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
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either not calm or quiet is both old and not brave.
If someone is both kind and not humble then someone is not creative and vice versa.
Everyone who is either brave or humble is rich.
Everyone who is not happy or not old is either not curious or brave.
Everyone who is both not generous and calm is humble and vice versa.
If someone is either patient or not patient then susan is not quiet or not old.
Everyone who is calm or rich is either not rich or not brave.
Everyone who is either not happy or not calm is either kind or calm.
Everyone who is both not creative and humble is both quiet and humble and vice versa.
If someone is either wise or not quiet then alice is both creative and humble and vice versa.
If paul is either generous or not generous then someone is both tall and creative.
If someone is not kind or not rich then mary is both not rich and patient.
Everyone who is both not strong and quiet is not generous or calm and vice versa.
If someone is both not funny and happy then john is both not happy and tall and vice versa.
If someone is both funny and creative then someone is not humble.
Someone is not funny or not patient.
Paul is both not tall and happy.
Alice is either not wise or curious.
Lucy is both creative and not strong.
Someone is kind.
John is not humble.
Someone is not rich.
John is either wise or not kind. | Mary is not humble. | entailment | (![X]:((~calm(X)<~>quiet(X))=>(old(X)&~brave(X))))&
((?[X]:((kind(X)&~humble(X))))<=>(?[X]:(~creative(X))))&
(![X]:((brave(X)<~>humble(X))=>rich(X)))&
(![X]:((~happy(X)|~old(X))=>(~curious(X)<~>brave(X))))&
(![X]:((~generous(X)&calm(X))<=>humble(X)))&
((?[X]:((patient(X)<~>~patient(X))))=>((~quiet(susan)|~old(susan))))&
(![X]:((calm(X)|rich(X))=>(~rich(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(kind(X)<~>calm(X))))&
(![X]:((~creative(X)&humble(X))<=>(quiet(X)&humble(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((creative(alice)&humble(alice))))&
(((generous(paul)<~>~generous(paul)))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~kind(X)|~rich(X))))=>((~rich(mary)&patient(mary))))&
(![X]:((~strong(X)&quiet(X))<=>(~generous(X)|calm(X))))&
((?[X]:((~funny(X)&happy(X))))<=>((~happy(john)&tall(john))))&
((?[X]:((funny(X)&creative(X))))=>(?[X]:(~humble(X))))&
(?[X]:((~funny(X)|~patient(X))))&
((~tall(paul)&happy(paul)))&
((~wise(alice)<~>curious(alice)))&
((creative(lucy)&~strong(lucy)))&
(?[X]:(kind(X)))&
(~humble(john))&
(?[X]:(~rich(X)))&
((wise(john)<~>~kind(john))) | ~humble(mary) | [
"p0",
"p2",
"p4",
"p11",
"p12",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 4884826287563696701852579
% SZS output start Proof for 4884826287563696701852579
1. ! [X0] : ((~calm(X0) <~> quiet(X0)) => (~brave(X0) & old(X0))) [input p0]
3. ! [X0] : ((brave(X0) <~> humble(X0)) => rich(X0)) [input p2]
5. ! [X0] : ((calm(X0) & ~generous(X0)) <=> humble(X0)) [input p4]
12. ? [X0] : (~rich(X0) | ~kind(X0)) => (patient(mary) & ~rich(mary)) [input p11]
13. ! [X0] : ((quiet(X0) & ~strong(X0)) <=> (calm(X0) | ~generous(X0))) [input p12]
22. ? [X0] : ~rich(X0) [input p21]
24. humble(mary) [input hypothesis]
27. ! [X0] : ((~brave(X0) & old(X0)) | (~calm(X0) <=> quiet(X0))) [ennf transformation 1]
28. ! [X0] : (rich(X0) | (brave(X0) <=> humble(X0))) [ennf transformation 3]
35. (patient(mary) & ~rich(mary)) | ! [X0] : (rich(X0) & kind(X0)) [ennf transformation 12]
37. ! [X0] : ((~brave(X0) & old(X0)) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) [nnf transformation 27]
43. ! [X0] : (rich(X0) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0)))) [nnf transformation 28]
45. ! [X0] : (((calm(X0) & ~generous(X0)) | ~humble(X0)) & (humble(X0) | (~calm(X0) | generous(X0)))) [nnf transformation 5]
46. ! [X0] : (((calm(X0) & ~generous(X0)) | ~humble(X0)) & (humble(X0) | ~calm(X0) | generous(X0))) [flattening 45]
60. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~calm(X0) & generous(X0))) & ((calm(X0) | ~generous(X0)) | (~quiet(X0) | strong(X0)))) [nnf transformation 13]
61. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~calm(X0) & generous(X0))) & (calm(X0) | ~generous(X0) | ~quiet(X0) | strong(X0))) [flattening 60]
75. ? [X0] : ~rich(X0) => ~rich(sK8) [choice axiom]
76. ~rich(sK8) [skolemisation 22,75]
81. ~brave(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 37]
86. ~humble(X0) | brave(X0) | rich(X0) [cnf transformation 43]
93. ~humble(X0) | calm(X0) [cnf transformation 46]
119. ~rich(mary) | rich(X0) [cnf transformation 35]
126. ~calm(X0) | quiet(X0) [cnf transformation 61]
141. ~rich(sK8) [cnf transformation 76]
144. humble(mary) [cnf transformation 24]
236. 19 <=> ! [X0] : rich(X0) [avatar definition]
237. rich(X0) <- (19) [avatar component clause 236]
248. 22 <=> rich(mary) [avatar definition]
250. ~rich(mary) <- (~22) [avatar component clause 248]
251. 19 | ~22 [avatar split clause 119,248,236]
313. calm(mary) [resolution 93,144]
316. quiet(mary) [resolution 126,313]
324. brave(mary) | rich(mary) [resolution 86,144]
326. brave(mary) <- (~22) [subsumption resolution 324,250]
344. ~calm(mary) | ~quiet(mary) <- (~22) [resolution 326,81]
346. ~quiet(mary) <- (~22) [subsumption resolution 344,313]
347. $false <- (~22) [subsumption resolution 346,316]
348. 22 [avatar contradiction clause 347]
354. $false <- (19) [resolution 237,141]
356. ~19 [avatar contradiction clause 354]
357. $false [avatar sat refutation 251,348,356]
% SZS output end Proof for 4884826287563696701852579
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not old is both not funny and wise. Everyone who is humble or not wise is both not brave and not curious and vice versa. If someone is either kind or rich then fred is wise or not strong. Everyone who is both not happy and calm is both not tall and old and vice versa. Everyone who is curious is patient. Everyone who is patient or not humble is either strong or not curious and vice versa. If someone is not kind then john is generous or creative. Everyone who is creative or not calm is either generous or curious and vice versa. If someone is not old then alice is wise and vice versa. Everyone who is strong is not quiet or not creative and vice versa. If mary is both not curious and rich then someone is old and vice versa. Everyone who is wise is both strong and not old and vice versa. If someone is not curious or rich then alice is not wise or not funny and vice versa. Everyone who is not funny is either humble or rich. Everyone who is wise or creative is both not patient and not wise and vice versa. Everyone who is happy or not quiet is either not creative or not funny. Lucy is either rich or quiet. Mary is either not kind or old. Mary is not strong. Lucy is tall or patient. | Alice is not tall. | contradiction | (![X]:((~tall(X)|~old(X))=>(~funny(X)&wise(X))))&
(![X]:((humble(X)|~wise(X))<=>(~brave(X)&~curious(X))))&
((?[X]:((kind(X)<~>rich(X))))=>((wise(fred)|~strong(fred))))&
(![X]:((~happy(X)&calm(X))<=>(~tall(X)&old(X))))&
(![X]:(curious(X)=>patient(X)))&
(![X]:((patient(X)|~humble(X))<=>(strong(X)<~>~curious(X))))&
((?[X]:(~kind(X)))=>((generous(john)|creative(john))))&
(![X]:((creative(X)|~calm(X))<=>(generous(X)<~>curious(X))))&
((?[X]:(~old(X)))<=>(wise(alice)))&
(![X]:(strong(X)<=>(~quiet(X)|~creative(X))))&
(((~curious(mary)&rich(mary)))<=>(?[X]:(old(X))))&
(![X]:(wise(X)<=>(strong(X)&~old(X))))&
((?[X]:((~curious(X)|rich(X))))<=>((~wise(alice)|~funny(alice))))&
(![X]:(~funny(X)=>(humble(X)<~>rich(X))))&
(![X]:((wise(X)|creative(X))<=>(~patient(X)&~wise(X))))&
(![X]:((happy(X)|~quiet(X))=>(~creative(X)<~>~funny(X))))&
((rich(lucy)<~>quiet(lucy)))&
((~kind(mary)<~>old(mary)))&
(~strong(mary))&
((tall(lucy)|patient(lucy))) | ~tall(alice) | [
"p0",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 1877965358219488641309324
% SZS output start Proof for 1877965358219488641309324
1. ! [X0] : ((~old(X0) | ~tall(X0)) => (wise(X0) & ~funny(X0))) [input p0]
15. ! [X0] : ((creative(X0) | wise(X0)) <=> (~wise(X0) & ~patient(X0))) [input p14]
21. ~tall(alice) [input hypothesis]
22. ! [X0] : ((wise(X0) & ~funny(X0)) | (old(X0) & tall(X0))) [ennf transformation 1]
58. ! [X0] : (((creative(X0) | wise(X0)) | (wise(X0) | patient(X0))) & ((~wise(X0) & ~patient(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 15]
59. ! [X0] : ((creative(X0) | wise(X0) | wise(X0) | patient(X0)) & ((~wise(X0) & ~patient(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 58]
65. wise(X0) | tall(X0) [cnf transformation 22]
111. ~wise(X0) | ~wise(X0) [cnf transformation 59]
124. ~tall(alice) [cnf transformation 21]
125. ~wise(X0) [duplicate literal removal 111]
249. tall(X0) [resolution 65,125]
250. $false [resolution 249,124]
% SZS output end Proof for 1877965358219488641309324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is patient is not strong or not curious and vice versa. If someone is creative or not humble then someone is either old or not happy and vice versa. Everyone who is either not curious or not funny is curious or not humble and vice versa. If someone is both rich and not humble then john is not brave or not calm and vice versa. If paul is not tall or rich then mary is both wise and not curious and vice versa. If someone is both kind and strong then john is not patient or happy. Everyone who is not brave is not quiet or not humble. Everyone who is either not old or humble is either creative or calm. Everyone who is either not wise or not creative is tall and vice versa. If john is tall then mary is either not curious or not old. If lucy is not happy then mary is not generous and vice versa. Everyone who is both not kind and not happy is not quiet and vice versa. Everyone who is both not curious and wise is both not old and not happy and vice versa. If someone is both not strong and quiet then someone is not calm or not happy. If susan is rich or funny then paul is old or patient and vice versa. Everyone who is both not generous and not wise is not brave. Someone is not curious or not kind. Mary is not rich. John is either not happy or not brave. Susan is not rich or funny. Someone is not brave or creative. Someone is not strong or generous. Someone is either not tall or patient. Fred is quiet or generous. | Susan is funny. | neutral | (![X]:(patient(X)<=>(~strong(X)|~curious(X))))&
((?[X]:((creative(X)|~humble(X))))<=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:((~curious(X)<~>~funny(X))<=>(curious(X)|~humble(X))))&
((?[X]:((rich(X)&~humble(X))))<=>((~brave(john)|~calm(john))))&
(((~tall(paul)|rich(paul)))<=>((wise(mary)&~curious(mary))))&
((?[X]:((kind(X)&strong(X))))=>((~patient(john)|happy(john))))&
(![X]:(~brave(X)=>(~quiet(X)|~humble(X))))&
(![X]:((~old(X)<~>humble(X))=>(creative(X)<~>calm(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>tall(X)))&
((tall(john))=>((~curious(mary)<~>~old(mary))))&
((~happy(lucy))<=>(~generous(mary)))&
(![X]:((~kind(X)&~happy(X))<=>~quiet(X)))&
(![X]:((~curious(X)&wise(X))<=>(~old(X)&~happy(X))))&
((?[X]:((~strong(X)&quiet(X))))=>(?[X]:((~calm(X)|~happy(X)))))&
(((rich(susan)|funny(susan)))<=>((old(paul)|patient(paul))))&
(![X]:((~generous(X)&~wise(X))=>~brave(X)))&
(?[X]:((~curious(X)|~kind(X))))&
(~rich(mary))&
((~happy(john)<~>~brave(john)))&
((~rich(susan)|funny(susan)))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((~strong(X)|generous(X))))&
(?[X]:((~tall(X)<~>patient(X))))&
((quiet(fred)|generous(fred))) | funny(susan) | []
| null | 0 |
If mary is not calm or old then someone is creative and vice versa.
Everyone who is curious or not quiet is curious or not humble and vice versa.
If someone is not quiet then someone is kind or humble.
If fred is either wise or not old then someone is either not patient or patient.
Everyone who is not old is both curious and kind.
If someone is brave or not kind then paul is either humble or not strong.
Everyone who is both rich and patient is either not strong or not calm and vice versa.
Everyone who is both curious and not quiet is both funny and not old and vice versa.
Everyone who is not wise is either curious or rich.
Everyone who is patient or rich is not patient or generous.
Everyone who is not patient or humble is generous or patient.
Everyone who is both tall and not brave is not creative.
If paul is either not humble or rich then someone is either not humble or not patient and vice versa.
Everyone who is not brave or not calm is not funny and vice versa.
Everyone who is not old is humble and vice versa.
Everyone who is both not old and curious is either not funny or not old.
Alice is both humble and not old.
Fred is patient or not kind.
Someone is both not wise and not funny.
Someone is not wise or not kind.
Someone is wise or not patient.
Someone is tall or calm.
Someone is patient or not rich. | Paul is not quiet. | neutral | (((~calm(mary)|old(mary)))<=>(?[X]:(creative(X))))&
(![X]:((curious(X)|~quiet(X))<=>(curious(X)|~humble(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((kind(X)|humble(X)))))&
(((wise(fred)<~>~old(fred)))=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:(~old(X)=>(curious(X)&kind(X))))&
((?[X]:((brave(X)|~kind(X))))=>((humble(paul)<~>~strong(paul))))&
(![X]:((rich(X)&patient(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:((curious(X)&~quiet(X))<=>(funny(X)&~old(X))))&
(![X]:(~wise(X)=>(curious(X)<~>rich(X))))&
(![X]:((patient(X)|rich(X))=>(~patient(X)|generous(X))))&
(![X]:((~patient(X)|humble(X))=>(generous(X)|patient(X))))&
(![X]:((tall(X)&~brave(X))=>~creative(X)))&
(((~humble(paul)<~>rich(paul)))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((~brave(X)|~calm(X))<=>~funny(X)))&
(![X]:(~old(X)<=>humble(X)))&
(![X]:((~old(X)&curious(X))=>(~funny(X)<~>~old(X))))&
((humble(alice)&~old(alice)))&
((patient(fred)|~kind(fred)))&
(?[X]:((~wise(X)&~funny(X))))&
(?[X]:((~wise(X)|~kind(X))))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:((patient(X)|~rich(X)))) | ~quiet(paul) | []
| null | 0 |
If john is either curious or wise then someone is creative or tall and vice versa. Everyone who is both not happy and not tall is both not funny and quiet. If someone is both not strong and humble then someone is either not tall or not quiet and vice versa. If someone is not humble or not wise then someone is curious or not quiet and vice versa. If someone is either not strong or tall then mary is humble or not happy and vice versa. If someone is either not quiet or not curious then someone is either strong or quiet and vice versa. Everyone who is curious or not old is wise or calm and vice versa. Everyone who is both strong and tall is either not patient or quiet and vice versa. If fred is humble then lucy is not wise and vice versa. If john is either not generous or not rich then susan is not rich and vice versa. Everyone who is either humble or happy is either not wise or happy and vice versa. Everyone who is either curious or generous is patient or quiet. If mary is either not patient or rich then someone is generous and vice versa. Everyone who is humble or creative is tall and vice versa. If fred is not wise or kind then someone is rich or patient. Everyone who is humble is both not quiet and not patient. John is not quiet or happy. Someone is not patient. Someone is either creative or rich. Lucy is calm or not generous. Paul is not patient or not creative. John is either not generous or calm. Fred is humble or not quiet. | Fred is humble. | contradiction | (((curious(john)<~>wise(john)))<=>(?[X]:((creative(X)|tall(X)))))&
(![X]:((~happy(X)&~tall(X))=>(~funny(X)&quiet(X))))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
((?[X]:((~humble(X)|~wise(X))))<=>(?[X]:((curious(X)|~quiet(X)))))&
((?[X]:((~strong(X)<~>tall(X))))<=>((humble(mary)|~happy(mary))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((curious(X)|~old(X))<=>(wise(X)|calm(X))))&
(![X]:((strong(X)&tall(X))<=>(~patient(X)<~>quiet(X))))&
((humble(fred))<=>(~wise(lucy)))&
(((~generous(john)<~>~rich(john)))<=>(~rich(susan)))&
(![X]:((humble(X)<~>happy(X))<=>(~wise(X)<~>happy(X))))&
(![X]:((curious(X)<~>generous(X))=>(patient(X)|quiet(X))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|creative(X))<=>tall(X)))&
(((~wise(fred)|kind(fred)))=>(?[X]:((rich(X)|patient(X)))))&
(![X]:(humble(X)=>(~quiet(X)&~patient(X))))&
((~quiet(john)|happy(john)))&
(?[X]:(~patient(X)))&
(?[X]:((creative(X)<~>rich(X))))&
((calm(lucy)|~generous(lucy)))&
((~patient(paul)|~creative(paul)))&
((~generous(john)<~>calm(john)))&
((humble(fred)|~quiet(fred))) | humble(fred) | [
"p2",
"p7",
"p13",
"p15",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 326821616095778544384739
% SZS output start Proof for 326821616095778544384739
3. ? [X0] : (humble(X0) & ~strong(X0)) <=> ? [X0] : (~tall(X0) <~> ~quiet(X0)) [input p2]
8. ! [X0] : ((tall(X0) & strong(X0)) <=> (~patient(X0) <~> quiet(X0))) [input p7]
14. ! [X0] : ((creative(X0) | humble(X0)) <=> tall(X0)) [input p13]
16. ! [X0] : (humble(X0) => (~patient(X0) & ~quiet(X0))) [input p15]
23. ~quiet(fred) | humble(fred) [input p22]
24. humble(fred) [input hypothesis]
25. ? [X0] : (humble(X0) & ~strong(X0)) <=> ? [X1] : (~tall(X1) <~> ~quiet(X1)) [rectify 3]
35. ! [X0] : ((~patient(X0) & ~quiet(X0)) | ~humble(X0)) [ennf transformation 16]
40. (? [X0] : (humble(X0) & ~strong(X0)) | ! [X1] : ((~tall(X1) | quiet(X1)) & (~quiet(X1) | tall(X1)))) & (? [X1] : ((quiet(X1) | tall(X1)) & (~quiet(X1) | ~tall(X1))) | ! [X0] : (~humble(X0) | strong(X0))) [nnf transformation 25]
41. (? [X0] : (humble(X0) & ~strong(X0)) | ! [X1] : ((~tall(X1) | quiet(X1)) & (~quiet(X1) | tall(X1)))) & (? [X2] : ((quiet(X2) | tall(X2)) & (~quiet(X2) | ~tall(X2))) | ! [X3] : (~humble(X3) | strong(X3))) [rectify 40]
42. ? [X0] : (humble(X0) & ~strong(X0)) => (humble(sK1) & ~strong(sK1)) [choice axiom]
43. ? [X2] : ((quiet(X2) | tall(X2)) & (~quiet(X2) | ~tall(X2))) => ((quiet(sK2) | tall(sK2)) & (~quiet(sK2) | ~tall(sK2))) [choice axiom]
44. ((humble(sK1) & ~strong(sK1)) | ! [X1] : ((~tall(X1) | quiet(X1)) & (~quiet(X1) | tall(X1)))) & (((quiet(sK2) | tall(sK2)) & (~quiet(sK2) | ~tall(sK2))) | ! [X3] : (~humble(X3) | strong(X3))) [skolemisation 41,43,42]
62. ! [X0] : (((tall(X0) & strong(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) & (((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (~tall(X0) | ~strong(X0)))) [nnf transformation 8]
63. ! [X0] : (((tall(X0) & strong(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) & (((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | ~tall(X0) | ~strong(X0))) [flattening 62]
72. ! [X0] : (((creative(X0) | humble(X0)) | ~tall(X0)) & (tall(X0) | (~creative(X0) & ~humble(X0)))) [nnf transformation 14]
73. ! [X0] : ((creative(X0) | humble(X0) | ~tall(X0)) & (tall(X0) | (~creative(X0) & ~humble(X0)))) [flattening 72]
92. ~strong(sK1) | ~tall(X1) | quiet(X1) [cnf transformation 44]
94. humble(sK1) | ~tall(X1) | quiet(X1) [cnf transformation 44]
119. patient(X0) | quiet(X0) | strong(X0) [cnf transformation 63]
143. ~humble(X0) | tall(X0) [cnf transformation 73]
147. ~humble(X0) | ~quiet(X0) [cnf transformation 35]
148. ~patient(X0) | ~humble(X0) [cnf transformation 35]
157. ~quiet(fred) | humble(fred) [cnf transformation 23]
158. humble(fred) [cnf transformation 24]
192. 7 <=> ! [X1] : (~tall(X1) | quiet(X1)) [avatar definition]
193. ~tall(X1) | quiet(X1) <- (7) [avatar component clause 192]
195. 8 <=> humble(sK1) [avatar definition]
197. humble(sK1) <- (8) [avatar component clause 195]
198. 7 | 8 [avatar split clause 94,195,192]
204. 10 <=> strong(sK1) [avatar definition]
206. ~strong(sK1) <- (~10) [avatar component clause 204]
207. 7 | ~10 [avatar split clause 92,204,192]
210. 11 <=> ! [X3] : (~humble(X3) | strong(X3)) [avatar definition]
211. ~humble(X3) | strong(X3) <- (11) [avatar component clause 210]
323. 37 <=> humble(fred) [avatar definition]
325. humble(fred) <- (37) [avatar component clause 323]
421. ~quiet(fred) [subsumption resolution 157,147]
422. 37 [avatar split clause 158,323]
424. tall(fred) <- (37) [resolution 143,325]
431. strong(sK1) <- (8, 11) [resolution 211,197]
433. $false <- (8, ~10, 11) [subsumption resolution 431,206]
434. ~8 | 10 | ~11 [avatar contradiction clause 433]
488. quiet(X0) | strong(X0) | ~humble(X0) [resolution 119,148]
492. strong(X0) | ~humble(X0) [subsumption resolution 488,147]
493. 11 [avatar split clause 492,210]
523. quiet(fred) <- (7, 37) [resolution 193,424]
530. $false <- (7, 37) [subsumption resolution 523,421]
531. ~7 | ~37 [avatar contradiction clause 530]
536. $false [avatar sat refutation 198,207,422,434,493,531]
% SZS output end Proof for 326821616095778544384739
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or brave is both strong and not brave.
If someone is wise or brave then susan is funny and vice versa.
If paul is not rich then someone is both not creative and creative and vice versa.
Everyone who is not rich is both not old and not patient.
If someone is both not funny and not kind then alice is both not creative and not old.
Everyone who is both not humble and curious is not funny or not strong and vice versa.
Everyone who is creative or not patient is funny and vice versa.
If someone is curious then paul is strong and vice versa.
Everyone who is either brave or happy is either quiet or not curious.
If mary is not rich or not creative then someone is old and vice versa.
Everyone who is either wise or kind is brave or humble and vice versa.
If someone is happy then john is happy or tall and vice versa.
If someone is not tall or not old then lucy is not patient and vice versa.
If paul is not funny then lucy is either not happy or calm.
If someone is either humble or rich then lucy is patient or brave.
Everyone who is not happy or brave is not kind and vice versa.
Someone is either kind or generous.
Susan is both calm and not creative.
Paul is not quiet or brave.
Lucy is not rich or not wise.
Someone is both not generous and not happy.
Lucy is patient.
Someone is funny.
Alice is not brave or not patient. | Lucy is wise. | contradiction | (![X]:((old(X)|brave(X))=>(strong(X)&~brave(X))))&
((?[X]:((wise(X)|brave(X))))<=>(funny(susan)))&
((~rich(paul))<=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:(~rich(X)=>(~old(X)&~patient(X))))&
((?[X]:((~funny(X)&~kind(X))))=>((~creative(alice)&~old(alice))))&
(![X]:((~humble(X)&curious(X))<=>(~funny(X)|~strong(X))))&
(![X]:((creative(X)|~patient(X))<=>funny(X)))&
((?[X]:(curious(X)))<=>(strong(paul)))&
(![X]:((brave(X)<~>happy(X))=>(quiet(X)<~>~curious(X))))&
(((~rich(mary)|~creative(mary)))<=>(?[X]:(old(X))))&
(![X]:((wise(X)<~>kind(X))<=>(brave(X)|humble(X))))&
((?[X]:(happy(X)))<=>((happy(john)|tall(john))))&
((?[X]:((~tall(X)|~old(X))))<=>(~patient(lucy)))&
((~funny(paul))=>((~happy(lucy)<~>calm(lucy))))&
((?[X]:((humble(X)<~>rich(X))))=>((patient(lucy)|brave(lucy))))&
(![X]:((~happy(X)|brave(X))<=>~kind(X)))&
(?[X]:((kind(X)<~>generous(X))))&
((calm(susan)&~creative(susan)))&
((~quiet(paul)|brave(paul)))&
((~rich(lucy)|~wise(lucy)))&
(?[X]:((~generous(X)&~happy(X))))&
(patient(lucy))&
(?[X]:(funny(X)))&
((~brave(alice)|~patient(alice))) | wise(lucy) | [
"p3",
"p12",
"p19",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 11725763628641876203231
% SZS output start Proof for 11725763628641876203231
4. ! [X0] : (~rich(X0) => (~patient(X0) & ~old(X0))) [input p3]
13. ? [X0] : (~old(X0) | ~tall(X0)) <=> ~patient(lucy) [input p12]
20. ~wise(lucy) | ~rich(lucy) [input p19]
22. patient(lucy) [input p21]
25. wise(lucy) [input hypothesis]
27. ! [X0] : ((~patient(X0) & ~old(X0)) | rich(X0)) [ennf transformation 4]
62. (? [X0] : (~old(X0) | ~tall(X0)) | patient(lucy)) & (~patient(lucy) | ! [X0] : (old(X0) & tall(X0))) [nnf transformation 13]
63. (? [X0] : (~old(X0) | ~tall(X0)) | patient(lucy)) & (~patient(lucy) | ! [X1] : (old(X1) & tall(X1))) [rectify 62]
64. ? [X0] : (~old(X0) | ~tall(X0)) => (~old(sK5) | ~tall(sK5)) [choice axiom]
65. ((~old(sK5) | ~tall(sK5)) | patient(lucy)) & (~patient(lucy) | ! [X1] : (old(X1) & tall(X1))) [skolemisation 63,64]
87. ~old(X0) | rich(X0) [cnf transformation 27]
118. ~patient(lucy) | old(X1) [cnf transformation 65]
132. ~wise(lucy) | ~rich(lucy) [cnf transformation 20]
135. patient(lucy) [cnf transformation 22]
138. wise(lucy) [cnf transformation 25]
231. 20 <=> patient(lucy) [avatar definition]
244. 23 <=> ! [X1] : old(X1) [avatar definition]
245. old(X1) <- (23) [avatar component clause 244]
246. 23 | ~20 [avatar split clause 118,231,244]
288. 32 <=> rich(lucy) [avatar definition]
290. ~rich(lucy) <- (~32) [avatar component clause 288]
292. 33 <=> wise(lucy) [avatar definition]
295. ~32 | ~33 [avatar split clause 132,292,288]
296. 20 [avatar split clause 135,231]
297. 33 [avatar split clause 138,292]
305. rich(X0) <- (23) [resolution 87,245]
306. $false <- (23, ~32) [resolution 305,290]
307. ~23 | 32 [avatar contradiction clause 306]
308. $false [avatar sat refutation 246,295,296,297,307]
% SZS output end Proof for 11725763628641876203231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not tall or not curious then someone is both humble and calm.
If someone is not curious then fred is not tall.
If someone is not strong then someone is both calm and not happy.
If susan is both not rich and wise then mary is either not kind or not wise and vice versa.
If lucy is either not generous or not calm then john is either wise or not old.
If alice is not strong or rich then fred is strong or not humble.
If someone is creative then fred is both happy and not patient and vice versa.
Everyone who is wise is either not happy or not patient and vice versa.
Everyone who is not patient or strong is both tall and not curious and vice versa.
Everyone who is both kind and old is either curious or quiet and vice versa.
If fred is both happy and funny then someone is either brave or patient and vice versa.
Everyone who is either kind or curious is both creative and patient and vice versa.
Everyone who is not kind or generous is curious.
If someone is both wise and not calm then paul is either calm or not generous and vice versa.
If someone is brave or not kind then alice is either happy or not generous.
If someone is humble or creative then someone is either not happy or not kind and vice versa.
John is either funny or not humble.
Someone is not quiet.
Someone is either brave or tall.
John is either tall or happy.
Alice is humble or old. | Fred is humble. | contradiction | (((~tall(lucy)|~curious(lucy)))=>(?[X]:((humble(X)&calm(X)))))&
((?[X]:(~curious(X)))=>(~tall(fred)))&
((?[X]:(~strong(X)))=>(?[X]:((calm(X)&~happy(X)))))&
(((~rich(susan)&wise(susan)))<=>((~kind(mary)<~>~wise(mary))))&
(((~generous(lucy)<~>~calm(lucy)))=>((wise(john)<~>~old(john))))&
(((~strong(alice)|rich(alice)))=>((strong(fred)|~humble(fred))))&
((?[X]:(creative(X)))<=>((happy(fred)&~patient(fred))))&
(![X]:(wise(X)<=>(~happy(X)<~>~patient(X))))&
(![X]:((~patient(X)|strong(X))<=>(tall(X)&~curious(X))))&
(![X]:((kind(X)&old(X))<=>(curious(X)<~>quiet(X))))&
(((happy(fred)&funny(fred)))<=>(?[X]:((brave(X)<~>patient(X)))))&
(![X]:((kind(X)<~>curious(X))<=>(creative(X)&patient(X))))&
(![X]:((~kind(X)|generous(X))=>curious(X)))&
((?[X]:((wise(X)&~calm(X))))<=>((calm(paul)<~>~generous(paul))))&
((?[X]:((brave(X)|~kind(X))))=>((happy(alice)<~>~generous(alice))))&
((?[X]:((humble(X)|creative(X))))<=>(?[X]:((~happy(X)<~>~kind(X)))))&
((funny(john)<~>~humble(john)))&
(?[X]:(~quiet(X)))&
(?[X]:((brave(X)<~>tall(X))))&
((tall(john)<~>happy(john)))&
((humble(alice)|old(alice))) | humble(fred) | [
"p1",
"p5",
"p6",
"p8",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 3020448991324189728742246
% SZS output start Proof for 3020448991324189728742246
2. ? [X0] : ~curious(X0) => ~tall(fred) [input p1]
6. (rich(alice) | ~strong(alice)) => (~humble(fred) | strong(fred)) [input p5]
7. ? [X0] : creative(X0) <=> (~patient(fred) & happy(fred)) [input p6]
9. ! [X0] : ((strong(X0) | ~patient(X0)) <=> (~curious(X0) & tall(X0))) [input p8]
12. ! [X0] : ((kind(X0) <~> curious(X0)) <=> (patient(X0) & creative(X0))) [input p11]
13. ! [X0] : ((generous(X0) | ~kind(X0)) => curious(X0)) [input p12]
22. humble(fred) [input hypothesis]
26. ~tall(fred) | ! [X0] : curious(X0) [ennf transformation 2]
29. (~humble(fred) | strong(fred)) | (~rich(alice) & strong(alice)) [ennf transformation 6]
30. ~humble(fred) | strong(fred) | (~rich(alice) & strong(alice)) [flattening 29]
31. ! [X0] : (curious(X0) | (~generous(X0) & kind(X0))) [ennf transformation 13]
41. (? [X0] : creative(X0) | (patient(fred) | ~happy(fred))) & ((~patient(fred) & happy(fred)) | ! [X0] : ~creative(X0)) [nnf transformation 7]
42. (? [X0] : creative(X0) | patient(fred) | ~happy(fred)) & ((~patient(fred) & happy(fred)) | ! [X0] : ~creative(X0)) [flattening 41]
43. (? [X0] : creative(X0) | patient(fred) | ~happy(fred)) & ((~patient(fred) & happy(fred)) | ! [X1] : ~creative(X1)) [rectify 42]
44. ? [X0] : creative(X0) => creative(sK2) [choice axiom]
45. (creative(sK2) | patient(fred) | ~happy(fred)) & ((~patient(fred) & happy(fred)) | ! [X1] : ~creative(X1)) [skolemisation 43,44]
47. ! [X0] : (((strong(X0) | ~patient(X0)) | (curious(X0) | ~tall(X0))) & ((~curious(X0) & tall(X0)) | (~strong(X0) & patient(X0)))) [nnf transformation 9]
48. ! [X0] : ((strong(X0) | ~patient(X0) | curious(X0) | ~tall(X0)) & ((~curious(X0) & tall(X0)) | (~strong(X0) & patient(X0)))) [flattening 47]
56. ! [X0] : ((((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | (~patient(X0) | ~creative(X0))) & ((patient(X0) & creative(X0)) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))))) [nnf transformation 12]
57. ! [X0] : ((((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | ~patient(X0) | ~creative(X0)) & ((patient(X0) & creative(X0)) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))))) [flattening 56]
79. ~tall(fred) | curious(X0) [cnf transformation 26]
92. ~humble(fred) | strong(fred) | strong(alice) [cnf transformation 30]
95. ~patient(fred) | ~creative(X1) [cnf transformation 45]
101. patient(X0) | tall(X0) [cnf transformation 48]
104. ~strong(X0) | ~curious(X0) [cnf transformation 48]
118. ~kind(X0) | curious(X0) | creative(X0) [cnf transformation 57]
124. kind(X0) | curious(X0) [cnf transformation 31]
150. humble(fred) [cnf transformation 22]
172. 5 <=> ! [X0] : curious(X0) [avatar definition]
173. curious(X0) <- (5) [avatar component clause 172]
175. 6 <=> tall(fred) [avatar definition]
177. ~tall(fred) <- (~6) [avatar component clause 175]
178. 5 | ~6 [avatar split clause 79,175,172]
239. 19 <=> strong(fred) [avatar definition]
241. strong(fred) <- (19) [avatar component clause 239]
243. 20 <=> humble(fred) [avatar definition]
248. 21 <=> strong(alice) [avatar definition]
250. strong(alice) <- (21) [avatar component clause 248]
251. 21 | 19 | ~20 [avatar split clause 92,243,239,248]
257. 23 <=> patient(fred) [avatar definition]
258. ~patient(fred) <- (~23) [avatar component clause 257]
266. 25 <=> ! [X1] : ~creative(X1) [avatar definition]
267. ~creative(X1) <- (25) [avatar component clause 266]
268. 25 | ~23 [avatar split clause 95,257,266]
409. 20 [avatar split clause 150,243]
410. tall(fred) <- (~23) [resolution 101,258]
411. $false <- (~6, ~23) [subsumption resolution 410,177]
412. 6 | 23 [avatar contradiction clause 411]
419. ~curious(alice) <- (21) [resolution 104,250]
470. curious(X0) | creative(X0) | curious(X0) [resolution 118,124]
471. curious(X0) | creative(X0) [duplicate literal removal 470]
472. curious(X0) <- (25) [subsumption resolution 471,267]
473. 5 | ~25 [avatar split clause 472,266,172]
477. $false <- (5, 21) [resolution 173,419]
478. ~5 | ~21 [avatar contradiction clause 477]
479. ~curious(fred) <- (19) [resolution 241,104]
481. $false <- (5, 19) [subsumption resolution 479,173]
482. ~5 | ~19 [avatar contradiction clause 481]
483. $false [avatar sat refutation 178,251,268,409,412,473,478,482]
% SZS output end Proof for 3020448991324189728742246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or tall is either not strong or not brave.
Everyone who is not calm is either old or not creative and vice versa.
Everyone who is wise is not patient.
Everyone who is brave is either curious or not brave and vice versa.
Everyone who is either not rich or not calm is not patient and vice versa.
If susan is happy then someone is both not tall and not humble and vice versa.
Everyone who is either not calm or not rich is both not quiet and old.
If someone is not curious then john is both not tall and not generous and vice versa.
If fred is generous then someone is happy.
If someone is either not patient or happy then someone is quiet and vice versa.
Everyone who is either not creative or not funny is not happy.
Everyone who is tall is either patient or not rich and vice versa.
Everyone who is either wise or not brave is either not generous or patient and vice versa.
If susan is both not patient and strong then someone is either quiet or happy.
If paul is both old and happy then someone is both old and quiet and vice versa.
If someone is patient then someone is either not humble or kind.
Lucy is either not tall or not generous.
Someone is funny.
Alice is both not brave and humble.
Someone is patient.
Someone is either strong or not calm.
Someone is not rich.
Fred is both not patient and not creative. | Alice is brave. | contradiction | (![X]:((calm(X)|tall(X))=>(~strong(X)<~>~brave(X))))&
(![X]:(~calm(X)<=>(old(X)<~>~creative(X))))&
(![X]:(wise(X)=>~patient(X)))&
(![X]:(brave(X)<=>(curious(X)<~>~brave(X))))&
(![X]:((~rich(X)<~>~calm(X))<=>~patient(X)))&
((happy(susan))<=>(?[X]:((~tall(X)&~humble(X)))))&
(![X]:((~calm(X)<~>~rich(X))=>(~quiet(X)&old(X))))&
((?[X]:(~curious(X)))<=>((~tall(john)&~generous(john))))&
((generous(fred))=>(?[X]:(happy(X))))&
((?[X]:((~patient(X)<~>happy(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~creative(X)<~>~funny(X))=>~happy(X)))&
(![X]:(tall(X)<=>(patient(X)<~>~rich(X))))&
(![X]:((wise(X)<~>~brave(X))<=>(~generous(X)<~>patient(X))))&
(((~patient(susan)&strong(susan)))=>(?[X]:((quiet(X)<~>happy(X)))))&
(((old(paul)&happy(paul)))<=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~humble(X)<~>kind(X)))))&
((~tall(lucy)<~>~generous(lucy)))&
(?[X]:(funny(X)))&
((~brave(alice)&humble(alice)))&
(?[X]:(patient(X)))&
(?[X]:((strong(X)<~>~calm(X))))&
(?[X]:(~rich(X)))&
((~patient(fred)&~creative(fred))) | brave(alice) | [
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 686281539952125449482990
% SZS output start Proof for 686281539952125449482990
19. humble(alice) & ~brave(alice) [input p18]
24. brave(alice) [input hypothesis]
138. ~brave(alice) [cnf transformation 19]
146. brave(alice) [cnf transformation 24]
290. $false [subsumption resolution 146,138]
% SZS output end Proof for 686281539952125449482990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both quiet and calm then paul is either quiet or not curious.
If lucy is either not brave or rich then susan is both not patient and humble.
Everyone who is either not calm or not funny is both not old and funny.
Everyone who is not wise or wise is strong.
Everyone who is happy or creative is both not funny and not quiet.
Everyone who is strong is either patient or not calm and vice versa.
If alice is both funny and not wise then susan is both not kind and funny and vice versa.
If someone is either not humble or patient then susan is both not strong and not happy.
If susan is rich or funny then lucy is not creative and vice versa.
Everyone who is both not creative and generous is both humble and calm.
If lucy is either wise or not funny then someone is wise and vice versa.
If someone is not strong or tall then someone is both calm and not creative.
If someone is both wise and generous then someone is both tall and patient.
Everyone who is brave is not calm or not strong and vice versa.
If fred is both not generous and rich then alice is either not curious or not generous and vice versa.
If susan is not funny or not wise then someone is old or not humble and vice versa.
Someone is either not strong or rich.
Someone is either not calm or not kind.
Someone is not calm or kind.
Someone is both kind and not funny.
Someone is not rich or funny.
Someone is either not curious or wise.
Fred is either humble or creative.
Someone is both not patient and not curious. | Paul is not strong. | contradiction | (((quiet(mary)&calm(mary)))=>((quiet(paul)<~>~curious(paul))))&
(((~brave(lucy)<~>rich(lucy)))=>((~patient(susan)&humble(susan))))&
(![X]:((~calm(X)<~>~funny(X))=>(~old(X)&funny(X))))&
(![X]:((~wise(X)|wise(X))=>strong(X)))&
(![X]:((happy(X)|creative(X))=>(~funny(X)&~quiet(X))))&
(![X]:(strong(X)<=>(patient(X)<~>~calm(X))))&
(((funny(alice)&~wise(alice)))<=>((~kind(susan)&funny(susan))))&
((?[X]:((~humble(X)<~>patient(X))))=>((~strong(susan)&~happy(susan))))&
(((rich(susan)|funny(susan)))<=>(~creative(lucy)))&
(![X]:((~creative(X)&generous(X))=>(humble(X)&calm(X))))&
(((wise(lucy)<~>~funny(lucy)))<=>(?[X]:(wise(X))))&
((?[X]:((~strong(X)|tall(X))))=>(?[X]:((calm(X)&~creative(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((tall(X)&patient(X)))))&
(![X]:(brave(X)<=>(~calm(X)|~strong(X))))&
(((~generous(fred)&rich(fred)))<=>((~curious(alice)<~>~generous(alice))))&
(((~funny(susan)|~wise(susan)))<=>(?[X]:((old(X)|~humble(X)))))&
(?[X]:((~strong(X)<~>rich(X))))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:((~calm(X)|kind(X))))&
(?[X]:((kind(X)&~funny(X))))&
(?[X]:((~rich(X)|funny(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
((humble(fred)<~>creative(fred)))&
(?[X]:((~patient(X)&~curious(X)))) | ~strong(paul) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 3822594363231078774886867
% SZS output start Proof for 3822594363231078774886867
4. ! [X0] : ((wise(X0) | ~wise(X0)) => strong(X0)) [input p3]
25. ~strong(paul) [input hypothesis]
34. ! [X0] : (strong(X0) | (~wise(X0) & wise(X0))) [ennf transformation 4]
97. strong(X0) | wise(X0) [cnf transformation 34]
98. strong(X0) | ~wise(X0) [cnf transformation 34]
153. ~strong(paul) [cnf transformation 25]
193. strong(X0) [subsumption resolution 97,98]
368. $false [subsumption resolution 153,193]
% SZS output end Proof for 3822594363231078774886867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not kind is either not old or not wise and vice versa.
Everyone who is not creative is either calm or not funny.
Everyone who is not tall is not curious or not strong and vice versa.
If alice is funny then mary is strong or patient.
Everyone who is either old or not creative is either strong or not wise.
Everyone who is both funny and not quiet is humble or creative and vice versa.
Everyone who is either humble or wise is not old.
If someone is not generous or not kind then susan is not rich or not calm and vice versa.
Everyone who is not strong or not creative is both not generous and not tall and vice versa.
If john is not brave then susan is either not quiet or not funny.
Everyone who is both tall and old is not humble and vice versa.
Everyone who is both not happy and not humble is either not kind or not quiet.
Everyone who is both not quiet and not brave is both not kind and not creative.
Everyone who is either rich or not old is brave.
Everyone who is strong or not curious is either calm or rich and vice versa.
Everyone who is both not kind and humble is generous or not strong.
Alice is kind or brave.
Someone is old.
Someone is calm or not generous.
Mary is strong or creative.
Alice is not old.
Someone is either not generous or not strong.
Someone is either not generous or not kind. | Mary is strong. | neutral | (![X]:((~humble(X)&~kind(X))<=>(~old(X)<~>~wise(X))))&
(![X]:(~creative(X)=>(calm(X)<~>~funny(X))))&
(![X]:(~tall(X)<=>(~curious(X)|~strong(X))))&
((funny(alice))=>((strong(mary)|patient(mary))))&
(![X]:((old(X)<~>~creative(X))=>(strong(X)<~>~wise(X))))&
(![X]:((funny(X)&~quiet(X))<=>(humble(X)|creative(X))))&
(![X]:((humble(X)<~>wise(X))=>~old(X)))&
((?[X]:((~generous(X)|~kind(X))))<=>((~rich(susan)|~calm(susan))))&
(![X]:((~strong(X)|~creative(X))<=>(~generous(X)&~tall(X))))&
((~brave(john))=>((~quiet(susan)<~>~funny(susan))))&
(![X]:((tall(X)&old(X))<=>~humble(X)))&
(![X]:((~happy(X)&~humble(X))=>(~kind(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&~brave(X))=>(~kind(X)&~creative(X))))&
(![X]:((rich(X)<~>~old(X))=>brave(X)))&
(![X]:((strong(X)|~curious(X))<=>(calm(X)<~>rich(X))))&
(![X]:((~kind(X)&humble(X))=>(generous(X)|~strong(X))))&
((kind(alice)|brave(alice)))&
(?[X]:(old(X)))&
(?[X]:((calm(X)|~generous(X))))&
((strong(mary)|creative(mary)))&
(~old(alice))&
(?[X]:((~generous(X)<~>~strong(X))))&
(?[X]:((~generous(X)<~>~kind(X)))) | strong(mary) | []
| null | 0 |
Everyone who is generous is not humble and vice versa. Everyone who is not brave is old. If fred is either creative or not wise then someone is not kind and vice versa. Everyone who is both brave and wise is both rich and tall. If someone is both not kind and tall then fred is old or curious. If lucy is not tall then someone is either not humble or kind and vice versa. Everyone who is either not strong or not tall is not quiet and vice versa. If alice is strong or not patient then someone is not happy. Everyone who is not tall or not old is not strong or not brave and vice versa. Everyone who is both rich and not happy is both not funny and not old and vice versa. If mary is either not quiet or generous then paul is both humble and not curious. If someone is humble or not curious then someone is both not generous and not brave and vice versa. Everyone who is not old or strong is both quiet and old. If fred is either not curious or happy then fred is not brave and vice versa. Everyone who is old is both creative and not funny and vice versa. Mary is either calm or patient. Someone is either not funny or wise. Someone is brave. Susan is not curious. John is generous. | Paul is quiet. | entailment | (![X]:(generous(X)<=>~humble(X)))&
(![X]:(~brave(X)=>old(X)))&
(((creative(fred)<~>~wise(fred)))<=>(?[X]:(~kind(X))))&
(![X]:((brave(X)&wise(X))=>(rich(X)&tall(X))))&
((?[X]:((~kind(X)&tall(X))))=>((old(fred)|curious(fred))))&
((~tall(lucy))<=>(?[X]:((~humble(X)<~>kind(X)))))&
(![X]:((~strong(X)<~>~tall(X))<=>~quiet(X)))&
(((strong(alice)|~patient(alice)))=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)|~old(X))<=>(~strong(X)|~brave(X))))&
(![X]:((rich(X)&~happy(X))<=>(~funny(X)&~old(X))))&
(((~quiet(mary)<~>generous(mary)))=>((humble(paul)&~curious(paul))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:((~generous(X)&~brave(X)))))&
(![X]:((~old(X)|strong(X))=>(quiet(X)&old(X))))&
(((~curious(fred)<~>happy(fred)))<=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
((calm(mary)<~>patient(mary)))&
(?[X]:((~funny(X)<~>wise(X))))&
(?[X]:(brave(X)))&
(~curious(susan))&
(generous(john)) | quiet(paul) | [
"p6",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 2758343934705065736912930
% SZS output start Proof for 2758343934705065736912930
7. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> ~quiet(X0)) [input p6]
9. ! [X0] : ((~old(X0) | ~tall(X0)) <=> (~brave(X0) | ~strong(X0))) [input p8]
13. ! [X0] : ((strong(X0) | ~old(X0)) => (old(X0) & quiet(X0))) [input p12]
21. ~quiet(paul) [input hypothesis]
30. ! [X0] : ((old(X0) & quiet(X0)) | (~strong(X0) & old(X0))) [ennf transformation 13]
40. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | quiet(X0)) & (~quiet(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 7]
43. ! [X0] : (((~old(X0) | ~tall(X0)) | (brave(X0) & strong(X0))) & ((~brave(X0) | ~strong(X0)) | (old(X0) & tall(X0)))) [nnf transformation 9]
44. ! [X0] : ((~old(X0) | ~tall(X0) | (brave(X0) & strong(X0))) & (~brave(X0) | ~strong(X0) | (old(X0) & tall(X0)))) [flattening 43]
79. quiet(X0) | strong(X0) | tall(X0) [cnf transformation 40]
84. ~tall(X0) | ~old(X0) | strong(X0) [cnf transformation 44]
100. ~strong(X0) | quiet(X0) [cnf transformation 30]
101. old(X0) | old(X0) [cnf transformation 30]
117. ~quiet(paul) [cnf transformation 21]
118. old(X0) [duplicate literal removal 101]
269. strong(paul) | tall(paul) [resolution 79,117]
276. 31 <=> tall(paul) [avatar definition]
278. tall(paul) <- (31) [avatar component clause 276]
280. 32 <=> strong(paul) [avatar definition]
282. strong(paul) <- (32) [avatar component clause 280]
283. 31 | 32 [avatar split clause 269,280,276]
299. ~old(paul) | strong(paul) <- (31) [resolution 84,278]
300. strong(paul) <- (31) [subsumption resolution 299,118]
301. 32 | ~31 [avatar split clause 300,276,280]
305. quiet(paul) <- (32) [resolution 282,100]
309. $false <- (32) [subsumption resolution 305,117]
310. ~32 [avatar contradiction clause 309]
311. $false [avatar sat refutation 283,301,310]
% SZS output end Proof for 2758343934705065736912930
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not kind is strong and vice versa. Everyone who is quiet or not tall is both curious and kind and vice versa. If mary is both not kind and not calm then susan is both not curious and not old. Everyone who is funny or not patient is funny or curious and vice versa. If someone is either not creative or tall then susan is not brave and vice versa. Everyone who is both not humble and strong is calm or not generous and vice versa. Everyone who is old is calm or not old and vice versa. Everyone who is both not creative and not wise is not generous or tall. If someone is both kind and wise then lucy is either not creative or not old. Everyone who is either curious or brave is both not quiet and not kind and vice versa. If fred is both calm and not happy then someone is not rich and vice versa. If alice is tall then someone is brave or humble. Everyone who is either not funny or not calm is either tall or not humble. Everyone who is either not quiet or not generous is not rich. Everyone who is both not calm and not funny is both not wise and generous and vice versa. Everyone who is both rich and not creative is not creative or not patient and vice versa. Fred is either not calm or calm. Someone is not creative. Someone is either not funny or not creative. Someone is both curious and not patient. Susan is not humble or not old. Someone is both tall and rich. | Alice is not creative. | neutral | (![X]:((brave(X)<~>~kind(X))<=>strong(X)))&
(![X]:((quiet(X)|~tall(X))<=>(curious(X)&kind(X))))&
(((~kind(mary)&~calm(mary)))=>((~curious(susan)&~old(susan))))&
(![X]:((funny(X)|~patient(X))<=>(funny(X)|curious(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>(~brave(susan)))&
(![X]:((~humble(X)&strong(X))<=>(calm(X)|~generous(X))))&
(![X]:(old(X)<=>(calm(X)|~old(X))))&
(![X]:((~creative(X)&~wise(X))=>(~generous(X)|tall(X))))&
((?[X]:((kind(X)&wise(X))))=>((~creative(lucy)<~>~old(lucy))))&
(![X]:((curious(X)<~>brave(X))<=>(~quiet(X)&~kind(X))))&
(((calm(fred)&~happy(fred)))<=>(?[X]:(~rich(X))))&
((tall(alice))=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~funny(X)<~>~calm(X))=>(tall(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>~rich(X)))&
(![X]:((~calm(X)&~funny(X))<=>(~wise(X)&generous(X))))&
(![X]:((rich(X)&~creative(X))<=>(~creative(X)|~patient(X))))&
((~calm(fred)<~>calm(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)<~>~creative(X))))&
(?[X]:((curious(X)&~patient(X))))&
((~humble(susan)|~old(susan)))&
(?[X]:((tall(X)&rich(X)))) | ~creative(alice) | []
| null | 0 |
Everyone who is not creative or strong is either kind or wise. Everyone who is either wise or funny is either not old or old. Everyone who is tall is creative. If someone is both old and not happy then john is not rich or not patient. Everyone who is creative is curious and vice versa. If someone is generous or not patient then paul is either not curious or not creative. Everyone who is brave or not patient is not brave or brave. Everyone who is both brave and humble is not calm and vice versa. If someone is not humble or humble then mary is either not rich or not happy. Everyone who is both not patient and funny is both calm and not kind and vice versa. If alice is both not kind and not wise then mary is either not quiet or humble and vice versa. Everyone who is not humble is not generous. If paul is strong or curious then someone is not kind. If john is both generous and not generous then someone is tall or not funny. If someone is not quiet then fred is funny and vice versa. If someone is not tall then someone is not curious. Someone is not quiet. Fred is both not humble and happy. Paul is rich. Someone is creative. Someone is not rich or not generous. Someone is not quiet or strong. | Alice is curious. | neutral | (![X]:((~creative(X)|strong(X))=>(kind(X)<~>wise(X))))&
(![X]:((wise(X)<~>funny(X))=>(~old(X)<~>old(X))))&
(![X]:(tall(X)=>creative(X)))&
((?[X]:((old(X)&~happy(X))))=>((~rich(john)|~patient(john))))&
(![X]:(creative(X)<=>curious(X)))&
((?[X]:((generous(X)|~patient(X))))=>((~curious(paul)<~>~creative(paul))))&
(![X]:((brave(X)|~patient(X))=>(~brave(X)|brave(X))))&
(![X]:((brave(X)&humble(X))<=>~calm(X)))&
((?[X]:((~humble(X)|humble(X))))=>((~rich(mary)<~>~happy(mary))))&
(![X]:((~patient(X)&funny(X))<=>(calm(X)&~kind(X))))&
(((~kind(alice)&~wise(alice)))<=>((~quiet(mary)<~>humble(mary))))&
(![X]:(~humble(X)=>~generous(X)))&
(((strong(paul)|curious(paul)))=>(?[X]:(~kind(X))))&
(((generous(john)&~generous(john)))=>(?[X]:((tall(X)|~funny(X)))))&
((?[X]:(~quiet(X)))<=>(funny(fred)))&
((?[X]:(~tall(X)))=>(?[X]:(~curious(X))))&
(?[X]:(~quiet(X)))&
((~humble(fred)&happy(fred)))&
(rich(paul))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:((~quiet(X)|strong(X)))) | curious(alice) | []
| null | 0 |
Everyone who is both generous and strong is either wise or kind and vice versa. Everyone who is not funny is either rich or not funny and vice versa. Everyone who is both rich and not strong is not old or rich. If someone is generous or quiet then someone is not calm or curious. Everyone who is both generous and not tall is both humble and not strong. Everyone who is not strong is not funny or not generous and vice versa. Everyone who is not rich is not generous or tall. If alice is both funny and generous then someone is kind and vice versa. If alice is not funny or not old then someone is not old and vice versa. Everyone who is either not generous or patient is both not kind and strong. Everyone who is either not tall or happy is not happy and vice versa. If someone is not brave or not quiet then someone is both calm and not calm and vice versa. If john is either not quiet or rich then paul is not old or quiet. If alice is both curious and not calm then lucy is humble or not humble. If lucy is not rich then paul is either funny or not kind and vice versa. Someone is not calm or not funny. Someone is either not calm or not rich. Someone is not strong or humble. Fred is not kind. Paul is not kind or kind. Someone is either creative or not generous. Susan is not tall or not happy. John is not curious. | Paul is rich. | contradiction | (![X]:((generous(X)&strong(X))<=>(wise(X)<~>kind(X))))&
(![X]:(~funny(X)<=>(rich(X)<~>~funny(X))))&
(![X]:((rich(X)&~strong(X))=>(~old(X)|rich(X))))&
((?[X]:((generous(X)|quiet(X))))=>(?[X]:((~calm(X)|curious(X)))))&
(![X]:((generous(X)&~tall(X))=>(humble(X)&~strong(X))))&
(![X]:(~strong(X)<=>(~funny(X)|~generous(X))))&
(![X]:(~rich(X)=>(~generous(X)|tall(X))))&
(((funny(alice)&generous(alice)))<=>(?[X]:(kind(X))))&
(((~funny(alice)|~old(alice)))<=>(?[X]:(~old(X))))&
(![X]:((~generous(X)<~>patient(X))=>(~kind(X)&strong(X))))&
(![X]:((~tall(X)<~>happy(X))<=>~happy(X)))&
((?[X]:((~brave(X)|~quiet(X))))<=>(?[X]:((calm(X)&~calm(X)))))&
(((~quiet(john)<~>rich(john)))=>((~old(paul)|quiet(paul))))&
(((curious(alice)&~calm(alice)))=>((humble(lucy)|~humble(lucy))))&
((~rich(lucy))<=>((funny(paul)<~>~kind(paul))))&
(?[X]:((~calm(X)|~funny(X))))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~strong(X)|humble(X))))&
(~kind(fred))&
((~kind(paul)|kind(paul)))&
(?[X]:((creative(X)<~>~generous(X))))&
((~tall(susan)|~happy(susan)))&
(~curious(john)) | rich(paul) | [
"p1",
"hypothesis"
]
| % SZS status Unsatisfiable for 841632921670437708482549
% SZS output start Proof for 841632921670437708482549
2. ! [X0] : (~funny(X0) <=> (rich(X0) <~> ~funny(X0))) [input p1]
24. rich(paul) [input hypothesis]
41. ! [X0] : ((~funny(X0) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | funny(X0))) [nnf transformation 2]
83. funny(X0) | ~rich(X0) | funny(X0) [cnf transformation 41]
84. ~funny(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 41]
131. rich(paul) [cnf transformation 24]
134. funny(X0) | ~rich(X0) [duplicate literal removal 83]
135. ~funny(X0) | ~rich(X0) [duplicate literal removal 84]
136. ~rich(X0) [subsumption resolution 134,135]
257. $false [subsumption resolution 131,136]
% SZS output end Proof for 841632921670437708482549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not humble is both not generous and patient.
Everyone who is not happy is not old and vice versa.
If alice is wise then fred is not curious or not funny and vice versa.
If someone is creative then someone is both quiet and not wise.
If lucy is strong then fred is funny.
If mary is both curious and calm then lucy is both patient and not patient.
Everyone who is not wise or not humble is rich or not wise and vice versa.
