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 wise or creative is not curious or not kind and vice versa.
Everyone who is not brave is either not wise or not generous.
Everyone who is either not rich or tall is funny and vice versa.
Everyone who is not calm is creative or happy and vice versa.
Everyone who is not tall or not calm is not creative and vice versa.
Everyone who is either not brave or creative is not humble.
If someone is curious or not quiet then someone is both not generous and not calm and vice versa.
Everyone who is either not humble or not creative is both not calm and funny.
If someone is not curious then alice is not funny or creative and vice versa.
If lucy is either patient or not strong then paul is both not wise and not brave.
If someone is calm or not old then lucy is not calm or not wise.
If john is both not rich and not strong then lucy is not strong.
If john is either patient or not rich then someone is both tall and old and vice versa.
Everyone who is either rich or not quiet is either not kind or not quiet.
If susan is tall then someone is calm or not old.
If paul is kind then someone is not strong or not patient.
Someone is not funny or tall.
Someone is either not rich or quiet.
Lucy is either not curious or not calm.
Someone is funny or not quiet.
Someone is both not calm and wise.
Someone is old or strong.
Susan is either brave or creative. | Lucy is brave. | neutral | (![X]:((~wise(X)<~>creative(X))<=>(~curious(X)|~kind(X))))&
(![X]:(~brave(X)=>(~wise(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>tall(X))<=>funny(X)))&
(![X]:(~calm(X)<=>(creative(X)|happy(X))))&
(![X]:((~tall(X)|~calm(X))<=>~creative(X)))&
(![X]:((~brave(X)<~>creative(X))=>~humble(X)))&
((?[X]:((curious(X)|~quiet(X))))<=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:((~humble(X)<~>~creative(X))=>(~calm(X)&funny(X))))&
((?[X]:(~curious(X)))<=>((~funny(alice)|creative(alice))))&
(((patient(lucy)<~>~strong(lucy)))=>((~wise(paul)&~brave(paul))))&
((?[X]:((calm(X)|~old(X))))=>((~calm(lucy)|~wise(lucy))))&
(((~rich(john)&~strong(john)))=>(~strong(lucy)))&
(((patient(john)<~>~rich(john)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:((rich(X)<~>~quiet(X))=>(~kind(X)<~>~quiet(X))))&
((tall(susan))=>(?[X]:((calm(X)|~old(X)))))&
((kind(paul))=>(?[X]:((~strong(X)|~patient(X)))))&
(?[X]:((~funny(X)|tall(X))))&
(?[X]:((~rich(X)<~>quiet(X))))&
((~curious(lucy)<~>~calm(lucy)))&
(?[X]:((funny(X)|~quiet(X))))&
(?[X]:((~calm(X)&wise(X))))&
(?[X]:((old(X)|strong(X))))&
((brave(susan)<~>creative(susan))) | brave(lucy) | [] | null | 0 |
Everyone who is not humble is not wise or old and vice versa.
If someone is either rich or not patient then someone is rich or not creative and vice versa.
Everyone who is either not brave or calm is both not strong and not quiet and vice versa.
Everyone who is wise is generous or not brave and vice versa.
Everyone who is not happy is both brave and not funny.
Everyone who is kind is not humble.
Everyone who is not strong is tall and vice versa.
Everyone who is brave is either brave or not generous.
Everyone who is both not kind and not tall is tall or not old.
If paul is rich or happy then someone is not old and vice versa.
If alice is kind or creative then someone is either not funny or generous.
Everyone who is rich is kind.
Everyone who is not creative or generous is quiet and vice versa.
Everyone who is quiet is both wise and patient.
If lucy is both patient and old then someone is both not creative and brave.
If someone is either tall or not generous then someone is either tall or not rich and vice versa.
Fred is both tall and not generous.
Mary is not funny or brave.
Paul is brave.
Paul is both curious and rich.
Lucy is curious or calm.
John is either not brave or not happy.
Someone is both not strong and not happy. | Paul is not old. | contradiction | (![X]:(~humble(X)<=>(~wise(X)|old(X))))&
((?[X]:((rich(X)<~>~patient(X))))<=>(?[X]:((rich(X)|~creative(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(~strong(X)&~quiet(X))))&
(![X]:(wise(X)<=>(generous(X)|~brave(X))))&
(![X]:(~happy(X)=>(brave(X)&~funny(X))))&
(![X]:(kind(X)=>~humble(X)))&
(![X]:(~strong(X)<=>tall(X)))&
(![X]:(brave(X)=>(brave(X)<~>~generous(X))))&
(![X]:((~kind(X)&~tall(X))=>(tall(X)|~old(X))))&
(((rich(paul)|happy(paul)))<=>(?[X]:(~old(X))))&
(((kind(alice)|creative(alice)))=>(?[X]:((~funny(X)<~>generous(X)))))&
(![X]:(rich(X)=>kind(X)))&
(![X]:((~creative(X)|generous(X))<=>quiet(X)))&
(![X]:(quiet(X)=>(wise(X)&patient(X))))&
(((patient(lucy)&old(lucy)))=>(?[X]:((~creative(X)&brave(X)))))&
((?[X]:((tall(X)<~>~generous(X))))<=>(?[X]:((tall(X)<~>~rich(X)))))&
((tall(fred)&~generous(fred)))&
((~funny(mary)|brave(mary)))&
(brave(paul))&
((curious(paul)&rich(paul)))&
((curious(lucy)|calm(lucy)))&
((~brave(john)<~>~happy(john)))&
(?[X]:((~strong(X)&~happy(X)))) | ~old(paul) | [
"p0",
"p3",
"p5",
"p7",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7837600935314206956863279
% SZS output start Proof for 7837600935314206956863279
1. ! [X0] : (~humble(X0) <=> (old(X0) | ~wise(X0))) [input p0]
4. ! [X0] : (wise(X0) <=> (~brave(X0) | generous(X0))) [input p3]
6. ! [X0] : (kind(X0) => ~humble(X0)) [input p5]
8. ! [X0] : (brave(X0) => (brave(X0) <~> ~generous(X0))) [input p7]
12. ! [X0] : (rich(X0) => kind(X0)) [input p11]
20. rich(paul) & curious(paul) [input p19]
24. ~old(paul) [input hypothesis]
27. ! [X0] : (~humble(X0) => (old(X0) | ~wise(X0))) [unused predicate definition removal 1]
29. rich(paul) [pure predicate removal 20]
30. ! [X0] : ((old(X0) | ~wise(X0)) | humble(X0)) [ennf transformation 27]
31. ! [X0] : (old(X0) | ~wise(X0) | humble(X0)) [flattening 30]
33. ! [X0] : (~humble(X0) | ~kind(X0)) [ennf transformation 6]
34. ! [X0] : ((brave(X0) <~> ~generous(X0)) | ~brave(X0)) [ennf transformation 8]
38. ! [X0] : (kind(X0) | ~rich(X0)) [ennf transformation 12]
49. ! [X0] : ((wise(X0) | (brave(X0) & ~generous(X0))) & ((~brave(X0) | generous(X0)) | ~wise(X0))) [nnf transformation 4]
50. ! [X0] : ((wise(X0) | (brave(X0) & ~generous(X0))) & (~brave(X0) | generous(X0) | ~wise(X0))) [flattening 49]
52. ! [X0] : (((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | ~brave(X0)) [nnf transformation 34]
73. ~wise(X0) | old(X0) | humble(X0) [cnf transformation 31]
87. ~generous(X0) | wise(X0) [cnf transformation 50]
88. brave(X0) | wise(X0) [cnf transformation 50]
91. ~kind(X0) | ~humble(X0) [cnf transformation 33]
95. generous(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 52]
104. ~rich(X0) | kind(X0) [cnf transformation 38]
124. rich(paul) [cnf transformation 29]
129. ~old(paul) [cnf transformation 24]
131. ~brave(X0) | generous(X0) [duplicate literal removal 95]
170. 10 <=> rich(paul) [avatar definition]
172. rich(paul) <- (10) [avatar component clause 170]
267. 10 [avatar split clause 124,170]
284. kind(paul) <- (10) [resolution 104,172]
285. ~humble(paul) <- (10) [resolution 284,91]
288. generous(X0) | wise(X0) [resolution 131,88]
292. wise(X0) [subsumption resolution 288,87]
322. old(X0) | humble(X0) [resolution 292,73]
444. humble(paul) [resolution 322,129]
447. $false <- (10) [subsumption resolution 444,285]
448. ~10 [avatar contradiction clause 447]
449. $false [avatar sat refutation 267,448]
% SZS output end Proof for 7837600935314206956863279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or humble is strong or creative. If someone is quiet then susan is either not curious or not generous and vice versa. If someone is not old or not happy then mary is both not happy and calm. If someone is both quiet and not humble then susan is either creative or not creative and vice versa. If someone is either happy or curious then someone is both curious and kind and vice versa. Everyone who is both not brave and quiet is not patient and vice versa. If someone is both creative and generous then paul is both not funny and kind and vice versa. If john is kind then mary is both not old and creative and vice versa. If someone is generous or not calm then mary is not funny or rich and vice versa. Everyone who is not quiet or not creative is both not brave and kind. Everyone who is not curious is brave or not quiet. Everyone who is wise or happy is old or calm. 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. Someone is strong. Someone is either happy or not tall. Someone is either not humble or calm. Paul is either not old or patient. Lucy is kind or happy. Susan is both curious and not quiet. Fred is both calm and rich. Lucy is not calm. | Lucy is not generous. | neutral | (![X]:((~kind(X)<~>humble(X))=>(strong(X)|creative(X))))&
((?[X]:(quiet(X)))<=>((~curious(susan)<~>~generous(susan))))&
((?[X]:((~old(X)|~happy(X))))=>((~happy(mary)&calm(mary))))&
((?[X]:((quiet(X)&~humble(X))))<=>((creative(susan)<~>~creative(susan))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:((curious(X)&kind(X)))))&
(![X]:((~brave(X)&quiet(X))<=>~patient(X)))&
((?[X]:((creative(X)&generous(X))))<=>((~funny(paul)&kind(paul))))&
((kind(john))<=>((~old(mary)&creative(mary))))&
((?[X]:((generous(X)|~calm(X))))<=>((~funny(mary)|rich(mary))))&
(![X]:((~quiet(X)|~creative(X))=>(~brave(X)&kind(X))))&
(![X]:(~curious(X)=>(brave(X)|~quiet(X))))&
(![X]:((wise(X)|happy(X))=>(old(X)|calm(X))))&
(![X]:((~patient(X)<~>creative(X))=>(calm(X)&funny(X))))&
((?[X]:((~strong(X)&creative(X))))<=>(?[X]:((rich(X)<~>~creative(X)))))&
(?[X]:(strong(X)))&
(?[X]:((happy(X)<~>~tall(X))))&
(?[X]:((~humble(X)<~>calm(X))))&
((~old(paul)<~>patient(paul)))&
((kind(lucy)|happy(lucy)))&
((curious(susan)&~quiet(susan)))&
((calm(fred)&rich(fred)))&
(~calm(lucy)) | ~generous(lucy) | [] | null | 0 |
If john is not kind or not humble then someone is both not strong and not generous.
Everyone who is either not rich or not happy is old and vice versa.
If someone is both not brave and not funny then someone is either not funny or generous and vice versa.
If someone is funny or not tall then john is both not tall and wise and vice versa.
If paul is either wise or humble then lucy is either funny or rich and vice versa.
Everyone who is either not happy or tall is tall.
If someone is not quiet then john is both not calm and curious.
Everyone who is either not rich or not old is either quiet or rich and vice versa.
If someone is generous or not funny then john is not strong.
Everyone who is not kind is not quiet and vice versa.
Everyone who is not wise or not calm is either not generous or not patient.
If fred is either patient or old then paul is not funny and vice versa.
If someone is both not quiet and not humble then john is both not generous and not funny.
Everyone who is not patient is both patient and not patient and vice versa.
Everyone who is not strong or not curious is both humble and not humble and vice versa.
Everyone who is not funny is either happy or curious and vice versa.
Someone is kind or not curious.
Someone is both calm and not wise.
John is either creative or kind.
John is either happy or not wise.
Susan is tall.
Alice is both not old and strong.
John is calm or wise. | Alice is not humble. | contradiction | (((~kind(john)|~humble(john)))=>(?[X]:((~strong(X)&~generous(X)))))&
(![X]:((~rich(X)<~>~happy(X))<=>old(X)))&
((?[X]:((~brave(X)&~funny(X))))<=>(?[X]:((~funny(X)<~>generous(X)))))&
((?[X]:((funny(X)|~tall(X))))<=>((~tall(john)&wise(john))))&
(((wise(paul)<~>humble(paul)))<=>((funny(lucy)<~>rich(lucy))))&
(![X]:((~happy(X)<~>tall(X))=>tall(X)))&
((?[X]:(~quiet(X)))=>((~calm(john)&curious(john))))&
(![X]:((~rich(X)<~>~old(X))<=>(quiet(X)<~>rich(X))))&
((?[X]:((generous(X)|~funny(X))))=>(~strong(john)))&
(![X]:(~kind(X)<=>~quiet(X)))&
(![X]:((~wise(X)|~calm(X))=>(~generous(X)<~>~patient(X))))&
(((patient(fred)<~>old(fred)))<=>(~funny(paul)))&
((?[X]:((~quiet(X)&~humble(X))))=>((~generous(john)&~funny(john))))&
(![X]:(~patient(X)<=>(patient(X)&~patient(X))))&
(![X]:((~strong(X)|~curious(X))<=>(humble(X)&~humble(X))))&
(![X]:(~funny(X)<=>(happy(X)<~>curious(X))))&
(?[X]:((kind(X)|~curious(X))))&
(?[X]:((calm(X)&~wise(X))))&
((creative(john)<~>kind(john)))&
((happy(john)<~>~wise(john)))&
(tall(susan))&
((~old(alice)&strong(alice)))&
((calm(john)|wise(john))) | ~humble(alice) | [
"p7",
"p8",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1118007364524807920589570
% SZS output start Proof for 1118007364524807920589570
8. ! [X0] : ((~rich(X0) <~> ~old(X0)) <=> (quiet(X0) <~> rich(X0))) [input p7]
9. ? [X0] : (~funny(X0) | generous(X0)) => ~strong(john) [input p8]
13. ? [X0] : (~humble(X0) & ~quiet(X0)) => (~funny(john) & ~generous(john)) [input p12]
15. ! [X0] : ((~curious(X0) | ~strong(X0)) <=> (~humble(X0) & humble(X0))) [input p14]
22. strong(alice) & ~old(alice) [input p21]
24. ~humble(alice) [input hypothesis]
29. ~strong(john) | ! [X0] : (funny(X0) & ~generous(X0)) [ennf transformation 9]
31. (~funny(john) & ~generous(john)) | ! [X0] : (humble(X0) | quiet(X0)) [ennf transformation 13]
47. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [nnf transformation 8]
53. ! [X0] : (((~curious(X0) | ~strong(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (curious(X0) & strong(X0)))) [nnf transformation 15]
54. ! [X0] : ((~curious(X0) | ~strong(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (curious(X0) & strong(X0)))) [flattening 53]
96. ~rich(X0) | ~quiet(X0) | ~rich(X0) | old(X0) [cnf transformation 47]
99. old(X0) | rich(X0) | rich(X0) | ~quiet(X0) [cnf transformation 47]
102. ~strong(john) | funny(X0) [cnf transformation 29]
114. ~funny(john) | humble(X0) | quiet(X0) [cnf transformation 31]
118. humble(X0) | strong(X0) [cnf transformation 54]
120. ~humble(X0) | strong(X0) [cnf transformation 54]
135. ~old(alice) [cnf transformation 22]
138. ~humble(alice) [cnf transformation 24]
142. ~rich(X0) | ~quiet(X0) | old(X0) [duplicate literal removal 96]
144. old(X0) | rich(X0) | ~quiet(X0) [duplicate literal removal 99]
261. ~quiet(X0) | old(X0) [subsumption resolution 142,144]
264. 25 <=> ! [X0] : funny(X0) [avatar definition]
265. funny(X0) <- (25) [avatar component clause 264]
267. 26 <=> strong(john) [avatar definition]
269. ~strong(john) <- (~26) [avatar component clause 267]
270. 25 | ~26 [avatar split clause 102,267,264]
292. 31 <=> ! [X0] : (humble(X0) | quiet(X0)) [avatar definition]
293. quiet(X0) | humble(X0) <- (31) [avatar component clause 292]
295. 32 <=> funny(john) [avatar definition]
297. ~funny(john) <- (~32) [avatar component clause 295]
298. 31 | ~32 [avatar split clause 114,295,292]
305. strong(X0) [subsumption resolution 118,120]
324. $false <- (~26) [subsumption resolution 269,305]
325. 26 [avatar contradiction clause 324]
340. $false <- (25, ~32) [resolution 297,265]
341. ~25 | 32 [avatar contradiction clause 340]
357. old(X0) | humble(X0) <- (31) [resolution 293,261]
400. humble(alice) <- (31) [resolution 357,135]
404. $false <- (31) [subsumption resolution 400,138]
405. ~31 [avatar contradiction clause 404]
407. $false [avatar sat refutation 270,298,325,341,405]
% SZS output end Proof for 1118007364524807920589570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny is both tall and not brave.
Everyone who is either wise or creative is both not old and funny.
Everyone who is not patient or brave is either not brave or generous.
Everyone who is both tall and calm is either strong or not strong and vice versa.
If someone is both not happy and not old then susan is either not calm or wise.
Everyone who is either not curious or rich is not brave or kind and vice versa.
If someone is either not quiet or humble then alice is either tall or strong and vice versa.
Everyone who is patient is either not curious or not patient and vice versa.
If someone is both brave and not calm then susan is not happy or wise and vice versa.
Everyone who is not patient or patient is either curious or rich and vice versa.
If john is not quiet or humble then alice is not curious.
If susan is either not patient or not calm then alice is curious and vice versa.
If someone is both wise and rich then alice is either curious or not calm.
Everyone who is generous is both rich and generous and vice versa.
If someone is both not old and not strong then john is not curious or wise.
If mary is both brave and not patient then mary is quiet or tall.
Lucy is either happy or calm.
Lucy is not wise or not calm.
Mary is not curious.
Someone is both not humble and not quiet.
Susan is calm or not humble.
Susan is both calm and old. | John is not tall. | contradiction | (![X]:(~funny(X)=>(tall(X)&~brave(X))))&
(![X]:((wise(X)<~>creative(X))=>(~old(X)&funny(X))))&
(![X]:((~patient(X)|brave(X))=>(~brave(X)<~>generous(X))))&
(![X]:((tall(X)&calm(X))<=>(strong(X)<~>~strong(X))))&
((?[X]:((~happy(X)&~old(X))))=>((~calm(susan)<~>wise(susan))))&
(![X]:((~curious(X)<~>rich(X))<=>(~brave(X)|kind(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>((tall(alice)<~>strong(alice))))&
(![X]:(patient(X)<=>(~curious(X)<~>~patient(X))))&
((?[X]:((brave(X)&~calm(X))))<=>((~happy(susan)|wise(susan))))&
(![X]:((~patient(X)|patient(X))<=>(curious(X)<~>rich(X))))&
(((~quiet(john)|humble(john)))=>(~curious(alice)))&
(((~patient(susan)<~>~calm(susan)))<=>(curious(alice)))&
((?[X]:((wise(X)&rich(X))))=>((curious(alice)<~>~calm(alice))))&
(![X]:(generous(X)<=>(rich(X)&generous(X))))&
((?[X]:((~old(X)&~strong(X))))=>((~curious(john)|wise(john))))&
(((brave(mary)&~patient(mary)))=>((quiet(mary)|tall(mary))))&
((happy(lucy)<~>calm(lucy)))&
((~wise(lucy)|~calm(lucy)))&
(~curious(mary))&
(?[X]:((~humble(X)&~quiet(X))))&
((calm(susan)|~humble(susan)))&
((calm(susan)&old(susan))) | ~tall(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3900401974433830662116351
% SZS output start Proof for 3900401974433830662116351
4. ! [X0] : ((calm(X0) & tall(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p3]
23. ~tall(john) [input hypothesis]
37. ! [X0] : (((calm(X0) & tall(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~calm(X0) | ~tall(X0)))) [nnf transformation 4]
38. ! [X0] : (((calm(X0) & tall(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~calm(X0) | ~tall(X0))) [flattening 37]
69. tall(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 38]
70. tall(X0) | strong(X0) | strong(X0) [cnf transformation 38]
126. ~tall(john) [cnf transformation 23]
129. tall(X0) | ~strong(X0) [duplicate literal removal 69]
130. tall(X0) | strong(X0) [duplicate literal removal 70]
135. tall(X0) [subsumption resolution 129,130]
189. $false [subsumption resolution 126,135]
% SZS output end Proof for 3900401974433830662116351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is either not humble or not old and vice versa.
If john is either not tall or not humble then someone is not humble.
Everyone who is rich or not old is both strong and calm and vice versa.
If paul is not brave or humble then someone is calm or not patient.
Everyone who is both not generous and kind is both patient and not kind and vice versa.
Everyone who is patient or not curious is both not funny and not happy and vice versa.
If someone is both not calm and not creative then someone is both creative and old and vice versa.
Everyone who is both patient and funny is creative or brave.
If someone is either not kind or generous then someone is both happy and brave.
If someone is tall then someone is either funny or brave and vice versa.
Everyone who is happy is both not brave and patient and vice versa.
Everyone who is not patient or happy is either not creative or not quiet.
If fred is either not brave or not kind then fred is either not patient or not tall.
Everyone who is not kind or creative is not calm.
Everyone who is not funny or not strong is both not kind and not curious.
Someone is not happy or wise.
Someone is both curious and strong.
Fred is not kind or happy.
Someone is funny. | Paul is not old. | contradiction | (![X]:(generous(X)<=>(~humble(X)<~>~old(X))))&
(((~tall(john)<~>~humble(john)))=>(?[X]:(~humble(X))))&
(![X]:((rich(X)|~old(X))<=>(strong(X)&calm(X))))&
(((~brave(paul)|humble(paul)))=>(?[X]:((calm(X)|~patient(X)))))&
(![X]:((~generous(X)&kind(X))<=>(patient(X)&~kind(X))))&
(![X]:((patient(X)|~curious(X))<=>(~funny(X)&~happy(X))))&
((?[X]:((~calm(X)&~creative(X))))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:((patient(X)&funny(X))=>(creative(X)|brave(X))))&
((?[X]:((~kind(X)<~>generous(X))))=>(?[X]:((happy(X)&brave(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:(happy(X)<=>(~brave(X)&patient(X))))&
(![X]:((~patient(X)|happy(X))=>(~creative(X)<~>~quiet(X))))&
(((~brave(fred)<~>~kind(fred)))=>((~patient(fred)<~>~tall(fred))))&
(![X]:((~kind(X)|creative(X))=>~calm(X)))&
(![X]:((~funny(X)|~strong(X))=>(~kind(X)&~curious(X))))&
(?[X]:((~happy(X)|wise(X))))&
(?[X]:((curious(X)&strong(X))))&
((~kind(fred)|happy(fred)))&
(?[X]:(funny(X))) | ~old(paul) | [
"p2",
"p4",
"p5",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7380848691196581424985249
% SZS output start Proof for 7380848691196581424985249
3. ! [X0] : ((~old(X0) | rich(X0)) <=> (calm(X0) & strong(X0))) [input p2]
5. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (~kind(X0) & patient(X0))) [input p4]
6. ! [X0] : ((~curious(X0) | patient(X0)) <=> (~happy(X0) & ~funny(X0))) [input p5]
9. ? [X0] : (~kind(X0) <~> generous(X0)) => ? [X0] : (brave(X0) & happy(X0)) [input p8]
11. ! [X0] : (happy(X0) <=> (patient(X0) & ~brave(X0))) [input p10]
14. ! [X0] : ((creative(X0) | ~kind(X0)) => ~calm(X0)) [input p13]
20. ~old(paul) [input hypothesis]
22. ? [X0] : (~kind(X0) <~> generous(X0)) => ? [X1] : (brave(X1) & happy(X1)) [rectify 9]
29. ? [X1] : (brave(X1) & happy(X1)) | ! [X0] : (~kind(X0) <=> generous(X0)) [ennf transformation 22]
32. ! [X0] : (~calm(X0) | (~creative(X0) & kind(X0))) [ennf transformation 14]
38. ! [X0] : (((~old(X0) | rich(X0)) | (~calm(X0) | ~strong(X0))) & ((calm(X0) & strong(X0)) | (old(X0) & ~rich(X0)))) [nnf transformation 3]
39. ! [X0] : ((~old(X0) | rich(X0) | ~calm(X0) | ~strong(X0)) & ((calm(X0) & strong(X0)) | (old(X0) & ~rich(X0)))) [flattening 38]
42. ! [X0] : (((kind(X0) & ~generous(X0)) | (kind(X0) | ~patient(X0))) & ((~kind(X0) & patient(X0)) | (~kind(X0) | generous(X0)))) [nnf transformation 5]
43. ! [X0] : (((kind(X0) & ~generous(X0)) | kind(X0) | ~patient(X0)) & ((~kind(X0) & patient(X0)) | ~kind(X0) | generous(X0))) [flattening 42]
44. ! [X0] : (((~curious(X0) | patient(X0)) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | (curious(X0) & ~patient(X0)))) [nnf transformation 6]
45. ! [X0] : ((~curious(X0) | patient(X0) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | (curious(X0) & ~patient(X0)))) [flattening 44]
51. ? [X1] : (brave(X1) & happy(X1)) | ! [X0] : ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))) [nnf transformation 29]
52. ? [X0] : (brave(X0) & happy(X0)) | ! [X1] : ((~kind(X1) | ~generous(X1)) & (generous(X1) | kind(X1))) [rectify 51]
53. ? [X0] : (brave(X0) & happy(X0)) => (brave(sK4) & happy(sK4)) [choice axiom]
54. (brave(sK4) & happy(sK4)) | ! [X1] : ((~kind(X1) | ~generous(X1)) & (generous(X1) | kind(X1))) [skolemisation 52,53]
60. ! [X0] : ((happy(X0) | (~patient(X0) | brave(X0))) & ((patient(X0) & ~brave(X0)) | ~happy(X0))) [nnf transformation 11]
61. ! [X0] : ((happy(X0) | ~patient(X0) | brave(X0)) & ((patient(X0) & ~brave(X0)) | ~happy(X0))) [flattening 60]
77. calm(X0) | old(X0) [cnf transformation 39]
82. ~kind(X0) | ~kind(X0) | generous(X0) [cnf transformation 43]
87. ~happy(X0) | ~patient(X0) [cnf transformation 45]
96. happy(sK4) | ~kind(X1) | ~generous(X1) [cnf transformation 54]
104. patient(X0) | ~happy(X0) [cnf transformation 61]
114. ~calm(X0) | kind(X0) [cnf transformation 32]
124. ~old(paul) [cnf transformation 20]
125. ~kind(X0) | generous(X0) [duplicate literal removal 82]
187. 14 <=> ! [X1] : ~kind(X1) [avatar definition]
188. ~kind(X1) <- (14) [avatar component clause 187]
199. happy(sK4) | ~kind(X1) [subsumption resolution 96,125]
201. 17 <=> happy(sK4) [avatar definition]
203. happy(sK4) <- (17) [avatar component clause 201]
204. 14 | 17 [avatar split clause 199,201,187]
233. ~happy(X0) [subsumption resolution 104,87]
257. kind(X0) | old(X0) [resolution 114,77]
258. old(X0) <- (14) [subsumption resolution 257,188]
259. $false <- (14) [resolution 258,124]
260. ~14 [avatar contradiction clause 259]
261. $false <- (17) [subsumption resolution 203,233]
262. ~17 [avatar contradiction clause 261]
263. $false [avatar sat refutation 204,260,262]
% SZS output end Proof for 7380848691196581424985249
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and rich then someone is not curious or generous.
Everyone who is both not generous and not humble is brave or not patient.
If john is both not humble and not wise then fred is either tall or not old.
If fred is either not wise or not rich then someone is either old or not kind.
If someone is creative or not humble then mary is rich.
Everyone who is either humble or wise is both patient and wise and vice versa.
Everyone who is not tall is both not generous and old.
If alice is patient or not curious then someone is not kind and vice versa.
If lucy is not generous or wise then mary is not curious.
If someone is happy or not quiet then someone is not rich.
Everyone who is not funny is both not strong and rich and vice versa.
Everyone who is both not generous and rich is not funny or not rich and vice versa.
Everyone who is not calm or not brave is creative and vice versa.
Everyone who is either not generous or not tall is quiet or wise and vice versa.
If someone is not strong or not rich then john is either not wise or happy and vice versa.
Mary is both not curious and not old.
Lucy is either kind or happy.
Susan is either brave or not funny.
Fred is old or not humble.
Alice is either not patient or tall.
John is not old. | Fred is not generous. | entailment | ((?[X]:((calm(X)&rich(X))))=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:((~generous(X)&~humble(X))=>(brave(X)|~patient(X))))&
(((~humble(john)&~wise(john)))=>((tall(fred)<~>~old(fred))))&
(((~wise(fred)<~>~rich(fred)))=>(?[X]:((old(X)<~>~kind(X)))))&
((?[X]:((creative(X)|~humble(X))))=>(rich(mary)))&
(![X]:((humble(X)<~>wise(X))<=>(patient(X)&wise(X))))&
(![X]:(~tall(X)=>(~generous(X)&old(X))))&
(((patient(alice)|~curious(alice)))<=>(?[X]:(~kind(X))))&
(((~generous(lucy)|wise(lucy)))=>(~curious(mary)))&
((?[X]:((happy(X)|~quiet(X))))=>(?[X]:(~rich(X))))&
(![X]:(~funny(X)<=>(~strong(X)&rich(X))))&
(![X]:((~generous(X)&rich(X))<=>(~funny(X)|~rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>creative(X)))&
(![X]:((~generous(X)<~>~tall(X))<=>(quiet(X)|wise(X))))&
((?[X]:((~strong(X)|~rich(X))))<=>((~wise(john)<~>happy(john))))&
((~curious(mary)&~old(mary)))&
((kind(lucy)<~>happy(lucy)))&
((brave(susan)<~>~funny(susan)))&
((old(fred)|~humble(fred)))&
((~patient(alice)<~>tall(alice)))&
(~old(john)) | ~generous(fred) | [
"p6",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8219563169715531899218869
% SZS output start Proof for 8219563169715531899218869
7. ! [X0] : (~tall(X0) => (old(X0) & ~generous(X0))) [input p6]
10. ? [X0] : (~quiet(X0) | happy(X0)) => ? [X0] : ~rich(X0) [input p9]
12. ! [X0] : ((rich(X0) & ~generous(X0)) <=> (~rich(X0) | ~funny(X0))) [input p11]
14. ! [X0] : ((~generous(X0) <~> ~tall(X0)) <=> (wise(X0) | quiet(X0))) [input p13]
22. generous(fred) [input hypothesis]
24. ? [X0] : (~quiet(X0) | happy(X0)) => ? [X1] : ~rich(X1) [rectify 10]
33. ! [X0] : ((old(X0) & ~generous(X0)) | tall(X0)) [ennf transformation 7]
35. ? [X1] : ~rich(X1) | ! [X0] : (quiet(X0) & ~happy(X0)) [ennf transformation 24]
51. ? [X0] : ~rich(X0) | ! [X1] : (quiet(X1) & ~happy(X1)) [rectify 35]
52. ? [X0] : ~rich(X0) => ~rich(sK3) [choice axiom]
53. ~rich(sK3) | ! [X1] : (quiet(X1) & ~happy(X1)) [skolemisation 51,52]
56. ! [X0] : (((rich(X0) & ~generous(X0)) | (rich(X0) & funny(X0))) & ((~rich(X0) | ~funny(X0)) | (~rich(X0) | generous(X0)))) [nnf transformation 12]
57. ! [X0] : (((rich(X0) & ~generous(X0)) | (rich(X0) & funny(X0))) & (~rich(X0) | ~funny(X0) | ~rich(X0) | generous(X0))) [flattening 56]
58. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (~wise(X0) & ~quiet(X0))) & ((wise(X0) | quiet(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [nnf transformation 14]
59. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (~wise(X0) & ~quiet(X0))) & (wise(X0) | quiet(X0) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [flattening 58]
83. ~generous(X0) | tall(X0) [cnf transformation 33]
91. ~rich(sK3) | quiet(X1) [cnf transformation 53]
99. rich(X0) | rich(X0) [cnf transformation 57]
104. ~tall(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 59]
106. tall(X0) | generous(X0) | ~quiet(X0) [cnf transformation 59]
124. generous(fred) [cnf transformation 22]
126. rich(X0) [duplicate literal removal 99]
224. 22 <=> ! [X1] : quiet(X1) [avatar definition]
225. quiet(X1) <- (22) [avatar component clause 224]
227. 23 <=> rich(sK3) [avatar definition]
229. ~rich(sK3) <- (~23) [avatar component clause 227]
230. 22 | ~23 [avatar split clause 91,227,224]
237. ~quiet(X0) | tall(X0) [subsumption resolution 106,83]
239. ~quiet(X0) | ~generous(X0) [subsumption resolution 104,237]
289. $false <- (~23) [subsumption resolution 229,126]
290. 23 [avatar contradiction clause 289]
309. ~generous(X0) <- (22) [resolution 239,225]
310. $false <- (22) [resolution 309,124]
311. ~22 [avatar contradiction clause 310]
312. $false [avatar sat refutation 230,290,311]
% SZS output end Proof for 8219563169715531899218869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or not humble then lucy is not old or creative.
Everyone who is either not generous or curious is either not happy or not quiet.
Everyone who is old is generous or not generous.
If john is either not tall or not patient then alice is either happy or curious and vice versa.
If fred is both creative and not happy then someone is both not funny and wise and vice versa.
If paul is either happy or brave then someone is both not kind and humble and vice versa.
If someone is not quiet or not brave then someone is creative or not curious and vice versa.
If someone is both happy and funny then someone is both tall and rich.
If someone is patient then lucy is happy and vice versa.
Everyone who is either not creative or not brave is either happy or patient.
Everyone who is not funny is wise and vice versa.
If someone is strong or generous then lucy is not rich and vice versa.
Everyone who is either happy or not brave is not generous or creative and vice versa.
Everyone who is both not patient and not happy is patient or calm and vice versa.
Everyone who is strong or not creative is old or creative and vice versa.
John is either wise or creative.
Alice is not generous or creative.
Mary is tall.
Someone is either not generous or calm.
Alice is both not brave and kind.
Someone is either humble or not strong.
Someone is curious or generous.
Paul is either not happy or funny. | John is not funny. | contradiction | ((?[X]:((~old(X)<~>~humble(X))))=>((~old(lucy)|creative(lucy))))&
(![X]:((~generous(X)<~>curious(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:(old(X)=>(generous(X)|~generous(X))))&
(((~tall(john)<~>~patient(john)))<=>((happy(alice)<~>curious(alice))))&
(((creative(fred)&~happy(fred)))<=>(?[X]:((~funny(X)&wise(X)))))&
(((happy(paul)<~>brave(paul)))<=>(?[X]:((~kind(X)&humble(X)))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(?[X]:((creative(X)|~curious(X)))))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:((tall(X)&rich(X)))))&
((?[X]:(patient(X)))<=>(happy(lucy)))&
(![X]:((~creative(X)<~>~brave(X))=>(happy(X)<~>patient(X))))&
(![X]:(~funny(X)<=>wise(X)))&
((?[X]:((strong(X)|generous(X))))<=>(~rich(lucy)))&
(![X]:((happy(X)<~>~brave(X))<=>(~generous(X)|creative(X))))&
(![X]:((~patient(X)&~happy(X))<=>(patient(X)|calm(X))))&
(![X]:((strong(X)|~creative(X))<=>(old(X)|creative(X))))&
((wise(john)<~>creative(john)))&
((~generous(alice)|creative(alice)))&
(tall(mary))&
(?[X]:((~generous(X)<~>calm(X))))&
((~brave(alice)&kind(alice)))&
(?[X]:((humble(X)<~>~strong(X))))&
(?[X]:((curious(X)|generous(X))))&
((~happy(paul)<~>funny(paul))) | ~funny(john) | [
"p4",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5312536711844618319865734
% SZS output start Proof for 5312536711844618319865734
5. (~happy(fred) & creative(fred)) <=> ? [X0] : (wise(X0) & ~funny(X0)) [input p4]
10. ! [X0] : ((~creative(X0) <~> ~brave(X0)) => (happy(X0) <~> patient(X0))) [input p9]
11. ! [X0] : (~funny(X0) <=> wise(X0)) [input p10]
13. ! [X0] : ((happy(X0) <~> ~brave(X0)) <=> (creative(X0) | ~generous(X0))) [input p12]
14. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (calm(X0) | patient(X0))) [input p13]
24. ~funny(john) [input hypothesis]
33. ! [X0] : ((happy(X0) <~> patient(X0)) | (~creative(X0) <=> ~brave(X0))) [ennf transformation 10]
37. ((~happy(fred) & creative(fred)) | ! [X0] : (~wise(X0) | funny(X0))) & (? [X0] : (wise(X0) & ~funny(X0)) | (happy(fred) | ~creative(fred))) [nnf transformation 5]
38. ((~happy(fred) & creative(fred)) | ! [X0] : (~wise(X0) | funny(X0))) & (? [X0] : (wise(X0) & ~funny(X0)) | happy(fred) | ~creative(fred)) [flattening 37]
39. ((~happy(fred) & creative(fred)) | ! [X0] : (~wise(X0) | funny(X0))) & (? [X1] : (wise(X1) & ~funny(X1)) | happy(fred) | ~creative(fred)) [rectify 38]
40. ? [X1] : (wise(X1) & ~funny(X1)) => (wise(sK0) & ~funny(sK0)) [choice axiom]
41. ((~happy(fred) & creative(fred)) | ! [X0] : (~wise(X0) | funny(X0))) & ((wise(sK0) & ~funny(sK0)) | happy(fred) | ~creative(fred)) [skolemisation 39,40]
58. ! [X0] : (((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) [nnf transformation 33]
59. ! [X0] : ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))) [nnf transformation 11]
64. ! [X0] : ((((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (~creative(X0) & generous(X0))) & ((creative(X0) | ~generous(X0)) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))))) [nnf transformation 13]
65. ! [X0] : ((((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (~creative(X0) & generous(X0))) & (creative(X0) | ~generous(X0) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))))) [flattening 64]
66. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~calm(X0) & ~patient(X0))) & ((calm(X0) | patient(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 14]
67. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~calm(X0) & ~patient(X0))) & (calm(X0) | patient(X0) | happy(X0) | patient(X0))) [flattening 66]
97. creative(fred) | ~wise(X0) | funny(X0) [cnf transformation 41]
98. ~happy(fred) | ~wise(X0) | funny(X0) [cnf transformation 41]
114. ~creative(X0) | happy(X0) | patient(X0) | brave(X0) [cnf transformation 58]
117. wise(X0) | funny(X0) [cnf transformation 59]
118. ~wise(X0) | ~funny(X0) [cnf transformation 59]
125. ~brave(X0) | happy(X0) | ~creative(X0) [cnf transformation 65]
129. ~patient(X0) | ~patient(X0) [cnf transformation 67]
150. ~funny(john) [cnf transformation 24]
154. ~patient(X0) [duplicate literal removal 129]
196. 9 <=> ! [X0] : (~wise(X0) | funny(X0)) [avatar definition]
197. ~wise(X0) | funny(X0) <- (9) [avatar component clause 196]
199. 10 <=> happy(fred) [avatar definition]
201. ~happy(fred) <- (~10) [avatar component clause 199]
202. 9 | ~10 [avatar split clause 98,199,196]
204. 11 <=> creative(fred) [avatar definition]
206. creative(fred) <- (11) [avatar component clause 204]
207. 9 | 11 [avatar split clause 97,204,196]
298. 32 <=> ! [X1] : ~patient(X1) [avatar definition]
299. ~patient(X1) <- (32) [avatar component clause 298]
322. 32 [avatar split clause 154,298]
324. 38 <=> wise(john) [avatar definition]
325. wise(john) <- (38) [avatar component clause 324]
326. ~wise(john) <- (~38) [avatar component clause 324]
377. ~wise(X0) <- (9) [subsumption resolution 197,118]
378. $false <- (9, 38) [resolution 377,325]
379. ~9 | ~38 [avatar contradiction clause 378]
444. happy(fred) | patient(fred) | brave(fred) <- (11) [resolution 114,206]
446. patient(fred) | brave(fred) <- (~10, 11) [subsumption resolution 444,201]
447. brave(fred) <- (~10, 11, 32) [subsumption resolution 446,299]
450. happy(fred) | ~creative(fred) <- (~10, 11, 32) [resolution 447,125]
452. ~creative(fred) <- (~10, 11, 32) [subsumption resolution 450,201]
453. $false <- (~10, 11, 32) [subsumption resolution 452,206]
454. 10 | ~11 | ~32 [avatar contradiction clause 453]
458. funny(john) <- (~38) [resolution 326,117]
459. $false <- (~38) [subsumption resolution 458,150]
460. 38 [avatar contradiction clause 459]
461. $false [avatar sat refutation 202,207,322,379,454,460]
% SZS output end Proof for 5312536711844618319865734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If john is either humble or not old then someone is both not curious and not generous. Everyone who is rich is either strong or not strong. Everyone who is either not calm or quiet is either not calm or humble and vice versa. Everyone who is not tall or not generous is both not patient and tall. Everyone who is curious or not tall is either not tall or kind and vice versa. Everyone who is both not strong and not calm is not funny or funny and vice versa. Everyone who is calm or not funny is not creative or not tall. Everyone who is not old is either brave or curious. Everyone who is happy is not patient. Everyone who is not tall is either not creative or curious and vice versa. If john is either not creative or not brave then paul is either tall or funny. Everyone who is curious is not old. If someone is either not happy or brave then alice is funny or tall. Everyone who is not old or calm is both strong and not funny. Everyone who is either happy or not curious is both generous and not old. Someone is happy. Someone is both quiet and funny. Someone is funny. Lucy is rich or old. Lucy is either not rich or humble. Fred is rich. | Lucy is not quiet. | neutral | (((humble(john)<~>~old(john)))=>(?[X]:((~curious(X)&~generous(X)))))&
(![X]:(rich(X)=>(strong(X)<~>~strong(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((~tall(X)|~generous(X))=>(~patient(X)&tall(X))))&
(![X]:((curious(X)|~tall(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((~strong(X)&~calm(X))<=>(~funny(X)|funny(X))))&
(![X]:((calm(X)|~funny(X))=>(~creative(X)|~tall(X))))&
(![X]:(~old(X)=>(brave(X)<~>curious(X))))&
(![X]:(happy(X)=>~patient(X)))&
(![X]:(~tall(X)<=>(~creative(X)<~>curious(X))))&
(((~creative(john)<~>~brave(john)))=>((tall(paul)<~>funny(paul))))&
(![X]:(curious(X)=>~old(X)))&
((?[X]:((~happy(X)<~>brave(X))))=>((funny(alice)|tall(alice))))&
(![X]:((~old(X)|calm(X))=>(strong(X)&~funny(X))))&
(![X]:((happy(X)<~>~curious(X))=>(generous(X)&~old(X))))&
(?[X]:(happy(X)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:(funny(X)))&
((rich(lucy)|old(lucy)))&
((~rich(lucy)<~>humble(lucy)))&
(rich(fred)) | ~quiet(lucy) | [] | null | 0 |
Everyone who is rich or not strong is not kind. Everyone who is rich is curious and vice versa. Everyone who is not wise or not funny is both not curious and not tall and vice versa. Everyone who is both not strong and not brave is both patient and brave. If fred is humble then someone is either not old or not creative and vice versa. Everyone who is calm is wise or strong. Everyone who is either quiet or rich is both quiet and brave. If someone is quiet then someone is generous or curious. If lucy is both not rich and brave then fred is tall. If lucy is both not generous and patient then someone is both old and not tall. If fred is humble or not calm then someone is kind or not curious. If someone is both wise and not funny then someone is wise. If susan is either not happy or not wise then susan is brave or not rich and vice versa. Everyone who is brave or old is both not tall and rich. If alice is not brave or not rich then mary is quiet. Everyone who is both patient and not tall is not brave or rich and vice versa. Someone is quiet or not old. Someone is either quiet or funny. Someone is both wise and not funny. Fred is happy or old. Someone is both not creative and old. Someone is both patient and not kind. Alice is quiet. Someone is not creative. | Fred is not patient. | contradiction | (![X]:((rich(X)|~strong(X))=>~kind(X)))&
(![X]:(rich(X)<=>curious(X)))&
(![X]:((~wise(X)|~funny(X))<=>(~curious(X)&~tall(X))))&
(![X]:((~strong(X)&~brave(X))=>(patient(X)&brave(X))))&
((humble(fred))<=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:(calm(X)=>(wise(X)|strong(X))))&
(![X]:((quiet(X)<~>rich(X))=>(quiet(X)&brave(X))))&
((?[X]:(quiet(X)))=>(?[X]:((generous(X)|curious(X)))))&
(((~rich(lucy)&brave(lucy)))=>(tall(fred)))&
(((~generous(lucy)&patient(lucy)))=>(?[X]:((old(X)&~tall(X)))))&
(((humble(fred)|~calm(fred)))=>(?[X]:((kind(X)|~curious(X)))))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:(wise(X))))&
(((~happy(susan)<~>~wise(susan)))<=>((brave(susan)|~rich(susan))))&
(![X]:((brave(X)|old(X))=>(~tall(X)&rich(X))))&
(((~brave(alice)|~rich(alice)))=>(quiet(mary)))&
(![X]:((patient(X)&~tall(X))<=>(~brave(X)|rich(X))))&
(?[X]:((quiet(X)|~old(X))))&
(?[X]:((quiet(X)<~>funny(X))))&
(?[X]:((wise(X)&~funny(X))))&
((happy(fred)|old(fred)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:((patient(X)&~kind(X))))&
(quiet(alice))&
(?[X]:(~creative(X))) | ~patient(fred) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6556563611939697800423730
% SZS output start Proof for 6556563611939697800423730
14. ! [X0] : ((old(X0) | brave(X0)) => (rich(X0) & ~tall(X0))) [input p13]
16. ! [X0] : ((~tall(X0) & patient(X0)) <=> (rich(X0) | ~brave(X0))) [input p15]
25. ~patient(fred) [input hypothesis]
40. ! [X0] : ((rich(X0) & ~tall(X0)) | (~old(X0) & ~brave(X0))) [ennf transformation 14]
57. ! [X0] : (((~tall(X0) & patient(X0)) | (~rich(X0) & brave(X0))) & ((rich(X0) | ~brave(X0)) | (tall(X0) | ~patient(X0)))) [nnf transformation 16]
58. ! [X0] : (((~tall(X0) & patient(X0)) | (~rich(X0) & brave(X0))) & (rich(X0) | ~brave(X0) | tall(X0) | ~patient(X0))) [flattening 57]
99. ~brave(X0) | rich(X0) [cnf transformation 40]
104. patient(X0) | brave(X0) [cnf transformation 58]
105. ~rich(X0) | patient(X0) [cnf transformation 58]
120. ~patient(fred) [cnf transformation 25]
249. brave(fred) [resolution 104,120]
253. rich(fred) [resolution 249,99]
292. patient(fred) [resolution 253,105]
294. $false [subsumption resolution 292,120]
% SZS output end Proof for 6556563611939697800423730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and rich is both curious and strong.
Everyone who is not brave is not tall and vice versa.
If someone is both generous and not rich then fred is not wise.
Everyone who is not curious or not patient is both brave and not rich.
If susan is both not humble and generous then alice is either not old or not tall.
Everyone who is not patient or not rich is generous and vice versa.
If someone is funny then someone is calm.
Everyone who is both rich and old is generous or not brave and vice versa.
If someone is not creative then lucy is not generous or not creative and vice versa.
If someone is not tall then lucy is either brave or not calm and vice versa.
If susan is not patient then john is both not quiet and humble and vice versa.
If someone is either not wise or calm then lucy is both patient and wise and vice versa.
Everyone who is not strong or funny is either not tall or patient and vice versa.
If someone is either humble or not rich then alice is kind.
If alice is either happy or funny then someone is either kind or not patient.
Someone is either tall or kind.
Someone is wise or strong.
Someone is either funny or not old.
Alice is both calm and happy.
Someone is not strong.
Lucy is either not calm or not quiet.
Someone is not quiet or not tall. | Lucy is not creative. | neutral | (![X]:((quiet(X)&rich(X))=>(curious(X)&strong(X))))&
(![X]:(~brave(X)<=>~tall(X)))&
((?[X]:((generous(X)&~rich(X))))=>(~wise(fred)))&
(![X]:((~curious(X)|~patient(X))=>(brave(X)&~rich(X))))&
(((~humble(susan)&generous(susan)))=>((~old(alice)<~>~tall(alice))))&
(![X]:((~patient(X)|~rich(X))<=>generous(X)))&
((?[X]:(funny(X)))=>(?[X]:(calm(X))))&
(![X]:((rich(X)&old(X))<=>(generous(X)|~brave(X))))&
((?[X]:(~creative(X)))<=>((~generous(lucy)|~creative(lucy))))&
((?[X]:(~tall(X)))<=>((brave(lucy)<~>~calm(lucy))))&
((~patient(susan))<=>((~quiet(john)&humble(john))))&
((?[X]:((~wise(X)<~>calm(X))))<=>((patient(lucy)&wise(lucy))))&
(![X]:((~strong(X)|funny(X))<=>(~tall(X)<~>patient(X))))&
((?[X]:((humble(X)<~>~rich(X))))=>(kind(alice)))&
(((happy(alice)<~>funny(alice)))=>(?[X]:((kind(X)<~>~patient(X)))))&
(?[X]:((tall(X)<~>kind(X))))&
(?[X]:((wise(X)|strong(X))))&
(?[X]:((funny(X)<~>~old(X))))&
((calm(alice)&happy(alice)))&
(?[X]:(~strong(X)))&
((~calm(lucy)<~>~quiet(lucy)))&
(?[X]:((~quiet(X)|~tall(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is not calm is not creative.
Everyone who is calm is not generous or not curious.
Everyone who is either funny or not old is either not rich or tall and vice versa.
If john is either not patient or not calm then john is both curious and not strong and vice versa.
Everyone who is not funny is not rich or not old.
If someone is tall then someone is kind or not wise and vice versa.
If paul is not generous or funny then someone is calm.
Everyone who is both rich and not funny is either quiet or generous and vice versa.
Everyone who is not kind or not curious is creative and vice versa.
If susan is rich then someone is either not kind or not calm.
If alice is both happy and not old then someone is either brave or patient.
Everyone who is not wise is either not generous or not wise and vice versa.
If john is both not happy and tall then lucy is either not wise or calm.
Everyone who is both not happy and not wise is not rich or wise and vice versa.
If paul is not curious or not patient then someone is not wise and vice versa.
If someone is not brave then fred is rich or old.
Paul is curious.
Paul is either kind or not old.
Someone is both not curious and brave.
Alice is both not creative and not brave.
Someone is calm or not quiet.
Someone is both humble and patient.
Mary is not tall. | Fred is old. | neutral | (![X]:(~calm(X)=>~creative(X)))&
(![X]:(calm(X)=>(~generous(X)|~curious(X))))&
(![X]:((funny(X)<~>~old(X))<=>(~rich(X)<~>tall(X))))&
(((~patient(john)<~>~calm(john)))<=>((curious(john)&~strong(john))))&
(![X]:(~funny(X)=>(~rich(X)|~old(X))))&
((?[X]:(tall(X)))<=>(?[X]:((kind(X)|~wise(X)))))&
(((~generous(paul)|funny(paul)))=>(?[X]:(calm(X))))&
(![X]:((rich(X)&~funny(X))<=>(quiet(X)<~>generous(X))))&
(![X]:((~kind(X)|~curious(X))<=>creative(X)))&
((rich(susan))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((happy(alice)&~old(alice)))=>(?[X]:((brave(X)<~>patient(X)))))&
(![X]:(~wise(X)<=>(~generous(X)<~>~wise(X))))&
(((~happy(john)&tall(john)))=>((~wise(lucy)<~>calm(lucy))))&
(![X]:((~happy(X)&~wise(X))<=>(~rich(X)|wise(X))))&
(((~curious(paul)|~patient(paul)))<=>(?[X]:(~wise(X))))&
((?[X]:(~brave(X)))=>((rich(fred)|old(fred))))&
(curious(paul))&
((kind(paul)<~>~old(paul)))&
(?[X]:((~curious(X)&brave(X))))&
((~creative(alice)&~brave(alice)))&
(?[X]:((calm(X)|~quiet(X))))&
(?[X]:((humble(X)&patient(X))))&
(~tall(mary)) | old(fred) | [] | null | 0 |
Everyone who is both funny and old is not patient or strong and vice versa.
If someone is both tall and not curious then someone is not strong or not happy and vice versa.
Everyone who is calm or kind is both tall and not rich and vice versa.
If susan is both not wise and not happy then someone is not strong.
If fred is curious or kind then someone is both not old and not 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.
Lucy is either not strong or not humble.
Someone is not rich.
Alice is not creative.
Someone is not generous.
Susan is both old and not tall.
