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 generous or brave is not quiet and vice versa.
Everyone who is either funny or not tall is funny or not tall and vice versa.
Everyone who is both tall and not curious is calm.
Everyone who is not generous or not brave is humble and vice versa.
Everyone who is both not generous and brave is rich and vice versa.
Everyone who is old is generous.
Everyone who is both creative and happy is happy or curious and vice versa.
Everyone who is either not calm or not wise is wise.
Everyone who is both strong and humble is either not creative or not quiet and vice versa.
If fred is both not quiet and tall then someone is curious.
Everyone who is kind is not calm and vice versa.
If susan is either patient or not wise then mary is not wise or curious.
If mary is not funny or not calm then susan is not curious.
If someone is not strong then fred is both generous and kind and vice versa.
Everyone who is both not quiet and creative is funny or happy.
If someone is not old or not rich then someone is either not quiet or kind.
Someone is both rich and tall.
Someone is not kind or wise.
Alice is either old or tall.
Someone is curious or kind.
Alice is both not calm and tall.
Alice is either kind or rich.
Someone is calm or not calm.
Someone is calm or not kind. | Alice is creative. | entailment | (![X]:((~generous(X)<~>brave(X))<=>~quiet(X)))&
(![X]:((funny(X)<~>~tall(X))<=>(funny(X)|~tall(X))))&
(![X]:((tall(X)&~curious(X))=>calm(X)))&
(![X]:((~generous(X)|~brave(X))<=>humble(X)))&
(![X]:((~generous(X)&brave(X))<=>rich(X)))&
(![X]:(old(X)=>generous(X)))&
(![X]:((creative(X)&happy(X))<=>(happy(X)|curious(X))))&
(![X]:((~calm(X)<~>~wise(X))=>wise(X)))&
(![X]:((strong(X)&humble(X))<=>(~creative(X)<~>~quiet(X))))&
(((~quiet(fred)&tall(fred)))=>(?[X]:(curious(X))))&
(![X]:(kind(X)<=>~calm(X)))&
(((patient(susan)<~>~wise(susan)))=>((~wise(mary)|curious(mary))))&
(((~funny(mary)|~calm(mary)))=>(~curious(susan)))&
((?[X]:(~strong(X)))<=>((generous(fred)&kind(fred))))&
(![X]:((~quiet(X)&creative(X))=>(funny(X)|happy(X))))&
((?[X]:((~old(X)|~rich(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((~kind(X)|wise(X))))&
((old(alice)<~>tall(alice)))&
(?[X]:((curious(X)|kind(X))))&
((~calm(alice)&tall(alice)))&
((kind(alice)<~>rich(alice)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((calm(X)|~kind(X)))) | creative(alice) | [
"p2",
"p6",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6242581582892325432629577
% SZS output start Proof for 6242581582892325432629577
3. ! [X0] : ((~curious(X0) & tall(X0)) => calm(X0)) [input p2]
7. ! [X0] : ((happy(X0) & creative(X0)) <=> (curious(X0) | happy(X0))) [input p6]
21. tall(alice) & ~calm(alice) [input p20]
25. ~creative(alice) [input hypothesis]
27. ! [X0] : (calm(X0) | (curious(X0) | ~tall(X0))) [ennf transformation 3]
28. ! [X0] : (calm(X0) | curious(X0) | ~tall(X0)) [flattening 27]
46. ! [X0] : (((happy(X0) & creative(X0)) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 7]
47. ! [X0] : (((happy(X0) & creative(X0)) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | ~happy(X0) | ~creative(X0))) [flattening 46]
86. ~tall(X0) | curious(X0) | calm(X0) [cnf transformation 28]
96. ~curious(X0) | creative(X0) [cnf transformation 47]
128. ~calm(alice) [cnf transformation 21]
129. tall(alice) [cnf transformation 21]
134. ~creative(alice) [cnf transformation 25]
235. 22 <=> tall(alice) [avatar definition]
236. tall(alice) <- (22) [avatar component clause 235]
249. 22 [avatar split clause 129,235]
291. curious(alice) | calm(alice) <- (22) [resolution 86,236]
301. curious(alice) <- (22) [subsumption resolution 291,128]
306. creative(alice) <- (22) [resolution 301,96]
307. $false <- (22) [subsumption resolution 306,134]
308. ~22 [avatar contradiction clause 307]
309. $false [avatar sat refutation 249,308]
% SZS output end Proof for 6242581582892325432629577
% ------------------------------
% 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 quiet and quiet then mary is both quiet and not patient and vice versa. If alice is either quiet or not brave then paul is either strong or wise and vice versa. If someone is not rich then john is either not tall or happy and vice versa. Everyone who is either old or generous is either curious or not curious. Everyone who is both generous and not rich is both not old and humble and vice versa. Everyone who is brave is not kind and vice versa. Everyone who is not calm is not quiet or humble. If lucy is old or wise then mary is either quiet or strong. Everyone who is both not brave and funny is not funny and vice versa. If someone is either not quiet or wise then someone is both rich and not old. Everyone who is either strong or generous is both quiet and funny and vice versa. If lucy is rich or not happy then john is not generous or rich and vice versa. Everyone who is both not humble and old is brave and vice versa. Everyone who is either not generous or old is kind or not tall. If someone is both not patient and not wise then john is creative and vice versa. If someone is not brave then someone is not curious. Someone is both not wise and funny. Someone is not generous. Lucy is rich. Lucy is both calm and happy. Lucy is funny. Alice is either wise or patient. Someone is rich or humble. | Mary is quiet. | neutral | ((?[X]:((~quiet(X)&quiet(X))))<=>((quiet(mary)&~patient(mary))))&
(((quiet(alice)<~>~brave(alice)))<=>((strong(paul)<~>wise(paul))))&
((?[X]:(~rich(X)))<=>((~tall(john)<~>happy(john))))&
(![X]:((old(X)<~>generous(X))=>(curious(X)<~>~curious(X))))&
(![X]:((generous(X)&~rich(X))<=>(~old(X)&humble(X))))&
(![X]:(brave(X)<=>~kind(X)))&
(![X]:(~calm(X)=>(~quiet(X)|humble(X))))&
(((old(lucy)|wise(lucy)))=>((quiet(mary)<~>strong(mary))))&
(![X]:((~brave(X)&funny(X))<=>~funny(X)))&
((?[X]:((~quiet(X)<~>wise(X))))=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((strong(X)<~>generous(X))<=>(quiet(X)&funny(X))))&
(((rich(lucy)|~happy(lucy)))<=>((~generous(john)|rich(john))))&
(![X]:((~humble(X)&old(X))<=>brave(X)))&
(![X]:((~generous(X)<~>old(X))=>(kind(X)|~tall(X))))&
((?[X]:((~patient(X)&~wise(X))))<=>(creative(john)))&
((?[X]:(~brave(X)))=>(?[X]:(~curious(X))))&
(?[X]:((~wise(X)&funny(X))))&
(?[X]:(~generous(X)))&
(rich(lucy))&
((calm(lucy)&happy(lucy)))&
(funny(lucy))&
((wise(alice)<~>patient(alice)))&
(?[X]:((rich(X)|humble(X)))) | quiet(mary) | [] | null | 0 |
Everyone who is curious or kind is either patient or generous.
If paul is both quiet and funny then lucy is both brave and not old.
If someone is not kind then someone is funny or not calm.
Everyone who is either not funny or kind is not rich or creative.
If someone is either not funny or curious then someone is not funny or not brave and vice versa.
Everyone who is either happy or not happy is wise or generous.
If mary is calm or not happy then fred is either kind or generous.
If someone is either wise or not humble then someone is not quiet and vice versa.
Everyone who is either not kind or wise is not patient or wise.
Everyone who is curious or strong is either generous or not tall.
Everyone who is kind or not quiet is not curious or humble and vice versa.
Everyone who is not generous or not tall is either not rich or not old and vice versa.
Everyone who is not wise is either patient or not happy.
Everyone who is either brave or not generous is tall.
If mary is happy then mary is both happy and not old.
If mary is either rich or calm then john is either calm or not generous and vice versa.
Alice is either wise or happy.
Someone is both not old and not humble.
Lucy is either patient or not calm.
Someone is not kind.
Someone is not kind or creative.
Someone is both not kind and not rich.
Someone is both not strong and brave.
Someone is not curious or old. | Alice is happy. | contradiction | (![X]:((curious(X)|kind(X))=>(patient(X)<~>generous(X))))&
(((quiet(paul)&funny(paul)))=>((brave(lucy)&~old(lucy))))&
((?[X]:(~kind(X)))=>(?[X]:((funny(X)|~calm(X)))))&
(![X]:((~funny(X)<~>kind(X))=>(~rich(X)|creative(X))))&
((?[X]:((~funny(X)<~>curious(X))))<=>(?[X]:((~funny(X)|~brave(X)))))&
(![X]:((happy(X)<~>~happy(X))=>(wise(X)|generous(X))))&
(((calm(mary)|~happy(mary)))=>((kind(fred)<~>generous(fred))))&
((?[X]:((wise(X)<~>~humble(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((~kind(X)<~>wise(X))=>(~patient(X)|wise(X))))&
(![X]:((curious(X)|strong(X))=>(generous(X)<~>~tall(X))))&
(![X]:((kind(X)|~quiet(X))<=>(~curious(X)|humble(X))))&
(![X]:((~generous(X)|~tall(X))<=>(~rich(X)<~>~old(X))))&
(![X]:(~wise(X)=>(patient(X)<~>~happy(X))))&
(![X]:((brave(X)<~>~generous(X))=>tall(X)))&
((happy(mary))=>((happy(mary)&~old(mary))))&
(((rich(mary)<~>calm(mary)))<=>((calm(john)<~>~generous(john))))&
((wise(alice)<~>happy(alice)))&
(?[X]:((~old(X)&~humble(X))))&
((patient(lucy)<~>~calm(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~kind(X)|creative(X))))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((~strong(X)&brave(X))))&
(?[X]:((~curious(X)|old(X)))) | happy(alice) | [
"p0",
"p5",
"p8",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3167441491369741919454587
% SZS output start Proof for 3167441491369741919454587
1. ! [X0] : ((kind(X0) | curious(X0)) => (patient(X0) <~> generous(X0))) [input p0]
6. ! [X0] : ((happy(X0) <~> ~happy(X0)) => (generous(X0) | wise(X0))) [input p5]
9. ! [X0] : ((~kind(X0) <~> wise(X0)) => (wise(X0) | ~patient(X0))) [input p8]
13. ! [X0] : (~wise(X0) => (patient(X0) <~> ~happy(X0))) [input p12]
17. wise(alice) <~> happy(alice) [input p16]
25. happy(alice) [input hypothesis]
33. ! [X0] : ((patient(X0) <~> generous(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 1]
37. ! [X0] : ((generous(X0) | wise(X0)) | (happy(X0) <=> ~happy(X0))) [ennf transformation 6]
38. ! [X0] : (generous(X0) | wise(X0) | (happy(X0) <=> ~happy(X0))) [flattening 37]
40. ! [X0] : ((wise(X0) | ~patient(X0)) | (~kind(X0) <=> wise(X0))) [ennf transformation 9]
41. ! [X0] : (wise(X0) | ~patient(X0) | (~kind(X0) <=> wise(X0))) [flattening 40]
43. ! [X0] : ((patient(X0) <~> ~happy(X0)) | wise(X0)) [ennf transformation 13]
46. ! [X0] : (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | (~kind(X0) & ~curious(X0))) [nnf transformation 33]
55. ! [X0] : (generous(X0) | wise(X0) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 38]
62. ! [X0] : (wise(X0) | ~patient(X0) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0)))) [nnf transformation 41]
68. ! [X0] : (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | wise(X0)) [nnf transformation 43]
71. (~happy(alice) | ~wise(alice)) & (happy(alice) | wise(alice)) [nnf transformation 17]
86. ~generous(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 46]
96. generous(X0) | wise(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 55]
97. generous(X0) | wise(X0) | happy(X0) | happy(X0) [cnf transformation 55]
106. wise(X0) | ~patient(X0) | wise(X0) | kind(X0) [cnf transformation 62]
120. ~happy(X0) | patient(X0) | wise(X0) [cnf transformation 68]
135. ~happy(alice) | ~wise(alice) [cnf transformation 71]
145. happy(alice) [cnf transformation 25]
146. ~patient(X0) | wise(X0) | kind(X0) [duplicate literal removal 106]
147. generous(X0) | wise(X0) | ~happy(X0) [duplicate literal removal 96]
148. generous(X0) | wise(X0) | happy(X0) [duplicate literal removal 97]
213. wise(X0) | generous(X0) [subsumption resolution 147,148]
285. 30 <=> wise(alice) [avatar definition]
287. ~wise(alice) <- (~30) [avatar component clause 285]
289. 31 <=> happy(alice) [avatar definition]
290. happy(alice) <- (31) [avatar component clause 289]
292. ~30 | ~31 [avatar split clause 135,289,285]
313. 31 [avatar split clause 145,289]
315. generous(alice) <- (~30) [resolution 213,287]
334. 39 <=> patient(alice) [avatar definition]
335. patient(alice) <- (39) [avatar component clause 334]
339. ~patient(alice) | ~kind(alice) <- (~30) [resolution 86,315]
399. patient(alice) | wise(alice) <- (31) [resolution 120,290]
403. patient(alice) <- (~30, 31) [subsumption resolution 399,287]
404. 39 | 30 | ~31 [avatar split clause 403,289,285,334]
406. 50 <=> kind(alice) [avatar definition]
408. ~kind(alice) <- (~50) [avatar component clause 406]
409. ~50 | ~39 | 30 [avatar split clause 339,285,334,406]
436. wise(alice) | kind(alice) <- (39) [resolution 146,335]
437. kind(alice) <- (~30, 39) [subsumption resolution 436,287]
438. $false <- (~30, 39, ~50) [subsumption resolution 437,408]
439. 30 | ~39 | 50 [avatar contradiction clause 438]
440. $false [avatar sat refutation 292,313,404,409,439]
% SZS output end Proof for 3167441491369741919454587
% ------------------------------
% 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is curious and vice versa.
If john is not old then paul is both creative and not brave.
Everyone who is both not quiet and not strong is not generous or humble and vice versa.
Everyone who is not strong or not curious is both not humble and not strong and vice versa.
Everyone who is either not creative or curious is curious and vice versa.
Everyone who is strong is calm or kind.
If someone is not tall then someone is humble or happy and vice versa.
If someone is curious or creative then lucy is either humble or curious and vice versa.
If someone is strong or not tall then someone is not kind and vice versa.
Everyone who is not patient or not kind is both creative and rich and vice versa.
Everyone who is either not creative or generous is funny and vice versa.
If alice is patient then someone is not kind.
Everyone who is either not brave or not wise is quiet or not calm and vice versa.
Everyone who is either not funny or patient is not generous.
Everyone who is either brave or generous is both wise and not kind.
Everyone who is both happy and not funny is both kind and not funny and vice versa.
Someone is not happy or wise.
Fred is either quiet or not happy.
Someone is generous.
Paul is either curious or not brave.
Susan is either not kind or not calm.
Someone is either happy or not happy. | Alice is wise. | neutral | (![X]:(~generous(X)<=>curious(X)))&
((~old(john))=>((creative(paul)&~brave(paul))))&
(![X]:((~quiet(X)&~strong(X))<=>(~generous(X)|humble(X))))&
(![X]:((~strong(X)|~curious(X))<=>(~humble(X)&~strong(X))))&
(![X]:((~creative(X)<~>curious(X))<=>curious(X)))&
(![X]:(strong(X)=>(calm(X)|kind(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((humble(X)|happy(X)))))&
((?[X]:((curious(X)|creative(X))))<=>((humble(lucy)<~>curious(lucy))))&
((?[X]:((strong(X)|~tall(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~patient(X)|~kind(X))<=>(creative(X)&rich(X))))&
(![X]:((~creative(X)<~>generous(X))<=>funny(X)))&
((patient(alice))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(quiet(X)|~calm(X))))&
(![X]:((~funny(X)<~>patient(X))=>~generous(X)))&
(![X]:((brave(X)<~>generous(X))=>(wise(X)&~kind(X))))&
(![X]:((happy(X)&~funny(X))<=>(kind(X)&~funny(X))))&
(?[X]:((~happy(X)|wise(X))))&
((quiet(fred)<~>~happy(fred)))&
(?[X]:(generous(X)))&
((curious(paul)<~>~brave(paul)))&
((~kind(susan)<~>~calm(susan)))&
(?[X]:((happy(X)<~>~happy(X)))) | wise(alice) | [] | null | 0 |
Everyone who is brave or not humble is either brave or not humble.
Everyone who is strong or curious is both rich and not patient.
If someone is creative or rich then someone is not rich or humble.
If lucy is either brave or not old then someone is either curious or calm.
Everyone who is either rich or quiet is not strong and vice versa.
If susan is either patient or not rich then someone is both wise and not wise.
Everyone who is quiet or not humble is either not kind or kind and vice versa.
Everyone who is kind or not strong is both kind and humble.
If someone is both brave and not tall then mary is either not generous or not humble and vice versa.
If susan is kind then someone is not strong.
If someone is either old or patient then mary is strong or not patient and vice versa.
Everyone who is either generous or creative is old and vice versa.
Everyone who is either not rich or not tall is rich.
If someone is both generous and not creative then lucy is not rich.
If someone is kind then someone is both old and brave.
If someone is rich then someone is strong or not tall.
Fred is not creative or not curious.
Someone is not creative or not happy.
Someone is not strong.
Susan is wise.
Fred is rich.
John is either not tall or not curious.
Paul is both brave and not happy. | John is rich. | entailment | (![X]:((brave(X)|~humble(X))=>(brave(X)<~>~humble(X))))&
(![X]:((strong(X)|curious(X))=>(rich(X)&~patient(X))))&
((?[X]:((creative(X)|rich(X))))=>(?[X]:((~rich(X)|humble(X)))))&
(((brave(lucy)<~>~old(lucy)))=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((rich(X)<~>quiet(X))<=>~strong(X)))&
(((patient(susan)<~>~rich(susan)))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((quiet(X)|~humble(X))<=>(~kind(X)<~>kind(X))))&
(![X]:((kind(X)|~strong(X))=>(kind(X)&humble(X))))&
((?[X]:((brave(X)&~tall(X))))<=>((~generous(mary)<~>~humble(mary))))&
((kind(susan))=>(?[X]:(~strong(X))))&
((?[X]:((old(X)<~>patient(X))))<=>((strong(mary)|~patient(mary))))&
(![X]:((generous(X)<~>creative(X))<=>old(X)))&
(![X]:((~rich(X)<~>~tall(X))=>rich(X)))&
((?[X]:((generous(X)&~creative(X))))=>(~rich(lucy)))&
((?[X]:(kind(X)))=>(?[X]:((old(X)&brave(X)))))&
((?[X]:(rich(X)))=>(?[X]:((strong(X)|~tall(X)))))&
((~creative(fred)|~curious(fred)))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:(~strong(X)))&
(wise(susan))&
(rich(fred))&
((~tall(john)<~>~curious(john)))&
((brave(paul)&~happy(paul))) | rich(john) | [
"p1",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7009678489642189090234103
% SZS output start Proof for 7009678489642189090234103
2. ! [X0] : ((curious(X0) | strong(X0)) => (~patient(X0) & rich(X0))) [input p1]
13. ! [X0] : ((~rich(X0) <~> ~tall(X0)) => rich(X0)) [input p12]
22. ~tall(john) <~> ~curious(john) [input p21]
24. ~rich(john) [input hypothesis]
31. ! [X0] : ((~patient(X0) & rich(X0)) | (~curious(X0) & ~strong(X0))) [ennf transformation 2]
37. ! [X0] : (rich(X0) | (~rich(X0) <=> ~tall(X0))) [ennf transformation 13]
66. ! [X0] : (rich(X0) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) [nnf transformation 37]
75. (curious(john) | tall(john)) & (~curious(john) | ~tall(john)) [nnf transformation 22]
81. ~curious(X0) | rich(X0) [cnf transformation 31]
125. rich(X0) | ~tall(X0) | rich(X0) [cnf transformation 66]
136. curious(john) | tall(john) [cnf transformation 75]
138. ~rich(john) [cnf transformation 24]
139. ~tall(X0) | rich(X0) [duplicate literal removal 125]
303. 34 <=> tall(john) [avatar definition]
305. tall(john) <- (34) [avatar component clause 303]
307. 35 <=> curious(john) [avatar definition]
309. curious(john) <- (35) [avatar component clause 307]
310. 34 | 35 [avatar split clause 136,307,303]
322. rich(john) <- (34) [resolution 139,305]
323. $false <- (34) [subsumption resolution 322,138]
324. ~34 [avatar contradiction clause 323]
325. rich(john) <- (35) [resolution 309,81]
326. $false <- (35) [subsumption resolution 325,138]
327. ~35 [avatar contradiction clause 326]
328. $false [avatar sat refutation 310,324,327]
% SZS output end Proof for 7009678489642189090234103
% ------------------------------
% 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 either not calm or rich then lucy is not quiet or not creative.
If someone is humble then someone is not quiet or not calm.
Everyone who is either not rich or quiet is not generous.
Everyone who is funny is not humble or wise and vice versa.
If john is happy or calm then someone is either not tall or funny.
If john is either generous or not kind then mary is rich or generous and vice versa.
If someone is not curious or not kind then john is both kind and not creative.
If someone is not calm or humble then someone is either old or kind.
Everyone who is either old or not rich is brave.
If susan is either old or curious then paul is both quiet and not creative.
Everyone who is not wise or not quiet is both tall and not patient and vice versa.
Everyone who is kind is humble.
Everyone who is quiet is creative.
If paul is either funny or patient then someone is either not creative or patient and vice versa.
Everyone who is both not wise and patient is both not funny and not brave and vice versa.
Fred is both funny and quiet.
Fred is not humble.
Susan is either generous or not curious.
Someone is both happy and kind.
John is either not brave or not strong.
Someone is happy. | Fred is not calm. | neutral | ((?[X]:((~calm(X)<~>rich(X))))=>((~quiet(lucy)|~creative(lucy))))&
((?[X]:(humble(X)))=>(?[X]:((~quiet(X)|~calm(X)))))&
(![X]:((~rich(X)<~>quiet(X))=>~generous(X)))&
(![X]:(funny(X)<=>(~humble(X)|wise(X))))&
(((happy(john)|calm(john)))=>(?[X]:((~tall(X)<~>funny(X)))))&
(((generous(john)<~>~kind(john)))<=>((rich(mary)|generous(mary))))&
((?[X]:((~curious(X)|~kind(X))))=>((kind(john)&~creative(john))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((old(X)<~>kind(X)))))&
(![X]:((old(X)<~>~rich(X))=>brave(X)))&
(((old(susan)<~>curious(susan)))=>((quiet(paul)&~creative(paul))))&
(![X]:((~wise(X)|~quiet(X))<=>(tall(X)&~patient(X))))&
(![X]:(kind(X)=>humble(X)))&
(![X]:(quiet(X)=>creative(X)))&
(((funny(paul)<~>patient(paul)))<=>(?[X]:((~creative(X)<~>patient(X)))))&
(![X]:((~wise(X)&patient(X))<=>(~funny(X)&~brave(X))))&
((funny(fred)&quiet(fred)))&
(~humble(fred))&
((generous(susan)<~>~curious(susan)))&
(?[X]:((happy(X)&kind(X))))&
((~brave(john)<~>~strong(john)))&
(?[X]:(happy(X))) | ~calm(fred) | [] | null | 0 |
If someone is both humble and tall then someone is either kind or not kind.
If mary is not tall then someone is both not funny and tall and vice versa.
Everyone who is not generous is old.
Everyone who is either not creative or humble is either not kind or not curious.
If paul is either not kind or wise then someone is both calm and funny and vice versa.
If fred is both humble and not humble then someone is either not wise or not strong.
If susan is creative or not funny then mary is wise or strong and vice versa.
Everyone who is either happy or not funny is tall or not quiet.
If john is either kind or rich then someone is either not rich or kind.
Everyone who is either not old or not strong is not happy or not brave and vice versa.
Everyone who is either not creative or not kind is generous or calm and vice versa.
If alice is either rich or happy then mary is both happy and not wise and vice versa.
Everyone who is either calm or strong is humble or not old and vice versa.
Everyone who is either brave or calm is either not humble or not strong and vice versa.
Everyone who is not funny is both not calm and curious.
If someone is quiet then someone is either humble or not strong and vice versa.
Paul is brave or not tall.
John is either not old or brave.
Susan is not quiet.
Mary is not generous.
Paul is both tall and creative.
Someone is either not tall or quiet.
John is both wise and not funny.
John is either funny or not tall. | John is not humble. | contradiction | ((?[X]:((humble(X)&tall(X))))=>(?[X]:((kind(X)<~>~kind(X)))))&
((~tall(mary))<=>(?[X]:((~funny(X)&tall(X)))))&
(![X]:(~generous(X)=>old(X)))&
(![X]:((~creative(X)<~>humble(X))=>(~kind(X)<~>~curious(X))))&
(((~kind(paul)<~>wise(paul)))<=>(?[X]:((calm(X)&funny(X)))))&
(((humble(fred)&~humble(fred)))=>(?[X]:((~wise(X)<~>~strong(X)))))&
(((creative(susan)|~funny(susan)))<=>((wise(mary)|strong(mary))))&
(![X]:((happy(X)<~>~funny(X))=>(tall(X)|~quiet(X))))&
(((kind(john)<~>rich(john)))=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:((~old(X)<~>~strong(X))<=>(~happy(X)|~brave(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>(generous(X)|calm(X))))&
(((rich(alice)<~>happy(alice)))<=>((happy(mary)&~wise(mary))))&
(![X]:((calm(X)<~>strong(X))<=>(humble(X)|~old(X))))&
(![X]:((brave(X)<~>calm(X))<=>(~humble(X)<~>~strong(X))))&
(![X]:(~funny(X)=>(~calm(X)&curious(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((humble(X)<~>~strong(X)))))&
((brave(paul)|~tall(paul)))&
((~old(john)<~>brave(john)))&
(~quiet(susan))&
(~generous(mary))&
((tall(paul)&creative(paul)))&
(?[X]:((~tall(X)<~>quiet(X))))&
((wise(john)&~funny(john)))&
((funny(john)<~>~tall(john))) | ~humble(john) | [
"p9",
"p12",
"p13",
"p14",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2630851654232776546305488
% SZS output start Proof for 2630851654232776546305488
10. ! [X0] : ((~old(X0) <~> ~strong(X0)) <=> (~brave(X0) | ~happy(X0))) [input p9]
13. ! [X0] : ((calm(X0) <~> strong(X0)) <=> (~old(X0) | humble(X0))) [input p12]
14. ! [X0] : ((brave(X0) <~> calm(X0)) <=> (~humble(X0) <~> ~strong(X0))) [input p13]
15. ! [X0] : (~funny(X0) => (curious(X0) & ~calm(X0))) [input p14]
18. ~old(john) <~> brave(john) [input p17]
23. ~funny(john) & wise(john) [input p22]
25. ~humble(john) [input hypothesis]
36. ! [X0] : ((curious(X0) & ~calm(X0)) | funny(X0)) [ennf transformation 15]
59. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (brave(X0) & happy(X0))) & ((~brave(X0) | ~happy(X0)) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [nnf transformation 10]
60. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (brave(X0) & happy(X0))) & (~brave(X0) | ~happy(X0) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [flattening 59]
65. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (old(X0) & ~humble(X0))) & ((~old(X0) | humble(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [nnf transformation 13]
66. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (old(X0) & ~humble(X0))) & (~old(X0) | humble(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [flattening 65]
67. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) & (((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [nnf transformation 14]
73. (~brave(john) | old(john)) & (brave(john) | ~old(john)) [nnf transformation 18]
111. brave(X0) | old(X0) | strong(X0) [cnf transformation 60]
125. ~strong(X0) | humble(X0) | calm(X0) | ~old(X0) [cnf transformation 66]
126. ~humble(X0) | calm(X0) | strong(X0) [cnf transformation 66]
129. ~strong(X0) | ~calm(X0) | old(X0) [cnf transformation 66]
132. strong(X0) | humble(X0) | calm(X0) | ~brave(X0) [cnf transformation 67]
134. ~strong(X0) | brave(X0) | calm(X0) | humble(X0) [cnf transformation 67]
137. ~calm(X0) | ~brave(X0) | ~humble(X0) | strong(X0) [cnf transformation 67]
138. ~calm(X0) | funny(X0) [cnf transformation 36]
145. brave(john) | ~old(john) [cnf transformation 73]
146. ~brave(john) | old(john) [cnf transformation 73]
154. ~funny(john) [cnf transformation 23]
157. ~humble(john) [cnf transformation 25]
259. ~brave(X0) | ~humble(X0) | strong(X0) [subsumption resolution 137,126]
261. ~brave(X0) | calm(X0) | strong(X0) [subsumption resolution 132,259]
298. 29 <=> old(john) [avatar definition]
299. ~old(john) <- (~29) [avatar component clause 298]
300. old(john) <- (29) [avatar component clause 298]
302. 30 <=> brave(john) [avatar definition]
303. brave(john) <- (30) [avatar component clause 302]
304. ~brave(john) <- (~30) [avatar component clause 302]
305. 29 | ~30 [avatar split clause 146,302,298]
306. ~29 | 30 [avatar split clause 145,302,298]
339. old(john) | strong(john) <- (~30) [resolution 111,304]
340. strong(john) <- (~29, ~30) [subsumption resolution 339,299]
356. ~calm(john) | old(john) <- (~29, ~30) [resolution 129,340]
497. ~calm(john) <- (~29, ~30) [subsumption resolution 356,299]
559. brave(john) | calm(john) | humble(john) <- (~29, ~30) [resolution 134,340]
562. calm(john) | humble(john) <- (~29, ~30) [subsumption resolution 559,304]
563. humble(john) <- (~29, ~30) [subsumption resolution 562,497]
564. $false <- (~29, ~30) [subsumption resolution 563,157]
565. 29 | 30 [avatar contradiction clause 564]
572. calm(john) | strong(john) <- (30) [resolution 303,261]
577. 60 <=> strong(john) [avatar definition]
579. strong(john) <- (60) [avatar component clause 577]
586. 62 <=> calm(john) [avatar definition]
587. ~calm(john) <- (~62) [avatar component clause 586]
588. calm(john) <- (62) [avatar component clause 586]
589. 60 | 62 | ~30 [avatar split clause 572,302,586,577]
675. funny(john) <- (62) [resolution 588,138]
681. $false <- (62) [subsumption resolution 675,154]
682. ~62 [avatar contradiction clause 681]
684. humble(john) | calm(john) | ~old(john) <- (60) [resolution 579,125]
689. calm(john) | ~old(john) <- (60) [subsumption resolution 684,157]
690. ~old(john) <- (60, ~62) [subsumption resolution 689,587]
691. $false <- (29, 60, ~62) [subsumption resolution 690,300]
692. ~29 | ~60 | 62 [avatar contradiction clause 691]
696. $false [avatar sat refutation 305,306,565,589,682,692]
% SZS output end Proof for 2630851654232776546305488
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not strong is both not quiet and not generous and vice versa.
If someone is both rich and calm then someone is not brave and vice versa.
If someone is both not brave and not wise then susan is not strong or not rich.
Everyone who is either rich or not strong is both not generous and not kind and vice versa.
Everyone who is calm or not curious is not humble.
Everyone who is funny is both kind and not wise and vice versa.
If susan is either not quiet or happy then alice is not funny.
If john is either not patient or not happy then susan is either humble or old and vice versa.
Everyone who is brave or not strong is either not brave or funny.
If susan is either patient or not humble then someone is curious or wise.
If paul is tall then someone is both not kind and not wise and vice versa.
Everyone who is curious or brave is both brave and not kind and vice versa.
If paul is not patient or not happy then john is old or generous.
Everyone who is rich is wise and vice versa.
Everyone who is either not rich or kind is either patient or not wise.
Everyone who is curious or not patient is humble or funny and vice versa.
John is both not generous and not strong.
Alice is either kind or generous.
Susan is both not funny and old.
Alice is both not happy and not brave.
Someone is strong.
Someone is not kind.
Someone is not wise.
Susan is not creative or not patient. | Paul is not curious. | entailment | (![X]:((curious(X)&~strong(X))<=>(~quiet(X)&~generous(X))))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((~brave(X)&~wise(X))))=>((~strong(susan)|~rich(susan))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~kind(X))))&
(![X]:((calm(X)|~curious(X))=>~humble(X)))&
(![X]:(funny(X)<=>(kind(X)&~wise(X))))&
(((~quiet(susan)<~>happy(susan)))=>(~funny(alice)))&
(((~patient(john)<~>~happy(john)))<=>((humble(susan)<~>old(susan))))&
(![X]:((brave(X)|~strong(X))=>(~brave(X)<~>funny(X))))&
(((patient(susan)<~>~humble(susan)))=>(?[X]:((curious(X)|wise(X)))))&
((tall(paul))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:((curious(X)|brave(X))<=>(brave(X)&~kind(X))))&
(((~patient(paul)|~happy(paul)))=>((old(john)|generous(john))))&
(![X]:(rich(X)<=>wise(X)))&
(![X]:((~rich(X)<~>kind(X))=>(patient(X)<~>~wise(X))))&
(![X]:((curious(X)|~patient(X))<=>(humble(X)|funny(X))))&
((~generous(john)&~strong(john)))&
((kind(alice)<~>generous(alice)))&
((~funny(susan)&old(susan)))&
((~happy(alice)&~brave(alice)))&
(?[X]:(strong(X)))&
(?[X]:(~kind(X)))&
(?[X]:(~wise(X)))&
((~creative(susan)|~patient(susan))) | ~curious(paul) | [
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 723938492976514868579730
% SZS output start Proof for 723938492976514868579730
6. ! [X0] : (funny(X0) <=> (~wise(X0) & kind(X0))) [input p5]
9. ! [X0] : ((~strong(X0) | brave(X0)) => (~brave(X0) <~> funny(X0))) [input p8]
12. ! [X0] : ((brave(X0) | curious(X0)) <=> (~kind(X0) & brave(X0))) [input p11]
25. curious(paul) [input hypothesis]
32. ! [X0] : ((~brave(X0) <~> funny(X0)) | (strong(X0) & ~brave(X0))) [ennf transformation 9]
46. ! [X0] : ((funny(X0) | (wise(X0) | ~kind(X0))) & ((~wise(X0) & kind(X0)) | ~funny(X0))) [nnf transformation 6]
47. ! [X0] : ((funny(X0) | wise(X0) | ~kind(X0)) & ((~wise(X0) & kind(X0)) | ~funny(X0))) [flattening 46]
50. ! [X0] : (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (strong(X0) & ~brave(X0))) [nnf transformation 32]
58. ! [X0] : (((brave(X0) | curious(X0)) | (kind(X0) | ~brave(X0))) & ((~kind(X0) & brave(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 12]
59. ! [X0] : ((brave(X0) | curious(X0) | kind(X0) | ~brave(X0)) & ((~kind(X0) & brave(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 58]
87. ~funny(X0) | kind(X0) [cnf transformation 47]
100. funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 50]
109. ~curious(X0) | brave(X0) [cnf transformation 59]
112. ~kind(X0) | ~brave(X0) [cnf transformation 59]
137. curious(paul) [cnf transformation 25]
138. ~brave(X0) | funny(X0) [duplicate literal removal 100]
276. brave(paul) [resolution 109,137]
282. funny(paul) [resolution 138,276]
287. kind(paul) [resolution 282,87]
588. ~brave(paul) [resolution 287,112]
601. $false [subsumption resolution 588,276]
% SZS output end Proof for 723938492976514868579730
% ------------------------------
% 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 lucy is either old or calm then someone is either patient or not wise and vice versa. If alice is not wise then mary is both brave and calm and vice versa. If someone is humble or not old then john is both not rich and strong. If susan is old or not old then lucy is funny. Everyone who is not creative or not patient is both not curious and kind. Everyone who is brave is not kind and vice versa. Everyone who is both calm and not humble is kind or strong and vice versa. Everyone who is not rich is either not rich or curious and vice versa. If fred is both tall and patient then someone is both curious and humble. Everyone who is either rich or humble is both humble and not patient and vice versa. Everyone who is both rich and funny is either not creative or creative. Everyone who is not quiet is both not creative and rich. Everyone who is not rich is not brave. Everyone who is not old or creative is both not brave and patient and vice versa. Everyone who is not happy or not kind is not calm. Everyone who is old or not generous is not strong or not brave and vice versa. Someone is not generous. John is tall or calm. Lucy is creative or not quiet. Mary is creative or not calm. Susan is old or tall. | Mary is not quiet. | contradiction | (((old(lucy)<~>calm(lucy)))<=>(?[X]:((patient(X)<~>~wise(X)))))&
((~wise(alice))<=>((brave(mary)&calm(mary))))&
((?[X]:((humble(X)|~old(X))))=>((~rich(john)&strong(john))))&
(((old(susan)|~old(susan)))=>(funny(lucy)))&
(![X]:((~creative(X)|~patient(X))=>(~curious(X)&kind(X))))&
(![X]:(brave(X)<=>~kind(X)))&
(![X]:((calm(X)&~humble(X))<=>(kind(X)|strong(X))))&
(![X]:(~rich(X)<=>(~rich(X)<~>curious(X))))&
(((tall(fred)&patient(fred)))=>(?[X]:((curious(X)&humble(X)))))&
(![X]:((rich(X)<~>humble(X))<=>(humble(X)&~patient(X))))&
(![X]:((rich(X)&funny(X))=>(~creative(X)<~>creative(X))))&
(![X]:(~quiet(X)=>(~creative(X)&rich(X))))&
(![X]:(~rich(X)=>~brave(X)))&
(![X]:((~old(X)|creative(X))<=>(~brave(X)&patient(X))))&
(![X]:((~happy(X)|~kind(X))=>~calm(X)))&
(![X]:((old(X)|~generous(X))<=>(~strong(X)|~brave(X))))&
(?[X]:(~generous(X)))&
((tall(john)|calm(john)))&
((creative(lucy)|~quiet(lucy)))&
((creative(mary)|~calm(mary)))&
((old(susan)|tall(susan))) | ~quiet(mary) | [
"p4",
"p5",
"p6",
"p11",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5378256179098796186851542
% SZS output start Proof for 5378256179098796186851542
5. ! [X0] : ((~patient(X0) | ~creative(X0)) => (kind(X0) & ~curious(X0))) [input p4]
6. ! [X0] : (brave(X0) <=> ~kind(X0)) [input p5]
7. ! [X0] : ((~humble(X0) & calm(X0)) <=> (strong(X0) | kind(X0))) [input p6]
12. ! [X0] : (~quiet(X0) => (rich(X0) & ~creative(X0))) [input p11]
14. ! [X0] : ((creative(X0) | ~old(X0)) <=> (patient(X0) & ~brave(X0))) [input p13]
20. ~calm(mary) | creative(mary) [input p19]
22. ~quiet(mary) [input hypothesis]
26. ! [X0] : ((kind(X0) & ~curious(X0)) | (patient(X0) & creative(X0))) [ennf transformation 5]
31. ! [X0] : ((rich(X0) & ~creative(X0)) | quiet(X0)) [ennf transformation 12]
40. ! [X0] : ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0))) [nnf transformation 6]
41. ! [X0] : (((~humble(X0) & calm(X0)) | (~strong(X0) & ~kind(X0))) & ((strong(X0) | kind(X0)) | (humble(X0) | ~calm(X0)))) [nnf transformation 7]
42. ! [X0] : (((~humble(X0) & calm(X0)) | (~strong(X0) & ~kind(X0))) & (strong(X0) | kind(X0) | humble(X0) | ~calm(X0))) [flattening 41]
49. ! [X0] : (((creative(X0) | ~old(X0)) | (~patient(X0) | brave(X0))) & ((patient(X0) & ~brave(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 14]
50. ! [X0] : ((creative(X0) | ~old(X0) | ~patient(X0) | brave(X0)) & ((patient(X0) & ~brave(X0)) | (~creative(X0) & old(X0)))) [flattening 49]
74. kind(X0) | creative(X0) [cnf transformation 26]
76. ~kind(X0) | ~brave(X0) [cnf transformation 40]
77. kind(X0) | brave(X0) [cnf transformation 40]
79. ~kind(X0) | calm(X0) [cnf transformation 42]
97. ~creative(X0) | quiet(X0) [cnf transformation 31]
101. ~brave(X0) | ~creative(X0) [cnf transformation 50]
113. ~calm(mary) | creative(mary) [cnf transformation 20]
115. ~quiet(mary) [cnf transformation 22]
155. 8 <=> calm(mary) [avatar definition]
157. ~calm(mary) <- (~8) [avatar component clause 155]
230. 23 <=> creative(mary) [avatar definition]
232. creative(mary) <- (23) [avatar component clause 230]
233. 23 | ~8 [avatar split clause 113,155,230]
240. ~brave(X1) | creative(X1) [resolution 76,74]
241. ~brave(X1) [subsumption resolution 240,101]
243. calm(X0) | brave(X0) [resolution 79,77]
246. calm(X0) [subsumption resolution 243,241]
248. $false <- (~8) [resolution 246,157]
249. 8 [avatar contradiction clause 248]
258. quiet(mary) <- (23) [resolution 97,232]
259. $false <- (23) [subsumption resolution 258,115]
260. ~23 [avatar contradiction clause 259]
261. $false [avatar sat refutation 233,249,260]
% SZS output end Proof for 5378256179098796186851542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or kind then fred is either not rich or brave.
If mary is patient or happy then mary is either quiet or strong.
Everyone who is either happy or old is either happy or not brave.
Everyone who is not brave is tall or brave and vice versa.
Everyone who is calm is not curious and vice versa.
If susan is either old or not patient then john is not calm or curious and vice versa.
Everyone who is old is either not rich or quiet and vice versa.
Everyone who is not generous or creative is humble.
Everyone who is not calm is not rich.
Everyone who is wise is both creative and not calm and vice versa.
If someone is both not patient and not kind then someone is either not kind or tall and vice versa.
Everyone who is either not brave or calm is either not brave or strong and vice versa.
Everyone who is not humble is not humble or tall.
If someone is either not curious or creative then susan is rich.
If mary is calm then someone is both not tall and curious.
Everyone who is rich or not humble is either not rich or not creative.
Someone is patient.
Someone is both tall and kind.
Alice is calm.
Paul is either tall or not patient.
Susan is not quiet.
Someone is both patient and kind.
Susan is old.
Someone is not funny or not creative. | Paul is not rich. | entailment | ((?[X]:((patient(X)<~>kind(X))))=>((~rich(fred)<~>brave(fred))))&
(((patient(mary)|happy(mary)))=>((quiet(mary)<~>strong(mary))))&
(![X]:((happy(X)<~>old(X))=>(happy(X)<~>~brave(X))))&
(![X]:(~brave(X)<=>(tall(X)|brave(X))))&
(![X]:(calm(X)<=>~curious(X)))&
(((old(susan)<~>~patient(susan)))<=>((~calm(john)|curious(john))))&
(![X]:(old(X)<=>(~rich(X)<~>quiet(X))))&
(![X]:((~generous(X)|creative(X))=>humble(X)))&
(![X]:(~calm(X)=>~rich(X)))&
(![X]:(wise(X)<=>(creative(X)&~calm(X))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:((~kind(X)<~>tall(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(~brave(X)<~>strong(X))))&
(![X]:(~humble(X)=>(~humble(X)|tall(X))))&
((?[X]:((~curious(X)<~>creative(X))))=>(rich(susan)))&
((calm(mary))=>(?[X]:((~tall(X)&curious(X)))))&
(![X]:((rich(X)|~humble(X))=>(~rich(X)<~>~creative(X))))&
(?[X]:(patient(X)))&
(?[X]:((tall(X)&kind(X))))&
(calm(alice))&
((tall(paul)<~>~patient(paul)))&
(~quiet(susan))&
(?[X]:((patient(X)&kind(X))))&
(old(susan))&
(?[X]:((~funny(X)|~creative(X)))) | ~rich(paul) | [
"p4",
"p6",
"p8",
"p13",
"p15",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 88488300005621587382622
% SZS output start Proof for 88488300005621587382622
5. ! [X0] : (calm(X0) <=> ~curious(X0)) [input p4]
7. ! [X0] : (old(X0) <=> (~rich(X0) <~> quiet(X0))) [input p6]
9. ! [X0] : (~calm(X0) => ~rich(X0)) [input p8]
14. ? [X0] : (~curious(X0) <~> creative(X0)) => rich(susan) [input p13]
16. ! [X0] : ((~humble(X0) | rich(X0)) => (~rich(X0) <~> ~creative(X0))) [input p15]
21. ~quiet(susan) [input p20]
23. old(susan) [input p22]
25. rich(paul) [input hypothesis]
33. ! [X0] : (~rich(X0) | calm(X0)) [ennf transformation 9]
36. rich(susan) | ! [X0] : (~curious(X0) <=> creative(X0)) [ennf transformation 14]
38. ! [X0] : ((~rich(X0) <~> ~creative(X0)) | (humble(X0) & ~rich(X0))) [ennf transformation 16]
44. ! [X0] : ((calm(X0) | curious(X0)) & (~curious(X0) | ~calm(X0))) [nnf transformation 5]
47. ! [X0] : ((old(X0) | ((~rich(X0) | ~quiet(X0)) & (quiet(X0) | rich(X0)))) & (((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | ~old(X0))) [nnf transformation 7]
54. rich(susan) | ! [X0] : ((~curious(X0) | ~creative(X0)) & (creative(X0) | curious(X0))) [nnf transformation 36]
57. ! [X0] : (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | (humble(X0) & ~rich(X0))) [nnf transformation 38]
80. ~curious(X0) | ~calm(X0) [cnf transformation 44]
88. ~old(X0) | ~rich(X0) | quiet(X0) [cnf transformation 47]
93. ~rich(X0) | calm(X0) [cnf transformation 33]
109. rich(susan) | creative(X0) | curious(X0) [cnf transformation 54]
113. ~creative(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 57]
123. ~quiet(susan) [cnf transformation 21]
126. old(susan) [cnf transformation 23]
127. rich(paul) [cnf transformation 25]
128. ~creative(X0) | ~rich(X0) [duplicate literal removal 113]
181. 10 <=> old(susan) [avatar definition]
182. old(susan) <- (10) [avatar component clause 181]
230. 19 <=> rich(susan) [avatar definition]
235. 20 <=> ! [X0] : (creative(X0) | curious(X0)) [avatar definition]
236. creative(X0) | curious(X0) <- (20) [avatar component clause 235]
237. 20 | 19 [avatar split clause 109,230,235]
251. 10 [avatar split clause 126,181]
253. calm(paul) [resolution 93,127]
268. ~rich(susan) | quiet(susan) <- (10) [resolution 88,182]
272. ~rich(susan) <- (10) [subsumption resolution 268,123]
273. ~19 | ~10 [avatar split clause 272,181,230]
275. ~rich(X1) | curious(X1) <- (20) [resolution 236,128]
278. curious(paul) <- (20) [resolution 275,127]
283. ~calm(paul) <- (20) [resolution 278,80]
284. $false <- (20) [subsumption resolution 283,253]
285. ~20 [avatar contradiction clause 284]
286. $false [avatar sat refutation 237,251,273,285]
% SZS output end Proof for 88488300005621587382622
% ------------------------------
% 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 susan is brave then paul is generous or not rich and vice versa.
Everyone who is either tall or not kind is both patient and strong and vice versa.
Everyone who is generous is both not tall and old and vice versa.
If lucy is old or not strong then susan is both old and not curious.
If susan is not kind then someone is creative and vice versa.
If someone is generous or not old then someone is not kind and vice versa.
Everyone who is not funny is kind and vice versa.
If someone is wise or not generous then john is both kind and not brave and vice versa.
Everyone who is both kind and not strong is not old and vice versa.
If someone is both funny and not quiet then alice is not curious or not patient and vice versa.
If fred is wise then lucy is not happy.
If john is not humble or not quiet then paul is both not old and not creative and vice versa.
If lucy is quiet then someone is both quiet and not happy.
Everyone who is either not strong or strong is funny.
If mary is both curious and not quiet then someone is old or not strong.
Someone is both not tall and not wise.
Someone is calm.
Susan is either not humble or not creative.
Someone is not kind.
Someone is quiet or kind. | Susan is tall. | contradiction | ((brave(susan))<=>((generous(paul)|~rich(paul))))&
(![X]:((tall(X)<~>~kind(X))<=>(patient(X)&strong(X))))&
(![X]:(generous(X)<=>(~tall(X)&old(X))))&
(((old(lucy)|~strong(lucy)))=>((old(susan)&~curious(susan))))&
((~kind(susan))<=>(?[X]:(creative(X))))&
((?[X]:((generous(X)|~old(X))))<=>(?[X]:(~kind(X))))&
(![X]:(~funny(X)<=>kind(X)))&
((?[X]:((wise(X)|~generous(X))))<=>((kind(john)&~brave(john))))&
(![X]:((kind(X)&~strong(X))<=>~old(X)))&
((?[X]:((funny(X)&~quiet(X))))<=>((~curious(alice)|~patient(alice))))&
((wise(fred))=>(~happy(lucy)))&
(((~humble(john)|~quiet(john)))<=>((~old(paul)&~creative(paul))))&
((quiet(lucy))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((~strong(X)<~>strong(X))=>funny(X)))&
(((curious(mary)&~quiet(mary)))=>(?[X]:((old(X)|~strong(X)))))&
(?[X]:((~tall(X)&~wise(X))))&
(?[X]:(calm(X)))&
((~humble(susan)<~>~creative(susan)))&
(?[X]:(~kind(X)))&
(?[X]:((quiet(X)|kind(X)))) | tall(susan) | [
"p2",
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8871318985500693168872587
% SZS output start Proof for 8871318985500693168872587
3. ! [X0] : (generous(X0) <=> (old(X0) & ~tall(X0))) [input p2]
7. ! [X0] : (~funny(X0) <=> kind(X0)) [input p6]
8. ? [X0] : (~generous(X0) | wise(X0)) <=> (~brave(john) & kind(john)) [input p7]
14. ! [X0] : ((~strong(X0) <~> strong(X0)) => funny(X0)) [input p13]
21. tall(susan) [input hypothesis]
28. ! [X0] : (funny(X0) | (~strong(X0) <=> strong(X0))) [ennf transformation 14]
35. ! [X0] : ((generous(X0) | (~old(X0) | tall(X0))) & ((old(X0) & ~tall(X0)) | ~generous(X0))) [nnf transformation 3]
36. ! [X0] : ((generous(X0) | ~old(X0) | tall(X0)) & ((old(X0) & ~tall(X0)) | ~generous(X0))) [flattening 35]
46. ! [X0] : ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))) [nnf transformation 7]
47. (? [X0] : (~generous(X0) | wise(X0)) | (brave(john) | ~kind(john))) & ((~brave(john) & kind(john)) | ! [X0] : (generous(X0) & ~wise(X0))) [nnf transformation 8]
48. (? [X0] : (~generous(X0) | wise(X0)) | brave(john) | ~kind(john)) & ((~brave(john) & kind(john)) | ! [X0] : (generous(X0) & ~wise(X0))) [flattening 47]
49. (? [X0] : (~generous(X0) | wise(X0)) | brave(john) | ~kind(john)) & ((~brave(john) & kind(john)) | ! [X1] : (generous(X1) & ~wise(X1))) [rectify 48]
50. ? [X0] : (~generous(X0) | wise(X0)) => (~generous(sK3) | wise(sK3)) [choice axiom]
51. ((~generous(sK3) | wise(sK3)) | brave(john) | ~kind(john)) & ((~brave(john) & kind(john)) | ! [X1] : (generous(X1) & ~wise(X1))) [skolemisation 49,50]
63. ! [X0] : (funny(X0) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 28]
82. ~tall(X0) | ~generous(X0) [cnf transformation 36]
95. ~funny(X0) | ~kind(X0) [cnf transformation 46]
97. kind(john) | generous(X1) [cnf transformation 51]
115. funny(X0) | strong(X0) | strong(X0) [cnf transformation 63]
116. funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 63]
124. tall(susan) [cnf transformation 21]
125. funny(X0) | strong(X0) [duplicate literal removal 115]
126. funny(X0) | ~strong(X0) [duplicate literal removal 116]
200. 17 <=> kind(john) [avatar definition]
201. kind(john) <- (17) [avatar component clause 200]
217. 21 <=> ! [X1] : generous(X1) [avatar definition]
218. generous(X1) <- (21) [avatar component clause 217]
224. 21 | 17 [avatar split clause 97,200,217]
280. funny(X0) [subsumption resolution 125,126]
300. ~generous(susan) [resolution 82,124]
302. ~kind(X1) [resolution 95,280]
314. $false <- (17) [resolution 302,201]
315. ~17 [avatar contradiction clause 314]
321. $false <- (21) [resolution 218,300]
322. ~21 [avatar contradiction clause 321]
325. $false [avatar sat refutation 224,315,322]
% SZS output end Proof for 8871318985500693168872587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and kind then someone is both tall and not curious.
Everyone who is wise or creative is either rich or curious.
If someone is either not creative or rich then john is either not kind or creative.
If someone is not old or curious then someone is not funny or not generous.
If fred is both not old and happy then someone is quiet or not rich.
If paul is either kind or not brave then someone is either kind or not tall and vice versa.
If someone is either not curious or not tall then someone is generous.
Everyone who is either not patient or funny is not calm or quiet.
If paul is both not quiet and quiet then someone is old and vice versa.
If john is curious or not old then someone is not tall and vice versa.
Everyone who is tall is not calm or not rich and vice versa.
If someone is both not rich and kind then someone is quiet.
If alice is brave then someone is both humble and curious and vice versa.
Everyone who is not calm or rich is either not generous or not old.
If someone is happy or not funny then lucy is both happy and not calm and vice versa.
If susan is humble then mary is kind.
Fred is calm.
Susan is old or curious.
Someone is both calm and quiet.
Someone is not funny or curious.
Someone is not patient or not wise.
Alice is not patient.
Mary is quiet or not tall.
Someone is not wise. | Fred is old. | contradiction | ((?[X]:((wise(X)&kind(X))))=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:((wise(X)|creative(X))=>(rich(X)<~>curious(X))))&
((?[X]:((~creative(X)<~>rich(X))))=>((~kind(john)<~>creative(john))))&
((?[X]:((~old(X)|curious(X))))=>(?[X]:((~funny(X)|~generous(X)))))&
(((~old(fred)&happy(fred)))=>(?[X]:((quiet(X)|~rich(X)))))&
(((kind(paul)<~>~brave(paul)))<=>(?[X]:((kind(X)<~>~tall(X)))))&
((?[X]:((~curious(X)<~>~tall(X))))=>(?[X]:(generous(X))))&
(![X]:((~patient(X)<~>funny(X))=>(~calm(X)|quiet(X))))&
(((~quiet(paul)&quiet(paul)))<=>(?[X]:(old(X))))&
(((curious(john)|~old(john)))<=>(?[X]:(~tall(X))))&
(![X]:(tall(X)<=>(~calm(X)|~rich(X))))&
((?[X]:((~rich(X)&kind(X))))=>(?[X]:(quiet(X))))&
((brave(alice))<=>(?[X]:((humble(X)&curious(X)))))&
(![X]:((~calm(X)|rich(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((happy(X)|~funny(X))))<=>((happy(lucy)&~calm(lucy))))&
((humble(susan))=>(kind(mary)))&
(calm(fred))&
((old(susan)|curious(susan)))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:((~patient(X)|~wise(X))))&
(~patient(alice))&
((quiet(mary)|~tall(mary)))&
(?[X]:(~wise(X))) | old(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3247596622092663989741900
% SZS output start Proof for 3247596622092663989741900
9. (quiet(paul) & ~quiet(paul)) <=> ? [X0] : old(X0) [input p8]
25. old(fred) [input hypothesis]
61. ((quiet(paul) & ~quiet(paul)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (~quiet(paul) | quiet(paul))) [nnf transformation 9]
62. ((quiet(paul) & ~quiet(paul)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ~quiet(paul) | quiet(paul)) [flattening 61]
63. ((quiet(paul) & ~quiet(paul)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ~quiet(paul) | quiet(paul)) [rectify 62]
64. ? [X1] : old(X1) => old(sK4) [choice axiom]
65. ((quiet(paul) & ~quiet(paul)) | ! [X0] : ~old(X0)) & (old(sK4) | ~quiet(paul) | quiet(paul)) [skolemisation 63,64]
112. ~quiet(paul) | ~old(X0) [cnf transformation 65]
113. quiet(paul) | ~old(X0) [cnf transformation 65]
141. old(fred) [cnf transformation 25]
177. 9 <=> old(fred) [avatar definition]
179. old(fred) <- (9) [avatar component clause 177]
236. 22 <=> ! [X0] : ~old(X0) [avatar definition]
237. ~old(X0) <- (22) [avatar component clause 236]
239. 23 <=> quiet(paul) [avatar definition]
242. 22 | 23 [avatar split clause 113,239,236]
243. 22 | ~23 [avatar split clause 112,239,236]
351. 9 [avatar split clause 141,177]
352. $false <- (9, 22) [subsumption resolution 179,237]
353. ~9 | ~22 [avatar contradiction clause 352]
354. $false [avatar sat refutation 242,243,351,353]
% SZS output end Proof for 3247596622092663989741900
% ------------------------------
% 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 not patient or kind is either not generous or quiet.
If alice is not happy then someone is either curious or not brave and vice versa.
If someone is both old and not kind then someone is not curious or generous and vice versa.
If someone is either creative or quiet then someone is not old and vice versa.