If someone is not funny then fred is both humble and not creative.
Everyone who is old or generous is both not funny and not patient.
Everyone who is either not creative or not strong is funny or not generous and vice versa.
If susan is not calm then mary is both not generous and funny and vice versa.
If fred is not strong or not generous then someone is calm or wise.
If someone is happy then someone is tall or not curious.
If paul is both humble and brave then lucy is either not rich or not curious.
If lucy is tall then someone is not wise.
Everyone who is not patient or not funny is either generous or not old.
Paul is old.
Susan is humble.
Paul is not old or kind.
Mary is both kind and not humble.
Someone is both old and not kind.
Lucy is either creative or not curious.
Paul is tall or not old.
Someone is not quiet. | Fred is not strong. | contradiction | (![X]:((~strong(X)|~humble(X))=>(~generous(X)&patient(X))))&
(![X]:(~happy(X)<=>~old(X)))&
((wise(alice))<=>((~curious(fred)|~funny(fred))))&
((?[X]:(creative(X)))=>(?[X]:((quiet(X)&~wise(X)))))&
((strong(lucy))=>(funny(fred)))&
(((curious(mary)&calm(mary)))=>((patient(lucy)&~patient(lucy))))&
(![X]:((~wise(X)|~humble(X))<=>(rich(X)|~wise(X))))&
((?[X]:(~funny(X)))=>((humble(fred)&~creative(fred))))&
(![X]:((old(X)|generous(X))=>(~funny(X)&~patient(X))))&
(![X]:((~creative(X)<~>~strong(X))<=>(funny(X)|~generous(X))))&
((~calm(susan))<=>((~generous(mary)&funny(mary))))&
(((~strong(fred)|~generous(fred)))=>(?[X]:((calm(X)|wise(X)))))&
((?[X]:(happy(X)))=>(?[X]:((tall(X)|~curious(X)))))&
(((humble(paul)&brave(paul)))=>((~rich(lucy)<~>~curious(lucy))))&
((tall(lucy))=>(?[X]:(~wise(X))))&
(![X]:((~patient(X)|~funny(X))=>(generous(X)<~>~old(X))))&
(old(paul))&
(humble(susan))&
((~old(paul)|kind(paul)))&
((kind(mary)&~humble(mary)))&
(?[X]:((old(X)&~kind(X))))&
((creative(lucy)<~>~curious(lucy)))&
((tall(paul)|~old(paul)))&
(?[X]:(~quiet(X))) | ~strong(fred) | [
"p0",
"p7",
"p8",
"p9",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 836853750606701714836934
% SZS output start Proof for 836853750606701714836934
1. ! [X0] : ((~humble(X0) | ~strong(X0)) => (patient(X0) & ~generous(X0))) [input p0]
8. ? [X0] : ~funny(X0) => (~creative(fred) & humble(fred)) [input p7]
9. ! [X0] : ((generous(X0) | old(X0)) => (~patient(X0) & ~funny(X0))) [input p8]
10. ! [X0] : ((~creative(X0) <~> ~strong(X0)) <=> (~generous(X0) | funny(X0))) [input p9]
17. old(paul) [input p16]
25. ~strong(fred) [input hypothesis]
30. ! [X0] : ((patient(X0) & ~generous(X0)) | (humble(X0) & strong(X0))) [ennf transformation 1]
36. (~creative(fred) & humble(fred)) | ! [X0] : funny(X0) [ennf transformation 8]
37. ! [X0] : ((~patient(X0) & ~funny(X0)) | (~generous(X0) & ~old(X0))) [ennf transformation 9]
49. ! [X0] : ((((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | (generous(X0) & ~funny(X0))) & ((~generous(X0) | funny(X0)) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0))))) [nnf transformation 10]
50. ! [X0] : ((((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | (generous(X0) & ~funny(X0))) & (~generous(X0) | funny(X0) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0))))) [flattening 49]
66. ~generous(X0) | strong(X0) [cnf transformation 30]
84. ~creative(fred) | funny(X0) [cnf transformation 36]
85. ~funny(X0) | ~old(X0) [cnf transformation 37]
94. strong(X0) | creative(X0) | generous(X0) [cnf transformation 50]
106. old(paul) [cnf transformation 17]
117. ~strong(fred) [cnf transformation 25]
166. 11 <=> ! [X0] : funny(X0) [avatar definition]
167. funny(X0) <- (11) [avatar component clause 166]
169. 12 <=> creative(fred) [avatar definition]
171. ~creative(fred) <- (~12) [avatar component clause 169]
172. 11 | ~12 [avatar split clause 84,169,166]
178. creative(X0) | strong(X0) [subsumption resolution 94,66]
211. 20 <=> strong(fred) [avatar definition]
212. ~strong(fred) <- (~20) [avatar component clause 211]
250. ~20 [avatar split clause 117,211]
253. ~old(X0) <- (11) [resolution 85,167]
259. $false <- (11) [resolution 253,106]
262. ~11 [avatar contradiction clause 259]
277. strong(fred) <- (~12) [resolution 171,178]
278. $false <- (~12, ~20) [subsumption resolution 277,212]
279. 12 | 20 [avatar contradiction clause 278]
280. $false [avatar sat refutation 172,250,262,279]
% SZS output end Proof for 836853750606701714836934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not wise then alice is not old and vice versa.
If susan is generous then someone is not tall or rich.
Everyone who is both not patient and not creative is brave and vice versa.
Everyone who is both not funny and funny is not curious or not tall and vice versa.
If someone is creative or not curious then someone is either patient or not quiet and vice versa.
If lucy is both calm and funny then mary is both rich and generous and vice versa.
Everyone who is both not brave and not old is either curious or not rich and vice versa.
Everyone who is generous is not curious and vice versa.
Everyone who is both not quiet and not humble is not generous and vice versa.
If someone is tall or patient then lucy is calm or brave and vice versa.
Everyone who is both not tall and not calm is either not creative or rich and vice versa.
If mary is calm then someone is not old or not generous.
Everyone who is both not strong and not funny is not strong.
If john is either quiet or brave then someone is either kind or not humble.
Everyone who is happy or wise is funny.
Someone is not kind.
Susan is either not tall or not happy.
John is not wise.
Someone is either patient or kind.
Lucy is patient or humble.
Someone is strong or not tall. | Alice is rich. | entailment | ((?[X]:((~curious(X)<~>~wise(X))))<=>(~old(alice)))&
((generous(susan))=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((~patient(X)&~creative(X))<=>brave(X)))&
(![X]:((~funny(X)&funny(X))<=>(~curious(X)|~tall(X))))&
((?[X]:((creative(X)|~curious(X))))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
(((calm(lucy)&funny(lucy)))<=>((rich(mary)&generous(mary))))&
(![X]:((~brave(X)&~old(X))<=>(curious(X)<~>~rich(X))))&
(![X]:(generous(X)<=>~curious(X)))&
(![X]:((~quiet(X)&~humble(X))<=>~generous(X)))&
((?[X]:((tall(X)|patient(X))))<=>((calm(lucy)|brave(lucy))))&
(![X]:((~tall(X)&~calm(X))<=>(~creative(X)<~>rich(X))))&
((calm(mary))=>(?[X]:((~old(X)|~generous(X)))))&
(![X]:((~strong(X)&~funny(X))=>~strong(X)))&
(((quiet(john)<~>brave(john)))=>(?[X]:((kind(X)<~>~humble(X)))))&
(![X]:((happy(X)|wise(X))=>funny(X)))&
(?[X]:(~kind(X)))&
((~tall(susan)<~>~happy(susan)))&
(~wise(john))&
(?[X]:((patient(X)<~>kind(X))))&
((patient(lucy)|humble(lucy)))&
(?[X]:((strong(X)|~tall(X)))) | rich(alice) | [
"p0",
"p2",
"p3",
"p6",
"p10",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 4743068212661093537478133
% SZS output start Proof for 4743068212661093537478133
1. ? [X0] : (~curious(X0) <~> ~wise(X0)) <=> ~old(alice) [input p0]
3. ! [X0] : ((~creative(X0) & ~patient(X0)) <=> brave(X0)) [input p2]
4. ! [X0] : ((funny(X0) & ~funny(X0)) <=> (~tall(X0) | ~curious(X0))) [input p3]
7. ! [X0] : ((~old(X0) & ~brave(X0)) <=> (curious(X0) <~> ~rich(X0))) [input p6]
11. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> (~creative(X0) <~> rich(X0))) [input p10]
18. ~wise(john) [input p17]
22. ~rich(alice) [input hypothesis]
30. (? [X0] : ((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | old(alice)) & (~old(alice) | ! [X0] : ((~curious(X0) | wise(X0)) & (~wise(X0) | curious(X0)))) [nnf transformation 1]
31. (? [X0] : ((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | old(alice)) & (~old(alice) | ! [X1] : ((~curious(X1) | wise(X1)) & (~wise(X1) | curious(X1)))) [rectify 30]
32. ? [X0] : ((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) => ((wise(sK0) | curious(sK0)) & (~wise(sK0) | ~curious(sK0))) [choice axiom]
33. (((wise(sK0) | curious(sK0)) & (~wise(sK0) | ~curious(sK0))) | old(alice)) & (~old(alice) | ! [X1] : ((~curious(X1) | wise(X1)) & (~wise(X1) | curious(X1)))) [skolemisation 31,32]
36. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~brave(X0)) & (brave(X0) | (creative(X0) | patient(X0)))) [nnf transformation 3]
37. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~brave(X0)) & (brave(X0) | creative(X0) | patient(X0))) [flattening 36]
38. ! [X0] : (((funny(X0) & ~funny(X0)) | (tall(X0) & curious(X0))) & ((~tall(X0) | ~curious(X0)) | (~funny(X0) | funny(X0)))) [nnf transformation 4]
39. ! [X0] : (((funny(X0) & ~funny(X0)) | (tall(X0) & curious(X0))) & (~tall(X0) | ~curious(X0) | ~funny(X0) | funny(X0))) [flattening 38]
47. ! [X0] : (((~old(X0) & ~brave(X0)) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) & (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | (old(X0) | brave(X0)))) [nnf transformation 7]
48. ! [X0] : (((~old(X0) & ~brave(X0)) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) & (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | old(X0) | brave(X0))) [flattening 47]
57. ! [X0] : (((~calm(X0) & ~tall(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | (calm(X0) | tall(X0)))) [nnf transformation 11]
58. ! [X0] : (((~calm(X0) & ~tall(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | calm(X0) | tall(X0))) [flattening 57]
73. ~old(alice) | ~curious(X1) | wise(X1) [cnf transformation 33]
79. ~brave(X0) | ~creative(X0) [cnf transformation 37]
81. ~funny(X0) | curious(X0) [cnf transformation 39]
82. ~funny(X0) | tall(X0) [cnf transformation 39]
83. funny(X0) | curious(X0) [cnf transformation 39]
84. funny(X0) | tall(X0) [cnf transformation 39]
96. rich(X0) | ~curious(X0) | old(X0) | brave(X0) [cnf transformation 48]
112. ~tall(X0) | rich(X0) | creative(X0) [cnf transformation 58]
113. ~tall(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 58]
127. ~wise(john) [cnf transformation 18]
132. ~rich(alice) [cnf transformation 22]
134. 1 <=> old(alice) [avatar definition]
148. 4 <=> ! [X1] : (~curious(X1) | wise(X1)) [avatar definition]
149. ~curious(X1) | wise(X1) <- (4) [avatar component clause 148]
150. 4 | ~1 [avatar split clause 73,134,148]
168. tall(X0) [subsumption resolution 82,84]
169. curious(X0) [subsumption resolution 81,83]
219. brave(X0) | old(X0) | rich(X0) [subsumption resolution 96,169]
233. ~creative(X0) | ~rich(X0) [subsumption resolution 113,168]
234. creative(X0) | rich(X0) [subsumption resolution 112,168]
291. old(X1) | rich(X1) | ~creative(X1) [resolution 219,79]
294. ~creative(X1) | old(X1) [subsumption resolution 291,233]
298. rich(X0) | old(X0) [resolution 294,234]
304. old(alice) [resolution 298,132]
309. 1 [avatar split clause 304,134]
310. wise(X1) <- (4) [subsumption resolution 149,169]
311. $false <- (4) [resolution 310,127]
315. ~4 [avatar contradiction clause 311]
316. $false [avatar sat refutation 150,309,315]
% SZS output end Proof for 4743068212661093537478133
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not kind then lucy is either not patient or not wise and vice versa.
Everyone who is not calm is either old or not humble and vice versa.
If john is not quiet or not creative then someone is not old or not patient.
Everyone who is not generous or not curious is brave or not old and vice versa.
Everyone who is not happy is generous and vice versa.
If someone is not strong or not brave then someone is both curious and not calm and vice versa.
Everyone who is either not brave or kind is either wise or old and vice versa.
If someone is calm then lucy is both quiet and creative.
Everyone who is either not old or humble is both quiet and curious.
Everyone who is curious is wise or not happy.
Everyone who is quiet or not patient is both old and strong.
Everyone who is rich is either tall or not curious and vice versa.
Everyone who is not humble is kind.
Everyone who is creative or rich is quiet and vice versa.
Everyone who is both old and not brave is not wise or brave and vice versa.
If someone is either funny or strong then john is either not rich or not kind and vice versa.
Fred is either patient or not tall.
Someone is funny or not generous.
Someone is calm.
John is either not old or not strong.
Someone is either kind or happy.
Someone is either not patient or quiet.
Someone is both strong and not happy. | John is not funny. | contradiction | ((?[X]:((~strong(X)&~kind(X))))<=>((~patient(lucy)<~>~wise(lucy))))&
(![X]:(~calm(X)<=>(old(X)<~>~humble(X))))&
(((~quiet(john)|~creative(john)))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~generous(X)|~curious(X))<=>(brave(X)|~old(X))))&
(![X]:(~happy(X)<=>generous(X)))&
((?[X]:((~strong(X)|~brave(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((~brave(X)<~>kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(calm(X)))=>((quiet(lucy)&creative(lucy))))&
(![X]:((~old(X)<~>humble(X))=>(quiet(X)&curious(X))))&
(![X]:(curious(X)=>(wise(X)|~happy(X))))&
(![X]:((quiet(X)|~patient(X))=>(old(X)&strong(X))))&
(![X]:(rich(X)<=>(tall(X)<~>~curious(X))))&
(![X]:(~humble(X)=>kind(X)))&
(![X]:((creative(X)|rich(X))<=>quiet(X)))&
(![X]:((old(X)&~brave(X))<=>(~wise(X)|brave(X))))&
((?[X]:((funny(X)<~>strong(X))))<=>((~rich(john)<~>~kind(john))))&
((patient(fred)<~>~tall(fred)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:(calm(X)))&
((~old(john)<~>~strong(john)))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((~patient(X)<~>quiet(X))))&
(?[X]:((strong(X)&~happy(X)))) | ~funny(john) | [
"p1",
"p6",
"p8",
"p10",
"p12",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 5622794817857445593271526
% SZS output start Proof for 5622794817857445593271526
2. ! [X0] : (~calm(X0) <=> (old(X0) <~> ~humble(X0))) [input p1]
7. ! [X0] : ((~brave(X0) <~> kind(X0)) <=> (wise(X0) <~> old(X0))) [input p6]
9. ! [X0] : ((~old(X0) <~> humble(X0)) => (curious(X0) & quiet(X0))) [input p8]
11. ! [X0] : ((~patient(X0) | quiet(X0)) => (strong(X0) & old(X0))) [input p10]
13. ! [X0] : (~humble(X0) => kind(X0)) [input p12]
14. ! [X0] : ((rich(X0) | creative(X0)) <=> quiet(X0)) [input p13]
15. ! [X0] : ((~brave(X0) & old(X0)) <=> (brave(X0) | ~wise(X0))) [input p14]
16. ? [X0] : (funny(X0) <~> strong(X0)) <=> (~rich(john) <~> ~kind(john)) [input p15]
20. ~old(john) <~> ~strong(john) [input p19]
24. ~funny(john) [input hypothesis]
28. ! [X0] : ((curious(X0) & quiet(X0)) | (~old(X0) <=> humble(X0))) [ennf transformation 9]
31. ! [X0] : ((strong(X0) & old(X0)) | (patient(X0) & ~quiet(X0))) [ennf transformation 11]
32. ! [X0] : (kind(X0) | humble(X0)) [ennf transformation 13]
37. ! [X0] : ((~calm(X0) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0)))) & (((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | calm(X0))) [nnf transformation 2]
48. ! [X0] : ((((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))))) [nnf transformation 7]
49. ! [X0] : ((curious(X0) & quiet(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) [nnf transformation 28]
51. ! [X0] : (((rich(X0) | creative(X0)) | ~quiet(X0)) & (quiet(X0) | (~rich(X0) & ~creative(X0)))) [nnf transformation 14]
52. ! [X0] : ((rich(X0) | creative(X0) | ~quiet(X0)) & (quiet(X0) | (~rich(X0) & ~creative(X0)))) [flattening 51]
53. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (brave(X0) | ~old(X0)))) [nnf transformation 15]
54. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | brave(X0) | ~old(X0))) [flattening 53]
55. (? [X0] : ((~strong(X0) | ~funny(X0)) & (strong(X0) | funny(X0))) | ((~rich(john) | kind(john)) & (~kind(john) | rich(john)))) & (((kind(john) | rich(john)) & (~kind(john) | ~rich(john))) | ! [X0] : ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0)))) [nnf transformation 16]
56. (? [X0] : ((~strong(X0) | ~funny(X0)) & (strong(X0) | funny(X0))) | ((~rich(john) | kind(john)) & (~kind(john) | rich(john)))) & (((kind(john) | rich(john)) & (~kind(john) | ~rich(john))) | ! [X1] : ((funny(X1) | ~strong(X1)) & (strong(X1) | ~funny(X1)))) [rectify 55]
57. ? [X0] : ((~strong(X0) | ~funny(X0)) & (strong(X0) | funny(X0))) => ((~strong(sK4) | ~funny(sK4)) & (strong(sK4) | funny(sK4))) [choice axiom]
58. (((~strong(sK4) | ~funny(sK4)) & (strong(sK4) | funny(sK4))) | ((~rich(john) | kind(john)) & (~kind(john) | rich(john)))) & (((kind(john) | rich(john)) & (~kind(john) | ~rich(john))) | ! [X1] : ((funny(X1) | ~strong(X1)) & (strong(X1) | ~funny(X1)))) [skolemisation 56,57]
64. (strong(john) | old(john)) & (~strong(john) | ~old(john)) [nnf transformation 20]
80. ~old(X0) | humble(X0) | calm(X0) [cnf transformation 37]
81. ~humble(X0) | ~calm(X0) | ~old(X0) [cnf transformation 37]
102. ~wise(X0) | brave(X0) | old(X0) | ~kind(X0) [cnf transformation 48]
103. ~old(X0) | brave(X0) | wise(X0) | ~kind(X0) [cnf transformation 48]
107. ~humble(X0) | ~old(X0) | quiet(X0) [cnf transformation 49]
111. ~quiet(X0) | old(X0) [cnf transformation 31]
113. ~quiet(X0) | strong(X0) [cnf transformation 31]
119. humble(X0) | kind(X0) [cnf transformation 32]
121. ~rich(X0) | quiet(X0) [cnf transformation 52]
123. brave(X0) | ~wise(X0) | brave(X0) | ~old(X0) [cnf transformation 54]
124. old(X0) | wise(X0) [cnf transformation 54]
127. ~brave(X0) | ~brave(X0) [cnf transformation 54]
131. kind(john) | rich(john) | funny(X1) | ~strong(X1) [cnf transformation 58]
140. ~strong(john) | ~old(john) [cnf transformation 64]
141. strong(john) | old(john) [cnf transformation 64]
148. ~funny(john) [cnf transformation 24]
149. brave(X0) | ~wise(X0) | ~old(X0) [duplicate literal removal 123]
150. ~brave(X0) [duplicate literal removal 127]
190. 9 <=> quiet(john) [avatar definition]
191. ~quiet(john) <- (~9) [avatar component clause 190]
192. quiet(john) <- (9) [avatar component clause 190]
237. ~old(X0) | ~wise(X0) [subsumption resolution 149,150]
239. 20 <=> kind(john) [avatar definition]
240. ~kind(john) <- (~20) [avatar component clause 239]
241. kind(john) <- (20) [avatar component clause 239]
243. 21 <=> rich(john) [avatar definition]
244. rich(john) <- (21) [avatar component clause 243]
259. 24 <=> ! [X1] : (funny(X1) | ~strong(X1)) [avatar definition]
260. ~strong(X1) | funny(X1) <- (24) [avatar component clause 259]
261. 24 | 21 | 20 [avatar split clause 131,239,243,259]
288. 30 <=> old(john) [avatar definition]
289. ~old(john) <- (~30) [avatar component clause 288]
290. old(john) <- (30) [avatar component clause 288]
292. 31 <=> strong(john) [avatar definition]
294. strong(john) <- (31) [avatar component clause 292]
295. 30 | 31 [avatar split clause 141,292,288]
296. ~30 | ~31 [avatar split clause 140,292,288]
338. ~wise(john) <- (30) [resolution 237,290]
356. 38 <=> calm(john) [avatar definition]
360. 39 <=> humble(john) [avatar definition]
362. humble(john) <- (39) [avatar component clause 360]
373. ~old(X0) | ~calm(X0) | kind(X0) [resolution 81,119]
524. brave(X0) | wise(X0) | ~kind(X0) | wise(X0) [resolution 103,124]
530. brave(X0) | wise(X0) | ~kind(X0) [duplicate literal removal 524]
531. ~kind(X0) | wise(X0) [subsumption resolution 530,150]
597. wise(john) <- (20) [resolution 531,241]
600. $false <- (20, 30) [subsumption resolution 597,338]
601. ~20 | ~30 [avatar contradiction clause 600]
618. brave(john) | old(john) | ~kind(john) <- (20) [resolution 597,102]
619. old(john) | ~kind(john) <- (20) [subsumption resolution 618,150]
620. ~kind(john) <- (20, ~30) [subsumption resolution 619,289]
621. $false <- (20, ~30) [subsumption resolution 620,241]
622. ~20 | 30 [avatar contradiction clause 621]
625. quiet(john) <- (21) [resolution 244,121]
635. 9 | ~21 [avatar split clause 625,243,190]
637. strong(john) <- (9) [resolution 192,113]
638. old(john) <- (9) [resolution 192,111]
641. 30 | ~9 [avatar split clause 638,190,288]
642. 31 | ~9 [avatar split clause 637,190,292]
649. humble(john) | calm(john) <- (30) [resolution 290,80]
690. ~calm(john) | kind(john) <- (30) [resolution 373,290]
702. ~calm(john) <- (~20, 30) [subsumption resolution 690,240]
703. ~38 | 20 | ~30 [avatar split clause 702,288,239,356]
704. 38 | 39 | ~30 [avatar split clause 649,288,360,356]
706. ~old(john) | quiet(john) <- (39) [resolution 362,107]
709. quiet(john) <- (30, 39) [subsumption resolution 706,290]
710. $false <- (~9, 30, 39) [subsumption resolution 709,191]
711. 9 | ~30 | ~39 [avatar contradiction clause 710]
725. funny(john) <- (24, 31) [resolution 294,260]
726. $false <- (24, 31) [subsumption resolution 725,148]
727. ~24 | ~31 [avatar contradiction clause 726]
728. $false [avatar sat refutation 261,295,296,601,622,635,641,642,703,704,711,727]
% SZS output end Proof for 5622794817857445593271526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or patient is not patient and vice versa. Everyone who is either not rich or not funny is old. If alice is not old then someone is both rich and not funny and vice versa. Everyone who is brave or calm is not funny or not quiet and vice versa. Everyone who is calm is either wise or happy and vice versa. Everyone who is either not rich or rich is both strong and not patient and vice versa. Everyone who is both happy and strong is either not kind or kind and vice versa. If someone is not rich or generous then someone is either calm or patient and vice versa. If paul is tall then someone is either funny or brave. If fred is either old or not quiet then someone is either not happy or not kind and vice versa. Everyone who is both creative and not generous is patient and vice versa. If susan is kind or not patient then someone is rich. Everyone who is either wise or quiet is both creative and humble and vice versa. Everyone who is not calm or old is not curious or curious and vice versa. If someone is humble then someone is either funny or kind. If someone is not generous then someone is either old or wise and vice versa. Someone is either not generous or calm. Someone is brave or not happy. Someone is both not tall and not creative. John is wise or curious. Someone is not rich or not generous. Lucy is either happy or curious. John is calm or not generous. | Susan is not strong. | contradiction | (![X]:((~wise(X)<~>patient(X))<=>~patient(X)))&
(![X]:((~rich(X)<~>~funny(X))=>old(X)))&
((~old(alice))<=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:((brave(X)|calm(X))<=>(~funny(X)|~quiet(X))))&
(![X]:(calm(X)<=>(wise(X)<~>happy(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(strong(X)&~patient(X))))&
(![X]:((happy(X)&strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((~rich(X)|generous(X))))<=>(?[X]:((calm(X)<~>patient(X)))))&
((tall(paul))=>(?[X]:((funny(X)<~>brave(X)))))&
(((old(fred)<~>~quiet(fred)))<=>(?[X]:((~happy(X)<~>~kind(X)))))&
(![X]:((creative(X)&~generous(X))<=>patient(X)))&
(((kind(susan)|~patient(susan)))=>(?[X]:(rich(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(creative(X)&humble(X))))&
(![X]:((~calm(X)|old(X))<=>(~curious(X)|curious(X))))&
((?[X]:(humble(X)))=>(?[X]:((funny(X)<~>kind(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((old(X)<~>wise(X)))))&
(?[X]:((~generous(X)<~>calm(X))))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:((~tall(X)&~creative(X))))&
((wise(john)|curious(john)))&
(?[X]:((~rich(X)|~generous(X))))&
((happy(lucy)<~>curious(lucy)))&
((calm(john)|~generous(john))) | ~strong(susan) | [
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 5020705565664787984216582
% SZS output start Proof for 5020705565664787984216582
6. ! [X0] : ((~rich(X0) <~> rich(X0)) <=> (~patient(X0) & strong(X0))) [input p5]
24. ~strong(susan) [input hypothesis]
42. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (patient(X0) | ~strong(X0))) & ((~patient(X0) & strong(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [nnf transformation 6]
43. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | patient(X0) | ~strong(X0)) & ((~patient(X0) & strong(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [flattening 42]
99. strong(X0) | rich(X0) | rich(X0) [cnf transformation 43]
100. strong(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 43]
155. ~strong(susan) [cnf transformation 24]
160. strong(X0) | rich(X0) [duplicate literal removal 99]
161. strong(X0) | ~rich(X0) [duplicate literal removal 100]
188. strong(X0) [subsumption resolution 160,161]
308. $false [subsumption resolution 155,188]
% SZS output end Proof for 5020705565664787984216582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and patient is not humble or kind and vice versa.
If john is not tall then john is either not quiet or wise.
If susan is tall or not happy then someone is both not curious and not old.
If someone is tall or not calm then someone is not quiet and vice versa.
Everyone who is either strong or not strong is both wise and happy and vice versa.
Everyone who is humble or generous is strong.
Everyone who is either happy or not creative is tall or brave.
If someone is either not wise or quiet then john is old and vice versa.
Everyone who is strong is curious and vice versa.
Everyone who is either not humble or not funny is not kind and vice versa.
If someone is both not creative and calm then fred is either tall or curious and vice versa.
If someone is not tall then fred is either rich or not calm and vice versa.
If someone is rich or not strong then someone is both not funny and not wise.
Everyone who is both not strong and not tall is calm or old and vice versa.
Everyone who is either funny or creative is not old or curious.
John is rich or wise.
John is either not old or patient.
Someone is not funny or not humble.
Someone is curious or not kind.
Someone is either not funny or happy.
John is both not kind and creative.
Someone is either kind or not kind. | Susan is not old. | entailment | (![X]:((strong(X)&patient(X))<=>(~humble(X)|kind(X))))&
((~tall(john))=>((~quiet(john)<~>wise(john))))&
(((tall(susan)|~happy(susan)))=>(?[X]:((~curious(X)&~old(X)))))&
((?[X]:((tall(X)|~calm(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((strong(X)<~>~strong(X))<=>(wise(X)&happy(X))))&
(![X]:((humble(X)|generous(X))=>strong(X)))&
(![X]:((happy(X)<~>~creative(X))=>(tall(X)|brave(X))))&
((?[X]:((~wise(X)<~>quiet(X))))<=>(old(john)))&
(![X]:(strong(X)<=>curious(X)))&
(![X]:((~humble(X)<~>~funny(X))<=>~kind(X)))&
((?[X]:((~creative(X)&calm(X))))<=>((tall(fred)<~>curious(fred))))&
((?[X]:(~tall(X)))<=>((rich(fred)<~>~calm(fred))))&
((?[X]:((rich(X)|~strong(X))))=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((~strong(X)&~tall(X))<=>(calm(X)|old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~old(X)|curious(X))))&
((rich(john)|wise(john)))&
((~old(john)<~>patient(john)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((curious(X)|~kind(X))))&
(?[X]:((~funny(X)<~>happy(X))))&
((~kind(john)&creative(john)))&
(?[X]:((kind(X)<~>~kind(X)))) | ~old(susan) | [
"p0",
"p5",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 2532363615272376190760218
% SZS output start Proof for 2532363615272376190760218
1. ! [X0] : ((patient(X0) & strong(X0)) <=> (kind(X0) | ~humble(X0))) [input p0]
6. ! [X0] : ((generous(X0) | humble(X0)) => strong(X0)) [input p5]
14. ! [X0] : ((~tall(X0) & ~strong(X0)) <=> (old(X0) | calm(X0))) [input p13]
23. old(susan) [input hypothesis]
27. ! [X0] : (humble(X0) => strong(X0)) [pure predicate removal 6]
30. ! [X0] : (strong(X0) | ~humble(X0)) [ennf transformation 27]
34. ! [X0] : (((patient(X0) & strong(X0)) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | (~patient(X0) | ~strong(X0)))) [nnf transformation 1]
35. ! [X0] : (((patient(X0) & strong(X0)) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | ~patient(X0) | ~strong(X0))) [flattening 34]
63. ! [X0] : (((~tall(X0) & ~strong(X0)) | (~old(X0) & ~calm(X0))) & ((old(X0) | calm(X0)) | (tall(X0) | strong(X0)))) [nnf transformation 14]
64. ! [X0] : (((~tall(X0) & ~strong(X0)) | (~old(X0) & ~calm(X0))) & (old(X0) | calm(X0) | tall(X0) | strong(X0))) [flattening 63]
78. strong(X0) | humble(X0) [cnf transformation 35]
97. strong(X0) | ~humble(X0) [cnf transformation 30]
124. ~strong(X0) | ~old(X0) [cnf transformation 64]
140. old(susan) [cnf transformation 23]
205. strong(X0) [subsumption resolution 97,78]
263. ~old(X0) [subsumption resolution 124,205]
276. $false [subsumption resolution 140,263]
% SZS output end Proof for 2532363615272376190760218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not wise and vice versa. Everyone who is not brave or generous is not happy. If susan is curious then someone is either curious or humble and vice versa. Everyone who is either not patient or not old is not happy or not humble. Everyone who is happy or tall is either creative or not kind and vice versa. Everyone who is both calm and not curious is not happy or not generous and vice versa. If paul is strong or brave then lucy is tall and vice versa. Everyone who is wise or not strong is not calm or not humble. If someone is not rich or not creative then lucy is either not tall or patient and vice versa. Everyone who is not humble or not curious is not patient or quiet and vice versa. Everyone who is both generous and not quiet is not curious and vice versa. If alice is either rich or not tall then someone is patient or not calm and vice versa. If someone is not wise then paul is curious or not generous. Everyone who is not funny is either brave or quiet and vice versa. If john is either calm or curious then lucy is generous and vice versa. John is strong or not creative. Someone is not strong or not happy. Mary is generous. | Lucy is kind. | entailment | (![X]:(~strong(X)<=>~wise(X)))&
(![X]:((~brave(X)|generous(X))=>~happy(X)))&
((curious(susan))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((~patient(X)<~>~old(X))=>(~happy(X)|~humble(X))))&
(![X]:((happy(X)|tall(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((calm(X)&~curious(X))<=>(~happy(X)|~generous(X))))&
(((strong(paul)|brave(paul)))<=>(tall(lucy)))&
(![X]:((wise(X)|~strong(X))=>(~calm(X)|~humble(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>((~tall(lucy)<~>patient(lucy))))&
(![X]:((~humble(X)|~curious(X))<=>(~patient(X)|quiet(X))))&
(![X]:((generous(X)&~quiet(X))<=>~curious(X)))&
(((rich(alice)<~>~tall(alice)))<=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:(~wise(X)))=>((curious(paul)|~generous(paul))))&
(![X]:(~funny(X)<=>(brave(X)<~>quiet(X))))&
(((calm(john)<~>curious(john)))<=>(generous(lucy)))&
((strong(john)|~creative(john)))&
(?[X]:((~strong(X)|~happy(X))))&
(generous(mary)) | kind(lucy) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 683900852496541838973884
% SZS output start Proof for 683900852496541838973884
1. ! [X0] : (~strong(X0) <=> ~wise(X0)) [input p0]
2. ! [X0] : ((generous(X0) | ~brave(X0)) => ~happy(X0)) [input p1]
3. curious(susan) <=> ? [X0] : (curious(X0) <~> humble(X0)) [input p2]
5. ! [X0] : ((tall(X0) | happy(X0)) <=> (creative(X0) <~> ~kind(X0))) [input p4]
6. ! [X0] : ((~curious(X0) & calm(X0)) <=> (~generous(X0) | ~happy(X0))) [input p5]
7. (brave(paul) | strong(paul)) <=> tall(lucy) [input p6]
8. ! [X0] : ((~strong(X0) | wise(X0)) => (~humble(X0) | ~calm(X0))) [input p7]
9. ? [X0] : (~creative(X0) | ~rich(X0)) <=> (~tall(lucy) <~> patient(lucy)) [input p8]
10. ! [X0] : ((~curious(X0) | ~humble(X0)) <=> (quiet(X0) | ~patient(X0))) [input p9]
11. ! [X0] : ((~quiet(X0) & generous(X0)) <=> ~curious(X0)) [input p10]
12. (rich(alice) <~> ~tall(alice)) <=> ? [X0] : (~calm(X0) | patient(X0)) [input p11]
13. ? [X0] : ~wise(X0) => (~generous(paul) | curious(paul)) [input p12]
19. ~kind(lucy) [input hypothesis]
20. ! [X0] : (~happy(X0) | (~generous(X0) & brave(X0))) [ennf transformation 2]
23. ! [X0] : ((~humble(X0) | ~calm(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 8]
24. ! [X0] : (~humble(X0) | ~calm(X0) | (strong(X0) & ~wise(X0))) [flattening 23]
25. (~generous(paul) | curious(paul)) | ! [X0] : wise(X0) [ennf transformation 13]
26. ~generous(paul) | curious(paul) | ! [X0] : wise(X0) [flattening 25]
27. ! [X0] : ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))) [nnf transformation 1]
28. (curious(susan) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (? [X0] : ((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | ~curious(susan)) [nnf transformation 3]
29. (curious(susan) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (? [X1] : ((~humble(X1) | ~curious(X1)) & (humble(X1) | curious(X1))) | ~curious(susan)) [rectify 28]
30. ? [X1] : ((~humble(X1) | ~curious(X1)) & (humble(X1) | curious(X1))) => ((~humble(sK0) | ~curious(sK0)) & (humble(sK0) | curious(sK0))) [choice axiom]
31. (curious(susan) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (((~humble(sK0) | ~curious(sK0)) & (humble(sK0) | curious(sK0))) | ~curious(susan)) [skolemisation 29,30]
33. ! [X0] : (((tall(X0) | happy(X0)) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (~tall(X0) & ~happy(X0)))) [nnf transformation 5]
34. ! [X0] : ((tall(X0) | happy(X0) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (~tall(X0) & ~happy(X0)))) [flattening 33]
35. ! [X0] : (((~curious(X0) & calm(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (curious(X0) | ~calm(X0)))) [nnf transformation 6]
36. ! [X0] : (((~curious(X0) & calm(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | curious(X0) | ~calm(X0))) [flattening 35]
37. ((brave(paul) | strong(paul)) | ~tall(lucy)) & (tall(lucy) | (~brave(paul) & ~strong(paul))) [nnf transformation 7]
38. (brave(paul) | strong(paul) | ~tall(lucy)) & (tall(lucy) | (~brave(paul) & ~strong(paul))) [flattening 37]
39. (? [X0] : (~creative(X0) | ~rich(X0)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X0] : (creative(X0) & rich(X0))) [nnf transformation 9]
40. (? [X0] : (~creative(X0) | ~rich(X0)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X1] : (creative(X1) & rich(X1))) [rectify 39]
41. ? [X0] : (~creative(X0) | ~rich(X0)) => (~creative(sK1) | ~rich(sK1)) [choice axiom]
42. ((~creative(sK1) | ~rich(sK1)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X1] : (creative(X1) & rich(X1))) [skolemisation 40,41]
43. ! [X0] : (((~curious(X0) | ~humble(X0)) | (~quiet(X0) & patient(X0))) & ((quiet(X0) | ~patient(X0)) | (curious(X0) & humble(X0)))) [nnf transformation 10]
44. ! [X0] : ((~curious(X0) | ~humble(X0) | (~quiet(X0) & patient(X0))) & (quiet(X0) | ~patient(X0) | (curious(X0) & humble(X0)))) [flattening 43]
45. ! [X0] : (((~quiet(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | (quiet(X0) | ~generous(X0)))) [nnf transformation 11]
46. ! [X0] : (((~quiet(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | quiet(X0) | ~generous(X0))) [flattening 45]
47. (((tall(alice) | ~rich(alice)) & (~tall(alice) | rich(alice))) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X0] : (~calm(X0) | patient(X0)) | ((rich(alice) | tall(alice)) & (~tall(alice) | ~rich(alice)))) [nnf transformation 12]
48. (((tall(alice) | ~rich(alice)) & (~tall(alice) | rich(alice))) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X1] : (~calm(X1) | patient(X1)) | ((rich(alice) | tall(alice)) & (~tall(alice) | ~rich(alice)))) [rectify 47]
49. ? [X1] : (~calm(X1) | patient(X1)) => (~calm(sK2) | patient(sK2)) [choice axiom]
50. (((tall(alice) | ~rich(alice)) & (~tall(alice) | rich(alice))) | ! [X0] : (calm(X0) & ~patient(X0))) & ((~calm(sK2) | patient(sK2)) | ((rich(alice) | tall(alice)) & (~tall(alice) | ~rich(alice)))) [skolemisation 48,49]
54. ~wise(X0) | strong(X0) [cnf transformation 27]
57. ~happy(X0) | ~generous(X0) [cnf transformation 20]
60. curious(susan) | humble(X0) | ~curious(X0) [cnf transformation 31]
67. ~creative(X0) | kind(X0) | ~tall(X0) [cnf transformation 34]
71. calm(X0) | happy(X0) [cnf transformation 36]
73. ~curious(X0) | happy(X0) [cnf transformation 36]
74. ~curious(X0) | generous(X0) [cnf transformation 36]
75. tall(lucy) | ~strong(paul) [cnf transformation 38]
78. ~calm(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 24]
81. patient(lucy) | ~tall(lucy) | creative(X1) [cnf transformation 42]
87. ~patient(X0) | quiet(X0) | curious(X0) [cnf transformation 44]
90. ~curious(X0) | quiet(X0) | ~generous(X0) [cnf transformation 46]
91. generous(X0) | curious(X0) [cnf transformation 46]
92. ~quiet(X0) | curious(X0) [cnf transformation 46]
93. ~calm(sK2) | patient(sK2) | ~tall(alice) | ~rich(alice) [cnf transformation 50]
94. ~calm(sK2) | patient(sK2) | rich(alice) | tall(alice) [cnf transformation 50]
95. ~tall(alice) | rich(alice) | ~patient(X0) [cnf transformation 50]
97. tall(alice) | ~rich(alice) | ~patient(X0) [cnf transformation 50]
99. ~generous(paul) | curious(paul) | wise(X0) [cnf transformation 26]
107. ~kind(lucy) [cnf transformation 19]
112. 2 <=> curious(susan) [avatar definition]
114. curious(susan) <- (2) [avatar component clause 112]
117. 3 <=> ! [X0] : (humble(X0) | ~curious(X0)) [avatar definition]
118. ~curious(X0) | humble(X0) <- (3) [avatar component clause 117]
119. 3 | 2 [avatar split clause 60,112,117]
131. 6 <=> tall(lucy) [avatar definition]
132. tall(lucy) <- (6) [avatar component clause 131]
135. 7 <=> strong(paul) [avatar definition]
136. ~strong(paul) <- (~7) [avatar component clause 135]
144. ~7 | 6 [avatar split clause 75,131,135]
146. 9 <=> patient(lucy) [avatar definition]
147. patient(lucy) <- (9) [avatar component clause 146]
160. 12 <=> ! [X1] : creative(X1) [avatar definition]
161. creative(X1) <- (12) [avatar component clause 160]
167. 12 | ~6 | 9 [avatar split clause 81,146,131,160]
169. generous(X0) [subsumption resolution 91,74]
170. ~curious(X0) | quiet(X0) [subsumption resolution 90,169]
175. 15 <=> rich(alice) [avatar definition]
179. 16 <=> tall(alice) [avatar definition]
184. 17 <=> ! [X0] : ~patient(X0) [avatar definition]
185. ~patient(X0) <- (17) [avatar component clause 184]
186. 17 | ~15 | 16 [avatar split clause 97,179,175,184]
188. 17 | 15 | ~16 [avatar split clause 95,179,175,184]
190. 18 <=> patient(sK2) [avatar definition]
192. patient(sK2) <- (18) [avatar component clause 190]
194. 19 <=> calm(sK2) [avatar definition]
195. calm(sK2) <- (19) [avatar component clause 194]
196. ~calm(sK2) <- (~19) [avatar component clause 194]
197. 16 | 15 | 18 | ~19 [avatar split clause 94,194,190,175,179]
198. ~15 | ~16 | 18 | ~19 [avatar split clause 93,194,190,179,175]
199. curious(paul) | wise(X0) [subsumption resolution 99,169]
201. 20 <=> ! [X0] : wise(X0) [avatar definition]
202. wise(X0) <- (20) [avatar component clause 201]
204. 21 <=> curious(paul) [avatar definition]
206. curious(paul) <- (21) [avatar component clause 204]
207. 20 | 21 [avatar split clause 199,204,201]
238. strong(X0) <- (20) [resolution 54,202]
239. $false <- (~7, 20) [resolution 238,136]
241. 7 | ~20 [avatar contradiction clause 239]
242. happy(sK2) <- (~19) [resolution 71,196]
243. ~generous(sK2) <- (~19) [resolution 242,57]
245. $false <- (~19) [subsumption resolution 243,169]
246. 19 [avatar contradiction clause 245]
247. $false <- (9, 17) [resolution 185,147]
248. ~9 | ~17 [avatar contradiction clause 247]
253. happy(susan) <- (2) [resolution 73,114]
255. happy(paul) <- (21) [resolution 73,206]
256. ~generous(susan) <- (2) [resolution 253,57]
258. $false <- (2) [subsumption resolution 256,169]
259. ~2 [avatar contradiction clause 258]
264. ~generous(paul) <- (21) [resolution 255,57]
266. $false <- (21) [subsumption resolution 264,169]
267. ~21 [avatar contradiction clause 266]
276. ~tall(X0) | kind(X0) <- (12) [resolution 67,161]
282. ~humble(sK2) | ~wise(sK2) <- (19) [resolution 78,195]
290. kind(lucy) <- (6, 12) [resolution 276,132]
291. $false <- (6, 12) [subsumption resolution 290,107]
292. ~6 | ~12 [avatar contradiction clause 291]
314. quiet(sK2) | curious(sK2) <- (18) [resolution 87,192]
332. 32 <=> humble(sK2) [avatar definition]
334. ~humble(sK2) <- (~32) [avatar component clause 332]
353. quiet(sK2) <- (18) [subsumption resolution 314,170]
355. ~humble(sK2) <- (19, 20) [subsumption resolution 282,202]
356. ~32 | ~19 | ~20 [avatar split clause 355,201,194,332]
366. curious(sK2) <- (18) [resolution 353,92]
370. humble(sK2) <- (3, 18) [resolution 366,118]
373. $false <- (3, 18, ~32) [subsumption resolution 370,334]
374. ~3 | ~18 | 32 [avatar contradiction clause 373]
376. $false [avatar sat refutation 119,144,167,186,188,197,198,207,241,246,248,259,267,292,356,374]
% SZS output end Proof for 683900852496541838973884
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or humble is brave and vice versa.
Everyone who is brave or calm is wise.
If alice is both tall and curious then someone is both not quiet and brave.
Everyone who is either tall or rich is not funny or not generous.
If someone is calm then john is both not brave and rich.
Everyone who is either curious or not brave is both brave and wise.
Everyone who is both kind and not humble is either brave or not humble and vice versa.
If someone is both not old and not humble then paul is not patient and vice versa.
Everyone who is not strong is patient.
Everyone who is old is not old or not rich and vice versa.
Everyone who is either humble or not kind is both not brave and not wise and vice versa.
If fred is either strong or not wise then susan is either kind or not wise and vice versa.
If fred is not old or not generous then mary is happy or not patient and vice versa.
If mary is either patient or not wise then someone is not kind or not calm and vice versa.
Everyone who is both humble and quiet is either not tall or not curious and vice versa.
Someone is either not brave or funny.
Someone is kind or not patient.
Someone is either quiet or not happy.
Someone is both curious and strong.
Someone is happy.
Someone is either not brave or not happy. | Mary is curious. | entailment | (![X]:((kind(X)<~>humble(X))<=>brave(X)))&
(![X]:((brave(X)|calm(X))=>wise(X)))&
(((tall(alice)&curious(alice)))=>(?[X]:((~quiet(X)&brave(X)))))&
(![X]:((tall(X)<~>rich(X))=>(~funny(X)|~generous(X))))&
((?[X]:(calm(X)))=>((~brave(john)&rich(john))))&
(![X]:((curious(X)<~>~brave(X))=>(brave(X)&wise(X))))&
(![X]:((kind(X)&~humble(X))<=>(brave(X)<~>~humble(X))))&
((?[X]:((~old(X)&~humble(X))))<=>(~patient(paul)))&
(![X]:(~strong(X)=>patient(X)))&
(![X]:(old(X)<=>(~old(X)|~rich(X))))&
(![X]:((humble(X)<~>~kind(X))<=>(~brave(X)&~wise(X))))&
(((strong(fred)<~>~wise(fred)))<=>((kind(susan)<~>~wise(susan))))&
(((~old(fred)|~generous(fred)))<=>((happy(mary)|~patient(mary))))&
(((patient(mary)<~>~wise(mary)))<=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:((humble(X)&quiet(X))<=>(~tall(X)<~>~curious(X))))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:((kind(X)|~patient(X))))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:((curious(X)&strong(X))))&
(?[X]:(happy(X)))&
(?[X]:((~brave(X)<~>~happy(X)))) | curious(mary) | [
"p0",
"p5",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 6077517592232609732451427
% SZS output start Proof for 6077517592232609732451427
1. ! [X0] : ((kind(X0) <~> humble(X0)) <=> brave(X0)) [input p0]
6. ! [X0] : ((curious(X0) <~> ~brave(X0)) => (wise(X0) & brave(X0))) [input p5]
7. ! [X0] : ((~humble(X0) & kind(X0)) <=> (brave(X0) <~> ~humble(X0))) [input p6]
22. ~curious(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & brave(X0)) | (curious(X0) <=> ~brave(X0))) [ennf transformation 6]
31. ! [X0] : ((((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | ~brave(X0)) & (brave(X0) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0))))) [nnf transformation 1]
35. ! [X0] : ((wise(X0) & brave(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) [nnf transformation 29]
36. ! [X0] : (((~humble(X0) & kind(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0)))) & (((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (humble(X0) | ~kind(X0)))) [nnf transformation 7]
37. ! [X0] : (((~humble(X0) & kind(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0)))) & (((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | humble(X0) | ~kind(X0))) [flattening 36]
70. ~kind(X0) | humble(X0) | brave(X0) [cnf transformation 31]
72. ~brave(X0) | kind(X0) | humble(X0) [cnf transformation 31]
73. ~humble(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 31]
83. brave(X0) | curious(X0) | brave(X0) [cnf transformation 35]
87. humble(X0) | ~brave(X0) | humble(X0) | ~kind(X0) [cnf transformation 37]
89. kind(X0) | brave(X0) | humble(X0) [cnf transformation 37]
90. ~humble(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 37]
139. ~curious(mary) [cnf transformation 22]
142. humble(X0) | ~brave(X0) | ~kind(X0) [duplicate literal removal 87]
143. ~brave(X0) | ~humble(X0) [duplicate literal removal 90]
144. curious(X0) | brave(X0) [duplicate literal removal 83]
177. brave(X0) | humble(X0) [subsumption resolution 89,70]
178. ~brave(X0) | ~kind(X0) [subsumption resolution 142,73]
307. brave(mary) [resolution 144,139]
309. ~humble(mary) [resolution 307,143]
321. ~kind(X0) | humble(X0) [resolution 178,177]
327. kind(X0) | humble(X0) | humble(X0) [resolution 72,177]
331. kind(X0) | humble(X0) [duplicate literal removal 327]
332. humble(X0) [subsumption resolution 331,321]
335. $false [resolution 332,309]
% SZS output end Proof for 6077517592232609732451427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is either humble or not patient.
If john is both brave and humble then someone is wise or tall.
If someone is either not brave or humble then someone is either not creative or tall and vice versa.
Everyone who is not wise or not quiet is not humble and vice versa.
Everyone who is both rich and curious is either not creative or not curious.
Everyone who is both generous and kind is not kind.
If someone is both not wise and generous then someone is not funny or not calm.
Everyone who is either brave or quiet is both not calm and funny.
Everyone who is both brave and not calm is either patient or funny.
If someone is funny or wise then susan is both not brave and generous.
If alice is either not old or quiet then someone is either rich or not generous and vice versa.
If susan is curious or not tall then someone is quiet or curious and vice versa.
Everyone who is not calm or brave is either brave or not funny.
Everyone who is not happy is both not tall and calm and vice versa.
Everyone who is both not happy and not rich is wise.
Everyone who is either not old or not funny is both funny and wise.
Paul is rich.
Susan is not generous.
Someone is not humble or not old.
Someone is both not wise and not kind.
John is not rich.
Fred is tall or brave.
Someone is both creative and not calm.
Someone is not brave or kind. | Paul is not tall. | neutral | (![X]:(rich(X)=>(humble(X)<~>~patient(X))))&
(((brave(john)&humble(john)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((~brave(X)<~>humble(X))))<=>(?[X]:((~creative(X)<~>tall(X)))))&
(![X]:((~wise(X)|~quiet(X))<=>~humble(X)))&
(![X]:((rich(X)&curious(X))=>(~creative(X)<~>~curious(X))))&
(![X]:((generous(X)&kind(X))=>~kind(X)))&
((?[X]:((~wise(X)&generous(X))))=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((brave(X)<~>quiet(X))=>(~calm(X)&funny(X))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)<~>funny(X))))&
((?[X]:((funny(X)|wise(X))))=>((~brave(susan)&generous(susan))))&
(((~old(alice)<~>quiet(alice)))<=>(?[X]:((rich(X)<~>~generous(X)))))&
(((curious(susan)|~tall(susan)))<=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((~calm(X)|brave(X))=>(brave(X)<~>~funny(X))))&
(![X]:(~happy(X)<=>(~tall(X)&calm(X))))&
(![X]:((~happy(X)&~rich(X))=>wise(X)))&
(![X]:((~old(X)<~>~funny(X))=>(funny(X)&wise(X))))&
(rich(paul))&
(~generous(susan))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:((~wise(X)&~kind(X))))&
(~rich(john))&
((tall(fred)|brave(fred)))&
(?[X]:((creative(X)&~calm(X))))&
(?[X]:((~brave(X)|kind(X)))) | ~tall(paul) | []
| null | 0 |
If someone is not curious then someone is both not rich and not quiet and vice versa. Everyone who is generous or not quiet is both not patient and strong and vice versa. If someone is either rich or wise then susan is both not humble and quiet. Everyone who is generous is creative or brave and vice versa. Everyone who is not funny or not brave is not creative or not patient. If someone is either not generous or not tall then someone is funny. Everyone who is not rich is either not kind or not old and vice versa. Everyone who is not creative or not calm is both brave and wise and vice versa. Everyone who is both funny and patient is not curious or not wise and vice versa. Everyone who is brave or not rich is not funny. If alice is not quiet then someone is both not happy and not calm and vice versa. Everyone who is not patient is not brave or patient and vice versa. If fred is either tall or not generous then someone is patient and vice versa. Everyone who is patient or not old is both old and happy and vice versa. If susan is either not tall or wise then someone is not brave or old and vice versa. Everyone who is not old is either not funny or rich. Someone is curious. Someone is not old or quiet. Someone is either not tall or curious. Someone is either curious or happy. Someone is humble or calm. Susan is not happy. | Fred is curious. | entailment | ((?[X]:(~curious(X)))<=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((generous(X)|~quiet(X))<=>(~patient(X)&strong(X))))&
((?[X]:((rich(X)<~>wise(X))))=>((~humble(susan)&quiet(susan))))&
(![X]:(generous(X)<=>(creative(X)|brave(X))))&
(![X]:((~funny(X)|~brave(X))=>(~creative(X)|~patient(X))))&
((?[X]:((~generous(X)<~>~tall(X))))=>(?[X]:(funny(X))))&
(![X]:(~rich(X)<=>(~kind(X)<~>~old(X))))&
(![X]:((~creative(X)|~calm(X))<=>(brave(X)&wise(X))))&
(![X]:((funny(X)&patient(X))<=>(~curious(X)|~wise(X))))&
(![X]:((brave(X)|~rich(X))=>~funny(X)))&
((~quiet(alice))<=>(?[X]:((~happy(X)&~calm(X)))))&
(![X]:(~patient(X)<=>(~brave(X)|patient(X))))&
(((tall(fred)<~>~generous(fred)))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)|~old(X))<=>(old(X)&happy(X))))&
(((~tall(susan)<~>wise(susan)))<=>(?[X]:((~brave(X)|old(X)))))&
(![X]:(~old(X)=>(~funny(X)<~>rich(X))))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)|quiet(X))))&
(?[X]:((~tall(X)<~>curious(X))))&
(?[X]:((curious(X)<~>happy(X))))&
(?[X]:((humble(X)|calm(X))))&
(~happy(susan)) | curious(fred) | [
"p8",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 232233271932667540124335
% SZS output start Proof for 232233271932667540124335
9. ! [X0] : ((patient(X0) & funny(X0)) <=> (~wise(X0) | ~curious(X0))) [input p8]
12. ! [X0] : (~patient(X0) <=> (patient(X0) | ~brave(X0))) [input p11]
23. ~curious(fred) [input hypothesis]
49. ! [X0] : (((patient(X0) & funny(X0)) | (wise(X0) & curious(X0))) & ((~wise(X0) | ~curious(X0)) | (~patient(X0) | ~funny(X0)))) [nnf transformation 9]
50. ! [X0] : (((patient(X0) & funny(X0)) | (wise(X0) & curious(X0))) & (~wise(X0) | ~curious(X0) | ~patient(X0) | ~funny(X0))) [flattening 49]
55. ! [X0] : ((~patient(X0) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | patient(X0))) [nnf transformation 12]
56. ! [X0] : ((~patient(X0) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | patient(X0))) [flattening 55]
111. patient(X0) | curious(X0) [cnf transformation 50]
120. ~patient(X0) | ~patient(X0) [cnf transformation 56]
146. ~curious(fred) [cnf transformation 23]
150. ~patient(X0) [duplicate literal removal 120]
160. 3 <=> ! [X3] : curious(X3) [avatar definition]
161. curious(X3) <- (3) [avatar component clause 160]
292. curious(X2) [resolution 111,150]
295. 3 [avatar split clause 292,160]
296. $false <- (3) [resolution 161,146]
301. ~3 [avatar contradiction clause 296]
302. $false [avatar sat refutation 295,301]
% SZS output end Proof for 232233271932667540124335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or tall is both happy and quiet.
Everyone who is either not wise or rich is both wise and not strong and vice versa.
Everyone who is both not humble and not creative is calm and vice versa.
Everyone who is rich or not generous is either brave or not curious.
Everyone who is both not strong and kind is either happy or not tall.
Everyone who is not happy is generous.
Everyone who is not generous is not old.
Everyone who is not tall is either not rich or creative.
Everyone who is both old and kind is both calm and curious and vice versa.
Everyone who is either not funny or not happy is tall.
If someone is not wise or not curious then someone is brave and vice versa.
If someone is both not humble and old then someone is either not wise or humble and vice versa.
If alice is either calm or wise then john is both not patient and not brave and vice versa.
If someone is strong or wise then someone is either not strong or not curious and vice versa.
Everyone who is creative is wise or patient and vice versa.
Everyone who is both not wise and tall is both not rich and not curious.
Someone is either not wise or not humble.
Someone is not rich or not humble.
Alice is either humble or not curious.
Alice is either quiet or generous.
Someone is humble or not calm.
Fred is both not brave and humble.
Susan is both rich and not patient.
