premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is either not humble or generous then john is not creative and vice versa.
Everyone who is generous or not quiet is either not strong or not funny.
If someone is both not creative and wise then john is quiet and vice versa.
Everyone who is not rich is not calm or not wise.
Everyone who is both generous and not patient is patient and vice versa.
If someone is not strong or not brave then john is both not patient and creative and vice versa.
Everyone who is not generous is brave or not rich and vice versa.
Everyone who is either funny or not creative is either calm or wise and vice versa.
Everyone who is either quiet or not old is both not strong and not quiet.
Everyone who is happy is either happy or strong.
If someone is either creative or patient then someone is creative.
If someone is either not generous or not wise then someone is either humble or not happy and vice versa.
Everyone who is creative or not calm is both creative and generous.
If john is not funny or brave then someone is either kind or not curious and vice versa.
Everyone who is either not tall or not funny is both generous and quiet and vice versa.
Someone is not wise or creative.
Alice is both not old and funny.
Susan is either happy or old.
Someone is both not rich and strong.
Someone is quiet or old. | John is not happy. | entailment | ((?[X]:((~humble(X)<~>generous(X))))<=>(~creative(john)))&
(![X]:((generous(X)|~quiet(X))=>(~strong(X)<~>~funny(X))))&
((?[X]:((~creative(X)&wise(X))))<=>(quiet(john)))&
(![X]:(~rich(X)=>(~calm(X)|~wise(X))))&
(![X]:((generous(X)&~patient(X))<=>patient(X)))&
((?[X]:((~strong(X)|~brave(X))))<=>((~patient(john)&creative(john))))&
(![X]:(~generous(X)<=>(brave(X)|~rich(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)<~>wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~strong(X)&~quiet(X))))&
(![X]:(happy(X)=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:(creative(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((creative(X)|~calm(X))=>(creative(X)&generous(X))))&
(((~funny(john)|brave(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~tall(X)<~>~funny(X))<=>(generous(X)&quiet(X))))&
(?[X]:((~wise(X)|creative(X))))&
((~old(alice)&funny(alice)))&
((happy(susan)<~>old(susan)))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((quiet(X)|old(X)))) | ~happy(john) | [
"p4",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1752391299733612775686514
% SZS output start Proof for 1752391299733612775686514
5. ! [X0] : ((~patient(X0) & generous(X0)) <=> patient(X0)) [input p4]
6. ? [X0] : (~brave(X0) | ~strong(X0)) <=> (creative(john) & ~patient(john)) [input p5]
10. ! [X0] : (happy(X0) => (happy(X0) <~> strong(X0))) [input p9]
13. ! [X0] : ((~calm(X0) | creative(X0)) => (generous(X0) & creative(X0))) [input p12]
21. happy(john) [input hypothesis]
28. ! [X0] : ((happy(X0) <~> strong(X0)) | ~happy(X0)) [ennf transformation 10]
30. ! [X0] : ((generous(X0) & creative(X0)) | (calm(X0) & ~creative(X0))) [ennf transformation 13]
40. ! [X0] : (((~patient(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) | ~generous(X0)))) [nnf transformation 5]
41. ! [X0] : (((~patient(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | patient(X0) | ~generous(X0))) [flattening 40]
42. (? [X0] : (~brave(X0) | ~strong(X0)) | (~creative(john) | patient(john))) & ((creative(john) & ~patient(john)) | ! [X0] : (brave(X0) & strong(X0))) [nnf transformation 6]
43. (? [X0] : (~brave(X0) | ~strong(X0)) | ~creative(john) | patient(john)) & ((creative(john) & ~patient(john)) | ! [X0] : (brave(X0) & strong(X0))) [flattening 42]
44. (? [X0] : (~brave(X0) | ~strong(X0)) | ~creative(john) | patient(john)) & ((creative(john) & ~patient(john)) | ! [X1] : (brave(X1) & strong(X1))) [rectify 43]
45. ? [X0] : (~brave(X0) | ~strong(X0)) => (~brave(sK2) | ~strong(sK2)) [choice axiom]
46. ((~brave(sK2) | ~strong(sK2)) | ~creative(john) | patient(john)) & ((creative(john) & ~patient(john)) | ! [X1] : (brave(X1) & strong(X1))) [skolemisation 44,45]
51. ! [X0] : (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | ~happy(X0)) [nnf transformation 28]
87. patient(X0) | patient(X0) | ~generous(X0) [cnf transformation 41]
89. ~patient(X0) | ~patient(X0) [cnf transformation 41]
92. creative(john) | strong(X1) [cnf transformation 46]
111. ~strong(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 51]
124. generous(X0) | ~creative(X0) [cnf transformation 30]
146. happy(john) [cnf transformation 21]
147. ~happy(X0) | ~strong(X0) [duplicate literal removal 111]
149. patient(X0) | ~generous(X0) [duplicate literal removal 87]
150. ~patient(X0) [duplicate literal removal 89]
152. 1 <=> creative(john) [avatar definition]
154. creative(john) <- (1) [avatar component clause 152]
191. ~generous(X0) [subsumption resolution 149,150]
207. 13 <=> ! [X1] : strong(X1) [avatar definition]
208. strong(X1) <- (13) [avatar component clause 207]
209. 13 | 1 [avatar split clause 92,152,207]
213. 14 <=> ! [X1] : ~creative(X1) [avatar definition]
214. ~creative(X1) <- (14) [avatar component clause 213]
250. ~creative(X0) [subsumption resolution 124,191]
251. 14 [avatar split clause 250,213]
310. ~strong(john) [resolution 147,146]
312. $false <- (13) [subsumption resolution 310,208]
313. ~13 [avatar contradiction clause 312]
317. $false <- (1, 14) [subsumption resolution 154,214]
318. ~1 | ~14 [avatar contradiction clause 317]
319. $false [avatar sat refutation 209,251,313,318]
% SZS output end Proof for 1752391299733612775686514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and brave is not calm or not tall and vice versa. Everyone who is wise or not kind is not humble or funny. If alice is not creative or humble then someone is both tall and rich and vice versa. Everyone who is either not brave or patient is either not brave or wise and vice versa. If john is both not old and not funny then paul is either tall or quiet and vice versa. Everyone who is creative is not quiet or not patient and vice versa. If someone is creative or not old then someone is not old and vice versa. If susan is creative or tall then someone is either not calm or not funny and vice versa. Everyone who is not rich or brave is both strong and old and vice versa. If someone is kind or brave then john is both quiet and calm and vice versa. If someone is quiet then paul is both not quiet and patient and vice versa. If someone is both old and not quiet then someone is either not wise or humble and vice versa. Everyone who is either happy or not happy is both not funny and strong. If someone is generous or brave then someone is both funny and brave. If someone is either patient or humble then mary is curious or funny. Paul is both not humble and not happy. Someone is not rich or not quiet. Someone is not rich. Someone is calm or not funny. Alice is creative or not funny. John is either not strong or curious. Someone is generous or not kind. | Paul is not patient. | contradiction | (![X]:((~calm(X)&brave(X))<=>(~calm(X)|~tall(X))))&
(![X]:((wise(X)|~kind(X))=>(~humble(X)|funny(X))))&
(((~creative(alice)|humble(alice)))<=>(?[X]:((tall(X)&rich(X)))))&
(![X]:((~brave(X)<~>patient(X))<=>(~brave(X)<~>wise(X))))&
(((~old(john)&~funny(john)))<=>((tall(paul)<~>quiet(paul))))&
(![X]:(creative(X)<=>(~quiet(X)|~patient(X))))&
((?[X]:((creative(X)|~old(X))))<=>(?[X]:(~old(X))))&
(((creative(susan)|tall(susan)))<=>(?[X]:((~calm(X)<~>~funny(X)))))&
(![X]:((~rich(X)|brave(X))<=>(strong(X)&old(X))))&
((?[X]:((kind(X)|brave(X))))<=>((quiet(john)&calm(john))))&
((?[X]:(quiet(X)))<=>((~quiet(paul)&patient(paul))))&
((?[X]:((old(X)&~quiet(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((happy(X)<~>~happy(X))=>(~funny(X)&strong(X))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:((funny(X)&brave(X)))))&
((?[X]:((patient(X)<~>humble(X))))=>((curious(mary)|funny(mary))))&
((~humble(paul)&~happy(paul)))&
(?[X]:((~rich(X)|~quiet(X))))&
(?[X]:(~rich(X)))&
(?[X]:((calm(X)|~funny(X))))&
((creative(alice)|~funny(alice)))&
((~strong(john)<~>curious(john)))&
(?[X]:((generous(X)|~kind(X)))) | ~patient(paul) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p8",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7604457710919555683351006
% SZS output start Proof for 7604457710919555683351006
1. ! [X0] : ((brave(X0) & ~calm(X0)) <=> (~tall(X0) | ~calm(X0))) [input p0]
2. ! [X0] : ((~kind(X0) | wise(X0)) => (funny(X0) | ~humble(X0))) [input p1]
3. (humble(alice) | ~creative(alice)) <=> ? [X0] : (rich(X0) & tall(X0)) [input p2]
5. (~funny(john) & ~old(john)) <=> (tall(paul) <~> quiet(paul)) [input p4]
6. ! [X0] : (creative(X0) <=> (~patient(X0) | ~quiet(X0))) [input p5]
9. ! [X0] : ((brave(X0) | ~rich(X0)) <=> (old(X0) & strong(X0))) [input p8]
10. ? [X0] : (brave(X0) | kind(X0)) <=> (calm(john) & quiet(john)) [input p9]
11. ? [X0] : quiet(X0) <=> (patient(paul) & ~quiet(paul)) [input p10]
13. ! [X0] : ((happy(X0) <~> ~happy(X0)) => (strong(X0) & ~funny(X0))) [input p12]
14. ? [X0] : (brave(X0) | generous(X0)) => ? [X0] : (brave(X0) & funny(X0)) [input p13]
23. ~patient(paul) [input hypothesis]
26. ? [X0] : (brave(X0) | generous(X0)) => ? [X1] : (brave(X1) & funny(X1)) [rectify 14]
27. ! [X0] : ((funny(X0) | ~humble(X0)) | (kind(X0) & ~wise(X0))) [ennf transformation 2]
28. ! [X0] : (funny(X0) | ~humble(X0) | (kind(X0) & ~wise(X0))) [flattening 27]
29. ! [X0] : ((strong(X0) & ~funny(X0)) | (happy(X0) <=> ~happy(X0))) [ennf transformation 13]
30. ? [X1] : (brave(X1) & funny(X1)) | ! [X0] : (~brave(X0) & ~generous(X0)) [ennf transformation 26]
33. ! [X0] : (((brave(X0) & ~calm(X0)) | (tall(X0) & calm(X0))) & ((~tall(X0) | ~calm(X0)) | (~brave(X0) | calm(X0)))) [nnf transformation 1]
34. ! [X0] : (((brave(X0) & ~calm(X0)) | (tall(X0) & calm(X0))) & (~tall(X0) | ~calm(X0) | ~brave(X0) | calm(X0))) [flattening 33]
35. ((humble(alice) | ~creative(alice)) | ! [X0] : (~rich(X0) | ~tall(X0))) & (? [X0] : (rich(X0) & tall(X0)) | (~humble(alice) & creative(alice))) [nnf transformation 3]
36. (humble(alice) | ~creative(alice) | ! [X0] : (~rich(X0) | ~tall(X0))) & (? [X0] : (rich(X0) & tall(X0)) | (~humble(alice) & creative(alice))) [flattening 35]
37. (humble(alice) | ~creative(alice) | ! [X0] : (~rich(X0) | ~tall(X0))) & (? [X1] : (rich(X1) & tall(X1)) | (~humble(alice) & creative(alice))) [rectify 36]
38. ? [X1] : (rich(X1) & tall(X1)) => (rich(sK0) & tall(sK0)) [choice axiom]
39. (humble(alice) | ~creative(alice) | ! [X0] : (~rich(X0) | ~tall(X0))) & ((rich(sK0) & tall(sK0)) | (~humble(alice) & creative(alice))) [skolemisation 37,38]
41. ((~funny(john) & ~old(john)) | ((tall(paul) | ~quiet(paul)) & (quiet(paul) | ~tall(paul)))) & (((~quiet(paul) | ~tall(paul)) & (quiet(paul) | tall(paul))) | (funny(john) | old(john))) [nnf transformation 5]
42. ((~funny(john) & ~old(john)) | ((tall(paul) | ~quiet(paul)) & (quiet(paul) | ~tall(paul)))) & (((~quiet(paul) | ~tall(paul)) & (quiet(paul) | tall(paul))) | funny(john) | old(john)) [flattening 41]
43. ! [X0] : ((creative(X0) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | ~creative(X0))) [nnf transformation 6]
44. ! [X0] : ((creative(X0) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~creative(X0))) [flattening 43]
55. ! [X0] : (((brave(X0) | ~rich(X0)) | (~old(X0) | ~strong(X0))) & ((old(X0) & strong(X0)) | (~brave(X0) & rich(X0)))) [nnf transformation 9]
56. ! [X0] : ((brave(X0) | ~rich(X0) | ~old(X0) | ~strong(X0)) & ((old(X0) & strong(X0)) | (~brave(X0) & rich(X0)))) [flattening 55]
57. (? [X0] : (brave(X0) | kind(X0)) | (~calm(john) | ~quiet(john))) & ((calm(john) & quiet(john)) | ! [X0] : (~brave(X0) & ~kind(X0))) [nnf transformation 10]
58. (? [X0] : (brave(X0) | kind(X0)) | ~calm(john) | ~quiet(john)) & ((calm(john) & quiet(john)) | ! [X0] : (~brave(X0) & ~kind(X0))) [flattening 57]
59. (? [X0] : (brave(X0) | kind(X0)) | ~calm(john) | ~quiet(john)) & ((calm(john) & quiet(john)) | ! [X1] : (~brave(X1) & ~kind(X1))) [rectify 58]
60. ? [X0] : (brave(X0) | kind(X0)) => (brave(sK4) | kind(sK4)) [choice axiom]
61. ((brave(sK4) | kind(sK4)) | ~calm(john) | ~quiet(john)) & ((calm(john) & quiet(john)) | ! [X1] : (~brave(X1) & ~kind(X1))) [skolemisation 59,60]
62. (? [X0] : quiet(X0) | (~patient(paul) | quiet(paul))) & ((patient(paul) & ~quiet(paul)) | ! [X0] : ~quiet(X0)) [nnf transformation 11]
63. (? [X0] : quiet(X0) | ~patient(paul) | quiet(paul)) & ((patient(paul) & ~quiet(paul)) | ! [X0] : ~quiet(X0)) [flattening 62]
64. (? [X0] : quiet(X0) | ~patient(paul) | quiet(paul)) & ((patient(paul) & ~quiet(paul)) | ! [X1] : ~quiet(X1)) [rectify 63]
65. ? [X0] : quiet(X0) => quiet(sK5) [choice axiom]
66. (quiet(sK5) | ~patient(paul) | quiet(paul)) & ((patient(paul) & ~quiet(paul)) | ! [X1] : ~quiet(X1)) [skolemisation 64,65]
72. ! [X0] : ((strong(X0) & ~funny(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 29]
73. ? [X0] : (brave(X0) & funny(X0)) | ! [X1] : (~brave(X1) & ~generous(X1)) [rectify 30]
74. ? [X0] : (brave(X0) & funny(X0)) => (brave(sK8) & funny(sK8)) [choice axiom]
75. (brave(sK8) & funny(sK8)) | ! [X1] : (~brave(X1) & ~generous(X1)) [skolemisation 73,74]
88. ~calm(X0) | tall(X0) [cnf transformation 34]
89. brave(X0) | calm(X0) [cnf transformation 34]
90. tall(X0) | brave(X0) [cnf transformation 34]
92. ~humble(X0) | funny(X0) | kind(X0) [cnf transformation 28]
97. humble(alice) | ~creative(alice) | ~rich(X0) | ~tall(X0) [cnf transformation 39]
108. ~old(john) | quiet(paul) | ~tall(paul) [cnf transformation 42]
113. quiet(X0) | creative(X0) [cnf transformation 44]
126. old(X0) | rich(X0) [cnf transformation 56]
129. quiet(john) | ~kind(X1) [cnf transformation 61]
135. patient(paul) | ~quiet(X1) [cnf transformation 66]
143. ~funny(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 72]
144. ~funny(X0) | happy(X0) | happy(X0) [cnf transformation 72]
148. funny(sK8) | ~brave(X1) [cnf transformation 75]
162. ~patient(paul) [cnf transformation 23]
163. ~funny(X0) | ~happy(X0) [duplicate literal removal 143]
164. ~funny(X0) | happy(X0) [duplicate literal removal 144]
172. 1 <=> ! [X0] : (~rich(X0) | ~tall(X0)) [avatar definition]
173. ~rich(X0) | ~tall(X0) <- (1) [avatar component clause 172]
175. 2 <=> creative(alice) [avatar definition]
177. ~creative(alice) <- (~2) [avatar component clause 175]
179. 3 <=> humble(alice) [avatar definition]
181. humble(alice) <- (3) [avatar component clause 179]
182. 1 | ~2 | 3 [avatar split clause 97,179,175,172]
198. 6 <=> quiet(paul) [avatar definition]
199. quiet(paul) <- (6) [avatar component clause 198]
202. 7 <=> tall(paul) [avatar definition]
203. ~tall(paul) <- (~7) [avatar component clause 202]
212. 9 <=> old(john) [avatar definition]
214. ~old(john) <- (~9) [avatar component clause 212]
216. ~7 | 6 | ~9 [avatar split clause 108,212,198,202]
269. 21 <=> quiet(john) [avatar definition]
270. quiet(john) <- (21) [avatar component clause 269]
286. 25 <=> ! [X1] : ~brave(X1) [avatar definition]
287. ~brave(X1) <- (25) [avatar component clause 286]
290. 26 <=> ! [X1] : ~kind(X1) [avatar definition]
291. ~kind(X1) <- (26) [avatar component clause 290]
294. 26 | 21 [avatar split clause 129,269,290]
296. 27 <=> patient(paul) [avatar definition]
305. 29 <=> ! [X1] : ~quiet(X1) [avatar definition]
306. ~quiet(X1) <- (29) [avatar component clause 305]
307. 29 | 27 [avatar split clause 135,296,305]
341. ~funny(X0) [subsumption resolution 163,164]
351. ~brave(X1) [subsumption resolution 148,341]
352. 25 [avatar split clause 351,286]
388. ~27 [avatar split clause 162,296]
389. $false <- (21, 29) [subsumption resolution 270,306]
390. ~21 | ~29 [avatar contradiction clause 389]
392. $false <- (6, 29) [subsumption resolution 199,306]
393. ~6 | ~29 [avatar contradiction clause 392]
398. calm(X0) <- (25) [resolution 89,287]
403. tall(X0) <- (25) [resolution 398,88]
404. brave(paul) <- (~7) [resolution 90,203]
405. $false <- (~7, 25) [subsumption resolution 404,287]
406. 7 | ~25 [avatar contradiction clause 405]
407. creative(X0) <- (29) [resolution 113,306]
415. rich(john) <- (~9) [resolution 126,214]
426. funny(alice) | kind(alice) <- (3) [resolution 92,181]
427. kind(alice) <- (3) [subsumption resolution 426,341]
428. $false <- (3, 26) [subsumption resolution 427,291]
429. ~3 | ~26 [avatar contradiction clause 428]
430. $false <- (~2, 29) [subsumption resolution 177,407]
431. 2 | ~29 [avatar contradiction clause 430]
432. ~rich(X0) <- (1, 25) [subsumption resolution 173,403]
433. $false <- (1, ~9, 25) [resolution 432,415]
440. ~1 | 9 | ~25 [avatar contradiction clause 433]
441. $false [avatar sat refutation 182,216,294,307,352,388,390,393,406,429,431,440]
% SZS output end Proof for 7604457710919555683351006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or rich is both not happy and not creative. If someone is both not wise and humble then paul is old or humble. Everyone who is both not humble and not quiet is either not tall or not humble and vice versa. Everyone who is old or happy is both not patient and not kind and vice versa. If fred is tall then someone is either not curious or creative and vice versa. If john is both calm and creative then someone is not strong and vice versa. If alice is either not humble or curious then fred is old or not tall. Everyone who is kind or not happy is either old or rich. If someone is not strong or old then paul is either not kind or humble and vice versa. If someone is not wise then fred is either quiet or funny and vice versa. Everyone who is not happy or brave is funny or quiet and vice versa. If lucy is generous then someone is humble or not calm. If someone is either happy or not old then mary is quiet or not calm. If paul is both not humble and not strong then someone is not strong or not kind. If someone is either patient or old then someone is not brave. If alice is both not funny and not brave then susan is not tall. Mary is both quiet and old. Someone is either old or not creative. Someone is not old or strong. Someone is both not strong and funny. Susan is not funny or calm. John is either old or tall. | Mary is patient. | contradiction | (![X]:((happy(X)|rich(X))=>(~happy(X)&~creative(X))))&
((?[X]:((~wise(X)&humble(X))))=>((old(paul)|humble(paul))))&
(![X]:((~humble(X)&~quiet(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((old(X)|happy(X))<=>(~patient(X)&~kind(X))))&
((tall(fred))<=>(?[X]:((~curious(X)<~>creative(X)))))&
(((calm(john)&creative(john)))<=>(?[X]:(~strong(X))))&
(((~humble(alice)<~>curious(alice)))=>((old(fred)|~tall(fred))))&
(![X]:((kind(X)|~happy(X))=>(old(X)<~>rich(X))))&
((?[X]:((~strong(X)|old(X))))<=>((~kind(paul)<~>humble(paul))))&
((?[X]:(~wise(X)))<=>((quiet(fred)<~>funny(fred))))&
(![X]:((~happy(X)|brave(X))<=>(funny(X)|quiet(X))))&
((generous(lucy))=>(?[X]:((humble(X)|~calm(X)))))&
((?[X]:((happy(X)<~>~old(X))))=>((quiet(mary)|~calm(mary))))&
(((~humble(paul)&~strong(paul)))=>(?[X]:((~strong(X)|~kind(X)))))&
((?[X]:((patient(X)<~>old(X))))=>(?[X]:(~brave(X))))&
(((~funny(alice)&~brave(alice)))=>(~tall(susan)))&
((quiet(mary)&old(mary)))&
(?[X]:((old(X)<~>~creative(X))))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:((~strong(X)&funny(X))))&
((~funny(susan)|calm(susan)))&
((old(john)<~>tall(john))) | patient(mary) | [
"p3",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5420611581650142821974282
% SZS output start Proof for 5420611581650142821974282
4. ! [X0] : ((happy(X0) | old(X0)) <=> (~kind(X0) & ~patient(X0))) [input p3]
17. old(mary) & quiet(mary) [input p16]
23. patient(mary) [input hypothesis]
41. ! [X0] : (((happy(X0) | old(X0)) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | (~happy(X0) & ~old(X0)))) [nnf transformation 4]
42. ! [X0] : ((happy(X0) | old(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | (~happy(X0) & ~old(X0)))) [flattening 41]
90. ~patient(X0) | ~old(X0) [cnf transformation 42]
129. old(mary) [cnf transformation 17]
138. patient(mary) [cnf transformation 23]
346. ~old(mary) [resolution 90,138]
347. $false [subsumption resolution 346,129]
% SZS output end Proof for 5420611581650142821974282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is calm then alice is both rich and patient and vice versa.
Everyone who is either calm or funny is not tall or quiet.
Everyone who is either not old or not funny is patient.
Everyone who is rich is either not funny or kind.
Everyone who is either generous or not tall is quiet or not funny and vice versa.
If someone is generous then someone is not creative and vice versa.
If someone is not quiet then paul is either funny or generous and vice versa.
Everyone who is generous is not humble and vice versa.
If paul is both patient and not rich then fred is not patient and vice versa.
Everyone who is both not generous and not wise is not kind or quiet.
If john is both not tall and not generous then paul is not curious or not funny and vice versa.
If someone is funny then someone is not tall or kind.
If lucy is old or creative then someone is both not brave and not calm.
If someone is not wise or not kind then paul is either not happy or rich.
Everyone who is calm is both patient and kind.
Everyone who is both not creative and not brave is kind and vice versa.
John is either not tall or curious.
Someone is happy or creative.
Alice is not wise or humble.
Fred is either wise or humble.
Lucy is either not humble or not creative.
Fred is either not strong or creative.
Susan is rich or curious.
Someone is both kind and calm. | Paul is not curious. | neutral | ((calm(paul))<=>((rich(alice)&patient(alice))))&
(![X]:((calm(X)<~>funny(X))=>(~tall(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))=>patient(X)))&
(![X]:(rich(X)=>(~funny(X)<~>kind(X))))&
(![X]:((generous(X)<~>~tall(X))<=>(quiet(X)|~funny(X))))&
((?[X]:(generous(X)))<=>(?[X]:(~creative(X))))&
((?[X]:(~quiet(X)))<=>((funny(paul)<~>generous(paul))))&
(![X]:(generous(X)<=>~humble(X)))&
(((patient(paul)&~rich(paul)))<=>(~patient(fred)))&
(![X]:((~generous(X)&~wise(X))=>(~kind(X)|quiet(X))))&
(((~tall(john)&~generous(john)))<=>((~curious(paul)|~funny(paul))))&
((?[X]:(funny(X)))=>(?[X]:((~tall(X)|kind(X)))))&
(((old(lucy)|creative(lucy)))=>(?[X]:((~brave(X)&~calm(X)))))&
((?[X]:((~wise(X)|~kind(X))))=>((~happy(paul)<~>rich(paul))))&
(![X]:(calm(X)=>(patient(X)&kind(X))))&
(![X]:((~creative(X)&~brave(X))<=>kind(X)))&
((~tall(john)<~>curious(john)))&
(?[X]:((happy(X)|creative(X))))&
((~wise(alice)|humble(alice)))&
((wise(fred)<~>humble(fred)))&
((~humble(lucy)<~>~creative(lucy)))&
((~strong(fred)<~>creative(fred)))&
((rich(susan)|curious(susan)))&
(?[X]:((kind(X)&calm(X)))) | ~curious(paul) | [] | null | 0 |
If someone is not happy then mary is both brave and quiet and vice versa. Everyone who is either curious or tall is brave or happy. Everyone who is quiet or tall is both not old and not rich and vice versa. If someone is either not curious or not creative then fred is rich and vice versa. If mary is not patient then mary is either kind or not old and vice versa. If someone is both patient and brave then lucy is not quiet and vice versa. Everyone who is either not humble or funny is either not kind or kind. Everyone who is not calm or not strong is either not kind or patient. Everyone who is both not quiet and not funny is not funny or not tall and vice versa. If someone is funny or not brave then someone is generous. Everyone who is strong or not creative is both quiet and not curious and vice versa. Everyone who is either not happy or creative is not rich and vice versa. If fred is both creative and humble then someone is both not wise and generous and vice versa. If someone is either rich or creative then someone is either patient or not strong. Everyone who is both not creative and calm is not brave. If someone is not curious or not creative then lucy is creative or brave and vice versa. Mary is not quiet or funny. Someone is old or tall. Susan is either not curious or rich. Someone is both not rich and humble. Someone is calm. Mary is either quiet or humble. Someone is not brave. Someone is not rich or not old. | Mary is quiet. | entailment | ((?[X]:(~happy(X)))<=>((brave(mary)&quiet(mary))))&
(![X]:((curious(X)<~>tall(X))=>(brave(X)|happy(X))))&
(![X]:((quiet(X)|tall(X))<=>(~old(X)&~rich(X))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(rich(fred)))&
((~patient(mary))<=>((kind(mary)<~>~old(mary))))&
((?[X]:((patient(X)&brave(X))))<=>(~quiet(lucy)))&
(![X]:((~humble(X)<~>funny(X))=>(~kind(X)<~>kind(X))))&
(![X]:((~calm(X)|~strong(X))=>(~kind(X)<~>patient(X))))&
(![X]:((~quiet(X)&~funny(X))<=>(~funny(X)|~tall(X))))&
((?[X]:((funny(X)|~brave(X))))=>(?[X]:(generous(X))))&
(![X]:((strong(X)|~creative(X))<=>(quiet(X)&~curious(X))))&
(![X]:((~happy(X)<~>creative(X))<=>~rich(X)))&
(((creative(fred)&humble(fred)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((rich(X)<~>creative(X))))=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:((~creative(X)&calm(X))=>~brave(X)))&
((?[X]:((~curious(X)|~creative(X))))<=>((creative(lucy)|brave(lucy))))&
((~quiet(mary)|funny(mary)))&
(?[X]:((old(X)|tall(X))))&
((~curious(susan)<~>rich(susan)))&
(?[X]:((~rich(X)&humble(X))))&
(?[X]:(calm(X)))&
((quiet(mary)<~>humble(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((~rich(X)|~old(X)))) | quiet(mary) | [
"p0",
"p2",
"p3",
"p10",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3702967379453260465263799
% SZS output start Proof for 3702967379453260465263799
1. ? [X0] : ~happy(X0) <=> (quiet(mary) & brave(mary)) [input p0]
3. ! [X0] : ((tall(X0) | quiet(X0)) <=> (~rich(X0) & ~old(X0))) [input p2]
4. ? [X0] : (~curious(X0) <~> ~creative(X0)) <=> rich(fred) [input p3]
11. ! [X0] : ((~creative(X0) | strong(X0)) <=> (~curious(X0) & quiet(X0))) [input p10]
12. ! [X0] : ((~happy(X0) <~> creative(X0)) <=> ~rich(X0)) [input p11]
19. ~curious(susan) <~> rich(susan) [input p18]
25. ~quiet(mary) [input hypothesis]
36. (? [X0] : ~happy(X0) | (~quiet(mary) | ~brave(mary))) & ((quiet(mary) & brave(mary)) | ! [X0] : happy(X0)) [nnf transformation 1]
37. (? [X0] : ~happy(X0) | ~quiet(mary) | ~brave(mary)) & ((quiet(mary) & brave(mary)) | ! [X0] : happy(X0)) [flattening 36]
38. (? [X0] : ~happy(X0) | ~quiet(mary) | ~brave(mary)) & ((quiet(mary) & brave(mary)) | ! [X1] : happy(X1)) [rectify 37]
39. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
40. (~happy(sK0) | ~quiet(mary) | ~brave(mary)) & ((quiet(mary) & brave(mary)) | ! [X1] : happy(X1)) [skolemisation 38,39]
42. ! [X0] : (((tall(X0) | quiet(X0)) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | (~tall(X0) & ~quiet(X0)))) [nnf transformation 3]
43. ! [X0] : ((tall(X0) | quiet(X0) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | (~tall(X0) & ~quiet(X0)))) [flattening 42]
44. (? [X0] : ((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ~rich(fred)) & (rich(fred) | ! [X0] : ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) [nnf transformation 4]
45. (? [X0] : ((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ~rich(fred)) & (rich(fred) | ! [X1] : ((~curious(X1) | creative(X1)) & (~creative(X1) | curious(X1)))) [rectify 44]
46. ? [X0] : ((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) => ((creative(sK1) | curious(sK1)) & (~creative(sK1) | ~curious(sK1))) [choice axiom]
47. (((creative(sK1) | curious(sK1)) & (~creative(sK1) | ~curious(sK1))) | ~rich(fred)) & (rich(fred) | ! [X1] : ((~curious(X1) | creative(X1)) & (~creative(X1) | curious(X1)))) [skolemisation 45,46]
60. ! [X0] : (((~creative(X0) | strong(X0)) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | (creative(X0) & ~strong(X0)))) [nnf transformation 11]
61. ! [X0] : ((~creative(X0) | strong(X0) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | (creative(X0) & ~strong(X0)))) [flattening 60]
62. ! [X0] : ((((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | rich(X0)) & (~rich(X0) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0))))) [nnf transformation 12]
79. (~rich(susan) | curious(susan)) & (rich(susan) | ~curious(susan)) [nnf transformation 19]
90. quiet(mary) | happy(X1) [cnf transformation 40]
96. ~rich(X0) | ~quiet(X0) [cnf transformation 43]
99. rich(fred) | ~creative(X1) | curious(X1) [cnf transformation 47]
126. creative(X0) | quiet(X0) [cnf transformation 61]
131. ~creative(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 62]
132. ~happy(X0) | creative(X0) | rich(X0) [cnf transformation 62]
149. rich(susan) | ~curious(susan) [cnf transformation 79]
158. ~quiet(mary) [cnf transformation 25]
164. 2 <=> quiet(mary) [avatar definition]
173. 4 <=> ! [X1] : happy(X1) [avatar definition]
174. happy(X1) <- (4) [avatar component clause 173]
175. 4 | 2 [avatar split clause 90,164,173]
178. 5 <=> rich(fred) [avatar definition]
179. rich(fred) <- (5) [avatar component clause 178]
196. 9 <=> ! [X1] : (~creative(X1) | curious(X1)) [avatar definition]
197. ~creative(X1) | curious(X1) <- (9) [avatar component clause 196]
198. 9 | 5 [avatar split clause 99,178,196]
306. 33 <=> ! [X1] : creative(X1) [avatar definition]
307. creative(X1) <- (33) [avatar component clause 306]
310. 34 <=> ! [X1] : curious(X1) [avatar definition]
311. curious(X1) <- (34) [avatar component clause 310]
323. 37 <=> curious(susan) [avatar definition]
324. ~curious(susan) <- (~37) [avatar component clause 323]
327. 38 <=> rich(susan) [avatar definition]
328. rich(susan) <- (38) [avatar component clause 327]
331. ~37 | 38 [avatar split clause 149,327,323]
347. ~2 [avatar split clause 158,164]
383. ~happy(X0) | ~rich(X0) | quiet(X0) [resolution 131,126]
385. ~rich(X0) | quiet(X0) <- (4) [subsumption resolution 383,174]
386. ~rich(X0) <- (4) [subsumption resolution 385,96]
387. creative(X0) | rich(X0) <- (4) [resolution 132,174]
388. creative(X0) <- (4) [subsumption resolution 387,386]
389. 33 | ~4 [avatar split clause 388,173,306]
391. curious(X1) <- (9, 33) [resolution 307,197]
392. 34 | ~9 | ~33 [avatar split clause 391,306,196,310]
393. $false <- (4, 5) [subsumption resolution 179,386]
394. ~4 | ~5 [avatar contradiction clause 393]
396. $false <- (34, ~37) [resolution 311,324]
401. ~34 | 37 [avatar contradiction clause 396]
402. $false <- (4, 38) [subsumption resolution 328,386]
403. ~4 | ~38 [avatar contradiction clause 402]
406. $false [avatar sat refutation 175,198,331,347,389,392,394,401,403]
% SZS output end Proof for 3702967379453260465263799
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either generous or wise then john is both wise and old. Everyone who is both not humble and humble is tall or not curious and vice versa. Everyone who is both brave and happy is both rich and not funny and vice versa. If someone is both not patient and not rich then someone is generous. Everyone who is not kind is funny and vice versa. Everyone who is humble is either old or not brave and vice versa. If someone is either not humble or not rich then someone is both not humble and humble. If john is brave then someone is both generous and creative and vice versa. If john is not patient then lucy is funny and vice versa. If fred is either tall or strong then someone is not curious and vice versa. Everyone who is both happy and not old is creative and vice versa. Everyone who is either old or not creative is not curious or not brave and vice versa. If someone is either not strong or strong then someone is either not quiet or wise. If someone is not kind then alice is curious and vice versa. If someone is not generous or strong then someone is not generous. Everyone who is either funny or not brave is brave or calm and vice versa. Someone is either calm or kind. Someone is not rich or humble. Someone is not wise or not generous. Someone is either humble or not humble. Someone is both wise and not old. Alice is either not generous or patient. | John is patient. | contradiction | (((generous(alice)<~>wise(alice)))=>((wise(john)&old(john))))&
(![X]:((~humble(X)&humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((brave(X)&happy(X))<=>(rich(X)&~funny(X))))&
((?[X]:((~patient(X)&~rich(X))))=>(?[X]:(generous(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:(humble(X)<=>(old(X)<~>~brave(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~humble(X)&humble(X)))))&
((brave(john))<=>(?[X]:((generous(X)&creative(X)))))&
((~patient(john))<=>(funny(lucy)))&
(((tall(fred)<~>strong(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((happy(X)&~old(X))<=>creative(X)))&
(![X]:((old(X)<~>~creative(X))<=>(~curious(X)|~brave(X))))&
((?[X]:((~strong(X)<~>strong(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:(~kind(X)))<=>(curious(alice)))&
((?[X]:((~generous(X)|strong(X))))=>(?[X]:(~generous(X))))&
(![X]:((funny(X)<~>~brave(X))<=>(brave(X)|calm(X))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((~rich(X)|humble(X))))&
(?[X]:((~wise(X)|~generous(X))))&
(?[X]:((humble(X)<~>~humble(X))))&
(?[X]:((wise(X)&~old(X))))&
((~generous(alice)<~>patient(alice))) | patient(john) | [
"p2",
"p5",
"p6",
"p8",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1750160566435043225355860
% SZS output start Proof for 1750160566435043225355860
3. ! [X0] : ((happy(X0) & brave(X0)) <=> (~funny(X0) & rich(X0))) [input p2]
6. ! [X0] : (humble(X0) <=> (old(X0) <~> ~brave(X0))) [input p5]
7. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X0] : (humble(X0) & ~humble(X0)) [input p6]
9. ~patient(john) <=> funny(lucy) [input p8]
11. ! [X0] : ((~old(X0) & happy(X0)) <=> creative(X0)) [input p10]
12. ! [X0] : ((old(X0) <~> ~creative(X0)) <=> (~brave(X0) | ~curious(X0))) [input p11]
16. ! [X0] : ((funny(X0) <~> ~brave(X0)) <=> (calm(X0) | brave(X0))) [input p15]
23. patient(john) [input hypothesis]
25. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X1] : (humble(X1) & ~humble(X1)) [rectify 7]
30. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : (~humble(X0) <=> ~rich(X0)) [ennf transformation 25]
36. ! [X0] : (((happy(X0) & brave(X0)) | (funny(X0) | ~rich(X0))) & ((~funny(X0) & rich(X0)) | (~happy(X0) | ~brave(X0)))) [nnf transformation 3]
37. ! [X0] : (((happy(X0) & brave(X0)) | funny(X0) | ~rich(X0)) & ((~funny(X0) & rich(X0)) | ~happy(X0) | ~brave(X0))) [flattening 36]
42. ! [X0] : ((humble(X0) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0)))) & (((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | ~humble(X0))) [nnf transformation 6]
43. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))) [nnf transformation 30]
44. ? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [rectify 43]
45. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK1) & ~humble(sK1)) [choice axiom]
46. (humble(sK1) & ~humble(sK1)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [skolemisation 44,45]
51. (~patient(john) | ~funny(lucy)) & (funny(lucy) | patient(john)) [nnf transformation 9]
56. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 11]
57. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | old(X0) | ~happy(X0))) [flattening 56]
58. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & ((~brave(X0) | ~curious(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [nnf transformation 12]
59. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & (~brave(X0) | ~curious(X0) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [flattening 58]
71. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | (~calm(X0) & ~brave(X0))) & ((calm(X0) | brave(X0)) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [nnf transformation 16]
72. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | (~calm(X0) & ~brave(X0))) & (calm(X0) | brave(X0) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [flattening 71]
97. ~rich(X0) | funny(X0) | brave(X0) [cnf transformation 37]
105. brave(X0) | old(X0) | humble(X0) [cnf transformation 42]
107. ~humble(sK1) | ~humble(X1) | rich(X1) [cnf transformation 46]
109. humble(sK1) | ~humble(X1) | rich(X1) [cnf transformation 46]
114. ~patient(john) | ~funny(lucy) [cnf transformation 51]
121. ~creative(X0) | ~old(X0) [cnf transformation 57]
127. creative(X0) | ~old(X0) | brave(X0) [cnf transformation 59]
138. ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 72]
152. patient(john) [cnf transformation 23]
154. ~brave(X0) | funny(X0) [duplicate literal removal 138]
190. 7 <=> ! [X1] : (~humble(X1) | rich(X1)) [avatar definition]
191. ~humble(X1) | rich(X1) <- (7) [avatar component clause 190]
193. 8 <=> humble(sK1) [avatar definition]
196. 7 | 8 [avatar split clause 109,193,190]
201. 7 | ~8 [avatar split clause 107,193,190]
222. 14 <=> funny(lucy) [avatar definition]
224. ~funny(lucy) <- (~14) [avatar component clause 222]
226. 15 <=> patient(john) [avatar definition]
229. ~14 | ~15 [avatar split clause 114,226,222]
233. ~old(X0) | brave(X0) [subsumption resolution 127,121]
299. 15 [avatar split clause 152,226]
342. funny(X2) | humble(X2) | old(X2) [resolution 105,154]
424. humble(lucy) | old(lucy) <- (~14) [resolution 342,224]
427. 40 <=> old(lucy) [avatar definition]
429. old(lucy) <- (40) [avatar component clause 427]
431. 41 <=> humble(lucy) [avatar definition]
433. humble(lucy) <- (41) [avatar component clause 431]
434. 40 | 41 | 14 [avatar split clause 424,222,431,427]
488. brave(lucy) <- (40) [resolution 429,233]
524. funny(lucy) <- (40) [resolution 488,154]
527. $false <- (~14, 40) [subsumption resolution 524,224]
528. 14 | ~40 [avatar contradiction clause 527]
530. rich(lucy) <- (7, 41) [resolution 433,191]
548. funny(lucy) | brave(lucy) <- (7, 41) [resolution 530,97]
551. brave(lucy) <- (7, ~14, 41) [subsumption resolution 548,224]
589. funny(lucy) <- (7, ~14, 41) [resolution 551,154]
595. $false <- (7, ~14, 41) [subsumption resolution 589,224]
596. ~7 | 14 | ~41 [avatar contradiction clause 595]
597. $false [avatar sat refutation 196,201,229,299,434,528,596]
% SZS output end Proof for 1750160566435043225355860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both calm and generous then someone is not generous or creative and vice versa.