Everyone who is not wise is quiet or not creative and vice versa.
Everyone who is not patient is either not calm or not quiet.
Everyone who is either not rich or brave is both kind and rich and vice versa.
Everyone who is wise is either wise or not wise and vice versa.
Everyone who is curious is not curious or not happy and vice versa.
Everyone who is both not generous and calm is both strong and not happy and vice versa.
Everyone who is either not kind or generous is either happy or not funny and vice versa.
Everyone who is tall or not old is not funny or not creative and vice versa.
If fred is not patient or quiet then someone is not brave.
Everyone who is either tall or not happy is quiet or not humble and vice versa.
If susan is either funny or not wise then someone is either not funny or not calm.
Everyone who is not happy is humble and vice versa.
Fred is not old or happy.
Susan is not kind.
Alice is patient or old.
Someone is not brave.
Someone is not calm.
Someone is either not creative or not kind.
Fred is either strong or old.
Someone is brave or not wise. | Alice is not humble. | contradiction | (![X]:((~patient(X)<~>kind(X))=>(~generous(X)<~>quiet(X))))&
((~happy(alice))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((?[X]:((old(X)&~kind(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:(~wise(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~patient(X)=>(~calm(X)<~>~quiet(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(kind(X)&rich(X))))&
(![X]:(wise(X)<=>(wise(X)<~>~wise(X))))&
(![X]:(curious(X)<=>(~curious(X)|~happy(X))))&
(![X]:((~generous(X)&calm(X))<=>(strong(X)&~happy(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((tall(X)|~old(X))<=>(~funny(X)|~creative(X))))&
(((~patient(fred)|quiet(fred)))=>(?[X]:(~brave(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(quiet(X)|~humble(X))))&
(((funny(susan)<~>~wise(susan)))=>(?[X]:((~funny(X)<~>~calm(X)))))&
(![X]:(~happy(X)<=>humble(X)))&
((~old(fred)|happy(fred)))&
(~kind(susan))&
((patient(alice)|old(alice)))&
(?[X]:(~brave(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~creative(X)<~>~kind(X))))&
((strong(fred)<~>old(fred)))&
(?[X]:((brave(X)|~wise(X)))) | ~humble(alice) | [
"p1",
"p7",
"p8",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4921850262170633991757281
% SZS output start Proof for 4921850262170633991757281
2. ~happy(alice) <=> ? [X0] : (curious(X0) <~> ~brave(X0)) [input p1]
8. ! [X0] : (wise(X0) <=> (wise(X0) <~> ~wise(X0))) [input p7]
9. ! [X0] : (curious(X0) <=> (~happy(X0) | ~curious(X0))) [input p8]
16. ! [X0] : (~happy(X0) <=> humble(X0)) [input p15]
24. ? [X0] : (~wise(X0) | brave(X0)) [input p23]
25. ~humble(alice) [input hypothesis]
33. (~happy(alice) | ! [X0] : ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (? [X0] : ((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | happy(alice)) [nnf transformation 2]
34. (~happy(alice) | ! [X0] : ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (? [X1] : ((brave(X1) | ~curious(X1)) & (~brave(X1) | curious(X1))) | happy(alice)) [rectify 33]
35. ? [X1] : ((brave(X1) | ~curious(X1)) & (~brave(X1) | curious(X1))) => ((brave(sK0) | ~curious(sK0)) & (~brave(sK0) | curious(sK0))) [choice axiom]
36. (~happy(alice) | ! [X0] : ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(sK0) | ~curious(sK0)) & (~brave(sK0) | curious(sK0))) | happy(alice)) [skolemisation 34,35]
52. ! [X0] : ((wise(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~wise(X0))) [nnf transformation 8]
53. ! [X0] : ((curious(X0) | (happy(X0) & curious(X0))) & ((~happy(X0) | ~curious(X0)) | ~curious(X0))) [nnf transformation 9]
54. ! [X0] : ((curious(X0) | (happy(X0) & curious(X0))) & (~happy(X0) | ~curious(X0) | ~curious(X0))) [flattening 53]
67. ! [X0] : ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))) [nnf transformation 16]
76. ? [X0] : (~wise(X0) | brave(X0)) => (~wise(sK10) | brave(sK10)) [choice axiom]
77. ~wise(sK10) | brave(sK10) [skolemisation 24,76]
84. ~happy(alice) | ~brave(X0) | ~curious(X0) [cnf transformation 36]
109. wise(X0) | wise(X0) | wise(X0) [cnf transformation 52]
111. curious(X0) | curious(X0) [cnf transformation 54]
141. humble(X0) | happy(X0) [cnf transformation 67]
152. ~wise(sK10) | brave(sK10) [cnf transformation 77]
153. ~humble(alice) [cnf transformation 25]
155. curious(X0) [duplicate literal removal 111]
159. wise(X0) [duplicate literal removal 109]
166. 2 <=> happy(alice) [avatar definition]
171. 3 <=> ! [X0] : (~brave(X0) | ~curious(X0)) [avatar definition]
172. ~brave(X0) | ~curious(X0) <- (3) [avatar component clause 171]
173. 3 | ~2 [avatar split clause 84,166,171]
193. 8 <=> ! [X1] : curious(X1) [avatar definition]
194. curious(X1) <- (8) [avatar component clause 193]
239. 8 [avatar split clause 155,193]
304. brave(sK10) [subsumption resolution 152,159]
314. happy(alice) [resolution 141,153]
317. 2 [avatar split clause 314,166]
318. ~brave(X0) <- (3, 8) [subsumption resolution 172,194]
320. $false <- (3, 8) [resolution 318,304]
321. ~3 | ~8 [avatar contradiction clause 320]
323. $false [avatar sat refutation 173,239,317,321]
% SZS output end Proof for 4921850262170633991757281
% ------------------------------
% 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 strong or humble is patient.
Everyone who is either not rich or creative is either rich or not tall.
If someone is either not wise or strong then fred is either not brave or not rich.
If paul is not quiet or not creative then someone is wise or not patient and vice versa.
Everyone who is either quiet or not quiet is either not brave or tall.
Everyone who is both brave and not humble is not kind or tall and vice versa.
Everyone who is both generous and humble is both not humble and not old and vice versa.
Everyone who is both wise and quiet is either calm or not creative and vice versa.
If someone is patient then fred is both humble and not kind.
If someone is either not rich or wise then someone is not funny.
If someone is either not brave or rich then mary is both not patient and not kind.
Everyone who is not curious or curious is either not strong or generous and vice versa.
If someone is either quiet or kind then paul is both curious and not old.
If mary is not strong or happy then someone is not tall or not happy.
If john is not brave or not happy then someone is funny.
Everyone who is not funny is not kind and vice versa.
John is not creative.
Someone is not creative or happy.
Someone is generous or curious.
Susan is funny.
Paul is not curious.
Fred is not strong. | Fred is not rich. | neutral | (![X]:((strong(X)<~>humble(X))=>patient(X)))&
(![X]:((~rich(X)<~>creative(X))=>(rich(X)<~>~tall(X))))&
((?[X]:((~wise(X)<~>strong(X))))=>((~brave(fred)<~>~rich(fred))))&
(((~quiet(paul)|~creative(paul)))<=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((quiet(X)<~>~quiet(X))=>(~brave(X)<~>tall(X))))&
(![X]:((brave(X)&~humble(X))<=>(~kind(X)|tall(X))))&
(![X]:((generous(X)&humble(X))<=>(~humble(X)&~old(X))))&
(![X]:((wise(X)&quiet(X))<=>(calm(X)<~>~creative(X))))&
((?[X]:(patient(X)))=>((humble(fred)&~kind(fred))))&
((?[X]:((~rich(X)<~>wise(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~brave(X)<~>rich(X))))=>((~patient(mary)&~kind(mary))))&
(![X]:((~curious(X)|curious(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:((quiet(X)<~>kind(X))))=>((curious(paul)&~old(paul))))&
(((~strong(mary)|happy(mary)))=>(?[X]:((~tall(X)|~happy(X)))))&
(((~brave(john)|~happy(john)))=>(?[X]:(funny(X))))&
(![X]:(~funny(X)<=>~kind(X)))&
(~creative(john))&
(?[X]:((~creative(X)|happy(X))))&
(?[X]:((generous(X)|curious(X))))&
(funny(susan))&
(~curious(paul))&
(~strong(fred)) | ~rich(fred) | [] | null | 0 |
Everyone who is either creative or generous is both old and not rich and vice versa. Everyone who is not patient is both not old and quiet and vice versa. Everyone who is both not brave and strong is either wise or not humble. If mary is not strong then mary is either not kind or calm and vice versa. Everyone who is not funny is either not happy or funny and vice versa. Everyone who is patient or calm is either not brave or not strong and vice versa. Everyone who is both rich and not patient is both old and not quiet and vice versa. Everyone who is strong or old is not old and vice versa. If someone is both rich and not humble then someone is either happy or creative. Everyone who is both strong and not brave is not kind and vice versa. If john is both wise and tall then fred is brave and vice versa. Everyone who is either calm or wise is both not kind and kind. If alice is either curious or not calm then someone is patient. Everyone who is both old and not curious is not quiet or not humble and vice versa. If someone is brave then someone is both not patient and curious. Everyone who is not humble or generous is creative. Someone is both not funny and curious. Someone is tall. Someone is either generous or not quiet. Someone is either not generous or tall. Alice is wise or not humble. Someone is strong. Paul is not funny. | Alice is curious. | contradiction | (![X]:((creative(X)<~>generous(X))<=>(old(X)&~rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&quiet(X))))&
(![X]:((~brave(X)&strong(X))=>(wise(X)<~>~humble(X))))&
((~strong(mary))<=>((~kind(mary)<~>calm(mary))))&
(![X]:(~funny(X)<=>(~happy(X)<~>funny(X))))&
(![X]:((patient(X)|calm(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:((rich(X)&~patient(X))<=>(old(X)&~quiet(X))))&
(![X]:((strong(X)|old(X))<=>~old(X)))&
((?[X]:((rich(X)&~humble(X))))=>(?[X]:((happy(X)<~>creative(X)))))&
(![X]:((strong(X)&~brave(X))<=>~kind(X)))&
(((wise(john)&tall(john)))<=>(brave(fred)))&
(![X]:((calm(X)<~>wise(X))=>(~kind(X)&kind(X))))&
(((curious(alice)<~>~calm(alice)))=>(?[X]:(patient(X))))&
(![X]:((old(X)&~curious(X))<=>(~quiet(X)|~humble(X))))&
((?[X]:(brave(X)))=>(?[X]:((~patient(X)&curious(X)))))&
(![X]:((~humble(X)|generous(X))=>creative(X)))&
(?[X]:((~funny(X)&curious(X))))&
(?[X]:(tall(X)))&
(?[X]:((generous(X)<~>~quiet(X))))&
(?[X]:((~generous(X)<~>tall(X))))&
((wise(alice)|~humble(alice)))&
(?[X]:(strong(X)))&
(~funny(paul)) | curious(alice) | [
"p1",
"p7",
"p11",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6740821836519827927334773
% SZS output start Proof for 6740821836519827927334773
2. ! [X0] : (~patient(X0) <=> (quiet(X0) & ~old(X0))) [input p1]
8. ! [X0] : ((old(X0) | strong(X0)) <=> ~old(X0)) [input p7]
12. ! [X0] : ((calm(X0) <~> wise(X0)) => (kind(X0) & ~kind(X0))) [input p11]
13. (curious(alice) <~> ~calm(alice)) => ? [X0] : patient(X0) [input p12]
14. ! [X0] : ((~curious(X0) & old(X0)) <=> (~humble(X0) | ~quiet(X0))) [input p13]
21. ~humble(alice) | wise(alice) [input p20]
24. curious(alice) [input hypothesis]
30. ! [X0] : ((kind(X0) & ~kind(X0)) | (calm(X0) <=> wise(X0))) [ennf transformation 12]
31. ? [X0] : patient(X0) | (curious(alice) <=> ~calm(alice)) [ennf transformation 13]
36. ! [X0] : ((~patient(X0) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | patient(X0))) [nnf transformation 2]
37. ! [X0] : ((~patient(X0) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | patient(X0))) [flattening 36]
45. ! [X0] : (((old(X0) | strong(X0)) | old(X0)) & (~old(X0) | (~old(X0) & ~strong(X0)))) [nnf transformation 8]
46. ! [X0] : ((old(X0) | strong(X0) | old(X0)) & (~old(X0) | (~old(X0) & ~strong(X0)))) [flattening 45]
55. ! [X0] : ((kind(X0) & ~kind(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) [nnf transformation 30]
56. ? [X0] : patient(X0) | ((curious(alice) | calm(alice)) & (~calm(alice) | ~curious(alice))) [nnf transformation 31]
57. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
58. patient(sK1) | ((curious(alice) | calm(alice)) & (~calm(alice) | ~curious(alice))) [skolemisation 56,57]
59. ! [X0] : (((~curious(X0) & old(X0)) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | (curious(X0) | ~old(X0)))) [nnf transformation 14]
60. ! [X0] : (((~curious(X0) & old(X0)) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | curious(X0) | ~old(X0))) [flattening 59]
84. ~quiet(X0) | ~patient(X0) | old(X0) [cnf transformation 37]
106. ~old(X0) | ~old(X0) [cnf transformation 46]
117. ~kind(X0) | calm(X0) | ~wise(X0) [cnf transformation 55]
119. kind(X0) | calm(X0) | ~wise(X0) [cnf transformation 55]
120. patient(sK1) | ~calm(alice) | ~curious(alice) [cnf transformation 58]
123. old(X0) | quiet(X0) [cnf transformation 60]
124. old(X0) | humble(X0) [cnf transformation 60]
138. ~humble(alice) | wise(alice) [cnf transformation 21]
141. curious(alice) [cnf transformation 24]
142. ~old(X0) [duplicate literal removal 106]
189. ~wise(X0) | calm(X0) [subsumption resolution 117,119]
192. 9 <=> calm(alice) [avatar definition]
196. 10 <=> curious(alice) [avatar definition]
200. 11 <=> patient(sK1) [avatar definition]
202. patient(sK1) <- (11) [avatar component clause 200]
204. ~10 | ~9 | 11 [avatar split clause 120,200,192,196]
205. humble(X0) [subsumption resolution 124,142]
206. quiet(X0) [subsumption resolution 123,142]
231. wise(alice) [subsumption resolution 138,205]
232. 10 [avatar split clause 141,196]
242. calm(alice) [resolution 189,231]
245. 9 [avatar split clause 242,192]
252. ~patient(X1) | old(X1) [resolution 84,206]
253. ~patient(X1) [subsumption resolution 252,142]
254. $false <- (11) [resolution 253,202]
255. ~11 [avatar contradiction clause 254]
256. $false [avatar sat refutation 204,232,245,255]
% SZS output end Proof for 6740821836519827927334773
% ------------------------------
% 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 susan is not kind or not rich then fred is wise or old and vice versa.
Everyone who is either not creative or old is either not happy or not wise and vice versa.
Everyone who is either rich or strong is both humble and not strong.
Everyone who is not kind or generous is curious or not calm.
If john is not wise then paul is both rich and patient.
Everyone who is rich is either not rich or generous.
Everyone who is either not funny or old is not creative or not wise and vice versa.
Everyone who is funny or rich is calm.
If someone is either happy or not quiet then someone is not wise.
Everyone who is happy is not funny or happy.
If mary is both not calm and kind then someone is not quiet and vice versa.
Everyone who is either not generous or not rich is both not humble and funny and vice versa.
Everyone who is not curious is strong or brave and vice versa.
Everyone who is either not patient or tall is either strong or not wise and vice versa.
If someone is generous or not humble then someone is either strong or not brave.
If someone is not tall or not funny then someone is both not humble and wise and vice versa.
Someone is either generous or not creative.
Someone is funny or not creative.
Fred is curious or tall.
Someone is both rich and funny.
Paul is creative.
Someone is not creative.
Susan is not patient or creative.
Fred is not wise. | Mary is not strong. | entailment | (((~kind(susan)|~rich(susan)))<=>((wise(fred)|old(fred))))&
(![X]:((~creative(X)<~>old(X))<=>(~happy(X)<~>~wise(X))))&
(![X]:((rich(X)<~>strong(X))=>(humble(X)&~strong(X))))&
(![X]:((~kind(X)|generous(X))=>(curious(X)|~calm(X))))&
((~wise(john))=>((rich(paul)&patient(paul))))&
(![X]:(rich(X)=>(~rich(X)<~>generous(X))))&
(![X]:((~funny(X)<~>old(X))<=>(~creative(X)|~wise(X))))&
(![X]:((funny(X)|rich(X))=>calm(X)))&
((?[X]:((happy(X)<~>~quiet(X))))=>(?[X]:(~wise(X))))&
(![X]:(happy(X)=>(~funny(X)|happy(X))))&
(((~calm(mary)&kind(mary)))<=>(?[X]:(~quiet(X))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~humble(X)&funny(X))))&
(![X]:(~curious(X)<=>(strong(X)|brave(X))))&
(![X]:((~patient(X)<~>tall(X))<=>(strong(X)<~>~wise(X))))&
((?[X]:((generous(X)|~humble(X))))=>(?[X]:((strong(X)<~>~brave(X)))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~humble(X)&wise(X)))))&
(?[X]:((generous(X)<~>~creative(X))))&
(?[X]:((funny(X)|~creative(X))))&
((curious(fred)|tall(fred)))&
(?[X]:((rich(X)&funny(X))))&
(creative(paul))&
(?[X]:(~creative(X)))&
((~patient(susan)|creative(susan)))&
(~wise(fred)) | ~strong(mary) | [
"p2",
"p3",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 118011506437494605822871
% SZS output start Proof for 118011506437494605822871
3. ! [X0] : ((rich(X0) <~> strong(X0)) => (~strong(X0) & humble(X0))) [input p2]
4. ! [X0] : ((generous(X0) | ~kind(X0)) => (~calm(X0) | curious(X0))) [input p3]
6. ! [X0] : (rich(X0) => (~rich(X0) <~> generous(X0))) [input p5]
8. ! [X0] : ((rich(X0) | funny(X0)) => calm(X0)) [input p7]
13. ! [X0] : (~curious(X0) <=> (brave(X0) | strong(X0))) [input p12]
25. strong(mary) [input hypothesis]
29. ! [X0] : ((brave(X0) | strong(X0)) => ~curious(X0)) [unused predicate definition removal 13]
30. ! [X0] : ((~strong(X0) & humble(X0)) | (rich(X0) <=> strong(X0))) [ennf transformation 3]
31. ! [X0] : ((~calm(X0) | curious(X0)) | (~generous(X0) & kind(X0))) [ennf transformation 4]
32. ! [X0] : (~calm(X0) | curious(X0) | (~generous(X0) & kind(X0))) [flattening 31]
34. ! [X0] : ((~rich(X0) <~> generous(X0)) | ~rich(X0)) [ennf transformation 6]
35. ! [X0] : (calm(X0) | (~rich(X0) & ~funny(X0))) [ennf transformation 8]
39. ! [X0] : (~curious(X0) | (~brave(X0) & ~strong(X0))) [ennf transformation 29]
44. ! [X0] : ((~strong(X0) & humble(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) [nnf transformation 30]
45. ! [X0] : (((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ~rich(X0)) [nnf transformation 34]
93. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 44]
95. ~calm(X0) | curious(X0) | ~generous(X0) [cnf transformation 32]
98. generous(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 45]
107. ~rich(X0) | calm(X0) [cnf transformation 35]
120. ~curious(X0) | ~strong(X0) [cnf transformation 39]
149. strong(mary) [cnf transformation 25]
150. ~rich(X0) | generous(X0) [duplicate literal removal 98]
151. ~strong(X0) | rich(X0) [duplicate literal removal 93]
207. 13 <=> calm(mary) [avatar definition]
208. calm(mary) <- (13) [avatar component clause 207]
310. rich(mary) [resolution 151,149]
332. generous(mary) [resolution 310,150]
333. calm(mary) [resolution 310,107]
334. 13 [avatar split clause 333,207]
351. 40 <=> curious(mary) [avatar definition]
353. curious(mary) <- (40) [avatar component clause 351]
356. curious(mary) | ~generous(mary) <- (13) [resolution 95,208]
359. curious(mary) <- (13) [subsumption resolution 356,332]
360. 40 | ~13 [avatar split clause 359,207,351]
361. ~strong(mary) <- (40) [resolution 353,120]
362. $false <- (40) [subsumption resolution 361,149]
363. ~40 [avatar contradiction clause 362]
364. $false [avatar sat refutation 334,360,363]
% SZS output end Proof for 118011506437494605822871
% ------------------------------
% 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 rich is either not creative or quiet and vice versa.
Everyone who is generous is either humble or rich and vice versa.
Everyone who is brave is either not generous or not tall and vice versa.
Everyone who is both not happy and curious is either not curious or kind and vice versa.
Everyone who is not patient or not happy is either not calm or curious and vice versa.
Everyone who is either not wise or curious is not brave or not tall and vice versa.
If someone is both not brave and patient then someone is either tall or not patient.
Everyone who is both not strong and not curious is either not humble or quiet and vice versa.
Everyone who is happy is not curious or not patient.
Everyone who is either tall or funny is brave and vice versa.
If mary is both rich and not strong then someone is either not kind or not rich.
If someone is old then alice is either funny or old and vice versa.
Everyone who is either happy or not tall is either not humble or not quiet and vice versa.
If paul is either patient or not calm then someone is not creative or old.
Everyone who is either not creative or not humble is both patient and not humble and vice versa.
Everyone who is not rich is either not patient or not kind and vice versa.
Lucy is either not patient or not generous.
Someone is either not humble or humble.
Alice is both curious and not tall.
Someone is calm.
Someone is either not brave or not quiet.
Lucy is either not kind or not rich.
Someone is funny or not generous. | Lucy is humble. | entailment | (![X]:(rich(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:(generous(X)<=>(humble(X)<~>rich(X))))&
(![X]:(brave(X)<=>(~generous(X)<~>~tall(X))))&
(![X]:((~happy(X)&curious(X))<=>(~curious(X)<~>kind(X))))&
(![X]:((~patient(X)|~happy(X))<=>(~calm(X)<~>curious(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(~brave(X)|~tall(X))))&
((?[X]:((~brave(X)&patient(X))))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:((~strong(X)&~curious(X))<=>(~humble(X)<~>quiet(X))))&
(![X]:(happy(X)=>(~curious(X)|~patient(X))))&
(![X]:((tall(X)<~>funny(X))<=>brave(X)))&
(((rich(mary)&~strong(mary)))=>(?[X]:((~kind(X)<~>~rich(X)))))&
((?[X]:(old(X)))<=>((funny(alice)<~>old(alice))))&
(![X]:((happy(X)<~>~tall(X))<=>(~humble(X)<~>~quiet(X))))&
(((patient(paul)<~>~calm(paul)))=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((~creative(X)<~>~humble(X))<=>(patient(X)&~humble(X))))&
(![X]:(~rich(X)<=>(~patient(X)<~>~kind(X))))&
((~patient(lucy)<~>~generous(lucy)))&
(?[X]:((~humble(X)<~>humble(X))))&
((curious(alice)&~tall(alice)))&
(?[X]:(calm(X)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:((funny(X)|~generous(X)))) | humble(lucy) | [
"p0",
"p1",
"p3",
"p7",
"p8",
"p14",
"p15",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6910831223867245442967625
% SZS output start Proof for 6910831223867245442967625
1. ! [X0] : (rich(X0) <=> (~creative(X0) <~> quiet(X0))) [input p0]
2. ! [X0] : (generous(X0) <=> (humble(X0) <~> rich(X0))) [input p1]
4. ! [X0] : ((curious(X0) & ~happy(X0)) <=> (~curious(X0) <~> kind(X0))) [input p3]
8. ! [X0] : ((~curious(X0) & ~strong(X0)) <=> (~humble(X0) <~> quiet(X0))) [input p7]
9. ! [X0] : (happy(X0) => (~patient(X0) | ~curious(X0))) [input p8]
15. ! [X0] : ((~creative(X0) <~> ~humble(X0)) <=> (~humble(X0) & patient(X0))) [input p14]
16. ! [X0] : (~rich(X0) <=> (~patient(X0) <~> ~kind(X0))) [input p15]
17. ~patient(lucy) <~> ~generous(lucy) [input p16]
22. ~kind(lucy) <~> ~rich(lucy) [input p21]
24. ~humble(lucy) [input hypothesis]
27. ! [X0] : ((~patient(X0) | ~curious(X0)) | ~happy(X0)) [ennf transformation 9]
28. ! [X0] : (~patient(X0) | ~curious(X0) | ~happy(X0)) [flattening 27]
32. ! [X0] : ((rich(X0) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0)))) & (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | ~rich(X0))) [nnf transformation 1]
33. ! [X0] : ((generous(X0) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ~generous(X0))) [nnf transformation 2]
35. ! [X0] : (((curious(X0) & ~happy(X0)) | ((~curious(X0) | ~kind(X0)) & (kind(X0) | curious(X0)))) & (((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) | (~curious(X0) | happy(X0)))) [nnf transformation 4]
36. ! [X0] : (((curious(X0) & ~happy(X0)) | ((~curious(X0) | ~kind(X0)) & (kind(X0) | curious(X0)))) & (((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) | ~curious(X0) | happy(X0))) [flattening 35]
45. ! [X0] : (((~curious(X0) & ~strong(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (curious(X0) | strong(X0)))) [nnf transformation 8]
46. ! [X0] : (((~curious(X0) & ~strong(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | curious(X0) | strong(X0))) [flattening 45]
59. ! [X0] : ((((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | (humble(X0) | ~patient(X0))) & ((~humble(X0) & patient(X0)) | ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0))))) [nnf transformation 15]
60. ! [X0] : ((((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | humble(X0) | ~patient(X0)) & ((~humble(X0) & patient(X0)) | ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0))))) [flattening 59]
61. ! [X0] : ((~rich(X0) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | rich(X0))) [nnf transformation 16]
62. (generous(lucy) | patient(lucy)) & (~generous(lucy) | ~patient(lucy)) [nnf transformation 17]
71. (rich(lucy) | kind(lucy)) & (~rich(lucy) | ~kind(lucy)) [nnf transformation 22]
75. ~quiet(X0) | creative(X0) | ~rich(X0) [cnf transformation 32]
78. ~generous(X0) | humble(X0) | rich(X0) [cnf transformation 33]
86. kind(X0) | ~curious(X0) | ~curious(X0) | happy(X0) [cnf transformation 36]
90. curious(X0) | kind(X0) | curious(X0) [cnf transformation 36]
110. ~curious(X0) | quiet(X0) | humble(X0) [cnf transformation 46]
112. ~patient(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 28]
134. ~creative(X0) | patient(X0) | humble(X0) [cnf transformation 60]
139. ~patient(X0) | ~kind(X0) | rich(X0) [cnf transformation 61]
144. generous(lucy) | patient(lucy) [cnf transformation 62]
152. ~rich(lucy) | ~kind(lucy) [cnf transformation 71]
153. rich(lucy) | kind(lucy) [cnf transformation 71]
155. ~humble(lucy) [cnf transformation 24]
158. kind(X0) | ~curious(X0) | happy(X0) [duplicate literal removal 86]
159. kind(X0) | curious(X0) [duplicate literal removal 90]
160. kind(X0) | happy(X0) [subsumption resolution 158,159]
230. 16 <=> patient(lucy) [avatar definition]
231. ~patient(lucy) <- (~16) [avatar component clause 230]
232. patient(lucy) <- (16) [avatar component clause 230]
234. 17 <=> generous(lucy) [avatar definition]
236. generous(lucy) <- (17) [avatar component clause 234]
237. 16 | 17 [avatar split clause 144,234,230]
250. 20 <=> kind(lucy) [avatar definition]
251. ~kind(lucy) <- (~20) [avatar component clause 250]
254. 21 <=> rich(lucy) [avatar definition]
256. rich(lucy) <- (21) [avatar component clause 254]
257. 20 | 21 [avatar split clause 153,254,250]
258. ~20 | ~21 [avatar split clause 152,254,250]
305. 28 <=> happy(lucy) [avatar definition]
309. 29 <=> curious(lucy) [avatar definition]
310. curious(lucy) <- (29) [avatar component clause 309]
417. ~curious(lucy) | ~happy(lucy) <- (16) [resolution 112,232]
449. ~kind(lucy) | rich(lucy) <- (16) [resolution 139,232]
455. 21 | ~20 | ~16 [avatar split clause 449,230,250,254]
456. happy(lucy) <- (~20) [resolution 251,160]
457. curious(lucy) <- (~20) [resolution 251,159]
460. 29 | 20 [avatar split clause 457,250,309]
461. 28 | 20 [avatar split clause 456,250,305]
462. ~28 | ~29 | ~16 [avatar split clause 417,230,309,305]
464. humble(lucy) | rich(lucy) <- (17) [resolution 236,78]
492. quiet(lucy) | humble(lucy) <- (29) [resolution 310,110]
497. quiet(lucy) <- (29) [subsumption resolution 492,155]
549. creative(lucy) | ~rich(lucy) <- (29) [resolution 497,75]
550. creative(lucy) <- (21, 29) [subsumption resolution 549,256]
666. patient(lucy) | humble(lucy) <- (21, 29) [resolution 550,134]
668. humble(lucy) <- (~16, 21, 29) [subsumption resolution 666,231]
669. $false <- (~16, 21, 29) [subsumption resolution 668,155]
670. 16 | ~21 | ~29 [avatar contradiction clause 669]
671. rich(lucy) <- (17) [subsumption resolution 464,155]
672. 21 | ~17 [avatar split clause 671,234,254]
677. $false [avatar sat refutation 237,257,258,455,460,461,462,670,672]
% SZS output end Proof for 6910831223867245442967625
% ------------------------------
% 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either rich or creative.
If someone is generous then someone is patient.
Everyone who is either tall or not rich is both patient and not wise.
If john is not humble then someone is either wise or brave and vice versa.
Everyone who is not rich or not curious is both not generous and not happy.
Everyone who is kind or not tall is happy and vice versa.
If alice is not brave or generous then paul is both quiet and humble and vice versa.
Everyone who is both funny and not quiet is both not funny and not happy and vice versa.
If someone is not old then fred is both quiet and not old and vice versa.
Everyone who is happy is either not wise or not old.
Everyone who is not kind is both generous and wise.
If someone is either not quiet or kind then fred is either not tall or not humble.
If someone is patient then lucy is both wise and not rich and vice versa.
If mary is both quiet and not funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
Mary is quiet.
Someone is strong.
Someone is kind.
Someone is both humble and rich.
John is not strong.
Someone is either creative or old.
Lucy is either rich or not happy. | Alice is wise. | contradiction | (![X]:(old(X)=>(rich(X)<~>creative(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
(![X]:((tall(X)<~>~rich(X))=>(patient(X)&~wise(X))))&
((~humble(john))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~generous(X)&~happy(X))))&
(![X]:((kind(X)|~tall(X))<=>happy(X)))&
(((~brave(alice)|generous(alice)))<=>((quiet(paul)&humble(paul))))&
(![X]:((funny(X)&~quiet(X))<=>(~funny(X)&~happy(X))))&
((?[X]:(~old(X)))<=>((quiet(fred)&~old(fred))))&
(![X]:(happy(X)=>(~wise(X)<~>~old(X))))&
(![X]:(~kind(X)=>(generous(X)&wise(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>((~tall(fred)<~>~humble(fred))))&
((?[X]:(patient(X)))<=>((wise(lucy)&~rich(lucy))))&
(((quiet(mary)&~funny(mary)))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(quiet(mary))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&rich(X))))&
(~strong(john))&
(?[X]:((creative(X)<~>old(X))))&
((rich(lucy)<~>~happy(lucy))) | wise(alice) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3555410812108341203812296
% SZS output start Proof for 3555410812108341203812296
2. ? [X0] : generous(X0) => ? [X0] : patient(X0) [input p1]
3. ! [X0] : ((tall(X0) <~> ~rich(X0)) => (~wise(X0) & patient(X0))) [input p2]
5. ! [X0] : ((~curious(X0) | ~rich(X0)) => (~happy(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~tall(X0) | kind(X0)) <=> happy(X0)) [input p5]
9. ? [X0] : ~old(X0) <=> (~old(fred) & quiet(fred)) [input p8]
10. ! [X0] : (happy(X0) => (~wise(X0) <~> ~old(X0))) [input p9]
11. ! [X0] : (~kind(X0) => (wise(X0) & generous(X0))) [input p10]
13. ? [X0] : patient(X0) <=> (~rich(lucy) & wise(lucy)) [input p12]
16. ! [X0] : ((~wise(X0) <~> ~generous(X0)) => (~quiet(X0) <~> tall(X0))) [input p15]
24. wise(alice) [input hypothesis]
25. ? [X0] : generous(X0) => ? [X1] : patient(X1) [rectify 2]
26. ! [X0] : (~rich(X0) => (~happy(X0) & ~generous(X0))) [pure predicate removal 5]
28. ? [X1] : patient(X1) | ! [X0] : ~generous(X0) [ennf transformation 25]
29. ! [X0] : ((~wise(X0) & patient(X0)) | (tall(X0) <=> ~rich(X0))) [ennf transformation 3]
30. ! [X0] : ((~happy(X0) & ~generous(X0)) | rich(X0)) [ennf transformation 26]
31. ! [X0] : ((~wise(X0) <~> ~old(X0)) | ~happy(X0)) [ennf transformation 10]
32. ! [X0] : ((wise(X0) & generous(X0)) | kind(X0)) [ennf transformation 11]
35. ! [X0] : ((~quiet(X0) <~> tall(X0)) | (~wise(X0) <=> ~generous(X0))) [ennf transformation 16]
37. ? [X0] : patient(X0) | ! [X1] : ~generous(X1) [rectify 28]
38. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
39. patient(sK0) | ! [X1] : ~generous(X1) [skolemisation 37,38]
40. ! [X0] : ((~wise(X0) & patient(X0)) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) [nnf transformation 29]
45. ! [X0] : (((~tall(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [nnf transformation 6]
46. ! [X0] : ((~tall(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [flattening 45]
51. (? [X0] : ~old(X0) | (old(fred) | ~quiet(fred))) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [nnf transformation 9]
52. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [flattening 51]
53. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [rectify 52]
54. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
55. (~old(sK2) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [skolemisation 53,54]
56. ! [X0] : (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | ~happy(X0)) [nnf transformation 31]
58. (? [X0] : patient(X0) | (rich(lucy) | ~wise(lucy))) & ((~rich(lucy) & wise(lucy)) | ! [X0] : ~patient(X0)) [nnf transformation 13]
59. (? [X0] : patient(X0) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X0] : ~patient(X0)) [flattening 58]
60. (? [X0] : patient(X0) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X1] : ~patient(X1)) [rectify 59]
61. ? [X0] : patient(X0) => patient(sK3) [choice axiom]
62. (patient(sK3) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X1] : ~patient(X1)) [skolemisation 60,61]
68. ! [X0] : (((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) [nnf transformation 35]
81. patient(sK0) | ~generous(X1) [cnf transformation 39]
82. ~tall(X0) | ~rich(X0) | patient(X0) [cnf transformation 40]
90. ~generous(X0) | rich(X0) [cnf transformation 30]
91. ~happy(X0) | rich(X0) [cnf transformation 30]
92. ~kind(X0) | happy(X0) [cnf transformation 46]
104. quiet(fred) | old(X1) [cnf transformation 55]
105. ~old(fred) | old(X1) [cnf transformation 55]
107. ~happy(X0) | ~wise(X0) | ~old(X0) [cnf transformation 56]
108. ~happy(X0) | wise(X0) | old(X0) [cnf transformation 56]
109. kind(X0) | generous(X0) [cnf transformation 32]
110. kind(X0) | wise(X0) [cnf transformation 32]
116. ~rich(lucy) | ~patient(X1) [cnf transformation 62]
124. ~quiet(X0) | tall(X0) | ~wise(X0) | generous(X0) [cnf transformation 68]
137. wise(alice) [cnf transformation 24]
141. 1 <=> ! [X1] : ~generous(X1) [avatar definition]
142. ~generous(X1) <- (1) [avatar component clause 141]
144. 2 <=> patient(sK0) [avatar definition]
146. patient(sK0) <- (2) [avatar component clause 144]
147. 1 | 2 [avatar split clause 81,144,141]
192. 12 <=> quiet(fred) [avatar definition]
193. quiet(fred) <- (12) [avatar component clause 192]
196. 13 <=> old(fred) [avatar definition]
205. 15 <=> ! [X1] : old(X1) [avatar definition]
206. old(X1) <- (15) [avatar component clause 205]
207. 15 | ~13 [avatar split clause 105,196,205]
208. 15 | 12 [avatar split clause 104,192,205]
213. 17 <=> tall(fred) [avatar definition]
214. ~tall(fred) <- (~17) [avatar component clause 213]
215. tall(fred) <- (17) [avatar component clause 213]
232. 21 <=> rich(lucy) [avatar definition]
233. ~rich(lucy) <- (~21) [avatar component clause 232]
241. 23 <=> ! [X1] : ~patient(X1) [avatar definition]
242. ~patient(X1) <- (23) [avatar component clause 241]
243. 23 | ~21 [avatar split clause 116,232,241]
293. happy(X0) | generous(X0) [resolution 109,92]
294. happy(X0) | wise(X0) [resolution 110,92]
306. ~rich(fred) | patient(fred) <- (17) [resolution 82,215]
309. 33 <=> patient(fred) [avatar definition]
311. patient(fred) <- (33) [avatar component clause 309]
313. 34 <=> rich(fred) [avatar definition]
315. ~rich(fred) <- (~34) [avatar component clause 313]
316. 33 | ~34 | ~17 [avatar split clause 306,213,313,309]
319. generous(X0) | rich(X0) [resolution 293,91]
320. rich(X0) [subsumption resolution 319,90]
328. $false <- (~21) [resolution 320,233]
329. $false <- (~34) [resolution 320,315]
330. 34 [avatar contradiction clause 329]
331. 21 [avatar contradiction clause 328]
335. $false <- (2, 23) [resolution 242,146]
338. ~2 | ~23 [avatar contradiction clause 335]
368. ~wise(X1) | ~old(X1) | generous(X1) [resolution 107,293]
373. ~wise(X1) | ~old(X1) <- (1) [subsumption resolution 368,142]
377. wise(X0) | old(X0) | wise(X0) [resolution 108,294]
384. wise(X0) | old(X0) [duplicate literal removal 377]
404. tall(fred) | ~wise(fred) | generous(fred) <- (12) [resolution 124,193]
408. ~wise(fred) | generous(fred) <- (12, ~17) [subsumption resolution 404,214]
409. ~wise(fred) <- (1, 12, ~17) [subsumption resolution 408,142]
414. ~old(alice) <- (1) [resolution 373,137]
422. old(fred) <- (1, 12, ~17) [resolution 384,409]
427. 13 | ~1 | ~12 | 17 [avatar split clause 422,213,192,141,196]
433. $false <- (1, 15) [resolution 414,206]
434. ~1 | ~15 [avatar contradiction clause 433]
441. $false <- (23, 33) [subsumption resolution 311,242]
442. ~23 | ~33 [avatar contradiction clause 441]
443. $false [avatar sat refutation 147,207,208,243,316,330,331,338,427,434,442]
% SZS output end Proof for 3555410812108341203812296
% ------------------------------
% 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 john is either old or tall then paul is both patient and strong and vice versa. Everyone who is either not happy or calm is not happy or generous. If paul is wise then someone is both not calm and not rich. If someone is not strong then paul is not brave or kind. If someone is creative then lucy is brave or not happy and vice versa. Everyone who is either humble or not wise is humble. Everyone who is both rich and not wise is strong. Everyone who is either curious or not kind is either humble or happy and vice versa. Everyone who is not strong or not curious is not strong or generous. If john is both not funny and tall then lucy is not quiet and vice versa. Everyone who is both curious and not wise is either curious or not creative and vice versa. Everyone who is humble or patient is old or quiet and vice versa. Everyone who is humble or brave is both not wise and not funny. Everyone who is either not kind or tall is either not curious or not creative and vice versa. Everyone who is both not happy and strong is not creative or wise. If paul is either funny or patient then someone is rich. Fred is either not tall or not rich. Someone is not old or humble. Someone is either rich or not generous. Someone is not kind or not wise. Someone is not rich. Someone is either quiet or wise. Someone is both not wise and old. Fred is both happy and rich. | Fred is wise. | entailment | (((old(john)<~>tall(john)))<=>((patient(paul)&strong(paul))))&
(![X]:((~happy(X)<~>calm(X))=>(~happy(X)|generous(X))))&
((wise(paul))=>(?[X]:((~calm(X)&~rich(X)))))&
((?[X]:(~strong(X)))=>((~brave(paul)|kind(paul))))&
((?[X]:(creative(X)))<=>((brave(lucy)|~happy(lucy))))&
(![X]:((humble(X)<~>~wise(X))=>humble(X)))&
(![X]:((rich(X)&~wise(X))=>strong(X)))&
(![X]:((curious(X)<~>~kind(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~strong(X)|~curious(X))=>(~strong(X)|generous(X))))&
(((~funny(john)&tall(john)))<=>(~quiet(lucy)))&
(![X]:((curious(X)&~wise(X))<=>(curious(X)<~>~creative(X))))&
(![X]:((humble(X)|patient(X))<=>(old(X)|quiet(X))))&
(![X]:((humble(X)|brave(X))=>(~wise(X)&~funny(X))))&
(![X]:((~kind(X)<~>tall(X))<=>(~curious(X)<~>~creative(X))))&
(![X]:((~happy(X)&strong(X))=>(~creative(X)|wise(X))))&
(((funny(paul)<~>patient(paul)))=>(?[X]:(rich(X))))&
((~tall(fred)<~>~rich(fred)))&
(?[X]:((~old(X)|humble(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:((~kind(X)|~wise(X))))&
(?[X]:(~rich(X)))&
(?[X]:((quiet(X)<~>wise(X))))&
(?[X]:((~wise(X)&old(X))))&
((happy(fred)&rich(fred))) | wise(fred) | [
"p5",
"p7",
"p10",
"p13",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7557600832232472352474767
% SZS output start Proof for 7557600832232472352474767
6. ! [X0] : ((humble(X0) <~> ~wise(X0)) => humble(X0)) [input p5]
8. ! [X0] : ((curious(X0) <~> ~kind(X0)) <=> (humble(X0) <~> happy(X0))) [input p7]
11. ! [X0] : ((~wise(X0) & curious(X0)) <=> (curious(X0) <~> ~creative(X0))) [input p10]
14. ! [X0] : ((~kind(X0) <~> tall(X0)) <=> (~curious(X0) <~> ~creative(X0))) [input p13]
17. ~tall(fred) <~> ~rich(fred) [input p16]
24. rich(fred) & happy(fred) [input p23]
25. ~wise(fred) [input hypothesis]
31. ! [X0] : (humble(X0) | (humble(X0) <=> ~wise(X0))) [ennf transformation 6]
50. ! [X0] : (humble(X0) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) [nnf transformation 31]
51. ! [X0] : ((((kind(X0) | ~curious(X0)) & (~kind(X0) | curious(X0))) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) & (((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0))))) [nnf transformation 8]
54. ! [X0] : (((~wise(X0) & curious(X0)) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0)))) & (((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | (wise(X0) | ~curious(X0)))) [nnf transformation 11]
55. ! [X0] : (((~wise(X0) & curious(X0)) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0)))) & (((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | wise(X0) | ~curious(X0))) [flattening 54]
58. ! [X0] : ((((~tall(X0) | kind(X0)) & (tall(X0) | ~kind(X0))) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0))))) [nnf transformation 14]
62. (rich(fred) | tall(fred)) & (~rich(fred) | ~tall(fred)) [nnf transformation 17]
92. humble(X0) | humble(X0) | wise(X0) [cnf transformation 50]
96. ~curious(X0) | ~humble(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 51]
97. ~humble(X0) | ~happy(X0) | curious(X0) | kind(X0) [cnf transformation 51]
108. creative(X0) | ~curious(X0) | wise(X0) | ~curious(X0) [cnf transformation 55]
110. curious(X0) | curious(X0) | creative(X0) [cnf transformation 55]
121. ~curious(X0) | ~creative(X0) | tall(X0) | kind(X0) [cnf transformation 58]
125. tall(X0) | ~kind(X0) | ~creative(X0) | curious(X0) [cnf transformation 58]
132. ~rich(fred) | ~tall(fred) [cnf transformation 62]
143. happy(fred) [cnf transformation 24]
144. rich(fred) [cnf transformation 24]
145. ~wise(fred) [cnf transformation 25]
146. creative(X0) | ~curious(X0) | wise(X0) [duplicate literal removal 108]
147. curious(X0) | creative(X0) [duplicate literal removal 110]
148. humble(X0) | wise(X0) [duplicate literal removal 92]
227. creative(X0) | wise(X0) [subsumption resolution 146,147]
231. ~kind(X0) | tall(X0) | curious(X0) [subsumption resolution 125,147]
244. 19 <=> tall(fred) [avatar definition]
245. ~tall(fred) <- (~19) [avatar component clause 244]
248. 20 <=> rich(fred) [avatar definition]
252. ~19 | ~20 [avatar split clause 132,248,244]
291. 20 [avatar split clause 144,248]
297. 29 <=> curious(fred) [avatar definition]
298. ~curious(fred) <- (~29) [avatar component clause 297]
299. curious(fred) <- (29) [avatar component clause 297]
403. 46 <=> kind(fred) [avatar definition]
404. kind(fred) <- (46) [avatar component clause 403]
407. 47 <=> humble(fred) [avatar definition]
409. ~humble(fred) <- (~47) [avatar component clause 407]
411. ~happy(X0) | curious(X0) | kind(X0) | wise(X0) [resolution 97,148]
448. curious(fred) | kind(fred) | wise(fred) [resolution 411,143]
449. kind(fred) | wise(fred) <- (~29) [subsumption resolution 448,298]
453. kind(fred) <- (~29) [subsumption resolution 449,145]
454. 46 | 29 [avatar split clause 453,297,403]
457. tall(fred) | curious(fred) <- (46) [resolution 404,231]
462. curious(fred) <- (~19, 46) [subsumption resolution 457,245]
466. 29 | 19 | ~46 [avatar split clause 462,403,244,297]
471. ~humble(fred) | ~kind(fred) | ~happy(fred) <- (29) [resolution 299,96]
475. ~creative(fred) | tall(fred) | kind(fred) <- (29) [resolution 299,121]
478. wise(fred) <- (~47) [resolution 409,148]
479. $false <- (~47) [subsumption resolution 478,145]
480. 47 [avatar contradiction clause 479]
481. ~creative(fred) | kind(fred) <- (~19, 29) [subsumption resolution 475,245]
483. 51 <=> creative(fred) [avatar definition]
485. ~creative(fred) <- (~51) [avatar component clause 483]
486. 46 | ~51 | 19 | ~29 [avatar split clause 481,297,244,483,403]
489. ~humble(fred) | ~kind(fred) <- (29) [subsumption resolution 471,143]
490. ~46 | ~47 | ~29 [avatar split clause 489,297,407,403]
549. wise(fred) <- (~51) [resolution 485,227]
550. $false <- (~51) [subsumption resolution 549,145]
551. 51 [avatar contradiction clause 550]
552. $false [avatar sat refutation 252,291,454,466,480,486,490,551]
% SZS output end Proof for 7557600832232472352474767
% ------------------------------
% 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 |
Everyone who is both funny and old is not patient or not strong and vice versa.
If someone is both funny and calm then paul is wise or not curious and vice versa.
If someone is both not rich and strong then john is both wise and curious.
If someone is both funny and not strong then someone is either not humble or funny.
Everyone who is both not old and happy is rich.
If susan is either creative or calm then lucy is both creative and wise and vice versa.
Everyone who is not strong or happy is both creative and not wise and vice versa.
Everyone who is kind is not generous or creative.
If someone is both not strong and kind then someone is kind and vice versa.
If someone is both generous and not generous then someone is kind or not calm.
If someone is strong or old then fred is humble.
Everyone who is generous or not wise is either happy or not wise.
Everyone who is not patient is quiet or not curious.
Everyone who is either not kind or old is both not brave and not old and vice versa.
Everyone who is brave or not curious is both not wise and not brave and vice versa.
Everyone who is both not creative and not humble is not rich and vice versa.
Alice is not creative.
Someone is not generous.
Susan is both old and not tall.
John is calm.
Someone is not creative or generous.
Someone is both quiet and not creative. | John is curious. | neutral | (![X]:((funny(X)&old(X))<=>(~patient(X)|~strong(X))))&
((?[X]:((funny(X)&calm(X))))<=>((wise(paul)|~curious(paul))))&
((?[X]:((~rich(X)&strong(X))))=>((wise(john)&curious(john))))&
((?[X]:((funny(X)&~strong(X))))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~old(X)&happy(X))=>rich(X)))&
(((creative(susan)<~>calm(susan)))<=>((creative(lucy)&wise(lucy))))&
(![X]:((~strong(X)|happy(X))<=>(creative(X)&~wise(X))))&
(![X]:(kind(X)=>(~generous(X)|creative(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(?[X]:(kind(X))))&
((?[X]:((generous(X)&~generous(X))))=>(?[X]:((kind(X)|~calm(X)))))&
((?[X]:((strong(X)|old(X))))=>(humble(fred)))&
(![X]:((generous(X)|~wise(X))=>(happy(X)<~>~wise(X))))&
(![X]:(~patient(X)=>(quiet(X)|~curious(X))))&
(![X]:((~kind(X)<~>old(X))<=>(~brave(X)&~old(X))))&
(![X]:((brave(X)|~curious(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~creative(X)&~humble(X))<=>~rich(X)))&
(~creative(alice))&
(?[X]:(~generous(X)))&
((old(susan)&~tall(susan)))&
(calm(john))&
(?[X]:((~creative(X)|generous(X))))&
(?[X]:((quiet(X)&~creative(X)))) | curious(john) | [] | null | 0 |
Everyone who is not kind is either not wise or funny.
If someone is not curious or not kind then alice is either not patient or quiet.
Everyone who is either not wise or brave is either not rich or kind and vice versa.
If paul is not brave then susan is either funny or not calm.
Everyone who is not humble or calm is both brave and not kind and vice versa.
If susan is either not curious or happy then someone is not wise or not funny and vice versa.
Everyone who is patient is both not kind and not quiet and vice versa.
Everyone who is either not calm or not creative is either rich or patient.
If someone is both strong and not old then john is both calm and not rich.
Everyone who is creative or not brave is not humble.
If someone is not old or not rich then someone is either not calm or not kind and vice versa.
Everyone who is patient is both curious and not curious and vice versa.
Everyone who is either strong or not old is kind or not wise and vice versa.
Everyone who is either calm or curious is not humble and vice versa.
If john is both wise and not tall then someone is both happy and tall and vice versa.
If alice is both not rich and creative then alice is not old or calm.
Lucy is either not happy or not old.
Someone is either patient or curious.
Someone is not tall.
Someone is either not generous or wise.
Someone is both not tall and brave.
Someone is not generous or not calm.
Someone is not wise or brave. | Lucy is wise. | neutral | (![X]:(~kind(X)=>(~wise(X)<~>funny(X))))&
((?[X]:((~curious(X)|~kind(X))))=>((~patient(alice)<~>quiet(alice))))&
(![X]:((~wise(X)<~>brave(X))<=>(~rich(X)<~>kind(X))))&
((~brave(paul))=>((funny(susan)<~>~calm(susan))))&
(![X]:((~humble(X)|calm(X))<=>(brave(X)&~kind(X))))&
(((~curious(susan)<~>happy(susan)))<=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:(patient(X)<=>(~kind(X)&~quiet(X))))&
(![X]:((~calm(X)<~>~creative(X))=>(rich(X)<~>patient(X))))&
((?[X]:((strong(X)&~old(X))))=>((calm(john)&~rich(john))))&
(![X]:((creative(X)|~brave(X))=>~humble(X)))&
((?[X]:((~old(X)|~rich(X))))<=>(?[X]:((~calm(X)<~>~kind(X)))))&
(![X]:(patient(X)<=>(curious(X)&~curious(X))))&
(![X]:((strong(X)<~>~old(X))<=>(kind(X)|~wise(X))))&
(![X]:((calm(X)<~>curious(X))<=>~humble(X)))&
(((wise(john)&~tall(john)))<=>(?[X]:((happy(X)&tall(X)))))&
(((~rich(alice)&creative(alice)))=>((~old(alice)|calm(alice))))&
((~happy(lucy)<~>~old(lucy)))&
(?[X]:((patient(X)<~>curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~generous(X)<~>wise(X))))&
(?[X]:((~tall(X)&brave(X))))&
(?[X]:((~generous(X)|~calm(X))))&
(?[X]:((~wise(X)|brave(X)))) | wise(lucy) | [] | null | 0 |
Everyone who is creative is either not curious or creative.
If someone is curious or not wise then someone is calm or patient.
Everyone who is generous is not rich.
Everyone who is either not humble or generous is creative or not old and vice versa.
Everyone who is funny or brave is either not quiet or funny.
Everyone who is either not calm or not curious is curious and vice versa.
If mary is both curious and happy then fred is not happy.
Everyone who is not patient is either wise or happy.
If someone is funny then someone is both not tall and not patient and vice versa.
Everyone who is humble or creative is not tall or happy and vice versa.
Everyone who is both funny and not generous is brave or not quiet.
Everyone who is not calm or not kind is curious.
If someone is patient then someone is creative and vice versa.
Everyone who is either not strong or old is not wise or calm.
Everyone who is strong is strong or not tall.
Everyone who is brave is not kind or quiet.
Paul is both rich and not tall.
Someone is tall or quiet.
Paul is not strong or not generous.
Someone is either not quiet or not old.
Someone is not patient.
Alice is either strong or wise.
Alice is brave.
Alice is both creative and generous. | Alice is not generous. | contradiction | (![X]:(creative(X)=>(~curious(X)<~>creative(X))))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:((calm(X)|patient(X)))))&
(![X]:(generous(X)=>~rich(X)))&
(![X]:((~humble(X)<~>generous(X))<=>(creative(X)|~old(X))))&
(![X]:((funny(X)|brave(X))=>(~quiet(X)<~>funny(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>curious(X)))&
(((curious(mary)&happy(mary)))=>(~happy(fred)))&
(![X]:(~patient(X)=>(wise(X)<~>happy(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~tall(X)&~patient(X)))))&
(![X]:((humble(X)|creative(X))<=>(~tall(X)|happy(X))))&
(![X]:((funny(X)&~generous(X))=>(brave(X)|~quiet(X))))&
(![X]:((~calm(X)|~kind(X))=>curious(X)))&
((?[X]:(patient(X)))<=>(?[X]:(creative(X))))&
(![X]:((~strong(X)<~>old(X))=>(~wise(X)|calm(X))))&
(![X]:(strong(X)=>(strong(X)|~tall(X))))&
(![X]:(brave(X)=>(~kind(X)|quiet(X))))&
((rich(paul)&~tall(paul)))&
(?[X]:((tall(X)|quiet(X))))&
((~strong(paul)|~generous(paul)))&
(?[X]:((~quiet(X)<~>~old(X))))&
(?[X]:(~patient(X)))&
((strong(alice)<~>wise(alice)))&
(brave(alice))&
((creative(alice)&generous(alice))) | ~generous(alice) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8481103581128360049763822
% SZS output start Proof for 8481103581128360049763822
24. generous(alice) & creative(alice) [input p23]
25. ~generous(alice) [input hypothesis]
124. generous(alice) [cnf transformation 24]
125. ~generous(alice) [cnf transformation 25]
239. $false [subsumption resolution 125,124]
% SZS output end Proof for 8481103581128360049763822
% ------------------------------
% 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 both not brave and not curious is funny or not wise and vice versa. If someone is not strong then john is happy or brave and vice versa. Everyone who is rich is either not patient or not quiet and vice versa. Everyone who is either curious or rich is rich and vice versa. Everyone who is both calm and creative is both funny and generous. Everyone who is rich is wise or not wise and vice versa. If someone is rich then mary is both not happy and not calm and vice versa. Everyone who is both not quiet and strong is either humble or curious and vice versa. If paul is not humble then someone is both wise and not rich. Everyone who is curious is not quiet or tall. Everyone who is generous or wise is old or calm and vice versa. If alice is tall or curious then someone is both not generous and brave and vice versa. Everyone who is either not humble or not funny is not generous. If paul is not happy or happy then someone is not quiet or not happy. Everyone who is curious or wise is either funny or wise. If lucy is curious or not generous then susan is rich or not kind. Someone is happy. Someone is either curious or not brave. Mary is tall or not tall. Someone is rich or not creative. Lucy is either creative or brave. | John is not curious. | entailment | (![X]:((~brave(X)&~curious(X))<=>(funny(X)|~wise(X))))&
((?[X]:(~strong(X)))<=>((happy(john)|brave(john))))&
(![X]:(rich(X)<=>(~patient(X)<~>~quiet(X))))&
(![X]:((curious(X)<~>rich(X))<=>rich(X)))&
(![X]:((calm(X)&creative(X))=>(funny(X)&generous(X))))&
(![X]:(rich(X)<=>(wise(X)|~wise(X))))&
((?[X]:(rich(X)))<=>((~happy(mary)&~calm(mary))))&
(![X]:((~quiet(X)&strong(X))<=>(humble(X)<~>curious(X))))&
((~humble(paul))=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:(curious(X)=>(~quiet(X)|tall(X))))&
(![X]:((generous(X)|wise(X))<=>(old(X)|calm(X))))&
(((tall(alice)|curious(alice)))<=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((~humble(X)<~>~funny(X))=>~generous(X)))&
(((~happy(paul)|happy(paul)))=>(?[X]:((~quiet(X)|~happy(X)))))&
(![X]:((curious(X)|wise(X))=>(funny(X)<~>wise(X))))&
(((curious(lucy)|~generous(lucy)))=>((rich(susan)|~kind(susan))))&
(?[X]:(happy(X)))&
(?[X]:((curious(X)<~>~brave(X))))&
((tall(mary)|~tall(mary)))&
(?[X]:((rich(X)|~creative(X))))&
((creative(lucy)<~>brave(lucy))) | ~curious(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 488706454226923868741979
% SZS output start Proof for 488706454226923868741979
4. ! [X0] : ((curious(X0) <~> rich(X0)) <=> rich(X0)) [input p3]
22. curious(john) [input hypothesis]
40. ! [X0] : ((((~rich(X0) | ~curious(X0)) & (rich(X0) | curious(X0))) | ~rich(X0)) & (rich(X0) | ((curious(X0) | ~rich(X0)) & (rich(X0) | ~curious(X0))))) [nnf transformation 4]
83. rich(X0) | rich(X0) | ~curious(X0) [cnf transformation 40]
86. ~rich(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 40]
128. curious(john) [cnf transformation 22]
130. rich(X0) | ~curious(X0) [duplicate literal removal 83]
131. ~rich(X0) | ~curious(X0) [duplicate literal removal 86]
150. ~curious(X0) [subsumption resolution 130,131]
202. $false [subsumption resolution 128,150]
% SZS output end Proof for 488706454226923868741979
% ------------------------------
% 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 lucy is funny then someone is not curious.