Mary is generous or wise. | Alice is not calm. | entailment | (![X]:((~humble(X)|tall(X))=>(happy(X)&quiet(X))))&
(![X]:((~wise(X)<~>rich(X))<=>(wise(X)&~strong(X))))&
(![X]:((~humble(X)&~creative(X))<=>calm(X)))&
(![X]:((rich(X)|~generous(X))=>(brave(X)<~>~curious(X))))&
(![X]:((~strong(X)&kind(X))=>(happy(X)<~>~tall(X))))&
(![X]:(~happy(X)=>generous(X)))&
(![X]:(~generous(X)=>~old(X)))&
(![X]:(~tall(X)=>(~rich(X)<~>creative(X))))&
(![X]:((old(X)&kind(X))<=>(calm(X)&curious(X))))&
(![X]:((~funny(X)<~>~happy(X))=>tall(X)))&
((?[X]:((~wise(X)|~curious(X))))<=>(?[X]:(brave(X))))&
((?[X]:((~humble(X)&old(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(((calm(alice)<~>wise(alice)))<=>((~patient(john)&~brave(john))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~strong(X)<~>~curious(X)))))&
(![X]:(creative(X)<=>(wise(X)|patient(X))))&
(![X]:((~wise(X)&tall(X))=>(~rich(X)&~curious(X))))&
(?[X]:((~wise(X)<~>~humble(X))))&
(?[X]:((~rich(X)|~humble(X))))&
((humble(alice)<~>~curious(alice)))&
((quiet(alice)<~>generous(alice)))&
(?[X]:((humble(X)|~calm(X))))&
((~brave(fred)&humble(fred)))&
((rich(susan)&~patient(susan)))&
((generous(mary)|wise(mary))) | ~calm(alice) | [
"p1",
"p2",
"p7",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 1476852735579262197437086
% SZS output start Proof for 1476852735579262197437086
2. ! [X0] : ((~wise(X0) <~> rich(X0)) <=> (~strong(X0) & wise(X0))) [input p1]
3. ! [X0] : ((~creative(X0) & ~humble(X0)) <=> calm(X0)) [input p2]
8. ! [X0] : (~tall(X0) => (~rich(X0) <~> creative(X0))) [input p7]
15. ! [X0] : (creative(X0) <=> (patient(X0) | wise(X0))) [input p14]
16. ! [X0] : ((tall(X0) & ~wise(X0)) => (~curious(X0) & ~rich(X0))) [input p15]
25. calm(alice) [input hypothesis]
35. ! [X0] : ((~rich(X0) <~> creative(X0)) | tall(X0)) [ennf transformation 8]
37. ! [X0] : ((~curious(X0) & ~rich(X0)) | (~tall(X0) | wise(X0))) [ennf transformation 16]
38. ! [X0] : ((~curious(X0) & ~rich(X0)) | ~tall(X0) | wise(X0)) [flattening 37]
39. ! [X0] : ((((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0))))) [flattening 39]
41. ! [X0] : (((~creative(X0) & ~humble(X0)) | ~calm(X0)) & (calm(X0) | (creative(X0) | humble(X0)))) [nnf transformation 3]
42. ! [X0] : (((~creative(X0) & ~humble(X0)) | ~calm(X0)) & (calm(X0) | creative(X0) | humble(X0))) [flattening 41]
45. ! [X0] : (((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | tall(X0)) [nnf transformation 35]
66. ! [X0] : ((creative(X0) | (~patient(X0) & ~wise(X0))) & ((patient(X0) | wise(X0)) | ~creative(X0))) [nnf transformation 15]
67. ! [X0] : ((creative(X0) | (~patient(X0) & ~wise(X0))) & (patient(X0) | wise(X0) | ~creative(X0))) [flattening 66]
81. wise(X0) | rich(X0) | wise(X0) [cnf transformation 40]
89. ~calm(X0) | ~creative(X0) [cnf transformation 42]
98. ~rich(X0) | creative(X0) | tall(X0) [cnf transformation 45]
128. ~wise(X0) | creative(X0) [cnf transformation 67]
130. ~rich(X0) | ~tall(X0) | wise(X0) [cnf transformation 38]
145. calm(alice) [cnf transformation 25]
146. rich(X0) | wise(X0) [duplicate literal removal 81]
213. 16 <=> calm(alice) [avatar definition]
214. calm(alice) <- (16) [avatar component clause 213]
217. 17 <=> wise(alice) [avatar definition]
218. wise(alice) <- (17) [avatar component clause 217]
260. ~tall(X0) | wise(X0) [subsumption resolution 130,146]
310. 16 [avatar split clause 145,213]
312. ~creative(alice) <- (16) [resolution 89,214]
366. creative(X0) | tall(X0) | wise(X0) [resolution 98,146]
376. creative(X0) | tall(X0) [subsumption resolution 366,128]
423. 53 <=> tall(alice) [avatar definition]
425. tall(alice) <- (53) [avatar component clause 423]
440. tall(alice) <- (16) [resolution 376,312]
444. 53 | ~16 [avatar split clause 440,213,423]
446. wise(alice) <- (53) [resolution 425,260]
451. 17 | ~53 [avatar split clause 446,423,217]
454. creative(alice) <- (17) [resolution 218,128]
464. $false <- (16, 17) [subsumption resolution 454,312]
465. ~16 | ~17 [avatar contradiction clause 464]
466. $false [avatar sat refutation 310,444,451,465]
% SZS output end Proof for 1476852735579262197437086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is kind or calm then someone is not wise and vice versa.
Everyone who is either not generous or humble is either not wise or not kind and vice versa.
Everyone who is not creative is both funny and creative.
Everyone who is not funny is either strong or not rich and vice versa.
If lucy is both rich and not happy then someone is not calm or humble.
If lucy is both not brave and not curious then someone is both generous and wise and vice versa.
Everyone who is not happy is curious and vice versa.
If someone is not kind then fred is both not wise and not patient and vice versa.
If mary is both not curious and not brave then someone is not generous and vice versa.
Everyone who is both not kind and not old is strong and vice versa.
Everyone who is tall or strong is both not calm and humble and vice versa.
Everyone who is either generous or not quiet is tall or calm.
Everyone who is both not humble and not calm is tall or not humble and vice versa.
If john is wise or not generous then someone is humble and vice versa.
Everyone who is both kind and not kind is either not creative or old and vice versa.
Everyone who is both not brave and not patient is funny.
Someone is both not wise and curious.
Lucy is either generous or not tall.
Paul is both curious and not patient.
Someone is both not curious and calm.
John is either not kind or funny.
Susan is either not quiet or quiet.
Someone is either tall or not happy.
Someone is not old or curious. | Susan is strong. | contradiction | (((kind(susan)|calm(susan)))<=>(?[X]:(~wise(X))))&
(![X]:((~generous(X)<~>humble(X))<=>(~wise(X)<~>~kind(X))))&
(![X]:(~creative(X)=>(funny(X)&creative(X))))&
(![X]:(~funny(X)<=>(strong(X)<~>~rich(X))))&
(((rich(lucy)&~happy(lucy)))=>(?[X]:((~calm(X)|humble(X)))))&
(((~brave(lucy)&~curious(lucy)))<=>(?[X]:((generous(X)&wise(X)))))&
(![X]:(~happy(X)<=>curious(X)))&
((?[X]:(~kind(X)))<=>((~wise(fred)&~patient(fred))))&
(((~curious(mary)&~brave(mary)))<=>(?[X]:(~generous(X))))&
(![X]:((~kind(X)&~old(X))<=>strong(X)))&
(![X]:((tall(X)|strong(X))<=>(~calm(X)&humble(X))))&
(![X]:((generous(X)<~>~quiet(X))=>(tall(X)|calm(X))))&
(![X]:((~humble(X)&~calm(X))<=>(tall(X)|~humble(X))))&
(((wise(john)|~generous(john)))<=>(?[X]:(humble(X))))&
(![X]:((kind(X)&~kind(X))<=>(~creative(X)<~>old(X))))&
(![X]:((~brave(X)&~patient(X))=>funny(X)))&
(?[X]:((~wise(X)&curious(X))))&
((generous(lucy)<~>~tall(lucy)))&
((curious(paul)&~patient(paul)))&
(?[X]:((~curious(X)&calm(X))))&
((~kind(john)<~>funny(john)))&
((~quiet(susan)<~>quiet(susan)))&
(?[X]:((tall(X)<~>~happy(X))))&
(?[X]:((~old(X)|curious(X)))) | strong(susan) | [
"p0",
"p9",
"p10",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 3062533126884719398310031
% SZS output start Proof for 3062533126884719398310031
1. (calm(susan) | kind(susan)) <=> ? [X0] : ~wise(X0) [input p0]
10. ! [X0] : ((~old(X0) & ~kind(X0)) <=> strong(X0)) [input p9]
11. ! [X0] : ((strong(X0) | tall(X0)) <=> (humble(X0) & ~calm(X0))) [input p10]
17. ? [X0] : (curious(X0) & ~wise(X0)) [input p16]
25. strong(susan) [input hypothesis]
33. ((calm(susan) | kind(susan)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | (~calm(susan) & ~kind(susan))) [nnf transformation 1]
34. (calm(susan) | kind(susan) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | (~calm(susan) & ~kind(susan))) [flattening 33]
35. (calm(susan) | kind(susan) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | (~calm(susan) & ~kind(susan))) [rectify 34]
36. ? [X1] : ~wise(X1) => ~wise(sK0) [choice axiom]
37. (calm(susan) | kind(susan) | ! [X0] : wise(X0)) & (~wise(sK0) | (~calm(susan) & ~kind(susan))) [skolemisation 35,36]
58. ! [X0] : (((~old(X0) & ~kind(X0)) | ~strong(X0)) & (strong(X0) | (old(X0) | kind(X0)))) [nnf transformation 10]
59. ! [X0] : (((~old(X0) & ~kind(X0)) | ~strong(X0)) & (strong(X0) | old(X0) | kind(X0))) [flattening 58]
60. ! [X0] : (((strong(X0) | tall(X0)) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | (~strong(X0) & ~tall(X0)))) [nnf transformation 11]
61. ! [X0] : ((strong(X0) | tall(X0) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | (~strong(X0) & ~tall(X0)))) [flattening 60]
72. ? [X0] : (curious(X0) & ~wise(X0)) => (curious(sK6) & ~wise(sK6)) [choice axiom]
73. curious(sK6) & ~wise(sK6) [skolemisation 17,72]
86. calm(susan) | kind(susan) | wise(X0) [cnf transformation 37]
115. ~strong(X0) | ~kind(X0) [cnf transformation 59]
118. ~strong(X0) | ~calm(X0) [cnf transformation 61]
139. ~wise(sK6) [cnf transformation 73]
154. strong(susan) [cnf transformation 25]
157. 1 <=> ! [X0] : wise(X0) [avatar definition]
158. wise(X0) <- (1) [avatar component clause 157]
160. 2 <=> kind(susan) [avatar definition]
164. 3 <=> calm(susan) [avatar definition]
167. 1 | 2 | 3 [avatar split clause 86,164,160,157]
291. ~kind(susan) [resolution 115,154]
294. ~2 [avatar split clause 291,160]
295. ~calm(susan) [resolution 118,154]
298. ~3 [avatar split clause 295,164]
302. $false <- (1) [resolution 158,139]
303. ~1 [avatar contradiction clause 302]
307. $false [avatar sat refutation 167,294,298,303]
% SZS output end Proof for 3062533126884719398310031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not brave then someone is calm or strong and vice versa. If someone is either not funny or not brave then someone is both not humble and not old. If someone is either rich or not creative then susan is not rich or not humble and vice versa. Everyone who is both funny and not patient is curious or not funny and vice versa. If someone is both rich and not patient then alice is either rich or not quiet. Everyone who is patient or not quiet is curious and vice versa. If fred is not strong or not old then mary is not creative or not patient and vice versa. If someone is either not rich or creative then someone is either not curious or not wise. If someone is either old or kind then someone is either not strong or old. Everyone who is not old or not tall is tall or not old and vice versa. Everyone who is not strong is both strong and not happy. Everyone who is both not calm and brave is either not creative or tall and vice versa. If someone is quiet or generous then someone is either quiet or generous. Everyone who is tall or not strong is not wise. If john is both not generous and old then mary is happy or not tall and vice versa. Someone is not brave. John is not brave or strong. Someone is tall. Someone is creative or not happy. Someone is either funny or old. | Susan is old. | contradiction | (((tall(mary)|~brave(mary)))<=>(?[X]:((calm(X)|strong(X)))))&
((?[X]:((~funny(X)<~>~brave(X))))=>(?[X]:((~humble(X)&~old(X)))))&
((?[X]:((rich(X)<~>~creative(X))))<=>((~rich(susan)|~humble(susan))))&
(![X]:((funny(X)&~patient(X))<=>(curious(X)|~funny(X))))&
((?[X]:((rich(X)&~patient(X))))=>((rich(alice)<~>~quiet(alice))))&
(![X]:((patient(X)|~quiet(X))<=>curious(X)))&
(((~strong(fred)|~old(fred)))<=>((~creative(mary)|~patient(mary))))&
((?[X]:((~rich(X)<~>creative(X))))=>(?[X]:((~curious(X)<~>~wise(X)))))&
((?[X]:((old(X)<~>kind(X))))=>(?[X]:((~strong(X)<~>old(X)))))&
(![X]:((~old(X)|~tall(X))<=>(tall(X)|~old(X))))&
(![X]:(~strong(X)=>(strong(X)&~happy(X))))&
(![X]:((~calm(X)&brave(X))<=>(~creative(X)<~>tall(X))))&
((?[X]:((quiet(X)|generous(X))))=>(?[X]:((quiet(X)<~>generous(X)))))&
(![X]:((tall(X)|~strong(X))=>~wise(X)))&
(((~generous(john)&old(john)))<=>((happy(mary)|~tall(mary))))&
(?[X]:(~brave(X)))&
((~brave(john)|strong(john)))&
(?[X]:(tall(X)))&
(?[X]:((creative(X)|~happy(X))))&
(?[X]:((funny(X)<~>old(X)))) | old(susan) | [
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 28759424737522349556630
% SZS output start Proof for 28759424737522349556630
10. ! [X0] : ((~tall(X0) | ~old(X0)) <=> (~old(X0) | tall(X0))) [input p9]
21. old(susan) [input hypothesis]
62. ! [X0] : (((~tall(X0) | ~old(X0)) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | (tall(X0) & old(X0)))) [nnf transformation 10]
63. ! [X0] : ((~tall(X0) | ~old(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | (tall(X0) & old(X0)))) [flattening 62]
118. ~old(X0) | tall(X0) | tall(X0) [cnf transformation 63]
119. ~tall(X0) | ~old(X0) | ~tall(X0) [cnf transformation 63]
146. old(susan) [cnf transformation 21]
148. ~old(X0) | tall(X0) [duplicate literal removal 118]
149. ~tall(X0) | ~old(X0) [duplicate literal removal 119]
286. ~old(X0) [subsumption resolution 148,149]
322. $false [subsumption resolution 146,286]
% SZS output end Proof for 28759424737522349556630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not strong and creative then john is both generous and patient. If someone is wise then susan is patient or not old and vice versa. If someone is either not rich or not old then susan is either humble or curious and vice versa. Everyone who is both not patient and not creative is both not brave and not quiet and vice versa. Everyone who is generous is happy or not generous and vice versa. Everyone who is either not funny or happy is either tall or not generous. If someone is not calm then someone is either not wise or calm. Everyone who is not quiet or calm is either not happy or patient. If someone is wise or curious then someone is both calm and not funny and vice versa. Everyone who is not generous or not strong is both not tall and not rich and vice versa. Everyone who is both generous and tall is both funny and not generous and vice versa. Everyone who is patient is either generous or kind. If susan is either not curious or humble then someone is kind and vice versa. Everyone who is not calm or happy is rich or not creative and vice versa. Everyone who is either generous or not strong is both curious and not patient. If susan is not curious or not kind then someone is not tall and vice versa. Someone is not kind. Someone is generous. Someone is patient. Someone is not humble. Susan is funny or generous. Someone is both patient and not old. | Susan is strong. | neutral | (((~strong(mary)&creative(mary)))=>((generous(john)&patient(john))))&
((?[X]:(wise(X)))<=>((patient(susan)|~old(susan))))&
((?[X]:((~rich(X)<~>~old(X))))<=>((humble(susan)<~>curious(susan))))&
(![X]:((~patient(X)&~creative(X))<=>(~brave(X)&~quiet(X))))&
(![X]:(generous(X)<=>(happy(X)|~generous(X))))&
(![X]:((~funny(X)<~>happy(X))=>(tall(X)<~>~generous(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:((~quiet(X)|calm(X))=>(~happy(X)<~>patient(X))))&
((?[X]:((wise(X)|curious(X))))<=>(?[X]:((calm(X)&~funny(X)))))&
(![X]:((~generous(X)|~strong(X))<=>(~tall(X)&~rich(X))))&
(![X]:((generous(X)&tall(X))<=>(funny(X)&~generous(X))))&
(![X]:(patient(X)=>(generous(X)<~>kind(X))))&
(((~curious(susan)<~>humble(susan)))<=>(?[X]:(kind(X))))&
(![X]:((~calm(X)|happy(X))<=>(rich(X)|~creative(X))))&
(![X]:((generous(X)<~>~strong(X))=>(curious(X)&~patient(X))))&
(((~curious(susan)|~kind(susan)))<=>(?[X]:(~tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:(generous(X)))&
(?[X]:(patient(X)))&
(?[X]:(~humble(X)))&
((funny(susan)|generous(susan)))&
(?[X]:((patient(X)&~old(X)))) | strong(susan) | []
| null | 0 |
Everyone who is either not happy or not creative is strong or brave.
If someone is not brave or funny then someone is both not happy and not humble and vice versa.
Everyone who is not old or kind is both not calm and not generous and vice versa.
Everyone who is either not old or not creative is both quiet and funny and vice versa.
If mary is calm then john is not quiet or creative.
If mary is not wise then someone is not curious.
Everyone who is either kind or not tall is not wise or not calm and vice versa.
Everyone who is both generous and not brave is not tall or not creative and vice versa.
Everyone who is not happy is either patient or generous.
Everyone who is both not rich and not tall is either old or happy and vice versa.
Everyone who is not humble or not calm is quiet.
Everyone who is creative is quiet.
If john is not old then someone is both not funny and kind and vice versa.
If someone is not curious then susan is either patient or not humble.
Everyone who is both not patient and not happy is both not tall and not generous.
If john is not strong or rich then someone is either not strong or old.
Someone is not generous.
John is both patient and not brave.
Someone is either quiet or funny.
Lucy is either not funny or quiet.
Lucy is creative.
Someone is both humble and not tall.
Someone is either curious or brave.
Susan is both tall and funny. | Lucy is funny. | entailment | (![X]:((~happy(X)<~>~creative(X))=>(strong(X)|brave(X))))&
((?[X]:((~brave(X)|funny(X))))<=>(?[X]:((~happy(X)&~humble(X)))))&
(![X]:((~old(X)|kind(X))<=>(~calm(X)&~generous(X))))&
(![X]:((~old(X)<~>~creative(X))<=>(quiet(X)&funny(X))))&
((calm(mary))=>((~quiet(john)|creative(john))))&
((~wise(mary))=>(?[X]:(~curious(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:((generous(X)&~brave(X))<=>(~tall(X)|~creative(X))))&
(![X]:(~happy(X)=>(patient(X)<~>generous(X))))&
(![X]:((~rich(X)&~tall(X))<=>(old(X)<~>happy(X))))&
(![X]:((~humble(X)|~calm(X))=>quiet(X)))&
(![X]:(creative(X)=>quiet(X)))&
((~old(john))<=>(?[X]:((~funny(X)&kind(X)))))&
((?[X]:(~curious(X)))=>((patient(susan)<~>~humble(susan))))&
(![X]:((~patient(X)&~happy(X))=>(~tall(X)&~generous(X))))&
(((~strong(john)|rich(john)))=>(?[X]:((~strong(X)<~>old(X)))))&
(?[X]:(~generous(X)))&
((patient(john)&~brave(john)))&
(?[X]:((quiet(X)<~>funny(X))))&
((~funny(lucy)<~>quiet(lucy)))&
(creative(lucy))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((curious(X)<~>brave(X))))&
((tall(susan)&funny(susan))) | funny(lucy) | [
"p11",
"p19",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 3767003774241982455320949
% SZS output start Proof for 3767003774241982455320949
12. ! [X0] : (creative(X0) => quiet(X0)) [input p11]
20. ~funny(lucy) <~> quiet(lucy) [input p19]
21. creative(lucy) [input p20]
25. ~funny(lucy) [input hypothesis]
34. ! [X0] : (quiet(X0) | ~creative(X0)) [ennf transformation 12]
71. (~quiet(lucy) | funny(lucy)) & (quiet(lucy) | ~funny(lucy)) [nnf transformation 20]
118. ~creative(X0) | quiet(X0) [cnf transformation 34]
136. ~quiet(lucy) | funny(lucy) [cnf transformation 71]
137. creative(lucy) [cnf transformation 21]
144. ~funny(lucy) [cnf transformation 25]
262. 26 <=> funny(lucy) [avatar definition]
266. 27 <=> quiet(lucy) [avatar definition]
268. ~quiet(lucy) <- (~27) [avatar component clause 266]
269. 26 | ~27 [avatar split clause 136,266,262]
281. ~26 [avatar split clause 144,262]
292. quiet(lucy) [resolution 118,137]
294. $false <- (~27) [subsumption resolution 292,268]
295. 27 [avatar contradiction clause 294]
296. $false [avatar sat refutation 269,281,295]
% SZS output end Proof for 3767003774241982455320949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious and not rich then someone is either not rich or not humble and vice versa.
Everyone who is either not creative or kind is not patient.
Everyone who is not happy is both not wise and not old.
If fred is humble then someone is either not humble or not tall.
If someone is both not quiet and tall then someone is quiet and vice versa.
Everyone who is not creative is not tall or creative and vice versa.
Everyone who is not quiet or not old is both not quiet and calm.
Everyone who is both calm and not generous is both kind and not rich and vice versa.
Everyone who is either generous or patient is both old and not old.
Everyone who is curious or not funny is not brave or strong.
If lucy is rich or generous then someone is either not old or not humble and vice versa.
Everyone who is not humble or kind is either not curious or brave and vice versa.
Everyone who is not wise is both not humble and kind and vice versa.
If someone is both humble and not quiet then someone is not quiet.
If fred is either generous or not patient then susan is not patient or tall and vice versa.
Someone is strong or happy.
Someone is either curious or not quiet.
Susan is either funny or generous.
Someone is curious or not rich.
John is wise.
Alice is not rich or humble.
Fred is not creative or happy. | Fred is not kind. | contradiction | ((?[X]:((~curious(X)&~rich(X))))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~creative(X)<~>kind(X))=>~patient(X)))&
(![X]:(~happy(X)=>(~wise(X)&~old(X))))&
((humble(fred))=>(?[X]:((~humble(X)<~>~tall(X)))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~tall(X)|creative(X))))&
(![X]:((~quiet(X)|~old(X))=>(~quiet(X)&calm(X))))&
(![X]:((calm(X)&~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((generous(X)<~>patient(X))=>(old(X)&~old(X))))&
(![X]:((curious(X)|~funny(X))=>(~brave(X)|strong(X))))&
(((rich(lucy)|generous(lucy)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|kind(X))<=>(~curious(X)<~>brave(X))))&
(![X]:(~wise(X)<=>(~humble(X)&kind(X))))&
((?[X]:((humble(X)&~quiet(X))))=>(?[X]:(~quiet(X))))&
(((generous(fred)<~>~patient(fred)))<=>((~patient(susan)|tall(susan))))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((curious(X)<~>~quiet(X))))&
((funny(susan)<~>generous(susan)))&
(?[X]:((curious(X)|~rich(X))))&
(wise(john))&
((~rich(alice)|humble(alice)))&
((~creative(fred)|happy(fred))) | ~kind(fred) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 8921984858013743313307874
% SZS output start Proof for 8921984858013743313307874
2. ! [X0] : ((~creative(X0) <~> kind(X0)) => ~patient(X0)) [input p1]
5. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X0] : quiet(X0) [input p4]
6. ! [X0] : (~creative(X0) <=> (creative(X0) | ~tall(X0))) [input p5]
7. ! [X0] : ((~old(X0) | ~quiet(X0)) => (calm(X0) & ~quiet(X0))) [input p6]
8. ! [X0] : ((~generous(X0) & calm(X0)) <=> (~rich(X0) & kind(X0))) [input p7]
9. ! [X0] : ((generous(X0) <~> patient(X0)) => (~old(X0) & old(X0))) [input p8]
23. ~kind(fred) [input hypothesis]
25. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X1] : quiet(X1) [rectify 5]
32. ! [X0] : (~patient(X0) | (~creative(X0) <=> kind(X0))) [ennf transformation 2]
34. ! [X0] : ((calm(X0) & ~quiet(X0)) | (old(X0) & quiet(X0))) [ennf transformation 7]
35. ! [X0] : ((~old(X0) & old(X0)) | (generous(X0) <=> patient(X0))) [ennf transformation 9]
44. ! [X0] : (~patient(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) [nnf transformation 32]
48. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : (~tall(X0) | quiet(X0))) [nnf transformation 25]
49. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : (~tall(X3) | quiet(X3))) [rectify 48]
50. ? [X0] : (tall(X0) & ~quiet(X0)) => (tall(sK3) & ~quiet(sK3)) [choice axiom]
51. ? [X2] : quiet(X2) => quiet(sK4) [choice axiom]
52. ((tall(sK3) & ~quiet(sK3)) | ! [X1] : ~quiet(X1)) & (quiet(sK4) | ! [X3] : (~tall(X3) | quiet(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & ((creative(X0) | ~tall(X0)) | creative(X0))) [nnf transformation 6]
54. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & (creative(X0) | ~tall(X0) | creative(X0))) [flattening 53]
55. ! [X0] : (((~generous(X0) & calm(X0)) | (rich(X0) | ~kind(X0))) & ((~rich(X0) & kind(X0)) | (generous(X0) | ~calm(X0)))) [nnf transformation 8]
56. ! [X0] : (((~generous(X0) & calm(X0)) | rich(X0) | ~kind(X0)) & ((~rich(X0) & kind(X0)) | generous(X0) | ~calm(X0))) [flattening 55]
57. ! [X0] : ((~old(X0) & old(X0)) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0)))) [nnf transformation 35]
82. ~patient(X0) | kind(X0) | creative(X0) [cnf transformation 44]
88. tall(sK3) | ~quiet(X1) [cnf transformation 52]
89. creative(X0) | ~tall(X0) | creative(X0) [cnf transformation 54]
91. ~creative(X0) | ~creative(X0) [cnf transformation 54]
94. calm(X0) | quiet(X0) [cnf transformation 34]
95. calm(X0) | old(X0) [cnf transformation 34]
96. ~calm(X0) | generous(X0) | kind(X0) [cnf transformation 56]
100. old(X0) | patient(X0) | ~generous(X0) [cnf transformation 57]
102. ~generous(X0) | patient(X0) | ~old(X0) [cnf transformation 57]
131. ~kind(fred) [cnf transformation 23]
132. creative(X0) | ~tall(X0) [duplicate literal removal 89]
133. ~creative(X0) [duplicate literal removal 91]
180. 11 <=> ! [X1] : ~quiet(X1) [avatar definition]
181. ~quiet(X1) <- (11) [avatar component clause 180]
183. 12 <=> tall(sK3) [avatar definition]
185. tall(sK3) <- (12) [avatar component clause 183]
186. 11 | 12 [avatar split clause 88,183,180]
200. ~tall(X0) [subsumption resolution 132,133]
202. ~generous(X0) | patient(X0) [subsumption resolution 100,102]
298. generous(X0) | kind(X0) | old(X0) [resolution 96,95]
299. generous(X1) | kind(X1) | quiet(X1) [resolution 96,94]
319. $false <- (12) [subsumption resolution 185,200]
320. ~12 [avatar contradiction clause 319]
353. old(X2) | kind(X2) | patient(X2) [resolution 298,202]
382. kind(X0) | quiet(X0) | patient(X0) | ~old(X0) [resolution 299,102]
386. kind(X0) | patient(X0) | ~old(X0) <- (11) [subsumption resolution 382,181]
387. patient(X0) | kind(X0) <- (11) [subsumption resolution 386,353]
569. kind(X1) | kind(X1) | creative(X1) <- (11) [resolution 387,82]
571. kind(X1) | creative(X1) <- (11) [duplicate literal removal 569]
572. kind(X1) <- (11) [subsumption resolution 571,133]
612. $false <- (11) [resolution 572,131]
617. ~11 [avatar contradiction clause 612]
618. $false [avatar sat refutation 186,320,617]
% SZS output end Proof for 8921984858013743313307874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is patient and vice versa. If someone is not creative or generous then someone is not old. Everyone who is either not kind or not generous is not humble. If john is patient or rich then mary is either not old or not generous. Everyone who is not strong or tall is creative or not rich. Everyone who is either not brave or not old is brave or calm. Everyone who is both not generous and not funny is not generous. Everyone who is not happy or not generous is not kind or creative and vice versa. Everyone who is not curious is not quiet. Everyone who is both calm and not kind is humble or not strong and vice versa. Everyone who is both not funny and not brave is either not calm or not patient and vice versa. If someone is not humble then someone is both humble and not tall and vice versa. Everyone who is either generous or not patient is not creative and vice versa. Everyone who is not old or not humble is not generous or humble. Everyone who is either wise or not strong is both not curious and old. If someone is tall then someone is wise or brave. Someone is creative or curious. Paul is both not calm and not kind. Someone is both not calm and curious. Susan is both not strong and old. Fred is not happy or humble. Someone is either not calm or rich. Someone is brave or old. Someone is both happy and not humble. | Paul is not generous. | entailment | (![X]:(~humble(X)<=>patient(X)))&
((?[X]:((~creative(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((~kind(X)<~>~generous(X))=>~humble(X)))&
(((patient(john)|rich(john)))=>((~old(mary)<~>~generous(mary))))&
(![X]:((~strong(X)|tall(X))=>(creative(X)|~rich(X))))&
(![X]:((~brave(X)<~>~old(X))=>(brave(X)|calm(X))))&
(![X]:((~generous(X)&~funny(X))=>~generous(X)))&
(![X]:((~happy(X)|~generous(X))<=>(~kind(X)|creative(X))))&
(![X]:(~curious(X)=>~quiet(X)))&
(![X]:((calm(X)&~kind(X))<=>(humble(X)|~strong(X))))&
(![X]:((~funny(X)&~brave(X))<=>(~calm(X)<~>~patient(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)&~tall(X)))))&
(![X]:((generous(X)<~>~patient(X))<=>~creative(X)))&
(![X]:((~old(X)|~humble(X))=>(~generous(X)|humble(X))))&
(![X]:((wise(X)<~>~strong(X))=>(~curious(X)&old(X))))&
((?[X]:(tall(X)))=>(?[X]:((wise(X)|brave(X)))))&
(?[X]:((creative(X)|curious(X))))&
((~calm(paul)&~kind(paul)))&
(?[X]:((~calm(X)&curious(X))))&
((~strong(susan)&old(susan)))&
((~happy(fred)|humble(fred)))&
(?[X]:((~calm(X)<~>rich(X))))&
(?[X]:((brave(X)|old(X))))&
(?[X]:((happy(X)&~humble(X)))) | ~generous(paul) | [
"p9",
"p13",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 711564776669104593698942
% SZS output start Proof for 711564776669104593698942
10. ! [X0] : ((~kind(X0) & calm(X0)) <=> (~strong(X0) | humble(X0))) [input p9]
14. ! [X0] : ((~humble(X0) | ~old(X0)) => (humble(X0) | ~generous(X0))) [input p13]
18. ~kind(paul) & ~calm(paul) [input p17]
25. generous(paul) [input hypothesis]
39. ! [X0] : ((humble(X0) | ~generous(X0)) | (humble(X0) & old(X0))) [ennf transformation 14]
40. ! [X0] : (humble(X0) | ~generous(X0) | (humble(X0) & old(X0))) [flattening 39]
52. ! [X0] : (((~kind(X0) & calm(X0)) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | (kind(X0) | ~calm(X0)))) [nnf transformation 10]
53. ! [X0] : (((~kind(X0) & calm(X0)) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | kind(X0) | ~calm(X0))) [flattening 52]
97. ~humble(X0) | calm(X0) [cnf transformation 53]
115. humble(X0) | ~generous(X0) | humble(X0) [cnf transformation 40]
122. ~calm(paul) [cnf transformation 18]
134. generous(paul) [cnf transformation 25]
135. ~generous(X0) | humble(X0) [duplicate literal removal 115]
251. humble(paul) [resolution 135,134]
252. calm(paul) [resolution 251,97]
253. $false [subsumption resolution 252,122]
% SZS output end Proof for 711564776669104593698942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then lucy is not funny or quiet and vice versa.
If someone is tall or not old then paul is quiet.
Everyone who is either tall or brave is either not strong or not creative and vice versa.
Everyone who is quiet or kind is either not generous or not patient and vice versa.
If mary is not quiet or happy then someone is either brave or curious.
Everyone who is not funny or not kind is either calm or not old and vice versa.
Everyone who is either creative or not calm is either not strong or patient and vice versa.
Everyone who is both not brave and strong is brave or generous and vice versa.
If alice is either not happy or not wise then someone is quiet or strong.
If someone is patient or not generous then someone is generous.
Everyone who is either strong or kind is calm and vice versa.
Everyone who is both funny and not tall is both happy and quiet.
Everyone who is not quiet is both not brave and not happy and vice versa.
Everyone who is patient or not kind is tall or not calm and vice versa.
If someone is tall or curious then someone is not brave or not rich.
If someone is both not brave and not calm then someone is either not patient or not old.
Someone is either not patient or old.
Mary is not humble or generous.
Lucy is both quiet and not creative.
Someone is funny or not funny.
Alice is not creative or creative.
Lucy is old.
Someone is rich.
Paul is either humble or not curious. | Lucy is patient. | contradiction | ((?[X]:(humble(X)))<=>((~funny(lucy)|quiet(lucy))))&
((?[X]:((tall(X)|~old(X))))=>(quiet(paul)))&
(![X]:((tall(X)<~>brave(X))<=>(~strong(X)<~>~creative(X))))&
(![X]:((quiet(X)|kind(X))<=>(~generous(X)<~>~patient(X))))&
(((~quiet(mary)|happy(mary)))=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:((~funny(X)|~kind(X))<=>(calm(X)<~>~old(X))))&
(![X]:((creative(X)<~>~calm(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((~brave(X)&strong(X))<=>(brave(X)|generous(X))))&
(((~happy(alice)<~>~wise(alice)))=>(?[X]:((quiet(X)|strong(X)))))&
((?[X]:((patient(X)|~generous(X))))=>(?[X]:(generous(X))))&
(![X]:((strong(X)<~>kind(X))<=>calm(X)))&
(![X]:((funny(X)&~tall(X))=>(happy(X)&quiet(X))))&
(![X]:(~quiet(X)<=>(~brave(X)&~happy(X))))&
(![X]:((patient(X)|~kind(X))<=>(tall(X)|~calm(X))))&
((?[X]:((tall(X)|curious(X))))=>(?[X]:((~brave(X)|~rich(X)))))&
((?[X]:((~brave(X)&~calm(X))))=>(?[X]:((~patient(X)<~>~old(X)))))&
(?[X]:((~patient(X)<~>old(X))))&
((~humble(mary)|generous(mary)))&
((quiet(lucy)&~creative(lucy)))&
(?[X]:((funny(X)|~funny(X))))&
((~creative(alice)|creative(alice)))&
(old(lucy))&
(?[X]:(rich(X)))&
((humble(paul)<~>~curious(paul))) | patient(lucy) | [
"p2",
"p3",
"p6",
"p7",
"p13",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 6940882103327846121408063
% SZS output start Proof for 6940882103327846121408063
3. ! [X0] : ((tall(X0) <~> brave(X0)) <=> (~strong(X0) <~> ~creative(X0))) [input p2]
4. ! [X0] : ((kind(X0) | quiet(X0)) <=> (~generous(X0) <~> ~patient(X0))) [input p3]
7. ! [X0] : ((creative(X0) <~> ~calm(X0)) <=> (~strong(X0) <~> patient(X0))) [input p6]
8. ! [X0] : ((strong(X0) & ~brave(X0)) <=> (generous(X0) | brave(X0))) [input p7]
14. ! [X0] : ((~kind(X0) | patient(X0)) <=> (~calm(X0) | tall(X0))) [input p13]
19. ~creative(lucy) & quiet(lucy) [input p18]
25. patient(lucy) [input hypothesis]
42. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0)))) & (((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [nnf transformation 3]
43. ! [X0] : (((kind(X0) | quiet(X0)) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 4]
44. ! [X0] : ((kind(X0) | quiet(X0) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (~kind(X0) & ~quiet(X0)))) [flattening 43]
50. ! [X0] : ((((calm(X0) | ~creative(X0)) & (~calm(X0) | creative(X0))) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0))))) [nnf transformation 7]
51. ! [X0] : (((strong(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (~strong(X0) | brave(X0)))) [nnf transformation 8]
52. ! [X0] : (((strong(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | ~strong(X0) | brave(X0))) [flattening 51]
62. ! [X0] : (((~kind(X0) | patient(X0)) | (calm(X0) & ~tall(X0))) & ((~calm(X0) | tall(X0)) | (kind(X0) & ~patient(X0)))) [nnf transformation 14]
63. ! [X0] : ((~kind(X0) | patient(X0) | (calm(X0) & ~tall(X0))) & (~calm(X0) | tall(X0) | (kind(X0) & ~patient(X0)))) [flattening 62]
86. ~tall(X0) | strong(X0) | brave(X0) | creative(X0) [cnf transformation 42]
92. ~patient(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 44]
111. ~patient(X0) | strong(X0) | creative(X0) | calm(X0) [cnf transformation 50]
116. generous(X0) | brave(X0) | ~strong(X0) | brave(X0) [cnf transformation 52]
117. ~brave(X0) | ~brave(X0) [cnf transformation 52]
134. ~calm(X0) | tall(X0) | ~patient(X0) [cnf transformation 63]
145. quiet(lucy) [cnf transformation 19]
146. ~creative(lucy) [cnf transformation 19]
153. patient(lucy) [cnf transformation 25]
154. generous(X0) | brave(X0) | ~strong(X0) [duplicate literal removal 116]
155. ~brave(X0) [duplicate literal removal 117]
157. 1 <=> quiet(lucy) [avatar definition]
158. quiet(lucy) <- (1) [avatar component clause 157]
206. ~strong(X0) | generous(X0) [subsumption resolution 154,155]
272. 1 [avatar split clause 145,157]
291. ~generous(lucy) | ~quiet(lucy) [resolution 92,153]
292. ~generous(lucy) <- (1) [subsumption resolution 291,158]
440. 38 <=> calm(lucy) [avatar definition]
441. ~calm(lucy) <- (~38) [avatar component clause 440]
442. calm(lucy) <- (38) [avatar component clause 440]
497. tall(lucy) | ~patient(lucy) <- (38) [resolution 442,134]
518. 49 <=> strong(lucy) [avatar definition]
520. strong(lucy) <- (49) [avatar component clause 518]
523. tall(lucy) <- (38) [subsumption resolution 497,153]
547. strong(lucy) | creative(lucy) | calm(lucy) [resolution 111,153]
627. strong(lucy) | brave(lucy) | creative(lucy) <- (38) [resolution 523,86]
632. strong(lucy) | creative(lucy) <- (38) [subsumption resolution 627,155]
633. strong(lucy) <- (38) [subsumption resolution 632,146]
634. 49 | ~38 [avatar split clause 633,440,518]
649. generous(lucy) <- (49) [resolution 520,206]
652. $false <- (1, 49) [subsumption resolution 649,292]
653. ~1 | ~49 [avatar contradiction clause 652]
656. strong(lucy) | calm(lucy) [subsumption resolution 547,146]
657. strong(lucy) <- (~38) [subsumption resolution 656,441]
658. 49 | 38 [avatar split clause 657,440,518]
659. $false [avatar sat refutation 272,634,653,658]
% SZS output end Proof for 6940882103327846121408063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or not humble then someone is not rich or not tall. Everyone who is both humble and tall is wise or not tall. Everyone who is either rich or not humble is wise or not old. If someone is not brave then paul is either rich or not funny. If someone is not rich then someone is either not old or funny and vice versa. If fred is old or not rich then someone is either not tall or wise. Everyone who is not quiet or kind is both not wise and patient. Everyone who is happy or strong is strong or not brave and vice versa. If someone is humble then someone is not wise or happy and vice versa. Everyone who is either brave or rich is generous and vice versa. Everyone who is not kind is both not humble and generous. If someone is patient or not quiet then someone is both creative and generous and vice versa. Everyone who is both rich and quiet is not humble or not calm and vice versa. Everyone who is either rich or not calm is calm or not strong. Everyone who is both not old and not creative is either not strong or humble and vice versa. Everyone who is not old or patient is not funny or not old. Susan is either not funny or calm. Alice is either not funny or not wise. Someone is not happy. John is calm or not calm. John is not kind or funny. Paul is wise. Someone is both not old and not wise. Someone is either not brave or kind. | John is not humble. | neutral | ((?[X]:((~strong(X)|~humble(X))))=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((humble(X)&tall(X))=>(wise(X)|~tall(X))))&
(![X]:((rich(X)<~>~humble(X))=>(wise(X)|~old(X))))&
((?[X]:(~brave(X)))=>((rich(paul)<~>~funny(paul))))&
((?[X]:(~rich(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(((old(fred)|~rich(fred)))=>(?[X]:((~tall(X)<~>wise(X)))))&
(![X]:((~quiet(X)|kind(X))=>(~wise(X)&patient(X))))&
(![X]:((happy(X)|strong(X))<=>(strong(X)|~brave(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((brave(X)<~>rich(X))<=>generous(X)))&
(![X]:(~kind(X)=>(~humble(X)&generous(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:((creative(X)&generous(X)))))&
(![X]:((rich(X)&quiet(X))<=>(~humble(X)|~calm(X))))&
(![X]:((rich(X)<~>~calm(X))=>(calm(X)|~strong(X))))&
(![X]:((~old(X)&~creative(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((~old(X)|patient(X))=>(~funny(X)|~old(X))))&
((~funny(susan)<~>calm(susan)))&
((~funny(alice)<~>~wise(alice)))&
(?[X]:(~happy(X)))&
((calm(john)|~calm(john)))&
((~kind(john)|funny(john)))&
(wise(paul))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:((~brave(X)<~>kind(X)))) | ~humble(john) | []
| null | 0 |
Everyone who is brave is either not wise or not kind and vice versa. Everyone who is either not wise or wise is both not patient and old and vice versa. Everyone who is humble is rich or creative. Everyone who is both not humble and generous is both not humble and not kind and vice versa. Everyone who is either not humble or not old is either happy or not funny and vice versa. If fred is either not strong or calm then fred is not calm or not rich. Everyone who is both old and calm is not kind. If someone is either not tall or kind then mary is both strong and rich and vice versa. If mary is not calm then someone is strong or not old. Everyone who is not brave or generous is either patient or not quiet. Everyone who is not happy is either not patient or not calm. Everyone who is not calm is either not generous or not curious. If alice is wise or old then mary is not rich or not generous. If susan is generous or not kind then alice is either wise or not generous and vice versa. Everyone who is not creative or brave is both humble and kind. Everyone who is either brave or not humble is not tall. Someone is both creative and not generous. Someone is either tall or calm. Mary is either humble or creative. Mary is both not patient and quiet. Someone is not calm. Someone is wise. Someone is not funny or rich. | Mary is not creative. | entailment | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~patient(X)&old(X))))&
(![X]:(humble(X)=>(rich(X)|creative(X))))&
(![X]:((~humble(X)&generous(X))<=>(~humble(X)&~kind(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(happy(X)<~>~funny(X))))&
(((~strong(fred)<~>calm(fred)))=>((~calm(fred)|~rich(fred))))&
(![X]:((old(X)&calm(X))=>~kind(X)))&
((?[X]:((~tall(X)<~>kind(X))))<=>((strong(mary)&rich(mary))))&
((~calm(mary))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((~brave(X)|generous(X))=>(patient(X)<~>~quiet(X))))&
(![X]:(~happy(X)=>(~patient(X)<~>~calm(X))))&
(![X]:(~calm(X)=>(~generous(X)<~>~curious(X))))&
(((wise(alice)|old(alice)))=>((~rich(mary)|~generous(mary))))&
(((generous(susan)|~kind(susan)))<=>((wise(alice)<~>~generous(alice))))&
(![X]:((~creative(X)|brave(X))=>(humble(X)&kind(X))))&
(![X]:((brave(X)<~>~humble(X))=>~tall(X)))&
(?[X]:((creative(X)&~generous(X))))&
(?[X]:((tall(X)<~>calm(X))))&
((humble(mary)<~>creative(mary)))&
((~patient(mary)&quiet(mary)))&
(?[X]:(~calm(X)))&
(?[X]:(wise(X)))&
(?[X]:((~funny(X)|rich(X)))) | ~creative(mary) | [
"p1",
"p9",
"p14",
"p18",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 227464183729815551312845
% SZS output start Proof for 227464183729815551312845
2. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (old(X0) & ~patient(X0))) [input p1]
10. ! [X0] : ((generous(X0) | ~brave(X0)) => (patient(X0) <~> ~quiet(X0))) [input p9]
15. ! [X0] : ((brave(X0) | ~creative(X0)) => (kind(X0) & humble(X0))) [input p14]
19. humble(mary) <~> creative(mary) [input p18]
20. quiet(mary) & ~patient(mary) [input p19]
24. creative(mary) [input hypothesis]
32. ! [X0] : ((patient(X0) <~> ~quiet(X0)) | (~generous(X0) & brave(X0))) [ennf transformation 10]
37. ! [X0] : ((kind(X0) & humble(X0)) | (~brave(X0) & creative(X0))) [ennf transformation 15]
40. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~old(X0) | patient(X0))) & ((old(X0) & ~patient(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 2]
41. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~old(X0) | patient(X0)) & ((old(X0) & ~patient(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 40]
53. ! [X0] : (((quiet(X0) | ~patient(X0)) & (~quiet(X0) | patient(X0))) | (~generous(X0) & brave(X0))) [nnf transformation 32]
64. (~creative(mary) | ~humble(mary)) & (creative(mary) | humble(mary)) [nnf transformation 19]
75. ~patient(X0) | wise(X0) | wise(X0) [cnf transformation 41]
76. ~patient(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 41]
104. ~quiet(X0) | patient(X0) | brave(X0) [cnf transformation 53]
121. ~brave(X0) | humble(X0) [cnf transformation 37]
131. ~creative(mary) | ~humble(mary) [cnf transformation 64]
133. quiet(mary) [cnf transformation 20]
137. creative(mary) [cnf transformation 24]
139. ~patient(X0) | wise(X0) [duplicate literal removal 75]
140. ~patient(X0) | ~wise(X0) [duplicate literal removal 76]
144. ~patient(X0) [subsumption resolution 139,140]
202. ~quiet(X0) | brave(X0) [subsumption resolution 104,144]
246. 19 <=> humble(mary) [avatar definition]
248. ~humble(mary) <- (~19) [avatar component clause 246]
250. 20 <=> creative(mary) [avatar definition]
253. ~19 | ~20 [avatar split clause 131,250,246]
263. 20 [avatar split clause 137,250]
267. brave(mary) [resolution 202,133]
269. humble(mary) [resolution 267,121]
272. $false <- (~19) [subsumption resolution 269,248]
273. 19 [avatar contradiction clause 272]
274. $false [avatar sat refutation 253,263,273]
% SZS output end Proof for 227464183729815551312845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or creative then paul is either patient or not humble.
Everyone who is both kind and rich is not funny and vice versa.
Everyone who is not humble is not rich.
If someone is either not calm or not strong then john is not kind or not patient and vice versa.
Everyone who is either not funny or calm is either not tall or not happy and vice versa.
Everyone who is either funny or curious is both old and patient.
Everyone who is both strong and not patient is not happy.
If someone is calm then lucy is both tall and not strong and vice versa.
Everyone who is both calm and kind is quiet or generous.
Everyone who is both rich and not funny is both generous and brave and vice versa.
Everyone who is either old or funny is either brave or not brave and vice versa.
Everyone who is not quiet is strong or not tall and vice versa.
If paul is either tall or happy then someone is not generous and vice versa.
Everyone who is either not generous or not strong is not old.
Everyone who is not kind is funny or not rich.
Everyone who is happy or rich is not happy and vice versa.
Alice is either tall or generous.
Alice is both not generous and not creative.
Someone is either not strong or not kind.
Fred is either creative or curious.
John is wise or not creative.
John is strong.
Susan is not wise.
Mary is not brave or not curious. | Lucy is happy. | contradiction | ((?[X]:((old(X)|creative(X))))=>((patient(paul)<~>~humble(paul))))&
(![X]:((kind(X)&rich(X))<=>~funny(X)))&
(![X]:(~humble(X)=>~rich(X)))&
((?[X]:((~calm(X)<~>~strong(X))))<=>((~kind(john)|~patient(john))))&
(![X]:((~funny(X)<~>calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((funny(X)<~>curious(X))=>(old(X)&patient(X))))&
(![X]:((strong(X)&~patient(X))=>~happy(X)))&
((?[X]:(calm(X)))<=>((tall(lucy)&~strong(lucy))))&
(![X]:((calm(X)&kind(X))=>(quiet(X)|generous(X))))&
(![X]:((rich(X)&~funny(X))<=>(generous(X)&brave(X))))&
(![X]:((old(X)<~>funny(X))<=>(brave(X)<~>~brave(X))))&
(![X]:(~quiet(X)<=>(strong(X)|~tall(X))))&
(((tall(paul)<~>happy(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((~generous(X)<~>~strong(X))=>~old(X)))&
(![X]:(~kind(X)=>(funny(X)|~rich(X))))&
(![X]:((happy(X)|rich(X))<=>~happy(X)))&
((tall(alice)<~>generous(alice)))&
((~generous(alice)&~creative(alice)))&
(?[X]:((~strong(X)<~>~kind(X))))&
((creative(fred)<~>curious(fred)))&
((wise(john)|~creative(john)))&
(strong(john))&
(~wise(susan))&
((~brave(mary)|~curious(mary))) | happy(lucy) | [
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 3497743117547967292814464
% SZS output start Proof for 3497743117547967292814464
16. ! [X0] : ((rich(X0) | happy(X0)) <=> ~happy(X0)) [input p15]
25. happy(lucy) [input hypothesis]
61. ! [X0] : (((rich(X0) | happy(X0)) | happy(X0)) & (~happy(X0) | (~rich(X0) & ~happy(X0)))) [nnf transformation 16]
62. ! [X0] : ((rich(X0) | happy(X0) | happy(X0)) & (~happy(X0) | (~rich(X0) & ~happy(X0)))) [flattening 61]
120. ~happy(X0) | ~happy(X0) [cnf transformation 62]
135. happy(lucy) [cnf transformation 25]
136. ~happy(X0) [duplicate literal removal 120]
279. $false [subsumption resolution 135,136]
% SZS output end Proof for 3497743117547967292814464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or humble is not wise.
Everyone who is not funny or brave is generous.
If alice is either rich or not quiet then someone is not tall or curious.
If paul is strong then someone is curious or rich.
If susan is not wise or humble then mary is not generous or kind and vice versa.
If someone is patient or not strong then someone is either rich or not calm.
If paul is both not creative and old then someone is both not generous and not creative and vice versa.
If alice is either not patient or humble then susan is both not patient and wise.
Everyone who is not brave or tall is both brave and not generous.
If someone is not patient or not wise then someone is both not generous and wise.
If alice is either funny or not old then fred is either tall or quiet and vice versa.
Everyone who is either not quiet or old is either generous or not generous.
If fred is creative or humble then mary is both old and not creative and vice versa.
If someone is old or funny then someone is both calm and humble.
Everyone who is both not curious and patient is brave.
Everyone who is not wise is either brave or not kind.
Mary is either not kind or strong.
Someone is either creative or not calm.
Mary is either rich or not old.
Someone is both patient and brave.
Alice is generous.
Someone is not brave or generous. | Susan is tall. | contradiction | (![X]:((~generous(X)<~>humble(X))=>~wise(X)))&
(![X]:((~funny(X)|brave(X))=>generous(X)))&
(((rich(alice)<~>~quiet(alice)))=>(?[X]:((~tall(X)|curious(X)))))&
((strong(paul))=>(?[X]:((curious(X)|rich(X)))))&
(((~wise(susan)|humble(susan)))<=>((~generous(mary)|kind(mary))))&
((?[X]:((patient(X)|~strong(X))))=>(?[X]:((rich(X)<~>~calm(X)))))&
(((~creative(paul)&old(paul)))<=>(?[X]:((~generous(X)&~creative(X)))))&
(((~patient(alice)<~>humble(alice)))=>((~patient(susan)&wise(susan))))&
(![X]:((~brave(X)|tall(X))=>(brave(X)&~generous(X))))&
((?[X]:((~patient(X)|~wise(X))))=>(?[X]:((~generous(X)&wise(X)))))&
(((funny(alice)<~>~old(alice)))<=>((tall(fred)<~>quiet(fred))))&
(![X]:((~quiet(X)<~>old(X))=>(generous(X)<~>~generous(X))))&
(((creative(fred)|humble(fred)))<=>((old(mary)&~creative(mary))))&
((?[X]:((old(X)|funny(X))))=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((~curious(X)&patient(X))=>brave(X)))&
(![X]:(~wise(X)=>(brave(X)<~>~kind(X))))&
((~kind(mary)<~>strong(mary)))&
(?[X]:((creative(X)<~>~calm(X))))&
((rich(mary)<~>~old(mary)))&
(?[X]:((patient(X)&brave(X))))&
(generous(alice))&
(?[X]:((~brave(X)|generous(X)))) | tall(susan) | [
"p1",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 620948098950582820472262
% SZS output start Proof for 620948098950582820472262
2. ! [X0] : ((brave(X0) | ~funny(X0)) => generous(X0)) [input p1]
9. ! [X0] : ((tall(X0) | ~brave(X0)) => (~generous(X0) & brave(X0))) [input p8]
23. tall(susan) [input hypothesis]
31. ! [X0] : (generous(X0) | (~brave(X0) & funny(X0))) [ennf transformation 2]
34. ! [X0] : ((~generous(X0) & brave(X0)) | (~tall(X0) & brave(X0))) [ennf transformation 9]
75. ~brave(X0) | generous(X0) [cnf transformation 31]
92. brave(X0) | brave(X0) [cnf transformation 34]
95. ~tall(X0) | ~generous(X0) [cnf transformation 34]
133. tall(susan) [cnf transformation 23]
134. brave(X0) [duplicate literal removal 92]
317. generous(X0) [resolution 75,134]
334. ~generous(susan) [resolution 95,133]
335. $false [subsumption resolution 334,317]
% SZS output end Proof for 620948098950582820472262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then someone is wise. Everyone who is not tall is either not happy or tall. If mary is either quiet or not tall then lucy is both not funny and rich and vice versa. If someone is either not funny or not tall then paul is not rich. Everyone who is not happy or quiet is both not brave and funny. Everyone who is both not creative and not humble is not calm or not rich. Everyone who is either curious or not funny is not rich or rich and vice versa. Everyone who is not creative or wise is not creative. Everyone who is not strong is either not quiet or rich. Everyone who is curious or happy is not rich and vice versa. Everyone who is not creative is either strong or not patient. If fred is creative or funny then someone is not brave or not funny. Everyone who is not kind or not brave is both not quiet and creative. Everyone who is patient is both not rich and not patient. Everyone who is not brave or not old is either not wise or tall. If fred is both not humble and funny then someone is either not happy or not generous and vice versa. Lucy is not patient. Paul is either happy or quiet. Paul is creative or not happy. Susan is not old or not strong. Someone is curious. Lucy is either calm or funny. Mary is not creative. Someone is funny or not quiet. | Mary is not kind. | contradiction | ((?[X]:(happy(X)))=>(?[X]:(wise(X))))&
(![X]:(~tall(X)=>(~happy(X)<~>tall(X))))&
(((quiet(mary)<~>~tall(mary)))<=>((~funny(lucy)&rich(lucy))))&
((?[X]:((~funny(X)<~>~tall(X))))=>(~rich(paul)))&
(![X]:((~happy(X)|quiet(X))=>(~brave(X)&funny(X))))&
(![X]:((~creative(X)&~humble(X))=>(~calm(X)|~rich(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(~rich(X)|rich(X))))&
(![X]:((~creative(X)|wise(X))=>~creative(X)))&
(![X]:(~strong(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((curious(X)|happy(X))<=>~rich(X)))&
(![X]:(~creative(X)=>(strong(X)<~>~patient(X))))&
(((creative(fred)|funny(fred)))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((~kind(X)|~brave(X))=>(~quiet(X)&creative(X))))&
(![X]:(patient(X)=>(~rich(X)&~patient(X))))&
(![X]:((~brave(X)|~old(X))=>(~wise(X)<~>tall(X))))&
(((~humble(fred)&funny(fred)))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
(~patient(lucy))&
((happy(paul)<~>quiet(paul)))&
((creative(paul)|~happy(paul)))&
((~old(susan)|~strong(susan)))&
(?[X]:(curious(X)))&
((calm(lucy)<~>funny(lucy)))&
(~creative(mary))&
(?[X]:((funny(X)|~quiet(X)))) | ~kind(mary) | [
"p12",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4910129088410597729910276
% SZS output start Proof for 4910129088410597729910276
13. ! [X0] : ((~brave(X0) | ~kind(X0)) => (creative(X0) & ~quiet(X0))) [input p12]
23. ~creative(mary) [input p22]
25. ~kind(mary) [input hypothesis]
37. ! [X0] : ((creative(X0) & ~quiet(X0)) | (brave(X0) & kind(X0))) [ennf transformation 13]
102. kind(X0) | creative(X0) [cnf transformation 37]
124. ~creative(mary) [cnf transformation 23]
126. ~kind(mary) [cnf transformation 25]
238. creative(mary) [resolution 102,126]
239. $false [subsumption resolution 238,124]
% SZS output end Proof for 4910129088410597729910276
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not wise and not quiet then someone is both not funny and tall and vice versa. If john is either not rich or not calm then john is both not wise and not kind. Everyone who is both not strong and not generous is funny or curious and vice versa. Everyone who is both generous and not patient is not humble. If alice is both not old and old then paul is strong or wise and vice versa. If someone is either curious or generous then someone is either calm or happy. Everyone who is rich or not creative is both kind and not generous. If someone is funny then someone is not curious and vice versa. If someone is not rich or not creative then someone is funny or not quiet and vice versa. Everyone who is not rich is either not old or creative and vice versa. Everyone who is calm is generous. If someone is calm or rich then susan is either not quiet or creative and vice versa. Everyone who is brave or not brave is not brave and vice versa. If someone is both not quiet and not happy then john is not rich and vice versa. Everyone who is both not strong and not brave is both not funny and not brave. Everyone who is not funny or not humble is wise or not creative. Mary is either wise or kind. Someone is not humble. Alice is either curious or brave. Fred is either happy or not quiet. Someone is either kind or generous. | Paul is calm. | contradiction | (((~wise(fred)&~quiet(fred)))<=>(?[X]:((~funny(X)&tall(X)))))&
(((~rich(john)<~>~calm(john)))=>((~wise(john)&~kind(john))))&
(![X]:((~strong(X)&~generous(X))<=>(funny(X)|curious(X))))&
(![X]:((generous(X)&~patient(X))=>~humble(X)))&
(((~old(alice)&old(alice)))<=>((strong(paul)|wise(paul))))&
((?[X]:((curious(X)<~>generous(X))))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((rich(X)|~creative(X))=>(kind(X)&~generous(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:(~rich(X)<=>(~old(X)<~>creative(X))))&
(![X]:(calm(X)=>generous(X)))&
((?[X]:((calm(X)|rich(X))))<=>((~quiet(susan)<~>creative(susan))))&
(![X]:((brave(X)|~brave(X))<=>~brave(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>(~rich(john)))&
(![X]:((~strong(X)&~brave(X))=>(~funny(X)&~brave(X))))&
(![X]:((~funny(X)|~humble(X))=>(wise(X)|~creative(X))))&
((wise(mary)<~>kind(mary)))&
(?[X]:(~humble(X)))&
((curious(alice)<~>brave(alice)))&
((happy(fred)<~>~quiet(fred)))&
(?[X]:((kind(X)<~>generous(X)))) | calm(paul) | [
"p2",
"p7",
"p10",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3564827800483168103481354
% SZS output start Proof for 3564827800483168103481354
3. ! [X0] : ((~generous(X0) & ~strong(X0)) <=> (curious(X0) | funny(X0))) [input p2]
8. ? [X0] : funny(X0) <=> ? [X0] : ~curious(X0) [input p7]
11. ! [X0] : (calm(X0) => generous(X0)) [input p10]
13. ! [X0] : ((~brave(X0) | brave(X0)) <=> ~brave(X0)) [input p12]
15. ! [X0] : ((~brave(X0) & ~strong(X0)) => (~brave(X0) & ~funny(X0))) [input p14]
22. calm(paul) [input hypothesis]
24. ? [X0] : funny(X0) <=> ? [X1] : ~curious(X1) [rectify 8]
30. ! [X0] : (generous(X0) | ~calm(X0)) [ennf transformation 11]
31. ! [X0] : ((~brave(X0) & ~funny(X0)) | (brave(X0) | strong(X0))) [ennf transformation 15]
32. ! [X0] : ((~brave(X0) & ~funny(X0)) | brave(X0) | strong(X0)) [flattening 31]
41. ! [X0] : (((~generous(X0) & ~strong(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (generous(X0) | strong(X0)))) [nnf transformation 3]
42. ! [X0] : (((~generous(X0) & ~strong(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | generous(X0) | strong(X0))) [flattening 41]
49. (? [X0] : funny(X0) | ! [X1] : curious(X1)) & (? [X1] : ~curious(X1) | ! [X0] : ~funny(X0)) [nnf transformation 24]
50. (? [X0] : funny(X0) | ! [X1] : curious(X1)) & (? [X2] : ~curious(X2) | ! [X3] : ~funny(X3)) [rectify 49]
51. ? [X0] : funny(X0) => funny(sK2) [choice axiom]
52. ? [X2] : ~curious(X2) => ~curious(sK3) [choice axiom]
53. (funny(sK2) | ! [X1] : curious(X1)) & (~curious(sK3) | ! [X3] : ~funny(X3)) [skolemisation 50,52,51]
64. ! [X0] : (((~brave(X0) | brave(X0)) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [nnf transformation 13]
65. ! [X0] : ((~brave(X0) | brave(X0) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [flattening 64]
87. ~strong(X0) | ~funny(X0) [cnf transformation 42]
90. ~curious(X0) | ~generous(X0) [cnf transformation 42]
105. funny(sK2) | curious(X1) [cnf transformation 53]
114. ~calm(X0) | generous(X0) [cnf transformation 30]
121. ~brave(X0) | ~brave(X0) [cnf transformation 65]
127. ~funny(X0) | brave(X0) | strong(X0) [cnf transformation 32]
140. calm(paul) [cnf transformation 22]
141. ~brave(X0) [duplicate literal removal 121]
204. 13 <=> ! [X1] : ~generous(X1) [avatar definition]
205. ~generous(X1) <- (13) [avatar component clause 204]
225. 17 <=> ! [X1] : curious(X1) [avatar definition]
226. curious(X1) <- (17) [avatar component clause 225]
228. 18 <=> funny(sK2) [avatar definition]
230. funny(sK2) <- (18) [avatar component clause 228]
231. 17 | 18 [avatar split clause 105,228,225]
233. 19 <=> ! [X3] : ~funny(X3) [avatar definition]
234. ~funny(X3) <- (19) [avatar component clause 233]
311. ~funny(X0) | strong(X0) [subsumption resolution 127,141]
312. ~funny(X0) [subsumption resolution 311,87]
313. 19 [avatar split clause 312,233]
343. ~generous(X0) <- (17) [resolution 90,226]
345. 13 | ~17 [avatar split clause 343,225,204]
347. generous(paul) [resolution 114,140]
350. $false <- (13) [subsumption resolution 347,205]
351. ~13 [avatar contradiction clause 350]
356. $false <- (18, 19) [subsumption resolution 230,234]
357. ~18 | ~19 [avatar contradiction clause 356]
358. $false [avatar sat refutation 231,313,345,351,357]
% SZS output end Proof for 3564827800483168103481354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either old or rich then alice is not rich or calm.