John is calm. | Lucy is not patient. | neutral | (![X]:((funny(X)&old(X))<=>(~patient(X)|strong(X))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((calm(X)|kind(X))<=>(tall(X)&~rich(X))))&
(((~wise(susan)&~happy(susan)))=>(?[X]:(~strong(X))))&
(((curious(fred)|kind(fred)))=>(?[X]:((~old(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))))&
((~strong(lucy)<~>~humble(lucy)))&
(?[X]:(~rich(X)))&
(~creative(alice))&
(?[X]:(~generous(X)))&
((old(susan)&~tall(susan)))&
(calm(john)) | ~patient(lucy) | [] | null | 0 |
If mary is humble or rich then someone is either kind or not old. Everyone who is rich is not tall. If alice is either calm or brave then someone is rich. Everyone who is either brave or patient is not rich and vice versa. Everyone who is not tall is not happy. Everyone who is either calm or tall is both not rich and not tall and vice versa. Everyone who is not kind is both not kind and kind. Everyone who is either not happy or creative is either old or not calm and vice versa. Everyone who is either creative or not kind is patient. Everyone who is humble is wise or happy and vice versa. If alice is either quiet or not creative then someone is not strong. Everyone who is generous or not rich is either not curious or creative. If someone is not humble or curious then paul is either not humble or not generous. Everyone who is either not rich or humble is either generous or not tall and vice versa. Everyone who is wise is either not tall or happy. Everyone who is humble or not humble is both not rich and brave and vice versa. Paul is not old or old. Someone is kind or rich. Someone is generous. Alice is not wise or quiet. Someone is old or brave. Mary is old or tall. | Alice is creative. | contradiction | (((humble(mary)|rich(mary)))=>(?[X]:((kind(X)<~>~old(X)))))&
(![X]:(rich(X)=>~tall(X)))&
(((calm(alice)<~>brave(alice)))=>(?[X]:(rich(X))))&
(![X]:((brave(X)<~>patient(X))<=>~rich(X)))&
(![X]:(~tall(X)=>~happy(X)))&
(![X]:((calm(X)<~>tall(X))<=>(~rich(X)&~tall(X))))&
(![X]:(~kind(X)=>(~kind(X)&kind(X))))&
(![X]:((~happy(X)<~>creative(X))<=>(old(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~kind(X))=>patient(X)))&
(![X]:(humble(X)<=>(wise(X)|happy(X))))&
(((quiet(alice)<~>~creative(alice)))=>(?[X]:(~strong(X))))&
(![X]:((generous(X)|~rich(X))=>(~curious(X)<~>creative(X))))&
((?[X]:((~humble(X)|curious(X))))=>((~humble(paul)<~>~generous(paul))))&
(![X]:((~rich(X)<~>humble(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(wise(X)=>(~tall(X)<~>happy(X))))&
(![X]:((humble(X)|~humble(X))<=>(~rich(X)&brave(X))))&
((~old(paul)|old(paul)))&
(?[X]:((kind(X)|rich(X))))&
(?[X]:(generous(X)))&
((~wise(alice)|quiet(alice)))&
(?[X]:((old(X)|brave(X))))&
((old(mary)|tall(mary))) | creative(alice) | [
"p3",
"p6",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6828946802125380857203755
% SZS output start Proof for 6828946802125380857203755
4. ! [X0] : ((brave(X0) <~> patient(X0)) <=> ~rich(X0)) [input p3]
7. ! [X0] : (~kind(X0) => (kind(X0) & ~kind(X0))) [input p6]
9. ! [X0] : ((creative(X0) <~> ~kind(X0)) => patient(X0)) [input p8]
16. ! [X0] : ((~humble(X0) | humble(X0)) <=> (brave(X0) & ~rich(X0))) [input p15]
23. creative(alice) [input hypothesis]
30. ! [X0] : ((kind(X0) & ~kind(X0)) | kind(X0)) [ennf transformation 7]
31. ! [X0] : (patient(X0) | (creative(X0) <=> ~kind(X0))) [ennf transformation 9]
41. ! [X0] : ((((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | rich(X0)) & (~rich(X0) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))))) [nnf transformation 4]
45. ! [X0] : (patient(X0) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) [nnf transformation 31]
52. ! [X0] : (((~humble(X0) | humble(X0)) | (~brave(X0) | rich(X0))) & ((brave(X0) & ~rich(X0)) | (humble(X0) & ~humble(X0)))) [nnf transformation 16]
53. ! [X0] : ((~humble(X0) | humble(X0) | ~brave(X0) | rich(X0)) & ((brave(X0) & ~rich(X0)) | (humble(X0) & ~humble(X0)))) [flattening 52]
70. ~patient(X0) | ~brave(X0) | rich(X0) [cnf transformation 41]
79. kind(X0) | kind(X0) [cnf transformation 30]
88. patient(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 45]
111. ~rich(X0) | ~humble(X0) [cnf transformation 53]
112. ~rich(X0) | humble(X0) [cnf transformation 53]
113. brave(X0) | ~humble(X0) [cnf transformation 53]
114. brave(X0) | humble(X0) [cnf transformation 53]
121. creative(alice) [cnf transformation 23]
122. kind(X0) [duplicate literal removal 79]
160. ~creative(X0) | patient(X0) [subsumption resolution 88,122]
183. brave(X0) [subsumption resolution 113,114]
184. ~rich(X0) [subsumption resolution 111,112]
197. patient(alice) [resolution 160,121]
203. ~brave(alice) | rich(alice) [resolution 70,197]
206. rich(alice) [subsumption resolution 203,183]
207. $false [subsumption resolution 206,184]
% SZS output end Proof for 6828946802125380857203755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not humble is either not funny or tall.
Everyone who is both not happy and not wise is either generous or not generous and vice versa.
Everyone who is not quiet or tall is not funny.
If someone is creative then mary is strong or patient.
If lucy is curious or quiet then paul is not patient or not calm and vice versa.
Everyone who is both rich and not kind is both rich and quiet and vice versa.
Everyone who is not strong or curious is not patient or not brave.
Everyone who is not wise or not calm is either curious or not creative.
If alice is both not quiet and not calm then john is humble or tall.
Everyone who is both generous and not wise is humble and vice versa.
If someone is brave then susan is both quiet and curious.
Everyone who is both not patient and funny is both not patient and curious and vice versa.
Everyone who is either not kind or not curious is not strong and vice versa.
If someone is humble then paul is both kind and not strong and vice versa.
Everyone who is rich is not kind or not quiet.
If someone is either not quiet or not creative then mary is either tall or wise.
Mary is not old.
Mary is not funny.
Someone is not kind or not brave.
Someone is not strong.
Lucy is kind.
Mary is not humble. | Alice is not strong. | neutral | (![X]:((~rich(X)<~>~humble(X))=>(~funny(X)<~>tall(X))))&
(![X]:((~happy(X)&~wise(X))<=>(generous(X)<~>~generous(X))))&
(![X]:((~quiet(X)|tall(X))=>~funny(X)))&
((?[X]:(creative(X)))=>((strong(mary)|patient(mary))))&
(((curious(lucy)|quiet(lucy)))<=>((~patient(paul)|~calm(paul))))&
(![X]:((rich(X)&~kind(X))<=>(rich(X)&quiet(X))))&
(![X]:((~strong(X)|curious(X))=>(~patient(X)|~brave(X))))&
(![X]:((~wise(X)|~calm(X))=>(curious(X)<~>~creative(X))))&
(((~quiet(alice)&~calm(alice)))=>((humble(john)|tall(john))))&
(![X]:((generous(X)&~wise(X))<=>humble(X)))&
((?[X]:(brave(X)))=>((quiet(susan)&curious(susan))))&
(![X]:((~patient(X)&funny(X))<=>(~patient(X)&curious(X))))&
(![X]:((~kind(X)<~>~curious(X))<=>~strong(X)))&
((?[X]:(humble(X)))<=>((kind(paul)&~strong(paul))))&
(![X]:(rich(X)=>(~kind(X)|~quiet(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))=>((tall(mary)<~>wise(mary))))&
(~old(mary))&
(~funny(mary))&
(?[X]:((~kind(X)|~brave(X))))&
(?[X]:(~strong(X)))&
(kind(lucy))&
(~humble(mary)) | ~strong(alice) | [] | null | 0 |
If paul is both tall and not patient then someone is both old and quiet.
If someone is not happy or funny then mary is both curious and creative.
Everyone who is both curious and generous is either not calm or not wise.
Everyone who is not brave or quiet is not generous and vice versa.
Everyone who is brave or creative is both not generous and curious.
If mary is happy or not calm then mary is not brave and vice versa.
Everyone who is either not humble or funny is tall.
Everyone who is old is patient and vice versa.
Everyone who is not rich is either not patient or strong and vice versa.
If someone is either tall or calm then someone is not generous or not patient and vice versa.
Everyone who is either not old or funny is both not funny and not creative.
Everyone who is not kind or not strong is old or not strong and vice versa.
If someone is both rich and old then someone is both not humble and calm and vice versa.
If mary is both wise and humble then someone is not calm or not brave.
Everyone who is not happy is kind and vice versa.
If someone is either brave or patient then someone is both not curious and not tall and vice versa.
Alice is not tall or not generous.
Someone is not creative or not calm.
Alice is not quiet.
Someone is either not kind or not tall.
Alice is either brave or not creative.
Someone is not curious or not wise.
Paul is not quiet.
Someone is either not curious or rich. | Mary is generous. | contradiction | (((tall(paul)&~patient(paul)))=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:((~happy(X)|funny(X))))=>((curious(mary)&creative(mary))))&
(![X]:((curious(X)&generous(X))=>(~calm(X)<~>~wise(X))))&
(![X]:((~brave(X)|quiet(X))<=>~generous(X)))&
(![X]:((brave(X)|creative(X))=>(~generous(X)&curious(X))))&
(((happy(mary)|~calm(mary)))<=>(~brave(mary)))&
(![X]:((~humble(X)<~>funny(X))=>tall(X)))&
(![X]:(old(X)<=>patient(X)))&
(![X]:(~rich(X)<=>(~patient(X)<~>strong(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(?[X]:((~generous(X)|~patient(X)))))&
(![X]:((~old(X)<~>funny(X))=>(~funny(X)&~creative(X))))&
(![X]:((~kind(X)|~strong(X))<=>(old(X)|~strong(X))))&
((?[X]:((rich(X)&old(X))))<=>(?[X]:((~humble(X)&calm(X)))))&
(((wise(mary)&humble(mary)))=>(?[X]:((~calm(X)|~brave(X)))))&
(![X]:(~happy(X)<=>kind(X)))&
((?[X]:((brave(X)<~>patient(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
((~tall(alice)|~generous(alice)))&
(?[X]:((~creative(X)|~calm(X))))&
(~quiet(alice))&
(?[X]:((~kind(X)<~>~tall(X))))&
((brave(alice)<~>~creative(alice)))&
(?[X]:((~curious(X)|~wise(X))))&
(~quiet(paul))&
(?[X]:((~curious(X)<~>rich(X)))) | generous(mary) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4035937673372504422268571
% SZS output start Proof for 4035937673372504422268571
4. ! [X0] : ((quiet(X0) | ~brave(X0)) <=> ~generous(X0)) [input p3]
5. ! [X0] : ((creative(X0) | brave(X0)) => (curious(X0) & ~generous(X0))) [input p4]
25. generous(mary) [input hypothesis]
34. ! [X0] : ((curious(X0) & ~generous(X0)) | (~creative(X0) & ~brave(X0))) [ennf transformation 5]
42. ! [X0] : (((quiet(X0) | ~brave(X0)) | generous(X0)) & (~generous(X0) | (~quiet(X0) & brave(X0)))) [nnf transformation 4]
43. ! [X0] : ((quiet(X0) | ~brave(X0) | generous(X0)) & (~generous(X0) | (~quiet(X0) & brave(X0)))) [flattening 42]
89. ~generous(X0) | brave(X0) [cnf transformation 43]
92. ~generous(X0) | ~brave(X0) [cnf transformation 34]
145. generous(mary) [cnf transformation 25]
183. ~generous(X0) [subsumption resolution 92,89]
338. $false [subsumption resolution 145,183]
% SZS output end Proof for 4035937673372504422268571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not old or not quiet then someone is both quiet and calm and vice versa. If someone is either wise or kind then alice is tall. Everyone who is either curious or funny is not humble or brave. Everyone who is wise is either funny or not patient and vice versa. Everyone who is patient or quiet is either wise or kind. Everyone who is not creative or not patient is not generous or creative and vice versa. Everyone who is patient is either patient or not quiet. Everyone who is either not patient or kind is not quiet or brave and vice versa. Everyone who is not old is not creative and vice versa. If john is calm then john is either not patient or happy and vice versa. Everyone who is either not generous or quiet is not humble. If someone is either strong or curious then someone is generous and vice versa. If paul is not humble then susan is both not patient and not creative. Everyone who is generous is not wise. If someone is either not generous or not wise then someone is both not rich and rich. If someone is humble then lucy is either calm or not tall. Someone is old. Lucy is strong or happy. Mary is both kind and humble. Susan is not creative or not wise. Someone is either not rich or not tall. Alice is either curious or not humble. | Susan is calm. | neutral | (((~old(lucy)|~quiet(lucy)))<=>(?[X]:((quiet(X)&calm(X)))))&
((?[X]:((wise(X)<~>kind(X))))=>(tall(alice)))&
(![X]:((curious(X)<~>funny(X))=>(~humble(X)|brave(X))))&
(![X]:(wise(X)<=>(funny(X)<~>~patient(X))))&
(![X]:((patient(X)|quiet(X))=>(wise(X)<~>kind(X))))&
(![X]:((~creative(X)|~patient(X))<=>(~generous(X)|creative(X))))&
(![X]:(patient(X)=>(patient(X)<~>~quiet(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~quiet(X)|brave(X))))&
(![X]:(~old(X)<=>~creative(X)))&
((calm(john))<=>((~patient(john)<~>happy(john))))&
(![X]:((~generous(X)<~>quiet(X))=>~humble(X)))&
((?[X]:((strong(X)<~>curious(X))))<=>(?[X]:(generous(X))))&
((~humble(paul))=>((~patient(susan)&~creative(susan))))&
(![X]:(generous(X)=>~wise(X)))&
((?[X]:((~generous(X)<~>~wise(X))))=>(?[X]:((~rich(X)&rich(X)))))&
((?[X]:(humble(X)))=>((calm(lucy)<~>~tall(lucy))))&
(?[X]:(old(X)))&
((strong(lucy)|happy(lucy)))&
((kind(mary)&humble(mary)))&
((~creative(susan)|~wise(susan)))&
(?[X]:((~rich(X)<~>~tall(X))))&
((curious(alice)<~>~humble(alice))) | calm(susan) | [] | null | 0 |
If someone is either not creative or not kind then someone is both happy and not wise.
Everyone who is not patient or not creative is both calm and strong and vice versa.
If someone is brave then lucy is both not tall and not calm and vice versa.
If someone is strong or patient then paul is creative or not patient and vice versa.
If someone is either not calm or creative then alice is either brave or humble and vice versa.
If someone is either generous or not wise then someone is either generous or funny.
If paul is either calm or not old then john is calm and vice versa.
Everyone who is brave is wise or happy.
Everyone who is not quiet is either rich or not humble.
Everyone who is old is not wise or not tall and vice versa.
Everyone who is strong or quiet is tall and vice versa.
Everyone who is either old or not funny is both not humble and not patient and vice versa.
If someone is not calm then someone is both old and strong and vice versa.
Everyone who is both brave and wise is not generous.
Everyone who is either not kind or kind is not quiet or humble and vice versa.
Everyone who is not rich or brave is not patient.
Paul is not happy.
Someone is creative or patient.
Fred is happy.
Someone is either strong or not old.
John is kind.
Lucy is generous.
Alice is strong or funny.
Lucy is not happy or strong. | Alice is creative. | neutral | ((?[X]:((~creative(X)<~>~kind(X))))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(calm(X)&strong(X))))&
((?[X]:(brave(X)))<=>((~tall(lucy)&~calm(lucy))))&
((?[X]:((strong(X)|patient(X))))<=>((creative(paul)|~patient(paul))))&
((?[X]:((~calm(X)<~>creative(X))))<=>((brave(alice)<~>humble(alice))))&
((?[X]:((generous(X)<~>~wise(X))))=>(?[X]:((generous(X)<~>funny(X)))))&
(((calm(paul)<~>~old(paul)))<=>(calm(john)))&
(![X]:(brave(X)=>(wise(X)|happy(X))))&
(![X]:(~quiet(X)=>(rich(X)<~>~humble(X))))&
(![X]:(old(X)<=>(~wise(X)|~tall(X))))&
(![X]:((strong(X)|quiet(X))<=>tall(X)))&
(![X]:((old(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((old(X)&strong(X)))))&
(![X]:((brave(X)&wise(X))=>~generous(X)))&
(![X]:((~kind(X)<~>kind(X))<=>(~quiet(X)|humble(X))))&
(![X]:((~rich(X)|brave(X))=>~patient(X)))&
(~happy(paul))&
(?[X]:((creative(X)|patient(X))))&
(happy(fred))&
(?[X]:((strong(X)<~>~old(X))))&
(kind(john))&
(generous(lucy))&
((strong(alice)|funny(alice)))&
((~happy(lucy)|strong(lucy))) | creative(alice) | [] | null | 0 |
Everyone who is either kind or curious is not strong or brave and vice versa.
If someone is patient then susan is tall.
Everyone who is not curious is rich and vice versa.
If someone is kind or not happy then john is either funny or not quiet and vice versa.
Everyone who is either not generous or not rich is not quiet or not kind and vice versa.
Everyone who is humble or generous is not humble or not funny and vice versa.
If someone is both not creative and patient then susan is not creative and vice versa.
If someone is both not rich and calm then someone is not creative or curious.
Everyone who is old is either curious or tall and vice versa.
If susan is both strong and patient then someone is either not quiet or not tall and vice versa.
Everyone who is either quiet or not calm is both humble and not quiet and vice versa.
Everyone who is humble is wise or not curious.
Everyone who is curious is either not old or brave and vice versa.
If someone is not brave then someone is old and vice versa.
If someone is not kind or curious then paul is either not funny or tall and vice versa.
If someone is happy or not quiet then alice is both not humble and rich and vice versa.
Susan is both tall and not funny.
Alice is both not curious and patient.
Lucy is both not funny and not calm.
Mary is not brave or not kind.
Lucy is either not curious or kind.
Mary is both kind and patient.
John is not funny or not strong.
Fred is patient. | Alice is not quiet. | contradiction | (![X]:((kind(X)<~>curious(X))<=>(~strong(X)|brave(X))))&
((?[X]:(patient(X)))=>(tall(susan)))&
(![X]:(~curious(X)<=>rich(X)))&
((?[X]:((kind(X)|~happy(X))))<=>((funny(john)<~>~quiet(john))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~quiet(X)|~kind(X))))&
(![X]:((humble(X)|generous(X))<=>(~humble(X)|~funny(X))))&
((?[X]:((~creative(X)&patient(X))))<=>(~creative(susan)))&
((?[X]:((~rich(X)&calm(X))))=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:(old(X)<=>(curious(X)<~>tall(X))))&
(((strong(susan)&patient(susan)))<=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(![X]:((quiet(X)<~>~calm(X))<=>(humble(X)&~quiet(X))))&
(![X]:(humble(X)=>(wise(X)|~curious(X))))&
(![X]:(curious(X)<=>(~old(X)<~>brave(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(old(X))))&
((?[X]:((~kind(X)|curious(X))))<=>((~funny(paul)<~>tall(paul))))&
((?[X]:((happy(X)|~quiet(X))))<=>((~humble(alice)&rich(alice))))&
((tall(susan)&~funny(susan)))&
((~curious(alice)&patient(alice)))&
((~funny(lucy)&~calm(lucy)))&
((~brave(mary)|~kind(mary)))&
((~curious(lucy)<~>kind(lucy)))&
((kind(mary)&patient(mary)))&
((~funny(john)|~strong(john)))&
(patient(fred)) | ~quiet(alice) | [
"p2",
"p4",
"p5",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6371942749172940648119217
% SZS output start Proof for 6371942749172940648119217
3. ! [X0] : (~curious(X0) <=> rich(X0)) [input p2]
5. ! [X0] : ((~generous(X0) <~> ~rich(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p4]
6. ! [X0] : ((generous(X0) | humble(X0)) <=> (~funny(X0) | ~humble(X0))) [input p5]
16. ? [X0] : (~quiet(X0) | happy(X0)) <=> (rich(alice) & ~humble(alice)) [input p15]
18. patient(alice) & ~curious(alice) [input p17]
25. ~quiet(alice) [input hypothesis]
33. ! [X0] : ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0))) [nnf transformation 3]
38. ! [X0] : ((((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))))) [nnf transformation 5]
39. ! [X0] : ((((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))))) [flattening 38]
40. ! [X0] : (((generous(X0) | humble(X0)) | (funny(X0) & humble(X0))) & ((~funny(X0) | ~humble(X0)) | (~generous(X0) & ~humble(X0)))) [nnf transformation 6]
41. ! [X0] : ((generous(X0) | humble(X0) | (funny(X0) & humble(X0))) & (~funny(X0) | ~humble(X0) | (~generous(X0) & ~humble(X0)))) [flattening 40]
67. (? [X0] : (~quiet(X0) | happy(X0)) | (~rich(alice) | humble(alice))) & ((rich(alice) & ~humble(alice)) | ! [X0] : (quiet(X0) & ~happy(X0))) [nnf transformation 16]
68. (? [X0] : (~quiet(X0) | happy(X0)) | ~rich(alice) | humble(alice)) & ((rich(alice) & ~humble(alice)) | ! [X0] : (quiet(X0) & ~happy(X0))) [flattening 67]
69. (? [X0] : (~quiet(X0) | happy(X0)) | ~rich(alice) | humble(alice)) & ((rich(alice) & ~humble(alice)) | ! [X1] : (quiet(X1) & ~happy(X1))) [rectify 68]
70. ? [X0] : (~quiet(X0) | happy(X0)) => (~quiet(sK7) | happy(sK7)) [choice axiom]
71. ((~quiet(sK7) | happy(sK7)) | ~rich(alice) | humble(alice)) & ((rich(alice) & ~humble(alice)) | ! [X1] : (quiet(X1) & ~happy(X1))) [skolemisation 69,70]
80. rich(X0) | curious(X0) [cnf transformation 33]
90. ~generous(X0) | ~rich(X0) | quiet(X0) [cnf transformation 39]
96. generous(X0) | humble(X0) | humble(X0) [cnf transformation 41]
131. ~humble(alice) | quiet(X1) [cnf transformation 71]
137. ~curious(alice) [cnf transformation 18]
148. ~quiet(alice) [cnf transformation 25]
152. humble(X0) | generous(X0) [duplicate literal removal 96]
292. 32 <=> humble(alice) [avatar definition]
293. ~humble(alice) <- (~32) [avatar component clause 292]
296. 33 <=> rich(alice) [avatar definition]
298. ~rich(alice) <- (~33) [avatar component clause 296]
309. 36 <=> ! [X1] : quiet(X1) [avatar definition]
310. quiet(X1) <- (36) [avatar component clause 309]
316. 36 | ~32 [avatar split clause 131,292,309]
352. generous(alice) <- (~32) [resolution 152,293]
356. ~rich(alice) | quiet(alice) <- (~32) [resolution 90,352]
360. ~rich(alice) <- (~32) [subsumption resolution 356,148]
361. ~33 | 32 [avatar split clause 360,292,296]
362. curious(alice) <- (~33) [resolution 298,80]
363. $false <- (~33) [subsumption resolution 362,137]
364. 33 [avatar contradiction clause 363]
369. $false <- (36) [resolution 310,148]
372. ~36 [avatar contradiction clause 369]
374. $false [avatar sat refutation 316,361,364,372]
% SZS output end Proof for 6371942749172940648119217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is both not strong and not old and vice versa.
If someone is not old then someone is old or not brave.
Everyone who is generous or not kind is both not quiet and humble and vice versa.
Everyone who is not curious is either not happy or not strong.
Everyone who is either not curious or not quiet is both creative and funny and vice versa.
Everyone who is generous or not funny is either not old or humble and vice versa.
If john is both not brave and not creative then someone is both not humble and old.
Everyone who is both calm and curious is either creative or quiet.
If susan is strong or not rich then mary is both funny and tall.
Everyone who is tall is not curious or not tall.
Everyone who is not old or not kind is not calm or not quiet.
Everyone who is not kind is humble or tall.
Everyone who is both kind and not brave is either not creative or not quiet.
If fred is not calm or creative then someone is not rich and vice versa.
Everyone who is not humble is both curious and humble and vice versa.
If alice is both happy and not patient then lucy is not wise or calm and vice versa.
Someone is tall.
Someone is both strong and not curious.
Someone is not strong or calm.
Someone is either old or calm.
John is tall.
Someone is both not strong and not generous.
Susan is tall or not quiet.
Someone is either funny or kind. | Alice is kind. | neutral | (![X]:(curious(X)<=>(~strong(X)&~old(X))))&
((?[X]:(~old(X)))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((generous(X)|~kind(X))<=>(~quiet(X)&humble(X))))&
(![X]:(~curious(X)=>(~happy(X)<~>~strong(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(creative(X)&funny(X))))&
(![X]:((generous(X)|~funny(X))<=>(~old(X)<~>humble(X))))&
(((~brave(john)&~creative(john)))=>(?[X]:((~humble(X)&old(X)))))&
(![X]:((calm(X)&curious(X))=>(creative(X)<~>quiet(X))))&
(((strong(susan)|~rich(susan)))=>((funny(mary)&tall(mary))))&
(![X]:(tall(X)=>(~curious(X)|~tall(X))))&
(![X]:((~old(X)|~kind(X))=>(~calm(X)|~quiet(X))))&
(![X]:(~kind(X)=>(humble(X)|tall(X))))&
(![X]:((kind(X)&~brave(X))=>(~creative(X)<~>~quiet(X))))&
(((~calm(fred)|creative(fred)))<=>(?[X]:(~rich(X))))&
(![X]:(~humble(X)<=>(curious(X)&humble(X))))&
(((happy(alice)&~patient(alice)))<=>((~wise(lucy)|calm(lucy))))&
(?[X]:(tall(X)))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:((~strong(X)|calm(X))))&
(?[X]:((old(X)<~>calm(X))))&
(tall(john))&
(?[X]:((~strong(X)&~generous(X))))&
((tall(susan)|~quiet(susan)))&
(?[X]:((funny(X)<~>kind(X)))) | kind(alice) | [] | null | 0 |
If someone is not curious then susan is curious or not humble and vice versa.
If alice is either old or not patient then someone is tall or curious.
Everyone who is both wise and not quiet is curious or strong and vice versa.
If lucy is either not wise or tall then someone is brave and vice versa.
Everyone who is both funny and curious is not wise.
Everyone who is both tall and funny is both old and not patient and vice versa.
If susan is calm then someone is both not strong and rich.
Everyone who is not tall or creative is rich or not old.
If someone is tall or not patient then mary is strong and vice versa.
If someone is not generous then someone is either not curious or generous.
Everyone who is strong is both not humble and kind.
If someone is not quiet or generous then alice is not curious and vice versa.
Everyone who is not patient or patient is both not curious and happy and vice versa.
If someone is both quiet and not rich then susan is strong.
Everyone who is either kind or not brave is both not brave and kind and vice versa.
If someone is not humble or kind then lucy is both not funny and not calm and vice versa.
Someone is either not funny or not calm.
John is either curious or not curious.
Paul is both creative and not curious.
Someone is patient.
Someone is either not funny or strong. | Susan is not old. | neutral | ((?[X]:(~curious(X)))<=>((curious(susan)|~humble(susan))))&
(((old(alice)<~>~patient(alice)))=>(?[X]:((tall(X)|curious(X)))))&
(![X]:((wise(X)&~quiet(X))<=>(curious(X)|strong(X))))&
(((~wise(lucy)<~>tall(lucy)))<=>(?[X]:(brave(X))))&
(![X]:((funny(X)&curious(X))=>~wise(X)))&
(![X]:((tall(X)&funny(X))<=>(old(X)&~patient(X))))&
((calm(susan))=>(?[X]:((~strong(X)&rich(X)))))&
(![X]:((~tall(X)|creative(X))=>(rich(X)|~old(X))))&
((?[X]:((tall(X)|~patient(X))))<=>(strong(mary)))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:(strong(X)=>(~humble(X)&kind(X))))&
((?[X]:((~quiet(X)|generous(X))))<=>(~curious(alice)))&
(![X]:((~patient(X)|patient(X))<=>(~curious(X)&happy(X))))&
((?[X]:((quiet(X)&~rich(X))))=>(strong(susan)))&
(![X]:((kind(X)<~>~brave(X))<=>(~brave(X)&kind(X))))&
((?[X]:((~humble(X)|kind(X))))<=>((~funny(lucy)&~calm(lucy))))&
(?[X]:((~funny(X)<~>~calm(X))))&
((curious(john)<~>~curious(john)))&
((creative(paul)&~curious(paul)))&
(?[X]:(patient(X)))&
(?[X]:((~funny(X)<~>strong(X)))) | ~old(susan) | [] | null | 0 |
Everyone who is not brave or not funny is not old or calm.
Everyone who is not funny is either tall or wise.
Everyone who is not strong is not curious or quiet and vice versa.
If alice is both happy and not wise then someone is not humble and vice versa.
Everyone who is either happy or not rich is creative or not tall.
If alice is happy then mary is not wise.
Everyone who is rich or kind is either generous or not funny.
If someone is both creative and not calm then alice is either strong or quiet.
Everyone who is not calm is both old and not generous and vice versa.
If someone is old or not happy then lucy is not kind and vice versa.
Everyone who is not old is quiet or funny and vice versa.
If lucy is either not curious or not old then someone is not wise or strong.
If alice is old then someone is strong.
Everyone who is not strong or not patient is creative or not quiet and vice versa.
Everyone who is not humble or old is both tall and patient.
Everyone who is both not generous and not patient is not patient or wise and vice versa.
Someone is not funny.
Mary is both not curious and patient.
Someone is not funny or curious.
Someone is either calm or happy.
Someone is strong or not brave.
Paul is not tall or rich.
Lucy is not happy.
Lucy is not brave. | Mary is not kind. | neutral | (![X]:((~brave(X)|~funny(X))=>(~old(X)|calm(X))))&
(![X]:(~funny(X)=>(tall(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(~curious(X)|quiet(X))))&
(((happy(alice)&~wise(alice)))<=>(?[X]:(~humble(X))))&
(![X]:((happy(X)<~>~rich(X))=>(creative(X)|~tall(X))))&
((happy(alice))=>(~wise(mary)))&
(![X]:((rich(X)|kind(X))=>(generous(X)<~>~funny(X))))&
((?[X]:((creative(X)&~calm(X))))=>((strong(alice)<~>quiet(alice))))&
(![X]:(~calm(X)<=>(old(X)&~generous(X))))&
((?[X]:((old(X)|~happy(X))))<=>(~kind(lucy)))&
(![X]:(~old(X)<=>(quiet(X)|funny(X))))&
(((~curious(lucy)<~>~old(lucy)))=>(?[X]:((~wise(X)|strong(X)))))&
((old(alice))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)|~patient(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~humble(X)|old(X))=>(tall(X)&patient(X))))&
(![X]:((~generous(X)&~patient(X))<=>(~patient(X)|wise(X))))&
(?[X]:(~funny(X)))&
((~curious(mary)&patient(mary)))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((strong(X)|~brave(X))))&
((~tall(paul)|rich(paul)))&
(~happy(lucy))&
(~brave(lucy)) | ~kind(mary) | [] | null | 0 |
If john is both strong and not curious then paul is both not funny and creative and vice versa. Everyone who is both curious and brave is either rich or strong and vice versa. If paul is either not brave or tall then someone is not patient. Everyone who is both generous and calm is not wise or calm. If someone is either not rich or not strong then someone is either not happy or not tall and vice versa. If someone is both not patient and rich then mary is both funny and not humble. Everyone who is either kind or calm is creative. Everyone who is not old or wise is both calm and not wise. If paul is strong then someone is not curious and vice versa. Everyone who is both not happy and not funny is creative or not brave and vice versa. Everyone who is creative or not tall is either happy or not curious and vice versa. Everyone who is funny is wise or not generous. Everyone who is not brave is humble and vice versa. If someone is curious then someone is not humble or not calm and vice versa. Everyone who is calm or not old is kind or brave. Everyone who is both not strong and brave is either not creative or not patient and vice versa. Lucy is creative or curious. Alice is both quiet and not strong. Someone is both not kind and happy. Lucy is old or happy. Someone is generous or not quiet. Lucy is either not generous or not calm. Fred is kind or not old. | Alice is happy. | neutral | (((strong(john)&~curious(john)))<=>((~funny(paul)&creative(paul))))&
(![X]:((curious(X)&brave(X))<=>(rich(X)<~>strong(X))))&
(((~brave(paul)<~>tall(paul)))=>(?[X]:(~patient(X))))&
(![X]:((generous(X)&calm(X))=>(~wise(X)|calm(X))))&
((?[X]:((~rich(X)<~>~strong(X))))<=>(?[X]:((~happy(X)<~>~tall(X)))))&
((?[X]:((~patient(X)&rich(X))))=>((funny(mary)&~humble(mary))))&
(![X]:((kind(X)<~>calm(X))=>creative(X)))&
(![X]:((~old(X)|wise(X))=>(calm(X)&~wise(X))))&
((strong(paul))<=>(?[X]:(~curious(X))))&
(![X]:((~happy(X)&~funny(X))<=>(creative(X)|~brave(X))))&
(![X]:((creative(X)|~tall(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(funny(X)=>(wise(X)|~generous(X))))&
(![X]:(~brave(X)<=>humble(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((calm(X)|~old(X))=>(kind(X)|brave(X))))&
(![X]:((~strong(X)&brave(X))<=>(~creative(X)<~>~patient(X))))&
((creative(lucy)|curious(lucy)))&
((quiet(alice)&~strong(alice)))&
(?[X]:((~kind(X)&happy(X))))&
((old(lucy)|happy(lucy)))&
(?[X]:((generous(X)|~quiet(X))))&
((~generous(lucy)<~>~calm(lucy)))&
((kind(fred)|~old(fred))) | happy(alice) | [] | null | 0 |
Everyone who is not strong or not kind is not humble. Everyone who is not tall is both not happy and not calm. Everyone who is both not generous and happy is brave or not old and vice versa. If mary is either happy or not generous then someone is either wise or patient. Everyone who is both not strong and strong is not curious or brave. If someone is either rich or brave then paul is not calm. If someone is either not rich or not curious then john is either tall or not humble and vice versa. Everyone who is not kind is either brave or wise. Everyone who is both strong and calm is not calm or not kind and vice versa. If someone is either not calm or brave then someone is both creative and humble. If someone is both patient and not wise then john is happy or rich and vice versa. If someone is either not creative or rich then someone is both funny and happy. If mary is either not curious or funny then someone is funny. If john is both not patient and not quiet then someone is both not quiet and calm. If someone is both not calm and not strong then mary is quiet and vice versa. Someone is either happy or quiet. Alice is not creative or not strong. Someone is both patient and not kind. Alice is old. Alice is both creative and tall. Someone is not wise or not quiet. Lucy is either not creative or not humble. Susan is not happy. | Susan is not rich. | entailment | (![X]:((~strong(X)|~kind(X))=>~humble(X)))&
(![X]:(~tall(X)=>(~happy(X)&~calm(X))))&
(![X]:((~generous(X)&happy(X))<=>(brave(X)|~old(X))))&
(((happy(mary)<~>~generous(mary)))=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:((~strong(X)&strong(X))=>(~curious(X)|brave(X))))&
((?[X]:((rich(X)<~>brave(X))))=>(~calm(paul)))&
((?[X]:((~rich(X)<~>~curious(X))))<=>((tall(john)<~>~humble(john))))&
(![X]:(~kind(X)=>(brave(X)<~>wise(X))))&
(![X]:((strong(X)&calm(X))<=>(~calm(X)|~kind(X))))&
((?[X]:((~calm(X)<~>brave(X))))=>(?[X]:((creative(X)&humble(X)))))&
((?[X]:((patient(X)&~wise(X))))<=>((happy(john)|rich(john))))&
((?[X]:((~creative(X)<~>rich(X))))=>(?[X]:((funny(X)&happy(X)))))&
(((~curious(mary)<~>funny(mary)))=>(?[X]:(funny(X))))&
(((~patient(john)&~quiet(john)))=>(?[X]:((~quiet(X)&calm(X)))))&
((?[X]:((~calm(X)&~strong(X))))<=>(quiet(mary)))&
(?[X]:((happy(X)<~>quiet(X))))&
((~creative(alice)|~strong(alice)))&
(?[X]:((patient(X)&~kind(X))))&
(old(alice))&
((creative(alice)&tall(alice)))&
(?[X]:((~wise(X)|~quiet(X))))&
((~creative(lucy)<~>~humble(lucy)))&
(~happy(susan)) | ~rich(susan) | [
"p2",
"p5",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4847611509156174951519123
% SZS output start Proof for 4847611509156174951519123
3. ! [X0] : ((happy(X0) & ~generous(X0)) <=> (~old(X0) | brave(X0))) [input p2]
6. ? [X0] : (rich(X0) <~> brave(X0)) => ~calm(paul) [input p5]
9. ! [X0] : ((calm(X0) & strong(X0)) <=> (~kind(X0) | ~calm(X0))) [input p8]
23. ~happy(susan) [input p22]
24. rich(susan) [input hypothesis]
32. ~calm(paul) | ! [X0] : (rich(X0) <=> brave(X0)) [ennf transformation 6]
39. ! [X0] : (((happy(X0) & ~generous(X0)) | (old(X0) & ~brave(X0))) & ((~old(X0) | brave(X0)) | (~happy(X0) | generous(X0)))) [nnf transformation 3]
40. ! [X0] : (((happy(X0) & ~generous(X0)) | (old(X0) & ~brave(X0))) & (~old(X0) | brave(X0) | ~happy(X0) | generous(X0))) [flattening 39]
44. ~calm(paul) | ! [X0] : ((rich(X0) | ~brave(X0)) & (brave(X0) | ~rich(X0))) [nnf transformation 32]
50. ! [X0] : (((calm(X0) & strong(X0)) | (kind(X0) & calm(X0))) & ((~kind(X0) | ~calm(X0)) | (~calm(X0) | ~strong(X0)))) [nnf transformation 9]
51. ! [X0] : (((calm(X0) & strong(X0)) | (kind(X0) & calm(X0))) & (~kind(X0) | ~calm(X0) | ~calm(X0) | ~strong(X0))) [flattening 50]
89. ~brave(X0) | happy(X0) [cnf transformation 40]
96. ~calm(paul) | brave(X0) | ~rich(X0) [cnf transformation 44]
111. calm(X0) | calm(X0) [cnf transformation 51]
144. ~happy(susan) [cnf transformation 23]
145. rich(susan) [cnf transformation 24]
147. calm(X0) [duplicate literal removal 111]
172. 6 <=> calm(paul) [avatar definition]
174. ~calm(paul) <- (~6) [avatar component clause 172]
177. 7 <=> ! [X0] : (brave(X0) | ~rich(X0)) [avatar definition]
178. ~rich(X0) | brave(X0) <- (7) [avatar component clause 177]
179. 7 | ~6 [avatar split clause 96,172,177]
345. $false <- (~6) [subsumption resolution 174,147]
346. 6 [avatar contradiction clause 345]
362. brave(susan) <- (7) [resolution 178,145]
373. happy(susan) <- (7) [resolution 362,89]
375. $false <- (7) [subsumption resolution 373,144]
376. ~7 [avatar contradiction clause 375]
377. $false [avatar sat refutation 179,346,376]
% SZS output end Proof for 4847611509156174951519123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either strong or not tall then susan is not humble and vice versa.
Everyone who is either not patient or creative is both not calm and curious and vice versa.
Everyone who is wise or not rich is not rich and vice versa.
If paul is either funny or kind then lucy is generous or curious and vice versa.
If lucy is both not strong and not quiet then susan is both kind and calm and vice versa.
If someone is funny then someone is not brave and vice versa.
Everyone who is both not strong and brave is either calm or not tall and vice versa.
Everyone who is not kind is both strong and not rich.
Everyone who is wise or tall is not old or happy.
Everyone who is calm is not kind or not strong.
Everyone who is either not happy or not generous is not happy or brave and vice versa.
If susan is not old or kind then lucy is calm or not creative.
Everyone who is calm is both not humble and curious and vice versa.
If john is both generous and tall then susan is either wise or not strong and vice versa.
If john is not funny or not old then someone is not old or not happy.
If lucy is funny then paul is generous or not humble and vice versa.
Fred is not curious.
Mary is rich.
Fred is either not curious or tall.
Alice is brave or not calm.
Someone is either happy or not rich.
Someone is both brave and not calm.
Mary is strong. | Alice is not creative. | neutral | (((strong(lucy)<~>~tall(lucy)))<=>(~humble(susan)))&
(![X]:((~patient(X)<~>creative(X))<=>(~calm(X)&curious(X))))&
(![X]:((wise(X)|~rich(X))<=>~rich(X)))&
(((funny(paul)<~>kind(paul)))<=>((generous(lucy)|curious(lucy))))&
(((~strong(lucy)&~quiet(lucy)))<=>((kind(susan)&calm(susan))))&
((?[X]:(funny(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~strong(X)&brave(X))<=>(calm(X)<~>~tall(X))))&
(![X]:(~kind(X)=>(strong(X)&~rich(X))))&
(![X]:((wise(X)|tall(X))=>(~old(X)|happy(X))))&
(![X]:(calm(X)=>(~kind(X)|~strong(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(~happy(X)|brave(X))))&
(((~old(susan)|kind(susan)))=>((calm(lucy)|~creative(lucy))))&
(![X]:(calm(X)<=>(~humble(X)&curious(X))))&
(((generous(john)&tall(john)))<=>((wise(susan)<~>~strong(susan))))&
(((~funny(john)|~old(john)))=>(?[X]:((~old(X)|~happy(X)))))&
((funny(lucy))<=>((generous(paul)|~humble(paul))))&
(~curious(fred))&
(rich(mary))&
((~curious(fred)<~>tall(fred)))&
((brave(alice)|~calm(alice)))&
(?[X]:((happy(X)<~>~rich(X))))&
(?[X]:((brave(X)&~calm(X))))&
(strong(mary)) | ~creative(alice) | [] | null | 0 |
Everyone who is kind or curious is not tall.
Everyone who is not curious is both generous and not kind and vice versa.
Everyone who is not brave is both quiet and humble.
Everyone who is both not quiet and quiet is not humble or kind and vice versa.
If someone is not quiet or funny then someone is not creative or old and vice versa.
If susan is both humble and calm then someone is not curious or not strong.
Everyone who is either creative or quiet is both not patient and not generous.
Everyone who is either rich or not humble is old and vice versa.
Everyone who is either not happy or patient is both funny and not creative and vice versa.
Everyone who is either old or creative is either not calm or not tall.
Everyone who is rich is tall or old and vice versa.
If someone is tall or not rich then someone is either quiet or creative and vice versa.
Everyone who is kind or not generous is either strong or not quiet and vice versa.
If someone is either calm or not wise then someone is not tall.
Everyone who is both not calm and brave is kind and vice versa.
If lucy is either not patient or not rich then susan is patient or not happy.
Someone is either not generous or not old.
Someone is calm.
Someone is not generous.
Susan is either humble or calm.
Someone is not patient or funny.
Paul is either not kind or calm.
Someone is kind or not happy. | Lucy is not calm. | neutral | (![X]:((kind(X)|curious(X))=>~tall(X)))&
(![X]:(~curious(X)<=>(generous(X)&~kind(X))))&
(![X]:(~brave(X)=>(quiet(X)&humble(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~quiet(X)|funny(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(((humble(susan)&calm(susan)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((rich(X)<~>~humble(X))<=>old(X)))&
(![X]:((~happy(X)<~>patient(X))<=>(funny(X)&~creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)&brave(X))<=>kind(X)))&
(((~patient(lucy)<~>~rich(lucy)))=>((patient(susan)|~happy(susan))))&
(?[X]:((~generous(X)<~>~old(X))))&
(?[X]:(calm(X)))&
(?[X]:(~generous(X)))&
((humble(susan)<~>calm(susan)))&
(?[X]:((~patient(X)|funny(X))))&
((~kind(paul)<~>calm(paul)))&
(?[X]:((kind(X)|~happy(X)))) | ~calm(lucy) | [] | null | 0 |
If someone is kind then alice is curious and vice versa. Everyone who is tall is not happy or wise and vice versa. Everyone who is not rich or strong is happy. Everyone who is either not creative or generous is not creative. Everyone who is not patient is not brave or brave and vice versa. Everyone who is not brave or not strong is brave or not rich and vice versa. If someone is both not old and wise then mary is either quiet or not generous and vice versa. If someone is both kind and not calm then someone is not tall or not wise and vice versa. If paul is funny or not brave then someone is either not rich or not curious and vice versa. If someone is not humble then mary is not tall and vice versa. If someone is patient or not calm then fred is either old or not patient and vice versa. Everyone who is either happy or wise is both not creative and creative and vice versa. If someone is both not happy and not creative then someone is either quiet or not patient. Everyone who is either not creative or humble is both quiet and not calm and vice versa. If someone is tall or not curious then alice is either old or not rich and vice versa. Everyone who is both tall and not brave is creative or not humble. Fred is either not wise or generous. Paul is not calm. Fred is creative. Someone is both wise and old. Someone is both kind and brave. Someone is either not quiet or happy. Someone is both not kind and not generous. Alice is both happy and not funny. | Paul is quiet. | neutral | ((?[X]:(kind(X)))<=>(curious(alice)))&
(![X]:(tall(X)<=>(~happy(X)|wise(X))))&
(![X]:((~rich(X)|strong(X))=>happy(X)))&
(![X]:((~creative(X)<~>generous(X))=>~creative(X)))&
(![X]:(~patient(X)<=>(~brave(X)|brave(X))))&
(![X]:((~brave(X)|~strong(X))<=>(brave(X)|~rich(X))))&
((?[X]:((~old(X)&wise(X))))<=>((quiet(mary)<~>~generous(mary))))&
((?[X]:((kind(X)&~calm(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
(((funny(paul)|~brave(paul)))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:(~humble(X)))<=>(~tall(mary)))&
((?[X]:((patient(X)|~calm(X))))<=>((old(fred)<~>~patient(fred))))&
(![X]:((happy(X)<~>wise(X))<=>(~creative(X)&creative(X))))&
((?[X]:((~happy(X)&~creative(X))))=>(?[X]:((quiet(X)<~>~patient(X)))))&
(![X]:((~creative(X)<~>humble(X))<=>(quiet(X)&~calm(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((old(alice)<~>~rich(alice))))&
(![X]:((tall(X)&~brave(X))=>(creative(X)|~humble(X))))&
((~wise(fred)<~>generous(fred)))&
(~calm(paul))&
(creative(fred))&
(?[X]:((wise(X)&old(X))))&
(?[X]:((kind(X)&brave(X))))&
(?[X]:((~quiet(X)<~>happy(X))))&
(?[X]:((~kind(X)&~generous(X))))&
((happy(alice)&~funny(alice))) | quiet(paul) | [] | null | 0 |
If susan is quiet then someone is both patient and funny.
Everyone who is either strong or calm is patient and vice versa.
If fred is either not kind or not funny then someone is not patient or curious.
If susan is not rich or funny then someone is generous and vice versa.
Everyone who is not creative is both patient and not patient.
If someone is both quiet and creative then paul is not curious and vice versa.
Everyone who is either calm or patient is not curious or creative.
If someone is either not calm or tall then susan is both not tall and not brave.
Everyone who is either not old or not kind is funny or humble and vice versa.
Everyone who is not generous is both not tall and strong and vice versa.
If lucy is either kind or brave then someone is curious or kind and vice versa.
Everyone who is both not kind and not calm is not kind or patient.
Everyone who is happy is kind or not funny and vice versa.
Everyone who is not wise is old or brave and vice versa.
If someone is both happy and not quiet then paul is both not happy and brave.
If alice is either not patient or not happy then someone is not quiet or curious.
Someone is both not happy and tall.
Someone is either not quiet or not old.
Someone is old or not patient.
Alice is either funny or generous.
Alice is not brave.
Susan is rich or funny.
Fred is kind.
Paul is both not strong and kind. | Paul is not curious. | entailment | ((quiet(susan))=>(?[X]:((patient(X)&funny(X)))))&
(![X]:((strong(X)<~>calm(X))<=>patient(X)))&
(((~kind(fred)<~>~funny(fred)))=>(?[X]:((~patient(X)|curious(X)))))&
(((~rich(susan)|funny(susan)))<=>(?[X]:(generous(X))))&
(![X]:(~creative(X)=>(patient(X)&~patient(X))))&
((?[X]:((quiet(X)&creative(X))))<=>(~curious(paul)))&
(![X]:((calm(X)<~>patient(X))=>(~curious(X)|creative(X))))&
((?[X]:((~calm(X)<~>tall(X))))=>((~tall(susan)&~brave(susan))))&
(![X]:((~old(X)<~>~kind(X))<=>(funny(X)|humble(X))))&
(![X]:(~generous(X)<=>(~tall(X)&strong(X))))&
(((kind(lucy)<~>brave(lucy)))<=>(?[X]:((curious(X)|kind(X)))))&
(![X]:((~kind(X)&~calm(X))=>(~kind(X)|patient(X))))&
(![X]:(happy(X)<=>(kind(X)|~funny(X))))&
(![X]:(~wise(X)<=>(old(X)|brave(X))))&
((?[X]:((happy(X)&~quiet(X))))=>((~happy(paul)&brave(paul))))&
(((~patient(alice)<~>~happy(alice)))=>(?[X]:((~quiet(X)|curious(X)))))&
(?[X]:((~happy(X)&tall(X))))&
(?[X]:((~quiet(X)<~>~old(X))))&
(?[X]:((old(X)|~patient(X))))&
((funny(alice)<~>generous(alice)))&
(~brave(alice))&
((rich(susan)|funny(susan)))&
(kind(fred))&
((~strong(paul)&kind(paul))) | ~curious(paul) | [
"p4",
"p5",
"p12",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 472071726807397360736049
% SZS output start Proof for 472071726807397360736049
5. ! [X0] : (~creative(X0) => (~patient(X0) & patient(X0))) [input p4]
6. ? [X0] : (creative(X0) & quiet(X0)) <=> ~curious(paul) [input p5]
13. ! [X0] : (happy(X0) <=> (~funny(X0) | kind(X0))) [input p12]
15. ? [X0] : (~quiet(X0) & happy(X0)) => (brave(paul) & ~happy(paul)) [input p14]
24. kind(paul) & ~strong(paul) [input p23]
25. curious(paul) [input hypothesis]
28. ! [X0] : ((~patient(X0) & patient(X0)) | creative(X0)) [ennf transformation 5]
34. (brave(paul) & ~happy(paul)) | ! [X0] : (quiet(X0) | ~happy(X0)) [ennf transformation 15]
47. (? [X0] : (creative(X0) & quiet(X0)) | curious(paul)) & (~curious(paul) | ! [X0] : (~creative(X0) | ~quiet(X0))) [nnf transformation 6]
48. (? [X0] : (creative(X0) & quiet(X0)) | curious(paul)) & (~curious(paul) | ! [X1] : (~creative(X1) | ~quiet(X1))) [rectify 47]
49. ? [X0] : (creative(X0) & quiet(X0)) => (creative(sK3) & quiet(sK3)) [choice axiom]
50. ((creative(sK3) & quiet(sK3)) | curious(paul)) & (~curious(paul) | ! [X1] : (~creative(X1) | ~quiet(X1))) [skolemisation 48,49]
61. ! [X0] : ((happy(X0) | (funny(X0) & ~kind(X0))) & ((~funny(X0) | kind(X0)) | ~happy(X0))) [nnf transformation 13]
62. ! [X0] : ((happy(X0) | (funny(X0) & ~kind(X0))) & (~funny(X0) | kind(X0) | ~happy(X0))) [flattening 61]
85. patient(X0) | creative(X0) [cnf transformation 28]
86. ~patient(X0) | creative(X0) [cnf transformation 28]
87. ~curious(paul) | ~creative(X1) | ~quiet(X1) [cnf transformation 50]
113. ~kind(X0) | happy(X0) [cnf transformation 62]
115. ~happy(paul) | quiet(X0) | ~happy(X0) [cnf transformation 34]
130. kind(paul) [cnf transformation 24]
131. curious(paul) [cnf transformation 25]
182. creative(X0) [subsumption resolution 85,86]
184. 12 <=> curious(paul) [avatar definition]
192. ~curious(paul) | ~quiet(X1) [subsumption resolution 87,182]
194. 14 <=> ! [X1] : ~quiet(X1) [avatar definition]
195. ~quiet(X1) <- (14) [avatar component clause 194]
196. 14 | ~12 [avatar split clause 192,184,194]
244. 25 <=> ! [X0] : (quiet(X0) | ~happy(X0)) [avatar definition]
245. ~happy(X0) | quiet(X0) <- (25) [avatar component clause 244]
252. 27 <=> happy(paul) [avatar definition]
253. happy(paul) <- (27) [avatar component clause 252]
255. 25 | ~27 [avatar split clause 115,252,244]
305. 12 [avatar split clause 131,184]
317. happy(paul) [resolution 113,130]
320. 27 [avatar split clause 317,252]
322. quiet(paul) <- (25, 27) [resolution 245,253]
325. $false <- (14, 25, 27) [subsumption resolution 322,195]
326. ~14 | ~25 | ~27 [avatar contradiction clause 325]
330. $false [avatar sat refutation 196,255,305,320,326]
% SZS output end Proof for 472071726807397360736049
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is wise then someone is not quiet or kind. Everyone who is either kind or not patient is both not patient and not humble and vice versa. If someone is both kind and rich then someone is not quiet or funny. If mary is either old or wise then someone is both not strong and not curious and vice versa. Everyone who is either quiet or generous is both not calm and not humble. Everyone who is not patient or not generous is either not rich or not creative. Everyone who is both strong and calm is funny or rich and vice versa. If someone is not strong then john is humble or not wise and vice versa. Everyone who is both not patient and humble is both not brave and rich. Everyone who is either not generous or old is either not creative or not generous and vice versa. If someone is not funny or not happy then someone is either not curious or patient and vice versa. If someone is both strong and old then someone is both not brave and not calm and vice versa. Everyone who is both not patient and not brave is wise or not curious and vice versa. Everyone who is generous is either strong or generous. If john is wise then someone is old or patient and vice versa. Everyone who is both not kind and not patient is both kind and curious and vice versa. Someone is either not curious or not strong. John is not calm or not tall. Mary is not patient. Someone is either not tall or not creative. Lucy is either not calm or kind. Someone is calm. John is wise. Someone is both curious and humble. | Mary is strong. | entailment | ((wise(paul))=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((kind(X)<~>~patient(X))<=>(~patient(X)&~humble(X))))&
((?[X]:((kind(X)&rich(X))))=>(?[X]:((~quiet(X)|funny(X)))))&
(((old(mary)<~>wise(mary)))<=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((quiet(X)<~>generous(X))=>(~calm(X)&~humble(X))))&
(![X]:((~patient(X)|~generous(X))=>(~rich(X)<~>~creative(X))))&
(![X]:((strong(X)&calm(X))<=>(funny(X)|rich(X))))&
((?[X]:(~strong(X)))<=>((humble(john)|~wise(john))))&
(![X]:((~patient(X)&humble(X))=>(~brave(X)&rich(X))))&
(![X]:((~generous(X)<~>old(X))<=>(~creative(X)<~>~generous(X))))&
((?[X]:((~funny(X)|~happy(X))))<=>(?[X]:((~curious(X)<~>patient(X)))))&
((?[X]:((strong(X)&old(X))))<=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:((~patient(X)&~brave(X))<=>(wise(X)|~curious(X))))&
(![X]:(generous(X)=>(strong(X)<~>generous(X))))&
((wise(john))<=>(?[X]:((old(X)|patient(X)))))&
(![X]:((~kind(X)&~patient(X))<=>(kind(X)&curious(X))))&
(?[X]:((~curious(X)<~>~strong(X))))&
((~calm(john)|~tall(john)))&
(~patient(mary))&
(?[X]:((~tall(X)<~>~creative(X))))&
((~calm(lucy)<~>kind(lucy)))&
(?[X]:(calm(X)))&
(wise(john))&
(?[X]:((curious(X)&humble(X)))) | strong(mary) | [
"p1",
"p6",
"p8",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8075332026710331717992648
% SZS output start Proof for 8075332026710331717992648
2. ! [X0] : ((kind(X0) <~> ~patient(X0)) <=> (~humble(X0) & ~patient(X0))) [input p1]
7. ! [X0] : ((calm(X0) & strong(X0)) <=> (rich(X0) | funny(X0))) [input p6]
9. ! [X0] : ((humble(X0) & ~patient(X0)) => (rich(X0) & ~brave(X0))) [input p8]
16. ! [X0] : ((~patient(X0) & ~kind(X0)) <=> (curious(X0) & kind(X0))) [input p15]
19. ~patient(mary) [input p18]
25. ~strong(mary) [input hypothesis]
33. ! [X0] : ((rich(X0) & ~brave(X0)) | (~humble(X0) | patient(X0))) [ennf transformation 9]
34. ! [X0] : ((rich(X0) & ~brave(X0)) | ~humble(X0) | patient(X0)) [flattening 33]
38. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (humble(X0) | patient(X0))) & ((~humble(X0) & ~patient(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [nnf transformation 2]
39. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | humble(X0) | patient(X0)) & ((~humble(X0) & ~patient(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [flattening 38]
49. ! [X0] : (((calm(X0) & strong(X0)) | (~rich(X0) & ~funny(X0))) & ((rich(X0) | funny(X0)) | (~calm(X0) | ~strong(X0)))) [nnf transformation 7]
50. ! [X0] : (((calm(X0) & strong(X0)) | (~rich(X0) & ~funny(X0))) & (rich(X0) | funny(X0) | ~calm(X0) | ~strong(X0))) [flattening 49]
74. ! [X0] : (((~patient(X0) & ~kind(X0)) | (~curious(X0) | ~kind(X0))) & ((curious(X0) & kind(X0)) | (patient(X0) | kind(X0)))) [nnf transformation 16]
75. ! [X0] : (((~patient(X0) & ~kind(X0)) | ~curious(X0) | ~kind(X0)) & ((curious(X0) & kind(X0)) | patient(X0) | kind(X0))) [flattening 74]
93. patient(X0) | ~kind(X0) | humble(X0) | patient(X0) [cnf transformation 39]
111. ~rich(X0) | strong(X0) [cnf transformation 50]
118. ~humble(X0) | rich(X0) | patient(X0) [cnf transformation 34]
147. kind(X0) | patient(X0) | kind(X0) [cnf transformation 75]
154. ~patient(mary) [cnf transformation 19]
163. ~strong(mary) [cnf transformation 25]
164. patient(X0) | kind(X0) [duplicate literal removal 147]
172. ~kind(X0) | patient(X0) | humble(X0) [duplicate literal removal 93]
361. kind(mary) [resolution 164,154]
501. patient(mary) | humble(mary) [resolution 172,361]
505. humble(mary) [subsumption resolution 501,154]
563. rich(mary) | patient(mary) [resolution 505,118]
567. rich(mary) [subsumption resolution 563,154]
691. strong(mary) [resolution 567,111]
697. $false [subsumption resolution 691,163]
% SZS output end Proof for 8075332026710331717992648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either creative or not kind then mary is both creative and strong.
