is both not old and quiet. Lucy is humble or generous.

Mary is not strong.

entailment

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

~strong(mary)

% SZS status Unsatisfiable for 5343897431589009516375046 % SZS output start Proof for 5343897431589009516375046 2. ! [X0] : ((creative(X0) | ~tall(X0)) => (~calm(X0) & ~happy(X0))) [input p1] 12. ! [X0] : ((~curious(X0) | strong(X0)) => (creative(X0) & ~humble(X0))) [input p11] 16. ! [X0] : ((~happy(X0) | patient(X0)) <=> (tall(X0) & calm(X0))) [input p15] 22. strong(mary) [input hypothesis] 25. ! [X0] : ((~calm(X0) & ~happy(X0)) | (~creative(X0) & tall(X0))) [ennf transformation 2] 37. ! [X0] : ((creative(X0) & ~humble(X0)) | (curious(X0) & ~strong(X0))) [ennf transformation 12] 65. ! [X0] : (((~happy(X0) | patient(X0)) | (~tall(X0) | ~calm(X0))) & ((tall(X0) & calm(X0)) | (happy(X0) & ~patient(X0)))) [nnf transformation 16] 66. ! [X0] : ((~happy(X0) | patient(X0) | ~tall(X0) | ~calm(X0)) & ((tall(X0) & calm(X0)) | (happy(X0) & ~patient(X0)))) [flattening 65] 78. ~creative(X0) | ~happy(X0) [cnf transformation 25] 80. ~creative(X0) | ~calm(X0) [cnf transformation 25] 105. ~strong(X0) | creative(X0) [cnf transformation 37] 120. calm(X0) | happy(X0) [cnf transformation 66] 130. strong(mary) [cnf transformation 22] 255. creative(mary) [resolution 105,130] 257. ~calm(mary) [resolution 255,80] 258. ~happy(mary) [resolution 255,78] 262. happy(mary) [resolution 257,120] 263. $false [subsumption resolution 262,258] % SZS output end Proof for 5343897431589009516375046 % ------------------------------ % 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 strong or not wise is either not generous or not humble. Everyone who is not curious is both quiet and tall and vice versa. If someone is either not tall or curious then someone is not happy or funny. If someone is not generous or wise then lucy is not brave. If someone is wise then someone is not happy or funny and vice versa. Everyone who is calm or tall is not funny and vice versa. Everyone who is either not tall or brave is tall and vice versa. Everyone who is not calm is both brave and not quiet. If someone is not quiet or not old then someone is humble and vice versa. If john is both kind and creative then someone is both not funny and not curious and vice versa. If someone is not humble then alice is both not old and not creative and vice versa. Everyone who is either not brave or not rich is either kind or not funny. If susan is not generous or not calm then paul is not generous or quiet and vice versa. Everyone who is creative or not happy is humble or not tall. If lucy is both not wise and not strong then lucy is both not happy and calm. Someone is old. Someone is not kind. Paul is both not tall and kind. Mary is either not tall or tall. Alice is both humble and not strong.

Paul is wise.

contradiction

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

wise(paul)

% SZS status Unsatisfiable for 8487772339088931166675943 % SZS output start Proof for 8487772339088931166675943 4. ? [X0] : (wise(X0) | ~generous(X0)) => ~brave(lucy) [input p3] 7. ! [X0] : ((~tall(X0) <~> brave(X0)) <=> tall(X0)) [input p6] 21. wise(paul) [input hypothesis] 27. ~brave(lucy) | ! [X0] : (~wise(X0) & generous(X0)) [ennf transformation 4] 48. ! [X0] : ((((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ~tall(X0)) & (tall(X0) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0))))) [nnf transformation 7] 82. ~brave(lucy) | ~wise(X0) [cnf transformation 27] 89. tall(X0) | brave(X0) | tall(X0) [cnf transformation 48] 91. brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 48] 125. wise(paul) [cnf transformation 21] 126. tall(X0) | brave(X0) [duplicate literal removal 89] 127. brave(X0) | ~tall(X0) [duplicate literal removal 91] 141. 4 <=> ! [X0] : ~wise(X0) [avatar definition] 142. ~wise(X0) <- (4) [avatar component clause 141] 144. 5 <=> brave(lucy) [avatar definition] 146. ~brave(lucy) <- (~5) [avatar component clause 144] 147. 4 | ~5 [avatar split clause 82,144,141] 173. brave(X0) [subsumption resolution 126,127] 279. $false <- (~5) [subsumption resolution 146,173] 280. 5 [avatar contradiction clause 279] 281. $false <- (4) [resolution 142,125] 282. ~4 [avatar contradiction clause 281] 283. $false [avatar sat refutation 147,280,282] % SZS output end Proof for 8487772339088931166675943 % ------------------------------ % 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 brave and not curious is both rich and funny. Everyone who is not old is either not brave or generous and vice versa. If lucy is not kind then someone is either not brave or not strong. Everyone who is both not wise and tall is humble and vice versa. If someone is rich then fred is both generous and curious. Everyone who is generous is not humble and vice versa. Everyone who is both calm and not calm is either old or patient. Everyone who is either not kind or wise is quiet or not wise and vice versa. If someone is curious or not tall then someone is both old and generous. Everyone who is curious is either strong or humble and vice versa. If someone is not quiet then someone is both generous and not quiet and vice versa. Everyone who is not tall or tall is either patient or not happy. Everyone who is either curious or happy is both brave and not brave and vice versa. Everyone who is both not happy and old is happy or quiet and vice versa. If mary is not creative then mary is either brave or tall and vice versa. Everyone who is not creative is generous. Paul is both strong and not kind. Someone is generous. Someone is not quiet. Someone is both not happy and not strong. Someone is not humble or not creative.

Lucy is not kind.

entailment

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

~kind(lucy)

% SZS status Unsatisfiable for 3979577640585593054220128 % SZS output start Proof for 3979577640585593054220128 1. ! [X0] : ((~curious(X0) & ~brave(X0)) => (funny(X0) & rich(X0))) [input p0] 2. ! [X0] : (~old(X0) <=> (~brave(X0) <~> generous(X0))) [input p1] 4. ! [X0] : ((tall(X0) & ~wise(X0)) <=> humble(X0)) [input p3] 5. ? [X0] : rich(X0) => (curious(fred) & generous(fred)) [input p4] 6. ! [X0] : (generous(X0) <=> ~humble(X0)) [input p5] 8. ! [X0] : ((~kind(X0) <~> wise(X0)) <=> (~wise(X0) | quiet(X0))) [input p7] 13. ! [X0] : ((curious(X0) <~> happy(X0)) <=> (~brave(X0) & brave(X0))) [input p12] 14. ! [X0] : ((old(X0) & ~happy(X0)) <=> (quiet(X0) | happy(X0))) [input p13] 22. kind(lucy) [input hypothesis] 25. ! [X0] : ((~curious(X0) & ~brave(X0)) => rich(X0)) [pure predicate removal 1] 26. ! [X0] : (rich(X0) | (curious(X0) | brave(X0))) [ennf transformation 25] 27. ! [X0] : (rich(X0) | curious(X0) | brave(X0)) [flattening 26] 29. (curious(fred) & generous(fred)) | ! [X0] : ~rich(X0) [ennf transformation 5] 35. ! [X0] : ((~old(X0) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0)))) & (((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | old(X0))) [nnf transformation 2] 39. ! [X0] : (((tall(X0) & ~wise(X0)) | ~humble(X0)) & (humble(X0) | (~tall(X0) | wise(X0)))) [nnf transformation 4] 40. ! [X0] : (((tall(X0) & ~wise(X0)) | ~humble(X0)) & (humble(X0) | ~tall(X0) | wise(X0))) [flattening 39] 41. ! [X0] : ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))) [nnf transformation 6] 43. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (wise(X0) & ~quiet(X0))) & ((~wise(X0) | quiet(X0)) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [nnf transformation 8] 44. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (wise(X0) & ~quiet(X0))) & (~wise(X0) | quiet(X0) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [flattening 43] 55. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [nnf transformation 13] 56. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [flattening 55] 57. ! [X0] : (((old(X0) & ~happy(X0)) | (~quiet(X0) & ~happy(X0))) & ((quiet(X0) | happy(X0)) | (~old(X0) | happy(X0)))) [nnf transformation 14] 58. ! [X0] : (((old(X0) & ~happy(X0)) | (~quiet(X0) & ~happy(X0))) & (quiet(X0) | happy(X0) | ~old(X0) | happy(X0))) [flattening 57] 68. rich(X0) | curious(X0) | brave(X0) [cnf transformation 27] 72. ~generous(X0) | ~brave(X0) | ~old(X0) [cnf transformation 35] 76. ~humble(X0) | ~wise(X0) [cnf transformation 40] 79. curious(fred) | ~rich(X0) [cnf transformation 29] 81. humble(X0) | generous(X0) [cnf transformation 41] 85. ~wise(X0) | quiet(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 44] 87. wise(X0) | ~kind(X0) | wise(X0) [cnf transformation 44] 105. brave(X0) | happy(X0) | ~curious(X0) [cnf transformation 56] 107. ~curious(X0) | happy(X0) | ~brave(X0) [cnf transformation 56] 112. ~happy(X0) | ~happy(X0) [cnf transformation 58] 115. ~quiet(X0) | old(X0) [cnf transformation 58] 128. kind(lucy) [cnf transformation 22] 130. ~happy(X0) [duplicate literal removal 112] 131. ~wise(X0) | quiet(X0) | ~kind(X0) [duplicate literal removal 85] 132. ~kind(X0) | wise(X0) [duplicate literal removal 87] 134. 1 <=> kind(lucy) [avatar definition] 136. kind(lucy) <- (1) [avatar component clause 134] 148. 4 <=> ! [X0] : ~rich(X0) [avatar definition] 149. ~rich(X0) <- (4) [avatar component clause 148] 151. 5 <=> curious(fred) [avatar definition] 153. curious(fred) <- (5) [avatar component clause 151] 154. 4 | 5 [avatar split clause 79,151,148] 160. ~kind(X0) | quiet(X0) [subsumption resolution 131,132] 203. ~curious(X0) | happy(X0) [subsumption resolution 105,107] 230. 1 [avatar split clause 128,134] 237. ~wise(X2) | generous(X2) [resolution 81,76] 241. wise(lucy) <- (1) [resolution 132,136] 242. quiet(lucy) <- (1) [resolution 160,136] 249. old(lucy) <- (1) [resolution 242,115] 257. curious(X0) | brave(X0) <- (4) [resolution 149,68] 310. 30 <=> generous(lucy) [avatar definition] 312. generous(lucy) <- (30) [avatar component clause 310] 368. generous(lucy) <- (1) [resolution 237,241] 369. 30 | ~1 [avatar split clause 368,134,310] 372. brave(X2) | happy(X2) <- (4) [resolution 257,203] 374. brave(X2) <- (4) [subsumption resolution 372,130] 412. ~brave(lucy) | ~old(lucy) <- (30) [resolution 312,72] 417. ~old(lucy) <- (4, 30) [subsumption resolution 412,374] 418. $false <- (1, 4, 30) [subsumption resolution 417,249] 419. ~1 | ~4 | ~30 [avatar contradiction clause 418] 438. happy(fred) <- (5) [resolution 153,203] 450. $false <- (5) [subsumption resolution 438,130] 451. ~5 [avatar contradiction clause 450] 452. $false [avatar sat refutation 154,230,369,419,451] % SZS output end Proof for 3979577640585593054220128 % ------------------------------ % 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: 0.025 s % ------------------------------ % ------------------------------

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

Alice is calm.

neutral

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

calm(alice)

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

Paul is not humble.

neutral

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

~humble(paul)

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

Lucy is not curious.

entailment

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

~curious(lucy)

% SZS status Unsatisfiable for 4468223538192700711624796 % SZS output start Proof for 4468223538192700711624796 5. ! [X0] : ((strong(X0) & ~happy(X0)) <=> (kind(X0) | rich(X0))) [input p4] 6. ! [X0] : ((~rich(X0) | ~old(X0)) <=> (~happy(X0) & ~funny(X0))) [input p5] 11. ! [X0] : ((~quiet(X0) <~> happy(X0)) <=> (~quiet(X0) | curious(X0))) [input p10] 14. ! [X0] : (~quiet(X0) => (patient(X0) & happy(X0))) [input p13] 25. curious(lucy) [input hypothesis] 39. ! [X0] : ((patient(X0) & happy(X0)) | quiet(X0)) [ennf transformation 14] 46. ! [X0] : (((strong(X0) & ~happy(X0)) | (~kind(X0) & ~rich(X0))) & ((kind(X0) | rich(X0)) | (~strong(X0) | happy(X0)))) [nnf transformation 5] 47. ! [X0] : (((strong(X0) & ~happy(X0)) | (~kind(X0) & ~rich(X0))) & (kind(X0) | rich(X0) | ~strong(X0) | happy(X0))) [flattening 46] 48. ! [X0] : (((~rich(X0) | ~old(X0)) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | (rich(X0) & old(X0)))) [nnf transformation 6] 49. ! [X0] : ((~rich(X0) | ~old(X0) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | (rich(X0) & old(X0)))) [flattening 48] 60. ! [X0] : ((((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))))) [nnf transformation 11] 61. ! [X0] : ((((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))))) [flattening 60] 87. ~rich(X0) | ~happy(X0) [cnf transformation 47] 94. ~happy(X0) | rich(X0) [cnf transformation 49] 106. happy(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 61] 113. happy(X0) | quiet(X0) [cnf transformation 39] 131. curious(lucy) [cnf transformation 25] 150. ~happy(X0) [subsumption resolution 94,87] 152. 4 <=> ! [X1] : quiet(X1) [avatar definition] 153. quiet(X1) <- (4) [avatar component clause 152] 190. ~curious(X0) | ~quiet(X0) [subsumption resolution 106,150] 207. quiet(X0) [subsumption resolution 113,150] 208. 4 [avatar split clause 207,152] 235. ~quiet(lucy) [resolution 190,131] 236. $false <- (4) [subsumption resolution 235,153] 237. ~4 [avatar contradiction clause 236] 238. $false [avatar sat refutation 208,237] % SZS output end Proof for 4468223538192700711624796 % ------------------------------ % 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 generous. If fred is either not humble or not kind then susan is either kind or wise. If someone is either calm or rich then someone is both not brave and quiet. Everyone who is both not quiet and wise is not happy. Everyone who is both humble and not funny is both strong and funny. If lucy is both rich and not brave then someone is kind and vice versa. Everyone who is both not rich and not wise is either happy or rich and vice versa. If someone is both patient and funny then someone is brave or humble and vice versa. Everyone who is both curious and not brave is not rich or brave and vice versa. Everyone who is not patient or old is either patient or not wise. Everyone who is both not funny and creative is not wise or not happy and vice versa. If someone is patient then lucy is either kind or tall and vice versa. Everyone who is patient is humble and vice versa. If someone is generous then alice is not old or strong and vice versa. If someone is not creative or quiet then someone is both not rich and humble and vice versa. Alice is either not strong or humble. Someone is humble or kind. Someone is both not curious and old. Fred is either not kind or not calm.

Lucy is calm.

entailment

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

calm(lucy)

% SZS status Unsatisfiable for 6171020456362299044764750 % SZS output start Proof for 6171020456362299044764750 3. ? [X0] : (calm(X0) <~> rich(X0)) => ? [X0] : (quiet(X0) & ~brave(X0)) [input p2] 4. ! [X0] : ((wise(X0) & ~quiet(X0)) => ~happy(X0)) [input p3] 5. ! [X0] : ((~funny(X0) & humble(X0)) => (funny(X0) & strong(X0))) [input p4] 6. (~brave(lucy) & rich(lucy)) <=> ? [X0] : kind(X0) [input p5] 7. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> (happy(X0) <~> rich(X0))) [input p6] 8. ? [X0] : (funny(X0) & patient(X0)) <=> ? [X0] : (humble(X0) | brave(X0)) [input p7] 11. ! [X0] : ((creative(X0) & ~funny(X0)) <=> (~happy(X0) | ~wise(X0))) [input p10] 13. ! [X0] : (patient(X0) <=> humble(X0)) [input p12] 15. ? [X0] : (quiet(X0) | ~creative(X0)) <=> ? [X0] : (humble(X0) & ~rich(X0)) [input p14] 17. ? [X0] : (kind(X0) | humble(X0)) [input p16] 20. ~calm(lucy) [input hypothesis] 21. ? [X0] : (calm(X0) <~> rich(X0)) => ? [X1] : (quiet(X1) & ~brave(X1)) [rectify 3] 22. ? [X0] : (funny(X0) & patient(X0)) <=> ? [X1] : (humble(X1) | brave(X1)) [rectify 8] 23. ? [X0] : (quiet(X0) | ~creative(X0)) <=> ? [X1] : (humble(X1) & ~rich(X1)) [rectify 15] 26. ? [X1] : (quiet(X1) & ~brave(X1)) | ! [X0] : (calm(X0) <=> rich(X0)) [ennf transformation 21] 27. ! [X0] : (~happy(X0) | (~wise(X0) | quiet(X0))) [ennf transformation 4] 28. ! [X0] : (~happy(X0) | ~wise(X0) | quiet(X0)) [flattening 27] 29. ! [X0] : ((funny(X0) & strong(X0)) | (funny(X0) | ~humble(X0))) [ennf transformation 5] 30. ! [X0] : ((funny(X0) & strong(X0)) | funny(X0) | ~humble(X0)) [flattening 29] 33. ? [X1] : (quiet(X1) & ~brave(X1)) | ! [X0] : ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0))) [nnf transformation 26] 34. ? [X0] : (quiet(X0) & ~brave(X0)) | ! [X1] : ((calm(X1) | ~rich(X1)) & (rich(X1) | ~calm(X1))) [rectify 33] 35. ? [X0] : (quiet(X0) & ~brave(X0)) => (quiet(sK0) & ~brave(sK0)) [choice axiom] 36. (quiet(sK0) & ~brave(sK0)) | ! [X1] : ((calm(X1) | ~rich(X1)) & (rich(X1) | ~calm(X1))) [skolemisation 34,35] 37. ((~brave(lucy) & rich(lucy)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | (brave(lucy) | ~rich(lucy))) [nnf transformation 6] 38. ((~brave(lucy) & rich(lucy)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | brave(lucy) | ~rich(lucy)) [flattening 37] 39. ((~brave(lucy) & rich(lucy)) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | brave(lucy) | ~rich(lucy)) [rectify 38] 40. ? [X1] : kind(X1) => kind(sK1) [choice axiom] 41. ((~brave(lucy) & rich(lucy)) | ! [X0] : ~kind(X0)) & (kind(sK1) | brave(lucy) | ~rich(lucy)) [skolemisation 39,40] 42. ! [X0] : (((~wise(X0) & ~rich(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0)))) & (((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (wise(X0) | rich(X0)))) [nnf transformation 7] 43. ! [X0] : (((~wise(X0) & ~rich(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0)))) & (((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | wise(X0) | rich(X0))) [flattening 42] 44. (? [X0] : (funny(X0) & patient(X0)) | ! [X1] : (~humble(X1) & ~brave(X1))) & (? [X1] : (humble(X1) | brave(X1)) | ! [X0] : (~funny(X0) | ~patient(X0))) [nnf transformation 22] 45. (? [X0] : (funny(X0) & patient(X0)) | ! [X1] : (~humble(X1) & ~brave(X1))) & (? [X2] : (humble(X2) | brave(X2)) | ! [X3] : (~funny(X3) | ~patient(X3))) [rectify 44] 46. ? [X0] : (funny(X0) & patient(X0)) => (funny(sK2) & patient(sK2)) [choice axiom] 47. ? [X2] : (humble(X2) | brave(X2)) => (humble(sK3) | brave(sK3)) [choice axiom] 48. ((funny(sK2) & patient(sK2)) | ! [X1] : (~humble(X1) & ~brave(X1))) & ((humble(sK3) | brave(sK3)) | ! [X3] : (~funny(X3) | ~patient(X3))) [skolemisation 45,47,46] 52. ! [X0] : (((creative(X0) & ~funny(X0)) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | (~creative(X0) | funny(X0)))) [nnf transformation 11] 53. ! [X0] : (((creative(X0) & ~funny(X0)) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | ~creative(X0) | funny(X0))) [flattening 52] 58. ! [X0] : ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))) [nnf transformation 13] 64. (? [X0] : (quiet(X0) | ~creative(X0)) | ! [X1] : (~humble(X1) | rich(X1))) & (? [X1] : (humble(X1) & ~rich(X1)) | ! [X0] : (~quiet(X0) & creative(X0))) [nnf transformation 23] 65. (? [X0] : (quiet(X0) | ~creative(X0)) | ! [X1] : (~humble(X1) | rich(X1))) & (? [X2] : (humble(X2) & ~rich(X2)) | ! [X3] : (~quiet(X3) & creative(X3))) [rectify 64] 66. ? [X0] : (quiet(X0) | ~creative(X0)) => (quiet(sK6) | ~creative(sK6)) [choice axiom] 67. ? [X2] : (humble(X2) & ~rich(X2)) => (humble(sK7) & ~rich(sK7)) [choice axiom] 68. ((quiet(sK6) | ~creative(sK6)) | ! [X1] : (~humble(X1) | rich(X1))) & ((humble(sK7) & ~rich(sK7)) | ! [X3] : (~quiet(X3) & creative(X3))) [skolemisation 65,67,66] 70. ? [X0] : (kind(X0) | humble(X0)) => (kind(sK8) | humble(sK8)) [choice axiom] 71. kind(sK8) | humble(sK8) [skolemisation 17,70] 83. quiet(sK0) | calm(X1) | ~rich(X1) [cnf transformation 36] 84. ~happy(X0) | ~wise(X0) | quiet(X0) [cnf transformation 28] 86. funny(X0) | funny(X0) | ~humble(X0) [cnf transformation 30] 88. rich(lucy) | ~kind(X0) [cnf transformation 41] 94. ~happy(X0) | rich(X0) | ~wise(X0) [cnf transformation 43] 98. patient(sK2) | ~humble(X1) [cnf transformation 48] 111. ~funny(X0) | wise(X0) [cnf transformation 53] 112. ~funny(X0) | happy(X0) [cnf transformation 53] 119. ~patient(X0) | humble(X0) [cnf transformation 58] 125. ~rich(sK7) | ~quiet(X3) [cnf transformation 68] 127. humble(sK7) | ~quiet(X3) [cnf transformation 68] 131. kind(sK8) | humble(sK8) [cnf transformation 71] 136. ~calm(lucy) [cnf transformation 20] 142. ~humble(X0) | funny(X0) [duplicate literal removal 86] 164. 5 <=> ! [X1] : (calm(X1) | ~rich(X1)) [avatar definition] 165. ~rich(X1) | calm(X1) <- (5) [avatar component clause 164] 167. 6 <=> quiet(sK0) [avatar definition] 169. quiet(sK0) <- (6) [avatar component clause 167] 170. 5 | 6 [avatar split clause 83,167,164] 182. 9 <=> ! [X0] : ~kind(X0) [avatar definition] 183. ~kind(X0) <- (9) [avatar component clause 182] 190. 11 <=> rich(lucy) [avatar definition] 192. rich(lucy) <- (11) [avatar component clause 190] 193. 9 | 11 [avatar split clause 88,190,182] 201. 13 <=> ! [X1] : ~humble(X1) [avatar definition] 202. ~humble(X1) <- (13) [avatar component clause 201] 204. 14 <=> funny(sK2) [avatar definition] 206. funny(sK2) <- (14) [avatar component clause 204] 213. 16 <=> patient(sK2) [avatar definition] 215. patient(sK2) <- (16) [avatar component clause 213] 216. 13 | 16 [avatar split clause 98,213,201] 281. 31 <=> ! [X3] : ~quiet(X3) [avatar definition] 282. ~quiet(X3) <- (31) [avatar component clause 281] 284. 32 <=> humble(sK7) [avatar definition] 286. humble(sK7) <- (32) [avatar component clause 284] 287. 31 | 32 [avatar split clause 127,284,281] 293. 34 <=> rich(sK7) [avatar definition] 295. ~rich(sK7) <- (~34) [avatar component clause 293] 296. 31 | ~34 [avatar split clause 125,293,281] 305. 36 <=> humble(sK8) [avatar definition] 307. humble(sK8) <- (36) [avatar component clause 305] 309. 37 <=> kind(sK8) [avatar definition] 311. kind(sK8) <- (37) [avatar component clause 309] 312. 36 | 37 [avatar split clause 131,309,305] 322. wise(sK2) <- (14) [resolution 111,206] 323. happy(sK2) <- (14) [resolution 112,206] 327. humble(sK2) <- (16) [resolution 119,215] 336. funny(sK2) <- (16) [resolution 142,327] 359. ~wise(sK2) | quiet(sK2) <- (14) [resolution 84,323] 362. quiet(sK2) <- (14) [subsumption resolution 359,322] 372. $false <- (6, 31) [resolution 282,169] 373. ~6 | ~31 [avatar contradiction clause 372] 419. $false <- (14, 31) [resolution 362,282] 420. ~14 | ~31 [avatar contradiction clause 419] 421. 14 | ~16 [avatar split clause 336,213,204] 424. $false <- (13, 36) [resolution 202,307] 425. ~13 | ~36 [avatar contradiction clause 424] 431. funny(sK7) <- (32) [resolution 286,142] 441. happy(sK7) <- (32) [resolution 431,112] 442. wise(sK7) <- (32) [resolution 431,111] 478. rich(sK7) | ~wise(sK7) <- (32) [resolution 441,94] 480. ~wise(sK7) <- (32, ~34) [subsumption resolution 478,295] 481. $false <- (32, ~34) [subsumption resolution 480,442] 482. ~32 | 34 [avatar contradiction clause 481] 484. $false <- (9, 37) [subsumption resolution 311,183] 485. ~9 | ~37 [avatar contradiction clause 484] 489. calm(lucy) <- (5, 11) [resolution 192,165] 492. $false <- (5, 11) [subsumption resolution 489,136] 493. ~5 | ~11 [avatar contradiction clause 492] 494. $false [avatar sat refutation 170,193,216,287,296,312,373,420,421,425,482,485,493] % SZS output end Proof for 6171020456362299044764750 % ------------------------------ % 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 % ------------------------------ % ------------------------------

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

John is not old.

entailment

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

~old(john)