Everyone who is patient or not creative is either old or rich.
Everyone who is either curious or brave is not brave.
Everyone who is either not kind or not brave is not rich or strong.
If someone is calm or not wise then someone is curious and vice versa.
If someone is either strong or not calm then someone is either not calm or calm and vice versa.
Everyone who is not kind or not happy is kind and vice versa.
Everyone who is not curious is kind.
If someone is rich then someone is not old and vice versa.
Everyone who is humble is both quiet and wise.
Everyone who is either not wise or calm is both kind and brave and vice versa.
Everyone who is kind or not creative is both kind and not wise.
Everyone who is creative or not happy is both patient and curious and vice versa.
Everyone who is either not tall or funny is both generous and not old.
If someone is not quiet then someone is either not brave or quiet and vice versa.
If mary is both not patient and brave then someone is both not strong and not creative and vice versa.
Mary is not brave.
Someone is either not humble or funny.
Someone is either tall or curious.
Someone is either calm or not wise.
Paul is both not creative and not brave. | Mary is not tall. | neutral | (((old(mary)<~>rich(mary)))=>((~rich(alice)|calm(alice))))&
(![X]:((patient(X)|~creative(X))=>(old(X)<~>rich(X))))&
(![X]:((curious(X)<~>brave(X))=>~brave(X)))&
(![X]:((~kind(X)<~>~brave(X))=>(~rich(X)|strong(X))))&
((?[X]:((calm(X)|~wise(X))))<=>(?[X]:(curious(X))))&
((?[X]:((strong(X)<~>~calm(X))))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((~kind(X)|~happy(X))<=>kind(X)))&
(![X]:(~curious(X)=>kind(X)))&
((?[X]:(rich(X)))<=>(?[X]:(~old(X))))&
(![X]:(humble(X)=>(quiet(X)&wise(X))))&
(![X]:((~wise(X)<~>calm(X))<=>(kind(X)&brave(X))))&
(![X]:((kind(X)|~creative(X))=>(kind(X)&~wise(X))))&
(![X]:((creative(X)|~happy(X))<=>(patient(X)&curious(X))))&
(![X]:((~tall(X)<~>funny(X))=>(generous(X)&~old(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((~patient(mary)&brave(mary)))<=>(?[X]:((~strong(X)&~creative(X)))))&
(~brave(mary))&
(?[X]:((~humble(X)<~>funny(X))))&
(?[X]:((tall(X)<~>curious(X))))&
(?[X]:((calm(X)<~>~wise(X))))&
((~creative(paul)&~brave(paul))) | ~tall(mary) | []
| null | 0 |
If lucy is either wise or not funny then lucy is quiet or not happy and vice versa.
If paul is curious or brave then someone is humble.
Everyone who is both wise and not humble is both calm and wise.
Everyone who is both old and not funny is both funny and strong and vice versa.
Everyone who is kind is both funny and not strong.
Everyone who is both rich and not curious is both not creative and creative and vice versa.
Everyone who is both not tall and not happy is not kind and vice versa.
If someone is not patient or generous then someone is both not strong and not funny.
Everyone who is both not quiet and not humble is not rich or not calm and vice versa.
Everyone who is curious or patient is either not funny or not happy.
Everyone who is either rich or not strong is either not curious or tall.
Everyone who is either not rich or strong is either not funny or not rich and vice versa.
If lucy is strong or not brave then susan is either not strong or not happy.
If paul is both not kind and not calm then someone is creative and vice versa.
Everyone who is wise or generous is rich or creative and vice versa.
Everyone who is either not creative or not strong is either calm or not calm.
Lucy is either strong or brave.
Someone is not generous.
Fred is humble.
Someone is curious or not humble.
Fred is not curious or funny.
Someone is either not happy or not creative. | Susan is curious. | neutral | (((wise(lucy)<~>~funny(lucy)))<=>((quiet(lucy)|~happy(lucy))))&
(((curious(paul)|brave(paul)))=>(?[X]:(humble(X))))&
(![X]:((wise(X)&~humble(X))=>(calm(X)&wise(X))))&
(![X]:((old(X)&~funny(X))<=>(funny(X)&strong(X))))&
(![X]:(kind(X)=>(funny(X)&~strong(X))))&
(![X]:((rich(X)&~curious(X))<=>(~creative(X)&creative(X))))&
(![X]:((~tall(X)&~happy(X))<=>~kind(X)))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:((~strong(X)&~funny(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(~rich(X)|~calm(X))))&
(![X]:((curious(X)|patient(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((rich(X)<~>~strong(X))=>(~curious(X)<~>tall(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(~funny(X)<~>~rich(X))))&
(((strong(lucy)|~brave(lucy)))=>((~strong(susan)<~>~happy(susan))))&
(((~kind(paul)&~calm(paul)))<=>(?[X]:(creative(X))))&
(![X]:((wise(X)|generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~creative(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
((strong(lucy)<~>brave(lucy)))&
(?[X]:(~generous(X)))&
(humble(fred))&
(?[X]:((curious(X)|~humble(X))))&
((~curious(fred)|funny(fred)))&
(?[X]:((~happy(X)<~>~creative(X)))) | curious(susan) | []
| null | 0 |
Everyone who is not happy or kind is both happy and humble.
Everyone who is strong or not quiet is not happy or not rich.
If someone is generous then mary is either not happy or rich and vice versa.
If john is not brave or not happy then someone is patient or not tall and vice versa.
Everyone who is kind or generous is both rich and not calm.
Everyone who is funny is either calm or not rich.
Everyone who is either not strong or not generous is tall or not strong.
If paul is either funny or creative then someone is funny or not curious.
If paul is both creative and not humble then someone is strong or not quiet.
Everyone who is either quiet or creative is not generous.
If mary is not creative then someone is not brave.
Everyone who is old or not old is kind.
Everyone who is generous is both not patient and not curious and vice versa.
If susan is kind or not strong then susan is not wise or generous and vice versa.
If someone is not strong then paul is rich or not kind.
Someone is either wise or strong.
Lucy is not patient or not happy.
Alice is humble or not happy.
Alice is rich.
Paul is both not strong and not tall. | Lucy is not happy. | contradiction | (![X]:((~happy(X)|kind(X))=>(happy(X)&humble(X))))&
(![X]:((strong(X)|~quiet(X))=>(~happy(X)|~rich(X))))&
((?[X]:(generous(X)))<=>((~happy(mary)<~>rich(mary))))&
(((~brave(john)|~happy(john)))<=>(?[X]:((patient(X)|~tall(X)))))&
(![X]:((kind(X)|generous(X))=>(rich(X)&~calm(X))))&
(![X]:(funny(X)=>(calm(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(tall(X)|~strong(X))))&
(((funny(paul)<~>creative(paul)))=>(?[X]:((funny(X)|~curious(X)))))&
(((creative(paul)&~humble(paul)))=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((quiet(X)<~>creative(X))=>~generous(X)))&
((~creative(mary))=>(?[X]:(~brave(X))))&
(![X]:((old(X)|~old(X))=>kind(X)))&
(![X]:(generous(X)<=>(~patient(X)&~curious(X))))&
(((kind(susan)|~strong(susan)))<=>((~wise(susan)|generous(susan))))&
((?[X]:(~strong(X)))=>((rich(paul)|~kind(paul))))&
(?[X]:((wise(X)<~>strong(X))))&
((~patient(lucy)|~happy(lucy)))&
((humble(alice)|~happy(alice)))&
(rich(alice))&
((~strong(paul)&~tall(paul))) | ~happy(lucy) | [
"p0",
"hypothesis"
]
| % SZS status Unsatisfiable for 1395066167433505316398215
% SZS output start Proof for 1395066167433505316398215
1. ! [X0] : ((kind(X0) | ~happy(X0)) => (humble(X0) & happy(X0))) [input p0]
21. ~happy(lucy) [input hypothesis]
22. ! [X0] : ((kind(X0) | ~happy(X0)) => happy(X0)) [pure predicate removal 1]
25. ! [X0] : (happy(X0) | (~kind(X0) & happy(X0))) [ennf transformation 22]
62. happy(X0) | happy(X0) [cnf transformation 25]
103. ~happy(lucy) [cnf transformation 21]
105. happy(X0) [duplicate literal removal 62]
200. $false [subsumption resolution 103,105]
% SZS output end Proof for 1395066167433505316398215
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble or generous then alice is not calm.
Everyone who is either brave or strong is both not humble and rich.
If john is not rich or not old then someone is patient or calm.
Everyone who is either tall or not kind is both not tall and not rich and vice versa.
If someone is both not old and happy then paul is not strong.
Everyone who is generous is either funny or patient.
If lucy is strong or not funny then susan is curious or wise and vice versa.
Everyone who is either curious or kind is both strong and funny and vice versa.
Everyone who is curious is both rich and funny.
Everyone who is not humble or not quiet is not tall.
Everyone who is not quiet or creative is either tall or funny and vice versa.
Everyone who is both humble and not quiet is either generous or wise and vice versa.
Everyone who is both not quiet and wise is either not generous or rich.
If someone is both curious and patient then someone is not creative and vice versa.
If someone is not patient or not creative then alice is either not patient or not funny and vice versa.
If someone is creative then someone is humble or patient and vice versa.
Susan is rich or not curious.
Someone is quiet.
Someone is kind or not happy.
John is happy or quiet.
John is not quiet.
Alice is funny.
Lucy is funny or patient.
Someone is either not old or not curious. | Alice is funny. | entailment | ((?[X]:((humble(X)|generous(X))))=>(~calm(alice)))&
(![X]:((brave(X)<~>strong(X))=>(~humble(X)&rich(X))))&
(((~rich(john)|~old(john)))=>(?[X]:((patient(X)|calm(X)))))&
(![X]:((tall(X)<~>~kind(X))<=>(~tall(X)&~rich(X))))&
((?[X]:((~old(X)&happy(X))))=>(~strong(paul)))&
(![X]:(generous(X)=>(funny(X)<~>patient(X))))&
(((strong(lucy)|~funny(lucy)))<=>((curious(susan)|wise(susan))))&
(![X]:((curious(X)<~>kind(X))<=>(strong(X)&funny(X))))&
(![X]:(curious(X)=>(rich(X)&funny(X))))&
(![X]:((~humble(X)|~quiet(X))=>~tall(X)))&
(![X]:((~quiet(X)|creative(X))<=>(tall(X)<~>funny(X))))&
(![X]:((humble(X)&~quiet(X))<=>(generous(X)<~>wise(X))))&
(![X]:((~quiet(X)&wise(X))=>(~generous(X)<~>rich(X))))&
((?[X]:((curious(X)&patient(X))))<=>(?[X]:(~creative(X))))&
((?[X]:((~patient(X)|~creative(X))))<=>((~patient(alice)<~>~funny(alice))))&
((?[X]:(creative(X)))<=>(?[X]:((humble(X)|patient(X)))))&
((rich(susan)|~curious(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((kind(X)|~happy(X))))&
((happy(john)|quiet(john)))&
(~quiet(john))&
(funny(alice))&
((funny(lucy)|patient(lucy)))&
(?[X]:((~old(X)<~>~curious(X)))) | funny(alice) | [
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 738970151947427765255541
% SZS output start Proof for 738970151947427765255541
22. funny(alice) [input p21]
25. ~funny(alice) [input hypothesis]
135. funny(alice) [cnf transformation 22]
139. ~funny(alice) [cnf transformation 25]
225. 19 <=> funny(alice) [avatar definition]
289. 19 [avatar split clause 135,225]
305. ~19 [avatar split clause 139,225]
306. $false [avatar sat refutation 289,305]
% SZS output end Proof for 738970151947427765255541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and not wise is calm or strong.
Everyone who is tall or not brave is both not kind and not rich and vice versa.
Everyone who is kind is not kind or old and vice versa.
Everyone who is old is not funny.
If alice is not calm then someone is either not curious or generous.
Everyone who is both brave and patient is humble and vice versa.
If paul is both patient and happy then john is not strong or not quiet.
If fred is quiet or happy then someone is quiet and vice versa.
If someone is tall then fred is either strong or not tall and vice versa.
Everyone who is kind or curious is both brave and creative and vice versa.
If someone is not brave then someone is not happy and vice versa.
Everyone who is old or quiet is quiet and vice versa.
If lucy is funny or strong then paul is both generous and patient.
If someone is humble then someone is either not patient or not rich and vice versa.
If alice is brave or funny then someone is either not quiet or not funny and vice versa.
Someone is happy or brave.
Alice is not strong or not quiet.
Mary is funny or generous.
Someone is not generous.
Susan is humble or not quiet.
Paul is either quiet or not quiet.
Alice is quiet.
Someone is strong. | Fred is happy. | entailment | (![X]:((happy(X)&~wise(X))=>(calm(X)|strong(X))))&
(![X]:((tall(X)|~brave(X))<=>(~kind(X)&~rich(X))))&
(![X]:(kind(X)<=>(~kind(X)|old(X))))&
(![X]:(old(X)=>~funny(X)))&
((~calm(alice))=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:((brave(X)&patient(X))<=>humble(X)))&
(((patient(paul)&happy(paul)))=>((~strong(john)|~quiet(john))))&
(((quiet(fred)|happy(fred)))<=>(?[X]:(quiet(X))))&
((?[X]:(tall(X)))<=>((strong(fred)<~>~tall(fred))))&
(![X]:((kind(X)|curious(X))<=>(brave(X)&creative(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(~happy(X))))&
(![X]:((old(X)|quiet(X))<=>quiet(X)))&
(((funny(lucy)|strong(lucy)))=>((generous(paul)&patient(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((~patient(X)<~>~rich(X)))))&
(((brave(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>~funny(X)))))&
(?[X]:((happy(X)|brave(X))))&
((~strong(alice)|~quiet(alice)))&
((funny(mary)|generous(mary)))&
(?[X]:(~generous(X)))&
((humble(susan)|~quiet(susan)))&
((quiet(paul)<~>~quiet(paul)))&
(quiet(alice))&
(?[X]:(strong(X))) | happy(fred) | [
"p1",
"p2",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 8647905852285695637463640
% SZS output start Proof for 8647905852285695637463640
2. ! [X0] : ((~brave(X0) | tall(X0)) <=> (~rich(X0) & ~kind(X0))) [input p1]
3. ! [X0] : (kind(X0) <=> (old(X0) | ~kind(X0))) [input p2]
11. ? [X0] : ~brave(X0) <=> ? [X0] : ~happy(X0) [input p10]
24. ~happy(fred) [input hypothesis]
25. ? [X0] : ~brave(X0) <=> ? [X1] : ~happy(X1) [rectify 11]
33. ! [X0] : (((~brave(X0) | tall(X0)) | (rich(X0) | kind(X0))) & ((~rich(X0) & ~kind(X0)) | (brave(X0) & ~tall(X0)))) [nnf transformation 2]
34. ! [X0] : ((~brave(X0) | tall(X0) | rich(X0) | kind(X0)) & ((~rich(X0) & ~kind(X0)) | (brave(X0) & ~tall(X0)))) [flattening 33]
35. ! [X0] : ((kind(X0) | (~old(X0) & kind(X0))) & ((old(X0) | ~kind(X0)) | ~kind(X0))) [nnf transformation 3]
36. ! [X0] : ((kind(X0) | (~old(X0) & kind(X0))) & (old(X0) | ~kind(X0) | ~kind(X0))) [flattening 35]
50. (? [X0] : ~brave(X0) | ! [X1] : happy(X1)) & (? [X1] : ~happy(X1) | ! [X0] : brave(X0)) [nnf transformation 25]
51. (? [X0] : ~brave(X0) | ! [X1] : happy(X1)) & (? [X2] : ~happy(X2) | ! [X3] : brave(X3)) [rectify 50]
52. ? [X0] : ~brave(X0) => ~brave(sK2) [choice axiom]
53. ? [X2] : ~happy(X2) => ~happy(sK3) [choice axiom]
54. (~brave(sK2) | ! [X1] : happy(X1)) & (~happy(sK3) | ! [X3] : brave(X3)) [skolemisation 51,53,52]
75. ~kind(X0) | brave(X0) [cnf transformation 34]
80. kind(X0) | kind(X0) [cnf transformation 36]
100. ~brave(sK2) | happy(X1) [cnf transformation 54]
127. ~happy(fred) [cnf transformation 24]
129. kind(X0) [duplicate literal removal 80]
157. 7 <=> happy(fred) [avatar definition]
158. ~happy(fred) <- (~7) [avatar component clause 157]
188. 13 <=> ! [X1] : happy(X1) [avatar definition]
189. happy(X1) <- (13) [avatar component clause 188]
191. 14 <=> brave(sK2) [avatar definition]
193. ~brave(sK2) <- (~14) [avatar component clause 191]
194. 13 | ~14 [avatar split clause 100,191,188]
196. 15 <=> ! [X3] : brave(X3) [avatar definition]
197. brave(X3) <- (15) [avatar component clause 196]
254. ~7 [avatar split clause 127,157]
267. brave(X0) [resolution 75,129]
268. 15 [avatar split clause 267,196]
269. $false <- (~14, 15) [resolution 197,193]
270. 14 | ~15 [avatar contradiction clause 269]
271. $false <- (~7, 13) [resolution 189,158]
274. 7 | ~13 [avatar contradiction clause 271]
275. $false [avatar sat refutation 194,254,268,270,274]
% SZS output end Proof for 8647905852285695637463640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or humble is rich or not strong and vice versa. If someone is both creative and kind then john is either brave or not kind and vice versa. If someone is happy then mary is not creative. If someone is either brave or humble then someone is not wise. Everyone who is not rich or funny is both not wise and creative and vice versa. Everyone who is either patient or not brave is either not tall or not old and vice versa. If john is both not quiet and not old then mary is either not creative or not calm and vice versa. If fred is both wise and not old then someone is both not brave and kind and vice versa. Everyone who is humble or not strong is both not quiet and not curious and vice versa. If john is either not humble or not rich then someone is both happy and wise and vice versa. If someone is not calm or humble then someone is tall. If mary is not strong then someone is not brave and vice versa. Everyone who is not quiet is both not old and not calm and vice versa. If someone is wise or not humble then someone is either not wise or generous. Everyone who is either strong or not funny is creative or funny and vice versa. Everyone who is generous or curious is patient. Someone is curious or not tall. Mary is humble. Susan is both not funny and brave. Fred is wise or not generous. Alice is either generous or not funny. | Fred is strong. | neutral | (![X]:((wise(X)|humble(X))<=>(rich(X)|~strong(X))))&
((?[X]:((creative(X)&kind(X))))<=>((brave(john)<~>~kind(john))))&
((?[X]:(happy(X)))=>(~creative(mary)))&
((?[X]:((brave(X)<~>humble(X))))=>(?[X]:(~wise(X))))&
(![X]:((~rich(X)|funny(X))<=>(~wise(X)&creative(X))))&
(![X]:((patient(X)<~>~brave(X))<=>(~tall(X)<~>~old(X))))&
(((~quiet(john)&~old(john)))<=>((~creative(mary)<~>~calm(mary))))&
(((wise(fred)&~old(fred)))<=>(?[X]:((~brave(X)&kind(X)))))&
(![X]:((humble(X)|~strong(X))<=>(~quiet(X)&~curious(X))))&
(((~humble(john)<~>~rich(john)))<=>(?[X]:((happy(X)&wise(X)))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:(tall(X))))&
((~strong(mary))<=>(?[X]:(~brave(X))))&
(![X]:(~quiet(X)<=>(~old(X)&~calm(X))))&
((?[X]:((wise(X)|~humble(X))))=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((strong(X)<~>~funny(X))<=>(creative(X)|funny(X))))&
(![X]:((generous(X)|curious(X))=>patient(X)))&
(?[X]:((curious(X)|~tall(X))))&
(humble(mary))&
((~funny(susan)&brave(susan)))&
((wise(fred)|~generous(fred)))&
((generous(alice)<~>~funny(alice))) | strong(fred) | []
| null | 0 |
If someone is both not funny and not brave then someone is wise.
If susan is either patient or curious then someone is both not quiet and not curious and vice versa.
If someone is not funny or not old then someone is either not creative or generous and vice versa.
Everyone who is creative is not generous and vice versa.
If someone is both patient and not happy then alice is both strong and not humble.
Everyone who is both generous and not curious is funny and vice versa.
If someone is either patient or tall then john is either not kind or not generous and vice versa.
Everyone who is either not wise or curious is humble or generous and vice versa.
If susan is wise or not strong then mary is not humble or not wise and vice versa.
If someone is rich then fred is happy or not creative and vice versa.
Everyone who is not strong is either not wise or not calm.
Everyone who is either rich or not creative is not patient and vice versa.
Everyone who is both not calm and wise is wise and vice versa.
Everyone who is both old and not strong is not curious.
Everyone who is either not rich or happy is calm or strong.
If mary is both funny and not humble then alice is rich or not calm.
Someone is not wise or curious.
Someone is not wise.
Someone is either not creative or not strong.
Alice is old or rich.
Paul is both not calm and old.
Someone is either wise or generous.
Someone is both happy and rich. | Mary is quiet. | neutral | ((?[X]:((~funny(X)&~brave(X))))=>(?[X]:(wise(X))))&
(((patient(susan)<~>curious(susan)))<=>(?[X]:((~quiet(X)&~curious(X)))))&
((?[X]:((~funny(X)|~old(X))))<=>(?[X]:((~creative(X)<~>generous(X)))))&
(![X]:(creative(X)<=>~generous(X)))&
((?[X]:((patient(X)&~happy(X))))=>((strong(alice)&~humble(alice))))&
(![X]:((generous(X)&~curious(X))<=>funny(X)))&
((?[X]:((patient(X)<~>tall(X))))<=>((~kind(john)<~>~generous(john))))&
(![X]:((~wise(X)<~>curious(X))<=>(humble(X)|generous(X))))&
(((wise(susan)|~strong(susan)))<=>((~humble(mary)|~wise(mary))))&
((?[X]:(rich(X)))<=>((happy(fred)|~creative(fred))))&
(![X]:(~strong(X)=>(~wise(X)<~>~calm(X))))&
(![X]:((rich(X)<~>~creative(X))<=>~patient(X)))&
(![X]:((~calm(X)&wise(X))<=>wise(X)))&
(![X]:((old(X)&~strong(X))=>~curious(X)))&
(![X]:((~rich(X)<~>happy(X))=>(calm(X)|strong(X))))&
(((funny(mary)&~humble(mary)))=>((rich(alice)|~calm(alice))))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~creative(X)<~>~strong(X))))&
((old(alice)|rich(alice)))&
((~calm(paul)&old(paul)))&
(?[X]:((wise(X)<~>generous(X))))&
(?[X]:((happy(X)&rich(X)))) | quiet(mary) | []
| null | 0 |
Everyone who is calm or kind is either old or not generous.
Everyone who is either kind or not happy is both not happy and humble and vice versa.
Everyone who is both not happy and not wise is not old and vice versa.
Everyone who is old or not strong is either patient or not creative.
If mary is humble then lucy is not curious and vice versa.
Everyone who is not calm is not wise and vice versa.
If someone is both strong and creative then john is old or tall and vice versa.
Everyone who is not old or happy is either not happy or not kind and vice versa.
Everyone who is rich or not generous is not brave.
If someone is either not curious or not funny then lucy is not calm or not old.
If fred is not humble then someone is either curious or not generous and vice versa.
Everyone who is not humble is both not quiet and not happy and vice versa.
Everyone who is rich or not curious is wise or not creative.
If john is either not old or curious then mary is not happy or not patient.
Everyone who is both happy and kind is not old.
Everyone who is both not creative and humble is patient or tall and vice versa.
Someone is both calm and not funny.
John is not happy or not brave.
Fred is either strong or rich.
Someone is not quiet or funny.
Someone is funny or humble. | Lucy is quiet. | neutral | (![X]:((calm(X)|kind(X))=>(old(X)<~>~generous(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~happy(X)&humble(X))))&
(![X]:((~happy(X)&~wise(X))<=>~old(X)))&
(![X]:((old(X)|~strong(X))=>(patient(X)<~>~creative(X))))&
((humble(mary))<=>(~curious(lucy)))&
(![X]:(~calm(X)<=>~wise(X)))&
((?[X]:((strong(X)&creative(X))))<=>((old(john)|tall(john))))&
(![X]:((~old(X)|happy(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((rich(X)|~generous(X))=>~brave(X)))&
((?[X]:((~curious(X)<~>~funny(X))))=>((~calm(lucy)|~old(lucy))))&
((~humble(fred))<=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:(~humble(X)<=>(~quiet(X)&~happy(X))))&
(![X]:((rich(X)|~curious(X))=>(wise(X)|~creative(X))))&
(((~old(john)<~>curious(john)))=>((~happy(mary)|~patient(mary))))&
(![X]:((happy(X)&kind(X))=>~old(X)))&
(![X]:((~creative(X)&humble(X))<=>(patient(X)|tall(X))))&
(?[X]:((calm(X)&~funny(X))))&
((~happy(john)|~brave(john)))&
((strong(fred)<~>rich(fred)))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((funny(X)|humble(X)))) | quiet(lucy) | []
| null | 0 |
If someone is curious or not tall then paul is both creative and not tall.
Everyone who is either funny or strong is either not generous or tall and vice versa.
Everyone who is both brave and kind is humble or kind.
Everyone who is patient is both not quiet and generous and vice versa.
Everyone who is old is kind and vice versa.
Everyone who is not humble or not generous is both old and wise and vice versa.
If fred is not brave then someone is either humble or old and vice versa.
Everyone who is not creative is not calm or creative and vice versa.
Everyone who is not generous or not calm is strong.
Everyone who is either strong or wise is both not humble and old.
Everyone who is not tall is either happy or not quiet and vice versa.
If john is either not patient or curious then lucy is not creative and vice versa.
Everyone who is not old is not kind and vice versa.
If fred is brave then alice is not wise.
If someone is wise then someone is both kind and not funny.
If alice is not brave or not happy then someone is not humble or not patient.
Fred is calm or patient.
Someone is not happy or rich.
Fred is kind.
Someone is brave.
Someone is not patient.
Susan is patient or not rich.
Someone is not happy. | Fred is curious. | contradiction | ((?[X]:((curious(X)|~tall(X))))=>((creative(paul)&~tall(paul))))&
(![X]:((funny(X)<~>strong(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((brave(X)&kind(X))=>(humble(X)|kind(X))))&
(![X]:(patient(X)<=>(~quiet(X)&generous(X))))&
(![X]:(old(X)<=>kind(X)))&
(![X]:((~humble(X)|~generous(X))<=>(old(X)&wise(X))))&
((~brave(fred))<=>(?[X]:((humble(X)<~>old(X)))))&
(![X]:(~creative(X)<=>(~calm(X)|creative(X))))&
(![X]:((~generous(X)|~calm(X))=>strong(X)))&
(![X]:((strong(X)<~>wise(X))=>(~humble(X)&old(X))))&
(![X]:(~tall(X)<=>(happy(X)<~>~quiet(X))))&
(((~patient(john)<~>curious(john)))<=>(~creative(lucy)))&
(![X]:(~old(X)<=>~kind(X)))&
((brave(fred))=>(~wise(alice)))&
((?[X]:(wise(X)))=>(?[X]:((kind(X)&~funny(X)))))&
(((~brave(alice)|~happy(alice)))=>(?[X]:((~humble(X)|~patient(X)))))&
((calm(fred)|patient(fred)))&
(?[X]:((~happy(X)|rich(X))))&
(kind(fred))&
(?[X]:(brave(X)))&
(?[X]:(~patient(X)))&
((patient(susan)|~rich(susan)))&
(?[X]:(~happy(X))) | curious(fred) | [
"p0",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 319010821259892568381276
% SZS output start Proof for 319010821259892568381276
1. ? [X0] : (~tall(X0) | curious(X0)) => (~tall(paul) & creative(paul)) [input p0]
8. ! [X0] : (~creative(X0) <=> (creative(X0) | ~calm(X0))) [input p7]
24. curious(fred) [input hypothesis]
26. (~tall(paul) & creative(paul)) | ! [X0] : (tall(X0) & ~curious(X0)) [ennf transformation 1]
44. ! [X0] : ((~creative(X0) | (~creative(X0) & calm(X0))) & ((creative(X0) | ~calm(X0)) | creative(X0))) [nnf transformation 8]
45. ! [X0] : ((~creative(X0) | (~creative(X0) & calm(X0))) & (creative(X0) | ~calm(X0) | creative(X0))) [flattening 44]
63. creative(paul) | ~curious(X0) [cnf transformation 26]
92. ~creative(X0) | ~creative(X0) [cnf transformation 45]
121. curious(fred) [cnf transformation 24]
123. ~creative(X0) [duplicate literal removal 92]
133. 3 <=> ! [X0] : ~curious(X0) [avatar definition]
134. ~curious(X0) <- (3) [avatar component clause 133]
137. 4 <=> creative(paul) [avatar definition]
139. creative(paul) <- (4) [avatar component clause 137]
141. 3 | 4 [avatar split clause 63,137,133]
223. $false <- (4) [subsumption resolution 139,123]
224. ~4 [avatar contradiction clause 223]
227. $false <- (3) [resolution 134,121]
228. ~3 [avatar contradiction clause 227]
229. $false [avatar sat refutation 141,224,228]
% SZS output end Proof for 319010821259892568381276
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both not quiet and not kind.
If mary is both not old and creative then someone is not patient or not quiet and vice versa.
If someone is generous then paul is both not rich and patient.
Everyone who is humble is rich and vice versa.
If someone is either not kind or not quiet then paul is not rich and vice versa.
Everyone who is either happy or not curious is both not wise and not strong and vice versa.
Everyone who is tall or not generous is not brave or generous and vice versa.
If someone is quiet or calm then someone is patient or not quiet.
Everyone who is kind is not old or not curious.
Everyone who is both quiet and not old is both old and not happy.
If fred is either kind or not happy then mary is both not humble and not calm and vice versa.
Everyone who is both tall and old is both curious and kind and vice versa.
If mary is not funny then fred is both not rich and kind.
If alice is funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
Mary is quiet.
Someone is strong.
Someone is kind.
Someone is both humble and rich.
John is not strong.
Someone is either creative or old.
Lucy is either rich or not happy.
Lucy is not kind. | Paul is quiet. | entailment | (![X]:(curious(X)=>(~quiet(X)&~kind(X))))&
(((~old(mary)&creative(mary)))<=>(?[X]:((~patient(X)|~quiet(X)))))&
((?[X]:(generous(X)))=>((~rich(paul)&patient(paul))))&
(![X]:(humble(X)<=>rich(X)))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(~rich(paul)))&
(![X]:((happy(X)<~>~curious(X))<=>(~wise(X)&~strong(X))))&
(![X]:((tall(X)|~generous(X))<=>(~brave(X)|generous(X))))&
((?[X]:((quiet(X)|calm(X))))=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:(kind(X)=>(~old(X)|~curious(X))))&
(![X]:((quiet(X)&~old(X))=>(old(X)&~happy(X))))&
(((kind(fred)<~>~happy(fred)))<=>((~humble(mary)&~calm(mary))))&
(![X]:((tall(X)&old(X))<=>(curious(X)&kind(X))))&
((~funny(mary))=>((~rich(fred)&kind(fred))))&
((funny(alice))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(quiet(mary))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&rich(X))))&
(~strong(john))&
(?[X]:((creative(X)<~>old(X))))&
((rich(lucy)<~>~happy(lucy)))&
(~kind(lucy)) | quiet(paul) | [
"p1",
"p9",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8457985221817882904944211
% SZS output start Proof for 8457985221817882904944211
2. (creative(mary) & ~old(mary)) <=> ? [X0] : (~quiet(X0) | ~patient(X0)) [input p1]
10. ! [X0] : ((~old(X0) & quiet(X0)) => (~happy(X0) & old(X0))) [input p9]
17. quiet(mary) [input p16]
25. ~quiet(paul) [input hypothesis]
32. ! [X0] : ((~happy(X0) & old(X0)) | (old(X0) | ~quiet(X0))) [ennf transformation 10]
33. ! [X0] : ((~happy(X0) & old(X0)) | old(X0) | ~quiet(X0)) [flattening 32]
37. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & (? [X0] : (~quiet(X0) | ~patient(X0)) | (~creative(mary) | old(mary))) [nnf transformation 2]
38. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & (? [X0] : (~quiet(X0) | ~patient(X0)) | ~creative(mary) | old(mary)) [flattening 37]
39. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & (? [X1] : (~quiet(X1) | ~patient(X1)) | ~creative(mary) | old(mary)) [rectify 38]
40. ? [X1] : (~quiet(X1) | ~patient(X1)) => (~quiet(sK0) | ~patient(sK0)) [choice axiom]
41. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & ((~quiet(sK0) | ~patient(sK0)) | ~creative(mary) | old(mary)) [skolemisation 39,40]
77. ~old(mary) | quiet(X0) [cnf transformation 41]
101. old(X0) | old(X0) | ~quiet(X0) [cnf transformation 33]
123. quiet(mary) [cnf transformation 17]
134. ~quiet(paul) [cnf transformation 25]
135. ~quiet(X0) | old(X0) [duplicate literal removal 101]
139. 1 <=> ! [X0] : quiet(X0) [avatar definition]
140. quiet(X0) <- (1) [avatar component clause 139]
151. 4 <=> old(mary) [avatar definition]
154. 1 | ~4 [avatar split clause 77,151,139]
298. old(mary) [resolution 135,123]
302. 4 [avatar split clause 298,151]
305. $false <- (1) [resolution 140,134]
310. ~1 [avatar contradiction clause 305]
311. $false [avatar sat refutation 154,302,310]
% SZS output end Proof for 8457985221817882904944211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is happy then john is either tall or not tall and vice versa.
If john is either generous or not kind then john is not strong or humble and vice versa.
Everyone who is tall is not curious or patient.
Everyone who is either quiet or not creative is not kind or happy and vice versa.
Everyone who is not rich or patient is both not strong and happy.
Everyone who is both calm and kind is not wise or calm and vice versa.
If paul is both not tall and quiet then mary is not funny and vice versa.
Everyone who is brave is both quiet and old.
Everyone who is calm or wise is both strong and not tall and vice versa.
Everyone who is not wise is not old or not humble and vice versa.
If mary is either curious or humble then someone is both not rich and quiet and vice versa.
If someone is both strong and not calm then john is either wise or rich.
Everyone who is either not quiet or brave is either happy or not kind.
Everyone who is humble or not funny is not strong.
Everyone who is not old or not calm is both not creative and old.
Someone is either wise or not quiet.
Someone is both not patient and not creative.
Susan is curious or not wise.
Someone is kind or not patient. | Susan is brave. | neutral | ((happy(susan))<=>((tall(john)<~>~tall(john))))&
(((generous(john)<~>~kind(john)))<=>((~strong(john)|humble(john))))&
(![X]:(tall(X)=>(~curious(X)|patient(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(~kind(X)|happy(X))))&
(![X]:((~rich(X)|patient(X))=>(~strong(X)&happy(X))))&
(![X]:((calm(X)&kind(X))<=>(~wise(X)|calm(X))))&
(((~tall(paul)&quiet(paul)))<=>(~funny(mary)))&
(![X]:(brave(X)=>(quiet(X)&old(X))))&
(![X]:((calm(X)|wise(X))<=>(strong(X)&~tall(X))))&
(![X]:(~wise(X)<=>(~old(X)|~humble(X))))&
(((curious(mary)<~>humble(mary)))<=>(?[X]:((~rich(X)&quiet(X)))))&
((?[X]:((strong(X)&~calm(X))))=>((wise(john)<~>rich(john))))&
(![X]:((~quiet(X)<~>brave(X))=>(happy(X)<~>~kind(X))))&
(![X]:((humble(X)|~funny(X))=>~strong(X)))&
(![X]:((~old(X)|~calm(X))=>(~creative(X)&old(X))))&
(?[X]:((wise(X)<~>~quiet(X))))&
(?[X]:((~patient(X)&~creative(X))))&
((curious(susan)|~wise(susan)))&
(?[X]:((kind(X)|~patient(X)))) | brave(susan) | []
| null | 0 |
If paul is both not strong and brave then someone is creative. If someone is either strong or not happy then mary is both not creative and wise. Everyone who is not rich or old is quiet and vice versa. If lucy is either not curious or quiet then someone is either rich or not strong and vice versa. Everyone who is not happy is wise and vice versa. If someone is both happy and not happy then paul is either humble or not quiet and vice versa. Everyone who is not curious or not funny is patient or not calm. If someone is not generous then someone is both patient and rich and vice versa. Everyone who is either rich or humble is not happy and vice versa. If mary is patient then someone is either not patient or funny and vice versa. If someone is funny or creative then john is either not curious or brave and vice versa. Everyone who is kind or not humble is not brave or not patient. Everyone who is not brave is not quiet. Everyone who is both not calm and not patient is either not wise or not generous. Everyone who is both not patient and not old is either generous or rich and vice versa. If someone is either creative or not creative then someone is either humble or not creative and vice versa. John is either not quiet or not happy. Someone is not strong. Alice is not wise or old. Alice is both not funny and not happy. Someone is not happy. Mary is both not generous and tall. Someone is both funny and not wise. Someone is tall or kind. | Alice is not quiet. | contradiction | (((~strong(paul)&brave(paul)))=>(?[X]:(creative(X))))&
((?[X]:((strong(X)<~>~happy(X))))=>((~creative(mary)&wise(mary))))&
(![X]:((~rich(X)|old(X))<=>quiet(X)))&
(((~curious(lucy)<~>quiet(lucy)))<=>(?[X]:((rich(X)<~>~strong(X)))))&
(![X]:(~happy(X)<=>wise(X)))&
((?[X]:((happy(X)&~happy(X))))<=>((humble(paul)<~>~quiet(paul))))&
(![X]:((~curious(X)|~funny(X))=>(patient(X)|~calm(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((patient(X)&rich(X)))))&
(![X]:((rich(X)<~>humble(X))<=>~happy(X)))&
((patient(mary))<=>(?[X]:((~patient(X)<~>funny(X)))))&
((?[X]:((funny(X)|creative(X))))<=>((~curious(john)<~>brave(john))))&
(![X]:((kind(X)|~humble(X))=>(~brave(X)|~patient(X))))&
(![X]:(~brave(X)=>~quiet(X)))&
(![X]:((~calm(X)&~patient(X))=>(~wise(X)<~>~generous(X))))&
(![X]:((~patient(X)&~old(X))<=>(generous(X)<~>rich(X))))&
((?[X]:((creative(X)<~>~creative(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~quiet(john)<~>~happy(john)))&
(?[X]:(~strong(X)))&
((~wise(alice)|old(alice)))&
((~funny(alice)&~happy(alice)))&
(?[X]:(~happy(X)))&
((~generous(mary)&tall(mary)))&
(?[X]:((funny(X)&~wise(X))))&
(?[X]:((tall(X)|kind(X)))) | ~quiet(alice) | [
"p2",
"p4",
"p18",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 3954825503081011788388726
% SZS output start Proof for 3954825503081011788388726
3. ! [X0] : ((old(X0) | ~rich(X0)) <=> quiet(X0)) [input p2]
5. ! [X0] : (~happy(X0) <=> wise(X0)) [input p4]
19. old(alice) | ~wise(alice) [input p18]
20. ~happy(alice) & ~funny(alice) [input p19]
25. ~quiet(alice) [input hypothesis]
44. ! [X0] : (((old(X0) | ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & rich(X0)))) [nnf transformation 3]
45. ! [X0] : ((old(X0) | ~rich(X0) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & rich(X0)))) [flattening 44]
50. ! [X0] : ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))) [nnf transformation 5]
90. ~old(X0) | quiet(X0) [cnf transformation 45]
100. wise(X0) | happy(X0) [cnf transformation 50]
148. old(alice) | ~wise(alice) [cnf transformation 19]
150. ~happy(alice) [cnf transformation 20]
155. ~quiet(alice) [cnf transformation 25]
334. 38 <=> wise(alice) [avatar definition]
336. ~wise(alice) <- (~38) [avatar component clause 334]
338. 39 <=> old(alice) [avatar definition]
340. old(alice) <- (39) [avatar component clause 338]
341. ~38 | 39 [avatar split clause 148,338,334]
349. happy(alice) <- (~38) [resolution 100,336]
350. $false <- (~38) [subsumption resolution 349,150]
351. 38 [avatar contradiction clause 350]
352. quiet(alice) <- (39) [resolution 340,90]
353. $false <- (39) [subsumption resolution 352,155]
354. ~39 [avatar contradiction clause 353]
355. $false [avatar sat refutation 341,351,354]
% SZS output end Proof for 3954825503081011788388726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not old is old and vice versa.
Everyone who is brave or calm is either strong or not funny.
Everyone who is either not strong or not quiet is either not happy or rich and vice versa.
Everyone who is tall or not kind is tall.
Everyone who is not creative or funny is both not rich and funny.
Everyone who is both old and rich is patient or strong.
If someone is either generous or quiet then someone is either not curious or brave.
Everyone who is either brave or not brave is both creative and kind.
If paul is either not kind or happy then john is either funny or happy and vice versa.
If someone is funny or quiet then someone is either funny or generous and vice versa.
If john is not brave then someone is both funny and not kind.
If fred is either brave or not happy then someone is both not curious and happy and vice versa.
Everyone who is not quiet is either funny or happy.
Everyone who is calm is tall or kind.
Everyone who is either not creative or generous is not humble.
If alice is not curious then someone is both kind and not calm.
Susan is both not happy and not generous.
Paul is quiet.
Fred is not tall.
Someone is strong or old.
Alice is either not tall or not brave. | Alice is humble. | neutral | (![X]:((brave(X)|~old(X))<=>old(X)))&
(![X]:((brave(X)|calm(X))=>(strong(X)<~>~funny(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(~happy(X)<~>rich(X))))&
(![X]:((tall(X)|~kind(X))=>tall(X)))&
(![X]:((~creative(X)|funny(X))=>(~rich(X)&funny(X))))&
(![X]:((old(X)&rich(X))=>(patient(X)|strong(X))))&
((?[X]:((generous(X)<~>quiet(X))))=>(?[X]:((~curious(X)<~>brave(X)))))&
(![X]:((brave(X)<~>~brave(X))=>(creative(X)&kind(X))))&
(((~kind(paul)<~>happy(paul)))<=>((funny(john)<~>happy(john))))&
((?[X]:((funny(X)|quiet(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
((~brave(john))=>(?[X]:((funny(X)&~kind(X)))))&
(((brave(fred)<~>~happy(fred)))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(~quiet(X)=>(funny(X)<~>happy(X))))&
(![X]:(calm(X)=>(tall(X)|kind(X))))&
(![X]:((~creative(X)<~>generous(X))=>~humble(X)))&
((~curious(alice))=>(?[X]:((kind(X)&~calm(X)))))&
((~happy(susan)&~generous(susan)))&
(quiet(paul))&
(~tall(fred))&
(?[X]:((strong(X)|old(X))))&
((~tall(alice)<~>~brave(alice))) | humble(alice) | []
| null | 0 |
Everyone who is not happy or strong is either generous or not rich.
Everyone who is both wise and creative is not creative or rich and vice versa.
Everyone who is either kind or not wise is not funny or not happy and vice versa.
Everyone who is not old is humble and vice versa.
If john is not strong then john is not calm.
Everyone who is brave or not funny is either not funny or not wise and vice versa.
Everyone who is either not kind or not creative is not strong or not wise.
If alice is either strong or not funny then susan is both funny and not patient and vice versa.
Everyone who is both not rich and not wise is curious.
Everyone who is either old or humble is patient or wise.
Everyone who is funny or not tall is either rich or wise and vice versa.
Everyone who is either not old or tall is either not generous or calm and vice versa.
If alice is not calm or not curious then someone is either creative or not generous.
Everyone who is not brave or not humble is either kind or creative and vice versa.
Everyone who is not happy or not old is not curious or not strong and vice versa.
If susan is both rich and funny then susan is quiet.
Fred is generous.
Paul is not happy or humble.
Someone is either humble or not kind.
Someone is quiet.
Mary is both creative and not curious.
Mary is either funny or wise.
Paul is both brave and happy. | Paul is not happy. | contradiction | (![X]:((~happy(X)|strong(X))=>(generous(X)<~>~rich(X))))&
(![X]:((wise(X)&creative(X))<=>(~creative(X)|rich(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(~funny(X)|~happy(X))))&
(![X]:(~old(X)<=>humble(X)))&
((~strong(john))=>(~calm(john)))&
(![X]:((brave(X)|~funny(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:((~kind(X)<~>~creative(X))=>(~strong(X)|~wise(X))))&
(((strong(alice)<~>~funny(alice)))<=>((funny(susan)&~patient(susan))))&
(![X]:((~rich(X)&~wise(X))=>curious(X)))&
(![X]:((old(X)<~>humble(X))=>(patient(X)|wise(X))))&
(![X]:((funny(X)|~tall(X))<=>(rich(X)<~>wise(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)<~>calm(X))))&
(((~calm(alice)|~curious(alice)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(kind(X)<~>creative(X))))&
(![X]:((~happy(X)|~old(X))<=>(~curious(X)|~strong(X))))&
(((rich(susan)&funny(susan)))=>(quiet(susan)))&
(generous(fred))&
((~happy(paul)|humble(paul)))&
(?[X]:((humble(X)<~>~kind(X))))&
(?[X]:(quiet(X)))&
((creative(mary)&~curious(mary)))&
((funny(mary)<~>wise(mary)))&
((brave(paul)&happy(paul))) | ~happy(paul) | [
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 9208580292782828439874237
% SZS output start Proof for 9208580292782828439874237
23. happy(paul) & brave(paul) [input p22]
24. ~happy(paul) [input hypothesis]
134. happy(paul) [cnf transformation 23]
135. ~happy(paul) [cnf transformation 24]
201. 10 <=> happy(paul) [avatar definition]
218. 10 [avatar split clause 134,201]
219. ~10 [avatar split clause 135,201]
220. $false [avatar sat refutation 218,219]
% SZS output end Proof for 9208580292782828439874237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not funny is either not creative or not old. If someone is not rich or happy then alice is both kind and not patient and vice versa. If someone is either not funny or wise then john is happy or not rich and vice versa. If someone is old then someone is both not rich and not old. Everyone who is generous or not humble is either not kind or patient. If someone is both rich and not happy then mary is not creative or not rich. Everyone who is not rich or generous is both not creative and not generous. Everyone who is curious is not tall or not strong. If someone is both not creative and generous then someone is both not calm and tall and vice versa. Everyone who is quiet or humble is patient. Everyone who is quiet is old. Everyone who is not generous is rich or patient. If someone is not patient then mary is not patient or creative and vice versa. Everyone who is strong is old or tall and vice versa. Everyone who is not generous is not kind or quiet and vice versa. If fred is not curious or not quiet then john is not patient. Someone is both not kind and creative. John is either creative or patient. Someone is both tall and funny. Alice is calm. Susan is either not humble or not wise. | Mary is not funny. | contradiction | (![X]:((wise(X)&~funny(X))=>(~creative(X)<~>~old(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((kind(alice)&~patient(alice))))&
((?[X]:((~funny(X)<~>wise(X))))<=>((happy(john)|~rich(john))))&
((?[X]:(old(X)))=>(?[X]:((~rich(X)&~old(X)))))&
(![X]:((generous(X)|~humble(X))=>(~kind(X)<~>patient(X))))&
((?[X]:((rich(X)&~happy(X))))=>((~creative(mary)|~rich(mary))))&
(![X]:((~rich(X)|generous(X))=>(~creative(X)&~generous(X))))&
(![X]:(curious(X)=>(~tall(X)|~strong(X))))&
((?[X]:((~creative(X)&generous(X))))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((quiet(X)|humble(X))=>patient(X)))&
(![X]:(quiet(X)=>old(X)))&
(![X]:(~generous(X)=>(rich(X)|patient(X))))&
((?[X]:(~patient(X)))<=>((~patient(mary)|creative(mary))))&
(![X]:(strong(X)<=>(old(X)|tall(X))))&
(![X]:(~generous(X)<=>(~kind(X)|quiet(X))))&
(((~curious(fred)|~quiet(fred)))=>(~patient(john)))&
(?[X]:((~kind(X)&creative(X))))&
((creative(john)<~>patient(john)))&
(?[X]:((tall(X)&funny(X))))&
(calm(alice))&
((~humble(susan)<~>~wise(susan))) | ~funny(mary) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p6",
"p9",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 795640501896478874757540
% SZS output start Proof for 795640501896478874757540
1. ! [X0] : ((~funny(X0) & wise(X0)) => (~creative(X0) <~> ~old(X0))) [input p0]
2. ? [X0] : (happy(X0) | ~rich(X0)) <=> (~patient(alice) & kind(alice)) [input p1]
3. ? [X0] : (~funny(X0) <~> wise(X0)) <=> (~rich(john) | happy(john)) [input p2]
4. ? [X0] : old(X0) => ? [X0] : (~old(X0) & ~rich(X0)) [input p3]
6. ? [X0] : (~happy(X0) & rich(X0)) => (~rich(mary) | ~creative(mary)) [input p5]
7. ! [X0] : ((generous(X0) | ~rich(X0)) => (~generous(X0) & ~creative(X0))) [input p6]
10. ! [X0] : ((humble(X0) | quiet(X0)) => patient(X0)) [input p9]
11. ! [X0] : (quiet(X0) => old(X0)) [input p10]
15. ! [X0] : (~generous(X0) <=> (quiet(X0) | ~kind(X0))) [input p14]
22. ~funny(mary) [input hypothesis]
23. ? [X0] : old(X0) => ? [X1] : (~old(X1) & ~rich(X1)) [rectify 4]
26. ! [X0] : ((~creative(X0) <~> ~old(X0)) | (funny(X0) | ~wise(X0))) [ennf transformation 1]
27. ! [X0] : ((~creative(X0) <~> ~old(X0)) | funny(X0) | ~wise(X0)) [flattening 26]
28. ? [X1] : (~old(X1) & ~rich(X1)) | ! [X0] : ~old(X0) [ennf transformation 23]
30. (~rich(mary) | ~creative(mary)) | ! [X0] : (happy(X0) | ~rich(X0)) [ennf transformation 6]
31. ~rich(mary) | ~creative(mary) | ! [X0] : (happy(X0) | ~rich(X0)) [flattening 30]
32. ! [X0] : ((~generous(X0) & ~creative(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 7]
35. ! [X0] : (patient(X0) | (~humble(X0) & ~quiet(X0))) [ennf transformation 10]
36. ! [X0] : (old(X0) | ~quiet(X0)) [ennf transformation 11]
41. ! [X0] : (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | funny(X0) | ~wise(X0)) [nnf transformation 27]
42. (? [X0] : (happy(X0) | ~rich(X0)) | (patient(alice) | ~kind(alice))) & ((~patient(alice) & kind(alice)) | ! [X0] : (~happy(X0) & rich(X0))) [nnf transformation 2]
43. (? [X0] : (happy(X0) | ~rich(X0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X0] : (~happy(X0) & rich(X0))) [flattening 42]
44. (? [X0] : (happy(X0) | ~rich(X0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X1] : (~happy(X1) & rich(X1))) [rectify 43]
45. ? [X0] : (happy(X0) | ~rich(X0)) => (happy(sK0) | ~rich(sK0)) [choice axiom]
46. ((happy(sK0) | ~rich(sK0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X1] : (~happy(X1) & rich(X1))) [skolemisation 44,45]
47. (? [X0] : ((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | (rich(john) & ~happy(john))) & ((~rich(john) | happy(john)) | ! [X0] : ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0)))) [nnf transformation 3]
48. (? [X0] : ((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | (rich(john) & ~happy(john))) & (~rich(john) | happy(john) | ! [X0] : ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0)))) [flattening 47]
49. (? [X0] : ((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | (rich(john) & ~happy(john))) & (~rich(john) | happy(john) | ! [X1] : ((~funny(X1) | ~wise(X1)) & (wise(X1) | funny(X1)))) [rectify 48]
50. ? [X0] : ((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) => ((~wise(sK1) | funny(sK1)) & (wise(sK1) | ~funny(sK1))) [choice axiom]
51. (((~wise(sK1) | funny(sK1)) & (wise(sK1) | ~funny(sK1))) | (rich(john) & ~happy(john))) & (~rich(john) | happy(john) | ! [X1] : ((~funny(X1) | ~wise(X1)) & (wise(X1) | funny(X1)))) [skolemisation 49,50]
52. ? [X0] : (~old(X0) & ~rich(X0)) | ! [X1] : ~old(X1) [rectify 28]
53. ? [X0] : (~old(X0) & ~rich(X0)) => (~old(sK2) & ~rich(sK2)) [choice axiom]
54. (~old(sK2) & ~rich(sK2)) | ! [X1] : ~old(X1) [skolemisation 52,53]
66. ! [X0] : ((~generous(X0) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | generous(X0))) [nnf transformation 15]
67. ! [X0] : ((~generous(X0) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | generous(X0))) [flattening 66]
75. ~wise(X0) | creative(X0) | funny(X0) | old(X0) [cnf transformation 41]
76. kind(alice) | rich(X1) [cnf transformation 46]
77. kind(alice) | ~happy(X1) [cnf transformation 46]
78. ~patient(alice) | rich(X1) [cnf transformation 46]
81. ~rich(john) | happy(john) | wise(X1) | funny(X1) [cnf transformation 51]
87. ~rich(sK2) | ~old(X1) [cnf transformation 54]
93. ~rich(mary) | ~creative(mary) | happy(X0) | ~rich(X0) [cnf transformation 31]
97. ~generous(X0) | ~generous(X0) [cnf transformation 32]
103. ~quiet(X0) | patient(X0) [cnf transformation 35]
105. ~quiet(X0) | old(X0) [cnf transformation 36]
112. quiet(X0) | ~kind(X0) | generous(X0) [cnf transformation 67]
126. ~funny(mary) [cnf transformation 22]
127. ~generous(X0) [duplicate literal removal 97]
129. 1 <=> kind(alice) [avatar definition]
130. kind(alice) <- (1) [avatar component clause 129]
133. 2 <=> patient(alice) [avatar definition]
134. ~patient(alice) <- (~2) [avatar component clause 133]
146. 5 <=> ! [X1] : ~happy(X1) [avatar definition]
147. ~happy(X1) <- (5) [avatar component clause 146]
150. 6 <=> ! [X1] : rich(X1) [avatar definition]
151. rich(X1) <- (6) [avatar component clause 150]
152. 6 | ~2 [avatar split clause 78,133,150]
153. 5 | 1 [avatar split clause 77,129,146]
154. 6 | 1 [avatar split clause 76,129,150]
156. 7 <=> rich(john) [avatar definition]
157. ~rich(john) <- (~7) [avatar component clause 156]
169. 10 <=> happy(john) [avatar definition]
170. happy(john) <- (10) [avatar component clause 169]
180. 12 <=> ! [X1] : (wise(X1) | funny(X1)) [avatar definition]
181. funny(X1) | wise(X1) <- (12) [avatar component clause 180]
182. 12 | 10 | ~7 [avatar split clause 81,156,169,180]
184. 13 <=> ! [X1] : ~old(X1) [avatar definition]
185. ~old(X1) <- (13) [avatar component clause 184]
192. 15 <=> rich(sK2) [avatar definition]
194. ~rich(sK2) <- (~15) [avatar component clause 192]
195. 13 | ~15 [avatar split clause 87,192,184]
197. 16 <=> ! [X0] : (happy(X0) | ~rich(X0)) [avatar definition]
198. happy(X0) | ~rich(X0) <- (16) [avatar component clause 197]
200. 17 <=> creative(mary) [avatar definition]
204. 18 <=> rich(mary) [avatar definition]
206. ~rich(mary) <- (~18) [avatar component clause 204]
207. 16 | ~17 | ~18 [avatar split clause 93,204,200,197]
224. ~kind(X0) | quiet(X0) [subsumption resolution 112,127]
255. $false <- (6, ~7) [resolution 157,151]
256. ~6 | 7 [avatar contradiction clause 255]
257. $false <- (5, 10) [subsumption resolution 170,147]
258. ~5 | ~10 [avatar contradiction clause 257]
259. $false <- (6, ~15) [resolution 194,151]
260. ~6 | 15 [avatar contradiction clause 259]
282. quiet(alice) <- (1) [resolution 224,130]
283. old(alice) <- (1) [resolution 282,105]
284. patient(alice) <- (1) [resolution 282,103]
285. $false <- (1, 13) [subsumption resolution 283,185]
286. ~1 | ~13 [avatar contradiction clause 285]
287. $false <- (1, ~2) [subsumption resolution 284,134]
288. ~1 | 2 [avatar contradiction clause 287]
292. wise(mary) <- (12) [resolution 181,126]
298. creative(mary) | funny(mary) | old(mary) <- (12) [resolution 75,292]
303. creative(mary) | old(mary) <- (12) [subsumption resolution 298,126]
304. creative(mary) <- (12, 13) [subsumption resolution 303,185]
305. 17 | ~12 | ~13 [avatar split clause 304,184,180,200]
306. $false <- (6, ~18) [subsumption resolution 206,151]
307. ~6 | 18 [avatar contradiction clause 306]
308. ~rich(X0) <- (5, 16) [subsumption resolution 198,147]
309. $false <- (5, 6, 16) [subsumption resolution 308,151]
310. ~5 | ~6 | ~16 [avatar contradiction clause 309]
311. $false [avatar sat refutation 152,153,154,182,195,207,256,258,260,286,288,305,307,310]
% SZS output end Proof for 795640501896478874757540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or generous is either not curious or not wise and vice versa.