If mary is not patient or not kind then paul is either not old or not kind.
If lucy is tall or strong then mary is generous or kind.
Everyone who is either not funny or tall is tall.
Everyone who is tall or not rich is either not strong or happy and vice versa.
If susan is generous or not strong then someone is kind or strong and vice versa.
Everyone who is both not patient and creative is either not brave or patient and vice versa.
Everyone who is calm or kind is not happy or strong and vice versa.
If someone is calm then susan is either patient or not generous and vice versa.
If fred is curious then fred is strong and vice versa.
Everyone who is both not generous and rich is either rich or not calm.
If fred is both humble and calm then paul is both not rich and wise and vice versa.
If someone is rich then john is both not brave and not generous.
Everyone who is either patient or not brave is either generous or not calm and vice versa.
If someone is both not kind and not quiet then susan is patient or happy and vice versa.
Everyone who is not brave is calm and vice versa.
Someone is both not tall and generous.
Someone is brave or quiet.
Someone is tall.
Someone is not kind or not wise.
Alice is not humble.
Someone is both funny and curious. | Paul is wise. | contradiction | ((funny(lucy))=>(?[X]:(~curious(X))))&
(((~patient(mary)|~kind(mary)))=>((~old(paul)<~>~kind(paul))))&
(((tall(lucy)|strong(lucy)))=>((generous(mary)|kind(mary))))&
(![X]:((~funny(X)<~>tall(X))=>tall(X)))&
(![X]:((tall(X)|~rich(X))<=>(~strong(X)<~>happy(X))))&
(((generous(susan)|~strong(susan)))<=>(?[X]:((kind(X)|strong(X)))))&
(![X]:((~patient(X)&creative(X))<=>(~brave(X)<~>patient(X))))&
(![X]:((calm(X)|kind(X))<=>(~happy(X)|strong(X))))&
((?[X]:(calm(X)))<=>((patient(susan)<~>~generous(susan))))&
((curious(fred))<=>(strong(fred)))&
(![X]:((~generous(X)&rich(X))=>(rich(X)<~>~calm(X))))&
(((humble(fred)&calm(fred)))<=>((~rich(paul)&wise(paul))))&
((?[X]:(rich(X)))=>((~brave(john)&~generous(john))))&
(![X]:((patient(X)<~>~brave(X))<=>(generous(X)<~>~calm(X))))&
((?[X]:((~kind(X)&~quiet(X))))<=>((patient(susan)|happy(susan))))&
(![X]:(~brave(X)<=>calm(X)))&
(?[X]:((~tall(X)&generous(X))))&
(?[X]:((brave(X)|quiet(X))))&
(?[X]:(tall(X)))&
(?[X]:((~kind(X)|~wise(X))))&
(~humble(alice))&
(?[X]:((funny(X)&curious(X)))) | wise(paul) | [
"p6",
"p8",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7244341863629147097224002
% SZS output start Proof for 7244341863629147097224002
7. ! [X0] : ((creative(X0) & ~patient(X0)) <=> (~brave(X0) <~> patient(X0))) [input p6]
9. ? [X0] : calm(X0) <=> (patient(susan) <~> ~generous(susan)) [input p8]
12. (calm(fred) & humble(fred)) <=> (wise(paul) & ~rich(paul)) [input p11]
13. ? [X0] : rich(X0) => (~generous(john) & ~brave(john)) [input p12]
14. ! [X0] : ((patient(X0) <~> ~brave(X0)) <=> (generous(X0) <~> ~calm(X0))) [input p13]
16. ! [X0] : (~brave(X0) <=> calm(X0)) [input p15]
23. wise(paul) [input hypothesis]
31. (~generous(john) & ~brave(john)) | ! [X0] : ~rich(X0) [ennf transformation 13]
43. ! [X0] : (((creative(X0) & ~patient(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) & (((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (~creative(X0) | patient(X0)))) [nnf transformation 7]
44. ! [X0] : (((creative(X0) & ~patient(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) & (((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | ~creative(X0) | patient(X0))) [flattening 43]
47. (? [X0] : calm(X0) | ((patient(susan) | generous(susan)) & (~generous(susan) | ~patient(susan)))) & (((generous(susan) | ~patient(susan)) & (~generous(susan) | patient(susan))) | ! [X0] : ~calm(X0)) [nnf transformation 9]
48. (? [X0] : calm(X0) | ((patient(susan) | generous(susan)) & (~generous(susan) | ~patient(susan)))) & (((generous(susan) | ~patient(susan)) & (~generous(susan) | patient(susan))) | ! [X1] : ~calm(X1)) [rectify 47]
49. ? [X0] : calm(X0) => calm(sK2) [choice axiom]
50. (calm(sK2) | ((patient(susan) | generous(susan)) & (~generous(susan) | ~patient(susan)))) & (((generous(susan) | ~patient(susan)) & (~generous(susan) | patient(susan))) | ! [X1] : ~calm(X1)) [skolemisation 48,49]
53. ((calm(fred) & humble(fred)) | (~wise(paul) | rich(paul))) & ((wise(paul) & ~rich(paul)) | (~calm(fred) | ~humble(fred))) [nnf transformation 12]
54. ((calm(fred) & humble(fred)) | ~wise(paul) | rich(paul)) & ((wise(paul) & ~rich(paul)) | ~calm(fred) | ~humble(fred)) [flattening 53]
55. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [nnf transformation 14]
61. ! [X0] : ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0))) [nnf transformation 16]
91. patient(X0) | ~brave(X0) | ~creative(X0) | patient(X0) [cnf transformation 44]
94. ~patient(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 44]
95. brave(X0) | patient(X0) | creative(X0) [cnf transformation 44]
101. ~generous(susan) | patient(susan) | ~calm(X1) [cnf transformation 50]
102. generous(susan) | ~patient(susan) | ~calm(X1) [cnf transformation 50]
112. calm(fred) | ~wise(paul) | rich(paul) [cnf transformation 54]
113. ~brave(john) | ~rich(X0) [cnf transformation 31]
116. ~calm(X0) | generous(X0) | patient(X0) | brave(X0) [cnf transformation 55]
120. ~brave(X0) | patient(X0) | generous(X0) | calm(X0) [cnf transformation 55]
121. brave(X0) | ~patient(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 55]
122. brave(X0) | ~patient(X0) | generous(X0) | calm(X0) [cnf transformation 55]
128. calm(X0) | brave(X0) [cnf transformation 61]
129. ~calm(X0) | ~brave(X0) [cnf transformation 61]
138. wise(paul) [cnf transformation 23]
140. patient(X0) | ~brave(X0) | ~creative(X0) [duplicate literal removal 91]
141. ~brave(X0) | ~patient(X0) [duplicate literal removal 94]
190. 11 <=> generous(susan) [avatar definition]
191. ~generous(susan) <- (~11) [avatar component clause 190]
192. generous(susan) <- (11) [avatar component clause 190]
212. ~brave(X0) | ~creative(X0) [subsumption resolution 140,141]
214. 16 <=> patient(susan) [avatar definition]
215. ~patient(susan) <- (~16) [avatar component clause 214]
216. patient(susan) <- (16) [avatar component clause 214]
224. 18 <=> ! [X1] : ~calm(X1) [avatar definition]
225. ~calm(X1) <- (18) [avatar component clause 224]
226. 18 | ~16 | 11 [avatar split clause 102,190,214,224]
227. 18 | 16 | ~11 [avatar split clause 101,190,214,224]
239. 21 <=> rich(paul) [avatar definition]
241. rich(paul) <- (21) [avatar component clause 239]
243. 22 <=> wise(paul) [avatar definition]
247. 23 <=> calm(fred) [avatar definition]
249. calm(fred) <- (23) [avatar component clause 247]
250. 21 | ~22 | 23 [avatar split clause 112,247,243,239]
259. 25 <=> ! [X0] : ~rich(X0) [avatar definition]
260. ~rich(X0) <- (25) [avatar component clause 259]
267. 27 <=> brave(john) [avatar definition]
269. ~brave(john) <- (~27) [avatar component clause 267]
270. 25 | ~27 [avatar split clause 113,267,259]
271. ~patient(X0) | generous(X0) | calm(X0) [subsumption resolution 122,141]
272. ~calm(X0) | ~patient(X0) | ~generous(X0) [subsumption resolution 121,141]
273. ~brave(X0) | generous(X0) | calm(X0) [subsumption resolution 120,271]
313. 22 [avatar split clause 138,243]
344. brave(X0) <- (18) [resolution 225,128]
345. $false <- (21, 25) [resolution 260,241]
346. ~21 | ~25 [avatar contradiction clause 345]
347. $false <- (18, 23) [subsumption resolution 249,225]
348. ~18 | ~23 [avatar contradiction clause 347]
349. $false <- (18, ~27) [subsumption resolution 269,344]
350. ~18 | 27 [avatar contradiction clause 349]
415. ~patient(X1) | ~generous(X1) | brave(X1) [resolution 272,128]
417. ~generous(X1) | ~patient(X1) [subsumption resolution 415,141]
426. generous(X0) | calm(X0) | patient(X0) | creative(X0) [resolution 273,95]
437. calm(X0) | generous(X0) | creative(X0) [subsumption resolution 426,271]
520. generous(X1) | patient(X1) | brave(X1) | brave(X1) [resolution 116,128]
523. brave(X1) | patient(X1) | generous(X1) [duplicate literal removal 520]
540. generous(X4) | creative(X4) | ~brave(X4) [resolution 437,129]
544. ~brave(X4) | generous(X4) [subsumption resolution 540,212]
618. generous(X0) | patient(X0) | generous(X0) [resolution 544,523]
621. generous(X0) | patient(X0) [duplicate literal removal 618]
644. patient(susan) <- (~11) [resolution 621,191]
649. $false <- (~11, ~16) [subsumption resolution 644,215]
650. 11 | 16 [avatar contradiction clause 649]
652. ~patient(susan) <- (11) [resolution 192,417]
656. $false <- (11, 16) [subsumption resolution 652,216]
657. ~11 | ~16 [avatar contradiction clause 656]
658. $false [avatar sat refutation 226,227,250,270,313,346,348,350,650,657]
% SZS output end Proof for 7244341863629147097224002
% ------------------------------
% 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 someone is not funny or not humble then someone is not happy and vice versa. Everyone who is not kind or old is both not tall and curious. If alice is either generous or not patient then someone is either tall or not wise. Everyone who is not curious is not generous or creative and vice versa. Everyone who is both patient and not old is not kind. Everyone who is both not patient and not calm is both calm and not tall. Everyone who is both not old and kind is happy or not generous and vice versa. If someone is both not patient and not quiet then someone is old and vice versa. If someone is either not generous or not calm then someone is not rich or calm. Everyone who is strong or not old is kind. Everyone who is creative or kind is not old or not creative. Everyone who is generous or not tall is not generous and vice versa. If someone is both generous and not creative then someone is not quiet and vice versa. If john is generous or wise then someone is rich and vice versa. If alice is brave or not creative then someone is both generous and calm and vice versa. Someone is either not generous or brave. Paul is kind. Someone is either strong or kind. Someone is not funny or curious. Someone is brave. Someone is not humble. Someone is humble or rich. | Alice is not tall. | entailment | ((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)|old(X))=>(~tall(X)&curious(X))))&
(((generous(alice)<~>~patient(alice)))=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:(~curious(X)<=>(~generous(X)|creative(X))))&
(![X]:((patient(X)&~old(X))=>~kind(X)))&
(![X]:((~patient(X)&~calm(X))=>(calm(X)&~tall(X))))&
(![X]:((~old(X)&kind(X))<=>(happy(X)|~generous(X))))&
((?[X]:((~patient(X)&~quiet(X))))<=>(?[X]:(old(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:((strong(X)|~old(X))=>kind(X)))&
(![X]:((creative(X)|kind(X))=>(~old(X)|~creative(X))))&
(![X]:((generous(X)|~tall(X))<=>~generous(X)))&
((?[X]:((generous(X)&~creative(X))))<=>(?[X]:(~quiet(X))))&
(((generous(john)|wise(john)))<=>(?[X]:(rich(X))))&
(((brave(alice)|~creative(alice)))<=>(?[X]:((generous(X)&calm(X)))))&
(?[X]:((~generous(X)<~>brave(X))))&
(kind(paul))&
(?[X]:((strong(X)<~>kind(X))))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:(brave(X)))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)|rich(X)))) | ~tall(alice) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5719002162591752348791665
% SZS output start Proof for 5719002162591752348791665
12. ! [X0] : ((~tall(X0) | generous(X0)) <=> ~generous(X0)) [input p11]
23. tall(alice) [input hypothesis]
59. ! [X0] : (((~tall(X0) | generous(X0)) | generous(X0)) & (~generous(X0) | (tall(X0) & ~generous(X0)))) [nnf transformation 12]
60. ! [X0] : ((~tall(X0) | generous(X0) | generous(X0)) & (~generous(X0) | (tall(X0) & ~generous(X0)))) [flattening 59]
120. ~generous(X0) | ~generous(X0) [cnf transformation 60]
122. ~tall(X0) | generous(X0) | generous(X0) [cnf transformation 60]
143. tall(alice) [cnf transformation 23]
144. ~generous(X0) [duplicate literal removal 120]
145. ~tall(X0) | generous(X0) [duplicate literal removal 122]
305. generous(alice) [resolution 145,143]
306. $false [subsumption resolution 305,144]
% SZS output end Proof for 5719002162591752348791665
% ------------------------------
% 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 creative and not generous then john is not tall or not wise and vice versa. Everyone who is not patient is not old and vice versa. Everyone who is not brave is not patient or calm and vice versa. Everyone who is not humble or wise is not strong or happy. If fred is both curious and not happy then someone is either not wise or not tall and vice versa. If someone is both rich and quiet then someone is either not strong or not old. If someone is either not creative or creative then alice is both generous and curious. Everyone who is both generous and creative is either happy or calm. If mary is either curious or old then someone is either curious or rich and vice versa. If alice is both old and rich then lucy is not rich and vice versa. Everyone who is both not patient and not rich is either creative or humble and vice versa. Everyone who is funny or generous is both not strong and not kind. If paul is either not old or not rich then paul is not creative and vice versa. Everyone who is not calm is happy and vice versa. Someone is humble or calm. Someone is not brave. John is both funny and happy. John is either not tall or not wise. Paul is quiet. Lucy is brave. Someone is both not curious and not humble. Someone is not strong. | Lucy is not brave. | contradiction | ((?[X]:((~creative(X)&~generous(X))))<=>((~tall(john)|~wise(john))))&
(![X]:(~patient(X)<=>~old(X)))&
(![X]:(~brave(X)<=>(~patient(X)|calm(X))))&
(![X]:((~humble(X)|wise(X))=>(~strong(X)|happy(X))))&
(((curious(fred)&~happy(fred)))<=>(?[X]:((~wise(X)<~>~tall(X)))))&
((?[X]:((rich(X)&quiet(X))))=>(?[X]:((~strong(X)<~>~old(X)))))&
((?[X]:((~creative(X)<~>creative(X))))=>((generous(alice)&curious(alice))))&
(![X]:((generous(X)&creative(X))=>(happy(X)<~>calm(X))))&
(((curious(mary)<~>old(mary)))<=>(?[X]:((curious(X)<~>rich(X)))))&
(((old(alice)&rich(alice)))<=>(~rich(lucy)))&
(![X]:((~patient(X)&~rich(X))<=>(creative(X)<~>humble(X))))&
(![X]:((funny(X)|generous(X))=>(~strong(X)&~kind(X))))&
(((~old(paul)<~>~rich(paul)))<=>(~creative(paul)))&
(![X]:(~calm(X)<=>happy(X)))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:(~brave(X)))&
((funny(john)&happy(john)))&
((~tall(john)<~>~wise(john)))&
(quiet(paul))&
(brave(lucy))&
(?[X]:((~curious(X)&~humble(X))))&
(?[X]:(~strong(X))) | ~brave(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 771318849425641048630357
% SZS output start Proof for 771318849425641048630357
20. brave(lucy) [input p19]
23. ~brave(lucy) [input hypothesis]
129. brave(lucy) [cnf transformation 20]
133. ~brave(lucy) [cnf transformation 23]
293. $false [subsumption resolution 133,129]
% SZS output end Proof for 771318849425641048630357
% ------------------------------
% 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 someone is both not wise and curious then john is both not humble and not funny.
Everyone who is old or strong is either brave or patient.
If alice is either strong or kind then someone is brave.
If susan is not wise or not old then paul is either not strong or not tall.
Everyone who is kind is either not kind or humble and vice versa.
Everyone who is quiet is both not brave and humble.
Everyone who is patient is wise.
Everyone who is not tall or strong is old.
If mary is both humble and old then fred is either kind or not old.
Everyone who is both strong and not kind is both patient and curious.
If susan is not rich or tall then someone is tall or wise.
If someone is not quiet or humble then alice is both not patient and not calm and vice versa.
Everyone who is happy or kind is both creative and humble and vice versa.
Everyone who is both creative and quiet is either strong or not humble and vice versa.
Everyone who is either wise or rich is strong.
If someone is quiet or not wise then susan is both not quiet and not funny and vice versa.
Someone is either curious or not old.
Someone is both quiet and not tall.
Someone is brave or not humble.
Fred is either not tall or patient.
Someone is both not quiet and curious.
Mary is funny or not wise.
Someone is not wise.
Someone is not brave. | Alice is humble. | entailment | ((?[X]:((~wise(X)&curious(X))))=>((~humble(john)&~funny(john))))&
(![X]:((old(X)|strong(X))=>(brave(X)<~>patient(X))))&
(((strong(alice)<~>kind(alice)))=>(?[X]:(brave(X))))&
(((~wise(susan)|~old(susan)))=>((~strong(paul)<~>~tall(paul))))&
(![X]:(kind(X)<=>(~kind(X)<~>humble(X))))&
(![X]:(quiet(X)=>(~brave(X)&humble(X))))&
(![X]:(patient(X)=>wise(X)))&
(![X]:((~tall(X)|strong(X))=>old(X)))&
(((humble(mary)&old(mary)))=>((kind(fred)<~>~old(fred))))&
(![X]:((strong(X)&~kind(X))=>(patient(X)&curious(X))))&
(((~rich(susan)|tall(susan)))=>(?[X]:((tall(X)|wise(X)))))&
((?[X]:((~quiet(X)|humble(X))))<=>((~patient(alice)&~calm(alice))))&
(![X]:((happy(X)|kind(X))<=>(creative(X)&humble(X))))&
(![X]:((creative(X)&quiet(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((wise(X)<~>rich(X))=>strong(X)))&
((?[X]:((quiet(X)|~wise(X))))<=>((~quiet(susan)&~funny(susan))))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:((quiet(X)&~tall(X))))&
(?[X]:((brave(X)|~humble(X))))&
((~tall(fred)<~>patient(fred)))&
(?[X]:((~quiet(X)&curious(X))))&
((funny(mary)|~wise(mary)))&
(?[X]:(~wise(X)))&
(?[X]:(~brave(X))) | humble(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5894141332609636260344062
% SZS output start Proof for 5894141332609636260344062
5. ! [X0] : (kind(X0) <=> (~kind(X0) <~> humble(X0))) [input p4]
25. ~humble(alice) [input hypothesis]
44. ! [X0] : ((kind(X0) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0)))) & (((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | ~kind(X0))) [nnf transformation 5]
89. humble(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 44]
91. kind(X0) | humble(X0) | kind(X0) [cnf transformation 44]
139. ~humble(alice) [cnf transformation 25]
140. humble(X0) | ~kind(X0) [duplicate literal removal 89]
141. kind(X0) | humble(X0) [duplicate literal removal 91]
189. humble(X0) [subsumption resolution 140,141]
287. $false [subsumption resolution 139,189]
% SZS output end Proof for 5894141332609636260344062
% ------------------------------
% 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 creative or happy is either not humble or not funny and vice versa. Everyone who is both creative and not curious is both not tall and not humble. Everyone who is both creative and not creative is generous and vice versa. If someone is tall then mary is happy. If someone is not patient then someone is calm or rich. If mary is either humble or tall then someone is old or not brave. Everyone who is patient is either not creative or wise and vice versa. Everyone who is not patient or creative is both not old and not strong and vice versa. If someone is both not humble and not patient then susan is either strong or not strong and vice versa. If lucy is not humble then susan is both calm and happy and vice versa. Everyone who is not patient is not rich or tall and vice versa. If someone is not funny or not calm then susan is rich or happy and vice versa. Everyone who is either not creative or funny is not generous. Everyone who is either not creative or brave is either curious or old. Everyone who is both curious and not quiet is both not rich and not humble. If alice is either happy or not curious then someone is either not brave or humble. Someone is both not humble and not tall. Susan is old. Someone is not kind or not tall. Fred is not humble or quiet. Someone is either generous or funny. Mary is both not kind and strong. Someone is humble. John is patient or not rich. | Mary is not tall. | entailment | (![X]:((~creative(X)|happy(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((creative(X)&~curious(X))=>(~tall(X)&~humble(X))))&
(![X]:((creative(X)&~creative(X))<=>generous(X)))&
((?[X]:(tall(X)))=>(happy(mary)))&
((?[X]:(~patient(X)))=>(?[X]:((calm(X)|rich(X)))))&
(((humble(mary)<~>tall(mary)))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:(patient(X)<=>(~creative(X)<~>wise(X))))&
(![X]:((~patient(X)|creative(X))<=>(~old(X)&~strong(X))))&
((?[X]:((~humble(X)&~patient(X))))<=>((strong(susan)<~>~strong(susan))))&
((~humble(lucy))<=>((calm(susan)&happy(susan))))&
(![X]:(~patient(X)<=>(~rich(X)|tall(X))))&
((?[X]:((~funny(X)|~calm(X))))<=>((rich(susan)|happy(susan))))&
(![X]:((~creative(X)<~>funny(X))=>~generous(X)))&
(![X]:((~creative(X)<~>brave(X))=>(curious(X)<~>old(X))))&
(![X]:((curious(X)&~quiet(X))=>(~rich(X)&~humble(X))))&
(((happy(alice)<~>~curious(alice)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(?[X]:((~humble(X)&~tall(X))))&
(old(susan))&
(?[X]:((~kind(X)|~tall(X))))&
((~humble(fred)|quiet(fred)))&
(?[X]:((generous(X)<~>funny(X))))&
((~kind(mary)&strong(mary)))&
(?[X]:(humble(X)))&
((patient(john)|~rich(john))) | ~tall(mary) | [
"p7",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5938724736278285687887822
% SZS output start Proof for 5938724736278285687887822
8. ! [X0] : ((creative(X0) | ~patient(X0)) <=> (~strong(X0) & ~old(X0))) [input p7]
11. ! [X0] : (~patient(X0) <=> (tall(X0) | ~rich(X0))) [input p10]
22. strong(mary) & ~kind(mary) [input p21]
25. tall(mary) [input hypothesis]
28. strong(mary) [pure predicate removal 22]
50. ! [X0] : (((creative(X0) | ~patient(X0)) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | (~creative(X0) & patient(X0)))) [nnf transformation 8]
51. ! [X0] : ((creative(X0) | ~patient(X0) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | (~creative(X0) & patient(X0)))) [flattening 50]
58. ! [X0] : ((~patient(X0) | (~tall(X0) & rich(X0))) & ((tall(X0) | ~rich(X0)) | patient(X0))) [nnf transformation 11]
59. ! [X0] : ((~patient(X0) | (~tall(X0) & rich(X0))) & (tall(X0) | ~rich(X0) | patient(X0))) [flattening 58]
98. ~strong(X0) | patient(X0) [cnf transformation 51]
112. ~patient(X0) | ~tall(X0) [cnf transformation 59]
132. strong(mary) [cnf transformation 28]
135. tall(mary) [cnf transformation 25]
162. 6 <=> tall(mary) [avatar definition]
163. tall(mary) <- (6) [avatar component clause 162]
264. 6 [avatar split clause 135,162]
269. patient(mary) [resolution 98,132]
275. ~tall(mary) [resolution 112,269]
276. $false <- (6) [subsumption resolution 275,163]
277. ~6 [avatar contradiction clause 276]
278. $false [avatar sat refutation 264,277]
% SZS output end Proof for 5938724736278285687887822
% ------------------------------
% 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 |
Everyone who is wise or brave is both not generous and funny and vice versa.
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.
Everyone who is both humble and rich is not brave and vice versa.
If mary is not patient or funny then john is either strong or not patient and vice versa.
Everyone who is either patient or kind is either strong or happy.
Everyone who is either wise or happy is happy.
If someone is not rich or kind then lucy is curious and vice versa.
Everyone who is either not strong or not quiet is not rich and vice versa.
Everyone who is not curious is creative or not patient and vice versa.
Everyone who is old or not quiet is either not creative or not curious and vice versa.
If someone is both not generous and not funny then someone is not quiet.
Someone is not curious.
Someone is either not kind or not old.
Susan is not wise or rich.
Someone is funny.
Someone is not strong or kind. | Fred is not brave. | neutral | (![X]:((wise(X)|brave(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]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(![X]:((old(X)|~quiet(X))<=>(~creative(X)<~>~curious(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:(~quiet(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~kind(X)<~>~old(X))))&
((~wise(susan)|rich(susan)))&
(?[X]:(funny(X)))&
(?[X]:((~strong(X)|kind(X)))) | ~brave(fred) | [] | null | 0 |
If someone is both kind and generous then someone is both not calm and not tall and vice versa. Everyone who is quiet or wise is either not humble or rich and vice versa. If susan is not generous or not wise then someone is not kind or creative and vice versa. Everyone who is not tall or strong is both tall and humble and vice versa. Everyone who is both creative and not tall is not wise or funny and vice versa. If fred is either not generous or wise then someone is both not wise and not curious and vice versa. Everyone who is brave or humble is either not quiet or humble and vice versa. If someone is either not humble or rich then john is wise. If someone is both rich and not tall then alice is not quiet. If fred is creative or funny then fred is not old or not tall. Everyone who is brave or quiet is either not tall or not kind. If fred is patient then mary is both humble and not kind. Everyone who is patient is either curious or wise and vice versa. If john is patient then someone is both not happy and generous. Everyone who is old is either not wise or not tall and vice versa. Someone is both happy and humble. John is either not old or calm. Paul is not funny or creative. Someone is either not tall or strong. Lucy is either not rich or wise. Mary is not rich or not brave. John is not kind. | Alice is not curious. | neutral | ((?[X]:((kind(X)&generous(X))))<=>(?[X]:((~calm(X)&~tall(X)))))&
(![X]:((quiet(X)|wise(X))<=>(~humble(X)<~>rich(X))))&
(((~generous(susan)|~wise(susan)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~tall(X)|strong(X))<=>(tall(X)&humble(X))))&
(![X]:((creative(X)&~tall(X))<=>(~wise(X)|funny(X))))&
(((~generous(fred)<~>wise(fred)))<=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((brave(X)|humble(X))<=>(~quiet(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>rich(X))))=>(wise(john)))&
((?[X]:((rich(X)&~tall(X))))=>(~quiet(alice)))&
(((creative(fred)|funny(fred)))=>((~old(fred)|~tall(fred))))&
(![X]:((brave(X)|quiet(X))=>(~tall(X)<~>~kind(X))))&
((patient(fred))=>((humble(mary)&~kind(mary))))&
(![X]:(patient(X)<=>(curious(X)<~>wise(X))))&
((patient(john))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:(old(X)<=>(~wise(X)<~>~tall(X))))&
(?[X]:((happy(X)&humble(X))))&
((~old(john)<~>calm(john)))&
((~funny(paul)|creative(paul)))&
(?[X]:((~tall(X)<~>strong(X))))&
((~rich(lucy)<~>wise(lucy)))&
((~rich(mary)|~brave(mary)))&
(~kind(john)) | ~curious(alice) | [] | null | 0 |
If susan is either tall or strong then paul is strong or not calm.
If mary is patient or not humble then fred is generous and vice versa.
Everyone who is either old or happy is either creative or humble and vice versa.
If paul is both not rich and not kind then someone is funny or happy and vice versa.
Everyone who is either tall or not quiet is both not generous and tall and vice versa.
Everyone who is patient or curious is patient and vice versa.
Everyone who is either strong or patient is both not tall and not old.
If paul is either generous or humble then mary is both not creative and calm.
Everyone who is both tall and not wise is strong and vice versa.
If susan is humble then someone is quiet or not patient and vice versa.
If mary is not funny or not calm then fred is both not calm and not happy and vice versa.
Everyone who is either happy or not quiet is both not strong and old.
If someone is brave or not happy then someone is either not brave or strong.
If paul is not brave or not old then lucy is not patient or happy and vice versa.
If paul is kind then mary is either not creative or not rich.
If someone is both old and not happy then someone is either rich or not funny and vice versa.
Someone is humble.
Mary is rich or kind.
Alice is strong or patient.
Someone is kind or not curious.
Alice is either not funny or not happy.
Alice is both not funny and not wise.
Someone is either calm or not humble. | Paul is not kind. | entailment | (((tall(susan)<~>strong(susan)))=>((strong(paul)|~calm(paul))))&
(((patient(mary)|~humble(mary)))<=>(generous(fred)))&
(![X]:((old(X)<~>happy(X))<=>(creative(X)<~>humble(X))))&
(((~rich(paul)&~kind(paul)))<=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((tall(X)<~>~quiet(X))<=>(~generous(X)&tall(X))))&
(![X]:((patient(X)|curious(X))<=>patient(X)))&
(![X]:((strong(X)<~>patient(X))=>(~tall(X)&~old(X))))&
(((generous(paul)<~>humble(paul)))=>((~creative(mary)&calm(mary))))&
(![X]:((tall(X)&~wise(X))<=>strong(X)))&
((humble(susan))<=>(?[X]:((quiet(X)|~patient(X)))))&
(((~funny(mary)|~calm(mary)))<=>((~calm(fred)&~happy(fred))))&
(![X]:((happy(X)<~>~quiet(X))=>(~strong(X)&old(X))))&
((?[X]:((brave(X)|~happy(X))))=>(?[X]:((~brave(X)<~>strong(X)))))&
(((~brave(paul)|~old(paul)))<=>((~patient(lucy)|happy(lucy))))&
((kind(paul))=>((~creative(mary)<~>~rich(mary))))&
((?[X]:((old(X)&~happy(X))))<=>(?[X]:((rich(X)<~>~funny(X)))))&
(?[X]:(humble(X)))&
((rich(mary)|kind(mary)))&
((strong(alice)|patient(alice)))&
(?[X]:((kind(X)|~curious(X))))&
((~funny(alice)<~>~happy(alice)))&
((~funny(alice)&~wise(alice)))&
(?[X]:((calm(X)<~>~humble(X)))) | ~kind(paul) | [
"p3",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3791537676556202233300803
% SZS output start Proof for 3791537676556202233300803
4. (~kind(paul) & ~rich(paul)) <=> ? [X0] : (happy(X0) | funny(X0)) [input p3]
21. ~funny(alice) <~> ~happy(alice) [input p20]
22. ~wise(alice) & ~funny(alice) [input p21]
24. kind(paul) [input hypothesis]
38. ((~kind(paul) & ~rich(paul)) | ! [X0] : (~happy(X0) & ~funny(X0))) & (? [X0] : (happy(X0) | funny(X0)) | (kind(paul) | rich(paul))) [nnf transformation 4]
39. ((~kind(paul) & ~rich(paul)) | ! [X0] : (~happy(X0) & ~funny(X0))) & (? [X0] : (happy(X0) | funny(X0)) | kind(paul) | rich(paul)) [flattening 38]
40. ((~kind(paul) & ~rich(paul)) | ! [X0] : (~happy(X0) & ~funny(X0))) & (? [X1] : (happy(X1) | funny(X1)) | kind(paul) | rich(paul)) [rectify 39]
41. ? [X1] : (happy(X1) | funny(X1)) => (happy(sK0) | funny(sK0)) [choice axiom]
42. ((~kind(paul) & ~rich(paul)) | ! [X0] : (~happy(X0) & ~funny(X0))) & ((happy(sK0) | funny(sK0)) | kind(paul) | rich(paul)) [skolemisation 40,41]
74. (happy(alice) | funny(alice)) & (~happy(alice) | ~funny(alice)) [nnf transformation 21]
95. ~kind(paul) | ~happy(X0) [cnf transformation 42]
149. happy(alice) | funny(alice) [cnf transformation 74]
150. ~funny(alice) [cnf transformation 22]
154. kind(paul) [cnf transformation 24]
191. 8 <=> ! [X0] : ~happy(X0) [avatar definition]
192. ~happy(X0) <- (8) [avatar component clause 191]
194. 9 <=> kind(paul) [avatar definition]
197. 8 | ~9 [avatar split clause 95,194,191]
374. 47 <=> funny(alice) [avatar definition]
378. 48 <=> happy(alice) [avatar definition]
380. happy(alice) <- (48) [avatar component clause 378]
381. 47 | 48 [avatar split clause 149,378,374]
383. ~47 [avatar split clause 150,374]
394. 9 [avatar split clause 154,194]
395. $false <- (8, 48) [resolution 380,192]
396. ~8 | ~48 [avatar contradiction clause 395]
397. $false [avatar sat refutation 197,381,383,394,396]
% SZS output end Proof for 3791537676556202233300803
% ------------------------------
% 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 happy or funny then someone is brave and vice versa. Everyone who is curious or strong is not funny. If someone is both tall and humble then someone is not rich or wise. If susan is calm then someone is both not calm and curious and vice versa. Everyone who is generous is kind or not generous and vice versa. Everyone who is either not rich or not tall is not rich. If alice is both not funny and not quiet then someone is kind and vice versa. Everyone who is curious or rich is not curious or not calm. Everyone who is generous or not humble is not brave. Everyone who is curious is either not patient or not funny and vice versa. If someone is humble then someone is not generous or not old and vice versa. Everyone who is either tall or kind is creative or tall. If fred is tall or creative then someone is brave or not patient and vice versa. If someone is either not brave or funny then someone is generous and vice versa. Everyone who is either not generous or tall is either calm or not funny and vice versa. Everyone who is humble or not strong is brave and vice versa. Someone is either curious or not rich. Someone is both strong and calm. Mary is either kind or brave. Someone is not strong or not rich. Alice is not wise. Someone is both not humble and curious. Paul is wise or not patient. | Alice is not old. | contradiction | (((happy(mary)|funny(mary)))<=>(?[X]:(brave(X))))&
(![X]:((curious(X)|strong(X))=>~funny(X)))&
((?[X]:((tall(X)&humble(X))))=>(?[X]:((~rich(X)|wise(X)))))&
((calm(susan))<=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:(generous(X)<=>(kind(X)|~generous(X))))&
(![X]:((~rich(X)<~>~tall(X))=>~rich(X)))&
(((~funny(alice)&~quiet(alice)))<=>(?[X]:(kind(X))))&
(![X]:((curious(X)|rich(X))=>(~curious(X)|~calm(X))))&
(![X]:((generous(X)|~humble(X))=>~brave(X)))&
(![X]:(curious(X)<=>(~patient(X)<~>~funny(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~generous(X)|~old(X)))))&
(![X]:((tall(X)<~>kind(X))=>(creative(X)|tall(X))))&
(((tall(fred)|creative(fred)))<=>(?[X]:((brave(X)|~patient(X)))))&
((?[X]:((~brave(X)<~>funny(X))))<=>(?[X]:(generous(X))))&
(![X]:((~generous(X)<~>tall(X))<=>(calm(X)<~>~funny(X))))&
(![X]:((humble(X)|~strong(X))<=>brave(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
(?[X]:((strong(X)&calm(X))))&
((kind(mary)<~>brave(mary)))&
(?[X]:((~strong(X)|~rich(X))))&
(~wise(alice))&
(?[X]:((~humble(X)&curious(X))))&
((wise(paul)|~patient(paul))) | ~old(alice) | [
"p4",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 139437283632449252401611
% SZS output start Proof for 139437283632449252401611
5. ! [X0] : (generous(X0) <=> (~generous(X0) | kind(X0))) [input p4]
9. ! [X0] : ((~humble(X0) | generous(X0)) => ~brave(X0)) [input p8]
11. ? [X0] : humble(X0) <=> ? [X0] : (~old(X0) | ~generous(X0)) [input p10]
16. ! [X0] : ((~strong(X0) | humble(X0)) <=> brave(X0)) [input p15]
24. ~old(alice) [input hypothesis]
26. ? [X0] : humble(X0) <=> ? [X1] : (~old(X1) | ~generous(X1)) [rectify 11]
33. ! [X0] : (~brave(X0) | (humble(X0) & ~generous(X0))) [ennf transformation 9]
48. ! [X0] : ((generous(X0) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | ~generous(X0))) [nnf transformation 5]
49. ! [X0] : ((generous(X0) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | ~generous(X0))) [flattening 48]
57. (? [X0] : humble(X0) | ! [X1] : (old(X1) & generous(X1))) & (? [X1] : (~old(X1) | ~generous(X1)) | ! [X0] : ~humble(X0)) [nnf transformation 26]
58. (? [X0] : humble(X0) | ! [X1] : (old(X1) & generous(X1))) & (? [X2] : (~old(X2) | ~generous(X2)) | ! [X3] : ~humble(X3)) [rectify 57]
59. ? [X0] : humble(X0) => humble(sK4) [choice axiom]
60. ? [X2] : (~old(X2) | ~generous(X2)) => (~old(sK5) | ~generous(sK5)) [choice axiom]
61. (humble(sK4) | ! [X1] : (old(X1) & generous(X1))) & ((~old(sK5) | ~generous(sK5)) | ! [X3] : ~humble(X3)) [skolemisation 58,60,59]
74. ! [X0] : (((~strong(X0) | humble(X0)) | ~brave(X0)) & (brave(X0) | (strong(X0) & ~humble(X0)))) [nnf transformation 16]
75. ! [X0] : ((~strong(X0) | humble(X0) | ~brave(X0)) & (brave(X0) | (strong(X0) & ~humble(X0)))) [flattening 74]
97. generous(X0) | generous(X0) [cnf transformation 49]
105. ~brave(X0) | ~generous(X0) [cnf transformation 33]
113. humble(sK4) | old(X1) [cnf transformation 61]
132. ~humble(X0) | brave(X0) [cnf transformation 75]
146. ~old(alice) [cnf transformation 24]
151. generous(X0) [duplicate literal removal 97]
153. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
154. ~brave(X0) <- (1) [avatar component clause 153]
203. ~brave(X0) [subsumption resolution 105,151]
204. 1 [avatar split clause 203,153]
208. 12 <=> ! [X1] : old(X1) [avatar definition]
209. old(X1) <- (12) [avatar component clause 208]
211. 13 <=> humble(sK4) [avatar definition]
213. humble(sK4) <- (13) [avatar component clause 211]
214. 12 | 13 [avatar split clause 113,211,208]
289. $false <- (12) [resolution 209,146]
290. ~12 [avatar contradiction clause 289]
296. brave(sK4) <- (13) [resolution 132,213]
297. $false <- (1, 13) [subsumption resolution 296,154]
298. ~1 | ~13 [avatar contradiction clause 297]
299. $false [avatar sat refutation 204,214,290,298]
% SZS output end Proof for 139437283632449252401611
% ------------------------------
% 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 mary is both not strong and not curious then fred is not strong or not curious and vice versa.
Everyone who is not funny is rich.
Everyone who is happy is both not creative and wise and vice versa.
Everyone who is either not rich or not old is either strong or patient.
If mary is not strong then someone is wise or quiet.
Everyone who is both not happy and not tall is either tall or happy.
If someone is not patient then fred is either not creative or generous.
Everyone who is either not strong or quiet is both not humble and not happy and vice versa.
If mary is either humble or wise then someone is either rich or happy and vice versa.
If paul is either not quiet or strong then someone is calm or not rich and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is not old or not rich is creative and vice versa.
If mary is either not calm or strong then someone is not calm or not brave and vice versa.
If someone is either not wise or not humble then someone is wise.
Everyone who is not humble is not creative or old and vice versa.
Susan is either kind or not funny.
Lucy is generous or not brave.
Alice is both not calm and wise.
Someone is either generous or not old.
Someone is not strong or kind. | Paul is not happy. | entailment | (((~strong(mary)&~curious(mary)))<=>((~strong(fred)|~curious(fred))))&
(![X]:(~funny(X)=>rich(X)))&
(![X]:(happy(X)<=>(~creative(X)&wise(X))))&
(![X]:((~rich(X)<~>~old(X))=>(strong(X)<~>patient(X))))&
((~strong(mary))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((~happy(X)&~tall(X))=>(tall(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>((~creative(fred)<~>generous(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~humble(X)&~happy(X))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((rich(X)<~>happy(X)))))&
(((~quiet(paul)<~>strong(paul)))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~old(X)|~rich(X))<=>creative(X)))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:((~calm(X)|~brave(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)<=>(~creative(X)|old(X))))&
((kind(susan)<~>~funny(susan)))&
((generous(lucy)|~brave(lucy)))&
((~calm(alice)&wise(alice)))&
(?[X]:((generous(X)<~>~old(X))))&
(?[X]:((~strong(X)|kind(X)))) | ~happy(paul) | [
"p2",
"p7",
"p8",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2834032511816702268539114
% SZS output start Proof for 2834032511816702268539114
3. ! [X0] : (happy(X0) <=> (wise(X0) & ~creative(X0))) [input p2]
8. ! [X0] : ((~strong(X0) <~> quiet(X0)) <=> (~happy(X0) & ~humble(X0))) [input p7]
9. (humble(mary) <~> wise(mary)) <=> ? [X0] : (rich(X0) <~> happy(X0)) [input p8]
10. (~quiet(paul) <~> strong(paul)) <=> ? [X0] : (~rich(X0) | calm(X0)) [input p9]
11. ! [X0] : (~old(X0) <=> wise(X0)) [input p10]
12. ! [X0] : ((~rich(X0) | ~old(X0)) <=> creative(X0)) [input p11]
15. ! [X0] : (~humble(X0) <=> (old(X0) | ~creative(X0))) [input p14]
21. happy(paul) [input hypothesis]
32. ! [X0] : ((happy(X0) | (~wise(X0) | creative(X0))) & ((wise(X0) & ~creative(X0)) | ~happy(X0))) [nnf transformation 3]
33. ! [X0] : ((happy(X0) | ~wise(X0) | creative(X0)) & ((wise(X0) & ~creative(X0)) | ~happy(X0))) [flattening 32]
39. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [nnf transformation 8]
40. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [flattening 39]
41. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [nnf transformation 9]
42. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [rectify 41]
43. ? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) => ((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) [choice axiom]
44. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [skolemisation 42,43]
45. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X0] : (~rich(X0) | calm(X0)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [nnf transformation 10]
46. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X1] : (~rich(X1) | calm(X1)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [rectify 45]
47. ? [X1] : (~rich(X1) | calm(X1)) => (~rich(sK2) | calm(sK2)) [choice axiom]
48. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & ((~rich(sK2) | calm(sK2)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [skolemisation 46,47]
49. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 11]
50. ! [X0] : (((~rich(X0) | ~old(X0)) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [nnf transformation 12]
51. ! [X0] : ((~rich(X0) | ~old(X0) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [flattening 50]
60. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & ((old(X0) | ~creative(X0)) | humble(X0))) [nnf transformation 15]
61. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & (old(X0) | ~creative(X0) | humble(X0))) [flattening 60]
74. ~creative(X0) | ~happy(X0) [cnf transformation 33]
75. ~happy(X0) | wise(X0) [cnf transformation 33]
88. ~happy(X0) | quiet(X0) | strong(X0) [cnf transformation 40]
89. ~quiet(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 40]
96. wise(mary) | humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 44]
98. ~wise(mary) | ~humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 44]
103. strong(paul) | ~quiet(paul) | rich(X0) [cnf transformation 48]
105. ~strong(paul) | quiet(paul) | rich(X0) [cnf transformation 48]
106. old(X0) | wise(X0) [cnf transformation 49]
107. ~old(X0) | ~wise(X0) [cnf transformation 49]
108. old(X0) | creative(X0) [cnf transformation 51]
119. old(X0) | ~creative(X0) | humble(X0) [cnf transformation 61]
121. ~humble(X0) | ~old(X0) [cnf transformation 61]
130. happy(paul) [cnf transformation 21]
179. 11 <=> humble(mary) [avatar definition]
180. humble(mary) <- (11) [avatar component clause 179]
181. ~humble(mary) <- (~11) [avatar component clause 179]
183. 12 <=> wise(mary) [avatar definition]
185. ~wise(mary) <- (~12) [avatar component clause 183]
188. 13 <=> ! [X0] : (happy(X0) | ~rich(X0)) [avatar definition]
189. ~rich(X0) | happy(X0) <- (13) [avatar component clause 188]
190. 13 | ~11 | ~12 [avatar split clause 98,183,179,188]
192. 13 | 11 | 12 [avatar split clause 96,183,179,188]
206. 16 <=> ! [X0] : rich(X0) [avatar definition]
207. rich(X0) <- (16) [avatar component clause 206]
209. 17 <=> quiet(paul) [avatar definition]
211. quiet(paul) <- (17) [avatar component clause 209]
213. 18 <=> strong(paul) [avatar definition]
215. ~strong(paul) <- (~18) [avatar component clause 213]
216. 16 | 17 | ~18 [avatar split clause 105,213,209,206]
221. 16 | ~17 | 18 [avatar split clause 103,213,209,206]
269. humble(X0) | old(X0) [subsumption resolution 119,108]
294. 35 <=> old(sK5) [avatar definition]
295. ~old(sK5) <- (~35) [avatar component clause 294]
296. old(sK5) <- (35) [avatar component clause 294]
312. creative(sK5) <- (~35) [resolution 108,295]
314. ~happy(sK5) <- (~35) [resolution 312,74]
323. old(mary) <- (~11) [resolution 269,181]
326. ~wise(mary) <- (~11) [resolution 323,107]
355. quiet(paul) | strong(paul) [resolution 88,130]
371. quiet(paul) <- (~18) [subsumption resolution 355,215]
372. 17 | 18 [avatar split clause 371,213,209]
374. happy(X0) <- (13, 16) [resolution 207,189]
377. ~strong(paul) | ~happy(paul) <- (17) [resolution 89,211]
381. wise(X2) <- (13, 16) [resolution 374,75]
382. $false <- (13, 16, ~35) [resolution 374,314]
385. ~13 | ~16 | 35 [avatar contradiction clause 382]
386. ~wise(sK5) <- (35) [resolution 296,107]
387. $false <- (13, 16, 35) [subsumption resolution 386,381]
388. ~13 | ~16 | ~35 [avatar contradiction clause 387]
398. ~strong(paul) <- (17) [subsumption resolution 377,130]
399. ~18 | ~17 [avatar split clause 398,209,213]
400. ~12 | 11 [avatar split clause 326,179,183]
405. ~old(mary) <- (11) [resolution 180,121]
435. wise(mary) <- (11) [resolution 405,106]
436. $false <- (11, ~12) [subsumption resolution 435,185]
437. ~11 | 12 [avatar contradiction clause 436]
438. $false [avatar sat refutation 190,192,216,221,372,385,388,399,400,437]
% SZS output end Proof for 2834032511816702268539114
% ------------------------------
% 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 someone is both tall and humble then susan is either not generous or curious. Everyone who is not tall is not happy and vice versa. Everyone who is either quiet or rich is either not strong or quiet and vice versa. Everyone who is both not curious and quiet is both not happy and old. If john is not calm then lucy is happy. Everyone who is quiet is kind or curious. Everyone who is either not kind or not happy is either humble or not patient and vice versa. If someone is either kind or creative then mary is creative and vice versa. If mary is not creative then mary is either not patient or not kind. If someone is both not wise and not tall then lucy is old or not wise. Everyone who is both not wise and creative is not humble and vice versa. Everyone who is both patient and creative is quiet or not patient and vice versa. If paul is either not old or kind then someone is both not kind and not tall and vice versa. Everyone who is both not brave and quiet is not kind or not rich and vice versa. If alice is old then someone is either generous or wise. If paul is generous or not strong then someone is both tall and creative. Lucy is not rich or happy. Alice is both generous and kind. Someone is wise or not patient. Someone is either not curious or not patient. Alice is not strong. Someone is both curious and happy. Someone is either funny or not calm. Fred is both not curious and not rich. | Alice is old. | neutral | ((?[X]:((tall(X)&humble(X))))=>((~generous(susan)<~>curious(susan))))&
(![X]:(~tall(X)<=>~happy(X)))&
(![X]:((quiet(X)<~>rich(X))<=>(~strong(X)<~>quiet(X))))&
(![X]:((~curious(X)&quiet(X))=>(~happy(X)&old(X))))&
((~calm(john))=>(happy(lucy)))&
(![X]:(quiet(X)=>(kind(X)|curious(X))))&
(![X]:((~kind(X)<~>~happy(X))<=>(humble(X)<~>~patient(X))))&
((?[X]:((kind(X)<~>creative(X))))<=>(creative(mary)))&
((~creative(mary))=>((~patient(mary)<~>~kind(mary))))&
((?[X]:((~wise(X)&~tall(X))))=>((old(lucy)|~wise(lucy))))&
(![X]:((~wise(X)&creative(X))<=>~humble(X)))&
(![X]:((patient(X)&creative(X))<=>(quiet(X)|~patient(X))))&
(((~old(paul)<~>kind(paul)))<=>(?[X]:((~kind(X)&~tall(X)))))&
(![X]:((~brave(X)&quiet(X))<=>(~kind(X)|~rich(X))))&
((old(alice))=>(?[X]:((generous(X)<~>wise(X)))))&
(((generous(paul)|~strong(paul)))=>(?[X]:((tall(X)&creative(X)))))&
((~rich(lucy)|happy(lucy)))&
((generous(alice)&kind(alice)))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:((~curious(X)<~>~patient(X))))&
(~strong(alice))&
(?[X]:((curious(X)&happy(X))))&
(?[X]:((funny(X)<~>~calm(X))))&
((~curious(fred)&~rich(fred))) | old(alice) | [] | null | 0 |
Everyone who is either calm or not tall is tall.
Everyone who is both not calm and not humble is both not old and quiet and vice versa.
Everyone who is both not humble and tall is kind.
Everyone who is quiet is rich.
If someone is both old and quiet then someone is both not patient and happy and vice versa.
If someone is both kind and not brave then susan is not old or not wise and vice versa.
If susan is either not humble or happy then someone is either not humble or not patient.
Everyone who is both not old and not funny is brave.
Everyone who is both not wise and not kind is either strong or curious.
If someone is both not rich and not calm then lucy is either wise or happy and vice versa.
If lucy is both happy and not strong then susan is old or happy and vice versa.
Everyone who is both humble and not rich is curious.
Everyone who is either not rich or wise is not calm or not brave.
Everyone who is either brave or patient is either not calm or wise and vice versa.
Everyone who is both brave and patient is both humble and curious.
Everyone who is either not wise or generous is generous or not old and vice versa.
Someone is both not funny and not calm.
Someone is either brave or not happy.
Someone is both not happy and not patient.
Lucy is not funny or kind.
Someone is either wise or creative.
Lucy is both not funny and not patient.
Mary is both tall and not creative.
Someone is not funny. | Susan is brave. | neutral | (![X]:((calm(X)<~>~tall(X))=>tall(X)))&
(![X]:((~calm(X)&~humble(X))<=>(~old(X)&quiet(X))))&
(![X]:((~humble(X)&tall(X))=>kind(X)))&
(![X]:(quiet(X)=>rich(X)))&
((?[X]:((old(X)&quiet(X))))<=>(?[X]:((~patient(X)&happy(X)))))&
((?[X]:((kind(X)&~brave(X))))<=>((~old(susan)|~wise(susan))))&
(((~humble(susan)<~>happy(susan)))=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((~old(X)&~funny(X))=>brave(X)))&
(![X]:((~wise(X)&~kind(X))=>(strong(X)<~>curious(X))))&
((?[X]:((~rich(X)&~calm(X))))<=>((wise(lucy)<~>happy(lucy))))&
(((happy(lucy)&~strong(lucy)))<=>((old(susan)|happy(susan))))&
(![X]:((humble(X)&~rich(X))=>curious(X)))&
(![X]:((~rich(X)<~>wise(X))=>(~calm(X)|~brave(X))))&
(![X]:((brave(X)<~>patient(X))<=>(~calm(X)<~>wise(X))))&
(![X]:((brave(X)&patient(X))=>(humble(X)&curious(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(generous(X)|~old(X))))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((brave(X)<~>~happy(X))))&
(?[X]:((~happy(X)&~patient(X))))&
((~funny(lucy)|kind(lucy)))&
(?[X]:((wise(X)<~>creative(X))))&
((~funny(lucy)&~patient(lucy)))&
((tall(mary)&~creative(mary)))&
(?[X]:(~funny(X))) | brave(susan) | [] | null | 0 |
If someone is humble then someone is not curious or kind.
Everyone who is both funny and not creative is either generous or not tall and vice versa.
If someone is both funny and humble then alice is both calm and not kind and vice versa.
If paul is creative then alice is strong or tall.
Everyone who is not tall is happy and vice versa.
Everyone who is either not calm or kind is not kind.
If paul is not calm then someone is both not generous and not patient.
Everyone who is quiet or strong is brave and vice versa.
If john is both old and not quiet then someone is both tall and not happy and vice versa.
Everyone who is either wise or not rich is both not curious and not humble.
Everyone who is both creative and strong is both calm and happy and vice versa.
If mary is either humble or creative then susan is both tall and not rich.
If paul is either not tall or humble then susan is either not wise or not quiet and vice versa.
If someone is old or tall then someone is patient and vice versa.
Everyone who is both tall and not funny is creative.
Everyone who is either not rich or happy is either not funny or not curious.
Someone is either funny or brave.
Susan is funny or not happy.
Paul is either calm or patient.
Mary is not wise or not funny.
Fred is humble or wise.
Susan is not calm or not happy.
Fred is not funny or patient.
Someone is strong. | Susan is happy. | neutral | ((?[X]:(humble(X)))=>(?[X]:((~curious(X)|kind(X)))))&
(![X]:((funny(X)&~creative(X))<=>(generous(X)<~>~tall(X))))&
((?[X]:((funny(X)&humble(X))))<=>((calm(alice)&~kind(alice))))&
((creative(paul))=>((strong(alice)|tall(alice))))&
(![X]:(~tall(X)<=>happy(X)))&
(![X]:((~calm(X)<~>kind(X))=>~kind(X)))&
((~calm(paul))=>(?[X]:((~generous(X)&~patient(X)))))&
(![X]:((quiet(X)|strong(X))<=>brave(X)))&
(((old(john)&~quiet(john)))<=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((wise(X)<~>~rich(X))=>(~curious(X)&~humble(X))))&
(![X]:((creative(X)&strong(X))<=>(calm(X)&happy(X))))&
(((humble(mary)<~>creative(mary)))=>((tall(susan)&~rich(susan))))&
(((~tall(paul)<~>humble(paul)))<=>((~wise(susan)<~>~quiet(susan))))&
((?[X]:((old(X)|tall(X))))<=>(?[X]:(patient(X))))&
(![X]:((tall(X)&~funny(X))=>creative(X)))&
(![X]:((~rich(X)<~>happy(X))=>(~funny(X)<~>~curious(X))))&
(?[X]:((funny(X)<~>brave(X))))&
((funny(susan)|~happy(susan)))&
((calm(paul)<~>patient(paul)))&
((~wise(mary)|~funny(mary)))&
((humble(fred)|wise(fred)))&
((~calm(susan)|~happy(susan)))&
((~funny(fred)|patient(fred)))&
(?[X]:(strong(X))) | happy(susan) | [] | null | 0 |
If someone is not funny then someone is both not kind and strong and vice versa.
If someone is rich or not happy then susan is both not funny and not calm.
If paul is either not brave or creative then someone is either humble or not generous.
Everyone who is both not strong and quiet is both quiet and not kind.
Everyone who is not generous is either not calm or not rich and vice versa.
Everyone who is either quiet or not generous is either tall or happy and vice versa.
If someone is either not curious or not funny then someone is wise and vice versa.
Everyone who is both tall and not wise is both tall and not patient.
If someone is not calm then someone is not wise.