Everyone who is not brave or creative is calm or not generous.
If someone is wise or not tall then paul is generous.
Everyone who is patient is not funny and vice versa.
Everyone who is either not rich or rich is not quiet or not generous and vice versa.
If someone is either not generous or calm then susan is either generous or not tall and vice versa.
If someone is not creative then paul is both curious and humble and vice versa.
Everyone who is both not wise and not tall is either not rich or quiet.
Everyone who is both funny and rich is either humble or tall and vice versa.
Everyone who is old is both not generous and happy.
Everyone who is both tall and not kind is both old and not tall and vice versa.
Everyone who is either not humble or not calm is both brave and not rich and vice versa.
If someone is not funny then someone is either not quiet or happy.
Everyone who is not happy or not calm is strong.
If someone is not old or humble then someone is both rich and not generous and vice versa.
If mary is not old or not happy then fred is not brave or funny.
Someone is not kind or not brave.
Mary is both old and not calm.
Someone is both tall and not old.
Alice is either funny or not quiet.
Someone is both old and rich.
Mary is either not quiet or tall.
Someone is old.
Someone is both not tall and generous. | Paul is tall. | neutral | ((?[X]:((calm(X)&generous(X))))<=>(?[X]:((~generous(X)|creative(X)))))&
(![X]:((~brave(X)|creative(X))=>(calm(X)|~generous(X))))&
((?[X]:((wise(X)|~tall(X))))=>(generous(paul)))&
(![X]:(patient(X)<=>~funny(X)))&
(![X]:((~rich(X)<~>rich(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((generous(susan)<~>~tall(susan))))&
((?[X]:(~creative(X)))<=>((curious(paul)&humble(paul))))&
(![X]:((~wise(X)&~tall(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((funny(X)&rich(X))<=>(humble(X)<~>tall(X))))&
(![X]:(old(X)=>(~generous(X)&happy(X))))&
(![X]:((tall(X)&~kind(X))<=>(old(X)&~tall(X))))&
(![X]:((~humble(X)<~>~calm(X))<=>(brave(X)&~rich(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((~happy(X)|~calm(X))=>strong(X)))&
((?[X]:((~old(X)|humble(X))))<=>(?[X]:((rich(X)&~generous(X)))))&
(((~old(mary)|~happy(mary)))=>((~brave(fred)|funny(fred))))&
(?[X]:((~kind(X)|~brave(X))))&
((old(mary)&~calm(mary)))&
(?[X]:((tall(X)&~old(X))))&
((funny(alice)<~>~quiet(alice)))&
(?[X]:((old(X)&rich(X))))&
((~quiet(mary)<~>tall(mary)))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)&generous(X)))) | tall(paul) | [] | null | 0 |
Everyone who is brave is either happy or tall. If lucy is both not rich and not generous then john is brave or not calm and vice versa. If someone is either not happy or not creative then someone is both old and happy and vice versa. If someone is not curious or calm then someone is humble and vice versa. Everyone who is either not humble or not quiet is both not strong and not funny. Everyone who is not old or not wise is both generous and wise. Everyone who is both happy and calm is kind. If fred is either not rich or not humble then someone is either humble or not humble. Everyone who is both tall and not brave is both not rich and not brave. If someone is creative then someone is both kind and not kind. If mary is not patient then someone is happy or not old and vice versa. Everyone who is both not tall and happy is not tall and vice versa. Everyone who is not curious is either tall or curious. Everyone who is both curious and not old is happy. Everyone who is not tall is not patient. Paul is either not rich or strong. Susan is both not happy and old. Someone is not old. Someone is both not happy and calm. Lucy is either happy or creative. Someone is both not curious and happy. Alice is both not creative and humble. | Mary is generous. | neutral | (![X]:(brave(X)=>(happy(X)<~>tall(X))))&
(((~rich(lucy)&~generous(lucy)))<=>((brave(john)|~calm(john))))&
((?[X]:((~happy(X)<~>~creative(X))))<=>(?[X]:((old(X)&happy(X)))))&
((?[X]:((~curious(X)|calm(X))))<=>(?[X]:(humble(X))))&
(![X]:((~humble(X)<~>~quiet(X))=>(~strong(X)&~funny(X))))&
(![X]:((~old(X)|~wise(X))=>(generous(X)&wise(X))))&
(![X]:((happy(X)&calm(X))=>kind(X)))&
(((~rich(fred)<~>~humble(fred)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((tall(X)&~brave(X))=>(~rich(X)&~brave(X))))&
((?[X]:(creative(X)))=>(?[X]:((kind(X)&~kind(X)))))&
((~patient(mary))<=>(?[X]:((happy(X)|~old(X)))))&
(![X]:((~tall(X)&happy(X))<=>~tall(X)))&
(![X]:(~curious(X)=>(tall(X)<~>curious(X))))&
(![X]:((curious(X)&~old(X))=>happy(X)))&
(![X]:(~tall(X)=>~patient(X)))&
((~rich(paul)<~>strong(paul)))&
((~happy(susan)&old(susan)))&
(?[X]:(~old(X)))&
(?[X]:((~happy(X)&calm(X))))&
((happy(lucy)<~>creative(lucy)))&
(?[X]:((~curious(X)&happy(X))))&
((~creative(alice)&humble(alice))) | generous(mary) | [] | null | 0 |
Everyone who is funny or old is not creative.
Everyone who is both brave and not quiet is both not kind and not creative.
If someone is brave or not brave then susan is not generous or not happy and vice versa.
Everyone who is wise is not patient and vice versa.
If someone is not happy or not kind then someone is both funny and not humble.
If someone is not quiet then someone is both not strong and humble and vice versa.
If someone is not rich or strong then john is both strong and not curious.
Everyone who is both wise and not humble is both funny and not brave.
If alice is humble then lucy is not patient or not generous and vice versa.
If alice is generous then lucy is kind.
Everyone who is not rich is tall.
Everyone who is either patient or not calm is not kind or brave and vice versa.
Everyone who is either old or not brave is happy or strong and vice versa.
If fred is both not brave and calm then someone is either humble or not patient and vice versa.
If mary is either not wise or not strong then someone is either patient or not rich.
Everyone who is both not tall and tall is strong and vice versa.
Someone is either strong or not creative.
Someone is not quiet or quiet.
John is either not strong or generous.
Someone is either patient or strong.
Someone is both curious and old.
Mary is patient. | Alice is not strong. | entailment | (![X]:((funny(X)|old(X))=>~creative(X)))&
(![X]:((brave(X)&~quiet(X))=>(~kind(X)&~creative(X))))&
((?[X]:((brave(X)|~brave(X))))<=>((~generous(susan)|~happy(susan))))&
(![X]:(wise(X)<=>~patient(X)))&
((?[X]:((~happy(X)|~kind(X))))=>(?[X]:((funny(X)&~humble(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~strong(X)&humble(X)))))&
((?[X]:((~rich(X)|strong(X))))=>((strong(john)&~curious(john))))&
(![X]:((wise(X)&~humble(X))=>(funny(X)&~brave(X))))&
((humble(alice))<=>((~patient(lucy)|~generous(lucy))))&
((generous(alice))=>(kind(lucy)))&
(![X]:(~rich(X)=>tall(X)))&
(![X]:((patient(X)<~>~calm(X))<=>(~kind(X)|brave(X))))&
(![X]:((old(X)<~>~brave(X))<=>(happy(X)|strong(X))))&
(((~brave(fred)&calm(fred)))<=>(?[X]:((humble(X)<~>~patient(X)))))&
(((~wise(mary)<~>~strong(mary)))=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:((~tall(X)&tall(X))<=>strong(X)))&
(?[X]:((strong(X)<~>~creative(X))))&
(?[X]:((~quiet(X)|quiet(X))))&
((~strong(john)<~>generous(john)))&
(?[X]:((patient(X)<~>strong(X))))&
(?[X]:((curious(X)&old(X))))&
(patient(mary)) | ~strong(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3596617220553919438362603
% SZS output start Proof for 3596617220553919438362603
16. ! [X0] : ((tall(X0) & ~tall(X0)) <=> strong(X0)) [input p15]
23. strong(alice) [input hypothesis]
64. ! [X0] : (((tall(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | (~tall(X0) | tall(X0)))) [nnf transformation 16]
65. ! [X0] : (((tall(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | ~tall(X0) | tall(X0))) [flattening 64]
128. ~tall(X0) | ~strong(X0) [cnf transformation 65]
129. tall(X0) | ~strong(X0) [cnf transformation 65]
140. strong(alice) [cnf transformation 23]
197. 14 <=> ! [X0] : ~strong(X0) [avatar definition]
198. ~strong(X0) <- (14) [avatar component clause 197]
286. ~strong(X0) [subsumption resolution 128,129]
287. 14 [avatar split clause 286,197]
317. $false <- (14) [resolution 198,140]
318. ~14 [avatar contradiction clause 317]
319. $false [avatar sat refutation 287,318]
% SZS output end Proof for 3596617220553919438362603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or curious then mary is not kind. If paul is either not rich or not humble then lucy is both not curious and not kind. Everyone who is not calm or old is both not wise and strong. Everyone who is not old or curious is strong. Everyone who is not brave or strong is both creative and not calm and vice versa. If someone is either not patient or not wise then someone is either creative or kind. If john is either funny or tall then someone is patient and vice versa. Everyone who is both not calm and not generous is both not old and not rich and vice versa. Everyone who is either not strong or strong is both not calm and not kind. If someone is not happy or not old then someone is either wise or not strong. Everyone who is both tall and patient is both not kind and strong. Everyone who is both not kind and creative is not kind. Everyone who is both brave and not kind is both not generous and quiet and vice versa. If mary is either not tall or not strong then someone is generous or strong. Everyone who is either not calm or happy is both patient and not curious. Fred is rich or not old. Someone is tall or not curious. Paul is both strong and humble. John is either calm or creative. Someone is happy. | Paul is not kind. | entailment | ((?[X]:((~creative(X)|curious(X))))=>(~kind(mary)))&
(((~rich(paul)<~>~humble(paul)))=>((~curious(lucy)&~kind(lucy))))&
(![X]:((~calm(X)|old(X))=>(~wise(X)&strong(X))))&
(![X]:((~old(X)|curious(X))=>strong(X)))&
(![X]:((~brave(X)|strong(X))<=>(creative(X)&~calm(X))))&
((?[X]:((~patient(X)<~>~wise(X))))=>(?[X]:((creative(X)<~>kind(X)))))&
(((funny(john)<~>tall(john)))<=>(?[X]:(patient(X))))&
(![X]:((~calm(X)&~generous(X))<=>(~old(X)&~rich(X))))&
(![X]:((~strong(X)<~>strong(X))=>(~calm(X)&~kind(X))))&
((?[X]:((~happy(X)|~old(X))))=>(?[X]:((wise(X)<~>~strong(X)))))&
(![X]:((tall(X)&patient(X))=>(~kind(X)&strong(X))))&
(![X]:((~kind(X)&creative(X))=>~kind(X)))&
(![X]:((brave(X)&~kind(X))<=>(~generous(X)&quiet(X))))&
(((~tall(mary)<~>~strong(mary)))=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((~calm(X)<~>happy(X))=>(patient(X)&~curious(X))))&
((rich(fred)|~old(fred)))&
(?[X]:((tall(X)|~curious(X))))&
((strong(paul)&humble(paul)))&
((calm(john)<~>creative(john)))&
(?[X]:(happy(X))) | ~kind(paul) | [
"p2",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2106057325584539487655125
% SZS output start Proof for 2106057325584539487655125
3. ! [X0] : ((old(X0) | ~calm(X0)) => (strong(X0) & ~wise(X0))) [input p2]
4. ! [X0] : ((curious(X0) | ~old(X0)) => strong(X0)) [input p3]
9. ! [X0] : ((~strong(X0) <~> strong(X0)) => (~kind(X0) & ~calm(X0))) [input p8]
21. kind(paul) [input hypothesis]
26. ! [X0] : (~old(X0) => strong(X0)) [pure predicate removal 4]
31. ! [X0] : ((strong(X0) & ~wise(X0)) | (~old(X0) & calm(X0))) [ennf transformation 3]
32. ! [X0] : (strong(X0) | old(X0)) [ennf transformation 26]
34. ! [X0] : ((~kind(X0) & ~calm(X0)) | (~strong(X0) <=> strong(X0))) [ennf transformation 9]
55. ! [X0] : ((~kind(X0) & ~calm(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 34]
75. strong(X0) | ~old(X0) [cnf transformation 31]
76. strong(X0) | old(X0) [cnf transformation 32]
97. ~kind(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 55]
119. kind(paul) [cnf transformation 21]
123. ~kind(X0) | ~strong(X0) [duplicate literal removal 97]
146. strong(X0) [subsumption resolution 76,75]
189. ~kind(X0) [subsumption resolution 123,146]
218. $false [subsumption resolution 119,189]
% SZS output end Proof for 2106057325584539487655125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is either happy or creative. If lucy is either generous or not brave then someone is old or kind and vice versa. If susan is both old and not brave then someone is both old and not funny and vice versa. If paul is either creative or not generous then john is either happy or humble. Everyone who is calm or not generous is not wise or not funny. Everyone who is either not wise or not funny is curious and vice versa. Everyone who is not humble is not calm and vice versa. Everyone who is both not rich and old is either not quiet or tall and vice versa. Everyone who is both not curious and patient is either brave or not curious. Everyone who is both not calm and not rich is not rich or not patient. If someone is both rich and not tall then lucy is rich or generous and vice versa. If someone is either not strong or not tall then someone is either wise or not happy and vice versa. Everyone who is curious is not patient or creative. If someone is both strong and kind then fred is kind. Everyone who is curious is old or tall and vice versa. If mary is not kind then john is not kind. Someone is either brave or not curious. Fred is old. Someone is curious. Lucy is either brave or not patient. Fred is both old and strong. Paul is either calm or not patient. Mary is both wise and funny. Someone is either happy or quiet. | Mary is generous. | entailment | (![X]:(calm(X)=>(happy(X)<~>creative(X))))&
(((generous(lucy)<~>~brave(lucy)))<=>(?[X]:((old(X)|kind(X)))))&
(((old(susan)&~brave(susan)))<=>(?[X]:((old(X)&~funny(X)))))&
(((creative(paul)<~>~generous(paul)))=>((happy(john)<~>humble(john))))&
(![X]:((calm(X)|~generous(X))=>(~wise(X)|~funny(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>curious(X)))&
(![X]:(~humble(X)<=>~calm(X)))&
(![X]:((~rich(X)&old(X))<=>(~quiet(X)<~>tall(X))))&
(![X]:((~curious(X)&patient(X))=>(brave(X)<~>~curious(X))))&
(![X]:((~calm(X)&~rich(X))=>(~rich(X)|~patient(X))))&
((?[X]:((rich(X)&~tall(X))))<=>((rich(lucy)|generous(lucy))))&
((?[X]:((~strong(X)<~>~tall(X))))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:(curious(X)=>(~patient(X)|creative(X))))&
((?[X]:((strong(X)&kind(X))))=>(kind(fred)))&
(![X]:(curious(X)<=>(old(X)|tall(X))))&
((~kind(mary))=>(~kind(john)))&
(?[X]:((brave(X)<~>~curious(X))))&
(old(fred))&
(?[X]:(curious(X)))&
((brave(lucy)<~>~patient(lucy)))&
((old(fred)&strong(fred)))&
((calm(paul)<~>~patient(paul)))&
((wise(mary)&funny(mary)))&
(?[X]:((happy(X)<~>quiet(X)))) | generous(mary) | [
"p4",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8933450721433036998412265
% SZS output start Proof for 8933450721433036998412265
5. ! [X0] : ((~generous(X0) | calm(X0)) => (~funny(X0) | ~wise(X0))) [input p4]
23. funny(mary) & wise(mary) [input p22]
25. ~generous(mary) [input hypothesis]
29. ! [X0] : ((~funny(X0) | ~wise(X0)) | (generous(X0) & ~calm(X0))) [ennf transformation 5]
30. ! [X0] : (~funny(X0) | ~wise(X0) | (generous(X0) & ~calm(X0))) [flattening 29]
94. ~wise(X0) | ~funny(X0) | generous(X0) [cnf transformation 30]
139. wise(mary) [cnf transformation 23]
140. funny(mary) [cnf transformation 23]
143. ~generous(mary) [cnf transformation 25]
334. ~funny(mary) | generous(mary) [resolution 94,139]
335. generous(mary) [subsumption resolution 334,140]
336. $false [subsumption resolution 335,143]
% SZS output end Proof for 8933450721433036998412265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or funny is both old and not creative.
Everyone who is old or patient is both not old and not strong.
Everyone who is not strong or not happy is both not happy and kind.
Everyone who is not kind or generous is calm and vice versa.
If john is both not quiet and tall then someone is tall or humble and vice versa.
Everyone who is curious or quiet is both funny and rich.
Everyone who is not patient is both not old and funny and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
If paul is not creative or not strong then someone is strong and vice versa.
Everyone who is quiet is kind.
Someone is brave or strong.
Alice is wise.
Someone is not strong or not rich.
Someone is happy or not kind.
Mary is rich. | Paul is humble. | contradiction | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|patient(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((brave(X)|strong(X))))&
(wise(alice))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((happy(X)|~kind(X))))&
(rich(mary)) | humble(paul) | [
"p0",
"p1",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3008249311704681017362140
% SZS output start Proof for 3008249311704681017362140
1. ! [X0] : ((~curious(X0) <~> funny(X0)) => (~creative(X0) & old(X0))) [input p0]
2. ! [X0] : ((patient(X0) | old(X0)) => (~strong(X0) & ~old(X0))) [input p1]
6. ! [X0] : ((quiet(X0) | curious(X0)) => (rich(X0) & funny(X0))) [input p5]
8. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (kind(X0) & ~humble(X0))) [input p7]
22. humble(paul) [input hypothesis]
25. ! [X0] : ((~creative(X0) & old(X0)) | (~curious(X0) <=> funny(X0))) [ennf transformation 1]
26. ! [X0] : ((~strong(X0) & ~old(X0)) | (~patient(X0) & ~old(X0))) [ennf transformation 2]
28. ! [X0] : ((rich(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0))) [ennf transformation 6]
34. ! [X0] : ((~creative(X0) & old(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) [nnf transformation 25]
42. ! [X0] : (((calm(X0) | ~curious(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 8]
43. ! [X0] : ((calm(X0) | ~curious(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [flattening 42]
68. ~funny(X0) | ~curious(X0) | old(X0) [cnf transformation 34]
71. ~old(X0) | ~old(X0) [cnf transformation 26]
87. ~curious(X0) | funny(X0) [cnf transformation 28]
93. ~humble(X0) | curious(X0) [cnf transformation 43]
128. humble(paul) [cnf transformation 22]
129. ~old(X0) [duplicate literal removal 71]
203. 15 <=> curious(paul) [avatar definition]
205. curious(paul) <- (15) [avatar component clause 203]
262. curious(paul) [resolution 93,128]
263. 15 [avatar split clause 262,203]
265. funny(paul) <- (15) [resolution 205,87]
271. ~curious(paul) | old(paul) <- (15) [resolution 68,265]
274. old(paul) <- (15) [subsumption resolution 271,205]
275. $false <- (15) [subsumption resolution 274,129]
276. ~15 [avatar contradiction clause 275]
278. $false [avatar sat refutation 263,276]
% SZS output end Proof for 3008249311704681017362140
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not brave is curious and vice versa. If someone is both not tall and not quiet then someone is both not tall and creative. Everyone who is either not kind or not rich is either strong or happy and vice versa. If someone is not quiet or brave then someone is curious and vice versa. Everyone who is both brave and not funny is not happy or not wise. If lucy is both funny and wise then paul is rich. Everyone who is calm or rich is not old and vice versa. If fred is either not calm or kind then alice is both not wise and patient. Everyone who is both not calm and not wise is not calm and vice versa. If paul is either not brave or not calm then someone is not wise or happy. Everyone who is either tall or not old is rich or curious. If susan is either brave or quiet then someone is not patient and vice versa. If alice is not tall then alice is not generous or kind. Everyone who is either calm or patient is both not patient and patient and vice versa. If someone is not quiet or not calm then someone is not calm and vice versa. Everyone who is both not wise and curious is not old or patient. Someone is both patient and happy. Someone is not calm. Lucy is not rich. Paul is old. Lucy is both generous and strong. Someone is both funny and not generous. Paul is not tall or kind. Someone is either calm or tall. | Paul is brave. | contradiction | (![X]:((~calm(X)<~>~brave(X))<=>curious(X)))&
((?[X]:((~tall(X)&~quiet(X))))=>(?[X]:((~tall(X)&creative(X)))))&
(![X]:((~kind(X)<~>~rich(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((~quiet(X)|brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((brave(X)&~funny(X))=>(~happy(X)|~wise(X))))&
(((funny(lucy)&wise(lucy)))=>(rich(paul)))&
(![X]:((calm(X)|rich(X))<=>~old(X)))&
(((~calm(fred)<~>kind(fred)))=>((~wise(alice)&patient(alice))))&
(![X]:((~calm(X)&~wise(X))<=>~calm(X)))&
(((~brave(paul)<~>~calm(paul)))=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((tall(X)<~>~old(X))=>(rich(X)|curious(X))))&
(((brave(susan)<~>quiet(susan)))<=>(?[X]:(~patient(X))))&
((~tall(alice))=>((~generous(alice)|kind(alice))))&
(![X]:((calm(X)<~>patient(X))<=>(~patient(X)&patient(X))))&
((?[X]:((~quiet(X)|~calm(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~wise(X)&curious(X))=>(~old(X)|patient(X))))&
(?[X]:((patient(X)&happy(X))))&
(?[X]:(~calm(X)))&
(~rich(lucy))&
(old(paul))&
((generous(lucy)&strong(lucy)))&
(?[X]:((funny(X)&~generous(X))))&
((~tall(paul)|kind(paul)))&
(?[X]:((calm(X)<~>tall(X)))) | brave(paul) | [
"p0",
"p6",
"p8",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 879690317072677780743267
% SZS output start Proof for 879690317072677780743267
1. ! [X0] : ((~calm(X0) <~> ~brave(X0)) <=> curious(X0)) [input p0]
7. ! [X0] : ((rich(X0) | calm(X0)) <=> ~old(X0)) [input p6]
9. ! [X0] : ((~wise(X0) & ~calm(X0)) <=> ~calm(X0)) [input p8]
14. ! [X0] : ((calm(X0) <~> patient(X0)) <=> (patient(X0) & ~patient(X0))) [input p13]
16. ! [X0] : ((curious(X0) & ~wise(X0)) => (patient(X0) | ~old(X0))) [input p15]
20. old(paul) [input p19]
25. brave(paul) [input hypothesis]
41. ! [X0] : ((patient(X0) | ~old(X0)) | (~curious(X0) | wise(X0))) [ennf transformation 16]
42. ! [X0] : (patient(X0) | ~old(X0) | ~curious(X0) | wise(X0)) [flattening 41]
43. ! [X0] : ((((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | ~curious(X0)) & (curious(X0) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0))))) [nnf transformation 1]
53. ! [X0] : (((rich(X0) | calm(X0)) | old(X0)) & (~old(X0) | (~rich(X0) & ~calm(X0)))) [nnf transformation 7]
54. ! [X0] : ((rich(X0) | calm(X0) | old(X0)) & (~old(X0) | (~rich(X0) & ~calm(X0)))) [flattening 53]
56. ! [X0] : (((~wise(X0) & ~calm(X0)) | calm(X0)) & (~calm(X0) | (wise(X0) | calm(X0)))) [nnf transformation 9]
57. ! [X0] : (((~wise(X0) & ~calm(X0)) | calm(X0)) & (~calm(X0) | wise(X0) | calm(X0))) [flattening 56]
66. ! [X0] : ((((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0))))) [nnf transformation 14]
67. ! [X0] : ((((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0))))) [flattening 66]
82. ~brave(X0) | curious(X0) | calm(X0) [cnf transformation 43]
100. ~old(X0) | ~calm(X0) [cnf transformation 54]
109. ~wise(X0) | calm(X0) [cnf transformation 57]
120. ~patient(X0) | calm(X0) | ~patient(X0) [cnf transformation 67]
128. ~old(X0) | patient(X0) | ~curious(X0) | wise(X0) [cnf transformation 42]
133. old(paul) [cnf transformation 20]
141. brave(paul) [cnf transformation 25]
142. ~patient(X0) | calm(X0) [duplicate literal removal 120]
212. 16 <=> calm(paul) [avatar definition]
213. ~calm(paul) <- (~16) [avatar component clause 212]
216. 17 <=> brave(paul) [avatar definition]
217. brave(paul) <- (17) [avatar component clause 216]
299. 17 [avatar split clause 141,216]
302. ~calm(paul) [resolution 100,133]
303. ~16 [avatar split clause 302,212]
310. curious(paul) | calm(paul) <- (17) [resolution 82,217]
312. curious(paul) <- (~16, 17) [subsumption resolution 310,213]
471. patient(paul) | ~curious(paul) | wise(paul) [resolution 128,133]
474. patient(paul) | wise(paul) <- (~16, 17) [subsumption resolution 471,312]
476. 57 <=> wise(paul) [avatar definition]
478. wise(paul) <- (57) [avatar component clause 476]
480. 58 <=> patient(paul) [avatar definition]
482. patient(paul) <- (58) [avatar component clause 480]
483. 57 | 58 | 16 | ~17 [avatar split clause 474,216,212,480,476]
486. calm(paul) <- (57) [resolution 478,109]
497. $false <- (~16, 57) [subsumption resolution 486,213]
498. 16 | ~57 [avatar contradiction clause 497]
499. calm(paul) <- (58) [resolution 482,142]
500. $false <- (~16, 58) [subsumption resolution 499,213]
501. 16 | ~58 [avatar contradiction clause 500]
502. $false [avatar sat refutation 299,303,483,498,501]
% SZS output end Proof for 879690317072677780743267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and kind is curious.
If lucy is not funny then someone is both not wise and brave and vice versa.
Everyone who is patient is not calm or not strong and vice versa.
If fred is both not tall and not wise then someone is either curious or not tall and vice versa.
Everyone who is not humble or not happy is both not creative and not old and vice versa.
If someone is calm then susan is both creative and not humble.
If someone is not wise or calm then john is both not calm and not funny and vice versa.
If someone is not old then someone is not tall and vice versa.
Everyone who is either not kind or wise is either not brave or not creative and vice versa.
Everyone who is both rich and calm is both not quiet and not funny and vice versa.
Everyone who is both wise and creative is either not generous or funny.
If someone is not wise or rich then alice is both not old and tall and vice versa.
Everyone who is both curious and not humble is either not creative or creative and vice versa.
If fred is tall or not generous then someone is either not wise or wise and vice versa.
If susan is both patient and not kind then someone is funny.
Someone is not strong.
John is either not humble or creative.
Susan is not calm.
Someone is either wise or tall.
Someone is happy or not patient.
Someone is either not kind or not tall.
Lucy is both not quiet and not wise. | Alice is humble. | contradiction | (![X]:((calm(X)&kind(X))=>curious(X)))&
((~funny(lucy))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:(patient(X)<=>(~calm(X)|~strong(X))))&
(((~tall(fred)&~wise(fred)))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~humble(X)|~happy(X))<=>(~creative(X)&~old(X))))&
((?[X]:(calm(X)))=>((creative(susan)&~humble(susan))))&
((?[X]:((~wise(X)|calm(X))))<=>((~calm(john)&~funny(john))))&
((?[X]:(~old(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~kind(X)<~>wise(X))<=>(~brave(X)<~>~creative(X))))&
(![X]:((rich(X)&calm(X))<=>(~quiet(X)&~funny(X))))&
(![X]:((wise(X)&creative(X))=>(~generous(X)<~>funny(X))))&
((?[X]:((~wise(X)|rich(X))))<=>((~old(alice)&tall(alice))))&
(![X]:((curious(X)&~humble(X))<=>(~creative(X)<~>creative(X))))&
(((tall(fred)|~generous(fred)))<=>(?[X]:((~wise(X)<~>wise(X)))))&
(((patient(susan)&~kind(susan)))=>(?[X]:(funny(X))))&
(?[X]:(~strong(X)))&
((~humble(john)<~>creative(john)))&
(~calm(susan))&
(?[X]:((wise(X)<~>tall(X))))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((~kind(X)<~>~tall(X))))&
((~quiet(lucy)&~wise(lucy))) | humble(alice) | [
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8977071021175643144218374
% SZS output start Proof for 8977071021175643144218374
5. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> (~old(X0) & ~creative(X0))) [input p4]
13. ! [X0] : ((~humble(X0) & curious(X0)) <=> (~creative(X0) <~> creative(X0))) [input p12]
23. humble(alice) [input hypothesis]
43. ! [X0] : (((~happy(X0) | ~humble(X0)) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [nnf transformation 5]
44. ! [X0] : ((~happy(X0) | ~humble(X0) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [flattening 43]
64. ! [X0] : (((~humble(X0) & curious(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (humble(X0) | ~curious(X0)))) [nnf transformation 13]
65. ! [X0] : (((~humble(X0) & curious(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | humble(X0) | ~curious(X0))) [flattening 64]
96. ~creative(X0) | humble(X0) [cnf transformation 44]
133. ~humble(X0) | creative(X0) | creative(X0) [cnf transformation 65]
134. ~humble(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 65]
153. humble(alice) [cnf transformation 23]
158. ~humble(X0) | creative(X0) [duplicate literal removal 133]
159. ~humble(X0) | ~creative(X0) [duplicate literal removal 134]
283. ~creative(X0) [subsumption resolution 159,96]
284. ~humble(X0) [subsumption resolution 158,283]
337. $false [subsumption resolution 153,284]
% SZS output end Proof for 8977071021175643144218374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or old is kind or tall. If fred is not curious or not creative then someone is not patient or funny. If someone is both tall and not curious then someone is strong or kind. If fred is either not creative or creative then paul is funny or not calm and vice versa. If someone is not creative then someone is both funny and not patient and vice versa. Everyone who is not humble is old or not old and vice versa. Everyone who is both not humble and brave is not calm or not tall and vice versa. If susan is not tall or tall then someone is both funny and not kind and vice versa. Everyone who is curious is not humble or brave. Everyone who is not rich is either not rich or not brave and vice versa. Everyone who is quiet is not wise and vice versa. If someone is not funny then susan is either not generous or brave. If mary is either not brave or not rich then fred is generous. Everyone who is not happy is happy. Everyone who is patient is either not humble or tall. If susan is both generous and funny then paul is rich or not curious and vice versa. Paul is not creative or not old. Susan is both not kind and wise. Alice is quiet. Someone is both strong and not generous. Someone is rich. Someone is both quiet and not wise. Susan is calm or quiet. Someone is both not humble and not old. | Susan is not tall. | entailment | (![X]:((kind(X)|old(X))=>(kind(X)|tall(X))))&
(((~curious(fred)|~creative(fred)))=>(?[X]:((~patient(X)|funny(X)))))&
((?[X]:((tall(X)&~curious(X))))=>(?[X]:((strong(X)|kind(X)))))&
(((~creative(fred)<~>creative(fred)))<=>((funny(paul)|~calm(paul))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:(~humble(X)<=>(old(X)|~old(X))))&
(![X]:((~humble(X)&brave(X))<=>(~calm(X)|~tall(X))))&
(((~tall(susan)|tall(susan)))<=>(?[X]:((funny(X)&~kind(X)))))&
(![X]:(curious(X)=>(~humble(X)|brave(X))))&
(![X]:(~rich(X)<=>(~rich(X)<~>~brave(X))))&
(![X]:(quiet(X)<=>~wise(X)))&
((?[X]:(~funny(X)))=>((~generous(susan)<~>brave(susan))))&
(((~brave(mary)<~>~rich(mary)))=>(generous(fred)))&
(![X]:(~happy(X)=>happy(X)))&
(![X]:(patient(X)=>(~humble(X)<~>tall(X))))&
(((generous(susan)&funny(susan)))<=>((rich(paul)|~curious(paul))))&
((~creative(paul)|~old(paul)))&
((~kind(susan)&wise(susan)))&
(quiet(alice))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:(rich(X)))&
(?[X]:((quiet(X)&~wise(X))))&
((calm(susan)|quiet(susan)))&
(?[X]:((~humble(X)&~old(X)))) | ~tall(susan) | [
"p5",
"p6",
"p9",
"p10",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 286198929734145372113039
% SZS output start Proof for 286198929734145372113039
6. ! [X0] : (~humble(X0) <=> (~old(X0) | old(X0))) [input p5]
7. ! [X0] : ((brave(X0) & ~humble(X0)) <=> (~tall(X0) | ~calm(X0))) [input p6]
10. ! [X0] : (~rich(X0) <=> (~rich(X0) <~> ~brave(X0))) [input p9]
11. ! [X0] : (quiet(X0) <=> ~wise(X0)) [input p10]
18. wise(susan) & ~kind(susan) [input p17]
23. quiet(susan) | calm(susan) [input p22]
25. tall(susan) [input hypothesis]
28. ! [X0] : (quiet(X0) => ~wise(X0)) [unused predicate definition removal 11]
37. ! [X0] : (~wise(X0) | ~quiet(X0)) [ennf transformation 28]
50. ! [X0] : ((~humble(X0) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | humble(X0))) [nnf transformation 6]
51. ! [X0] : ((~humble(X0) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | humble(X0))) [flattening 50]
52. ! [X0] : (((brave(X0) & ~humble(X0)) | (tall(X0) & calm(X0))) & ((~tall(X0) | ~calm(X0)) | (~brave(X0) | humble(X0)))) [nnf transformation 7]
53. ! [X0] : (((brave(X0) & ~humble(X0)) | (tall(X0) & calm(X0))) & (~tall(X0) | ~calm(X0) | ~brave(X0) | humble(X0))) [flattening 52]
59. ! [X0] : ((~rich(X0) | ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0)))) & (((brave(X0) | rich(X0)) & (~brave(X0) | ~rich(X0))) | rich(X0))) [nnf transformation 10]
87. ~humble(X0) | ~old(X0) [cnf transformation 51]
88. ~humble(X0) | old(X0) [cnf transformation 51]
89. ~tall(X0) | ~calm(X0) | ~brave(X0) | humble(X0) [cnf transformation 53]
101. brave(X0) | rich(X0) | rich(X0) [cnf transformation 59]
103. ~rich(X0) | ~rich(X0) | brave(X0) [cnf transformation 59]
104. ~wise(X0) | ~quiet(X0) [cnf transformation 37]
118. wise(susan) [cnf transformation 18]
124. quiet(susan) | calm(susan) [cnf transformation 23]
127. tall(susan) [cnf transformation 25]
128. brave(X0) | rich(X0) [duplicate literal removal 101]
129. ~rich(X0) | brave(X0) [duplicate literal removal 103]
181. ~humble(X0) [subsumption resolution 87,88]
182. ~brave(X0) | ~calm(X0) | ~tall(X0) [subsumption resolution 89,181]
184. 12 <=> tall(susan) [avatar definition]
185. tall(susan) <- (12) [avatar component clause 184]
199. brave(X0) [subsumption resolution 128,129]
247. 24 <=> calm(susan) [avatar definition]
249. calm(susan) <- (24) [avatar component clause 247]
251. 25 <=> quiet(susan) [avatar definition]
254. 24 | 25 [avatar split clause 124,251,247]
255. 12 [avatar split clause 127,184]
261. ~quiet(susan) [resolution 104,118]
262. ~25 [avatar split clause 261,251]
269. ~calm(X2) | ~tall(X2) [resolution 182,199]
270. ~tall(susan) <- (24) [resolution 269,249]
271. $false <- (12, 24) [subsumption resolution 270,185]
272. ~12 | ~24 [avatar contradiction clause 271]
273. $false [avatar sat refutation 254,255,262,272]
% SZS output end Proof for 286198929734145372113039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If john is strong then alice is not rich or not curious.
If paul is not tall or not old then someone is both not wise and tall and vice versa.
If fred is either not wise or not happy then someone is either funny or not quiet.
Everyone who is both strong and funny is not tall or happy and vice versa.
Everyone who is either not funny or old is both not calm and brave.
Everyone who is both not happy and not kind is either patient or tall and vice versa.
Everyone who is either not rich or quiet is either curious or calm.
If fred is both brave and happy then fred is not humble.
Everyone who is funny or wise is curious.
Everyone who is both not patient and not old is not kind and vice versa.
If someone is either rich or not old then someone is wise or humble and vice versa.
Everyone who is funny or creative is patient.
Everyone who is both not brave and curious is both curious and creative and vice versa.
Everyone who is both creative and not curious is not kind or wise.
If paul is kind then someone is both not rich and not strong and vice versa.
Everyone who is creative or not generous is not funny and vice versa.
Fred is not old or not funny.
Lucy is wise.
Paul is not wise or strong.
John is either curious or not humble.
Someone is both old and not quiet.
Someone is calm or quiet.
Someone is both creative and not strong. | Paul is not tall. | contradiction | ((strong(john))=>((~rich(alice)|~curious(alice))))&
(((~tall(paul)|~old(paul)))<=>(?[X]:((~wise(X)&tall(X)))))&
(((~wise(fred)<~>~happy(fred)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((strong(X)&funny(X))<=>(~tall(X)|happy(X))))&
(![X]:((~funny(X)<~>old(X))=>(~calm(X)&brave(X))))&
(![X]:((~happy(X)&~kind(X))<=>(patient(X)<~>tall(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(curious(X)<~>calm(X))))&
(((brave(fred)&happy(fred)))=>(~humble(fred)))&
(![X]:((funny(X)|wise(X))=>curious(X)))&
(![X]:((~patient(X)&~old(X))<=>~kind(X)))&
((?[X]:((rich(X)<~>~old(X))))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((funny(X)|creative(X))=>patient(X)))&
(![X]:((~brave(X)&curious(X))<=>(curious(X)&creative(X))))&
(![X]:((creative(X)&~curious(X))=>(~kind(X)|wise(X))))&
((kind(paul))<=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((creative(X)|~generous(X))<=>~funny(X)))&
((~old(fred)|~funny(fred)))&
(wise(lucy))&
((~wise(paul)|strong(paul)))&
((curious(john)<~>~humble(john)))&
(?[X]:((old(X)&~quiet(X))))&
(?[X]:((calm(X)|quiet(X))))&
(?[X]:((creative(X)&~strong(X)))) | ~tall(paul) | [
"p3",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7854104861096638140146122
% SZS output start Proof for 7854104861096638140146122
4. ! [X0] : ((funny(X0) & strong(X0)) <=> (happy(X0) | ~tall(X0))) [input p3]
6. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> (patient(X0) <~> tall(X0))) [input p5]
10. ! [X0] : ((~old(X0) & ~patient(X0)) <=> ~kind(X0)) [input p9]
12. ! [X0] : ((creative(X0) | funny(X0)) => patient(X0)) [input p11]
24. ~tall(paul) [input hypothesis]
34. ! [X0] : (patient(X0) | (~creative(X0) & ~funny(X0))) [ennf transformation 12]
45. ! [X0] : (((funny(X0) & strong(X0)) | (~happy(X0) & tall(X0))) & ((happy(X0) | ~tall(X0)) | (~funny(X0) | ~strong(X0)))) [nnf transformation 4]
46. ! [X0] : (((funny(X0) & strong(X0)) | (~happy(X0) & tall(X0))) & (happy(X0) | ~tall(X0) | ~funny(X0) | ~strong(X0))) [flattening 45]
48. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (kind(X0) | happy(X0)))) [nnf transformation 6]
49. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | kind(X0) | happy(X0))) [flattening 48]
51. ! [X0] : (((~old(X0) & ~patient(X0)) | kind(X0)) & (~kind(X0) | (old(X0) | patient(X0)))) [nnf transformation 10]
52. ! [X0] : (((~old(X0) & ~patient(X0)) | kind(X0)) & (~kind(X0) | old(X0) | patient(X0))) [flattening 51]
86. funny(X0) | tall(X0) [cnf transformation 46]
96. ~patient(X0) | tall(X0) | ~kind(X0) [cnf transformation 49]
106. ~patient(X0) | kind(X0) [cnf transformation 52]
114. ~funny(X0) | patient(X0) [cnf transformation 34]
137. ~tall(paul) [cnf transformation 24]
155. 5 <=> tall(paul) [avatar definition]
157. ~tall(paul) <- (~5) [avatar component clause 155]
294. ~5 [avatar split clause 137,155]
301. patient(X0) | tall(X0) [resolution 114,86]
323. tall(X1) | kind(X1) [resolution 301,106]
326. tall(X0) | ~kind(X0) | tall(X0) [resolution 96,301]
327. tall(X0) | ~kind(X0) [duplicate literal removal 326]
328. tall(X0) [subsumption resolution 327,323]
329. $false <- (~5) [resolution 328,157]
330. 5 [avatar contradiction clause 329]
331. $false [avatar sat refutation 294,330]
% SZS output end Proof for 7854104861096638140146122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not brave and not generous then someone is not generous and vice versa.
Everyone who is patient or not tall is both patient and not strong and vice versa.
Everyone who is not generous or generous is either not wise or calm and vice versa.
If mary is not calm then someone is old and vice versa.
Everyone who is funny is wise or rich and vice versa.
If someone is not old then susan is either not strong or happy.
Everyone who is either creative or not strong is not humble or patient and vice versa.
Everyone who is both not funny and generous is wise or tall and vice versa.
If john is calm or strong then susan is both not calm and not humble.
Everyone who is both not calm and not humble is not old and vice versa.
If someone is either not funny or generous then someone is both curious and not humble and vice versa.
Everyone who is humble or not creative is old and vice versa.
If susan is not generous or not patient then someone is both happy and quiet and vice versa.
Everyone who is not funny or generous is either strong or not strong.
Everyone who is both not curious and generous is both not rich and not happy.
Someone is either funny or patient.
Someone is funny or not strong.
Someone is tall.