Everyone who is both wise and not old is both not quiet and wise and vice versa.
Everyone who is both humble and quiet is calm.
If lucy is not quiet or not creative then mary is both not patient and quiet.
Everyone who is not wise is not kind and vice versa.
Everyone who is either tall or not curious is calm or not patient.
If paul is happy then fred is either not creative or generous and vice versa.
Everyone who is both quiet and curious is either rich or not brave and vice versa.
If lucy is not kind or not curious then alice is tall.
Everyone who is both wise and not patient is not funny or strong and vice versa.
Everyone who is either not tall or curious is not tall.
If susan is generous then mary is quiet or not funny and vice versa.
Everyone who is patient is strong and vice versa.
Everyone who is either rich or calm is not quiet.
Everyone who is both not creative and patient is not brave and vice versa.
Everyone who is quiet is kind or strong and vice versa.
John is quiet.
Fred is happy.
Someone is not curious.
Lucy is not generous or funny.
Someone is not quiet or not old.
Someone is kind or not wise.
Mary is generous or not generous.
Someone is either not brave or curious. | John is wise. | entailment | ((?[X]:((creative(X)<~>~kind(X))))=>((creative(mary)&strong(mary))))&
(![X]:((wise(X)&~old(X))<=>(~quiet(X)&wise(X))))&
(![X]:((humble(X)&quiet(X))=>calm(X)))&
(((~quiet(lucy)|~creative(lucy)))=>((~patient(mary)&quiet(mary))))&
(![X]:(~wise(X)<=>~kind(X)))&
(![X]:((tall(X)<~>~curious(X))=>(calm(X)|~patient(X))))&
((happy(paul))<=>((~creative(fred)<~>generous(fred))))&
(![X]:((quiet(X)&curious(X))<=>(rich(X)<~>~brave(X))))&
(((~kind(lucy)|~curious(lucy)))=>(tall(alice)))&
(![X]:((wise(X)&~patient(X))<=>(~funny(X)|strong(X))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
(quiet(john))&
(happy(fred))&
(?[X]:(~curious(X)))&
((~generous(lucy)|funny(lucy)))&
(?[X]:((~quiet(X)|~old(X))))&
(?[X]:((kind(X)|~wise(X))))&
((generous(mary)|~generous(mary)))&
(?[X]:((~brave(X)<~>curious(X)))) | wise(john) | [
"p4",
"p9",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1477144052163762919165964
% SZS output start Proof for 1477144052163762919165964
5. ! [X0] : (~wise(X0) <=> ~kind(X0)) [input p4]
10. ! [X0] : ((~patient(X0) & wise(X0)) <=> (strong(X0) | ~funny(X0))) [input p9]
13. ! [X0] : (patient(X0) <=> strong(X0)) [input p12]
16. ! [X0] : (quiet(X0) <=> (strong(X0) | kind(X0))) [input p15]
17. quiet(john) [input p16]
25. ~wise(john) [input hypothesis]
37. ! [X0] : ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))) [nnf transformation 5]
42. ! [X0] : (((~patient(X0) & wise(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (patient(X0) | ~wise(X0)))) [nnf transformation 10]
43. ! [X0] : (((~patient(X0) & wise(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | patient(X0) | ~wise(X0))) [flattening 42]
47. ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 13]
51. ! [X0] : ((quiet(X0) | (~strong(X0) & ~kind(X0))) & ((strong(X0) | kind(X0)) | ~quiet(X0))) [nnf transformation 16]
52. ! [X0] : ((quiet(X0) | (~strong(X0) & ~kind(X0))) & (strong(X0) | kind(X0) | ~quiet(X0))) [flattening 51]
74. ~kind(X0) | wise(X0) [cnf transformation 37]
94. ~patient(X0) | ~strong(X0) [cnf transformation 43]
101. patient(X0) | ~strong(X0) [cnf transformation 47]
107. strong(X0) | kind(X0) | ~quiet(X0) [cnf transformation 52]
110. quiet(john) [cnf transformation 17]
119. ~wise(john) [cnf transformation 25]
200. ~strong(X0) [subsumption resolution 101,94]
203. ~quiet(X0) | kind(X0) [subsumption resolution 107,200]
229. kind(john) [resolution 203,110]
252. wise(john) [resolution 229,74]
253. $false [subsumption resolution 252,119]
% SZS output end Proof for 1477144052163762919165964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not creative is either rich or not happy and vice versa.
If john is both patient and not quiet then someone is both not funny and not brave and vice versa.
Everyone who is kind or quiet is not quiet or tall.
Everyone who is quiet is both not creative and not calm and vice versa.
If alice is not kind then alice is both not kind and calm and vice versa.
Everyone who is both not happy and not patient is either not kind or not humble and vice versa.
Everyone who is generous or kind is creative and vice versa.
Everyone who is either not funny or not generous is not wise or funny.
If paul is either strong or brave then someone is both brave and quiet and vice versa.
If someone is both rich and not calm then someone is either curious or funny and vice versa.
Everyone who is either humble or patient is either not funny or curious.
If someone is both humble and not happy then susan is both humble and curious.
Everyone who is not calm is both not quiet and not generous.
If someone is quiet then someone is not calm or not rich.
Everyone who is both not curious and not wise is both not happy and not brave and vice versa.
Everyone who is not creative is both old and humble and vice versa.
Someone is both not patient and funny.
Someone is both strong and not happy.
Mary is not kind or wise.
Paul is either not creative or not curious.
Lucy is either not strong or funny.
Mary is either generous or brave.
Someone is either not rich or wise. | Alice is not curious. | neutral | (![X]:((~curious(X)&~creative(X))<=>(rich(X)<~>~happy(X))))&
(((patient(john)&~quiet(john)))<=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|tall(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~calm(X))))&
((~kind(alice))<=>((~kind(alice)&calm(alice))))&
(![X]:((~happy(X)&~patient(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((generous(X)|kind(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~wise(X)|funny(X))))&
(((strong(paul)<~>brave(paul)))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~funny(X)<~>curious(X))))&
((?[X]:((humble(X)&~happy(X))))=>((humble(susan)&curious(susan))))&
(![X]:(~calm(X)=>(~quiet(X)&~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((~curious(X)&~wise(X))<=>(~happy(X)&~brave(X))))&
(![X]:(~creative(X)<=>(old(X)&humble(X))))&
(?[X]:((~patient(X)&funny(X))))&
(?[X]:((strong(X)&~happy(X))))&
((~kind(mary)|wise(mary)))&
((~creative(paul)<~>~curious(paul)))&
((~strong(lucy)<~>funny(lucy)))&
((generous(mary)<~>brave(mary)))&
(?[X]:((~rich(X)<~>wise(X)))) | ~curious(alice) | [] | null | 0 |
If fred is patient or happy then alice is either not curious or humble.
Everyone who is either patient or not rich is happy and vice versa.
Everyone who is patient is either not humble or tall.
Everyone who is not patient is both curious and wise and vice versa.
Everyone who is rich or happy is happy.
Everyone who is quiet or not kind is old and vice versa.
Everyone who is both strong and brave is kind or tall.
If someone is kind or not funny then susan is both quiet and not old and vice versa.
Everyone who is both not wise and not patient is either rich or wise.
If someone is either creative or patient then someone is both funny and not brave.
Everyone who is either tall or brave is kind.
Everyone who is not funny is either humble or patient and vice versa.
If someone is either rich or not curious then lucy is kind or generous.
If someone is not old then someone is either rich or strong and vice versa.
Everyone who is not quiet or not calm is both old and not calm.
Everyone who is strong is not calm or funny.
Fred is both brave and patient.
Mary is not rich.
Someone is either kind or not quiet.
Someone is not strong.
Someone is either not happy or not rich.
Susan is strong. | Alice is not brave. | contradiction | (((patient(fred)|happy(fred)))=>((~curious(alice)<~>humble(alice))))&
(![X]:((patient(X)<~>~rich(X))<=>happy(X)))&
(![X]:(patient(X)=>(~humble(X)<~>tall(X))))&
(![X]:(~patient(X)<=>(curious(X)&wise(X))))&
(![X]:((rich(X)|happy(X))=>happy(X)))&
(![X]:((quiet(X)|~kind(X))<=>old(X)))&
(![X]:((strong(X)&brave(X))=>(kind(X)|tall(X))))&
((?[X]:((kind(X)|~funny(X))))<=>((quiet(susan)&~old(susan))))&
(![X]:((~wise(X)&~patient(X))=>(rich(X)<~>wise(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((tall(X)<~>brave(X))=>kind(X)))&
(![X]:(~funny(X)<=>(humble(X)<~>patient(X))))&
((?[X]:((rich(X)<~>~curious(X))))=>((kind(lucy)|generous(lucy))))&
((?[X]:(~old(X)))<=>(?[X]:((rich(X)<~>strong(X)))))&
(![X]:((~quiet(X)|~calm(X))=>(old(X)&~calm(X))))&
(![X]:(strong(X)=>(~calm(X)|funny(X))))&
((brave(fred)&patient(fred)))&
(~rich(mary))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(strong(susan)) | ~brave(alice) | [
"p0",
"p2",
"p3",
"p5",
"p7",
"p10",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2794445777957921508769937
% SZS output start Proof for 2794445777957921508769937
1. (happy(fred) | patient(fred)) => (~curious(alice) <~> humble(alice)) [input p0]
3. ! [X0] : (patient(X0) => (~humble(X0) <~> tall(X0))) [input p2]
4. ! [X0] : (~patient(X0) <=> (wise(X0) & curious(X0))) [input p3]
6. ! [X0] : ((~kind(X0) | quiet(X0)) <=> old(X0)) [input p5]
8. ? [X0] : (~funny(X0) | kind(X0)) <=> (~old(susan) & quiet(susan)) [input p7]
11. ! [X0] : ((tall(X0) <~> brave(X0)) => kind(X0)) [input p10]
12. ! [X0] : (~funny(X0) <=> (humble(X0) <~> patient(X0))) [input p11]
15. ! [X0] : ((~calm(X0) | ~quiet(X0)) => (~calm(X0) & old(X0))) [input p14]
17. patient(fred) & brave(fred) [input p16]
23. ~brave(alice) [input hypothesis]
27. (~curious(alice) <~> humble(alice)) | (~happy(fred) & ~patient(fred)) [ennf transformation 1]
28. ! [X0] : ((~humble(X0) <~> tall(X0)) | ~patient(X0)) [ennf transformation 3]
35. ! [X0] : (kind(X0) | (tall(X0) <=> brave(X0))) [ennf transformation 11]
36. ! [X0] : ((~calm(X0) & old(X0)) | (calm(X0) & quiet(X0))) [ennf transformation 15]
39. ((~humble(alice) | curious(alice)) & (humble(alice) | ~curious(alice))) | (~happy(fred) & ~patient(fred)) [nnf transformation 27]
41. ! [X0] : (((~tall(X0) | humble(X0)) & (tall(X0) | ~humble(X0))) | ~patient(X0)) [nnf transformation 28]
42. ! [X0] : ((~patient(X0) | (~wise(X0) | ~curious(X0))) & ((wise(X0) & curious(X0)) | patient(X0))) [nnf transformation 4]
43. ! [X0] : ((~patient(X0) | ~wise(X0) | ~curious(X0)) & ((wise(X0) & curious(X0)) | patient(X0))) [flattening 42]
44. ! [X0] : (((~kind(X0) | quiet(X0)) | ~old(X0)) & (old(X0) | (kind(X0) & ~quiet(X0)))) [nnf transformation 6]
45. ! [X0] : ((~kind(X0) | quiet(X0) | ~old(X0)) & (old(X0) | (kind(X0) & ~quiet(X0)))) [flattening 44]
46. (? [X0] : (~funny(X0) | kind(X0)) | (old(susan) | ~quiet(susan))) & ((~old(susan) & quiet(susan)) | ! [X0] : (funny(X0) & ~kind(X0))) [nnf transformation 8]
47. (? [X0] : (~funny(X0) | kind(X0)) | old(susan) | ~quiet(susan)) & ((~old(susan) & quiet(susan)) | ! [X0] : (funny(X0) & ~kind(X0))) [flattening 46]
48. (? [X0] : (~funny(X0) | kind(X0)) | old(susan) | ~quiet(susan)) & ((~old(susan) & quiet(susan)) | ! [X1] : (funny(X1) & ~kind(X1))) [rectify 47]
49. ? [X0] : (~funny(X0) | kind(X0)) => (~funny(sK0) | kind(sK0)) [choice axiom]
50. ((~funny(sK0) | kind(sK0)) | old(susan) | ~quiet(susan)) & ((~old(susan) & quiet(susan)) | ! [X1] : (funny(X1) & ~kind(X1))) [skolemisation 48,49]
56. ! [X0] : (kind(X0) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0)))) [nnf transformation 35]
57. ! [X0] : ((~funny(X0) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0)))) & (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | funny(X0))) [nnf transformation 12]
71. humble(alice) | ~curious(alice) | ~patient(fred) [cnf transformation 39]
79. ~humble(X0) | tall(X0) | ~patient(X0) [cnf transformation 41]
81. curious(X0) | patient(X0) [cnf transformation 43]
86. ~quiet(X0) | old(X0) [cnf transformation 45]
92. ~old(susan) | ~kind(X1) [cnf transformation 50]
93. ~old(susan) | funny(X1) [cnf transformation 50]
101. ~tall(X0) | brave(X0) | kind(X0) [cnf transformation 56]
105. ~funny(X0) | patient(X0) | ~humble(X0) [cnf transformation 57]
106. ~funny(X0) | humble(X0) | ~patient(X0) [cnf transformation 57]
111. old(X0) | quiet(X0) [cnf transformation 36]
117. patient(fred) [cnf transformation 17]
125. ~brave(alice) [cnf transformation 23]
132. 2 <=> curious(alice) [avatar definition]
133. ~curious(alice) <- (~2) [avatar component clause 132]
136. 3 <=> humble(alice) [avatar definition]
137. humble(alice) <- (3) [avatar component clause 136]
138. ~humble(alice) <- (~3) [avatar component clause 136]
141. 4 <=> patient(fred) [avatar definition]
146. ~4 | ~2 | 3 [avatar split clause 71,136,132,141]
148. 5 <=> ! [X1] : funny(X1) [avatar definition]
149. funny(X1) <- (5) [avatar component clause 148]
151. 6 <=> old(susan) [avatar definition]
153. ~old(susan) <- (~6) [avatar component clause 151]
154. 5 | ~6 [avatar split clause 93,151,148]
156. 7 <=> ! [X1] : ~kind(X1) [avatar definition]
157. ~kind(X1) <- (7) [avatar component clause 156]
158. 7 | ~6 [avatar split clause 92,151,156]
196. 16 <=> ! [X3] : old(X3) [avatar definition]
197. old(X3) <- (16) [avatar component clause 196]
208. old(X0) [subsumption resolution 111,86]
209. 16 [avatar split clause 208,196]
210. 4 [avatar split clause 117,141]
225. patient(alice) <- (~2) [resolution 81,133]
280. ~patient(X1) | humble(X1) <- (5) [resolution 106,149]
283. humble(alice) <- (~2, 5) [resolution 280,225]
285. $false <- (~2, ~3, 5) [subsumption resolution 283,138]
286. 2 | 3 | ~5 [avatar contradiction clause 285]
288. $false <- (~6, 16) [subsumption resolution 153,197]
289. 6 | ~16 [avatar contradiction clause 288]
291. tall(alice) | ~patient(alice) <- (3) [resolution 137,79]
293. 23 <=> patient(alice) [avatar definition]
297. 24 <=> tall(alice) [avatar definition]
299. tall(alice) <- (24) [avatar component clause 297]
300. ~23 | 24 | ~3 [avatar split clause 291,136,297,293]
302. ~humble(X1) | patient(X1) <- (5) [resolution 149,105]
314. patient(alice) <- (3, 5) [resolution 302,137]
318. 23 | ~3 | ~5 [avatar split clause 314,148,136,293]
321. brave(alice) | kind(alice) <- (24) [resolution 299,101]
323. kind(alice) <- (24) [subsumption resolution 321,125]
324. $false <- (7, 24) [subsumption resolution 323,157]
325. ~7 | ~24 [avatar contradiction clause 324]
326. $false [avatar sat refutation 146,154,158,209,210,286,289,300,318,325]
% SZS output end Proof for 2794445777957921508769937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not strong or curious.
If someone is either not curious or strong then fred is not quiet.
If someone is either wise or curious then john is either rich or not happy and vice versa.
Everyone who is not humble or kind is not kind.
Everyone who is either not funny or strong is either brave or not funny.
If mary is either wise or not kind then fred is both strong and curious and vice versa.
Everyone who is calm or not rich is creative and vice versa.
If paul is either strong or patient then paul is both not creative and funny and vice versa.
If paul is either strong or wise then mary is curious.
If fred is both not old and not strong then someone is not kind or not tall.
Everyone who is not funny is not old or happy.
If someone is either humble or not kind then paul is both curious and humble and vice versa.
Everyone who is both not old and curious is wise and vice versa.
If someone is not creative or kind then lucy is both creative and not patient.
If someone is quiet or creative then someone is either not kind or not curious and vice versa.
Everyone who is either not funny or not curious is both not brave and not patient.
Someone is both funny and creative.
Fred is rich or not funny.
Someone is both strong and not generous.
Lucy is not brave.
Mary is both not wise and old.
Someone is creative or not funny.
Someone is creative or brave.
Someone is wise or old. | Paul is humble. | entailment | (![X]:(~creative(X)=>(~strong(X)|curious(X))))&
((?[X]:((~curious(X)<~>strong(X))))=>(~quiet(fred)))&
((?[X]:((wise(X)<~>curious(X))))<=>((rich(john)<~>~happy(john))))&
(![X]:((~humble(X)|kind(X))=>~kind(X)))&
(![X]:((~funny(X)<~>strong(X))=>(brave(X)<~>~funny(X))))&
(((wise(mary)<~>~kind(mary)))<=>((strong(fred)&curious(fred))))&
(![X]:((calm(X)|~rich(X))<=>creative(X)))&
(((strong(paul)<~>patient(paul)))<=>((~creative(paul)&funny(paul))))&
(((strong(paul)<~>wise(paul)))=>(curious(mary)))&
(((~old(fred)&~strong(fred)))=>(?[X]:((~kind(X)|~tall(X)))))&
(![X]:(~funny(X)=>(~old(X)|happy(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>((curious(paul)&humble(paul))))&
(![X]:((~old(X)&curious(X))<=>wise(X)))&
((?[X]:((~creative(X)|kind(X))))=>((creative(lucy)&~patient(lucy))))&
((?[X]:((quiet(X)|creative(X))))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
(![X]:((~funny(X)<~>~curious(X))=>(~brave(X)&~patient(X))))&
(?[X]:((funny(X)&creative(X))))&
((rich(fred)|~funny(fred)))&
(?[X]:((strong(X)&~generous(X))))&
(~brave(lucy))&
((~wise(mary)&old(mary)))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:((wise(X)|old(X)))) | humble(paul) | [
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3063845147457338330196901
% SZS output start Proof for 3063845147457338330196901
4. ! [X0] : ((kind(X0) | ~humble(X0)) => ~kind(X0)) [input p3]
12. ? [X0] : (humble(X0) <~> ~kind(X0)) <=> (humble(paul) & curious(paul)) [input p11]
25. ~humble(paul) [input hypothesis]
32. ! [X0] : (~kind(X0) | (~kind(X0) & humble(X0))) [ennf transformation 4]
52. (? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | (~humble(paul) | ~curious(paul))) & ((humble(paul) & curious(paul)) | ! [X0] : ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) [nnf transformation 12]
53. (? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | ~humble(paul) | ~curious(paul)) & ((humble(paul) & curious(paul)) | ! [X0] : ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) [flattening 52]
54. (? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | ~humble(paul) | ~curious(paul)) & ((humble(paul) & curious(paul)) | ! [X1] : ((humble(X1) | kind(X1)) & (~kind(X1) | ~humble(X1)))) [rectify 53]
55. ? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) => ((kind(sK1) | ~humble(sK1)) & (~kind(sK1) | humble(sK1))) [choice axiom]
56. (((kind(sK1) | ~humble(sK1)) & (~kind(sK1) | humble(sK1))) | ~humble(paul) | ~curious(paul)) & ((humble(paul) & curious(paul)) | ! [X1] : ((humble(X1) | kind(X1)) & (~kind(X1) | ~humble(X1)))) [skolemisation 54,55]
87. ~kind(X0) | ~kind(X0) [cnf transformation 32]
113. humble(paul) | humble(X1) | kind(X1) [cnf transformation 56]
143. ~humble(paul) [cnf transformation 25]
146. ~kind(X0) [duplicate literal removal 87]
245. 20 <=> humble(paul) [avatar definition]
247. ~humble(paul) <- (~20) [avatar component clause 245]
253. humble(paul) | humble(X1) [subsumption resolution 113,146]
255. 22 <=> ! [X1] : humble(X1) [avatar definition]
256. humble(X1) <- (22) [avatar component clause 255]
257. 22 | 20 [avatar split clause 253,245,255]
338. ~20 [avatar split clause 143,245]
339. $false <- (~20, 22) [subsumption resolution 247,256]
340. 20 | ~22 [avatar contradiction clause 339]
346. $false [avatar sat refutation 257,338,340]
% SZS output end Proof for 3063845147457338330196901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not creative is not strong.
If susan is not creative or not tall then lucy is either not strong or not creative.
Everyone who is rich or not wise is both calm and not calm.
If someone is not wise then someone is quiet or humble and vice versa.
Everyone who is not tall is both wise and not wise.
If someone is both not funny and not brave then someone is not quiet.
If john is either humble or brave then mary is both happy and not old and vice versa.
If someone is both kind and wise then someone is not kind or humble.
Everyone who is generous or curious is humble.
Everyone who is both not patient and strong is either not humble or strong and vice versa.
If someone is both humble and old then john is generous.
If someone is curious or humble then susan is not wise or not patient.
If susan is curious or rich then someone is either funny or rich.
Everyone who is funny is not creative or kind and vice versa.
Everyone who is not brave or not kind is not generous and vice versa.
Susan is both not curious and not funny.
Lucy is either not tall or creative.
Mary is happy.
Fred is quiet or wise.
Someone is not creative or calm.
Fred is either not happy or curious. | Lucy is rich. | contradiction | (![X]:((calm(X)&~creative(X))=>~strong(X)))&
(((~creative(susan)|~tall(susan)))=>((~strong(lucy)<~>~creative(lucy))))&
(![X]:((rich(X)|~wise(X))=>(calm(X)&~calm(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((quiet(X)|humble(X)))))&
(![X]:(~tall(X)=>(wise(X)&~wise(X))))&
((?[X]:((~funny(X)&~brave(X))))=>(?[X]:(~quiet(X))))&
(((humble(john)<~>brave(john)))<=>((happy(mary)&~old(mary))))&
((?[X]:((kind(X)&wise(X))))=>(?[X]:((~kind(X)|humble(X)))))&
(![X]:((generous(X)|curious(X))=>humble(X)))&
(![X]:((~patient(X)&strong(X))<=>(~humble(X)<~>strong(X))))&
((?[X]:((humble(X)&old(X))))=>(generous(john)))&
((?[X]:((curious(X)|humble(X))))=>((~wise(susan)|~patient(susan))))&
(((curious(susan)|rich(susan)))=>(?[X]:((funny(X)<~>rich(X)))))&
(![X]:(funny(X)<=>(~creative(X)|kind(X))))&
(![X]:((~brave(X)|~kind(X))<=>~generous(X)))&
((~curious(susan)&~funny(susan)))&
((~tall(lucy)<~>creative(lucy)))&
(happy(mary))&
((quiet(fred)|wise(fred)))&
(?[X]:((~creative(X)|calm(X))))&
((~happy(fred)<~>curious(fred))) | rich(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5425790149612381710318950
% SZS output start Proof for 5425790149612381710318950
3. ! [X0] : ((~wise(X0) | rich(X0)) => (~calm(X0) & calm(X0))) [input p2]
22. rich(lucy) [input hypothesis]
29. ! [X0] : ((~calm(X0) & calm(X0)) | (wise(X0) & ~rich(X0))) [ennf transformation 3]
70. calm(X0) | ~rich(X0) [cnf transformation 29]
72. ~calm(X0) | ~rich(X0) [cnf transformation 29]
117. rich(lucy) [cnf transformation 22]
141. ~rich(X0) [subsumption resolution 70,72]
192. $false [subsumption resolution 117,141]
% SZS output end Proof for 5425790149612381710318950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is tall. Everyone who is tall or patient is patient. Everyone who is calm is not patient or quiet. If someone is both not strong and rich then someone is not old and vice versa. Everyone who is either patient or kind is both strong and funny. If someone is kind or old then someone is either quiet or tall and vice versa. If someone is not strong or generous then alice is strong and vice versa. Everyone who is both curious and not creative is not brave or not tall and vice versa. If someone is not patient then someone is both not humble and tall. If someone is both tall and happy then paul is either not quiet or not kind. Everyone who is strong is rich. If someone is curious or calm then someone is either brave or not rich. If mary is not calm then john is patient. If susan is either creative or not funny then someone is tall and vice versa. Everyone who is either creative or tall is not generous or kind. Everyone who is both not calm and rich is not curious. Lucy is either creative or not happy. Mary is both curious and brave. Someone is both not brave and generous. Someone is either not patient or not generous. John is either not happy or not brave. Someone is calm or not strong. | Paul is not calm. | neutral | (![X]:(patient(X)=>tall(X)))&
(![X]:((tall(X)|patient(X))=>patient(X)))&
(![X]:(calm(X)=>(~patient(X)|quiet(X))))&
((?[X]:((~strong(X)&rich(X))))<=>(?[X]:(~old(X))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)&funny(X))))&
((?[X]:((kind(X)|old(X))))<=>(?[X]:((quiet(X)<~>tall(X)))))&
((?[X]:((~strong(X)|generous(X))))<=>(strong(alice)))&
(![X]:((curious(X)&~creative(X))<=>(~brave(X)|~tall(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~humble(X)&tall(X)))))&
((?[X]:((tall(X)&happy(X))))=>((~quiet(paul)<~>~kind(paul))))&
(![X]:(strong(X)=>rich(X)))&
((?[X]:((curious(X)|calm(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
((~calm(mary))=>(patient(john)))&
(((creative(susan)<~>~funny(susan)))<=>(?[X]:(tall(X))))&
(![X]:((creative(X)<~>tall(X))=>(~generous(X)|kind(X))))&
(![X]:((~calm(X)&rich(X))=>~curious(X)))&
((creative(lucy)<~>~happy(lucy)))&
((curious(mary)&brave(mary)))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:((~patient(X)<~>~generous(X))))&
((~happy(john)<~>~brave(john)))&
(?[X]:((calm(X)|~strong(X)))) | ~calm(paul) | [] | null | 0 |
Everyone who is both calm and patient is both brave and quiet.
If someone is both not kind and strong then mary is not patient and vice versa.
If paul is not kind or generous then someone is not quiet or not humble and vice versa.
If john is not wise or not rich then lucy is not quiet and vice versa.
Everyone who is both happy and brave is both strong and quiet.
If someone is old then someone is both not funny and humble and vice versa.
Everyone who is either not tall or quiet is both not tall and not patient and vice versa.
Everyone who is both not tall and creative is funny or curious and vice versa.
Everyone who is strong is humble.
If someone is not old or not patient then paul is both creative and strong.
Everyone who is either humble or brave is both happy and quiet.
If fred is either not brave or not humble then someone is both rich and not rich and vice versa.
If someone is either not rich or not patient then someone is both not wise and not generous and vice versa.
Everyone who is old or brave is both rich and not strong.
Everyone who is not kind is both not creative and wise and vice versa.
If mary is funny then someone is rich and vice versa.
Someone is either patient or not rich.
Someone is both not happy and humble.
Someone is not quiet or old.
Someone is both not patient and creative.
Mary is both creative and old.
Fred is old.
Lucy is either tall or calm. | Mary is tall. | contradiction | (![X]:((calm(X)&patient(X))=>(brave(X)&quiet(X))))&
((?[X]:((~kind(X)&strong(X))))<=>(~patient(mary)))&
(((~kind(paul)|generous(paul)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(((~wise(john)|~rich(john)))<=>(~quiet(lucy)))&
(![X]:((happy(X)&brave(X))=>(strong(X)&quiet(X))))&
((?[X]:(old(X)))<=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&creative(X))<=>(funny(X)|curious(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~old(X)|~patient(X))))=>((creative(paul)&strong(paul))))&
(![X]:((humble(X)<~>brave(X))=>(happy(X)&quiet(X))))&
(((~brave(fred)<~>~humble(fred)))<=>(?[X]:((rich(X)&~rich(X)))))&
((?[X]:((~rich(X)<~>~patient(X))))<=>(?[X]:((~wise(X)&~generous(X)))))&
(![X]:((old(X)|brave(X))=>(rich(X)&~strong(X))))&
(![X]:(~kind(X)<=>(~creative(X)&wise(X))))&
((funny(mary))<=>(?[X]:(rich(X))))&
(?[X]:((patient(X)<~>~rich(X))))&
(?[X]:((~happy(X)&humble(X))))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:((~patient(X)&creative(X))))&
((creative(mary)&old(mary)))&
(old(fred))&
((tall(lucy)<~>calm(lucy))) | tall(mary) | [
"p7",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5360287713292840291821859
% SZS output start Proof for 5360287713292840291821859
8. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (curious(X0) | funny(X0))) [input p7]
14. ! [X0] : ((brave(X0) | old(X0)) => (~strong(X0) & rich(X0))) [input p13]
16. funny(mary) <=> ? [X0] : rich(X0) [input p15]
22. old(fred) [input p21]
24. tall(mary) [input hypothesis]
34. ! [X0] : ((~strong(X0) & rich(X0)) | (~brave(X0) & ~old(X0))) [ennf transformation 14]
53. ! [X0] : (((creative(X0) & ~tall(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 8]
54. ! [X0] : (((creative(X0) & ~tall(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | ~creative(X0) | tall(X0))) [flattening 53]
67. (funny(mary) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | ~funny(mary)) [nnf transformation 16]
68. (funny(mary) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | ~funny(mary)) [rectify 67]
69. ? [X1] : rich(X1) => rich(sK7) [choice axiom]
70. (funny(mary) | ! [X0] : ~rich(X0)) & (rich(sK7) | ~funny(mary)) [skolemisation 68,69]
105. ~tall(X0) | ~funny(X0) [cnf transformation 54]
130. ~old(X0) | rich(X0) [cnf transformation 34]
138. funny(mary) | ~rich(X0) [cnf transformation 70]
148. old(fred) [cnf transformation 22]
151. tall(mary) [cnf transformation 24]
300. 33 <=> ! [X0] : ~rich(X0) [avatar definition]
301. ~rich(X0) <- (33) [avatar component clause 300]
303. 34 <=> funny(mary) [avatar definition]
306. 33 | 34 [avatar split clause 138,303,300]
345. ~funny(mary) [resolution 105,151]
350. rich(fred) [resolution 130,148]
354. $false <- (33) [subsumption resolution 350,301]
355. ~33 [avatar contradiction clause 354]
358. ~34 [avatar split clause 345,303]
359. $false [avatar sat refutation 306,355,358]
% SZS output end Proof for 5360287713292840291821859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not curious and not patient then susan is not happy.
Everyone who is not happy or not funny is either tall or not kind and vice versa.
Everyone who is not humble or generous is both not strong and patient.
If alice is calm or quiet then susan is either calm or tall and vice versa.
If someone is not creative then lucy is rich.
If someone is quiet then mary is tall.
If someone is calm or not brave then john is both patient and not patient.
Everyone who is not kind or not quiet is not rich.
Everyone who is old is generous or calm and vice versa.
Everyone who is brave is calm or curious.
Everyone who is both not tall and creative is not calm or not quiet.
Everyone who is both not quiet and happy is either not calm or kind.
Everyone who is either old or not funny is not curious.
Everyone who is not curious or not wise is rich and vice versa.
If lucy is either wise or not creative then alice is either not strong or calm.
Everyone who is either not old or not happy is both patient and not funny and vice versa.
Paul is either not funny or not humble.
Someone is both brave and curious.
Mary is both creative and tall.
Mary is strong.
John is not humble or not brave.
Alice is not creative or not curious. | Lucy is curious. | entailment | (((~curious(alice)&~patient(alice)))=>(~happy(susan)))&
(![X]:((~happy(X)|~funny(X))<=>(tall(X)<~>~kind(X))))&
(![X]:((~humble(X)|generous(X))=>(~strong(X)&patient(X))))&
(((calm(alice)|quiet(alice)))<=>((calm(susan)<~>tall(susan))))&
((?[X]:(~creative(X)))=>(rich(lucy)))&
((?[X]:(quiet(X)))=>(tall(mary)))&
((?[X]:((calm(X)|~brave(X))))=>((patient(john)&~patient(john))))&
(![X]:((~kind(X)|~quiet(X))=>~rich(X)))&
(![X]:(old(X)<=>(generous(X)|calm(X))))&
(![X]:(brave(X)=>(calm(X)|curious(X))))&
(![X]:((~tall(X)&creative(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~quiet(X)&happy(X))=>(~calm(X)<~>kind(X))))&
(![X]:((old(X)<~>~funny(X))=>~curious(X)))&
(![X]:((~curious(X)|~wise(X))<=>rich(X)))&
(((wise(lucy)<~>~creative(lucy)))=>((~strong(alice)<~>calm(alice))))&
(![X]:((~old(X)<~>~happy(X))<=>(patient(X)&~funny(X))))&
((~funny(paul)<~>~humble(paul)))&
(?[X]:((brave(X)&curious(X))))&
((creative(mary)&tall(mary)))&
(strong(mary))&
((~humble(john)|~brave(john)))&
((~creative(alice)|~curious(alice))) | curious(lucy) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 187327848347902247822624
% SZS output start Proof for 187327848347902247822624
7. ? [X0] : (~brave(X0) | calm(X0)) => (~patient(john) & patient(john)) [input p6]
10. ! [X0] : (brave(X0) => (curious(X0) | calm(X0))) [input p9]
23. ~curious(lucy) [input hypothesis]
29. (~patient(john) & patient(john)) | ! [X0] : (brave(X0) & ~calm(X0)) [ennf transformation 7]
31. ! [X0] : ((curious(X0) | calm(X0)) | ~brave(X0)) [ennf transformation 10]
32. ! [X0] : (curious(X0) | calm(X0) | ~brave(X0)) [flattening 31]
74. patient(john) | ~calm(X0) [cnf transformation 29]
75. patient(john) | brave(X0) [cnf transformation 29]
76. ~patient(john) | ~calm(X0) [cnf transformation 29]
77. ~patient(john) | brave(X0) [cnf transformation 29]
83. ~brave(X0) | calm(X0) | curious(X0) [cnf transformation 32]
111. ~curious(lucy) [cnf transformation 23]
164. 12 <=> ! [X0] : brave(X0) [avatar definition]
165. brave(X0) <- (12) [avatar component clause 164]
167. 13 <=> patient(john) [avatar definition]
170. 12 | ~13 [avatar split clause 77,167,164]
172. 14 <=> ! [X0] : ~calm(X0) [avatar definition]
173. ~calm(X0) <- (14) [avatar component clause 172]
174. 14 | ~13 [avatar split clause 76,167,172]
175. 12 | 13 [avatar split clause 75,167,164]
176. 14 | 13 [avatar split clause 74,167,172]
272. calm(X0) | curious(X0) <- (12) [resolution 83,165]
273. curious(X0) <- (12, 14) [subsumption resolution 272,173]
274. $false <- (12, 14) [resolution 273,111]
277. ~12 | ~14 [avatar contradiction clause 274]
278. $false [avatar sat refutation 170,174,175,176,277]
% SZS output end Proof for 187327848347902247822624
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is kind or creative and vice versa.
If john is not rich then someone is kind or wise.
If someone is not generous then someone is both strong and curious and vice versa.
Everyone who is tall or strong is either patient or curious.
If someone is patient then lucy is rich or not patient.
Everyone who is not patient is curious or wise and vice versa.
Everyone who is both not kind and old is both happy and not patient.
Everyone who is both tall and not generous is either not curious or rich and vice versa.
If someone is not creative then mary is not curious and vice versa.
If mary is either strong or tall then paul is rich and vice versa.
Everyone who is both humble and brave is strong and vice versa.
Everyone who is quiet or not wise is both strong and old.
Everyone who is not tall is tall or not curious.
Everyone who is not wise or not quiet is either not brave or strong and vice versa.
Everyone who is calm is not rich or not happy and vice versa.
Everyone who is quiet or not generous is not brave.
Lucy is either not humble or wise.
Mary is both not old and rich.
Someone is both funny and not patient.
Susan is either not creative or not kind.
Fred is rich or kind.
Lucy is not wise or not funny.
Paul is both not wise and strong.
Lucy is both tall and curious. | Lucy is not quiet. | entailment | (![X]:(wise(X)<=>(kind(X)|creative(X))))&
((~rich(john))=>(?[X]:((kind(X)|wise(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((tall(X)|strong(X))=>(patient(X)<~>curious(X))))&
((?[X]:(patient(X)))=>((rich(lucy)|~patient(lucy))))&
(![X]:(~patient(X)<=>(curious(X)|wise(X))))&
(![X]:((~kind(X)&old(X))=>(happy(X)&~patient(X))))&
(![X]:((tall(X)&~generous(X))<=>(~curious(X)<~>rich(X))))&
((?[X]:(~creative(X)))<=>(~curious(mary)))&
(((strong(mary)<~>tall(mary)))<=>(rich(paul)))&
(![X]:((humble(X)&brave(X))<=>strong(X)))&
(![X]:((quiet(X)|~wise(X))=>(strong(X)&old(X))))&
(![X]:(~tall(X)=>(tall(X)|~curious(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(~brave(X)<~>strong(X))))&
(![X]:(calm(X)<=>(~rich(X)|~happy(X))))&
(![X]:((quiet(X)|~generous(X))=>~brave(X)))&
((~humble(lucy)<~>wise(lucy)))&
((~old(mary)&rich(mary)))&
(?[X]:((funny(X)&~patient(X))))&
((~creative(susan)<~>~kind(susan)))&
((rich(fred)|kind(fred)))&
((~wise(lucy)|~funny(lucy)))&
((~wise(paul)&strong(paul)))&
((tall(lucy)&curious(lucy))) | ~quiet(lucy) | [
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1993568085694712202560411
% SZS output start Proof for 1993568085694712202560411
11. ! [X0] : ((brave(X0) & humble(X0)) <=> strong(X0)) [input p10]
12. ! [X0] : ((~wise(X0) | quiet(X0)) => (old(X0) & strong(X0))) [input p11]
16. ! [X0] : ((~generous(X0) | quiet(X0)) => ~brave(X0)) [input p15]
25. quiet(lucy) [input hypothesis]
34. ! [X0] : ((old(X0) & strong(X0)) | (wise(X0) & ~quiet(X0))) [ennf transformation 12]
37. ! [X0] : (~brave(X0) | (generous(X0) & ~quiet(X0))) [ennf transformation 16]
57. ! [X0] : (((brave(X0) & humble(X0)) | ~strong(X0)) & (strong(X0) | (~brave(X0) | ~humble(X0)))) [nnf transformation 11]
58. ! [X0] : (((brave(X0) & humble(X0)) | ~strong(X0)) & (strong(X0) | ~brave(X0) | ~humble(X0))) [flattening 57]
95. ~strong(X0) | brave(X0) [cnf transformation 58]
96. ~quiet(X0) | strong(X0) [cnf transformation 34]
107. ~quiet(X0) | ~brave(X0) [cnf transformation 37]
123. quiet(lucy) [cnf transformation 25]
241. strong(lucy) [resolution 96,123]
246. brave(lucy) [resolution 241,95]
252. ~brave(lucy) [resolution 107,123]
253. $false [subsumption resolution 252,246]
% SZS output end Proof for 1993568085694712202560411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not quiet is not old or not curious. Everyone who is either creative or rich is not rich and vice versa. If lucy is rich then alice is both not old and not funny. If someone is not old or not wise then lucy is kind. Everyone who is not wise or brave is both not generous and not curious. If lucy is both strong and tall then someone is either not strong or not brave and vice versa. Everyone who is rich is either strong or old and vice versa. If someone is patient then someone is either not brave or not creative and vice versa. Everyone who is brave is either strong or not quiet and vice versa. Everyone who is humble is both kind and brave. Everyone who is both old and brave is either creative or not wise and vice versa. If someone is both curious and old then fred is both not strong and not old and vice versa. If someone is not quiet or old then someone is both not tall and calm. If someone is not tall or wise then someone is both wise and creative. If someone is either not humble or not funny then mary is both not creative and tall and vice versa. If john is either not patient or rich then someone is either not kind or not brave. Someone is either not calm or rich. Someone is both not rich and funny. Lucy is not wise. John is both not kind and not funny. Someone is generous or not generous. Mary is either not old or not happy. Lucy is either not brave or not quiet. Susan is either not rich or not quiet. | Mary is not quiet. | contradiction | (![X]:((~generous(X)<~>~quiet(X))=>(~old(X)|~curious(X))))&
(![X]:((creative(X)<~>rich(X))<=>~rich(X)))&
((rich(lucy))=>((~old(alice)&~funny(alice))))&
((?[X]:((~old(X)|~wise(X))))=>(kind(lucy)))&
(![X]:((~wise(X)|brave(X))=>(~generous(X)&~curious(X))))&
(((strong(lucy)&tall(lucy)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:(rich(X)<=>(strong(X)<~>old(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)<~>~creative(X)))))&
(![X]:(brave(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:(humble(X)=>(kind(X)&brave(X))))&
(![X]:((old(X)&brave(X))<=>(creative(X)<~>~wise(X))))&
((?[X]:((curious(X)&old(X))))<=>((~strong(fred)&~old(fred))))&
((?[X]:((~quiet(X)|old(X))))=>(?[X]:((~tall(X)&calm(X)))))&
((?[X]:((~tall(X)|wise(X))))=>(?[X]:((wise(X)&creative(X)))))&
((?[X]:((~humble(X)<~>~funny(X))))<=>((~creative(mary)&tall(mary))))&
(((~patient(john)<~>rich(john)))=>(?[X]:((~kind(X)<~>~brave(X)))))&
(?[X]:((~calm(X)<~>rich(X))))&
(?[X]:((~rich(X)&funny(X))))&
(~wise(lucy))&
((~kind(john)&~funny(john)))&
(?[X]:((generous(X)|~generous(X))))&
((~old(mary)<~>~happy(mary)))&
((~brave(lucy)<~>~quiet(lucy)))&
((~rich(susan)<~>~quiet(susan))) | ~quiet(mary) | [
"p5",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2642825171462896532808922
% SZS output start Proof for 2642825171462896532808922
6. (tall(lucy) & strong(lucy)) <=> ? [X0] : (~strong(X0) <~> ~brave(X0)) [input p5]
9. ! [X0] : (brave(X0) <=> (strong(X0) <~> ~quiet(X0))) [input p8]
23. ~brave(lucy) <~> ~quiet(lucy) [input p22]
25. ~quiet(mary) [input hypothesis]
40. ((tall(lucy) & strong(lucy)) | ! [X0] : ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0)))) & (? [X0] : ((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | (~tall(lucy) | ~strong(lucy))) [nnf transformation 6]
41. ((tall(lucy) & strong(lucy)) | ! [X0] : ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0)))) & (? [X0] : ((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | ~tall(lucy) | ~strong(lucy)) [flattening 40]
42. ((tall(lucy) & strong(lucy)) | ! [X0] : ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0)))) & (? [X1] : ((brave(X1) | strong(X1)) & (~brave(X1) | ~strong(X1))) | ~tall(lucy) | ~strong(lucy)) [rectify 41]
43. ? [X1] : ((brave(X1) | strong(X1)) & (~brave(X1) | ~strong(X1))) => ((brave(sK0) | strong(sK0)) & (~brave(sK0) | ~strong(sK0))) [choice axiom]
44. ((tall(lucy) & strong(lucy)) | ! [X0] : ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0)))) & (((brave(sK0) | strong(sK0)) & (~brave(sK0) | ~strong(sK0))) | ~tall(lucy) | ~strong(lucy)) [skolemisation 42,43]
51. ! [X0] : ((brave(X0) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | ~brave(X0))) [nnf transformation 9]
81. (quiet(lucy) | brave(lucy)) & (~quiet(lucy) | ~brave(lucy)) [nnf transformation 23]
99. strong(lucy) | ~brave(X0) | strong(X0) [cnf transformation 44]
100. strong(lucy) | ~strong(X0) | brave(X0) [cnf transformation 44]
112. ~strong(X0) | quiet(X0) | ~brave(X0) [cnf transformation 51]
113. ~strong(X0) | ~quiet(X0) | brave(X0) [cnf transformation 51]
114. strong(X0) | brave(X0) | quiet(X0) [cnf transformation 51]
155. ~quiet(lucy) | ~brave(lucy) [cnf transformation 81]
156. quiet(lucy) | brave(lucy) [cnf transformation 81]
159. ~quiet(mary) [cnf transformation 25]
190. 7 <=> ! [X0] : (~strong(X0) | brave(X0)) [avatar definition]
191. ~strong(X0) | brave(X0) <- (7) [avatar component clause 190]
198. 9 <=> ! [X0] : (~brave(X0) | strong(X0)) [avatar definition]
199. ~brave(X0) | strong(X0) <- (9) [avatar component clause 198]
202. 10 <=> strong(lucy) [avatar definition]
204. strong(lucy) <- (10) [avatar component clause 202]
205. 7 | 10 [avatar split clause 100,202,190]
206. 9 | 10 [avatar split clause 99,202,198]
270. 24 <=> ! [X1] : quiet(X1) [avatar definition]
271. quiet(X1) <- (24) [avatar component clause 270]
348. 40 <=> brave(lucy) [avatar definition]
349. ~brave(lucy) <- (~40) [avatar component clause 348]
350. brave(lucy) <- (40) [avatar component clause 348]
352. 41 <=> quiet(lucy) [avatar definition]
354. quiet(lucy) <- (41) [avatar component clause 352]
355. 40 | 41 [avatar split clause 156,352,348]
356. ~40 | ~41 [avatar split clause 155,352,348]
376. strong(lucy) <- (9, 40) [resolution 199,350]
379. 10 | ~9 | ~40 [avatar split clause 376,348,198,202]
458. quiet(lucy) | ~brave(lucy) <- (10) [resolution 112,204]
465. ~40 | 41 | ~10 [avatar split clause 458,202,352,348]
486. ~quiet(lucy) | brave(lucy) <- (10) [resolution 113,204]
489. brave(lucy) <- (10, 41) [subsumption resolution 486,354]
490. $false <- (10, ~40, 41) [subsumption resolution 489,349]
491. ~10 | 40 | ~41 [avatar contradiction clause 490]
497. brave(X0) | quiet(X0) | brave(X0) <- (7) [resolution 114,191]
507. brave(X0) | quiet(X0) <- (7) [duplicate literal removal 497]
545. strong(X2) | quiet(X2) <- (7, 9) [resolution 507,199]
576. quiet(X2) | quiet(X2) | ~brave(X2) <- (7, 9) [resolution 545,112]
582. quiet(X2) | ~brave(X2) <- (7, 9) [duplicate literal removal 576]
583. quiet(X2) <- (7, 9) [subsumption resolution 582,507]
584. 24 | ~7 | ~9 [avatar split clause 583,198,190,270]
585. $false <- (24) [resolution 271,159]
590. ~24 [avatar contradiction clause 585]
591. $false [avatar sat refutation 205,206,355,356,379,465,491,584,590]
% SZS output end Proof for 2642825171462896532808922
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is either funny or quiet and vice versa.
Everyone who is not brave or wise is both not calm and calm.
Everyone who is funny is either quiet or not kind and vice versa.
If someone is both not old and not calm then someone is both not wise and not brave.
If someone is happy then someone is not brave and vice versa.
Everyone who is both not generous and curious is both not tall and patient.
Everyone who is not generous is both brave and not rich and vice versa.
If someone is either not curious or curious then someone is calm.
If someone is not funny or funny then someone is either not rich or strong and vice versa.
Everyone who is both not wise and old is both not tall and happy and vice versa.
If someone is either not old or not wise then mary is rich or not brave.
Everyone who is either tall or not brave is kind or not funny and vice versa.
If fred is either not tall or wise then fred is kind and vice versa.
Everyone who is not calm or not funny is brave.
If lucy is either not funny or old then someone is quiet or generous and vice versa.
If someone is both rich and brave then someone is tall or calm and vice versa.
Someone is patient.
Mary is both not funny and not generous.
John is rich.
Someone is both not strong and not old.
