premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either not calm or not rich is not rich or not humble.
Everyone who is not curious is either not strong or not happy.
Everyone who is calm or humble is either happy or not creative.
Everyone who is rich is kind.
Everyone who is both not kind and not calm is not wise or not humble and vice versa.
Everyone who is not wise or strong is not tall.
If someone is either rich or patient then paul is either rich or funny.
If mary is either patient or brave then alice is either funny or rich.
If someone is both rich and not patient then mary is not wise or not rich.
Everyone who is not tall or old is both tall and wise.
If mary is not rich then john is wise.
Everyone who is either not generous or not rich is either curious or funny and vice versa.
Everyone who is either wise or old is both kind and humble and vice versa.
Everyone who is both tall and curious is either not humble or humble and vice versa.
If fred is both not rich and strong then someone is not creative or not generous.
If fred is not wise then someone is either humble or not creative.
Susan is generous or calm.
Someone is either calm or old.
Paul is either kind or quiet.
Someone is creative.
John is either funny or not rich.
Someone is not quiet.
Someone is both generous and not quiet.
Someone is either not tall or not calm. | Mary is not strong. | entailment | (![X]:((~calm(X)<~>~rich(X))=>(~rich(X)|~humble(X))))&
(![X]:(~curious(X)=>(~strong(X)<~>~happy(X))))&
(![X]:((calm(X)|humble(X))=>(happy(X)<~>~creative(X))))&
(![X]:(rich(X)=>kind(X)))&
(![X]:((~kind(X)&~calm(X))<=>(~wise(X)|~humble(X))))&
(![X]:((~wise(X)|strong(X))=>~tall(X)))&
((?[X]:((rich(X)<~>patient(X))))=>((rich(paul)<~>funny(paul))))&
(((patient(mary)<~>brave(mary)))=>((funny(alice)<~>rich(alice))))&
((?[X]:((rich(X)&~patient(X))))=>((~wise(mary)|~rich(mary))))&
(![X]:((~tall(X)|old(X))=>(tall(X)&wise(X))))&
((~rich(mary))=>(wise(john)))&
(![X]:((~generous(X)<~>~rich(X))<=>(curious(X)<~>funny(X))))&
(![X]:((wise(X)<~>old(X))<=>(kind(X)&humble(X))))&
(![X]:((tall(X)&curious(X))<=>(~humble(X)<~>humble(X))))&
(((~rich(fred)&strong(fred)))=>(?[X]:((~creative(X)|~generous(X)))))&
((~wise(fred))=>(?[X]:((humble(X)<~>~creative(X)))))&
((generous(susan)|calm(susan)))&
(?[X]:((calm(X)<~>old(X))))&
((kind(paul)<~>quiet(paul)))&
(?[X]:(creative(X)))&
((funny(john)<~>~rich(john)))&
(?[X]:(~quiet(X)))&
(?[X]:((generous(X)&~quiet(X))))&
(?[X]:((~tall(X)<~>~calm(X)))) | ~strong(mary) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2693652752183017921337688
% SZS output start Proof for 2693652752183017921337688
6. ! [X0] : ((strong(X0) | ~wise(X0)) => ~tall(X0)) [input p5]
10. ! [X0] : ((old(X0) | ~tall(X0)) => (wise(X0) & tall(X0))) [input p9]
25. strong(mary) [input hypothesis]
31. ! [X0] : (~tall(X0) | (~strong(X0) & wise(X0))) [ennf transformation 6]
36. ! [X0] : ((wise(X0) & tall(X0)) | (~old(X0) & tall(X0))) [ennf transformation 10]
87. ~tall(X0) | ~strong(X0) [cnf transformation 31]
97. tall(X0) | tall(X0) [cnf transformation 36]
138. strong(mary) [cnf transformation 25]
143. tall(X0) [duplicate literal removal 97]
261. ~strong(X0) [resolution 87,143]
262. $false [resolution 261,138]
% SZS output end Proof for 2693652752183017921337688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or funny then someone is both not funny and not patient. Everyone who is either not tall or not humble is humble or calm. Everyone who is not funny is curious or tall. If someone is quiet then someone is either brave or not happy. Everyone who is not curious is curious or not quiet and vice versa. If alice is both not happy and not curious then someone is not quiet and vice versa. If someone is both not old and not calm then someone is humble or generous. If paul is not patient then someone is either not wise or not strong. Everyone who is either not generous or not funny is not happy or calm. Everyone who is both old and not wise is calm or humble. If someone is either not funny or tall then someone is not funny and vice versa. Everyone who is not kind or not rich is either not kind or happy. Everyone who is not curious is generous and vice versa. If someone is brave then lucy is either not curious or calm. If someone is patient or creative then someone is strong and vice versa. Paul is both not old and calm. Paul is either not tall or strong. Lucy is brave or not humble. Alice is wise or humble. John is both not funny and tall. | Alice is not creative. | neutral | ((?[X]:((patient(X)<~>funny(X))))=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:((~tall(X)<~>~humble(X))=>(humble(X)|calm(X))))&
(![X]:(~funny(X)=>(curious(X)|tall(X))))&
((?[X]:(quiet(X)))=>(?[X]:((brave(X)<~>~happy(X)))))&
(![X]:(~curious(X)<=>(curious(X)|~quiet(X))))&
(((~happy(alice)&~curious(alice)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~old(X)&~calm(X))))=>(?[X]:((humble(X)|generous(X)))))&
((~patient(paul))=>(?[X]:((~wise(X)<~>~strong(X)))))&
(![X]:((~generous(X)<~>~funny(X))=>(~happy(X)|calm(X))))&
(![X]:((old(X)&~wise(X))=>(calm(X)|humble(X))))&
((?[X]:((~funny(X)<~>tall(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~kind(X)|~rich(X))=>(~kind(X)<~>happy(X))))&
(![X]:(~curious(X)<=>generous(X)))&
((?[X]:(brave(X)))=>((~curious(lucy)<~>calm(lucy))))&
((?[X]:((patient(X)|creative(X))))<=>(?[X]:(strong(X))))&
((~old(paul)&calm(paul)))&
((~tall(paul)<~>strong(paul)))&
((brave(lucy)|~humble(lucy)))&
((wise(alice)|humble(alice)))&
((~funny(john)&tall(john))) | ~creative(alice) | [] | null | 0 |
Everyone who is both not old and quiet is rich or generous and vice versa.
If fred is both brave and old then someone is brave or generous and vice versa.
Everyone who is brave is wise or quiet.
If someone is either not rich or patient then paul is not old.
Everyone who is not wise or quiet is brave and vice versa.
Everyone who is both not strong and not calm is both tall and calm.
If lucy is not brave then someone is either patient or not creative.
If someone is both not old and strong then mary is either not strong or not calm and vice versa.
Everyone who is either not rich or creative is either not old or patient.
If someone is either kind or generous then someone is creative or funny.
If paul is not happy then someone is either not rich or brave and vice versa.
If someone is not wise then paul is not creative.
Everyone who is not quiet or quiet is not curious.
If fred is either not patient or calm then someone is both wise and curious.
If someone is either happy or curious then someone is humble and vice versa.
If someone is not quiet or not brave then paul is not quiet and vice versa.
Paul is both not strong and brave.
Someone is brave or wise.
Paul is rich or patient.
Paul is quiet.
John is not curious or not kind.
Alice is not rich.
Susan is either not curious or creative.
Someone is patient or rich. | Alice is curious. | contradiction | (![X]:((~old(X)&quiet(X))<=>(rich(X)|generous(X))))&
(((brave(fred)&old(fred)))<=>(?[X]:((brave(X)|generous(X)))))&
(![X]:(brave(X)=>(wise(X)|quiet(X))))&
((?[X]:((~rich(X)<~>patient(X))))=>(~old(paul)))&
(![X]:((~wise(X)|quiet(X))<=>brave(X)))&
(![X]:((~strong(X)&~calm(X))=>(tall(X)&calm(X))))&
((~brave(lucy))=>(?[X]:((patient(X)<~>~creative(X)))))&
((?[X]:((~old(X)&strong(X))))<=>((~strong(mary)<~>~calm(mary))))&
(![X]:((~rich(X)<~>creative(X))=>(~old(X)<~>patient(X))))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:((creative(X)|funny(X)))))&
((~happy(paul))<=>(?[X]:((~rich(X)<~>brave(X)))))&
((?[X]:(~wise(X)))=>(~creative(paul)))&
(![X]:((~quiet(X)|quiet(X))=>~curious(X)))&
(((~patient(fred)<~>calm(fred)))=>(?[X]:((wise(X)&curious(X)))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(~quiet(paul)))&
((~strong(paul)&brave(paul)))&
(?[X]:((brave(X)|wise(X))))&
((rich(paul)|patient(paul)))&
(quiet(paul))&
((~curious(john)|~kind(john)))&
(~rich(alice))&
((~curious(susan)<~>creative(susan)))&
(?[X]:((patient(X)|rich(X)))) | curious(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4512876478373790374539877
% SZS output start Proof for 4512876478373790374539877
13. ! [X0] : ((quiet(X0) | ~quiet(X0)) => ~curious(X0)) [input p12]
25. curious(alice) [input hypothesis]
39. ! [X0] : (~curious(X0) | (~quiet(X0) & quiet(X0))) [ennf transformation 13]
114. ~curious(X0) | quiet(X0) [cnf transformation 39]
115. ~curious(X0) | ~quiet(X0) [cnf transformation 39]
136. curious(alice) [cnf transformation 25]
252. ~curious(X0) [subsumption resolution 114,115]
327. $false [subsumption resolution 136,252]
% SZS output end Proof for 4512876478373790374539877
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If alice is not calm or not creative then someone is either old or wise.
Everyone who is both not happy and not patient is either old or not happy and vice versa.
If mary is either not brave or brave then lucy is not funny.
If someone is either generous or old then someone is either creative or wise and vice versa.
Everyone who is not kind or not curious is either not generous or not happy.
Everyone who is not old or funny is not calm and vice versa.
If someone is both rich and not curious then someone is either not kind or brave and vice versa.
If someone is humble then someone is funny.
If alice is kind then alice is either creative or kind and vice versa.
If someone is patient or funny then fred is not strong and vice versa.
Everyone who is both old and not happy is either rich or calm.
If someone is not old then fred is brave and vice versa.
Everyone who is creative or generous is either happy or not old and vice versa.
Everyone who is both not rich and generous is either not calm or funny and vice versa.
Everyone who is generous or curious is patient.
If paul is patient or funny then alice is not happy or not patient and vice versa.
Someone is both curious and humble.
Lucy is not creative.
Lucy is either not generous or humble.
Fred is either creative or not wise.
Someone is either not quiet or patient.
Mary is both not curious and quiet.
Someone is both patient and not quiet. | Mary is calm. | contradiction | (((~calm(alice)|~creative(alice)))=>(?[X]:((old(X)<~>wise(X)))))&
(![X]:((~happy(X)&~patient(X))<=>(old(X)<~>~happy(X))))&
(((~brave(mary)<~>brave(mary)))=>(~funny(lucy)))&
((?[X]:((generous(X)<~>old(X))))<=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:((~kind(X)|~curious(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((~old(X)|funny(X))<=>~calm(X)))&
((?[X]:((rich(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>brave(X)))))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
((kind(alice))<=>((creative(alice)<~>kind(alice))))&
((?[X]:((patient(X)|funny(X))))<=>(~strong(fred)))&
(![X]:((old(X)&~happy(X))=>(rich(X)<~>calm(X))))&
((?[X]:(~old(X)))<=>(brave(fred)))&
(![X]:((creative(X)|generous(X))<=>(happy(X)<~>~old(X))))&
(![X]:((~rich(X)&generous(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((generous(X)|curious(X))=>patient(X)))&
(((patient(paul)|funny(paul)))<=>((~happy(alice)|~patient(alice))))&
(?[X]:((curious(X)&humble(X))))&
(~creative(lucy))&
((~generous(lucy)<~>humble(lucy)))&
((creative(fred)<~>~wise(fred)))&
(?[X]:((~quiet(X)<~>patient(X))))&
((~curious(mary)&quiet(mary)))&
(?[X]:((patient(X)&~quiet(X)))) | calm(mary) | [
"p1",
"p4",
"p5",
"p10",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5320768743684665605489291
% SZS output start Proof for 5320768743684665605489291
2. ! [X0] : ((~patient(X0) & ~happy(X0)) <=> (old(X0) <~> ~happy(X0))) [input p1]
5. ! [X0] : ((~curious(X0) | ~kind(X0)) => (~generous(X0) <~> ~happy(X0))) [input p4]
6. ! [X0] : ((funny(X0) | ~old(X0)) <=> ~calm(X0)) [input p5]
11. ! [X0] : ((~happy(X0) & old(X0)) => (rich(X0) <~> calm(X0))) [input p10]
14. ! [X0] : ((generous(X0) & ~rich(X0)) <=> (~calm(X0) <~> funny(X0))) [input p13]
22. quiet(mary) & ~curious(mary) [input p21]
24. calm(mary) [input hypothesis]
30. ! [X0] : ((~generous(X0) <~> ~happy(X0)) | (curious(X0) & kind(X0))) [ennf transformation 5]
32. ! [X0] : ((rich(X0) <~> calm(X0)) | (happy(X0) | ~old(X0))) [ennf transformation 11]
33. ! [X0] : ((rich(X0) <~> calm(X0)) | happy(X0) | ~old(X0)) [flattening 32]
38. ! [X0] : (((~patient(X0) & ~happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | (patient(X0) | happy(X0)))) [nnf transformation 2]
39. ! [X0] : (((~patient(X0) & ~happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | patient(X0) | happy(X0))) [flattening 38]
46. ! [X0] : (((happy(X0) | generous(X0)) & (~happy(X0) | ~generous(X0))) | (curious(X0) & kind(X0))) [nnf transformation 30]
47. ! [X0] : (((funny(X0) | ~old(X0)) | calm(X0)) & (~calm(X0) | (~funny(X0) & old(X0)))) [nnf transformation 6]
48. ! [X0] : ((funny(X0) | ~old(X0) | calm(X0)) & (~calm(X0) | (~funny(X0) & old(X0)))) [flattening 47]
62. ! [X0] : (((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | happy(X0) | ~old(X0)) [nnf transformation 33]
69. ! [X0] : (((generous(X0) & ~rich(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (~generous(X0) | rich(X0)))) [nnf transformation 14]
70. ! [X0] : (((generous(X0) & ~rich(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | ~generous(X0) | rich(X0))) [flattening 69]
88. ~happy(X0) | ~happy(X0) | ~old(X0) [cnf transformation 39]
105. curious(X0) | generous(X0) | happy(X0) [cnf transformation 46]
106. ~calm(X0) | old(X0) [cnf transformation 48]
107. ~funny(X0) | ~calm(X0) [cnf transformation 48]
124. ~calm(X0) | ~rich(X0) | happy(X0) | ~old(X0) [cnf transformation 62]
133. funny(X0) | ~calm(X0) | ~generous(X0) | rich(X0) [cnf transformation 70]
134. ~funny(X0) | calm(X0) | ~generous(X0) | rich(X0) [cnf transformation 70]
154. ~curious(mary) [cnf transformation 22]
158. calm(mary) [cnf transformation 24]
164. ~happy(X0) | ~old(X0) [duplicate literal removal 88]
298. ~calm(X0) | ~rich(X0) | ~old(X0) [subsumption resolution 124,164]
299. ~rich(X0) | ~calm(X0) [subsumption resolution 298,106]
319. ~generous(X0) | ~funny(X0) | rich(X0) [subsumption resolution 134,107]
320. ~calm(X0) | ~generous(X0) | rich(X0) [subsumption resolution 133,319]
321. ~generous(X0) | ~calm(X0) [subsumption resolution 320,299]
374. old(mary) [resolution 106,158]
465. generous(mary) | happy(mary) [resolution 105,154]
469. 53 <=> happy(mary) [avatar definition]
471. happy(mary) <- (53) [avatar component clause 469]
473. 54 <=> generous(mary) [avatar definition]
475. generous(mary) <- (54) [avatar component clause 473]
476. 53 | 54 [avatar split clause 465,473,469]
545. ~old(mary) <- (53) [resolution 471,164]
546. $false <- (53) [subsumption resolution 545,374]
547. ~53 [avatar contradiction clause 546]
573. ~calm(mary) <- (54) [resolution 475,321]
585. $false <- (54) [subsumption resolution 573,158]
586. ~54 [avatar contradiction clause 585]
587. $false [avatar sat refutation 476,547,586]
% SZS output end Proof for 5320768743684665605489291
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not calm is both not brave and not happy.
Everyone who is not happy is both brave and not humble and vice versa.
Everyone who is not rich or humble is kind or generous and vice versa.
Everyone who is brave or not old is both not wise and curious.
If someone is not patient or not wise then lucy is wise and vice versa.
Everyone who is both not creative and patient is both not humble and happy.
If someone is either not generous or tall then someone is either not happy or generous and vice versa.
If someone is both generous and humble then lucy is both kind and generous and vice versa.
Everyone who is not quiet or creative is not happy or funny.
Everyone who is not creative is funny or not humble and vice versa.
If someone is happy or brave then someone is both not generous and funny.
If susan is either creative or not humble then paul is not patient and vice versa.
Everyone who is either wise or patient is either not generous or not humble.
If susan is generous then susan is happy and vice versa.
If someone is both kind and not humble then fred is either not funny or creative.
Everyone who is curious or wise is not curious.
Someone is not generous or rich.
Mary is not brave.
Paul is both not generous and not kind.
Someone is both not calm and not tall.
Alice is both old and wise.
Susan is not quiet. | Paul is not calm. | contradiction | (![X]:((~generous(X)&~calm(X))=>(~brave(X)&~happy(X))))&
(![X]:(~happy(X)<=>(brave(X)&~humble(X))))&
(![X]:((~rich(X)|humble(X))<=>(kind(X)|generous(X))))&
(![X]:((brave(X)|~old(X))=>(~wise(X)&curious(X))))&
((?[X]:((~patient(X)|~wise(X))))<=>(wise(lucy)))&
(![X]:((~creative(X)&patient(X))=>(~humble(X)&happy(X))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:((~happy(X)<~>generous(X)))))&
((?[X]:((generous(X)&humble(X))))<=>((kind(lucy)&generous(lucy))))&
(![X]:((~quiet(X)|creative(X))=>(~happy(X)|funny(X))))&
(![X]:(~creative(X)<=>(funny(X)|~humble(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(?[X]:((~generous(X)|rich(X))))&
(~brave(mary))&
((~generous(paul)&~kind(paul)))&
(?[X]:((~calm(X)&~tall(X))))&
((old(alice)&wise(alice)))&
(~quiet(susan)) | ~calm(paul) | [
"p0",
"p1",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1588735447832530229930116
% SZS output start Proof for 1588735447832530229930116
1. ! [X0] : ((~calm(X0) & ~generous(X0)) => (~happy(X0) & ~brave(X0))) [input p0]
2. ! [X0] : (~happy(X0) <=> (~humble(X0) & brave(X0))) [input p1]
19. ~kind(paul) & ~generous(paul) [input p18]
23. ~calm(paul) [input hypothesis]
28. ! [X0] : ((~happy(X0) & ~brave(X0)) | (calm(X0) | generous(X0))) [ennf transformation 1]
29. ! [X0] : ((~happy(X0) & ~brave(X0)) | calm(X0) | generous(X0)) [flattening 28]
39. ! [X0] : ((~happy(X0) | (humble(X0) | ~brave(X0))) & ((~humble(X0) & brave(X0)) | happy(X0))) [nnf transformation 2]
40. ! [X0] : ((~happy(X0) | humble(X0) | ~brave(X0)) & ((~humble(X0) & brave(X0)) | happy(X0))) [flattening 39]
70. ~brave(X0) | calm(X0) | generous(X0) [cnf transformation 29]
71. ~happy(X0) | calm(X0) | generous(X0) [cnf transformation 29]
72. happy(X0) | brave(X0) [cnf transformation 40]
123. ~generous(paul) [cnf transformation 19]
129. ~calm(paul) [cnf transformation 23]
300. calm(X0) | generous(X0) | brave(X0) [resolution 71,72]
323. calm(X0) | generous(X0) [subsumption resolution 300,70]
368. generous(paul) [resolution 323,129]
369. $false [subsumption resolution 368,123]
% SZS output end Proof for 1588735447832530229930116
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or tall is both not calm and not brave.
If someone is either not rich or not creative then someone is curious.
Everyone who is either funny or happy is funny or happy.
Everyone who is either quiet or calm is tall or not quiet and vice versa.
If alice is either not quiet or curious then someone is either not wise or funny and vice versa.
If fred is tall then fred is both brave and strong.
Everyone who is rich is either strong or old and vice versa.
Everyone who is kind or generous is both humble and wise.
Everyone who is either not funny or not brave is either not old or not rich and vice versa.
Everyone who is either not happy or rich is either not generous or quiet and vice versa.
If alice is kind or humble then someone is both not humble and brave.
Everyone who is both strong and calm is either not curious or rich and vice versa.
Everyone who is both strong and brave is brave and vice versa.
Someone is both tall and strong.
Someone is not calm.
Someone is both strong and curious.
Mary is not curious or old.
John is patient or quiet.
Someone is tall or not calm.
Someone is not generous or not funny. | Fred is happy. | neutral | (![X]:((kind(X)|tall(X))=>(~calm(X)&~brave(X))))&
((?[X]:((~rich(X)<~>~creative(X))))=>(?[X]:(curious(X))))&
(![X]:((funny(X)<~>happy(X))=>(funny(X)|happy(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(tall(X)|~quiet(X))))&
(((~quiet(alice)<~>curious(alice)))<=>(?[X]:((~wise(X)<~>funny(X)))))&
((tall(fred))=>((brave(fred)&strong(fred))))&
(![X]:(rich(X)<=>(strong(X)<~>old(X))))&
(![X]:((kind(X)|generous(X))=>(humble(X)&wise(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~old(X)<~>~rich(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~generous(X)<~>quiet(X))))&
(((kind(alice)|humble(alice)))=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((strong(X)&calm(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((strong(X)&brave(X))<=>brave(X)))&
(?[X]:((tall(X)&strong(X))))&
(?[X]:(~calm(X)))&
(?[X]:((strong(X)&curious(X))))&
((~curious(mary)|old(mary)))&
((patient(john)|quiet(john)))&
(?[X]:((tall(X)|~calm(X))))&
(?[X]:((~generous(X)|~funny(X)))) | happy(fred) | [] | null | 0 |
Everyone who is both not generous and strong is creative and vice versa. Everyone who is brave is either humble or not patient. Everyone who is either old or not funny is not curious. Everyone who is both not rich and not wise is not kind and vice versa. If john is not calm then fred is either happy or not generous and vice versa. Everyone who is not funny is not calm or not kind and vice versa. Everyone who is rich is not creative. If someone is patient then someone is tall and vice versa. If john is both calm and not happy then paul is not creative or not strong. Everyone who is not generous or not old is both quiet and not quiet. If someone is not curious then someone is kind or not rich. If john is tall or brave then someone is both not quiet and not tall and vice versa. If john is not humble then someone is both not brave and brave. If fred is not rich then someone is both brave and not old and vice versa. If susan is either wise or calm then someone is either kind or not humble. If someone is either not creative or not generous then fred is either funny or old and vice versa. Someone is not creative. Someone is not brave or old. Mary is brave. Someone is either not patient or not rich. Someone is either not humble or not quiet. Mary is either not old or not wise. | Susan is calm. | neutral | (![X]:((~generous(X)&strong(X))<=>creative(X)))&
(![X]:(brave(X)=>(humble(X)<~>~patient(X))))&
(![X]:((old(X)<~>~funny(X))=>~curious(X)))&
(![X]:((~rich(X)&~wise(X))<=>~kind(X)))&
((~calm(john))<=>((happy(fred)<~>~generous(fred))))&
(![X]:(~funny(X)<=>(~calm(X)|~kind(X))))&
(![X]:(rich(X)=>~creative(X)))&
((?[X]:(patient(X)))<=>(?[X]:(tall(X))))&
(((calm(john)&~happy(john)))=>((~creative(paul)|~strong(paul))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&~quiet(X))))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~rich(X)))))&
(((tall(john)|brave(john)))<=>(?[X]:((~quiet(X)&~tall(X)))))&
((~humble(john))=>(?[X]:((~brave(X)&brave(X)))))&
((~rich(fred))<=>(?[X]:((brave(X)&~old(X)))))&
(((wise(susan)<~>calm(susan)))=>(?[X]:((kind(X)<~>~humble(X)))))&
((?[X]:((~creative(X)<~>~generous(X))))<=>((funny(fred)<~>old(fred))))&
(?[X]:(~creative(X)))&
(?[X]:((~brave(X)|old(X))))&
(brave(mary))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:((~humble(X)<~>~quiet(X))))&
((~old(mary)<~>~wise(mary))) | calm(susan) | [] | null | 0 |
If someone is funny or patient then paul is old or curious. Everyone who is not quiet is either patient or not curious and vice versa. Everyone who is humble is rich or not quiet. Everyone who is strong or not wise is either funny or not happy. If john is not curious or patient then alice is not calm or not funny. If fred is not strong then someone is quiet and vice versa. If fred is not generous or not funny then lucy is not strong. If someone is not funny then someone is either not rich or strong and vice versa. Everyone who is either not curious or not old is happy. Everyone who is rich or creative is both not creative and not curious. Everyone who is either not rich or not wise is not happy or brave and vice versa. Everyone who is not rich is both brave and not rich and vice versa. Everyone who is creative or not curious is humble or brave. If susan is either patient or curious then john is both not old and not quiet and vice versa. Everyone who is either not calm or strong is generous or not kind and vice versa. Everyone who is curious or tall is either quiet or not rich. Fred is tall or not quiet. Susan is not humble. Fred is either kind or quiet. Paul is either happy or rich. Alice is humble. Susan is either old or not humble. Someone is kind. | Lucy is curious. | neutral | ((?[X]:((funny(X)|patient(X))))=>((old(paul)|curious(paul))))&
(![X]:(~quiet(X)<=>(patient(X)<~>~curious(X))))&
(![X]:(humble(X)=>(rich(X)|~quiet(X))))&
(![X]:((strong(X)|~wise(X))=>(funny(X)<~>~happy(X))))&
(((~curious(john)|patient(john)))=>((~calm(alice)|~funny(alice))))&
((~strong(fred))<=>(?[X]:(quiet(X))))&
(((~generous(fred)|~funny(fred)))=>(~strong(lucy)))&
((?[X]:(~funny(X)))<=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:((~curious(X)<~>~old(X))=>happy(X)))&
(![X]:((rich(X)|creative(X))=>(~creative(X)&~curious(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>(~happy(X)|brave(X))))&
(![X]:(~rich(X)<=>(brave(X)&~rich(X))))&
(![X]:((creative(X)|~curious(X))=>(humble(X)|brave(X))))&
(((patient(susan)<~>curious(susan)))<=>((~old(john)&~quiet(john))))&
(![X]:((~calm(X)<~>strong(X))<=>(generous(X)|~kind(X))))&
(![X]:((curious(X)|tall(X))=>(quiet(X)<~>~rich(X))))&
((tall(fred)|~quiet(fred)))&
(~humble(susan))&
((kind(fred)<~>quiet(fred)))&
((happy(paul)<~>rich(paul)))&
(humble(alice))&
((old(susan)<~>~humble(susan)))&
(?[X]:(kind(X))) | curious(lucy) | [] | null | 0 |
If someone is quiet or not funny then john is either generous or not old and vice versa.
Everyone who is not wise is either creative or not wise.
Everyone who is not wise is wise or funny and vice versa.
Everyone who is both happy and creative is not tall and vice versa.
If paul is not wise or not calm then lucy is either happy or funny and vice versa.
Everyone who is not kind or not strong is tall and vice versa.
If mary is either funny or humble then alice is both not calm and not quiet.
If someone is either strong or tall then someone is calm or not quiet and vice versa.
If lucy is either creative or curious then susan is either funny or not creative and vice versa.
If someone is kind then alice is strong.
Everyone who is both brave and humble is both curious and not creative and vice versa.
Everyone who is not funny is not patient or not quiet.
If someone is not old then someone is not wise.
If someone is quiet or brave then someone is both not old and old.
Everyone who is either strong or not quiet is not happy.
Everyone who is patient is both not wise and humble and vice versa.
Fred is old or creative.
Someone is either not rich or not creative.
Fred is either happy or not rich.
Paul is either not funny or kind.
Someone is not brave.
Fred is not creative.
Lucy is wise or not quiet. | Alice is curious. | contradiction | ((?[X]:((quiet(X)|~funny(X))))<=>((generous(john)<~>~old(john))))&
(![X]:(~wise(X)=>(creative(X)<~>~wise(X))))&
(![X]:(~wise(X)<=>(wise(X)|funny(X))))&
(![X]:((happy(X)&creative(X))<=>~tall(X)))&
(((~wise(paul)|~calm(paul)))<=>((happy(lucy)<~>funny(lucy))))&
(![X]:((~kind(X)|~strong(X))<=>tall(X)))&
(((funny(mary)<~>humble(mary)))=>((~calm(alice)&~quiet(alice))))&
((?[X]:((strong(X)<~>tall(X))))<=>(?[X]:((calm(X)|~quiet(X)))))&
(((creative(lucy)<~>curious(lucy)))<=>((funny(susan)<~>~creative(susan))))&
((?[X]:(kind(X)))=>(strong(alice)))&
(![X]:((brave(X)&humble(X))<=>(curious(X)&~creative(X))))&
(![X]:(~funny(X)=>(~patient(X)|~quiet(X))))&
((?[X]:(~old(X)))=>(?[X]:(~wise(X))))&
((?[X]:((quiet(X)|brave(X))))=>(?[X]:((~old(X)&old(X)))))&
(![X]:((strong(X)<~>~quiet(X))=>~happy(X)))&
(![X]:(patient(X)<=>(~wise(X)&humble(X))))&
((old(fred)|creative(fred)))&
(?[X]:((~rich(X)<~>~creative(X))))&
((happy(fred)<~>~rich(fred)))&
((~funny(paul)<~>kind(paul)))&
(?[X]:(~brave(X)))&
(~creative(fred))&
((wise(lucy)|~quiet(lucy))) | curious(alice) | [
"p1",
"p2",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2603763527365673833724065
% SZS output start Proof for 2603763527365673833724065
2. ! [X0] : (~wise(X0) => (creative(X0) <~> ~wise(X0))) [input p1]
3. ! [X0] : (~wise(X0) <=> (funny(X0) | wise(X0))) [input p2]
11. ! [X0] : ((humble(X0) & brave(X0)) <=> (~creative(X0) & curious(X0))) [input p10]
14. ? [X0] : (brave(X0) | quiet(X0)) => ? [X0] : (old(X0) & ~old(X0)) [input p13]
24. curious(alice) [input hypothesis]
27. ? [X0] : (brave(X0) | quiet(X0)) => ? [X1] : (old(X1) & ~old(X1)) [rectify 14]
29. ! [X0] : ((creative(X0) <~> ~wise(X0)) | wise(X0)) [ennf transformation 2]
35. ? [X1] : (old(X1) & ~old(X1)) | ! [X0] : (~brave(X0) & ~quiet(X0)) [ennf transformation 27]
43. ! [X0] : (((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | wise(X0)) [nnf transformation 29]
44. ! [X0] : ((~wise(X0) | (~funny(X0) & ~wise(X0))) & ((funny(X0) | wise(X0)) | wise(X0))) [nnf transformation 3]
45. ! [X0] : ((~wise(X0) | (~funny(X0) & ~wise(X0))) & (funny(X0) | wise(X0) | wise(X0))) [flattening 44]
59. ! [X0] : (((humble(X0) & brave(X0)) | (creative(X0) | ~curious(X0))) & ((~creative(X0) & curious(X0)) | (~humble(X0) | ~brave(X0)))) [nnf transformation 11]
60. ! [X0] : (((humble(X0) & brave(X0)) | creative(X0) | ~curious(X0)) & ((~creative(X0) & curious(X0)) | ~humble(X0) | ~brave(X0))) [flattening 59]
64. ? [X0] : (old(X0) & ~old(X0)) | ! [X1] : (~brave(X1) & ~quiet(X1)) [rectify 35]
65. ? [X0] : (old(X0) & ~old(X0)) => (old(sK4) & ~old(sK4)) [choice axiom]
66. (old(sK4) & ~old(sK4)) | ! [X1] : (~brave(X1) & ~quiet(X1)) [skolemisation 64,65]
82. wise(X0) | ~creative(X0) | wise(X0) [cnf transformation 43]
84. ~wise(X0) | ~wise(X0) [cnf transformation 45]
119. ~curious(X0) | creative(X0) | brave(X0) [cnf transformation 60]
124. ~old(sK4) | ~brave(X1) [cnf transformation 66]
126. old(sK4) | ~brave(X1) [cnf transformation 66]
140. curious(alice) [cnf transformation 24]
142. ~wise(X0) [duplicate literal removal 84]
143. ~creative(X0) | wise(X0) [duplicate literal removal 82]
279. 28 <=> ! [X1] : ~brave(X1) [avatar definition]
280. ~brave(X1) <- (28) [avatar component clause 279]
282. 29 <=> old(sK4) [avatar definition]
285. 28 | 29 [avatar split clause 126,282,279]
287. 28 | ~29 [avatar split clause 124,282,279]
381. creative(alice) | brave(alice) [resolution 119,140]
382. creative(alice) <- (28) [subsumption resolution 381,280]
387. wise(alice) <- (28) [resolution 382,143]
388. $false <- (28) [subsumption resolution 387,142]
389. ~28 [avatar contradiction clause 388]
390. $false [avatar sat refutation 285,287,389]
% SZS output end Proof for 2603763527365673833724065
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not rich is both happy and funny and vice versa.
Everyone who is either strong or not old is both wise and not happy and vice versa.
If someone is brave or not brave then someone is both happy and kind.
If john is both calm and not curious then someone is not calm or not creative and vice versa.
Everyone who is both wise and patient is either not wise or not tall and vice versa.
Everyone who is not humble or generous is both not funny and funny.
Everyone who is not humble is both kind and not old.
If lucy is not strong or brave then mary is quiet or not kind and vice versa.
Everyone who is generous is patient or wise and vice versa.
Everyone who is not happy or not patient is either old or tall and vice versa.
Everyone who is not rich is either not calm or not happy and vice versa.
If paul is both not creative and not calm then susan is both funny and not happy and vice versa.
If lucy is old then someone is both not creative and not wise and vice versa.
Everyone who is calm or old is wise or old.
If fred is not creative then someone is either strong or not humble and vice versa.
Susan is both brave and not rich.
Someone is creative.
Alice is curious or not funny.
Someone is either curious or creative.
Someone is not creative.
Susan is not generous. | Lucy is patient. | contradiction | (![X]:((~patient(X)|~rich(X))<=>(happy(X)&funny(X))))&
(![X]:((strong(X)<~>~old(X))<=>(wise(X)&~happy(X))))&
((?[X]:((brave(X)|~brave(X))))=>(?[X]:((happy(X)&kind(X)))))&
(((calm(john)&~curious(john)))<=>(?[X]:((~calm(X)|~creative(X)))))&
(![X]:((wise(X)&patient(X))<=>(~wise(X)<~>~tall(X))))&
(![X]:((~humble(X)|generous(X))=>(~funny(X)&funny(X))))&
(![X]:(~humble(X)=>(kind(X)&~old(X))))&
(((~strong(lucy)|brave(lucy)))<=>((quiet(mary)|~kind(mary))))&
(![X]:(generous(X)<=>(patient(X)|wise(X))))&
(![X]:((~happy(X)|~patient(X))<=>(old(X)<~>tall(X))))&
(![X]:(~rich(X)<=>(~calm(X)<~>~happy(X))))&
(((~creative(paul)&~calm(paul)))<=>((funny(susan)&~happy(susan))))&
((old(lucy))<=>(?[X]:((~creative(X)&~wise(X)))))&
(![X]:((calm(X)|old(X))=>(wise(X)|old(X))))&
((~creative(fred))<=>(?[X]:((strong(X)<~>~humble(X)))))&
((brave(susan)&~rich(susan)))&
(?[X]:(creative(X)))&
((curious(alice)|~funny(alice)))&
(?[X]:((curious(X)<~>creative(X))))&
(?[X]:(~creative(X)))&
(~generous(susan)) | patient(lucy) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 949061198156397446495753
% SZS output start Proof for 949061198156397446495753
6. ! [X0] : ((generous(X0) | ~humble(X0)) => (funny(X0) & ~funny(X0))) [input p5]
9. ! [X0] : (generous(X0) <=> (wise(X0) | patient(X0))) [input p8]
22. patient(lucy) [input hypothesis]
24. ! [X0] : ((wise(X0) | patient(X0)) => generous(X0)) [unused predicate definition removal 9]
26. ! [X0] : ((funny(X0) & ~funny(X0)) | (~generous(X0) & humble(X0))) [ennf transformation 6]
28. ! [X0] : (generous(X0) | (~wise(X0) & ~patient(X0))) [ennf transformation 24]
94. ~funny(X0) | ~generous(X0) [cnf transformation 26]
96. funny(X0) | ~generous(X0) [cnf transformation 26]
103. generous(X0) | ~patient(X0) [cnf transformation 28]
136. patient(lucy) [cnf transformation 22]
185. ~generous(X0) [subsumption resolution 94,96]
208. ~patient(X0) [subsumption resolution 103,185]
279. $false [subsumption resolution 136,208]
% SZS output end Proof for 949061198156397446495753
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then someone is not tall or not generous and vice versa. Everyone who is generous is both funny and rich. Everyone who is either humble or old is both generous and funny. Everyone who is humble is calm and vice versa. Everyone who is humble is generous and vice versa. If someone is either happy or not humble then someone is either patient or not creative. Everyone who is both not strong and not creative is not brave or tall and vice versa. Everyone who is calm or not quiet is generous or patient and vice versa. Everyone who is not strong is either not kind or funny and vice versa. Everyone who is not happy or brave is either not brave or not creative and vice versa. If alice is old then paul is both not happy and generous. Everyone who is either humble or strong is both curious and not creative. Everyone who is both not strong and not creative is either brave or not calm and vice versa. Everyone who is both not old and tall is patient. Everyone who is old or tall is both not strong and happy. Susan is either not creative or not old. Someone is quiet or not brave. Fred is not wise or not old. Someone is not calm or old. Someone is either patient or rich. Susan is rich or not generous. | Susan is curious. | entailment | ((?[X]:(creative(X)))<=>(?[X]:((~tall(X)|~generous(X)))))&
(![X]:(generous(X)=>(funny(X)&rich(X))))&
(![X]:((humble(X)<~>old(X))=>(generous(X)&funny(X))))&
(![X]:(humble(X)<=>calm(X)))&
(![X]:(humble(X)<=>generous(X)))&
((?[X]:((happy(X)<~>~humble(X))))=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((~strong(X)&~creative(X))<=>(~brave(X)|tall(X))))&
(![X]:((calm(X)|~quiet(X))<=>(generous(X)|patient(X))))&
(![X]:(~strong(X)<=>(~kind(X)<~>funny(X))))&
(![X]:((~happy(X)|brave(X))<=>(~brave(X)<~>~creative(X))))&
((old(alice))=>((~happy(paul)&generous(paul))))&
(![X]:((humble(X)<~>strong(X))=>(curious(X)&~creative(X))))&
(![X]:((~strong(X)&~creative(X))<=>(brave(X)<~>~calm(X))))&
(![X]:((~old(X)&tall(X))=>patient(X)))&
(![X]:((old(X)|tall(X))=>(~strong(X)&happy(X))))&
((~creative(susan)<~>~old(susan)))&
(?[X]:((quiet(X)|~brave(X))))&
((~wise(fred)|~old(fred)))&
(?[X]:((~calm(X)|old(X))))&
(?[X]:((patient(X)<~>rich(X))))&
((rich(susan)|~generous(susan))) | curious(susan) | [
"p0",
"p3",
"p4",
"p6",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 9010293761004548722255846
% SZS output start Proof for 9010293761004548722255846
1. ? [X0] : creative(X0) <=> ? [X0] : (~generous(X0) | ~tall(X0)) [input p0]
4. ! [X0] : (humble(X0) <=> calm(X0)) [input p3]
5. ! [X0] : (humble(X0) <=> generous(X0)) [input p4]
7. ! [X0] : ((~creative(X0) & ~strong(X0)) <=> (tall(X0) | ~brave(X0))) [input p6]
10. ! [X0] : ((brave(X0) | ~happy(X0)) <=> (~brave(X0) <~> ~creative(X0))) [input p9]
12. ! [X0] : ((humble(X0) <~> strong(X0)) => (~creative(X0) & curious(X0))) [input p11]
13. ! [X0] : ((~creative(X0) & ~strong(X0)) <=> (brave(X0) <~> ~calm(X0))) [input p12]
22. ~curious(susan) [input hypothesis]
23. ? [X0] : creative(X0) <=> ? [X1] : (~generous(X1) | ~tall(X1)) [rectify 1]
30. ! [X0] : ((~creative(X0) & curious(X0)) | (humble(X0) <=> strong(X0))) [ennf transformation 12]
34. (? [X0] : creative(X0) | ! [X1] : (generous(X1) & tall(X1))) & (? [X1] : (~generous(X1) | ~tall(X1)) | ! [X0] : ~creative(X0)) [nnf transformation 23]
35. (? [X0] : creative(X0) | ! [X1] : (generous(X1) & tall(X1))) & (? [X2] : (~generous(X2) | ~tall(X2)) | ! [X3] : ~creative(X3)) [rectify 34]
36. ? [X0] : creative(X0) => creative(sK0) [choice axiom]
37. ? [X2] : (~generous(X2) | ~tall(X2)) => (~generous(sK1) | ~tall(sK1)) [choice axiom]
38. (creative(sK0) | ! [X1] : (generous(X1) & tall(X1))) & ((~generous(sK1) | ~tall(sK1)) | ! [X3] : ~creative(X3)) [skolemisation 35,37,36]
40. ! [X0] : ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0))) [nnf transformation 4]
41. ! [X0] : ((humble(X0) | ~generous(X0)) & (generous(X0) | ~humble(X0))) [nnf transformation 5]
46. ! [X0] : (((~creative(X0) & ~strong(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (creative(X0) | strong(X0)))) [nnf transformation 7]
47. ! [X0] : (((~creative(X0) & ~strong(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | creative(X0) | strong(X0))) [flattening 46]
51. ! [X0] : (((brave(X0) | ~happy(X0)) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~brave(X0) & happy(X0)))) [nnf transformation 10]
52. ! [X0] : ((brave(X0) | ~happy(X0) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~brave(X0) & happy(X0)))) [flattening 51]
53. ! [X0] : ((~creative(X0) & curious(X0)) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0)))) [nnf transformation 30]
54. ! [X0] : (((~creative(X0) & ~strong(X0)) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0)))) & (((calm(X0) | ~brave(X0)) & (~calm(X0) | brave(X0))) | (creative(X0) | strong(X0)))) [nnf transformation 13]
55. ! [X0] : (((~creative(X0) & ~strong(X0)) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0)))) & (((calm(X0) | ~brave(X0)) & (~calm(X0) | brave(X0))) | creative(X0) | strong(X0))) [flattening 54]
66. creative(sK0) | generous(X1) [cnf transformation 38]
73. ~humble(X0) | calm(X0) [cnf transformation 40]
76. ~generous(X0) | humble(X0) [cnf transformation 41]
82. ~strong(X0) | brave(X0) [cnf transformation 47]
84. ~creative(X0) | brave(X0) [cnf transformation 47]
95. ~creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 52]
102. ~humble(X0) | strong(X0) | curious(X0) [cnf transformation 53]
108. ~strong(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 55]
124. ~curious(susan) [cnf transformation 22]
125. ~creative(X0) | ~brave(X0) [duplicate literal removal 95]
128. 1 <=> ! [X1] : generous(X1) [avatar definition]
129. generous(X1) <- (1) [avatar component clause 128]
131. 2 <=> creative(sK0) [avatar definition]
133. creative(sK0) <- (2) [avatar component clause 131]
134. 1 | 2 [avatar split clause 66,131,128]
140. 4 <=> ! [X3] : ~creative(X3) [avatar definition]
141. ~creative(X3) <- (4) [avatar component clause 140]
170. ~creative(X0) [subsumption resolution 125,84]
171. 4 [avatar split clause 170,140]
188. ~strong(X0) | ~calm(X0) [subsumption resolution 108,82]
229. $false <- (2, 4) [subsumption resolution 133,141]
230. ~2 | ~4 [avatar contradiction clause 229]
237. humble(X0) <- (1) [resolution 76,129]
239. calm(X1) <- (1) [resolution 237,73]
267. curious(X0) | strong(X0) <- (1) [resolution 102,237]
268. strong(susan) <- (1) [resolution 267,124]
271. ~calm(susan) <- (1) [resolution 268,188]
275. $false <- (1) [subsumption resolution 271,239]
276. ~1 [avatar contradiction clause 275]
281. $false [avatar sat refutation 134,171,230,276]
% SZS output end Proof for 9010293761004548722255846
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is both not wise and wise and vice versa.
Everyone who is either happy or quiet is either not creative or not kind.
If mary is either old or calm then john is not creative and vice versa.
If someone is either tall or curious then john is either not rich or strong.
If someone is humble then someone is calm and vice versa.
Everyone who is either not tall or happy is both not tall and generous and vice versa.
If someone is not quiet or calm then someone is either not rich or curious.
If paul is both not happy and not creative then paul is both humble and not kind.
If paul is brave then someone is both not tall and funny and vice versa.
If someone is brave or calm then someone is old or patient and vice versa.
If someone is quiet then someone is both wise and happy.
If susan is wise then alice is brave and vice versa.
If someone is brave then paul is not happy and vice versa.
If john is both not tall and tall then someone is either wise or not old.
Everyone who is either old or rich is creative and vice versa.
If someone is rich then someone is calm or not strong.
Susan is curious.
Someone is curious.
John is not funny.
Someone is not strong or not rich.
Someone is not kind or creative.
Mary is either not patient or not calm.
Alice is either creative or wise.
Alice is both patient and not funny. | Susan is quiet. | contradiction | (![X]:(~generous(X)<=>(~wise(X)&wise(X))))&
(![X]:((happy(X)<~>quiet(X))=>(~creative(X)<~>~kind(X))))&
(((old(mary)<~>calm(mary)))<=>(~creative(john)))&
((?[X]:((tall(X)<~>curious(X))))=>((~rich(john)<~>strong(john))))&
((?[X]:(humble(X)))<=>(?[X]:(calm(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(~tall(X)&generous(X))))&
((?[X]:((~quiet(X)|calm(X))))=>(?[X]:((~rich(X)<~>curious(X)))))&
(((~happy(paul)&~creative(paul)))=>((humble(paul)&~kind(paul))))&
((brave(paul))<=>(?[X]:((~tall(X)&funny(X)))))&
((?[X]:((brave(X)|calm(X))))<=>(?[X]:((old(X)|patient(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((wise(X)&happy(X)))))&
((wise(susan))<=>(brave(alice)))&
((?[X]:(brave(X)))<=>(~happy(paul)))&
(((~tall(john)&tall(john)))=>(?[X]:((wise(X)<~>~old(X)))))&
(![X]:((old(X)<~>rich(X))<=>creative(X)))&
((?[X]:(rich(X)))=>(?[X]:((calm(X)|~strong(X)))))&
(curious(susan))&
(?[X]:(curious(X)))&
(~funny(john))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((~kind(X)|creative(X))))&
((~patient(mary)<~>~calm(mary)))&
((creative(alice)<~>wise(alice)))&
((patient(alice)&~funny(alice))) | quiet(susan) | [
"p0",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3797075026535647309751897
% SZS output start Proof for 3797075026535647309751897
1. ! [X0] : (~generous(X0) <=> (wise(X0) & ~wise(X0))) [input p0]
6. ! [X0] : ((~tall(X0) <~> happy(X0)) <=> (generous(X0) & ~tall(X0))) [input p5]
11. ? [X0] : quiet(X0) => ? [X0] : (happy(X0) & wise(X0)) [input p10]
25. quiet(susan) [input hypothesis]
29. ? [X0] : quiet(X0) => ? [X1] : (happy(X1) & wise(X1)) [rectify 11]
36. ? [X1] : (happy(X1) & wise(X1)) | ! [X0] : ~quiet(X0) [ennf transformation 29]
40. ! [X0] : ((~generous(X0) | (~wise(X0) | wise(X0))) & ((wise(X0) & ~wise(X0)) | generous(X0))) [nnf transformation 1]
41. ! [X0] : ((~generous(X0) | ~wise(X0) | wise(X0)) & ((wise(X0) & ~wise(X0)) | generous(X0))) [flattening 40]
50. ! [X0] : ((((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0))))) [nnf transformation 6]
51. ! [X0] : ((((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0))))) [flattening 50]
65. ? [X0] : (happy(X0) & wise(X0)) | ! [X1] : ~quiet(X1) [rectify 36]
66. ? [X0] : (happy(X0) & wise(X0)) => (happy(sK6) & wise(sK6)) [choice axiom]
67. (happy(sK6) & wise(sK6)) | ! [X1] : ~quiet(X1) [skolemisation 65,66]
88. ~wise(X0) | generous(X0) [cnf transformation 41]
89. wise(X0) | generous(X0) [cnf transformation 41]
106. ~tall(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 51]
110. ~happy(X0) | tall(X0) | ~generous(X0) | tall(X0) [cnf transformation 51]
125. happy(sK6) | ~quiet(X1) [cnf transformation 67]
148. quiet(susan) [cnf transformation 25]
149. ~tall(X0) | ~happy(X0) [duplicate literal removal 106]
150. ~happy(X0) | tall(X0) | ~generous(X0) [duplicate literal removal 110]
151. generous(X0) [subsumption resolution 88,89]
202. ~happy(X0) | tall(X0) [subsumption resolution 150,151]
203. ~happy(X0) [subsumption resolution 149,202]
282. ~quiet(X1) [subsumption resolution 125,203]
340. $false [subsumption resolution 148,282]
% SZS output end Proof for 3797075026535647309751897
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or humble is not curious.
If someone is not curious or humble then someone is either kind or not wise.
Everyone who is funny or tall is both strong and not happy and vice versa.
If john is both not brave and not generous then mary is both funny and not curious.
If someone is not humble then lucy is either strong or creative.
If someone is either strong or not funny then someone is strong or not wise and vice versa.
Everyone who is either not kind or not tall is not patient or funny.
Everyone who is both patient and not tall is both tall and patient and vice versa.
Everyone who is either not tall or not old is patient and vice versa.
If someone is either not kind or not funny then lucy is not creative.
If someone is kind then alice is not quiet or curious.
Everyone who is either not calm or generous is patient or not calm and vice versa.
If paul is either generous or not strong then mary is not patient and vice versa.
If someone is both quiet and not humble then susan is strong and vice versa.
If someone is tall then lucy is not brave and vice versa.
Everyone who is either not wise or not brave is patient or curious and vice versa.
Someone is not calm or not tall.
Lucy is humble or not calm.
Lucy is quiet.
Someone is not funny or patient.
Paul is either happy or humble.
Someone is not kind or not quiet.