% SZS status Unsatisfiable for 8539645846699635079586140 % SZS output start Proof for 8539645846699635079586140 2. ! [X0] : ((~strong(X0) <~> ~wise(X0)) <=> (~kind(X0) & curious(X0))) [input p1] 3. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (calm(X0) & ~funny(X0))) [input p2] 4. ? [X0] : (~kind(X0) | ~humble(X0)) => ~wise(john) [input p3] 7. ! [X0] : ((~patient(X0) | ~generous(X0)) => (strong(X0) & ~curious(X0))) [input p6] 8. ? [X0] : (patient(X0) & ~patient(X0)) <=> ? [X0] : (old(X0) & patient(X0)) [input p7] 11. (~funny(john) | rich(john)) => ? [X0] : ~kind(X0) [input p10] 20. old(john) [input hypothesis] 21. ? [X0] : (patient(X0) & ~patient(X0)) <=> ? [X1] : (old(X1) & patient(X1)) [rectify 8] 26. ~wise(john) | ! [X0] : (kind(X0) & humble(X0)) [ennf transformation 4] 28. ! [X0] : ((strong(X0) & ~curious(X0)) | (patient(X0) & generous(X0))) [ennf transformation 7] 29. ? [X0] : ~kind(X0) | (funny(john) & ~rich(john)) [ennf transformation 11] 32. ! [X0] : ((((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | (kind(X0) | ~curious(X0))) & ((~kind(X0) & curious(X0)) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))))) [nnf transformation 2] 33. ! [X0] : ((((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | kind(X0) | ~curious(X0)) & ((~kind(X0) & curious(X0)) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))))) [flattening 32] 34. ! [X0] : (((generous(X0) | ~generous(X0)) | (~calm(X0) | funny(X0))) & ((calm(X0) & ~funny(X0)) | (~generous(X0) & generous(X0)))) [nnf transformation 3] 35. ! [X0] : ((generous(X0) | ~generous(X0) | ~calm(X0) | funny(X0)) & ((calm(X0) & ~funny(X0)) | (~generous(X0) & generous(X0)))) [flattening 34] 38. (? [X0] : (patient(X0) & ~patient(X0)) | ! [X1] : (~old(X1) | ~patient(X1))) & (? [X1] : (old(X1) & patient(X1)) | ! [X0] : (~patient(X0) | patient(X0))) [nnf transformation 21] 39. (? [X0] : (patient(X0) & ~patient(X0)) | ! [X1] : (~old(X1) | ~patient(X1))) & (? [X2] : (old(X2) & patient(X2)) | ! [X3] : (~patient(X3) | patient(X3))) [rectify 38] 40. ? [X0] : (patient(X0) & ~patient(X0)) => (patient(sK0) & ~patient(sK0)) [choice axiom] 41. ? [X2] : (old(X2) & patient(X2)) => (old(sK1) & patient(sK1)) [choice axiom] 42. ((patient(sK0) & ~patient(sK0)) | ! [X1] : (~old(X1) | ~patient(X1))) & ((old(sK1) & patient(sK1)) | ! [X3] : (~patient(X3) | patient(X3))) [skolemisation 39,41,40] 49. ? [X0] : ~kind(X0) => ~kind(sK4) [choice axiom] 50. ~kind(sK4) | (funny(john) & ~rich(john)) [skolemisation 29,49] 71. ~strong(X0) | curious(X0) | wise(X0) [cnf transformation 33] 76. ~funny(X0) | generous(X0) [cnf transformation 35] 77. ~generous(X0) | ~funny(X0) [cnf transformation 35] 82. ~wise(john) | kind(X0) [cnf transformation 26] 90. ~curious(X0) | patient(X0) [cnf transformation 28] 92. patient(X0) | strong(X0) [cnf transformation 28] 95. ~patient(sK0) | ~old(X1) | ~patient(X1) [cnf transformation 42] 96. patient(sK0) | ~old(X1) | ~patient(X1) [cnf transformation 42] 103. ~kind(sK4) | funny(john) [cnf transformation 50] 127. old(john) [cnf transformation 20] 129. ~funny(X0) [subsumption resolution 76,77] 131. 1 <=> ! [X0] : kind(X0) [avatar definition] 132. kind(X0) <- (1) [avatar component clause 131] 134. 2 <=> wise(john) [avatar definition] 136. ~wise(john) <- (~2) [avatar component clause 134] 137. 1 | ~2 [avatar split clause 82,134,131] 159. 7 <=> ! [X1] : (~old(X1) | ~patient(X1)) [avatar definition] 160. ~old(X1) | ~patient(X1) <- (7) [avatar component clause 159] 162. 8 <=> patient(sK0) [avatar definition] 165. 7 | 8 [avatar split clause 96,162,159] 166. 7 | ~8 [avatar split clause 95,162,159] 185. ~kind(sK4) [subsumption resolution 103,129] 265. ~patient(john) <- (7) [resolution 160,127] 266. strong(john) <- (7) [resolution 265,92] 279. curious(john) | wise(john) <- (7) [resolution 71,266] 283. curious(john) <- (~2, 7) [subsumption resolution 279,136] 320. patient(john) <- (~2, 7) [resolution 283,90] 322. $false <- (~2, 7) [subsumption resolution 320,265] 323. 2 | ~7 [avatar contradiction clause 322] 333. $false <- (1) [resolution 132,185] 336. ~1 [avatar contradiction clause 333] 337. $false [avatar sat refutation 137,165,166,323,336] % SZS output end Proof for 8539645846699635079586140 % ------------------------------ % 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 wise or strong is calm or curious and vice versa. If someone is strong then paul is quiet. Everyone who is both not creative and not happy is not old and vice versa. If someone is rich or old then susan is patient. Everyone who is both not old and curious is funny. Everyone who is funny is either not funny or funny and vice versa. If susan is wise then someone is not rich or creative and vice versa. Everyone who is curious or calm is both wise and old and vice versa. Everyone who is either not old or old is either strong or generous and vice versa. If mary is either not curious or brave then paul is not old. If someone is both old and funny then alice is both strong and not curious. If lucy is both not calm and not patient then someone is both creative and not old and vice versa. Everyone who is kind or tall is both not tall and old and vice versa. Everyone who is quiet is both calm and not funny. Someone is wise or not curious. Alice is rich. Paul is not kind. Alice is either creative or patient. John is both brave and not tall. Alice is either humble or brave.

Mary is not strong.

entailment

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

~strong(mary)

% SZS status Unsatisfiable for 2056495771396609276401255 % SZS output start Proof for 2056495771396609276401255 2. ? [X0] : strong(X0) => quiet(paul) [input p1] 6. ! [X0] : (funny(X0) <=> (~funny(X0) <~> funny(X0))) [input p5] 14. ! [X0] : (quiet(X0) => (~funny(X0) & calm(X0))) [input p13] 21. strong(mary) [input hypothesis] 22. quiet(paul) | ! [X0] : ~strong(X0) [ennf transformation 2] 28. ! [X0] : ((~funny(X0) & calm(X0)) | ~quiet(X0)) [ennf transformation 14] 33. ! [X0] : ((funny(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ~funny(X0))) [nnf transformation 6] 59. quiet(paul) | ~strong(X0) [cnf transformation 22] 68. funny(X0) | funny(X0) | funny(X0) [cnf transformation 33] 100. ~funny(X0) | ~quiet(X0) [cnf transformation 28] 110. strong(mary) [cnf transformation 21] 119. funny(X0) [duplicate literal removal 68] 122. 1 <=> ! [X0] : ~strong(X0) [avatar definition] 123. ~strong(X0) <- (1) [avatar component clause 122] 125. 2 <=> quiet(paul) [avatar definition] 127. quiet(paul) <- (2) [avatar component clause 125] 128. 1 | 2 [avatar split clause 59,125,122] 208. ~quiet(X0) [subsumption resolution 100,119] 229. $false <- (2) [subsumption resolution 127,208] 230. ~2 [avatar contradiction clause 229] 231. $false <- (1) [resolution 123,110] 232. ~1 [avatar contradiction clause 231] 233. $false [avatar sat refutation 128,230,232] % SZS output end Proof for 2056495771396609276401255 % ------------------------------ % 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 not quiet or happy then someone is both funny and not humble. If fred is funny then paul is not quiet or old. If someone is both not generous and wise then john is either not happy or happy and vice versa. Everyone who is not curious or not tall is either not rich or funny. If someone is either not strong or generous then paul is happy or curious. Everyone who is happy or not wise is both not rich and not curious. Everyone who is both not curious and not quiet is not creative or not quiet and vice versa. Everyone who is both happy and humble is not wise or strong and vice versa. Everyone who is not happy or humble is either kind or not brave and vice versa. Everyone who is both calm and not calm is not curious and vice versa. If susan is old or not wise then fred is not wise or rich. Everyone who is calm or curious is either not creative or not rich and vice versa. Everyone who is not humble is not curious and vice versa. If alice is not calm or brave then someone is either funny or creative and vice versa. If someone is not curious then lucy is not strong or not creative. Someone is not wise or not brave. Someone is not patient or quiet. Lucy is generous or kind. Someone is both not generous and not happy. Someone is not patient.

John is quiet.

entailment

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

quiet(john)

% SZS status Unsatisfiable for 5689821570198753519272154 % SZS output start Proof for 5689821570198753519272154 7. ! [X0] : ((~quiet(X0) & ~curious(X0)) <=> (~quiet(X0) | ~creative(X0))) [input p6] 10. ! [X0] : ((~calm(X0) & calm(X0)) <=> ~curious(X0)) [input p9] 21. ~quiet(john) [input hypothesis] 47. ! [X0] : (((~quiet(X0) & ~curious(X0)) | (quiet(X0) & creative(X0))) & ((~quiet(X0) | ~creative(X0)) | (quiet(X0) | curious(X0)))) [nnf transformation 7] 48. ! [X0] : (((~quiet(X0) & ~curious(X0)) | (quiet(X0) & creative(X0))) & (~quiet(X0) | ~creative(X0) | quiet(X0) | curious(X0))) [flattening 47] 53. ! [X0] : (((~calm(X0) & calm(X0)) | curious(X0)) & (~curious(X0) | (calm(X0) | ~calm(X0)))) [nnf transformation 10] 54. ! [X0] : (((~calm(X0) & calm(X0)) | curious(X0)) & (~curious(X0) | calm(X0) | ~calm(X0))) [flattening 53] 88. ~curious(X0) | quiet(X0) [cnf transformation 48] 103. calm(X0) | curious(X0) [cnf transformation 54] 104. ~calm(X0) | curious(X0) [cnf transformation 54] 126. ~quiet(john) [cnf transformation 21] 194. curious(X0) [subsumption resolution 103,104] 272. quiet(X0) [resolution 88,194] 273. $false [resolution 272,126] % SZS output end Proof for 5689821570198753519272154 % ------------------------------ % 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 paul is wise then alice is either creative or not generous and vice versa. Everyone who is either not old or not creative is either not calm or calm and vice versa. Everyone who is rich is either not quiet or creative. If someone is not curious or tall then fred is not old or not curious. If lucy is not curious then someone is either not quiet or not strong and vice versa. If someone is creative or not happy then fred is both brave and tall and vice versa. Everyone who is rich or not patient is both curious and quiet. Everyone who is both not wise and not generous is not brave or wise and vice versa. If someone is both not creative and not funny then paul is not curious or not happy. Everyone who is old or generous is not patient. If someone is both not humble and happy then lucy is either not strong or creative and vice versa. Everyone who is not old or happy is not tall. If lucy is not curious then someone is strong. If someone is not rich or old then alice is happy and vice versa. If susan is not rich or quiet then someone is strong or not generous. If someone is both creative and not funny then john is both funny and brave. Mary is either not old or not tall. Someone is calm or happy. Lucy is not creative. Mary is old or strong.

Susan is brave.

neutral

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

brave(susan)

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

Susan is not tall.

contradiction

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

~tall(susan)

% SZS status Unsatisfiable for 1247380666375956282563624 % SZS output start Proof for 1247380666375956282563624 3. ! [X0] : (kind(X0) <=> (~tall(X0) | ~humble(X0))) [input p2] 12. ! [X0] : ((~calm(X0) | kind(X0)) => tall(X0)) [input p11] 25. ~tall(susan) [input hypothesis] 40. ! [X0] : (tall(X0) | (calm(X0) & ~kind(X0))) [ennf transformation 12] 44. ! [X0] : ((kind(X0) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | ~kind(X0))) [nnf transformation 3] 45. ! [X0] : ((kind(X0) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | ~kind(X0))) [flattening 44] 88. kind(X0) | tall(X0) [cnf transformation 45] 106. tall(X0) | ~kind(X0) [cnf transformation 40] 134. ~tall(susan) [cnf transformation 25] 216. 19 <=> ! [X3] : tall(X3) [avatar definition] 217. tall(X3) <- (19) [avatar component clause 216] 227. tall(X0) [subsumption resolution 106,88] 228. 19 [avatar split clause 227,216] 340. $false <- (19) [resolution 217,134] 341. ~19 [avatar contradiction clause 340] 342. $false [avatar sat refutation 228,341] % SZS output end Proof for 1247380666375956282563624 % ------------------------------ % 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 not generous then paul is not strong. If someone is either calm or happy then paul is both not generous and not old. Everyone who is both not tall and tall is not kind and vice versa. If fred is either not kind or happy then someone is both not creative and wise. If someone is brave then someone is rich or generous and vice versa. Everyone who is not calm is old. If someone is kind or not generous then someone is either tall or old. Everyone who is both patient and rich is calm or not kind and vice versa. If someone is both brave and kind then paul is both old and quiet. If susan is patient then someone is both not strong and happy. If lucy is both not patient and not wise then mary is creative. Everyone who is both not tall and not wise is both quiet and strong. Everyone who is not rich is either not happy or calm and vice versa. Everyone who is both not rich and not wise is old. If john is either not generous or not calm then someone is both not wise and kind and vice versa. If alice is not old or not kind then someone is both not strong and not funny and vice versa. Someone is not quiet. Fred is both not curious and tall. John is both not funny and not calm. Alice is either not funny or not strong. Mary is either not quiet or brave. John is not creative or calm. Paul is either not quiet or brave. Fred is happy or not happy.

Mary is not happy.

entailment

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

~happy(mary)

% SZS status Unsatisfiable for 2427008745495446010253227 % SZS output start Proof for 2427008745495446010253227 2. ? [X0] : (calm(X0) <~> happy(X0)) => (~old(paul) & ~generous(paul)) [input p1] 3. ! [X0] : ((tall(X0) & ~tall(X0)) <=> ~kind(X0)) [input p2] 5. ? [X0] : brave(X0) <=> ? [X0] : (generous(X0) | rich(X0)) [input p4] 6. ! [X0] : (~calm(X0) => old(X0)) [input p5] 8. ! [X0] : ((rich(X0) & patient(X0)) <=> (~kind(X0) | calm(X0))) [input p7] 9. ? [X0] : (kind(X0) & brave(X0)) => (quiet(paul) & old(paul)) [input p8] 13. ! [X0] : (~rich(X0) <=> (~happy(X0) <~> calm(X0))) [input p12] 25. happy(mary) [input hypothesis] 26. ? [X0] : brave(X0) <=> ? [X1] : (generous(X1) | rich(X1)) [rectify 5] 30. (~old(paul) & ~generous(paul)) | ! [X0] : (calm(X0) <=> happy(X0)) [ennf transformation 2] 32. ! [X0] : (old(X0) | calm(X0)) [ennf transformation 6] 34. (quiet(paul) & old(paul)) | ! [X0] : (~kind(X0) | ~brave(X0)) [ennf transformation 9] 42. (~old(paul) & ~generous(paul)) | ! [X0] : ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))) [nnf transformation 30] 43. ! [X0] : (((tall(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (~tall(X0) | tall(X0)))) [nnf transformation 3] 44. ! [X0] : (((tall(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | ~tall(X0) | tall(X0))) [flattening 43] 48. (? [X0] : brave(X0) | ! [X1] : (~generous(X1) & ~rich(X1))) & (? [X1] : (generous(X1) | rich(X1)) | ! [X0] : ~brave(X0)) [nnf transformation 26] 49. (? [X0] : brave(X0) | ! [X1] : (~generous(X1) & ~rich(X1))) & (? [X2] : (generous(X2) | rich(X2)) | ! [X3] : ~brave(X3)) [rectify 48] 50. ? [X0] : brave(X0) => brave(sK1) [choice axiom] 51. ? [X2] : (generous(X2) | rich(X2)) => (generous(sK2) | rich(sK2)) [choice axiom] 52. (brave(sK1) | ! [X1] : (~generous(X1) & ~rich(X1))) & ((generous(sK2) | rich(sK2)) | ! [X3] : ~brave(X3)) [skolemisation 49,51,50] 57. ! [X0] : (((rich(X0) & patient(X0)) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 8] 58. ! [X0] : (((rich(X0) & patient(X0)) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | ~rich(X0) | ~patient(X0))) [flattening 57] 61. ! [X0] : ((~rich(X0) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0)))) & (((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | rich(X0))) [nnf transformation 13] 79. ~old(paul) | happy(X0) | ~calm(X0) [cnf transformation 42] 80. ~old(paul) | calm(X0) | ~happy(X0) [cnf transformation 42] 82. ~tall(X0) | kind(X0) [cnf transformation 44] 83. kind(X0) | tall(X0) [cnf transformation 44] 89. brave(sK1) | ~rich(X1) [cnf transformation 52] 91. old(X0) | calm(X0) [cnf transformation 32] 99. ~calm(X0) | rich(X0) [cnf transformation 58] 101. old(paul) | ~kind(X0) | ~brave(X0) [cnf transformation 34] 111. ~rich(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 61] 136. happy(mary) [cnf transformation 25] 146. 3 <=> ! [X0] : (calm(X0) | ~happy(X0)) [avatar definition] 147. calm(X0) | ~happy(X0) <- (3) [avatar component clause 146] 149. 4 <=> old(paul) [avatar definition] 151. ~old(paul) <- (~4) [avatar component clause 149] 152. 3 | ~4 [avatar split clause 80,149,146] 154. 5 <=> ! [X0] : (happy(X0) | ~calm(X0)) [avatar definition] 155. happy(X0) | ~calm(X0) <- (5) [avatar component clause 154] 156. 5 | ~4 [avatar split clause 79,149,154] 163. kind(X0) [subsumption resolution 82,83] 184. 11 <=> brave(sK1) [avatar definition] 186. brave(sK1) <- (11) [avatar component clause 184] 189. 12 <=> ! [X1] : ~rich(X1) [avatar definition] 190. ~rich(X1) <- (12) [avatar component clause 189] 191. 12 | 11 [avatar split clause 89,184,189] 193. 13 <=> ! [X3] : ~brave(X3) [avatar definition] 194. ~brave(X3) <- (13) [avatar component clause 193] 225. old(paul) | ~brave(X0) [subsumption resolution 101,163] 226. 13 | 4 [avatar split clause 225,149,193] 254. ~happy(X0) | ~calm(X0) [subsumption resolution 111,99] 328. $false <- (11, 13) [subsumption resolution 186,194] 329. ~11 | ~13 [avatar contradiction clause 328] 334. calm(paul) <- (~4) [resolution 91,151] 338. rich(paul) <- (~4) [resolution 99,334] 339. $false <- (~4, 12) [subsumption resolution 338,190] 340. 4 | ~12 [avatar contradiction clause 339] 341. ~calm(X0) <- (5) [subsumption resolution 155,254] 342. ~happy(X0) <- (3, 5) [subsumption resolution 147,341] 343. $false <- (3, 5) [resolution 342,136] 344. ~3 | ~5 [avatar contradiction clause 343] 345. $false [avatar sat refutation 152,156,191,226,329,340,344] % SZS output end Proof for 2427008745495446010253227 % ------------------------------ % 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 old is either not creative or humble. If someone is both wise and brave then someone is either patient or brave. If susan is strong or not patient then lucy is both not patient and wise and vice versa. Everyone who is not old is funny. If someone is old or not generous then john is not old and vice versa. If susan is both happy and not kind then someone is either not quiet or not humble and vice versa. If paul is not kind or old then john is not strong and vice versa. If someone is generous or not brave then someone is not funny. Everyone who is both patient and brave is both generous and not patient. If lucy is patient or not tall then someone is both happy and generous and vice versa. If someone is not calm then fred is not kind or not strong and vice versa. If someone is humble or not tall then someone is both kind and tall. If susan is either not calm or curious then susan is humble and vice versa. Everyone who is both not funny and not creative is both not rich and not brave and vice versa. Everyone who is either old or not tall is either calm or patient. Everyone who is both generous and strong is not creative. John is not rich or not old. Alice is not generous. Paul is both not funny and tall. Alice is either funny or generous. Lucy is tall or funny. Someone is not creative. Lucy is not generous. Someone is brave or not calm.

John is funny.

entailment

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

funny(john)

% SZS status Unsatisfiable for 9067099769704591716179352 % SZS output start Proof for 9067099769704591716179352 4. ! [X0] : (~old(X0) => funny(X0)) [input p3] 5. ? [X0] : (~generous(X0) | old(X0)) <=> ~old(john) [input p4] 25. ~funny(john) [input hypothesis] 31. ! [X0] : (funny(X0) | old(X0)) [ennf transformation 4] 46. (? [X0] : (~generous(X0) | old(X0)) | old(john)) & (~old(john) | ! [X0] : (generous(X0) & ~old(X0))) [nnf transformation 5] 47. (? [X0] : (~generous(X0) | old(X0)) | old(john)) & (~old(john) | ! [X1] : (generous(X1) & ~old(X1))) [rectify 46] 48. ? [X0] : (~generous(X0) | old(X0)) => (~generous(sK1) | old(sK1)) [choice axiom] 49. ((~generous(sK1) | old(sK1)) | old(john)) & (~old(john) | ! [X1] : (generous(X1) & ~old(X1))) [skolemisation 47,48] 91. funny(X0) | old(X0) [cnf transformation 31] 92. ~old(john) | ~old(X1) [cnf transformation 49] 143. ~funny(john) [cnf transformation 25] 180. 8 <=> old(john) [avatar definition] 182. old(john) <- (8) [avatar component clause 180] 197. 12 <=> ! [X1] : ~old(X1) [avatar definition] 198. ~old(X1) <- (12) [avatar component clause 197] 199. 12 | ~8 [avatar split clause 92,180,197] 351. old(john) [resolution 91,143] 356. 8 [avatar split clause 351,180] 357. $false <- (8, 12) [subsumption resolution 182,198] 358. ~8 | ~12 [avatar contradiction clause 357] 359. $false [avatar sat refutation 199,356,358] % SZS output end Proof for 9067099769704591716179352 % ------------------------------ % 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 lucy is either not wise or old then someone is either not curious or not wise. Everyone who is either not happy or patient is either tall or curious. If someone is either not old or not brave then alice is either not funny or not happy and vice versa. Everyone who is happy or humble is either not kind or rich. Everyone who is either calm or not wise is funny and vice versa. If someone is kind then mary is not tall and vice versa. Everyone who is either calm or quiet is not generous and vice versa. If lucy is both happy and funny then john is old and vice versa. Everyone who is wise is either not brave or tall and vice versa. Everyone who is either not strong or not quiet is either not creative or creative and vice versa. Everyone who is both not old and creative is either kind or brave. If someone is both happy and not creative then paul is not creative and vice versa. If someone is either brave or old then fred is patient or not patient and vice versa. If someone is either not curious or brave then someone is both not wise and not generous and vice versa. Everyone who is rich or wise is either not kind or not wise. Everyone who is not patient or not funny is both not calm and not quiet and vice versa. Someone is not patient or not kind. Someone is both not kind and humble. Someone is curious. Alice is both not calm and happy. Someone is not old. John is quiet. Someone is generous. Fred is either funny or not funny.

Alice is wise.

entailment

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

wise(alice)

% SZS status Unsatisfiable for 8841359678954647498784631 % SZS output start Proof for 8841359678954647498784631 3. ? [X0] : (~old(X0) <~> ~brave(X0)) <=> (~funny(alice) <~> ~happy(alice)) [input p2] 5. ! [X0] : ((calm(X0) <~> ~wise(X0)) <=> funny(X0)) [input p4] 13. ? [X0] : (brave(X0) <~> old(X0)) <=> (~patient(fred) | patient(fred)) [input p12] 20. happy(alice) & ~calm(alice) [input p19] 25. ~wise(alice) [input hypothesis] 37. (? [X0] : ((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | ((~funny(alice) | happy(alice)) & (~happy(alice) | funny(alice)))) & (((happy(alice) | funny(alice)) & (~happy(alice) | ~funny(alice))) | ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) [nnf transformation 3] 38. (? [X0] : ((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | ((~funny(alice) | happy(alice)) & (~happy(alice) | funny(alice)))) & (((happy(alice) | funny(alice)) & (~happy(alice) | ~funny(alice))) | ! [X1] : ((~old(X1) | brave(X1)) & (~brave(X1) | old(X1)))) [rectify 37] 39. ? [X0] : ((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) => ((brave(sK1) | old(sK1)) & (~brave(sK1) | ~old(sK1))) [choice axiom] 40. (((brave(sK1) | old(sK1)) & (~brave(sK1) | ~old(sK1))) | ((~funny(alice) | happy(alice)) & (~happy(alice) | funny(alice)))) & (((happy(alice) | funny(alice)) & (~happy(alice) | ~funny(alice))) | ! [X1] : ((~old(X1) | brave(X1)) & (~brave(X1) | old(X1)))) [skolemisation 38,39] 42. ! [X0] : ((((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | ~funny(X0)) & (funny(X0) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0))))) [nnf transformation 5] 57. (? [X0] : ((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | (patient(fred) & ~patient(fred))) & ((~patient(fred) | patient(fred)) | ! [X0] : ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) [nnf transformation 13] 58. (? [X0] : ((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | (patient(fred) & ~patient(fred))) & (~patient(fred) | patient(fred) | ! [X0] : ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) [flattening 57] 59. (? [X0] : ((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | (patient(fred) & ~patient(fred))) & (~patient(fred) | patient(fred) | ! [X1] : ((brave(X1) | ~old(X1)) & (old(X1) | ~brave(X1)))) [rectify 58] 60. ? [X0] : ((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) => ((~old(sK4) | ~brave(sK4)) & (old(sK4) | brave(sK4))) [choice axiom] 61. (((~old(sK4) | ~brave(sK4)) & (old(sK4) | brave(sK4))) | (patient(fred) & ~patient(fred))) & (~patient(fred) | patient(fred) | ! [X1] : ((brave(X1) | ~old(X1)) & (old(X1) | ~brave(X1)))) [skolemisation 59,60] 89. ~happy(alice) | ~funny(alice) | ~brave(X1) | old(X1) [cnf transformation 40] 90. ~happy(alice) | ~funny(alice) | ~old(X1) | brave(X1) [cnf transformation 40] 102. calm(X0) | funny(X0) | wise(X0) [cnf transformation 42] 133. old(sK4) | brave(sK4) | ~patient(fred) [cnf transformation 61] 134. old(sK4) | brave(sK4) | patient(fred) [cnf transformation 61] 135. ~old(sK4) | ~brave(sK4) | ~patient(fred) [cnf transformation 61] 136. ~old(sK4) | ~brave(sK4) | patient(fred) [cnf transformation 61] 156. ~calm(alice) [cnf transformation 20] 157. happy(alice) [cnf transformation 20] 163. ~wise(alice) [cnf transformation 25] 190. 5 <=> happy(alice) [avatar definition] 194. 6 <=> funny(alice) [avatar definition] 196. ~funny(alice) <- (~6) [avatar component clause 194] 210. 9 <=> ! [X1] : (~old(X1) | brave(X1)) [avatar definition] 211. ~old(X1) | brave(X1) <- (9) [avatar component clause 210] 214. 10 <=> ! [X1] : (~brave(X1) | old(X1)) [avatar definition] 215. ~brave(X1) | old(X1) <- (10) [avatar component clause 214] 217. 9 | ~6 | ~5 [avatar split clause 90,190,194,210] 218. 10 | ~6 | ~5 [avatar split clause 89,190,194,214] 268. 21 <=> patient(fred) [avatar definition] 272. 22 <=> brave(sK4) [avatar definition] 273. brave(sK4) <- (22) [avatar component clause 272] 274. ~brave(sK4) <- (~22) [avatar component clause 272] 276. 23 <=> old(sK4) [avatar definition] 277. old(sK4) <- (23) [avatar component clause 276] 278. ~old(sK4) <- (~23) [avatar component clause 276] 279. 21 | ~22 | ~23 [avatar split clause 136,276,272,268] 280. ~21 | ~22 | ~23 [avatar split clause 135,276,272,268] 281. 21 | 22 | 23 [avatar split clause 134,276,272,268] 282. ~21 | 22 | 23 [avatar split clause 133,276,272,268] 323. 5 [avatar split clause 157,190] 344. funny(alice) | wise(alice) [resolution 102,156] 350. wise(alice) <- (~6) [subsumption resolution 344,196] 351. $false <- (~6) [subsumption resolution 350,163] 352. 6 [avatar contradiction clause 351] 357. old(sK4) <- (10, 22) [resolution 215,273] 359. $false <- (10, 22, ~23) [subsumption resolution 357,278] 360. ~10 | ~22 | 23 [avatar contradiction clause 359] 361. brave(sK4) <- (9, 23) [resolution 277,211] 362. $false <- (9, ~22, 23) [subsumption resolution 361,274] 363. ~9 | 22 | ~23 [avatar contradiction clause 362] 364. $false [avatar sat refutation 217,218,279,280,281,282,323,352,360,363] % SZS output end Proof for 8841359678954647498784631 % ------------------------------ % 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: 0.035 s % ------------------------------ % ------------------------------

