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 calm is both generous and not brave and vice versa.
If someone is both not rich and not happy then someone is both calm and creative.
Everyone who is either not rich or happy is either patient or calm.
Everyone who is either generous or old is not strong.
If someone is both creative and not curious then mary is old.
If someone is curious then someone is either not creative or not happy.
If susan is both not generous and not calm then fred is not creative or not quiet.
Everyone who is rich or brave is funny.
If someone is funny or old then someone is either patient or generous.
Everyone who is generous or brave is not funny and vice versa.
Everyone who is funny is not wise.
If someone is both strong and creative then someone is strong or wise.
Everyone who is both patient and generous is both not funny and not brave.
Everyone who is both not humble and humble is either not curious or creative and vice versa.
Everyone who is not curious is strong and vice versa.
Everyone who is quiet or not patient is not calm.
Someone is either not kind or not brave.
Alice is not happy.
Someone is calm.
Lucy is kind.
Someone is happy.
Someone is not rich.
Lucy is either creative or not happy.
Someone is humble or funny. | Alice is not calm. | entailment | (![X]:(calm(X)<=>(generous(X)&~brave(X))))&
((?[X]:((~rich(X)&~happy(X))))=>(?[X]:((calm(X)&creative(X)))))&
(![X]:((~rich(X)<~>happy(X))=>(patient(X)<~>calm(X))))&
(![X]:((generous(X)<~>old(X))=>~strong(X)))&
((?[X]:((creative(X)&~curious(X))))=>(old(mary)))&
((?[X]:(curious(X)))=>(?[X]:((~creative(X)<~>~happy(X)))))&
(((~generous(susan)&~calm(susan)))=>((~creative(fred)|~quiet(fred))))&
(![X]:((rich(X)|brave(X))=>funny(X)))&
((?[X]:((funny(X)|old(X))))=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:((generous(X)|brave(X))<=>~funny(X)))&
(![X]:(funny(X)=>~wise(X)))&
((?[X]:((strong(X)&creative(X))))=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((patient(X)&generous(X))=>(~funny(X)&~brave(X))))&
(![X]:((~humble(X)&humble(X))<=>(~curious(X)<~>creative(X))))&
(![X]:(~curious(X)<=>strong(X)))&
(![X]:((quiet(X)|~patient(X))=>~calm(X)))&
(?[X]:((~kind(X)<~>~brave(X))))&
(~happy(alice))&
(?[X]:(calm(X)))&
(kind(lucy))&
(?[X]:(happy(X)))&
(?[X]:(~rich(X)))&
((creative(lucy)<~>~happy(lucy)))&
(?[X]:((humble(X)|funny(X)))) | ~calm(alice) | [
"p0",
"p2",
"p7",
"p9",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 151993668999100228830228
% SZS output start Proof for 151993668999100228830228
1. ! [X0] : (calm(X0) <=> (~brave(X0) & generous(X0))) [input p0]
3. ! [X0] : ((~rich(X0) <~> happy(X0)) => (patient(X0) <~> calm(X0))) [input p2]
8. ! [X0] : ((brave(X0) | rich(X0)) => funny(X0)) [input p7]
10. ! [X0] : ((brave(X0) | generous(X0)) <=> ~funny(X0)) [input p9]
16. ! [X0] : ((~patient(X0) | quiet(X0)) => ~calm(X0)) [input p15]
18. ~happy(alice) [input p17]
25. calm(alice) [input hypothesis]
31. ! [X0] : (~patient(X0) => ~calm(X0)) [pure predicate removal 16]
33. ! [X0] : ((patient(X0) <~> calm(X0)) | (~rich(X0) <=> happy(X0))) [ennf transformation 3]
37. ! [X0] : (funny(X0) | (~brave(X0) & ~rich(X0))) [ennf transformation 8]
43. ! [X0] : (~calm(X0) | patient(X0)) [ennf transformation 31]
44. ! [X0] : ((calm(X0) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | ~calm(X0))) [nnf transformation 1]
45. ! [X0] : ((calm(X0) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | ~calm(X0))) [flattening 44]
49. ! [X0] : (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0)))) [nnf transformation 33]
59. ! [X0] : (((brave(X0) | generous(X0)) | funny(X0)) & (~funny(X0) | (~brave(X0) & ~generous(X0)))) [nnf transformation 10]
60. ! [X0] : ((brave(X0) | generous(X0) | funny(X0)) & (~funny(X0) | (~brave(X0) & ~generous(X0)))) [flattening 59]
79. ~calm(X0) | generous(X0) [cnf transformation 45]
86. ~patient(X0) | ~calm(X0) | happy(X0) | rich(X0) [cnf transformation 49]
93. ~rich(X0) | funny(X0) [cnf transformation 37]
99. ~funny(X0) | ~generous(X0) [cnf transformation 60]
114. ~calm(X0) | patient(X0) [cnf transformation 43]
117. ~happy(alice) [cnf transformation 18]
125. calm(alice) [cnf transformation 25]
223. generous(alice) [resolution 79,125]
227. patient(alice) [resolution 114,125]
290. ~calm(alice) | happy(alice) | rich(alice) [resolution 86,227]
295. happy(alice) | rich(alice) [subsumption resolution 290,125]
296. rich(alice) [subsumption resolution 295,117]
343. funny(alice) [resolution 296,93]
347. ~generous(alice) [resolution 343,99]
348. $false [subsumption resolution 347,223]
% SZS output end Proof for 151993668999100228830228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either rich or kind then alice is kind or not brave and vice versa.
If someone is not calm or creative then someone is curious or not patient and vice versa.
If someone is curious or humble then someone is either funny or strong and vice versa.
Everyone who is not curious is not rich or happy.
If alice is both not happy and not old then mary is not happy and vice versa.
Everyone who is either quiet or kind is not generous.
If someone is either rich or not rich then alice is generous or not curious.
If alice is generous or not funny then lucy is funny or not curious and vice versa.
Everyone who is either funny or humble is tall.
Everyone who is either kind or not happy is either rich or humble and vice versa.
Everyone who is not funny is wise or calm.
Everyone who is either not kind or not rich is either not generous or old.
Everyone who is either not funny or quiet is rich.
If john is either funny or not tall then mary is both brave and not old.
Everyone who is either calm or not happy is not generous and vice versa.
If paul is either not happy or not creative then someone is both funny and brave and vice versa.
Someone is wise.
Alice is not generous.
Someone is either not generous or not wise.
Someone is not rich or not patient.
Someone is either tall or humble.
Lucy is both not brave and not quiet.
Someone is not curious.
Susan is funny or creative. | Alice is not curious. | entailment | (((rich(alice)<~>kind(alice)))<=>((kind(alice)|~brave(alice))))&
((?[X]:((~calm(X)|creative(X))))<=>(?[X]:((curious(X)|~patient(X)))))&
((?[X]:((curious(X)|humble(X))))<=>(?[X]:((funny(X)<~>strong(X)))))&
(![X]:(~curious(X)=>(~rich(X)|happy(X))))&
(((~happy(alice)&~old(alice)))<=>(~happy(mary)))&
(![X]:((quiet(X)<~>kind(X))=>~generous(X)))&
((?[X]:((rich(X)<~>~rich(X))))=>((generous(alice)|~curious(alice))))&
(((generous(alice)|~funny(alice)))<=>((funny(lucy)|~curious(lucy))))&
(![X]:((funny(X)<~>humble(X))=>tall(X)))&
(![X]:((kind(X)<~>~happy(X))<=>(rich(X)<~>humble(X))))&
(![X]:(~funny(X)=>(wise(X)|calm(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~generous(X)<~>old(X))))&
(![X]:((~funny(X)<~>quiet(X))=>rich(X)))&
(((funny(john)<~>~tall(john)))=>((brave(mary)&~old(mary))))&
(![X]:((calm(X)<~>~happy(X))<=>~generous(X)))&
(((~happy(paul)<~>~creative(paul)))<=>(?[X]:((funny(X)&brave(X)))))&
(?[X]:(wise(X)))&
(~generous(alice))&
(?[X]:((~generous(X)<~>~wise(X))))&
(?[X]:((~rich(X)|~patient(X))))&
(?[X]:((tall(X)<~>humble(X))))&
((~brave(lucy)&~quiet(lucy)))&
(?[X]:(~curious(X)))&
((funny(susan)|creative(susan))) | ~curious(alice) | [
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 396159380009590143971840
% SZS output start Proof for 396159380009590143971840
7. ? [X0] : (rich(X0) <~> ~rich(X0)) => (~curious(alice) | generous(alice)) [input p6]
18. ~generous(alice) [input p17]
25. curious(alice) [input hypothesis]
31. (~curious(alice) | generous(alice)) | ! [X0] : (rich(X0) <=> ~rich(X0)) [ennf transformation 7]
32. ~curious(alice) | generous(alice) | ! [X0] : (rich(X0) <=> ~rich(X0)) [flattening 31]
54. ~curious(alice) | generous(alice) | ! [X0] : ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))) [nnf transformation 32]
101. ~curious(alice) | generous(alice) | ~rich(X0) | ~rich(X0) [cnf transformation 54]
102. ~curious(alice) | generous(alice) | rich(X0) | rich(X0) [cnf transformation 54]
139. ~generous(alice) [cnf transformation 18]
149. curious(alice) [cnf transformation 25]
150. ~curious(alice) | generous(alice) | ~rich(X0) [duplicate literal removal 101]
151. ~curious(alice) | generous(alice) | rich(X0) [duplicate literal removal 102]
249. 22 <=> ! [X0] : rich(X0) [avatar definition]
250. rich(X0) <- (22) [avatar component clause 249]
252. 23 <=> generous(alice) [avatar definition]
256. 24 <=> curious(alice) [avatar definition]
259. 22 | 23 | ~24 [avatar split clause 151,256,252,249]
261. 25 <=> ! [X0] : ~rich(X0) [avatar definition]
262. ~rich(X0) <- (25) [avatar component clause 261]
263. 25 | 23 | ~24 [avatar split clause 150,256,252,261]
325. ~23 [avatar split clause 139,252]
364. 24 [avatar split clause 149,256]
365. $false <- (22, 25) [subsumption resolution 250,262]
366. ~22 | ~25 [avatar contradiction clause 365]
369. $false [avatar sat refutation 259,263,325,364,366]
% SZS output end Proof for 396159380009590143971840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is both humble and happy. Everyone who is either brave or tall is tall or not old and vice versa. Everyone who is quiet is either not creative or tall. If susan is both creative and not funny then someone is not curious. Everyone who is not brave is both generous and not curious and vice versa. Everyone who is either not patient or humble is either quiet or funny and vice versa. Everyone who is both not quiet and not humble is both humble and not brave and vice versa. If susan is kind or not creative then lucy is creative and vice versa. If someone is both not humble and not rich then john is not creative or humble. If someone is quiet then fred is both calm and not tall. Everyone who is both not humble and funny is both not generous and not wise and vice versa. Everyone who is either not quiet or strong is either not rich or humble. Everyone who is either kind or not patient is both old and calm. Everyone who is either funny or not happy is either not tall or rich. Everyone who is not kind is not curious or not patient. Everyone who is brave or not creative is either not calm or humble and vice versa. Alice is kind. Lucy is either patient or funny. Fred is either not old or not generous. Someone is patient or strong. Someone is not patient. Someone is either brave or not humble. Lucy is either not brave or funny. | Lucy is not humble. | contradiction | (![X]:(~rich(X)=>(humble(X)&happy(X))))&
(![X]:((brave(X)<~>tall(X))<=>(tall(X)|~old(X))))&
(![X]:(quiet(X)=>(~creative(X)<~>tall(X))))&
(((creative(susan)&~funny(susan)))=>(?[X]:(~curious(X))))&
(![X]:(~brave(X)<=>(generous(X)&~curious(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(quiet(X)<~>funny(X))))&
(![X]:((~quiet(X)&~humble(X))<=>(humble(X)&~brave(X))))&
(((kind(susan)|~creative(susan)))<=>(creative(lucy)))&
((?[X]:((~humble(X)&~rich(X))))=>((~creative(john)|humble(john))))&
((?[X]:(quiet(X)))=>((calm(fred)&~tall(fred))))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)&~wise(X))))&
(![X]:((~quiet(X)<~>strong(X))=>(~rich(X)<~>humble(X))))&
(![X]:((kind(X)<~>~patient(X))=>(old(X)&calm(X))))&
(![X]:((funny(X)<~>~happy(X))=>(~tall(X)<~>rich(X))))&
(![X]:(~kind(X)=>(~curious(X)|~patient(X))))&
(![X]:((brave(X)|~creative(X))<=>(~calm(X)<~>humble(X))))&
(kind(alice))&
((patient(lucy)<~>funny(lucy)))&
((~old(fred)<~>~generous(fred)))&
(?[X]:((patient(X)|strong(X))))&
(?[X]:(~patient(X)))&
(?[X]:((brave(X)<~>~humble(X))))&
((~brave(lucy)<~>funny(lucy))) | ~humble(lucy) | [
"p5",
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6454619987676628428589002
% SZS output start Proof for 6454619987676628428589002
6. ! [X0] : ((~patient(X0) <~> humble(X0)) <=> (quiet(X0) <~> funny(X0))) [input p5]
7. ! [X0] : ((~humble(X0) & ~quiet(X0)) <=> (~brave(X0) & humble(X0))) [input p6]
18. patient(lucy) <~> funny(lucy) [input p17]
24. ~humble(lucy) [input hypothesis]
44. ! [X0] : ((((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) & (((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0))))) [nnf transformation 6]
45. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (brave(X0) | ~humble(X0))) & ((~brave(X0) & humble(X0)) | (humble(X0) | quiet(X0)))) [nnf transformation 7]
46. ! [X0] : (((~humble(X0) & ~quiet(X0)) | brave(X0) | ~humble(X0)) & ((~brave(X0) & humble(X0)) | humble(X0) | quiet(X0))) [flattening 45]
56. (~funny(lucy) | ~patient(lucy)) & (funny(lucy) | patient(lucy)) [nnf transformation 18]
82. ~funny(X0) | ~quiet(X0) | humble(X0) | patient(X0) [cnf transformation 44]
84. ~patient(X0) | humble(X0) | funny(X0) | ~quiet(X0) [cnf transformation 44]
88. humble(X0) | humble(X0) | quiet(X0) [cnf transformation 46]
122. funny(lucy) | patient(lucy) [cnf transformation 56]
123. ~funny(lucy) | ~patient(lucy) [cnf transformation 56]
132. ~humble(lucy) [cnf transformation 24]
133. quiet(X0) | humble(X0) [duplicate literal removal 88]
184. 9 <=> patient(lucy) [avatar definition]
185. patient(lucy) <- (9) [avatar component clause 184]
186. ~patient(lucy) <- (~9) [avatar component clause 184]
188. 10 <=> funny(lucy) [avatar definition]
189. funny(lucy) <- (10) [avatar component clause 188]
190. ~funny(lucy) <- (~10) [avatar component clause 188]
191. ~9 | ~10 [avatar split clause 123,188,184]
192. 9 | 10 [avatar split clause 122,188,184]
244. 18 <=> quiet(lucy) [avatar definition]
245. quiet(lucy) <- (18) [avatar component clause 244]
246. ~quiet(lucy) <- (~18) [avatar component clause 244]
252. humble(lucy) <- (~18) [resolution 246,133]
253. $false <- (~18) [subsumption resolution 252,132]
254. 18 [avatar contradiction clause 253]
409. humble(lucy) | funny(lucy) | ~quiet(lucy) <- (9) [resolution 84,185]
413. funny(lucy) | ~quiet(lucy) <- (9) [subsumption resolution 409,132]
414. ~quiet(lucy) <- (9, ~10) [subsumption resolution 413,190]
415. $false <- (9, ~10, 18) [subsumption resolution 414,245]
416. ~9 | 10 | ~18 [avatar contradiction clause 415]
457. ~quiet(lucy) | humble(lucy) | patient(lucy) <- (10) [resolution 189,82]
460. humble(lucy) | patient(lucy) <- (10, 18) [subsumption resolution 457,245]
461. patient(lucy) <- (10, 18) [subsumption resolution 460,132]
462. $false <- (~9, 10, 18) [subsumption resolution 461,186]
463. 9 | ~10 | ~18 [avatar contradiction clause 462]
464. $false [avatar sat refutation 191,192,254,416,463]
% SZS output end Proof for 6454619987676628428589002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not rich is old.
Everyone who is not wise is both rich and not quiet and vice versa.
Everyone who is both patient and happy is both tall and happy.
Everyone who is generous is not generous or quiet and vice versa.
If someone is either strong or not generous then john is either not happy or quiet and vice versa.
If someone is not patient then someone is either wise or not happy and vice versa.
Everyone who is not generous is either not kind or not happy.
If alice is either brave or wise then someone is either not creative or not happy.
If someone is both old and not generous then paul is either not creative or not humble and vice versa.
If someone is humble or not kind then someone is not curious or not quiet and vice versa.
If john is not funny then someone is either not rich or not funny.
If john is rich then someone is either happy or old.
Everyone who is curious is generous and vice versa.
If mary is patient then someone is creative or curious and vice versa.
If someone is not kind or tall then john is not old and vice versa.
If someone is not rich then alice is calm or generous and vice versa.
Someone is curious or not wise.
Paul is not wise or not happy.
Fred is funny.
Paul is strong or quiet.
John is not wise or tall.
Someone is both not humble and not patient.
Someone is funny or not old. | Alice is not wise. | contradiction | (![X]:((~happy(X)|~rich(X))=>old(X)))&
(![X]:(~wise(X)<=>(rich(X)&~quiet(X))))&
(![X]:((patient(X)&happy(X))=>(tall(X)&happy(X))))&
(![X]:(generous(X)<=>(~generous(X)|quiet(X))))&
((?[X]:((strong(X)<~>~generous(X))))<=>((~happy(john)<~>quiet(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:(~generous(X)=>(~kind(X)<~>~happy(X))))&
(((brave(alice)<~>wise(alice)))=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((old(X)&~generous(X))))<=>((~creative(paul)<~>~humble(paul))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~curious(X)|~quiet(X)))))&
((~funny(john))=>(?[X]:((~rich(X)<~>~funny(X)))))&
((rich(john))=>(?[X]:((happy(X)<~>old(X)))))&
(![X]:(curious(X)<=>generous(X)))&
((patient(mary))<=>(?[X]:((creative(X)|curious(X)))))&
((?[X]:((~kind(X)|tall(X))))<=>(~old(john)))&
((?[X]:(~rich(X)))<=>((calm(alice)|generous(alice))))&
(?[X]:((curious(X)|~wise(X))))&
((~wise(paul)|~happy(paul)))&
(funny(fred))&
((strong(paul)|quiet(paul)))&
((~wise(john)|tall(john)))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((funny(X)|~old(X)))) | ~wise(alice) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7425614720199639613167203
% SZS output start Proof for 7425614720199639613167203
2. ! [X0] : (~wise(X0) <=> (~quiet(X0) & rich(X0))) [input p1]
4. ! [X0] : (generous(X0) <=> (quiet(X0) | ~generous(X0))) [input p3]
24. ~wise(alice) [input hypothesis]
34. ! [X0] : ((~wise(X0) | (quiet(X0) | ~rich(X0))) & ((~quiet(X0) & rich(X0)) | wise(X0))) [nnf transformation 2]
35. ! [X0] : ((~wise(X0) | quiet(X0) | ~rich(X0)) & ((~quiet(X0) & rich(X0)) | wise(X0))) [flattening 34]
36. ! [X0] : ((generous(X0) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | ~generous(X0))) [nnf transformation 4]
37. ! [X0] : ((generous(X0) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | ~generous(X0))) [flattening 36]
89. ~quiet(X0) | wise(X0) [cnf transformation 35]
93. quiet(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 37]
94. generous(X0) | generous(X0) [cnf transformation 37]
147. ~wise(alice) [cnf transformation 24]
148. quiet(X0) | ~generous(X0) [duplicate literal removal 93]
149. generous(X0) [duplicate literal removal 94]
150. quiet(X0) [subsumption resolution 148,149]
194. 10 <=> wise(alice) [avatar definition]
196. ~wise(alice) <- (~10) [avatar component clause 194]
362. ~10 [avatar split clause 147,194]
386. wise(X0) [resolution 89,150]
393. $false <- (~10) [resolution 386,196]
398. 10 [avatar contradiction clause 393]
400. $false [avatar sat refutation 362,398]
% SZS output end Proof for 7425614720199639613167203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and calm is not curious or tall. Everyone who is not old is either not generous or old. Everyone who is curious is brave. Everyone who is not happy or not creative is old or generous and vice versa. Everyone who is both not curious and not creative is quiet or kind. If someone is tall or generous then someone is both not patient and humble and vice versa. Everyone who is both not quiet and not kind is happy. Everyone who is either not brave or not quiet is both old and wise. Everyone who is both not brave and quiet is not old. Everyone who is both not rich and creative is both funny and not curious. Everyone who is either not brave or not generous is funny or rich. Everyone who is both patient and curious is either wise or brave and vice versa. If someone is curious then lucy is both creative and not humble. Everyone who is either generous or calm is not brave or patient. If mary is either funny or wise then someone is both curious and not kind. Everyone who is both not tall and rich is calm or not curious and vice versa. Mary is both not brave and patient. Susan is either not humble or not generous. Someone is either rich or not quiet. Someone is not rich. Mary is not curious or kind. Susan is either funny or not curious. Susan is both curious and not old. | Lucy is tall. | neutral | (![X]:((brave(X)&calm(X))=>(~curious(X)|tall(X))))&
(![X]:(~old(X)=>(~generous(X)<~>old(X))))&
(![X]:(curious(X)=>brave(X)))&
(![X]:((~happy(X)|~creative(X))<=>(old(X)|generous(X))))&
(![X]:((~curious(X)&~creative(X))=>(quiet(X)|kind(X))))&
((?[X]:((tall(X)|generous(X))))<=>(?[X]:((~patient(X)&humble(X)))))&
(![X]:((~quiet(X)&~kind(X))=>happy(X)))&
(![X]:((~brave(X)<~>~quiet(X))=>(old(X)&wise(X))))&
(![X]:((~brave(X)&quiet(X))=>~old(X)))&
(![X]:((~rich(X)&creative(X))=>(funny(X)&~curious(X))))&
(![X]:((~brave(X)<~>~generous(X))=>(funny(X)|rich(X))))&
(![X]:((patient(X)&curious(X))<=>(wise(X)<~>brave(X))))&
((?[X]:(curious(X)))=>((creative(lucy)&~humble(lucy))))&
(![X]:((generous(X)<~>calm(X))=>(~brave(X)|patient(X))))&
(((funny(mary)<~>wise(mary)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((~tall(X)&rich(X))<=>(calm(X)|~curious(X))))&
((~brave(mary)&patient(mary)))&
((~humble(susan)<~>~generous(susan)))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:(~rich(X)))&
((~curious(mary)|kind(mary)))&
((funny(susan)<~>~curious(susan)))&
((curious(susan)&~old(susan))) | tall(lucy) | [] | null | 0 |
If someone is both curious and not kind then someone is not tall and vice versa. Everyone who is calm is wise or not tall. If alice is both happy and old then someone is not humble or happy. If someone is tall then lucy is both wise and not tall and vice versa. If someone is either not tall or happy then someone is humble or not rich and vice versa. Everyone who is both not creative and not tall is not strong or wise and vice versa. If fred is tall or strong then john is both not kind and rich. Everyone who is both not calm and rich is not tall or kind. Everyone who is patient is either strong or funny and vice versa. If alice is not tall or not patient then john is both not kind and not humble and vice versa. Everyone who is both not tall and patient is both strong and happy. If someone is both not funny and not creative then alice is both not rich and humble and vice versa. Everyone who is either patient or creative is either humble or not old. If someone is strong then paul is not kind. Everyone who is not rich is both not calm and happy and vice versa. If someone is either not quiet or not curious then someone is either humble or not patient. Paul is both not wise and not strong. Someone is both kind and not generous. Someone is either calm or not patient. Alice is either not happy or curious. John is both humble and rich. Mary is not funny or not humble. Susan is not tall or not wise. Alice is generous. | Lucy is creative. | contradiction | ((?[X]:((curious(X)&~kind(X))))<=>(?[X]:(~tall(X))))&
(![X]:(calm(X)=>(wise(X)|~tall(X))))&
(((happy(alice)&old(alice)))=>(?[X]:((~humble(X)|happy(X)))))&
((?[X]:(tall(X)))<=>((wise(lucy)&~tall(lucy))))&
((?[X]:((~tall(X)<~>happy(X))))<=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:((~creative(X)&~tall(X))<=>(~strong(X)|wise(X))))&
(((tall(fred)|strong(fred)))=>((~kind(john)&rich(john))))&
(![X]:((~calm(X)&rich(X))=>(~tall(X)|kind(X))))&
(![X]:(patient(X)<=>(strong(X)<~>funny(X))))&
(((~tall(alice)|~patient(alice)))<=>((~kind(john)&~humble(john))))&
(![X]:((~tall(X)&patient(X))=>(strong(X)&happy(X))))&
((?[X]:((~funny(X)&~creative(X))))<=>((~rich(alice)&humble(alice))))&
(![X]:((patient(X)<~>creative(X))=>(humble(X)<~>~old(X))))&
((?[X]:(strong(X)))=>(~kind(paul)))&
(![X]:(~rich(X)<=>(~calm(X)&happy(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))=>(?[X]:((humble(X)<~>~patient(X)))))&
((~wise(paul)&~strong(paul)))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:((calm(X)<~>~patient(X))))&
((~happy(alice)<~>curious(alice)))&
((humble(john)&rich(john)))&
((~funny(mary)|~humble(mary)))&
((~tall(susan)|~wise(susan)))&
(generous(alice)) | creative(lucy) | [
"p3",
"p5",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4953473107815680930999393
% SZS output start Proof for 4953473107815680930999393
4. ? [X0] : tall(X0) <=> (~tall(lucy) & wise(lucy)) [input p3]
6. ! [X0] : ((~tall(X0) & ~creative(X0)) <=> (wise(X0) | ~strong(X0))) [input p5]
10. (~patient(alice) | ~tall(alice)) <=> (~humble(john) & ~kind(john)) [input p9]
21. rich(john) & humble(john) [input p20]
25. creative(lucy) [input hypothesis]
48. (? [X0] : tall(X0) | (tall(lucy) | ~wise(lucy))) & ((~tall(lucy) & wise(lucy)) | ! [X0] : ~tall(X0)) [nnf transformation 4]
49. (? [X0] : tall(X0) | tall(lucy) | ~wise(lucy)) & ((~tall(lucy) & wise(lucy)) | ! [X0] : ~tall(X0)) [flattening 48]
50. (? [X0] : tall(X0) | tall(lucy) | ~wise(lucy)) & ((~tall(lucy) & wise(lucy)) | ! [X1] : ~tall(X1)) [rectify 49]
51. ? [X0] : tall(X0) => tall(sK3) [choice axiom]
52. (tall(sK3) | tall(lucy) | ~wise(lucy)) & ((~tall(lucy) & wise(lucy)) | ! [X1] : ~tall(X1)) [skolemisation 50,51]
58. ! [X0] : (((~tall(X0) & ~creative(X0)) | (~wise(X0) & strong(X0))) & ((wise(X0) | ~strong(X0)) | (tall(X0) | creative(X0)))) [nnf transformation 6]
59. ! [X0] : (((~tall(X0) & ~creative(X0)) | (~wise(X0) & strong(X0))) & (wise(X0) | ~strong(X0) | tall(X0) | creative(X0))) [flattening 58]
61. ((~patient(alice) | ~tall(alice)) | (humble(john) | kind(john))) & ((~humble(john) & ~kind(john)) | (patient(alice) & tall(alice))) [nnf transformation 10]
62. (~patient(alice) | ~tall(alice) | humble(john) | kind(john)) & ((~humble(john) & ~kind(john)) | (patient(alice) & tall(alice))) [flattening 61]
86. wise(lucy) | ~tall(X1) [cnf transformation 52]
97. ~creative(X0) | ~wise(X0) [cnf transformation 59]
111. ~humble(john) | tall(alice) [cnf transformation 62]
140. humble(john) [cnf transformation 21]
145. creative(lucy) [cnf transformation 25]
185. 10 <=> wise(lucy) [avatar definition]
198. 13 <=> ! [X1] : ~tall(X1) [avatar definition]
199. ~tall(X1) <- (13) [avatar component clause 198]
201. 13 | 10 [avatar split clause 86,185,198]
257. 26 <=> humble(john) [avatar definition]
261. 27 <=> tall(alice) [avatar definition]
262. tall(alice) <- (27) [avatar component clause 261]
270. 27 | ~26 [avatar split clause 111,257,261]
340. 26 [avatar split clause 140,257]
351. ~wise(lucy) [resolution 97,145]
354. ~10 [avatar split clause 351,185]
356. $false <- (13, 27) [resolution 199,262]
357. ~13 | ~27 [avatar contradiction clause 356]
359. $false [avatar sat refutation 201,270,340,354,357]
% SZS output end Proof for 4953473107815680930999393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then mary is wise. Everyone who is both kind and old is not wise or not old and vice versa. Everyone who is not patient is either not rich or wise. If someone is either not calm or not tall then fred is either strong or creative and vice versa. Everyone who is both not brave and not rich is creative. Everyone who is humble is both old and brave and vice versa. If someone is either not old or not quiet then someone is happy and vice versa. If someone is humble then someone is happy or not brave. Everyone who is quiet is not funny or patient and vice versa. Everyone who is not quiet or not patient is either curious or not brave and vice versa. If someone is not funny or not wise then someone is brave or not patient. If alice is not patient or tall then someone is either not rich or calm. If someone is not brave then someone is both not generous and not humble. Everyone who is not patient is either not patient or not curious and vice versa. Everyone who is both quiet and not strong is either not humble or humble. Everyone who is not brave is patient. Someone is either not happy or brave. Fred is both not kind and not quiet. Fred is funny. Lucy is both not calm and curious. Someone is either not old or not happy. Mary is both not funny and not creative. | Lucy is curious. | entailment | ((?[X]:(creative(X)))=>(wise(mary)))&
(![X]:((kind(X)&old(X))<=>(~wise(X)|~old(X))))&
(![X]:(~patient(X)=>(~rich(X)<~>wise(X))))&
((?[X]:((~calm(X)<~>~tall(X))))<=>((strong(fred)<~>creative(fred))))&
(![X]:((~brave(X)&~rich(X))=>creative(X)))&
(![X]:(humble(X)<=>(old(X)&brave(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:(happy(X))))&
((?[X]:(humble(X)))=>(?[X]:((happy(X)|~brave(X)))))&
(![X]:(quiet(X)<=>(~funny(X)|patient(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(curious(X)<~>~brave(X))))&
((?[X]:((~funny(X)|~wise(X))))=>(?[X]:((brave(X)|~patient(X)))))&
(((~patient(alice)|tall(alice)))=>(?[X]:((~rich(X)<~>calm(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:(~patient(X)<=>(~patient(X)<~>~curious(X))))&
(![X]:((quiet(X)&~strong(X))=>(~humble(X)<~>humble(X))))&
(![X]:(~brave(X)=>patient(X)))&
(?[X]:((~happy(X)<~>brave(X))))&
((~kind(fred)&~quiet(fred)))&
(funny(fred))&
((~calm(lucy)&curious(lucy)))&
(?[X]:((~old(X)<~>~happy(X))))&
((~funny(mary)&~creative(mary))) | curious(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5685951532072560790195003
% SZS output start Proof for 5685951532072560790195003
14. ! [X0] : (~patient(X0) <=> (~patient(X0) <~> ~curious(X0))) [input p13]
23. ~curious(lucy) [input hypothesis]
70. ! [X0] : ((~patient(X0) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | patient(X0))) [nnf transformation 14]
120. curious(X0) | patient(X0) | patient(X0) [cnf transformation 70]
122. ~patient(X0) | ~patient(X0) | curious(X0) [cnf transformation 70]
137. ~curious(lucy) [cnf transformation 23]
138. curious(X0) | patient(X0) [duplicate literal removal 120]
139. ~patient(X0) | curious(X0) [duplicate literal removal 122]
258. curious(X0) [subsumption resolution 138,139]
270. $false [subsumption resolution 137,258]
% SZS output end Proof for 5685951532072560790195003
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or kind then alice is both not patient and not strong and vice versa. Everyone who is both not quiet and not curious is kind or curious and vice versa. If someone is old then fred is not humble and vice versa. Everyone who is tall is generous and vice versa. If someone is both curious and funny then someone is either curious or not humble and vice versa. If paul is both not wise and not kind then someone is not rich or not calm and vice versa. Everyone who is either not humble or not old is not generous. If alice is old or not calm then susan is both curious and not tall. Everyone who is old is strong or brave. Everyone who is not old is both patient and rich and vice versa. Everyone who is both not humble and not tall is wise or not tall. If alice is not happy then paul is both funny and calm. If mary is either not rich or patient then someone is both not happy and calm and vice versa. If lucy is not humble then alice is generous or not quiet. If someone is not calm or not quiet then someone is not brave or not strong. Everyone who is both not happy and strong is either happy or not quiet. Mary is quiet. Fred is either not patient or not funny. Someone is both happy and not kind. Paul is both not wise and brave. Someone is calm or not old. | Susan is not rich. | contradiction | ((?[X]:((tall(X)|kind(X))))<=>((~patient(alice)&~strong(alice))))&
(![X]:((~quiet(X)&~curious(X))<=>(kind(X)|curious(X))))&
((?[X]:(old(X)))<=>(~humble(fred)))&
(![X]:(tall(X)<=>generous(X)))&
((?[X]:((curious(X)&funny(X))))<=>(?[X]:((curious(X)<~>~humble(X)))))&
(((~wise(paul)&~kind(paul)))<=>(?[X]:((~rich(X)|~calm(X)))))&
(![X]:((~humble(X)<~>~old(X))=>~generous(X)))&
(((old(alice)|~calm(alice)))=>((curious(susan)&~tall(susan))))&
(![X]:(old(X)=>(strong(X)|brave(X))))&
(![X]:(~old(X)<=>(patient(X)&rich(X))))&
(![X]:((~humble(X)&~tall(X))=>(wise(X)|~tall(X))))&
((~happy(alice))=>((funny(paul)&calm(paul))))&
(((~rich(mary)<~>patient(mary)))<=>(?[X]:((~happy(X)&calm(X)))))&
((~humble(lucy))=>((generous(alice)|~quiet(alice))))&
((?[X]:((~calm(X)|~quiet(X))))=>(?[X]:((~brave(X)|~strong(X)))))&
(![X]:((~happy(X)&strong(X))=>(happy(X)<~>~quiet(X))))&
(quiet(mary))&
((~patient(fred)<~>~funny(fred)))&
(?[X]:((happy(X)&~kind(X))))&
((~wise(paul)&brave(paul)))&
(?[X]:((calm(X)|~old(X)))) | ~rich(susan) | [
"p1",
"p2",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3430659383785531487248639
% SZS output start Proof for 3430659383785531487248639
2. ! [X0] : ((~curious(X0) & ~quiet(X0)) <=> (curious(X0) | kind(X0))) [input p1]
3. ? [X0] : old(X0) <=> ~humble(fred) [input p2]
5. ? [X0] : (funny(X0) & curious(X0)) <=> ? [X0] : (curious(X0) <~> ~humble(X0)) [input p4]
10. ! [X0] : (~old(X0) <=> (rich(X0) & patient(X0))) [input p9]
22. ~rich(susan) [input hypothesis]
23. ? [X0] : (funny(X0) & curious(X0)) <=> ? [X1] : (curious(X1) <~> ~humble(X1)) [rectify 5]
42. ! [X0] : (((~curious(X0) & ~quiet(X0)) | (~curious(X0) & ~kind(X0))) & ((curious(X0) | kind(X0)) | (curious(X0) | quiet(X0)))) [nnf transformation 2]
43. ! [X0] : (((~curious(X0) & ~quiet(X0)) | (~curious(X0) & ~kind(X0))) & (curious(X0) | kind(X0) | curious(X0) | quiet(X0))) [flattening 42]
44. (? [X0] : old(X0) | humble(fred)) & (~humble(fred) | ! [X0] : ~old(X0)) [nnf transformation 3]
45. (? [X0] : old(X0) | humble(fred)) & (~humble(fred) | ! [X1] : ~old(X1)) [rectify 44]
46. ? [X0] : old(X0) => old(sK1) [choice axiom]
47. (old(sK1) | humble(fred)) & (~humble(fred) | ! [X1] : ~old(X1)) [skolemisation 45,46]
49. (? [X0] : (funny(X0) & curious(X0)) | ! [X1] : ((curious(X1) | humble(X1)) & (~humble(X1) | ~curious(X1)))) & (? [X1] : ((humble(X1) | ~curious(X1)) & (~humble(X1) | curious(X1))) | ! [X0] : (~funny(X0) | ~curious(X0))) [nnf transformation 23]
50. (? [X0] : (funny(X0) & curious(X0)) | ! [X1] : ((curious(X1) | humble(X1)) & (~humble(X1) | ~curious(X1)))) & (? [X2] : ((humble(X2) | ~curious(X2)) & (~humble(X2) | curious(X2))) | ! [X3] : (~funny(X3) | ~curious(X3))) [rectify 49]
51. ? [X0] : (funny(X0) & curious(X0)) => (funny(sK2) & curious(sK2)) [choice axiom]
52. ? [X2] : ((humble(X2) | ~curious(X2)) & (~humble(X2) | curious(X2))) => ((humble(sK3) | ~curious(sK3)) & (~humble(sK3) | curious(sK3))) [choice axiom]
53. ((funny(sK2) & curious(sK2)) | ! [X1] : ((curious(X1) | humble(X1)) & (~humble(X1) | ~curious(X1)))) & (((humble(sK3) | ~curious(sK3)) & (~humble(sK3) | curious(sK3))) | ! [X3] : (~funny(X3) | ~curious(X3))) [skolemisation 50,52,51]
60. ! [X0] : ((~old(X0) | (~rich(X0) | ~patient(X0))) & ((rich(X0) & patient(X0)) | old(X0))) [nnf transformation 10]
61. ! [X0] : ((~old(X0) | ~rich(X0) | ~patient(X0)) & ((rich(X0) & patient(X0)) | old(X0))) [flattening 60]
84. ~curious(X0) | ~curious(X0) [cnf transformation 43]
85. ~humble(fred) | ~old(X1) [cnf transformation 47]
92. curious(sK2) | curious(X1) | humble(X1) [cnf transformation 53]
108. rich(X0) | old(X0) [cnf transformation 61]
132. ~rich(susan) [cnf transformation 22]
135. ~curious(X0) [duplicate literal removal 84]
165. 7 <=> humble(fred) [avatar definition]
166. ~humble(fred) <- (~7) [avatar component clause 165]
174. 9 <=> ! [X1] : ~old(X1) [avatar definition]
175. ~old(X1) <- (9) [avatar component clause 174]
176. 9 | ~7 [avatar split clause 85,165,174]
179. 10 <=> ! [X1] : humble(X1) [avatar definition]
180. humble(X1) <- (10) [avatar component clause 179]
186. curious(X1) | humble(X1) [subsumption resolution 92,135]
187. humble(X1) [subsumption resolution 186,135]
188. 10 [avatar split clause 187,179]
319. $false <- (~7, 10) [subsumption resolution 166,180]
320. 7 | ~10 [avatar contradiction clause 319]
329. old(susan) [resolution 108,132]
331. $false <- (9) [subsumption resolution 329,175]
332. ~9 [avatar contradiction clause 331]
335. $false [avatar sat refutation 176,188,320,332]
% SZS output end Proof for 3430659383785531487248639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and happy is strong. If someone is both not patient and rich then lucy is funny or not brave and vice versa. If john is quiet then susan is both not brave and not tall. Everyone who is quiet or not patient is both not rich and quiet and vice versa. Everyone who is both quiet and happy is not kind and vice versa. Everyone who is both happy and kind is kind or not tall and vice versa. Everyone who is patient or not old is rich and vice versa. Everyone who is not creative is not calm or brave. If someone is either happy or not funny then someone is both brave and not brave and vice versa. Everyone who is not kind is not patient. If john is either generous or old then someone is not funny. Everyone who is both not curious and curious is both wise and funny. Everyone who is both calm and happy is both not curious and not humble and vice versa. Everyone who is not humble is both not funny and quiet. Everyone who is both brave and not generous is either not tall or quiet and vice versa. Everyone who is old is either not quiet or not patient and vice versa. Lucy is both strong and generous. John is not quiet or old. Susan is both humble and rich. Paul is creative or not strong. Alice is strong or not quiet. Mary is either not calm or curious. | Susan is kind. | entailment | (![X]:((~happy(X)&happy(X))=>strong(X)))&
((?[X]:((~patient(X)&rich(X))))<=>((funny(lucy)|~brave(lucy))))&
((quiet(john))=>((~brave(susan)&~tall(susan))))&
(![X]:((quiet(X)|~patient(X))<=>(~rich(X)&quiet(X))))&
(![X]:((quiet(X)&happy(X))<=>~kind(X)))&
(![X]:((happy(X)&kind(X))<=>(kind(X)|~tall(X))))&
(![X]:((patient(X)|~old(X))<=>rich(X)))&
(![X]:(~creative(X)=>(~calm(X)|brave(X))))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:(~kind(X)=>~patient(X)))&
(((generous(john)<~>old(john)))=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)&curious(X))=>(wise(X)&funny(X))))&
(![X]:((calm(X)&happy(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~humble(X)=>(~funny(X)&quiet(X))))&
(![X]:((brave(X)&~generous(X))<=>(~tall(X)<~>quiet(X))))&
(![X]:(old(X)<=>(~quiet(X)<~>~patient(X))))&
((strong(lucy)&generous(lucy)))&
((~quiet(john)|old(john)))&
((humble(susan)&rich(susan)))&
((creative(paul)|~strong(paul)))&
((strong(alice)|~quiet(alice)))&
((~calm(mary)<~>curious(mary))) | kind(susan) | [
"p3",
"p4",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 394486846001163193561413
% SZS output start Proof for 394486846001163193561413
4. ! [X0] : ((~patient(X0) | quiet(X0)) <=> (quiet(X0) & ~rich(X0))) [input p3]
5. ! [X0] : ((happy(X0) & quiet(X0)) <=> ~kind(X0)) [input p4]
19. rich(susan) & humble(susan) [input p18]
23. ~kind(susan) [input hypothesis]
42. ! [X0] : (((~patient(X0) | quiet(X0)) | (~quiet(X0) | rich(X0))) & ((quiet(X0) & ~rich(X0)) | (patient(X0) & ~quiet(X0)))) [nnf transformation 4]
43. ! [X0] : ((~patient(X0) | quiet(X0) | ~quiet(X0) | rich(X0)) & ((quiet(X0) & ~rich(X0)) | (patient(X0) & ~quiet(X0)))) [flattening 42]
44. ! [X0] : (((happy(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) | ~quiet(X0)))) [nnf transformation 5]
45. ! [X0] : (((happy(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | ~happy(X0) | ~quiet(X0))) [flattening 44]
71. ~quiet(X0) | ~rich(X0) [cnf transformation 43]
77. kind(X0) | quiet(X0) [cnf transformation 45]
116. rich(susan) [cnf transformation 19]
119. ~kind(susan) [cnf transformation 23]
195. quiet(susan) [resolution 77,119]
197. ~rich(susan) [resolution 195,71]
198. $false [subsumption resolution 197,116]
% SZS output end Proof for 394486846001163193561413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not happy or tall then someone is both not funny and not wise and vice versa.
Everyone who is not strong is kind.
Everyone who is not strong or brave is not humble.
If susan is not wise then susan is not tall or not calm and vice versa.
Everyone who is not strong or creative is creative and vice versa.
If susan is both old and not strong then someone is not brave or strong.
Everyone who is quiet is either not generous or not humble.
If someone is either generous or not rich then alice is both not kind and quiet and vice versa.
If someone is not funny then someone is both patient and brave and vice versa.
Everyone who is either not brave or old is either happy or creative.
Everyone who is either old or humble is generous.
Everyone who is wise is both rich and not calm and vice versa.
Everyone who is strong is brave and vice versa.
If someone is rich then someone is either not brave or not old and vice versa.
If paul is not patient or strong then alice is not brave or curious and vice versa.
Everyone who is both not curious and curious is generous or not strong and vice versa.
Someone is either kind or funny.
Someone is either curious or brave.
Mary is curious.
Lucy is generous or brave.
Mary is either strong or quiet. | Mary is old. | contradiction | (((~happy(alice)<~>tall(alice)))<=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:(~strong(X)=>kind(X)))&
(![X]:((~strong(X)|brave(X))=>~humble(X)))&
((~wise(susan))<=>((~tall(susan)|~calm(susan))))&
(![X]:((~strong(X)|creative(X))<=>creative(X)))&
(((old(susan)&~strong(susan)))=>(?[X]:((~brave(X)|strong(X)))))&
(![X]:(quiet(X)=>(~generous(X)<~>~humble(X))))&
((?[X]:((generous(X)<~>~rich(X))))<=>((~kind(alice)&quiet(alice))))&
((?[X]:(~funny(X)))<=>(?[X]:((patient(X)&brave(X)))))&
(![X]:((~brave(X)<~>old(X))=>(happy(X)<~>creative(X))))&
(![X]:((old(X)<~>humble(X))=>generous(X)))&
(![X]:(wise(X)<=>(rich(X)&~calm(X))))&
(![X]:(strong(X)<=>brave(X)))&
((?[X]:(rich(X)))<=>(?[X]:((~brave(X)<~>~old(X)))))&
(((~patient(paul)|strong(paul)))<=>((~brave(alice)|curious(alice))))&
(![X]:((~curious(X)&curious(X))<=>(generous(X)|~strong(X))))&
(?[X]:((kind(X)<~>funny(X))))&
(?[X]:((curious(X)<~>brave(X))))&
(curious(mary))&
((generous(lucy)|brave(lucy)))&
((strong(mary)<~>quiet(mary))) | old(mary) | [
"p2",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7384257301955459406488891
% SZS output start Proof for 7384257301955459406488891
3. ! [X0] : ((brave(X0) | ~strong(X0)) => ~humble(X0)) [input p2]
11. ! [X0] : ((old(X0) <~> humble(X0)) => generous(X0)) [input p10]
13. ! [X0] : (strong(X0) <=> brave(X0)) [input p12]
16. ! [X0] : ((curious(X0) & ~curious(X0)) <=> (~strong(X0) | generous(X0))) [input p15]
22. old(mary) [input hypothesis]
26. ! [X0] : (~humble(X0) | (~brave(X0) & strong(X0))) [ennf transformation 3]
31. ! [X0] : (generous(X0) | (old(X0) <=> humble(X0))) [ennf transformation 11]
54. ! [X0] : (generous(X0) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) [nnf transformation 31]
57. ! [X0] : ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0))) [nnf transformation 13]
65. ! [X0] : (((curious(X0) & ~curious(X0)) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | (~curious(X0) | curious(X0)))) [nnf transformation 16]
66. ! [X0] : (((curious(X0) & ~curious(X0)) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ~curious(X0) | curious(X0))) [flattening 65]
82. ~humble(X0) | ~brave(X0) [cnf transformation 26]
105. ~old(X0) | humble(X0) | generous(X0) [cnf transformation 54]
110. ~strong(X0) | brave(X0) [cnf transformation 57]
121. ~curious(X0) | ~generous(X0) [cnf transformation 66]
122. ~curious(X0) | strong(X0) [cnf transformation 66]
123. ~generous(X0) | curious(X0) [cnf transformation 66]
124. curious(X0) | strong(X0) [cnf transformation 66]
133. old(mary) [cnf transformation 22]
285. strong(X0) [subsumption resolution 122,124]
286. ~generous(X0) [subsumption resolution 121,123]
316. brave(X0) [resolution 110,285]
346. humble(mary) | generous(mary) [resolution 105,133]
347. humble(mary) [subsumption resolution 346,286]
349. ~brave(mary) [resolution 347,82]
351. $false [subsumption resolution 349,316]
% SZS output end Proof for 7384257301955459406488891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or not funny then paul is patient or not wise. Everyone who is both not rich and curious is humble or quiet and vice versa. If fred is not patient or old then someone is old and vice versa. Everyone who is not quiet is either not curious or not patient and vice versa. If someone is both old and not curious then someone is not old and vice versa. Everyone who is not strong is wise or not patient and vice versa. Everyone who is both kind and not strong is not generous and vice versa. Everyone who is not kind or kind is both kind and strong and vice versa. Everyone who is both not rich and kind is funny or creative. If someone is curious or calm then alice is either kind or brave. Everyone who is both not brave and not strong is not quiet and vice versa. If someone is creative then lucy is either calm or quiet and vice versa. Everyone who is not quiet is humble or not curious and vice versa. If someone is happy or not happy then mary is creative. If lucy is not strong then fred is both humble and quiet and vice versa. If someone is either brave or not tall then someone is either not creative or not humble and vice versa. Someone is not patient or old. Fred is creative or not creative. Someone is funny or not happy. Susan is not tall or not creative. Someone is not rich or generous. Someone is either not brave or not curious. John is patient. | Fred is not old. | contradiction | ((?[X]:((~rich(X)<~>~funny(X))))=>((patient(paul)|~wise(paul))))&
(![X]:((~rich(X)&curious(X))<=>(humble(X)|quiet(X))))&
(((~patient(fred)|old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~quiet(X)<=>(~curious(X)<~>~patient(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:(~old(X))))&
(![X]:(~strong(X)<=>(wise(X)|~patient(X))))&
(![X]:((kind(X)&~strong(X))<=>~generous(X)))&
(![X]:((~kind(X)|kind(X))<=>(kind(X)&strong(X))))&
(![X]:((~rich(X)&kind(X))=>(funny(X)|creative(X))))&
((?[X]:((curious(X)|calm(X))))=>((kind(alice)<~>brave(alice))))&
(![X]:((~brave(X)&~strong(X))<=>~quiet(X)))&
((?[X]:(creative(X)))<=>((calm(lucy)<~>quiet(lucy))))&
(![X]:(~quiet(X)<=>(humble(X)|~curious(X))))&
((?[X]:((happy(X)|~happy(X))))=>(creative(mary)))&
((~strong(lucy))<=>((humble(fred)&quiet(fred))))&
((?[X]:((brave(X)<~>~tall(X))))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(?[X]:((~patient(X)|old(X))))&
((creative(fred)|~creative(fred)))&
(?[X]:((funny(X)|~happy(X))))&
((~tall(susan)|~creative(susan)))&
(?[X]:((~rich(X)|generous(X))))&
(?[X]:((~brave(X)<~>~curious(X))))&
(patient(john)) | ~old(fred) | [
"p1",
"p4",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5362289087776496775830938
% SZS output start Proof for 5362289087776496775830938
2. ! [X0] : ((curious(X0) & ~rich(X0)) <=> (quiet(X0) | humble(X0))) [input p1]
5. ? [X0] : (~curious(X0) & old(X0)) <=> ? [X0] : ~old(X0) [input p4]
8. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (strong(X0) & kind(X0))) [input p7]
11. ! [X0] : ((~strong(X0) & ~brave(X0)) <=> ~quiet(X0)) [input p10]
24. ~old(fred) [input hypothesis]
25. ? [X0] : (~curious(X0) & old(X0)) <=> ? [X1] : ~old(X1) [rectify 5]
37. ! [X0] : (((curious(X0) & ~rich(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (~curious(X0) | rich(X0)))) [nnf transformation 2]
38. ! [X0] : (((curious(X0) & ~rich(X0)) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | ~curious(X0) | rich(X0))) [flattening 37]
45. (? [X0] : (~curious(X0) & old(X0)) | ! [X1] : old(X1)) & (? [X1] : ~old(X1) | ! [X0] : (curious(X0) | ~old(X0))) [nnf transformation 25]
46. (? [X0] : (~curious(X0) & old(X0)) | ! [X1] : old(X1)) & (? [X2] : ~old(X2) | ! [X3] : (curious(X3) | ~old(X3))) [rectify 45]
47. ? [X0] : (~curious(X0) & old(X0)) => (~curious(sK1) & old(sK1)) [choice axiom]
48. ? [X2] : ~old(X2) => ~old(sK2) [choice axiom]
49. ((~curious(sK1) & old(sK1)) | ! [X1] : old(X1)) & (~old(sK2) | ! [X3] : (curious(X3) | ~old(X3))) [skolemisation 46,48,47]
52. ! [X0] : (((kind(X0) | ~kind(X0)) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 8]
53. ! [X0] : ((kind(X0) | ~kind(X0) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [flattening 52]
55. ! [X0] : (((~strong(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | (strong(X0) | brave(X0)))) [nnf transformation 11]
56. ! [X0] : (((~strong(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | strong(X0) | brave(X0))) [flattening 55]
85. ~quiet(X0) | curious(X0) [cnf transformation 38]
95. ~curious(sK1) | old(X1) [cnf transformation 49]
102. strong(X0) | kind(X0) [cnf transformation 53]
103. strong(X0) | ~kind(X0) [cnf transformation 53]
112. ~strong(X0) | quiet(X0) [cnf transformation 56]
141. ~old(fred) [cnf transformation 24]
168. 7 <=> old(fred) [avatar definition]
169. ~old(fred) <- (~7) [avatar component clause 168]
181. 9 <=> ! [X1] : old(X1) [avatar definition]
182. old(X1) <- (9) [avatar component clause 181]
184. 10 <=> curious(sK1) [avatar definition]
186. ~curious(sK1) <- (~10) [avatar component clause 184]
187. 9 | ~10 [avatar split clause 95,184,181]
201. strong(X0) [subsumption resolution 102,103]
217. quiet(X0) [subsumption resolution 112,201]
318. ~7 [avatar split clause 141,168]
319. $false <- (~7, 9) [subsumption resolution 169,182]
320. 7 | ~9 [avatar contradiction clause 319]
326. curious(X0) [resolution 85,217]
327. $false <- (~10) [resolution 326,186]
330. 10 [avatar contradiction clause 327]
331. $false [avatar sat refutation 187,318,320,330]
% SZS output end Proof for 5362289087776496775830938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or tall is brave and vice versa.
Everyone who is not strong is not funny or happy.
Everyone who is either tall or not quiet is not happy or not tall.
If someone is not happy or tall then someone is not generous.
If paul is wise then someone is both not curious and generous and vice versa.
If someone is either not patient or not humble then someone is patient and vice versa.
If paul is not funny then alice is not brave.
If someone is curious then someone is calm or curious and vice versa.
Everyone who is not tall or not rich is not funny.
If susan is not calm then someone is either not tall or humble and vice versa.
Everyone who is either happy or old is funny.
Everyone who is both not humble and not strong is humble and vice versa.
Everyone who is either wise or not generous is either funny or tall.
If someone is both not wise and not rich then paul is both tall and rich.
If paul is not quiet or kind then someone is happy or curious and vice versa.
Everyone who is not patient or not wise is not curious or curious.
Someone is patient or brave.
Someone is either not strong or rich.
Alice is both creative and strong.
Susan is not tall or funny.
Susan is kind.
Paul is either brave or rich.
Mary is both not humble and not generous.
Someone is both not funny and kind. | Paul is not old. | neutral | (![X]:((kind(X)|tall(X))<=>brave(X)))&
(![X]:(~strong(X)=>(~funny(X)|happy(X))))&
(![X]:((tall(X)<~>~quiet(X))=>(~happy(X)|~tall(X))))&
((?[X]:((~happy(X)|tall(X))))=>(?[X]:(~generous(X))))&
((wise(paul))<=>(?[X]:((~curious(X)&generous(X)))))&
((?[X]:((~patient(X)<~>~humble(X))))<=>(?[X]:(patient(X))))&
((~funny(paul))=>(~brave(alice)))&
((?[X]:(curious(X)))<=>(?[X]:((calm(X)|curious(X)))))&
(![X]:((~tall(X)|~rich(X))=>~funny(X)))&
((~calm(susan))<=>(?[X]:((~tall(X)<~>humble(X)))))&
(![X]:((happy(X)<~>old(X))=>funny(X)))&
(![X]:((~humble(X)&~strong(X))<=>humble(X)))&
(![X]:((wise(X)<~>~generous(X))=>(funny(X)<~>tall(X))))&
((?[X]:((~wise(X)&~rich(X))))=>((tall(paul)&rich(paul))))&
(((~quiet(paul)|kind(paul)))<=>(?[X]:((happy(X)|curious(X)))))&
(![X]:((~patient(X)|~wise(X))=>(~curious(X)|curious(X))))&
(?[X]:((patient(X)|brave(X))))&
(?[X]:((~strong(X)<~>rich(X))))&
((creative(alice)&strong(alice)))&
((~tall(susan)|funny(susan)))&
(kind(susan))&
((brave(paul)<~>rich(paul)))&
((~humble(mary)&~generous(mary)))&
(?[X]:((~funny(X)&kind(X)))) | ~old(paul) | [] | null | 0 |
Everyone who is rich or not brave is either not strong or calm.
If susan is either brave or not funny then someone is both not generous and generous and vice versa.
If someone is either not curious or funny then paul is both strong and not creative and vice versa.
Everyone who is both curious and kind is either kind or tall.
If mary is both patient and not old then john is tall or happy.
Everyone who is either quiet or not rich is funny.
Everyone who is both quiet and not brave is not humble and vice versa.
Everyone who is either old or not tall is both not kind and not brave and vice versa.
Everyone who is either not rich or quiet is both funny and not generous.
If someone is not brave then paul is both patient and funny and vice versa.
If someone is humble then someone is either calm or not kind and vice versa.
Everyone who is not happy or not old is either not old or kind.
If someone is wise or humble then someone is both not strong and patient and vice versa.
If alice is both not funny and calm then fred is both not humble and not creative.
Everyone who is not tall is curious and vice versa.
Everyone who is not generous is not brave.
Lucy is either calm or kind.
Someone is generous or not quiet.
Lucy is rich.
John is not curious or not old.
Fred is either not rich or old.
Someone is both not patient and curious.
Lucy is both not curious and not brave.
Someone is both happy and not wise. | Lucy is not brave. | entailment | (![X]:((rich(X)|~brave(X))=>(~strong(X)<~>calm(X))))&
(((brave(susan)<~>~funny(susan)))<=>(?[X]:((~generous(X)&generous(X)))))&
((?[X]:((~curious(X)<~>funny(X))))<=>((strong(paul)&~creative(paul))))&
(![X]:((curious(X)&kind(X))=>(kind(X)<~>tall(X))))&
(((patient(mary)&~old(mary)))=>((tall(john)|happy(john))))&
(![X]:((quiet(X)<~>~rich(X))=>funny(X)))&
(![X]:((quiet(X)&~brave(X))<=>~humble(X)))&
(![X]:((old(X)<~>~tall(X))<=>(~kind(X)&~brave(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(funny(X)&~generous(X))))&
((?[X]:(~brave(X)))<=>((patient(paul)&funny(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((calm(X)<~>~kind(X)))))&
(![X]:((~happy(X)|~old(X))=>(~old(X)<~>kind(X))))&
((?[X]:((wise(X)|humble(X))))<=>(?[X]:((~strong(X)&patient(X)))))&
(((~funny(alice)&calm(alice)))=>((~humble(fred)&~creative(fred))))&
(![X]:(~tall(X)<=>curious(X)))&
(![X]:(~generous(X)=>~brave(X)))&
((calm(lucy)<~>kind(lucy)))&
(?[X]:((generous(X)|~quiet(X))))&
(rich(lucy))&
((~curious(john)|~old(john)))&
((~rich(fred)<~>old(fred)))&
(?[X]:((~patient(X)&curious(X))))&
((~curious(lucy)&~brave(lucy)))&
(?[X]:((happy(X)&~wise(X)))) | ~brave(lucy) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 288332878787652642329448
% SZS output start Proof for 288332878787652642329448
23. ~brave(lucy) & ~curious(lucy) [input p22]
25. brave(lucy) [input hypothesis]
144. ~brave(lucy) [cnf transformation 23]
146. brave(lucy) [cnf transformation 25]
319. $false [subsumption resolution 146,144]
% SZS output end Proof for 288332878787652642329448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or not funny then someone is generous or not creative.
Everyone who is both generous and not generous is either not curious or tall and vice versa.
If mary is both not patient and not creative then someone is either quiet or happy and vice versa.