Fred is quiet or not humble. | Mary is not patient. | entailment | (![X]:((~old(X)|humble(X))=>~curious(X)))&
((?[X]:((~curious(X)|humble(X))))=>(?[X]:((kind(X)<~>~wise(X)))))&
(![X]:((funny(X)|tall(X))<=>(strong(X)&~happy(X))))&
(((~brave(john)&~generous(john)))=>((funny(mary)&~curious(mary))))&
((?[X]:(~humble(X)))=>((strong(lucy)<~>creative(lucy))))&
((?[X]:((strong(X)<~>~funny(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
(![X]:((~kind(X)<~>~tall(X))=>(~patient(X)|funny(X))))&
(![X]:((patient(X)&~tall(X))<=>(tall(X)&patient(X))))&
(![X]:((~tall(X)<~>~old(X))<=>patient(X)))&
((?[X]:((~kind(X)<~>~funny(X))))=>(~creative(lucy)))&
((?[X]:(kind(X)))=>((~quiet(alice)|curious(alice))))&
(![X]:((~calm(X)<~>generous(X))<=>(patient(X)|~calm(X))))&
(((generous(paul)<~>~strong(paul)))<=>(~patient(mary)))&
((?[X]:((quiet(X)&~humble(X))))<=>(strong(susan)))&
((?[X]:(tall(X)))<=>(~brave(lucy)))&
(![X]:((~wise(X)<~>~brave(X))<=>(patient(X)|curious(X))))&
(?[X]:((~calm(X)|~tall(X))))&
((humble(lucy)|~calm(lucy)))&
(quiet(lucy))&
(?[X]:((~funny(X)|patient(X))))&
((happy(paul)<~>humble(paul)))&
(?[X]:((~kind(X)|~quiet(X))))&
((quiet(fred)|~humble(fred))) | ~patient(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7661002452062218206200045
% SZS output start Proof for 7661002452062218206200045
8. ! [X0] : ((~tall(X0) & patient(X0)) <=> (patient(X0) & tall(X0))) [input p7]
24. patient(mary) [input hypothesis]
50. ! [X0] : (((~tall(X0) & patient(X0)) | (~patient(X0) | ~tall(X0))) & ((patient(X0) & tall(X0)) | (tall(X0) | ~patient(X0)))) [nnf transformation 8]
51. ! [X0] : (((~tall(X0) & patient(X0)) | ~patient(X0) | ~tall(X0)) & ((patient(X0) & tall(X0)) | tall(X0) | ~patient(X0))) [flattening 50]
97. tall(X0) | tall(X0) | ~patient(X0) [cnf transformation 51]
100. ~tall(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 51]
137. patient(mary) [cnf transformation 24]
140. tall(X0) | ~patient(X0) [duplicate literal removal 97]
141. ~tall(X0) | ~patient(X0) [duplicate literal removal 100]
225. ~patient(X0) [subsumption resolution 140,141]
332. $false [subsumption resolution 137,225]
% SZS output end Proof for 7661002452062218206200045
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and old is strong. Everyone who is funny or not kind is either happy or not tall and vice versa. If someone is happy or strong then mary is not generous. Everyone who is not generous is either brave or not quiet and vice versa. If someone is either strong or happy then lucy is tall or generous. Everyone who is both rich and not kind is creative and vice versa. Everyone who is not humble is rich and vice versa. Everyone who is not generous is both not humble and old and vice versa. If someone is both not tall and humble then someone is either not funny or not strong. If someone is either not patient or quiet then john is either kind or calm. Everyone who is funny is old. If someone is either happy or not brave then someone is either generous or not quiet and vice versa. If lucy is either not rich or old then someone is generous. Everyone who is not brave or not calm is both not humble and curious and vice versa. If someone is both tall and curious then fred is both strong and not happy and vice versa. Everyone who is both calm and not patient is happy or rich and vice versa. Someone is not old. Someone is not tall or calm. Mary is both kind and not creative. Fred is either brave or tall. Mary is either old or not humble. Alice is patient or generous. Paul is not old. | Fred is tall. | contradiction | (![X]:((~happy(X)&old(X))=>strong(X)))&
(![X]:((funny(X)|~kind(X))<=>(happy(X)<~>~tall(X))))&
((?[X]:((happy(X)|strong(X))))=>(~generous(mary)))&
(![X]:(~generous(X)<=>(brave(X)<~>~quiet(X))))&
((?[X]:((strong(X)<~>happy(X))))=>((tall(lucy)|generous(lucy))))&
(![X]:((rich(X)&~kind(X))<=>creative(X)))&
(![X]:(~humble(X)<=>rich(X)))&
(![X]:(~generous(X)<=>(~humble(X)&old(X))))&
((?[X]:((~tall(X)&humble(X))))=>(?[X]:((~funny(X)<~>~strong(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((kind(john)<~>calm(john))))&
(![X]:(funny(X)=>old(X)))&
((?[X]:((happy(X)<~>~brave(X))))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
(((~rich(lucy)<~>old(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~humble(X)&curious(X))))&
((?[X]:((tall(X)&curious(X))))<=>((strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~patient(X))<=>(happy(X)|rich(X))))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)|calm(X))))&
((kind(mary)&~creative(mary)))&
((brave(fred)<~>tall(fred)))&
((old(mary)<~>~humble(mary)))&
((patient(alice)|generous(alice)))&
(~old(paul)) | tall(fred) | [
"p2",
"p7",
"p13",
"p14",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 277383277183181826124417
% SZS output start Proof for 277383277183181826124417
3. ? [X0] : (strong(X0) | happy(X0)) => ~generous(mary) [input p2]
8. ! [X0] : (~generous(X0) <=> (old(X0) & ~humble(X0))) [input p7]
14. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> (curious(X0) & ~humble(X0))) [input p13]
15. ? [X0] : (curious(X0) & tall(X0)) <=> (~happy(fred) & strong(fred)) [input p14]
20. brave(fred) <~> tall(fred) [input p19]
21. old(mary) <~> ~humble(mary) [input p20]
24. tall(fred) [input hypothesis]
30. ~generous(mary) | ! [X0] : (~strong(X0) & ~happy(X0)) [ennf transformation 3]
44. ! [X0] : ((~generous(X0) | (~old(X0) | humble(X0))) & ((old(X0) & ~humble(X0)) | generous(X0))) [nnf transformation 8]
45. ! [X0] : ((~generous(X0) | ~old(X0) | humble(X0)) & ((old(X0) & ~humble(X0)) | generous(X0))) [flattening 44]
59. ! [X0] : (((~calm(X0) | ~brave(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [nnf transformation 14]
60. ! [X0] : ((~calm(X0) | ~brave(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [flattening 59]
61. (? [X0] : (curious(X0) & tall(X0)) | (happy(fred) | ~strong(fred))) & ((~happy(fred) & strong(fred)) | ! [X0] : (~curious(X0) | ~tall(X0))) [nnf transformation 15]
62. (? [X0] : (curious(X0) & tall(X0)) | happy(fred) | ~strong(fred)) & ((~happy(fred) & strong(fred)) | ! [X0] : (~curious(X0) | ~tall(X0))) [flattening 61]
63. (? [X0] : (curious(X0) & tall(X0)) | happy(fred) | ~strong(fred)) & ((~happy(fred) & strong(fred)) | ! [X1] : (~curious(X1) | ~tall(X1))) [rectify 62]
64. ? [X0] : (curious(X0) & tall(X0)) => (curious(sK4) & tall(sK4)) [choice axiom]
65. ((curious(sK4) & tall(sK4)) | happy(fred) | ~strong(fred)) & ((~happy(fred) & strong(fred)) | ! [X1] : (~curious(X1) | ~tall(X1))) [skolemisation 63,64]
72. (~tall(fred) | ~brave(fred)) & (tall(fred) | brave(fred)) [nnf transformation 20]
73. (humble(mary) | ~old(mary)) & (~humble(mary) | old(mary)) [nnf transformation 21]
82. ~generous(mary) | ~strong(X0) [cnf transformation 30]
92. ~humble(X0) | generous(X0) [cnf transformation 45]
93. generous(X0) | old(X0) [cnf transformation 45]
114. curious(X0) | brave(X0) [cnf transformation 60]
117. strong(fred) | ~curious(X1) | ~tall(X1) [cnf transformation 65]
131. ~tall(fred) | ~brave(fred) [cnf transformation 72]
133. humble(mary) | ~old(mary) [cnf transformation 73]
136. tall(fred) [cnf transformation 24]
138. 1 <=> ! [X0] : ~strong(X0) [avatar definition]
139. ~strong(X0) <- (1) [avatar component clause 138]
141. 2 <=> generous(mary) [avatar definition]
143. ~generous(mary) <- (~2) [avatar component clause 141]
144. 1 | ~2 [avatar split clause 82,141,138]
247. 26 <=> strong(fred) [avatar definition]
248. strong(fred) <- (26) [avatar component clause 247]
265. 30 <=> ! [X1] : (~curious(X1) | ~tall(X1)) [avatar definition]
266. ~curious(X1) | ~tall(X1) <- (30) [avatar component clause 265]
268. 30 | 26 [avatar split clause 117,247,265]
279. 33 <=> brave(fred) [avatar definition]
281. ~brave(fred) <- (~33) [avatar component clause 279]
283. 34 <=> tall(fred) [avatar definition]
284. tall(fred) <- (34) [avatar component clause 283]
286. ~33 | ~34 [avatar split clause 131,283,279]
289. 35 <=> old(mary) [avatar definition]
293. 36 <=> humble(mary) [avatar definition]
295. humble(mary) <- (36) [avatar component clause 293]
296. ~35 | 36 [avatar split clause 133,293,289]
307. 34 [avatar split clause 136,283]
311. old(mary) <- (~2) [resolution 93,143]
315. 35 | 2 [avatar split clause 311,141,289]
316. generous(mary) <- (36) [resolution 295,92]
320. 2 | ~36 [avatar split clause 316,293,141]
321. $false <- (1, 26) [resolution 139,248]
322. ~1 | ~26 [avatar contradiction clause 321]
336. ~tall(X1) | brave(X1) <- (30) [resolution 266,114]
487. brave(fred) <- (30, 34) [resolution 336,284]
490. $false <- (30, ~33, 34) [subsumption resolution 487,281]
491. ~30 | 33 | ~34 [avatar contradiction clause 490]
492. $false [avatar sat refutation 144,268,286,296,307,315,320,322,491]
% SZS output end Proof for 277383277183181826124417
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If lucy is tall then someone is not calm or not old and vice versa.
If john is either not tall or rich then lucy is old or patient and vice versa.
Everyone who is patient is both humble and rich.
Everyone who is both quiet and not generous is both not rich and curious.
Everyone who is funny is either not happy or not patient.
Everyone who is both calm and not quiet is either not humble or not wise.
If someone is either generous or curious then someone is humble and vice versa.
Everyone who is either tall or kind is wise.
If someone is not calm then john is either funny or not humble.
Everyone who is both not strong and kind is both not humble and brave and vice versa.
Everyone who is creative is generous or not strong and vice versa.
If john is calm then lucy is tall and vice versa.
Everyone who is not humble is either not humble or creative and vice versa.
Everyone who is either not rich or not quiet is creative and vice versa.
If someone is patient or not creative then someone is either old or generous and vice versa.
Everyone who is not brave is strong or not tall and vice versa.
Lucy is tall.
Paul is either wise or not humble.
Someone is either quiet or not rich.
Mary is both not creative and wise.
Lucy is both strong and not rich.
Someone is not brave or not generous. | Lucy is generous. | contradiction | ((tall(lucy))<=>(?[X]:((~calm(X)|~old(X)))))&
(((~tall(john)<~>rich(john)))<=>((old(lucy)|patient(lucy))))&
(![X]:(patient(X)=>(humble(X)&rich(X))))&
(![X]:((quiet(X)&~generous(X))=>(~rich(X)&curious(X))))&
(![X]:(funny(X)=>(~happy(X)<~>~patient(X))))&
(![X]:((calm(X)&~quiet(X))=>(~humble(X)<~>~wise(X))))&
((?[X]:((generous(X)<~>curious(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)<~>kind(X))=>wise(X)))&
((?[X]:(~calm(X)))=>((funny(john)<~>~humble(john))))&
(![X]:((~strong(X)&kind(X))<=>(~humble(X)&brave(X))))&
(![X]:(creative(X)<=>(generous(X)|~strong(X))))&
((calm(john))<=>(tall(lucy)))&
(![X]:(~humble(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>creative(X)))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:(~brave(X)<=>(strong(X)|~tall(X))))&
(tall(lucy))&
((wise(paul)<~>~humble(paul)))&
(?[X]:((quiet(X)<~>~rich(X))))&
((~creative(mary)&wise(mary)))&
((strong(lucy)&~rich(lucy)))&
(?[X]:((~brave(X)|~generous(X)))) | generous(lucy) | [
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6029683247648960261627550
% SZS output start Proof for 6029683247648960261627550
11. ! [X0] : (creative(X0) <=> (~strong(X0) | generous(X0))) [input p10]
13. ! [X0] : (~humble(X0) <=> (~humble(X0) <~> creative(X0))) [input p12]
23. generous(lucy) [input hypothesis]
51. ! [X0] : ((creative(X0) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ~creative(X0))) [nnf transformation 11]
52. ! [X0] : ((creative(X0) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ~creative(X0))) [flattening 51]
54. ! [X0] : ((~humble(X0) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0)))) & (((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | humble(X0))) [nnf transformation 13]
99. ~generous(X0) | creative(X0) [cnf transformation 52]
104. ~creative(X0) | humble(X0) | humble(X0) [cnf transformation 54]
106. ~humble(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 54]
130. generous(lucy) [cnf transformation 23]
131. ~creative(X0) | humble(X0) [duplicate literal removal 104]
132. ~humble(X0) | ~creative(X0) [duplicate literal removal 106]
217. ~creative(X0) [subsumption resolution 131,132]
263. creative(lucy) [resolution 99,130]
265. $false [subsumption resolution 263,217]
% SZS output end Proof for 6029683247648960261627550
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If john is both not kind and not rich then mary is either creative or happy and vice versa.
Everyone who is not happy is kind or funny.
Everyone who is patient is either not old or not calm and vice versa.
Everyone who is either not quiet or happy is not patient or wise.
Everyone who is funny or not brave is both wise and not generous.
If alice is both not creative and old then alice is calm.
If lucy is either quiet or not kind then someone is not strong.
If john is not curious then someone is both kind and not patient and vice versa.
Everyone who is both not quiet and not humble is both not humble and curious and vice versa.
If paul is strong or not old then someone is either not creative or not brave.
Everyone who is both old and happy is both not wise and curious and vice versa.
Everyone who is both not curious and humble is either tall or humble.
Everyone who is humble or not brave is both patient and quiet.
If fred is both not funny and kind then mary is not creative and vice versa.
Everyone who is either curious or tall is not patient.
Everyone who is either not old or not generous is either not old or not humble.
Mary is not generous or not kind.
John is creative.
Susan is both generous and curious.
Paul is either not old or kind.
Fred is both generous and patient.
Susan is old or not generous.
Alice is both funny and old. | Alice is not old. | contradiction | (((~kind(john)&~rich(john)))<=>((creative(mary)<~>happy(mary))))&
(![X]:(~happy(X)=>(kind(X)|funny(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~calm(X))))&
(![X]:((~quiet(X)<~>happy(X))=>(~patient(X)|wise(X))))&
(![X]:((funny(X)|~brave(X))=>(wise(X)&~generous(X))))&
(((~creative(alice)&old(alice)))=>(calm(alice)))&
(((quiet(lucy)<~>~kind(lucy)))=>(?[X]:(~strong(X))))&
((~curious(john))<=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(~humble(X)&curious(X))))&
(((strong(paul)|~old(paul)))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((old(X)&happy(X))<=>(~wise(X)&curious(X))))&
(![X]:((~curious(X)&humble(X))=>(tall(X)<~>humble(X))))&
(![X]:((humble(X)|~brave(X))=>(patient(X)&quiet(X))))&
(((~funny(fred)&kind(fred)))<=>(~creative(mary)))&
(![X]:((curious(X)<~>tall(X))=>~patient(X)))&
(![X]:((~old(X)<~>~generous(X))=>(~old(X)<~>~humble(X))))&
((~generous(mary)|~kind(mary)))&
(creative(john))&
((generous(susan)&curious(susan)))&
((~old(paul)<~>kind(paul)))&
((generous(fred)&patient(fred)))&
((old(susan)|~generous(susan)))&
((funny(alice)&old(alice))) | ~old(alice) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 519886159153758724442814
% SZS output start Proof for 519886159153758724442814
23. old(alice) & funny(alice) [input p22]
24. ~old(alice) [input hypothesis]
117. old(alice) [cnf transformation 23]
118. ~old(alice) [cnf transformation 24]
149. 6 <=> old(alice) [avatar definition]
216. 6 [avatar split clause 117,149]
217. ~6 [avatar split clause 118,149]
218. $false [avatar sat refutation 216,217]
% SZS output end Proof for 519886159153758724442814
% ------------------------------
% 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and quiet then lucy is both humble and not creative.
If lucy is either tall or rich then fred is kind or tall.
If lucy is not quiet then john is both not happy and not old.
If someone is happy then someone is both kind and not kind and vice versa.
If susan is both old and not creative then someone is not brave and vice versa.
Everyone who is curious is either curious or quiet.
If john is either funny or not kind then someone is not funny or brave.
Everyone who is curious is not wise or not creative and vice versa.
If mary is not patient or not curious then someone is both creative and not patient.
If someone is both not rich and quiet then john is old and vice versa.
If someone is not patient or funny then john is not humble or wise.
If john is rich then mary is both generous and humble.
If someone is either curious or not old then someone is not wise and vice versa.
If alice is either not strong or strong then fred is both not happy and rich and vice versa.
Everyone who is both not generous and funny is both creative and not brave and vice versa.
Everyone who is both not kind and not generous is not funny and vice versa.
Alice is funny.
Mary is not calm.
Someone is either not quiet or rich.
Someone is not strong.
Mary is both strong and wise.
Alice is both humble and rich.
Someone is either not creative or not funny. | John is not happy. | entailment | ((?[X]:((~generous(X)&quiet(X))))=>((humble(lucy)&~creative(lucy))))&
(((tall(lucy)<~>rich(lucy)))=>((kind(fred)|tall(fred))))&
((~quiet(lucy))=>((~happy(john)&~old(john))))&
((?[X]:(happy(X)))<=>(?[X]:((kind(X)&~kind(X)))))&
(((old(susan)&~creative(susan)))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>(curious(X)<~>quiet(X))))&
(((funny(john)<~>~kind(john)))=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:(curious(X)<=>(~wise(X)|~creative(X))))&
(((~patient(mary)|~curious(mary)))=>(?[X]:((creative(X)&~patient(X)))))&
((?[X]:((~rich(X)&quiet(X))))<=>(old(john)))&
((?[X]:((~patient(X)|funny(X))))=>((~humble(john)|wise(john))))&
((rich(john))=>((generous(mary)&humble(mary))))&
((?[X]:((curious(X)<~>~old(X))))<=>(?[X]:(~wise(X))))&
(((~strong(alice)<~>strong(alice)))<=>((~happy(fred)&rich(fred))))&
(![X]:((~generous(X)&funny(X))<=>(creative(X)&~brave(X))))&
(![X]:((~kind(X)&~generous(X))<=>~funny(X)))&
(funny(alice))&
(~calm(mary))&
(?[X]:((~quiet(X)<~>rich(X))))&
(?[X]:(~strong(X)))&
((strong(mary)&wise(mary)))&
((humble(alice)&rich(alice)))&
(?[X]:((~creative(X)<~>~funny(X)))) | ~happy(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 4215484112142543548425141
% SZS output start Proof for 4215484112142543548425141
4. ? [X0] : happy(X0) <=> ? [X0] : (~kind(X0) & kind(X0)) [input p3]
24. happy(john) [input hypothesis]
25. ? [X0] : happy(X0) <=> ? [X1] : (~kind(X1) & kind(X1)) [rectify 4]
39. (? [X0] : happy(X0) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X1] : (~kind(X1) & kind(X1)) | ! [X0] : ~happy(X0)) [nnf transformation 25]
40. (? [X0] : happy(X0) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X2] : (~kind(X2) & kind(X2)) | ! [X3] : ~happy(X3)) [rectify 39]
41. ? [X0] : happy(X0) => happy(sK0) [choice axiom]
42. ? [X2] : (~kind(X2) & kind(X2)) => (~kind(sK1) & kind(sK1)) [choice axiom]
43. (happy(sK0) | ! [X1] : (kind(X1) | ~kind(X1))) & ((~kind(sK1) & kind(sK1)) | ! [X3] : ~happy(X3)) [skolemisation 40,42,41]
86. kind(sK1) | ~happy(X3) [cnf transformation 43]
87. ~kind(sK1) | ~happy(X3) [cnf transformation 43]
137. happy(john) [cnf transformation 24]
184. 10 <=> happy(john) [avatar definition]
185. happy(john) <- (10) [avatar component clause 184]
189. 11 <=> ! [X3] : ~happy(X3) [avatar definition]
190. ~happy(X3) <- (11) [avatar component clause 189]
192. 12 <=> kind(sK1) [avatar definition]
195. 11 | ~12 [avatar split clause 87,192,189]
196. 11 | 12 [avatar split clause 86,192,189]
358. 10 [avatar split clause 137,184]
359. $false <- (10, 11) [subsumption resolution 185,190]
360. ~10 | ~11 [avatar contradiction clause 359]
361. $false [avatar sat refutation 195,196,358,360]
% SZS output end Proof for 4215484112142543548425141
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either generous or wise then john is both wise and old. Everyone who is both not humble and humble is tall or not curious and vice versa. Everyone who is both brave and happy is both rich and not funny and vice versa. If someone is both not patient and not rich then someone is generous. Everyone who is not kind is funny and vice versa. Everyone who is humble is either old or not brave and vice versa. If someone is either not humble or not rich then someone is both not humble and humble. If john is brave then someone is both generous and creative and vice versa. If john is not patient then lucy is funny and vice versa. If fred is either tall or strong then someone is not curious and vice versa. Everyone who is both happy and not old is creative and vice versa. Everyone who is either old or not creative is not curious or not brave and vice versa. If someone is either not strong or strong then someone is either not quiet or wise. If someone is not kind then alice is curious and vice versa. If someone is not generous or strong then someone is not generous. Everyone who is either funny or not brave is brave or calm and vice versa. Someone is either calm or kind. Someone is not rich or humble. Someone is not wise or not generous. Someone is either humble or not humble. Someone is both wise and not old. Alice is either not generous or patient. | John is patient. | contradiction | (((generous(alice)<~>wise(alice)))=>((wise(john)&old(john))))&
(![X]:((~humble(X)&humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((brave(X)&happy(X))<=>(rich(X)&~funny(X))))&
((?[X]:((~patient(X)&~rich(X))))=>(?[X]:(generous(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:(humble(X)<=>(old(X)<~>~brave(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~humble(X)&humble(X)))))&
((brave(john))<=>(?[X]:((generous(X)&creative(X)))))&
((~patient(john))<=>(funny(lucy)))&
(((tall(fred)<~>strong(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((happy(X)&~old(X))<=>creative(X)))&
(![X]:((old(X)<~>~creative(X))<=>(~curious(X)|~brave(X))))&
((?[X]:((~strong(X)<~>strong(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:(~kind(X)))<=>(curious(alice)))&
((?[X]:((~generous(X)|strong(X))))=>(?[X]:(~generous(X))))&
(![X]:((funny(X)<~>~brave(X))<=>(brave(X)|calm(X))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((~rich(X)|humble(X))))&
(?[X]:((~wise(X)|~generous(X))))&
(?[X]:((humble(X)<~>~humble(X))))&
(?[X]:((wise(X)&~old(X))))&
((~generous(alice)<~>patient(alice))) | patient(john) | [
"p2",
"p5",
"p6",
"p8",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1750160566435043225958334
% SZS output start Proof for 1750160566435043225958334
3. ! [X0] : ((happy(X0) & brave(X0)) <=> (~funny(X0) & rich(X0))) [input p2]
6. ! [X0] : (humble(X0) <=> (old(X0) <~> ~brave(X0))) [input p5]
7. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X0] : (humble(X0) & ~humble(X0)) [input p6]
9. ~patient(john) <=> funny(lucy) [input p8]
11. ! [X0] : ((~old(X0) & happy(X0)) <=> creative(X0)) [input p10]
12. ! [X0] : ((old(X0) <~> ~creative(X0)) <=> (~brave(X0) | ~curious(X0))) [input p11]
16. ! [X0] : ((funny(X0) <~> ~brave(X0)) <=> (calm(X0) | brave(X0))) [input p15]
23. patient(john) [input hypothesis]
25. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X1] : (humble(X1) & ~humble(X1)) [rectify 7]
30. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : (~humble(X0) <=> ~rich(X0)) [ennf transformation 25]
36. ! [X0] : (((happy(X0) & brave(X0)) | (funny(X0) | ~rich(X0))) & ((~funny(X0) & rich(X0)) | (~happy(X0) | ~brave(X0)))) [nnf transformation 3]
37. ! [X0] : (((happy(X0) & brave(X0)) | funny(X0) | ~rich(X0)) & ((~funny(X0) & rich(X0)) | ~happy(X0) | ~brave(X0))) [flattening 36]
42. ! [X0] : ((humble(X0) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0)))) & (((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | ~humble(X0))) [nnf transformation 6]
43. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))) [nnf transformation 30]
44. ? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [rectify 43]
45. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK1) & ~humble(sK1)) [choice axiom]
46. (humble(sK1) & ~humble(sK1)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [skolemisation 44,45]
51. (~patient(john) | ~funny(lucy)) & (funny(lucy) | patient(john)) [nnf transformation 9]
56. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 11]
57. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | old(X0) | ~happy(X0))) [flattening 56]
58. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & ((~brave(X0) | ~curious(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [nnf transformation 12]
59. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & (~brave(X0) | ~curious(X0) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [flattening 58]
71. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | (~calm(X0) & ~brave(X0))) & ((calm(X0) | brave(X0)) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [nnf transformation 16]
72. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | (~calm(X0) & ~brave(X0))) & (calm(X0) | brave(X0) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [flattening 71]
97. ~rich(X0) | funny(X0) | brave(X0) [cnf transformation 37]
105. brave(X0) | old(X0) | humble(X0) [cnf transformation 42]
107. ~humble(sK1) | ~humble(X1) | rich(X1) [cnf transformation 46]
109. humble(sK1) | ~humble(X1) | rich(X1) [cnf transformation 46]
114. ~patient(john) | ~funny(lucy) [cnf transformation 51]
121. ~creative(X0) | ~old(X0) [cnf transformation 57]
127. creative(X0) | ~old(X0) | brave(X0) [cnf transformation 59]
138. ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 72]
152. patient(john) [cnf transformation 23]
154. ~brave(X0) | funny(X0) [duplicate literal removal 138]
190. 7 <=> ! [X1] : (~humble(X1) | rich(X1)) [avatar definition]
191. ~humble(X1) | rich(X1) <- (7) [avatar component clause 190]
193. 8 <=> humble(sK1) [avatar definition]
196. 7 | 8 [avatar split clause 109,193,190]
201. 7 | ~8 [avatar split clause 107,193,190]
222. 14 <=> funny(lucy) [avatar definition]
224. ~funny(lucy) <- (~14) [avatar component clause 222]
226. 15 <=> patient(john) [avatar definition]
229. ~14 | ~15 [avatar split clause 114,226,222]
233. ~old(X0) | brave(X0) [subsumption resolution 127,121]
299. 15 [avatar split clause 152,226]
342. funny(X2) | humble(X2) | old(X2) [resolution 105,154]
424. humble(lucy) | old(lucy) <- (~14) [resolution 342,224]
427. 40 <=> old(lucy) [avatar definition]
429. old(lucy) <- (40) [avatar component clause 427]
431. 41 <=> humble(lucy) [avatar definition]
433. humble(lucy) <- (41) [avatar component clause 431]
434. 40 | 41 | 14 [avatar split clause 424,222,431,427]
488. brave(lucy) <- (40) [resolution 429,233]
524. funny(lucy) <- (40) [resolution 488,154]
527. $false <- (~14, 40) [subsumption resolution 524,224]
528. 14 | ~40 [avatar contradiction clause 527]
530. rich(lucy) <- (7, 41) [resolution 433,191]
548. funny(lucy) | brave(lucy) <- (7, 41) [resolution 530,97]
551. brave(lucy) <- (7, ~14, 41) [subsumption resolution 548,224]
589. funny(lucy) <- (7, ~14, 41) [resolution 551,154]
595. $false <- (7, ~14, 41) [subsumption resolution 589,224]
596. ~7 | 14 | ~41 [avatar contradiction clause 595]
597. $false [avatar sat refutation 196,201,229,299,434,528,596]
% SZS output end Proof for 1750160566435043225958334
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or creative is either happy or not brave and vice versa.
Everyone who is either not humble or curious is kind and vice versa.
Everyone who is either not curious or strong is not creative and vice versa.
If john is creative or not patient then alice is either calm or not brave and vice versa.
If someone is either strong or not old then alice is both not humble and brave and vice versa.
If john is both not generous and not humble then someone is wise or not funny.
If someone is not patient then paul is both not humble and old and vice versa.
If fred is brave or not humble then fred is not strong and vice versa.
If susan is either not quiet or creative then fred is kind.
If someone is quiet then someone is either wise or not curious and vice versa.
If lucy is not kind or tall then mary is strong or not old.
If someone is not quiet then someone is not tall and vice versa.
Everyone who is either calm or not curious is either old or tall.
If someone is both not humble and not rich then paul is not quiet or not patient and vice versa.
If someone is not generous then lucy is humble and vice versa.
If someone is both kind and quiet then someone is both not wise and rich and vice versa.
Susan is not kind or not humble.
Someone is happy.
Someone is either not patient or generous.
Someone is not patient.
Mary is rich.
Lucy is humble.
Someone is not kind.
John is both not generous and not kind. | Paul is funny. | neutral | (![X]:((wise(X)|creative(X))<=>(happy(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>curious(X))<=>kind(X)))&
(![X]:((~curious(X)<~>strong(X))<=>~creative(X)))&
(((creative(john)|~patient(john)))<=>((calm(alice)<~>~brave(alice))))&
((?[X]:((strong(X)<~>~old(X))))<=>((~humble(alice)&brave(alice))))&
(((~generous(john)&~humble(john)))=>(?[X]:((wise(X)|~funny(X)))))&
((?[X]:(~patient(X)))<=>((~humble(paul)&old(paul))))&
(((brave(fred)|~humble(fred)))<=>(~strong(fred)))&
(((~quiet(susan)<~>creative(susan)))=>(kind(fred)))&
((?[X]:(quiet(X)))<=>(?[X]:((wise(X)<~>~curious(X)))))&
(((~kind(lucy)|tall(lucy)))=>((strong(mary)|~old(mary))))&
((?[X]:(~quiet(X)))<=>(?[X]:(~tall(X))))&
(![X]:((calm(X)<~>~curious(X))=>(old(X)<~>tall(X))))&
((?[X]:((~humble(X)&~rich(X))))<=>((~quiet(paul)|~patient(paul))))&
((?[X]:(~generous(X)))<=>(humble(lucy)))&
((?[X]:((kind(X)&quiet(X))))<=>(?[X]:((~wise(X)&rich(X)))))&
((~kind(susan)|~humble(susan)))&
(?[X]:(happy(X)))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:(~patient(X)))&
(rich(mary))&
(humble(lucy))&
(?[X]:(~kind(X)))&
((~generous(john)&~kind(john))) | funny(paul) | [] | null | 0 |
Everyone who is both not funny and curious is either not patient or not strong. If someone is both not humble and not quiet then someone is either curious or calm. If paul is not creative then paul is not curious or not rich. Everyone who is either not creative or calm is not calm or not kind. Everyone who is quiet is both not creative and not strong and vice versa. If john is kind then someone is not generous. If susan is funny then someone is tall or not patient. Everyone who is not generous is not kind. If someone is not humble then paul is both not rich and quiet and vice versa. If alice is both humble and funny then mary is generous or creative. Everyone who is either generous or not generous is either creative or not rich. If paul is both rich and generous then someone is either not humble or not tall and vice versa. Everyone who is not kind is either not tall or not happy. If lucy is either funny or not brave then susan is either wise or not curious and vice versa. Everyone who is either wise or not wise is not strong or not tall. Everyone who is tall is not humble and vice versa. Someone is both not calm and creative. Someone is both humble and not happy. Someone is either old or strong. Alice is not calm or not kind. Someone is either patient or not happy. Susan is both generous and not funny. Someone is not wise. Paul is not wise or not brave. | John is tall. | contradiction | (![X]:((~funny(X)&curious(X))=>(~patient(X)<~>~strong(X))))&
((?[X]:((~humble(X)&~quiet(X))))=>(?[X]:((curious(X)<~>calm(X)))))&
((~creative(paul))=>((~curious(paul)|~rich(paul))))&
(![X]:((~creative(X)<~>calm(X))=>(~calm(X)|~kind(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~strong(X))))&
((kind(john))=>(?[X]:(~generous(X))))&
((funny(susan))=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:(~generous(X)=>~kind(X)))&
((?[X]:(~humble(X)))<=>((~rich(paul)&quiet(paul))))&
(((humble(alice)&funny(alice)))=>((generous(mary)|creative(mary))))&
(![X]:((generous(X)<~>~generous(X))=>(creative(X)<~>~rich(X))))&
(((rich(paul)&generous(paul)))<=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(~kind(X)=>(~tall(X)<~>~happy(X))))&
(((funny(lucy)<~>~brave(lucy)))<=>((wise(susan)<~>~curious(susan))))&
(![X]:((wise(X)<~>~wise(X))=>(~strong(X)|~tall(X))))&
(![X]:(tall(X)<=>~humble(X)))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((humble(X)&~happy(X))))&
(?[X]:((old(X)<~>strong(X))))&
((~calm(alice)|~kind(alice)))&
(?[X]:((patient(X)<~>~happy(X))))&
((generous(susan)&~funny(susan)))&
(?[X]:(~wise(X)))&
((~wise(paul)|~brave(paul))) | tall(john) | [
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1503993184093609595103538
% SZS output start Proof for 1503993184093609595103538
9. ? [X0] : ~humble(X0) <=> (quiet(paul) & ~rich(paul)) [input p8]
12. (generous(paul) & rich(paul)) <=> ? [X0] : (~humble(X0) <~> ~tall(X0)) [input p11]
16. ! [X0] : (tall(X0) <=> ~humble(X0)) [input p15]
25. tall(john) [input hypothesis]
55. (? [X0] : ~humble(X0) | (~quiet(paul) | rich(paul))) & ((quiet(paul) & ~rich(paul)) | ! [X0] : humble(X0)) [nnf transformation 9]
56. (? [X0] : ~humble(X0) | ~quiet(paul) | rich(paul)) & ((quiet(paul) & ~rich(paul)) | ! [X0] : humble(X0)) [flattening 55]
57. (? [X0] : ~humble(X0) | ~quiet(paul) | rich(paul)) & ((quiet(paul) & ~rich(paul)) | ! [X1] : humble(X1)) [rectify 56]
58. ? [X0] : ~humble(X0) => ~humble(sK3) [choice axiom]
59. (~humble(sK3) | ~quiet(paul) | rich(paul)) & ((quiet(paul) & ~rich(paul)) | ! [X1] : humble(X1)) [skolemisation 57,58]
61. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | (~generous(paul) | ~rich(paul))) [nnf transformation 12]
62. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | ~generous(paul) | ~rich(paul)) [flattening 61]
63. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X1] : ((tall(X1) | humble(X1)) & (~tall(X1) | ~humble(X1))) | ~generous(paul) | ~rich(paul)) [rectify 62]
64. ? [X1] : ((tall(X1) | humble(X1)) & (~tall(X1) | ~humble(X1))) => ((tall(sK4) | humble(sK4)) & (~tall(sK4) | ~humble(sK4))) [choice axiom]
65. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (((tall(sK4) | humble(sK4)) & (~tall(sK4) | ~humble(sK4))) | ~generous(paul) | ~rich(paul)) [skolemisation 63,64]
69. ! [X0] : ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))) [nnf transformation 16]
95. ~rich(paul) | humble(X1) [cnf transformation 59]
105. rich(paul) | ~tall(X0) | humble(X0) [cnf transformation 65]
121. ~tall(X0) | ~humble(X0) [cnf transformation 69]
136. tall(john) [cnf transformation 25]
166. 6 <=> rich(paul) [avatar definition]
202. 14 <=> ! [X1] : humble(X1) [avatar definition]
203. humble(X1) <- (14) [avatar component clause 202]
205. 14 | ~6 [avatar split clause 95,166,202]
234. 21 <=> ! [X0] : (~tall(X0) | humble(X0)) [avatar definition]
235. ~tall(X0) | humble(X0) <- (21) [avatar component clause 234]
238. 21 | 6 [avatar split clause 105,166,234]
313. ~tall(X0) <- (21) [subsumption resolution 235,121]
317. $false <- (21) [resolution 313,136]
318. ~21 [avatar contradiction clause 317]
328. ~humble(john) [resolution 121,136]
329. $false <- (14) [subsumption resolution 328,203]
330. ~14 [avatar contradiction clause 329]
331. $false [avatar sat refutation 205,238,318,330]
% SZS output end Proof for 1503993184093609595103538
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or rich is either curious or not wise and vice versa. Everyone who is both not rich and not patient is both brave and humble. Everyone who is not brave is either brave or not rich and vice versa. Everyone who is either not patient or not brave is brave or old. Everyone who is either not patient or not curious is not creative or not calm and vice versa. Everyone who is both quiet and not creative is either quiet or funny. Everyone who is both not quiet and not brave is not funny. If mary is either brave or not kind then susan is not rich or not humble and vice versa. Everyone who is kind is not brave or not generous. If someone is funny or tall then mary is not quiet or rich and vice versa. Everyone who is old is strong or old. Everyone who is both humble and patient is happy. Everyone who is both not patient and not happy is not humble. Everyone who is not patient or generous is not wise. Everyone who is old or generous is not creative or humble. If someone is either rich or not generous then paul is both tall and brave. Someone is strong or not patient. Someone is not calm or not old. Someone is either not humble or brave. Someone is humble or not rich. Someone is both happy and wise. Someone is not curious. Paul is wise. Mary is not patient or not humble. | Susan is not brave. | neutral | (![X]:((~calm(X)|rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((~rich(X)&~patient(X))=>(brave(X)&humble(X))))&
(![X]:(~brave(X)<=>(brave(X)<~>~rich(X))))&
(![X]:((~patient(X)<~>~brave(X))=>(brave(X)|old(X))))&
(![X]:((~patient(X)<~>~curious(X))<=>(~creative(X)|~calm(X))))&
(![X]:((quiet(X)&~creative(X))=>(quiet(X)<~>funny(X))))&
(![X]:((~quiet(X)&~brave(X))=>~funny(X)))&
(((brave(mary)<~>~kind(mary)))<=>((~rich(susan)|~humble(susan))))&
(![X]:(kind(X)=>(~brave(X)|~generous(X))))&
((?[X]:((funny(X)|tall(X))))<=>((~quiet(mary)|rich(mary))))&
(![X]:(old(X)=>(strong(X)|old(X))))&
(![X]:((humble(X)&patient(X))=>happy(X)))&
(![X]:((~patient(X)&~happy(X))=>~humble(X)))&
(![X]:((~patient(X)|generous(X))=>~wise(X)))&
(![X]:((old(X)|generous(X))=>(~creative(X)|humble(X))))&
((?[X]:((rich(X)<~>~generous(X))))=>((tall(paul)&brave(paul))))&
(?[X]:((strong(X)|~patient(X))))&
(?[X]:((~calm(X)|~old(X))))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:((happy(X)&wise(X))))&
(?[X]:(~curious(X)))&
(wise(paul))&
((~patient(mary)|~humble(mary))) | ~brave(susan) | [] | null | 0 |
If fred is calm then paul is generous.
Everyone who is patient or not strong is both calm and not strong.
If someone is not patient then lucy is old or not patient and vice versa.
If susan is patient or happy then alice is both strong and wise and vice versa.
Everyone who is patient or not funny is old or not old and vice versa.
Everyone who is old or not old is tall or curious and vice versa.
If someone is not funny then someone is both not brave and happy.
If someone is happy then someone is not kind and vice versa.
Everyone who is not wise or brave is quiet or not funny.
Everyone who is both not curious and brave is not patient or not calm and vice versa.
If alice is both funny and curious then alice is either not calm or funny.
Everyone who is not happy or not strong is quiet or not calm.
If someone is both not curious and calm then alice is not tall or rich and vice versa.
If someone is either wise or not strong then someone is kind or curious and vice versa.
Everyone who is both humble and quiet is both not old and not humble and vice versa.
Fred is either not patient or rich.
Paul is not patient or patient.
Lucy is both not generous and not tall.
Someone is quiet or not rich.
Someone is either not kind or not tall.
Paul is not calm. | Lucy is not old. | contradiction | ((calm(fred))=>(generous(paul)))&
(![X]:((patient(X)|~strong(X))=>(calm(X)&~strong(X))))&
((?[X]:(~patient(X)))<=>((old(lucy)|~patient(lucy))))&
(((patient(susan)|happy(susan)))<=>((strong(alice)&wise(alice))))&
(![X]:((patient(X)|~funny(X))<=>(old(X)|~old(X))))&
(![X]:((old(X)|~old(X))<=>(tall(X)|curious(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~brave(X)&happy(X)))))&
((?[X]:(happy(X)))<=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)|brave(X))=>(quiet(X)|~funny(X))))&
(![X]:((~curious(X)&brave(X))<=>(~patient(X)|~calm(X))))&
(((funny(alice)&curious(alice)))=>((~calm(alice)<~>funny(alice))))&
(![X]:((~happy(X)|~strong(X))=>(quiet(X)|~calm(X))))&
((?[X]:((~curious(X)&calm(X))))<=>((~tall(alice)|rich(alice))))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((humble(X)&quiet(X))<=>(~old(X)&~humble(X))))&
((~patient(fred)<~>rich(fred)))&
((~patient(paul)|patient(paul)))&
((~generous(lucy)&~tall(lucy)))&
(?[X]:((quiet(X)|~rich(X))))&
(?[X]:((~kind(X)<~>~tall(X))))&
(~calm(paul)) | ~old(lucy) | [
"p1",
"p2",
"p3",
"p5",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 64183152068917807383095
% SZS output start Proof for 64183152068917807383095
2. ! [X0] : ((~strong(X0) | patient(X0)) => (~strong(X0) & calm(X0))) [input p1]
3. ? [X0] : ~patient(X0) <=> (~patient(lucy) | old(lucy)) [input p2]
4. (happy(susan) | patient(susan)) <=> (wise(alice) & strong(alice)) [input p3]
6. ! [X0] : ((~old(X0) | old(X0)) <=> (curious(X0) | tall(X0))) [input p5]
10. ! [X0] : ((brave(X0) & ~curious(X0)) <=> (~calm(X0) | ~patient(X0))) [input p9]
18. ~tall(lucy) & ~generous(lucy) [input p17]
22. ~old(lucy) [input hypothesis]
27. ! [X0] : ((~strong(X0) & calm(X0)) | (strong(X0) & ~patient(X0))) [ennf transformation 2]
35. (? [X0] : ~patient(X0) | (patient(lucy) & ~old(lucy))) & ((~patient(lucy) | old(lucy)) | ! [X0] : patient(X0)) [nnf transformation 3]
36. (? [X0] : ~patient(X0) | (patient(lucy) & ~old(lucy))) & (~patient(lucy) | old(lucy) | ! [X0] : patient(X0)) [flattening 35]
37. (? [X0] : ~patient(X0) | (patient(lucy) & ~old(lucy))) & (~patient(lucy) | old(lucy) | ! [X1] : patient(X1)) [rectify 36]
38. ? [X0] : ~patient(X0) => ~patient(sK0) [choice axiom]
39. (~patient(sK0) | (patient(lucy) & ~old(lucy))) & (~patient(lucy) | old(lucy) | ! [X1] : patient(X1)) [skolemisation 37,38]
40. ((happy(susan) | patient(susan)) | (~wise(alice) | ~strong(alice))) & ((wise(alice) & strong(alice)) | (~happy(susan) & ~patient(susan))) [nnf transformation 4]
41. (happy(susan) | patient(susan) | ~wise(alice) | ~strong(alice)) & ((wise(alice) & strong(alice)) | (~happy(susan) & ~patient(susan))) [flattening 40]
44. ! [X0] : (((~old(X0) | old(X0)) | (~curious(X0) & ~tall(X0))) & ((curious(X0) | tall(X0)) | (old(X0) & ~old(X0)))) [nnf transformation 6]
45. ! [X0] : ((~old(X0) | old(X0) | (~curious(X0) & ~tall(X0))) & (curious(X0) | tall(X0) | (old(X0) & ~old(X0)))) [flattening 44]
54. ! [X0] : (((brave(X0) & ~curious(X0)) | (calm(X0) & patient(X0))) & ((~calm(X0) | ~patient(X0)) | (~brave(X0) | curious(X0)))) [nnf transformation 10]
55. ! [X0] : (((brave(X0) & ~curious(X0)) | (calm(X0) & patient(X0))) & (~calm(X0) | ~patient(X0) | ~brave(X0) | curious(X0))) [flattening 54]
78. ~strong(X0) | ~patient(X0) [cnf transformation 27]
80. ~patient(lucy) | old(lucy) | patient(X1) [cnf transformation 39]
83. strong(alice) | ~patient(susan) [cnf transformation 41]
92. curious(X0) | tall(X0) | ~old(X0) [cnf transformation 45]
93. curious(X0) | tall(X0) | old(X0) [cnf transformation 45]
103. ~curious(X0) | patient(X0) [cnf transformation 55]
130. ~tall(lucy) [cnf transformation 18]
135. ~old(lucy) [cnf transformation 22]
149. 3 <=> patient(lucy) [avatar definition]
158. 5 <=> old(lucy) [avatar definition]
163. 6 <=> ! [X1] : patient(X1) [avatar definition]
164. patient(X1) <- (6) [avatar component clause 163]
165. 6 | 5 | ~3 [avatar split clause 80,149,158,163]
167. 7 <=> strong(alice) [avatar definition]
168. strong(alice) <- (7) [avatar component clause 167]
175. 9 <=> patient(susan) [avatar definition]
176. ~patient(susan) <- (~9) [avatar component clause 175]
186. ~9 | 7 [avatar split clause 83,167,175]
188. curious(X0) | tall(X0) [subsumption resolution 92,93]
307. ~5 [avatar split clause 135,158]
319. $false <- (6, ~9) [resolution 164,176]
322. ~6 | 9 [avatar contradiction clause 319]
329. tall(X1) | patient(X1) [resolution 188,103]
401. patient(lucy) [resolution 329,130]
404. 3 [avatar split clause 401,149]
408. ~patient(alice) <- (7) [resolution 168,78]
409. $false <- (6, 7) [subsumption resolution 408,164]
410. ~6 | ~7 [avatar contradiction clause 409]
411. $false [avatar sat refutation 165,186,307,322,404,410]
% SZS output end Proof for 64183152068917807383095
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or humble is both not funny and strong.
Everyone who is not patient is generous or not brave.
Everyone who is both not funny and quiet is brave or not generous and vice versa.
Everyone who is patient or not wise is not brave or not wise.
Everyone who is not brave or tall is curious or rich.
Everyone who is patient or rich is not humble or kind and vice versa.
If alice is tall or generous then someone is both brave and old.
If lucy is both happy and generous then someone is either creative or not old.
Everyone who is both strong and not funny is both not old and not tall.
If susan is both not quiet and calm then john is either strong or not brave.
If someone is both happy and kind then fred is both generous and not rich.
If mary is both not strong and kind then fred is creative and vice versa.
If someone is not quiet then someone is either patient or not brave.
Everyone who is either not wise or not patient is wise.
Everyone who is either curious or calm is both not kind and not strong.
If someone is both curious and not generous then someone is both quiet and creative and vice versa.
Someone is not wise or funny.
Alice is old or patient.
Someone is generous.
Fred is not kind or not strong.
Someone is not old or not humble.
Someone is not creative or calm.
John is both not brave and rich. | Alice is quiet. | entailment | (![X]:((~humble(X)<~>humble(X))=>(~funny(X)&strong(X))))&
(![X]:(~patient(X)=>(generous(X)|~brave(X))))&
(![X]:((~funny(X)&quiet(X))<=>(brave(X)|~generous(X))))&
(![X]:((patient(X)|~wise(X))=>(~brave(X)|~wise(X))))&
(![X]:((~brave(X)|tall(X))=>(curious(X)|rich(X))))&
(![X]:((patient(X)|rich(X))<=>(~humble(X)|kind(X))))&
(((tall(alice)|generous(alice)))=>(?[X]:((brave(X)&old(X)))))&
(((happy(lucy)&generous(lucy)))=>(?[X]:((creative(X)<~>~old(X)))))&
(![X]:((strong(X)&~funny(X))=>(~old(X)&~tall(X))))&
(((~quiet(susan)&calm(susan)))=>((strong(john)<~>~brave(john))))&
((?[X]:((happy(X)&kind(X))))=>((generous(fred)&~rich(fred))))&
(((~strong(mary)&kind(mary)))<=>(creative(fred)))&
((?[X]:(~quiet(X)))=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((~wise(X)<~>~patient(X))=>wise(X)))&
(![X]:((curious(X)<~>calm(X))=>(~kind(X)&~strong(X))))&
((?[X]:((curious(X)&~generous(X))))<=>(?[X]:((quiet(X)&creative(X)))))&
(?[X]:((~wise(X)|funny(X))))&
((old(alice)|patient(alice)))&
(?[X]:(generous(X)))&
((~kind(fred)|~strong(fred)))&
(?[X]:((~old(X)|~humble(X))))&
(?[X]:((~creative(X)|calm(X))))&
((~brave(john)&rich(john))) | quiet(alice) | [
"p0",
"p2",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2920235352146045567833204
% SZS output start Proof for 2920235352146045567833204
1. ! [X0] : ((~humble(X0) <~> humble(X0)) => (strong(X0) & ~funny(X0))) [input p0]
3. ! [X0] : ((quiet(X0) & ~funny(X0)) <=> (~generous(X0) | brave(X0))) [input p2]
7. (generous(alice) | tall(alice)) => ? [X0] : (old(X0) & brave(X0)) [input p6]
9. ! [X0] : ((~funny(X0) & strong(X0)) => (~tall(X0) & ~old(X0))) [input p8]
24. ~quiet(alice) [input hypothesis]
29. ! [X0] : ((~funny(X0) & strong(X0)) => ~old(X0)) [pure predicate removal 9]
30. generous(alice) => ? [X0] : (old(X0) & brave(X0)) [pure predicate removal 7]
32. ! [X0] : ((strong(X0) & ~funny(X0)) | (~humble(X0) <=> humble(X0))) [ennf transformation 1]
39. ? [X0] : (old(X0) & brave(X0)) | ~generous(alice) [ennf transformation 30]
40. ! [X0] : (~old(X0) | (funny(X0) | ~strong(X0))) [ennf transformation 29]
41. ! [X0] : (~old(X0) | funny(X0) | ~strong(X0)) [flattening 40]
47. ! [X0] : ((strong(X0) & ~funny(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 32]
48. ! [X0] : (((quiet(X0) & ~funny(X0)) | (generous(X0) & ~brave(X0))) & ((~generous(X0) | brave(X0)) | (~quiet(X0) | funny(X0)))) [nnf transformation 3]
49. ! [X0] : (((quiet(X0) & ~funny(X0)) | (generous(X0) & ~brave(X0))) & (~generous(X0) | brave(X0) | ~quiet(X0) | funny(X0))) [flattening 48]
52. ? [X0] : (old(X0) & brave(X0)) => (old(sK0) & brave(sK0)) [choice axiom]
53. (old(sK0) & brave(sK0)) | ~generous(alice) [skolemisation 39,52]
76. ~funny(X0) | humble(X0) | humble(X0) [cnf transformation 47]
77. ~funny(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47]
78. strong(X0) | humble(X0) | humble(X0) [cnf transformation 47]
79. strong(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47]
85. quiet(X0) | generous(X0) [cnf transformation 49]
94. old(sK0) | ~generous(alice) [cnf transformation 53]
95. ~old(X0) | funny(X0) | ~strong(X0) [cnf transformation 41]
121. ~quiet(alice) [cnf transformation 24]
123. ~funny(X0) | humble(X0) [duplicate literal removal 76]
124. ~funny(X0) | ~humble(X0) [duplicate literal removal 77]
125. strong(X0) | humble(X0) [duplicate literal removal 78]
126. strong(X0) | ~humble(X0) [duplicate literal removal 79]
127. strong(X0) [subsumption resolution 125,126]
128. ~funny(X0) [subsumption resolution 123,124]
131. 1 <=> generous(alice) [avatar definition]
135. 2 <=> old(sK0) [avatar definition]
137. old(sK0) <- (2) [avatar component clause 135]
138. ~1 | 2 [avatar split clause 94,135,131]
144. ~old(X0) | ~strong(X0) [subsumption resolution 95,128]
145. ~old(X0) [subsumption resolution 144,127]
225. generous(alice) [resolution 85,121]
228. 1 [avatar split clause 225,131]
229. $false <- (2) [subsumption resolution 137,145]
230. ~2 [avatar contradiction clause 229]
231. $false [avatar sat refutation 138,228,230]
% SZS output end Proof for 2920235352146045567833204
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is both brave and creative and vice versa.
If fred is creative or not rich then someone is not calm.
Everyone who is both not tall and generous is not old and vice versa.
If susan is either not wise or not funny then someone is not rich or not patient and vice versa.
If alice is either quiet or funny then someone is not creative.
If paul is either wise or not calm then lucy is both funny and curious.
If someone is either not funny or not creative then paul is both not funny and strong.
Everyone who is not generous or not strong is both not quiet and funny.
If alice is both not humble and humble then john is quiet or not happy.
Everyone who is either not quiet or curious is not generous or not kind and vice versa.
Everyone who is not creative or not funny is both not creative and not happy and vice versa.
If paul is not old or happy then john is either not rich or strong and vice versa.
Everyone who is curious is either not strong or not calm and vice versa.
If someone is either not kind or not generous then someone is not tall or not brave and vice versa.
Everyone who is old is either not creative or not calm.
Everyone who is both not creative and not wise is both calm and not tall and vice versa.
Someone is not happy.
Someone is both not creative and old.
Someone is not old.
Someone is not creative.
Someone is both not funny and wise.
Susan is quiet.
John is either patient or humble. | Fred is not rich. | neutral | (![X]:(curious(X)<=>(brave(X)&creative(X))))&
(((creative(fred)|~rich(fred)))=>(?[X]:(~calm(X))))&
(![X]:((~tall(X)&generous(X))<=>~old(X)))&
(((~wise(susan)<~>~funny(susan)))<=>(?[X]:((~rich(X)|~patient(X)))))&
(((quiet(alice)<~>funny(alice)))=>(?[X]:(~creative(X))))&
(((wise(paul)<~>~calm(paul)))=>((funny(lucy)&curious(lucy))))&
((?[X]:((~funny(X)<~>~creative(X))))=>((~funny(paul)&strong(paul))))&
(![X]:((~generous(X)|~strong(X))=>(~quiet(X)&funny(X))))&
(((~humble(alice)&humble(alice)))=>((quiet(john)|~happy(john))))&
(![X]:((~quiet(X)<~>curious(X))<=>(~generous(X)|~kind(X))))&
(![X]:((~creative(X)|~funny(X))<=>(~creative(X)&~happy(X))))&
(((~old(paul)|happy(paul)))<=>((~rich(john)<~>strong(john))))&
(![X]:(curious(X)<=>(~strong(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(old(X)=>(~creative(X)<~>~calm(X))))&
(![X]:((~creative(X)&~wise(X))<=>(calm(X)&~tall(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:(~old(X)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)&wise(X))))&
(quiet(susan))&
((patient(john)<~>humble(john))) | ~rich(fred) | [] | null | 0 |
Everyone who is both creative and not kind is both creative and not happy and vice versa.
Everyone who is both wise and not calm is not creative or calm.
Everyone who is old is funny.
Everyone who is creative or old is generous and vice versa.
Everyone who is both not rich and tall is both not curious and not wise.
If mary is either calm or not wise then someone is either tall or old and vice versa.
If someone is not humble then someone is humble or not patient and vice versa.
If someone is kind then someone is both not brave and quiet.
Everyone who is both not old and curious is old or wise.
Everyone who is wise or happy is both not happy and not strong and vice versa.
Everyone who is both calm and funny is not kind or not generous.
If paul is either not rich or not strong then someone is either not calm or creative and vice versa.
If someone is creative or not wise then someone is not calm or humble.
Everyone who is both not funny and strong is not kind or not creative.
If someone is wise or generous then someone is quiet or strong.
If someone is both not funny and not old then paul is both not strong and happy.
Someone is strong or tall.
Someone is humble.
Someone is old.
Someone is not old.
Lucy is calm.
Someone is funny or wise. | Paul is creative. | neutral | (![X]:((creative(X)&~kind(X))<=>(creative(X)&~happy(X))))&
(![X]:((wise(X)&~calm(X))=>(~creative(X)|calm(X))))&
(![X]:(old(X)=>funny(X)))&
(![X]:((creative(X)|old(X))<=>generous(X)))&
(![X]:((~rich(X)&tall(X))=>(~curious(X)&~wise(X))))&
(((calm(mary)<~>~wise(mary)))<=>(?[X]:((tall(X)<~>old(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:(kind(X)))=>(?[X]:((~brave(X)&quiet(X)))))&
(![X]:((~old(X)&curious(X))=>(old(X)|wise(X))))&
(![X]:((wise(X)|happy(X))<=>(~happy(X)&~strong(X))))&
(![X]:((calm(X)&funny(X))=>(~kind(X)|~generous(X))))&
(((~rich(paul)<~>~strong(paul)))<=>(?[X]:((~calm(X)<~>creative(X)))))&
((?[X]:((creative(X)|~wise(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~funny(X)&strong(X))=>(~kind(X)|~creative(X))))&
((?[X]:((wise(X)|generous(X))))=>(?[X]:((quiet(X)|strong(X)))))&
((?[X]:((~funny(X)&~old(X))))=>((~strong(paul)&happy(paul))))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:(humble(X)))&
(?[X]:(old(X)))&
(?[X]:(~old(X)))&
(calm(lucy))&
(?[X]:((funny(X)|wise(X)))) | creative(paul) | [] | null | 0 |
Everyone who is either not creative or brave is both not tall and strong.
Everyone who is both not wise and curious is not quiet and vice versa.
Everyone who is either old or not rich is both not old and calm and vice versa.
Everyone who is both not happy and kind is either not generous or not funny.
If someone is rich then lucy is quiet and vice versa.
Everyone who is not strong or not creative is not tall and vice versa.
If someone is both strong and brave then someone is not funny and vice versa.
If someone is both funny and creative then mary is both not funny and not old and vice versa.
Everyone who is not curious or old is both curious and happy.
If someone is curious then mary is patient.
Everyone who is humble or old is not strong.
If someone is not strong then fred is funny and vice versa.
Everyone who is both rich and not calm is not strong or not wise and vice versa.
If someone is either not funny or quiet then someone is either not rich or creative and vice versa.
If someone is not generous then fred is either rich or kind and vice versa.
If mary is not happy or humble then someone is not happy or not generous and vice versa.
Someone is both not humble and not generous.
Someone is generous.
Lucy is both tall and kind.
Paul is both not funny and rich.
Mary is either generous or not old.
Someone is not old.