If someone is not rich or not humble then susan is both creative and not old and vice versa.
Everyone who is both strong and patient is not rich or tall and vice versa.
If someone is strong then mary is both strong and generous.
If john is not creative or generous then fred is wise or rich and vice versa.
Everyone who is generous is curious.
Everyone who is either wise or not curious is not humble.
Everyone who is brave or not generous is either not curious or not generous and vice versa.
Alice is not happy or not kind.
Someone is either calm or not tall.
Someone is kind.
Mary is not wise. | Fred is not rich. | neutral | ((?[X]:(~funny(X)))<=>(?[X]:((~kind(X)&strong(X)))))&
((?[X]:((rich(X)|~happy(X))))=>((~funny(susan)&~calm(susan))))&
(((~brave(paul)<~>creative(paul)))=>(?[X]:((humble(X)<~>~generous(X)))))&
(![X]:((~strong(X)&quiet(X))=>(quiet(X)&~kind(X))))&
(![X]:(~generous(X)<=>(~calm(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>~generous(X))<=>(tall(X)<~>happy(X))))&
((?[X]:((~curious(X)<~>~funny(X))))<=>(?[X]:(wise(X))))&
(![X]:((tall(X)&~wise(X))=>(tall(X)&~patient(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~wise(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>((creative(susan)&~old(susan))))&
(![X]:((strong(X)&patient(X))<=>(~rich(X)|tall(X))))&
((?[X]:(strong(X)))=>((strong(mary)&generous(mary))))&
(((~creative(john)|generous(john)))<=>((wise(fred)|rich(fred))))&
(![X]:(generous(X)=>curious(X)))&
(![X]:((wise(X)<~>~curious(X))=>~humble(X)))&
(![X]:((brave(X)|~generous(X))<=>(~curious(X)<~>~generous(X))))&
((~happy(alice)|~kind(alice)))&
(?[X]:((calm(X)<~>~tall(X))))&
(?[X]:(kind(X)))&
(~wise(mary)) | ~rich(fred) | [] | null | 0 |
If someone is not strong or tall then someone is happy or humble. Everyone who is not happy is both not rich and happy. If mary is curious then mary is happy or not generous. If mary is both happy and not rich then fred is either kind or tall and vice versa. If alice is both generous and not funny then someone is old or not funny. If someone is either not humble or not funny then alice is either strong or tall and vice versa. Everyone who is tall is strong or not rich. Everyone who is not calm or funny is not curious and vice versa. Everyone who is wise or creative is both not creative and not rich. Everyone who is either patient or not rich is not rich or not humble. Everyone who is either patient or not quiet is both not kind and rich. Everyone who is not old is either not old or generous. Everyone who is either not tall or strong is either not curious or not patient. Everyone who is kind or not patient is either not happy or not tall. If mary is patient or not brave then someone is either not strong or patient. Everyone who is either not rich or quiet is old or calm and vice versa. Someone is either not rich or patient. Fred is not funny or calm. Mary is rich or kind. Someone is not brave. Susan is not humble. Lucy is wise or strong. Someone is both not brave and not kind. Someone is not humble or not patient. | Susan is not creative. | entailment | ((?[X]:((~strong(X)|tall(X))))=>(?[X]:((happy(X)|humble(X)))))&
(![X]:(~happy(X)=>(~rich(X)&happy(X))))&
((curious(mary))=>((happy(mary)|~generous(mary))))&
(((happy(mary)&~rich(mary)))<=>((kind(fred)<~>tall(fred))))&
(((generous(alice)&~funny(alice)))=>(?[X]:((old(X)|~funny(X)))))&
((?[X]:((~humble(X)<~>~funny(X))))<=>((strong(alice)<~>tall(alice))))&
(![X]:(tall(X)=>(strong(X)|~rich(X))))&
(![X]:((~calm(X)|funny(X))<=>~curious(X)))&
(![X]:((wise(X)|creative(X))=>(~creative(X)&~rich(X))))&
(![X]:((patient(X)<~>~rich(X))=>(~rich(X)|~humble(X))))&
(![X]:((patient(X)<~>~quiet(X))=>(~kind(X)&rich(X))))&
(![X]:(~old(X)=>(~old(X)<~>generous(X))))&
(![X]:((~tall(X)<~>strong(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((kind(X)|~patient(X))=>(~happy(X)<~>~tall(X))))&
(((patient(mary)|~brave(mary)))=>(?[X]:((~strong(X)<~>patient(X)))))&
(![X]:((~rich(X)<~>quiet(X))<=>(old(X)|calm(X))))&
(?[X]:((~rich(X)<~>patient(X))))&
((~funny(fred)|calm(fred)))&
((rich(mary)|kind(mary)))&
(?[X]:(~brave(X)))&
(~humble(susan))&
((wise(lucy)|strong(lucy)))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:((~humble(X)|~patient(X)))) | ~creative(susan) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 880320284271884085966300
% SZS output start Proof for 880320284271884085966300
9. ! [X0] : ((creative(X0) | wise(X0)) => (~rich(X0) & ~creative(X0))) [input p8]
25. creative(susan) [input hypothesis]
35. ! [X0] : ((~rich(X0) & ~creative(X0)) | (~creative(X0) & ~wise(X0))) [ennf transformation 9]
100. ~creative(X0) | ~creative(X0) [cnf transformation 35]
139. creative(susan) [cnf transformation 25]
142. ~creative(X0) [duplicate literal removal 100]
289. $false [subsumption resolution 139,142]
% SZS output end Proof for 880320284271884085966300
% ------------------------------
% 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 paul is both kind and not rich then someone is both rich and not tall.
If someone is both creative and tall then susan is tall and vice versa.
Everyone who is both not calm and not old is patient and vice versa.
Everyone who is both patient and not curious is either happy or not quiet and vice versa.
If someone is funny or quiet then someone is both rich and creative and vice versa.
Everyone who is not patient is either not strong or not creative.
If john is either creative or quiet then someone is not creative and vice versa.
Everyone who is strong is not old or not kind and vice versa.
Everyone who is either not humble or rich is both wise and not funny.
Everyone who is generous or old is both not rich and not humble and vice versa.
If fred is both quiet and humble then mary is old or not humble.
Everyone who is creative is not kind and vice versa.
If someone is not humble then paul is either not humble or curious.
If alice is either generous or not kind then paul is either not happy or brave and vice versa.
Everyone who is either not generous or brave is both funny and not curious.
If someone is happy then fred is either not brave or curious and vice versa.
Someone is both happy and not calm.
John is not happy or brave.
Someone is both not creative and rich.
Someone is either not tall or not wise.
Someone is not generous or not calm.
Someone is both not curious and kind. | Fred is quiet. | neutral | (((kind(paul)&~rich(paul)))=>(?[X]:((rich(X)&~tall(X)))))&
((?[X]:((creative(X)&tall(X))))<=>(tall(susan)))&
(![X]:((~calm(X)&~old(X))<=>patient(X)))&
(![X]:((patient(X)&~curious(X))<=>(happy(X)<~>~quiet(X))))&
((?[X]:((funny(X)|quiet(X))))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~patient(X)=>(~strong(X)<~>~creative(X))))&
(((creative(john)<~>quiet(john)))<=>(?[X]:(~creative(X))))&
(![X]:(strong(X)<=>(~old(X)|~kind(X))))&
(![X]:((~humble(X)<~>rich(X))=>(wise(X)&~funny(X))))&
(![X]:((generous(X)|old(X))<=>(~rich(X)&~humble(X))))&
(((quiet(fred)&humble(fred)))=>((old(mary)|~humble(mary))))&
(![X]:(creative(X)<=>~kind(X)))&
((?[X]:(~humble(X)))=>((~humble(paul)<~>curious(paul))))&
(((generous(alice)<~>~kind(alice)))<=>((~happy(paul)<~>brave(paul))))&
(![X]:((~generous(X)<~>brave(X))=>(funny(X)&~curious(X))))&
((?[X]:(happy(X)))<=>((~brave(fred)<~>curious(fred))))&
(?[X]:((happy(X)&~calm(X))))&
((~happy(john)|brave(john)))&
(?[X]:((~creative(X)&rich(X))))&
(?[X]:((~tall(X)<~>~wise(X))))&
(?[X]:((~generous(X)|~calm(X))))&
(?[X]:((~curious(X)&kind(X)))) | quiet(fred) | [] | null | 0 |
Everyone who is patient or kind is not rich. If someone is kind or not quiet then someone is either wise or humble and vice versa. If susan is both not calm and quiet then someone is not patient and vice versa. If someone is both creative and generous then someone is strong or not happy and vice versa. Everyone who is calm is not wise and vice versa. If someone is quiet then alice is either not tall or not old. Everyone who is patient or strong is both not curious and not kind. If paul is kind or not tall then someone is old or kind and vice versa. Everyone who is both not tall and rich is either creative or patient. If someone is either calm or not tall then someone is kind or rich and vice versa. Everyone who is both not kind and not humble is not creative. Everyone who is not strong or not funny is both not calm and not kind and vice versa. If someone is not tall then john is not quiet and vice versa. Everyone who is old is both not old and not tall and vice versa. If someone is not creative then paul is funny and vice versa. If paul is either creative or not creative then alice is not quiet. Someone is either brave or kind. Someone is either not wise or rich. Someone is both not quiet and not patient. Susan is either kind or tall. Someone is not calm or quiet. Someone is patient or creative. Someone is both strong and not rich. Someone is either not old or creative. | Alice is not tall. | contradiction | (![X]:((patient(X)|kind(X))=>~rich(X)))&
((?[X]:((kind(X)|~quiet(X))))<=>(?[X]:((wise(X)<~>humble(X)))))&
(((~calm(susan)&quiet(susan)))<=>(?[X]:(~patient(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((strong(X)|~happy(X)))))&
(![X]:(calm(X)<=>~wise(X)))&
((?[X]:(quiet(X)))=>((~tall(alice)<~>~old(alice))))&
(![X]:((patient(X)|strong(X))=>(~curious(X)&~kind(X))))&
(((kind(paul)|~tall(paul)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:((~tall(X)&rich(X))=>(creative(X)<~>patient(X))))&
((?[X]:((calm(X)<~>~tall(X))))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((~kind(X)&~humble(X))=>~creative(X)))&
(![X]:((~strong(X)|~funny(X))<=>(~calm(X)&~kind(X))))&
((?[X]:(~tall(X)))<=>(~quiet(john)))&
(![X]:(old(X)<=>(~old(X)&~tall(X))))&
((?[X]:(~creative(X)))<=>(funny(paul)))&
(((creative(paul)<~>~creative(paul)))=>(~quiet(alice)))&
(?[X]:((brave(X)<~>kind(X))))&
(?[X]:((~wise(X)<~>rich(X))))&
(?[X]:((~quiet(X)&~patient(X))))&
((kind(susan)<~>tall(susan)))&
(?[X]:((~calm(X)|quiet(X))))&
(?[X]:((patient(X)|creative(X))))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:((~old(X)<~>creative(X)))) | ~tall(alice) | [
"p2",
"p5",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3740493118653441121156292
% SZS output start Proof for 3740493118653441121156292
3. (quiet(susan) & ~calm(susan)) <=> ? [X0] : ~patient(X0) [input p2]
6. ? [X0] : quiet(X0) => (~tall(alice) <~> ~old(alice)) [input p5]
14. ! [X0] : (old(X0) <=> (~tall(X0) & ~old(X0))) [input p13]
19. ? [X0] : (~patient(X0) & ~quiet(X0)) [input p18]
25. ~tall(alice) [input hypothesis]
31. (~tall(alice) <~> ~old(alice)) | ! [X0] : ~quiet(X0) [ennf transformation 6]
43. ((quiet(susan) & ~calm(susan)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (~quiet(susan) | calm(susan))) [nnf transformation 3]
44. ((quiet(susan) & ~calm(susan)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ~quiet(susan) | calm(susan)) [flattening 43]
45. ((quiet(susan) & ~calm(susan)) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ~quiet(susan) | calm(susan)) [rectify 44]
46. ? [X1] : ~patient(X1) => ~patient(sK2) [choice axiom]
47. ((quiet(susan) & ~calm(susan)) | ! [X0] : patient(X0)) & (~patient(sK2) | ~quiet(susan) | calm(susan)) [skolemisation 45,46]
54. ((old(alice) | tall(alice)) & (~old(alice) | ~tall(alice))) | ! [X0] : ~quiet(X0) [nnf transformation 31]
72. ! [X0] : ((old(X0) | (tall(X0) | old(X0))) & ((~tall(X0) & ~old(X0)) | ~old(X0))) [nnf transformation 14]
73. ! [X0] : ((old(X0) | tall(X0) | old(X0)) & ((~tall(X0) & ~old(X0)) | ~old(X0))) [flattening 72]
85. ? [X0] : (~patient(X0) & ~quiet(X0)) => (~patient(sK12) & ~quiet(sK12)) [choice axiom]
86. ~patient(sK12) & ~quiet(sK12) [skolemisation 19,85]
107. quiet(susan) | patient(X0) [cnf transformation 47]
116. old(alice) | tall(alice) | ~quiet(X0) [cnf transformation 54]
139. ~old(X0) | ~old(X0) [cnf transformation 73]
151. ~patient(sK12) [cnf transformation 86]
160. ~tall(alice) [cnf transformation 25]
163. ~old(X0) [duplicate literal removal 139]
200. 9 <=> ! [X0] : patient(X0) [avatar definition]
201. patient(X0) <- (9) [avatar component clause 200]
203. 10 <=> quiet(susan) [avatar definition]
205. quiet(susan) <- (10) [avatar component clause 203]
206. 9 | 10 [avatar split clause 107,203,200]
248. 20 <=> ! [X0] : ~quiet(X0) [avatar definition]
249. ~quiet(X0) <- (20) [avatar component clause 248]
251. 21 <=> tall(alice) [avatar definition]
255. 22 <=> old(alice) [avatar definition]
257. old(alice) <- (22) [avatar component clause 255]
258. 20 | 21 | 22 [avatar split clause 116,255,251,248]
270. 25 <=> ! [X0] : ~old(X0) [avatar definition]
271. ~old(X0) <- (25) [avatar component clause 270]
331. 25 [avatar split clause 163,270]
413. ~21 [avatar split clause 160,251]
416. $false <- (9) [resolution 201,151]
417. ~9 [avatar contradiction clause 416]
418. $false <- (10, 20) [subsumption resolution 205,249]
419. ~10 | ~20 [avatar contradiction clause 418]
420. $false <- (22, 25) [subsumption resolution 257,271]
421. ~22 | ~25 [avatar contradiction clause 420]
422. $false [avatar sat refutation 206,258,331,413,417,419,421]
% SZS output end Proof for 3740493118653441121156292
% ------------------------------
% 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 |
Everyone who is either not brave or not tall is both wise and not kind and vice versa. Everyone who is both wise and patient is either not wise or funny. If susan is both old and not curious then someone is humble. Everyone who is not wise is creative and vice versa. Everyone who is calm or happy is both not creative and not happy and vice versa. If someone is not funny or not brave then someone is either not calm or kind and vice versa. If someone is both not strong and not quiet then someone is both not kind and funny and vice versa. Everyone who is either tall or not calm is happy and vice versa. If someone is either not kind or not creative then someone is tall or not funny. Everyone who is either creative or generous is happy or old. Everyone who is both quiet and kind is not creative or quiet and vice versa. If someone is wise then someone is not patient or not rich. If alice is quiet or not brave then lucy is not generous and vice versa. Everyone who is both not calm and not brave is not generous or not kind and vice versa. Everyone who is either humble or not calm is either not humble or strong. If someone is either not humble or not tall then fred is curious and vice versa. Someone is either generous or not brave. Fred is either funny or happy. Someone is either not funny or not kind. Someone is patient. Someone is not quiet. Lucy is rich. Paul is both creative and curious. Lucy is brave or calm. | Paul is not generous. | contradiction | (![X]:((~brave(X)<~>~tall(X))<=>(wise(X)&~kind(X))))&
(![X]:((wise(X)&patient(X))=>(~wise(X)<~>funny(X))))&
(((old(susan)&~curious(susan)))=>(?[X]:(humble(X))))&
(![X]:(~wise(X)<=>creative(X)))&
(![X]:((calm(X)|happy(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((~funny(X)|~brave(X))))<=>(?[X]:((~calm(X)<~>kind(X)))))&
((?[X]:((~strong(X)&~quiet(X))))<=>(?[X]:((~kind(X)&funny(X)))))&
(![X]:((tall(X)<~>~calm(X))<=>happy(X)))&
((?[X]:((~kind(X)<~>~creative(X))))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((creative(X)<~>generous(X))=>(happy(X)|old(X))))&
(![X]:((quiet(X)&kind(X))<=>(~creative(X)|quiet(X))))&
((?[X]:(wise(X)))=>(?[X]:((~patient(X)|~rich(X)))))&
(((quiet(alice)|~brave(alice)))<=>(~generous(lucy)))&
(![X]:((~calm(X)&~brave(X))<=>(~generous(X)|~kind(X))))&
(![X]:((humble(X)<~>~calm(X))=>(~humble(X)<~>strong(X))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(curious(fred)))&
(?[X]:((generous(X)<~>~brave(X))))&
((funny(fred)<~>happy(fred)))&
(?[X]:((~funny(X)<~>~kind(X))))&
(?[X]:(patient(X)))&
(?[X]:(~quiet(X)))&
(rich(lucy))&
((creative(paul)&curious(paul)))&
((brave(lucy)|calm(lucy))) | ~generous(paul) | [
"p0",
"p3",
"p4",
"p7",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5953383127987058465803816
% SZS output start Proof for 5953383127987058465803816
1. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> (~kind(X0) & wise(X0))) [input p0]
4. ! [X0] : (~wise(X0) <=> creative(X0)) [input p3]
5. ! [X0] : ((happy(X0) | calm(X0)) <=> (~happy(X0) & ~creative(X0))) [input p4]
8. ! [X0] : ((tall(X0) <~> ~calm(X0)) <=> happy(X0)) [input p7]
14. ! [X0] : ((~brave(X0) & ~calm(X0)) <=> (~kind(X0) | ~generous(X0))) [input p13]
23. curious(paul) & creative(paul) [input p22]
25. ~generous(paul) [input hypothesis]
39. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | (kind(X0) | ~wise(X0))) & ((~kind(X0) & wise(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 1]
40. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | kind(X0) | ~wise(X0)) & ((~kind(X0) & wise(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [flattening 39]
44. ! [X0] : ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0))) [nnf transformation 4]
45. ! [X0] : (((happy(X0) | calm(X0)) | (happy(X0) | creative(X0))) & ((~happy(X0) & ~creative(X0)) | (~happy(X0) & ~calm(X0)))) [nnf transformation 5]
46. ! [X0] : ((happy(X0) | calm(X0) | happy(X0) | creative(X0)) & ((~happy(X0) & ~creative(X0)) | (~happy(X0) & ~calm(X0)))) [flattening 45]
57. ! [X0] : ((((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | ~happy(X0)) & (happy(X0) | ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0))))) [nnf transformation 8]
70. ! [X0] : (((~brave(X0) & ~calm(X0)) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | (brave(X0) | calm(X0)))) [nnf transformation 14]
71. ! [X0] : (((~brave(X0) & ~calm(X0)) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | brave(X0) | calm(X0))) [flattening 70]
88. ~tall(X0) | wise(X0) | brave(X0) [cnf transformation 40]
98. ~creative(X0) | ~wise(X0) [cnf transformation 44]
102. ~happy(X0) | ~happy(X0) [cnf transformation 46]
115. happy(X0) | tall(X0) | calm(X0) [cnf transformation 57]
132. ~calm(X0) | generous(X0) [cnf transformation 71]
134. ~brave(X0) | generous(X0) [cnf transformation 71]
153. creative(paul) [cnf transformation 23]
156. ~generous(paul) [cnf transformation 25]
159. ~happy(X0) [duplicate literal removal 102]
235. calm(X0) | tall(X0) [subsumption resolution 115,159]
333. ~wise(paul) [resolution 98,153]
364. generous(X1) | tall(X1) [resolution 235,132]
614. tall(paul) [resolution 364,156]
695. wise(paul) | brave(paul) [resolution 614,88]
696. brave(paul) [subsumption resolution 695,333]
775. generous(paul) [resolution 696,134]
776. $false [subsumption resolution 775,156]
% SZS output end Proof for 5953383127987058465803816
% ------------------------------
% 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 |
If paul is old or not quiet then john is either not humble or patient and vice versa. If someone is both not generous and not funny then someone is not quiet. Everyone who is quiet or not curious is both not funny and generous and vice versa. If fred is both humble and not creative then someone is brave or not curious and vice versa. If fred is generous then john is funny and vice versa. Everyone who is not strong is creative or not generous and vice versa. If someone is either kind or not old then mary is both tall and not calm. Everyone who is both strong and not old is not happy or not generous and vice versa. Everyone who is calm is not quiet. Everyone who is both happy and not creative is not quiet or generous and vice versa. Everyone who is not calm is not funny or old and vice versa. Everyone who is both generous and not happy is not wise or not generous and vice versa. If someone is both quiet and rich then someone is either not kind or not humble and vice versa. If someone is either not happy or not wise then someone is rich or not quiet. Everyone who is both kind and strong is not quiet or not kind. Someone is strong. Someone is either not calm or not humble. Alice is both humble and not funny. Paul is either not funny or not curious. Someone is both old and not rich. | Mary is creative. | contradiction | (((old(paul)|~quiet(paul)))<=>((~humble(john)<~>patient(john))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~curious(X))<=>(~funny(X)&generous(X))))&
(((humble(fred)&~creative(fred)))<=>(?[X]:((brave(X)|~curious(X)))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(![X]:((happy(X)&~creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:(~calm(X)<=>(~funny(X)|old(X))))&
(![X]:((generous(X)&~happy(X))<=>(~wise(X)|~generous(X))))&
((?[X]:((quiet(X)&rich(X))))<=>(?[X]:((~kind(X)<~>~humble(X)))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((kind(X)&strong(X))=>(~quiet(X)|~kind(X))))&
(?[X]:(strong(X)))&
(?[X]:((~calm(X)<~>~humble(X))))&
((humble(alice)&~funny(alice)))&
((~funny(paul)<~>~curious(paul)))&
(?[X]:((old(X)&~rich(X)))) | creative(mary) | [
"p5",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4730029136550855706568952
% SZS output start Proof for 4730029136550855706568952
6. ! [X0] : (~strong(X0) <=> (~generous(X0) | creative(X0))) [input p5]
8. ! [X0] : ((~old(X0) & strong(X0)) <=> (~generous(X0) | ~happy(X0))) [input p7]
10. ! [X0] : ((~creative(X0) & happy(X0)) <=> (generous(X0) | ~quiet(X0))) [input p9]
21. creative(mary) [input hypothesis]
45. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | strong(X0))) [nnf transformation 6]
46. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | strong(X0))) [flattening 45]
48. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (old(X0) | ~strong(X0)))) [nnf transformation 8]
49. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0))) [flattening 48]
50. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 10]
51. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | creative(X0) | ~happy(X0))) [flattening 50]
94. ~strong(X0) | generous(X0) [cnf transformation 46]
99. strong(X0) | generous(X0) [cnf transformation 49]
107. ~creative(X0) | ~generous(X0) [cnf transformation 51]
134. creative(mary) [cnf transformation 21]
217. generous(X0) [subsumption resolution 99,94]
219. ~creative(X0) [subsumption resolution 107,217]
265. $false [subsumption resolution 134,219]
% SZS output end Proof for 4730029136550855706568952
% ------------------------------
% 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 strong then someone is either old or not brave and vice versa. Everyone who is not generous or not wise is brave. If john is happy or humble then lucy is both not patient and happy and vice versa. If someone is old or not brave then someone is not wise or brave. If someone is either funny or strong then john is either not rich or not kind and vice versa. Everyone who is humble is either not tall or not rich. Everyone who is funny or happy is tall and vice versa. Everyone who is both not curious and happy is either happy or not brave and vice versa. If someone is generous or wise then someone is not wise and vice versa. Everyone who is either not creative or wise is both not quiet and not rich and vice versa. Everyone who is rich is both patient and not rich and vice versa. Everyone who is either not rich or not kind is not funny or not humble and vice versa. Everyone who is both not funny and not curious is either tall or creative and vice versa. If paul is not quiet or old then paul is either wise or not calm and vice versa. Everyone who is either not funny or brave is either curious or creative and vice versa. Everyone who is either strong or wise is old. Someone is not old. Someone is both not patient and not happy. Someone is both happy and curious. Someone is either kind or tall. Alice is creative. Mary is kind. Someone is tall. Lucy is patient or not humble. | Alice is not rich. | entailment | ((?[X]:(~strong(X)))<=>(?[X]:((old(X)<~>~brave(X)))))&
(![X]:((~generous(X)|~wise(X))=>brave(X)))&
(((happy(john)|humble(john)))<=>((~patient(lucy)&happy(lucy))))&
((?[X]:((old(X)|~brave(X))))=>(?[X]:((~wise(X)|brave(X)))))&
((?[X]:((funny(X)<~>strong(X))))<=>((~rich(john)<~>~kind(john))))&
(![X]:(humble(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((funny(X)|happy(X))<=>tall(X)))&
(![X]:((~curious(X)&happy(X))<=>(happy(X)<~>~brave(X))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:(~wise(X))))&
(![X]:((~creative(X)<~>wise(X))<=>(~quiet(X)&~rich(X))))&
(![X]:(rich(X)<=>(patient(X)&~rich(X))))&
(![X]:((~rich(X)<~>~kind(X))<=>(~funny(X)|~humble(X))))&
(![X]:((~funny(X)&~curious(X))<=>(tall(X)<~>creative(X))))&
(((~quiet(paul)|old(paul)))<=>((wise(paul)<~>~calm(paul))))&
(![X]:((~funny(X)<~>brave(X))<=>(curious(X)<~>creative(X))))&
(![X]:((strong(X)<~>wise(X))=>old(X)))&
(?[X]:(~old(X)))&
(?[X]:((~patient(X)&~happy(X))))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((kind(X)<~>tall(X))))&
(creative(alice))&
(kind(mary))&
(?[X]:(tall(X)))&
((patient(lucy)|~humble(lucy))) | ~rich(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5028554356242455924981586
% SZS output start Proof for 5028554356242455924981586
11. ! [X0] : (rich(X0) <=> (~rich(X0) & patient(X0))) [input p10]
25. rich(alice) [input hypothesis]
59. ! [X0] : ((rich(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | ~rich(X0))) [nnf transformation 11]
60. ! [X0] : ((rich(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | ~rich(X0))) [flattening 59]
122. ~rich(X0) | ~rich(X0) [cnf transformation 60]
163. rich(alice) [cnf transformation 25]
164. ~rich(X0) [duplicate literal removal 122]
329. $false [subsumption resolution 163,164]
% SZS output end Proof for 5028554356242455924981586
% ------------------------------
% 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 tall or generous and vice versa.
If mary is not kind then lucy is not funny or not patient.
Everyone who is not brave or not funny is both not calm and creative and vice versa.
Everyone who is not strong or patient is either happy or not quiet and vice versa.
Everyone who is both not rich and brave is wise or quiet and vice versa.
If someone is both patient and not quiet then fred is both brave and not old.
If lucy is either not generous or not quiet then someone is brave and vice versa.
Everyone who is wise is either rich or not calm.
If someone is both not quiet and old then john is both not humble and tall and vice versa.
If lucy is not curious then alice is rich and vice versa.
Everyone who is strong or not tall is both not rich and not humble.
Everyone who is both not brave and old is either tall or not curious.
If someone is not calm then someone is not tall and vice versa.
If paul is curious then fred is funny and vice versa.
Everyone who is not tall or patient is both not strong and not humble.
If alice is not curious or not humble then paul is both not strong and funny and vice versa.
Paul is not calm.
Someone is either not tall or not strong.
Lucy is not old or not brave.
Fred is not strong or not funny.
Fred is happy.
Lucy is both not curious and happy.
Someone is not curious or creative.
Lucy is both patient and not old. | Alice is not wise. | entailment | (![X]:(quiet(X)<=>(tall(X)<~>generous(X))))&
((~kind(mary))=>((~funny(lucy)|~patient(lucy))))&
(![X]:((~brave(X)|~funny(X))<=>(~calm(X)&creative(X))))&
(![X]:((~strong(X)|patient(X))<=>(happy(X)<~>~quiet(X))))&
(![X]:((~rich(X)&brave(X))<=>(wise(X)|quiet(X))))&
((?[X]:((patient(X)&~quiet(X))))=>((brave(fred)&~old(fred))))&
(((~generous(lucy)<~>~quiet(lucy)))<=>(?[X]:(brave(X))))&
(![X]:(wise(X)=>(rich(X)<~>~calm(X))))&
((?[X]:((~quiet(X)&old(X))))<=>((~humble(john)&tall(john))))&
((~curious(lucy))<=>(rich(alice)))&
(![X]:((strong(X)|~tall(X))=>(~rich(X)&~humble(X))))&
(![X]:((~brave(X)&old(X))=>(tall(X)<~>~curious(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~tall(X))))&
((curious(paul))<=>(funny(fred)))&
(![X]:((~tall(X)|patient(X))=>(~strong(X)&~humble(X))))&
(((~curious(alice)|~humble(alice)))<=>((~strong(paul)&funny(paul))))&
(~calm(paul))&
(?[X]:((~tall(X)<~>~strong(X))))&
((~old(lucy)|~brave(lucy)))&
((~strong(fred)|~funny(fred)))&
(happy(fred))&
((~curious(lucy)&happy(lucy)))&
(?[X]:((~curious(X)|creative(X))))&
((patient(lucy)&~old(lucy))) | ~wise(alice) | [
"p4",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7033705588115759798959757
% SZS output start Proof for 7033705588115759798959757
5. ! [X0] : ((brave(X0) & ~rich(X0)) <=> (quiet(X0) | wise(X0))) [input p4]
10. ~curious(lucy) <=> rich(alice) [input p9]
22. happy(lucy) & ~curious(lucy) [input p21]
25. wise(alice) [input hypothesis]
39. ! [X0] : (((brave(X0) & ~rich(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (~brave(X0) | rich(X0)))) [nnf transformation 5]
40. ! [X0] : (((brave(X0) & ~rich(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ~brave(X0) | rich(X0))) [flattening 39]
51. (~curious(lucy) | ~rich(alice)) & (rich(alice) | curious(lucy)) [nnf transformation 10]
82. ~wise(X0) | ~rich(X0) [cnf transformation 40]
98. rich(alice) | curious(lucy) [cnf transformation 51]
125. ~curious(lucy) [cnf transformation 22]
130. wise(alice) [cnf transformation 25]
188. 13 <=> rich(alice) [avatar definition]
189. rich(alice) <- (13) [avatar component clause 188]
192. 14 <=> curious(lucy) [avatar definition]
196. 14 | 13 [avatar split clause 98,188,192]
260. ~14 [avatar split clause 125,192]
273. ~rich(alice) [resolution 82,130]
274. $false <- (13) [subsumption resolution 273,189]
275. ~13 [avatar contradiction clause 274]
276. $false [avatar sat refutation 196,260,275]
% SZS output end Proof for 7033705588115759798959757
% ------------------------------
% 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 both wise and kind is either not old or brave.
Everyone who is not generous is calm and vice versa.
Everyone who is either not generous or not rich is not kind and vice versa.
If paul is either generous or patient then someone is not tall or not generous and vice versa.
If someone is strong then mary is either curious or not calm.
Everyone who is not brave is not happy or not funny.
Everyone who is not wise or brave is calm and vice versa.
If someone is not generous then susan is both kind and patient.
If someone is happy or generous then fred is creative.
If mary is either not wise or brave then someone is both not brave and not tall and vice versa.
Everyone who is not old or curious is either humble or generous.
Everyone who is both not calm and humble is either not wise or calm.
If fred is both strong and creative then fred is not curious or humble.
If lucy is either not tall or not humble then mary is both happy and not wise and vice versa.
Everyone who is either curious or quiet is either wise or calm.
If fred is not creative or calm then lucy is both not happy and not strong and vice versa.
Someone is both not brave and patient.
Someone is rich.
Someone is strong or not strong.
Someone is not funny.
Fred is not calm.
John is rich or not humble.
John is either kind or humble.
Someone is either not old or not wise. | Susan is kind. | entailment | (![X]:((wise(X)&kind(X))=>(~old(X)<~>brave(X))))&
(![X]:(~generous(X)<=>calm(X)))&
(![X]:((~generous(X)<~>~rich(X))<=>~kind(X)))&
(((generous(paul)<~>patient(paul)))<=>(?[X]:((~tall(X)|~generous(X)))))&
((?[X]:(strong(X)))=>((curious(mary)<~>~calm(mary))))&
(![X]:(~brave(X)=>(~happy(X)|~funny(X))))&
(![X]:((~wise(X)|brave(X))<=>calm(X)))&
((?[X]:(~generous(X)))=>((kind(susan)&patient(susan))))&
((?[X]:((happy(X)|generous(X))))=>(creative(fred)))&
(((~wise(mary)<~>brave(mary)))<=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((~old(X)|curious(X))=>(humble(X)<~>generous(X))))&
(![X]:((~calm(X)&humble(X))=>(~wise(X)<~>calm(X))))&
(((strong(fred)&creative(fred)))=>((~curious(fred)|humble(fred))))&
(((~tall(lucy)<~>~humble(lucy)))<=>((happy(mary)&~wise(mary))))&
(![X]:((curious(X)<~>quiet(X))=>(wise(X)<~>calm(X))))&
(((~creative(fred)|calm(fred)))<=>((~happy(lucy)&~strong(lucy))))&
(?[X]:((~brave(X)&patient(X))))&
(?[X]:(rich(X)))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:(~funny(X)))&
(~calm(fred))&
((rich(john)|~humble(john)))&
((kind(john)<~>humble(john)))&
(?[X]:((~old(X)<~>~wise(X)))) | kind(susan) | [
"p1",
"p3",
"p6",
"p7",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8675779520783065566538147
% SZS output start Proof for 8675779520783065566538147
2. ! [X0] : (~generous(X0) <=> calm(X0)) [input p1]
4. (generous(paul) <~> patient(paul)) <=> ? [X0] : (~generous(X0) | ~tall(X0)) [input p3]
7. ! [X0] : ((brave(X0) | ~wise(X0)) <=> calm(X0)) [input p6]
8. ? [X0] : ~generous(X0) => (patient(susan) & kind(susan)) [input p7]
10. (~wise(mary) <~> brave(mary)) <=> ? [X0] : (~tall(X0) & ~brave(X0)) [input p9]
12. ! [X0] : ((humble(X0) & ~calm(X0)) => (~wise(X0) <~> calm(X0))) [input p11]
14. (~tall(lucy) <~> ~humble(lucy)) <=> (~wise(mary) & happy(mary)) [input p13]
25. ~kind(susan) [input hypothesis]
31. (patient(susan) & kind(susan)) | ! [X0] : generous(X0) [ennf transformation 8]
34. ! [X0] : ((~wise(X0) <~> calm(X0)) | (~humble(X0) | calm(X0))) [ennf transformation 12]
35. ! [X0] : ((~wise(X0) <~> calm(X0)) | ~humble(X0) | calm(X0)) [flattening 34]
40. ! [X0] : ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0))) [nnf transformation 2]
42. (((~patient(paul) | ~generous(paul)) & (patient(paul) | generous(paul))) | ! [X0] : (generous(X0) & tall(X0))) & (? [X0] : (~generous(X0) | ~tall(X0)) | ((generous(paul) | ~patient(paul)) & (patient(paul) | ~generous(paul)))) [nnf transformation 4]
43. (((~patient(paul) | ~generous(paul)) & (patient(paul) | generous(paul))) | ! [X0] : (generous(X0) & tall(X0))) & (? [X1] : (~generous(X1) | ~tall(X1)) | ((generous(paul) | ~patient(paul)) & (patient(paul) | ~generous(paul)))) [rectify 42]
44. ? [X1] : (~generous(X1) | ~tall(X1)) => (~generous(sK0) | ~tall(sK0)) [choice axiom]
45. (((~patient(paul) | ~generous(paul)) & (patient(paul) | generous(paul))) | ! [X0] : (generous(X0) & tall(X0))) & ((~generous(sK0) | ~tall(sK0)) | ((generous(paul) | ~patient(paul)) & (patient(paul) | ~generous(paul)))) [skolemisation 43,44]
47. ! [X0] : (((brave(X0) | ~wise(X0)) | ~calm(X0)) & (calm(X0) | (~brave(X0) & wise(X0)))) [nnf transformation 7]
48. ! [X0] : ((brave(X0) | ~wise(X0) | ~calm(X0)) & (calm(X0) | (~brave(X0) & wise(X0)))) [flattening 47]
49. (((~brave(mary) | wise(mary)) & (brave(mary) | ~wise(mary))) | ! [X0] : (tall(X0) | brave(X0))) & (? [X0] : (~tall(X0) & ~brave(X0)) | ((~wise(mary) | ~brave(mary)) & (brave(mary) | wise(mary)))) [nnf transformation 10]
50. (((~brave(mary) | wise(mary)) & (brave(mary) | ~wise(mary))) | ! [X0] : (tall(X0) | brave(X0))) & (? [X1] : (~tall(X1) & ~brave(X1)) | ((~wise(mary) | ~brave(mary)) & (brave(mary) | wise(mary)))) [rectify 49]
51. ? [X1] : (~tall(X1) & ~brave(X1)) => (~tall(sK1) & ~brave(sK1)) [choice axiom]
52. (((~brave(mary) | wise(mary)) & (brave(mary) | ~wise(mary))) | ! [X0] : (tall(X0) | brave(X0))) & ((~tall(sK1) & ~brave(sK1)) | ((~wise(mary) | ~brave(mary)) & (brave(mary) | wise(mary)))) [skolemisation 50,51]
54. ! [X0] : (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ~humble(X0) | calm(X0)) [nnf transformation 35]
55. (((humble(lucy) | tall(lucy)) & (~humble(lucy) | ~tall(lucy))) | (wise(mary) | ~happy(mary))) & ((~wise(mary) & happy(mary)) | ((~tall(lucy) | humble(lucy)) & (~humble(lucy) | tall(lucy)))) [nnf transformation 14]
56. (((humble(lucy) | tall(lucy)) & (~humble(lucy) | ~tall(lucy))) | wise(mary) | ~happy(mary)) & ((~wise(mary) & happy(mary)) | ((~tall(lucy) | humble(lucy)) & (~humble(lucy) | tall(lucy)))) [flattening 55]
73. ~calm(X0) | ~generous(X0) [cnf transformation 40]
78. ~generous(sK0) | ~tall(sK0) | patient(paul) | ~generous(paul) [cnf transformation 45]
82. ~patient(paul) | ~generous(paul) | tall(X0) [cnf transformation 45]
86. calm(X0) | wise(X0) [cnf transformation 48]
87. ~brave(X0) | calm(X0) [cnf transformation 48]
89. kind(susan) | generous(X0) [cnf transformation 31]
97. brave(mary) | ~wise(mary) | tall(X0) | brave(X0) [cnf transformation 52]
103. calm(X0) | ~wise(X0) | ~humble(X0) | calm(X0) [cnf transformation 54]
109. ~wise(mary) | ~tall(lucy) | humble(lucy) [cnf transformation 56]
131. ~kind(susan) [cnf transformation 25]
132. calm(X0) | ~wise(X0) | ~humble(X0) [duplicate literal removal 103]
134. 1 <=> ! [X0] : generous(X0) [avatar definition]
135. generous(X0) <- (1) [avatar component clause 134]
137. 2 <=> generous(paul) [avatar definition]
139. ~generous(paul) <- (~2) [avatar component clause 137]
141. 3 <=> patient(paul) [avatar definition]
146. 4 <=> ! [X0] : tall(X0) [avatar definition]
147. tall(X0) <- (4) [avatar component clause 146]
148. 4 | ~2 | ~3 [avatar split clause 82,141,137,146]
152. 5 <=> tall(sK0) [avatar definition]
154. ~tall(sK0) <- (~5) [avatar component clause 152]
156. 6 <=> generous(sK0) [avatar definition]
158. ~generous(sK0) <- (~6) [avatar component clause 156]
160. ~2 | 3 | ~5 | ~6 [avatar split clause 78,156,152,141,137]
169. 9 <=> calm(mary) [avatar definition]
170. ~calm(mary) <- (~9) [avatar component clause 169]
171. calm(mary) <- (9) [avatar component clause 169]
180. 11 <=> kind(susan) [avatar definition]
183. 1 | 11 [avatar split clause 89,180,134]
197. 15 <=> ! [X0] : (tall(X0) | brave(X0)) [avatar definition]
198. tall(X0) | brave(X0) <- (15) [avatar component clause 197]
200. 16 <=> wise(mary) [avatar definition]
201. ~wise(mary) <- (~16) [avatar component clause 200]
204. 17 <=> brave(mary) [avatar definition]
205. brave(mary) <- (17) [avatar component clause 204]
208. 15 | ~16 | 17 [avatar split clause 97,204,200,197]
221. ~humble(X0) | calm(X0) [subsumption resolution 132,86]
240. 24 <=> tall(lucy) [avatar definition]
241. ~tall(lucy) <- (~24) [avatar component clause 240]
244. 25 <=> humble(lucy) [avatar definition]
246. humble(lucy) <- (25) [avatar component clause 244]
249. 25 | ~24 | ~16 [avatar split clause 109,200,240,244]
296. ~11 [avatar split clause 131,180]
299. $false <- (1, ~2) [subsumption resolution 139,135]
300. ~1 | 2 [avatar contradiction clause 299]
301. $false <- (1, ~6) [subsumption resolution 158,135]
302. ~1 | 6 [avatar contradiction clause 301]
308. wise(mary) <- (~9) [resolution 86,170]
311. $false <- (~9, ~16) [subsumption resolution 308,201]
312. 9 | 16 [avatar contradiction clause 311]
314. ~generous(mary) <- (9) [resolution 171,73]
315. $false <- (1, 9) [subsumption resolution 314,135]
316. ~1 | ~9 [avatar contradiction clause 315]
326. calm(mary) <- (17) [resolution 205,87]
327. $false <- (~9, 17) [subsumption resolution 326,170]
328. 9 | ~17 [avatar contradiction clause 327]
329. brave(sK0) <- (~5, 15) [resolution 198,154]
332. calm(sK0) <- (~5, 15) [resolution 329,87]
347. ~generous(sK0) <- (~5, 15) [resolution 332,73]
348. $false <- (1, ~5, 15) [subsumption resolution 347,135]
349. ~1 | 5 | ~15 [avatar contradiction clause 348]
350. $false <- (4, ~24) [resolution 147,241]
351. ~4 | 24 [avatar contradiction clause 350]
352. calm(lucy) <- (25) [resolution 246,221]
356. ~generous(lucy) <- (25) [resolution 352,73]
358. $false <- (1, 25) [subsumption resolution 356,135]
359. ~1 | ~25 [avatar contradiction clause 358]
360. $false [avatar sat refutation 148,160,183,208,249,296,300,302,312,316,328,349,351,359]
% SZS output end Proof for 8675779520783065566538147
% ------------------------------
% 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or calm then someone is not strong or strong and vice versa. Everyone who is either brave or not rich is brave and vice versa. Everyone who is generous is either old or not patient. If someone is either kind or not brave then someone is not curious and vice versa. If john is generous then someone is both happy and tall and vice versa. If fred is either strong or humble then john is either rich or not patient. Everyone who is either not funny or calm is not rich or generous. If paul is not quiet or creative then mary is tall and vice versa. Everyone who is not generous is not creative. If someone is both strong and curious then someone is either humble or not rich and vice versa. If mary is either not brave or not calm then someone is not old and vice versa. Everyone who is both calm and not old is both not quiet and not old and vice versa. If someone is humble or tall then paul is not old. If someone is either funny or not brave then someone is both creative and not wise. Everyone who is either humble or not rich is curious or kind and vice versa. If john is old or not generous then paul is both rich and quiet and vice versa. Someone is both strong and patient. Susan is either not wise or creative. Someone is curious. Someone is humble. Alice is both not creative and funny. Lucy is both brave and not calm. Someone is either not humble or wise. | Paul is not quiet. | neutral | ((?[X]:((~quiet(X)<~>calm(X))))<=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:((brave(X)<~>~rich(X))<=>brave(X)))&
(![X]:(generous(X)=>(old(X)<~>~patient(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:(~curious(X))))&
((generous(john))<=>(?[X]:((happy(X)&tall(X)))))&
(((strong(fred)<~>humble(fred)))=>((rich(john)<~>~patient(john))))&
(![X]:((~funny(X)<~>calm(X))=>(~rich(X)|generous(X))))&
(((~quiet(paul)|creative(paul)))<=>(tall(mary)))&
(![X]:(~generous(X)=>~creative(X)))&
((?[X]:((strong(X)&curious(X))))<=>(?[X]:((humble(X)<~>~rich(X)))))&
(((~brave(mary)<~>~calm(mary)))<=>(?[X]:(~old(X))))&
(![X]:((calm(X)&~old(X))<=>(~quiet(X)&~old(X))))&
((?[X]:((humble(X)|tall(X))))=>(~old(paul)))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((creative(X)&~wise(X)))))&
(![X]:((humble(X)<~>~rich(X))<=>(curious(X)|kind(X))))&
(((old(john)|~generous(john)))<=>((rich(paul)&quiet(paul))))&
(?[X]:((strong(X)&patient(X))))&
((~wise(susan)<~>creative(susan)))&
(?[X]:(curious(X)))&
(?[X]:(humble(X)))&
((~creative(alice)&funny(alice)))&
((brave(lucy)&~calm(lucy)))&
(?[X]:((~humble(X)<~>wise(X)))) | ~quiet(paul) | [] | null | 0 |
Everyone who is strong or kind is both not humble and not funny and vice versa.
If someone is either not humble or old then someone is both kind and not generous and vice versa.
If someone is both tall and brave then someone is generous or not wise and vice versa.
If fred is not creative or strong then alice is both kind and not tall.
Everyone who is not kind is not humble and vice versa.
Everyone who is humble is strong or not calm.
Everyone who is either tall or generous is not humble or not kind and vice versa.
If lucy is either not patient or not generous then someone is both generous and calm.
Everyone who is not tall or not wise is both tall and not curious.
If fred is rich or not curious then someone is funny or not rich and vice versa.
Everyone who is both not strong and not generous is not calm or brave.
Everyone who is calm or not wise is either not happy or not tall and vice versa.
If paul is tall then someone is tall or brave.
Everyone who is both not generous and not happy is not funny.
If alice is either not creative or rich then lucy is either calm or strong.
Someone is happy.
John is not happy.
Someone is old or not brave.
Lucy is either happy or not funny.
Someone is wise.
Someone is curious. | Fred is not kind. | entailment | (![X]:((strong(X)|kind(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((~humble(X)<~>old(X))))<=>(?[X]:((kind(X)&~generous(X)))))&
((?[X]:((tall(X)&brave(X))))<=>(?[X]:((generous(X)|~wise(X)))))&
(((~creative(fred)|strong(fred)))=>((kind(alice)&~tall(alice))))&
(![X]:(~kind(X)<=>~humble(X)))&
(![X]:(humble(X)=>(strong(X)|~calm(X))))&
(![X]:((tall(X)<~>generous(X))<=>(~humble(X)|~kind(X))))&
(((~patient(lucy)<~>~generous(lucy)))=>(?[X]:((generous(X)&calm(X)))))&
(![X]:((~tall(X)|~wise(X))=>(tall(X)&~curious(X))))&
(((rich(fred)|~curious(fred)))<=>(?[X]:((funny(X)|~rich(X)))))&
(![X]:((~strong(X)&~generous(X))=>(~calm(X)|brave(X))))&
(![X]:((calm(X)|~wise(X))<=>(~happy(X)<~>~tall(X))))&
((tall(paul))=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~generous(X)&~happy(X))=>~funny(X)))&
(((~creative(alice)<~>rich(alice)))=>((calm(lucy)<~>strong(lucy))))&
(?[X]:(happy(X)))&
(~happy(john))&
(?[X]:((old(X)|~brave(X))))&
((happy(lucy)<~>~funny(lucy)))&
(?[X]:(wise(X)))&
(?[X]:(curious(X))) | ~kind(fred) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1051597004531501865956369
% SZS output start Proof for 1051597004531501865956369
1. ! [X0] : ((kind(X0) | strong(X0)) <=> (~funny(X0) & ~humble(X0))) [input p0]
5. ! [X0] : (~kind(X0) <=> ~humble(X0)) [input p4]
22. kind(fred) [input hypothesis]
36. ! [X0] : (((kind(X0) | strong(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~kind(X0) & ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : ((kind(X0) | strong(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~kind(X0) & ~strong(X0)))) [flattening 36]
48. ! [X0] : ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))) [nnf transformation 5]
74. ~humble(X0) | ~kind(X0) [cnf transformation 37]
94. ~kind(X0) | humble(X0) [cnf transformation 48]
134. kind(fred) [cnf transformation 22]
217. ~kind(X0) [subsumption resolution 94,74]
309. $false [subsumption resolution 134,217]
% SZS output end Proof for 1051597004531501865956369
% ------------------------------
% 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then mary is both wise and not calm. If john is both not calm and quiet then someone is not creative and vice versa. If john is humble or not creative then someone is both not quiet and funny and vice versa. Everyone who is tall or funny is both kind and happy. Everyone who is rich is either not funny or not happy and vice versa. If someone is tall or not curious then someone is either funny or tall and vice versa. Everyone who is not rich is either not funny or kind. If lucy is either not humble or funny then someone is brave or calm and vice versa. Everyone who is calm or not old is old and vice versa. Everyone who is not brave or not happy is curious or funny. If someone is either not old or not brave then fred is both not wise and not calm and vice versa. Everyone who is either generous or not humble is either wise or not tall and vice versa. Everyone who is either humble or rich is happy or not old and vice versa. Everyone who is not brave or curious is either not creative or not strong. If paul is not curious or strong then someone is generous and vice versa. Everyone who is creative or not happy is tall or not strong. Someone is quiet or patient. Someone is not funny. Someone is wise or creative. Alice is either not humble or wise. Alice is not patient or strong. Someone is either not rich or not wise. John is either not patient or patient. | Lucy is not brave. | contradiction | ((?[X]:(kind(X)))=>((wise(mary)&~calm(mary))))&
(((~calm(john)&quiet(john)))<=>(?[X]:(~creative(X))))&
(((humble(john)|~creative(john)))<=>(?[X]:((~quiet(X)&funny(X)))))&
(![X]:((tall(X)|funny(X))=>(kind(X)&happy(X))))&
(![X]:(rich(X)<=>(~funny(X)<~>~happy(X))))&
((?[X]:((tall(X)|~curious(X))))<=>(?[X]:((funny(X)<~>tall(X)))))&
(![X]:(~rich(X)=>(~funny(X)<~>kind(X))))&
(((~humble(lucy)<~>funny(lucy)))<=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((calm(X)|~old(X))<=>old(X)))&
(![X]:((~brave(X)|~happy(X))=>(curious(X)|funny(X))))&
((?[X]:((~old(X)<~>~brave(X))))<=>((~wise(fred)&~calm(fred))))&
(![X]:((generous(X)<~>~humble(X))<=>(wise(X)<~>~tall(X))))&
(![X]:((humble(X)<~>rich(X))<=>(happy(X)|~old(X))))&
(![X]:((~brave(X)|curious(X))=>(~creative(X)<~>~strong(X))))&
(((~curious(paul)|strong(paul)))<=>(?[X]:(generous(X))))&
(![X]:((creative(X)|~happy(X))=>(tall(X)|~strong(X))))&
(?[X]:((quiet(X)|patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:((wise(X)|creative(X))))&
((~humble(alice)<~>wise(alice)))&
((~patient(alice)|strong(alice)))&
(?[X]:((~rich(X)<~>~wise(X))))&
((~patient(john)<~>patient(john))) | ~brave(lucy) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2847371806243684323242215
% SZS output start Proof for 2847371806243684323242215
9. ! [X0] : ((~old(X0) | calm(X0)) <=> old(X0)) [input p8]
11. ? [X0] : (~old(X0) <~> ~brave(X0)) <=> (~calm(fred) & ~wise(fred)) [input p10]
24. ~brave(lucy) [input hypothesis]
55. ! [X0] : (((~old(X0) | calm(X0)) | ~old(X0)) & (old(X0) | (old(X0) & ~calm(X0)))) [nnf transformation 9]
56. ! [X0] : ((~old(X0) | calm(X0) | ~old(X0)) & (old(X0) | (old(X0) & ~calm(X0)))) [flattening 55]
57. (? [X0] : ((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | (calm(fred) | wise(fred))) & ((~calm(fred) & ~wise(fred)) | ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) [nnf transformation 11]
58. (? [X0] : ((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | calm(fred) | wise(fred)) & ((~calm(fred) & ~wise(fred)) | ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) [flattening 57]
59. (? [X0] : ((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | calm(fred) | wise(fred)) & ((~calm(fred) & ~wise(fred)) | ! [X1] : ((~old(X1) | brave(X1)) & (~brave(X1) | old(X1)))) [rectify 58]
60. ? [X0] : ((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) => ((brave(sK5) | old(sK5)) & (~brave(sK5) | ~old(sK5))) [choice axiom]
61. (((brave(sK5) | old(sK5)) & (~brave(sK5) | ~old(sK5))) | calm(fred) | wise(fred)) & ((~calm(fred) & ~wise(fred)) | ! [X1] : ((~old(X1) | brave(X1)) & (~brave(X1) | old(X1)))) [skolemisation 59,60]
115. old(X0) | old(X0) [cnf transformation 56]
116. ~old(X0) | calm(X0) | ~old(X0) [cnf transformation 56]
122. ~calm(fred) | ~old(X1) | brave(X1) [cnf transformation 61]
158. ~brave(lucy) [cnf transformation 24]
159. old(X0) [duplicate literal removal 115]
160. ~old(X0) | calm(X0) [duplicate literal removal 116]
287. 28 <=> calm(fred) [avatar definition]
288. ~calm(fred) <- (~28) [avatar component clause 287]
295. ~calm(fred) | brave(X1) [subsumption resolution 122,159]
297. 30 <=> ! [X1] : brave(X1) [avatar definition]
298. brave(X1) <- (30) [avatar component clause 297]
299. 30 | ~28 [avatar split clause 295,287,297]
377. calm(X0) [resolution 160,159]
399. $false <- (~28) [resolution 377,288]
400. 28 [avatar contradiction clause 399]
403. $false <- (30) [resolution 298,158]
406. ~30 [avatar contradiction clause 403]
407. $false [avatar sat refutation 299,400,406]
% SZS output end Proof for 2847371806243684323242215
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If john is either tall or rich then fred is either not happy or not creative and vice versa. Everyone who is patient or creative is both not generous and humble. Everyone who is not wise or humble is generous and vice versa. If lucy is generous or not quiet then lucy is not tall. If fred is either patient or not generous then alice is rich. Everyone who is not curious or not patient is both not wise and not calm. If alice is either wise or brave then someone is both not happy and not brave. Everyone who is wise is both strong and humble. Everyone who is rich is both not strong and not calm and vice versa. Everyone who is either strong or not funny is not happy or not funny and vice versa. Everyone who is brave or not calm is kind or not funny. If someone is humble then alice is not happy and vice versa. If john is not brave then mary is either old or not kind and vice versa. Everyone who is either not rich or funny is either not kind or old. Everyone who is both not old and not generous is patient or not kind. Someone is humble. Someone is either not humble or not funny. Someone is not old. Paul is kind. Fred is not creative or not brave. Susan is either not strong or old. | Mary is tall. | neutral | (((tall(john)<~>rich(john)))<=>((~happy(fred)<~>~creative(fred))))&
(![X]:((patient(X)|creative(X))=>(~generous(X)&humble(X))))&
(![X]:((~wise(X)|humble(X))<=>generous(X)))&
(((generous(lucy)|~quiet(lucy)))=>(~tall(lucy)))&
(((patient(fred)<~>~generous(fred)))=>(rich(alice)))&
(![X]:((~curious(X)|~patient(X))=>(~wise(X)&~calm(X))))&
(((wise(alice)<~>brave(alice)))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(wise(X)=>(strong(X)&humble(X))))&
(![X]:(rich(X)<=>(~strong(X)&~calm(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~happy(X)|~funny(X))))&
(![X]:((brave(X)|~calm(X))=>(kind(X)|~funny(X))))&
((?[X]:(humble(X)))<=>(~happy(alice)))&
((~brave(john))<=>((old(mary)<~>~kind(mary))))&
(![X]:((~rich(X)<~>funny(X))=>(~kind(X)<~>old(X))))&
(![X]:((~old(X)&~generous(X))=>(patient(X)|~kind(X))))&
(?[X]:(humble(X)))&
(?[X]:((~humble(X)<~>~funny(X))))&
(?[X]:(~old(X)))&
(kind(paul))&
((~creative(fred)|~brave(fred)))&
((~strong(susan)<~>old(susan))) | tall(mary) | [] | null | 0 |
Everyone who is both not quiet and rich is brave or not brave and vice versa.
Everyone who is not wise or patient is old or not humble and vice versa.
Everyone who is either not happy or not generous is old.
If mary is either not happy or not calm then susan is not tall.
Everyone who is curious or not curious is generous.
If someone is strong or humble then someone is both kind and generous and vice versa.
Everyone who is not curious or not generous is both patient and not funny.
If someone is funny then someone is not creative or not calm and vice versa.
Everyone who is either not tall or not generous is not creative or creative and vice versa.
If fred is both not creative and not funny then someone is both not wise and kind and vice versa.