Everyone who is brave or kind is brave or funny and vice versa.
If lucy is brave or creative then lucy is not curious.
If alice is tall then john is strong.
Everyone who is both generous and calm is either not patient or not funny and vice versa.
If someone is either creative or kind then john is quiet and vice versa.
Everyone who is either not funny or generous is not old and vice versa.
Everyone who is either brave or happy is generous.
Everyone who is both old and quiet is not humble or not wise.
Everyone who is either not patient or patient is both generous and not happy.
Everyone who is old is either not happy or patient and vice versa.
Everyone who is creative or not creative is not wise.
If paul is both not quiet and old then mary is humble or not tall and vice versa.
Everyone who is both not tall and not kind is both humble and not brave.
John is both not humble and strong.
Someone is either not calm or not kind.
Someone is either not wise or funny.
John is both creative and not tall.
Someone is quiet.
Susan is either not brave or creative.
Someone is either not happy or rich. | John is not calm. | entailment | ((?[X]:((patient(X)<~>~funny(X))))=>(?[X]:((generous(X)|~creative(X)))))&
(![X]:((generous(X)&~generous(X))<=>(~curious(X)<~>tall(X))))&
(((~patient(mary)&~creative(mary)))<=>(?[X]:((quiet(X)<~>happy(X)))))&
(![X]:((brave(X)|kind(X))<=>(brave(X)|funny(X))))&
(((brave(lucy)|creative(lucy)))=>(~curious(lucy)))&
((tall(alice))=>(strong(john)))&
(![X]:((generous(X)&calm(X))<=>(~patient(X)<~>~funny(X))))&
((?[X]:((creative(X)<~>kind(X))))<=>(quiet(john)))&
(![X]:((~funny(X)<~>generous(X))<=>~old(X)))&
(![X]:((brave(X)<~>happy(X))=>generous(X)))&
(![X]:((old(X)&quiet(X))=>(~humble(X)|~wise(X))))&
(![X]:((~patient(X)<~>patient(X))=>(generous(X)&~happy(X))))&
(![X]:(old(X)<=>(~happy(X)<~>patient(X))))&
(![X]:((creative(X)|~creative(X))=>~wise(X)))&
(((~quiet(paul)&old(paul)))<=>((humble(mary)|~tall(mary))))&
(![X]:((~tall(X)&~kind(X))=>(humble(X)&~brave(X))))&
((~humble(john)&strong(john)))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:((~wise(X)<~>funny(X))))&
((creative(john)&~tall(john)))&
(?[X]:(quiet(X)))&
((~brave(susan)<~>creative(susan)))&
(?[X]:((~happy(X)<~>rich(X)))) | ~calm(john) | [
"p6",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 685669077355112760040014
% SZS output start Proof for 685669077355112760040014
7. ! [X0] : ((calm(X0) & generous(X0)) <=> (~patient(X0) <~> ~funny(X0))) [input p6]
9. ! [X0] : ((~funny(X0) <~> generous(X0)) <=> ~old(X0)) [input p8]
12. ! [X0] : ((~patient(X0) <~> patient(X0)) => (~happy(X0) & generous(X0))) [input p11]
13. ! [X0] : (old(X0) <=> (~happy(X0) <~> patient(X0))) [input p12]
24. calm(john) [input hypothesis]
33. ! [X0] : ((~happy(X0) & generous(X0)) | (~patient(X0) <=> patient(X0))) [ennf transformation 12]
50. ! [X0] : (((calm(X0) & generous(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 7]
51. ! [X0] : (((calm(X0) & generous(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ~calm(X0) | ~generous(X0))) [flattening 50]
56. ! [X0] : ((((~generous(X0) | funny(X0)) & (generous(X0) | ~funny(X0))) | old(X0)) & (~old(X0) | ((~funny(X0) | ~generous(X0)) & (generous(X0) | funny(X0))))) [nnf transformation 9]
58. ! [X0] : ((~happy(X0) & generous(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 33]
59. ! [X0] : ((old(X0) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ~old(X0))) [nnf transformation 13]
94. ~calm(X0) | ~patient(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 51]
95. ~calm(X0) | patient(X0) | funny(X0) | ~generous(X0) [cnf transformation 51]
105. ~old(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 56]
107. ~generous(X0) | funny(X0) | old(X0) [cnf transformation 56]
111. generous(X0) | patient(X0) | patient(X0) [cnf transformation 58]
112. generous(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 58]
113. ~happy(X0) | patient(X0) | patient(X0) [cnf transformation 58]
114. ~happy(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 58]
116. ~patient(X0) | happy(X0) | ~old(X0) [cnf transformation 59]
117. old(X0) | patient(X0) | happy(X0) [cnf transformation 59]
140. calm(john) [cnf transformation 24]
141. generous(X0) | patient(X0) [duplicate literal removal 111]
142. ~patient(X0) | generous(X0) [duplicate literal removal 112]
143. ~happy(X0) | patient(X0) [duplicate literal removal 113]
144. ~happy(X0) | ~patient(X0) [duplicate literal removal 114]
227. ~happy(X0) [subsumption resolution 143,144]
228. generous(X0) [subsumption resolution 141,142]
229. old(X0) | patient(X0) [subsumption resolution 117,227]
230. ~old(X0) | ~patient(X0) [subsumption resolution 116,227]
304. ~funny(X0) | ~generous(X0) | patient(X0) [resolution 105,229]
306. ~funny(X0) | patient(X0) [subsumption resolution 304,228]
309. old(X0) | funny(X0) [resolution 107,228]
312. ~patient(X2) | funny(X2) [resolution 309,230]
320. 29 <=> funny(john) [avatar definition]
328. ~patient(john) | ~funny(john) | ~generous(john) [resolution 94,140]
344. patient(john) | funny(john) | ~generous(john) [resolution 95,140]
376. patient(john) | funny(john) [subsumption resolution 344,228]
377. funny(john) [subsumption resolution 376,312]
378. 29 [avatar split clause 377,320]
379. ~patient(john) | ~funny(john) [subsumption resolution 328,228]
380. ~funny(john) [subsumption resolution 379,306]
381. ~29 [avatar split clause 380,320]
382. $false [avatar sat refutation 378,381]
% SZS output end Proof for 685669077355112760040014
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is funny then fred is not humble and vice versa.
Everyone who is both not calm and not strong is not brave or generous and vice versa.
Everyone who is not curious is both brave and not tall and vice versa.
Everyone who is either not calm or not creative is not strong or calm and vice versa.
Everyone who is either not strong or kind is both not tall and not creative and vice versa.
If fred is either not curious or not funny then fred is either not humble or humble.
If someone is not generous or rich then john is creative or not brave.
If paul is both not generous and humble then john is not kind.
Everyone who is both generous and not calm is not kind and vice versa.
Everyone who is quiet is patient or curious.
If someone is either not strong or not creative then someone is either humble or not curious.
Everyone who is not curious is calm or patient and vice versa.
Everyone who is both old and not brave is either creative or not old and vice versa.
Everyone who is both creative and not generous is old and vice versa.
Everyone who is either old or not happy is not creative and vice versa.
John is funny or patient.
Susan is old or happy.
Someone is either not rich or humble.
Someone is not funny. | Fred is not generous. | entailment | ((funny(mary))<=>(~humble(fred)))&
(![X]:((~calm(X)&~strong(X))<=>(~brave(X)|generous(X))))&
(![X]:(~curious(X)<=>(brave(X)&~tall(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(~strong(X)|calm(X))))&
(![X]:((~strong(X)<~>kind(X))<=>(~tall(X)&~creative(X))))&
(((~curious(fred)<~>~funny(fred)))=>((~humble(fred)<~>humble(fred))))&
((?[X]:((~generous(X)|rich(X))))=>((creative(john)|~brave(john))))&
(((~generous(paul)&humble(paul)))=>(~kind(john)))&
(![X]:((generous(X)&~calm(X))<=>~kind(X)))&
(![X]:(quiet(X)=>(patient(X)|curious(X))))&
((?[X]:((~strong(X)<~>~creative(X))))=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:(~curious(X)<=>(calm(X)|patient(X))))&
(![X]:((old(X)&~brave(X))<=>(creative(X)<~>~old(X))))&
(![X]:((creative(X)&~generous(X))<=>old(X)))&
(![X]:((old(X)<~>~happy(X))<=>~creative(X)))&
((funny(john)|patient(john)))&
((old(susan)|happy(susan)))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:(~funny(X))) | ~generous(fred) | [
"p1",
"p3",
"p4",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2280315478725413971307228
% SZS output start Proof for 2280315478725413971307228
2. ! [X0] : ((~strong(X0) & ~calm(X0)) <=> (generous(X0) | ~brave(X0))) [input p1]
4. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (calm(X0) | ~strong(X0))) [input p3]
5. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (~creative(X0) & ~tall(X0))) [input p4]
9. ! [X0] : ((~calm(X0) & generous(X0)) <=> ~kind(X0)) [input p8]
13. ! [X0] : ((~brave(X0) & old(X0)) <=> (creative(X0) <~> ~old(X0))) [input p12]
14. ! [X0] : ((~generous(X0) & creative(X0)) <=> old(X0)) [input p13]
20. generous(fred) [input hypothesis]
30. ! [X0] : (((~strong(X0) & ~calm(X0)) | (~generous(X0) & brave(X0))) & ((generous(X0) | ~brave(X0)) | (strong(X0) | calm(X0)))) [nnf transformation 2]
31. ! [X0] : (((~strong(X0) & ~calm(X0)) | (~generous(X0) & brave(X0))) & (generous(X0) | ~brave(X0) | strong(X0) | calm(X0))) [flattening 30]
34. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 4]
35. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [flattening 34]
36. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [flattening 36]
39. ! [X0] : (((~calm(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | (calm(X0) | ~generous(X0)))) [nnf transformation 9]
40. ! [X0] : (((~calm(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | calm(X0) | ~generous(X0))) [flattening 39]
47. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | (brave(X0) | ~old(X0)))) [nnf transformation 13]
48. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | brave(X0) | ~old(X0))) [flattening 47]
49. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | (generous(X0) | ~creative(X0)))) [nnf transformation 14]
50. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | generous(X0) | ~creative(X0))) [flattening 49]
61. ~generous(X0) | ~calm(X0) [cnf transformation 31]
67. calm(X0) | ~strong(X0) | ~creative(X0) | calm(X0) [cnf transformation 35]
70. ~creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 35]
75. ~creative(X0) | kind(X0) | strong(X0) [cnf transformation 37]
86. ~kind(X0) | calm(X0) | ~generous(X0) [cnf transformation 40]
99. old(X0) | creative(X0) | old(X0) [cnf transformation 48]
103. creative(X0) | ~old(X0) [cnf transformation 50]
114. generous(fred) [cnf transformation 20]
116. old(X0) | creative(X0) [duplicate literal removal 99]
117. calm(X0) | ~strong(X0) | ~creative(X0) [duplicate literal removal 67]
118. ~creative(X0) | ~calm(X0) [duplicate literal removal 70]
129. ~creative(X0) | ~strong(X0) [subsumption resolution 117,118]
131. ~creative(X0) | kind(X0) [subsumption resolution 75,129]
161. ~kind(X0) | ~generous(X0) [subsumption resolution 86,61]
185. creative(X0) [subsumption resolution 103,116]
219. kind(X0) [resolution 131,185]
222. ~generous(X0) [resolution 219,161]
224. $false [resolution 222,114]
% SZS output end Proof for 2280315478725413971307228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not quiet or not calm is tall or not rich and vice versa.
If mary is humble then susan is generous or creative.
If someone is either patient or quiet then john is not tall or not curious.
If paul is brave then paul is both not wise and not calm and vice versa.
Everyone who is wise is both not wise and not calm and vice versa.
If someone is not strong then someone is either wise or rich.
Everyone who is both not strong and not patient is both not calm and old.
If someone is both curious and old then john is not kind and vice versa.
Everyone who is not strong is patient and vice versa.
If someone is patient then someone is not kind or happy.
Everyone who is both kind and generous is both calm and not brave and vice versa.
If mary is either strong or brave then someone is either not humble or creative.
If someone is curious or not quiet then lucy is not calm and vice versa.
If john is brave then alice is both not kind and not brave and vice versa.
Everyone who is quiet is both not happy and not creative.
John is funny or not strong.
Mary is either not happy or curious.
Paul is not creative.
Someone is both not brave and patient.
Lucy is either calm or not brave. | Susan is not brave. | neutral | (![X]:((~quiet(X)<~>~calm(X))<=>(tall(X)|~rich(X))))&
((humble(mary))=>((generous(susan)|creative(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>((~tall(john)|~curious(john))))&
((brave(paul))<=>((~wise(paul)&~calm(paul))))&
(![X]:(wise(X)<=>(~wise(X)&~calm(X))))&
((?[X]:(~strong(X)))=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~strong(X)&~patient(X))=>(~calm(X)&old(X))))&
((?[X]:((curious(X)&old(X))))<=>(~kind(john)))&
(![X]:(~strong(X)<=>patient(X)))&
((?[X]:(patient(X)))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((kind(X)&generous(X))<=>(calm(X)&~brave(X))))&
(((strong(mary)<~>brave(mary)))=>(?[X]:((~humble(X)<~>creative(X)))))&
((?[X]:((curious(X)|~quiet(X))))<=>(~calm(lucy)))&
((brave(john))<=>((~kind(alice)&~brave(alice))))&
(![X]:(quiet(X)=>(~happy(X)&~creative(X))))&
((funny(john)|~strong(john)))&
((~happy(mary)<~>curious(mary)))&
(~creative(paul))&
(?[X]:((~brave(X)&patient(X))))&
((calm(lucy)<~>~brave(lucy))) | ~brave(susan) | [] | null | 0 |
If john is either tall or generous then someone is not strong and vice versa.
Everyone who is either tall or wise is humble.
If someone is both not curious and not old then mary is rich or not old and vice versa.
Everyone who is both quiet and curious is either generous or not old.
Everyone who is either quiet or not curious is creative and vice versa.
If susan is not humble then fred is either patient or tall and vice versa.
Everyone who is both not tall and old is either not calm or not creative and vice versa.
Everyone who is both not humble and not tall is curious or not rich and vice versa.
If alice is both not wise and quiet then susan is both wise and not calm.
If someone is both not calm and not generous then someone is not wise or generous.
If someone is both old and not quiet then fred is not rich or not creative.
Everyone who is either not calm or generous is both quiet and old.
Everyone who is strong is happy.
If paul is patient then john is kind and vice versa.
Everyone who is either not humble or rich is not old or not humble and vice versa.
If someone is either kind or not kind then alice is curious or not happy and vice versa.
John is either not brave or not creative.
Paul is either not kind or curious.
Someone is not generous or curious.
Someone is generous.
Someone is both not wise and old.
Someone is either old or not calm.
Someone is both not generous and funny. | Paul is curious. | neutral | (((tall(john)<~>generous(john)))<=>(?[X]:(~strong(X))))&
(![X]:((tall(X)<~>wise(X))=>humble(X)))&
((?[X]:((~curious(X)&~old(X))))<=>((rich(mary)|~old(mary))))&
(![X]:((quiet(X)&curious(X))=>(generous(X)<~>~old(X))))&
(![X]:((quiet(X)<~>~curious(X))<=>creative(X)))&
((~humble(susan))<=>((patient(fred)<~>tall(fred))))&
(![X]:((~tall(X)&old(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~humble(X)&~tall(X))<=>(curious(X)|~rich(X))))&
(((~wise(alice)&quiet(alice)))=>((wise(susan)&~calm(susan))))&
((?[X]:((~calm(X)&~generous(X))))=>(?[X]:((~wise(X)|generous(X)))))&
((?[X]:((old(X)&~quiet(X))))=>((~rich(fred)|~creative(fred))))&
(![X]:((~calm(X)<~>generous(X))=>(quiet(X)&old(X))))&
(![X]:(strong(X)=>happy(X)))&
((patient(paul))<=>(kind(john)))&
(![X]:((~humble(X)<~>rich(X))<=>(~old(X)|~humble(X))))&
((?[X]:((kind(X)<~>~kind(X))))<=>((curious(alice)|~happy(alice))))&
((~brave(john)<~>~creative(john)))&
((~kind(paul)<~>curious(paul)))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:(generous(X)))&
(?[X]:((~wise(X)&old(X))))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:((~generous(X)&funny(X)))) | curious(paul) | [] | null | 0 |
If fred is not brave then someone is not patient.
If someone is both not strong and generous then someone is not tall or old.
If someone is either not brave or not calm then someone is happy.
If fred is both patient and generous then someone is rich or strong.
If someone is either not strong or not happy then paul is both not strong and not creative.
If someone is not funny or not happy then paul is either not curious or quiet and vice versa.
Everyone who is both not kind and humble is both not kind and rich.
If mary is funny then someone is both strong and old and vice versa.
Everyone who is funny is both not strong and rich.
Everyone who is brave or calm is either brave or quiet.
If someone is both not humble and creative then someone is either kind or not tall.
If someone is not wise or not creative then john is both not generous and not brave.
If someone is both not wise and not patient then someone is old or not quiet.
Everyone who is not kind is not happy or not brave.
If someone is old or patient then mary is both kind and not rich.
Everyone who is both not wise and patient is calm and vice versa.
Someone is both generous and strong.
Someone is patient or not strong.
Mary is both not funny and not quiet.
Someone is both tall and not wise.
Someone is both not brave and calm.
Someone is both not wise and not happy.
Someone is either brave or not wise.
Mary is not rich. | Mary is kind. | entailment | ((~brave(fred))=>(?[X]:(~patient(X))))&
((?[X]:((~strong(X)&generous(X))))=>(?[X]:((~tall(X)|old(X)))))&
((?[X]:((~brave(X)<~>~calm(X))))=>(?[X]:(happy(X))))&
(((patient(fred)&generous(fred)))=>(?[X]:((rich(X)|strong(X)))))&
((?[X]:((~strong(X)<~>~happy(X))))=>((~strong(paul)&~creative(paul))))&
((?[X]:((~funny(X)|~happy(X))))<=>((~curious(paul)<~>quiet(paul))))&
(![X]:((~kind(X)&humble(X))=>(~kind(X)&rich(X))))&
((funny(mary))<=>(?[X]:((strong(X)&old(X)))))&
(![X]:(funny(X)=>(~strong(X)&rich(X))))&
(![X]:((brave(X)|calm(X))=>(brave(X)<~>quiet(X))))&
((?[X]:((~humble(X)&creative(X))))=>(?[X]:((kind(X)<~>~tall(X)))))&
((?[X]:((~wise(X)|~creative(X))))=>((~generous(john)&~brave(john))))&
((?[X]:((~wise(X)&~patient(X))))=>(?[X]:((old(X)|~quiet(X)))))&
(![X]:(~kind(X)=>(~happy(X)|~brave(X))))&
((?[X]:((old(X)|patient(X))))=>((kind(mary)&~rich(mary))))&
(![X]:((~wise(X)&patient(X))<=>calm(X)))&
(?[X]:((generous(X)&strong(X))))&
(?[X]:((patient(X)|~strong(X))))&
((~funny(mary)&~quiet(mary)))&
(?[X]:((tall(X)&~wise(X))))&
(?[X]:((~brave(X)&calm(X))))&
(?[X]:((~wise(X)&~happy(X))))&
(?[X]:((brave(X)<~>~wise(X))))&
(~rich(mary)) | kind(mary) | [
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5612405574727794186369189
% SZS output start Proof for 5612405574727794186369189
15. ? [X0] : (patient(X0) | old(X0)) => (~rich(mary) & kind(mary)) [input p14]
16. ! [X0] : ((patient(X0) & ~wise(X0)) <=> calm(X0)) [input p15]
21. ? [X0] : (calm(X0) & ~brave(X0)) [input p20]
25. ~kind(mary) [input hypothesis]
45. (~rich(mary) & kind(mary)) | ! [X0] : (~patient(X0) & ~old(X0)) [ennf transformation 15]
74. ! [X0] : (((patient(X0) & ~wise(X0)) | ~calm(X0)) & (calm(X0) | (~patient(X0) | wise(X0)))) [nnf transformation 16]
75. ! [X0] : (((patient(X0) & ~wise(X0)) | ~calm(X0)) & (calm(X0) | ~patient(X0) | wise(X0))) [flattening 74]
82. ? [X0] : (calm(X0) & ~brave(X0)) => (calm(sK11) & ~brave(sK11)) [choice axiom]
83. calm(sK11) & ~brave(sK11) [skolemisation 21,82]
124. kind(mary) | ~patient(X0) [cnf transformation 45]
129. ~calm(X0) | patient(X0) [cnf transformation 75]
138. calm(sK11) [cnf transformation 83]
144. ~kind(mary) [cnf transformation 25]
304. 37 <=> ! [X0] : ~patient(X0) [avatar definition]
305. ~patient(X0) <- (37) [avatar component clause 304]
316. 40 <=> kind(mary) [avatar definition]
319. 37 | 40 [avatar split clause 124,316,304]
342. ~40 [avatar split clause 144,316]
343. patient(sK11) [resolution 129,138]
344. $false <- (37) [subsumption resolution 343,305]
345. ~37 [avatar contradiction clause 344]
346. $false [avatar sat refutation 319,342,345]
% SZS output end Proof for 5612405574727794186369189
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and tall then lucy is either wise or brave and vice versa. If someone is not brave then paul is either generous or not patient. Everyone who is both not tall and funny is both not creative and tall and vice versa. If fred is patient then paul is both generous and not calm and vice versa. If someone is calm or not strong then john is either not generous or not brave and vice versa. Everyone who is either strong or generous is both funny and not curious. Everyone who is both generous and humble is not curious or tall and vice versa. Everyone who is both strong and not happy is not quiet or humble. If someone is not kind or creative then john 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 generous is either generous or old and vice versa. Mary is both rich and not curious. Someone is not strong. Someone is both not happy and patient. John is not kind. Paul is old or not humble. Paul is not kind or not tall. Alice is strong. Mary is both calm and wise. | John is not tall. | entailment | ((?[X]:((humble(X)&tall(X))))<=>((wise(lucy)<~>brave(lucy))))&
((?[X]:(~brave(X)))=>((generous(paul)<~>~patient(paul))))&
(![X]:((~tall(X)&funny(X))<=>(~creative(X)&tall(X))))&
((patient(fred))<=>((generous(paul)&~calm(paul))))&
((?[X]:((calm(X)|~strong(X))))<=>((~generous(john)<~>~brave(john))))&
(![X]:((strong(X)<~>generous(X))=>(funny(X)&~curious(X))))&
(![X]:((generous(X)&humble(X))<=>(~curious(X)|tall(X))))&
(![X]:((strong(X)&~happy(X))=>(~quiet(X)|humble(X))))&
((?[X]:((~kind(X)|creative(X))))<=>(wise(john)))&
((?[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]:(generous(X)<=>(generous(X)<~>old(X))))&
((rich(mary)&~curious(mary)))&
(?[X]:(~strong(X)))&
(?[X]:((~happy(X)&patient(X))))&
(~kind(john))&
((old(paul)|~humble(paul)))&
((~kind(paul)|~tall(paul)))&
(strong(alice))&
((calm(mary)&wise(mary))) | ~tall(john) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2743221489806108498491362
% SZS output start Proof for 2743221489806108498491362
7. ! [X0] : ((humble(X0) & generous(X0)) <=> (tall(X0) | ~curious(X0))) [input p6]
13. ! [X0] : (tall(X0) => (~patient(X0) & ~humble(X0))) [input p12]
25. tall(john) [input hypothesis]
36. ! [X0] : ((~patient(X0) & ~humble(X0)) | ~tall(X0)) [ennf transformation 13]
54. ! [X0] : (((humble(X0) & generous(X0)) | (~tall(X0) & curious(X0))) & ((tall(X0) | ~curious(X0)) | (~humble(X0) | ~generous(X0)))) [nnf transformation 7]
55. ! [X0] : (((humble(X0) & generous(X0)) | (~tall(X0) & curious(X0))) & (tall(X0) | ~curious(X0) | ~humble(X0) | ~generous(X0))) [flattening 54]
99. humble(X0) | ~tall(X0) [cnf transformation 55]
114. ~humble(X0) | ~tall(X0) [cnf transformation 36]
133. tall(john) [cnf transformation 25]
250. ~tall(X0) [subsumption resolution 114,99]
261. $false [subsumption resolution 133,250]
% SZS output end Proof for 2743221489806108498491362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not generous and generous then fred is creative and vice versa.
Everyone who is both calm and not calm is not humble and vice versa.
If susan is both calm and tall then someone is curious.
Everyone who is creative or humble is either humble or not wise and vice versa.
If fred is both kind and old then someone is both not strong and not humble.
If fred is both quiet and funny then someone is either curious or not rich.
Everyone who is not tall is not creative or wise and vice versa.
Everyone who is not strong is either not curious or quiet and vice versa.
If mary is not kind or curious then lucy is either generous or humble.
Everyone who is not funny or tall is rich.
If someone is not old then someone is curious.
Everyone who is quiet is not brave and vice versa.
If lucy is both not generous and not patient then lucy is brave or not quiet.
Everyone who is both wise and humble is patient.
Everyone who is humble or calm is both not quiet and not calm.
Everyone who is humble is either strong or patient and vice versa.
Lucy is wise.
Susan is happy or not calm.
Someone is not wise or brave.
Paul is not tall.
Mary is rich.
Someone is not old or old.
Someone is not creative or old. | Mary is quiet. | contradiction | (((~generous(john)&generous(john)))<=>(creative(fred)))&
(![X]:((calm(X)&~calm(X))<=>~humble(X)))&
(((calm(susan)&tall(susan)))=>(?[X]:(curious(X))))&
(![X]:((creative(X)|humble(X))<=>(humble(X)<~>~wise(X))))&
(((kind(fred)&old(fred)))=>(?[X]:((~strong(X)&~humble(X)))))&
(((quiet(fred)&funny(fred)))=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:(~tall(X)<=>(~creative(X)|wise(X))))&
(![X]:(~strong(X)<=>(~curious(X)<~>quiet(X))))&
(((~kind(mary)|curious(mary)))=>((generous(lucy)<~>humble(lucy))))&
(![X]:((~funny(X)|tall(X))=>rich(X)))&
((?[X]:(~old(X)))=>(?[X]:(curious(X))))&
(![X]:(quiet(X)<=>~brave(X)))&
(((~generous(lucy)&~patient(lucy)))=>((brave(lucy)|~quiet(lucy))))&
(![X]:((wise(X)&humble(X))=>patient(X)))&
(![X]:((humble(X)|calm(X))=>(~quiet(X)&~calm(X))))&
(![X]:(humble(X)<=>(strong(X)<~>patient(X))))&
(wise(lucy))&
((happy(susan)|~calm(susan)))&
(?[X]:((~wise(X)|brave(X))))&
(~tall(paul))&
(rich(mary))&
(?[X]:((~old(X)|old(X))))&
(?[X]:((~creative(X)|old(X)))) | quiet(mary) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3435707907256021208790
% SZS output start Proof for 3435707907256021208790
2. ! [X0] : ((~calm(X0) & calm(X0)) <=> ~humble(X0)) [input p1]
15. ! [X0] : ((calm(X0) | humble(X0)) => (~calm(X0) & ~quiet(X0))) [input p14]
24. quiet(mary) [input hypothesis]
43. ! [X0] : ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & ~humble(X0))) [ennf transformation 15]
46. ! [X0] : (((~calm(X0) & calm(X0)) | humble(X0)) & (~humble(X0) | (calm(X0) | ~calm(X0)))) [nnf transformation 2]
47. ! [X0] : (((~calm(X0) & calm(X0)) | humble(X0)) & (~humble(X0) | calm(X0) | ~calm(X0))) [flattening 46]
74. calm(X0) | humble(X0) [cnf transformation 47]
75. ~calm(X0) | humble(X0) [cnf transformation 47]
103. ~quiet(X0) | ~humble(X0) [cnf transformation 43]
117. quiet(mary) [cnf transformation 24]
131. humble(X0) [subsumption resolution 74,75]
215. ~quiet(X0) [subsumption resolution 103,131]
228. $false [subsumption resolution 117,215]
% SZS output end Proof for 3435707907256021208790
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not creative then someone is either not quiet or not calm. Everyone who is either quiet or brave is funny or not tall and vice versa. If someone is happy then someone is either curious or not generous and vice versa. Everyone who is not old or tall is not kind or not rich and vice versa. If john is not creative then someone is both rich and not generous. If someone is wise then john is both funny and curious and vice versa. Everyone who is both not humble and not curious is either happy or calm. Everyone who is both generous and creative is not patient. Everyone who is brave or not tall is both creative and not kind and vice versa. If someone is both rich and wise then paul is not rich or generous. Everyone who is both tall and not rich is both happy and not generous. If someone is both quiet and not funny then paul is either not calm or not old and vice versa. Everyone who is both not funny and not brave is either happy or not wise and vice versa. Everyone who is funny or not strong is not tall or patient. If someone is strong then paul is both not strong and funny. Everyone who is quiet is both not rich and curious. Someone is either not calm or tall. Someone is not happy or funny. Alice is either wise or happy. Someone is kind. Someone is either calm or not strong. Someone is brave or kind. Alice is calm. Alice is kind or wise. | John is creative. | neutral | ((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~quiet(X)<~>~calm(X)))))&
(![X]:((quiet(X)<~>brave(X))<=>(funny(X)|~tall(X))))&
((?[X]:(happy(X)))<=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:((~old(X)|tall(X))<=>(~kind(X)|~rich(X))))&
((~creative(john))=>(?[X]:((rich(X)&~generous(X)))))&
((?[X]:(wise(X)))<=>((funny(john)&curious(john))))&
(![X]:((~humble(X)&~curious(X))=>(happy(X)<~>calm(X))))&
(![X]:((generous(X)&creative(X))=>~patient(X)))&
(![X]:((brave(X)|~tall(X))<=>(creative(X)&~kind(X))))&
((?[X]:((rich(X)&wise(X))))=>((~rich(paul)|generous(paul))))&
(![X]:((tall(X)&~rich(X))=>(happy(X)&~generous(X))))&
((?[X]:((quiet(X)&~funny(X))))<=>((~calm(paul)<~>~old(paul))))&
(![X]:((~funny(X)&~brave(X))<=>(happy(X)<~>~wise(X))))&
(![X]:((funny(X)|~strong(X))=>(~tall(X)|patient(X))))&
((?[X]:(strong(X)))=>((~strong(paul)&funny(paul))))&
(![X]:(quiet(X)=>(~rich(X)&curious(X))))&
(?[X]:((~calm(X)<~>tall(X))))&
(?[X]:((~happy(X)|funny(X))))&
((wise(alice)<~>happy(alice)))&
(?[X]:(kind(X)))&
(?[X]:((calm(X)<~>~strong(X))))&
(?[X]:((brave(X)|kind(X))))&
(calm(alice))&
((kind(alice)|wise(alice))) | creative(john) | [] | null | 0 |
If someone is both not strong and not creative then someone is both not calm and not brave.
Everyone who is either not old or kind is funny or strong and vice versa.
Everyone who is either not quiet or patient is either curious or not generous.
If susan is not generous or not wise then someone is either not funny or not humble.
If someone is either happy or not patient then alice is both not funny and not strong.
If susan is strong then someone is not wise and vice versa.
Everyone who is old is both not wise and not humble and vice versa.
Everyone who is both tall and not old is both not creative and brave and vice versa.
Everyone who is not happy is both not generous and not wise.
If alice is not strong then susan is not brave or patient.
Everyone who is either not kind or not humble is not wise.
If susan is either not strong or not funny then someone is not strong or not patient and vice versa.
Everyone who is either not creative or wise is both happy and not brave.
If fred is generous or not creative then someone is both not quiet and not creative.
Everyone who is not strong or not happy is not wise.
Everyone who is either funny or not kind is both humble and not brave.
John is not brave or not humble.
Someone is not rich or not calm.
Susan is not old.
Someone is both not funny and not humble.
Mary is funny or brave.
Someone is brave.
Paul is wise or curious. | Fred is not curious. | neutral | ((?[X]:((~strong(X)&~creative(X))))=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((~old(X)<~>kind(X))<=>(funny(X)|strong(X))))&
(![X]:((~quiet(X)<~>patient(X))=>(curious(X)<~>~generous(X))))&
(((~generous(susan)|~wise(susan)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
((?[X]:((happy(X)<~>~patient(X))))=>((~funny(alice)&~strong(alice))))&
((strong(susan))<=>(?[X]:(~wise(X))))&
(![X]:(old(X)<=>(~wise(X)&~humble(X))))&
(![X]:((tall(X)&~old(X))<=>(~creative(X)&brave(X))))&
(![X]:(~happy(X)=>(~generous(X)&~wise(X))))&
((~strong(alice))=>((~brave(susan)|patient(susan))))&
(![X]:((~kind(X)<~>~humble(X))=>~wise(X)))&
(((~strong(susan)<~>~funny(susan)))<=>(?[X]:((~strong(X)|~patient(X)))))&
(![X]:((~creative(X)<~>wise(X))=>(happy(X)&~brave(X))))&
(((generous(fred)|~creative(fred)))=>(?[X]:((~quiet(X)&~creative(X)))))&
(![X]:((~strong(X)|~happy(X))=>~wise(X)))&
(![X]:((funny(X)<~>~kind(X))=>(humble(X)&~brave(X))))&
((~brave(john)|~humble(john)))&
(?[X]:((~rich(X)|~calm(X))))&
(~old(susan))&
(?[X]:((~funny(X)&~humble(X))))&
((funny(mary)|brave(mary)))&
(?[X]:(brave(X)))&
((wise(paul)|curious(paul))) | ~curious(fred) | [] | null | 0 |
Everyone who is not creative is both funny and rich. If someone is either not rich or not strong then someone is not patient or not brave. Everyone who is either humble or not brave is not patient and vice versa. Everyone who is either patient or not curious is both rich and patient and vice versa. If alice is brave then someone is both happy and strong. If someone is not curious or old then alice is either patient or kind and vice versa. Everyone who is not wise is strong and vice versa. If someone is not curious or not patient then alice is quiet or strong. If someone is both not curious and not generous then alice is both quiet and brave and vice versa. Everyone who is either old or not curious is not funny and vice versa. Everyone who is brave or not strong is both funny and not creative. Everyone who is either not strong or not kind is old or generous. Everyone who is both wise and creative is not brave or not calm. Everyone who is not creative or not funny is calm and vice versa. Everyone who is either calm or not kind is rich or quiet. Everyone who is not calm or not humble is not strong and vice versa. Someone is not quiet or calm. Mary is creative or not rich. Someone is happy or brave. Someone is either wise or not wise. Mary is both not kind and old. Someone is both not rich and not old. Someone is not creative. Someone is either patient or not brave. | Mary is humble. | entailment | (![X]:(~creative(X)=>(funny(X)&rich(X))))&
((?[X]:((~rich(X)<~>~strong(X))))=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((humble(X)<~>~brave(X))<=>~patient(X)))&
(![X]:((patient(X)<~>~curious(X))<=>(rich(X)&patient(X))))&
((brave(alice))=>(?[X]:((happy(X)&strong(X)))))&
((?[X]:((~curious(X)|old(X))))<=>((patient(alice)<~>kind(alice))))&
(![X]:(~wise(X)<=>strong(X)))&
((?[X]:((~curious(X)|~patient(X))))=>((quiet(alice)|strong(alice))))&
((?[X]:((~curious(X)&~generous(X))))<=>((quiet(alice)&brave(alice))))&
(![X]:((old(X)<~>~curious(X))<=>~funny(X)))&
(![X]:((brave(X)|~strong(X))=>(funny(X)&~creative(X))))&
(![X]:((~strong(X)<~>~kind(X))=>(old(X)|generous(X))))&
(![X]:((wise(X)&creative(X))=>(~brave(X)|~calm(X))))&
(![X]:((~creative(X)|~funny(X))<=>calm(X)))&
(![X]:((calm(X)<~>~kind(X))=>(rich(X)|quiet(X))))&
(![X]:((~calm(X)|~humble(X))<=>~strong(X)))&
(?[X]:((~quiet(X)|calm(X))))&
((creative(mary)|~rich(mary)))&
(?[X]:((happy(X)|brave(X))))&
(?[X]:((wise(X)<~>~wise(X))))&
((~kind(mary)&old(mary)))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:(~creative(X)))&
(?[X]:((patient(X)<~>~brave(X)))) | humble(mary) | [
"p0",
"p10",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 189739535843234416448635
% SZS output start Proof for 189739535843234416448635
1. ! [X0] : (~creative(X0) => (rich(X0) & funny(X0))) [input p0]
11. ! [X0] : ((~strong(X0) | brave(X0)) => (~creative(X0) & funny(X0))) [input p10]
16. ! [X0] : ((~humble(X0) | ~calm(X0)) <=> ~strong(X0)) [input p15]
18. ~rich(mary) | creative(mary) [input p17]
25. ~humble(mary) [input hypothesis]
29. ! [X0] : ((rich(X0) & funny(X0)) | creative(X0)) [ennf transformation 1]
34. ! [X0] : ((~creative(X0) & funny(X0)) | (strong(X0) & ~brave(X0))) [ennf transformation 11]
65. ! [X0] : (((~humble(X0) | ~calm(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) & calm(X0)))) [nnf transformation 16]
66. ! [X0] : ((~humble(X0) | ~calm(X0) | strong(X0)) & (~strong(X0) | (humble(X0) & calm(X0)))) [flattening 65]
80. rich(X0) | creative(X0) [cnf transformation 29]
115. ~creative(X0) | strong(X0) [cnf transformation 34]
125. ~strong(X0) | humble(X0) [cnf transformation 66]
128. ~rich(mary) | creative(mary) [cnf transformation 18]
138. ~humble(mary) [cnf transformation 25]
231. creative(mary) [subsumption resolution 128,80]
246. strong(mary) [resolution 115,231]
253. humble(mary) [resolution 125,246]
256. $false [subsumption resolution 253,138]
% SZS output end Proof for 189739535843234416448635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not old or curious then someone is not happy or not humble.
Everyone who is either not old or not happy is curious.
Everyone who is patient is not old or not calm.
If alice is not brave then john is not calm and vice versa.
Everyone who is both not rich and funny is tall or not patient.
If someone is not wise or not funny then someone is both kind and old and vice versa.
Everyone who is not quiet is both not funny and old and vice versa.
Everyone who is funny is not calm and vice versa.
Everyone who is not curious is tall and vice versa.
Everyone who is patient or strong is creative and vice versa.
Everyone who is strong is wise and vice versa.
Everyone who is either funny or not old is not tall or not strong.
If alice is both not happy and not funny then mary is both patient and not tall and vice versa.
If someone is both creative and old then someone is patient or not brave.
Everyone who is not strong is either not rich or humble.
If alice is funny then someone is both not rich and not quiet.
Paul is not happy.
Someone is either not humble or not happy.
Alice is either not kind or tall.
Susan is quiet.
Someone is not old.
Someone is quiet.
John is old or not curious.
Paul is either generous or not humble. | Mary is not old. | neutral | (((~old(mary)|curious(mary)))=>(?[X]:((~happy(X)|~humble(X)))))&
(![X]:((~old(X)<~>~happy(X))=>curious(X)))&
(![X]:(patient(X)=>(~old(X)|~calm(X))))&
((~brave(alice))<=>(~calm(john)))&
(![X]:((~rich(X)&funny(X))=>(tall(X)|~patient(X))))&
((?[X]:((~wise(X)|~funny(X))))<=>(?[X]:((kind(X)&old(X)))))&
(![X]:(~quiet(X)<=>(~funny(X)&old(X))))&
(![X]:(funny(X)<=>~calm(X)))&
(![X]:(~curious(X)<=>tall(X)))&
(![X]:((patient(X)|strong(X))<=>creative(X)))&
(![X]:(strong(X)<=>wise(X)))&
(![X]:((funny(X)<~>~old(X))=>(~tall(X)|~strong(X))))&
(((~happy(alice)&~funny(alice)))<=>((patient(mary)&~tall(mary))))&
((?[X]:((creative(X)&old(X))))=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:(~strong(X)=>(~rich(X)<~>humble(X))))&
((funny(alice))=>(?[X]:((~rich(X)&~quiet(X)))))&
(~happy(paul))&
(?[X]:((~humble(X)<~>~happy(X))))&
((~kind(alice)<~>tall(alice)))&
(quiet(susan))&
(?[X]:(~old(X)))&
(?[X]:(quiet(X)))&
((old(john)|~curious(john)))&
((generous(paul)<~>~humble(paul))) | ~old(mary) | [] | null | 0 |
If mary is patient or calm then mary is both generous and kind.
If someone is not curious or tall then fred is both not happy and not generous and vice versa.
Everyone who is both not patient and not happy is kind or patient and vice versa.
If someone is not quiet or not kind then fred is either not rich or funny and vice versa.
If lucy is either not kind or not funny then someone is not wise or funny.
Everyone who is not creative or not quiet is happy or kind and vice versa.
Everyone who is both curious and brave is both rich and humble.
If someone is either patient or tall then someone is both not kind and not calm and vice versa.
Everyone who is not rich or not funny is not funny or not tall.
Everyone who is wise or not kind is both not quiet and humble.
If mary is both not strong and kind then john is either funny or tall.
Everyone who is not happy is wise and vice versa.
If susan is not tall or not quiet then mary is funny or not funny.
If paul is either rich or not brave then john is happy or strong and vice versa.
If someone is either not generous or generous then mary is curious.
Everyone who is not patient or strong is creative or not tall.
Alice is both tall and not happy.
Someone is not happy.
Mary is either happy or calm.
Lucy is not happy.
Susan is humble.
Mary is not kind or rich. | Paul is creative. | neutral | (((patient(mary)|calm(mary)))=>((generous(mary)&kind(mary))))&
((?[X]:((~curious(X)|tall(X))))<=>((~happy(fred)&~generous(fred))))&
(![X]:((~patient(X)&~happy(X))<=>(kind(X)|patient(X))))&
((?[X]:((~quiet(X)|~kind(X))))<=>((~rich(fred)<~>funny(fred))))&
(((~kind(lucy)<~>~funny(lucy)))=>(?[X]:((~wise(X)|funny(X)))))&
(![X]:((~creative(X)|~quiet(X))<=>(happy(X)|kind(X))))&
(![X]:((curious(X)&brave(X))=>(rich(X)&humble(X))))&
((?[X]:((patient(X)<~>tall(X))))<=>(?[X]:((~kind(X)&~calm(X)))))&
(![X]:((~rich(X)|~funny(X))=>(~funny(X)|~tall(X))))&
(![X]:((wise(X)|~kind(X))=>(~quiet(X)&humble(X))))&
(((~strong(mary)&kind(mary)))=>((funny(john)<~>tall(john))))&
(![X]:(~happy(X)<=>wise(X)))&
(((~tall(susan)|~quiet(susan)))=>((funny(mary)|~funny(mary))))&
(((rich(paul)<~>~brave(paul)))<=>((happy(john)|strong(john))))&
((?[X]:((~generous(X)<~>generous(X))))=>(curious(mary)))&
(![X]:((~patient(X)|strong(X))=>(creative(X)|~tall(X))))&
((tall(alice)&~happy(alice)))&
(?[X]:(~happy(X)))&
((happy(mary)<~>calm(mary)))&
(~happy(lucy))&
(humble(susan))&
((~kind(mary)|rich(mary))) | creative(paul) | [] | null | 0 |
If someone is not quiet or calm then alice is both not humble and not brave and vice versa.
Everyone who is both curious and not humble is both not patient and not curious and vice versa.
If lucy is either humble or not humble then lucy is either not wise or not rich.
If someone is not wise or not quiet then someone is not curious and vice versa.
If someone is wise or humble then lucy is either not kind or tall and vice versa.
Everyone who is both old and wise is either not strong or humble and vice versa.
Everyone who is not old or tall is both humble and not old.
If someone is either quiet or patient then susan is either not humble or tall.
Everyone who is happy is either not curious or creative.
Everyone who is either not kind or wise is not humble or not kind.
If alice is quiet then someone is both rich and not patient.
Everyone who is both not creative and not curious is both funny and wise and vice versa.
If someone is either funny or not kind then john is not wise or not strong.
Everyone who is both humble and not old is either old or strong.
If someone is not funny or kind then someone is either not patient or rich.
If susan is not strong then someone is either not quiet or not strong and vice versa.
Someone is both funny and not curious.
Lucy is rich.
Susan is curious.
Someone is not generous or not kind.
Someone is both strong and not kind.
Someone is either not kind or brave.
Mary is both not rich and not creative. | Alice is not patient. | contradiction | ((?[X]:((~quiet(X)|calm(X))))<=>((~humble(alice)&~brave(alice))))&
(![X]:((curious(X)&~humble(X))<=>(~patient(X)&~curious(X))))&
(((humble(lucy)<~>~humble(lucy)))=>((~wise(lucy)<~>~rich(lucy))))&
((?[X]:((~wise(X)|~quiet(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|humble(X))))<=>((~kind(lucy)<~>tall(lucy))))&
(![X]:((old(X)&wise(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((~old(X)|tall(X))=>(humble(X)&~old(X))))&
((?[X]:((quiet(X)<~>patient(X))))=>((~humble(susan)<~>tall(susan))))&
(![X]:(happy(X)=>(~curious(X)<~>creative(X))))&
(![X]:((~kind(X)<~>wise(X))=>(~humble(X)|~kind(X))))&
((quiet(alice))=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:((~creative(X)&~curious(X))<=>(funny(X)&wise(X))))&
((?[X]:((funny(X)<~>~kind(X))))=>((~wise(john)|~strong(john))))&
(![X]:((humble(X)&~old(X))=>(old(X)<~>strong(X))))&
((?[X]:((~funny(X)|kind(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
((~strong(susan))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(?[X]:((funny(X)&~curious(X))))&
(rich(lucy))&
(curious(susan))&
(?[X]:((~generous(X)|~kind(X))))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:((~kind(X)<~>brave(X))))&
((~rich(mary)&~creative(mary))) | ~patient(alice) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5726070059072861602821957
% SZS output start Proof for 5726070059072861602821957
1. ? [X0] : (calm(X0) | ~quiet(X0)) <=> (~brave(alice) & ~humble(alice)) [input p0]
2. ! [X0] : ((~humble(X0) & curious(X0)) <=> (~curious(X0) & ~patient(X0))) [input p1]
6. ! [X0] : ((wise(X0) & old(X0)) <=> (~strong(X0) <~> humble(X0))) [input p5]
7. ! [X0] : ((tall(X0) | ~old(X0)) => (~old(X0) & humble(X0))) [input p6]
8. ? [X0] : (quiet(X0) <~> patient(X0)) => (~humble(susan) <~> tall(susan)) [input p7]
14. ! [X0] : ((~old(X0) & humble(X0)) => (old(X0) <~> strong(X0))) [input p13]
19. curious(susan) [input p18]
24. ~patient(alice) [input hypothesis]
30. ! [X0] : ((~old(X0) & humble(X0)) | (~tall(X0) & old(X0))) [ennf transformation 7]
31. (~humble(susan) <~> tall(susan)) | ! [X0] : (quiet(X0) <=> patient(X0)) [ennf transformation 8]
37. ! [X0] : ((old(X0) <~> strong(X0)) | (old(X0) | ~humble(X0))) [ennf transformation 14]
38. ! [X0] : ((old(X0) <~> strong(X0)) | old(X0) | ~humble(X0)) [flattening 37]
40. (? [X0] : (calm(X0) | ~quiet(X0)) | (brave(alice) | humble(alice))) & ((~brave(alice) & ~humble(alice)) | ! [X0] : (~calm(X0) & quiet(X0))) [nnf transformation 1]
41. (? [X0] : (calm(X0) | ~quiet(X0)) | brave(alice) | humble(alice)) & ((~brave(alice) & ~humble(alice)) | ! [X0] : (~calm(X0) & quiet(X0))) [flattening 40]
42. (? [X0] : (calm(X0) | ~quiet(X0)) | brave(alice) | humble(alice)) & ((~brave(alice) & ~humble(alice)) | ! [X1] : (~calm(X1) & quiet(X1))) [rectify 41]
43. ? [X0] : (calm(X0) | ~quiet(X0)) => (calm(sK0) | ~quiet(sK0)) [choice axiom]
44. ((calm(sK0) | ~quiet(sK0)) | brave(alice) | humble(alice)) & ((~brave(alice) & ~humble(alice)) | ! [X1] : (~calm(X1) & quiet(X1))) [skolemisation 42,43]
45. ! [X0] : (((~humble(X0) & curious(X0)) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | (humble(X0) | ~curious(X0)))) [nnf transformation 2]
46. ! [X0] : (((~humble(X0) & curious(X0)) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | humble(X0) | ~curious(X0))) [flattening 45]
57. ! [X0] : (((wise(X0) & old(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~wise(X0) | ~old(X0)))) [nnf transformation 6]
58. ! [X0] : (((wise(X0) & old(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ~wise(X0) | ~old(X0))) [flattening 57]
59. ((~tall(susan) | humble(susan)) & (tall(susan) | ~humble(susan))) | ! [X0] : ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))) [nnf transformation 31]
66. ! [X0] : (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | old(X0) | ~humble(X0)) [nnf transformation 38]
82. ~humble(alice) | quiet(X1) [cnf transformation 44]
88. ~curious(X0) | humble(X0) | ~curious(X0) [cnf transformation 46]
89. curious(X0) | curious(X0) | patient(X0) [cnf transformation 46]
107. ~strong(X0) | old(X0) | ~humble(X0) [cnf transformation 58]
110. old(X0) | humble(X0) [cnf transformation 30]
113. ~old(X0) | ~tall(X0) [cnf transformation 30]
114. tall(susan) | ~humble(susan) | patient(X0) | ~quiet(X0) [cnf transformation 59]
128. strong(X0) | old(X0) | old(X0) | ~humble(X0) [cnf transformation 66]
141. curious(susan) [cnf transformation 19]
148. ~patient(alice) [cnf transformation 24]
149. strong(X0) | old(X0) | ~humble(X0) [duplicate literal removal 128]
155. ~curious(X0) | humble(X0) [duplicate literal removal 88]
156. patient(X0) | curious(X0) [duplicate literal removal 89]
158. 1 <=> humble(alice) [avatar definition]
179. 6 <=> ! [X1] : quiet(X1) [avatar definition]
180. quiet(X1) <- (6) [avatar component clause 179]
183. 6 | ~1 [avatar split clause 82,158,179]
253. 22 <=> humble(susan) [avatar definition]
257. 23 <=> tall(susan) [avatar definition]
259. tall(susan) <- (23) [avatar component clause 257]
262. 24 <=> ! [X0] : (patient(X0) | ~quiet(X0)) [avatar definition]
263. patient(X0) | ~quiet(X0) <- (24) [avatar component clause 262]
264. 24 | ~22 | 23 [avatar split clause 114,257,253,262]
295. strong(X0) | old(X0) [subsumption resolution 149,110]
348. humble(susan) [resolution 155,141]
351. 22 [avatar split clause 348,253]
353. curious(alice) [resolution 156,148]
356. humble(alice) [resolution 353,155]
359. 1 [avatar split clause 356,158]
386. old(X2) | ~humble(X2) | old(X2) [resolution 107,295]
387. old(X2) | ~humble(X2) [duplicate literal removal 386]
402. old(X2) [subsumption resolution 387,110]
420. ~tall(X0) [resolution 402,113]
477. $false <- (23) [resolution 420,259]
478. ~23 [avatar contradiction clause 477]
479. patient(X0) <- (6, 24) [subsumption resolution 263,180]
480. $false <- (6, 24) [resolution 479,148]
485. ~6 | ~24 [avatar contradiction clause 480]
486. $false [avatar sat refutation 183,264,351,359,478,485]
% SZS output end Proof for 5726070059072861602821957
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not kind is both not creative and not humble. If mary is quiet then someone is quiet or not tall. Everyone who is either not happy or not kind is calm or not patient. Everyone who is either not funny or creative is not creative and vice versa. Everyone who is either not rich or not happy is rich. Everyone who is not strong or rich is both calm and quiet and vice versa. If someone is either not old or creative then someone is both calm and not brave. Everyone who is either not wise or kind is both not old and not tall and vice versa. Everyone who is creative is not generous or not creative and vice versa. If paul is either not happy or not generous then someone is wise or not rich. If susan is old or not humble then someone is either generous or not humble and vice versa. Everyone who is not wise is either rich or strong and vice versa. Everyone who is happy or creative is either not calm or not quiet and vice versa. If mary is wise then fred is either not rich or not humble and vice versa. If alice is not curious then alice is both old and curious. Everyone who is either not curious or humble is both calm and not tall and vice versa. Someone is creative or calm. Someone is either brave or not wise. Someone is strong. Susan is either old or not funny. Someone is not wise. | Mary is generous. | contradiction | (![X]:((creative(X)<~>~kind(X))=>(~creative(X)&~humble(X))))&
((quiet(mary))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~happy(X)<~>~kind(X))=>(calm(X)|~patient(X))))&
(![X]:((~funny(X)<~>creative(X))<=>~creative(X)))&
(![X]:((~rich(X)<~>~happy(X))=>rich(X)))&
(![X]:((~strong(X)|rich(X))<=>(calm(X)&quiet(X))))&
((?[X]:((~old(X)<~>creative(X))))=>(?[X]:((calm(X)&~brave(X)))))&
(![X]:((~wise(X)<~>kind(X))<=>(~old(X)&~tall(X))))&
(![X]:(creative(X)<=>(~generous(X)|~creative(X))))&
(((~happy(paul)<~>~generous(paul)))=>(?[X]:((wise(X)|~rich(X)))))&
(((old(susan)|~humble(susan)))<=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:(~wise(X)<=>(rich(X)<~>strong(X))))&
(![X]:((happy(X)|creative(X))<=>(~calm(X)<~>~quiet(X))))&
((wise(mary))<=>((~rich(fred)<~>~humble(fred))))&
((~curious(alice))=>((old(alice)&curious(alice))))&
(![X]:((~curious(X)<~>humble(X))<=>(calm(X)&~tall(X))))&
(?[X]:((creative(X)|calm(X))))&
(?[X]:((brave(X)<~>~wise(X))))&
(?[X]:(strong(X)))&
((old(susan)<~>~funny(susan)))&
(?[X]:(~wise(X))) | generous(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6507867368348965757317726
% SZS output start Proof for 6507867368348965757317726
9. ! [X0] : (creative(X0) <=> (~creative(X0) | ~generous(X0))) [input p8]
22. generous(mary) [input hypothesis]
44. ! [X0] : ((creative(X0) | (creative(X0) & generous(X0))) & ((~creative(X0) | ~generous(X0)) | ~creative(X0))) [nnf transformation 9]
45. ! [X0] : ((creative(X0) | (creative(X0) & generous(X0))) & (~creative(X0) | ~generous(X0) | ~creative(X0))) [flattening 44]
96. ~creative(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 45]
98. creative(X0) | creative(X0) [cnf transformation 45]
136. generous(mary) [cnf transformation 22]
138. ~creative(X0) | ~generous(X0) [duplicate literal removal 96]
139. creative(X0) [duplicate literal removal 98]
176. ~generous(X0) [subsumption resolution 138,139]
242. $false [subsumption resolution 136,176]
% SZS output end Proof for 6507867368348965757317726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not wise or not funny then fred is both not quiet and happy and vice versa.
If someone is happy or not curious then lucy is either tall or not generous.
If susan is both not wise and not generous then someone is either generous or not humble.
Everyone who is both creative and wise is not generous and vice versa.
If someone is funny then someone is not kind or not generous and vice versa.
If someone is both not brave and curious then someone is generous or funny and vice versa.
Everyone who is either curious or not brave is not tall.
Everyone who is both strong and humble is both not kind and tall.
If someone is both strong and not wise then fred is not calm or not wise and vice versa.
If someone is not patient then lucy is brave and vice versa.
Everyone who is both not old and not quiet is both old and not calm.
Everyone who is either creative or funny is either kind or tall and vice versa.
Everyone who is rich is not tall or not quiet.
If fred is not wise then someone is both not humble and happy.
Everyone who is happy is either not wise or calm and vice versa.
If someone is not rich or patient then lucy is quiet or wise and vice versa.
Fred is both not creative and patient.
Someone is both not strong and generous.
Someone is not strong.
Lucy is funny or creative.
John is both not calm and not funny.
Someone is not quiet.
Mary is not kind or rich.
Someone is both patient and generous. | Fred is quiet. | neutral | (((~wise(alice)|~funny(alice)))<=>((~quiet(fred)&happy(fred))))&
((?[X]:((happy(X)|~curious(X))))=>((tall(lucy)<~>~generous(lucy))))&
(((~wise(susan)&~generous(susan)))=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:((creative(X)&wise(X))<=>~generous(X)))&
((?[X]:(funny(X)))<=>(?[X]:((~kind(X)|~generous(X)))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((generous(X)|funny(X)))))&
(![X]:((curious(X)<~>~brave(X))=>~tall(X)))&
(![X]:((strong(X)&humble(X))=>(~kind(X)&tall(X))))&
((?[X]:((strong(X)&~wise(X))))<=>((~calm(fred)|~wise(fred))))&
((?[X]:(~patient(X)))<=>(brave(lucy)))&
(![X]:((~old(X)&~quiet(X))=>(old(X)&~calm(X))))&
(![X]:((creative(X)<~>funny(X))<=>(kind(X)<~>tall(X))))&
(![X]:(rich(X)=>(~tall(X)|~quiet(X))))&
((~wise(fred))=>(?[X]:((~humble(X)&happy(X)))))&
(![X]:(happy(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((~rich(X)|patient(X))))<=>((quiet(lucy)|wise(lucy))))&
((~creative(fred)&patient(fred)))&
(?[X]:((~strong(X)&generous(X))))&
(?[X]:(~strong(X)))&
((funny(lucy)|creative(lucy)))&
((~calm(john)&~funny(john)))&
(?[X]:(~quiet(X)))&
((~kind(mary)|rich(mary)))&
(?[X]:((patient(X)&generous(X)))) | quiet(fred) | [] | null | 0 |
Everyone who is not brave is both not rich and creative and vice versa.
If someone is either not calm or not happy then someone is either old or creative.
Everyone who is either not patient or kind is strong or not curious and vice versa.
If someone is creative or humble then someone is quiet or not creative.
Everyone who is either quiet or not old is either not rich or quiet and vice versa.
Everyone who is either not tall or funny is either not rich or not calm.
If someone is both not kind and humble then fred is either not strong or not brave and vice versa.
Everyone who is creative or not rich is either funny or not funny and vice versa.
If someone is both not patient and not humble then someone is both not old and not creative and vice versa.
If paul is not creative or not rich then someone is either brave or not creative and vice versa.
If someone is both not curious and not tall then someone is either not rich or not old and vice versa.
Everyone who is either not calm or not rich is either rich or not humble and vice versa.
If someone is either not humble or happy then mary is not generous.
Everyone who is tall is brave.
Everyone who is not quiet is calm or not generous.
Alice is not generous or brave.
Mary is not kind.
Someone is not brave.
Someone is both creative and wise.
Fred is not kind or funny.
Someone is not generous.
Someone is both tall and generous. | Alice is not brave. | neutral | (![X]:(~brave(X)<=>(~rich(X)&creative(X))))&
((?[X]:((~calm(X)<~>~happy(X))))=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((~patient(X)<~>kind(X))<=>(strong(X)|~curious(X))))&
((?[X]:((creative(X)|humble(X))))=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:((quiet(X)<~>~old(X))<=>(~rich(X)<~>quiet(X))))&
(![X]:((~tall(X)<~>funny(X))=>(~rich(X)<~>~calm(X))))&
((?[X]:((~kind(X)&humble(X))))<=>((~strong(fred)<~>~brave(fred))))&
(![X]:((creative(X)|~rich(X))<=>(funny(X)<~>~funny(X))))&
((?[X]:((~patient(X)&~humble(X))))<=>(?[X]:((~old(X)&~creative(X)))))&
(((~creative(paul)|~rich(paul)))<=>(?[X]:((brave(X)<~>~creative(X)))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((~rich(X)<~>~old(X)))))&
(![X]:((~calm(X)<~>~rich(X))<=>(rich(X)<~>~humble(X))))&
((?[X]:((~humble(X)<~>happy(X))))=>(~generous(mary)))&
(![X]:(tall(X)=>brave(X)))&
(![X]:(~quiet(X)=>(calm(X)|~generous(X))))&
((~generous(alice)|brave(alice)))&
(~kind(mary))&
(?[X]:(~brave(X)))&
(?[X]:((creative(X)&wise(X))))&
((~kind(fred)|funny(fred)))&
(?[X]:(~generous(X)))&
(?[X]:((tall(X)&generous(X)))) | ~brave(alice) | [] | null | 0 |
If john is not wise or happy then lucy is either not humble or not wise and vice versa.