Someone is both not funny and not strong.
Lucy is both not humble and not calm.
Lucy is happy or quiet.
Mary is either generous or wise.
Susan is either calm or creative. | John is not happy. | neutral | (((~brave(paul)&~generous(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((patient(X)|~tall(X))<=>(patient(X)&~strong(X))))&
(![X]:((~generous(X)|generous(X))<=>(~wise(X)<~>calm(X))))&
((~calm(mary))<=>(?[X]:(old(X))))&
(![X]:(funny(X)<=>(wise(X)|rich(X))))&
((?[X]:(~old(X)))=>((~strong(susan)<~>happy(susan))))&
(![X]:((creative(X)<~>~strong(X))<=>(~humble(X)|patient(X))))&
(![X]:((~funny(X)&generous(X))<=>(wise(X)|tall(X))))&
(((calm(john)|strong(john)))=>((~calm(susan)&~humble(susan))))&
(![X]:((~calm(X)&~humble(X))<=>~old(X)))&
((?[X]:((~funny(X)<~>generous(X))))<=>(?[X]:((curious(X)&~humble(X)))))&
(![X]:((humble(X)|~creative(X))<=>old(X)))&
(((~generous(susan)|~patient(susan)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:((~funny(X)|generous(X))=>(strong(X)<~>~strong(X))))&
(![X]:((~curious(X)&generous(X))=>(~rich(X)&~happy(X))))&
(?[X]:((funny(X)<~>patient(X))))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:(tall(X)))&
(?[X]:((~funny(X)&~strong(X))))&
((~humble(lucy)&~calm(lucy)))&
((happy(lucy)|quiet(lucy)))&
((generous(mary)<~>wise(mary)))&
((calm(susan)<~>creative(susan))) | ~happy(john) | [] | null | 0 |
Everyone who is either not strong or not wise is either not generous or not humble.
Everyone who is not curious is both quiet and tall and vice versa.
If someone is either not tall or curious then someone is not happy or funny.
If someone is not generous or wise then lucy is not brave.
If someone is wise then someone is not happy or funny and vice versa.
Everyone who is calm or tall is not funny and vice versa.
Everyone who is either not tall or brave is tall and vice versa.
Everyone who is not calm is both brave and not quiet.
If someone is not quiet or not old then someone is humble and vice versa.
If john is both kind and creative then someone is both not funny and not curious and vice versa.
If someone is not humble then alice is both not old and not creative and vice versa.
Everyone who is either not brave or not rich is either kind or not funny.
If susan is not generous or not calm then paul is not generous or quiet and vice versa.
Everyone who is creative or not happy is humble or not tall.
If lucy is both not wise and not strong then lucy is both not happy and calm.
Someone is old.
Someone is not kind.
Paul is both not tall and kind.
Mary is either not tall or tall.
Alice is both humble and not strong. | Susan is generous. | entailment | (![X]:((~strong(X)<~>~wise(X))=>(~generous(X)<~>~humble(X))))&
(![X]:(~curious(X)<=>(quiet(X)&tall(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>(?[X]:((~happy(X)|funny(X)))))&
((?[X]:((~generous(X)|wise(X))))=>(~brave(lucy)))&
((?[X]:(wise(X)))<=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:((calm(X)|tall(X))<=>~funny(X)))&
(![X]:((~tall(X)<~>brave(X))<=>tall(X)))&
(![X]:(~calm(X)=>(brave(X)&~quiet(X))))&
((?[X]:((~quiet(X)|~old(X))))<=>(?[X]:(humble(X))))&
(((kind(john)&creative(john)))<=>(?[X]:((~funny(X)&~curious(X)))))&
((?[X]:(~humble(X)))<=>((~old(alice)&~creative(alice))))&
(![X]:((~brave(X)<~>~rich(X))=>(kind(X)<~>~funny(X))))&
(((~generous(susan)|~calm(susan)))<=>((~generous(paul)|quiet(paul))))&
(![X]:((creative(X)|~happy(X))=>(humble(X)|~tall(X))))&
(((~wise(lucy)&~strong(lucy)))=>((~happy(lucy)&calm(lucy))))&
(?[X]:(old(X)))&
(?[X]:(~kind(X)))&
((~tall(paul)&kind(paul)))&
((~tall(mary)<~>tall(mary)))&
((humble(alice)&~strong(alice))) | generous(susan) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 679099076493304552171393
% SZS output start Proof for 679099076493304552171393
4. ? [X0] : (wise(X0) | ~generous(X0)) => ~brave(lucy) [input p3]
7. ! [X0] : ((~tall(X0) <~> brave(X0)) <=> tall(X0)) [input p6]
21. ~generous(susan) [input hypothesis]
27. ~brave(lucy) | ! [X0] : (~wise(X0) & generous(X0)) [ennf transformation 4]
48. ! [X0] : ((((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ~tall(X0)) & (tall(X0) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0))))) [nnf transformation 7]
81. ~brave(lucy) | generous(X0) [cnf transformation 27]
89. tall(X0) | brave(X0) | tall(X0) [cnf transformation 48]
91. brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 48]
125. ~generous(susan) [cnf transformation 21]
126. tall(X0) | brave(X0) [duplicate literal removal 89]
127. brave(X0) | ~tall(X0) [duplicate literal removal 91]
144. 5 <=> brave(lucy) [avatar definition]
146. ~brave(lucy) <- (~5) [avatar component clause 144]
149. 6 <=> ! [X0] : generous(X0) [avatar definition]
150. generous(X0) <- (6) [avatar component clause 149]
151. 6 | ~5 [avatar split clause 81,144,149]
173. brave(X0) [subsumption resolution 126,127]
246. 28 <=> generous(susan) [avatar definition]
248. ~generous(susan) <- (~28) [avatar component clause 246]
279. ~28 [avatar split clause 125,246]
280. $false <- (~5) [subsumption resolution 146,173]
281. 5 [avatar contradiction clause 280]
290. $false <- (6, ~28) [resolution 248,150]
291. ~6 | 28 [avatar contradiction clause 290]
292. $false [avatar sat refutation 151,279,281,291]
% SZS output end Proof for 679099076493304552171393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is curious.
Everyone who is either quiet or kind is not wise and vice versa.
If paul is not curious or funny then someone is not quiet and vice versa.
Everyone who is happy is both creative and not strong and vice versa.
Everyone who is quiet is creative or not generous.
If paul is not kind then fred is both curious and not happy.
If someone is quiet or not generous then someone is both not old and not tall and vice versa.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
If paul is creative or wise then lucy is rich or happy and vice versa.
Everyone who is both calm and not quiet is not rich or not wise.
Everyone who is patient or wise is quiet and vice versa.
Everyone who is both tall and generous is not tall or not creative and vice versa.
Everyone who is brave or not wise is happy or not humble and vice versa.
If john is either kind or not humble then someone is not curious and vice versa.
Everyone who is both not curious and happy is quiet or curious.
Someone is both not quiet and not calm.
Fred is either not kind or brave.
John is both not rich and not strong. | Fred is not calm. | neutral | (![X]:(generous(X)=>curious(X)))&
(![X]:((quiet(X)<~>kind(X))<=>~wise(X)))&
(((~curious(paul)|funny(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(happy(X)<=>(creative(X)&~strong(X))))&
(![X]:(quiet(X)=>(creative(X)|~generous(X))))&
((~kind(paul))=>((curious(fred)&~happy(fred))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
(((creative(paul)|wise(paul)))<=>((rich(lucy)|happy(lucy))))&
(![X]:((calm(X)&~quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(![X]:((tall(X)&generous(X))<=>(~tall(X)|~creative(X))))&
(![X]:((brave(X)|~wise(X))<=>(happy(X)|~humble(X))))&
(((kind(john)<~>~humble(john)))<=>(?[X]:(~curious(X))))&
(![X]:((~curious(X)&happy(X))=>(quiet(X)|curious(X))))&
(?[X]:((~quiet(X)&~calm(X))))&
((~kind(fred)<~>brave(fred)))&
((~rich(john)&~strong(john))) | ~calm(fred) | [] | null | 0 |
Everyone who is both kind and not curious is curious. If paul is not old or patient then paul is both not generous and patient. If someone is both not rich and not brave then lucy is not patient or not creative and vice versa. If susan is both curious and rich then paul is not tall and vice versa. Everyone who is both not wise and happy is both quiet and not old. If john is either happy or wise then fred is wise and vice versa. Everyone who is both not happy and not curious is wise and vice versa. If lucy is not funny or kind then fred is either not wise or not quiet and vice versa. If mary is both kind and not brave then someone is either humble or not rich and vice versa. If someone is both wise and not quiet then fred is either not wise or generous and vice versa. Everyone who is not funny is strong or happy. If someone is not strong then someone is strong and vice versa. If someone is either not brave or not creative then lucy is not curious or quiet. Everyone who is either generous or not happy is not curious or not rich. If mary is both not brave and patient then susan is not wise or strong and vice versa. If someone is wise or funny then someone is either curious or funny. Susan is not humble. Paul is patient or not rich. Mary is happy. Someone is either not brave or not rich. Alice is either not quiet or not curious. Someone is both rich and not old. Paul is either not humble or generous. | John is not patient. | neutral | (![X]:((kind(X)&~curious(X))=>curious(X)))&
(((~old(paul)|patient(paul)))=>((~generous(paul)&patient(paul))))&
((?[X]:((~rich(X)&~brave(X))))<=>((~patient(lucy)|~creative(lucy))))&
(((curious(susan)&rich(susan)))<=>(~tall(paul)))&
(![X]:((~wise(X)&happy(X))=>(quiet(X)&~old(X))))&
(((happy(john)<~>wise(john)))<=>(wise(fred)))&
(![X]:((~happy(X)&~curious(X))<=>wise(X)))&
(((~funny(lucy)|kind(lucy)))<=>((~wise(fred)<~>~quiet(fred))))&
(((kind(mary)&~brave(mary)))<=>(?[X]:((humble(X)<~>~rich(X)))))&
((?[X]:((wise(X)&~quiet(X))))<=>((~wise(fred)<~>generous(fred))))&
(![X]:(~funny(X)=>(strong(X)|happy(X))))&
((?[X]:(~strong(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>~creative(X))))=>((~curious(lucy)|quiet(lucy))))&
(![X]:((generous(X)<~>~happy(X))=>(~curious(X)|~rich(X))))&
(((~brave(mary)&patient(mary)))<=>((~wise(susan)|strong(susan))))&
((?[X]:((wise(X)|funny(X))))=>(?[X]:((curious(X)<~>funny(X)))))&
(~humble(susan))&
((patient(paul)|~rich(paul)))&
(happy(mary))&
(?[X]:((~brave(X)<~>~rich(X))))&
((~quiet(alice)<~>~curious(alice)))&
(?[X]:((rich(X)&~old(X))))&
((~humble(paul)<~>generous(paul))) | ~patient(john) | [] | null | 0 |
If alice is humble or patient then someone is both not quiet and brave.
If someone is not curious then mary is both wise and not wise.
If someone is humble then paul is both humble and not patient and vice versa.
Everyone who is either creative or humble is either quiet or kind.
If john is not funny or not happy then paul is both humble and rich.
If someone is not kind or kind then someone is both old and humble and vice versa.
Everyone who is not kind is either patient or quiet.
If john is brave or creative then john is brave or not happy and vice versa.
Everyone who is not old or curious is not calm and vice versa.
Everyone who is quiet or not curious is both not brave and kind and vice versa.
If john is both not quiet and wise then someone is humble and vice versa.
If susan is not rich then mary is either not funny or not tall.
If someone is either rich or not tall then someone is either not kind or creative and vice versa.
If paul is both generous and not kind then someone is funny or not old and vice versa.
Everyone who is not curious or not humble is both funny and humble.
If someone is both not quiet and not curious then someone is not humble and vice versa.
Paul is not happy.
Mary is not quiet.
Alice is either wise or quiet.
Someone is tall.
Someone is either not creative or happy.
John is brave.
Someone is old or not tall. | Susan is not funny. | entailment | (((humble(alice)|patient(alice)))=>(?[X]:((~quiet(X)&brave(X)))))&
((?[X]:(~curious(X)))=>((wise(mary)&~wise(mary))))&
((?[X]:(humble(X)))<=>((humble(paul)&~patient(paul))))&
(![X]:((creative(X)<~>humble(X))=>(quiet(X)<~>kind(X))))&
(((~funny(john)|~happy(john)))=>((humble(paul)&rich(paul))))&
((?[X]:((~kind(X)|kind(X))))<=>(?[X]:((old(X)&humble(X)))))&
(![X]:(~kind(X)=>(patient(X)<~>quiet(X))))&
(((brave(john)|creative(john)))<=>((brave(john)|~happy(john))))&
(![X]:((~old(X)|curious(X))<=>~calm(X)))&
(![X]:((quiet(X)|~curious(X))<=>(~brave(X)&kind(X))))&
(((~quiet(john)&wise(john)))<=>(?[X]:(humble(X))))&
((~rich(susan))=>((~funny(mary)<~>~tall(mary))))&
((?[X]:((rich(X)<~>~tall(X))))<=>(?[X]:((~kind(X)<~>creative(X)))))&
(((generous(paul)&~kind(paul)))<=>(?[X]:((funny(X)|~old(X)))))&
(![X]:((~curious(X)|~humble(X))=>(funny(X)&humble(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>(?[X]:(~humble(X))))&
(~happy(paul))&
(~quiet(mary))&
((wise(alice)<~>quiet(alice)))&
(?[X]:(tall(X)))&
(?[X]:((~creative(X)<~>happy(X))))&
(brave(john))&
(?[X]:((old(X)|~tall(X)))) | ~funny(susan) | [
"p2",
"p6",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6214002640595710193198278
% SZS output start Proof for 6214002640595710193198278
3. ? [X0] : humble(X0) <=> (~patient(paul) & humble(paul)) [input p2]
7. ! [X0] : (~kind(X0) => (patient(X0) <~> quiet(X0))) [input p6]
10. ! [X0] : ((~curious(X0) | quiet(X0)) <=> (kind(X0) & ~brave(X0))) [input p9]
14. (~kind(paul) & generous(paul)) <=> ? [X0] : (~old(X0) | funny(X0)) [input p13]
15. ! [X0] : ((~humble(X0) | ~curious(X0)) => (humble(X0) & funny(X0))) [input p14]
24. funny(susan) [input hypothesis]
32. ! [X0] : ((patient(X0) <~> quiet(X0)) | kind(X0)) [ennf transformation 7]
34. ! [X0] : ((humble(X0) & funny(X0)) | (humble(X0) & curious(X0))) [ennf transformation 15]
37. (? [X0] : humble(X0) | (patient(paul) | ~humble(paul))) & ((~patient(paul) & humble(paul)) | ! [X0] : ~humble(X0)) [nnf transformation 3]
38. (? [X0] : humble(X0) | patient(paul) | ~humble(paul)) & ((~patient(paul) & humble(paul)) | ! [X0] : ~humble(X0)) [flattening 37]
39. (? [X0] : humble(X0) | patient(paul) | ~humble(paul)) & ((~patient(paul) & humble(paul)) | ! [X1] : ~humble(X1)) [rectify 38]
40. ? [X0] : humble(X0) => humble(sK1) [choice axiom]
41. (humble(sK1) | patient(paul) | ~humble(paul)) & ((~patient(paul) & humble(paul)) | ! [X1] : ~humble(X1)) [skolemisation 39,40]
48. ! [X0] : (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | kind(X0)) [nnf transformation 32]
51. ! [X0] : (((~curious(X0) | quiet(X0)) | (~kind(X0) | brave(X0))) & ((kind(X0) & ~brave(X0)) | (curious(X0) & ~quiet(X0)))) [nnf transformation 10]
52. ! [X0] : ((~curious(X0) | quiet(X0) | ~kind(X0) | brave(X0)) & ((kind(X0) & ~brave(X0)) | (curious(X0) & ~quiet(X0)))) [flattening 51]
64. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & (? [X0] : (~old(X0) | funny(X0)) | (kind(paul) | ~generous(paul))) [nnf transformation 14]
65. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & (? [X0] : (~old(X0) | funny(X0)) | kind(paul) | ~generous(paul)) [flattening 64]
66. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & (? [X1] : (~old(X1) | funny(X1)) | kind(paul) | ~generous(paul)) [rectify 65]
67. ? [X1] : (~old(X1) | funny(X1)) => (~old(sK7) | funny(sK7)) [choice axiom]
68. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & ((~old(sK7) | funny(sK7)) | kind(paul) | ~generous(paul)) [skolemisation 66,67]
89. ~patient(paul) | ~humble(X1) [cnf transformation 41]
104. kind(X0) | patient(X0) | quiet(X0) [cnf transformation 48]
112. ~quiet(X0) | kind(X0) [cnf transformation 52]
131. ~kind(paul) | ~funny(X0) [cnf transformation 68]
136. humble(X0) | humble(X0) [cnf transformation 34]
149. funny(susan) [cnf transformation 24]
150. humble(X0) [duplicate literal removal 136]
185. 8 <=> patient(paul) [avatar definition]
186. ~patient(paul) <- (~8) [avatar component clause 185]
194. 10 <=> ! [X1] : ~humble(X1) [avatar definition]
195. ~humble(X1) <- (10) [avatar component clause 194]
196. 10 | ~8 [avatar split clause 89,185,194]
311. 35 <=> kind(paul) [avatar definition]
313. ~kind(paul) <- (~35) [avatar component clause 311]
316. 36 <=> ! [X0] : ~funny(X0) [avatar definition]
317. ~funny(X0) <- (36) [avatar component clause 316]
318. 36 | ~35 [avatar split clause 131,311,316]
367. $false <- (10) [subsumption resolution 195,150]
368. ~10 [avatar contradiction clause 367]
373. $false <- (36) [resolution 317,149]
374. ~36 [avatar contradiction clause 373]
384. patient(paul) | quiet(paul) <- (~35) [resolution 104,313]
385. quiet(paul) <- (~8, ~35) [subsumption resolution 384,186]
387. kind(paul) <- (~8, ~35) [resolution 385,112]
388. $false <- (~8, ~35) [subsumption resolution 387,313]
389. 8 | 35 [avatar contradiction clause 388]
390. $false [avatar sat refutation 196,318,368,374,389]
% SZS output end Proof for 6214002640595710193198278
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both funny and wise is either not quiet or wise and vice versa.
If someone is not funny or calm then john is not creative.
Everyone who is both kind and not happy is both not old and quiet and vice versa.
Everyone who is not patient is either tall or not patient and vice versa.
If someone is both brave and not old then paul is both wise and not patient and vice versa.
Everyone who is either strong or not rich is not old or not strong.
If paul is kind then lucy is not patient and vice versa.
If someone is rich then susan is not funny and vice versa.
Everyone who is patient is quiet or not tall.
If lucy is happy or funny then paul is both not happy and not quiet.
If mary is not strong then fred is both not rich and not old and vice versa.
Everyone who is either wise or not tall is not creative.
Everyone who is both humble and not strong is not wise.
If someone is not strong then lucy is strong.
Everyone who is strong is not old or happy.
If fred is happy or not happy then lucy is funny or not strong and vice versa.
Fred is wise or not brave.
Someone is tall or not tall.
Someone is both not curious and patient.
Someone is either not curious or not brave.
Someone is not humble.
Susan is not tall.
Mary is either generous or not patient.
Susan is either not creative or curious. | John is creative. | contradiction | (![X]:((funny(X)&wise(X))<=>(~quiet(X)<~>wise(X))))&
((?[X]:((~funny(X)|calm(X))))=>(~creative(john)))&
(![X]:((kind(X)&~happy(X))<=>(~old(X)&quiet(X))))&
(![X]:(~patient(X)<=>(tall(X)<~>~patient(X))))&
((?[X]:((brave(X)&~old(X))))<=>((wise(paul)&~patient(paul))))&
(![X]:((strong(X)<~>~rich(X))=>(~old(X)|~strong(X))))&
((kind(paul))<=>(~patient(lucy)))&
((?[X]:(rich(X)))<=>(~funny(susan)))&
(![X]:(patient(X)=>(quiet(X)|~tall(X))))&
(((happy(lucy)|funny(lucy)))=>((~happy(paul)&~quiet(paul))))&
((~strong(mary))<=>((~rich(fred)&~old(fred))))&
(![X]:((wise(X)<~>~tall(X))=>~creative(X)))&
(![X]:((humble(X)&~strong(X))=>~wise(X)))&
((?[X]:(~strong(X)))=>(strong(lucy)))&
(![X]:(strong(X)=>(~old(X)|happy(X))))&
(((happy(fred)|~happy(fred)))<=>((funny(lucy)|~strong(lucy))))&
((wise(fred)|~brave(fred)))&
(?[X]:((tall(X)|~tall(X))))&
(?[X]:((~curious(X)&patient(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:(~humble(X)))&
(~tall(susan))&
((generous(mary)<~>~patient(mary)))&
((~creative(susan)<~>curious(susan))) | creative(john) | [
"p0",
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2781203671994912784410179
% SZS output start Proof for 2781203671994912784410179
1. ! [X0] : ((wise(X0) & funny(X0)) <=> (~quiet(X0) <~> wise(X0))) [input p0]
2. ? [X0] : (calm(X0) | ~funny(X0)) => ~creative(john) [input p1]
10. (funny(lucy) | happy(lucy)) => (~quiet(paul) & ~happy(paul)) [input p9]
25. creative(john) [input hypothesis]
28. ? [X0] : ~funny(X0) => ~creative(john) [pure predicate removal 2]
29. ~creative(john) | ! [X0] : funny(X0) [ennf transformation 28]
34. (~quiet(paul) & ~happy(paul)) | (~funny(lucy) & ~happy(lucy)) [ennf transformation 10]
39. ! [X0] : (((wise(X0) & funny(X0)) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) & (((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | (~wise(X0) | ~funny(X0)))) [nnf transformation 1]
40. ! [X0] : (((wise(X0) & funny(X0)) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) & (((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~wise(X0) | ~funny(X0))) [flattening 39]
70. ~wise(X0) | quiet(X0) | ~wise(X0) | ~funny(X0) [cnf transformation 40]
73. wise(X0) | wise(X0) | quiet(X0) [cnf transformation 40]
75. ~creative(john) | funny(X0) [cnf transformation 29]
98. ~quiet(paul) | ~funny(lucy) [cnf transformation 34]
121. creative(john) [cnf transformation 25]
125. ~wise(X0) | quiet(X0) | ~funny(X0) [duplicate literal removal 70]
126. quiet(X0) | wise(X0) [duplicate literal removal 73]
127. ~funny(X0) | quiet(X0) [subsumption resolution 125,126]
129. 1 <=> ! [X0] : funny(X0) [avatar definition]
130. funny(X0) <- (1) [avatar component clause 129]
132. 2 <=> creative(john) [avatar definition]
135. 1 | ~2 [avatar split clause 75,132,129]
184. 13 <=> funny(lucy) [avatar definition]
186. ~funny(lucy) <- (~13) [avatar component clause 184]
188. 14 <=> quiet(paul) [avatar definition]
190. ~quiet(paul) <- (~14) [avatar component clause 188]
191. ~13 | ~14 [avatar split clause 98,188,184]
272. 2 [avatar split clause 121,132]
279. $false <- (1, ~13) [resolution 186,130]
280. ~1 | 13 [avatar contradiction clause 279]
289. quiet(X0) <- (1) [resolution 127,130]
290. $false <- (1, ~14) [resolution 289,190]
291. ~1 | 14 [avatar contradiction clause 290]
292. $false [avatar sat refutation 135,191,272,280,291]
% SZS output end Proof for 2781203671994912784410179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not wise or happy then alice is both not brave and not tall.
If alice is kind then fred is not kind or not funny and vice versa.
Everyone who is both not rich and not curious is not quiet or not curious and vice versa.
Everyone who is patient is either not kind or not quiet and vice versa.
Everyone who is patient or old is either not rich or not kind.
If someone is either brave or not generous then someone is either generous or not calm.
Everyone who is either creative or calm is patient or not generous and vice versa.
If someone is both not generous and not old then mary is either not humble or not wise.
If someone is not funny or rich then lucy is either humble or funny and vice versa.
Everyone who is generous or not patient is either not quiet or quiet and vice versa.
Everyone who is both kind and not calm is not kind or brave.
If alice is both not creative and not happy then someone is either not strong or not rich.
If someone is rich or not generous then paul is both wise and not old and vice versa.
Everyone who is not quiet or creative is either not brave or not wise and vice versa.
Everyone who is both not patient and quiet is not strong and vice versa.
Someone is rich or not calm.
Someone is both strong and not creative.
Someone is both not patient and creative.
Someone is not rich or tall.
John is either not wise or tall.
Paul is either not kind or not old.
Fred is funny.
Someone is not tall. | John is rich. | neutral | ((?[X]:((~wise(X)<~>happy(X))))=>((~brave(alice)&~tall(alice))))&
((kind(alice))<=>((~kind(fred)|~funny(fred))))&
(![X]:((~rich(X)&~curious(X))<=>(~quiet(X)|~curious(X))))&
(![X]:(patient(X)<=>(~kind(X)<~>~quiet(X))))&
(![X]:((patient(X)|old(X))=>(~rich(X)<~>~kind(X))))&
((?[X]:((brave(X)<~>~generous(X))))=>(?[X]:((generous(X)<~>~calm(X)))))&
(![X]:((creative(X)<~>calm(X))<=>(patient(X)|~generous(X))))&
((?[X]:((~generous(X)&~old(X))))=>((~humble(mary)<~>~wise(mary))))&
((?[X]:((~funny(X)|rich(X))))<=>((humble(lucy)<~>funny(lucy))))&
(![X]:((generous(X)|~patient(X))<=>(~quiet(X)<~>quiet(X))))&
(![X]:((kind(X)&~calm(X))=>(~kind(X)|brave(X))))&
(((~creative(alice)&~happy(alice)))=>(?[X]:((~strong(X)<~>~rich(X)))))&
((?[X]:((rich(X)|~generous(X))))<=>((wise(paul)&~old(paul))))&
(![X]:((~quiet(X)|creative(X))<=>(~brave(X)<~>~wise(X))))&
(![X]:((~patient(X)&quiet(X))<=>~strong(X)))&
(?[X]:((rich(X)|~calm(X))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:((~rich(X)|tall(X))))&
((~wise(john)<~>tall(john)))&
((~kind(paul)<~>~old(paul)))&
(funny(fred))&
(?[X]:(~tall(X))) | rich(john) | [] | null | 0 |
Everyone who is either not curious or rich is patient and vice versa. Everyone who is not rich or happy is both brave and not strong and vice versa. Everyone who is either not brave or quiet is not humble and vice versa. If susan is creative then someone is both not kind and not funny and vice versa. Everyone who is both not rich and patient is either not happy or strong and vice versa. If someone is either not funny or not old then mary is not generous or not strong and vice versa. If fred is generous or patient then mary is either kind or strong. Everyone who is humble or not rich is either not quiet or not creative. Everyone who is both calm and funny is not brave or kind and vice versa. If someone is not curious or not rich then someone is not brave. If someone is tall then fred is brave and vice versa. Everyone who is not humble or old is both not wise and wise and vice versa. Everyone who is humble is rich or not curious and vice versa. Everyone who is not tall is generous. Someone is not wise. Someone is both not tall and not strong. Alice is brave or quiet. Someone is curious. Someone is not kind or not creative. | Susan is not patient. | neutral | (![X]:((~curious(X)<~>rich(X))<=>patient(X)))&
(![X]:((~rich(X)|happy(X))<=>(brave(X)&~strong(X))))&
(![X]:((~brave(X)<~>quiet(X))<=>~humble(X)))&
((creative(susan))<=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((~rich(X)&patient(X))<=>(~happy(X)<~>strong(X))))&
((?[X]:((~funny(X)<~>~old(X))))<=>((~generous(mary)|~strong(mary))))&
(((generous(fred)|patient(fred)))=>((kind(mary)<~>strong(mary))))&
(![X]:((humble(X)|~rich(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:((calm(X)&funny(X))<=>(~brave(X)|kind(X))))&
((?[X]:((~curious(X)|~rich(X))))=>(?[X]:(~brave(X))))&
((?[X]:(tall(X)))<=>(brave(fred)))&
(![X]:((~humble(X)|old(X))<=>(~wise(X)&wise(X))))&
(![X]:(humble(X)<=>(rich(X)|~curious(X))))&
(![X]:(~tall(X)=>generous(X)))&
(?[X]:(~wise(X)))&
(?[X]:((~tall(X)&~strong(X))))&
((brave(alice)|quiet(alice)))&
(?[X]:(curious(X)))&
(?[X]:((~kind(X)|~creative(X)))) | ~patient(susan) | [] | null | 0 |
If susan is not patient or not calm then someone is either funny or not calm and vice versa.
If fred is both not creative and not tall then paul is kind and vice versa.
Everyone who is not creative or quiet is both not creative and quiet and vice versa.
Everyone who is brave or not wise is both not rich and creative and vice versa.
Everyone who is curious is either curious or humble and vice versa.
If alice is either not creative or curious then mary is quiet.
If someone is either not humble or not kind then lucy is both generous and not quiet and vice versa.
Everyone who is both calm and strong is both quiet and wise.
If lucy is both rich and not generous then paul is either creative or not tall and vice versa.
If someone is rich then paul is both not old and strong.
If someone is not creative or wise then fred is humble.
Everyone who is not kind or funny is either patient or tall and vice versa.
If alice is not patient then someone is brave.
Everyone who is either not funny or funny is either not kind or quiet and vice versa.
If lucy is both funny and tall then someone is either quiet or kind.
If fred is humble then john is both brave and happy and vice versa.
Someone is both calm and brave.
Someone is not funny.
Someone is both curious and patient.
Fred is not kind or quiet.
Someone is not kind or happy. | Mary is wise. | contradiction | (((~patient(susan)|~calm(susan)))<=>(?[X]:((funny(X)<~>~calm(X)))))&
(((~creative(fred)&~tall(fred)))<=>(kind(paul)))&
(![X]:((~creative(X)|quiet(X))<=>(~creative(X)&quiet(X))))&
(![X]:((brave(X)|~wise(X))<=>(~rich(X)&creative(X))))&
(![X]:(curious(X)<=>(curious(X)<~>humble(X))))&
(((~creative(alice)<~>curious(alice)))=>(quiet(mary)))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((generous(lucy)&~quiet(lucy))))&
(![X]:((calm(X)&strong(X))=>(quiet(X)&wise(X))))&
(((rich(lucy)&~generous(lucy)))<=>((creative(paul)<~>~tall(paul))))&
((?[X]:(rich(X)))=>((~old(paul)&strong(paul))))&
((?[X]:((~creative(X)|wise(X))))=>(humble(fred)))&
(![X]:((~kind(X)|funny(X))<=>(patient(X)<~>tall(X))))&
((~patient(alice))=>(?[X]:(brave(X))))&
(![X]:((~funny(X)<~>funny(X))<=>(~kind(X)<~>quiet(X))))&
(((funny(lucy)&tall(lucy)))=>(?[X]:((quiet(X)<~>kind(X)))))&
((humble(fred))<=>((brave(john)&happy(john))))&
(?[X]:((calm(X)&brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((curious(X)&patient(X))))&
((~kind(fred)|quiet(fred)))&
(?[X]:((~kind(X)|happy(X)))) | wise(mary) | [
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6838675676975167718202209
% SZS output start Proof for 6838675676975167718202209
5. ! [X0] : (curious(X0) <=> (curious(X0) <~> humble(X0))) [input p4]
11. ? [X0] : (wise(X0) | ~creative(X0)) => humble(fred) [input p10]
22. wise(mary) [input hypothesis]
28. humble(fred) | ! [X0] : (~wise(X0) & creative(X0)) [ennf transformation 11]
43. ! [X0] : ((curious(X0) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | ~curious(X0))) [nnf transformation 5]
90. ~humble(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 43]
92. curious(X0) | curious(X0) | ~humble(X0) [cnf transformation 43]
111. humble(fred) | ~wise(X0) [cnf transformation 28]
139. wise(mary) [cnf transformation 22]
144. ~humble(X0) | ~curious(X0) [duplicate literal removal 90]
145. curious(X0) | ~humble(X0) [duplicate literal removal 92]
189. ~humble(X0) [subsumption resolution 144,145]
251. ~wise(X0) [subsumption resolution 111,189]
299. $false [subsumption resolution 139,251]
% SZS output end Proof for 6838675676975167718202209
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or calm is either creative or not wise.
Everyone who is not tall is kind.
Everyone who is either creative or not curious is either not kind or funny and vice versa.
Everyone who is not humble or not happy is strong and vice versa.
Everyone who is not calm or generous is either not generous or curious and vice versa.
If fred is not brave or humble then someone is both not funny and not humble and vice versa.
Everyone who is both wise and not kind is either tall or not calm.
Everyone who is generous or curious is wise or not curious and vice versa.
If someone is tall then susan is not creative and vice versa.
If alice is either not kind or not patient then lucy is calm and vice versa.
If someone is generous or rich then lucy is not old.
If someone is quiet or brave then lucy is generous or kind and vice versa.
Everyone who is rich or tall is both happy and quiet and vice versa.
Everyone who is wise is not patient or wise.
If alice is either generous or not tall then paul is not creative or kind.
If someone is not rich then fred is both happy and not patient and vice versa.
John is both funny and not old.
Lucy is wise.
Someone is both creative and not tall.
Someone is brave or not brave.
Lucy is calm or old.
Someone is old or kind.
Someone is strong or not generous.
Fred is not tall or tall. | Lucy is creative. | entailment | (![X]:((creative(X)|calm(X))=>(creative(X)<~>~wise(X))))&
(![X]:(~tall(X)=>kind(X)))&
(![X]:((creative(X)<~>~curious(X))<=>(~kind(X)<~>funny(X))))&
(![X]:((~humble(X)|~happy(X))<=>strong(X)))&
(![X]:((~calm(X)|generous(X))<=>(~generous(X)<~>curious(X))))&
(((~brave(fred)|humble(fred)))<=>(?[X]:((~funny(X)&~humble(X)))))&
(![X]:((wise(X)&~kind(X))=>(tall(X)<~>~calm(X))))&
(![X]:((generous(X)|curious(X))<=>(wise(X)|~curious(X))))&
((?[X]:(tall(X)))<=>(~creative(susan)))&
(((~kind(alice)<~>~patient(alice)))<=>(calm(lucy)))&
((?[X]:((generous(X)|rich(X))))=>(~old(lucy)))&
((?[X]:((quiet(X)|brave(X))))<=>((generous(lucy)|kind(lucy))))&
(![X]:((rich(X)|tall(X))<=>(happy(X)&quiet(X))))&
(![X]:(wise(X)=>(~patient(X)|wise(X))))&
(((generous(alice)<~>~tall(alice)))=>((~creative(paul)|kind(paul))))&
((?[X]:(~rich(X)))<=>((happy(fred)&~patient(fred))))&
((funny(john)&~old(john)))&
(wise(lucy))&
(?[X]:((creative(X)&~tall(X))))&
(?[X]:((brave(X)|~brave(X))))&
((calm(lucy)|old(lucy)))&
(?[X]:((old(X)|kind(X))))&
(?[X]:((strong(X)|~generous(X))))&
((~tall(fred)|tall(fred))) | creative(lucy) | [
"p0",
"p4",
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 474568397890415805615564
% SZS output start Proof for 474568397890415805615564
1. ! [X0] : ((calm(X0) | creative(X0)) => (creative(X0) <~> ~wise(X0))) [input p0]
5. ! [X0] : ((generous(X0) | ~calm(X0)) <=> (~generous(X0) <~> curious(X0))) [input p4]
8. ! [X0] : ((curious(X0) | generous(X0)) <=> (~curious(X0) | wise(X0))) [input p7]
11. ? [X0] : (rich(X0) | generous(X0)) => ~old(lucy) [input p10]
21. old(lucy) | calm(lucy) [input p20]
25. ~creative(lucy) [input hypothesis]
27. ! [X0] : ((creative(X0) <~> ~wise(X0)) | (~calm(X0) & ~creative(X0))) [ennf transformation 1]
33. ~old(lucy) | ! [X0] : (~rich(X0) & ~generous(X0)) [ennf transformation 11]
38. ! [X0] : (((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (~calm(X0) & ~creative(X0))) [nnf transformation 27]
40. ! [X0] : (((generous(X0) | ~calm(X0)) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) & (((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | (~generous(X0) & calm(X0)))) [nnf transformation 5]
41. ! [X0] : ((generous(X0) | ~calm(X0) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) & (((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | (~generous(X0) & calm(X0)))) [flattening 40]
48. ! [X0] : (((curious(X0) | generous(X0)) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | (~curious(X0) & ~generous(X0)))) [nnf transformation 8]
49. ! [X0] : ((curious(X0) | generous(X0) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | (~curious(X0) & ~generous(X0)))) [flattening 48]
77. ~wise(X0) | creative(X0) | ~calm(X0) [cnf transformation 38]
91. curious(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 41]
92. ~curious(X0) | generous(X0) | calm(X0) [cnf transformation 41]
104. ~curious(X0) | wise(X0) | ~curious(X0) [cnf transformation 49]
106. curious(X0) | generous(X0) | curious(X0) [cnf transformation 49]
113. ~old(lucy) | ~generous(X0) [cnf transformation 33]
136. old(lucy) | calm(lucy) [cnf transformation 21]
140. ~creative(lucy) [cnf transformation 25]
141. ~curious(X0) | wise(X0) [duplicate literal removal 104]
142. curious(X0) | generous(X0) [duplicate literal removal 106]
143. ~generous(X0) | curious(X0) [duplicate literal removal 91]
171. curious(X0) [subsumption resolution 142,143]
172. wise(X0) [subsumption resolution 141,171]
187. 9 <=> calm(lucy) [avatar definition]
188. calm(lucy) <- (9) [avatar component clause 187]
189. ~calm(lucy) <- (~9) [avatar component clause 187]
206. 13 <=> old(lucy) [avatar definition]
211. 14 <=> ! [X0] : ~generous(X0) [avatar definition]
212. ~generous(X0) <- (14) [avatar component clause 211]
213. 14 | ~13 [avatar split clause 113,206,211]
276. 9 | 13 [avatar split clause 136,206,187]
298. ~calm(X0) | creative(X0) [resolution 77,172]
300. creative(lucy) <- (9) [resolution 298,188]
301. $false <- (9) [subsumption resolution 300,140]
302. ~9 [avatar contradiction clause 301]
305. generous(X0) | calm(X0) [resolution 92,171]
306. calm(X0) <- (14) [subsumption resolution 305,212]
309. $false <- (~9, 14) [resolution 306,189]
310. 9 | ~14 [avatar contradiction clause 309]
311. $false [avatar sat refutation 213,276,302,310]
% SZS output end Proof for 474568397890415805615564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not creative and happy is not tall. If someone is rich or patient then someone is either happy or not strong. Everyone who is brave is either not generous or brave. Everyone who is old or not patient is calm or kind. If alice is rich or kind then mary is either not calm or humble and vice versa. If someone is funny then john is both not kind and not rich. If someone is both quiet and not funny then mary is not kind or curious. Everyone who is patient is either wise or patient and vice versa. If susan is generous or not humble then lucy is either wise or quiet and vice versa. Everyone who is either not quiet or humble is not wise or brave. Everyone who is not rich or not wise is either wise or generous and vice versa. If paul is both rich and not strong then alice is both not strong and quiet. Everyone who is not old or not brave is happy or rich and vice versa. Everyone who is old or brave is not happy. Everyone who is both not patient and not funny is either strong or not quiet. Everyone who is not tall or wise is not creative. John is both quiet and not humble. Someone is both not humble and strong. Paul is either not patient or not funny. Someone is both calm and not kind. Susan is either not quiet or not rich. Someone is rich. Someone is either curious or not wise. Someone is either not kind or not quiet. | Mary is wise. | contradiction | (![X]:((~creative(X)&happy(X))=>~tall(X)))&
((?[X]:((rich(X)|patient(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(brave(X)=>(~generous(X)<~>brave(X))))&
(![X]:((old(X)|~patient(X))=>(calm(X)|kind(X))))&
(((rich(alice)|kind(alice)))<=>((~calm(mary)<~>humble(mary))))&
((?[X]:(funny(X)))=>((~kind(john)&~rich(john))))&
((?[X]:((quiet(X)&~funny(X))))=>((~kind(mary)|curious(mary))))&
(![X]:(patient(X)<=>(wise(X)<~>patient(X))))&
(((generous(susan)|~humble(susan)))<=>((wise(lucy)<~>quiet(lucy))))&
(![X]:((~quiet(X)<~>humble(X))=>(~wise(X)|brave(X))))&
(![X]:((~rich(X)|~wise(X))<=>(wise(X)<~>generous(X))))&
(((rich(paul)&~strong(paul)))=>((~strong(alice)&quiet(alice))))&
(![X]:((~old(X)|~brave(X))<=>(happy(X)|rich(X))))&
(![X]:((old(X)|brave(X))=>~happy(X)))&
(![X]:((~patient(X)&~funny(X))=>(strong(X)<~>~quiet(X))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
((quiet(john)&~humble(john)))&
(?[X]:((~humble(X)&strong(X))))&
((~patient(paul)<~>~funny(paul)))&
(?[X]:((calm(X)&~kind(X))))&
((~quiet(susan)<~>~rich(susan)))&
(?[X]:(rich(X)))&
(?[X]:((curious(X)<~>~wise(X))))&
(?[X]:((~kind(X)<~>~quiet(X)))) | wise(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1559696138249922327330093
% SZS output start Proof for 1559696138249922327330093
8. ! [X0] : (patient(X0) <=> (wise(X0) <~> patient(X0))) [input p7]
25. wise(mary) [input hypothesis]
51. ! [X0] : ((patient(X0) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0)))) & (((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | ~patient(X0))) [nnf transformation 8]
93. ~patient(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 51]
94. patient(X0) | patient(X0) | ~wise(X0) [cnf transformation 51]
137. wise(mary) [cnf transformation 25]
140. ~patient(X0) | ~wise(X0) [duplicate literal removal 93]
141. patient(X0) | ~wise(X0) [duplicate literal removal 94]
208. ~wise(X0) [subsumption resolution 140,141]
277. $false [subsumption resolution 137,208]
% SZS output end Proof for 1559696138249922327330093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not quiet is either brave or calm and vice versa.