Someone is not humble. | John is not calm. | contradiction | (![X]:(~creative(X)<=>(funny(X)<~>quiet(X))))&
(![X]:((~brave(X)|wise(X))=>(~calm(X)&calm(X))))&
(![X]:(funny(X)<=>(quiet(X)<~>~kind(X))))&
((?[X]:((~old(X)&~calm(X))))=>(?[X]:((~wise(X)&~brave(X)))))&
((?[X]:(happy(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~generous(X)&curious(X))=>(~tall(X)&patient(X))))&
(![X]:(~generous(X)<=>(brave(X)&~rich(X))))&
((?[X]:((~curious(X)<~>curious(X))))=>(?[X]:(calm(X))))&
((?[X]:((~funny(X)|funny(X))))<=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:((~wise(X)&old(X))<=>(~tall(X)&happy(X))))&
((?[X]:((~old(X)<~>~wise(X))))=>((rich(mary)|~brave(mary))))&
(![X]:((tall(X)<~>~brave(X))<=>(kind(X)|~funny(X))))&
(((~tall(fred)<~>wise(fred)))<=>(kind(fred)))&
(![X]:((~calm(X)|~funny(X))=>brave(X)))&
(((~funny(lucy)<~>old(lucy)))<=>(?[X]:((quiet(X)|generous(X)))))&
((?[X]:((rich(X)&brave(X))))<=>(?[X]:((tall(X)|calm(X)))))&
(?[X]:(patient(X)))&
((~funny(mary)&~generous(mary)))&
(rich(john))&
(?[X]:((~strong(X)&~old(X))))&
(?[X]:(~humble(X))) | ~calm(john) | [
"p1",
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 435408406402445669727989
% SZS output start Proof for 435408406402445669727989
2. ! [X0] : ((wise(X0) | ~brave(X0)) => (calm(X0) & ~calm(X0))) [input p1]
4. ? [X0] : (~calm(X0) & ~old(X0)) => ? [X0] : (~brave(X0) & ~wise(X0)) [input p3]
5. ? [X0] : happy(X0) <=> ? [X0] : ~brave(X0) [input p4]
10. ! [X0] : ((old(X0) & ~wise(X0)) <=> (happy(X0) & ~tall(X0))) [input p9]
22. ~calm(john) [input hypothesis]
23. ? [X0] : (~calm(X0) & ~old(X0)) => ? [X1] : (~brave(X1) & ~wise(X1)) [rectify 4]
24. ? [X0] : happy(X0) <=> ? [X1] : ~brave(X1) [rectify 5]
31. ! [X0] : ((calm(X0) & ~calm(X0)) | (~wise(X0) & brave(X0))) [ennf transformation 2]
32. ? [X1] : (~brave(X1) & ~wise(X1)) | ! [X0] : (calm(X0) | old(X0)) [ennf transformation 23]
40. ? [X0] : (~brave(X0) & ~wise(X0)) | ! [X1] : (calm(X1) | old(X1)) [rectify 32]
41. ? [X0] : (~brave(X0) & ~wise(X0)) => (~brave(sK0) & ~wise(sK0)) [choice axiom]
42. (~brave(sK0) & ~wise(sK0)) | ! [X1] : (calm(X1) | old(X1)) [skolemisation 40,41]
43. (? [X0] : happy(X0) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : ~happy(X0)) [nnf transformation 24]
44. (? [X0] : happy(X0) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : ~happy(X3)) [rectify 43]
45. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
46. ? [X2] : ~brave(X2) => ~brave(sK2) [choice axiom]
47. (happy(sK1) | ! [X1] : brave(X1)) & (~brave(sK2) | ! [X3] : ~happy(X3)) [skolemisation 44,46,45]
59. ! [X0] : (((old(X0) & ~wise(X0)) | (~happy(X0) | tall(X0))) & ((happy(X0) & ~tall(X0)) | (~old(X0) | wise(X0)))) [nnf transformation 10]
60. ! [X0] : (((old(X0) & ~wise(X0)) | ~happy(X0) | tall(X0)) & ((happy(X0) & ~tall(X0)) | ~old(X0) | wise(X0))) [flattening 59]
76. ~calm(X0) | brave(X0) [cnf transformation 31]
77. ~calm(X0) | ~wise(X0) [cnf transformation 31]
78. calm(X0) | brave(X0) [cnf transformation 31]
79. ~wise(X0) | calm(X0) [cnf transformation 31]
85. ~brave(sK0) | calm(X1) | old(X1) [cnf transformation 42]
86. ~brave(sK2) | ~happy(X3) [cnf transformation 47]
101. happy(X0) | ~old(X0) | wise(X0) [cnf transformation 60]
134. ~calm(john) [cnf transformation 22]
137. ~wise(X0) [subsumption resolution 77,79]
138. brave(X0) [subsumption resolution 76,78]
139. old(X1) | calm(X1) [subsumption resolution 85,138]
140. ~happy(X3) [subsumption resolution 86,138]
172. ~old(X0) | wise(X0) [subsumption resolution 101,140]
173. ~old(X0) [subsumption resolution 172,137]
245. calm(X0) [resolution 139,173]
248. $false [resolution 245,134]
% SZS output end Proof for 435408406402445669727989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not quiet is either generous or not creative and vice versa. If someone is not wise then alice is not patient and vice versa. If someone is not creative then someone is both brave and not old. Everyone who is quiet is curious. If mary is both strong and not curious then someone is not humble or not brave and vice versa. Everyone who is not happy or not brave is both not patient and not creative and vice versa. Everyone who is brave is not humble or calm and vice versa. Everyone who is either not old or not brave is kind and vice versa. If someone is both not strong and creative then lucy is both not calm and strong and vice versa. If someone is both not creative and not humble then someone is humble or quiet and vice versa. Everyone who is not curious is patient. If john is either creative or humble then lucy is kind and vice versa. Everyone who is both not generous and calm is not creative or generous. If someone is not generous then lucy is calm or old. If someone is both not strong and curious then lucy is both not calm and not patient and vice versa. Everyone who is not generous is humble or kind. John is not humble. Alice is either creative or not generous. Mary is both not tall and not calm. Alice is either old or not patient. Someone is kind. Someone is either not rich or not brave. Someone is either humble or wise. | Mary is not humble. | entailment | (![X]:((creative(X)|~quiet(X))<=>(generous(X)<~>~creative(X))))&
((?[X]:(~wise(X)))<=>(~patient(alice)))&
((?[X]:(~creative(X)))=>(?[X]:((brave(X)&~old(X)))))&
(![X]:(quiet(X)=>curious(X)))&
(((strong(mary)&~curious(mary)))<=>(?[X]:((~humble(X)|~brave(X)))))&
(![X]:((~happy(X)|~brave(X))<=>(~patient(X)&~creative(X))))&
(![X]:(brave(X)<=>(~humble(X)|calm(X))))&
(![X]:((~old(X)<~>~brave(X))<=>kind(X)))&
((?[X]:((~strong(X)&creative(X))))<=>((~calm(lucy)&strong(lucy))))&
((?[X]:((~creative(X)&~humble(X))))<=>(?[X]:((humble(X)|quiet(X)))))&
(![X]:(~curious(X)=>patient(X)))&
(((creative(john)<~>humble(john)))<=>(kind(lucy)))&
(![X]:((~generous(X)&calm(X))=>(~creative(X)|generous(X))))&
((?[X]:(~generous(X)))=>((calm(lucy)|old(lucy))))&
((?[X]:((~strong(X)&curious(X))))<=>((~calm(lucy)&~patient(lucy))))&
(![X]:(~generous(X)=>(humble(X)|kind(X))))&
(~humble(john))&
((creative(alice)<~>~generous(alice)))&
((~tall(mary)&~calm(mary)))&
((old(alice)<~>~patient(alice)))&
(?[X]:(kind(X)))&
(?[X]:((~rich(X)<~>~brave(X))))&
(?[X]:((humble(X)<~>wise(X)))) | ~humble(mary) | [
"p4",
"p5",
"p6",
"p9",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4039477387570353460852716
% SZS output start Proof for 4039477387570353460852716
5. (~curious(mary) & strong(mary)) <=> ? [X0] : (~brave(X0) | ~humble(X0)) [input p4]
6. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> (~creative(X0) & ~patient(X0))) [input p5]
7. ! [X0] : (brave(X0) <=> (calm(X0) | ~humble(X0))) [input p6]
10. ? [X0] : (~humble(X0) & ~creative(X0)) <=> ? [X0] : (quiet(X0) | humble(X0)) [input p9]
11. ! [X0] : (~curious(X0) => patient(X0)) [input p10]
19. ~calm(mary) & ~tall(mary) [input p18]
24. humble(mary) [input hypothesis]
26. ? [X0] : (~humble(X0) & ~creative(X0)) <=> ? [X1] : (quiet(X1) | humble(X1)) [rectify 10]
27. ~calm(mary) [pure predicate removal 19]
30. ! [X0] : (patient(X0) | curious(X0)) [ennf transformation 11]
46. ((~curious(mary) & strong(mary)) | ! [X0] : (brave(X0) & humble(X0))) & (? [X0] : (~brave(X0) | ~humble(X0)) | (curious(mary) | ~strong(mary))) [nnf transformation 5]
47. ((~curious(mary) & strong(mary)) | ! [X0] : (brave(X0) & humble(X0))) & (? [X0] : (~brave(X0) | ~humble(X0)) | curious(mary) | ~strong(mary)) [flattening 46]
48. ((~curious(mary) & strong(mary)) | ! [X0] : (brave(X0) & humble(X0))) & (? [X1] : (~brave(X1) | ~humble(X1)) | curious(mary) | ~strong(mary)) [rectify 47]
49. ? [X1] : (~brave(X1) | ~humble(X1)) => (~brave(sK2) | ~humble(sK2)) [choice axiom]
50. ((~curious(mary) & strong(mary)) | ! [X0] : (brave(X0) & humble(X0))) & ((~brave(sK2) | ~humble(sK2)) | curious(mary) | ~strong(mary)) [skolemisation 48,49]
51. ! [X0] : (((~brave(X0) | ~happy(X0)) | (creative(X0) | patient(X0))) & ((~creative(X0) & ~patient(X0)) | (brave(X0) & happy(X0)))) [nnf transformation 6]
52. ! [X0] : ((~brave(X0) | ~happy(X0) | creative(X0) | patient(X0)) & ((~creative(X0) & ~patient(X0)) | (brave(X0) & happy(X0)))) [flattening 51]
53. ! [X0] : ((brave(X0) | (~calm(X0) & humble(X0))) & ((calm(X0) | ~humble(X0)) | ~brave(X0))) [nnf transformation 7]
54. ! [X0] : ((brave(X0) | (~calm(X0) & humble(X0))) & (calm(X0) | ~humble(X0) | ~brave(X0))) [flattening 53]
61. (? [X0] : (~humble(X0) & ~creative(X0)) | ! [X1] : (~quiet(X1) & ~humble(X1))) & (? [X1] : (quiet(X1) | humble(X1)) | ! [X0] : (humble(X0) | creative(X0))) [nnf transformation 26]
62. (? [X0] : (~humble(X0) & ~creative(X0)) | ! [X1] : (~quiet(X1) & ~humble(X1))) & (? [X2] : (quiet(X2) | humble(X2)) | ! [X3] : (humble(X3) | creative(X3))) [rectify 61]
63. ? [X0] : (~humble(X0) & ~creative(X0)) => (~humble(sK4) & ~creative(sK4)) [choice axiom]
64. ? [X2] : (quiet(X2) | humble(X2)) => (quiet(sK5) | humble(sK5)) [choice axiom]
65. ((~humble(sK4) & ~creative(sK4)) | ! [X1] : (~quiet(X1) & ~humble(X1))) & ((quiet(sK5) | humble(sK5)) | ! [X3] : (humble(X3) | creative(X3))) [skolemisation 62,64,63]
96. ~curious(mary) | humble(X0) [cnf transformation 50]
99. ~patient(X0) | brave(X0) [cnf transformation 52]
103. ~humble(X0) | calm(X0) | ~brave(X0) [cnf transformation 54]
117. ~humble(sK4) | ~humble(X1) [cnf transformation 65]
119. curious(X0) | patient(X0) [cnf transformation 30]
134. ~calm(mary) [cnf transformation 27]
142. humble(mary) [cnf transformation 24]
176. 8 <=> curious(mary) [avatar definition]
178. ~curious(mary) <- (~8) [avatar component clause 176]
181. 9 <=> ! [X0] : humble(X0) [avatar definition]
182. humble(X0) <- (9) [avatar component clause 181]
183. 9 | ~8 [avatar split clause 96,176,181]
226. 19 <=> humble(sK4) [avatar definition]
228. ~humble(sK4) <- (~19) [avatar component clause 226]
231. 20 <=> ! [X1] : ~humble(X1) [avatar definition]
232. ~humble(X1) <- (20) [avatar component clause 231]
233. 20 | ~19 [avatar split clause 117,226,231]
333. $false <- (9, ~19) [resolution 228,182]
334. ~9 | 19 [avatar contradiction clause 333]
337. $false <- (20) [resolution 232,142]
338. ~20 [avatar contradiction clause 337]
345. patient(mary) <- (~8) [resolution 119,178]
346. brave(mary) <- (~8) [resolution 345,99]
358. calm(mary) | ~brave(mary) [resolution 103,142]
361. ~brave(mary) [subsumption resolution 358,134]
362. $false <- (~8) [subsumption resolution 361,346]
363. 8 [avatar contradiction clause 362]
382. $false [avatar sat refutation 183,233,334,338,363]
% SZS output end Proof for 4039477387570353460852716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both funny and not funny is either not patient or not tall and vice versa. Everyone who is calm or rich is not rich and vice versa. Everyone who is creative is humble and vice versa. Everyone who is wise or old is either not wise or not kind. Everyone who is not rich or not funny is either quiet or creative and vice versa. Everyone who is happy or not wise is calm. If someone is both curious and not kind then alice is either not kind or generous and vice versa. Everyone who is calm or generous is both calm and not humble and vice versa. If paul is strong then someone is either calm or not humble and vice versa. If someone is calm or brave then alice is both wise and not kind and vice versa. Everyone who is both not calm and patient is not old or brave and vice versa. Everyone who is either not calm or rich is both not creative and curious and vice versa. If mary is both tall and not strong then someone is either not happy or not rich and vice versa. If susan is calm then fred is not generous or not curious. Someone is happy or not happy. Lucy is not funny or calm. Someone is both not tall and kind. Someone is not kind or wise. Mary is either strong or not strong. Someone is either not humble or brave. | Lucy is strong. | neutral | (![X]:((funny(X)&~funny(X))<=>(~patient(X)<~>~tall(X))))&
(![X]:((calm(X)|rich(X))<=>~rich(X)))&
(![X]:(creative(X)<=>humble(X)))&
(![X]:((wise(X)|old(X))=>(~wise(X)<~>~kind(X))))&
(![X]:((~rich(X)|~funny(X))<=>(quiet(X)<~>creative(X))))&
(![X]:((happy(X)|~wise(X))=>calm(X)))&
((?[X]:((curious(X)&~kind(X))))<=>((~kind(alice)<~>generous(alice))))&
(![X]:((calm(X)|generous(X))<=>(calm(X)&~humble(X))))&
((strong(paul))<=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((calm(X)|brave(X))))<=>((wise(alice)&~kind(alice))))&
(![X]:((~calm(X)&patient(X))<=>(~old(X)|brave(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(~creative(X)&curious(X))))&
(((tall(mary)&~strong(mary)))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
((calm(susan))=>((~generous(fred)|~curious(fred))))&
(?[X]:((happy(X)|~happy(X))))&
((~funny(lucy)|calm(lucy)))&
(?[X]:((~tall(X)&kind(X))))&
(?[X]:((~kind(X)|wise(X))))&
((strong(mary)<~>~strong(mary)))&
(?[X]:((~humble(X)<~>brave(X)))) | strong(lucy) | [] | null | 0 |
If susan is not quiet or not generous then someone is both patient and not curious.
Everyone who is either not calm or not happy is either not old or not wise and vice versa.
If paul is curious or not creative then paul is both not funny and not old and vice versa.
Everyone who is not brave is brave or not tall.
Everyone who is both not curious and happy is not tall and vice versa.
If someone is both not brave and not wise then someone is both not wise and not tall and vice versa.
If mary is both not rich and patient then someone is not humble.
Everyone who is creative or old is either brave or tall.
Everyone who is generous or happy is not wise and vice versa.
Everyone who is both funny and strong is both not calm and tall and vice versa.
Everyone who is brave is either kind or wise.
If someone is curious then susan is both not tall and not rich and vice versa.
Everyone who is either quiet or strong is either creative or tall.
Everyone who is not brave is both tall and not patient.
Everyone who is both old and not humble is both not happy and not humble and vice versa.
If mary is not wise or funny then fred is both not patient and not tall and vice versa.
Someone is either old or quiet.
Someone is not tall or not rich.
Someone is curious or patient.
Paul is rich.
Lucy is generous or not happy. | Paul is old. | contradiction | (((~quiet(susan)|~generous(susan)))=>(?[X]:((patient(X)&~curious(X)))))&
(![X]:((~calm(X)<~>~happy(X))<=>(~old(X)<~>~wise(X))))&
(((curious(paul)|~creative(paul)))<=>((~funny(paul)&~old(paul))))&
(![X]:(~brave(X)=>(brave(X)|~tall(X))))&
(![X]:((~curious(X)&happy(X))<=>~tall(X)))&
((?[X]:((~brave(X)&~wise(X))))<=>(?[X]:((~wise(X)&~tall(X)))))&
(((~rich(mary)&patient(mary)))=>(?[X]:(~humble(X))))&
(![X]:((creative(X)|old(X))=>(brave(X)<~>tall(X))))&
(![X]:((generous(X)|happy(X))<=>~wise(X)))&
(![X]:((funny(X)&strong(X))<=>(~calm(X)&tall(X))))&
(![X]:(brave(X)=>(kind(X)<~>wise(X))))&
((?[X]:(curious(X)))<=>((~tall(susan)&~rich(susan))))&
(![X]:((quiet(X)<~>strong(X))=>(creative(X)<~>tall(X))))&
(![X]:(~brave(X)=>(tall(X)&~patient(X))))&
(![X]:((old(X)&~humble(X))<=>(~happy(X)&~humble(X))))&
(((~wise(mary)|funny(mary)))<=>((~patient(fred)&~tall(fred))))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul))&
((generous(lucy)|~happy(lucy))) | old(paul) | [
"p3",
"p4",
"p5",
"p7",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 892334791118912899667271
% SZS output start Proof for 892334791118912899667271
4. ! [X0] : (~brave(X0) => (~tall(X0) | brave(X0))) [input p3]
5. ! [X0] : ((happy(X0) & ~curious(X0)) <=> ~tall(X0)) [input p4]
6. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X0] : (~tall(X0) & ~wise(X0)) [input p5]
8. ! [X0] : ((old(X0) | creative(X0)) => (brave(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((happy(X0) | generous(X0)) <=> ~wise(X0)) [input p8]
12. ? [X0] : curious(X0) <=> (~rich(susan) & ~tall(susan)) [input p11]
14. ! [X0] : (~brave(X0) => (~patient(X0) & tall(X0))) [input p13]
22. old(paul) [input hypothesis]
23. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X1] : (~tall(X1) & ~wise(X1)) [rectify 6]
25. ! [X0] : ((~tall(X0) | brave(X0)) | brave(X0)) [ennf transformation 4]
26. ! [X0] : (~tall(X0) | brave(X0) | brave(X0)) [flattening 25]
29. ! [X0] : ((brave(X0) <~> tall(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 8]
32. ! [X0] : ((~patient(X0) & tall(X0)) | brave(X0)) [ennf transformation 14]
38. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | (~happy(X0) | curious(X0)))) [nnf transformation 5]
39. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | ~happy(X0) | curious(X0))) [flattening 38]
40. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : (tall(X1) | wise(X1))) & (? [X1] : (~tall(X1) & ~wise(X1)) | ! [X0] : (wise(X0) | brave(X0))) [nnf transformation 23]
41. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : (tall(X1) | wise(X1))) & (? [X2] : (~tall(X2) & ~wise(X2)) | ! [X3] : (wise(X3) | brave(X3))) [rectify 40]
42. ? [X0] : (~wise(X0) & ~brave(X0)) => (~wise(sK1) & ~brave(sK1)) [choice axiom]
43. ? [X2] : (~tall(X2) & ~wise(X2)) => (~tall(sK2) & ~wise(sK2)) [choice axiom]
44. ((~wise(sK1) & ~brave(sK1)) | ! [X1] : (tall(X1) | wise(X1))) & ((~tall(sK2) & ~wise(sK2)) | ! [X3] : (wise(X3) | brave(X3))) [skolemisation 41,43,42]
47. ! [X0] : (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | (~old(X0) & ~creative(X0))) [nnf transformation 29]
48. ! [X0] : (((happy(X0) | generous(X0)) | wise(X0)) & (~wise(X0) | (~happy(X0) & ~generous(X0)))) [nnf transformation 9]
49. ! [X0] : ((happy(X0) | generous(X0) | wise(X0)) & (~wise(X0) | (~happy(X0) & ~generous(X0)))) [flattening 48]
53. (? [X0] : curious(X0) | (rich(susan) | tall(susan))) & ((~rich(susan) & ~tall(susan)) | ! [X0] : ~curious(X0)) [nnf transformation 12]
54. (? [X0] : curious(X0) | rich(susan) | tall(susan)) & ((~rich(susan) & ~tall(susan)) | ! [X0] : ~curious(X0)) [flattening 53]
55. (? [X0] : curious(X0) | rich(susan) | tall(susan)) & ((~rich(susan) & ~tall(susan)) | ! [X1] : ~curious(X1)) [rectify 54]
56. ? [X0] : curious(X0) => curious(sK4) [choice axiom]
57. (curious(sK4) | rich(susan) | tall(susan)) & ((~rich(susan) & ~tall(susan)) | ! [X1] : ~curious(X1)) [skolemisation 55,56]
87. ~tall(X0) | brave(X0) | brave(X0) [cnf transformation 26]
88. ~tall(X0) | ~happy(X0) | curious(X0) [cnf transformation 39]
90. tall(X0) | happy(X0) [cnf transformation 39]
93. ~brave(sK1) | tall(X1) | wise(X1) [cnf transformation 44]
99. ~tall(X0) | ~brave(X0) | ~old(X0) [cnf transformation 47]
101. ~wise(X0) | ~happy(X0) [cnf transformation 49]
109. ~tall(susan) | ~curious(X1) [cnf transformation 57]
116. tall(X0) | brave(X0) [cnf transformation 32]
133. old(paul) [cnf transformation 22]
134. ~tall(X0) | brave(X0) [duplicate literal removal 87]
160. 6 <=> old(paul) [avatar definition]
162. old(paul) <- (6) [avatar component clause 160]
177. 9 <=> ! [X1] : (tall(X1) | wise(X1)) [avatar definition]
178. tall(X1) | wise(X1) <- (9) [avatar component clause 177]
185. 11 <=> brave(sK1) [avatar definition]
187. ~brave(sK1) <- (~11) [avatar component clause 185]
188. 9 | ~11 [avatar split clause 93,185,177]
215. ~tall(X0) | ~old(X0) [subsumption resolution 99,134]
220. 18 <=> tall(susan) [avatar definition]
221. ~tall(susan) <- (~18) [avatar component clause 220]
233. 21 <=> ! [X1] : ~curious(X1) [avatar definition]
234. ~curious(X1) <- (21) [avatar component clause 233]
236. 21 | ~18 [avatar split clause 109,220,233]
237. brave(X0) [subsumption resolution 116,134]
296. 6 [avatar split clause 133,160]
297. $false <- (~11) [subsumption resolution 187,237]
298. 11 [avatar contradiction clause 297]
301. happy(susan) <- (~18) [resolution 90,221]
310. wise(susan) <- (9, ~18) [resolution 178,221]
318. ~old(X1) | happy(X1) [resolution 215,90]
327. ~happy(susan) <- (9, ~18) [resolution 310,101]
329. $false <- (9, ~18) [subsumption resolution 327,301]
330. ~9 | 18 [avatar contradiction clause 329]
359. ~happy(X0) | curious(X0) | wise(X0) <- (9) [resolution 88,178]
365. ~happy(X0) | wise(X0) <- (9, 21) [subsumption resolution 359,234]
366. ~happy(X0) <- (9, 21) [subsumption resolution 365,101]
434. happy(paul) <- (6) [resolution 318,162]
437. $false <- (6, 9, 21) [subsumption resolution 434,366]
438. ~6 | ~9 | ~21 [avatar contradiction clause 437]
443. $false [avatar sat refutation 188,236,296,298,330,438]
% SZS output end Proof for 892334791118912899667271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or generous is not old and vice versa. If someone is not wise or not creative then john is patient and vice versa. Everyone who is not kind or not patient is either not generous or not wise and vice versa. If john is both rich and not brave then someone is not generous. Everyone who is not humble or not brave is not kind and vice versa. If fred is both not curious and not quiet then john is both wise and rich and vice versa. If someone is either old or strong then paul is both not funny and creative. If someone is both brave and not patient then someone is not tall or not wise and vice versa. If someone is either creative or not old then someone is either curious or old. Everyone who is curious or happy is not tall and vice versa. Everyone who is either not kind or humble is both happy and brave and vice versa. If lucy is both not creative and kind then someone is either brave or not old and vice versa. Everyone who is tall is not generous. If someone is not rich or not patient then someone is not brave or wise. Everyone who is both strong and rich is not tall and vice versa. Everyone who is both quiet and rich is generous. Someone is both creative and not happy. Someone is both not generous and not kind. Fred is kind or funny. Someone is funny. Alice is generous or brave. Someone is not strong or happy. Lucy is both not curious and funny. Mary is both not strong and patient. | Mary is not patient. | contradiction | (![X]:((humble(X)|generous(X))<=>~old(X)))&
((?[X]:((~wise(X)|~creative(X))))<=>(patient(john)))&
(![X]:((~kind(X)|~patient(X))<=>(~generous(X)<~>~wise(X))))&
(((rich(john)&~brave(john)))=>(?[X]:(~generous(X))))&
(![X]:((~humble(X)|~brave(X))<=>~kind(X)))&
(((~curious(fred)&~quiet(fred)))<=>((wise(john)&rich(john))))&
((?[X]:((old(X)<~>strong(X))))=>((~funny(paul)&creative(paul))))&
((?[X]:((brave(X)&~patient(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
((?[X]:((creative(X)<~>~old(X))))=>(?[X]:((curious(X)<~>old(X)))))&
(![X]:((curious(X)|happy(X))<=>~tall(X)))&
(![X]:((~kind(X)<~>humble(X))<=>(happy(X)&brave(X))))&
(((~creative(lucy)&kind(lucy)))<=>(?[X]:((brave(X)<~>~old(X)))))&
(![X]:(tall(X)=>~generous(X)))&
((?[X]:((~rich(X)|~patient(X))))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((strong(X)&rich(X))<=>~tall(X)))&
(![X]:((quiet(X)&rich(X))=>generous(X)))&
(?[X]:((creative(X)&~happy(X))))&
(?[X]:((~generous(X)&~kind(X))))&
((kind(fred)|funny(fred)))&
(?[X]:(funny(X)))&
((generous(alice)|brave(alice)))&
(?[X]:((~strong(X)|happy(X))))&
((~curious(lucy)&funny(lucy)))&
((~strong(mary)&patient(mary))) | ~patient(mary) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3387781990865401536444195
% SZS output start Proof for 3387781990865401536444195
24. patient(mary) & ~strong(mary) [input p23]
25. ~patient(mary) [input hypothesis]
149. patient(mary) [cnf transformation 24]
150. ~patient(mary) [cnf transformation 25]
338. $false [subsumption resolution 150,149]
% SZS output end Proof for 3387781990865401536444195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and old is humble. If someone is both not tall and not curious then someone is not brave. If susan is old or generous then someone is both old and not rich. Everyone who is not patient is not quiet or humble and vice versa. Everyone who is not funny is calm or kind. Everyone who is not patient is either funny or creative. Everyone who is not brave or not kind is generous and vice versa. Everyone who is both not tall and not happy is either generous or calm. Everyone who is not wise or generous is both wise and not brave and vice versa. Everyone who is either not curious or not patient is both funny and rich. Everyone who is not wise is not quiet or strong and vice versa. If someone is either humble or not strong then lucy is not happy and vice versa. Everyone who is either not rich or creative is both not funny and not kind and vice versa. Everyone who is not rich is either calm or not humble and vice versa. If alice is not curious or not funny then someone is calm or funny. Everyone who is both not strong and generous is both not calm and wise and vice versa. Susan is humble or creative. Paul is not patient. Lucy is either humble or not generous. Susan is either patient or quiet. Fred is either calm or kind. Someone is not calm or not tall. Someone is curious or not strong. Someone is patient or not curious. | Lucy is not creative. | entailment | (![X]:((~wise(X)&old(X))=>humble(X)))&
((?[X]:((~tall(X)&~curious(X))))=>(?[X]:(~brave(X))))&
(((old(susan)|generous(susan)))=>(?[X]:((old(X)&~rich(X)))))&
(![X]:(~patient(X)<=>(~quiet(X)|humble(X))))&
(![X]:(~funny(X)=>(calm(X)|kind(X))))&
(![X]:(~patient(X)=>(funny(X)<~>creative(X))))&
(![X]:((~brave(X)|~kind(X))<=>generous(X)))&
(![X]:((~tall(X)&~happy(X))=>(generous(X)<~>calm(X))))&
(![X]:((~wise(X)|generous(X))<=>(wise(X)&~brave(X))))&
(![X]:((~curious(X)<~>~patient(X))=>(funny(X)&rich(X))))&
(![X]:(~wise(X)<=>(~quiet(X)|strong(X))))&
((?[X]:((humble(X)<~>~strong(X))))<=>(~happy(lucy)))&
(![X]:((~rich(X)<~>creative(X))<=>(~funny(X)&~kind(X))))&
(![X]:(~rich(X)<=>(calm(X)<~>~humble(X))))&
(((~curious(alice)|~funny(alice)))=>(?[X]:((calm(X)|funny(X)))))&
(![X]:((~strong(X)&generous(X))<=>(~calm(X)&wise(X))))&
((humble(susan)|creative(susan)))&
(~patient(paul))&
((humble(lucy)<~>~generous(lucy)))&
((patient(susan)<~>quiet(susan)))&
((calm(fred)<~>kind(fred)))&
(?[X]:((~calm(X)|~tall(X))))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:((patient(X)|~curious(X)))) | ~creative(lucy) | [
"p4",
"p6",
"p8",
"p10",
"p12",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5899197968801762360898761
% SZS output start Proof for 5899197968801762360898761
5. ! [X0] : (~funny(X0) => (kind(X0) | calm(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | ~brave(X0)) <=> generous(X0)) [input p6]
9. ! [X0] : ((generous(X0) | ~wise(X0)) <=> (~brave(X0) & wise(X0))) [input p8]
11. ! [X0] : (~wise(X0) <=> (strong(X0) | ~quiet(X0))) [input p10]
13. ! [X0] : ((~rich(X0) <~> creative(X0)) <=> (~kind(X0) & ~funny(X0))) [input p12]
14. ! [X0] : (~rich(X0) <=> (calm(X0) <~> ~humble(X0))) [input p13]
16. ! [X0] : ((generous(X0) & ~strong(X0)) <=> (wise(X0) & ~calm(X0))) [input p15]
19. humble(lucy) <~> ~generous(lucy) [input p18]
25. creative(lucy) [input hypothesis]
31. ! [X0] : ((kind(X0) | calm(X0)) | funny(X0)) [ennf transformation 5]
32. ! [X0] : (kind(X0) | calm(X0) | funny(X0)) [flattening 31]
46. ! [X0] : (((~kind(X0) | ~brave(X0)) | ~generous(X0)) & (generous(X0) | (kind(X0) & brave(X0)))) [nnf transformation 7]
47. ! [X0] : ((~kind(X0) | ~brave(X0) | ~generous(X0)) & (generous(X0) | (kind(X0) & brave(X0)))) [flattening 46]
49. ! [X0] : (((generous(X0) | ~wise(X0)) | (brave(X0) | ~wise(X0))) & ((~brave(X0) & wise(X0)) | (~generous(X0) & wise(X0)))) [nnf transformation 9]
50. ! [X0] : ((generous(X0) | ~wise(X0) | brave(X0) | ~wise(X0)) & ((~brave(X0) & wise(X0)) | (~generous(X0) & wise(X0)))) [flattening 49]
52. ! [X0] : ((~wise(X0) | (~strong(X0) & quiet(X0))) & ((strong(X0) | ~quiet(X0)) | wise(X0))) [nnf transformation 11]
53. ! [X0] : ((~wise(X0) | (~strong(X0) & quiet(X0))) & (strong(X0) | ~quiet(X0) | wise(X0))) [flattening 52]
58. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (kind(X0) | funny(X0))) & ((~kind(X0) & ~funny(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [nnf transformation 13]
59. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | kind(X0) | funny(X0)) & ((~kind(X0) & ~funny(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [flattening 58]
60. ! [X0] : ((~rich(X0) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0)))) & (((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | rich(X0))) [nnf transformation 14]
63. ! [X0] : (((generous(X0) & ~strong(X0)) | (~wise(X0) | calm(X0))) & ((wise(X0) & ~calm(X0)) | (~generous(X0) | strong(X0)))) [nnf transformation 16]
64. ! [X0] : (((generous(X0) & ~strong(X0)) | ~wise(X0) | calm(X0)) & ((wise(X0) & ~calm(X0)) | ~generous(X0) | strong(X0))) [flattening 63]
65. (generous(lucy) | ~humble(lucy)) & (~generous(lucy) | humble(lucy)) [nnf transformation 19]
83. kind(X0) | calm(X0) | funny(X0) [cnf transformation 32]
87. kind(X0) | generous(X0) [cnf transformation 47]
91. wise(X0) | wise(X0) [cnf transformation 50]
102. ~wise(X0) | ~strong(X0) [cnf transformation 53]
108. ~creative(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 59]
110. ~creative(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 59]
113. ~humble(X0) | calm(X0) | rich(X0) [cnf transformation 60]
114. ~calm(X0) | humble(X0) | rich(X0) [cnf transformation 60]
119. ~calm(X0) | ~generous(X0) | strong(X0) [cnf transformation 64]
122. generous(X0) | ~wise(X0) | calm(X0) [cnf transformation 64]
125. ~generous(lucy) | humble(lucy) [cnf transformation 65]
126. generous(lucy) | ~humble(lucy) [cnf transformation 65]
134. creative(lucy) [cnf transformation 25]
135. wise(X0) [duplicate literal removal 91]
165. ~strong(X0) [subsumption resolution 102,135]
200. calm(X0) | generous(X0) [subsumption resolution 122,135]
201. ~calm(X0) | ~generous(X0) [subsumption resolution 119,165]
212. 16 <=> humble(lucy) [avatar definition]
213. humble(lucy) <- (16) [avatar component clause 212]
214. ~humble(lucy) <- (~16) [avatar component clause 212]
216. 17 <=> generous(lucy) [avatar definition]
217. ~generous(lucy) <- (~17) [avatar component clause 216]
218. generous(lucy) <- (17) [avatar component clause 216]
219. ~16 | 17 [avatar split clause 126,216,212]
220. 16 | ~17 [avatar split clause 125,216,212]
281. 25 <=> funny(lucy) [avatar definition]
294. ~rich(lucy) | ~funny(lucy) [resolution 108,134]
309. ~rich(lucy) | ~kind(lucy) [resolution 110,134]
312. 28 <=> kind(lucy) [avatar definition]
314. ~kind(lucy) <- (~28) [avatar component clause 312]
316. 29 <=> rich(lucy) [avatar definition]
317. rich(lucy) <- (29) [avatar component clause 316]
318. ~rich(lucy) <- (~29) [avatar component clause 316]
319. ~28 | ~29 [avatar split clause 309,316,312]
348. generous(lucy) <- (~28) [resolution 314,87]
352. 17 | 28 [avatar split clause 348,312,216]
353. calm(lucy) | rich(lucy) <- (16) [resolution 213,113]
357. rich(X0) | humble(X0) | generous(X0) [resolution 114,200]
433. 41 <=> calm(lucy) [avatar definition]
434. ~calm(lucy) <- (~41) [avatar component clause 433]
435. calm(lucy) <- (41) [avatar component clause 433]
436. 29 | 41 | ~16 [avatar split clause 353,212,433,316]
447. ~generous(lucy) <- (41) [resolution 435,201]
450. $false <- (17, 41) [subsumption resolution 447,218]
451. ~17 | ~41 [avatar contradiction clause 450]
472. humble(lucy) | generous(lucy) <- (~29) [resolution 357,318]
474. generous(lucy) <- (~16, ~29) [subsumption resolution 472,214]
475. $false <- (~16, ~17, ~29) [subsumption resolution 474,217]
476. 16 | 17 | 29 [avatar contradiction clause 475]
480. calm(lucy) | funny(lucy) <- (~28) [resolution 314,83]
482. funny(lucy) <- (~28, ~41) [subsumption resolution 480,434]
485. 25 | 28 | 41 [avatar split clause 482,433,312,281]
486. ~funny(lucy) <- (29) [subsumption resolution 294,317]
487. ~25 | ~29 [avatar split clause 486,316,281]
488. $false [avatar sat refutation 219,220,319,352,436,451,476,485,487]
% SZS output end Proof for 5899197968801762360898761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not calm or not quiet then lucy is tall or generous. Everyone who is either not humble or not old is both not quiet and rich. Everyone who is either not tall or not creative is not tall or brave and vice versa. If john is either patient or kind then john is not kind. If fred is calm then susan is both not funny and kind. Everyone who is both kind and wise is not calm and vice versa. Everyone who is patient is not patient. Everyone who is not curious is wise. If someone is patient then mary is brave or not funny and vice versa. If someone is either rich or not brave then alice is not humble or old. Everyone who is rich or curious is both brave and old and vice versa. Everyone who is not kind or calm is both humble and tall and vice versa. Everyone who is either not quiet or not patient is wise or not creative. Everyone who is wise or happy is either tall or creative and vice versa. If someone is both not creative and not kind then someone is both tall and funny. Everyone who is generous is either old or not humble and vice versa. Lucy is either wise or patient. Lucy is not patient or not wise. Lucy is both curious and wise. Susan is not brave. Someone is both not patient and not funny. Someone is creative. Alice is both quiet and not brave. | Mary is not calm. | entailment | (((~calm(john)|~quiet(john)))=>((tall(lucy)|generous(lucy))))&
(![X]:((~humble(X)<~>~old(X))=>(~quiet(X)&rich(X))))&
(![X]:((~tall(X)<~>~creative(X))<=>(~tall(X)|brave(X))))&
(((patient(john)<~>kind(john)))=>(~kind(john)))&
((calm(fred))=>((~funny(susan)&kind(susan))))&
(![X]:((kind(X)&wise(X))<=>~calm(X)))&
(![X]:(patient(X)=>~patient(X)))&
(![X]:(~curious(X)=>wise(X)))&
((?[X]:(patient(X)))<=>((brave(mary)|~funny(mary))))&
((?[X]:((rich(X)<~>~brave(X))))=>((~humble(alice)|old(alice))))&
(![X]:((rich(X)|curious(X))<=>(brave(X)&old(X))))&
(![X]:((~kind(X)|calm(X))<=>(humble(X)&tall(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(wise(X)|~creative(X))))&
(![X]:((wise(X)|happy(X))<=>(tall(X)<~>creative(X))))&
((?[X]:((~creative(X)&~kind(X))))=>(?[X]:((tall(X)&funny(X)))))&
(![X]:(generous(X)<=>(old(X)<~>~humble(X))))&
((wise(lucy)<~>patient(lucy)))&
((~patient(lucy)|~wise(lucy)))&
((curious(lucy)&wise(lucy)))&
(~brave(susan))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:(creative(X)))&
((quiet(alice)&~brave(alice))) | ~calm(mary) | [
"p2",
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4913383551376933616293501
% SZS output start Proof for 4913383551376933616293501
3. ! [X0] : ((~tall(X0) <~> ~creative(X0)) <=> (brave(X0) | ~tall(X0))) [input p2]
7. ! [X0] : (patient(X0) => ~patient(X0)) [input p6]
8. ! [X0] : (~curious(X0) => wise(X0)) [input p7]
9. ? [X0] : patient(X0) <=> (~funny(mary) | brave(mary)) [input p8]
11. ! [X0] : ((curious(X0) | rich(X0)) <=> (old(X0) & brave(X0))) [input p10]
12. ! [X0] : ((calm(X0) | ~kind(X0)) <=> (tall(X0) & humble(X0))) [input p11]
14. ! [X0] : ((happy(X0) | wise(X0)) <=> (tall(X0) <~> creative(X0))) [input p13]
24. calm(mary) [input hypothesis]
32. ! [X0] : (~patient(X0) | ~patient(X0)) [ennf transformation 7]
33. ! [X0] : (wise(X0) | curious(X0)) [ennf transformation 8]
41. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~brave(X0) & tall(X0))) & ((brave(X0) | ~tall(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [nnf transformation 3]
42. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~brave(X0) & tall(X0))) & (brave(X0) | ~tall(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [flattening 41]
46. (? [X0] : patient(X0) | (funny(mary) & ~brave(mary))) & ((~funny(mary) | brave(mary)) | ! [X0] : ~patient(X0)) [nnf transformation 9]
47. (? [X0] : patient(X0) | (funny(mary) & ~brave(mary))) & (~funny(mary) | brave(mary) | ! [X0] : ~patient(X0)) [flattening 46]
48. (? [X0] : patient(X0) | (funny(mary) & ~brave(mary))) & (~funny(mary) | brave(mary) | ! [X1] : ~patient(X1)) [rectify 47]
49. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
50. (patient(sK0) | (funny(mary) & ~brave(mary))) & (~funny(mary) | brave(mary) | ! [X1] : ~patient(X1)) [skolemisation 48,49]
52. ! [X0] : (((curious(X0) | rich(X0)) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | (~curious(X0) & ~rich(X0)))) [nnf transformation 11]
53. ! [X0] : ((curious(X0) | rich(X0) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | (~curious(X0) & ~rich(X0)))) [flattening 52]
54. ! [X0] : (((calm(X0) | ~kind(X0)) | (~tall(X0) | ~humble(X0))) & ((tall(X0) & humble(X0)) | (~calm(X0) & kind(X0)))) [nnf transformation 12]
55. ! [X0] : ((calm(X0) | ~kind(X0) | ~tall(X0) | ~humble(X0)) & ((tall(X0) & humble(X0)) | (~calm(X0) & kind(X0)))) [flattening 54]
57. ! [X0] : (((happy(X0) | wise(X0)) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | (~happy(X0) & ~wise(X0)))) [nnf transformation 14]
58. ! [X0] : ((happy(X0) | wise(X0) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | (~happy(X0) & ~wise(X0)))) [flattening 57]
75. brave(X0) | ~tall(X0) | ~tall(X0) | creative(X0) [cnf transformation 42]
78. creative(X0) | tall(X0) | tall(X0) [cnf transformation 42]
87. ~patient(X0) | ~patient(X0) [cnf transformation 32]
88. curious(X0) | wise(X0) [cnf transformation 33]
90. patient(sK0) | ~brave(mary) [cnf transformation 50]
95. ~curious(X0) | brave(X0) [cnf transformation 53]
102. ~calm(X0) | tall(X0) [cnf transformation 55]
108. ~wise(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 58]
127. calm(mary) [cnf transformation 24]
128. ~patient(X0) [duplicate literal removal 87]
130. brave(X0) | ~tall(X0) | creative(X0) [duplicate literal removal 75]
131. creative(X0) | tall(X0) [duplicate literal removal 78]
150. brave(X0) | creative(X0) [subsumption resolution 130,131]
175. ~brave(mary) [subsumption resolution 90,128]
213. wise(X0) | brave(X0) [resolution 95,88]
220. tall(mary) [resolution 102,127]
343. brave(X0) | ~tall(X0) | ~creative(X0) [resolution 213,108]
345. ~tall(X0) | brave(X0) [subsumption resolution 343,150]
399. brave(mary) [resolution 345,220]
401. $false [subsumption resolution 399,175]
% SZS output end Proof for 4913383551376933616293501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not quiet is brave or funny.
Everyone who is either creative or not funny is either not generous or not calm.
Everyone who is not creative is humble and vice versa.
Everyone who is not creative is rich or funny and vice versa.
Everyone who is not humble or not funny is both tall and not funny and vice versa.
Everyone who is either not generous or humble is both not kind and not tall and vice versa.
If someone is kind or not creative then fred is both humble and not rich.
Everyone who is wise is generous or not calm and vice versa.
If someone is not kind or strong then susan is not rich.
If lucy is both not calm and patient then susan is not brave or patient.
Everyone who is both not brave and not rich is not curious or not creative and vice versa.
Everyone who is not quiet is not funny or old and vice versa.
Everyone who is both not wise and kind is tall.
Everyone who is both not patient and old is either funny or strong and vice versa.
If john is either not humble or not quiet then alice is either tall or not brave and vice versa.
Everyone who is either kind or not patient is both funny and not wise and vice versa.
John is not tall or not rich.
John is not generous.
Someone is kind or not calm.
Lucy is either funny or not strong.
Someone is both old and not rich.
Fred is either wise or not generous.
Someone is not generous or funny. | Lucy is brave. | neutral | (![X]:(~quiet(X)=>(brave(X)|funny(X))))&
(![X]:((creative(X)<~>~funny(X))=>(~generous(X)<~>~calm(X))))&
(![X]:(~creative(X)<=>humble(X)))&
(![X]:(~creative(X)<=>(rich(X)|funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(tall(X)&~funny(X))))&
(![X]:((~generous(X)<~>humble(X))<=>(~kind(X)&~tall(X))))&
((?[X]:((kind(X)|~creative(X))))=>((humble(fred)&~rich(fred))))&
(![X]:(wise(X)<=>(generous(X)|~calm(X))))&
((?[X]:((~kind(X)|strong(X))))=>(~rich(susan)))&
(((~calm(lucy)&patient(lucy)))=>((~brave(susan)|patient(susan))))&
(![X]:((~brave(X)&~rich(X))<=>(~curious(X)|~creative(X))))&
(![X]:(~quiet(X)<=>(~funny(X)|old(X))))&
(![X]:((~wise(X)&kind(X))=>tall(X)))&
(![X]:((~patient(X)&old(X))<=>(funny(X)<~>strong(X))))&
(((~humble(john)<~>~quiet(john)))<=>((tall(alice)<~>~brave(alice))))&
(![X]:((kind(X)<~>~patient(X))<=>(funny(X)&~wise(X))))&
((~tall(john)|~rich(john)))&
(~generous(john))&
(?[X]:((kind(X)|~calm(X))))&
((funny(lucy)<~>~strong(lucy)))&
(?[X]:((old(X)&~rich(X))))&
((wise(fred)<~>~generous(fred)))&
(?[X]:((~generous(X)|funny(X)))) | brave(lucy) | [] | null | 0 |
If john is not quiet then john is either not old or brave and vice versa. If someone is both kind and patient then someone is not funny or wise and vice versa. Everyone who is not strong is both not old and patient and vice versa. Everyone who is not strong is calm and vice versa. If alice is both not brave and not tall then someone is creative or brave. Everyone who is either humble or generous is old. If john is both old and not calm then mary is both not funny and not old and vice versa. If alice is rich or not rich then alice is both humble and not quiet. Everyone who is either brave or not strong is both calm and brave and vice versa. Everyone who is either patient or quiet is not humble or not tall and vice versa. Everyone who is either not creative or not happy is either quiet or not creative. Everyone who is humble or patient is either rich or not brave. If alice is not old then fred is not kind or tall. If john is not patient or brave then mary is not funny and vice versa. Everyone who is not funny is creative or not kind and vice versa. If someone is quiet then someone is not calm or old. Fred is both rich and not kind. Mary is both curious and happy. Susan is not curious. Paul is either not quiet or not tall. John is both quiet and kind. Mary is curious or brave. | Mary is calm. | contradiction | ((~quiet(john))<=>((~old(john)<~>brave(john))))&
((?[X]:((kind(X)&patient(X))))<=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:(~strong(X)<=>(~old(X)&patient(X))))&
(![X]:(~strong(X)<=>calm(X)))&
(((~brave(alice)&~tall(alice)))=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((humble(X)<~>generous(X))=>old(X)))&
(((old(john)&~calm(john)))<=>((~funny(mary)&~old(mary))))&
(((rich(alice)|~rich(alice)))=>((humble(alice)&~quiet(alice))))&
(![X]:((brave(X)<~>~strong(X))<=>(calm(X)&brave(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~humble(X)|~tall(X))))&
(![X]:((~creative(X)<~>~happy(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((humble(X)|patient(X))=>(rich(X)<~>~brave(X))))&
((~old(alice))=>((~kind(fred)|tall(fred))))&
(((~patient(john)|brave(john)))<=>(~funny(mary)))&
(![X]:(~funny(X)<=>(creative(X)|~kind(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|old(X)))))&
((rich(fred)&~kind(fred)))&
((curious(mary)&happy(mary)))&
(~curious(susan))&
((~quiet(paul)<~>~tall(paul)))&
((quiet(john)&kind(john)))&
((curious(mary)|brave(mary))) | calm(mary) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2595637204021357882979072
% SZS output start Proof for 2595637204021357882979072
4. ! [X0] : (~strong(X0) <=> calm(X0)) [input p3]
9. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (brave(X0) & calm(X0))) [input p8]
23. calm(mary) [input hypothesis]
43. ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0))) [nnf transformation 4]
49. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 9]
50. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 49]
75. calm(X0) | strong(X0) [cnf transformation 43]
76. ~calm(X0) | ~strong(X0) [cnf transformation 43]
88. calm(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 50]
91. brave(X0) | brave(X0) | strong(X0) [cnf transformation 50]
93. strong(X0) | ~brave(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 50]
126. calm(mary) [cnf transformation 23]
129. strong(X0) | brave(X0) [duplicate literal removal 91]
130. strong(X0) | ~brave(X0) | ~calm(X0) [duplicate literal removal 93]
226. ~brave(X0) | ~calm(X0) [subsumption resolution 130,76]
227. calm(X0) | ~brave(X0) [subsumption resolution 88,75]
228. ~brave(X0) [subsumption resolution 227,226]
282. ~strong(mary) [resolution 76,126]
285. brave(mary) [resolution 129,282]
286. $false [subsumption resolution 285,228]
% SZS output end Proof for 2595637204021357882979072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not kind or patient then someone is both not generous and not quiet and vice versa. If someone is strong or not patient then someone is not funny and vice versa. Everyone who is happy is patient or not calm and vice versa. If fred is either not brave or not funny then paul is both patient and not creative and vice versa. If susan is wise then someone is strong. If someone is both not generous and not creative then mary is funny or not calm. If someone is not rich or rich then someone is both rich and funny. If mary is both not funny and generous then susan is rich and vice versa. Everyone who is either wise or not calm is not quiet and vice versa. If someone is either tall or quiet then paul is both happy and not old and vice versa. If someone is not quiet or strong then someone is both kind and not kind. Everyone who is both not calm and not rich is not funny or not kind. Everyone who is either not rich or generous is both humble and not generous. If someone is calm or not kind then mary is brave and vice versa. If someone is either kind or not funny then lucy is tall. Fred is both not kind and not strong. Someone is both not happy and not generous. Mary is either not calm or quiet. Fred is not kind or creative. Someone is creative or humble. | Fred is not quiet. | contradiction | (((~kind(susan)|patient(susan)))<=>(?[X]:((~generous(X)&~quiet(X)))))&
((?[X]:((strong(X)|~patient(X))))<=>(?[X]:(~funny(X))))&
(![X]:(happy(X)<=>(patient(X)|~calm(X))))&
(((~brave(fred)<~>~funny(fred)))<=>((patient(paul)&~creative(paul))))&
((wise(susan))=>(?[X]:(strong(X))))&
((?[X]:((~generous(X)&~creative(X))))=>((funny(mary)|~calm(mary))))&
((?[X]:((~rich(X)|rich(X))))=>(?[X]:((rich(X)&funny(X)))))&
(((~funny(mary)&generous(mary)))<=>(rich(susan)))&
(![X]:((wise(X)<~>~calm(X))<=>~quiet(X)))&
((?[X]:((tall(X)<~>quiet(X))))<=>((happy(paul)&~old(paul))))&
((?[X]:((~quiet(X)|strong(X))))=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((~calm(X)&~rich(X))=>(~funny(X)|~kind(X))))&
(![X]:((~rich(X)<~>generous(X))=>(humble(X)&~generous(X))))&
((?[X]:((calm(X)|~kind(X))))<=>(brave(mary)))&
((?[X]:((kind(X)<~>~funny(X))))=>(tall(lucy)))&
((~kind(fred)&~strong(fred)))&
(?[X]:((~happy(X)&~generous(X))))&
((~calm(mary)<~>quiet(mary)))&
((~kind(fred)|creative(fred)))&
(?[X]:((creative(X)|humble(X)))) | ~quiet(fred) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6484309739265084654542979
% SZS output start Proof for 6484309739265084654542979
11. ? [X0] : (strong(X0) | ~quiet(X0)) => ? [X0] : (~kind(X0) & kind(X0)) [input p10]
21. ~quiet(fred) [input hypothesis]
24. ? [X0] : (strong(X0) | ~quiet(X0)) => ? [X1] : (~kind(X1) & kind(X1)) [rectify 11]
31. ? [X1] : (~kind(X1) & kind(X1)) | ! [X0] : (~strong(X0) & quiet(X0)) [ennf transformation 24]
63. ? [X0] : (~kind(X0) & kind(X0)) | ! [X1] : (~strong(X1) & quiet(X1)) [rectify 31]
64. ? [X0] : (~kind(X0) & kind(X0)) => (~kind(sK6) & kind(sK6)) [choice axiom]
65. (~kind(sK6) & kind(sK6)) | ! [X1] : (~strong(X1) & quiet(X1)) [skolemisation 63,64]
111. kind(sK6) | quiet(X1) [cnf transformation 65]
113. ~kind(sK6) | quiet(X1) [cnf transformation 65]
130. ~quiet(fred) [cnf transformation 21]
281. 33 <=> kind(sK6) [avatar definition]
286. 34 <=> ! [X1] : quiet(X1) [avatar definition]
287. quiet(X1) <- (34) [avatar component clause 286]
288. 34 | ~33 [avatar split clause 113,281,286]
290. 34 | 33 [avatar split clause 111,281,286]
338. $false <- (34) [resolution 287,130]
339. ~34 [avatar contradiction clause 338]
340. $false [avatar sat refutation 288,290,339]
% SZS output end Proof for 6484309739265084654542979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not tall or tall then alice is not kind and vice versa.
If someone is not quiet then someone is not old or not quiet.
Everyone who is either not generous or not wise is either curious or brave and vice versa.
Everyone who is not quiet or not kind is both not brave and not creative.
Everyone who is both funny and old is humble.
If someone is both patient and not quiet then someone is either humble or not generous and vice versa.
Everyone who is both not happy and tall is either humble or tall and vice versa.
If susan is not calm then mary is quiet or rich and vice versa.
Everyone who is patient is both brave and wise and vice versa.
Everyone who is brave is curious.
Everyone who is both not patient and quiet is both curious and not humble.
Everyone who is creative or not funny is calm.
If mary is tall or not curious then someone is not patient and vice versa.
If someone is brave or calm then someone is either brave or curious and vice versa.
If paul is either not wise or not creative then susan is either creative or not kind and vice versa.
Everyone who is both not quiet and not funny is not curious and vice versa.
Mary is either kind or not old.
Paul is humble.
Someone is either brave or not kind.
Someone is not wise.
Fred is either calm or not rich.
Lucy is either not tall or old.
Someone is both rich and old.