Someone is not funny or not brave. | Lucy is not rich. | entailment | (![X]:((~creative(X)<~>brave(X))=>(~tall(X)&strong(X))))&
(![X]:((~wise(X)&curious(X))<=>~quiet(X)))&
(![X]:((old(X)<~>~rich(X))<=>(~old(X)&calm(X))))&
(![X]:((~happy(X)&kind(X))=>(~generous(X)<~>~funny(X))))&
((?[X]:(rich(X)))<=>(quiet(lucy)))&
(![X]:((~strong(X)|~creative(X))<=>~tall(X)))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((funny(X)&creative(X))))<=>((~funny(mary)&~old(mary))))&
(![X]:((~curious(X)|old(X))=>(curious(X)&happy(X))))&
((?[X]:(curious(X)))=>(patient(mary)))&
(![X]:((humble(X)|old(X))=>~strong(X)))&
((?[X]:(~strong(X)))<=>(funny(fred)))&
(![X]:((rich(X)&~calm(X))<=>(~strong(X)|~wise(X))))&
((?[X]:((~funny(X)<~>quiet(X))))<=>(?[X]:((~rich(X)<~>creative(X)))))&
((?[X]:(~generous(X)))<=>((rich(fred)<~>kind(fred))))&
(((~happy(mary)|humble(mary)))<=>(?[X]:((~happy(X)|~generous(X)))))&
(?[X]:((~humble(X)&~generous(X))))&
(?[X]:(generous(X)))&
((tall(lucy)&kind(lucy)))&
((~funny(paul)&rich(paul)))&
((generous(mary)<~>~old(mary)))&
(?[X]:(~old(X)))&
(?[X]:((~funny(X)|~brave(X)))) | ~rich(lucy) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p10",
"p12",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8422474207637708450236642
% SZS output start Proof for 8422474207637708450236642
2. ! [X0] : ((curious(X0) & ~wise(X0)) <=> ~quiet(X0)) [input p1]
3. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> (calm(X0) & ~old(X0))) [input p2]
5. ? [X0] : rich(X0) <=> quiet(lucy) [input p4]
6. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> ~tall(X0)) [input p5]
9. ! [X0] : ((old(X0) | ~curious(X0)) => (happy(X0) & curious(X0))) [input p8]
11. ! [X0] : ((old(X0) | humble(X0)) => ~strong(X0)) [input p10]
13. ! [X0] : ((~calm(X0) & rich(X0)) <=> (~wise(X0) | ~strong(X0))) [input p12]
19. kind(lucy) & tall(lucy) [input p18]
20. rich(paul) & ~funny(paul) [input p19]
24. rich(lucy) [input hypothesis]
31. ! [X0] : ((happy(X0) & curious(X0)) | (~old(X0) & curious(X0))) [ennf transformation 9]
32. ! [X0] : (~strong(X0) | (~old(X0) & ~humble(X0))) [ennf transformation 11]
34. ! [X0] : (((curious(X0) & ~wise(X0)) | quiet(X0)) & (~quiet(X0) | (~curious(X0) | wise(X0)))) [nnf transformation 2]
35. ! [X0] : (((curious(X0) & ~wise(X0)) | quiet(X0)) & (~quiet(X0) | ~curious(X0) | wise(X0))) [flattening 34]
36. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | (~calm(X0) | old(X0))) & ((calm(X0) & ~old(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 3]
37. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~calm(X0) | old(X0)) & ((calm(X0) & ~old(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [flattening 36]
39. (? [X0] : rich(X0) | ~quiet(lucy)) & (quiet(lucy) | ! [X0] : ~rich(X0)) [nnf transformation 5]
40. (? [X0] : rich(X0) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : ~rich(X1)) [rectify 39]
41. ? [X0] : rich(X0) => rich(sK0) [choice axiom]
42. (rich(sK0) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : ~rich(X1)) [skolemisation 40,41]
43. ! [X0] : (((~creative(X0) | ~strong(X0)) | tall(X0)) & (~tall(X0) | (creative(X0) & strong(X0)))) [nnf transformation 6]
44. ! [X0] : ((~creative(X0) | ~strong(X0) | tall(X0)) & (~tall(X0) | (creative(X0) & strong(X0)))) [flattening 43]
59. ! [X0] : (((~calm(X0) & rich(X0)) | (wise(X0) & strong(X0))) & ((~wise(X0) | ~strong(X0)) | (calm(X0) | ~rich(X0)))) [nnf transformation 13]
60. ! [X0] : (((~calm(X0) & rich(X0)) | (wise(X0) & strong(X0))) & (~wise(X0) | ~strong(X0) | calm(X0) | ~rich(X0))) [flattening 59]
88. ~quiet(X0) | ~curious(X0) | wise(X0) [cnf transformation 35]
91. ~old(X0) | ~rich(X0) | ~old(X0) [cnf transformation 37]
95. ~rich(X0) | old(X0) | ~calm(X0) | old(X0) [cnf transformation 37]
99. quiet(lucy) | ~rich(X1) [cnf transformation 42]
101. ~tall(X0) | strong(X0) [cnf transformation 44]
111. curious(X0) | curious(X0) [cnf transformation 31]
116. ~old(X0) | ~strong(X0) [cnf transformation 32]
119. ~rich(X0) | ~strong(X0) | calm(X0) | ~wise(X0) [cnf transformation 60]
120. rich(X0) | strong(X0) [cnf transformation 60]
143. tall(lucy) [cnf transformation 19]
146. rich(paul) [cnf transformation 20]
151. rich(lucy) [cnf transformation 24]
152. curious(X0) [duplicate literal removal 111]
153. ~rich(X0) | ~old(X0) [duplicate literal removal 91]
154. ~calm(X0) | old(X0) | ~rich(X0) [duplicate literal removal 95]
156. 1 <=> quiet(lucy) [avatar definition]
157. quiet(lucy) <- (1) [avatar component clause 156]
165. 3 <=> ! [X1] : ~rich(X1) [avatar definition]
166. ~rich(X1) <- (3) [avatar component clause 165]
167. 3 | 1 [avatar split clause 99,156,165]
318. $false <- (3) [resolution 166,146]
321. ~3 [avatar contradiction clause 318]
325. strong(lucy) [resolution 101,143]
335. ~old(X1) | strong(X1) [resolution 153,120]
339. ~old(X1) [subsumption resolution 335,116]
356. ~curious(lucy) | wise(lucy) <- (1) [resolution 88,157]
359. wise(lucy) <- (1) [subsumption resolution 356,152]
421. ~strong(lucy) | calm(lucy) | ~wise(lucy) [resolution 119,151]
425. calm(lucy) | ~wise(lucy) [subsumption resolution 421,325]
426. calm(lucy) <- (1) [subsumption resolution 425,359]
457. old(lucy) | ~rich(lucy) <- (1) [resolution 426,154]
460. ~rich(lucy) <- (1) [subsumption resolution 457,339]
461. $false <- (1) [subsumption resolution 460,151]
462. ~1 [avatar contradiction clause 461]
463. $false [avatar sat refutation 167,321,462]
% SZS output end Proof for 8422474207637708450236642
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or tall is either rich or humble. If someone is not brave then someone is either calm or not calm. Everyone who is both not funny and not rich is calm and vice versa. Everyone who is wise or brave is either happy or not calm. Everyone who is either old or not calm is not generous and vice versa. Everyone who is both not funny and strong is rich. Everyone who is not funny or not quiet is generous or old. If john is either strong or not humble then someone is either not calm or not curious. If someone is not brave then someone is not patient or not kind. Everyone who is both not old and humble is not creative and vice versa. Everyone who is either not strong or not creative is not strong or not quiet. If fred is either calm or creative then someone is curious and vice versa. Everyone who is either not curious or creative is generous or creative and vice versa. If paul is both rich and not rich then someone is both not patient and not wise and vice versa. Everyone who is either not happy or calm is not quiet or not funny. Susan is not rich or not funny. Someone is either not humble or funny. Lucy is not happy. Someone is patient or creative. Someone is rich or not funny. John is kind. Someone is either not kind or not curious. Someone is not happy or not old. | Susan is not strong. | neutral | (![X]:((~humble(X)|tall(X))=>(rich(X)<~>humble(X))))&
((?[X]:(~brave(X)))=>(?[X]:((calm(X)<~>~calm(X)))))&
(![X]:((~funny(X)&~rich(X))<=>calm(X)))&
(![X]:((wise(X)|brave(X))=>(happy(X)<~>~calm(X))))&
(![X]:((old(X)<~>~calm(X))<=>~generous(X)))&
(![X]:((~funny(X)&strong(X))=>rich(X)))&
(![X]:((~funny(X)|~quiet(X))=>(generous(X)|old(X))))&
(((strong(john)<~>~humble(john)))=>(?[X]:((~calm(X)<~>~curious(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~patient(X)|~kind(X)))))&
(![X]:((~old(X)&humble(X))<=>~creative(X)))&
(![X]:((~strong(X)<~>~creative(X))=>(~strong(X)|~quiet(X))))&
(((calm(fred)<~>creative(fred)))<=>(?[X]:(curious(X))))&
(![X]:((~curious(X)<~>creative(X))<=>(generous(X)|creative(X))))&
(((rich(paul)&~rich(paul)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:((~happy(X)<~>calm(X))=>(~quiet(X)|~funny(X))))&
((~rich(susan)|~funny(susan)))&
(?[X]:((~humble(X)<~>funny(X))))&
(~happy(lucy))&
(?[X]:((patient(X)|creative(X))))&
(?[X]:((rich(X)|~funny(X))))&
(kind(john))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:((~happy(X)|~old(X)))) | ~strong(susan) | [] | null | 0 |
Everyone who is either patient or brave is curious and vice versa.
If mary is not creative or not funny then someone is either not wise or not humble and vice versa.
Everyone who is rich or generous is either patient or not tall and vice versa.
Everyone who is both wise and patient is either happy or not calm and vice versa.
Everyone who is both not quiet and strong is either not tall or brave.
If someone is not curious or not patient then someone is brave.
If mary is not creative or brave then someone is not brave or not patient and vice versa.
If mary is not happy then susan is both not wise and quiet and vice versa.
Everyone who is not generous or not happy is patient or not patient and vice versa.
If someone is either not kind or not rich then someone is not funny and vice versa.
Everyone who is not patient is brave or wise and vice versa.
If someone is curious or brave then susan is either wise or funny and vice versa.
If someone is not brave or not tall then someone is both not brave and not creative and vice versa.
If someone is humble then john is both not generous and brave.
Everyone who is either funny or not funny is not calm.
Everyone who is old or kind is either calm or happy and vice versa.
Someone is wise or strong.
Lucy is quiet or curious.
Lucy is either old or not rich.
Someone is both not humble and creative.
Alice is either not strong or creative. | Mary is strong. | neutral | (![X]:((patient(X)<~>brave(X))<=>curious(X)))&
(((~creative(mary)|~funny(mary)))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((rich(X)|generous(X))<=>(patient(X)<~>~tall(X))))&
(![X]:((wise(X)&patient(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((~quiet(X)&strong(X))=>(~tall(X)<~>brave(X))))&
((?[X]:((~curious(X)|~patient(X))))=>(?[X]:(brave(X))))&
(((~creative(mary)|brave(mary)))<=>(?[X]:((~brave(X)|~patient(X)))))&
((~happy(mary))<=>((~wise(susan)&quiet(susan))))&
(![X]:((~generous(X)|~happy(X))<=>(patient(X)|~patient(X))))&
((?[X]:((~kind(X)<~>~rich(X))))<=>(?[X]:(~funny(X))))&
(![X]:(~patient(X)<=>(brave(X)|wise(X))))&
((?[X]:((curious(X)|brave(X))))<=>((wise(susan)<~>funny(susan))))&
((?[X]:((~brave(X)|~tall(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
((?[X]:(humble(X)))=>((~generous(john)&brave(john))))&
(![X]:((funny(X)<~>~funny(X))=>~calm(X)))&
(![X]:((old(X)|kind(X))<=>(calm(X)<~>happy(X))))&
(?[X]:((wise(X)|strong(X))))&
((quiet(lucy)|curious(lucy)))&
((old(lucy)<~>~rich(lucy)))&
(?[X]:((~humble(X)&creative(X))))&
((~strong(alice)<~>creative(alice))) | strong(mary) | [] | null | 0 |
If mary is not strong or wise then susan is humble and vice versa.
If lucy is not creative then fred is not wise or not happy.
If someone is not old then fred is kind or strong.
If someone is both not strong and kind then susan is not generous and vice versa.
Everyone who is both not curious and not wise is either curious or funny.
Everyone who is not quiet or not happy is tall or strong and vice versa.
If john is both strong and not curious then someone is either creative or not creative and vice versa.
If paul is both not tall and not generous then someone is old or happy and vice versa.
Everyone who is not creative is tall and vice versa.
Everyone who is both kind and rich is not calm.
Everyone who is either not kind or brave is curious or wise.
If someone is both not humble and not strong then susan is either wise or rich.
Everyone who is both quiet and rich is old or not creative and vice versa.
Everyone who is either not strong or quiet is both not kind and not rich.
If someone is not patient or not generous then someone is either kind or not happy.
Everyone who is both strong and kind is not calm or quiet and vice versa.
Fred is not tall or not wise.
Someone is either not wise or not generous.
Someone is both not kind and strong.
Someone is not wise.
Paul is not humble.
Someone is both not funny and not rich.
Someone is patient or creative.
Susan is either not rich or not kind. | Paul is not creative. | contradiction | (((~strong(mary)|wise(mary)))<=>(humble(susan)))&
((~creative(lucy))=>((~wise(fred)|~happy(fred))))&
((?[X]:(~old(X)))=>((kind(fred)|strong(fred))))&
((?[X]:((~strong(X)&kind(X))))<=>(~generous(susan)))&
(![X]:((~curious(X)&~wise(X))=>(curious(X)<~>funny(X))))&
(![X]:((~quiet(X)|~happy(X))<=>(tall(X)|strong(X))))&
(((strong(john)&~curious(john)))<=>(?[X]:((creative(X)<~>~creative(X)))))&
(((~tall(paul)&~generous(paul)))<=>(?[X]:((old(X)|happy(X)))))&
(![X]:(~creative(X)<=>tall(X)))&
(![X]:((kind(X)&rich(X))=>~calm(X)))&
(![X]:((~kind(X)<~>brave(X))=>(curious(X)|wise(X))))&
((?[X]:((~humble(X)&~strong(X))))=>((wise(susan)<~>rich(susan))))&
(![X]:((quiet(X)&rich(X))<=>(old(X)|~creative(X))))&
(![X]:((~strong(X)<~>quiet(X))=>(~kind(X)&~rich(X))))&
((?[X]:((~patient(X)|~generous(X))))=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((strong(X)&kind(X))<=>(~calm(X)|quiet(X))))&
((~tall(fred)|~wise(fred)))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:((~kind(X)&strong(X))))&
(?[X]:(~wise(X)))&
(~humble(paul))&
(?[X]:((~funny(X)&~rich(X))))&
(?[X]:((patient(X)|creative(X))))&
((~rich(susan)<~>~kind(susan))) | ~creative(paul) | [
"p5",
"p8",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4746235381229824066650048
% SZS output start Proof for 4746235381229824066650048
6. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (strong(X0) | tall(X0))) [input p5]
9. ! [X0] : (~creative(X0) <=> tall(X0)) [input p8]
13. ! [X0] : ((rich(X0) & quiet(X0)) <=> (~creative(X0) | old(X0))) [input p12]
14. ! [X0] : ((~strong(X0) <~> quiet(X0)) => (~rich(X0) & ~kind(X0))) [input p13]
16. ! [X0] : ((kind(X0) & strong(X0)) <=> (quiet(X0) | ~calm(X0))) [input p15]
25. ~creative(paul) [input hypothesis]
40. ! [X0] : ((~rich(X0) & ~kind(X0)) | (~strong(X0) <=> quiet(X0))) [ennf transformation 14]
49. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 6]
50. ! [X0] : ((~happy(X0) | ~quiet(X0) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | (happy(X0) & quiet(X0)))) [flattening 49]
61. ! [X0] : ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))) [nnf transformation 9]
64. ! [X0] : (((rich(X0) & quiet(X0)) | (creative(X0) & ~old(X0))) & ((~creative(X0) | old(X0)) | (~rich(X0) | ~quiet(X0)))) [nnf transformation 13]
65. ! [X0] : (((rich(X0) & quiet(X0)) | (creative(X0) & ~old(X0))) & (~creative(X0) | old(X0) | ~rich(X0) | ~quiet(X0))) [flattening 64]
66. ! [X0] : ((~rich(X0) & ~kind(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) [nnf transformation 40]
71. ! [X0] : (((kind(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | (~kind(X0) | ~strong(X0)))) [nnf transformation 16]
72. ! [X0] : (((kind(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ~kind(X0) | ~strong(X0))) [flattening 71]
93. tall(X0) | strong(X0) | quiet(X0) [cnf transformation 50]
109. ~tall(X0) | ~creative(X0) [cnf transformation 61]
117. quiet(X0) | creative(X0) [cnf transformation 65]
121. ~quiet(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 66]
128. ~quiet(X0) | strong(X0) [cnf transformation 72]
130. ~quiet(X0) | kind(X0) [cnf transformation 72]
142. ~creative(paul) [cnf transformation 25]
207. 14 <=> ! [X0] : creative(X0) [avatar definition]
208. creative(X0) <- (14) [avatar component clause 207]
311. creative(X0) | strong(X0) [resolution 128,117]
312. kind(X0) | creative(X0) [resolution 130,117]
313. strong(X0) | quiet(X0) | ~creative(X0) [resolution 93,109]
314. strong(X0) | ~creative(X0) [subsumption resolution 313,128]
315. strong(X0) [subsumption resolution 314,311]
333. ~strong(X0) | ~kind(X0) | creative(X0) [resolution 121,117]
334. ~kind(X0) | creative(X0) [subsumption resolution 333,315]
335. creative(X0) [subsumption resolution 334,312]
336. 14 [avatar split clause 335,207]
337. $false <- (14) [resolution 208,142]
338. ~14 [avatar contradiction clause 337]
339. $false [avatar sat refutation 336,338]
% SZS output end Proof for 4746235381229824066650048
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and generous then someone is wise and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Everyone who is not strong is both not brave and funny and vice versa.
Everyone who is calm or quiet is both not funny and wise and vice versa.
Everyone who is not generous is both humble and curious and vice versa.
If someone is not curious or not generous then fred is both creative and old and vice versa.
If someone is funny then alice is not brave or not wise.
If someone is either not calm or rich then susan is not calm and vice versa.
Everyone who is either not generous or rich is not funny or wise and vice versa.
If paul is either rich or not brave then alice is not generous.
If mary is either not funny or quiet then someone is both brave and creative and vice versa.
Everyone who is both kind and not wise is both not rich and curious.
If fred is both calm and not calm then lucy is rich or strong and vice versa.
If someone is both not generous and not quiet then alice is both not rich and curious and vice versa.
Fred is both curious and not brave.
Someone is brave or humble.
John is humble or not patient.
Fred is not happy.
Mary is tall or not strong.
Mary is both not calm and not kind. | Susan is not patient. | neutral | ((?[X]:((~wise(X)&generous(X))))<=>(?[X]:(wise(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((creative(fred)&old(fred))))&
((?[X]:(funny(X)))=>((~brave(alice)|~wise(alice))))&
((?[X]:((~calm(X)<~>rich(X))))<=>(~calm(susan)))&
(![X]:((~generous(X)<~>rich(X))<=>(~funny(X)|wise(X))))&
(((rich(paul)<~>~brave(paul)))=>(~generous(alice)))&
(((~funny(mary)<~>quiet(mary)))<=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((kind(X)&~wise(X))=>(~rich(X)&curious(X))))&
(((calm(fred)&~calm(fred)))<=>((rich(lucy)|strong(lucy))))&
((?[X]:((~generous(X)&~quiet(X))))<=>((~rich(alice)&curious(alice))))&
((curious(fred)&~brave(fred)))&
(?[X]:((brave(X)|humble(X))))&
((humble(john)|~patient(john)))&
(~happy(fred))&
((tall(mary)|~strong(mary)))&
((~calm(mary)&~kind(mary))) | ~patient(susan) | [] | null | 0 |
Everyone who is happy or brave is either not generous or rich.
Everyone who is both brave and not humble is both not rich and kind.
Everyone who is either not strong or humble is brave or not kind.
Everyone who is not strong is not creative.
Everyone who is either patient or brave is either patient or not kind and vice versa.
If mary is generous then someone is tall or strong.
Everyone who is not calm is not humble and vice versa.
If alice is not generous or not happy then someone is old.
If fred is curious or not humble then john is either strong or not generous and vice versa.
Everyone who is both happy and humble is both calm and not curious and vice versa.
Everyone who is brave or kind is either not funny or generous.
If someone is both not humble and humble then someone is humble or not tall and vice versa.
If someone is both not quiet and curious then someone is either calm or quiet and vice versa.
Everyone who is both old and curious is not brave or patient and vice versa.
If john is strong then someone is creative or not quiet and vice versa.
Everyone who is either not curious or not wise is not generous and vice versa.
Someone is both quiet and kind.
Mary is either creative or brave.
Someone is either not tall or not quiet.
Someone is both not patient and not funny.
Someone is either not wise or generous. | Mary is creative. | entailment | (![X]:((happy(X)|brave(X))=>(~generous(X)<~>rich(X))))&
(![X]:((brave(X)&~humble(X))=>(~rich(X)&kind(X))))&
(![X]:((~strong(X)<~>humble(X))=>(brave(X)|~kind(X))))&
(![X]:(~strong(X)=>~creative(X)))&
(![X]:((patient(X)<~>brave(X))<=>(patient(X)<~>~kind(X))))&
((generous(mary))=>(?[X]:((tall(X)|strong(X)))))&
(![X]:(~calm(X)<=>~humble(X)))&
(((~generous(alice)|~happy(alice)))=>(?[X]:(old(X))))&
(((curious(fred)|~humble(fred)))<=>((strong(john)<~>~generous(john))))&
(![X]:((happy(X)&humble(X))<=>(calm(X)&~curious(X))))&
(![X]:((brave(X)|kind(X))=>(~funny(X)<~>generous(X))))&
((?[X]:((~humble(X)&humble(X))))<=>(?[X]:((humble(X)|~tall(X)))))&
((?[X]:((~quiet(X)&curious(X))))<=>(?[X]:((calm(X)<~>quiet(X)))))&
(![X]:((old(X)&curious(X))<=>(~brave(X)|patient(X))))&
((strong(john))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((~curious(X)<~>~wise(X))<=>~generous(X)))&
(?[X]:((quiet(X)&kind(X))))&
((creative(mary)<~>brave(mary)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:((~wise(X)<~>generous(X)))) | creative(mary) | [
"p1",
"p4",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2957023930771056305648856
% SZS output start Proof for 2957023930771056305648856
2. ! [X0] : ((~humble(X0) & brave(X0)) => (kind(X0) & ~rich(X0))) [input p1]
5. ! [X0] : ((patient(X0) <~> brave(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p4]
12. ? [X0] : (humble(X0) & ~humble(X0)) <=> ? [X0] : (~tall(X0) | humble(X0)) [input p11]
18. creative(mary) <~> brave(mary) [input p17]
22. ~creative(mary) [input hypothesis]
23. ? [X0] : (humble(X0) & ~humble(X0)) <=> ? [X1] : (~tall(X1) | humble(X1)) [rectify 12]
26. ! [X0] : ((kind(X0) & ~rich(X0)) | (humble(X0) | ~brave(X0))) [ennf transformation 2]
27. ! [X0] : ((kind(X0) & ~rich(X0)) | humble(X0) | ~brave(X0)) [flattening 26]
36. ! [X0] : ((((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))))) [nnf transformation 5]
47. (? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : (tall(X1) & ~humble(X1))) & (? [X1] : (~tall(X1) | humble(X1)) | ! [X0] : (~humble(X0) | humble(X0))) [nnf transformation 23]
48. (? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : (tall(X1) & ~humble(X1))) & (? [X2] : (~tall(X2) | humble(X2)) | ! [X3] : (~humble(X3) | humble(X3))) [rectify 47]
49. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK2) & ~humble(sK2)) [choice axiom]
50. ? [X2] : (~tall(X2) | humble(X2)) => (~tall(sK3) | humble(sK3)) [choice axiom]
51. ((humble(sK2) & ~humble(sK2)) | ! [X1] : (tall(X1) & ~humble(X1))) & ((~tall(sK3) | humble(sK3)) | ! [X3] : (~humble(X3) | humble(X3))) [skolemisation 48,50,49]
66. (~brave(mary) | ~creative(mary)) & (brave(mary) | creative(mary)) [nnf transformation 18]
80. ~brave(X0) | humble(X0) | kind(X0) [cnf transformation 27]
85. ~kind(X0) | patient(X0) | patient(X0) | ~brave(X0) [cnf transformation 36]
90. ~brave(X0) | ~patient(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 36]
112. ~humble(sK2) | ~humble(X1) [cnf transformation 51]
114. humble(sK2) | ~humble(X1) [cnf transformation 51]
136. brave(mary) | creative(mary) [cnf transformation 66]
144. ~creative(mary) [cnf transformation 22]
145. ~kind(X0) | patient(X0) | ~brave(X0) [duplicate literal removal 85]
148. ~brave(X0) | ~patient(X0) | ~kind(X0) [duplicate literal removal 90]
150. ~kind(X0) | ~brave(X0) [subsumption resolution 145,148]
204. 12 <=> humble(sK2) [avatar definition]
209. 13 <=> ! [X1] : ~humble(X1) [avatar definition]
210. ~humble(X1) <- (13) [avatar component clause 209]
211. 13 | 12 [avatar split clause 114,204,209]
213. 13 | ~12 [avatar split clause 112,204,209]
263. 25 <=> creative(mary) [avatar definition]
267. 26 <=> brave(mary) [avatar definition]
268. brave(mary) <- (26) [avatar component clause 267]
271. 25 | 26 [avatar split clause 136,267,263]
292. ~25 [avatar split clause 144,263]
327. humble(mary) | kind(mary) <- (26) [resolution 80,268]
328. kind(mary) <- (13, 26) [subsumption resolution 327,210]
331. ~brave(mary) <- (13, 26) [resolution 328,150]
332. $false <- (13, 26) [subsumption resolution 331,268]
333. ~13 | ~26 [avatar contradiction clause 332]
334. $false [avatar sat refutation 211,213,271,292,333]
% SZS output end Proof for 2957023930771056305648856
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is wise or calm. If mary is both patient and creative then someone is old or curious. Everyone who is not funny is both creative and not creative. If someone is kind then someone is not kind or curious. Everyone who is both not wise and quiet is both not quiet and not rich. Everyone who is not rich or not happy is not happy or tall. Everyone who is generous or kind is both not kind and creative. If someone is both not calm and not funny then someone is humble or not funny. If someone is wise or not tall then lucy is humble. If someone is both not rich and not patient then lucy is both rich and funny. Everyone who is either not quiet or not old is either not wise or generous. Everyone who is both not creative and not quiet is both generous and tall. If mary is both not tall and not generous then someone is humble or creative and vice versa. Everyone who is either kind or not generous is not wise or not calm. Everyone who is either not rich or wise is creative. Lucy is strong. Someone is humble or not generous. Susan is not curious. Someone is not creative. Mary is either wise or old. Someone is either not creative or not rich. | Lucy is humble. | entailment | ((?[X]:(~creative(X)))=>(?[X]:((wise(X)|calm(X)))))&
(((patient(mary)&creative(mary)))=>(?[X]:((old(X)|curious(X)))))&
(![X]:(~funny(X)=>(creative(X)&~creative(X))))&
((?[X]:(kind(X)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~wise(X)&quiet(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~rich(X)|~happy(X))=>(~happy(X)|tall(X))))&
(![X]:((generous(X)|kind(X))=>(~kind(X)&creative(X))))&
((?[X]:((~calm(X)&~funny(X))))=>(?[X]:((humble(X)|~funny(X)))))&
((?[X]:((wise(X)|~tall(X))))=>(humble(lucy)))&
((?[X]:((~rich(X)&~patient(X))))=>((rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)<~>~old(X))=>(~wise(X)<~>generous(X))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)&tall(X))))&
(((~tall(mary)&~generous(mary)))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:((kind(X)<~>~generous(X))=>(~wise(X)|~calm(X))))&
(![X]:((~rich(X)<~>wise(X))=>creative(X)))&
(strong(lucy))&
(?[X]:((humble(X)|~generous(X))))&
(~curious(susan))&
(?[X]:(~creative(X)))&
((wise(mary)<~>old(mary)))&
(?[X]:((~creative(X)<~>~rich(X)))) | humble(lucy) | [
"p4",
"p6",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4089770639742810809840845
% SZS output start Proof for 4089770639742810809840845
5. ! [X0] : ((quiet(X0) & ~wise(X0)) => (~rich(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : ((kind(X0) | generous(X0)) => (creative(X0) & ~kind(X0))) [input p6]
9. ? [X0] : (~tall(X0) | wise(X0)) => humble(lucy) [input p8]
12. ! [X0] : ((~quiet(X0) & ~creative(X0)) => (tall(X0) & generous(X0))) [input p11]
13. (~generous(mary) & ~tall(mary)) <=> ? [X0] : (creative(X0) | humble(X0)) [input p12]
22. ~humble(lucy) [input hypothesis]
32. ! [X0] : ((~rich(X0) & ~quiet(X0)) | (~quiet(X0) | wise(X0))) [ennf transformation 5]
33. ! [X0] : ((~rich(X0) & ~quiet(X0)) | ~quiet(X0) | wise(X0)) [flattening 32]
36. ! [X0] : ((creative(X0) & ~kind(X0)) | (~kind(X0) & ~generous(X0))) [ennf transformation 7]
38. humble(lucy) | ! [X0] : (tall(X0) & ~wise(X0)) [ennf transformation 9]
41. ! [X0] : ((tall(X0) & generous(X0)) | (quiet(X0) | creative(X0))) [ennf transformation 12]
42. ! [X0] : ((tall(X0) & generous(X0)) | quiet(X0) | creative(X0)) [flattening 41]
58. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & (? [X0] : (creative(X0) | humble(X0)) | (generous(mary) | tall(mary))) [nnf transformation 13]
59. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & (? [X0] : (creative(X0) | humble(X0)) | generous(mary) | tall(mary)) [flattening 58]
60. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & (? [X1] : (creative(X1) | humble(X1)) | generous(mary) | tall(mary)) [rectify 59]
61. ? [X1] : (creative(X1) | humble(X1)) => (creative(sK4) | humble(sK4)) [choice axiom]
62. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & ((creative(sK4) | humble(sK4)) | generous(mary) | tall(mary)) [skolemisation 60,61]
78. ~quiet(X0) | ~quiet(X0) | wise(X0) [cnf transformation 33]
84. ~generous(X0) | creative(X0) [cnf transformation 36]
87. humble(lucy) | ~wise(X0) [cnf transformation 38]
88. humble(lucy) | tall(X0) [cnf transformation 38]
95. generous(X0) | quiet(X0) | creative(X0) [cnf transformation 42]
99. ~tall(mary) | ~creative(X0) [cnf transformation 62]
113. ~humble(lucy) [cnf transformation 22]
115. ~quiet(X0) | wise(X0) [duplicate literal removal 78]
160. 11 <=> ! [X0] : tall(X0) [avatar definition]
161. tall(X0) <- (11) [avatar component clause 160]
163. 12 <=> humble(lucy) [avatar definition]
166. 11 | 12 [avatar split clause 88,163,160]
168. 13 <=> ! [X0] : ~wise(X0) [avatar definition]
169. ~wise(X0) <- (13) [avatar component clause 168]
170. 13 | 12 [avatar split clause 87,163,168]
181. quiet(X0) | creative(X0) [subsumption resolution 95,84]
183. 16 <=> ! [X0] : ~creative(X0) [avatar definition]
184. ~creative(X0) <- (16) [avatar component clause 183]
195. 19 <=> tall(mary) [avatar definition]
197. ~tall(mary) <- (~19) [avatar component clause 195]
198. 16 | ~19 [avatar split clause 99,195,183]
238. ~12 [avatar split clause 113,163]
241. $false <- (11, ~19) [resolution 197,161]
242. ~11 | 19 [avatar contradiction clause 241]
251. creative(X0) | wise(X0) [resolution 181,115]
252. wise(X0) <- (16) [subsumption resolution 251,184]
253. $false <- (13, 16) [subsumption resolution 252,169]
254. ~13 | ~16 [avatar contradiction clause 253]
255. $false [avatar sat refutation 166,170,198,238,242,254]
% SZS output end Proof for 4089770639742810809840845
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is both not patient and not rich.
If fred is either not calm or patient then fred is kind or creative.
Everyone who is either not old or old is not generous or wise.
If someone is not rich or not funny then fred is both tall and strong and vice versa.
Everyone who is kind or humble is both not happy and funny and vice versa.
Everyone who is not generous is either not kind or generous.
Everyone who is calm or generous is both calm and not humble and vice versa.
If paul is strong then someone is either calm or not humble and vice versa.
If someone is calm or brave then alice is both wise and not kind and vice versa.
Everyone who is not old or quiet is both not calm and humble and vice versa.
Everyone who is both not calm and patient is not old or brave and vice versa.
Everyone who is either not calm or rich is both not creative and curious and vice versa.
If mary is both tall and not strong then someone is either not happy or not rich and vice versa.
If susan is calm then fred is not generous or not curious.
Everyone who is curious or not calm is kind and vice versa.
Everyone who is not happy or generous is both kind and not funny and vice versa.
John is strong.
Fred is not brave.
Alice is old or not old.
Paul is either not humble or brave.
Someone is wise. | Fred is humble. | contradiction | (![X]:(creative(X)=>(~patient(X)&~rich(X))))&
(((~calm(fred)<~>patient(fred)))=>((kind(fred)|creative(fred))))&
(![X]:((~old(X)<~>old(X))=>(~generous(X)|wise(X))))&
((?[X]:((~rich(X)|~funny(X))))<=>((tall(fred)&strong(fred))))&
(![X]:((kind(X)|humble(X))<=>(~happy(X)&funny(X))))&
(![X]:(~generous(X)=>(~kind(X)<~>generous(X))))&
(![X]:((calm(X)|generous(X))<=>(calm(X)&~humble(X))))&
((strong(paul))<=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((calm(X)|brave(X))))<=>((wise(alice)&~kind(alice))))&
(![X]:((~old(X)|quiet(X))<=>(~calm(X)&humble(X))))&
(![X]:((~calm(X)&patient(X))<=>(~old(X)|brave(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(~creative(X)&curious(X))))&
(((tall(mary)&~strong(mary)))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
((calm(susan))=>((~generous(fred)|~curious(fred))))&
(![X]:((curious(X)|~calm(X))<=>kind(X)))&
(![X]:((~happy(X)|generous(X))<=>(kind(X)&~funny(X))))&
(strong(john))&
(~brave(fred))&
((old(alice)|~old(alice)))&
((~humble(paul)<~>brave(paul)))&
(?[X]:(wise(X))) | humble(fred) | [
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8676694496192249000540389
% SZS output start Proof for 8676694496192249000540389
5. ! [X0] : ((humble(X0) | kind(X0)) <=> (funny(X0) & ~happy(X0))) [input p4]
16. ! [X0] : ((generous(X0) | ~happy(X0)) <=> (~funny(X0) & kind(X0))) [input p15]
22. humble(fred) [input hypothesis]
38. ! [X0] : (((humble(X0) | kind(X0)) | (~funny(X0) | happy(X0))) & ((funny(X0) & ~happy(X0)) | (~humble(X0) & ~kind(X0)))) [nnf transformation 5]
39. ! [X0] : ((humble(X0) | kind(X0) | ~funny(X0) | happy(X0)) & ((funny(X0) & ~happy(X0)) | (~humble(X0) & ~kind(X0)))) [flattening 38]
65. ! [X0] : (((generous(X0) | ~happy(X0)) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | (~generous(X0) & happy(X0)))) [nnf transformation 16]
66. ! [X0] : ((generous(X0) | ~happy(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | (~generous(X0) & happy(X0)))) [flattening 65]
82. ~happy(X0) | ~humble(X0) [cnf transformation 39]
84. ~humble(X0) | funny(X0) [cnf transformation 39]
130. ~funny(X0) | happy(X0) [cnf transformation 66]
139. humble(fred) [cnf transformation 22]
291. funny(fred) [resolution 84,139]
308. happy(fred) [resolution 130,291]
310. ~humble(fred) [resolution 308,82]
312. $false [subsumption resolution 310,139]
% SZS output end Proof for 8676694496192249000540389
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then someone is patient.
Everyone who is not happy or kind is happy or not tall and vice versa.
Everyone who is strong is both curious and not strong and vice versa.
If john is both not quiet and happy then someone is not tall.
Everyone who is either not happy or quiet is not brave.
Everyone who is either brave or not creative is happy.
If someone is both not old and not quiet then someone is calm or not funny.
If someone is calm or not calm then alice is not happy and vice versa.
Everyone who is not funny is both not happy and not brave and vice versa.
Everyone who is creative is not generous and vice versa.
If someone is both not tall and humble then john is both quiet and not quiet.
Everyone who is not calm is both calm and funny and vice versa.
If john is both not rich and happy then someone is not funny or not happy.
If someone is either not wise or not patient then lucy is generous and vice versa.
If mary is both calm and not brave then someone is kind or not funny and vice versa.
Everyone who is either tall or not old is both not happy and not quiet.
Alice is either not wise or not humble.
Mary is not rich.
Someone is not generous.
Susan is either old or not wise.
Someone is kind or tall. | Alice is tall. | contradiction | ((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
(![X]:((~happy(X)|kind(X))<=>(happy(X)|~tall(X))))&
(![X]:(strong(X)<=>(curious(X)&~strong(X))))&
(((~quiet(john)&happy(john)))=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)<~>quiet(X))=>~brave(X)))&
(![X]:((brave(X)<~>~creative(X))=>happy(X)))&
((?[X]:((~old(X)&~quiet(X))))=>(?[X]:((calm(X)|~funny(X)))))&
((?[X]:((calm(X)|~calm(X))))<=>(~happy(alice)))&
(![X]:(~funny(X)<=>(~happy(X)&~brave(X))))&
(![X]:(creative(X)<=>~generous(X)))&
((?[X]:((~tall(X)&humble(X))))=>((quiet(john)&~quiet(john))))&
(![X]:(~calm(X)<=>(calm(X)&funny(X))))&
(((~rich(john)&happy(john)))=>(?[X]:((~funny(X)|~happy(X)))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>(generous(lucy)))&
(((calm(mary)&~brave(mary)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((tall(X)<~>~old(X))=>(~happy(X)&~quiet(X))))&
((~wise(alice)<~>~humble(alice)))&
(~rich(mary))&
(?[X]:(~generous(X)))&
((old(susan)<~>~wise(susan)))&
(?[X]:((kind(X)|tall(X)))) | tall(alice) | [
"p1",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2690044392486881501942955
% SZS output start Proof for 2690044392486881501942955
2. ! [X0] : ((kind(X0) | ~happy(X0)) <=> (~tall(X0) | happy(X0))) [input p1]
8. ? [X0] : (~calm(X0) | calm(X0)) <=> ~happy(alice) [input p7]
12. ! [X0] : (~calm(X0) <=> (funny(X0) & calm(X0))) [input p11]
22. tall(alice) [input hypothesis]
38. ! [X0] : (((kind(X0) | ~happy(X0)) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | (~kind(X0) & happy(X0)))) [nnf transformation 2]
39. ! [X0] : ((kind(X0) | ~happy(X0) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | (~kind(X0) & happy(X0)))) [flattening 38]
49. (? [X0] : (~calm(X0) | calm(X0)) | happy(alice)) & (~happy(alice) | ! [X0] : (calm(X0) & ~calm(X0))) [nnf transformation 8]
50. (? [X0] : (~calm(X0) | calm(X0)) | happy(alice)) & (~happy(alice) | ! [X1] : (calm(X1) & ~calm(X1))) [rectify 49]
51. ? [X0] : (~calm(X0) | calm(X0)) => (~calm(sK3) | calm(sK3)) [choice axiom]
52. ((~calm(sK3) | calm(sK3)) | happy(alice)) & (~happy(alice) | ! [X1] : (calm(X1) & ~calm(X1))) [skolemisation 50,51]
56. ! [X0] : ((~calm(X0) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | calm(X0))) [nnf transformation 12]
57. ! [X0] : ((~calm(X0) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | calm(X0))) [flattening 56]
77. ~tall(X0) | happy(X0) | happy(X0) [cnf transformation 39]
90. ~happy(alice) | ~calm(X1) [cnf transformation 52]
100. calm(X0) | calm(X0) [cnf transformation 57]
124. tall(alice) [cnf transformation 22]
125. calm(X0) [duplicate literal removal 100]
129. ~tall(X0) | happy(X0) [duplicate literal removal 77]
165. 9 <=> ! [X1] : calm(X1) [avatar definition]
166. calm(X1) <- (9) [avatar component clause 165]
168. 10 <=> happy(alice) [avatar definition]
173. 11 <=> ! [X1] : ~calm(X1) [avatar definition]
174. ~calm(X1) <- (11) [avatar component clause 173]
175. 11 | ~10 [avatar split clause 90,168,173]
181. 9 [avatar split clause 125,165]
284. happy(alice) [resolution 129,124]
287. 10 [avatar split clause 284,168]
288. $false <- (9, 11) [subsumption resolution 174,166]
289. ~9 | ~11 [avatar contradiction clause 288]
290. $false [avatar sat refutation 175,181,287,289]
% SZS output end Proof for 2690044392486881501942955
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or calm is both funny and not kind and vice versa.
Everyone who is either quiet or not creative is either not humble or not wise and vice versa.
If paul is brave or curious then someone is not tall or not funny and vice versa.
If susan is tall then someone is either kind or not happy and vice versa.
Everyone who is not old or not funny is funny or not old and vice versa.
Everyone who is either rich or not old is not curious.
Everyone who is patient or not creative is not generous.
Everyone who is either quiet or brave is either not funny or humble and vice versa.
If someone is both not humble and not curious then paul is both not kind and not quiet.
If someone is either old or not rich then fred is quiet and vice versa.
If someone is not curious then paul is rich or not happy and vice versa.
Everyone who is either humble or rich is either not curious or not happy and vice versa.
If someone is quiet or not curious then someone is not generous and vice versa.
Everyone who is either not generous or humble is either not tall or not rich.
Everyone who is not brave or generous is both not curious and not creative.
Everyone who is calm or not wise is both humble and generous.
Someone is not happy.
Someone is humble or generous.
Paul is happy.
Mary is wise.
Fred is both not quiet and not patient.
Susan is both not curious and not tall. | Paul is rich. | entailment | (![X]:((quiet(X)<~>calm(X))<=>(funny(X)&~kind(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(~humble(X)<~>~wise(X))))&
(((brave(paul)|curious(paul)))<=>(?[X]:((~tall(X)|~funny(X)))))&
((tall(susan))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((~old(X)|~funny(X))<=>(funny(X)|~old(X))))&
(![X]:((rich(X)<~>~old(X))=>~curious(X)))&
(![X]:((patient(X)|~creative(X))=>~generous(X)))&
(![X]:((quiet(X)<~>brave(X))<=>(~funny(X)<~>humble(X))))&
((?[X]:((~humble(X)&~curious(X))))=>((~kind(paul)&~quiet(paul))))&
((?[X]:((old(X)<~>~rich(X))))<=>(quiet(fred)))&
((?[X]:(~curious(X)))<=>((rich(paul)|~happy(paul))))&
(![X]:((humble(X)<~>rich(X))<=>(~curious(X)<~>~happy(X))))&
((?[X]:((quiet(X)|~curious(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~generous(X)<~>humble(X))=>(~tall(X)<~>~rich(X))))&
(![X]:((~brave(X)|generous(X))=>(~curious(X)&~creative(X))))&
(![X]:((calm(X)|~wise(X))=>(humble(X)&generous(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)|generous(X))))&
(happy(paul))&
(wise(mary))&
((~quiet(fred)&~patient(fred)))&
((~curious(susan)&~tall(susan))) | rich(paul) | [
"p4",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6094714323284276118791956
% SZS output start Proof for 6094714323284276118791956
5. ! [X0] : ((~funny(X0) | ~old(X0)) <=> (~old(X0) | funny(X0))) [input p4]
10. ? [X0] : (old(X0) <~> ~rich(X0)) <=> quiet(fred) [input p9]
21. ~patient(fred) & ~quiet(fred) [input p20]
23. ~rich(paul) [input hypothesis]
25. ~quiet(fred) [pure predicate removal 21]
45. ! [X0] : (((~funny(X0) | ~old(X0)) | (old(X0) & ~funny(X0))) & ((~old(X0) | funny(X0)) | (funny(X0) & old(X0)))) [nnf transformation 5]
46. ! [X0] : ((~funny(X0) | ~old(X0) | (old(X0) & ~funny(X0))) & (~old(X0) | funny(X0) | (funny(X0) & old(X0)))) [flattening 45]
49. (? [X0] : ((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~quiet(fred)) & (quiet(fred) | ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0)))) [nnf transformation 10]
50. (? [X0] : ((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~quiet(fred)) & (quiet(fred) | ! [X1] : ((old(X1) | rich(X1)) & (~rich(X1) | ~old(X1)))) [rectify 49]
51. ? [X0] : ((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) => ((rich(sK2) | ~old(sK2)) & (~rich(sK2) | old(sK2))) [choice axiom]
52. (((rich(sK2) | ~old(sK2)) & (~rich(sK2) | old(sK2))) | ~quiet(fred)) & (quiet(fred) | ! [X1] : ((old(X1) | rich(X1)) & (~rich(X1) | ~old(X1)))) [skolemisation 50,51]
92. ~old(X0) | funny(X0) | funny(X0) [cnf transformation 46]
93. ~funny(X0) | ~old(X0) | ~funny(X0) [cnf transformation 46]
109. quiet(fred) | old(X1) | rich(X1) [cnf transformation 52]
142. ~quiet(fred) [cnf transformation 25]
145. ~rich(paul) [cnf transformation 23]
146. ~old(X0) | funny(X0) [duplicate literal removal 92]
147. ~funny(X0) | ~old(X0) [duplicate literal removal 93]
196. ~old(X0) [subsumption resolution 146,147]
213. 15 <=> quiet(fred) [avatar definition]
221. quiet(fred) | rich(X1) [subsumption resolution 109,196]
223. 17 <=> ! [X1] : rich(X1) [avatar definition]
224. rich(X1) <- (17) [avatar component clause 223]
225. 17 | 15 [avatar split clause 221,213,223]
236. 20 <=> rich(paul) [avatar definition]
238. ~rich(paul) <- (~20) [avatar component clause 236]
274. ~15 [avatar split clause 142,213]
276. ~20 [avatar split clause 145,236]
277. $false <- (17, ~20) [resolution 238,224]
278. ~17 | 20 [avatar contradiction clause 277]
279. $false [avatar sat refutation 225,274,276,278]
% SZS output end Proof for 6094714323284276118791956
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is either not patient or funny and vice versa.
If fred is patient or humble then someone is quiet and vice versa.
If lucy is either not kind or kind then someone is both not humble and not strong.
If alice is happy or not happy then john is not wise or rich and vice versa.
If someone is not wise or tall then susan is not wise.
Everyone who is not patient is both not patient and not generous.
If someone is not funny or not old then someone is either not creative or generous and vice versa.
Everyone who is creative is not generous and vice versa.
If someone is both patient and not happy then alice is both strong and not humble.
Everyone who is both generous and not curious is funny and vice versa.
If someone is either patient or tall then john is either not kind or not generous and vice versa.
Everyone who is either not wise or curious is humble or generous and vice versa.
If susan is wise or not strong then mary is not humble or not wise and vice versa.
If someone is rich then fred is happy or not creative and vice versa.
Everyone who is not strong is either not wise or not calm.
Everyone who is either rich or not creative is not patient and vice versa.
Lucy is wise or kind.
Fred is funny.
Susan is either not curious or brave.
Someone is either not patient or patient.
Someone is both not humble and strong. | Susan is patient. | entailment | (![X]:(quiet(X)<=>(~patient(X)<~>funny(X))))&
(((patient(fred)|humble(fred)))<=>(?[X]:(quiet(X))))&
(((~kind(lucy)<~>kind(lucy)))=>(?[X]:((~humble(X)&~strong(X)))))&
(((happy(alice)|~happy(alice)))<=>((~wise(john)|rich(john))))&
((?[X]:((~wise(X)|tall(X))))=>(~wise(susan)))&
(![X]:(~patient(X)=>(~patient(X)&~generous(X))))&
((?[X]:((~funny(X)|~old(X))))<=>(?[X]:((~creative(X)<~>generous(X)))))&
(![X]:(creative(X)<=>~generous(X)))&
((?[X]:((patient(X)&~happy(X))))=>((strong(alice)&~humble(alice))))&
(![X]:((generous(X)&~curious(X))<=>funny(X)))&
((?[X]:((patient(X)<~>tall(X))))<=>((~kind(john)<~>~generous(john))))&
(![X]:((~wise(X)<~>curious(X))<=>(humble(X)|generous(X))))&
(((wise(susan)|~strong(susan)))<=>((~humble(mary)|~wise(mary))))&
((?[X]:(rich(X)))<=>((happy(fred)|~creative(fred))))&
(![X]:(~strong(X)=>(~wise(X)<~>~calm(X))))&
(![X]:((rich(X)<~>~creative(X))<=>~patient(X)))&
((wise(lucy)|kind(lucy)))&
(funny(fred))&
((~curious(susan)<~>brave(susan)))&
(?[X]:((~patient(X)<~>patient(X))))&
(?[X]:((~humble(X)&strong(X)))) | patient(susan) | [
"p5",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 30124361301602334248267
% SZS output start Proof for 30124361301602334248267
6. ! [X0] : (~patient(X0) => (~generous(X0) & ~patient(X0))) [input p5]
7. ? [X0] : (~old(X0) | ~funny(X0)) <=> ? [X0] : (~creative(X0) <~> generous(X0)) [input p6]
8. ! [X0] : (creative(X0) <=> ~generous(X0)) [input p7]
10. ! [X0] : ((~curious(X0) & generous(X0)) <=> funny(X0)) [input p9]
22. ~patient(susan) [input hypothesis]
23. ? [X0] : (~old(X0) | ~funny(X0)) <=> ? [X1] : (~creative(X1) <~> generous(X1)) [rectify 7]
26. ! [X0] : ((~generous(X0) & ~patient(X0)) | patient(X0)) [ennf transformation 6]
40. (? [X0] : (~old(X0) | ~funny(X0)) | ! [X1] : ((~creative(X1) | ~generous(X1)) & (generous(X1) | creative(X1)))) & (? [X1] : ((~generous(X1) | creative(X1)) & (generous(X1) | ~creative(X1))) | ! [X0] : (old(X0) & funny(X0))) [nnf transformation 23]
41. (? [X0] : (~old(X0) | ~funny(X0)) | ! [X1] : ((~creative(X1) | ~generous(X1)) & (generous(X1) | creative(X1)))) & (? [X2] : ((~generous(X2) | creative(X2)) & (generous(X2) | ~creative(X2))) | ! [X3] : (old(X3) & funny(X3))) [rectify 40]
42. ? [X0] : (~old(X0) | ~funny(X0)) => (~old(sK2) | ~funny(sK2)) [choice axiom]
43. ? [X2] : ((~generous(X2) | creative(X2)) & (generous(X2) | ~creative(X2))) => ((~generous(sK3) | creative(sK3)) & (generous(sK3) | ~creative(sK3))) [choice axiom]
44. ((~old(sK2) | ~funny(sK2)) | ! [X1] : ((~creative(X1) | ~generous(X1)) & (generous(X1) | creative(X1)))) & (((~generous(sK3) | creative(sK3)) & (generous(sK3) | ~creative(sK3))) | ! [X3] : (old(X3) & funny(X3))) [skolemisation 41,43,42]
45. ! [X0] : ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0))) [nnf transformation 8]
46. ! [X0] : (((~curious(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | (curious(X0) | ~generous(X0)))) [nnf transformation 10]
47. ! [X0] : (((~curious(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | curious(X0) | ~generous(X0))) [flattening 46]
87. ~generous(X0) | patient(X0) [cnf transformation 26]
88. generous(sK3) | ~creative(sK3) | funny(X3) [cnf transformation 44]
90. ~generous(sK3) | creative(sK3) | funny(X3) [cnf transformation 44]
94. ~generous(X0) | ~creative(X0) [cnf transformation 45]
95. creative(X0) | generous(X0) [cnf transformation 45]
99. ~funny(X0) | generous(X0) [cnf transformation 47]
136. ~patient(susan) [cnf transformation 22]
202. 14 <=> ! [X1] : (~creative(X1) | ~generous(X1)) [avatar definition]
203. ~creative(X1) | ~generous(X1) <- (14) [avatar component clause 202]
214. 17 <=> ! [X1] : (generous(X1) | creative(X1)) [avatar definition]
215. creative(X1) | generous(X1) <- (17) [avatar component clause 214]
221. 19 <=> creative(sK3) [avatar definition]
222. ~creative(sK3) <- (~19) [avatar component clause 221]
223. creative(sK3) <- (19) [avatar component clause 221]
225. 20 <=> generous(sK3) [avatar definition]
227. ~generous(sK3) <- (~20) [avatar component clause 225]
230. 21 <=> ! [X3] : funny(X3) [avatar definition]
231. funny(X3) <- (21) [avatar component clause 230]
232. 21 | 19 | ~20 [avatar split clause 90,225,221,230]
234. 21 | ~19 | 20 [avatar split clause 88,225,221,230]
235. 17 [avatar split clause 95,214]
236. 14 [avatar split clause 94,202]
332. generous(sK3) <- (17, ~19) [resolution 215,222]
335. $false <- (17, ~19, ~20) [subsumption resolution 332,227]
336. ~17 | 19 | 20 [avatar contradiction clause 335]
337. ~generous(sK3) <- (14, 19) [resolution 223,203]
340. ~20 | ~14 | ~19 [avatar split clause 337,221,202,225]
341. generous(X0) <- (21) [resolution 231,99]
342. patient(X0) <- (21) [resolution 341,87]
346. $false <- (21) [resolution 342,136]
347. ~21 [avatar contradiction clause 346]
348. $false [avatar sat refutation 232,234,235,236,336,340,347]
% SZS output end Proof for 30124361301602334248267
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If susan is not wise then fred is either not curious or funny.
If alice is not quiet then someone is happy and vice versa.
Everyone who is not wise or generous is either not rich or not old.
If someone is quiet then paul is happy and vice versa.
Everyone who is not humble is both not happy and not curious and vice versa.
If someone is both not rich and not quiet then someone is not creative or patient and vice versa.
If someone is wise or humble then john is tall and vice versa.
If someone is quiet or not rich then someone is either not tall or not calm.
If lucy is either happy or not kind then john is either not funny or funny.
If mary is both tall and not old then mary is patient or rich and vice versa.
If someone is either not tall or kind then someone is either creative or kind.
If john is both kind and old then john is both brave and not generous.
Everyone who is either calm or generous is either curious or generous and vice versa.
Everyone who is either generous or tall is not tall and vice versa.
If mary is not quiet then lucy is either not funny or happy.
Everyone who is curious or not old is either not calm or rich and vice versa.
Mary is calm or strong.
Someone is both not patient and funny.
Someone is not strong or not old.