Everyone who is not rich is funny or tall and vice versa.
If susan is creative then alice is kind and vice versa.
If alice is curious then john is either humble or not funny and vice versa.
If someone is either brave or not humble then paul is either quiet or creative.
If someone is either generous or not patient then alice is either not old or old and vice versa.
If someone is not creative or not strong then paul is either not patient or happy.
Everyone who is not creative is either humble or not creative.
Everyone who is both not calm and calm is not rich or not patient.
Everyone who is old or happy is not curious.
If paul is brave or not creative then john is funny.
Everyone who is not funny is both not wise and humble.
Everyone who is funny or rich is either not rich or not kind.
If paul is either not humble or not quiet then john is not happy or not tall.
If john is either strong or not quiet then john is either quiet or not creative.
Everyone who is both strong and not humble is tall or creative and vice versa.
Mary is not generous or curious.
Paul is funny.
Someone is either kind or not tall.
Someone is both strong and not humble.
Paul is either not creative or not old.
Someone is old or brave.
Someone is either rich or not curious.
Paul is either wise or not funny. | Lucy is not rich. | entailment | (((~wise(john)|happy(john)))<=>((~humble(lucy)<~>~wise(lucy))))&
(![X]:(~rich(X)<=>(funny(X)|tall(X))))&
((creative(susan))<=>(kind(alice)))&
((curious(alice))<=>((humble(john)<~>~funny(john))))&
((?[X]:((brave(X)<~>~humble(X))))=>((quiet(paul)<~>creative(paul))))&
((?[X]:((generous(X)<~>~patient(X))))<=>((~old(alice)<~>old(alice))))&
((?[X]:((~creative(X)|~strong(X))))=>((~patient(paul)<~>happy(paul))))&
(![X]:(~creative(X)=>(humble(X)<~>~creative(X))))&
(![X]:((~calm(X)&calm(X))=>(~rich(X)|~patient(X))))&
(![X]:((old(X)|happy(X))=>~curious(X)))&
(((brave(paul)|~creative(paul)))=>(funny(john)))&
(![X]:(~funny(X)=>(~wise(X)&humble(X))))&
(![X]:((funny(X)|rich(X))=>(~rich(X)<~>~kind(X))))&
(((~humble(paul)<~>~quiet(paul)))=>((~happy(john)|~tall(john))))&
(((strong(john)<~>~quiet(john)))=>((quiet(john)<~>~creative(john))))&
(![X]:((strong(X)&~humble(X))<=>(tall(X)|creative(X))))&
((~generous(mary)|curious(mary)))&
(funny(paul))&
(?[X]:((kind(X)<~>~tall(X))))&
(?[X]:((strong(X)&~humble(X))))&
((~creative(paul)<~>~old(paul)))&
(?[X]:((old(X)|brave(X))))&
(?[X]:((rich(X)<~>~curious(X))))&
((wise(paul)<~>~funny(paul))) | ~rich(lucy) | [
"p1",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8683952877358009274444918
% SZS output start Proof for 8683952877358009274444918
2. ! [X0] : (~rich(X0) <=> (tall(X0) | funny(X0))) [input p1]
8. ! [X0] : (~creative(X0) => (humble(X0) <~> ~creative(X0))) [input p7]
12. ! [X0] : (~funny(X0) => (humble(X0) & ~wise(X0))) [input p11]
16. ! [X0] : ((~humble(X0) & strong(X0)) <=> (creative(X0) | tall(X0))) [input p15]
25. rich(lucy) [input hypothesis]
28. ! [X0] : ((humble(X0) <~> ~creative(X0)) | creative(X0)) [ennf transformation 8]
33. ! [X0] : ((humble(X0) & ~wise(X0)) | funny(X0)) [ennf transformation 12]
40. ! [X0] : ((~rich(X0) | (~tall(X0) & ~funny(X0))) & ((tall(X0) | funny(X0)) | rich(X0))) [nnf transformation 2]
41. ! [X0] : ((~rich(X0) | (~tall(X0) & ~funny(X0))) & (tall(X0) | funny(X0) | rich(X0))) [flattening 40]
50. ! [X0] : (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | creative(X0)) [nnf transformation 28]
54. ! [X0] : (((~humble(X0) & strong(X0)) | (~creative(X0) & ~tall(X0))) & ((creative(X0) | tall(X0)) | (humble(X0) | ~strong(X0)))) [nnf transformation 16]
55. ! [X0] : (((~humble(X0) & strong(X0)) | (~creative(X0) & ~tall(X0))) & (creative(X0) | tall(X0) | humble(X0) | ~strong(X0))) [flattening 54]
75. ~funny(X0) | ~rich(X0) [cnf transformation 41]
100. creative(X0) | ~humble(X0) | creative(X0) [cnf transformation 50]
107. funny(X0) | humble(X0) [cnf transformation 33]
122. ~humble(X0) | ~creative(X0) [cnf transformation 55]
136. rich(lucy) [cnf transformation 25]
140. creative(X0) | ~humble(X0) [duplicate literal removal 100]
276. ~humble(X0) [subsumption resolution 122,140]
330. humble(X0) | ~rich(X0) [resolution 107,75]
331. ~rich(X0) [subsumption resolution 330,276]
332. $false [resolution 331,136]
% SZS output end Proof for 8683952877358009274444918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either not brave or not happy.
If fred is not patient then alice is humble or not quiet and vice versa.
Everyone who is either creative or tall is not funny or humble and vice versa.
Everyone who is not patient or humble is not humble.
If susan is both creative and not calm then someone is funny and vice versa.
Everyone who is rich is brave or not patient.
Everyone who is not humble or wise is both not curious and patient.
Everyone who is calm is either patient or wise and vice versa.
Everyone who is either humble or brave is both not funny and not calm.
Everyone who is not tall is both tall and not brave.
Everyone who is either kind or not generous is both not humble and quiet and vice versa.
If john is happy or not humble then someone is both creative and not rich.
Everyone who is not quiet or not kind is either kind or brave.
If fred is not patient then susan is not rich or not generous.
Everyone who is both patient and not patient is either kind or happy and vice versa.
Someone is wise or not curious.
Susan is either not old or rich.
Someone is not happy or not kind.
Someone is either not kind or curious.
Mary is not brave or not old.
Someone is not strong. | Susan is not happy. | contradiction | (![X]:(wise(X)=>(~brave(X)<~>~happy(X))))&
((~patient(fred))<=>((humble(alice)|~quiet(alice))))&
(![X]:((creative(X)<~>tall(X))<=>(~funny(X)|humble(X))))&
(![X]:((~patient(X)|humble(X))=>~humble(X)))&
(((creative(susan)&~calm(susan)))<=>(?[X]:(funny(X))))&
(![X]:(rich(X)=>(brave(X)|~patient(X))))&
(![X]:((~humble(X)|wise(X))=>(~curious(X)&patient(X))))&
(![X]:(calm(X)<=>(patient(X)<~>wise(X))))&
(![X]:((humble(X)<~>brave(X))=>(~funny(X)&~calm(X))))&
(![X]:(~tall(X)=>(tall(X)&~brave(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(~humble(X)&quiet(X))))&
(((happy(john)|~humble(john)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((~quiet(X)|~kind(X))=>(kind(X)<~>brave(X))))&
((~patient(fred))=>((~rich(susan)|~generous(susan))))&
(![X]:((patient(X)&~patient(X))<=>(kind(X)<~>happy(X))))&
(?[X]:((wise(X)|~curious(X))))&
((~old(susan)<~>rich(susan)))&
(?[X]:((~happy(X)|~kind(X))))&
(?[X]:((~kind(X)<~>curious(X))))&
((~brave(mary)|~old(mary)))&
(?[X]:(~strong(X))) | ~happy(susan) | [
"p2",
"p3",
"p4",
"p6",
"p8",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8505737868713252461208840
% SZS output start Proof for 8505737868713252461208840
3. ! [X0] : ((creative(X0) <~> tall(X0)) <=> (humble(X0) | ~funny(X0))) [input p2]
4. ! [X0] : ((humble(X0) | ~patient(X0)) => ~humble(X0)) [input p3]
5. (~calm(susan) & creative(susan)) <=> ? [X0] : funny(X0) [input p4]
7. ! [X0] : ((wise(X0) | ~humble(X0)) => (patient(X0) & ~curious(X0))) [input p6]
9. ! [X0] : ((humble(X0) <~> brave(X0)) => (~calm(X0) & ~funny(X0))) [input p8]
10. ! [X0] : (~tall(X0) => (~brave(X0) & tall(X0))) [input p9]
12. (~humble(john) | happy(john)) => ? [X0] : (~rich(X0) & creative(X0)) [input p11]
13. ! [X0] : ((~kind(X0) | ~quiet(X0)) => (kind(X0) <~> brave(X0))) [input p12]
15. ! [X0] : ((~patient(X0) & patient(X0)) <=> (kind(X0) <~> happy(X0))) [input p14]
22. ~happy(susan) [input hypothesis]
25. ! [X0] : (~humble(X0) | (~humble(X0) & patient(X0))) [ennf transformation 4]
28. ! [X0] : ((patient(X0) & ~curious(X0)) | (~wise(X0) & humble(X0))) [ennf transformation 7]
29. ! [X0] : ((~calm(X0) & ~funny(X0)) | (humble(X0) <=> brave(X0))) [ennf transformation 9]
30. ! [X0] : ((~brave(X0) & tall(X0)) | tall(X0)) [ennf transformation 10]
31. ? [X0] : (~rich(X0) & creative(X0)) | (humble(john) & ~happy(john)) [ennf transformation 12]
32. ! [X0] : ((kind(X0) <~> brave(X0)) | (kind(X0) & quiet(X0))) [ennf transformation 13]
38. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~humble(X0) & funny(X0))) & ((humble(X0) | ~funny(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [nnf transformation 3]
39. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~humble(X0) & funny(X0))) & (humble(X0) | ~funny(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [flattening 38]
40. ((~calm(susan) & creative(susan)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | (calm(susan) | ~creative(susan))) [nnf transformation 5]
41. ((~calm(susan) & creative(susan)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | calm(susan) | ~creative(susan)) [flattening 40]
42. ((~calm(susan) & creative(susan)) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | calm(susan) | ~creative(susan)) [rectify 41]
43. ? [X1] : funny(X1) => funny(sK0) [choice axiom]
44. ((~calm(susan) & creative(susan)) | ! [X0] : ~funny(X0)) & (funny(sK0) | calm(susan) | ~creative(susan)) [skolemisation 42,43]
46. ! [X0] : ((~calm(X0) & ~funny(X0)) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) [nnf transformation 29]
49. ? [X0] : (~rich(X0) & creative(X0)) => (~rich(sK1) & creative(sK1)) [choice axiom]
50. (~rich(sK1) & creative(sK1)) | (humble(john) & ~happy(john)) [skolemisation 31,49]
51. ! [X0] : (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | (kind(X0) & quiet(X0))) [nnf transformation 32]
52. ! [X0] : (((~patient(X0) & patient(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (patient(X0) | ~patient(X0)))) [nnf transformation 15]
53. ! [X0] : (((~patient(X0) & patient(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | patient(X0) | ~patient(X0))) [flattening 52]
71. ~tall(X0) | ~creative(X0) | funny(X0) [cnf transformation 39]
74. ~humble(X0) | ~humble(X0) [cnf transformation 25]
76. creative(susan) | ~funny(X0) [cnf transformation 44]
81. patient(X0) | humble(X0) [cnf transformation 28]
88. ~funny(X0) | humble(X0) | ~brave(X0) [cnf transformation 46]
91. tall(X0) | tall(X0) [cnf transformation 30]
100. creative(sK1) | humble(john) [cnf transformation 50]
104. brave(X0) | kind(X0) | kind(X0) [cnf transformation 51]
112. ~patient(X0) | happy(X0) | ~kind(X0) [cnf transformation 53]
121. ~happy(susan) [cnf transformation 22]
122. kind(X0) | brave(X0) [duplicate literal removal 104]
123. tall(X0) [duplicate literal removal 91]
124. ~humble(X0) [duplicate literal removal 74]
141. 4 <=> ! [X0] : ~funny(X0) [avatar definition]
142. ~funny(X0) <- (4) [avatar component clause 141]
149. 6 <=> creative(susan) [avatar definition]
151. creative(susan) <- (6) [avatar component clause 149]
152. 4 | 6 [avatar split clause 76,149,141]
158. patient(X0) [subsumption resolution 81,124]
163. ~funny(X0) | ~brave(X0) [subsumption resolution 88,124]
167. creative(sK1) [subsumption resolution 100,124]
169. ~kind(X0) | happy(X0) [subsumption resolution 112,158]
199. happy(X0) | brave(X0) [resolution 169,122]
208. brave(susan) [resolution 199,121]
211. ~creative(X0) | funny(X0) [resolution 71,123]
212. ~creative(X0) <- (4) [subsumption resolution 211,142]
213. $false <- (4) [resolution 212,167]
214. ~4 [avatar contradiction clause 213]
223. funny(susan) <- (6) [resolution 211,151]
228. ~brave(susan) <- (6) [resolution 223,163]
229. $false <- (6) [subsumption resolution 228,208]
230. ~6 [avatar contradiction clause 229]
231. $false [avatar sat refutation 152,214,230]
% SZS output end Proof for 8505737868713252461208840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not curious is either strong or generous.
If lucy is tall then lucy is not happy or happy and vice versa.
If someone is not calm then lucy is either not wise or humble.
Everyone who is humble or strong is both not patient and patient.
If mary is creative then someone is either quiet or kind and vice versa.
If someone is either kind or quiet then someone is not wise and vice versa.
Everyone who is either tall or not rich is happy or creative and vice versa.
If alice is both not funny and not kind then someone is not old and vice versa.
Everyone who is brave is not kind and vice versa.
Everyone who is both curious and not funny is curious or happy.
Everyone who is brave or calm is both not brave and not quiet and vice versa.
If someone is either not calm or not curious then susan is not creative or not old and vice versa.
Everyone who is both kind and not calm is rich or kind.
Everyone who is rich or not wise is generous.
Everyone who is not strong is not tall or patient.
Everyone who is both not creative and not generous is not calm and vice versa.
Someone is not calm.
Someone is either happy or not humble.
Someone is quiet.
Someone is both not quiet and not patient.
Susan is either not curious or not creative.
Someone is old or tall.
Mary is wise or not patient. | Susan is strong. | contradiction | (![X]:((kind(X)<~>~curious(X))=>(strong(X)<~>generous(X))))&
((tall(lucy))<=>((~happy(lucy)|happy(lucy))))&
((?[X]:(~calm(X)))=>((~wise(lucy)<~>humble(lucy))))&
(![X]:((humble(X)|strong(X))=>(~patient(X)&patient(X))))&
((creative(mary))<=>(?[X]:((quiet(X)<~>kind(X)))))&
((?[X]:((kind(X)<~>quiet(X))))<=>(?[X]:(~wise(X))))&
(![X]:((tall(X)<~>~rich(X))<=>(happy(X)|creative(X))))&
(((~funny(alice)&~kind(alice)))<=>(?[X]:(~old(X))))&
(![X]:(brave(X)<=>~kind(X)))&
(![X]:((curious(X)&~funny(X))=>(curious(X)|happy(X))))&
(![X]:((brave(X)|calm(X))<=>(~brave(X)&~quiet(X))))&
((?[X]:((~calm(X)<~>~curious(X))))<=>((~creative(susan)|~old(susan))))&
(![X]:((kind(X)&~calm(X))=>(rich(X)|kind(X))))&
(![X]:((rich(X)|~wise(X))=>generous(X)))&
(![X]:(~strong(X)=>(~tall(X)|patient(X))))&
(![X]:((~creative(X)&~generous(X))<=>~calm(X)))&
(?[X]:(~calm(X)))&
(?[X]:((happy(X)<~>~humble(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~quiet(X)&~patient(X))))&
((~curious(susan)<~>~creative(susan)))&
(?[X]:((old(X)|tall(X))))&
((wise(mary)|~patient(mary))) | strong(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8573554120412444773406340
% SZS output start Proof for 8573554120412444773406340
4. ! [X0] : ((strong(X0) | humble(X0)) => (patient(X0) & ~patient(X0))) [input p3]
24. strong(susan) [input hypothesis]
28. ! [X0] : ((patient(X0) & ~patient(X0)) | (~strong(X0) & ~humble(X0))) [ennf transformation 4]
88. ~patient(X0) | ~strong(X0) [cnf transformation 28]
90. patient(X0) | ~strong(X0) [cnf transformation 28]
139. strong(susan) [cnf transformation 24]
165. ~strong(X0) [subsumption resolution 88,90]
280. $false [subsumption resolution 139,165]
% SZS output end Proof for 8573554120412444773406340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is curious or brave and vice versa.
Everyone who is not curious or not generous is curious.
If lucy is both not wise and not quiet then john is both not curious and quiet.
Everyone who is both funny and not old is both not strong and creative.
Everyone who is both not brave and not patient is both brave and tall.
Everyone who is either creative or tall is not old or wise and vice versa.
Everyone who is either not rich or not strong is not wise.
If paul is both kind and tall then someone is not brave and vice versa.
Everyone who is either curious or old is not rich or rich.
Everyone who is not brave is either not strong or not wise and vice versa.
Everyone who is not humble is both humble and strong and vice versa.
If mary is not strong or old then someone is funny or brave.
Everyone who is both humble and not rich is either funny or kind.
Everyone who is rich or quiet is curious or strong.
If someone is both funny and strong then someone is both not tall and not kind.
Everyone who is humble is calm and vice versa.
Someone is patient.
Lucy is both not tall and not generous.
Mary is both not generous and old.
Alice is not creative or humble.
Someone is either funny or curious.
Someone is happy.
Paul is old.
Mary is either not quiet or not curious. | Paul is not creative. | entailment | (![X]:(~tall(X)<=>(curious(X)|brave(X))))&
(![X]:((~curious(X)|~generous(X))=>curious(X)))&
(((~wise(lucy)&~quiet(lucy)))=>((~curious(john)&quiet(john))))&
(![X]:((funny(X)&~old(X))=>(~strong(X)&creative(X))))&
(![X]:((~brave(X)&~patient(X))=>(brave(X)&tall(X))))&
(![X]:((creative(X)<~>tall(X))<=>(~old(X)|wise(X))))&
(![X]:((~rich(X)<~>~strong(X))=>~wise(X)))&
(((kind(paul)&tall(paul)))<=>(?[X]:(~brave(X))))&
(![X]:((curious(X)<~>old(X))=>(~rich(X)|rich(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~wise(X))))&
(![X]:(~humble(X)<=>(humble(X)&strong(X))))&
(((~strong(mary)|old(mary)))=>(?[X]:((funny(X)|brave(X)))))&
(![X]:((humble(X)&~rich(X))=>(funny(X)<~>kind(X))))&
(![X]:((rich(X)|quiet(X))=>(curious(X)|strong(X))))&
((?[X]:((funny(X)&strong(X))))=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:(humble(X)<=>calm(X)))&
(?[X]:(patient(X)))&
((~tall(lucy)&~generous(lucy)))&
((~generous(mary)&old(mary)))&
((~creative(alice)|humble(alice)))&
(?[X]:((funny(X)<~>curious(X))))&
(?[X]:(happy(X)))&
(old(paul))&
((~quiet(mary)<~>~curious(mary))) | ~creative(paul) | [
"p0",
"p1",
"p5",
"p7",
"p9",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2073612464108907437525565
% SZS output start Proof for 2073612464108907437525565
1. ! [X0] : (~tall(X0) <=> (brave(X0) | curious(X0))) [input p0]
2. ! [X0] : ((~generous(X0) | ~curious(X0)) => curious(X0)) [input p1]
6. ! [X0] : ((creative(X0) <~> tall(X0)) <=> (wise(X0) | ~old(X0))) [input p5]
8. (tall(paul) & kind(paul)) <=> ? [X0] : ~brave(X0) [input p7]
10. ! [X0] : (~brave(X0) <=> (~strong(X0) <~> ~wise(X0))) [input p9]
11. ! [X0] : (~humble(X0) <=> (strong(X0) & humble(X0))) [input p10]
23. old(paul) [input p22]
25. creative(paul) [input hypothesis]
30. ! [X0] : (curious(X0) | (generous(X0) & curious(X0))) [ennf transformation 2]
44. ! [X0] : ((~tall(X0) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | tall(X0))) [nnf transformation 1]
45. ! [X0] : ((~tall(X0) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | tall(X0))) [flattening 44]
46. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~wise(X0) & old(X0))) & ((wise(X0) | ~old(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [nnf transformation 6]
47. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~wise(X0) & old(X0))) & (wise(X0) | ~old(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [flattening 46]
49. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~tall(paul) | ~kind(paul))) [nnf transformation 8]
50. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~tall(paul) | ~kind(paul)) [flattening 49]
51. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~tall(paul) | ~kind(paul)) [rectify 50]
52. ? [X1] : ~brave(X1) => ~brave(sK0) [choice axiom]
53. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (~brave(sK0) | ~tall(paul) | ~kind(paul)) [skolemisation 51,52]
55. ! [X0] : ((~brave(X0) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | brave(X0))) [nnf transformation 10]
56. ! [X0] : ((~humble(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | humble(X0))) [nnf transformation 11]
57. ! [X0] : ((~humble(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | humble(X0))) [flattening 56]
70. ~curious(X0) | ~tall(X0) [cnf transformation 45]
72. curious(X0) | curious(X0) [cnf transformation 30]
78. ~creative(X0) | ~old(X0) | tall(X0) | wise(X0) [cnf transformation 47]
88. tall(paul) | brave(X0) [cnf transformation 53]
93. ~wise(X0) | ~brave(X0) | strong(X0) [cnf transformation 55]
95. humble(X0) | humble(X0) [cnf transformation 57]
97. ~humble(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 57]
115. old(paul) [cnf transformation 23]
118. creative(paul) [cnf transformation 25]
119. humble(X0) [duplicate literal removal 95]
120. ~humble(X0) | ~strong(X0) [duplicate literal removal 97]
121. curious(X0) [duplicate literal removal 72]
138. 4 <=> ! [X0] : brave(X0) [avatar definition]
139. brave(X0) <- (4) [avatar component clause 138]
141. 5 <=> tall(paul) [avatar definition]
142. ~tall(paul) <- (~5) [avatar component clause 141]
143. tall(paul) <- (5) [avatar component clause 141]
144. 4 | 5 [avatar split clause 88,141,138]
192. ~tall(X0) [resolution 70,121]
197. ~strong(X1) [resolution 120,119]
235. ~old(paul) | tall(paul) | wise(paul) [resolution 78,118]
238. tall(paul) | wise(paul) [subsumption resolution 235,115]
239. wise(paul) <- (~5) [subsumption resolution 238,142]
242. ~brave(paul) | strong(paul) <- (~5) [resolution 239,93]
244. strong(paul) <- (4, ~5) [subsumption resolution 242,139]
245. $false <- (4, ~5) [subsumption resolution 244,197]
246. ~4 | 5 [avatar contradiction clause 245]
250. $false <- (5) [subsumption resolution 143,192]
251. ~5 [avatar contradiction clause 250]
252. $false [avatar sat refutation 144,246,251]
% SZS output end Proof for 2073612464108907437525565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both patient and wise then someone is both tall and not curious.
Everyone who is funny is either wise or old and vice versa.
Everyone who is either wise or calm is not creative and vice versa.
If john is either not rich or brave then someone is both not quiet and not generous and vice versa.
If paul is funny then paul is not funny or wise and vice versa.
Everyone who is either quiet or not creative is quiet and vice versa.
If someone is curious then mary is old.
If someone is either quiet or rich then fred is not quiet or not rich.
If susan is both not strong and not humble then mary is either not humble or kind and vice versa.
If someone is quiet then fred is either not tall or not generous.
Everyone who is either calm or funny is both strong and not brave.
If someone is kind then someone is either patient or happy.
If someone is both not happy and funny then mary is brave or not generous and vice versa.
Everyone who is not rich or generous is either humble or not quiet and vice versa.
Everyone who is not quiet or creative is both brave and quiet.
Everyone who is not brave is both not quiet and not patient and vice versa.
Alice is either not tall or not calm.
Susan is either rich or old.
Fred is both happy and wise.
Fred is happy.
Someone is both creative and generous.
Someone is not generous or creative. | Paul is patient. | neutral | ((?[X]:((patient(X)&wise(X))))=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:(funny(X)<=>(wise(X)<~>old(X))))&
(![X]:((wise(X)<~>calm(X))<=>~creative(X)))&
(((~rich(john)<~>brave(john)))<=>(?[X]:((~quiet(X)&~generous(X)))))&
((funny(paul))<=>((~funny(paul)|wise(paul))))&
(![X]:((quiet(X)<~>~creative(X))<=>quiet(X)))&
((?[X]:(curious(X)))=>(old(mary)))&
((?[X]:((quiet(X)<~>rich(X))))=>((~quiet(fred)|~rich(fred))))&
(((~strong(susan)&~humble(susan)))<=>((~humble(mary)<~>kind(mary))))&
((?[X]:(quiet(X)))=>((~tall(fred)<~>~generous(fred))))&
(![X]:((calm(X)<~>funny(X))=>(strong(X)&~brave(X))))&
((?[X]:(kind(X)))=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((~happy(X)&funny(X))))<=>((brave(mary)|~generous(mary))))&
(![X]:((~rich(X)|generous(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|creative(X))=>(brave(X)&quiet(X))))&
(![X]:(~brave(X)<=>(~quiet(X)&~patient(X))))&
((~tall(alice)<~>~calm(alice)))&
((rich(susan)<~>old(susan)))&
((happy(fred)&wise(fred)))&
(happy(fred))&
(?[X]:((creative(X)&generous(X))))&
(?[X]:((~generous(X)|creative(X)))) | patient(paul) | [] | null | 0 |
Everyone who is either not wise or wise is both not funny and old and vice versa.
Everyone who is both wise and rich is both happy and not curious.
Everyone who is strong is wise and vice versa.
Everyone who is both quiet and tall is either strong or not old and vice versa.
Everyone who is both old and quiet is both strong and not strong and vice versa.
If lucy is both not brave and not creative then someone is not old or not quiet and vice versa.
Everyone who is not generous or not curious is either happy or wise.
If alice is both tall and not creative then lucy is not curious.
If someone is wise then john is both brave and not curious and vice versa.
Everyone who is not rich is quiet or not funny.
If someone is not patient then someone is wise or kind and vice versa.
Everyone who is both not happy and calm is not creative.
Everyone who is either old or generous is brave or not patient and vice versa.
Everyone who is both creative and not rich is brave or kind.
If someone is both patient and not old then someone is not calm or humble.
Everyone who is not humble or not curious is both not patient and not tall.
Someone is both kind and not strong.
Someone is not wise or happy.
Someone is not rich or not humble.
Fred is either not wise or kind.
Susan is generous.
Someone is either not funny or kind.
Someone is both not tall and calm. | Susan is not patient. | contradiction | (![X]:((~wise(X)<~>wise(X))<=>(~funny(X)&old(X))))&
(![X]:((wise(X)&rich(X))=>(happy(X)&~curious(X))))&
(![X]:(strong(X)<=>wise(X)))&
(![X]:((quiet(X)&tall(X))<=>(strong(X)<~>~old(X))))&
(![X]:((old(X)&quiet(X))<=>(strong(X)&~strong(X))))&
(((~brave(lucy)&~creative(lucy)))<=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:((~generous(X)|~curious(X))=>(happy(X)<~>wise(X))))&
(((tall(alice)&~creative(alice)))=>(~curious(lucy)))&
((?[X]:(wise(X)))<=>((brave(john)&~curious(john))))&
(![X]:(~rich(X)=>(quiet(X)|~funny(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((~happy(X)&calm(X))=>~creative(X)))&
(![X]:((old(X)<~>generous(X))<=>(brave(X)|~patient(X))))&
(![X]:((creative(X)&~rich(X))=>(brave(X)|kind(X))))&
((?[X]:((patient(X)&~old(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~humble(X)|~curious(X))=>(~patient(X)&~tall(X))))&
(?[X]:((kind(X)&~strong(X))))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((~rich(X)|~humble(X))))&
((~wise(fred)<~>kind(fred)))&
(generous(susan))&
(?[X]:((~funny(X)<~>kind(X))))&
(?[X]:((~tall(X)&calm(X)))) | ~patient(susan) | [
"p0",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 740211501530104601526672
% SZS output start Proof for 740211501530104601526672
1. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (old(X0) & ~funny(X0))) [input p0]
13. ! [X0] : ((old(X0) <~> generous(X0)) <=> (~patient(X0) | brave(X0))) [input p12]
21. generous(susan) [input p20]
24. ~patient(susan) [input hypothesis]
40. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 1]
41. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 40]
63. ! [X0] : ((((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (patient(X0) & ~brave(X0))) & ((~patient(X0) | brave(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))))) [nnf transformation 13]
64. ! [X0] : ((((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (patient(X0) & ~brave(X0))) & (~patient(X0) | brave(X0) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))))) [flattening 63]
82. old(X0) | wise(X0) | wise(X0) [cnf transformation 41]
83. old(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 41]
123. ~generous(X0) | ~old(X0) | patient(X0) [cnf transformation 64]
136. generous(susan) [cnf transformation 21]
141. ~patient(susan) [cnf transformation 24]
144. old(X0) | wise(X0) [duplicate literal removal 82]
145. ~wise(X0) | old(X0) [duplicate literal removal 83]
146. old(X0) [subsumption resolution 144,145]
209. ~generous(X0) | patient(X0) [subsumption resolution 123,146]
255. patient(susan) [resolution 209,136]
256. $false [subsumption resolution 255,141]
% SZS output end Proof for 740211501530104601526672
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or patient is not creative and vice versa. If someone is both not generous and not curious then someone is not tall or not kind. Everyone who is both calm and happy is not curious and vice versa. Everyone who is either quiet or happy is either not patient or not quiet and vice versa. Everyone who is not happy is not tall. If lucy is not quiet or not tall then fred is both not tall and not strong and vice versa. Everyone who is not calm is brave or happy. If someone is either not generous or generous then susan is not creative and vice versa. If susan is either creative or happy then mary is either generous or curious and vice versa. If someone is either old or not calm then alice is both wise and not happy and vice versa. Everyone who is patient or not kind is not humble. If susan is not rich then alice is both not generous and humble and vice versa. Everyone who is not creative or not funny is not rich or not patient and vice versa. Everyone who is brave is both curious and rich and vice versa. If alice is strong then someone is either tall or funny. Everyone who is not funny or brave is either not happy or not strong and vice versa. Fred is patient or creative. Someone is either not generous or strong. Mary is both wise and happy. Someone is either quiet or generous. Someone is either not curious or old. Fred is both not humble and brave. Someone is both not generous and not happy. Paul is either rich or quiet. | Mary is not humble. | entailment | (![X]:((~brave(X)<~>patient(X))<=>~creative(X)))&
((?[X]:((~generous(X)&~curious(X))))=>(?[X]:((~tall(X)|~kind(X)))))&
(![X]:((calm(X)&happy(X))<=>~curious(X)))&
(![X]:((quiet(X)<~>happy(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:(~happy(X)=>~tall(X)))&
(((~quiet(lucy)|~tall(lucy)))<=>((~tall(fred)&~strong(fred))))&
(![X]:(~calm(X)=>(brave(X)|happy(X))))&
((?[X]:((~generous(X)<~>generous(X))))<=>(~creative(susan)))&
(((creative(susan)<~>happy(susan)))<=>((generous(mary)<~>curious(mary))))&
((?[X]:((old(X)<~>~calm(X))))<=>((wise(alice)&~happy(alice))))&
(![X]:((patient(X)|~kind(X))=>~humble(X)))&
((~rich(susan))<=>((~generous(alice)&humble(alice))))&
(![X]:((~creative(X)|~funny(X))<=>(~rich(X)|~patient(X))))&
(![X]:(brave(X)<=>(curious(X)&rich(X))))&
((strong(alice))=>(?[X]:((tall(X)<~>funny(X)))))&
(![X]:((~funny(X)|brave(X))<=>(~happy(X)<~>~strong(X))))&
((patient(fred)|creative(fred)))&
(?[X]:((~generous(X)<~>strong(X))))&
((wise(mary)&happy(mary)))&
(?[X]:((quiet(X)<~>generous(X))))&
(?[X]:((~curious(X)<~>old(X))))&
((~humble(fred)&brave(fred)))&
(?[X]:((~generous(X)&~happy(X))))&
((rich(paul)<~>quiet(paul))) | ~humble(mary) | [
"p3",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8396933654466366387106893
% SZS output start Proof for 8396933654466366387106893
4. ! [X0] : ((quiet(X0) <~> happy(X0)) <=> (~patient(X0) <~> ~quiet(X0))) [input p3]
11. ! [X0] : ((~kind(X0) | patient(X0)) => ~humble(X0)) [input p10]
19. happy(mary) & wise(mary) [input p18]
25. humble(mary) [input hypothesis]
31. ! [X0] : (~humble(X0) | (kind(X0) & ~patient(X0))) [ennf transformation 11]
39. ! [X0] : ((((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0))))) [nnf transformation 4]
86. quiet(X0) | patient(X0) | quiet(X0) | ~happy(X0) [cnf transformation 39]
89. ~happy(X0) | ~quiet(X0) | ~quiet(X0) | patient(X0) [cnf transformation 39]
116. ~humble(X0) | ~patient(X0) [cnf transformation 31]
140. happy(mary) [cnf transformation 19]
151. humble(mary) [cnf transformation 25]
155. quiet(X0) | patient(X0) | ~happy(X0) [duplicate literal removal 86]
157. ~happy(X0) | ~quiet(X0) | patient(X0) [duplicate literal removal 89]
170. ~happy(X0) | patient(X0) [subsumption resolution 155,157]
335. ~patient(mary) [resolution 116,151]
341. patient(mary) [resolution 170,140]
343. $false [subsumption resolution 341,335]
% SZS output end Proof for 8396933654466366387106893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is rich then john is both curious and not kind and vice versa. If someone is both not brave and kind then fred is either not rich or happy and vice versa. Everyone who is both not old and kind is both tall and quiet and vice versa. If someone is not strong then paul is both not creative and not happy and vice versa. Everyone who is both strong and not rich is either not funny or happy and vice versa. If someone is patient then someone is either old or not curious and vice versa. If someone is both not old and funny then john is not humble or creative. If john is both not creative and not humble then someone is not brave and vice versa. If someone is patient or tall then alice is patient and vice versa. If fred is both not kind and not happy then someone is either not happy or strong and vice versa. If mary is both not calm and not creative then someone is both kind and not old and vice versa. If susan is both brave and not quiet then paul is both generous and tall. Everyone who is happy or funny is not rich. Everyone who is either not tall or tall is either humble or rich and vice versa. If john is not tall or not wise then someone is both calm and not generous and vice versa. Everyone who is either not calm or not wise is either humble or not curious. John is not kind or kind. Someone is not brave or not wise. Someone is either not old or not wise. Susan is not curious. Lucy is not patient. Someone is creative or not patient. | Susan is brave. | entailment | ((rich(alice))<=>((curious(john)&~kind(john))))&
((?[X]:((~brave(X)&kind(X))))<=>((~rich(fred)<~>happy(fred))))&
(![X]:((~old(X)&kind(X))<=>(tall(X)&quiet(X))))&
((?[X]:(~strong(X)))<=>((~creative(paul)&~happy(paul))))&
(![X]:((strong(X)&~rich(X))<=>(~funny(X)<~>happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((old(X)<~>~curious(X)))))&
((?[X]:((~old(X)&funny(X))))=>((~humble(john)|creative(john))))&
(((~creative(john)&~humble(john)))<=>(?[X]:(~brave(X))))&
((?[X]:((patient(X)|tall(X))))<=>(patient(alice)))&
(((~kind(fred)&~happy(fred)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(((~calm(mary)&~creative(mary)))<=>(?[X]:((kind(X)&~old(X)))))&
(((brave(susan)&~quiet(susan)))=>((generous(paul)&tall(paul))))&
(![X]:((happy(X)|funny(X))=>~rich(X)))&
(![X]:((~tall(X)<~>tall(X))<=>(humble(X)<~>rich(X))))&
(((~tall(john)|~wise(john)))<=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((~calm(X)<~>~wise(X))=>(humble(X)<~>~curious(X))))&
((~kind(john)|kind(john)))&
(?[X]:((~brave(X)|~wise(X))))&
(?[X]:((~old(X)<~>~wise(X))))&
(~curious(susan))&
(~patient(lucy))&
(?[X]:((creative(X)|~patient(X)))) | brave(susan) | [
"p4",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4198991412377436671142477
% SZS output start Proof for 4198991412377436671142477
5. ! [X0] : ((~rich(X0) & strong(X0)) <=> (~funny(X0) <~> happy(X0))) [input p4]
8. (~humble(john) & ~creative(john)) <=> ? [X0] : ~brave(X0) [input p7]
13. ! [X0] : ((funny(X0) | happy(X0)) => ~rich(X0)) [input p12]
14. ! [X0] : ((~tall(X0) <~> tall(X0)) <=> (humble(X0) <~> rich(X0))) [input p13]
23. ~brave(susan) [input hypothesis]
29. ! [X0] : (~rich(X0) | (~funny(X0) & ~happy(X0))) [ennf transformation 13]
44. ! [X0] : (((~rich(X0) & strong(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (rich(X0) | ~strong(X0)))) [nnf transformation 5]
45. ! [X0] : (((~rich(X0) & strong(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | rich(X0) | ~strong(X0))) [flattening 44]
51. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (humble(john) | creative(john))) [nnf transformation 8]
52. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | humble(john) | creative(john)) [flattening 51]
53. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | humble(john) | creative(john)) [rectify 52]
54. ? [X1] : ~brave(X1) => ~brave(sK4) [choice axiom]
55. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (~brave(sK4) | humble(john) | creative(john)) [skolemisation 53,54]
70. ! [X0] : ((((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))))) [nnf transformation 14]
104. ~rich(X0) | happy(X0) | funny(X0) [cnf transformation 45]
113. ~humble(john) | brave(X0) [cnf transformation 55]
129. ~happy(X0) | ~rich(X0) [cnf transformation 29]
130. ~funny(X0) | ~rich(X0) [cnf transformation 29]
131. rich(X0) | humble(X0) | tall(X0) | tall(X0) [cnf transformation 70]
132. rich(X0) | humble(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 70]
155. ~brave(susan) [cnf transformation 23]
156. rich(X0) | humble(X0) | tall(X0) [duplicate literal removal 131]
157. ~tall(X0) | humble(X0) | rich(X0) [duplicate literal removal 132]
247. 20 <=> humble(john) [avatar definition]
249. ~humble(john) <- (~20) [avatar component clause 247]
256. 22 <=> ! [X0] : brave(X0) [avatar definition]
257. brave(X0) <- (22) [avatar component clause 256]
258. 22 | ~20 [avatar split clause 113,247,256]
331. 38 <=> brave(susan) [avatar definition]
333. ~brave(susan) <- (~38) [avatar component clause 331]
349. humble(X0) | rich(X0) [subsumption resolution 156,157]
402. ~38 [avatar split clause 155,331]
415. 53 <=> funny(john) [avatar definition]
417. funny(john) <- (53) [avatar component clause 415]
419. 54 <=> happy(john) [avatar definition]
421. happy(john) <- (54) [avatar component clause 419]
424. $false <- (22, ~38) [resolution 257,333]
431. ~22 | 38 [avatar contradiction clause 424]
432. rich(john) <- (~20) [resolution 249,349]
434. happy(john) | funny(john) <- (~20) [resolution 432,104]
440. ~rich(john) <- (53) [resolution 417,130]
441. $false <- (~20, 53) [subsumption resolution 440,432]
442. 20 | ~53 [avatar contradiction clause 441]
443. 53 | 54 | 20 [avatar split clause 434,247,419,415]
447. ~rich(john) <- (54) [resolution 421,129]
448. $false <- (~20, 54) [subsumption resolution 447,432]
449. 20 | ~54 [avatar contradiction clause 448]
450. $false [avatar sat refutation 258,402,431,442,443,449]
% SZS output end Proof for 4198991412377436671142477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not rich then lucy is either creative or calm and vice versa. Everyone who is both not curious and not humble is not strong or not patient and vice versa. If someone is both not happy and old then john is humble or happy. If mary is kind or creative then someone is not calm or not curious. If someone is either not kind or not curious then someone is not tall and vice versa. Everyone who is not humble is not quiet or not kind and vice versa. Everyone who is strong or curious is either patient or not rich. Everyone who is either happy or strong is both calm and not funny. Everyone who is either not patient or not humble is either not happy or generous and vice versa. Everyone who is wise is both not humble and humble. If someone is strong or not calm then someone is either not funny or not wise and vice versa. Everyone who is either curious or not generous is humble or brave and vice versa. Everyone who is both not happy and kind is brave or not tall and vice versa. Everyone who is not humble is both kind and calm. Everyone who is either kind or not tall is not patient and vice versa. Everyone who is not humble is either not funny or not brave. Someone is old or not creative. Mary is both calm and not old. John is not wise. John is either kind or happy. | John is old. | contradiction | ((~rich(paul))<=>((creative(lucy)<~>calm(lucy))))&
(![X]:((~curious(X)&~humble(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((~happy(X)&old(X))))=>((humble(john)|happy(john))))&
(((kind(mary)|creative(mary)))=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~kind(X)<~>~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:(~humble(X)<=>(~quiet(X)|~kind(X))))&
(![X]:((strong(X)|curious(X))=>(patient(X)<~>~rich(X))))&
(![X]:((happy(X)<~>strong(X))=>(calm(X)&~funny(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>(~happy(X)<~>generous(X))))&
(![X]:(wise(X)=>(~humble(X)&humble(X))))&
((?[X]:((strong(X)|~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:((curious(X)<~>~generous(X))<=>(humble(X)|brave(X))))&
(![X]:((~happy(X)&kind(X))<=>(brave(X)|~tall(X))))&
(![X]:(~humble(X)=>(kind(X)&calm(X))))&
(![X]:((kind(X)<~>~tall(X))<=>~patient(X)))&
(![X]:(~humble(X)=>(~funny(X)<~>~brave(X))))&
(?[X]:((old(X)|~creative(X))))&
((calm(mary)&~old(mary)))&
(~wise(john))&
((kind(john)<~>happy(john))) | old(john) | [
"p1",
"p2",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 171113513196987480316564
% SZS output start Proof for 171113513196987480316564
2. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (~patient(X0) | ~strong(X0))) [input p1]
3. ? [X0] : (old(X0) & ~happy(X0)) => (happy(john) | humble(john)) [input p2]
6. ! [X0] : (~humble(X0) <=> (~kind(X0) | ~quiet(X0))) [input p5]
8. ! [X0] : ((happy(X0) <~> strong(X0)) => (~funny(X0) & calm(X0))) [input p7]
9. ! [X0] : ((~patient(X0) <~> ~humble(X0)) <=> (~happy(X0) <~> generous(X0))) [input p8]
10. ! [X0] : (wise(X0) => (humble(X0) & ~humble(X0))) [input p9]
11. ? [X0] : (~calm(X0) | strong(X0)) <=> ? [X0] : (~funny(X0) <~> ~wise(X0)) [input p10]
12. ! [X0] : ((curious(X0) <~> ~generous(X0)) <=> (brave(X0) | humble(X0))) [input p11]
13. ! [X0] : ((kind(X0) & ~happy(X0)) <=> (~tall(X0) | brave(X0))) [input p12]
14. ! [X0] : (~humble(X0) => (calm(X0) & kind(X0))) [input p13]
15. ! [X0] : ((kind(X0) <~> ~tall(X0)) <=> ~patient(X0)) [input p14]
16. ! [X0] : (~humble(X0) => (~funny(X0) <~> ~brave(X0))) [input p15]
20. kind(john) <~> happy(john) [input p19]
21. old(john) [input hypothesis]
23. ? [X0] : (~calm(X0) | strong(X0)) <=> ? [X1] : (~funny(X1) <~> ~wise(X1)) [rectify 11]
24. (happy(john) | humble(john)) | ! [X0] : (~old(X0) | happy(X0)) [ennf transformation 3]
25. happy(john) | humble(john) | ! [X0] : (~old(X0) | happy(X0)) [flattening 24]
28. ! [X0] : ((~funny(X0) & calm(X0)) | (happy(X0) <=> strong(X0))) [ennf transformation 8]
29. ! [X0] : ((humble(X0) & ~humble(X0)) | ~wise(X0)) [ennf transformation 10]
30. ! [X0] : ((calm(X0) & kind(X0)) | humble(X0)) [ennf transformation 14]
31. ! [X0] : ((~funny(X0) <~> ~brave(X0)) | humble(X0)) [ennf transformation 16]
33. ! [X0] : (((~humble(X0) & ~curious(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (humble(X0) | curious(X0)))) [nnf transformation 2]
34. ! [X0] : (((~humble(X0) & ~curious(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | humble(X0) | curious(X0))) [flattening 33]
42. ! [X0] : ((~humble(X0) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | humble(X0))) [nnf transformation 6]
43. ! [X0] : ((~humble(X0) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | humble(X0))) [flattening 42]
45. ! [X0] : ((~funny(X0) & calm(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) [nnf transformation 28]
46. ! [X0] : ((((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0))))) [nnf transformation 9]
47. (? [X0] : (~calm(X0) | strong(X0)) | ! [X1] : ((~funny(X1) | wise(X1)) & (~wise(X1) | funny(X1)))) & (? [X1] : ((wise(X1) | funny(X1)) & (~wise(X1) | ~funny(X1))) | ! [X0] : (calm(X0) & ~strong(X0))) [nnf transformation 23]
48. (? [X0] : (~calm(X0) | strong(X0)) | ! [X1] : ((~funny(X1) | wise(X1)) & (~wise(X1) | funny(X1)))) & (? [X2] : ((wise(X2) | funny(X2)) & (~wise(X2) | ~funny(X2))) | ! [X3] : (calm(X3) & ~strong(X3))) [rectify 47]
49. ? [X0] : (~calm(X0) | strong(X0)) => (~calm(sK3) | strong(sK3)) [choice axiom]
50. ? [X2] : ((wise(X2) | funny(X2)) & (~wise(X2) | ~funny(X2))) => ((wise(sK4) | funny(sK4)) & (~wise(sK4) | ~funny(sK4))) [choice axiom]
51. ((~calm(sK3) | strong(sK3)) | ! [X1] : ((~funny(X1) | wise(X1)) & (~wise(X1) | funny(X1)))) & (((wise(sK4) | funny(sK4)) & (~wise(sK4) | ~funny(sK4))) | ! [X3] : (calm(X3) & ~strong(X3))) [skolemisation 48,50,49]
52. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [nnf transformation 12]
53. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [flattening 52]
54. ! [X0] : (((kind(X0) & ~happy(X0)) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | (~kind(X0) | happy(X0)))) [nnf transformation 13]
55. ! [X0] : (((kind(X0) & ~happy(X0)) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | ~kind(X0) | happy(X0))) [flattening 54]
56. ! [X0] : ((((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | patient(X0)) & (~patient(X0) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0))))) [nnf transformation 15]
57. ! [X0] : (((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | humble(X0)) [nnf transformation 31]
60. (~happy(john) | ~kind(john)) & (happy(john) | kind(john)) [nnf transformation 20]
66. ~curious(X0) | strong(X0) [cnf transformation 34]
67. ~curious(X0) | patient(X0) [cnf transformation 34]
68. ~humble(X0) | strong(X0) [cnf transformation 34]
69. ~humble(X0) | patient(X0) [cnf transformation 34]
70. happy(john) | humble(john) | ~old(X0) | happy(X0) [cnf transformation 25]
79. ~humble(X0) | kind(X0) [cnf transformation 43]
87. ~funny(X0) | happy(X0) | ~strong(X0) [cnf transformation 45]
91. ~generous(X0) | happy(X0) | ~patient(X0) | humble(X0) [cnf transformation 46]
92. ~humble(X0) | ~patient(X0) | generous(X0) | happy(X0) [cnf transformation 46]
94. humble(X0) | patient(X0) | generous(X0) | happy(X0) [cnf transformation 46]
95. humble(X0) | patient(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 46]
96. ~humble(X0) | ~wise(X0) [cnf transformation 29]
97. ~wise(X0) | humble(X0) [cnf transformation 29]
100. wise(sK4) | funny(sK4) | ~strong(X3) [cnf transformation 51]
105. brave(X0) | humble(X0) | curious(X0) | generous(X0) [cnf transformation 53]
106. ~generous(X0) | curious(X0) | ~humble(X0) [cnf transformation 53]
107. ~brave(X0) | curious(X0) | ~generous(X0) [cnf transformation 53]
110. ~tall(X0) | brave(X0) | ~kind(X0) | happy(X0) [cnf transformation 55]
112. ~happy(X0) | tall(X0) [cnf transformation 55]
115. kind(X0) | humble(X0) [cnf transformation 30]
117. ~patient(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 56]
120. tall(X0) | ~kind(X0) | patient(X0) [cnf transformation 56]
121. ~brave(X0) | ~funny(X0) | humble(X0) [cnf transformation 57]
122. brave(X0) | funny(X0) | humble(X0) [cnf transformation 57]
128. ~happy(john) | ~kind(john) [cnf transformation 60]
129. old(john) [cnf transformation 21]
147. 4 <=> ! [X0] : (~old(X0) | happy(X0)) [avatar definition]
148. ~old(X0) | happy(X0) <- (4) [avatar component clause 147]
150. 5 <=> humble(john) [avatar definition]
152. humble(john) <- (5) [avatar component clause 150]
154. 6 <=> happy(john) [avatar definition]
155. ~happy(john) <- (~6) [avatar component clause 154]
157. 4 | 5 | 6 [avatar split clause 70,154,150,147]
202. ~generous(X0) | ~happy(X0) | patient(X0) [subsumption resolution 95,69]
203. generous(X0) | patient(X0) | happy(X0) [subsumption resolution 94,69]
205. ~humble(X0) | generous(X0) | happy(X0) [subsumption resolution 92,203]
206. ~wise(X0) [subsumption resolution 96,97]
225. 21 <=> funny(sK4) [avatar definition]
227. funny(sK4) <- (21) [avatar component clause 225]
229. funny(sK4) | ~strong(X3) [subsumption resolution 100,206]
231. 22 <=> ! [X3] : ~strong(X3) [avatar definition]
232. ~strong(X3) <- (22) [avatar component clause 231]
233. 22 | 21 [avatar split clause 229,225,231]
234. kind(X0) [subsumption resolution 115,79]
235. tall(X0) | patient(X0) [subsumption resolution 120,234]
236. ~tall(X0) | ~patient(X0) [subsumption resolution 117,234]
246. ~happy(john) [subsumption resolution 128,234]
247. ~6 [avatar split clause 246,154]
255. happy(john) <- (4) [resolution 148,129]
256. $false <- (4, ~6) [subsumption resolution 255,155]
257. ~4 | 6 [avatar contradiction clause 256]
261. strong(john) <- (5) [resolution 152,68]
286. 27 <=> happy(sK4) [avatar definition]
287. happy(sK4) <- (27) [avatar component clause 286]
288. ~happy(sK4) <- (~27) [avatar component clause 286]
290. 28 <=> strong(sK4) [avatar definition]
318. funny(X2) | humble(X2) | curious(X2) | ~generous(X2) [resolution 122,107]
323. ~generous(X2) | curious(X2) | funny(X2) [subsumption resolution 318,106]
382. humble(X0) | curious(X0) | generous(X0) | ~funny(X0) | humble(X0) [resolution 105,121]
389. ~funny(X0) | curious(X0) | generous(X0) | humble(X0) [duplicate literal removal 382]
392. brave(X1) | ~kind(X1) | happy(X1) | patient(X1) [resolution 110,235]
394. brave(X1) | happy(X1) | patient(X1) [subsumption resolution 392,234]
395. curious(X0) | funny(X0) | patient(X0) | happy(X0) [resolution 323,203]
397. funny(X0) | patient(X0) | happy(X0) [subsumption resolution 395,67]
398. happy(X0) | patient(X0) | ~funny(X0) | humble(X0) [resolution 394,121]
403. happy(X0) | patient(X0) | ~funny(X0) [subsumption resolution 398,69]
404. happy(X0) | patient(X0) [subsumption resolution 403,397]
420. 33 <=> humble(sK4) [avatar definition]
421. ~humble(sK4) <- (~33) [avatar component clause 420]
422. humble(sK4) <- (33) [avatar component clause 420]
424. 34 <=> generous(sK4) [avatar definition]
426. generous(sK4) <- (34) [avatar component clause 424]
428. 35 <=> curious(sK4) [avatar definition]
430. curious(sK4) <- (35) [avatar component clause 428]
432. $false <- (5, 22) [resolution 232,261]
436. ~5 | ~22 [avatar contradiction clause 432]
437. curious(sK4) | generous(sK4) | humble(sK4) <- (21) [resolution 227,389]
438. happy(sK4) | ~strong(sK4) <- (21) [resolution 227,87]
440. generous(sK4) | happy(sK4) <- (33) [resolution 422,205]
444. patient(sK4) <- (33) [resolution 422,69]
445. strong(sK4) <- (33) [resolution 422,68]
451. 27 | 34 | ~33 [avatar split clause 440,420,424,286]
453. 28 | ~33 [avatar split clause 445,420,290]
454. ~28 | 27 | ~21 [avatar split clause 438,225,286,290]
459. tall(sK4) <- (27) [resolution 287,112]
463. ~patient(sK4) <- (27) [resolution 459,236]
464. $false <- (27, 33) [subsumption resolution 463,444]
465. ~27 | ~33 [avatar contradiction clause 464]
476. ~happy(sK4) | patient(sK4) <- (34) [resolution 426,202]
478. patient(sK4) <- (27, 34) [subsumption resolution 476,287]
479. $false <- (27, 34) [subsumption resolution 478,463]
480. ~27 | ~34 [avatar contradiction clause 479]
481. curious(sK4) | generous(sK4) <- (21, ~33) [subsumption resolution 437,421]
482. 34 | 35 | ~21 | 33 [avatar split clause 481,420,225,428,424]
489. patient(sK4) <- (35) [resolution 430,67]
490. strong(sK4) <- (35) [resolution 430,66]
493. $false <- (27, 35) [subsumption resolution 489,463]
494. ~27 | ~35 [avatar contradiction clause 493]
495. 28 | ~35 [avatar split clause 490,428,290]
496. patient(sK4) <- (~27) [resolution 288,404]
501. happy(sK4) | ~patient(sK4) | humble(sK4) <- (34) [resolution 426,91]
505. ~patient(sK4) | humble(sK4) <- (~27, 34) [subsumption resolution 501,288]
506. humble(sK4) <- (~27, 34) [subsumption resolution 505,496]
507. $false <- (~27, ~33, 34) [subsumption resolution 506,421]
508. 27 | 33 | ~34 [avatar contradiction clause 507]
509. $false [avatar sat refutation 157,233,247,257,436,451,453,454,465,480,482,494,495,508]
% SZS output end Proof for 171113513196987480316564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or not humble then fred is both not rich and not funny and vice versa. Everyone who is kind is either strong or patient. Everyone who is generous or not happy is both calm and not creative and vice versa. Everyone who is either quiet or not calm is both funny and creative and vice versa. If fred is both funny and humble then fred is creative. Everyone who is old is either not happy or not strong and vice versa. If someone is either generous or not rich then susan is both not creative and not happy. If fred is not brave or wise then susan is humble or generous and vice versa. Everyone who is not quiet or tall is generous and vice versa. If someone is tall then someone is not funny and vice versa. If mary is brave then john is not generous and vice versa. If someone is either not generous or not patient then someone is not old. Everyone who is quiet or generous is either generous or calm and vice versa. Everyone who is either not calm or old is both tall and curious. Everyone who is both curious and rich is generous and vice versa. Everyone who is both not quiet and not curious is not patient or not quiet. Paul is not old or not quiet. Someone is calm or not wise. Paul is either generous or wise. Someone is not patient or not tall. Mary is not humble. Someone is not tall. Someone is not patient. | Fred is not curious. | entailment | ((?[X]:((~kind(X)<~>~humble(X))))<=>((~rich(fred)&~funny(fred))))&
(![X]:(kind(X)=>(strong(X)<~>patient(X))))&
(![X]:((generous(X)|~happy(X))<=>(calm(X)&~creative(X))))&
(![X]:((quiet(X)<~>~calm(X))<=>(funny(X)&creative(X))))&
(((funny(fred)&humble(fred)))=>(creative(fred)))&
(![X]:(old(X)<=>(~happy(X)<~>~strong(X))))&
((?[X]:((generous(X)<~>~rich(X))))=>((~creative(susan)&~happy(susan))))&
(((~brave(fred)|wise(fred)))<=>((humble(susan)|generous(susan))))&
(![X]:((~quiet(X)|tall(X))<=>generous(X)))&
((?[X]:(tall(X)))<=>(?[X]:(~funny(X))))&
((brave(mary))<=>(~generous(john)))&
((?[X]:((~generous(X)<~>~patient(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|generous(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~calm(X)<~>old(X))=>(tall(X)&curious(X))))&
(![X]:((curious(X)&rich(X))<=>generous(X)))&
(![X]:((~quiet(X)&~curious(X))=>(~patient(X)|~quiet(X))))&
((~old(paul)|~quiet(paul)))&
(?[X]:((calm(X)|~wise(X))))&
((generous(paul)<~>wise(paul)))&
(?[X]:((~patient(X)|~tall(X))))&
(~humble(mary))&
(?[X]:(~tall(X)))&
(?[X]:(~patient(X))) | ~curious(fred) | [
"p2",
"p3",
"p6",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 899336842263745529111219
% SZS output start Proof for 899336842263745529111219
3. ! [X0] : ((~happy(X0) | generous(X0)) <=> (~creative(X0) & calm(X0))) [input p2]
4. ! [X0] : ((quiet(X0) <~> ~calm(X0)) <=> (creative(X0) & funny(X0))) [input p3]
7. ? [X0] : (generous(X0) <~> ~rich(X0)) => (~happy(susan) & ~creative(susan)) [input p6]
9. ! [X0] : ((tall(X0) | ~quiet(X0)) <=> generous(X0)) [input p8]
13. ! [X0] : ((generous(X0) | quiet(X0)) <=> (generous(X0) <~> calm(X0))) [input p12]
15. ! [X0] : ((rich(X0) & curious(X0)) <=> generous(X0)) [input p14]
24. curious(fred) [input hypothesis]
30. (~happy(susan) & ~creative(susan)) | ! [X0] : (generous(X0) <=> ~rich(X0)) [ennf transformation 7]
41. ! [X0] : (((~happy(X0) | generous(X0)) | (creative(X0) | ~calm(X0))) & ((~creative(X0) & calm(X0)) | (happy(X0) & ~generous(X0)))) [nnf transformation 3]
42. ! [X0] : ((~happy(X0) | generous(X0) | creative(X0) | ~calm(X0)) & ((~creative(X0) & calm(X0)) | (happy(X0) & ~generous(X0)))) [flattening 41]
43. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | (~creative(X0) | ~funny(X0))) & ((creative(X0) & funny(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [nnf transformation 4]
44. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | ~creative(X0) | ~funny(X0)) & ((creative(X0) & funny(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [flattening 43]
46. (~happy(susan) & ~creative(susan)) | ! [X0] : ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))) [nnf transformation 30]
49. ! [X0] : (((tall(X0) | ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (~tall(X0) & quiet(X0)))) [nnf transformation 9]
50. ! [X0] : ((tall(X0) | ~quiet(X0) | ~generous(X0)) & (generous(X0) | (~tall(X0) & quiet(X0)))) [flattening 49]
61. ! [X0] : (((generous(X0) | quiet(X0)) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (~generous(X0) & ~quiet(X0)))) [nnf transformation 13]
62. ! [X0] : ((generous(X0) | quiet(X0) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (~generous(X0) & ~quiet(X0)))) [flattening 61]
64. ! [X0] : (((rich(X0) & curious(X0)) | ~generous(X0)) & (generous(X0) | (~rich(X0) | ~curious(X0)))) [nnf transformation 15]
65. ! [X0] : (((rich(X0) & curious(X0)) | ~generous(X0)) & (generous(X0) | ~rich(X0) | ~curious(X0))) [flattening 64]
83. ~generous(X0) | calm(X0) [cnf transformation 42]
90. ~quiet(X0) | ~calm(X0) | creative(X0) [cnf transformation 44]
100. ~creative(susan) | generous(X0) | rich(X0) [cnf transformation 46]
107. quiet(X0) | generous(X0) [cnf transformation 50]
116. calm(X0) | generous(X0) | ~quiet(X0) [cnf transformation 62]
119. ~calm(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 62]
126. generous(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 65]
138. curious(fred) [cnf transformation 24]
139. ~calm(X0) | ~generous(X0) [duplicate literal removal 119]
179. 9 <=> ! [X0] : (generous(X0) | rich(X0)) [avatar definition]
180. generous(X0) | rich(X0) <- (9) [avatar component clause 179]
191. 12 <=> creative(susan) [avatar definition]
193. ~creative(susan) <- (~12) [avatar component clause 191]
194. 9 | ~12 [avatar split clause 100,191,179]
254. ~generous(X0) [subsumption resolution 139,83]
255. ~quiet(X0) | calm(X0) [subsumption resolution 116,254]
256. ~curious(X0) | ~rich(X0) [subsumption resolution 126,254]
304. calm(X0) | generous(X0) [resolution 255,107]
306. calm(X0) [subsumption resolution 304,254]
307. ~rich(fred) [resolution 256,138]
326. ~calm(X1) | creative(X1) | generous(X1) [resolution 90,107]
328. creative(X1) | generous(X1) [subsumption resolution 326,306]
329. creative(X1) [subsumption resolution 328,254]
330. $false <- (~12) [resolution 329,193]
333. 12 [avatar contradiction clause 330]
334. rich(X0) <- (9) [subsumption resolution 180,254]
337. $false <- (9) [subsumption resolution 307,334]
338. ~9 [avatar contradiction clause 337]
339. $false [avatar sat refutation 194,333,338]
% SZS output end Proof for 899336842263745529111219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not rich or not quiet then fred is generous or strong and vice versa.