Paul is not calm or not old. | Paul is not old. | neutral | (((~tall(lucy)<~>tall(lucy)))<=>(~kind(alice)))&
((?[X]:(~quiet(X)))=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:((~generous(X)<~>~wise(X))<=>(curious(X)<~>brave(X))))&
(![X]:((~quiet(X)|~kind(X))=>(~brave(X)&~creative(X))))&
(![X]:((funny(X)&old(X))=>humble(X)))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:((humble(X)<~>~generous(X)))))&
(![X]:((~happy(X)&tall(X))<=>(humble(X)<~>tall(X))))&
((~calm(susan))<=>((quiet(mary)|rich(mary))))&
(![X]:(patient(X)<=>(brave(X)&wise(X))))&
(![X]:(brave(X)=>curious(X)))&
(![X]:((~patient(X)&quiet(X))=>(curious(X)&~humble(X))))&
(![X]:((creative(X)|~funny(X))=>calm(X)))&
(((tall(mary)|~curious(mary)))<=>(?[X]:(~patient(X))))&
((?[X]:((brave(X)|calm(X))))<=>(?[X]:((brave(X)<~>curious(X)))))&
(((~wise(paul)<~>~creative(paul)))<=>((creative(susan)<~>~kind(susan))))&
(![X]:((~quiet(X)&~funny(X))<=>~curious(X)))&
((kind(mary)<~>~old(mary)))&
(humble(paul))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:(~wise(X)))&
((calm(fred)<~>~rich(fred)))&
((~tall(lucy)<~>old(lucy)))&
(?[X]:((rich(X)&old(X))))&
((~calm(paul)|~old(paul))) | ~old(paul) | [] | null | 0 |
If mary is either not wise or humble then someone is both not old and not generous.
If someone is both generous and not funny then mary is both not curious and not funny.
Everyone who is funny or not tall is both rich and strong.
Everyone who is both curious and creative is old and vice versa.
Everyone who is either creative or not curious is not brave and vice versa.
Everyone who is both strong and tall is not funny.
If john is either not rich or calm then someone is both tall and not funny and vice versa.
Everyone who is calm or creative is both brave and rich.
Everyone who is either patient or not strong is either not old or not humble.
Everyone who is both patient and not funny is either wise or not old and vice versa.
If alice is not quiet or happy then someone is not brave or not curious and vice versa.
Everyone who is rich or tall is either kind or not tall.
If someone is both happy and creative then someone is not old or not funny and vice versa.
If fred is both curious and not wise then someone is kind.
If someone is quiet then john is not calm and vice versa.
Everyone who is generous is either creative or not rich and vice versa.
Paul is not strong.
Paul is either not calm or curious.
Lucy is both not patient and rich.
Someone is not generous or not rich.
Someone is both not kind and funny.
Lucy is both not curious and creative.
Lucy is not rich or not patient.
Someone is not kind or rich. | Lucy is generous. | entailment | (((~wise(mary)<~>humble(mary)))=>(?[X]:((~old(X)&~generous(X)))))&
((?[X]:((generous(X)&~funny(X))))=>((~curious(mary)&~funny(mary))))&
(![X]:((funny(X)|~tall(X))=>(rich(X)&strong(X))))&
(![X]:((curious(X)&creative(X))<=>old(X)))&
(![X]:((creative(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((strong(X)&tall(X))=>~funny(X)))&
(((~rich(john)<~>calm(john)))<=>(?[X]:((tall(X)&~funny(X)))))&
(![X]:((calm(X)|creative(X))=>(brave(X)&rich(X))))&
(![X]:((patient(X)<~>~strong(X))=>(~old(X)<~>~humble(X))))&
(![X]:((patient(X)&~funny(X))<=>(wise(X)<~>~old(X))))&
(((~quiet(alice)|happy(alice)))<=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:((rich(X)|tall(X))=>(kind(X)<~>~tall(X))))&
((?[X]:((happy(X)&creative(X))))<=>(?[X]:((~old(X)|~funny(X)))))&
(((curious(fred)&~wise(fred)))=>(?[X]:(kind(X))))&
((?[X]:(quiet(X)))<=>(~calm(john)))&
(![X]:(generous(X)<=>(creative(X)<~>~rich(X))))&
(~strong(paul))&
((~calm(paul)<~>curious(paul)))&
((~patient(lucy)&rich(lucy)))&
(?[X]:((~generous(X)|~rich(X))))&
(?[X]:((~kind(X)&funny(X))))&
((~curious(lucy)&creative(lucy)))&
((~rich(lucy)|~patient(lucy)))&
(?[X]:((~kind(X)|rich(X)))) | generous(lucy) | [
"p7",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2503550286981178363958385
% SZS output start Proof for 2503550286981178363958385
8. ! [X0] : ((creative(X0) | calm(X0)) => (rich(X0) & brave(X0))) [input p7]
16. ! [X0] : (generous(X0) <=> (creative(X0) <~> ~rich(X0))) [input p15]
22. creative(lucy) & ~curious(lucy) [input p21]
25. ~generous(lucy) [input hypothesis]
27. ! [X0] : ((creative(X0) <~> ~rich(X0)) => generous(X0)) [unused predicate definition removal 16]
33. ! [X0] : ((rich(X0) & brave(X0)) | (~creative(X0) & ~calm(X0))) [ennf transformation 8]
38. ! [X0] : (generous(X0) | (creative(X0) <=> ~rich(X0))) [ennf transformation 27]
69. ! [X0] : (generous(X0) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 38]
104. ~creative(X0) | rich(X0) [cnf transformation 33]
131. generous(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 69]
142. creative(lucy) [cnf transformation 22]
145. ~generous(lucy) [cnf transformation 25]
288. ~creative(X0) | generous(X0) [subsumption resolution 131,104]
352. generous(lucy) [resolution 288,142]
354. $false [subsumption resolution 352,145]
% SZS output end Proof for 2503550286981178363958385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is kind is not generous.
Everyone who is humble or curious is kind.
Everyone who is both creative and not patient is either not happy or calm.
If someone is both not tall and creative then someone is strong or old.
Everyone who is both not creative and tall is not happy and vice versa.
If alice is not curious or not brave then someone is either not quiet or not strong and vice versa.
If someone is not curious then susan is either not tall or curious and vice versa.
Everyone who is not quiet is either humble or not quiet.
Everyone who is both not wise and curious is both not old and not brave.
If someone is both humble and not rich then someone is not patient.
Everyone who is not strong or humble is not quiet.
If lucy is humble or not patient then someone is both tall and wise and vice versa.
Everyone who is calm is not humble or curious.
If alice is not calm or kind then someone is both creative and not tall.
Everyone who is not old is not patient and vice versa.
If someone is not quiet then someone is both not wise and generous and vice versa.
Someone is not strong or old.
Someone is both not brave and not patient.
John is both kind and not happy.
Someone is either tall or strong.
Someone is not curious or not rich.
John is curious or not happy.
Someone is not kind or patient. | Alice is curious. | neutral | (![X]:(kind(X)=>~generous(X)))&
(![X]:((humble(X)|curious(X))=>kind(X)))&
(![X]:((creative(X)&~patient(X))=>(~happy(X)<~>calm(X))))&
((?[X]:((~tall(X)&creative(X))))=>(?[X]:((strong(X)|old(X)))))&
(![X]:((~creative(X)&tall(X))<=>~happy(X)))&
(((~curious(alice)|~brave(alice)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
((?[X]:(~curious(X)))<=>((~tall(susan)<~>curious(susan))))&
(![X]:(~quiet(X)=>(humble(X)<~>~quiet(X))))&
(![X]:((~wise(X)&curious(X))=>(~old(X)&~brave(X))))&
((?[X]:((humble(X)&~rich(X))))=>(?[X]:(~patient(X))))&
(![X]:((~strong(X)|humble(X))=>~quiet(X)))&
(((humble(lucy)|~patient(lucy)))<=>(?[X]:((tall(X)&wise(X)))))&
(![X]:(calm(X)=>(~humble(X)|curious(X))))&
(((~calm(alice)|kind(alice)))=>(?[X]:((creative(X)&~tall(X)))))&
(![X]:(~old(X)<=>~patient(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:((~wise(X)&generous(X)))))&
(?[X]:((~strong(X)|old(X))))&
(?[X]:((~brave(X)&~patient(X))))&
((kind(john)&~happy(john)))&
(?[X]:((tall(X)<~>strong(X))))&
(?[X]:((~curious(X)|~rich(X))))&
((curious(john)|~happy(john)))&
(?[X]:((~kind(X)|patient(X)))) | curious(alice) | [] | null | 0 |
If john is humble or funny then someone is patient and vice versa.
If fred is funny or not old then someone is old and vice versa.
Everyone who is not calm is happy or not humble.
Everyone who is either rich or not tall is not funny and vice versa.
Everyone who is either not rich or old is not calm or not happy and vice versa.
Everyone who is either not calm or not old is both not kind and curious.
Everyone who is both not generous and not kind is generous.
Everyone who is both not strong and not brave is either not tall or not brave.
Everyone who is both not creative and not calm is funny or not patient and vice versa.
If someone is both not generous and not funny then someone is either generous or not funny.
If john is not calm then someone is either generous or happy.
Everyone who is both patient and not humble is strong or not kind and vice versa.
If john is generous or not quiet then mary is both not kind and quiet.
Everyone who is both not brave and generous is funny or not generous and vice versa.
Everyone who is both not wise and not tall is tall or not wise and vice versa.
Everyone who is both strong and not calm is not quiet.
Someone is not tall or old.
Someone is wise or not strong.
Fred is humble or wise.
Mary is not kind or not curious.
John is both not humble and old. | Fred is not creative. | neutral | (((humble(john)|funny(john)))<=>(?[X]:(patient(X))))&
(((funny(fred)|~old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~calm(X)=>(happy(X)|~humble(X))))&
(![X]:((rich(X)<~>~tall(X))<=>~funny(X)))&
(![X]:((~rich(X)<~>old(X))<=>(~calm(X)|~happy(X))))&
(![X]:((~calm(X)<~>~old(X))=>(~kind(X)&curious(X))))&
(![X]:((~generous(X)&~kind(X))=>generous(X)))&
(![X]:((~strong(X)&~brave(X))=>(~tall(X)<~>~brave(X))))&
(![X]:((~creative(X)&~calm(X))<=>(funny(X)|~patient(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:((generous(X)<~>~funny(X)))))&
((~calm(john))=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:((patient(X)&~humble(X))<=>(strong(X)|~kind(X))))&
(((generous(john)|~quiet(john)))=>((~kind(mary)&quiet(mary))))&
(![X]:((~brave(X)&generous(X))<=>(funny(X)|~generous(X))))&
(![X]:((~wise(X)&~tall(X))<=>(tall(X)|~wise(X))))&
(![X]:((strong(X)&~calm(X))=>~quiet(X)))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((wise(X)|~strong(X))))&
((humble(fred)|wise(fred)))&
((~kind(mary)|~curious(mary)))&
((~humble(john)&old(john))) | ~creative(fred) | [] | null | 0 |
Everyone who is not old is both wise and not wise.
If john is not calm then mary is humble.
Everyone who is either not rich or calm is either not funny or quiet.
Everyone who is both not generous and tall is brave and vice versa.
If lucy is not happy or funny then john is both humble and happy and vice versa.
Everyone who is both funny and brave is either curious or generous and vice versa.
Everyone who is either strong or not old is either not happy or not humble and vice versa.
Everyone who is both wise and happy is curious and vice versa.
If john is not old or not rich then someone is both not creative and not kind and vice versa.
If someone is either wise or rich then someone is both kind and humble and vice versa.
Everyone who is both wise and tall is either kind or not creative and vice versa.
If someone is either quiet or generous then paul is not creative.
If paul is both not rich and not strong then someone is either creative or not generous.
If someone is happy or brave then john is either funny or humble and vice versa.
If someone is wise or not humble then fred is both creative and not strong and vice versa.
Everyone who is either funny or quiet is both rich and not patient and vice versa.
Someone is both quiet and wise.
Alice is either not brave or curious.
Someone is not calm or quiet.
Paul is either wise or not humble.
Someone is rich or happy.
Someone is either not patient or generous.
Mary is both brave and old.
Fred is not wise. | Paul is old. | entailment | (![X]:(~old(X)=>(wise(X)&~wise(X))))&
((~calm(john))=>(humble(mary)))&
(![X]:((~rich(X)<~>calm(X))=>(~funny(X)<~>quiet(X))))&
(![X]:((~generous(X)&tall(X))<=>brave(X)))&
(((~happy(lucy)|funny(lucy)))<=>((humble(john)&happy(john))))&
(![X]:((funny(X)&brave(X))<=>(curious(X)<~>generous(X))))&
(![X]:((strong(X)<~>~old(X))<=>(~happy(X)<~>~humble(X))))&
(![X]:((wise(X)&happy(X))<=>curious(X)))&
(((~old(john)|~rich(john)))<=>(?[X]:((~creative(X)&~kind(X)))))&
((?[X]:((wise(X)<~>rich(X))))<=>(?[X]:((kind(X)&humble(X)))))&
(![X]:((wise(X)&tall(X))<=>(kind(X)<~>~creative(X))))&
((?[X]:((quiet(X)<~>generous(X))))=>(~creative(paul)))&
(((~rich(paul)&~strong(paul)))=>(?[X]:((creative(X)<~>~generous(X)))))&
((?[X]:((happy(X)|brave(X))))<=>((funny(john)<~>humble(john))))&
((?[X]:((wise(X)|~humble(X))))<=>((creative(fred)&~strong(fred))))&
(![X]:((funny(X)<~>quiet(X))<=>(rich(X)&~patient(X))))&
(?[X]:((quiet(X)&wise(X))))&
((~brave(alice)<~>curious(alice)))&
(?[X]:((~calm(X)|quiet(X))))&
((wise(paul)<~>~humble(paul)))&
(?[X]:((rich(X)|happy(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
((brave(mary)&old(mary)))&
(~wise(fred)) | old(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 4836434806102090149504439
% SZS output start Proof for 4836434806102090149504439
1. ! [X0] : (~old(X0) => (~wise(X0) & wise(X0))) [input p0]
25. ~old(paul) [input hypothesis]
27. ! [X0] : ((~wise(X0) & wise(X0)) | old(X0)) [ennf transformation 1]
81. wise(X0) | old(X0) [cnf transformation 27]
82. ~wise(X0) | old(X0) [cnf transformation 27]
164. ~old(paul) [cnf transformation 25]
165. old(X0) [subsumption resolution 81,82]
381. $false [subsumption resolution 164,165]
% SZS output end Proof for 4836434806102090149504439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not happy and not old then john is funny or patient and vice versa.
If someone is either generous or not old then someone is not generous and vice versa.
Everyone who is either not generous or quiet is not wise or not kind and vice versa.
Everyone who is not funny is both not tall and brave.
Everyone who is both strong and not generous is calm or not old and vice versa.
Everyone who is brave or not rich is generous or old.
If john is both not tall and brave then alice is not kind or old and vice versa.
Everyone who is not curious is either patient or creative and vice versa.
Everyone who is not calm or kind is both not humble and creative and vice versa.
If john is either not funny or curious then john is either creative or generous and vice versa.
Everyone who is not patient or not creative is humble and vice versa.
If susan is either not curious or curious then alice is not rich.
If someone is both happy and not strong then someone is quiet and vice versa.
Everyone who is patient or creative is tall or not brave.
If someone is either happy or kind then alice is not curious or creative and vice versa.
Fred is both tall and funny.
Fred is either not funny or calm.
Alice is both brave and curious.
Someone is quiet or not humble.
Someone is not humble.
Mary is not kind or not patient.
John is curious or old.
Paul is either not strong or kind. | Mary is humble. | neutral | (((~happy(lucy)&~old(lucy)))<=>((funny(john)|patient(john))))&
((?[X]:((generous(X)<~>~old(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(~wise(X)|~kind(X))))&
(![X]:(~funny(X)=>(~tall(X)&brave(X))))&
(![X]:((strong(X)&~generous(X))<=>(calm(X)|~old(X))))&
(![X]:((brave(X)|~rich(X))=>(generous(X)|old(X))))&
(((~tall(john)&brave(john)))<=>((~kind(alice)|old(alice))))&
(![X]:(~curious(X)<=>(patient(X)<~>creative(X))))&
(![X]:((~calm(X)|kind(X))<=>(~humble(X)&creative(X))))&
(((~funny(john)<~>curious(john)))<=>((creative(john)<~>generous(john))))&
(![X]:((~patient(X)|~creative(X))<=>humble(X)))&
(((~curious(susan)<~>curious(susan)))=>(~rich(alice)))&
((?[X]:((happy(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
(![X]:((patient(X)|creative(X))=>(tall(X)|~brave(X))))&
((?[X]:((happy(X)<~>kind(X))))<=>((~curious(alice)|creative(alice))))&
((tall(fred)&funny(fred)))&
((~funny(fred)<~>calm(fred)))&
((brave(alice)&curious(alice)))&
(?[X]:((quiet(X)|~humble(X))))&
(?[X]:(~humble(X)))&
((~kind(mary)|~patient(mary)))&
((curious(john)|old(john)))&
((~strong(paul)<~>kind(paul))) | humble(mary) | [] | null | 0 |
If someone is not funny or not generous then someone is both not rich and calm.
Everyone who is kind is both curious and not rich.
If someone is both not calm and creative then fred is not humble or brave.
Everyone who is not calm is funny or creative.
Everyone who is happy is either not humble or rich.
Everyone who is not wise is both not creative and old and vice versa.
If someone is both funny and not quiet then someone is both not generous and curious and vice versa.
Everyone who is either not wise or calm is calm and vice versa.
Everyone who is either creative or not creative is both not creative and not happy and vice versa.
Everyone who is calm or not strong is tall and vice versa.
Everyone who is either curious or not quiet is not brave or not curious and vice versa.
If someone is brave or not generous then john is either not creative or not humble and vice versa.
Everyone who is not calm or quiet is both not strong and not calm and vice versa.
Everyone who is not tall or wise is not curious or happy and vice versa.
Someone is not rich.
Fred is quiet or patient.
Mary is either not calm or tall.
Someone is either not quiet or not brave. | Mary is quiet. | contradiction | ((?[X]:((~funny(X)|~generous(X))))=>(?[X]:((~rich(X)&calm(X)))))&
(![X]:(kind(X)=>(curious(X)&~rich(X))))&
((?[X]:((~calm(X)&creative(X))))=>((~humble(fred)|brave(fred))))&
(![X]:(~calm(X)=>(funny(X)|creative(X))))&
(![X]:(happy(X)=>(~humble(X)<~>rich(X))))&
(![X]:(~wise(X)<=>(~creative(X)&old(X))))&
((?[X]:((funny(X)&~quiet(X))))<=>(?[X]:((~generous(X)&curious(X)))))&
(![X]:((~wise(X)<~>calm(X))<=>calm(X)))&
(![X]:((creative(X)<~>~creative(X))<=>(~creative(X)&~happy(X))))&
(![X]:((calm(X)|~strong(X))<=>tall(X)))&
(![X]:((curious(X)<~>~quiet(X))<=>(~brave(X)|~curious(X))))&
((?[X]:((brave(X)|~generous(X))))<=>((~creative(john)<~>~humble(john))))&
(![X]:((~calm(X)|quiet(X))<=>(~strong(X)&~calm(X))))&
(![X]:((~tall(X)|wise(X))<=>(~curious(X)|happy(X))))&
(?[X]:(~rich(X)))&
((quiet(fred)|patient(fred)))&
((~calm(mary)<~>tall(mary)))&
(?[X]:((~quiet(X)<~>~brave(X)))) | quiet(mary) | [
"p9",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3532676266608155749680734
% SZS output start Proof for 3532676266608155749680734
10. ! [X0] : ((~strong(X0) | calm(X0)) <=> tall(X0)) [input p9]
13. ! [X0] : ((quiet(X0) | ~calm(X0)) <=> (~calm(X0) & ~strong(X0))) [input p12]
17. ~calm(mary) <~> tall(mary) [input p16]
19. quiet(mary) [input hypothesis]
44. ! [X0] : (((~strong(X0) | calm(X0)) | ~tall(X0)) & (tall(X0) | (strong(X0) & ~calm(X0)))) [nnf transformation 10]
45. ! [X0] : ((~strong(X0) | calm(X0) | ~tall(X0)) & (tall(X0) | (strong(X0) & ~calm(X0)))) [flattening 44]
52. ! [X0] : (((quiet(X0) | ~calm(X0)) | (calm(X0) | strong(X0))) & ((~calm(X0) & ~strong(X0)) | (~quiet(X0) & calm(X0)))) [nnf transformation 13]
53. ! [X0] : ((quiet(X0) | ~calm(X0) | calm(X0) | strong(X0)) & ((~calm(X0) & ~strong(X0)) | (~quiet(X0) & calm(X0)))) [flattening 52]
58. (~tall(mary) | calm(mary)) & (tall(mary) | ~calm(mary)) [nnf transformation 17]
88. tall(X0) | strong(X0) [cnf transformation 45]
102. ~strong(X0) | calm(X0) [cnf transformation 53]
105. ~quiet(X0) | ~calm(X0) [cnf transformation 53]
113. ~tall(mary) | calm(mary) [cnf transformation 58]
116. quiet(mary) [cnf transformation 19]
210. 18 <=> calm(mary) [avatar definition]
212. calm(mary) <- (18) [avatar component clause 210]
214. 19 <=> tall(mary) [avatar definition]
216. ~tall(mary) <- (~19) [avatar component clause 214]
217. 18 | ~19 [avatar split clause 113,214,210]
228. strong(mary) <- (~19) [resolution 88,216]
229. calm(mary) <- (~19) [resolution 102,228]
230. 18 | 19 [avatar split clause 229,214,210]
235. ~calm(mary) [resolution 105,116]
237. $false <- (18) [subsumption resolution 235,212]
238. ~18 [avatar contradiction clause 237]
239. $false [avatar sat refutation 217,230,238]
% SZS output end Proof for 3532676266608155749680734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or happy is either not kind or not calm and vice versa.
Everyone who is both not tall and curious is either not brave or old and vice versa.
If someone is not calm then someone is not tall or wise and vice versa.
If john is rich then john is either brave or not quiet.
Everyone who is either not kind or not wise is either wise or not quiet and vice versa.
Everyone who is both not patient and not wise is not funny or rich.
Everyone who is both not curious and not calm is not creative and vice versa.
Everyone who is either not calm or not happy is not patient.
If paul is not kind or curious then someone is brave or not kind and vice versa.
If alice is not tall then someone is brave.
Everyone who is rich or calm is both not funny and not tall.
Everyone who is not quiet is patient.
If susan is both not wise and brave then fred is strong or wise.
If susan is both not generous and quiet then someone is not funny.
Everyone who is both not happy and brave is curious and vice versa.
Fred is either not old or tall.
Someone is not quiet.
Someone is not generous.
Mary is patient.
Someone is both brave and kind.
Someone is both humble and not patient.
Someone is happy. | John is brave. | neutral | (![X]:((old(X)<~>happy(X))<=>(~kind(X)<~>~calm(X))))&
(![X]:((~tall(X)&curious(X))<=>(~brave(X)<~>old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)|wise(X)))))&
((rich(john))=>((brave(john)<~>~quiet(john))))&
(![X]:((~kind(X)<~>~wise(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~patient(X)&~wise(X))=>(~funny(X)|rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>~creative(X)))&
(![X]:((~calm(X)<~>~happy(X))=>~patient(X)))&
(((~kind(paul)|curious(paul)))<=>(?[X]:((brave(X)|~kind(X)))))&
((~tall(alice))=>(?[X]:(brave(X))))&
(![X]:((rich(X)|calm(X))=>(~funny(X)&~tall(X))))&
(![X]:(~quiet(X)=>patient(X)))&
(((~wise(susan)&brave(susan)))=>((strong(fred)|wise(fred))))&
(((~generous(susan)&quiet(susan)))=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)&brave(X))<=>curious(X)))&
((~old(fred)<~>tall(fred)))&
(?[X]:(~quiet(X)))&
(?[X]:(~generous(X)))&
(patient(mary))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:(happy(X))) | brave(john) | [] | null | 0 |
Everyone who is old or creative is not humble.
If someone is either funny or strong then paul is not strong or not funny and vice versa.
Everyone who is tall or not tall is brave.
Everyone who is not happy is not kind.
Everyone who is both not calm and curious is both wise and tall.
If someone is both generous and not happy then someone is not strong.
If john is both not happy and happy then someone is kind or tall.
If fred is both not patient and brave then someone is both not quiet and wise.
Everyone who is not wise or not curious is not humble or quiet.
If fred is either not strong or not tall then fred is both funny and not brave and vice versa.
If someone is both generous and funny then someone is both not brave and curious.
If someone is either not funny or funny then someone is not patient and vice versa.
Everyone who is calm or not patient is not calm.
Everyone who is either curious or calm is both not funny and not tall.
If someone is calm or not humble then someone is both creative and curious and vice versa.
Everyone who is not humble is strong or rich and vice versa.
Lucy is either happy or not happy.
John is tall or not calm.
Alice is not quiet or not funny.
Alice is either old or not happy.
Lucy is either happy or not kind.
Lucy is funny or not old. | Fred is not strong. | entailment | (![X]:((old(X)|creative(X))=>~humble(X)))&
((?[X]:((funny(X)<~>strong(X))))<=>((~strong(paul)|~funny(paul))))&
(![X]:((tall(X)|~tall(X))=>brave(X)))&
(![X]:(~happy(X)=>~kind(X)))&
(![X]:((~calm(X)&curious(X))=>(wise(X)&tall(X))))&
((?[X]:((generous(X)&~happy(X))))=>(?[X]:(~strong(X))))&
(((~happy(john)&happy(john)))=>(?[X]:((kind(X)|tall(X)))))&
(((~patient(fred)&brave(fred)))=>(?[X]:((~quiet(X)&wise(X)))))&
(![X]:((~wise(X)|~curious(X))=>(~humble(X)|quiet(X))))&
(((~strong(fred)<~>~tall(fred)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((generous(X)&funny(X))))=>(?[X]:((~brave(X)&curious(X)))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:(~patient(X))))&
(![X]:((calm(X)|~patient(X))=>~calm(X)))&
(![X]:((curious(X)<~>calm(X))=>(~funny(X)&~tall(X))))&
((?[X]:((calm(X)|~humble(X))))<=>(?[X]:((creative(X)&curious(X)))))&
(![X]:(~humble(X)<=>(strong(X)|rich(X))))&
((happy(lucy)<~>~happy(lucy)))&
((tall(john)|~calm(john)))&
((~quiet(alice)|~funny(alice)))&
((old(alice)<~>~happy(alice)))&
((happy(lucy)<~>~kind(lucy)))&
((funny(lucy)|~old(lucy))) | ~strong(fred) | [
"p4",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 878682216276406728800433
% SZS output start Proof for 878682216276406728800433
5. ! [X0] : ((curious(X0) & ~calm(X0)) => (tall(X0) & wise(X0))) [input p4]
13. ! [X0] : ((~patient(X0) | calm(X0)) => ~calm(X0)) [input p12]
14. ! [X0] : ((curious(X0) <~> calm(X0)) => (~tall(X0) & ~funny(X0))) [input p13]
15. ? [X0] : (~humble(X0) | calm(X0)) <=> ? [X0] : (curious(X0) & creative(X0)) [input p14]
16. ! [X0] : (~humble(X0) <=> (rich(X0) | strong(X0))) [input p15]
23. strong(fred) [input hypothesis]
27. ? [X0] : (~humble(X0) | calm(X0)) <=> ? [X1] : (curious(X1) & creative(X1)) [rectify 15]
32. ! [X0] : ((curious(X0) & ~calm(X0)) => tall(X0)) [pure predicate removal 5]
36. ! [X0] : (tall(X0) | (~curious(X0) | calm(X0))) [ennf transformation 32]
37. ! [X0] : (tall(X0) | ~curious(X0) | calm(X0)) [flattening 36]
44. ! [X0] : (~calm(X0) | (patient(X0) & ~calm(X0))) [ennf transformation 13]
45. ! [X0] : ((~tall(X0) & ~funny(X0)) | (curious(X0) <=> calm(X0))) [ennf transformation 14]
62. ! [X0] : ((~tall(X0) & ~funny(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) [nnf transformation 45]
63. (? [X0] : (~humble(X0) | calm(X0)) | ! [X1] : (~curious(X1) | ~creative(X1))) & (? [X1] : (curious(X1) & creative(X1)) | ! [X0] : (humble(X0) & ~calm(X0))) [nnf transformation 27]
64. (? [X0] : (~humble(X0) | calm(X0)) | ! [X1] : (~curious(X1) | ~creative(X1))) & (? [X2] : (curious(X2) & creative(X2)) | ! [X3] : (humble(X3) & ~calm(X3))) [rectify 63]
65. ? [X0] : (~humble(X0) | calm(X0)) => (~humble(sK5) | calm(sK5)) [choice axiom]
66. ? [X2] : (curious(X2) & creative(X2)) => (curious(sK6) & creative(sK6)) [choice axiom]
67. ((~humble(sK5) | calm(sK5)) | ! [X1] : (~curious(X1) | ~creative(X1))) & ((curious(sK6) & creative(sK6)) | ! [X3] : (humble(X3) & ~calm(X3))) [skolemisation 64,66,65]
68. ! [X0] : ((~humble(X0) | (~rich(X0) & ~strong(X0))) & ((rich(X0) | strong(X0)) | humble(X0))) [nnf transformation 16]
69. ! [X0] : ((~humble(X0) | (~rich(X0) & ~strong(X0))) & (rich(X0) | strong(X0) | humble(X0))) [flattening 68]
84. ~curious(X0) | tall(X0) | calm(X0) [cnf transformation 37]
98. ~calm(X0) | ~calm(X0) [cnf transformation 44]
102. ~tall(X0) | calm(X0) | ~curious(X0) [cnf transformation 62]
107. curious(sK6) | humble(X3) [cnf transformation 67]
110. ~strong(X0) | ~humble(X0) [cnf transformation 69]
121. strong(fred) [cnf transformation 23]
122. ~calm(X0) [duplicate literal removal 98]
170. 10 <=> strong(fred) [avatar definition]
171. strong(fred) <- (10) [avatar component clause 170]
194. ~curious(X0) | ~tall(X0) [subsumption resolution 102,122]
206. 17 <=> ! [X3] : humble(X3) [avatar definition]
207. humble(X3) <- (17) [avatar component clause 206]
209. 18 <=> curious(sK6) [avatar definition]
211. curious(sK6) <- (18) [avatar component clause 209]
212. 17 | 18 [avatar split clause 107,209,206]
255. 10 [avatar split clause 121,170]
260. ~humble(fred) <- (10) [resolution 110,171]
261. $false <- (10, 17) [subsumption resolution 260,207]
262. ~10 | ~17 [avatar contradiction clause 261]
265. ~tall(sK6) <- (18) [resolution 194,211]
270. tall(sK6) | calm(sK6) <- (18) [resolution 84,211]
271. calm(sK6) <- (18) [subsumption resolution 270,265]
272. $false <- (18) [subsumption resolution 271,122]
273. ~18 [avatar contradiction clause 272]
274. $false [avatar sat refutation 212,255,262,273]
% SZS output end Proof for 878682216276406728800433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or rich is both patient and not patient and vice versa.
If someone is generous or not strong then fred is both not rich and not happy.
Everyone who is either not generous or calm is either strong or quiet and vice versa.
Everyone who is happy is both quiet and not funny and vice versa.
If someone is creative then someone is both rich and creative and vice versa.
Everyone who is not kind or not curious is not quiet and vice versa.
Everyone who is not quiet or not generous is not brave or not patient and vice versa.
If someone is either old or kind then someone is not happy or not calm.
If lucy is not old then someone is both not old and patient and vice versa.
If john is either not brave or creative then someone is generous.
If susan is either kind or tall then paul is both wise and quiet and vice versa.
Everyone who is not happy is strong and vice versa.
If john is not generous then fred is either not curious or not patient.
Everyone who is either not kind or not rich is either happy or wise.
Everyone who is either curious or patient is not tall and vice versa.
Everyone who is either not funny or kind is rich or not old and vice versa.
Someone is either old or not humble.
John is curious.
Lucy is both quiet and tall.
Paul is happy.
Someone is creative or old.
Lucy is not old or not tall.
Alice is either happy or quiet. | Alice is brave. | entailment | (![X]:((calm(X)|rich(X))<=>(patient(X)&~patient(X))))&
((?[X]:((generous(X)|~strong(X))))=>((~rich(fred)&~happy(fred))))&
(![X]:((~generous(X)<~>calm(X))<=>(strong(X)<~>quiet(X))))&
(![X]:(happy(X)<=>(quiet(X)&~funny(X))))&
((?[X]:(creative(X)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:((~kind(X)|~curious(X))<=>~quiet(X)))&
(![X]:((~quiet(X)|~generous(X))<=>(~brave(X)|~patient(X))))&
((?[X]:((old(X)<~>kind(X))))=>(?[X]:((~happy(X)|~calm(X)))))&
((~old(lucy))<=>(?[X]:((~old(X)&patient(X)))))&
(((~brave(john)<~>creative(john)))=>(?[X]:(generous(X))))&
(((kind(susan)<~>tall(susan)))<=>((wise(paul)&quiet(paul))))&
(![X]:(~happy(X)<=>strong(X)))&
((~generous(john))=>((~curious(fred)<~>~patient(fred))))&
(![X]:((~kind(X)<~>~rich(X))=>(happy(X)<~>wise(X))))&
(![X]:((curious(X)<~>patient(X))<=>~tall(X)))&
(![X]:((~funny(X)<~>kind(X))<=>(rich(X)|~old(X))))&
(?[X]:((old(X)<~>~humble(X))))&
(curious(john))&
((quiet(lucy)&tall(lucy)))&
(happy(paul))&
(?[X]:((creative(X)|old(X))))&
((~old(lucy)|~tall(lucy)))&
((happy(alice)<~>quiet(alice))) | brave(alice) | [
"p0",
"p2",
"p3",
"p6",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2215748215359940816558397
% SZS output start Proof for 2215748215359940816558397
1. ! [X0] : ((rich(X0) | calm(X0)) <=> (~patient(X0) & patient(X0))) [input p0]
3. ! [X0] : ((~generous(X0) <~> calm(X0)) <=> (strong(X0) <~> quiet(X0))) [input p2]
4. ! [X0] : (happy(X0) <=> (~funny(X0) & quiet(X0))) [input p3]
7. ! [X0] : ((~generous(X0) | ~quiet(X0)) <=> (~patient(X0) | ~brave(X0))) [input p6]
12. ! [X0] : (~happy(X0) <=> strong(X0)) [input p11]
23. happy(alice) <~> quiet(alice) [input p22]
24. ~brave(alice) [input hypothesis]
32. ! [X0] : (((rich(X0) | calm(X0)) | (patient(X0) | ~patient(X0))) & ((~patient(X0) & patient(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 1]
33. ! [X0] : ((rich(X0) | calm(X0) | patient(X0) | ~patient(X0)) & ((~patient(X0) & patient(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 32]
34. ! [X0] : ((((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0)))) & (((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0))))) [nnf transformation 3]
35. ! [X0] : ((happy(X0) | (funny(X0) | ~quiet(X0))) & ((~funny(X0) & quiet(X0)) | ~happy(X0))) [nnf transformation 4]
36. ! [X0] : ((happy(X0) | funny(X0) | ~quiet(X0)) & ((~funny(X0) & quiet(X0)) | ~happy(X0))) [flattening 35]
44. ! [X0] : (((~generous(X0) | ~quiet(X0)) | (patient(X0) & brave(X0))) & ((~patient(X0) | ~brave(X0)) | (generous(X0) & quiet(X0)))) [nnf transformation 7]
45. ! [X0] : ((~generous(X0) | ~quiet(X0) | (patient(X0) & brave(X0))) & (~patient(X0) | ~brave(X0) | (generous(X0) & quiet(X0)))) [flattening 44]
59. ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))) [nnf transformation 12]
70. (~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice)) [nnf transformation 23]
71. patient(X0) | ~calm(X0) [cnf transformation 33]
73. ~patient(X0) | ~calm(X0) [cnf transformation 33]
82. ~quiet(X0) | ~strong(X0) | calm(X0) | generous(X0) [cnf transformation 34]
88. ~happy(X0) | quiet(X0) [cnf transformation 36]
99. ~quiet(X0) | ~generous(X0) | brave(X0) [cnf transformation 45]
114. happy(X0) | strong(X0) [cnf transformation 59]
140. quiet(alice) | happy(alice) [cnf transformation 70]
141. ~quiet(alice) | ~happy(alice) [cnf transformation 70]
142. ~brave(alice) [cnf transformation 24]
144. ~calm(X0) [subsumption resolution 71,73]
159. ~quiet(X0) | ~strong(X0) | generous(X0) [subsumption resolution 82,144]
264. ~happy(alice) [subsumption resolution 141,88]
265. quiet(alice) [subsumption resolution 140,264]
281. strong(alice) [resolution 114,264]
319. ~generous(alice) | brave(alice) [resolution 99,265]
330. ~generous(alice) [subsumption resolution 319,142]
425. ~strong(alice) | generous(alice) [resolution 159,265]
430. generous(alice) [subsumption resolution 425,281]
431. $false [subsumption resolution 430,330]
% SZS output end Proof for 2215748215359940816558397
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not patient is either funny or tall and vice versa.
Everyone who is both kind and not happy is both not brave and not humble and vice versa.
If someone is calm then someone is both not creative and patient and vice versa.
Everyone who is either not calm or calm is tall or not rich.
Everyone who is not calm or generous is not patient or brave.
Everyone who is both not kind and patient is either not creative or not calm and vice versa.
Everyone who is curious or humble is wise or not brave.
Everyone who is either not quiet or generous is both old and not curious and vice versa.
Everyone who is not quiet or not wise is strong.
Everyone who is not kind or not wise is not creative and vice versa.
If fred is tall or not brave then susan is both old and strong and vice versa.
If someone is wise then mary is not creative or not calm.
Everyone who is either not wise or not brave is both quiet and wise and vice versa.
Everyone who is both strong and rich is either not funny or curious and vice versa.
Everyone who is brave or not generous is happy and vice versa.
If john is both strong and not kind then someone is both creative and old.
Mary is either not curious or not brave.
Someone is either kind or not kind.
Mary is either happy or not generous.
Fred is rich.
Someone is either rich or not rich.
John is calm. | Mary is creative. | contradiction | (![X]:((~old(X)&~patient(X))<=>(funny(X)<~>tall(X))))&
(![X]:((kind(X)&~happy(X))<=>(~brave(X)&~humble(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:((~calm(X)<~>calm(X))=>(tall(X)|~rich(X))))&
(![X]:((~calm(X)|generous(X))=>(~patient(X)|brave(X))))&
(![X]:((~kind(X)&patient(X))<=>(~creative(X)<~>~calm(X))))&
(![X]:((curious(X)|humble(X))=>(wise(X)|~brave(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(old(X)&~curious(X))))&
(![X]:((~quiet(X)|~wise(X))=>strong(X)))&
(![X]:((~kind(X)|~wise(X))<=>~creative(X)))&
(((tall(fred)|~brave(fred)))<=>((old(susan)&strong(susan))))&
((?[X]:(wise(X)))=>((~creative(mary)|~calm(mary))))&
(![X]:((~wise(X)<~>~brave(X))<=>(quiet(X)&wise(X))))&
(![X]:((strong(X)&rich(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((brave(X)|~generous(X))<=>happy(X)))&
(((strong(john)&~kind(john)))=>(?[X]:((creative(X)&old(X)))))&
((~curious(mary)<~>~brave(mary)))&
(?[X]:((kind(X)<~>~kind(X))))&
((happy(mary)<~>~generous(mary)))&
(rich(fred))&
(?[X]:((rich(X)<~>~rich(X))))&
(calm(john)) | creative(mary) | [
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1561540580687793302211073
% SZS output start Proof for 1561540580687793302211073
6. ! [X0] : ((patient(X0) & ~kind(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p5]
10. ! [X0] : ((~wise(X0) | ~kind(X0)) <=> ~creative(X0)) [input p9]
12. ? [X0] : wise(X0) => (~calm(mary) | ~creative(mary)) [input p11]
23. creative(mary) [input hypothesis]
32. (~calm(mary) | ~creative(mary)) | ! [X0] : ~wise(X0) [ennf transformation 12]
33. ~calm(mary) | ~creative(mary) | ! [X0] : ~wise(X0) [flattening 32]
46. ! [X0] : (((patient(X0) & ~kind(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (~patient(X0) | kind(X0)))) [nnf transformation 6]
47. ! [X0] : (((patient(X0) & ~kind(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ~patient(X0) | kind(X0))) [flattening 46]
50. ! [X0] : (((~wise(X0) | ~kind(X0)) | creative(X0)) & (~creative(X0) | (wise(X0) & kind(X0)))) [nnf transformation 10]
51. ! [X0] : ((~wise(X0) | ~kind(X0) | creative(X0)) & (~creative(X0) | (wise(X0) & kind(X0)))) [flattening 50]
90. ~creative(X0) | ~kind(X0) | calm(X0) [cnf transformation 47]
103. ~creative(X0) | kind(X0) [cnf transformation 51]
104. ~creative(X0) | wise(X0) [cnf transformation 51]
111. ~calm(mary) | ~creative(mary) | ~wise(X0) [cnf transformation 33]
139. creative(mary) [cnf transformation 23]
188. 10 <=> ! [X0] : ~wise(X0) [avatar definition]
189. ~wise(X0) <- (10) [avatar component clause 188]
191. 11 <=> creative(mary) [avatar definition]
192. creative(mary) <- (11) [avatar component clause 191]
195. 12 <=> calm(mary) [avatar definition]
198. 10 | ~11 | ~12 [avatar split clause 111,195,191,188]
229. 11 [avatar split clause 139,191]
236. kind(mary) <- (11) [resolution 103,192]
237. wise(mary) <- (11) [resolution 104,192]
295. ~kind(mary) | calm(mary) <- (11) [resolution 90,192]
296. calm(mary) <- (11) [subsumption resolution 295,236]
299. 12 | ~11 [avatar split clause 296,191,195]
301. $false <- (10, 11) [resolution 189,237]
302. ~10 | ~11 [avatar contradiction clause 301]
304. $false [avatar sat refutation 198,229,299,302]
% SZS output end Proof for 1561540580687793302211073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then mary is either not curious or humble.
Everyone who is both not tall and kind is wise.
If someone is both quiet and funny then mary is either not wise or not strong.
If someone is kind or not old then mary is either creative or brave and vice versa.
Everyone who is not kind is both creative and not creative.
Everyone who is creative or tall is both happy and not generous.
Everyone who is not wise or not patient is happy or not humble and vice versa.
Everyone who is either not tall or not happy is not wise or not patient.
Everyone who is brave is either curious or patient.
Everyone who is either not strong or old is both patient and generous.
If fred is either not strong or tall then susan is curious.
Everyone who is either curious or brave is both not curious and generous and vice versa.
Everyone who is quiet is either brave or not patient.
Everyone who is not wise is not happy and vice versa.
If someone is not humble or not kind then alice is happy or old and vice versa.
Everyone who is not humble or patient is not curious or not creative.
Someone is not brave.
Someone is either old or brave.
Someone is either not calm or rich.
Fred is curious or tall.
Mary is either not happy or humble. | Fred is not patient. | entailment | ((?[X]:(tall(X)))=>((~curious(mary)<~>humble(mary))))&
(![X]:((~tall(X)&kind(X))=>wise(X)))&
((?[X]:((quiet(X)&funny(X))))=>((~wise(mary)<~>~strong(mary))))&
((?[X]:((kind(X)|~old(X))))<=>((creative(mary)<~>brave(mary))))&
(![X]:(~kind(X)=>(creative(X)&~creative(X))))&
(![X]:((creative(X)|tall(X))=>(happy(X)&~generous(X))))&
(![X]:((~wise(X)|~patient(X))<=>(happy(X)|~humble(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(~wise(X)|~patient(X))))&
(![X]:(brave(X)=>(curious(X)<~>patient(X))))&
(![X]:((~strong(X)<~>old(X))=>(patient(X)&generous(X))))&
(((~strong(fred)<~>tall(fred)))=>(curious(susan)))&
(![X]:((curious(X)<~>brave(X))<=>(~curious(X)&generous(X))))&
(![X]:(quiet(X)=>(brave(X)<~>~patient(X))))&
(![X]:(~wise(X)<=>~happy(X)))&
((?[X]:((~humble(X)|~kind(X))))<=>((happy(alice)|old(alice))))&
(![X]:((~humble(X)|patient(X))=>(~curious(X)|~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:((old(X)<~>brave(X))))&
(?[X]:((~calm(X)<~>rich(X))))&
((curious(fred)|tall(fred)))&
((~happy(mary)<~>humble(mary))) | ~patient(fred) | [
"p1",
"p4",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7423237933087858261475185
% SZS output start Proof for 7423237933087858261475185
2. ! [X0] : ((kind(X0) & ~tall(X0)) => wise(X0)) [input p1]
5. ! [X0] : (~kind(X0) => (~creative(X0) & creative(X0))) [input p4]
6. ! [X0] : ((tall(X0) | creative(X0)) => (~generous(X0) & happy(X0))) [input p5]
7. ! [X0] : ((~patient(X0) | ~wise(X0)) <=> (~humble(X0) | happy(X0))) [input p6]
14. ! [X0] : (~wise(X0) <=> ~happy(X0)) [input p13]
22. patient(fred) [input hypothesis]
26. ! [X0] : (wise(X0) | (~kind(X0) | tall(X0))) [ennf transformation 2]
27. ! [X0] : (wise(X0) | ~kind(X0) | tall(X0)) [flattening 26]
28. ! [X0] : ((~creative(X0) & creative(X0)) | kind(X0)) [ennf transformation 5]
29. ! [X0] : ((~generous(X0) & happy(X0)) | (~tall(X0) & ~creative(X0))) [ennf transformation 6]
42. ! [X0] : (((~patient(X0) | ~wise(X0)) | (humble(X0) & ~happy(X0))) & ((~humble(X0) | happy(X0)) | (patient(X0) & wise(X0)))) [nnf transformation 7]
43. ! [X0] : ((~patient(X0) | ~wise(X0) | (humble(X0) & ~happy(X0))) & (~humble(X0) | happy(X0) | (patient(X0) & wise(X0)))) [flattening 42]
50. ! [X0] : ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))) [nnf transformation 14]
67. ~kind(X0) | wise(X0) | tall(X0) [cnf transformation 27]
74. creative(X0) | kind(X0) [cnf transformation 28]
75. ~creative(X0) | kind(X0) [cnf transformation 28]
77. ~tall(X0) | happy(X0) [cnf transformation 29]
82. ~patient(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 43]
100. ~happy(X0) | wise(X0) [cnf transformation 50]
101. ~wise(X0) | happy(X0) [cnf transformation 50]
116. patient(fred) [cnf transformation 22]
160. kind(X0) [subsumption resolution 74,75]
229. wise(X0) | tall(X0) [resolution 67,160]
230. tall(X0) | happy(X0) [resolution 229,101]
231. happy(X0) [subsumption resolution 230,77]
233. wise(X0) [resolution 231,100]
239. ~wise(fred) | ~happy(fred) [resolution 82,116]
243. ~happy(fred) [subsumption resolution 239,233]
244. $false [subsumption resolution 243,231]
% SZS output end Proof for 7423237933087858261475185
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or not calm then someone is either humble or old. If john is both not rich and not kind then fred is not creative. Everyone who is not creative or not quiet is both not strong and not quiet and vice versa. Everyone who is both kind and not strong is strong. Everyone who is not old or not humble is both quiet and curious and vice versa. Everyone who is both rich and not kind is strong and vice versa. Everyone who is either not patient or not wise is rich or not creative and vice versa. If someone is wise then someone is humble or not patient and vice versa. If someone is wise or humble then someone is not quiet or funny and vice versa. Everyone who is either not kind or kind is strong or not creative. If john is either quiet or patient then someone is generous or not calm. If mary is either rich or not quiet then mary is either curious or not tall and vice versa. If someone is both not quiet and not calm then someone is not patient or calm and vice versa. If someone is both curious and not rich then lucy is both not brave and not wise and vice versa. Everyone who is both patient and old is both not old and happy and vice versa. If alice is wise then john is rich or not curious and vice versa. John is happy. Someone is both not funny and not quiet. Alice is either old or strong. Someone is not rich. Fred is not rich. John is either not rich or not patient. Susan is both not kind and not brave. | Fred is not wise. | contradiction | ((?[X]:((~patient(X)|~calm(X))))=>(?[X]:((humble(X)<~>old(X)))))&
(((~rich(john)&~kind(john)))=>(~creative(fred)))&
(![X]:((~creative(X)|~quiet(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((kind(X)&~strong(X))=>strong(X)))&
(![X]:((~old(X)|~humble(X))<=>(quiet(X)&curious(X))))&
(![X]:((rich(X)&~kind(X))<=>strong(X)))&
(![X]:((~patient(X)<~>~wise(X))<=>(rich(X)|~creative(X))))&
((?[X]:(wise(X)))<=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:((wise(X)|humble(X))))<=>(?[X]:((~quiet(X)|funny(X)))))&
(![X]:((~kind(X)<~>kind(X))=>(strong(X)|~creative(X))))&
(((quiet(john)<~>patient(john)))=>(?[X]:((generous(X)|~calm(X)))))&
(((rich(mary)<~>~quiet(mary)))<=>((curious(mary)<~>~tall(mary))))&
((?[X]:((~quiet(X)&~calm(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:((curious(X)&~rich(X))))<=>((~brave(lucy)&~wise(lucy))))&
(![X]:((patient(X)&old(X))<=>(~old(X)&happy(X))))&
((wise(alice))<=>((rich(john)|~curious(john))))&
(happy(john))&
(?[X]:((~funny(X)&~quiet(X))))&
((old(alice)<~>strong(alice)))&
(?[X]:(~rich(X)))&
(~rich(fred))&
((~rich(john)<~>~patient(john)))&
((~kind(susan)&~brave(susan))) | ~wise(fred) | [
"p2",
"p3",
"p4",
"p5",
"p6",
"p9",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2049395737565256519498926
% SZS output start Proof for 2049395737565256519498926
3. ! [X0] : ((~quiet(X0) | ~creative(X0)) <=> (~quiet(X0) & ~strong(X0))) [input p2]
4. ! [X0] : ((~strong(X0) & kind(X0)) => strong(X0)) [input p3]
5. ! [X0] : ((~humble(X0) | ~old(X0)) <=> (curious(X0) & quiet(X0))) [input p4]
6. ! [X0] : ((~kind(X0) & rich(X0)) <=> strong(X0)) [input p5]
7. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> (~creative(X0) | rich(X0))) [input p6]
10. ! [X0] : ((~kind(X0) <~> kind(X0)) => (~creative(X0) | strong(X0))) [input p9]
15. ! [X0] : ((old(X0) & patient(X0)) <=> (happy(X0) & ~old(X0))) [input p14]
21. ~rich(fred) [input p20]
24. ~wise(fred) [input hypothesis]
33. ! [X0] : (strong(X0) | (strong(X0) | ~kind(X0))) [ennf transformation 4]
34. ! [X0] : (strong(X0) | strong(X0) | ~kind(X0)) [flattening 33]
35. ! [X0] : ((~creative(X0) | strong(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 10]
36. ! [X0] : (~creative(X0) | strong(X0) | (~kind(X0) <=> kind(X0))) [flattening 35]
41. ! [X0] : (((~quiet(X0) | ~creative(X0)) | (quiet(X0) | strong(X0))) & ((~quiet(X0) & ~strong(X0)) | (quiet(X0) & creative(X0)))) [nnf transformation 3]
42. ! [X0] : ((~quiet(X0) | ~creative(X0) | quiet(X0) | strong(X0)) & ((~quiet(X0) & ~strong(X0)) | (quiet(X0) & creative(X0)))) [flattening 41]
43. ! [X0] : (((~humble(X0) | ~old(X0)) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | (humble(X0) & old(X0)))) [nnf transformation 5]
44. ! [X0] : ((~humble(X0) | ~old(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | (humble(X0) & old(X0)))) [flattening 43]
45. ! [X0] : (((~kind(X0) & rich(X0)) | ~strong(X0)) & (strong(X0) | (kind(X0) | ~rich(X0)))) [nnf transformation 6]
46. ! [X0] : (((~kind(X0) & rich(X0)) | ~strong(X0)) & (strong(X0) | kind(X0) | ~rich(X0))) [flattening 45]
47. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (creative(X0) & ~rich(X0))) & ((~creative(X0) | rich(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 7]
48. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (creative(X0) & ~rich(X0))) & (~creative(X0) | rich(X0) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [flattening 47]
59. ! [X0] : (~creative(X0) | strong(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 36]
71. ! [X0] : (((old(X0) & patient(X0)) | (~happy(X0) | old(X0))) & ((happy(X0) & ~old(X0)) | (~old(X0) | ~patient(X0)))) [nnf transformation 15]
72. ! [X0] : (((old(X0) & patient(X0)) | ~happy(X0) | old(X0)) & ((happy(X0) & ~old(X0)) | ~old(X0) | ~patient(X0))) [flattening 71]
88. ~quiet(X0) | creative(X0) [cnf transformation 42]
91. strong(X0) | strong(X0) | ~kind(X0) [cnf transformation 34]
92. quiet(X0) | old(X0) [cnf transformation 44]
98. ~strong(X0) | rich(X0) [cnf transformation 46]
99. ~kind(X0) | ~strong(X0) [cnf transformation 46]
105. wise(X0) | patient(X0) | creative(X0) [cnf transformation 48]
113. ~creative(X0) | strong(X0) | kind(X0) | kind(X0) [cnf transformation 59]
132. ~old(X0) | ~old(X0) | ~patient(X0) [cnf transformation 72]
145. ~rich(fred) [cnf transformation 21]
150. ~wise(fred) [cnf transformation 24]
151. ~old(X0) | ~patient(X0) [duplicate literal removal 132]
153. ~creative(X0) | strong(X0) | kind(X0) [duplicate literal removal 113]
155. ~kind(X0) | strong(X0) [duplicate literal removal 91]
183. 7 <=> creative(fred) [avatar definition]
184. creative(fred) <- (7) [avatar component clause 183]
185. ~creative(fred) <- (~7) [avatar component clause 183]
187. ~kind(X0) [subsumption resolution 99,155]
236. ~creative(X0) | strong(X0) [subsumption resolution 153,187]
338. creative(X0) | old(X0) [resolution 92,88]
392. patient(fred) | creative(fred) [resolution 105,150]
398. 44 <=> patient(fred) [avatar definition]
400. patient(fred) <- (44) [avatar component clause 398]
401. 7 | 44 [avatar split clause 392,398,183]
411. strong(fred) <- (7) [resolution 184,236]
469. rich(fred) <- (7) [resolution 411,98]
472. $false <- (7) [subsumption resolution 469,145]
473. ~7 [avatar contradiction clause 472]
488. old(fred) <- (~7) [resolution 338,185]
519. ~patient(fred) <- (~7) [resolution 488,151]
521. $false <- (~7, 44) [subsumption resolution 519,400]
522. 7 | ~44 [avatar contradiction clause 521]
523. $false [avatar sat refutation 401,473,522]
% SZS output end Proof for 2049395737565256519498926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not brave is wise or not strong. If someone is both not generous and not rich then someone is both humble and calm and vice versa. If someone is not happy then someone is both brave and not rich and vice versa. If john is creative then paul is creative. If someone is creative or not curious then lucy is not brave and vice versa. If paul is either brave or happy then someone is both not creative and curious and vice versa. Everyone who is either patient or not humble is not curious. Everyone who is not strong is both quiet and not happy. If someone is either not generous or humble then mary is happy or quiet. If paul is both not humble and humble then someone is not happy. Everyone who is not quiet is tall or funny and vice versa. If someone is not calm or not wise then someone is creative or generous and vice versa. If someone is curious then someone is either curious or not old. Everyone who is both old and kind is tall or calm. Everyone who is not humble is not humble or not brave and vice versa. Someone is funny or brave. John is generous. Mary is both rich and tall. Alice is generous. Someone is either creative or not generous. Someone is both funny and rich. | Mary is strong. | entailment | (![X]:((~quiet(X)|~brave(X))=>(wise(X)|~strong(X))))&
((?[X]:((~generous(X)&~rich(X))))<=>(?[X]:((humble(X)&calm(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((brave(X)&~rich(X)))))&
((creative(john))=>(creative(paul)))&
((?[X]:((creative(X)|~curious(X))))<=>(~brave(lucy)))&
(((brave(paul)<~>happy(paul)))<=>(?[X]:((~creative(X)&curious(X)))))&
(![X]:((patient(X)<~>~humble(X))=>~curious(X)))&
(![X]:(~strong(X)=>(quiet(X)&~happy(X))))&
((?[X]:((~generous(X)<~>humble(X))))=>((happy(mary)|quiet(mary))))&
(((~humble(paul)&humble(paul)))=>(?[X]:(~happy(X))))&
(![X]:(~quiet(X)<=>(tall(X)|funny(X))))&
((?[X]:((~calm(X)|~wise(X))))<=>(?[X]:((creative(X)|generous(X)))))&
((?[X]:(curious(X)))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((old(X)&kind(X))=>(tall(X)|calm(X))))&
(![X]:(~humble(X)<=>(~humble(X)|~brave(X))))&
(?[X]:((funny(X)|brave(X))))&
(generous(john))&
((rich(mary)&tall(mary)))&
(generous(alice))&
(?[X]:((creative(X)<~>~generous(X))))&
(?[X]:((funny(X)&rich(X)))) | strong(mary) | [
"p7",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2285050839785427770150459
% SZS output start Proof for 2285050839785427770150459
8. ! [X0] : (~strong(X0) => (~happy(X0) & quiet(X0))) [input p7]
11. ! [X0] : (~quiet(X0) <=> (funny(X0) | tall(X0))) [input p10]
18. tall(mary) & rich(mary) [input p17]
22. ~strong(mary) [input hypothesis]
27. ! [X0] : ((funny(X0) | tall(X0)) => ~quiet(X0)) [unused predicate definition removal 11]
33. ! [X0] : ((~happy(X0) & quiet(X0)) | strong(X0)) [ennf transformation 8]
38. ! [X0] : (~quiet(X0) | (~funny(X0) & ~tall(X0))) [ennf transformation 27]
101. strong(X0) | quiet(X0) [cnf transformation 33]
106. ~tall(X0) | ~quiet(X0) [cnf transformation 38]
120. tall(mary) [cnf transformation 18]
126. ~strong(mary) [cnf transformation 22]
237. 26 <=> quiet(mary) [avatar definition]
239. quiet(mary) <- (26) [avatar component clause 237]
310. quiet(mary) [resolution 101,126]
311. 26 [avatar split clause 310,237]
316. ~quiet(mary) [resolution 106,120]
317. $false <- (26) [subsumption resolution 316,239]
318. ~26 [avatar contradiction clause 317]
319. $false [avatar sat refutation 311,318]
% SZS output end Proof for 2285050839785427770150459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not patient or not creative and vice versa.