Alice is either wise or patient. | John is old. | contradiction | ((~wise(susan))=>((~curious(fred)<~>funny(fred))))&
((~quiet(alice))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)|generous(X))=>(~rich(X)<~>~old(X))))&
((?[X]:(quiet(X)))<=>(happy(paul)))&
(![X]:(~humble(X)<=>(~happy(X)&~curious(X))))&
((?[X]:((~rich(X)&~quiet(X))))<=>(?[X]:((~creative(X)|patient(X)))))&
((?[X]:((wise(X)|humble(X))))<=>(tall(john)))&
((?[X]:((quiet(X)|~rich(X))))=>(?[X]:((~tall(X)<~>~calm(X)))))&
(((happy(lucy)<~>~kind(lucy)))=>((~funny(john)<~>funny(john))))&
(((tall(mary)&~old(mary)))<=>((patient(mary)|rich(mary))))&
((?[X]:((~tall(X)<~>kind(X))))=>(?[X]:((creative(X)<~>kind(X)))))&
(((kind(john)&old(john)))=>((brave(john)&~generous(john))))&
(![X]:((calm(X)<~>generous(X))<=>(curious(X)<~>generous(X))))&
(![X]:((generous(X)<~>tall(X))<=>~tall(X)))&
((~quiet(mary))=>((~funny(lucy)<~>happy(lucy))))&
(![X]:((curious(X)|~old(X))<=>(~calm(X)<~>rich(X))))&
((calm(mary)|strong(mary)))&
(?[X]:((~patient(X)&funny(X))))&
(?[X]:((~strong(X)|~old(X))))&
((wise(alice)<~>patient(alice))) | old(john) | [
"p2",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7471638218730718062850920
% SZS output start Proof for 7471638218730718062850920
3. ! [X0] : ((generous(X0) | ~wise(X0)) => (~rich(X0) <~> ~old(X0))) [input p2]
13. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (curious(X0) <~> generous(X0))) [input p12]
14. ! [X0] : ((generous(X0) <~> tall(X0)) <=> ~tall(X0)) [input p13]
16. ! [X0] : ((~old(X0) | curious(X0)) <=> (~calm(X0) <~> rich(X0))) [input p15]
21. old(john) [input hypothesis]
27. ! [X0] : ((~rich(X0) <~> ~old(X0)) | (~generous(X0) & wise(X0))) [ennf transformation 3]
39. ! [X0] : (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (~generous(X0) & wise(X0))) [nnf transformation 27]
66. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0)))) & (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 13]
67. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | tall(X0)) & (~tall(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [nnf transformation 14]
69. ! [X0] : (((~old(X0) | curious(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (old(X0) & ~curious(X0)))) [nnf transformation 16]
70. ! [X0] : ((~old(X0) | curious(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (old(X0) & ~curious(X0)))) [flattening 69]
81. ~old(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 39]
83. ~generous(X0) | rich(X0) | old(X0) [cnf transformation 39]
115. generous(X0) | curious(X0) | generous(X0) | ~calm(X0) [cnf transformation 66]
118. ~generous(X0) | ~curious(X0) | calm(X0) | ~generous(X0) [cnf transformation 66]
119. generous(X0) | calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 66]
122. ~generous(X0) | ~calm(X0) | curious(X0) | ~generous(X0) [cnf transformation 66]
124. ~tall(X0) | generous(X0) | ~tall(X0) [cnf transformation 67]
125. tall(X0) | generous(X0) | tall(X0) [cnf transformation 67]
129. rich(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 70]
133. ~old(X0) | curious(X0) | rich(X0) | calm(X0) [cnf transformation 70]
141. old(john) [cnf transformation 21]
142. ~tall(X0) | generous(X0) [duplicate literal removal 124]
143. tall(X0) | generous(X0) [duplicate literal removal 125]
144. generous(X0) | curious(X0) | ~calm(X0) [duplicate literal removal 115]
145. ~generous(X0) | ~curious(X0) | calm(X0) [duplicate literal removal 118]
146. ~curious(X0) | calm(X0) | generous(X0) [duplicate literal removal 119]
147. ~calm(X0) | ~generous(X0) | curious(X0) [duplicate literal removal 122]
240. 22 <=> ! [X1] : rich(X1) [avatar definition]
241. rich(X1) <- (22) [avatar component clause 240]
298. 34 <=> old(john) [avatar definition]
299. old(john) <- (34) [avatar component clause 298]
306. ~curious(X0) | calm(X0) [subsumption resolution 145,146]
307. ~calm(X0) | curious(X0) [subsumption resolution 144,147]
308. generous(X0) [subsumption resolution 142,143]
323. ~old(X0) | rich(X0) | calm(X0) [subsumption resolution 133,306]
324. ~calm(X0) | rich(X0) [subsumption resolution 129,307]
353. 34 [avatar split clause 141,298]
389. ~rich(john) | ~generous(john) <- (34) [resolution 81,299]
404. old(X0) | rich(X0) [resolution 83,308]
426. rich(X0) | calm(X0) | rich(X0) [resolution 323,404]
429. rich(X0) | calm(X0) [duplicate literal removal 426]
431. rich(X0) [subsumption resolution 429,324]
432. 22 [avatar split clause 431,240]
437. ~generous(john) <- (22, 34) [subsumption resolution 389,241]
438. $false <- (22, 34) [subsumption resolution 437,308]
439. ~22 | ~34 [avatar contradiction clause 438]
440. $false [avatar sat refutation 353,432,439]
% SZS output end Proof for 7471638218730718062850920
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If mary is either not old or not creative then someone is both tall and old.
If someone is both not humble and creative then fred is either not funny or tall and vice versa.
Everyone who is either calm or not kind is calm and vice versa.
If someone is both strong and wise then fred is either wise or tall and vice versa.
Everyone who is either not quiet or not humble is humble or tall.
If john is not patient then mary is both brave and calm and vice versa.
If someone is either patient or wise then someone is both humble and wise.
Everyone who is wise or creative is both rich and strong.
If lucy is either patient or not quiet then mary is either not creative or not humble and vice versa.
Everyone who is both not wise and not humble is curious.
Everyone who is both curious and not strong is either humble or not brave and vice versa.
Everyone who is curious or not old is either not happy or tall and vice versa.
Everyone who is happy or kind is either not patient or generous and vice versa.
If someone is not strong then someone is both not calm and patient and vice versa.
If someone is not creative then fred is not humble or old.
Everyone who is not patient is both strong and old.
Someone is tall or old.
Someone is both kind and wise.
Someone is both not quiet and curious.
Lucy is either not generous or strong.
Fred is either brave or not funny.
Paul is both rich and creative.
Someone is curious or not humble.
Someone is not wise or generous. | Mary is not kind. | contradiction | (((~old(mary)<~>~creative(mary)))=>(?[X]:((tall(X)&old(X)))))&
((?[X]:((~humble(X)&creative(X))))<=>((~funny(fred)<~>tall(fred))))&
(![X]:((calm(X)<~>~kind(X))<=>calm(X)))&
((?[X]:((strong(X)&wise(X))))<=>((wise(fred)<~>tall(fred))))&
(![X]:((~quiet(X)<~>~humble(X))=>(humble(X)|tall(X))))&
((~patient(john))<=>((brave(mary)&calm(mary))))&
((?[X]:((patient(X)<~>wise(X))))=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((wise(X)|creative(X))=>(rich(X)&strong(X))))&
(((patient(lucy)<~>~quiet(lucy)))<=>((~creative(mary)<~>~humble(mary))))&
(![X]:((~wise(X)&~humble(X))=>curious(X)))&
(![X]:((curious(X)&~strong(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((curious(X)|~old(X))<=>(~happy(X)<~>tall(X))))&
(![X]:((happy(X)|kind(X))<=>(~patient(X)<~>generous(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~calm(X)&patient(X)))))&
((?[X]:(~creative(X)))=>((~humble(fred)|old(fred))))&
(![X]:(~patient(X)=>(strong(X)&old(X))))&
(?[X]:((tall(X)|old(X))))&
(?[X]:((kind(X)&wise(X))))&
(?[X]:((~quiet(X)&curious(X))))&
((~generous(lucy)<~>strong(lucy)))&
((brave(fred)<~>~funny(fred)))&
((rich(paul)&creative(paul)))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((~wise(X)|generous(X)))) | ~kind(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1499018317645767042165300
% SZS output start Proof for 1499018317645767042165300
3. ! [X0] : ((calm(X0) <~> ~kind(X0)) <=> calm(X0)) [input p2]
25. ~kind(mary) [input hypothesis]
47. ! [X0] : ((((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | ~calm(X0)) & (calm(X0) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0))))) [nnf transformation 3]
94. calm(X0) | calm(X0) | kind(X0) [cnf transformation 47]
96. kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 47]
159. ~kind(mary) [cnf transformation 25]
161. calm(X0) | kind(X0) [duplicate literal removal 94]
162. kind(X0) | ~calm(X0) [duplicate literal removal 96]
208. kind(X0) [subsumption resolution 161,162]
361. $false [subsumption resolution 159,208]
% SZS output end Proof for 1499018317645767042165300
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or strong is either not generous or kind and vice versa. If someone is either not old or not patient then fred is both calm and quiet. If alice is calm then alice is not quiet. Everyone who is both not calm and not generous is either patient or not wise. If someone is both creative and generous then lucy is both not old and not kind. Everyone who is not rich or not creative is not old and vice versa. Everyone who is not wise is not humble or not creative. Everyone who is not funny is either not generous or not kind and vice versa. If someone is not generous then paul is both wise and funny and vice versa. If lucy is either rich or tall then someone is either not old or brave. Everyone who is not quiet or wise is both creative and generous and vice versa. Everyone who is curious or not strong is both happy and quiet and vice versa. Everyone who is patient or not rich is both wise and funny and vice versa. Everyone who is tall or not old is both not brave and not tall and vice versa. If someone is either happy or kind then lucy is calm and vice versa. Everyone who is both not happy and not brave is both not wise and rich and vice versa. Mary is both happy and calm. Someone is not curious. Someone is both quiet and not kind. Lucy is either funny or happy. Someone is not strong or curious. Susan is wise or calm. Someone is both not calm and creative. | Lucy is not strong. | contradiction | (![X]:((generous(X)|strong(X))<=>(~generous(X)<~>kind(X))))&
((?[X]:((~old(X)<~>~patient(X))))=>((calm(fred)&quiet(fred))))&
((calm(alice))=>(~quiet(alice)))&
(![X]:((~calm(X)&~generous(X))=>(patient(X)<~>~wise(X))))&
((?[X]:((creative(X)&generous(X))))=>((~old(lucy)&~kind(lucy))))&
(![X]:((~rich(X)|~creative(X))<=>~old(X)))&
(![X]:(~wise(X)=>(~humble(X)|~creative(X))))&
(![X]:(~funny(X)<=>(~generous(X)<~>~kind(X))))&
((?[X]:(~generous(X)))<=>((wise(paul)&funny(paul))))&
(((rich(lucy)<~>tall(lucy)))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~quiet(X)|wise(X))<=>(creative(X)&generous(X))))&
(![X]:((curious(X)|~strong(X))<=>(happy(X)&quiet(X))))&
(![X]:((patient(X)|~rich(X))<=>(wise(X)&funny(X))))&
(![X]:((tall(X)|~old(X))<=>(~brave(X)&~tall(X))))&
((?[X]:((happy(X)<~>kind(X))))<=>(calm(lucy)))&
(![X]:((~happy(X)&~brave(X))<=>(~wise(X)&rich(X))))&
((happy(mary)&calm(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((quiet(X)&~kind(X))))&
((funny(lucy)<~>happy(lucy)))&
(?[X]:((~strong(X)|curious(X))))&
((wise(susan)|calm(susan)))&
(?[X]:((~calm(X)&creative(X)))) | ~strong(lucy) | [
"p0",
"p4",
"p7",
"p8",
"p10",
"p11",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8998122266920900703609924
% SZS output start Proof for 8998122266920900703609924
1. ! [X0] : ((strong(X0) | generous(X0)) <=> (~generous(X0) <~> kind(X0))) [input p0]
5. ? [X0] : (generous(X0) & creative(X0)) => (~kind(lucy) & ~old(lucy)) [input p4]
8. ! [X0] : (~funny(X0) <=> (~generous(X0) <~> ~kind(X0))) [input p7]
9. ? [X0] : ~generous(X0) <=> (funny(paul) & wise(paul)) [input p8]
11. ! [X0] : ((wise(X0) | ~quiet(X0)) <=> (generous(X0) & creative(X0))) [input p10]
12. ! [X0] : ((~strong(X0) | curious(X0)) <=> (quiet(X0) & happy(X0))) [input p11]
20. funny(lucy) <~> happy(lucy) [input p19]
23. ? [X0] : (creative(X0) & ~calm(X0)) [input p22]
24. ~strong(lucy) [input hypothesis]
30. (~kind(lucy) & ~old(lucy)) | ! [X0] : (~generous(X0) | ~creative(X0)) [ennf transformation 5]
32. ! [X0] : (((strong(X0) | generous(X0)) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (~strong(X0) & ~generous(X0)))) [nnf transformation 1]
33. ! [X0] : ((strong(X0) | generous(X0) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (~strong(X0) & ~generous(X0)))) [flattening 32]
38. ! [X0] : ((~funny(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | funny(X0))) [nnf transformation 8]
39. (? [X0] : ~generous(X0) | (~funny(paul) | ~wise(paul))) & ((funny(paul) & wise(paul)) | ! [X0] : generous(X0)) [nnf transformation 9]
40. (? [X0] : ~generous(X0) | ~funny(paul) | ~wise(paul)) & ((funny(paul) & wise(paul)) | ! [X0] : generous(X0)) [flattening 39]
41. (? [X0] : ~generous(X0) | ~funny(paul) | ~wise(paul)) & ((funny(paul) & wise(paul)) | ! [X1] : generous(X1)) [rectify 40]
42. ? [X0] : ~generous(X0) => ~generous(sK0) [choice axiom]
43. (~generous(sK0) | ~funny(paul) | ~wise(paul)) & ((funny(paul) & wise(paul)) | ! [X1] : generous(X1)) [skolemisation 41,42]
47. ! [X0] : (((wise(X0) | ~quiet(X0)) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | (~wise(X0) & quiet(X0)))) [nnf transformation 11]
48. ! [X0] : ((wise(X0) | ~quiet(X0) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | (~wise(X0) & quiet(X0)))) [flattening 47]
49. ! [X0] : (((~strong(X0) | curious(X0)) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | (strong(X0) & ~curious(X0)))) [nnf transformation 12]
50. ! [X0] : ((~strong(X0) | curious(X0) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | (strong(X0) & ~curious(X0)))) [flattening 49]
65. (~happy(lucy) | ~funny(lucy)) & (happy(lucy) | funny(lucy)) [nnf transformation 20]
68. ? [X0] : (creative(X0) & ~calm(X0)) => (creative(sK6) & ~calm(sK6)) [choice axiom]
69. creative(sK6) & ~calm(sK6) [skolemisation 23,68]
70. kind(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 33]
84. ~kind(lucy) | ~generous(X0) | ~creative(X0) [cnf transformation 30]
89. kind(X0) | generous(X0) | funny(X0) [cnf transformation 38]
92. wise(paul) | generous(X1) [cnf transformation 43]
100. ~wise(X0) | creative(X0) [cnf transformation 48]
102. ~wise(X0) | generous(X0) [cnf transformation 48]
105. happy(X0) | strong(X0) [cnf transformation 50]
133. ~happy(lucy) | ~funny(lucy) [cnf transformation 65]
137. creative(sK6) [cnf transformation 69]
138. ~strong(lucy) [cnf transformation 24]
141. ~generous(X0) | kind(X0) [duplicate literal removal 70]
171. 7 <=> ! [X0] : (~generous(X0) | ~creative(X0)) [avatar definition]
172. ~creative(X0) | ~generous(X0) <- (7) [avatar component clause 171]
174. 8 <=> kind(lucy) [avatar definition]
177. 7 | ~8 [avatar split clause 84,174,171]
183. funny(X0) | kind(X0) [subsumption resolution 89,141]
186. 10 <=> wise(paul) [avatar definition]
187. wise(paul) <- (10) [avatar component clause 186]
199. 13 <=> ! [X1] : generous(X1) [avatar definition]
200. generous(X1) <- (13) [avatar component clause 199]
202. 13 | 10 [avatar split clause 92,186,199]
248. 23 <=> funny(lucy) [avatar definition]
250. ~funny(lucy) <- (~23) [avatar component clause 248]
252. 24 <=> happy(lucy) [avatar definition]
254. ~happy(lucy) <- (~24) [avatar component clause 252]
255. ~23 | ~24 [avatar split clause 133,252,248]
275. creative(paul) <- (10) [resolution 100,187]
277. generous(paul) <- (10) [resolution 102,187]
279. strong(lucy) <- (~24) [resolution 105,254]
280. $false <- (~24) [subsumption resolution 279,138]
281. 24 [avatar contradiction clause 280]
291. kind(lucy) <- (~23) [resolution 183,250]
294. 8 | 23 [avatar split clause 291,248,174]
296. ~generous(paul) <- (7, 10) [resolution 172,275]
298. ~generous(sK6) <- (7) [resolution 172,137]
300. $false <- (7, 10) [subsumption resolution 296,277]
301. ~7 | ~10 [avatar contradiction clause 300]
307. $false <- (7, 13) [resolution 298,200]
308. ~7 | ~13 [avatar contradiction clause 307]
309. $false [avatar sat refutation 177,202,255,281,294,301,308]
% SZS output end Proof for 8998122266920900703609924
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or happy is both curious and not funny.
If john is both creative and tall then lucy is not rich or rich and vice versa.
Everyone who is both strong and patient is either quiet or not quiet and vice versa.
If someone is quiet then fred is not humble or not happy.
If fred is not generous or not curious then fred is not strong or old.
If someone is humble then alice is calm or funny.
Everyone who is humble or calm is rich and vice versa.
If someone is either humble or not funny then someone is not generous or not wise and vice versa.
Everyone who is not generous or old is rich or wise.
If someone is brave or not old then someone is not curious.
Everyone who is either quiet or not generous is generous.
If someone is either not generous or not old then someone is calm and vice versa.
Everyone who is either humble or not curious is kind or calm.
If someone is either not happy or not wise then someone is either not happy or not calm.
Everyone who is calm or not humble is not kind and vice versa.
Everyone who is not calm is quiet or not quiet and vice versa.
Someone is either not old or quiet.
Fred is humble.
Someone is not rich.
Mary is not old or quiet.
Susan is strong.
Someone is not calm.
Alice is either strong or quiet.
Someone is not tall. | Susan is not calm. | entailment | (![X]:((~tall(X)|happy(X))=>(curious(X)&~funny(X))))&
(((creative(john)&tall(john)))<=>((~rich(lucy)|rich(lucy))))&
(![X]:((strong(X)&patient(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:(quiet(X)))=>((~humble(fred)|~happy(fred))))&
(((~generous(fred)|~curious(fred)))=>((~strong(fred)|old(fred))))&
((?[X]:(humble(X)))=>((calm(alice)|funny(alice))))&
(![X]:((humble(X)|calm(X))<=>rich(X)))&
((?[X]:((humble(X)<~>~funny(X))))<=>(?[X]:((~generous(X)|~wise(X)))))&
(![X]:((~generous(X)|old(X))=>(rich(X)|wise(X))))&
((?[X]:((brave(X)|~old(X))))=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)<~>~generous(X))=>generous(X)))&
((?[X]:((~generous(X)<~>~old(X))))<=>(?[X]:(calm(X))))&
(![X]:((humble(X)<~>~curious(X))=>(kind(X)|calm(X))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((calm(X)|~humble(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>(quiet(X)|~quiet(X))))&
(?[X]:((~old(X)<~>quiet(X))))&
(humble(fred))&
(?[X]:(~rich(X)))&
((~old(mary)|quiet(mary)))&
(strong(susan))&
(?[X]:(~calm(X)))&
((strong(alice)<~>quiet(alice)))&
(?[X]:(~tall(X))) | ~calm(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5672126689788591347450706
% SZS output start Proof for 5672126689788591347450706
16. ! [X0] : (~calm(X0) <=> (~quiet(X0) | quiet(X0))) [input p15]
25. calm(susan) [input hypothesis]
72. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | calm(X0))) [nnf transformation 16]
73. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | calm(X0))) [flattening 72]
130. ~calm(X0) | ~quiet(X0) [cnf transformation 73]
131. ~calm(X0) | quiet(X0) [cnf transformation 73]
142. calm(susan) [cnf transformation 25]
249. 23 <=> ! [X1] : ~calm(X1) [avatar definition]
250. ~calm(X1) <- (23) [avatar component clause 249]
291. ~calm(X0) [subsumption resolution 130,131]
292. 23 [avatar split clause 291,249]
318. $false <- (23) [resolution 250,142]
319. ~23 [avatar contradiction clause 318]
320. $false [avatar sat refutation 292,319]
% SZS output end Proof for 5672126689788591347450706
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If alice is either not strong or creative then someone is happy and vice versa. Everyone who is old is both patient and not old and vice versa. Everyone who is not tall is both not kind and funny and vice versa. If fred is tall then someone is creative and vice versa. Everyone who is both wise and not curious is strong. If alice is either creative or not patient then someone is creative or rich and vice versa. If someone is patient or generous then paul is either not happy or kind. If someone is not quiet or curious then paul is not quiet or brave. Everyone who is rich or wise is both not funny and generous. Everyone who is both strong and kind is humble and vice versa. If mary is not curious or not humble then someone is either happy or strong and vice versa. If someone is not kind then someone is either not kind or not generous. If someone is both not happy and not curious then someone is not calm or curious and vice versa. If mary is either quiet or not generous then someone is either old or not quiet. Everyone who is both quiet and tall is both not humble and rich and vice versa. Alice is rich or not creative. Someone is both brave and calm. Lucy is brave. Someone is either not old or creative. Mary is not tall or not funny. Someone is not calm or not humble. Alice is both tall and happy. | Alice is not creative. | entailment | (((~strong(alice)<~>creative(alice)))<=>(?[X]:(happy(X))))&
(![X]:(old(X)<=>(patient(X)&~old(X))))&
(![X]:(~tall(X)<=>(~kind(X)&funny(X))))&
((tall(fred))<=>(?[X]:(creative(X))))&
(![X]:((wise(X)&~curious(X))=>strong(X)))&
(((creative(alice)<~>~patient(alice)))<=>(?[X]:((creative(X)|rich(X)))))&
((?[X]:((patient(X)|generous(X))))=>((~happy(paul)<~>kind(paul))))&
((?[X]:((~quiet(X)|curious(X))))=>((~quiet(paul)|brave(paul))))&
(![X]:((rich(X)|wise(X))=>(~funny(X)&generous(X))))&
(![X]:((strong(X)&kind(X))<=>humble(X)))&
(((~curious(mary)|~humble(mary)))<=>(?[X]:((happy(X)<~>strong(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~kind(X)<~>~generous(X)))))&
((?[X]:((~happy(X)&~curious(X))))<=>(?[X]:((~calm(X)|curious(X)))))&
(((quiet(mary)<~>~generous(mary)))=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&tall(X))<=>(~humble(X)&rich(X))))&
((rich(alice)|~creative(alice)))&
(?[X]:((brave(X)&calm(X))))&
(brave(lucy))&
(?[X]:((~old(X)<~>creative(X))))&
((~tall(mary)|~funny(mary)))&
(?[X]:((~calm(X)|~humble(X))))&
((tall(alice)&happy(alice))) | ~creative(alice) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6838472579688699150912380
% SZS output start Proof for 6838472579688699150912380
2. ! [X0] : (old(X0) <=> (~old(X0) & patient(X0))) [input p1]
6. (creative(alice) <~> ~patient(alice)) <=> ? [X0] : (rich(X0) | creative(X0)) [input p5]
23. creative(alice) [input hypothesis]
39. ! [X0] : ((old(X0) | (old(X0) | ~patient(X0))) & ((~old(X0) & patient(X0)) | ~old(X0))) [nnf transformation 2]
40. ! [X0] : ((old(X0) | old(X0) | ~patient(X0)) & ((~old(X0) & patient(X0)) | ~old(X0))) [flattening 39]
47. (((patient(alice) | ~creative(alice)) & (~patient(alice) | creative(alice))) | ! [X0] : (~rich(X0) & ~creative(X0))) & (? [X0] : (rich(X0) | creative(X0)) | ((creative(alice) | patient(alice)) & (~patient(alice) | ~creative(alice)))) [nnf transformation 6]
48. (((patient(alice) | ~creative(alice)) & (~patient(alice) | creative(alice))) | ! [X0] : (~rich(X0) & ~creative(X0))) & (? [X1] : (rich(X1) | creative(X1)) | ((creative(alice) | patient(alice)) & (~patient(alice) | ~creative(alice)))) [rectify 47]
49. ? [X1] : (rich(X1) | creative(X1)) => (rich(sK2) | creative(sK2)) [choice axiom]
50. (((patient(alice) | ~creative(alice)) & (~patient(alice) | creative(alice))) | ! [X0] : (~rich(X0) & ~creative(X0))) & ((rich(sK2) | creative(sK2)) | ((creative(alice) | patient(alice)) & (~patient(alice) | ~creative(alice)))) [skolemisation 48,49]
85. ~old(X0) | ~old(X0) [cnf transformation 40]
86. old(X0) | old(X0) | ~patient(X0) [cnf transformation 40]
96. patient(alice) | ~creative(alice) | ~creative(X0) [cnf transformation 50]
136. creative(alice) [cnf transformation 23]
137. ~old(X0) [duplicate literal removal 85]
138. ~patient(X0) | old(X0) [duplicate literal removal 86]
147. 3 <=> creative(alice) [avatar definition]
148. creative(alice) <- (3) [avatar component clause 147]
159. 5 <=> ! [X0] : ~creative(X0) [avatar definition]
160. ~creative(X0) <- (5) [avatar component clause 159]
175. 9 <=> patient(alice) [avatar definition]
177. patient(alice) <- (9) [avatar component clause 175]
179. 5 | ~3 | 9 [avatar split clause 96,175,147,159]
321. 3 [avatar split clause 136,147]
324. $false <- (3, 5) [subsumption resolution 148,160]
325. ~3 | ~5 [avatar contradiction clause 324]
338. old(alice) <- (9) [resolution 138,177]
339. $false <- (9) [subsumption resolution 338,137]
340. ~9 [avatar contradiction clause 339]
341. $false [avatar sat refutation 179,321,325,340]
% SZS output end Proof for 6838472579688699150912380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or brave then someone is both curious and wise and vice versa.
Everyone who is not creative or humble is both strong and not tall and vice versa.
Everyone who is either not strong or brave is curious or generous and vice versa.
If susan is patient or quiet then john is either not humble or not happy.
Everyone who is not creative or quiet is both curious and not creative.
Everyone who is either patient or strong is both not kind and creative and vice versa.
If someone is either not strong or patient then someone is strong or wise and vice versa.
Everyone who is either happy or not creative is either tall or brave.
If mary is generous or not curious then john is either not generous or curious.
Everyone who is strong or not generous is either not humble or not generous and vice versa.
Everyone who is both not humble and not wise is both not wise and not rich and vice versa.
Everyone who is not brave is quiet or kind.
Everyone who is brave is not strong and vice versa.
If someone is brave then someone is both not wise and funny and vice versa.
Everyone who is both patient and kind is both rich and wise and vice versa.
Fred is not brave.
Someone is either creative or not funny.
Someone is happy or creative.
Lucy is curious or not brave.
Paul is both creative and not tall.
Alice is rich or strong.
Someone is either generous or patient. | Paul is not generous. | entailment | ((?[X]:((quiet(X)<~>brave(X))))<=>(?[X]:((curious(X)&wise(X)))))&
(![X]:((~creative(X)|humble(X))<=>(strong(X)&~tall(X))))&
(![X]:((~strong(X)<~>brave(X))<=>(curious(X)|generous(X))))&
(((patient(susan)|quiet(susan)))=>((~humble(john)<~>~happy(john))))&
(![X]:((~creative(X)|quiet(X))=>(curious(X)&~creative(X))))&
(![X]:((patient(X)<~>strong(X))<=>(~kind(X)&creative(X))))&
((?[X]:((~strong(X)<~>patient(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((happy(X)<~>~creative(X))=>(tall(X)<~>brave(X))))&
(((generous(mary)|~curious(mary)))=>((~generous(john)<~>curious(john))))&
(![X]:((strong(X)|~generous(X))<=>(~humble(X)<~>~generous(X))))&
(![X]:((~humble(X)&~wise(X))<=>(~wise(X)&~rich(X))))&
(![X]:(~brave(X)=>(quiet(X)|kind(X))))&
(![X]:(brave(X)<=>~strong(X)))&
((?[X]:(brave(X)))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((patient(X)&kind(X))<=>(rich(X)&wise(X))))&
(~brave(fred))&
(?[X]:((creative(X)<~>~funny(X))))&
(?[X]:((happy(X)|creative(X))))&
((curious(lucy)|~brave(lucy)))&
((creative(paul)&~tall(paul)))&
((rich(alice)|strong(alice)))&
(?[X]:((generous(X)<~>patient(X)))) | ~generous(paul) | [
"p1",
"p2",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1315021428168402510262008
% SZS output start Proof for 1315021428168402510262008
2. ! [X0] : ((humble(X0) | ~creative(X0)) <=> (~tall(X0) & strong(X0))) [input p1]
3. ! [X0] : ((~strong(X0) <~> brave(X0)) <=> (generous(X0) | curious(X0))) [input p2]
10. ! [X0] : ((~generous(X0) | strong(X0)) <=> (~humble(X0) <~> ~generous(X0))) [input p9]
13. ! [X0] : (brave(X0) <=> ~strong(X0)) [input p12]
23. generous(paul) [input hypothesis]
38. ! [X0] : (((humble(X0) | ~creative(X0)) | (tall(X0) | ~strong(X0))) & ((~tall(X0) & strong(X0)) | (~humble(X0) & creative(X0)))) [nnf transformation 2]
39. ! [X0] : ((humble(X0) | ~creative(X0) | tall(X0) | ~strong(X0)) & ((~tall(X0) & strong(X0)) | (~humble(X0) & creative(X0)))) [flattening 38]
40. ! [X0] : ((((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))))) [nnf transformation 3]
41. ! [X0] : ((((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))))) [flattening 40]
52. ! [X0] : (((~generous(X0) | strong(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) & (((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (generous(X0) & ~strong(X0)))) [nnf transformation 10]
53. ! [X0] : ((~generous(X0) | strong(X0) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) & (((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (generous(X0) & ~strong(X0)))) [flattening 52]
56. ! [X0] : ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))) [nnf transformation 13]
79. ~humble(X0) | strong(X0) [cnf transformation 39]
86. ~generous(X0) | ~strong(X0) | brave(X0) [cnf transformation 41]
121. ~generous(X0) | strong(X0) | ~generous(X0) | humble(X0) [cnf transformation 53]
128. ~strong(X0) | ~brave(X0) [cnf transformation 56]
147. generous(paul) [cnf transformation 23]
149. ~generous(X0) | strong(X0) | humble(X0) [duplicate literal removal 121]
259. ~generous(X0) | strong(X0) [subsumption resolution 149,79]
352. strong(paul) [resolution 259,147]
360. ~brave(paul) [resolution 352,128]
373. ~strong(paul) | brave(paul) [resolution 86,147]
376. brave(paul) [subsumption resolution 373,352]
387. $false [subsumption resolution 360,376]
% SZS output end Proof for 1315021428168402510262008
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or funny then someone is both quiet and creative. Everyone who is happy is either patient or wise. If susan is not rich or curious then someone is both not brave and rich and vice versa. Everyone who is not humble or not happy is brave and vice versa. Everyone who is not creative or humble is both not tall and tall. If someone is either old or not happy then alice is humble or not creative. If paul is either patient or not humble then someone is either not brave or not generous. Everyone who is kind is generous or not tall and vice versa. If someone is either strong or not patient then someone is not humble or kind. If mary is strong then someone is not tall or not quiet and vice versa. Everyone who is both tall and patient is both not generous and creative. Everyone who is not kind is both not rich and curious. Everyone who is not humble is not funny or creative. If someone is curious or tall then someone is either not strong or not quiet and vice versa. Everyone who is not kind is either not generous or quiet. Mary is either wise or not happy. Someone is either quiet or funny. Fred is not calm or tall. Paul is both creative and brave. Mary is wise or happy. Someone is rich. Lucy is either generous or not wise. | Alice is not funny. | neutral | ((?[X]:((generous(X)|funny(X))))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:(happy(X)=>(patient(X)<~>wise(X))))&
(((~rich(susan)|curious(susan)))<=>(?[X]:((~brave(X)&rich(X)))))&
(![X]:((~humble(X)|~happy(X))<=>brave(X)))&
(![X]:((~creative(X)|humble(X))=>(~tall(X)&tall(X))))&
((?[X]:((old(X)<~>~happy(X))))=>((humble(alice)|~creative(alice))))&
(((patient(paul)<~>~humble(paul)))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:(kind(X)<=>(generous(X)|~tall(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~humble(X)|kind(X)))))&
((strong(mary))<=>(?[X]:((~tall(X)|~quiet(X)))))&
(![X]:((tall(X)&patient(X))=>(~generous(X)&creative(X))))&
(![X]:(~kind(X)=>(~rich(X)&curious(X))))&
(![X]:(~humble(X)=>(~funny(X)|creative(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:(~kind(X)=>(~generous(X)<~>quiet(X))))&
((wise(mary)<~>~happy(mary)))&
(?[X]:((quiet(X)<~>funny(X))))&
((~calm(fred)|tall(fred)))&
((creative(paul)&brave(paul)))&
((wise(mary)|happy(mary)))&
(?[X]:(rich(X)))&
((generous(lucy)<~>~wise(lucy))) | ~funny(alice) | [] | null | 0 |
Everyone who is not calm or brave is not wise.
If someone is creative or funny then someone is either not happy or happy.
If john is either old or not wise then lucy is either not generous or happy and vice versa.
If someone is humble or not tall then mary is not rich.
If someone is both not old and creative then someone is funny.
Everyone who is quiet is not brave or generous and vice versa.
Everyone who is both not funny and not kind is either funny or not funny and vice versa.
Everyone who is either wise or old is both kind and funny and vice versa.
If alice is not generous then john is brave or kind.
If alice is creative then someone is not calm or creative and vice versa.
Everyone who is both patient and old is not quiet.
Everyone who is not wise is creative.
If someone is either funny or curious then someone is both not generous and brave and vice versa.
Everyone who is brave is strong.
If susan is both funny and not happy then someone is funny and vice versa.
Mary is happy or tall.
Someone is not brave.
Someone is either not quiet or not strong.
Someone is either not rich or not brave. | Susan is not brave. | entailment | (![X]:((~calm(X)|brave(X))=>~wise(X)))&
((?[X]:((creative(X)|funny(X))))=>(?[X]:((~happy(X)<~>happy(X)))))&
(((old(john)<~>~wise(john)))<=>((~generous(lucy)<~>happy(lucy))))&
((?[X]:((humble(X)|~tall(X))))=>(~rich(mary)))&
((?[X]:((~old(X)&creative(X))))=>(?[X]:(funny(X))))&
(![X]:(quiet(X)<=>(~brave(X)|generous(X))))&
(![X]:((~funny(X)&~kind(X))<=>(funny(X)<~>~funny(X))))&
(![X]:((wise(X)<~>old(X))<=>(kind(X)&funny(X))))&
((~generous(alice))=>((brave(john)|kind(john))))&
((creative(alice))<=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((patient(X)&old(X))=>~quiet(X)))&
(![X]:(~wise(X)=>creative(X)))&
((?[X]:((funny(X)<~>curious(X))))<=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:(brave(X)=>strong(X)))&
(((funny(susan)&~happy(susan)))<=>(?[X]:(funny(X))))&
((happy(mary)|tall(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>~brave(X)))) | ~brave(susan) | [
"p0",
"p4",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4261376086414698201234194
% SZS output start Proof for 4261376086414698201234194
1. ! [X0] : ((brave(X0) | ~calm(X0)) => ~wise(X0)) [input p0]
5. ? [X0] : (creative(X0) & ~old(X0)) => ? [X0] : funny(X0) [input p4]
7. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (funny(X0) <~> ~funny(X0))) [input p6]
8. ! [X0] : ((wise(X0) <~> old(X0)) <=> (funny(X0) & kind(X0))) [input p7]
12. ! [X0] : (~wise(X0) => creative(X0)) [input p11]
20. brave(susan) [input hypothesis]
22. ? [X0] : (creative(X0) & ~old(X0)) => ? [X1] : funny(X1) [rectify 5]
28. ! [X0] : (~wise(X0) | (~brave(X0) & calm(X0))) [ennf transformation 1]
30. ? [X1] : funny(X1) | ! [X0] : (~creative(X0) | old(X0)) [ennf transformation 22]
33. ! [X0] : (creative(X0) | wise(X0)) [ennf transformation 12]
40. ? [X0] : funny(X0) | ! [X1] : (~creative(X1) | old(X1)) [rectify 30]
41. ? [X0] : funny(X0) => funny(sK1) [choice axiom]
42. funny(sK1) | ! [X1] : (~creative(X1) | old(X1)) [skolemisation 40,41]
45. ! [X0] : (((~kind(X0) & ~funny(X0)) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0)))) & (((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | (kind(X0) | funny(X0)))) [nnf transformation 7]
46. ! [X0] : (((~kind(X0) & ~funny(X0)) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0)))) & (((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | kind(X0) | funny(X0))) [flattening 45]
47. ! [X0] : ((((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | (~funny(X0) | ~kind(X0))) & ((funny(X0) & kind(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0))))) [nnf transformation 8]
48. ! [X0] : ((((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ~funny(X0) | ~kind(X0)) & ((funny(X0) & kind(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0))))) [flattening 47]
72. ~wise(X0) | ~brave(X0) [cnf transformation 28]
85. funny(sK1) | ~creative(X1) | old(X1) [cnf transformation 42]
91. ~funny(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 46]
97. funny(X0) | old(X0) | ~wise(X0) [cnf transformation 48]
98. funny(X0) | wise(X0) | ~old(X0) [cnf transformation 48]
105. creative(X0) | wise(X0) [cnf transformation 33]
121. brave(susan) [cnf transformation 20]
124. ~funny(X0) [duplicate literal removal 91]
153. 5 <=> ! [X1] : (~creative(X1) | old(X1)) [avatar definition]
154. ~creative(X1) | old(X1) <- (5) [avatar component clause 153]
156. 6 <=> funny(sK1) [avatar definition]
158. funny(sK1) <- (6) [avatar component clause 156]
159. 5 | 6 [avatar split clause 85,156,153]
161. ~old(X0) | wise(X0) [subsumption resolution 98,124]
162. ~wise(X0) | old(X0) [subsumption resolution 97,124]
259. $false <- (6) [subsumption resolution 158,124]
260. ~6 [avatar contradiction clause 259]
270. old(X0) | wise(X0) <- (5) [resolution 154,105]
278. old(X0) <- (5) [subsumption resolution 270,162]
281. wise(X0) <- (5) [resolution 278,161]
283. ~brave(X1) <- (5) [resolution 281,72]
285. $false <- (5) [resolution 283,121]
286. ~5 [avatar contradiction clause 285]
287. $false [avatar sat refutation 159,260,286]
% SZS output end Proof for 4261376086414698201234194
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or old is either rich or not old.
Everyone who is not calm is both not happy and patient.
If someone is either not brave or brave then john is wise.
Everyone who is tall or creative is both calm and not patient.
Everyone who is not brave is both brave and not curious and vice versa.
If lucy is both not strong and quiet then lucy is not brave and vice versa.
Everyone who is either humble or patient is either funny or happy and vice versa.
If someone is either not calm or patient then someone is both wise and brave.
If someone is happy or not strong then mary is either not strong or humble.
Everyone who is both not creative and tall is not creative and vice versa.
Everyone who is not tall or not funny is brave.
If someone is both patient and not happy then someone is not generous or not creative.
If fred is either not happy or not funny then someone is either tall or not generous.
If alice is both generous and strong then mary is both not quiet and strong and vice versa.
If someone is either not kind or generous then someone is not generous.
Everyone who is either funny or quiet is generous.
Alice is both not old and kind.
Someone is not patient.
Someone is not patient or not wise.
Alice is wise or patient.
Someone is humble.
Lucy is both curious and strong.
Someone is not wise. | Fred is not patient. | entailment | (![X]:((~rich(X)<~>old(X))=>(rich(X)<~>~old(X))))&
(![X]:(~calm(X)=>(~happy(X)&patient(X))))&
((?[X]:((~brave(X)<~>brave(X))))=>(wise(john)))&
(![X]:((tall(X)|creative(X))=>(calm(X)&~patient(X))))&
(![X]:(~brave(X)<=>(brave(X)&~curious(X))))&
(((~strong(lucy)&quiet(lucy)))<=>(~brave(lucy)))&
(![X]:((humble(X)<~>patient(X))<=>(funny(X)<~>happy(X))))&
((?[X]:((~calm(X)<~>patient(X))))=>(?[X]:((wise(X)&brave(X)))))&
((?[X]:((happy(X)|~strong(X))))=>((~strong(mary)<~>humble(mary))))&
(![X]:((~creative(X)&tall(X))<=>~creative(X)))&
(![X]:((~tall(X)|~funny(X))=>brave(X)))&
((?[X]:((patient(X)&~happy(X))))=>(?[X]:((~generous(X)|~creative(X)))))&
(((~happy(fred)<~>~funny(fred)))=>(?[X]:((tall(X)<~>~generous(X)))))&
(((generous(alice)&strong(alice)))<=>((~quiet(mary)&strong(mary))))&
((?[X]:((~kind(X)<~>generous(X))))=>(?[X]:(~generous(X))))&
(![X]:((funny(X)<~>quiet(X))=>generous(X)))&
((~old(alice)&kind(alice)))&
(?[X]:(~patient(X)))&
(?[X]:((~patient(X)|~wise(X))))&
((wise(alice)|patient(alice)))&
(?[X]:(humble(X)))&
((curious(lucy)&strong(lucy)))&
(?[X]:(~wise(X))) | ~patient(fred) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1247500788564926991431334
% SZS output start Proof for 1247500788564926991431334
4. ! [X0] : ((creative(X0) | tall(X0)) => (~patient(X0) & calm(X0))) [input p3]
10. ! [X0] : ((tall(X0) & ~creative(X0)) <=> ~creative(X0)) [input p9]
24. patient(fred) [input hypothesis]
31. ! [X0] : ((~patient(X0) & calm(X0)) | (~creative(X0) & ~tall(X0))) [ennf transformation 4]
51. ! [X0] : (((tall(X0) & ~creative(X0)) | creative(X0)) & (~creative(X0) | (~tall(X0) | creative(X0)))) [nnf transformation 10]
52. ! [X0] : (((tall(X0) & ~creative(X0)) | creative(X0)) & (~creative(X0) | ~tall(X0) | creative(X0))) [flattening 51]
84. ~tall(X0) | ~patient(X0) [cnf transformation 31]
85. ~creative(X0) | ~patient(X0) [cnf transformation 31]
110. creative(X0) | tall(X0) [cnf transformation 52]
135. patient(fred) [cnf transformation 24]
285. tall(X0) | ~patient(X0) [resolution 110,85]
287. ~patient(X0) [subsumption resolution 285,84]
289. $false [resolution 287,135]
% SZS output end Proof for 1247500788564926991431334
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not funny is both rich and not tall. Everyone who is curious is both not funny and not happy. Everyone who is both quiet and not generous is either funny or wise. Everyone who is either brave or not funny is both kind and not happy and vice versa. If paul is both not calm and humble then paul is both humble and not tall. Everyone who is funny or not generous is either not funny or brave and vice versa. If someone is both not calm and funny then someone is not rich or strong. Everyone who is strong is creative or not brave. Everyone who is brave or not old is not kind and vice versa. Everyone who is both rich and funny is both strong and calm and vice versa. Everyone who is not creative is not happy. Everyone who is strong or humble is either quiet or creative. If alice is not funny then lucy is not old. If mary is not wise or not tall then paul is both quiet and not brave and vice versa. Everyone who is brave or not generous is not funny. Lucy is strong or brave. Lucy is not old. Lucy is either not happy or old. Someone is kind or quiet. Someone is either not quiet or wise. Someone is strong or not humble. Lucy is either kind or brave. | Mary is funny. | contradiction | (![X]:((calm(X)|~funny(X))=>(rich(X)&~tall(X))))&
(![X]:(curious(X)=>(~funny(X)&~happy(X))))&
(![X]:((quiet(X)&~generous(X))=>(funny(X)<~>wise(X))))&
(![X]:((brave(X)<~>~funny(X))<=>(kind(X)&~happy(X))))&
(((~calm(paul)&humble(paul)))=>((humble(paul)&~tall(paul))))&
(![X]:((funny(X)|~generous(X))<=>(~funny(X)<~>brave(X))))&
((?[X]:((~calm(X)&funny(X))))=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:(strong(X)=>(creative(X)|~brave(X))))&
(![X]:((brave(X)|~old(X))<=>~kind(X)))&
(![X]:((rich(X)&funny(X))<=>(strong(X)&calm(X))))&
(![X]:(~creative(X)=>~happy(X)))&
(![X]:((strong(X)|humble(X))=>(quiet(X)<~>creative(X))))&
((~funny(alice))=>(~old(lucy)))&
(((~wise(mary)|~tall(mary)))<=>((quiet(paul)&~brave(paul))))&
(![X]:((brave(X)|~generous(X))=>~funny(X)))&
((strong(lucy)|brave(lucy)))&
(~old(lucy))&
((~happy(lucy)<~>old(lucy)))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((~quiet(X)<~>wise(X))))&
(?[X]:((strong(X)|~humble(X))))&
((kind(lucy)<~>brave(lucy))) | funny(mary) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2888004648743189916389103
% SZS output start Proof for 2888004648743189916389103
6. ! [X0] : ((~generous(X0) | funny(X0)) <=> (~funny(X0) <~> brave(X0))) [input p5]
15. ! [X0] : ((~generous(X0) | brave(X0)) => ~funny(X0)) [input p14]
23. funny(mary) [input hypothesis]
37. ! [X0] : (~funny(X0) | (generous(X0) & ~brave(X0))) [ennf transformation 15]
41. ! [X0] : (((~generous(X0) | funny(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) & (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (generous(X0) & ~funny(X0)))) [nnf transformation 6]
42. ! [X0] : ((~generous(X0) | funny(X0) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) & (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (generous(X0) & ~funny(X0)))) [flattening 41]
76. brave(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 42]
102. ~funny(X0) | ~brave(X0) [cnf transformation 37]
114. funny(mary) [cnf transformation 23]
115. brave(X0) | ~funny(X0) [duplicate literal removal 76]
169. ~funny(X0) [subsumption resolution 102,115]
219. $false [subsumption resolution 114,169]
% SZS output end Proof for 2888004648743189916389103
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If mary is either not generous or not wise then lucy is either not curious or kind and vice versa. If paul is both not generous and not creative then lucy is not patient or not creative. Everyone who is not rich or wise is not old or not quiet. Everyone who is both not creative and not strong is not patient or not strong and vice versa. If alice is not brave or kind then mary is either not rich or kind and vice versa. Everyone who is patient or calm is either humble or not kind. If susan is old or funny then someone is both not tall and generous and vice versa. If someone is not rich or not quiet then someone is funny or not rich and vice versa. Everyone who is either not quiet or happy is not strong and vice versa. Everyone who is patient is either curious or funny. Everyone who is both not humble and not quiet is either not funny or funny. Everyone who is either creative or not strong is both patient and not generous. Everyone who is both not happy and not rich is happy or not quiet. Everyone who is either not wise or patient is either not humble or not wise and vice versa. Everyone who is not rich or calm is not funny or not creative. Everyone who is both not quiet and funny is funny or quiet. Fred is not rich or curious. Someone is both happy and calm. Fred is both not brave and not quiet. Fred is either rich or not curious. Someone is not old. Someone is not generous. Paul is not strong or wise. Someone is either not strong or generous. | Mary is not kind. | entailment | (((~generous(mary)<~>~wise(mary)))<=>((~curious(lucy)<~>kind(lucy))))&
(((~generous(paul)&~creative(paul)))=>((~patient(lucy)|~creative(lucy))))&
(![X]:((~rich(X)|wise(X))=>(~old(X)|~quiet(X))))&
(![X]:((~creative(X)&~strong(X))<=>(~patient(X)|~strong(X))))&
(((~brave(alice)|kind(alice)))<=>((~rich(mary)<~>kind(mary))))&
(![X]:((patient(X)|calm(X))=>(humble(X)<~>~kind(X))))&
(((old(susan)|funny(susan)))<=>(?[X]:((~tall(X)&generous(X)))))&
((?[X]:((~rich(X)|~quiet(X))))<=>(?[X]:((funny(X)|~rich(X)))))&
(![X]:((~quiet(X)<~>happy(X))<=>~strong(X)))&
(![X]:(patient(X)=>(curious(X)<~>funny(X))))&
(![X]:((~humble(X)&~quiet(X))=>(~funny(X)<~>funny(X))))&
(![X]:((creative(X)<~>~strong(X))=>(patient(X)&~generous(X))))&
(![X]:((~happy(X)&~rich(X))=>(happy(X)|~quiet(X))))&
(![X]:((~wise(X)<~>patient(X))<=>(~humble(X)<~>~wise(X))))&
(![X]:((~rich(X)|calm(X))=>(~funny(X)|~creative(X))))&
(![X]:((~quiet(X)&funny(X))=>(funny(X)|quiet(X))))&
((~rich(fred)|curious(fred)))&
(?[X]:((happy(X)&calm(X))))&
((~brave(fred)&~quiet(fred)))&
((rich(fred)<~>~curious(fred)))&
(?[X]:(~old(X)))&
(?[X]:(~generous(X)))&
((~strong(paul)|wise(paul)))&
(?[X]:((~strong(X)<~>generous(X)))) | ~kind(mary) | [
"p3",
"p5",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7712661558055958740464395
% SZS output start Proof for 7712661558055958740464395
4. ! [X0] : ((~strong(X0) & ~creative(X0)) <=> (~strong(X0) | ~patient(X0))) [input p3]
6. ! [X0] : ((calm(X0) | patient(X0)) => (humble(X0) <~> ~kind(X0))) [input p5]
12. ! [X0] : ((creative(X0) <~> ~strong(X0)) => (~generous(X0) & patient(X0))) [input p11]
14. ! [X0] : ((~wise(X0) <~> patient(X0)) <=> (~humble(X0) <~> ~wise(X0))) [input p13]
25. kind(mary) [input hypothesis]
31. ! [X0] : ((humble(X0) <~> ~kind(X0)) | (~calm(X0) & ~patient(X0))) [ennf transformation 6]
35. ! [X0] : ((~generous(X0) & patient(X0)) | (creative(X0) <=> ~strong(X0))) [ennf transformation 12]
43. ! [X0] : (((~strong(X0) & ~creative(X0)) | (strong(X0) & patient(X0))) & ((~strong(X0) | ~patient(X0)) | (strong(X0) | creative(X0)))) [nnf transformation 4]
44. ! [X0] : (((~strong(X0) & ~creative(X0)) | (strong(X0) & patient(X0))) & (~strong(X0) | ~patient(X0) | strong(X0) | creative(X0))) [flattening 43]
47. ! [X0] : (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | (~calm(X0) & ~patient(X0))) [nnf transformation 31]
61. ! [X0] : ((~generous(X0) & patient(X0)) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) [nnf transformation 35]
62. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0)))) & (((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [nnf transformation 14]
86. ~creative(X0) | strong(X0) [cnf transformation 44]
87. ~strong(X0) | patient(X0) [cnf transformation 44]
95. ~patient(X0) | humble(X0) | ~kind(X0) [cnf transformation 47]
117. patient(X0) | creative(X0) | strong(X0) [cnf transformation 61]
122. ~wise(X0) | ~humble(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 62]
128. ~patient(X0) | wise(X0) | ~humble(X0) | wise(X0) [cnf transformation 62]
144. kind(mary) [cnf transformation 25]
146. ~wise(X0) | ~humble(X0) | ~patient(X0) [duplicate literal removal 122]
149. ~patient(X0) | wise(X0) | ~humble(X0) [duplicate literal removal 128]
193. 9 <=> kind(mary) [avatar definition]
194. kind(mary) <- (9) [avatar component clause 193]
269. patient(X0) | strong(X0) [subsumption resolution 117,86]
270. patient(X0) [subsumption resolution 269,87]
271. ~humble(X0) | wise(X0) [subsumption resolution 149,270]
272. ~wise(X0) | ~humble(X0) [subsumption resolution 146,270]
273. ~humble(X0) [subsumption resolution 272,271]
303. 9 [avatar split clause 144,193]
306. humble(X0) | ~kind(X0) [resolution 95,270]
307. ~kind(X0) [subsumption resolution 306,273]
308. $false <- (9) [resolution 307,194]
309. ~9 [avatar contradiction clause 308]
310. $false [avatar sat refutation 303,309]
% SZS output end Proof for 7712661558055958740464395
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not happy is brave and vice versa. Everyone who is quiet or patient is not strong. Everyone who is either calm or not funny is both not curious and not generous. Everyone who is not generous or creative is either brave or kind and vice versa. Everyone who is humble or not rich is not rich or not brave. Everyone who is both patient and calm is either not funny or not kind and vice versa. Everyone who is brave is not funny or not calm. Everyone who is creative is not funny or not wise and vice versa. Everyone who is not tall or funny is tall or generous and vice versa. Everyone who is brave or not funny is not curious or not calm. Everyone who is strong or quiet is both patient and not strong. Everyone who is both humble and not rich is both generous and quiet and vice versa. If lucy is quiet or not curious then someone is humble. If susan is not kind then someone is creative and vice versa. Everyone who is both quiet and funny is both brave and generous and vice versa. Everyone who is both not wise and quiet is not happy and vice versa. Someone is both not tall and patient. Someone is happy. Susan is tall or not quiet. Susan is either kind or not calm. Someone is either patient or not curious. | Lucy is not creative. | entailment | (![X]:((humble(X)<~>~happy(X))<=>brave(X)))&
(![X]:((quiet(X)|patient(X))=>~strong(X)))&
(![X]:((calm(X)<~>~funny(X))=>(~curious(X)&~generous(X))))&
(![X]:((~generous(X)|creative(X))<=>(brave(X)<~>kind(X))))&
(![X]:((humble(X)|~rich(X))=>(~rich(X)|~brave(X))))&
(![X]:((patient(X)&calm(X))<=>(~funny(X)<~>~kind(X))))&
(![X]:(brave(X)=>(~funny(X)|~calm(X))))&
(![X]:(creative(X)<=>(~funny(X)|~wise(X))))&
(![X]:((~tall(X)|funny(X))<=>(tall(X)|generous(X))))&
(![X]:((brave(X)|~funny(X))=>(~curious(X)|~calm(X))))&
(![X]:((strong(X)|quiet(X))=>(patient(X)&~strong(X))))&
(![X]:((humble(X)&~rich(X))<=>(generous(X)&quiet(X))))&
(((quiet(lucy)|~curious(lucy)))=>(?[X]:(humble(X))))&
((~kind(susan))<=>(?[X]:(creative(X))))&
(![X]:((quiet(X)&funny(X))<=>(brave(X)&generous(X))))&
(![X]:((~wise(X)&quiet(X))<=>~happy(X)))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:(happy(X)))&
((tall(susan)|~quiet(susan)))&
((kind(susan)<~>~calm(susan)))&
(?[X]:((patient(X)<~>~curious(X)))) | ~creative(lucy) | [
"p2",
"p5",
"p8",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 821362518540589627053048
% SZS output start Proof for 821362518540589627053048
3. ! [X0] : ((calm(X0) <~> ~funny(X0)) => (~generous(X0) & ~curious(X0))) [input p2]