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

Fred is generous.

entailment

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

generous(fred)

% SZS status Unsatisfiable for 4051037363683680852540867 % SZS output start Proof for 4051037363683680852540867 2. ! [X0] : ((~funny(X0) & generous(X0)) <=> humble(X0)) [input p1] 11. ! [X0] : (~quiet(X0) => (quiet(X0) | creative(X0))) [input p10] 13. ! [X0] : ((~generous(X0) & ~quiet(X0)) <=> (tall(X0) <~> ~patient(X0))) [input p12] 14. ! [X0] : ((~strong(X0) | humble(X0)) <=> (~patient(X0) <~> ~funny(X0))) [input p13] 16. ? [X0] : (generous(X0) & ~tall(X0)) => (tall(fred) & generous(fred)) [input p15] 22. humble(susan) & ~creative(susan) [input p21] 24. ~generous(fred) [input hypothesis] 35. ! [X0] : ((quiet(X0) | creative(X0)) | quiet(X0)) [ennf transformation 11] 36. ! [X0] : (quiet(X0) | creative(X0) | quiet(X0)) [flattening 35] 39. (tall(fred) & generous(fred)) | ! [X0] : (~generous(X0) | tall(X0)) [ennf transformation 16] 42. ! [X0] : (((~funny(X0) & generous(X0)) | ~humble(X0)) & (humble(X0) | (funny(X0) | ~generous(X0)))) [nnf transformation 2] 43. ! [X0] : (((~funny(X0) & generous(X0)) | ~humble(X0)) & (humble(X0) | funny(X0) | ~generous(X0))) [flattening 42] 67. ! [X0] : (((~generous(X0) & ~quiet(X0)) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) & (((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | (generous(X0) | quiet(X0)))) [nnf transformation 13] 68. ! [X0] : (((~generous(X0) & ~quiet(X0)) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) & (((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | generous(X0) | quiet(X0))) [flattening 67] 69. ! [X0] : (((~strong(X0) | humble(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (strong(X0) & ~humble(X0)))) [nnf transformation 14] 70. ! [X0] : ((~strong(X0) | humble(X0) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (strong(X0) & ~humble(X0)))) [flattening 69] 80. ~humble(X0) | generous(X0) [cnf transformation 43] 81. ~humble(X0) | ~funny(X0) [cnf transformation 43] 106. quiet(X0) | creative(X0) | quiet(X0) [cnf transformation 36] 117. ~patient(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 68] 123. funny(X0) | patient(X0) | ~humble(X0) [cnf transformation 70] 128. generous(fred) | ~generous(X0) | tall(X0) [cnf transformation 39] 137. ~creative(susan) [cnf transformation 22] 138. humble(susan) [cnf transformation 22] 140. ~generous(fred) [cnf transformation 24] 141. creative(X0) | quiet(X0) [duplicate literal removal 106] 261. ~humble(X0) | patient(X0) [subsumption resolution 123,81] 263. 28 <=> ! [X0] : (~generous(X0) | tall(X0)) [avatar definition] 264. ~generous(X0) | tall(X0) <- (28) [avatar component clause 263] 271. 30 <=> generous(fred) [avatar definition] 274. 28 | 30 [avatar split clause 128,271,263] 294. ~30 [avatar split clause 140,271] 295. generous(susan) [resolution 80,138] 299. quiet(susan) [resolution 141,137] 302. patient(susan) [resolution 261,138] 304. tall(susan) <- (28) [resolution 264,295] 358. ~quiet(susan) | ~tall(susan) [resolution 117,302] 369. ~tall(susan) [subsumption resolution 358,299] 370. $false <- (28) [subsumption resolution 369,304] 371. ~28 [avatar contradiction clause 370] 373. $false [avatar sat refutation 274,294,371] % SZS output end Proof for 4051037363683680852540867 % ------------------------------ % 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: 0.024 s % ------------------------------ % ------------------------------

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

Lucy is brave.

neutral

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

brave(lucy)

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

Lucy is generous.

neutral

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

generous(lucy)

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

John is kind.

neutral

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

kind(john)

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

Alice is calm.

neutral

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

calm(alice)

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

Mary is curious.

neutral

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

curious(mary)

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

Paul is quiet.

contradiction

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

quiet(paul)

% SZS status Unsatisfiable for 3903580915170679690158552 % SZS output start Proof for 3903580915170679690158552 1. ! [X0] : ((kind(X0) <~> ~kind(X0)) => old(X0)) [input p0] 10. ! [X0] : (~old(X0) <=> (old(X0) <~> ~quiet(X0))) [input p9] 23. quiet(paul) [input hypothesis] 29. ! [X0] : (old(X0) | (kind(X0) <=> ~kind(X0))) [ennf transformation 1] 34. ! [X0] : (old(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 29] 53. ! [X0] : ((~old(X0) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | old(X0))) [nnf transformation 10] 69. old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 34] 70. old(X0) | kind(X0) | kind(X0) [cnf transformation 34] 95. ~old(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 53] 121. quiet(paul) [cnf transformation 23] 124. ~old(X0) | ~quiet(X0) [duplicate literal removal 95] 126. old(X0) | ~kind(X0) [duplicate literal removal 69] 127. old(X0) | kind(X0) [duplicate literal removal 70] 128. old(X0) [subsumption resolution 126,127] 222. ~quiet(X0) [subsumption resolution 124,128] 266. $false [subsumption resolution 121,222] % SZS output end Proof for 3903580915170679690158552 % ------------------------------ % 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 both rich and not happy is not old or calm and vice versa. Everyone who is happy or not humble is happy and vice versa. Everyone who is both not brave and humble is both kind and not wise and vice versa. Everyone who is both tall and old is humble or not strong and vice versa. If fred is not calm then someone is either generous or calm and vice versa. Everyone who is kind or old is quiet. Everyone who is not happy or not tall is either not strong or tall and vice versa. Everyone who is not creative is either not funny or funny. If john is wise then someone is either old or creative and vice versa. If mary is not happy or brave then someone is not strong or funny and vice versa. Everyone who is either not patient or not calm is both not old and funny. Everyone who is not patient is not kind. Everyone who is both calm and not tall is rich. Everyone who is strong is either not brave or humble and vice versa. If someone is both rich and not quiet then fred is both curious and not brave. If fred is brave or not kind then paul is wise and vice versa. Someone is either not generous or old. Someone is either humble or patient. Someone is not humble. Paul is quiet or not quiet. Someone is either rich or not funny. Paul is either not curious or kind.

Fred is not brave.

contradiction

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

~brave(fred)

% SZS status Unsatisfiable for 6858963284964478481324353 % SZS output start Proof for 6858963284964478481324353 1. ! [X0] : ((~happy(X0) & rich(X0)) <=> (calm(X0) | ~old(X0))) [input p0] 2. ! [X0] : ((~humble(X0) | happy(X0)) <=> happy(X0)) [input p1] 3. ! [X0] : ((humble(X0) & ~brave(X0)) <=> (~wise(X0) & kind(X0))) [input p2] 4. ! [X0] : ((old(X0) & tall(X0)) <=> (~strong(X0) | humble(X0))) [input p3] 7. ! [X0] : ((~tall(X0) | ~happy(X0)) <=> (~strong(X0) <~> tall(X0))) [input p6] 11. ! [X0] : ((~patient(X0) <~> ~calm(X0)) => (funny(X0) & ~old(X0))) [input p10] 12. ! [X0] : (~patient(X0) => ~kind(X0)) [input p11] 14. ! [X0] : (strong(X0) <=> (~brave(X0) <~> humble(X0))) [input p13] 23. ~brave(fred) [input hypothesis] 26. ! [X0] : ((funny(X0) & ~old(X0)) | (~patient(X0) <=> ~calm(X0))) [ennf transformation 11] 27. ! [X0] : (~kind(X0) | patient(X0)) [ennf transformation 12] 31. ! [X0] : (((~happy(X0) & rich(X0)) | (~calm(X0) & old(X0))) & ((calm(X0) | ~old(X0)) | (happy(X0) | ~rich(X0)))) [nnf transformation 1] 32. ! [X0] : (((~happy(X0) & rich(X0)) | (~calm(X0) & old(X0))) & (calm(X0) | ~old(X0) | happy(X0) | ~rich(X0))) [flattening 31] 33. ! [X0] : (((~humble(X0) | happy(X0)) | ~happy(X0)) & (happy(X0) | (humble(X0) & ~happy(X0)))) [nnf transformation 2] 34. ! [X0] : ((~humble(X0) | happy(X0) | ~happy(X0)) & (happy(X0) | (humble(X0) & ~happy(X0)))) [flattening 33] 35. ! [X0] : (((humble(X0) & ~brave(X0)) | (wise(X0) | ~kind(X0))) & ((~wise(X0) & kind(X0)) | (~humble(X0) | brave(X0)))) [nnf transformation 3] 36. ! [X0] : (((humble(X0) & ~brave(X0)) | wise(X0) | ~kind(X0)) & ((~wise(X0) & kind(X0)) | ~humble(X0) | brave(X0))) [flattening 35] 37. ! [X0] : (((old(X0) & tall(X0)) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | (~old(X0) | ~tall(X0)))) [nnf transformation 4] 38. ! [X0] : (((old(X0) & tall(X0)) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | ~old(X0) | ~tall(X0))) [flattening 37] 43. ! [X0] : (((~tall(X0) | ~happy(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (tall(X0) & happy(X0)))) [nnf transformation 7] 44. ! [X0] : ((~tall(X0) | ~happy(X0) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (tall(X0) & happy(X0)))) [flattening 43] 55. ! [X0] : ((funny(X0) & ~old(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) [nnf transformation 26] 56. ! [X0] : ((strong(X0) | ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) & (((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | ~strong(X0))) [nnf transformation 14] 74. ~happy(X0) | old(X0) [cnf transformation 32] 75. ~calm(X0) | ~happy(X0) [cnf transformation 32] 77. humble(X0) | happy(X0) [cnf transformation 34] 79. ~humble(X0) | kind(X0) | brave(X0) [cnf transformation 36] 85. strong(X0) | tall(X0) [cnf transformation 38] 86. ~humble(X0) | old(X0) [cnf transformation 38] 95. tall(X0) | ~strong(X0) | tall(X0) [cnf transformation 44] 96. ~tall(X0) | strong(X0) | happy(X0) [cnf transformation 44] 99. ~tall(X0) | ~happy(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 44] 111. ~patient(X0) | ~old(X0) | calm(X0) [cnf transformation 55] 114. ~kind(X0) | patient(X0) [cnf transformation 27] 117. ~strong(X0) | brave(X0) | ~humble(X0) [cnf transformation 56] 118. strong(X0) | humble(X0) | brave(X0) [cnf transformation 56] 135. ~brave(fred) [cnf transformation 23] 136. tall(X0) | ~strong(X0) [duplicate literal removal 95] 137. ~strong(X0) | ~happy(X0) | ~tall(X0) [duplicate literal removal 99] 142. 2 <=> calm(fred) [avatar definition] 143. calm(fred) <- (2) [avatar component clause 142] 160. strong(X0) | happy(X0) [subsumption resolution 96,85] 161. tall(X0) [subsumption resolution 136,85] 214. 18 <=> brave(fred) [avatar definition] 216. ~brave(fred) <- (~18) [avatar component clause 214] 228. 21 <=> kind(fred) [avatar definition] 229. kind(fred) <- (21) [avatar component clause 228] 274. ~18 [avatar split clause 135,214] 282. old(X0) | happy(X0) [resolution 86,77] 283. old(X0) [subsumption resolution 282,74] 337. brave(X0) | ~humble(X0) | happy(X0) [resolution 117,160] 340. brave(X0) | happy(X0) [subsumption resolution 337,77] 361. happy(fred) <- (~18) [resolution 340,216] 365. ~happy(X1) | ~tall(X1) | humble(X1) | brave(X1) [resolution 137,118] 378. ~happy(X1) | humble(X1) | brave(X1) [subsumption resolution 365,161] 379. brave(X1) | humble(X1) [subsumption resolution 378,340] 411. humble(fred) <- (~18) [resolution 379,216] 425. kind(fred) | brave(fred) <- (~18) [resolution 411,79] 431. kind(fred) <- (~18) [subsumption resolution 425,216] 432. 21 | 18 [avatar split clause 431,214,228] 435. patient(fred) <- (21) [resolution 229,114] 438. ~old(fred) | calm(fred) <- (21) [resolution 435,111] 440. calm(fred) <- (21) [subsumption resolution 438,283] 443. 2 | ~21 [avatar split clause 440,228,142] 451. ~happy(fred) <- (2) [resolution 143,75] 453. $false <- (2, ~18) [subsumption resolution 451,361] 454. ~2 | 18 [avatar contradiction clause 453] 455. $false [avatar sat refutation 274,432,443,454] % SZS output end Proof for 6858963284964478481324353 % ------------------------------ % 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 not tall then alice is not calm. Everyone who is kind is both not patient and not brave and vice versa. Everyone who is either not calm or not strong is not happy or not humble. Everyone who is generous is either not quiet or not calm and vice versa. Everyone who is not generous is either generous or not generous and vice versa. If lucy is both strong and not wise then someone is both humble and not quiet and vice versa. Everyone who is not strong is kind and vice versa. Everyone who is both not patient and not curious is not creative. If paul is either funny or brave then lucy is either not humble or not funny and vice versa. Everyone who is not brave is both not calm and not strong. Everyone who is not happy or not calm is either not humble or patient and vice versa. If alice is both not rich and tall then someone is either not tall or not funny. Everyone who is either not patient or quiet is not calm and vice versa. Everyone who is generous or not generous is either wise or funny and vice versa. Everyone who is both not strong and not wise is not kind. If mary is both patient and not happy then john is both not calm and rich and vice versa. Someone is creative. Paul is either not old or patient. Someone is both happy and strong. Someone is either happy or strong. Someone is either not tall or not patient. Someone is humble or generous. John is either not creative or curious.

Lucy is not old.

neutral

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

~old(lucy)

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

Alice is strong.

neutral

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

strong(alice)

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

Lucy is humble.

contradiction

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

humble(lucy)

% SZS status Unsatisfiable for 9159970916034808483118483 % SZS output start Proof for 9159970916034808483118483 4. ? [X0] : (rich(X0) | ~quiet(X0)) => tall(susan) [input p3] 9. ! [X0] : ((rich(X0) | humble(X0)) <=> (~quiet(X0) & wise(X0))) [input p8] 15. ? [X0] : (~wise(X0) <~> tall(X0)) => ~wise(susan) [input p14] 16. ! [X0] : ((~wise(X0) | patient(X0)) => (rich(X0) & curious(X0))) [input p15] 21. humble(lucy) [input hypothesis] 23. ! [X0] : ((~wise(X0) | patient(X0)) => rich(X0)) [pure predicate removal 16] 28. tall(susan) | ! [X0] : (~rich(X0) & quiet(X0)) [ennf transformation 4] 33. ~wise(susan) | ! [X0] : (~wise(X0) <=> tall(X0)) [ennf transformation 15] 34. ! [X0] : (rich(X0) | (wise(X0) & ~patient(X0))) [ennf transformation 23] 42. ! [X0] : (((rich(X0) | humble(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (~rich(X0) & ~humble(X0)))) [nnf transformation 9] 43. ! [X0] : ((rich(X0) | humble(X0) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | (~rich(X0) & ~humble(X0)))) [flattening 42] 49. ~wise(susan) | ! [X0] : ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0))) [nnf transformation 33] 66. tall(susan) | quiet(X0) [cnf transformation 28] 80. ~rich(X0) | wise(X0) [cnf transformation 43] 81. ~humble(X0) | ~quiet(X0) [cnf transformation 43] 101. ~wise(susan) | ~wise(X0) | ~tall(X0) [cnf transformation 49] 103. rich(X0) | wise(X0) [cnf transformation 34] 112. humble(lucy) [cnf transformation 21] 136. 6 <=> tall(susan) [avatar definition] 138. tall(susan) <- (6) [avatar component clause 136] 141. 7 <=> ! [X0] : quiet(X0) [avatar definition] 142. quiet(X0) <- (7) [avatar component clause 141] 143. 7 | 6 [avatar split clause 66,136,141] 209. 20 <=> ! [X0] : (~wise(X0) | ~tall(X0)) [avatar definition] 210. ~wise(X0) | ~tall(X0) <- (20) [avatar component clause 209] 212. 21 <=> wise(susan) [avatar definition] 214. ~wise(susan) <- (~21) [avatar component clause 212] 215. 20 | ~21 [avatar split clause 101,212,209] 220. wise(X0) [subsumption resolution 103,80] 231. $false <- (~21) [subsumption resolution 214,220] 232. 21 [avatar contradiction clause 231] 233. ~tall(X0) <- (20) [subsumption resolution 210,220] 234. $false <- (6, 20) [resolution 233,138] 235. ~6 | ~20 [avatar contradiction clause 234] 239. ~quiet(lucy) [resolution 81,112] 240. $false <- (7) [subsumption resolution 239,142] 241. ~7 [avatar contradiction clause 240] 242. $false [avatar sat refutation 143,215,232,235,241] % SZS output end Proof for 9159970916034808483118483 % ------------------------------ % 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 both creative and funny is both strong and rich and vice versa. Everyone who is not humble is either rich or patient. If alice is happy or curious then someone is kind and vice versa. If mary is either strong or creative then mary is not tall or wise. Everyone who is rich is generous. If mary is both not patient and not brave then someone is both not quiet and not strong and vice versa. Everyone who is creative or not quiet is either not wise or not happy. If someone is not rich or humble then someone is not calm. Everyone who is creative is not patient. Everyone who is wise is old. Everyone who is both not kind and wise is rich and vice versa. Everyone who is not funny or not tall is either not calm or strong and vice versa. If paul is either not wise or not funny then someone is not brave or wise and vice versa. If someone is not tall or curious then lucy is not tall or not strong. If someone is both calm and not humble then someone is brave or old. If someone is either not curious or not brave then someone is both kind and not strong. Someone is not funny or happy. Mary is not rich. Mary is both wise and not calm. Paul is not wise or patient. Someone is brave. Someone is both generous and not funny. Someone is both not patient and not calm. Someone is patient.

Lucy is rich.

neutral

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

rich(lucy)

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

Lucy is generous.

neutral

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

generous(lucy)

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

Alice is quiet.

contradiction

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

quiet(alice)

% SZS status Unsatisfiable for 171369430443909891892756 % SZS output start Proof for 171369430443909891892756 17. ~patient(alice) & ~quiet(alice) [input p16] 25. quiet(alice) [input hypothesis] 126. ~quiet(alice) [cnf transformation 17] 136. quiet(alice) [cnf transformation 25] 334. $false [subsumption resolution 136,126] % SZS output end Proof for 171369430443909891892756 % ------------------------------ % 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 either not curious or generous is humble and vice versa. Everyone who is old is either happy or not creative. Everyone who is both old and not happy is generous or not rich and vice versa. If someone is both generous and funny then mary is not happy or not generous and vice versa. If paul is either kind or quiet then susan is either rich or old and vice versa. Everyone who is either not curious or not happy is both not humble and not curious. Everyone who is either not rich or funny is both happy and not brave. Everyone who is not kind is not humble or not quiet and vice versa. Everyone who is either rich or tall is happy or not strong and vice versa. Everyone who is both not kind and not happy is humble or not humble and vice versa. Everyone who is both strong and not generous is not tall. Everyone who is funny or not humble is not calm or generous and vice versa. If someone is generous then john is tall and vice versa. If alice is both not humble and not tall then fred is not rich or not humble. Everyone who is brave or not brave is not funny or not wise. Fred is either not generous or quiet. Someone is not generous or rich. Someone is humble.

John is not old.

contradiction

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

~old(john)

% SZS status Unsatisfiable for 3163308653172333317604665 % SZS output start Proof for 3163308653172333317604665 3. ! [X0] : ((~happy(X0) & old(X0)) <=> (~rich(X0) | generous(X0))) [input p2] 4. ? [X0] : (funny(X0) & generous(X0)) <=> (~generous(mary) | ~happy(mary)) [input p3] 9. ! [X0] : ((rich(X0) <~> tall(X0)) <=> (~strong(X0) | happy(X0))) [input p8] 10. ! [X0] : ((~happy(X0) & ~kind(X0)) <=> (~humble(X0) | humble(X0))) [input p9] 11. ! [X0] : ((~generous(X0) & strong(X0)) => ~tall(X0)) [input p10] 13. ? [X0] : generous(X0) <=> tall(john) [input p12] 19. ~old(john) [input hypothesis] 25. ! [X0] : (~tall(X0) | (generous(X0) | ~strong(X0))) [ennf transformation 11] 26. ! [X0] : (~tall(X0) | generous(X0) | ~strong(X0)) [flattening 25] 31. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & ((~rich(X0) | generous(X0)) | (happy(X0) | ~old(X0)))) [nnf transformation 3] 32. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & (~rich(X0) | generous(X0) | happy(X0) | ~old(X0))) [flattening 31] 33. (? [X0] : (funny(X0) & generous(X0)) | (generous(mary) & happy(mary))) & ((~generous(mary) | ~happy(mary)) | ! [X0] : (~funny(X0) | ~generous(X0))) [nnf transformation 4] 34. (? [X0] : (funny(X0) & generous(X0)) | (generous(mary) & happy(mary))) & (~generous(mary) | ~happy(mary) | ! [X0] : (~funny(X0) | ~generous(X0))) [flattening 33] 35. (? [X0] : (funny(X0) & generous(X0)) | (generous(mary) & happy(mary))) & (~generous(mary) | ~happy(mary) | ! [X1] : (~funny(X1) | ~generous(X1))) [rectify 34] 36. ? [X0] : (funny(X0) & generous(X0)) => (funny(sK0) & generous(sK0)) [choice axiom] 37. ((funny(sK0) & generous(sK0)) | (generous(mary) & happy(mary))) & (~generous(mary) | ~happy(mary) | ! [X1] : (~funny(X1) | ~generous(X1))) [skolemisation 35,36] 43. ! [X0] : ((((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0))))) [nnf transformation 9] 44. ! [X0] : ((((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0))))) [flattening 43] 45. ! [X0] : (((~happy(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | (happy(X0) | kind(X0)))) [nnf transformation 10] 46. ! [X0] : (((~happy(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | happy(X0) | kind(X0))) [flattening 45] 49. (? [X0] : generous(X0) | ~tall(john)) & (tall(john) | ! [X0] : ~generous(X0)) [nnf transformation 13] 50. (? [X0] : generous(X0) | ~tall(john)) & (tall(john) | ! [X1] : ~generous(X1)) [rectify 49] 51. ? [X0] : generous(X0) => generous(sK1) [choice axiom] 52. (generous(sK1) | ~tall(john)) & (tall(john) | ! [X1] : ~generous(X1)) [skolemisation 50,51] 65. ~generous(X0) | old(X0) [cnf transformation 32] 66. rich(X0) | old(X0) [cnf transformation 32] 70. generous(sK0) | happy(mary) [cnf transformation 37] 96. ~tall(X0) | ~rich(X0) | strong(X0) [cnf transformation 44] 100. ~happy(X0) | ~humble(X0) [cnf transformation 46] 101. ~happy(X0) | humble(X0) [cnf transformation 46] 102. ~strong(X0) | generous(X0) | ~tall(X0) [cnf transformation 26] 107. tall(john) | ~generous(X1) [cnf transformation 52] 114. ~old(john) [cnf transformation 19] 126. 3 <=> happy(mary) [avatar definition] 128. happy(mary) <- (3) [avatar component clause 126] 131. 4 <=> generous(sK0) [avatar definition] 133. generous(sK0) <- (4) [avatar component clause 131] 135. 3 | 4 [avatar split clause 70,131,126] 165. ~happy(X0) [subsumption resolution 100,101] 168. 9 <=> tall(john) [avatar definition] 169. tall(john) <- (9) [avatar component clause 168] 177. 11 <=> ! [X1] : ~generous(X1) [avatar definition] 178. ~generous(X1) <- (11) [avatar component clause 177] 179. 11 | 9 [avatar split clause 107,168,177] 283. ~rich(john) | strong(john) <- (9) [resolution 96,169] 285. 28 <=> strong(john) [avatar definition] 287. strong(john) <- (28) [avatar component clause 285] 289. 29 <=> rich(john) [avatar definition] 291. ~rich(john) <- (~29) [avatar component clause 289] 292. 28 | ~29 | ~9 [avatar split clause 283,168,289,285] 293. old(john) <- (~29) [resolution 291,66] 294. $false <- (~29) [subsumption resolution 293,114] 295. 29 [avatar contradiction clause 294] 296. $false <- (4, 11) [resolution 178,133] 299. ~4 | ~11 [avatar contradiction clause 296] 303. generous(john) | ~tall(john) <- (28) [resolution 102,287] 304. generous(john) <- (9, 28) [subsumption resolution 303,169] 309. old(john) <- (9, 28) [resolution 304,65] 319. $false <- (9, 28) [subsumption resolution 309,114] 320. ~9 | ~28 [avatar contradiction clause 319] 326. $false <- (3) [subsumption resolution 128,165] 327. ~3 [avatar contradiction clause 326] 330. $false [avatar sat refutation 135,179,292,295,299,320,327] % SZS output end Proof for 3163308653172333317604665 % ------------------------------ % 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 not creative and tall then someone is wise or generous and vice versa. If alice is both brave and wise then lucy is tall and vice versa. If someone is either not strong or strong then someone is not wise or not quiet. If mary is both calm and not calm then john is not curious or not quiet and vice versa. If fred is either not creative or not happy then someone is either quiet or wise and vice versa. If someone is both brave and old then mary is either not old or not quiet and vice versa. Everyone who is both not kind and generous is not curious or not rich and vice versa. Everyone who is not wise is creative or generous and vice versa. If someone is brave then lucy is either humble or funny and vice versa. If someone is both patient and tall then john is not tall or not brave and vice versa. Everyone who is not happy is both not tall and not old. If someone is either not tall or not happy then someone is not rich or not patient and vice versa. If lucy is either rich or not generous then mary is not old or not brave and vice versa. If someone is kind then someone is either strong or quiet. Everyone who is either brave or rich is brave and vice versa. If paul is quiet or not brave then alice is humble or kind and vice versa. Fred is kind or not humble. Someone is either humble or not strong. Alice is not wise. Someone is funny. Someone is both not humble and not calm. Someone is both not strong and old.