Everyone who is not brave or not kind is strong.
If fred is not happy then someone is either creative or not old.
Everyone who is either funny or wise is both not funny and happy.
Everyone who is either old or funny is either generous or not brave.
Everyone who is calm is kind or happy and vice versa.
Everyone who is both not brave and creative is not creative and vice versa.
Everyone who is both not old and quiet is both not humble and old.
If mary is both old and not wise then someone is not generous and vice versa.
Everyone who is not humble or not creative is creative or kind.
If john is both not kind and not strong then someone is both not quiet and not funny.
If someone is wise then fred is brave or wise and vice versa.
If mary is not rich then alice is both not humble and rich.
If someone is either not tall or not kind then someone is patient.
Everyone who is patient is rich or not creative.
Alice is either creative or rich.
Alice is generous.
Mary is not happy or kind.
Someone is curious or tall.
Paul is creative or curious.
Paul is not old.
Mary is funny or not wise. | Paul is not wise. | neutral | (![X]:(~funny(X)<=>(~patient(X)|~creative(X))))&
(![X]:((~brave(X)|~kind(X))=>strong(X)))&
((~happy(fred))=>(?[X]:((creative(X)<~>~old(X)))))&
(![X]:((funny(X)<~>wise(X))=>(~funny(X)&happy(X))))&
(![X]:((old(X)<~>funny(X))=>(generous(X)<~>~brave(X))))&
(![X]:(calm(X)<=>(kind(X)|happy(X))))&
(![X]:((~brave(X)&creative(X))<=>~creative(X)))&
(![X]:((~old(X)&quiet(X))=>(~humble(X)&old(X))))&
(((old(mary)&~wise(mary)))<=>(?[X]:(~generous(X))))&
(![X]:((~humble(X)|~creative(X))=>(creative(X)|kind(X))))&
(((~kind(john)&~strong(john)))=>(?[X]:((~quiet(X)&~funny(X)))))&
((?[X]:(wise(X)))<=>((brave(fred)|wise(fred))))&
((~rich(mary))=>((~humble(alice)&rich(alice))))&
((?[X]:((~tall(X)<~>~kind(X))))=>(?[X]:(patient(X))))&
(![X]:(patient(X)=>(rich(X)|~creative(X))))&
((creative(alice)<~>rich(alice)))&
(generous(alice))&
((~happy(mary)|kind(mary)))&
(?[X]:((curious(X)|tall(X))))&
((creative(paul)|curious(paul)))&
(~old(paul))&
((funny(mary)|~wise(mary))) | ~wise(paul) | [] | null | 0 |
If someone is kind or not creative then mary is either wise or old and vice versa.
If paul is both not quiet and not rich then paul is creative and vice versa.
If mary is rich then someone is not curious.
Everyone who is both generous and not patient is not quiet and vice versa.
Everyone who is not quiet or curious is creative or not calm.
Everyone who is either not creative or creative is generous or creative and vice versa.
Everyone who is old is not tall and vice versa.
If someone is humble then paul is either tall or wise.
If paul is both not quiet and not old then someone is both not quiet and calm.
Everyone who is not tall or tall is both brave and not happy.
Everyone who is both rich and not kind is kind.
If someone is either not tall or calm then someone is not tall or not creative.
Everyone who is patient or happy is both creative and not kind and vice versa.
If someone is either not wise or not generous then susan is both not tall and strong.
If mary is both not curious and humble then susan is either not tall or not wise.
If someone is funny or rich then mary is either curious or strong and vice versa.
Paul is strong or tall.
Paul is not old or not patient.
Paul is both not strong and humble.
Fred is not brave or not generous.
Someone is wise.
Someone is old.
Mary is creative or funny. | Paul is rich. | neutral | ((?[X]:((kind(X)|~creative(X))))<=>((wise(mary)<~>old(mary))))&
(((~quiet(paul)&~rich(paul)))<=>(creative(paul)))&
((rich(mary))=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&~patient(X))<=>~quiet(X)))&
(![X]:((~quiet(X)|curious(X))=>(creative(X)|~calm(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(generous(X)|creative(X))))&
(![X]:(old(X)<=>~tall(X)))&
((?[X]:(humble(X)))=>((tall(paul)<~>wise(paul))))&
(((~quiet(paul)&~old(paul)))=>(?[X]:((~quiet(X)&calm(X)))))&
(![X]:((~tall(X)|tall(X))=>(brave(X)&~happy(X))))&
(![X]:((rich(X)&~kind(X))=>kind(X)))&
((?[X]:((~tall(X)<~>calm(X))))=>(?[X]:((~tall(X)|~creative(X)))))&
(![X]:((patient(X)|happy(X))<=>(creative(X)&~kind(X))))&
((?[X]:((~wise(X)<~>~generous(X))))=>((~tall(susan)&strong(susan))))&
(((~curious(mary)&humble(mary)))=>((~tall(susan)<~>~wise(susan))))&
((?[X]:((funny(X)|rich(X))))<=>((curious(mary)<~>strong(mary))))&
((strong(paul)|tall(paul)))&
((~old(paul)|~patient(paul)))&
((~strong(paul)&humble(paul)))&
((~brave(fred)|~generous(fred)))&
(?[X]:(wise(X)))&
(?[X]:(old(X)))&
((creative(mary)|funny(mary))) | rich(paul) | [] | null | 0 |
Everyone who is funny or not strong is not happy or not creative and vice versa.
If someone is both kind and old then someone is both happy and old.
Everyone who is not rich is strong and vice versa.
If someone is wise then someone is either tall or not calm and vice versa.
Everyone who is kind is both not wise and calm and vice versa.
Everyone who is both not happy and not wise is both not quiet and tall and vice versa.
Everyone who is either not brave or not old is both quiet and wise.
If someone is both strong and humble then someone is not creative or old and vice versa.
Everyone who is both not patient and not happy is quiet or old and vice versa.
If susan is not generous or creative then mary is not rich or not brave.
Everyone who is both brave and strong is both not curious and brave.
Everyone who is both not curious and not happy is both not kind and not calm.
If someone is either creative or not calm then someone is wise and vice versa.
Everyone who is strong is either happy or brave and vice versa.
Everyone who is not generous or not strong is not curious.
Everyone who is kind or not rich is happy and vice versa.
Paul is both kind and humble.
Someone is not humble.
John is both strong and not rich.
Paul is either quiet or humble.
Paul is either humble or quiet.
Paul is humble. | Mary is not brave. | entailment | (![X]:((funny(X)|~strong(X))<=>(~happy(X)|~creative(X))))&
((?[X]:((kind(X)&old(X))))=>(?[X]:((happy(X)&old(X)))))&
(![X]:(~rich(X)<=>strong(X)))&
((?[X]:(wise(X)))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(![X]:(kind(X)<=>(~wise(X)&calm(X))))&
(![X]:((~happy(X)&~wise(X))<=>(~quiet(X)&tall(X))))&
(![X]:((~brave(X)<~>~old(X))=>(quiet(X)&wise(X))))&
((?[X]:((strong(X)&humble(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((~patient(X)&~happy(X))<=>(quiet(X)|old(X))))&
(((~generous(susan)|creative(susan)))=>((~rich(mary)|~brave(mary))))&
(![X]:((brave(X)&strong(X))=>(~curious(X)&brave(X))))&
(![X]:((~curious(X)&~happy(X))=>(~kind(X)&~calm(X))))&
((?[X]:((creative(X)<~>~calm(X))))<=>(?[X]:(wise(X))))&
(![X]:(strong(X)<=>(happy(X)<~>brave(X))))&
(![X]:((~generous(X)|~strong(X))=>~curious(X)))&
(![X]:((kind(X)|~rich(X))<=>happy(X)))&
((kind(paul)&humble(paul)))&
(?[X]:(~humble(X)))&
((strong(john)&~rich(john)))&
((quiet(paul)<~>humble(paul)))&
((humble(paul)<~>quiet(paul)))&
(humble(paul)) | ~brave(mary) | [
"p2",
"p6",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7116212096173579704404997
% SZS output start Proof for 7116212096173579704404997
3. ! [X0] : (~rich(X0) <=> strong(X0)) [input p2]
7. ! [X0] : ((~brave(X0) <~> ~old(X0)) => (wise(X0) & quiet(X0))) [input p6]
9. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (old(X0) | quiet(X0))) [input p8]
14. ! [X0] : (strong(X0) <=> (happy(X0) <~> brave(X0))) [input p13]
16. ! [X0] : ((~rich(X0) | kind(X0)) <=> happy(X0)) [input p15]
23. brave(mary) [input hypothesis]
31. ! [X0] : ((wise(X0) & quiet(X0)) | (~brave(X0) <=> ~old(X0))) [ennf transformation 7]
44. ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))) [nnf transformation 3]
54. ! [X0] : ((wise(X0) & quiet(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) [nnf transformation 31]
60. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~old(X0) & ~quiet(X0))) & ((old(X0) | quiet(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 9]
61. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~old(X0) & ~quiet(X0))) & (old(X0) | quiet(X0) | happy(X0) | patient(X0))) [flattening 60]
67. ! [X0] : ((strong(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ~strong(X0))) [nnf transformation 14]
68. ! [X0] : (((~rich(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((~rich(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [flattening 68]
81. ~rich(X0) | ~strong(X0) [cnf transformation 44]
94. ~brave(X0) | quiet(X0) | old(X0) [cnf transformation 54]
105. ~quiet(X0) | ~happy(X0) [cnf transformation 61]
106. ~old(X0) | ~happy(X0) [cnf transformation 61]
119. ~brave(X0) | happy(X0) | strong(X0) [cnf transformation 67]
122. rich(X0) | happy(X0) [cnf transformation 69]
134. brave(mary) [cnf transformation 23]
208. 18 <=> rich(mary) [avatar definition]
209. rich(mary) <- (18) [avatar component clause 208]
210. ~rich(mary) <- (~18) [avatar component clause 208]
212. 19 <=> brave(mary) [avatar definition]
213. brave(mary) <- (19) [avatar component clause 212]
239. 19 [avatar split clause 134,212]
256. happy(mary) <- (~18) [resolution 122,210]
324. quiet(mary) | old(mary) <- (19) [resolution 94,213]
326. 35 <=> old(mary) [avatar definition]
328. old(mary) <- (35) [avatar component clause 326]
330. 36 <=> quiet(mary) [avatar definition]
332. quiet(mary) <- (36) [avatar component clause 330]
333. 35 | 36 | ~19 [avatar split clause 324,212,330,326]
339. ~happy(mary) <- (36) [resolution 332,105]
340. $false <- (~18, 36) [subsumption resolution 339,256]
341. 18 | ~36 [avatar contradiction clause 340]
343. ~strong(mary) <- (18) [resolution 209,81]
364. happy(mary) | strong(mary) <- (19) [resolution 119,213]
365. strong(mary) <- (19, 36) [subsumption resolution 364,339]
366. $false <- (18, 19, 36) [subsumption resolution 365,343]
367. ~18 | ~19 | ~36 [avatar contradiction clause 366]
368. happy(mary) <- (18, 19) [subsumption resolution 364,343]
377. ~happy(mary) <- (35) [resolution 328,106]
378. $false <- (18, 19, 35) [subsumption resolution 377,368]
379. ~18 | ~19 | ~35 [avatar contradiction clause 378]
381. happy(mary) <- (~18) [resolution 210,122]
383. $false <- (~18, 35) [subsumption resolution 381,377]
384. 18 | ~35 [avatar contradiction clause 383]
385. $false [avatar sat refutation 239,333,341,367,379,384]
% SZS output end Proof for 7116212096173579704404997
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is either not kind or quiet. If alice is both kind and wise then someone is not rich or old and vice versa. Everyone who is not generous or tall is not wise or curious. If someone is both not kind and wise then someone is wise or not generous and vice versa. Everyone who is not kind is both not generous and strong. If fred is both funny and not brave then someone is either not happy or creative. Everyone who is both quiet and not curious is either humble or calm and vice versa. If mary is not curious then alice is old or quiet and vice versa. Everyone who is both kind and creative is kind and vice versa. If fred is either not old or not happy then someone is either not calm or kind. Everyone who is both quiet and strong is not happy or quiet and vice versa. Everyone who is either not old or not funny is either strong or humble and vice versa. If paul is both not humble and not old then lucy is patient or not tall and vice versa. Everyone who is either kind or creative is either old or not tall and vice versa. Everyone who is not creative is either not creative or creative and vice versa. If someone is rich then fred is either not curious or brave. Someone is either not generous or not calm. Mary is wise. Someone is not brave or wise. Someone is brave or not quiet. Alice is generous or patient. Someone is strong or humble. Someone is either strong or quiet. | Lucy is generous. | contradiction | (![X]:(wise(X)=>(~kind(X)<~>quiet(X))))&
(((kind(alice)&wise(alice)))<=>(?[X]:((~rich(X)|old(X)))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)|curious(X))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~generous(X)&strong(X))))&
(((funny(fred)&~brave(fred)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(humble(X)<~>calm(X))))&
((~curious(mary))<=>((old(alice)|quiet(alice))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>creative(X))))&
((?[X]:(rich(X)))=>((~curious(fred)<~>brave(fred))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(wise(mary))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice)))&
(?[X]:((strong(X)|humble(X))))&
(?[X]:((strong(X)<~>quiet(X)))) | generous(lucy) | [
"p4",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3541741135143665657240880
% SZS output start Proof for 3541741135143665657240880
5. ! [X0] : (~kind(X0) => (strong(X0) & ~generous(X0))) [input p4]
9. ! [X0] : ((creative(X0) & kind(X0)) <=> kind(X0)) [input p8]
15. ! [X0] : (~creative(X0) <=> (~creative(X0) <~> creative(X0))) [input p14]
24. generous(lucy) [input hypothesis]
29. ! [X0] : ((strong(X0) & ~generous(X0)) | kind(X0)) [ennf transformation 5]
52. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | (~creative(X0) | ~kind(X0)))) [nnf transformation 9]
53. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | ~creative(X0) | ~kind(X0))) [flattening 52]
63. ! [X0] : ((~creative(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | creative(X0))) [nnf transformation 15]
91. ~generous(X0) | kind(X0) [cnf transformation 29]
106. ~kind(X0) | creative(X0) [cnf transformation 53]
140. ~creative(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 63]
152. generous(lucy) [cnf transformation 24]
156. ~creative(X0) [duplicate literal removal 140]
349. kind(lucy) [resolution 91,152]
353. creative(lucy) [resolution 106,349]
357. $false [subsumption resolution 353,156]
% SZS output end Proof for 3541741135143665657240880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both kind and not brave is not quiet and vice versa.
Everyone who is either not funny or not curious is not funny or rich.
Everyone who is both not tall and not old is strong and vice versa.
If someone is humble then someone is humble or happy and vice versa.
Everyone who is not curious is either calm or not calm and vice versa.
If paul is either not quiet or quiet then paul is both not rich and humble.
Everyone who is funny is curious and vice versa.
Everyone who is not curious or not rich is either humble or not humble and vice versa.
Everyone who is both old and wise is both old and rich and vice versa.
Everyone who is tall is not calm or not tall and vice versa.
If lucy is either wise or calm then someone is not rich or calm and vice versa.
If someone is either not happy or not wise then someone is both creative and not creative and vice versa.
Everyone who is not funny or creative is either brave or not patient.
Everyone who is not old or not humble is either strong or patient and vice versa.
If fred is not calm or tall then susan is patient or not strong.
Fred is both humble and patient.
Someone is either not tall or not patient.
Someone is both not rich and old.
Someone is generous.
Someone is either not calm or curious. | Paul is not tall. | contradiction | (![X]:((kind(X)&~brave(X))<=>~quiet(X)))&
(![X]:((~funny(X)<~>~curious(X))=>(~funny(X)|rich(X))))&
(![X]:((~tall(X)&~old(X))<=>strong(X)))&
((?[X]:(humble(X)))<=>(?[X]:((humble(X)|happy(X)))))&
(![X]:(~curious(X)<=>(calm(X)<~>~calm(X))))&
(((~quiet(paul)<~>quiet(paul)))=>((~rich(paul)&humble(paul))))&
(![X]:(funny(X)<=>curious(X)))&
(![X]:((~curious(X)|~rich(X))<=>(humble(X)<~>~humble(X))))&
(![X]:((old(X)&wise(X))<=>(old(X)&rich(X))))&
(![X]:(tall(X)<=>(~calm(X)|~tall(X))))&
(((wise(lucy)<~>calm(lucy)))<=>(?[X]:((~rich(X)|calm(X)))))&
((?[X]:((~happy(X)<~>~wise(X))))<=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((~funny(X)|creative(X))=>(brave(X)<~>~patient(X))))&
(![X]:((~old(X)|~humble(X))<=>(strong(X)<~>patient(X))))&
(((~calm(fred)|tall(fred)))=>((patient(susan)|~strong(susan))))&
((humble(fred)&patient(fred)))&
(?[X]:((~tall(X)<~>~patient(X))))&
(?[X]:((~rich(X)&old(X))))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)<~>curious(X)))) | ~tall(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6268013075016182997934458
% SZS output start Proof for 6268013075016182997934458
10. ! [X0] : (tall(X0) <=> (~tall(X0) | ~calm(X0))) [input p9]
21. ~tall(paul) [input hypothesis]
48. ! [X0] : ((tall(X0) | (tall(X0) & calm(X0))) & ((~tall(X0) | ~calm(X0)) | ~tall(X0))) [nnf transformation 10]
49. ! [X0] : ((tall(X0) | (tall(X0) & calm(X0))) & (~tall(X0) | ~calm(X0) | ~tall(X0))) [flattening 48]
103. tall(X0) | tall(X0) [cnf transformation 49]
136. ~tall(paul) [cnf transformation 21]
138. tall(X0) [duplicate literal removal 103]
225. $false [subsumption resolution 136,138]
% SZS output end Proof for 6268013075016182997934458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is both patient and creative and vice versa.
Everyone who is both not tall and not kind is not happy or not quiet and vice versa.
Everyone who is not brave is either tall or creative.
Everyone who is not generous is either not old or funny and vice versa.
Everyone who is both old and not tall is both creative and patient.
If someone is humble then susan is either not creative or not happy.
If john is either not patient or calm then someone is old and vice versa.
If someone is not generous then someone is either not rich or creative and vice versa.
Everyone who is kind or not old is both strong and calm and vice versa.
Everyone who is either not happy or strong is not happy and vice versa.
If someone is either humble or patient then someone is either not strong or generous and vice versa.
Everyone who is humble is both humble and not kind.
Everyone who is both curious and quiet is either not rich or kind.
Everyone who is both creative and not quiet is humble or not strong.
Everyone who is either wise or not humble is not strong or not happy and vice versa.
Lucy is humble.
Someone is either generous or not humble.
Susan is tall or curious.
Paul is not happy.
Fred is not funny.
Mary is either tall or not tall.
Someone is not patient or not curious. | John is patient. | entailment | (![X]:(~calm(X)<=>(patient(X)&creative(X))))&
(![X]:((~tall(X)&~kind(X))<=>(~happy(X)|~quiet(X))))&
(![X]:(~brave(X)=>(tall(X)<~>creative(X))))&
(![X]:(~generous(X)<=>(~old(X)<~>funny(X))))&
(![X]:((old(X)&~tall(X))=>(creative(X)&patient(X))))&
((?[X]:(humble(X)))=>((~creative(susan)<~>~happy(susan))))&
(((~patient(john)<~>calm(john)))<=>(?[X]:(old(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((kind(X)|~old(X))<=>(strong(X)&calm(X))))&
(![X]:((~happy(X)<~>strong(X))<=>~happy(X)))&
((?[X]:((humble(X)<~>patient(X))))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:(humble(X)=>(humble(X)&~kind(X))))&
(![X]:((curious(X)&quiet(X))=>(~rich(X)<~>kind(X))))&
(![X]:((creative(X)&~quiet(X))=>(humble(X)|~strong(X))))&
(![X]:((wise(X)<~>~humble(X))<=>(~strong(X)|~happy(X))))&
(humble(lucy))&
(?[X]:((generous(X)<~>~humble(X))))&
((tall(susan)|curious(susan)))&
(~happy(paul))&
(~funny(fred))&
((tall(mary)<~>~tall(mary)))&
(?[X]:((~patient(X)|~curious(X)))) | patient(john) | [
"p0",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2430214717254073918663038
% SZS output start Proof for 2430214717254073918663038
1. ! [X0] : (~calm(X0) <=> (creative(X0) & patient(X0))) [input p0]
7. (~patient(john) <~> calm(john)) <=> ? [X0] : old(X0) [input p6]
9. ! [X0] : ((~old(X0) | kind(X0)) <=> (calm(X0) & strong(X0))) [input p8]
10. ! [X0] : ((~happy(X0) <~> strong(X0)) <=> ~happy(X0)) [input p9]
23. ~patient(john) [input hypothesis]
35. ! [X0] : ((~calm(X0) | (~creative(X0) | ~patient(X0))) & ((creative(X0) & patient(X0)) | calm(X0))) [nnf transformation 1]
36. ! [X0] : ((~calm(X0) | ~creative(X0) | ~patient(X0)) & ((creative(X0) & patient(X0)) | calm(X0))) [flattening 35]
41. (((~calm(john) | patient(john)) & (calm(john) | ~patient(john))) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ((~patient(john) | ~calm(john)) & (calm(john) | patient(john)))) [nnf transformation 7]
42. (((~calm(john) | patient(john)) & (calm(john) | ~patient(john))) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ((~patient(john) | ~calm(john)) & (calm(john) | patient(john)))) [rectify 41]
43. ? [X1] : old(X1) => old(sK0) [choice axiom]
44. (((~calm(john) | patient(john)) & (calm(john) | ~patient(john))) | ! [X0] : ~old(X0)) & (old(sK0) | ((~patient(john) | ~calm(john)) & (calm(john) | patient(john)))) [skolemisation 42,43]
50. ! [X0] : (((~old(X0) | kind(X0)) | (~calm(X0) | ~strong(X0))) & ((calm(X0) & strong(X0)) | (old(X0) & ~kind(X0)))) [nnf transformation 9]
51. ! [X0] : ((~old(X0) | kind(X0) | ~calm(X0) | ~strong(X0)) & ((calm(X0) & strong(X0)) | (old(X0) & ~kind(X0)))) [flattening 50]
52. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | happy(X0)) & (~happy(X0) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [nnf transformation 10]
67. patient(X0) | calm(X0) [cnf transformation 36]
86. ~calm(john) | patient(john) | ~old(X0) [cnf transformation 44]
92. strong(X0) | old(X0) [cnf transformation 51]
97. ~happy(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 52]
99. ~strong(X0) | happy(X0) | happy(X0) [cnf transformation 52]
128. ~patient(john) [cnf transformation 23]
129. ~happy(X0) | ~strong(X0) [duplicate literal removal 97]
130. ~strong(X0) | happy(X0) [duplicate literal removal 99]
144. patient(john) | ~old(X0) [subsumption resolution 86,67]
146. 4 <=> ! [X0] : ~old(X0) [avatar definition]
147. ~old(X0) <- (4) [avatar component clause 146]
149. 5 <=> patient(john) [avatar definition]
152. 4 | 5 [avatar split clause 144,149,146]
189. ~strong(X0) [subsumption resolution 129,130]
247. ~5 [avatar split clause 128,149]
259. old(X0) [resolution 92,189]
260. $false <- (4) [subsumption resolution 259,147]
261. ~4 [avatar contradiction clause 260]
262. $false [avatar sat refutation 152,247,261]
% SZS output end Proof for 2430214717254073918663038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is curious or not kind then someone is not funny or not tall and vice versa. If mary is not quiet or not funny then someone is not quiet or quiet and vice versa. If someone is not brave then someone is either generous or calm and vice versa. Everyone who is either rich or old is both calm and not quiet and vice versa. If someone is both old and not old then fred is both not old and not wise and vice versa. Everyone who is funny is not quiet. Everyone who is both not wise and happy is both not funny and tall. Everyone who is not tall is not funny or not patient. Everyone who is kind or quiet is both not old and not brave. If someone is either not old or brave then alice is not wise and vice versa. If someone is not wise then john is not curious and vice versa. If someone is old then fred is rich or not old and vice versa. If susan is both tall and not happy then someone is not generous or not creative and vice versa. Everyone who is not old or not strong is kind or not funny. If susan is either not humble or happy then mary is either not rich or creative. Everyone who is not happy is both not generous and not happy. John is not calm or calm. Fred is either not tall or humble. Lucy is humble or tall. Fred is both happy and not generous. Paul is rich. Someone is both humble and not generous. Lucy is both quiet and patient. Alice is either wise or creative. | John is curious. | contradiction | ((?[X]:((curious(X)|~kind(X))))<=>(?[X]:((~funny(X)|~tall(X)))))&
(((~quiet(mary)|~funny(mary)))<=>(?[X]:((~quiet(X)|quiet(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((generous(X)<~>calm(X)))))&
(![X]:((rich(X)<~>old(X))<=>(calm(X)&~quiet(X))))&
((?[X]:((old(X)&~old(X))))<=>((~old(fred)&~wise(fred))))&
(![X]:(funny(X)=>~quiet(X)))&
(![X]:((~wise(X)&happy(X))=>(~funny(X)&tall(X))))&
(![X]:(~tall(X)=>(~funny(X)|~patient(X))))&
(![X]:((kind(X)|quiet(X))=>(~old(X)&~brave(X))))&
((?[X]:((~old(X)<~>brave(X))))<=>(~wise(alice)))&
((?[X]:(~wise(X)))<=>(~curious(john)))&
((?[X]:(old(X)))<=>((rich(fred)|~old(fred))))&
(((tall(susan)&~happy(susan)))<=>(?[X]:((~generous(X)|~creative(X)))))&
(![X]:((~old(X)|~strong(X))=>(kind(X)|~funny(X))))&
(((~humble(susan)<~>happy(susan)))=>((~rich(mary)<~>creative(mary))))&
(![X]:(~happy(X)=>(~generous(X)&~happy(X))))&
((~calm(john)|calm(john)))&
((~tall(fred)<~>humble(fred)))&
((humble(lucy)|tall(lucy)))&
((happy(fred)&~generous(fred)))&
(rich(paul))&
(?[X]:((humble(X)&~generous(X))))&
((quiet(lucy)&patient(lucy)))&
((wise(alice)<~>creative(alice))) | curious(john) | [
"p8",
"p9",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3763883490252023915967211
% SZS output start Proof for 3763883490252023915967211
9. ! [X0] : ((quiet(X0) | kind(X0)) => (~brave(X0) & ~old(X0))) [input p8]
10. ? [X0] : (~old(X0) <~> brave(X0)) <=> ~wise(alice) [input p9]
11. ? [X0] : ~wise(X0) <=> ~curious(john) [input p10]
23. patient(lucy) & quiet(lucy) [input p22]
25. curious(john) [input hypothesis]
34. ! [X0] : ((~brave(X0) & ~old(X0)) | (~quiet(X0) & ~kind(X0))) [ennf transformation 9]
61. (? [X0] : ((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | wise(alice)) & (~wise(alice) | ! [X0] : ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0)))) [nnf transformation 10]
62. (? [X0] : ((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | wise(alice)) & (~wise(alice) | ! [X1] : ((~old(X1) | ~brave(X1)) & (brave(X1) | old(X1)))) [rectify 61]
63. ? [X0] : ((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) => ((~brave(sK6) | old(sK6)) & (brave(sK6) | ~old(sK6))) [choice axiom]
64. (((~brave(sK6) | old(sK6)) & (brave(sK6) | ~old(sK6))) | wise(alice)) & (~wise(alice) | ! [X1] : ((~old(X1) | ~brave(X1)) & (brave(X1) | old(X1)))) [skolemisation 62,63]
65. (? [X0] : ~wise(X0) | curious(john)) & (~curious(john) | ! [X0] : wise(X0)) [nnf transformation 11]
66. (? [X0] : ~wise(X0) | curious(john)) & (~curious(john) | ! [X1] : wise(X1)) [rectify 65]
67. ? [X0] : ~wise(X0) => ~wise(sK7) [choice axiom]
68. (~wise(sK7) | curious(john)) & (~curious(john) | ! [X1] : wise(X1)) [skolemisation 66,67]
111. ~old(X0) | ~quiet(X0) [cnf transformation 34]
113. ~brave(X0) | ~quiet(X0) [cnf transformation 34]
114. ~wise(alice) | brave(X1) | old(X1) [cnf transformation 64]
118. ~curious(john) | wise(X1) [cnf transformation 68]
144. quiet(lucy) [cnf transformation 23]
148. curious(john) [cnf transformation 25]
182. 9 <=> ! [X0] : ~quiet(X0) [avatar definition]
183. ~quiet(X0) <- (9) [avatar component clause 182]
237. 22 <=> wise(alice) [avatar definition]
238. ~wise(alice) <- (~22) [avatar component clause 237]
255. 26 <=> ! [X1] : (brave(X1) | old(X1)) [avatar definition]
256. old(X1) | brave(X1) <- (26) [avatar component clause 255]
257. 26 | ~22 [avatar split clause 114,237,255]
259. 27 <=> curious(john) [avatar definition]
268. 29 <=> ! [X1] : wise(X1) [avatar definition]
269. wise(X1) <- (29) [avatar component clause 268]
270. 29 | ~27 [avatar split clause 118,259,268]
353. 27 [avatar split clause 148,259]
369. $false <- (9) [resolution 183,144]
370. ~9 [avatar contradiction clause 369]
380. brave(X1) | ~quiet(X1) <- (26) [resolution 256,111]
382. ~quiet(X1) <- (26) [subsumption resolution 380,113]
383. 9 | ~26 [avatar split clause 382,255,182]
385. $false <- (~22, 29) [subsumption resolution 238,269]
386. 22 | ~29 [avatar contradiction clause 385]
387. $false [avatar sat refutation 257,270,353,370,383,386]
% SZS output end Proof for 3763883490252023915967211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either tall or humble then susan is not strong and vice versa. Everyone who is not strong is both not old and funny. Everyone who is either strong or funny is either generous or strong. Everyone who is not calm is old and vice versa. If someone is either not happy or not patient then lucy is both kind and not quiet and vice versa. Everyone who is either not rich or not tall is quiet or not kind. If someone is not tall or not happy then alice is funny or tall and vice versa. Everyone who is not quiet is not wise and vice versa. If someone is either calm or generous then fred is both patient and old and vice versa. If susan is both patient and strong then someone is both not quiet and curious and vice versa. If john is humble or strong then fred is either brave or not funny. Everyone who is humble or not strong is not generous or not humble. Everyone who is not wise is happy and vice versa. Everyone who is either generous or humble is not calm and vice versa. Everyone who is both not strong and humble is either not funny or old. If someone is either happy or not humble then fred is either not generous or not humble. Lucy is either tall or not strong. Paul is not calm. Paul is kind. Lucy is both not humble and strong. Paul is both not tall and not rich. Fred is not calm or not happy. Someone is both rich and not funny. | Fred is not humble. | neutral | (((tall(alice)<~>humble(alice)))<=>(~strong(susan)))&
(![X]:(~strong(X)=>(~old(X)&funny(X))))&
(![X]:((strong(X)<~>funny(X))=>(generous(X)<~>strong(X))))&
(![X]:(~calm(X)<=>old(X)))&
((?[X]:((~happy(X)<~>~patient(X))))<=>((kind(lucy)&~quiet(lucy))))&
(![X]:((~rich(X)<~>~tall(X))=>(quiet(X)|~kind(X))))&
((?[X]:((~tall(X)|~happy(X))))<=>((funny(alice)|tall(alice))))&
(![X]:(~quiet(X)<=>~wise(X)))&
((?[X]:((calm(X)<~>generous(X))))<=>((patient(fred)&old(fred))))&
(((patient(susan)&strong(susan)))<=>(?[X]:((~quiet(X)&curious(X)))))&
(((humble(john)|strong(john)))=>((brave(fred)<~>~funny(fred))))&
(![X]:((humble(X)|~strong(X))=>(~generous(X)|~humble(X))))&
(![X]:(~wise(X)<=>happy(X)))&
(![X]:((generous(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~strong(X)&humble(X))=>(~funny(X)<~>old(X))))&
((?[X]:((happy(X)<~>~humble(X))))=>((~generous(fred)<~>~humble(fred))))&
((tall(lucy)<~>~strong(lucy)))&
(~calm(paul))&
(kind(paul))&
((~humble(lucy)&strong(lucy)))&
((~tall(paul)&~rich(paul)))&
((~calm(fred)|~happy(fred)))&
(?[X]:((rich(X)&~funny(X)))) | ~humble(fred) | [] | null | 0 |
If someone is not calm or not strong then someone is both old and not kind.
Everyone who is not kind is either not creative or patient.
If paul is not patient or not funny then someone is both not curious and not quiet and vice versa.
Everyone who is either humble or not curious is either not tall or not wise.
Everyone who is tall is either patient or strong and vice versa.
Everyone who is both happy and not calm is strong or not patient.
If someone is either not strong or not humble then someone is strong and vice versa.
If someone is wise or kind then fred is not patient and vice versa.
If someone is not strong or happy then fred is either calm or not kind and vice versa.
Everyone who is either humble or not strong is not strong or not kind.
If someone is either quiet or patient then someone is not happy or strong and vice versa.
Everyone who is not rich or calm is both creative and not tall and vice versa.
Everyone who is either calm or tall is not old or funny and vice versa.
Everyone who is either not brave or not rich is both not quiet and patient and vice versa.
If john is not creative then lucy is not patient and vice versa.
Everyone who is calm or curious is creative and vice versa.
Someone is strong or not funny.
Someone is not rich or not old.
Someone is either not quiet or old.
Someone is both kind and not creative.
Someone is not funny.
Lucy is either strong or not generous.
Fred is either happy or not quiet.
Someone is both old and curious. | Fred is funny. | neutral | ((?[X]:((~calm(X)|~strong(X))))=>(?[X]:((old(X)&~kind(X)))))&
(![X]:(~kind(X)=>(~creative(X)<~>patient(X))))&
(((~patient(paul)|~funny(paul)))<=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((humble(X)<~>~curious(X))=>(~tall(X)<~>~wise(X))))&
(![X]:(tall(X)<=>(patient(X)<~>strong(X))))&
(![X]:((happy(X)&~calm(X))=>(strong(X)|~patient(X))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>(?[X]:(strong(X))))&
((?[X]:((wise(X)|kind(X))))<=>(~patient(fred)))&
((?[X]:((~strong(X)|happy(X))))<=>((calm(fred)<~>~kind(fred))))&
(![X]:((humble(X)<~>~strong(X))=>(~strong(X)|~kind(X))))&
((?[X]:((quiet(X)<~>patient(X))))<=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~rich(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~old(X)|funny(X))))&
(![X]:((~brave(X)<~>~rich(X))<=>(~quiet(X)&patient(X))))&
((~creative(john))<=>(~patient(lucy)))&
(![X]:((calm(X)|curious(X))<=>creative(X)))&
(?[X]:((strong(X)|~funny(X))))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((~quiet(X)<~>old(X))))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:(~funny(X)))&
((strong(lucy)<~>~generous(lucy)))&
((happy(fred)<~>~quiet(fred)))&
(?[X]:((old(X)&curious(X)))) | funny(fred) | [] | null | 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 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.
Everyone who is rich is not curious or creative.
Someone is not rich or calm.
Lucy is funny.
Someone is either not old or brave.
Alice is either tall or kind.
Mary is brave or not quiet.
Someone is tall. | Paul is curious. | neutral | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(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))))&
(![X]:(rich(X)=>(~curious(X)|creative(X))))&
(?[X]:((~rich(X)|calm(X))))&
(funny(lucy))&
(?[X]:((~old(X)<~>brave(X))))&
((tall(alice)<~>kind(alice)))&
((brave(mary)|~quiet(mary)))&
(?[X]:(tall(X))) | curious(paul) | [] | null | 0 |
Everyone who is creative or not strong is not happy. Everyone who is both patient and not rich is not happy. Everyone who is either not kind or not curious is either not patient or not old. If alice is kind or not humble then lucy is patient. If someone is either kind or patient then someone is either not kind or tall. Everyone who is both old and curious is both not patient and not funny. Everyone who is not happy is both wise and kind and vice versa. If lucy is happy or brave then lucy is rich and vice versa. If someone is either not kind or not creative then susan is old and vice versa. Everyone who is either funny or not brave is either tall or not calm and vice versa. Everyone who is either brave or patient is curious or quiet. Everyone who is both funny and not generous is not brave and vice versa. If fred is both old and not wise then paul is either quiet or wise. If someone is happy then someone is both not generous and creative and vice versa. Everyone who is not kind is not patient and vice versa. Everyone who is both not kind and curious is both patient and not generous and vice versa. Mary is both not tall and humble. Fred is not quiet. Mary is kind or not happy. Someone is both not strong and not tall. Lucy is patient or not generous. | Alice is humble. | neutral | (![X]:((creative(X)|~strong(X))=>~happy(X)))&
(![X]:((patient(X)&~rich(X))=>~happy(X)))&
(![X]:((~kind(X)<~>~curious(X))=>(~patient(X)<~>~old(X))))&
(((kind(alice)|~humble(alice)))=>(patient(lucy)))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)<~>tall(X)))))&
(![X]:((old(X)&curious(X))=>(~patient(X)&~funny(X))))&
(![X]:(~happy(X)<=>(wise(X)&kind(X))))&
(((happy(lucy)|brave(lucy)))<=>(rich(lucy)))&
((?[X]:((~kind(X)<~>~creative(X))))<=>(old(susan)))&
(![X]:((funny(X)<~>~brave(X))<=>(tall(X)<~>~calm(X))))&
(![X]:((brave(X)<~>patient(X))=>(curious(X)|quiet(X))))&
(![X]:((funny(X)&~generous(X))<=>~brave(X)))&
(((old(fred)&~wise(fred)))=>((quiet(paul)<~>wise(paul))))&
((?[X]:(happy(X)))<=>(?[X]:((~generous(X)&creative(X)))))&
(![X]:(~kind(X)<=>~patient(X)))&
(![X]:((~kind(X)&curious(X))<=>(patient(X)&~generous(X))))&
((~tall(mary)&humble(mary)))&
(~quiet(fred))&
((kind(mary)|~happy(mary)))&
(?[X]:((~strong(X)&~tall(X))))&
((patient(lucy)|~generous(lucy))) | humble(alice) | [] | null | 0 |
Everyone who is not humble is both not brave and not strong and vice versa.
Everyone who is quiet is both tall and not wise.
Everyone who is rich is either not quiet or curious and vice versa.
Everyone who is both patient and not kind is curious or not tall.
If someone is not quiet then someone is strong and vice versa.
If someone is either not old or rich then someone is either not generous or kind and vice versa.
If someone is both happy and rich then paul is either not wise or strong.
Everyone who is not quiet or not wise is both strong and rich and vice versa.
Everyone who is both rich and happy is both not strong and rich and vice versa.
If someone is either tall or happy then lucy is calm and vice versa.
Everyone who is either wise or not funny is not generous.
If someone is calm then susan is both rich and not generous and vice versa.
Everyone who is both calm and funny is not quiet or not kind and vice versa.
If lucy is both kind and not wise then someone is not strong or tall and vice versa.
If alice is both creative and not rich then john is creative or not tall and vice versa.
If someone is both not happy and not calm then someone is either not patient or brave and vice versa.
Susan is not curious or not generous.
Mary is not happy or brave.
Someone is both brave and patient.
Mary is quiet or not rich.
Someone is either not strong or not patient. | Alice is not strong. | contradiction | (![X]:(~humble(X)<=>(~brave(X)&~strong(X))))&
(![X]:(quiet(X)=>(tall(X)&~wise(X))))&
(![X]:(rich(X)<=>(~quiet(X)<~>curious(X))))&
(![X]:((patient(X)&~kind(X))=>(curious(X)|~tall(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~old(X)<~>rich(X))))<=>(?[X]:((~generous(X)<~>kind(X)))))&
((?[X]:((happy(X)&rich(X))))=>((~wise(paul)<~>strong(paul))))&
(![X]:((~quiet(X)|~wise(X))<=>(strong(X)&rich(X))))&
(![X]:((rich(X)&happy(X))<=>(~strong(X)&rich(X))))&
((?[X]:((tall(X)<~>happy(X))))<=>(calm(lucy)))&
(![X]:((wise(X)<~>~funny(X))=>~generous(X)))&
((?[X]:(calm(X)))<=>((rich(susan)&~generous(susan))))&
(![X]:((calm(X)&funny(X))<=>(~quiet(X)|~kind(X))))&
(((kind(lucy)&~wise(lucy)))<=>(?[X]:((~strong(X)|tall(X)))))&
(((creative(alice)&~rich(alice)))<=>((creative(john)|~tall(john))))&
((?[X]:((~happy(X)&~calm(X))))<=>(?[X]:((~patient(X)<~>brave(X)))))&
((~curious(susan)|~generous(susan)))&
((~happy(mary)|brave(mary)))&
(?[X]:((brave(X)&patient(X))))&
((quiet(mary)|~rich(mary)))&
(?[X]:((~strong(X)<~>~patient(X)))) | ~strong(alice) | [
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8253689977451685359688863
% SZS output start Proof for 8253689977451685359688863
2. ! [X0] : (quiet(X0) => (~wise(X0) & tall(X0))) [input p1]
8. ! [X0] : ((~wise(X0) | ~quiet(X0)) <=> (rich(X0) & strong(X0))) [input p7]
22. ~strong(alice) [input hypothesis]
26. ! [X0] : ((~wise(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 2]
43. ! [X0] : (((~wise(X0) | ~quiet(X0)) | (~rich(X0) | ~strong(X0))) & ((rich(X0) & strong(X0)) | (wise(X0) & quiet(X0)))) [nnf transformation 8]
44. ! [X0] : ((~wise(X0) | ~quiet(X0) | ~rich(X0) | ~strong(X0)) & ((rich(X0) & strong(X0)) | (wise(X0) & quiet(X0)))) [flattening 43]
77. ~wise(X0) | ~quiet(X0) [cnf transformation 26]
95. quiet(X0) | strong(X0) [cnf transformation 44]
96. wise(X0) | strong(X0) [cnf transformation 44]
141. ~strong(alice) [cnf transformation 22]
256. 27 <=> ! [X0] : strong(X0) [avatar definition]
257. strong(X0) <- (27) [avatar component clause 256]
372. strong(X0) | ~quiet(X0) [resolution 96,77]
380. strong(X0) [subsumption resolution 372,95]
381. 27 [avatar split clause 380,256]
384. $false <- (27) [resolution 257,141]
387. ~27 [avatar contradiction clause 384]
388. $false [avatar sat refutation 381,387]
% SZS output end Proof for 8253689977451685359688863
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or not calm is calm and vice versa. If someone is both not patient and not wise then mary is not rich and vice versa. Everyone who is happy is both creative and not wise and vice versa. Everyone who is not strong or calm is not humble or not happy and vice versa. Everyone who is both calm and creative is both rich and not wise and vice versa. Everyone who is not patient is rich. Everyone who is both not kind and not generous is both not rich and not strong and vice versa. Everyone who is both happy and not calm is humble or not calm. If mary is either patient or not calm then paul is not brave or happy and vice versa. Everyone who is either not wise or tall is not rich and vice versa. If someone is either strong or not strong then someone is either generous or not strong. Everyone who is happy or not generous is not tall or quiet and vice versa. Everyone who is old or humble is curious or not generous. Someone is not kind or wise. John is either not patient or not funny. Someone is not generous. Someone is not old or rich. John is not creative. Alice is either old or not calm. | Paul is not old. | neutral | (![X]:((patient(X)<~>~calm(X))<=>calm(X)))&
((?[X]:((~patient(X)&~wise(X))))<=>(~rich(mary)))&
(![X]:(happy(X)<=>(creative(X)&~wise(X))))&
(![X]:((~strong(X)|calm(X))<=>(~humble(X)|~happy(X))))&
(![X]:((calm(X)&creative(X))<=>(rich(X)&~wise(X))))&
(![X]:(~patient(X)=>rich(X)))&
(![X]:((~kind(X)&~generous(X))<=>(~rich(X)&~strong(X))))&
(![X]:((happy(X)&~calm(X))=>(humble(X)|~calm(X))))&
(((patient(mary)<~>~calm(mary)))<=>((~brave(paul)|happy(paul))))&
(![X]:((~wise(X)<~>tall(X))<=>~rich(X)))&
((?[X]:((strong(X)<~>~strong(X))))=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((happy(X)|~generous(X))<=>(~tall(X)|quiet(X))))&
(![X]:((old(X)|humble(X))=>(curious(X)|~generous(X))))&
(?[X]:((~kind(X)|wise(X))))&
((~patient(john)<~>~funny(john)))&
(?[X]:(~generous(X)))&
(?[X]:((~old(X)|rich(X))))&
(~creative(john))&
((old(alice)<~>~calm(alice))) | ~old(paul) | [] | null | 0 |
Everyone who is funny or not wise is creative.
Everyone who is both humble and not brave is either not happy or wise.
If someone is not brave then lucy is tall.
Everyone who is either not happy or not brave is either not rich or not tall and vice versa.
Everyone who is patient is both not kind and humble and vice versa.
Everyone who is tall or not rich is strong.
If someone is not patient then someone is either creative or not generous.
Everyone who is not generous is not wise.
Everyone who is both not rich and tall is not generous.
Everyone who is either not funny or rich is patient.
Everyone who is both kind and not generous is either not calm or rich and vice versa.
Everyone who is not generous is patient and vice versa.
Everyone who is creative is either rich or not quiet and vice versa.
If someone is kind or not happy then someone is both not generous and not humble and vice versa.
Everyone who is either generous or strong is both not wise and not brave and vice versa.
Everyone who is both curious and not wise is not generous and vice versa.
Someone is funny.
John is creative.
Someone is quiet or generous.
Someone is not happy or not quiet.
Someone is creative.
Susan is not patient.
Alice is humble or funny.