If mary is not brave or not patient then lucy is both not calm and not funny and vice versa.
If susan is both patient and calm then someone is both old and curious and vice versa.
Everyone who is both not strong and creative is not humble or patient and vice versa.
If john is both creative and not calm then lucy is either calm or not rich and vice versa.
If someone is happy or not curious then alice is tall.
If susan is not happy then someone is strong or generous and vice versa.
If john is generous then someone is both curious and not brave and vice versa.
If john is either not happy or kind then someone is both not kind and not brave.
If someone is strong then someone is either not quiet or not brave and vice versa.
If someone is both tall and creative then paul is both not funny and brave and vice versa.
Everyone who is creative or tall is both not curious and brave and vice versa.
Everyone who is not funny is both not old and not curious and vice versa.
If lucy is humble then mary is curious or old and vice versa.
If lucy is both not generous and not tall then susan is not kind or humble.
Everyone who is not rich or tall is both calm and not creative.
Mary is both not funny and not happy.
Someone is either curious or patient.
Someone is humble or brave.
Someone is not kind or humble.
Someone is kind or quiet.
Someone is either kind or strong.
Fred is kind.
Lucy is kind or patient. | Alice is not curious. | entailment | (((~rich(alice)|~quiet(alice)))<=>((generous(fred)|strong(fred))))&
(((~brave(mary)|~patient(mary)))<=>((~calm(lucy)&~funny(lucy))))&
(((patient(susan)&calm(susan)))<=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~strong(X)&creative(X))<=>(~humble(X)|patient(X))))&
(((creative(john)&~calm(john)))<=>((calm(lucy)<~>~rich(lucy))))&
((?[X]:((happy(X)|~curious(X))))=>(tall(alice)))&
((~happy(susan))<=>(?[X]:((strong(X)|generous(X)))))&
((generous(john))<=>(?[X]:((curious(X)&~brave(X)))))&
(((~happy(john)<~>kind(john)))=>(?[X]:((~kind(X)&~brave(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((~quiet(X)<~>~brave(X)))))&
((?[X]:((tall(X)&creative(X))))<=>((~funny(paul)&brave(paul))))&
(![X]:((creative(X)|tall(X))<=>(~curious(X)&brave(X))))&
(![X]:(~funny(X)<=>(~old(X)&~curious(X))))&
((humble(lucy))<=>((curious(mary)|old(mary))))&
(((~generous(lucy)&~tall(lucy)))=>((~kind(susan)|humble(susan))))&
(![X]:((~rich(X)|tall(X))=>(calm(X)&~creative(X))))&
((~funny(mary)&~happy(mary)))&
(?[X]:((curious(X)<~>patient(X))))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:((~kind(X)|humble(X))))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((kind(X)<~>strong(X))))&
(kind(fred))&
((kind(lucy)|patient(lucy))) | ~curious(alice) | [
"p5",
"p11",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3120613756347158395379988
% SZS output start Proof for 3120613756347158395379988
6. ? [X0] : (~curious(X0) | happy(X0)) => tall(alice) [input p5]
12. ! [X0] : ((tall(X0) | creative(X0)) <=> (brave(X0) & ~curious(X0))) [input p11]
13. ! [X0] : (~funny(X0) <=> (~curious(X0) & ~old(X0))) [input p12]
17. ~happy(mary) & ~funny(mary) [input p16]
25. curious(alice) [input hypothesis]
27. tall(alice) | ! [X0] : (curious(X0) & ~happy(X0)) [ennf transformation 6]
66. ! [X0] : (((tall(X0) | creative(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 12]
67. ! [X0] : ((tall(X0) | creative(X0) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 66]
68. ! [X0] : ((~funny(X0) | (curious(X0) | old(X0))) & ((~curious(X0) & ~old(X0)) | funny(X0))) [nnf transformation 13]
69. ! [X0] : ((~funny(X0) | curious(X0) | old(X0)) & ((~curious(X0) & ~old(X0)) | funny(X0))) [flattening 68]
109. tall(alice) | curious(X0) [cnf transformation 27]
129. ~tall(X0) | ~curious(X0) [cnf transformation 67]
134. ~curious(X0) | funny(X0) [cnf transformation 69]
144. ~funny(mary) [cnf transformation 17]
155. curious(alice) [cnf transformation 25]
239. 17 <=> ! [X0] : curious(X0) [avatar definition]
240. curious(X0) <- (17) [avatar component clause 239]
242. 18 <=> tall(alice) [avatar definition]
244. tall(alice) <- (18) [avatar component clause 242]
245. 17 | 18 [avatar split clause 109,242,239]
450. ~curious(alice) <- (18) [resolution 129,244]
451. $false <- (18) [subsumption resolution 450,155]
452. ~18 [avatar contradiction clause 451]
465. funny(X0) <- (17) [resolution 134,240]
468. $false <- (17) [resolution 465,144]
471. ~17 [avatar contradiction clause 468]
472. $false [avatar sat refutation 245,452,471]
% SZS output end Proof for 3120613756347158395379988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or curious is both wise and not humble.
If someone is generous then mary is not old and vice versa.
If someone is creative then paul is not brave and vice versa.
Everyone who is both not funny and not strong is either quiet or not quiet and vice versa.
Everyone who is happy is not generous and vice versa.
Everyone who is calm or not quiet is both creative and brave and vice versa.
If someone is both kind and not generous then someone is rich or not quiet and vice versa.
Everyone who is either not curious or not quiet is old and vice versa.
Everyone who is either patient or curious is either not creative or calm and vice versa.
If someone is strong or not quiet then fred is both not kind and curious.
Everyone who is both wise and not brave is not creative or quiet and vice versa.
If paul is not patient then someone is brave or not wise and vice versa.
Everyone who is both quiet and not quiet is either rich or strong and vice versa.
If mary is humble or not creative then fred is either brave or not rich and vice versa.
If alice is both kind and happy then alice is funny or happy and vice versa.
John is not patient or not funny.
Someone is brave or kind.
Mary is not curious or old.
Someone is not tall.
Mary is not patient.
Paul is not patient or not tall. | Fred is tall. | neutral | (![X]:((~humble(X)<~>curious(X))=>(wise(X)&~humble(X))))&
((?[X]:(generous(X)))<=>(~old(mary)))&
((?[X]:(creative(X)))<=>(~brave(paul)))&
(![X]:((~funny(X)&~strong(X))<=>(quiet(X)<~>~quiet(X))))&
(![X]:(happy(X)<=>~generous(X)))&
(![X]:((calm(X)|~quiet(X))<=>(creative(X)&brave(X))))&
((?[X]:((kind(X)&~generous(X))))<=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((~curious(X)<~>~quiet(X))<=>old(X)))&
(![X]:((patient(X)<~>curious(X))<=>(~creative(X)<~>calm(X))))&
((?[X]:((strong(X)|~quiet(X))))=>((~kind(fred)&curious(fred))))&
(![X]:((wise(X)&~brave(X))<=>(~creative(X)|quiet(X))))&
((~patient(paul))<=>(?[X]:((brave(X)|~wise(X)))))&
(![X]:((quiet(X)&~quiet(X))<=>(rich(X)<~>strong(X))))&
(((humble(mary)|~creative(mary)))<=>((brave(fred)<~>~rich(fred))))&
(((kind(alice)&happy(alice)))<=>((funny(alice)|happy(alice))))&
((~patient(john)|~funny(john)))&
(?[X]:((brave(X)|kind(X))))&
((~curious(mary)|old(mary)))&
(?[X]:(~tall(X)))&
(~patient(mary))&
((~patient(paul)|~tall(paul))) | tall(fred) | [] | null | 0 |
Everyone who is not tall or happy is both curious and not funny. If john is both creative and tall then john is not rich or old and vice versa. If lucy is not creative then someone is not generous or not curious and vice versa. If someone is either patient or old then fred is not calm or wise. Everyone who is not old or not humble is not strong and vice versa. If someone is not tall or curious then paul is not wise or strong and vice versa. If someone is tall then someone is calm or funny and vice versa. Everyone who is either rich or not creative is not funny. If alice is not brave or not humble then paul is not wise and vice versa. If someone is not calm or not old then someone is either not patient or creative and vice versa. If fred is brave or not humble then someone is either kind or happy. Everyone who is either funny or not quiet is curious or not calm and vice versa. Everyone who is calm or not humble is not kind and vice versa. Everyone who is not calm is quiet or not quiet and vice versa. If lucy is not strong or not curious then fred is both not generous and patient and vice versa. If someone is not creative then lucy is patient or strong and vice versa. Paul is not happy or strong. Someone is either quiet or not rich. Lucy is both funny and not old. Someone is not kind. John is both not rich and humble. Someone is not strong or not brave. Someone is not patient or not calm. | Lucy is calm. | contradiction | (![X]:((~tall(X)|happy(X))=>(curious(X)&~funny(X))))&
(((creative(john)&tall(john)))<=>((~rich(john)|old(john))))&
((~creative(lucy))<=>(?[X]:((~generous(X)|~curious(X)))))&
((?[X]:((patient(X)<~>old(X))))=>((~calm(fred)|wise(fred))))&
(![X]:((~old(X)|~humble(X))<=>~strong(X)))&
((?[X]:((~tall(X)|curious(X))))<=>((~wise(paul)|strong(paul))))&
((?[X]:(tall(X)))<=>(?[X]:((calm(X)|funny(X)))))&
(![X]:((rich(X)<~>~creative(X))=>~funny(X)))&
(((~brave(alice)|~humble(alice)))<=>(~wise(paul)))&
((?[X]:((~calm(X)|~old(X))))<=>(?[X]:((~patient(X)<~>creative(X)))))&
(((brave(fred)|~humble(fred)))=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((funny(X)<~>~quiet(X))<=>(curious(X)|~calm(X))))&
(![X]:((calm(X)|~humble(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>(quiet(X)|~quiet(X))))&
(((~strong(lucy)|~curious(lucy)))<=>((~generous(fred)&patient(fred))))&
((?[X]:(~creative(X)))<=>((patient(lucy)|strong(lucy))))&
((~happy(paul)|strong(paul)))&
(?[X]:((quiet(X)<~>~rich(X))))&
((funny(lucy)&~old(lucy)))&
(?[X]:(~kind(X)))&
((~rich(john)&humble(john)))&
(?[X]:((~strong(X)|~brave(X))))&
(?[X]:((~patient(X)|~calm(X)))) | calm(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6575534227330218323944588
% SZS output start Proof for 6575534227330218323944588
14. ! [X0] : (~calm(X0) <=> (~quiet(X0) | quiet(X0))) [input p13]
24. calm(lucy) [input hypothesis]
66. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | calm(X0))) [nnf transformation 14]
67. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | calm(X0))) [flattening 66]
133. ~calm(X0) | ~quiet(X0) [cnf transformation 67]
134. ~calm(X0) | quiet(X0) [cnf transformation 67]
153. calm(lucy) [cnf transformation 24]
245. 21 <=> ! [X1] : ~calm(X1) [avatar definition]
246. ~calm(X1) <- (21) [avatar component clause 245]
325. ~calm(X0) [subsumption resolution 133,134]
326. 21 [avatar split clause 325,245]
402. $false <- (21) [resolution 246,153]
403. ~21 [avatar contradiction clause 402]
404. $false [avatar sat refutation 326,403]
% SZS output end Proof for 6575534227330218323944588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is patient or quiet then someone is happy and vice versa.
Everyone who is kind is both calm and brave and vice versa.
If paul is either not wise or tall then someone is both not creative and patient.
Everyone who is not quiet or strong is not strong.
Everyone who is strong or not old is rich or not old.
Everyone who is either not calm or old is not happy.
If fred is both generous and not curious then someone is humble.
If john is either brave or generous then susan is both tall and not rich and vice versa.
Everyone who is either not rich or not happy is curious or not rich and vice versa.
Everyone who is either not strong or generous is wise.
Everyone who is both humble and wise is either not rich or not old.
Everyone who is either not generous or quiet is either rich or curious and vice versa.
If john is either wise or kind then someone is rich or not kind and vice versa.
Everyone who is either not wise or curious is not brave and vice versa.
If someone is both kind and brave then lucy is not brave and vice versa.
Everyone who is either not old or curious is not kind or brave.
Fred is not funny or not tall.
Someone is either not curious or strong.
John is both not old and humble.
Lucy is both calm and not quiet.
Someone is both not patient and curious.
Someone is not funny or not creative.
Someone is either not patient or humble.
Paul is either not curious or curious. | John is not curious. | contradiction | ((?[X]:((patient(X)|quiet(X))))<=>(?[X]:(happy(X))))&
(![X]:(kind(X)<=>(calm(X)&brave(X))))&
(((~wise(paul)<~>tall(paul)))=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:((~quiet(X)|strong(X))=>~strong(X)))&
(![X]:((strong(X)|~old(X))=>(rich(X)|~old(X))))&
(![X]:((~calm(X)<~>old(X))=>~happy(X)))&
(((generous(fred)&~curious(fred)))=>(?[X]:(humble(X))))&
(((brave(john)<~>generous(john)))<=>((tall(susan)&~rich(susan))))&
(![X]:((~rich(X)<~>~happy(X))<=>(curious(X)|~rich(X))))&
(![X]:((~strong(X)<~>generous(X))=>wise(X)))&
(![X]:((humble(X)&wise(X))=>(~rich(X)<~>~old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(rich(X)<~>curious(X))))&
(((wise(john)<~>kind(john)))<=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>~brave(X)))&
((?[X]:((kind(X)&brave(X))))<=>(~brave(lucy)))&
(![X]:((~old(X)<~>curious(X))=>(~kind(X)|brave(X))))&
((~funny(fred)|~tall(fred)))&
(?[X]:((~curious(X)<~>strong(X))))&
((~old(john)&humble(john)))&
((calm(lucy)&~quiet(lucy)))&
(?[X]:((~patient(X)&curious(X))))&
(?[X]:((~funny(X)|~creative(X))))&
(?[X]:((~patient(X)<~>humble(X))))&
((~curious(paul)<~>curious(paul))) | ~curious(john) | [
"p1",
"p5",
"p8",
"p10",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5444067368904215467438447
% SZS output start Proof for 5444067368904215467438447
2. ! [X0] : (kind(X0) <=> (brave(X0) & calm(X0))) [input p1]
6. ! [X0] : ((~calm(X0) <~> old(X0)) => ~happy(X0)) [input p5]
9. ! [X0] : ((~rich(X0) <~> ~happy(X0)) <=> (~rich(X0) | curious(X0))) [input p8]
11. ! [X0] : ((wise(X0) & humble(X0)) => (~rich(X0) <~> ~old(X0))) [input p10]
13. (wise(john) <~> kind(john)) <=> ? [X0] : (~kind(X0) | rich(X0)) [input p12]
14. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> ~brave(X0)) [input p13]
19. humble(john) & ~old(john) [input p18]
25. ~curious(john) [input hypothesis]
34. ! [X0] : (~happy(X0) | (~calm(X0) <=> old(X0))) [ennf transformation 6]
38. ! [X0] : ((~rich(X0) <~> ~old(X0)) | (~wise(X0) | ~humble(X0))) [ennf transformation 11]
39. ! [X0] : ((~rich(X0) <~> ~old(X0)) | ~wise(X0) | ~humble(X0)) [flattening 38]
47. ! [X0] : ((kind(X0) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | ~kind(X0))) [nnf transformation 2]
48. ! [X0] : ((kind(X0) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | ~kind(X0))) [flattening 47]
52. ! [X0] : (~happy(X0) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) [nnf transformation 34]
57. ! [X0] : ((((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (rich(X0) & ~curious(X0))) & ((~rich(X0) | curious(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0))))) [nnf transformation 9]
58. ! [X0] : ((((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (rich(X0) & ~curious(X0))) & (~rich(X0) | curious(X0) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0))))) [flattening 57]
60. ! [X0] : (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ~wise(X0) | ~humble(X0)) [nnf transformation 39]
62. (((~kind(john) | ~wise(john)) & (kind(john) | wise(john))) | ! [X0] : (kind(X0) & ~rich(X0))) & (? [X0] : (~kind(X0) | rich(X0)) | ((wise(john) | ~kind(john)) & (kind(john) | ~wise(john)))) [nnf transformation 13]
63. (((~kind(john) | ~wise(john)) & (kind(john) | wise(john))) | ! [X0] : (kind(X0) & ~rich(X0))) & (? [X1] : (~kind(X1) | rich(X1)) | ((wise(john) | ~kind(john)) & (kind(john) | ~wise(john)))) [rectify 62]
64. ? [X1] : (~kind(X1) | rich(X1)) => (~kind(sK4) | rich(sK4)) [choice axiom]
65. (((~kind(john) | ~wise(john)) & (kind(john) | wise(john))) | ! [X0] : (kind(X0) & ~rich(X0))) & ((~kind(sK4) | rich(sK4)) | ((wise(john) | ~kind(john)) & (kind(john) | ~wise(john)))) [skolemisation 63,64]
66. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | brave(X0)) & (~brave(X0) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 14]
85. ~kind(X0) | brave(X0) [cnf transformation 48]
86. ~brave(X0) | kind(X0) | ~calm(X0) [cnf transformation 48]
93. ~happy(X0) | old(X0) | calm(X0) [cnf transformation 52]
103. ~rich(X0) | curious(X0) | ~rich(X0) | happy(X0) [cnf transformation 58]
107. happy(X0) | rich(X0) | rich(X0) [cnf transformation 58]
111. ~humble(X0) | rich(X0) | ~wise(X0) | old(X0) [cnf transformation 60]
122. kind(john) | wise(john) | ~rich(X0) [cnf transformation 65]
123. kind(john) | wise(john) | kind(X0) [cnf transformation 65]
124. ~kind(john) | ~wise(john) | ~rich(X0) [cnf transformation 65]
126. ~brave(X0) | curious(X0) | wise(X0) [cnf transformation 66]
128. ~wise(X0) | curious(X0) | brave(X0) [cnf transformation 66]
137. ~old(john) [cnf transformation 19]
138. humble(john) [cnf transformation 19]
147. ~curious(john) [cnf transformation 25]
148. ~rich(X0) | curious(X0) | happy(X0) [duplicate literal removal 103]
149. rich(X0) | happy(X0) [duplicate literal removal 107]
211. 15 <=> brave(john) [avatar definition]
212. brave(john) <- (15) [avatar component clause 211]
213. ~brave(john) <- (~15) [avatar component clause 211]
224. curious(X0) | happy(X0) [subsumption resolution 148,149]
227. 17 <=> ! [X0] : kind(X0) [avatar definition]
228. kind(X0) <- (17) [avatar component clause 227]
230. 18 <=> wise(john) [avatar definition]
231. wise(john) <- (18) [avatar component clause 230]
234. 19 <=> kind(john) [avatar definition]
235. kind(john) <- (19) [avatar component clause 234]
236. ~kind(john) <- (~19) [avatar component clause 234]
239. 20 <=> ! [X0] : ~rich(X0) [avatar definition]
240. ~rich(X0) <- (20) [avatar component clause 239]
241. 20 | ~18 | ~19 [avatar split clause 124,234,230,239]
242. 17 | 18 | 19 [avatar split clause 123,234,230,227]
243. 20 | 18 | 19 [avatar split clause 122,234,230,239]
286. happy(john) [resolution 224,147]
292. old(john) | calm(john) [resolution 93,286]
303. calm(john) [subsumption resolution 292,137]
369. curious(john) | brave(john) <- (18) [resolution 128,231]
372. brave(john) <- (18) [subsumption resolution 369,147]
373. $false <- (~15, 18) [subsumption resolution 372,213]
374. 15 | ~18 [avatar contradiction clause 373]
395. curious(john) | wise(john) <- (15) [resolution 212,126]
396. kind(john) | ~calm(john) <- (15) [resolution 212,86]
400. wise(john) <- (15) [subsumption resolution 395,147]
401. 18 | ~15 [avatar split clause 400,211,230]
402. kind(john) <- (15) [subsumption resolution 396,303]
403. 19 | ~15 [avatar split clause 402,211,234]
409. brave(john) <- (19) [resolution 235,85]
418. rich(john) | ~wise(john) | old(john) [resolution 111,138]
419. ~wise(john) | old(john) <- (20) [subsumption resolution 418,240]
423. 15 | ~19 [avatar split clause 409,234,211]
435. ~wise(john) <- (20) [subsumption resolution 419,137]
436. ~18 | ~20 [avatar split clause 435,239,230]
439. $false <- (17, ~19) [resolution 236,228]
440. ~17 | 19 [avatar contradiction clause 439]
441. $false [avatar sat refutation 241,242,243,374,401,403,423,436,440]
% SZS output end Proof for 5444067368904215467438447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and old then paul is both not brave and not quiet.
If susan is not rich or tall then someone is calm and vice versa.
If susan is either not quiet or not happy then someone is either brave or quiet and vice versa.
Everyone who is not generous or not rich is both funny and not old and vice versa.
Everyone who is either wise or rich is both kind and not rich.
Everyone who is either kind or tall is either funny or rich and vice versa.
Everyone who is brave or not calm is patient.
Everyone who is not generous or not old is both not generous and happy.
If someone is either tall or calm then alice is either not patient or quiet and vice versa.
If mary is not quiet then john is both not curious and creative and vice versa.
Everyone who is not old or not kind is not creative.
Everyone who is both generous and not tall is not curious or not quiet and vice versa.
Everyone who is kind or not rich is both not old and not generous.
Everyone who is not tall or quiet is not calm and vice versa.
Everyone who is quiet is generous or old.
If someone is not strong or patient then lucy is strong or patient and vice versa.
Mary is either wise or not curious.
Paul is both strong and humble.
Mary is not kind or not curious.
Lucy is either curious or old.
Someone is either not humble or curious.
Someone is humble.
Someone is wise. | Susan is old. | entailment | ((?[X]:((brave(X)&old(X))))=>((~brave(paul)&~quiet(paul))))&
(((~rich(susan)|tall(susan)))<=>(?[X]:(calm(X))))&
(((~quiet(susan)<~>~happy(susan)))<=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((~generous(X)|~rich(X))<=>(funny(X)&~old(X))))&
(![X]:((wise(X)<~>rich(X))=>(kind(X)&~rich(X))))&
(![X]:((kind(X)<~>tall(X))<=>(funny(X)<~>rich(X))))&
(![X]:((brave(X)|~calm(X))=>patient(X)))&
(![X]:((~generous(X)|~old(X))=>(~generous(X)&happy(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((~patient(alice)<~>quiet(alice))))&
((~quiet(mary))<=>((~curious(john)&creative(john))))&
(![X]:((~old(X)|~kind(X))=>~creative(X)))&
(![X]:((generous(X)&~tall(X))<=>(~curious(X)|~quiet(X))))&
(![X]:((kind(X)|~rich(X))=>(~old(X)&~generous(X))))&
(![X]:((~tall(X)|quiet(X))<=>~calm(X)))&
(![X]:(quiet(X)=>(generous(X)|old(X))))&
((?[X]:((~strong(X)|patient(X))))<=>((strong(lucy)|patient(lucy))))&
((wise(mary)<~>~curious(mary)))&
((strong(paul)&humble(paul)))&
((~kind(mary)|~curious(mary)))&
((curious(lucy)<~>old(lucy)))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:(humble(X)))&
(?[X]:(wise(X))) | old(susan) | [
"p3",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4027159373894486728333209
% SZS output start Proof for 4027159373894486728333209
4. ! [X0] : ((~rich(X0) | ~generous(X0)) <=> (~old(X0) & funny(X0))) [input p3]
8. ! [X0] : ((~old(X0) | ~generous(X0)) => (happy(X0) & ~generous(X0))) [input p7]
12. ! [X0] : ((~tall(X0) & generous(X0)) <=> (~quiet(X0) | ~curious(X0))) [input p11]
15. ! [X0] : (quiet(X0) => (old(X0) | generous(X0))) [input p14]
24. ~old(susan) [input hypothesis]
28. ! [X0] : ((happy(X0) & ~generous(X0)) | (old(X0) & generous(X0))) [ennf transformation 8]
31. ! [X0] : ((old(X0) | generous(X0)) | ~quiet(X0)) [ennf transformation 15]
32. ! [X0] : (old(X0) | generous(X0) | ~quiet(X0)) [flattening 31]
42. ! [X0] : (((~rich(X0) | ~generous(X0)) | (old(X0) | ~funny(X0))) & ((~old(X0) & funny(X0)) | (rich(X0) & generous(X0)))) [nnf transformation 4]
43. ! [X0] : ((~rich(X0) | ~generous(X0) | old(X0) | ~funny(X0)) & ((~old(X0) & funny(X0)) | (rich(X0) & generous(X0)))) [flattening 42]
52. ! [X0] : (((~tall(X0) & generous(X0)) | (quiet(X0) & curious(X0))) & ((~quiet(X0) | ~curious(X0)) | (tall(X0) | ~generous(X0)))) [nnf transformation 12]
53. ! [X0] : (((~tall(X0) & generous(X0)) | (quiet(X0) & curious(X0))) & (~quiet(X0) | ~curious(X0) | tall(X0) | ~generous(X0))) [flattening 52]
85. ~old(X0) | generous(X0) [cnf transformation 43]
103. ~generous(X0) | old(X0) [cnf transformation 28]
121. generous(X0) | quiet(X0) [cnf transformation 53]
131. old(X0) | generous(X0) | ~quiet(X0) [cnf transformation 32]
147. ~old(susan) [cnf transformation 24]
260. old(X0) | generous(X0) [subsumption resolution 131,121]
261. generous(X0) [subsumption resolution 260,85]
324. old(X0) [resolution 103,261]
326. $false [resolution 324,147]
% SZS output end Proof for 4027159373894486728333209
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not humble then someone is not old or not kind and vice versa. Everyone who is tall or not patient is either not brave or quiet. Everyone who is generous is not old and vice versa. Everyone who is not kind is not funny or not old. Everyone who is both generous and old is both not calm and kind. Everyone who is not patient is brave and vice versa. Everyone who is brave is both not strong and not happy and vice versa. If someone is both not creative and wise then mary is both not brave and calm. If john is funny or curious then paul is curious or tall and vice versa. If someone is both not patient and patient then someone is not happy. If lucy is either not wise or not humble then paul is both not happy and old. Everyone who is not brave is both not calm and not curious and vice versa. If someone is both not kind and brave then alice is either curious or creative. If fred is either not old or tall then lucy is not generous or not rich and vice versa. If someone is either not brave or humble then alice is not curious or not brave. Everyone who is both not patient and not humble is curious or creative. Someone is both strong and not generous. Someone is strong or not wise. Someone is not kind. Mary is not funny or old. Someone is both not rich and tall. Someone is both curious and wise. Susan is either quiet or calm. John is both not tall and not happy. | Mary is humble. | neutral | ((~humble(fred))<=>(?[X]:((~old(X)|~kind(X)))))&
(![X]:((tall(X)|~patient(X))=>(~brave(X)<~>quiet(X))))&
(![X]:(generous(X)<=>~old(X)))&
(![X]:(~kind(X)=>(~funny(X)|~old(X))))&
(![X]:((generous(X)&old(X))=>(~calm(X)&kind(X))))&
(![X]:(~patient(X)<=>brave(X)))&
(![X]:(brave(X)<=>(~strong(X)&~happy(X))))&
((?[X]:((~creative(X)&wise(X))))=>((~brave(mary)&calm(mary))))&
(((funny(john)|curious(john)))<=>((curious(paul)|tall(paul))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:(~happy(X))))&
(((~wise(lucy)<~>~humble(lucy)))=>((~happy(paul)&old(paul))))&
(![X]:(~brave(X)<=>(~calm(X)&~curious(X))))&
((?[X]:((~kind(X)&brave(X))))=>((curious(alice)<~>creative(alice))))&
(((~old(fred)<~>tall(fred)))<=>((~generous(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)<~>humble(X))))=>((~curious(alice)|~brave(alice))))&
(![X]:((~patient(X)&~humble(X))=>(curious(X)|creative(X))))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:((strong(X)|~wise(X))))&
(?[X]:(~kind(X)))&
((~funny(mary)|old(mary)))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((curious(X)&wise(X))))&
((quiet(susan)<~>calm(susan)))&
((~tall(john)&~happy(john))) | humble(mary) | [] | null | 0 |
Everyone who is either quiet or not funny is both kind and not patient and vice versa.
If mary is rich or not generous then susan is happy and vice versa.
If fred is either happy or not kind then alice is generous.
Everyone who is either not rich or not tall is not creative and vice versa.
Everyone who is both rich and humble is not humble or not calm and vice versa.
Everyone who is happy is not curious or not kind.
If someone is rich or creative then mary is creative.
Everyone who is brave is patient.
If someone is either not calm or not rich then someone is strong or curious and vice versa.
If someone is not generous or old then someone is either kind or not brave.
If someone is both not happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
If susan is generous or kind then paul is not creative or not generous.
Everyone who is humble is either rich or not happy and vice versa.
Everyone who is wise or calm is both brave and not wise.
Everyone who is both patient and not strong is not patient and vice versa.
John is not rich.
Someone is curious or generous.
Susan is both curious and humble.
Lucy is both not quiet and patient.
Someone is either not rich or kind.
Someone is rich or not wise.
Fred is both not tall and strong. | Susan is curious. | entailment | (![X]:((quiet(X)<~>~funny(X))<=>(kind(X)&~patient(X))))&
(((rich(mary)|~generous(mary)))<=>(happy(susan)))&
(((happy(fred)<~>~kind(fred)))=>(generous(alice)))&
(![X]:((~rich(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((rich(X)&humble(X))<=>(~humble(X)|~calm(X))))&
(![X]:(happy(X)=>(~curious(X)|~kind(X))))&
((?[X]:((rich(X)|creative(X))))=>(creative(mary)))&
(![X]:(brave(X)=>patient(X)))&
((?[X]:((~calm(X)<~>~rich(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
(((generous(susan)|kind(susan)))=>((~creative(paul)|~generous(paul))))&
(![X]:(humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)&~wise(X))))&
(![X]:((patient(X)&~strong(X))<=>~patient(X)))&
(~rich(john))&
(?[X]:((curious(X)|generous(X))))&
((curious(susan)&humble(susan)))&
((~quiet(lucy)&patient(lucy)))&
(?[X]:((~rich(X)<~>kind(X))))&
(?[X]:((rich(X)|~wise(X))))&
((~tall(fred)&strong(fred))) | curious(susan) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 605060941909180030046762
% SZS output start Proof for 605060941909180030046762
19. humble(susan) & curious(susan) [input p18]
24. ~curious(susan) [input hypothesis]
125. curious(susan) [cnf transformation 19]
133. ~curious(susan) [cnf transformation 24]
282. $false [subsumption resolution 133,125]
% SZS output end Proof for 605060941909180030046762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and strong then someone is both not humble and patient.
Everyone who is generous is both not calm and quiet.
Everyone who is not curious is not brave.
Everyone who is wise or strong is either humble or creative.
Everyone who is not strong is both creative and not quiet and vice versa.
Everyone who is not rich or rich is either not rich or not kind and vice versa.
Everyone who is either not funny or not patient is either not wise or not rich and vice versa.
Everyone who is either happy or quiet is both happy and tall and vice versa.
If someone is either not kind or not old then lucy is not funny and vice versa.
Everyone who is both not tall and not funny is either curious or not patient and vice versa.
Everyone who is not old or quiet is happy.
If fred is strong or generous then someone is both strong and not calm and vice versa.
Everyone who is not rich is both brave and not strong.
Everyone who is either creative or strong is not brave and vice versa.
If someone is both curious and kind then someone is not humble or not happy and vice versa.
Everyone who is not rich or not wise is quiet or creative and vice versa.
Fred is either not patient or not happy.
Someone is either brave or not calm.
Alice is either creative or not old.
Someone is curious.
Someone is either not humble or funny.
Alice is not tall.
Someone is not creative. | Alice is not humble. | contradiction | ((?[X]:((patient(X)&strong(X))))=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:(generous(X)=>(~calm(X)&quiet(X))))&
(![X]:(~curious(X)=>~brave(X)))&
(![X]:((wise(X)|strong(X))=>(humble(X)<~>creative(X))))&
(![X]:(~strong(X)<=>(creative(X)&~quiet(X))))&
(![X]:((~rich(X)|rich(X))<=>(~rich(X)<~>~kind(X))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((happy(X)<~>quiet(X))<=>(happy(X)&tall(X))))&
((?[X]:((~kind(X)<~>~old(X))))<=>(~funny(lucy)))&
(![X]:((~tall(X)&~funny(X))<=>(curious(X)<~>~patient(X))))&
(![X]:((~old(X)|quiet(X))=>happy(X)))&
(((strong(fred)|generous(fred)))<=>(?[X]:((strong(X)&~calm(X)))))&
(![X]:(~rich(X)=>(brave(X)&~strong(X))))&
(![X]:((creative(X)<~>strong(X))<=>~brave(X)))&
((?[X]:((curious(X)&kind(X))))<=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((~rich(X)|~wise(X))<=>(quiet(X)|creative(X))))&
((~patient(fred)<~>~happy(fred)))&
(?[X]:((brave(X)<~>~calm(X))))&
((creative(alice)<~>~old(alice)))&
(?[X]:(curious(X)))&
(?[X]:((~humble(X)<~>funny(X))))&
(~tall(alice))&
(?[X]:(~creative(X))) | ~humble(alice) | [
"p4",
"p5",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 663380490837119447198927
% SZS output start Proof for 663380490837119447198927
5. ! [X0] : (~strong(X0) <=> (~quiet(X0) & creative(X0))) [input p4]
6. ! [X0] : ((rich(X0) | ~rich(X0)) <=> (~rich(X0) <~> ~kind(X0))) [input p5]
13. ! [X0] : (~rich(X0) => (~strong(X0) & brave(X0))) [input p12]
14. ! [X0] : ((creative(X0) <~> strong(X0)) <=> ~brave(X0)) [input p13]
15. ? [X0] : (kind(X0) & curious(X0)) <=> ? [X0] : (~happy(X0) | ~humble(X0)) [input p14]
24. ~humble(alice) [input hypothesis]
26. ? [X0] : (kind(X0) & curious(X0)) <=> ? [X1] : (~happy(X1) | ~humble(X1)) [rectify 15]
32. ! [X0] : ((~strong(X0) & brave(X0)) | rich(X0)) [ennf transformation 13]
37. ! [X0] : ((~strong(X0) | (quiet(X0) | ~creative(X0))) & ((~quiet(X0) & creative(X0)) | strong(X0))) [nnf transformation 5]
38. ! [X0] : ((~strong(X0) | quiet(X0) | ~creative(X0)) & ((~quiet(X0) & creative(X0)) | strong(X0))) [flattening 37]
39. ! [X0] : (((rich(X0) | ~rich(X0)) | ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0)))) & (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | (~rich(X0) & rich(X0)))) [nnf transformation 6]
40. ! [X0] : ((rich(X0) | ~rich(X0) | ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0)))) & (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | (~rich(X0) & rich(X0)))) [flattening 39]
55. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | brave(X0)) & (~brave(X0) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [nnf transformation 14]
56. (? [X0] : (kind(X0) & curious(X0)) | ! [X1] : (happy(X1) & humble(X1))) & (? [X1] : (~happy(X1) | ~humble(X1)) | ! [X0] : (~kind(X0) | ~curious(X0))) [nnf transformation 26]
57. (? [X0] : (kind(X0) & curious(X0)) | ! [X1] : (happy(X1) & humble(X1))) & (? [X2] : (~happy(X2) | ~humble(X2)) | ! [X3] : (~kind(X3) | ~curious(X3))) [rectify 56]
58. ? [X0] : (kind(X0) & curious(X0)) => (kind(sK3) & curious(sK3)) [choice axiom]
59. ? [X2] : (~happy(X2) | ~humble(X2)) => (~happy(sK4) | ~humble(sK4)) [choice axiom]
60. ((kind(sK3) & curious(sK3)) | ! [X1] : (happy(X1) & humble(X1))) & ((~happy(sK4) | ~humble(sK4)) | ! [X3] : (~kind(X3) | ~curious(X3))) [skolemisation 57,59,58]
84. creative(X0) | strong(X0) [cnf transformation 38]
88. ~kind(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 40]
124. rich(X0) | brave(X0) [cnf transformation 32]
125. ~strong(X0) | rich(X0) [cnf transformation 32]
126. ~brave(X0) | strong(X0) | ~creative(X0) [cnf transformation 55]
127. ~brave(X0) | creative(X0) | ~strong(X0) [cnf transformation 55]
133. kind(sK3) | humble(X1) [cnf transformation 60]
150. ~humble(alice) [cnf transformation 24]
153. ~kind(X0) | ~rich(X0) [duplicate literal removal 88]
216. ~brave(X0) | creative(X0) [subsumption resolution 127,84]
217. ~brave(X0) | strong(X0) [subsumption resolution 126,216]
222. 15 <=> kind(sK3) [avatar definition]
224. kind(sK3) <- (15) [avatar component clause 222]
227. 16 <=> ! [X1] : humble(X1) [avatar definition]
228. humble(X1) <- (16) [avatar component clause 227]
229. 16 | 15 [avatar split clause 133,222,227]
299. ~rich(sK3) <- (15) [resolution 153,224]
302. brave(sK3) <- (15) [resolution 299,124]
308. strong(sK3) <- (15) [resolution 302,217]
357. rich(sK3) <- (15) [resolution 308,125]
358. $false <- (15) [subsumption resolution 357,299]
359. ~15 [avatar contradiction clause 358]
364. $false <- (16) [resolution 228,150]
367. ~16 [avatar contradiction clause 364]
368. $false [avatar sat refutation 229,359,367]
% SZS output end Proof for 663380490837119447198927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is both not quiet and rich. Everyone who is not rich or calm is either not happy or not humble. Everyone who is both tall and patient is not old. Everyone who is both calm and tall is not creative and vice versa. Everyone who is rich or not happy is either not brave or not kind and vice versa. Everyone who is either old or brave is curious or not strong. If someone is both not wise and not creative then john is wise. If paul is not tall or not creative then someone is both not generous and creative. If someone is either not calm or funny then someone is kind and vice versa. Everyone who is both not strong and brave is not quiet or kind. If someone is either not funny or not wise then someone is both patient and not wise and vice versa. Everyone who is both tall and patient is both not patient and strong. If john is rich or not generous then someone is brave and vice versa. Everyone who is not humble or humble is old or quiet and vice versa. Everyone who is both not funny and not kind is not patient. Everyone who is both strong and tall is wise. Susan is calm or not humble. Lucy is either not curious or curious. Someone is either not strong or funny. Fred is both not quiet and strong. John is either brave or not humble. Someone is patient. Paul is either not brave or not strong. Alice is both not creative and not happy. | John is not strong. | neutral | (![X]:(generous(X)=>(~quiet(X)&rich(X))))&
(![X]:((~rich(X)|calm(X))=>(~happy(X)<~>~humble(X))))&
(![X]:((tall(X)&patient(X))=>~old(X)))&
(![X]:((calm(X)&tall(X))<=>~creative(X)))&
(![X]:((rich(X)|~happy(X))<=>(~brave(X)<~>~kind(X))))&
(![X]:((old(X)<~>brave(X))=>(curious(X)|~strong(X))))&
((?[X]:((~wise(X)&~creative(X))))=>(wise(john)))&
(((~tall(paul)|~creative(paul)))=>(?[X]:((~generous(X)&creative(X)))))&
((?[X]:((~calm(X)<~>funny(X))))<=>(?[X]:(kind(X))))&
(![X]:((~strong(X)&brave(X))=>(~quiet(X)|kind(X))))&
((?[X]:((~funny(X)<~>~wise(X))))<=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((tall(X)&patient(X))=>(~patient(X)&strong(X))))&
(((rich(john)|~generous(john)))<=>(?[X]:(brave(X))))&
(![X]:((~humble(X)|humble(X))<=>(old(X)|quiet(X))))&
(![X]:((~funny(X)&~kind(X))=>~patient(X)))&
(![X]:((strong(X)&tall(X))=>wise(X)))&
((calm(susan)|~humble(susan)))&
((~curious(lucy)<~>curious(lucy)))&
(?[X]:((~strong(X)<~>funny(X))))&
((~quiet(fred)&strong(fred)))&
((brave(john)<~>~humble(john)))&
(?[X]:(patient(X)))&
((~brave(paul)<~>~strong(paul)))&
((~creative(alice)&~happy(alice))) | ~strong(john) | [] | null | 0 |
Everyone who is both not funny and not generous is either generous or not brave. Everyone who is quiet is both quiet and not wise and vice versa. Everyone who is both calm and not kind is rich. Everyone who is not happy is not curious or calm. If someone is curious or quiet then someone is not happy and vice versa. Everyone who is both not strong and wise is both not funny and rich and vice versa. Everyone who is either not rich or wise is either not strong or not calm and vice versa. Everyone who is both not tall and not quiet is wise. If someone is creative then lucy is both tall and not generous. If someone is strong or not funny then someone is not humble or not generous and vice versa. Everyone who is both funny and not rich is kind. Everyone who is both brave and not funny is not tall or not kind and vice versa. Everyone who is either not humble or patient is both creative and not kind and vice versa. If john is not humble or curious then alice is both funny and kind and vice versa. If someone is not rich then someone is both happy and not funny and vice versa. If alice is either curious or not kind then someone is strong. Mary is both not happy and curious. Lucy is either not brave or curious. Lucy is not generous. Lucy is either not quiet or not creative. John is either generous or not kind. Alice is not tall or not humble. Someone is both not generous and wise. Someone is either not calm or not brave. | Alice is not humble. | neutral | (![X]:((~funny(X)&~generous(X))=>(generous(X)<~>~brave(X))))&
(![X]:(quiet(X)<=>(quiet(X)&~wise(X))))&
(![X]:((calm(X)&~kind(X))=>rich(X)))&
(![X]:(~happy(X)=>(~curious(X)|calm(X))))&
((?[X]:((curious(X)|quiet(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)&wise(X))<=>(~funny(X)&rich(X))))&
(![X]:((~rich(X)<~>wise(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:((~tall(X)&~quiet(X))=>wise(X)))&
((?[X]:(creative(X)))=>((tall(lucy)&~generous(lucy))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((funny(X)&~rich(X))=>kind(X)))&
(![X]:((brave(X)&~funny(X))<=>(~tall(X)|~kind(X))))&
(![X]:((~humble(X)<~>patient(X))<=>(creative(X)&~kind(X))))&
(((~humble(john)|curious(john)))<=>((funny(alice)&kind(alice))))&
((?[X]:(~rich(X)))<=>(?[X]:((happy(X)&~funny(X)))))&
(((curious(alice)<~>~kind(alice)))=>(?[X]:(strong(X))))&
((~happy(mary)&curious(mary)))&
((~brave(lucy)<~>curious(lucy)))&
(~generous(lucy))&
((~quiet(lucy)<~>~creative(lucy)))&
((generous(john)<~>~kind(john)))&
((~tall(alice)|~humble(alice)))&
(?[X]:((~generous(X)&wise(X))))&
(?[X]:((~calm(X)<~>~brave(X)))) | ~humble(alice) | [] | null | 0 |
Everyone who is patient is either curious or not strong and vice versa.
Everyone who is both old and tall is wise.
Everyone who is not strong is either not generous or brave.
Everyone who is curious is both not patient and not strong.
Everyone who is not tall or not strong is either calm or generous.
Everyone who is both not brave and not funny is happy and vice versa.
If john is either kind or funny then lucy is not patient or not tall.
If paul is not quiet or not humble then someone is brave or not happy.
Everyone who is both quiet and not kind is either not brave or not rich and vice versa.
If alice is not rich or creative then someone is either generous or funny and vice versa.
If someone is not wise or creative then someone is either not brave or not funny and vice versa.
Everyone who is calm is not brave and vice versa.
If paul is either not rich or not quiet then john is funny and vice versa.
Everyone who is curious is happy.
Everyone who is either generous or not curious is curious and vice versa.
Everyone who is either not wise or not brave is not creative or not kind.
Alice is humble.
Someone is calm or old.
Someone is both tall and rich.
Someone is not funny or not humble. | Paul is not kind. | neutral | (![X]:(patient(X)<=>(curious(X)<~>~strong(X))))&
(![X]:((old(X)&tall(X))=>wise(X)))&
(![X]:(~strong(X)=>(~generous(X)<~>brave(X))))&
(![X]:(curious(X)=>(~patient(X)&~strong(X))))&
(![X]:((~tall(X)|~strong(X))=>(calm(X)<~>generous(X))))&
(![X]:((~brave(X)&~funny(X))<=>happy(X)))&
(((kind(john)<~>funny(john)))=>((~patient(lucy)|~tall(lucy))))&
(((~quiet(paul)|~humble(paul)))=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(~brave(X)<~>~rich(X))))&
(((~rich(alice)|creative(alice)))<=>(?[X]:((generous(X)<~>funny(X)))))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(![X]:(calm(X)<=>~brave(X)))&
(((~rich(paul)<~>~quiet(paul)))<=>(funny(john)))&
(![X]:(curious(X)=>happy(X)))&
(![X]:((generous(X)<~>~curious(X))<=>curious(X)))&
(![X]:((~wise(X)<~>~brave(X))=>(~creative(X)|~kind(X))))&
(humble(alice))&
(?[X]:((calm(X)|old(X))))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:((~funny(X)|~humble(X)))) | ~kind(paul) | [] | null | 0 |
If someone is patient then someone is not kind and vice versa. If fred is generous then fred is not brave. Everyone who is not brave or brave is either creative or curious. Everyone who is both brave and rich is both rich and not funny and vice versa. Everyone who is both tall and not kind is both not generous and creative and vice versa. Everyone who is either curious or generous is either tall or wise. If someone is not calm or happy then someone is brave or not curious and vice versa. Everyone who is both not calm and funny is either curious or not curious and vice versa. Everyone who is not brave or generous is either calm or not brave and vice versa. Everyone who is generous or not creative is not quiet or brave and vice versa. Everyone who is either rich or strong is kind and vice versa. Everyone who is funny or calm is either not generous or not creative. If alice is not creative or not funny then someone is either generous or happy. Everyone who is curious is either tall or not patient. If someone is both not kind and not wise then someone is both not curious and not rich and vice versa. If john is either not brave or tall then someone is either tall or not old. Susan is curious. Lucy is rich or not tall. Someone is happy or not calm. Fred is generous or funny. John is both not patient and not happy. Lucy is old or curious. Lucy is either quiet or not funny. | John is not generous. | neutral | ((?[X]:(patient(X)))<=>(?[X]:(~kind(X))))&
((generous(fred))=>(~brave(fred)))&
(![X]:((~brave(X)|brave(X))=>(creative(X)<~>curious(X))))&
(![X]:((brave(X)&rich(X))<=>(rich(X)&~funny(X))))&
(![X]:((tall(X)&~kind(X))<=>(~generous(X)&creative(X))))&
(![X]:((curious(X)<~>generous(X))=>(tall(X)<~>wise(X))))&
((?[X]:((~calm(X)|happy(X))))<=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((~calm(X)&funny(X))<=>(curious(X)<~>~curious(X))))&
(![X]:((~brave(X)|generous(X))<=>(calm(X)<~>~brave(X))))&
(![X]:((generous(X)|~creative(X))<=>(~quiet(X)|brave(X))))&
(![X]:((rich(X)<~>strong(X))<=>kind(X)))&
(![X]:((funny(X)|calm(X))=>(~generous(X)<~>~creative(X))))&
(((~creative(alice)|~funny(alice)))=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:(curious(X)=>(tall(X)<~>~patient(X))))&
((?[X]:((~kind(X)&~wise(X))))<=>(?[X]:((~curious(X)&~rich(X)))))&
(((~brave(john)<~>tall(john)))=>(?[X]:((tall(X)<~>~old(X)))))&
(curious(susan))&
((rich(lucy)|~tall(lucy)))&
(?[X]:((happy(X)|~calm(X))))&
((generous(fred)|funny(fred)))&
((~patient(john)&~happy(john)))&
((old(lucy)|curious(lucy)))&
((quiet(lucy)<~>~funny(lucy))) | ~generous(john) | [] | null | 0 |
Everyone who is both patient and not wise is both not patient and tall and vice versa.
If someone is both tall and patient then someone is either happy or strong and vice versa.
Everyone who is either old or not curious is both creative and not generous.
Everyone who is both not creative and kind is not curious or strong.
Everyone who is not happy or brave is curious or not curious and vice versa.
Everyone who is creative is both not curious and not brave.
If john is not old then fred is not calm and vice versa.
If susan is generous or creative then someone is both not happy and funny and vice versa.
Everyone who is not tall or calm is creative or not curious.
If john is either generous or wise then someone is curious.
Everyone who is either creative or quiet is both patient and calm.
If someone is strong or generous then alice is either funny or not tall.
Everyone who is either old or not brave is not generous or patient and vice versa.
If paul is both not brave and not happy then paul is either strong or curious.
Everyone who is humble is not wise.
Everyone who is either not strong or kind is not funny or strong.
Mary is patient or not old.
Someone is both strong and happy.
Someone is generous or not quiet.
Mary is not rich or calm.
Fred is not creative.
Fred is old or not tall. | John is not quiet. | neutral | (![X]:((patient(X)&~wise(X))<=>(~patient(X)&tall(X))))&
((?[X]:((tall(X)&patient(X))))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:((old(X)<~>~curious(X))=>(creative(X)&~generous(X))))&
(![X]:((~creative(X)&kind(X))=>(~curious(X)|strong(X))))&
(![X]:((~happy(X)|brave(X))<=>(curious(X)|~curious(X))))&
(![X]:(creative(X)=>(~curious(X)&~brave(X))))&
((~old(john))<=>(~calm(fred)))&
(((generous(susan)|creative(susan)))<=>(?[X]:((~happy(X)&funny(X)))))&
(![X]:((~tall(X)|calm(X))=>(creative(X)|~curious(X))))&
(((generous(john)<~>wise(john)))=>(?[X]:(curious(X))))&
(![X]:((creative(X)<~>quiet(X))=>(patient(X)&calm(X))))&
((?[X]:((strong(X)|generous(X))))=>((funny(alice)<~>~tall(alice))))&
(![X]:((old(X)<~>~brave(X))<=>(~generous(X)|patient(X))))&
(((~brave(paul)&~happy(paul)))=>((strong(paul)<~>curious(paul))))&
(![X]:(humble(X)=>~wise(X)))&
(![X]:((~strong(X)<~>kind(X))=>(~funny(X)|strong(X))))&
((patient(mary)|~old(mary)))&
(?[X]:((strong(X)&happy(X))))&
(?[X]:((generous(X)|~quiet(X))))&
((~rich(mary)|calm(mary)))&
(~creative(fred))&
((old(fred)|~tall(fred))) | ~quiet(john) | [] | null | 0 |
If fred is either not kind or rich then fred is both not curious and not generous and vice versa.
If someone is either not strong or not old then someone is both not generous and not rich.
Everyone who is not quiet or not brave is tall and vice versa.
Everyone who is both not tall and curious is either not patient or happy and vice versa.
Everyone who is both not rich and not old is old and vice versa.
Everyone who is not patient or not calm is either not happy or not quiet and vice versa.
If someone is both not brave and wise then john is either curious or tall.
If fred is either old or happy then lucy is either curious or not quiet and vice versa.
Everyone who is either rich or happy is humble or quiet and vice versa.
Everyone who is not funny is either kind or not happy.
Everyone who is not curious is curious or not strong and vice versa.
If someone is creative or calm then someone is both wise and not calm and vice versa.
Everyone who is kind or not humble is either not old or not curious and vice versa.
If paul is not old then lucy is either creative or not rich.
Everyone who is humble or not generous is either happy or creative and vice versa.
Someone is wise or quiet.
Paul is humble.
Someone is not funny or funny.
Someone is either not tall or not patient.
Paul is either not rich or rich.
Alice is kind or not strong.
Susan is patient. | Susan is creative. | entailment | (((~kind(fred)<~>rich(fred)))<=>((~curious(fred)&~generous(fred))))&
((?[X]:((~strong(X)<~>~old(X))))=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((~quiet(X)|~brave(X))<=>tall(X)))&
(![X]:((~tall(X)&curious(X))<=>(~patient(X)<~>happy(X))))&
(![X]:((~rich(X)&~old(X))<=>old(X)))&
(![X]:((~patient(X)|~calm(X))<=>(~happy(X)<~>~quiet(X))))&
((?[X]:((~brave(X)&wise(X))))=>((curious(john)<~>tall(john))))&
(((old(fred)<~>happy(fred)))<=>((curious(lucy)<~>~quiet(lucy))))&
(![X]:((rich(X)<~>happy(X))<=>(humble(X)|quiet(X))))&
(![X]:(~funny(X)=>(kind(X)<~>~happy(X))))&
(![X]:(~curious(X)<=>(curious(X)|~strong(X))))&
((?[X]:((creative(X)|calm(X))))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((kind(X)|~humble(X))<=>(~old(X)<~>~curious(X))))&
((~old(paul))=>((creative(lucy)<~>~rich(lucy))))&
(![X]:((humble(X)|~generous(X))<=>(happy(X)<~>creative(X))))&
(?[X]:((wise(X)|quiet(X))))&
(humble(paul))&
(?[X]:((~funny(X)|funny(X))))&
(?[X]:((~tall(X)<~>~patient(X))))&
((~rich(paul)<~>rich(paul)))&
((kind(alice)|~strong(alice)))&
(patient(susan)) | creative(susan) | [
"p4",
"p8",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4325698614031620800334065
% SZS output start Proof for 4325698614031620800334065
5. ! [X0] : ((~old(X0) & ~rich(X0)) <=> old(X0)) [input p4]
9. ! [X0] : ((rich(X0) <~> happy(X0)) <=> (quiet(X0) | humble(X0))) [input p8]
11. ! [X0] : (~curious(X0) <=> (~strong(X0) | curious(X0))) [input p10]
13. ! [X0] : ((~humble(X0) | kind(X0)) <=> (~old(X0) <~> ~curious(X0))) [input p12]
15. ! [X0] : ((~generous(X0) | humble(X0)) <=> (happy(X0) <~> creative(X0))) [input p14]
23. ~creative(susan) [input hypothesis]
40. ! [X0] : (((~old(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | (old(X0) | rich(X0)))) [nnf transformation 5]
41. ! [X0] : (((~old(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | old(X0) | rich(X0))) [flattening 40]
46. ! [X0] : ((((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0))))) [flattening 46]
49. ! [X0] : ((~curious(X0) | (strong(X0) & ~curious(X0))) & ((~strong(X0) | curious(X0)) | curious(X0))) [nnf transformation 11]
50. ! [X0] : ((~curious(X0) | (strong(X0) & ~curious(X0))) & (~strong(X0) | curious(X0) | curious(X0))) [flattening 49]
56. ! [X0] : (((~humble(X0) | kind(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (humble(X0) & ~kind(X0)))) [nnf transformation 13]
57. ! [X0] : ((~humble(X0) | kind(X0) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (humble(X0) & ~kind(X0)))) [flattening 56]
59. ! [X0] : (((~generous(X0) | humble(X0)) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | (generous(X0) & ~humble(X0)))) [nnf transformation 15]
60. ! [X0] : ((~generous(X0) | humble(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | (generous(X0) & ~humble(X0)))) [flattening 59]
88. old(X0) | old(X0) | rich(X0) [cnf transformation 41]
90. ~old(X0) | ~old(X0) [cnf transformation 41]
111. ~happy(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 47]
116. ~curious(X0) | ~curious(X0) [cnf transformation 50]
126. curious(X0) | old(X0) | humble(X0) [cnf transformation 57]
131. creative(X0) | happy(X0) | ~humble(X0) [cnf transformation 60]
146. ~creative(susan) [cnf transformation 23]
148. ~curious(X0) [duplicate literal removal 116]
149. old(X0) | rich(X0) [duplicate literal removal 88]
150. ~old(X0) [duplicate literal removal 90]
191. rich(X0) [subsumption resolution 149,150]
226. ~humble(X0) | ~happy(X0) [subsumption resolution 111,191]
259. old(X0) | humble(X0) [subsumption resolution 126,148]
260. humble(X0) [subsumption resolution 259,150]
265. creative(X0) | happy(X0) [subsumption resolution 131,260]
300. ~happy(X0) [resolution 226,260]
301. happy(susan) [resolution 265,146]
302. $false [subsumption resolution 301,300]
% SZS output end Proof for 4325698614031620800334065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not strong is both kind and not funny and vice versa.
Everyone who is not old or tall is happy.
Everyone who is both not kind and rich is humble.
Everyone who is generous is wise.
Everyone who is both quiet and humble is quiet or strong and vice versa.
Everyone who is kind or tall is both strong and generous.
Everyone who is either curious or not funny is either not brave or strong and vice versa.
If someone is both not creative and curious then mary is generous or calm and vice versa.
Everyone who is both not calm and strong is either wise or kind and vice versa.
Everyone who is both not calm and rich is not generous.
Everyone who is not generous or not curious is either happy or generous and vice versa.
Everyone who is either creative or tall is either patient or not funny.
Everyone who is not rich or not humble is not patient or not rich.
Everyone who is both not strong and rich is either not kind or wise.
If someone is either not creative or not patient then someone is not humble or not generous and vice versa.
Everyone who is funny or humble is creative or not creative.
Mary is not humble or quiet.
Someone is either creative or humble.
John is either happy or not tall.
Mary is kind.