Mary is not old.

contradiction

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

~old(mary)

% SZS status Unsatisfiable for 4554249384761945177195001 % SZS output start Proof for 4554249384761945177195001 7. ! [X0] : ((generous(X0) & ~kind(X0)) <=> (~rich(X0) | ~curious(X0))) [input p6] 13. (rich(lucy) <~> ~generous(lucy)) <=> (~brave(mary) | ~old(mary)) [input p12] 15. ! [X0] : ((brave(X0) <~> rich(X0)) <=> brave(X0)) [input p14] 23. ~old(mary) [input hypothesis] 51. ! [X0] : (((generous(X0) & ~kind(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (~generous(X0) | kind(X0)))) [nnf transformation 7] 52. ! [X0] : (((generous(X0) & ~kind(X0)) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | ~generous(X0) | kind(X0))) [flattening 51] 69. (((generous(lucy) | ~rich(lucy)) & (~generous(lucy) | rich(lucy))) | (brave(mary) & old(mary))) & ((~brave(mary) | ~old(mary)) | ((rich(lucy) | generous(lucy)) & (~generous(lucy) | ~rich(lucy)))) [nnf transformation 13] 70. (((generous(lucy) | ~rich(lucy)) & (~generous(lucy) | rich(lucy))) | (brave(mary) & old(mary))) & (~brave(mary) | ~old(mary) | ((rich(lucy) | generous(lucy)) & (~generous(lucy) | ~rich(lucy)))) [flattening 69] 75. ! [X0] : ((((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | ~brave(X0)) & (brave(X0) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0))))) [nnf transformation 15] 120. generous(X0) | rich(X0) [cnf transformation 52] 143. ~generous(lucy) | rich(lucy) | old(mary) [cnf transformation 70] 150. brave(X0) | brave(X0) | ~rich(X0) [cnf transformation 75] 152. ~rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 75] 166. ~old(mary) [cnf transformation 23] 167. brave(X0) | ~rich(X0) [duplicate literal removal 150] 168. ~rich(X0) | ~brave(X0) [duplicate literal removal 152] 280. 24 <=> old(mary) [avatar definition] 387. 45 <=> rich(lucy) [avatar definition] 389. rich(lucy) <- (45) [avatar component clause 387] 391. rich(lucy) | old(mary) [subsumption resolution 143,120] 392. 24 | 45 [avatar split clause 391,387,280] 407. ~rich(X0) [subsumption resolution 167,168] 448. ~24 [avatar split clause 166,280] 449. $false <- (45) [subsumption resolution 389,407] 450. ~45 [avatar contradiction clause 449] 451. $false [avatar sat refutation 392,448,450] % SZS output end Proof for 4554249384761945177195001 % ------------------------------ % 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 not tall then someone is either generous or quiet and vice versa. Everyone who is wise is funny or not tall. Everyone who is tall is both rich and funny and vice versa. Everyone who is either creative or strong is both not calm and not brave and vice versa. Everyone who is not tall or rich is both tall and calm. Everyone who is generous or patient is quiet or not quiet and vice versa. Everyone who is both tall and humble is creative or kind and vice versa. Everyone who is both not happy and quiet is calm or patient and vice versa. Everyone who is strong is either kind or not humble and vice versa. If lucy is funny or not rich then paul is either not brave or not happy and vice versa. If someone is both happy and not humble then fred is both not funny and not brave and vice versa. Everyone who is either creative or calm is happy. Everyone who is not old or not brave is both not quiet and humble. Everyone who is not tall is either not rich or patient and vice versa. Someone is either generous or not calm. Paul is not tall or wise. Someone is tall or not strong. Someone is not curious. Someone is either not old or brave.

Fred is funny.

entailment

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

funny(fred)

% SZS status Unsatisfiable for 1559693926765746578582163 % SZS output start Proof for 1559693926765746578582163 3. ! [X0] : (tall(X0) <=> (funny(X0) & rich(X0))) [input p2] 5. ! [X0] : ((rich(X0) | ~tall(X0)) => (calm(X0) & tall(X0))) [input p4] 20. ~funny(fred) [input hypothesis] 25. ! [X0] : ((calm(X0) & tall(X0)) | (~rich(X0) & tall(X0))) [ennf transformation 5] 33. ! [X0] : ((tall(X0) | (~funny(X0) | ~rich(X0))) & ((funny(X0) & rich(X0)) | ~tall(X0))) [nnf transformation 3] 34. ! [X0] : ((tall(X0) | ~funny(X0) | ~rich(X0)) & ((funny(X0) & rich(X0)) | ~tall(X0))) [flattening 33] 67. ~tall(X0) | funny(X0) [cnf transformation 34] 75. tall(X0) | tall(X0) [cnf transformation 25] 123. ~funny(fred) [cnf transformation 20] 124. tall(X0) [duplicate literal removal 75] 138. 4 <=> ! [X3] : tall(X3) [avatar definition] 139. tall(X3) <- (4) [avatar component clause 138] 150. 4 [avatar split clause 124,138] 177. 11 <=> funny(fred) [avatar definition] 178. ~funny(fred) <- (~11) [avatar component clause 177] 241. ~11 [avatar split clause 123,177] 247. funny(X0) <- (4) [resolution 67,139] 253. $false <- (4, ~11) [resolution 247,178] 254. ~4 | 11 [avatar contradiction clause 253] 255. $false [avatar sat refutation 150,241,254] % SZS output end Proof for 1559693926765746578582163 % ------------------------------ % 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 not tall or strong is either calm or not funny and vice versa. If someone is not brave or not rich then someone is both not quiet and quiet and vice versa. If mary is not funny or not brave then paul is strong and vice versa. If john is either not rich or wise then someone is either old or not wise. Everyone who is not generous or brave is not wise and vice versa. If lucy is not brave then someone is not patient. Everyone who is either strong or not calm is either rich or not strong and vice versa. If john is not old or brave then someone is either old or not creative. Everyone who is not happy is creative or not humble and vice versa. Everyone who is either old or tall is either not funny or not creative. If lucy is either not kind or brave then paul is both not quiet and not creative. If someone is both wise and strong then someone is strong or not funny. If lucy is not strong then lucy is either rich or not rich and vice versa. Everyone who is both not creative and quiet is either curious or calm and vice versa. If someone is quiet or brave then john is rich and vice versa. Everyone who is both not generous and brave is curious. Someone is either not brave or not wise. Mary is humble or brave. Paul is either happy or brave. Someone is either humble or not kind. Someone is strong or rich. Mary is not strong or humble. Lucy is patient or calm.

Lucy is rich.

entailment

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

rich(lucy)

% SZS status Unsatisfiable for 3458516778857406317757284 % SZS output start Proof for 3458516778857406317757284 2. ? [X0] : (~rich(X0) | ~brave(X0)) <=> ? [X0] : (quiet(X0) & ~quiet(X0)) [input p1] 24. ~rich(lucy) [input hypothesis] 25. ? [X0] : (~rich(X0) | ~brave(X0)) <=> ? [X1] : (quiet(X1) & ~quiet(X1)) [rectify 2] 37. (? [X0] : (~rich(X0) | ~brave(X0)) | ! [X1] : (~quiet(X1) | quiet(X1))) & (? [X1] : (quiet(X1) & ~quiet(X1)) | ! [X0] : (rich(X0) & brave(X0))) [nnf transformation 25] 38. (? [X0] : (~rich(X0) | ~brave(X0)) | ! [X1] : (~quiet(X1) | quiet(X1))) & (? [X2] : (quiet(X2) & ~quiet(X2)) | ! [X3] : (rich(X3) & brave(X3))) [rectify 37] 39. ? [X0] : (~rich(X0) | ~brave(X0)) => (~rich(sK0) | ~brave(sK0)) [choice axiom] 40. ? [X2] : (quiet(X2) & ~quiet(X2)) => (quiet(sK1) & ~quiet(sK1)) [choice axiom] 41. ((~rich(sK0) | ~brave(sK0)) | ! [X1] : (~quiet(X1) | quiet(X1))) & ((quiet(sK1) & ~quiet(sK1)) | ! [X3] : (rich(X3) & brave(X3))) [skolemisation 38,40,39] 85. ~quiet(sK1) | rich(X3) [cnf transformation 41] 87. quiet(sK1) | rich(X3) [cnf transformation 41] 148. ~rich(lucy) [cnf transformation 24] 156. 1 <=> ! [X3] : rich(X3) [avatar definition] 157. rich(X3) <- (1) [avatar component clause 156] 159. 2 <=> quiet(sK1) [avatar definition] 162. 1 | 2 [avatar split clause 87,159,156] 167. 1 | ~2 [avatar split clause 85,159,156] 264. 23 <=> rich(lucy) [avatar definition] 265. ~rich(lucy) <- (~23) [avatar component clause 264] 347. ~23 [avatar split clause 148,264] 350. $false <- (1, ~23) [resolution 265,157] 351. ~1 | 23 [avatar contradiction clause 350] 352. $false [avatar sat refutation 162,167,347,351] % SZS output end Proof for 3458516778857406317757284 % ------------------------------ % 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 susan is either creative or generous then mary is not funny or not kind. If alice is either not rich or wise then someone is quiet and vice versa. If lucy is curious or not calm then fred is not wise and vice versa. Everyone who is either calm or not patient is both calm and tall and vice versa. If susan is either calm or not wise then paul is either not patient or generous and vice versa. If someone is either not rich or strong then someone is either tall or not brave. Everyone who is not strong is not curious or happy. Everyone who is either not brave or not old is both calm and funny and vice versa. Everyone who is not brave or old is not humble. If mary is both not strong and curious then someone is both tall and not happy and vice versa. If someone is either quiet or old then someone is either tall or not curious. Everyone who is calm or not humble is quiet or patient and vice versa. Everyone who is not strong is either not wise or funny and vice versa. Everyone who is not brave or not calm is both patient and not wise. Everyone who is both tall and quiet is either old or not quiet and vice versa. Everyone who is generous is humble or not humble and vice versa. Someone is both generous and brave. Mary is either brave or generous. Someone is kind. Someone is strong or not tall. John is calm or not funny. Alice is both not wise and not curious. Paul is tall.

Paul is not creative.

neutral

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

~creative(paul)

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

Fred is rich.

neutral

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

rich(fred)

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

Alice is not wise.

neutral

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

~wise(alice)

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

Mary is not rich.

neutral

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

~rich(mary)

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

Susan is happy.

contradiction

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

happy(susan)

% SZS status Unsatisfiable for 7508563259804004345303458 % SZS output start Proof for 7508563259804004345303458 3. ! [X0] : ((~rich(X0) & rich(X0)) <=> (kind(X0) | tall(X0))) [input p2] 10. ! [X0] : ((happy(X0) | ~rich(X0)) => (strong(X0) & tall(X0))) [input p9] 22. happy(susan) [input hypothesis] 28. ! [X0] : ((strong(X0) & tall(X0)) | (~happy(X0) & rich(X0))) [ennf transformation 10] 34. ! [X0] : (((~rich(X0) & rich(X0)) | (~kind(X0) & ~tall(X0))) & ((kind(X0) | tall(X0)) | (rich(X0) | ~rich(X0)))) [nnf transformation 3] 35. ! [X0] : (((~rich(X0) & rich(X0)) | (~kind(X0) & ~tall(X0))) & (kind(X0) | tall(X0) | rich(X0) | ~rich(X0))) [flattening 34] 77. rich(X0) | ~tall(X0) [cnf transformation 35] 79. ~rich(X0) | ~tall(X0) [cnf transformation 35] 102. tall(X0) | ~happy(X0) [cnf transformation 28] 139. happy(susan) [cnf transformation 22] 161. ~tall(X0) [subsumption resolution 77,79] 232. ~happy(X0) [subsumption resolution 102,161] 350. $false [subsumption resolution 139,232] % SZS output end Proof for 7508563259804004345303458 % ------------------------------ % 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 tall then someone is either happy or tall. If paul is both strong and happy then someone is old and vice versa. Everyone who is creative is not wise and vice versa. Everyone who is rich is not funny and vice versa. If fred is either not quiet or wise then john is either not patient or wise. Everyone who is both not happy and curious is not kind. If susan is either strong or wise then someone is both calm and not humble. Everyone who is either not curious or tall is not funny or humble and vice versa. Everyone who is both quiet and curious is both happy and not humble. Everyone who is not rich is funny or tall and vice versa. If paul is both not quiet and not happy then lucy is both wise and curious. Everyone who is not patient or not generous is both not tall and rich and vice versa. If paul is either creative or not strong then someone is not kind or not rich and vice versa. If susan is both not humble and rich then someone is either rich or not generous. If alice is either strong or not funny then someone is both not strong and tall and vice versa. Everyone who is both not old and patient is either not generous or tall. Someone is happy or kind. Lucy is humble. Paul is either not quiet or not generous. John is not kind. Paul is not humble or not old. Alice is old or rich. Someone is not strong. John is not wise or tall.

Susan is not humble.

neutral

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

~humble(susan)

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

Paul is kind.

contradiction

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

kind(paul)

% SZS status Unsatisfiable for 6852449131501170005204369 % SZS output start Proof for 6852449131501170005204369 5. ! [X0] : ((~curious(X0) <~> curious(X0)) <=> ~kind(X0)) [input p4] 25. kind(paul) [input hypothesis] 48. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | kind(X0)) & (~kind(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [nnf transformation 5] 88. ~kind(X0) | curious(X0) | curious(X0) [cnf transformation 48] 89. ~kind(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 48] 135. kind(paul) [cnf transformation 25] 136. ~kind(X0) | curious(X0) [duplicate literal removal 88] 137. ~kind(X0) | ~curious(X0) [duplicate literal removal 89] 170. ~kind(X0) [subsumption resolution 136,137] 285. $false [subsumption resolution 135,170] % SZS output end Proof for 6852449131501170005204369 % ------------------------------ % 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 john is wise or strong then someone is both brave and not patient. If alice is both not brave and not patient then someone is either kind or rich. If someone is not generous then john is not rich or rich and vice versa. Everyone who is either old or not old is either humble or curious. Everyone who is either not brave or not creative is not curious or happy and vice versa. Everyone who is not creative is both not curious and not tall and vice versa. Everyone who is both kind and quiet is either wise or not wise and vice versa. Everyone who is rich or not curious is not funny or curious and vice versa. If susan is both wise and not old then someone is both quiet and brave. Everyone who is creative or not quiet is both not calm and not wise and vice versa. Everyone who is calm or humble is either not quiet or happy. Everyone who is humble is both strong and tall and vice versa. If lucy is both not curious and not quiet then someone is not kind and vice versa. Everyone who is not humble or tall is both brave and funny and vice versa. If someone is both not wise and generous then susan is either rich or patient. Everyone who is not quiet or not generous is strong or calm and vice versa. Someone is both quiet and strong. Someone is rich or quiet. Mary is either not creative or not wise. Someone is either old or not rich. Someone is either rich or not strong. Someone is brave.

Mary is not rich.

contradiction

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

~rich(mary)

% SZS status Unsatisfiable for 780266105661242212046655 % SZS output start Proof for 780266105661242212046655 4. ! [X0] : ((old(X0) <~> ~old(X0)) => (humble(X0) <~> curious(X0))) [input p3] 5. ! [X0] : ((~brave(X0) <~> ~creative(X0)) <=> (happy(X0) | ~curious(X0))) [input p4] 6. ! [X0] : (~creative(X0) <=> (~tall(X0) & ~curious(X0))) [input p5] 8. ! [X0] : ((~curious(X0) | rich(X0)) <=> (curious(X0) | ~funny(X0))) [input p7] 12. ! [X0] : (humble(X0) <=> (tall(X0) & strong(X0))) [input p11] 14. ! [X0] : ((tall(X0) | ~humble(X0)) <=> (funny(X0) & brave(X0))) [input p13] 23. ~rich(mary) [input hypothesis] 27. ! [X0] : ((humble(X0) <~> curious(X0)) | (old(X0) <=> ~old(X0))) [ennf transformation 4] 42. ! [X0] : (((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 27] 43. ! [X0] : ((((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~happy(X0) & curious(X0))) & ((happy(X0) | ~curious(X0)) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))))) [nnf transformation 5] 44. ! [X0] : ((((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~happy(X0) & curious(X0))) & (happy(X0) | ~curious(X0) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))))) [flattening 43] 45. ! [X0] : ((~creative(X0) | (tall(X0) | curious(X0))) & ((~tall(X0) & ~curious(X0)) | creative(X0))) [nnf transformation 6] 46. ! [X0] : ((~creative(X0) | tall(X0) | curious(X0)) & ((~tall(X0) & ~curious(X0)) | creative(X0))) [flattening 45] 49. ! [X0] : (((~curious(X0) | rich(X0)) | (~curious(X0) & funny(X0))) & ((curious(X0) | ~funny(X0)) | (curious(X0) & ~rich(X0)))) [nnf transformation 8] 50. ! [X0] : ((~curious(X0) | rich(X0) | (~curious(X0) & funny(X0))) & (curious(X0) | ~funny(X0) | (curious(X0) & ~rich(X0)))) [flattening 49] 56. ! [X0] : ((humble(X0) | (~tall(X0) | ~strong(X0))) & ((tall(X0) & strong(X0)) | ~humble(X0))) [nnf transformation 12] 57. ! [X0] : ((humble(X0) | ~tall(X0) | ~strong(X0)) & ((tall(X0) & strong(X0)) | ~humble(X0))) [flattening 56] 63. ! [X0] : (((tall(X0) | ~humble(X0)) | (~funny(X0) | ~brave(X0))) & ((funny(X0) & brave(X0)) | (~tall(X0) & humble(X0)))) [nnf transformation 14] 64. ! [X0] : ((tall(X0) | ~humble(X0) | ~funny(X0) | ~brave(X0)) & ((funny(X0) & brave(X0)) | (~tall(X0) & humble(X0)))) [flattening 63] 90. curious(X0) | humble(X0) | ~old(X0) | ~old(X0) [cnf transformation 42] 91. curious(X0) | humble(X0) | old(X0) | old(X0) [cnf transformation 42] 96. ~creative(X0) | ~brave(X0) | curious(X0) [cnf transformation 44] 100. ~curious(X0) | creative(X0) [cnf transformation 46] 101. ~tall(X0) | creative(X0) [cnf transformation 46] 112. ~curious(X0) | rich(X0) | ~curious(X0) [cnf transformation 50] 125. ~humble(X0) | tall(X0) [cnf transformation 57] 130. humble(X0) | brave(X0) [cnf transformation 64] 131. ~tall(X0) | brave(X0) [cnf transformation 64] 151. ~rich(mary) [cnf transformation 23] 153. ~curious(X0) | rich(X0) [duplicate literal removal 112] 158. curious(X0) | humble(X0) | ~old(X0) [duplicate literal removal 90] 159. curious(X0) | humble(X0) | old(X0) [duplicate literal removal 91] 211. curious(X0) | humble(X0) [subsumption resolution 158,159] 246. 17 <=> creative(mary) [avatar definition] 247. ~creative(mary) <- (~17) [avatar component clause 246] 248. creative(mary) <- (17) [avatar component clause 246] 276. brave(X0) | tall(X0) [resolution 130,125] 278. brave(X0) [subsumption resolution 276,131] 282. creative(X2) | humble(X2) [resolution 211,100] 287. ~brave(mary) | curious(mary) <- (17) [resolution 96,248] 288. curious(mary) <- (17) [subsumption resolution 287,278] 290. rich(mary) <- (17) [resolution 288,153] 292. $false <- (17) [subsumption resolution 290,151] 293. ~17 [avatar contradiction clause 292] 296. humble(mary) <- (~17) [resolution 282,247] 302. tall(mary) <- (~17) [resolution 296,125] 311. creative(mary) <- (~17) [resolution 302,101] 312. $false <- (~17) [subsumption resolution 311,247] 313. 17 [avatar contradiction clause 312] 314. $false [avatar sat refutation 293,313] % SZS output end Proof for 780266105661242212046655 % ------------------------------ % 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 curious or strong then fred is brave. Everyone who is brave is not humble and vice versa. If lucy is not funny or strong then fred is not rich. Everyone who is either not brave or old is either not funny or not tall and vice versa. If alice is both not kind and not funny then someone is either not quiet or not humble. If lucy is not generous then paul is either not funny or not rich and vice versa. Everyone who is both not old and not curious is not rich or generous and vice versa. Everyone who is both not old and not curious is not kind or not quiet. If fred is not brave or humble then alice is not wise or humble. Everyone who is not rich or not quiet is not patient. Everyone who is tall or quiet is curious and vice versa. Everyone who is either not strong or not calm is not happy and vice versa. Everyone who is not happy or calm is not calm or curious. Everyone who is not funny or patient is both brave and creative. Everyone who is both not tall and wise is kind or not creative and vice versa. If john is both not old and not strong then paul is happy. Someone is either not tall or humble. Fred is not funny. Alice is either not quiet or brave. Someone is kind or wise. Someone is either not old or not quiet. Fred is either not quiet or kind. Someone is tall or creative. Alice is happy or not kind.

Fred is quiet.

neutral

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

quiet(fred)

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

Susan is not calm.

entailment

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

~calm(susan)

% SZS status Unsatisfiable for 8663849980661687182278518 % SZS output start Proof for 8663849980661687182278518 5. ! [X0] : ((~quiet(X0) | funny(X0)) <=> ~calm(X0)) [input p4] 14. ! [X0] : (brave(X0) => (quiet(X0) & funny(X0))) [input p13] 20. brave(susan) & rich(susan) [input p19] 25. calm(susan) [input hypothesis] 37. ! [X0] : ((quiet(X0) & funny(X0)) | ~brave(X0)) [ennf transformation 14] 51. ! [X0] : (((~quiet(X0) | funny(X0)) | calm(X0)) & (~calm(X0) | (quiet(X0) & ~funny(X0)))) [nnf transformation 5] 52. ! [X0] : ((~quiet(X0) | funny(X0) | calm(X0)) & (~calm(X0) | (quiet(X0) & ~funny(X0)))) [flattening 51] 102. ~calm(X0) | ~funny(X0) [cnf transformation 52] 125. ~brave(X0) | funny(X0) [cnf transformation 37] 139. brave(susan) [cnf transformation 20] 146. calm(susan) [cnf transformation 25] 239. ~funny(susan) [resolution 102,146] 242. funny(susan) [resolution 125,139] 243. $false [subsumption resolution 242,239] % SZS output end Proof for 8663849980661687182278518 % ------------------------------ % 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 generous is not happy and vice versa. Everyone who is both not generous and not old is old or tall. Everyone who is either creative or calm is either not funny or curious. If paul is not curious or not tall then someone is both not curious and not old. Everyone who is old or not quiet is both not happy and funny. Everyone who is not tall is either not wise or wise. Everyone who is either strong or not generous is not happy. If someone is creative or calm then someone is both not patient and not old. Everyone who is either brave or rich is not patient and vice versa. Everyone who is creative is either quiet or funny and vice versa. Everyone who is either not generous or not rich is not humble or not creative. Everyone who is both funny and kind is either not wise or not quiet. Everyone who is funny is not brave. If paul is not funny then mary is not kind or quiet. If someone is generous or happy then mary is both not wise and quiet and vice versa. Everyone who is patient is quiet and vice versa. Fred is rich. Someone is rich or not quiet. Someone is humble or not curious. Someone is either wise or kind. Someone is both not old and not creative. Paul is generous. Fred is not funny. Someone is both funny and not kind.

Paul is happy.

entailment

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

happy(paul)

% SZS status Unsatisfiable for 2272314673549608555187600 % SZS output start Proof for 2272314673549608555187600 1. ! [X0] : (~generous(X0) <=> ~happy(X0)) [input p0] 22. generous(paul) [input p21] 25. ~happy(paul) [input hypothesis] 46. ! [X0] : ((~generous(X0) | happy(X0)) & (~happy(X0) | generous(X0))) [nnf transformation 1] 76. ~generous(X0) | happy(X0) [cnf transformation 46] 115. generous(paul) [cnf transformation 22] 119. ~happy(paul) [cnf transformation 25] 207. happy(paul) [resolution 76,115] 208. $false [subsumption resolution 207,119] % SZS output end Proof for 2272314673549608555187600 % ------------------------------ % 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 both not patient and not old is rich and vice versa. Everyone who is either quiet or not quiet is either quiet or not humble and vice versa. If mary is not humble then someone is not quiet and vice versa. Everyone who is not tall or humble is not creative. If alice is humble then fred is either not rich or not wise and vice versa. Everyone who is either generous or brave is not quiet or not creative. Everyone who is tall is calm. Everyone who is happy is either patient or not quiet. Everyone who is not old is calm and vice versa. Everyone who is not generous or not quiet is both creative and not humble. Everyone who is either old or calm is tall or not curious. If fred is humble or not curious then someone is either old or not wise and vice versa. If someone is not humble or not rich then john is rich or old. Everyone who is both brave and not humble is either not funny or brave. If mary is not calm then someone is both not calm and kind. Everyone who is either wise or not creative is not wise or rich and vice versa. Alice is not funny or not generous. Mary is creative or generous. Someone is both not funny and brave. Someone is not humble. Someone is kind. Paul is both not old and not creative. Alice is not humble.