Someone is not wise or quiet. | Lucy is not generous. | contradiction | (![X]:((funny(X)|~wise(X))=>creative(X)))&
(![X]:((humble(X)&~brave(X))=>(~happy(X)<~>wise(X))))&
((?[X]:(~brave(X)))=>(tall(lucy)))&
(![X]:((~happy(X)<~>~brave(X))<=>(~rich(X)<~>~tall(X))))&
(![X]:(patient(X)<=>(~kind(X)&humble(X))))&
(![X]:((tall(X)|~rich(X))=>strong(X)))&
((?[X]:(~patient(X)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:((~funny(X)<~>rich(X))=>patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(creative(X)<=>(rich(X)<~>~quiet(X))))&
((?[X]:((kind(X)|~happy(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~wise(X)&~brave(X))))&
(![X]:((curious(X)&~wise(X))<=>~generous(X)))&
(?[X]:(funny(X)))&
(creative(john))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:(creative(X)))&
(~patient(susan))&
((humble(alice)|funny(alice)))&
(?[X]:((~wise(X)|quiet(X)))) | ~generous(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3034228291595798509200303
% SZS output start Proof for 3034228291595798509200303
2. ! [X0] : ((~brave(X0) & humble(X0)) => (~happy(X0) <~> wise(X0))) [input p1]
3. ? [X0] : ~brave(X0) => tall(lucy) [input p2]
4. ! [X0] : ((~happy(X0) <~> ~brave(X0)) <=> (~rich(X0) <~> ~tall(X0))) [input p3]
5. ! [X0] : (patient(X0) <=> (humble(X0) & ~kind(X0))) [input p4]
6. ! [X0] : ((~rich(X0) | tall(X0)) => strong(X0)) [input p5]
8. ! [X0] : (~generous(X0) => ~wise(X0)) [input p7]
12. ! [X0] : (~generous(X0) <=> patient(X0)) [input p11]
14. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X0] : (~humble(X0) & ~generous(X0)) [input p13]
15. ! [X0] : ((generous(X0) <~> strong(X0)) <=> (~brave(X0) & ~wise(X0))) [input p14]
25. ~generous(lucy) [input hypothesis]
27. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X1] : (~humble(X1) & ~generous(X1)) [rectify 14]
29. ! [X0] : ((~happy(X0) <~> wise(X0)) | (brave(X0) | ~humble(X0))) [ennf transformation 2]
30. ! [X0] : ((~happy(X0) <~> wise(X0)) | brave(X0) | ~humble(X0)) [flattening 29]
31. tall(lucy) | ! [X0] : brave(X0) [ennf transformation 3]
32. ! [X0] : (strong(X0) | (rich(X0) & ~tall(X0))) [ennf transformation 6]
34. ! [X0] : (~wise(X0) | generous(X0)) [ennf transformation 8]
38. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | brave(X0) | ~humble(X0)) [nnf transformation 30]
39. ! [X0] : ((((brave(X0) | happy(X0)) & (~brave(X0) | ~happy(X0))) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) & (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ((~happy(X0) | brave(X0)) & (~brave(X0) | happy(X0))))) [nnf transformation 4]
40. ! [X0] : ((patient(X0) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [nnf transformation 5]
41. ! [X0] : ((patient(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [flattening 40]
49. ! [X0] : ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))) [nnf transformation 12]
51. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X1] : (~humble(X1) & ~generous(X1)) | ! [X0] : (happy(X0) & ~kind(X0))) [nnf transformation 27]
52. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X2] : (~humble(X2) & ~generous(X2)) | ! [X3] : (happy(X3) & ~kind(X3))) [rectify 51]
53. ? [X0] : (~happy(X0) | kind(X0)) => (~happy(sK1) | kind(sK1)) [choice axiom]
54. ? [X2] : (~humble(X2) & ~generous(X2)) => (~humble(sK2) & ~generous(sK2)) [choice axiom]
55. ((~happy(sK1) | kind(sK1)) | ! [X1] : (humble(X1) | generous(X1))) & ((~humble(sK2) & ~generous(sK2)) | ! [X3] : (happy(X3) & ~kind(X3))) [skolemisation 52,54,53]
56. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [nnf transformation 15]
57. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [flattening 56]
72. ~happy(X0) | wise(X0) | brave(X0) | ~humble(X0) [cnf transformation 38]
74. tall(lucy) | brave(X0) [cnf transformation 31]
80. ~rich(X0) | ~happy(X0) | ~brave(X0) | tall(X0) [cnf transformation 39]
84. ~patient(X0) | humble(X0) [cnf transformation 41]
86. ~tall(X0) | strong(X0) [cnf transformation 32]
87. strong(X0) | rich(X0) [cnf transformation 32]
90. ~wise(X0) | generous(X0) [cnf transformation 34]
100. generous(X0) | patient(X0) [cnf transformation 49]
107. ~generous(sK2) | happy(X3) [cnf transformation 55]
109. ~humble(sK2) | happy(X3) [cnf transformation 55]
114. ~strong(X0) | generous(X0) | ~brave(X0) [cnf transformation 57]
128. ~generous(lucy) [cnf transformation 25]
130. 1 <=> ! [X0] : brave(X0) [avatar definition]
131. brave(X0) <- (1) [avatar component clause 130]
133. 2 <=> tall(lucy) [avatar definition]
134. ~tall(lucy) <- (~2) [avatar component clause 133]
135. tall(lucy) <- (2) [avatar component clause 133]
136. 1 | 2 [avatar split clause 74,133,130]
163. 9 <=> ! [X3] : happy(X3) [avatar definition]
164. happy(X3) <- (9) [avatar component clause 163]
166. 10 <=> humble(sK2) [avatar definition]
168. ~humble(sK2) <- (~10) [avatar component clause 166]
169. 9 | ~10 [avatar split clause 109,166,163]
175. 12 <=> generous(sK2) [avatar definition]
177. ~generous(sK2) <- (~12) [avatar component clause 175]
178. 9 | ~12 [avatar split clause 107,175,163]
220. strong(lucy) <- (2) [resolution 86,135]
224. patient(lucy) [resolution 100,128]
225. patient(sK2) <- (~12) [resolution 100,177]
226. humble(lucy) [resolution 224,84]
229. humble(sK2) <- (~12) [resolution 225,84]
230. $false <- (~10, ~12) [subsumption resolution 229,168]
231. 10 | 12 [avatar contradiction clause 230]
368. generous(lucy) | ~brave(lucy) <- (2) [resolution 114,220]
369. ~brave(X0) | generous(X0) | rich(X0) [resolution 114,87]
370. ~brave(lucy) <- (2) [subsumption resolution 368,128]
392. ~humble(X0) | brave(X0) | wise(X0) <- (9) [resolution 72,164]
505. brave(lucy) | wise(lucy) <- (9) [resolution 392,226]
507. wise(lucy) <- (2, 9) [subsumption resolution 505,370]
665. generous(lucy) <- (2, 9) [resolution 507,90]
666. $false <- (2, 9) [subsumption resolution 665,128]
667. ~2 | ~9 [avatar contradiction clause 666]
683. generous(X0) | rich(X0) <- (1) [resolution 131,369]
736. rich(lucy) <- (1) [resolution 683,128]
757. ~happy(lucy) | ~brave(lucy) | tall(lucy) <- (1) [resolution 736,80]
762. ~brave(lucy) | tall(lucy) <- (1, 9) [subsumption resolution 757,164]
763. tall(lucy) <- (1, 9) [subsumption resolution 762,131]
764. $false <- (1, ~2, 9) [subsumption resolution 763,134]
765. ~1 | 2 | ~9 [avatar contradiction clause 764]
775. $false [avatar sat refutation 136,169,178,231,667,765]
% SZS output end Proof for 3034228291595798509200303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is brave. Everyone who is both curious and not kind is not rich or happy. Everyone who is generous is not rich. Everyone who is strong is both not humble and not brave and vice versa. Everyone who is both creative and not curious is both funny and not calm and vice versa. If fred is not happy then someone is calm or curious and vice versa. If john is not creative or humble then someone is wise or patient and vice versa. Everyone who is both not quiet and not creative is happy and vice versa. Everyone who is both not old and not strong is curious or not patient. If someone is not happy or not curious then someone is both kind and quiet. If fred is either wise or quiet then someone is brave or not humble. If susan is either not quiet or old then someone is kind or curious and vice versa. Everyone who is either generous or old is either brave or not generous and vice versa. Everyone who is both not tall and not kind is strong and vice versa. Everyone who is not curious or wise is rich or not old and vice versa. Everyone who is not quiet is not creative or strong and vice versa. Someone is either tall or creative. Alice is rich or not brave. Someone is both not calm and not generous. Paul is either rich or kind. Someone is either creative or not wise. Someone is not humble or not quiet. Someone is not creative. | Paul is not rich. | neutral | (![X]:(rich(X)=>brave(X)))&
(![X]:((curious(X)&~kind(X))=>(~rich(X)|happy(X))))&
(![X]:(generous(X)=>~rich(X)))&
(![X]:(strong(X)<=>(~humble(X)&~brave(X))))&
(![X]:((creative(X)&~curious(X))<=>(funny(X)&~calm(X))))&
((~happy(fred))<=>(?[X]:((calm(X)|curious(X)))))&
(((~creative(john)|humble(john)))<=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((~quiet(X)&~creative(X))<=>happy(X)))&
(![X]:((~old(X)&~strong(X))=>(curious(X)|~patient(X))))&
((?[X]:((~happy(X)|~curious(X))))=>(?[X]:((kind(X)&quiet(X)))))&
(((wise(fred)<~>quiet(fred)))=>(?[X]:((brave(X)|~humble(X)))))&
(((~quiet(susan)<~>old(susan)))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((generous(X)<~>old(X))<=>(brave(X)<~>~generous(X))))&
(![X]:((~tall(X)&~kind(X))<=>strong(X)))&
(![X]:((~curious(X)|wise(X))<=>(rich(X)|~old(X))))&
(![X]:(~quiet(X)<=>(~creative(X)|strong(X))))&
(?[X]:((tall(X)<~>creative(X))))&
((rich(alice)|~brave(alice)))&
(?[X]:((~calm(X)&~generous(X))))&
((rich(paul)<~>kind(paul)))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((~humble(X)|~quiet(X))))&
(?[X]:(~creative(X))) | ~rich(paul) | [] | null | 0 |
Everyone who is generous or happy is either curious or not patient.
If someone is brave then someone is not funny.
If someone is curious or happy then lucy is both not curious and rich and vice versa.
Everyone who is not strong or quiet is calm or strong.
Everyone who is not humble or calm is brave.
Everyone who is brave or generous is both kind and not brave and vice versa.
If someone is not old or not creative then someone is both not strong and patient and vice versa.
Everyone who is not tall or not patient is not kind.
Everyone who is either quiet or patient is not calm.
If someone is both calm and rich then lucy is kind or not rich.
Everyone who is either creative or kind is either humble or not rich.
Everyone who is patient is not humble and vice versa.
If someone is either not patient or generous then someone is both not wise and funny.
Everyone who is not humble is not tall.
If fred is creative or happy then fred is either not wise or not creative and vice versa.
Everyone who is not rich is either tall or not generous.
Someone is not kind.
Someone is funny or not strong.
Someone is not wise or wise.
Lucy is strong.
Susan is kind or funny.
Susan is not brave.
Someone is either old or not curious. | Susan is generous. | contradiction | (![X]:((generous(X)|happy(X))=>(curious(X)<~>~patient(X))))&
((?[X]:(brave(X)))=>(?[X]:(~funny(X))))&
((?[X]:((curious(X)|happy(X))))<=>((~curious(lucy)&rich(lucy))))&
(![X]:((~strong(X)|quiet(X))=>(calm(X)|strong(X))))&
(![X]:((~humble(X)|calm(X))=>brave(X)))&
(![X]:((brave(X)|generous(X))<=>(kind(X)&~brave(X))))&
((?[X]:((~old(X)|~creative(X))))<=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~tall(X)|~patient(X))=>~kind(X)))&
(![X]:((quiet(X)<~>patient(X))=>~calm(X)))&
((?[X]:((calm(X)&rich(X))))=>((kind(lucy)|~rich(lucy))))&
(![X]:((creative(X)<~>kind(X))=>(humble(X)<~>~rich(X))))&
(![X]:(patient(X)<=>~humble(X)))&
((?[X]:((~patient(X)<~>generous(X))))=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:(~humble(X)=>~tall(X)))&
(((creative(fred)|happy(fred)))<=>((~wise(fred)<~>~creative(fred))))&
(![X]:(~rich(X)=>(tall(X)<~>~generous(X))))&
(?[X]:(~kind(X)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((~wise(X)|wise(X))))&
(strong(lucy))&
((kind(susan)|funny(susan)))&
(~brave(susan))&
(?[X]:((old(X)<~>~curious(X)))) | generous(susan) | [
"p4",
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2149227383974133301850455
% SZS output start Proof for 2149227383974133301850455
5. ! [X0] : ((calm(X0) | ~humble(X0)) => brave(X0)) [input p4]
6. ! [X0] : ((generous(X0) | brave(X0)) <=> (~brave(X0) & kind(X0))) [input p5]
8. ! [X0] : ((~patient(X0) | ~tall(X0)) => ~kind(X0)) [input p7]
12. ! [X0] : (patient(X0) <=> ~humble(X0)) [input p11]
24. generous(susan) [input hypothesis]
32. ! [X0] : (brave(X0) | (~calm(X0) & humble(X0))) [ennf transformation 5]
33. ! [X0] : (~kind(X0) | (patient(X0) & tall(X0))) [ennf transformation 8]
50. ! [X0] : (((generous(X0) | brave(X0)) | (brave(X0) | ~kind(X0))) & ((~brave(X0) & kind(X0)) | (~generous(X0) & ~brave(X0)))) [nnf transformation 6]
51. ! [X0] : ((generous(X0) | brave(X0) | brave(X0) | ~kind(X0)) & ((~brave(X0) & kind(X0)) | (~generous(X0) & ~brave(X0)))) [flattening 50]
59. ! [X0] : ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))) [nnf transformation 12]
88. humble(X0) | brave(X0) [cnf transformation 32]
91. ~generous(X0) | kind(X0) [cnf transformation 51]
92. ~brave(X0) | ~brave(X0) [cnf transformation 51]
101. ~kind(X0) | patient(X0) [cnf transformation 33]
109. ~humble(X0) | ~patient(X0) [cnf transformation 59]
132. generous(susan) [cnf transformation 24]
135. ~brave(X0) [duplicate literal removal 92]
139. 1 <=> ! [X1] : ~brave(X1) [avatar definition]
140. ~brave(X1) <- (1) [avatar component clause 139]
173. 1 [avatar split clause 135,139]
256. 27 <=> kind(susan) [avatar definition]
258. kind(susan) <- (27) [avatar component clause 256]
274. kind(susan) [resolution 91,132]
276. patient(susan) <- (27) [resolution 101,258]
277. ~patient(X0) | brave(X0) [resolution 109,88]
278. ~patient(X0) <- (1) [subsumption resolution 277,140]
281. $false <- (1, 27) [resolution 278,276]
282. ~1 | ~27 [avatar contradiction clause 281]
284. 27 [avatar split clause 274,256]
285. $false [avatar sat refutation 173,282,284]
% SZS output end Proof for 2149227383974133301850455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both humble and not happy is either not curious or not calm and vice versa.
If fred is both not rich and not patient then susan is either not brave or not patient.
If someone is both old and funny then someone is both rich and kind and vice versa.
If someone is creative then someone is not tall or not brave and vice versa.
Everyone who is either not old or patient is kind and vice versa.
If someone is either not patient or not quiet then someone is both wise and not curious.
If lucy is not happy then someone is both not humble and not wise and vice versa.
Everyone who is not humble or not calm is either tall or brave.
If someone is both not tall and not quiet then someone is patient and vice versa.
If susan is not rich or not calm then someone is not quiet and vice versa.
If someone is not wise then someone is both curious and strong.
Everyone who is not quiet is both not wise and not brave.
Everyone who is both not tall and not brave is not kind or calm and vice versa.
Everyone who is both not humble and not kind is either rich or not funny and vice versa.
If someone is not funny or rich then john is either patient or curious.
Everyone who is creative is both strong and old and vice versa.
Someone is quiet.
Lucy is creative.
Mary is either strong or not strong.
Someone is both creative and tall.
Someone is tall or funny.
Fred is not patient.
Someone is both quiet and not curious.
Paul is both happy and not calm. | Fred is not wise. | neutral | (![X]:((humble(X)&~happy(X))<=>(~curious(X)<~>~calm(X))))&
(((~rich(fred)&~patient(fred)))=>((~brave(susan)<~>~patient(susan))))&
((?[X]:((old(X)&funny(X))))<=>(?[X]:((rich(X)&kind(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:((~old(X)<~>patient(X))<=>kind(X)))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:((wise(X)&~curious(X)))))&
((~happy(lucy))<=>(?[X]:((~humble(X)&~wise(X)))))&
(![X]:((~humble(X)|~calm(X))=>(tall(X)<~>brave(X))))&
((?[X]:((~tall(X)&~quiet(X))))<=>(?[X]:(patient(X))))&
(((~rich(susan)|~calm(susan)))<=>(?[X]:(~quiet(X))))&
((?[X]:(~wise(X)))=>(?[X]:((curious(X)&strong(X)))))&
(![X]:(~quiet(X)=>(~wise(X)&~brave(X))))&
(![X]:((~tall(X)&~brave(X))<=>(~kind(X)|calm(X))))&
(![X]:((~humble(X)&~kind(X))<=>(rich(X)<~>~funny(X))))&
((?[X]:((~funny(X)|rich(X))))=>((patient(john)<~>curious(john))))&
(![X]:(creative(X)<=>(strong(X)&old(X))))&
(?[X]:(quiet(X)))&
(creative(lucy))&
((strong(mary)<~>~strong(mary)))&
(?[X]:((creative(X)&tall(X))))&
(?[X]:((tall(X)|funny(X))))&
(~patient(fred))&
(?[X]:((quiet(X)&~curious(X))))&
((happy(paul)&~calm(paul))) | ~wise(fred) | [] | null | 0 |
If someone is both not patient and not funny then someone is both patient and not creative.
Everyone who is rich is both creative and not rich and vice versa.
If someone is not happy then alice is not old and vice versa.
If fred is both not kind and curious then someone is both creative and calm and vice versa.
Everyone who is happy or not creative is both not happy and brave.
If fred is generous or not patient then someone is not happy or not generous.
If someone is creative or not old then mary is not quiet or strong and vice versa.
If john is both not creative and not old then someone is generous or not patient and vice versa.
Everyone who is both curious and wise is not brave or quiet and vice versa.
If alice is not curious then someone is both quiet and brave.
Everyone who is both not humble and quiet is tall or funny.
If john is happy or not wise then someone is both not rich and not old and vice versa.
Everyone who is not funny is either kind or not patient.
Everyone who is either not old or not strong is not curious.
Everyone who is not strong or not calm is not strong and vice versa.
If someone is either strong or kind then fred is not tall and vice versa.
Lucy is not curious or strong.
Someone is either not happy or old.
Alice is either not patient or kind.
Paul is either happy or not quiet.
Someone is either old or not happy.
Someone is both curious and not rich.
Someone is either quiet or not wise. | John is wise. | contradiction | ((?[X]:((~patient(X)&~funny(X))))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:(rich(X)<=>(creative(X)&~rich(X))))&
((?[X]:(~happy(X)))<=>(~old(alice)))&
(((~kind(fred)&curious(fred)))<=>(?[X]:((creative(X)&calm(X)))))&
(![X]:((happy(X)|~creative(X))=>(~happy(X)&brave(X))))&
(((generous(fred)|~patient(fred)))=>(?[X]:((~happy(X)|~generous(X)))))&
((?[X]:((creative(X)|~old(X))))<=>((~quiet(mary)|strong(mary))))&
(((~creative(john)&~old(john)))<=>(?[X]:((generous(X)|~patient(X)))))&
(![X]:((curious(X)&wise(X))<=>(~brave(X)|quiet(X))))&
((~curious(alice))=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((~humble(X)&quiet(X))=>(tall(X)|funny(X))))&
(((happy(john)|~wise(john)))<=>(?[X]:((~rich(X)&~old(X)))))&
(![X]:(~funny(X)=>(kind(X)<~>~patient(X))))&
(![X]:((~old(X)<~>~strong(X))=>~curious(X)))&
(![X]:((~strong(X)|~calm(X))<=>~strong(X)))&
((?[X]:((strong(X)<~>kind(X))))<=>(~tall(fred)))&
((~curious(lucy)|strong(lucy)))&
(?[X]:((~happy(X)<~>old(X))))&
((~patient(alice)<~>kind(alice)))&
((happy(paul)<~>~quiet(paul)))&
(?[X]:((old(X)<~>~happy(X))))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((quiet(X)<~>~wise(X)))) | wise(john) | [
"p1",
"p2",
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3784373616853883609275438
% SZS output start Proof for 3784373616853883609275438
2. ! [X0] : (rich(X0) <=> (~rich(X0) & creative(X0))) [input p1]
3. ? [X0] : ~happy(X0) <=> ~old(alice) [input p2]
5. ! [X0] : ((~creative(X0) | happy(X0)) => (brave(X0) & ~happy(X0))) [input p4]
12. (~wise(john) | happy(john)) <=> ? [X0] : (~old(X0) & ~rich(X0)) [input p11]
24. wise(john) [input hypothesis]
29. ! [X0] : ((brave(X0) & ~happy(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 5]
33. ! [X0] : ((rich(X0) | (rich(X0) | ~creative(X0))) & ((~rich(X0) & creative(X0)) | ~rich(X0))) [nnf transformation 2]
34. ! [X0] : ((rich(X0) | rich(X0) | ~creative(X0)) & ((~rich(X0) & creative(X0)) | ~rich(X0))) [flattening 33]
35. (? [X0] : ~happy(X0) | old(alice)) & (~old(alice) | ! [X0] : happy(X0)) [nnf transformation 3]
36. (? [X0] : ~happy(X0) | old(alice)) & (~old(alice) | ! [X1] : happy(X1)) [rectify 35]
37. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
38. (~happy(sK0) | old(alice)) & (~old(alice) | ! [X1] : happy(X1)) [skolemisation 36,37]
60. ((~wise(john) | happy(john)) | ! [X0] : (old(X0) | rich(X0))) & (? [X0] : (~old(X0) & ~rich(X0)) | (wise(john) & ~happy(john))) [nnf transformation 12]
61. (~wise(john) | happy(john) | ! [X0] : (old(X0) | rich(X0))) & (? [X0] : (~old(X0) & ~rich(X0)) | (wise(john) & ~happy(john))) [flattening 60]
62. (~wise(john) | happy(john) | ! [X0] : (old(X0) | rich(X0))) & (? [X1] : (~old(X1) & ~rich(X1)) | (wise(john) & ~happy(john))) [rectify 61]
63. ? [X1] : (~old(X1) & ~rich(X1)) => (~old(sK6) & ~rich(sK6)) [choice axiom]
64. (~wise(john) | happy(john) | ! [X0] : (old(X0) | rich(X0))) & ((~old(sK6) & ~rich(sK6)) | (wise(john) & ~happy(john))) [skolemisation 62,63]
86. ~rich(X0) | ~rich(X0) [cnf transformation 34]
88. ~old(alice) | happy(X1) [cnf transformation 38]
94. ~happy(X0) | ~happy(X0) [cnf transformation 29]
120. ~wise(john) | happy(john) | old(X0) | rich(X0) [cnf transformation 64]
143. wise(john) [cnf transformation 24]
144. ~happy(X0) [duplicate literal removal 94]
145. ~rich(X0) [duplicate literal removal 86]
148. 1 <=> old(alice) [avatar definition]
149. ~old(alice) <- (~1) [avatar component clause 148]
157. 3 <=> ! [X1] : happy(X1) [avatar definition]
158. happy(X1) <- (3) [avatar component clause 157]
159. 3 | ~1 [avatar split clause 88,148,157]
202. 13 <=> ! [X1] : old(X1) [avatar definition]
203. old(X1) <- (13) [avatar component clause 202]
250. ~wise(john) | old(X0) | rich(X0) [subsumption resolution 120,144]
251. ~wise(john) | old(X0) [subsumption resolution 250,145]
253. 24 <=> wise(john) [avatar definition]
256. 13 | ~24 [avatar split clause 251,253,202]
315. 24 [avatar split clause 143,253]
318. $false <- (~1, 13) [subsumption resolution 149,203]
319. 1 | ~13 [avatar contradiction clause 318]
320. $false <- (3) [subsumption resolution 158,144]
321. ~3 [avatar contradiction clause 320]
322. $false [avatar sat refutation 159,256,315,319,321]
% SZS output end Proof for 3784373616853883609275438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or quiet is both not strong and strong. Everyone who is not rich or not happy is happy. If someone is both funny and kind then someone is not quiet or happy and vice versa. If lucy is not curious or tall then john is humble or not wise. Everyone who is not old is both curious and not kind. If susan is creative then someone is wise and vice versa. If someone is humble or kind then lucy is both not humble and not wise. Everyone who is calm or humble is either not strong or generous. Everyone who is not quiet is both not happy and not wise and vice versa. Everyone who is tall is both not humble and not patient. Everyone who is either strong or calm is not kind or patient. If someone is both old and calm then someone is not funny. Everyone who is either rich or not curious is generous. Everyone who is both kind and not quiet is quiet or not old. Lucy is either not curious or not patient. Someone is wise or generous. Alice is not wise or not strong. Someone is either not kind or strong. Paul is calm. Paul is not wise or kind. Someone is either not patient or brave. Someone is either humble or generous. | Alice is not quiet. | contradiction | (![X]:((funny(X)<~>quiet(X))=>(~strong(X)&strong(X))))&
(![X]:((~rich(X)|~happy(X))=>happy(X)))&
((?[X]:((funny(X)&kind(X))))<=>(?[X]:((~quiet(X)|happy(X)))))&
(((~curious(lucy)|tall(lucy)))=>((humble(john)|~wise(john))))&
(![X]:(~old(X)=>(curious(X)&~kind(X))))&
((creative(susan))<=>(?[X]:(wise(X))))&
((?[X]:((humble(X)|kind(X))))=>((~humble(lucy)&~wise(lucy))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)<~>generous(X))))&
(![X]:(~quiet(X)<=>(~happy(X)&~wise(X))))&
(![X]:(tall(X)=>(~humble(X)&~patient(X))))&
(![X]:((strong(X)<~>calm(X))=>(~kind(X)|patient(X))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:(~funny(X))))&
(![X]:((rich(X)<~>~curious(X))=>generous(X)))&
(![X]:((kind(X)&~quiet(X))=>(quiet(X)|~old(X))))&
((~curious(lucy)<~>~patient(lucy)))&
(?[X]:((wise(X)|generous(X))))&
((~wise(alice)|~strong(alice)))&
(?[X]:((~kind(X)<~>strong(X))))&
(calm(paul))&
((~wise(paul)|kind(paul)))&
(?[X]:((~patient(X)<~>brave(X))))&
(?[X]:((humble(X)<~>generous(X)))) | ~quiet(alice) | [
"p1",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5157212887100714162208900
% SZS output start Proof for 5157212887100714162208900
2. ! [X0] : ((~happy(X0) | ~rich(X0)) => happy(X0)) [input p1]
9. ! [X0] : (~quiet(X0) <=> (~wise(X0) & ~happy(X0))) [input p8]
23. ~quiet(alice) [input hypothesis]
29. ! [X0] : (happy(X0) | (happy(X0) & rich(X0))) [ennf transformation 2]
52. ! [X0] : ((~quiet(X0) | (wise(X0) | happy(X0))) & ((~wise(X0) & ~happy(X0)) | quiet(X0))) [nnf transformation 9]
53. ! [X0] : ((~quiet(X0) | wise(X0) | happy(X0)) & ((~wise(X0) & ~happy(X0)) | quiet(X0))) [flattening 52]
76. happy(X0) | happy(X0) [cnf transformation 29]
95. ~happy(X0) | quiet(X0) [cnf transformation 53]
116. ~quiet(alice) [cnf transformation 23]
118. happy(X0) [duplicate literal removal 76]
167. quiet(X0) [subsumption resolution 95,118]
239. $false [subsumption resolution 116,167]
% SZS output end Proof for 5157212887100714162208900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is calm.
Everyone who is both not humble and kind is brave.
If someone is creative or not brave then someone is not wise.
Everyone who is not funny is both not generous and curious and vice versa.
Everyone who is creative is either funny or not calm.
If mary is either generous or calm then someone is not old.
Everyone who is both not happy and not quiet is either not strong or not humble and vice versa.
Everyone who is kind is generous or wise and vice versa.
Everyone who is not calm is rich and vice versa.
If mary is both generous and kind then lucy is not creative or old and vice versa.
If someone is both not quiet and happy then paul is both creative and not happy.
If lucy is not wise then john is both funny and tall.
If lucy is patient or not patient then mary is both not humble and strong and vice versa.
If someone is generous then john is brave or not old and vice versa.
Everyone who is either not patient or not generous is old.
If someone is either not rich or not generous then mary is both not generous and old.
Alice is both calm and brave.
John is creative or funny.
Someone is either not creative or not rich.
Someone is not tall.
Someone is not humble or not creative.
Someone is both curious and not kind. | Lucy is rich. | contradiction | (![X]:(~calm(X)=>calm(X)))&
(![X]:((~humble(X)&kind(X))=>brave(X)))&
((?[X]:((creative(X)|~brave(X))))=>(?[X]:(~wise(X))))&
(![X]:(~funny(X)<=>(~generous(X)&curious(X))))&
(![X]:(creative(X)=>(funny(X)<~>~calm(X))))&
(((generous(mary)<~>calm(mary)))=>(?[X]:(~old(X))))&
(![X]:((~happy(X)&~quiet(X))<=>(~strong(X)<~>~humble(X))))&
(![X]:(kind(X)<=>(generous(X)|wise(X))))&
(![X]:(~calm(X)<=>rich(X)))&
(((generous(mary)&kind(mary)))<=>((~creative(lucy)|old(lucy))))&
((?[X]:((~quiet(X)&happy(X))))=>((creative(paul)&~happy(paul))))&
((~wise(lucy))=>((funny(john)&tall(john))))&
(((patient(lucy)|~patient(lucy)))<=>((~humble(mary)&strong(mary))))&
((?[X]:(generous(X)))<=>((brave(john)|~old(john))))&
(![X]:((~patient(X)<~>~generous(X))=>old(X)))&
((?[X]:((~rich(X)<~>~generous(X))))=>((~generous(mary)&old(mary))))&
((calm(alice)&brave(alice)))&
((creative(john)|funny(john)))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~humble(X)|~creative(X))))&
(?[X]:((curious(X)&~kind(X)))) | rich(lucy) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 49173609888262994768243
% SZS output start Proof for 49173609888262994768243
1. ! [X0] : (~calm(X0) => calm(X0)) [input p0]
9. ! [X0] : (~calm(X0) <=> rich(X0)) [input p8]
23. rich(lucy) [input hypothesis]
25. ! [X0] : (calm(X0) | calm(X0)) [ennf transformation 1]
48. ! [X0] : ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0))) [nnf transformation 9]
69. calm(X0) | calm(X0) [cnf transformation 25]
90. ~calm(X0) | ~rich(X0) [cnf transformation 48]
123. rich(lucy) [cnf transformation 23]
124. calm(X0) [duplicate literal removal 69]
148. ~rich(X0) [subsumption resolution 90,124]
248. $false [subsumption resolution 123,148]
% SZS output end Proof for 49173609888262994768243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not brave is either not quiet or old. Everyone who is either creative or not strong is either patient or not creative. Everyone who is not generous is both humble and not quiet. Everyone who is kind is curious or not rich. If someone is curious or funny then someone is both not generous and not wise. If someone is humble or strong then susan is either not wise or kind. If mary is either not creative or not brave then mary is either rich or not patient. If lucy is either not patient or not calm then someone is either not wise or curious and vice versa. If paul is not creative or not brave then someone is either humble or not patient and vice versa. If someone is not tall then someone is both not calm and calm. If paul is not funny then someone is calm or kind. Everyone who is either not tall or not happy is either not happy or wise and vice versa. If fred is tall or not wise then mary is either happy or not curious. Everyone who is either generous or not creative is both not wise and humble and vice versa. Everyone who is either happy or not strong is either not rich or not curious and vice versa. If someone is not kind or not old then someone is calm or not wise. Someone is both not brave and not happy. Someone is both strong and not old. Someone is tall. Alice is quiet or funny. Someone is either creative or humble. Someone is not rich. | Mary is not rich. | neutral | (![X]:((~tall(X)|~brave(X))=>(~quiet(X)<~>old(X))))&
(![X]:((creative(X)<~>~strong(X))=>(patient(X)<~>~creative(X))))&
(![X]:(~generous(X)=>(humble(X)&~quiet(X))))&
(![X]:(kind(X)=>(curious(X)|~rich(X))))&
((?[X]:((curious(X)|funny(X))))=>(?[X]:((~generous(X)&~wise(X)))))&
((?[X]:((humble(X)|strong(X))))=>((~wise(susan)<~>kind(susan))))&
(((~creative(mary)<~>~brave(mary)))=>((rich(mary)<~>~patient(mary))))&
(((~patient(lucy)<~>~calm(lucy)))<=>(?[X]:((~wise(X)<~>curious(X)))))&
(((~creative(paul)|~brave(paul)))<=>(?[X]:((humble(X)<~>~patient(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((~calm(X)&calm(X)))))&
((~funny(paul))=>(?[X]:((calm(X)|kind(X)))))&
(![X]:((~tall(X)<~>~happy(X))<=>(~happy(X)<~>wise(X))))&
(((tall(fred)|~wise(fred)))=>((happy(mary)<~>~curious(mary))))&
(![X]:((generous(X)<~>~creative(X))<=>(~wise(X)&humble(X))))&
(![X]:((happy(X)<~>~strong(X))<=>(~rich(X)<~>~curious(X))))&
((?[X]:((~kind(X)|~old(X))))=>(?[X]:((calm(X)|~wise(X)))))&
(?[X]:((~brave(X)&~happy(X))))&
(?[X]:((strong(X)&~old(X))))&
(?[X]:(tall(X)))&
((quiet(alice)|funny(alice)))&
(?[X]:((creative(X)<~>humble(X))))&
(?[X]:(~rich(X))) | ~rich(mary) | [] | null | 0 |
Everyone who is not generous is rich or wise and vice versa.
Everyone who is not kind is either not generous or wise.
Everyone who is patient is either not wise or strong.
Everyone who is rich or patient is both wise and not patient and vice versa.
Everyone who is both humble and happy is wise or happy and vice versa.
Everyone who is not strong or not generous is either tall or not curious and vice versa.
If someone is either not quiet or not curious then someone is both not old and funny.
Everyone who is patient or not kind is not strong or happy and vice versa.
Everyone who is not old or not happy is curious and vice versa.
Everyone who is either creative or not patient is either not quiet or not tall and vice versa.
Everyone who is either not calm or old is either not quiet or not kind.
Everyone who is not strong is either strong or generous.
If paul is either curious or quiet then alice is rich or wise.
Everyone who is not humble is not generous or not quiet and vice versa.
John is not happy or tall.
Someone is either not funny or not curious.
Someone is not creative or rich.
Fred is calm.
Someone is either not kind or not funny. | John is creative. | neutral | (![X]:(~generous(X)<=>(rich(X)|wise(X))))&
(![X]:(~kind(X)=>(~generous(X)<~>wise(X))))&
(![X]:(patient(X)=>(~wise(X)<~>strong(X))))&
(![X]:((rich(X)|patient(X))<=>(wise(X)&~patient(X))))&
(![X]:((humble(X)&happy(X))<=>(wise(X)|happy(X))))&
(![X]:((~strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((patient(X)|~kind(X))<=>(~strong(X)|happy(X))))&
(![X]:((~old(X)|~happy(X))<=>curious(X)))&
(![X]:((creative(X)<~>~patient(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((~calm(X)<~>old(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:(~strong(X)=>(strong(X)<~>generous(X))))&
(((curious(paul)<~>quiet(paul)))=>((rich(alice)|wise(alice))))&
(![X]:(~humble(X)<=>(~generous(X)|~quiet(X))))&
((~happy(john)|tall(john)))&
(?[X]:((~funny(X)<~>~curious(X))))&
(?[X]:((~creative(X)|rich(X))))&
(calm(fred))&
(?[X]:((~kind(X)<~>~funny(X)))) | creative(john) | [] | null | 0 |
If alice is funny or rich then alice is brave.
If someone is either wise or patient then someone is humble and vice versa.
Everyone who is both tall and happy is both rich and not calm and vice versa.
Everyone who is not patient or curious is either old or wise and vice versa.
If someone is not tall then someone is wise or old and vice versa.
If someone is either wise or humble then mary is not tall or not patient.
Everyone who is funny or tall is both humble and funny.
If paul is both not funny and calm then someone is both not strong and not tall and vice versa.
If someone is not funny or old then lucy is either not funny or not wise and vice versa.
If fred is either not wise or generous then someone is not kind or creative and vice versa.
Everyone who is not strong or strong is brave or calm.
Everyone who is both not humble and not calm is not happy or quiet and vice versa.
Everyone who is not strong is either strong or humble and vice versa.
If someone is either not rich or tall then someone is both brave and generous and vice versa.
Everyone who is both humble and not wise is quiet or not wise and vice versa.
If lucy is not quiet or tall then someone is either not creative or quiet.
Someone is curious.
Someone is wise.
Someone is either not humble or calm.
Someone is either generous or not rich.
Mary is not patient.
Someone is not happy or kind. | Lucy is not funny. | neutral | (((funny(alice)|rich(alice)))=>(brave(alice)))&
((?[X]:((wise(X)<~>patient(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)&happy(X))<=>(rich(X)&~calm(X))))&
(![X]:((~patient(X)|curious(X))<=>(old(X)<~>wise(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((wise(X)|old(X)))))&
((?[X]:((wise(X)<~>humble(X))))=>((~tall(mary)|~patient(mary))))&
(![X]:((funny(X)|tall(X))=>(humble(X)&funny(X))))&
(((~funny(paul)&calm(paul)))<=>(?[X]:((~strong(X)&~tall(X)))))&
((?[X]:((~funny(X)|old(X))))<=>((~funny(lucy)<~>~wise(lucy))))&
(((~wise(fred)<~>generous(fred)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~strong(X)|strong(X))=>(brave(X)|calm(X))))&
(![X]:((~humble(X)&~calm(X))<=>(~happy(X)|quiet(X))))&
(![X]:(~strong(X)<=>(strong(X)<~>humble(X))))&
((?[X]:((~rich(X)<~>tall(X))))<=>(?[X]:((brave(X)&generous(X)))))&
(![X]:((humble(X)&~wise(X))<=>(quiet(X)|~wise(X))))&
(((~quiet(lucy)|tall(lucy)))=>(?[X]:((~creative(X)<~>quiet(X)))))&
(?[X]:(curious(X)))&
(?[X]:(wise(X)))&
(?[X]:((~humble(X)<~>calm(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
(~patient(mary))&
(?[X]:((~happy(X)|kind(X)))) | ~funny(lucy) | [] | null | 0 |
If someone is not curious then mary is not generous and vice versa.
Everyone who is not rich or not patient is generous.
If someone is creative or not happy then someone is either not wise or curious and vice versa.
If someone is not calm or not curious then someone is not tall or wise and vice versa.
If susan is old then alice is tall or not humble and vice versa.
If someone is either strong or not happy then someone is both not strong and not old.
Everyone who is tall is not humble and vice versa.
If john is either patient or not tall then someone is both kind and strong.
Everyone who is either not brave or generous is not funny and vice versa.
If someone is both not rich and humble then someone is both not wise and not humble.
Everyone who is not wise or curious is quiet.
If john is both happy and calm then someone is kind or not rich and vice versa.
Everyone who is patient is either strong or humble.
If someone is either creative or not old then someone is happy.
Everyone who is quiet or not curious is both not calm and not brave.
Everyone who is both not brave and not calm is not kind or wise and vice versa.
Someone is not generous.
Alice is tall or wise.
Someone is not generous or old.
Someone is not happy.
Someone is either humble or not curious.
Lucy is strong or not calm. | John is not calm. | entailment | ((?[X]:(~curious(X)))<=>(~generous(mary)))&
(![X]:((~rich(X)|~patient(X))=>generous(X)))&
((?[X]:((creative(X)|~happy(X))))<=>(?[X]:((~wise(X)<~>curious(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:((~tall(X)|wise(X)))))&
((old(susan))<=>((tall(alice)|~humble(alice))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:(tall(X)<=>~humble(X)))&
(((patient(john)<~>~tall(john)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((~brave(X)<~>generous(X))<=>~funny(X)))&
((?[X]:((~rich(X)&humble(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~wise(X)|curious(X))=>quiet(X)))&
(((happy(john)&calm(john)))<=>(?[X]:((kind(X)|~rich(X)))))&
(![X]:(patient(X)=>(strong(X)<~>humble(X))))&
((?[X]:((creative(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(![X]:((quiet(X)|~curious(X))=>(~calm(X)&~brave(X))))&
(![X]:((~brave(X)&~calm(X))<=>(~kind(X)|wise(X))))&
(?[X]:(~generous(X)))&
((tall(alice)|wise(alice)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)<~>~curious(X))))&
((strong(lucy)|~calm(lucy))) | ~calm(john) | [
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3765204448465984437163512
% SZS output start Proof for 3765204448465984437163512
11. ! [X0] : ((curious(X0) | ~wise(X0)) => quiet(X0)) [input p10]
15. ! [X0] : ((~curious(X0) | quiet(X0)) => (~brave(X0) & ~calm(X0))) [input p14]
16. ! [X0] : ((~calm(X0) & ~brave(X0)) <=> (wise(X0) | ~kind(X0))) [input p15]
23. calm(john) [input hypothesis]
33. ! [X0] : (quiet(X0) | (~curious(X0) & wise(X0))) [ennf transformation 11]
36. ! [X0] : ((~brave(X0) & ~calm(X0)) | (curious(X0) & ~quiet(X0))) [ennf transformation 15]
74. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & kind(X0))) & ((wise(X0) | ~kind(X0)) | (calm(X0) | brave(X0)))) [nnf transformation 16]
75. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & kind(X0))) & (wise(X0) | ~kind(X0) | calm(X0) | brave(X0))) [flattening 74]
114. quiet(X0) | wise(X0) [cnf transformation 33]
125. ~quiet(X0) | ~calm(X0) [cnf transformation 36]
133. ~calm(X0) | ~wise(X0) [cnf transformation 75]
141. calm(john) [cnf transformation 23]
288. 34 <=> calm(john) [avatar definition]
290. calm(john) <- (34) [avatar component clause 288]
356. 34 [avatar split clause 141,288]
361. ~calm(X0) | wise(X0) [resolution 125,114]
362. ~calm(X0) [subsumption resolution 361,133]
363. $false <- (34) [resolution 362,290]
364. ~34 [avatar contradiction clause 363]
365. $false [avatar sat refutation 356,364]
% SZS output end Proof for 3765204448465984437163512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not generous is both not brave and not tall and vice versa.
Everyone who is not funny is either strong or not strong.
If someone is both happy and patient then someone is not kind or curious and vice versa.
Everyone who is not strong is not humble or not brave.
If someone is either not rich or old then alice is not rich or not old and vice versa.
Everyone who is both not patient and humble is both not patient and not curious and vice versa.
If fred is kind or quiet then someone is either curious or humble and vice versa.
Everyone who is strong or funny is quiet and vice versa.
If someone is not strong then someone is both calm and not calm and vice versa.
Everyone who is both not happy and quiet is either generous or not happy and vice versa.
If john is either strong or not humble then john is both brave and not wise.
Everyone who is not funny or not wise is both strong and not wise.
Everyone who is both not curious and tall is both brave and not wise and vice versa.
Everyone who is both not tall and tall is not wise or not calm and vice versa.
Everyone who is rich is not happy or not generous and vice versa.
Alice is not quiet or quiet.
John is curious.
Someone is either not funny or not happy.
Mary is either humble or strong.
Someone is either not happy or happy.
Someone is both not brave and rich. | Mary is curious. | entailment | (![X]:((~brave(X)<~>~generous(X))<=>(~brave(X)&~tall(X))))&
(![X]:(~funny(X)=>(strong(X)<~>~strong(X))))&
((?[X]:((happy(X)&patient(X))))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:(~strong(X)=>(~humble(X)|~brave(X))))&
((?[X]:((~rich(X)<~>old(X))))<=>((~rich(alice)|~old(alice))))&
(![X]:((~patient(X)&humble(X))<=>(~patient(X)&~curious(X))))&
(((kind(fred)|quiet(fred)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((strong(X)|funny(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(generous(X)<~>~happy(X))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:(rich(X)<=>(~happy(X)|~generous(X))))&
((~quiet(alice)|quiet(alice)))&
(curious(john))&
(?[X]:((~funny(X)<~>~happy(X))))&
((humble(mary)<~>strong(mary)))&
(?[X]:((~happy(X)<~>happy(X))))&
(?[X]:((~brave(X)&rich(X)))) | curious(mary) | [
"p0",
"p7",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1821788120524434419686021
% SZS output start Proof for 1821788120524434419686021
1. ! [X0] : ((~brave(X0) <~> ~generous(X0)) <=> (~tall(X0) & ~brave(X0))) [input p0]
8. ! [X0] : ((funny(X0) | strong(X0)) <=> quiet(X0)) [input p7]
9. ? [X0] : ~strong(X0) <=> ? [X0] : (~calm(X0) & calm(X0)) [input p8]
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (generous(X0) <~> ~happy(X0))) [input p9]
13. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~wise(X0) & brave(X0))) [input p12]
14. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | ~wise(X0))) [input p13]
22. ~curious(mary) [input hypothesis]
24. ? [X0] : ~strong(X0) <=> ? [X1] : (~calm(X1) & calm(X1)) [rectify 9]
30. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [nnf transformation 1]
31. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [flattening 30]
50. ! [X0] : (((funny(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) & ~strong(X0)))) [nnf transformation 8]
51. ! [X0] : ((funny(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) & ~strong(X0)))) [flattening 50]
52. (? [X0] : ~strong(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X1] : (~calm(X1) & calm(X1)) | ! [X0] : strong(X0)) [nnf transformation 24]
53. (? [X0] : ~strong(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X2] : (~calm(X2) & calm(X2)) | ! [X3] : strong(X3)) [rectify 52]
54. ? [X0] : ~strong(X0) => ~strong(sK4) [choice axiom]
55. ? [X2] : (~calm(X2) & calm(X2)) => (~calm(sK5) & calm(sK5)) [choice axiom]
56. (~strong(sK4) | ! [X1] : (calm(X1) | ~calm(X1))) & ((~calm(sK5) & calm(sK5)) | ! [X3] : strong(X3)) [skolemisation 53,55,54]
57. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 10]
58. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | ~quiet(X0) | happy(X0))) [flattening 57]
60. ! [X0] : (((tall(X0) & ~curious(X0)) | (wise(X0) | ~brave(X0))) & ((~wise(X0) & brave(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 13]
61. ! [X0] : (((tall(X0) & ~curious(X0)) | wise(X0) | ~brave(X0)) & ((~wise(X0) & brave(X0)) | ~tall(X0) | curious(X0))) [flattening 60]
62. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 14]
63. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0) | tall(X0))) [flattening 62]
76. ~brave(X0) | ~brave(X0) | generous(X0) [cnf transformation 31]
80. generous(X0) | brave(X0) | tall(X0) | brave(X0) [cnf transformation 31]
105. ~strong(X0) | quiet(X0) [cnf transformation 51]
108. calm(sK5) | strong(X3) [cnf transformation 56]
109. ~calm(sK5) | strong(X3) [cnf transformation 56]
112. happy(X0) | ~generous(X0) | ~quiet(X0) | happy(X0) [cnf transformation 58]
113. ~happy(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 58]
126. ~wise(X0) | ~tall(X0) | curious(X0) [cnf transformation 61]
130. ~tall(X0) | wise(X0) [cnf transformation 63]
132. wise(X0) | tall(X0) [cnf transformation 63]
147. ~curious(mary) [cnf transformation 22]
148. happy(X0) | ~generous(X0) | ~quiet(X0) [duplicate literal removal 112]
149. ~happy(X0) | ~generous(X0) [duplicate literal removal 113]
150. ~brave(X0) | generous(X0) [duplicate literal removal 76]
151. tall(X0) | brave(X0) | generous(X0) [duplicate literal removal 80]
239. 20 <=> ! [X3] : strong(X3) [avatar definition]
240. strong(X3) <- (20) [avatar component clause 239]
242. 21 <=> calm(sK5) [avatar definition]
245. 20 | ~21 [avatar split clause 109,242,239]
246. 20 | 21 [avatar split clause 108,242,239]
247. ~quiet(X0) | ~generous(X0) [subsumption resolution 148,149]
269. wise(X0) [subsumption resolution 130,132]
294. quiet(X0) <- (20) [resolution 105,240]
315. ~generous(X0) <- (20) [resolution 247,294]
331. ~tall(X2) | curious(X2) [resolution 126,269]
335. brave(X0) | generous(X0) | curious(X0) [resolution 151,331]
342. curious(X0) | brave(X0) <- (20) [subsumption resolution 335,315]
343. brave(mary) <- (20) [resolution 342,147]
346. generous(mary) <- (20) [resolution 343,150]
347. $false <- (20) [subsumption resolution 346,315]
348. ~20 [avatar contradiction clause 347]
349. $false [avatar sat refutation 245,246,348]
% SZS output end Proof for 1821788120524434419686021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not happy is curious or not happy and vice versa.
Everyone who is either wise or strong is both not quiet and not wise and vice versa.
If alice is not curious then someone is rich or not brave.
Everyone who is both not old and not humble is wise.
Everyone who is happy or not happy is either generous or not rich.
If john is tall or quiet then someone is either not wise or not patient.
If someone is either happy or tall then alice is either funny or rich.
Everyone who is either not strong or not curious is not funny and vice versa.
Everyone who is either not tall or generous is either not tall or not old.
Everyone who is curious is both not quiet and generous and vice versa.
If john is not humble then someone is not rich and vice versa.
If alice is both not old and rich then paul is not generous.
Everyone who is both not brave and not humble is not brave.
Everyone who is brave is either curious or wise and vice versa.
Everyone who is both curious and happy is funny or generous and vice versa.
Susan is rich or not happy.
Someone is not kind or not tall.
Mary is humble.
Someone is calm or wise.
Someone is both brave and not rich.
Susan is curious or creative. | Alice is happy. | contradiction | (![X]:((~funny(X)|~happy(X))<=>(curious(X)|~happy(X))))&
(![X]:((wise(X)<~>strong(X))<=>(~quiet(X)&~wise(X))))&
((~curious(alice))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:((~old(X)&~humble(X))=>wise(X)))&
(![X]:((happy(X)|~happy(X))=>(generous(X)<~>~rich(X))))&
(((tall(john)|quiet(john)))=>(?[X]:((~wise(X)<~>~patient(X)))))&
((?[X]:((happy(X)<~>tall(X))))=>((funny(alice)<~>rich(alice))))&
(![X]:((~strong(X)<~>~curious(X))<=>~funny(X)))&
(![X]:((~tall(X)<~>generous(X))=>(~tall(X)<~>~old(X))))&
(![X]:(curious(X)<=>(~quiet(X)&generous(X))))&
((~humble(john))<=>(?[X]:(~rich(X))))&
(((~old(alice)&rich(alice)))=>(~generous(paul)))&
(![X]:((~brave(X)&~humble(X))=>~brave(X)))&
(![X]:(brave(X)<=>(curious(X)<~>wise(X))))&
(![X]:((curious(X)&happy(X))<=>(funny(X)|generous(X))))&
((rich(susan)|~happy(susan)))&
(?[X]:((~kind(X)|~tall(X))))&
(humble(mary))&
(?[X]:((calm(X)|wise(X))))&
(?[X]:((brave(X)&~rich(X))))&
((curious(susan)|creative(susan))) | happy(alice) | [
"p0",
"p1",
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3418988403403417799581715
% SZS output start Proof for 3418988403403417799581715
1. ! [X0] : ((~happy(X0) | ~funny(X0)) <=> (~happy(X0) | curious(X0))) [input p0]
2. ! [X0] : ((wise(X0) <~> strong(X0)) <=> (~wise(X0) & ~quiet(X0))) [input p1]
8. ! [X0] : ((~strong(X0) <~> ~curious(X0)) <=> ~funny(X0)) [input p7]
10. ! [X0] : (curious(X0) <=> (generous(X0) & ~quiet(X0))) [input p9]
15. ! [X0] : ((happy(X0) & curious(X0)) <=> (generous(X0) | funny(X0))) [input p14]
22. happy(alice) [input hypothesis]
37. ! [X0] : (((~happy(X0) | ~funny(X0)) | (happy(X0) & ~curious(X0))) & ((~happy(X0) | curious(X0)) | (happy(X0) & funny(X0)))) [nnf transformation 1]
38. ! [X0] : ((~happy(X0) | ~funny(X0) | (happy(X0) & ~curious(X0))) & (~happy(X0) | curious(X0) | (happy(X0) & funny(X0)))) [flattening 37]
39. ! [X0] : ((((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | (wise(X0) | quiet(X0))) & ((~wise(X0) & ~quiet(X0)) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | wise(X0) | quiet(X0)) & ((~wise(X0) & ~quiet(X0)) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0))))) [flattening 39]
48. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | funny(X0)) & (~funny(X0) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [nnf transformation 8]
50. ! [X0] : ((curious(X0) | (~generous(X0) | quiet(X0))) & ((generous(X0) & ~quiet(X0)) | ~curious(X0))) [nnf transformation 10]
51. ! [X0] : ((curious(X0) | ~generous(X0) | quiet(X0)) & ((generous(X0) & ~quiet(X0)) | ~curious(X0))) [flattening 50]
57. ! [X0] : (((happy(X0) & curious(X0)) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 15]
58. ! [X0] : (((happy(X0) & curious(X0)) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | ~happy(X0) | ~curious(X0))) [flattening 57]
61. ~happy(X0) | curious(X0) | funny(X0) [cnf transformation 38]
63. ~curious(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 38]
67. ~wise(X0) | strong(X0) | ~wise(X0) [cnf transformation 40]
69. strong(X0) | wise(X0) | wise(X0) | quiet(X0) [cnf transformation 40]
87. ~strong(X0) | ~curious(X0) | funny(X0) [cnf transformation 48]
93. ~quiet(X0) | ~curious(X0) [cnf transformation 51]
105. ~funny(X0) | curious(X0) [cnf transformation 58]
113. happy(alice) [cnf transformation 22]
116. ~wise(X0) | strong(X0) [duplicate literal removal 67]
117. quiet(X0) | wise(X0) | strong(X0) [duplicate literal removal 69]
119. 1 <=> curious(alice) [avatar definition]
121. curious(alice) <- (1) [avatar component clause 119]
157. 9 <=> funny(alice) [avatar definition]
158. funny(alice) <- (9) [avatar component clause 157]
159. ~funny(alice) <- (~9) [avatar component clause 157]
202. curious(alice) <- (9) [resolution 105,158]
203. 1 | ~9 [avatar split clause 202,157,119]
211. curious(alice) | funny(alice) [resolution 61,113]
212. curious(alice) <- (~9) [subsumption resolution 211,159]
213. 1 | 9 [avatar split clause 212,157,119]
215. ~funny(alice) | ~happy(alice) <- (1) [resolution 63,121]
285. wise(X1) | strong(X1) | ~curious(X1) [resolution 117,93]
288. ~curious(X1) | strong(X1) [subsumption resolution 285,116]
303. strong(alice) <- (1) [resolution 288,121]
304. ~curious(alice) | funny(alice) <- (1) [resolution 303,87]
306. funny(alice) <- (1) [subsumption resolution 304,121]
309. 9 | ~1 [avatar split clause 306,119,157]
310. ~funny(alice) <- (1) [subsumption resolution 215,113]
311. ~9 | ~1 [avatar split clause 310,119,157]
312. $false [avatar sat refutation 203,213,309,311]
% SZS output end Proof for 3418988403403417799581715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not wise is kind. Everyone who is humble or not humble is tall or not brave and vice versa. If fred is not calm or humble then paul is not strong. If someone is tall then alice is both not funny and not quiet and vice versa. Everyone who is creative is either not tall or not strong. If someone is old or not happy then someone is kind and vice versa. Everyone who is both not humble and humble is both not strong and creative and vice versa. If someone is either not patient or not curious then paul is happy. Everyone who is both not funny and rich is either not patient or strong. Everyone who is either patient or not patient is either not kind or brave. Everyone who is either creative or not quiet is either rich or wise. Everyone who is both humble and curious is both not happy and patient. Everyone who is quiet is kind or wise. Everyone who is not funny or rich is old and vice versa. If someone is not rich or strong then alice is either not rich or calm and vice versa. If someone is not kind or not patient then fred is both tall and curious and vice versa. Someone is not happy. Someone is not happy or generous. Susan is creative. Someone is not curious or not quiet. Susan is both not rich and happy. Someone is not creative. Someone is either strong or not brave. | Fred is not creative. | entailment | (![X]:((rich(X)<~>~wise(X))=>kind(X)))&
(![X]:((humble(X)|~humble(X))<=>(tall(X)|~brave(X))))&
(((~calm(fred)|humble(fred)))=>(~strong(paul)))&
((?[X]:(tall(X)))<=>((~funny(alice)&~quiet(alice))))&
(![X]:(creative(X)=>(~tall(X)<~>~strong(X))))&
((?[X]:((old(X)|~happy(X))))<=>(?[X]:(kind(X))))&
(![X]:((~humble(X)&humble(X))<=>(~strong(X)&creative(X))))&
((?[X]:((~patient(X)<~>~curious(X))))=>(happy(paul)))&
(![X]:((~funny(X)&rich(X))=>(~patient(X)<~>strong(X))))&
(![X]:((patient(X)<~>~patient(X))=>(~kind(X)<~>brave(X))))&
(![X]:((creative(X)<~>~quiet(X))=>(rich(X)<~>wise(X))))&
(![X]:((humble(X)&curious(X))=>(~happy(X)&patient(X))))&
(![X]:(quiet(X)=>(kind(X)|wise(X))))&
(![X]:((~funny(X)|rich(X))<=>old(X)))&
((?[X]:((~rich(X)|strong(X))))<=>((~rich(alice)<~>calm(alice))))&
((?[X]:((~kind(X)|~patient(X))))<=>((tall(fred)&curious(fred))))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)|generous(X))))&
(creative(susan))&
(?[X]:((~curious(X)|~quiet(X))))&
((~rich(susan)&happy(susan)))&
(?[X]:(~creative(X)))&
(?[X]:((strong(X)<~>~brave(X)))) | ~creative(fred) | [
"p1",
"p4",
"p6",
"p9",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 180138516792478088913688
% SZS output start Proof for 180138516792478088913688
2. ! [X0] : ((~humble(X0) | humble(X0)) <=> (~brave(X0) | tall(X0))) [input p1]
5. ! [X0] : (creative(X0) => (~tall(X0) <~> ~strong(X0))) [input p4]
7. ! [X0] : ((humble(X0) & ~humble(X0)) <=> (creative(X0) & ~strong(X0))) [input p6]
10. ! [X0] : ((patient(X0) <~> ~patient(X0)) => (~kind(X0) <~> brave(X0))) [input p9]
16. ? [X0] : (~patient(X0) | ~kind(X0)) <=> (curious(fred) & tall(fred)) [input p15]
19. creative(susan) [input p18]
24. creative(fred) [input hypothesis]
29. ! [X0] : ((~tall(X0) <~> ~strong(X0)) | ~creative(X0)) [ennf transformation 5]
33. ! [X0] : ((~kind(X0) <~> brave(X0)) | (patient(X0) <=> ~patient(X0))) [ennf transformation 10]
40. ! [X0] : (((~humble(X0) | humble(X0)) | (brave(X0) & ~tall(X0))) & ((~brave(X0) | tall(X0)) | (humble(X0) & ~humble(X0)))) [nnf transformation 2]
41. ! [X0] : ((~humble(X0) | humble(X0) | (brave(X0) & ~tall(X0))) & (~brave(X0) | tall(X0) | (humble(X0) & ~humble(X0)))) [flattening 40]
47. ! [X0] : (((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ~creative(X0)) [nnf transformation 29]
53. ! [X0] : (((humble(X0) & ~humble(X0)) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | (~humble(X0) | humble(X0)))) [nnf transformation 7]
54. ! [X0] : (((humble(X0) & ~humble(X0)) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | ~humble(X0) | humble(X0))) [flattening 53]
57. ! [X0] : (((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) [nnf transformation 33]
65. (? [X0] : (~patient(X0) | ~kind(X0)) | (~curious(fred) | ~tall(fred))) & ((curious(fred) & tall(fred)) | ! [X0] : (patient(X0) & kind(X0))) [nnf transformation 16]
66. (? [X0] : (~patient(X0) | ~kind(X0)) | ~curious(fred) | ~tall(fred)) & ((curious(fred) & tall(fred)) | ! [X0] : (patient(X0) & kind(X0))) [flattening 65]
67. (? [X0] : (~patient(X0) | ~kind(X0)) | ~curious(fred) | ~tall(fred)) & ((curious(fred) & tall(fred)) | ! [X1] : (patient(X1) & kind(X1))) [rectify 66]
68. ? [X0] : (~patient(X0) | ~kind(X0)) => (~patient(sK4) | ~kind(sK4)) [choice axiom]
69. ((~patient(sK4) | ~kind(sK4)) | ~curious(fred) | ~tall(fred)) & ((curious(fred) & tall(fred)) | ! [X1] : (patient(X1) & kind(X1))) [skolemisation 67,68]
81. ~brave(X0) | tall(X0) | ~humble(X0) [cnf transformation 41]
82. ~brave(X0) | tall(X0) | humble(X0) [cnf transformation 41]
90. ~creative(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 47]
97. ~humble(X0) | ~creative(X0) | strong(X0) [cnf transformation 54]
98. ~creative(X0) | humble(X0) | strong(X0) [cnf transformation 54]
103. brave(X0) | ~kind(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 57]
104. brave(X0) | ~kind(X0) | patient(X0) | patient(X0) [cnf transformation 57]
123. tall(fred) | kind(X1) [cnf transformation 69]
129. creative(susan) [cnf transformation 19]
136. creative(fred) [cnf transformation 24]
137. brave(X0) | ~kind(X0) | ~patient(X0) [duplicate literal removal 103]
138. brave(X0) | ~kind(X0) | patient(X0) [duplicate literal removal 104]
141. ~brave(X0) | tall(X0) [subsumption resolution 81,82]
198. ~creative(X0) | strong(X0) [subsumption resolution 97,98]
212. ~kind(X0) | brave(X0) [subsumption resolution 137,138]
242. 23 <=> tall(fred) [avatar definition]
263. 28 <=> ! [X1] : kind(X1) [avatar definition]
264. kind(X1) <- (28) [avatar component clause 263]
267. 28 | 23 [avatar split clause 123,242,263]
287. strong(susan) [resolution 198,129]
288. strong(fred) [resolution 198,136]
294. ~tall(susan) | ~strong(susan) [resolution 90,129]
295. ~tall(fred) | ~strong(fred) [resolution 90,136]
296. ~tall(susan) [subsumption resolution 294,287]
300. ~tall(fred) [subsumption resolution 295,288]
301. ~23 [avatar split clause 300,242]
304. brave(X0) <- (28) [resolution 264,212]
312. tall(X2) <- (28) [resolution 304,141]
315. $false <- (28) [resolution 312,296]
316. ~28 [avatar contradiction clause 315]
318. $false [avatar sat refutation 267,301,316]
% SZS output end Proof for 180138516792478088913688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or wise is both strong and not wise.