Everyone who is both happy and not rich is not generous and vice versa.
Everyone who is both kind and old is both not patient and wise and vice versa.
Everyone who is humble or not happy is tall and vice versa.
If lucy is tall or wise then susan is not calm or not brave.
If lucy is quiet then lucy is both humble and rich and vice versa.
Everyone who is both patient and kind is either humble or not strong.
If lucy is both not funny and humble then someone is not wise.
Everyone who is not generous or not funny is not patient or generous.
Everyone who is both patient and brave is not tall or generous and vice versa.
Everyone who is not curious or patient is not wise or brave and vice versa.
Everyone who is both quiet and funny is both patient and wise and vice versa.
Everyone who is creative or wise is brave.
If alice is either tall or not generous then fred is not old or not kind.
Everyone who is both brave and quiet is either not wise or wise and vice versa.
Everyone who is brave or not rich is not calm.
Someone is not strong.
Someone is either not rich or old.
Mary is happy.
Someone is either not kind or not wise.
Someone is either generous or old. | Fred is not calm. | entailment | (![X]:((~funny(X)|generous(X))<=>(~curious(X)<~>~wise(X))))&
(![X]:((happy(X)&~rich(X))<=>~generous(X)))&
(![X]:((kind(X)&old(X))<=>(~patient(X)&wise(X))))&
(![X]:((humble(X)|~happy(X))<=>tall(X)))&
(((tall(lucy)|wise(lucy)))=>((~calm(susan)|~brave(susan))))&
((quiet(lucy))<=>((humble(lucy)&rich(lucy))))&
(![X]:((patient(X)&kind(X))=>(humble(X)<~>~strong(X))))&
(((~funny(lucy)&humble(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((~generous(X)|~funny(X))=>(~patient(X)|generous(X))))&
(![X]:((patient(X)&brave(X))<=>(~tall(X)|generous(X))))&
(![X]:((~curious(X)|patient(X))<=>(~wise(X)|brave(X))))&
(![X]:((quiet(X)&funny(X))<=>(patient(X)&wise(X))))&
(![X]:((creative(X)|wise(X))=>brave(X)))&
(((tall(alice)<~>~generous(alice)))=>((~old(fred)|~kind(fred))))&
(![X]:((brave(X)&quiet(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((brave(X)|~rich(X))=>~calm(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~rich(X)<~>old(X))))&
(happy(mary))&
(?[X]:((~kind(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>old(X)))) | ~calm(fred) | [
"p12",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 7504427010272974137562792
% SZS output start Proof for 7504427010272974137562792
13. ! [X0] : ((wise(X0) | creative(X0)) => brave(X0)) [input p12]
15. ! [X0] : ((quiet(X0) & brave(X0)) <=> (~wise(X0) <~> wise(X0))) [input p14]
16. ! [X0] : ((~rich(X0) | brave(X0)) => ~calm(X0)) [input p15]
22. calm(fred) [input hypothesis]
23. ! [X0] : (wise(X0) => brave(X0)) [pure predicate removal 13]
32. ! [X0] : (brave(X0) | ~wise(X0)) [ennf transformation 23]
35. ! [X0] : (~calm(X0) | (rich(X0) & ~brave(X0))) [ennf transformation 16]
56. ! [X0] : (((quiet(X0) & brave(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~quiet(X0) | ~brave(X0)))) [nnf transformation 15]
57. ! [X0] : (((quiet(X0) & brave(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~quiet(X0) | ~brave(X0))) [flattening 56]
108. brave(X0) | ~wise(X0) [cnf transformation 32]
113. brave(X0) | wise(X0) | wise(X0) [cnf transformation 57]
117. ~calm(X0) | ~brave(X0) [cnf transformation 35]
127. calm(fred) [cnf transformation 22]
128. brave(X0) | wise(X0) [duplicate literal removal 113]
194. brave(X0) [subsumption resolution 128,108]
195. ~calm(X0) [subsumption resolution 117,194]
226. $false [subsumption resolution 127,195]
% SZS output end Proof for 7504427010272974137562792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not rich is both not curious and calm and vice versa.
Everyone who is funny is brave and vice versa.
Everyone who is both not curious and not wise is either happy or not old and vice versa.
Everyone who is either patient or not kind is both not tall and old and vice versa.
If susan is rich or brave then mary is not tall.
If mary is not kind or not happy then someone is both not funny and not rich and vice versa.
If susan is curious or generous then mary is not calm.
Everyone who is not rich is both kind and not quiet and vice versa.
If susan is not humble then someone is not rich.
If john is not creative or patient then someone is both tall and not quiet.
Everyone who is both not tall and patient is rich or not tall and vice versa.
If john is both not creative and not funny then someone is both kind and not creative and vice versa.
If john is both calm and old then fred is not quiet or not rich.
If someone is not funny or strong then john is both not strong and generous.
Everyone who is not patient or not curious is both not humble and generous.
Everyone who is curious or tall is either calm or kind.
Alice is either not funny or not rich.
Someone is not kind.
Someone is either not funny or tall.
Someone is either creative or tall.
Lucy is either not generous or generous.
Someone is quiet or rich.
Susan is not patient. | John is not strong. | entailment | (![X]:((old(X)<~>~rich(X))<=>(~curious(X)&calm(X))))&
(![X]:(funny(X)<=>brave(X)))&
(![X]:((~curious(X)&~wise(X))<=>(happy(X)<~>~old(X))))&
(![X]:((patient(X)<~>~kind(X))<=>(~tall(X)&old(X))))&
(((rich(susan)|brave(susan)))=>(~tall(mary)))&
(((~kind(mary)|~happy(mary)))<=>(?[X]:((~funny(X)&~rich(X)))))&
(((curious(susan)|generous(susan)))=>(~calm(mary)))&
(![X]:(~rich(X)<=>(kind(X)&~quiet(X))))&
((~humble(susan))=>(?[X]:(~rich(X))))&
(((~creative(john)|patient(john)))=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:((~tall(X)&patient(X))<=>(rich(X)|~tall(X))))&
(((~creative(john)&~funny(john)))<=>(?[X]:((kind(X)&~creative(X)))))&
(((calm(john)&old(john)))=>((~quiet(fred)|~rich(fred))))&
((?[X]:((~funny(X)|strong(X))))=>((~strong(john)&generous(john))))&
(![X]:((~patient(X)|~curious(X))=>(~humble(X)&generous(X))))&
(![X]:((curious(X)|tall(X))=>(calm(X)<~>kind(X))))&
((~funny(alice)<~>~rich(alice)))&
(?[X]:(~kind(X)))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:((creative(X)<~>tall(X))))&
((~generous(lucy)<~>generous(lucy)))&
(?[X]:((quiet(X)|rich(X))))&
(~patient(susan)) | ~strong(john) | [
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 1734782449500696013775531
% SZS output start Proof for 1734782449500696013775531
14. ? [X0] : (strong(X0) | ~funny(X0)) => (generous(john) & ~strong(john)) [input p13]
24. strong(john) [input hypothesis]
31. (generous(john) & ~strong(john)) | ! [X0] : (~strong(X0) & funny(X0)) [ennf transformation 14]
120. ~strong(john) | ~strong(X0) [cnf transformation 31]
142. strong(john) [cnf transformation 24]
258. 25 <=> ! [X0] : ~strong(X0) [avatar definition]
259. ~strong(X0) <- (25) [avatar component clause 258]
270. 28 <=> strong(john) [avatar definition]
271. strong(john) <- (28) [avatar component clause 270]
273. 25 | ~28 [avatar split clause 120,270,258]
306. 28 [avatar split clause 142,270]
309. $false <- (25, 28) [resolution 271,259]
310. ~25 | ~28 [avatar contradiction clause 309]
311. $false [avatar sat refutation 273,306,310]
% SZS output end Proof for 1734782449500696013775531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not calm is both rich and quiet.
Everyone who is not quiet is either not humble or wise.
If someone is tall then someone is happy and vice versa.
If someone is both not creative and not patient then someone is curious or old.
If susan is either not kind or not calm then alice is either not happy or strong.
If mary is tall or not tall then paul is not wise and vice versa.
Everyone who is either patient or generous is not curious or not funny and vice versa.
If someone is either not old or not happy then john is either kind or funny and vice versa.
Everyone who is either not humble or not patient is either rich or not rich and vice versa.
Everyone who is not old or not tall is both rich and kind.
Everyone who is humble or wise is strong.
Everyone who is wise is creative or not generous and vice versa.
Everyone who is not old is either happy or calm and vice versa.
If paul is both not happy and not patient then john is not funny.
If alice is not calm then fred is patient.
If someone is both funny and strong then someone is not funny and vice versa.
Mary is either not generous or funny.
Someone is creative or happy.
Alice is either curious or strong.
Alice is both curious and not calm.
Paul is not curious.
Someone is either patient or not wise.
Someone is not strong.
Paul is not creative or brave. | Alice is not patient. | contradiction | (![X]:((generous(X)<~>~calm(X))=>(rich(X)&quiet(X))))&
(![X]:(~quiet(X)=>(~humble(X)<~>wise(X))))&
((?[X]:(tall(X)))<=>(?[X]:(happy(X))))&
((?[X]:((~creative(X)&~patient(X))))=>(?[X]:((curious(X)|old(X)))))&
(((~kind(susan)<~>~calm(susan)))=>((~happy(alice)<~>strong(alice))))&
(((tall(mary)|~tall(mary)))<=>(~wise(paul)))&
(![X]:((patient(X)<~>generous(X))<=>(~curious(X)|~funny(X))))&
((?[X]:((~old(X)<~>~happy(X))))<=>((kind(john)<~>funny(john))))&
(![X]:((~humble(X)<~>~patient(X))<=>(rich(X)<~>~rich(X))))&
(![X]:((~old(X)|~tall(X))=>(rich(X)&kind(X))))&
(![X]:((humble(X)|wise(X))=>strong(X)))&
(![X]:(wise(X)<=>(creative(X)|~generous(X))))&
(![X]:(~old(X)<=>(happy(X)<~>calm(X))))&
(((~happy(paul)&~patient(paul)))=>(~funny(john)))&
((~calm(alice))=>(patient(fred)))&
((?[X]:((funny(X)&strong(X))))<=>(?[X]:(~funny(X))))&
((~generous(mary)<~>funny(mary)))&
(?[X]:((creative(X)|happy(X))))&
((curious(alice)<~>strong(alice)))&
((curious(alice)&~calm(alice)))&
(~curious(paul))&
(?[X]:((patient(X)<~>~wise(X))))&
(?[X]:(~strong(X)))&
((~creative(paul)|brave(paul))) | ~patient(alice) | [
"p8",
"p10",
"p18",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 3127766989910395190763395
% SZS output start Proof for 3127766989910395190763395
9. ! [X0] : ((~humble(X0) <~> ~patient(X0)) <=> (rich(X0) <~> ~rich(X0))) [input p8]
11. ! [X0] : ((wise(X0) | humble(X0)) => strong(X0)) [input p10]
19. curious(alice) <~> strong(alice) [input p18]
20. ~calm(alice) & curious(alice) [input p19]
25. ~patient(alice) [input hypothesis]
36. ! [X0] : (strong(X0) | (~wise(X0) & ~humble(X0))) [ennf transformation 11]
58. ! [X0] : ((((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) & (((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0))))) [nnf transformation 9]
70. (~strong(alice) | ~curious(alice)) & (strong(alice) | curious(alice)) [nnf transformation 19]
108. patient(X0) | humble(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
109. patient(X0) | humble(X0) | rich(X0) | rich(X0) [cnf transformation 58]
114. ~humble(X0) | strong(X0) [cnf transformation 36]
132. ~strong(alice) | ~curious(alice) [cnf transformation 70]
133. curious(alice) [cnf transformation 20]
139. ~patient(alice) [cnf transformation 25]
142. patient(X0) | humble(X0) | ~rich(X0) [duplicate literal removal 108]
143. patient(X0) | humble(X0) | rich(X0) [duplicate literal removal 109]
185. 11 <=> strong(alice) [avatar definition]
187. ~strong(alice) <- (~11) [avatar component clause 185]
232. patient(X0) | humble(X0) [subsumption resolution 142,143]
293. 33 <=> curious(alice) [avatar definition]
296. ~33 | ~11 [avatar split clause 132,185,293]
299. 33 [avatar split clause 133,293]
334. humble(alice) [resolution 232,139]
346. strong(alice) [resolution 334,114]
347. $false <- (~11) [subsumption resolution 346,187]
348. 11 [avatar contradiction clause 347]
349. $false [avatar sat refutation 296,299,348]
% SZS output end Proof for 3127766989910395190763395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or tall then paul is either strong or not generous and vice versa.
Everyone who is curious or patient is both not kind and not happy.
If mary is not wise then someone is both quiet and not patient and vice versa.
Everyone who is not generous is not patient and vice versa.
Everyone who is tall or not curious is both strong and not strong.
Everyone who is old is both not kind and not calm and vice versa.
Everyone who is patient is old or not quiet.
If someone is both tall and brave then someone is both not wise and funny and vice versa.
Everyone who is either not strong or not brave is both not happy and not creative and vice versa.
Everyone who is generous or funny is brave.
Everyone who is not creative is not quiet or wise.
If alice is not generous then paul is brave or not strong and vice versa.
Everyone who is either not brave or not rich is not old or patient.
Everyone who is strong or tall is not patient and vice versa.
If someone is tall then john is creative or not calm and vice versa.
Everyone who is creative or calm is not tall or quiet.
Fred is either not funny or not quiet.
Someone is not funny or strong.
Someone is both not patient and old.
Someone is not funny or not happy.
Alice is both not tall and patient.
John is not old. | Mary is old. | neutral | ((?[X]:((kind(X)|tall(X))))<=>((strong(paul)<~>~generous(paul))))&
(![X]:((curious(X)|patient(X))=>(~kind(X)&~happy(X))))&
((~wise(mary))<=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:(~generous(X)<=>~patient(X)))&
(![X]:((tall(X)|~curious(X))=>(strong(X)&~strong(X))))&
(![X]:(old(X)<=>(~kind(X)&~calm(X))))&
(![X]:(patient(X)=>(old(X)|~quiet(X))))&
((?[X]:((tall(X)&brave(X))))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((~strong(X)<~>~brave(X))<=>(~happy(X)&~creative(X))))&
(![X]:((generous(X)|funny(X))=>brave(X)))&
(![X]:(~creative(X)=>(~quiet(X)|wise(X))))&
((~generous(alice))<=>((brave(paul)|~strong(paul))))&
(![X]:((~brave(X)<~>~rich(X))=>(~old(X)|patient(X))))&
(![X]:((strong(X)|tall(X))<=>~patient(X)))&
((?[X]:(tall(X)))<=>((creative(john)|~calm(john))))&
(![X]:((creative(X)|calm(X))=>(~tall(X)|quiet(X))))&
((~funny(fred)<~>~quiet(fred)))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((~patient(X)&old(X))))&
(?[X]:((~funny(X)|~happy(X))))&
((~tall(alice)&patient(alice)))&
(~old(john)) | old(mary) | []
| null | 0 |
If susan is calm then mary is either happy or humble and vice versa. If someone is not creative or tall then someone is either creative or brave and vice versa. Everyone who is not brave or kind is not wise or calm and vice versa. Everyone who is not tall is both not humble and not old and vice versa. Everyone who is not kind is funny. Everyone who is either not strong or wise is not happy and vice versa. Everyone who is both old and not strong is both quiet and not brave. If someone is both not old and not generous then mary is not patient and vice versa. If someone is kind or strong then someone is not tall or happy and vice versa. Everyone who is kind is tall and vice versa. Everyone who is both not happy and not calm is not brave or not wise and vice versa. If someone is both not humble and not happy then someone is both wise and not brave and vice versa. Everyone who is either not humble or funny is calm or wise. Everyone who is either curious or funny is both not humble and not brave and vice versa. Everyone who is tall is both brave and not creative. If someone is both strong and curious then someone is humble. Alice is not calm. Alice is either not generous or not wise. Mary is brave or not strong. Someone is not funny. Lucy is both rich and not wise. Someone is either rich or not creative. Someone is either generous or not rich. Susan is both tall and kind. | Lucy is not brave. | contradiction | ((calm(susan))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((creative(X)<~>brave(X)))))&
(![X]:((~brave(X)|kind(X))<=>(~wise(X)|calm(X))))&
(![X]:(~tall(X)<=>(~humble(X)&~old(X))))&
(![X]:(~kind(X)=>funny(X)))&
(![X]:((~strong(X)<~>wise(X))<=>~happy(X)))&
(![X]:((old(X)&~strong(X))=>(quiet(X)&~brave(X))))&
((?[X]:((~old(X)&~generous(X))))<=>(~patient(mary)))&
((?[X]:((kind(X)|strong(X))))<=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:(kind(X)<=>tall(X)))&
(![X]:((~happy(X)&~calm(X))<=>(~brave(X)|~wise(X))))&
((?[X]:((~humble(X)&~happy(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((~humble(X)<~>funny(X))=>(calm(X)|wise(X))))&
(![X]:((curious(X)<~>funny(X))<=>(~humble(X)&~brave(X))))&
(![X]:(tall(X)=>(brave(X)&~creative(X))))&
((?[X]:((strong(X)&curious(X))))=>(?[X]:(humble(X))))&
(~calm(alice))&
((~generous(alice)<~>~wise(alice)))&
((brave(mary)|~strong(mary)))&
(?[X]:(~funny(X)))&
((rich(lucy)&~wise(lucy)))&
(?[X]:((rich(X)<~>~creative(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
((tall(susan)&kind(susan))) | ~brave(lucy) | [
"p2",
"p3",
"p10",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 7011382642660808763578919
% SZS output start Proof for 7011382642660808763578919
3. ! [X0] : ((kind(X0) | ~brave(X0)) <=> (calm(X0) | ~wise(X0))) [input p2]
4. ! [X0] : (~tall(X0) <=> (~old(X0) & ~humble(X0))) [input p3]
11. ! [X0] : ((~calm(X0) & ~happy(X0)) <=> (~wise(X0) | ~brave(X0))) [input p10]
12. ? [X0] : (~happy(X0) & ~humble(X0)) <=> ? [X0] : (~brave(X0) & wise(X0)) [input p11]
15. ! [X0] : (tall(X0) => (~creative(X0) & brave(X0))) [input p14]
25. ~brave(lucy) [input hypothesis]
28. ? [X0] : (~happy(X0) & ~humble(X0)) <=> ? [X1] : (~brave(X1) & wise(X1)) [rectify 12]
36. ! [X0] : ((~creative(X0) & brave(X0)) | ~tall(X0)) [ennf transformation 15]
44. ! [X0] : (((kind(X0) | ~brave(X0)) | (~calm(X0) & wise(X0))) & ((calm(X0) | ~wise(X0)) | (~kind(X0) & brave(X0)))) [nnf transformation 3]
45. ! [X0] : ((kind(X0) | ~brave(X0) | (~calm(X0) & wise(X0))) & (calm(X0) | ~wise(X0) | (~kind(X0) & brave(X0)))) [flattening 44]
46. ! [X0] : ((~tall(X0) | (old(X0) | humble(X0))) & ((~old(X0) & ~humble(X0)) | tall(X0))) [nnf transformation 4]
47. ! [X0] : ((~tall(X0) | old(X0) | humble(X0)) & ((~old(X0) & ~humble(X0)) | tall(X0))) [flattening 46]
59. ! [X0] : (((~calm(X0) & ~happy(X0)) | (wise(X0) & brave(X0))) & ((~wise(X0) | ~brave(X0)) | (calm(X0) | happy(X0)))) [nnf transformation 11]
60. ! [X0] : (((~calm(X0) & ~happy(X0)) | (wise(X0) & brave(X0))) & (~wise(X0) | ~brave(X0) | calm(X0) | happy(X0))) [flattening 59]
61. (? [X0] : (~happy(X0) & ~humble(X0)) | ! [X1] : (brave(X1) | ~wise(X1))) & (? [X1] : (~brave(X1) & wise(X1)) | ! [X0] : (happy(X0) | humble(X0))) [nnf transformation 28]
62. (? [X0] : (~happy(X0) & ~humble(X0)) | ! [X1] : (brave(X1) | ~wise(X1))) & (? [X2] : (~brave(X2) & wise(X2)) | ! [X3] : (happy(X3) | humble(X3))) [rectify 61]
63. ? [X0] : (~happy(X0) & ~humble(X0)) => (~happy(sK5) & ~humble(sK5)) [choice axiom]
64. ? [X2] : (~brave(X2) & wise(X2)) => (~brave(sK6) & wise(sK6)) [choice axiom]
65. ((~happy(sK5) & ~humble(sK5)) | ! [X1] : (brave(X1) | ~wise(X1))) & ((~brave(sK6) & wise(sK6)) | ! [X3] : (happy(X3) | humble(X3))) [skolemisation 62,64,63]
91. ~wise(X0) | calm(X0) | brave(X0) [cnf transformation 45]
95. ~humble(X0) | tall(X0) [cnf transformation 47]
114. ~happy(X0) | brave(X0) [cnf transformation 60]
116. ~calm(X0) | brave(X0) [cnf transformation 60]
118. wise(sK6) | happy(X3) | humble(X3) [cnf transformation 65]
119. ~brave(sK6) | happy(X3) | humble(X3) [cnf transformation 65]
130. ~tall(X0) | brave(X0) [cnf transformation 36]
146. ~brave(lucy) [cnf transformation 25]
262. 27 <=> ! [X3] : (happy(X3) | humble(X3)) [avatar definition]
263. humble(X3) | happy(X3) <- (27) [avatar component clause 262]
265. 28 <=> brave(sK6) [avatar definition]
267. ~brave(sK6) <- (~28) [avatar component clause 265]
268. 27 | ~28 [avatar split clause 119,265,262]
270. 29 <=> wise(sK6) [avatar definition]
272. wise(sK6) <- (29) [avatar component clause 270]
273. 27 | 29 [avatar split clause 118,270,262]
343. calm(sK6) | brave(sK6) <- (29) [resolution 91,272]
344. calm(sK6) <- (~28, 29) [subsumption resolution 343,267]
346. brave(sK6) <- (~28, 29) [resolution 344,116]
347. $false <- (~28, 29) [subsumption resolution 346,267]
348. 28 | ~29 [avatar contradiction clause 347]
365. tall(X0) | happy(X0) <- (27) [resolution 263,95]
491. happy(X2) | brave(X2) <- (27) [resolution 365,130]
494. brave(X2) <- (27) [subsumption resolution 491,114]
526. $false <- (27) [resolution 494,146]
531. ~27 [avatar contradiction clause 526]
532. $false [avatar sat refutation 268,273,348,531]
% SZS output end Proof for 7011382642660808763578919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is brave then someone is generous or not generous and vice versa.
If lucy is both not kind and not humble then someone is either wise or old and vice versa.
Everyone who is both old and funny is both calm and not humble and vice versa.
If susan is both not happy and not tall then susan is both calm and not quiet.
Everyone who is curious is funny or not creative and vice versa.
Everyone who is either funny or kind is patient and vice versa.
If someone is funny then lucy is both not patient and not creative.
Everyone who is old is both not generous and not old.
Everyone who is not rich is not calm or not wise and vice versa.
Everyone who is not patient is happy.
Everyone who is not old is both not kind and not strong and vice versa.
Everyone who is both not generous and curious is both brave and not funny and vice versa.
Everyone who is not quiet is either not funny or quiet.
Everyone who is not quiet or not tall is both not wise and not patient.
Everyone who is quiet or calm is old and vice versa.
If lucy is calm or quiet then someone is not tall or not humble and vice versa.
Paul is not kind.
Mary is not creative.
Susan is either brave or not happy.
Paul is not brave. | Lucy is strong. | contradiction | ((brave(mary))<=>(?[X]:((generous(X)|~generous(X)))))&
(((~kind(lucy)&~humble(lucy)))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((old(X)&funny(X))<=>(calm(X)&~humble(X))))&
(((~happy(susan)&~tall(susan)))=>((calm(susan)&~quiet(susan))))&
(![X]:(curious(X)<=>(funny(X)|~creative(X))))&
(![X]:((funny(X)<~>kind(X))<=>patient(X)))&
((?[X]:(funny(X)))=>((~patient(lucy)&~creative(lucy))))&
(![X]:(old(X)=>(~generous(X)&~old(X))))&
(![X]:(~rich(X)<=>(~calm(X)|~wise(X))))&
(![X]:(~patient(X)=>happy(X)))&
(![X]:(~old(X)<=>(~kind(X)&~strong(X))))&
(![X]:((~generous(X)&curious(X))<=>(brave(X)&~funny(X))))&
(![X]:(~quiet(X)=>(~funny(X)<~>quiet(X))))&
(![X]:((~quiet(X)|~tall(X))=>(~wise(X)&~patient(X))))&
(![X]:((quiet(X)|calm(X))<=>old(X)))&
(((calm(lucy)|quiet(lucy)))<=>(?[X]:((~tall(X)|~humble(X)))))&
(~kind(paul))&
(~creative(mary))&
((brave(susan)<~>~happy(susan)))&
(~brave(paul)) | strong(lucy) | [
"p7",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 3016947919112316170638341
% SZS output start Proof for 3016947919112316170638341
8. ! [X0] : (old(X0) => (~old(X0) & ~generous(X0))) [input p7]
11. ! [X0] : (~old(X0) <=> (~strong(X0) & ~kind(X0))) [input p10]
21. strong(lucy) [input hypothesis]
25. ! [X0] : ((~old(X0) & ~generous(X0)) | ~old(X0)) [ennf transformation 8]
43. ! [X0] : ((~old(X0) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | old(X0))) [nnf transformation 11]
44. ! [X0] : ((~old(X0) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | old(X0))) [flattening 43]
81. ~old(X0) | ~old(X0) [cnf transformation 25]
84. ~strong(X0) | old(X0) [cnf transformation 44]
108. strong(lucy) [cnf transformation 21]
110. ~old(X0) [duplicate literal removal 81]
182. ~strong(X0) [subsumption resolution 84,110]
198. $false [subsumption resolution 108,182]
% SZS output end Proof for 3016947919112316170638341
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and happy then someone is either not funny or old. Everyone who is either brave or patient is both generous and not happy. If someone is calm then someone is not humble or not funny and vice versa. Everyone who is both old and not funny is strong or not happy and vice versa. Everyone who is not rich or not quiet is wise. Everyone who is calm or not quiet is not wise or not rich and vice versa. If lucy is either not generous or not quiet then fred is not calm. Everyone who is happy or not brave is not rich or not humble and vice versa. If alice is not calm then paul is not brave or curious. Everyone who is tall or generous is creative or not wise. Everyone who is generous is not kind or not old and vice versa. Everyone who is both not strong and humble is either patient or not kind and vice versa. Everyone who is either brave or not wise is humble or not funny and vice versa. Everyone who is generous is not calm and vice versa. If someone is wise or brave then someone is both not calm and kind and vice versa. If susan is happy or rich then fred is brave and vice versa. Someone is either creative or calm. Lucy is either not creative or not patient. Someone is both not strong and not kind. Lucy is not happy or wise. Someone is either creative or rich. Mary is not curious or brave. Someone is either happy or not happy. Someone is not happy or not quiet. | Fred is wise. | entailment | ((?[X]:((tall(X)&happy(X))))=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((brave(X)<~>patient(X))=>(generous(X)&~happy(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((old(X)&~funny(X))<=>(strong(X)|~happy(X))))&
(![X]:((~rich(X)|~quiet(X))=>wise(X)))&
(![X]:((calm(X)|~quiet(X))<=>(~wise(X)|~rich(X))))&
(((~generous(lucy)<~>~quiet(lucy)))=>(~calm(fred)))&
(![X]:((happy(X)|~brave(X))<=>(~rich(X)|~humble(X))))&
((~calm(alice))=>((~brave(paul)|curious(paul))))&
(![X]:((tall(X)|generous(X))=>(creative(X)|~wise(X))))&
(![X]:(generous(X)<=>(~kind(X)|~old(X))))&
(![X]:((~strong(X)&humble(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((brave(X)<~>~wise(X))<=>(humble(X)|~funny(X))))&
(![X]:(generous(X)<=>~calm(X)))&
((?[X]:((wise(X)|brave(X))))<=>(?[X]:((~calm(X)&kind(X)))))&
(((happy(susan)|rich(susan)))<=>(brave(fred)))&
(?[X]:((creative(X)<~>calm(X))))&
((~creative(lucy)<~>~patient(lucy)))&
(?[X]:((~strong(X)&~kind(X))))&
((~happy(lucy)|wise(lucy)))&
(?[X]:((creative(X)<~>rich(X))))&
((~curious(mary)|brave(mary)))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((~happy(X)|~quiet(X)))) | wise(fred) | [
"p1",
"p3",
"p4",
"p5",
"p7",
"p10",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 7790401095697070018846250
% SZS output start Proof for 7790401095697070018846250
2. ! [X0] : ((brave(X0) <~> patient(X0)) => (~happy(X0) & generous(X0))) [input p1]
4. ! [X0] : ((~funny(X0) & old(X0)) <=> (~happy(X0) | strong(X0))) [input p3]
5. ! [X0] : ((~quiet(X0) | ~rich(X0)) => wise(X0)) [input p4]
6. ! [X0] : ((~quiet(X0) | calm(X0)) <=> (~rich(X0) | ~wise(X0))) [input p5]
8. ! [X0] : ((~brave(X0) | happy(X0)) <=> (~humble(X0) | ~rich(X0))) [input p7]
11. ! [X0] : (generous(X0) <=> (~old(X0) | ~kind(X0))) [input p10]
12. ! [X0] : ((humble(X0) & ~strong(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p11]
13. ! [X0] : ((brave(X0) <~> ~wise(X0)) <=> (~funny(X0) | humble(X0))) [input p12]
14. ! [X0] : (generous(X0) <=> ~calm(X0)) [input p13]
16. (rich(susan) | happy(susan)) <=> brave(fred) [input p15]
25. ~wise(fred) [input hypothesis]
31. ! [X0] : ((~happy(X0) & generous(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 2]
32. ! [X0] : (wise(X0) | (quiet(X0) & rich(X0))) [ennf transformation 5]
38. ! [X0] : ((~happy(X0) & generous(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 31]
44. ! [X0] : (((~funny(X0) & old(X0)) | (happy(X0) & ~strong(X0))) & ((~happy(X0) | strong(X0)) | (funny(X0) | ~old(X0)))) [nnf transformation 4]
45. ! [X0] : (((~funny(X0) & old(X0)) | (happy(X0) & ~strong(X0))) & (~happy(X0) | strong(X0) | funny(X0) | ~old(X0))) [flattening 44]
46. ! [X0] : (((~quiet(X0) | calm(X0)) | (rich(X0) & wise(X0))) & ((~rich(X0) | ~wise(X0)) | (quiet(X0) & ~calm(X0)))) [nnf transformation 6]
47. ! [X0] : ((~quiet(X0) | calm(X0) | (rich(X0) & wise(X0))) & (~rich(X0) | ~wise(X0) | (quiet(X0) & ~calm(X0)))) [flattening 46]
49. ! [X0] : (((~brave(X0) | happy(X0)) | (humble(X0) & rich(X0))) & ((~humble(X0) | ~rich(X0)) | (brave(X0) & ~happy(X0)))) [nnf transformation 8]
50. ! [X0] : ((~brave(X0) | happy(X0) | (humble(X0) & rich(X0))) & (~humble(X0) | ~rich(X0) | (brave(X0) & ~happy(X0)))) [flattening 49]
51. ! [X0] : ((generous(X0) | (old(X0) & kind(X0))) & ((~old(X0) | ~kind(X0)) | ~generous(X0))) [nnf transformation 11]
52. ! [X0] : ((generous(X0) | (old(X0) & kind(X0))) & (~old(X0) | ~kind(X0) | ~generous(X0))) [flattening 51]
53. ! [X0] : (((humble(X0) & ~strong(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~humble(X0) | strong(X0)))) [nnf transformation 12]
54. ! [X0] : (((humble(X0) & ~strong(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ~humble(X0) | strong(X0))) [flattening 53]
55. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (funny(X0) & ~humble(X0))) & ((~funny(X0) | humble(X0)) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [nnf transformation 13]
56. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (funny(X0) & ~humble(X0))) & (~funny(X0) | humble(X0) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [flattening 55]
57. ! [X0] : ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0))) [nnf transformation 14]
63. ((rich(susan) | happy(susan)) | ~brave(fred)) & (brave(fred) | (~rich(susan) & ~happy(susan))) [nnf transformation 16]
64. (rich(susan) | happy(susan) | ~brave(fred)) & (brave(fred) | (~rich(susan) & ~happy(susan))) [flattening 63]
79. ~brave(X0) | patient(X0) | generous(X0) [cnf transformation 38]
90. ~funny(X0) | happy(X0) [cnf transformation 45]
91. wise(X0) | rich(X0) [cnf transformation 32]
92. wise(X0) | quiet(X0) [cnf transformation 32]
95. ~quiet(X0) | calm(X0) | wise(X0) [cnf transformation 47]
99. ~rich(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 50]
101. ~brave(X0) | happy(X0) | rich(X0) [cnf transformation 50]
106. kind(X0) | generous(X0) [cnf transformation 52]
112. ~kind(X0) | humble(X0) | ~patient(X0) [cnf transformation 54]
117. ~wise(X0) | brave(X0) | funny(X0) [cnf transformation 56]
119. ~brave(X0) | wise(X0) | funny(X0) [cnf transformation 56]
120. ~calm(X0) | ~generous(X0) [cnf transformation 57]
127. brave(fred) | ~happy(susan) [cnf transformation 64]
128. brave(fred) | ~rich(susan) [cnf transformation 64]
143. ~wise(fred) [cnf transformation 25]
168. wise(X0) | calm(X0) [subsumption resolution 95,92]
179. 9 <=> calm(fred) [avatar definition]
180. calm(fred) <- (9) [avatar component clause 179]
228. 20 <=> brave(fred) [avatar definition]
229. brave(fred) <- (20) [avatar component clause 228]
232. 21 <=> happy(susan) [avatar definition]
233. ~happy(susan) <- (~21) [avatar component clause 232]
236. 22 <=> rich(susan) [avatar definition]
237. ~rich(susan) <- (~22) [avatar component clause 236]
240. ~22 | 20 [avatar split clause 128,228,236]
241. ~21 | 20 [avatar split clause 127,228,232]
299. rich(fred) [resolution 91,143]
308. calm(fred) [resolution 168,143]
311. 9 [avatar split clause 308,179]
313. ~generous(fred) <- (9) [resolution 180,120]
335. ~humble(fred) | ~happy(fred) [resolution 99,299]
337. 37 <=> happy(fred) [avatar definition]
339. ~happy(fred) <- (~37) [avatar component clause 337]
341. 38 <=> humble(fred) [avatar definition]
344. ~37 | ~38 [avatar split clause 335,341,337]
370. ~patient(X0) | humble(X0) | generous(X0) [resolution 112,106]
392. rich(X2) | funny(X2) | brave(X2) [resolution 117,91]
572. funny(susan) | brave(susan) <- (~22) [resolution 392,237]
579. 66 <=> brave(susan) [avatar definition]
581. brave(susan) <- (66) [avatar component clause 579]
583. 67 <=> funny(susan) [avatar definition]
585. funny(susan) <- (67) [avatar component clause 583]
586. 66 | 67 | 22 [avatar split clause 572,236,583,579]
756. happy(susan) | rich(susan) <- (66) [resolution 581,101]
771. rich(susan) <- (~21, 66) [subsumption resolution 756,233]
772. $false <- (~21, ~22, 66) [subsumption resolution 771,237]
773. 21 | 22 | ~66 [avatar contradiction clause 772]
781. happy(susan) <- (67) [resolution 585,90]
788. $false <- (~21, 67) [subsumption resolution 781,233]
789. 21 | ~67 [avatar contradiction clause 788]
790. patient(fred) | generous(fred) <- (20) [resolution 229,79]
794. wise(fred) | funny(fred) <- (20) [resolution 229,119]
798. patient(fred) <- (9, 20) [subsumption resolution 790,313]
802. funny(fred) <- (20) [subsumption resolution 794,143]
805. humble(fred) | generous(fred) <- (9, 20) [resolution 798,370]
811. humble(fred) <- (9, 20) [subsumption resolution 805,313]
812. 38 | ~9 | ~20 [avatar split clause 811,228,179,341]
815. happy(fred) <- (20) [resolution 802,90]
816. $false <- (20, ~37) [subsumption resolution 815,339]
817. ~20 | 37 [avatar contradiction clause 816]
818. $false [avatar sat refutation 240,241,311,344,586,773,789,812,817]
% SZS output end Proof for 7790401095697070018846250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not curious is both rich and happy and vice versa.
Everyone who is either not funny or not tall is not brave.
If someone is either not strong or not calm then paul is both quiet and humble.
If someone is both not happy and not curious then someone is curious or not kind and vice versa.
Everyone who is not curious or not happy is either not kind or not patient.
Everyone who is humble is old or happy.
If fred is either brave or quiet then someone is either not tall or not generous.
Everyone who is not happy or not humble is not brave or not funny and vice versa.
Everyone who is either quiet or tall is either not patient or funny and vice versa.
Everyone who is patient or humble is not old and vice versa.
If someone is tall then someone is either not strong or tall and vice versa.
If susan is rich or generous then paul is humble or not funny.
If someone is either not rich or not humble then someone is both curious and not tall and vice versa.
If alice is curious or not funny then fred is happy or not strong and vice versa.
Everyone who is either not tall or not patient is both not happy and not curious and vice versa.
If someone is both generous and not humble then fred is either kind or not humble and vice versa.
Lucy is both not curious and strong.
Susan is either not rich or happy.
Someone is not rich or not tall.
John is not funny or rich.
Susan is both patient and not funny.
Paul is curious or not curious.
Someone is either not calm or not kind. | Paul is not happy. | neutral | (![X]:((~tall(X)<~>~curious(X))<=>(rich(X)&happy(X))))&
(![X]:((~funny(X)<~>~tall(X))=>~brave(X)))&
((?[X]:((~strong(X)<~>~calm(X))))=>((quiet(paul)&humble(paul))))&
((?[X]:((~happy(X)&~curious(X))))<=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:((~curious(X)|~happy(X))=>(~kind(X)<~>~patient(X))))&
(![X]:(humble(X)=>(old(X)|happy(X))))&
(((brave(fred)<~>quiet(fred)))=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:((~happy(X)|~humble(X))<=>(~brave(X)|~funny(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~patient(X)<~>funny(X))))&
(![X]:((patient(X)|humble(X))<=>~old(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~strong(X)<~>tall(X)))))&
(((rich(susan)|generous(susan)))=>((humble(paul)|~funny(paul))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>(?[X]:((curious(X)&~tall(X)))))&
(((curious(alice)|~funny(alice)))<=>((happy(fred)|~strong(fred))))&
(![X]:((~tall(X)<~>~patient(X))<=>(~happy(X)&~curious(X))))&
((?[X]:((generous(X)&~humble(X))))<=>((kind(fred)<~>~humble(fred))))&
((~curious(lucy)&strong(lucy)))&
((~rich(susan)<~>happy(susan)))&
(?[X]:((~rich(X)|~tall(X))))&
((~funny(john)|rich(john)))&
((patient(susan)&~funny(susan)))&
((curious(paul)|~curious(paul)))&
(?[X]:((~calm(X)<~>~kind(X)))) | ~happy(paul) | []
| null | 0 |
If fred is not happy or not old then someone is either not brave or not generous and vice versa. If someone is happy or not creative then alice is not old. If someone is not tall or not generous then someone is both kind and curious. Everyone who is not happy or brave is not creative and vice versa. Everyone who is either not creative or funny is both kind and patient. If someone is not patient then someone is not calm. If mary is not kind or not patient then someone is old or patient and vice versa. If someone is both quiet and not funny then someone is both wise and not wise. Everyone who is not kind or old is both not quiet and not wise. If someone is both not calm and calm then someone is either not quiet or patient and vice versa. Everyone who is both humble and quiet is either not rich or humble. Everyone who is wise is either brave or rich. Everyone who is both not tall and old is either happy or not rich. If mary is both not curious and tall then fred is not old and vice versa. If someone is funny then someone is both rich and not generous. Everyone who is kind is both brave and creative. Someone is either not wise or kind. Susan is either old or not strong. Alice is either not brave or not happy. Someone is either not kind or not humble. Lucy is not calm or kind. Someone is not rich. | Mary is creative. | entailment | (((~happy(fred)|~old(fred)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((?[X]:((happy(X)|~creative(X))))=>(~old(alice)))&
((?[X]:((~tall(X)|~generous(X))))=>(?[X]:((kind(X)&curious(X)))))&
(![X]:((~happy(X)|brave(X))<=>~creative(X)))&
(![X]:((~creative(X)<~>funny(X))=>(kind(X)&patient(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~calm(X))))&
(((~kind(mary)|~patient(mary)))<=>(?[X]:((old(X)|patient(X)))))&
((?[X]:((quiet(X)&~funny(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~kind(X)|old(X))=>(~quiet(X)&~wise(X))))&
((?[X]:((~calm(X)&calm(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
(![X]:((humble(X)&quiet(X))=>(~rich(X)<~>humble(X))))&
(![X]:(wise(X)=>(brave(X)<~>rich(X))))&
(![X]:((~tall(X)&old(X))=>(happy(X)<~>~rich(X))))&
(((~curious(mary)&tall(mary)))<=>(~old(fred)))&
((?[X]:(funny(X)))=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:(kind(X)=>(brave(X)&creative(X))))&
(?[X]:((~wise(X)<~>kind(X))))&
((old(susan)<~>~strong(susan)))&
((~brave(alice)<~>~happy(alice)))&
(?[X]:((~kind(X)<~>~humble(X))))&
((~calm(lucy)|kind(lucy)))&
(?[X]:(~rich(X))) | creative(mary) | [
"p2",
"p3",
"p4",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 5990518642677123612442962
% SZS output start Proof for 5990518642677123612442962
3. ? [X0] : (~generous(X0) | ~tall(X0)) => ? [X0] : (curious(X0) & kind(X0)) [input p2]
4. ! [X0] : ((brave(X0) | ~happy(X0)) <=> ~creative(X0)) [input p3]
5. ! [X0] : ((~creative(X0) <~> funny(X0)) => (patient(X0) & kind(X0))) [input p4]
15. ? [X0] : funny(X0) => ? [X0] : (~generous(X0) & rich(X0)) [input p14]
16. ! [X0] : (kind(X0) => (creative(X0) & brave(X0))) [input p15]
23. ~creative(mary) [input hypothesis]
24. ? [X0] : (~generous(X0) | ~tall(X0)) => ? [X1] : (curious(X1) & kind(X1)) [rectify 3]
28. ? [X0] : funny(X0) => ? [X1] : (~generous(X1) & rich(X1)) [rectify 15]
30. ? [X1] : (curious(X1) & kind(X1)) | ! [X0] : (generous(X0) & tall(X0)) [ennf transformation 24]
31. ! [X0] : ((patient(X0) & kind(X0)) | (~creative(X0) <=> funny(X0))) [ennf transformation 5]
40. ? [X1] : (~generous(X1) & rich(X1)) | ! [X0] : ~funny(X0) [ennf transformation 28]
41. ! [X0] : ((creative(X0) & brave(X0)) | ~kind(X0)) [ennf transformation 16]
47. ? [X0] : (curious(X0) & kind(X0)) | ! [X1] : (generous(X1) & tall(X1)) [rectify 30]
48. ? [X0] : (curious(X0) & kind(X0)) => (curious(sK1) & kind(sK1)) [choice axiom]
49. (curious(sK1) & kind(sK1)) | ! [X1] : (generous(X1) & tall(X1)) [skolemisation 47,48]
50. ! [X0] : (((brave(X0) | ~happy(X0)) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [nnf transformation 4]
51. ! [X0] : ((brave(X0) | ~happy(X0) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [flattening 50]
52. ! [X0] : ((patient(X0) & kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) [nnf transformation 31]
74. ? [X0] : (~generous(X0) & rich(X0)) | ! [X1] : ~funny(X1) [rectify 40]
75. ? [X0] : (~generous(X0) & rich(X0)) => (~generous(sK7) & rich(sK7)) [choice axiom]
76. (~generous(sK7) & rich(sK7)) | ! [X1] : ~funny(X1) [skolemisation 74,75]
96. kind(sK1) | generous(X1) [cnf transformation 49]
100. ~creative(X0) | ~brave(X0) [cnf transformation 51]
102. funny(X0) | kind(X0) | creative(X0) [cnf transformation 52]
133. ~generous(sK7) | ~funny(X1) [cnf transformation 76]
134. ~kind(X0) | brave(X0) [cnf transformation 41]
135. ~kind(X0) | creative(X0) [cnf transformation 41]
146. ~creative(mary) [cnf transformation 23]
177. 7 <=> ! [X0] : creative(X0) [avatar definition]
178. creative(X0) <- (7) [avatar component clause 177]
189. 10 <=> ! [X1] : generous(X1) [avatar definition]
190. generous(X1) <- (10) [avatar component clause 189]
201. 13 <=> kind(sK1) [avatar definition]
203. kind(sK1) <- (13) [avatar component clause 201]
204. 10 | 13 [avatar split clause 96,201,189]
275. 29 <=> ! [X1] : ~funny(X1) [avatar definition]
276. ~funny(X1) <- (29) [avatar component clause 275]
278. 30 <=> generous(sK7) [avatar definition]
280. ~generous(sK7) <- (~30) [avatar component clause 278]
281. 29 | ~30 [avatar split clause 133,278,275]
338. brave(sK1) <- (13) [resolution 134,203]
341. creative(sK1) <- (13) [resolution 135,203]
349. ~brave(sK1) <- (13) [resolution 341,100]
351. $false <- (13) [subsumption resolution 349,338]
352. ~13 [avatar contradiction clause 351]
372. $false <- (10, ~30) [subsumption resolution 280,190]
373. ~10 | 30 [avatar contradiction clause 372]
390. kind(X0) | creative(X0) <- (29) [resolution 102,276]
391. creative(X0) <- (29) [subsumption resolution 390,135]
392. 7 | ~29 [avatar split clause 391,275,177]
393. $false <- (7) [resolution 178,146]
396. ~7 [avatar contradiction clause 393]
397. $false [avatar sat refutation 204,281,352,373,392,396]
% SZS output end Proof for 5990518642677123612442962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet then someone is strong or creative.
Everyone who is not calm or quiet is either not curious or humble.
Everyone who is not happy or not rich is either quiet or calm.
Everyone who is not tall or humble is both funny and not old.
If alice is creative then someone is both old and strong.
If lucy is not tall or kind then fred is old.
If alice is both funny and not wise then someone is quiet or not old.
Everyone who is both rich and not funny is not tall or wise and vice versa.
If mary is not humble then fred is not patient.
If someone is both not generous and brave then john is not happy and vice versa.
Everyone who is both not happy and not old is brave.
Everyone who is generous or old is strong and vice versa.
Everyone who is not patient or strong is either creative or tall and vice versa.
If susan is not generous then someone is both not creative and not happy and vice versa.
Everyone who is both humble and rich is either not humble or not calm and vice versa.
Everyone who is not happy is both brave and happy.
Someone is either generous or quiet.
Someone is both not kind and not patient.
Someone is kind.
Someone is either not generous or generous.
Fred is either not calm or generous.
Someone is either quiet or funny.
John is either not humble or not old.
Someone is humble. | Susan is happy. | entailment | ((?[X]:(~quiet(X)))=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((~calm(X)|quiet(X))=>(~curious(X)<~>humble(X))))&
(![X]:((~happy(X)|~rich(X))=>(quiet(X)<~>calm(X))))&
(![X]:((~tall(X)|humble(X))=>(funny(X)&~old(X))))&
((creative(alice))=>(?[X]:((old(X)&strong(X)))))&
(((~tall(lucy)|kind(lucy)))=>(old(fred)))&
(((funny(alice)&~wise(alice)))=>(?[X]:((quiet(X)|~old(X)))))&
(![X]:((rich(X)&~funny(X))<=>(~tall(X)|wise(X))))&
((~humble(mary))=>(~patient(fred)))&
((?[X]:((~generous(X)&brave(X))))<=>(~happy(john)))&
(![X]:((~happy(X)&~old(X))=>brave(X)))&
(![X]:((generous(X)|old(X))<=>strong(X)))&
(![X]:((~patient(X)|strong(X))<=>(creative(X)<~>tall(X))))&
((~generous(susan))<=>(?[X]:((~creative(X)&~happy(X)))))&
(![X]:((humble(X)&rich(X))<=>(~humble(X)<~>~calm(X))))&
(![X]:(~happy(X)=>(brave(X)&happy(X))))&
(?[X]:((generous(X)<~>quiet(X))))&
(?[X]:((~kind(X)&~patient(X))))&
(?[X]:(kind(X)))&
(?[X]:((~generous(X)<~>generous(X))))&
((~calm(fred)<~>generous(fred)))&
(?[X]:((quiet(X)<~>funny(X))))&
((~humble(john)<~>~old(john)))&
(?[X]:(humble(X))) | happy(susan) | [
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 286031306028060996298328
% SZS output start Proof for 286031306028060996298328
16. ! [X0] : (~happy(X0) => (happy(X0) & brave(X0))) [input p15]
25. ~happy(susan) [input hypothesis]
38. ! [X0] : ((happy(X0) & brave(X0)) | happy(X0)) [ennf transformation 16]
128. happy(X0) | happy(X0) [cnf transformation 38]
143. ~happy(susan) [cnf transformation 25]
144. happy(X0) [duplicate literal removal 128]
294. $false [subsumption resolution 143,144]
% SZS output end Proof for 286031306028060996298328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If susan is either kind or patient then someone is both calm and not creative and vice versa.
Everyone who is either happy or kind is either not funny or rich and vice versa.
If someone is brave or not calm then paul is both not patient and not strong and vice versa.
If someone is patient or quiet then someone is either patient or humble.
Everyone who is both not generous and patient is both creative and kind and vice versa.
Everyone who is funny is brave or tall.
Everyone who is either old or not happy is either tall or funny and vice versa.
Everyone who is curious is not generous or rich.
If lucy is both not creative and old then someone is either curious or not tall.
If paul is either happy or not curious then someone is not tall.
Everyone who is both not curious and not kind is generous or not calm.
Everyone who is either generous or not wise is both calm and strong and vice versa.
If someone is not curious then someone is humble.
Everyone who is not kind or generous is not calm and vice versa.
Everyone who is either funny or not calm is strong or curious and vice versa.
Everyone who is not calm is both not kind and not patient and vice versa.
Someone is both not strong and creative.
Someone is creative or funny.
Paul is both not patient and creative.
Someone is both not humble and not strong.
Someone is generous.
Someone is not quiet.
Someone is not kind or brave.
Someone is curious or not creative. | Paul is old. | neutral | (((kind(susan)<~>patient(susan)))<=>(?[X]:((calm(X)&~creative(X)))))&
(![X]:((happy(X)<~>kind(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((brave(X)|~calm(X))))<=>((~patient(paul)&~strong(paul))))&
((?[X]:((patient(X)|quiet(X))))=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~generous(X)&patient(X))<=>(creative(X)&kind(X))))&
(![X]:(funny(X)=>(brave(X)|tall(X))))&
(![X]:((old(X)<~>~happy(X))<=>(tall(X)<~>funny(X))))&
(![X]:(curious(X)=>(~generous(X)|rich(X))))&
(((~creative(lucy)&old(lucy)))=>(?[X]:((curious(X)<~>~tall(X)))))&
(((happy(paul)<~>~curious(paul)))=>(?[X]:(~tall(X))))&
(![X]:((~curious(X)&~kind(X))=>(generous(X)|~calm(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(calm(X)&strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:(humble(X))))&
(![X]:((~kind(X)|generous(X))<=>~calm(X)))&
(![X]:((funny(X)<~>~calm(X))<=>(strong(X)|curious(X))))&
(![X]:(~calm(X)<=>(~kind(X)&~patient(X))))&
(?[X]:((~strong(X)&creative(X))))&
(?[X]:((creative(X)|funny(X))))&
((~patient(paul)&creative(paul)))&
(?[X]:((~humble(X)&~strong(X))))&
(?[X]:(generous(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((curious(X)|~creative(X)))) | old(paul) | []
| null | 0 |
If mary is funny then lucy is both not happy and patient and vice versa. If someone is humble or quiet then mary is not happy and vice versa. If someone is both not generous and patient then someone is both not brave and tall and vice versa. Everyone who is both not generous and funny is generous and vice versa. Everyone who is either kind or not patient is funny or not kind and vice versa. If susan is brave then someone is patient or funny. If someone is generous or not quiet then paul is both curious and happy and vice versa. If john is funny then someone is either not quiet or not happy and vice versa. Everyone who is not brave or wise is calm or quiet. If someone is both tall and not creative then someone is either not tall or not quiet. Everyone who is either not kind or not happy is either wise or not creative and vice versa. Everyone who is both not old and not generous is either strong or humble and vice versa. Everyone who is both not kind and funny is not curious and vice versa. If susan is not humble or not brave then paul is not humble. Everyone who is both not happy and not quiet is not strong and vice versa. If someone is not quiet then someone is strong or funny and vice versa. Mary is calm. Mary is both calm and humble. Mary is either not curious or calm. Someone is either quiet or not kind. Fred is not happy. | Paul is tall. | neutral | ((funny(mary))<=>((~happy(lucy)&patient(lucy))))&
((?[X]:((humble(X)|quiet(X))))<=>(~happy(mary)))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(![X]:((~generous(X)&funny(X))<=>generous(X)))&
(![X]:((kind(X)<~>~patient(X))<=>(funny(X)|~kind(X))))&
((brave(susan))=>(?[X]:((patient(X)|funny(X)))))&
((?[X]:((generous(X)|~quiet(X))))<=>((curious(paul)&happy(paul))))&
((funny(john))<=>(?[X]:((~quiet(X)<~>~happy(X)))))&
(![X]:((~brave(X)|wise(X))=>(calm(X)|quiet(X))))&
((?[X]:((tall(X)&~creative(X))))=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(![X]:((~kind(X)<~>~happy(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((~old(X)&~generous(X))<=>(strong(X)<~>humble(X))))&
(![X]:((~kind(X)&funny(X))<=>~curious(X)))&
(((~humble(susan)|~brave(susan)))=>(~humble(paul)))&
(![X]:((~happy(X)&~quiet(X))<=>~strong(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:((strong(X)|funny(X)))))&
(calm(mary))&
((calm(mary)&humble(mary)))&
((~curious(mary)<~>calm(mary)))&
(?[X]:((quiet(X)<~>~kind(X))))&
(~happy(fred)) | tall(paul) | []
| null | 0 |
Everyone who is not calm is both curious and not calm.
Everyone who is old or generous is not old or not quiet.
If susan is both brave and old then alice is rich and vice versa.
If someone is either brave or not generous then someone is both not funny and not happy.
Everyone who is not funny is both not kind and not patient and vice versa.
If someone is not calm then john is either patient or not brave and vice versa.