If someone is humble or wise then fred is not rich and vice versa.
If someone is not happy or funny then mary is creative.
Everyone who is both not happy and patient is either not patient or not calm.
Everyone who is old or not happy is either generous or not tall and vice versa.
Everyone who is not kind or not strong is calm or not quiet and vice versa.
Lucy is calm or rich.
Someone is both not kind and not brave.
Someone is creative or humble.
Someone is rich or curious.
John is brave or not humble.
Someone is creative or not kind.
Someone is wise or not wise. | Fred is wise. | contradiction | (![X]:((~quiet(X)&rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~wise(X)|patient(X))<=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>~generous(X))=>old(X)))&
(((~happy(mary)<~>~calm(mary)))=>(~tall(susan)))&
(![X]:((curious(X)|~curious(X))=>generous(X)))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:((kind(X)&generous(X)))))&
(![X]:((~curious(X)|~generous(X))=>(patient(X)&~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~creative(X)|creative(X))))&
(((~creative(fred)&~funny(fred)))<=>(?[X]:((~wise(X)&kind(X)))))&
((?[X]:((humble(X)|wise(X))))<=>(~rich(fred)))&
((?[X]:((~happy(X)|funny(X))))=>(creative(mary)))&
(![X]:((~happy(X)&patient(X))=>(~patient(X)<~>~calm(X))))&
(![X]:((old(X)|~happy(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((~kind(X)|~strong(X))<=>(calm(X)|~quiet(X))))&
((calm(lucy)|rich(lucy)))&
(?[X]:((~kind(X)&~brave(X))))&
(?[X]:((creative(X)|humble(X))))&
(?[X]:((rich(X)|curious(X))))&
((brave(john)|~humble(john)))&
(?[X]:((creative(X)|~kind(X))))&
(?[X]:((wise(X)|~wise(X)))) | wise(fred) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6127199199790466686870353
% SZS output start Proof for 6127199199790466686870353
1. ! [X0] : ((rich(X0) & ~quiet(X0)) <=> (~brave(X0) | brave(X0))) [input p0]
11. ? [X0] : (wise(X0) | humble(X0)) <=> ~rich(fred) [input p10]
23. wise(fred) [input hypothesis]
33. ! [X0] : (((rich(X0) & ~quiet(X0)) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | (~rich(X0) | quiet(X0)))) [nnf transformation 1]
34. ! [X0] : (((rich(X0) & ~quiet(X0)) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | ~rich(X0) | quiet(X0))) [flattening 33]
56. (? [X0] : (wise(X0) | humble(X0)) | rich(fred)) & (~rich(fred) | ! [X0] : (~wise(X0) & ~humble(X0))) [nnf transformation 11]
57. (? [X0] : (wise(X0) | humble(X0)) | rich(fred)) & (~rich(fred) | ! [X1] : (~wise(X1) & ~humble(X1))) [rectify 56]
58. ? [X0] : (wise(X0) | humble(X0)) => (wise(sK5) | humble(sK5)) [choice axiom]
59. ((wise(sK5) | humble(sK5)) | rich(fred)) & (~rich(fred) | ! [X1] : (~wise(X1) & ~humble(X1))) [skolemisation 57,58]
78. rich(X0) | ~brave(X0) [cnf transformation 34]
79. rich(X0) | brave(X0) [cnf transformation 34]
113. ~rich(fred) | ~wise(X1) [cnf transformation 59]
137. wise(fred) [cnf transformation 23]
139. rich(X0) [subsumption resolution 78,79]
231. ~wise(X1) [subsumption resolution 113,139]
276. $false [subsumption resolution 137,231]
% SZS output end Proof for 6127199199790466686870353
% ------------------------------
% 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or curious is both humble and not wise and vice versa.
Everyone who is not happy or funny is both not humble and not wise.
Everyone who is not tall or wise is either not quiet or not kind and vice versa.
Everyone who is not wise is not humble or kind and vice versa.
Everyone who is both rich and not funny is either humble or old and vice versa.
Everyone who is brave or not generous is not rich or happy and vice versa.
If someone is both not strong and not quiet then paul is both not kind and old.
Everyone who is not rich or not strong is not strong or curious and vice versa.
Everyone who is not calm is both not funny and patient and vice versa.
If lucy is old then mary is patient.
If alice is either not curious or tall then susan is both funny and not old and vice versa.
Everyone who is either kind or not curious is happy or not humble and vice versa.
Everyone who is both not humble and not calm is either patient or not creative and vice versa.
Everyone who is both not strong and rich is not humble.
Everyone who is calm is not patient or not strong.
If someone is quiet or brave then susan is tall.
Someone is not generous.
Lucy is funny or not calm.
Someone is both not creative and humble.
Someone is funny.
Susan is both not humble and kind.
Someone is either rich or generous.
Lucy is not funny. | Paul is kind. | neutral | (![X]:((rich(X)<~>curious(X))<=>(humble(X)&~wise(X))))&
(![X]:((~happy(X)|funny(X))=>(~humble(X)&~wise(X))))&
(![X]:((~tall(X)|wise(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:(~wise(X)<=>(~humble(X)|kind(X))))&
(![X]:((rich(X)&~funny(X))<=>(humble(X)<~>old(X))))&
(![X]:((brave(X)|~generous(X))<=>(~rich(X)|happy(X))))&
((?[X]:((~strong(X)&~quiet(X))))=>((~kind(paul)&old(paul))))&
(![X]:((~rich(X)|~strong(X))<=>(~strong(X)|curious(X))))&
(![X]:(~calm(X)<=>(~funny(X)&patient(X))))&
((old(lucy))=>(patient(mary)))&
(((~curious(alice)<~>tall(alice)))<=>((funny(susan)&~old(susan))))&
(![X]:((kind(X)<~>~curious(X))<=>(happy(X)|~humble(X))))&
(![X]:((~humble(X)&~calm(X))<=>(patient(X)<~>~creative(X))))&
(![X]:((~strong(X)&rich(X))=>~humble(X)))&
(![X]:(calm(X)=>(~patient(X)|~strong(X))))&
((?[X]:((quiet(X)|brave(X))))=>(tall(susan)))&
(?[X]:(~generous(X)))&
((funny(lucy)|~calm(lucy)))&
(?[X]:((~creative(X)&humble(X))))&
(?[X]:(funny(X)))&
((~humble(susan)&kind(susan)))&
(?[X]:((rich(X)<~>generous(X))))&
(~funny(lucy)) | kind(paul) | [] | null | 0 |
If someone is rich then paul is not happy.
If someone is both humble and quiet then mary is strong or patient and vice versa.
Everyone who is brave or generous is either not funny or not generous and vice versa.
Everyone who is either not creative or curious is both not rich and happy.
If someone is either creative or brave then someone is both not funny and not kind and vice versa.
Everyone who is both not wise and old is both not creative and not rich.
Everyone who is both generous and not calm is happy and vice versa.
If fred is not generous then someone is both not quiet and happy and vice versa.
Everyone who is either not curious or not creative is both creative and happy and vice versa.
If someone is not old or not strong then susan is not creative and vice versa.
Everyone who is both strong and calm is wise and vice versa.
Everyone who is happy is kind.
Everyone who is both not old and not funny is rich.
If someone is both not funny and not happy then fred is both happy and not humble and vice versa.
Everyone who is both not funny and not brave is tall or not patient and vice versa.
Someone is quiet or not brave.
Susan is either not humble or patient.
Someone is strong.
Someone is not curious. | Fred is funny. | contradiction | ((?[X]:(rich(X)))=>(~happy(paul)))&
((?[X]:((humble(X)&quiet(X))))<=>((strong(mary)|patient(mary))))&
(![X]:((brave(X)|generous(X))<=>(~funny(X)<~>~generous(X))))&
(![X]:((~creative(X)<~>curious(X))=>(~rich(X)&happy(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>(?[X]:((~funny(X)&~kind(X)))))&
(![X]:((~wise(X)&old(X))=>(~creative(X)&~rich(X))))&
(![X]:((generous(X)&~calm(X))<=>happy(X)))&
((~generous(fred))<=>(?[X]:((~quiet(X)&happy(X)))))&
(![X]:((~curious(X)<~>~creative(X))<=>(creative(X)&happy(X))))&
((?[X]:((~old(X)|~strong(X))))<=>(~creative(susan)))&
(![X]:((strong(X)&calm(X))<=>wise(X)))&
(![X]:(happy(X)=>kind(X)))&
(![X]:((~old(X)&~funny(X))=>rich(X)))&
((?[X]:((~funny(X)&~happy(X))))<=>((happy(fred)&~humble(fred))))&
(![X]:((~funny(X)&~brave(X))<=>(tall(X)|~patient(X))))&
(?[X]:((quiet(X)|~brave(X))))&
((~humble(susan)<~>patient(susan)))&
(?[X]:(strong(X)))&
(?[X]:(~curious(X))) | funny(fred) | [
"p2",
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2015794130249982452634682
% SZS output start Proof for 2015794130249982452634682
3. ! [X0] : ((generous(X0) | brave(X0)) <=> (~funny(X0) <~> ~generous(X0))) [input p2]
4. ! [X0] : ((~creative(X0) <~> curious(X0)) => (happy(X0) & ~rich(X0))) [input p3]
7. ! [X0] : ((~calm(X0) & generous(X0)) <=> happy(X0)) [input p6]
9. ! [X0] : ((~curious(X0) <~> ~creative(X0)) <=> (happy(X0) & creative(X0))) [input p8]
20. funny(fred) [input hypothesis]
24. ! [X0] : ((happy(X0) & ~rich(X0)) | (~creative(X0) <=> curious(X0))) [ennf transformation 4]
36. ! [X0] : (((generous(X0) | brave(X0)) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) & (((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | (~generous(X0) & ~brave(X0)))) [nnf transformation 3]
37. ! [X0] : ((generous(X0) | brave(X0) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) & (((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | (~generous(X0) & ~brave(X0)))) [flattening 36]
38. ! [X0] : ((happy(X0) & ~rich(X0)) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) [nnf transformation 24]
44. ! [X0] : (((~calm(X0) & generous(X0)) | ~happy(X0)) & (happy(X0) | (calm(X0) | ~generous(X0)))) [nnf transformation 7]
45. ! [X0] : (((~calm(X0) & generous(X0)) | ~happy(X0)) & (happy(X0) | calm(X0) | ~generous(X0))) [flattening 44]
50. ! [X0] : ((((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | (~happy(X0) | ~creative(X0))) & ((happy(X0) & creative(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0))))) [nnf transformation 9]
51. ! [X0] : ((((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ~happy(X0) | ~creative(X0)) & ((happy(X0) & creative(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0))))) [flattening 50]
77. ~generous(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 37]
84. happy(X0) | curious(X0) | creative(X0) [cnf transformation 38]
85. happy(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 38]
95. ~happy(X0) | generous(X0) [cnf transformation 45]
102. happy(X0) | ~creative(X0) | curious(X0) [cnf transformation 51]
103. happy(X0) | ~curious(X0) | creative(X0) [cnf transformation 51]
127. funny(fred) [cnf transformation 20]
130. ~funny(X0) | ~generous(X0) [duplicate literal removal 77]
214. happy(X0) | ~curious(X0) [subsumption resolution 103,85]
215. happy(X0) | curious(X0) [subsumption resolution 102,84]
216. happy(X0) [subsumption resolution 215,214]
266. generous(X0) [resolution 95,216]
268. ~generous(fred) [resolution 130,127]
271. $false [subsumption resolution 268,266]
% SZS output end Proof for 2015794130249982452634682
% ------------------------------
% 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 happy is quiet.
If someone is both tall and not quiet then someone is both not creative and not wise.
If someone is either not tall or not happy then someone is quiet.
If fred is old then susan is either happy or not happy.
If someone is either not wise or not patient then alice is both not tall and not funny and vice versa.
If fred is not humble then someone is either funny or not generous and vice versa.
Everyone who is not patient or not wise is wise and vice versa.
Everyone who is not curious is both patient and brave and vice versa.
If alice is either not old or not rich then someone is both not happy and not tall and vice versa.
If someone is not brave or not wise then alice is both not kind and not curious.
If alice is not rich then someone is both not humble and rich.
If john is funny or not rich then fred is not old or not quiet.
Everyone who is both brave and generous is either not wise or quiet and vice versa.
If someone is both calm and generous then paul is either rich or quiet.
If someone is not kind then someone is not tall or patient and vice versa.
Someone is both not old and creative.
Someone is old or tall.
Someone is both rich and calm.
Lucy is both calm and not creative.
Someone is not curious or not quiet.
Someone is both not creative and tall. | Lucy is not brave. | contradiction | (![X]:(happy(X)=>quiet(X)))&
((?[X]:((tall(X)&~quiet(X))))=>(?[X]:((~creative(X)&~wise(X)))))&
((?[X]:((~tall(X)<~>~happy(X))))=>(?[X]:(quiet(X))))&
((old(fred))=>((happy(susan)<~>~happy(susan))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>((~tall(alice)&~funny(alice))))&
((~humble(fred))<=>(?[X]:((funny(X)<~>~generous(X)))))&
(![X]:((~patient(X)|~wise(X))<=>wise(X)))&
(![X]:(~curious(X)<=>(patient(X)&brave(X))))&
(((~old(alice)<~>~rich(alice)))<=>(?[X]:((~happy(X)&~tall(X)))))&
((?[X]:((~brave(X)|~wise(X))))=>((~kind(alice)&~curious(alice))))&
((~rich(alice))=>(?[X]:((~humble(X)&rich(X)))))&
(((funny(john)|~rich(john)))=>((~old(fred)|~quiet(fred))))&
(![X]:((brave(X)&generous(X))<=>(~wise(X)<~>quiet(X))))&
((?[X]:((calm(X)&generous(X))))=>((rich(paul)<~>quiet(paul))))&
((?[X]:(~kind(X)))<=>(?[X]:((~tall(X)|patient(X)))))&
(?[X]:((~old(X)&creative(X))))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((rich(X)&calm(X))))&
((calm(lucy)&~creative(lucy)))&
(?[X]:((~curious(X)|~quiet(X))))&
(?[X]:((~creative(X)&tall(X)))) | ~brave(lucy) | [
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 474148234946459599146963
% SZS output start Proof for 474148234946459599146963
7. ! [X0] : ((~wise(X0) | ~patient(X0)) <=> wise(X0)) [input p6]
8. ! [X0] : (~curious(X0) <=> (brave(X0) & patient(X0))) [input p7]
10. ? [X0] : (~wise(X0) | ~brave(X0)) => (~curious(alice) & ~kind(alice)) [input p9]
22. ~brave(lucy) [input hypothesis]
26. ! [X0] : (~curious(X0) => (brave(X0) & patient(X0))) [unused predicate definition removal 8]
31. ! [X0] : ((brave(X0) & patient(X0)) | curious(X0)) [ennf transformation 26]
32. (~curious(alice) & ~kind(alice)) | ! [X0] : (wise(X0) & brave(X0)) [ennf transformation 10]
54. ! [X0] : (((~wise(X0) | ~patient(X0)) | ~wise(X0)) & (wise(X0) | (wise(X0) & patient(X0)))) [nnf transformation 7]
55. ! [X0] : ((~wise(X0) | ~patient(X0) | ~wise(X0)) & (wise(X0) | (wise(X0) & patient(X0)))) [flattening 54]
98. wise(X0) | wise(X0) [cnf transformation 55]
99. ~wise(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 55]
100. curious(X0) | patient(X0) [cnf transformation 31]
110. ~curious(alice) | brave(X0) [cnf transformation 32]
137. ~brave(lucy) [cnf transformation 22]
138. wise(X0) [duplicate literal removal 98]
139. ~patient(X0) | ~wise(X0) [duplicate literal removal 99]
241. 23 <=> ! [X0] : brave(X0) [avatar definition]
242. brave(X0) <- (23) [avatar component clause 241]
244. 24 <=> curious(alice) [avatar definition]
246. ~curious(alice) <- (~24) [avatar component clause 244]
247. 23 | ~24 [avatar split clause 110,244,241]
341. patient(alice) <- (~24) [resolution 100,246]
343. ~wise(alice) <- (~24) [resolution 139,341]
344. $false <- (~24) [subsumption resolution 343,138]
345. 24 [avatar contradiction clause 344]
346. $false <- (23) [resolution 242,137]
347. ~23 [avatar contradiction clause 346]
348. $false [avatar sat refutation 247,345,347]
% SZS output end Proof for 474148234946459599146963
% ------------------------------
% 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or wise is both calm and not patient and vice versa.
If susan is happy or calm then lucy is kind or not tall and vice versa.
If alice is either not rich or not quiet then someone is creative or not curious.
If someone is both not humble and not generous then paul is not generous.
Everyone who is both calm and strong is not quiet or quiet.
Everyone who is both not rich and curious is both funny and not brave and vice versa.
Everyone who is both not humble and strong is not brave or not calm.
Everyone who is both strong and happy is either not generous or quiet and vice versa.
If john is either kind or not patient then fred is both not calm and not quiet.
If someone is brave or creative then someone is either not quiet or quiet.
Everyone who is not wise is both old and not tall.
Everyone who is not kind is either not patient or not strong.
If mary is not kind or not tall then john is not quiet or not calm.
Everyone who is both not quiet and humble is humble or not happy and vice versa.
Everyone who is both not quiet and quiet is calm or not rich and vice versa.
If someone is either wise or generous then someone is either not strong or old and vice versa.
Alice is patient or not happy.
Someone is not strong or wise.
John is both not creative and not brave.
Fred is either brave or curious.
Paul is brave.
Someone is not creative or creative.
Someone is either funny or not funny.
Someone is not curious or not tall. | Mary is not calm. | entailment | (![X]:((~creative(X)<~>wise(X))<=>(calm(X)&~patient(X))))&
(((happy(susan)|calm(susan)))<=>((kind(lucy)|~tall(lucy))))&
(((~rich(alice)<~>~quiet(alice)))=>(?[X]:((creative(X)|~curious(X)))))&
((?[X]:((~humble(X)&~generous(X))))=>(~generous(paul)))&
(![X]:((calm(X)&strong(X))=>(~quiet(X)|quiet(X))))&
(![X]:((~rich(X)&curious(X))<=>(funny(X)&~brave(X))))&
(![X]:((~humble(X)&strong(X))=>(~brave(X)|~calm(X))))&
(![X]:((strong(X)&happy(X))<=>(~generous(X)<~>quiet(X))))&
(((kind(john)<~>~patient(john)))=>((~calm(fred)&~quiet(fred))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:(~wise(X)=>(old(X)&~tall(X))))&
(![X]:(~kind(X)=>(~patient(X)<~>~strong(X))))&
(((~kind(mary)|~tall(mary)))=>((~quiet(john)|~calm(john))))&
(![X]:((~quiet(X)&humble(X))<=>(humble(X)|~happy(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(calm(X)|~rich(X))))&
((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:((~strong(X)<~>old(X)))))&
((patient(alice)|~happy(alice)))&
(?[X]:((~strong(X)|wise(X))))&
((~creative(john)&~brave(john)))&
((brave(fred)<~>curious(fred)))&
(brave(paul))&
(?[X]:((~creative(X)|creative(X))))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((~curious(X)|~tall(X)))) | ~calm(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7040595164623850836801611
% SZS output start Proof for 7040595164623850836801611
15. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (~rich(X0) | calm(X0))) [input p14]
25. calm(mary) [input hypothesis]
59. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (rich(X0) & ~calm(X0))) & ((~rich(X0) | calm(X0)) | (~quiet(X0) | quiet(X0)))) [nnf transformation 15]
60. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (rich(X0) & ~calm(X0))) & (~rich(X0) | calm(X0) | ~quiet(X0) | quiet(X0))) [flattening 59]
121. ~quiet(X0) | ~calm(X0) [cnf transformation 60]
123. quiet(X0) | ~calm(X0) [cnf transformation 60]
144. calm(mary) [cnf transformation 25]
230. ~calm(X0) [subsumption resolution 121,123]
304. $false [subsumption resolution 144,230]
% SZS output end Proof for 7040595164623850836801611
% ------------------------------
% 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 brave is both not brave and not creative.
Everyone who is both not tall and not humble is both not curious and not tall and vice versa.
Everyone who is not brave or not generous is both not kind and strong and vice versa.
Everyone who is both not humble and not generous is curious and vice versa.
Everyone who is wise is not strong.
Everyone who is both not calm and rich is not brave or calm.
Everyone who is not patient or rich is either not creative or not quiet and vice versa.
Everyone who is either not funny or not rich is quiet and vice versa.
If someone is not rich then someone is curious and vice versa.
Everyone who is both not funny and calm is funny or not patient.
If someone is not happy or not brave then someone is patient and vice versa.
Everyone who is not generous or kind is both not brave and not creative.
Everyone who is either not old or not creative is not old or not quiet.
Everyone who is not happy or not strong is either wise or not strong.
If john is not happy or not quiet then someone is either not quiet or wise.
Everyone who is both curious and strong is either strong or tall and vice versa.
John is not generous.
Someone is both not wise and not curious.
Someone is either generous or not tall.
Someone is not strong.
Someone is happy.
Paul is both not curious and brave.
Someone is either patient or not humble. | Paul is rich. | entailment | (![X]:(~brave(X)=>(~brave(X)&~creative(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~curious(X)&~tall(X))))&
(![X]:((~brave(X)|~generous(X))<=>(~kind(X)&strong(X))))&
(![X]:((~humble(X)&~generous(X))<=>curious(X)))&
(![X]:(wise(X)=>~strong(X)))&
(![X]:((~calm(X)&rich(X))=>(~brave(X)|calm(X))))&
(![X]:((~patient(X)|rich(X))<=>(~creative(X)<~>~quiet(X))))&
(![X]:((~funny(X)<~>~rich(X))<=>quiet(X)))&
((?[X]:(~rich(X)))<=>(?[X]:(curious(X))))&
(![X]:((~funny(X)&calm(X))=>(funny(X)|~patient(X))))&
((?[X]:((~happy(X)|~brave(X))))<=>(?[X]:(patient(X))))&
(![X]:((~generous(X)|kind(X))=>(~brave(X)&~creative(X))))&
(![X]:((~old(X)<~>~creative(X))=>(~old(X)|~quiet(X))))&
(![X]:((~happy(X)|~strong(X))=>(wise(X)<~>~strong(X))))&
(((~happy(john)|~quiet(john)))=>(?[X]:((~quiet(X)<~>wise(X)))))&
(![X]:((curious(X)&strong(X))<=>(strong(X)<~>tall(X))))&
(~generous(john))&
(?[X]:((~wise(X)&~curious(X))))&
(?[X]:((generous(X)<~>~tall(X))))&
(?[X]:(~strong(X)))&
(?[X]:(happy(X)))&
((~curious(paul)&brave(paul)))&
(?[X]:((patient(X)<~>~humble(X)))) | rich(paul) | [
"p1",
"p3",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 86929422312664244711205
% SZS output start Proof for 86929422312664244711205
2. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> (~tall(X0) & ~curious(X0))) [input p1]
4. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> curious(X0)) [input p3]
9. ? [X0] : ~rich(X0) <=> ? [X0] : curious(X0) [input p8]
16. ! [X0] : ((strong(X0) & curious(X0)) <=> (strong(X0) <~> tall(X0))) [input p15]
24. ~rich(paul) [input hypothesis]
25. ? [X0] : ~rich(X0) <=> ? [X1] : curious(X1) [rectify 9]
38. ! [X0] : (((~humble(X0) & ~tall(X0)) | (tall(X0) | curious(X0))) & ((~tall(X0) & ~curious(X0)) | (humble(X0) | tall(X0)))) [nnf transformation 2]
39. ! [X0] : (((~humble(X0) & ~tall(X0)) | tall(X0) | curious(X0)) & ((~tall(X0) & ~curious(X0)) | humble(X0) | tall(X0))) [flattening 38]
42. ! [X0] : (((~generous(X0) & ~humble(X0)) | ~curious(X0)) & (curious(X0) | (generous(X0) | humble(X0)))) [nnf transformation 4]
43. ! [X0] : (((~generous(X0) & ~humble(X0)) | ~curious(X0)) & (curious(X0) | generous(X0) | humble(X0))) [flattening 42]
47. (? [X0] : ~rich(X0) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : rich(X0)) [nnf transformation 25]
48. (? [X0] : ~rich(X0) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : rich(X3)) [rectify 47]
49. ? [X0] : ~rich(X0) => ~rich(sK0) [choice axiom]
50. ? [X2] : curious(X2) => curious(sK1) [choice axiom]
51. (~rich(sK0) | ! [X1] : ~curious(X1)) & (curious(sK1) | ! [X3] : rich(X3)) [skolemisation 48,50,49]
62. ! [X0] : (((strong(X0) & curious(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | (~strong(X0) | ~curious(X0)))) [nnf transformation 16]
63. ! [X0] : (((strong(X0) & curious(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | ~strong(X0) | ~curious(X0))) [flattening 62]
78. ~curious(X0) | humble(X0) | tall(X0) [cnf transformation 39]
88. ~curious(X0) | ~humble(X0) [cnf transformation 43]
102. curious(sK1) | rich(X3) [cnf transformation 51]
123. ~tall(X0) | ~strong(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 63]
127. strong(X0) | strong(X0) | ~tall(X0) [cnf transformation 63]
139. ~rich(paul) [cnf transformation 24]
140. ~tall(X0) | ~strong(X0) | ~curious(X0) [duplicate literal removal 123]
141. ~tall(X0) | strong(X0) [duplicate literal removal 127]
155. 3 <=> ! [X3] : rich(X3) [avatar definition]
156. rich(X3) <- (3) [avatar component clause 155]
158. 4 <=> curious(sK1) [avatar definition]
160. curious(sK1) <- (4) [avatar component clause 158]
161. 3 | 4 [avatar split clause 102,158,155]
205. ~curious(X0) | ~tall(X0) [subsumption resolution 140,141]
228. $false <- (3) [resolution 156,139]
229. ~3 [avatar contradiction clause 228]
234. ~humble(sK1) <- (4) [resolution 88,160]
241. ~tall(sK1) <- (4) [resolution 205,160]
242. humble(sK1) | tall(sK1) <- (4) [resolution 78,160]
243. tall(sK1) <- (4) [subsumption resolution 242,234]
244. $false <- (4) [subsumption resolution 243,241]
245. ~4 [avatar contradiction clause 244]
246. $false [avatar sat refutation 161,229,245]
% SZS output end Proof for 86929422312664244711205
% ------------------------------
% 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 happy or not quiet is both not humble and not funny and vice versa. Everyone who is not kind or strong is humble or quiet and vice versa. If mary is old or generous then someone is tall and vice versa. Everyone who is quiet or kind is brave and vice versa. If paul is both humble and not strong then someone is old or kind and vice versa. Everyone who is humble is either humble or not wise. Everyone who is either not wise or quiet is not kind. If susan is either tall or wise then paul is both quiet and old. Everyone who is both rich and old is either not rich or not patient and vice versa. Everyone who is not strong is tall and vice versa. Everyone who is both curious and not patient is either patient or strong. If someone is not strong then someone is either funny or not humble and vice versa. Everyone who is either not patient or humble is not happy or not kind and vice versa. If fred is either not wise or not calm then john is not generous or wise and vice versa. Someone is not creative or not happy. Paul is wise or not funny. Someone is not patient. Someone is either kind or funny. Susan is either curious or rich. Someone is not patient or not creative. | Mary is humble. | neutral | (![X]:((~happy(X)|~quiet(X))<=>(~humble(X)&~funny(X))))&
(![X]:((~kind(X)|strong(X))<=>(humble(X)|quiet(X))))&
(((old(mary)|generous(mary)))<=>(?[X]:(tall(X))))&
(![X]:((quiet(X)|kind(X))<=>brave(X)))&
(((humble(paul)&~strong(paul)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:(humble(X)=>(humble(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>quiet(X))=>~kind(X)))&
(((tall(susan)<~>wise(susan)))=>((quiet(paul)&old(paul))))&
(![X]:((rich(X)&old(X))<=>(~rich(X)<~>~patient(X))))&
(![X]:(~strong(X)<=>tall(X)))&
(![X]:((curious(X)&~patient(X))=>(patient(X)<~>strong(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((funny(X)<~>~humble(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(~happy(X)|~kind(X))))&
(((~wise(fred)<~>~calm(fred)))<=>((~generous(john)|wise(john))))&
(?[X]:((~creative(X)|~happy(X))))&
((wise(paul)|~funny(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((kind(X)<~>funny(X))))&
((curious(susan)<~>rich(susan)))&
(?[X]:((~patient(X)|~creative(X)))) | humble(mary) | [] | null | 0 |
If someone is not creative then someone is both not kind and curious.
If someone is both quiet and not quiet then someone is both old and creative and vice versa.
If mary is either not strong or creative then someone is either kind or brave and vice versa.
If mary is not creative or not curious then someone is both not strong and not kind.
Everyone who is not creative is both not quiet and tall and vice versa.
Everyone who is either creative or not kind is both not humble and not rich.
Everyone who is either brave or not wise is not brave.
Everyone who is not creative is either not calm or creative.
Everyone who is both not strong and not kind is not funny or not wise.
Everyone who is both not creative and rich is either creative or not quiet and vice versa.
Everyone who is not tall is not tall or calm.
If someone is kind then paul is calm or wise.
Everyone who is both old and strong is either not curious or curious.
Everyone who is either not brave or curious is both not old and not happy and vice versa.
Paul is not strong or kind.
Someone is either kind or not funny.
John is not old. | John is humble. | neutral | ((?[X]:(~creative(X)))=>(?[X]:((~kind(X)&curious(X)))))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((old(X)&creative(X)))))&
(((~strong(mary)<~>creative(mary)))<=>(?[X]:((kind(X)<~>brave(X)))))&
(((~creative(mary)|~curious(mary)))=>(?[X]:((~strong(X)&~kind(X)))))&
(![X]:(~creative(X)<=>(~quiet(X)&tall(X))))&
(![X]:((creative(X)<~>~kind(X))=>(~humble(X)&~rich(X))))&
(![X]:((brave(X)<~>~wise(X))=>~brave(X)))&
(![X]:(~creative(X)=>(~calm(X)<~>creative(X))))&
(![X]:((~strong(X)&~kind(X))=>(~funny(X)|~wise(X))))&
(![X]:((~creative(X)&rich(X))<=>(creative(X)<~>~quiet(X))))&
(![X]:(~tall(X)=>(~tall(X)|calm(X))))&
((?[X]:(kind(X)))=>((calm(paul)|wise(paul))))&
(![X]:((old(X)&strong(X))=>(~curious(X)<~>curious(X))))&
(![X]:((~brave(X)<~>curious(X))<=>(~old(X)&~happy(X))))&
((~strong(paul)|kind(paul)))&
(?[X]:((kind(X)<~>~funny(X))))&
(~old(john)) | humble(john) | [] | null | 0 |
Everyone who is both not funny and tall is not generous or not happy and vice versa.
If paul is either quiet or not quiet then paul is not funny or not curious.
If susan is either strong or creative then fred is both not brave and not kind.
Everyone who is wise is either quiet or not rich and vice versa.
Everyone who is both strong and curious is either not wise or old and vice versa.
If susan is strong then someone is either not kind or not brave.
Everyone who is not curious or not kind is not quiet.
Everyone who is both calm and not humble is wise and vice versa.
Everyone who is funny is not patient or tall and vice versa.
If someone is not calm or not tall then fred is either rich or old.
Everyone who is not funny or not rich is both not humble and not old and vice versa.
Everyone who is both strong and not quiet is not kind and vice versa.
If someone is patient or not wise then someone is both kind and old.
If someone is not funny then susan is either brave or funny and vice versa.
Everyone who is calm or brave is either brave or not generous.
Everyone who is kind is creative or not brave and vice versa.
Paul is not tall.
Lucy is not brave.
Lucy is both not patient and funny.
Someone is both not brave and funny.
John is not funny or wise.
Paul is either not creative or strong.
Someone is generous. | Fred is not quiet. | neutral | (![X]:((~funny(X)&tall(X))<=>(~generous(X)|~happy(X))))&
(((quiet(paul)<~>~quiet(paul)))=>((~funny(paul)|~curious(paul))))&
(((strong(susan)<~>creative(susan)))=>((~brave(fred)&~kind(fred))))&
(![X]:(wise(X)<=>(quiet(X)<~>~rich(X))))&
(![X]:((strong(X)&curious(X))<=>(~wise(X)<~>old(X))))&
((strong(susan))=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:((~curious(X)|~kind(X))=>~quiet(X)))&
(![X]:((calm(X)&~humble(X))<=>wise(X)))&
(![X]:(funny(X)<=>(~patient(X)|tall(X))))&
((?[X]:((~calm(X)|~tall(X))))=>((rich(fred)<~>old(fred))))&
(![X]:((~funny(X)|~rich(X))<=>(~humble(X)&~old(X))))&
(![X]:((strong(X)&~quiet(X))<=>~kind(X)))&
((?[X]:((patient(X)|~wise(X))))=>(?[X]:((kind(X)&old(X)))))&
((?[X]:(~funny(X)))<=>((brave(susan)<~>funny(susan))))&
(![X]:((calm(X)|brave(X))=>(brave(X)<~>~generous(X))))&
(![X]:(kind(X)<=>(creative(X)|~brave(X))))&
(~tall(paul))&
(~brave(lucy))&
((~patient(lucy)&funny(lucy)))&
(?[X]:((~brave(X)&funny(X))))&
((~funny(john)|wise(john)))&
((~creative(paul)<~>strong(paul)))&
(?[X]:(generous(X))) | ~quiet(fred) | [] | null | 0 |
Everyone who is both not happy and brave is both strong and not wise and vice versa.
Everyone who is either patient or quiet is kind or calm and vice versa.
Everyone who is both not patient and strong is either not creative or not tall and vice versa.
Everyone who is generous is either generous or curious.
If someone is either not curious or curious then paul is humble and vice versa.
Everyone who is not rich or not calm is either not calm or not brave and vice versa.
Everyone who is funny is curious or not patient and vice versa.
If someone is both strong and brave then someone is not rich or tall and vice versa.
Everyone who is strong is not quiet or brave and vice versa.
If someone is both not old and happy then someone is both brave and not old and vice versa.
Everyone who is both not funny and not calm is either calm or not generous and vice versa.
If someone is both kind and happy then mary is both humble and not quiet and vice versa.
Everyone who is either patient or brave is both kind and not old.
If someone is not kind then someone is not curious.
If someone is tall or generous then fred is happy or not patient.
Everyone who is either not rich or happy is not calm or calm.
Someone is either brave or tall.
Mary is both not strong and not curious.
John is either not funny or wise.
John is either not old or humble.
Alice is not happy or not patient.
Fred is funny.
Susan is curious.
Paul is old. | John is not generous. | entailment | (![X]:((~happy(X)&brave(X))<=>(strong(X)&~wise(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(kind(X)|calm(X))))&
(![X]:((~patient(X)&strong(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:(generous(X)=>(generous(X)<~>curious(X))))&
((?[X]:((~curious(X)<~>curious(X))))<=>(humble(paul)))&
(![X]:((~rich(X)|~calm(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:(funny(X)<=>(curious(X)|~patient(X))))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:((~rich(X)|tall(X)))))&
(![X]:(strong(X)<=>(~quiet(X)|brave(X))))&
((?[X]:((~old(X)&happy(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((~funny(X)&~calm(X))<=>(calm(X)<~>~generous(X))))&
((?[X]:((kind(X)&happy(X))))<=>((humble(mary)&~quiet(mary))))&
(![X]:((patient(X)<~>brave(X))=>(kind(X)&~old(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~curious(X))))&
((?[X]:((tall(X)|generous(X))))=>((happy(fred)|~patient(fred))))&
(![X]:((~rich(X)<~>happy(X))=>(~calm(X)|calm(X))))&
(?[X]:((brave(X)<~>tall(X))))&
((~strong(mary)&~curious(mary)))&
((~funny(john)<~>wise(john)))&
((~old(john)<~>humble(john)))&
((~happy(alice)|~patient(alice)))&
(funny(fred))&
(curious(susan))&
(old(paul)) | ~generous(john) | [
"p0",
"p3",
"p5",
"p6",
"p8",
"p10",
"p11",
"p12",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8153647200820319703244
% SZS output start Proof for 8153647200820319703244
1. ! [X0] : ((brave(X0) & ~happy(X0)) <=> (~wise(X0) & strong(X0))) [input p0]
4. ! [X0] : (generous(X0) => (generous(X0) <~> curious(X0))) [input p3]
6. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> (~calm(X0) <~> ~brave(X0))) [input p5]
7. ! [X0] : (funny(X0) <=> (~patient(X0) | curious(X0))) [input p6]
9. ! [X0] : (strong(X0) <=> (brave(X0) | ~quiet(X0))) [input p8]
11. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (calm(X0) <~> ~generous(X0))) [input p10]
12. ? [X0] : (happy(X0) & kind(X0)) <=> (~quiet(mary) & humble(mary)) [input p11]
13. ! [X0] : ((patient(X0) <~> brave(X0)) => (~old(X0) & kind(X0))) [input p12]
18. ~curious(mary) & ~strong(mary) [input p17]
19. ~funny(john) <~> wise(john) [input p18]
25. generous(john) [input hypothesis]
29. ! [X0] : ((generous(X0) <~> curious(X0)) | ~generous(X0)) [ennf transformation 4]
30. ! [X0] : ((~old(X0) & kind(X0)) | (patient(X0) <=> brave(X0))) [ennf transformation 13]
36. ! [X0] : (((brave(X0) & ~happy(X0)) | (wise(X0) | ~strong(X0))) & ((~wise(X0) & strong(X0)) | (~brave(X0) | happy(X0)))) [nnf transformation 1]
37. ! [X0] : (((brave(X0) & ~happy(X0)) | wise(X0) | ~strong(X0)) & ((~wise(X0) & strong(X0)) | ~brave(X0) | happy(X0))) [flattening 36]
42. ! [X0] : (((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | ~generous(X0)) [nnf transformation 29]
47. ! [X0] : (((~calm(X0) | ~rich(X0)) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0)))) & (((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | (calm(X0) & rich(X0)))) [nnf transformation 6]
48. ! [X0] : ((~calm(X0) | ~rich(X0) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0)))) & (((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | (calm(X0) & rich(X0)))) [flattening 47]
49. ! [X0] : ((funny(X0) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | ~funny(X0))) [nnf transformation 7]
50. ! [X0] : ((funny(X0) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | ~funny(X0))) [flattening 49]
56. ! [X0] : ((strong(X0) | (~brave(X0) & quiet(X0))) & ((brave(X0) | ~quiet(X0)) | ~strong(X0))) [nnf transformation 9]
57. ! [X0] : ((strong(X0) | (~brave(X0) & quiet(X0))) & (brave(X0) | ~quiet(X0) | ~strong(X0))) [flattening 56]
63. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (calm(X0) | funny(X0)))) [nnf transformation 11]
64. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | calm(X0) | funny(X0))) [flattening 63]
65. (? [X0] : (happy(X0) & kind(X0)) | (quiet(mary) | ~humble(mary))) & ((~quiet(mary) & humble(mary)) | ! [X0] : (~happy(X0) | ~kind(X0))) [nnf transformation 12]
66. (? [X0] : (happy(X0) & kind(X0)) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X0] : (~happy(X0) | ~kind(X0))) [flattening 65]
67. (? [X0] : (happy(X0) & kind(X0)) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X1] : (~happy(X1) | ~kind(X1))) [rectify 66]
68. ? [X0] : (happy(X0) & kind(X0)) => (happy(sK5) & kind(sK5)) [choice axiom]
69. ((happy(sK5) & kind(sK5)) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X1] : (~happy(X1) | ~kind(X1))) [skolemisation 67,68]
70. ! [X0] : ((~old(X0) & kind(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) [nnf transformation 30]
78. (~wise(john) | funny(john)) & (wise(john) | ~funny(john)) [nnf transformation 19]
81. ~wise(X0) | ~brave(X0) | happy(X0) [cnf transformation 37]
97. ~curious(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 42]
105. brave(X0) | calm(X0) | calm(X0) [cnf transformation 48]
108. ~funny(X0) | curious(X0) | ~patient(X0) [cnf transformation 50]
117. quiet(X0) | strong(X0) [cnf transformation 57]
123. ~generous(X0) | calm(X0) | calm(X0) | funny(X0) [cnf transformation 64]
127. ~calm(X0) | ~generous(X0) | ~calm(X0) [cnf transformation 64]
130. ~quiet(mary) | ~happy(X1) | ~kind(X1) [cnf transformation 69]
134. ~brave(X0) | patient(X0) | kind(X0) [cnf transformation 70]
144. ~strong(mary) [cnf transformation 18]
146. wise(john) | ~funny(john) [cnf transformation 78]
154. generous(john) [cnf transformation 25]
155. ~generous(X0) | calm(X0) | funny(X0) [duplicate literal removal 123]
156. ~generous(X0) | ~calm(X0) [duplicate literal removal 127]
157. calm(X0) | brave(X0) [duplicate literal removal 105]
161. ~curious(X0) | ~generous(X0) [duplicate literal removal 97]
230. ~generous(X0) | funny(X0) [subsumption resolution 155,156]
236. 18 <=> quiet(mary) [avatar definition]
237. ~quiet(mary) <- (~18) [avatar component clause 236]
250. 21 <=> ! [X1] : (~happy(X1) | ~kind(X1)) [avatar definition]
251. ~kind(X1) | ~happy(X1) <- (21) [avatar component clause 250]
252. 21 | ~18 [avatar split clause 130,236,250]
286. 29 <=> funny(john) [avatar definition]
288. funny(john) <- (29) [avatar component clause 286]
290. 30 <=> wise(john) [avatar definition]
291. wise(john) <- (30) [avatar component clause 290]
294. ~29 | 30 [avatar split clause 146,290,286]
318. strong(mary) <- (~18) [resolution 117,237]
319. $false <- (~18) [subsumption resolution 318,144]
320. 18 [avatar contradiction clause 319]
323. ~calm(john) [resolution 156,154]
324. brave(john) [resolution 157,323]
337. funny(john) [resolution 230,154]
340. 29 [avatar split clause 337,286]
349. ~brave(john) | happy(john) <- (30) [resolution 81,291]
350. happy(john) <- (30) [subsumption resolution 349,324]
401. curious(john) | ~patient(john) <- (29) [resolution 108,288]
404. 43 <=> patient(john) [avatar definition]
408. 44 <=> curious(john) [avatar definition]
410. curious(john) <- (44) [avatar component clause 408]
411. ~43 | 44 | ~29 [avatar split clause 401,286,408,404]
432. patient(john) | kind(john) [resolution 134,324]
542. 63 <=> kind(john) [avatar definition]
544. kind(john) <- (63) [avatar component clause 542]
545. 63 | 43 [avatar split clause 432,404,542]
550. ~generous(john) <- (44) [resolution 410,161]
552. $false <- (44) [subsumption resolution 550,154]
553. ~44 [avatar contradiction clause 552]
712. ~happy(john) <- (21, 63) [resolution 544,251]
714. $false <- (21, 30, 63) [subsumption resolution 712,350]
715. ~21 | ~30 | ~63 [avatar contradiction clause 714]
716. $false [avatar sat refutation 252,294,320,340,411,545,553,715]
% SZS output end Proof for 8153647200820319703244
% ------------------------------
% 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not brave is either happy or not wise and vice versa. If someone is both not kind and not happy then lucy is kind or not creative and vice versa. Everyone who is either wise or kind is not old or not funny. Everyone who is not creative or not happy is generous. Everyone who is either humble or old is both not curious and not humble and vice versa. Everyone who is patient or not generous is rich. Everyone who is either generous or rich is generous and vice versa. Everyone who is not humble is both happy and strong and vice versa. If someone is not wise then fred is both happy and not happy. If someone is tall then lucy is not generous or not patient and vice versa. If someone is not kind then someone is quiet or generous. If fred is brave or not kind then mary is humble. If someone is either not strong or strong then someone is not tall or strong and vice versa. If someone is both happy and not calm then lucy is not creative or strong. Everyone who is either not curious or not strong is calm or not quiet. If susan is wise or not old then someone is curious or rich. Susan is not old. Someone is strong or funny. Alice is both funny and old. Susan is calm or not happy. Alice is not tall or rich. Someone is not strong or not tall. | Lucy is not old. | neutral | (![X]:((~kind(X)<~>~brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:((~kind(X)&~happy(X))))<=>((kind(lucy)|~creative(lucy))))&
(![X]:((wise(X)<~>kind(X))=>(~old(X)|~funny(X))))&
(![X]:((~creative(X)|~happy(X))=>generous(X)))&
(![X]:((humble(X)<~>old(X))<=>(~curious(X)&~humble(X))))&
(![X]:((patient(X)|~generous(X))=>rich(X)))&
(![X]:((generous(X)<~>rich(X))<=>generous(X)))&
(![X]:(~humble(X)<=>(happy(X)&strong(X))))&
((?[X]:(~wise(X)))=>((happy(fred)&~happy(fred))))&
((?[X]:(tall(X)))<=>((~generous(lucy)|~patient(lucy))))&
((?[X]:(~kind(X)))=>(?[X]:((quiet(X)|generous(X)))))&
(((brave(fred)|~kind(fred)))=>(humble(mary)))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~tall(X)|strong(X)))))&
((?[X]:((happy(X)&~calm(X))))=>((~creative(lucy)|strong(lucy))))&
(![X]:((~curious(X)<~>~strong(X))=>(calm(X)|~quiet(X))))&
(((wise(susan)|~old(susan)))=>(?[X]:((curious(X)|rich(X)))))&
(~old(susan))&
(?[X]:((strong(X)|funny(X))))&
((funny(alice)&old(alice)))&
((calm(susan)|~happy(susan)))&
((~tall(alice)|rich(alice)))&
(?[X]:((~strong(X)|~tall(X)))) | ~old(lucy) | [] | null | 0 |
If someone is not old or tall then susan is both humble and not quiet. Everyone who is either kind or not strong is humble or not rich and vice versa. Everyone who is either generous or not calm is both not curious and not old and vice versa. If paul is both kind and creative then fred is not calm. Everyone who is either happy or creative is either not old or not curious and vice versa. Everyone who is both rich and not wise is both not rich and not calm and vice versa. If paul is not generous then susan is not creative and vice versa. Everyone who is kind is not strong and vice versa. If someone is either kind or curious then fred is tall and vice versa. If someone is both not brave and rich then alice is either not brave or not happy and vice versa. Everyone who is rich is either not brave or old and vice versa. If someone is not generous or not funny then someone is either quiet or tall. If someone is either not kind or old then someone is not creative or creative. Everyone who is either quiet or funny is both happy and humble. Everyone who is not strong is both not strong and brave and vice versa. Lucy is either not tall or curious. John is not calm or not creative. John is happy. Someone is not quiet or not creative. Fred is creative or not rich. Paul is either wise or happy. Susan is not patient. | Alice is brave. | entailment | ((?[X]:((~old(X)|tall(X))))=>((humble(susan)&~quiet(susan))))&
(![X]:((kind(X)<~>~strong(X))<=>(humble(X)|~rich(X))))&
(![X]:((generous(X)<~>~calm(X))<=>(~curious(X)&~old(X))))&
(((kind(paul)&creative(paul)))=>(~calm(fred)))&
(![X]:((happy(X)<~>creative(X))<=>(~old(X)<~>~curious(X))))&
(![X]:((rich(X)&~wise(X))<=>(~rich(X)&~calm(X))))&
((~generous(paul))<=>(~creative(susan)))&
(![X]:(kind(X)<=>~strong(X)))&
((?[X]:((kind(X)<~>curious(X))))<=>(tall(fred)))&
((?[X]:((~brave(X)&rich(X))))<=>((~brave(alice)<~>~happy(alice))))&
(![X]:(rich(X)<=>(~brave(X)<~>old(X))))&
((?[X]:((~generous(X)|~funny(X))))=>(?[X]:((quiet(X)<~>tall(X)))))&
((?[X]:((~kind(X)<~>old(X))))=>(?[X]:((~creative(X)|creative(X)))))&
(![X]:((quiet(X)<~>funny(X))=>(happy(X)&humble(X))))&
(![X]:(~strong(X)<=>(~strong(X)&brave(X))))&
((~tall(lucy)<~>curious(lucy)))&
((~calm(john)|~creative(john)))&
(happy(john))&
(?[X]:((~quiet(X)|~creative(X))))&
((creative(fred)|~rich(fred)))&
((wise(paul)<~>happy(paul)))&
(~patient(susan)) | brave(alice) | [
"p0",
"p1",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 924996175110809259909970
% SZS output start Proof for 924996175110809259909970
1. ? [X0] : (tall(X0) | ~old(X0)) => (~quiet(susan) & humble(susan)) [input p0]
2. ! [X0] : ((kind(X0) <~> ~strong(X0)) <=> (~rich(X0) | humble(X0))) [input p1]
8. ! [X0] : (kind(X0) <=> ~strong(X0)) [input p7]
11. ! [X0] : (rich(X0) <=> (~brave(X0) <~> old(X0))) [input p10]
15. ! [X0] : (~strong(X0) <=> (brave(X0) & ~strong(X0))) [input p14]
23. ~brave(alice) [input hypothesis]
27. (~quiet(susan) & humble(susan)) | ! [X0] : (~tall(X0) & old(X0)) [ennf transformation 1]
33. ! [X0] : ((((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (rich(X0) & ~humble(X0))) & ((~rich(X0) | humble(X0)) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))))) [nnf transformation 2]
34. ! [X0] : ((((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (rich(X0) & ~humble(X0))) & (~rich(X0) | humble(X0) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))))) [flattening 33]
41. ! [X0] : ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))) [nnf transformation 8]
50. ! [X0] : ((rich(X0) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) & (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | ~rich(X0))) [nnf transformation 11]
60. ! [X0] : ((~strong(X0) | (~brave(X0) | strong(X0))) & ((brave(X0) & ~strong(X0)) | strong(X0))) [nnf transformation 15]
61. ! [X0] : ((~strong(X0) | ~brave(X0) | strong(X0)) & ((brave(X0) & ~strong(X0)) | strong(X0))) [flattening 60]
66. humble(susan) | old(X0) [cnf transformation 27]
72. ~strong(X0) | kind(X0) | ~humble(X0) [cnf transformation 34]
73. ~strong(X0) | kind(X0) | rich(X0) [cnf transformation 34]
74. ~kind(X0) | strong(X0) | ~humble(X0) [cnf transformation 34]
97. ~strong(X0) | ~kind(X0) [cnf transformation 41]
98. strong(X0) | kind(X0) [cnf transformation 41]
110. ~rich(X0) | brave(X0) | ~old(X0) [cnf transformation 50]
124. brave(X0) | strong(X0) [cnf transformation 61]
134. ~brave(alice) [cnf transformation 23]
146. 3 <=> ! [X0] : old(X0) [avatar definition]
147. old(X0) <- (3) [avatar component clause 146]
150. 4 <=> humble(susan) [avatar definition]
152. humble(susan) <- (4) [avatar component clause 150]
154. 3 | 4 [avatar split clause 66,150,146]
205. 16 <=> brave(alice) [avatar definition]
207. ~brave(alice) <- (~16) [avatar component clause 205]
290. ~16 [avatar split clause 134,205]
292. strong(alice) <- (~16) [resolution 124,207]
295. ~kind(alice) <- (~16) [resolution 292,97]
297. kind(X0) | ~humble(X0) | kind(X0) [resolution 72,98]
300. ~humble(X0) | kind(X0) [duplicate literal removal 297]
301. kind(X0) | rich(X0) | kind(X0) [resolution 73,98]
304. rich(X0) | kind(X0) [duplicate literal removal 301]
334. kind(susan) <- (4) [resolution 300,152]
338. strong(susan) | ~humble(susan) <- (4) [resolution 334,74]
344. 40 <=> strong(susan) [avatar definition]
346. strong(susan) <- (40) [avatar component clause 344]
348. strong(susan) <- (4) [subsumption resolution 338,152]
349. 40 | ~4 [avatar split clause 348,150,344]
401. kind(susan) <- (4) [resolution 152,300]
407. 44 <=> rich(alice) [avatar definition]
408. ~rich(alice) <- (~44) [avatar component clause 407]
409. rich(alice) <- (44) [avatar component clause 407]
411. 45 <=> old(alice) [avatar definition]
412. ~old(alice) <- (~45) [avatar component clause 411]
430. brave(alice) | ~old(alice) <- (44) [resolution 409,110]
432. ~old(alice) <- (~16, 44) [subsumption resolution 430,207]
433. ~45 | 16 | ~44 [avatar split clause 432,407,205,411]
444. ~kind(susan) <- (40) [resolution 346,97]
445. $false <- (4, 40) [subsumption resolution 444,401]
446. ~4 | ~40 [avatar contradiction clause 445]
454. $false <- (3, ~45) [resolution 147,412]
455. ~3 | 45 [avatar contradiction clause 454]
487. kind(alice) <- (~44) [resolution 408,304]
488. $false <- (~16, ~44) [subsumption resolution 487,295]
489. 16 | 44 [avatar contradiction clause 488]
490. $false [avatar sat refutation 154,290,349,433,446,455,489]
% SZS output end Proof for 924996175110809259909970
% ------------------------------
% 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 |
Everyone who is not generous is happy or not brave.
Everyone who is rich or not creative is both patient and not tall and vice versa.
Everyone who is either not quiet or not kind is wise or not curious.
If someone is either funny or patient then someone is not patient and vice versa.
Everyone who is either not quiet or tall is quiet.
Everyone who is both creative and not wise is either wise or calm.
If someone is either not tall or patient then someone is either quiet or not calm.
If someone is either not quiet or not strong then paul is happy and vice versa.
Everyone who is not curious is not old or not humble.
If someone is not tall or not kind then john is not calm or not kind and vice versa.
If someone is either creative or not tall then someone is both funny and not generous.
If someone is either not curious or happy then fred is not humble or calm and vice versa.
If susan is either not creative or not patient then paul is either not patient or not wise and vice versa.
If someone is both not generous and creative then mary is both not generous and not calm.
Everyone who is wise is both happy and not wise and vice versa.
Everyone who is both kind and not creative is not calm and vice versa.
Lucy is not generous or quiet.
Mary is both rich and strong.
John is either brave or not calm.
Alice is either old or not brave.
Someone is not wise or tall.
Lucy is either humble or generous.
Alice is not rich or not tall. | Susan is strong. | neutral | (![X]:(~generous(X)=>(happy(X)|~brave(X))))&
(![X]:((rich(X)|~creative(X))<=>(patient(X)&~tall(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(wise(X)|~curious(X))))&
((?[X]:((funny(X)<~>patient(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~quiet(X)<~>tall(X))=>quiet(X)))&
(![X]:((creative(X)&~wise(X))=>(wise(X)<~>calm(X))))&
((?[X]:((~tall(X)<~>patient(X))))=>(?[X]:((quiet(X)<~>~calm(X)))))&
((?[X]:((~quiet(X)<~>~strong(X))))<=>(happy(paul)))&
(![X]:(~curious(X)=>(~old(X)|~humble(X))))&
((?[X]:((~tall(X)|~kind(X))))<=>((~calm(john)|~kind(john))))&
((?[X]:((creative(X)<~>~tall(X))))=>(?[X]:((funny(X)&~generous(X)))))&
((?[X]:((~curious(X)<~>happy(X))))<=>((~humble(fred)|calm(fred))))&
(((~creative(susan)<~>~patient(susan)))<=>((~patient(paul)<~>~wise(paul))))&
((?[X]:((~generous(X)&creative(X))))=>((~generous(mary)&~calm(mary))))&
(![X]:(wise(X)<=>(happy(X)&~wise(X))))&
(![X]:((kind(X)&~creative(X))<=>~calm(X)))&
((~generous(lucy)|quiet(lucy)))&
((rich(mary)&strong(mary)))&
((brave(john)<~>~calm(john)))&
((old(alice)<~>~brave(alice)))&
(?[X]:((~wise(X)|tall(X))))&
((humble(lucy)<~>generous(lucy)))&
((~rich(alice)|~tall(alice))) | strong(susan) | [] | null | 0 |
If someone is creative then john is quiet or old.
Everyone who is not creative or strong is either not quiet or humble and vice versa.
Everyone who is not brave is creative and vice versa.
Everyone who is not funny or humble is both calm and rich.
If john is either not quiet or not generous then john is creative.
If someone is both not brave and patient then fred is both kind and not humble and vice versa.
If someone is either not funny or not rich then fred is both humble and rich.
Everyone who is not wise is not creative.
If mary is not generous then susan is either not funny or wise.
Everyone who is both not patient and not quiet is brave or not wise and vice versa.
If someone is not curious or brave then someone is not tall and vice versa.
Everyone who is both rich and not humble is both not curious and quiet.
Everyone who is both quiet and not strong is both not humble and not wise.
If someone is not humble then someone is both quiet and not patient and vice versa.
If lucy is quiet then someone is either not kind or not curious and vice versa.
If someone is either wise or rich then mary is generous.
Mary is not creative.
Mary is either not creative or not happy.
Someone is not humble.
Lucy is not old.
Fred is not quiet or not curious.