Someone is both generous and not creative. | John is kind. | entailment | (![X]:((quiet(X)|~strong(X))<=>(kind(X)&~funny(X))))&
(![X]:((~old(X)|tall(X))=>happy(X)))&
(![X]:((~kind(X)&rich(X))=>humble(X)))&
(![X]:(generous(X)=>wise(X)))&
(![X]:((quiet(X)&humble(X))<=>(quiet(X)|strong(X))))&
(![X]:((kind(X)|tall(X))=>(strong(X)&generous(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(~brave(X)<~>strong(X))))&
((?[X]:((~creative(X)&curious(X))))<=>((generous(mary)|calm(mary))))&
(![X]:((~calm(X)&strong(X))<=>(wise(X)<~>kind(X))))&
(![X]:((~calm(X)&rich(X))=>~generous(X)))&
(![X]:((~generous(X)|~curious(X))<=>(happy(X)<~>generous(X))))&
(![X]:((creative(X)<~>tall(X))=>(patient(X)<~>~funny(X))))&
(![X]:((~rich(X)|~humble(X))=>(~patient(X)|~rich(X))))&
(![X]:((~strong(X)&rich(X))=>(~kind(X)<~>wise(X))))&
((?[X]:((~creative(X)<~>~patient(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((funny(X)|humble(X))=>(creative(X)|~creative(X))))&
((~humble(mary)|quiet(mary)))&
(?[X]:((creative(X)<~>humble(X))))&
((happy(john)<~>~tall(john)))&
(kind(mary))&
(?[X]:((generous(X)&~creative(X)))) | kind(john) | [
"p0",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5927056034277696408533792
% SZS output start Proof for 5927056034277696408533792
1. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (~funny(X0) & kind(X0))) [input p0]
5. ! [X0] : ((humble(X0) & quiet(X0)) <=> (strong(X0) | quiet(X0))) [input p4]
6. ! [X0] : ((tall(X0) | kind(X0)) => (generous(X0) & strong(X0))) [input p5]
22. ~kind(john) [input hypothesis]
29. ! [X0] : ((generous(X0) & strong(X0)) | (~tall(X0) & ~kind(X0))) [ennf transformation 6]
39. ! [X0] : (((~strong(X0) | quiet(X0)) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | (strong(X0) & ~quiet(X0)))) [nnf transformation 1]
40. ! [X0] : ((~strong(X0) | quiet(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | (strong(X0) & ~quiet(X0)))) [flattening 39]
41. ! [X0] : (((humble(X0) & quiet(X0)) | (~strong(X0) & ~quiet(X0))) & ((strong(X0) | quiet(X0)) | (~humble(X0) | ~quiet(X0)))) [nnf transformation 5]
42. ! [X0] : (((humble(X0) & quiet(X0)) | (~strong(X0) & ~quiet(X0))) & (strong(X0) | quiet(X0) | ~humble(X0) | ~quiet(X0))) [flattening 41]
66. ~quiet(X0) | kind(X0) [cnf transformation 40]
67. kind(X0) | strong(X0) [cnf transformation 40]
76. ~strong(X0) | quiet(X0) [cnf transformation 42]
79. strong(X0) | ~kind(X0) [cnf transformation 29]
133. ~kind(john) [cnf transformation 22]
136. strong(X0) [subsumption resolution 79,67]
232. quiet(X0) [resolution 76,136]
234. kind(X1) [resolution 232,66]
241. $false [resolution 234,133]
% SZS output end Proof for 5927056034277696408533792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is either kind or not rich and vice versa.
Everyone who is funny is not tall or not funny and vice versa.
If mary is either not kind or strong then fred is either not happy or not humble and vice versa.
If paul is old then someone is humble and vice versa.
Everyone who is wise or not generous is not calm or not creative.
If someone is not calm then someone is both creative and strong and vice versa.
If susan is generous or quiet then someone is either quiet or happy.
Everyone who is both calm and not rich is both rich and not funny.
Everyone who is kind is both not tall and happy.
Everyone who is old or strong is wise.
Everyone who is both not creative and humble is curious or not humble and vice versa.
Everyone who is either not funny or not wise is both not quiet and kind.
If paul is generous then alice is not strong or strong and vice versa.
Everyone who is either not old or not tall is patient or quiet and vice versa.
If someone is both not humble and creative then lucy is both not funny and patient.
Everyone who is either patient or not generous is both creative and tall and vice versa.
Susan is humble or not brave.
Susan is either not generous or not rich.
John is funny or not quiet.
Alice is not kind or not curious.
Someone is either not funny or strong.
Someone is both not quiet and not tall. | Susan is kind. | entailment | (![X]:((~rich(X)<~>humble(X))<=>(kind(X)<~>~rich(X))))&
(![X]:(funny(X)<=>(~tall(X)|~funny(X))))&
(((~kind(mary)<~>strong(mary)))<=>((~happy(fred)<~>~humble(fred))))&
((old(paul))<=>(?[X]:(humble(X))))&
(![X]:((wise(X)|~generous(X))=>(~calm(X)|~creative(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((creative(X)&strong(X)))))&
(((generous(susan)|quiet(susan)))=>(?[X]:((quiet(X)<~>happy(X)))))&
(![X]:((calm(X)&~rich(X))=>(rich(X)&~funny(X))))&
(![X]:(kind(X)=>(~tall(X)&happy(X))))&
(![X]:((old(X)|strong(X))=>wise(X)))&
(![X]:((~creative(X)&humble(X))<=>(curious(X)|~humble(X))))&
(![X]:((~funny(X)<~>~wise(X))=>(~quiet(X)&kind(X))))&
((generous(paul))<=>((~strong(alice)|strong(alice))))&
(![X]:((~old(X)<~>~tall(X))<=>(patient(X)|quiet(X))))&
((?[X]:((~humble(X)&creative(X))))=>((~funny(lucy)&patient(lucy))))&
(![X]:((patient(X)<~>~generous(X))<=>(creative(X)&tall(X))))&
((humble(susan)|~brave(susan)))&
((~generous(susan)<~>~rich(susan)))&
((funny(john)|~quiet(john)))&
((~kind(alice)|~curious(alice)))&
(?[X]:((~funny(X)<~>strong(X))))&
(?[X]:((~quiet(X)&~tall(X)))) | kind(susan) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7040961690090940821956046
% SZS output start Proof for 7040961690090940821956046
1. ! [X0] : ((~rich(X0) <~> humble(X0)) <=> (kind(X0) <~> ~rich(X0))) [input p0]
11. ! [X0] : ((humble(X0) & ~creative(X0)) <=> (~humble(X0) | curious(X0))) [input p10]
23. ~kind(susan) [input hypothesis]
35. ! [X0] : ((((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | ((kind(X0) | rich(X0)) & (~rich(X0) | ~kind(X0)))) & (((rich(X0) | ~kind(X0)) & (~rich(X0) | kind(X0))) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))))) [nnf transformation 1]
51. ! [X0] : (((humble(X0) & ~creative(X0)) | (humble(X0) & ~curious(X0))) & ((~humble(X0) | curious(X0)) | (~humble(X0) | creative(X0)))) [nnf transformation 11]
52. ! [X0] : (((humble(X0) & ~creative(X0)) | (humble(X0) & ~curious(X0))) & (~humble(X0) | curious(X0) | ~humble(X0) | creative(X0))) [flattening 51]
67. ~rich(X0) | kind(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 35]
73. ~humble(X0) | rich(X0) | kind(X0) | rich(X0) [cnf transformation 35]
106. humble(X0) | humble(X0) [cnf transformation 52]
136. ~kind(susan) [cnf transformation 23]
138. humble(X0) [duplicate literal removal 106]
142. ~rich(X0) | kind(X0) | ~humble(X0) [duplicate literal removal 67]
145. ~humble(X0) | rich(X0) | kind(X0) [duplicate literal removal 73]
147. ~humble(X0) | kind(X0) [subsumption resolution 142,145]
268. kind(X0) [resolution 147,138]
272. $false [resolution 268,136]
% SZS output end Proof for 7040961690090940821956046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not 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. | Mary is not creative. | contradiction | (![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))) | ~creative(mary) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1986854452337611901783748
% SZS output start Proof for 1986854452337611901783748
2. ! [X0] : ((~funny(X0) | ~kind(X0)) <=> (wise(X0) <~> ~funny(X0))) [input p1]
5. ! [X0] : ((strong(X0) & tall(X0)) <=> (generous(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | funny(X0)) <=> (rich(X0) & tall(X0))) [input p5]
7. ! [X0] : ((~patient(X0) | happy(X0)) => patient(X0)) [input p6]
8. ! [X0] : (tall(X0) <=> (humble(X0) & strong(X0))) [input p7]
9. ? [X0] : (happy(X0) <~> brave(X0)) <=> ? [X0] : ~patient(X0) [input p8]
15. ! [X0] : ((~creative(X0) & rich(X0)) => (~happy(X0) <~> curious(X0))) [input p14]
16. ! [X0] : (rich(X0) => (creative(X0) | ~curious(X0))) [input p15]
23. ~creative(mary) [input hypothesis]
24. ? [X0] : (happy(X0) <~> brave(X0)) <=> ? [X1] : ~patient(X1) [rectify 9]
30. ! [X0] : (patient(X0) | (patient(X0) & ~happy(X0))) [ennf transformation 7]
35. ! [X0] : ((~happy(X0) <~> curious(X0)) | (creative(X0) | ~rich(X0))) [ennf transformation 15]
36. ! [X0] : ((~happy(X0) <~> curious(X0)) | creative(X0) | ~rich(X0)) [flattening 35]
37. ! [X0] : ((creative(X0) | ~curious(X0)) | ~rich(X0)) [ennf transformation 16]
38. ! [X0] : (creative(X0) | ~curious(X0) | ~rich(X0)) [flattening 37]
41. ! [X0] : (((~funny(X0) | ~kind(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [nnf transformation 2]
42. ! [X0] : ((~funny(X0) | ~kind(X0) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [flattening 41]
45. ! [X0] : (((strong(X0) & tall(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 5]
46. ! [X0] : (((strong(X0) & tall(X0)) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | ~strong(X0) | ~tall(X0))) [flattening 45]
47. ! [X0] : (((~wise(X0) | funny(X0)) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [nnf transformation 6]
48. ! [X0] : ((~wise(X0) | funny(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [flattening 47]
49. ! [X0] : ((tall(X0) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | ~tall(X0))) [nnf transformation 8]
50. ! [X0] : ((tall(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | ~tall(X0))) [flattening 49]
51. (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) [nnf transformation 24]
52. (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : ((happy(X3) | ~brave(X3)) & (brave(X3) | ~happy(X3)))) [rectify 51]
53. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) => ((~brave(sK0) | ~happy(sK0)) & (brave(sK0) | happy(sK0))) [choice axiom]
54. ? [X2] : ~patient(X2) => ~patient(sK1) [choice axiom]
55. (((~brave(sK0) | ~happy(sK0)) & (brave(sK0) | happy(sK0))) | ! [X1] : patient(X1)) & (~patient(sK1) | ! [X3] : ((happy(X3) | ~brave(X3)) & (brave(X3) | ~happy(X3)))) [skolemisation 52,54,53]
70. ! [X0] : (((~curious(X0) | happy(X0)) & (curious(X0) | ~happy(X0))) | creative(X0) | ~rich(X0)) [nnf transformation 36]
88. funny(X0) | ~wise(X0) | funny(X0) [cnf transformation 42]
95. ~strong(X0) | brave(X0) | ~tall(X0) [cnf transformation 46]
99. ~funny(X0) | tall(X0) [cnf transformation 48]
100. wise(X0) | tall(X0) [cnf transformation 48]
101. ~funny(X0) | rich(X0) [cnf transformation 48]
102. rich(X0) | wise(X0) [cnf transformation 48]
105. patient(X0) | patient(X0) [cnf transformation 30]
106. ~tall(X0) | strong(X0) [cnf transformation 50]
110. ~patient(sK1) | happy(X3) | ~brave(X3) [cnf transformation 55]
130. ~rich(X0) | ~happy(X0) | creative(X0) | curious(X0) [cnf transformation 70]
132. ~curious(X0) | creative(X0) | ~rich(X0) [cnf transformation 38]
141. ~creative(mary) [cnf transformation 23]
142. patient(X0) [duplicate literal removal 105]
144. ~wise(X0) | funny(X0) [duplicate literal removal 88]
151. 2 <=> creative(mary) [avatar definition]
153. ~creative(mary) <- (~2) [avatar component clause 151]
160. ~brave(X3) | happy(X3) [subsumption resolution 110,142]
277. ~2 [avatar split clause 141,151]
297. funny(X0) | tall(X0) [resolution 144,100]
299. tall(X0) [subsumption resolution 297,99]
302. strong(X1) [resolution 299,106]
331. brave(X0) | ~tall(X0) [resolution 95,302]
336. brave(X0) [subsumption resolution 331,299]
337. happy(X0) [resolution 336,160]
386. ~happy(X0) | creative(X0) | curious(X0) | wise(X0) [resolution 130,102]
398. curious(X0) | creative(X0) | wise(X0) [subsumption resolution 386,337]
415. creative(X1) | wise(X1) | creative(X1) | ~rich(X1) [resolution 398,132]
416. creative(X1) | wise(X1) | ~rich(X1) [duplicate literal removal 415]
427. creative(X1) | wise(X1) [subsumption resolution 416,102]
432. wise(mary) <- (~2) [resolution 427,153]
435. funny(mary) <- (~2) [resolution 432,144]
453. rich(mary) <- (~2) [resolution 435,101]
458. ~happy(mary) | creative(mary) | curious(mary) <- (~2) [resolution 453,130]
459. creative(mary) | curious(mary) <- (~2) [subsumption resolution 458,337]
460. curious(mary) <- (~2) [subsumption resolution 459,153]
465. creative(mary) | ~rich(mary) <- (~2) [resolution 460,132]
466. ~rich(mary) <- (~2) [subsumption resolution 465,153]
467. $false <- (~2) [subsumption resolution 466,453]
468. 2 [avatar contradiction clause 467]
469. $false [avatar sat refutation 277,468]
% SZS output end Proof for 1986854452337611901783748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is both not happy and quiet and vice versa.
Everyone who is either curious or not patient is either rich or tall.
If john is both not strong and not tall then susan is either curious or not happy and vice versa.
If someone is not rich then someone is either quiet or strong and vice versa.
Everyone who is not wise or not creative is either funny or calm and vice versa.
If someone is either generous or funny then mary is both not generous and not wise.
If someone is both not creative and not funny then someone is both rich and kind.
Everyone who is curious or kind is both strong and patient and vice versa.
Everyone who is either strong or generous is both not strong and curious.
If someone is tall or not humble then someone is funny and vice versa.
Everyone who is not curious is both not wise and kind.
If susan is patient then someone is old or funny.
If someone is patient then someone is generous.
If someone is both not generous and not patient then lucy is either humble or not creative.
If someone is both not old and brave then someone is either quiet or not generous and vice versa.
Everyone who is either not humble or not calm is kind and vice versa.
Fred is not tall or not funny.
Fred is quiet or calm.
Someone is both funny and curious.
Susan is either not calm or not wise.
Susan is both not old and not creative.
John is not creative or patient. | Mary is quiet. | entailment | (![X]:(patient(X)<=>(~happy(X)&quiet(X))))&
(![X]:((curious(X)<~>~patient(X))=>(rich(X)<~>tall(X))))&
(((~strong(john)&~tall(john)))<=>((curious(susan)<~>~happy(susan))))&
((?[X]:(~rich(X)))<=>(?[X]:((quiet(X)<~>strong(X)))))&
(![X]:((~wise(X)|~creative(X))<=>(funny(X)<~>calm(X))))&
((?[X]:((generous(X)<~>funny(X))))=>((~generous(mary)&~wise(mary))))&
((?[X]:((~creative(X)&~funny(X))))=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((curious(X)|kind(X))<=>(strong(X)&patient(X))))&
(![X]:((strong(X)<~>generous(X))=>(~strong(X)&curious(X))))&
((?[X]:((tall(X)|~humble(X))))<=>(?[X]:(funny(X))))&
(![X]:(~curious(X)=>(~wise(X)&kind(X))))&
((patient(susan))=>(?[X]:((old(X)|funny(X)))))&
((?[X]:(patient(X)))=>(?[X]:(generous(X))))&
((?[X]:((~generous(X)&~patient(X))))=>((humble(lucy)<~>~creative(lucy))))&
((?[X]:((~old(X)&brave(X))))<=>(?[X]:((quiet(X)<~>~generous(X)))))&
(![X]:((~humble(X)<~>~calm(X))<=>kind(X)))&
((~tall(fred)|~funny(fred)))&
((quiet(fred)|calm(fred)))&
(?[X]:((funny(X)&curious(X))))&
((~calm(susan)<~>~wise(susan)))&
((~old(susan)&~creative(susan)))&
((~creative(john)|patient(john))) | quiet(mary) | [
"p0",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2419320914755239543292718
% SZS output start Proof for 2419320914755239543292718
1. ! [X0] : (patient(X0) <=> (quiet(X0) & ~happy(X0))) [input p0]
8. ! [X0] : ((kind(X0) | curious(X0)) <=> (patient(X0) & strong(X0))) [input p7]
11. ! [X0] : (~curious(X0) => (kind(X0) & ~wise(X0))) [input p10]
23. ~quiet(mary) [input hypothesis]
33. ! [X0] : ((kind(X0) & ~wise(X0)) | curious(X0)) [ennf transformation 11]
37. ! [X0] : ((patient(X0) | (~quiet(X0) | happy(X0))) & ((quiet(X0) & ~happy(X0)) | ~patient(X0))) [nnf transformation 1]
38. ! [X0] : ((patient(X0) | ~quiet(X0) | happy(X0)) & ((quiet(X0) & ~happy(X0)) | ~patient(X0))) [flattening 37]
53. ! [X0] : (((kind(X0) | curious(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~kind(X0) & ~curious(X0)))) [nnf transformation 8]
54. ! [X0] : ((kind(X0) | curious(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~kind(X0) & ~curious(X0)))) [flattening 53]
77. ~patient(X0) | quiet(X0) [cnf transformation 38]
107. ~curious(X0) | patient(X0) [cnf transformation 54]
108. ~kind(X0) | patient(X0) [cnf transformation 54]
118. kind(X0) | curious(X0) [cnf transformation 33]
142. ~quiet(mary) [cnf transformation 23]
356. curious(X0) | patient(X0) [resolution 118,108]
358. patient(X0) [subsumption resolution 356,107]
361. quiet(X0) [resolution 358,77]
371. $false [resolution 361,142]
% SZS output end Proof for 2419320914755239543292718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is rich or tall and vice versa.
If someone is rich then someone is not calm or rich and vice versa.
Everyone who is creative or not curious is either not kind or wise and vice versa.
If someone is not brave or not quiet then someone is not humble or not strong.
If alice is either kind or not creative then someone is tall.
Everyone who is tall is not quiet.
Everyone who is both not humble and not patient is both calm and generous and vice versa.
If someone is both not tall and not calm then john is not wise or calm.
If someone is both not tall and creative then mary is both tall and not quiet and vice versa.
If susan is both not curious and not kind then susan is not curious or not generous.
Everyone who is both not humble and not creative is both not humble and patient and vice versa.
Everyone who is both wise and not curious is either not tall or not strong and vice versa.
If someone is either not rich or creative then someone is either not strong or quiet and vice versa.
Everyone who is either happy or strong is either not curious or brave and vice versa.
Everyone who is either not quiet or rich is both not patient and not curious and vice versa.
If someone is both not happy and calm then someone is not tall or generous.
Someone is not strong or not brave.
Fred is either humble or not wise.
Someone is both quiet and not funny.
Lucy is tall or quiet.
Someone is either not strong or creative.
Lucy is both not brave and old. | Susan is not curious. | entailment | (![X]:(~tall(X)<=>(rich(X)|tall(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:((creative(X)|~curious(X))<=>(~kind(X)<~>wise(X))))&
((?[X]:((~brave(X)|~quiet(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(((kind(alice)<~>~creative(alice)))=>(?[X]:(tall(X))))&
(![X]:(tall(X)=>~quiet(X)))&
(![X]:((~humble(X)&~patient(X))<=>(calm(X)&generous(X))))&
((?[X]:((~tall(X)&~calm(X))))=>((~wise(john)|calm(john))))&
((?[X]:((~tall(X)&creative(X))))<=>((tall(mary)&~quiet(mary))))&
(((~curious(susan)&~kind(susan)))=>((~curious(susan)|~generous(susan))))&
(![X]:((~humble(X)&~creative(X))<=>(~humble(X)&patient(X))))&
(![X]:((wise(X)&~curious(X))<=>(~tall(X)<~>~strong(X))))&
((?[X]:((~rich(X)<~>creative(X))))<=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:((happy(X)<~>strong(X))<=>(~curious(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>rich(X))<=>(~patient(X)&~curious(X))))&
((?[X]:((~happy(X)&calm(X))))=>(?[X]:((~tall(X)|generous(X)))))&
(?[X]:((~strong(X)|~brave(X))))&
((humble(fred)<~>~wise(fred)))&
(?[X]:((quiet(X)&~funny(X))))&
((tall(lucy)|quiet(lucy)))&
(?[X]:((~strong(X)<~>creative(X))))&
((~brave(lucy)&old(lucy))) | ~curious(susan) | [
"p0",
"p8",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3181806026123817383717057
% SZS output start Proof for 3181806026123817383717057
1. ! [X0] : (~tall(X0) <=> (tall(X0) | rich(X0))) [input p0]
9. ? [X0] : (creative(X0) & ~tall(X0)) <=> (~quiet(mary) & tall(mary)) [input p8]
12. ! [X0] : ((~curious(X0) & wise(X0)) <=> (~tall(X0) <~> ~strong(X0))) [input p11]
13. ? [X0] : (~rich(X0) <~> creative(X0)) <=> ? [X0] : (~strong(X0) <~> quiet(X0)) [input p12]
15. ! [X0] : ((~quiet(X0) <~> rich(X0)) <=> (~curious(X0) & ~patient(X0))) [input p14]
23. curious(susan) [input hypothesis]
26. ? [X0] : (~rich(X0) <~> creative(X0)) <=> ? [X1] : (~strong(X1) <~> quiet(X1)) [rectify 13]
38. ! [X0] : ((~tall(X0) | (~tall(X0) & ~rich(X0))) & ((tall(X0) | rich(X0)) | tall(X0))) [nnf transformation 1]
39. ! [X0] : ((~tall(X0) | (~tall(X0) & ~rich(X0))) & (tall(X0) | rich(X0) | tall(X0))) [flattening 38]
55. (? [X0] : (creative(X0) & ~tall(X0)) | (quiet(mary) | ~tall(mary))) & ((~quiet(mary) & tall(mary)) | ! [X0] : (~creative(X0) | tall(X0))) [nnf transformation 9]
56. (? [X0] : (creative(X0) & ~tall(X0)) | quiet(mary) | ~tall(mary)) & ((~quiet(mary) & tall(mary)) | ! [X0] : (~creative(X0) | tall(X0))) [flattening 55]
57. (? [X0] : (creative(X0) & ~tall(X0)) | quiet(mary) | ~tall(mary)) & ((~quiet(mary) & tall(mary)) | ! [X1] : (~creative(X1) | tall(X1))) [rectify 56]
58. ? [X0] : (creative(X0) & ~tall(X0)) => (creative(sK4) & ~tall(sK4)) [choice axiom]
59. ((creative(sK4) & ~tall(sK4)) | quiet(mary) | ~tall(mary)) & ((~quiet(mary) & tall(mary)) | ! [X1] : (~creative(X1) | tall(X1))) [skolemisation 57,58]
62. ! [X0] : (((~curious(X0) & wise(X0)) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) & (((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | (curious(X0) | ~wise(X0)))) [nnf transformation 12]
63. ! [X0] : (((~curious(X0) & wise(X0)) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) & (((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | curious(X0) | ~wise(X0))) [flattening 62]
64. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ! [X1] : ((~strong(X1) | ~quiet(X1)) & (quiet(X1) | strong(X1)))) & (? [X1] : ((~quiet(X1) | strong(X1)) & (quiet(X1) | ~strong(X1))) | ! [X0] : ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) [nnf transformation 26]
65. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ! [X1] : ((~strong(X1) | ~quiet(X1)) & (quiet(X1) | strong(X1)))) & (? [X2] : ((~quiet(X2) | strong(X2)) & (quiet(X2) | ~strong(X2))) | ! [X3] : ((~rich(X3) | ~creative(X3)) & (creative(X3) | rich(X3)))) [rectify 64]
66. ? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) => ((~creative(sK5) | rich(sK5)) & (creative(sK5) | ~rich(sK5))) [choice axiom]
67. ? [X2] : ((~quiet(X2) | strong(X2)) & (quiet(X2) | ~strong(X2))) => ((~quiet(sK6) | strong(sK6)) & (quiet(sK6) | ~strong(sK6))) [choice axiom]
68. (((~creative(sK5) | rich(sK5)) & (creative(sK5) | ~rich(sK5))) | ! [X1] : ((~strong(X1) | ~quiet(X1)) & (quiet(X1) | strong(X1)))) & (((~quiet(sK6) | strong(sK6)) & (quiet(sK6) | ~strong(sK6))) | ! [X3] : ((~rich(X3) | ~creative(X3)) & (creative(X3) | rich(X3)))) [skolemisation 65,67,66]
70. ! [X0] : ((((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0))))) [nnf transformation 15]
71. ! [X0] : ((((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0))))) [flattening 70]
83. tall(X0) | rich(X0) | tall(X0) [cnf transformation 39]
85. ~tall(X0) | ~tall(X0) [cnf transformation 39]
105. tall(mary) | ~creative(X1) | tall(X1) [cnf transformation 59]
118. ~curious(X0) | ~strong(X0) | tall(X0) [cnf transformation 63]
124. creative(sK5) | ~rich(sK5) | quiet(X1) | strong(X1) [cnf transformation 68]
139. ~curious(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 71]
151. curious(susan) [cnf transformation 23]
152. tall(X0) | rich(X0) [duplicate literal removal 83]
153. ~tall(X0) [duplicate literal removal 85]
154. rich(X0) [subsumption resolution 152,153]
198. 10 <=> ! [X1] : ~creative(X1) [avatar definition]
199. ~creative(X1) <- (10) [avatar component clause 198]
205. ~creative(X1) | tall(X1) [subsumption resolution 105,153]
206. ~creative(X1) [subsumption resolution 205,153]
207. 10 [avatar split clause 206,198]
208. ~strong(X0) | ~curious(X0) [subsumption resolution 118,153]
216. 13 <=> creative(sK5) [avatar definition]
218. creative(sK5) <- (13) [avatar component clause 216]
220. creative(sK5) | quiet(X1) | strong(X1) [subsumption resolution 124,154]
222. 14 <=> ! [X1] : (quiet(X1) | strong(X1)) [avatar definition]
223. strong(X1) | quiet(X1) <- (14) [avatar component clause 222]
224. 14 | 13 [avatar split clause 220,216,222]
242. ~quiet(X0) | ~curious(X0) [subsumption resolution 139,154]
276. $false <- (10, 13) [resolution 218,199]
277. ~10 | ~13 [avatar contradiction clause 276]
281. quiet(X2) | ~curious(X2) <- (14) [resolution 223,208]
282. ~curious(X2) <- (14) [subsumption resolution 281,242]
286. $false <- (14) [resolution 282,151]
287. ~14 [avatar contradiction clause 286]
288. $false [avatar sat refutation 207,224,277,287]
% SZS output end Proof for 3181806026123817383717057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not creative is either not patient or not happy and vice versa. If someone is not humble or not brave then paul is curious. If someone is not happy then paul is not old. If someone is either not old or funny then someone is both patient and happy. Everyone who is either not patient or not calm is either brave or not wise. If someone is both not humble and not creative then paul is old and vice versa. Everyone who is not rich is brave. If mary is not curious then someone is not patient or not tall and vice versa. Everyone who is not strong or not happy is not wise or not generous. If susan is either not strong or quiet then someone is both not strong and not tall and vice versa. Everyone who is brave is not generous. If susan is not strong then alice is either not curious or not patient. If someone is both not quiet and not happy then someone is not wise and vice versa. If someone is brave then someone is not quiet and vice versa. Everyone who is either not strong or not funny is either not old or patient and vice versa. Everyone who is strong is not rich and vice versa. Mary is either generous or wise. Paul is not tall. Someone is both happy and not calm. Alice is quiet. Someone is patient. Someone is either not happy or not patient. Susan is wise or not curious. Alice is either brave or rich. | Susan is not wise. | neutral | (![X]:((~generous(X)&~creative(X))<=>(~patient(X)<~>~happy(X))))&
((?[X]:((~humble(X)|~brave(X))))=>(curious(paul)))&
((?[X]:(~happy(X)))=>(~old(paul)))&
((?[X]:((~old(X)<~>funny(X))))=>(?[X]:((patient(X)&happy(X)))))&
(![X]:((~patient(X)<~>~calm(X))=>(brave(X)<~>~wise(X))))&
((?[X]:((~humble(X)&~creative(X))))<=>(old(paul)))&
(![X]:(~rich(X)=>brave(X)))&
((~curious(mary))<=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:((~strong(X)|~happy(X))=>(~wise(X)|~generous(X))))&
(((~strong(susan)<~>quiet(susan)))<=>(?[X]:((~strong(X)&~tall(X)))))&
(![X]:(brave(X)=>~generous(X)))&
((~strong(susan))=>((~curious(alice)<~>~patient(alice))))&
((?[X]:((~quiet(X)&~happy(X))))<=>(?[X]:(~wise(X))))&
((?[X]:(brave(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>(~old(X)<~>patient(X))))&
(![X]:(strong(X)<=>~rich(X)))&
((generous(mary)<~>wise(mary)))&
(~tall(paul))&
(?[X]:((happy(X)&~calm(X))))&
(quiet(alice))&
(?[X]:(patient(X)))&
(?[X]:((~happy(X)<~>~patient(X))))&
((wise(susan)|~curious(susan)))&
((brave(alice)<~>rich(alice))) | ~wise(susan) | [] | null | 0 |
Everyone who is not happy is both not happy and not tall.
Everyone who is old is wise.
If alice is either kind or not happy then someone is not quiet and vice versa.
Everyone who is both humble and not creative is either not happy or not tall and vice versa.
If someone is rich then someone is both generous and not generous.
If someone is brave or strong then someone is both old and not humble and vice versa.
If fred is brave then someone is creative or brave and vice versa.
If john is both calm and brave then someone is not humble or quiet.
Everyone who is both generous and not patient is not strong or not patient and vice versa.
Everyone who is not rich is not tall or not quiet.
Everyone who is not patient is both strong and not patient and vice versa.
Everyone who is strong or wise is not rich or tall and vice versa.
If someone is both not happy and not tall then john is strong and vice versa.
If someone is either humble or tall then someone is either not humble or strong.
Everyone who is either not wise or not old is not funny and vice versa.
If fred is both patient and curious then john is either not creative or curious.
Susan is both quiet and wise.
Someone is curious.
Fred is either not kind or humble.
Fred is humble or calm.
Someone is both not funny and not tall.
Lucy is either not calm or funny.
Someone is brave or rich.
Alice is both curious and creative. | Lucy is not strong. | contradiction | (![X]:(~happy(X)=>(~happy(X)&~tall(X))))&
(![X]:(old(X)=>wise(X)))&
(((kind(alice)<~>~happy(alice)))<=>(?[X]:(~quiet(X))))&
(![X]:((humble(X)&~creative(X))<=>(~happy(X)<~>~tall(X))))&
((?[X]:(rich(X)))=>(?[X]:((generous(X)&~generous(X)))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((old(X)&~humble(X)))))&
((brave(fred))<=>(?[X]:((creative(X)|brave(X)))))&
(((calm(john)&brave(john)))=>(?[X]:((~humble(X)|quiet(X)))))&
(![X]:((generous(X)&~patient(X))<=>(~strong(X)|~patient(X))))&
(![X]:(~rich(X)=>(~tall(X)|~quiet(X))))&
(![X]:(~patient(X)<=>(strong(X)&~patient(X))))&
(![X]:((strong(X)|wise(X))<=>(~rich(X)|tall(X))))&
((?[X]:((~happy(X)&~tall(X))))<=>(strong(john)))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:((~humble(X)<~>strong(X)))))&
(![X]:((~wise(X)<~>~old(X))<=>~funny(X)))&
(((patient(fred)&curious(fred)))=>((~creative(john)<~>curious(john))))&
((quiet(susan)&wise(susan)))&
(?[X]:(curious(X)))&
((~kind(fred)<~>humble(fred)))&
((humble(fred)|calm(fred)))&
(?[X]:((~funny(X)&~tall(X))))&
((~calm(lucy)<~>funny(lucy)))&
(?[X]:((brave(X)|rich(X))))&
((curious(alice)&creative(alice))) | ~strong(lucy) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7019956825770690778631456
% SZS output start Proof for 7019956825770690778631456
9. ! [X0] : ((~patient(X0) & generous(X0)) <=> (~patient(X0) | ~strong(X0))) [input p8]
11. ! [X0] : (~patient(X0) <=> (~patient(X0) & strong(X0))) [input p10]
25. ~strong(lucy) [input hypothesis]
59. ! [X0] : (((~patient(X0) & generous(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (patient(X0) | ~generous(X0)))) [nnf transformation 9]
60. ! [X0] : (((~patient(X0) & generous(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | patient(X0) | ~generous(X0))) [flattening 59]
61. ! [X0] : ((~patient(X0) | (patient(X0) | ~strong(X0))) & ((~patient(X0) & strong(X0)) | patient(X0))) [nnf transformation 11]
62. ! [X0] : ((~patient(X0) | patient(X0) | ~strong(X0)) & ((~patient(X0) & strong(X0)) | patient(X0))) [flattening 61]
110. ~patient(X0) | strong(X0) [cnf transformation 60]
113. strong(X0) | patient(X0) [cnf transformation 62]
146. ~strong(lucy) [cnf transformation 25]
242. strong(X0) [subsumption resolution 113,110]
314. $false [subsumption resolution 146,242]
% SZS output end Proof for 7019956825770690778631456
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both humble and not strong and vice versa.
If someone is both tall and not old then paul is not creative or strong.
If alice is not humble or not curious then susan is both creative and not tall.
If someone is both calm and not funny then someone is both quiet and patient.
If john is both not tall and not creative then someone is curious.
Everyone who is not old is calm and vice versa.
Everyone who is both kind and generous is not humble or patient and vice versa.
If someone is not quiet or not tall then susan is either not patient or wise and vice versa.
If someone is not wise or not calm then alice is not curious.
If someone is not rich or not humble then someone is patient.
Everyone who is not kind or quiet is both not happy and not creative.
If someone is either not rich or funny then someone is both not calm and not old and vice versa.
Everyone who is quiet is either not patient or funny and vice versa.
Everyone who is happy or wise is either happy or not rich and vice versa.
Everyone who is both old and not strong is not strong or wise and vice versa.
If someone is not quiet or tall then someone is not funny or not calm and vice versa.
Alice is not generous or brave.
Susan is either funny or not strong.
Someone is both not strong and not wise.
Lucy is quiet or not tall.
Mary is humble or brave.
Someone is either wise or not rich.
John is not happy or calm.
Paul is either funny or kind. | Susan is not happy. | contradiction | (![X]:(wise(X)<=>(humble(X)&~strong(X))))&
((?[X]:((tall(X)&~old(X))))=>((~creative(paul)|strong(paul))))&
(((~humble(alice)|~curious(alice)))=>((creative(susan)&~tall(susan))))&
((?[X]:((calm(X)&~funny(X))))=>(?[X]:((quiet(X)&patient(X)))))&
(((~tall(john)&~creative(john)))=>(?[X]:(curious(X))))&
(![X]:(~old(X)<=>calm(X)))&
(![X]:((kind(X)&generous(X))<=>(~humble(X)|patient(X))))&
((?[X]:((~quiet(X)|~tall(X))))<=>((~patient(susan)<~>wise(susan))))&
((?[X]:((~wise(X)|~calm(X))))=>(~curious(alice)))&
((?[X]:((~rich(X)|~humble(X))))=>(?[X]:(patient(X))))&
(![X]:((~kind(X)|quiet(X))=>(~happy(X)&~creative(X))))&
((?[X]:((~rich(X)<~>funny(X))))<=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:(quiet(X)<=>(~patient(X)<~>funny(X))))&
(![X]:((happy(X)|wise(X))<=>(happy(X)<~>~rich(X))))&
(![X]:((old(X)&~strong(X))<=>(~strong(X)|wise(X))))&
((?[X]:((~quiet(X)|tall(X))))<=>(?[X]:((~funny(X)|~calm(X)))))&
((~generous(alice)|brave(alice)))&
((funny(susan)<~>~strong(susan)))&
(?[X]:((~strong(X)&~wise(X))))&
((quiet(lucy)|~tall(lucy)))&
((humble(mary)|brave(mary)))&
(?[X]:((wise(X)<~>~rich(X))))&
((~happy(john)|calm(john)))&
((funny(paul)<~>kind(paul))) | ~happy(susan) | [
"p0",
"p2",
"p5",
"p7",
"p8",
"p10",
"p11",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8212616061616996060852993
% SZS output start Proof for 8212616061616996060852993
1. ! [X0] : (wise(X0) <=> (~strong(X0) & humble(X0))) [input p0]
3. (~curious(alice) | ~humble(alice)) => (~tall(susan) & creative(susan)) [input p2]
6. ! [X0] : (~old(X0) <=> calm(X0)) [input p5]
8. ? [X0] : (~tall(X0) | ~quiet(X0)) <=> (~patient(susan) <~> wise(susan)) [input p7]
9. ? [X0] : (~calm(X0) | ~wise(X0)) => ~curious(alice) [input p8]
11. ! [X0] : ((quiet(X0) | ~kind(X0)) => (~creative(X0) & ~happy(X0))) [input p10]
12. ? [X0] : (~rich(X0) <~> funny(X0)) <=> ? [X0] : (~old(X0) & ~calm(X0)) [input p11]
13. ! [X0] : (quiet(X0) <=> (~patient(X0) <~> funny(X0))) [input p12]
14. ! [X0] : ((wise(X0) | happy(X0)) <=> (happy(X0) <~> ~rich(X0))) [input p13]
18. funny(susan) <~> ~strong(susan) [input p17]
25. ~happy(susan) [input hypothesis]
28. ? [X0] : (~rich(X0) <~> funny(X0)) <=> ? [X1] : (~old(X1) & ~calm(X1)) [rectify 12]
34. (~tall(susan) & creative(susan)) | (curious(alice) & humble(alice)) [ennf transformation 3]
38. ~curious(alice) | ! [X0] : (calm(X0) & wise(X0)) [ennf transformation 9]
40. ! [X0] : ((~creative(X0) & ~happy(X0)) | (~quiet(X0) & kind(X0))) [ennf transformation 11]
41. ! [X0] : ((wise(X0) | (strong(X0) | ~humble(X0))) & ((~strong(X0) & humble(X0)) | ~wise(X0))) [nnf transformation 1]
42. ! [X0] : ((wise(X0) | strong(X0) | ~humble(X0)) & ((~strong(X0) & humble(X0)) | ~wise(X0))) [flattening 41]
48. ! [X0] : ((~old(X0) | ~calm(X0)) & (calm(X0) | old(X0))) [nnf transformation 6]
51. (? [X0] : (~tall(X0) | ~quiet(X0)) | ((~patient(susan) | ~wise(susan)) & (wise(susan) | patient(susan)))) & (((~wise(susan) | patient(susan)) & (wise(susan) | ~patient(susan))) | ! [X0] : (tall(X0) & quiet(X0))) [nnf transformation 8]
52. (? [X0] : (~tall(X0) | ~quiet(X0)) | ((~patient(susan) | ~wise(susan)) & (wise(susan) | patient(susan)))) & (((~wise(susan) | patient(susan)) & (wise(susan) | ~patient(susan))) | ! [X1] : (tall(X1) & quiet(X1))) [rectify 51]
53. ? [X0] : (~tall(X0) | ~quiet(X0)) => (~tall(sK2) | ~quiet(sK2)) [choice axiom]
54. ((~tall(sK2) | ~quiet(sK2)) | ((~patient(susan) | ~wise(susan)) & (wise(susan) | patient(susan)))) & (((~wise(susan) | patient(susan)) & (wise(susan) | ~patient(susan))) | ! [X1] : (tall(X1) & quiet(X1))) [skolemisation 52,53]
58. (? [X0] : ((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | ! [X1] : (old(X1) | calm(X1))) & (? [X1] : (~old(X1) & ~calm(X1)) | ! [X0] : ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) [nnf transformation 28]
59. (? [X0] : ((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | ! [X1] : (old(X1) | calm(X1))) & (? [X2] : (~old(X2) & ~calm(X2)) | ! [X3] : ((~rich(X3) | ~funny(X3)) & (funny(X3) | rich(X3)))) [rectify 58]
60. ? [X0] : ((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) => ((~funny(sK4) | rich(sK4)) & (funny(sK4) | ~rich(sK4))) [choice axiom]
61. ? [X2] : (~old(X2) & ~calm(X2)) => (~old(sK5) & ~calm(sK5)) [choice axiom]
62. (((~funny(sK4) | rich(sK4)) & (funny(sK4) | ~rich(sK4))) | ! [X1] : (old(X1) | calm(X1))) & ((~old(sK5) & ~calm(sK5)) | ! [X3] : ((~rich(X3) | ~funny(X3)) & (funny(X3) | rich(X3)))) [skolemisation 59,61,60]
63. ! [X0] : ((quiet(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | ~quiet(X0))) [nnf transformation 13]
64. ! [X0] : (((wise(X0) | happy(X0)) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) & (((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | (~wise(X0) & ~happy(X0)))) [nnf transformation 14]
65. ! [X0] : ((wise(X0) | happy(X0) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) & (((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | (~wise(X0) & ~happy(X0)))) [flattening 64]
73. (strong(susan) | ~funny(susan)) & (~strong(susan) | funny(susan)) [nnf transformation 18]
81. ~strong(X0) | ~wise(X0) [cnf transformation 42]
85. creative(susan) | curious(alice) [cnf transformation 34]
87. ~tall(susan) | curious(alice) [cnf transformation 34]
91. calm(X0) | old(X0) [cnf transformation 48]
99. wise(susan) | ~patient(susan) | tall(X1) [cnf transformation 54]
104. ~curious(alice) | wise(X0) [cnf transformation 38]
111. ~quiet(X0) | ~creative(X0) [cnf transformation 40]
112. ~calm(sK5) | funny(X3) | rich(X3) [cnf transformation 62]
113. ~calm(sK5) | ~rich(X3) | ~funny(X3) [cnf transformation 62]
114. ~old(sK5) | funny(X3) | rich(X3) [cnf transformation 62]
115. ~old(sK5) | ~rich(X3) | ~funny(X3) [cnf transformation 62]
120. patient(X0) | funny(X0) | quiet(X0) [cnf transformation 63]
123. ~rich(X0) | happy(X0) | ~wise(X0) [cnf transformation 65]
124. rich(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 65]
127. wise(X0) | happy(X0) | happy(X0) | rich(X0) [cnf transformation 65]
138. strong(susan) | ~funny(susan) [cnf transformation 73]
147. ~happy(susan) [cnf transformation 25]
148. ~happy(X0) | rich(X0) [duplicate literal removal 124]
149. happy(X0) | wise(X0) | rich(X0) [duplicate literal removal 127]
163. 4 <=> curious(alice) [avatar definition]
167. 5 <=> tall(susan) [avatar definition]
169. ~tall(susan) <- (~5) [avatar component clause 167]
170. 4 | ~5 [avatar split clause 87,167,163]
177. 7 <=> creative(susan) [avatar definition]
179. creative(susan) <- (7) [avatar component clause 177]
180. 4 | 7 [avatar split clause 85,177,163]
209. 14 <=> wise(susan) [avatar definition]
210. wise(susan) <- (14) [avatar component clause 209]
211. ~wise(susan) <- (~14) [avatar component clause 209]
213. 15 <=> patient(susan) [avatar definition]
215. ~patient(susan) <- (~15) [avatar component clause 213]
227. 18 <=> ! [X1] : tall(X1) [avatar definition]
228. tall(X1) <- (18) [avatar component clause 227]
234. 18 | ~15 | 14 [avatar split clause 99,209,213,227]
241. 21 <=> ! [X0] : wise(X0) [avatar definition]
242. wise(X0) <- (21) [avatar component clause 241]
243. 21 | ~4 [avatar split clause 104,163,241]
257. 25 <=> ! [X3] : (~rich(X3) | ~funny(X3)) [avatar definition]
258. ~rich(X3) | ~funny(X3) <- (25) [avatar component clause 257]
260. 26 <=> old(sK5) [avatar definition]
263. 25 | ~26 [avatar split clause 115,260,257]
265. 27 <=> ! [X3] : (funny(X3) | rich(X3)) [avatar definition]
266. rich(X3) | funny(X3) <- (27) [avatar component clause 265]
267. 27 | ~26 [avatar split clause 114,260,265]
269. 28 <=> calm(sK5) [avatar definition]
271. ~calm(sK5) <- (~28) [avatar component clause 269]
272. 25 | ~28 [avatar split clause 113,269,257]
273. 27 | ~28 [avatar split clause 112,269,265]
301. 35 <=> funny(susan) [avatar definition]
302. funny(susan) <- (35) [avatar component clause 301]
303. ~funny(susan) <- (~35) [avatar component clause 301]
305. 36 <=> strong(susan) [avatar definition]
307. strong(susan) <- (36) [avatar component clause 305]
308. ~35 | 36 [avatar split clause 138,305,301]
348. old(sK5) <- (~28) [resolution 91,271]
352. 26 | 28 [avatar split clause 348,269,260]
379. funny(susan) | quiet(susan) <- (~15) [resolution 120,215]
384. quiet(susan) <- (~15, ~35) [subsumption resolution 379,303]
386. ~creative(susan) <- (~15, ~35) [resolution 384,111]
387. $false <- (7, ~15, ~35) [subsumption resolution 386,179]
388. ~7 | 15 | 35 [avatar contradiction clause 387]
402. ~wise(X0) | happy(X0) | funny(X0) <- (27) [resolution 123,266]
407. wise(X1) | rich(X1) | rich(X1) [resolution 149,148]
410. rich(X1) | wise(X1) [duplicate literal removal 407]
452. ~funny(X1) | wise(X1) <- (25) [resolution 410,258]
468. happy(susan) | funny(susan) <- (14, 27) [resolution 402,210]
470. funny(susan) <- (14, 27) [subsumption resolution 468,147]
473. 35 | ~14 | ~27 [avatar split clause 470,265,209,301]
480. ~wise(susan) <- (36) [resolution 307,81]
481. $false <- (14, 36) [subsumption resolution 480,210]
482. ~14 | ~36 [avatar contradiction clause 481]
483. $false <- (~14, 21) [subsumption resolution 211,242]
484. 14 | ~21 [avatar contradiction clause 483]
519. wise(susan) <- (25, 35) [resolution 452,302]
520. $false <- (~14, 25, 35) [subsumption resolution 519,211]
521. 14 | ~25 | ~35 [avatar contradiction clause 520]
526. $false <- (~5, 18) [resolution 228,169]
531. 5 | ~18 [avatar contradiction clause 526]
532. $false [avatar sat refutation 170,180,234,243,263,267,272,273,308,352,388,473,482,484,521,531]
% SZS output end Proof for 8212616061616996060852993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and generous is creative.
If someone is either not humble or not tall then someone is not quiet and vice versa.
If someone is either not kind or kind then susan is creative.
Everyone who is not quiet or not rich is both rich and not wise.
Everyone who is both old and quiet is both strong and kind.
Everyone who is both patient and not old is either calm or brave and vice versa.
If someone is both not generous and wise then lucy is either not old or not rich and vice versa.
If paul is curious or not funny then alice is both curious and not kind.
If fred is either not rich or rich then someone is creative and vice versa.
Everyone who is either kind or not curious is either wise or generous and vice versa.
Everyone who is patient is either curious or not patient and vice versa.
If someone is both kind and generous then alice is patient.
Everyone who is creative is rich and vice versa.
If alice is patient or old then john is humble or not curious and vice versa.
If mary is both curious and not strong then someone is patient or not creative.
Everyone who is not kind is both not kind and not calm and vice versa.
Mary is both patient and humble.
John is rich or not calm.
Someone is not rich or strong.
Alice is curious or brave.
Lucy is funny or patient.
Lucy is either not old or calm.
Susan is calm or quiet. | Fred is not patient. | neutral | (![X]:((curious(X)&generous(X))=>creative(X)))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((~kind(X)<~>kind(X))))=>(creative(susan)))&
(![X]:((~quiet(X)|~rich(X))=>(rich(X)&~wise(X))))&
(![X]:((old(X)&quiet(X))=>(strong(X)&kind(X))))&
(![X]:((patient(X)&~old(X))<=>(calm(X)<~>brave(X))))&
((?[X]:((~generous(X)&wise(X))))<=>((~old(lucy)<~>~rich(lucy))))&
(((curious(paul)|~funny(paul)))=>((curious(alice)&~kind(alice))))&
(((~rich(fred)<~>rich(fred)))<=>(?[X]:(creative(X))))&
(![X]:((kind(X)<~>~curious(X))<=>(wise(X)<~>generous(X))))&
(![X]:(patient(X)<=>(curious(X)<~>~patient(X))))&
((?[X]:((kind(X)&generous(X))))=>(patient(alice)))&
(![X]:(creative(X)<=>rich(X)))&
(((patient(alice)|old(alice)))<=>((humble(john)|~curious(john))))&
(((curious(mary)&~strong(mary)))=>(?[X]:((patient(X)|~creative(X)))))&
(![X]:(~kind(X)<=>(~kind(X)&~calm(X))))&
((patient(mary)&humble(mary)))&
((rich(john)|~calm(john)))&
(?[X]:((~rich(X)|strong(X))))&
((curious(alice)|brave(alice)))&
((funny(lucy)|patient(lucy)))&
((~old(lucy)<~>calm(lucy)))&
((calm(susan)|quiet(susan))) | ~patient(fred) | [] | null | 0 |
If someone is funny then someone is not funny. Everyone who is both creative and happy is rich or tall. Everyone who is brave or quiet is both not funny and not tall. Everyone who is both strong and not patient is both not funny and patient and vice versa. If fred is brave or not funny then someone is not patient. If fred is both humble and not creative then someone is kind or not kind and vice versa. If someone is either not humble or not creative then someone is either creative or funny. If someone is quiet or not kind then paul is both funny and not funny. If susan is not old then someone is not old or happy and vice versa. If someone is either tall or not kind then fred is either not patient or rich. Everyone who is both not creative and tall is not generous. Everyone who is tall is both brave and rich. Everyone who is both patient and not quiet is humble and vice versa. Everyone who is either kind or not kind is strong or not old and vice versa. If alice is wise or humble then someone is not funny or patient and vice versa. Everyone who is not old or not strong is both not funny and not generous and vice versa. John is funny or wise. Someone is either wise or not brave. Someone is brave or humble. Lucy is not quiet or old. Paul is not tall. Someone is strong or not kind. | Fred is old. | entailment | ((?[X]:(funny(X)))=>(?[X]:(~funny(X))))&
(![X]:((creative(X)&happy(X))=>(rich(X)|tall(X))))&
(![X]:((brave(X)|quiet(X))=>(~funny(X)&~tall(X))))&
(![X]:((strong(X)&~patient(X))<=>(~funny(X)&patient(X))))&
(((brave(fred)|~funny(fred)))=>(?[X]:(~patient(X))))&
(((humble(fred)&~creative(fred)))<=>(?[X]:((kind(X)|~kind(X)))))&
((?[X]:((~humble(X)<~>~creative(X))))=>(?[X]:((creative(X)<~>funny(X)))))&
((?[X]:((quiet(X)|~kind(X))))=>((funny(paul)&~funny(paul))))&
((~old(susan))<=>(?[X]:((~old(X)|happy(X)))))&
((?[X]:((tall(X)<~>~kind(X))))=>((~patient(fred)<~>rich(fred))))&
(![X]:((~creative(X)&tall(X))=>~generous(X)))&
(![X]:(tall(X)=>(brave(X)&rich(X))))&
(![X]:((patient(X)&~quiet(X))<=>humble(X)))&
(![X]:((kind(X)<~>~kind(X))<=>(strong(X)|~old(X))))&
(((wise(alice)|humble(alice)))<=>(?[X]:((~funny(X)|patient(X)))))&
(![X]:((~old(X)|~strong(X))<=>(~funny(X)&~generous(X))))&
((funny(john)|wise(john)))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((brave(X)|humble(X))))&
((~quiet(lucy)|old(lucy)))&
(~tall(paul))&
(?[X]:((strong(X)|~kind(X)))) | old(fred) | [
"p3",
"p5",
"p7",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7103454191873335547154673
% SZS output start Proof for 7103454191873335547154673
4. ! [X0] : ((~patient(X0) & strong(X0)) <=> (patient(X0) & ~funny(X0))) [input p3]
6. (~creative(fred) & humble(fred)) <=> ? [X0] : (~kind(X0) | kind(X0)) [input p5]
8. ? [X0] : (~kind(X0) | quiet(X0)) => (~funny(paul) & funny(paul)) [input p7]
13. ! [X0] : ((~quiet(X0) & patient(X0)) <=> humble(X0)) [input p12]
16. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (~generous(X0) & ~funny(X0))) [input p15]
23. ~old(fred) [input hypothesis]
32. (~funny(paul) & funny(paul)) | ! [X0] : (kind(X0) & ~quiet(X0)) [ennf transformation 8]
40. ! [X0] : (((~patient(X0) & strong(X0)) | (~patient(X0) | funny(X0))) & ((patient(X0) & ~funny(X0)) | (patient(X0) | ~strong(X0)))) [nnf transformation 4]
41. ! [X0] : (((~patient(X0) & strong(X0)) | ~patient(X0) | funny(X0)) & ((patient(X0) & ~funny(X0)) | patient(X0) | ~strong(X0))) [flattening 40]
44. ((~creative(fred) & humble(fred)) | ! [X0] : (kind(X0) & ~kind(X0))) & (? [X0] : (~kind(X0) | kind(X0)) | (creative(fred) | ~humble(fred))) [nnf transformation 6]
45. ((~creative(fred) & humble(fred)) | ! [X0] : (kind(X0) & ~kind(X0))) & (? [X0] : (~kind(X0) | kind(X0)) | creative(fred) | ~humble(fred)) [flattening 44]
46. ((~creative(fred) & humble(fred)) | ! [X0] : (kind(X0) & ~kind(X0))) & (? [X1] : (~kind(X1) | kind(X1)) | creative(fred) | ~humble(fred)) [rectify 45]
47. ? [X1] : (~kind(X1) | kind(X1)) => (~kind(sK2) | kind(sK2)) [choice axiom]
48. ((~creative(fred) & humble(fred)) | ! [X0] : (kind(X0) & ~kind(X0))) & ((~kind(sK2) | kind(sK2)) | creative(fred) | ~humble(fred)) [skolemisation 46,47]
58. ! [X0] : (((~quiet(X0) & patient(X0)) | ~humble(X0)) & (humble(X0) | (quiet(X0) | ~patient(X0)))) [nnf transformation 13]
59. ! [X0] : (((~quiet(X0) & patient(X0)) | ~humble(X0)) & (humble(X0) | quiet(X0) | ~patient(X0))) [flattening 58]
67. ! [X0] : (((~strong(X0) | ~old(X0)) | (generous(X0) | funny(X0))) & ((~generous(X0) & ~funny(X0)) | (strong(X0) & old(X0)))) [nnf transformation 16]
68. ! [X0] : ((~strong(X0) | ~old(X0) | generous(X0) | funny(X0)) & ((~generous(X0) & ~funny(X0)) | (strong(X0) & old(X0)))) [flattening 67]
85. ~patient(X0) | ~patient(X0) | funny(X0) [cnf transformation 41]
89. humble(fred) | ~kind(X0) [cnf transformation 48]
98. funny(paul) | kind(X0) [cnf transformation 32]
100. ~funny(paul) | kind(X0) [cnf transformation 32]
112. ~humble(X0) | patient(X0) [cnf transformation 59]
124. ~funny(X0) | old(X0) [cnf transformation 68]
136. ~old(fred) [cnf transformation 23]
140. ~patient(X0) | funny(X0) [duplicate literal removal 85]
150. 3 <=> funny(fred) [avatar definition]
152. funny(fred) <- (3) [avatar component clause 150]
164. 6 <=> ! [X0] : kind(X0) [avatar definition]
165. kind(X0) <- (6) [avatar component clause 164]
172. 8 <=> ! [X0] : ~kind(X0) [avatar definition]
173. ~kind(X0) <- (8) [avatar component clause 172]
176. 9 <=> humble(fred) [avatar definition]
178. humble(fred) <- (9) [avatar component clause 176]
180. 8 | 9 [avatar split clause 89,176,172]
200. 14 <=> funny(paul) [avatar definition]
203. 6 | ~14 [avatar split clause 100,200,164]
208. 6 | 14 [avatar split clause 98,200,164]
235. 22 <=> patient(fred) [avatar definition]
237. patient(fred) <- (22) [avatar component clause 235]
324. $false <- (6, 8) [subsumption resolution 165,173]
325. ~6 | ~8 [avatar contradiction clause 324]
330. patient(fred) <- (9) [resolution 112,178]
333. 22 | ~9 [avatar split clause 330,176,235]
339. funny(fred) <- (22) [resolution 140,237]
341. 3 | ~22 [avatar split clause 339,235,150]
343. old(fred) <- (3) [resolution 152,124]
344. $false <- (3) [subsumption resolution 343,136]
345. ~3 [avatar contradiction clause 344]
346. $false [avatar sat refutation 180,203,208,325,333,341,345]
% SZS output end Proof for 7103454191873335547154673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either curious or not wise and vice versa.
Everyone who is not patient or generous is either not strong or calm and vice versa.
Everyone who is both not funny and calm is not humble and vice versa.
If fred is either not calm or brave then someone is calm.
If someone is both not funny and not patient then susan is either old or not quiet.
Everyone who is either humble or quiet is either creative or not happy.
Everyone who is both not brave and generous is either strong or brave and vice versa.
If someone is either not quiet or strong then someone is either not calm or not rich and vice versa.
Everyone who is not kind or patient is both brave and not generous.
Everyone who is kind is both generous and not wise and vice versa.
If fred is either not wise or not tall then someone is either creative or not happy.
If someone is not tall then alice is both not generous and not happy and vice versa.
If someone is curious then someone is not old or not tall and vice versa.
If someone is both calm and not patient then someone is both not wise and wise.
If someone is quiet then paul is not calm.
If someone is both not strong and not tall then someone is tall or not old and vice versa.
Someone is either not funny or not strong.
Someone is not wise.
Someone is brave or not old.
Paul is not tall.
John is both brave and curious.