If paul is either not funny or not generous then john is both not funny and patient and vice versa.
If someone is not curious then someone is either not old or not creative and vice versa.
Everyone who is either not kind or not humble is not brave and vice versa.
Everyone who is not patient is both not funny and not curious.
If someone is either not calm or not kind then john is both wise and not funny.
If someone is both funny and humble then someone is not patient and vice versa.
Everyone who is both patient and not tall is either funny or not kind and vice versa.
If fred is funny or not rich then someone is not patient or rich and vice versa.
Everyone who is quiet or humble is both wise and not calm and vice versa.
If alice is not tall then john is not strong or not tall.
Lucy is both not old and not quiet.
Someone is not rich.
John is either strong or generous.
Mary is happy or calm.
Lucy is not kind or not humble.
Paul is not quiet or quiet.
Alice is either quiet or creative. | Mary is not kind. | neutral | (![X]:(~calm(X)=>(curious(X)&~calm(X))))&
(![X]:((old(X)|generous(X))=>(~old(X)|~quiet(X))))&
(((brave(susan)&old(susan)))<=>(rich(alice)))&
((?[X]:((brave(X)<~>~generous(X))))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:(~funny(X)<=>(~kind(X)&~patient(X))))&
((?[X]:(~calm(X)))<=>((patient(john)<~>~brave(john))))&
(((~funny(paul)<~>~generous(paul)))<=>((~funny(john)&patient(john))))&
((?[X]:(~curious(X)))<=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:((~kind(X)<~>~humble(X))<=>~brave(X)))&
(![X]:(~patient(X)=>(~funny(X)&~curious(X))))&
((?[X]:((~calm(X)<~>~kind(X))))=>((wise(john)&~funny(john))))&
((?[X]:((funny(X)&humble(X))))<=>(?[X]:(~patient(X))))&
(![X]:((patient(X)&~tall(X))<=>(funny(X)<~>~kind(X))))&
(((funny(fred)|~rich(fred)))<=>(?[X]:((~patient(X)|rich(X)))))&
(![X]:((quiet(X)|humble(X))<=>(wise(X)&~calm(X))))&
((~tall(alice))=>((~strong(john)|~tall(john))))&
((~old(lucy)&~quiet(lucy)))&
(?[X]:(~rich(X)))&
((strong(john)<~>generous(john)))&
((happy(mary)|calm(mary)))&
((~kind(lucy)|~humble(lucy)))&
((~quiet(paul)|quiet(paul)))&
((quiet(alice)<~>creative(alice))) | ~kind(mary) | []
| null | 0 |
Everyone who is either tall or calm is both not quiet and not creative and vice versa. If susan is kind then someone is either not kind or brave. Everyone who is either curious or patient is either not strong or not wise and vice versa. If someone is both humble and not calm then someone is not kind or not happy and vice versa. If alice is old or funny then someone is both quiet and not brave. If someone is both generous and wise then paul is not curious or old and vice versa. Everyone who is not calm is both patient and happy and vice versa. Everyone who is not kind or happy is either brave or not funny. Everyone who is either not quiet or rich is either happy or funny. Everyone who is not calm is either not old or not rich and vice versa. Everyone who is not old or curious is either not tall or happy. If susan is both calm and funny then someone is not generous and vice versa. If someone is both humble and not tall then someone is brave. Everyone who is both not generous and not patient is both rich and not happy. If susan is both curious and not curious then fred is not curious. Someone is happy or strong. Someone is both creative and strong. Paul is happy or creative. Someone is either humble or happy. Someone is not strong. Susan is either not generous or old. | Alice is not generous. | neutral | (![X]:((tall(X)<~>calm(X))<=>(~quiet(X)&~creative(X))))&
((kind(susan))=>(?[X]:((~kind(X)<~>brave(X)))))&
(![X]:((curious(X)<~>patient(X))<=>(~strong(X)<~>~wise(X))))&
((?[X]:((humble(X)&~calm(X))))<=>(?[X]:((~kind(X)|~happy(X)))))&
(((old(alice)|funny(alice)))=>(?[X]:((quiet(X)&~brave(X)))))&
((?[X]:((generous(X)&wise(X))))<=>((~curious(paul)|old(paul))))&
(![X]:(~calm(X)<=>(patient(X)&happy(X))))&
(![X]:((~kind(X)|happy(X))=>(brave(X)<~>~funny(X))))&
(![X]:((~quiet(X)<~>rich(X))=>(happy(X)<~>funny(X))))&
(![X]:(~calm(X)<=>(~old(X)<~>~rich(X))))&
(![X]:((~old(X)|curious(X))=>(~tall(X)<~>happy(X))))&
(((calm(susan)&funny(susan)))<=>(?[X]:(~generous(X))))&
((?[X]:((humble(X)&~tall(X))))=>(?[X]:(brave(X))))&
(![X]:((~generous(X)&~patient(X))=>(rich(X)&~happy(X))))&
(((curious(susan)&~curious(susan)))=>(~curious(fred)))&
(?[X]:((happy(X)|strong(X))))&
(?[X]:((creative(X)&strong(X))))&
((happy(paul)|creative(paul)))&
(?[X]:((humble(X)<~>happy(X))))&
(?[X]:(~strong(X)))&
((~generous(susan)<~>old(susan))) | ~generous(alice) | []
| null | 0 |
Everyone who is not happy is either rich or not curious and vice versa.
Everyone who is either brave or funny is not kind.
Everyone who is not funny or generous is both not happy and happy and vice versa.
Everyone who is quiet or wise is rich or not curious and vice versa.
Everyone who is quiet is either quiet or happy and vice versa.
Everyone who is either not wise or not strong is either rich or not patient.
Everyone who is generous is both funny and strong and vice versa.
Everyone who is both brave and not rich is not old and vice versa.
If someone is both brave and not humble then someone is either not rich or curious.
Everyone who is both not funny and generous is patient.
Everyone who is both funny and not tall is not creative and vice versa.
Everyone who is not generous or not tall is tall.
If someone is either tall or not kind then mary is not calm.
If someone is not wise then someone is either not patient or curious and vice versa.
Everyone who is both not tall and not brave is both not calm and kind and vice versa.
If john is both funny and not brave then someone is generous or funny.
Someone is not tall or not old.
Someone is not wise or brave.
Alice is creative or not happy.
John is not curious.
Someone is not patient.
Someone is not funny or not humble.
Paul is not old or not creative.
Fred is funny or wise. | Fred is not generous. | entailment | (![X]:(~happy(X)<=>(rich(X)<~>~curious(X))))&
(![X]:((brave(X)<~>funny(X))=>~kind(X)))&
(![X]:((~funny(X)|generous(X))<=>(~happy(X)&happy(X))))&
(![X]:((quiet(X)|wise(X))<=>(rich(X)|~curious(X))))&
(![X]:(quiet(X)<=>(quiet(X)<~>happy(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(rich(X)<~>~patient(X))))&
(![X]:(generous(X)<=>(funny(X)&strong(X))))&
(![X]:((brave(X)&~rich(X))<=>~old(X)))&
((?[X]:((brave(X)&~humble(X))))=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:((~funny(X)&generous(X))=>patient(X)))&
(![X]:((funny(X)&~tall(X))<=>~creative(X)))&
(![X]:((~generous(X)|~tall(X))=>tall(X)))&
((?[X]:((tall(X)<~>~kind(X))))=>(~calm(mary)))&
((?[X]:(~wise(X)))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((~tall(X)&~brave(X))<=>(~calm(X)&kind(X))))&
(((funny(john)&~brave(john)))=>(?[X]:((generous(X)|funny(X)))))&
(?[X]:((~tall(X)|~old(X))))&
(?[X]:((~wise(X)|brave(X))))&
((creative(alice)|~happy(alice)))&
(~curious(john))&
(?[X]:(~patient(X)))&
(?[X]:((~funny(X)|~humble(X))))&
((~old(paul)|~creative(paul)))&
((funny(fred)|wise(fred))) | ~generous(fred) | [
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 8059649774165219821786152
% SZS output start Proof for 8059649774165219821786152
3. ! [X0] : ((generous(X0) | ~funny(X0)) <=> (happy(X0) & ~happy(X0))) [input p2]
25. generous(fred) [input hypothesis]
41. ! [X0] : (((generous(X0) | ~funny(X0)) | (~happy(X0) | happy(X0))) & ((happy(X0) & ~happy(X0)) | (~generous(X0) & funny(X0)))) [nnf transformation 3]
42. ! [X0] : ((generous(X0) | ~funny(X0) | ~happy(X0) | happy(X0)) & ((happy(X0) & ~happy(X0)) | (~generous(X0) & funny(X0)))) [flattening 41]
80. ~happy(X0) | ~generous(X0) [cnf transformation 42]
82. happy(X0) | ~generous(X0) [cnf transformation 42]
128. generous(fred) [cnf transformation 25]
132. ~generous(X0) [subsumption resolution 80,82]
206. $false [subsumption resolution 128,132]
% SZS output end Proof for 8059649774165219821786152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is both brave and not happy and vice versa.
If someone is tall then someone is happy and vice versa.
If someone is not creative or strong then john is either not calm or funny and vice versa.
If alice is kind or not wise then someone is old or not kind.
If someone is creative or tall then someone is both old and not funny.
Everyone who is either humble or not calm is not funny.
If susan is either not patient or wise then fred is either not rich or happy and vice versa.
Everyone who is either generous or kind is brave or creative and vice versa.
Everyone who is either humble or quiet is both quiet and not strong.
Everyone who is calm is either calm or generous.
If someone is both generous and quiet then paul is both generous and not kind and vice versa.
Everyone who is either happy or not humble is either patient or brave and vice versa.
Everyone who is not brave or not generous is not kind or creative.
If someone is humble then someone is old or not happy and vice versa.
If mary is patient or humble then lucy is strong and vice versa.
If someone is not funny then someone is both not humble and tall and vice versa.
Fred is both not curious and happy.
Mary is either not humble or not funny.
Alice is both not quiet and not wise.
Someone is not generous or not happy.
Fred is not generous or funny.
Someone is both not humble and not creative.
Someone is both not humble and not happy.
Alice is not calm. | Alice is wise. | contradiction | (![X]:(~kind(X)<=>(brave(X)&~happy(X))))&
((?[X]:(tall(X)))<=>(?[X]:(happy(X))))&
((?[X]:((~creative(X)|strong(X))))<=>((~calm(john)<~>funny(john))))&
(((kind(alice)|~wise(alice)))=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((creative(X)|tall(X))))=>(?[X]:((old(X)&~funny(X)))))&
(![X]:((humble(X)<~>~calm(X))=>~funny(X)))&
(((~patient(susan)<~>wise(susan)))<=>((~rich(fred)<~>happy(fred))))&
(![X]:((generous(X)<~>kind(X))<=>(brave(X)|creative(X))))&
(![X]:((humble(X)<~>quiet(X))=>(quiet(X)&~strong(X))))&
(![X]:(calm(X)=>(calm(X)<~>generous(X))))&
((?[X]:((generous(X)&quiet(X))))<=>((generous(paul)&~kind(paul))))&
(![X]:((happy(X)<~>~humble(X))<=>(patient(X)<~>brave(X))))&
(![X]:((~brave(X)|~generous(X))=>(~kind(X)|creative(X))))&
((?[X]:(humble(X)))<=>(?[X]:((old(X)|~happy(X)))))&
(((patient(mary)|humble(mary)))<=>(strong(lucy)))&
((?[X]:(~funny(X)))<=>(?[X]:((~humble(X)&tall(X)))))&
((~curious(fred)&happy(fred)))&
((~humble(mary)<~>~funny(mary)))&
((~quiet(alice)&~wise(alice)))&
(?[X]:((~generous(X)|~happy(X))))&
((~generous(fred)|funny(fred)))&
(?[X]:((~humble(X)&~creative(X))))&
(?[X]:((~humble(X)&~happy(X))))&
(~calm(alice)) | wise(alice) | [
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 5340541901372738251602700
% SZS output start Proof for 5340541901372738251602700
19. ~wise(alice) & ~quiet(alice) [input p18]
25. wise(alice) [input hypothesis]
151. ~wise(alice) [cnf transformation 19]
159. wise(alice) [cnf transformation 25]
207. 11 <=> wise(alice) [avatar definition]
359. ~11 [avatar split clause 151,207]
378. 11 [avatar split clause 159,207]
379. $false [avatar sat refutation 359,378]
% SZS output end Proof for 5340541901372738251602700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or kind is both tall and rich.
If someone is either humble or not kind then someone is humble or not wise and vice versa.
Everyone who is not happy is either not brave or patient and vice versa.
If someone is not happy or strong then fred is wise or not generous.
If someone is either brave or happy then john is both not quiet and quiet.
Everyone who is generous is either happy or creative and vice versa.
Everyone who is humble or not rich is generous or not humble.
If alice is either not calm or not funny then someone is kind.
Everyone who is both patient and quiet is not humble.
Everyone who is not creative is not tall or not funny and vice versa.
If someone is either not creative or wise then someone is both creative and wise.
If alice is not tall then fred is humble or not kind and vice versa.
Everyone who is not strong is either not strong or calm and vice versa.
Everyone who is both not generous and brave is both rich and not humble and vice versa.
If john is both humble and quiet then alice is either not generous or wise and vice versa.
If alice is not happy then someone is both not calm and not generous and vice versa.
John is tall or rich.
John is either humble or not generous.
Someone is both tall and rich.
Someone is not kind.
Someone is both not humble and quiet.
Someone is either not rich or not creative.
Someone is either generous or not happy.
Someone is not curious. | Alice is not happy. | neutral | (![X]:((calm(X)<~>kind(X))=>(tall(X)&rich(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:(~happy(X)<=>(~brave(X)<~>patient(X))))&
((?[X]:((~happy(X)|strong(X))))=>((wise(fred)|~generous(fred))))&
((?[X]:((brave(X)<~>happy(X))))=>((~quiet(john)&quiet(john))))&
(![X]:(generous(X)<=>(happy(X)<~>creative(X))))&
(![X]:((humble(X)|~rich(X))=>(generous(X)|~humble(X))))&
(((~calm(alice)<~>~funny(alice)))=>(?[X]:(kind(X))))&
(![X]:((patient(X)&quiet(X))=>~humble(X)))&
(![X]:(~creative(X)<=>(~tall(X)|~funny(X))))&
((?[X]:((~creative(X)<~>wise(X))))=>(?[X]:((creative(X)&wise(X)))))&
((~tall(alice))<=>((humble(fred)|~kind(fred))))&
(![X]:(~strong(X)<=>(~strong(X)<~>calm(X))))&
(![X]:((~generous(X)&brave(X))<=>(rich(X)&~humble(X))))&
(((humble(john)&quiet(john)))<=>((~generous(alice)<~>wise(alice))))&
((~happy(alice))<=>(?[X]:((~calm(X)&~generous(X)))))&
((tall(john)|rich(john)))&
((humble(john)<~>~generous(john)))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~humble(X)&quiet(X))))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:((generous(X)<~>~happy(X))))&
(?[X]:(~curious(X))) | ~happy(alice) | []
| null | 0 |
If someone is not humble or not funny then lucy is both wise and not creative and vice versa.
Everyone who is not tall or funny is both not happy and not rich and vice versa.
If mary is not old then john is calm and vice versa.
Everyone who is not brave is rich or not patient.
Everyone who is not wise is either not brave or not wise and vice versa.
Everyone who is both funny and strong is quiet and vice versa.
Everyone who is not wise or not generous is both not strong and quiet.
If lucy is funny or wise then someone is rich or not curious and vice versa.
If someone is creative then someone is both not patient and strong and vice versa.
If someone is either not calm or funny then someone is funny or curious.
Everyone who is both rich and strong is both not funny and not quiet.
If paul is both creative and not patient then paul is both rich and funny.
Everyone who is either tall or wise is both not generous and rich and vice versa.
Everyone who is not patient or brave is either not creative or not kind and vice versa.
If someone is wise or strong then someone is either not rich or not generous.
Everyone who is not humble is either not old or old and vice versa.
Someone is either not old or strong.
Mary is tall or not kind.
Lucy is either creative or kind.
Someone is not funny or humble.
Mary is both calm and happy.
John is not tall or patient.
Someone is wise. | Paul is quiet. | neutral | ((?[X]:((~humble(X)|~funny(X))))<=>((wise(lucy)&~creative(lucy))))&
(![X]:((~tall(X)|funny(X))<=>(~happy(X)&~rich(X))))&
((~old(mary))<=>(calm(john)))&
(![X]:(~brave(X)=>(rich(X)|~patient(X))))&
(![X]:(~wise(X)<=>(~brave(X)<~>~wise(X))))&
(![X]:((funny(X)&strong(X))<=>quiet(X)))&
(![X]:((~wise(X)|~generous(X))=>(~strong(X)&quiet(X))))&
(((funny(lucy)|wise(lucy)))<=>(?[X]:((rich(X)|~curious(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:((~calm(X)<~>funny(X))))=>(?[X]:((funny(X)|curious(X)))))&
(![X]:((rich(X)&strong(X))=>(~funny(X)&~quiet(X))))&
(((creative(paul)&~patient(paul)))=>((rich(paul)&funny(paul))))&
(![X]:((tall(X)<~>wise(X))<=>(~generous(X)&rich(X))))&
(![X]:((~patient(X)|brave(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:((wise(X)|strong(X))))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:(~humble(X)<=>(~old(X)<~>old(X))))&
(?[X]:((~old(X)<~>strong(X))))&
((tall(mary)|~kind(mary)))&
((creative(lucy)<~>kind(lucy)))&
(?[X]:((~funny(X)|humble(X))))&
((calm(mary)&happy(mary)))&
((~tall(john)|patient(john)))&
(?[X]:(wise(X))) | quiet(paul) | []
| null | 0 |
Everyone who is either strong or not patient is not old and vice versa.
Everyone who is either not funny or quiet is both not wise and generous and vice versa.
If paul is both not creative and creative then someone is strong.
If lucy is not old then someone is not brave or quiet.
If someone is both wise and calm then someone is funny or brave and vice versa.
If someone is both not old and not wise then someone is not humble and vice versa.
Everyone who is either not wise or not patient is old.
Everyone who is patient is kind and vice versa.
Everyone who is both not old and kind is happy or quiet and vice versa.
If lucy is either humble or not tall then john is either not humble or not curious.
Everyone who is both creative and not calm is strong.
If someone is generous or tall then someone is patient or not generous.
Everyone who is either happy or brave is not calm or generous and vice versa.
Everyone who is both not kind and not generous is humble or not calm.
If mary is both not brave and quiet then john is not kind.
Everyone who is not rich is not brave or not wise and vice versa.
Someone is either not funny or creative.
Someone is both brave and generous.
John is either not rich or not humble.
Someone is both humble and not patient.
Mary is wise or happy.
John is kind.
John is not old or not generous.
Someone is humble. | John is not happy. | neutral | (![X]:((strong(X)<~>~patient(X))<=>~old(X)))&
(![X]:((~funny(X)<~>quiet(X))<=>(~wise(X)&generous(X))))&
(((~creative(paul)&creative(paul)))=>(?[X]:(strong(X))))&
((~old(lucy))=>(?[X]:((~brave(X)|quiet(X)))))&
((?[X]:((wise(X)&calm(X))))<=>(?[X]:((funny(X)|brave(X)))))&
((?[X]:((~old(X)&~wise(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~wise(X)<~>~patient(X))=>old(X)))&
(![X]:(patient(X)<=>kind(X)))&
(![X]:((~old(X)&kind(X))<=>(happy(X)|quiet(X))))&
(((humble(lucy)<~>~tall(lucy)))=>((~humble(john)<~>~curious(john))))&
(![X]:((creative(X)&~calm(X))=>strong(X)))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~calm(X)|generous(X))))&
(![X]:((~kind(X)&~generous(X))=>(humble(X)|~calm(X))))&
(((~brave(mary)&quiet(mary)))=>(~kind(john)))&
(![X]:(~rich(X)<=>(~brave(X)|~wise(X))))&
(?[X]:((~funny(X)<~>creative(X))))&
(?[X]:((brave(X)&generous(X))))&
((~rich(john)<~>~humble(john)))&
(?[X]:((humble(X)&~patient(X))))&
((wise(mary)|happy(mary)))&
(kind(john))&
((~old(john)|~generous(john)))&
(?[X]:(humble(X))) | ~happy(john) | []
| null | 0 |
If someone is brave or wise then alice is not patient and vice versa.
Everyone who is rich or not strong is both not calm and old.
Everyone who is both creative and not rich is not brave.
Everyone who is both happy and patient is either not old or humble.
Everyone who is both patient and tall is both not happy and strong.
Everyone who is either not wise or brave is both generous and funny and vice versa.
If mary is either not tall or not curious then paul is both not rich and tall.
Everyone who is old is either creative or calm.
Everyone who is either not generous or not rich is not old and vice versa.
Everyone who is humble is either brave or not calm.
Everyone who is either not tall or not patient is not wise or generous.
If alice is kind then someone is humble or old.
Everyone who is not wise or generous is both not strong and quiet and vice versa.
Everyone who is both kind and humble is either humble or not old and vice versa.
If someone is either kind or old then mary is tall or not kind.
Everyone who is not calm or not happy is both strong and not tall.
Mary is strong or curious.
Someone is not humble.
Susan is either not happy or calm.
Mary is not creative.
Someone is wise. | Mary is not tall. | entailment | ((?[X]:((brave(X)|wise(X))))<=>(~patient(alice)))&
(![X]:((rich(X)|~strong(X))=>(~calm(X)&old(X))))&
(![X]:((creative(X)&~rich(X))=>~brave(X)))&
(![X]:((happy(X)&patient(X))=>(~old(X)<~>humble(X))))&
(![X]:((patient(X)&tall(X))=>(~happy(X)&strong(X))))&
(![X]:((~wise(X)<~>brave(X))<=>(generous(X)&funny(X))))&
(((~tall(mary)<~>~curious(mary)))=>((~rich(paul)&tall(paul))))&
(![X]:(old(X)=>(creative(X)<~>calm(X))))&
(![X]:((~generous(X)<~>~rich(X))<=>~old(X)))&
(![X]:(humble(X)=>(brave(X)<~>~calm(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(~wise(X)|generous(X))))&
((kind(alice))=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~strong(X)&quiet(X))))&
(![X]:((kind(X)&humble(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((kind(X)<~>old(X))))=>((tall(mary)|~kind(mary))))&
(![X]:((~calm(X)|~happy(X))=>(strong(X)&~tall(X))))&
((strong(mary)|curious(mary)))&
(?[X]:(~humble(X)))&
((~happy(susan)<~>calm(susan)))&
(~creative(mary))&
(?[X]:(wise(X))) | ~tall(mary) | [
"p1",
"p4",
"p10",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 4721782039349458994455464
% SZS output start Proof for 4721782039349458994455464
2. ! [X0] : ((~strong(X0) | rich(X0)) => (old(X0) & ~calm(X0))) [input p1]
5. ! [X0] : ((tall(X0) & patient(X0)) => (strong(X0) & ~happy(X0))) [input p4]
11. ! [X0] : ((~tall(X0) <~> ~patient(X0)) => (generous(X0) | ~wise(X0))) [input p10]
13. ! [X0] : ((generous(X0) | ~wise(X0)) <=> (quiet(X0) & ~strong(X0))) [input p12]
16. ! [X0] : ((~happy(X0) | ~calm(X0)) => (~tall(X0) & strong(X0))) [input p15]
22. tall(mary) [input hypothesis]
23. ! [X0] : ((old(X0) & ~calm(X0)) | (strong(X0) & ~rich(X0))) [ennf transformation 2]
28. ! [X0] : ((strong(X0) & ~happy(X0)) | (~tall(X0) | ~patient(X0))) [ennf transformation 5]
29. ! [X0] : ((strong(X0) & ~happy(X0)) | ~tall(X0) | ~patient(X0)) [flattening 28]
33. ! [X0] : ((generous(X0) | ~wise(X0)) | (~tall(X0) <=> ~patient(X0))) [ennf transformation 11]
34. ! [X0] : (generous(X0) | ~wise(X0) | (~tall(X0) <=> ~patient(X0))) [flattening 33]
38. ! [X0] : ((~tall(X0) & strong(X0)) | (happy(X0) & calm(X0))) [ennf transformation 16]
50. ! [X0] : (generous(X0) | ~wise(X0) | ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0)))) [nnf transformation 34]
53. ! [X0] : (((generous(X0) | ~wise(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [nnf transformation 13]
54. ! [X0] : ((generous(X0) | ~wise(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [flattening 53]
67. ~calm(X0) | strong(X0) [cnf transformation 23]
73. ~tall(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 29]
94. ~tall(X0) | ~wise(X0) | generous(X0) | patient(X0) [cnf transformation 50]
96. ~strong(X0) | wise(X0) [cnf transformation 54]
97. ~generous(X0) | ~strong(X0) [cnf transformation 54]
109. strong(X0) | calm(X0) [cnf transformation 38]
112. ~tall(X0) | happy(X0) [cnf transformation 38]
119. tall(mary) [cnf transformation 22]
148. 7 <=> tall(mary) [avatar definition]
149. tall(mary) <- (7) [avatar component clause 148]
187. strong(X0) [subsumption resolution 109,67]
198. 7 [avatar split clause 119,148]
199. wise(X0) [resolution 96,187]
204. happy(mary) <- (7) [resolution 112,149]
209. ~happy(mary) | ~patient(mary) <- (7) [resolution 73,149]
210. ~patient(mary) <- (7) [subsumption resolution 209,204]
251. ~wise(mary) | generous(mary) | patient(mary) <- (7) [resolution 94,149]
252. generous(mary) | patient(mary) <- (7) [subsumption resolution 251,199]
253. generous(mary) <- (7) [subsumption resolution 252,210]
256. ~strong(mary) <- (7) [resolution 253,97]
260. $false <- (7) [subsumption resolution 256,187]
261. ~7 [avatar contradiction clause 260]
262. $false [avatar sat refutation 198,261]
% SZS output end Proof for 4721782039349458994455464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is both old and not curious and vice versa. Everyone who is both not rich and curious is strong or not curious. If mary is both not tall and not curious then someone is both funny and creative. If john is either quiet or brave then lucy is rich or happy and vice versa. Everyone who is not kind is not quiet or not happy and vice versa. If fred is humble then someone is both not old and not tall. Everyone who is both not calm and funny is both funny and brave and vice versa. Everyone who is generous is both not generous and not calm. Everyone who is either generous or not rich is both rich and strong. Everyone who is either not old or generous is either not humble or not curious and vice versa. If someone is both not quiet and not wise then john is both not happy and not humble. Everyone who is either strong or tall is both not tall and patient and vice versa. If someone is not patient then mary is both not happy and not rich. Everyone who is both tall and brave is not strong or creative. Everyone who is not happy is brave. Everyone who is funny or creative is either not wise or calm and vice versa. Lucy is either strong or not kind. Someone is either not wise or generous. John is both old and not happy. Someone is tall or not curious. Paul is patient. Someone is not kind or not wise. Someone is not kind. Paul is creative or happy. | Lucy is not kind. | contradiction | (![X]:((generous(X)<~>~strong(X))<=>(old(X)&~curious(X))))&
(![X]:((~rich(X)&curious(X))=>(strong(X)|~curious(X))))&
(((~tall(mary)&~curious(mary)))=>(?[X]:((funny(X)&creative(X)))))&
(((quiet(john)<~>brave(john)))<=>((rich(lucy)|happy(lucy))))&
(![X]:(~kind(X)<=>(~quiet(X)|~happy(X))))&
((humble(fred))=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((~calm(X)&funny(X))<=>(funny(X)&brave(X))))&
(![X]:(generous(X)=>(~generous(X)&~calm(X))))&
(![X]:((generous(X)<~>~rich(X))=>(rich(X)&strong(X))))&
(![X]:((~old(X)<~>generous(X))<=>(~humble(X)<~>~curious(X))))&
((?[X]:((~quiet(X)&~wise(X))))=>((~happy(john)&~humble(john))))&
(![X]:((strong(X)<~>tall(X))<=>(~tall(X)&patient(X))))&
((?[X]:(~patient(X)))=>((~happy(mary)&~rich(mary))))&
(![X]:((tall(X)&brave(X))=>(~strong(X)|creative(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:((funny(X)|creative(X))<=>(~wise(X)<~>calm(X))))&
((strong(lucy)<~>~kind(lucy)))&
(?[X]:((~wise(X)<~>generous(X))))&
((old(john)&~happy(john)))&
(?[X]:((tall(X)|~curious(X))))&
(patient(paul))&
(?[X]:((~kind(X)|~wise(X))))&
(?[X]:(~kind(X)))&
((creative(paul)|happy(paul))) | ~kind(lucy) | [
"p7",
"p8",
"p11",
"p12",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 6164624828665929800909245
% SZS output start Proof for 6164624828665929800909245
8. ! [X0] : (generous(X0) => (~calm(X0) & ~generous(X0))) [input p7]
9. ! [X0] : ((generous(X0) <~> ~rich(X0)) => (strong(X0) & rich(X0))) [input p8]
12. ! [X0] : ((strong(X0) <~> tall(X0)) <=> (patient(X0) & ~tall(X0))) [input p11]
13. ? [X0] : ~patient(X0) => (~rich(mary) & ~happy(mary)) [input p12]
17. strong(lucy) <~> ~kind(lucy) [input p16]
25. ~kind(lucy) [input hypothesis]
31. ! [X0] : ((~calm(X0) & ~generous(X0)) | ~generous(X0)) [ennf transformation 8]
32. ! [X0] : ((strong(X0) & rich(X0)) | (generous(X0) <=> ~rich(X0))) [ennf transformation 9]
34. (~rich(mary) & ~happy(mary)) | ! [X0] : patient(X0) [ennf transformation 13]
50. ! [X0] : ((strong(X0) & rich(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) [nnf transformation 32]
52. ! [X0] : ((((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | (~patient(X0) | tall(X0))) & ((patient(X0) & ~tall(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))))) [nnf transformation 12]
53. ! [X0] : ((((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | ~patient(X0) | tall(X0)) & ((patient(X0) & ~tall(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))))) [flattening 52]
56. (kind(lucy) | ~strong(lucy)) & (~kind(lucy) | strong(lucy)) [nnf transformation 17]
90. ~generous(X0) | ~generous(X0) [cnf transformation 31]
93. rich(X0) | generous(X0) | rich(X0) [cnf transformation 50]
107. ~tall(X0) | strong(X0) | ~tall(X0) [cnf transformation 53]
110. tall(X0) | strong(X0) | ~patient(X0) | tall(X0) [cnf transformation 53]
113. ~rich(mary) | patient(X0) [cnf transformation 34]
123. kind(lucy) | ~strong(lucy) [cnf transformation 56]
133. ~kind(lucy) [cnf transformation 25]
134. ~tall(X0) | strong(X0) [duplicate literal removal 107]
135. ~patient(X0) | strong(X0) | tall(X0) [duplicate literal removal 110]
136. rich(X0) | generous(X0) [duplicate literal removal 93]
137. ~generous(X0) [duplicate literal removal 90]
194. rich(X0) [subsumption resolution 136,137]
212. patient(X0) [subsumption resolution 113,194]
215. 15 <=> strong(lucy) [avatar definition]
217. ~strong(lucy) <- (~15) [avatar component clause 215]
219. 16 <=> kind(lucy) [avatar definition]
222. ~15 | 16 [avatar split clause 123,219,215]
253. ~16 [avatar split clause 133,219]
267. strong(X0) | tall(X0) [resolution 135,212]
268. strong(X0) [subsumption resolution 267,134]
269. $false <- (~15) [resolution 268,217]
272. 15 [avatar contradiction clause 269]
273. $false [avatar sat refutation 222,253,272]
% SZS output end Proof for 6164624828665929800909245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not brave and quiet then alice is both not calm and creative. Everyone who is not quiet is not strong and vice versa. If someone is not creative then alice is either not strong or old. If someone is either calm or quiet then lucy is not generous. Everyone who is either rich or not brave is both humble and not creative. If fred is old or not humble then susan is either generous or curious. Everyone who is not creative or kind is not calm or not creative and vice versa. Everyone who is either brave or not happy is both not wise and not rich. If someone is not calm then lucy is either curious or not calm. Everyone who is rich or not strong is either not kind or kind and vice versa. If someone is either not strong or not wise then someone is either not wise or not tall. Everyone who is both not rich and not happy is either not brave or not funny and vice versa. If lucy is both not wise and wise then paul is either not generous or not funny and vice versa. If someone is not curious then someone is not brave or not patient and vice versa. If paul is tall or not kind then someone is old and vice versa. Everyone who is not brave or strong is both not happy and patient and vice versa. Paul is strong. Alice is not old. Someone is both humble and quiet. Mary is either brave or strong. Mary is brave or not calm. Someone is creative or not kind. Paul is quiet. Fred is not happy or not patient. | Paul is not generous. | contradiction | (((~brave(alice)&quiet(alice)))=>((~calm(alice)&creative(alice))))&
(![X]:(~quiet(X)<=>~strong(X)))&
((?[X]:(~creative(X)))=>((~strong(alice)<~>old(alice))))&
((?[X]:((calm(X)<~>quiet(X))))=>(~generous(lucy)))&
(![X]:((rich(X)<~>~brave(X))=>(humble(X)&~creative(X))))&
(((old(fred)|~humble(fred)))=>((generous(susan)<~>curious(susan))))&
(![X]:((~creative(X)|kind(X))<=>(~calm(X)|~creative(X))))&
(![X]:((brave(X)<~>~happy(X))=>(~wise(X)&~rich(X))))&
((?[X]:(~calm(X)))=>((curious(lucy)<~>~calm(lucy))))&
(![X]:((rich(X)|~strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((~strong(X)<~>~wise(X))))=>(?[X]:((~wise(X)<~>~tall(X)))))&
(![X]:((~rich(X)&~happy(X))<=>(~brave(X)<~>~funny(X))))&
(((~wise(lucy)&wise(lucy)))<=>((~generous(paul)<~>~funny(paul))))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)|~patient(X)))))&
(((tall(paul)|~kind(paul)))<=>(?[X]:(old(X))))&
(![X]:((~brave(X)|strong(X))<=>(~happy(X)&patient(X))))&
(strong(paul))&
(~old(alice))&
(?[X]:((humble(X)&quiet(X))))&
((brave(mary)<~>strong(mary)))&
((brave(mary)|~calm(mary)))&
(?[X]:((creative(X)|~kind(X))))&
(quiet(paul))&
((~happy(fred)|~patient(fred))) | ~generous(paul) | [
"p7",
"p9",
"p11",
"p12",
"p15",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 5540390450130496118851195
% SZS output start Proof for 5540390450130496118851195
8. ! [X0] : ((brave(X0) <~> ~happy(X0)) => (~rich(X0) & ~wise(X0))) [input p7]
10. ! [X0] : ((~strong(X0) | rich(X0)) <=> (~kind(X0) <~> kind(X0))) [input p9]
12. ! [X0] : ((~happy(X0) & ~rich(X0)) <=> (~brave(X0) <~> ~funny(X0))) [input p11]
13. (wise(lucy) & ~wise(lucy)) <=> (~generous(paul) <~> ~funny(paul)) [input p12]
16. ! [X0] : ((strong(X0) | ~brave(X0)) <=> (patient(X0) & ~happy(X0))) [input p15]
17. strong(paul) [input p16]
25. ~generous(paul) [input hypothesis]
37. ! [X0] : ((~rich(X0) & ~wise(X0)) | (brave(X0) <=> ~happy(X0))) [ennf transformation 8]
47. ! [X0] : ((~rich(X0) & ~wise(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) [nnf transformation 37]
49. ! [X0] : (((~strong(X0) | rich(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (strong(X0) & ~rich(X0)))) [nnf transformation 10]
50. ! [X0] : ((~strong(X0) | rich(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (strong(X0) & ~rich(X0)))) [flattening 49]
55. ! [X0] : (((~happy(X0) & ~rich(X0)) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (happy(X0) | rich(X0)))) [nnf transformation 12]
56. ! [X0] : (((~happy(X0) & ~rich(X0)) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | happy(X0) | rich(X0))) [flattening 55]
57. ((wise(lucy) & ~wise(lucy)) | ((~generous(paul) | funny(paul)) & (~funny(paul) | generous(paul)))) & (((funny(paul) | generous(paul)) & (~funny(paul) | ~generous(paul))) | (~wise(lucy) | wise(lucy))) [nnf transformation 13]
58. ((wise(lucy) & ~wise(lucy)) | ((~generous(paul) | funny(paul)) & (~funny(paul) | generous(paul)))) & (((funny(paul) | generous(paul)) & (~funny(paul) | ~generous(paul))) | ~wise(lucy) | wise(lucy)) [flattening 57]
69. ! [X0] : (((strong(X0) | ~brave(X0)) | (~patient(X0) | happy(X0))) & ((patient(X0) & ~happy(X0)) | (~strong(X0) & brave(X0)))) [nnf transformation 16]
70. ! [X0] : ((strong(X0) | ~brave(X0) | ~patient(X0) | happy(X0)) & ((patient(X0) & ~happy(X0)) | (~strong(X0) & brave(X0)))) [flattening 69]
95. ~rich(X0) | brave(X0) | happy(X0) [cnf transformation 47]
102. ~strong(X0) | rich(X0) | kind(X0) | kind(X0) [cnf transformation 50]
103. ~strong(X0) | rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 50]
111. ~rich(X0) | ~brave(X0) | funny(X0) [cnf transformation 56]
116. ~wise(lucy) | ~funny(paul) | generous(paul) [cnf transformation 58]
118. wise(lucy) | ~funny(paul) | generous(paul) [cnf transformation 58]
126. ~happy(X0) | brave(X0) [cnf transformation 70]
131. strong(paul) [cnf transformation 17]
140. ~generous(paul) [cnf transformation 25]
141. ~strong(X0) | rich(X0) | kind(X0) [duplicate literal removal 102]
142. ~strong(X0) | rich(X0) | ~kind(X0) [duplicate literal removal 103]
213. ~strong(X0) | rich(X0) [subsumption resolution 141,142]
234. 21 <=> funny(paul) [avatar definition]
235. ~funny(paul) <- (~21) [avatar component clause 234]
238. 22 <=> generous(paul) [avatar definition]
242. 23 <=> wise(lucy) [avatar definition]
246. 22 | ~21 | 23 [avatar split clause 118,242,234,238]
248. 22 | ~21 | ~23 [avatar split clause 116,242,234,238]
325. ~22 [avatar split clause 140,238]
334. rich(paul) [resolution 213,131]
342. 42 <=> brave(paul) [avatar definition]
343. brave(paul) <- (42) [avatar component clause 342]
361. brave(paul) | happy(paul) [resolution 95,334]
363. brave(paul) [subsumption resolution 361,126]
364. 42 [avatar split clause 363,342]
367. ~brave(paul) | funny(paul) [resolution 111,334]
369. funny(paul) <- (42) [subsumption resolution 367,343]
370. $false <- (~21, 42) [subsumption resolution 369,235]
371. 21 | ~42 [avatar contradiction clause 370]
373. $false [avatar sat refutation 246,248,325,364,371]
% SZS output end Proof for 5540390450130496118851195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or not calm. If john is strong then john is both not funny and happy. Everyone who is generous or not kind is either not wise or not patient. Everyone who is wise or humble is generous and vice versa. If someone is generous then john is both not brave and wise. Everyone who is either strong or brave is kind. Everyone who is both not calm and not patient is brave. Everyone who is not old or not rich is either not funny or curious and vice versa. Everyone who is both not kind and not brave is either not wise or generous and vice versa. If lucy is both not generous and not tall then lucy is either calm or not generous and vice versa. Everyone who is both kind and not patient is either not brave or patient and vice versa. If john is either brave or not old then someone is both not quiet and not brave and vice versa. Everyone who is calm is both not happy and not funny. Everyone who is tall or curious is not humble or curious and vice versa. Everyone who is wise or kind is both not brave and not calm. If alice is both quiet and wise then mary is either not rich or not calm. Someone is both rich and not calm. Mary is rich. Alice is either not tall or happy. Susan is both patient and not curious. Someone is not humble. | John is not strong. | entailment | (![X]:(~tall(X)=>(wise(X)<~>~calm(X))))&
((strong(john))=>((~funny(john)&happy(john))))&
(![X]:((generous(X)|~kind(X))=>(~wise(X)<~>~patient(X))))&
(![X]:((wise(X)|humble(X))<=>generous(X)))&
((?[X]:(generous(X)))=>((~brave(john)&wise(john))))&
(![X]:((strong(X)<~>brave(X))=>kind(X)))&
(![X]:((~calm(X)&~patient(X))=>brave(X)))&
(![X]:((~old(X)|~rich(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((~kind(X)&~brave(X))<=>(~wise(X)<~>generous(X))))&
(((~generous(lucy)&~tall(lucy)))<=>((calm(lucy)<~>~generous(lucy))))&
(![X]:((kind(X)&~patient(X))<=>(~brave(X)<~>patient(X))))&
(((brave(john)<~>~old(john)))<=>(?[X]:((~quiet(X)&~brave(X)))))&
(![X]:(calm(X)=>(~happy(X)&~funny(X))))&
(![X]:((tall(X)|curious(X))<=>(~humble(X)|curious(X))))&
(![X]:((wise(X)|kind(X))=>(~brave(X)&~calm(X))))&
(((quiet(alice)&wise(alice)))=>((~rich(mary)<~>~calm(mary))))&
(?[X]:((rich(X)&~calm(X))))&
(rich(mary))&
((~tall(alice)<~>happy(alice)))&
((patient(susan)&~curious(susan)))&
(?[X]:(~humble(X))) | ~strong(john) | [
"p3",
"p4",
"p5",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 4323484848565275476965496
% SZS output start Proof for 4323484848565275476965496
4. ! [X0] : ((humble(X0) | wise(X0)) <=> generous(X0)) [input p3]
5. ? [X0] : generous(X0) => (wise(john) & ~brave(john)) [input p4]
6. ! [X0] : ((strong(X0) <~> brave(X0)) => kind(X0)) [input p5]
9. ! [X0] : ((~brave(X0) & ~kind(X0)) <=> (~wise(X0) <~> generous(X0))) [input p8]
22. strong(john) [input hypothesis]
26. (wise(john) & ~brave(john)) | ! [X0] : ~generous(X0) [ennf transformation 5]
27. ! [X0] : (kind(X0) | (strong(X0) <=> brave(X0))) [ennf transformation 6]
36. ! [X0] : (((humble(X0) | wise(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) & ~wise(X0)))) [nnf transformation 4]
37. ! [X0] : ((humble(X0) | wise(X0) | ~generous(X0)) & (generous(X0) | (~humble(X0) & ~wise(X0)))) [flattening 36]
38. ! [X0] : (kind(X0) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) [nnf transformation 27]
41. ! [X0] : (((~brave(X0) & ~kind(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (brave(X0) | kind(X0)))) [nnf transformation 9]
42. ! [X0] : (((~brave(X0) & ~kind(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | brave(X0) | kind(X0))) [flattening 41]
67. ~wise(X0) | generous(X0) [cnf transformation 37]
70. ~brave(john) | ~generous(X0) [cnf transformation 26]
71. wise(john) | ~generous(X0) [cnf transformation 26]
72. ~strong(X0) | brave(X0) | kind(X0) [cnf transformation 38]
83. ~kind(X0) | generous(X0) | wise(X0) [cnf transformation 42]
84. ~kind(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 42]
85. ~brave(X0) | generous(X0) | wise(X0) [cnf transformation 42]
86. ~brave(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 42]
125. strong(john) [cnf transformation 22]
131. 1 <=> strong(john) [avatar definition]
132. strong(john) <- (1) [avatar component clause 131]
145. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
146. ~generous(X0) <- (4) [avatar component clause 145]
148. 5 <=> wise(john) [avatar definition]
151. 4 | 5 [avatar split clause 71,148,145]
153. 6 <=> brave(john) [avatar definition]
154. brave(john) <- (6) [avatar component clause 153]
155. ~brave(john) <- (~6) [avatar component clause 153]
156. 4 | ~6 [avatar split clause 70,153,145]
157. ~brave(X0) | ~wise(X0) [subsumption resolution 86,67]
158. ~brave(X0) | generous(X0) [subsumption resolution 85,157]
159. ~kind(X0) | ~wise(X0) [subsumption resolution 84,67]
160. ~kind(X0) | generous(X0) [subsumption resolution 83,159]
228. 1 [avatar split clause 125,131]
241. brave(john) | kind(john) <- (1) [resolution 72,132]
242. kind(john) <- (1, ~6) [subsumption resolution 241,155]
243. generous(john) <- (1, ~6) [resolution 242,160]
244. ~wise(john) <- (1, ~6) [resolution 242,159]
248. ~5 | ~1 | 6 [avatar split clause 244,153,131,148]
273. $false <- (1, 4, ~6) [resolution 243,146]
276. ~1 | ~4 | 6 [avatar contradiction clause 273]
285. generous(john) <- (6) [resolution 154,158]
289. $false <- (4, 6) [subsumption resolution 285,146]
290. ~4 | ~6 [avatar contradiction clause 289]
291. $false [avatar sat refutation 151,156,228,248,276,290]
% SZS output end Proof for 4323484848565275476965496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not old then paul is either not humble or tall and vice versa.
Everyone who is rich is either humble or calm and vice versa.
Everyone who is brave is funny and vice versa.
Everyone who is either not old or kind is both funny and curious.
If alice is humble or not kind then someone is either curious or tall.
Everyone who is not humble or calm is either not strong or quiet.
If someone is not curious or generous then someone is both not brave and not kind.
Everyone who is either not happy or not old is either quiet or generous and vice versa.
Everyone who is not generous is not quiet or creative and vice versa.
Everyone who is not kind or strong is either not brave or not kind and vice versa.
If alice is not quiet then someone is both rich and not generous and vice versa.
Everyone who is either not humble or quiet is quiet or patient and vice versa.
Everyone who is not wise is not generous and vice versa.
If fred is humble then someone is either rich or not humble.
If fred is either not kind or curious then someone is not kind and vice versa.
If lucy is both kind and not quiet then alice is not funny or not kind and vice versa.
Alice is not generous or not rich.
Someone is both old and curious.
Fred is either creative or not happy.
Alice is not rich.
Someone is either humble or old.
Mary is either not humble or calm. | Alice is wise. | contradiction | ((?[X]:((~strong(X)&~old(X))))<=>((~humble(paul)<~>tall(paul))))&
(![X]:(rich(X)<=>(humble(X)<~>calm(X))))&
(![X]:(brave(X)<=>funny(X)))&
(![X]:((~old(X)<~>kind(X))=>(funny(X)&curious(X))))&
(((humble(alice)|~kind(alice)))=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~humble(X)|calm(X))=>(~strong(X)<~>quiet(X))))&
((?[X]:((~curious(X)|generous(X))))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((~happy(X)<~>~old(X))<=>(quiet(X)<~>generous(X))))&
(![X]:(~generous(X)<=>(~quiet(X)|creative(X))))&
(![X]:((~kind(X)|strong(X))<=>(~brave(X)<~>~kind(X))))&
((~quiet(alice))<=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((~humble(X)<~>quiet(X))<=>(quiet(X)|patient(X))))&
(![X]:(~wise(X)<=>~generous(X)))&
((humble(fred))=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~kind(fred)<~>curious(fred)))<=>(?[X]:(~kind(X))))&
(((kind(lucy)&~quiet(lucy)))<=>((~funny(alice)|~kind(alice))))&
((~generous(alice)|~rich(alice)))&
(?[X]:((old(X)&curious(X))))&
((creative(fred)<~>~happy(fred)))&
(~rich(alice))&
(?[X]:((humble(X)<~>old(X))))&
((~humble(mary)<~>calm(mary))) | wise(alice) | [
"p6",
"p9",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 3681678738455230758788232
% SZS output start Proof for 3681678738455230758788232
7. ? [X0] : (generous(X0) | ~curious(X0)) => ? [X0] : (~kind(X0) & ~brave(X0)) [input p6]
10. ! [X0] : ((strong(X0) | ~kind(X0)) <=> (~brave(X0) <~> ~kind(X0))) [input p9]
13. ! [X0] : (~wise(X0) <=> ~generous(X0)) [input p12]
23. wise(alice) [input hypothesis]
24. ? [X0] : (generous(X0) | ~curious(X0)) => ? [X1] : (~kind(X1) & ~brave(X1)) [rectify 7]
25. ! [X0] : (~generous(X0) => ~wise(X0)) [unused predicate definition removal 13]
29. ? [X1] : (~kind(X1) & ~brave(X1)) | ! [X0] : (~generous(X0) & curious(X0)) [ennf transformation 24]
30. ! [X0] : (~wise(X0) | generous(X0)) [ennf transformation 25]
43. ? [X0] : (~kind(X0) & ~brave(X0)) | ! [X1] : (~generous(X1) & curious(X1)) [rectify 29]
44. ? [X0] : (~kind(X0) & ~brave(X0)) => (~kind(sK2) & ~brave(sK2)) [choice axiom]
45. (~kind(sK2) & ~brave(sK2)) | ! [X1] : (~generous(X1) & curious(X1)) [skolemisation 43,44]
49. ! [X0] : (((strong(X0) | ~kind(X0)) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0)))) & (((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | (~strong(X0) & kind(X0)))) [nnf transformation 10]
50. ! [X0] : ((strong(X0) | ~kind(X0) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0)))) & (((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | (~strong(X0) & kind(X0)))) [flattening 49]
98. ~brave(sK2) | ~generous(X1) [cnf transformation 45]
100. ~kind(sK2) | ~generous(X1) [cnf transformation 45]
114. kind(X0) | brave(X0) | kind(X0) [cnf transformation 50]
127. ~wise(X0) | generous(X0) [cnf transformation 30]
149. wise(alice) [cnf transformation 23]
152. kind(X0) | brave(X0) [duplicate literal removal 114]
200. 10 <=> ! [X1] : ~generous(X1) [avatar definition]
201. ~generous(X1) <- (10) [avatar component clause 200]
203. 11 <=> kind(sK2) [avatar definition]
205. ~kind(sK2) <- (~11) [avatar component clause 203]
206. 10 | ~11 [avatar split clause 100,203,200]
212. 13 <=> brave(sK2) [avatar definition]
214. ~brave(sK2) <- (~13) [avatar component clause 212]
215. 10 | ~13 [avatar split clause 98,212,200]
287. 28 <=> generous(alice) [avatar definition]
288. generous(alice) <- (28) [avatar component clause 287]
328. generous(alice) [resolution 127,149]
329. 28 [avatar split clause 328,287]
337. brave(sK2) <- (~11) [resolution 152,205]
339. $false <- (~11, ~13) [subsumption resolution 337,214]
340. 11 | 13 [avatar contradiction clause 339]
341. $false <- (10, 28) [resolution 201,288]
342. ~10 | ~28 [avatar contradiction clause 341]
343. $false [avatar sat refutation 206,215,329,340,342]
% SZS output end Proof for 3681678738455230758788232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative then paul is rich or not calm and vice versa.
If someone is strong then alice is either generous or not calm.
If someone is not tall then someone is either not brave or quiet.
If fred is either tall or humble then lucy is either not funny or kind.
Everyone who is either old or not generous is patient.
Everyone who is tall or rich is both not tall and rich and vice versa.
Everyone who is not curious or rich is either funny or happy.
If someone is funny or kind then someone is either not wise or humble and vice versa.
Everyone who is happy is not old and vice versa.
Everyone who is not happy is both generous and calm.
Everyone who is old or rich is kind.
Everyone who is funny is not creative or not kind.
Everyone who is not humble or old is rich or not curious.
If lucy is curious then fred is either strong or creative.
Everyone who is both humble and generous is both kind and happy.
Everyone who is either not generous or not curious is either not brave or not tall and vice versa.
Someone is not brave or not calm.
Someone is not old.
Someone is both not humble and not creative.
Mary is either not humble or happy.
Fred is not old.
John is either calm or not wise.
Someone is quiet.
Someone is strong. | Alice is creative. | neutral | ((~creative(alice))<=>((rich(paul)|~calm(paul))))&
((?[X]:(strong(X)))=>((generous(alice)<~>~calm(alice))))&
((?[X]:(~tall(X)))=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((tall(fred)<~>humble(fred)))=>((~funny(lucy)<~>kind(lucy))))&
(![X]:((old(X)<~>~generous(X))=>patient(X)))&
(![X]:((tall(X)|rich(X))<=>(~tall(X)&rich(X))))&
(![X]:((~curious(X)|rich(X))=>(funny(X)<~>happy(X))))&
((?[X]:((funny(X)|kind(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(happy(X)<=>~old(X)))&
(![X]:(~happy(X)=>(generous(X)&calm(X))))&
(![X]:((old(X)|rich(X))=>kind(X)))&
(![X]:(funny(X)=>(~creative(X)|~kind(X))))&
(![X]:((~humble(X)|old(X))=>(rich(X)|~curious(X))))&
((curious(lucy))=>((strong(fred)<~>creative(fred))))&
(![X]:((humble(X)&generous(X))=>(kind(X)&happy(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~brave(X)<~>~tall(X))))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:(~old(X)))&
(?[X]:((~humble(X)&~creative(X))))&
((~humble(mary)<~>happy(mary)))&
(~old(fred))&
((calm(john)<~>~wise(john)))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X))) | creative(alice) | []
| null | 0 |
If someone is strong or kind then lucy is tall and vice versa.
If someone is either not brave or strong then someone is either not funny or old.
If someone is curious then someone is not wise or not brave.
If someone is either patient or humble then someone is curious and vice versa.
Everyone who is either not creative or rich is both not patient and not curious and vice versa.
If john is not curious then someone is rich and vice versa.
If fred is either not humble or quiet then susan is both rich and wise and vice versa.
If susan is not happy or old then someone is both creative and rich and vice versa.
Everyone who is creative is either not kind or kind and vice versa.
If someone is both not brave and not tall then lucy is rich or not curious.
If alice is not generous then paul is both not rich and not tall.
If someone is both quiet and not funny then mary is not happy or strong.
If someone is rich or patient then someone is not curious or tall and vice versa.
Everyone who is both not kind and not funny is not funny.
If john is curious or not creative then someone is calm or curious and vice versa.
Everyone who is not tall or curious is either not curious or not creative and vice versa.
Someone is funny.
Someone is old or kind.
Paul is either not humble or calm.
Lucy is kind or not tall.
Alice is both not curious and not wise.
Mary is not patient or not quiet. | Paul is not patient. | entailment | ((?[X]:((strong(X)|kind(X))))<=>(tall(lucy)))&
((?[X]:((~brave(X)<~>strong(X))))=>(?[X]:((~funny(X)<~>old(X)))))&
((?[X]:(curious(X)))=>(?[X]:((~wise(X)|~brave(X)))))&
((?[X]:((patient(X)<~>humble(X))))<=>(?[X]:(curious(X))))&
(![X]:((~creative(X)<~>rich(X))<=>(~patient(X)&~curious(X))))&
((~curious(john))<=>(?[X]:(rich(X))))&
(((~humble(fred)<~>quiet(fred)))<=>((rich(susan)&wise(susan))))&
(((~happy(susan)|old(susan)))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:(creative(X)<=>(~kind(X)<~>kind(X))))&
((?[X]:((~brave(X)&~tall(X))))=>((rich(lucy)|~curious(lucy))))&
((~generous(alice))=>((~rich(paul)&~tall(paul))))&
((?[X]:((quiet(X)&~funny(X))))=>((~happy(mary)|strong(mary))))&
((?[X]:((rich(X)|patient(X))))<=>(?[X]:((~curious(X)|tall(X)))))&
(![X]:((~kind(X)&~funny(X))=>~funny(X)))&
(((curious(john)|~creative(john)))<=>(?[X]:((calm(X)|curious(X)))))&
(![X]:((~tall(X)|curious(X))<=>(~curious(X)<~>~creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((old(X)|kind(X))))&
((~humble(paul)<~>calm(paul)))&
((kind(lucy)|~tall(lucy)))&
((~curious(alice)&~wise(alice)))&
((~patient(mary)|~quiet(mary))) | ~patient(paul) | [
"p3",
"p8",
"p14",
"p15",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 3745711345256500858245861
% SZS output start Proof for 3745711345256500858245861
4. ? [X0] : (patient(X0) <~> humble(X0)) <=> ? [X0] : curious(X0) [input p3]
9. ! [X0] : (creative(X0) <=> (~kind(X0) <~> kind(X0))) [input p8]
15. (~creative(john) | curious(john)) <=> ? [X0] : (curious(X0) | calm(X0)) [input p14]
16. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~curious(X0) <~> ~creative(X0))) [input p15]
19. ~humble(paul) <~> calm(paul) [input p18]
23. patient(paul) [input hypothesis]
26. ? [X0] : (patient(X0) <~> humble(X0)) <=> ? [X1] : curious(X1) [rectify 4]
48. (? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) [nnf transformation 26]
49. (? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : ((patient(X3) | ~humble(X3)) & (humble(X3) | ~patient(X3)))) [rectify 48]
50. ? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) => ((~humble(sK3) | ~patient(sK3)) & (humble(sK3) | patient(sK3))) [choice axiom]
51. ? [X2] : curious(X2) => curious(sK4) [choice axiom]
52. (((~humble(sK3) | ~patient(sK3)) & (humble(sK3) | patient(sK3))) | ! [X1] : ~curious(X1)) & (curious(sK4) | ! [X3] : ((patient(X3) | ~humble(X3)) & (humble(X3) | ~patient(X3)))) [skolemisation 49,51,50]
66. ! [X0] : ((creative(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~creative(X0))) [nnf transformation 9]
72. ((~creative(john) | curious(john)) | ! [X0] : (~curious(X0) & ~calm(X0))) & (? [X0] : (curious(X0) | calm(X0)) | (creative(john) & ~curious(john))) [nnf transformation 15]
73. (~creative(john) | curious(john) | ! [X0] : (~curious(X0) & ~calm(X0))) & (? [X0] : (curious(X0) | calm(X0)) | (creative(john) & ~curious(john))) [flattening 72]
74. (~creative(john) | curious(john) | ! [X0] : (~curious(X0) & ~calm(X0))) & (? [X1] : (curious(X1) | calm(X1)) | (creative(john) & ~curious(john))) [rectify 73]
75. ? [X1] : (curious(X1) | calm(X1)) => (curious(sK9) | calm(sK9)) [choice axiom]
76. (~creative(john) | curious(john) | ! [X0] : (~curious(X0) & ~calm(X0))) & ((curious(sK9) | calm(sK9)) | (creative(john) & ~curious(john))) [skolemisation 74,75]
77. ! [X0] : (((curious(X0) | ~tall(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | (~curious(X0) & tall(X0)))) [nnf transformation 16]
78. ! [X0] : ((curious(X0) | ~tall(X0) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | (~curious(X0) & tall(X0)))) [flattening 77]
83. (~calm(paul) | humble(paul)) & (calm(paul) | ~humble(paul)) [nnf transformation 19]
92. curious(sK4) | humble(X3) | ~patient(X3) [cnf transformation 52]
117. creative(X0) | kind(X0) | kind(X0) [cnf transformation 66]
118. creative(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 66]
128. ~creative(john) | curious(john) | ~calm(X0) [cnf transformation 76]
131. ~creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 78]
138. calm(paul) | ~humble(paul) [cnf transformation 83]
144. patient(paul) [cnf transformation 23]
145. ~creative(X0) | ~curious(X0) [duplicate literal removal 131]
147. creative(X0) | kind(X0) [duplicate literal removal 117]
148. ~kind(X0) | creative(X0) [duplicate literal removal 118]
189. 10 <=> ! [X1] : ~curious(X1) [avatar definition]
190. ~curious(X1) <- (10) [avatar component clause 189]
214. 16 <=> curious(sK4) [avatar definition]
216. curious(sK4) <- (16) [avatar component clause 214]
219. 17 <=> ! [X3] : (humble(X3) | ~patient(X3)) [avatar definition]
220. ~patient(X3) | humble(X3) <- (17) [avatar component clause 219]
221. 17 | 16 [avatar split clause 92,214,219]
226. 19 <=> curious(john) [avatar definition]
227. curious(john) <- (19) [avatar component clause 226]
281. creative(X0) [subsumption resolution 147,148]
337. curious(john) | ~calm(X0) [subsumption resolution 128,281]
339. 43 <=> ! [X0] : ~calm(X0) [avatar definition]
340. ~calm(X0) <- (43) [avatar component clause 339]
341. 43 | 19 [avatar split clause 337,226,339]
352. ~curious(X0) [subsumption resolution 145,281]
353. 10 [avatar split clause 352,189]
365. 48 <=> humble(paul) [avatar definition]
369. 49 <=> calm(paul) [avatar definition]
370. calm(paul) <- (49) [avatar component clause 369]
373. ~48 | 49 [avatar split clause 138,369,365]
390. $false <- (10, 16) [resolution 216,190]
391. ~10 | ~16 [avatar contradiction clause 390]
394. humble(paul) <- (17) [resolution 220,144]
397. 48 | ~17 [avatar split clause 394,219,365]
398. $false <- (43, 49) [subsumption resolution 370,340]
399. ~43 | ~49 [avatar contradiction clause 398]
400. $false <- (10, 19) [subsumption resolution 227,190]
401. ~10 | ~19 [avatar contradiction clause 400]
402. $false [avatar sat refutation 221,341,353,373,391,397,399,401]
% SZS output end Proof for 3745711345256500858245861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old or not patient is brave or not patient and vice versa.