Someone is both brave and tall. | Fred is wise. | entailment | ((?[X]:(creative(X)))=>((quiet(john)|old(john))))&
(![X]:((~creative(X)|strong(X))<=>(~quiet(X)<~>humble(X))))&
(![X]:(~brave(X)<=>creative(X)))&
(![X]:((~funny(X)|humble(X))=>(calm(X)&rich(X))))&
(((~quiet(john)<~>~generous(john)))=>(creative(john)))&
((?[X]:((~brave(X)&patient(X))))<=>((kind(fred)&~humble(fred))))&
((?[X]:((~funny(X)<~>~rich(X))))=>((humble(fred)&rich(fred))))&
(![X]:(~wise(X)=>~creative(X)))&
((~generous(mary))=>((~funny(susan)<~>wise(susan))))&
(![X]:((~patient(X)&~quiet(X))<=>(brave(X)|~wise(X))))&
((?[X]:((~curious(X)|brave(X))))<=>(?[X]:(~tall(X))))&
(![X]:((rich(X)&~humble(X))=>(~curious(X)&quiet(X))))&
(![X]:((quiet(X)&~strong(X))=>(~humble(X)&~wise(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((quiet(X)&~patient(X)))))&
((quiet(lucy))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
((?[X]:((wise(X)<~>rich(X))))=>(generous(mary)))&
(~creative(mary))&
((~creative(mary)<~>~happy(mary)))&
(?[X]:(~humble(X)))&
(~old(lucy))&
((~quiet(fred)|~curious(fred)))&
(?[X]:((brave(X)&tall(X)))) | wise(fred) | [
"p1",
"p2",
"p3",
"p6",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1013840362585577959739679
% SZS output start Proof for 1013840362585577959739679
2. ! [X0] : ((strong(X0) | ~creative(X0)) <=> (~quiet(X0) <~> humble(X0))) [input p1]
3. ! [X0] : (~brave(X0) <=> creative(X0)) [input p2]
4. ! [X0] : ((humble(X0) | ~funny(X0)) => (rich(X0) & calm(X0))) [input p3]
7. ? [X0] : (~funny(X0) <~> ~rich(X0)) => (rich(fred) & humble(fred)) [input p6]
8. ! [X0] : (~wise(X0) => ~creative(X0)) [input p7]
10. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (~wise(X0) | brave(X0))) [input p9]
12. ! [X0] : ((~humble(X0) & rich(X0)) => (quiet(X0) & ~curious(X0))) [input p11]
23. ~wise(fred) [input hypothesis]
26. ! [X0] : ((humble(X0) | ~funny(X0)) => rich(X0)) [pure predicate removal 4]
29. ! [X0] : (rich(X0) | (~humble(X0) & funny(X0))) [ennf transformation 26]
31. (rich(fred) & humble(fred)) | ! [X0] : (~funny(X0) <=> ~rich(X0)) [ennf transformation 7]
32. ! [X0] : (~creative(X0) | wise(X0)) [ennf transformation 8]
34. ! [X0] : ((quiet(X0) & ~curious(X0)) | (humble(X0) | ~rich(X0))) [ennf transformation 12]
35. ! [X0] : ((quiet(X0) & ~curious(X0)) | humble(X0) | ~rich(X0)) [flattening 34]
39. ! [X0] : (((strong(X0) | ~creative(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0)))) & (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & creative(X0)))) [nnf transformation 2]
40. ! [X0] : ((strong(X0) | ~creative(X0) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0)))) & (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & creative(X0)))) [flattening 39]
41. ! [X0] : ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))) [nnf transformation 3]
48. (rich(fred) & humble(fred)) | ! [X0] : ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))) [nnf transformation 31]
50. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (wise(X0) & ~brave(X0))) & ((~wise(X0) | brave(X0)) | (quiet(X0) | patient(X0)))) [nnf transformation 10]
51. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (wise(X0) & ~brave(X0))) & (~wise(X0) | brave(X0) | quiet(X0) | patient(X0))) [flattening 50]
75. ~humble(X0) | quiet(X0) | creative(X0) [cnf transformation 40]
79. brave(X0) | creative(X0) [cnf transformation 41]
81. rich(X0) | funny(X0) [cnf transformation 29]
90. humble(fred) | ~funny(X0) | rich(X0) [cnf transformation 48]
93. ~creative(X0) | wise(X0) [cnf transformation 32]
99. ~brave(X0) | ~quiet(X0) [cnf transformation 51]
100. ~quiet(X0) | wise(X0) [cnf transformation 51]
105. ~rich(X0) | humble(X0) | quiet(X0) [cnf transformation 35]
125. ~wise(fred) [cnf transformation 23]
153. 7 <=> humble(fred) [avatar definition]
154. ~humble(fred) <- (~7) [avatar component clause 153]
155. humble(fred) <- (7) [avatar component clause 153]
173. 11 <=> ! [X0] : rich(X0) [avatar definition]
174. rich(X0) <- (11) [avatar component clause 173]
176. 12 <=> rich(fred) [avatar definition]
177. ~rich(fred) <- (~12) [avatar component clause 176]
178. rich(fred) <- (12) [avatar component clause 176]
185. humble(fred) | rich(X0) [subsumption resolution 90,81]
186. 11 | 7 [avatar split clause 185,153,173]
281. 35 <=> quiet(fred) [avatar definition]
282. quiet(fred) <- (35) [avatar component clause 281]
305. ~quiet(X0) | creative(X0) [resolution 99,79]
325. humble(fred) | quiet(fred) <- (12) [resolution 105,178]
328. quiet(fred) <- (~7, 12) [subsumption resolution 325,154]
329. 35 | 7 | ~12 [avatar split clause 328,176,153,281]
331. quiet(fred) | creative(fred) <- (7) [resolution 155,75]
338. creative(fred) <- (7) [subsumption resolution 331,305]
342. wise(fred) <- (7) [resolution 338,93]
343. $false <- (7) [subsumption resolution 342,125]
344. ~7 [avatar contradiction clause 343]
345. $false <- (11, ~12) [subsumption resolution 177,174]
346. ~11 | 12 [avatar contradiction clause 345]
350. wise(fred) <- (35) [resolution 282,100]
354. $false <- (35) [subsumption resolution 350,125]
355. ~35 [avatar contradiction clause 354]
356. $false [avatar sat refutation 186,329,344,346,355]
% SZS output end Proof for 1013840362585577959739679
% ------------------------------
% 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not old is calm and vice versa. If someone is patient then mary is patient. If someone is not brave or kind then lucy is both not creative and not humble and vice versa. Everyone who is wise is either not funny or not calm. Everyone who is either not generous or curious is either not funny or not calm. If someone is not patient then fred is either patient or brave. Everyone who is either not creative or patient is not tall or not brave. If susan is quiet or not kind then someone is not tall or not strong. Everyone who is both not generous and not calm is funny. Everyone who is not creative is either not happy or wise. Everyone who is not patient is both not quiet and not happy. Everyone who is either quiet or not happy is either not funny or brave and vice versa. Everyone who is not happy or curious is both not kind and brave. If paul is both not quiet and brave then susan is quiet and vice versa. If someone is either brave or curious then someone is not curious or not kind and vice versa. If john is not strong then susan is either not brave or brave. Someone is both not quiet and not rich. Someone is either not humble or not creative. Alice is not humble or happy. Lucy is either happy or not quiet. Paul is either not patient or brave. Mary is either strong or not rich. Someone is tall or not kind. Someone is both creative and not quiet. | Lucy is not calm. | contradiction | (![X]:((old(X)|~old(X))<=>calm(X)))&
((?[X]:(patient(X)))=>(patient(mary)))&
((?[X]:((~brave(X)|kind(X))))<=>((~creative(lucy)&~humble(lucy))))&
(![X]:(wise(X)=>(~funny(X)<~>~calm(X))))&
(![X]:((~generous(X)<~>curious(X))=>(~funny(X)<~>~calm(X))))&
((?[X]:(~patient(X)))=>((patient(fred)<~>brave(fred))))&
(![X]:((~creative(X)<~>patient(X))=>(~tall(X)|~brave(X))))&
(((quiet(susan)|~kind(susan)))=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:((~generous(X)&~calm(X))=>funny(X)))&
(![X]:(~creative(X)=>(~happy(X)<~>wise(X))))&
(![X]:(~patient(X)=>(~quiet(X)&~happy(X))))&
(![X]:((quiet(X)<~>~happy(X))<=>(~funny(X)<~>brave(X))))&
(![X]:((~happy(X)|curious(X))=>(~kind(X)&brave(X))))&
(((~quiet(paul)&brave(paul)))<=>(quiet(susan)))&
((?[X]:((brave(X)<~>curious(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((~strong(john))=>((~brave(susan)<~>brave(susan))))&
(?[X]:((~quiet(X)&~rich(X))))&
(?[X]:((~humble(X)<~>~creative(X))))&
((~humble(alice)|happy(alice)))&
((happy(lucy)<~>~quiet(lucy)))&
((~patient(paul)<~>brave(paul)))&
((strong(mary)<~>~rich(mary)))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((creative(X)&~quiet(X)))) | ~calm(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1219507177677192752942123
% SZS output start Proof for 1219507177677192752942123
1. ! [X0] : ((~old(X0) | old(X0)) <=> calm(X0)) [input p0]
25. ~calm(lucy) [input hypothesis]
40. ! [X0] : (((~old(X0) | old(X0)) | ~calm(X0)) & (calm(X0) | (old(X0) & ~old(X0)))) [nnf transformation 1]
41. ! [X0] : ((~old(X0) | old(X0) | ~calm(X0)) & (calm(X0) | (old(X0) & ~old(X0)))) [flattening 40]
75. calm(X0) | ~old(X0) [cnf transformation 41]
76. calm(X0) | old(X0) [cnf transformation 41]
138. ~calm(lucy) [cnf transformation 25]
139. calm(X0) [subsumption resolution 75,76]
296. $false [subsumption resolution 138,139]
% SZS output end Proof for 1219507177677192752942123
% ------------------------------
% 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 mary is not kind then someone is rich and vice versa. If someone is not generous then someone is not funny and vice versa. If someone is either not brave or not old then someone is not strong or kind and vice versa. Everyone who is strong is tall or humble. Everyone who is both not generous and tall is generous or quiet and vice versa. Everyone who is not humble is happy or not funny and vice versa. Everyone who is both not kind and rich is not calm and vice versa. Everyone who is humble is humble or happy. If susan is either not creative or wise then someone is either creative or not strong. Everyone who is quiet or not rich is not tall or curious and vice versa. Everyone who is either not tall or creative is both not humble and not curious. Everyone who is both not rich and patient is both creative and not creative and vice versa. Everyone who is patient is strong or not tall. Everyone who is either kind or brave is either not wise or not quiet and vice versa. If someone is both not old and curious then mary is not kind. Alice is curious or not generous. Someone is not humble or not tall. Fred is old or generous. Fred is either kind or not quiet. Lucy is not wise or brave. Someone is old. Susan is not wise or not humble. Someone is quiet or funny. | Lucy is not generous. | entailment | ((~kind(mary))<=>(?[X]:(rich(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~brave(X)<~>~old(X))))<=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:(strong(X)=>(tall(X)|humble(X))))&
(![X]:((~generous(X)&tall(X))<=>(generous(X)|quiet(X))))&
(![X]:(~humble(X)<=>(happy(X)|~funny(X))))&
(![X]:((~kind(X)&rich(X))<=>~calm(X)))&
(![X]:(humble(X)=>(humble(X)|happy(X))))&
(((~creative(susan)<~>wise(susan)))=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((quiet(X)|~rich(X))<=>(~tall(X)|curious(X))))&
(![X]:((~tall(X)<~>creative(X))=>(~humble(X)&~curious(X))))&
(![X]:((~rich(X)&patient(X))<=>(creative(X)&~creative(X))))&
(![X]:(patient(X)=>(strong(X)|~tall(X))))&
(![X]:((kind(X)<~>brave(X))<=>(~wise(X)<~>~quiet(X))))&
((?[X]:((~old(X)&curious(X))))=>(~kind(mary)))&
((curious(alice)|~generous(alice)))&
(?[X]:((~humble(X)|~tall(X))))&
((old(fred)|generous(fred)))&
((kind(fred)<~>~quiet(fred)))&
((~wise(lucy)|brave(lucy)))&
(?[X]:(old(X)))&
((~wise(susan)|~humble(susan)))&
(?[X]:((quiet(X)|funny(X)))) | ~generous(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8352380912870922115700489
% SZS output start Proof for 8352380912870922115700489
5. ! [X0] : ((tall(X0) & ~generous(X0)) <=> (quiet(X0) | generous(X0))) [input p4]
24. generous(lucy) [input hypothesis]
50. ! [X0] : (((tall(X0) & ~generous(X0)) | (~quiet(X0) & ~generous(X0))) & ((quiet(X0) | generous(X0)) | (~tall(X0) | generous(X0)))) [nnf transformation 5]
51. ! [X0] : (((tall(X0) & ~generous(X0)) | (~quiet(X0) & ~generous(X0))) & (quiet(X0) | generous(X0) | ~tall(X0) | generous(X0))) [flattening 50]
82. ~generous(X0) | ~generous(X0) [cnf transformation 51]
125. generous(lucy) [cnf transformation 24]
127. ~generous(X0) [duplicate literal removal 82]
262. $false [subsumption resolution 125,127]
% SZS output end Proof for 8352380912870922115700489
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or kind then alice is funny and vice versa. Everyone who is either wise or calm is funny. If paul is not brave then someone is not curious and vice versa. Everyone who is patient or quiet is both old and not humble. Everyone who is happy or creative is either curious or not old and vice versa. Everyone who is both quiet and not funny is not kind or rich. Everyone who is both not calm and not humble is both not rich and creative and vice versa. Everyone who is either not happy or not quiet is not happy. If fred is happy then someone is calm or strong. If paul is not funny then someone is both generous and happy and vice versa. Everyone who is both not happy and not quiet is both not kind and not old. Everyone who is either generous or strong is not strong or not generous and vice versa. If someone is both not rich and kind then paul is either not tall or curious and vice versa. Everyone who is not kind is both funny and curious and vice versa. If someone is both not humble and strong then susan is humble or not creative. Everyone who is creative or not happy is funny or not creative and vice versa. Someone is both not funny and tall. Someone is tall or old. Someone is not quiet. Someone is either happy or brave. Someone is both humble and not calm. Someone is rich. | Fred is not old. | neutral | ((?[X]:((strong(X)|kind(X))))<=>(funny(alice)))&
(![X]:((wise(X)<~>calm(X))=>funny(X)))&
((~brave(paul))<=>(?[X]:(~curious(X))))&
(![X]:((patient(X)|quiet(X))=>(old(X)&~humble(X))))&
(![X]:((happy(X)|creative(X))<=>(curious(X)<~>~old(X))))&
(![X]:((quiet(X)&~funny(X))=>(~kind(X)|rich(X))))&
(![X]:((~calm(X)&~humble(X))<=>(~rich(X)&creative(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>~happy(X)))&
((happy(fred))=>(?[X]:((calm(X)|strong(X)))))&
((~funny(paul))<=>(?[X]:((generous(X)&happy(X)))))&
(![X]:((~happy(X)&~quiet(X))=>(~kind(X)&~old(X))))&
(![X]:((generous(X)<~>strong(X))<=>(~strong(X)|~generous(X))))&
((?[X]:((~rich(X)&kind(X))))<=>((~tall(paul)<~>curious(paul))))&
(![X]:(~kind(X)<=>(funny(X)&curious(X))))&
((?[X]:((~humble(X)&strong(X))))=>((humble(susan)|~creative(susan))))&
(![X]:((creative(X)|~happy(X))<=>(funny(X)|~creative(X))))&
(?[X]:((~funny(X)&tall(X))))&
(?[X]:((tall(X)|old(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((happy(X)<~>brave(X))))&
(?[X]:((humble(X)&~calm(X))))&
(?[X]:(rich(X))) | ~old(fred) | [] | null | 0 |
Everyone who is not creative is both creative and happy and vice versa.
If someone is quiet or wise then susan is both not brave and not wise.
If someone is both not old and strong then someone is both not calm and brave and vice versa.
Everyone who is strong or not quiet is not happy or not rich.
If someone is generous then mary is either not happy or rich and vice versa.
If john is not brave or not happy then someone is patient or not tall and vice versa.
Everyone who is kind or generous is both rich and not calm.
Everyone who is funny is either calm or not rich.
Everyone who is either not strong or not generous is tall or not strong.
If paul is either funny or creative then someone is funny or not curious.
If paul is both creative and not humble then someone is strong or not quiet.
Everyone who is either quiet or creative is not generous.
If mary is not creative then someone is not brave.
Everyone who is old or not old is kind.
Everyone who is generous is both not patient and not curious and vice versa.
Someone is rich.
Paul is either not funny or not curious.
Someone is either wise or not tall.
Fred is either not brave or not quiet.
Someone is strong.
John is both not tall and patient. | Fred is not happy. | entailment | (![X]:(~creative(X)<=>(creative(X)&happy(X))))&
((?[X]:((quiet(X)|wise(X))))=>((~brave(susan)&~wise(susan))))&
((?[X]:((~old(X)&strong(X))))<=>(?[X]:((~calm(X)&brave(X)))))&
(![X]:((strong(X)|~quiet(X))=>(~happy(X)|~rich(X))))&
((?[X]:(generous(X)))<=>((~happy(mary)<~>rich(mary))))&
(((~brave(john)|~happy(john)))<=>(?[X]:((patient(X)|~tall(X)))))&
(![X]:((kind(X)|generous(X))=>(rich(X)&~calm(X))))&
(![X]:(funny(X)=>(calm(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(tall(X)|~strong(X))))&
(((funny(paul)<~>creative(paul)))=>(?[X]:((funny(X)|~curious(X)))))&
(((creative(paul)&~humble(paul)))=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((quiet(X)<~>creative(X))=>~generous(X)))&
((~creative(mary))=>(?[X]:(~brave(X))))&
(![X]:((old(X)|~old(X))=>kind(X)))&
(![X]:(generous(X)<=>(~patient(X)&~curious(X))))&
(?[X]:(rich(X)))&
((~funny(paul)<~>~curious(paul)))&
(?[X]:((wise(X)<~>~tall(X))))&
((~brave(fred)<~>~quiet(fred)))&
(?[X]:(strong(X)))&
((~tall(john)&patient(john))) | ~happy(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8672374082275296251677723
% SZS output start Proof for 8672374082275296251677723
1. ! [X0] : (~creative(X0) <=> (happy(X0) & creative(X0))) [input p0]
22. happy(fred) [input hypothesis]
36. ! [X0] : ((~creative(X0) | (~happy(X0) | ~creative(X0))) & ((happy(X0) & creative(X0)) | creative(X0))) [nnf transformation 1]
37. ! [X0] : ((~creative(X0) | ~happy(X0) | ~creative(X0)) & ((happy(X0) & creative(X0)) | creative(X0))) [flattening 36]
71. creative(X0) | creative(X0) [cnf transformation 37]
73. ~creative(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 37]
120. happy(fred) [cnf transformation 22]
122. creative(X0) [duplicate literal removal 71]
123. ~happy(X0) | ~creative(X0) [duplicate literal removal 73]
265. ~creative(fred) [resolution 123,120]
267. $false [subsumption resolution 265,122]
% SZS output end Proof for 8672374082275296251677723
% ------------------------------
% 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 brave and not calm is patient. Everyone who is generous or calm is old and vice versa. If someone is either not rich or not generous then someone is both not happy and old and vice versa. Everyone who is curious or not rich is either not humble or not quiet and vice versa. If alice is curious then someone is either generous or curious and vice versa. Everyone who is both not generous and not quiet is not calm and vice versa. Everyone who is either not patient or tall is not creative. If lucy is not quiet or not calm then someone is rich or strong and vice versa. If fred is calm or not generous then susan is quiet or not creative and vice versa. If someone is not generous then someone is either not wise or not happy and vice versa. If someone is not curious or not kind then someone is both not happy and humble and vice versa. Everyone who is not funny or old is quiet. Everyone who is both not quiet and quiet is either patient or not old and vice versa. Everyone who is creative is either not brave or not old and vice versa. If mary is both happy and generous then someone is not curious or humble and vice versa. If someone is either kind or not old then someone is both not creative and tall. Lucy is not patient or not humble. Someone is not quiet or strong. Fred is both not funny and not wise. Someone is curious. Paul is patient. Mary is not old or not humble. Fred is either not strong or funny. Someone is not generous or not tall. | Fred is not strong. | entailment | (![X]:((~brave(X)&~calm(X))=>patient(X)))&
(![X]:((generous(X)|calm(X))<=>old(X)))&
((?[X]:((~rich(X)<~>~generous(X))))<=>(?[X]:((~happy(X)&old(X)))))&
(![X]:((curious(X)|~rich(X))<=>(~humble(X)<~>~quiet(X))))&
((curious(alice))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~generous(X)&~quiet(X))<=>~calm(X)))&
(![X]:((~patient(X)<~>tall(X))=>~creative(X)))&
(((~quiet(lucy)|~calm(lucy)))<=>(?[X]:((rich(X)|strong(X)))))&
(((calm(fred)|~generous(fred)))<=>((quiet(susan)|~creative(susan))))&
((?[X]:(~generous(X)))<=>(?[X]:((~wise(X)<~>~happy(X)))))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((~happy(X)&humble(X)))))&
(![X]:((~funny(X)|old(X))=>quiet(X)))&
(![X]:((~quiet(X)&quiet(X))<=>(patient(X)<~>~old(X))))&
(![X]:(creative(X)<=>(~brave(X)<~>~old(X))))&
(((happy(mary)&generous(mary)))<=>(?[X]:((~curious(X)|humble(X)))))&
((?[X]:((kind(X)<~>~old(X))))=>(?[X]:((~creative(X)&tall(X)))))&
((~patient(lucy)|~humble(lucy)))&
(?[X]:((~quiet(X)|strong(X))))&
((~funny(fred)&~wise(fred)))&
(?[X]:(curious(X)))&
(patient(paul))&
((~old(mary)|~humble(mary)))&
((~strong(fred)<~>funny(fred)))&
(?[X]:((~generous(X)|~tall(X)))) | ~strong(fred) | [
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6783910929968962428945096
% SZS output start Proof for 6783910929968962428945096
19. ~wise(fred) & ~funny(fred) [input p18]
23. ~strong(fred) <~> funny(fred) [input p22]
25. strong(fred) [input hypothesis]
84. (~funny(fred) | strong(fred)) & (funny(fred) | ~strong(fred)) [nnf transformation 23]
152. ~funny(fred) [cnf transformation 19]
157. funny(fred) | ~strong(fred) [cnf transformation 84]
160. strong(fred) [cnf transformation 25]
387. ~strong(fred) [subsumption resolution 157,152]
397. $false [subsumption resolution 160,387]
% SZS output end Proof for 6783910929968962428945096
% ------------------------------
% 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both quiet and not old then someone is not patient or not brave and vice versa.
Everyone who is both curious and not tall is either funny or quiet.
If someone is either happy or rich then john is either creative or curious.
If susan is both not curious and not calm then someone is tall or not quiet and vice versa.
Everyone who is either not patient or not rich is not rich or not strong and vice versa.
Everyone who is either not generous or not old is both brave and generous and vice versa.
Everyone who is not wise or not brave is both not patient and not humble and vice versa.
If someone is both not humble and not kind then fred is not quiet or old and vice versa.
If someone is rich or not calm then fred is either not humble or old and vice versa.
Everyone who is generous or humble is either not funny or patient and vice versa.
If someone is old then someone is both brave and not old.
If someone is both happy and wise then someone is both not generous and funny.
If alice is either humble or funny then alice is quiet or kind.
Everyone who is not curious or not quiet is not strong and vice versa.
Everyone who is not creative is both not patient and happy and vice versa.
Everyone who is rich or happy is not creative or kind and vice versa.
Someone is funny or not creative.
Alice is patient.
Someone is curious.
Fred is tall.
Fred is kind.
Alice is not strong.
Alice is not rich or not old. | Susan is calm. | contradiction | (((quiet(paul)&~old(paul)))<=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((curious(X)&~tall(X))=>(funny(X)<~>quiet(X))))&
((?[X]:((happy(X)<~>rich(X))))=>((creative(john)<~>curious(john))))&
(((~curious(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~quiet(X)))))&
(![X]:((~patient(X)<~>~rich(X))<=>(~rich(X)|~strong(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(brave(X)&generous(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~patient(X)&~humble(X))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~quiet(fred)|old(fred))))&
((?[X]:((rich(X)|~calm(X))))<=>((~humble(fred)<~>old(fred))))&
(![X]:((generous(X)|humble(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:(old(X)))=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((humble(alice)<~>funny(alice)))=>((quiet(alice)|kind(alice))))&
(![X]:((~curious(X)|~quiet(X))<=>~strong(X)))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(![X]:((rich(X)|happy(X))<=>(~creative(X)|kind(X))))&
(?[X]:((funny(X)|~creative(X))))&
(patient(alice))&
(?[X]:(curious(X)))&
(tall(fred))&
(kind(fred))&
(~strong(alice))&
((~rich(alice)|~old(alice))) | calm(susan) | [
"p3",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2153933563051467236230815
% SZS output start Proof for 2153933563051467236230815
4. (~calm(susan) & ~curious(susan)) <=> ? [X0] : (~quiet(X0) | tall(X0)) [input p3]
20. tall(fred) [input p19]
24. calm(susan) [input hypothesis]
41. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & (? [X0] : (~quiet(X0) | tall(X0)) | (calm(susan) | curious(susan))) [nnf transformation 4]
42. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & (? [X0] : (~quiet(X0) | tall(X0)) | calm(susan) | curious(susan)) [flattening 41]
43. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & (? [X1] : (~quiet(X1) | tall(X1)) | calm(susan) | curious(susan)) [rectify 42]
44. ? [X1] : (~quiet(X1) | tall(X1)) => (~quiet(sK1) | tall(sK1)) [choice axiom]
45. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & ((~quiet(sK1) | tall(sK1)) | calm(susan) | curious(susan)) [skolemisation 43,44]
94. ~calm(susan) | ~tall(X0) [cnf transformation 45]
149. tall(fred) [cnf transformation 20]
153. calm(susan) [cnf transformation 24]
207. 12 <=> calm(susan) [avatar definition]
212. 13 <=> ! [X0] : ~tall(X0) [avatar definition]
213. ~tall(X0) <- (13) [avatar component clause 212]
214. 13 | ~12 [avatar split clause 94,207,212]
341. 12 [avatar split clause 153,207]
342. $false <- (13) [resolution 213,149]
343. ~13 [avatar contradiction clause 342]
344. $false [avatar sat refutation 214,341,343]
% SZS output end Proof for 2153933563051467236230815
% ------------------------------
% 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 both happy and not old is either not curious or not rich and vice versa.
If someone is both not calm and not humble then lucy is both not funny and not curious.
Everyone who is either not strong or patient is calm or patient.
Everyone who is either not kind or not quiet is not strong.
If someone is either not quiet or old then lucy is not quiet or tall and vice versa.
Everyone who is either not tall or not calm is either brave or not calm.
If someone is not kind then fred is either not wise or not humble and vice versa.
If john is generous or not brave then someone is wise.
If someone is both generous and not quiet then susan is not kind or strong.
Everyone who is both strong and not kind is either quiet or not wise.
Everyone who is both humble and quiet is both not kind and not rich.
If someone is not patient or rich then someone is not rich or not quiet.
Everyone who is either patient or not happy is generous and vice versa.
Everyone who is tall is either quiet or curious.
Everyone who is either not old or kind is funny or not rich.
Everyone who is either not brave or funny is not happy and vice versa.
Fred is strong.
Susan is either quiet or not curious.
Fred is either not humble or not brave.
Someone is strong or rich.
Susan is funny or happy.
Someone is both tall and not rich.
Alice is generous.
Fred is not happy or not curious. | Alice is kind. | neutral | (![X]:((happy(X)&~old(X))<=>(~curious(X)<~>~rich(X))))&
((?[X]:((~calm(X)&~humble(X))))=>((~funny(lucy)&~curious(lucy))))&
(![X]:((~strong(X)<~>patient(X))=>(calm(X)|patient(X))))&
(![X]:((~kind(X)<~>~quiet(X))=>~strong(X)))&
((?[X]:((~quiet(X)<~>old(X))))<=>((~quiet(lucy)|tall(lucy))))&
(![X]:((~tall(X)<~>~calm(X))=>(brave(X)<~>~calm(X))))&
((?[X]:(~kind(X)))<=>((~wise(fred)<~>~humble(fred))))&
(((generous(john)|~brave(john)))=>(?[X]:(wise(X))))&
((?[X]:((generous(X)&~quiet(X))))=>((~kind(susan)|strong(susan))))&
(![X]:((strong(X)&~kind(X))=>(quiet(X)<~>~wise(X))))&
(![X]:((humble(X)&quiet(X))=>(~kind(X)&~rich(X))))&
((?[X]:((~patient(X)|rich(X))))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((patient(X)<~>~happy(X))<=>generous(X)))&
(![X]:(tall(X)=>(quiet(X)<~>curious(X))))&
(![X]:((~old(X)<~>kind(X))=>(funny(X)|~rich(X))))&
(![X]:((~brave(X)<~>funny(X))<=>~happy(X)))&
(strong(fred))&
((quiet(susan)<~>~curious(susan)))&
((~humble(fred)<~>~brave(fred)))&
(?[X]:((strong(X)|rich(X))))&
((funny(susan)|happy(susan)))&
(?[X]:((tall(X)&~rich(X))))&
(generous(alice))&
((~happy(fred)|~curious(fred))) | kind(alice) | [] | null | 0 |
Everyone who is either tall or rich is both rich and not strong and vice versa. If alice is funny then paul is not old or strong. Everyone who is happy is not patient and vice versa. Everyone who is not quiet or rich is curious. Everyone who is either curious or not patient is funny. Everyone who is brave or humble is both humble and not humble and vice versa. Everyone who is either not strong or not quiet is not calm. Everyone who is generous is both humble and generous and vice versa. Everyone who is either rich or not strong is either not quiet or not tall and vice versa. Everyone who is either funny or happy is both wise and quiet. If someone is generous or rich then someone is not curious or not humble. Everyone who is brave is either not generous or tall. If someone is not curious or wise then someone is either not old or happy. Everyone who is not generous or not happy is not calm and vice versa. Everyone who is either wise or not calm is not humble or not curious. Everyone who is not calm is either not brave or creative. Fred is patient. Paul is not tall or not rich. Susan is both kind and not creative. Someone is curious. Susan is not quiet or not creative. Someone is strong or generous. | Fred is generous. | contradiction | (![X]:((tall(X)<~>rich(X))<=>(rich(X)&~strong(X))))&
((funny(alice))=>((~old(paul)|strong(paul))))&
(![X]:(happy(X)<=>~patient(X)))&
(![X]:((~quiet(X)|rich(X))=>curious(X)))&
(![X]:((curious(X)<~>~patient(X))=>funny(X)))&
(![X]:((brave(X)|humble(X))<=>(humble(X)&~humble(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>~calm(X)))&
(![X]:(generous(X)<=>(humble(X)&generous(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((funny(X)<~>happy(X))=>(wise(X)&quiet(X))))&
((?[X]:((generous(X)|rich(X))))=>(?[X]:((~curious(X)|~humble(X)))))&
(![X]:(brave(X)=>(~generous(X)<~>tall(X))))&
((?[X]:((~curious(X)|wise(X))))=>(?[X]:((~old(X)<~>happy(X)))))&
(![X]:((~generous(X)|~happy(X))<=>~calm(X)))&
(![X]:((wise(X)<~>~calm(X))=>(~humble(X)|~curious(X))))&
(![X]:(~calm(X)=>(~brave(X)<~>creative(X))))&
(patient(fred))&
((~tall(paul)|~rich(paul)))&
((kind(susan)&~creative(susan)))&
(?[X]:(curious(X)))&
((~quiet(susan)|~creative(susan)))&
(?[X]:((strong(X)|generous(X)))) | generous(fred) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2229690577314777360976003
% SZS output start Proof for 2229690577314777360976003
6. ! [X0] : ((humble(X0) | brave(X0)) <=> (~humble(X0) & humble(X0))) [input p5]
8. ! [X0] : (generous(X0) <=> (generous(X0) & humble(X0))) [input p7]
23. generous(fred) [input hypothesis]
43. ! [X0] : (((humble(X0) | brave(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (~humble(X0) & ~brave(X0)))) [nnf transformation 6]
44. ! [X0] : ((humble(X0) | brave(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (~humble(X0) & ~brave(X0)))) [flattening 43]
46. ! [X0] : ((generous(X0) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | ~generous(X0))) [nnf transformation 8]
47. ! [X0] : ((generous(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | ~generous(X0))) [flattening 46]
82. ~humble(X0) | ~humble(X0) [cnf transformation 44]
86. humble(X0) | ~generous(X0) [cnf transformation 47]
122. generous(fred) [cnf transformation 23]
123. ~humble(X0) [duplicate literal removal 82]
141. ~generous(X0) [subsumption resolution 86,123]
170. $false [subsumption resolution 122,141]
% SZS output end Proof for 2229690577314777360976003
% ------------------------------
% 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not old or not wise then paul is either not patient or not wise. If someone is both not strong and brave then john is both patient and not creative and vice versa. If someone is either not tall or not old then someone is happy. Everyone who is either kind or wise is either not kind or not brave and vice versa. If someone is both humble and old then john is not tall or not wise and vice versa. If alice is not kind then someone is quiet or wise and vice versa. Everyone who is humble or tall is not strong and vice versa. If lucy is curious or not brave then alice is patient or not curious. If john is both happy and funny then alice is either not tall or not brave. Everyone who is not funny or quiet is either kind or brave and vice versa. Everyone who is both not kind and patient is both not funny and humble. Everyone who is calm or old is either kind or not brave. If john is either generous or rich then someone is either not funny or not curious and vice versa. Everyone who is not brave or strong is both not rich and curious. Everyone who is not wise or creative is both not rich and not happy. Everyone who is not brave is happy or not strong and vice versa. Fred is either not brave or not old. John is both not rich and kind. Someone is not happy or curious. Lucy is either curious or strong. Lucy is both not kind and not wise. Someone is either happy or generous. | John is not curious. | contradiction | (((~old(paul)<~>~wise(paul)))=>((~patient(paul)<~>~wise(paul))))&
((?[X]:((~strong(X)&brave(X))))<=>((patient(john)&~creative(john))))&
((?[X]:((~tall(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(![X]:((kind(X)<~>wise(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:((humble(X)&old(X))))<=>((~tall(john)|~wise(john))))&
((~kind(alice))<=>(?[X]:((quiet(X)|wise(X)))))&
(![X]:((humble(X)|tall(X))<=>~strong(X)))&
(((curious(lucy)|~brave(lucy)))=>((patient(alice)|~curious(alice))))&
(((happy(john)&funny(john)))=>((~tall(alice)<~>~brave(alice))))&
(![X]:((~funny(X)|quiet(X))<=>(kind(X)<~>brave(X))))&
(![X]:((~kind(X)&patient(X))=>(~funny(X)&humble(X))))&
(![X]:((calm(X)|old(X))=>(kind(X)<~>~brave(X))))&
(((generous(john)<~>rich(john)))<=>(?[X]:((~funny(X)<~>~curious(X)))))&
(![X]:((~brave(X)|strong(X))=>(~rich(X)&curious(X))))&
(![X]:((~wise(X)|creative(X))=>(~rich(X)&~happy(X))))&
(![X]:(~brave(X)<=>(happy(X)|~strong(X))))&
((~brave(fred)<~>~old(fred)))&
((~rich(john)&kind(john)))&
(?[X]:((~happy(X)|curious(X))))&
((curious(lucy)<~>strong(lucy)))&
((~kind(lucy)&~wise(lucy)))&
(?[X]:((happy(X)<~>generous(X)))) | ~curious(john) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5906605581534702814552944
% SZS output start Proof for 5906605581534702814552944
14. ! [X0] : ((strong(X0) | ~brave(X0)) => (curious(X0) & ~rich(X0))) [input p13]
16. ! [X0] : (~brave(X0) <=> (~strong(X0) | happy(X0))) [input p15]
23. ~curious(john) [input hypothesis]
35. ! [X0] : ((curious(X0) & ~rich(X0)) | (~strong(X0) & brave(X0))) [ennf transformation 14]
67. ! [X0] : ((~brave(X0) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | brave(X0))) [nnf transformation 16]
68. ! [X0] : ((~brave(X0) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | brave(X0))) [flattening 67]
129. curious(X0) | brave(X0) [cnf transformation 35]
130. ~strong(X0) | curious(X0) [cnf transformation 35]
137. ~brave(X0) | strong(X0) [cnf transformation 68]
149. ~curious(john) [cnf transformation 23]
189. 8 <=> ! [X1] : (~brave(X1) | strong(X1)) [avatar definition]
190. ~brave(X1) | strong(X1) <- (8) [avatar component clause 189]
318. 8 [avatar split clause 137,189]
353. brave(john) [resolution 129,149]
363. strong(john) <- (8) [resolution 190,353]
368. curious(john) <- (8) [resolution 363,130]
369. $false <- (8) [subsumption resolution 368,149]
370. ~8 [avatar contradiction clause 369]
371. $false [avatar sat refutation 318,370]
% SZS output end Proof for 5906605581534702814552944
% ------------------------------
% 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 funny or not old then fred is curious and vice versa. Everyone who is kind is both patient and tall and vice versa. Everyone who is both not happy and tall is both curious and creative. Everyone who is not creative is either not kind or not rich and vice versa. If someone is both not strong and kind then alice is quiet. Everyone who is brave or quiet is not creative or not brave and vice versa. If susan is either wise or not humble then someone is not strong or creative. Everyone who is generous or not generous is both humble and creative and vice versa. Everyone who is either humble or not quiet is both tall and not old and vice versa. If mary is strong or not rich then paul is both not strong and not wise. Everyone who is generous or not brave is either old or not funny. If someone is both not wise and not calm then lucy is not happy or funny and vice versa. Everyone who is both tall and not rich is not tall and vice versa. If john is tall or not patient then someone is both kind and calm. Everyone who is calm or curious is both not brave and not wise and vice versa. Everyone who is calm or not rich is either not generous or patient and vice versa. Someone is both not happy and creative. Someone is either curious or not patient. Lucy is either not old or not kind. Someone is generous. Fred is rich. Someone is old or happy. John is either not brave or not quiet. | Paul is not funny. | entailment | (((~funny(susan)|~old(susan)))<=>(curious(fred)))&
(![X]:(kind(X)<=>(patient(X)&tall(X))))&
(![X]:((~happy(X)&tall(X))=>(curious(X)&creative(X))))&
(![X]:(~creative(X)<=>(~kind(X)<~>~rich(X))))&
((?[X]:((~strong(X)&kind(X))))=>(quiet(alice)))&
(![X]:((brave(X)|quiet(X))<=>(~creative(X)|~brave(X))))&
(((wise(susan)<~>~humble(susan)))=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:((generous(X)|~generous(X))<=>(humble(X)&creative(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(tall(X)&~old(X))))&
(((strong(mary)|~rich(mary)))=>((~strong(paul)&~wise(paul))))&
(![X]:((generous(X)|~brave(X))=>(old(X)<~>~funny(X))))&
((?[X]:((~wise(X)&~calm(X))))<=>((~happy(lucy)|funny(lucy))))&
(![X]:((tall(X)&~rich(X))<=>~tall(X)))&
(((tall(john)|~patient(john)))=>(?[X]:((kind(X)&calm(X)))))&
(![X]:((calm(X)|curious(X))<=>(~brave(X)&~wise(X))))&
(![X]:((calm(X)|~rich(X))<=>(~generous(X)<~>patient(X))))&
(?[X]:((~happy(X)&creative(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
((~old(lucy)<~>~kind(lucy)))&
(?[X]:(generous(X)))&
(rich(fred))&
(?[X]:((old(X)|happy(X))))&
((~brave(john)<~>~quiet(john))) | ~funny(paul) | [
"p5",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5855238225235188336514466
% SZS output start Proof for 5855238225235188336514466
6. ! [X0] : ((quiet(X0) | brave(X0)) <=> (~brave(X0) | ~creative(X0))) [input p5]
8. ! [X0] : ((~generous(X0) | generous(X0)) <=> (creative(X0) & humble(X0))) [input p7]
9. ! [X0] : ((humble(X0) <~> ~quiet(X0)) <=> (~old(X0) & tall(X0))) [input p8]
11. ! [X0] : ((~brave(X0) | generous(X0)) => (old(X0) <~> ~funny(X0))) [input p10]
24. funny(paul) [input hypothesis]
30. ! [X0] : ((old(X0) <~> ~funny(X0)) | (brave(X0) & ~generous(X0))) [ennf transformation 11]
37. ! [X0] : (((quiet(X0) | brave(X0)) | (brave(X0) & creative(X0))) & ((~brave(X0) | ~creative(X0)) | (~quiet(X0) & ~brave(X0)))) [nnf transformation 6]
38. ! [X0] : ((quiet(X0) | brave(X0) | (brave(X0) & creative(X0))) & (~brave(X0) | ~creative(X0) | (~quiet(X0) & ~brave(X0)))) [flattening 37]
42. ! [X0] : (((~generous(X0) | generous(X0)) | (~creative(X0) | ~humble(X0))) & ((creative(X0) & humble(X0)) | (generous(X0) & ~generous(X0)))) [nnf transformation 8]
43. ! [X0] : ((~generous(X0) | generous(X0) | ~creative(X0) | ~humble(X0)) & ((creative(X0) & humble(X0)) | (generous(X0) & ~generous(X0)))) [flattening 42]
44. ! [X0] : ((((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (old(X0) | ~tall(X0))) & ((~old(X0) & tall(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0))))) [nnf transformation 9]
45. ! [X0] : ((((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | old(X0) | ~tall(X0)) & ((~old(X0) & tall(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0))))) [flattening 44]
46. ! [X0] : (((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | (brave(X0) & ~generous(X0))) [nnf transformation 30]
84. ~brave(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 38]
85. ~brave(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 38]
87. quiet(X0) | brave(X0) | brave(X0) [cnf transformation 38]
90. humble(X0) | ~generous(X0) [cnf transformation 43]
91. generous(X0) | humble(X0) [cnf transformation 43]
92. creative(X0) | ~generous(X0) [cnf transformation 43]
93. generous(X0) | creative(X0) [cnf transformation 43]
97. ~old(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 45]
106. ~funny(X0) | old(X0) | brave(X0) [cnf transformation 46]
143. funny(paul) [cnf transformation 24]
146. ~brave(X0) | ~creative(X0) [duplicate literal removal 84]
147. brave(X0) | quiet(X0) [duplicate literal removal 87]
189. creative(X0) [subsumption resolution 92,93]
190. humble(X0) [subsumption resolution 90,91]
192. ~quiet(X0) | ~old(X0) [subsumption resolution 97,190]
304. quiet(X0) | ~creative(X0) [resolution 147,146]
307. quiet(X0) [subsumption resolution 304,189]
312. ~old(X0) [resolution 192,307]
356. old(paul) | brave(paul) [resolution 106,143]
358. brave(paul) [subsumption resolution 356,312]
363. ~creative(paul) | ~quiet(paul) [resolution 358,85]
366. ~quiet(paul) [subsumption resolution 363,189]
367. $false [subsumption resolution 366,307]
% SZS output end Proof for 5855238225235188336514466
% ------------------------------
% 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and calm then lucy is both not creative and not wise. If fred is both happy and not curious then alice is both generous and not creative and vice versa. If someone is rich or not brave then someone is not tall and vice versa. If someone is not funny or quiet then someone is not quiet. If someone is not old then mary is either generous or brave. Everyone who is not curious is not generous or not kind. If susan is not generous then alice is strong or rich and vice versa. Everyone who is patient is creative and vice versa. If susan is either not creative or creative then someone is not strong. Everyone who is either not strong or not creative is not brave and vice versa. Everyone who is wise or not calm is both not kind and patient and vice versa. If paul is not happy then susan is either not brave or old. Everyone who is creative or generous is both not old and not calm and vice versa. If john is both not quiet and creative then john is calm and vice versa. Everyone who is both not creative and not curious is both rich and patient and vice versa. If someone is not wise or tall then someone is both not wise and not patient. Mary is not brave. Someone is not funny. Someone is not strong. Someone is not kind. Someone is either not calm or not patient. Someone is not happy. | Mary is kind. | contradiction | ((?[X]:((kind(X)&calm(X))))=>((~creative(lucy)&~wise(lucy))))&
(((happy(fred)&~curious(fred)))<=>((generous(alice)&~creative(alice))))&
((?[X]:((rich(X)|~brave(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~funny(X)|quiet(X))))=>(?[X]:(~quiet(X))))&
((?[X]:(~old(X)))=>((generous(mary)<~>brave(mary))))&
(![X]:(~curious(X)=>(~generous(X)|~kind(X))))&
((~generous(susan))<=>((strong(alice)|rich(alice))))&
(![X]:(patient(X)<=>creative(X)))&
(((~creative(susan)<~>creative(susan)))=>(?[X]:(~strong(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>~brave(X)))&
(![X]:((wise(X)|~calm(X))<=>(~kind(X)&patient(X))))&
((~happy(paul))=>((~brave(susan)<~>old(susan))))&
(![X]:((creative(X)|generous(X))<=>(~old(X)&~calm(X))))&
(((~quiet(john)&creative(john)))<=>(calm(john)))&
(![X]:((~creative(X)&~curious(X))<=>(rich(X)&patient(X))))&
((?[X]:((~wise(X)|tall(X))))=>(?[X]:((~wise(X)&~patient(X)))))&
(~brave(mary))&
(?[X]:(~funny(X)))&
(?[X]:(~strong(X)))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)<~>~patient(X))))&
(?[X]:(~happy(X))) | kind(mary) | [
"p4",
"p7",
"p10",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7127560135145434023641264
% SZS output start Proof for 7127560135145434023641264
5. ? [X0] : ~old(X0) => (generous(mary) <~> brave(mary)) [input p4]
8. ! [X0] : (patient(X0) <=> creative(X0)) [input p7]
11. ! [X0] : ((~calm(X0) | wise(X0)) <=> (patient(X0) & ~kind(X0))) [input p10]
13. ! [X0] : ((generous(X0) | creative(X0)) <=> (~calm(X0) & ~old(X0))) [input p12]
14. (creative(john) & ~quiet(john)) <=> calm(john) [input p13]
17. ~brave(mary) [input p16]
23. kind(mary) [input hypothesis]
29. (generous(mary) <~> brave(mary)) | ! [X0] : old(X0) [ennf transformation 5]
45. ((~brave(mary) | ~generous(mary)) & (brave(mary) | generous(mary))) | ! [X0] : old(X0) [nnf transformation 29]
48. ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 8]
53. ! [X0] : (((~calm(X0) | wise(X0)) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | (calm(X0) & ~wise(X0)))) [nnf transformation 11]
54. ! [X0] : ((~calm(X0) | wise(X0) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | (calm(X0) & ~wise(X0)))) [flattening 53]
56. ! [X0] : (((generous(X0) | creative(X0)) | (calm(X0) | old(X0))) & ((~calm(X0) & ~old(X0)) | (~generous(X0) & ~creative(X0)))) [nnf transformation 13]
57. ! [X0] : ((generous(X0) | creative(X0) | calm(X0) | old(X0)) & ((~calm(X0) & ~old(X0)) | (~generous(X0) & ~creative(X0)))) [flattening 56]
58. ((creative(john) & ~quiet(john)) | ~calm(john)) & (calm(john) | (~creative(john) | quiet(john))) [nnf transformation 14]
59. ((creative(john) & ~quiet(john)) | ~calm(john)) & (calm(john) | ~creative(john) | quiet(john)) [flattening 58]
87. brave(mary) | generous(mary) | old(X0) [cnf transformation 45]
93. ~patient(X0) | creative(X0) [cnf transformation 48]
102. ~kind(X0) | calm(X0) [cnf transformation 54]
104. patient(X0) | calm(X0) [cnf transformation 54]
108. ~old(X0) | ~creative(X0) [cnf transformation 57]
110. ~creative(X0) | ~calm(X0) [cnf transformation 57]
111. ~generous(X0) | ~calm(X0) [cnf transformation 57]
115. creative(john) | ~calm(john) [cnf transformation 59]
124. ~brave(mary) [cnf transformation 17]
131. kind(mary) [cnf transformation 23]
204. 17 <=> ! [X0] : old(X0) [avatar definition]
205. old(X0) <- (17) [avatar component clause 204]
207. 18 <=> generous(mary) [avatar definition]
208. generous(mary) <- (18) [avatar component clause 207]
211. 19 <=> brave(mary) [avatar definition]
215. 17 | 18 | 19 [avatar split clause 87,211,207,204]
255. ~calm(john) [subsumption resolution 115,110]
262. 29 <=> creative(john) [avatar definition]
263. creative(john) <- (29) [avatar component clause 262]
264. ~creative(john) <- (~29) [avatar component clause 262]
286. ~19 [avatar split clause 124,211]
298. calm(mary) [resolution 102,131]
301. creative(X0) | calm(X0) [resolution 104,93]
303. ~calm(mary) <- (18) [resolution 111,208]
304. $false <- (18) [subsumption resolution 303,298]
305. ~18 [avatar contradiction clause 304]
307. ~creative(X1) <- (17) [resolution 205,108]
312. calm(john) <- (~29) [resolution 301,264]
316. $false <- (~29) [subsumption resolution 312,255]
317. 29 [avatar contradiction clause 316]
318. $false <- (17, 29) [subsumption resolution 263,307]
319. ~17 | ~29 [avatar contradiction clause 318]
320. $false [avatar sat refutation 215,286,305,317,319]
% SZS output end Proof for 7127560135145434023641264
% ------------------------------
% 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 creative or kind is either humble or not rich.
Everyone who is either wise or humble is either not quiet or humble.
Everyone who is patient or not wise is strong or brave.
If someone is quiet then fred is either kind or tall and vice versa.
If someone is happy then mary is happy or generous and vice versa.
Everyone who is either not funny or not humble is both not tall and tall.
If someone is creative then susan is rich or not generous and vice versa.
Everyone who is happy is not kind or kind and vice versa.
If someone is not happy then someone is patient or funny and vice versa.
If fred is both not old and not rich then paul is both not strong and old and vice versa.
Everyone who is patient is both creative and not creative and vice versa.
Everyone who is either tall or not patient is both creative and not kind and vice versa.
Everyone who is either kind or not quiet is both generous and not strong.
Everyone who is tall is not strong or kind.
Everyone who is kind or strong is not kind or not calm and vice versa.
Fred is either not calm or not rich.
Someone is not brave or funny.
Someone is both rich and not wise.
Someone is either calm or not quiet.
Susan is creative.
Someone is either funny or not strong. | Mary is humble. | contradiction | (![X]:((creative(X)<~>kind(X))=>(humble(X)<~>~rich(X))))&
(![X]:((wise(X)<~>humble(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((patient(X)|~wise(X))=>(strong(X)|brave(X))))&
((?[X]:(quiet(X)))<=>((kind(fred)<~>tall(fred))))&
((?[X]:(happy(X)))<=>((happy(mary)|generous(mary))))&
(![X]:((~funny(X)<~>~humble(X))=>(~tall(X)&tall(X))))&
((?[X]:(creative(X)))<=>((rich(susan)|~generous(susan))))&
(![X]:(happy(X)<=>(~kind(X)|kind(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((patient(X)|funny(X)))))&
(((~old(fred)&~rich(fred)))<=>((~strong(paul)&old(paul))))&
(![X]:(patient(X)<=>(creative(X)&~creative(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(creative(X)&~kind(X))))&
(![X]:((kind(X)<~>~quiet(X))=>(generous(X)&~strong(X))))&
(![X]:(tall(X)=>(~strong(X)|kind(X))))&
(![X]:((kind(X)|strong(X))<=>(~kind(X)|~calm(X))))&
((~calm(fred)<~>~rich(fred)))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((rich(X)&~wise(X))))&
(?[X]:((calm(X)<~>~quiet(X))))&
(creative(susan))&
(?[X]:((funny(X)<~>~strong(X)))) | humble(mary) | [
"p5",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8610569002307157886638656
% SZS output start Proof for 8610569002307157886638656
6. ! [X0] : ((~funny(X0) <~> ~humble(X0)) => (tall(X0) & ~tall(X0))) [input p5]
8. ! [X0] : (happy(X0) <=> (kind(X0) | ~kind(X0))) [input p7]
9. ? [X0] : ~happy(X0) <=> ? [X0] : (funny(X0) | patient(X0)) [input p8]
22. humble(mary) [input hypothesis]
23. ? [X0] : ~happy(X0) <=> ? [X1] : (funny(X1) | patient(X1)) [rectify 9]
28. ! [X0] : ((tall(X0) & ~tall(X0)) | (~funny(X0) <=> ~humble(X0))) [ennf transformation 6]
43. ! [X0] : ((tall(X0) & ~tall(X0)) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0)))) [nnf transformation 28]
49. ! [X0] : ((happy(X0) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | ~happy(X0))) [nnf transformation 8]
50. ! [X0] : ((happy(X0) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ~happy(X0))) [flattening 49]
51. (? [X0] : ~happy(X0) | ! [X1] : (~funny(X1) & ~patient(X1))) & (? [X1] : (funny(X1) | patient(X1)) | ! [X0] : happy(X0)) [nnf transformation 23]
52. (? [X0] : ~happy(X0) | ! [X1] : (~funny(X1) & ~patient(X1))) & (? [X2] : (funny(X2) | patient(X2)) | ! [X3] : happy(X3)) [rectify 51]
53. ? [X0] : ~happy(X0) => ~happy(sK3) [choice axiom]
54. ? [X2] : (funny(X2) | patient(X2)) => (funny(sK4) | patient(sK4)) [choice axiom]
55. (~happy(sK3) | ! [X1] : (~funny(X1) & ~patient(X1))) & ((funny(sK4) | patient(sK4)) | ! [X3] : happy(X3)) [skolemisation 52,54,53]
93. ~tall(X0) | ~humble(X0) | funny(X0) [cnf transformation 43]
95. tall(X0) | ~humble(X0) | funny(X0) [cnf transformation 43]
101. happy(X0) | kind(X0) [cnf transformation 50]
102. ~kind(X0) | happy(X0) [cnf transformation 50]
105. ~happy(sK3) | ~funny(X1) [cnf transformation 55]
138. humble(mary) [cnf transformation 22]
181. ~humble(X0) | funny(X0) [subsumption resolution 93,95]
200. happy(X0) [subsumption resolution 101,102]
201. ~funny(X1) [subsumption resolution 105,200]
247. funny(mary) [resolution 181,138]
248. $false [subsumption resolution 247,201]
% SZS output end Proof for 8610569002307157886638656
% ------------------------------
% 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 john is not calm then mary is not kind or happy.
Everyone who is not funny or not wise is both funny and not humble.
If someone is humble or not tall then someone is either not tall or not patient.
Everyone who is both not strong and not tall is either not creative or funny and vice versa.
If fred is both tall and humble then someone is either kind or not strong.
If someone is either funny or curious then mary is either generous or wise.
Everyone who is either not happy or calm is either happy or humble.
Everyone who is either strong or not humble is either happy or tall and vice versa.
Everyone who is both calm and funny is both happy and not curious and vice versa.
Everyone who is not funny is either humble or not wise and vice versa.
If fred is not kind then someone is curious or not patient and vice versa.
Everyone who is not strong is not creative or rich and vice versa.
Everyone who is both not creative and rich is both not creative and not strong.
If lucy is either not humble or generous then someone is either kind or generous and vice versa.
If someone is patient or not quiet then someone is wise and vice versa.
Everyone who is kind or not strong is either generous or not kind.
Paul is not quiet or not rich.
Mary is curious or humble.
Someone is either quiet or curious.
Susan is rich or not strong.