Susan is both not calm and patient. | John is tall. | contradiction | (![X]:(~funny(X)<=>(curious(X)<~>~wise(X))))&
(![X]:((~patient(X)|generous(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((~funny(X)&calm(X))<=>~humble(X)))&
(((~calm(fred)<~>brave(fred)))=>(?[X]:(calm(X))))&
((?[X]:((~funny(X)&~patient(X))))=>((old(susan)<~>~quiet(susan))))&
(![X]:((humble(X)<~>quiet(X))=>(creative(X)<~>~happy(X))))&
(![X]:((~brave(X)&generous(X))<=>(strong(X)<~>brave(X))))&
((?[X]:((~quiet(X)<~>strong(X))))<=>(?[X]:((~calm(X)<~>~rich(X)))))&
(![X]:((~kind(X)|patient(X))=>(brave(X)&~generous(X))))&
(![X]:(kind(X)<=>(generous(X)&~wise(X))))&
(((~wise(fred)<~>~tall(fred)))=>(?[X]:((creative(X)<~>~happy(X)))))&
((?[X]:(~tall(X)))<=>((~generous(alice)&~happy(alice))))&
((?[X]:(curious(X)))<=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:((calm(X)&~patient(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:(quiet(X)))=>(~calm(paul)))&
((?[X]:((~strong(X)&~tall(X))))<=>(?[X]:((tall(X)|~old(X)))))&
(?[X]:((~funny(X)<~>~strong(X))))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)|~old(X))))&
(~tall(paul))&
((brave(john)&curious(john)))&
((~calm(susan)&patient(susan))) | tall(john) | [
"p6",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8938552369809339049489609
% SZS output start Proof for 8938552369809339049489609
7. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (strong(X0) <~> brave(X0))) [input p6]
9. ! [X0] : ((patient(X0) | ~kind(X0)) => (~generous(X0) & brave(X0))) [input p8]
10. ! [X0] : (kind(X0) <=> (~wise(X0) & generous(X0))) [input p9]
16. ? [X0] : (~tall(X0) & ~strong(X0)) <=> ? [X0] : (~old(X0) | tall(X0)) [input p15]
23. tall(john) [input hypothesis]
27. ? [X0] : (~tall(X0) & ~strong(X0)) <=> ? [X1] : (~old(X1) | tall(X1)) [rectify 16]
28. ! [X0] : (kind(X0) => (~wise(X0) & generous(X0))) [unused predicate definition removal 10]
32. ! [X0] : ((~generous(X0) & brave(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 9]
33. ! [X0] : ((~wise(X0) & generous(X0)) | ~kind(X0)) [ennf transformation 28]
47. ! [X0] : (((generous(X0) & ~brave(X0)) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | (~generous(X0) | brave(X0)))) [nnf transformation 7]
48. ! [X0] : (((generous(X0) & ~brave(X0)) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | ~generous(X0) | brave(X0))) [flattening 47]
70. (? [X0] : (~tall(X0) & ~strong(X0)) | ! [X1] : (old(X1) & ~tall(X1))) & (? [X1] : (~old(X1) | tall(X1)) | ! [X0] : (tall(X0) | strong(X0))) [nnf transformation 27]
71. (? [X0] : (~tall(X0) & ~strong(X0)) | ! [X1] : (old(X1) & ~tall(X1))) & (? [X2] : (~old(X2) | tall(X2)) | ! [X3] : (tall(X3) | strong(X3))) [rectify 70]
72. ? [X0] : (~tall(X0) & ~strong(X0)) => (~tall(sK8) & ~strong(sK8)) [choice axiom]
73. ? [X2] : (~old(X2) | tall(X2)) => (~old(sK9) | tall(sK9)) [choice axiom]
74. ((~tall(sK8) & ~strong(sK8)) | ! [X1] : (old(X1) & ~tall(X1))) & ((~old(sK9) | tall(sK9)) | ! [X3] : (tall(X3) | strong(X3))) [skolemisation 71,73,72]
103. brave(X0) | strong(X0) | ~generous(X0) | brave(X0) [cnf transformation 48]
106. ~brave(X0) | strong(X0) | ~brave(X0) [cnf transformation 48]
108. ~brave(X0) | strong(X0) | generous(X0) [cnf transformation 48]
117. kind(X0) | brave(X0) [cnf transformation 32]
121. ~kind(X0) | generous(X0) [cnf transformation 33]
137. ~strong(sK8) | ~tall(X1) [cnf transformation 74]
150. tall(john) [cnf transformation 23]
151. brave(X0) | strong(X0) | ~generous(X0) [duplicate literal removal 103]
152. ~brave(X0) | strong(X0) [duplicate literal removal 106]
180. ~generous(X0) | strong(X0) [subsumption resolution 151,152]
299. 33 <=> ! [X1] : ~tall(X1) [avatar definition]
300. ~tall(X1) <- (33) [avatar component clause 299]
303. 34 <=> strong(sK8) [avatar definition]
305. ~strong(sK8) <- (~34) [avatar component clause 303]
307. 33 | ~34 [avatar split clause 137,303,299]
341. brave(X0) | generous(X0) [resolution 121,117]
480. generous(X0) | strong(X0) | generous(X0) [resolution 341,108]
482. generous(X0) | strong(X0) [duplicate literal removal 480]
483. strong(X0) [subsumption resolution 482,180]
487. $false <- (~34) [resolution 483,305]
491. 34 [avatar contradiction clause 487]
494. $false <- (33) [resolution 300,150]
495. ~33 [avatar contradiction clause 494]
496. $false [avatar sat refutation 307,491,495]
% SZS output end Proof for 8938552369809339049489609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or creative is strong.
If someone is not calm then mary is both old and generous.
Everyone who is both rich and not curious is tall.
If someone is not curious or not strong then susan is either not tall or quiet.
If someone is either kind or not humble then john is either brave or not generous and vice versa.
If someone is funny or not old then someone is not quiet or not creative.
Everyone who is strong or quiet is either not humble or funny.
Everyone who is either old or strong is not old or not funny and vice versa.
If someone is either not happy or calm then lucy is not curious or generous and vice versa.
Everyone who is both humble and kind is both not old and happy and vice versa.
Everyone who is humble is patient and vice versa.
Everyone who is either quiet or not brave is either not strong or generous and vice versa.
If someone is not kind then someone is not brave.
If mary is quiet then john is both calm and not kind and vice versa.
Everyone who is either generous or funny is not generous or tall and vice versa.
If paul is tall then someone is either tall or calm and vice versa.
Someone is patient or not kind.
Someone is tall.
Lucy is both not brave and not funny.
Someone is both generous and not brave.
Someone is either not patient or curious.
Someone is humble or not calm.
Alice is both funny and not calm.
Someone is not happy or funny. | Lucy is not patient. | entailment | (![X]:((~calm(X)<~>creative(X))=>strong(X)))&
((?[X]:(~calm(X)))=>((old(mary)&generous(mary))))&
(![X]:((rich(X)&~curious(X))=>tall(X)))&
((?[X]:((~curious(X)|~strong(X))))=>((~tall(susan)<~>quiet(susan))))&
((?[X]:((kind(X)<~>~humble(X))))<=>((brave(john)<~>~generous(john))))&
((?[X]:((funny(X)|~old(X))))=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:((strong(X)|quiet(X))=>(~humble(X)<~>funny(X))))&
(![X]:((old(X)<~>strong(X))<=>(~old(X)|~funny(X))))&
((?[X]:((~happy(X)<~>calm(X))))<=>((~curious(lucy)|generous(lucy))))&
(![X]:((humble(X)&kind(X))<=>(~old(X)&happy(X))))&
(![X]:(humble(X)<=>patient(X)))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~brave(X))))&
((quiet(mary))<=>((calm(john)&~kind(john))))&
(![X]:((generous(X)<~>funny(X))<=>(~generous(X)|tall(X))))&
((tall(paul))<=>(?[X]:((tall(X)<~>calm(X)))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:(tall(X)))&
((~brave(lucy)&~funny(lucy)))&
(?[X]:((generous(X)&~brave(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((humble(X)|~calm(X))))&
((funny(alice)&~calm(alice)))&
(?[X]:((~happy(X)|funny(X)))) | ~patient(lucy) | [
"p6",
"p7",
"p10",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3337918057855914778178733
% SZS output start Proof for 3337918057855914778178733
7. ! [X0] : ((quiet(X0) | strong(X0)) => (~humble(X0) <~> funny(X0))) [input p6]
8. ! [X0] : ((old(X0) <~> strong(X0)) <=> (~funny(X0) | ~old(X0))) [input p7]
11. ! [X0] : (humble(X0) <=> patient(X0)) [input p10]
12. ! [X0] : ((quiet(X0) <~> ~brave(X0)) <=> (~strong(X0) <~> generous(X0))) [input p11]
15. ! [X0] : ((generous(X0) <~> funny(X0)) <=> (tall(X0) | ~generous(X0))) [input p14]
19. ~funny(lucy) & ~brave(lucy) [input p18]
25. patient(lucy) [input hypothesis]
33. ! [X0] : ((~humble(X0) <~> funny(X0)) | (~quiet(X0) & ~strong(X0))) [ennf transformation 7]
44. ! [X0] : (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~quiet(X0) & ~strong(X0))) [nnf transformation 33]
45. ! [X0] : ((((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (funny(X0) & old(X0))) & ((~funny(X0) | ~old(X0)) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (funny(X0) & old(X0))) & (~funny(X0) | ~old(X0) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))))) [flattening 45]
54. ! [X0] : ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))) [nnf transformation 11]
55. ! [X0] : ((((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0))))) [nnf transformation 12]
61. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (~tall(X0) & generous(X0))) & ((tall(X0) | ~generous(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (~tall(X0) & generous(X0))) & (tall(X0) | ~generous(X0) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [flattening 61]
98. ~humble(X0) | funny(X0) | ~strong(X0) [cnf transformation 44]
99. ~humble(X0) | funny(X0) | ~quiet(X0) [cnf transformation 44]
102. ~funny(X0) | ~old(X0) | strong(X0) | ~old(X0) [cnf transformation 46]
104. strong(X0) | old(X0) | old(X0) [cnf transformation 46]
119. ~patient(X0) | humble(X0) [cnf transformation 54]
123. ~generous(X0) | strong(X0) | quiet(X0) | brave(X0) [cnf transformation 55]
134. funny(X0) | generous(X0) | generous(X0) [cnf transformation 62]
144. ~brave(lucy) [cnf transformation 19]
145. ~funny(lucy) [cnf transformation 19]
154. patient(lucy) [cnf transformation 25]
156. funny(X0) | generous(X0) [duplicate literal removal 134]
157. ~funny(X0) | ~old(X0) | strong(X0) [duplicate literal removal 102]
158. old(X0) | strong(X0) [duplicate literal removal 104]
236. ~funny(X0) | strong(X0) [subsumption resolution 157,158]
348. humble(lucy) [resolution 119,154]
355. generous(X0) | strong(X0) [resolution 236,156]
363. funny(lucy) | ~strong(lucy) [resolution 98,348]
364. ~strong(lucy) [subsumption resolution 363,145]
365. funny(lucy) | ~quiet(lucy) [resolution 99,348]
366. ~quiet(lucy) [subsumption resolution 365,145]
490. strong(X0) | quiet(X0) | brave(X0) | strong(X0) [resolution 123,355]
495. brave(X0) | quiet(X0) | strong(X0) [duplicate literal removal 490]
606. quiet(lucy) | strong(lucy) [resolution 495,144]
612. strong(lucy) [subsumption resolution 606,366]
613. $false [subsumption resolution 612,364]
% SZS output end Proof for 3337918057855914778178733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not tall is both not happy and not brave. Everyone who is not happy or not strong is both not generous and old. If someone is both wise and not creative then lucy is both quiet and happy. Everyone who is happy or not curious is strong and vice versa. If someone is either funny or not rich then someone is either not patient or not old. Everyone who is rich is creative or humble and vice versa. If mary is either not tall or not old then alice is humble or not tall. Everyone who is strong or not patient is not tall and vice versa. Everyone who is both rich and strong is either happy or generous. If mary is either not kind or strong then someone is both not brave and generous and vice versa. Everyone who is either creative or old is strong or kind. Everyone who is tall or generous is not curious and vice versa. Everyone who is not wise is either tall or not quiet. Everyone who is not old is rich and vice versa. If someone is either not strong or not calm then john is brave or not quiet. If paul is not happy or not creative then someone is not strong or wise. Someone is both not quiet and strong. Someone is funny. Someone is both curious and funny. Someone is either not generous or quiet. Fred is either not creative or not generous. Someone is either patient or not old. Susan is happy or not creative. Mary is not humble. | John is tall. | contradiction | (![X]:((~creative(X)<~>~tall(X))=>(~happy(X)&~brave(X))))&
(![X]:((~happy(X)|~strong(X))=>(~generous(X)&old(X))))&
((?[X]:((wise(X)&~creative(X))))=>((quiet(lucy)&happy(lucy))))&
(![X]:((happy(X)|~curious(X))<=>strong(X)))&
((?[X]:((funny(X)<~>~rich(X))))=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:(rich(X)<=>(creative(X)|humble(X))))&
(((~tall(mary)<~>~old(mary)))=>((humble(alice)|~tall(alice))))&
(![X]:((strong(X)|~patient(X))<=>~tall(X)))&
(![X]:((rich(X)&strong(X))=>(happy(X)<~>generous(X))))&
(((~kind(mary)<~>strong(mary)))<=>(?[X]:((~brave(X)&generous(X)))))&
(![X]:((creative(X)<~>old(X))=>(strong(X)|kind(X))))&
(![X]:((tall(X)|generous(X))<=>~curious(X)))&
(![X]:(~wise(X)=>(tall(X)<~>~quiet(X))))&
(![X]:(~old(X)<=>rich(X)))&
((?[X]:((~strong(X)<~>~calm(X))))=>((brave(john)|~quiet(john))))&
(((~happy(paul)|~creative(paul)))=>(?[X]:((~strong(X)|wise(X)))))&
(?[X]:((~quiet(X)&strong(X))))&
(?[X]:(funny(X)))&
(?[X]:((curious(X)&funny(X))))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~creative(fred)<~>~generous(fred)))&
(?[X]:((patient(X)<~>~old(X))))&
((happy(susan)|~creative(susan)))&
(~humble(mary)) | tall(john) | [
"p3",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5758236159127255987921353
% SZS output start Proof for 5758236159127255987921353
4. ! [X0] : ((~curious(X0) | happy(X0)) <=> strong(X0)) [input p3]
8. ! [X0] : ((~patient(X0) | strong(X0)) <=> ~tall(X0)) [input p7]
12. ! [X0] : ((generous(X0) | tall(X0)) <=> ~curious(X0)) [input p11]
25. tall(john) [input hypothesis]
42. ! [X0] : (((~curious(X0) | happy(X0)) | ~strong(X0)) & (strong(X0) | (curious(X0) & ~happy(X0)))) [nnf transformation 4]
43. ! [X0] : ((~curious(X0) | happy(X0) | ~strong(X0)) & (strong(X0) | (curious(X0) & ~happy(X0)))) [flattening 42]
51. ! [X0] : (((~patient(X0) | strong(X0)) | tall(X0)) & (~tall(X0) | (patient(X0) & ~strong(X0)))) [nnf transformation 8]
52. ! [X0] : ((~patient(X0) | strong(X0) | tall(X0)) & (~tall(X0) | (patient(X0) & ~strong(X0)))) [flattening 51]
59. ! [X0] : (((generous(X0) | tall(X0)) | curious(X0)) & (~curious(X0) | (~generous(X0) & ~tall(X0)))) [nnf transformation 12]
60. ! [X0] : ((generous(X0) | tall(X0) | curious(X0)) & (~curious(X0) | (~generous(X0) & ~tall(X0)))) [flattening 59]
90. curious(X0) | strong(X0) [cnf transformation 43]
101. ~strong(X0) | ~tall(X0) [cnf transformation 52]
114. ~curious(X0) | ~tall(X0) [cnf transformation 60]
138. tall(john) [cnf transformation 25]
304. ~tall(X0) | strong(X0) [resolution 114,90]
305. ~tall(X0) [subsumption resolution 304,101]
308. $false [resolution 305,138]
% SZS output end Proof for 5758236159127255987921353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind and patient and vice versa. Everyone who is not brave or curious is both tall and kind. Everyone who is both not calm and not humble is funny and vice versa. Everyone who is not creative or happy is brave. Everyone who is either not humble or wise is not kind or strong. Everyone who is either not generous or strong is both not brave and not wise and vice versa. Everyone who is either not wise or not patient is not creative or creative and vice versa. If someone is either quiet or wise then someone is either rich or not patient. Everyone who is both not tall and not quiet is both not quiet and strong and vice versa. Everyone who is both not creative and tall is either not quiet or not creative. Everyone who is not quiet or not brave is either not curious or old and vice versa. Everyone who is strong or not tall is both not calm and not creative. Everyone who is both humble and not happy is humble and vice versa. Everyone who is either not old or not kind is both not happy and curious. Everyone who is brave or not quiet is not patient or curious and vice versa. Everyone who is both not funny and curious is not happy and vice versa. Susan is either not quiet or not generous. Mary is both calm and not wise. Someone is generous or not strong. Alice is not humble or old. Someone is humble or tall. Alice is either humble or not patient. Someone is patient or quiet. | Alice is not brave. | neutral | (![X]:(~calm(X)<=>(~kind(X)&patient(X))))&
(![X]:((~brave(X)|curious(X))=>(tall(X)&kind(X))))&
(![X]:((~calm(X)&~humble(X))<=>funny(X)))&
(![X]:((~creative(X)|happy(X))=>brave(X)))&
(![X]:((~humble(X)<~>wise(X))=>(~kind(X)|strong(X))))&
(![X]:((~generous(X)<~>strong(X))<=>(~brave(X)&~wise(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~creative(X)|creative(X))))&
((?[X]:((quiet(X)<~>wise(X))))=>(?[X]:((rich(X)<~>~patient(X)))))&
(![X]:((~tall(X)&~quiet(X))<=>(~quiet(X)&strong(X))))&
(![X]:((~creative(X)&tall(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(~curious(X)<~>old(X))))&
(![X]:((strong(X)|~tall(X))=>(~calm(X)&~creative(X))))&
(![X]:((humble(X)&~happy(X))<=>humble(X)))&
(![X]:((~old(X)<~>~kind(X))=>(~happy(X)&curious(X))))&
(![X]:((brave(X)|~quiet(X))<=>(~patient(X)|curious(X))))&
(![X]:((~funny(X)&curious(X))<=>~happy(X)))&
((~quiet(susan)<~>~generous(susan)))&
((calm(mary)&~wise(mary)))&
(?[X]:((generous(X)|~strong(X))))&
((~humble(alice)|old(alice)))&
(?[X]:((humble(X)|tall(X))))&
((humble(alice)<~>~patient(alice)))&
(?[X]:((patient(X)|quiet(X)))) | ~brave(alice) | [] | null | 0 |
Everyone who is not happy is calm or rich. Everyone who is both not tall and old is not old or quiet. If someone is patient then john is creative or rich. If someone is either kind or not strong then someone is not calm. Everyone who is either tall or not curious is wise or patient. Everyone who is both happy and not strong is old or not calm and vice versa. Everyone who is generous is not rich or not happy and vice versa. Everyone who is both curious and old is both humble and wise. Everyone who is not quiet or strong is both generous and not generous. If someone is funny or not kind then lucy is not brave or quiet. If someone is either funny or brave then alice is kind or rich. If someone is wise or not curious then alice is kind or generous. If someone is rich or not calm then susan is either not creative or patient. Everyone who is not curious is tall or kind. If paul is not brave then someone is patient or wise and vice versa. If john is both old and not happy then someone is old and vice versa. Paul is both not kind and not curious. Someone is creative. Someone is either quiet or not tall. Fred is both not patient and calm. Someone is not funny or patient. Mary is both funny and curious. | Fred is generous. | entailment | (![X]:(~happy(X)=>(calm(X)|rich(X))))&
(![X]:((~tall(X)&old(X))=>(~old(X)|quiet(X))))&
((?[X]:(patient(X)))=>((creative(john)|rich(john))))&
((?[X]:((kind(X)<~>~strong(X))))=>(?[X]:(~calm(X))))&
(![X]:((tall(X)<~>~curious(X))=>(wise(X)|patient(X))))&
(![X]:((happy(X)&~strong(X))<=>(old(X)|~calm(X))))&
(![X]:(generous(X)<=>(~rich(X)|~happy(X))))&
(![X]:((curious(X)&old(X))=>(humble(X)&wise(X))))&
(![X]:((~quiet(X)|strong(X))=>(generous(X)&~generous(X))))&
((?[X]:((funny(X)|~kind(X))))=>((~brave(lucy)|quiet(lucy))))&
((?[X]:((funny(X)<~>brave(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((wise(X)|~curious(X))))=>((kind(alice)|generous(alice))))&
((?[X]:((rich(X)|~calm(X))))=>((~creative(susan)<~>patient(susan))))&
(![X]:(~curious(X)=>(tall(X)|kind(X))))&
((~brave(paul))<=>(?[X]:((patient(X)|wise(X)))))&
(((old(john)&~happy(john)))<=>(?[X]:(old(X))))&
((~kind(paul)&~curious(paul)))&
(?[X]:(creative(X)))&
(?[X]:((quiet(X)<~>~tall(X))))&
((~patient(fred)&calm(fred)))&
(?[X]:((~funny(X)|patient(X))))&
((funny(mary)&curious(mary))) | generous(fred) | [
"p5",
"p6",
"p8",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5325725555972312703542774
% SZS output start Proof for 5325725555972312703542774
6. ! [X0] : ((~strong(X0) & happy(X0)) <=> (~calm(X0) | old(X0))) [input p5]
7. ! [X0] : (generous(X0) <=> (~happy(X0) | ~rich(X0))) [input p6]
9. ! [X0] : ((strong(X0) | ~quiet(X0)) => (~generous(X0) & generous(X0))) [input p8]
16. (~happy(john) & old(john)) <=> ? [X0] : old(X0) [input p15]
20. calm(fred) & ~patient(fred) [input p19]
23. ~generous(fred) [input hypothesis]
37. ! [X0] : ((~generous(X0) & generous(X0)) | (~strong(X0) & quiet(X0))) [ennf transformation 9]
52. ! [X0] : (((~strong(X0) & happy(X0)) | (calm(X0) & ~old(X0))) & ((~calm(X0) | old(X0)) | (strong(X0) | ~happy(X0)))) [nnf transformation 6]
53. ! [X0] : (((~strong(X0) & happy(X0)) | (calm(X0) & ~old(X0))) & (~calm(X0) | old(X0) | strong(X0) | ~happy(X0))) [flattening 52]
54. ! [X0] : ((generous(X0) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | ~generous(X0))) [nnf transformation 7]
55. ! [X0] : ((generous(X0) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | ~generous(X0))) [flattening 54]
62. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (happy(john) | ~old(john))) [nnf transformation 16]
63. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | happy(john) | ~old(john)) [flattening 62]
64. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | happy(john) | ~old(john)) [rectify 63]
65. ? [X1] : old(X1) => old(sK2) [choice axiom]
66. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (old(sK2) | happy(john) | ~old(john)) [skolemisation 64,65]
81. ~calm(X0) | old(X0) | strong(X0) | ~happy(X0) [cnf transformation 53]
82. ~old(X0) | happy(X0) [cnf transformation 53]
88. generous(X0) | happy(X0) [cnf transformation 55]
91. generous(X0) | ~strong(X0) [cnf transformation 37]
93. ~generous(X0) | ~strong(X0) [cnf transformation 37]
109. old(john) | ~old(X0) [cnf transformation 66]
110. ~happy(john) | ~old(X0) [cnf transformation 66]
117. calm(fred) [cnf transformation 20]
121. ~generous(fred) [cnf transformation 23]
147. ~strong(X0) [subsumption resolution 91,93]
211. 21 <=> ! [X0] : ~old(X0) [avatar definition]
212. ~old(X0) <- (21) [avatar component clause 211]
214. 22 <=> happy(john) [avatar definition]
216. ~happy(john) <- (~22) [avatar component clause 214]
217. 21 | ~22 [avatar split clause 110,214,211]
219. 23 <=> old(john) [avatar definition]
221. old(john) <- (23) [avatar component clause 219]
222. 21 | 23 [avatar split clause 109,219,211]
235. happy(fred) [resolution 88,121]
261. old(fred) | strong(fred) | ~happy(fred) [resolution 81,117]
263. strong(fred) | ~happy(fred) <- (21) [subsumption resolution 261,212]
264. ~happy(fred) <- (21) [subsumption resolution 263,147]
265. $false <- (21) [subsumption resolution 264,235]
266. ~21 [avatar contradiction clause 265]
275. happy(john) <- (23) [resolution 221,82]
276. $false <- (~22, 23) [subsumption resolution 275,216]
277. 22 | ~23 [avatar contradiction clause 276]
278. $false [avatar sat refutation 217,222,266,277]
% SZS output end Proof for 5325725555972312703542774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not patient is calm or not rich and vice versa.
If someone is either not creative or not tall then someone is either not rich or not curious and vice versa.
If someone is both strong and wise then mary is both not humble and not generous and vice versa.
If someone is either creative or not creative then mary is generous and vice versa.
If lucy is either generous or rich then alice is both not generous and curious.
If paul is both humble and not calm then someone is either not patient or not humble.
If alice is both not creative and not patient then someone is either brave or wise and vice versa.
Everyone who is either wise or not rich is patient.
Everyone who is both not tall and wise is either curious or creative.
Everyone who is both wise and humble is both not tall and rich and vice versa.
If john is both kind and not rich then john is not creative.
If someone is either kind or generous then someone is not brave.
Everyone who is not old or creative is old or not wise and vice versa.
Everyone who is not wise is both not calm and not tall and vice versa.
Everyone who is not quiet is both not funny and kind.
Everyone who is both patient and creative is both not creative and old and vice versa.
Someone is both curious and creative.
Someone is not generous.
Alice is both not patient and old.
Someone is funny.
Someone is either not quiet or old.
Paul is both generous and calm. | John is not quiet. | contradiction | (![X]:((old(X)|~patient(X))<=>(calm(X)|~rich(X))))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:((strong(X)&wise(X))))<=>((~humble(mary)&~generous(mary))))&
((?[X]:((creative(X)<~>~creative(X))))<=>(generous(mary)))&
(((generous(lucy)<~>rich(lucy)))=>((~generous(alice)&curious(alice))))&
(((humble(paul)&~calm(paul)))=>(?[X]:((~patient(X)<~>~humble(X)))))&
(((~creative(alice)&~patient(alice)))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((wise(X)<~>~rich(X))=>patient(X)))&
(![X]:((~tall(X)&wise(X))=>(curious(X)<~>creative(X))))&
(![X]:((wise(X)&humble(X))<=>(~tall(X)&rich(X))))&
(((kind(john)&~rich(john)))=>(~creative(john)))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|creative(X))<=>(old(X)|~wise(X))))&
(![X]:(~wise(X)<=>(~calm(X)&~tall(X))))&
(![X]:(~quiet(X)=>(~funny(X)&kind(X))))&
(![X]:((patient(X)&creative(X))<=>(~creative(X)&old(X))))&
(?[X]:((curious(X)&creative(X))))&
(?[X]:(~generous(X)))&
((~patient(alice)&old(alice)))&
(?[X]:(funny(X)))&
(?[X]:((~quiet(X)<~>old(X))))&
((generous(paul)&calm(paul))) | ~quiet(john) | [
"p0",
"p7",
"p9",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 59760311196554235549699
% SZS output start Proof for 59760311196554235549699
1. ! [X0] : ((~patient(X0) | old(X0)) <=> (~rich(X0) | calm(X0))) [input p0]
8. ! [X0] : ((wise(X0) <~> ~rich(X0)) => patient(X0)) [input p7]
10. ! [X0] : ((humble(X0) & wise(X0)) <=> (rich(X0) & ~tall(X0))) [input p9]
11. (~rich(john) & kind(john)) => ~creative(john) [input p10]
13. ! [X0] : ((creative(X0) | ~old(X0)) <=> (~wise(X0) | old(X0))) [input p12]
14. ! [X0] : (~wise(X0) <=> (~tall(X0) & ~calm(X0))) [input p13]
15. ! [X0] : (~quiet(X0) => (kind(X0) & ~funny(X0))) [input p14]
16. ! [X0] : ((creative(X0) & patient(X0)) <=> (old(X0) & ~creative(X0))) [input p15]
23. ~quiet(john) [input hypothesis]
29. ! [X0] : (patient(X0) | (wise(X0) <=> ~rich(X0))) [ennf transformation 8]
32. ~creative(john) | (rich(john) | ~kind(john)) [ennf transformation 11]
33. ~creative(john) | rich(john) | ~kind(john) [flattening 32]
35. ! [X0] : ((kind(X0) & ~funny(X0)) | quiet(X0)) [ennf transformation 15]
36. ! [X0] : (((~patient(X0) | old(X0)) | (rich(X0) & ~calm(X0))) & ((~rich(X0) | calm(X0)) | (patient(X0) & ~old(X0)))) [nnf transformation 1]
37. ! [X0] : ((~patient(X0) | old(X0) | (rich(X0) & ~calm(X0))) & (~rich(X0) | calm(X0) | (patient(X0) & ~old(X0)))) [flattening 36]
61. ! [X0] : (patient(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0)))) [nnf transformation 29]
63. ! [X0] : (((humble(X0) & wise(X0)) | (~rich(X0) | tall(X0))) & ((rich(X0) & ~tall(X0)) | (~humble(X0) | ~wise(X0)))) [nnf transformation 10]
64. ! [X0] : (((humble(X0) & wise(X0)) | ~rich(X0) | tall(X0)) & ((rich(X0) & ~tall(X0)) | ~humble(X0) | ~wise(X0))) [flattening 63]
69. ! [X0] : (((creative(X0) | ~old(X0)) | (wise(X0) & ~old(X0))) & ((~wise(X0) | old(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 13]
70. ! [X0] : ((creative(X0) | ~old(X0) | (wise(X0) & ~old(X0))) & (~wise(X0) | old(X0) | (~creative(X0) & old(X0)))) [flattening 69]
71. ! [X0] : ((~wise(X0) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | wise(X0))) [nnf transformation 14]
72. ! [X0] : ((~wise(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | wise(X0))) [flattening 71]
73. ! [X0] : (((creative(X0) & patient(X0)) | (~old(X0) | creative(X0))) & ((old(X0) & ~creative(X0)) | (~creative(X0) | ~patient(X0)))) [nnf transformation 16]
74. ! [X0] : (((creative(X0) & patient(X0)) | ~old(X0) | creative(X0)) & ((old(X0) & ~creative(X0)) | ~creative(X0) | ~patient(X0))) [flattening 73]
87. ~patient(X0) | old(X0) | rich(X0) [cnf transformation 37]
116. ~wise(X0) | ~rich(X0) | patient(X0) [cnf transformation 61]
117. wise(X0) | patient(X0) | rich(X0) [cnf transformation 61]
122. ~rich(X0) | wise(X0) | tall(X0) [cnf transformation 64]
124. ~creative(john) | rich(john) | ~kind(john) [cnf transformation 33]
127. ~wise(X0) | old(X0) | old(X0) [cnf transformation 70]
129. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 70]
132. ~tall(X0) | wise(X0) [cnf transformation 72]
135. quiet(X0) | kind(X0) [cnf transformation 35]
136. ~creative(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 74]
150. ~quiet(john) [cnf transformation 23]
151. ~creative(X0) | ~patient(X0) [duplicate literal removal 136]
153. ~wise(X0) | old(X0) [duplicate literal removal 127]
154. ~old(X0) | creative(X0) [duplicate literal removal 129]
217. 14 <=> ! [X1] : creative(X1) [avatar definition]
218. creative(X1) <- (14) [avatar component clause 217]
291. 30 <=> kind(john) [avatar definition]
295. 31 <=> rich(john) [avatar definition]
297. rich(john) <- (31) [avatar component clause 295]
299. 32 <=> creative(john) [avatar definition]
301. ~creative(john) <- (~32) [avatar component clause 299]
302. ~30 | 31 | ~32 [avatar split clause 124,299,295,291]
329. kind(john) [resolution 135,150]
333. 30 [avatar split clause 329,291]
366. patient(X3) | rich(X3) | old(X3) [resolution 117,153]
368. rich(X3) | old(X3) [subsumption resolution 366,87]
378. wise(X0) | tall(X0) | old(X0) [resolution 122,368]
379. wise(X0) | old(X0) [subsumption resolution 378,132]
380. old(X0) [subsumption resolution 379,153]
393. creative(X1) [resolution 380,154]
395. 14 [avatar split clause 393,217]
396. $false <- (14, ~32) [resolution 218,301]
397. ~patient(X0) <- (14) [resolution 218,151]
398. ~14 | 32 [avatar contradiction clause 396]
400. wise(john) | tall(john) <- (31) [resolution 297,122]
412. wise(john) <- (31) [subsumption resolution 400,132]
426. ~rich(john) | patient(john) <- (31) [resolution 412,116]
430. patient(john) <- (31) [subsumption resolution 426,297]
431. $false <- (14, 31) [subsumption resolution 430,397]
432. ~14 | ~31 [avatar contradiction clause 431]
433. $false [avatar sat refutation 302,333,395,398,432]
% SZS output end Proof for 59760311196554235549699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not generous is either not patient or kind and vice versa.
If someone is both not brave and calm then fred is humble or brave and vice versa.
If someone is generous then lucy is either not humble or happy and vice versa.
Everyone who is both not happy and not kind is either happy or calm and vice versa.
Everyone who is not tall is either not kind or tall and vice versa.
Everyone who is not happy is both old and not tall.
Everyone who is either not old or not happy is both patient and curious and vice versa.
Everyone who is either not happy or not quiet is either not curious or not generous.
Everyone who is tall is either calm or not funny.
If someone is either not happy or not rich then someone is not kind and vice versa.
Everyone who is either wise or patient is either humble or calm.
If someone is not creative or not calm then someone is both not calm and rich and vice versa.
If fred is either not calm or not creative then someone is not funny and vice versa.
If paul is both not funny and not creative then someone is either not quiet or funny.
If john is generous then someone is either funny or not kind and vice versa.
Everyone who is either tall or curious is generous or creative and vice versa.
Mary is funny or not brave.
Someone is not tall.
Paul is either not brave or kind.
Susan is either brave or rich.
Paul is generous or not rich. | Susan is not wise. | neutral | (![X]:((old(X)|~generous(X))<=>(~patient(X)<~>kind(X))))&
((?[X]:((~brave(X)&calm(X))))<=>((humble(fred)|brave(fred))))&
((?[X]:(generous(X)))<=>((~humble(lucy)<~>happy(lucy))))&
(![X]:((~happy(X)&~kind(X))<=>(happy(X)<~>calm(X))))&
(![X]:(~tall(X)<=>(~kind(X)<~>tall(X))))&
(![X]:(~happy(X)=>(old(X)&~tall(X))))&
(![X]:((~old(X)<~>~happy(X))<=>(patient(X)&curious(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>(~curious(X)<~>~generous(X))))&
(![X]:(tall(X)=>(calm(X)<~>~funny(X))))&
((?[X]:((~happy(X)<~>~rich(X))))<=>(?[X]:(~kind(X))))&
(![X]:((wise(X)<~>patient(X))=>(humble(X)<~>calm(X))))&
((?[X]:((~creative(X)|~calm(X))))<=>(?[X]:((~calm(X)&rich(X)))))&
(((~calm(fred)<~>~creative(fred)))<=>(?[X]:(~funny(X))))&
(((~funny(paul)&~creative(paul)))=>(?[X]:((~quiet(X)<~>funny(X)))))&
((generous(john))<=>(?[X]:((funny(X)<~>~kind(X)))))&
(![X]:((tall(X)<~>curious(X))<=>(generous(X)|creative(X))))&
((funny(mary)|~brave(mary)))&
(?[X]:(~tall(X)))&
((~brave(paul)<~>kind(paul)))&
((brave(susan)<~>rich(susan)))&
((generous(paul)|~rich(paul))) | ~wise(susan) | [] | null | 0 |
Everyone who is either humble or old is funny or generous and vice versa. Everyone who is either not strong or humble is not tall and vice versa. Everyone who is happy or not creative is both not brave and tall. If someone is tall then mary is either calm or strong. Everyone who is curious is happy and vice versa. Everyone who is both brave and not kind is quiet and vice versa. Everyone who is kind or old is brave or not quiet and vice versa. Everyone who is not kind or calm is not brave or not funny. Everyone who is wise is not humble. Everyone who is humble or wise is both not generous and not creative. Everyone who is humble is rich or brave and vice versa. If someone is brave then lucy is not patient or not generous and vice versa. If someone is not quiet or calm then someone is not happy and vice versa. If alice is either wise or not generous then someone is both not brave and old and vice versa. Everyone who is kind is old and vice versa. If someone is both wise and not patient then someone is either wise or not wise and vice versa. Someone is not quiet or not curious. John is tall or creative. Alice is not curious. Someone is either rich or not tall. Susan is either old or not generous. Someone is both wise and patient. John is not tall or not calm. | Mary is not old. | contradiction | (![X]:((humble(X)<~>old(X))<=>(funny(X)|generous(X))))&
(![X]:((~strong(X)<~>humble(X))<=>~tall(X)))&
(![X]:((happy(X)|~creative(X))=>(~brave(X)&tall(X))))&
((?[X]:(tall(X)))=>((calm(mary)<~>strong(mary))))&
(![X]:(curious(X)<=>happy(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((kind(X)|old(X))<=>(brave(X)|~quiet(X))))&
(![X]:((~kind(X)|calm(X))=>(~brave(X)|~funny(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))=>(~generous(X)&~creative(X))))&
(![X]:(humble(X)<=>(rich(X)|brave(X))))&
((?[X]:(brave(X)))<=>((~patient(lucy)|~generous(lucy))))&
((?[X]:((~quiet(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((~brave(X)&old(X)))))&
(![X]:(kind(X)<=>old(X)))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(?[X]:((~quiet(X)|~curious(X))))&
((tall(john)|creative(john)))&
(~curious(alice))&
(?[X]:((rich(X)<~>~tall(X))))&
((old(susan)<~>~generous(susan)))&
(?[X]:((wise(X)&patient(X))))&
((~tall(john)|~calm(john))) | ~old(mary) | [
"p2",
"p5",
"p6",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5185625987282541140308003
% SZS output start Proof for 5185625987282541140308003
3. ! [X0] : ((~creative(X0) | happy(X0)) => (tall(X0) & ~brave(X0))) [input p2]
6. ! [X0] : ((~kind(X0) & brave(X0)) <=> quiet(X0)) [input p5]
7. ! [X0] : ((old(X0) | kind(X0)) <=> (~quiet(X0) | brave(X0))) [input p6]
10. ! [X0] : ((wise(X0) | humble(X0)) => (~creative(X0) & ~generous(X0))) [input p9]
11. ! [X0] : (humble(X0) <=> (brave(X0) | rich(X0))) [input p10]
12. ? [X0] : brave(X0) <=> (~generous(lucy) | ~patient(lucy)) [input p11]
15. ! [X0] : (kind(X0) <=> old(X0)) [input p14]
24. ~old(mary) [input hypothesis]
28. ! [X0] : ((tall(X0) & ~brave(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 3]
34. ! [X0] : ((~creative(X0) & ~generous(X0)) | (~wise(X0) & ~humble(X0))) [ennf transformation 10]
39. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | (kind(X0) | ~brave(X0)))) [nnf transformation 6]
40. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | kind(X0) | ~brave(X0))) [flattening 39]
41. ! [X0] : (((old(X0) | kind(X0)) | (quiet(X0) & ~brave(X0))) & ((~quiet(X0) | brave(X0)) | (~old(X0) & ~kind(X0)))) [nnf transformation 7]
42. ! [X0] : ((old(X0) | kind(X0) | (quiet(X0) & ~brave(X0))) & (~quiet(X0) | brave(X0) | (~old(X0) & ~kind(X0)))) [flattening 41]
43. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ~humble(X0))) [nnf transformation 11]
44. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ~humble(X0))) [flattening 43]
45. (? [X0] : brave(X0) | (generous(lucy) & patient(lucy))) & ((~generous(lucy) | ~patient(lucy)) | ! [X0] : ~brave(X0)) [nnf transformation 12]
46. (? [X0] : brave(X0) | (generous(lucy) & patient(lucy))) & (~generous(lucy) | ~patient(lucy) | ! [X0] : ~brave(X0)) [flattening 45]
47. (? [X0] : brave(X0) | (generous(lucy) & patient(lucy))) & (~generous(lucy) | ~patient(lucy) | ! [X1] : ~brave(X1)) [rectify 46]
48. ? [X0] : brave(X0) => brave(sK0) [choice axiom]
49. (brave(sK0) | (generous(lucy) & patient(lucy))) & (~generous(lucy) | ~patient(lucy) | ! [X1] : ~brave(X1)) [skolemisation 47,48]
59. ! [X0] : ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))) [nnf transformation 15]
84. ~brave(X0) | creative(X0) [cnf transformation 28]
91. ~quiet(X0) | brave(X0) [cnf transformation 40]
96. quiet(X0) | kind(X0) | old(X0) [cnf transformation 42]
102. ~creative(X0) | ~humble(X0) [cnf transformation 34]
106. ~brave(X0) | humble(X0) [cnf transformation 44]
107. ~generous(lucy) | ~patient(lucy) | ~brave(X1) [cnf transformation 49]
108. brave(sK0) | patient(lucy) [cnf transformation 49]
109. brave(sK0) | generous(lucy) [cnf transformation 49]
119. ~kind(X0) | old(X0) [cnf transformation 59]
137. ~old(mary) [cnf transformation 24]
156. 4 <=> generous(lucy) [avatar definition]
160. 5 <=> brave(sK0) [avatar definition]
162. brave(sK0) <- (5) [avatar component clause 160]
163. 4 | 5 [avatar split clause 109,160,156]
165. 6 <=> patient(lucy) [avatar definition]
168. 6 | 5 [avatar split clause 108,160,165]
170. 7 <=> ! [X1] : ~brave(X1) [avatar definition]
171. ~brave(X1) <- (7) [avatar component clause 170]
172. 7 | ~6 | ~4 [avatar split clause 107,156,165,170]
285. creative(sK0) <- (5) [resolution 84,162]
291. ~humble(sK0) <- (5) [resolution 102,285]
296. humble(sK0) <- (5) [resolution 106,162]
297. $false <- (5) [subsumption resolution 296,291]
298. ~5 [avatar contradiction clause 297]
330. kind(X1) | old(X1) | brave(X1) [resolution 96,91]
332. kind(X1) | old(X1) <- (7) [subsumption resolution 330,171]
333. old(X1) <- (7) [subsumption resolution 332,119]
335. $false <- (7) [resolution 333,137]
339. ~7 [avatar contradiction clause 335]
340. $false [avatar sat refutation 163,168,172,298,339]
% SZS output end Proof for 5185625987282541140308003
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or funny is both not patient and humble and vice versa.
Everyone who is both quiet and tall is rich.
If paul is either not strong or not wise then john is either not humble or not calm and vice versa.
If someone is not kind or generous then john is rich and vice versa.
If someone is not generous then lucy is either patient or tall and vice versa.
If john is both not creative and not old then alice is not kind or humble and vice versa.
If someone is either wise or not strong then someone is calm or rich.
Everyone who is not rich is not rich or happy and vice versa.
Everyone who is not generous is either curious or not curious and vice versa.
Everyone who is either rich or not calm is not old or happy and vice versa.
Everyone who is humble or not happy is not humble.
If alice is not curious then someone is both creative and not old.
Everyone who is not happy or not tall is not wise or wise and vice versa.
Everyone who is either not funny or patient is either not calm or not rich.
If susan is either not happy or not brave then fred is either humble or not tall and vice versa.
Everyone who is either not rich or tall is both not brave and generous.
Someone is not brave or rich.
Someone is not brave.
Lucy is either not generous or rich.
Susan is not tall or not patient.
Someone is humble or wise.
Someone is both not wise and not happy.
Mary is not funny or not creative. | Paul is not kind. | neutral | (![X]:((creative(X)<~>funny(X))<=>(~patient(X)&humble(X))))&
(![X]:((quiet(X)&tall(X))=>rich(X)))&
(((~strong(paul)<~>~wise(paul)))<=>((~humble(john)<~>~calm(john))))&
((?[X]:((~kind(X)|generous(X))))<=>(rich(john)))&
((?[X]:(~generous(X)))<=>((patient(lucy)<~>tall(lucy))))&
(((~creative(john)&~old(john)))<=>((~kind(alice)|humble(alice))))&
((?[X]:((wise(X)<~>~strong(X))))=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~rich(X)|happy(X))))&
(![X]:(~generous(X)<=>(curious(X)<~>~curious(X))))&
(![X]:((rich(X)<~>~calm(X))<=>(~old(X)|happy(X))))&
(![X]:((humble(X)|~happy(X))=>~humble(X)))&
((~curious(alice))=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((~happy(X)|~tall(X))<=>(~wise(X)|wise(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~calm(X)<~>~rich(X))))&
(((~happy(susan)<~>~brave(susan)))<=>((humble(fred)<~>~tall(fred))))&
(![X]:((~rich(X)<~>tall(X))=>(~brave(X)&generous(X))))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:(~brave(X)))&
((~generous(lucy)<~>rich(lucy)))&
((~tall(susan)|~patient(susan)))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:((~wise(X)&~happy(X))))&
((~funny(mary)|~creative(mary))) | ~kind(paul) | [] | null | 0 |
Everyone who is calm or patient is both kind and wise and vice versa.
Everyone who is both not kind and kind is either patient or not calm and vice versa.
Everyone who is not happy is not rich or not quiet.
Everyone who is creative or not wise is not strong or humble and vice versa.
Everyone who is not rich or not curious is kind or not happy.
Everyone who is both not happy and not rich is either strong or not curious.
Everyone who is humble is either not rich or not humble and vice versa.
If john is both tall and not humble then fred is either kind or calm and vice versa.
If lucy is either generous or not brave then someone is both humble and not curious.
If someone is not humble or not rich then susan is patient and vice versa.
If fred is brave or funny then mary is either humble or funny and vice versa.
If someone is humble then mary is both rich and kind and vice versa.
If someone is either not happy or not brave then someone is both not quiet and happy and vice versa.
If someone is either kind or tall then alice is not funny.
Everyone who is not strong is generous.
If susan is both not calm and calm then someone is strong and vice versa.
Alice is both calm and not patient.
Someone is patient or tall.
Mary is both funny and not calm.
Someone is not brave.
Someone is creative or generous.
Fred is not brave.
Someone is either not kind or creative. | Alice is curious. | neutral | (![X]:((calm(X)|patient(X))<=>(kind(X)&wise(X))))&
(![X]:((~kind(X)&kind(X))<=>(patient(X)<~>~calm(X))))&
(![X]:(~happy(X)=>(~rich(X)|~quiet(X))))&
(![X]:((creative(X)|~wise(X))<=>(~strong(X)|humble(X))))&
(![X]:((~rich(X)|~curious(X))=>(kind(X)|~happy(X))))&
(![X]:((~happy(X)&~rich(X))=>(strong(X)<~>~curious(X))))&
(![X]:(humble(X)<=>(~rich(X)<~>~humble(X))))&
(((tall(john)&~humble(john)))<=>((kind(fred)<~>calm(fred))))&
(((generous(lucy)<~>~brave(lucy)))=>(?[X]:((humble(X)&~curious(X)))))&
((?[X]:((~humble(X)|~rich(X))))<=>(patient(susan)))&
(((brave(fred)|funny(fred)))<=>((humble(mary)<~>funny(mary))))&
((?[X]:(humble(X)))<=>((rich(mary)&kind(mary))))&
((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:((kind(X)<~>tall(X))))=>(~funny(alice)))&
(![X]:(~strong(X)=>generous(X)))&
(((~calm(susan)&calm(susan)))<=>(?[X]:(strong(X))))&
((calm(alice)&~patient(alice)))&
(?[X]:((patient(X)|tall(X))))&
((funny(mary)&~calm(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((creative(X)|generous(X))))&
(~brave(fred))&
(?[X]:((~kind(X)<~>creative(X)))) | curious(alice) | [] | null | 0 |
If someone is kind then lucy is either not strong or creative. If someone is either not strong or not brave then john is not wise or not creative and vice versa. If someone is generous or happy then someone is both not strong and curious. Everyone who is curious is not wise and vice versa. Everyone who is not wise is both not quiet and not curious. Everyone who is kind or not creative is humble or not calm and vice versa. Everyone who is quiet or rich is either not generous or not old. If someone is both not creative and humble then someone is not happy. If someone is not patient then someone is both not patient and not brave and vice versa. If someone is generous or not quiet then someone is both not kind and rich. Everyone who is not brave is strong. If paul is either humble or quiet then alice is old or wise and vice versa. Everyone who is both old and kind is quiet or not generous and vice versa. Everyone who is not curious is tall and vice versa. Everyone who is either not humble or strong is kind or not curious and vice versa. Someone is calm. Paul is either not generous or calm. Someone is either not funny or calm. Someone is patient. Lucy is brave. Someone is either patient or not happy. | John is not tall. | contradiction | ((?[X]:(kind(X)))=>((~strong(lucy)<~>creative(lucy))))&
((?[X]:((~strong(X)<~>~brave(X))))<=>((~wise(john)|~creative(john))))&
((?[X]:((generous(X)|happy(X))))=>(?[X]:((~strong(X)&curious(X)))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:(~wise(X)=>(~quiet(X)&~curious(X))))&
(![X]:((kind(X)|~creative(X))<=>(humble(X)|~calm(X))))&
(![X]:((quiet(X)|rich(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((~creative(X)&humble(X))))=>(?[X]:(~happy(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~patient(X)&~brave(X)))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:(~brave(X)=>strong(X)))&
(((humble(paul)<~>quiet(paul)))<=>((old(alice)|wise(alice))))&
(![X]:((old(X)&kind(X))<=>(quiet(X)|~generous(X))))&
(![X]:(~curious(X)<=>tall(X)))&
(![X]:((~humble(X)<~>strong(X))<=>(kind(X)|~curious(X))))&
(?[X]:(calm(X)))&
((~generous(paul)<~>calm(paul)))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:(patient(X)))&
(brave(lucy))&
(?[X]:((patient(X)<~>~happy(X)))) | ~tall(john) | [
"p3",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1856693756050847657369613
% SZS output start Proof for 1856693756050847657369613
4. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p3]
5. ! [X0] : (~wise(X0) => (~curious(X0) & ~quiet(X0))) [input p4]
14. ! [X0] : (~curious(X0) <=> tall(X0)) [input p13]
22. ~tall(john) [input hypothesis]
29. ! [X0] : ((~curious(X0) & ~quiet(X0)) | wise(X0)) [ennf transformation 5]
43. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 4]
62. ! [X0] : ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0))) [nnf transformation 14]
88. ~curious(X0) | ~wise(X0) [cnf transformation 43]
89. curious(X0) | wise(X0) [cnf transformation 43]
91. ~curious(X0) | wise(X0) [cnf transformation 29]
120. tall(X0) | curious(X0) [cnf transformation 62]
137. ~tall(john) [cnf transformation 22]
197. wise(X0) [subsumption resolution 91,89]
298. curious(john) [resolution 120,137]
313. ~wise(john) [resolution 298,88]
314. $false [subsumption resolution 313,197]
% SZS output end Proof for 1856693756050847657369613
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm is old and vice versa.
If paul is strong then lucy is both quiet and strong and vice versa.
Everyone who is either old or not creative is both calm and curious.
If someone is either not rich or not wise then someone is both creative and curious and vice versa.
If someone is both wise and not funny then someone is both not happy and kind.
Everyone who is either not strong or not brave is old or not brave and vice versa.
If paul is not calm or creative then alice is either humble or not calm.
If someone is rich or kind then someone is not brave or not funny and vice versa.
Everyone who is not happy is both quiet and brave.
Everyone who is either not brave or not strong is both not calm and not tall.
Everyone who is both generous and tall is funny or not creative and vice versa.
If lucy is not quiet then john is not old.
If someone is not wise then paul is quiet or not funny.
Everyone who is either happy or not calm is either not wise or rich and vice versa.
If someone is strong or curious then someone is creative.
Everyone who is not patient or brave is either not patient or not funny and vice versa.
Alice is not kind or not funny.
Alice is funny.
Someone is funny.
Susan is both generous and not humble.
Susan is not humble or not wise.
Someone is both not old and curious.
Fred is not brave or curious.
Someone is not kind or rich. | Lucy is brave. | entailment | (![X]:(~calm(X)<=>old(X)))&
((strong(paul))<=>((quiet(lucy)&strong(lucy))))&
(![X]:((old(X)<~>~creative(X))=>(calm(X)&curious(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(?[X]:((creative(X)&curious(X)))))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:((~happy(X)&kind(X)))))&
(![X]:((~strong(X)<~>~brave(X))<=>(old(X)|~brave(X))))&
(((~calm(paul)|creative(paul)))=>((humble(alice)<~>~calm(alice))))&
((?[X]:((rich(X)|kind(X))))<=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:(~happy(X)=>(quiet(X)&brave(X))))&
(![X]:((~brave(X)<~>~strong(X))=>(~calm(X)&~tall(X))))&
(![X]:((generous(X)&tall(X))<=>(funny(X)|~creative(X))))&
((~quiet(lucy))=>(~old(john)))&
((?[X]:(~wise(X)))=>((quiet(paul)|~funny(paul))))&
(![X]:((happy(X)<~>~calm(X))<=>(~wise(X)<~>rich(X))))&
((?[X]:((strong(X)|curious(X))))=>(?[X]:(creative(X))))&
(![X]:((~patient(X)|brave(X))<=>(~patient(X)<~>~funny(X))))&
((~kind(alice)|~funny(alice)))&
(funny(alice))&
(?[X]:(funny(X)))&
((generous(susan)&~humble(susan)))&
((~humble(susan)|~wise(susan)))&
(?[X]:((~old(X)&curious(X))))&
((~brave(fred)|curious(fred)))&
(?[X]:((~kind(X)|rich(X)))) | brave(lucy) | [
"p0",
"p2",
"p5",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7029473588752737803232986
% SZS output start Proof for 7029473588752737803232986
1. ! [X0] : (~calm(X0) <=> old(X0)) [input p0]
3. ! [X0] : ((old(X0) <~> ~creative(X0)) => (curious(X0) & calm(X0))) [input p2]
6. ! [X0] : ((~strong(X0) <~> ~brave(X0)) <=> (~brave(X0) | old(X0))) [input p5]
10. ! [X0] : ((~brave(X0) <~> ~strong(X0)) => (~tall(X0) & ~calm(X0))) [input p9]
11. ! [X0] : ((tall(X0) & generous(X0)) <=> (~creative(X0) | funny(X0))) [input p10]
25. ~brave(lucy) [input hypothesis]
30. ! [X0] : ((curious(X0) & calm(X0)) | (old(X0) <=> ~creative(X0))) [ennf transformation 3]
34. ! [X0] : ((~tall(X0) & ~calm(X0)) | (~brave(X0) <=> ~strong(X0))) [ennf transformation 10]
39. ! [X0] : ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0))) [nnf transformation 1]
42. ! [X0] : ((curious(X0) & calm(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0)))) [nnf transformation 30]
51. ! [X0] : ((((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0))))) [nnf transformation 6]
52. ! [X0] : ((((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0))))) [flattening 51]
59. ! [X0] : ((~tall(X0) & ~calm(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0)))) [nnf transformation 34]
60. ! [X0] : (((tall(X0) & generous(X0)) | (creative(X0) & ~funny(X0))) & ((~creative(X0) | funny(X0)) | (~tall(X0) | ~generous(X0)))) [nnf transformation 11]
61. ! [X0] : (((tall(X0) & generous(X0)) | (creative(X0) & ~funny(X0))) & (~creative(X0) | funny(X0) | ~tall(X0) | ~generous(X0))) [flattening 60]
74. old(X0) | calm(X0) [cnf transformation 39]
75. ~old(X0) | ~calm(X0) [cnf transformation 39]
79. calm(X0) | ~creative(X0) | ~old(X0) [cnf transformation 42]
91. ~brave(X0) | old(X0) | ~brave(X0) | strong(X0) [cnf transformation 52]
93. ~brave(X0) | ~strong(X0) | ~old(X0) [cnf transformation 52]
96. brave(X0) | strong(X0) | brave(X0) [cnf transformation 52]
107. ~calm(X0) | ~strong(X0) | brave(X0) [cnf transformation 59]
109. ~tall(X0) | ~strong(X0) | brave(X0) [cnf transformation 59]
110. ~tall(X0) | ~brave(X0) | strong(X0) [cnf transformation 59]
115. tall(X0) | creative(X0) [cnf transformation 61]
144. ~brave(lucy) [cnf transformation 25]
147. ~brave(X0) | old(X0) | strong(X0) [duplicate literal removal 91]
148. brave(X0) | strong(X0) [duplicate literal removal 96]
164. ~creative(X0) | ~old(X0) [subsumption resolution 79,75]
209. strong(X0) | old(X0) [subsumption resolution 147,148]
262. ~tall(X0) | strong(X0) [subsumption resolution 110,148]
263. ~tall(X0) | brave(X0) [subsumption resolution 109,148]
265. ~calm(X0) | brave(X0) [subsumption resolution 107,148]
346. creative(X0) | strong(X0) [resolution 262,115]
349. brave(X0) | creative(X0) [resolution 263,115]
513. 61 <=> calm(lucy) [avatar definition]
514. calm(lucy) <- (61) [avatar component clause 513]
515. ~calm(lucy) <- (~61) [avatar component clause 513]
595. strong(X1) | ~old(X1) [resolution 346,164]
600. strong(X1) [subsumption resolution 595,209]
609. creative(X1) | ~strong(X1) | ~old(X1) [resolution 349,93]
610. creative(X1) | ~old(X1) [subsumption resolution 609,600]
611. ~old(X1) [subsumption resolution 610,164]
672. brave(lucy) <- (61) [resolution 514,265]
674. $false <- (61) [subsumption resolution 672,144]
675. ~61 [avatar contradiction clause 674]
759. calm(X0) [resolution 611,74]
802. $false <- (~61) [resolution 759,515]
807. 61 [avatar contradiction clause 802]
811. $false [avatar sat refutation 675,807]
% SZS output end Proof for 7029473588752737803232986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and wise is either calm or not calm and vice versa.
If someone is both happy and not funny then susan is either brave or not funny and vice versa.
Everyone who is both not curious and funny is either not brave or rich.
Everyone who is both generous and funny is not quiet or not patient and vice versa.
Everyone who is not wise is old or tall and vice versa.
If someone is not generous then someone is calm and vice versa.
If susan is either not patient or humble then someone is either tall or old.
Everyone who is both not wise and strong is either rich or not calm.
If fred is not creative or not strong then someone is tall or not funny and vice versa.
Everyone who is both not strong and not funny is both not brave and not wise.
If someone is either strong or not kind then someone is both not rich and not humble.
Everyone who is not creative or not quiet is not creative or patient.
Everyone who is generous is both not tall and not kind.
Everyone who is both not old and not brave is not strong or not calm and vice versa.
If someone is either happy or old then fred is generous.
Everyone who is both creative and old is both quiet and humble.
Someone is either not creative or not rich.
Someone is either humble or generous.
Paul is creative or tall.
Someone is kind or creative.
Someone is not curious.
Alice is brave or creative.
Alice is wise.
Mary is not old. | Fred is not wise. | contradiction | (![X]:((funny(X)&wise(X))<=>(calm(X)<~>~calm(X))))&
((?[X]:((happy(X)&~funny(X))))<=>((brave(susan)<~>~funny(susan))))&
(![X]:((~curious(X)&funny(X))=>(~brave(X)<~>rich(X))))&
(![X]:((generous(X)&funny(X))<=>(~quiet(X)|~patient(X))))&
(![X]:(~wise(X)<=>(old(X)|tall(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(calm(X))))&
(((~patient(susan)<~>humble(susan)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((~wise(X)&strong(X))=>(rich(X)<~>~calm(X))))&
(((~creative(fred)|~strong(fred)))<=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((~strong(X)&~funny(X))=>(~brave(X)&~wise(X))))&
((?[X]:((strong(X)<~>~kind(X))))=>(?[X]:((~rich(X)&~humble(X)))))&
(![X]:((~creative(X)|~quiet(X))=>(~creative(X)|patient(X))))&
(![X]:(generous(X)=>(~tall(X)&~kind(X))))&
(![X]:((~old(X)&~brave(X))<=>(~strong(X)|~calm(X))))&
((?[X]:((happy(X)<~>old(X))))=>(generous(fred)))&
(![X]:((creative(X)&old(X))=>(quiet(X)&humble(X))))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((humble(X)<~>generous(X))))&
((creative(paul)|tall(paul)))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:(~curious(X)))&
((brave(alice)|creative(alice)))&
(wise(alice))&
(~old(mary)) | ~wise(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1225404250107294537619356
% SZS output start Proof for 1225404250107294537619356
1. ! [X0] : ((wise(X0) & funny(X0)) <=> (calm(X0) <~> ~calm(X0))) [input p0]
25. ~wise(fred) [input hypothesis]
42. ! [X0] : (((wise(X0) & funny(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | (~wise(X0) | ~funny(X0)))) [nnf transformation 1]
43. ! [X0] : (((wise(X0) & funny(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | ~wise(X0) | ~funny(X0))) [flattening 42]
88. wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 43]
89. wise(X0) | calm(X0) | calm(X0) [cnf transformation 43]
147. ~wise(fred) [cnf transformation 25]
150. wise(X0) | ~calm(X0) [duplicate literal removal 88]
151. wise(X0) | calm(X0) [duplicate literal removal 89]
152. wise(X0) [subsumption resolution 150,151]
262. $false [subsumption resolution 147,152]
% SZS output end Proof for 1225404250107294537619356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then someone is brave or quiet and vice versa.
Everyone who is either not old or creative is not funny and vice versa.
If mary is either not curious or funny then someone is either not wise or tall and vice versa.
If lucy is not creative then someone is quiet and vice versa.
Everyone who is not old or tall is both not generous and not creative and vice versa.
If someone is both humble and wise then someone is calm.
Everyone who is both old and strong is brave or not curious and vice versa.
Everyone who is not funny or not creative is not quiet and vice versa.