Everyone who is either strong or not generous is both happy and not patient and vice versa.
Everyone who is brave or not happy is both kind and not calm.
Everyone who is rich is wise or not tall.
Everyone who is either not curious or not calm is curious and vice versa.
Everyone who is both tall and not generous is either wise or not happy.
Everyone who is not rich is both not calm and calm and vice versa.
If someone is humble or brave then someone is not rich.
If someone is not funny then lucy is brave.
Everyone who is either not curious or humble is both not patient and tall.
Everyone who is old is not kind.
If someone is not creative or humble then john is both quiet and not strong and vice versa.
If john is both creative and not happy then paul is not strong.
If mary is brave or not strong then someone is either strong or not patient and vice versa.
Everyone who is either quiet or calm is both not wise and funny and vice versa.
If someone is both humble and curious then someone is either humble or not creative and vice versa.
Fred is either not generous or old.
Alice is either patient or rich.
Lucy is both tall and not curious.
Someone is either not calm or generous.
Susan is either not wise or rich.
Someone is not tall. | Susan is brave. | contradiction | (![X]:((~old(X)|~patient(X))<=>(brave(X)|~patient(X))))&
(![X]:((strong(X)<~>~generous(X))<=>(happy(X)&~patient(X))))&
(![X]:((brave(X)|~happy(X))=>(kind(X)&~calm(X))))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
((?[X]:(~funny(X)))=>(brave(lucy)))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~wise(X)&funny(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~generous(fred)<~>old(fred)))&
((patient(alice)<~>rich(alice)))&
((tall(lucy)&~curious(lucy)))&
(?[X]:((~calm(X)<~>generous(X))))&
((~wise(susan)<~>rich(susan)))&
(?[X]:(~tall(X))) | brave(susan) | [
"p4",
"p6",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 420515648517569424284733
% SZS output start Proof for 420515648517569424284733
5. ! [X0] : ((~curious(X0) <~> ~calm(X0)) <=> curious(X0)) [input p4]
7. ! [X0] : (~rich(X0) <=> (calm(X0) & ~calm(X0))) [input p6]
8. ? [X0] : (brave(X0) | humble(X0)) => ? [X0] : ~rich(X0) [input p7]
23. brave(susan) [input hypothesis]
24. ? [X0] : (brave(X0) | humble(X0)) => ? [X1] : ~rich(X1) [rectify 8]
31. ? [X1] : ~rich(X1) | ! [X0] : (~brave(X0) & ~humble(X0)) [ennf transformation 24]
41. ! [X0] : ((((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | ~curious(X0)) & (curious(X0) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))))) [nnf transformation 5]
43. ! [X0] : ((~rich(X0) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | rich(X0))) [nnf transformation 7]
44. ! [X0] : ((~rich(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | rich(X0))) [flattening 43]
45. ? [X0] : ~rich(X0) | ! [X1] : (~brave(X1) & ~humble(X1)) [rectify 31]
46. ? [X0] : ~rich(X0) => ~rich(sK0) [choice axiom]
47. ~rich(sK0) | ! [X1] : (~brave(X1) & ~humble(X1)) [skolemisation 45,46]
89. curious(X0) | ~calm(X0) | curious(X0) [cnf transformation 41]
91. ~calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 41]
96. calm(X0) | rich(X0) [cnf transformation 44]
99. ~rich(sK0) | ~brave(X1) [cnf transformation 47]
141. brave(susan) [cnf transformation 23]
142. curious(X0) | ~calm(X0) [duplicate literal removal 89]
143. ~calm(X0) | ~curious(X0) [duplicate literal removal 91]
144. ~calm(X0) [subsumption resolution 142,143]
145. rich(X0) [subsumption resolution 96,144]
146. ~brave(X1) [subsumption resolution 99,145]
232. $false [subsumption resolution 141,146]
% SZS output end Proof for 420515648517569424284733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is creative then fred is both patient and curious and vice versa.
Everyone who is calm or not rich is not kind or strong and vice versa.
If someone is not happy then fred is humble or creative.
Everyone who is not humble or happy is both kind and patient.
Everyone who is not kind is not wise or not quiet.
If john is not old then someone is brave and vice versa.
Everyone who is either not quiet or old is not wise.
If alice is both humble and not kind then paul is not patient and vice versa.
If paul is not quiet or kind then someone is either creative or not strong and vice versa.
Everyone who is either kind or patient is kind and vice versa.
If someone is patient then john is not old.
If someone is rich or curious then someone is not calm.
Everyone who is not brave or not strong is either rich or not curious.
If someone is generous or not happy then someone is rich or not tall.
Everyone who is quiet is both calm and brave.
Everyone who is either not kind or not old is both rich and not wise and vice versa.
Susan is humble or brave.
Susan is both humble and not old.
Lucy is creative.
Paul is both humble and not tall.
Someone is kind.
Paul is humble or not brave. | Lucy is rich. | neutral | ((creative(john))<=>((patient(fred)&curious(fred))))&
(![X]:((calm(X)|~rich(X))<=>(~kind(X)|strong(X))))&
((?[X]:(~happy(X)))=>((humble(fred)|creative(fred))))&
(![X]:((~humble(X)|happy(X))=>(kind(X)&patient(X))))&
(![X]:(~kind(X)=>(~wise(X)|~quiet(X))))&
((~old(john))<=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)<~>old(X))=>~wise(X)))&
(((humble(alice)&~kind(alice)))<=>(~patient(paul)))&
(((~quiet(paul)|kind(paul)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((kind(X)<~>patient(X))<=>kind(X)))&
((?[X]:(patient(X)))=>(~old(john)))&
((?[X]:((rich(X)|curious(X))))=>(?[X]:(~calm(X))))&
(![X]:((~brave(X)|~strong(X))=>(rich(X)<~>~curious(X))))&
((?[X]:((generous(X)|~happy(X))))=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:(quiet(X)=>(calm(X)&brave(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(rich(X)&~wise(X))))&
((humble(susan)|brave(susan)))&
((humble(susan)&~old(susan)))&
(creative(lucy))&
((humble(paul)&~tall(paul)))&
(?[X]:(kind(X)))&
((humble(paul)|~brave(paul))) | rich(lucy) | []
| null | 0 |
Everyone who is creative is happy or not generous.
Everyone who is rich or wise is not creative or happy and vice versa.
Everyone who is either not patient or not brave is creative or not tall.
Everyone who is funny is not quiet or rich and vice versa.
If lucy is wise then someone is both wise and not patient.
Everyone who is happy or not calm is both not strong and humble and vice versa.
Everyone who is tall or not brave is either rich or not curious and vice versa.
Everyone who is rich or tall is either not curious or happy and vice versa.
Everyone who is either calm or not humble is rich or brave and vice versa.
Everyone who is not curious is either not tall or humble.
Everyone who is both not brave and not old is either not calm or not wise and vice versa.
If someone is both not generous and not strong then alice is either strong or patient and vice versa.
If lucy is either old or humble then someone is both old and not kind and vice versa.
Everyone who is not wise or creative is curious or not kind and vice versa.
Everyone who is not happy is not brave and vice versa.
Someone is not funny or calm.
Alice is not humble or brave.
John is not old or not brave.
Someone is either not generous or not curious.
Mary is old or not patient.
Someone is either not patient or tall.
Someone is not rich or not humble. | Alice is not brave. | contradiction | (![X]:(creative(X)=>(happy(X)|~generous(X))))&
(![X]:((rich(X)|wise(X))<=>(~creative(X)|happy(X))))&
(![X]:((~patient(X)<~>~brave(X))=>(creative(X)|~tall(X))))&
(![X]:(funny(X)<=>(~quiet(X)|rich(X))))&
((wise(lucy))=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:((happy(X)|~calm(X))<=>(~strong(X)&humble(X))))&
(![X]:((tall(X)|~brave(X))<=>(rich(X)<~>~curious(X))))&
(![X]:((rich(X)|tall(X))<=>(~curious(X)<~>happy(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(rich(X)|brave(X))))&
(![X]:(~curious(X)=>(~tall(X)<~>humble(X))))&
(![X]:((~brave(X)&~old(X))<=>(~calm(X)<~>~wise(X))))&
((?[X]:((~generous(X)&~strong(X))))<=>((strong(alice)<~>patient(alice))))&
(((old(lucy)<~>humble(lucy)))<=>(?[X]:((old(X)&~kind(X)))))&
(![X]:((~wise(X)|creative(X))<=>(curious(X)|~kind(X))))&
(![X]:(~happy(X)<=>~brave(X)))&
(?[X]:((~funny(X)|calm(X))))&
((~humble(alice)|brave(alice)))&
((~old(john)|~brave(john)))&
(?[X]:((~generous(X)<~>~curious(X))))&
((old(mary)|~patient(mary)))&
(?[X]:((~patient(X)<~>tall(X))))&
(?[X]:((~rich(X)|~humble(X)))) | ~brave(alice) | [
"p5",
"p6",
"p7",
"p8",
"p9",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 689021932178335844724875
% SZS output start Proof for 689021932178335844724875
6. ! [X0] : ((~calm(X0) | happy(X0)) <=> (humble(X0) & ~strong(X0))) [input p5]
7. ! [X0] : ((~brave(X0) | tall(X0)) <=> (rich(X0) <~> ~curious(X0))) [input p6]
8. ! [X0] : ((tall(X0) | rich(X0)) <=> (~curious(X0) <~> happy(X0))) [input p7]
9. ! [X0] : ((calm(X0) <~> ~humble(X0)) <=> (brave(X0) | rich(X0))) [input p8]
10. ! [X0] : (~curious(X0) => (~tall(X0) <~> humble(X0))) [input p9]
15. ! [X0] : (~happy(X0) <=> ~brave(X0)) [input p14]
17. brave(alice) | ~humble(alice) [input p16]
23. ~brave(alice) [input hypothesis]
32. ! [X0] : ((~tall(X0) <~> humble(X0)) | curious(X0)) [ennf transformation 10]
38. ! [X0] : (((~calm(X0) | happy(X0)) | (~humble(X0) | strong(X0))) & ((humble(X0) & ~strong(X0)) | (calm(X0) & ~happy(X0)))) [nnf transformation 6]
39. ! [X0] : ((~calm(X0) | happy(X0) | ~humble(X0) | strong(X0)) & ((humble(X0) & ~strong(X0)) | (calm(X0) & ~happy(X0)))) [flattening 38]
40. ! [X0] : (((~brave(X0) | tall(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (brave(X0) & ~tall(X0)))) [nnf transformation 7]
41. ! [X0] : ((~brave(X0) | tall(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (brave(X0) & ~tall(X0)))) [flattening 40]
42. ! [X0] : (((tall(X0) | rich(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) & (((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~tall(X0) & ~rich(X0)))) [nnf transformation 8]
43. ! [X0] : ((tall(X0) | rich(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) & (((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~tall(X0) & ~rich(X0)))) [flattening 42]
44. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [nnf transformation 9]
45. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [flattening 44]
46. ! [X0] : (((~humble(X0) | tall(X0)) & (humble(X0) | ~tall(X0))) | curious(X0)) [nnf transformation 32]
59. ! [X0] : ((~happy(X0) | brave(X0)) & (~brave(X0) | happy(X0))) [nnf transformation 15]
83. humble(X0) | calm(X0) [cnf transformation 39]
86. ~curious(X0) | rich(X0) | brave(X0) [cnf transformation 41]
95. curious(X0) | rich(X0) | happy(X0) | tall(X0) [cnf transformation 43]
101. humble(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 45]
102. humble(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 45]
103. ~tall(X0) | humble(X0) | curious(X0) [cnf transformation 46]
128. ~happy(X0) | brave(X0) [cnf transformation 59]
130. brave(alice) | ~humble(alice) [cnf transformation 17]
138. ~brave(alice) [cnf transformation 23]
154. ~brave(X0) | humble(X0) [subsumption resolution 102,83]
155. ~rich(X0) | humble(X0) [subsumption resolution 101,83]
220. 16 <=> humble(alice) [avatar definition]
222. ~humble(alice) <- (~16) [avatar component clause 220]
224. 17 <=> brave(alice) [avatar definition]
227. ~16 | 17 [avatar split clause 130,224,220]
267. ~17 [avatar split clause 138,224]
350. rich(X1) | happy(X1) | tall(X1) | rich(X1) | brave(X1) [resolution 95,86]
361. rich(X1) | happy(X1) | tall(X1) | brave(X1) [duplicate literal removal 350]
363. tall(X1) | rich(X1) | brave(X1) [subsumption resolution 361,128]
414. rich(X2) | brave(X2) | humble(X2) | curious(X2) [resolution 363,103]
427. rich(X2) | humble(X2) | curious(X2) [subsumption resolution 414,154]
428. curious(X2) | humble(X2) [subsumption resolution 427,155]
529. humble(X1) | rich(X1) | brave(X1) [resolution 428,86]
538. humble(X1) | rich(X1) [subsumption resolution 529,154]
539. humble(X1) [subsumption resolution 538,155]
557. $false <- (~16) [resolution 539,222]
561. 16 [avatar contradiction clause 557]
563. $false [avatar sat refutation 227,267,561]
% SZS output end Proof for 689021932178335844724875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either rich or not generous is both not old and generous.
Everyone who is not kind or quiet is calm or patient and vice versa.
If someone is either not happy or not generous then lucy is not happy or not curious and vice versa.
If someone is humble then someone is not curious or not quiet and vice versa.
Everyone who is both brave and calm is not tall or strong and vice versa.
Everyone who is either patient or not brave is patient and vice versa.
Everyone who is not generous or calm is old.
Everyone who is not funny is both quiet and not patient and vice versa.
If someone is not quiet or kind then someone is both patient and funny.
If alice is both kind and tall then someone is humble and vice versa.
If someone is not generous then someone is either not old or not patient and vice versa.
If paul is both strong and calm then fred is both not humble and not old.
Everyone who is not wise is either humble or not quiet and vice versa.
If fred is either strong or not wise then lucy is not kind and vice versa.
Everyone who is both quiet and happy is either strong or brave and vice versa.
If someone is either rich or not humble then someone is both old and not old.
Someone is both not old and not rich.
Paul is rich.
Fred is either not brave or not old.
Someone is not creative or patient.
Fred is either generous or curious.
Someone is both strong and kind.
Someone is either not old or not patient. | Lucy is not brave. | contradiction | (![X]:((rich(X)<~>~generous(X))=>(~old(X)&generous(X))))&
(![X]:((~kind(X)|quiet(X))<=>(calm(X)|patient(X))))&
((?[X]:((~happy(X)<~>~generous(X))))<=>((~happy(lucy)|~curious(lucy))))&
((?[X]:(humble(X)))<=>(?[X]:((~curious(X)|~quiet(X)))))&
(![X]:((brave(X)&calm(X))<=>(~tall(X)|strong(X))))&
(![X]:((patient(X)<~>~brave(X))<=>patient(X)))&
(![X]:((~generous(X)|calm(X))=>old(X)))&
(![X]:(~funny(X)<=>(quiet(X)&~patient(X))))&
((?[X]:((~quiet(X)|kind(X))))=>(?[X]:((patient(X)&funny(X)))))&
(((kind(alice)&tall(alice)))<=>(?[X]:(humble(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~old(X)<~>~patient(X)))))&
(((strong(paul)&calm(paul)))=>((~humble(fred)&~old(fred))))&
(![X]:(~wise(X)<=>(humble(X)<~>~quiet(X))))&
(((strong(fred)<~>~wise(fred)))<=>(~kind(lucy)))&
(![X]:((quiet(X)&happy(X))<=>(strong(X)<~>brave(X))))&
((?[X]:((rich(X)<~>~humble(X))))=>(?[X]:((old(X)&~old(X)))))&
(?[X]:((~old(X)&~rich(X))))&
(rich(paul))&
((~brave(fred)<~>~old(fred)))&
(?[X]:((~creative(X)|patient(X))))&
((generous(fred)<~>curious(fred)))&
(?[X]:((strong(X)&kind(X))))&
(?[X]:((~old(X)<~>~patient(X)))) | ~brave(lucy) | [
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 8046786120367141500582708
% SZS output start Proof for 8046786120367141500582708
6. ! [X0] : ((patient(X0) <~> ~brave(X0)) <=> patient(X0)) [input p5]
24. ~brave(lucy) [input hypothesis]
54. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ~patient(X0)) & (patient(X0) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [nnf transformation 6]
108. patient(X0) | patient(X0) | brave(X0) [cnf transformation 54]
110. brave(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 54]
156. ~brave(lucy) [cnf transformation 24]
157. patient(X0) | brave(X0) [duplicate literal removal 108]
158. brave(X0) | ~patient(X0) [duplicate literal removal 110]
212. brave(X0) [subsumption resolution 157,158]
339. $false [subsumption resolution 156,212]
% SZS output end Proof for 8046786120367141500582708
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and old then lucy is not patient and vice versa.
Everyone who is not calm or not quiet is both not patient and patient.
Everyone who is either humble or not kind is not brave or not funny and vice versa.
Everyone who is both not calm and not happy is not generous or not rich.
Everyone who is either funny or creative is kind or funny and vice versa.
If lucy is either not curious or not patient then someone is both wise and not funny and vice versa.
Everyone who is either not old or tall is both generous and old.
Everyone who is curious or generous is not creative or not tall and vice versa.
Everyone who is both not tall and humble is strong and vice versa.
If fred is both funny and not kind then someone is not humble or calm and vice versa.
If susan is either rich or wise then someone is calm or wise and vice versa.
Everyone who is patient is either generous or not tall and vice versa.
Everyone who is not tall or not rich is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
If someone is either not funny or strong then mary is either tall or not calm and vice versa.
Someone is not creative.
Someone is either not calm or not rich.
Someone is not creative or humble.
Someone is either old or not tall.
Fred is both not humble and quiet.
Someone is not old or kind.
Alice is either rich or not creative. | Fred is not rich. | neutral | ((?[X]:((humble(X)&old(X))))<=>(~patient(lucy)))&
(![X]:((~calm(X)|~quiet(X))=>(~patient(X)&patient(X))))&
(![X]:((humble(X)<~>~kind(X))<=>(~brave(X)|~funny(X))))&
(![X]:((~calm(X)&~happy(X))=>(~generous(X)|~rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>(kind(X)|funny(X))))&
(((~curious(lucy)<~>~patient(lucy)))<=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((~old(X)<~>tall(X))=>(generous(X)&old(X))))&
(![X]:((curious(X)|generous(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~tall(X)&humble(X))<=>strong(X)))&
(((funny(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(((rich(susan)<~>wise(susan)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)|~rich(X))=>calm(X)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((tall(mary)<~>~calm(mary))))&
(?[X]:(~creative(X)))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:((old(X)<~>~tall(X))))&
((~humble(fred)&quiet(fred)))&
(?[X]:((~old(X)|kind(X))))&
((rich(alice)<~>~creative(alice))) | ~rich(fred) | []
| null | 0 |
If someone is both not wise and calm then someone is not strong or funny and vice versa.
Everyone who is happy is not old and vice versa.
If someone is either not rich or not quiet then alice is not rich and vice versa.
Everyone who is either not rich or calm is not rich and vice versa.
Everyone who is not tall or not creative is both not quiet and not happy.
If someone is either generous or not wise then someone is creative or not quiet.
Everyone who is not quiet is either strong or calm and vice versa.
Everyone who is wise is either not generous or creative.
If susan is either not creative or not wise then lucy is both not strong and not happy and vice versa.
If mary is both not patient and not wise then alice is both not tall and generous.
If john is both strong and kind then someone is both not quiet and funny.
Everyone who is not happy is both not funny and creative.
If someone is either not old or not funny then susan is either generous or humble and vice versa.
If someone is not strong or not wise then paul is either curious or quiet and vice versa.
If paul is not generous or not rich then someone is not happy or strong.
Everyone who is either not humble or not rich is either not creative or wise.
Lucy is funny or not quiet.
Someone is not humble.
Susan is not quiet or kind.
Alice is not patient or curious.
Someone is generous or quiet.
John is either not happy or creative.
Fred is both kind and not humble.
Someone is either curious or humble. | Paul is not funny. | entailment | ((?[X]:((~wise(X)&calm(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:(happy(X)<=>~old(X)))&
((?[X]:((~rich(X)<~>~quiet(X))))<=>(~rich(alice)))&
(![X]:((~rich(X)<~>calm(X))<=>~rich(X)))&
(![X]:((~tall(X)|~creative(X))=>(~quiet(X)&~happy(X))))&
((?[X]:((generous(X)<~>~wise(X))))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:(~quiet(X)<=>(strong(X)<~>calm(X))))&
(![X]:(wise(X)=>(~generous(X)<~>creative(X))))&
(((~creative(susan)<~>~wise(susan)))<=>((~strong(lucy)&~happy(lucy))))&
(((~patient(mary)&~wise(mary)))=>((~tall(alice)&generous(alice))))&
(((strong(john)&kind(john)))=>(?[X]:((~quiet(X)&funny(X)))))&
(![X]:(~happy(X)=>(~funny(X)&creative(X))))&
((?[X]:((~old(X)<~>~funny(X))))<=>((generous(susan)<~>humble(susan))))&
((?[X]:((~strong(X)|~wise(X))))<=>((curious(paul)<~>quiet(paul))))&
(((~generous(paul)|~rich(paul)))=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~humble(X)<~>~rich(X))=>(~creative(X)<~>wise(X))))&
((funny(lucy)|~quiet(lucy)))&
(?[X]:(~humble(X)))&
((~quiet(susan)|kind(susan)))&
((~patient(alice)|curious(alice)))&
(?[X]:((generous(X)|quiet(X))))&
((~happy(john)<~>creative(john)))&
((kind(fred)&~humble(fred)))&
(?[X]:((curious(X)<~>humble(X)))) | ~funny(paul) | [
"p0",
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 2098943814636656172180695
% SZS output start Proof for 2098943814636656172180695
1. ? [X0] : (calm(X0) & ~wise(X0)) <=> ? [X0] : (funny(X0) | ~strong(X0)) [input p0]
4. ! [X0] : ((~rich(X0) <~> calm(X0)) <=> ~rich(X0)) [input p3]
25. funny(paul) [input hypothesis]
26. ? [X0] : (calm(X0) & ~wise(X0)) <=> ? [X1] : (funny(X1) | ~strong(X1)) [rectify 1]
38. (? [X0] : (calm(X0) & ~wise(X0)) | ! [X1] : (~funny(X1) & strong(X1))) & (? [X1] : (funny(X1) | ~strong(X1)) | ! [X0] : (~calm(X0) | wise(X0))) [nnf transformation 26]
39. (? [X0] : (calm(X0) & ~wise(X0)) | ! [X1] : (~funny(X1) & strong(X1))) & (? [X2] : (funny(X2) | ~strong(X2)) | ! [X3] : (~calm(X3) | wise(X3))) [rectify 38]
40. ? [X0] : (calm(X0) & ~wise(X0)) => (calm(sK0) & ~wise(sK0)) [choice axiom]
41. ? [X2] : (funny(X2) | ~strong(X2)) => (funny(sK1) | ~strong(sK1)) [choice axiom]
42. ((calm(sK0) & ~wise(sK0)) | ! [X1] : (~funny(X1) & strong(X1))) & ((funny(sK1) | ~strong(sK1)) | ! [X3] : (~calm(X3) | wise(X3))) [skolemisation 39,41,40]
48. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | rich(X0)) & (~rich(X0) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [nnf transformation 4]
82. calm(sK0) | ~funny(X1) [cnf transformation 42]
90. ~rich(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 48]
92. ~calm(X0) | rich(X0) | rich(X0) [cnf transformation 48]
148. funny(paul) [cnf transformation 25]
149. ~rich(X0) | ~calm(X0) [duplicate literal removal 90]
150. ~calm(X0) | rich(X0) [duplicate literal removal 92]
152. 1 <=> ! [X1] : ~funny(X1) [avatar definition]
153. ~funny(X1) <- (1) [avatar component clause 152]
155. 2 <=> calm(sK0) [avatar definition]
157. calm(sK0) <- (2) [avatar component clause 155]
158. 1 | 2 [avatar split clause 82,155,152]
203. ~calm(X0) [subsumption resolution 149,150]
389. $false <- (2) [subsumption resolution 157,203]
390. ~2 [avatar contradiction clause 389]
391. $false <- (1) [resolution 153,148]
392. ~1 [avatar contradiction clause 391]
393. $false [avatar sat refutation 158,390,392]
% SZS output end Proof for 2098943814636656172180695
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either brave or not kind is either happy or not kind and vice versa.
Everyone who is both happy and not quiet is not old or not tall.
If john is either rich or not brave then mary is not brave.
Everyone who is tall is both not happy and generous and vice versa.
If someone is not kind then fred is wise or not creative.
Everyone who is either not creative or strong is funny and vice versa.
If someone is not generous or not strong then someone is either not rich or humble.
Everyone who is not wise or not tall is both not curious and not creative.
Everyone who is both wise and not creative is both not patient and happy and vice versa.
If someone is either tall or not quiet then susan is creative and vice versa.
Everyone who is not patient or creative is not quiet and vice versa.
Everyone who is not kind or tall is quiet.
If someone is funny then someone is creative.
If lucy is both creative and not generous then someone is either rich or happy.
Everyone who is both not patient and not old is not kind or not happy and vice versa.
If john is patient or old then someone is both not tall and not rich and vice versa.
Someone is either not quiet or kind.
Someone is either curious or kind.
Someone is not curious.
Someone is not generous or rich.
Fred is generous or not brave.
John is both happy and generous. | Mary is not generous. | neutral | (![X]:((brave(X)<~>~kind(X))<=>(happy(X)<~>~kind(X))))&
(![X]:((happy(X)&~quiet(X))=>(~old(X)|~tall(X))))&
(((rich(john)<~>~brave(john)))=>(~brave(mary)))&
(![X]:(tall(X)<=>(~happy(X)&generous(X))))&
((?[X]:(~kind(X)))=>((wise(fred)|~creative(fred))))&
(![X]:((~creative(X)<~>strong(X))<=>funny(X)))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~wise(X)|~tall(X))=>(~curious(X)&~creative(X))))&
(![X]:((wise(X)&~creative(X))<=>(~patient(X)&happy(X))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>(creative(susan)))&
(![X]:((~patient(X)|creative(X))<=>~quiet(X)))&
(![X]:((~kind(X)|tall(X))=>quiet(X)))&
((?[X]:(funny(X)))=>(?[X]:(creative(X))))&
(((creative(lucy)&~generous(lucy)))=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((~patient(X)&~old(X))<=>(~kind(X)|~happy(X))))&
(((patient(john)|old(john)))<=>(?[X]:((~tall(X)&~rich(X)))))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~generous(X)|rich(X))))&
((generous(fred)|~brave(fred)))&
((happy(john)&generous(john))) | ~generous(mary) | []
| null | 0 |
Everyone who is funny is quiet. Everyone who is generous or not funny is not quiet or not kind and vice versa. Everyone who is patient or not wise is tall or not wise and vice versa. Everyone who is either kind or generous is either not old or tall and vice versa. Everyone who is not wise is either not patient or strong. If susan is old then someone is either funny or not brave and vice versa. Everyone who is not curious is both generous and not happy and vice versa. Everyone who is tall is happy or not tall. If someone is both not patient and not kind then someone is both calm and old and vice versa. If mary is both not creative and wise then someone is not old or not creative and vice versa. Everyone who is not strong or quiet is patient and vice versa. If john is not rich then someone is old. Everyone who is not tall or not rich is tall and vice versa. Everyone who is not quiet or strong is either not curious or not old. If susan is not tall then alice is calm. Everyone who is either not brave or wise is both kind and not tall. Someone is quiet. Someone is either not wise or curious. Someone is either generous or old. Someone is either not creative or wise. Someone is either not old or not humble. John is generous. | Mary is wise. | entailment | (![X]:(funny(X)=>quiet(X)))&
(![X]:((generous(X)|~funny(X))<=>(~quiet(X)|~kind(X))))&
(![X]:((patient(X)|~wise(X))<=>(tall(X)|~wise(X))))&
(![X]:((kind(X)<~>generous(X))<=>(~old(X)<~>tall(X))))&
(![X]:(~wise(X)=>(~patient(X)<~>strong(X))))&
((old(susan))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:(~curious(X)<=>(generous(X)&~happy(X))))&
(![X]:(tall(X)=>(happy(X)|~tall(X))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:((calm(X)&old(X)))))&
(((~creative(mary)&wise(mary)))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((~strong(X)|quiet(X))<=>patient(X)))&
((~rich(john))=>(?[X]:(old(X))))&
(![X]:((~tall(X)|~rich(X))<=>tall(X)))&
(![X]:((~quiet(X)|strong(X))=>(~curious(X)<~>~old(X))))&
((~tall(susan))=>(calm(alice)))&
(![X]:((~brave(X)<~>wise(X))=>(kind(X)&~tall(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((generous(X)<~>old(X))))&
(?[X]:((~creative(X)<~>wise(X))))&
(?[X]:((~old(X)<~>~humble(X))))&
(generous(john)) | wise(mary) | [
"p2",
"p4",
"p6",
"p7",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5435267992007181899245136
% SZS output start Proof for 5435267992007181899245136
3. ! [X0] : ((~wise(X0) | patient(X0)) <=> (~wise(X0) | tall(X0))) [input p2]
5. ! [X0] : (~wise(X0) => (~patient(X0) <~> strong(X0))) [input p4]
7. ! [X0] : (~curious(X0) <=> (~happy(X0) & generous(X0))) [input p6]
8. ! [X0] : (tall(X0) => (~tall(X0) | happy(X0))) [input p7]
10. (wise(mary) & ~creative(mary)) <=> ? [X0] : (~creative(X0) | ~old(X0)) [input p9]
11. ! [X0] : ((quiet(X0) | ~strong(X0)) <=> patient(X0)) [input p10]
13. ! [X0] : ((~rich(X0) | ~tall(X0)) <=> tall(X0)) [input p12]
14. ! [X0] : ((strong(X0) | ~quiet(X0)) => (~curious(X0) <~> ~old(X0))) [input p13]
23. ~wise(mary) [input hypothesis]
26. ! [X0] : ((~patient(X0) <~> strong(X0)) | wise(X0)) [ennf transformation 5]
27. ! [X0] : ((~tall(X0) | happy(X0)) | ~tall(X0)) [ennf transformation 8]
28. ! [X0] : (~tall(X0) | happy(X0) | ~tall(X0)) [flattening 27]
30. ! [X0] : ((~curious(X0) <~> ~old(X0)) | (~strong(X0) & quiet(X0))) [ennf transformation 14]
35. ! [X0] : (((~wise(X0) | patient(X0)) | (wise(X0) & ~tall(X0))) & ((~wise(X0) | tall(X0)) | (wise(X0) & ~patient(X0)))) [nnf transformation 3]
36. ! [X0] : ((~wise(X0) | patient(X0) | (wise(X0) & ~tall(X0))) & (~wise(X0) | tall(X0) | (wise(X0) & ~patient(X0)))) [flattening 35]
38. ! [X0] : (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | wise(X0)) [nnf transformation 26]
43. ! [X0] : ((~curious(X0) | (happy(X0) | ~generous(X0))) & ((~happy(X0) & generous(X0)) | curious(X0))) [nnf transformation 7]
44. ! [X0] : ((~curious(X0) | happy(X0) | ~generous(X0)) & ((~happy(X0) & generous(X0)) | curious(X0))) [flattening 43]
50. ((wise(mary) & ~creative(mary)) | ! [X0] : (creative(X0) & old(X0))) & (? [X0] : (~creative(X0) | ~old(X0)) | (~wise(mary) | creative(mary))) [nnf transformation 10]
51. ((wise(mary) & ~creative(mary)) | ! [X0] : (creative(X0) & old(X0))) & (? [X0] : (~creative(X0) | ~old(X0)) | ~wise(mary) | creative(mary)) [flattening 50]
52. ((wise(mary) & ~creative(mary)) | ! [X0] : (creative(X0) & old(X0))) & (? [X1] : (~creative(X1) | ~old(X1)) | ~wise(mary) | creative(mary)) [rectify 51]
53. ? [X1] : (~creative(X1) | ~old(X1)) => (~creative(sK3) | ~old(sK3)) [choice axiom]
54. ((wise(mary) & ~creative(mary)) | ! [X0] : (creative(X0) & old(X0))) & ((~creative(sK3) | ~old(sK3)) | ~wise(mary) | creative(mary)) [skolemisation 52,53]
55. ! [X0] : (((quiet(X0) | ~strong(X0)) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & strong(X0)))) [nnf transformation 11]
56. ! [X0] : ((quiet(X0) | ~strong(X0) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & strong(X0)))) [flattening 55]
59. ! [X0] : (((~rich(X0) | ~tall(X0)) | ~tall(X0)) & (tall(X0) | (rich(X0) & tall(X0)))) [nnf transformation 13]
60. ! [X0] : ((~rich(X0) | ~tall(X0) | ~tall(X0)) & (tall(X0) | (rich(X0) & tall(X0)))) [flattening 59]
61. ! [X0] : (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~strong(X0) & quiet(X0))) [nnf transformation 30]
84. ~tall(X0) | patient(X0) | ~wise(X0) [cnf transformation 36]
94. ~patient(X0) | strong(X0) | wise(X0) [cnf transformation 38]
95. ~strong(X0) | patient(X0) | wise(X0) [cnf transformation 38]
101. ~happy(X0) | curious(X0) [cnf transformation 44]
103. ~tall(X0) | happy(X0) | ~tall(X0) [cnf transformation 28]
111. wise(mary) | old(X0) [cnf transformation 54]
113. strong(X0) | patient(X0) [cnf transformation 56]
117. tall(X0) | tall(X0) [cnf transformation 60]
121. ~curious(X0) | ~old(X0) | ~strong(X0) [cnf transformation 61]
139. ~wise(mary) [cnf transformation 23]
140. tall(X0) [duplicate literal removal 117]
142. ~tall(X0) | happy(X0) [duplicate literal removal 103]
195. 13 <=> wise(mary) [avatar definition]
196. ~wise(mary) <- (~13) [avatar component clause 195]
200. 14 <=> ! [X0] : old(X0) [avatar definition]
201. old(X0) <- (14) [avatar component clause 200]
202. 14 | 13 [avatar split clause 111,195,200]
269. ~13 [avatar split clause 139,195]
281. happy(X0) [resolution 142,140]
287. curious(X0) [resolution 281,101]
311. ~wise(X0) | patient(X0) [resolution 84,140]
324. patient(X0) | wise(X0) | patient(X0) [resolution 95,113]
325. patient(X0) | wise(X0) [duplicate literal removal 324]
326. patient(X0) [subsumption resolution 325,311]
328. strong(X0) | wise(X0) [resolution 326,94]
350. ~old(X0) | ~strong(X0) [resolution 121,287]
352. ~strong(X0) <- (14) [subsumption resolution 350,201]
353. wise(X0) <- (14) [resolution 352,328]
359. $false <- (~13, 14) [resolution 353,196]
362. 13 | ~14 [avatar contradiction clause 359]
363. $false [avatar sat refutation 202,269,362]
% SZS output end Proof for 5435267992007181899245136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is humble or strong then lucy is funny or not quiet. Everyone who is either kind or quiet is either not curious or not tall and vice versa. Everyone who is not humble is humble or brave and vice versa. Everyone who is strong is brave or not strong and vice versa. Everyone who is either tall or funny is either happy or not kind and vice versa. Everyone who is both strong and rich is both not strong and not happy and vice versa. Everyone who is not funny is not generous. Everyone who is curious is humble. Everyone who is both not wise and quiet is both patient and not generous and vice versa. If susan is not tall or not funny then lucy is happy and vice versa. Everyone who is either not humble or not funny is either not brave or not old. If someone is either funny or patient then mary is either curious or creative and vice versa. If alice is either happy or wise then someone is funny or kind. If someone is not creative or tall then mary is either not tall or not wise. If susan is not funny or old then someone is either not wise or not calm. If lucy is either not funny or not humble then paul is happy and vice versa. Someone is generous or not generous. Someone is not happy or not curious. Someone is both funny and strong. Someone is not brave or not quiet. Alice is both not kind and wise. Someone is either not old or strong. Someone is rich or creative. | Susan is humble. | contradiction | (((humble(paul)|strong(paul)))=>((funny(lucy)|~quiet(lucy))))&
(![X]:((kind(X)<~>quiet(X))<=>(~curious(X)<~>~tall(X))))&
(![X]:(~humble(X)<=>(humble(X)|brave(X))))&
(![X]:(strong(X)<=>(brave(X)|~strong(X))))&
(![X]:((tall(X)<~>funny(X))<=>(happy(X)<~>~kind(X))))&
(![X]:((strong(X)&rich(X))<=>(~strong(X)&~happy(X))))&
(![X]:(~funny(X)=>~generous(X)))&
(![X]:(curious(X)=>humble(X)))&
(![X]:((~wise(X)&quiet(X))<=>(patient(X)&~generous(X))))&
(((~tall(susan)|~funny(susan)))<=>(happy(lucy)))&
(![X]:((~humble(X)<~>~funny(X))=>(~brave(X)<~>~old(X))))&
((?[X]:((funny(X)<~>patient(X))))<=>((curious(mary)<~>creative(mary))))&
(((happy(alice)<~>wise(alice)))=>(?[X]:((funny(X)|kind(X)))))&
((?[X]:((~creative(X)|tall(X))))=>((~tall(mary)<~>~wise(mary))))&
(((~funny(susan)|old(susan)))=>(?[X]:((~wise(X)<~>~calm(X)))))&
(((~funny(lucy)<~>~humble(lucy)))<=>(happy(paul)))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((~happy(X)|~curious(X))))&
(?[X]:((funny(X)&strong(X))))&
(?[X]:((~brave(X)|~quiet(X))))&
((~kind(alice)&wise(alice)))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:((rich(X)|creative(X)))) | humble(susan) | [
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 2559029938074972591559382
% SZS output start Proof for 2559029938074972591559382
3. ! [X0] : (~humble(X0) <=> (brave(X0) | humble(X0))) [input p2]
24. humble(susan) [input hypothesis]
34. ! [X0] : ((~humble(X0) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | humble(X0))) [nnf transformation 3]
35. ! [X0] : ((~humble(X0) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | humble(X0))) [flattening 34]
82. ~humble(X0) | ~humble(X0) [cnf transformation 35]
144. humble(susan) [cnf transformation 24]
150. ~humble(X0) [duplicate literal removal 82]
280. $false [subsumption resolution 144,150]
% SZS output end Proof for 2559029938074972591559382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or quiet is both kind and tall. If susan is not funny or strong then susan is either funny or not quiet and vice versa. If fred is not wise or not humble then alice is creative or humble. Everyone who is brave or old is both funny and calm. If paul is both creative and not calm then someone is either not old or curious. Everyone who is both humble and brave is quiet and vice versa. Everyone who is not wise is old or not creative. If lucy is both not old and not kind then john is not generous or not wise and vice versa. If john is not calm then alice is either strong or happy and vice versa. Everyone who is both happy and not strong is calm. Everyone who is happy is kind or curious. If fred is not quiet or not brave then someone is either not rich or wise and vice versa. Everyone who is either wise or not quiet is not funny. Everyone who is both not humble and brave is not rich or not curious and vice versa. If mary is either not kind or not happy then john is either not funny or not quiet. Someone is either rich or not funny. Someone is both not old and not curious. Alice is kind. Mary is generous or happy. Someone is strong or patient. Someone is calm. Fred is not brave or not strong. Someone is not old. | John is quiet. | contradiction | (![X]:((~quiet(X)<~>quiet(X))=>(kind(X)&tall(X))))&
(((~funny(susan)|strong(susan)))<=>((funny(susan)<~>~quiet(susan))))&
(((~wise(fred)|~humble(fred)))=>((creative(alice)|humble(alice))))&
(![X]:((brave(X)|old(X))=>(funny(X)&calm(X))))&
(((creative(paul)&~calm(paul)))=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((humble(X)&brave(X))<=>quiet(X)))&
(![X]:(~wise(X)=>(old(X)|~creative(X))))&
(((~old(lucy)&~kind(lucy)))<=>((~generous(john)|~wise(john))))&
((~calm(john))<=>((strong(alice)<~>happy(alice))))&
(![X]:((happy(X)&~strong(X))=>calm(X)))&
(![X]:(happy(X)=>(kind(X)|curious(X))))&
(((~quiet(fred)|~brave(fred)))<=>(?[X]:((~rich(X)<~>wise(X)))))&
(![X]:((wise(X)<~>~quiet(X))=>~funny(X)))&
(![X]:((~humble(X)&brave(X))<=>(~rich(X)|~curious(X))))&
(((~kind(mary)<~>~happy(mary)))=>((~funny(john)<~>~quiet(john))))&
(?[X]:((rich(X)<~>~funny(X))))&
(?[X]:((~old(X)&~curious(X))))&
(kind(alice))&
((generous(mary)|happy(mary)))&
(?[X]:((strong(X)|patient(X))))&
(?[X]:(calm(X)))&
((~brave(fred)|~strong(fred)))&
(?[X]:(~old(X))) | quiet(john) | [
"p0",
"p3",
"p5",
"p7",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 2012548044096247245324955
% SZS output start Proof for 2012548044096247245324955
1. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => (tall(X0) & kind(X0))) [input p0]
4. ! [X0] : ((old(X0) | brave(X0)) => (calm(X0) & funny(X0))) [input p3]
6. ! [X0] : ((brave(X0) & humble(X0)) <=> quiet(X0)) [input p5]
8. (~kind(lucy) & ~old(lucy)) <=> (~wise(john) | ~generous(john)) [input p7]
13. ! [X0] : ((wise(X0) <~> ~quiet(X0)) => ~funny(X0)) [input p12]
24. quiet(john) [input hypothesis]
26. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => kind(X0)) [pure predicate removal 1]
27. ! [X0] : (kind(X0) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 26]
30. ! [X0] : ((calm(X0) & funny(X0)) | (~old(X0) & ~brave(X0))) [ennf transformation 4]
39. ! [X0] : (~funny(X0) | (wise(X0) <=> ~quiet(X0))) [ennf transformation 13]
41. ! [X0] : (kind(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 27]
47. ! [X0] : (((brave(X0) & humble(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) | ~humble(X0)))) [nnf transformation 6]
48. ! [X0] : (((brave(X0) & humble(X0)) | ~quiet(X0)) & (quiet(X0) | ~brave(X0) | ~humble(X0))) [flattening 47]
49. ((~kind(lucy) & ~old(lucy)) | (wise(john) & generous(john))) & ((~wise(john) | ~generous(john)) | (kind(lucy) | old(lucy))) [nnf transformation 8]
50. ((~kind(lucy) & ~old(lucy)) | (wise(john) & generous(john))) & (~wise(john) | ~generous(john) | kind(lucy) | old(lucy)) [flattening 49]
57. ! [X0] : (~funny(X0) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 39]
70. kind(X0) | quiet(X0) | quiet(X0) [cnf transformation 41]
71. kind(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 41]
80. ~brave(X0) | funny(X0) [cnf transformation 30]
88. ~quiet(X0) | brave(X0) [cnf transformation 48]
94. ~kind(lucy) | wise(john) [cnf transformation 50]
107. ~wise(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 57]
127. quiet(john) [cnf transformation 24]
130. kind(X0) | quiet(X0) [duplicate literal removal 70]
131. ~quiet(X0) | kind(X0) [duplicate literal removal 71]
132. kind(X0) [subsumption resolution 130,131]
185. wise(john) [subsumption resolution 94,132]
239. 22 <=> funny(john) [avatar definition]
241. funny(john) <- (22) [avatar component clause 239]
243. 23 <=> quiet(john) [avatar definition]
245. quiet(john) <- (23) [avatar component clause 243]
269. 23 [avatar split clause 127,243]
271. brave(john) <- (23) [resolution 88,245]
274. funny(john) <- (23) [resolution 271,80]
277. 22 | ~23 [avatar split clause 274,243,239]
335. ~quiet(john) | ~funny(john) [resolution 107,185]
336. ~funny(john) <- (23) [subsumption resolution 335,245]
337. $false <- (22, 23) [subsumption resolution 336,241]
338. ~22 | ~23 [avatar contradiction clause 337]
339. $false [avatar sat refutation 269,277,338]
% SZS output end Proof for 2012548044096247245324955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or old is either not generous or old. Everyone who is both not calm and not strong is not generous or strong. Everyone who is both generous and happy is both not strong and curious. Everyone who is funny or wise is both strong and not calm and vice versa. If someone is either strong or rich then someone is either not calm or creative and vice versa. Everyone who is both not funny and humble is funny or rich and vice versa. Everyone who is not curious or not tall is funny or not quiet and vice versa. Everyone who is wise is both not old and not kind and vice versa. If someone is either not humble or not wise then alice is not rich. If someone is rich or not old then someone is both not happy and not tall. Everyone who is either kind or brave is both old and not calm and vice versa. Everyone who is not happy or humble is not kind or not brave. Everyone who is curious is both not funny and curious. Everyone who is not curious or not kind is either wise or curious and vice versa. If someone is either wise or generous then someone is either not creative or not happy. Everyone who is not funny is both tall and strong. Alice is creative or not brave. Someone is not happy. Susan is not kind or not wise. Someone is both not humble and tall. Susan is patient. Mary is either not creative or tall. Someone is generous or humble. | Alice is not kind. | entailment | (![X]:((tall(X)<~>old(X))=>(~generous(X)<~>old(X))))&
(![X]:((~calm(X)&~strong(X))=>(~generous(X)|strong(X))))&
(![X]:((generous(X)&happy(X))=>(~strong(X)&curious(X))))&
(![X]:((funny(X)|wise(X))<=>(strong(X)&~calm(X))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~funny(X)&humble(X))<=>(funny(X)|rich(X))))&
(![X]:((~curious(X)|~tall(X))<=>(funny(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~old(X)&~kind(X))))&
((?[X]:((~humble(X)<~>~wise(X))))=>(~rich(alice)))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((~happy(X)&~tall(X)))))&
(![X]:((kind(X)<~>brave(X))<=>(old(X)&~calm(X))))&
(![X]:((~happy(X)|humble(X))=>(~kind(X)|~brave(X))))&
(![X]:(curious(X)=>(~funny(X)&curious(X))))&
(![X]:((~curious(X)|~kind(X))<=>(wise(X)<~>curious(X))))&
((?[X]:((wise(X)<~>generous(X))))=>(?[X]:((~creative(X)<~>~happy(X)))))&
(![X]:(~funny(X)=>(tall(X)&strong(X))))&
((creative(alice)|~brave(alice)))&
(?[X]:(~happy(X)))&
((~kind(susan)|~wise(susan)))&
(?[X]:((~humble(X)&tall(X))))&
(patient(susan))&
((~creative(mary)<~>tall(mary)))&
(?[X]:((generous(X)|humble(X)))) | ~kind(alice) | [
"p5",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 4849014487319471072845916
% SZS output start Proof for 4849014487319471072845916
6. ! [X0] : ((humble(X0) & ~funny(X0)) <=> (rich(X0) | funny(X0))) [input p5]
8. ! [X0] : (wise(X0) <=> (~kind(X0) & ~old(X0))) [input p7]
10. ? [X0] : (~old(X0) | rich(X0)) => ? [X0] : (~tall(X0) & ~happy(X0)) [input p9]
14. ! [X0] : ((~kind(X0) | ~curious(X0)) <=> (wise(X0) <~> curious(X0))) [input p13]
16. ! [X0] : (~funny(X0) => (strong(X0) & tall(X0))) [input p15]
24. kind(alice) [input hypothesis]
26. ? [X0] : (~old(X0) | rich(X0)) => ? [X1] : (~tall(X1) & ~happy(X1)) [rectify 10]
35. ? [X1] : (~tall(X1) & ~happy(X1)) | ! [X0] : (old(X0) & ~rich(X0)) [ennf transformation 26]
40. ! [X0] : ((strong(X0) & tall(X0)) | funny(X0)) [ennf transformation 16]
49. ! [X0] : (((humble(X0) & ~funny(X0)) | (~rich(X0) & ~funny(X0))) & ((rich(X0) | funny(X0)) | (~humble(X0) | funny(X0)))) [nnf transformation 6]
50. ! [X0] : (((humble(X0) & ~funny(X0)) | (~rich(X0) & ~funny(X0))) & (rich(X0) | funny(X0) | ~humble(X0) | funny(X0))) [flattening 49]
53. ! [X0] : ((wise(X0) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | ~wise(X0))) [nnf transformation 8]
54. ! [X0] : ((wise(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | ~wise(X0))) [flattening 53]
56. ? [X0] : (~tall(X0) & ~happy(X0)) | ! [X1] : (old(X1) & ~rich(X1)) [rectify 35]
57. ? [X0] : (~tall(X0) & ~happy(X0)) => (~tall(sK2) & ~happy(sK2)) [choice axiom]
58. (~tall(sK2) & ~happy(sK2)) | ! [X1] : (old(X1) & ~rich(X1)) [skolemisation 56,57]
61. ! [X0] : (((~kind(X0) | ~curious(X0)) | ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0)))) & (((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | (kind(X0) & curious(X0)))) [nnf transformation 14]
62. ! [X0] : ((~kind(X0) | ~curious(X0) | ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0)))) & (((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | (kind(X0) & curious(X0)))) [flattening 61]
95. ~funny(X0) | ~funny(X0) [cnf transformation 50]
103. ~wise(X0) | ~old(X0) [cnf transformation 54]
104. ~kind(X0) | ~wise(X0) [cnf transformation 54]
111. ~tall(sK2) | old(X1) [cnf transformation 58]
122. curious(X0) | wise(X0) | curious(X0) [cnf transformation 62]
127. ~kind(X0) | ~curious(X0) | wise(X0) | ~curious(X0) [cnf transformation 62]
132. tall(X0) | funny(X0) [cnf transformation 40]
142. kind(alice) [cnf transformation 24]
143. wise(X0) | curious(X0) [duplicate literal removal 122]
144. ~kind(X0) | ~curious(X0) | wise(X0) [duplicate literal removal 127]
146. ~funny(X0) [duplicate literal removal 95]
202. 12 <=> ! [X1] : old(X1) [avatar definition]
203. old(X1) <- (12) [avatar component clause 202]
205. 13 <=> tall(sK2) [avatar definition]
207. ~tall(sK2) <- (~13) [avatar component clause 205]
208. 12 | ~13 [avatar split clause 111,205,202]
219. ~kind(X0) | ~curious(X0) [subsumption resolution 144,104]
240. tall(X0) [subsumption resolution 132,146]
260. $false <- (~13) [subsumption resolution 207,240]
261. 13 [avatar contradiction clause 260]
263. curious(X0) | ~old(X0) [resolution 143,103]
266. curious(X0) <- (12) [subsumption resolution 263,203]
268. ~curious(alice) [resolution 219,142]
269. $false <- (12) [subsumption resolution 268,266]
270. ~12 [avatar contradiction clause 269]
271. $false [avatar sat refutation 208,261,270]
% SZS output end Proof for 4849014487319471072845916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is patient is old or not generous and vice versa. If alice is curious then someone is wise. Everyone who is not brave or not funny is both not generous and not strong. If someone is not wise or rich then someone is old or not brave and vice versa. Everyone who is either not happy or not tall is both curious and strong and vice versa. Everyone who is either not patient or strong is both kind and not funny and vice versa. If susan is both not tall and not old then someone is both wise and not rich. Everyone who is generous is not kind or not wise and vice versa. Everyone who is both wise and not creative is curious and vice versa. If someone is either not kind or creative then someone is either not patient or old. Everyone who is brave is not tall or generous and vice versa. Everyone who is generous or calm is either happy or tall. If someone is either not curious or rich then paul is creative or not curious and vice versa. Everyone who is either creative or old is not patient or quiet. If susan is curious or not generous then fred is both not patient and tall and vice versa. Someone is both not tall and not happy. Someone is both not brave and kind. John is not wise or not creative. Lucy is kind or not patient. Someone is not kind. Someone is either not quiet or not kind. Paul is either not calm or tall. | Fred is not kind. | entailment | (![X]:(patient(X)<=>(old(X)|~generous(X))))&
((curious(alice))=>(?[X]:(wise(X))))&
(![X]:((~brave(X)|~funny(X))=>(~generous(X)&~strong(X))))&
((?[X]:((~wise(X)|rich(X))))<=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((~happy(X)<~>~tall(X))<=>(curious(X)&strong(X))))&
(![X]:((~patient(X)<~>strong(X))<=>(kind(X)&~funny(X))))&
(((~tall(susan)&~old(susan)))=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:(generous(X)<=>(~kind(X)|~wise(X))))&
(![X]:((wise(X)&~creative(X))<=>curious(X)))&
((?[X]:((~kind(X)<~>creative(X))))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(brave(X)<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((~brave(X)&kind(X))))&
((~wise(john)|~creative(john)))&
((kind(lucy)|~patient(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
((~calm(paul)<~>tall(paul))) | ~kind(fred) | [
"p0",
"p4",
"p7",
"p8",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2656938619168904077945543
% SZS output start Proof for 2656938619168904077945543
1. ! [X0] : (patient(X0) <=> (~generous(X0) | old(X0))) [input p0]
5. ! [X0] : ((~happy(X0) <~> ~tall(X0)) <=> (strong(X0) & curious(X0))) [input p4]
8. ! [X0] : (generous(X0) <=> (~wise(X0) | ~kind(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & wise(X0)) <=> curious(X0)) [input p8]
12. ! [X0] : ((calm(X0) | generous(X0)) => (happy(X0) <~> tall(X0))) [input p11]
15. (~generous(susan) | curious(susan)) <=> (tall(fred) & ~patient(fred)) [input p14]
23. kind(fred) [input hypothesis]
31. ! [X0] : ((happy(X0) <~> tall(X0)) | (~calm(X0) & ~generous(X0))) [ennf transformation 12]
34. ! [X0] : ((patient(X0) | (generous(X0) & ~old(X0))) & ((~generous(X0) | old(X0)) | ~patient(X0))) [nnf transformation 1]
35. ! [X0] : ((patient(X0) | (generous(X0) & ~old(X0))) & (~generous(X0) | old(X0) | ~patient(X0))) [flattening 34]
43. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (~strong(X0) | ~curious(X0))) & ((strong(X0) & curious(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [nnf transformation 5]
44. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | ~strong(X0) | ~curious(X0)) & ((strong(X0) & curious(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [flattening 43]
49. ! [X0] : ((generous(X0) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | ~generous(X0))) [nnf transformation 8]
50. ! [X0] : ((generous(X0) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | ~generous(X0))) [flattening 49]
51. ! [X0] : (((~creative(X0) & wise(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) | ~wise(X0)))) [nnf transformation 9]
52. ! [X0] : (((~creative(X0) & wise(X0)) | ~curious(X0)) & (curious(X0) | creative(X0) | ~wise(X0))) [flattening 51]
59. ! [X0] : (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (~calm(X0) & ~generous(X0))) [nnf transformation 31]
66. ((~generous(susan) | curious(susan)) | (~tall(fred) | patient(fred))) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [nnf transformation 15]
67. (~generous(susan) | curious(susan) | ~tall(fred) | patient(fred)) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [flattening 66]
80. generous(X0) | patient(X0) [cnf transformation 35]
90. ~tall(X0) | curious(X0) | happy(X0) [cnf transformation 44]
91. ~happy(X0) | curious(X0) | tall(X0) [cnf transformation 44]
104. ~kind(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 50]
108. ~curious(X0) | wise(X0) [cnf transformation 52]
117. ~generous(X0) | happy(X0) | tall(X0) [cnf transformation 59]
119. ~tall(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 59]
129. ~patient(fred) | ~curious(susan) [cnf transformation 67]
130. ~patient(fred) | generous(susan) [cnf transformation 67]
131. tall(fred) | ~curious(susan) [cnf transformation 67]
132. tall(fred) | generous(susan) [cnf transformation 67]
145. kind(fred) [cnf transformation 23]
190. 11 <=> tall(susan) [avatar definition]
191. ~tall(susan) <- (~11) [avatar component clause 190]
192. tall(susan) <- (11) [avatar component clause 190]
255. 25 <=> patient(fred) [avatar definition]
256. ~patient(fred) <- (~25) [avatar component clause 255]
259. 26 <=> tall(fred) [avatar definition]
260. tall(fred) <- (26) [avatar component clause 259]
263. 27 <=> curious(susan) [avatar definition]
267. 28 <=> generous(susan) [avatar definition]
268. generous(susan) <- (28) [avatar component clause 267]
271. 28 | 26 [avatar split clause 132,259,267]
272. ~27 | 26 [avatar split clause 131,259,263]
273. 28 | ~25 [avatar split clause 130,255,267]
274. ~27 | ~25 [avatar split clause 129,255,263]
371. curious(susan) | happy(susan) <- (11) [resolution 90,192]
375. 45 <=> happy(susan) [avatar definition]
377. happy(susan) <- (45) [avatar component clause 375]
378. 45 | 27 | ~11 [avatar split clause 371,190,263,375]
380. 46 <=> happy(fred) [avatar definition]
384. 47 <=> curious(fred) [avatar definition]
386. curious(fred) <- (47) [avatar component clause 384]
405. ~wise(fred) | ~generous(fred) [resolution 104,145]
418. 50 <=> generous(fred) [avatar definition]
419. generous(fred) <- (50) [avatar component clause 418]
420. ~generous(fred) <- (~50) [avatar component clause 418]
422. 51 <=> wise(fred) [avatar definition]
425. ~50 | ~51 [avatar split clause 405,422,418]
436. happy(susan) | tall(susan) <- (28) [resolution 117,268]
441. happy(susan) <- (~11, 28) [subsumption resolution 436,191]
442. 45 | 11 | ~28 [avatar split clause 441,267,190,375]
502. curious(susan) | tall(susan) <- (45) [resolution 377,91]
511. curious(fred) | happy(fred) <- (26) [resolution 260,90]
516. ~happy(fred) | ~generous(fred) <- (26) [resolution 119,260]
520. ~happy(fred) <- (26, 50) [subsumption resolution 516,419]
521. ~46 | ~26 | ~50 [avatar split clause 520,418,259,380]
522. 46 | 47 | ~26 [avatar split clause 511,259,384,380]
528. wise(fred) <- (47) [resolution 386,108]
536. 51 | ~47 [avatar split clause 528,384,422]
544. patient(fred) <- (~50) [resolution 420,80]
545. $false <- (~25, ~50) [subsumption resolution 544,256]
546. 25 | 50 [avatar contradiction clause 545]
547. 11 | 27 | ~45 [avatar split clause 502,375,263,190]
553. ~happy(susan) | ~generous(susan) <- (11) [resolution 192,119]
557. ~generous(susan) <- (11, 45) [subsumption resolution 553,377]
558. $false <- (11, 28, 45) [subsumption resolution 557,268]
559. ~11 | ~28 | ~45 [avatar contradiction clause 558]
560. $false [avatar sat refutation 271,272,273,274,378,425,442,521,522,536,546,547,559]
% SZS output end Proof for 2656938619168904077945543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then john is either curious or not rich. Everyone who is either tall or old is both generous and not rich and vice versa. Everyone who is not rich is both not humble and old and vice versa. Everyone who is quiet is either not brave or brave. Everyone who is humble is not kind or rich and vice versa. Everyone who is not funny is either calm or quiet and vice versa. Everyone who is not kind or not brave is both creative and not humble. If alice is not strong then someone is either old or not tall. Everyone who is both brave and not curious is not quiet and vice versa. If someone is creative or rich then mary is either tall or old. If lucy is either creative or kind then someone is not wise or not calm. Everyone who is either old or brave is both generous and not funny and vice versa. Everyone who is both not patient and calm is tall. Everyone who is not funny or generous is not creative. If mary is happy or not strong then susan is happy. If someone is creative or calm then someone is not calm or brave and vice versa. Someone is funny. Someone is not humble or not old. Susan is not old. Fred is not funny. Lucy is either not brave or calm. Fred is either patient or not tall. Lucy is either not rich or wise. Alice is both not old and rich. | Susan is not kind. | contradiction | ((?[X]:(tall(X)))=>((curious(john)<~>~rich(john))))&
(![X]:((tall(X)<~>old(X))<=>(generous(X)&~rich(X))))&
(![X]:(~rich(X)<=>(~humble(X)&old(X))))&
(![X]:(quiet(X)=>(~brave(X)<~>brave(X))))&
(![X]:(humble(X)<=>(~kind(X)|rich(X))))&
(![X]:(~funny(X)<=>(calm(X)<~>quiet(X))))&
(![X]:((~kind(X)|~brave(X))=>(creative(X)&~humble(X))))&
((~strong(alice))=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((brave(X)&~curious(X))<=>~quiet(X)))&
((?[X]:((creative(X)|rich(X))))=>((tall(mary)<~>old(mary))))&
(((creative(lucy)<~>kind(lucy)))=>(?[X]:((~wise(X)|~calm(X)))))&
(![X]:((old(X)<~>brave(X))<=>(generous(X)&~funny(X))))&
(![X]:((~patient(X)&calm(X))=>tall(X)))&
(![X]:((~funny(X)|generous(X))=>~creative(X)))&
(((happy(mary)|~strong(mary)))=>(happy(susan)))&
((?[X]:((creative(X)|calm(X))))<=>(?[X]:((~calm(X)|brave(X)))))&
(?[X]:(funny(X)))&
(?[X]:((~humble(X)|~old(X))))&
(~old(susan))&
(~funny(fred))&
((~brave(lucy)<~>calm(lucy)))&
((patient(fred)<~>~tall(fred)))&
((~rich(lucy)<~>wise(lucy)))&
((~old(alice)&rich(alice))) | ~kind(susan) | [
"p4",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 5304523548875803283131073
% SZS output start Proof for 5304523548875803283131073
5. ! [X0] : (humble(X0) <=> (rich(X0) | ~kind(X0))) [input p4]
7. ! [X0] : ((~brave(X0) | ~kind(X0)) => (~humble(X0) & creative(X0))) [input p6]
25. ~kind(susan) [input hypothesis]
31. ! [X0] : ((~humble(X0) & creative(X0)) | (brave(X0) & kind(X0))) [ennf transformation 7]
44. ! [X0] : ((humble(X0) | (~rich(X0) & kind(X0))) & ((rich(X0) | ~kind(X0)) | ~humble(X0))) [nnf transformation 5]
45. ! [X0] : ((humble(X0) | (~rich(X0) & kind(X0))) & (rich(X0) | ~kind(X0) | ~humble(X0))) [flattening 44]
81. humble(X0) | kind(X0) [cnf transformation 45]
89. ~humble(X0) | kind(X0) [cnf transformation 31]
126. ~kind(susan) [cnf transformation 25]
140. kind(X0) [subsumption resolution 89,81]
250. $false [subsumption resolution 126,140]
% SZS output end Proof for 5304523548875803283131073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or tall is calm and vice versa.