If someone is both calm and not wise then someone is patient or calm and vice versa.
If someone is either not happy or quiet then mary is both not patient and not calm and vice versa.
If paul is both creative and not rich then mary is not tall or creative.
Everyone who is not old or funny is either old or not patient.
If john is not wise then fred is not creative or not tall and vice versa.
Everyone who is not calm is creative or not wise and vice versa.
Everyone who is old is both wise and not calm and vice versa.
If mary is not generous then mary is not happy.
Everyone who is both kind and strong is not tall or funny and vice versa.
Everyone who is old or brave is old.
Everyone who is humble or not funny is not generous and vice versa.
Everyone who is either patient or funny is either not old or creative.
If someone is both kind and not brave then lucy is both curious and quiet and vice versa.
Everyone who is either old or generous is both humble and funny and vice versa.
Everyone who is not creative or generous is kind and vice versa.
Susan is not humble.
Someone is not kind.
Someone is strong.
Mary is both not funny and strong.
Someone is not patient.
Someone is not humble or happy.
Someone is either old or not generous. | Fred is generous. | contradiction | (![X]:((curious(X)&~quiet(X))<=>(brave(X)<~>calm(X))))&
((?[X]:((calm(X)&~wise(X))))<=>(?[X]:((patient(X)|calm(X)))))&
((?[X]:((~happy(X)<~>quiet(X))))<=>((~patient(mary)&~calm(mary))))&
(((creative(paul)&~rich(paul)))=>((~tall(mary)|creative(mary))))&
(![X]:((~old(X)|funny(X))=>(old(X)<~>~patient(X))))&
((~wise(john))<=>((~creative(fred)|~tall(fred))))&
(![X]:(~calm(X)<=>(creative(X)|~wise(X))))&
(![X]:(old(X)<=>(wise(X)&~calm(X))))&
((~generous(mary))=>(~happy(mary)))&
(![X]:((kind(X)&strong(X))<=>(~tall(X)|funny(X))))&
(![X]:((old(X)|brave(X))=>old(X)))&
(![X]:((humble(X)|~funny(X))<=>~generous(X)))&
(![X]:((patient(X)<~>funny(X))=>(~old(X)<~>creative(X))))&
((?[X]:((kind(X)&~brave(X))))<=>((curious(lucy)&quiet(lucy))))&
(![X]:((old(X)<~>generous(X))<=>(humble(X)&funny(X))))&
(![X]:((~creative(X)|generous(X))<=>kind(X)))&
(~humble(susan))&
(?[X]:(~kind(X)))&
(?[X]:(strong(X)))&
((~funny(mary)&strong(mary)))&
(?[X]:(~patient(X)))&
(?[X]:((~humble(X)|happy(X))))&
(?[X]:((old(X)<~>~generous(X)))) | generous(fred) | [
"p1",
"p4",
"p6",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 873047069107953227343339
% SZS output start Proof for 873047069107953227343339
2. ? [X0] : (~wise(X0) & calm(X0)) <=> ? [X0] : (calm(X0) | patient(X0)) [input p1]
5. ! [X0] : ((funny(X0) | ~old(X0)) => (old(X0) <~> ~patient(X0))) [input p4]
7. ! [X0] : (~calm(X0) <=> (~wise(X0) | creative(X0))) [input p6]
12. ! [X0] : ((~funny(X0) | humble(X0)) <=> ~generous(X0)) [input p11]
15. ! [X0] : ((old(X0) <~> generous(X0)) <=> (funny(X0) & humble(X0))) [input p14]
24. generous(fred) [input hypothesis]
25. ? [X0] : (~wise(X0) & calm(X0)) <=> ? [X1] : (calm(X1) | patient(X1)) [rectify 2]
27. ! [X0] : ((old(X0) <~> ~patient(X0)) | (~funny(X0) & old(X0))) [ennf transformation 5]
33. (? [X0] : (~wise(X0) & calm(X0)) | ! [X1] : (~calm(X1) & ~patient(X1))) & (? [X1] : (calm(X1) | patient(X1)) | ! [X0] : (wise(X0) | ~calm(X0))) [nnf transformation 25]
34. (? [X0] : (~wise(X0) & calm(X0)) | ! [X1] : (~calm(X1) & ~patient(X1))) & (? [X2] : (calm(X2) | patient(X2)) | ! [X3] : (wise(X3) | ~calm(X3))) [rectify 33]
35. ? [X0] : (~wise(X0) & calm(X0)) => (~wise(sK0) & calm(sK0)) [choice axiom]
36. ? [X2] : (calm(X2) | patient(X2)) => (calm(sK1) | patient(sK1)) [choice axiom]
37. ((~wise(sK0) & calm(sK0)) | ! [X1] : (~calm(X1) & ~patient(X1))) & ((calm(sK1) | patient(sK1)) | ! [X3] : (wise(X3) | ~calm(X3))) [skolemisation 34,36,35]
43. ! [X0] : (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | (~funny(X0) & old(X0))) [nnf transformation 27]
46. ! [X0] : ((~calm(X0) | (wise(X0) & ~creative(X0))) & ((~wise(X0) | creative(X0)) | calm(X0))) [nnf transformation 7]
47. ! [X0] : ((~calm(X0) | (wise(X0) & ~creative(X0))) & (~wise(X0) | creative(X0) | calm(X0))) [flattening 46]
52. ! [X0] : (((~funny(X0) | humble(X0)) | generous(X0)) & (~generous(X0) | (funny(X0) & ~humble(X0)))) [nnf transformation 12]
53. ! [X0] : ((~funny(X0) | humble(X0) | generous(X0)) & (~generous(X0) | (funny(X0) & ~humble(X0)))) [flattening 52]
60. ! [X0] : ((((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))))) [flattening 60]
82. calm(sK0) | ~patient(X1) [cnf transformation 37]
84. ~wise(sK0) | ~patient(X1) [cnf transformation 37]
95. ~funny(X0) | ~old(X0) | patient(X0) [cnf transformation 43]
101. ~calm(X0) | wise(X0) [cnf transformation 47]
113. ~humble(X0) | ~generous(X0) [cnf transformation 53]
114. ~generous(X0) | funny(X0) [cnf transformation 53]
125. humble(X0) | old(X0) | ~generous(X0) [cnf transformation 61]
142. generous(fred) [cnf transformation 24]
148. 2 <=> wise(sK0) [avatar definition]
153. 3 <=> ! [X1] : ~patient(X1) [avatar definition]
154. ~patient(X1) <- (3) [avatar component clause 153]
155. 3 | ~2 [avatar split clause 84,148,153]
157. 4 <=> calm(sK0) [avatar definition]
159. calm(sK0) <- (4) [avatar component clause 157]
161. 3 | 4 [avatar split clause 82,157,153]
163. 5 <=> ! [X3] : (wise(X3) | ~calm(X3)) [avatar definition]
164. ~calm(X3) | wise(X3) <- (5) [avatar component clause 163]
217. 5 [avatar split clause 101,163]
254. ~generous(X0) | old(X0) [subsumption resolution 125,113]
274. funny(fred) [resolution 114,142]
280. wise(sK0) <- (4, 5) [resolution 164,159]
283. 2 | ~4 | ~5 [avatar split clause 280,163,157,148]
286. old(fred) [resolution 254,142]
291. ~old(fred) | patient(fred) [resolution 95,274]
292. patient(fred) [subsumption resolution 291,286]
293. $false <- (3) [subsumption resolution 292,154]
294. ~3 [avatar contradiction clause 293]
295. $false [avatar sat refutation 155,161,217,283,294]
% SZS output end Proof for 873047069107953227343339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not rich then someone is both quiet and not curious and vice versa. Everyone who is curious or generous is both rich and not wise and vice versa. If someone is humble then someone is not old or not tall and vice versa. Everyone who is not happy is either brave or generous. Everyone who is not brave or funny is tall and vice versa. Everyone who is humble or not rich is not creative. Everyone who is not wise is either curious or patient. If paul is either curious or brave then john is either curious or generous and vice versa. Everyone who is either not calm or not old is both old and quiet. If someone is both not rich and old then someone is rich and vice versa. If susan is either not rich or wise then someone is both not rich and not humble and vice versa. If fred is either old or not quiet then fred is either not strong or strong. If someone is both rich and generous then someone is both happy and wise. If fred is both not humble and strong then paul is both generous and funny and vice versa. If someone is either not wise or kind then mary is calm and vice versa. Everyone who is not calm or old is either patient or not tall. John is both not tall and curious. Paul is both not funny and not creative. Lucy is not rich or not quiet. Someone is strong or old. Someone is either not kind or not funny. Susan is both not tall and not quiet. Someone is strong. Paul is wise. | Susan is wise. | neutral | ((?[X]:((quiet(X)&~rich(X))))<=>(?[X]:((quiet(X)&~curious(X)))))&
(![X]:((curious(X)|generous(X))<=>(rich(X)&~wise(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:(~happy(X)=>(brave(X)<~>generous(X))))&
(![X]:((~brave(X)|funny(X))<=>tall(X)))&
(![X]:((humble(X)|~rich(X))=>~creative(X)))&
(![X]:(~wise(X)=>(curious(X)<~>patient(X))))&
(((curious(paul)<~>brave(paul)))<=>((curious(john)<~>generous(john))))&
(![X]:((~calm(X)<~>~old(X))=>(old(X)&quiet(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:(rich(X))))&
(((~rich(susan)<~>wise(susan)))<=>(?[X]:((~rich(X)&~humble(X)))))&
(((old(fred)<~>~quiet(fred)))=>((~strong(fred)<~>strong(fred))))&
((?[X]:((rich(X)&generous(X))))=>(?[X]:((happy(X)&wise(X)))))&
(((~humble(fred)&strong(fred)))<=>((generous(paul)&funny(paul))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(calm(mary)))&
(![X]:((~calm(X)|old(X))=>(patient(X)<~>~tall(X))))&
((~tall(john)&curious(john)))&
((~funny(paul)&~creative(paul)))&
((~rich(lucy)|~quiet(lucy)))&
(?[X]:((strong(X)|old(X))))&
(?[X]:((~kind(X)<~>~funny(X))))&
((~tall(susan)&~quiet(susan)))&
(?[X]:(strong(X)))&
(wise(paul)) | wise(susan) | [] | null | 0 |
If someone is quiet then paul is both humble and not strong and vice versa.
If someone is both not curious and funny then susan is patient.
Everyone who is not happy is old.
If someone is both not strong and funny then paul is generous and vice versa.
Everyone who is both humble and not quiet is not brave or happy.
Everyone who is both not calm and humble is not wise or not strong.
If susan is both not strong and rich then someone is generous.
Everyone who is either not kind or not humble is kind and vice versa.
Everyone who is humble or not calm is humble or wise.
Everyone who is either not rich or not strong is creative or quiet.
Everyone who is humble or creative is both wise and old and vice versa.
If someone is patient then susan is generous or creative.
Everyone who is both not calm and not wise is creative and vice versa.
If someone is funny or rich then someone is either rich or not curious.
If lucy is calm then paul is either not calm or not brave and vice versa.
Everyone who is not rich is tall.
John is both not curious and not old.
Alice is not generous.
John is humble or tall.
Someone is either not brave or creative.
Someone is either brave or strong.
Someone is either quiet or not curious.
Someone is both brave and not wise.
Someone is not kind or creative. | Lucy is not creative. | entailment | ((?[X]:(quiet(X)))<=>((humble(paul)&~strong(paul))))&
((?[X]:((~curious(X)&funny(X))))=>(patient(susan)))&
(![X]:(~happy(X)=>old(X)))&
((?[X]:((~strong(X)&funny(X))))<=>(generous(paul)))&
(![X]:((humble(X)&~quiet(X))=>(~brave(X)|happy(X))))&
(![X]:((~calm(X)&humble(X))=>(~wise(X)|~strong(X))))&
(((~strong(susan)&rich(susan)))=>(?[X]:(generous(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>kind(X)))&
(![X]:((humble(X)|~calm(X))=>(humble(X)|wise(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(creative(X)|quiet(X))))&
(![X]:((humble(X)|creative(X))<=>(wise(X)&old(X))))&
((?[X]:(patient(X)))=>((generous(susan)|creative(susan))))&
(![X]:((~calm(X)&~wise(X))<=>creative(X)))&
((?[X]:((funny(X)|rich(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
((calm(lucy))<=>((~calm(paul)<~>~brave(paul))))&
(![X]:(~rich(X)=>tall(X)))&
((~curious(john)&~old(john)))&
(~generous(alice))&
((humble(john)|tall(john)))&
(?[X]:((~brave(X)<~>creative(X))))&
(?[X]:((brave(X)<~>strong(X))))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((brave(X)&~wise(X))))&
(?[X]:((~kind(X)|creative(X)))) | ~creative(lucy) | [
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7290990640804670648475176
% SZS output start Proof for 7290990640804670648475176
11. ! [X0] : ((creative(X0) | humble(X0)) <=> (old(X0) & wise(X0))) [input p10]
13. ! [X0] : ((~wise(X0) & ~calm(X0)) <=> creative(X0)) [input p12]
25. creative(lucy) [input hypothesis]
56. ! [X0] : (((creative(X0) | humble(X0)) | (~old(X0) | ~wise(X0))) & ((old(X0) & wise(X0)) | (~creative(X0) & ~humble(X0)))) [nnf transformation 11]
57. ! [X0] : ((creative(X0) | humble(X0) | ~old(X0) | ~wise(X0)) & ((old(X0) & wise(X0)) | (~creative(X0) & ~humble(X0)))) [flattening 56]
58. ! [X0] : (((~wise(X0) & ~calm(X0)) | ~creative(X0)) & (creative(X0) | (wise(X0) | calm(X0)))) [nnf transformation 13]
59. ! [X0] : (((~wise(X0) & ~calm(X0)) | ~creative(X0)) & (creative(X0) | wise(X0) | calm(X0))) [flattening 58]
96. wise(X0) | ~creative(X0) [cnf transformation 57]
103. ~wise(X0) | ~creative(X0) [cnf transformation 59]
124. creative(lucy) [cnf transformation 25]
199. ~creative(X0) [subsumption resolution 103,96]
256. $false [subsumption resolution 124,199]
% SZS output end Proof for 7290990640804670648475176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either funny or not creative then someone is not creative or not generous and vice versa.
If mary is both not strong and creative then fred is either not strong or patient and vice versa.
Everyone who is brave is either funny or tall and vice versa.
Everyone who is both not strong and not old is tall.
Everyone who is either generous or not tall is rich and vice versa.
If susan is not kind or humble then someone is either not tall or not quiet and vice versa.
If fred is either not humble or wise then someone is either not creative or patient and vice versa.
Everyone who is either wise or rich is not kind or patient and vice versa.
Everyone who is both creative and happy is both tall and humble and vice versa.
If susan is not kind or not patient then someone is either not quiet or happy and vice versa.
If paul is not quiet then someone is not brave or not generous.
If someone is either not strong or not rich then someone is either tall or not curious.
Everyone who is not happy is either not kind or funny and vice versa.
If john is both patient and not quiet then someone is both not brave and quiet and vice versa.
If lucy is happy then alice is not calm or rich.
Everyone who is not happy or not curious is both tall and brave.
Alice is both calm and quiet.
Someone is either strong or not patient.
Someone is not generous or wise.
John is both wise and not old.
Someone is not patient.
Fred is either not generous or not creative.
Fred is humble.
Fred is either patient or not creative. | Fred is funny. | entailment | (((funny(fred)<~>~creative(fred)))<=>(?[X]:((~creative(X)|~generous(X)))))&
(((~strong(mary)&creative(mary)))<=>((~strong(fred)<~>patient(fred))))&
(![X]:(brave(X)<=>(funny(X)<~>tall(X))))&
(![X]:((~strong(X)&~old(X))=>tall(X)))&
(![X]:((generous(X)<~>~tall(X))<=>rich(X)))&
(((~kind(susan)|humble(susan)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(((~humble(fred)<~>wise(fred)))<=>(?[X]:((~creative(X)<~>patient(X)))))&
(![X]:((wise(X)<~>rich(X))<=>(~kind(X)|patient(X))))&
(![X]:((creative(X)&happy(X))<=>(tall(X)&humble(X))))&
(((~kind(susan)|~patient(susan)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
((~quiet(paul))=>(?[X]:((~brave(X)|~generous(X)))))&
((?[X]:((~strong(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:(~happy(X)<=>(~kind(X)<~>funny(X))))&
(((patient(john)&~quiet(john)))<=>(?[X]:((~brave(X)&quiet(X)))))&
((happy(lucy))=>((~calm(alice)|rich(alice))))&
(![X]:((~happy(X)|~curious(X))=>(tall(X)&brave(X))))&
((calm(alice)&quiet(alice)))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:((~generous(X)|wise(X))))&
((wise(john)&~old(john)))&
(?[X]:(~patient(X)))&
((~generous(fred)<~>~creative(fred)))&
(humble(fred))&
((patient(fred)<~>~creative(fred))) | funny(fred) | [
"p0",
"p4",
"p6",
"p7",
"p8",
"p12",
"p15",
"p21",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 86652979352590933544808
% SZS output start Proof for 86652979352590933544808
1. (funny(fred) <~> ~creative(fred)) <=> ? [X0] : (~generous(X0) | ~creative(X0)) [input p0]
5. ! [X0] : ((generous(X0) <~> ~tall(X0)) <=> rich(X0)) [input p4]
7. (~humble(fred) <~> wise(fred)) <=> ? [X0] : (~creative(X0) <~> patient(X0)) [input p6]
8. ! [X0] : ((wise(X0) <~> rich(X0)) <=> (patient(X0) | ~kind(X0))) [input p7]
9. ! [X0] : ((happy(X0) & creative(X0)) <=> (humble(X0) & tall(X0))) [input p8]
13. ! [X0] : (~happy(X0) <=> (~kind(X0) <~> funny(X0))) [input p12]
16. ! [X0] : ((~curious(X0) | ~happy(X0)) => (brave(X0) & tall(X0))) [input p15]
22. ~generous(fred) <~> ~creative(fred) [input p21]
23. humble(fred) [input p22]
24. patient(fred) <~> ~creative(fred) [input p23]
25. ~funny(fred) [input hypothesis]
33. ! [X0] : ((brave(X0) & tall(X0)) | (curious(X0) & happy(X0))) [ennf transformation 16]
34. (((creative(fred) | ~funny(fred)) & (~creative(fred) | funny(fred))) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | ((funny(fred) | creative(fred)) & (~creative(fred) | ~funny(fred)))) [nnf transformation 1]
35. (((creative(fred) | ~funny(fred)) & (~creative(fred) | funny(fred))) | ! [X0] : (generous(X0) & creative(X0))) & (? [X1] : (~generous(X1) | ~creative(X1)) | ((funny(fred) | creative(fred)) & (~creative(fred) | ~funny(fred)))) [rectify 34]
36. ? [X1] : (~generous(X1) | ~creative(X1)) => (~generous(sK0) | ~creative(sK0)) [choice axiom]
37. (((creative(fred) | ~funny(fred)) & (~creative(fred) | funny(fred))) | ! [X0] : (generous(X0) & creative(X0))) & ((~generous(sK0) | ~creative(sK0)) | ((funny(fred) | creative(fred)) & (~creative(fred) | ~funny(fred)))) [skolemisation 35,36]
41. ! [X0] : ((((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | ~rich(X0)) & (rich(X0) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0))))) [nnf transformation 5]
47. (((~wise(fred) | humble(fred)) & (wise(fred) | ~humble(fred))) | ! [X0] : ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (? [X0] : ((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | ((~humble(fred) | ~wise(fred)) & (wise(fred) | humble(fred)))) [nnf transformation 7]
48. (((~wise(fred) | humble(fred)) & (wise(fred) | ~humble(fred))) | ! [X0] : ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (? [X1] : ((~patient(X1) | creative(X1)) & (patient(X1) | ~creative(X1))) | ((~humble(fred) | ~wise(fred)) & (wise(fred) | humble(fred)))) [rectify 47]
49. ? [X1] : ((~patient(X1) | creative(X1)) & (patient(X1) | ~creative(X1))) => ((~patient(sK2) | creative(sK2)) & (patient(sK2) | ~creative(sK2))) [choice axiom]
50. (((~wise(fred) | humble(fred)) & (wise(fred) | ~humble(fred))) | ! [X0] : ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(sK2) | creative(sK2)) & (patient(sK2) | ~creative(sK2))) | ((~humble(fred) | ~wise(fred)) & (wise(fred) | humble(fred)))) [skolemisation 48,49]
51. ! [X0] : ((((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | (~patient(X0) & kind(X0))) & ((patient(X0) | ~kind(X0)) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0))))) [nnf transformation 8]
52. ! [X0] : ((((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | (~patient(X0) & kind(X0))) & (patient(X0) | ~kind(X0) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0))))) [flattening 51]
53. ! [X0] : (((happy(X0) & creative(X0)) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 9]
54. ! [X0] : (((happy(X0) & creative(X0)) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | ~happy(X0) | ~creative(X0))) [flattening 53]
66. ! [X0] : ((~happy(X0) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0)))) & (((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | happy(X0))) [nnf transformation 13]
79. (creative(fred) | generous(fred)) & (~creative(fred) | ~generous(fred)) [nnf transformation 22]
80. (creative(fred) | ~patient(fred)) & (~creative(fred) | patient(fred)) [nnf transformation 24]
84. ~creative(fred) | funny(fred) | generous(X0) [cnf transformation 37]
101. ~rich(X0) | ~generous(X0) | tall(X0) [cnf transformation 41]
112. wise(fred) | ~humble(fred) | patient(X0) | creative(X0) [cnf transformation 50]
116. ~wise(X0) | ~kind(X0) | rich(X0) | patient(X0) [cnf transformation 52]
124. ~humble(X0) | creative(X0) | ~tall(X0) [cnf transformation 54]
139. ~happy(X0) | funny(X0) | kind(X0) [cnf transformation 66]
146. happy(X0) | tall(X0) [cnf transformation 33]
158. ~creative(fred) | ~generous(fred) [cnf transformation 79]
159. creative(fred) | generous(fred) [cnf transformation 79]
160. humble(fred) [cnf transformation 23]
162. creative(fred) | ~patient(fred) [cnf transformation 80]
163. ~funny(fred) [cnf transformation 25]
165. 1 <=> ! [X0] : generous(X0) [avatar definition]
166. generous(X0) <- (1) [avatar component clause 165]
168. 2 <=> funny(fred) [avatar definition]
170. ~funny(fred) <- (~2) [avatar component clause 168]
172. 3 <=> creative(fred) [avatar definition]
173. ~creative(fred) <- (~3) [avatar component clause 172]
180. 1 | 2 | ~3 [avatar split clause 84,172,168,165]
193. 7 <=> patient(fred) [avatar definition]
195. ~patient(fred) <- (~7) [avatar component clause 193]
246. 18 <=> humble(fred) [avatar definition]
248. humble(fred) <- (18) [avatar component clause 246]
250. 19 <=> wise(fred) [avatar definition]
251. wise(fred) <- (19) [avatar component clause 250]
255. 20 <=> ! [X0] : (patient(X0) | creative(X0)) [avatar definition]
256. patient(X0) | creative(X0) <- (20) [avatar component clause 255]
259. 20 | ~18 | 19 [avatar split clause 112,250,246,255]
384. 47 <=> generous(fred) [avatar definition]
385. ~generous(fred) <- (~47) [avatar component clause 384]
386. generous(fred) <- (47) [avatar component clause 384]
387. 47 | 3 [avatar split clause 159,172,384]
388. ~47 | ~3 [avatar split clause 158,172,384]
389. 18 [avatar split clause 160,246]
390. ~7 | 3 [avatar split clause 162,172,193]
392. ~2 [avatar split clause 163,168]
522. 65 <=> kind(fred) [avatar definition]
523. ~kind(fred) <- (~65) [avatar component clause 522]
526. 66 <=> rich(fred) [avatar definition]
527. rich(fred) <- (66) [avatar component clause 526]
548. creative(fred) | ~tall(fred) <- (18) [resolution 124,248]
550. ~tall(fred) <- (~3, 18) [subsumption resolution 548,173]
607. kind(X1) | funny(X1) | tall(X1) [resolution 139,146]
611. ~kind(fred) | rich(fred) | patient(fred) <- (19) [resolution 116,251]
653. funny(fred) | tall(fred) <- (~65) [resolution 607,523]
655. tall(fred) <- (~2, ~65) [subsumption resolution 653,170]
656. $false <- (~2, ~3, 18, ~65) [subsumption resolution 655,550]
657. 2 | 3 | ~18 | 65 [avatar contradiction clause 656]
658. ~kind(fred) | rich(fred) <- (~7, 19) [subsumption resolution 611,195]
659. 66 | ~65 | 7 | ~19 [avatar split clause 658,250,193,522,526]
663. ~generous(fred) | tall(fred) <- (66) [resolution 527,101]
665. tall(fred) <- (47, 66) [subsumption resolution 663,386]
666. $false <- (~3, 18, 47, 66) [subsumption resolution 665,550]
667. 3 | ~18 | ~47 | ~66 [avatar contradiction clause 666]
674. creative(fred) <- (~7, 20) [resolution 256,195]
680. $false <- (~3, ~7, 20) [subsumption resolution 674,173]
681. 3 | 7 | ~20 [avatar contradiction clause 680]
797. $false <- (1, ~47) [resolution 385,166]
798. ~1 | 47 [avatar contradiction clause 797]
799. $false [avatar sat refutation 180,259,387,388,389,390,392,657,659,667,681,798]
% SZS output end Proof for 86652979352590933544808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and strong then someone is both calm and not brave and vice versa.
If mary is either not tall or not funny then mary is both happy and not humble.
Everyone who is calm or not tall is both rich and not old.
If someone is patient or generous then lucy is both generous and not funny.
If paul is both not calm and not patient then someone is either strong or curious and vice versa.
Everyone who is either not curious or not brave is either creative or not happy.
If fred is either not humble or not creative then lucy is both not generous and humble.
Everyone who is creative or not tall is not happy.
Everyone who is both not old and strong is either calm or brave and vice versa.
If someone is both brave and not calm then someone is either not wise or creative and vice versa.
Everyone who is both not strong and not curious is creative and vice versa.
If paul is both brave and not kind then someone is not old or not funny and vice versa.
Everyone who is generous or strong is both rich and kind.
If fred is brave or generous then mary is generous or calm.
Someone is not wise.
Someone is happy or not generous.
Someone is not brave or not rich.
Someone is either not quiet or not funny.
Someone is either not happy or not tall.
Someone is wise or humble. | Lucy is old. | entailment | ((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((calm(X)&~brave(X)))))&
(((~tall(mary)<~>~funny(mary)))=>((happy(mary)&~humble(mary))))&
(![X]:((calm(X)|~tall(X))=>(rich(X)&~old(X))))&
((?[X]:((patient(X)|generous(X))))=>((generous(lucy)&~funny(lucy))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:((strong(X)<~>curious(X)))))&
(![X]:((~curious(X)<~>~brave(X))=>(creative(X)<~>~happy(X))))&
(((~humble(fred)<~>~creative(fred)))=>((~generous(lucy)&humble(lucy))))&
(![X]:((creative(X)|~tall(X))=>~happy(X)))&
(![X]:((~old(X)&strong(X))<=>(calm(X)<~>brave(X))))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((~wise(X)<~>creative(X)))))&
(![X]:((~strong(X)&~curious(X))<=>creative(X)))&
(((brave(paul)&~kind(paul)))<=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((generous(X)|strong(X))=>(rich(X)&kind(X))))&
(((brave(fred)|generous(fred)))=>((generous(mary)|calm(mary))))&
(?[X]:(~wise(X)))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:((~happy(X)<~>~tall(X))))&
(?[X]:((wise(X)|humble(X)))) | old(lucy) | [
"p4",
"p5",
"p7",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6533449285750169603218775
% SZS output start Proof for 6533449285750169603218775
5. (~patient(paul) & ~calm(paul)) <=> ? [X0] : (strong(X0) <~> curious(X0)) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~brave(X0)) => (creative(X0) <~> ~happy(X0))) [input p5]
8. ! [X0] : ((~tall(X0) | creative(X0)) => ~happy(X0)) [input p7]
9. ! [X0] : ((strong(X0) & ~old(X0)) <=> (calm(X0) <~> brave(X0))) [input p8]
11. ! [X0] : ((~curious(X0) & ~strong(X0)) <=> creative(X0)) [input p10]
12. (~kind(paul) & brave(paul)) <=> ? [X0] : (~funny(X0) | ~old(X0)) [input p11]
13. ! [X0] : ((strong(X0) | generous(X0)) => (kind(X0) & rich(X0))) [input p12]
21. ~old(lucy) [input hypothesis]
27. ! [X0] : ((creative(X0) <~> ~happy(X0)) | (~curious(X0) <=> ~brave(X0))) [ennf transformation 6]
29. ! [X0] : (~happy(X0) | (tall(X0) & ~creative(X0))) [ennf transformation 8]
30. ! [X0] : ((kind(X0) & rich(X0)) | (~strong(X0) & ~generous(X0))) [ennf transformation 13]
39. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (patient(paul) | calm(paul))) [nnf transformation 5]
40. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | patient(paul) | calm(paul)) [flattening 39]
41. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X1] : ((~curious(X1) | ~strong(X1)) & (curious(X1) | strong(X1))) | patient(paul) | calm(paul)) [rectify 40]
42. ? [X1] : ((~curious(X1) | ~strong(X1)) & (curious(X1) | strong(X1))) => ((~curious(sK2) | ~strong(sK2)) & (curious(sK2) | strong(sK2))) [choice axiom]
43. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(sK2) | ~strong(sK2)) & (curious(sK2) | strong(sK2))) | patient(paul) | calm(paul)) [skolemisation 41,42]
44. ! [X0] : (((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) [nnf transformation 27]
46. ! [X0] : (((strong(X0) & ~old(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~strong(X0) | old(X0)))) [nnf transformation 9]
47. ! [X0] : (((strong(X0) & ~old(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | ~strong(X0) | old(X0))) [flattening 46]
53. ! [X0] : (((~curious(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | (curious(X0) | strong(X0)))) [nnf transformation 11]
54. ! [X0] : (((~curious(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | curious(X0) | strong(X0))) [flattening 53]
55. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X0] : (~funny(X0) | ~old(X0)) | (kind(paul) | ~brave(paul))) [nnf transformation 12]
56. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X0] : (~funny(X0) | ~old(X0)) | kind(paul) | ~brave(paul)) [flattening 55]
57. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X1] : (~funny(X1) | ~old(X1)) | kind(paul) | ~brave(paul)) [rectify 56]
58. ? [X1] : (~funny(X1) | ~old(X1)) => (~funny(sK5) | ~old(sK5)) [choice axiom]
59. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & ((~funny(sK5) | ~old(sK5)) | kind(paul) | ~brave(paul)) [skolemisation 57,58]
92. ~calm(paul) | curious(X0) | ~strong(X0) [cnf transformation 43]
93. ~calm(paul) | strong(X0) | ~curious(X0) [cnf transformation 43]
98. ~creative(X0) | happy(X0) | ~brave(X0) | curious(X0) [cnf transformation 44]
104. ~creative(X0) | ~happy(X0) [cnf transformation 29]
111. ~brave(X0) | calm(X0) | strong(X0) [cnf transformation 47]
118. creative(X0) | curious(X0) | strong(X0) [cnf transformation 54]
122. brave(paul) | old(X0) [cnf transformation 59]
124. ~kind(paul) | old(X0) [cnf transformation 59]
129. ~strong(X0) | kind(X0) [cnf transformation 30]
140. ~old(lucy) [cnf transformation 21]
189. 11 <=> ! [X0] : (strong(X0) | ~curious(X0)) [avatar definition]
190. ~curious(X0) | strong(X0) <- (11) [avatar component clause 189]
197. 13 <=> ! [X0] : (curious(X0) | ~strong(X0)) [avatar definition]
198. ~strong(X0) | curious(X0) <- (13) [avatar component clause 197]
201. 14 <=> calm(paul) [avatar definition]
204. 11 | ~14 [avatar split clause 93,201,189]
205. 13 | ~14 [avatar split clause 92,201,197]
269. 28 <=> kind(paul) [avatar definition]
271. ~kind(paul) <- (~28) [avatar component clause 269]
274. 29 <=> ! [X0] : old(X0) [avatar definition]
275. old(X0) <- (29) [avatar component clause 274]
276. 29 | ~28 [avatar split clause 124,269,274]
278. 30 <=> brave(paul) [avatar definition]
280. brave(paul) <- (30) [avatar component clause 278]
282. 29 | 30 [avatar split clause 122,278,274]
351. $false <- (29) [resolution 275,140]
352. ~29 [avatar contradiction clause 351]
381. calm(paul) | strong(paul) <- (30) [resolution 111,280]
386. curious(X2) | strong(X2) | ~happy(X2) [resolution 118,104]
389. ~happy(X2) | curious(X2) <- (13) [subsumption resolution 386,198]
420. happy(X0) | ~brave(X0) | curious(X0) | curious(X0) | strong(X0) [resolution 98,118]
421. happy(X0) | ~brave(X0) | curious(X0) | strong(X0) [duplicate literal removal 420]
424. happy(X0) | ~brave(X0) | curious(X0) <- (13) [subsumption resolution 421,198]
425. ~brave(X0) | curious(X0) <- (13) [subsumption resolution 424,389]
478. 55 <=> strong(paul) [avatar definition]
479. strong(paul) <- (55) [avatar component clause 478]
480. ~strong(paul) <- (~55) [avatar component clause 478]
482. 55 | 14 | ~30 [avatar split clause 381,278,201,478]
502. kind(paul) <- (55) [resolution 479,129]
504. $false <- (~28, 55) [subsumption resolution 502,271]
505. 28 | ~55 [avatar contradiction clause 504]
513. curious(paul) <- (13, 30) [resolution 425,280]
517. strong(paul) <- (11, 13, 30) [resolution 513,190]
519. $false <- (11, 13, 30, ~55) [subsumption resolution 517,480]
520. ~11 | ~13 | ~30 | 55 [avatar contradiction clause 519]
521. $false [avatar sat refutation 204,205,276,282,352,482,505,520]
% SZS output end Proof for 6533449285750169603218775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and funny then john is not kind or not curious. If someone is both quiet and old then someone is both strong and not strong. Everyone who is not kind or patient is both not quiet and creative. If john is not strong then someone is either rich or not humble and vice versa. If someone is either creative or kind then mary is both patient and not old. Everyone who is wise is kind and vice versa. Everyone who is either not quiet or not calm is not strong or not calm and vice versa. Everyone who is creative is not quiet or kind and vice versa. If someone is kind then someone is tall. If alice is either not creative or patient then someone is either creative or not happy. If john is both quiet and not tall then someone is both not strong and not tall. If alice is both not calm and calm then someone is either tall or happy. Everyone who is both not funny and not calm is either happy or not funny and vice versa. Everyone who is either not creative or happy is not happy or old and vice versa. Everyone who is both wise and humble is not old and vice versa. Everyone who is either wise or not quiet is not quiet. Someone is not patient or not quiet. Susan is either patient or humble. Fred is strong or rich. Mary is either not funny or curious. | John is old. | entailment | ((?[X]:((~patient(X)&funny(X))))=>((~kind(john)|~curious(john))))&
((?[X]:((quiet(X)&old(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~kind(X)|patient(X))=>(~quiet(X)&creative(X))))&
((~strong(john))<=>(?[X]:((rich(X)<~>~humble(X)))))&
((?[X]:((creative(X)<~>kind(X))))=>((patient(mary)&~old(mary))))&
(![X]:(wise(X)<=>kind(X)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~strong(X)|~calm(X))))&
(![X]:(creative(X)<=>(~quiet(X)|kind(X))))&
((?[X]:(kind(X)))=>(?[X]:(tall(X))))&
(((~creative(alice)<~>patient(alice)))=>(?[X]:((creative(X)<~>~happy(X)))))&
(((quiet(john)&~tall(john)))=>(?[X]:((~strong(X)&~tall(X)))))&
(((~calm(alice)&calm(alice)))=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:((~funny(X)&~calm(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(~happy(X)|old(X))))&
(![X]:((wise(X)&humble(X))<=>~old(X)))&
(![X]:((wise(X)<~>~quiet(X))=>~quiet(X)))&
(?[X]:((~patient(X)|~quiet(X))))&
((patient(susan)<~>humble(susan)))&
((strong(fred)|rich(fred)))&
((~funny(mary)<~>curious(mary))) | old(john) | [
"p1",
"p7",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2262196358422542274490699
% SZS output start Proof for 2262196358422542274490699
2. ? [X0] : (old(X0) & quiet(X0)) => ? [X0] : (~strong(X0) & strong(X0)) [input p1]
8. ! [X0] : (creative(X0) <=> (kind(X0) | ~quiet(X0))) [input p7]
14. ! [X0] : ((~creative(X0) <~> happy(X0)) <=> (old(X0) | ~happy(X0))) [input p13]
15. ! [X0] : ((humble(X0) & wise(X0)) <=> ~old(X0)) [input p14]
16. ! [X0] : ((wise(X0) <~> ~quiet(X0)) => ~quiet(X0)) [input p15]
21. ~old(john) [input hypothesis]
22. ? [X0] : (old(X0) & quiet(X0)) => ? [X1] : (~strong(X1) & strong(X1)) [rectify 2]
26. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (~old(X0) | ~quiet(X0)) [ennf transformation 22]
35. ! [X0] : (~quiet(X0) | (wise(X0) <=> ~quiet(X0))) [ennf transformation 16]
36. ? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (~old(X1) | ~quiet(X1)) [rectify 26]
37. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK0) & strong(sK0)) [choice axiom]
38. (~strong(sK0) & strong(sK0)) | ! [X1] : (~old(X1) | ~quiet(X1)) [skolemisation 36,37]
47. ! [X0] : ((creative(X0) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ~creative(X0))) [nnf transformation 8]
48. ! [X0] : ((creative(X0) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ~creative(X0))) [flattening 47]
62. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [nnf transformation 14]
63. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [flattening 62]
64. ! [X0] : (((humble(X0) & wise(X0)) | old(X0)) & (~old(X0) | (~humble(X0) | ~wise(X0)))) [nnf transformation 15]
65. ! [X0] : (((humble(X0) & wise(X0)) | old(X0)) & (~old(X0) | ~humble(X0) | ~wise(X0))) [flattening 64]
66. ! [X0] : (~quiet(X0) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 35]
72. strong(sK0) | ~old(X1) | ~quiet(X1) [cnf transformation 38]
73. ~strong(sK0) | ~old(X1) | ~quiet(X1) [cnf transformation 38]
95. creative(X0) | quiet(X0) [cnf transformation 48]
113. old(X0) | ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 63]
114. happy(X0) | ~creative(X0) | happy(X0) [cnf transformation 63]
119. wise(X0) | old(X0) [cnf transformation 65]
121. ~quiet(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 66]
129. ~old(john) [cnf transformation 21]
130. ~wise(X0) | ~quiet(X0) [duplicate literal removal 121]
131. old(X0) | ~happy(X0) | ~creative(X0) [duplicate literal removal 113]
132. ~creative(X0) | happy(X0) [duplicate literal removal 114]
150. 4 <=> ! [X1] : (~old(X1) | ~quiet(X1)) [avatar definition]
151. ~old(X1) | ~quiet(X1) <- (4) [avatar component clause 150]
153. 5 <=> strong(sK0) [avatar definition]
156. 4 | ~5 [avatar split clause 73,153,150]
157. 4 | 5 [avatar split clause 72,153,150]
256. ~creative(X0) | old(X0) [subsumption resolution 131,132]
300. ~quiet(X0) | old(X0) [resolution 130,119]
301. ~quiet(X0) <- (4) [subsumption resolution 300,151]
315. old(X0) | quiet(X0) [resolution 256,95]
318. old(X0) <- (4) [subsumption resolution 315,301]
319. $false <- (4) [resolution 318,129]
323. ~4 [avatar contradiction clause 319]
324. $false [avatar sat refutation 156,157,323]
% SZS output end Proof for 2262196358422542274490699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is either brave or not rich and vice versa.
Everyone who is old is not rich and vice versa.
If fred is patient then lucy is not curious or happy.
Everyone who is both not patient and rich is both creative and not humble and vice versa.
Everyone who is not old or rich is generous or not kind and vice versa.
Everyone who is either not brave or creative is not quiet or quiet and vice versa.
Everyone who is not happy is either generous or not generous.
If john is quiet then someone is either old or kind.
If alice is not kind then alice is either not happy or not generous.
Everyone who is funny is either not calm or not old and vice versa.
If mary is not calm or not brave then someone is both kind and creative and vice versa.
If someone is not generous or creative then john is happy or kind.
Everyone who is either not kind or not tall is either not kind or not generous.
Everyone who is either not rich or wise is calm.
If paul is either generous or kind then alice is either not calm or not tall.
Everyone who is both kind and wise is either generous or not funny and vice versa.
Someone is either not wise or humble.
Fred is either not calm or not brave.
Someone is either calm or rich.