Paul is not happy.

neutral

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

~happy(paul)

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

Alice is kind.

neutral

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

kind(alice)

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

Susan is tall.

neutral

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

tall(susan)

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

John is not humble.

entailment

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

~humble(john)

% SZS status Unsatisfiable for 6299707685867399730609762 % SZS output start Proof for 6299707685867399730609762 2. ! [X0] : ((old(X0) | ~creative(X0)) <=> (~brave(X0) <~> humble(X0))) [input p1] 6. ! [X0] : ((creative(X0) & old(X0)) <=> (brave(X0) & generous(X0))) [input p5] 7. ! [X0] : (generous(X0) => (~generous(X0) | ~quiet(X0))) [input p6] 16. ! [X0] : ((generous(X0) & ~creative(X0)) <=> (~generous(X0) | ~quiet(X0))) [input p15] 24. humble(john) [input hypothesis] 34. ! [X0] : ((~generous(X0) | ~quiet(X0)) | ~generous(X0)) [ennf transformation 7] 35. ! [X0] : (~generous(X0) | ~quiet(X0) | ~generous(X0)) [flattening 34] 42. ! [X0] : (((old(X0) | ~creative(X0)) | ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) & (((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | (~old(X0) & creative(X0)))) [nnf transformation 2] 43. ! [X0] : ((old(X0) | ~creative(X0) | ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) & (((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | (~old(X0) & creative(X0)))) [flattening 42] 58. ! [X0] : (((creative(X0) & old(X0)) | (~brave(X0) | ~generous(X0))) & ((brave(X0) & generous(X0)) | (~creative(X0) | ~old(X0)))) [nnf transformation 6] 59. ! [X0] : (((creative(X0) & old(X0)) | ~brave(X0) | ~generous(X0)) & ((brave(X0) & generous(X0)) | ~creative(X0) | ~old(X0))) [flattening 58] 73. ! [X0] : (((generous(X0) & ~creative(X0)) | (generous(X0) & quiet(X0))) & ((~generous(X0) | ~quiet(X0)) | (~generous(X0) | creative(X0)))) [nnf transformation 16] 74. ! [X0] : (((generous(X0) & ~creative(X0)) | (generous(X0) & quiet(X0))) & (~generous(X0) | ~quiet(X0) | ~generous(X0) | creative(X0))) [flattening 73] 80. ~humble(X0) | brave(X0) | creative(X0) [cnf transformation 43] 99. ~brave(X0) | creative(X0) | ~generous(X0) [cnf transformation 59] 100. ~generous(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 35] 129. ~creative(X0) | quiet(X0) [cnf transformation 74] 132. generous(X0) | generous(X0) [cnf transformation 74] 140. humble(john) [cnf transformation 24] 142. generous(X0) [duplicate literal removal 132] 143. ~quiet(X0) | ~generous(X0) [duplicate literal removal 100] 256. 26 <=> quiet(john) [avatar definition] 257. quiet(john) <- (26) [avatar component clause 256] 375. brave(john) | creative(john) [resolution 80,140] 377. 47 <=> creative(john) [avatar definition] 378. ~creative(john) <- (~47) [avatar component clause 377] 379. creative(john) <- (47) [avatar component clause 377] 381. 48 <=> brave(john) [avatar definition] 383. brave(john) <- (48) [avatar component clause 381] 384. 47 | 48 [avatar split clause 375,381,377] 385. quiet(john) <- (47) [resolution 379,129] 388. 26 | ~47 [avatar split clause 385,377,256] 389. ~generous(john) <- (26) [resolution 257,143] 390. $false <- (26) [subsumption resolution 389,142] 391. ~26 [avatar contradiction clause 390] 402. creative(john) | ~generous(john) <- (48) [resolution 99,383] 403. ~generous(john) <- (~47, 48) [subsumption resolution 402,378] 404. $false <- (~47, 48) [subsumption resolution 403,142] 405. 47 | ~48 [avatar contradiction clause 404] 406. $false [avatar sat refutation 384,388,391,405] % SZS output end Proof for 6299707685867399730609762 % ------------------------------ % 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 both rich and kind is both not creative and rich and vice versa. Everyone who is not quiet is wise or not calm and vice versa. Everyone who is either tall or calm is not quiet and vice versa. Everyone who is tall is not funny or not rich and vice versa. Everyone who is not strong is either rich or wise. Everyone who is not old is not kind. If paul is either calm or not rich then john is not humble or kind. If lucy is not funny then someone is rich. Everyone who is rich or not tall is both tall and old. Everyone who is both happy and humble is not generous. Everyone who is both generous and not creative is not old or not humble. Everyone who is either generous or not generous is either not curious or funny and vice versa. Everyone who is both not strong and humble is not humble and vice versa. If someone is either tall or funny then someone is both kind and strong. If someone is old or not patient then fred is not patient. If alice is happy then fred is not rich and vice versa. Mary is not funny or not brave. Someone is either not generous or humble. Someone is both happy and not generous. Paul is both not curious and not old. Mary is wise or tall. Susan is either not wise or happy.

Paul is humble.

entailment

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

humble(paul)

% SZS status Unsatisfiable for 2091416641952933615873419 % SZS output start Proof for 2091416641952933615873419 13. ! [X0] : ((humble(X0) & ~strong(X0)) <=> ~humble(X0)) [input p12] 23. ~humble(paul) [input hypothesis] 50. ! [X0] : (((humble(X0) & ~strong(X0)) | humble(X0)) & (~humble(X0) | (~humble(X0) | strong(X0)))) [nnf transformation 13] 51. ! [X0] : (((humble(X0) & ~strong(X0)) | humble(X0)) & (~humble(X0) | ~humble(X0) | strong(X0))) [flattening 50] 99. humble(X0) | humble(X0) [cnf transformation 51] 117. ~humble(paul) [cnf transformation 23] 119. humble(X0) [duplicate literal removal 99] 199. $false [subsumption resolution 117,119] % SZS output end Proof for 2091416641952933615873419 % ------------------------------ % 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: 0.037 s % ------------------------------ % ------------------------------

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

Lucy is creative.

contradiction

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

creative(lucy)

% SZS status Unsatisfiable for 5748213026564184608135229 % SZS output start Proof for 5748213026564184608135229 9. ! [X0] : ((strong(X0) | humble(X0)) => (~wise(X0) & tall(X0))) [input p8] 11. ! [X0] : (~happy(X0) <=> creative(X0)) [input p10] 16. ? [X0] : (~happy(X0) | ~tall(X0)) => (~tall(susan) & ~funny(susan)) [input p15] 20. ~humble(susan) & strong(susan) [input p19] 25. creative(lucy) [input hypothesis] 31. ! [X0] : ((strong(X0) | humble(X0)) => tall(X0)) [pure predicate removal 9] 38. ! [X0] : (tall(X0) | (~strong(X0) & ~humble(X0))) [ennf transformation 31] 42. (~tall(susan) & ~funny(susan)) | ! [X0] : (happy(X0) & tall(X0)) [ennf transformation 16] 55. ! [X0] : ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0))) [nnf transformation 11] 92. ~strong(X0) | tall(X0) [cnf transformation 38] 96. ~happy(X0) | ~creative(X0) [cnf transformation 55] 112. ~tall(susan) | happy(X0) [cnf transformation 42] 117. strong(susan) [cnf transformation 20] 124. creative(lucy) [cnf transformation 25] 199. 16 <=> ! [X0] : happy(X0) [avatar definition] 200. happy(X0) <- (16) [avatar component clause 199] 202. 17 <=> tall(susan) [avatar definition] 205. 16 | ~17 [avatar split clause 112,202,199] 239. tall(susan) [resolution 92,117] 243. 17 [avatar split clause 239,202] 252. ~creative(X1) <- (16) [resolution 96,200] 253. $false <- (16) [resolution 252,124] 254. ~16 [avatar contradiction clause 253] 255. $false [avatar sat refutation 205,243,254] % SZS output end Proof for 5748213026564184608135229 % ------------------------------ % 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 paul is either not tall or not strong then paul is not funny or funny. If susan is either not creative or patient then someone is either not old or tall and vice versa. Everyone who is not strong is not tall or happy. Everyone who is both not tall and calm is both rich and kind. Everyone who is calm is both humble and not kind and vice versa. Everyone who is either generous or creative is not wise and vice versa. Everyone who is both not kind and old is not old. If someone is rich then someone is rich or not strong and vice versa. If someone is not tall then susan is either quiet or happy. Everyone who is not strong is either not humble or happy. If someone is both happy and tall then someone is not generous or rich and vice versa. Everyone who is both not tall and kind is not patient or patient. If someone is kind then someone is either wise or not kind. If someone is happy or not brave then alice is not patient. Everyone who is either not wise or not happy is either strong or happy. If someone is not tall or funny then someone is not happy and vice versa. Mary is not curious or rich. Mary is not kind or brave. Someone is not humble or quiet. Paul is curious or strong. Paul is humble or rich. Someone is not old or not strong. Someone is not kind or not happy. Mary is not kind or calm.

Susan is quiet.

neutral

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

quiet(susan)

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

John is calm.

entailment

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

calm(john)

% SZS status Unsatisfiable for 8395074567908267381164998 % SZS output start Proof for 8395074567908267381164998 12. ! [X0] : (humble(X0) <=> (humble(X0) <~> ~calm(X0))) [input p11] 23. ~calm(john) [input hypothesis] 47. ! [X0] : ((humble(X0) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0)))) & (((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 12] 105. calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47] 107. humble(X0) | humble(X0) | calm(X0) [cnf transformation 47] 138. ~calm(john) [cnf transformation 23] 139. calm(X0) | ~humble(X0) [duplicate literal removal 105] 140. humble(X0) | calm(X0) [duplicate literal removal 107] 220. calm(X0) [subsumption resolution 139,140] 290. $false [subsumption resolution 138,220] % SZS output end Proof for 8395074567908267381164998 % ------------------------------ % 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 not rich then someone is either curious or wise and vice versa. If paul is not calm then someone is not patient or not funny. Everyone who is rich or not humble is both rich and not patient and vice versa. Everyone who is generous or kind is both strong and not creative and vice versa. Everyone who is either rich or tall is calm and vice versa. Everyone who is creative is either not tall or not generous. Everyone who is both not curious and not patient is humble or generous and vice versa. Everyone who is curious or not rich is either creative or not patient. If someone is both not happy and calm then someone is curious or kind and vice versa. If john is old or brave then someone is either strong or brave. If mary is not curious or not quiet then fred is either kind or quiet and vice versa. If someone is both curious and tall then alice is either patient or old. Everyone who is both creative and not tall is either not rich or not curious and vice versa. Everyone who is creative or not creative is not strong. Everyone who is both not creative and not kind is not rich and vice versa. Everyone who is calm or not tall is either tall or happy and vice versa. Someone is happy or not humble. Someone is not quiet or creative. Alice is either not quiet or patient. Someone is either not generous or old. Fred is either happy or not happy. Someone is not funny. Someone is either humble or not humble.

Mary is curious.

contradiction

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

curious(mary)

% SZS status Unsatisfiable for 8483828089262819239927334 % SZS output start Proof for 8483828089262819239927334 3. ! [X0] : ((~humble(X0) | rich(X0)) <=> (~patient(X0) & rich(X0))) [input p2] 4. ! [X0] : ((kind(X0) | generous(X0)) <=> (~creative(X0) & strong(X0))) [input p3] 7. ! [X0] : ((~patient(X0) & ~curious(X0)) <=> (generous(X0) | humble(X0))) [input p6] 8. ! [X0] : ((~rich(X0) | curious(X0)) => (creative(X0) <~> ~patient(X0))) [input p7] 9. ? [X0] : (calm(X0) & ~happy(X0)) <=> ? [X0] : (kind(X0) | curious(X0)) [input p8] 13. ! [X0] : ((~tall(X0) & creative(X0)) <=> (~rich(X0) <~> ~curious(X0))) [input p12] 14. ! [X0] : ((~creative(X0) | creative(X0)) => ~strong(X0)) [input p13] 15. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> ~rich(X0)) [input p14] 24. curious(mary) [input hypothesis] 26. ? [X0] : (calm(X0) & ~happy(X0)) <=> ? [X1] : (kind(X1) | curious(X1)) [rectify 9] 30. ! [X0] : ((creative(X0) <~> ~patient(X0)) | (rich(X0) & ~curious(X0))) [ennf transformation 8] 33. ! [X0] : (~strong(X0) | (creative(X0) & ~creative(X0))) [ennf transformation 14] 39. ! [X0] : (((~humble(X0) | rich(X0)) | (patient(X0) | ~rich(X0))) & ((~patient(X0) & rich(X0)) | (humble(X0) & ~rich(X0)))) [nnf transformation 3] 40. ! [X0] : ((~humble(X0) | rich(X0) | patient(X0) | ~rich(X0)) & ((~patient(X0) & rich(X0)) | (humble(X0) & ~rich(X0)))) [flattening 39] 41. ! [X0] : (((kind(X0) | generous(X0)) | (creative(X0) | ~strong(X0))) & ((~creative(X0) & strong(X0)) | (~kind(X0) & ~generous(X0)))) [nnf transformation 4] 42. ! [X0] : ((kind(X0) | generous(X0) | creative(X0) | ~strong(X0)) & ((~creative(X0) & strong(X0)) | (~kind(X0) & ~generous(X0)))) [flattening 41] 45. ! [X0] : (((~patient(X0) & ~curious(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (patient(X0) | curious(X0)))) [nnf transformation 7] 46. ! [X0] : (((~patient(X0) & ~curious(X0)) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | patient(X0) | curious(X0))) [flattening 45] 47. ! [X0] : (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (rich(X0) & ~curious(X0))) [nnf transformation 30] 48. (? [X0] : (calm(X0) & ~happy(X0)) | ! [X1] : (~kind(X1) & ~curious(X1))) & (? [X1] : (kind(X1) | curious(X1)) | ! [X0] : (~calm(X0) | happy(X0))) [nnf transformation 26] 49. (? [X0] : (calm(X0) & ~happy(X0)) | ! [X1] : (~kind(X1) & ~curious(X1))) & (? [X2] : (kind(X2) | curious(X2)) | ! [X3] : (~calm(X3) | happy(X3))) [rectify 48] 50. ? [X0] : (calm(X0) & ~happy(X0)) => (calm(sK2) & ~happy(sK2)) [choice axiom] 51. ? [X2] : (kind(X2) | curious(X2)) => (kind(sK3) | curious(sK3)) [choice axiom] 52. ((calm(sK2) & ~happy(sK2)) | ! [X1] : (~kind(X1) & ~curious(X1))) & ((kind(sK3) | curious(sK3)) | ! [X3] : (~calm(X3) | happy(X3))) [skolemisation 49,51,50] 59. ! [X0] : (((~tall(X0) & creative(X0)) | ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) & (((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) | (tall(X0) | ~creative(X0)))) [nnf transformation 13] 60. ! [X0] : (((~tall(X0) & creative(X0)) | ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) & (((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) | tall(X0) | ~creative(X0))) [flattening 59] 61. ! [X0] : (((~kind(X0) & ~creative(X0)) | rich(X0)) & (~rich(X0) | (kind(X0) | creative(X0)))) [nnf transformation 15] 62. ! [X0] : (((~kind(X0) & ~creative(X0)) | rich(X0)) & (~rich(X0) | kind(X0) | creative(X0))) [flattening 61] 84. ~patient(X0) | humble(X0) [cnf transformation 40] 87. ~kind(X0) | strong(X0) [cnf transformation 42] 100. ~patient(X0) | ~humble(X0) [cnf transformation 46] 104. patient(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 47] 106. kind(sK3) | curious(sK3) | ~calm(X3) | happy(X3) [cnf transformation 52] 107. ~happy(sK2) | ~curious(X1) [cnf transformation 52] 109. calm(sK2) | ~curious(X1) [cnf transformation 52] 125. creative(X0) | ~curious(X0) | rich(X0) [cnf transformation 60] 129. ~strong(X0) | ~creative(X0) [cnf transformation 33] 130. ~strong(X0) | creative(X0) [cnf transformation 33] 131. ~rich(X0) | kind(X0) | creative(X0) [cnf transformation 62] 150. curious(mary) [cnf transformation 24] 179. ~patient(X0) [subsumption resolution 100,84] 182. ~creative(X0) | ~curious(X0) [subsumption resolution 104,179] 187. 8 <=> calm(sK2) [avatar definition] 189. calm(sK2) <- (8) [avatar component clause 187] 192. 9 <=> ! [X1] : ~curious(X1) [avatar definition] 193. ~curious(X1) <- (9) [avatar component clause 192] 194. 9 | 8 [avatar split clause 109,187,192] 196. 10 <=> happy(sK2) [avatar definition] 198. ~happy(sK2) <- (~10) [avatar component clause 196] 200. 9 | ~10 [avatar split clause 107,196,192] 202. 11 <=> ! [X3] : (~calm(X3) | happy(X3)) [avatar definition] 203. ~calm(X3) | happy(X3) <- (11) [avatar component clause 202] 205. 12 <=> curious(sK3) [avatar definition] 207. curious(sK3) <- (12) [avatar component clause 205] 209. 13 <=> kind(sK3) [avatar definition] 211. kind(sK3) <- (13) [avatar component clause 209] 212. 11 | 12 | 13 [avatar split clause 106,209,205,202] 242. 20 <=> curious(mary) [avatar definition] 243. curious(mary) <- (20) [avatar component clause 242] 264. ~curious(X0) | rich(X0) [subsumption resolution 125,182] 265. ~strong(X0) [subsumption resolution 129,130] 295. 20 [avatar split clause 150,242] 301. happy(sK2) <- (8, 11) [resolution 203,189] 302. $false <- (8, ~10, 11) [subsumption resolution 301,198] 303. ~8 | 10 | ~11 [avatar contradiction clause 302] 305. $false <- (9, 20) [resolution 193,243] 306. ~9 | ~20 [avatar contradiction clause 305] 311. rich(sK3) <- (12) [resolution 264,207] 364. kind(sK3) | creative(sK3) <- (12) [resolution 131,311] 376. 38 <=> creative(sK3) [avatar definition] 378. creative(sK3) <- (38) [avatar component clause 376] 379. 38 | 13 | ~12 [avatar split clause 364,205,209,376] 390. strong(sK3) <- (13) [resolution 211,87] 391. $false <- (13) [subsumption resolution 390,265] 392. ~13 [avatar contradiction clause 391] 397. ~curious(sK3) <- (38) [resolution 378,182] 402. $false <- (12, 38) [subsumption resolution 397,207] 403. ~12 | ~38 [avatar contradiction clause 402] 405. $false [avatar sat refutation 194,200,212,295,303,306,379,392,403] % SZS output end Proof for 8483828089262819239927334 % ------------------------------ % 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 % ------------------------------ % ------------------------------

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

Fred is not humble.

neutral

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

~humble(fred)

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

Lucy is creative.

neutral

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

creative(lucy)

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

Susan is not patient.

neutral

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

~patient(susan)

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

Paul is not happy.

contradiction

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

~happy(paul)

% SZS status Unsatisfiable for 5514623700451642724319241 % SZS output start Proof for 5514623700451642724319241 1. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~creative(X0) <~> funny(X0))) [input p0] 6. (~funny(paul) <~> ~kind(paul)) => (~creative(paul) | rich(paul)) [input p5] 9. ! [X0] : ((~happy(X0) | ~funny(X0)) <=> (~strong(X0) & ~rich(X0))) [input p8] 11. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p10] 13. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p12] 14. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> (kind(X0) | wise(X0))) [input p13] 15. ! [X0] : ((funny(X0) <~> creative(X0)) <=> (humble(X0) & rich(X0))) [input p14] 20. ~happy(paul) [input hypothesis] 24. (~creative(paul) | rich(paul)) | (~funny(paul) <=> ~kind(paul)) [ennf transformation 6] 25. ~creative(paul) | rich(paul) | (~funny(paul) <=> ~kind(paul)) [flattening 24] 26. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 11] 29. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (wise(X0) | kind(X0)))) [nnf transformation 1] 30. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | wise(X0) | kind(X0))) [flattening 29] 37. ~creative(paul) | rich(paul) | ((~funny(paul) | kind(paul)) & (~kind(paul) | funny(paul))) [nnf transformation 25] 42. ! [X0] : (((~happy(X0) | ~funny(X0)) | (strong(X0) | rich(X0))) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [nnf transformation 9] 43. ! [X0] : ((~happy(X0) | ~funny(X0) | strong(X0) | rich(X0)) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [flattening 42] 47. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 13] 48. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 47] 49. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 14] 50. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [flattening 49] 51. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~humble(X0) | ~rich(X0))) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 15] 52. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ~humble(X0) | ~rich(X0)) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [flattening 51] 61. ~kind(X0) | funny(X0) | creative(X0) [cnf transformation 30] 62. ~funny(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 30] 63. ~wise(X0) | funny(X0) | creative(X0) [cnf transformation 30] 75. ~creative(paul) | rich(paul) | ~kind(paul) | funny(paul) [cnf transformation 37] 76. ~creative(paul) | rich(paul) | ~funny(paul) | kind(paul) [cnf transformation 37] 86. ~rich(X0) | funny(X0) [cnf transformation 43] 87. ~rich(X0) | happy(X0) [cnf transformation 43] 95. ~happy(X0) | funny(X0) [cnf transformation 26] 99. funny(X0) | ~old(X0) | brave(X0) | happy(X0) [cnf transformation 48] 102. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 48] 103. ~brave(X0) | happy(X0) | old(X0) [cnf transformation 48] 105. ~brave(X0) | wise(X0) | ~old(X0) | kind(X0) [cnf transformation 50] 106. brave(X0) | wise(X0) | kind(X0) | old(X0) [cnf transformation 50] 111. ~funny(X0) | creative(X0) | rich(X0) [cnf transformation 52] 112. rich(X0) | funny(X0) | ~creative(X0) [cnf transformation 52] 122. ~happy(paul) [cnf transformation 20] 169. ~creative(paul) | rich(paul) | ~funny(paul) [subsumption resolution 76,62] 171. 11 <=> funny(paul) [avatar definition] 172. funny(paul) <- (11) [avatar component clause 171] 173. ~funny(paul) <- (~11) [avatar component clause 171] 175. 12 <=> rich(paul) [avatar definition] 176. ~rich(paul) <- (~12) [avatar component clause 175] 177. rich(paul) <- (12) [avatar component clause 175] 179. 13 <=> creative(paul) [avatar definition] 180. creative(paul) <- (13) [avatar component clause 179] 181. ~creative(paul) <- (~13) [avatar component clause 179] 182. ~11 | 12 | ~13 [avatar split clause 169,179,175,171] 183. rich(paul) | ~kind(paul) | funny(paul) [subsumption resolution 75,61] 185. 14 <=> kind(paul) [avatar definition] 187. ~kind(paul) <- (~14) [avatar component clause 185] 188. 11 | ~14 | 12 [avatar split clause 183,175,185,171] 189. ~happy(X0) | brave(X0) [subsumption resolution 102,95] 190. ~old(X0) | funny(X0) | brave(X0) [subsumption resolution 99,189] 192. ~creative(X0) | funny(X0) [subsumption resolution 112,86] 404. wise(X4) | kind(X4) | old(X4) | happy(X4) | old(X4) [resolution 106,103] 405. old(X4) | kind(X4) | wise(X4) | happy(X4) [duplicate literal removal 404] 426. kind(X0) | wise(X0) | happy(X0) | funny(X0) | brave(X0) [resolution 405,190] 444. brave(X0) | wise(X0) | funny(X0) | kind(X0) [subsumption resolution 426,189] 515. happy(paul) <- (12) [resolution 177,87] 517. $false <- (12) [subsumption resolution 515,122] 518. ~12 [avatar contradiction clause 517] 524. creative(paul) | rich(paul) <- (11) [resolution 172,111] 530. rich(paul) <- (11, ~13) [subsumption resolution 524,181] 531. $false <- (11, ~12, ~13) [subsumption resolution 530,176] 532. ~11 | 12 | 13 [avatar contradiction clause 531] 625. wise(X0) | funny(X0) | kind(X0) | wise(X0) | ~old(X0) | kind(X0) [resolution 444,105] 630. ~old(X0) | funny(X0) | kind(X0) | wise(X0) [duplicate literal removal 625] 661. funny(X0) | kind(X0) | wise(X0) | kind(X0) | wise(X0) | happy(X0) [resolution 630,405] 662. funny(X0) | kind(X0) | wise(X0) | happy(X0) [duplicate literal removal 661] 663. funny(X0) | kind(X0) | wise(X0) [subsumption resolution 662,95] 673. kind(paul) | wise(paul) <- (~11) [resolution 663,173] 676. wise(paul) <- (~11, ~14) [subsumption resolution 673,187] 678. funny(paul) | creative(paul) <- (~11, ~14) [resolution 676,63] 680. creative(paul) <- (~11, ~14) [subsumption resolution 678,173] 683. 13 | 11 | 14 [avatar split clause 680,185,171,179] 691. funny(paul) <- (13) [resolution 180,192] 693. $false <- (~11, 13) [subsumption resolution 691,173] 694. 11 | ~13 [avatar contradiction clause 693] 695. $false [avatar sat refutation 182,188,518,532,683,694] % SZS output end Proof for 5514623700451642724319241 % ------------------------------ % 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: 0.041 s % ------------------------------ % ------------------------------

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

Lucy is wise.

contradiction

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

wise(lucy)

% SZS status Unsatisfiable for 7138829533642485218289559 % SZS output start Proof for 7138829533642485218289559 15. ! [X0] : ((wise(X0) | old(X0)) <=> (~wise(X0) & ~kind(X0))) [input p14] 25. wise(lucy) [input hypothesis] 67. ! [X0] : (((wise(X0) | old(X0)) | (wise(X0) | kind(X0))) & ((~wise(X0) & ~kind(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 15] 68. ! [X0] : ((wise(X0) | old(X0) | wise(X0) | kind(X0)) & ((~wise(X0) & ~kind(X0)) | (~wise(X0) & ~old(X0)))) [flattening 67] 123. ~wise(X0) | ~wise(X0) [cnf transformation 68] 139. wise(lucy) [cnf transformation 25] 140. ~wise(X0) [duplicate literal removal 123] 299. $false [subsumption resolution 139,140] % SZS output end Proof for 7138829533642485218289559 % ------------------------------ % 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 calm and not brave is humble or not curious and vice versa. If someone is not brave or wise then mary is both not tall and creative. Everyone who is wise or humble is not strong. Everyone who is either strong or rich is both not rich and not curious and vice versa. If mary is both not calm and creative then susan is brave or curious and vice versa. Everyone who is either not tall or generous is not generous or creative. Everyone who is either not humble or funny is strong. Everyone who is either brave or generous is both brave and quiet. Everyone who is funny is either humble or tall. If mary is either not kind or not creative then john is both not creative and not generous and vice versa. Everyone who is not wise is either wise or generous and vice versa. Everyone who is both curious and happy is strong or not brave and vice versa. If someone is both not funny and curious then lucy is both not creative and not happy and vice versa. Everyone who is not curious or brave is not patient or not generous. If mary is rich then someone is not patient or happy and vice versa. Someone is creative or kind. Someone is not old. Fred is either not wise or not old. Susan is not patient or funny.

Mary is not humble.

entailment

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

~humble(mary)

% SZS status Unsatisfiable for 9037544488431048458496410 % SZS output start Proof for 9037544488431048458496410 1. ! [X0] : ((~brave(X0) & calm(X0)) <=> (~curious(X0) | humble(X0))) [input p0] 5. (creative(mary) & ~calm(mary)) <=> (curious(susan) | brave(susan)) [input p4] 12. ! [X0] : ((happy(X0) & curious(X0)) <=> (~brave(X0) | strong(X0))) [input p11] 20. humble(mary) [input hypothesis] 31. ! [X0] : (((~brave(X0) & calm(X0)) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | (brave(X0) | ~calm(X0)))) [nnf transformation 1] 32. ! [X0] : (((~brave(X0) & calm(X0)) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | brave(X0) | ~calm(X0))) [flattening 31] 35. ((creative(mary) & ~calm(mary)) | (~curious(susan) & ~brave(susan))) & ((curious(susan) | brave(susan)) | (~creative(mary) | calm(mary))) [nnf transformation 5] 36. ((creative(mary) & ~calm(mary)) | (~curious(susan) & ~brave(susan))) & (curious(susan) | brave(susan) | ~creative(mary) | calm(mary)) [flattening 35] 44. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & ((~brave(X0) | strong(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 12] 45. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & (~brave(X0) | strong(X0) | ~happy(X0) | ~curious(X0))) [flattening 44] 61. ~humble(X0) | calm(X0) [cnf transformation 32] 64. ~brave(X0) | curious(X0) [cnf transformation 32] 79. ~calm(mary) | ~curious(susan) [cnf transformation 36] 102. curious(X0) | brave(X0) [cnf transformation 45] 119. humble(mary) [cnf transformation 20] 145. 5 <=> curious(susan) [avatar definition] 147. ~curious(susan) <- (~5) [avatar component clause 145] 155. 7 <=> calm(mary) [avatar definition] 158. ~5 | ~7 [avatar split clause 79,155,145] 183. curious(X0) [subsumption resolution 102,64] 257. calm(mary) [resolution 61,119] 260. 7 [avatar split clause 257,155] 261. $false <- (~5) [subsumption resolution 147,183] 262. 5 [avatar contradiction clause 261] 263. $false [avatar sat refutation 158,260,262] % SZS output end Proof for 9037544488431048458496410 % ------------------------------ % 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 mary is not humble then mary is not humble or kind. Everyone who is not rich or not calm is not kind or not curious and vice versa. Everyone who is either creative or not wise is funny. If paul is both old and generous then fred is not brave or tall and vice versa. If someone is either brave or not strong then john is funny and vice versa. Everyone who is happy or creative is either not rich or creative and vice versa. Everyone who is not calm is not strong. If someone is not funny then someone is not funny or not creative and vice versa. Everyone who is either not rich or not calm is generous or funny. Everyone who is either not old or humble is either not brave or strong and vice versa. If someone is not patient then paul is not curious. If john is both kind and curious then susan is kind and vice versa. If mary is not strong then susan is not patient. Everyone who is both old and not rich is patient or not rich. If someone is creative or happy then mary is both strong and not brave. If lucy is either not curious or curious then alice is funny and vice versa. John is not wise or funny. Mary is not creative. Mary is either wise or not funny. Fred is generous or kind. Someone is happy or not brave. Lucy is both not creative and brave. Someone is both not tall and funny. Someone is not calm or not kind.