If john is not old or not patient then someone is both not quiet and tall.
Everyone who is both not patient and not generous is either not kind or calm.
Everyone who is kind is either generous or wise.
Everyone who is both not brave and not tall is not happy.
If someone is creative or brave then someone is both tall and quiet.
If someone is both rich and not old then someone is old or not quiet and vice versa.
Everyone who is happy or funny is both creative and kind.
If lucy is both not funny and not tall then someone is either not curious or not wise.
Everyone who is both not curious and creative is both not quiet and not generous.
Everyone who is either not tall or old is humble.
If alice is quiet or strong then someone is either calm or not tall.
Everyone who is happy is both not funny and not generous and vice versa.
If alice is old or rich then alice is brave and vice versa.
If susan is not rich or patient then someone is wise or not strong.
Everyone who is either quiet or not funny is not humble or not creative and vice versa.
Susan is generous or not generous.
Fred is both not rich and not brave.
Susan is not rich.
John is either not calm or creative.
Someone is funny or generous.
John is either not rich or not brave.
Someone is not humble.
Someone is generous. | Fred is brave. | contradiction | (![X]:((kind(X)|wise(X))=>(strong(X)&~wise(X))))&
(((~old(john)|~patient(john)))=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((~patient(X)&~generous(X))=>(~kind(X)<~>calm(X))))&
(![X]:(kind(X)=>(generous(X)<~>wise(X))))&
(![X]:((~brave(X)&~tall(X))=>~happy(X)))&
((?[X]:((creative(X)|brave(X))))=>(?[X]:((tall(X)&quiet(X)))))&
((?[X]:((rich(X)&~old(X))))<=>(?[X]:((old(X)|~quiet(X)))))&
(![X]:((happy(X)|funny(X))=>(creative(X)&kind(X))))&
(((~funny(lucy)&~tall(lucy)))=>(?[X]:((~curious(X)<~>~wise(X)))))&
(![X]:((~curious(X)&creative(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~tall(X)<~>old(X))=>humble(X)))&
(((quiet(alice)|strong(alice)))=>(?[X]:((calm(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>(~funny(X)&~generous(X))))&
(((old(alice)|rich(alice)))<=>(brave(alice)))&
(((~rich(susan)|patient(susan)))=>(?[X]:((wise(X)|~strong(X)))))&
(![X]:((quiet(X)<~>~funny(X))<=>(~humble(X)|~creative(X))))&
((generous(susan)|~generous(susan)))&
((~rich(fred)&~brave(fred)))&
(~rich(susan))&
((~calm(john)<~>creative(john)))&
(?[X]:((funny(X)|generous(X))))&
((~rich(john)<~>~brave(john)))&
(?[X]:(~humble(X)))&
(?[X]:(generous(X))) | brave(fred) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6159826560531619005876595
% SZS output start Proof for 6159826560531619005876595
18. ~brave(fred) & ~rich(fred) [input p17]
25. brave(fred) [input hypothesis]
130. ~brave(fred) [cnf transformation 18]
139. brave(fred) [cnf transformation 25]
307. $false [subsumption resolution 139,130]
% SZS output end Proof for 6159826560531619005876595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious and not tall then someone is not strong and vice versa.
Everyone who is either strong or creative is wise and vice versa.
Everyone who is creative is not quiet or generous and vice versa.
Everyone who is not brave or curious is both not rich and not quiet and vice versa.
Everyone who is not quiet is both not creative and kind and vice versa.
If someone is rich then someone is both brave and tall and vice versa.
Everyone who is calm or wise is not creative.
Everyone who is not patient is both generous and not humble.
Everyone who is rich is either creative or not quiet.
Everyone who is either not patient or not funny is both not curious and funny and vice versa.
Everyone who is not curious or patient is not kind or curious.
If lucy is either quiet or humble then paul is not rich and vice versa.
Everyone who is both brave and not humble is funny and vice versa.
If fred is not brave then susan is creative or not wise.
Everyone who is both rich and not quiet is both not creative and not happy.
Everyone who is both not funny and quiet is rich or not old.
John is either tall or kind.
Lucy is patient or not happy.
Someone is not old or strong.
Someone is creative.
Alice is rich or generous. | Lucy is not generous. | contradiction | ((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:(~strong(X))))&
(![X]:((strong(X)<~>creative(X))<=>wise(X)))&
(![X]:(creative(X)<=>(~quiet(X)|generous(X))))&
(![X]:((~brave(X)|curious(X))<=>(~rich(X)&~quiet(X))))&
(![X]:(~quiet(X)<=>(~creative(X)&kind(X))))&
((?[X]:(rich(X)))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((calm(X)|wise(X))=>~creative(X)))&
(![X]:(~patient(X)=>(generous(X)&~humble(X))))&
(![X]:(rich(X)=>(creative(X)<~>~quiet(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(~curious(X)&funny(X))))&
(![X]:((~curious(X)|patient(X))=>(~kind(X)|curious(X))))&
(((quiet(lucy)<~>humble(lucy)))<=>(~rich(paul)))&
(![X]:((brave(X)&~humble(X))<=>funny(X)))&
((~brave(fred))=>((creative(susan)|~wise(susan))))&
(![X]:((rich(X)&~quiet(X))=>(~creative(X)&~happy(X))))&
(![X]:((~funny(X)&quiet(X))=>(rich(X)|~old(X))))&
((tall(john)<~>kind(john)))&
((patient(lucy)|~happy(lucy)))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:(creative(X)))&
((rich(alice)|generous(alice))) | ~generous(lucy) | [
"p2",
"p3",
"p4",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 764329091556320156114237
% SZS output start Proof for 764329091556320156114237
3. ! [X0] : (creative(X0) <=> (generous(X0) | ~quiet(X0))) [input p2]
4. ! [X0] : ((curious(X0) | ~brave(X0)) <=> (~quiet(X0) & ~rich(X0))) [input p3]
5. ! [X0] : (~quiet(X0) <=> (kind(X0) & ~creative(X0))) [input p4]
8. ! [X0] : (~patient(X0) => (~humble(X0) & generous(X0))) [input p7]
10. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (funny(X0) & ~curious(X0))) [input p9]
22. ~generous(lucy) [input hypothesis]
33. ! [X0] : ((~humble(X0) & generous(X0)) | patient(X0)) [ennf transformation 8]
47. ! [X0] : ((creative(X0) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | ~creative(X0))) [nnf transformation 3]
48. ! [X0] : ((creative(X0) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~creative(X0))) [flattening 47]
49. ! [X0] : (((curious(X0) | ~brave(X0)) | (quiet(X0) | rich(X0))) & ((~quiet(X0) & ~rich(X0)) | (~curious(X0) & brave(X0)))) [nnf transformation 4]
50. ! [X0] : ((curious(X0) | ~brave(X0) | quiet(X0) | rich(X0)) & ((~quiet(X0) & ~rich(X0)) | (~curious(X0) & brave(X0)))) [flattening 49]
51. ! [X0] : ((~quiet(X0) | (~kind(X0) | creative(X0))) & ((kind(X0) & ~creative(X0)) | quiet(X0))) [nnf transformation 5]
52. ! [X0] : ((~quiet(X0) | ~kind(X0) | creative(X0)) & ((kind(X0) & ~creative(X0)) | quiet(X0))) [flattening 51]
59. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 10]
60. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [flattening 59]
73. quiet(X0) | creative(X0) [cnf transformation 48]
78. ~quiet(X0) | ~curious(X0) [cnf transformation 50]
80. ~creative(X0) | quiet(X0) [cnf transformation 52]
87. patient(X0) | generous(X0) [cnf transformation 33]
94. funny(X0) | ~patient(X0) | funny(X0) [cnf transformation 60]
95. ~funny(X0) | ~patient(X0) | ~funny(X0) | curious(X0) [cnf transformation 60]
112. ~generous(lucy) [cnf transformation 22]
114. ~patient(X0) | funny(X0) [duplicate literal removal 94]
115. ~funny(X0) | ~patient(X0) | curious(X0) [duplicate literal removal 95]
138. quiet(X0) [subsumption resolution 80,73]
209. ~curious(X1) [resolution 78,138]
212. funny(X0) | generous(X0) [resolution 114,87]
301. generous(X0) | ~patient(X0) | curious(X0) [resolution 212,115]
305. generous(X0) | ~patient(X0) [subsumption resolution 301,209]
306. generous(X0) [subsumption resolution 305,87]
329. $false [resolution 306,112]
% SZS output end Proof for 764329091556320156114237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not brave and kind is both wise and happy and vice versa.
Everyone who is not calm or not happy is wise or curious.
Everyone who is both kind and not humble is not strong or not patient and vice versa.
If someone is both old and humble then someone is either not humble or wise.
If someone is both strong and funny then someone is either curious or old and vice versa.
If susan is either not humble or generous then someone is not strong and vice versa.
If lucy is either not strong or brave then lucy is either funny or rich.
Everyone who is both patient and curious is generous and vice versa.
Everyone who is calm is creative and vice versa.
Everyone who is both not calm and not humble is both wise and not curious and vice versa.
Everyone who is both not strong and old is both curious and not happy.
Everyone who is not wise or not curious is not old and vice versa.
Everyone who is generous or not strong is either curious or wise.
If someone is calm or not generous then john is happy or brave.
Everyone who is old is brave or not generous.
Everyone who is either quiet or not creative is not humble or not curious and vice versa.
Someone is either not humble or tall.
John is either tall or not rich.
John is calm.
Susan is either not wise or rich.
Someone is not happy.
Someone is tall or not old.
Alice is strong. | John is creative. | entailment | (![X]:((~brave(X)&kind(X))<=>(wise(X)&happy(X))))&
(![X]:((~calm(X)|~happy(X))=>(wise(X)|curious(X))))&
(![X]:((kind(X)&~humble(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((old(X)&humble(X))))=>(?[X]:((~humble(X)<~>wise(X)))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:((curious(X)<~>old(X)))))&
(((~humble(susan)<~>generous(susan)))<=>(?[X]:(~strong(X))))&
(((~strong(lucy)<~>brave(lucy)))=>((funny(lucy)<~>rich(lucy))))&
(![X]:((patient(X)&curious(X))<=>generous(X)))&
(![X]:(calm(X)<=>creative(X)))&
(![X]:((~calm(X)&~humble(X))<=>(wise(X)&~curious(X))))&
(![X]:((~strong(X)&old(X))=>(curious(X)&~happy(X))))&
(![X]:((~wise(X)|~curious(X))<=>~old(X)))&
(![X]:((generous(X)|~strong(X))=>(curious(X)<~>wise(X))))&
((?[X]:((calm(X)|~generous(X))))=>((happy(john)|brave(john))))&
(![X]:(old(X)=>(brave(X)|~generous(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(~humble(X)|~curious(X))))&
(?[X]:((~humble(X)<~>tall(X))))&
((tall(john)<~>~rich(john)))&
(calm(john))&
((~wise(susan)<~>rich(susan)))&
(?[X]:(~happy(X)))&
(?[X]:((tall(X)|~old(X))))&
(strong(alice)) | creative(john) | [
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3103495239613185202374554
% SZS output start Proof for 3103495239613185202374554
9. ! [X0] : (calm(X0) <=> creative(X0)) [input p8]
19. calm(john) [input p18]
24. ~creative(john) [input hypothesis]
58. ! [X0] : ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))) [nnf transformation 9]
105. ~calm(X0) | creative(X0) [cnf transformation 58]
133. calm(john) [cnf transformation 19]
139. ~creative(john) [cnf transformation 24]
282. creative(john) [resolution 105,133]
283. $false [subsumption resolution 282,139]
% SZS output end Proof for 3103495239613185202374554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not curious or funny is both old and not creative.
Everyone who is both old and patient is both not old and not strong.
Everyone who is not strong or not happy is both not happy and kind.
Everyone who is not kind or generous is calm and vice versa.
If john is both not quiet and tall then someone is tall or humble and vice versa.
Everyone who is curious or quiet is both funny and rich.
Everyone who is not patient is both not old and funny and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
If paul is not creative or not strong then someone is strong and vice versa.
Everyone who is quiet is kind.
Someone is brave or strong.
Alice is wise.
Someone is not strong or not rich.
Someone is happy or not kind.
Mary is rich. | Alice is not quiet. | entailment | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)&patient(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((brave(X)|strong(X))))&
(wise(alice))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((happy(X)|~kind(X))))&
(rich(mary)) | ~quiet(alice) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7862654950715214836696663
% SZS output start Proof for 7862654950715214836696663
1. ! [X0] : ((~curious(X0) <~> funny(X0)) => (~creative(X0) & old(X0))) [input p0]
2. ! [X0] : ((patient(X0) & old(X0)) => (~strong(X0) & ~old(X0))) [input p1]
6. ! [X0] : ((quiet(X0) | curious(X0)) => (rich(X0) & funny(X0))) [input p5]
7. ! [X0] : (~patient(X0) <=> (funny(X0) & ~old(X0))) [input p6]
8. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (kind(X0) & ~humble(X0))) [input p7]
14. ! [X0] : (quiet(X0) <=> (~creative(X0) & humble(X0))) [input p13]
22. quiet(alice) [input hypothesis]
23. ! [X0] : (~patient(X0) => (funny(X0) & ~old(X0))) [unused predicate definition removal 7]
25. ! [X0] : ((~creative(X0) & old(X0)) | (~curious(X0) <=> funny(X0))) [ennf transformation 1]
26. ! [X0] : ((~strong(X0) & ~old(X0)) | (~patient(X0) | ~old(X0))) [ennf transformation 2]
27. ! [X0] : ((~strong(X0) & ~old(X0)) | ~patient(X0) | ~old(X0)) [flattening 26]
29. ! [X0] : ((rich(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0))) [ennf transformation 6]
30. ! [X0] : ((funny(X0) & ~old(X0)) | patient(X0)) [ennf transformation 23]
35. ! [X0] : ((~creative(X0) & old(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) [nnf transformation 25]
43. ! [X0] : (((calm(X0) | ~curious(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 8]
44. ! [X0] : ((calm(X0) | ~curious(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [flattening 43]
55. ! [X0] : ((quiet(X0) | (creative(X0) | ~humble(X0))) & ((~creative(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 14]
56. ! [X0] : ((quiet(X0) | creative(X0) | ~humble(X0)) & ((~creative(X0) & humble(X0)) | ~quiet(X0))) [flattening 55]
69. ~funny(X0) | ~curious(X0) | old(X0) [cnf transformation 35]
72. ~old(X0) | ~patient(X0) | ~old(X0) [cnf transformation 27]
87. ~quiet(X0) | funny(X0) [cnf transformation 29]
90. ~old(X0) | patient(X0) [cnf transformation 30]
92. ~humble(X0) | curious(X0) [cnf transformation 44]
116. ~quiet(X0) | humble(X0) [cnf transformation 56]
127. quiet(alice) [cnf transformation 22]
128. ~patient(X0) | ~old(X0) [duplicate literal removal 72]
156. ~old(X0) [subsumption resolution 90,128]
171. 9 <=> quiet(alice) [avatar definition]
172. quiet(alice) <- (9) [avatar component clause 171]
252. 9 [avatar split clause 127,171]
257. funny(alice) <- (9) [resolution 87,172]
261. humble(alice) <- (9) [resolution 116,172]
264. curious(alice) <- (9) [resolution 261,92]
269. ~curious(alice) | old(alice) <- (9) [resolution 69,257]
274. old(alice) <- (9) [subsumption resolution 269,264]
275. $false <- (9) [subsumption resolution 274,156]
276. ~9 [avatar contradiction clause 275]
278. $false [avatar sat refutation 252,276]
% SZS output end Proof for 7862654950715214836696663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not calm is old and vice versa.
Everyone who is not creative or not happy is not calm or not funny and vice versa.
Everyone who is both not calm and not rich is either not curious or not brave and vice versa.
Everyone who is either not funny or not happy is not curious or not humble.
Everyone who is either happy or not generous is both not patient and curious and vice versa.
If mary is happy or not funny then paul is both not patient and humble.
Everyone who is kind is either not rich or not kind and vice versa.
If alice is either quiet or old then mary is either not wise or patient and vice versa.
If fred is either generous or not wise then fred is both calm and funny.
Everyone who is both not brave and not humble is either generous or not strong and vice versa.
Everyone who is brave or generous is quiet.
If someone is wise or not quiet then someone is either not quiet or not patient and vice versa.
Everyone who is either not funny or not patient is not wise or not calm and vice versa.
If someone is rich then someone is patient or happy.
Everyone who is not generous or brave is both rich and strong and vice versa.
Everyone who is kind or not brave is not humble or not old and vice versa.
Paul is either old or not kind.
Someone is creative or not curious.
Susan is not creative.
Susan is both quiet and not happy.
Someone is calm.
Lucy is strong. | Fred is not humble. | neutral | (![X]:((~generous(X)<~>~calm(X))<=>old(X)))&
(![X]:((~creative(X)|~happy(X))<=>(~calm(X)|~funny(X))))&
(![X]:((~calm(X)&~rich(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((~funny(X)<~>~happy(X))=>(~curious(X)|~humble(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~patient(X)&curious(X))))&
(((happy(mary)|~funny(mary)))=>((~patient(paul)&humble(paul))))&
(![X]:(kind(X)<=>(~rich(X)<~>~kind(X))))&
(((quiet(alice)<~>old(alice)))<=>((~wise(mary)<~>patient(mary))))&
(((generous(fred)<~>~wise(fred)))=>((calm(fred)&funny(fred))))&
(![X]:((~brave(X)&~humble(X))<=>(generous(X)<~>~strong(X))))&
(![X]:((brave(X)|generous(X))=>quiet(X)))&
((?[X]:((wise(X)|~quiet(X))))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~wise(X)|~calm(X))))&
((?[X]:(rich(X)))=>(?[X]:((patient(X)|happy(X)))))&
(![X]:((~generous(X)|brave(X))<=>(rich(X)&strong(X))))&
(![X]:((kind(X)|~brave(X))<=>(~humble(X)|~old(X))))&
((old(paul)<~>~kind(paul)))&
(?[X]:((creative(X)|~curious(X))))&
(~creative(susan))&
((quiet(susan)&~happy(susan)))&
(?[X]:(calm(X)))&
(strong(lucy)) | ~humble(fred) | [] | null | 0 |
Everyone who is humble is either not generous or kind. Everyone who is generous or not wise is not humble or not generous. Everyone who is either old or not funny is humble or not brave and vice versa. If someone is either funny or calm then someone is both not brave and funny. If someone is not kind or generous then fred is not patient. If someone is both humble and tall then mary is either not quiet or wise. If paul is both not curious and not patient then lucy is old or not humble and vice versa. Everyone who is both not humble and humble is either strong or not quiet and vice versa. Everyone who is either calm or not quiet is both wise and curious and vice versa. Everyone who is not old or happy is both generous and not quiet and vice versa. If mary is strong or curious then someone is not rich or kind. If someone is both generous and strong then fred is calm or brave and vice versa. If someone is either tall or not happy then someone is both strong and brave and vice versa. If someone is not strong or tall then someone is old. Everyone who is both not rich and not strong is either happy or wise. Everyone who is strong or not wise is both not generous and tall and vice versa. Susan is humble or not calm. Paul is not happy or not curious. Lucy is wise. Someone is wise. Someone is either funny or not humble. Fred is not curious or not brave. Someone is kind. | Fred is not happy. | entailment | (![X]:(humble(X)=>(~generous(X)<~>kind(X))))&
(![X]:((generous(X)|~wise(X))=>(~humble(X)|~generous(X))))&
(![X]:((old(X)<~>~funny(X))<=>(humble(X)|~brave(X))))&
((?[X]:((funny(X)<~>calm(X))))=>(?[X]:((~brave(X)&funny(X)))))&
((?[X]:((~kind(X)|generous(X))))=>(~patient(fred)))&
((?[X]:((humble(X)&tall(X))))=>((~quiet(mary)<~>wise(mary))))&
(((~curious(paul)&~patient(paul)))<=>((old(lucy)|~humble(lucy))))&
(![X]:((~humble(X)&humble(X))<=>(strong(X)<~>~quiet(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>(wise(X)&curious(X))))&
(![X]:((~old(X)|happy(X))<=>(generous(X)&~quiet(X))))&
(((strong(mary)|curious(mary)))=>(?[X]:((~rich(X)|kind(X)))))&
((?[X]:((generous(X)&strong(X))))<=>((calm(fred)|brave(fred))))&
((?[X]:((tall(X)<~>~happy(X))))<=>(?[X]:((strong(X)&brave(X)))))&
((?[X]:((~strong(X)|tall(X))))=>(?[X]:(old(X))))&
(![X]:((~rich(X)&~strong(X))=>(happy(X)<~>wise(X))))&
(![X]:((strong(X)|~wise(X))<=>(~generous(X)&tall(X))))&
((humble(susan)|~calm(susan)))&
((~happy(paul)|~curious(paul)))&
(wise(lucy))&
(?[X]:(wise(X)))&
(?[X]:((funny(X)<~>~humble(X))))&
((~curious(fred)|~brave(fred)))&
(?[X]:(kind(X))) | ~happy(fred) | [
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 23397248100446214459791
% SZS output start Proof for 23397248100446214459791
8. ! [X0] : ((humble(X0) & ~humble(X0)) <=> (strong(X0) <~> ~quiet(X0))) [input p7]
10. ! [X0] : ((happy(X0) | ~old(X0)) <=> (~quiet(X0) & generous(X0))) [input p9]
16. ! [X0] : ((~wise(X0) | strong(X0)) <=> (tall(X0) & ~generous(X0))) [input p15]
24. happy(fred) [input hypothesis]
48. ! [X0] : (((humble(X0) & ~humble(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (~humble(X0) | humble(X0)))) [nnf transformation 8]
49. ! [X0] : (((humble(X0) & ~humble(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | ~humble(X0) | humble(X0))) [flattening 48]
52. ! [X0] : (((happy(X0) | ~old(X0)) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 10]
53. ! [X0] : ((happy(X0) | ~old(X0) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | (~happy(X0) & old(X0)))) [flattening 52]
70. ! [X0] : (((~wise(X0) | strong(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (wise(X0) & ~strong(X0)))) [nnf transformation 16]
71. ! [X0] : ((~wise(X0) | strong(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (wise(X0) & ~strong(X0)))) [flattening 70]
105. ~humble(X0) | strong(X0) | quiet(X0) [cnf transformation 49]
107. strong(X0) | humble(X0) | quiet(X0) [cnf transformation 49]
115. ~happy(X0) | generous(X0) [cnf transformation 53]
117. ~happy(X0) | ~quiet(X0) [cnf transformation 53]
136. ~generous(X0) | ~strong(X0) [cnf transformation 71]
149. happy(fred) [cnf transformation 24]
215. strong(X0) | quiet(X0) [subsumption resolution 105,107]
256. 23 <=> ! [X1] : (~strong(X1) | ~generous(X1)) [avatar definition]
257. ~strong(X1) | ~generous(X1) <- (23) [avatar component clause 256]
302. 23 [avatar split clause 136,256]
332. generous(fred) [resolution 115,149]
333. ~quiet(fred) [resolution 117,149]
339. ~generous(X0) | quiet(X0) <- (23) [resolution 257,215]
560. quiet(fred) <- (23) [resolution 339,332]
562. $false <- (23) [subsumption resolution 560,333]
563. ~23 [avatar contradiction clause 562]
566. $false [avatar sat refutation 302,563]
% SZS output end Proof for 23397248100446214459791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or tall is both humble and not humble and vice versa. If susan is both quiet and brave then someone is either not rich or rich. If someone is calm then mary is both not kind and not rich. Everyone who is either curious or rich is either calm or not calm and vice versa. Everyone who is calm is wise. Everyone who is not quiet or funny is both not tall and creative and vice versa. If fred is not old then alice is both calm and not kind. If alice is not kind or not curious then someone is rich or not creative and vice versa. If someone is both not tall and old then someone is not kind. If someone is either humble or kind then lucy is not quiet or creative. Everyone who is wise is both not wise and not strong. Everyone who is not brave is either not old or quiet and vice versa. If mary is creative or funny then someone is both not creative and quiet and vice versa. Everyone who is curious is either not quiet or brave and vice versa. Everyone who is not old or not wise is brave. Paul is either wise or creative. Someone is both quiet and not humble. Someone is patient or calm. Someone is quiet or not wise. Lucy is not generous. Someone is either rich or strong. Someone is curious. | Fred is quiet. | contradiction | (![X]:((~old(X)<~>tall(X))<=>(humble(X)&~humble(X))))&
(((quiet(susan)&brave(susan)))=>(?[X]:((~rich(X)<~>rich(X)))))&
((?[X]:(calm(X)))=>((~kind(mary)&~rich(mary))))&
(![X]:((curious(X)<~>rich(X))<=>(calm(X)<~>~calm(X))))&
(![X]:(calm(X)=>wise(X)))&
(![X]:((~quiet(X)|funny(X))<=>(~tall(X)&creative(X))))&
((~old(fred))=>((calm(alice)&~kind(alice))))&
(((~kind(alice)|~curious(alice)))<=>(?[X]:((rich(X)|~creative(X)))))&
((?[X]:((~tall(X)&old(X))))=>(?[X]:(~kind(X))))&
((?[X]:((humble(X)<~>kind(X))))=>((~quiet(lucy)|creative(lucy))))&
(![X]:(wise(X)=>(~wise(X)&~strong(X))))&
(![X]:(~brave(X)<=>(~old(X)<~>quiet(X))))&
(((creative(mary)|funny(mary)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:(curious(X)<=>(~quiet(X)<~>brave(X))))&
(![X]:((~old(X)|~wise(X))=>brave(X)))&
((wise(paul)<~>creative(paul)))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((patient(X)|calm(X))))&
(?[X]:((quiet(X)|~wise(X))))&
(~generous(lucy))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:(curious(X))) | quiet(fred) | [
"p4",
"p6",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3790273113923712758785908
% SZS output start Proof for 3790273113923712758785908
5. ! [X0] : (calm(X0) => wise(X0)) [input p4]
7. ~old(fred) => (~kind(alice) & calm(alice)) [input p6]
11. ! [X0] : (wise(X0) => (~strong(X0) & ~wise(X0))) [input p10]
12. ! [X0] : (~brave(X0) <=> (~old(X0) <~> quiet(X0))) [input p11]
15. ! [X0] : ((~wise(X0) | ~old(X0)) => brave(X0)) [input p14]
23. quiet(fred) [input hypothesis]
30. ! [X0] : (wise(X0) | ~calm(X0)) [ennf transformation 5]
31. (~kind(alice) & calm(alice)) | old(fred) [ennf transformation 7]
35. ! [X0] : ((~strong(X0) & ~wise(X0)) | ~wise(X0)) [ennf transformation 11]
36. ! [X0] : (brave(X0) | (wise(X0) & old(X0))) [ennf transformation 15]
54. ! [X0] : ((~brave(X0) | ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0)))) & (((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | brave(X0))) [nnf transformation 12]
89. ~calm(X0) | wise(X0) [cnf transformation 30]
95. calm(alice) | old(fred) [cnf transformation 31]
104. ~wise(X0) | ~wise(X0) [cnf transformation 35]
109. ~brave(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 54]
120. brave(X0) | wise(X0) [cnf transformation 36]
129. quiet(fred) [cnf transformation 23]
130. ~wise(X0) [duplicate literal removal 104]
153. 4 <=> old(fred) [avatar definition]
162. 6 <=> calm(alice) [avatar definition]
164. calm(alice) <- (6) [avatar component clause 162]
165. 4 | 6 [avatar split clause 95,162,153]
234. brave(X0) [subsumption resolution 120,130]
264. ~quiet(X0) | ~old(X0) [resolution 109,234]
266. ~old(fred) [resolution 264,129]
271. ~4 [avatar split clause 266,153]
272. wise(alice) <- (6) [resolution 164,89]
273. $false <- (6) [subsumption resolution 272,130]
274. ~6 [avatar contradiction clause 273]
275. $false [avatar sat refutation 165,271,274]
% SZS output end Proof for 3790273113923712758785908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is both not curious and not calm.
Everyone who is either not strong or wise is either funny or creative and vice versa.
Everyone who is not calm or curious is either not tall or not old.
If someone is either generous or not creative then someone is both not patient and patient and vice versa.
If paul is quiet then someone is both not tall and generous and vice versa.
Everyone who is both humble and not happy is funny or not patient and vice versa.
Everyone who is both wise and kind is not brave or tall and vice versa.
If mary is either not kind or not tall then susan is either patient or happy and vice versa.
If alice is not kind or calm then alice is both not tall and not quiet.
If lucy is not humble or not kind then someone is both humble and strong.
If someone is kind or not calm then john is either old or happy and vice versa.
Everyone who is both not old and creative is both generous and not creative.
Everyone who is not patient or wise is both not old and curious.
If someone is both humble and not strong then mary is creative or not calm.
Everyone who is both not generous and not quiet is tall or not happy and vice versa.
Everyone who is either tall or not generous is tall or rich and vice versa.
Susan is both not happy and strong.
Alice is not strong.
Someone is not kind.
John is funny.
Someone is either not funny or strong.
Someone is both curious and rich. | John is not wise. | entailment | (![X]:(quiet(X)=>(~curious(X)&~calm(X))))&
(![X]:((~strong(X)<~>wise(X))<=>(funny(X)<~>creative(X))))&
(![X]:((~calm(X)|curious(X))=>(~tall(X)<~>~old(X))))&
((?[X]:((generous(X)<~>~creative(X))))<=>(?[X]:((~patient(X)&patient(X)))))&
((quiet(paul))<=>(?[X]:((~tall(X)&generous(X)))))&
(![X]:((humble(X)&~happy(X))<=>(funny(X)|~patient(X))))&
(![X]:((wise(X)&kind(X))<=>(~brave(X)|tall(X))))&
(((~kind(mary)<~>~tall(mary)))<=>((patient(susan)<~>happy(susan))))&
(((~kind(alice)|calm(alice)))=>((~tall(alice)&~quiet(alice))))&
(((~humble(lucy)|~kind(lucy)))=>(?[X]:((humble(X)&strong(X)))))&
((?[X]:((kind(X)|~calm(X))))<=>((old(john)<~>happy(john))))&
(![X]:((~old(X)&creative(X))=>(generous(X)&~creative(X))))&
(![X]:((~patient(X)|wise(X))=>(~old(X)&curious(X))))&
((?[X]:((humble(X)&~strong(X))))=>((creative(mary)|~calm(mary))))&
(![X]:((~generous(X)&~quiet(X))<=>(tall(X)|~happy(X))))&
(![X]:((tall(X)<~>~generous(X))<=>(tall(X)|rich(X))))&
((~happy(susan)&strong(susan)))&
(~strong(alice))&
(?[X]:(~kind(X)))&
(funny(john))&
(?[X]:((~funny(X)<~>strong(X))))&
(?[X]:((curious(X)&rich(X)))) | ~wise(john) | [
"p0",
"p3",
"p4",
"p5",
"p10",
"p11",
"p12",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5911403942970391017918457
% SZS output start Proof for 5911403942970391017918457
1. ! [X0] : (quiet(X0) => (~calm(X0) & ~curious(X0))) [input p0]
4. ? [X0] : (generous(X0) <~> ~creative(X0)) <=> ? [X0] : (patient(X0) & ~patient(X0)) [input p3]
5. quiet(paul) <=> ? [X0] : (generous(X0) & ~tall(X0)) [input p4]
6. ! [X0] : ((~happy(X0) & humble(X0)) <=> (~patient(X0) | funny(X0))) [input p5]
11. ? [X0] : (~calm(X0) | kind(X0)) <=> (old(john) <~> happy(john)) [input p10]
12. ! [X0] : ((creative(X0) & ~old(X0)) => (~creative(X0) & generous(X0))) [input p11]
13. ! [X0] : ((wise(X0) | ~patient(X0)) => (curious(X0) & ~old(X0))) [input p12]
15. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> (~happy(X0) | tall(X0))) [input p14]
16. ! [X0] : ((tall(X0) <~> ~generous(X0)) <=> (rich(X0) | tall(X0))) [input p15]
20. funny(john) [input p19]
23. wise(john) [input hypothesis]
24. ? [X0] : (generous(X0) <~> ~creative(X0)) <=> ? [X1] : (patient(X1) & ~patient(X1)) [rectify 4]
25. ! [X0] : ((~calm(X0) & ~curious(X0)) | ~quiet(X0)) [ennf transformation 1]
29. ! [X0] : ((~creative(X0) & generous(X0)) | (~creative(X0) | old(X0))) [ennf transformation 12]
30. ! [X0] : ((~creative(X0) & generous(X0)) | ~creative(X0) | old(X0)) [flattening 29]
31. ! [X0] : ((curious(X0) & ~old(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 13]
36. (? [X0] : ((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | ! [X1] : (~patient(X1) | patient(X1))) & (? [X1] : (patient(X1) & ~patient(X1)) | ! [X0] : ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0)))) [nnf transformation 24]
37. (? [X0] : ((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | ! [X1] : (~patient(X1) | patient(X1))) & (? [X2] : (patient(X2) & ~patient(X2)) | ! [X3] : ((generous(X3) | creative(X3)) & (~creative(X3) | ~generous(X3)))) [rectify 36]
38. ? [X0] : ((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) => ((creative(sK0) | ~generous(sK0)) & (~creative(sK0) | generous(sK0))) [choice axiom]
39. ? [X2] : (patient(X2) & ~patient(X2)) => (patient(sK1) & ~patient(sK1)) [choice axiom]
40. (((creative(sK0) | ~generous(sK0)) & (~creative(sK0) | generous(sK0))) | ! [X1] : (~patient(X1) | patient(X1))) & ((patient(sK1) & ~patient(sK1)) | ! [X3] : ((generous(X3) | creative(X3)) & (~creative(X3) | ~generous(X3)))) [skolemisation 37,39,38]
41. (quiet(paul) | ! [X0] : (~generous(X0) | tall(X0))) & (? [X0] : (generous(X0) & ~tall(X0)) | ~quiet(paul)) [nnf transformation 5]
42. (quiet(paul) | ! [X0] : (~generous(X0) | tall(X0))) & (? [X1] : (generous(X1) & ~tall(X1)) | ~quiet(paul)) [rectify 41]
43. ? [X1] : (generous(X1) & ~tall(X1)) => (generous(sK2) & ~tall(sK2)) [choice axiom]
44. (quiet(paul) | ! [X0] : (~generous(X0) | tall(X0))) & ((generous(sK2) & ~tall(sK2)) | ~quiet(paul)) [skolemisation 42,43]
45. ! [X0] : (((~happy(X0) & humble(X0)) | (patient(X0) & ~funny(X0))) & ((~patient(X0) | funny(X0)) | (happy(X0) | ~humble(X0)))) [nnf transformation 6]
46. ! [X0] : (((~happy(X0) & humble(X0)) | (patient(X0) & ~funny(X0))) & (~patient(X0) | funny(X0) | happy(X0) | ~humble(X0))) [flattening 45]
52. (? [X0] : (~calm(X0) | kind(X0)) | ((old(john) | ~happy(john)) & (happy(john) | ~old(john)))) & (((~happy(john) | ~old(john)) & (happy(john) | old(john))) | ! [X0] : (calm(X0) & ~kind(X0))) [nnf transformation 11]
53. (? [X0] : (~calm(X0) | kind(X0)) | ((old(john) | ~happy(john)) & (happy(john) | ~old(john)))) & (((~happy(john) | ~old(john)) & (happy(john) | old(john))) | ! [X1] : (calm(X1) & ~kind(X1))) [rectify 52]
54. ? [X0] : (~calm(X0) | kind(X0)) => (~calm(sK4) | kind(sK4)) [choice axiom]
55. ((~calm(sK4) | kind(sK4)) | ((old(john) | ~happy(john)) & (happy(john) | ~old(john)))) & (((~happy(john) | ~old(john)) & (happy(john) | old(john))) | ! [X1] : (calm(X1) & ~kind(X1))) [skolemisation 53,54]
56. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (happy(X0) & ~tall(X0))) & ((~happy(X0) | tall(X0)) | (quiet(X0) | generous(X0)))) [nnf transformation 15]
57. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (happy(X0) & ~tall(X0))) & (~happy(X0) | tall(X0) | quiet(X0) | generous(X0))) [flattening 56]
58. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [nnf transformation 16]
59. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [flattening 58]
68. ~calm(X0) | ~quiet(X0) [cnf transformation 25]
82. ~patient(sK1) | generous(X3) | creative(X3) [cnf transformation 40]
84. patient(sK1) | generous(X3) | creative(X3) [cnf transformation 40]
89. quiet(paul) | ~generous(X0) | tall(X0) [cnf transformation 44]
93. ~happy(X0) | ~funny(X0) [cnf transformation 46]
117. happy(john) | old(john) | calm(X1) [cnf transformation 55]
123. ~creative(X0) | ~creative(X0) | old(X0) [cnf transformation 30]
125. ~old(X0) | ~wise(X0) [cnf transformation 31]
130. ~generous(X0) | ~tall(X0) [cnf transformation 57]
138. generous(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 59]
144. funny(john) [cnf transformation 20]
149. wise(john) [cnf transformation 23]
151. generous(X0) | ~tall(X0) [duplicate literal removal 138]
152. ~creative(X0) | old(X0) [duplicate literal removal 123]
154. 1 <=> ! [X3] : (generous(X3) | creative(X3)) [avatar definition]
155. generous(X3) | creative(X3) <- (1) [avatar component clause 154]
157. 2 <=> patient(sK1) [avatar definition]
160. 1 | 2 [avatar split clause 84,157,154]
165. 1 | ~2 [avatar split clause 82,157,154]
168. 4 <=> ! [X0] : (~generous(X0) | tall(X0)) [avatar definition]
169. ~generous(X0) | tall(X0) <- (4) [avatar component clause 168]
171. 5 <=> quiet(paul) [avatar definition]
173. quiet(paul) <- (5) [avatar component clause 171]
174. 4 | 5 [avatar split clause 89,171,168]
248. 20 <=> happy(john) [avatar definition]
249. happy(john) <- (20) [avatar component clause 248]
252. 21 <=> old(john) [avatar definition]
253. ~old(john) <- (~21) [avatar component clause 252]
254. old(john) <- (21) [avatar component clause 252]
266. 24 <=> ! [X1] : calm(X1) [avatar definition]
267. calm(X1) <- (24) [avatar component clause 266]
273. 24 | 21 | 20 [avatar split clause 117,248,252,266]
288. ~tall(X0) [subsumption resolution 151,130]
302. ~generous(X0) <- (4) [subsumption resolution 169,288]
303. creative(X3) <- (1, 4) [subsumption resolution 155,302]
306. ~funny(john) <- (20) [resolution 93,249]
307. $false <- (20) [subsumption resolution 306,144]
308. ~20 [avatar contradiction clause 307]
310. ~wise(john) <- (21) [resolution 125,254]
311. $false <- (21) [subsumption resolution 310,149]
312. ~21 [avatar contradiction clause 311]
315. ~quiet(X0) <- (24) [resolution 267,68]
324. old(X0) <- (1, 4) [resolution 152,303]
331. $false <- (1, 4, ~21) [resolution 324,253]
332. ~1 | ~4 | 21 [avatar contradiction clause 331]
333. $false <- (5, 24) [subsumption resolution 173,315]
334. ~5 | ~24 [avatar contradiction clause 333]
335. $false [avatar sat refutation 160,165,174,273,308,312,332,334]
% SZS output end Proof for 5911403942970391017918457
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and old is both calm and patient and vice versa.
Everyone who is patient is both old and not creative.
If paul is either calm or old then someone is not kind or humble and vice versa.
Everyone who is both curious and strong is not creative and vice versa.
Everyone who is wise is both wise and kind and vice versa.
If someone is humble then someone is either not old or brave.
Everyone who is curious or not generous is not brave and vice versa.
If fred is both generous and old then john is both generous and patient.
If someone is not funny or not quiet then someone is happy or humble.
If lucy is curious then alice is happy.
If someone is either not strong or not generous then john is either creative or curious.
Everyone who is not brave is both humble and kind and vice versa.
Everyone who is humble is both not generous and not patient.
Everyone who is both not creative and curious is not patient or not rich and vice versa.
Everyone who is both curious and patient is either kind or curious and vice versa.
Everyone who is both rich and not quiet is either rich or tall and vice versa.
Susan is either not humble or not calm.
Someone is not happy.
Someone is either not happy or not funny.
Mary is either not brave or generous.
Susan is humble or old.
Someone is either rich or not wise. | John is old. | contradiction | (![X]:((kind(X)&old(X))<=>(calm(X)&patient(X))))&
(![X]:(patient(X)=>(old(X)&~creative(X))))&
(((calm(paul)<~>old(paul)))<=>(?[X]:((~kind(X)|humble(X)))))&
(![X]:((curious(X)&strong(X))<=>~creative(X)))&
(![X]:(wise(X)<=>(wise(X)&kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((curious(X)|~generous(X))<=>~brave(X)))&
(((generous(fred)&old(fred)))=>((generous(john)&patient(john))))&
((?[X]:((~funny(X)|~quiet(X))))=>(?[X]:((happy(X)|humble(X)))))&
((curious(lucy))=>(happy(alice)))&
((?[X]:((~strong(X)<~>~generous(X))))=>((creative(john)<~>curious(john))))&
(![X]:(~brave(X)<=>(humble(X)&kind(X))))&
(![X]:(humble(X)=>(~generous(X)&~patient(X))))&
(![X]:((~creative(X)&curious(X))<=>(~patient(X)|~rich(X))))&
(![X]:((curious(X)&patient(X))<=>(kind(X)<~>curious(X))))&
(![X]:((rich(X)&~quiet(X))<=>(rich(X)<~>tall(X))))&
((~humble(susan)<~>~calm(susan)))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)<~>~funny(X))))&
((~brave(mary)<~>generous(mary)))&
((humble(susan)|old(susan)))&
(?[X]:((rich(X)<~>~wise(X)))) | old(john) | [
"p0",
"p1",
"p3",
"p6",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 103960164322186613246386
% SZS output start Proof for 103960164322186613246386
1. ! [X0] : ((old(X0) & kind(X0)) <=> (patient(X0) & calm(X0))) [input p0]
2. ! [X0] : (patient(X0) => (~creative(X0) & old(X0))) [input p1]
4. ! [X0] : ((strong(X0) & curious(X0)) <=> ~creative(X0)) [input p3]
7. ! [X0] : ((~generous(X0) | curious(X0)) <=> ~brave(X0)) [input p6]
12. ! [X0] : (~brave(X0) <=> (kind(X0) & humble(X0))) [input p11]
13. ! [X0] : (humble(X0) => (~patient(X0) & ~generous(X0))) [input p12]
14. ! [X0] : ((curious(X0) & ~creative(X0)) <=> (~rich(X0) | ~patient(X0))) [input p13]
23. old(john) [input hypothesis]
26. ! [X0] : ((~creative(X0) & old(X0)) | ~patient(X0)) [ennf transformation 2]
33. ! [X0] : ((~patient(X0) & ~generous(X0)) | ~humble(X0)) [ennf transformation 13]
34. ! [X0] : (((old(X0) & kind(X0)) | (~patient(X0) | ~calm(X0))) & ((patient(X0) & calm(X0)) | (~old(X0) | ~kind(X0)))) [nnf transformation 1]
35. ! [X0] : (((old(X0) & kind(X0)) | ~patient(X0) | ~calm(X0)) & ((patient(X0) & calm(X0)) | ~old(X0) | ~kind(X0))) [flattening 34]
40. ! [X0] : (((strong(X0) & curious(X0)) | creative(X0)) & (~creative(X0) | (~strong(X0) | ~curious(X0)))) [nnf transformation 4]
41. ! [X0] : (((strong(X0) & curious(X0)) | creative(X0)) & (~creative(X0) | ~strong(X0) | ~curious(X0))) [flattening 40]
48. ! [X0] : (((~generous(X0) | curious(X0)) | brave(X0)) & (~brave(X0) | (generous(X0) & ~curious(X0)))) [nnf transformation 7]
49. ! [X0] : ((~generous(X0) | curious(X0) | brave(X0)) & (~brave(X0) | (generous(X0) & ~curious(X0)))) [flattening 48]
54. ! [X0] : ((~brave(X0) | (~kind(X0) | ~humble(X0))) & ((kind(X0) & humble(X0)) | brave(X0))) [nnf transformation 12]
55. ! [X0] : ((~brave(X0) | ~kind(X0) | ~humble(X0)) & ((kind(X0) & humble(X0)) | brave(X0))) [flattening 54]
56. ! [X0] : (((curious(X0) & ~creative(X0)) | (rich(X0) & patient(X0))) & ((~rich(X0) | ~patient(X0)) | (~curious(X0) | creative(X0)))) [nnf transformation 14]
57. ! [X0] : (((curious(X0) & ~creative(X0)) | (rich(X0) & patient(X0))) & (~rich(X0) | ~patient(X0) | ~curious(X0) | creative(X0))) [flattening 56]
73. ~old(X0) | patient(X0) | ~kind(X0) [cnf transformation 35]
77. ~creative(X0) | ~patient(X0) [cnf transformation 26]
85. curious(X0) | creative(X0) [cnf transformation 41]
92. ~brave(X0) | ~curious(X0) [cnf transformation 49]
93. ~brave(X0) | generous(X0) [cnf transformation 49]
104. brave(X0) | humble(X0) [cnf transformation 55]
105. brave(X0) | kind(X0) [cnf transformation 55]
107. ~generous(X0) | ~humble(X0) [cnf transformation 33]
108. ~humble(X0) | ~patient(X0) [cnf transformation 33]
110. ~creative(X0) | patient(X0) [cnf transformation 57]
136. old(john) [cnf transformation 23]
154. 4 <=> ! [X0] : kind(X0) [avatar definition]
155. kind(X0) <- (4) [avatar component clause 154]
238. ~creative(X0) [subsumption resolution 110,77]
292. ~curious(X1) | humble(X1) [resolution 104,92]
294. generous(X0) | kind(X0) [resolution 105,93]
315. patient(john) | ~kind(john) [resolution 73,136]
335. humble(X1) | creative(X1) [resolution 292,85]
342. humble(X1) [subsumption resolution 335,238]
343. ~patient(X0) [resolution 342,108]
347. kind(X1) | ~humble(X1) [resolution 294,107]
348. kind(X1) [subsumption resolution 347,342]
349. 4 [avatar split clause 348,154]
355. ~kind(john) [subsumption resolution 315,343]
356. $false <- (4) [subsumption resolution 355,155]
357. ~4 [avatar contradiction clause 356]
358. $false [avatar sat refutation 349,357]
% SZS output end Proof for 103960164322186613246386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or kind is either not kind or funny and vice versa. If susan is not brave or quiet then mary is both not brave and humble and vice versa. Everyone who is both tall and not creative is quiet. Everyone who is creative or not old is funny. If someone is either not generous or old then someone is both tall and not happy and vice versa. Everyone who is either not happy or not brave is calm. Everyone who is both not quiet and not wise is either not happy or funny. If someone is either old or not humble then susan is either generous or not wise. Everyone who is both tall and humble is rich or not brave. If someone is either not kind or not old then someone is curious. If someone is not strong then someone is both not rich and patient and vice versa. If someone is both not curious and not patient then susan is creative or generous. Everyone who is both not tall and patient is either not funny or funny and vice versa. If mary is either not curious or creative then mary is both not humble and humble. If someone is happy or not calm then someone is kind or not tall and vice versa. Everyone who is both creative and strong is brave and vice versa. Someone is not creative. Someone is not brave or wise. Alice is rich. Paul is happy. Someone is both not brave and not strong. Lucy is both not brave and old. Someone is either not brave or not old. | Paul is not patient. | contradiction | (![X]:((calm(X)|kind(X))<=>(~kind(X)<~>funny(X))))&
(((~brave(susan)|quiet(susan)))<=>((~brave(mary)&humble(mary))))&
(![X]:((tall(X)&~creative(X))=>quiet(X)))&
(![X]:((creative(X)|~old(X))=>funny(X)))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~happy(X)<~>~brave(X))=>calm(X)))&
(![X]:((~quiet(X)&~wise(X))=>(~happy(X)<~>funny(X))))&
((?[X]:((old(X)<~>~humble(X))))=>((generous(susan)<~>~wise(susan))))&
(![X]:((tall(X)&humble(X))=>(rich(X)|~brave(X))))&
((?[X]:((~kind(X)<~>~old(X))))=>(?[X]:(curious(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~rich(X)&patient(X)))))&
((?[X]:((~curious(X)&~patient(X))))=>((creative(susan)|generous(susan))))&
(![X]:((~tall(X)&patient(X))<=>(~funny(X)<~>funny(X))))&
(((~curious(mary)<~>creative(mary)))=>((~humble(mary)&humble(mary))))&
((?[X]:((happy(X)|~calm(X))))<=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:((creative(X)&strong(X))<=>brave(X)))&
(?[X]:(~creative(X)))&
(?[X]:((~brave(X)|wise(X))))&
(rich(alice))&
(happy(paul))&
(?[X]:((~brave(X)&~strong(X))))&
((~brave(lucy)&old(lucy)))&
(?[X]:((~brave(X)<~>~old(X)))) | ~patient(paul) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3164465493195820174769075
% SZS output start Proof for 3164465493195820174769075
13. ! [X0] : ((patient(X0) & ~tall(X0)) <=> (~funny(X0) <~> funny(X0))) [input p12]
24. ~patient(paul) [input hypothesis]
63. ! [X0] : (((patient(X0) & ~tall(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (~patient(X0) | tall(X0)))) [nnf transformation 13]
64. ! [X0] : (((patient(X0) & ~tall(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ~patient(X0) | tall(X0))) [flattening 63]
121. patient(X0) | funny(X0) | funny(X0) [cnf transformation 64]
122. patient(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 64]
144. ~patient(paul) [cnf transformation 24]
147. patient(X0) | funny(X0) [duplicate literal removal 121]
148. patient(X0) | ~funny(X0) [duplicate literal removal 122]
262. patient(X0) [subsumption resolution 147,148]
309. $false [subsumption resolution 144,262]
% SZS output end Proof for 3164465493195820174769075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
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