Susan is not brave or rich. | John is patient. | neutral | ((~calm(john))=>((~kind(mary)|happy(mary))))&
(![X]:((~funny(X)|~wise(X))=>(funny(X)&~humble(X))))&
((?[X]:((humble(X)|~tall(X))))=>(?[X]:((~tall(X)<~>~patient(X)))))&
(![X]:((~strong(X)&~tall(X))<=>(~creative(X)<~>funny(X))))&
(((tall(fred)&humble(fred)))=>(?[X]:((kind(X)<~>~strong(X)))))&
((?[X]:((funny(X)<~>curious(X))))=>((generous(mary)<~>wise(mary))))&
(![X]:((~happy(X)<~>calm(X))=>(happy(X)<~>humble(X))))&
(![X]:((strong(X)<~>~humble(X))<=>(happy(X)<~>tall(X))))&
(![X]:((calm(X)&funny(X))<=>(happy(X)&~curious(X))))&
(![X]:(~funny(X)<=>(humble(X)<~>~wise(X))))&
((~kind(fred))<=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:(~strong(X)<=>(~creative(X)|rich(X))))&
(![X]:((~creative(X)&rich(X))=>(~creative(X)&~strong(X))))&
(((~humble(lucy)<~>generous(lucy)))<=>(?[X]:((kind(X)<~>generous(X)))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
((~quiet(paul)|~rich(paul)))&
((curious(mary)|humble(mary)))&
(?[X]:((quiet(X)<~>curious(X))))&
((rich(susan)|~strong(susan)))&
((~brave(susan)|rich(susan))) | patient(john) | [] | null | 0 |
If someone is either kind or brave then someone is either funny or strong. Everyone who is either not wise or funny is creative or not happy. If lucy is not humble or not old then susan is both not old and not patient. Everyone who is either old or wise is both not calm and not tall and vice versa. Everyone who is either not humble or not old is either not tall or not quiet and vice versa. If alice is both creative and not curious then someone is generous or strong and vice versa. Everyone who is not funny is both not happy and not humble. If someone is wise or not tall then someone is either old or wise. If fred is wise then someone is funny and vice versa. If someone is patient or not rich then someone is either not quiet or not brave. Everyone who is not funny or patient is rich and vice versa. If someone is not rich or happy then someone is not kind or happy and vice versa. Everyone who is rich or not funny is happy or generous. Everyone who is not tall is either not old or not calm and vice versa. If susan is both wise and patient then someone is creative or brave and vice versa. If susan is either happy or creative then susan is both not curious and old. Someone is both generous and humble. Someone is not brave. Mary is both not generous and not creative. Someone is either not old or not calm. Alice is both tall and not curious. Paul is not curious. Someone is both rich and happy. Alice is not generous or curious. | Alice is funny. | entailment | ((?[X]:((kind(X)<~>brave(X))))=>(?[X]:((funny(X)<~>strong(X)))))&
(![X]:((~wise(X)<~>funny(X))=>(creative(X)|~happy(X))))&
(((~humble(lucy)|~old(lucy)))=>((~old(susan)&~patient(susan))))&
(![X]:((old(X)<~>wise(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(~tall(X)<~>~quiet(X))))&
(((creative(alice)&~curious(alice)))<=>(?[X]:((generous(X)|strong(X)))))&
(![X]:(~funny(X)=>(~happy(X)&~humble(X))))&
((?[X]:((wise(X)|~tall(X))))=>(?[X]:((old(X)<~>wise(X)))))&
((wise(fred))<=>(?[X]:(funny(X))))&
((?[X]:((patient(X)|~rich(X))))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(![X]:((~funny(X)|patient(X))<=>rich(X)))&
((?[X]:((~rich(X)|happy(X))))<=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((rich(X)|~funny(X))=>(happy(X)|generous(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>~calm(X))))&
(((wise(susan)&patient(susan)))<=>(?[X]:((creative(X)|brave(X)))))&
(((happy(susan)<~>creative(susan)))=>((~curious(susan)&old(susan))))&
(?[X]:((generous(X)&humble(X))))&
(?[X]:(~brave(X)))&
((~generous(mary)&~creative(mary)))&
(?[X]:((~old(X)<~>~calm(X))))&
((tall(alice)&~curious(alice)))&
(~curious(paul))&
(?[X]:((rich(X)&happy(X))))&
((~generous(alice)|curious(alice))) | funny(alice) | [
"p6",
"p12",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3356972959157713092793551
% SZS output start Proof for 3356972959157713092793551
7. ! [X0] : (~funny(X0) => (~humble(X0) & ~happy(X0))) [input p6]
13. ! [X0] : ((~funny(X0) | rich(X0)) => (generous(X0) | happy(X0))) [input p12]
21. ~curious(alice) & tall(alice) [input p20]
24. curious(alice) | ~generous(alice) [input p23]
25. ~funny(alice) [input hypothesis]
34. ! [X0] : ((~humble(X0) & ~happy(X0)) | funny(X0)) [ennf transformation 7]
37. ! [X0] : ((generous(X0) | happy(X0)) | (funny(X0) & ~rich(X0))) [ennf transformation 13]
38. ! [X0] : (generous(X0) | happy(X0) | (funny(X0) & ~rich(X0))) [flattening 37]
117. ~happy(X0) | funny(X0) [cnf transformation 34]
137. generous(X0) | happy(X0) | funny(X0) [cnf transformation 38]
159. ~curious(alice) [cnf transformation 21]
163. curious(alice) | ~generous(alice) [cnf transformation 24]
164. ~funny(alice) [cnf transformation 25]
207. 10 <=> curious(alice) [avatar definition]
305. generous(X0) | funny(X0) [subsumption resolution 137,117]
355. ~10 [avatar split clause 159,207]
357. 42 <=> generous(alice) [avatar definition]
359. ~generous(alice) <- (~42) [avatar component clause 357]
360. ~42 | 10 [avatar split clause 163,207,357]
373. funny(alice) <- (~42) [resolution 305,359]
374. $false <- (~42) [subsumption resolution 373,164]
375. 42 [avatar contradiction clause 374]
376. $false [avatar sat refutation 355,360,375]
% SZS output end Proof for 3356972959157713092793551
% ------------------------------
% 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 |
Everyone who is either funny or not curious is either not tall or generous and vice versa.
If someone is kind then lucy is tall and vice versa.
Everyone who is both not rich and not generous is wise or not old.
If lucy is both calm and old then someone is either not brave or not old and vice versa.
If someone is either not tall or old then someone is both tall and not rich.
Everyone who is either quiet or rich is not brave or tall.
Everyone who is both not brave and not quiet is both humble and old.
If alice is not humble or calm then someone is tall and vice versa.
Everyone who is either not funny or happy is rich and vice versa.
If someone is both not patient and humble then alice is not rich or not calm.
Everyone who is curious is curious or not wise.
Everyone who is either not humble or curious is both generous and happy and vice versa.
If alice is not quiet or kind then john is either tall or happy and vice versa.
Everyone who is both not brave and tall is either not funny or not strong and vice versa.
If someone is brave then mary is either not funny or not humble and vice versa.
Everyone who is not quiet or quiet is generous or rich and vice versa.
Someone is either tall or strong.
Fred is both wise and rich.
Susan is not happy or calm.
Mary is either not strong or wise.
Mary is both not tall and not generous.
Someone is not curious or calm.
Paul is both funny and calm. | Lucy is calm. | neutral | (![X]:((funny(X)<~>~curious(X))<=>(~tall(X)<~>generous(X))))&
((?[X]:(kind(X)))<=>(tall(lucy)))&
(![X]:((~rich(X)&~generous(X))=>(wise(X)|~old(X))))&
(((calm(lucy)&old(lucy)))<=>(?[X]:((~brave(X)<~>~old(X)))))&
((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((tall(X)&~rich(X)))))&
(![X]:((quiet(X)<~>rich(X))=>(~brave(X)|tall(X))))&
(![X]:((~brave(X)&~quiet(X))=>(humble(X)&old(X))))&
(((~humble(alice)|calm(alice)))<=>(?[X]:(tall(X))))&
(![X]:((~funny(X)<~>happy(X))<=>rich(X)))&
((?[X]:((~patient(X)&humble(X))))=>((~rich(alice)|~calm(alice))))&
(![X]:(curious(X)=>(curious(X)|~wise(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(generous(X)&happy(X))))&
(((~quiet(alice)|kind(alice)))<=>((tall(john)<~>happy(john))))&
(![X]:((~brave(X)&tall(X))<=>(~funny(X)<~>~strong(X))))&
((?[X]:(brave(X)))<=>((~funny(mary)<~>~humble(mary))))&
(![X]:((~quiet(X)|quiet(X))<=>(generous(X)|rich(X))))&
(?[X]:((tall(X)<~>strong(X))))&
((wise(fred)&rich(fred)))&
((~happy(susan)|calm(susan)))&
((~strong(mary)<~>wise(mary)))&
((~tall(mary)&~generous(mary)))&
(?[X]:((~curious(X)|calm(X))))&
((funny(paul)&calm(paul))) | calm(lucy) | [] | null | 0 |
Everyone who is either quiet or tall is both not strong and wise.
Everyone who is kind or strong is either not tall or not quiet.
Everyone who is rich or not patient is either not generous or quiet and vice versa.
Everyone who is either tall or not creative is strong or patient and vice versa.
Everyone who is either not wise or not funny is kind and vice versa.
If someone is either happy or wise then someone is both wise and not rich and vice versa.
Everyone who is either not funny or old is both old and patient and vice versa.
If susan is rich or not patient then alice is both not calm and curious.
Everyone who is not funny or not patient is both creative and patient and vice versa.
Everyone who is both not rich and kind is humble.
Everyone who is not kind or not wise is not rich or not tall.
If paul is patient or funny then someone is rich and vice versa.
Everyone who is either not brave or brave is kind or not old and vice versa.
Everyone who is not calm is both not brave and not rich.
If alice is both not patient and quiet then someone is either generous or calm and vice versa.
Alice is not humble or patient.
Fred is both funny and wise.
Someone is either not humble or not strong.
Someone is either not quiet or not happy.
John is either not wise or not strong.
Fred is either quiet or not humble.
Someone is not kind. | John is not patient. | contradiction | (![X]:((quiet(X)<~>tall(X))=>(~strong(X)&wise(X))))&
(![X]:((kind(X)|strong(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:((rich(X)|~patient(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(strong(X)|patient(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>kind(X)))&
((?[X]:((happy(X)<~>wise(X))))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~funny(X)<~>old(X))<=>(old(X)&patient(X))))&
(((rich(susan)|~patient(susan)))=>((~calm(alice)&curious(alice))))&
(![X]:((~funny(X)|~patient(X))<=>(creative(X)&patient(X))))&
(![X]:((~rich(X)&kind(X))=>humble(X)))&
(![X]:((~kind(X)|~wise(X))=>(~rich(X)|~tall(X))))&
(((patient(paul)|funny(paul)))<=>(?[X]:(rich(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(kind(X)|~old(X))))&
(![X]:(~calm(X)=>(~brave(X)&~rich(X))))&
(((~patient(alice)&quiet(alice)))<=>(?[X]:((generous(X)<~>calm(X)))))&
((~humble(alice)|patient(alice)))&
((funny(fred)&wise(fred)))&
(?[X]:((~humble(X)<~>~strong(X))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((~wise(john)<~>~strong(john)))&
((quiet(fred)<~>~humble(fred)))&
(?[X]:(~kind(X))) | ~patient(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3220482374897906890409059
% SZS output start Proof for 3220482374897906890409059
9. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> (patient(X0) & creative(X0))) [input p8]
23. ~patient(john) [input hypothesis]
48. ! [X0] : (((~patient(X0) | ~funny(X0)) | (~patient(X0) | ~creative(X0))) & ((patient(X0) & creative(X0)) | (patient(X0) & funny(X0)))) [nnf transformation 9]
49. ! [X0] : ((~patient(X0) | ~funny(X0) | ~patient(X0) | ~creative(X0)) & ((patient(X0) & creative(X0)) | (patient(X0) & funny(X0)))) [flattening 48]
113. patient(X0) | patient(X0) [cnf transformation 49]
147. ~patient(john) [cnf transformation 23]
150. patient(X0) [duplicate literal removal 113]
271. $false [subsumption resolution 147,150]
% SZS output end Proof for 3220482374897906890409059
% ------------------------------
% 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 both not creative and not funny then mary is generous or happy.
Everyone who is both patient and not curious is patient and vice versa.
If someone is tall or not happy then paul is brave.
Everyone who is either rich or not old is either quiet or not curious.
If someone is quiet then someone is both patient and not strong and vice versa.
If lucy is both not generous and not humble then someone is either generous or kind and vice versa.
Everyone who is humble or not happy is old.
Everyone who is either creative or not funny is not happy or not wise and vice versa.
Everyone who is both funny and happy is either curious or brave and vice versa.
If paul is brave then someone is both happy and old.
If lucy is not calm or curious then someone is either rich or humble.
Everyone who is both generous and not generous is tall or creative and vice versa.
If someone is either not funny or not rich then someone is not strong.
If fred is both not happy and not calm then someone is wise and vice versa.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
Someone is both not tall and not patient.
Mary is generous.
Someone is kind or strong.
Lucy is not tall or not rich.
Someone is both not curious and strong.
Fred is generous.
Alice is calm or strong. | Fred is calm. | neutral | ((?[X]:((~creative(X)&~funny(X))))=>((generous(mary)|happy(mary))))&
(![X]:((patient(X)&~curious(X))<=>patient(X)))&
((?[X]:((tall(X)|~happy(X))))=>(brave(paul)))&
(![X]:((rich(X)<~>~old(X))=>(quiet(X)<~>~curious(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((patient(X)&~strong(X)))))&
(((~generous(lucy)&~humble(lucy)))<=>(?[X]:((generous(X)<~>kind(X)))))&
(![X]:((humble(X)|~happy(X))=>old(X)))&
(![X]:((creative(X)<~>~funny(X))<=>(~happy(X)|~wise(X))))&
(![X]:((funny(X)&happy(X))<=>(curious(X)<~>brave(X))))&
((brave(paul))=>(?[X]:((happy(X)&old(X)))))&
(((~calm(lucy)|curious(lucy)))=>(?[X]:((rich(X)<~>humble(X)))))&
(![X]:((generous(X)&~generous(X))<=>(tall(X)|creative(X))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(?[X]:(~strong(X))))&
(((~happy(fred)&~calm(fred)))<=>(?[X]:(wise(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
(?[X]:((~tall(X)&~patient(X))))&
(generous(mary))&
(?[X]:((kind(X)|strong(X))))&
((~tall(lucy)|~rich(lucy)))&
(?[X]:((~curious(X)&strong(X))))&
(generous(fred))&
((calm(alice)|strong(alice))) | calm(fred) | [] | null | 0 |
Everyone who is patient is old or not generous and vice versa. If alice is curious then someone is wise. Everyone who is not brave or not funny is both not generous and not strong. If someone is not wise or rich then someone is old or not brave and vice versa. Everyone who is either not happy or not tall is both curious and strong and vice versa. Everyone who is either not patient or strong is both kind and not funny and vice versa. If susan is both not tall and not old then someone is both wise and not rich. Everyone who is generous is not kind or not wise and vice versa. Everyone who is both wise and not creative is curious and vice versa. If someone is either not kind or creative then someone is either not patient or old. Everyone who is brave is not tall or generous and vice versa. Everyone who is generous or calm is either happy or tall. If someone is either not curious or rich then paul is creative or not curious and vice versa. Everyone who is either creative or old is not patient or quiet. If susan is curious or not generous then fred is both not patient and tall and vice versa. Someone is both not tall and not happy. Someone is both not brave and kind. John is not wise or not creative. Lucy is kind or not patient. Someone is not kind. Someone is either not quiet or not kind. Paul is either not calm or tall. | Fred is not brave. | contradiction | (![X]:(patient(X)<=>(old(X)|~generous(X))))&
((curious(alice))=>(?[X]:(wise(X))))&
(![X]:((~brave(X)|~funny(X))=>(~generous(X)&~strong(X))))&
((?[X]:((~wise(X)|rich(X))))<=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((~happy(X)<~>~tall(X))<=>(curious(X)&strong(X))))&
(![X]:((~patient(X)<~>strong(X))<=>(kind(X)&~funny(X))))&
(((~tall(susan)&~old(susan)))=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:(generous(X)<=>(~kind(X)|~wise(X))))&
(![X]:((wise(X)&~creative(X))<=>curious(X)))&
((?[X]:((~kind(X)<~>creative(X))))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(brave(X)<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((~brave(X)&kind(X))))&
((~wise(john)|~creative(john)))&
((kind(lucy)|~patient(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
((~calm(paul)<~>tall(paul))) | ~brave(fred) | [
"p0",
"p2",
"p4",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4958450868746012553527529
% SZS output start Proof for 4958450868746012553527529
1. ! [X0] : (patient(X0) <=> (~generous(X0) | old(X0))) [input p0]
3. ! [X0] : ((~funny(X0) | ~brave(X0)) => (~strong(X0) & ~generous(X0))) [input p2]
5. ! [X0] : ((~happy(X0) <~> ~tall(X0)) <=> (strong(X0) & curious(X0))) [input p4]
11. ! [X0] : (brave(X0) <=> (generous(X0) | ~tall(X0))) [input p10]
12. ! [X0] : ((calm(X0) | generous(X0)) => (happy(X0) <~> tall(X0))) [input p11]
15. (~generous(susan) | curious(susan)) <=> (tall(fred) & ~patient(fred)) [input p14]
23. ~brave(fred) [input hypothesis]
27. ! [X0] : ((~strong(X0) & ~generous(X0)) | (funny(X0) & brave(X0))) [ennf transformation 3]
31. ! [X0] : ((happy(X0) <~> tall(X0)) | (~calm(X0) & ~generous(X0))) [ennf transformation 12]
34. ! [X0] : ((patient(X0) | (generous(X0) & ~old(X0))) & ((~generous(X0) | old(X0)) | ~patient(X0))) [nnf transformation 1]
35. ! [X0] : ((patient(X0) | (generous(X0) & ~old(X0))) & (~generous(X0) | old(X0) | ~patient(X0))) [flattening 34]
43. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (~strong(X0) | ~curious(X0))) & ((strong(X0) & curious(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [nnf transformation 5]
44. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | ~strong(X0) | ~curious(X0)) & ((strong(X0) & curious(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [flattening 43]
57. ! [X0] : ((brave(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | ~brave(X0))) [nnf transformation 11]
58. ! [X0] : ((brave(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | ~brave(X0))) [flattening 57]
59. ! [X0] : (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (~calm(X0) & ~generous(X0))) [nnf transformation 31]
66. ((~generous(susan) | curious(susan)) | (~tall(fred) | patient(fred))) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [nnf transformation 15]
67. (~generous(susan) | curious(susan) | ~tall(fred) | patient(fred)) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [flattening 66]
80. generous(X0) | patient(X0) [cnf transformation 35]
84. ~strong(X0) | brave(X0) [cnf transformation 27]
90. ~tall(X0) | curious(X0) | happy(X0) [cnf transformation 44]
91. ~happy(X0) | curious(X0) | tall(X0) [cnf transformation 44]
92. ~tall(X0) | strong(X0) | happy(X0) [cnf transformation 44]
115. tall(X0) | brave(X0) [cnf transformation 58]
117. ~generous(X0) | happy(X0) | tall(X0) [cnf transformation 59]
119. ~tall(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 59]
129. ~patient(fred) | ~curious(susan) [cnf transformation 67]
130. ~patient(fred) | generous(susan) [cnf transformation 67]
145. ~brave(fred) [cnf transformation 23]
190. 11 <=> tall(susan) [avatar definition]
191. ~tall(susan) <- (~11) [avatar component clause 190]
192. tall(susan) <- (11) [avatar component clause 190]
255. 25 <=> patient(fred) [avatar definition]
259. 26 <=> tall(fred) [avatar definition]
260. tall(fred) <- (26) [avatar component clause 259]
261. ~tall(fred) <- (~26) [avatar component clause 259]
263. 27 <=> curious(susan) [avatar definition]
267. 28 <=> generous(susan) [avatar definition]
268. generous(susan) <- (28) [avatar component clause 267]
273. 28 | ~25 [avatar split clause 130,255,267]
274. ~27 | ~25 [avatar split clause 129,255,263]
371. curious(susan) | happy(susan) <- (11) [resolution 90,192]
375. 45 <=> happy(susan) [avatar definition]
377. happy(susan) <- (45) [avatar component clause 375]
378. 45 | 27 | ~11 [avatar split clause 371,190,263,375]
380. 46 <=> happy(fred) [avatar definition]
382. happy(fred) <- (46) [avatar component clause 380]
390. brave(fred) <- (~26) [resolution 261,115]
391. $false <- (~26) [subsumption resolution 390,145]
392. 26 [avatar contradiction clause 391]
399. strong(fred) | happy(fred) <- (26) [resolution 92,260]
432. happy(susan) | tall(susan) <- (28) [resolution 117,268]
475. 11 | 45 | ~28 [avatar split clause 432,267,375,190]
515. ~happy(fred) | ~generous(fred) <- (26) [resolution 119,260]
516. ~generous(fred) <- (26, 46) [subsumption resolution 515,382]
540. ~happy(susan) | ~generous(susan) <- (11) [resolution 192,119]
546. curious(susan) | tall(susan) <- (45) [resolution 377,91]
552. 65 <=> strong(fred) [avatar definition]
553. strong(fred) <- (65) [avatar component clause 552]
560. patient(fred) <- (26, 46) [resolution 516,80]
563. 25 | ~26 | ~46 [avatar split clause 560,380,259,255]
569. ~generous(susan) <- (11, 45) [subsumption resolution 540,377]
570. ~28 | ~11 | ~45 [avatar split clause 569,375,190,267]
577. 46 | 65 | ~26 [avatar split clause 399,259,552,380]
583. curious(susan) <- (~11, 45) [subsumption resolution 546,191]
584. 27 | 11 | ~45 [avatar split clause 583,375,190,263]
624. brave(fred) <- (65) [resolution 553,84]
625. $false <- (65) [subsumption resolution 624,145]
626. ~65 [avatar contradiction clause 625]
627. $false [avatar sat refutation 273,274,378,392,475,563,570,577,584,626]
% SZS output end Proof for 4958450868746012553527529
% ------------------------------
% 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 someone is either not wise or funny then fred is not humble.
If alice is both quiet and humble then alice is both not curious and funny.
If fred is not funny or happy then susan is not calm.
Everyone who is either happy or not happy is not creative.
Everyone who is either not funny or not rich is either curious or not wise.
If someone is kind then someone is funny.
Everyone who is patient is quiet and vice versa.
Everyone who is either creative or not funny is both not generous and tall.
Everyone who is both not creative and funny is not strong and vice versa.
If susan is not old or old then alice is not wise or rich.
Everyone who is happy or not rich is strong and vice versa.
If mary is both calm and not wise then fred is either not rich or not strong and vice versa.
If fred is humble or not happy then mary is both not calm and not brave and vice versa.
If someone is either not rich or not humble then alice is both rich and strong and vice versa.
Everyone who is either strong or funny is both curious and quiet and vice versa.
Everyone who is funny or not wise is either not strong or not kind and vice versa.
Mary is either rich or not wise.
Fred is not kind.
Someone is both not creative and brave.
Paul is both patient and not happy.
Alice is both tall and not humble.
Someone is not happy. | Mary is not strong. | contradiction | ((?[X]:((~wise(X)<~>funny(X))))=>(~humble(fred)))&
(((quiet(alice)&humble(alice)))=>((~curious(alice)&funny(alice))))&
(((~funny(fred)|happy(fred)))=>(~calm(susan)))&
(![X]:((happy(X)<~>~happy(X))=>~creative(X)))&
(![X]:((~funny(X)<~>~rich(X))=>(curious(X)<~>~wise(X))))&
((?[X]:(kind(X)))=>(?[X]:(funny(X))))&
(![X]:(patient(X)<=>quiet(X)))&
(![X]:((creative(X)<~>~funny(X))=>(~generous(X)&tall(X))))&
(![X]:((~creative(X)&funny(X))<=>~strong(X)))&
(((~old(susan)|old(susan)))=>((~wise(alice)|rich(alice))))&
(![X]:((happy(X)|~rich(X))<=>strong(X)))&
(((calm(mary)&~wise(mary)))<=>((~rich(fred)<~>~strong(fred))))&
(((humble(fred)|~happy(fred)))<=>((~calm(mary)&~brave(mary))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((rich(alice)&strong(alice))))&
(![X]:((strong(X)<~>funny(X))<=>(curious(X)&quiet(X))))&
(![X]:((funny(X)|~wise(X))<=>(~strong(X)<~>~kind(X))))&
((rich(mary)<~>~wise(mary)))&
(~kind(fred))&
(?[X]:((~creative(X)&brave(X))))&
((patient(paul)&~happy(paul)))&
((tall(alice)&~humble(alice)))&
(?[X]:(~happy(X))) | ~strong(mary) | [
"p3",
"p4",
"p8",
"p10",
"p11",
"p14",
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 627823263503042634188166
% SZS output start Proof for 627823263503042634188166
4. ! [X0] : ((happy(X0) <~> ~happy(X0)) => ~creative(X0)) [input p3]
5. ! [X0] : ((~funny(X0) <~> ~rich(X0)) => (curious(X0) <~> ~wise(X0))) [input p4]
9. ! [X0] : ((funny(X0) & ~creative(X0)) <=> ~strong(X0)) [input p8]
11. ! [X0] : ((~rich(X0) | happy(X0)) <=> strong(X0)) [input p10]
12. (~wise(mary) & calm(mary)) <=> (~rich(fred) <~> ~strong(fred)) [input p11]
15. ! [X0] : ((strong(X0) <~> funny(X0)) <=> (quiet(X0) & curious(X0))) [input p14]
16. ! [X0] : ((~wise(X0) | funny(X0)) <=> (~strong(X0) <~> ~kind(X0))) [input p15]
17. rich(mary) <~> ~wise(mary) [input p16]
18. ~kind(fred) [input p17]
23. ~strong(mary) [input hypothesis]
33. ! [X0] : (~creative(X0) | (happy(X0) <=> ~happy(X0))) [ennf transformation 4]
34. ! [X0] : ((curious(X0) <~> ~wise(X0)) | (~funny(X0) <=> ~rich(X0))) [ennf transformation 5]
40. ! [X0] : (~creative(X0) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 33]
41. ! [X0] : (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0)))) [nnf transformation 34]
45. ! [X0] : (((funny(X0) & ~creative(X0)) | strong(X0)) & (~strong(X0) | (~funny(X0) | creative(X0)))) [nnf transformation 9]
46. ! [X0] : (((funny(X0) & ~creative(X0)) | strong(X0)) & (~strong(X0) | ~funny(X0) | creative(X0))) [flattening 45]
47. ! [X0] : (((~rich(X0) | happy(X0)) | ~strong(X0)) & (strong(X0) | (rich(X0) & ~happy(X0)))) [nnf transformation 11]
48. ! [X0] : ((~rich(X0) | happy(X0) | ~strong(X0)) & (strong(X0) | (rich(X0) & ~happy(X0)))) [flattening 47]
49. ((~wise(mary) & calm(mary)) | ((~rich(fred) | strong(fred)) & (~strong(fred) | rich(fred)))) & (((strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred))) | (wise(mary) | ~calm(mary))) [nnf transformation 12]
50. ((~wise(mary) & calm(mary)) | ((~rich(fred) | strong(fred)) & (~strong(fred) | rich(fred)))) & (((strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred))) | wise(mary) | ~calm(mary)) [flattening 49]
58. ! [X0] : ((((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0))))) [nnf transformation 15]
59. ! [X0] : ((((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0))))) [flattening 58]
60. ! [X0] : (((~wise(X0) | funny(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (wise(X0) & ~funny(X0)))) [nnf transformation 16]
61. ! [X0] : ((~wise(X0) | funny(X0) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (wise(X0) & ~funny(X0)))) [flattening 60]
62. (wise(mary) | ~rich(mary)) & (~wise(mary) | rich(mary)) [nnf transformation 17]
73. ~creative(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 40]
74. ~creative(X0) | happy(X0) | happy(X0) [cnf transformation 40]
77. ~rich(X0) | ~curious(X0) | wise(X0) | funny(X0) [cnf transformation 41]
81. ~strong(X0) | ~funny(X0) | creative(X0) [cnf transformation 46]
83. strong(X0) | funny(X0) [cnf transformation 46]
87. strong(X0) | rich(X0) [cnf transformation 48]
93. ~wise(mary) | ~strong(fred) | rich(fred) [cnf transformation 50]
94. ~wise(mary) | ~rich(fred) | strong(fred) [cnf transformation 50]
106. curious(X0) | funny(X0) | ~strong(X0) [cnf transformation 59]
107. curious(X0) | strong(X0) | ~funny(X0) [cnf transformation 59]
117. ~wise(X0) | funny(X0) | ~strong(X0) | kind(X0) [cnf transformation 61]
119. wise(mary) | ~rich(mary) [cnf transformation 62]
120. ~kind(fred) [cnf transformation 18]
127. ~strong(mary) [cnf transformation 23]
128. ~creative(X0) | ~happy(X0) [duplicate literal removal 73]
129. ~creative(X0) | happy(X0) [duplicate literal removal 74]
170. 10 <=> funny(fred) [avatar definition]
171. ~funny(fred) <- (~10) [avatar component clause 170]
174. ~creative(X0) [subsumption resolution 128,129]
183. ~strong(X0) | ~funny(X0) [subsumption resolution 81,174]
198. ~wise(mary) | strong(fred) [subsumption resolution 94,87]
200. 16 <=> strong(fred) [avatar definition]
202. strong(fred) <- (16) [avatar component clause 200]
204. 17 <=> wise(mary) [avatar definition]
207. 16 | ~17 [avatar split clause 198,204,200]
208. ~wise(mary) | rich(fred) [subsumption resolution 93,87]
210. 18 <=> rich(fred) [avatar definition]
212. rich(fred) <- (18) [avatar component clause 210]
213. 18 | ~17 [avatar split clause 208,204,210]
259. strong(X0) | curious(X0) [subsumption resolution 107,83]
260. curious(X0) | ~strong(X0) [subsumption resolution 106,183]
261. curious(X0) [subsumption resolution 260,259]
262. ~strong(X0) | ~wise(X0) | kind(X0) [subsumption resolution 117,183]
265. 26 <=> rich(mary) [avatar definition]
268. ~26 | 17 [avatar split clause 119,204,265]
273. rich(mary) [resolution 87,127]
276. 26 [avatar split clause 273,265]
277. ~funny(fred) <- (16) [resolution 183,202]
281. ~10 | ~16 [avatar split clause 277,200,170]
324. ~wise(fred) | kind(fred) <- (16) [resolution 262,202]
334. ~wise(fred) <- (16) [subsumption resolution 324,120]
345. ~curious(fred) | wise(fred) | funny(fred) <- (18) [resolution 77,212]
349. wise(fred) | funny(fred) <- (18) [subsumption resolution 345,261]
350. funny(fred) <- (16, 18) [subsumption resolution 349,334]
351. $false <- (~10, 16, 18) [subsumption resolution 350,171]
352. 10 | ~16 | ~18 [avatar contradiction clause 351]
367. $false [avatar sat refutation 207,213,268,276,281,352]
% SZS output end Proof for 627823263503042634188166
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or old is both brave and kind and vice versa. Everyone who is happy or not patient is not patient. Everyone who is both not quiet and not brave is not patient or funny. Everyone who is both not calm and creative is not humble or not creative and vice versa. Everyone who is either wise or not quiet is not patient. Everyone who is either not creative or not kind is rich or not patient and vice versa. If someone is not funny then someone is both wise and not humble. If someone is strong then alice is not rich. If someone is tall or not patient then someone is both not patient and creative and vice versa. Everyone who is not creative is both not funny and not quiet. If someone is not creative then someone is not tall or old. If alice is both strong and not old then someone is either not tall or tall and vice versa. Everyone who is quiet or not tall is calm. Everyone who is both wise and happy is both not happy and not old. Someone is either not rich or not strong. Paul is wise or strong. Mary is either old or creative. Someone is either old or not kind. | Alice is not rich. | entailment | (![X]:((~old(X)<~>old(X))<=>(brave(X)&kind(X))))&
(![X]:((happy(X)|~patient(X))=>~patient(X)))&
(![X]:((~quiet(X)&~brave(X))=>(~patient(X)|funny(X))))&
(![X]:((~calm(X)&creative(X))<=>(~humble(X)|~creative(X))))&
(![X]:((wise(X)<~>~quiet(X))=>~patient(X)))&
(![X]:((~creative(X)<~>~kind(X))<=>(rich(X)|~patient(X))))&
((?[X]:(~funny(X)))=>(?[X]:((wise(X)&~humble(X)))))&
((?[X]:(strong(X)))=>(~rich(alice)))&
((?[X]:((tall(X)|~patient(X))))<=>(?[X]:((~patient(X)&creative(X)))))&
(![X]:(~creative(X)=>(~funny(X)&~quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)|old(X)))))&
(((strong(alice)&~old(alice)))<=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((quiet(X)|~tall(X))=>calm(X)))&
(![X]:((wise(X)&happy(X))=>(~happy(X)&~old(X))))&
(?[X]:((~rich(X)<~>~strong(X))))&
((wise(paul)|strong(paul)))&
((old(mary)<~>creative(mary)))&
(?[X]:((old(X)<~>~kind(X)))) | ~rich(alice) | [
"p0",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 55414517257697728018733
% SZS output start Proof for 55414517257697728018733
1. ! [X0] : ((~old(X0) <~> old(X0)) <=> (kind(X0) & brave(X0))) [input p0]
4. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (~creative(X0) | ~humble(X0))) [input p3]
6. ! [X0] : ((~creative(X0) <~> ~kind(X0)) <=> (~patient(X0) | rich(X0))) [input p5]
19. rich(alice) [input hypothesis]
34. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | (~kind(X0) | ~brave(X0))) & ((kind(X0) & brave(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [nnf transformation 1]
35. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~kind(X0) | ~brave(X0)) & ((kind(X0) & brave(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [flattening 34]
36. ! [X0] : (((creative(X0) & ~calm(X0)) | (creative(X0) & humble(X0))) & ((~creative(X0) | ~humble(X0)) | (~creative(X0) | calm(X0)))) [nnf transformation 4]
37. ! [X0] : (((creative(X0) & ~calm(X0)) | (creative(X0) & humble(X0))) & (~creative(X0) | ~humble(X0) | ~creative(X0) | calm(X0))) [flattening 36]
39. ! [X0] : ((((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (patient(X0) & ~rich(X0))) & ((~patient(X0) | rich(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0))))) [nnf transformation 6]
40. ! [X0] : ((((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (patient(X0) & ~rich(X0))) & (~patient(X0) | rich(X0) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0))))) [flattening 39]
66. kind(X0) | old(X0) | old(X0) [cnf transformation 35]
67. kind(X0) | ~old(X0) | ~old(X0) [cnf transformation 35]
76. creative(X0) | creative(X0) [cnf transformation 37]
81. ~kind(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 40]
111. rich(alice) [cnf transformation 19]
117. creative(X0) [duplicate literal removal 76]
120. kind(X0) | old(X0) [duplicate literal removal 66]
121. kind(X0) | ~old(X0) [duplicate literal removal 67]
122. kind(X0) [subsumption resolution 120,121]
127. ~creative(X0) | ~rich(X0) [subsumption resolution 81,122]
128. ~rich(X0) [subsumption resolution 127,117]
158. $false [subsumption resolution 111,128]
% SZS output end Proof for 55414517257697728018733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is both strong and creative and vice versa. If susan is calm or not humble then fred is not wise and vice versa. Everyone who is not creative or not happy is both not patient and not kind. If someone is either not quiet or not funny then someone is curious. If someone is either not creative or not happy then susan is not old and vice versa. Everyone who is either not happy or not funny is not creative. If someone is not brave or funny then paul is kind or not happy. Everyone who is either funny or generous is both patient and generous and vice versa. Everyone who is not wise or not strong is either not rich or not old and vice versa. Everyone who is not old is curious and vice versa. Everyone who is both tall and not generous is either old or tall. Everyone who is either not creative or patient is both not brave and not happy. Everyone who is either not tall or creative is happy and vice versa. If john is either not brave or not strong then someone is either not curious or wise and vice versa. Everyone who is not brave or creative is happy. If someone is strong then susan is either strong or tall and vice versa. John is humble. Lucy is either not brave or rich. Alice is either kind or tall. Someone is both old and humble. Someone is both curious and not wise. Someone is not old. | Paul is happy. | entailment | (![X]:(curious(X)<=>(strong(X)&creative(X))))&
(((calm(susan)|~humble(susan)))<=>(~wise(fred)))&
(![X]:((~creative(X)|~happy(X))=>(~patient(X)&~kind(X))))&
((?[X]:((~quiet(X)<~>~funny(X))))=>(?[X]:(curious(X))))&
((?[X]:((~creative(X)<~>~happy(X))))<=>(~old(susan)))&
(![X]:((~happy(X)<~>~funny(X))=>~creative(X)))&
((?[X]:((~brave(X)|funny(X))))=>((kind(paul)|~happy(paul))))&
(![X]:((funny(X)<~>generous(X))<=>(patient(X)&generous(X))))&
(![X]:((~wise(X)|~strong(X))<=>(~rich(X)<~>~old(X))))&
(![X]:(~old(X)<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(old(X)<~>tall(X))))&
(![X]:((~creative(X)<~>patient(X))=>(~brave(X)&~happy(X))))&
(![X]:((~tall(X)<~>creative(X))<=>happy(X)))&
(((~brave(john)<~>~strong(john)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(![X]:((~brave(X)|creative(X))=>happy(X)))&
((?[X]:(strong(X)))<=>((strong(susan)<~>tall(susan))))&
(humble(john))&
((~brave(lucy)<~>rich(lucy)))&
((kind(alice)<~>tall(alice)))&
(?[X]:((old(X)&humble(X))))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:(~old(X))) | happy(paul) | [
"p2",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 96337807482879507981562
% SZS output start Proof for 96337807482879507981562
3. ! [X0] : ((~happy(X0) | ~creative(X0)) => (~kind(X0) & ~patient(X0))) [input p2]
12. ! [X0] : ((~creative(X0) <~> patient(X0)) => (~happy(X0) & ~brave(X0))) [input p11]
15. ! [X0] : ((creative(X0) | ~brave(X0)) => happy(X0)) [input p14]
23. ~happy(paul) [input hypothesis]
25. ! [X0] : ((~kind(X0) & ~patient(X0)) | (happy(X0) & creative(X0))) [ennf transformation 3]
32. ! [X0] : ((~happy(X0) & ~brave(X0)) | (~creative(X0) <=> patient(X0))) [ennf transformation 12]
33. ! [X0] : (happy(X0) | (~creative(X0) & brave(X0))) [ennf transformation 15]
53. ! [X0] : ((~happy(X0) & ~brave(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) [nnf transformation 32]
77. ~patient(X0) | creative(X0) [cnf transformation 25]
78. ~patient(X0) | happy(X0) [cnf transformation 25]
107. ~brave(X0) | patient(X0) | creative(X0) [cnf transformation 53]
110. ~happy(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 53]
123. brave(X0) | happy(X0) [cnf transformation 33]
124. happy(X0) | ~creative(X0) [cnf transformation 33]
139. ~happy(paul) [cnf transformation 23]
185. 10 <=> ! [X1] : (~creative(X1) | happy(X1)) [avatar definition]
186. ~creative(X1) | happy(X1) <- (10) [avatar component clause 185]
200. 14 <=> happy(paul) [avatar definition]
202. ~happy(paul) <- (~14) [avatar component clause 200]
208. ~creative(X0) | ~patient(X0) [subsumption resolution 110,78]
209. ~patient(X0) [subsumption resolution 208,77]
212. ~brave(X0) | creative(X0) [subsumption resolution 107,209]
243. 10 [avatar split clause 124,185]
283. ~14 [avatar split clause 139,200]
309. creative(X0) | happy(X0) [resolution 212,123]
310. happy(X0) <- (10) [subsumption resolution 309,186]
335. $false <- (10, ~14) [resolution 310,202]
337. ~10 | 14 [avatar contradiction clause 335]
338. $false [avatar sat refutation 243,283,337]
% SZS output end Proof for 96337807482879507981562
% ------------------------------
% 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 both not humble and brave is both humble and old and vice versa.
If someone is wise then mary is both curious and kind.
If lucy is either not rich or not happy then someone is both not quiet and not happy.
Everyone who is both rich and not quiet is either tall or not quiet.
Everyone who is tall is both rich and old.
Everyone who is calm or not calm is both brave and wise.
If john is both not happy and funny then someone is either quiet or wise and vice versa.
Everyone who is both not patient and creative is both old and wise and vice versa.
Everyone who is both not funny and calm is both not wise and creative.
Everyone who is not generous is both creative and generous and vice versa.
If someone is both rich and tall then alice is not quiet or creative.
Everyone who is both not happy and humble is either not calm or funny and vice versa.
Everyone who is not kind or not old is both not old and not happy.
Everyone who is old or generous is both calm and not quiet and vice versa.
Lucy is either not happy or not strong.
Someone is rich or not happy.
Fred is not brave or not creative.
Someone is strong or wise.
Someone is both not kind and not rich.
Someone is either rich or not tall. | Alice is not funny. | contradiction | (![X]:((~humble(X)&brave(X))<=>(humble(X)&old(X))))&
((?[X]:(wise(X)))=>((curious(mary)&kind(mary))))&
(((~rich(lucy)<~>~happy(lucy)))=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:((rich(X)&~quiet(X))=>(tall(X)<~>~quiet(X))))&
(![X]:(tall(X)=>(rich(X)&old(X))))&
(![X]:((calm(X)|~calm(X))=>(brave(X)&wise(X))))&
(((~happy(john)&funny(john)))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:((~patient(X)&creative(X))<=>(old(X)&wise(X))))&
(![X]:((~funny(X)&calm(X))=>(~wise(X)&creative(X))))&
(![X]:(~generous(X)<=>(creative(X)&generous(X))))&
((?[X]:((rich(X)&tall(X))))=>((~quiet(alice)|creative(alice))))&
(![X]:((~happy(X)&humble(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((~kind(X)|~old(X))=>(~old(X)&~happy(X))))&
(![X]:((old(X)|generous(X))<=>(calm(X)&~quiet(X))))&
((~happy(lucy)<~>~strong(lucy)))&
(?[X]:((rich(X)|~happy(X))))&
((~brave(fred)|~creative(fred)))&
(?[X]:((strong(X)|wise(X))))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((rich(X)<~>~tall(X)))) | ~funny(alice) | [
"p5",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8791146322940069198266470
% SZS output start Proof for 8791146322940069198266470
6. ! [X0] : ((~calm(X0) | calm(X0)) => (wise(X0) & brave(X0))) [input p5]
9. ! [X0] : ((calm(X0) & ~funny(X0)) => (creative(X0) & ~wise(X0))) [input p8]
10. ! [X0] : (~generous(X0) <=> (generous(X0) & creative(X0))) [input p9]
14. ! [X0] : ((generous(X0) | old(X0)) <=> (~quiet(X0) & calm(X0))) [input p13]
21. ~funny(alice) [input hypothesis]
28. ! [X0] : ((wise(X0) & brave(X0)) | (calm(X0) & ~calm(X0))) [ennf transformation 6]
29. ! [X0] : ((creative(X0) & ~wise(X0)) | (~calm(X0) | funny(X0))) [ennf transformation 9]
30. ! [X0] : ((creative(X0) & ~wise(X0)) | ~calm(X0) | funny(X0)) [flattening 29]
47. ! [X0] : ((~generous(X0) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | generous(X0))) [nnf transformation 10]
48. ! [X0] : ((~generous(X0) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | generous(X0))) [flattening 47]
51. ! [X0] : (((generous(X0) | old(X0)) | (quiet(X0) | ~calm(X0))) & ((~quiet(X0) & calm(X0)) | (~generous(X0) & ~old(X0)))) [nnf transformation 14]
52. ! [X0] : ((generous(X0) | old(X0) | quiet(X0) | ~calm(X0)) & ((~quiet(X0) & calm(X0)) | (~generous(X0) & ~old(X0)))) [flattening 51]
78. wise(X0) | ~calm(X0) [cnf transformation 28]
79. calm(X0) | wise(X0) [cnf transformation 28]
90. ~wise(X0) | ~calm(X0) | funny(X0) [cnf transformation 30]
93. generous(X0) | generous(X0) [cnf transformation 48]
107. calm(X0) | ~generous(X0) [cnf transformation 52]
120. ~funny(alice) [cnf transformation 21]
121. generous(X0) [duplicate literal removal 93]
154. wise(X0) [subsumption resolution 78,79]
179. ~calm(X0) | funny(X0) [subsumption resolution 90,154]
198. calm(X0) [subsumption resolution 107,121]
236. funny(X2) [resolution 179,198]
237. $false [resolution 236,120]
% SZS output end Proof for 8791146322940069198266470
% ------------------------------
% 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 brave is either brave or not kind. If someone is humble or wise then someone is either tall or brave and vice versa. If fred is not calm then someone is not humble or not funny and vice versa. Everyone who is both not brave and not rich is not old and vice versa. Everyone who is either quiet or strong is not strong or not humble and vice versa. Everyone who is not wise is both funny and old and vice versa. Everyone who is either tall or not tall is not brave. Everyone who is either generous or not rich is either not strong or brave and vice versa. Everyone who is not quiet or curious is generous. If fred is both wise and not brave then paul is curious. If alice is either not wise or not calm then someone is either wise or creative. If someone is creative then alice is humble or not patient. Everyone who is generous or not creative is either not funny or not rich and vice versa. If paul is both patient and not old then mary is funny. Everyone who is either curious or not calm is not tall and vice versa. John is either not strong or not happy. Someone is not brave. Someone is either brave or not kind. John is not wise. Someone is patient. Susan is not curious or calm. Lucy is not creative. | Fred is quiet. | neutral | (![X]:(~brave(X)=>(brave(X)<~>~kind(X))))&
((?[X]:((humble(X)|wise(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
((~calm(fred))<=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((~brave(X)&~rich(X))<=>~old(X)))&
(![X]:((quiet(X)<~>strong(X))<=>(~strong(X)|~humble(X))))&
(![X]:(~wise(X)<=>(funny(X)&old(X))))&
(![X]:((tall(X)<~>~tall(X))=>~brave(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(~strong(X)<~>brave(X))))&
(![X]:((~quiet(X)|curious(X))=>generous(X)))&
(((wise(fred)&~brave(fred)))=>(curious(paul)))&
(((~wise(alice)<~>~calm(alice)))=>(?[X]:((wise(X)<~>creative(X)))))&
((?[X]:(creative(X)))=>((humble(alice)|~patient(alice))))&
(![X]:((generous(X)|~creative(X))<=>(~funny(X)<~>~rich(X))))&
(((patient(paul)&~old(paul)))=>(funny(mary)))&
(![X]:((curious(X)<~>~calm(X))<=>~tall(X)))&
((~strong(john)<~>~happy(john)))&
(?[X]:(~brave(X)))&
(?[X]:((brave(X)<~>~kind(X))))&
(~wise(john))&
(?[X]:(patient(X)))&
((~curious(susan)|calm(susan)))&
(~creative(lucy)) | quiet(fred) | [] | null | 0 |
If mary is not humble or not kind then paul is either not patient or curious. Everyone who is calm or wise is either quiet or brave and vice versa. Everyone who is patient or not happy is either not happy or not kind. If someone is either not strong or old then susan is both not calm and not curious. If someone is not quiet then alice is both not happy and not wise and vice versa. Everyone who is both not calm and not creative is tall. If someone is tall or not old then someone is both brave and not generous and vice versa. Everyone who is creative is not funny and vice versa. Everyone who is both generous and not quiet is either not strong or not humble and vice versa. If fred is either not patient or not strong then susan is either strong or not quiet and vice versa. Everyone who is creative is both calm and strong and vice versa. Everyone who is both not quiet and not creative is rich or not happy and vice versa. Everyone who is both brave and not strong is either not tall or not creative and vice versa. If someone is both kind and brave then someone is not curious or not humble and vice versa. If fred is both not patient and generous then someone is curious. If someone is both not generous and not creative then someone is not patient or humble. John is both curious and not wise. John is not happy. Someone is wise or not patient. Someone is not brave. Someone is not curious or not patient. Susan is not happy. Mary is rich or not tall. | Mary is curious. | neutral | (((~humble(mary)|~kind(mary)))=>((~patient(paul)<~>curious(paul))))&
(![X]:((calm(X)|wise(X))<=>(quiet(X)<~>brave(X))))&
(![X]:((patient(X)|~happy(X))=>(~happy(X)<~>~kind(X))))&
((?[X]:((~strong(X)<~>old(X))))=>((~calm(susan)&~curious(susan))))&
((?[X]:(~quiet(X)))<=>((~happy(alice)&~wise(alice))))&
(![X]:((~calm(X)&~creative(X))=>tall(X)))&
((?[X]:((tall(X)|~old(X))))<=>(?[X]:((brave(X)&~generous(X)))))&
(![X]:(creative(X)<=>~funny(X)))&
(![X]:((generous(X)&~quiet(X))<=>(~strong(X)<~>~humble(X))))&
(((~patient(fred)<~>~strong(fred)))<=>((strong(susan)<~>~quiet(susan))))&
(![X]:(creative(X)<=>(calm(X)&strong(X))))&
(![X]:((~quiet(X)&~creative(X))<=>(rich(X)|~happy(X))))&
(![X]:((brave(X)&~strong(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:((~curious(X)|~humble(X)))))&
(((~patient(fred)&generous(fred)))=>(?[X]:(curious(X))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:((~patient(X)|humble(X)))))&
((curious(john)&~wise(john)))&
(~happy(john))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~curious(X)|~patient(X))))&
(~happy(susan))&
((rich(mary)|~tall(mary))) | curious(mary) | [] | null | 0 |
Everyone who is either creative or humble is tall and vice versa.
If someone is either tall or old then someone is both not creative and not kind.
If someone is not quiet then mary is not generous or not tall.
Everyone who is either generous or happy is both old and not creative.
If someone is not kind then paul is either quiet or curious.
Everyone who is not strong or calm is both humble and not wise and vice versa.
If alice is not rich or strong then someone is not happy or patient and vice versa.
Everyone who is both not generous and old is either generous or strong and vice versa.
Everyone who is not wise is both kind and not kind.
Everyone who is happy or not curious is humble.
Everyone who is either not happy or brave is both not strong and not rich.
Everyone who is not calm or not quiet is either funny or wise.
Everyone who is not strong is either rich or strong and vice versa.
Everyone who is either rich or strong is either creative or not brave and vice versa.
If alice is either wise or tall then paul is not curious.
If someone is both not creative and not wise then susan is patient.
Someone is not patient.
Susan is curious or not old.
Alice is patient.
John is either not patient or not kind.
Paul is both tall and not quiet.
Alice is either not kind or humble.
John is happy or humble. | Alice is not funny. | entailment | (![X]:((creative(X)<~>humble(X))<=>tall(X)))&
((?[X]:((tall(X)<~>old(X))))=>(?[X]:((~creative(X)&~kind(X)))))&
((?[X]:(~quiet(X)))=>((~generous(mary)|~tall(mary))))&
(![X]:((generous(X)<~>happy(X))=>(old(X)&~creative(X))))&
((?[X]:(~kind(X)))=>((quiet(paul)<~>curious(paul))))&
(![X]:((~strong(X)|calm(X))<=>(humble(X)&~wise(X))))&
(((~rich(alice)|strong(alice)))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)<~>strong(X))))&
(![X]:(~wise(X)=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|~curious(X))=>humble(X)))&
(![X]:((~happy(X)<~>brave(X))=>(~strong(X)&~rich(X))))&
(![X]:((~calm(X)|~quiet(X))=>(funny(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>strong(X))))&
(![X]:((rich(X)<~>strong(X))<=>(creative(X)<~>~brave(X))))&
(((wise(alice)<~>tall(alice)))=>(~curious(paul)))&
((?[X]:((~creative(X)&~wise(X))))=>(patient(susan)))&
(?[X]:(~patient(X)))&
((curious(susan)|~old(susan)))&
(patient(alice))&
((~patient(john)<~>~kind(john)))&
((tall(paul)&~quiet(paul)))&
((~kind(alice)<~>humble(alice)))&
((happy(john)|humble(john))) | ~funny(alice) | [
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 414503974291706173764457
% SZS output start Proof for 414503974291706173764457
6. ! [X0] : ((calm(X0) | ~strong(X0)) <=> (~wise(X0) & humble(X0))) [input p5]
9. ! [X0] : (~wise(X0) => (~kind(X0) & kind(X0))) [input p8]
12. ! [X0] : ((~quiet(X0) | ~calm(X0)) => (funny(X0) <~> wise(X0))) [input p11]
24. funny(alice) [input hypothesis]
31. ! [X0] : ((~kind(X0) & kind(X0)) | wise(X0)) [ennf transformation 9]
34. ! [X0] : ((funny(X0) <~> wise(X0)) | (quiet(X0) & calm(X0))) [ennf transformation 12]
44. ! [X0] : (((calm(X0) | ~strong(X0)) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [nnf transformation 6]
45. ! [X0] : ((calm(X0) | ~strong(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [flattening 44]
54. ! [X0] : (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | (quiet(X0) & calm(X0))) [nnf transformation 34]
80. ~wise(X0) | ~calm(X0) [cnf transformation 45]
92. kind(X0) | wise(X0) [cnf transformation 31]
93. ~kind(X0) | wise(X0) [cnf transformation 31]
102. ~wise(X0) | ~funny(X0) | calm(X0) [cnf transformation 54]
129. funny(alice) [cnf transformation 24]
204. wise(X0) [subsumption resolution 92,93]
206. ~funny(X0) | calm(X0) [subsumption resolution 102,204]
254. ~calm(X0) [resolution 80,204]
259. calm(alice) [resolution 206,129]
260. $false [subsumption resolution 259,254]
% SZS output end Proof for 414503974291706173764457
% ------------------------------
% 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 fred is not patient then someone is creative and vice versa.
If fred is either kind or quiet then someone is not happy and vice versa.
Everyone who is not kind or not brave is brave and vice versa.
Everyone who is funny is humble and vice versa.
If lucy is both humble and not generous then paul is not old.
Everyone who is not rich or calm is either old or tall.
Everyone who is not calm is either not tall or quiet.
If someone is not creative or patient then someone is creative or happy and vice versa.
Everyone who is not brave is either not strong or not kind.
If someone is both not tall and not wise then lucy is quiet or not calm.
Everyone who is not quiet is both tall and not strong and vice versa.
If someone is patient then john is both funny and not humble.
If john is not old or not kind then someone is funny or not funny and vice versa.
Everyone who is either patient or not funny is not wise or not rich.
Everyone who is both patient and creative is either not patient or not generous and vice versa.
Everyone who is either wise or quiet is either not tall or not old and vice versa.
Someone is either curious or not quiet.
Someone is either not humble or brave.
Someone is either calm or humble.
Someone is funny or brave.
Someone is both not humble and not rich.