John is funny.

neutral

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

funny(john)

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

Lucy is not patient.

contradiction

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

~patient(lucy)

% SZS status Unsatisfiable for 3972739402953713402393078 % SZS output start Proof for 3972739402953713402393078 1. (~patient(lucy) <~> ~old(lucy)) => (tall(lucy) | humble(lucy)) [input p0] 6. ! [X0] : (tall(X0) <=> generous(X0)) [input p5] 13. ! [X0] : ((humble(X0) | ~old(X0)) => (~old(X0) & generous(X0))) [input p12] 16. ! [X0] : ((~tall(X0) <~> ~curious(X0)) => (~brave(X0) & humble(X0))) [input p15] 21. ~curious(lucy) & ~humble(lucy) [input p20] 25. ~patient(lucy) [input hypothesis] 27. (tall(lucy) | humble(lucy)) | (~patient(lucy) <=> ~old(lucy)) [ennf transformation 1] 28. tall(lucy) | humble(lucy) | (~patient(lucy) <=> ~old(lucy)) [flattening 27] 41. ! [X0] : ((~old(X0) & generous(X0)) | (~humble(X0) & old(X0))) [ennf transformation 13] 43. ! [X0] : ((~brave(X0) & humble(X0)) | (~tall(X0) <=> ~curious(X0))) [ennf transformation 16] 44. tall(lucy) | humble(lucy) | ((~patient(lucy) | old(lucy)) & (~old(lucy) | patient(lucy))) [nnf transformation 28] 50. ! [X0] : ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))) [nnf transformation 6] 62. ! [X0] : ((~brave(X0) & humble(X0)) | ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0)))) [nnf transformation 43] 72. tall(lucy) | humble(lucy) | ~old(lucy) | patient(lucy) [cnf transformation 44] 87. ~generous(X0) | tall(X0) [cnf transformation 50] 105. generous(X0) | old(X0) [cnf transformation 41] 115. ~tall(X0) | humble(X0) | curious(X0) [cnf transformation 62] 123. ~humble(lucy) [cnf transformation 21] 124. ~curious(lucy) [cnf transformation 21] 129. ~patient(lucy) [cnf transformation 25] 131. 1 <=> old(lucy) [avatar definition] 132. ~old(lucy) <- (~1) [avatar component clause 131] 135. 2 <=> patient(lucy) [avatar definition] 139. 3 <=> humble(lucy) [avatar definition] 140. ~humble(lucy) <- (~3) [avatar component clause 139] 143. 4 <=> tall(lucy) [avatar definition] 144. ~tall(lucy) <- (~4) [avatar component clause 143] 145. tall(lucy) <- (4) [avatar component clause 143] 147. 2 | ~1 | 3 | 4 [avatar split clause 72,143,139,131,135] 284. ~3 [avatar split clause 123,139] 285. ~2 [avatar split clause 129,135] 290. tall(X0) | old(X0) [resolution 105,87] 300. old(lucy) <- (~4) [resolution 290,144] 301. $false <- (~1, ~4) [subsumption resolution 300,132] 302. 1 | 4 [avatar contradiction clause 301] 348. humble(lucy) | curious(lucy) <- (4) [resolution 115,145] 350. curious(lucy) <- (~3, 4) [subsumption resolution 348,140] 351. $false <- (~3, 4) [subsumption resolution 350,124] 352. 3 | ~4 [avatar contradiction clause 351] 353. $false [avatar sat refutation 147,284,285,302,352] % SZS output end Proof for 3972739402953713402393078 % ------------------------------ % 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 kind or funny is not strong and vice versa. If someone is either not brave or curious then someone is calm. If someone is both wise and quiet then someone is not kind or generous. Everyone who is not tall is either quiet or not patient. If paul is funny or quiet then lucy is either not rich or not strong and vice versa. Everyone who is both not tall and funny is not old and vice versa. Everyone who is generous is not generous or old and vice versa. If paul is both calm and not calm then someone is kind or funny. If someone is either patient or kind then lucy is either not wise or strong and vice versa. If mary is not quiet or happy then someone is both creative and not rich. Everyone who is both funny and kind is both brave and not tall and vice versa. If paul is calm then someone is not rich or humble and vice versa. If someone is both not brave and not calm then someone is happy or humble and vice versa. Everyone who is both not kind and not funny is not quiet and vice versa. Everyone who is not creative is both not happy and not calm. Everyone who is tall or not calm is both not brave and humble. John is either not humble or not happy. Someone is not wise. Someone is both not kind and not tall. Susan is not tall or creative. Someone is creative or wise.

Lucy is funny.

neutral

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

funny(lucy)

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

Susan is strong.

neutral

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

strong(susan)

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

Paul is not humble.

entailment

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

~humble(paul)

% SZS status Unsatisfiable for 5006128961383096828849178 % SZS output start Proof for 5006128961383096828849178 15. ! [X0] : ((~humble(X0) & curious(X0)) <=> (~creative(X0) | ~calm(X0))) [input p14] 16. ! [X0] : ((~old(X0) | creative(X0)) => ~calm(X0)) [input p15] 23. humble(paul) [input hypothesis] 34. ! [X0] : (~calm(X0) | (old(X0) & ~creative(X0))) [ennf transformation 16] 53. ! [X0] : (((~humble(X0) & curious(X0)) | (creative(X0) & calm(X0))) & ((~creative(X0) | ~calm(X0)) | (humble(X0) | ~curious(X0)))) [nnf transformation 15] 54. ! [X0] : (((~humble(X0) & curious(X0)) | (creative(X0) & calm(X0))) & (~creative(X0) | ~calm(X0) | humble(X0) | ~curious(X0))) [flattening 53] 112. ~humble(X0) | calm(X0) [cnf transformation 54] 113. ~humble(X0) | creative(X0) [cnf transformation 54] 114. ~creative(X0) | ~calm(X0) [cnf transformation 34] 124. humble(paul) [cnf transformation 23] 205. 17 <=> calm(paul) [avatar definition] 206. calm(paul) <- (17) [avatar component clause 205] 237. 24 <=> humble(paul) [avatar definition] 238. humble(paul) <- (24) [avatar component clause 237] 242. 24 [avatar split clause 124,237] 246. calm(paul) <- (24) [resolution 112,238] 249. 17 | ~24 [avatar split clause 246,237,205] 250. creative(paul) <- (24) [resolution 113,238] 253. ~calm(paul) <- (24) [resolution 250,114] 254. $false <- (17, 24) [subsumption resolution 253,206] 255. ~17 | ~24 [avatar contradiction clause 254] 256. $false [avatar sat refutation 242,249,255] % SZS output end Proof for 5006128961383096828849178 % ------------------------------ % 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 fred is both not calm and curious then fred is both not tall and not generous. Everyone who is tall or not wise is both quiet and not happy. If paul is both not creative and generous then someone is curious or not rich. Everyone who is not calm or not wise is not happy or patient. Everyone who is both happy and not wise is either not curious or not patient and vice versa. If fred is not funny then paul is both not funny and quiet. Everyone who is both not patient and wise is either not rich or humble and vice versa. Everyone who is strong or tall is either not strong or happy and vice versa. Everyone who is not patient is both generous and strong. Everyone who is either kind or brave is both not rich and not funny and vice versa. Everyone who is either not wise or rich is not happy. If someone is both tall and strong then someone is generous or tall and vice versa. If someone is both not quiet and humble then alice is not strong or not patient. Everyone who is both creative and tall is either old or not old. Everyone who is not rich is either not calm or kind and vice versa. Everyone who is strong or not funny is quiet or not tall and vice versa. Someone is not brave or not quiet. Fred is not quiet or generous. Someone is both quiet and curious. Someone is not strong or quiet. Susan is not rich or patient. Someone is both strong and not kind. Someone is either quiet or not quiet.

Paul is curious.

entailment

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

curious(paul)

% SZS status Unsatisfiable for 2974363702064071091513533 % SZS output start Proof for 2974363702064071091513533 2. ! [X0] : ((~wise(X0) | tall(X0)) => (~happy(X0) & quiet(X0))) [input p1] 5. ! [X0] : ((~wise(X0) & happy(X0)) <=> (~curious(X0) <~> ~patient(X0))) [input p4] 8. ! [X0] : ((tall(X0) | strong(X0)) <=> (~strong(X0) <~> happy(X0))) [input p7] 9. ! [X0] : (~patient(X0) => (strong(X0) & generous(X0))) [input p8] 12. ? [X0] : (strong(X0) & tall(X0)) <=> ? [X0] : (tall(X0) | generous(X0)) [input p11] 24. ~curious(paul) [input hypothesis] 25. ? [X0] : (strong(X0) & tall(X0)) <=> ? [X1] : (tall(X1) | generous(X1)) [rectify 12] 28. ! [X0] : ((~happy(X0) & quiet(X0)) | (wise(X0) & ~tall(X0))) [ennf transformation 2] 34. ! [X0] : ((strong(X0) & generous(X0)) | patient(X0)) [ennf transformation 9] 42. ! [X0] : (((~wise(X0) & happy(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | (wise(X0) | ~happy(X0)))) [nnf transformation 5] 43. ! [X0] : (((~wise(X0) & happy(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | wise(X0) | ~happy(X0))) [flattening 42] 46. ! [X0] : (((tall(X0) | strong(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~tall(X0) & ~strong(X0)))) [nnf transformation 8] 47. ! [X0] : ((tall(X0) | strong(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~tall(X0) & ~strong(X0)))) [flattening 46] 51. (? [X0] : (strong(X0) & tall(X0)) | ! [X1] : (~tall(X1) & ~generous(X1))) & (? [X1] : (tall(X1) | generous(X1)) | ! [X0] : (~strong(X0) | ~tall(X0))) [nnf transformation 25] 52. (? [X0] : (strong(X0) & tall(X0)) | ! [X1] : (~tall(X1) & ~generous(X1))) & (? [X2] : (tall(X2) | generous(X2)) | ! [X3] : (~strong(X3) | ~tall(X3))) [rectify 51] 53. ? [X0] : (strong(X0) & tall(X0)) => (strong(sK1) & tall(sK1)) [choice axiom] 54. ? [X2] : (tall(X2) | generous(X2)) => (tall(sK2) | generous(sK2)) [choice axiom] 55. ((strong(sK1) & tall(sK1)) | ! [X1] : (~tall(X1) & ~generous(X1))) & ((tall(sK2) | generous(sK2)) | ! [X3] : (~strong(X3) | ~tall(X3))) [skolemisation 52,54,53] 75. ~happy(X0) | ~tall(X0) [cnf transformation 28] 76. ~happy(X0) | wise(X0) [cnf transformation 28] 82. ~patient(X0) | happy(X0) | curious(X0) [cnf transformation 43] 84. ~patient(X0) | ~wise(X0) | curious(X0) [cnf transformation 43] 95. happy(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 47] 100. patient(X0) | generous(X0) [cnf transformation 34] 111. tall(sK1) | ~generous(X1) [cnf transformation 55] 113. strong(sK1) | ~generous(X1) [cnf transformation 55] 136. ~curious(paul) [cnf transformation 24] 188. ~strong(X0) | ~tall(X0) [subsumption resolution 95,75] 194. 13 <=> strong(sK1) [avatar definition] 196. strong(sK1) <- (13) [avatar component clause 194] 199. 14 <=> ! [X1] : ~generous(X1) [avatar definition] 200. ~generous(X1) <- (14) [avatar component clause 199] 201. 14 | 13 [avatar split clause 113,194,199] 203. 15 <=> tall(sK1) [avatar definition] 207. 14 | 15 [avatar split clause 111,203,199] 265. ~tall(sK1) <- (13) [resolution 188,196] 269. ~15 | ~13 [avatar split clause 265,194,203] 295. happy(X0) | curious(X0) | generous(X0) [resolution 82,100] 298. happy(X0) | curious(X0) <- (14) [subsumption resolution 295,200] 300. ~wise(X0) | curious(X0) | generous(X0) [resolution 84,100] 303. ~wise(X0) | curious(X0) <- (14) [subsumption resolution 300,200] 335. curious(X1) | wise(X1) <- (14) [resolution 298,76] 337. curious(X1) <- (14) [subsumption resolution 335,303] 340. $false <- (14) [resolution 337,136] 343. ~14 [avatar contradiction clause 340] 345. $false [avatar sat refutation 201,207,269,343] % SZS output end Proof for 2974363702064071091513533 % ------------------------------ % 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 either calm or not old is not calm. Everyone who is not creative is both not tall and tall and vice versa. Everyone who is happy is either wise or not calm and vice versa. If someone is happy or generous then paul is wise or calm. If someone is either not rich or patient then alice is curious. Everyone who is not rich is tall or not calm and vice versa. Everyone who is not happy or not strong is both not funny and strong. Everyone who is not curious is strong or quiet and vice versa. Everyone who is not patient is either kind or creative and vice versa. If paul is not generous or not tall then paul is not wise or humble and vice versa. Everyone who is both kind and not wise is not wise or generous and vice versa. Everyone who is both not rich and not calm is both not creative and humble. If someone is old then someone is either not quiet or not tall. If mary is either not rich or funny then someone is either generous or strong. Everyone who is brave is not patient. Everyone who is not wise or strong is not patient. Lucy is either generous or not old. Fred is either not old or not creative. Someone is not generous. Alice is both not funny and happy. Someone is either wise or humble. John is either funny or not patient.

Mary is happy.

entailment

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

happy(mary)

% SZS status Unsatisfiable for 6543969935726781482136160 % SZS output start Proof for 6543969935726781482136160 2. ! [X0] : (~creative(X0) <=> (tall(X0) & ~tall(X0))) [input p1] 3. ! [X0] : (happy(X0) <=> (wise(X0) <~> ~calm(X0))) [input p2] 6. ! [X0] : (~rich(X0) <=> (~calm(X0) | tall(X0))) [input p5] 7. ! [X0] : ((~strong(X0) | ~happy(X0)) => (strong(X0) & ~funny(X0))) [input p6] 9. ! [X0] : (~patient(X0) <=> (kind(X0) <~> creative(X0))) [input p8] 11. ! [X0] : ((~wise(X0) & kind(X0)) <=> (generous(X0) | ~wise(X0))) [input p10] 12. ! [X0] : ((~calm(X0) & ~rich(X0)) => (humble(X0) & ~creative(X0))) [input p11] 16. ! [X0] : ((strong(X0) | ~wise(X0)) => ~patient(X0)) [input p15] 23. ~happy(mary) [input hypothesis] 31. ! [X0] : ((strong(X0) & ~funny(X0)) | (strong(X0) & happy(X0))) [ennf transformation 7] 33. ! [X0] : ((humble(X0) & ~creative(X0)) | (calm(X0) | rich(X0))) [ennf transformation 12] 34. ! [X0] : ((humble(X0) & ~creative(X0)) | calm(X0) | rich(X0)) [flattening 33] 37. ! [X0] : (~patient(X0) | (~strong(X0) & wise(X0))) [ennf transformation 16] 39. ! [X0] : ((~creative(X0) | (~tall(X0) | tall(X0))) & ((tall(X0) & ~tall(X0)) | creative(X0))) [nnf transformation 2] 40. ! [X0] : ((~creative(X0) | ~tall(X0) | tall(X0)) & ((tall(X0) & ~tall(X0)) | creative(X0))) [flattening 39] 41. ! [X0] : ((happy(X0) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0)))) & (((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | ~happy(X0))) [nnf transformation 3] 43. ! [X0] : ((~rich(X0) | (calm(X0) & ~tall(X0))) & ((~calm(X0) | tall(X0)) | rich(X0))) [nnf transformation 6] 44. ! [X0] : ((~rich(X0) | (calm(X0) & ~tall(X0))) & (~calm(X0) | tall(X0) | rich(X0))) [flattening 43] 45. ! [X0] : ((~patient(X0) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | patient(X0))) [nnf transformation 9] 48. ! [X0] : (((~wise(X0) & kind(X0)) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | (wise(X0) | ~kind(X0)))) [nnf transformation 11] 49. ! [X0] : (((~wise(X0) & kind(X0)) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | wise(X0) | ~kind(X0))) [flattening 48] 67. ~tall(X0) | creative(X0) [cnf transformation 40] 68. tall(X0) | creative(X0) [cnf transformation 40] 72. ~wise(X0) | ~calm(X0) | happy(X0) [cnf transformation 41] 80. ~rich(X0) | calm(X0) [cnf transformation 44] 84. strong(X0) | strong(X0) [cnf transformation 31] 88. ~creative(X0) | ~kind(X0) | patient(X0) [cnf transformation 45] 96. kind(X0) | wise(X0) [cnf transformation 49] 100. ~creative(X0) | calm(X0) | rich(X0) [cnf transformation 34] 109. ~patient(X0) | ~strong(X0) [cnf transformation 37] 121. ~happy(mary) [cnf transformation 23] 122. strong(X0) [duplicate literal removal 84] 124. creative(X0) [subsumption resolution 67,68] 155. ~kind(X0) | patient(X0) [subsumption resolution 88,124] 173. calm(X0) | rich(X0) [subsumption resolution 100,124] 174. calm(X0) [subsumption resolution 173,80] 204. ~patient(X0) [subsumption resolution 109,122] 233. patient(X0) | wise(X0) [resolution 155,96] 234. wise(X0) [subsumption resolution 233,204] 242. ~calm(X0) | happy(X0) [resolution 72,234] 244. happy(X0) [subsumption resolution 242,174] 250. $false [resolution 244,121] % SZS output end Proof for 6543969935726781482136160 % ------------------------------ % 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 % ------------------------------ % ------------------------------

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

Paul is wise.

neutral

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

wise(paul)

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

Paul is not brave.

neutral

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

~brave(paul)

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

John is not tall.

entailment

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

~tall(john)

% SZS status Unsatisfiable for 2393009109006268192642032 % SZS output start Proof for 2393009109006268192642032 1. ! [X0] : (quiet(X0) => (~rich(X0) <~> strong(X0))) [input p0] 2. ! [X0] : ((~generous(X0) <~> ~calm(X0)) <=> (~rich(X0) | creative(X0))) [input p1] 5. ! [X0] : ((~curious(X0) | strong(X0)) <=> (~tall(X0) & patient(X0))) [input p4] 8. ! [X0] : (~calm(X0) <=> curious(X0)) [input p7] 16. ! [X0] : ((~quiet(X0) & tall(X0)) <=> (patient(X0) & ~patient(X0))) [input p15] 17. ~generous(john) [input p16] 25. tall(john) [input hypothesis] 29. ! [X0] : ((~rich(X0) <~> strong(X0)) | ~quiet(X0)) [ennf transformation 1] 41. ! [X0] : (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ~quiet(X0)) [nnf transformation 29] 42. ! [X0] : ((((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (rich(X0) & ~creative(X0))) & ((~rich(X0) | creative(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))))) [nnf transformation 2] 43. ! [X0] : ((((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (rich(X0) & ~creative(X0))) & (~rich(X0) | creative(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))))) [flattening 42] 44. ! [X0] : (((~curious(X0) | strong(X0)) | (tall(X0) | ~patient(X0))) & ((~tall(X0) & patient(X0)) | (curious(X0) & ~strong(X0)))) [nnf transformation 5] 45. ! [X0] : ((~curious(X0) | strong(X0) | tall(X0) | ~patient(X0)) & ((~tall(X0) & patient(X0)) | (curious(X0) & ~strong(X0)))) [flattening 44] 54. ! [X0] : ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0))) [nnf transformation 8] 73. ! [X0] : (((~quiet(X0) & tall(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (quiet(X0) | ~tall(X0)))) [nnf transformation 16] 74. ! [X0] : (((~quiet(X0) & tall(X0)) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | quiet(X0) | ~tall(X0))) [flattening 73] 84. ~rich(X0) | strong(X0) | ~quiet(X0) [cnf transformation 41] 91. calm(X0) | generous(X0) | rich(X0) [cnf transformation 43] 98. ~tall(X0) | ~strong(X0) [cnf transformation 45] 99. ~tall(X0) | curious(X0) [cnf transformation 45] 112. ~curious(X0) | ~calm(X0) [cnf transformation 54] 131. ~patient(X0) | quiet(X0) | ~tall(X0) [cnf transformation 74] 132. ~tall(X0) | quiet(X0) | patient(X0) [cnf transformation 74] 135. ~generous(john) [cnf transformation 17] 145. tall(john) [cnf transformation 25] 291. ~tall(X0) | quiet(X0) [subsumption resolution 131,132] 344. ~strong(john) [resolution 98,145] 346. curious(john) [resolution 99,145] 357. ~calm(john) [resolution 346,112] 359. quiet(john) [resolution 291,145] 484. generous(john) | rich(john) [resolution 357,91] 485. rich(john) [subsumption resolution 484,135] 515. strong(john) | ~quiet(john) [resolution 485,84] 516. ~quiet(john) [subsumption resolution 515,344] 517. $false [subsumption resolution 516,359] % SZS output end Proof for 2393009109006268192642032 % ------------------------------ % 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 wise or not generous then someone is either funny or not quiet. Everyone who is old or not brave is humble or not wise and vice versa. Everyone who is not quiet or calm is quiet and vice versa. If alice is kind or not creative then lucy is both not curious and not generous and vice versa. Everyone who is either funny or strong is not generous. If someone is either not strong or not old then susan is funny or not wise. If john is both not brave and curious then someone is either not humble or not old and vice versa. If someone is either not curious or curious then someone is not calm or not funny. Everyone who is not funny is not rich or not generous. Everyone who is both not strong and not wise is both not patient and tall. If someone is either brave or wise then someone is not quiet or tall. Everyone who is not calm is not kind or strong and vice versa. Everyone who is not patient is not wise or humble. If susan is either not strong or rich then someone is rich or not wise and vice versa. If someone is either creative or not calm then someone is quiet or not rich. If someone is not quiet or strong then mary is both not quiet and creative. Someone is wise or not happy. Alice is calm or not creative. Someone is either wise or brave. Someone is both not brave and not tall. Fred is funny. Someone is quiet or not old. John is both not generous and funny. John is either calm or rich.

John is generous.

contradiction

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

generous(john)

% SZS status Unsatisfiable for 2579368212536987909377717 % SZS output start Proof for 2579368212536987909377717 23. funny(john) & ~generous(john) [input p22] 25. generous(john) [input hypothesis] 144. ~generous(john) [cnf transformation 23] 148. generous(john) [cnf transformation 25] 329. $false [subsumption resolution 148,144] % SZS output end Proof for 2579368212536987909377717 % ------------------------------ % 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 funny or humble is humble and vice versa. Everyone who is not tall or not generous is not tall. If someone is either not quiet or not creative then alice is not calm or not tall and vice versa. Everyone who is both not funny and not curious is not generous or generous. Everyone who is not calm is either funny or quiet. Everyone who is either old or not tall is funny or old and vice versa. If lucy is both not humble and not creative then mary is not rich or patient. If paul is both not creative and funny then someone is humble or calm. Everyone who is not calm is rich and vice versa. Everyone who is either quiet or not generous is both not curious and not wise. If fred is both quiet and happy then john is either generous or not wise. Everyone who is tall is not kind or patient. Everyone who is not tall or calm is calm. Everyone who is not kind is both not calm and calm and vice versa. If paul is not calm then someone is either creative or not calm. Everyone who is either quiet or not rich is both rich and generous and vice versa. Someone is wise or not rich. Someone is either tall or not patient. Paul is either not kind or patient. John is both not rich and not funny. Paul is both rich and patient. Someone is not calm. Someone is both tall and not strong.

Lucy is kind.

entailment

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

kind(lucy)

% SZS status Unsatisfiable for 428181823107340765162643 % SZS output start Proof for 428181823107340765162643 14. ! [X0] : (~kind(X0) <=> (calm(X0) & ~calm(X0))) [input p13] 24. ~kind(lucy) [input hypothesis] 54. ! [X0] : ((~kind(X0) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | kind(X0))) [nnf transformation 14] 55. ! [X0] : ((~kind(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | kind(X0))) [flattening 54] 102. ~calm(X0) | kind(X0) [cnf transformation 55] 103. calm(X0) | kind(X0) [cnf transformation 55] 124. ~kind(lucy) [cnf transformation 24] 192. kind(X0) [subsumption resolution 102,103] 227. $false [subsumption resolution 124,192] % SZS output end Proof for 428181823107340765162643 % ------------------------------ % 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 creative then john is quiet or old. Everyone who is not creative or strong is either not quiet or humble and vice versa. Everyone who is not brave is creative and vice versa. Everyone who is not funny or humble is both calm and rich. If john is either not quiet or not generous then john is creative. If someone is both not brave and patient then fred is both kind and not humble and vice versa. If someone is either not funny or not rich then fred is both humble and rich. Everyone who is not wise is not creative. If mary is not generous then susan is either not funny or wise. Everyone who is both not patient and not quiet is brave or not wise and vice versa. If someone is not curious or brave then someone is not tall and vice versa. Everyone who is both rich and not humble is both not curious and quiet. Everyone who is both quiet and not strong is both not humble and not wise. If someone is not humble then someone is both quiet and not patient and vice versa. If lucy is quiet then someone is either not kind or not curious and vice versa. If someone is either wise or rich then mary is generous. Mary is not creative. Mary is either not creative or not happy. Someone is not humble. Lucy is not old. Fred is not quiet or not curious. Someone is both brave and tall.