6. ! [X0] : ((calm(X0) & patient(X0)) <=> (~funny(X0) <~> ~kind(X0))) [input p5]
9. ! [X0] : ((funny(X0) | ~tall(X0)) <=> (generous(X0) | tall(X0))) [input p8]
14. ~kind(susan) <=> ? [X0] : creative(X0) [input p13]
20. kind(susan) <~> ~calm(susan) [input p19]
22. creative(lucy) [input hypothesis]
25. ! [X0] : ((~generous(X0) & ~curious(X0)) | (calm(X0) <=> ~funny(X0))) [ennf transformation 3]
35. ! [X0] : ((~generous(X0) & ~curious(X0)) | ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) [nnf transformation 25]
38. ! [X0] : (((calm(X0) & patient(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (~calm(X0) | ~patient(X0)))) [nnf transformation 6]
39. ! [X0] : (((calm(X0) & patient(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | ~calm(X0) | ~patient(X0))) [flattening 38]
42. ! [X0] : (((funny(X0) | ~tall(X0)) | (~generous(X0) & ~tall(X0))) & ((generous(X0) | tall(X0)) | (~funny(X0) & tall(X0)))) [nnf transformation 9]
43. ! [X0] : ((funny(X0) | ~tall(X0) | (~generous(X0) & ~tall(X0))) & (generous(X0) | tall(X0) | (~funny(X0) & tall(X0)))) [flattening 42]
48. (~kind(susan) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | kind(susan)) [nnf transformation 14]
49. (~kind(susan) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | kind(susan)) [rectify 48]
50. ? [X1] : creative(X1) => creative(sK1) [choice axiom]
51. (~kind(susan) | ! [X0] : ~creative(X0)) & (creative(sK1) | kind(susan)) [skolemisation 49,50]
60. (calm(susan) | ~kind(susan)) & (~calm(susan) | kind(susan)) [nnf transformation 20]
71. ~generous(X0) | calm(X0) | funny(X0) [cnf transformation 35]
85. ~funny(X0) | calm(X0) | kind(X0) [cnf transformation 39]
90. generous(X0) | tall(X0) | tall(X0) [cnf transformation 43]
92. funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 43]
104. ~kind(susan) | ~creative(X0) [cnf transformation 51]
116. ~calm(susan) | kind(susan) [cnf transformation 60]
120. creative(lucy) [cnf transformation 22]
121. tall(X0) | generous(X0) [duplicate literal removal 90]
122. ~tall(X0) | funny(X0) [duplicate literal removal 92]
139. 4 <=> ! [X0] : ~creative(X0) [avatar definition]
140. ~creative(X0) <- (4) [avatar component clause 139]
142. 5 <=> kind(susan) [avatar definition]
144. ~kind(susan) <- (~5) [avatar component clause 142]
145. 4 | ~5 [avatar split clause 104,142,139]
161. 9 <=> calm(susan) [avatar definition]
162. ~calm(susan) <- (~9) [avatar component clause 161]
165. 5 | ~9 [avatar split clause 116,161,142]
180. generous(X0) | funny(X0) [resolution 122,121]
232. 20 <=> generous(susan) [avatar definition]
233. ~generous(susan) <- (~20) [avatar component clause 232]
234. generous(susan) <- (20) [avatar component clause 232]
265. $false <- (4) [resolution 140,120]
268. ~4 [avatar contradiction clause 265]
359. calm(susan) | funny(susan) <- (20) [resolution 234,71]
361. funny(susan) <- (~9, 20) [subsumption resolution 359,162]
442. calm(susan) | kind(susan) <- (~9, 20) [resolution 361,85]
444. kind(susan) <- (~9, 20) [subsumption resolution 442,162]
445. $false <- (~5, ~9, 20) [subsumption resolution 444,144]
446. 5 | 9 | ~20 [avatar contradiction clause 445]
457. funny(susan) <- (~20) [resolution 180,233]
489. calm(susan) | kind(susan) <- (~20) [resolution 457,85]
491. kind(susan) <- (~9, ~20) [subsumption resolution 489,162]
492. $false <- (~5, ~9, ~20) [subsumption resolution 491,144]
493. 5 | 9 | 20 [avatar contradiction clause 492]
495. $false [avatar sat refutation 145,165,268,446,493]
% SZS output end Proof for 821362518540589627053048
% ------------------------------
% 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then mary is brave or not rich and vice versa. If someone is both not brave and humble then someone is not strong or not humble. Everyone who is either patient or creative is both old and quiet. Everyone who is both not happy and generous is not calm and vice versa. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. If lucy is brave or old then lucy is either rich or humble. Everyone who is strong is humble and vice versa. If mary is both not calm and rich then someone is not old and vice versa. Everyone who is calm is either old or kind. Fred is both tall and not strong. Someone is not strong or happy. Someone is not wise or strong. Someone is curious. Someone is either generous or calm. Someone is either not happy or strong. | Fred is creative. | entailment | ((?[X]:(generous(X)))<=>((brave(mary)|~rich(mary))))&
((?[X]:((~brave(X)&humble(X))))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((patient(X)<~>creative(X))=>(old(X)&quiet(X))))&
(![X]:((~happy(X)&generous(X))<=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
(((brave(lucy)|old(lucy)))=>((rich(lucy)<~>humble(lucy))))&
(![X]:(strong(X)<=>humble(X)))&
(((~calm(mary)&rich(mary)))<=>(?[X]:(~old(X))))&
(![X]:(calm(X)=>(old(X)<~>kind(X))))&
((tall(fred)&~strong(fred)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~wise(X)|strong(X))))&
(?[X]:(curious(X)))&
(?[X]:((generous(X)<~>calm(X))))&
(?[X]:((~happy(X)<~>strong(X)))) | creative(fred) | [
"p5",
"p6",
"p7",
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 833065675300661779680903
% SZS output start Proof for 833065675300661779680903
6. ! [X0] : ((old(X0) | kind(X0)) <=> quiet(X0)) [input p5]
7. ! [X0] : ((funny(X0) & ~humble(X0)) <=> (~generous(X0) <~> creative(X0))) [input p6]
8. ! [X0] : ((generous(X0) | funny(X0)) => ~quiet(X0)) [input p7]
9. ? [X0] : (tall(X0) <~> kind(X0)) => calm(fred) [input p8]
16. ! [X0] : (calm(X0) => (old(X0) <~> kind(X0))) [input p15]
17. ~strong(fred) & tall(fred) [input p16]
23. ~creative(fred) [input hypothesis]
28. ! [X0] : (~quiet(X0) | (~generous(X0) & ~funny(X0))) [ennf transformation 8]
29. calm(fred) | ! [X0] : (tall(X0) <=> kind(X0)) [ennf transformation 9]
32. ! [X0] : ((old(X0) <~> kind(X0)) | ~calm(X0)) [ennf transformation 16]
46. ! [X0] : (((old(X0) | kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & ~kind(X0)))) [nnf transformation 6]
47. ! [X0] : ((old(X0) | kind(X0) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & ~kind(X0)))) [flattening 46]
48. ! [X0] : (((funny(X0) & ~humble(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | (~funny(X0) | humble(X0)))) [nnf transformation 7]
49. ! [X0] : (((funny(X0) & ~humble(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | ~funny(X0) | humble(X0))) [flattening 48]
50. calm(fred) | ! [X0] : ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0))) [nnf transformation 29]
62. ! [X0] : (((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | ~calm(X0)) [nnf transformation 32]
87. ~kind(X0) | quiet(X0) [cnf transformation 47]
88. ~old(X0) | quiet(X0) [cnf transformation 47]
94. funny(X0) | creative(X0) | generous(X0) [cnf transformation 49]
96. ~funny(X0) | ~quiet(X0) [cnf transformation 28]
97. ~quiet(X0) | ~generous(X0) [cnf transformation 28]
98. calm(fred) | kind(X0) | ~tall(X0) [cnf transformation 50]
120. ~calm(X0) | old(X0) | kind(X0) [cnf transformation 62]
122. tall(fred) [cnf transformation 17]
130. ~creative(fred) [cnf transformation 23]
165. 9 <=> calm(fred) [avatar definition]
167. calm(fred) <- (9) [avatar component clause 165]
170. 10 <=> ! [X0] : (kind(X0) | ~tall(X0)) [avatar definition]
171. ~tall(X0) | kind(X0) <- (10) [avatar component clause 170]
172. 10 | 9 [avatar split clause 98,165,170]
178. 12 <=> quiet(fred) [avatar definition]
179. quiet(fred) <- (12) [avatar component clause 178]
180. ~quiet(fred) <- (~12) [avatar component clause 178]
296. creative(X0) | generous(X0) | ~quiet(X0) [resolution 94,96]
305. ~quiet(X0) | creative(X0) [subsumption resolution 296,97]
332. 33 <=> old(fred) [avatar definition]
334. old(fred) <- (33) [avatar component clause 332]
357. kind(fred) <- (10) [resolution 171,122]
363. quiet(fred) <- (10) [resolution 357,87]
365. 12 | ~10 [avatar split clause 363,170,178]
370. old(fred) | kind(fred) <- (9) [resolution 120,167]
372. quiet(fred) <- (33) [resolution 334,88]
374. 12 | ~33 [avatar split clause 372,332,178]
376. 37 <=> kind(fred) [avatar definition]
378. kind(fred) <- (37) [avatar component clause 376]
379. 37 | 33 | ~9 [avatar split clause 370,165,332,376]
437. creative(fred) <- (12) [resolution 305,179]
438. $false <- (12) [subsumption resolution 437,130]
439. ~12 [avatar contradiction clause 438]
448. quiet(fred) <- (37) [resolution 378,87]
450. $false <- (~12, 37) [subsumption resolution 448,180]
451. 12 | ~37 [avatar contradiction clause 450]
452. $false [avatar sat refutation 172,365,374,379,439,451]
% SZS output end Proof for 833065675300661779680903
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If alice is both not quiet and generous then someone is curious or not generous and vice versa. If someone is both creative and brave then fred is either not wise or not patient. If alice is both not wise and strong then someone is both not rich and not patient. If mary is not happy then susan is not curious. Everyone who is either brave or not brave is not funny. Everyone who is not calm is both not generous and not wise and vice versa. If someone is not brave then someone is either curious or strong and vice versa. If someone is patient then alice is either not rich or humble. If someone is either happy or not generous then someone is both not kind and generous and vice versa. If someone is not humble or not kind then john is either not calm or kind. Everyone who is not patient is either not curious or not wise and vice versa. Everyone who is either tall or not brave is either old or strong and vice versa. Everyone who is both not tall and not creative is quiet or wise and vice versa. If someone is funny then paul is humble. If someone is either not funny or happy then paul is patient and vice versa. Everyone who is either not wise or not humble is both rich and not happy and vice versa. Someone is strong or generous. Susan is either not humble or not kind. Someone is not wise. Susan is both curious and old. Someone is not tall. Someone is tall. Someone is either tall or not rich. | Fred is funny. | contradiction | (((~quiet(alice)&generous(alice)))<=>(?[X]:((curious(X)|~generous(X)))))&
((?[X]:((creative(X)&brave(X))))=>((~wise(fred)<~>~patient(fred))))&
(((~wise(alice)&strong(alice)))=>(?[X]:((~rich(X)&~patient(X)))))&
((~happy(mary))=>(~curious(susan)))&
(![X]:((brave(X)<~>~brave(X))=>~funny(X)))&
(![X]:(~calm(X)<=>(~generous(X)&~wise(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((curious(X)<~>strong(X)))))&
((?[X]:(patient(X)))=>((~rich(alice)<~>humble(alice))))&
((?[X]:((happy(X)<~>~generous(X))))<=>(?[X]:((~kind(X)&generous(X)))))&
((?[X]:((~humble(X)|~kind(X))))=>((~calm(john)<~>kind(john))))&
(![X]:(~patient(X)<=>(~curious(X)<~>~wise(X))))&
(![X]:((tall(X)<~>~brave(X))<=>(old(X)<~>strong(X))))&
(![X]:((~tall(X)&~creative(X))<=>(quiet(X)|wise(X))))&
((?[X]:(funny(X)))=>(humble(paul)))&
((?[X]:((~funny(X)<~>happy(X))))<=>(patient(paul)))&
(![X]:((~wise(X)<~>~humble(X))<=>(rich(X)&~happy(X))))&
(?[X]:((strong(X)|generous(X))))&
((~humble(susan)<~>~kind(susan)))&
(?[X]:(~wise(X)))&
((curious(susan)&old(susan)))&
(?[X]:(~tall(X)))&
(?[X]:(tall(X)))&
(?[X]:((tall(X)<~>~rich(X)))) | funny(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4631001969251647460963693
% SZS output start Proof for 4631001969251647460963693
5. ! [X0] : ((brave(X0) <~> ~brave(X0)) => ~funny(X0)) [input p4]
24. funny(fred) [input hypothesis]
31. ! [X0] : (~funny(X0) | (brave(X0) <=> ~brave(X0))) [ennf transformation 5]
43. ! [X0] : (~funny(X0) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 31]
90. ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 43]
91. ~funny(X0) | brave(X0) | brave(X0) [cnf transformation 43]
149. funny(fred) [cnf transformation 24]
150. ~funny(X0) | ~brave(X0) [duplicate literal removal 90]
151. ~funny(X0) | brave(X0) [duplicate literal removal 91]
219. ~funny(X0) [subsumption resolution 150,151]
352. $false [subsumption resolution 149,219]
% SZS output end Proof for 4631001969251647460963693
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is either not tall or not calm and vice versa. Everyone who is both patient and rich is not calm or calm. Everyone who is either not old or not kind is both wise and not tall. Everyone who is both not wise and not humble is both tall and not happy and vice versa. Everyone who is not brave is curious or brave. If someone is both not calm and not patient then someone is not funny or rich and vice versa. Everyone who is either not curious or humble is not creative or funny. Everyone who is not curious is both creative and old. If someone is not creative or not calm then someone is not patient. Everyone who is both curious and old is curious or not wise and vice versa. Everyone who is funny or brave is both not happy and not creative and vice versa. If someone is not patient or patient then someone is both not creative and curious and vice versa. Everyone who is calm is not old or humble and vice versa. Everyone who is both humble and wise is wise or tall. If someone is not wise then susan is either curious or humble. Everyone who is not rich is either funny or strong. John is both not rich and not creative. Susan is not funny. Someone is both brave and not patient. Someone is either not patient or tall. Susan is either old or tall. Someone is not humble or not funny. | Susan is patient. | neutral | (![X]:(~kind(X)<=>(~tall(X)<~>~calm(X))))&
(![X]:((patient(X)&rich(X))=>(~calm(X)|calm(X))))&
(![X]:((~old(X)<~>~kind(X))=>(wise(X)&~tall(X))))&
(![X]:((~wise(X)&~humble(X))<=>(tall(X)&~happy(X))))&
(![X]:(~brave(X)=>(curious(X)|brave(X))))&
((?[X]:((~calm(X)&~patient(X))))<=>(?[X]:((~funny(X)|rich(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(~creative(X)|funny(X))))&
(![X]:(~curious(X)=>(creative(X)&old(X))))&
((?[X]:((~creative(X)|~calm(X))))=>(?[X]:(~patient(X))))&
(![X]:((curious(X)&old(X))<=>(curious(X)|~wise(X))))&
(![X]:((funny(X)|brave(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((~patient(X)|patient(X))))<=>(?[X]:((~creative(X)&curious(X)))))&
(![X]:(calm(X)<=>(~old(X)|humble(X))))&
(![X]:((humble(X)&wise(X))=>(wise(X)|tall(X))))&
((?[X]:(~wise(X)))=>((curious(susan)<~>humble(susan))))&
(![X]:(~rich(X)=>(funny(X)<~>strong(X))))&
((~rich(john)&~creative(john)))&
(~funny(susan))&
(?[X]:((brave(X)&~patient(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((old(susan)<~>tall(susan)))&
(?[X]:((~humble(X)|~funny(X)))) | patient(susan) | [] | null | 0 |
Everyone who is both rich and funny is rich or happy. If john is both generous and strong then someone is not old and vice versa. Everyone who is either not happy or not strong is brave and vice versa. Everyone who is old or creative is either not wise or generous and vice versa. Everyone who is wise is happy or not old. Everyone who is either not patient or quiet is calm. Everyone who is kind or old is both not tall and not funny and vice versa. Everyone who is patient or tall is either wise or not patient and vice versa. Everyone who is not generous is humble or kind and vice versa. Everyone who is both not curious and not patient is either not generous or not strong and vice versa. If fred is either generous or not funny then someone is both calm and not funny and vice versa. If susan is both not rich and not brave then someone is both brave and rich and vice versa. Everyone who is quiet is not curious. If someone is either not strong or rich then fred is both old and wise. If lucy is both not quiet and not happy then someone is either not brave or rich and vice versa. Everyone who is both wise and not brave is both not humble and quiet. Someone is either not curious or calm. Mary is both generous and old. Mary is not creative. Someone is rich or not tall. Alice is either brave or not strong. Someone is either calm or not calm. Alice is both not humble and not curious. | John is humble. | contradiction | (![X]:((rich(X)&funny(X))=>(rich(X)|happy(X))))&
(((generous(john)&strong(john)))<=>(?[X]:(~old(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>brave(X)))&
(![X]:((old(X)|creative(X))<=>(~wise(X)<~>generous(X))))&
(![X]:(wise(X)=>(happy(X)|~old(X))))&
(![X]:((~patient(X)<~>quiet(X))=>calm(X)))&
(![X]:((kind(X)|old(X))<=>(~tall(X)&~funny(X))))&
(![X]:((patient(X)|tall(X))<=>(wise(X)<~>~patient(X))))&
(![X]:(~generous(X)<=>(humble(X)|kind(X))))&
(![X]:((~curious(X)&~patient(X))<=>(~generous(X)<~>~strong(X))))&
(((generous(fred)<~>~funny(fred)))<=>(?[X]:((calm(X)&~funny(X)))))&
(((~rich(susan)&~brave(susan)))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:(quiet(X)=>~curious(X)))&
((?[X]:((~strong(X)<~>rich(X))))=>((old(fred)&wise(fred))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:((~brave(X)<~>rich(X)))))&
(![X]:((wise(X)&~brave(X))=>(~humble(X)&quiet(X))))&
(?[X]:((~curious(X)<~>calm(X))))&
((generous(mary)&old(mary)))&
(~creative(mary))&
(?[X]:((rich(X)|~tall(X))))&
((brave(alice)<~>~strong(alice)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~humble(alice)&~curious(alice))) | humble(john) | [
"p1",
"p3",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8441592591759729386945364
% SZS output start Proof for 8441592591759729386945364
2. (strong(john) & generous(john)) <=> ? [X0] : ~old(X0) [input p1]
4. ! [X0] : ((creative(X0) | old(X0)) <=> (~wise(X0) <~> generous(X0))) [input p3]
7. ! [X0] : ((old(X0) | kind(X0)) <=> (~funny(X0) & ~tall(X0))) [input p6]
8. ! [X0] : ((tall(X0) | patient(X0)) <=> (wise(X0) <~> ~patient(X0))) [input p7]
9. ! [X0] : (~generous(X0) <=> (kind(X0) | humble(X0))) [input p8]
24. humble(john) [input hypothesis]
34. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | (~strong(john) | ~generous(john))) [nnf transformation 2]
35. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~strong(john) | ~generous(john)) [flattening 34]
36. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~strong(john) | ~generous(john)) [rectify 35]
37. ? [X1] : ~old(X1) => ~old(sK0) [choice axiom]
38. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (~old(sK0) | ~strong(john) | ~generous(john)) [skolemisation 36,37]
40. ! [X0] : (((creative(X0) | old(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~creative(X0) & ~old(X0)))) [nnf transformation 4]
41. ! [X0] : ((creative(X0) | old(X0) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~creative(X0) & ~old(X0)))) [flattening 40]
43. ! [X0] : (((old(X0) | kind(X0)) | (funny(X0) | tall(X0))) & ((~funny(X0) & ~tall(X0)) | (~old(X0) & ~kind(X0)))) [nnf transformation 7]
44. ! [X0] : ((old(X0) | kind(X0) | funny(X0) | tall(X0)) & ((~funny(X0) & ~tall(X0)) | (~old(X0) & ~kind(X0)))) [flattening 43]
45. ! [X0] : (((tall(X0) | patient(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~tall(X0) & ~patient(X0)))) [nnf transformation 8]
46. ! [X0] : ((tall(X0) | patient(X0) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~tall(X0) & ~patient(X0)))) [flattening 45]
47. ! [X0] : ((~generous(X0) | (~kind(X0) & ~humble(X0))) & ((kind(X0) | humble(X0)) | generous(X0))) [nnf transformation 9]
48. ! [X0] : ((~generous(X0) | (~kind(X0) & ~humble(X0))) & (kind(X0) | humble(X0) | generous(X0))) [flattening 47]
77. generous(john) | old(X0) [cnf transformation 38]
83. ~wise(X0) | generous(X0) | ~old(X0) [cnf transformation 41]
93. ~tall(X0) | ~old(X0) [cnf transformation 44]
97. ~patient(X0) | wise(X0) | ~patient(X0) [cnf transformation 46]
102. tall(X0) | patient(X0) | wise(X0) | patient(X0) [cnf transformation 46]
104. ~humble(X0) | ~generous(X0) [cnf transformation 48]
147. humble(john) [cnf transformation 24]
148. ~patient(X0) | wise(X0) [duplicate literal removal 97]
149. tall(X0) | patient(X0) | wise(X0) [duplicate literal removal 102]
151. 1 <=> ! [X0] : old(X0) [avatar definition]
152. old(X0) <- (1) [avatar component clause 151]
159. 3 <=> generous(john) [avatar definition]
160. ~generous(john) <- (~3) [avatar component clause 159]
162. 1 | 3 [avatar split clause 77,159,151]
289. ~generous(john) [resolution 104,147]
292. ~3 [avatar split clause 289,159]
431. patient(X2) | wise(X2) | ~old(X2) [resolution 149,93]
436. patient(X2) | wise(X2) <- (1) [subsumption resolution 431,152]
437. wise(X2) <- (1) [subsumption resolution 436,148]
474. generous(X3) | ~old(X3) <- (1) [resolution 437,83]
480. generous(X3) <- (1) [subsumption resolution 474,152]
555. $false <- (1, ~3) [resolution 480,160]
558. ~1 | 3 [avatar contradiction clause 555]
559. $false [avatar sat refutation 162,292,558]
% SZS output end Proof for 8441592591759729386945364
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not happy then someone is both not brave and not tall and vice versa.
Everyone who is either creative or wise is both brave and not creative and vice versa.
Everyone who is either generous or not rich is either quiet or rich and vice versa.
Everyone who is not calm is either quiet or not patient.
Everyone who is not creative is strong or rich.
Everyone who is not old or generous is both happy and quiet.
If mary is rich or patient then lucy is both curious and wise.
Everyone who is both not kind and rich is both not curious and funny.
If someone is both old and not calm then someone is creative.
Everyone who is both not curious and happy is both calm and not humble.
Everyone who is creative is generous and vice versa.
If alice is not funny then someone is not calm.
If paul is either not patient or not tall then someone is both not generous and not rich.
Everyone who is not rich is rich or brave and vice versa.
Everyone who is not brave is both curious and tall.
Everyone who is not calm or not strong is not strong.
Paul is not strong or happy.
Someone is either not old or not wise.
Someone is happy.
Fred is not funny or wise.
Fred is wise.
Someone is both curious and not rich. | Fred is rich. | contradiction | ((?[X]:((strong(X)&~happy(X))))<=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((creative(X)<~>wise(X))<=>(brave(X)&~creative(X))))&
(![X]:((generous(X)<~>~rich(X))<=>(quiet(X)<~>rich(X))))&
(![X]:(~calm(X)=>(quiet(X)<~>~patient(X))))&
(![X]:(~creative(X)=>(strong(X)|rich(X))))&
(![X]:((~old(X)|generous(X))=>(happy(X)&quiet(X))))&
(((rich(mary)|patient(mary)))=>((curious(lucy)&wise(lucy))))&
(![X]:((~kind(X)&rich(X))=>(~curious(X)&funny(X))))&
((?[X]:((old(X)&~calm(X))))=>(?[X]:(creative(X))))&
(![X]:((~curious(X)&happy(X))=>(calm(X)&~humble(X))))&
(![X]:(creative(X)<=>generous(X)))&
((~funny(alice))=>(?[X]:(~calm(X))))&
(((~patient(paul)<~>~tall(paul)))=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:(~rich(X)<=>(rich(X)|brave(X))))&
(![X]:(~brave(X)=>(curious(X)&tall(X))))&
(![X]:((~calm(X)|~strong(X))=>~strong(X)))&
((~strong(paul)|happy(paul)))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:(happy(X)))&
((~funny(fred)|wise(fred)))&
(wise(fred))&
(?[X]:((curious(X)&~rich(X)))) | rich(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 410701068831987074711739
% SZS output start Proof for 410701068831987074711739
14. ! [X0] : (~rich(X0) <=> (brave(X0) | rich(X0))) [input p13]
23. rich(fred) [input hypothesis]
60. ! [X0] : ((~rich(X0) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | rich(X0))) [nnf transformation 14]
61. ! [X0] : ((~rich(X0) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | rich(X0))) [flattening 60]
105. ~rich(X0) | ~rich(X0) [cnf transformation 61]
117. rich(fred) [cnf transformation 23]
119. ~rich(X0) [duplicate literal removal 105]
236. $false [subsumption resolution 117,119]
% SZS output end Proof for 410701068831987074711739
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not calm is both not wise and calm. If fred is not calm then alice is not humble or old and vice versa. Everyone who is patient is either not funny or brave. Everyone who is both not funny and not rich is wise and vice versa. Everyone who is both quiet and not happy is not creative and vice versa. Everyone who is either not quiet or creative is both not creative and wise and vice versa. If someone is generous or curious then someone is not patient and vice versa. If someone is either kind or funny then someone is not funny. Everyone who is both wise and not brave is either kind or not brave. Everyone who is not generous or funny is not rich. If mary is creative or not generous then john is humble or not calm and vice versa. If john is both generous and calm then mary is curious and vice versa. If someone is both not strong and curious then someone is both not kind and calm and vice versa. Everyone who is both not kind and strong is either not quiet or not generous and vice versa. If someone is both happy and creative then someone is wise or creative. Everyone who is either old or not tall is not quiet or not brave. Paul is curious. Someone is either not calm or generous. Someone is not curious. John is either tall or quiet. Paul is not calm. Alice is either rich or not old. Mary is either not funny or strong. Fred is both tall and funny. | Fred is rich. | contradiction | (![X]:((funny(X)&~calm(X))=>(~wise(X)&calm(X))))&
((~calm(fred))<=>((~humble(alice)|old(alice))))&
(![X]:(patient(X)=>(~funny(X)<~>brave(X))))&
(![X]:((~funny(X)&~rich(X))<=>wise(X)))&
(![X]:((quiet(X)&~happy(X))<=>~creative(X)))&
(![X]:((~quiet(X)<~>creative(X))<=>(~creative(X)&wise(X))))&
((?[X]:((generous(X)|curious(X))))<=>(?[X]:(~patient(X))))&
((?[X]:((kind(X)<~>funny(X))))=>(?[X]:(~funny(X))))&
(![X]:((wise(X)&~brave(X))=>(kind(X)<~>~brave(X))))&
(![X]:((~generous(X)|funny(X))=>~rich(X)))&
(((creative(mary)|~generous(mary)))<=>((humble(john)|~calm(john))))&
(((generous(john)&calm(john)))<=>(curious(mary)))&
((?[X]:((~strong(X)&curious(X))))<=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:((~kind(X)&strong(X))<=>(~quiet(X)<~>~generous(X))))&
((?[X]:((happy(X)&creative(X))))=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((old(X)<~>~tall(X))=>(~quiet(X)|~brave(X))))&
(curious(paul))&
(?[X]:((~calm(X)<~>generous(X))))&
(?[X]:(~curious(X)))&
((tall(john)<~>quiet(john)))&
(~calm(paul))&
((rich(alice)<~>~old(alice)))&
((~funny(mary)<~>strong(mary)))&
((tall(fred)&funny(fred))) | rich(fred) | [
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6404537369661888811937250
% SZS output start Proof for 6404537369661888811937250
10. ! [X0] : ((funny(X0) | ~generous(X0)) => ~rich(X0)) [input p9]
24. funny(fred) & tall(fred) [input p23]
25. rich(fred) [input hypothesis]
36. ! [X0] : (~rich(X0) | (~funny(X0) & generous(X0))) [ennf transformation 10]
109. ~rich(X0) | ~funny(X0) [cnf transformation 36]
142. funny(fred) [cnf transformation 24]
143. rich(fred) [cnf transformation 25]
307. ~funny(fred) [resolution 109,143]
308. $false [subsumption resolution 307,142]
% SZS output end Proof for 6404537369661888811937250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not tall or not brave then mary is kind and vice versa.
Everyone who is not happy is strong and vice versa.
If someone is not brave or old then someone is either generous or strong and vice versa.
Everyone who is humble is both happy and not wise and vice versa.
Everyone who is either not kind or brave is both not calm and old and vice versa.
If someone is both generous and not wise then john is not strong.
Everyone who is not strong is not quiet and vice versa.
Everyone who is generous is either not kind or old and vice versa.
If susan is curious or humble then someone is tall or kind and vice versa.
Everyone who is quiet is either not kind or creative and vice versa.
If someone is either not curious or humble then someone is both wise and patient and vice versa.
If someone is either rich or calm then someone is not creative or quiet.
Everyone who is both generous and not strong is both calm and brave.
Everyone who is either old or not kind is tall and vice versa.
If someone is either old or curious then someone is not happy and vice versa.
Everyone who is both not strong and funny is not humble and vice versa.
Someone is either brave or not humble.
Paul is not old or wise.
Someone is both not brave and funny.
Susan is not tall or curious.
Someone is rich or quiet.
Fred is either wise or not calm.
Someone is not quiet or not generous. | Paul is not funny. | neutral | (((~tall(paul)<~>~brave(paul)))<=>(kind(mary)))&
(![X]:(~happy(X)<=>strong(X)))&
((?[X]:((~brave(X)|old(X))))<=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:(humble(X)<=>(happy(X)&~wise(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(~calm(X)&old(X))))&
((?[X]:((generous(X)&~wise(X))))=>(~strong(john)))&
(![X]:(~strong(X)<=>~quiet(X)))&
(![X]:(generous(X)<=>(~kind(X)<~>old(X))))&
(((curious(susan)|humble(susan)))<=>(?[X]:((tall(X)|kind(X)))))&
(![X]:(quiet(X)<=>(~kind(X)<~>creative(X))))&
((?[X]:((~curious(X)<~>humble(X))))<=>(?[X]:((wise(X)&patient(X)))))&
((?[X]:((rich(X)<~>calm(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
(![X]:((generous(X)&~strong(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)<~>~kind(X))<=>tall(X)))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)&funny(X))<=>~humble(X)))&
(?[X]:((brave(X)<~>~humble(X))))&
((~old(paul)|wise(paul)))&
(?[X]:((~brave(X)&funny(X))))&
((~tall(susan)|curious(susan)))&
(?[X]:((rich(X)|quiet(X))))&
((wise(fred)<~>~calm(fred)))&
(?[X]:((~quiet(X)|~generous(X)))) | ~funny(paul) | [] | null | 0 |
If john is not humble or old then paul is tall or rich and vice versa.
Everyone who is either not curious or wise is not generous.
If someone is either tall or curious then someone is wise or not curious.
Everyone who is not old or funny is both not brave and rich and vice versa.
Everyone who is generous or kind is old.
If someone is not patient or old then fred is either curious or brave and vice versa.
Everyone who is calm is both not brave and wise and vice versa.
Everyone who is curious or not rich is not patient.
Everyone who is either not curious or generous is either quiet or curious and vice versa.
If susan is not strong or humble then alice is both wise and not wise.
Everyone who is brave or not humble is both not generous and not happy.
Everyone who is patient is either not curious or happy.
Everyone who is both not strong and not humble is not patient or not funny and vice versa.
If lucy is not wise or tall then someone is either not kind or humble and vice versa.
If fred is kind then paul is not tall or funny and vice versa.
Lucy is brave or kind.
Someone is either not tall or creative.
Mary is brave.
Someone is not old or not patient.
Susan is old.
Someone is either strong or old.
Paul is both not rich and not funny. | Fred is quiet. | entailment | (((~humble(john)|old(john)))<=>((tall(paul)|rich(paul))))&
(![X]:((~curious(X)<~>wise(X))=>~generous(X)))&
((?[X]:((tall(X)<~>curious(X))))=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:((~old(X)|funny(X))<=>(~brave(X)&rich(X))))&
(![X]:((generous(X)|kind(X))=>old(X)))&
((?[X]:((~patient(X)|old(X))))<=>((curious(fred)<~>brave(fred))))&
(![X]:(calm(X)<=>(~brave(X)&wise(X))))&
(![X]:((curious(X)|~rich(X))=>~patient(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(quiet(X)<~>curious(X))))&
(((~strong(susan)|humble(susan)))=>((wise(alice)&~wise(alice))))&
(![X]:((brave(X)|~humble(X))=>(~generous(X)&~happy(X))))&
(![X]:(patient(X)=>(~curious(X)<~>happy(X))))&
(![X]:((~strong(X)&~humble(X))<=>(~patient(X)|~funny(X))))&
(((~wise(lucy)|tall(lucy)))<=>(?[X]:((~kind(X)<~>humble(X)))))&
((kind(fred))<=>((~tall(paul)|funny(paul))))&
((brave(lucy)|kind(lucy)))&
(?[X]:((~tall(X)<~>creative(X))))&
(brave(mary))&
(?[X]:((~old(X)|~patient(X))))&
(old(susan))&
(?[X]:((strong(X)<~>old(X))))&
((~rich(paul)&~funny(paul))) | quiet(fred) | [
"p5",
"p7",
"p8",
"p10",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3476679267509666284570788
% SZS output start Proof for 3476679267509666284570788
6. ? [X0] : (old(X0) | ~patient(X0)) <=> (curious(fred) <~> brave(fred)) [input p5]
8. ! [X0] : ((~rich(X0) | curious(X0)) => ~patient(X0)) [input p7]
9. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> (quiet(X0) <~> curious(X0))) [input p8]
11. ! [X0] : ((~humble(X0) | brave(X0)) => (~happy(X0) & ~generous(X0))) [input p10]
13. ! [X0] : ((~humble(X0) & ~strong(X0)) <=> (~funny(X0) | ~patient(X0))) [input p12]
20. old(susan) [input p19]
23. ~quiet(fred) [input hypothesis]
28. ! [X0] : (~patient(X0) | (rich(X0) & ~curious(X0))) [ennf transformation 8]
30. ! [X0] : ((~happy(X0) & ~generous(X0)) | (humble(X0) & ~brave(X0))) [ennf transformation 11]
41. (? [X0] : (old(X0) | ~patient(X0)) | ((curious(fred) | ~brave(fred)) & (brave(fred) | ~curious(fred)))) & (((~brave(fred) | ~curious(fred)) & (brave(fred) | curious(fred))) | ! [X0] : (~old(X0) & patient(X0))) [nnf transformation 6]
42. (? [X0] : (old(X0) | ~patient(X0)) | ((curious(fred) | ~brave(fred)) & (brave(fred) | ~curious(fred)))) & (((~brave(fred) | ~curious(fred)) & (brave(fred) | curious(fred))) | ! [X1] : (~old(X1) & patient(X1))) [rectify 41]
43. ? [X0] : (old(X0) | ~patient(X0)) => (old(sK1) | ~patient(sK1)) [choice axiom]
44. ((old(sK1) | ~patient(sK1)) | ((curious(fred) | ~brave(fred)) & (brave(fred) | ~curious(fred)))) & (((~brave(fred) | ~curious(fred)) & (brave(fred) | curious(fred))) | ! [X1] : (~old(X1) & patient(X1))) [skolemisation 42,43]
45. ! [X0] : ((((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))))) [nnf transformation 9]
47. ! [X0] : (((~humble(X0) & ~strong(X0)) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | (humble(X0) | strong(X0)))) [nnf transformation 13]
48. ! [X0] : (((~humble(X0) & ~strong(X0)) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | humble(X0) | strong(X0))) [flattening 47]
80. brave(fred) | curious(fred) | ~old(X1) [cnf transformation 44]
85. ~patient(X0) | ~curious(X0) [cnf transformation 28]
87. curious(X0) | quiet(X0) | generous(X0) | curious(X0) [cnf transformation 45]
92. generous(X0) | ~curious(X0) | quiet(X0) | ~curious(X0) [cnf transformation 45]
99. ~brave(X0) | ~generous(X0) [cnf transformation 30]
100. ~generous(X0) | humble(X0) [cnf transformation 30]
108. ~humble(X0) | patient(X0) [cnf transformation 48]
124. old(susan) [cnf transformation 20]
129. ~quiet(fred) [cnf transformation 23]
130. curious(X0) | quiet(X0) | generous(X0) [duplicate literal removal 87]
132. ~curious(X0) | generous(X0) | quiet(X0) [duplicate literal removal 92]
171. 9 <=> brave(fred) [avatar definition]
172. brave(fred) <- (9) [avatar component clause 171]
175. 10 <=> curious(fred) [avatar definition]
177. curious(fred) <- (10) [avatar component clause 175]
189. 13 <=> ! [X1] : ~old(X1) [avatar definition]
190. ~old(X1) <- (13) [avatar component clause 189]
196. 13 | 10 | 9 [avatar split clause 80,171,175,189]
199. quiet(X0) | generous(X0) [subsumption resolution 130,132]
304. ~generous(fred) <- (9) [resolution 99,172]
316. generous(fred) [resolution 199,129]
318. $false <- (9) [subsumption resolution 316,304]
319. ~9 [avatar contradiction clause 318]
321. $false <- (13) [resolution 190,124]
326. ~13 [avatar contradiction clause 321]
334. humble(fred) [resolution 316,100]
342. patient(fred) [resolution 334,108]
351. ~curious(fred) [resolution 342,85]
352. $false <- (10) [subsumption resolution 351,177]
353. ~10 [avatar contradiction clause 352]
354. $false [avatar sat refutation 196,319,326,353]
% SZS output end Proof for 3476679267509666284570788
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and curious is not strong or humble and vice versa. Everyone who is both generous and happy is kind or not calm. Everyone who is either not kind or kind is calm. Everyone who is either not patient or wise is either funny or not tall. If paul is curious then someone is not rich. Everyone who is not tall is calm. Everyone who is creative is not rich and vice versa. If someone is both brave and strong then susan is either kind or not quiet and vice versa. If someone is either not curious or rich then someone is not calm. Everyone who is either strong or funny is not calm or rich and vice versa. If lucy is old then susan is not curious. Everyone who is both not funny and kind is either patient or not old. If mary is not rich or not quiet then someone is either not old or not brave and vice versa. Everyone who is either wise or not old is creative and vice versa. Everyone who is either brave or tall is both rich and humble and vice versa. Everyone who is not tall or not happy is either tall or brave. Someone is both curious and brave. Someone is both quiet and creative. Someone is not creative or rich. Someone is either not rich or not wise. | Paul is not quiet. | neutral | (![X]:((happy(X)&curious(X))<=>(~strong(X)|humble(X))))&
(![X]:((generous(X)&happy(X))=>(kind(X)|~calm(X))))&
(![X]:((~kind(X)<~>kind(X))=>calm(X)))&
(![X]:((~patient(X)<~>wise(X))=>(funny(X)<~>~tall(X))))&
((curious(paul))=>(?[X]:(~rich(X))))&
(![X]:(~tall(X)=>calm(X)))&
(![X]:(creative(X)<=>~rich(X)))&
((?[X]:((brave(X)&strong(X))))<=>((kind(susan)<~>~quiet(susan))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>funny(X))<=>(~calm(X)|rich(X))))&
((old(lucy))=>(~curious(susan)))&
(![X]:((~funny(X)&kind(X))=>(patient(X)<~>~old(X))))&
(((~rich(mary)|~quiet(mary)))<=>(?[X]:((~old(X)<~>~brave(X)))))&
(![X]:((wise(X)<~>~old(X))<=>creative(X)))&
(![X]:((brave(X)<~>tall(X))<=>(rich(X)&humble(X))))&
(![X]:((~tall(X)|~happy(X))=>(tall(X)<~>brave(X))))&
(?[X]:((curious(X)&brave(X))))&
(?[X]:((quiet(X)&creative(X))))&
(?[X]:((~creative(X)|rich(X))))&
(?[X]:((~rich(X)<~>~wise(X)))) | ~quiet(paul) | [] | null | 0 |
Everyone who is not curious or not strong is either curious or quiet.
If alice is not wise then someone is brave or wise and vice versa.
Everyone who is not happy or curious is curious.
Everyone who is both generous and patient is not calm or not happy and vice versa.
Everyone who is quiet or not wise is either not generous or not calm.
Everyone who is not old or strong is both not generous and curious and vice versa.
If someone is both not creative and not old then someone is either not patient or rich and vice versa.
If fred is not rich then someone is kind and vice versa.
Everyone who is not curious is both not curious and brave.
Everyone who is not humble is wise.
If someone is either not humble or not calm then lucy is either not generous or not old and vice versa.
Everyone who is either rich or calm is curious.
If someone is old or generous then someone is either old or not curious.
Everyone who is not happy is both quiet and brave.
Everyone who is both not creative and happy is either quiet or old.
Everyone who is either humble or not patient is both not patient and funny and vice versa.
Someone is rich.
Alice is calm.
Someone is both not kind and old.
Fred is not brave.
Fred is not wise or not old.
Susan is either funny or patient.
Someone is either calm or funny.
John is either funny or patient. | John is wise. | entailment | (![X]:((~curious(X)|~strong(X))=>(curious(X)<~>quiet(X))))&
((~wise(alice))<=>(?[X]:((brave(X)|wise(X)))))&
(![X]:((~happy(X)|curious(X))=>curious(X)))&
(![X]:((generous(X)&patient(X))<=>(~calm(X)|~happy(X))))&
(![X]:((quiet(X)|~wise(X))=>(~generous(X)<~>~calm(X))))&
(![X]:((~old(X)|strong(X))<=>(~generous(X)&curious(X))))&
((?[X]:((~creative(X)&~old(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
((~rich(fred))<=>(?[X]:(kind(X))))&
(![X]:(~curious(X)=>(~curious(X)&brave(X))))&
(![X]:(~humble(X)=>wise(X)))&
((?[X]:((~humble(X)<~>~calm(X))))<=>((~generous(lucy)<~>~old(lucy))))&
(![X]:((rich(X)<~>calm(X))=>curious(X)))&
((?[X]:((old(X)|generous(X))))=>(?[X]:((old(X)<~>~curious(X)))))&
(![X]:(~happy(X)=>(quiet(X)&brave(X))))&
(![X]:((~creative(X)&happy(X))=>(quiet(X)<~>old(X))))&
(![X]:((humble(X)<~>~patient(X))<=>(~patient(X)&funny(X))))&
(?[X]:(rich(X)))&
(calm(alice))&
(?[X]:((~kind(X)&old(X))))&
(~brave(fred))&
((~wise(fred)|~old(fred)))&
((funny(susan)<~>patient(susan)))&
(?[X]:((calm(X)<~>funny(X))))&
((funny(john)<~>patient(john))) | wise(john) | [
"p9",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8121430958379549064467905
% SZS output start Proof for 8121430958379549064467905
10. ! [X0] : (~humble(X0) => wise(X0)) [input p9]
16. ! [X0] : ((humble(X0) <~> ~patient(X0)) <=> (funny(X0) & ~patient(X0))) [input p15]
24. funny(john) <~> patient(john) [input p23]
25. ~wise(john) [input hypothesis]
32. ! [X0] : (wise(X0) | humble(X0)) [ennf transformation 10]
67. ! [X0] : ((((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (~funny(X0) | patient(X0))) & ((funny(X0) & ~patient(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0))))) [nnf transformation 16]
68. ! [X0] : ((((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | ~funny(X0) | patient(X0)) & ((funny(X0) & ~patient(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0))))) [flattening 67]
77. (~patient(john) | ~funny(john)) & (patient(john) | funny(john)) [nnf transformation 24]
111. humble(X0) | wise(X0) [cnf transformation 32]
130. ~patient(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 68]
135. patient(X0) | ~humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 68]
146. patient(john) | funny(john) [cnf transformation 77]
148. ~wise(john) [cnf transformation 25]
149. ~humble(X0) | ~patient(X0) [duplicate literal removal 130]
150. ~funny(X0) | ~humble(X0) | patient(X0) [duplicate literal removal 135]
302. 32 <=> funny(john) [avatar definition]
303. funny(john) <- (32) [avatar component clause 302]
306. 33 <=> patient(john) [avatar definition]
307. patient(john) <- (33) [avatar component clause 306]
308. ~patient(john) <- (~33) [avatar component clause 306]
310. 32 | 33 [avatar split clause 146,306,302]
329. ~patient(X0) | wise(X0) [resolution 149,111]
383. ~humble(john) | patient(john) <- (32) [resolution 150,303]
392. ~humble(john) <- (32, ~33) [subsumption resolution 383,308]
539. wise(john) <- (32, ~33) [resolution 392,111]
540. $false <- (32, ~33) [subsumption resolution 539,148]
541. ~32 | 33 [avatar contradiction clause 540]
543. wise(john) <- (33) [resolution 307,329]
544. $false <- (33) [subsumption resolution 543,148]
545. ~33 [avatar contradiction clause 544]
546. $false [avatar sat refutation 310,541,545]
% SZS output end Proof for 8121430958379549064467905
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If susan is generous then someone is strong.
Everyone who is not brave or curious is brave.
Everyone who is both brave and not brave is not creative and vice versa.
If someone is both not happy and kind then someone is creative and vice versa.
If mary is both tall and not humble then someone is both creative and tall.
Everyone who is either not old or patient is kind and vice versa.
Everyone who is both kind and not tall is either not strong or curious.
If someone is either tall or funny then john is either quiet or patient.
Everyone who is both humble and not humble is not old or not rich and vice versa.
If someone is either not rich or not strong then someone is both not funny and strong.
If mary is either not rich or not patient then paul is both rich and brave.
Everyone who is not kind is either calm or not funny and vice versa.
If someone is happy or not happy then someone is calm.
Everyone who is either not old or not brave is wise.
If someone is both not brave and calm then fred is either not curious or not old and vice versa.
If someone is both brave and generous then alice is wise or not old and vice versa.
John is calm.
Fred is not calm.
Fred is both kind and humble.
Alice is not tall or not happy.
Someone is calm.
Fred is either kind or not brave.
Lucy is either not patient or patient.
Someone is not strong. | Mary is not rich. | contradiction | ((generous(susan))=>(?[X]:(strong(X))))&
(![X]:((~brave(X)|curious(X))=>brave(X)))&
(![X]:((brave(X)&~brave(X))<=>~creative(X)))&
((?[X]:((~happy(X)&kind(X))))<=>(?[X]:(creative(X))))&
(((tall(mary)&~humble(mary)))=>(?[X]:((creative(X)&tall(X)))))&
(![X]:((~old(X)<~>patient(X))<=>kind(X)))&
(![X]:((kind(X)&~tall(X))=>(~strong(X)<~>curious(X))))&
((?[X]:((tall(X)<~>funny(X))))=>((quiet(john)<~>patient(john))))&
(![X]:((humble(X)&~humble(X))<=>(~old(X)|~rich(X))))&
((?[X]:((~rich(X)<~>~strong(X))))=>(?[X]:((~funny(X)&strong(X)))))&
(((~rich(mary)<~>~patient(mary)))=>((rich(paul)&brave(paul))))&
(![X]:(~kind(X)<=>(calm(X)<~>~funny(X))))&
((?[X]:((happy(X)|~happy(X))))=>(?[X]:(calm(X))))&
(![X]:((~old(X)<~>~brave(X))=>wise(X)))&
((?[X]:((~brave(X)&calm(X))))<=>((~curious(fred)<~>~old(fred))))&
((?[X]:((brave(X)&generous(X))))<=>((wise(alice)|~old(alice))))&
(calm(john))&
(~calm(fred))&
((kind(fred)&humble(fred)))&
((~tall(alice)|~happy(alice)))&
(?[X]:(calm(X)))&
((kind(fred)<~>~brave(fred)))&
((~patient(lucy)<~>patient(lucy)))&
(?[X]:(~strong(X))) | ~rich(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7034413829356533825503603
% SZS output start Proof for 7034413829356533825503603
9. ! [X0] : ((~humble(X0) & humble(X0)) <=> (~rich(X0) | ~old(X0))) [input p8]
25. ~rich(mary) [input hypothesis]
54. ! [X0] : (((~humble(X0) & humble(X0)) | (rich(X0) & old(X0))) & ((~rich(X0) | ~old(X0)) | (humble(X0) | ~humble(X0)))) [nnf transformation 9]
55. ! [X0] : (((~humble(X0) & humble(X0)) | (rich(X0) & old(X0))) & (~rich(X0) | ~old(X0) | humble(X0) | ~humble(X0))) [flattening 54]
104. humble(X0) | rich(X0) [cnf transformation 55]
106. ~humble(X0) | rich(X0) [cnf transformation 55]
145. ~rich(mary) [cnf transformation 25]
190. rich(X0) [subsumption resolution 104,106]
256. $false [subsumption resolution 145,190]
% SZS output end Proof for 7034413829356533825503603
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is kind or not wise and vice versa.
Everyone who is both not patient and not curious is either happy or not kind and vice versa.
If someone is not tall or not wise then paul is either calm or happy.
Everyone who is not quiet or humble is both not generous and not patient and vice versa.
If someone is funny or not creative then lucy is either funny or not strong and vice versa.
Everyone who is not old or not humble is either not creative or not kind and vice versa.
Everyone who is both not funny and not patient is either rich or wise.
Everyone who is not patient or not creative is not creative.
If mary is either not calm or wise then someone is either strong or not wise and vice versa.
If fred is either creative or not calm then paul is old.
Everyone who is wise or not happy is brave and vice versa.
Everyone who is quiet or not calm is either quiet or calm and vice versa.
Everyone who is not happy is both tall and kind.
If john is humble then someone is not rich and vice versa.
If susan is either not patient or strong then susan is both brave and wise.
If someone is not creative or calm then lucy is either not strong or brave.
Fred is both not brave and creative.
Paul is both brave and not patient.
Lucy is either brave or not patient.
Someone is both not rich and funny.
Someone is either not happy or brave.
Someone is happy or not brave.
Fred is both not funny and not humble.
Lucy is strong or not happy. | John is generous. | contradiction | (![X]:(~calm(X)<=>(kind(X)|~wise(X))))&
(![X]:((~patient(X)&~curious(X))<=>(happy(X)<~>~kind(X))))&
((?[X]:((~tall(X)|~wise(X))))=>((calm(paul)<~>happy(paul))))&
(![X]:((~quiet(X)|humble(X))<=>(~generous(X)&~patient(X))))&
((?[X]:((funny(X)|~creative(X))))<=>((funny(lucy)<~>~strong(lucy))))&
(![X]:((~old(X)|~humble(X))<=>(~creative(X)<~>~kind(X))))&
(![X]:((~funny(X)&~patient(X))=>(rich(X)<~>wise(X))))&
(![X]:((~patient(X)|~creative(X))=>~creative(X)))&
(((~calm(mary)<~>wise(mary)))<=>(?[X]:((strong(X)<~>~wise(X)))))&
(((creative(fred)<~>~calm(fred)))=>(old(paul)))&
(![X]:((wise(X)|~happy(X))<=>brave(X)))&
(![X]:((quiet(X)|~calm(X))<=>(quiet(X)<~>calm(X))))&
(![X]:(~happy(X)=>(tall(X)&kind(X))))&
((humble(john))<=>(?[X]:(~rich(X))))&
(((~patient(susan)<~>strong(susan)))=>((brave(susan)&wise(susan))))&
((?[X]:((~creative(X)|calm(X))))=>((~strong(lucy)<~>brave(lucy))))&
((~brave(fred)&creative(fred)))&
((brave(paul)&~patient(paul)))&
((brave(lucy)<~>~patient(lucy)))&
(?[X]:((~rich(X)&funny(X))))&
(?[X]:((~happy(X)<~>brave(X))))&
(?[X]:((happy(X)|~brave(X))))&
((~funny(fred)&~humble(fred)))&
((strong(lucy)|~happy(lucy))) | generous(john) | [
"p3",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6678260853124966958235074
% SZS output start Proof for 6678260853124966958235074
4. ! [X0] : ((humble(X0) | ~quiet(X0)) <=> (~patient(X0) & ~generous(X0))) [input p3]
14. humble(john) <=> ? [X0] : ~rich(X0) [input p13]
20. ? [X0] : (funny(X0) & ~rich(X0)) [input p19]
25. generous(john) [input hypothesis]
41. ! [X0] : (((humble(X0) | ~quiet(X0)) | (patient(X0) | generous(X0))) & ((~patient(X0) & ~generous(X0)) | (~humble(X0) & quiet(X0)))) [nnf transformation 4]
42. ! [X0] : ((humble(X0) | ~quiet(X0) | patient(X0) | generous(X0)) & ((~patient(X0) & ~generous(X0)) | (~humble(X0) & quiet(X0)))) [flattening 41]
59. (humble(john) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | ~humble(john)) [nnf transformation 14]
60. (humble(john) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | ~humble(john)) [rectify 59]
61. ? [X1] : ~rich(X1) => ~rich(sK2) [choice axiom]
62. (humble(john) | ! [X0] : rich(X0)) & (~rich(sK2) | ~humble(john)) [skolemisation 60,61]
66. ? [X0] : (funny(X0) & ~rich(X0)) => (funny(sK3) & ~rich(sK3)) [choice axiom]
67. funny(sK3) & ~rich(sK3) [skolemisation 20,66]
85. ~generous(X0) | ~humble(X0) [cnf transformation 42]
126. humble(john) | rich(X0) [cnf transformation 62]
141. ~rich(sK3) [cnf transformation 67]
149. generous(john) [cnf transformation 25]
243. 19 <=> ! [X0] : rich(X0) [avatar definition]
244. rich(X0) <- (19) [avatar component clause 243]
246. 20 <=> humble(john) [avatar definition]
248. humble(john) <- (20) [avatar component clause 246]
249. 19 | 20 [avatar split clause 126,246,243]
298. $false <- (19) [resolution 244,141]
299. ~19 [avatar contradiction clause 298]
301. ~humble(john) [resolution 85,149]
302. $false <- (20) [subsumption resolution 301,248]
303. ~20 [avatar contradiction clause 302]
304. $false [avatar sat refutation 249,299,303]
% SZS output end Proof for 6678260853124966958235074
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not happy or humble then john is not rich.
Everyone who is creative or not strong is not generous or not kind and vice versa.
Everyone who is both generous and tall is quiet and vice versa.
Everyone who is not calm or not strong is not kind or funny.
Everyone who is not happy is either not wise or kind and vice versa.
If someone is quiet then john is both not strong and quiet.
If someone is tall or happy then john is not creative.
Everyone who is not calm is both wise and not quiet and vice versa.
Everyone who is not patient is not old or wise.
If lucy is either not humble or not brave then john is either not generous or tall and vice versa.
Everyone who is both rich and not curious is not old or not wise and vice versa.
If someone is either not generous or wise then someone is both funny and strong and vice versa.
Everyone who is funny is wise.
If someone is either quiet or not strong then lucy is either not old or creative and vice versa.
If paul is either not happy or not curious then lucy is either curious or not brave and vice versa.
If fred is tall or not curious then fred is funny.
Fred is both not old and not calm.
Someone is either kind or not patient.
Someone is not creative.
Someone is curious.
Susan is both not rich and not tall.
Susan is either not patient or old.
John is both not generous and strong.