Someone is not humble or not strong. | Paul is not humble. | neutral | (![X]:(~creative(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(old(X)<=>~rich(X)))&
((patient(fred))=>((~curious(lucy)|happy(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(creative(X)&~humble(X))))&
(![X]:((~old(X)|rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(![X]:((~kind(X)<~>~tall(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>wise(X))=>calm(X)))&
(((generous(paul)<~>kind(paul)))=>((~calm(alice)<~>~tall(alice))))&
(![X]:((kind(X)&wise(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~humble(X)|~strong(X)))) | ~humble(paul) | [] | null | 0 |
If fred is not humble then someone is not old or not kind and vice versa. Everyone who is tall or not patient is either not brave or quiet. Everyone who is generous is not old and vice versa. Everyone who is not kind is not funny or not old. Everyone who is both generous and old is both not calm and kind. Everyone who is not patient is brave and vice versa. Everyone who is brave is both not strong and not happy and vice versa. If someone is both not creative and wise then mary is both not brave and calm. If john is funny or curious then paul is curious or tall and vice versa. If someone is both not patient and patient then someone is not happy. If lucy is either not wise or not humble then paul is both not happy and old. Everyone who is not brave is both not calm and not curious and vice versa. If someone is both not kind and brave then alice is either curious or creative. If fred is either not old or tall then lucy is not generous or not rich and vice versa. If someone is either not brave or humble then alice is not curious or not brave. Everyone who is both not patient and not humble is curious or creative. Someone is both strong and not generous. Someone is strong or not wise. Someone is not kind. Mary is not funny or old. Someone is both not rich and tall. Someone is both curious and wise. Susan is either quiet or calm. John is both not tall and not happy. | John is not brave. | neutral | ((~humble(fred))<=>(?[X]:((~old(X)|~kind(X)))))&
(![X]:((tall(X)|~patient(X))=>(~brave(X)<~>quiet(X))))&
(![X]:(generous(X)<=>~old(X)))&
(![X]:(~kind(X)=>(~funny(X)|~old(X))))&
(![X]:((generous(X)&old(X))=>(~calm(X)&kind(X))))&
(![X]:(~patient(X)<=>brave(X)))&
(![X]:(brave(X)<=>(~strong(X)&~happy(X))))&
((?[X]:((~creative(X)&wise(X))))=>((~brave(mary)&calm(mary))))&
(((funny(john)|curious(john)))<=>((curious(paul)|tall(paul))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:(~happy(X))))&
(((~wise(lucy)<~>~humble(lucy)))=>((~happy(paul)&old(paul))))&
(![X]:(~brave(X)<=>(~calm(X)&~curious(X))))&
((?[X]:((~kind(X)&brave(X))))=>((curious(alice)<~>creative(alice))))&
(((~old(fred)<~>tall(fred)))<=>((~generous(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)<~>humble(X))))=>((~curious(alice)|~brave(alice))))&
(![X]:((~patient(X)&~humble(X))=>(curious(X)|creative(X))))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:((strong(X)|~wise(X))))&
(?[X]:(~kind(X)))&
((~funny(mary)|old(mary)))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((curious(X)&wise(X))))&
((quiet(susan)<~>calm(susan)))&
((~tall(john)&~happy(john))) | ~brave(john) | [] | null | 0 |
If mary is either tall or not kind then someone is old.
Everyone who is strong or generous is old and vice versa.
Everyone who is both not old and wise is both humble and funny and vice versa.
Everyone who is both generous and not quiet is not happy or not quiet.
If alice is either tall or not humble then alice is either not funny or funny and vice versa.
Everyone who is creative or tall is both generous and not funny and vice versa.
Everyone who is both not kind and not wise is either not funny or not tall and vice versa.
If someone is curious then lucy is not funny.
Everyone who is either happy or not quiet is both quiet and not rich.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
Everyone who is curious or not patient is both not humble and quiet.
Someone is strong or brave.
Someone is brave.
Someone is either old or humble. | Alice is quiet. | contradiction | (((tall(mary)<~>~kind(mary)))=>(?[X]:(old(X))))&
(![X]:((strong(X)|generous(X))<=>old(X)))&
(![X]:((~old(X)&wise(X))<=>(humble(X)&funny(X))))&
(![X]:((generous(X)&~quiet(X))=>(~happy(X)|~quiet(X))))&
(((tall(alice)<~>~humble(alice)))<=>((~funny(alice)<~>funny(alice))))&
(![X]:((creative(X)|tall(X))<=>(generous(X)&~funny(X))))&
(![X]:((~kind(X)&~wise(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:(curious(X)))=>(~funny(lucy)))&
(![X]:((happy(X)<~>~quiet(X))=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:((curious(X)|~patient(X))=>(~humble(X)&quiet(X))))&
(?[X]:((strong(X)|brave(X))))&
(?[X]:(brave(X)))&
(?[X]:((old(X)<~>humble(X)))) | quiet(alice) | [
"p5",
"p6",
"p8",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8647743260934424691905322
% SZS output start Proof for 8647743260934424691905322
6. ! [X0] : ((tall(X0) | creative(X0)) <=> (~funny(X0) & generous(X0))) [input p5]
7. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p6]
9. ! [X0] : ((happy(X0) <~> ~quiet(X0)) => (~rich(X0) & quiet(X0))) [input p8]
10. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p9]
11. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X0] : (~tall(X0) & wise(X0)) [input p10]
12. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~happy(X0) | wise(X0))) [input p11]
19. quiet(alice) [input hypothesis]
20. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X1] : (~tall(X1) & wise(X1)) [rectify 11]
30. ! [X0] : ((~rich(X0) & quiet(X0)) | (happy(X0) <=> ~quiet(X0))) [ennf transformation 9]
31. ! [X0] : ((~happy(X0) | wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 12]
32. ! [X0] : (~happy(X0) | wise(X0) | (rich(X0) & creative(X0))) [flattening 31]
42. ! [X0] : (((tall(X0) | creative(X0)) | (funny(X0) | ~generous(X0))) & ((~funny(X0) & generous(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 6]
43. ! [X0] : ((tall(X0) | creative(X0) | funny(X0) | ~generous(X0)) & ((~funny(X0) & generous(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 42]
44. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (wise(X0) | kind(X0)))) [nnf transformation 7]
45. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | wise(X0) | kind(X0))) [flattening 44]
46. ! [X0] : ((~rich(X0) & quiet(X0)) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0)))) [nnf transformation 30]
47. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 10]
48. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 47]
49. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X1] : (~tall(X1) & wise(X1)) | ! [X0] : (~generous(X0) | ~kind(X0))) [nnf transformation 20]
50. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X2] : (~tall(X2) & wise(X2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [rectify 49]
51. ? [X0] : (generous(X0) & kind(X0)) => (generous(sK1) & kind(sK1)) [choice axiom]
52. ? [X2] : (~tall(X2) & wise(X2)) => (~tall(sK2) & wise(sK2)) [choice axiom]
53. ((generous(sK1) & kind(sK1)) | ! [X1] : (tall(X1) | ~wise(X1))) & ((~tall(sK2) & wise(sK2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [skolemisation 50,52,51]
81. ~funny(X0) | ~tall(X0) [cnf transformation 43]
87. ~wise(X0) | ~tall(X0) | funny(X0) [cnf transformation 45]
91. ~rich(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 46]
93. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 48]
94. happy(X0) | happy(X0) [cnf transformation 48]
98. kind(sK1) | tall(X1) | ~wise(X1) [cnf transformation 53]
101. ~happy(X0) | wise(X0) | rich(X0) [cnf transformation 32]
108. quiet(alice) [cnf transformation 19]
109. ~kind(X0) | ~happy(X0) [duplicate literal removal 93]
110. happy(X0) [duplicate literal removal 94]
147. ~wise(X0) | ~tall(X0) [subsumption resolution 87,81]
150. ~kind(X0) [subsumption resolution 109,110]
153. 7 <=> ! [X1] : ~wise(X1) [avatar definition]
154. ~wise(X1) <- (7) [avatar component clause 153]
160. tall(X1) | ~wise(X1) [subsumption resolution 98,150]
161. ~wise(X1) [subsumption resolution 160,147]
162. 7 [avatar split clause 161,153]
163. rich(X0) | wise(X0) [subsumption resolution 101,110]
201. ~quiet(X0) | ~happy(X0) | wise(X0) [resolution 91,163]
202. ~quiet(X0) | wise(X0) [subsumption resolution 201,110]
203. ~quiet(X0) <- (7) [subsumption resolution 202,154]
204. $false <- (7) [resolution 203,108]
205. ~7 [avatar contradiction clause 204]
206. $false [avatar sat refutation 162,205]
% SZS output end Proof for 8647743260934424691905322
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious or patient is both not wise and happy.
If paul is not brave then someone is quiet or not strong and vice versa.
If john is kind then someone is rich or wise.
Everyone who is either not old or happy is tall.
If mary is not tall then someone is old or generous and vice versa.
If someone is either not funny or not happy then susan is either not happy or not humble and vice versa.
Everyone who is either not wise or humble is both strong and not curious and vice versa.
Everyone who is both wise and not generous is kind or not quiet and vice versa.
Everyone who is curious is either not humble or generous.
If fred is old or patient then someone is both creative and patient.
Everyone who is both not patient and not humble is either curious or wise.
Everyone who is either not strong or happy is not happy.
If someone is both wise and not patient then someone is quiet or not kind.
Everyone who is either tall or not old is either not funny or not creative and vice versa.
If paul is either not quiet or not wise then someone is not strong or not quiet and vice versa.
Everyone who is rich or not tall is either quiet or patient.
Lucy is not calm or funny.
Someone is either funny or strong.
Someone is both not kind and not calm.
Someone is either curious or strong.
Paul is both not wise and not old. | Paul is not funny. | neutral | (![X]:((~curious(X)|patient(X))=>(~wise(X)&happy(X))))&
((~brave(paul))<=>(?[X]:((quiet(X)|~strong(X)))))&
((kind(john))=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((~old(X)<~>happy(X))=>tall(X)))&
((~tall(mary))<=>(?[X]:((old(X)|generous(X)))))&
((?[X]:((~funny(X)<~>~happy(X))))<=>((~happy(susan)<~>~humble(susan))))&
(![X]:((~wise(X)<~>humble(X))<=>(strong(X)&~curious(X))))&
(![X]:((wise(X)&~generous(X))<=>(kind(X)|~quiet(X))))&
(![X]:(curious(X)=>(~humble(X)<~>generous(X))))&
(((old(fred)|patient(fred)))=>(?[X]:((creative(X)&patient(X)))))&
(![X]:((~patient(X)&~humble(X))=>(curious(X)<~>wise(X))))&
(![X]:((~strong(X)<~>happy(X))=>~happy(X)))&
((?[X]:((wise(X)&~patient(X))))=>(?[X]:((quiet(X)|~kind(X)))))&
(![X]:((tall(X)<~>~old(X))<=>(~funny(X)<~>~creative(X))))&
(((~quiet(paul)<~>~wise(paul)))<=>(?[X]:((~strong(X)|~quiet(X)))))&
(![X]:((rich(X)|~tall(X))=>(quiet(X)<~>patient(X))))&
((~calm(lucy)|funny(lucy)))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((curious(X)<~>strong(X))))&
((~wise(paul)&~old(paul))) | ~funny(paul) | [] | null | 0 |
If susan is either not rich or generous then someone is not strong.
Everyone who is generous is not wise and vice versa.
Everyone who is curious is either patient or wise and vice versa.
Everyone who is not curious is not generous or not patient.
Everyone who is both old and tall is not generous and vice versa.
Everyone who is either tall or not quiet is both rich and wise.
If paul is calm then someone is generous or not humble.
Everyone who is either wise or not curious is not old.
Everyone who is both not patient and not kind is not happy.
If someone is both not kind and patient then lucy is both tall and quiet.
Everyone who is not old is either not rich or not kind.
If fred is either curious or not happy then paul is both not generous and not tall and vice versa.
If john is not wise or happy then someone is not kind or not wise and vice versa.
If paul is wise or strong then susan is either not happy or not wise and vice versa.
Everyone who is not calm or curious is rich or kind.
If mary is patient or not kind then someone is both not patient and rich and vice versa.
Mary is strong.
Alice is generous.
John is either old or not wise.
Paul is either calm or generous.
Someone is either wise or not creative.
Fred is either kind or calm.
Paul is patient or not old.
Susan is not funny. | Alice is wise. | contradiction | (((~rich(susan)<~>generous(susan)))=>(?[X]:(~strong(X))))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:(curious(X)<=>(patient(X)<~>wise(X))))&
(![X]:(~curious(X)=>(~generous(X)|~patient(X))))&
(![X]:((old(X)&tall(X))<=>~generous(X)))&
(![X]:((tall(X)<~>~quiet(X))=>(rich(X)&wise(X))))&
((calm(paul))=>(?[X]:((generous(X)|~humble(X)))))&
(![X]:((wise(X)<~>~curious(X))=>~old(X)))&
(![X]:((~patient(X)&~kind(X))=>~happy(X)))&
((?[X]:((~kind(X)&patient(X))))=>((tall(lucy)&quiet(lucy))))&
(![X]:(~old(X)=>(~rich(X)<~>~kind(X))))&
(((curious(fred)<~>~happy(fred)))<=>((~generous(paul)&~tall(paul))))&
(((~wise(john)|happy(john)))<=>(?[X]:((~kind(X)|~wise(X)))))&
(((wise(paul)|strong(paul)))<=>((~happy(susan)<~>~wise(susan))))&
(![X]:((~calm(X)|curious(X))=>(rich(X)|kind(X))))&
(((patient(mary)|~kind(mary)))<=>(?[X]:((~patient(X)&rich(X)))))&
(strong(mary))&
(generous(alice))&
((old(john)<~>~wise(john)))&
((calm(paul)<~>generous(paul)))&
(?[X]:((wise(X)<~>~creative(X))))&
((kind(fred)<~>calm(fred)))&
((patient(paul)|~old(paul)))&
(~funny(susan)) | wise(alice) | [
"p1",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3039011100667640145619995
% SZS output start Proof for 3039011100667640145619995
2. ! [X0] : (generous(X0) <=> ~wise(X0)) [input p1]
18. generous(alice) [input p17]
25. wise(alice) [input hypothesis]
42. ! [X0] : ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0))) [nnf transformation 2]
71. ~wise(X0) | ~generous(X0) [cnf transformation 42]
116. generous(alice) [cnf transformation 18]
126. wise(alice) [cnf transformation 25]
287. ~generous(alice) [resolution 71,126]
288. $false [subsumption resolution 287,116]
% SZS output end Proof for 3039011100667640145619995
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then someone is either not funny or not patient. Everyone who is either patient or strong is creative. Everyone who is either not creative or tall is strong or calm and vice versa. Everyone who is either creative or patient is either rich or curious. If lucy is both quiet and not wise then fred is both not generous and not brave and vice versa. Everyone who is not wise is calm or humble and vice versa. If lucy is strong then someone is either kind or calm and vice versa. If someone is either funny or creative then someone is both calm and not quiet and vice versa. If someone is quiet then fred is both wise and not humble and vice versa. If someone is both happy and tall then someone is both brave and tall. Everyone who is not rich is wise and vice versa. If someone is either curious or rich then lucy is either patient or quiet and vice versa. Everyone who is not kind or funny is either not calm or not strong. Everyone who is both strong and old is wise or patient and vice versa. Everyone who is either old or not wise is not brave or not quiet. If someone is rich then fred is both tall and quiet and vice versa. Someone is both creative and calm. Someone is old or wise. Someone is both not curious and not tall. Someone is calm or not happy. Someone is funny or not generous. Alice is not patient. Lucy is either humble or not wise. | Fred is not creative. | contradiction | ((?[X]:(~happy(X)))=>(?[X]:((~funny(X)<~>~patient(X)))))&
(![X]:((patient(X)<~>strong(X))=>creative(X)))&
(![X]:((~creative(X)<~>tall(X))<=>(strong(X)|calm(X))))&
(![X]:((creative(X)<~>patient(X))=>(rich(X)<~>curious(X))))&
(((quiet(lucy)&~wise(lucy)))<=>((~generous(fred)&~brave(fred))))&
(![X]:(~wise(X)<=>(calm(X)|humble(X))))&
((strong(lucy))<=>(?[X]:((kind(X)<~>calm(X)))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((calm(X)&~quiet(X)))))&
((?[X]:(quiet(X)))<=>((wise(fred)&~humble(fred))))&
((?[X]:((happy(X)&tall(X))))=>(?[X]:((brave(X)&tall(X)))))&
(![X]:(~rich(X)<=>wise(X)))&
((?[X]:((curious(X)<~>rich(X))))<=>((patient(lucy)<~>quiet(lucy))))&
(![X]:((~kind(X)|funny(X))=>(~calm(X)<~>~strong(X))))&
(![X]:((strong(X)&old(X))<=>(wise(X)|patient(X))))&
(![X]:((old(X)<~>~wise(X))=>(~brave(X)|~quiet(X))))&
((?[X]:(rich(X)))<=>((tall(fred)&quiet(fred))))&
(?[X]:((creative(X)&calm(X))))&
(?[X]:((old(X)|wise(X))))&
(?[X]:((~curious(X)&~tall(X))))&
(?[X]:((calm(X)|~happy(X))))&
(?[X]:((funny(X)|~generous(X))))&
(~patient(alice))&
((humble(lucy)<~>~wise(lucy))) | ~creative(fred) | [
"p2",
"p5",
"p8",
"p10",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2337292042754499718710154
% SZS output start Proof for 2337292042754499718710154
3. ! [X0] : ((~creative(X0) <~> tall(X0)) <=> (calm(X0) | strong(X0))) [input p2]
6. ! [X0] : (~wise(X0) <=> (humble(X0) | calm(X0))) [input p5]
9. ? [X0] : quiet(X0) <=> (~humble(fred) & wise(fred)) [input p8]
11. ! [X0] : (~rich(X0) <=> wise(X0)) [input p10]
14. ! [X0] : ((old(X0) & strong(X0)) <=> (patient(X0) | wise(X0))) [input p13]
16. ? [X0] : rich(X0) <=> (quiet(fred) & tall(fred)) [input p15]
23. humble(lucy) <~> ~wise(lucy) [input p22]
24. ~creative(fred) [input hypothesis]
40. ! [X0] : ((((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))))) [nnf transformation 3]
41. ! [X0] : ((((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))))) [flattening 40]
45. ! [X0] : ((~wise(X0) | (~humble(X0) & ~calm(X0))) & ((humble(X0) | calm(X0)) | wise(X0))) [nnf transformation 6]
46. ! [X0] : ((~wise(X0) | (~humble(X0) & ~calm(X0))) & (humble(X0) | calm(X0) | wise(X0))) [flattening 45]
56. (? [X0] : quiet(X0) | (humble(fred) | ~wise(fred))) & ((~humble(fred) & wise(fred)) | ! [X0] : ~quiet(X0)) [nnf transformation 9]
57. (? [X0] : quiet(X0) | humble(fred) | ~wise(fred)) & ((~humble(fred) & wise(fred)) | ! [X0] : ~quiet(X0)) [flattening 56]
58. (? [X0] : quiet(X0) | humble(fred) | ~wise(fred)) & ((~humble(fred) & wise(fred)) | ! [X1] : ~quiet(X1)) [rectify 57]
59. ? [X0] : quiet(X0) => quiet(sK4) [choice axiom]
60. (quiet(sK4) | humble(fred) | ~wise(fred)) & ((~humble(fred) & wise(fred)) | ! [X1] : ~quiet(X1)) [skolemisation 58,59]
64. ! [X0] : ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0))) [nnf transformation 11]
70. ! [X0] : (((old(X0) & strong(X0)) | (~patient(X0) & ~wise(X0))) & ((patient(X0) | wise(X0)) | (~old(X0) | ~strong(X0)))) [nnf transformation 14]
71. ! [X0] : (((old(X0) & strong(X0)) | (~patient(X0) & ~wise(X0))) & (patient(X0) | wise(X0) | ~old(X0) | ~strong(X0))) [flattening 70]
73. (? [X0] : rich(X0) | (~quiet(fred) | ~tall(fred))) & ((quiet(fred) & tall(fred)) | ! [X0] : ~rich(X0)) [nnf transformation 16]
74. (? [X0] : rich(X0) | ~quiet(fred) | ~tall(fred)) & ((quiet(fred) & tall(fred)) | ! [X0] : ~rich(X0)) [flattening 73]
75. (? [X0] : rich(X0) | ~quiet(fred) | ~tall(fred)) & ((quiet(fred) & tall(fred)) | ! [X1] : ~rich(X1)) [rectify 74]
76. ? [X0] : rich(X0) => rich(sK7) [choice axiom]
77. (rich(sK7) | ~quiet(fred) | ~tall(fred)) & ((quiet(fred) & tall(fred)) | ! [X1] : ~rich(X1)) [skolemisation 75,76]
88. (wise(lucy) | ~humble(lucy)) & (~wise(lucy) | humble(lucy)) [nnf transformation 23]
97. ~tall(X0) | creative(X0) | ~strong(X0) [cnf transformation 41]
109. ~humble(X0) | ~wise(X0) [cnf transformation 46]
120. wise(fred) | ~quiet(X1) [cnf transformation 60]
125. wise(X0) | rich(X0) [cnf transformation 64]
140. ~wise(X0) | strong(X0) [cnf transformation 71]
146. tall(fred) | ~rich(X1) [cnf transformation 77]
147. quiet(fred) | ~rich(X1) [cnf transformation 77]
157. ~wise(lucy) | humble(lucy) [cnf transformation 88]
158. wise(lucy) | ~humble(lucy) [cnf transformation 88]
159. ~creative(fred) [cnf transformation 24]
182. 6 <=> wise(lucy) [avatar definition]
184. ~wise(lucy) <- (~6) [avatar component clause 182]
248. 20 <=> wise(fred) [avatar definition]
249. wise(fred) <- (20) [avatar component clause 248]
257. 22 <=> ! [X1] : ~quiet(X1) [avatar definition]
258. ~quiet(X1) <- (22) [avatar component clause 257]
264. 22 | 20 [avatar split clause 120,248,257]
307. 32 <=> tall(fred) [avatar definition]
308. tall(fred) <- (32) [avatar component clause 307]
311. 33 <=> quiet(fred) [avatar definition]
312. quiet(fred) <- (33) [avatar component clause 311]
320. 35 <=> ! [X1] : ~rich(X1) [avatar definition]
321. ~rich(X1) <- (35) [avatar component clause 320]
322. 35 | 33 [avatar split clause 147,311,320]
323. 35 | 32 [avatar split clause 146,307,320]
343. ~humble(lucy) [subsumption resolution 158,109]
344. ~wise(lucy) [subsumption resolution 157,343]
345. ~6 [avatar split clause 344,182]
347. rich(lucy) <- (~6) [resolution 125,184]
351. strong(fred) <- (20) [resolution 140,249]
392. creative(fred) | ~strong(fred) <- (32) [resolution 97,308]
394. ~strong(fred) <- (32) [subsumption resolution 392,159]
395. $false <- (20, 32) [subsumption resolution 394,351]
396. ~20 | ~32 [avatar contradiction clause 395]
399. $false <- (22, 33) [resolution 258,312]
404. ~22 | ~33 [avatar contradiction clause 399]
411. $false <- (~6, 35) [resolution 321,347]
412. 6 | ~35 [avatar contradiction clause 411]
414. $false [avatar sat refutation 264,322,323,345,396,404,412]
% SZS output end Proof for 2337292042754499718710154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or brave is either not rich or not quiet. If susan is not patient then someone is not calm or not kind. Everyone who is either brave or not generous is not generous. If alice is both not kind and not happy then someone is generous or not old. Everyone who is both not humble and not kind is wise. Everyone who is calm or not rich is not calm. If someone is either calm or generous then susan is either funny or not kind. Everyone who is both rich and not calm is not creative or quiet and vice versa. If someone is not kind or happy then someone is not wise and vice versa. Everyone who is either not rich or creative is either wise or creative and vice versa. Everyone who is both not patient and not calm is not kind. Everyone who is brave is not patient or generous and vice versa. If john is not funny then someone is either not brave or not happy. Everyone who is not kind or calm is not curious or humble. Everyone who is not patient is not tall or not kind and vice versa. If someone is both not patient and kind then someone is both not curious and funny and vice versa. John is either not happy or old. Someone is both not calm and happy. Someone is not curious. Mary is either not kind or not wise. Someone is both rich and old. Someone is not wise. Someone is either not happy or not curious. Someone is either creative or not tall. | John is not generous. | entailment | (![X]:((kind(X)<~>brave(X))=>(~rich(X)<~>~quiet(X))))&
((~patient(susan))=>(?[X]:((~calm(X)|~kind(X)))))&
(![X]:((brave(X)<~>~generous(X))=>~generous(X)))&
(((~kind(alice)&~happy(alice)))=>(?[X]:((generous(X)|~old(X)))))&
(![X]:((~humble(X)&~kind(X))=>wise(X)))&
(![X]:((calm(X)|~rich(X))=>~calm(X)))&
((?[X]:((calm(X)<~>generous(X))))=>((funny(susan)<~>~kind(susan))))&
(![X]:((rich(X)&~calm(X))<=>(~creative(X)|quiet(X))))&
((?[X]:((~kind(X)|happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((~rich(X)<~>creative(X))<=>(wise(X)<~>creative(X))))&
(![X]:((~patient(X)&~calm(X))=>~kind(X)))&
(![X]:(brave(X)<=>(~patient(X)|generous(X))))&
((~funny(john))=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:((~kind(X)|calm(X))=>(~curious(X)|humble(X))))&
(![X]:(~patient(X)<=>(~tall(X)|~kind(X))))&
((?[X]:((~patient(X)&kind(X))))<=>(?[X]:((~curious(X)&funny(X)))))&
((~happy(john)<~>old(john)))&
(?[X]:((~calm(X)&happy(X))))&
(?[X]:(~curious(X)))&
((~kind(mary)<~>~wise(mary)))&
(?[X]:((rich(X)&old(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~happy(X)<~>~curious(X))))&
(?[X]:((creative(X)<~>~tall(X)))) | ~generous(john) | [
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5320157273933577330575407
% SZS output start Proof for 5320157273933577330575407
3. ! [X0] : ((brave(X0) <~> ~generous(X0)) => ~generous(X0)) [input p2]
12. ! [X0] : (brave(X0) <=> (generous(X0) | ~patient(X0))) [input p11]
25. generous(john) [input hypothesis]
32. ! [X0] : (~generous(X0) | (brave(X0) <=> ~generous(X0))) [ennf transformation 3]
43. ! [X0] : (~generous(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) [nnf transformation 32]
55. ! [X0] : ((brave(X0) | (~generous(X0) & patient(X0))) & ((generous(X0) | ~patient(X0)) | ~brave(X0))) [nnf transformation 12]
56. ! [X0] : ((brave(X0) | (~generous(X0) & patient(X0))) & (generous(X0) | ~patient(X0) | ~brave(X0))) [flattening 55]
88. ~generous(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 43]
116. brave(X0) | ~generous(X0) [cnf transformation 56]
140. generous(john) [cnf transformation 25]
146. ~generous(X0) | ~brave(X0) [duplicate literal removal 88]
179. 8 <=> ! [X0] : ~generous(X0) [avatar definition]
180. ~generous(X0) <- (8) [avatar component clause 179]
221. ~generous(X0) [subsumption resolution 116,146]
222. 8 [avatar split clause 221,179]
291. $false <- (8) [resolution 180,140]
292. ~8 [avatar contradiction clause 291]
293. $false [avatar sat refutation 222,292]
% SZS output end Proof for 5320157273933577330575407
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or brave then someone is wise or generous and vice versa. If someone is both curious and not old then someone is both not quiet and humble and vice versa. If mary is strong or generous then susan is not calm. Everyone who is both not calm and creative is both tall and old. If someone is both not calm and not creative then mary is not patient. Everyone who is either patient or not patient is both wise and not rich. If john is either not wise or not old then someone is funny or patient and vice versa. Everyone who is not patient is either not brave or wise. Everyone who is both kind and curious is rich. If paul is strong then alice is either creative or patient and vice versa. If someone is both not happy and creative then someone is either not calm or not old and vice versa. Everyone who is both not strong and creative is not humble or not rich. Everyone who is calm is both not creative and not generous. If mary is not happy then someone is creative and vice versa. Everyone who is rich or wise is both not generous and calm and vice versa. If john is humble or not curious then john is either happy or not old and vice versa. Someone is not humble or not quiet. Susan is either not generous or rich. Someone is both kind and not quiet. Someone is kind. Paul is humble or not kind. | Paul is brave. | entailment | ((?[X]:((tall(X)<~>brave(X))))<=>(?[X]:((wise(X)|generous(X)))))&
((?[X]:((curious(X)&~old(X))))<=>(?[X]:((~quiet(X)&humble(X)))))&
(((strong(mary)|generous(mary)))=>(~calm(susan)))&
(![X]:((~calm(X)&creative(X))=>(tall(X)&old(X))))&
((?[X]:((~calm(X)&~creative(X))))=>(~patient(mary)))&
(![X]:((patient(X)<~>~patient(X))=>(wise(X)&~rich(X))))&
(((~wise(john)<~>~old(john)))<=>(?[X]:((funny(X)|patient(X)))))&
(![X]:(~patient(X)=>(~brave(X)<~>wise(X))))&
(![X]:((kind(X)&curious(X))=>rich(X)))&
((strong(paul))<=>((creative(alice)<~>patient(alice))))&
((?[X]:((~happy(X)&creative(X))))<=>(?[X]:((~calm(X)<~>~old(X)))))&
(![X]:((~strong(X)&creative(X))=>(~humble(X)|~rich(X))))&
(![X]:(calm(X)=>(~creative(X)&~generous(X))))&
((~happy(mary))<=>(?[X]:(creative(X))))&
(![X]:((rich(X)|wise(X))<=>(~generous(X)&calm(X))))&
(((humble(john)|~curious(john)))<=>((happy(john)<~>~old(john))))&
(?[X]:((~humble(X)|~quiet(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((kind(X)&~quiet(X))))&
(?[X]:(kind(X)))&
((humble(paul)|~kind(paul))) | brave(paul) | [
"p5",
"p6",
"p7",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 702602256131480846921794
% SZS output start Proof for 702602256131480846921794
6. ! [X0] : ((patient(X0) <~> ~patient(X0)) => (~rich(X0) & wise(X0))) [input p5]
7. (~wise(john) <~> ~old(john)) <=> ? [X0] : (patient(X0) | funny(X0)) [input p6]
8. ! [X0] : (~patient(X0) => (~brave(X0) <~> wise(X0))) [input p7]
11. ? [X0] : (creative(X0) & ~happy(X0)) <=> ? [X0] : (~calm(X0) <~> ~old(X0)) [input p10]
13. ! [X0] : (calm(X0) => (~generous(X0) & ~creative(X0))) [input p12]
15. ! [X0] : ((wise(X0) | rich(X0)) <=> (calm(X0) & ~generous(X0))) [input p14]
22. ~brave(paul) [input hypothesis]
25. ? [X0] : (creative(X0) & ~happy(X0)) <=> ? [X1] : (~calm(X1) <~> ~old(X1)) [rectify 11]
30. ! [X0] : ((~rich(X0) & wise(X0)) | (patient(X0) <=> ~patient(X0))) [ennf transformation 6]
31. ! [X0] : ((~brave(X0) <~> wise(X0)) | patient(X0)) [ennf transformation 8]
36. ! [X0] : ((~generous(X0) & ~creative(X0)) | ~calm(X0)) [ennf transformation 13]
47. ! [X0] : ((~rich(X0) & wise(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) [nnf transformation 30]
48. (((old(john) | wise(john)) & (~old(john) | ~wise(john))) | ! [X0] : (~patient(X0) & ~funny(X0))) & (? [X0] : (patient(X0) | funny(X0)) | ((~wise(john) | old(john)) & (~old(john) | wise(john)))) [nnf transformation 7]
49. (((old(john) | wise(john)) & (~old(john) | ~wise(john))) | ! [X0] : (~patient(X0) & ~funny(X0))) & (? [X1] : (patient(X1) | funny(X1)) | ((~wise(john) | old(john)) & (~old(john) | wise(john)))) [rectify 48]
50. ? [X1] : (patient(X1) | funny(X1)) => (patient(sK4) | funny(sK4)) [choice axiom]
51. (((old(john) | wise(john)) & (~old(john) | ~wise(john))) | ! [X0] : (~patient(X0) & ~funny(X0))) & ((patient(sK4) | funny(sK4)) | ((~wise(john) | old(john)) & (~old(john) | wise(john)))) [skolemisation 49,50]
52. ! [X0] : (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | patient(X0)) [nnf transformation 31]
54. (? [X0] : (creative(X0) & ~happy(X0)) | ! [X1] : ((~calm(X1) | old(X1)) & (~old(X1) | calm(X1)))) & (? [X1] : ((old(X1) | calm(X1)) & (~old(X1) | ~calm(X1))) | ! [X0] : (~creative(X0) | happy(X0))) [nnf transformation 25]
55. (? [X0] : (creative(X0) & ~happy(X0)) | ! [X1] : ((~calm(X1) | old(X1)) & (~old(X1) | calm(X1)))) & (? [X2] : ((old(X2) | calm(X2)) & (~old(X2) | ~calm(X2))) | ! [X3] : (~creative(X3) | happy(X3))) [rectify 54]
56. ? [X0] : (creative(X0) & ~happy(X0)) => (creative(sK5) & ~happy(sK5)) [choice axiom]
57. ? [X2] : ((old(X2) | calm(X2)) & (~old(X2) | ~calm(X2))) => ((old(sK6) | calm(sK6)) & (~old(sK6) | ~calm(sK6))) [choice axiom]
58. ((creative(sK5) & ~happy(sK5)) | ! [X1] : ((~calm(X1) | old(X1)) & (~old(X1) | calm(X1)))) & (((old(sK6) | calm(sK6)) & (~old(sK6) | ~calm(sK6))) | ! [X3] : (~creative(X3) | happy(X3))) [skolemisation 55,57,56]
63. ! [X0] : (((wise(X0) | rich(X0)) | (~calm(X0) | generous(X0))) & ((calm(X0) & ~generous(X0)) | (~wise(X0) & ~rich(X0)))) [nnf transformation 15]
64. ! [X0] : ((wise(X0) | rich(X0) | ~calm(X0) | generous(X0)) & ((calm(X0) & ~generous(X0)) | (~wise(X0) & ~rich(X0)))) [flattening 63]
89. wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 47]
90. wise(X0) | patient(X0) | patient(X0) [cnf transformation 47]
96. ~old(john) | ~wise(john) | ~patient(X0) [cnf transformation 51]
100. ~wise(X0) | brave(X0) | patient(X0) [cnf transformation 52]
111. creative(sK5) | ~calm(X1) | old(X1) [cnf transformation 58]
113. ~creative(X0) | ~calm(X0) [cnf transformation 36]
120. calm(X0) | ~wise(X0) [cnf transformation 64]
135. ~brave(paul) [cnf transformation 22]
136. wise(X0) | ~patient(X0) [duplicate literal removal 89]
137. patient(X0) | wise(X0) [duplicate literal removal 90]
223. wise(X0) [subsumption resolution 136,137]
224. ~old(john) | ~patient(X0) [subsumption resolution 96,223]
226. 20 <=> ! [X0] : ~patient(X0) [avatar definition]
227. ~patient(X0) <- (20) [avatar component clause 226]
229. 21 <=> old(john) [avatar definition]
231. ~old(john) <- (~21) [avatar component clause 229]
232. 20 | ~21 [avatar split clause 224,229,226]
248. patient(X0) | brave(X0) [subsumption resolution 100,223]
267. 28 <=> ! [X1] : (~calm(X1) | old(X1)) [avatar definition]
268. ~calm(X1) | old(X1) <- (28) [avatar component clause 267]
270. 29 <=> creative(sK5) [avatar definition]
272. creative(sK5) <- (29) [avatar component clause 270]
273. 28 | 29 [avatar split clause 111,270,267]
310. calm(X0) [subsumption resolution 120,223]
354. old(X1) <- (28) [subsumption resolution 268,310]
355. $false <- (~21, 28) [resolution 354,231]
356. 21 | ~28 [avatar contradiction clause 355]
357. ~calm(sK5) <- (29) [resolution 113,272]
359. $false <- (29) [subsumption resolution 357,310]
360. ~29 [avatar contradiction clause 359]
372. brave(X0) <- (20) [resolution 248,227]
375. $false <- (20) [resolution 372,135]
376. ~20 [avatar contradiction clause 375]
377. $false [avatar sat refutation 232,273,356,360,376]
% SZS output end Proof for 702602256131480846921794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or rich is either quiet or not wise.
If paul is either kind or not happy then someone is rich or strong and vice versa.
If someone is either not patient or old then someone is not funny or not humble.
If someone is either kind or humble then someone is not funny or patient and vice versa.
Everyone who is either not calm or curious is not old or not kind.
If paul is kind then someone is old or not creative.
Everyone who is both not funny and not kind is both not rich and not happy and vice versa.
Everyone who is either brave or patient is calm.
Everyone who is either not brave or patient is quiet and vice versa.
If someone is quiet then someone is wise and vice versa.
Everyone who is both happy and not strong is not happy or not kind.
Everyone who is creative or wise is funny.
If someone is rich then someone is both creative and old.
If someone is both happy and not funny then someone is not creative and vice versa.
Everyone who is either not quiet or calm is not creative.
Everyone who is quiet is both curious and not generous.
Someone is either not humble or rich.
Alice is both strong and not old.
Someone is either brave or happy.
Someone is both not strong and not wise.
Someone is not funny.
John is quiet.
Susan is not calm.
Fred is creative or not generous. | Alice is old. | contradiction | (![X]:((kind(X)<~>rich(X))=>(quiet(X)<~>~wise(X))))&
(((kind(paul)<~>~happy(paul)))<=>(?[X]:((rich(X)|strong(X)))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:((~funny(X)|~humble(X)))))&
((?[X]:((kind(X)<~>humble(X))))<=>(?[X]:((~funny(X)|patient(X)))))&
(![X]:((~calm(X)<~>curious(X))=>(~old(X)|~kind(X))))&
((kind(paul))=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(~rich(X)&~happy(X))))&
(![X]:((brave(X)<~>patient(X))=>calm(X)))&
(![X]:((~brave(X)<~>patient(X))<=>quiet(X)))&
((?[X]:(quiet(X)))<=>(?[X]:(wise(X))))&
(![X]:((happy(X)&~strong(X))=>(~happy(X)|~kind(X))))&
(![X]:((creative(X)|wise(X))=>funny(X)))&
((?[X]:(rich(X)))=>(?[X]:((creative(X)&old(X)))))&
((?[X]:((happy(X)&~funny(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)<~>calm(X))=>~creative(X)))&
(![X]:(quiet(X)=>(curious(X)&~generous(X))))&
(?[X]:((~humble(X)<~>rich(X))))&
((strong(alice)&~old(alice)))&
(?[X]:((brave(X)<~>happy(X))))&
(?[X]:((~strong(X)&~wise(X))))&
(?[X]:(~funny(X)))&
(quiet(john))&
(~calm(susan))&
((creative(fred)|~generous(fred))) | old(alice) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6125213520763615562381384
% SZS output start Proof for 6125213520763615562381384
18. ~old(alice) & strong(alice) [input p17]
25. old(alice) [input hypothesis]
137. ~old(alice) [cnf transformation 18]
145. old(alice) [cnf transformation 25]
301. $false [subsumption resolution 145,137]
% SZS output end Proof for 6125213520763615562381384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then john is curious or not old.
If john is both not kind and not wise then alice is either not brave or not curious.
If someone is creative then susan is calm or not strong.
Everyone who is both not funny and brave is not generous and vice versa.
If someone is either old or not patient then lucy is both humble and not humble and vice versa.
Everyone who is both not funny and not patient is not tall or not wise and vice versa.
Everyone who is not brave or humble is both tall and not creative and vice versa.
Everyone who is both not wise and rich is generous.
If paul is patient then paul is not old or not quiet.
If someone is both not brave and brave then someone is either not curious or not funny.
Everyone who is both creative and happy is both not rich and wise.
If mary is brave or humble then someone is either happy or calm.
If someone is not funny then susan is either not curious or funny and vice versa.
Everyone who is either humble or patient is not strong or not rich and vice versa.
Everyone who is funny is either curious or not quiet.
If someone is either not calm or old then someone is humble.
Mary is funny or humble.
Fred is either kind or not funny.
Someone is both not calm and not old.
Someone is either rich or tall.
Someone is both happy and tall.
Someone is not calm.
Someone is rich or generous.