Fred is not wise.

contradiction

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

~wise(fred)

% SZS status Unsatisfiable for 8271117704970669966167834 % SZS output start Proof for 8271117704970669966167834 2. ! [X0] : ((strong(X0) | ~creative(X0)) <=> (~quiet(X0) <~> humble(X0))) [input p1] 3. ! [X0] : (~brave(X0) <=> creative(X0)) [input p2] 4. ! [X0] : ((humble(X0) | ~funny(X0)) => (rich(X0) & calm(X0))) [input p3] 7. ? [X0] : (~funny(X0) <~> ~rich(X0)) => (rich(fred) & humble(fred)) [input p6] 8. ! [X0] : (~wise(X0) => ~creative(X0)) [input p7] 10. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (~wise(X0) | brave(X0))) [input p9] 12. ! [X0] : ((~humble(X0) & rich(X0)) => (quiet(X0) & ~curious(X0))) [input p11] 23. ~wise(fred) [input hypothesis] 26. ! [X0] : ((humble(X0) | ~funny(X0)) => rich(X0)) [pure predicate removal 4] 29. ! [X0] : (rich(X0) | (~humble(X0) & funny(X0))) [ennf transformation 26] 31. (rich(fred) & humble(fred)) | ! [X0] : (~funny(X0) <=> ~rich(X0)) [ennf transformation 7] 32. ! [X0] : (~creative(X0) | wise(X0)) [ennf transformation 8] 34. ! [X0] : ((quiet(X0) & ~curious(X0)) | (humble(X0) | ~rich(X0))) [ennf transformation 12] 35. ! [X0] : ((quiet(X0) & ~curious(X0)) | humble(X0) | ~rich(X0)) [flattening 34] 39. ! [X0] : (((strong(X0) | ~creative(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0)))) & (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & creative(X0)))) [nnf transformation 2] 40. ! [X0] : ((strong(X0) | ~creative(X0) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0)))) & (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & creative(X0)))) [flattening 39] 41. ! [X0] : ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))) [nnf transformation 3] 48. (rich(fred) & humble(fred)) | ! [X0] : ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))) [nnf transformation 31] 50. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (wise(X0) & ~brave(X0))) & ((~wise(X0) | brave(X0)) | (quiet(X0) | patient(X0)))) [nnf transformation 10] 51. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (wise(X0) & ~brave(X0))) & (~wise(X0) | brave(X0) | quiet(X0) | patient(X0))) [flattening 50] 75. ~humble(X0) | quiet(X0) | creative(X0) [cnf transformation 40] 79. brave(X0) | creative(X0) [cnf transformation 41] 81. rich(X0) | funny(X0) [cnf transformation 29] 90. humble(fred) | ~funny(X0) | rich(X0) [cnf transformation 48] 93. ~creative(X0) | wise(X0) [cnf transformation 32] 99. ~brave(X0) | ~quiet(X0) [cnf transformation 51] 100. ~quiet(X0) | wise(X0) [cnf transformation 51] 105. ~rich(X0) | humble(X0) | quiet(X0) [cnf transformation 35] 125. ~wise(fred) [cnf transformation 23] 153. 7 <=> humble(fred) [avatar definition] 154. ~humble(fred) <- (~7) [avatar component clause 153] 155. humble(fred) <- (7) [avatar component clause 153] 173. 11 <=> ! [X0] : rich(X0) [avatar definition] 174. rich(X0) <- (11) [avatar component clause 173] 176. 12 <=> rich(fred) [avatar definition] 177. ~rich(fred) <- (~12) [avatar component clause 176] 178. rich(fred) <- (12) [avatar component clause 176] 185. humble(fred) | rich(X0) [subsumption resolution 90,81] 186. 11 | 7 [avatar split clause 185,153,173] 281. 35 <=> quiet(fred) [avatar definition] 282. quiet(fred) <- (35) [avatar component clause 281] 305. ~quiet(X0) | creative(X0) [resolution 99,79] 325. humble(fred) | quiet(fred) <- (12) [resolution 105,178] 328. quiet(fred) <- (~7, 12) [subsumption resolution 325,154] 329. 35 | 7 | ~12 [avatar split clause 328,176,153,281] 331. quiet(fred) | creative(fred) <- (7) [resolution 155,75] 338. creative(fred) <- (7) [subsumption resolution 331,305] 342. wise(fred) <- (7) [resolution 338,93] 343. $false <- (7) [subsumption resolution 342,125] 344. ~7 [avatar contradiction clause 343] 345. $false <- (11, ~12) [subsumption resolution 177,174] 346. ~11 | 12 [avatar contradiction clause 345] 350. wise(fred) <- (35) [resolution 282,100] 354. $false <- (35) [subsumption resolution 350,125] 355. ~35 [avatar contradiction clause 354] 356. $false [avatar sat refutation 186,329,344,346,355] % SZS output end Proof for 8271117704970669966167834 % ------------------------------ % 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 brave or not creative is both not quiet and not patient and vice versa. If mary is either not quiet or not humble then john is both strong and not old. If susan is happy then paul is either not wise or happy. Everyone who is not happy is not curious and vice versa. If susan is both curious and not generous then john is both not calm and wise and vice versa. Everyone who is both creative and not tall is either not quiet or not rich. If someone is not creative then paul is not rich or brave. Everyone who is not generous or not curious is either rich or strong. Everyone who is rich or not rich is either patient or brave and vice versa. If someone is both humble and tall then someone is either not strong or not wise. If john is calm then someone is either not creative or kind and vice versa. Everyone who is generous or strong is both not rich and rich and vice versa. Everyone who is both kind and curious is not happy or not curious and vice versa. Everyone who is not old is patient or tall and vice versa. If someone is not funny or strong then lucy is quiet or curious. If someone is curious or not quiet then someone is both not patient and not funny and vice versa. Someone is not generous. Someone is either quiet or happy. Susan is both not strong and funny. John is both not kind and not brave. Someone is tall or not calm. Someone is not rich or calm. Alice is not quiet or not calm. Someone is not happy or not brave.

Susan is generous.

contradiction

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

generous(susan)

% SZS status Unsatisfiable for 3104323618827206858186312 % SZS output start Proof for 3104323618827206858186312 12. ! [X0] : ((strong(X0) | generous(X0)) <=> (rich(X0) & ~rich(X0))) [input p11] 25. generous(susan) [input hypothesis] 60. ! [X0] : (((strong(X0) | generous(X0)) | (~rich(X0) | rich(X0))) & ((rich(X0) & ~rich(X0)) | (~strong(X0) & ~generous(X0)))) [nnf transformation 12] 61. ! [X0] : ((strong(X0) | generous(X0) | ~rich(X0) | rich(X0)) & ((rich(X0) & ~rich(X0)) | (~strong(X0) & ~generous(X0)))) [flattening 60] 116. ~rich(X0) | ~generous(X0) [cnf transformation 61] 118. rich(X0) | ~generous(X0) [cnf transformation 61] 145. generous(susan) [cnf transformation 25] 248. ~generous(X0) [subsumption resolution 116,118] 313. $false [subsumption resolution 145,248] % SZS output end Proof for 3104323618827206858186312 % ------------------------------ % 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 % ------------------------------ % ------------------------------

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

Alice is not tall.

entailment

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

~tall(alice)

% SZS status Unsatisfiable for 7213051666667753812759173 % SZS output start Proof for 7213051666667753812759173 11. ! [X0] : ((~tall(X0) | ~patient(X0)) <=> (kind(X0) | ~kind(X0))) [input p10] 19. ~creative(alice) & ~wise(alice) [input p18] 23. wise(alice) <~> patient(alice) [input p22] 25. tall(alice) [input hypothesis] 66. ! [X0] : (((~tall(X0) | ~patient(X0)) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | (tall(X0) & patient(X0)))) [nnf transformation 11] 67. ! [X0] : ((~tall(X0) | ~patient(X0) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | (tall(X0) & patient(X0)))) [flattening 66] 76. (~patient(alice) | ~wise(alice)) & (patient(alice) | wise(alice)) [nnf transformation 23] 105. ~tall(X0) | ~patient(X0) | kind(X0) [cnf transformation 67] 106. ~tall(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 67] 118. ~wise(alice) [cnf transformation 19] 123. patient(alice) | wise(alice) [cnf transformation 76] 126. tall(alice) [cnf transformation 25] 216. ~patient(X0) | ~tall(X0) [subsumption resolution 105,106] 258. patient(alice) [subsumption resolution 123,118] 277. ~tall(alice) [resolution 216,258] 278. $false [subsumption resolution 277,126] % SZS output end Proof for 7213051666667753812759173 % ------------------------------ % 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 kind and not humble then lucy is both not calm and not rich. Everyone who is quiet is not old and vice versa. Everyone who is not brave or not quiet is both creative and funny. Everyone who is brave is both not patient and not strong. Everyone who is either not wise or not creative is patient or calm. If alice is both old and wise then someone is generous and vice versa. If someone is not happy or wise then susan is both not rich and not strong and vice versa. If mary is either strong or not creative then mary is either happy or generous and vice versa. Everyone who is either rich or not brave is not calm or generous and vice versa. Everyone who is either humble or not patient is either creative or not old. If someone is quiet then mary is either quiet or not generous and vice versa. If someone is both kind and not calm then someone is not tall or not wise and vice versa. If paul is funny or not brave then someone is either not rich or not curious and vice versa. If someone is not humble then mary is not tall and vice versa. If someone is patient or not calm then fred is either old or not patient and vice versa. Everyone who is either happy or wise is both not creative and creative and vice versa. Mary is not happy or not creative. Someone is either quiet or not patient. John is both kind and not brave. Someone is tall. Someone is not kind. Someone is not strong or not rich. Someone is curious or wise.

Susan is rich.

contradiction

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

rich(susan)

% SZS status Unsatisfiable for 3074436126770856888669181 % SZS output start Proof for 3074436126770856888669181 3. ! [X0] : ((~quiet(X0) | ~brave(X0)) => (funny(X0) & creative(X0))) [input p2] 6. (wise(alice) & old(alice)) <=> ? [X0] : generous(X0) [input p5] 7. ? [X0] : (wise(X0) | ~happy(X0)) <=> (~strong(susan) & ~rich(susan)) [input p6] 11. ? [X0] : quiet(X0) <=> (quiet(mary) <~> ~generous(mary)) [input p10] 17. ~creative(mary) | ~happy(mary) [input p16] 24. rich(susan) [input hypothesis] 27. ! [X0] : ((funny(X0) & creative(X0)) | (quiet(X0) & brave(X0))) [ennf transformation 3] 34. ((wise(alice) & old(alice)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (~wise(alice) | ~old(alice))) [nnf transformation 6] 35. ((wise(alice) & old(alice)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | ~wise(alice) | ~old(alice)) [flattening 34] 36. ((wise(alice) & old(alice)) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | ~wise(alice) | ~old(alice)) [rectify 35] 37. ? [X1] : generous(X1) => generous(sK0) [choice axiom] 38. ((wise(alice) & old(alice)) | ! [X0] : ~generous(X0)) & (generous(sK0) | ~wise(alice) | ~old(alice)) [skolemisation 36,37] 39. (? [X0] : (wise(X0) | ~happy(X0)) | (strong(susan) | rich(susan))) & ((~strong(susan) & ~rich(susan)) | ! [X0] : (~wise(X0) & happy(X0))) [nnf transformation 7] 40. (? [X0] : (wise(X0) | ~happy(X0)) | strong(susan) | rich(susan)) & ((~strong(susan) & ~rich(susan)) | ! [X0] : (~wise(X0) & happy(X0))) [flattening 39] 41. (? [X0] : (wise(X0) | ~happy(X0)) | strong(susan) | rich(susan)) & ((~strong(susan) & ~rich(susan)) | ! [X1] : (~wise(X1) & happy(X1))) [rectify 40] 42. ? [X0] : (wise(X0) | ~happy(X0)) => (wise(sK1) | ~happy(sK1)) [choice axiom] 43. ((wise(sK1) | ~happy(sK1)) | strong(susan) | rich(susan)) & ((~strong(susan) & ~rich(susan)) | ! [X1] : (~wise(X1) & happy(X1))) [skolemisation 41,42] 48. (? [X0] : quiet(X0) | ((quiet(mary) | generous(mary)) & (~generous(mary) | ~quiet(mary)))) & (((generous(mary) | ~quiet(mary)) & (~generous(mary) | quiet(mary))) | ! [X0] : ~quiet(X0)) [nnf transformation 11] 49. (? [X0] : quiet(X0) | ((quiet(mary) | generous(mary)) & (~generous(mary) | ~quiet(mary)))) & (((generous(mary) | ~quiet(mary)) & (~generous(mary) | quiet(mary))) | ! [X1] : ~quiet(X1)) [rectify 48] 50. ? [X0] : quiet(X0) => quiet(sK2) [choice axiom] 51. (quiet(sK2) | ((quiet(mary) | generous(mary)) & (~generous(mary) | ~quiet(mary)))) & (((generous(mary) | ~quiet(mary)) & (~generous(mary) | quiet(mary))) | ! [X1] : ~quiet(X1)) [skolemisation 49,50] 88. creative(X0) | quiet(X0) [cnf transformation 27] 97. wise(alice) | ~generous(X0) [cnf transformation 38] 98. ~rich(susan) | happy(X1) [cnf transformation 43] 99. ~rich(susan) | ~wise(X1) [cnf transformation 43] 122. generous(mary) | ~quiet(mary) | ~quiet(X1) [cnf transformation 51] 150. ~creative(mary) | ~happy(mary) [cnf transformation 17] 159. rich(susan) [cnf transformation 24] 174. 4 <=> ! [X0] : ~generous(X0) [avatar definition] 175. ~generous(X0) <- (4) [avatar component clause 174] 177. 5 <=> wise(alice) [avatar definition] 179. wise(alice) <- (5) [avatar component clause 177] 180. 4 | 5 [avatar split clause 97,177,174] 192. 8 <=> rich(susan) [avatar definition] 209. 12 <=> ! [X1] : ~wise(X1) [avatar definition] 210. ~wise(X1) <- (12) [avatar component clause 209] 213. 13 <=> ! [X1] : happy(X1) [avatar definition] 214. happy(X1) <- (13) [avatar component clause 213] 216. 12 | ~8 [avatar split clause 99,192,209] 217. 13 | ~8 [avatar split clause 98,192,213] 219. 14 <=> generous(mary) [avatar definition] 220. generous(mary) <- (14) [avatar component clause 219] 223. 15 <=> happy(mary) [avatar definition] 224. ~happy(mary) <- (~15) [avatar component clause 223] 231. 17 <=> creative(mary) [avatar definition] 232. ~creative(mary) <- (~17) [avatar component clause 231] 243. 18 <=> quiet(mary) [avatar definition] 245. quiet(mary) <- (18) [avatar component clause 243] 253. 20 <=> ! [X1] : ~quiet(X1) [avatar definition] 254. ~quiet(X1) <- (20) [avatar component clause 253] 255. 20 | ~18 | 14 [avatar split clause 122,219,243,253] 360. ~15 | ~17 [avatar split clause 150,231,223] 389. 8 [avatar split clause 159,192] 394. $false <- (13, ~15) [resolution 224,214] 395. ~13 | 15 [avatar contradiction clause 394] 401. quiet(mary) <- (~17) [resolution 88,232] 404. 18 | 17 [avatar split clause 401,231,243] 405. $false <- (4, 14) [subsumption resolution 220,175] 406. ~4 | ~14 [avatar contradiction clause 405] 407. $false <- (5, 12) [subsumption resolution 179,210] 408. ~5 | ~12 [avatar contradiction clause 407] 414. $false <- (18, 20) [resolution 254,245] 415. ~18 | ~20 [avatar contradiction clause 414] 418. $false [avatar sat refutation 180,216,217,255,360,389,395,404,406,408,415] % SZS output end Proof for 3074436126770856888669181 % ------------------------------ % 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 % ------------------------------ % ------------------------------

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

Mary is not humble.

contradiction

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

~humble(mary)

% SZS status Unsatisfiable for 8749762774157674166992070 % SZS output start Proof for 8749762774157674166992070 2. ! [X0] : ((humble(X0) & ~patient(X0)) <=> (wise(X0) | ~patient(X0))) [input p1] 7. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> (~old(X0) & ~quiet(X0))) [input p6] 8. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (~tall(X0) & wise(X0))) [input p7] 23. ~humble(mary) [input hypothesis] 37. ! [X0] : (((humble(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (~humble(X0) | patient(X0)))) [nnf transformation 2] 38. ! [X0] : (((humble(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | ~humble(X0) | patient(X0))) [flattening 37] 44. ! [X0] : (((~rich(X0) | ~wise(X0)) | (old(X0) | quiet(X0))) & ((~old(X0) & ~quiet(X0)) | (rich(X0) & wise(X0)))) [nnf transformation 7] 45. ! [X0] : ((~rich(X0) | ~wise(X0) | old(X0) | quiet(X0)) & ((~old(X0) & ~quiet(X0)) | (rich(X0) & wise(X0)))) [flattening 44] 46. ! [X0] : (((~patient(X0) | ~quiet(X0)) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | (patient(X0) & quiet(X0)))) [nnf transformation 8] 47. ! [X0] : ((~patient(X0) | ~quiet(X0) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | (patient(X0) & quiet(X0)))) [flattening 46] 68. ~wise(X0) | ~patient(X0) [cnf transformation 38] 69. humble(X0) | patient(X0) [cnf transformation 38] 78. ~quiet(X0) | wise(X0) [cnf transformation 45] 83. wise(X0) | quiet(X0) [cnf transformation 47] 119. ~humble(mary) [cnf transformation 23] 166. wise(X0) [subsumption resolution 83,78] 255. ~patient(X0) [resolution 68,166] 256. patient(mary) [resolution 69,119] 259. $false [subsumption resolution 256,255] % SZS output end Proof for 8749762774157674166992070 % ------------------------------ % 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 generous or humble is both not funny and not patient and vice versa. If someone is curious or not brave then someone is not humble. If someone is both patient and brave then susan is not funny. If john is both kind and not kind then someone is old and vice versa. Everyone who is either not quiet or curious is both patient and not funny and vice versa. Everyone who is either rich or not strong is wise or patient and vice versa. Everyone who is curious is not wise or not strong. Everyone who is not tall or not generous is both tall and not old and vice versa. Everyone who is tall or generous is both not generous and rich. Everyone who is strong or not quiet is either generous or not strong and vice versa. If fred is not humble or not generous then mary is either not wise or patient. Everyone who is not rich is funny and vice versa. Everyone who is not creative is old or not happy and vice versa. If mary is kind or not curious then mary is either not strong or not rich and vice versa. Someone is both not strong and not funny. Paul is either kind or patient. Alice is either not calm or not patient. Someone is either calm or not happy. Fred is curious or not strong.

Alice is happy.

neutral

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

happy(alice)

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

Paul is tall.

entailment

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

tall(paul)

% SZS status Unsatisfiable for 6977580448645442728844341 % SZS output start Proof for 6977580448645442728844341 2. ! [X0] : (humble(X0) <=> (~humble(X0) | tall(X0))) [input p1] 25. ~tall(paul) [input hypothesis] 47. ! [X0] : ((humble(X0) | (humble(X0) & ~tall(X0))) & ((~humble(X0) | tall(X0)) | ~humble(X0))) [nnf transformation 2] 48. ! [X0] : ((humble(X0) | (humble(X0) & ~tall(X0))) & (~humble(X0) | tall(X0) | ~humble(X0))) [flattening 47] 75. ~humble(X0) | tall(X0) | ~humble(X0) [cnf transformation 48] 77. humble(X0) | humble(X0) [cnf transformation 48] 112. ~tall(paul) [cnf transformation 25] 113. ~humble(X0) | tall(X0) [duplicate literal removal 75] 114. humble(X0) [duplicate literal removal 77] 124. 3 <=> ! [X0] : humble(X0) [avatar definition] 125. humble(X0) <- (3) [avatar component clause 124] 133. 3 [avatar split clause 114,124] 239. tall(X0) <- (3) [resolution 113,125] 245. $false <- (3) [resolution 239,112] 248. ~3 [avatar contradiction clause 245] 249. $false [avatar sat refutation 133,248] % SZS output end Proof for 6977580448645442728844341 % ------------------------------ % 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 % ------------------------------ % ------------------------------

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

Paul is quiet.

contradiction

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

quiet(paul)

% SZS status Unsatisfiable for 5533515416314928051899268 % SZS output start Proof for 5533515416314928051899268 2. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X0] : (~patient(X0) | ~calm(X0)) [input p1] 6. (curious(paul) & funny(paul)) => (~old(mary) & ~calm(mary)) [input p5] 14. ! [X0] : ((strong(X0) & curious(X0)) <=> (~quiet(X0) <~> patient(X0))) [input p13] 19. funny(paul) [input p18] 24. quiet(paul) [input hypothesis] 25. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X1] : (~patient(X1) | ~calm(X1)) [rectify 2] 28. (~old(mary) & ~calm(mary)) | (~curious(paul) | ~funny(paul)) [ennf transformation 6] 29. (~old(mary) & ~calm(mary)) | ~curious(paul) | ~funny(paul) [flattening 28] 41. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (patient(X1) & calm(X1))) & (? [X1] : (~patient(X1) | ~calm(X1)) | ! [X0] : (~wise(X0) | wise(X0))) [nnf transformation 25] 42. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (patient(X1) & calm(X1))) & (? [X2] : (~patient(X2) | ~calm(X2)) | ! [X3] : (~wise(X3) | wise(X3))) [rectify 41] 43. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK1) & ~wise(sK1)) [choice axiom] 44. ? [X2] : (~patient(X2) | ~calm(X2)) => (~patient(sK2) | ~calm(sK2)) [choice axiom] 45. ((wise(sK1) & ~wise(sK1)) | ! [X1] : (patient(X1) & calm(X1))) & ((~patient(sK2) | ~calm(sK2)) | ! [X3] : (~wise(X3) | wise(X3))) [skolemisation 42,44,43] 70. ! [X0] : (((strong(X0) & curious(X0)) | ((~quiet(X0) | ~patient(X0)) & (patient(X0) | quiet(X0)))) & (((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | (~strong(X0) | ~curious(X0)))) [nnf transformation 14] 71. ! [X0] : (((strong(X0) & curious(X0)) | ((~quiet(X0) | ~patient(X0)) & (patient(X0) | quiet(X0)))) & (((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | ~strong(X0) | ~curious(X0))) [flattening 70] 83. ~wise(sK1) | calm(X1) [cnf transformation 45] 84. ~wise(sK1) | patient(X1) [cnf transformation 45] 85. wise(sK1) | calm(X1) [cnf transformation 45] 86. wise(sK1) | patient(X1) [cnf transformation 45] 96. ~calm(mary) | ~curious(paul) | ~funny(paul) [cnf transformation 29] 126. ~patient(X0) | ~quiet(X0) | curious(X0) [cnf transformation 71] 135. funny(paul) [cnf transformation 19] 143. quiet(paul) [cnf transformation 24] 165. 5 <=> ! [X1] : patient(X1) [avatar definition] 166. patient(X1) <- (5) [avatar component clause 165] 168. 6 <=> wise(sK1) [avatar definition] 171. 5 | 6 [avatar split clause 86,168,165] 173. 7 <=> ! [X1] : calm(X1) [avatar definition] 174. calm(X1) <- (7) [avatar component clause 173] 175. 7 | 6 [avatar split clause 85,168,173] 176. 5 | ~6 [avatar split clause 84,168,165] 177. 7 | ~6 [avatar split clause 83,168,173] 195. 11 <=> funny(paul) [avatar definition] 199. 12 <=> curious(paul) [avatar definition] 208. 14 <=> calm(mary) [avatar definition] 210. ~calm(mary) <- (~14) [avatar component clause 208] 211. ~11 | ~12 | ~14 [avatar split clause 96,208,199,195] 279. 11 [avatar split clause 135,195] 356. ~quiet(X0) | curious(X0) <- (5) [resolution 126,166] 358. curious(paul) <- (5) [resolution 356,143] 362. 12 | ~5 [avatar split clause 358,165,199] 363. $false <- (7, ~14) [subsumption resolution 210,174] 364. ~7 | 14 [avatar contradiction clause 363] 365. $false [avatar sat refutation 171,175,176,177,211,279,362,364] % SZS output end Proof for 5533515416314928051899268 % ------------------------------ % 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: 0.039 s % ------------------------------ % ------------------------------

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

Alice is old.

neutral

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

old(alice)

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

John is not humble.

contradiction

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

~humble(john)

% SZS status Unsatisfiable for 2456779539174918144309837 % SZS output start Proof for 2456779539174918144309837 10. ! [X0] : ((wise(X0) <~> humble(X0)) <=> ~wise(X0)) [input p9] 25. ~humble(john) [input hypothesis] 62. ! [X0] : ((((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | wise(X0)) & (~wise(X0) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0))))) [nnf transformation 10] 121. ~wise(X0) | humble(X0) | ~wise(X0) [cnf transformation 62] 123. humble(X0) | wise(X0) | wise(X0) [cnf transformation 62] 155. ~humble(john) [cnf transformation 25] 158. ~wise(X0) | humble(X0) [duplicate literal removal 121] 159. humble(X0) | wise(X0) [duplicate literal removal 123] 209. 12 <=> ! [X1] : (humble(X1) | wise(X1)) [avatar definition] 210. humble(X1) | wise(X1) <- (12) [avatar component clause 209] 270. 12 [avatar split clause 159,209] 375. 47 <=> humble(john) [avatar definition] 377. ~humble(john) <- (~47) [avatar component clause 375] 392. ~47 [avatar split clause 155,375] 393. humble(X1) <- (12) [subsumption resolution 210,158] 397. $false <- (12, ~47) [resolution 393,377] 398. ~12 | 47 [avatar contradiction clause 397] 400. $false [avatar sat refutation 270,392,398] % SZS output end Proof for 2456779539174918144309837 % ------------------------------ % 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 either not brave or not rich is not curious or not quiet and vice versa. Everyone who is not strong is humble or old and vice versa. Everyone who is humble is not old. If alice is old then susan is either old or tall. Everyone who is not kind or not creative is generous. Everyone who is either old or quiet is either not funny or wise. Everyone who is both curious and not strong is either not happy or not funny. If someone is either brave or not happy then john is both generous and not happy. If someone is either not curious or humble then someone is both not patient and not quiet. If lucy is not humble or tall then someone is both brave and not patient and vice versa. If susan is strong or not humble then someone is both not calm and curious. If someone is both happy and quiet then john is both rich and not patient. Everyone who is strong is kind and vice versa. Everyone who is either strong or not quiet is creative and vice versa. Everyone who is both patient and curious is not rich and vice versa. Everyone who is not patient is tall or strong and vice versa. Lucy is both calm and quiet. Someone is either strong or brave. Someone is not rich or brave. Someone is generous. John is either not calm or not tall. Someone is either not kind or not quiet. John is strong. Someone is creative or tall.