Susan is quiet or not tall. | Lucy is patient. | contradiction | ((~patient(fred))<=>(?[X]:(creative(X))))&
(((kind(fred)<~>quiet(fred)))<=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)|~brave(X))<=>brave(X)))&
(![X]:(funny(X)<=>humble(X)))&
(((humble(lucy)&~generous(lucy)))=>(~old(paul)))&
(![X]:((~rich(X)|calm(X))=>(old(X)<~>tall(X))))&
(![X]:(~calm(X)=>(~tall(X)<~>quiet(X))))&
((?[X]:((~creative(X)|patient(X))))<=>(?[X]:((creative(X)|happy(X)))))&
(![X]:(~brave(X)=>(~strong(X)<~>~kind(X))))&
((?[X]:((~tall(X)&~wise(X))))=>((quiet(lucy)|~calm(lucy))))&
(![X]:(~quiet(X)<=>(tall(X)&~strong(X))))&
((?[X]:(patient(X)))=>((funny(john)&~humble(john))))&
(((~old(john)|~kind(john)))<=>(?[X]:((funny(X)|~funny(X)))))&
(![X]:((patient(X)<~>~funny(X))=>(~wise(X)|~rich(X))))&
(![X]:((patient(X)&creative(X))<=>(~patient(X)<~>~generous(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(~tall(X)<~>~old(X))))&
(?[X]:((curious(X)<~>~quiet(X))))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((calm(X)<~>humble(X))))&
(?[X]:((funny(X)|brave(X))))&
(?[X]:((~humble(X)&~rich(X))))&
((quiet(susan)|~tall(susan))) | patient(lucy) | [
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 35011860429523667919501
% SZS output start Proof for 35011860429523667919501
4. ! [X0] : (funny(X0) <=> humble(X0)) [input p3]
12. ? [X0] : patient(X0) => (~humble(john) & funny(john)) [input p11]
23. patient(lucy) [input hypothesis]
32. (~humble(john) & funny(john)) | ! [X0] : ~patient(X0) [ennf transformation 12]
45. ! [X0] : ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))) [nnf transformation 4]
87. ~funny(X0) | humble(X0) [cnf transformation 45]
106. funny(john) | ~patient(X0) [cnf transformation 32]
107. ~humble(john) | ~patient(X0) [cnf transformation 32]
138. patient(lucy) [cnf transformation 23]
202. 14 <=> ! [X3] : ~patient(X3) [avatar definition]
203. ~patient(X3) <- (14) [avatar component clause 202]
230. 21 <=> humble(john) [avatar definition]
232. ~humble(john) <- (~21) [avatar component clause 230]
233. 14 | ~21 [avatar split clause 107,230,202]
235. 22 <=> funny(john) [avatar definition]
237. funny(john) <- (22) [avatar component clause 235]
238. 14 | 22 [avatar split clause 106,235,202]
282. $false <- (14) [resolution 203,138]
283. ~14 [avatar contradiction clause 282]
284. humble(john) <- (22) [resolution 87,237]
285. $false <- (~21, 22) [subsumption resolution 284,232]
286. 21 | ~22 [avatar contradiction clause 285]
287. $false [avatar sat refutation 233,238,283,286]
% SZS output end Proof for 35011860429523667919501
% ------------------------------
% 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 not strong or funny is not humble. Everyone who is humble or wise is humble. If someone is both not funny and rich then fred is not calm or wise and vice versa. If mary is strong or tall then fred is not creative and vice versa. Everyone who is tall or not generous is calm. Everyone who is tall is either kind or calm. Everyone who is not old or creative is rich. Everyone who is either not patient or calm is curious or not calm and vice versa. Everyone who is either wise or not rich is not humble or patient and vice versa. Everyone who is patient or tall is both not curious and creative and vice versa. Everyone who is both not happy and funny is either not calm or not strong and vice versa. Everyone who is not wise or not kind is both creative and not curious and vice versa. If john is both creative and not patient then someone is brave or not curious. If someone is both not strong and not curious then someone is either not calm or brave. Everyone who is either not kind or old is both not generous and kind. If susan is strong then someone is not happy or humble and vice versa. Paul is not generous or not rich. Paul is either humble or rich. Fred is brave or humble. Someone is wise or not funny. Susan is both not happy and brave. Someone is either rich or curious. Alice is either not humble or not creative. | Fred is not calm. | contradiction | (![X]:((~strong(X)|funny(X))=>~humble(X)))&
(![X]:((humble(X)|wise(X))=>humble(X)))&
((?[X]:((~funny(X)&rich(X))))<=>((~calm(fred)|wise(fred))))&
(((strong(mary)|tall(mary)))<=>(~creative(fred)))&
(![X]:((tall(X)|~generous(X))=>calm(X)))&
(![X]:(tall(X)=>(kind(X)<~>calm(X))))&
(![X]:((~old(X)|creative(X))=>rich(X)))&
(![X]:((~patient(X)<~>calm(X))<=>(curious(X)|~calm(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(~humble(X)|patient(X))))&
(![X]:((patient(X)|tall(X))<=>(~curious(X)&creative(X))))&
(![X]:((~happy(X)&funny(X))<=>(~calm(X)<~>~strong(X))))&
(![X]:((~wise(X)|~kind(X))<=>(creative(X)&~curious(X))))&
(((creative(john)&~patient(john)))=>(?[X]:((brave(X)|~curious(X)))))&
((?[X]:((~strong(X)&~curious(X))))=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:((~kind(X)<~>old(X))=>(~generous(X)&kind(X))))&
((strong(susan))<=>(?[X]:((~happy(X)|humble(X)))))&
((~generous(paul)|~rich(paul)))&
((humble(paul)<~>rich(paul)))&
((brave(fred)|humble(fred)))&
(?[X]:((wise(X)|~funny(X))))&
((~happy(susan)&brave(susan)))&
(?[X]:((rich(X)<~>curious(X))))&
((~humble(alice)<~>~creative(alice))) | ~calm(fred) | [
"p0",
"p1",
"p6",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 523668768048031044576075
% SZS output start Proof for 523668768048031044576075
1. ! [X0] : ((funny(X0) | ~strong(X0)) => ~humble(X0)) [input p0]
2. ! [X0] : ((wise(X0) | humble(X0)) => humble(X0)) [input p1]
7. ! [X0] : ((creative(X0) | ~old(X0)) => rich(X0)) [input p6]
9. ! [X0] : ((wise(X0) <~> ~rich(X0)) <=> (patient(X0) | ~humble(X0))) [input p8]
11. ! [X0] : ((funny(X0) & ~happy(X0)) <=> (~calm(X0) <~> ~strong(X0))) [input p10]
12. ! [X0] : ((~kind(X0) | ~wise(X0)) <=> (~curious(X0) & creative(X0))) [input p11]
24. ~calm(fred) [input hypothesis]
26. ! [X0] : (~humble(X0) | (~funny(X0) & strong(X0))) [ennf transformation 1]
27. ! [X0] : (humble(X0) | (~wise(X0) & ~humble(X0))) [ennf transformation 2]
30. ! [X0] : (rich(X0) | (~creative(X0) & old(X0))) [ennf transformation 7]
45. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (~patient(X0) & humble(X0))) & ((patient(X0) | ~humble(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [nnf transformation 9]
46. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (~patient(X0) & humble(X0))) & (patient(X0) | ~humble(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [flattening 45]
49. ! [X0] : (((funny(X0) & ~happy(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | (~funny(X0) | happy(X0)))) [nnf transformation 11]
50. ! [X0] : (((funny(X0) & ~happy(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | ~funny(X0) | happy(X0))) [flattening 49]
51. ! [X0] : (((~kind(X0) | ~wise(X0)) | (curious(X0) | ~creative(X0))) & ((~curious(X0) & creative(X0)) | (kind(X0) & wise(X0)))) [nnf transformation 12]
52. ! [X0] : ((~kind(X0) | ~wise(X0) | curious(X0) | ~creative(X0)) & ((~curious(X0) & creative(X0)) | (kind(X0) & wise(X0)))) [flattening 51]
71. ~humble(X0) | strong(X0) [cnf transformation 26]
72. ~humble(X0) | ~funny(X0) [cnf transformation 26]
74. ~wise(X0) | humble(X0) [cnf transformation 27]
88. ~creative(X0) | rich(X0) [cnf transformation 30]
97. ~rich(X0) | wise(X0) | humble(X0) [cnf transformation 46]
110. ~strong(X0) | funny(X0) | calm(X0) [cnf transformation 50]
112. creative(X0) | wise(X0) [cnf transformation 52]
138. ~calm(fred) [cnf transformation 24]
143. 1 <=> wise(fred) [avatar definition]
144. wise(fred) <- (1) [avatar component clause 143]
152. 3 <=> calm(fred) [avatar definition]
153. ~calm(fred) <- (~3) [avatar component clause 152]
167. 6 <=> creative(fred) [avatar definition]
168. ~creative(fred) <- (~6) [avatar component clause 167]
169. creative(fred) <- (6) [avatar component clause 167]
183. ~rich(X0) | humble(X0) [subsumption resolution 97,74]
252. 23 <=> humble(fred) [avatar definition]
254. humble(fred) <- (23) [avatar component clause 252]
285. ~3 [avatar split clause 138,152]
290. rich(fred) <- (6) [resolution 88,169]
301. humble(fred) <- (6) [resolution 183,290]
302. 23 | ~6 [avatar split clause 301,167,252]
303. wise(fred) <- (~6) [resolution 168,112]
304. 1 | 6 [avatar split clause 303,167,143]
305. humble(fred) <- (1) [resolution 144,74]
306. 23 | ~1 [avatar split clause 305,143,252]
307. ~funny(fred) <- (23) [resolution 254,72]
308. strong(fred) <- (23) [resolution 254,71]
313. funny(fred) | calm(fred) <- (23) [resolution 110,308]
320. calm(fred) <- (23) [subsumption resolution 313,307]
321. $false <- (~3, 23) [subsumption resolution 320,153]
322. 3 | ~23 [avatar contradiction clause 321]
345. $false [avatar sat refutation 285,302,304,306,322]
% SZS output end Proof for 523668768048031044576075
% ------------------------------
% 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 not patient or rich is both generous and tall and vice versa.
If susan is either rich or tall then someone is both strong and not rich and vice versa.
If someone is both creative and not brave then lucy is not old.
If lucy is either not wise or generous then someone is both creative and curious.
If lucy is both calm and curious then mary is both quiet and tall.
Everyone who is either not funny or funny is not generous.
Everyone who is either not generous or tall is not curious or strong and vice versa.
If john is tall or not kind then mary is both not happy and not rich and vice versa.
If someone is calm or not creative then susan is either wise or calm and vice versa.
If mary is both not tall and strong then someone is both not funny and not tall and vice versa.
Everyone who is both not patient and happy is not generous.
Everyone who is both patient and not tall is tall.
If paul is both tall and calm then someone is quiet and vice versa.
If susan is either not happy or tall then someone is curious and vice versa.
Everyone who is brave is both not brave and not humble.
Mary is either strong or old.
Susan is both humble and not kind.
Paul is either not old or not generous.
Someone is not creative or tall.
Susan is either not generous or not wise.
Paul is either not creative or not rich.
Lucy is not humble. | Susan is not curious. | contradiction | (![X]:((~patient(X)<~>rich(X))<=>(generous(X)&tall(X))))&
(((rich(susan)<~>tall(susan)))<=>(?[X]:((strong(X)&~rich(X)))))&
((?[X]:((creative(X)&~brave(X))))=>(~old(lucy)))&
(((~wise(lucy)<~>generous(lucy)))=>(?[X]:((creative(X)&curious(X)))))&
(((calm(lucy)&curious(lucy)))=>((quiet(mary)&tall(mary))))&
(![X]:((~funny(X)<~>funny(X))=>~generous(X)))&
(![X]:((~generous(X)<~>tall(X))<=>(~curious(X)|strong(X))))&
(((tall(john)|~kind(john)))<=>((~happy(mary)&~rich(mary))))&
((?[X]:((calm(X)|~creative(X))))<=>((wise(susan)<~>calm(susan))))&
(((~tall(mary)&strong(mary)))<=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:((~patient(X)&happy(X))=>~generous(X)))&
(![X]:((patient(X)&~tall(X))=>tall(X)))&
(((tall(paul)&calm(paul)))<=>(?[X]:(quiet(X))))&
(((~happy(susan)<~>tall(susan)))<=>(?[X]:(curious(X))))&
(![X]:(brave(X)=>(~brave(X)&~humble(X))))&
((strong(mary)<~>old(mary)))&
((humble(susan)&~kind(susan)))&
((~old(paul)<~>~generous(paul)))&
(?[X]:((~creative(X)|tall(X))))&
((~generous(susan)<~>~wise(susan)))&
((~creative(paul)<~>~rich(paul)))&
(~humble(lucy)) | ~curious(susan) | [
"p0",
"p1",
"p5",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 745462685701532876310923
% SZS output start Proof for 745462685701532876310923
1. ! [X0] : ((~patient(X0) <~> rich(X0)) <=> (tall(X0) & generous(X0))) [input p0]
2. (rich(susan) <~> tall(susan)) <=> ? [X0] : (~rich(X0) & strong(X0)) [input p1]
6. ! [X0] : ((~funny(X0) <~> funny(X0)) => ~generous(X0)) [input p5]
7. ! [X0] : ((~generous(X0) <~> tall(X0)) <=> (strong(X0) | ~curious(X0))) [input p6]
12. ! [X0] : ((~tall(X0) & patient(X0)) => tall(X0)) [input p11]
23. ~curious(susan) [input hypothesis]
28. ! [X0] : (~generous(X0) | (~funny(X0) <=> funny(X0))) [ennf transformation 6]
31. ! [X0] : (tall(X0) | (tall(X0) | ~patient(X0))) [ennf transformation 12]
32. ! [X0] : (tall(X0) | tall(X0) | ~patient(X0)) [flattening 31]
34. ! [X0] : ((((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0))))) [nnf transformation 1]
35. ! [X0] : ((((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0))))) [flattening 34]
36. (((~tall(susan) | ~rich(susan)) & (tall(susan) | rich(susan))) | ! [X0] : (rich(X0) | ~strong(X0))) & (? [X0] : (~rich(X0) & strong(X0)) | ((rich(susan) | ~tall(susan)) & (tall(susan) | ~rich(susan)))) [nnf transformation 2]
37. (((~tall(susan) | ~rich(susan)) & (tall(susan) | rich(susan))) | ! [X0] : (rich(X0) | ~strong(X0))) & (? [X1] : (~rich(X1) & strong(X1)) | ((rich(susan) | ~tall(susan)) & (tall(susan) | ~rich(susan)))) [rectify 36]
38. ? [X1] : (~rich(X1) & strong(X1)) => (~rich(sK0) & strong(sK0)) [choice axiom]
39. (((~tall(susan) | ~rich(susan)) & (tall(susan) | rich(susan))) | ! [X0] : (rich(X0) | ~strong(X0))) & ((~rich(sK0) & strong(sK0)) | ((rich(susan) | ~tall(susan)) & (tall(susan) | ~rich(susan)))) [skolemisation 37,38]
43. ! [X0] : (~generous(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) [nnf transformation 28]
44. ! [X0] : ((((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | (~strong(X0) & curious(X0))) & ((strong(X0) | ~curious(X0)) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0))))) [nnf transformation 7]
45. ! [X0] : ((((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | (~strong(X0) & curious(X0))) & (strong(X0) | ~curious(X0) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0))))) [flattening 44]
72. generous(X0) | rich(X0) | patient(X0) [cnf transformation 35]
78. strong(sK0) | tall(susan) | ~rich(susan) [cnf transformation 39]
80. ~rich(sK0) | tall(susan) | ~rich(susan) [cnf transformation 39]
91. ~generous(X0) | funny(X0) | funny(X0) [cnf transformation 43]
92. ~generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 43]
97. ~tall(X0) | generous(X0) | curious(X0) [cnf transformation 45]
98. ~tall(X0) | generous(X0) | ~strong(X0) [cnf transformation 45]
115. tall(X0) | tall(X0) | ~patient(X0) [cnf transformation 32]
137. ~curious(susan) [cnf transformation 23]
139. ~patient(X0) | tall(X0) [duplicate literal removal 115]
140. ~generous(X0) | funny(X0) [duplicate literal removal 91]
141. ~funny(X0) | ~generous(X0) [duplicate literal removal 92]
146. 2 <=> rich(susan) [avatar definition]
148. ~rich(susan) <- (~2) [avatar component clause 146]
150. 3 <=> tall(susan) [avatar definition]
151. tall(susan) <- (3) [avatar component clause 150]
152. ~tall(susan) <- (~3) [avatar component clause 150]
156. 4 <=> rich(sK0) [avatar definition]
158. ~rich(sK0) <- (~4) [avatar component clause 156]
160. ~2 | 3 | ~4 [avatar split clause 80,156,150,146]
162. 5 <=> strong(sK0) [avatar definition]
164. strong(sK0) <- (5) [avatar component clause 162]
166. ~2 | 3 | 5 [avatar split clause 78,162,150,146]
213. ~generous(X0) [subsumption resolution 140,141]
214. ~strong(X0) | ~tall(X0) [subsumption resolution 98,213]
215. ~tall(X0) | curious(X0) [subsumption resolution 97,213]
351. ~tall(sK0) <- (5) [resolution 214,164]
353. curious(susan) <- (3) [resolution 215,151]
354. $false <- (3) [subsumption resolution 353,137]
355. ~3 [avatar contradiction clause 354]
356. rich(X0) | patient(X0) [resolution 72,213]
359. patient(sK0) <- (~4) [resolution 356,158]
401. tall(sK0) <- (~4) [resolution 359,139]
402. $false <- (~4, 5) [subsumption resolution 401,351]
403. 4 | ~5 [avatar contradiction clause 402]
404. patient(susan) <- (~2) [resolution 148,356]
406. tall(susan) <- (~2) [resolution 404,139]
407. $false <- (~2, ~3) [subsumption resolution 406,152]
408. 2 | 3 [avatar contradiction clause 407]
409. $false [avatar sat refutation 160,166,355,403,408]
% SZS output end Proof for 745462685701532876310923
% ------------------------------
% 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 |
If fred is both not creative and happy then john is either rich or curious and vice versa. Everyone who is either funny or creative is kind and vice versa. If someone is either not creative or quiet then susan is not quiet or old. If someone is either not tall or calm then someone is both not patient and tall and vice versa. If someone is both humble and generous then mary is not generous and vice versa. If john is either patient or creative then mary is wise or funny. Everyone who is both not strong and wise is not curious and vice versa. Everyone who is not kind or kind is either kind or calm. Everyone who is both humble and tall is either old or not rich. If someone is both old and not rich then someone is patient or curious and vice versa. Everyone who is patient is not patient or not humble and vice versa. If someone is not quiet or rich then someone is both calm and creative and vice versa. If someone is old or tall then susan is both generous and wise. If someone is patient then someone is not quiet or not happy. Everyone who is not curious or not happy is creative. Everyone who is curious or not calm is humble or not patient and vice versa. Someone is both calm and old. Someone is not quiet. Someone is either not wise or not rich. Someone is creative. Someone is quiet or tall. John is not tall or humble. | John is rich. | contradiction | (((~creative(fred)&happy(fred)))<=>((rich(john)<~>curious(john))))&
(![X]:((funny(X)<~>creative(X))<=>kind(X)))&
((?[X]:((~creative(X)<~>quiet(X))))=>((~quiet(susan)|old(susan))))&
((?[X]:((~tall(X)<~>calm(X))))<=>(?[X]:((~patient(X)&tall(X)))))&
((?[X]:((humble(X)&generous(X))))<=>(~generous(mary)))&
(((patient(john)<~>creative(john)))=>((wise(mary)|funny(mary))))&
(![X]:((~strong(X)&wise(X))<=>~curious(X)))&
(![X]:((~kind(X)|kind(X))=>(kind(X)<~>calm(X))))&
(![X]:((humble(X)&tall(X))=>(old(X)<~>~rich(X))))&
((?[X]:((old(X)&~rich(X))))<=>(?[X]:((patient(X)|curious(X)))))&
(![X]:(patient(X)<=>(~patient(X)|~humble(X))))&
((?[X]:((~quiet(X)|rich(X))))<=>(?[X]:((calm(X)&creative(X)))))&
((?[X]:((old(X)|tall(X))))=>((generous(susan)&wise(susan))))&
((?[X]:(patient(X)))=>(?[X]:((~quiet(X)|~happy(X)))))&
(![X]:((~curious(X)|~happy(X))=>creative(X)))&
(![X]:((curious(X)|~calm(X))<=>(humble(X)|~patient(X))))&
(?[X]:((calm(X)&old(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(?[X]:(creative(X)))&
(?[X]:((quiet(X)|tall(X))))&
((~tall(john)|humble(john))) | rich(john) | [
"p0",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7129600394525875547942732
% SZS output start Proof for 7129600394525875547942732
1. (happy(fred) & ~creative(fred)) <=> (rich(john) <~> curious(john)) [input p0]
11. ! [X0] : (patient(X0) <=> (~humble(X0) | ~patient(X0))) [input p10]
15. ! [X0] : ((~happy(X0) | ~curious(X0)) => creative(X0)) [input p14]
16. ! [X0] : ((~calm(X0) | curious(X0)) <=> (~patient(X0) | humble(X0))) [input p15]
23. rich(john) [input hypothesis]
37. ! [X0] : (creative(X0) | (happy(X0) & curious(X0))) [ennf transformation 15]
38. ((happy(fred) & ~creative(fred)) | ((rich(john) | ~curious(john)) & (curious(john) | ~rich(john)))) & (((~curious(john) | ~rich(john)) & (curious(john) | rich(john))) | (~happy(fred) | creative(fred))) [nnf transformation 1]
39. ((happy(fred) & ~creative(fred)) | ((rich(john) | ~curious(john)) & (curious(john) | ~rich(john)))) & (((~curious(john) | ~rich(john)) & (curious(john) | rich(john))) | ~happy(fred) | creative(fred)) [flattening 38]
61. ! [X0] : ((patient(X0) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 11]
62. ! [X0] : ((patient(X0) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | ~patient(X0))) [flattening 61]
71. ! [X0] : (((~calm(X0) | curious(X0)) | (patient(X0) & ~humble(X0))) & ((~patient(X0) | humble(X0)) | (calm(X0) & ~curious(X0)))) [nnf transformation 16]
72. ! [X0] : ((~calm(X0) | curious(X0) | (patient(X0) & ~humble(X0))) & (~patient(X0) | humble(X0) | (calm(X0) & ~curious(X0)))) [flattening 71]
86. ~creative(fred) | curious(john) | ~rich(john) [cnf transformation 39]
121. ~humble(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 62]
122. patient(X0) | patient(X0) [cnf transformation 62]
134. curious(X0) | creative(X0) [cnf transformation 37]
136. ~patient(X0) | humble(X0) | ~curious(X0) [cnf transformation 72]
148. rich(john) [cnf transformation 23]
149. ~humble(X0) | ~patient(X0) [duplicate literal removal 121]
150. patient(X0) [duplicate literal removal 122]
154. 1 <=> curious(john) [avatar definition]
155. curious(john) <- (1) [avatar component clause 154]
158. 2 <=> rich(john) [avatar definition]
168. 4 <=> creative(fred) [avatar definition]
170. ~creative(fred) <- (~4) [avatar component clause 168]
172. ~2 | 1 | ~4 [avatar split clause 86,168,154,158]
259. 24 <=> ! [X1] : ~curious(X1) [avatar definition]
260. ~curious(X1) <- (24) [avatar component clause 259]
288. ~humble(X0) [subsumption resolution 149,150]
349. humble(X0) | ~curious(X0) [subsumption resolution 136,150]
350. ~curious(X0) [subsumption resolution 349,288]
351. 24 [avatar split clause 350,259]
372. 2 [avatar split clause 148,158]
405. creative(X0) <- (24) [resolution 134,260]
406. $false <- (~4, 24) [resolution 405,170]
409. 4 | ~24 [avatar contradiction clause 406]
410. $false <- (1, 24) [subsumption resolution 155,260]
411. ~1 | ~24 [avatar contradiction clause 410]
412. $false [avatar sat refutation 172,351,372,409,411]
% SZS output end Proof for 7129600394525875547942732
% ------------------------------
% 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 |
Everyone who is not wise is kind or not calm.
Everyone who is not kind or not funny is both funny and not old.
If someone is both generous and not rich then someone is not generous or not happy and vice versa.
Everyone who is rich is not patient.
Everyone who is both not kind and curious is either quiet or not old and vice versa.
If paul is both creative and not strong then alice is creative and vice versa.
Everyone who is old is either not brave or not quiet.
If john is both kind and patient then someone is not generous.
If paul is either calm or wise then someone is funny.
Everyone who is calm is both creative and wise.
Everyone who is either not wise or calm is either humble or not creative and vice versa.
Everyone who is both not old and wise is either not quiet or not patient and vice versa.
If someone is not happy or wise then paul is either not funny or kind.
Everyone who is not kind is not rich or not happy and vice versa.
Everyone who is both not tall and creative is not brave and vice versa.
Everyone who is tall is not old or creative and vice versa.
John is either old or strong.
Someone is both not humble and not rich.
Someone is quiet or not creative.
Lucy is not humble.
Someone is rich or not old.
Mary is kind or not brave.
Alice is not patient or not kind. | Mary is not brave. | contradiction | (![X]:(~wise(X)=>(kind(X)|~calm(X))))&
(![X]:((~kind(X)|~funny(X))=>(funny(X)&~old(X))))&
((?[X]:((generous(X)&~rich(X))))<=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:(rich(X)=>~patient(X)))&
(![X]:((~kind(X)&curious(X))<=>(quiet(X)<~>~old(X))))&
(((creative(paul)&~strong(paul)))<=>(creative(alice)))&
(![X]:(old(X)=>(~brave(X)<~>~quiet(X))))&
(((kind(john)&patient(john)))=>(?[X]:(~generous(X))))&
(((calm(paul)<~>wise(paul)))=>(?[X]:(funny(X))))&
(![X]:(calm(X)=>(creative(X)&wise(X))))&
(![X]:((~wise(X)<~>calm(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((~old(X)&wise(X))<=>(~quiet(X)<~>~patient(X))))&
((?[X]:((~happy(X)|wise(X))))=>((~funny(paul)<~>kind(paul))))&
(![X]:(~kind(X)<=>(~rich(X)|~happy(X))))&
(![X]:((~tall(X)&creative(X))<=>~brave(X)))&
(![X]:(tall(X)<=>(~old(X)|creative(X))))&
((old(john)<~>strong(john)))&
(?[X]:((~humble(X)&~rich(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(~humble(lucy))&
(?[X]:((rich(X)|~old(X))))&
((kind(mary)|~brave(mary)))&
((~patient(alice)|~kind(alice))) | ~brave(mary) | [
"p1",
"p4",
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5363619838491796274908642
% SZS output start Proof for 5363619838491796274908642
2. ! [X0] : ((~funny(X0) | ~kind(X0)) => (~old(X0) & funny(X0))) [input p1]
5. ! [X0] : ((curious(X0) & ~kind(X0)) <=> (quiet(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : (old(X0) => (~brave(X0) <~> ~quiet(X0))) [input p6]
15. ! [X0] : ((creative(X0) & ~tall(X0)) <=> ~brave(X0)) [input p14]
16. ! [X0] : (tall(X0) <=> (creative(X0) | ~old(X0))) [input p15]
24. ~brave(mary) [input hypothesis]
28. ! [X0] : ((~old(X0) & funny(X0)) | (funny(X0) & kind(X0))) [ennf transformation 2]
30. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) | ~old(X0)) [ennf transformation 7]
41. ! [X0] : (((curious(X0) & ~kind(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | (~curious(X0) | kind(X0)))) [nnf transformation 5]
42. ! [X0] : (((curious(X0) & ~kind(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ~curious(X0) | kind(X0))) [flattening 41]
45. ! [X0] : (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | ~old(X0)) [nnf transformation 30]
57. ! [X0] : (((creative(X0) & ~tall(X0)) | brave(X0)) & (~brave(X0) | (~creative(X0) | tall(X0)))) [nnf transformation 15]
58. ! [X0] : (((creative(X0) & ~tall(X0)) | brave(X0)) & (~brave(X0) | ~creative(X0) | tall(X0))) [flattening 57]
59. ! [X0] : ((tall(X0) | (~creative(X0) & old(X0))) & ((creative(X0) | ~old(X0)) | ~tall(X0))) [nnf transformation 16]
60. ! [X0] : ((tall(X0) | (~creative(X0) & old(X0))) & (creative(X0) | ~old(X0) | ~tall(X0))) [flattening 59]
71. ~old(X0) | kind(X0) [cnf transformation 28]
81. ~kind(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 42]
89. quiet(X0) | brave(X0) | ~old(X0) [cnf transformation 45]
117. ~tall(X0) | brave(X0) [cnf transformation 58]
120. tall(X0) | old(X0) [cnf transformation 60]
131. ~brave(mary) [cnf transformation 24]
163. ~old(X0) | ~quiet(X0) [subsumption resolution 81,71]
180. brave(X0) | ~old(X0) [subsumption resolution 89,163]
245. 23 <=> brave(mary) [avatar definition]
247. ~brave(mary) <- (~23) [avatar component clause 245]
258. ~23 [avatar split clause 131,245]
267. old(X0) | brave(X0) [resolution 120,117]
268. brave(X0) [subsumption resolution 267,180]
270. $false <- (~23) [resolution 268,247]
271. 23 [avatar contradiction clause 270]
272. $false [avatar sat refutation 258,271]
% SZS output end Proof for 5363619838491796274908642
% ------------------------------
% 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 patient is not strong and vice versa.
If john is happy then someone is humble or not funny and vice versa.
If paul is brave then fred is not creative or not old.
If someone is both brave and not generous then someone is either tall or not creative.
Everyone who is either not rich or kind is both kind and humble and vice versa.
Everyone who is both kind and wise is brave or not quiet.
Everyone who is not curious or curious is not quiet and vice versa.
Everyone who is wise or happy is old or calm.
Everyone who is happy is not creative or not happy and vice versa.
Everyone who is either not patient or creative is both calm and funny.
If someone is both not strong and creative then someone is either rich or not creative and vice versa.
Everyone who is either strong or calm is not tall and vice versa.
If lucy is not creative or not happy then someone is calm and vice versa.
Everyone who is creative or tall is funny and vice versa.
If someone is patient or not tall then someone is wise.
Everyone who is kind is either tall or not quiet and vice versa.
Someone is happy.
Someone is funny.
Someone is either not humble or generous.
Mary is not happy or tall.
Lucy is either not rich or not tall.
Someone is wise or happy.
Mary is either not creative or not funny. | Paul is not calm. | neutral | (![X]:(~patient(X)<=>~strong(X)))&
((happy(john))<=>(?[X]:((humble(X)|~funny(X)))))&
((brave(paul))=>((~creative(fred)|~old(fred))))&
((?[X]:((brave(X)&~generous(X))))=>(?[X]:((tall(X)<~>~creative(X)))))&
(![X]:((~rich(X)<~>kind(X))<=>(kind(X)&humble(X))))&
(![X]:((kind(X)&wise(X))=>(brave(X)|~quiet(X))))&
(![X]:((~curious(X)|curious(X))<=>~quiet(X)))&
(![X]:((wise(X)|happy(X))=>(old(X)|calm(X))))&
(![X]:(happy(X)<=>(~creative(X)|~happy(X))))&
(![X]:((~patient(X)<~>creative(X))=>(calm(X)&funny(X))))&
((?[X]:((~strong(X)&creative(X))))<=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((strong(X)<~>calm(X))<=>~tall(X)))&
(((~creative(lucy)|~happy(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((creative(X)|tall(X))<=>funny(X)))&
((?[X]:((patient(X)|~tall(X))))=>(?[X]:(wise(X))))&
(![X]:(kind(X)<=>(tall(X)<~>~quiet(X))))&
(?[X]:(happy(X)))&
(?[X]:(funny(X)))&
(?[X]:((~humble(X)<~>generous(X))))&
((~happy(mary)|tall(mary)))&
((~rich(lucy)<~>~tall(lucy)))&
(?[X]:((wise(X)|happy(X))))&
((~creative(mary)<~>~funny(mary))) | ~calm(paul) | [] | null | 0 |
If susan is not strong or rich then alice is either funny or not brave and vice versa.
Everyone who is curious is generous or curious and vice versa.
If someone is not quiet or calm then someone is tall or creative.
Everyone who is either quiet or tall is wise and vice versa.
If someone is either funny or not brave then mary is patient and vice versa.
If fred is not rich or not kind then susan is both old and not old.
If someone is either happy or not curious then someone is both not brave and brave.
If someone is not curious or creative then someone is not creative.
If someone is happy or not calm then susan is not quiet and vice versa.
Everyone who is both strong and rich is not calm or quiet and vice versa.
Everyone who is quiet or tall is not rich or not brave.
Everyone who is both calm and old is wise or curious and vice versa.
If someone is tall then john is both strong and not wise.
Everyone who is either strong or not generous is not wise and vice versa.
If someone is both not tall and not old then mary is rich or not generous and vice versa.
If alice is either strong or not funny then someone is either not humble or patient and vice versa.
Mary is not old or generous.
Paul is tall or not creative.
Someone is either not brave or strong.
Someone is patient.
Fred is both not strong and happy.
Someone is either not humble or not wise.
Lucy is both generous and tall. | John is not curious. | contradiction | (((~strong(susan)|rich(susan)))<=>((funny(alice)<~>~brave(alice))))&
(![X]:(curious(X)<=>(generous(X)|curious(X))))&
((?[X]:((~quiet(X)|calm(X))))=>(?[X]:((tall(X)|creative(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>wise(X)))&
((?[X]:((funny(X)<~>~brave(X))))<=>(patient(mary)))&
(((~rich(fred)|~kind(fred)))=>((old(susan)&~old(susan))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&brave(X)))))&
((?[X]:((~curious(X)|creative(X))))=>(?[X]:(~creative(X))))&
((?[X]:((happy(X)|~calm(X))))<=>(~quiet(susan)))&
(![X]:((strong(X)&rich(X))<=>(~calm(X)|quiet(X))))&
(![X]:((quiet(X)|tall(X))=>(~rich(X)|~brave(X))))&
(![X]:((calm(X)&old(X))<=>(wise(X)|curious(X))))&
((?[X]:(tall(X)))=>((strong(john)&~wise(john))))&
(![X]:((strong(X)<~>~generous(X))<=>~wise(X)))&
((?[X]:((~tall(X)&~old(X))))<=>((rich(mary)|~generous(mary))))&
(((strong(alice)<~>~funny(alice)))<=>(?[X]:((~humble(X)<~>patient(X)))))&
((~old(mary)|generous(mary)))&
((tall(paul)|~creative(paul)))&
(?[X]:((~brave(X)<~>strong(X))))&
(?[X]:(patient(X)))&
((~strong(fred)&happy(fred)))&
(?[X]:((~humble(X)<~>~wise(X))))&
((generous(lucy)&tall(lucy))) | ~curious(john) | [
"p1",
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5643718461237983436203206
% SZS output start Proof for 5643718461237983436203206
2. ! [X0] : (curious(X0) <=> (curious(X0) | generous(X0))) [input p1]
13. ? [X0] : tall(X0) => (~wise(john) & strong(john)) [input p12]
14. ! [X0] : ((strong(X0) <~> ~generous(X0)) <=> ~wise(X0)) [input p13]
23. tall(lucy) & generous(lucy) [input p22]
24. ~curious(john) [input hypothesis]
35. (~wise(john) & strong(john)) | ! [X0] : ~tall(X0) [ennf transformation 13]
38. ! [X0] : ((curious(X0) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | ~curious(X0))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | ~curious(X0))) [flattening 38]
63. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | wise(X0)) & (~wise(X0) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [nnf transformation 14]
88. ~generous(X0) | curious(X0) [cnf transformation 39]
123. strong(john) | ~tall(X0) [cnf transformation 35]
124. ~wise(john) | ~tall(X0) [cnf transformation 35]
128. ~strong(X0) | generous(X0) | wise(X0) [cnf transformation 63]
152. tall(lucy) [cnf transformation 23]
153. ~curious(john) [cnf transformation 24]
273. 27 <=> ! [X0] : ~tall(X0) [avatar definition]
274. ~tall(X0) <- (27) [avatar component clause 273]
276. 28 <=> wise(john) [avatar definition]
278. ~wise(john) <- (~28) [avatar component clause 276]
279. 27 | ~28 [avatar split clause 124,276,273]
281. 29 <=> strong(john) [avatar definition]
283. strong(john) <- (29) [avatar component clause 281]
284. 27 | 29 [avatar split clause 123,281,273]
371. $false <- (27) [resolution 274,152]
372. ~27 [avatar contradiction clause 371]
410. generous(john) | wise(john) <- (29) [resolution 128,283]
412. generous(john) <- (~28, 29) [subsumption resolution 410,278]
424. curious(john) <- (~28, 29) [resolution 412,88]
425. $false <- (~28, 29) [subsumption resolution 424,153]
426. 28 | ~29 [avatar contradiction clause 425]
427. $false [avatar sat refutation 279,284,372,426]
% SZS output end Proof for 5643718461237983436203206
% ------------------------------
% 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 |
If someone is kind or not rich then lucy is funny or not wise.
If someone is funny or not funny then someone is not tall or not brave.
Everyone who is not tall or generous is both not humble and kind and vice versa.
Everyone who is either happy or tall is not generous.
Everyone who is either not creative or creative is either kind or wise.
If fred is either not kind or not patient then fred is both not generous and not old.
If someone is patient then paul is either curious or not generous.
Everyone who is either brave or not strong is kind or brave and vice versa.
Everyone who is calm or rich is both not creative and not strong and vice versa.
Everyone who is not old or not generous is both happy and wise.
Everyone who is either not patient or not funny is either creative or calm and vice versa.
If alice is either not wise or patient then john is not generous or not calm and vice versa.
Everyone who is either not patient or creative is both kind and strong and vice versa.
Everyone who is either not happy or not generous is patient or humble and vice versa.
Everyone who is not quiet or kind is not kind or quiet.
Lucy is not calm.
Alice is patient or not creative.
Susan is both not rich and quiet.
Lucy is either not creative or curious.
John is both curious and not quiet.
Someone is not kind. | Alice is not kind. | neutral | ((?[X]:((kind(X)|~rich(X))))=>((funny(lucy)|~wise(lucy))))&
((?[X]:((funny(X)|~funny(X))))=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:((~tall(X)|generous(X))<=>(~humble(X)&kind(X))))&
(![X]:((happy(X)<~>tall(X))=>~generous(X)))&
(![X]:((~creative(X)<~>creative(X))=>(kind(X)<~>wise(X))))&
(((~kind(fred)<~>~patient(fred)))=>((~generous(fred)&~old(fred))))&
((?[X]:(patient(X)))=>((curious(paul)<~>~generous(paul))))&
(![X]:((brave(X)<~>~strong(X))<=>(kind(X)|brave(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)&~strong(X))))&
(![X]:((~old(X)|~generous(X))=>(happy(X)&wise(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(creative(X)<~>calm(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~generous(john)|~calm(john))))&
(![X]:((~patient(X)<~>creative(X))<=>(kind(X)&strong(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(patient(X)|humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(~kind(X)|quiet(X))))&
(~calm(lucy))&
((patient(alice)|~creative(alice)))&
((~rich(susan)&quiet(susan)))&
((~creative(lucy)<~>curious(lucy)))&
((curious(john)&~quiet(john)))&
(?[X]:(~kind(X))) | ~kind(alice) | [] | null | 0 |
Everyone who is not curious is either not rich or creative and vice versa.
Everyone who is either kind or quiet is rich and vice versa.
Everyone who is brave is not rich and vice versa.
Everyone who is creative is both kind and quiet.
If fred is either tall or calm then someone is not quiet.
If alice is either not rich or not wise then mary is either not creative or curious and vice versa.
Everyone who is both funny and humble is either not rich or not humble and vice versa.
If someone is generous or tall then someone is not old.
If john is both wise and brave then susan is either funny or not curious and vice versa.
Everyone who is either not curious or not rich is either creative or not calm.
Everyone who is either not patient or humble is old or generous.
If someone is not brave or funny then fred is not old or not calm.
Everyone who is not humble is both not rich and strong and vice versa.
Everyone who is either creative or not creative is either not quiet or calm and vice versa.
If fred is not curious then lucy is both curious and not humble.
Everyone who is brave is both not brave and not happy.
Fred is tall.
Someone is either not strong or not generous.
Lucy is either funny or not tall.
Susan is either not generous or not rich.
Someone is either curious or not patient.
Someone is old.
Someone is either old or happy.
Fred is not happy. | Alice is funny. | contradiction | (![X]:(~curious(X)<=>(~rich(X)<~>creative(X))))&
(![X]:((kind(X)<~>quiet(X))<=>rich(X)))&
(![X]:(brave(X)<=>~rich(X)))&
(![X]:(creative(X)=>(kind(X)&quiet(X))))&
(((tall(fred)<~>calm(fred)))=>(?[X]:(~quiet(X))))&
(((~rich(alice)<~>~wise(alice)))<=>((~creative(mary)<~>curious(mary))))&
(![X]:((funny(X)&humble(X))<=>(~rich(X)<~>~humble(X))))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:(~old(X))))&
(((wise(john)&brave(john)))<=>((funny(susan)<~>~curious(susan))))&
(![X]:((~curious(X)<~>~rich(X))=>(creative(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>humble(X))=>(old(X)|generous(X))))&
((?[X]:((~brave(X)|funny(X))))=>((~old(fred)|~calm(fred))))&
(![X]:(~humble(X)<=>(~rich(X)&strong(X))))&
(![X]:((creative(X)<~>~creative(X))<=>(~quiet(X)<~>calm(X))))&
((~curious(fred))=>((curious(lucy)&~humble(lucy))))&
(![X]:(brave(X)=>(~brave(X)&~happy(X))))&
(tall(fred))&
(?[X]:((~strong(X)<~>~generous(X))))&
((funny(lucy)<~>~tall(lucy)))&
((~generous(susan)<~>~rich(susan)))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:(old(X)))&
(?[X]:((old(X)<~>happy(X))))&
(~happy(fred)) | funny(alice) | [
"p2",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2707547421214633526940786
% SZS output start Proof for 2707547421214633526940786
3. ! [X0] : (brave(X0) <=> ~rich(X0)) [input p2]
7. ! [X0] : ((humble(X0) & funny(X0)) <=> (~rich(X0) <~> ~humble(X0))) [input p6]
16. ! [X0] : (brave(X0) => (~happy(X0) & ~brave(X0))) [input p15]
25. funny(alice) [input hypothesis]
36. ! [X0] : ((~happy(X0) & ~brave(X0)) | ~brave(X0)) [ennf transformation 16]
39. ! [X0] : ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))) [nnf transformation 3]
44. ! [X0] : (((humble(X0) & funny(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0)))) & (((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | (~humble(X0) | ~funny(X0)))) [nnf transformation 7]
45. ! [X0] : (((humble(X0) & funny(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0)))) & (((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | ~humble(X0) | ~funny(X0))) [flattening 44]
78. brave(X0) | rich(X0) [cnf transformation 39]
91. ~humble(X0) | ~rich(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 45]
96. humble(X0) | ~rich(X0) | humble(X0) [cnf transformation 45]
126. ~brave(X0) | ~brave(X0) [cnf transformation 36]
141. funny(alice) [cnf transformation 25]
142. ~brave(X0) [duplicate literal removal 126]
147. ~humble(X0) | ~rich(X0) | ~funny(X0) [duplicate literal removal 91]
148. ~rich(X0) | humble(X0) [duplicate literal removal 96]
187. ~funny(X0) | ~rich(X0) [subsumption resolution 147,148]
304. rich(X1) [resolution 78,142]
312. ~rich(alice) [resolution 187,141]
313. $false [subsumption resolution 312,304]
% SZS output end Proof for 2707547421214633526940786
% ------------------------------
% 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 humble or not humble is not strong and vice versa.
Everyone who is either not calm or not kind is not humble.
Everyone who is curious is not quiet or strong.
Everyone who is old is rich and vice versa.
Everyone who is brave or happy is wise and vice versa.
If alice is both old and not creative then mary is not calm or not strong.
Everyone who is curious is creative and vice versa.
Everyone who is not happy is both not rich and not generous.
If mary is creative then someone is either old or not rich.
Everyone who is curious or quiet is both not patient and not tall.
Everyone who is not rich is either calm or wise.
If someone is both calm and not generous then someone is both not happy and not generous.
If someone is not wise or not quiet then someone is not old.
If someone is either tall or not happy then susan is not happy or strong and vice versa.
If someone is not quiet then someone is strong and vice versa.
If someone is either not brave or curious then someone is both happy and not creative.
Someone is either not funny or generous.
Lucy is creative or not tall.
Mary is either quiet or not wise.
Paul is happy or not kind.
Susan is either not quiet or not funny.
Someone is not happy or not humble.
Someone is kind or not patient. | Lucy is not rich. | neutral | (![X]:((humble(X)|~humble(X))<=>~strong(X)))&
(![X]:((~calm(X)<~>~kind(X))=>~humble(X)))&
(![X]:(curious(X)=>(~quiet(X)|strong(X))))&
(![X]:(old(X)<=>rich(X)))&
(![X]:((brave(X)|happy(X))<=>wise(X)))&
(((old(alice)&~creative(alice)))=>((~calm(mary)|~strong(mary))))&
(![X]:(curious(X)<=>creative(X)))&
(![X]:(~happy(X)=>(~rich(X)&~generous(X))))&
((creative(mary))=>(?[X]:((old(X)<~>~rich(X)))))&
(![X]:((curious(X)|quiet(X))=>(~patient(X)&~tall(X))))&
(![X]:(~rich(X)=>(calm(X)<~>wise(X))))&
((?[X]:((calm(X)&~generous(X))))=>(?[X]:((~happy(X)&~generous(X)))))&
((?[X]:((~wise(X)|~quiet(X))))=>(?[X]:(~old(X))))&
((?[X]:((tall(X)<~>~happy(X))))<=>((~happy(susan)|strong(susan))))&
((?[X]:(~quiet(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>curious(X))))=>(?[X]:((happy(X)&~creative(X)))))&
(?[X]:((~funny(X)<~>generous(X))))&
((creative(lucy)|~tall(lucy)))&
((quiet(mary)<~>~wise(mary)))&
((happy(paul)|~kind(paul)))&
((~quiet(susan)<~>~funny(susan)))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((kind(X)|~patient(X)))) | ~rich(lucy) | [] | null | 0 |
Everyone who is either not patient or not funny is not tall or not old.
If paul is both funny and not curious then alice is either creative or funny.
If susan is both not kind and not tall then susan is not strong and vice versa.
Everyone who is either happy or funny is both generous and not strong and vice versa.
If mary is old or kind then lucy is both not funny and not curious and vice versa.
Everyone who is either not strong or creative is both strong and tall and vice versa.
Everyone who is happy or not creative is either not tall or generous and vice versa.
Everyone who is both old and not happy is not brave or not quiet and vice versa.
Everyone who is not kind is either not tall or rich and vice versa.
If someone is both creative and not strong then susan is curious or not generous.
If someone is either not tall or curious then someone is not happy and vice versa.
Everyone who is either funny or not wise is kind or not brave and vice versa.
If paul is both humble and not strong then fred is not tall and vice versa.
If fred is both curious and rich then susan is humble.
If lucy is not kind then paul is both wise and brave and vice versa.
Everyone who is both not tall and funny is both not quiet and not generous and vice versa.
Someone is both curious and not wise.
Someone is strong.
Someone is both not humble and not funny.
Alice is both not wise and not old.
Someone is old.
Someone is not tall or not humble.
Someone is either strong or curious.
Someone is both not brave and not strong. | Susan is quiet. | entailment | (![X]:((~patient(X)<~>~funny(X))=>(~tall(X)|~old(X))))&
(((funny(paul)&~curious(paul)))=>((creative(alice)<~>funny(alice))))&
(((~kind(susan)&~tall(susan)))<=>(~strong(susan)))&
(![X]:((happy(X)<~>funny(X))<=>(generous(X)&~strong(X))))&
(((old(mary)|kind(mary)))<=>((~funny(lucy)&~curious(lucy))))&
(![X]:((~strong(X)<~>creative(X))<=>(strong(X)&tall(X))))&
(![X]:((happy(X)|~creative(X))<=>(~tall(X)<~>generous(X))))&
(![X]:((old(X)&~happy(X))<=>(~brave(X)|~quiet(X))))&
(![X]:(~kind(X)<=>(~tall(X)<~>rich(X))))&
((?[X]:((creative(X)&~strong(X))))=>((curious(susan)|~generous(susan))))&
((?[X]:((~tall(X)<~>curious(X))))<=>(?[X]:(~happy(X))))&
(![X]:((funny(X)<~>~wise(X))<=>(kind(X)|~brave(X))))&
(((humble(paul)&~strong(paul)))<=>(~tall(fred)))&
(((curious(fred)&rich(fred)))=>(humble(susan)))&
((~kind(lucy))<=>((wise(paul)&brave(paul))))&
(![X]:((~tall(X)&funny(X))<=>(~quiet(X)&~generous(X))))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:(strong(X)))&
(?[X]:((~humble(X)&~funny(X))))&
((~wise(alice)&~old(alice)))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)|~humble(X))))&
(?[X]:((strong(X)<~>curious(X))))&
(?[X]:((~brave(X)&~strong(X)))) | quiet(susan) | [
"p3",
"p5",
"p6",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4023055948905903722616624
% SZS output start Proof for 4023055948905903722616624
4. ! [X0] : ((happy(X0) <~> funny(X0)) <=> (~strong(X0) & generous(X0))) [input p3]
6. ! [X0] : ((~strong(X0) <~> creative(X0)) <=> (tall(X0) & strong(X0))) [input p5]
7. ! [X0] : ((~creative(X0) | happy(X0)) <=> (~tall(X0) <~> generous(X0))) [input p6]
8. ! [X0] : ((~happy(X0) & old(X0)) <=> (~quiet(X0) | ~brave(X0))) [input p7]
16. ! [X0] : ((funny(X0) & ~tall(X0)) <=> (~generous(X0) & ~quiet(X0))) [input p15]
25. ~quiet(susan) [input hypothesis]
39. ! [X0] : ((((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) | (strong(X0) | ~generous(X0))) & ((~strong(X0) & generous(X0)) | ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0))))) [nnf transformation 4]
40. ! [X0] : ((((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) | strong(X0) | ~generous(X0)) & ((~strong(X0) & generous(X0)) | ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0))))) [flattening 39]
43. ! [X0] : ((((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | (~tall(X0) | ~strong(X0))) & ((tall(X0) & strong(X0)) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))))) [nnf transformation 6]
44. ! [X0] : ((((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | ~tall(X0) | ~strong(X0)) & ((tall(X0) & strong(X0)) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))))) [flattening 43]
45. ! [X0] : (((~creative(X0) | happy(X0)) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0)))) & (((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | (creative(X0) & ~happy(X0)))) [nnf transformation 7]
46. ! [X0] : ((~creative(X0) | happy(X0) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0)))) & (((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | (creative(X0) & ~happy(X0)))) [flattening 45]
47. ! [X0] : (((~happy(X0) & old(X0)) | (quiet(X0) & brave(X0))) & ((~quiet(X0) | ~brave(X0)) | (happy(X0) | ~old(X0)))) [nnf transformation 8]
48. ! [X0] : (((~happy(X0) & old(X0)) | (quiet(X0) & brave(X0))) & (~quiet(X0) | ~brave(X0) | happy(X0) | ~old(X0))) [flattening 47]
61. ! [X0] : (((funny(X0) & ~tall(X0)) | (generous(X0) | quiet(X0))) & ((~generous(X0) & ~quiet(X0)) | (~funny(X0) | tall(X0)))) [nnf transformation 16]
62. ! [X0] : (((funny(X0) & ~tall(X0)) | generous(X0) | quiet(X0)) & ((~generous(X0) & ~quiet(X0)) | ~funny(X0) | tall(X0))) [flattening 61]
86. ~funny(X0) | happy(X0) | generous(X0) [cnf transformation 40]
89. ~generous(X0) | happy(X0) | strong(X0) | funny(X0) [cnf transformation 40]
96. strong(X0) | creative(X0) | strong(X0) [cnf transformation 44]
99. ~strong(X0) | tall(X0) | ~creative(X0) [cnf transformation 44]
100. creative(X0) | ~strong(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 44]
104. ~generous(X0) | tall(X0) | ~happy(X0) [cnf transformation 46]
105. ~generous(X0) | tall(X0) | creative(X0) [cnf transformation 46]
107. ~generous(X0) | happy(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 46]
112. ~happy(X0) | quiet(X0) [cnf transformation 48]
136. ~generous(X0) | ~funny(X0) | tall(X0) [cnf transformation 62]
138. quiet(X0) | generous(X0) | funny(X0) [cnf transformation 62]
152. ~quiet(susan) [cnf transformation 25]
153. strong(X0) | creative(X0) [duplicate literal removal 96]
154. ~strong(X0) | creative(X0) | ~tall(X0) [duplicate literal removal 100]
174. 5 <=> strong(susan) [avatar definition]
175. ~strong(susan) <- (~5) [avatar component clause 174]
176. strong(susan) <- (5) [avatar component clause 174]
178. 6 <=> tall(susan) [avatar definition]
180. ~tall(susan) <- (~6) [avatar component clause 178]
218. 14 <=> generous(susan) [avatar definition]
219. generous(susan) <- (14) [avatar component clause 218]
422. generous(susan) | funny(susan) [resolution 138,152]
438. 53 <=> funny(susan) [avatar definition]
439. ~funny(susan) <- (~53) [avatar component clause 438]
440. funny(susan) <- (53) [avatar component clause 438]
441. 53 | 14 [avatar split clause 422,218,438]
448. ~funny(susan) | tall(susan) <- (14) [resolution 219,136]
450. tall(susan) | ~happy(susan) <- (14) [resolution 219,104]
451. ~funny(susan) <- (~6, 14) [subsumption resolution 448,180]
452. ~53 | 6 | ~14 [avatar split clause 451,218,178,438]
453. ~happy(susan) <- (~6, 14) [subsumption resolution 450,180]
455. creative(X1) | ~tall(X1) | creative(X1) [resolution 154,153]
459. ~tall(X1) | creative(X1) [duplicate literal removal 455]
496. happy(susan) | strong(susan) | funny(susan) <- (14) [resolution 89,219]
507. strong(susan) | funny(susan) <- (~6, 14) [subsumption resolution 496,453]
508. funny(susan) <- (~5, ~6, 14) [subsumption resolution 507,175]
509. $false <- (~5, ~6, 14, ~53) [subsumption resolution 508,439]
510. 5 | 6 | ~14 | 53 [avatar contradiction clause 509]
513. happy(susan) | generous(susan) <- (53) [resolution 440,86]
557. 65 <=> happy(susan) [avatar definition]
558. ~happy(susan) <- (~65) [avatar component clause 557]
559. happy(susan) <- (65) [avatar component clause 557]
560. 14 | 65 | ~53 [avatar split clause 513,438,557,218]
562. tall(susan) | ~creative(susan) <- (5) [resolution 176,99]
578. happy(susan) | ~tall(susan) | ~creative(susan) <- (14) [resolution 219,107]
582. tall(susan) | creative(susan) <- (14) [resolution 219,105]
702. quiet(susan) <- (65) [resolution 559,112]
704. $false <- (65) [subsumption resolution 702,152]
705. ~65 [avatar contradiction clause 704]
715. ~tall(susan) | ~creative(susan) <- (14, ~65) [subsumption resolution 578,558]
716. ~tall(susan) <- (14, ~65) [subsumption resolution 715,459]
717. ~6 | ~14 | 65 [avatar split clause 716,557,218,178]
722. creative(susan) <- (14) [subsumption resolution 582,459]
723. tall(susan) <- (5, 14) [subsumption resolution 562,722]
724. 6 | ~5 | ~14 [avatar split clause 723,218,174,178]
728. $false [avatar sat refutation 441,452,510,560,705,717,724]
% SZS output end Proof for 4023055948905903722616624
% ------------------------------
% 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa.
Everyone who is not kind or not funny is either wise or not funny and vice versa.
Everyone who is either happy or not calm is either not happy or not calm.
Everyone who is either quiet or not kind is quiet or kind.
If alice is not patient then mary is either creative or not brave.
Everyone who is both tall and strong is both brave and generous and vice versa.
Everyone who is funny or not wise is both tall and rich and vice versa.
Everyone who is happy or not patient is patient.
Everyone who is tall is both strong and humble and vice versa.
If someone is either happy or brave then someone is not patient and vice versa.
If someone is not kind then someone is brave or not creative.
If lucy is brave or old then someone is either not strong or patient and vice versa.
If alice is both not brave and humble then alice is either quiet or calm.
If someone is either happy or not creative then someone is either not humble or patient.
If paul is curious then susan is either not humble or old and vice versa.
Everyone who is both rich and not creative is either not happy or curious.
Paul is both rich and not creative.
Paul is either curious or funny.
Someone is either not old or brave.
Someone is not creative. | Paul is wise. | contradiction | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~calm(X))=>(~happy(X)<~>~calm(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(quiet(X)|kind(X))))&
((~patient(alice))=>((creative(mary)<~>~brave(mary))))&
(![X]:((tall(X)&strong(X))<=>(brave(X)&generous(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)&rich(X))))&
(![X]:((happy(X)|~patient(X))=>patient(X)))&
(![X]:(tall(X)<=>(strong(X)&humble(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)|~creative(X)))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~brave(alice)&humble(alice)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
((curious(paul))<=>((~humble(susan)<~>old(susan))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)<~>curious(X))))&
((rich(paul)&~creative(paul)))&
((curious(paul)<~>funny(paul)))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:(~creative(X))) | wise(paul) | [
"p0",
"p1",
"p2",
"p6",
"p8",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4474098369202958164774544
% SZS output start Proof for 4474098369202958164774544
1. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (~tall(X0) <~> ~happy(X0))) [input p0]
2. ! [X0] : ((~funny(X0) | ~kind(X0)) <=> (wise(X0) <~> ~funny(X0))) [input p1]
3. ! [X0] : ((happy(X0) <~> ~calm(X0)) => (~happy(X0) <~> ~calm(X0))) [input p2]
7. ! [X0] : ((~wise(X0) | funny(X0)) <=> (rich(X0) & tall(X0))) [input p6]
9. ! [X0] : (tall(X0) <=> (humble(X0) & strong(X0))) [input p8]
15. curious(paul) <=> (~humble(susan) <~> old(susan)) [input p14]
18. curious(paul) <~> funny(paul) [input p17]
21. wise(paul) [input hypothesis]
25. ! [X0] : ((~happy(X0) <~> ~calm(X0)) | (happy(X0) <=> ~calm(X0))) [ennf transformation 3]
36. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | (calm(X0) | old(X0)))) [nnf transformation 1]
37. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | calm(X0) | old(X0))) [flattening 36]
38. ! [X0] : (((~funny(X0) | ~kind(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [nnf transformation 2]
39. ! [X0] : ((~funny(X0) | ~kind(X0) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [flattening 38]
40. ! [X0] : (((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 25]
45. ! [X0] : (((~wise(X0) | funny(X0)) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [nnf transformation 7]
46. ! [X0] : ((~wise(X0) | funny(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [flattening 45]
47. ! [X0] : ((tall(X0) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | ~tall(X0))) [nnf transformation 9]
48. ! [X0] : ((tall(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | ~tall(X0))) [flattening 47]
67. (curious(paul) | ((~humble(susan) | ~old(susan)) & (old(susan) | humble(susan)))) & (((~old(susan) | humble(susan)) & (old(susan) | ~humble(susan))) | ~curious(paul)) [nnf transformation 15]
69. (~funny(paul) | ~curious(paul)) & (funny(paul) | curious(paul)) [nnf transformation 18]
75. ~happy(X0) | ~tall(X0) | calm(X0) | old(X0) [cnf transformation 37]
80. ~tall(X0) | ~calm(X0) | happy(X0) [cnf transformation 37]
84. funny(X0) | ~wise(X0) | funny(X0) [cnf transformation 39]
87. ~calm(X0) | ~happy(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 40]
90. calm(X0) | happy(X0) | happy(X0) | calm(X0) [cnf transformation 40]
99. ~funny(X0) | tall(X0) [cnf transformation 46]
100. wise(X0) | tall(X0) [cnf transformation 46]
107. ~tall(X0) | humble(X0) [cnf transformation 48]
129. curious(paul) | ~humble(susan) | ~old(susan) [cnf transformation 67]
135. ~funny(paul) | ~curious(paul) [cnf transformation 69]
139. wise(paul) [cnf transformation 21]
142. ~happy(X0) | ~calm(X0) [duplicate literal removal 87]
143. happy(X0) | calm(X0) [duplicate literal removal 90]
144. ~wise(X0) | funny(X0) [duplicate literal removal 84]
228. 18 <=> old(susan) [avatar definition]
230. ~old(susan) <- (~18) [avatar component clause 228]
232. 19 <=> humble(susan) [avatar definition]
234. ~humble(susan) <- (~19) [avatar component clause 232]
236. 20 <=> curious(paul) [avatar definition]
239. ~18 | ~19 | 20 [avatar split clause 129,236,232,228]
244. 21 <=> funny(paul) [avatar definition]
247. ~20 | ~21 [avatar split clause 135,244,236]
260. funny(paul) [resolution 144,139]
261. funny(X0) | tall(X0) [resolution 144,100]
264. tall(X0) [subsumption resolution 261,99]
265. 21 [avatar split clause 260,244]
268. humble(X0) [resolution 264,107]
273. $false <- (~19) [resolution 268,234]
274. 19 [avatar contradiction clause 273]
290. ~calm(X0) | happy(X0) [resolution 80,264]
291. happy(X0) [subsumption resolution 290,143]
295. ~calm(X3) [resolution 291,142]
316. ~tall(X0) | calm(X0) | old(X0) [resolution 75,291]
320. calm(X0) | old(X0) [subsumption resolution 316,264]
321. old(X0) [subsumption resolution 320,295]
330. $false <- (~18) [resolution 321,230]
332. 18 [avatar contradiction clause 330]
333. $false [avatar sat refutation 239,247,265,274,332]
% SZS output end Proof for 4474098369202958164774544
% ------------------------------
% 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 |
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