Paul is not calm or kind. | Mary is tall. | entailment | ((?[X]:(old(X)))=>((curious(john)|~old(john))))&
(((~kind(john)&~wise(john)))=>((~brave(alice)<~>~curious(alice))))&
((?[X]:(creative(X)))=>((calm(susan)|~strong(susan))))&
(![X]:((~funny(X)&brave(X))<=>~generous(X)))&
((?[X]:((old(X)<~>~patient(X))))<=>((humble(lucy)&~humble(lucy))))&
(![X]:((~funny(X)&~patient(X))<=>(~tall(X)|~wise(X))))&
(![X]:((~brave(X)|humble(X))<=>(tall(X)&~creative(X))))&
(![X]:((~wise(X)&rich(X))=>generous(X)))&
((patient(paul))=>((~old(paul)|~quiet(paul))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:((~curious(X)<~>~funny(X)))))&
(![X]:((creative(X)&happy(X))=>(~rich(X)&wise(X))))&
(((brave(mary)|humble(mary)))=>(?[X]:((happy(X)<~>calm(X)))))&
((?[X]:(~funny(X)))<=>((~curious(susan)<~>funny(susan))))&
(![X]:((humble(X)<~>patient(X))<=>(~strong(X)|~rich(X))))&
(![X]:(funny(X)=>(curious(X)<~>~quiet(X))))&
((?[X]:((~calm(X)<~>old(X))))=>(?[X]:(humble(X))))&
((funny(mary)|humble(mary)))&
((kind(fred)<~>~funny(fred)))&
(?[X]:((~calm(X)&~old(X))))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:((happy(X)&tall(X))))&
(?[X]:(~calm(X)))&
(?[X]:((rich(X)|generous(X))))&
((~calm(paul)|kind(paul))) | tall(mary) | [
"p5",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3945384303395690770667134
% SZS output start Proof for 3945384303395690770667134
6. ! [X0] : ((~patient(X0) & ~funny(X0)) <=> (~wise(X0) | ~tall(X0))) [input p5]
7. ! [X0] : ((humble(X0) | ~brave(X0)) <=> (~creative(X0) & tall(X0))) [input p6]
17. humble(mary) | funny(mary) [input p16]
25. ~tall(mary) [input hypothesis]
53. ! [X0] : (((~patient(X0) & ~funny(X0)) | (wise(X0) & tall(X0))) & ((~wise(X0) | ~tall(X0)) | (patient(X0) | funny(X0)))) [nnf transformation 6]
54. ! [X0] : (((~patient(X0) & ~funny(X0)) | (wise(X0) & tall(X0))) & (~wise(X0) | ~tall(X0) | patient(X0) | funny(X0))) [flattening 53]
55. ! [X0] : (((humble(X0) | ~brave(X0)) | (creative(X0) | ~tall(X0))) & ((~creative(X0) & tall(X0)) | (~humble(X0) & brave(X0)))) [nnf transformation 7]
56. ! [X0] : ((humble(X0) | ~brave(X0) | creative(X0) | ~tall(X0)) & ((~creative(X0) & tall(X0)) | (~humble(X0) & brave(X0)))) [flattening 55]
99. ~funny(X0) | tall(X0) [cnf transformation 54]
104. ~humble(X0) | tall(X0) [cnf transformation 56]
132. humble(mary) | funny(mary) [cnf transformation 17]
144. ~tall(mary) [cnf transformation 25]
215. 17 <=> humble(mary) [avatar definition]
216. humble(mary) <- (17) [avatar component clause 215]
266. 28 <=> funny(mary) [avatar definition]
268. funny(mary) <- (28) [avatar component clause 266]
269. 28 | 17 [avatar split clause 132,215,266]
311. tall(mary) <- (17) [resolution 104,216]
313. $false <- (17) [subsumption resolution 311,144]
314. ~17 [avatar contradiction clause 313]
316. tall(mary) <- (28) [resolution 268,99]
317. $false <- (28) [subsumption resolution 316,144]
318. ~28 [avatar contradiction clause 317]
319. $false [avatar sat refutation 269,314,318]
% SZS output end Proof for 3945384303395690770667134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not generous or kind then alice is funny or not brave. If someone is either patient or not patient then lucy is creative and vice versa. Everyone who is both happy and not brave is either not wise or strong and vice versa. If fred is rich or not generous then paul is not curious or tall. If someone is either not rich or quiet then paul is either not generous or not quiet and vice versa. If lucy is both not creative and not tall then someone is both generous and not rich and vice versa. If someone is not strong then someone is not calm. If someone is not calm then mary is either calm or strong and vice versa. Everyone who is not wise or not tall is either humble or quiet and vice versa. If lucy is curious then paul is not kind or not happy. If susan is not wise then someone is not kind or not generous. Everyone who is both not old and not kind is either not tall or not brave. Everyone who is not old is generous or not tall and vice versa. Everyone who is both not wise and not happy is brave and vice versa. Everyone who is not humble or not happy is not generous or rich and vice versa. If fred is not rich or not happy then someone is either quiet or patient and vice versa. John is both kind and old. Fred is creative. Susan is both old and not brave. Someone is either happy or wise. Lucy is either not brave or not old. Someone is kind or not quiet. Someone is both strong and not happy. Someone is not strong or not generous. | Alice is funny. | neutral | (((~generous(fred)|kind(fred)))=>((funny(alice)|~brave(alice))))&
((?[X]:((patient(X)<~>~patient(X))))<=>(creative(lucy)))&
(![X]:((happy(X)&~brave(X))<=>(~wise(X)<~>strong(X))))&
(((rich(fred)|~generous(fred)))=>((~curious(paul)|tall(paul))))&
((?[X]:((~rich(X)<~>quiet(X))))<=>((~generous(paul)<~>~quiet(paul))))&
(((~creative(lucy)&~tall(lucy)))<=>(?[X]:((generous(X)&~rich(X)))))&
((?[X]:(~strong(X)))=>(?[X]:(~calm(X))))&
((?[X]:(~calm(X)))<=>((calm(mary)<~>strong(mary))))&
(![X]:((~wise(X)|~tall(X))<=>(humble(X)<~>quiet(X))))&
((curious(lucy))=>((~kind(paul)|~happy(paul))))&
((~wise(susan))=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:((~old(X)&~kind(X))=>(~tall(X)<~>~brave(X))))&
(![X]:(~old(X)<=>(generous(X)|~tall(X))))&
(![X]:((~wise(X)&~happy(X))<=>brave(X)))&
(![X]:((~humble(X)|~happy(X))<=>(~generous(X)|rich(X))))&
(((~rich(fred)|~happy(fred)))<=>(?[X]:((quiet(X)<~>patient(X)))))&
((kind(john)&old(john)))&
(creative(fred))&
((old(susan)&~brave(susan)))&
(?[X]:((happy(X)<~>wise(X))))&
((~brave(lucy)<~>~old(lucy)))&
(?[X]:((kind(X)|~quiet(X))))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((~strong(X)|~generous(X)))) | funny(alice) | [] | null | 0 |
Everyone who is calm or not generous is both quiet and brave and vice versa. If someone is either not generous or calm then mary is generous. Everyone who is not humble or not kind is funny. If fred is either tall or not patient then alice is both not happy and strong. If someone is both not generous and not old then someone is either not brave or brave and vice versa. If someone is both patient and tall then someone is both creative and kind and vice versa. Everyone who is not humble or funny is both not humble and not funny. Everyone who is either tall or not creative is not rich and vice versa. If mary is either not curious or curious then someone is either not funny or funny. If alice is quiet then paul is not patient or not rich. Everyone who is quiet or not quiet is either funny or quiet. If someone is either old or humble then fred is calm or rich and vice versa. Everyone who is quiet is creative and vice versa. Everyone who is both not curious and funny is either tall or not curious and vice versa. If alice is old or happy then john is humble and vice versa. Everyone who is quiet or creative is brave or kind. Susan is not strong. Paul is either wise or rich. Someone is both wise and tall. Lucy is creative or not tall. John is both wise and not curious. | Susan is not tall. | neutral | (![X]:((calm(X)|~generous(X))<=>(quiet(X)&brave(X))))&
((?[X]:((~generous(X)<~>calm(X))))=>(generous(mary)))&
(![X]:((~humble(X)|~kind(X))=>funny(X)))&
(((tall(fred)<~>~patient(fred)))=>((~happy(alice)&strong(alice))))&
((?[X]:((~generous(X)&~old(X))))<=>(?[X]:((~brave(X)<~>brave(X)))))&
((?[X]:((patient(X)&tall(X))))<=>(?[X]:((creative(X)&kind(X)))))&
(![X]:((~humble(X)|funny(X))=>(~humble(X)&~funny(X))))&
(![X]:((tall(X)<~>~creative(X))<=>~rich(X)))&
(((~curious(mary)<~>curious(mary)))=>(?[X]:((~funny(X)<~>funny(X)))))&
((quiet(alice))=>((~patient(paul)|~rich(paul))))&
(![X]:((quiet(X)|~quiet(X))=>(funny(X)<~>quiet(X))))&
((?[X]:((old(X)<~>humble(X))))<=>((calm(fred)|rich(fred))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:((~curious(X)&funny(X))<=>(tall(X)<~>~curious(X))))&
(((old(alice)|happy(alice)))<=>(humble(john)))&
(![X]:((quiet(X)|creative(X))=>(brave(X)|kind(X))))&
(~strong(susan))&
((wise(paul)<~>rich(paul)))&
(?[X]:((wise(X)&tall(X))))&
((creative(lucy)|~tall(lucy)))&
((wise(john)&~curious(john))) | ~tall(susan) | [] | null | 0 |
If someone is quiet then lucy is either not strong or not rich.
If someone is either not patient or not quiet then someone is curious.
Everyone who is patient is both not tall and happy.
Everyone who is not rich is not brave or not creative and vice versa.
If someone is either tall or patient then someone is either happy or curious and vice versa.
Everyone who is creative or not creative is kind or not quiet and vice versa.
If paul is not calm or creative then someone is both wise and rich and vice versa.
If alice is not funny then john is humble and vice versa.
If someone is not strong then someone is either not kind or not old.
If fred is curious then someone is both not strong and not brave and vice versa.
Everyone who is kind or not calm is not old.
Everyone who is not old is both not creative and not strong and vice versa.
Everyone who is brave is either humble or not funny and vice versa.
Everyone who is rich is creative and vice versa.
If mary is happy or creative then someone is not funny and vice versa.
Everyone who is either not old or not kind is kind.
Someone is either generous or kind.
Mary is rich or calm.
Lucy is not calm or brave.
Someone is both not wise and curious.
Someone is not quiet.
Someone is either not generous or not patient.
Susan is not patient. | Alice is not funny. | neutral | ((?[X]:(quiet(X)))=>((~strong(lucy)<~>~rich(lucy))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:(curious(X))))&
(![X]:(patient(X)=>(~tall(X)&happy(X))))&
(![X]:(~rich(X)<=>(~brave(X)|~creative(X))))&
((?[X]:((tall(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>curious(X)))))&
(![X]:((creative(X)|~creative(X))<=>(kind(X)|~quiet(X))))&
(((~calm(paul)|creative(paul)))<=>(?[X]:((wise(X)&rich(X)))))&
((~funny(alice))<=>(humble(john)))&
((?[X]:(~strong(X)))=>(?[X]:((~kind(X)<~>~old(X)))))&
((curious(fred))<=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((kind(X)|~calm(X))=>~old(X)))&
(![X]:(~old(X)<=>(~creative(X)&~strong(X))))&
(![X]:(brave(X)<=>(humble(X)<~>~funny(X))))&
(![X]:(rich(X)<=>creative(X)))&
(((happy(mary)|creative(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)<~>~kind(X))=>kind(X)))&
(?[X]:((generous(X)<~>kind(X))))&
((rich(mary)|calm(mary)))&
((~calm(lucy)|brave(lucy)))&
(?[X]:((~wise(X)&curious(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)<~>~patient(X))))&
(~patient(susan)) | ~funny(alice) | [] | null | 0 |
Everyone who is both humble and strong is old and vice versa. Everyone who is both patient and not kind is not kind. Everyone who is either not happy or strong is happy or humble and vice versa. If someone is humble or not wise then someone is rich. Everyone who is not patient is either not quiet or kind and vice versa. If someone is either strong or calm then susan is curious or not generous and vice versa. If someone is quiet then alice is not wise or not strong. Everyone who is both not curious and not brave is either creative or not wise and vice versa. Everyone who is calm is both not wise and happy and vice versa. Everyone who is either not kind or happy is not old. If fred is both not generous and not curious then someone is not curious. If john is not curious or humble then someone is both quiet and not calm. Everyone who is old or humble is both curious and brave. If mary is either quiet or not patient then someone is not rich. Everyone who is not old or not creative is both quiet and not curious and vice versa. If mary is both tall and not happy then someone is tall or not rich and vice versa. John is not tall or not kind. Paul is both kind and not calm. Someone is not humble or not happy. Alice is not strong or not quiet. John is not curious. Susan is either curious or not wise. Fred is both happy and not humble. Mary is not patient. | Susan is not quiet. | contradiction | (![X]:((humble(X)&strong(X))<=>old(X)))&
(![X]:((patient(X)&~kind(X))=>~kind(X)))&
(![X]:((~happy(X)<~>strong(X))<=>(happy(X)|humble(X))))&
((?[X]:((humble(X)|~wise(X))))=>(?[X]:(rich(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>kind(X))))&
((?[X]:((strong(X)<~>calm(X))))<=>((curious(susan)|~generous(susan))))&
((?[X]:(quiet(X)))=>((~wise(alice)|~strong(alice))))&
(![X]:((~curious(X)&~brave(X))<=>(creative(X)<~>~wise(X))))&
(![X]:(calm(X)<=>(~wise(X)&happy(X))))&
(![X]:((~kind(X)<~>happy(X))=>~old(X)))&
(((~generous(fred)&~curious(fred)))=>(?[X]:(~curious(X))))&
(((~curious(john)|humble(john)))=>(?[X]:((quiet(X)&~calm(X)))))&
(![X]:((old(X)|humble(X))=>(curious(X)&brave(X))))&
(((quiet(mary)<~>~patient(mary)))=>(?[X]:(~rich(X))))&
(![X]:((~old(X)|~creative(X))<=>(quiet(X)&~curious(X))))&
(((tall(mary)&~happy(mary)))<=>(?[X]:((tall(X)|~rich(X)))))&
((~tall(john)|~kind(john)))&
((kind(paul)&~calm(paul)))&
(?[X]:((~humble(X)|~happy(X))))&
((~strong(alice)|~quiet(alice)))&
(~curious(john))&
((curious(susan)<~>~wise(susan)))&
((happy(fred)&~humble(fred)))&
(~patient(mary)) | ~quiet(susan) | [
"p7",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2587193785835042975329387
% SZS output start Proof for 2587193785835042975329387
8. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> (creative(X0) <~> ~wise(X0))) [input p7]
13. ! [X0] : ((humble(X0) | old(X0)) => (brave(X0) & curious(X0))) [input p12]
15. ! [X0] : ((~creative(X0) | ~old(X0)) <=> (~curious(X0) & quiet(X0))) [input p14]
22. curious(susan) <~> ~wise(susan) [input p21]
25. ~quiet(susan) [input hypothesis]
36. ! [X0] : ((brave(X0) & curious(X0)) | (~humble(X0) & ~old(X0))) [ennf transformation 13]
51. ! [X0] : (((~brave(X0) & ~curious(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (brave(X0) | curious(X0)))) [nnf transformation 8]
52. ! [X0] : (((~brave(X0) & ~curious(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | brave(X0) | curious(X0))) [flattening 51]
63. ! [X0] : (((~creative(X0) | ~old(X0)) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | (creative(X0) & old(X0)))) [nnf transformation 15]
64. ! [X0] : ((~creative(X0) | ~old(X0) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | (creative(X0) & old(X0)))) [flattening 63]
72. (wise(susan) | ~curious(susan)) & (~wise(susan) | curious(susan)) [nnf transformation 22]
98. ~creative(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 52]
112. ~old(X0) | curious(X0) [cnf transformation 36]
118. quiet(X0) | old(X0) [cnf transformation 64]
121. ~curious(X0) | creative(X0) [cnf transformation 64]
135. wise(susan) | ~curious(susan) [cnf transformation 72]
139. ~quiet(susan) [cnf transformation 25]
169. 7 <=> curious(susan) [avatar definition]
170. curious(susan) <- (7) [avatar component clause 169]
294. 34 <=> wise(susan) [avatar definition]
296. wise(susan) <- (34) [avatar component clause 294]
297. ~7 | 34 [avatar split clause 135,294,169]
302. old(susan) [resolution 118,139]
304. curious(susan) [resolution 302,112]
309. 7 [avatar split clause 304,169]
311. creative(susan) <- (7) [resolution 121,170]
369. ~wise(susan) | ~curious(susan) <- (7) [resolution 98,311]
370. ~curious(susan) <- (7, 34) [subsumption resolution 369,296]
371. $false <- (7, 34) [subsumption resolution 370,170]
372. ~7 | ~34 [avatar contradiction clause 371]
373. $false [avatar sat refutation 297,309,372]
% SZS output end Proof for 2587193785835042975329387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not kind or creative then fred is either not curious or old and vice versa. If someone is either not kind or not rich then someone is not brave or not generous. Everyone who is both creative and not rich is both not patient and quiet and vice versa. Everyone who is not happy or not rich is not humble and vice versa. Everyone who is not funny or not quiet is either creative or not tall. Everyone who is tall is old and vice versa. Everyone who is not patient is quiet and vice versa. Everyone who is wise is old. If mary is quiet or not kind then someone is either funny or calm and vice versa. Everyone who is either not rich or creative is either old or happy and vice versa. If paul is both strong and tall then someone is not patient and vice versa. If mary is not kind or not patient then alice is both not funny and creative. Everyone who is not curious or not quiet is kind. If fred is both not funny and quiet then john is not curious. Everyone who is either not curious or generous is both not kind and not strong. If someone is either kind or wise then fred is generous and vice versa. John is calm or wise. Susan is not strong or not happy. Paul is both not curious and not creative. Susan is both not tall and not generous. Someone is not calm or not patient. Someone is either humble or curious. | Mary is not rich. | neutral | ((?[X]:((~kind(X)<~>creative(X))))<=>((~curious(fred)<~>old(fred))))&
((?[X]:((~kind(X)<~>~rich(X))))=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((creative(X)&~rich(X))<=>(~patient(X)&quiet(X))))&
(![X]:((~happy(X)|~rich(X))<=>~humble(X)))&
(![X]:((~funny(X)|~quiet(X))=>(creative(X)<~>~tall(X))))&
(![X]:(tall(X)<=>old(X)))&
(![X]:(~patient(X)<=>quiet(X)))&
(![X]:(wise(X)=>old(X)))&
(((quiet(mary)|~kind(mary)))<=>(?[X]:((funny(X)<~>calm(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(old(X)<~>happy(X))))&
(((strong(paul)&tall(paul)))<=>(?[X]:(~patient(X))))&
(((~kind(mary)|~patient(mary)))=>((~funny(alice)&creative(alice))))&
(![X]:((~curious(X)|~quiet(X))=>kind(X)))&
(((~funny(fred)&quiet(fred)))=>(~curious(john)))&
(![X]:((~curious(X)<~>generous(X))=>(~kind(X)&~strong(X))))&
((?[X]:((kind(X)<~>wise(X))))<=>(generous(fred)))&
((calm(john)|wise(john)))&
((~strong(susan)|~happy(susan)))&
((~curious(paul)&~creative(paul)))&
((~tall(susan)&~generous(susan)))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:((humble(X)<~>curious(X)))) | ~rich(mary) | [] | null | 0 |
If someone is not humble then john is not patient.
If paul is either humble or not patient then someone is not calm.
If john is either not happy or rich then someone is old or not strong and vice versa.
Everyone who is not quiet or not happy is both not funny and rich and vice versa.
Everyone who is either not quiet or calm is both kind and not brave and vice versa.
Everyone who is either old or not strong is both patient and not happy and vice versa.
Everyone who is both not curious and rich is not strong.
Everyone who is both not calm and not quiet is both calm and not creative.
Everyone who is both not calm and curious is not funny or not quiet and vice versa.
If someone is not creative or strong then fred is quiet or humble.
If mary is either humble or happy then someone is not happy or humble and vice versa.
Everyone who is either quiet or tall is either not tall or brave and vice versa.
Everyone who is not curious or not calm is both not quiet and old and vice versa.
Everyone who is quiet or not rich is both quiet and not wise.
If someone is calm or brave then someone is both not brave and humble.
Everyone who is either creative or not tall is both not rich and funny.
Lucy is creative.
Susan is either generous or not quiet.
Susan is not rich or old.
Mary is not kind or not tall.
Fred is both not rich and generous.
Mary is not rich.
Susan is humble or not humble. | Mary is funny. | entailment | ((?[X]:(~humble(X)))=>(~patient(john)))&
(((humble(paul)<~>~patient(paul)))=>(?[X]:(~calm(X))))&
(((~happy(john)<~>rich(john)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~quiet(X)|~happy(X))<=>(~funny(X)&rich(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(kind(X)&~brave(X))))&
(![X]:((old(X)<~>~strong(X))<=>(patient(X)&~happy(X))))&
(![X]:((~curious(X)&rich(X))=>~strong(X)))&
(![X]:((~calm(X)&~quiet(X))=>(calm(X)&~creative(X))))&
(![X]:((~calm(X)&curious(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)|strong(X))))=>((quiet(fred)|humble(fred))))&
(((humble(mary)<~>happy(mary)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((~curious(X)|~calm(X))<=>(~quiet(X)&old(X))))&
(![X]:((quiet(X)|~rich(X))=>(quiet(X)&~wise(X))))&
((?[X]:((calm(X)|brave(X))))=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((creative(X)<~>~tall(X))=>(~rich(X)&funny(X))))&
(creative(lucy))&
((generous(susan)<~>~quiet(susan)))&
((~rich(susan)|old(susan)))&
((~kind(mary)|~tall(mary)))&
((~rich(fred)&generous(fred)))&
(~rich(mary))&
((humble(susan)|~humble(susan))) | funny(mary) | [
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 879319848237747605945982
% SZS output start Proof for 879319848237747605945982
8. ! [X0] : ((~quiet(X0) & ~calm(X0)) => (~creative(X0) & calm(X0))) [input p7]
9. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p8]
13. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> (old(X0) & ~quiet(X0))) [input p12]
24. ~funny(mary) [input hypothesis]
31. ! [X0] : ((~creative(X0) & calm(X0)) | (quiet(X0) | calm(X0))) [ennf transformation 8]
32. ! [X0] : ((~creative(X0) & calm(X0)) | quiet(X0) | calm(X0)) [flattening 31]
51. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | (~curious(X0) | calm(X0)))) [nnf transformation 9]
52. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~curious(X0) | calm(X0))) [flattening 51]
58. ! [X0] : (((~calm(X0) | ~curious(X0)) | (~old(X0) | quiet(X0))) & ((old(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [nnf transformation 13]
59. ! [X0] : ((~calm(X0) | ~curious(X0) | ~old(X0) | quiet(X0)) & ((old(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [flattening 58]
92. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 32]
95. ~calm(X0) | funny(X0) [cnf transformation 52]
96. ~calm(X0) | quiet(X0) [cnf transformation 52]
116. ~quiet(X0) | calm(X0) [cnf transformation 59]
139. ~funny(mary) [cnf transformation 24]
144. calm(X0) | quiet(X0) [duplicate literal removal 92]
195. quiet(X0) [subsumption resolution 96,144]
228. calm(X0) [subsumption resolution 116,195]
261. funny(X0) [resolution 95,228]
262. $false [resolution 261,139]
% SZS output end Proof for 879319848237747605945982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both humble and not brave then mary is both kind and wise and vice versa. If someone is funny or not tall then someone is either strong or patient. Everyone who is either calm or wise is generous or not calm. Everyone who is both kind and humble is creative or calm. If susan is not tall or brave then mary is both not curious and calm. Everyone who is not kind or strong is both curious and not wise. Everyone who is not curious is not generous or not funny. If john is either old or not brave then alice is wise or tall. Everyone who is both not humble and curious is not old and vice versa. Everyone who is either humble or not old is creative and vice versa. Everyone who is either brave or not funny is brave and vice versa. Everyone who is not happy is either quiet or not rich. If john is either tall or strong then paul is brave or rich. Everyone who is either patient or not rich is either old or happy and vice versa. Everyone who is generous or not generous is not curious. If someone is rich then someone is either strong or patient and vice versa. Someone is quiet or not tall. Someone is either calm or wise. Paul is both not quiet and not patient. Someone is not quiet or wise. Lucy is either tall or not wise. Fred is either strong or not calm. | Mary is humble. | neutral | (((humble(fred)&~brave(fred)))<=>((kind(mary)&wise(mary))))&
((?[X]:((funny(X)|~tall(X))))=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((calm(X)<~>wise(X))=>(generous(X)|~calm(X))))&
(![X]:((kind(X)&humble(X))=>(creative(X)|calm(X))))&
(((~tall(susan)|brave(susan)))=>((~curious(mary)&calm(mary))))&
(![X]:((~kind(X)|strong(X))=>(curious(X)&~wise(X))))&
(![X]:(~curious(X)=>(~generous(X)|~funny(X))))&
(((old(john)<~>~brave(john)))=>((wise(alice)|tall(alice))))&
(![X]:((~humble(X)&curious(X))<=>~old(X)))&
(![X]:((humble(X)<~>~old(X))<=>creative(X)))&
(![X]:((brave(X)<~>~funny(X))<=>brave(X)))&
(![X]:(~happy(X)=>(quiet(X)<~>~rich(X))))&
(((tall(john)<~>strong(john)))=>((brave(paul)|rich(paul))))&
(![X]:((patient(X)<~>~rich(X))<=>(old(X)<~>happy(X))))&
(![X]:((generous(X)|~generous(X))=>~curious(X)))&
((?[X]:(rich(X)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(?[X]:((quiet(X)|~tall(X))))&
(?[X]:((calm(X)<~>wise(X))))&
((~quiet(paul)&~patient(paul)))&
(?[X]:((~quiet(X)|wise(X))))&
((tall(lucy)<~>~wise(lucy)))&
((strong(fred)<~>~calm(fred))) | humble(mary) | [] | null | 0 |
Everyone who is either funny or curious is either quiet or kind.
If john is both happy and wise then lucy is both tall and funny.
Everyone who is not kind is either not patient or patient.
If mary is not strong or old then someone is rich or happy and vice versa.
Everyone who is not wise is either humble or not wise.
Everyone who is both quiet and not humble is not curious or not funny and vice versa.
Everyone who is not funny is not brave and vice versa.
If paul is not old or old then someone is both not old and quiet and vice versa.
Everyone who is either wise or humble is not kind or not generous.
If someone is either not wise or old then mary is both funny and not old and vice versa.
Everyone who is both not quiet and tall is either patient or tall.
Everyone who is not patient or funny is not patient and vice versa.
If john is tall or brave then john is both not funny and kind.
If someone is happy or tall then fred is both not happy and not curious and vice versa.
Everyone who is both funny and creative is either not brave or not patient.
If someone is both not kind and not calm then mary is both funny and not creative.
Someone is wise or tall.
Susan is rich.
Mary is either not creative or strong.
Someone is not creative.
Someone is not brave or not humble.
Paul is not rich.
Alice is strong or curious. | Paul is old. | neutral | (![X]:((funny(X)<~>curious(X))=>(quiet(X)<~>kind(X))))&
(((happy(john)&wise(john)))=>((tall(lucy)&funny(lucy))))&
(![X]:(~kind(X)=>(~patient(X)<~>patient(X))))&
(((~strong(mary)|old(mary)))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:(~wise(X)=>(humble(X)<~>~wise(X))))&
(![X]:((quiet(X)&~humble(X))<=>(~curious(X)|~funny(X))))&
(![X]:(~funny(X)<=>~brave(X)))&
(((~old(paul)|old(paul)))<=>(?[X]:((~old(X)&quiet(X)))))&
(![X]:((wise(X)<~>humble(X))=>(~kind(X)|~generous(X))))&
((?[X]:((~wise(X)<~>old(X))))<=>((funny(mary)&~old(mary))))&
(![X]:((~quiet(X)&tall(X))=>(patient(X)<~>tall(X))))&
(![X]:((~patient(X)|funny(X))<=>~patient(X)))&
(((tall(john)|brave(john)))=>((~funny(john)&kind(john))))&
((?[X]:((happy(X)|tall(X))))<=>((~happy(fred)&~curious(fred))))&
(![X]:((funny(X)&creative(X))=>(~brave(X)<~>~patient(X))))&
((?[X]:((~kind(X)&~calm(X))))=>((funny(mary)&~creative(mary))))&
(?[X]:((wise(X)|tall(X))))&
(rich(susan))&
((~creative(mary)<~>strong(mary)))&
(?[X]:(~creative(X)))&
(?[X]:((~brave(X)|~humble(X))))&
(~rich(paul))&
((strong(alice)|curious(alice))) | old(paul) | [] | null | 0 |
If someone is either not tall or not strong then someone is both happy and not quiet and vice versa. Everyone who is not strong or old is both creative and patient. If mary is either quiet or patient then fred is either not patient or not calm. If john is both not quiet and not patient then fred is both patient and not strong and vice versa. Everyone who is rich or patient is either not kind or not happy and vice versa. If alice is both curious and not kind then alice is not humble or tall and vice versa. If someone is both not calm and not happy then john is either not old or strong. If mary is either not funny or not creative then mary is not humble and vice versa. Everyone who is not old is both not humble and funny and vice versa. If susan is either not creative or not humble then paul is curious and vice versa. Everyone who is either not quiet or wise is wise and vice versa. Everyone who is not wise or not funny is not calm and vice versa. Everyone who is either not happy or wise is both creative and wise and vice versa. If someone is either not quiet or patient then someone is either not quiet or not generous and vice versa. Everyone who is not old or old is quiet or wise and vice versa. Everyone who is either brave or patient is brave and vice versa. John is not creative. Paul is either rich or patient. Fred is curious or not rich. Fred is kind. Someone is either not strong or funny. | Fred is calm. | entailment | ((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:((~strong(X)|old(X))=>(creative(X)&patient(X))))&
(((quiet(mary)<~>patient(mary)))=>((~patient(fred)<~>~calm(fred))))&
(((~quiet(john)&~patient(john)))<=>((patient(fred)&~strong(fred))))&
(![X]:((rich(X)|patient(X))<=>(~kind(X)<~>~happy(X))))&
(((curious(alice)&~kind(alice)))<=>((~humble(alice)|tall(alice))))&
((?[X]:((~calm(X)&~happy(X))))=>((~old(john)<~>strong(john))))&
(((~funny(mary)<~>~creative(mary)))<=>(~humble(mary)))&
(![X]:(~old(X)<=>(~humble(X)&funny(X))))&
(((~creative(susan)<~>~humble(susan)))<=>(curious(paul)))&
(![X]:((~quiet(X)<~>wise(X))<=>wise(X)))&
(![X]:((~wise(X)|~funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(creative(X)&wise(X))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:((~old(X)|old(X))<=>(quiet(X)|wise(X))))&
(![X]:((brave(X)<~>patient(X))<=>brave(X)))&
(~creative(john))&
((rich(paul)<~>patient(paul)))&
((curious(fred)|~rich(fred)))&
(kind(fred))&
(?[X]:((~strong(X)<~>funny(X)))) | calm(fred) | [
"p2",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 218238860312549639492435
% SZS output start Proof for 218238860312549639492435
3. (quiet(mary) <~> patient(mary)) => (~patient(fred) <~> ~calm(fred)) [input p2]
11. ! [X0] : ((~quiet(X0) <~> wise(X0)) <=> wise(X0)) [input p10]
16. ! [X0] : ((brave(X0) <~> patient(X0)) <=> brave(X0)) [input p15]
22. ~calm(fred) [input hypothesis]
26. (~patient(fred) <~> ~calm(fred)) | (quiet(mary) <=> patient(mary)) [ennf transformation 3]
33. ((calm(fred) | patient(fred)) & (~calm(fred) | ~patient(fred))) | ((quiet(mary) | ~patient(mary)) & (patient(mary) | ~quiet(mary))) [nnf transformation 26]
45. ! [X0] : ((((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~wise(X0)) & (wise(X0) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))))) [nnf transformation 11]
57. ! [X0] : ((((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~brave(X0)) & (brave(X0) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))))) [nnf transformation 16]
74. calm(fred) | patient(fred) | patient(mary) | ~quiet(mary) [cnf transformation 33]
104. wise(X0) | wise(X0) | quiet(X0) [cnf transformation 45]
107. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 45]
130. brave(X0) | brave(X0) | ~patient(X0) [cnf transformation 57]
132. ~patient(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 57]
140. ~calm(fred) [cnf transformation 22]
141. brave(X0) | ~patient(X0) [duplicate literal removal 130]
142. ~patient(X0) | ~brave(X0) [duplicate literal removal 132]
145. wise(X0) | quiet(X0) [duplicate literal removal 104]
146. ~wise(X0) | quiet(X0) [duplicate literal removal 107]
179. 8 <=> patient(mary) [avatar definition]
180. patient(mary) <- (8) [avatar component clause 179]
183. 9 <=> quiet(mary) [avatar definition]
184. ~quiet(mary) <- (~9) [avatar component clause 183]
187. 10 <=> patient(fred) [avatar definition]
189. patient(fred) <- (10) [avatar component clause 187]
191. 11 <=> calm(fred) [avatar definition]
195. ~9 | 8 | 10 | 11 [avatar split clause 74,191,187,179,183]
282. quiet(X0) [subsumption resolution 145,146]
296. 30 <=> ! [X3] : ~patient(X3) [avatar definition]
297. ~patient(X3) <- (30) [avatar component clause 296]
303. ~patient(X0) [subsumption resolution 141,142]
304. 30 [avatar split clause 303,296]
334. ~11 [avatar split clause 140,191]
337. $false <- (10, 30) [subsumption resolution 189,297]
338. ~10 | ~30 [avatar contradiction clause 337]
341. $false <- (~9) [subsumption resolution 184,282]
342. 9 [avatar contradiction clause 341]
343. $false <- (8, 30) [subsumption resolution 180,297]
344. ~8 | ~30 [avatar contradiction clause 343]
345. $false [avatar sat refutation 195,304,334,338,342,344]
% SZS output end Proof for 218238860312549639492435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not generous is not happy or not creative and vice versa.
If someone is not patient or quiet then someone is not calm or not old.
If alice is not kind then someone is either funny or strong and vice versa.
If someone is not humble then paul is either quiet or not kind.
Everyone who is strong is humble or not strong and vice versa.
If someone is either kind or not curious then paul is both not wise and not generous and vice versa.
If mary is brave then someone is not patient and vice versa.
If someone is creative or not old then someone is quiet or rich.
If mary is both patient and not wise then someone is not patient or not happy and vice versa.
If someone is not humble or not kind then john is either not calm or not tall.
Everyone who is not tall is not strong or patient.
Everyone who is curious or not humble is humble.
If fred is both brave and rich then john is not old or tall and vice versa.
Everyone who is either brave or not old is not kind.
If mary is not old then paul is wise or not tall.
Everyone who is not tall is not curious.
Alice is either not humble or patient.
Paul is either not generous or not calm.
Lucy is calm.
Someone is both curious and not generous.
Fred is not brave or not wise.
Mary is wise or not generous. | Lucy is creative. | neutral | (![X]:((tall(X)<~>~generous(X))<=>(~happy(X)|~creative(X))))&
((?[X]:((~patient(X)|quiet(X))))=>(?[X]:((~calm(X)|~old(X)))))&
((~kind(alice))<=>(?[X]:((funny(X)<~>strong(X)))))&
((?[X]:(~humble(X)))=>((quiet(paul)<~>~kind(paul))))&
(![X]:(strong(X)<=>(humble(X)|~strong(X))))&
((?[X]:((kind(X)<~>~curious(X))))<=>((~wise(paul)&~generous(paul))))&
((brave(mary))<=>(?[X]:(~patient(X))))&
((?[X]:((creative(X)|~old(X))))=>(?[X]:((quiet(X)|rich(X)))))&
(((patient(mary)&~wise(mary)))<=>(?[X]:((~patient(X)|~happy(X)))))&
((?[X]:((~humble(X)|~kind(X))))=>((~calm(john)<~>~tall(john))))&
(![X]:(~tall(X)=>(~strong(X)|patient(X))))&
(![X]:((curious(X)|~humble(X))=>humble(X)))&
(((brave(fred)&rich(fred)))<=>((~old(john)|tall(john))))&
(![X]:((brave(X)<~>~old(X))=>~kind(X)))&
((~old(mary))=>((wise(paul)|~tall(paul))))&
(![X]:(~tall(X)=>~curious(X)))&
((~humble(alice)<~>patient(alice)))&
((~generous(paul)<~>~calm(paul)))&
(calm(lucy))&
(?[X]:((curious(X)&~generous(X))))&
((~brave(fred)|~wise(fred)))&
((wise(mary)|~generous(mary))) | creative(lucy) | [] | null | 0 |
If john is either not calm or not patient then susan is not old or not creative.
If someone is old or not rich then lucy is not curious or not generous.
If someone is quiet or not quiet then fred is happy.
If someone is both not quiet and not wise then someone is humble or not tall and vice versa.
Everyone who is both not kind and generous is quiet or not patient and vice versa.
If fred is strong then someone is either generous or wise.
If lucy is both not rich and not happy then fred is not patient or rich and vice versa.
Everyone who is either creative or not strong is both kind and not happy.
Everyone who is not tall or not wise is tall or not calm and vice versa.
If someone is generous or not curious then someone is wise or not creative and vice versa.
If someone is both not wise and not creative then lucy is either not kind or not patient and vice versa.
If someone is both funny and wise then someone is both not generous and not creative.
If lucy is both creative and patient then someone is patient or not tall and vice versa.
If someone is both not funny and creative then someone is brave.
If someone is both not kind and not strong then fred is not generous and vice versa.
If john is either wise or creative then john is either wise or funny.
Someone is not old or generous.
Someone is either not brave or not happy.
Alice is not strong or not patient.
Someone is not patient or quiet.
Someone is both not calm and curious.
Someone is not patient.
Someone is curious.