If someone is either rich or not wise then someone is both strong and not rich and vice versa.
Everyone who is not old or old is either rich or not tall and vice versa.
If mary is both curious and calm then someone is not strong.
Everyone who is either not quiet or not strong is either curious or creative and vice versa.
If someone is old or patient then alice is not kind or not old and vice versa.
If john is either calm or not generous then someone is not brave and vice versa.
If lucy is not wise or humble then paul is curious and vice versa.
If fred is either generous or not generous then someone is not generous.
Everyone who is both brave and kind is not generous or curious and vice versa.
If someone is both not funny and humble then mary is not happy or not calm.
If someone is both not generous and not quiet then someone is kind or funny.
If fred is both not calm and not kind then susan is both not humble and quiet.
Everyone who is not kind is either tall or generous and vice versa.
If someone is both rich and not rich then paul is either not calm or not patient and vice versa.
Everyone who is strong or not patient is either not quiet or strong and vice versa.
Someone is not rich.
John is either not rich or not brave.
Someone is strong.
John is both not wise and generous.
Someone is not happy.
Someone is wise or strong.
Someone is both quiet and not creative.
John is both not calm and not funny. | John is not curious. | entailment | (![X]:((quiet(X)<~>tall(X))<=>calm(X)))&
((?[X]:((rich(X)<~>~wise(X))))<=>(?[X]:((strong(X)&~rich(X)))))&
(![X]:((~old(X)|old(X))<=>(rich(X)<~>~tall(X))))&
(((curious(mary)&calm(mary)))=>(?[X]:(~strong(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>(curious(X)<~>creative(X))))&
((?[X]:((old(X)|patient(X))))<=>((~kind(alice)|~old(alice))))&
(((calm(john)<~>~generous(john)))<=>(?[X]:(~brave(X))))&
(((~wise(lucy)|humble(lucy)))<=>(curious(paul)))&
(((generous(fred)<~>~generous(fred)))=>(?[X]:(~generous(X))))&
(![X]:((brave(X)&kind(X))<=>(~generous(X)|curious(X))))&
((?[X]:((~funny(X)&humble(X))))=>((~happy(mary)|~calm(mary))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((kind(X)|funny(X)))))&
(((~calm(fred)&~kind(fred)))=>((~humble(susan)&quiet(susan))))&
(![X]:(~kind(X)<=>(tall(X)<~>generous(X))))&
((?[X]:((rich(X)&~rich(X))))<=>((~calm(paul)<~>~patient(paul))))&
(![X]:((strong(X)|~patient(X))<=>(~quiet(X)<~>strong(X))))&
(?[X]:(~rich(X)))&
((~rich(john)<~>~brave(john)))&
(?[X]:(strong(X)))&
((~wise(john)&generous(john)))&
(?[X]:(~happy(X)))&
(?[X]:((wise(X)|strong(X))))&
(?[X]:((quiet(X)&~creative(X))))&
((~calm(john)&~funny(john))) | ~curious(john) | [
"p2",
"p6",
"p9",
"p13",
"p17",
"p19",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 6762106275813428536456500
% SZS output start Proof for 6762106275813428536456500
3. ! [X0] : ((old(X0) | ~old(X0)) <=> (rich(X0) <~> ~tall(X0))) [input p2]
7. (calm(john) <~> ~generous(john)) <=> ? [X0] : ~brave(X0) [input p6]
10. ! [X0] : ((kind(X0) & brave(X0)) <=> (curious(X0) | ~generous(X0))) [input p9]
14. ! [X0] : (~kind(X0) <=> (tall(X0) <~> generous(X0))) [input p13]
18. ~rich(john) <~> ~brave(john) [input p17]
20. generous(john) & ~wise(john) [input p19]
24. ~funny(john) & ~calm(john) [input p23]
25. curious(john) [input hypothesis]
42. ! [X0] : (((old(X0) | ~old(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | (~old(X0) & old(X0)))) [nnf transformation 3]
43. ! [X0] : ((old(X0) | ~old(X0) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | (~old(X0) & old(X0)))) [flattening 42]
52. (((generous(john) | ~calm(john)) & (~generous(john) | calm(john))) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ((calm(john) | generous(john)) & (~generous(john) | ~calm(john)))) [nnf transformation 7]
53. (((generous(john) | ~calm(john)) & (~generous(john) | calm(john))) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ((calm(john) | generous(john)) & (~generous(john) | ~calm(john)))) [rectify 52]
54. ? [X1] : ~brave(X1) => ~brave(sK4) [choice axiom]
55. (((generous(john) | ~calm(john)) & (~generous(john) | calm(john))) | ! [X0] : brave(X0)) & (~brave(sK4) | ((calm(john) | generous(john)) & (~generous(john) | ~calm(john)))) [skolemisation 53,54]
61. ! [X0] : (((kind(X0) & brave(X0)) | (~curious(X0) & generous(X0))) & ((curious(X0) | ~generous(X0)) | (~kind(X0) | ~brave(X0)))) [nnf transformation 10]
62. ! [X0] : (((kind(X0) & brave(X0)) | (~curious(X0) & generous(X0))) & (curious(X0) | ~generous(X0) | ~kind(X0) | ~brave(X0))) [flattening 61]
66. ! [X0] : ((~kind(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0)))) & (((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | kind(X0))) [nnf transformation 14]
75. (brave(john) | rich(john)) & (~brave(john) | ~rich(john)) [nnf transformation 18]
92. ~tall(X0) | rich(X0) | old(X0) [cnf transformation 43]
93. ~old(X0) | rich(X0) | ~tall(X0) [cnf transformation 43]
113. ~generous(john) | calm(john) | brave(X0) [cnf transformation 55]
124. ~curious(X0) | kind(X0) [cnf transformation 62]
131. ~generous(X0) | tall(X0) | ~kind(X0) [cnf transformation 66]
145. ~brave(john) | ~rich(john) [cnf transformation 75]
149. generous(john) [cnf transformation 20]
153. ~calm(john) [cnf transformation 24]
155. curious(john) [cnf transformation 25]
192. ~tall(X0) | rich(X0) [subsumption resolution 92,93]
233. 17 <=> ! [X0] : brave(X0) [avatar definition]
234. brave(X0) <- (17) [avatar component clause 233]
236. 18 <=> calm(john) [avatar definition]
240. 19 <=> generous(john) [avatar definition]
242. generous(john) <- (19) [avatar component clause 240]
244. 17 | 18 | ~19 [avatar split clause 113,240,236,233]
325. 36 <=> rich(john) [avatar definition]
326. ~rich(john) <- (~36) [avatar component clause 325]
329. 37 <=> brave(john) [avatar definition]
330. ~brave(john) <- (~37) [avatar component clause 329]
333. ~36 | ~37 [avatar split clause 145,329,325]
334. 19 [avatar split clause 149,240]
344. ~18 [avatar split clause 153,236]
345. $false <- (17, ~37) [resolution 330,234]
346. ~17 | 37 [avatar contradiction clause 345]
350. kind(john) [resolution 124,155]
427. tall(john) | ~kind(john) <- (19) [resolution 131,242]
429. tall(john) <- (19) [subsumption resolution 427,350]
433. rich(john) <- (19) [resolution 429,192]
435. $false <- (19, ~36) [subsumption resolution 433,326]
436. ~19 | 36 [avatar contradiction clause 435]
437. $false [avatar sat refutation 244,333,334,344,346,436]
% SZS output end Proof for 6762106275813428536456500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not strong or not generous is not calm.
If fred is either not funny or calm then mary is both funny and brave and vice versa.
If someone is both happy and not strong then susan is old.
Everyone who is either not curious or calm is not quiet and vice versa.
Everyone who is not tall or not curious is either curious or not patient.
If lucy is both quiet and not curious then someone is not creative.
If fred is both calm and not quiet then john is quiet and vice versa.
If john is not tall then someone is either curious or not calm and vice versa.
Everyone who is wise or not wise is both old and calm.
If someone is not creative or not tall then fred is both tall and strong and vice versa.
If john is happy then someone is either wise or old.
Everyone who is humble or kind is not patient or not wise and vice versa.
Everyone who is either not curious or humble is both curious and not kind and vice versa.
Everyone who is either not patient or not tall is brave or not quiet.
Everyone who is either not happy or old is not humble or curious and vice versa.
If mary is both brave and funny then lucy is either generous or strong and vice versa.
Alice is not tall.
Someone is either kind or not patient.
Someone is either not wise or strong.
Someone is both old and rich.
Someone is not happy or not kind.
Someone is either tall or wise.
Fred is either not curious or wise. | Lucy is not calm. | contradiction | (![X]:((~strong(X)|~generous(X))=>~calm(X)))&
(((~funny(fred)<~>calm(fred)))<=>((funny(mary)&brave(mary))))&
((?[X]:((happy(X)&~strong(X))))=>(old(susan)))&
(![X]:((~curious(X)<~>calm(X))<=>~quiet(X)))&
(![X]:((~tall(X)|~curious(X))=>(curious(X)<~>~patient(X))))&
(((quiet(lucy)&~curious(lucy)))=>(?[X]:(~creative(X))))&
(((calm(fred)&~quiet(fred)))<=>(quiet(john)))&
((~tall(john))<=>(?[X]:((curious(X)<~>~calm(X)))))&
(![X]:((wise(X)|~wise(X))=>(old(X)&calm(X))))&
((?[X]:((~creative(X)|~tall(X))))<=>((tall(fred)&strong(fred))))&
((happy(john))=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((humble(X)|kind(X))<=>(~patient(X)|~wise(X))))&
(![X]:((~curious(X)<~>humble(X))<=>(curious(X)&~kind(X))))&
(![X]:((~patient(X)<~>~tall(X))=>(brave(X)|~quiet(X))))&
(![X]:((~happy(X)<~>old(X))<=>(~humble(X)|curious(X))))&
(((brave(mary)&funny(mary)))<=>((generous(lucy)<~>strong(lucy))))&
(~tall(alice))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((old(X)&rich(X))))&
(?[X]:((~happy(X)|~kind(X))))&
(?[X]:((tall(X)<~>wise(X))))&
((~curious(fred)<~>wise(fred))) | ~calm(lucy) | [
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 8396624993477540274979385
% SZS output start Proof for 8396624993477540274979385
9. ! [X0] : ((~wise(X0) | wise(X0)) => (calm(X0) & old(X0))) [input p8]
24. ~calm(lucy) [input hypothesis]
31. ! [X0] : ((calm(X0) & old(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 9]
105. calm(X0) | ~wise(X0) [cnf transformation 31]
106. calm(X0) | wise(X0) [cnf transformation 31]
149. ~calm(lucy) [cnf transformation 24]
229. calm(X0) [subsumption resolution 105,106]
335. $false [subsumption resolution 149,229]
% SZS output end Proof for 8396624993477540274979385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then susan is both not curious and patient. Everyone who is both wise and quiet is funny and vice versa. If paul is both not old and not rich then someone is either happy or not patient. If john is happy then someone is calm and vice versa. Everyone who is either not strong or not brave is not quiet. If someone is quiet or calm then susan is not wise or kind and vice versa. Everyone who is not funny is not patient. Everyone who is both not quiet and old is not humble and vice versa. If fred is either not strong or not tall then paul is not tall and vice versa. Everyone who is not patient is both quiet and not quiet. If someone is either not rich or brave then mary is both humble and generous. Everyone who is both not quiet and not tall is not brave or brave. If someone is not brave or patient then someone is both not tall and not kind and vice versa. Everyone who is wise or funny is either rich or old and vice versa. Everyone who is creative is either brave or not rich and vice versa. If someone is brave then mary is brave or quiet. Someone is brave. Someone is either curious or not strong. Mary is either strong or creative. Someone is not rich. Susan is both strong and not creative. Paul is either not creative or tall. | John is wise. | entailment | ((?[X]:(~rich(X)))=>((~curious(susan)&patient(susan))))&
(![X]:((wise(X)&quiet(X))<=>funny(X)))&
(((~old(paul)&~rich(paul)))=>(?[X]:((happy(X)<~>~patient(X)))))&
((happy(john))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)<~>~brave(X))=>~quiet(X)))&
((?[X]:((quiet(X)|calm(X))))<=>((~wise(susan)|kind(susan))))&
(![X]:(~funny(X)=>~patient(X)))&
(![X]:((~quiet(X)&old(X))<=>~humble(X)))&
(((~strong(fred)<~>~tall(fred)))<=>(~tall(paul)))&
(![X]:(~patient(X)=>(quiet(X)&~quiet(X))))&
((?[X]:((~rich(X)<~>brave(X))))=>((humble(mary)&generous(mary))))&
(![X]:((~quiet(X)&~tall(X))=>(~brave(X)|brave(X))))&
((?[X]:((~brave(X)|patient(X))))<=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:((wise(X)|funny(X))<=>(rich(X)<~>old(X))))&
(![X]:(creative(X)<=>(brave(X)<~>~rich(X))))&
((?[X]:(brave(X)))=>((brave(mary)|quiet(mary))))&
(?[X]:(brave(X)))&
(?[X]:((curious(X)<~>~strong(X))))&
((strong(mary)<~>creative(mary)))&
(?[X]:(~rich(X)))&
((strong(susan)&~creative(susan)))&
((~creative(paul)<~>tall(paul))) | wise(john) | [
"p1",
"p6",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 3069189806457269619202311
% SZS output start Proof for 3069189806457269619202311
2. ! [X0] : ((quiet(X0) & wise(X0)) <=> funny(X0)) [input p1]
7. ! [X0] : (~funny(X0) => ~patient(X0)) [input p6]
10. ! [X0] : (~patient(X0) => (~quiet(X0) & quiet(X0))) [input p9]
23. ~wise(john) [input hypothesis]
31. ! [X0] : (~patient(X0) | funny(X0)) [ennf transformation 7]
34. ! [X0] : ((~quiet(X0) & quiet(X0)) | patient(X0)) [ennf transformation 10]
40. ! [X0] : (((quiet(X0) & wise(X0)) | ~funny(X0)) & (funny(X0) | (~quiet(X0) | ~wise(X0)))) [nnf transformation 2]
41. ! [X0] : (((quiet(X0) & wise(X0)) | ~funny(X0)) & (funny(X0) | ~quiet(X0) | ~wise(X0))) [flattening 40]
77. ~funny(X0) | wise(X0) [cnf transformation 41]
89. ~patient(X0) | funny(X0) [cnf transformation 31]
95. quiet(X0) | patient(X0) [cnf transformation 34]
96. ~quiet(X0) | patient(X0) [cnf transformation 34]
126. ~wise(john) [cnf transformation 23]
210. patient(X0) [subsumption resolution 95,96]
269. funny(X0) [resolution 89,210]
272. wise(X1) [resolution 269,77]
288. $false [resolution 272,126]
% SZS output end Proof for 3069189806457269619202311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious is either not humble or calm and vice versa. If alice is not humble or generous then fred is either not humble or not strong. Everyone who is old is not quiet and vice versa. Everyone who is old is not curious or not calm and vice versa. Everyone who is not wise is either happy or not curious and vice versa. Everyone who is calm or not humble is happy or not curious. Everyone who is both creative and not brave is both not brave and not patient. Everyone who is either not rich or not old is humble. Everyone who is brave or not wise is both quiet and strong. If someone is both not generous and creative then lucy is rich or not old and vice versa. Everyone who is not humble or not kind is both generous and not calm and vice versa. If susan is either kind or patient then someone is not quiet or brave and vice versa. If someone is not generous or tall then someone is either curious or generous. If someone is curious then lucy is not rich or rich. Everyone who is not tall or not calm is either kind or quiet and vice versa. Alice is both kind and wise. Mary is both patient and wise. Someone is both tall and not creative. Someone is both creative and wise. Someone is either curious or not humble. | Fred is generous. | contradiction | (![X]:((~happy(X)&~curious(X))<=>(~humble(X)<~>calm(X))))&
(((~humble(alice)|generous(alice)))=>((~humble(fred)<~>~strong(fred))))&
(![X]:(old(X)<=>~quiet(X)))&
(![X]:(old(X)<=>(~curious(X)|~calm(X))))&
(![X]:(~wise(X)<=>(happy(X)<~>~curious(X))))&
(![X]:((calm(X)|~humble(X))=>(happy(X)|~curious(X))))&
(![X]:((creative(X)&~brave(X))=>(~brave(X)&~patient(X))))&
(![X]:((~rich(X)<~>~old(X))=>humble(X)))&
(![X]:((brave(X)|~wise(X))=>(quiet(X)&strong(X))))&
((?[X]:((~generous(X)&creative(X))))<=>((rich(lucy)|~old(lucy))))&
(![X]:((~humble(X)|~kind(X))<=>(generous(X)&~calm(X))))&
(((kind(susan)<~>patient(susan)))<=>(?[X]:((~quiet(X)|brave(X)))))&
((?[X]:((~generous(X)|tall(X))))=>(?[X]:((curious(X)<~>generous(X)))))&
((?[X]:(curious(X)))=>((~rich(lucy)|rich(lucy))))&
(![X]:((~tall(X)|~calm(X))<=>(kind(X)<~>quiet(X))))&
((kind(alice)&wise(alice)))&
((patient(mary)&wise(mary)))&
(?[X]:((tall(X)&~creative(X))))&
(?[X]:((creative(X)&wise(X))))&
(?[X]:((curious(X)<~>~humble(X)))) | generous(fred) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p8",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 8926006977061141171641360
% SZS output start Proof for 8926006977061141171641360
1. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> (~humble(X0) <~> calm(X0))) [input p0]
3. ! [X0] : (old(X0) <=> ~quiet(X0)) [input p2]
4. ! [X0] : (old(X0) <=> (~calm(X0) | ~curious(X0))) [input p3]
5. ! [X0] : (~wise(X0) <=> (happy(X0) <~> ~curious(X0))) [input p4]
6. ! [X0] : ((~humble(X0) | calm(X0)) => (~curious(X0) | happy(X0))) [input p5]
9. ! [X0] : ((~wise(X0) | brave(X0)) => (strong(X0) & quiet(X0))) [input p8]
11. ! [X0] : ((~kind(X0) | ~humble(X0)) <=> (~calm(X0) & generous(X0))) [input p10]
15. ! [X0] : ((~calm(X0) | ~tall(X0)) <=> (kind(X0) <~> quiet(X0))) [input p14]
21. generous(fred) [input hypothesis]
23. ! [X0] : ((happy(X0) <~> ~curious(X0)) => ~wise(X0)) [unused predicate definition removal 5]
25. ! [X0] : (~wise(X0) | (happy(X0) <=> ~curious(X0))) [ennf transformation 23]
26. ! [X0] : ((~curious(X0) | happy(X0)) | (humble(X0) & ~calm(X0))) [ennf transformation 6]
27. ! [X0] : (~curious(X0) | happy(X0) | (humble(X0) & ~calm(X0))) [flattening 26]
31. ! [X0] : ((strong(X0) & quiet(X0)) | (wise(X0) & ~brave(X0))) [ennf transformation 9]
35. ! [X0] : (((~curious(X0) & ~happy(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) & (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (curious(X0) | happy(X0)))) [nnf transformation 1]
36. ! [X0] : (((~curious(X0) & ~happy(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) & (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | curious(X0) | happy(X0))) [flattening 35]
38. ! [X0] : ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0))) [nnf transformation 3]
39. ! [X0] : ((old(X0) | (calm(X0) & curious(X0))) & ((~calm(X0) | ~curious(X0)) | ~old(X0))) [nnf transformation 4]
40. ! [X0] : ((old(X0) | (calm(X0) & curious(X0))) & (~calm(X0) | ~curious(X0) | ~old(X0))) [flattening 39]
41. ! [X0] : (~wise(X0) | ((happy(X0) | curious(X0)) & (~curious(X0) | ~happy(X0)))) [nnf transformation 25]
48. ! [X0] : (((~kind(X0) | ~humble(X0)) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | (kind(X0) & humble(X0)))) [nnf transformation 11]
49. ! [X0] : ((~kind(X0) | ~humble(X0) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | (kind(X0) & humble(X0)))) [flattening 48]
58. ! [X0] : (((~calm(X0) | ~tall(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0)))) & (((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | (calm(X0) & tall(X0)))) [nnf transformation 15]
59. ! [X0] : ((~calm(X0) | ~tall(X0) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0)))) & (((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | (calm(X0) & tall(X0)))) [flattening 58]
69. ~happy(X0) | calm(X0) | humble(X0) [cnf transformation 36]
70. ~calm(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 36]
72. ~calm(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 36]
77. ~quiet(X0) | ~old(X0) [cnf transformation 38]
80. old(X0) | curious(X0) [cnf transformation 40]
81. old(X0) | calm(X0) [cnf transformation 40]
83. ~wise(X0) | happy(X0) | curious(X0) [cnf transformation 41]
85. ~curious(X0) | happy(X0) | humble(X0) [cnf transformation 27]
91. wise(X0) | quiet(X0) [cnf transformation 31]
101. ~calm(X0) | humble(X0) [cnf transformation 49]
102. ~calm(X0) | kind(X0) [cnf transformation 49]
103. ~kind(X0) | ~humble(X0) | calm(X0) | ~generous(X0) [cnf transformation 49]
116. quiet(X0) | kind(X0) | calm(X0) [cnf transformation 59]
131. generous(fred) [cnf transformation 21]
137. 2 <=> humble(fred) [avatar definition]
138. ~humble(fred) <- (~2) [avatar component clause 137]
139. humble(fred) <- (2) [avatar component clause 137]
223. kind(X0) | quiet(X0) [subsumption resolution 116,102]
307. quiet(X1) | curious(X1) | happy(X1) [resolution 83,91]
410. 43 <=> happy(fred) [avatar definition]
411. ~happy(fred) <- (~43) [avatar component clause 410]
412. happy(fred) <- (43) [avatar component clause 410]
414. 44 <=> curious(fred) [avatar definition]
415. ~curious(fred) <- (~44) [avatar component clause 414]
418. 45 <=> calm(fred) [avatar definition]
419. ~calm(fred) <- (~45) [avatar component clause 418]
420. calm(fred) <- (45) [avatar component clause 418]
436. ~generous(X0) | calm(X0) | ~humble(X0) | quiet(X0) [resolution 103,223]
488. curious(X0) | happy(X0) | ~old(X0) [resolution 307,77]
491. curious(X0) | happy(X0) [subsumption resolution 488,80]
502. calm(fred) | ~humble(fred) | quiet(fred) [resolution 436,131]
516. happy(X2) | happy(X2) | humble(X2) [resolution 491,85]
524. humble(X2) | happy(X2) [duplicate literal removal 516]
589. happy(fred) <- (~2) [resolution 524,138]
593. 43 | 2 [avatar split clause 589,137,410]
594. calm(fred) | humble(fred) <- (43) [resolution 412,69]
595. calm(fred) <- (~2, 43) [subsumption resolution 594,138]
596. 45 | 2 | ~43 [avatar split clause 595,410,137,418]
599. ~humble(fred) | ~curious(fred) <- (45) [resolution 420,72]
600. ~humble(fred) | ~happy(fred) <- (45) [resolution 420,70]
602. humble(fred) <- (45) [resolution 420,101]
605. 2 | ~45 [avatar split clause 602,418,137]
606. ~humble(fred) <- (43, 45) [subsumption resolution 600,412]
607. ~2 | ~43 | ~45 [avatar split clause 606,418,410,137]
608. ~44 | ~2 | ~45 [avatar split clause 599,418,137,414]
609. calm(fred) | quiet(fred) <- (2) [subsumption resolution 502,139]
611. 58 <=> quiet(fred) [avatar definition]
613. quiet(fred) <- (58) [avatar component clause 611]
614. 58 | 45 | ~2 [avatar split clause 609,137,418,611]
618. ~old(fred) <- (58) [resolution 613,77]
620. calm(fred) <- (58) [resolution 618,81]
622. $false <- (~45, 58) [subsumption resolution 620,419]
623. 45 | ~58 [avatar contradiction clause 622]
625. happy(fred) <- (~44) [resolution 415,491]
626. $false <- (~43, ~44) [subsumption resolution 625,411]
627. 43 | 44 [avatar contradiction clause 626]
628. $false [avatar sat refutation 593,596,605,607,608,614,623,627]
% SZS output end Proof for 8926006977061141171641360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then susan is not kind and vice versa.
Everyone who is not humble is either generous or not calm.
If someone is either creative or not funny then someone is either not calm or old.
Everyone who is not rich is either curious or wise and vice versa.
If john is either creative or not tall then paul is kind.
If paul is not tall or wise then susan is not tall and vice versa.
Everyone who is not tall is either not patient or kind.
Everyone who is happy is funny and vice versa.
If someone is both funny and happy then someone is rich.
Everyone who is either not tall or kind is both not calm and humble.
If john is not rich or brave then fred is calm and vice versa.
Everyone who is both not wise and kind is tall and vice versa.
If lucy is both not funny and not calm then susan is rich or not tall.
If someone is not funny or happy then someone is both kind and old.
If susan is both tall and humble then paul is not humble and vice versa.
Everyone who is not patient is patient.
Alice is either not curious or rich.
Someone is both strong and not old.
Someone is both patient and not happy.
Someone is old.
Lucy is either not tall or not rich.
Paul is both creative and old. | Alice is not wise. | contradiction | ((?[X]:(~wise(X)))<=>(~kind(susan)))&
(![X]:(~humble(X)=>(generous(X)<~>~calm(X))))&
((?[X]:((creative(X)<~>~funny(X))))=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:(~rich(X)<=>(curious(X)<~>wise(X))))&
(((creative(john)<~>~tall(john)))=>(kind(paul)))&
(((~tall(paul)|wise(paul)))<=>(~tall(susan)))&
(![X]:(~tall(X)=>(~patient(X)<~>kind(X))))&
(![X]:(happy(X)<=>funny(X)))&
((?[X]:((funny(X)&happy(X))))=>(?[X]:(rich(X))))&
(![X]:((~tall(X)<~>kind(X))=>(~calm(X)&humble(X))))&
(((~rich(john)|brave(john)))<=>(calm(fred)))&
(![X]:((~wise(X)&kind(X))<=>tall(X)))&
(((~funny(lucy)&~calm(lucy)))=>((rich(susan)|~tall(susan))))&
((?[X]:((~funny(X)|happy(X))))=>(?[X]:((kind(X)&old(X)))))&
(((tall(susan)&humble(susan)))<=>(~humble(paul)))&
(![X]:(~patient(X)=>patient(X)))&
((~curious(alice)<~>rich(alice)))&
(?[X]:((strong(X)&~old(X))))&
(?[X]:((patient(X)&~happy(X))))&
(?[X]:(old(X)))&
((~tall(lucy)<~>~rich(lucy)))&
((creative(paul)&old(paul))) | ~wise(alice) | [
"p3",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 2926308687540726683790485
% SZS output start Proof for 2926308687540726683790485
4. ! [X0] : (~rich(X0) <=> (curious(X0) <~> wise(X0))) [input p3]
17. ~curious(alice) <~> rich(alice) [input p16]
23. ~wise(alice) [input hypothesis]
49. ! [X0] : ((~rich(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | rich(X0))) [nnf transformation 4]
67. (~rich(alice) | curious(alice)) & (rich(alice) | ~curious(alice)) [nnf transformation 17]
83. curious(X0) | wise(X0) | rich(X0) [cnf transformation 49]
85. ~curious(X0) | wise(X0) | ~rich(X0) [cnf transformation 49]
115. rich(alice) | ~curious(alice) [cnf transformation 67]
116. ~rich(alice) | curious(alice) [cnf transformation 67]
125. ~wise(alice) [cnf transformation 23]
254. 28 <=> curious(alice) [avatar definition]
255. ~curious(alice) <- (~28) [avatar component clause 254]
256. curious(alice) <- (28) [avatar component clause 254]
258. 29 <=> rich(alice) [avatar definition]
259. rich(alice) <- (29) [avatar component clause 258]
260. ~rich(alice) <- (~29) [avatar component clause 258]
261. 28 | ~29 [avatar split clause 116,258,254]
262. ~28 | 29 [avatar split clause 115,258,254]
292. wise(alice) | rich(alice) <- (~28) [resolution 83,255]
293. rich(alice) <- (~28) [subsumption resolution 292,125]
294. $false <- (~28, ~29) [subsumption resolution 293,260]
295. 28 | 29 [avatar contradiction clause 294]
301. wise(alice) | ~rich(alice) <- (28) [resolution 85,256]
303. ~rich(alice) <- (28) [subsumption resolution 301,125]
304. $false <- (28, 29) [subsumption resolution 303,259]
305. ~28 | ~29 [avatar contradiction clause 304]
306. $false [avatar sat refutation 261,262,295,305]
% SZS output end Proof for 2926308687540726683790485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and patient then susan is either not brave or not humble.
Everyone who is both not curious and not humble is not old.
If someone is happy or not creative then mary is either humble or generous.
Everyone who is not patient is both calm and kind.
If someone is not kind then fred is generous.
Everyone who is either not humble or not funny is both not quiet and quiet.
Everyone who is either not strong or quiet is either creative or not old and vice versa.
Everyone who is both not rich and not strong is both not humble and not old.
If someone is tall then lucy is either not kind or not old and vice versa.
If someone is patient then mary is both patient and tall.
Everyone who is either not old or tall is either happy or wise and vice versa.
If alice is either not curious or not wise then someone is not creative.
Everyone who is not funny is both creative and happy.
Everyone who is creative is not creative or rich and vice versa.
If lucy is wise then alice is curious or humble.
If someone is not strong then someone is not strong or not wise and vice versa.
Mary is either rich or not tall.
Paul is patient.
John is not funny.
Someone is not calm or not rich.
Someone is either not kind or rich.
Someone is funny or not quiet.
Paul is not brave or not creative.
Mary is not funny or not calm. | John is not creative. | contradiction | ((?[X]:((generous(X)&patient(X))))=>((~brave(susan)<~>~humble(susan))))&
(![X]:((~curious(X)&~humble(X))=>~old(X)))&
((?[X]:((happy(X)|~creative(X))))=>((humble(mary)<~>generous(mary))))&
(![X]:(~patient(X)=>(calm(X)&kind(X))))&
((?[X]:(~kind(X)))=>(generous(fred)))&
(![X]:((~humble(X)<~>~funny(X))=>(~quiet(X)&quiet(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>(creative(X)<~>~old(X))))&
(![X]:((~rich(X)&~strong(X))=>(~humble(X)&~old(X))))&
((?[X]:(tall(X)))<=>((~kind(lucy)<~>~old(lucy))))&
((?[X]:(patient(X)))=>((patient(mary)&tall(mary))))&
(![X]:((~old(X)<~>tall(X))<=>(happy(X)<~>wise(X))))&
(((~curious(alice)<~>~wise(alice)))=>(?[X]:(~creative(X))))&
(![X]:(~funny(X)=>(creative(X)&happy(X))))&
(![X]:(creative(X)<=>(~creative(X)|rich(X))))&
((wise(lucy))=>((curious(alice)|humble(alice))))&
((?[X]:(~strong(X)))<=>(?[X]:((~strong(X)|~wise(X)))))&
((rich(mary)<~>~tall(mary)))&
(patient(paul))&
(~funny(john))&
(?[X]:((~calm(X)|~rich(X))))&
(?[X]:((~kind(X)<~>rich(X))))&
(?[X]:((funny(X)|~quiet(X))))&
((~brave(paul)|~creative(paul)))&
((~funny(mary)|~calm(mary))) | ~creative(john) | [
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 506985091724340084870427
% SZS output start Proof for 506985091724340084870427
14. ! [X0] : (creative(X0) <=> (rich(X0) | ~creative(X0))) [input p13]
25. ~creative(john) [input hypothesis]
53. ! [X0] : ((creative(X0) | (~rich(X0) & creative(X0))) & ((rich(X0) | ~creative(X0)) | ~creative(X0))) [nnf transformation 14]
54. ! [X0] : ((creative(X0) | (~rich(X0) & creative(X0))) & (rich(X0) | ~creative(X0) | ~creative(X0))) [flattening 53]
111. creative(X0) | creative(X0) [cnf transformation 54]
127. ~creative(john) [cnf transformation 25]
129. creative(X0) [duplicate literal removal 111]
144. 4 <=> ! [X0] : creative(X0) [avatar definition]
145. creative(X0) <- (4) [avatar component clause 144]
217. 4 [avatar split clause 129,144]
300. $false <- (4) [resolution 145,127]
301. ~4 [avatar contradiction clause 300]
302. $false [avatar sat refutation 217,301]
% SZS output end Proof for 506985091724340084870427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and kind is tall or not rich and vice versa. If someone is rich or brave then someone is not old and vice versa. Everyone who is either not kind or kind is curious and vice versa. Everyone who is patient is happy and vice versa. Everyone who is not wise or not calm is calm or not generous. If lucy is generous then someone is both humble and brave and vice versa. If john is not strong or not brave then someone is kind or strong and vice versa. Everyone who is rich is either creative or calm and vice versa. If someone is both funny and not funny then someone is both not patient and not tall and vice versa. If someone is either calm or not tall then someone is either generous or not wise. Everyone who is kind or not generous is quiet or creative and vice versa. If mary is both wise and calm then lucy is brave or not funny. Everyone who is both humble and not quiet is both wise and not humble and vice versa. Everyone who is either not rich or brave is either quiet or happy and vice versa. Everyone who is not old or humble is not rich or strong and vice versa. If john is either not patient or funny then someone is both not tall and generous and vice versa. John is both calm and not kind. Someone is not patient or not funny. Someone is wise or patient. Alice is either humble or not curious. Someone is both not rich and not old. Someone is either generous or funny. | Lucy is not generous. | entailment | (![X]:((~quiet(X)&kind(X))<=>(tall(X)|~rich(X))))&
((?[X]:((rich(X)|brave(X))))<=>(?[X]:(~old(X))))&
(![X]:((~kind(X)<~>kind(X))<=>curious(X)))&
(![X]:(patient(X)<=>happy(X)))&
(![X]:((~wise(X)|~calm(X))=>(calm(X)|~generous(X))))&
((generous(lucy))<=>(?[X]:((humble(X)&brave(X)))))&
(((~strong(john)|~brave(john)))<=>(?[X]:((kind(X)|strong(X)))))&
(![X]:(rich(X)<=>(creative(X)<~>calm(X))))&
((?[X]:((funny(X)&~funny(X))))<=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:((calm(X)<~>~tall(X))))=>(?[X]:((generous(X)<~>~wise(X)))))&
(![X]:((kind(X)|~generous(X))<=>(quiet(X)|creative(X))))&
(((wise(mary)&calm(mary)))=>((brave(lucy)|~funny(lucy))))&
(![X]:((humble(X)&~quiet(X))<=>(wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((~old(X)|humble(X))<=>(~rich(X)|strong(X))))&
(((~patient(john)<~>funny(john)))<=>(?[X]:((~tall(X)&generous(X)))))&
((calm(john)&~kind(john)))&
(?[X]:((~patient(X)|~funny(X))))&
(?[X]:((wise(X)|patient(X))))&
((humble(alice)<~>~curious(alice)))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:((generous(X)<~>funny(X)))) | ~generous(lucy) | [
"p0",
"p3",
"p5",
"p8",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 4060214071782155051917221
% SZS output start Proof for 4060214071782155051917221
1. ! [X0] : ((kind(X0) & ~quiet(X0)) <=> (~rich(X0) | tall(X0))) [input p0]
4. ! [X0] : (patient(X0) <=> happy(X0)) [input p3]
6. generous(lucy) <=> ? [X0] : (brave(X0) & humble(X0)) [input p5]
9. ? [X0] : (~funny(X0) & funny(X0)) <=> ? [X0] : (~tall(X0) & ~patient(X0)) [input p8]
13. ! [X0] : ((~quiet(X0) & humble(X0)) <=> (~humble(X0) & wise(X0))) [input p12]
14. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (quiet(X0) <~> happy(X0))) [input p13]
23. generous(lucy) [input hypothesis]
25. ? [X0] : (~funny(X0) & funny(X0)) <=> ? [X1] : (~tall(X1) & ~patient(X1)) [rectify 9]
32. ! [X0] : (((kind(X0) & ~quiet(X0)) | (rich(X0) & ~tall(X0))) & ((~rich(X0) | tall(X0)) | (~kind(X0) | quiet(X0)))) [nnf transformation 1]
33. ! [X0] : (((kind(X0) & ~quiet(X0)) | (rich(X0) & ~tall(X0))) & (~rich(X0) | tall(X0) | ~kind(X0) | quiet(X0))) [flattening 32]
40. ! [X0] : ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0))) [nnf transformation 4]
41. (generous(lucy) | ! [X0] : (~brave(X0) | ~humble(X0))) & (? [X0] : (brave(X0) & humble(X0)) | ~generous(lucy)) [nnf transformation 6]
42. (generous(lucy) | ! [X0] : (~brave(X0) | ~humble(X0))) & (? [X1] : (brave(X1) & humble(X1)) | ~generous(lucy)) [rectify 41]
43. ? [X1] : (brave(X1) & humble(X1)) => (brave(sK2) & humble(sK2)) [choice axiom]
44. (generous(lucy) | ! [X0] : (~brave(X0) | ~humble(X0))) & ((brave(sK2) & humble(sK2)) | ~generous(lucy)) [skolemisation 42,43]
51. (? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : (tall(X1) | patient(X1))) & (? [X1] : (~tall(X1) & ~patient(X1)) | ! [X0] : (funny(X0) | ~funny(X0))) [nnf transformation 25]
52. (? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : (tall(X1) | patient(X1))) & (? [X2] : (~tall(X2) & ~patient(X2)) | ! [X3] : (funny(X3) | ~funny(X3))) [rectify 51]
53. ? [X0] : (~funny(X0) & funny(X0)) => (~funny(sK4) & funny(sK4)) [choice axiom]
54. ? [X2] : (~tall(X2) & ~patient(X2)) => (~tall(sK5) & ~patient(sK5)) [choice axiom]
55. ((~funny(sK4) & funny(sK4)) | ! [X1] : (tall(X1) | patient(X1))) & ((~tall(sK5) & ~patient(sK5)) | ! [X3] : (funny(X3) | ~funny(X3))) [skolemisation 52,54,53]
62. ! [X0] : (((~quiet(X0) & humble(X0)) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | (quiet(X0) | ~humble(X0)))) [nnf transformation 13]
63. ! [X0] : (((~quiet(X0) & humble(X0)) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | quiet(X0) | ~humble(X0))) [flattening 62]
64. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 14]
82. ~tall(X0) | ~quiet(X0) [cnf transformation 33]
83. ~quiet(X0) | rich(X0) [cnf transformation 33]
93. ~patient(X0) | happy(X0) [cnf transformation 40]
97. humble(sK2) | ~generous(lucy) [cnf transformation 44]
98. brave(sK2) | ~generous(lucy) [cnf transformation 44]
110. funny(sK4) | tall(X1) | patient(X1) [cnf transformation 55]
111. ~funny(sK4) | tall(X1) | patient(X1) [cnf transformation 55]
122. ~humble(X0) | quiet(X0) | ~humble(X0) [cnf transformation 63]
128. ~happy(X0) | ~quiet(X0) | ~rich(X0) | ~brave(X0) [cnf transformation 64]
132. ~brave(X0) | rich(X0) | quiet(X0) | ~happy(X0) [cnf transformation 64]
153. generous(lucy) [cnf transformation 23]
154. ~humble(X0) | quiet(X0) [duplicate literal removal 122]
188. 8 <=> generous(lucy) [avatar definition]
193. 9 <=> brave(sK2) [avatar definition]
195. brave(sK2) <- (9) [avatar component clause 193]
196. ~8 | 9 [avatar split clause 98,193,188]
198. 10 <=> humble(sK2) [avatar definition]
200. humble(sK2) <- (10) [avatar component clause 198]
201. ~8 | 10 [avatar split clause 97,198,188]
229. 17 <=> ! [X1] : (tall(X1) | patient(X1)) [avatar definition]
230. patient(X1) | tall(X1) <- (17) [avatar component clause 229]
232. 18 <=> funny(sK4) [avatar definition]
235. 17 | ~18 [avatar split clause 111,232,229]
236. 17 | 18 [avatar split clause 110,232,229]
272. ~happy(X0) | rich(X0) | ~brave(X0) [subsumption resolution 132,83]
274. ~happy(X0) | ~quiet(X0) | ~brave(X0) [subsumption resolution 128,272]
330. 8 [avatar split clause 153,188]
338. quiet(sK2) <- (10) [resolution 154,200]
348. happy(X0) | tall(X0) <- (17) [resolution 230,93]
618. tall(X1) | ~quiet(X1) | ~brave(X1) <- (17) [resolution 348,274]
621. ~brave(X1) | ~quiet(X1) <- (17) [subsumption resolution 618,82]
780. ~quiet(sK2) <- (9, 17) [resolution 621,195]
783. $false <- (9, 10, 17) [subsumption resolution 780,338]
784. ~9 | ~10 | ~17 [avatar contradiction clause 783]
787. $false [avatar sat refutation 196,201,235,236,330,784]
% SZS output end Proof for 4060214071782155051917221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either tall or rich then someone is both patient and not brave.
Everyone who is both patient and not kind is creative and vice versa.
If mary is both not happy and not tall then susan is happy or not wise and vice versa.
Everyone who is generous or kind is either not humble or brave and vice versa.
Everyone who is not quiet is both not patient and not creative.
Everyone who is humble or not wise is either creative or not happy.
If someone is either not tall or calm then someone is either patient or curious.
If paul is both curious and not tall then someone is not humble and vice versa.
Everyone who is not brave or not patient is either brave or not strong.
If someone is either not quiet or not generous then paul is either not calm or not old.
If someone is both creative and not quiet then paul is old or not kind and vice versa.
If someone is patient or generous then mary is not rich or wise.
Everyone who is not curious or not kind is either not rich or calm and vice versa.
If mary is either not patient or not kind then someone is generous or not tall.
If someone is both not humble and not creative then lucy is both not patient and brave.
If someone is both brave and curious then fred is not quiet.
Susan is funny.
Lucy is creative.
Someone is humble or tall.
Someone is both not kind and not rich.
Lucy is either not patient or patient.
John is not wise or not kind.
Mary is both generous and not old.
Someone is not generous. | Paul is not brave. | contradiction | (((tall(paul)<~>rich(paul)))=>(?[X]:((patient(X)&~brave(X)))))&
(![X]:((patient(X)&~kind(X))<=>creative(X)))&
(((~happy(mary)&~tall(mary)))<=>((happy(susan)|~wise(susan))))&
(![X]:((generous(X)|kind(X))<=>(~humble(X)<~>brave(X))))&
(![X]:(~quiet(X)=>(~patient(X)&~creative(X))))&
(![X]:((humble(X)|~wise(X))=>(creative(X)<~>~happy(X))))&
((?[X]:((~tall(X)<~>calm(X))))=>(?[X]:((patient(X)<~>curious(X)))))&
(((curious(paul)&~tall(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)|~patient(X))=>(brave(X)<~>~strong(X))))&
((?[X]:((~quiet(X)<~>~generous(X))))=>((~calm(paul)<~>~old(paul))))&
((?[X]:((creative(X)&~quiet(X))))<=>((old(paul)|~kind(paul))))&
((?[X]:((patient(X)|generous(X))))=>((~rich(mary)|wise(mary))))&
(![X]:((~curious(X)|~kind(X))<=>(~rich(X)<~>calm(X))))&
(((~patient(mary)<~>~kind(mary)))=>(?[X]:((generous(X)|~tall(X)))))&
((?[X]:((~humble(X)&~creative(X))))=>((~patient(lucy)&brave(lucy))))&
((?[X]:((brave(X)&curious(X))))=>(~quiet(fred)))&
(funny(susan))&
(creative(lucy))&
(?[X]:((humble(X)|tall(X))))&
(?[X]:((~kind(X)&~rich(X))))&
((~patient(lucy)<~>patient(lucy)))&
((~wise(john)|~kind(john)))&
((generous(mary)&~old(mary)))&
(?[X]:(~generous(X))) | ~brave(paul) | [
"p1",
"p3",
"p4",
"p10",
"p14",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 7217994479950586733779713
% SZS output start Proof for 7217994479950586733779713
2. ! [X0] : ((~kind(X0) & patient(X0)) <=> creative(X0)) [input p1]
4. ! [X0] : ((kind(X0) | generous(X0)) <=> (~humble(X0) <~> brave(X0))) [input p3]
5. ! [X0] : (~quiet(X0) => (~creative(X0) & ~patient(X0))) [input p4]
11. ? [X0] : (~quiet(X0) & creative(X0)) <=> (~kind(paul) | old(paul)) [input p10]
15. ? [X0] : (~creative(X0) & ~humble(X0)) => (brave(lucy) & ~patient(lucy)) [input p14]
18. creative(lucy) [input p17]
25. ~brave(paul) [input hypothesis]
29. ! [X0] : ((~creative(X0) & ~patient(X0)) | quiet(X0)) [ennf transformation 5]
37. (brave(lucy) & ~patient(lucy)) | ! [X0] : (creative(X0) | humble(X0)) [ennf transformation 15]
42. ! [X0] : (((~kind(X0) & patient(X0)) | ~creative(X0)) & (creative(X0) | (kind(X0) | ~patient(X0)))) [nnf transformation 2]
43. ! [X0] : (((~kind(X0) & patient(X0)) | ~creative(X0)) & (creative(X0) | kind(X0) | ~patient(X0))) [flattening 42]
46. ! [X0] : (((kind(X0) | generous(X0)) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0)))) & (((~brave(X0) | humble(X0)) & (brave(X0) | ~humble(X0))) | (~kind(X0) & ~generous(X0)))) [nnf transformation 4]
47. ! [X0] : ((kind(X0) | generous(X0) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0)))) & (((~brave(X0) | humble(X0)) & (brave(X0) | ~humble(X0))) | (~kind(X0) & ~generous(X0)))) [flattening 46]
60. (? [X0] : (~quiet(X0) & creative(X0)) | (kind(paul) & ~old(paul))) & ((~kind(paul) | old(paul)) | ! [X0] : (quiet(X0) | ~creative(X0))) [nnf transformation 11]
61. (? [X0] : (~quiet(X0) & creative(X0)) | (kind(paul) & ~old(paul))) & (~kind(paul) | old(paul) | ! [X0] : (quiet(X0) | ~creative(X0))) [flattening 60]
62. (? [X0] : (~quiet(X0) & creative(X0)) | (kind(paul) & ~old(paul))) & (~kind(paul) | old(paul) | ! [X1] : (quiet(X1) | ~creative(X1))) [rectify 61]
63. ? [X0] : (~quiet(X0) & creative(X0)) => (~quiet(sK3) & creative(sK3)) [choice axiom]
64. ((~quiet(sK3) & creative(sK3)) | (kind(paul) & ~old(paul))) & (~kind(paul) | old(paul) | ! [X1] : (quiet(X1) | ~creative(X1))) [skolemisation 62,63]
82. ~creative(X0) | patient(X0) [cnf transformation 43]
83. ~creative(X0) | ~kind(X0) [cnf transformation 43]
90. ~humble(X0) | brave(X0) | ~kind(X0) [cnf transformation 47]
96. ~creative(X0) | quiet(X0) [cnf transformation 29]
118. creative(sK3) | kind(paul) [cnf transformation 64]
120. ~quiet(sK3) | kind(paul) [cnf transformation 64]
131. ~patient(lucy) | creative(X0) | humble(X0) [cnf transformation 37]
134. creative(lucy) [cnf transformation 18]
144. ~brave(paul) [cnf transformation 25]
238. 20 <=> kind(paul) [avatar definition]
240. kind(paul) <- (20) [avatar component clause 238]
242. 21 <=> quiet(sK3) [avatar definition]
244. ~quiet(sK3) <- (~21) [avatar component clause 242]
245. 20 | ~21 [avatar split clause 120,242,238]
248. 22 <=> creative(sK3) [avatar definition]
250. creative(sK3) <- (22) [avatar component clause 248]
251. 20 | 22 [avatar split clause 118,248,238]
288. 31 <=> ! [X0] : (creative(X0) | humble(X0)) [avatar definition]
289. humble(X0) | creative(X0) <- (31) [avatar component clause 288]
296. 33 <=> patient(lucy) [avatar definition]
299. 31 | ~33 [avatar split clause 131,296,288]
326. patient(lucy) [resolution 82,134]
327. 33 [avatar split clause 326,296]
347. brave(X0) | ~kind(X0) | creative(X0) <- (31) [resolution 90,289]
350. ~kind(X0) | brave(X0) <- (31) [subsumption resolution 347,83]
352. brave(paul) <- (20, 31) [resolution 350,240]
353. $false <- (20, 31) [subsumption resolution 352,144]
354. ~20 | ~31 [avatar contradiction clause 353]
355. quiet(sK3) <- (22) [resolution 250,96]
358. $false <- (~21, 22) [subsumption resolution 355,244]
359. 21 | ~22 [avatar contradiction clause 358]
360. $false [avatar sat refutation 245,251,299,327,354,359]
% SZS output end Proof for 7217994479950586733779713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or quiet is either not generous or generous and vice versa. If someone is not calm then someone is old or not funny and vice versa. Everyone who is not brave is kind and vice versa. Everyone who is either not happy or strong is both not rich and not calm. Everyone who is tall or strong is both not curious and wise and vice versa. If someone is both old and not kind then someone is humble. If susan is both funny and patient then someone is either not strong or rich and vice versa. Everyone who is both kind and brave is either not strong or kind. Everyone who is both tall and not brave is happy. If someone is either not generous or not rich then someone is not rich or kind. Everyone who is not humble or not generous is either patient or strong and vice versa. Everyone who is either humble or not wise is either not calm or humble. If mary is either not generous or not happy then someone is both not funny and tall and vice versa. Everyone who is not funny is not rich or quiet. If mary is not calm then john is not rich and vice versa. Everyone who is either funny or calm is both creative and brave and vice versa. John is either not creative or not old. Someone is brave or tall. Mary is rich. Someone is not old or not generous. Lucy is either not strong or humble. Someone is not quiet or quiet. Someone is calm. Mary is both calm and quiet. | Mary is not generous. | neutral | (![X]:((wise(X)<~>quiet(X))<=>(~generous(X)<~>generous(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((old(X)|~funny(X)))))&
(![X]:(~brave(X)<=>kind(X)))&
(![X]:((~happy(X)<~>strong(X))=>(~rich(X)&~calm(X))))&
(![X]:((tall(X)|strong(X))<=>(~curious(X)&wise(X))))&
((?[X]:((old(X)&~kind(X))))=>(?[X]:(humble(X))))&
(((funny(susan)&patient(susan)))<=>(?[X]:((~strong(X)<~>rich(X)))))&
(![X]:((kind(X)&brave(X))=>(~strong(X)<~>kind(X))))&
(![X]:((tall(X)&~brave(X))=>happy(X)))&
((?[X]:((~generous(X)<~>~rich(X))))=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~humble(X)|~generous(X))<=>(patient(X)<~>strong(X))))&
(![X]:((humble(X)<~>~wise(X))=>(~calm(X)<~>humble(X))))&
(((~generous(mary)<~>~happy(mary)))<=>(?[X]:((~funny(X)&tall(X)))))&
(![X]:(~funny(X)=>(~rich(X)|quiet(X))))&
((~calm(mary))<=>(~rich(john)))&
(![X]:((funny(X)<~>calm(X))<=>(creative(X)&brave(X))))&
((~creative(john)<~>~old(john)))&
(?[X]:((brave(X)|tall(X))))&
(rich(mary))&
(?[X]:((~old(X)|~generous(X))))&
((~strong(lucy)<~>humble(lucy)))&
(?[X]:((~quiet(X)|quiet(X))))&
(?[X]:(calm(X)))&
((calm(mary)&quiet(mary))) | ~generous(mary) | []
| null | 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.