Susan is both not humble and wise. | Lucy is not old. | neutral | (((~happy(john)<~>humble(john)))=>(~rich(john)))&
(![X]:((creative(X)|~strong(X))<=>(~generous(X)|~kind(X))))&
(![X]:((generous(X)&tall(X))<=>quiet(X)))&
(![X]:((~calm(X)|~strong(X))=>(~kind(X)|funny(X))))&
(![X]:(~happy(X)<=>(~wise(X)<~>kind(X))))&
((?[X]:(quiet(X)))=>((~strong(john)&quiet(john))))&
((?[X]:((tall(X)|happy(X))))=>(~creative(john)))&
(![X]:(~calm(X)<=>(wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>(~old(X)|wise(X))))&
(((~humble(lucy)<~>~brave(lucy)))<=>((~generous(john)<~>tall(john))))&
(![X]:((rich(X)&~curious(X))<=>(~old(X)|~wise(X))))&
((?[X]:((~generous(X)<~>wise(X))))<=>(?[X]:((funny(X)&strong(X)))))&
(![X]:(funny(X)=>wise(X)))&
((?[X]:((quiet(X)<~>~strong(X))))<=>((~old(lucy)<~>creative(lucy))))&
(((~happy(paul)<~>~curious(paul)))<=>((curious(lucy)<~>~brave(lucy))))&
(((tall(fred)|~curious(fred)))=>(funny(fred)))&
((~old(fred)&~calm(fred)))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:(~creative(X)))&
(?[X]:(curious(X)))&
((~rich(susan)&~tall(susan)))&
((~patient(susan)<~>old(susan)))&
((~generous(john)&strong(john)))&
((~humble(susan)&wise(susan))) | ~old(lucy) | [] | null | 0 |
Everyone who is brave is both patient and not wise and vice versa. Everyone who is both not happy and not rich is either quiet or not strong and vice versa. If alice is not tall then mary is either patient or not generous. Everyone who is both not old and not calm is either strong or not kind and vice versa. Everyone who is not kind or wise is not curious or funny and vice versa. If lucy is both not funny and old then someone is quiet. If someone is not old or not creative then someone is quiet and vice versa. If someone is both kind and not humble then someone is either not tall or curious and vice versa. Everyone who is wise is kind or quiet and vice versa. If mary is either not humble or not generous then alice is both not rich and generous. If someone is both generous and not wise then someone is either creative or not brave. If someone is either old or humble then paul is funny or wise and vice versa. If susan is either quiet or humble then someone is humble. Everyone who is both not humble and not calm is both not brave and tall. Everyone who is generous is wise and vice versa. Everyone who is either strong or not kind is both happy and humble and vice versa. Alice is patient or not wise. John is either not happy or old. Paul is both wise and not calm. Mary is strong. Lucy is not generous or creative. Someone is not funny or brave. John is strong. Lucy is either happy or not quiet. | John is kind. | contradiction | (![X]:(brave(X)<=>(patient(X)&~wise(X))))&
(![X]:((~happy(X)&~rich(X))<=>(quiet(X)<~>~strong(X))))&
((~tall(alice))=>((patient(mary)<~>~generous(mary))))&
(![X]:((~old(X)&~calm(X))<=>(strong(X)<~>~kind(X))))&
(![X]:((~kind(X)|wise(X))<=>(~curious(X)|funny(X))))&
(((~funny(lucy)&old(lucy)))=>(?[X]:(quiet(X))))&
((?[X]:((~old(X)|~creative(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((kind(X)&~humble(X))))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:(wise(X)<=>(kind(X)|quiet(X))))&
(((~humble(mary)<~>~generous(mary)))=>((~rich(alice)&generous(alice))))&
((?[X]:((generous(X)&~wise(X))))=>(?[X]:((creative(X)<~>~brave(X)))))&
((?[X]:((old(X)<~>humble(X))))<=>((funny(paul)|wise(paul))))&
(((quiet(susan)<~>humble(susan)))=>(?[X]:(humble(X))))&
(![X]:((~humble(X)&~calm(X))=>(~brave(X)&tall(X))))&
(![X]:(generous(X)<=>wise(X)))&
(![X]:((strong(X)<~>~kind(X))<=>(happy(X)&humble(X))))&
((patient(alice)|~wise(alice)))&
((~happy(john)<~>old(john)))&
((wise(paul)&~calm(paul)))&
(strong(mary))&
((~generous(lucy)|creative(lucy)))&
(?[X]:((~funny(X)|brave(X))))&
(strong(john))&
((happy(lucy)<~>~quiet(lucy))) | kind(john) | [
"p3",
"p15",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7462893205653013801474524
% SZS output start Proof for 7462893205653013801474524
4. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (strong(X0) <~> ~kind(X0))) [input p3]
16. ! [X0] : ((strong(X0) <~> ~kind(X0)) <=> (humble(X0) & happy(X0))) [input p15]
18. ~happy(john) <~> old(john) [input p17]
23. strong(john) [input p22]
25. kind(john) [input hypothesis]
42. ! [X0] : (((~calm(X0) & ~old(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | (calm(X0) | old(X0)))) [nnf transformation 4]
43. ! [X0] : (((~calm(X0) & ~old(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | calm(X0) | old(X0))) [flattening 42]
74. ! [X0] : ((((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | (~humble(X0) | ~happy(X0))) & ((humble(X0) & happy(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0))))) [nnf transformation 16]
75. ! [X0] : ((((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ~humble(X0) | ~happy(X0)) & ((humble(X0) & happy(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0))))) [flattening 74]
76. (~old(john) | happy(john)) & (old(john) | ~happy(john)) [nnf transformation 18]
93. ~kind(X0) | ~old(X0) | ~strong(X0) [cnf transformation 43]
132. ~kind(X0) | happy(X0) | ~strong(X0) [cnf transformation 75]
139. old(john) | ~happy(john) [cnf transformation 76]
146. strong(john) [cnf transformation 23]
149. kind(john) [cnf transformation 25]
314. 37 <=> happy(john) [avatar definition]
318. 38 <=> old(john) [avatar definition]
322. ~37 | 38 [avatar split clause 139,318,314]
392. ~old(john) | ~strong(john) [resolution 93,149]
508. happy(john) | ~strong(john) [resolution 132,149]
513. happy(john) [subsumption resolution 508,146]
514. 37 [avatar split clause 513,314]
515. ~old(john) [subsumption resolution 392,146]
516. ~38 [avatar split clause 515,318]
517. $false [avatar sat refutation 322,514,516]
% SZS output end Proof for 7462893205653013801474524
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or happy then someone is wise or curious and vice versa. If mary is both patient and not generous then someone is not calm or humble. Everyone who is either rich or calm is strong or not creative and vice versa. Everyone who is both not humble and not patient is both brave and not wise and vice versa. If someone is not old then john is both quiet and not tall and vice versa. Everyone who is either funny or not funny is both not rich and humble. Everyone who is both not happy and generous is humble. Everyone who is either rich or patient is funny. Everyone who is quiet is either generous or not generous. Everyone who is rich or curious is either not generous or not curious. If john is either not patient or not brave then someone is not funny and vice versa. Everyone who is either not generous or not brave is calm. Everyone who is not wise or quiet is quiet and vice versa. Everyone who is brave or quiet is curious or not kind and vice versa. Everyone who is both generous and curious is either wise or not creative and vice versa. If paul is not tall then mary is not creative or happy and vice versa. Someone is both happy and not kind. Paul is either kind or not rich. Mary is not calm. Mary is tall. Someone is not kind or tall. Susan is brave or not funny. Paul is both brave and not happy. Susan is not strong. | Mary is strong. | contradiction | ((?[X]:((~funny(X)|happy(X))))<=>(?[X]:((wise(X)|curious(X)))))&
(((patient(mary)&~generous(mary)))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((rich(X)<~>calm(X))<=>(strong(X)|~creative(X))))&
(![X]:((~humble(X)&~patient(X))<=>(brave(X)&~wise(X))))&
((?[X]:(~old(X)))<=>((quiet(john)&~tall(john))))&
(![X]:((funny(X)<~>~funny(X))=>(~rich(X)&humble(X))))&
(![X]:((~happy(X)&generous(X))=>humble(X)))&
(![X]:((rich(X)<~>patient(X))=>funny(X)))&
(![X]:(quiet(X)=>(generous(X)<~>~generous(X))))&
(![X]:((rich(X)|curious(X))=>(~generous(X)<~>~curious(X))))&
(((~patient(john)<~>~brave(john)))<=>(?[X]:(~funny(X))))&
(![X]:((~generous(X)<~>~brave(X))=>calm(X)))&
(![X]:((~wise(X)|quiet(X))<=>quiet(X)))&
(![X]:((brave(X)|quiet(X))<=>(curious(X)|~kind(X))))&
(![X]:((generous(X)&curious(X))<=>(wise(X)<~>~creative(X))))&
((~tall(paul))<=>((~creative(mary)|happy(mary))))&
(?[X]:((happy(X)&~kind(X))))&
((kind(paul)<~>~rich(paul)))&
(~calm(mary))&
(tall(mary))&
(?[X]:((~kind(X)|tall(X))))&
((brave(susan)|~funny(susan)))&
((brave(paul)&~happy(paul)))&
(~strong(susan)) | strong(mary) | [
"p2",
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1582981665421137116813853
% SZS output start Proof for 1582981665421137116813853
3. ! [X0] : ((rich(X0) <~> calm(X0)) <=> (~creative(X0) | strong(X0))) [input p2]
6. ! [X0] : ((funny(X0) <~> ~funny(X0)) => (humble(X0) & ~rich(X0))) [input p5]
19. ~calm(mary) [input p18]
25. strong(mary) [input hypothesis]
29. ! [X0] : ((humble(X0) & ~rich(X0)) | (funny(X0) <=> ~funny(X0))) [ennf transformation 6]
43. ! [X0] : ((((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | (creative(X0) & ~strong(X0))) & ((~creative(X0) | strong(X0)) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))))) [nnf transformation 3]
44. ! [X0] : ((((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | (creative(X0) & ~strong(X0))) & (~creative(X0) | strong(X0) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))))) [flattening 43]
52. ! [X0] : ((humble(X0) & ~rich(X0)) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0)))) [nnf transformation 29]
81. ~strong(X0) | rich(X0) | calm(X0) [cnf transformation 44]
92. ~rich(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 52]
93. ~rich(X0) | funny(X0) | funny(X0) [cnf transformation 52]
131. ~calm(mary) [cnf transformation 19]
138. strong(mary) [cnf transformation 25]
140. ~rich(X0) | ~funny(X0) [duplicate literal removal 92]
141. ~rich(X0) | funny(X0) [duplicate literal removal 93]
212. ~rich(X0) [subsumption resolution 140,141]
269. rich(mary) | calm(mary) [resolution 81,138]
270. calm(mary) [subsumption resolution 269,212]
271. $false [subsumption resolution 270,131]
% SZS output end Proof for 1582981665421137116813853
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is not tall and vice versa. Everyone who is generous is both not calm and kind. If alice is not wise or not kind then someone is both strong and not kind. Everyone who is either tall or funny is both funny and not generous and vice versa. If lucy is both wise and not curious then lucy is not funny. Everyone who is not kind or not patient is either not calm or happy. Everyone who is not tall is both calm and wise. Everyone who is not wise or not happy is not creative or not calm and vice versa. If someone is both humble and quiet then mary is wise or old. If someone is either wise or kind then john is not curious. If someone is both not happy and not creative then fred is not creative or humble and vice versa. Everyone who is both tall and not curious is creative or generous. Everyone who is either not tall or quiet is both not tall and not patient and vice versa. Everyone who is both not tall and creative is funny or curious and vice versa. Everyone who is strong is humble. If someone is not old or not patient then paul is both creative and strong. Mary is both not patient and brave. Mary is old. Someone is quiet or not wise. Someone is generous or wise. Someone is not rich or not generous. Paul is rich. Someone is both old and brave. | John is brave. | entailment | (![X]:(brave(X)<=>~tall(X)))&
(![X]:(generous(X)=>(~calm(X)&kind(X))))&
(((~wise(alice)|~kind(alice)))=>(?[X]:((strong(X)&~kind(X)))))&
(![X]:((tall(X)<~>funny(X))<=>(funny(X)&~generous(X))))&
(((wise(lucy)&~curious(lucy)))=>(~funny(lucy)))&
(![X]:((~kind(X)|~patient(X))=>(~calm(X)<~>happy(X))))&
(![X]:(~tall(X)=>(calm(X)&wise(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~creative(X)|~calm(X))))&
((?[X]:((humble(X)&quiet(X))))=>((wise(mary)|old(mary))))&
((?[X]:((wise(X)<~>kind(X))))=>(~curious(john)))&
((?[X]:((~happy(X)&~creative(X))))<=>((~creative(fred)|humble(fred))))&
(![X]:((tall(X)&~curious(X))=>(creative(X)|generous(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&creative(X))<=>(funny(X)|curious(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~old(X)|~patient(X))))=>((creative(paul)&strong(paul))))&
((~patient(mary)&brave(mary)))&
(old(mary))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((~rich(X)|~generous(X))))&
(rich(paul))&
(?[X]:((old(X)&brave(X)))) | brave(john) | [
"p0",
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6438527267290073807188569
% SZS output start Proof for 6438527267290073807188569
1. ! [X0] : (brave(X0) <=> ~tall(X0)) [input p0]
4. ! [X0] : ((tall(X0) <~> funny(X0)) <=> (~generous(X0) & funny(X0))) [input p3]
14. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (curious(X0) | funny(X0))) [input p13]
24. ~brave(john) [input hypothesis]
40. ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))) [nnf transformation 1]
43. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (generous(X0) | ~funny(X0))) & ((~generous(X0) & funny(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | generous(X0) | ~funny(X0)) & ((~generous(X0) & funny(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [flattening 43]
56. ! [X0] : (((creative(X0) & ~tall(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 14]
57. ! [X0] : (((creative(X0) & ~tall(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | ~creative(X0) | tall(X0))) [flattening 56]
67. tall(X0) | brave(X0) [cnf transformation 40]
74. funny(X0) | funny(X0) | ~tall(X0) [cnf transformation 44]
106. ~tall(X0) | ~funny(X0) [cnf transformation 57]
120. ~brave(john) [cnf transformation 24]
123. funny(X0) | ~tall(X0) [duplicate literal removal 74]
194. ~tall(X0) [subsumption resolution 106,123]
239. brave(X1) [resolution 67,194]
240. $false [resolution 239,120]
% SZS output end Proof for 6438527267290073807188569
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is wise then paul is either not tall or kind.
Everyone who is not tall is not patient or curious.
If susan is either not funny or not curious then fred is either not wise or tall.
If someone is not old or kind then someone is not kind or not curious.
Everyone who is not patient is both quiet and not quiet and vice versa.
Everyone who is either curious or not creative is both not kind and not patient.
If someone is rich then lucy is both strong and not wise and vice versa.
If someone is not humble then someone is not happy.
Everyone who is not tall is both not kind and not old.
If someone is strong then fred is patient and vice versa.
If lucy is humble then someone is not kind or not patient.
Everyone who is wise is either not tall or not happy and vice versa.
Everyone who is both not quiet and not curious is either funny or not brave and vice versa.
If someone is patient then paul is not rich and vice versa.
Everyone who is either not funny or brave is kind or calm and vice versa.
Everyone who is not rich is old and vice versa.
Fred is funny.
Someone is wise.
Mary is both not brave and calm.
Someone is both kind and funny.
Someone is rich.
Someone is not rich or wise.
Paul is both not funny and not happy. | Paul is patient. | entailment | ((?[X]:(wise(X)))=>((~tall(paul)<~>kind(paul))))&
(![X]:(~tall(X)=>(~patient(X)|curious(X))))&
(((~funny(susan)<~>~curious(susan)))=>((~wise(fred)<~>tall(fred))))&
((?[X]:((~old(X)|kind(X))))=>(?[X]:((~kind(X)|~curious(X)))))&
(![X]:(~patient(X)<=>(quiet(X)&~quiet(X))))&
(![X]:((curious(X)<~>~creative(X))=>(~kind(X)&~patient(X))))&
((?[X]:(rich(X)))<=>((strong(lucy)&~wise(lucy))))&
((?[X]:(~humble(X)))=>(?[X]:(~happy(X))))&
(![X]:(~tall(X)=>(~kind(X)&~old(X))))&
((?[X]:(strong(X)))<=>(patient(fred)))&
((humble(lucy))=>(?[X]:((~kind(X)|~patient(X)))))&
(![X]:(wise(X)<=>(~tall(X)<~>~happy(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(funny(X)<~>~brave(X))))&
((?[X]:(patient(X)))<=>(~rich(paul)))&
(![X]:((~funny(X)<~>brave(X))<=>(kind(X)|calm(X))))&
(![X]:(~rich(X)<=>old(X)))&
(funny(fred))&
(?[X]:(wise(X)))&
((~brave(mary)&calm(mary)))&
(?[X]:((kind(X)&funny(X))))&
(?[X]:(rich(X)))&
(?[X]:((~rich(X)|wise(X))))&
((~funny(paul)&~happy(paul))) | patient(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8925477941364098363900844
% SZS output start Proof for 8925477941364098363900844
5. ! [X0] : (~patient(X0) <=> (~quiet(X0) & quiet(X0))) [input p4]
24. ~patient(paul) [input hypothesis]
41. ! [X0] : ((~patient(X0) | (quiet(X0) | ~quiet(X0))) & ((~quiet(X0) & quiet(X0)) | patient(X0))) [nnf transformation 5]
42. ! [X0] : ((~patient(X0) | quiet(X0) | ~quiet(X0)) & ((~quiet(X0) & quiet(X0)) | patient(X0))) [flattening 41]
85. quiet(X0) | patient(X0) [cnf transformation 42]
86. ~quiet(X0) | patient(X0) [cnf transformation 42]
131. ~patient(paul) [cnf transformation 24]
181. patient(X0) [subsumption resolution 85,86]
231. $false [subsumption resolution 131,181]
% SZS output end Proof for 8925477941364098363900844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not kind and creative then someone is both kind and generous. Everyone who is not patient is either not wise or not tall and vice versa. Everyone who is curious is either kind or tall. If someone is either kind or brave then someone is not generous and vice versa. If someone is not funny or not creative then lucy is both curious and not funny and vice versa. If someone is calm then someone is either not brave or creative and vice versa. If someone is both brave and humble then someone is both calm and wise and vice versa. Everyone who is both not creative and not quiet is generous or kind. If someone is wise then lucy is curious or quiet. If someone is either creative or not old then someone is both not kind and not happy and vice versa. If someone is either not brave or happy then fred is both curious and not strong and vice versa. Everyone who is not kind or not calm is both creative and calm and vice versa. If mary is both creative and not happy then someone is strong. If mary is not funny then paul is not old. If someone is either rich or tall then someone is kind and vice versa. If mary is quiet or humble then paul is both creative and wise. Someone is funny. Someone is either brave or not funny. Fred is not kind. Fred is either funny or not kind. Alice is both not generous and wise. Someone is either not patient or happy. Someone is both not brave and not kind. Lucy is calm or not generous. | Lucy is curious. | entailment | (((~kind(john)&creative(john)))=>(?[X]:((kind(X)&generous(X)))))&
(![X]:(~patient(X)<=>(~wise(X)<~>~tall(X))))&
(![X]:(curious(X)=>(kind(X)<~>tall(X))))&
((?[X]:((kind(X)<~>brave(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((~funny(X)|~creative(X))))<=>((curious(lucy)&~funny(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>creative(X)))))&
((?[X]:((brave(X)&humble(X))))<=>(?[X]:((calm(X)&wise(X)))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)|kind(X))))&
((?[X]:(wise(X)))=>((curious(lucy)|quiet(lucy))))&
((?[X]:((creative(X)<~>~old(X))))<=>(?[X]:((~kind(X)&~happy(X)))))&
((?[X]:((~brave(X)<~>happy(X))))<=>((curious(fred)&~strong(fred))))&
(![X]:((~kind(X)|~calm(X))<=>(creative(X)&calm(X))))&
(((creative(mary)&~happy(mary)))=>(?[X]:(strong(X))))&
((~funny(mary))=>(~old(paul)))&
((?[X]:((rich(X)<~>tall(X))))<=>(?[X]:(kind(X))))&
(((quiet(mary)|humble(mary)))=>((creative(paul)&wise(paul))))&
(?[X]:(funny(X)))&
(?[X]:((brave(X)<~>~funny(X))))&
(~kind(fred))&
((funny(fred)<~>~kind(fred)))&
((~generous(alice)&wise(alice)))&
(?[X]:((~patient(X)<~>happy(X))))&
(?[X]:((~brave(X)&~kind(X))))&
((calm(lucy)|~generous(lucy))) | curious(lucy) | [
"p4",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8792668121007168828112615
% SZS output start Proof for 8792668121007168828112615
5. ? [X0] : (~creative(X0) | ~funny(X0)) <=> (~funny(lucy) & curious(lucy)) [input p4]
19. ~kind(fred) [input p18]
20. funny(fred) <~> ~kind(fred) [input p19]
25. ~curious(lucy) [input hypothesis]
51. (? [X0] : (~creative(X0) | ~funny(X0)) | (funny(lucy) | ~curious(lucy))) & ((~funny(lucy) & curious(lucy)) | ! [X0] : (creative(X0) & funny(X0))) [nnf transformation 5]
52. (? [X0] : (~creative(X0) | ~funny(X0)) | funny(lucy) | ~curious(lucy)) & ((~funny(lucy) & curious(lucy)) | ! [X0] : (creative(X0) & funny(X0))) [flattening 51]
53. (? [X0] : (~creative(X0) | ~funny(X0)) | funny(lucy) | ~curious(lucy)) & ((~funny(lucy) & curious(lucy)) | ! [X1] : (creative(X1) & funny(X1))) [rectify 52]
54. ? [X0] : (~creative(X0) | ~funny(X0)) => (~creative(sK3) | ~funny(sK3)) [choice axiom]
55. ((~creative(sK3) | ~funny(sK3)) | funny(lucy) | ~curious(lucy)) & ((~funny(lucy) & curious(lucy)) | ! [X1] : (creative(X1) & funny(X1))) [skolemisation 53,54]
90. (kind(fred) | ~funny(fred)) & (~kind(fred) | funny(fred)) [nnf transformation 20]
108. curious(lucy) | funny(X1) [cnf transformation 55]
153. ~kind(fred) [cnf transformation 19]
155. kind(fred) | ~funny(fred) [cnf transformation 90]
163. ~curious(lucy) [cnf transformation 25]
210. 11 <=> curious(lucy) [avatar definition]
231. 16 <=> ! [X1] : funny(X1) [avatar definition]
232. funny(X1) <- (16) [avatar component clause 231]
235. 16 | 11 [avatar split clause 108,210,231]
431. ~funny(fred) [subsumption resolution 155,153]
442. ~11 [avatar split clause 163,210]
463. $false <- (16) [resolution 431,232]
464. ~16 [avatar contradiction clause 463]
465. $false [avatar sat refutation 235,442,464]
% SZS output end Proof for 8792668121007168828112615
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If alice is not tall then someone is funny and vice versa. If someone is strong or not wise then someone is either not tall or not calm and vice versa. If alice is both kind and calm then paul is either curious or kind and vice versa. If someone is either patient or not old then mary is not kind. If someone is not funny or not wise then someone is both old and not old. If someone is not quiet then someone is patient. Everyone who is brave is both not patient and not tall. If john is patient or not wise then someone is both generous and tall. Everyone who is old is not quiet. If someone is curious then fred is not happy. If someone is both not old and old then someone is both not creative and tall and vice versa. Everyone who is patient is both old and not funny. If someone is not funny then someone is either curious or brave and vice versa. Everyone who is happy or not generous is both humble and patient. Everyone who is both not humble and not patient is kind or not old and vice versa. Someone is tall. Susan is either not curious or not humble. Someone is both not rich and not calm. Alice is either humble or strong. Someone is tall or not rich. Someone is either not generous or not happy. Mary is both not tall and quiet. Someone is brave or not calm. | Susan is not humble. | entailment | ((~tall(alice))<=>(?[X]:(funny(X))))&
((?[X]:((strong(X)|~wise(X))))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(((kind(alice)&calm(alice)))<=>((curious(paul)<~>kind(paul))))&
((?[X]:((patient(X)<~>~old(X))))=>(~kind(mary)))&
((?[X]:((~funny(X)|~wise(X))))=>(?[X]:((old(X)&~old(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:(patient(X))))&
(![X]:(brave(X)=>(~patient(X)&~tall(X))))&
(((patient(john)|~wise(john)))=>(?[X]:((generous(X)&tall(X)))))&
(![X]:(old(X)=>~quiet(X)))&
((?[X]:(curious(X)))=>(~happy(fred)))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:(patient(X)=>(old(X)&~funny(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:((happy(X)|~generous(X))=>(humble(X)&patient(X))))&
(![X]:((~humble(X)&~patient(X))<=>(kind(X)|~old(X))))&
(?[X]:(tall(X)))&
((~curious(susan)<~>~humble(susan)))&
(?[X]:((~rich(X)&~calm(X))))&
((humble(alice)<~>strong(alice)))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((~generous(X)<~>~happy(X))))&
((~tall(mary)&quiet(mary)))&
(?[X]:((brave(X)|~calm(X)))) | ~humble(susan) | [
"p4",
"p5",
"p8",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 222282691748219820271173
% SZS output start Proof for 222282691748219820271173
5. ? [X0] : (~wise(X0) | ~funny(X0)) => ? [X0] : (~old(X0) & old(X0)) [input p4]
6. ? [X0] : ~quiet(X0) => ? [X0] : patient(X0) [input p5]
9. ! [X0] : (old(X0) => ~quiet(X0)) [input p8]
12. ! [X0] : (patient(X0) => (~funny(X0) & old(X0))) [input p11]
15. ! [X0] : ((~patient(X0) & ~humble(X0)) <=> (~old(X0) | kind(X0))) [input p14]
24. humble(susan) [input hypothesis]
26. ? [X0] : (~wise(X0) | ~funny(X0)) => ? [X1] : (~old(X1) & old(X1)) [rectify 5]
27. ? [X0] : ~quiet(X0) => ? [X1] : patient(X1) [rectify 6]
33. ? [X1] : (~old(X1) & old(X1)) | ! [X0] : (wise(X0) & funny(X0)) [ennf transformation 26]
34. ? [X1] : patient(X1) | ! [X0] : quiet(X0) [ennf transformation 27]
37. ! [X0] : (~quiet(X0) | ~old(X0)) [ennf transformation 9]
39. ! [X0] : ((~funny(X0) & old(X0)) | ~patient(X0)) [ennf transformation 12]
53. ? [X0] : (~old(X0) & old(X0)) | ! [X1] : (wise(X1) & funny(X1)) [rectify 33]
54. ? [X0] : (~old(X0) & old(X0)) => (~old(sK3) & old(sK3)) [choice axiom]
55. (~old(sK3) & old(sK3)) | ! [X1] : (wise(X1) & funny(X1)) [skolemisation 53,54]
56. ? [X0] : patient(X0) | ! [X1] : quiet(X1) [rectify 34]
57. ? [X0] : patient(X0) => patient(sK4) [choice axiom]
58. patient(sK4) | ! [X1] : quiet(X1) [skolemisation 56,57]
71. ! [X0] : (((~patient(X0) & ~humble(X0)) | (old(X0) & ~kind(X0))) & ((~old(X0) | kind(X0)) | (patient(X0) | humble(X0)))) [nnf transformation 15]
72. ! [X0] : (((~patient(X0) & ~humble(X0)) | (old(X0) & ~kind(X0))) & (~old(X0) | kind(X0) | patient(X0) | humble(X0))) [flattening 71]
100. old(sK3) | funny(X1) [cnf transformation 55]
102. ~old(sK3) | funny(X1) [cnf transformation 55]
104. patient(sK4) | quiet(X1) [cnf transformation 58]
111. ~quiet(X0) | ~old(X0) [cnf transformation 37]
118. ~patient(X0) | ~funny(X0) [cnf transformation 39]
129. ~humble(X0) | old(X0) [cnf transformation 72]
143. humble(susan) [cnf transformation 24]
226. 19 <=> old(sK3) [avatar definition]
231. 20 <=> ! [X1] : funny(X1) [avatar definition]
232. funny(X1) <- (20) [avatar component clause 231]
233. 20 | ~19 [avatar split clause 102,226,231]
235. 20 | 19 [avatar split clause 100,226,231]
237. 21 <=> ! [X1] : quiet(X1) [avatar definition]
238. quiet(X1) <- (21) [avatar component clause 237]
240. 22 <=> patient(sK4) [avatar definition]
242. patient(sK4) <- (22) [avatar component clause 240]
243. 21 | 22 [avatar split clause 104,240,237]
308. 37 <=> humble(susan) [avatar definition]
310. humble(susan) <- (37) [avatar component clause 308]
342. 37 [avatar split clause 143,308]
348. ~old(X0) <- (21) [resolution 111,238]
353. old(susan) <- (37) [resolution 129,310]
356. $false <- (21, 37) [subsumption resolution 353,348]
357. ~21 | ~37 [avatar contradiction clause 356]
361. ~funny(sK4) <- (22) [resolution 242,118]
363. $false <- (20, 22) [subsumption resolution 361,232]
364. ~20 | ~22 [avatar contradiction clause 363]
365. $false [avatar sat refutation 233,235,243,342,357,364]
% SZS output end Proof for 222282691748219820271173
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or patient is either not creative or not tall and vice versa. Everyone who is not humble or not happy is old. Everyone who is both not kind and not humble is not creative and vice versa. If someone is either not patient or not rich then someone is not patient or not tall. Everyone who is not rich is both not creative and happy and vice versa. If mary is old then paul is not wise or not happy. Everyone who is not humble or old is both old and not rich and vice versa. Everyone who is curious or tall is either humble or not patient and vice versa. If fred is either calm or not funny then john is either not quiet or old and vice versa. If someone is not old or not quiet then mary is both not funny and not curious and vice versa. Everyone who is tall or wise is both humble and patient and vice versa. Everyone who is not funny or not wise is funny. Everyone who is both humble and funny is not happy or creative and vice versa. If someone is both wise and humble then susan is both quiet and not calm and vice versa. If mary is either funny or creative then someone is both not rich and not brave. If lucy is both not calm and brave then someone is both not brave and rich. Someone is curious or strong. Susan is either brave or not generous. Someone is either funny or patient. | Susan is rich. | contradiction | (![X]:((~old(X)|patient(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((~humble(X)|~happy(X))=>old(X)))&
(![X]:((~kind(X)&~humble(X))<=>~creative(X)))&
((?[X]:((~patient(X)<~>~rich(X))))=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:(~rich(X)<=>(~creative(X)&happy(X))))&
((old(mary))=>((~wise(paul)|~happy(paul))))&
(![X]:((~humble(X)|old(X))<=>(old(X)&~rich(X))))&
(![X]:((curious(X)|tall(X))<=>(humble(X)<~>~patient(X))))&
(((calm(fred)<~>~funny(fred)))<=>((~quiet(john)<~>old(john))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~funny(mary)&~curious(mary))))&
(![X]:((tall(X)|wise(X))<=>(humble(X)&patient(X))))&
(![X]:((~funny(X)|~wise(X))=>funny(X)))&
(![X]:((humble(X)&funny(X))<=>(~happy(X)|creative(X))))&
((?[X]:((wise(X)&humble(X))))<=>((quiet(susan)&~calm(susan))))&
(((funny(mary)<~>creative(mary)))=>(?[X]:((~rich(X)&~brave(X)))))&
(((~calm(lucy)&brave(lucy)))=>(?[X]:((~brave(X)&rich(X)))))&
(?[X]:((curious(X)|strong(X))))&
((brave(susan)<~>~generous(susan)))&
(?[X]:((funny(X)<~>patient(X)))) | rich(susan) | [
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1392206440147535871189117
% SZS output start Proof for 1392206440147535871189117
7. ! [X0] : ((old(X0) | ~humble(X0)) <=> (~rich(X0) & old(X0))) [input p6]
10. ? [X0] : (~quiet(X0) | ~old(X0)) <=> (~curious(mary) & ~funny(mary)) [input p9]
12. ! [X0] : ((~wise(X0) | ~funny(X0)) => funny(X0)) [input p11]
20. rich(susan) [input hypothesis]
27. ! [X0] : (funny(X0) | (wise(X0) & funny(X0))) [ennf transformation 12]
41. ! [X0] : (((old(X0) | ~humble(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (~old(X0) & humble(X0)))) [nnf transformation 7]
42. ! [X0] : ((old(X0) | ~humble(X0) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | (~old(X0) & humble(X0)))) [flattening 41]
46. (? [X0] : (~quiet(X0) | ~old(X0)) | (curious(mary) | funny(mary))) & ((~curious(mary) & ~funny(mary)) | ! [X0] : (quiet(X0) & old(X0))) [nnf transformation 10]
47. (? [X0] : (~quiet(X0) | ~old(X0)) | curious(mary) | funny(mary)) & ((~curious(mary) & ~funny(mary)) | ! [X0] : (quiet(X0) & old(X0))) [flattening 46]
48. (? [X0] : (~quiet(X0) | ~old(X0)) | curious(mary) | funny(mary)) & ((~curious(mary) & ~funny(mary)) | ! [X1] : (quiet(X1) & old(X1))) [rectify 47]
49. ? [X0] : (~quiet(X0) | ~old(X0)) => (~quiet(sK1) | ~old(sK1)) [choice axiom]
50. ((~quiet(sK1) | ~old(sK1)) | curious(mary) | funny(mary)) & ((~curious(mary) & ~funny(mary)) | ! [X1] : (quiet(X1) & old(X1))) [skolemisation 48,49]
89. ~rich(X0) | ~old(X0) [cnf transformation 42]
105. ~funny(mary) | old(X1) [cnf transformation 50]
115. funny(X0) | funny(X0) [cnf transformation 27]
136. rich(susan) [cnf transformation 20]
137. funny(X0) [duplicate literal removal 115]
192. 12 <=> funny(mary) [avatar definition]
193. ~funny(mary) <- (~12) [avatar component clause 192]
213. 17 <=> ! [X1] : old(X1) [avatar definition]
214. old(X1) <- (17) [avatar component clause 213]
217. 17 | ~12 [avatar split clause 105,192,213]
288. $false <- (~12) [subsumption resolution 193,137]
289. 12 [avatar contradiction clause 288]
305. ~old(susan) [resolution 89,136]
307. $false <- (17) [subsumption resolution 305,214]
308. ~17 [avatar contradiction clause 307]
310. $false [avatar sat refutation 217,289,308]
% SZS output end Proof for 1392206440147535871189117
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not kind is old. Everyone who is both not brave and kind is not tall. Everyone who is both not strong and not creative is both wise and not curious. Everyone who is either not rich or calm is either not wise or wise and vice versa. Everyone who is strong is not quiet or not patient and vice versa. If someone is both old and not brave then someone is either not happy or not brave and vice versa. If someone is not rich then mary is either not strong or old and vice versa. Everyone who is not brave or patient is rich and vice versa. If mary is both old and tall then paul is not strong. Everyone who is strong or rich is either not calm or not patient and vice versa. If someone is both calm and not funny then alice is either generous or not creative. If paul is both quiet and not creative then someone is not tall or rich and vice versa. Everyone who is both tall and not calm is either not generous or strong. If mary is not wise then someone is both creative and curious. Everyone who is strong or curious is funny or creative. Fred is not creative or humble. Someone is kind. Someone is funny. Someone is not calm or rich. Someone is not happy or not curious. Alice is not funny or not calm. Someone is either curious or funny. Someone is not tall or rich. | Alice is not calm. | contradiction | (![X]:((happy(X)|~kind(X))=>old(X)))&
(![X]:((~brave(X)&kind(X))=>~tall(X)))&
(![X]:((~strong(X)&~creative(X))=>(wise(X)&~curious(X))))&
(![X]:((~rich(X)<~>calm(X))<=>(~wise(X)<~>wise(X))))&
(![X]:(strong(X)<=>(~quiet(X)|~patient(X))))&
((?[X]:((old(X)&~brave(X))))<=>(?[X]:((~happy(X)<~>~brave(X)))))&
((?[X]:(~rich(X)))<=>((~strong(mary)<~>old(mary))))&
(![X]:((~brave(X)|patient(X))<=>rich(X)))&
(((old(mary)&tall(mary)))=>(~strong(paul)))&
(![X]:((strong(X)|rich(X))<=>(~calm(X)<~>~patient(X))))&
((?[X]:((calm(X)&~funny(X))))=>((generous(alice)<~>~creative(alice))))&
(((quiet(paul)&~creative(paul)))<=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((tall(X)&~calm(X))=>(~generous(X)<~>strong(X))))&
((~wise(mary))=>(?[X]:((creative(X)&curious(X)))))&
(![X]:((strong(X)|curious(X))=>(funny(X)|creative(X))))&
((~creative(fred)|humble(fred)))&
(?[X]:(kind(X)))&
(?[X]:(funny(X)))&
(?[X]:((~calm(X)|rich(X))))&
(?[X]:((~happy(X)|~curious(X))))&
((~funny(alice)|~calm(alice)))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:((~tall(X)|rich(X)))) | ~calm(alice) | [
"p3",
"p4",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6000019540683720661821409
% SZS output start Proof for 6000019540683720661821409
4. ! [X0] : ((~rich(X0) <~> calm(X0)) <=> (~wise(X0) <~> wise(X0))) [input p3]
5. ! [X0] : (strong(X0) <=> (~patient(X0) | ~quiet(X0))) [input p4]
8. ! [X0] : ((patient(X0) | ~brave(X0)) <=> rich(X0)) [input p7]
10. ! [X0] : ((rich(X0) | strong(X0)) <=> (~calm(X0) <~> ~patient(X0))) [input p9]
24. ~calm(alice) [input hypothesis]
40. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [nnf transformation 4]
41. ! [X0] : ((strong(X0) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | ~strong(X0))) [nnf transformation 5]
42. ! [X0] : ((strong(X0) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~strong(X0))) [flattening 41]
52. ! [X0] : (((patient(X0) | ~brave(X0)) | ~rich(X0)) & (rich(X0) | (~patient(X0) & brave(X0)))) [nnf transformation 8]
53. ! [X0] : ((patient(X0) | ~brave(X0) | ~rich(X0)) & (rich(X0) | (~patient(X0) & brave(X0)))) [flattening 52]
54. ! [X0] : (((rich(X0) | strong(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~rich(X0) & ~strong(X0)))) [nnf transformation 10]
55. ! [X0] : ((rich(X0) | strong(X0) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~rich(X0) & ~strong(X0)))) [flattening 54]
87. calm(X0) | ~rich(X0) | wise(X0) | wise(X0) [cnf transformation 40]
88. calm(X0) | ~rich(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 40]
93. patient(X0) | strong(X0) [cnf transformation 42]
105. ~patient(X0) | rich(X0) [cnf transformation 53]
110. patient(X0) | calm(X0) | ~strong(X0) [cnf transformation 55]
135. ~calm(alice) [cnf transformation 24]
136. calm(X0) | ~rich(X0) | wise(X0) [duplicate literal removal 87]
137. calm(X0) | ~rich(X0) | ~wise(X0) [duplicate literal removal 88]
141. ~rich(X0) | calm(X0) [subsumption resolution 136,137]
201. patient(X0) | calm(X0) [subsumption resolution 110,93]
271. 29 <=> calm(alice) [avatar definition]
273. ~calm(alice) <- (~29) [avatar component clause 271]
294. ~29 [avatar split clause 135,271]
312. calm(X0) | rich(X0) [resolution 201,105]
313. calm(X0) [subsumption resolution 312,141]
319. $false <- (~29) [resolution 313,273]
321. 29 [avatar contradiction clause 319]
323. $false [avatar sat refutation 294,321]
% SZS output end Proof for 6000019540683720661821409
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If susan is kind or quiet then fred is either generous or calm and vice versa.
Everyone who is both not old and not creative is both creative and not wise and vice versa.
Everyone who is old or not calm is brave or generous and vice versa.
Everyone who is not brave is brave or tall and vice versa.
If someone is old or wise then someone is funny and vice versa.
Everyone who is either not funny or kind is rich and vice versa.
Everyone who is kind or curious is not patient and vice versa.
Everyone who is not generous or calm is patient or not old.
If alice is both wise and funny then someone is creative or rich.
Everyone who is not wise is not calm or wise.
If fred is not calm or not brave then paul is brave or quiet and vice versa.
Everyone who is either curious or generous is humble and vice versa.
Everyone who is either tall or not humble is either creative or strong and vice versa.
Everyone who is humble is creative or not patient and vice versa.
If paul is either humble or generous then someone is either brave or not quiet and vice versa.
Someone is old or tall.
Someone is either humble or not quiet.
Lucy is not generous.
Someone is strong.
Someone is either not calm or not tall. | Paul is strong. | neutral | (((kind(susan)|quiet(susan)))<=>((generous(fred)<~>calm(fred))))&
(![X]:((~old(X)&~creative(X))<=>(creative(X)&~wise(X))))&
(![X]:((old(X)|~calm(X))<=>(brave(X)|generous(X))))&
(![X]:(~brave(X)<=>(brave(X)|tall(X))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:(funny(X))))&
(![X]:((~funny(X)<~>kind(X))<=>rich(X)))&
(![X]:((kind(X)|curious(X))<=>~patient(X)))&
(![X]:((~generous(X)|calm(X))=>(patient(X)|~old(X))))&
(((wise(alice)&funny(alice)))=>(?[X]:((creative(X)|rich(X)))))&
(![X]:(~wise(X)=>(~calm(X)|wise(X))))&
(((~calm(fred)|~brave(fred)))<=>((brave(paul)|quiet(paul))))&
(![X]:((curious(X)<~>generous(X))<=>humble(X)))&
(![X]:((tall(X)<~>~humble(X))<=>(creative(X)<~>strong(X))))&
(![X]:(humble(X)<=>(creative(X)|~patient(X))))&
(((humble(paul)<~>generous(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(~generous(lucy))&
(?[X]:(strong(X)))&
(?[X]:((~calm(X)<~>~tall(X)))) | strong(paul) | [] | null | 0 |
Everyone who is not tall or brave is both not funny and old.
If lucy is both kind and funny then susan is either not tall or not kind.
If lucy is generous then alice is creative.
Everyone who is old is either patient or happy.
Everyone who is both not patient and not tall is wise or not curious and vice versa.
Everyone who is not humble is both not patient and not curious and vice versa.
Everyone who is strong or not old is both not humble and tall and vice versa.
If john is patient then someone is curious.
If someone is either not rich or not patient then someone is not rich or not brave and vice versa.
Everyone who is either not wise or not patient is not old and vice versa.
Everyone who is not quiet is both not patient and not curious.
Everyone who is not happy or not rich is curious and vice versa.
If someone is strong or not brave then alice is not funny or not humble.
If alice is generous then paul is both strong and old and vice versa.
Someone is not strong.
Paul is creative or not rich.
Alice is both not calm and not kind. | Paul is not old. | contradiction | (![X]:((~tall(X)|brave(X))=>(~funny(X)&old(X))))&
(((kind(lucy)&funny(lucy)))=>((~tall(susan)<~>~kind(susan))))&
((generous(lucy))=>(creative(alice)))&
(![X]:(old(X)=>(patient(X)<~>happy(X))))&
(![X]:((~patient(X)&~tall(X))<=>(wise(X)|~curious(X))))&
(![X]:(~humble(X)<=>(~patient(X)&~curious(X))))&
(![X]:((strong(X)|~old(X))<=>(~humble(X)&tall(X))))&
((patient(john))=>(?[X]:(curious(X))))&
((?[X]:((~rich(X)<~>~patient(X))))<=>(?[X]:((~rich(X)|~brave(X)))))&
(![X]:((~wise(X)<~>~patient(X))<=>~old(X)))&
(![X]:(~quiet(X)=>(~patient(X)&~curious(X))))&
(![X]:((~happy(X)|~rich(X))<=>curious(X)))&
((?[X]:((strong(X)|~brave(X))))=>((~funny(alice)|~humble(alice))))&
((generous(alice))<=>((strong(paul)&old(paul))))&
(?[X]:(~strong(X)))&
((creative(paul)|~rich(paul)))&
((~calm(alice)&~kind(alice))) | ~old(paul) | [
"p0",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 266026978434750848961801
% SZS output start Proof for 266026978434750848961801
1. ! [X0] : ((brave(X0) | ~tall(X0)) => (old(X0) & ~funny(X0))) [input p0]
5. ! [X0] : ((~tall(X0) & ~patient(X0)) <=> (~curious(X0) | wise(X0))) [input p4]
6. ! [X0] : (~humble(X0) <=> (~curious(X0) & ~patient(X0))) [input p5]
7. ! [X0] : ((~old(X0) | strong(X0)) <=> (tall(X0) & ~humble(X0))) [input p6]
18. ~old(paul) [input hypothesis]
25. ! [X0] : ((brave(X0) | ~tall(X0)) => old(X0)) [pure predicate removal 1]
28. ! [X0] : (old(X0) | (~brave(X0) & tall(X0))) [ennf transformation 25]
32. ! [X0] : (((~tall(X0) & ~patient(X0)) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | (tall(X0) | patient(X0)))) [nnf transformation 5]
33. ! [X0] : (((~tall(X0) & ~patient(X0)) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | tall(X0) | patient(X0))) [flattening 32]
34. ! [X0] : ((~humble(X0) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | humble(X0))) [nnf transformation 6]
35. ! [X0] : ((~humble(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | humble(X0))) [flattening 34]
36. ! [X0] : (((~old(X0) | strong(X0)) | (~tall(X0) | humble(X0))) & ((tall(X0) & ~humble(X0)) | (old(X0) & ~strong(X0)))) [nnf transformation 7]
37. ! [X0] : ((~old(X0) | strong(X0) | ~tall(X0) | humble(X0)) & ((tall(X0) & ~humble(X0)) | (old(X0) & ~strong(X0)))) [flattening 36]
52. old(X0) | tall(X0) [cnf transformation 28]
60. ~tall(X0) | curious(X0) [cnf transformation 33]
62. ~curious(X0) | humble(X0) [cnf transformation 35]
65. ~humble(X0) | old(X0) [cnf transformation 37]
87. ~old(paul) [cnf transformation 18]
139. 12 <=> old(paul) [avatar definition]
141. ~old(paul) <- (~12) [avatar component clause 139]
149. ~12 [avatar split clause 87,139]
150. tall(paul) <- (~12) [resolution 52,141]
151. curious(paul) <- (~12) [resolution 60,150]
152. humble(paul) <- (~12) [resolution 62,151]
153. old(paul) <- (~12) [resolution 65,152]
154. $false <- (~12) [subsumption resolution 153,141]
155. 12 [avatar contradiction clause 154]
156. $false [avatar sat refutation 149,155]
% SZS output end Proof for 266026978434750848961801
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or tall is both humble and not humble and vice versa. If susan is both quiet and brave then someone is either not rich or rich. If someone is calm then mary is both not kind and not rich. Everyone who is either curious or rich is either calm or not calm and vice versa. Everyone who is calm is wise. Everyone who is not quiet or funny is both not tall and creative and vice versa. If fred is not old then alice is both calm and not kind. If alice is not kind or not curious then someone is rich or not creative and vice versa. If someone is both not tall and old then someone is not kind. If someone is either humble or kind then lucy is not quiet or creative. Everyone who is wise is both not wise and not strong. Everyone who is not brave is either not old or quiet and vice versa. If mary is creative or funny then someone is both not creative and quiet and vice versa. Everyone who is curious is either not quiet or brave and vice versa. Everyone who is not old or not wise is brave. Paul is either wise or creative. Someone is both quiet and not humble. Someone is patient or calm. Someone is quiet or not wise. Lucy is not generous. Someone is either rich or strong. Someone is curious. | Mary is creative. | entailment | (![X]:((~old(X)<~>tall(X))<=>(humble(X)&~humble(X))))&
(((quiet(susan)&brave(susan)))=>(?[X]:((~rich(X)<~>rich(X)))))&
((?[X]:(calm(X)))=>((~kind(mary)&~rich(mary))))&
(![X]:((curious(X)<~>rich(X))<=>(calm(X)<~>~calm(X))))&
(![X]:(calm(X)=>wise(X)))&
(![X]:((~quiet(X)|funny(X))<=>(~tall(X)&creative(X))))&
((~old(fred))=>((calm(alice)&~kind(alice))))&
(((~kind(alice)|~curious(alice)))<=>(?[X]:((rich(X)|~creative(X)))))&
((?[X]:((~tall(X)&old(X))))=>(?[X]:(~kind(X))))&
((?[X]:((humble(X)<~>kind(X))))=>((~quiet(lucy)|creative(lucy))))&
(![X]:(wise(X)=>(~wise(X)&~strong(X))))&
(![X]:(~brave(X)<=>(~old(X)<~>quiet(X))))&
(((creative(mary)|funny(mary)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:(curious(X)<=>(~quiet(X)<~>brave(X))))&
(![X]:((~old(X)|~wise(X))=>brave(X)))&
((wise(paul)<~>creative(paul)))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((patient(X)|calm(X))))&
(?[X]:((quiet(X)|~wise(X))))&
(~generous(lucy))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:(curious(X))) | creative(mary) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6111281968706054386826141
% SZS output start Proof for 6111281968706054386826141
6. ! [X0] : ((funny(X0) | ~quiet(X0)) <=> (creative(X0) & ~tall(X0))) [input p5]
13. (funny(mary) | creative(mary)) <=> ? [X0] : (quiet(X0) & ~creative(X0)) [input p12]
23. ~creative(mary) [input hypothesis]
43. ! [X0] : (((funny(X0) | ~quiet(X0)) | (~creative(X0) | tall(X0))) & ((creative(X0) & ~tall(X0)) | (~funny(X0) & quiet(X0)))) [nnf transformation 6]
44. ! [X0] : ((funny(X0) | ~quiet(X0) | ~creative(X0) | tall(X0)) & ((creative(X0) & ~tall(X0)) | (~funny(X0) & quiet(X0)))) [flattening 43]
55. ((funny(mary) | creative(mary)) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X0] : (quiet(X0) & ~creative(X0)) | (~funny(mary) & ~creative(mary))) [nnf transformation 13]
56. (funny(mary) | creative(mary) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X0] : (quiet(X0) & ~creative(X0)) | (~funny(mary) & ~creative(mary))) [flattening 55]
57. (funny(mary) | creative(mary) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X1] : (quiet(X1) & ~creative(X1)) | (~funny(mary) & ~creative(mary))) [rectify 56]
58. ? [X1] : (quiet(X1) & ~creative(X1)) => (quiet(sK3) & ~creative(sK3)) [choice axiom]
59. (funny(mary) | creative(mary) | ! [X0] : (~quiet(X0) | creative(X0))) & ((quiet(sK3) & ~creative(sK3)) | (~funny(mary) & ~creative(mary))) [skolemisation 57,58]
92. creative(X0) | quiet(X0) [cnf transformation 44]
93. creative(X0) | ~funny(X0) [cnf transformation 44]
114. funny(mary) | creative(mary) | ~quiet(X0) | creative(X0) [cnf transformation 59]
129. ~creative(mary) [cnf transformation 23]
167. 7 <=> ! [X0] : creative(X0) [avatar definition]
168. creative(X0) <- (7) [avatar component clause 167]
211. funny(mary) | creative(mary) | creative(X0) [subsumption resolution 114,92]
212. creative(mary) | creative(X0) [subsumption resolution 211,93]
214. 17 <=> creative(mary) [avatar definition]
215. ~creative(mary) <- (~17) [avatar component clause 214]
217. 7 | 17 [avatar split clause 212,214,167]
246. ~17 [avatar split clause 129,214]
249. $false <- (7, ~17) [resolution 215,168]
250. ~7 | 17 [avatar contradiction clause 249]
251. $false [avatar sat refutation 217,246,250]
% SZS output end Proof for 6111281968706054386826141
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and funny is both strong and wise and vice versa. Everyone who is not rich is either not curious or quiet. If someone is calm then alice is both not calm and not quiet. Everyone who is not happy is not rich and vice versa. If mary is either strong or old then someone is not happy. If someone is funny then john is not brave or quiet and vice versa. Everyone who is not brave or not patient is not patient or calm and vice versa. If paul is not creative or not wise then john is rich and vice versa. Everyone who is not old or wise is kind and vice versa. Everyone who is not calm or curious is not funny. Everyone who is either not humble or funny is happy and vice versa. Everyone who is quiet or not brave is not humble or patient. Everyone who is not quiet or not brave is either brave or humble and vice versa. Everyone who is happy is both generous and kind and vice versa. Everyone who is both not generous and not calm is either not happy or not rich. If someone is both not calm and not happy then john is not curious. Someone is both not happy and old. Paul is brave or not curious. Someone is either patient or creative. Someone is either calm or happy. Someone is either not brave or not generous. Someone is kind. John is rich. Someone is not curious or not rich. | Alice is quiet. | contradiction | (![X]:((wise(X)&funny(X))<=>(strong(X)&wise(X))))&
(![X]:(~rich(X)=>(~curious(X)<~>quiet(X))))&
((?[X]:(calm(X)))=>((~calm(alice)&~quiet(alice))))&
(![X]:(~happy(X)<=>~rich(X)))&
(((strong(mary)<~>old(mary)))=>(?[X]:(~happy(X))))&
((?[X]:(funny(X)))<=>((~brave(john)|quiet(john))))&
(![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))&
(((~creative(paul)|~wise(paul)))<=>(rich(john)))&
(![X]:((~old(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)|curious(X))=>~funny(X)))&
(![X]:((~humble(X)<~>funny(X))<=>happy(X)))&
(![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))&
(![X]:(happy(X)<=>(generous(X)&kind(X))))&
(![X]:((~generous(X)&~calm(X))=>(~happy(X)<~>~rich(X))))&
((?[X]:((~calm(X)&~happy(X))))=>(~curious(john)))&
(?[X]:((~happy(X)&old(X))))&
((brave(paul)|~curious(paul)))&
(?[X]:((patient(X)<~>creative(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((~brave(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
(rich(john))&
(?[X]:((~curious(X)|~rich(X)))) | quiet(alice) | [
"p2",
"p3",
"p5",
"p6",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8284368291033128096446605
% SZS output start Proof for 8284368291033128096446605
3. ? [X0] : calm(X0) => (~quiet(alice) & ~calm(alice)) [input p2]
4. ! [X0] : (~happy(X0) <=> ~rich(X0)) [input p3]
6. ? [X0] : funny(X0) <=> (quiet(john) | ~brave(john)) [input p5]
7. ! [X0] : ((~patient(X0) | ~brave(X0)) <=> (calm(X0) | ~patient(X0))) [input p6]
10. ! [X0] : ((curious(X0) | ~calm(X0)) => ~funny(X0)) [input p9]
11. ! [X0] : ((~humble(X0) <~> funny(X0)) <=> happy(X0)) [input p10]
12. ! [X0] : ((~brave(X0) | quiet(X0)) => (patient(X0) | ~humble(X0))) [input p11]
13. ! [X0] : ((~brave(X0) | ~quiet(X0)) <=> (brave(X0) <~> humble(X0))) [input p12]
14. ! [X0] : (happy(X0) <=> (kind(X0) & generous(X0))) [input p13]
15. ! [X0] : ((~calm(X0) & ~generous(X0)) => (~happy(X0) <~> ~rich(X0))) [input p14]
21. ? [X0] : (~brave(X0) <~> ~generous(X0)) [input p20]
25. quiet(alice) [input hypothesis]
27. (~quiet(alice) & ~calm(alice)) | ! [X0] : ~calm(X0) [ennf transformation 3]
29. ! [X0] : (~funny(X0) | (~curious(X0) & calm(X0))) [ennf transformation 10]
30. ! [X0] : ((patient(X0) | ~humble(X0)) | (brave(X0) & ~quiet(X0))) [ennf transformation 12]
31. ! [X0] : (patient(X0) | ~humble(X0) | (brave(X0) & ~quiet(X0))) [flattening 30]
32. ! [X0] : ((~happy(X0) <~> ~rich(X0)) | (calm(X0) | generous(X0))) [ennf transformation 15]
33. ! [X0] : ((~happy(X0) <~> ~rich(X0)) | calm(X0) | generous(X0)) [flattening 32]
38. ! [X0] : ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0))) [nnf transformation 4]
42. (? [X0] : funny(X0) | (~quiet(john) & brave(john))) & ((quiet(john) | ~brave(john)) | ! [X0] : ~funny(X0)) [nnf transformation 6]
43. (? [X0] : funny(X0) | (~quiet(john) & brave(john))) & (quiet(john) | ~brave(john) | ! [X0] : ~funny(X0)) [flattening 42]
44. (? [X0] : funny(X0) | (~quiet(john) & brave(john))) & (quiet(john) | ~brave(john) | ! [X1] : ~funny(X1)) [rectify 43]
45. ? [X0] : funny(X0) => funny(sK1) [choice axiom]
46. (funny(sK1) | (~quiet(john) & brave(john))) & (quiet(john) | ~brave(john) | ! [X1] : ~funny(X1)) [skolemisation 44,45]
47. ! [X0] : (((~patient(X0) | ~brave(X0)) | (~calm(X0) & patient(X0))) & ((calm(X0) | ~patient(X0)) | (patient(X0) & brave(X0)))) [nnf transformation 7]
48. ! [X0] : ((~patient(X0) | ~brave(X0) | (~calm(X0) & patient(X0))) & (calm(X0) | ~patient(X0) | (patient(X0) & brave(X0)))) [flattening 47]
53. ! [X0] : ((((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | ~happy(X0)) & (happy(X0) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0))))) [nnf transformation 11]
54. ! [X0] : (((~brave(X0) | ~quiet(X0)) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0)))) & (((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | (brave(X0) & quiet(X0)))) [nnf transformation 13]
55. ! [X0] : ((~brave(X0) | ~quiet(X0) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0)))) & (((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | (brave(X0) & quiet(X0)))) [flattening 54]
56. ! [X0] : ((happy(X0) | (~kind(X0) | ~generous(X0))) & ((kind(X0) & generous(X0)) | ~happy(X0))) [nnf transformation 14]
57. ! [X0] : ((happy(X0) | ~kind(X0) | ~generous(X0)) & ((kind(X0) & generous(X0)) | ~happy(X0))) [flattening 56]
58. ! [X0] : (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | calm(X0) | generous(X0)) [nnf transformation 33]
67. ? [X0] : ((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) [nnf transformation 21]
68. ? [X0] : ((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) => ((generous(sK5) | brave(sK5)) & (~generous(sK5) | ~brave(sK5))) [choice axiom]
69. (generous(sK5) | brave(sK5)) & (~generous(sK5) | ~brave(sK5)) [skolemisation 67,68]
81. ~quiet(alice) | ~calm(X0) [cnf transformation 27]
82. ~rich(X0) | happy(X0) [cnf transformation 38]
86. quiet(john) | ~brave(john) | ~funny(X1) [cnf transformation 46]
87. funny(sK1) | brave(john) [cnf transformation 46]
88. funny(sK1) | ~quiet(john) [cnf transformation 46]
89. ~patient(X0) | calm(X0) | brave(X0) [cnf transformation 48]
99. ~funny(X0) | calm(X0) [cnf transformation 29]
101. humble(X0) | funny(X0) | happy(X0) [cnf transformation 53]
103. ~humble(X0) | funny(X0) | ~happy(X0) [cnf transformation 53]
106. ~humble(X0) | patient(X0) | brave(X0) [cnf transformation 31]
108. humble(X0) | brave(X0) | brave(X0) [cnf transformation 55]
113. ~happy(X0) | generous(X0) [cnf transformation 57]
117. rich(X0) | happy(X0) | calm(X0) | generous(X0) [cnf transformation 58]
126. ~generous(sK5) | ~brave(sK5) [cnf transformation 69]
131. quiet(alice) [cnf transformation 25]
132. humble(X0) | brave(X0) [duplicate literal removal 108]
135. 1 <=> ! [X0] : ~calm(X0) [avatar definition]
136. ~calm(X0) <- (1) [avatar component clause 135]
138. 2 <=> quiet(alice) [avatar definition]
141. 1 | ~2 [avatar split clause 81,138,135]
162. 7 <=> quiet(john) [avatar definition]
166. 8 <=> funny(sK1) [avatar definition]
168. funny(sK1) <- (8) [avatar component clause 166]
169. ~7 | 8 [avatar split clause 88,166,162]
171. 9 <=> brave(john) [avatar definition]
174. 9 | 8 [avatar split clause 87,166,171]
176. 10 <=> ! [X1] : ~funny(X1) [avatar definition]
177. ~funny(X1) <- (10) [avatar component clause 176]
178. 10 | ~9 | 7 [avatar split clause 86,162,171,176]
194. generous(X0) | calm(X0) | rich(X0) [subsumption resolution 117,113]
233. 22 <=> brave(sK5) [avatar definition]
234. ~brave(sK5) <- (~22) [avatar component clause 233]
237. 23 <=> generous(sK5) [avatar definition]
238. ~generous(sK5) <- (~23) [avatar component clause 237]
241. ~22 | ~23 [avatar split clause 126,237,233]
252. 2 [avatar split clause 131,138]
259. calm(sK1) <- (8) [resolution 99,168]
260. $false <- (1, 8) [subsumption resolution 259,136]
261. ~1 | ~8 [avatar contradiction clause 260]
318. funny(X1) | ~happy(X1) | brave(X1) [resolution 103,132]
320. ~happy(X1) | brave(X1) <- (10) [subsumption resolution 318,177]
337. patient(X0) | brave(X0) | funny(X0) | happy(X0) [resolution 106,101]
340. patient(X0) | brave(X0) | happy(X0) <- (10) [subsumption resolution 337,177]
341. patient(X0) | brave(X0) <- (10) [subsumption resolution 340,320]
382. calm(sK5) | rich(sK5) <- (~23) [resolution 194,238]
384. rich(sK5) <- (1, ~23) [subsumption resolution 382,136]
387. happy(sK5) <- (1, ~23) [resolution 384,82]
389. brave(X1) | calm(X1) | brave(X1) <- (10) [resolution 341,89]
390. brave(X1) | calm(X1) <- (10) [duplicate literal removal 389]
391. brave(X1) <- (1, 10) [subsumption resolution 390,136]
400. generous(sK5) <- (1, ~23) [resolution 387,113]
402. $false <- (1, ~23) [subsumption resolution 400,238]
403. ~1 | 23 [avatar contradiction clause 402]
404. $false <- (1, 10, ~22) [subsumption resolution 234,391]
405. ~1 | ~10 | 22 [avatar contradiction clause 404]
406. $false [avatar sat refutation 141,169,174,178,241,252,261,403,405]
% SZS output end Proof for 8284368291033128096446605
% ------------------------------
% 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or strong is tall or calm. Everyone who is not humble or not quiet is either strong or happy and vice versa. If someone is either brave or generous then someone is both quiet and tall. If someone is either wise or not calm then someone is not rich. If someone is curious or happy then lucy is either not strong or not funny. If someone is not calm or kind then someone is wise. Everyone who is not curious is both kind and creative. Everyone who is wise is funny or not calm and vice versa. If fred is both humble and not humble then mary is either calm or wise. Everyone who is either not kind or not brave is both not brave and not happy. Everyone who is not wise is either patient or creative and vice versa. Everyone who is both not happy and brave is both not tall and not rich. If someone is either brave or happy then paul is both humble and old and vice versa. If someone is either not rich or old then alice is kind. Everyone who is strong is either wise or not kind. If someone is both not humble and funny then someone is not kind or not creative and vice versa. Fred is both rich and not kind. Mary is happy. Susan is both not old and not humble. Lucy is not generous or old. Susan is both not brave and not curious. Someone is both creative and funny. Paul is both tall and wise. Lucy is either old or not strong. | Susan is old. | contradiction | (![X]:((~generous(X)<~>strong(X))=>(tall(X)|calm(X))))&
(![X]:((~humble(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((brave(X)<~>generous(X))))=>(?[X]:((quiet(X)&tall(X)))))&
((?[X]:((wise(X)<~>~calm(X))))=>(?[X]:(~rich(X))))&
((?[X]:((curious(X)|happy(X))))=>((~strong(lucy)<~>~funny(lucy))))&
((?[X]:((~calm(X)|kind(X))))=>(?[X]:(wise(X))))&
(![X]:(~curious(X)=>(kind(X)&creative(X))))&
(![X]:(wise(X)<=>(funny(X)|~calm(X))))&
(((humble(fred)&~humble(fred)))=>((calm(mary)<~>wise(mary))))&
(![X]:((~kind(X)<~>~brave(X))=>(~brave(X)&~happy(X))))&
(![X]:(~wise(X)<=>(patient(X)<~>creative(X))))&
(![X]:((~happy(X)&brave(X))=>(~tall(X)&~rich(X))))&
((?[X]:((brave(X)<~>happy(X))))<=>((humble(paul)&old(paul))))&
((?[X]:((~rich(X)<~>old(X))))=>(kind(alice)))&
(![X]:(strong(X)=>(wise(X)<~>~kind(X))))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:((~kind(X)|~creative(X)))))&
((rich(fred)&~kind(fred)))&
(happy(mary))&
((~old(susan)&~humble(susan)))&
((~generous(lucy)|old(lucy)))&
((~brave(susan)&~curious(susan)))&
(?[X]:((creative(X)&funny(X))))&
((tall(paul)&wise(paul)))&
((old(lucy)<~>~strong(lucy))) | old(susan) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5654539198954160735764909
% SZS output start Proof for 5654539198954160735764909
19. ~humble(susan) & ~old(susan) [input p18]
25. old(susan) [input hypothesis]
134. ~old(susan) [cnf transformation 19]
145. old(susan) [cnf transformation 25]
289. $false [subsumption resolution 145,134]
% SZS output end Proof for 5654539198954160735764909
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or happy is both not curious and not wise and vice versa.