Someone is not kind. | John is not calm. | neutral | (((~calm(john)<~>~patient(john)))=>((~old(susan)|~creative(susan))))&
((?[X]:((old(X)|~rich(X))))=>((~curious(lucy)|~generous(lucy))))&
((?[X]:((quiet(X)|~quiet(X))))=>(happy(fred)))&
((?[X]:((~quiet(X)&~wise(X))))<=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~kind(X)&generous(X))<=>(quiet(X)|~patient(X))))&
((strong(fred))=>(?[X]:((generous(X)<~>wise(X)))))&
(((~rich(lucy)&~happy(lucy)))<=>((~patient(fred)|rich(fred))))&
(![X]:((creative(X)<~>~strong(X))=>(kind(X)&~happy(X))))&
(![X]:((~tall(X)|~wise(X))<=>(tall(X)|~calm(X))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((wise(X)|~creative(X)))))&
((?[X]:((~wise(X)&~creative(X))))<=>((~kind(lucy)<~>~patient(lucy))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:((~generous(X)&~creative(X)))))&
(((creative(lucy)&patient(lucy)))<=>(?[X]:((patient(X)|~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:(brave(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(~generous(fred)))&
(((wise(john)<~>creative(john)))=>((wise(john)<~>funny(john))))&
(?[X]:((~old(X)|generous(X))))&
(?[X]:((~brave(X)<~>~happy(X))))&
((~strong(alice)|~patient(alice)))&
(?[X]:((~patient(X)|quiet(X))))&
(?[X]:((~calm(X)&curious(X))))&
(?[X]:(~patient(X)))&
(?[X]:(curious(X)))&
(?[X]:(~kind(X))) | ~calm(john) | [] | null | 0 |
If alice is either not quiet or not generous then someone is both kind and not kind and vice versa. If someone is either not old or kind then someone is either not happy or happy and vice versa. If paul is both old and not old then someone is both not humble and kind. If alice is either not rich or kind then someone is rich and vice versa. Everyone who is both not wise and brave is not kind and vice versa. If someone is either patient or creative then someone is both funny and not funny. Everyone who is not tall or humble is patient and vice versa. If someone is not kind then someone is both creative and not calm. If someone is kind or creative then susan is patient and vice versa. If someone is strong or not happy then alice is both tall and not patient and vice versa. If mary is rich or not patient then alice is not happy. Everyone who is both not humble and not curious is both not kind and not tall and vice versa. Everyone who is either not rich or not humble is not wise or happy and vice versa. Everyone who is not curious is either happy or brave. Everyone who is strong or quiet is not kind or not happy and vice versa. If john is both not generous and quiet then someone is not patient. Someone is not happy or curious. Someone is rich. Someone is not generous or funny. John is both not curious and not calm. Alice is either humble or wise. Someone is both not strong and not creative. Someone is both not creative and not kind. | John is not creative. | contradiction | (((~quiet(alice)<~>~generous(alice)))<=>(?[X]:((kind(X)&~kind(X)))))&
((?[X]:((~old(X)<~>kind(X))))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(((old(paul)&~old(paul)))=>(?[X]:((~humble(X)&kind(X)))))&
(((~rich(alice)<~>kind(alice)))<=>(?[X]:(rich(X))))&
(![X]:((~wise(X)&brave(X))<=>~kind(X)))&
((?[X]:((patient(X)<~>creative(X))))=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((~tall(X)|humble(X))<=>patient(X)))&
((?[X]:(~kind(X)))=>(?[X]:((creative(X)&~calm(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(patient(susan)))&
((?[X]:((strong(X)|~happy(X))))<=>((tall(alice)&~patient(alice))))&
(((rich(mary)|~patient(mary)))=>(~happy(alice)))&
(![X]:((~humble(X)&~curious(X))<=>(~kind(X)&~tall(X))))&
(![X]:((~rich(X)<~>~humble(X))<=>(~wise(X)|happy(X))))&
(![X]:(~curious(X)=>(happy(X)<~>brave(X))))&
(![X]:((strong(X)|quiet(X))<=>(~kind(X)|~happy(X))))&
(((~generous(john)&quiet(john)))=>(?[X]:(~patient(X))))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:(rich(X)))&
(?[X]:((~generous(X)|funny(X))))&
((~curious(john)&~calm(john)))&
((humble(alice)<~>wise(alice)))&
(?[X]:((~strong(X)&~creative(X))))&
(?[X]:((~creative(X)&~kind(X)))) | ~creative(john) | [
"p5",
"p6",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6817909751088665822398815
% SZS output start Proof for 6817909751088665822398815
6. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X0] : (~funny(X0) & funny(X0)) [input p5]
7. ! [X0] : ((humble(X0) | ~tall(X0)) <=> patient(X0)) [input p6]
12. ! [X0] : ((~curious(X0) & ~humble(X0)) <=> (~tall(X0) & ~kind(X0))) [input p11]
20. ~calm(john) & ~curious(john) [input p19]
24. ~creative(john) [input hypothesis]
26. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X1] : (~funny(X1) & funny(X1)) [rectify 6]
29. ~curious(john) [pure predicate removal 20]
32. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : (patient(X0) <=> creative(X0)) [ennf transformation 26]
55. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 32]
56. ? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [rectify 55]
57. ? [X0] : (~funny(X0) & funny(X0)) => (~funny(sK5) & funny(sK5)) [choice axiom]
58. (~funny(sK5) & funny(sK5)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [skolemisation 56,57]
59. ! [X0] : (((humble(X0) | ~tall(X0)) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [nnf transformation 7]
60. ! [X0] : ((humble(X0) | ~tall(X0) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [flattening 59]
73. ! [X0] : (((~curious(X0) & ~humble(X0)) | (tall(X0) | kind(X0))) & ((~tall(X0) & ~kind(X0)) | (curious(X0) | humble(X0)))) [nnf transformation 12]
74. ! [X0] : (((~curious(X0) & ~humble(X0)) | tall(X0) | kind(X0)) & ((~tall(X0) & ~kind(X0)) | curious(X0) | humble(X0))) [flattening 73]
116. funny(sK5) | creative(X1) | ~patient(X1) [cnf transformation 58]
118. ~funny(sK5) | creative(X1) | ~patient(X1) [cnf transformation 58]
120. tall(X0) | patient(X0) [cnf transformation 60]
121. ~humble(X0) | patient(X0) [cnf transformation 60]
135. ~tall(X0) | curious(X0) | humble(X0) [cnf transformation 74]
154. ~curious(john) [cnf transformation 29]
161. ~creative(john) [cnf transformation 24]
223. 13 <=> funny(sK5) [avatar definition]
228. 14 <=> ! [X1] : (creative(X1) | ~patient(X1)) [avatar definition]
229. ~patient(X1) | creative(X1) <- (14) [avatar component clause 228]
230. 14 | ~13 [avatar split clause 118,223,228]
232. 14 | 13 [avatar split clause 116,223,228]
393. curious(X0) | humble(X0) | patient(X0) [resolution 135,120]
394. curious(X0) | patient(X0) [subsumption resolution 393,121]
397. patient(john) [resolution 394,154]
424. creative(john) <- (14) [resolution 397,229]
425. $false <- (14) [subsumption resolution 424,161]
426. ~14 [avatar contradiction clause 425]
427. $false [avatar sat refutation 230,232,426]
% SZS output end Proof for 6817909751088665822398815
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either humble or not quiet then fred is either not rich or generous and vice versa. Everyone who is not brave is either not wise or not happy and vice versa. Everyone who is creative or not patient is wise. Everyone who is either not tall or wise is wise. Everyone who is both not quiet and not funny is not quiet or patient and vice versa. If paul is humble or not funny then paul is both creative and calm and vice versa. If fred is either not tall or old then someone is either calm or not wise and vice versa. Everyone who is either generous or humble is both patient and not strong. Everyone who is both strong and not quiet is not old and vice versa. Everyone who is creative is both not wise and brave. If someone is humble or not funny then someone is either not wise or not patient and vice versa. Everyone who is creative is strong. If someone is patient then mary is either kind or not humble and vice versa. Everyone who is either not kind or not funny is either creative or calm. Everyone who is both not brave and humble is patient and vice versa. Everyone who is calm or not happy is happy or strong. Someone is not curious or not funny. Someone is either kind or not patient. Someone is not curious. Someone is patient or strong. Paul is not quiet or not curious. Someone is not creative or wise. Alice is either not patient or not kind. | Paul is not old. | contradiction | (((humble(alice)<~>~quiet(alice)))<=>((~rich(fred)<~>generous(fred))))&
(![X]:(~brave(X)<=>(~wise(X)<~>~happy(X))))&
(![X]:((creative(X)|~patient(X))=>wise(X)))&
(![X]:((~tall(X)<~>wise(X))=>wise(X)))&
(![X]:((~quiet(X)&~funny(X))<=>(~quiet(X)|patient(X))))&
(((humble(paul)|~funny(paul)))<=>((creative(paul)&calm(paul))))&
(((~tall(fred)<~>old(fred)))<=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:((generous(X)<~>humble(X))=>(patient(X)&~strong(X))))&
(![X]:((strong(X)&~quiet(X))<=>~old(X)))&
(![X]:(creative(X)=>(~wise(X)&brave(X))))&
((?[X]:((humble(X)|~funny(X))))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:(creative(X)=>strong(X)))&
((?[X]:(patient(X)))<=>((kind(mary)<~>~humble(mary))))&
(![X]:((~kind(X)<~>~funny(X))=>(creative(X)<~>calm(X))))&
(![X]:((~brave(X)&humble(X))<=>patient(X)))&
(![X]:((calm(X)|~happy(X))=>(happy(X)|strong(X))))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:(~curious(X)))&
(?[X]:((patient(X)|strong(X))))&
((~quiet(paul)|~curious(paul)))&
(?[X]:((~creative(X)|wise(X))))&
((~patient(alice)<~>~kind(alice))) | ~old(paul) | [
"p2",
"p4",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6279898154919544611744468
% SZS output start Proof for 6279898154919544611744468
3. ! [X0] : ((~patient(X0) | creative(X0)) => wise(X0)) [input p2]
5. ! [X0] : ((~funny(X0) & ~quiet(X0)) <=> (patient(X0) | ~quiet(X0))) [input p4]
6. (~funny(paul) | humble(paul)) <=> (calm(paul) & creative(paul)) [input p5]
9. ! [X0] : ((~quiet(X0) & strong(X0)) <=> ~old(X0)) [input p8]
10. ! [X0] : (creative(X0) => (brave(X0) & ~wise(X0))) [input p9]
24. ~old(paul) [input hypothesis]
29. ! [X0] : (wise(X0) | (patient(X0) & ~creative(X0))) [ennf transformation 3]
32. ! [X0] : ((brave(X0) & ~wise(X0)) | ~creative(X0)) [ennf transformation 10]
40. ! [X0] : (((~funny(X0) & ~quiet(X0)) | (~patient(X0) & quiet(X0))) & ((patient(X0) | ~quiet(X0)) | (funny(X0) | quiet(X0)))) [nnf transformation 5]
41. ! [X0] : (((~funny(X0) & ~quiet(X0)) | (~patient(X0) & quiet(X0))) & (patient(X0) | ~quiet(X0) | funny(X0) | quiet(X0))) [flattening 40]
42. ((~funny(paul) | humble(paul)) | (~calm(paul) | ~creative(paul))) & ((calm(paul) & creative(paul)) | (funny(paul) & ~humble(paul))) [nnf transformation 6]
43. (~funny(paul) | humble(paul) | ~calm(paul) | ~creative(paul)) & ((calm(paul) & creative(paul)) | (funny(paul) & ~humble(paul))) [flattening 42]
49. ! [X0] : (((~quiet(X0) & strong(X0)) | old(X0)) & (~old(X0) | (quiet(X0) | ~strong(X0)))) [nnf transformation 9]
50. ! [X0] : (((~quiet(X0) & strong(X0)) | old(X0)) & (~old(X0) | quiet(X0) | ~strong(X0))) [flattening 49]
83. ~creative(X0) | wise(X0) [cnf transformation 29]
90. ~funny(X0) | quiet(X0) [cnf transformation 41]
93. creative(paul) | funny(paul) [cnf transformation 43]
111. ~quiet(X0) | old(X0) [cnf transformation 50]
112. ~wise(X0) | ~creative(X0) [cnf transformation 32]
140. ~old(paul) [cnf transformation 24]
168. 5 <=> creative(paul) [avatar definition]
169. creative(paul) <- (5) [avatar component clause 168]
180. 8 <=> funny(paul) [avatar definition]
181. funny(paul) <- (8) [avatar component clause 180]
186. 8 | 5 [avatar split clause 93,168,180]
218. ~creative(X0) [subsumption resolution 112,83]
308. quiet(paul) <- (8) [resolution 90,181]
310. old(paul) <- (8) [resolution 111,308]
311. $false <- (8) [subsumption resolution 310,140]
312. ~8 [avatar contradiction clause 311]
313. $false <- (5) [subsumption resolution 169,218]
314. ~5 [avatar contradiction clause 313]
315. $false [avatar sat refutation 186,312,314]
% SZS output end Proof for 6279898154919544611744468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not old then someone is not funny and vice versa.
Everyone who is both creative and not humble is quiet or strong.
Everyone who is not creative or not tall is not patient or brave and vice versa.
Everyone who is both not generous and funny is either not creative or quiet and vice versa.
Everyone who is either humble or strong is not old.
If john is either happy or tall then paul is patient or tall.
Everyone who is both funny and curious is either humble or not kind.
Everyone who is both generous and kind is curious or brave and vice versa.
Everyone who is happy or funny is patient and vice versa.
If mary is either not creative or not rich then lucy is not kind and vice versa.
Everyone who is curious is generous.
Everyone who is both not strong and not kind is not humble.
If lucy is both not creative and not generous then someone is not curious and vice versa.
If someone is wise or patient then john is funny and vice versa.
If alice is both humble and happy then someone is not wise and vice versa.
If someone is old then alice is not strong or not humble and vice versa.
Susan is not creative.
Fred is either not funny or not creative.
Someone is not happy.
Paul is not calm.
Someone is not patient or not strong.
Fred is either generous or not humble.
Mary is both not tall and not curious.
Someone is both curious and creative. | Lucy is happy. | contradiction | ((~old(mary))<=>(?[X]:(~funny(X))))&
(![X]:((creative(X)&~humble(X))=>(quiet(X)|strong(X))))&
(![X]:((~creative(X)|~tall(X))<=>(~patient(X)|brave(X))))&
(![X]:((~generous(X)&funny(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:((humble(X)<~>strong(X))=>~old(X)))&
(((happy(john)<~>tall(john)))=>((patient(paul)|tall(paul))))&
(![X]:((funny(X)&curious(X))=>(humble(X)<~>~kind(X))))&
(![X]:((generous(X)&kind(X))<=>(curious(X)|brave(X))))&
(![X]:((happy(X)|funny(X))<=>patient(X)))&
(((~creative(mary)<~>~rich(mary)))<=>(~kind(lucy)))&
(![X]:(curious(X)=>generous(X)))&
(![X]:((~strong(X)&~kind(X))=>~humble(X)))&
(((~creative(lucy)&~generous(lucy)))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|patient(X))))<=>(funny(john)))&
(((humble(alice)&happy(alice)))<=>(?[X]:(~wise(X))))&
((?[X]:(old(X)))<=>((~strong(alice)|~humble(alice))))&
(~creative(susan))&
((~funny(fred)<~>~creative(fred)))&
(?[X]:(~happy(X)))&
(~calm(paul))&
(?[X]:((~patient(X)|~strong(X))))&
((generous(fred)<~>~humble(fred)))&
((~tall(mary)&~curious(mary)))&
(?[X]:((curious(X)&creative(X)))) | happy(lucy) | [
"p2",
"p7",
"p8",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1617481178785789884792020
% SZS output start Proof for 1617481178785789884792020
3. ! [X0] : ((~tall(X0) | ~creative(X0)) <=> (brave(X0) | ~patient(X0))) [input p2]
8. ! [X0] : ((kind(X0) & generous(X0)) <=> (brave(X0) | curious(X0))) [input p7]
9. ! [X0] : ((funny(X0) | happy(X0)) <=> patient(X0)) [input p8]
13. (~generous(lucy) & ~creative(lucy)) <=> ? [X0] : ~curious(X0) [input p12]
23. ~curious(mary) & ~tall(mary) [input p22]
25. happy(lucy) [input hypothesis]
41. ! [X0] : (((~tall(X0) | ~creative(X0)) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | (tall(X0) & creative(X0)))) [nnf transformation 3]
42. ! [X0] : ((~tall(X0) | ~creative(X0) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | (tall(X0) & creative(X0)))) [flattening 41]
48. ! [X0] : (((kind(X0) & generous(X0)) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | (~kind(X0) | ~generous(X0)))) [nnf transformation 8]
49. ! [X0] : (((kind(X0) & generous(X0)) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | ~kind(X0) | ~generous(X0))) [flattening 48]
50. ! [X0] : (((funny(X0) | happy(X0)) | ~patient(X0)) & (patient(X0) | (~funny(X0) & ~happy(X0)))) [nnf transformation 9]
51. ! [X0] : ((funny(X0) | happy(X0) | ~patient(X0)) & (patient(X0) | (~funny(X0) & ~happy(X0)))) [flattening 50]
53. ((~generous(lucy) & ~creative(lucy)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (generous(lucy) | creative(lucy))) [nnf transformation 13]
54. ((~generous(lucy) & ~creative(lucy)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | generous(lucy) | creative(lucy)) [flattening 53]
55. ((~generous(lucy) & ~creative(lucy)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | generous(lucy) | creative(lucy)) [rectify 54]
56. ? [X1] : ~curious(X1) => ~curious(sK1) [choice axiom]
57. ((~generous(lucy) & ~creative(lucy)) | ! [X0] : curious(X0)) & (~curious(sK1) | generous(lucy) | creative(lucy)) [skolemisation 55,56]
83. ~patient(X0) | brave(X0) | creative(X0) [cnf transformation 42]
101. ~brave(X0) | generous(X0) [cnf transformation 49]
104. ~happy(X0) | patient(X0) [cnf transformation 51]
114. ~creative(lucy) | curious(X0) [cnf transformation 57]
115. ~generous(lucy) | curious(X0) [cnf transformation 57]
133. ~curious(mary) [cnf transformation 23]
136. happy(lucy) [cnf transformation 25]
185. 11 <=> ! [X0] : curious(X0) [avatar definition]
186. curious(X0) <- (11) [avatar component clause 185]
188. 12 <=> generous(lucy) [avatar definition]
191. 11 | ~12 [avatar split clause 115,188,185]
193. 13 <=> creative(lucy) [avatar definition]
195. ~creative(lucy) <- (~13) [avatar component clause 193]
196. 11 | ~13 [avatar split clause 114,193,185]
286. patient(lucy) [resolution 104,136]
289. brave(lucy) | creative(lucy) [resolution 83,286]
290. brave(lucy) <- (~13) [subsumption resolution 289,195]
358. generous(lucy) <- (~13) [resolution 290,101]
361. 12 | 13 [avatar split clause 358,193,188]
362. $false <- (11) [resolution 186,133]
367. ~11 [avatar contradiction clause 362]
368. $false [avatar sat refutation 191,196,361,367]
% SZS output end Proof for 1617481178785789884792020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either funny or not kind then alice is curious and vice versa.
Everyone who is both strong and not wise is wise and vice versa.
If fred is patient then someone is both rich and wise.
Everyone who is not rich or kind is not happy.
Everyone who is not brave is not funny or not kind.
If someone is either not humble or not old then susan is both tall and not humble.
If alice is not generous then lucy is strong.
If alice is either strong or not wise then someone is not calm or humble.
Everyone who is funny or calm is both not brave and not calm.
If someone is both not humble and brave then someone is happy.
If paul is either not brave or not wise then susan is tall or not calm.
Everyone who is either brave or curious is both not generous and not quiet and vice versa.
Everyone who is curious is both wise and creative and vice versa.
If someone is generous or not generous then someone is either wise or generous.
If someone is either patient or humble then susan is either brave or generous and vice versa.
Everyone who is either strong or not brave is either old or patient and vice versa.
Someone is not wise.
Someone is not kind or wise.
Paul is not quiet.
Someone is not generous.
Fred is brave or kind.
Someone is not tall.
Alice is either not strong or not tall. | Alice is not brave. | entailment | ((?[X]:((funny(X)<~>~kind(X))))<=>(curious(alice)))&
(![X]:((strong(X)&~wise(X))<=>wise(X)))&
((patient(fred))=>(?[X]:((rich(X)&wise(X)))))&
(![X]:((~rich(X)|kind(X))=>~happy(X)))&
(![X]:(~brave(X)=>(~funny(X)|~kind(X))))&
((?[X]:((~humble(X)<~>~old(X))))=>((tall(susan)&~humble(susan))))&
((~generous(alice))=>(strong(lucy)))&
(((strong(alice)<~>~wise(alice)))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((funny(X)|calm(X))=>(~brave(X)&~calm(X))))&
((?[X]:((~humble(X)&brave(X))))=>(?[X]:(happy(X))))&
(((~brave(paul)<~>~wise(paul)))=>((tall(susan)|~calm(susan))))&
(![X]:((brave(X)<~>curious(X))<=>(~generous(X)&~quiet(X))))&
(![X]:(curious(X)<=>(wise(X)&creative(X))))&
((?[X]:((generous(X)|~generous(X))))=>(?[X]:((wise(X)<~>generous(X)))))&
((?[X]:((patient(X)<~>humble(X))))<=>((brave(susan)<~>generous(susan))))&
(![X]:((strong(X)<~>~brave(X))<=>(old(X)<~>patient(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~kind(X)|wise(X))))&
(~quiet(paul))&
(?[X]:(~generous(X)))&
((brave(fred)|kind(fred)))&
(?[X]:(~tall(X)))&
((~strong(alice)<~>~tall(alice))) | ~brave(alice) | [
"p1",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7379908724153479634814045
% SZS output start Proof for 7379908724153479634814045
2. ! [X0] : ((~wise(X0) & strong(X0)) <=> wise(X0)) [input p1]
7. ~generous(alice) => strong(lucy) [input p6]
12. ! [X0] : ((brave(X0) <~> curious(X0)) <=> (~quiet(X0) & ~generous(X0))) [input p11]
13. ! [X0] : (curious(X0) <=> (creative(X0) & wise(X0))) [input p12]
24. brave(alice) [input hypothesis]
37. strong(lucy) | generous(alice) [ennf transformation 7]
45. ! [X0] : (((~wise(X0) & strong(X0)) | ~wise(X0)) & (wise(X0) | (wise(X0) | ~strong(X0)))) [nnf transformation 2]
46. ! [X0] : (((~wise(X0) & strong(X0)) | ~wise(X0)) & (wise(X0) | wise(X0) | ~strong(X0))) [flattening 45]
53. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (quiet(X0) | generous(X0))) & ((~quiet(X0) & ~generous(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [nnf transformation 12]
54. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | quiet(X0) | generous(X0)) & ((~quiet(X0) & ~generous(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [flattening 53]
55. ! [X0] : ((curious(X0) | (~creative(X0) | ~wise(X0))) & ((creative(X0) & wise(X0)) | ~curious(X0))) [nnf transformation 13]
56. ! [X0] : ((curious(X0) | ~creative(X0) | ~wise(X0)) & ((creative(X0) & wise(X0)) | ~curious(X0))) [flattening 55]
79. wise(X0) | wise(X0) | ~strong(X0) [cnf transformation 46]
81. ~wise(X0) | ~wise(X0) [cnf transformation 46]
89. strong(lucy) | generous(alice) [cnf transformation 37]
92. ~generous(X0) | curious(X0) | ~brave(X0) [cnf transformation 54]
98. wise(X0) | ~curious(X0) [cnf transformation 56]
129. brave(alice) [cnf transformation 24]
130. wise(X0) | ~strong(X0) [duplicate literal removal 79]
131. ~wise(X0) [duplicate literal removal 81]
154. ~strong(X0) [subsumption resolution 130,131]
174. generous(alice) [subsumption resolution 89,154]
183. ~curious(X0) [subsumption resolution 98,131]
252. curious(alice) | ~brave(alice) [resolution 92,174]
255. ~brave(alice) [subsumption resolution 252,183]
256. $false [subsumption resolution 255,129]
% SZS output end Proof for 7379908724153479634814045
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old or humble then mary is either kind or curious and vice versa.
If mary is quiet then lucy is generous.
Everyone who is either not strong or brave is either patient or quiet and vice versa.
If someone is not creative then someone is not curious.
Everyone who is both humble and not rich is not patient.
If someone is rich or funny then alice is not strong or generous and vice versa.
If someone is both patient and brave then alice is calm and vice versa.
Everyone who is kind is not creative and vice versa.
Everyone who is either strong or humble is not calm and vice versa.
Everyone who is both not patient and kind is both not funny and old.
If lucy is funny then someone is either not old or not calm and vice versa.
Everyone who is not quiet or not creative is both strong and humble.
If paul is humble then susan is not generous and vice versa.
Everyone who is not wise is either not wise or not kind and vice versa.
Everyone who is either wise or tall is both creative and not funny.
Everyone who is humble is either not patient or rich.
Lucy is not quiet or not humble.
Paul is not humble or rich.
Someone is both not curious and happy.
Susan is either not rich or kind.
Fred is both not creative and humble.
John is either brave or calm. | Susan is wise. | neutral | ((?[X]:((~old(X)|humble(X))))<=>((kind(mary)<~>curious(mary))))&
((quiet(mary))=>(generous(lucy)))&
(![X]:((~strong(X)<~>brave(X))<=>(patient(X)<~>quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~curious(X))))&
(![X]:((humble(X)&~rich(X))=>~patient(X)))&
((?[X]:((rich(X)|funny(X))))<=>((~strong(alice)|generous(alice))))&
((?[X]:((patient(X)&brave(X))))<=>(calm(alice)))&
(![X]:(kind(X)<=>~creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~patient(X)&kind(X))=>(~funny(X)&old(X))))&
((funny(lucy))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:((~quiet(X)|~creative(X))=>(strong(X)&humble(X))))&
((humble(paul))<=>(~generous(susan)))&
(![X]:(~wise(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((wise(X)<~>tall(X))=>(creative(X)&~funny(X))))&
(![X]:(humble(X)=>(~patient(X)<~>rich(X))))&
((~quiet(lucy)|~humble(lucy)))&
((~humble(paul)|rich(paul)))&
(?[X]:((~curious(X)&happy(X))))&
((~rich(susan)<~>kind(susan)))&
((~creative(fred)&humble(fred)))&
((brave(john)<~>calm(john))) | wise(susan) | [] | null | 0 |
Everyone who is either not happy or not patient is not old. If alice is brave then someone is not quiet and vice versa. If someone is both rich and quiet then alice is strong or brave and vice versa. Everyone who is not old or not funny is both tall and not humble. If susan is rich then someone is either not brave or not rich. If alice is both quiet and not wise then fred is not calm. Everyone who is both curious and calm is not patient and vice versa. Everyone who is not wise is both strong and not quiet and vice versa. Everyone who is generous or rich is either not generous or not old. If someone is both not old and happy then someone is both not kind and curious and vice versa. If someone is curious then alice is either not brave or not quiet. Everyone who is patient is not rich or not happy. Everyone who is not generous or not calm is both not funny and not generous and vice versa. Everyone who is either curious or not happy is both not old and humble and vice versa. If someone is not generous then someone is not quiet or not kind and vice versa. Everyone who is wise or happy is both not generous and calm. Someone is either not wise or not quiet. Fred is not kind or not calm. Mary is both wise and old. Mary is both strong and old. Someone is tall. Alice is both wise and brave. Someone is brave. | Mary is not generous. | entailment | (![X]:((~happy(X)<~>~patient(X))=>~old(X)))&
((brave(alice))<=>(?[X]:(~quiet(X))))&
((?[X]:((rich(X)&quiet(X))))<=>((strong(alice)|brave(alice))))&
(![X]:((~old(X)|~funny(X))=>(tall(X)&~humble(X))))&
((rich(susan))=>(?[X]:((~brave(X)<~>~rich(X)))))&
(((quiet(alice)&~wise(alice)))=>(~calm(fred)))&
(![X]:((curious(X)&calm(X))<=>~patient(X)))&
(![X]:(~wise(X)<=>(strong(X)&~quiet(X))))&
(![X]:((generous(X)|rich(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((~old(X)&happy(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
((?[X]:(curious(X)))=>((~brave(alice)<~>~quiet(alice))))&
(![X]:(patient(X)=>(~rich(X)|~happy(X))))&
(![X]:((~generous(X)|~calm(X))<=>(~funny(X)&~generous(X))))&
(![X]:((curious(X)<~>~happy(X))<=>(~old(X)&humble(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~quiet(X)|~kind(X)))))&
(![X]:((wise(X)|happy(X))=>(~generous(X)&calm(X))))&
(?[X]:((~wise(X)<~>~quiet(X))))&
((~kind(fred)|~calm(fred)))&
((wise(mary)&old(mary)))&
((strong(mary)&old(mary)))&
(?[X]:(tall(X)))&
((wise(alice)&brave(alice)))&
(?[X]:(brave(X))) | ~generous(mary) | [
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6962830465782378938407538
% SZS output start Proof for 6962830465782378938407538
16. ! [X0] : ((happy(X0) | wise(X0)) => (calm(X0) & ~generous(X0))) [input p15]
19. old(mary) & wise(mary) [input p18]
24. generous(mary) [input hypothesis]
38. ! [X0] : ((calm(X0) & ~generous(X0)) | (~happy(X0) & ~wise(X0))) [ennf transformation 16]
122. ~generous(X0) | ~wise(X0) [cnf transformation 38]
129. wise(mary) [cnf transformation 19]
136. generous(mary) [cnf transformation 24]
262. ~wise(mary) [resolution 122,136]
263. $false [subsumption resolution 262,129]
% SZS output end Proof for 6962830465782378938407538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or not brave then paul is not patient and vice versa.
If someone is both not calm and strong then john is rich and vice versa.
If paul is either patient or strong then paul is calm or generous.
If paul is strong then lucy is both curious and not brave and vice versa.
Everyone who is either rich or not happy is not wise and vice versa.
If someone is either not curious or patient then someone is either creative or not happy and vice versa.
Everyone who is both happy and brave is both humble and rich and vice versa.
Everyone who is strong is both rich and strong and vice versa.
If mary is not tall then lucy is both not patient and rich.
If someone is wise or tall then paul is both wise and not happy.
Everyone who is patient or not strong is not rich.
If john is both not patient and brave then john is not strong or not happy.
Everyone who is both not humble and not funny is both not tall and not strong.
Everyone who is calm is humble.
If alice is either not calm or not quiet then someone is both creative and not calm and vice versa.
If susan is both quiet and not strong then john is either generous or patient and vice versa.
Someone is both calm and creative.
Someone is not rich or not quiet.
Someone is either not rich or not brave.
Someone is both creative and funny.
Someone is not rich or not generous.
Mary is not happy or not tall.
Lucy is not calm or happy.
Someone is either not humble or not rich. | Susan is not funny. | neutral | ((?[X]:((quiet(X)<~>~brave(X))))<=>(~patient(paul)))&
((?[X]:((~calm(X)&strong(X))))<=>(rich(john)))&
(((patient(paul)<~>strong(paul)))=>((calm(paul)|generous(paul))))&
((strong(paul))<=>((curious(lucy)&~brave(lucy))))&
(![X]:((rich(X)<~>~happy(X))<=>~wise(X)))&
((?[X]:((~curious(X)<~>patient(X))))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(![X]:((happy(X)&brave(X))<=>(humble(X)&rich(X))))&
(![X]:(strong(X)<=>(rich(X)&strong(X))))&
((~tall(mary))=>((~patient(lucy)&rich(lucy))))&
((?[X]:((wise(X)|tall(X))))=>((wise(paul)&~happy(paul))))&
(![X]:((patient(X)|~strong(X))=>~rich(X)))&
(((~patient(john)&brave(john)))=>((~strong(john)|~happy(john))))&
(![X]:((~humble(X)&~funny(X))=>(~tall(X)&~strong(X))))&
(![X]:(calm(X)=>humble(X)))&
(((~calm(alice)<~>~quiet(alice)))<=>(?[X]:((creative(X)&~calm(X)))))&
(((quiet(susan)&~strong(susan)))<=>((generous(john)<~>patient(john))))&
(?[X]:((calm(X)&creative(X))))&
(?[X]:((~rich(X)|~quiet(X))))&
(?[X]:((~rich(X)<~>~brave(X))))&
(?[X]:((creative(X)&funny(X))))&
(?[X]:((~rich(X)|~generous(X))))&
((~happy(mary)|~tall(mary)))&
((~calm(lucy)|happy(lucy)))&
(?[X]:((~humble(X)<~>~rich(X)))) | ~funny(susan) | [] | null | 0 |
Everyone who is either not tall or humble is both not calm and creative. Everyone who is not rich or kind is wise and vice versa. If someone is humble or not creative then fred is not wise and vice versa. If paul is either creative or not humble then someone is not tall and vice versa. If someone is either not curious or kind then susan is quiet or not quiet. Everyone who is funny or generous is kind. If someone is generous then susan is both not generous and rich. Everyone who is not brave or not curious is humble or quiet and vice versa. If fred is both wise and curious then someone is both wise and not generous and vice versa. Everyone who is not humble is patient or tall and vice versa. If mary is happy then john is curious. If john is both not humble and rich then john is calm or creative and vice versa. If someone is creative or not generous then susan is creative or patient and vice versa. If someone is both generous and not funny then paul is wise. Everyone who is both not humble and curious is quiet and vice versa. Everyone who is not quiet or wise is either not kind or not happy and vice versa. Paul is tall or quiet. Someone is both not tall and not strong. Mary is not patient or strong. Someone is either not kind or tall. Someone is both not kind and not calm. Someone is not patient or not strong. John is not rich. Someone is not creative or wise. | Paul is not brave. | entailment | (![X]:((~tall(X)<~>humble(X))=>(~calm(X)&creative(X))))&
(![X]:((~rich(X)|kind(X))<=>wise(X)))&
((?[X]:((humble(X)|~creative(X))))<=>(~wise(fred)))&
(((creative(paul)<~>~humble(paul)))<=>(?[X]:(~tall(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>((quiet(susan)|~quiet(susan))))&
(![X]:((funny(X)|generous(X))=>kind(X)))&
((?[X]:(generous(X)))=>((~generous(susan)&rich(susan))))&
(![X]:((~brave(X)|~curious(X))<=>(humble(X)|quiet(X))))&
(((wise(fred)&curious(fred)))<=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:(~humble(X)<=>(patient(X)|tall(X))))&
((happy(mary))=>(curious(john)))&
(((~humble(john)&rich(john)))<=>((calm(john)|creative(john))))&
((?[X]:((creative(X)|~generous(X))))<=>((creative(susan)|patient(susan))))&
((?[X]:((generous(X)&~funny(X))))=>(wise(paul)))&
(![X]:((~humble(X)&curious(X))<=>quiet(X)))&
(![X]:((~quiet(X)|wise(X))<=>(~kind(X)<~>~happy(X))))&
((tall(paul)|quiet(paul)))&
(?[X]:((~tall(X)&~strong(X))))&
((~patient(mary)|strong(mary)))&
(?[X]:((~kind(X)<~>tall(X))))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((~patient(X)|~strong(X))))&
(~rich(john))&
(?[X]:((~creative(X)|wise(X)))) | ~brave(paul) | [
"p7",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8058159405448070903523990
% SZS output start Proof for 8058159405448070903523990
8. ! [X0] : ((~curious(X0) | ~brave(X0)) <=> (quiet(X0) | humble(X0))) [input p7]
10. ! [X0] : (~humble(X0) <=> (tall(X0) | patient(X0))) [input p9]
15. ! [X0] : ((curious(X0) & ~humble(X0)) <=> quiet(X0)) [input p14]
17. quiet(paul) | tall(paul) [input p16]
25. brave(paul) [input hypothesis]
45. ! [X0] : (((~curious(X0) | ~brave(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (curious(X0) & brave(X0)))) [nnf transformation 8]
46. ! [X0] : ((~curious(X0) | ~brave(X0) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | (curious(X0) & brave(X0)))) [flattening 45]
52. ! [X0] : ((~humble(X0) | (~tall(X0) & ~patient(X0))) & ((tall(X0) | patient(X0)) | humble(X0))) [nnf transformation 10]
53. ! [X0] : ((~humble(X0) | (~tall(X0) & ~patient(X0))) & (tall(X0) | patient(X0) | humble(X0))) [flattening 52]
61. ! [X0] : (((curious(X0) & ~humble(X0)) | ~quiet(X0)) & (quiet(X0) | (~curious(X0) | humble(X0)))) [nnf transformation 15]
62. ! [X0] : (((curious(X0) & ~humble(X0)) | ~quiet(X0)) & (quiet(X0) | ~curious(X0) | humble(X0))) [flattening 61]
97. quiet(X0) | humble(X0) | curious(X0) [cnf transformation 46]
99. ~brave(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 46]
106. ~humble(X0) | ~tall(X0) [cnf transformation 53]
118. quiet(X0) | ~curious(X0) | humble(X0) [cnf transformation 62]
120. ~quiet(X0) | curious(X0) [cnf transformation 62]
127. quiet(paul) | tall(paul) [cnf transformation 17]
138. brave(paul) [cnf transformation 25]
168. 8 <=> humble(paul) [avatar definition]
170. humble(paul) <- (8) [avatar component clause 168]
275. quiet(X0) | humble(X0) [subsumption resolution 118,97]
279. 31 <=> tall(paul) [avatar definition]
281. tall(paul) <- (31) [avatar component clause 279]
283. 32 <=> quiet(paul) [avatar definition]
284. ~quiet(paul) <- (~32) [avatar component clause 283]
286. 31 | 32 [avatar split clause 127,283,279]
380. ~curious(paul) | ~quiet(paul) [resolution 99,138]
382. ~quiet(paul) [subsumption resolution 380,120]
383. ~32 [avatar split clause 382,283]
385. humble(paul) <- (~32) [resolution 284,275]
388. 8 | 32 [avatar split clause 385,283,168]
405. ~tall(paul) <- (8) [resolution 170,106]
406. $false <- (8, 31) [subsumption resolution 405,281]
407. ~8 | ~31 [avatar contradiction clause 406]
408. $false [avatar sat refutation 286,383,388,407]
% SZS output end Proof for 8058159405448070903523990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is humble then someone is both rich and not generous and vice versa.
Everyone who is not curious or not brave is not calm or wise and vice versa.
If someone is both funny and not kind then susan is both kind and calm.
Everyone who is both tall and not tall is not old and vice versa.
If mary is both humble and not brave then susan is not humble or not funny and vice versa.
If paul is not tall or generous then susan is wise or not wise.
If lucy is both humble and creative then lucy is generous.
Everyone who is either generous or wise is not rich.
Everyone who is both creative and not funny is both tall and generous and vice versa.
If someone is either old or not humble then susan is strong or funny and vice versa.
Everyone who is calm is not curious or generous.
Everyone who is either not strong or not creative is both kind and not creative and vice versa.
Everyone who is not strong or patient is tall or wise and vice versa.
If someone is not calm or not quiet then someone is either not old or curious and vice versa.
Everyone who is either creative or kind is brave and vice versa.
If paul is not creative or not curious then someone is not happy.
Someone is both rich and funny.
Someone is either not curious or wise.
Someone is either not tall or generous.
Susan is kind.
Mary is not rich. | Alice is happy. | neutral | ((humble(alice))<=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((~curious(X)|~brave(X))<=>(~calm(X)|wise(X))))&
((?[X]:((funny(X)&~kind(X))))=>((kind(susan)&calm(susan))))&
(![X]:((tall(X)&~tall(X))<=>~old(X)))&
(((humble(mary)&~brave(mary)))<=>((~humble(susan)|~funny(susan))))&
(((~tall(paul)|generous(paul)))=>((wise(susan)|~wise(susan))))&
(((humble(lucy)&creative(lucy)))=>(generous(lucy)))&
(![X]:((generous(X)<~>wise(X))=>~rich(X)))&
(![X]:((creative(X)&~funny(X))<=>(tall(X)&generous(X))))&
((?[X]:((old(X)<~>~humble(X))))<=>((strong(susan)|funny(susan))))&
(![X]:(calm(X)=>(~curious(X)|generous(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>(kind(X)&~creative(X))))&
(![X]:((~strong(X)|patient(X))<=>(tall(X)|wise(X))))&
((?[X]:((~calm(X)|~quiet(X))))<=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((creative(X)<~>kind(X))<=>brave(X)))&
(((~creative(paul)|~curious(paul)))=>(?[X]:(~happy(X))))&
(?[X]:((rich(X)&funny(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:((~tall(X)<~>generous(X))))&
(kind(susan))&
(~rich(mary)) | happy(alice) | [] | null | 0 |
If someone is both not kind and not tall then fred is tall and vice versa. Everyone who is either kind or strong is not happy. Everyone who is humble or not brave is both wise and not brave and vice versa. If susan is old or tall then mary is quiet or not kind. Everyone who is wise or curious is either generous or not happy. If someone is either humble or not quiet then lucy is not curious. If someone is not generous then lucy is both not creative and kind and vice versa. Everyone who is not calm or not patient is either not generous or tall. Everyone who is not quiet is tall or not kind. If someone is either not old or quiet then alice is both not strong and not creative and vice versa. Everyone who is both humble and curious is either old or patient and vice versa. If paul is both not quiet and happy then susan is either patient or not old and vice versa. Everyone who is not calm or quiet is either not old or old and vice versa. If someone is humble then mary is brave. Everyone who is not wise or strong is either patient or creative and vice versa. Everyone who is not brave is both quiet and not creative. Someone is either not generous or kind. Susan is wise. Paul is humble. Someone is not calm. Someone is humble. Susan is both old and not strong. Someone is either happy or patient. Someone is both not curious and not wise. | Susan is not curious. | contradiction | ((?[X]:((~kind(X)&~tall(X))))<=>(tall(fred)))&
(![X]:((kind(X)<~>strong(X))=>~happy(X)))&
(![X]:((humble(X)|~brave(X))<=>(wise(X)&~brave(X))))&
(((old(susan)|tall(susan)))=>((quiet(mary)|~kind(mary))))&
(![X]:((wise(X)|curious(X))=>(generous(X)<~>~happy(X))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(~curious(lucy)))&
((?[X]:(~generous(X)))<=>((~creative(lucy)&kind(lucy))))&
(![X]:((~calm(X)|~patient(X))=>(~generous(X)<~>tall(X))))&
(![X]:(~quiet(X)=>(tall(X)|~kind(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>((~strong(alice)&~creative(alice))))&
(![X]:((humble(X)&curious(X))<=>(old(X)<~>patient(X))))&
(((~quiet(paul)&happy(paul)))<=>((patient(susan)<~>~old(susan))))&
(![X]:((~calm(X)|quiet(X))<=>(~old(X)<~>old(X))))&
((?[X]:(humble(X)))=>(brave(mary)))&
(![X]:((~wise(X)|strong(X))<=>(patient(X)<~>creative(X))))&
(![X]:(~brave(X)=>(quiet(X)&~creative(X))))&
(?[X]:((~generous(X)<~>kind(X))))&
(wise(susan))&
(humble(paul))&
(?[X]:(~calm(X)))&
(?[X]:(humble(X)))&
((old(susan)&~strong(susan)))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((~curious(X)&~wise(X)))) | ~curious(susan) | [
"p2",
"p10",
"p11",
"p15",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 193953783132546398371753
% SZS output start Proof for 193953783132546398371753
3. ! [X0] : ((~brave(X0) | humble(X0)) <=> (~brave(X0) & wise(X0))) [input p2]
11. ! [X0] : ((curious(X0) & humble(X0)) <=> (old(X0) <~> patient(X0))) [input p10]
12. (happy(paul) & ~quiet(paul)) <=> (patient(susan) <~> ~old(susan)) [input p11]
16. ! [X0] : (~brave(X0) => (~creative(X0) & quiet(X0))) [input p15]
19. humble(paul) [input p18]
22. ~strong(susan) & old(susan) [input p21]
25. ~curious(susan) [input hypothesis]
35. ! [X0] : ((~creative(X0) & quiet(X0)) | brave(X0)) [ennf transformation 16]
41. ! [X0] : (((~brave(X0) | humble(X0)) | (brave(X0) | ~wise(X0))) & ((~brave(X0) & wise(X0)) | (brave(X0) & ~humble(X0)))) [nnf transformation 3]
42. ! [X0] : ((~brave(X0) | humble(X0) | brave(X0) | ~wise(X0)) & ((~brave(X0) & wise(X0)) | (brave(X0) & ~humble(X0)))) [flattening 41]
56. ! [X0] : (((curious(X0) & humble(X0)) | ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0)))) & (((~patient(X0) | ~old(X0)) & (patient(X0) | old(X0))) | (~curious(X0) | ~humble(X0)))) [nnf transformation 11]
57. ! [X0] : (((curious(X0) & humble(X0)) | ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0)))) & (((~patient(X0) | ~old(X0)) & (patient(X0) | old(X0))) | ~curious(X0) | ~humble(X0))) [flattening 56]
58. ((happy(paul) & ~quiet(paul)) | ((patient(susan) | old(susan)) & (~old(susan) | ~patient(susan)))) & (((old(susan) | ~patient(susan)) & (~old(susan) | patient(susan))) | (~happy(paul) | quiet(paul))) [nnf transformation 12]
59. ((happy(paul) & ~quiet(paul)) | ((patient(susan) | old(susan)) & (~old(susan) | ~patient(susan)))) & (((old(susan) | ~patient(susan)) & (~old(susan) | patient(susan))) | ~happy(paul) | quiet(paul)) [flattening 58]
83. ~brave(X0) | ~humble(X0) [cnf transformation 42]
112. ~old(X0) | patient(X0) | curious(X0) [cnf transformation 57]
116. ~quiet(paul) | ~old(susan) | ~patient(susan) [cnf transformation 59]
133. quiet(X0) | brave(X0) [cnf transformation 35]
138. humble(paul) [cnf transformation 19]
141. old(susan) [cnf transformation 22]
147. ~curious(susan) [cnf transformation 25]
182. 8 <=> old(susan) [avatar definition]
183. old(susan) <- (8) [avatar component clause 182]
245. 22 <=> patient(susan) [avatar definition]
255. 24 <=> quiet(paul) [avatar definition]
257. ~quiet(paul) <- (~24) [avatar component clause 255]
259. ~22 | ~8 | ~24 [avatar split clause 116,255,182,245]
281. 8 [avatar split clause 141,182]
375. patient(susan) | curious(susan) <- (8) [resolution 112,183]
379. patient(susan) <- (8) [subsumption resolution 375,147]
380. 22 | ~8 [avatar split clause 379,182,245]
404. brave(paul) <- (~24) [resolution 257,133]
438. ~humble(paul) <- (~24) [resolution 404,83]
439. $false <- (~24) [subsumption resolution 438,138]
440. 24 [avatar contradiction clause 439]
441. $false [avatar sat refutation 259,281,380,440]
% SZS output end Proof for 193953783132546398371753
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is not quiet or not humble.
If alice is both not generous and kind then someone is patient.
If susan is patient then someone is not rich.
If someone is either creative or not calm then lucy is both happy and generous and vice versa.
Everyone who is not quiet or creative is either humble or not humble and vice versa.