If alice is humble or not strong then someone is either not curious or not generous and vice versa.
Everyone who is both not wise and not kind is not quiet or not rich and vice versa.
Everyone who is both not happy and not old is brave or not strong.
If someone is curious then someone is both not quiet and brave.
If someone is both quiet and not old then someone is either tall or not old and vice versa.
If fred is not strong or not generous then john is not tall or not kind and vice versa.
If lucy is not rich then someone is not patient and vice versa.
Everyone who is not curious or patient is not humble.
Someone is not generous or not rich.
Someone is not kind or patient.
Someone is not calm.
Lucy is not quiet.
Fred is both not brave and rich.
Lucy is either not brave or curious. | Lucy is not brave. | entailment | ((?[X]:(quiet(X)))<=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:((~old(X)<~>creative(X))<=>~funny(X)))&
(((~curious(mary)<~>funny(mary)))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((~creative(lucy))<=>(?[X]:(quiet(X))))&
(![X]:((~old(X)|tall(X))<=>(~generous(X)&~creative(X))))&
((?[X]:((humble(X)&wise(X))))=>(?[X]:(calm(X))))&
(![X]:((old(X)&strong(X))<=>(brave(X)|~curious(X))))&
(![X]:((~funny(X)|~creative(X))<=>~quiet(X)))&
(((humble(alice)|~strong(alice)))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
(![X]:((~wise(X)&~kind(X))<=>(~quiet(X)|~rich(X))))&
(![X]:((~happy(X)&~old(X))=>(brave(X)|~strong(X))))&
((?[X]:(curious(X)))=>(?[X]:((~quiet(X)&brave(X)))))&
((?[X]:((quiet(X)&~old(X))))<=>(?[X]:((tall(X)<~>~old(X)))))&
(((~strong(fred)|~generous(fred)))<=>((~tall(john)|~kind(john))))&
((~rich(lucy))<=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)|patient(X))=>~humble(X)))&
(?[X]:((~generous(X)|~rich(X))))&
(?[X]:((~kind(X)|patient(X))))&
(?[X]:(~calm(X)))&
(~quiet(lucy))&
((~brave(fred)&rich(fred)))&
((~brave(lucy)<~>curious(lucy))) | ~brave(lucy) | [
"p0",
"p1",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4947323749099996353564173
% SZS output start Proof for 4947323749099996353564173
1. ? [X0] : quiet(X0) <=> ? [X0] : (quiet(X0) | brave(X0)) [input p0]
2. ! [X0] : ((~old(X0) <~> creative(X0)) <=> ~funny(X0)) [input p1]
5. ! [X0] : ((tall(X0) | ~old(X0)) <=> (~creative(X0) & ~generous(X0))) [input p4]
8. ! [X0] : ((~creative(X0) | ~funny(X0)) <=> ~quiet(X0)) [input p7]
23. brave(lucy) [input hypothesis]
24. ? [X0] : quiet(X0) <=> ? [X1] : (quiet(X1) | brave(X1)) [rectify 1]
32. (? [X0] : quiet(X0) | ! [X1] : (~quiet(X1) & ~brave(X1))) & (? [X1] : (quiet(X1) | brave(X1)) | ! [X0] : ~quiet(X0)) [nnf transformation 24]
33. (? [X0] : quiet(X0) | ! [X1] : (~quiet(X1) & ~brave(X1))) & (? [X2] : (quiet(X2) | brave(X2)) | ! [X3] : ~quiet(X3)) [rectify 32]
34. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom]
35. ? [X2] : (quiet(X2) | brave(X2)) => (quiet(sK1) | brave(sK1)) [choice axiom]
36. (quiet(sK0) | ! [X1] : (~quiet(X1) & ~brave(X1))) & ((quiet(sK1) | brave(sK1)) | ! [X3] : ~quiet(X3)) [skolemisation 33,35,34]
37. ! [X0] : ((((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | funny(X0)) & (~funny(X0) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0))))) [nnf transformation 2]
46. ! [X0] : (((tall(X0) | ~old(X0)) | (creative(X0) | generous(X0))) & ((~creative(X0) & ~generous(X0)) | (~tall(X0) & old(X0)))) [nnf transformation 5]
47. ! [X0] : ((tall(X0) | ~old(X0) | creative(X0) | generous(X0)) & ((~creative(X0) & ~generous(X0)) | (~tall(X0) & old(X0)))) [flattening 46]
53. ! [X0] : (((~creative(X0) | ~funny(X0)) | quiet(X0)) & (~quiet(X0) | (creative(X0) & funny(X0)))) [nnf transformation 8]
54. ! [X0] : ((~creative(X0) | ~funny(X0) | quiet(X0)) & (~quiet(X0) | (creative(X0) & funny(X0)))) [flattening 53]
84. quiet(sK0) | ~brave(X1) [cnf transformation 36]
87. ~funny(X0) | ~old(X0) | ~creative(X0) [cnf transformation 37]
102. ~creative(X0) | old(X0) [cnf transformation 47]
111. ~quiet(X0) | funny(X0) [cnf transformation 54]
112. ~quiet(X0) | creative(X0) [cnf transformation 54]
149. brave(lucy) [cnf transformation 23]
154. 2 <=> quiet(sK0) [avatar definition]
156. quiet(sK0) <- (2) [avatar component clause 154]
159. 3 <=> ! [X1] : ~brave(X1) [avatar definition]
160. ~brave(X1) <- (3) [avatar component clause 159]
161. 3 | 2 [avatar split clause 84,154,159]
343. 43 <=> brave(lucy) [avatar definition]
345. brave(lucy) <- (43) [avatar component clause 343]
352. 43 [avatar split clause 149,343]
364. funny(sK0) <- (2) [resolution 111,156]
366. creative(sK0) <- (2) [resolution 112,156]
368. old(sK0) <- (2) [resolution 366,102]
398. ~old(sK0) | ~creative(sK0) <- (2) [resolution 87,364]
401. ~creative(sK0) <- (2) [subsumption resolution 398,368]
402. $false <- (2) [subsumption resolution 401,366]
403. ~2 [avatar contradiction clause 402]
411. $false <- (3, 43) [resolution 160,345]
414. ~3 | ~43 [avatar contradiction clause 411]
416. $false [avatar sat refutation 161,352,403,414]
% SZS output end Proof for 4947323749099996353564173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not funny or not calm then mary is either not rich or curious and vice versa.
Everyone who is either creative or funny is not funny or patient and vice versa.
Everyone who is tall is brave and vice versa.
Everyone who is not brave or not wise is either not calm or tall and vice versa.
If john is not kind then mary is not funny or humble.
If someone is both not patient and curious then john is not calm.
Everyone who is rich is both not humble and calm and vice versa.
Everyone who is not kind is either not curious or funny and vice versa.
Everyone who is not brave or not creative is not old or not quiet.
Everyone who is not strong is not curious.
Everyone who is both not strong and not rich is not happy and vice versa.
Everyone who is not calm is both not kind and curious.
If someone is both curious and not humble then paul is generous or calm.
Everyone who is either creative or not generous is not quiet and vice versa.
If someone is not funny then someone is not strong or curious.
If mary is curious or not generous then alice is generous.
Someone is not creative or old.
Paul is not curious.
Someone is both creative and not happy.
Lucy is not calm.
Susan is not calm.
Mary is either not quiet or not strong.
Someone is either creative or not old.
Someone is either calm or not curious. | Susan is not kind. | entailment | (((~funny(paul)|~calm(paul)))<=>((~rich(mary)<~>curious(mary))))&
(![X]:((creative(X)<~>funny(X))<=>(~funny(X)|patient(X))))&
(![X]:(tall(X)<=>brave(X)))&
(![X]:((~brave(X)|~wise(X))<=>(~calm(X)<~>tall(X))))&
((~kind(john))=>((~funny(mary)|humble(mary))))&
((?[X]:((~patient(X)&curious(X))))=>(~calm(john)))&
(![X]:(rich(X)<=>(~humble(X)&calm(X))))&
(![X]:(~kind(X)<=>(~curious(X)<~>funny(X))))&
(![X]:((~brave(X)|~creative(X))=>(~old(X)|~quiet(X))))&
(![X]:(~strong(X)=>~curious(X)))&
(![X]:((~strong(X)&~rich(X))<=>~happy(X)))&
(![X]:(~calm(X)=>(~kind(X)&curious(X))))&
((?[X]:((curious(X)&~humble(X))))=>((generous(paul)|calm(paul))))&
(![X]:((creative(X)<~>~generous(X))<=>~quiet(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~strong(X)|curious(X)))))&
(((curious(mary)|~generous(mary)))=>(generous(alice)))&
(?[X]:((~creative(X)|old(X))))&
(~curious(paul))&
(?[X]:((creative(X)&~happy(X))))&
(~calm(lucy))&
(~calm(susan))&
((~quiet(mary)<~>~strong(mary)))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:((calm(X)<~>~curious(X)))) | ~kind(susan) | [
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8482462278843075546167767
% SZS output start Proof for 8482462278843075546167767
12. ! [X0] : (~calm(X0) => (curious(X0) & ~kind(X0))) [input p11]
21. ~calm(susan) [input p20]
25. kind(susan) [input hypothesis]
35. ! [X0] : ((curious(X0) & ~kind(X0)) | calm(X0)) [ennf transformation 12]
99. ~kind(X0) | calm(X0) [cnf transformation 35]
114. ~calm(susan) [cnf transformation 21]
121. kind(susan) [cnf transformation 25]
233. calm(susan) [resolution 99,121]
234. $false [subsumption resolution 233,114]
% SZS output end Proof for 8482462278843075546167767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not tall is either not happy or humble. Everyone who is strong is tall. Everyone who is creative is old or calm. Everyone who is either brave or generous is both not brave and funny. If someone is either not creative or not wise then mary is patient or not wise. Everyone who is creative is not tall or funny. Everyone who is not funny is both brave and not kind. Everyone who is not generous or creative is creative or happy. Everyone who is patient or not generous is both not generous and not funny. Everyone who is wise is wise or calm. If john is not old or strong then fred is either not happy or old and vice versa. If paul is either calm or not strong then someone is both not curious and generous and vice versa. If someone is brave then mary is creative. If alice is humble then someone is not calm and vice versa. Everyone who is either not happy or brave is happy or not creative. If mary is funny then fred is both generous and not brave and vice versa. Someone is either happy or rich. Someone is either not rich or quiet. Someone is either strong or not curious. Someone is wise or not old. Someone is not patient or not tall. Lucy is not happy or not quiet. Susan is patient or not curious. Alice is not generous or not happy. | Paul is generous. | entailment | (![X]:((humble(X)<~>~tall(X))=>(~happy(X)<~>humble(X))))&
(![X]:(strong(X)=>tall(X)))&
(![X]:(creative(X)=>(old(X)|calm(X))))&
(![X]:((brave(X)<~>generous(X))=>(~brave(X)&funny(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>((patient(mary)|~wise(mary))))&
(![X]:(creative(X)=>(~tall(X)|funny(X))))&
(![X]:(~funny(X)=>(brave(X)&~kind(X))))&
(![X]:((~generous(X)|creative(X))=>(creative(X)|happy(X))))&
(![X]:((patient(X)|~generous(X))=>(~generous(X)&~funny(X))))&
(![X]:(wise(X)=>(wise(X)|calm(X))))&
(((~old(john)|strong(john)))<=>((~happy(fred)<~>old(fred))))&
(((calm(paul)<~>~strong(paul)))<=>(?[X]:((~curious(X)&generous(X)))))&
((?[X]:(brave(X)))=>(creative(mary)))&
((humble(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~happy(X)<~>brave(X))=>(happy(X)|~creative(X))))&
((funny(mary))<=>((generous(fred)&~brave(fred))))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:((~rich(X)<~>quiet(X))))&
(?[X]:((strong(X)<~>~curious(X))))&
(?[X]:((wise(X)|~old(X))))&
(?[X]:((~patient(X)|~tall(X))))&
((~happy(lucy)|~quiet(lucy)))&
((patient(susan)|~curious(susan)))&
((~generous(alice)|~happy(alice))) | generous(paul) | [
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2426982942179795529725596
% SZS output start Proof for 2426982942179795529725596
4. ! [X0] : ((brave(X0) <~> generous(X0)) => (funny(X0) & ~brave(X0))) [input p3]
7. ! [X0] : (~funny(X0) => (~kind(X0) & brave(X0))) [input p6]
9. ! [X0] : ((~generous(X0) | patient(X0)) => (~funny(X0) & ~generous(X0))) [input p8]
25. ~generous(paul) [input hypothesis]
26. ! [X0] : (~funny(X0) => brave(X0)) [pure predicate removal 7]
31. ! [X0] : ((funny(X0) & ~brave(X0)) | (brave(X0) <=> generous(X0))) [ennf transformation 4]
36. ! [X0] : (brave(X0) | funny(X0)) [ennf transformation 26]
39. ! [X0] : ((~funny(X0) & ~generous(X0)) | (generous(X0) & ~patient(X0))) [ennf transformation 9]
46. ! [X0] : ((funny(X0) & ~brave(X0)) | ((brave(X0) | ~generous(X0)) & (generous(X0) | ~brave(X0)))) [nnf transformation 31]
80. ~brave(X0) | generous(X0) | ~brave(X0) [cnf transformation 46]
87. funny(X0) | brave(X0) [cnf transformation 36]
93. ~funny(X0) | generous(X0) [cnf transformation 39]
126. ~generous(paul) [cnf transformation 25]
128. ~brave(X0) | generous(X0) [duplicate literal removal 80]
308. generous(X0) | brave(X0) [resolution 93,87]
309. generous(X0) [subsumption resolution 308,128]
311. $false [resolution 309,126]
% SZS output end Proof for 2426982942179795529725596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not creative is both not old and not patient. If someone is creative then susan is not tall. If alice is either not brave or patient then someone is either kind or not creative and vice versa. If lucy is humble or not patient then paul is either old or happy. Everyone who is both quiet and not kind is either not kind or not humble and vice versa. Everyone who is not tall is strong and vice versa. Everyone who is old or not kind is brave and vice versa. Everyone who is both not brave and not calm is curious. If someone is creative then susan is either patient or calm. If someone is humble then someone is both not creative and not brave and vice versa. Everyone who is not funny or not strong is wise or calm. If someone is not kind or generous then someone is not rich or not calm. If alice is either not funny or not wise then someone is either not humble or creative. Everyone who is both kind and happy is patient and vice versa. Everyone who is both tall and strong is curious or not generous and vice versa. Everyone who is creative or not happy is both not humble and not happy. Alice is calm. Susan is both strong and not brave. Paul is both old and not creative. Someone is rich or not curious. John is either creative or not calm. Someone is wise. | Alice is humble. | entailment | (![X]:((generous(X)<~>~creative(X))=>(~old(X)&~patient(X))))&
((?[X]:(creative(X)))=>(~tall(susan)))&
(((~brave(alice)<~>patient(alice)))<=>(?[X]:((kind(X)<~>~creative(X)))))&
(((humble(lucy)|~patient(lucy)))=>((old(paul)<~>happy(paul))))&
(![X]:((quiet(X)&~kind(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:(~tall(X)<=>strong(X)))&
(![X]:((old(X)|~kind(X))<=>brave(X)))&
(![X]:((~brave(X)&~calm(X))=>curious(X)))&
((?[X]:(creative(X)))=>((patient(susan)<~>calm(susan))))&
((?[X]:(humble(X)))<=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((~funny(X)|~strong(X))=>(wise(X)|calm(X))))&
((?[X]:((~kind(X)|generous(X))))=>(?[X]:((~rich(X)|~calm(X)))))&
(((~funny(alice)<~>~wise(alice)))=>(?[X]:((~humble(X)<~>creative(X)))))&
(![X]:((kind(X)&happy(X))<=>patient(X)))&
(![X]:((tall(X)&strong(X))<=>(curious(X)|~generous(X))))&
(![X]:((creative(X)|~happy(X))=>(~humble(X)&~happy(X))))&
(calm(alice))&
((strong(susan)&~brave(susan)))&
((old(paul)&~creative(paul)))&
(?[X]:((rich(X)|~curious(X))))&
((creative(john)<~>~calm(john)))&
(?[X]:(wise(X))) | humble(alice) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p6",
"p13",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 411521696527387807589992
% SZS output start Proof for 411521696527387807589992
1. ! [X0] : ((generous(X0) <~> ~creative(X0)) => (~patient(X0) & ~old(X0))) [input p0]
3. (~brave(alice) <~> patient(alice)) <=> ? [X0] : (kind(X0) <~> ~creative(X0)) [input p2]
4. (~patient(lucy) | humble(lucy)) => (old(paul) <~> happy(paul)) [input p3]
5. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (~kind(X0) <~> ~humble(X0))) [input p4]
6. ! [X0] : (~tall(X0) <=> strong(X0)) [input p5]
7. ! [X0] : ((~kind(X0) | old(X0)) <=> brave(X0)) [input p6]
14. ! [X0] : ((happy(X0) & kind(X0)) <=> patient(X0)) [input p13]
15. ! [X0] : ((strong(X0) & tall(X0)) <=> (~generous(X0) | curious(X0))) [input p14]
16. ! [X0] : ((~happy(X0) | creative(X0)) => (~happy(X0) & ~humble(X0))) [input p15]
19. ~creative(paul) & old(paul) [input p18]
23. ~humble(alice) [input hypothesis]
26. ! [X0] : ((~patient(X0) & ~old(X0)) | (generous(X0) <=> ~creative(X0))) [ennf transformation 1]
28. (old(paul) <~> happy(paul)) | (patient(lucy) & ~humble(lucy)) [ennf transformation 4]
36. ! [X0] : ((~happy(X0) & ~humble(X0)) | (happy(X0) & ~creative(X0))) [ennf transformation 16]
37. ! [X0] : ((~patient(X0) & ~old(X0)) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0)))) [nnf transformation 26]
38. (((~patient(alice) | brave(alice)) & (patient(alice) | ~brave(alice))) | ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0)))) & (? [X0] : ((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | ((~brave(alice) | ~patient(alice)) & (patient(alice) | brave(alice)))) [nnf transformation 3]
39. (((~patient(alice) | brave(alice)) & (patient(alice) | ~brave(alice))) | ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0)))) & (? [X1] : ((creative(X1) | ~kind(X1)) & (~creative(X1) | kind(X1))) | ((~brave(alice) | ~patient(alice)) & (patient(alice) | brave(alice)))) [rectify 38]
40. ? [X1] : ((creative(X1) | ~kind(X1)) & (~creative(X1) | kind(X1))) => ((creative(sK0) | ~kind(sK0)) & (~creative(sK0) | kind(sK0))) [choice axiom]
41. (((~patient(alice) | brave(alice)) & (patient(alice) | ~brave(alice))) | ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0)))) & (((creative(sK0) | ~kind(sK0)) & (~creative(sK0) | kind(sK0))) | ((~brave(alice) | ~patient(alice)) & (patient(alice) | brave(alice)))) [skolemisation 39,40]
42. ((~happy(paul) | ~old(paul)) & (happy(paul) | old(paul))) | (patient(lucy) & ~humble(lucy)) [nnf transformation 28]
43. ! [X0] : (((~kind(X0) & quiet(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (kind(X0) | ~quiet(X0)))) [nnf transformation 5]
44. ! [X0] : (((~kind(X0) & quiet(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | kind(X0) | ~quiet(X0))) [flattening 43]
45. ! [X0] : ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))) [nnf transformation 6]
46. ! [X0] : (((~kind(X0) | old(X0)) | ~brave(X0)) & (brave(X0) | (kind(X0) & ~old(X0)))) [nnf transformation 7]
47. ! [X0] : ((~kind(X0) | old(X0) | ~brave(X0)) & (brave(X0) | (kind(X0) & ~old(X0)))) [flattening 46]
60. ! [X0] : (((happy(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | (~happy(X0) | ~kind(X0)))) [nnf transformation 14]
61. ! [X0] : (((happy(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | ~happy(X0) | ~kind(X0))) [flattening 60]
62. ! [X0] : (((strong(X0) & tall(X0)) | (generous(X0) & ~curious(X0))) & ((~generous(X0) | curious(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((strong(X0) & tall(X0)) | (generous(X0) & ~curious(X0))) & (~generous(X0) | curious(X0) | ~strong(X0) | ~tall(X0))) [flattening 62]
71. ~patient(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 37]
79. patient(alice) | ~brave(alice) | kind(X0) | creative(X0) [cnf transformation 41]
84. ~happy(paul) | ~old(paul) | ~humble(lucy) [cnf transformation 42]
85. ~happy(paul) | ~old(paul) | patient(lucy) [cnf transformation 42]
91. ~kind(X0) | ~kind(X0) | humble(X0) [cnf transformation 44]
93. ~strong(X0) | ~tall(X0) [cnf transformation 45]
95. kind(X0) | brave(X0) [cnf transformation 47]
112. ~patient(X0) | kind(X0) [cnf transformation 61]
116. tall(X0) | generous(X0) [cnf transformation 63]
118. strong(X0) | generous(X0) [cnf transformation 63]
120. ~humble(X0) | happy(X0) [cnf transformation 36]
126. old(paul) [cnf transformation 19]
127. ~creative(paul) [cnf transformation 19]
132. ~humble(alice) [cnf transformation 23]
134. ~kind(X0) | humble(X0) [duplicate literal removal 91]
144. 3 <=> ! [X0] : (kind(X0) | creative(X0)) [avatar definition]
145. kind(X0) | creative(X0) <- (3) [avatar component clause 144]
147. 4 <=> brave(alice) [avatar definition]
151. 5 <=> patient(alice) [avatar definition]
152. patient(alice) <- (5) [avatar component clause 151]
159. 3 | ~4 | 5 [avatar split clause 79,151,147,144]
174. 9 <=> patient(lucy) [avatar definition]
176. patient(lucy) <- (9) [avatar component clause 174]
178. 10 <=> old(paul) [avatar definition]
182. 11 <=> happy(paul) [avatar definition]
184. ~happy(paul) <- (~11) [avatar component clause 182]
185. 9 | ~10 | ~11 [avatar split clause 85,182,178,174]
187. 12 <=> humble(lucy) [avatar definition]
189. ~humble(lucy) <- (~12) [avatar component clause 187]
190. ~12 | ~10 | ~11 [avatar split clause 84,182,178,187]
261. 10 [avatar split clause 126,178]
288. generous(X0) | ~tall(X0) [resolution 118,93]
289. generous(X0) [subsumption resolution 288,116]
291. humble(X0) | brave(X0) [resolution 134,95]
307. brave(alice) [resolution 291,132]
312. 4 [avatar split clause 307,147]
314. kind(alice) <- (5) [resolution 152,112]
321. humble(alice) <- (5) [resolution 314,134]
322. $false <- (5) [subsumption resolution 321,132]
323. ~5 [avatar contradiction clause 322]
325. humble(X0) | creative(X0) <- (3) [resolution 145,134]
392. happy(X1) | creative(X1) <- (3) [resolution 325,120]
442. creative(paul) <- (3, ~11) [resolution 392,184]
445. $false <- (3, ~11) [subsumption resolution 442,127]
446. ~3 | 11 [avatar contradiction clause 445]
449. ~creative(lucy) | ~generous(lucy) <- (9) [resolution 176,71]
452. ~creative(lucy) <- (9) [subsumption resolution 449,289]
455. creative(lucy) <- (3, ~12) [resolution 189,325]
457. $false <- (3, 9, ~12) [subsumption resolution 455,452]
458. ~3 | ~9 | 12 [avatar contradiction clause 457]
459. $false [avatar sat refutation 159,185,190,261,312,323,446,458]
% SZS output end Proof for 411521696527387807589992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is quiet or not funny and vice versa. If someone is wise or not generous then someone is not funny or rich. If someone is rich then mary is both rich and tall. If someone is not patient or not rich then mary is both not wise and kind and vice versa. If someone is humble or not happy then someone is both happy and quiet. Everyone who is not funny or not generous is not kind and vice versa. If john is not rich then someone is not quiet. Everyone who is either generous or wise is both calm and brave. Everyone who is not curious is not calm or not creative. Everyone who is curious is both generous and not rich. If someone is not strong or strong then someone is either wise or patient and vice versa. Everyone who is funny or wise is both not patient and wise. Everyone who is either generous or wise is either not wise or not happy. Mary is kind or not kind. Paul is not brave or happy. Someone is not wise or calm. Paul is kind or not curious. Someone is not brave. Lucy is not curious. | Mary is not rich. | contradiction | (![X]:(~strong(X)<=>(quiet(X)|~funny(X))))&
((?[X]:((wise(X)|~generous(X))))=>(?[X]:((~funny(X)|rich(X)))))&
((?[X]:(rich(X)))=>((rich(mary)&tall(mary))))&
((?[X]:((~patient(X)|~rich(X))))<=>((~wise(mary)&kind(mary))))&
((?[X]:((humble(X)|~happy(X))))=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:((~funny(X)|~generous(X))<=>~kind(X)))&
((~rich(john))=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)<~>wise(X))=>(calm(X)&brave(X))))&
(![X]:(~curious(X)=>(~calm(X)|~creative(X))))&
(![X]:(curious(X)=>(generous(X)&~rich(X))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:((funny(X)|wise(X))=>(~patient(X)&wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(~wise(X)<~>~happy(X))))&
((kind(mary)|~kind(mary)))&
((~brave(paul)|happy(paul)))&
(?[X]:((~wise(X)|calm(X))))&
((kind(paul)|~curious(paul)))&
(?[X]:(~brave(X)))&
(~curious(lucy)) | ~rich(mary) | [
"p2",
"p3",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7816873147279346863150254
% SZS output start Proof for 7816873147279346863150254
3. ? [X0] : rich(X0) => (tall(mary) & rich(mary)) [input p2]
4. ? [X0] : (~rich(X0) | ~patient(X0)) <=> (kind(mary) & ~wise(mary)) [input p3]
6. ! [X0] : ((~generous(X0) | ~funny(X0)) <=> ~kind(X0)) [input p5]
12. ! [X0] : ((wise(X0) | funny(X0)) => (wise(X0) & ~patient(X0))) [input p11]
20. ~rich(mary) [input hypothesis]
31. ? [X0] : rich(X0) => rich(mary) [pure predicate removal 3]
33. rich(mary) | ! [X0] : ~rich(X0) [ennf transformation 31]
37. ! [X0] : ((wise(X0) & ~patient(X0)) | (~wise(X0) & ~funny(X0))) [ennf transformation 12]
44. (? [X0] : (~rich(X0) | ~patient(X0)) | (~kind(mary) | wise(mary))) & ((kind(mary) & ~wise(mary)) | ! [X0] : (rich(X0) & patient(X0))) [nnf transformation 4]
45. (? [X0] : (~rich(X0) | ~patient(X0)) | ~kind(mary) | wise(mary)) & ((kind(mary) & ~wise(mary)) | ! [X0] : (rich(X0) & patient(X0))) [flattening 44]
46. (? [X0] : (~rich(X0) | ~patient(X0)) | ~kind(mary) | wise(mary)) & ((kind(mary) & ~wise(mary)) | ! [X1] : (rich(X1) & patient(X1))) [rectify 45]
47. ? [X0] : (~rich(X0) | ~patient(X0)) => (~rich(sK1) | ~patient(sK1)) [choice axiom]
48. ((~rich(sK1) | ~patient(sK1)) | ~kind(mary) | wise(mary)) & ((kind(mary) & ~wise(mary)) | ! [X1] : (rich(X1) & patient(X1))) [skolemisation 46,47]
52. ! [X0] : (((~generous(X0) | ~funny(X0)) | kind(X0)) & (~kind(X0) | (generous(X0) & funny(X0)))) [nnf transformation 6]
53. ! [X0] : ((~generous(X0) | ~funny(X0) | kind(X0)) & (~kind(X0) | (generous(X0) & funny(X0)))) [flattening 52]
70. rich(mary) | ~rich(X0) [cnf transformation 33]
72. ~wise(mary) | rich(X1) [cnf transformation 48]
74. kind(mary) | rich(X1) [cnf transformation 48]
78. ~kind(X0) | funny(X0) [cnf transformation 53]
92. ~funny(X0) | wise(X0) [cnf transformation 37]
101. ~rich(mary) [cnf transformation 20]
121. 5 <=> ! [X0] : ~rich(X0) [avatar definition]
122. ~rich(X0) <- (5) [avatar component clause 121]
124. 6 <=> rich(mary) [avatar definition]
127. 5 | 6 [avatar split clause 70,124,121]
129. 7 <=> wise(mary) [avatar definition]
130. ~wise(mary) <- (~7) [avatar component clause 129]
133. 8 <=> kind(mary) [avatar definition]
134. kind(mary) <- (8) [avatar component clause 133]
146. 11 <=> ! [X1] : rich(X1) [avatar definition]
147. rich(X1) <- (11) [avatar component clause 146]
148. 11 | 8 [avatar split clause 74,133,146]
153. 11 | ~7 [avatar split clause 72,129,146]
204. ~6 [avatar split clause 101,124]
205. funny(mary) <- (8) [resolution 78,134]
207. wise(mary) <- (8) [resolution 92,205]
208. $false <- (~7, 8) [subsumption resolution 207,130]
209. 7 | ~8 [avatar contradiction clause 208]
210. $false <- (5, 11) [subsumption resolution 147,122]
211. ~5 | ~11 [avatar contradiction clause 210]
212. $false [avatar sat refutation 127,148,153,204,209,211]
% SZS output end Proof for 7816873147279346863150254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and kind then someone is either not brave or kind.
If someone is not funny then john is not happy or happy.
Everyone who is creative or not calm is not kind or not curious and vice versa.
Everyone who is rich or not strong is not brave or not kind and vice versa.
Everyone who is not kind or patient is both not brave and not tall.
Everyone who is creative is rich and vice versa.
If alice is rich then mary is both patient and not happy and vice versa.
Everyone who is not kind is funny or creative.
If susan is not happy then someone is both not happy and not kind.
Everyone who is not generous or not calm is either funny or patient and vice versa.
Everyone who is both quiet and not tall is both generous and not wise and vice versa.
Everyone who is not curious or not generous is generous.
Everyone who is either creative or not happy is old or happy.
Everyone who is both not curious and not funny is not patient or happy and vice versa.
Everyone who is either not old or not funny is both kind and not strong and vice versa.
Everyone who is quiet is generous and vice versa.
Someone is not old.
Someone is either not tall or kind.
Mary is both not curious and not creative.
Someone is either kind or not funny.
Someone is wise. | Alice is patient. | entailment | ((?[X]:((tall(X)&kind(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
((?[X]:(~funny(X)))=>((~happy(john)|happy(john))))&
(![X]:((creative(X)|~calm(X))<=>(~kind(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(![X]:(quiet(X)<=>generous(X)))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)<~>kind(X))))&
((~curious(mary)&~creative(mary)))&
(?[X]:((kind(X)<~>~funny(X))))&
(?[X]:(wise(X))) | patient(alice) | [
"p2",
"p5",
"p6",
"p9",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8512401049969237055721837
% SZS output start Proof for 8512401049969237055721837
3. ! [X0] : ((~calm(X0) | creative(X0)) <=> (~curious(X0) | ~kind(X0))) [input p2]
6. ! [X0] : (creative(X0) <=> rich(X0)) [input p5]
7. rich(alice) <=> (~happy(mary) & patient(mary)) [input p6]
10. ! [X0] : ((~calm(X0) | ~generous(X0)) <=> (funny(X0) <~> patient(X0))) [input p9]
14. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (happy(X0) | ~patient(X0))) [input p13]
19. ~creative(mary) & ~curious(mary) [input p18]
22. ~patient(alice) [input hypothesis]
38. ! [X0] : (((~calm(X0) | creative(X0)) | (curious(X0) & kind(X0))) & ((~curious(X0) | ~kind(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 3]
39. ! [X0] : ((~calm(X0) | creative(X0) | (curious(X0) & kind(X0))) & (~curious(X0) | ~kind(X0) | (calm(X0) & ~creative(X0)))) [flattening 38]
42. ! [X0] : ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))) [nnf transformation 6]
43. (rich(alice) | (happy(mary) | ~patient(mary))) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [nnf transformation 7]
44. (rich(alice) | happy(mary) | ~patient(mary)) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [flattening 43]
47. ! [X0] : (((~calm(X0) | ~generous(X0)) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [nnf transformation 10]
48. ! [X0] : ((~calm(X0) | ~generous(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [flattening 47]
52. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 14]
53. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | curious(X0))) [flattening 52]
73. ~calm(X0) | creative(X0) | curious(X0) [cnf transformation 39]
82. ~creative(X0) | rich(X0) [cnf transformation 42]
84. patient(mary) | ~rich(alice) [cnf transformation 44]
85. ~happy(mary) | ~rich(alice) [cnf transformation 44]
91. patient(X0) | funny(X0) | calm(X0) [cnf transformation 48]
93. ~patient(X0) | ~funny(X0) | calm(X0) [cnf transformation 48]
104. ~patient(X0) | happy(X0) | funny(X0) | curious(X0) [cnf transformation 53]
105. ~curious(X0) | patient(X0) [cnf transformation 53]
107. ~funny(X0) | patient(X0) [cnf transformation 53]
120. ~curious(mary) [cnf transformation 19]
121. ~creative(mary) [cnf transformation 19]
125. ~patient(alice) [cnf transformation 22]
142. 4 <=> patient(mary) [avatar definition]
143. patient(mary) <- (4) [avatar component clause 142]
146. 5 <=> happy(mary) [avatar definition]
147. ~happy(mary) <- (~5) [avatar component clause 146]
150. 6 <=> rich(alice) [avatar definition]
154. ~6 | ~5 [avatar split clause 85,146,150]
155. ~6 | 4 [avatar split clause 84,142,150]
197. 15 <=> funny(mary) [avatar definition]
201. funny(alice) | calm(alice) [resolution 91,125]
206. 16 <=> calm(alice) [avatar definition]
208. calm(alice) <- (16) [avatar component clause 206]
210. 17 <=> funny(alice) [avatar definition]
212. funny(alice) <- (17) [avatar component clause 210]
213. 16 | 17 [avatar split clause 201,210,206]
215. 18 <=> calm(mary) [avatar definition]
216. ~calm(mary) <- (~18) [avatar component clause 215]
217. calm(mary) <- (18) [avatar component clause 215]
228. 19 <=> curious(alice) [avatar definition]
230. curious(alice) <- (19) [avatar component clause 228]
232. 20 <=> creative(alice) [avatar definition]
234. creative(alice) <- (20) [avatar component clause 232]
244. patient(alice) <- (17) [resolution 212,107]
245. $false <- (17) [subsumption resolution 244,125]
246. ~17 [avatar contradiction clause 245]
249. creative(alice) | curious(alice) <- (16) [resolution 208,73]
255. creative(mary) | curious(mary) <- (18) [resolution 217,73]
257. curious(mary) <- (18) [subsumption resolution 255,121]
258. $false <- (18) [subsumption resolution 257,120]
259. ~18 [avatar contradiction clause 258]
260. ~funny(mary) | calm(mary) <- (4) [resolution 143,93]
285. rich(alice) <- (20) [resolution 234,82]
288. 6 | ~20 [avatar split clause 285,232,150]
293. happy(mary) | funny(mary) | curious(mary) <- (4) [resolution 104,143]
295. funny(mary) | curious(mary) <- (4, ~5) [subsumption resolution 293,147]
299. funny(mary) <- (4, ~5) [subsumption resolution 295,120]
300. 15 | ~4 | 5 [avatar split clause 299,146,142,197]
301. ~funny(mary) <- (4, ~18) [subsumption resolution 260,216]
302. ~15 | ~4 | 18 [avatar split clause 301,215,142,197]
306. 19 | 20 | ~16 [avatar split clause 249,206,232,228]
313. patient(alice) <- (19) [resolution 230,105]
314. $false <- (19) [subsumption resolution 313,125]
315. ~19 [avatar contradiction clause 314]
316. $false [avatar sat refutation 154,155,213,246,259,288,300,302,306,315]
% SZS output end Proof for 8512401049969237055721837
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or wise is both creative and brave and vice versa. Everyone who is either not old or generous is both not humble and not curious. If someone is not patient or not humble then someone is strong and vice versa. Everyone who is both not funny and not curious is wise and vice versa. Everyone who is happy or funny is either not tall or not patient and vice versa. If someone is old or not generous then alice is kind or generous and vice versa. If someone is not generous or not happy then someone is old. If someone is wise or old then alice is both funny and not happy and vice versa. Everyone who is not old is either patient or not generous. If someone is either funny or not creative then someone is either curious or not rich and vice versa. If someone is either not patient or strong then someone is either not brave or not curious. If lucy is either old or not humble then someone is not wise or not patient. Everyone who is funny is brave or not brave and vice versa. If alice is both not curious and tall then someone is not wise. Everyone who is either funny or not rich is either kind or not tall. If paul is either patient or old then someone is creative and vice versa. Someone is not humble. Fred is either old or not funny. Fred is either not brave or tall. Someone is either patient or not calm. Paul is happy or funny. Someone is curious or not strong. Someone is either tall or not wise. Someone is not generous. | Fred is not old. | contradiction | (![X]:((~humble(X)<~>wise(X))<=>(creative(X)&brave(X))))&
(![X]:((~old(X)<~>generous(X))=>(~humble(X)&~curious(X))))&
((?[X]:((~patient(X)|~humble(X))))<=>(?[X]:(strong(X))))&
(![X]:((~funny(X)&~curious(X))<=>wise(X)))&
(![X]:((happy(X)|funny(X))<=>(~tall(X)<~>~patient(X))))&
((?[X]:((old(X)|~generous(X))))<=>((kind(alice)|generous(alice))))&
((?[X]:((~generous(X)|~happy(X))))=>(?[X]:(old(X))))&
((?[X]:((wise(X)|old(X))))<=>((funny(alice)&~happy(alice))))&
(![X]:(~old(X)=>(patient(X)<~>~generous(X))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:((curious(X)<~>~rich(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:((~brave(X)<~>~curious(X)))))&
(((old(lucy)<~>~humble(lucy)))=>(?[X]:((~wise(X)|~patient(X)))))&
(![X]:(funny(X)<=>(brave(X)|~brave(X))))&
(((~curious(alice)&tall(alice)))=>(?[X]:(~wise(X))))&
(![X]:((funny(X)<~>~rich(X))=>(kind(X)<~>~tall(X))))&
(((patient(paul)<~>old(paul)))<=>(?[X]:(creative(X))))&
(?[X]:(~humble(X)))&
((old(fred)<~>~funny(fred)))&
((~brave(fred)<~>tall(fred)))&
(?[X]:((patient(X)<~>~calm(X))))&
((happy(paul)|funny(paul)))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
(?[X]:(~generous(X))) | ~old(fred) | [
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8834698478549187675670270
% SZS output start Proof for 8834698478549187675670270
13. ! [X0] : (funny(X0) <=> (~brave(X0) | brave(X0))) [input p12]
18. old(fred) <~> ~funny(fred) [input p17]
25. ~old(fred) [input hypothesis]
76. ! [X0] : ((funny(X0) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | ~funny(X0))) [nnf transformation 13]
77. ! [X0] : ((funny(X0) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | ~funny(X0))) [flattening 76]
87. (funny(fred) | ~old(fred)) & (~funny(fred) | old(fred)) [nnf transformation 18]
149. funny(X0) | ~brave(X0) [cnf transformation 77]
150. funny(X0) | brave(X0) [cnf transformation 77]
161. ~funny(fred) | old(fred) [cnf transformation 87]
172. ~old(fred) [cnf transformation 25]
328. funny(X0) [subsumption resolution 149,150]
363. old(fred) [subsumption resolution 161,328]
403. $false [subsumption resolution 172,363]
% SZS output end Proof for 8834698478549187675670270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and patient is curious or not patient. Everyone who is tall or brave is brave and vice versa. Everyone who is both not quiet and calm is either patient or happy. Everyone who is not generous or not quiet is not kind. Everyone who is quiet is both not quiet and strong. Everyone who is not wise is both not wise and rich. If someone is tall or not wise then mary is either brave or curious and vice versa. Everyone who is both not wise and curious is both not curious and not rich. If fred is brave or kind then alice is both kind and old and vice versa. If someone is not humble then john is both kind and not patient and vice versa. Everyone who is not wise is strong or humble and vice versa. If someone is either creative or humble then someone is not curious or not happy. If john is not creative or kind then lucy is either humble or not old and vice versa. Everyone who is generous or humble is either not calm or happy and vice versa. Everyone who is either not curious or old is both not old and not humble and vice versa. Everyone who is not funny or creative is patient or kind and vice versa. Someone is not kind. Someone is tall. John is not creative or not wise. Susan is not tall. | Fred is generous. | neutral | (![X]:((rich(X)&patient(X))=>(curious(X)|~patient(X))))&
(![X]:((tall(X)|brave(X))<=>brave(X)))&
(![X]:((~quiet(X)&calm(X))=>(patient(X)<~>happy(X))))&
(![X]:((~generous(X)|~quiet(X))=>~kind(X)))&
(![X]:(quiet(X)=>(~quiet(X)&strong(X))))&
(![X]:(~wise(X)=>(~wise(X)&rich(X))))&
((?[X]:((tall(X)|~wise(X))))<=>((brave(mary)<~>curious(mary))))&
(![X]:((~wise(X)&curious(X))=>(~curious(X)&~rich(X))))&
(((brave(fred)|kind(fred)))<=>((kind(alice)&old(alice))))&
((?[X]:(~humble(X)))<=>((kind(john)&~patient(john))))&
(![X]:(~wise(X)<=>(strong(X)|humble(X))))&
((?[X]:((creative(X)<~>humble(X))))=>(?[X]:((~curious(X)|~happy(X)))))&
(((~creative(john)|kind(john)))<=>((humble(lucy)<~>~old(lucy))))&
(![X]:((generous(X)|humble(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((~curious(X)<~>old(X))<=>(~old(X)&~humble(X))))&
(![X]:((~funny(X)|creative(X))<=>(patient(X)|kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:(tall(X)))&
((~creative(john)|~wise(john)))&
(~tall(susan)) | generous(fred) | [] | null | 0 |
If lucy is curious then john is both funny and not calm. Everyone who is both humble and not wise is not tall or tall and vice versa. Everyone who is brave or not humble is either old or not generous. Everyone who is either not wise or old is both not creative and not strong and vice versa. If someone is quiet then someone is either quiet or calm. If someone is both not rich and curious then someone is both not happy and not generous and vice versa. If lucy is both not old and rich then someone is strong or calm and vice versa. Everyone who is both not strong and not rich is not old or quiet and vice versa. If alice is not strong then someone is either not kind or wise and vice versa. If alice is wise then alice is creative or not patient and vice versa. If someone is not humble then someone is generous. If someone is either tall or humble then fred is both not quiet and not humble and vice versa. Everyone who is both not calm and not happy is not curious and vice versa. Everyone who is humble or not rich is not happy or generous. Everyone who is old or generous is either rich or not happy. Paul is funny. Someone is not calm or humble. Someone is either not wise or not happy. Someone is brave or not old. Someone is tall or old. Susan is not strong. | Fred is not generous. | contradiction | ((curious(lucy))=>((funny(john)&~calm(john))))&
(![X]:((humble(X)&~wise(X))<=>(~tall(X)|tall(X))))&
(![X]:((brave(X)|~humble(X))=>(old(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>old(X))<=>(~creative(X)&~strong(X))))&
((?[X]:(quiet(X)))=>(?[X]:((quiet(X)<~>calm(X)))))&
((?[X]:((~rich(X)&curious(X))))<=>(?[X]:((~happy(X)&~generous(X)))))&
(((~old(lucy)&rich(lucy)))<=>(?[X]:((strong(X)|calm(X)))))&
(![X]:((~strong(X)&~rich(X))<=>(~old(X)|quiet(X))))&
((~strong(alice))<=>(?[X]:((~kind(X)<~>wise(X)))))&
((wise(alice))<=>((creative(alice)|~patient(alice))))&
((?[X]:(~humble(X)))=>(?[X]:(generous(X))))&
((?[X]:((tall(X)<~>humble(X))))<=>((~quiet(fred)&~humble(fred))))&
(![X]:((~calm(X)&~happy(X))<=>~curious(X)))&
(![X]:((humble(X)|~rich(X))=>(~happy(X)|generous(X))))&
(![X]:((old(X)|generous(X))=>(rich(X)<~>~happy(X))))&
(funny(paul))&
(?[X]:((~calm(X)|humble(X))))&
(?[X]:((~wise(X)<~>~happy(X))))&
(?[X]:((brave(X)|~old(X))))&
(?[X]:((tall(X)|old(X))))&
(~strong(susan)) | ~generous(fred) | [
"p1",
"p5",
"p6",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6118844314673028557638186
% SZS output start Proof for 6118844314673028557638186
2. ! [X0] : ((~wise(X0) & humble(X0)) <=> (tall(X0) | ~tall(X0))) [input p1]
6. ? [X0] : (curious(X0) & ~rich(X0)) <=> ? [X0] : (~generous(X0) & ~happy(X0)) [input p5]
7. (rich(lucy) & ~old(lucy)) <=> ? [X0] : (calm(X0) | strong(X0)) [input p6]
8. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> (quiet(X0) | ~old(X0))) [input p7]
13. ! [X0] : ((~happy(X0) & ~calm(X0)) <=> ~curious(X0)) [input p12]
14. ! [X0] : ((~rich(X0) | humble(X0)) => (generous(X0) | ~happy(X0))) [input p13]
15. ! [X0] : ((generous(X0) | old(X0)) => (rich(X0) <~> ~happy(X0))) [input p14]
22. ~generous(fred) [input hypothesis]
24. ? [X0] : (curious(X0) & ~rich(X0)) <=> ? [X1] : (~generous(X1) & ~happy(X1)) [rectify 6]
32. ! [X0] : ((generous(X0) | ~happy(X0)) | (rich(X0) & ~humble(X0))) [ennf transformation 14]
33. ! [X0] : (generous(X0) | ~happy(X0) | (rich(X0) & ~humble(X0))) [flattening 32]
34. ! [X0] : ((rich(X0) <~> ~happy(X0)) | (~generous(X0) & ~old(X0))) [ennf transformation 15]
35. ! [X0] : (((~wise(X0) & humble(X0)) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | (wise(X0) | ~humble(X0)))) [nnf transformation 2]
36. ! [X0] : (((~wise(X0) & humble(X0)) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | wise(X0) | ~humble(X0))) [flattening 35]
44. (? [X0] : (curious(X0) & ~rich(X0)) | ! [X1] : (generous(X1) | happy(X1))) & (? [X1] : (~generous(X1) & ~happy(X1)) | ! [X0] : (~curious(X0) | rich(X0))) [nnf transformation 24]
45. (? [X0] : (curious(X0) & ~rich(X0)) | ! [X1] : (generous(X1) | happy(X1))) & (? [X2] : (~generous(X2) & ~happy(X2)) | ! [X3] : (~curious(X3) | rich(X3))) [rectify 44]
46. ? [X0] : (curious(X0) & ~rich(X0)) => (curious(sK1) & ~rich(sK1)) [choice axiom]
47. ? [X2] : (~generous(X2) & ~happy(X2)) => (~generous(sK2) & ~happy(sK2)) [choice axiom]
48. ((curious(sK1) & ~rich(sK1)) | ! [X1] : (generous(X1) | happy(X1))) & ((~generous(sK2) & ~happy(sK2)) | ! [X3] : (~curious(X3) | rich(X3))) [skolemisation 45,47,46]
49. ((rich(lucy) & ~old(lucy)) | ! [X0] : (~calm(X0) & ~strong(X0))) & (? [X0] : (calm(X0) | strong(X0)) | (~rich(lucy) | old(lucy))) [nnf transformation 7]
50. ((rich(lucy) & ~old(lucy)) | ! [X0] : (~calm(X0) & ~strong(X0))) & (? [X0] : (calm(X0) | strong(X0)) | ~rich(lucy) | old(lucy)) [flattening 49]
51. ((rich(lucy) & ~old(lucy)) | ! [X0] : (~calm(X0) & ~strong(X0))) & (? [X1] : (calm(X1) | strong(X1)) | ~rich(lucy) | old(lucy)) [rectify 50]
52. ? [X1] : (calm(X1) | strong(X1)) => (calm(sK3) | strong(sK3)) [choice axiom]
53. ((rich(lucy) & ~old(lucy)) | ! [X0] : (~calm(X0) & ~strong(X0))) & ((calm(sK3) | strong(sK3)) | ~rich(lucy) | old(lucy)) [skolemisation 51,52]
54. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (rich(X0) | strong(X0)))) [nnf transformation 8]
55. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | rich(X0) | strong(X0))) [flattening 54]
70. ! [X0] : (((~happy(X0) & ~calm(X0)) | curious(X0)) & (~curious(X0) | (happy(X0) | calm(X0)))) [nnf transformation 13]
71. ! [X0] : (((~happy(X0) & ~calm(X0)) | curious(X0)) & (~curious(X0) | happy(X0) | calm(X0))) [flattening 70]
72. ! [X0] : (((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~generous(X0) & ~old(X0))) [nnf transformation 34]
84. humble(X0) | tall(X0) [cnf transformation 36]
85. ~tall(X0) | humble(X0) [cnf transformation 36]
102. ~rich(sK1) | generous(X1) | happy(X1) [cnf transformation 48]
103. curious(sK1) | generous(X1) | happy(X1) [cnf transformation 48]
106. ~old(lucy) | ~calm(X0) [cnf transformation 53]
108. rich(lucy) | ~calm(X0) [cnf transformation 53]
112. ~rich(X0) | old(X0) [cnf transformation 55]
128. ~curious(X0) | happy(X0) | calm(X0) [cnf transformation 71]
131. generous(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 33]
132. generous(X0) | ~happy(X0) | rich(X0) [cnf transformation 33]
134. ~happy(X0) | rich(X0) | ~generous(X0) [cnf transformation 72]
143. ~generous(fred) [cnf transformation 22]
154. humble(X0) [subsumption resolution 84,85]
172. 6 <=> ! [X1] : (generous(X1) | happy(X1)) [avatar definition]
173. generous(X1) | happy(X1) <- (6) [avatar component clause 172]
175. 7 <=> curious(sK1) [avatar definition]
177. curious(sK1) <- (7) [avatar component clause 175]
178. 6 | 7 [avatar split clause 103,175,172]
180. 8 <=> rich(sK1) [avatar definition]
182. ~rich(sK1) <- (~8) [avatar component clause 180]
183. 6 | ~8 [avatar split clause 102,180,172]
198. 12 <=> ! [X0] : ~calm(X0) [avatar definition]
199. ~calm(X0) <- (12) [avatar component clause 198]
201. 13 <=> rich(lucy) [avatar definition]
203. rich(lucy) <- (13) [avatar component clause 201]
204. 12 | 13 [avatar split clause 108,201,198]
210. 15 <=> old(lucy) [avatar definition]
212. ~old(lucy) <- (~15) [avatar component clause 210]
213. 12 | ~15 [avatar split clause 106,210,198]
243. ~happy(X0) | generous(X0) [subsumption resolution 131,154]
245. ~happy(X0) | rich(X0) [subsumption resolution 134,132]
256. generous(X1) <- (6) [subsumption resolution 173,243]
257. $false <- (6) [resolution 256,143]
260. ~6 [avatar contradiction clause 257]
280. happy(sK1) | calm(sK1) <- (7) [resolution 128,177]
282. happy(sK1) <- (7, 12) [subsumption resolution 280,199]
283. rich(sK1) <- (7, 12) [resolution 282,245]
286. $false <- (7, ~8, 12) [subsumption resolution 283,182]
287. ~7 | 8 | ~12 [avatar contradiction clause 286]
301. old(lucy) <- (13) [resolution 203,112]
302. $false <- (13, ~15) [subsumption resolution 301,212]
303. ~13 | 15 [avatar contradiction clause 302]
304. $false [avatar sat refutation 178,183,204,213,260,287,303]
% SZS output end Proof for 6118844314673028557638186
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not wise is both generous and not calm and vice versa.
If someone is not tall then someone is either calm or not generous and vice versa.
Everyone who is either not creative or rich is brave and vice versa.
Everyone who is both funny and curious is both not rich and funny.
Everyone who is brave is not patient or brave and vice versa.
If alice is not humble or wise then someone is patient or not old and vice versa.
If someone is not wise or funny then someone is both not kind and not patient and vice versa.
Everyone who is not old or curious is not humble and vice versa.
If someone is either creative or not brave then someone is creative.
Everyone who is not patient is both tall and not humble.
If mary is both not generous and tall then alice is both brave and calm.
Everyone who is creative is either not strong or not calm and vice versa.
If someone is either creative or strong then mary is either not generous or not rich and vice versa.
If someone is not creative or strong then someone is patient.
If alice is both tall and wise then someone is either not strong or not calm and vice versa.
Everyone who is both not rich and not humble is both not calm and strong.
Someone is not wise.
Someone is not kind.
John is not rich.
Fred is either brave or not humble.
Someone is either tall or not strong.
Fred is both wise and not curious.
Mary is both not happy and not quiet.