If john is not brave then someone is both curious and tall and vice versa.
Everyone who is either humble or tall is either not wise or humble.
Everyone who is either curious or patient is rich.
If alice is both not kind and tall then someone is either tall or curious and vice versa.
Everyone who is both tall and not patient is either strong or not funny and vice versa.
Everyone who is both curious and not patient is either strong or old and vice versa.
If mary is not strong then lucy is not old and vice versa.
If someone is curious then john is kind and vice versa.
If lucy is creative then someone is both happy and funny.
Everyone who is both quiet and humble is both not old and not funny and vice versa.
Everyone who is old is both humble and not tall and vice versa.
If mary is not curious or funny then john is either wise or kind and vice versa.
If alice is both wise and not calm then alice is funny.
Everyone who is calm is both not generous and curious and vice versa.
If someone is quiet then paul is generous or humble and vice versa.
Someone is either not generous or not creative.
Someone is both old and curious.
Paul is either not old or strong.
Someone is not brave.
Someone is humble or not humble.
Someone is either not funny or calm.
Susan is both happy and generous. | Alice is funny. | neutral | (![X]:((strong(X)<~>happy(X))<=>(~curious(X)&~wise(X))))&
((~brave(john))<=>(?[X]:((curious(X)&tall(X)))))&
(![X]:((humble(X)<~>tall(X))=>(~wise(X)<~>humble(X))))&
(![X]:((curious(X)<~>patient(X))=>rich(X)))&
(((~kind(alice)&tall(alice)))<=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:((tall(X)&~patient(X))<=>(strong(X)<~>~funny(X))))&
(![X]:((curious(X)&~patient(X))<=>(strong(X)<~>old(X))))&
((~strong(mary))<=>(~old(lucy)))&
((?[X]:(curious(X)))<=>(kind(john)))&
((creative(lucy))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~old(X)&~funny(X))))&
(![X]:(old(X)<=>(humble(X)&~tall(X))))&
(((~curious(mary)|funny(mary)))<=>((wise(john)<~>kind(john))))&
(((wise(alice)&~calm(alice)))=>(funny(alice)))&
(![X]:(calm(X)<=>(~generous(X)&curious(X))))&
((?[X]:(quiet(X)))<=>((generous(paul)|humble(paul))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((old(X)&curious(X))))&
((~old(paul)<~>strong(paul)))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)|~humble(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
((happy(susan)&generous(susan))) | funny(alice) | [] | null | 0 |
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 not quiet. | contradiction | ((?[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)))) | ~quiet(fred) | [
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1051084978580399911263601
% SZS output start Proof for 1051084978580399911263601
3. ! [X0] : (tall(X0) <=> (funny(X0) & rich(X0))) [input p2]
5. ! [X0] : ((rich(X0) | ~tall(X0)) => (calm(X0) & tall(X0))) [input p4]
8. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (patient(X0) | calm(X0))) [input p7]
20. ~quiet(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]
41. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~patient(X0) & ~calm(X0))) & ((patient(X0) | calm(X0)) | (~quiet(X0) | happy(X0)))) [nnf transformation 8]
42. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~patient(X0) & ~calm(X0))) & (patient(X0) | calm(X0) | ~quiet(X0) | happy(X0))) [flattening 41]
66. ~tall(X0) | rich(X0) [cnf transformation 34]
75. tall(X0) | tall(X0) [cnf transformation 25]
78. ~rich(X0) | calm(X0) [cnf transformation 25]
91. ~calm(X0) | quiet(X0) [cnf transformation 42]
123. ~quiet(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]
245. rich(X0) <- (4) [resolution 66,139]
255. calm(X0) <- (4) [resolution 78,245]
261. quiet(X0) <- (4) [resolution 91,255]
263. $false <- (4) [resolution 261,123]
264. ~4 [avatar contradiction clause 263]
265. $false [avatar sat refutation 150,264]
% SZS output end Proof for 1051084978580399911263601
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not happy is either wise or rich.
Everyone who is not kind or patient is not patient.
Everyone who is rich is brave or creative and vice versa.
If someone is either humble or patient then someone is both happy and not calm.
Everyone who is not strong is either happy or not kind.
If someone is old or curious then lucy is not patient.
Everyone who is not calm or calm is either generous or not generous and vice versa.
If someone is not patient then mary is not rich or quiet.
If someone is not curious or not funny then someone is not calm and vice versa.
If mary is both generous and strong then someone is both not happy and humble and vice versa.
If susan is curious then someone is either funny or not happy.
If someone is not curious then someone is both wise and not creative and vice versa.
Everyone who is either wise or not curious is both generous and curious and vice versa.
Everyone who is not old or not funny is either not brave or not kind and vice versa.
If mary is either not old or wise then someone is humble and vice versa.
If mary is either not calm or kind then paul is rich.
Someone is humble or happy.
Paul is not strong or not kind.
Lucy is either not patient or not funny.
Alice is both wise and not funny.
Someone is not quiet.
Someone is either generous or wise.
Susan is either strong or not humble.
Mary is both kind and creative. | Paul is kind. | neutral | (![X]:((~brave(X)|~happy(X))=>(wise(X)<~>rich(X))))&
(![X]:((~kind(X)|patient(X))=>~patient(X)))&
(![X]:(rich(X)<=>(brave(X)|creative(X))))&
((?[X]:((humble(X)<~>patient(X))))=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:(~strong(X)=>(happy(X)<~>~kind(X))))&
((?[X]:((old(X)|curious(X))))=>(~patient(lucy)))&
(![X]:((~calm(X)|calm(X))<=>(generous(X)<~>~generous(X))))&
((?[X]:(~patient(X)))=>((~rich(mary)|quiet(mary))))&
((?[X]:((~curious(X)|~funny(X))))<=>(?[X]:(~calm(X))))&
(((generous(mary)&strong(mary)))<=>(?[X]:((~happy(X)&humble(X)))))&
((curious(susan))=>(?[X]:((funny(X)<~>~happy(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((wise(X)&~creative(X)))))&
(![X]:((wise(X)<~>~curious(X))<=>(generous(X)&curious(X))))&
(![X]:((~old(X)|~funny(X))<=>(~brave(X)<~>~kind(X))))&
(((~old(mary)<~>wise(mary)))<=>(?[X]:(humble(X))))&
(((~calm(mary)<~>kind(mary)))=>(rich(paul)))&
(?[X]:((humble(X)|happy(X))))&
((~strong(paul)|~kind(paul)))&
((~patient(lucy)<~>~funny(lucy)))&
((wise(alice)&~funny(alice)))&
(?[X]:(~quiet(X)))&
(?[X]:((generous(X)<~>wise(X))))&
((strong(susan)<~>~humble(susan)))&
((kind(mary)&creative(mary))) | kind(paul) | [] | null | 0 |
Everyone who is either not kind or not calm is not kind or brave. Everyone who is quiet is not brave or not kind. Everyone who is not rich is tall. If mary is curious or kind then fred is both not curious and rich and vice versa. If someone is both calm and not strong then someone is either generous or funny and vice versa. Everyone who is both not patient and happy is not brave or brave and vice versa. Everyone who is not strong or rich is both generous and funny and vice versa. If susan is both creative and not wise then john is not tall and vice versa. If fred is funny then someone is both creative and not patient and vice versa. If mary is generous then fred is either quiet or humble and vice versa. Everyone who is not strong or not generous is either not rich or curious. If paul is either quiet or not brave then someone is both not generous and not brave and vice versa. If paul is not creative or not humble then mary is both happy and funny and vice versa. Everyone who is either not generous or kind is both not happy and not quiet. Everyone who is humble or not wise is both brave and rich and vice versa. If someone is both not curious and rich then someone is either not old or rich. Someone is either strong or not tall. John is either not brave or curious. Susan is not funny or not brave. Someone is both not curious and not patient. Alice is either tall or wise. Fred is not kind. Someone is either not humble or wise. Someone is curious or tall. | Alice is not rich. | contradiction | (![X]:((~kind(X)<~>~calm(X))=>(~kind(X)|brave(X))))&
(![X]:(quiet(X)=>(~brave(X)|~kind(X))))&
(![X]:(~rich(X)=>tall(X)))&
(((curious(mary)|kind(mary)))<=>((~curious(fred)&rich(fred))))&
((?[X]:((calm(X)&~strong(X))))<=>(?[X]:((generous(X)<~>funny(X)))))&
(![X]:((~patient(X)&happy(X))<=>(~brave(X)|brave(X))))&
(![X]:((~strong(X)|rich(X))<=>(generous(X)&funny(X))))&
(((creative(susan)&~wise(susan)))<=>(~tall(john)))&
((funny(fred))<=>(?[X]:((creative(X)&~patient(X)))))&
((generous(mary))<=>((quiet(fred)<~>humble(fred))))&
(![X]:((~strong(X)|~generous(X))=>(~rich(X)<~>curious(X))))&
(((quiet(paul)<~>~brave(paul)))<=>(?[X]:((~generous(X)&~brave(X)))))&
(((~creative(paul)|~humble(paul)))<=>((happy(mary)&funny(mary))))&
(![X]:((~generous(X)<~>kind(X))=>(~happy(X)&~quiet(X))))&
(![X]:((humble(X)|~wise(X))<=>(brave(X)&rich(X))))&
((?[X]:((~curious(X)&rich(X))))=>(?[X]:((~old(X)<~>rich(X)))))&
(?[X]:((strong(X)<~>~tall(X))))&
((~brave(john)<~>curious(john)))&
((~funny(susan)|~brave(susan)))&
(?[X]:((~curious(X)&~patient(X))))&
((tall(alice)<~>wise(alice)))&
(~kind(fred))&
(?[X]:((~humble(X)<~>wise(X))))&
(?[X]:((curious(X)|tall(X)))) | ~rich(alice) | [
"p2",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5947561640178898235883382
% SZS output start Proof for 5947561640178898235883382
3. ! [X0] : (~rich(X0) => tall(X0)) [input p2]
15. ! [X0] : ((~wise(X0) | humble(X0)) <=> (rich(X0) & brave(X0))) [input p14]
21. tall(alice) <~> wise(alice) [input p20]
25. ~rich(alice) [input hypothesis]
32. ! [X0] : (tall(X0) | rich(X0)) [ennf transformation 3]
63. ! [X0] : (((~wise(X0) | humble(X0)) | (~rich(X0) | ~brave(X0))) & ((rich(X0) & brave(X0)) | (wise(X0) & ~humble(X0)))) [nnf transformation 15]
64. ! [X0] : ((~wise(X0) | humble(X0) | ~rich(X0) | ~brave(X0)) & ((rich(X0) & brave(X0)) | (wise(X0) & ~humble(X0)))) [flattening 63]
75. (~wise(alice) | ~tall(alice)) & (wise(alice) | tall(alice)) [nnf transformation 21]
84. tall(X0) | rich(X0) [cnf transformation 32]
138. wise(X0) | rich(X0) [cnf transformation 64]
150. ~wise(alice) | ~tall(alice) [cnf transformation 75]
155. ~rich(alice) [cnf transformation 25]
343. 38 <=> tall(alice) [avatar definition]
345. ~tall(alice) <- (~38) [avatar component clause 343]
347. 39 <=> wise(alice) [avatar definition]
349. ~wise(alice) <- (~39) [avatar component clause 347]
350. ~38 | ~39 [avatar split clause 150,347,343]
381. rich(alice) <- (~39) [resolution 138,349]
383. $false <- (~39) [subsumption resolution 381,155]
384. 39 [avatar contradiction clause 383]
385. rich(alice) <- (~38) [resolution 345,84]
386. $false <- (~38) [subsumption resolution 385,155]
387. 38 [avatar contradiction clause 386]
388. $false [avatar sat refutation 350,384,387]
% SZS output end Proof for 5947561640178898235883382
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then mary is either calm or brave. Everyone who is either happy or strong is both rich and not generous and vice versa. Everyone who is either funny or not curious is generous or patient. If someone is both kind and happy then fred is not generous and vice versa. Everyone who is both not tall and not humble is either brave or not humble and vice versa. Everyone who is not wise or not quiet is kind. Everyone who is both not generous and not funny is either wise or humble and vice versa. If john is both curious and not strong then lucy is calm or strong and vice versa. Everyone who is not calm is both not happy and not wise and vice versa. Everyone who is not rich or quiet is not rich or old. Everyone who is both not old and patient is either not kind or generous. If someone is tall or old then someone is either not funny or curious. Everyone who is not strong or not calm is both calm and quiet. If fred is both not curious and patient then lucy is either not brave or generous. Everyone who is either rich or wise is curious. If fred is patient or not humble then susan is both not curious and not funny and vice versa. Someone is calm. Fred is generous. Alice is either not humble or not strong. Susan is either rich or not funny. John is not curious or not patient. John is not happy. Lucy is both tall and wise. | Susan is wise. | entailment | ((?[X]:(~creative(X)))=>((calm(mary)<~>brave(mary))))&
(![X]:((happy(X)<~>strong(X))<=>(rich(X)&~generous(X))))&
(![X]:((funny(X)<~>~curious(X))=>(generous(X)|patient(X))))&
((?[X]:((kind(X)&happy(X))))<=>(~generous(fred)))&
(![X]:((~tall(X)&~humble(X))<=>(brave(X)<~>~humble(X))))&
(![X]:((~wise(X)|~quiet(X))=>kind(X)))&
(![X]:((~generous(X)&~funny(X))<=>(wise(X)<~>humble(X))))&
(((curious(john)&~strong(john)))<=>((calm(lucy)|strong(lucy))))&
(![X]:(~calm(X)<=>(~happy(X)&~wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(~rich(X)|old(X))))&
(![X]:((~old(X)&patient(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((tall(X)|old(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)&quiet(X))))&
(((~curious(fred)&patient(fred)))=>((~brave(lucy)<~>generous(lucy))))&
(![X]:((rich(X)<~>wise(X))=>curious(X)))&
(((patient(fred)|~humble(fred)))<=>((~curious(susan)&~funny(susan))))&
(?[X]:(calm(X)))&
(generous(fred))&
((~humble(alice)<~>~strong(alice)))&
((rich(susan)<~>~funny(susan)))&
((~curious(john)|~patient(john)))&
(~happy(john))&
((tall(lucy)&wise(lucy))) | wise(susan) | [
"p3",
"p5",
"p8",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 133412733846016035252363
% SZS output start Proof for 133412733846016035252363
4. ? [X0] : (happy(X0) & kind(X0)) <=> ~generous(fred) [input p3]
6. ! [X0] : ((~quiet(X0) | ~wise(X0)) => kind(X0)) [input p5]
9. ! [X0] : (~calm(X0) <=> (~wise(X0) & ~happy(X0))) [input p8]
13. ! [X0] : ((~calm(X0) | ~strong(X0)) => (quiet(X0) & calm(X0))) [input p12]
18. generous(fred) [input p17]
24. ~wise(susan) [input hypothesis]
29. ! [X0] : (kind(X0) | (quiet(X0) & wise(X0))) [ennf transformation 6]
35. ! [X0] : ((quiet(X0) & calm(X0)) | (calm(X0) & strong(X0))) [ennf transformation 13]
42. (? [X0] : (happy(X0) & kind(X0)) | generous(fred)) & (~generous(fred) | ! [X0] : (~happy(X0) | ~kind(X0))) [nnf transformation 4]
43. (? [X0] : (happy(X0) & kind(X0)) | generous(fred)) & (~generous(fred) | ! [X1] : (~happy(X1) | ~kind(X1))) [rectify 42]
44. ? [X0] : (happy(X0) & kind(X0)) => (happy(sK0) & kind(sK0)) [choice axiom]
45. ((happy(sK0) & kind(sK0)) | generous(fred)) & (~generous(fred) | ! [X1] : (~happy(X1) | ~kind(X1))) [skolemisation 43,44]
52. ! [X0] : ((~calm(X0) | (wise(X0) | happy(X0))) & ((~wise(X0) & ~happy(X0)) | calm(X0))) [nnf transformation 9]
53. ! [X0] : ((~calm(X0) | wise(X0) | happy(X0)) & ((~wise(X0) & ~happy(X0)) | calm(X0))) [flattening 52]
75. ~generous(fred) | ~happy(X1) | ~kind(X1) [cnf transformation 45]
84. wise(X0) | kind(X0) [cnf transformation 29]
99. ~calm(X0) | wise(X0) | happy(X0) [cnf transformation 53]
109. calm(X0) | calm(X0) [cnf transformation 35]
122. generous(fred) [cnf transformation 18]
131. ~wise(susan) [cnf transformation 24]
132. calm(X0) [duplicate literal removal 109]
136. 1 <=> generous(fred) [avatar definition]
150. 4 <=> ! [X1] : (~happy(X1) | ~kind(X1)) [avatar definition]
151. ~kind(X1) | ~happy(X1) <- (4) [avatar component clause 150]
152. 4 | ~1 [avatar split clause 75,136,150]
228. 1 [avatar split clause 122,136]
252. kind(susan) [resolution 84,131]
256. ~happy(susan) <- (4) [resolution 151,252]
303. wise(X0) | happy(X0) [resolution 99,132]
304. happy(susan) [resolution 303,131]
308. $false <- (4) [subsumption resolution 304,256]
309. ~4 [avatar contradiction clause 308]
310. $false [avatar sat refutation 152,228,309]
% SZS output end Proof for 133412733846016035252363
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not kind is both wise and not humble and vice versa. Everyone who is not brave or rich is both not kind and happy and vice versa. If someone is rich or not brave then alice is either not wise or funny. If fred is both not patient and strong then someone is both strong and not quiet and vice versa. Everyone who is both calm and kind is not wise or not strong. If mary is happy then paul is not kind or calm and vice versa. Everyone who is both quiet and not patient is not strong or not kind and vice versa. If alice is wise or brave then someone is tall or not generous. If someone is both not tall and not curious then someone is old or not kind and vice versa. If someone is rich or old then susan is not brave or old and vice versa. Everyone who is brave or wise is either not calm or not rich and vice versa. If susan is patient then someone is curious. Everyone who is tall is not creative. Everyone who is either tall or not strong is either not curious or kind and vice versa. Everyone who is either patient or not calm is not happy and vice versa. If lucy is wise then fred is either kind or not calm. Lucy is either not happy or not brave. Someone is either tall or happy. Paul is both rich and strong. Susan is either funny or wise. Someone is creative or curious. Mary is not old or not brave. Susan is not quiet or not wise. Someone is not curious or not generous. | Fred is not quiet. | contradiction | (![X]:((~wise(X)<~>~kind(X))<=>(wise(X)&~humble(X))))&
(![X]:((~brave(X)|rich(X))<=>(~kind(X)&happy(X))))&
((?[X]:((rich(X)|~brave(X))))=>((~wise(alice)<~>funny(alice))))&
(((~patient(fred)&strong(fred)))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((calm(X)&kind(X))=>(~wise(X)|~strong(X))))&
((happy(mary))<=>((~kind(paul)|calm(paul))))&
(![X]:((quiet(X)&~patient(X))<=>(~strong(X)|~kind(X))))&
(((wise(alice)|brave(alice)))=>(?[X]:((tall(X)|~generous(X)))))&
((?[X]:((~tall(X)&~curious(X))))<=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((rich(X)|old(X))))<=>((~brave(susan)|old(susan))))&
(![X]:((brave(X)|wise(X))<=>(~calm(X)<~>~rich(X))))&
((patient(susan))=>(?[X]:(curious(X))))&
(![X]:(tall(X)=>~creative(X)))&
(![X]:((tall(X)<~>~strong(X))<=>(~curious(X)<~>kind(X))))&
(![X]:((patient(X)<~>~calm(X))<=>~happy(X)))&
((wise(lucy))=>((kind(fred)<~>~calm(fred))))&
((~happy(lucy)<~>~brave(lucy)))&
(?[X]:((tall(X)<~>happy(X))))&
((rich(paul)&strong(paul)))&
((funny(susan)<~>wise(susan)))&
(?[X]:((creative(X)|curious(X))))&
((~old(mary)|~brave(mary)))&
((~quiet(susan)|~wise(susan)))&
(?[X]:((~curious(X)|~generous(X)))) | ~quiet(fred) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7877057382806184464751194
% SZS output start Proof for 7877057382806184464751194
1. ! [X0] : ((~wise(X0) <~> ~kind(X0)) <=> (~humble(X0) & wise(X0))) [input p0]
2. ! [X0] : ((rich(X0) | ~brave(X0)) <=> (happy(X0) & ~kind(X0))) [input p1]
4. (strong(fred) & ~patient(fred)) <=> ? [X0] : (~quiet(X0) & strong(X0)) [input p3]
5. ! [X0] : ((kind(X0) & calm(X0)) => (~strong(X0) | ~wise(X0))) [input p4]
7. ! [X0] : ((~patient(X0) & quiet(X0)) <=> (~kind(X0) | ~strong(X0))) [input p6]
11. ! [X0] : ((wise(X0) | brave(X0)) <=> (~calm(X0) <~> ~rich(X0))) [input p10]
25. ~quiet(fred) [input hypothesis]
30. ! [X0] : ((~strong(X0) | ~wise(X0)) | (~kind(X0) | ~calm(X0))) [ennf transformation 5]
31. ! [X0] : (~strong(X0) | ~wise(X0) | ~kind(X0) | ~calm(X0)) [flattening 30]
35. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [nnf transformation 1]
36. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [flattening 35]
37. ! [X0] : (((rich(X0) | ~brave(X0)) | (~happy(X0) | kind(X0))) & ((happy(X0) & ~kind(X0)) | (~rich(X0) & brave(X0)))) [nnf transformation 2]
38. ! [X0] : ((rich(X0) | ~brave(X0) | ~happy(X0) | kind(X0)) & ((happy(X0) & ~kind(X0)) | (~rich(X0) & brave(X0)))) [flattening 37]
40. ((strong(fred) & ~patient(fred)) | ! [X0] : (quiet(X0) | ~strong(X0))) & (? [X0] : (~quiet(X0) & strong(X0)) | (~strong(fred) | patient(fred))) [nnf transformation 4]
41. ((strong(fred) & ~patient(fred)) | ! [X0] : (quiet(X0) | ~strong(X0))) & (? [X0] : (~quiet(X0) & strong(X0)) | ~strong(fred) | patient(fred)) [flattening 40]
42. ((strong(fred) & ~patient(fred)) | ! [X0] : (quiet(X0) | ~strong(X0))) & (? [X1] : (~quiet(X1) & strong(X1)) | ~strong(fred) | patient(fred)) [rectify 41]
43. ? [X1] : (~quiet(X1) & strong(X1)) => (~quiet(sK0) & strong(sK0)) [choice axiom]
44. ((strong(fred) & ~patient(fred)) | ! [X0] : (quiet(X0) | ~strong(X0))) & ((~quiet(sK0) & strong(sK0)) | ~strong(fred) | patient(fred)) [skolemisation 42,43]
47. ! [X0] : (((~patient(X0) & quiet(X0)) | (kind(X0) & strong(X0))) & ((~kind(X0) | ~strong(X0)) | (patient(X0) | ~quiet(X0)))) [nnf transformation 7]
48. ! [X0] : (((~patient(X0) & quiet(X0)) | (kind(X0) & strong(X0))) & (~kind(X0) | ~strong(X0) | patient(X0) | ~quiet(X0))) [flattening 47]
59. ! [X0] : (((wise(X0) | brave(X0)) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) & (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | (~wise(X0) & ~brave(X0)))) [nnf transformation 11]
60. ! [X0] : ((wise(X0) | brave(X0) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) & (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | (~wise(X0) & ~brave(X0)))) [flattening 59]
73. wise(X0) | ~kind(X0) | wise(X0) [cnf transformation 36]
80. ~rich(X0) | ~kind(X0) [cnf transformation 38]
91. strong(fred) | quiet(X0) | ~strong(X0) [cnf transformation 44]
92. ~strong(X0) | ~wise(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 31]
97. quiet(X0) | strong(X0) [cnf transformation 48]
98. quiet(X0) | kind(X0) [cnf transformation 48]
113. ~wise(X0) | calm(X0) | rich(X0) [cnf transformation 60]
143. ~quiet(fred) [cnf transformation 25]
144. ~kind(X0) | wise(X0) [duplicate literal removal 73]
165. 5 <=> ! [X0] : (quiet(X0) | ~strong(X0)) [avatar definition]
166. quiet(X0) | ~strong(X0) <- (5) [avatar component clause 165]
168. 6 <=> strong(fred) [avatar definition]
170. strong(fred) <- (6) [avatar component clause 168]
171. 5 | 6 [avatar split clause 91,168,165]
187. ~calm(X0) | ~kind(X0) | ~strong(X0) [subsumption resolution 92,144]
267. 27 <=> kind(fred) [avatar definition]
268. kind(fred) <- (27) [avatar component clause 267]
271. 28 <=> calm(fred) [avatar definition]
273. calm(fred) <- (28) [avatar component clause 271]
328. quiet(X0) <- (5) [subsumption resolution 166,97]
329. $false <- (5) [resolution 328,143]
330. ~5 [avatar contradiction clause 329]
340. kind(fred) [resolution 98,143]
342. 27 [avatar split clause 340,267]
346. wise(fred) <- (27) [resolution 144,268]
361. 42 <=> rich(fred) [avatar definition]
363. rich(fred) <- (42) [avatar component clause 361]
380. calm(fred) | rich(fred) <- (27) [resolution 113,346]
476. ~kind(fred) | ~strong(fred) <- (28) [resolution 187,273]
480. ~strong(fred) <- (27, 28) [subsumption resolution 476,268]
481. $false <- (6, 27, 28) [subsumption resolution 480,170]
482. ~6 | ~27 | ~28 [avatar contradiction clause 481]
501. 42 | 28 | ~27 [avatar split clause 380,267,271,361]
627. ~kind(fred) <- (42) [resolution 363,80]
628. $false <- (27, 42) [subsumption resolution 627,268]
629. ~27 | ~42 [avatar contradiction clause 628]
630. $false [avatar sat refutation 171,330,342,482,501,629]
% SZS output end Proof for 7877057382806184464751194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not creative is both not old and not tall.
If susan is not quiet then someone is brave or not humble.
If someone is both funny and not curious then mary is either patient or tall.
Everyone who is old is not patient or tall and vice versa.
Everyone who is happy is not generous and vice versa.
Everyone who is either not old or not rich is either not wise or wise.
Everyone who is rich is either not creative or not patient.
If someone is both tall and not patient then susan is either not tall or patient.
If someone is not kind or not happy then someone is humble.
If someone is not strong then susan is both not tall and not humble and vice versa.
Everyone who is both not quiet and quiet is both not quiet and not generous and vice versa.
If alice is either not generous or not wise then lucy is both not rich and funny.
Everyone who is not quiet or not old is not strong and vice versa.
Everyone who is not brave or not curious is brave or not humble.
If fred is either strong or not rich then someone is not strong or not creative.
Mary is either old or quiet.
Susan is both not creative and calm.
Fred is strong or not kind.
Alice is tall.
John is either calm or generous.
Someone is both wise and not old.
Lucy is either not wise or rich.
Fred is strong or not funny. | John is old. | neutral | (![X]:((~happy(X)|~creative(X))=>(~old(X)&~tall(X))))&
((~quiet(susan))=>(?[X]:((brave(X)|~humble(X)))))&
((?[X]:((funny(X)&~curious(X))))=>((patient(mary)<~>tall(mary))))&
(![X]:(old(X)<=>(~patient(X)|tall(X))))&
(![X]:(happy(X)<=>~generous(X)))&
(![X]:((~old(X)<~>~rich(X))=>(~wise(X)<~>wise(X))))&
(![X]:(rich(X)=>(~creative(X)<~>~patient(X))))&
((?[X]:((tall(X)&~patient(X))))=>((~tall(susan)<~>patient(susan))))&
((?[X]:((~kind(X)|~happy(X))))=>(?[X]:(humble(X))))&
((?[X]:(~strong(X)))<=>((~tall(susan)&~humble(susan))))&
(![X]:((~quiet(X)&quiet(X))<=>(~quiet(X)&~generous(X))))&
(((~generous(alice)<~>~wise(alice)))=>((~rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)|~old(X))<=>~strong(X)))&
(![X]:((~brave(X)|~curious(X))=>(brave(X)|~humble(X))))&
(((strong(fred)<~>~rich(fred)))=>(?[X]:((~strong(X)|~creative(X)))))&
((old(mary)<~>quiet(mary)))&
((~creative(susan)&calm(susan)))&
((strong(fred)|~kind(fred)))&
(tall(alice))&
((calm(john)<~>generous(john)))&
(?[X]:((wise(X)&~old(X))))&
((~wise(lucy)<~>rich(lucy)))&
((strong(fred)|~funny(fred))) | old(john) | [] | null | 0 |
Everyone who is not brave is not generous or not funny.
Everyone who is not brave or not wise is brave or calm and vice versa.
Everyone who is brave or not wise is either not creative or not humble and vice versa.
If someone is either tall or generous then someone is both tall and not generous and vice versa.
If lucy is either brave or wise then someone is either not patient or humble and vice versa.
If lucy is creative then lucy is not old or not patient.
If susan is both not creative and not tall then fred is creative and vice versa.
Everyone who is either not quiet or creative is both strong and funny.
Everyone who is not old or not happy is both not rich and not calm.
Everyone who is both brave and not strong is not tall and vice versa.
If someone is both wise and not curious then someone is both generous and tall and vice versa.
If alice is both not generous and kind then fred is curious or not patient and vice versa.
Everyone who is not humble is strong.
Everyone who is either kind or not curious is either not quiet or not wise and vice versa.
If someone is either not old or old then someone is not curious or not kind and vice versa.
Everyone who is not strong is not old or not quiet.
Someone is both not humble and not calm.
Mary is not wise.
Someone is both quiet and not creative.
Alice is not wise.
Mary is happy.
Someone is both strong and happy.
Lucy is either brave or not calm.
Fred is both creative and generous. | Alice is not generous. | neutral | (![X]:(~brave(X)=>(~generous(X)|~funny(X))))&
(![X]:((~brave(X)|~wise(X))<=>(brave(X)|calm(X))))&
(![X]:((brave(X)|~wise(X))<=>(~creative(X)<~>~humble(X))))&
((?[X]:((tall(X)<~>generous(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(((brave(lucy)<~>wise(lucy)))<=>(?[X]:((~patient(X)<~>humble(X)))))&
((creative(lucy))=>((~old(lucy)|~patient(lucy))))&
(((~creative(susan)&~tall(susan)))<=>(creative(fred)))&
(![X]:((~quiet(X)<~>creative(X))=>(strong(X)&funny(X))))&
(![X]:((~old(X)|~happy(X))=>(~rich(X)&~calm(X))))&
(![X]:((brave(X)&~strong(X))<=>~tall(X)))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((generous(X)&tall(X)))))&
(((~generous(alice)&kind(alice)))<=>((curious(fred)|~patient(fred))))&
(![X]:(~humble(X)=>strong(X)))&
(![X]:((kind(X)<~>~curious(X))<=>(~quiet(X)<~>~wise(X))))&
((?[X]:((~old(X)<~>old(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:(~strong(X)=>(~old(X)|~quiet(X))))&
(?[X]:((~humble(X)&~calm(X))))&
(~wise(mary))&
(?[X]:((quiet(X)&~creative(X))))&
(~wise(alice))&
(happy(mary))&
(?[X]:((strong(X)&happy(X))))&
((brave(lucy)<~>~calm(lucy)))&
((creative(fred)&generous(fred))) | ~generous(alice) | [] | null | 0 |
Everyone who is either creative or generous is not quiet or not brave.
Everyone who is both not generous and not wise is not happy.
Everyone who is not rich is both curious and not kind.
If someone is both not patient and rich then alice is both strong and not generous and vice versa.
Everyone who is happy is either happy or not kind.
If susan is both not rich and not brave then someone is both not calm and not wise.
Everyone who is not wise is either strong or not curious and vice versa.
Everyone who is not creative is both old and generous.
If alice is both patient and not tall then someone is either not happy or old.
If paul is not rich or creative then someone is not humble.
Everyone who is not creative or rich is not strong and vice versa.
Everyone who is not wise or tall is not happy or quiet and vice versa.
Everyone who is kind is not happy or rich and vice versa.
If someone is not brave or funny then someone is not strong.
If lucy is both generous and tall then paul is either not generous or not strong.
Everyone who is not creative or not humble is not generous or patient and vice versa.
Someone is generous.
Someone is both rich and creative.
Fred is not generous or wise.
Someone is generous or happy.
Someone is not humble or creative.
Fred is not brave or funny. | Paul is not old. | neutral | (![X]:((creative(X)<~>generous(X))=>(~quiet(X)|~brave(X))))&
(![X]:((~generous(X)&~wise(X))=>~happy(X)))&
(![X]:(~rich(X)=>(curious(X)&~kind(X))))&
((?[X]:((~patient(X)&rich(X))))<=>((strong(alice)&~generous(alice))))&
(![X]:(happy(X)=>(happy(X)<~>~kind(X))))&
(((~rich(susan)&~brave(susan)))=>(?[X]:((~calm(X)&~wise(X)))))&
(![X]:(~wise(X)<=>(strong(X)<~>~curious(X))))&
(![X]:(~creative(X)=>(old(X)&generous(X))))&
(((patient(alice)&~tall(alice)))=>(?[X]:((~happy(X)<~>old(X)))))&
(((~rich(paul)|creative(paul)))=>(?[X]:(~humble(X))))&
(![X]:((~creative(X)|rich(X))<=>~strong(X)))&
(![X]:((~wise(X)|tall(X))<=>(~happy(X)|quiet(X))))&
(![X]:(kind(X)<=>(~happy(X)|rich(X))))&
((?[X]:((~brave(X)|funny(X))))=>(?[X]:(~strong(X))))&
(((generous(lucy)&tall(lucy)))=>((~generous(paul)<~>~strong(paul))))&
(![X]:((~creative(X)|~humble(X))<=>(~generous(X)|patient(X))))&
(?[X]:(generous(X)))&
(?[X]:((rich(X)&creative(X))))&
((~generous(fred)|wise(fred)))&
(?[X]:((generous(X)|happy(X))))&
(?[X]:((~humble(X)|creative(X))))&
((~brave(fred)|funny(fred))) | ~old(paul) | [] | null | 0 |
If alice is tall or not generous then fred is either happy or strong and vice versa. Everyone who is either not rich or not happy is both happy and calm and vice versa. Everyone who is both not patient and not creative is both not curious and happy. If susan is both not creative and funny then alice is calm and vice versa. If john is either curious or calm then someone is wise and vice versa. If mary is not brave then someone is both not kind and not old and vice versa. If alice is not patient or creative then lucy is curious. Everyone who is either funny or curious is either rich or not old. Everyone who is not tall is funny and vice versa. Everyone who is not wise or generous is creative. Everyone who is not funny is rich or not curious and vice versa. Everyone who is quiet or strong is either curious or not kind and vice versa. If someone is either not humble or old then someone is either brave or not calm. Everyone who is humble or not happy is not rich and vice versa. If paul is either not kind or quiet then someone is not creative or curious and vice versa. Everyone who is tall or not kind is rich or not patient and vice versa. Mary is both strong and not brave. Someone is not tall or creative. Someone is both wise and funny. Alice is happy. Fred is both not kind and calm. Someone is brave. Someone is both calm and not quiet. Fred is tall or not kind. | Paul is tall. | neutral | (((tall(alice)|~generous(alice)))<=>((happy(fred)<~>strong(fred))))&
(![X]:((~rich(X)<~>~happy(X))<=>(happy(X)&calm(X))))&
(![X]:((~patient(X)&~creative(X))=>(~curious(X)&happy(X))))&
(((~creative(susan)&funny(susan)))<=>(calm(alice)))&
(((curious(john)<~>calm(john)))<=>(?[X]:(wise(X))))&
((~brave(mary))<=>(?[X]:((~kind(X)&~old(X)))))&
(((~patient(alice)|creative(alice)))=>(curious(lucy)))&
(![X]:((funny(X)<~>curious(X))=>(rich(X)<~>~old(X))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~wise(X)|generous(X))=>creative(X)))&
(![X]:(~funny(X)<=>(rich(X)|~curious(X))))&
(![X]:((quiet(X)|strong(X))<=>(curious(X)<~>~kind(X))))&
((?[X]:((~humble(X)<~>old(X))))=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((humble(X)|~happy(X))<=>~rich(X)))&
(((~kind(paul)<~>quiet(paul)))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:((tall(X)|~kind(X))<=>(rich(X)|~patient(X))))&
((strong(mary)&~brave(mary)))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:((wise(X)&funny(X))))&
(happy(alice))&
((~kind(fred)&calm(fred)))&
(?[X]:(brave(X)))&
(?[X]:((calm(X)&~quiet(X))))&
((tall(fred)|~kind(fred))) | tall(paul) | [] | null | 0 |
If alice is not tall or rich then someone is either strong or curious and vice versa. Everyone who is rich is both not brave and happy. If alice is brave or strong then john is both brave and strong. If john is either not tall or happy then someone is both generous and not calm. If someone is old then someone is kind. Everyone who is both kind and not old is both patient and quiet and vice versa. If john is strong then john is patient or not tall. Everyone who is funny or not patient is funny or not happy and vice versa. Everyone who is both wise and old is either not kind or funny. If alice is not generous then someone is not rich. Everyone who is not calm is either calm or not tall and vice versa. If someone is not strong then someone is both rich and not kind. Everyone who is wise is either not kind or happy and vice versa. Everyone who is not humble is either humble or not curious and vice versa. Everyone who is both quiet and not happy is either curious or not tall and vice versa. Everyone who is both curious and funny is both not tall and creative. Susan is not strong or brave. Mary is quiet or old. Someone is either creative or not calm. Paul is brave or not strong. Someone is either not funny or not humble. Someone is kind or not rich. | Susan is not brave. | contradiction | (((~tall(alice)|rich(alice)))<=>(?[X]:((strong(X)<~>curious(X)))))&
(![X]:(rich(X)=>(~brave(X)&happy(X))))&
(((brave(alice)|strong(alice)))=>((brave(john)&strong(john))))&
(((~tall(john)<~>happy(john)))=>(?[X]:((generous(X)&~calm(X)))))&
((?[X]:(old(X)))=>(?[X]:(kind(X))))&
(![X]:((kind(X)&~old(X))<=>(patient(X)&quiet(X))))&
((strong(john))=>((patient(john)|~tall(john))))&
(![X]:((funny(X)|~patient(X))<=>(funny(X)|~happy(X))))&
(![X]:((wise(X)&old(X))=>(~kind(X)<~>funny(X))))&
((~generous(alice))=>(?[X]:(~rich(X))))&
(![X]:(~calm(X)<=>(calm(X)<~>~tall(X))))&
((?[X]:(~strong(X)))=>(?[X]:((rich(X)&~kind(X)))))&
(![X]:(wise(X)<=>(~kind(X)<~>happy(X))))&
(![X]:(~humble(X)<=>(humble(X)<~>~curious(X))))&
(![X]:((quiet(X)&~happy(X))<=>(curious(X)<~>~tall(X))))&
(![X]:((curious(X)&funny(X))=>(~tall(X)&creative(X))))&
((~strong(susan)|brave(susan)))&
((quiet(mary)|old(mary)))&
(?[X]:((creative(X)<~>~calm(X))))&
((brave(paul)|~strong(paul)))&
(?[X]:((~funny(X)<~>~humble(X))))&
(?[X]:((kind(X)|~rich(X)))) | ~brave(susan) | [
"p1",
"p10",
"p11",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3007679753644405906408582
% SZS output start Proof for 3007679753644405906408582
2. ! [X0] : (rich(X0) => (happy(X0) & ~brave(X0))) [input p1]
11. ! [X0] : (~calm(X0) <=> (calm(X0) <~> ~tall(X0))) [input p10]
12. ? [X0] : ~strong(X0) => ? [X0] : (~kind(X0) & rich(X0)) [input p11]
14. ! [X0] : (~humble(X0) <=> (humble(X0) <~> ~curious(X0))) [input p13]
15. ! [X0] : ((~happy(X0) & quiet(X0)) <=> (curious(X0) <~> ~tall(X0))) [input p14]
17. brave(susan) | ~strong(susan) [input p16]
23. ~brave(susan) [input hypothesis]
25. ? [X0] : ~strong(X0) => ? [X1] : (~kind(X1) & rich(X1)) [rectify 12]
29. ! [X0] : ((happy(X0) & ~brave(X0)) | ~rich(X0)) [ennf transformation 2]
37. ? [X1] : (~kind(X1) & rich(X1)) | ! [X0] : strong(X0) [ennf transformation 25]
57. ! [X0] : ((~calm(X0) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | calm(X0))) [nnf transformation 11]
58. ? [X0] : (~kind(X0) & rich(X0)) | ! [X1] : strong(X1) [rectify 37]
59. ? [X0] : (~kind(X0) & rich(X0)) => (~kind(sK3) & rich(sK3)) [choice axiom]
60. (~kind(sK3) & rich(sK3)) | ! [X1] : strong(X1) [skolemisation 58,59]
62. ! [X0] : ((~humble(X0) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0)))) & (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | humble(X0))) [nnf transformation 14]
63. ! [X0] : (((~happy(X0) & quiet(X0)) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) & (((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (happy(X0) | ~quiet(X0)))) [nnf transformation 15]
64. ! [X0] : (((~happy(X0) & quiet(X0)) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) & (((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | happy(X0) | ~quiet(X0))) [flattening 63]
80. ~rich(X0) | happy(X0) [cnf transformation 29]
99. ~tall(X0) | calm(X0) | calm(X0) [cnf transformation 57]
101. ~calm(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 57]
103. rich(sK3) | strong(X1) [cnf transformation 60]
107. ~curious(X0) | humble(X0) | humble(X0) [cnf transformation 62]
109. ~humble(X0) | ~curious(X0) | ~humble(X0) [cnf transformation 62]
116. ~happy(X0) | curious(X0) | tall(X0) [cnf transformation 64]
119. brave(susan) | ~strong(susan) [cnf transformation 17]
127. ~brave(susan) [cnf transformation 23]
128. ~curious(X0) | humble(X0) [duplicate literal removal 107]
129. ~humble(X0) | ~curious(X0) [duplicate literal removal 109]
130. ~tall(X0) | calm(X0) [duplicate literal removal 99]
131. ~calm(X0) | ~tall(X0) [duplicate literal removal 101]
207. ~tall(X0) [subsumption resolution 130,131]
209. 17 <=> ! [X1] : strong(X1) [avatar definition]
210. strong(X1) <- (17) [avatar component clause 209]
217. 19 <=> rich(sK3) [avatar definition]
219. rich(sK3) <- (19) [avatar component clause 217]
220. 17 | 19 [avatar split clause 103,217,209]
221. ~curious(X0) [subsumption resolution 128,129]
222. ~happy(X0) | tall(X0) [subsumption resolution 116,221]
223. ~happy(X0) [subsumption resolution 222,207]
227. 20 <=> strong(susan) [avatar definition]
229. ~strong(susan) <- (~20) [avatar component clause 227]
231. 21 <=> brave(susan) [avatar definition]
234. ~20 | 21 [avatar split clause 119,231,227]
273. ~21 [avatar split clause 127,231]
278. $false <- (17, ~20) [resolution 229,210]
279. ~17 | 20 [avatar contradiction clause 278]
282. happy(sK3) <- (19) [resolution 80,219]
285. $false <- (19) [subsumption resolution 282,223]
286. ~19 [avatar contradiction clause 285]
287. $false [avatar sat refutation 220,234,273,279,286]
% SZS output end Proof for 3007679753644405906408582
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
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. | Paul is not strong. | neutral | ((~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)))) | ~strong(paul) | [] | null | 0 |
Everyone who is creative or humble is both not kind and rich.
Everyone who is both kind and not humble is both not happy and not curious and vice versa.
Everyone who is both calm and curious is both not kind and humble and vice versa.
Everyone who is rich or not creative is creative.
If alice is both old and creative then someone is rich or wise.
If susan is brave or tall then john is generous or not patient.
Everyone who is either curious or not brave is calm.
If someone is not calm or humble then john is either not brave or quiet and vice versa.
Everyone who is brave is not calm or happy and vice versa.
If someone is old or funny then susan is not patient and vice versa.
Everyone who is tall is either tall or funny.
Everyone who is both curious and not quiet is both not wise and kind and vice versa.
If someone is both not wise and quiet then paul is either not curious or funny.
Everyone who is funny or happy is either not happy or tall.
Everyone who is happy or not creative is happy or not rich.
Everyone who is not funny or not brave is generous or not strong and vice versa.
Someone is not curious or patient.
Mary is creative or old.
Alice is not humble.
Fred is both tall and not wise.
Mary is not patient.
Someone is not funny.
Fred is patient.