John is rich.

entailment

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

rich(john)

% SZS status Unsatisfiable for 1360716449347758299436955 % SZS output start Proof for 1360716449347758299436955 15. ! [X0] : ((curious(X0) & patient(X0)) <=> ~rich(X0)) [input p14] 16. ! [X0] : (~patient(X0) <=> (strong(X0) | tall(X0))) [input p15] 23. strong(john) [input p22] 25. ~rich(john) [input hypothesis] 62. ! [X0] : (((curious(X0) & patient(X0)) | rich(X0)) & (~rich(X0) | (~curious(X0) | ~patient(X0)))) [nnf transformation 15] 63. ! [X0] : (((curious(X0) & patient(X0)) | rich(X0)) & (~rich(X0) | ~curious(X0) | ~patient(X0))) [flattening 62] 64. ! [X0] : ((~patient(X0) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | patient(X0))) [nnf transformation 16] 65. ! [X0] : ((~patient(X0) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | patient(X0))) [flattening 64] 117. patient(X0) | rich(X0) [cnf transformation 63] 121. ~patient(X0) | ~strong(X0) [cnf transformation 65] 131. strong(john) [cnf transformation 23] 133. ~rich(john) [cnf transformation 25] 231. 22 <=> rich(john) [avatar definition] 232. ~rich(john) <- (~22) [avatar component clause 231] 283. ~22 [avatar split clause 133,231] 294. ~strong(X0) | rich(X0) [resolution 121,117] 306. rich(john) [resolution 294,131] 309. $false <- (~22) [subsumption resolution 306,232] 310. 22 [avatar contradiction clause 309] 311. $false [avatar sat refutation 283,310] % SZS output end Proof for 1360716449347758299436955 % ------------------------------ % 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 old or not brave is quiet and vice versa. If john is both curious and not tall then someone is both not rich and not wise. Everyone who is wise is not old. Everyone who is either kind or not quiet is either calm or funny and vice versa. Everyone who is not strong is both quiet and calm and vice versa. Everyone who is not happy or not curious is either not strong or not happy. If lucy is either not funny or patient then paul is strong and vice versa. Everyone who is either not generous or not wise is patient and vice versa. Everyone who is not happy is either patient or not strong and vice versa. If someone is not old or tall then alice is not humble and vice versa. Everyone who is both not humble and brave is either rich or not tall and vice versa. Everyone who is both not strong and old is calm or quiet and vice versa. If someone is either not patient or old then someone is not brave. If someone is tall or rich then someone is calm and vice versa. Everyone who is both not calm and funny is patient or brave and vice versa. Everyone who is both rich and not humble is both old and not strong. Alice is not calm. Susan is either humble or not tall. Fred is not generous or not old. Someone is not wise. Alice is both not curious and not tall. John is strong.

Lucy is kind.

contradiction

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

kind(lucy)

% SZS status Unsatisfiable for 7353699083041588538853557 % SZS output start Proof for 7353699083041588538853557 4. ! [X0] : ((kind(X0) <~> ~quiet(X0)) <=> (calm(X0) <~> funny(X0))) [input p3] 5. ! [X0] : (~strong(X0) <=> (calm(X0) & quiet(X0))) [input p4] 6. ! [X0] : ((~curious(X0) | ~happy(X0)) => (~strong(X0) <~> ~happy(X0))) [input p5] 9. ! [X0] : (~happy(X0) <=> (patient(X0) <~> ~strong(X0))) [input p8] 11. ! [X0] : ((brave(X0) & ~humble(X0)) <=> (rich(X0) <~> ~tall(X0))) [input p10] 12. ! [X0] : ((old(X0) & ~strong(X0)) <=> (quiet(X0) | calm(X0))) [input p11] 14. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X0] : calm(X0) [input p13] 15. ! [X0] : ((funny(X0) & ~calm(X0)) <=> (brave(X0) | patient(X0))) [input p14] 23. kind(lucy) [input hypothesis] 25. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X1] : calm(X1) [rectify 14] 29. ! [X0] : ((~strong(X0) <~> ~happy(X0)) | (curious(X0) & happy(X0))) [ennf transformation 6] 36. ! [X0] : ((((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0))))) [nnf transformation 4] 37. ! [X0] : ((~strong(X0) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | strong(X0))) [nnf transformation 5] 38. ! [X0] : ((~strong(X0) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | strong(X0))) [flattening 37] 39. ! [X0] : (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | (curious(X0) & happy(X0))) [nnf transformation 29] 42. ! [X0] : ((~happy(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) & (((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | happy(X0))) [nnf transformation 9] 47. ! [X0] : (((brave(X0) & ~humble(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | (~brave(X0) | humble(X0)))) [nnf transformation 11] 48. ! [X0] : (((brave(X0) & ~humble(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | ~brave(X0) | humble(X0))) [flattening 47] 49. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (~old(X0) | strong(X0)))) [nnf transformation 12] 50. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | ~old(X0) | strong(X0))) [flattening 49] 55. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : (~rich(X0) & ~tall(X0))) [nnf transformation 25] 56. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : (~rich(X3) & ~tall(X3))) [rectify 55] 57. ? [X0] : (rich(X0) | tall(X0)) => (rich(sK3) | tall(sK3)) [choice axiom] 58. ? [X2] : calm(X2) => calm(sK4) [choice axiom] 59. ((rich(sK3) | tall(sK3)) | ! [X1] : ~calm(X1)) & (calm(sK4) | ! [X3] : (~rich(X3) & ~tall(X3))) [skolemisation 56,58,57] 60. ! [X0] : (((funny(X0) & ~calm(X0)) | (~brave(X0) & ~patient(X0))) & ((brave(X0) | patient(X0)) | (~funny(X0) | calm(X0)))) [nnf transformation 15] 61. ! [X0] : (((funny(X0) & ~calm(X0)) | (~brave(X0) & ~patient(X0))) & (brave(X0) | patient(X0) | ~funny(X0) | calm(X0))) [flattening 60] 79. ~funny(X0) | ~kind(X0) | calm(X0) | quiet(X0) [cnf transformation 36] 81. strong(X0) | calm(X0) [cnf transformation 38] 85. happy(X0) | strong(X0) | happy(X0) [cnf transformation 39] 98. ~happy(X0) | patient(X0) | strong(X0) [cnf transformation 42] 107. rich(X0) | brave(X0) | tall(X0) [cnf transformation 48] 109. ~strong(X0) | ~calm(X0) [cnf transformation 50] 110. ~strong(X0) | ~quiet(X0) [cnf transformation 50] 115. calm(sK4) | ~tall(X3) [cnf transformation 59] 116. calm(sK4) | ~rich(X3) [cnf transformation 59] 119. ~patient(X0) | ~calm(X0) [cnf transformation 61] 122. ~brave(X0) | funny(X0) [cnf transformation 61] 133. kind(lucy) [cnf transformation 23] 134. happy(X0) | strong(X0) [duplicate literal removal 85] 158. 6 <=> funny(lucy) [avatar definition] 159. ~funny(lucy) <- (~6) [avatar component clause 158] 160. funny(lucy) <- (6) [avatar component clause 158] 169. patient(X0) | strong(X0) [subsumption resolution 98,134] 185. 11 <=> ! [X1] : ~tall(X1) [avatar definition] 186. ~tall(X1) <- (11) [avatar component clause 185] 205. 16 <=> ! [X1] : ~calm(X1) [avatar definition] 206. ~calm(X1) <- (16) [avatar component clause 205] 217. 19 <=> ! [X3] : ~rich(X3) [avatar definition] 218. ~rich(X3) <- (19) [avatar component clause 217] 220. 20 <=> calm(sK4) [avatar definition] 222. calm(sK4) <- (20) [avatar component clause 220] 223. 19 | 20 [avatar split clause 116,220,217] 224. 11 | 20 [avatar split clause 115,220,185] 255. strong(X1) | ~calm(X1) [resolution 169,119] 290. ~calm(X1) [subsumption resolution 255,109] 291. 16 [avatar split clause 290,205] 329. brave(X1) | tall(X1) <- (19) [resolution 107,218] 331. brave(X1) <- (11, 19) [subsumption resolution 329,186] 334. funny(X1) <- (11, 19) [resolution 331,122] 338. $false <- (~6, 11, 19) [resolution 334,159] 339. 6 | ~11 | ~19 [avatar contradiction clause 338] 340. $false <- (16, 20) [subsumption resolution 222,206] 341. ~16 | ~20 [avatar contradiction clause 340] 352. 30 <=> strong(lucy) [avatar definition] 353. strong(lucy) <- (30) [avatar component clause 352] 354. ~strong(lucy) <- (~30) [avatar component clause 352] 400. calm(lucy) <- (~30) [resolution 354,81] 402. $false <- (16, ~30) [subsumption resolution 400,206] 403. ~16 | 30 [avatar contradiction clause 402] 412. ~quiet(lucy) <- (30) [resolution 353,110] 433. ~kind(lucy) | calm(lucy) | quiet(lucy) <- (6) [resolution 79,160] 439. calm(lucy) | quiet(lucy) <- (6) [subsumption resolution 433,133] 440. quiet(lucy) <- (6, 16) [subsumption resolution 439,206] 441. $false <- (6, 16, 30) [subsumption resolution 440,412] 442. ~6 | ~16 | ~30 [avatar contradiction clause 441] 451. $false [avatar sat refutation 223,224,291,339,341,403,442] % SZS output end Proof for 7353699083041588538853557 % ------------------------------ % 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 not patient or quiet is either brave or happy. If susan is not generous then mary is patient and vice versa. If someone is both not creative and curious then someone is either not humble or not wise. If paul is either strong or not humble then alice is funny and vice versa. If someone is both not humble and not generous then someone is both not generous and brave. If someone is brave then someone is not patient. Everyone who is brave is both tall and not kind. Everyone who is not tall or not humble is both rich and not old and vice versa. Everyone who is both curious and tall is not kind. Everyone who is brave is not humble or not rich and vice versa. If fred is either not quiet or not wise then john is both strong and generous. Everyone who is both not old and strong is not strong or quiet. Everyone who is both not patient and not tall is old or funny and vice versa. Everyone who is patient or not wise is funny and vice versa. Everyone who is either not brave or not tall is brave and vice versa. Someone is both not generous and curious. Someone is both not tall and creative. Someone is both not kind and quiet. Someone is both quiet and rich. John is not old.

Fred is quiet.

neutral

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

quiet(fred)

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

Alice is not happy.

contradiction

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

~happy(alice)

% SZS status Unsatisfiable for 8029677207301842256126694 % SZS output start Proof for 8029677207301842256126694 2. ! [X0] : ((kind(X0) | ~brave(X0)) => (~funny(X0) & quiet(X0))) [input p1] 9. ! [X0] : ((~patient(X0) & happy(X0)) <=> ~rich(X0)) [input p8] 10. ! [X0] : (~old(X0) <=> (~strong(X0) | ~calm(X0))) [input p9] 15. ! [X0] : ((patient(X0) | ~kind(X0)) <=> old(X0)) [input p14] 16. ! [X0] : ((patient(X0) | ~quiet(X0)) <=> (rich(X0) | brave(X0))) [input p15] 18. ~strong(alice) [input p17] 25. ~happy(alice) [input hypothesis] 29. ! [X0] : ((~funny(X0) & quiet(X0)) | (~kind(X0) & brave(X0))) [ennf transformation 2] 53. ! [X0] : (((~patient(X0) & happy(X0)) | rich(X0)) & (~rich(X0) | (patient(X0) | ~happy(X0)))) [nnf transformation 9] 54. ! [X0] : (((~patient(X0) & happy(X0)) | rich(X0)) & (~rich(X0) | patient(X0) | ~happy(X0))) [flattening 53] 55. ! [X0] : ((~old(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | old(X0))) [nnf transformation 10] 56. ! [X0] : ((~old(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | old(X0))) [flattening 55] 68. ! [X0] : (((patient(X0) | ~kind(X0)) | ~old(X0)) & (old(X0) | (~patient(X0) & kind(X0)))) [nnf transformation 15] 69. ! [X0] : ((patient(X0) | ~kind(X0) | ~old(X0)) & (old(X0) | (~patient(X0) & kind(X0)))) [flattening 68] 70. ! [X0] : (((patient(X0) | ~quiet(X0)) | (~rich(X0) & ~brave(X0))) & ((rich(X0) | brave(X0)) | (~patient(X0) & quiet(X0)))) [nnf transformation 16] 71. ! [X0] : ((patient(X0) | ~quiet(X0) | (~rich(X0) & ~brave(X0))) & (rich(X0) | brave(X0) | (~patient(X0) & quiet(X0)))) [flattening 70] 87. ~kind(X0) | quiet(X0) [cnf transformation 29] 109. rich(X0) | happy(X0) [cnf transformation 54] 113. ~old(X0) | strong(X0) [cnf transformation 56] 127. old(X0) | kind(X0) [cnf transformation 69] 128. ~patient(X0) | old(X0) [cnf transformation 69] 133. ~rich(X0) | ~quiet(X0) | patient(X0) [cnf transformation 71] 135. ~strong(alice) [cnf transformation 18] 145. ~happy(alice) [cnf transformation 25] 247. 24 <=> rich(alice) [avatar definition] 248. rich(alice) <- (24) [avatar component clause 247] 249. ~rich(alice) <- (~24) [avatar component clause 247] 364. happy(alice) <- (~24) [resolution 249,109] 365. $false <- (~24) [subsumption resolution 364,145] 366. 24 [avatar contradiction clause 365] 367. strong(X0) | kind(X0) [resolution 127,113] 402. kind(alice) [resolution 367,135] 426. quiet(alice) [resolution 402,87] 429. ~quiet(alice) | patient(alice) <- (24) [resolution 133,248] 435. patient(alice) <- (24) [subsumption resolution 429,426] 437. old(alice) <- (24) [resolution 435,128] 471. strong(alice) <- (24) [resolution 437,113] 473. $false <- (24) [subsumption resolution 471,135] 474. ~24 [avatar contradiction clause 473] 475. $false [avatar sat refutation 366,474] % SZS output end Proof for 8029677207301842256126694 % ------------------------------ % 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 curious or strong then fred is brave. If someone is not humble or happy then someone is not brave or creative and vice versa. Everyone who is generous or not tall is either kind or not strong. If someone is not old then lucy is either not curious or not generous and vice versa. Everyone who is either tall or kind is either kind or not kind and vice versa. Everyone who is either patient or not strong is not patient or old and vice versa. Everyone who is either calm or not strong is either kind or not brave and vice versa. Everyone who is both not patient and not funny is both old and not quiet. Everyone who is not quiet or wise is not strong or funny and vice versa. If someone is either curious or tall then someone is either not calm or rich. If lucy is creative then someone is not quiet. Everyone who is creative or not brave is not funny or patient and vice versa. Everyone who is either not calm or curious is both not tall and wise. Everyone who is kind or not creative is either not curious or not quiet and vice versa. Everyone who is wise or not humble is not creative or not calm and vice versa. Everyone who is either calm or not quiet is not quiet or kind and vice versa. Lucy is both tall and not patient. Fred is not happy. Someone is both not rich and not creative. Alice is both brave and curious. Mary is quiet or tall. Someone is not kind. Lucy is either happy or patient.

Lucy is not brave.

entailment

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

~brave(lucy)

% SZS status Unsatisfiable for 1997216752816041566204845 % SZS output start Proof for 1997216752816041566204845 5. ! [X0] : ((tall(X0) <~> kind(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p4] 6. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (old(X0) | ~patient(X0))) [input p5] 7. ! [X0] : ((calm(X0) <~> ~strong(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p6] 16. ! [X0] : ((calm(X0) <~> ~quiet(X0)) <=> (kind(X0) | ~quiet(X0))) [input p15] 17. ~patient(lucy) & tall(lucy) [input p16] 24. brave(lucy) [input hypothesis] 44. ! [X0] : ((((~kind(X0) | ~tall(X0)) & (kind(X0) | tall(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0))))) [nnf transformation 5] 45. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 6] 46. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 45] 47. ! [X0] : ((((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))))) [nnf transformation 7] 63. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [nnf transformation 16] 64. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [flattening 63] 90. ~kind(X0) | ~tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 44] 94. ~strong(X0) | patient(X0) | patient(X0) [cnf transformation 46] 99. ~brave(X0) | kind(X0) | calm(X0) | strong(X0) [cnf transformation 47] 135. kind(X0) | ~quiet(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 64] 139. quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 64] 141. tall(lucy) [cnf transformation 17] 142. ~patient(lucy) [cnf transformation 17] 152. brave(lucy) [cnf transformation 24] 153. kind(X0) | ~quiet(X0) | ~calm(X0) [duplicate literal removal 135] 154. ~calm(X0) | quiet(X0) [duplicate literal removal 139] 156. ~strong(X0) | patient(X0) [duplicate literal removal 94] 163. ~kind(X0) | ~tall(X0) [duplicate literal removal 90] 256. ~calm(X0) | kind(X0) [subsumption resolution 153,154] 271. 24 <=> strong(lucy) [avatar definition] 272. strong(lucy) <- (24) [avatar component clause 271] 275. 25 <=> kind(lucy) [avatar definition] 277. kind(lucy) <- (25) [avatar component clause 275] 384. kind(lucy) | calm(lucy) | strong(lucy) [resolution 99,152] 401. ~tall(lucy) <- (25) [resolution 277,163] 402. $false <- (25) [subsumption resolution 401,141] 403. ~25 [avatar contradiction clause 402] 404. kind(lucy) | strong(lucy) [subsumption resolution 384,256] 405. 24 | 25 [avatar split clause 404,275,271] 472. patient(lucy) <- (24) [resolution 272,156] 473. $false <- (24) [subsumption resolution 472,142] 474. ~24 [avatar contradiction clause 473] 475. $false [avatar sat refutation 403,405,474] % SZS output end Proof for 1997216752816041566204845 % ------------------------------ % 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 paul is either not generous or not old then someone is not generous or humble. Everyone who is both not tall and not quiet is not quiet and vice versa. Everyone who is either creative or patient is either not tall or not happy. Everyone who is curious is both not creative and funny. If someone is not tall then alice is not generous and vice versa. Everyone who is not patient or rich is wise. Everyone who is both not quiet and old is either not creative or not old. Everyone who is either not creative or humble is either not calm or not strong. Everyone who is both not calm and patient is not brave and vice versa. Everyone who is curious is not curious or old and vice versa. Everyone who is either not funny or not old is not kind or not tall and vice versa. If someone is tall or not kind then someone is curious or not curious and vice versa. Everyone who is either tall or not kind is curious and vice versa. Everyone who is either not strong or not rich is either not wise or not funny and vice versa. Everyone who is not strong is calm or curious and vice versa. Everyone who is both not curious and kind is both curious and not happy. John is curious or not funny. Someone is either wise or rich. Mary is either kind or not brave. Mary is both kind and not calm. John is either not tall or not happy.

John is not funny.

contradiction

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

~funny(john)

% SZS status Unsatisfiable for 5083317872188871122452155 % SZS output start Proof for 5083317872188871122452155 4. ! [X0] : (curious(X0) => (funny(X0) & ~creative(X0))) [input p3] 10. ! [X0] : (curious(X0) <=> (old(X0) | ~curious(X0))) [input p9] 22. ~funny(john) [input hypothesis] 26. ! [X0] : ((funny(X0) & ~creative(X0)) | ~curious(X0)) [ennf transformation 4] 47. ! [X0] : ((curious(X0) | (~old(X0) & curious(X0))) & ((old(X0) | ~curious(X0)) | ~curious(X0))) [nnf transformation 10] 48. ! [X0] : ((curious(X0) | (~old(X0) & curious(X0))) & (old(X0) | ~curious(X0) | ~curious(X0))) [flattening 47] 75. ~curious(X0) | funny(X0) [cnf transformation 26] 90. curious(X0) | curious(X0) [cnf transformation 48] 128. ~funny(john) [cnf transformation 22] 131. curious(X0) [duplicate literal removal 90] 210. funny(X0) [resolution 75,131] 211. $false [resolution 210,128] % SZS output end Proof for 5083317872188871122452155 % ------------------------------ % 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 susan is not quiet then someone is either quiet or not strong and vice versa. If someone is tall then alice is both funny and not humble and vice versa. Everyone who is both not generous and not humble is either not tall or not generous. Everyone who is both creative and generous is both funny and humble and vice versa. Everyone who is old or not brave is both generous and curious. If alice is brave then fred is either not curious or not quiet. Everyone who is either quiet or wise is either tall or patient. If paul is strong then lucy is both strong and humble. If john is both generous and curious then lucy is not kind or not rich. Everyone who is either not brave or kind is either not rich or creative. Everyone who is both not old and funny is not strong and vice versa. Everyone who is both brave and happy is happy. Everyone who is strong or not creative is either not kind or tall and vice versa. Everyone who is rich is generous. Everyone who is not calm or not brave is either tall or quiet and vice versa. Everyone who is not brave or creative is not funny or tall. Lucy is either brave or calm. Fred is either strong or generous. Mary is both not patient and not creative. Susan is both not funny and not happy. Lucy is not creative. Alice is both happy and humble. Paul is both not happy and wise. Someone is not funny or not happy.

Susan is brave.

entailment

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

brave(susan)

% SZS status Unsatisfiable for 184273502094308013123508 % SZS output start Proof for 184273502094308013123508 1. ~quiet(susan) <=> ? [X0] : (quiet(X0) <~> ~strong(X0)) [input p0] 2. ? [X0] : tall(X0) <=> (~humble(alice) & funny(alice)) [input p1] 11. ! [X0] : ((funny(X0) & ~old(X0)) <=> ~strong(X0)) [input p10] 15. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (tall(X0) <~> quiet(X0))) [input p14] 20. ~happy(susan) & ~funny(susan) [input p19] 22. humble(alice) & happy(alice) [input p21] 25. ~brave(susan) [input hypothesis] 40. (~quiet(susan) | ! [X0] : ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (? [X0] : ((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | quiet(susan)) [nnf transformation 1] 41. (~quiet(susan) | ! [X0] : ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (? [X1] : ((strong(X1) | ~quiet(X1)) & (~strong(X1) | quiet(X1))) | quiet(susan)) [rectify 40] 42. ? [X1] : ((strong(X1) | ~quiet(X1)) & (~strong(X1) | quiet(X1))) => ((strong(sK0) | ~quiet(sK0)) & (~strong(sK0) | quiet(sK0))) [choice axiom] 43. (~quiet(susan) | ! [X0] : ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(sK0) | ~quiet(sK0)) & (~strong(sK0) | quiet(sK0))) | quiet(susan)) [skolemisation 41,42] 44. (? [X0] : tall(X0) | (humble(alice) | ~funny(alice))) & ((~humble(alice) & funny(alice)) | ! [X0] : ~tall(X0)) [nnf transformation 2] 45. (? [X0] : tall(X0) | humble(alice) | ~funny(alice)) & ((~humble(alice) & funny(alice)) | ! [X0] : ~tall(X0)) [flattening 44] 46. (? [X0] : tall(X0) | humble(alice) | ~funny(alice)) & ((~humble(alice) & funny(alice)) | ! [X1] : ~tall(X1)) [rectify 45] 47. ? [X0] : tall(X0) => tall(sK1) [choice axiom] 48. (tall(sK1) | humble(alice) | ~funny(alice)) & ((~humble(alice) & funny(alice)) | ! [X1] : ~tall(X1)) [skolemisation 46,47] 55. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | (~funny(X0) | old(X0)))) [nnf transformation 11] 56. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | ~funny(X0) | old(X0))) [flattening 55] 59. ! [X0] : (((~brave(X0) | ~calm(X0)) | ((tall(X0) | ~quiet(X0)) & (quiet(X0) | ~tall(X0)))) & (((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | (brave(X0) & calm(X0)))) [nnf transformation 15] 60. ! [X0] : ((~brave(X0) | ~calm(X0) | ((tall(X0) | ~quiet(X0)) & (quiet(X0) | ~tall(X0)))) & (((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | (brave(X0) & calm(X0)))) [flattening 59] 67. ~quiet(susan) | ~strong(X0) | ~quiet(X0) [cnf transformation 43] 70. ~humble(alice) | ~tall(X1) [cnf transformation 48] 97. funny(X0) | strong(X0) [cnf transformation 56] 107. brave(X0) | tall(X0) | quiet(X0) [cnf transformation 60] 120. ~funny(susan) [cnf transformation 20] 124. humble(alice) [cnf transformation 22] 128. ~brave(susan) [cnf transformation 25] 134. 2 <=> quiet(susan) [avatar definition] 135. quiet(susan) <- (2) [avatar component clause 134] 139. 3 <=> ! [X0] : (~strong(X0) | ~quiet(X0)) [avatar definition] 140. ~strong(X0) | ~quiet(X0) <- (3) [avatar component clause 139] 141. 3 | ~2 [avatar split clause 67,134,139] 157. 7 <=> humble(alice) [avatar definition] 166. 9 <=> ! [X1] : ~tall(X1) [avatar definition] 167. ~tall(X1) <- (9) [avatar component clause 166] 168. 9 | ~7 [avatar split clause 70,157,166] 235. 7 [avatar split clause 124,157] 247. strong(susan) [resolution 97,120] 259. tall(susan) | quiet(susan) [resolution 107,128] 261. quiet(susan) <- (9) [subsumption resolution 259,167] 265. 2 | ~9 [avatar split clause 261,166,134] 272. ~quiet(susan) <- (3) [resolution 140,247] 275. $false <- (2, 3) [subsumption resolution 272,135] 276. ~2 | ~3 [avatar contradiction clause 275] 280. $false [avatar sat refutation 141,168,235,265,276] % SZS output end Proof for 184273502094308013123508 % ------------------------------ % 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 not strong or calm then someone is either curious or not happy. If someone is patient or not curious then someone is both not wise and tall and vice versa. If paul is happy then fred is both brave and old. If john is not creative or funny then someone is either generous or not patient and vice versa. If mary is both not wise and not patient then someone is both funny and patient and vice versa. If mary is generous or creative then someone is both not kind and curious. Everyone who is both not generous and happy is curious and vice versa. If paul is either brave or not calm then alice is both not wise and kind. If someone is both not creative and humble then john is old or calm and vice versa. Everyone who is both not brave and generous is either kind or not calm and vice versa. If fred is either not generous or rich then john is both not curious and not rich and vice versa. If someone is not tall or wise then paul is quiet or rich. If fred is not happy then someone is either curious or not old and vice versa. Everyone who is not humble is generous and vice versa. Everyone who is not rich is both wise and not rich. Everyone who is either not calm or not patient is both not patient and not humble and vice versa. Alice is both not old and calm. Lucy is calm. Paul is both brave and curious. Someone is not quiet. Someone is either not patient or not rich. Someone is either not tall or brave. Someone is tall or not strong. Paul is calm.

Paul is not humble.

contradiction

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

~humble(paul)

% SZS status Unsatisfiable for 3074182821123288916239247 % SZS output start Proof for 3074182821123288916239247 7. ! [X0] : ((happy(X0) & ~generous(X0)) <=> curious(X0)) [input p6] 14. ! [X0] : (~humble(X0) <=> generous(X0)) [input p13] 19. curious(paul) & brave(paul) [input p18] 25. ~humble(paul) [input hypothesis] 56. ! [X0] : (((happy(X0) & ~generous(X0)) | ~curious(X0)) & (curious(X0) | (~happy(X0) | generous(X0)))) [nnf transformation 7] 57. ! [X0] : (((happy(X0) & ~generous(X0)) | ~curious(X0)) & (curious(X0) | ~happy(X0) | generous(X0))) [flattening 56] 72. ! [X0] : ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))) [nnf transformation 14] 111. ~generous(X0) | ~curious(X0) [cnf transformation 57] 140. humble(X0) | generous(X0) [cnf transformation 72] 154. curious(paul) [cnf transformation 19] 162. ~humble(paul) [cnf transformation 25] 437. generous(paul) [resolution 140,162] 438. ~curious(paul) [resolution 437,111] 439. $false [subsumption resolution 438,154] % SZS output end Proof for 3074182821123288916239247 % ------------------------------ % 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 % ------------------------------ % ------------------------------