Someone is either quiet or happy. | Alice is not wise. | contradiction | (![X]:((wise(X)&~wise(X))<=>(generous(X)&~calm(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((calm(X)<~>~generous(X)))))&
(![X]:((~creative(X)<~>rich(X))<=>brave(X)))&
(![X]:((funny(X)&curious(X))=>(~rich(X)&funny(X))))&
(![X]:(brave(X)<=>(~patient(X)|brave(X))))&
(((~humble(alice)|wise(alice)))<=>(?[X]:((patient(X)|~old(X)))))&
((?[X]:((~wise(X)|funny(X))))<=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:((~old(X)|curious(X))<=>~humble(X)))&
((?[X]:((creative(X)<~>~brave(X))))=>(?[X]:(creative(X))))&
(![X]:(~patient(X)=>(tall(X)&~humble(X))))&
(((~generous(mary)&tall(mary)))=>((brave(alice)&calm(alice))))&
(![X]:(creative(X)<=>(~strong(X)<~>~calm(X))))&
((?[X]:((creative(X)<~>strong(X))))<=>((~generous(mary)<~>~rich(mary))))&
((?[X]:((~creative(X)|strong(X))))=>(?[X]:(patient(X))))&
(((tall(alice)&wise(alice)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((~rich(X)&~humble(X))=>(~calm(X)&strong(X))))&
(?[X]:(~wise(X)))&
(?[X]:(~kind(X)))&
(~rich(john))&
((brave(fred)<~>~humble(fred)))&
(?[X]:((tall(X)<~>~strong(X))))&
((wise(fred)&~curious(fred)))&
((~happy(mary)&~quiet(mary)))&
(?[X]:((quiet(X)<~>happy(X)))) | ~wise(alice) | [
"p2",
"p5",
"p8",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2342290947339840888556112
% SZS output start Proof for 2342290947339840888556112
3. ! [X0] : ((~creative(X0) <~> rich(X0)) <=> brave(X0)) [input p2]
6. (wise(alice) | ~humble(alice)) <=> ? [X0] : (~old(X0) | patient(X0)) [input p5]
9. ? [X0] : (creative(X0) <~> ~brave(X0)) => ? [X0] : creative(X0) [input p8]
10. ! [X0] : (~patient(X0) => (~humble(X0) & tall(X0))) [input p9]
12. ! [X0] : (creative(X0) <=> (~strong(X0) <~> ~calm(X0))) [input p11]
15. (wise(alice) & tall(alice)) <=> ? [X0] : (~strong(X0) <~> ~calm(X0)) [input p14]
16. ! [X0] : ((~humble(X0) & ~rich(X0)) => (strong(X0) & ~calm(X0))) [input p15]
25. ~wise(alice) [input hypothesis]
28. ? [X0] : (creative(X0) <~> ~brave(X0)) => ? [X1] : creative(X1) [rectify 9]
32. ? [X1] : creative(X1) | ! [X0] : (creative(X0) <=> ~brave(X0)) [ennf transformation 28]
33. ! [X0] : ((~humble(X0) & tall(X0)) | patient(X0)) [ennf transformation 10]
37. ! [X0] : ((strong(X0) & ~calm(X0)) | (humble(X0) | rich(X0))) [ennf transformation 16]
38. ! [X0] : ((strong(X0) & ~calm(X0)) | humble(X0) | rich(X0)) [flattening 37]
46. ! [X0] : ((((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | ~brave(X0)) & (brave(X0) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0))))) [nnf transformation 3]
49. ((wise(alice) | ~humble(alice)) | ! [X0] : (old(X0) & ~patient(X0))) & (? [X0] : (~old(X0) | patient(X0)) | (~wise(alice) & humble(alice))) [nnf transformation 6]
50. (wise(alice) | ~humble(alice) | ! [X0] : (old(X0) & ~patient(X0))) & (? [X0] : (~old(X0) | patient(X0)) | (~wise(alice) & humble(alice))) [flattening 49]
51. (wise(alice) | ~humble(alice) | ! [X0] : (old(X0) & ~patient(X0))) & (? [X1] : (~old(X1) | patient(X1)) | (~wise(alice) & humble(alice))) [rectify 50]
52. ? [X1] : (~old(X1) | patient(X1)) => (~old(sK2) | patient(sK2)) [choice axiom]
53. (wise(alice) | ~humble(alice) | ! [X0] : (old(X0) & ~patient(X0))) & ((~old(sK2) | patient(sK2)) | (~wise(alice) & humble(alice))) [skolemisation 51,52]
61. ? [X1] : creative(X1) | ! [X0] : ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))) [nnf transformation 32]
62. ? [X0] : creative(X0) | ! [X1] : ((creative(X1) | brave(X1)) & (~brave(X1) | ~creative(X1))) [rectify 61]
63. ? [X0] : creative(X0) => creative(sK5) [choice axiom]
64. creative(sK5) | ! [X1] : ((creative(X1) | brave(X1)) & (~brave(X1) | ~creative(X1))) [skolemisation 62,63]
65. ! [X0] : ((creative(X0) | ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | ~creative(X0))) [nnf transformation 12]
73. ((wise(alice) & tall(alice)) | ! [X0] : ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (? [X0] : ((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | (~wise(alice) | ~tall(alice))) [nnf transformation 15]
74. ((wise(alice) & tall(alice)) | ! [X0] : ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (? [X0] : ((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | ~wise(alice) | ~tall(alice)) [flattening 73]
75. ((wise(alice) & tall(alice)) | ! [X0] : ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (? [X1] : ((calm(X1) | strong(X1)) & (~calm(X1) | ~strong(X1))) | ~wise(alice) | ~tall(alice)) [rectify 74]
76. ? [X1] : ((calm(X1) | strong(X1)) & (~calm(X1) | ~strong(X1))) => ((calm(sK8) | strong(sK8)) & (~calm(sK8) | ~strong(sK8))) [choice axiom]
77. ((wise(alice) & tall(alice)) | ! [X0] : ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (((calm(sK8) | strong(sK8)) & (~calm(sK8) | ~strong(sK8))) | ~wise(alice) | ~tall(alice)) [skolemisation 75,76]
98. ~rich(X0) | ~creative(X0) | brave(X0) [cnf transformation 46]
100. ~brave(X0) | creative(X0) | ~rich(X0) [cnf transformation 46]
108. wise(alice) | ~humble(alice) | ~patient(X0) [cnf transformation 53]
118. creative(sK5) | ~brave(X1) | ~creative(X1) [cnf transformation 64]
119. creative(sK5) | creative(X1) | brave(X1) [cnf transformation 64]
121. ~humble(X0) | patient(X0) [cnf transformation 33]
124. ~strong(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 65]
125. ~creative(X0) | strong(X0) | calm(X0) [cnf transformation 65]
127. ~strong(X0) | creative(X0) | calm(X0) [cnf transformation 65]
142. wise(alice) | ~calm(X0) | strong(X0) [cnf transformation 77]
143. wise(alice) | ~strong(X0) | calm(X0) [cnf transformation 77]
144. ~calm(X0) | humble(X0) | rich(X0) [cnf transformation 38]
145. strong(X0) | humble(X0) | rich(X0) [cnf transformation 38]
159. ~wise(alice) [cnf transformation 25]
191. 8 <=> humble(alice) [avatar definition]
192. humble(alice) <- (8) [avatar component clause 191]
193. ~humble(alice) <- (~8) [avatar component clause 191]
195. 9 <=> wise(alice) [avatar definition]
200. 10 <=> ! [X0] : ~patient(X0) [avatar definition]
201. ~patient(X0) <- (10) [avatar component clause 200]
202. 10 | ~8 | 9 [avatar split clause 108,195,191,200]
244. 20 <=> ! [X1] : (creative(X1) | brave(X1)) [avatar definition]
245. brave(X1) | creative(X1) <- (20) [avatar component clause 244]
247. 21 <=> creative(sK5) [avatar definition]
249. creative(sK5) <- (21) [avatar component clause 247]
250. 20 | 21 [avatar split clause 119,247,244]
252. 22 <=> ! [X1] : (~brave(X1) | ~creative(X1)) [avatar definition]
253. ~brave(X1) | ~creative(X1) <- (22) [avatar component clause 252]
254. 22 | 21 [avatar split clause 118,247,252]
269. 26 <=> brave(alice) [avatar definition]
271. brave(alice) <- (26) [avatar component clause 269]
312. 35 <=> ! [X0] : (~strong(X0) | calm(X0)) [avatar definition]
313. ~strong(X0) | calm(X0) <- (35) [avatar component clause 312]
314. 35 | 9 [avatar split clause 143,195,312]
316. 36 <=> ! [X0] : (~calm(X0) | strong(X0)) [avatar definition]
317. ~calm(X0) | strong(X0) <- (36) [avatar component clause 316]
318. 36 | 9 [avatar split clause 142,195,316]
365. ~9 [avatar split clause 159,195]
401. strong(sK5) | calm(sK5) <- (21) [resolution 125,249]
404. strong(sK5) <- (21, 36) [subsumption resolution 401,317]
407. ~calm(sK5) | ~creative(sK5) <- (21, 36) [resolution 404,124]
408. calm(sK5) <- (21, 35, 36) [resolution 404,313]
409. ~calm(sK5) <- (21, 36) [subsumption resolution 407,249]
410. $false <- (21, 35, 36) [subsumption resolution 408,409]
411. ~21 | ~35 | ~36 [avatar contradiction clause 410]
423. creative(X0) | creative(X0) | ~rich(X0) <- (20) [resolution 245,100]
425. ~rich(X0) | creative(X0) <- (20) [duplicate literal removal 423]
472. humble(X0) | rich(X0) | creative(X0) | calm(X0) [resolution 145,127]
474. humble(X2) | rich(X2) | calm(X2) <- (35) [resolution 145,313]
476. humble(X0) | rich(X0) | creative(X0) [subsumption resolution 472,144]
477. humble(X0) | creative(X0) <- (20) [subsumption resolution 476,425]
478. humble(X2) | rich(X2) <- (35) [subsumption resolution 474,144]
484. creative(alice) <- (~8, 20) [resolution 477,193]
492. rich(alice) <- (~8, 35) [resolution 478,193]
505. ~creative(alice) | brave(alice) <- (~8, 35) [resolution 492,98]
506. brave(alice) <- (~8, 20, 35) [subsumption resolution 505,484]
507. 26 | 8 | ~20 | ~35 [avatar split clause 506,312,244,191,269]
508. ~creative(alice) <- (22, 26) [resolution 271,253]
511. $false <- (~8, 20, 22, 26) [subsumption resolution 508,484]
512. 8 | ~20 | ~22 | ~26 [avatar contradiction clause 511]
526. patient(alice) <- (8) [resolution 192,121]
529. $false <- (8, 10) [subsumption resolution 526,201]
530. ~8 | ~10 [avatar contradiction clause 529]
531. $false [avatar sat refutation 202,250,254,314,318,365,411,507,512,530]
% SZS output end Proof for 2342290947339840888556112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either wise or creative then someone is brave. If lucy is both funny and calm then someone is both not tall and wise. Everyone who is rich or not brave is brave or not patient. If someone is not old then paul is both patient and not rich and vice versa. If fred is not old then paul is either happy or creative. If susan is happy then someone is both not calm and not generous and vice versa. Everyone who is funny or not happy is both quiet and not brave. Everyone who is both calm and curious is either creative or calm and vice versa. Everyone who is both old and creative is not funny or not tall. Everyone who is not funny is old. Everyone who is either rich or curious is either calm or not funny and vice versa. Everyone who is both patient and brave is either not curious or not patient. Everyone who is funny is not wise or rich. Everyone who is not generous or kind is generous and vice versa. If someone is patient or old then someone is either patient or tall and vice versa. If someone is humble or curious then someone is both rich and humble and vice versa. Alice is both not old and not strong. Fred is tall. Fred is not creative. Mary is not kind or not happy. Someone is either brave or not kind. Someone is quiet or not brave. Lucy is tall. | Paul is not calm. | contradiction | (((wise(fred)<~>creative(fred)))=>(?[X]:(brave(X))))&
(((funny(lucy)&calm(lucy)))=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((rich(X)|~brave(X))=>(brave(X)|~patient(X))))&
((?[X]:(~old(X)))<=>((patient(paul)&~rich(paul))))&
((~old(fred))=>((happy(paul)<~>creative(paul))))&
((happy(susan))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((funny(X)|~happy(X))=>(quiet(X)&~brave(X))))&
(![X]:((calm(X)&curious(X))<=>(creative(X)<~>calm(X))))&
(![X]:((old(X)&creative(X))=>(~funny(X)|~tall(X))))&
(![X]:(~funny(X)=>old(X)))&
(![X]:((rich(X)<~>curious(X))<=>(calm(X)<~>~funny(X))))&
(![X]:((patient(X)&brave(X))=>(~curious(X)<~>~patient(X))))&
(![X]:(funny(X)=>(~wise(X)|rich(X))))&
(![X]:((~generous(X)|kind(X))<=>generous(X)))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:((patient(X)<~>tall(X)))))&
((?[X]:((humble(X)|curious(X))))<=>(?[X]:((rich(X)&humble(X)))))&
((~old(alice)&~strong(alice)))&
(tall(fred))&
(~creative(fred))&
((~kind(mary)|~happy(mary)))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(tall(lucy)) | ~calm(paul) | [
"p2",
"p3",
"p6",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 289837921765827103202833
% SZS output start Proof for 289837921765827103202833
3. ! [X0] : ((~brave(X0) | rich(X0)) => (~patient(X0) | brave(X0))) [input p2]
4. ? [X0] : ~old(X0) <=> (~rich(paul) & patient(paul)) [input p3]
7. ! [X0] : ((~happy(X0) | funny(X0)) => (~brave(X0) & quiet(X0))) [input p6]
11. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (calm(X0) <~> ~funny(X0))) [input p10]
12. ! [X0] : ((brave(X0) & patient(X0)) => (~curious(X0) <~> ~patient(X0))) [input p11]
17. ~strong(alice) & ~old(alice) [input p16]
24. ~calm(paul) [input hypothesis]
27. ~old(alice) [pure predicate removal 17]
28. ! [X0] : ((~happy(X0) | funny(X0)) => ~brave(X0)) [pure predicate removal 7]
33. ! [X0] : ((~patient(X0) | brave(X0)) | (brave(X0) & ~rich(X0))) [ennf transformation 3]
34. ! [X0] : (~patient(X0) | brave(X0) | (brave(X0) & ~rich(X0))) [flattening 33]
36. ! [X0] : (~brave(X0) | (happy(X0) & ~funny(X0))) [ennf transformation 28]
40. ! [X0] : ((~curious(X0) <~> ~patient(X0)) | (~brave(X0) | ~patient(X0))) [ennf transformation 12]
41. ! [X0] : ((~curious(X0) <~> ~patient(X0)) | ~brave(X0) | ~patient(X0)) [flattening 40]
49. (? [X0] : ~old(X0) | (rich(paul) | ~patient(paul))) & ((~rich(paul) & patient(paul)) | ! [X0] : old(X0)) [nnf transformation 4]
50. (? [X0] : ~old(X0) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X0] : old(X0)) [flattening 49]
51. (? [X0] : ~old(X0) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X1] : old(X1)) [rectify 50]
52. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
53. (~old(sK2) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X1] : old(X1)) [skolemisation 51,52]
61. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0)))) & (((funny(X0) | ~calm(X0)) & (~funny(X0) | calm(X0))) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 11]
62. ! [X0] : (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ~brave(X0) | ~patient(X0)) [nnf transformation 41]
83. ~patient(X0) | brave(X0) | brave(X0) [cnf transformation 34]
84. patient(paul) | old(X1) [cnf transformation 53]
85. ~rich(paul) | old(X1) [cnf transformation 53]
92. ~funny(X0) | ~brave(X0) [cnf transformation 36]
107. curious(X0) | rich(X0) | calm(X0) | funny(X0) [cnf transformation 61]
110. ~patient(X0) | ~curious(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 62]
127. ~old(alice) [cnf transformation 27]
134. ~calm(paul) [cnf transformation 24]
137. ~patient(X0) | ~curious(X0) | ~brave(X0) [duplicate literal removal 110]
140. ~patient(X0) | brave(X0) [duplicate literal removal 83]
174. 8 <=> patient(paul) [avatar definition]
175. patient(paul) <- (8) [avatar component clause 174]
178. 9 <=> rich(paul) [avatar definition]
179. ~rich(paul) <- (~9) [avatar component clause 178]
187. 11 <=> ! [X1] : old(X1) [avatar definition]
188. old(X1) <- (11) [avatar component clause 187]
189. 11 | ~9 [avatar split clause 85,178,187]
190. 11 | 8 [avatar split clause 84,174,187]
224. ~curious(X0) | ~patient(X0) [subsumption resolution 137,140]
323. $false <- (11) [resolution 188,127]
326. ~11 [avatar contradiction clause 323]
327. brave(paul) <- (8) [resolution 175,140]
355. ~patient(X2) | calm(X2) | funny(X2) | rich(X2) [resolution 107,224]
397. calm(paul) | funny(paul) | rich(paul) <- (8) [resolution 355,175]
424. funny(paul) | rich(paul) <- (8) [subsumption resolution 397,134]
425. funny(paul) <- (8, ~9) [subsumption resolution 424,179]
437. ~brave(paul) <- (8, ~9) [resolution 425,92]
439. $false <- (8, ~9) [subsumption resolution 437,327]
440. ~8 | 9 [avatar contradiction clause 439]
441. $false [avatar sat refutation 189,190,326,440]
% SZS output end Proof for 289837921765827103202833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If mary is creative or not funny then someone is either quiet or not rich and vice versa.
If paul is both not brave and creative then john is wise and vice versa.
If someone is not funny then someone is not curious or old and vice versa.
Everyone who is either not brave or strong is happy or not wise and vice versa.
Everyone who is either happy or not curious is both not rich and kind.
Everyone who is both not patient and creative is both not old and creative and vice versa.
If someone is both humble and quiet then someone is not funny or tall and vice versa.
Everyone who is either not strong or happy is not funny or not rich.
Everyone who is quiet or creative is both tall and not humble.
Everyone who is both not happy and not strong is both strong and not rich.
Everyone who is either not happy or kind is both brave and rich.
Everyone who is both not tall and calm is both humble and not brave.
Everyone who is either old or rich is not wise or not quiet.
If someone is both creative and wise then someone is both not patient and not tall.
Everyone who is funny or not patient is rich or not calm and vice versa.
Someone is either not brave or not wise.
Someone is either patient or not calm.
Susan is either not happy or creative.
Someone is patient.
Lucy is either not creative or creative. | Susan is kind. | neutral | (((creative(mary)|~funny(mary)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(((~brave(paul)&creative(paul)))<=>(wise(john)))&
((?[X]:(~funny(X)))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(happy(X)|~wise(X))))&
(![X]:((happy(X)<~>~curious(X))=>(~rich(X)&kind(X))))&
(![X]:((~patient(X)&creative(X))<=>(~old(X)&creative(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((~funny(X)|tall(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~funny(X)|~rich(X))))&
(![X]:((quiet(X)|creative(X))=>(tall(X)&~humble(X))))&
(![X]:((~happy(X)&~strong(X))=>(strong(X)&~rich(X))))&
(![X]:((~happy(X)<~>kind(X))=>(brave(X)&rich(X))))&
(![X]:((~tall(X)&calm(X))=>(humble(X)&~brave(X))))&
(![X]:((old(X)<~>rich(X))=>(~wise(X)|~quiet(X))))&
((?[X]:((creative(X)&wise(X))))=>(?[X]:((~patient(X)&~tall(X)))))&
(![X]:((funny(X)|~patient(X))<=>(rich(X)|~calm(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
(?[X]:((patient(X)<~>~calm(X))))&
((~happy(susan)<~>creative(susan)))&
(?[X]:(patient(X)))&
((~creative(lucy)<~>creative(lucy))) | kind(susan) | [] | null | 0 |
Everyone who is both patient and kind is old and vice versa.
If someone is both not rich and not old then lucy is both generous and not generous.
If someone is either patient or not rich then mary is either old or creative and vice versa.
Everyone who is creative is not tall.
If mary is humble or not creative then mary is happy.
Everyone who is wise or creative is both rich and generous and vice versa.
Everyone who is happy is either rich or not curious and vice versa.
Everyone who is not curious or old is strong or not humble and vice versa.
Everyone who is rich is brave or not patient and vice versa.
If fred is not patient then paul is both not generous and not quiet.
Everyone who is not curious is either creative or generous.
If paul is not strong or not quiet then john is either curious or not calm.
If paul is not humble or generous then someone is curious.
Everyone who is creative or not calm is both not rich and not funny.
If susan is kind or not quiet then someone is either not rich or funny.
If alice is both patient and not rich then mary is not patient.
Someone is either not happy or not humble.
Fred is kind.
John is either not funny or brave.
Paul is not patient.
Someone is not creative.
Someone is not humble or not tall.
Someone is not kind or not generous.
Someone is quiet or not humble. | Mary is not happy. | contradiction | (![X]:((patient(X)&kind(X))<=>old(X)))&
((?[X]:((~rich(X)&~old(X))))=>((generous(lucy)&~generous(lucy))))&
((?[X]:((patient(X)<~>~rich(X))))<=>((old(mary)<~>creative(mary))))&
(![X]:(creative(X)=>~tall(X)))&
(((humble(mary)|~creative(mary)))=>(happy(mary)))&
(![X]:((wise(X)|creative(X))<=>(rich(X)&generous(X))))&
(![X]:(happy(X)<=>(rich(X)<~>~curious(X))))&
(![X]:((~curious(X)|old(X))<=>(strong(X)|~humble(X))))&
(![X]:(rich(X)<=>(brave(X)|~patient(X))))&
((~patient(fred))=>((~generous(paul)&~quiet(paul))))&
(![X]:(~curious(X)=>(creative(X)<~>generous(X))))&
(((~strong(paul)|~quiet(paul)))=>((curious(john)<~>~calm(john))))&
(((~humble(paul)|generous(paul)))=>(?[X]:(curious(X))))&
(![X]:((creative(X)|~calm(X))=>(~rich(X)&~funny(X))))&
(((kind(susan)|~quiet(susan)))=>(?[X]:((~rich(X)<~>funny(X)))))&
(((patient(alice)&~rich(alice)))=>(~patient(mary)))&
(?[X]:((~happy(X)<~>~humble(X))))&
(kind(fred))&
((~funny(john)<~>brave(john)))&
(~patient(paul))&
(?[X]:(~creative(X)))&
(?[X]:((~humble(X)|~tall(X))))&
(?[X]:((~kind(X)|~generous(X))))&
(?[X]:((quiet(X)|~humble(X)))) | ~happy(mary) | [
"p4",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9121208977891824624732947
% SZS output start Proof for 9121208977891824624732947
5. (~creative(mary) | humble(mary)) => happy(mary) [input p4]
6. ! [X0] : ((creative(X0) | wise(X0)) <=> (generous(X0) & rich(X0))) [input p5]
14. ! [X0] : ((~calm(X0) | creative(X0)) => (~funny(X0) & ~rich(X0))) [input p13]
25. ~happy(mary) [input hypothesis]
29. happy(mary) | (creative(mary) & ~humble(mary)) [ennf transformation 5]
34. ! [X0] : ((~funny(X0) & ~rich(X0)) | (calm(X0) & ~creative(X0))) [ennf transformation 14]
44. ! [X0] : (((creative(X0) | wise(X0)) | (~generous(X0) | ~rich(X0))) & ((generous(X0) & rich(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 6]
45. ! [X0] : ((creative(X0) | wise(X0) | ~generous(X0) | ~rich(X0)) & ((generous(X0) & rich(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 44]
82. happy(mary) | creative(mary) [cnf transformation 29]
84. rich(X0) | ~creative(X0) [cnf transformation 45]
109. ~rich(X0) | ~creative(X0) [cnf transformation 34]
127. ~happy(mary) [cnf transformation 25]
138. 3 <=> creative(mary) [avatar definition]
139. creative(mary) <- (3) [avatar component clause 138]
168. 9 <=> happy(mary) [avatar definition]
171. 3 | 9 [avatar split clause 82,168,138]
220. ~creative(X0) [subsumption resolution 109,84]
292. ~9 [avatar split clause 127,168]
293. $false <- (3) [subsumption resolution 139,220]
294. ~3 [avatar contradiction clause 293]
295. $false [avatar sat refutation 171,292,294]
% SZS output end Proof for 9121208977891824624732947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not funny then someone is not patient or brave and vice versa. Everyone who is both not curious and curious is not brave and vice versa. If someone is either happy or kind then john is either not generous or not wise. If lucy is either not humble or curious then mary is generous and vice versa. If someone is both funny and tall then fred is calm or strong. Everyone who is not rich or not funny is both not happy and not patient. If lucy is not patient then someone is not wise and vice versa. If someone is not tall or generous then someone is both not generous and kind and vice versa. Everyone who is both not quiet and not calm is either not strong or generous. Everyone who is either quiet or funny is not tall. If someone is either generous or curious then lucy is curious and vice versa. If someone is either old or not funny then someone is either not curious or not kind and vice versa. Everyone who is either generous or not funny is old or not curious and vice versa. Everyone who is either tall or not curious is both not old and funny. Everyone who is patient or not happy is brave and vice versa. Everyone who is both not generous and not patient is both not patient and rich and vice versa. Someone is either not generous or not creative. Someone is both tall and rich. Alice is either creative or not brave. Someone is either not wise or calm. Mary is either quiet or not calm. Mary is funny. Susan is old. Someone is not curious. | Alice is creative. | entailment | ((?[X]:((funny(X)|~funny(X))))<=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:((~curious(X)&curious(X))<=>~brave(X)))&
((?[X]:((happy(X)<~>kind(X))))=>((~generous(john)<~>~wise(john))))&
(((~humble(lucy)<~>curious(lucy)))<=>(generous(mary)))&
((?[X]:((funny(X)&tall(X))))=>((calm(fred)|strong(fred))))&
(![X]:((~rich(X)|~funny(X))=>(~happy(X)&~patient(X))))&
((~patient(lucy))<=>(?[X]:(~wise(X))))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:((~quiet(X)&~calm(X))=>(~strong(X)<~>generous(X))))&
(![X]:((quiet(X)<~>funny(X))=>~tall(X)))&
((?[X]:((generous(X)<~>curious(X))))<=>(curious(lucy)))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~kind(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(old(X)|~curious(X))))&
(![X]:((tall(X)<~>~curious(X))=>(~old(X)&funny(X))))&
(![X]:((patient(X)|~happy(X))<=>brave(X)))&
(![X]:((~generous(X)&~patient(X))<=>(~patient(X)&rich(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((tall(X)&rich(X))))&
((creative(alice)<~>~brave(alice)))&
(?[X]:((~wise(X)<~>calm(X))))&
((quiet(mary)<~>~calm(mary)))&
(funny(mary))&
(old(susan))&
(?[X]:(~curious(X))) | creative(alice) | [
"p1",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6334814802749062630579612
% SZS output start Proof for 6334814802749062630579612
2. ! [X0] : ((curious(X0) & ~curious(X0)) <=> ~brave(X0)) [input p1]
19. creative(alice) <~> ~brave(alice) [input p18]
25. ~creative(alice) [input hypothesis]
42. ! [X0] : (((curious(X0) & ~curious(X0)) | brave(X0)) & (~brave(X0) | (~curious(X0) | curious(X0)))) [nnf transformation 2]
43. ! [X0] : (((curious(X0) & ~curious(X0)) | brave(X0)) & (~brave(X0) | ~curious(X0) | curious(X0))) [flattening 42]
78. (brave(alice) | ~creative(alice)) & (~brave(alice) | creative(alice)) [nnf transformation 19]
90. ~curious(X0) | brave(X0) [cnf transformation 43]
91. curious(X0) | brave(X0) [cnf transformation 43]
149. ~brave(alice) | creative(alice) [cnf transformation 78]
158. ~creative(alice) [cnf transformation 25]
175. brave(X0) [subsumption resolution 90,91]
331. creative(alice) [subsumption resolution 149,175]
352. $false [subsumption resolution 158,331]
% SZS output end Proof for 6334814802749062630579612
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or happy is both not creative and not funny and vice versa. If someone is not brave then alice is not humble or creative and vice versa. Everyone who is brave or not calm is either not rich or not wise. If someone is both not wise and not quiet then someone is either curious or patient and vice versa. If mary is rich or not funny then someone is not tall or not funny. Everyone who is both quiet and rich is either not tall or not old and vice versa. Everyone who is either not old or strong is patient or brave. If fred is generous then someone is both generous and not generous. If someone is both rich and calm then fred is quiet or calm and vice versa. Everyone who is calm or rich is not quiet. Everyone who is not strong is not rich or not quiet. If someone is not happy or calm then someone is not brave or not creative. Everyone who is both wise and not humble is either funny or generous and vice versa. Everyone who is both patient and not generous is both patient and humble. Everyone who is both kind and wise is either not kind or not quiet. Someone is either not strong or brave. Someone is both not creative and brave. John is either patient or not tall. Someone is both not humble and not tall. John is rich or brave. Someone is wise. Someone is either brave or not funny. Lucy is not curious. | Alice is humble. | neutral | (![X]:((~kind(X)|happy(X))<=>(~creative(X)&~funny(X))))&
((?[X]:(~brave(X)))<=>((~humble(alice)|creative(alice))))&
(![X]:((brave(X)|~calm(X))=>(~rich(X)<~>~wise(X))))&
((?[X]:((~wise(X)&~quiet(X))))<=>(?[X]:((curious(X)<~>patient(X)))))&
(((rich(mary)|~funny(mary)))=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:((quiet(X)&rich(X))<=>(~tall(X)<~>~old(X))))&
(![X]:((~old(X)<~>strong(X))=>(patient(X)|brave(X))))&
((generous(fred))=>(?[X]:((generous(X)&~generous(X)))))&
((?[X]:((rich(X)&calm(X))))<=>((quiet(fred)|calm(fred))))&
(![X]:((calm(X)|rich(X))=>~quiet(X)))&
(![X]:(~strong(X)=>(~rich(X)|~quiet(X))))&
((?[X]:((~happy(X)|calm(X))))=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:((wise(X)&~humble(X))<=>(funny(X)<~>generous(X))))&
(![X]:((patient(X)&~generous(X))=>(patient(X)&humble(X))))&
(![X]:((kind(X)&wise(X))=>(~kind(X)<~>~quiet(X))))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:((~creative(X)&brave(X))))&
((patient(john)<~>~tall(john)))&
(?[X]:((~humble(X)&~tall(X))))&
((rich(john)|brave(john)))&
(?[X]:(wise(X)))&
(?[X]:((brave(X)<~>~funny(X))))&
(~curious(lucy)) | humble(alice) | [] | null | 0 |
Everyone who is rich or generous is humble or not generous.
If john is either tall or not brave then someone is not calm or quiet and vice versa.
Everyone who is either calm or not creative is funny or not happy.
Everyone who is both not patient and not calm is either calm or funny and vice versa.
Everyone who is humble is either not humble or brave.
Everyone who is either not creative or creative is either not funny or kind and vice versa.
Everyone who is rich or creative is not creative and vice versa.
Everyone who is quiet is rich or quiet and vice versa.
Everyone who is generous or not happy is not strong and vice versa.
If someone is both not quiet and calm then fred is happy or not generous and vice versa.
Everyone who is either not rich or not humble is both not quiet and not wise and vice versa.
If fred is not kind or not strong then fred is not tall or quiet and vice versa.
Everyone who is happy is patient.
Everyone who is both tall and not strong is both wise and not humble and vice versa.
Everyone who is either brave or not wise is rich.
If someone is either tall or not old then lucy is not humble.
Fred is both old and not calm.
Fred is not kind.
Someone is strong or not funny.
Lucy is either creative or humble.
Lucy is either not happy or humble.
Alice is not old. | John is humble. | entailment | (![X]:((rich(X)|generous(X))=>(humble(X)|~generous(X))))&
(((tall(john)<~>~brave(john)))<=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((calm(X)<~>~creative(X))=>(funny(X)|~happy(X))))&
(![X]:((~patient(X)&~calm(X))<=>(calm(X)<~>funny(X))))&
(![X]:(humble(X)=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((rich(X)|creative(X))<=>~creative(X)))&
(![X]:(quiet(X)<=>(rich(X)|quiet(X))))&
(![X]:((generous(X)|~happy(X))<=>~strong(X)))&
((?[X]:((~quiet(X)&calm(X))))<=>((happy(fred)|~generous(fred))))&
(![X]:((~rich(X)<~>~humble(X))<=>(~quiet(X)&~wise(X))))&
(((~kind(fred)|~strong(fred)))<=>((~tall(fred)|quiet(fred))))&
(![X]:(happy(X)=>patient(X)))&
(![X]:((tall(X)&~strong(X))<=>(wise(X)&~humble(X))))&
(![X]:((brave(X)<~>~wise(X))=>rich(X)))&
((?[X]:((tall(X)<~>~old(X))))=>(~humble(lucy)))&
((old(fred)&~calm(fred)))&
(~kind(fred))&
(?[X]:((strong(X)|~funny(X))))&
((creative(lucy)<~>humble(lucy)))&
((~happy(lucy)<~>humble(lucy)))&
(~old(alice)) | humble(john) | [
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3173993338563729372302894
% SZS output start Proof for 3173993338563729372302894
7. ! [X0] : ((creative(X0) | rich(X0)) <=> ~creative(X0)) [input p6]
8. ! [X0] : (quiet(X0) <=> (quiet(X0) | rich(X0))) [input p7]
11. ! [X0] : ((~rich(X0) <~> ~humble(X0)) <=> (~wise(X0) & ~quiet(X0))) [input p10]
23. ~humble(john) [input hypothesis]
41. ! [X0] : (((creative(X0) | rich(X0)) | creative(X0)) & (~creative(X0) | (~creative(X0) & ~rich(X0)))) [nnf transformation 7]
42. ! [X0] : ((creative(X0) | rich(X0) | creative(X0)) & (~creative(X0) | (~creative(X0) & ~rich(X0)))) [flattening 41]
43. ! [X0] : ((quiet(X0) | (~quiet(X0) & ~rich(X0))) & ((quiet(X0) | rich(X0)) | ~quiet(X0))) [nnf transformation 8]
44. ! [X0] : ((quiet(X0) | (~quiet(X0) & ~rich(X0))) & (quiet(X0) | rich(X0) | ~quiet(X0))) [flattening 43]
52. ! [X0] : ((((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | (wise(X0) | quiet(X0))) & ((~wise(X0) & ~quiet(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))))) [nnf transformation 11]
53. ! [X0] : ((((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | wise(X0) | quiet(X0)) & ((~wise(X0) & ~quiet(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))))) [flattening 52]
91. ~creative(X0) | ~creative(X0) [cnf transformation 42]
92. creative(X0) | rich(X0) | creative(X0) [cnf transformation 42]
94. ~rich(X0) | quiet(X0) [cnf transformation 44]
105. ~quiet(X0) | ~rich(X0) | humble(X0) [cnf transformation 53]
132. ~humble(john) [cnf transformation 23]
133. ~creative(X0) [duplicate literal removal 91]
134. creative(X0) | rich(X0) [duplicate literal removal 92]
199. ~rich(X0) | humble(X0) [subsumption resolution 105,94]
251. rich(X0) [resolution 134,133]
261. humble(X0) [resolution 199,251]
262. $false [resolution 261,132]
% SZS output end Proof for 3173993338563729372302894
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either brave or not patient.
If someone is happy or not rich then someone is not humble or not tall and vice versa.
Everyone who is both not wise and not tall is funny or happy and vice versa.
Everyone who is either not generous or curious is not kind and vice versa.
If someone is curious or calm then john is either rich or old.
Everyone who is either not brave or not old is kind or not humble and vice versa.
Everyone who is tall is not calm or curious.
Everyone who is both not quiet and not calm is not patient or curious and vice versa.
Everyone who is funny or not strong is strong.
If paul is either rich or not patient then someone is patient.
Everyone who is both not tall and wise is not creative or not kind and vice versa.
Everyone who is not wise is wise.
Everyone who is both not calm and calm is either old or patient.
Everyone who is not wise or not tall is both not tall and not calm.
Everyone who is either not tall or not funny is humble or not old and vice versa.
Everyone who is either old or not wise is either strong or quiet.
Someone is not funny.
Mary is either kind or not generous.
Someone is either patient or humble.
Fred is either not creative or quiet.
Mary is not curious or not brave.
Fred is either not brave or not curious. | John is strong. | entailment | (![X]:(~curious(X)=>(brave(X)<~>~patient(X))))&
((?[X]:((happy(X)|~rich(X))))<=>(?[X]:((~humble(X)|~tall(X)))))&
(![X]:((~wise(X)&~tall(X))<=>(funny(X)|happy(X))))&
(![X]:((~generous(X)<~>curious(X))<=>~kind(X)))&
((?[X]:((curious(X)|calm(X))))=>((rich(john)<~>old(john))))&
(![X]:((~brave(X)<~>~old(X))<=>(kind(X)|~humble(X))))&
(![X]:(tall(X)=>(~calm(X)|curious(X))))&
(![X]:((~quiet(X)&~calm(X))<=>(~patient(X)|curious(X))))&
(![X]:((funny(X)|~strong(X))=>strong(X)))&
(((rich(paul)<~>~patient(paul)))=>(?[X]:(patient(X))))&
(![X]:((~tall(X)&wise(X))<=>(~creative(X)|~kind(X))))&
(![X]:(~wise(X)=>wise(X)))&
(![X]:((~calm(X)&calm(X))=>(old(X)<~>patient(X))))&
(![X]:((~wise(X)|~tall(X))=>(~tall(X)&~calm(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>(humble(X)|~old(X))))&
(![X]:((old(X)<~>~wise(X))=>(strong(X)<~>quiet(X))))&
(?[X]:(~funny(X)))&
((kind(mary)<~>~generous(mary)))&
(?[X]:((patient(X)<~>humble(X))))&
((~creative(fred)<~>quiet(fred)))&
((~curious(mary)|~brave(mary)))&
((~brave(fred)<~>~curious(fred))) | strong(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6040154426990073576939143
% SZS output start Proof for 6040154426990073576939143
9. ! [X0] : ((~strong(X0) | funny(X0)) => strong(X0)) [input p8]
23. ~strong(john) [input hypothesis]
29. ! [X0] : (strong(X0) | (strong(X0) & ~funny(X0))) [ennf transformation 9]
99. strong(X0) | strong(X0) [cnf transformation 29]
134. ~strong(john) [cnf transformation 23]
136. strong(X0) [duplicate literal removal 99]
254. $false [subsumption resolution 134,136]
% SZS output end Proof for 6040154426990073576939143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not creative and brave is happy and vice versa.
Everyone who is not rich or strong is both not generous and not brave and vice versa.
If someone is strong then someone is both not strong and not tall and vice versa.
Everyone who is both not tall and not generous is kind or strong and vice versa.
Everyone who is both creative and wise is both not tall and tall.
If someone is not brave or kind then someone is both not rich and generous.
If someone is both creative and not old then susan is both brave and not tall and vice versa.
If paul is kind then john is not rich or not wise.
If lucy is not quiet or not brave then alice is not calm or generous and vice versa.
Everyone who is not funny or not old is either not curious or tall.
If someone is both quiet and tall then paul is both rich and humble.
Everyone who is not patient is not kind and vice versa.
Everyone who is either patient or kind is either not old or happy and vice versa.
Everyone who is both not happy and generous is either wise or calm.
Everyone who is both not generous and tall is not humble and vice versa.
Everyone who is not curious or not calm is both old and not patient and vice versa.
Someone is creative or not humble.
Susan is not calm or quiet.
Someone is both wise and curious.
John is both not patient and quiet.
John is either not curious or not humble.
Alice is not humble.
Mary is not strong or funny. | Mary is strong. | contradiction | (![X]:((~creative(X)&brave(X))<=>happy(X)))&
(![X]:((~rich(X)|strong(X))<=>(~generous(X)&~brave(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~strong(X)&~tall(X)))))&
(![X]:((~tall(X)&~generous(X))<=>(kind(X)|strong(X))))&
(![X]:((creative(X)&wise(X))=>(~tall(X)&tall(X))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((~rich(X)&generous(X)))))&
((?[X]:((creative(X)&~old(X))))<=>((brave(susan)&~tall(susan))))&
((kind(paul))=>((~rich(john)|~wise(john))))&
(((~quiet(lucy)|~brave(lucy)))<=>((~calm(alice)|generous(alice))))&
(![X]:((~funny(X)|~old(X))=>(~curious(X)<~>tall(X))))&
((?[X]:((quiet(X)&tall(X))))=>((rich(paul)&humble(paul))))&
(![X]:(~patient(X)<=>~kind(X)))&
(![X]:((patient(X)<~>kind(X))<=>(~old(X)<~>happy(X))))&
(![X]:((~happy(X)&generous(X))=>(wise(X)<~>calm(X))))&
(![X]:((~generous(X)&tall(X))<=>~humble(X)))&
(![X]:((~curious(X)|~calm(X))<=>(old(X)&~patient(X))))&
(?[X]:((creative(X)|~humble(X))))&
((~calm(susan)|quiet(susan)))&
(?[X]:((wise(X)&curious(X))))&
((~patient(john)&quiet(john)))&
((~curious(john)<~>~humble(john)))&
(~humble(alice))&
((~strong(mary)|funny(mary))) | strong(mary) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3319120135963528035852465
% SZS output start Proof for 3319120135963528035852465
2. ! [X0] : ((strong(X0) | ~rich(X0)) <=> (~brave(X0) & ~generous(X0))) [input p1]
6. ? [X0] : (kind(X0) | ~brave(X0)) => ? [X0] : (generous(X0) & ~rich(X0)) [input p5]
24. strong(mary) [input hypothesis]
26. ? [X0] : (kind(X0) | ~brave(X0)) => ? [X1] : (generous(X1) & ~rich(X1)) [rectify 6]
31. ? [X1] : (generous(X1) & ~rich(X1)) | ! [X0] : (~kind(X0) & brave(X0)) [ennf transformation 26]
40. ! [X0] : (((strong(X0) | ~rich(X0)) | (brave(X0) | generous(X0))) & ((~brave(X0) & ~generous(X0)) | (~strong(X0) & rich(X0)))) [nnf transformation 2]
41. ! [X0] : ((strong(X0) | ~rich(X0) | brave(X0) | generous(X0)) & ((~brave(X0) & ~generous(X0)) | (~strong(X0) & rich(X0)))) [flattening 40]
49. ? [X0] : (generous(X0) & ~rich(X0)) | ! [X1] : (~kind(X1) & brave(X1)) [rectify 31]
50. ? [X0] : (generous(X0) & ~rich(X0)) => (generous(sK2) & ~rich(sK2)) [choice axiom]
51. (generous(sK2) & ~rich(sK2)) | ! [X1] : (~kind(X1) & brave(X1)) [skolemisation 49,50]
75. ~generous(X0) | rich(X0) [cnf transformation 41]
78. ~strong(X0) | ~brave(X0) [cnf transformation 41]
90. ~rich(sK2) | brave(X1) [cnf transformation 51]
92. generous(sK2) | brave(X1) [cnf transformation 51]
136. strong(mary) [cnf transformation 24]
163. 7 <=> generous(sK2) [avatar definition]
165. generous(sK2) <- (7) [avatar component clause 163]
168. 8 <=> ! [X1] : brave(X1) [avatar definition]
169. brave(X1) <- (8) [avatar component clause 168]
170. 8 | 7 [avatar split clause 92,163,168]
172. 9 <=> rich(sK2) [avatar definition]
174. ~rich(sK2) <- (~9) [avatar component clause 172]
176. 8 | ~9 [avatar split clause 90,172,168]
279. rich(sK2) <- (7) [resolution 75,165]
280. $false <- (7, ~9) [subsumption resolution 279,174]
281. ~7 | 9 [avatar contradiction clause 280]
284. ~brave(mary) [resolution 78,136]
286. $false <- (8) [subsumption resolution 284,169]
287. ~8 [avatar contradiction clause 286]
290. $false [avatar sat refutation 170,176,281,287]
% SZS output end Proof for 3319120135963528035852465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both creative and curious.
Everyone who is either strong or not funny is not quiet or not humble.
If someone is not quiet then alice is kind or calm and vice versa.
Everyone who is creative is either calm or creative and vice versa.
Everyone who is not calm is both old and wise.
If someone is not brave then someone is not old and vice versa.
If someone is not happy then someone is not wise or humble and vice versa.
Everyone who is both not tall and curious is not humble.
If someone is either not generous or happy then someone is wise or tall and vice versa.
Everyone who is either not quiet or not brave is both rich and humble.
If someone is both tall and kind then alice is not old.
Everyone who is not humble is either not funny or creative and vice versa.
Everyone who is curious or tall is not brave.
Everyone who is old is creative or not humble and vice versa.
Mary is not patient or not humble.
Someone is either not humble or generous.
Someone is both not tall and not patient.
Susan is generous.
Someone is humble or quiet.
Lucy is not strong or not humble.
Fred is not patient. | Susan is happy. | entailment | (![X]:(creative(X)=>(creative(X)&curious(X))))&
(![X]:((strong(X)<~>~funny(X))=>(~quiet(X)|~humble(X))))&
((?[X]:(~quiet(X)))<=>((kind(alice)|calm(alice))))&
(![X]:(creative(X)<=>(calm(X)<~>creative(X))))&
(![X]:(~calm(X)=>(old(X)&wise(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((~tall(X)&curious(X))=>~humble(X)))&
((?[X]:((~generous(X)<~>happy(X))))<=>(?[X]:((wise(X)|tall(X)))))&
(![X]:((~quiet(X)<~>~brave(X))=>(rich(X)&humble(X))))&
((?[X]:((tall(X)&kind(X))))=>(~old(alice)))&
(![X]:(~humble(X)<=>(~funny(X)<~>creative(X))))&
(![X]:((curious(X)|tall(X))=>~brave(X)))&
(![X]:(old(X)<=>(creative(X)|~humble(X))))&
((~patient(mary)|~humble(mary)))&
(?[X]:((~humble(X)<~>generous(X))))&
(?[X]:((~tall(X)&~patient(X))))&
(generous(susan))&
(?[X]:((humble(X)|quiet(X))))&
((~strong(lucy)|~humble(lucy)))&
(~patient(fred)) | happy(susan) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 964976698960779853539673
% SZS output start Proof for 964976698960779853539673
1. ! [X0] : (creative(X0) => (curious(X0) & creative(X0))) [input p0]
4. ! [X0] : (creative(X0) <=> (calm(X0) <~> creative(X0))) [input p3]
5. ! [X0] : (~calm(X0) => (wise(X0) & old(X0))) [input p4]
6. ? [X0] : ~brave(X0) <=> ? [X0] : ~old(X0) [input p5]
7. ? [X0] : ~happy(X0) <=> ? [X0] : (humble(X0) | ~wise(X0)) [input p6]
13. ! [X0] : ((tall(X0) | curious(X0)) => ~brave(X0)) [input p12]
14. ! [X0] : (old(X0) <=> (~humble(X0) | creative(X0))) [input p13]
22. ~happy(susan) [input hypothesis]
23. ? [X0] : ~brave(X0) <=> ? [X1] : ~old(X1) [rectify 6]
24. ? [X0] : ~happy(X0) <=> ? [X1] : (humble(X1) | ~wise(X1)) [rectify 7]
30. ! [X0] : ((curious(X0) & creative(X0)) | ~creative(X0)) [ennf transformation 1]
33. ! [X0] : ((wise(X0) & old(X0)) | calm(X0)) [ennf transformation 5]
38. ! [X0] : (~brave(X0) | (~tall(X0) & ~curious(X0))) [ennf transformation 13]
45. ! [X0] : ((creative(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ~creative(X0))) [nnf transformation 4]
46. (? [X0] : ~brave(X0) | ! [X1] : old(X1)) & (? [X1] : ~old(X1) | ! [X0] : brave(X0)) [nnf transformation 23]
47. (? [X0] : ~brave(X0) | ! [X1] : old(X1)) & (? [X2] : ~old(X2) | ! [X3] : brave(X3)) [rectify 46]
48. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
49. ? [X2] : ~old(X2) => ~old(sK2) [choice axiom]
50. (~brave(sK1) | ! [X1] : old(X1)) & (~old(sK2) | ! [X3] : brave(X3)) [skolemisation 47,49,48]
51. (? [X0] : ~happy(X0) | ! [X1] : (~humble(X1) & wise(X1))) & (? [X1] : (humble(X1) | ~wise(X1)) | ! [X0] : happy(X0)) [nnf transformation 24]
52. (? [X0] : ~happy(X0) | ! [X1] : (~humble(X1) & wise(X1))) & (? [X2] : (humble(X2) | ~wise(X2)) | ! [X3] : happy(X3)) [rectify 51]
53. ? [X0] : ~happy(X0) => ~happy(sK3) [choice axiom]
54. ? [X2] : (humble(X2) | ~wise(X2)) => (humble(sK4) | ~wise(sK4)) [choice axiom]
55. (~happy(sK3) | ! [X1] : (~humble(X1) & wise(X1))) & ((humble(sK4) | ~wise(sK4)) | ! [X3] : happy(X3)) [skolemisation 52,54,53]
63. ! [X0] : ((old(X0) | (humble(X0) & ~creative(X0))) & ((~humble(X0) | creative(X0)) | ~old(X0))) [nnf transformation 14]
64. ! [X0] : ((old(X0) | (humble(X0) & ~creative(X0))) & (~humble(X0) | creative(X0) | ~old(X0))) [flattening 63]
73. ~creative(X0) | curious(X0) [cnf transformation 30]
80. ~creative(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 45]
81. creative(X0) | creative(X0) | ~calm(X0) [cnf transformation 45]
83. old(X0) | calm(X0) [cnf transformation 33]
84. wise(X0) | calm(X0) [cnf transformation 33]
85. ~old(sK2) | brave(X3) [cnf transformation 50]
87. humble(sK4) | ~wise(sK4) | happy(X3) [cnf transformation 55]
104. ~brave(X0) | ~curious(X0) [cnf transformation 38]
106. ~humble(X0) | creative(X0) | ~old(X0) [cnf transformation 64]
115. ~happy(susan) [cnf transformation 22]
116. ~creative(X0) | ~calm(X0) [duplicate literal removal 80]
117. ~calm(X0) | creative(X0) [duplicate literal removal 81]
136. ~calm(X0) [subsumption resolution 116,117]
137. wise(X0) [subsumption resolution 84,136]
138. old(X0) [subsumption resolution 83,136]
139. brave(X3) [subsumption resolution 85,138]
148. humble(sK4) | happy(X3) [subsumption resolution 87,137]
150. 7 <=> ! [X3] : happy(X3) [avatar definition]
151. happy(X3) <- (7) [avatar component clause 150]
153. 8 <=> humble(sK4) [avatar definition]
155. humble(sK4) <- (8) [avatar component clause 153]
156. 7 | 8 [avatar split clause 148,153,150]
178. ~curious(X0) [subsumption resolution 104,139]
179. ~humble(X0) | creative(X0) [subsumption resolution 106,138]
201. $false <- (7) [resolution 151,115]
202. ~7 [avatar contradiction clause 201]
207. creative(sK4) <- (8) [resolution 179,155]
211. curious(sK4) <- (8) [resolution 207,73]
212. $false <- (8) [subsumption resolution 211,178]
213. ~8 [avatar contradiction clause 212]
214. $false [avatar sat refutation 156,202,213]
% SZS output end Proof for 964976698960779853539673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not strong is not tall and vice versa. If someone is not generous then john is not strong. Everyone who is both calm and not humble is not humble or rich. If someone is both happy and brave then mary is strong or happy. Everyone who is old is both quiet and not wise and vice versa. Everyone who is both not strong and rich is wise. If someone is not quiet then someone is generous. Everyone who is wise is either not kind or not happy and vice versa. Everyone who is either funny or happy is strong and vice versa. If someone is both kind and funny then susan is curious and vice versa. Everyone who is happy is either wise or old and vice versa. Everyone who is not quiet or not happy is both quiet and calm. If lucy is both old and rich then someone is both not rich and tall and vice versa. If paul is both humble and brave then mary is both not old and brave. If susan is both curious and not rich then someone is either not wise or calm. Everyone who is not kind is rich. Susan is either not humble or quiet. John is either kind or humble. Someone is not strong. Someone is both brave and funny. Mary is either not rich or tall. Lucy is both not funny and curious. | Lucy is not brave. | neutral | (![X]:((humble(X)&~strong(X))<=>~tall(X)))&
((?[X]:(~generous(X)))=>(~strong(john)))&
(![X]:((calm(X)&~humble(X))=>(~humble(X)|rich(X))))&
((?[X]:((happy(X)&brave(X))))=>((strong(mary)|happy(mary))))&
(![X]:(old(X)<=>(quiet(X)&~wise(X))))&
(![X]:((~strong(X)&rich(X))=>wise(X)))&
((?[X]:(~quiet(X)))=>(?[X]:(generous(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>~happy(X))))&
(![X]:((funny(X)<~>happy(X))<=>strong(X)))&
((?[X]:((kind(X)&funny(X))))<=>(curious(susan)))&
(![X]:(happy(X)<=>(wise(X)<~>old(X))))&
(![X]:((~quiet(X)|~happy(X))=>(quiet(X)&calm(X))))&
(((old(lucy)&rich(lucy)))<=>(?[X]:((~rich(X)&tall(X)))))&
(((humble(paul)&brave(paul)))=>((~old(mary)&brave(mary))))&
(((curious(susan)&~rich(susan)))=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:(~kind(X)=>rich(X)))&
((~humble(susan)<~>quiet(susan)))&
((kind(john)<~>humble(john)))&
(?[X]:(~strong(X)))&
(?[X]:((brave(X)&funny(X))))&
((~rich(mary)<~>tall(mary)))&
((~funny(lucy)&curious(lucy))) | ~brave(lucy) | [] | null | 0 |
Everyone who is funny is not happy.
If paul is either not strong or not creative then someone is both not happy and not patient and vice versa.
If someone is not happy then paul is both not humble and not funny and vice versa.
Everyone who is both quiet and not humble is generous and vice versa.
If john is either not generous or not patient then someone is not rich and vice versa.
If someone is both not tall and rich then john is either old or humble.
If someone is either kind or calm then alice is not calm and vice versa.
If paul is either tall or not curious then paul is curious and vice versa.
Everyone who is calm or not calm is humble and vice versa.
Everyone who is generous is not curious.
Everyone who is both generous and happy is not curious or not humble.
If someone is not curious then someone is both not curious and not calm and vice versa.
If someone is not generous or funny then john is not curious.
If alice is either creative or wise then someone is either old or creative.
If someone is not curious or not funny then someone is both not calm and not patient and vice versa.
If alice is not creative or not humble then paul is patient.
Someone is not patient or quiet.
John is either not calm or not creative.
Susan is tall.
Fred is not generous or funny.
Someone is either creative or not quiet.
Paul is both not strong and not curious. | Susan is not creative. | neutral | (![X]:(funny(X)=>~happy(X)))&
(((~strong(paul)<~>~creative(paul)))<=>(?[X]:((~happy(X)&~patient(X)))))&
((?[X]:(~happy(X)))<=>((~humble(paul)&~funny(paul))))&
(![X]:((quiet(X)&~humble(X))<=>generous(X)))&
(((~generous(john)<~>~patient(john)))<=>(?[X]:(~rich(X))))&
((?[X]:((~tall(X)&rich(X))))=>((old(john)<~>humble(john))))&
((?[X]:((kind(X)<~>calm(X))))<=>(~calm(alice)))&
(((tall(paul)<~>~curious(paul)))<=>(curious(paul)))&
(![X]:((calm(X)|~calm(X))<=>humble(X)))&
(![X]:(generous(X)=>~curious(X)))&
(![X]:((generous(X)&happy(X))=>(~curious(X)|~humble(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((~generous(X)|funny(X))))=>(~curious(john)))&
(((creative(alice)<~>wise(alice)))=>(?[X]:((old(X)<~>creative(X)))))&
((?[X]:((~curious(X)|~funny(X))))<=>(?[X]:((~calm(X)&~patient(X)))))&
(((~creative(alice)|~humble(alice)))=>(patient(paul)))&
(?[X]:((~patient(X)|quiet(X))))&
((~calm(john)<~>~creative(john)))&
(tall(susan))&
((~generous(fred)|funny(fred)))&
(?[X]:((creative(X)<~>~quiet(X))))&
((~strong(paul)&~curious(paul))) | ~creative(susan) | [] | null | 0 |
If someone is kind then someone is humble or not generous.
If mary is both calm and not wise then someone is either quiet or brave.
Everyone who is either humble or not old is not curious.
If someone is generous then someone is wise.
If someone is both not quiet and old then mary is either kind or funny.
Everyone who is quiet or not brave is both brave and rich and vice versa.
If paul is either tall or strong then lucy is either calm or not generous and vice versa.
Everyone who is both kind and not brave is not strong or not brave.
If fred is both generous and not old then fred is both rich and creative and vice versa.
Everyone who is both not calm and not kind is either not creative or funny.
Everyone who is kind is either curious or rich.
If mary is either patient or not kind then paul is both not humble and strong.
Everyone who is not generous or not quiet is brave or not curious.
Everyone who is both not humble and not generous is not funny and vice versa.
If someone is not strong then john is both strong and tall and vice versa.
Everyone who is not wise or brave is not patient.
Someone is either not quiet or not happy.
John is both funny and generous.
Alice is both kind and quiet.
Someone is either calm or not patient.
Someone is both strong and not creative.
Someone is either not old or wise.
Someone is brave or not quiet.
Someone is both wise and rich. | John is patient. | contradiction | ((?[X]:(kind(X)))=>(?[X]:((humble(X)|~generous(X)))))&
(((calm(mary)&~wise(mary)))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:((humble(X)<~>~old(X))=>~curious(X)))&
((?[X]:(generous(X)))=>(?[X]:(wise(X))))&
((?[X]:((~quiet(X)&old(X))))=>((kind(mary)<~>funny(mary))))&
(![X]:((quiet(X)|~brave(X))<=>(brave(X)&rich(X))))&
(((tall(paul)<~>strong(paul)))<=>((calm(lucy)<~>~generous(lucy))))&
(![X]:((kind(X)&~brave(X))=>(~strong(X)|~brave(X))))&
(((generous(fred)&~old(fred)))<=>((rich(fred)&creative(fred))))&
(![X]:((~calm(X)&~kind(X))=>(~creative(X)<~>funny(X))))&
(![X]:(kind(X)=>(curious(X)<~>rich(X))))&
(((patient(mary)<~>~kind(mary)))=>((~humble(paul)&strong(paul))))&
(![X]:((~generous(X)|~quiet(X))=>(brave(X)|~curious(X))))&
(![X]:((~humble(X)&~generous(X))<=>~funny(X)))&
((?[X]:(~strong(X)))<=>((strong(john)&tall(john))))&
(![X]:((~wise(X)|brave(X))=>~patient(X)))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((funny(john)&generous(john)))&
((kind(alice)&quiet(alice)))&
(?[X]:((calm(X)<~>~patient(X))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
(?[X]:((wise(X)&rich(X)))) | patient(john) | [
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4760051435688218025222699
% SZS output start Proof for 4760051435688218025222699
6. ! [X0] : ((~brave(X0) | quiet(X0)) <=> (rich(X0) & brave(X0))) [input p5]
16. ! [X0] : ((brave(X0) | ~wise(X0)) => ~patient(X0)) [input p15]
25. patient(john) [input hypothesis]
42. ! [X0] : (~patient(X0) | (~brave(X0) & wise(X0))) [ennf transformation 16]
54. ! [X0] : (((~brave(X0) | quiet(X0)) | (~rich(X0) | ~brave(X0))) & ((rich(X0) & brave(X0)) | (brave(X0) & ~quiet(X0)))) [nnf transformation 6]
55. ! [X0] : ((~brave(X0) | quiet(X0) | ~rich(X0) | ~brave(X0)) & ((rich(X0) & brave(X0)) | (brave(X0) & ~quiet(X0)))) [flattening 54]
93. brave(X0) | brave(X0) [cnf transformation 55]
127. ~patient(X0) | ~brave(X0) [cnf transformation 42]
143. patient(john) [cnf transformation 25]
144. brave(X0) [duplicate literal removal 93]
271. ~patient(X0) [subsumption resolution 127,144]
293. $false [subsumption resolution 143,271]
% SZS output end Proof for 4760051435688218025222699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and strong is not creative or creative.
If someone is both not brave and curious then someone is either not happy or creative and vice versa.
Everyone who is both funny and kind is not strong.
Everyone who is tall or calm is both not calm and creative and vice versa.
If john is not kind or not patient then lucy is both humble and creative and vice versa.
Everyone who is happy or not funny is both not strong and not happy and vice versa.
Everyone who is both brave and not generous is both curious and quiet and vice versa.
If someone is both not curious and not wise then paul is wise or patient.
If alice is rich then someone is either funny or brave and vice versa.
If someone is patient or not funny then someone is not humble or not happy.
If mary is brave or generous then mary is not humble.
Everyone who is either kind or quiet is strong and vice versa.
Everyone who is tall or wise is not quiet or happy and vice versa.
Everyone who is not strong or not creative is either curious or not funny and vice versa.
Everyone who is both not happy and not brave is not tall.
If mary is strong then mary is not creative or not brave and vice versa.
Mary is either not happy or wise.
Someone is either humble or tall.
Someone is both old and not funny.
Lucy is either patient or not happy.
Paul is either not happy or old. | Lucy is not patient. | entailment | (![X]:((old(X)&strong(X))=>(~creative(X)|creative(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((funny(X)&kind(X))=>~strong(X)))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(![X]:((happy(X)|~funny(X))<=>(~strong(X)&~happy(X))))&
(![X]:((brave(X)&~generous(X))<=>(curious(X)&quiet(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((wise(paul)|patient(paul))))&
((rich(alice))<=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~humble(X)|~happy(X)))))&
(((brave(mary)|generous(mary)))=>(~humble(mary)))&
(![X]:((kind(X)<~>quiet(X))<=>strong(X)))&
(![X]:((tall(X)|wise(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~strong(X)|~creative(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&~brave(X))=>~tall(X)))&
((strong(mary))<=>((~creative(mary)|~brave(mary))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((old(X)&~funny(X))))&
((patient(lucy)<~>~happy(lucy)))&
((~happy(paul)<~>old(paul))) | ~patient(lucy) | [
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1364599297898013881611958
% SZS output start Proof for 1364599297898013881611958
6. ! [X0] : ((~funny(X0) | happy(X0)) <=> (~happy(X0) & ~strong(X0))) [input p5]
20. patient(lucy) <~> ~happy(lucy) [input p19]
22. patient(lucy) [input hypothesis]
44. ! [X0] : (((~funny(X0) | happy(X0)) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [nnf transformation 6]
45. ! [X0] : ((~funny(X0) | happy(X0) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [flattening 44]
68. (happy(lucy) | ~patient(lucy)) & (~happy(lucy) | patient(lucy)) [nnf transformation 20]
90. ~happy(X0) | ~happy(X0) [cnf transformation 45]
131. happy(lucy) | ~patient(lucy) [cnf transformation 68]
134. patient(lucy) [cnf transformation 22]
135. ~happy(X0) [duplicate literal removal 90]
266. ~patient(lucy) [subsumption resolution 131,135]
268. $false [subsumption resolution 134,266]
% SZS output end Proof for 1364599297898013881611958
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not strong or funny is humble. If fred is either funny or not old then someone is either not humble or creative and vice versa. If lucy is not rich or creative then fred is both not funny and generous. Everyone who is both old and not wise is not tall or not creative and vice versa. Everyone who is creative is old and vice versa. If susan is curious then lucy is not rich or rich. Everyone who is either not funny or quiet is both generous and humble. Everyone who is funny is not strong or strong. If someone is not patient or patient then fred is creative or humble and vice versa. If someone is either not creative or not wise then alice is not rich or not quiet. If susan is either rich or not quiet then someone is both not wise and calm and vice versa. If john is not tall or not brave then someone is either calm or generous. Everyone who is both funny and not humble is both generous and not quiet and vice versa. If john is either not generous or not rich then someone is not creative or not wise. If mary is both not generous and brave then susan is not rich and vice versa. Someone is either not rich or humble. Someone is either not generous or not calm. Someone is not patient or not humble. Someone is either brave or strong. Mary is both not patient and not curious. Someone is either not brave or quiet. | Fred is funny. | contradiction | (![X]:((~strong(X)<~>funny(X))=>humble(X)))&
(((funny(fred)<~>~old(fred)))<=>(?[X]:((~humble(X)<~>creative(X)))))&
(((~rich(lucy)|creative(lucy)))=>((~funny(fred)&generous(fred))))&
(![X]:((old(X)&~wise(X))<=>(~tall(X)|~creative(X))))&
(![X]:(creative(X)<=>old(X)))&
((curious(susan))=>((~rich(lucy)|rich(lucy))))&
(![X]:((~funny(X)<~>quiet(X))=>(generous(X)&humble(X))))&
(![X]:(funny(X)=>(~strong(X)|strong(X))))&
((?[X]:((~patient(X)|patient(X))))<=>((creative(fred)|humble(fred))))&
((?[X]:((~creative(X)<~>~wise(X))))=>((~rich(alice)|~quiet(alice))))&
(((rich(susan)<~>~quiet(susan)))<=>(?[X]:((~wise(X)&calm(X)))))&
(((~tall(john)|~brave(john)))=>(?[X]:((calm(X)<~>generous(X)))))&
(![X]:((funny(X)&~humble(X))<=>(generous(X)&~quiet(X))))&
(((~generous(john)<~>~rich(john)))=>(?[X]:((~creative(X)|~wise(X)))))&
(((~generous(mary)&brave(mary)))<=>(~rich(susan)))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(?[X]:((~patient(X)|~humble(X))))&
(?[X]:((brave(X)<~>strong(X))))&
((~patient(mary)&~curious(mary)))&
(?[X]:((~brave(X)<~>quiet(X)))) | funny(fred) | [
"p2",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 306808900768598532118387
% SZS output start Proof for 306808900768598532118387
3. (creative(lucy) | ~rich(lucy)) => (generous(fred) & ~funny(fred)) [input p2]
4. ! [X0] : ((~wise(X0) & old(X0)) <=> (~creative(X0) | ~tall(X0))) [input p3]
5. ! [X0] : (creative(X0) <=> old(X0)) [input p4]
22. funny(fred) [input hypothesis]
26. (generous(fred) & ~funny(fred)) | (~creative(lucy) & rich(lucy)) [ennf transformation 3]
39. ! [X0] : (((~wise(X0) & old(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 4]
40. ! [X0] : (((~wise(X0) & old(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | wise(X0) | ~old(X0))) [flattening 39]
41. ! [X0] : ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))) [nnf transformation 5]
88. ~funny(fred) | ~creative(lucy) [cnf transformation 26]
93. old(X0) | creative(X0) [cnf transformation 40]
97. creative(X0) | ~old(X0) [cnf transformation 41]
138. funny(fred) [cnf transformation 22]
143. 2 <=> funny(fred) [avatar definition]
170. 7 <=> creative(lucy) [avatar definition]
172. ~creative(lucy) <- (~7) [avatar component clause 170]
183. ~7 | ~2 [avatar split clause 88,143,170]
185. creative(X0) [subsumption resolution 97,93]
322. 2 [avatar split clause 138,143]
323. $false <- (~7) [subsumption resolution 172,185]
324. 7 [avatar contradiction clause 323]
327. $false [avatar sat refutation 183,322,324]
% SZS output end Proof for 306808900768598532118387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
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