Mary is either funny or quiet. | Susan is not tall. | neutral | (![X]:((creative(X)|humble(X))=>(~kind(X)&rich(X))))&
(![X]:((kind(X)&~humble(X))<=>(~happy(X)&~curious(X))))&
(![X]:((calm(X)&curious(X))<=>(~kind(X)&humble(X))))&
(![X]:((rich(X)|~creative(X))=>creative(X)))&
(((old(alice)&creative(alice)))=>(?[X]:((rich(X)|wise(X)))))&
(((brave(susan)|tall(susan)))=>((generous(john)|~patient(john))))&
(![X]:((curious(X)<~>~brave(X))=>calm(X)))&
((?[X]:((~calm(X)|humble(X))))<=>((~brave(john)<~>quiet(john))))&
(![X]:(brave(X)<=>(~calm(X)|happy(X))))&
((?[X]:((old(X)|funny(X))))<=>(~patient(susan)))&
(![X]:(tall(X)=>(tall(X)<~>funny(X))))&
(![X]:((curious(X)&~quiet(X))<=>(~wise(X)&kind(X))))&
((?[X]:((~wise(X)&quiet(X))))=>((~curious(paul)<~>funny(paul))))&
(![X]:((funny(X)|happy(X))=>(~happy(X)<~>tall(X))))&
(![X]:((happy(X)|~creative(X))=>(happy(X)|~rich(X))))&
(![X]:((~funny(X)|~brave(X))<=>(generous(X)|~strong(X))))&
(?[X]:((~curious(X)|patient(X))))&
((creative(mary)|old(mary)))&
(~humble(alice))&
((tall(fred)&~wise(fred)))&
(~patient(mary))&
(?[X]:(~funny(X)))&
(patient(fred))&
((funny(mary)<~>quiet(mary))) | ~tall(susan) | [] | null | 0 |
Everyone who is patient or not calm is both not tall and not curious. Everyone who is either strong or wise is not wise or not kind and vice versa. If someone is calm then susan is both rich and wise. If someone is not calm then john is kind or quiet. Everyone who is either not humble or not strong is both tall and funny and vice versa. If lucy is old or generous then mary is both not humble and strong and vice versa. Everyone who is not calm or tall is not calm or curious and vice versa. Everyone who is both not tall and strong is quiet or strong and vice versa. If alice is tall or not patient then fred is not rich and vice versa. If fred is both wise and not creative then someone is not creative or not strong and vice versa. If someone is either old or not generous then fred is not wise. If someone is rich then paul is humble. If lucy is both not strong and curious then mary is either not strong or not wise. Everyone who is kind is both tall and brave and vice versa. If lucy is wise then someone is quiet. Everyone who is either not quiet or kind is not old. Someone is both creative and not brave. Susan is either generous or tall. Paul is either not kind or not brave. Lucy is either generous or humble. Someone is both not kind and not old. Susan is either patient or rich. | Susan is strong. | entailment | (![X]:((patient(X)|~calm(X))=>(~tall(X)&~curious(X))))&
(![X]:((strong(X)<~>wise(X))<=>(~wise(X)|~kind(X))))&
((?[X]:(calm(X)))=>((rich(susan)&wise(susan))))&
((?[X]:(~calm(X)))=>((kind(john)|quiet(john))))&
(![X]:((~humble(X)<~>~strong(X))<=>(tall(X)&funny(X))))&
(((old(lucy)|generous(lucy)))<=>((~humble(mary)&strong(mary))))&
(![X]:((~calm(X)|tall(X))<=>(~calm(X)|curious(X))))&
(![X]:((~tall(X)&strong(X))<=>(quiet(X)|strong(X))))&
(((tall(alice)|~patient(alice)))<=>(~rich(fred)))&
(((wise(fred)&~creative(fred)))<=>(?[X]:((~creative(X)|~strong(X)))))&
((?[X]:((old(X)<~>~generous(X))))=>(~wise(fred)))&
((?[X]:(rich(X)))=>(humble(paul)))&
(((~strong(lucy)&curious(lucy)))=>((~strong(mary)<~>~wise(mary))))&
(![X]:(kind(X)<=>(tall(X)&brave(X))))&
((wise(lucy))=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)<~>kind(X))=>~old(X)))&
(?[X]:((creative(X)&~brave(X))))&
((generous(susan)<~>tall(susan)))&
((~kind(paul)<~>~brave(paul)))&
((generous(lucy)<~>humble(lucy)))&
(?[X]:((~kind(X)&~old(X))))&
((patient(susan)<~>rich(susan))) | strong(susan) | [
"p4",
"p5",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1972651405880807128922663
% SZS output start Proof for 1972651405880807128922663
5. ! [X0] : ((~humble(X0) <~> ~strong(X0)) <=> (funny(X0) & tall(X0))) [input p4]
6. (generous(lucy) | old(lucy)) <=> (strong(mary) & ~humble(mary)) [input p5]
8. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (strong(X0) | quiet(X0))) [input p7]
10. (~creative(fred) & wise(fred)) <=> ? [X0] : (~strong(X0) | ~creative(X0)) [input p9]
11. ? [X0] : (old(X0) <~> ~generous(X0)) => ~wise(fred) [input p10]
23. ~strong(susan) [input hypothesis]
28. ~wise(fred) | ! [X0] : (old(X0) <=> ~generous(X0)) [ennf transformation 11]
36. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (~funny(X0) | ~tall(X0))) & ((funny(X0) & tall(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [nnf transformation 5]
37. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ~funny(X0) | ~tall(X0)) & ((funny(X0) & tall(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [flattening 36]
38. ((generous(lucy) | old(lucy)) | (~strong(mary) | humble(mary))) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [nnf transformation 6]
39. (generous(lucy) | old(lucy) | ~strong(mary) | humble(mary)) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [flattening 38]
42. ! [X0] : (((strong(X0) & ~tall(X0)) | (~strong(X0) & ~quiet(X0))) & ((strong(X0) | quiet(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 8]
43. ! [X0] : (((strong(X0) & ~tall(X0)) | (~strong(X0) & ~quiet(X0))) & (strong(X0) | quiet(X0) | ~strong(X0) | tall(X0))) [flattening 42]
46. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | (creative(fred) | ~wise(fred))) [nnf transformation 10]
47. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | creative(fred) | ~wise(fred)) [flattening 46]
48. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X1] : (~strong(X1) | ~creative(X1)) | creative(fred) | ~wise(fred)) [rectify 47]
49. ? [X1] : (~strong(X1) | ~creative(X1)) => (~strong(sK0) | ~creative(sK0)) [choice axiom]
50. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & ((~strong(sK0) | ~creative(sK0)) | creative(fred) | ~wise(fred)) [skolemisation 48,49]
51. ~wise(fred) | ! [X0] : ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0))) [nnf transformation 28]
79. ~strong(X0) | tall(X0) | humble(X0) [cnf transformation 37]
85. ~humble(mary) | ~old(lucy) [cnf transformation 39]
86. ~humble(mary) | ~generous(lucy) [cnf transformation 39]
87. strong(mary) | ~old(lucy) [cnf transformation 39]
88. strong(mary) | ~generous(lucy) [cnf transformation 39]
96. ~strong(X0) | ~tall(X0) [cnf transformation 43]
104. wise(fred) | strong(X0) [cnf transformation 50]
108. ~wise(fred) | old(X0) | generous(X0) [cnf transformation 51]
130. ~strong(susan) [cnf transformation 23]
160. 7 <=> humble(mary) [avatar definition]
164. 8 <=> strong(mary) [avatar definition]
165. strong(mary) <- (8) [avatar component clause 164]
168. 9 <=> old(lucy) [avatar definition]
169. ~old(lucy) <- (~9) [avatar component clause 168]
172. 10 <=> generous(lucy) [avatar definition]
173. ~generous(lucy) <- (~10) [avatar component clause 172]
176. ~10 | 8 [avatar split clause 88,164,172]
177. ~9 | 8 [avatar split clause 87,164,168]
178. ~10 | ~7 [avatar split clause 86,160,172]
179. ~9 | ~7 [avatar split clause 85,160,168]
199. 14 <=> ! [X0] : strong(X0) [avatar definition]
200. strong(X0) <- (14) [avatar component clause 199]
211. 17 <=> wise(fred) [avatar definition]
214. 14 | 17 [avatar split clause 104,211,199]
226. 20 <=> ! [X0] : (old(X0) | generous(X0)) [avatar definition]
227. generous(X0) | old(X0) <- (20) [avatar component clause 226]
228. 20 | ~17 [avatar split clause 108,211,226]
289. $false <- (14) [resolution 200,130]
290. ~14 [avatar contradiction clause 289]
295. ~tall(mary) <- (8) [resolution 96,165]
321. tall(mary) | humble(mary) <- (8) [resolution 79,165]
323. humble(mary) <- (8) [subsumption resolution 321,295]
329. 7 | ~8 [avatar split clause 323,164,160]
331. old(lucy) <- (~10, 20) [resolution 173,227]
332. $false <- (~9, ~10, 20) [subsumption resolution 331,169]
333. 9 | 10 | ~20 [avatar contradiction clause 332]
334. $false [avatar sat refutation 176,177,178,179,214,228,290,329,333]
% SZS output end Proof for 1972651405880807128922663
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is rich.
Everyone who is either not humble or quiet is either happy or not old.
Everyone who is generous or not patient is humble or quiet and vice versa.
Everyone who is either creative or old is both happy and not rich and vice versa.
Everyone who is both funny and not generous is kind and vice versa.
Everyone who is both not wise and not rich is either not humble or patient.
Everyone who is either not creative or happy is humble or calm and vice versa.
Everyone who is kind is both quiet and not strong and vice versa.
If someone is funny then mary is either curious or wise and vice versa.
Everyone who is not creative is both not generous and patient.
Everyone who is not wise or not creative is patient.
If someone is either kind or not tall then someone is calm or kind.
If someone is both old and calm then john is both tall and rich.
Everyone who is either not rich or happy is either old or quiet.
Everyone who is either not curious or patient is wise and vice versa.
Everyone who is either wise or generous is funny and vice versa.
Someone is wise or humble.
Paul is either rich or not funny.
Someone is either tall or strong.
Someone is both not creative and not kind.
Lucy is both calm and not happy.
Paul is not brave or not rich.
Someone is either not creative or brave.
Someone is either not happy or funny. | Lucy is not quiet. | entailment | (![X]:(~curious(X)=>rich(X)))&
(![X]:((~humble(X)<~>quiet(X))=>(happy(X)<~>~old(X))))&
(![X]:((generous(X)|~patient(X))<=>(humble(X)|quiet(X))))&
(![X]:((creative(X)<~>old(X))<=>(happy(X)&~rich(X))))&
(![X]:((funny(X)&~generous(X))<=>kind(X)))&
(![X]:((~wise(X)&~rich(X))=>(~humble(X)<~>patient(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(humble(X)|calm(X))))&
(![X]:(kind(X)<=>(quiet(X)&~strong(X))))&
((?[X]:(funny(X)))<=>((curious(mary)<~>wise(mary))))&
(![X]:(~creative(X)=>(~generous(X)&patient(X))))&
(![X]:((~wise(X)|~creative(X))=>patient(X)))&
((?[X]:((kind(X)<~>~tall(X))))=>(?[X]:((calm(X)|kind(X)))))&
((?[X]:((old(X)&calm(X))))=>((tall(john)&rich(john))))&
(![X]:((~rich(X)<~>happy(X))=>(old(X)<~>quiet(X))))&
(![X]:((~curious(X)<~>patient(X))<=>wise(X)))&
(![X]:((wise(X)<~>generous(X))<=>funny(X)))&
(?[X]:((wise(X)|humble(X))))&
((rich(paul)<~>~funny(paul)))&
(?[X]:((tall(X)<~>strong(X))))&
(?[X]:((~creative(X)&~kind(X))))&
((calm(lucy)&~happy(lucy)))&
((~brave(paul)|~rich(paul)))&
(?[X]:((~creative(X)<~>brave(X))))&
(?[X]:((~happy(X)<~>funny(X)))) | ~quiet(lucy) | [
"p2",
"p6",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 798808644080102709665
% SZS output start Proof for 798808644080102709665
3. ! [X0] : ((~patient(X0) | generous(X0)) <=> (quiet(X0) | humble(X0))) [input p2]
7. ! [X0] : ((~creative(X0) <~> happy(X0)) <=> (calm(X0) | humble(X0))) [input p6]
10. ! [X0] : (~creative(X0) => (patient(X0) & ~generous(X0))) [input p9]
21. ~happy(lucy) & calm(lucy) [input p20]
25. quiet(lucy) [input hypothesis]
31. ! [X0] : ((patient(X0) & ~generous(X0)) | creative(X0)) [ennf transformation 10]
37. ! [X0] : (((~patient(X0) | generous(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (patient(X0) & ~generous(X0)))) [nnf transformation 3]
38. ! [X0] : ((~patient(X0) | generous(X0) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | (patient(X0) & ~generous(X0)))) [flattening 37]
44. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~calm(X0) & ~humble(X0))) & ((calm(X0) | humble(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [nnf transformation 7]
45. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~calm(X0) & ~humble(X0))) & (calm(X0) | humble(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [flattening 44]
81. ~patient(X0) | generous(X0) | ~quiet(X0) [cnf transformation 38]
96. ~calm(X0) | ~creative(X0) | happy(X0) [cnf transformation 45]
106. ~generous(X0) | creative(X0) [cnf transformation 31]
107. creative(X0) | patient(X0) [cnf transformation 31]
133. calm(lucy) [cnf transformation 21]
134. ~happy(lucy) [cnf transformation 21]
140. quiet(lucy) [cnf transformation 25]
326. ~creative(lucy) | happy(lucy) [resolution 96,133]
328. ~creative(lucy) [subsumption resolution 326,134]
338. patient(lucy) [resolution 328,107]
479. generous(lucy) | ~quiet(lucy) [resolution 338,81]
490. 56 <=> generous(lucy) [avatar definition]
492. generous(lucy) <- (56) [avatar component clause 490]
494. generous(lucy) [subsumption resolution 479,140]
495. 56 [avatar split clause 494,490]
850. creative(lucy) <- (56) [resolution 492,106]
856. $false <- (56) [subsumption resolution 850,328]
857. ~56 [avatar contradiction clause 856]
858. $false [avatar sat refutation 495,857]
% SZS output end Proof for 798808644080102709665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
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. | Lucy is not wise. | 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))) | ~wise(lucy) | [
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3849713161321021341466710
% SZS output start Proof for 3849713161321021341466710
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. ~wise(lucy) [input hypothesis]
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]
78. ~quiet(X0) | wise(X0) [cnf transformation 45]
83. wise(X0) | quiet(X0) [cnf transformation 47]
119. ~wise(lucy) [cnf transformation 23]
166. wise(X0) [subsumption resolution 83,78]
255. $false [subsumption resolution 119,166]
% SZS output end Proof for 3849713161321021341466710
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then someone is both not tall and patient and vice versa. Everyone who is not tall or not calm is tall or strong. If someone is either happy or not calm then someone is kind or tall. Everyone who is kind is not happy and vice versa. If john is both quiet and funny then someone is either not creative or humble and vice versa. If someone is old then john is both brave and not rich and vice versa. Everyone who is either calm or not tall is both not creative and calm. If someone is tall or quiet then someone is not funny and vice versa. If someone is happy then someone is either quiet or not old. Everyone who is not kind or not funny is either not kind or humble and vice versa. Everyone who is both quiet and not generous is both not patient and not old. If paul is both happy and not calm then lucy is calm or strong and vice versa. If fred is not quiet then someone is both old and generous and vice versa. If someone is not curious or funny then mary is both not wise and old. Everyone who is either not strong or not funny is both happy and not brave and vice versa. Everyone who is not humble is either wise or old and vice versa. Someone is either not old or calm. John is both not strong and kind. Fred is both not humble and not calm. Susan is both not happy and generous. Someone is funny. Someone is not calm. | John is not creative. | entailment | ((?[X]:(~happy(X)))<=>(?[X]:((~tall(X)&patient(X)))))&
(![X]:((~tall(X)|~calm(X))=>(tall(X)|strong(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((kind(X)|tall(X)))))&
(![X]:(kind(X)<=>~happy(X)))&
(((quiet(john)&funny(john)))<=>(?[X]:((~creative(X)<~>humble(X)))))&
((?[X]:(old(X)))<=>((brave(john)&~rich(john))))&
(![X]:((calm(X)<~>~tall(X))=>(~creative(X)&calm(X))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:(~funny(X))))&
((?[X]:(happy(X)))=>(?[X]:((quiet(X)<~>~old(X)))))&
(![X]:((~kind(X)|~funny(X))<=>(~kind(X)<~>humble(X))))&
(![X]:((quiet(X)&~generous(X))=>(~patient(X)&~old(X))))&
(((happy(paul)&~calm(paul)))<=>((calm(lucy)|strong(lucy))))&
((~quiet(fred))<=>(?[X]:((old(X)&generous(X)))))&
((?[X]:((~curious(X)|funny(X))))=>((~wise(mary)&old(mary))))&
(![X]:((~strong(X)<~>~funny(X))<=>(happy(X)&~brave(X))))&
(![X]:(~humble(X)<=>(wise(X)<~>old(X))))&
(?[X]:((~old(X)<~>calm(X))))&
((~strong(john)&kind(john)))&
((~humble(fred)&~calm(fred)))&
((~happy(susan)&generous(susan)))&
(?[X]:(funny(X)))&
(?[X]:(~calm(X))) | ~creative(john) | [
"p3",
"p4",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8571557146202712972189998
% SZS output start Proof for 8571557146202712972189998
4. ! [X0] : (kind(X0) <=> ~happy(X0)) [input p3]
5. (funny(john) & quiet(john)) <=> ? [X0] : (~creative(X0) <~> humble(X0)) [input p4]
10. ! [X0] : ((~funny(X0) | ~kind(X0)) <=> (~kind(X0) <~> humble(X0))) [input p9]
15. ! [X0] : ((~strong(X0) <~> ~funny(X0)) <=> (~brave(X0) & happy(X0))) [input p14]
18. kind(john) & ~strong(john) [input p17]
23. creative(john) [input hypothesis]
46. ! [X0] : ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))) [nnf transformation 4]
47. ((funny(john) & quiet(john)) | ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0)))) & (? [X0] : ((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | (~funny(john) | ~quiet(john))) [nnf transformation 5]
48. ((funny(john) & quiet(john)) | ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0)))) & (? [X0] : ((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | ~funny(john) | ~quiet(john)) [flattening 47]
49. ((funny(john) & quiet(john)) | ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0)))) & (? [X1] : ((~humble(X1) | creative(X1)) & (humble(X1) | ~creative(X1))) | ~funny(john) | ~quiet(john)) [rectify 48]
50. ? [X1] : ((~humble(X1) | creative(X1)) & (humble(X1) | ~creative(X1))) => ((~humble(sK3) | creative(sK3)) & (humble(sK3) | ~creative(sK3))) [choice axiom]
51. ((funny(john) & quiet(john)) | ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0)))) & (((~humble(sK3) | creative(sK3)) & (humble(sK3) | ~creative(sK3))) | ~funny(john) | ~quiet(john)) [skolemisation 49,50]
67. ! [X0] : (((~funny(X0) | ~kind(X0)) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0)))) & (((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | (funny(X0) & kind(X0)))) [nnf transformation 10]
68. ! [X0] : ((~funny(X0) | ~kind(X0) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0)))) & (((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | (funny(X0) & kind(X0)))) [flattening 67]
75. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [nnf transformation 15]
76. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [flattening 75]
92. ~kind(X0) | ~happy(X0) [cnf transformation 46]
99. funny(john) | ~creative(X0) | ~humble(X0) [cnf transformation 51]
113. ~kind(X0) | humble(X0) | funny(X0) [cnf transformation 68]
130. ~funny(X0) | happy(X0) | strong(X0) [cnf transformation 76]
142. ~strong(john) [cnf transformation 18]
143. kind(john) [cnf transformation 18]
150. creative(john) [cnf transformation 23]
193. 10 <=> ! [X0] : (~creative(X0) | ~humble(X0)) [avatar definition]
194. ~humble(X0) | ~creative(X0) <- (10) [avatar component clause 193]
196. 11 <=> funny(john) [avatar definition]
198. funny(john) <- (11) [avatar component clause 196]
199. 10 | 11 [avatar split clause 99,196,193]
345. ~happy(john) [resolution 92,143]
366. humble(john) | funny(john) [resolution 113,143]
370. 42 <=> humble(john) [avatar definition]
372. humble(john) <- (42) [avatar component clause 370]
373. 11 | 42 [avatar split clause 366,370,196]
416. happy(john) | strong(john) <- (11) [resolution 130,198]
427. strong(john) <- (11) [subsumption resolution 416,345]
428. $false <- (11) [subsumption resolution 427,142]
429. ~11 [avatar contradiction clause 428]
434. ~creative(john) <- (10, 42) [resolution 372,194]
436. $false <- (10, 42) [subsumption resolution 434,150]
437. ~10 | ~42 [avatar contradiction clause 436]
438. $false [avatar sat refutation 199,373,429,437]
% SZS output end Proof for 8571557146202712972189998
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or creative is either creative or old.
Everyone who is both curious and not rich is not funny or humble.
Everyone who is not happy is both not patient and not brave.
Everyone who is humble or kind is either creative or not curious and vice versa.
If alice is not humble then someone is both not old and generous and vice versa.
If someone is both not tall and not patient then lucy is both not creative and not calm and vice versa.
If someone is both not kind and patient then someone is not humble or not calm and vice versa.
If someone is quiet then someone is not kind and vice versa.
If someone is not wise then someone is both curious and strong.
Everyone who is happy is strong.
If someone is not quiet then susan is not tall or quiet.
Everyone who is not strong is both happy and strong and vice versa.
If someone is both not generous and generous then susan is kind or not generous and vice versa.
Everyone who is generous is not happy or not tall.
Someone is humble or not creative.
Someone is brave or not patient.
John is either not strong or calm.
Someone is not brave.
Someone is both not wise and not old.
Paul is not happy or not brave. | John is brave. | contradiction | (![X]:((funny(X)|creative(X))=>(creative(X)<~>old(X))))&
(![X]:((curious(X)&~rich(X))=>(~funny(X)|humble(X))))&
(![X]:(~happy(X)=>(~patient(X)&~brave(X))))&
(![X]:((humble(X)|kind(X))<=>(creative(X)<~>~curious(X))))&
((~humble(alice))<=>(?[X]:((~old(X)&generous(X)))))&
((?[X]:((~tall(X)&~patient(X))))<=>((~creative(lucy)&~calm(lucy))))&
((?[X]:((~kind(X)&patient(X))))<=>(?[X]:((~humble(X)|~calm(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:(~kind(X))))&
((?[X]:(~wise(X)))=>(?[X]:((curious(X)&strong(X)))))&
(![X]:(happy(X)=>strong(X)))&
((?[X]:(~quiet(X)))=>((~tall(susan)|quiet(susan))))&
(![X]:(~strong(X)<=>(happy(X)&strong(X))))&
((?[X]:((~generous(X)&generous(X))))<=>((kind(susan)|~generous(susan))))&
(![X]:(generous(X)=>(~happy(X)|~tall(X))))&
(?[X]:((humble(X)|~creative(X))))&
(?[X]:((brave(X)|~patient(X))))&
((~strong(john)<~>calm(john)))&
(?[X]:(~brave(X)))&
(?[X]:((~wise(X)&~old(X))))&
((~happy(paul)|~brave(paul))) | brave(john) | [
"p2",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5487159645364466274813916
% SZS output start Proof for 5487159645364466274813916
3. ! [X0] : (~happy(X0) => (~brave(X0) & ~patient(X0))) [input p2]
10. ! [X0] : (happy(X0) => strong(X0)) [input p9]
12. ! [X0] : (~strong(X0) <=> (strong(X0) & happy(X0))) [input p11]
21. brave(john) [input hypothesis]
28. ! [X0] : ((~brave(X0) & ~patient(X0)) | happy(X0)) [ennf transformation 3]
30. ! [X0] : (strong(X0) | ~happy(X0)) [ennf transformation 10]
60. ! [X0] : ((~strong(X0) | (~strong(X0) | ~happy(X0))) & ((strong(X0) & happy(X0)) | strong(X0))) [nnf transformation 12]
61. ! [X0] : ((~strong(X0) | ~strong(X0) | ~happy(X0)) & ((strong(X0) & happy(X0)) | strong(X0))) [flattening 60]
79. ~brave(X0) | happy(X0) [cnf transformation 28]
102. strong(X0) | ~happy(X0) [cnf transformation 30]
106. ~strong(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 61]
121. brave(john) [cnf transformation 21]
123. ~strong(X0) | ~happy(X0) [duplicate literal removal 106]
237. ~happy(X0) [subsumption resolution 123,102]
288. happy(john) [resolution 79,121]
289. $false [subsumption resolution 288,237]
% SZS output end Proof for 5487159645364466274813916
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is both old and calm and vice versa.
Everyone who is both not creative and not old is tall.
Everyone who is either creative or not rich is both quiet and not wise.
Everyone who is either not wise or strong is either creative or patient.
Everyone who is not brave is curious or old.
If someone is both old and wise then lucy is either creative or not brave.
If someone is calm then someone is happy or not wise and vice versa.
Everyone who is not patient or strong is both quiet and not funny and vice versa.
If someone is not tall then john is both not brave and not creative.
Everyone who is not wise or rich is both funny and not curious.
If someone is not patient or not rich then someone is either not tall or not strong.
If paul is not strong or not quiet then john is both not tall and not brave.
If lucy is both old and creative then john is not humble.
If john is either creative or not kind then paul is both not brave and not rich and vice versa.
If lucy is either generous or quiet then lucy is not old.
Mary is either not tall or not curious.
Someone is quiet.
Susan is both not generous and happy.
Alice is strong or not tall.
Alice is either not happy or not brave.
Someone is either not happy or rich.
Someone is strong or patient. | Mary is tall. | entailment | (![X]:(~calm(X)<=>(old(X)&calm(X))))&
(![X]:((~creative(X)&~old(X))=>tall(X)))&
(![X]:((creative(X)<~>~rich(X))=>(quiet(X)&~wise(X))))&
(![X]:((~wise(X)<~>strong(X))=>(creative(X)<~>patient(X))))&
(![X]:(~brave(X)=>(curious(X)|old(X))))&
((?[X]:((old(X)&wise(X))))=>((creative(lucy)<~>~brave(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((happy(X)|~wise(X)))))&
(![X]:((~patient(X)|strong(X))<=>(quiet(X)&~funny(X))))&
((?[X]:(~tall(X)))=>((~brave(john)&~creative(john))))&
(![X]:((~wise(X)|rich(X))=>(funny(X)&~curious(X))))&
((?[X]:((~patient(X)|~rich(X))))=>(?[X]:((~tall(X)<~>~strong(X)))))&
(((~strong(paul)|~quiet(paul)))=>((~tall(john)&~brave(john))))&
(((old(lucy)&creative(lucy)))=>(~humble(john)))&
(((creative(john)<~>~kind(john)))<=>((~brave(paul)&~rich(paul))))&
(((generous(lucy)<~>quiet(lucy)))=>(~old(lucy)))&
((~tall(mary)<~>~curious(mary)))&
(?[X]:(quiet(X)))&
((~generous(susan)&happy(susan)))&
((strong(alice)|~tall(alice)))&
((~happy(alice)<~>~brave(alice)))&
(?[X]:((~happy(X)<~>rich(X))))&
(?[X]:((strong(X)|patient(X)))) | tall(mary) | [
"p0",
"p2",
"p4",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8226462589537779799191776
% SZS output start Proof for 8226462589537779799191776
1. ! [X0] : (~calm(X0) <=> (calm(X0) & old(X0))) [input p0]
3. ! [X0] : ((creative(X0) <~> ~rich(X0)) => (~wise(X0) & quiet(X0))) [input p2]
5. ! [X0] : (~brave(X0) => (old(X0) | curious(X0))) [input p4]
9. ? [X0] : ~tall(X0) => (~creative(john) & ~brave(john)) [input p8]
10. ! [X0] : ((rich(X0) | ~wise(X0)) => (~curious(X0) & funny(X0))) [input p9]
23. ~tall(mary) [input hypothesis]
29. ! [X0] : ((~wise(X0) & quiet(X0)) | (creative(X0) <=> ~rich(X0))) [ennf transformation 3]
31. ! [X0] : ((old(X0) | curious(X0)) | brave(X0)) [ennf transformation 5]
32. ! [X0] : (old(X0) | curious(X0) | brave(X0)) [flattening 31]
34. (~creative(john) & ~brave(john)) | ! [X0] : tall(X0) [ennf transformation 9]
35. ! [X0] : ((~curious(X0) & funny(X0)) | (~rich(X0) & wise(X0))) [ennf transformation 10]
39. ! [X0] : ((~calm(X0) | (~calm(X0) | ~old(X0))) & ((calm(X0) & old(X0)) | calm(X0))) [nnf transformation 1]
40. ! [X0] : ((~calm(X0) | ~calm(X0) | ~old(X0)) & ((calm(X0) & old(X0)) | calm(X0))) [flattening 39]
41. ! [X0] : ((~wise(X0) & quiet(X0)) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 29]
68. calm(X0) | calm(X0) [cnf transformation 40]
69. ~calm(X0) | ~calm(X0) | ~old(X0) [cnf transformation 40]
74. ~wise(X0) | creative(X0) | rich(X0) [cnf transformation 41]
79. curious(X0) | old(X0) | brave(X0) [cnf transformation 32]
90. ~brave(john) | tall(X0) [cnf transformation 34]
91. ~creative(john) | tall(X0) [cnf transformation 34]
94. ~curious(X0) | wise(X0) [cnf transformation 35]
95. ~curious(X0) | ~rich(X0) [cnf transformation 35]
123. ~tall(mary) [cnf transformation 23]
124. calm(X0) [duplicate literal removal 68]
125. ~old(X0) | ~calm(X0) [duplicate literal removal 69]
150. 6 <=> ! [X0] : tall(X0) [avatar definition]
151. tall(X0) <- (6) [avatar component clause 150]
153. 7 <=> creative(john) [avatar definition]
155. ~creative(john) <- (~7) [avatar component clause 153]
156. 6 | ~7 [avatar split clause 91,153,150]
158. 8 <=> brave(john) [avatar definition]
160. ~brave(john) <- (~8) [avatar component clause 158]
161. 6 | ~8 [avatar split clause 90,158,150]
229. 22 <=> tall(mary) [avatar definition]
230. ~tall(mary) <- (~22) [avatar component clause 229]
276. ~22 [avatar split clause 123,229]
337. ~rich(X0) | brave(X0) | old(X0) [resolution 79,95]
338. brave(X1) | old(X1) | wise(X1) [resolution 79,94]
383. old(john) | wise(john) <- (~8) [resolution 338,160]
388. 41 <=> wise(john) [avatar definition]
390. wise(john) <- (41) [avatar component clause 388]
392. 42 <=> old(john) [avatar definition]
394. old(john) <- (42) [avatar component clause 392]
395. 41 | 42 | 8 [avatar split clause 383,158,392,388]
402. creative(john) | rich(john) <- (41) [resolution 390,74]
404. rich(john) <- (~7, 41) [subsumption resolution 402,155]
433. brave(john) | old(john) <- (~7, 41) [resolution 404,337]
441. $false <- (6, ~22) [resolution 151,230]
444. ~6 | 22 [avatar contradiction clause 441]
450. 42 | 8 | 7 | ~41 [avatar split clause 433,388,153,158,392]
457. ~calm(john) <- (42) [resolution 394,125]
458. $false <- (42) [subsumption resolution 457,124]
459. ~42 [avatar contradiction clause 458]
460. $false [avatar sat refutation 156,161,276,395,444,450,459]
% SZS output end Proof for 8226462589537779799191776
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If alice is not humble or not wise then paul is either not quiet or not strong and vice versa.
If someone is generous or not tall then alice is kind or brave.
If fred is either not happy or tall then someone is old and vice versa.
Everyone who is not creative is creative or tall and vice versa.
Everyone who is humble or not funny is not rich and vice versa.
Everyone who is either tall or funny is both not generous and not old and vice versa.
Everyone who is not wise is not tall and vice versa.
Everyone who is funny or happy is either not funny or brave.
Everyone who is either brave or not quiet is either patient or funny.
If someone is funny then someone is not generous or generous and vice versa.
Everyone who is either not old or strong is either patient or not wise.
If someone is either not old or not rich then someone is either strong or calm.
Everyone who is not strong or patient is either brave or not happy.
Everyone who is not tall or not curious is not tall.
If susan is not tall or not humble then someone is either quiet or not calm.
Everyone who is either happy or humble is generous and vice versa.
Lucy is both happy and brave.
John is either humble or tall.
Someone is old.
Paul is funny or not tall.
Someone is either not brave or calm.
Someone is calm.
Someone is either not curious or curious. | Lucy is not creative. | entailment | (((~humble(alice)|~wise(alice)))<=>((~quiet(paul)<~>~strong(paul))))&
((?[X]:((generous(X)|~tall(X))))=>((kind(alice)|brave(alice))))&
(((~happy(fred)<~>tall(fred)))<=>(?[X]:(old(X))))&
(![X]:(~creative(X)<=>(creative(X)|tall(X))))&
(![X]:((humble(X)|~funny(X))<=>~rich(X)))&
(![X]:((tall(X)<~>funny(X))<=>(~generous(X)&~old(X))))&
(![X]:(~wise(X)<=>~tall(X)))&
(![X]:((funny(X)|happy(X))=>(~funny(X)<~>brave(X))))&
(![X]:((brave(X)<~>~quiet(X))=>(patient(X)<~>funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:((~old(X)<~>strong(X))=>(patient(X)<~>~wise(X))))&
((?[X]:((~old(X)<~>~rich(X))))=>(?[X]:((strong(X)<~>calm(X)))))&
(![X]:((~strong(X)|patient(X))=>(brave(X)<~>~happy(X))))&
(![X]:((~tall(X)|~curious(X))=>~tall(X)))&
(((~tall(susan)|~humble(susan)))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((happy(X)<~>humble(X))<=>generous(X)))&
((happy(lucy)&brave(lucy)))&
((humble(john)<~>tall(john)))&
(?[X]:(old(X)))&
((funny(paul)|~tall(paul)))&
(?[X]:((~brave(X)<~>calm(X))))&
(?[X]:(calm(X)))&
(?[X]:((~curious(X)<~>curious(X)))) | ~creative(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7601112572886172358310075
% SZS output start Proof for 7601112572886172358310075
4. ! [X0] : (~creative(X0) <=> (tall(X0) | creative(X0))) [input p3]
24. creative(lucy) [input hypothesis]
41. ! [X0] : ((~creative(X0) | (~tall(X0) & ~creative(X0))) & ((tall(X0) | creative(X0)) | creative(X0))) [nnf transformation 4]
42. ! [X0] : ((~creative(X0) | (~tall(X0) & ~creative(X0))) & (tall(X0) | creative(X0) | creative(X0))) [flattening 41]
87. ~creative(X0) | ~creative(X0) [cnf transformation 42]
144. creative(lucy) [cnf transformation 24]
147. ~creative(X0) [duplicate literal removal 87]
255. $false [subsumption resolution 144,147]
% SZS output end Proof for 7601112572886172358310075
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and calm is generous or calm and vice versa. If someone is both rich and not kind then mary is kind or not strong. Everyone who is either funny or not rich is old or generous. If someone is either happy or not patient then fred is not kind and vice versa. Everyone who is either not wise or happy is calm or old. If someone is either not patient or old then lucy is not tall or not old and vice versa. If fred is humble or calm then someone is not kind or tall. Everyone who is either not humble or not wise is humble. Everyone who is brave or funny is either funny or rich. If someone is either happy or not patient then paul is both patient and not rich. Everyone who is both not happy and not patient is not curious or funny and vice versa. Everyone who is both not calm and not strong is both not tall and brave and vice versa. Everyone who is either not old or not kind is not quiet. If john is both not strong and strong then someone is not wise and vice versa. If fred is strong or tall then john is both not old and rich and vice versa. Everyone who is humble or kind is happy. Alice is not rich. Alice is not kind. Susan is wise. Someone is not brave. John is either kind or wise. Someone is quiet or wise. | Mary is funny. | contradiction | (![X]:((~old(X)&calm(X))<=>(generous(X)|calm(X))))&
((?[X]:((rich(X)&~kind(X))))=>((kind(mary)|~strong(mary))))&
(![X]:((funny(X)<~>~rich(X))=>(old(X)|generous(X))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(~kind(fred)))&
(![X]:((~wise(X)<~>happy(X))=>(calm(X)|old(X))))&
((?[X]:((~patient(X)<~>old(X))))<=>((~tall(lucy)|~old(lucy))))&
(((humble(fred)|calm(fred)))=>(?[X]:((~kind(X)|tall(X)))))&
(![X]:((~humble(X)<~>~wise(X))=>humble(X)))&
(![X]:((brave(X)|funny(X))=>(funny(X)<~>rich(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>((patient(paul)&~rich(paul))))&
(![X]:((~happy(X)&~patient(X))<=>(~curious(X)|funny(X))))&
(![X]:((~calm(X)&~strong(X))<=>(~tall(X)&brave(X))))&
(![X]:((~old(X)<~>~kind(X))=>~quiet(X)))&
(((~strong(john)&strong(john)))<=>(?[X]:(~wise(X))))&
(((strong(fred)|tall(fred)))<=>((~old(john)&rich(john))))&
(![X]:((humble(X)|kind(X))=>happy(X)))&
(~rich(alice))&
(~kind(alice))&
(wise(susan))&
(?[X]:(~brave(X)))&
((kind(john)<~>wise(john)))&
(?[X]:((quiet(X)|wise(X)))) | funny(mary) | [
"p7",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1648440029127161652933294
% SZS output start Proof for 1648440029127161652933294
8. ! [X0] : ((~humble(X0) <~> ~wise(X0)) => humble(X0)) [input p7]
11. ! [X0] : ((~patient(X0) & ~happy(X0)) <=> (funny(X0) | ~curious(X0))) [input p10]
14. (strong(john) & ~strong(john)) <=> ? [X0] : ~wise(X0) [input p13]
16. ! [X0] : ((kind(X0) | humble(X0)) => happy(X0)) [input p15]
23. funny(mary) [input hypothesis]
31. ! [X0] : (humble(X0) | (~humble(X0) <=> ~wise(X0))) [ennf transformation 8]
35. ! [X0] : (happy(X0) | (~kind(X0) & ~humble(X0))) [ennf transformation 16]
51. ! [X0] : (humble(X0) | ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0)))) [nnf transformation 31]
54. ! [X0] : (((~patient(X0) & ~happy(X0)) | (~funny(X0) & curious(X0))) & ((funny(X0) | ~curious(X0)) | (patient(X0) | happy(X0)))) [nnf transformation 11]
55. ! [X0] : (((~patient(X0) & ~happy(X0)) | (~funny(X0) & curious(X0))) & (funny(X0) | ~curious(X0) | patient(X0) | happy(X0))) [flattening 54]
59. ((strong(john) & ~strong(john)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | (~strong(john) | strong(john))) [nnf transformation 14]
60. ((strong(john) & ~strong(john)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | ~strong(john) | strong(john)) [flattening 59]
61. ((strong(john) & ~strong(john)) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | ~strong(john) | strong(john)) [rectify 60]
62. ? [X1] : ~wise(X1) => ~wise(sK3) [choice axiom]
63. ((strong(john) & ~strong(john)) | ! [X0] : wise(X0)) & (~wise(sK3) | ~strong(john) | strong(john)) [skolemisation 61,62]
93. humble(X0) | ~wise(X0) | humble(X0) [cnf transformation 51]
105. ~happy(X0) | ~funny(X0) [cnf transformation 55]
115. ~strong(john) | wise(X0) [cnf transformation 63]
116. strong(john) | wise(X0) [cnf transformation 63]
122. ~humble(X0) | happy(X0) [cnf transformation 35]
131. funny(mary) [cnf transformation 23]
133. ~wise(X0) | humble(X0) [duplicate literal removal 93]
227. 21 <=> ! [X0] : wise(X0) [avatar definition]
228. wise(X0) <- (21) [avatar component clause 227]
230. 22 <=> strong(john) [avatar definition]
233. 21 | 22 [avatar split clause 116,230,227]
234. 21 | ~22 [avatar split clause 115,230,227]
279. humble(X0) <- (21) [resolution 133,228]
294. happy(X0) <- (21) [resolution 279,122]
399. ~funny(X0) <- (21) [resolution 294,105]
427. $false <- (21) [resolution 399,131]
430. ~21 [avatar contradiction clause 427]
431. $false [avatar sat refutation 233,234,430]
% SZS output end Proof for 1648440029127161652933294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If paul is rich or not tall then someone is tall.
Everyone who is kind is either kind or happy and vice versa.
If someone is both kind and calm then someone is calm or quiet and vice versa.
Everyone who is not old is both old and funny and vice versa.
Everyone who is creative is both rich and not quiet and vice versa.
If alice is not rich then someone is not creative.
If someone is either not calm or not kind then someone is either not patient or funny and vice versa.
If someone is not calm then someone is both tall and strong.
If lucy is either not tall or quiet then someone is creative or not generous and vice versa.
If paul is both not creative and patient then susan is both not creative and rich.
Everyone who is either not funny or not old is calm or kind.
If paul is both not kind and not patient then someone is quiet or not strong.
If someone is both wise and not calm then alice is not patient.
If john is both not wise and quiet then someone is not funny or happy and vice versa.
Everyone who is not generous is not rich or not old and vice versa.
Everyone who is either rich or brave is not humble or not rich.
Mary is not strong.
Someone is not humble or not patient.
Someone is strong.
Someone is not humble or not calm.
Someone is not creative or calm.
Alice is not wise or not humble.
Lucy is creative or not rich.
Someone is not funny. | Alice is patient. | neutral | (((rich(paul)|~tall(paul)))=>(?[X]:(tall(X))))&
(![X]:(kind(X)<=>(kind(X)<~>happy(X))))&
((?[X]:((kind(X)&calm(X))))<=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:(~old(X)<=>(old(X)&funny(X))))&
(![X]:(creative(X)<=>(rich(X)&~quiet(X))))&
((~rich(alice))=>(?[X]:(~creative(X))))&
((?[X]:((~calm(X)<~>~kind(X))))<=>(?[X]:((~patient(X)<~>funny(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((tall(X)&strong(X)))))&
(((~tall(lucy)<~>quiet(lucy)))<=>(?[X]:((creative(X)|~generous(X)))))&
(((~creative(paul)&patient(paul)))=>((~creative(susan)&rich(susan))))&
(![X]:((~funny(X)<~>~old(X))=>(calm(X)|kind(X))))&
(((~kind(paul)&~patient(paul)))=>(?[X]:((quiet(X)|~strong(X)))))&
((?[X]:((wise(X)&~calm(X))))=>(~patient(alice)))&
(((~wise(john)&quiet(john)))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:(~generous(X)<=>(~rich(X)|~old(X))))&
(![X]:((rich(X)<~>brave(X))=>(~humble(X)|~rich(X))))&
(~strong(mary))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:(strong(X)))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((~creative(X)|calm(X))))&
((~wise(alice)|~humble(alice)))&
((creative(lucy)|~rich(lucy)))&
(?[X]:(~funny(X))) | patient(alice) | [] | null | 0 |
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Everyone who is not funny is either funny or not wise and vice versa.
If lucy is either not happy or quiet then john is generous.
Everyone who is both brave and rich is old or not wise and vice versa.
If someone is either curious or not creative then alice is tall.
Someone is either not wise or patient.
Fred is either tall or not humble.
Lucy is not humble.
Someone is quiet or not calm.
Someone is both not kind and old. | Susan is not generous. | entailment | (![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(![X]:(~funny(X)<=>(funny(X)<~>~wise(X))))&
(((~happy(lucy)<~>quiet(lucy)))=>(generous(john)))&
(![X]:((brave(X)&rich(X))<=>(old(X)|~wise(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(tall(alice)))&
(?[X]:((~wise(X)<~>patient(X))))&
((tall(fred)<~>~humble(fred)))&
(~humble(lucy))&
(?[X]:((quiet(X)|~calm(X))))&
(?[X]:((~kind(X)&old(X)))) | ~generous(susan) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 2249144627447361157130102
% SZS output start Proof for 2249144627447361157130102
5. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p4]
22. generous(susan) [input hypothesis]
39. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 5]
40. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 39]
83. strong(X0) | strong(X0) [cnf transformation 40]
85. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 40]
130. generous(susan) [cnf transformation 22]
133. strong(X0) [duplicate literal removal 83]
134. ~strong(X0) | ~generous(X0) [duplicate literal removal 85]
260. ~generous(X1) [resolution 134,133]
266. $false [resolution 260,130]
% SZS output end Proof for 2249144627447361157130102
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or quiet then fred is either wise or funny. If john is either not calm or not humble then someone is either not creative or not happy. If lucy is either rich or strong then alice is either not generous or not old and vice versa. Everyone who is both funny and patient is both not brave and not patient. Everyone who is either old or rich is either calm or kind and vice versa. If mary is either not funny or kind then john is not old. Everyone who is not wise or humble is either wise or not funny. Everyone who is either not old or quiet is strong. Everyone who is brave or not tall is wise and vice versa. Everyone who is curious is both not creative and creative. If someone is not old or not patient then mary is both kind and tall and vice versa. Everyone who is quiet is either creative or not happy and vice versa. If lucy is both not creative and wise then mary is generous or rich and vice versa. Everyone who is either kind or curious is either not kind or humble and vice versa. Everyone who is strong is either not creative or quiet and vice versa. Everyone who is either not happy or not generous is not wise or not generous. Lucy is not happy or not creative. Mary is not old or humble. Someone is either not wise or old. Alice is either generous or not kind. Paul is both rich and calm. Lucy is both brave and not strong. Someone is both not curious and calm. | Mary is funny. | entailment | ((?[X]:((~brave(X)|quiet(X))))=>((wise(fred)<~>funny(fred))))&
(((~calm(john)<~>~humble(john)))=>(?[X]:((~creative(X)<~>~happy(X)))))&
(((rich(lucy)<~>strong(lucy)))<=>((~generous(alice)<~>~old(alice))))&
(![X]:((funny(X)&patient(X))=>(~brave(X)&~patient(X))))&
(![X]:((old(X)<~>rich(X))<=>(calm(X)<~>kind(X))))&
(((~funny(mary)<~>kind(mary)))=>(~old(john)))&
(![X]:((~wise(X)|humble(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~old(X)<~>quiet(X))=>strong(X)))&
(![X]:((brave(X)|~tall(X))<=>wise(X)))&
(![X]:(curious(X)=>(~creative(X)&creative(X))))&
((?[X]:((~old(X)|~patient(X))))<=>((kind(mary)&tall(mary))))&
(![X]:(quiet(X)<=>(creative(X)<~>~happy(X))))&
(((~creative(lucy)&wise(lucy)))<=>((generous(mary)|rich(mary))))&
(![X]:((kind(X)<~>curious(X))<=>(~kind(X)<~>humble(X))))&
(![X]:(strong(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:((~happy(X)<~>~generous(X))=>(~wise(X)|~generous(X))))&
((~happy(lucy)|~creative(lucy)))&
((~old(mary)|humble(mary)))&
(?[X]:((~wise(X)<~>old(X))))&
((generous(alice)<~>~kind(alice)))&
((rich(paul)&calm(paul)))&
((brave(lucy)&~strong(lucy)))&
(?[X]:((~curious(X)&calm(X)))) | funny(mary) | [
"p0",
"p6",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7607362066447723663732186
% SZS output start Proof for 7607362066447723663732186
1. ? [X0] : (quiet(X0) | ~brave(X0)) => (wise(fred) <~> funny(fred)) [input p0]
7. ! [X0] : ((humble(X0) | ~wise(X0)) => (wise(X0) <~> ~funny(X0))) [input p6]
9. ! [X0] : ((~tall(X0) | brave(X0)) <=> wise(X0)) [input p8]
10. ! [X0] : (curious(X0) => (creative(X0) & ~creative(X0))) [input p9]
14. ! [X0] : ((kind(X0) <~> curious(X0)) <=> (~kind(X0) <~> humble(X0))) [input p13]
24. ~funny(mary) [input hypothesis]
25. (wise(fred) <~> funny(fred)) | ! [X0] : (~quiet(X0) & brave(X0)) [ennf transformation 1]
30. ! [X0] : ((wise(X0) <~> ~funny(X0)) | (~humble(X0) & wise(X0))) [ennf transformation 7]
32. ! [X0] : ((creative(X0) & ~creative(X0)) | ~curious(X0)) [ennf transformation 10]
35. ((~funny(fred) | ~wise(fred)) & (funny(fred) | wise(fred))) | ! [X0] : (~quiet(X0) & brave(X0)) [nnf transformation 25]
42. ! [X0] : (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (~humble(X0) & wise(X0))) [nnf transformation 30]
44. ! [X0] : (((~tall(X0) | brave(X0)) | ~wise(X0)) & (wise(X0) | (tall(X0) & ~brave(X0)))) [nnf transformation 9]
45. ! [X0] : ((~tall(X0) | brave(X0) | ~wise(X0)) & (wise(X0) | (tall(X0) & ~brave(X0)))) [flattening 44]
54. ! [X0] : ((((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0)))) & (((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))))) [nnf transformation 14]
63. funny(fred) | wise(fred) | brave(X0) [cnf transformation 35]
65. ~funny(fred) | ~wise(fred) | brave(X0) [cnf transformation 35]
91. ~funny(X0) | wise(X0) | wise(X0) [cnf transformation 42]
94. ~humble(X0) | ~wise(X0) | funny(X0) [cnf transformation 42]
97. ~brave(X0) | wise(X0) [cnf transformation 45]
100. ~creative(X0) | ~curious(X0) [cnf transformation 32]
101. ~curious(X0) | creative(X0) [cnf transformation 32]
116. humble(X0) | ~kind(X0) | curious(X0) | ~kind(X0) [cnf transformation 54]
120. curious(X0) | kind(X0) | humble(X0) | kind(X0) [cnf transformation 54]
142. ~funny(mary) [cnf transformation 24]
144. humble(X0) | ~kind(X0) | curious(X0) [duplicate literal removal 116]
146. curious(X0) | kind(X0) | humble(X0) [duplicate literal removal 120]
148. ~funny(X0) | wise(X0) [duplicate literal removal 91]
154. 2 <=> wise(fred) [avatar definition]
155. wise(fred) <- (2) [avatar component clause 154]
156. ~wise(fred) <- (~2) [avatar component clause 154]
158. 3 <=> funny(fred) [avatar definition]
159. funny(fred) <- (3) [avatar component clause 158]
160. ~funny(fred) <- (~3) [avatar component clause 158]
163. 4 <=> ! [X0] : brave(X0) [avatar definition]
164. brave(X0) <- (4) [avatar component clause 163]
165. 4 | ~2 | ~3 [avatar split clause 65,158,154,163]
167. 4 | 2 | 3 [avatar split clause 63,158,154,163]
217. 14 <=> funny(mary) [avatar definition]
219. ~funny(mary) <- (~14) [avatar component clause 217]
226. ~curious(X0) [subsumption resolution 100,101]
271. kind(X0) | humble(X0) [subsumption resolution 146,226]
272. humble(X0) | ~kind(X0) [subsumption resolution 144,226]
273. humble(X0) [subsumption resolution 272,271]
296. ~14 [avatar split clause 142,217]
305. ~wise(X0) | funny(X0) [resolution 94,273]
306. funny(fred) <- (2) [resolution 305,155]
308. $false <- (2, ~3) [subsumption resolution 306,160]
309. ~2 | 3 [avatar contradiction clause 308]
310. wise(fred) <- (3) [resolution 159,148]
311. $false <- (~2, 3) [subsumption resolution 310,156]
312. 2 | ~3 [avatar contradiction clause 311]
313. wise(X0) <- (4) [resolution 164,97]
315. funny(X0) <- (4) [resolution 313,305]
326. $false <- (4, ~14) [resolution 315,219]
327. ~4 | 14 [avatar contradiction clause 326]
328. $false [avatar sat refutation 165,167,296,309,312,327]
% SZS output end Proof for 7607362066447723663732186
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
If mary is both not curious and kind then someone is both quiet and not tall and vice versa.
Everyone who is both not tall and not curious is both not brave and curious and vice versa.
Everyone who is either brave or generous is both brave and curious and vice versa.
Everyone who is either not rich or strong is either strong or brave and vice versa.
If someone is not old or generous then someone is both not kind and calm and vice versa.
If someone is both not creative and patient then someone is creative.
If someone is not patient then someone is both brave and wise.
If someone is both tall and not wise then susan is tall or funny and vice versa.
Everyone who is both not kind and funny is both not calm and curious.
Everyone who is either not quiet or rich is both funny and not happy.
If fred is both humble and generous then lucy is both creative and not wise.
Everyone who is quiet or not quiet is tall.
If alice is generous then someone is happy.
Everyone who is both not creative and wise is old.
Everyone who is either not generous or not tall is wise or not humble.
If someone is either not patient or tall then someone is either creative or funny.
Someone is not creative or funny.
Susan is happy or generous.
Mary is wise.
Someone is not funny.
Someone is not quiet.
Someone is wise or creative.
Susan is generous or not humble. | Lucy is quiet. | neutral | (((~curious(mary)&kind(mary)))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~tall(X)&~curious(X))<=>(~brave(X)&curious(X))))&
(![X]:((brave(X)<~>generous(X))<=>(brave(X)&curious(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(strong(X)<~>brave(X))))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((~kind(X)&calm(X)))))&
((?[X]:((~creative(X)&patient(X))))=>(?[X]:(creative(X))))&
((?[X]:(~patient(X)))=>(?[X]:((brave(X)&wise(X)))))&
((?[X]:((tall(X)&~wise(X))))<=>((tall(susan)|funny(susan))))&
(![X]:((~kind(X)&funny(X))=>(~calm(X)&curious(X))))&
(![X]:((~quiet(X)<~>rich(X))=>(funny(X)&~happy(X))))&
(((humble(fred)&generous(fred)))=>((creative(lucy)&~wise(lucy))))&
(![X]:((quiet(X)|~quiet(X))=>tall(X)))&
((generous(alice))=>(?[X]:(happy(X))))&
(![X]:((~creative(X)&wise(X))=>old(X)))&
(![X]:((~generous(X)<~>~tall(X))=>(wise(X)|~humble(X))))&
((?[X]:((~patient(X)<~>tall(X))))=>(?[X]:((creative(X)<~>funny(X)))))&
(?[X]:((~creative(X)|funny(X))))&
((happy(susan)|generous(susan)))&
(wise(mary))&
(?[X]:(~funny(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((wise(X)|creative(X))))&
((generous(susan)|~humble(susan))) | quiet(lucy) | [] | null | 0 |
If lucy is both not kind and not strong then john is generous or not calm and vice versa.
Everyone who is either not humble or strong is happy.
If someone is funny or curious then someone is not humble or not generous and vice versa.
Everyone who is either not wise or not brave is not quiet.
Everyone who is both happy and old is not happy or quiet.
If someone is both not kind and not tall then someone is either curious or not creative.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is either humble or old then paul is either patient or happy.
If someone is calm or generous then someone is not old.
Everyone who is quiet or funny is either not patient or not calm.
If someone is kind then paul is curious and vice versa.
If someone is both not curious and brave then someone is not old or not funny.
Everyone who is old or not humble is not humble or not patient and vice versa.
Everyone who is both humble and not calm is both happy and kind.
Everyone who is tall is either kind or not brave and vice versa.
Everyone who is either not old or not generous is not generous and vice versa.
Someone is either wise or rich.
Someone is both not generous and not wise.
Someone is not kind or not tall.
Someone is either tall or generous.
Fred is kind or not calm.
Someone is either not quiet or not happy.
Susan is not brave.
Someone is both not calm and not curious. | John is generous. | contradiction | (((~kind(lucy)&~strong(lucy)))<=>((generous(john)|~calm(john))))&
(![X]:((~humble(X)<~>strong(X))=>happy(X)))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>~quiet(X)))&
(![X]:((happy(X)&old(X))=>(~happy(X)|quiet(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>((patient(paul)<~>happy(paul))))&
((?[X]:((calm(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|funny(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:(kind(X)))<=>(curious(paul)))&
((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((old(X)|~humble(X))<=>(~humble(X)|~patient(X))))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&kind(X))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
(![X]:((~old(X)<~>~generous(X))<=>~generous(X)))&
(?[X]:((wise(X)<~>rich(X))))&
(?[X]:((~generous(X)&~wise(X))))&
(?[X]:((~kind(X)|~tall(X))))&
(?[X]:((tall(X)<~>generous(X))))&
((kind(fred)|~calm(fred)))&
(?[X]:((~quiet(X)<~>~happy(X))))&
(~brave(susan))&
(?[X]:((~calm(X)&~curious(X)))) | generous(john) | [
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 525093311355391158561867
% SZS output start Proof for 525093311355391158561867
9. ? [X0] : (generous(X0) | calm(X0)) => ? [X0] : ~old(X0) [input p8]
16. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> ~generous(X0)) [input p15]
25. generous(john) [input hypothesis]
28. ? [X0] : (generous(X0) | calm(X0)) => ? [X1] : ~old(X1) [rectify 9]
36. ? [X1] : ~old(X1) | ! [X0] : (~generous(X0) & ~calm(X0)) [ennf transformation 28]
57. ? [X0] : ~old(X0) | ! [X1] : (~generous(X1) & ~calm(X1)) [rectify 36]
58. ? [X0] : ~old(X0) => ~old(sK3) [choice axiom]
59. ~old(sK3) | ! [X1] : (~generous(X1) & ~calm(X1)) [skolemisation 57,58]
71. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | generous(X0)) & (~generous(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 16]
113. ~old(sK3) | ~generous(X1) [cnf transformation 59]
131. ~generous(X0) | ~generous(X0) | old(X0) [cnf transformation 71]
134. generous(X0) | old(X0) | generous(X0) [cnf transformation 71]
148. generous(john) [cnf transformation 25]
149. ~generous(X0) | old(X0) [duplicate literal removal 131]
150. generous(X0) | old(X0) [duplicate literal removal 134]
162. 3 <=> generous(john) [avatar definition]
163. generous(john) <- (3) [avatar component clause 162]
237. 20 <=> ! [X1] : ~generous(X1) [avatar definition]
238. ~generous(X1) <- (20) [avatar component clause 237]
240. 21 <=> old(sK3) [avatar definition]
242. ~old(sK3) <- (~21) [avatar component clause 240]
243. 20 | ~21 [avatar split clause 113,240,237]
273. old(X0) [subsumption resolution 149,150]
322. 3 [avatar split clause 148,162]
325. $false <- (~21) [subsumption resolution 242,273]
326. 21 [avatar contradiction clause 325]
327. $false <- (3, 20) [resolution 238,163]
328. ~3 | ~20 [avatar contradiction clause 327]
329. $false [avatar sat refutation 243,322,326,328]
% SZS output end Proof for 525093311355391158561867
% ------------------------------
% 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
% ------------------------------
% ------------------------------
| 0 |
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