Everyone who is happy or humble is both not humble and not strong.
If susan is happy then someone is both not brave and not curious.
If john is generous or calm then someone is either generous or rich.
Everyone who is tall or not curious is not creative.
If someone is both calm and rich then alice is humble.
If susan is not calm or not creative then someone is not kind or not funny.
If someone is not wise then someone is brave.
Everyone who is calm or generous is both brave and calm and vice versa.
If john is either not quiet or not happy then lucy is either creative or funny and vice versa.
If someone is not funny then john is both not wise and not strong and vice versa.
If susan is not old then alice is either quiet or not tall.
Someone is patient.
Someone is not creative.
Fred is both tall and rich.
Someone is strong or not tall.
Someone is not wise or not calm.
Someone is creative or not creative.
Someone is not strong.
Someone is not calm or old. | Alice is humble. | contradiction | (![X]:(wise(X)=>(~quiet(X)|~humble(X))))&
(((~generous(alice)&kind(alice)))=>(?[X]:(patient(X))))&
((patient(susan))=>(?[X]:(~rich(X))))&
((?[X]:((creative(X)<~>~calm(X))))<=>((happy(lucy)&generous(lucy))))&
(![X]:((~quiet(X)|creative(X))<=>(humble(X)<~>~humble(X))))&
(![X]:((happy(X)|humble(X))=>(~humble(X)&~strong(X))))&
((happy(susan))=>(?[X]:((~brave(X)&~curious(X)))))&
(((generous(john)|calm(john)))=>(?[X]:((generous(X)<~>rich(X)))))&
(![X]:((tall(X)|~curious(X))=>~creative(X)))&
((?[X]:((calm(X)&rich(X))))=>(humble(alice)))&
(((~calm(susan)|~creative(susan)))=>(?[X]:((~kind(X)|~funny(X)))))&
((?[X]:(~wise(X)))=>(?[X]:(brave(X))))&
(![X]:((calm(X)|generous(X))<=>(brave(X)&calm(X))))&
(((~quiet(john)<~>~happy(john)))<=>((creative(lucy)<~>funny(lucy))))&
((?[X]:(~funny(X)))<=>((~wise(john)&~strong(john))))&
((~old(susan))=>((quiet(alice)<~>~tall(alice))))&
(?[X]:(patient(X)))&
(?[X]:(~creative(X)))&
((tall(fred)&rich(fred)))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((creative(X)|~creative(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~calm(X)|old(X)))) | humble(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6815834521605662863803002
% SZS output start Proof for 6815834521605662863803002
6. ! [X0] : ((humble(X0) | happy(X0)) => (~strong(X0) & ~humble(X0))) [input p5]
25. humble(alice) [input hypothesis]
34. ! [X0] : ((~strong(X0) & ~humble(X0)) | (~humble(X0) & ~happy(X0))) [ennf transformation 6]
92. ~humble(X0) | ~humble(X0) [cnf transformation 34]
129. humble(alice) [cnf transformation 25]
130. ~humble(X0) [duplicate literal removal 92]
274. $false [subsumption resolution 129,130]
% SZS output end Proof for 6815834521605662863803002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and happy is happy or wise and vice versa. If alice is tall or not rich then someone is either not brave or not wise and vice versa. If paul is both brave and tall then someone is both happy and not curious and vice versa. If susan is not old then fred is not wise or not old. Everyone who is either humble or rich is not quiet and vice versa. If someone is both not rich and brave then someone is old or rich. Everyone who is not calm or patient is strong or not happy. Everyone who is either wise or kind is either patient or brave. If someone is not funny then paul is not tall and vice versa. Everyone who is calm is creative. If someone is not tall or not curious then someone is strong and vice versa. If someone is strong or quiet then someone is generous or old. Everyone who is either not creative or rich is both not quiet and calm. Everyone who is not humble or not rich is both generous and quiet and vice versa. Everyone who is either patient or funny is either strong or tall and vice versa. Everyone who is brave is not quiet and vice versa. Mary is not creative or generous. Mary is calm or not happy. Someone is rich or not tall. Someone is not patient or quiet. Paul is strong or not creative. Mary is not kind or calm. Someone is humble or not funny. | Paul is old. | neutral | (![X]:((patient(X)&happy(X))<=>(happy(X)|wise(X))))&
(((tall(alice)|~rich(alice)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(((brave(paul)&tall(paul)))<=>(?[X]:((happy(X)&~curious(X)))))&
((~old(susan))=>((~wise(fred)|~old(fred))))&
(![X]:((humble(X)<~>rich(X))<=>~quiet(X)))&
((?[X]:((~rich(X)&brave(X))))=>(?[X]:((old(X)|rich(X)))))&
(![X]:((~calm(X)|patient(X))=>(strong(X)|~happy(X))))&
(![X]:((wise(X)<~>kind(X))=>(patient(X)<~>brave(X))))&
((?[X]:(~funny(X)))<=>(~tall(paul)))&
(![X]:(calm(X)=>creative(X)))&
((?[X]:((~tall(X)|~curious(X))))<=>(?[X]:(strong(X))))&
((?[X]:((strong(X)|quiet(X))))=>(?[X]:((generous(X)|old(X)))))&
(![X]:((~creative(X)<~>rich(X))=>(~quiet(X)&calm(X))))&
(![X]:((~humble(X)|~rich(X))<=>(generous(X)&quiet(X))))&
(![X]:((patient(X)<~>funny(X))<=>(strong(X)<~>tall(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
((~creative(mary)|generous(mary)))&
((calm(mary)|~happy(mary)))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:((~patient(X)|quiet(X))))&
((strong(paul)|~creative(paul)))&
((~kind(mary)|calm(mary)))&
(?[X]:((humble(X)|~funny(X)))) | old(paul) | [] | null | 0 |
If someone is curious or not old then someone is not humble or kind and vice versa.
Everyone who is both humble and calm is not tall or not brave and vice versa.
Everyone who is either kind or not patient is not wise or not strong and vice versa.
Everyone who is not quiet or old is both patient and happy and vice versa.
If someone is not funny or generous then alice is quiet or not rich and vice versa.
If lucy is not curious then paul is either humble or old.
Everyone who is tall is both not curious and kind and vice versa.
If lucy is quiet or tall then susan is humble or not patient.
If john is either not calm or not strong then someone is not creative or not humble and vice versa.
If lucy is not curious then fred is both not patient and curious.
Everyone who is either happy or not curious is either not kind or humble and vice versa.
Everyone who is both not quiet and not wise is strong or quiet and vice versa.
If someone is not strong or rich then mary is not curious or not tall.
Everyone who is either not curious or strong is not kind and vice versa.
If paul is either not kind or not strong then mary is not old or brave and vice versa.
Everyone who is either not old or not humble is both rich and not funny and vice versa.
Someone is either not creative or not calm.
Someone is either quiet or not curious.
Someone is either funny or not old.
Someone is both not wise and strong.
Someone is either patient or not generous.
Someone is rich or not wise. | Susan is wise. | neutral | ((?[X]:((curious(X)|~old(X))))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((humble(X)&calm(X))<=>(~tall(X)|~brave(X))))&
(![X]:((kind(X)<~>~patient(X))<=>(~wise(X)|~strong(X))))&
(![X]:((~quiet(X)|old(X))<=>(patient(X)&happy(X))))&
((?[X]:((~funny(X)|generous(X))))<=>((quiet(alice)|~rich(alice))))&
((~curious(lucy))=>((humble(paul)<~>old(paul))))&
(![X]:(tall(X)<=>(~curious(X)&kind(X))))&
(((quiet(lucy)|tall(lucy)))=>((humble(susan)|~patient(susan))))&
(((~calm(john)<~>~strong(john)))<=>(?[X]:((~creative(X)|~humble(X)))))&
((~curious(lucy))=>((~patient(fred)&curious(fred))))&
(![X]:((happy(X)<~>~curious(X))<=>(~kind(X)<~>humble(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(strong(X)|quiet(X))))&
((?[X]:((~strong(X)|rich(X))))=>((~curious(mary)|~tall(mary))))&
(![X]:((~curious(X)<~>strong(X))<=>~kind(X)))&
(((~kind(paul)<~>~strong(paul)))<=>((~old(mary)|brave(mary))))&
(![X]:((~old(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
(?[X]:((~creative(X)<~>~calm(X))))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((funny(X)<~>~old(X))))&
(?[X]:((~wise(X)&strong(X))))&
(?[X]:((patient(X)<~>~generous(X))))&
(?[X]:((rich(X)|~wise(X)))) | wise(susan) | [] | null | 0 |
If someone is both strong and patient then someone is both happy and kind and vice versa.
If someone is either not calm or strong then lucy is generous or tall.
If someone is either not creative or creative then someone is both not kind and not creative.
Everyone who is both not quiet and not funny is not humble and vice versa.
Everyone who is patient is brave or not patient.
Everyone who is both calm and happy is not calm.
If paul is both patient and not brave then susan is either tall or kind.
Everyone who is patient is curious or brave.
Everyone who is both funny and not humble is either not calm or strong.
If someone is either creative or not kind then someone is both not tall and rich.
Everyone who is humble or curious is both not funny and generous.
If someone is not curious or funny then susan is not old.
If someone is either not humble or not tall then lucy is both curious and not wise.
Everyone who is both kind and brave is not old.
Everyone who is patient is either not calm or not quiet and vice versa.
If susan is not wise then mary is either generous or wise.
Someone is either happy or not brave.
Lucy is either not quiet or happy.
Someone is both not quiet and not strong.
Someone is either not old or generous.
Someone is both wise and not generous.
Someone is not quiet.
Susan is humble.
Someone is brave or not tall. | Susan is not wise. | neutral | ((?[X]:((strong(X)&patient(X))))<=>(?[X]:((happy(X)&kind(X)))))&
((?[X]:((~calm(X)<~>strong(X))))=>((generous(lucy)|tall(lucy))))&
((?[X]:((~creative(X)<~>creative(X))))=>(?[X]:((~kind(X)&~creative(X)))))&
(![X]:((~quiet(X)&~funny(X))<=>~humble(X)))&
(![X]:(patient(X)=>(brave(X)|~patient(X))))&
(![X]:((calm(X)&happy(X))=>~calm(X)))&
(((patient(paul)&~brave(paul)))=>((tall(susan)<~>kind(susan))))&
(![X]:(patient(X)=>(curious(X)|brave(X))))&
(![X]:((funny(X)&~humble(X))=>(~calm(X)<~>strong(X))))&
((?[X]:((creative(X)<~>~kind(X))))=>(?[X]:((~tall(X)&rich(X)))))&
(![X]:((humble(X)|curious(X))=>(~funny(X)&generous(X))))&
((?[X]:((~curious(X)|funny(X))))=>(~old(susan)))&
((?[X]:((~humble(X)<~>~tall(X))))=>((curious(lucy)&~wise(lucy))))&
(![X]:((kind(X)&brave(X))=>~old(X)))&
(![X]:(patient(X)<=>(~calm(X)<~>~quiet(X))))&
((~wise(susan))=>((generous(mary)<~>wise(mary))))&
(?[X]:((happy(X)<~>~brave(X))))&
((~quiet(lucy)<~>happy(lucy)))&
(?[X]:((~quiet(X)&~strong(X))))&
(?[X]:((~old(X)<~>generous(X))))&
(?[X]:((wise(X)&~generous(X))))&
(?[X]:(~quiet(X)))&
(humble(susan))&
(?[X]:((brave(X)|~tall(X)))) | ~wise(susan) | [] | null | 0 |
Everyone who is both creative and not brave is both tall and not curious and vice versa.
Everyone who is not creative or strong is either not funny or generous.
Everyone who is happy or calm is both not old and generous and vice versa.
Everyone who is either not tall or generous is either not funny or calm.
If someone is both not rich and not kind then someone is rich.
Everyone who is not curious or patient is wise or not patient.
If someone is either patient or not brave then john is both generous and kind.
If susan is both not kind and funny then someone is either tall or not patient and vice versa.
If someone is both not quiet and not calm then someone is both humble and tall.
If someone is either not calm or tall then someone is either brave or quiet and vice versa.
Everyone who is either old or not funny is both not generous and funny and vice versa.
Everyone who is either curious or funny is not wise or old and vice versa.
If someone is either curious or funny then someone is either kind or not rich and vice versa.
Everyone who is not wise is either not brave or not patient and vice versa.
Everyone who is both not rich and humble is both humble and not funny and vice versa.
If someone is both not creative and not generous then someone is both not funny and wise and vice versa.
Fred is either not strong or not quiet.
Someone is not kind.
Alice is happy.
Someone is not brave.
Someone is strong.
Someone is patient or brave.
Someone is both not rich and not strong. | Alice is generous. | entailment | (![X]:((creative(X)&~brave(X))<=>(tall(X)&~curious(X))))&
(![X]:((~creative(X)|strong(X))=>(~funny(X)<~>generous(X))))&
(![X]:((happy(X)|calm(X))<=>(~old(X)&generous(X))))&
(![X]:((~tall(X)<~>generous(X))=>(~funny(X)<~>calm(X))))&
((?[X]:((~rich(X)&~kind(X))))=>(?[X]:(rich(X))))&
(![X]:((~curious(X)|patient(X))=>(wise(X)|~patient(X))))&
((?[X]:((patient(X)<~>~brave(X))))=>((generous(john)&kind(john))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:((tall(X)<~>~patient(X)))))&
((?[X]:((~quiet(X)&~calm(X))))=>(?[X]:((humble(X)&tall(X)))))&
((?[X]:((~calm(X)<~>tall(X))))<=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((old(X)<~>~funny(X))<=>(~generous(X)&funny(X))))&
(![X]:((curious(X)<~>funny(X))<=>(~wise(X)|old(X))))&
((?[X]:((curious(X)<~>funny(X))))<=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:(~wise(X)<=>(~brave(X)<~>~patient(X))))&
(![X]:((~rich(X)&humble(X))<=>(humble(X)&~funny(X))))&
((?[X]:((~creative(X)&~generous(X))))<=>(?[X]:((~funny(X)&wise(X)))))&
((~strong(fred)<~>~quiet(fred)))&
(?[X]:(~kind(X)))&
(happy(alice))&
(?[X]:(~brave(X)))&
(?[X]:(strong(X)))&
(?[X]:((patient(X)|brave(X))))&
(?[X]:((~rich(X)&~strong(X)))) | generous(alice) | [
"p2",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 253017498165948647136604
% SZS output start Proof for 253017498165948647136604
3. ! [X0] : ((calm(X0) | happy(X0)) <=> (generous(X0) & ~old(X0))) [input p2]
19. happy(alice) [input p18]
24. ~generous(alice) [input hypothesis]
40. ! [X0] : (((calm(X0) | happy(X0)) | (~generous(X0) | old(X0))) & ((generous(X0) & ~old(X0)) | (~calm(X0) & ~happy(X0)))) [nnf transformation 3]
41. ! [X0] : ((calm(X0) | happy(X0) | ~generous(X0) | old(X0)) & ((generous(X0) & ~old(X0)) | (~calm(X0) & ~happy(X0)))) [flattening 40]
98. ~happy(X0) | generous(X0) [cnf transformation 41]
163. happy(alice) [cnf transformation 19]
169. ~generous(alice) [cnf transformation 24]
358. generous(alice) [resolution 98,163]
359. $false [subsumption resolution 358,169]
% SZS output end Proof for 253017498165948647136604
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not happy is not humble or tall and vice versa.
If alice is strong then alice is humble and vice versa.
Everyone who is both wise and creative is patient and vice versa.
If someone is kind or not tall then fred is both not patient and quiet.
Everyone who is both creative and strong is either not calm or not strong and vice versa.
If susan is either brave or calm then someone is not humble.
Everyone who is not tall or strong is both quiet and not strong and vice versa.
If john is both not rich and not quiet then alice is calm.
If someone is both curious and patient then alice is either not humble or old and vice versa.
If someone is either not happy or not funny then someone is brave or not quiet.
If someone is both not generous and not happy then mary is both not old and not happy and vice versa.
Everyone who is both funny and not brave is funny and vice versa.
If john is not curious or quiet then someone is not tall or brave.
Everyone who is both curious and not kind is either curious or not humble.
If someone is both not creative and happy then fred is either generous or not curious and vice versa.
Someone is either not brave or not strong.
Alice is either not humble or not quiet.
Someone is either not rich or not patient.
Susan is either tall or not brave.
John is not wise. | Alice is patient. | neutral | (![X]:((~old(X)&~happy(X))<=>(~humble(X)|tall(X))))&
((strong(alice))<=>(humble(alice)))&
(![X]:((wise(X)&creative(X))<=>patient(X)))&
((?[X]:((kind(X)|~tall(X))))=>((~patient(fred)&quiet(fred))))&
(![X]:((creative(X)&strong(X))<=>(~calm(X)<~>~strong(X))))&
(((brave(susan)<~>calm(susan)))=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)|strong(X))<=>(quiet(X)&~strong(X))))&
(((~rich(john)&~quiet(john)))=>(calm(alice)))&
((?[X]:((curious(X)&patient(X))))<=>((~humble(alice)<~>old(alice))))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:((brave(X)|~quiet(X)))))&
((?[X]:((~generous(X)&~happy(X))))<=>((~old(mary)&~happy(mary))))&
(![X]:((funny(X)&~brave(X))<=>funny(X)))&
(((~curious(john)|quiet(john)))=>(?[X]:((~tall(X)|brave(X)))))&
(![X]:((curious(X)&~kind(X))=>(curious(X)<~>~humble(X))))&
((?[X]:((~creative(X)&happy(X))))<=>((generous(fred)<~>~curious(fred))))&
(?[X]:((~brave(X)<~>~strong(X))))&
((~humble(alice)<~>~quiet(alice)))&
(?[X]:((~rich(X)<~>~patient(X))))&
((tall(susan)<~>~brave(susan)))&
(~wise(john)) | patient(alice) | [] | null | 0 |
If john is wise or tall then someone is both not wise and humble and vice versa. If someone is not quiet then fred is old. Everyone who is either not curious or not happy is brave. If john is both not wise and old then someone is calm or not patient and vice versa. Everyone who is either brave or not brave is both generous and curious. If someone is either not wise or humble then someone is wise or quiet and vice versa. Everyone who is both calm and not kind is both not humble and not curious. If someone is not kind then susan is not happy. If someone is either not wise or tall then someone is not patient and vice versa. Everyone who is both curious and calm is either quiet or not rich. Everyone who is not old is both not brave and not strong. Everyone who is not kind is not humble or not quiet. Everyone who is either not creative or not generous is funny. Everyone who is both creative and calm is either quiet or funny and vice versa. If susan is either generous or not quiet then someone is humble or brave. Everyone who is both not tall and rich is not calm and vice versa. Someone is not tall. Lucy is both not calm and generous. Susan is both quiet and curious. Someone is old or not creative. Paul is both patient and calm. Someone is both not strong and funny. Mary is brave or humble. Someone is either patient or not tall. | John is not wise. | entailment | (((wise(john)|tall(john)))<=>(?[X]:((~wise(X)&humble(X)))))&
((?[X]:(~quiet(X)))=>(old(fred)))&
(![X]:((~curious(X)<~>~happy(X))=>brave(X)))&
(((~wise(john)&old(john)))<=>(?[X]:((calm(X)|~patient(X)))))&
(![X]:((brave(X)<~>~brave(X))=>(generous(X)&curious(X))))&
((?[X]:((~wise(X)<~>humble(X))))<=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((calm(X)&~kind(X))=>(~humble(X)&~curious(X))))&
((?[X]:(~kind(X)))=>(~happy(susan)))&
((?[X]:((~wise(X)<~>tall(X))))<=>(?[X]:(~patient(X))))&
(![X]:((curious(X)&calm(X))=>(quiet(X)<~>~rich(X))))&
(![X]:(~old(X)=>(~brave(X)&~strong(X))))&
(![X]:(~kind(X)=>(~humble(X)|~quiet(X))))&
(![X]:((~creative(X)<~>~generous(X))=>funny(X)))&
(![X]:((creative(X)&calm(X))<=>(quiet(X)<~>funny(X))))&
(((generous(susan)<~>~quiet(susan)))=>(?[X]:((humble(X)|brave(X)))))&
(![X]:((~tall(X)&rich(X))<=>~calm(X)))&
(?[X]:(~tall(X)))&
((~calm(lucy)&generous(lucy)))&
((quiet(susan)&curious(susan)))&
(?[X]:((old(X)|~creative(X))))&
((patient(paul)&calm(paul)))&
(?[X]:((~strong(X)&funny(X))))&
((brave(mary)|humble(mary)))&
(?[X]:((patient(X)<~>~tall(X)))) | ~wise(john) | [
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2716370372022926515494722
% SZS output start Proof for 2716370372022926515494722
4. (old(john) & ~wise(john)) <=> ? [X0] : (~patient(X0) | calm(X0)) [input p3]
21. calm(paul) & patient(paul) [input p20]
25. wise(john) [input hypothesis]
47. ((old(john) & ~wise(john)) | ! [X0] : (patient(X0) & ~calm(X0))) & (? [X0] : (~patient(X0) | calm(X0)) | (~old(john) | wise(john))) [nnf transformation 4]
48. ((old(john) & ~wise(john)) | ! [X0] : (patient(X0) & ~calm(X0))) & (? [X0] : (~patient(X0) | calm(X0)) | ~old(john) | wise(john)) [flattening 47]
49. ((old(john) & ~wise(john)) | ! [X0] : (patient(X0) & ~calm(X0))) & (? [X1] : (~patient(X1) | calm(X1)) | ~old(john) | wise(john)) [rectify 48]
50. ? [X1] : (~patient(X1) | calm(X1)) => (~patient(sK1) | calm(sK1)) [choice axiom]
51. ((old(john) & ~wise(john)) | ! [X0] : (patient(X0) & ~calm(X0))) & ((~patient(sK1) | calm(sK1)) | ~old(john) | wise(john)) [skolemisation 49,50]
90. ~wise(john) | ~calm(X0) [cnf transformation 51]
131. calm(paul) [cnf transformation 21]
136. wise(john) [cnf transformation 25]
145. 2 <=> wise(john) [avatar definition]
182. 10 <=> ! [X0] : ~calm(X0) [avatar definition]
183. ~calm(X0) <- (10) [avatar component clause 182]
186. 10 | ~2 [avatar split clause 90,145,182]
302. 2 [avatar split clause 136,145]
303. $false <- (10) [resolution 183,131]
304. ~10 [avatar contradiction clause 303]
305. $false [avatar sat refutation 186,302,304]
% SZS output end Proof for 2716370372022926515494722
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not happy is both generous and not strong and vice versa.
If fred is both quiet and generous then paul is quiet or tall and vice versa.
Everyone who is either not kind or not strong is both happy and not old and vice versa.
Everyone who is not old or brave is funny and vice versa.
If someone is not brave or not curious then john is either not wise or not patient and vice versa.
Everyone who is wise is both not wise and not quiet and vice versa.
Everyone who is tall or not kind is both patient and not humble.
Everyone who is curious is not brave.
Everyone who is curious or strong is both not patient and rich.
If fred is not patient or generous then someone is brave.
If someone is wise or happy then someone is either kind or not old and vice versa.
If someone is not wise or brave then someone is not strong and vice versa.
Everyone who is both not curious and not funny is either patient or happy and vice versa.
If alice is both old and not kind then someone is curious.
If someone is wise then susan is either quiet or not strong.
If someone is both not old and strong then someone is both not humble and calm.
Lucy is funny or not wise.
Lucy is not humble or not curious.
Someone is either not humble or not curious.
Someone is both generous and humble.
John is not generous.
Someone is either not happy or not rich.
Someone is both not brave and not curious.
Someone is not happy or wise. | John is not tall. | neutral | (![X]:((funny(X)&~happy(X))<=>(generous(X)&~strong(X))))&
(((quiet(fred)&generous(fred)))<=>((quiet(paul)|tall(paul))))&
(![X]:((~kind(X)<~>~strong(X))<=>(happy(X)&~old(X))))&
(![X]:((~old(X)|brave(X))<=>funny(X)))&
((?[X]:((~brave(X)|~curious(X))))<=>((~wise(john)<~>~patient(john))))&
(![X]:(wise(X)<=>(~wise(X)&~quiet(X))))&
(![X]:((tall(X)|~kind(X))=>(patient(X)&~humble(X))))&
(![X]:(curious(X)=>~brave(X)))&
(![X]:((curious(X)|strong(X))=>(~patient(X)&rich(X))))&
(((~patient(fred)|generous(fred)))=>(?[X]:(brave(X))))&
((?[X]:((wise(X)|happy(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~wise(X)|brave(X))))<=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&~funny(X))<=>(patient(X)<~>happy(X))))&
(((old(alice)&~kind(alice)))=>(?[X]:(curious(X))))&
((?[X]:(wise(X)))=>((quiet(susan)<~>~strong(susan))))&
((?[X]:((~old(X)&strong(X))))=>(?[X]:((~humble(X)&calm(X)))))&
((funny(lucy)|~wise(lucy)))&
((~humble(lucy)|~curious(lucy)))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:((generous(X)&humble(X))))&
(~generous(john))&
(?[X]:((~happy(X)<~>~rich(X))))&
(?[X]:((~brave(X)&~curious(X))))&
(?[X]:((~happy(X)|wise(X)))) | ~tall(john) | [] | null | 0 |
If someone is not curious or not happy then john is both old and curious.
Everyone who is strong is not tall or old.
Everyone who is both old and not quiet is both not humble and strong and vice versa.
Everyone who is either old or not happy is wise or not brave.
Everyone who is both not generous and not strong is old and vice versa.
If susan is creative or not creative then lucy is either not tall or happy and vice versa.
Everyone who is both quiet and not old is creative or happy.
Everyone who is both not creative and not humble is either not calm or not kind and vice versa.
If lucy is not strong then susan is both strong and not kind.
If lucy is either not rich or not calm then alice is either not creative or not curious and vice versa.
If someone is tall then someone is not generous or kind.
Everyone who is humble is not funny or not creative and vice versa.
Everyone who is both not rich and not generous is both not strong and curious and vice versa.
Everyone who is either curious or not wise is both funny and humble.
Everyone who is either not kind or not generous is both not curious and calm.
If someone is not creative or curious then someone is not quiet or not humble.
Fred is not wise.
Susan is not humble.
Someone is both wise and humble.
Lucy is brave.
Someone is either not happy or not creative.
Someone is both not wise and not curious.
Susan is curious or strong.
Someone is both not humble and happy. | Susan is strong. | contradiction | ((?[X]:((~curious(X)|~happy(X))))=>((old(john)&curious(john))))&
(![X]:(strong(X)=>(~tall(X)|old(X))))&
(![X]:((old(X)&~quiet(X))<=>(~humble(X)&strong(X))))&
(![X]:((old(X)<~>~happy(X))=>(wise(X)|~brave(X))))&
(![X]:((~generous(X)&~strong(X))<=>old(X)))&
(((creative(susan)|~creative(susan)))<=>((~tall(lucy)<~>happy(lucy))))&
(![X]:((quiet(X)&~old(X))=>(creative(X)|happy(X))))&
(![X]:((~creative(X)&~humble(X))<=>(~calm(X)<~>~kind(X))))&
((~strong(lucy))=>((strong(susan)&~kind(susan))))&
(((~rich(lucy)<~>~calm(lucy)))<=>((~creative(alice)<~>~curious(alice))))&
((?[X]:(tall(X)))=>(?[X]:((~generous(X)|kind(X)))))&
(![X]:(humble(X)<=>(~funny(X)|~creative(X))))&
(![X]:((~rich(X)&~generous(X))<=>(~strong(X)&curious(X))))&
(![X]:((curious(X)<~>~wise(X))=>(funny(X)&humble(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(~curious(X)&calm(X))))&
((?[X]:((~creative(X)|curious(X))))=>(?[X]:((~quiet(X)|~humble(X)))))&
(~wise(fred))&
(~humble(susan))&
(?[X]:((wise(X)&humble(X))))&
(brave(lucy))&
(?[X]:((~happy(X)<~>~creative(X))))&
(?[X]:((~wise(X)&~curious(X))))&
((curious(susan)|strong(susan)))&
(?[X]:((~humble(X)&happy(X)))) | strong(susan) | [
"p2",
"p4",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8782863222557795166172431
% SZS output start Proof for 8782863222557795166172431
3. ! [X0] : ((~quiet(X0) & old(X0)) <=> (strong(X0) & ~humble(X0))) [input p2]
5. ! [X0] : ((~strong(X0) & ~generous(X0)) <=> old(X0)) [input p4]
18. ~humble(susan) [input p17]
25. strong(susan) [input hypothesis]
40. ! [X0] : (((~quiet(X0) & old(X0)) | (~strong(X0) | humble(X0))) & ((strong(X0) & ~humble(X0)) | (quiet(X0) | ~old(X0)))) [nnf transformation 3]
41. ! [X0] : (((~quiet(X0) & old(X0)) | ~strong(X0) | humble(X0)) & ((strong(X0) & ~humble(X0)) | quiet(X0) | ~old(X0))) [flattening 40]
43. ! [X0] : (((~strong(X0) & ~generous(X0)) | ~old(X0)) & (old(X0) | (strong(X0) | generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((~strong(X0) & ~generous(X0)) | ~old(X0)) & (old(X0) | strong(X0) | generous(X0))) [flattening 43]
78. ~strong(X0) | old(X0) | humble(X0) [cnf transformation 41]
84. ~strong(X0) | ~old(X0) [cnf transformation 44]
127. ~humble(susan) [cnf transformation 18]
138. strong(susan) [cnf transformation 25]
183. 10 <=> strong(susan) [avatar definition]
185. strong(susan) <- (10) [avatar component clause 183]
254. 10 [avatar split clause 138,183]
255. ~old(susan) <- (10) [resolution 84,185]
305. old(susan) | humble(susan) <- (10) [resolution 78,185]
306. humble(susan) <- (10) [subsumption resolution 305,255]
307. $false <- (10) [subsumption resolution 306,127]
308. ~10 [avatar contradiction clause 307]
309. $false [avatar sat refutation 254,308]
% SZS output end Proof for 8782863222557795166172431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not strong is old and vice versa.
If fred is not quiet or not funny then alice is either not happy or quiet.
Everyone who is either curious or not calm is not wise.
Everyone who is both not old and old is either strong or not humble.
Everyone who is either not strong or strong is not creative and vice versa.
Everyone who is kind is not kind or humble.
Everyone who is either creative or not quiet is either not curious or not rich and vice versa.
If fred is both patient and not strong then alice is both not tall and generous.
Everyone who is humble is both quiet and strong.
If someone is patient then alice is both old and wise.
If someone is not humble then paul is not curious or not rich.
If someone is kind or not kind then alice is not calm.
If someone is either funny or curious then someone is old or not happy and vice versa.
If fred is either brave or curious then lucy is not old or funny.
Everyone who is not funny is both tall and rich.
If alice is either not generous or not brave then someone is both happy and not generous.
Someone is tall.
Someone is tall or humble.
Susan is kind.
Paul is patient or wise.
Someone is both not brave and old.
John is curious or not kind.
Mary is both not old and tall. | Fred is patient. | contradiction | (![X]:((calm(X)&~strong(X))<=>old(X)))&
(((~quiet(fred)|~funny(fred)))=>((~happy(alice)<~>quiet(alice))))&
(![X]:((curious(X)<~>~calm(X))=>~wise(X)))&
(![X]:((~old(X)&old(X))=>(strong(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>strong(X))<=>~creative(X)))&
(![X]:(kind(X)=>(~kind(X)|humble(X))))&
(![X]:((creative(X)<~>~quiet(X))<=>(~curious(X)<~>~rich(X))))&
(((patient(fred)&~strong(fred)))=>((~tall(alice)&generous(alice))))&
(![X]:(humble(X)=>(quiet(X)&strong(X))))&
((?[X]:(patient(X)))=>((old(alice)&wise(alice))))&
((?[X]:(~humble(X)))=>((~curious(paul)|~rich(paul))))&
((?[X]:((kind(X)|~kind(X))))=>(~calm(alice)))&
((?[X]:((funny(X)<~>curious(X))))<=>(?[X]:((old(X)|~happy(X)))))&
(((brave(fred)<~>curious(fred)))=>((~old(lucy)|funny(lucy))))&
(![X]:(~funny(X)=>(tall(X)&rich(X))))&
(((~generous(alice)<~>~brave(alice)))=>(?[X]:((happy(X)&~generous(X)))))&
(?[X]:(tall(X)))&
(?[X]:((tall(X)|humble(X))))&
(kind(susan))&
((patient(paul)|wise(paul)))&
(?[X]:((~brave(X)&old(X))))&
((curious(john)|~kind(john)))&
((~old(mary)&tall(mary))) | patient(fred) | [
"p0",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 172972014434084084366620
% SZS output start Proof for 172972014434084084366620
1. ! [X0] : ((~strong(X0) & calm(X0)) <=> old(X0)) [input p0]
10. ? [X0] : patient(X0) => (wise(alice) & old(alice)) [input p9]
12. ? [X0] : (~kind(X0) | kind(X0)) => ~calm(alice) [input p11]
24. patient(fred) [input hypothesis]
35. (wise(alice) & old(alice)) | ! [X0] : ~patient(X0) [ennf transformation 10]
38. ~calm(alice) | ! [X0] : (kind(X0) & ~kind(X0)) [ennf transformation 12]
43. ! [X0] : (((~strong(X0) & calm(X0)) | ~old(X0)) & (old(X0) | (strong(X0) | ~calm(X0)))) [nnf transformation 1]
44. ! [X0] : (((~strong(X0) & calm(X0)) | ~old(X0)) & (old(X0) | strong(X0) | ~calm(X0))) [flattening 43]
66. ~old(X0) | calm(X0) [cnf transformation 44]
93. old(alice) | ~patient(X0) [cnf transformation 35]
96. ~calm(alice) | ~kind(X0) [cnf transformation 38]
97. ~calm(alice) | kind(X0) [cnf transformation 38]
121. patient(fred) [cnf transformation 24]
151. 5 <=> patient(fred) [avatar definition]
152. patient(fred) <- (5) [avatar component clause 151]
169. 9 <=> ! [X0] : ~patient(X0) [avatar definition]
170. ~patient(X0) <- (9) [avatar component clause 169]
177. 11 <=> old(alice) [avatar definition]
179. old(alice) <- (11) [avatar component clause 177]
180. 9 | 11 [avatar split clause 93,177,169]
194. 15 <=> ! [X0] : kind(X0) [avatar definition]
195. kind(X0) <- (15) [avatar component clause 194]
197. 16 <=> calm(alice) [avatar definition]
200. 15 | ~16 [avatar split clause 97,197,194]
202. 17 <=> ! [X0] : ~kind(X0) [avatar definition]
203. ~kind(X0) <- (17) [avatar component clause 202]
204. 17 | ~16 [avatar split clause 96,197,202]
300. 5 [avatar split clause 121,151]
301. $false <- (5, 9) [subsumption resolution 152,170]
302. ~5 | ~9 [avatar contradiction clause 301]
304. calm(alice) <- (11) [resolution 66,179]
307. 16 | ~11 [avatar split clause 304,177,197]
308. $false <- (15, 17) [subsumption resolution 195,203]
309. ~15 | ~17 [avatar contradiction clause 308]
310. $false [avatar sat refutation 180,200,204,300,302,307,309]
% SZS output end Proof for 172972014434084084366620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is rich then someone is old or not generous.
If john is either kind or not patient then someone is tall or curious.
If lucy is creative then fred is either not happy or not creative and vice versa.
Everyone who is either not quiet or humble is not humble or curious and vice versa.
If fred is either creative or rich then fred is not creative.
If someone is happy or patient then someone is both not kind and not funny.
Everyone who is both creative and not patient is calm or happy.
If alice is both not creative and rich then lucy is both happy and humble and vice versa.
If someone is either not humble or strong then someone is humble or strong and vice versa.
If someone is not funny or old then lucy is both not strong and not creative and vice versa.
Everyone who is both not old and not patient is happy.
Everyone who is either kind or quiet is not tall.
Everyone who is not old or wise is not quiet or not curious and vice versa.
Everyone who is both not happy and not old is either kind or rich and vice versa.
If john is both not rich and funny then someone is either not wise or not quiet and vice versa.
Everyone who is curious is either not humble or not tall.
Paul is either brave or not kind.
Fred is brave or not humble.
Fred is not happy.
Paul is curious.
Lucy is both happy and not patient.
John is both not funny and not tall.
Someone is both not quiet and not old.
Paul is funny or not old. | Paul is brave. | contradiction | ((rich(lucy))=>(?[X]:((old(X)|~generous(X)))))&
(((kind(john)<~>~patient(john)))=>(?[X]:((tall(X)|curious(X)))))&
((creative(lucy))<=>((~happy(fred)<~>~creative(fred))))&
(![X]:((~quiet(X)<~>humble(X))<=>(~humble(X)|curious(X))))&
(((creative(fred)<~>rich(fred)))=>(~creative(fred)))&
((?[X]:((happy(X)|patient(X))))=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((creative(X)&~patient(X))=>(calm(X)|happy(X))))&
(((~creative(alice)&rich(alice)))<=>((happy(lucy)&humble(lucy))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:((humble(X)|strong(X)))))&
((?[X]:((~funny(X)|old(X))))<=>((~strong(lucy)&~creative(lucy))))&
(![X]:((~old(X)&~patient(X))=>happy(X)))&
(![X]:((kind(X)<~>quiet(X))=>~tall(X)))&
(![X]:((~old(X)|wise(X))<=>(~quiet(X)|~curious(X))))&
(![X]:((~happy(X)&~old(X))<=>(kind(X)<~>rich(X))))&
(((~rich(john)&funny(john)))<=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:(curious(X)=>(~humble(X)<~>~tall(X))))&
((brave(paul)<~>~kind(paul)))&
((brave(fred)|~humble(fred)))&
(~happy(fred))&
(curious(paul))&
((happy(lucy)&~patient(lucy)))&
((~funny(john)&~tall(john)))&
(?[X]:((~quiet(X)&~old(X))))&
((funny(paul)|~old(paul))) | brave(paul) | [
"p3",
"p11",
"p12",
"p14",
"p15",
"p16",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8169110592620001764234287
% SZS output start Proof for 8169110592620001764234287
4. ! [X0] : ((~quiet(X0) <~> humble(X0)) <=> (curious(X0) | ~humble(X0))) [input p3]
12. ! [X0] : ((kind(X0) <~> quiet(X0)) => ~tall(X0)) [input p11]
13. ! [X0] : ((wise(X0) | ~old(X0)) <=> (~curious(X0) | ~quiet(X0))) [input p12]
15. (funny(john) & ~rich(john)) <=> ? [X0] : (~wise(X0) <~> ~quiet(X0)) [input p14]
16. ! [X0] : (curious(X0) => (~humble(X0) <~> ~tall(X0))) [input p15]
17. brave(paul) <~> ~kind(paul) [input p16]
20. curious(paul) [input p19]
22. ~tall(john) & ~funny(john) [input p21]
25. brave(paul) [input hypothesis]
35. ! [X0] : (~tall(X0) | (kind(X0) <=> quiet(X0))) [ennf transformation 12]
36. ! [X0] : ((~humble(X0) <~> ~tall(X0)) | ~curious(X0)) [ennf transformation 16]
41. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~curious(X0) & humble(X0))) & ((curious(X0) | ~humble(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~curious(X0) & humble(X0))) & (curious(X0) | ~humble(X0) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [flattening 41]
59. ! [X0] : (~tall(X0) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0)))) [nnf transformation 35]
60. ! [X0] : (((wise(X0) | ~old(X0)) | (curious(X0) & quiet(X0))) & ((~curious(X0) | ~quiet(X0)) | (~wise(X0) & old(X0)))) [nnf transformation 13]
61. ! [X0] : ((wise(X0) | ~old(X0) | (curious(X0) & quiet(X0))) & (~curious(X0) | ~quiet(X0) | (~wise(X0) & old(X0)))) [flattening 60]
64. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (? [X0] : ((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | (~funny(john) | rich(john))) [nnf transformation 15]
65. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (? [X0] : ((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ~funny(john) | rich(john)) [flattening 64]
66. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (? [X1] : ((quiet(X1) | wise(X1)) & (~quiet(X1) | ~wise(X1))) | ~funny(john) | rich(john)) [rectify 65]
67. ? [X1] : ((quiet(X1) | wise(X1)) & (~quiet(X1) | ~wise(X1))) => ((quiet(sK5) | wise(sK5)) & (~quiet(sK5) | ~wise(sK5))) [choice axiom]
68. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (((quiet(sK5) | wise(sK5)) & (~quiet(sK5) | ~wise(sK5))) | ~funny(john) | rich(john)) [skolemisation 66,67]
69. ! [X0] : (((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | ~curious(X0)) [nnf transformation 36]
70. (kind(paul) | ~brave(paul)) & (~kind(paul) | brave(paul)) [nnf transformation 17]
80. curious(X0) | ~humble(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 42]
81. humble(X0) | ~quiet(X0) | humble(X0) [cnf transformation 42]
84. ~humble(X0) | quiet(X0) | ~curious(X0) [cnf transformation 42]
107. ~tall(X0) | quiet(X0) | ~kind(X0) [cnf transformation 59]
110. ~curious(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 61]
123. funny(john) | ~quiet(X0) | wise(X0) [cnf transformation 68]
126. ~curious(X0) | humble(X0) | tall(X0) [cnf transformation 69]
128. kind(paul) | ~brave(paul) [cnf transformation 70]
131. curious(paul) [cnf transformation 20]
134. ~funny(john) [cnf transformation 22]
139. brave(paul) [cnf transformation 25]
141. curious(X0) | ~humble(X0) | ~quiet(X0) [duplicate literal removal 80]
142. ~quiet(X0) | humble(X0) [duplicate literal removal 81]
177. ~quiet(X0) | curious(X0) [subsumption resolution 141,142]
278. ~wise(X0) | ~quiet(X0) [subsumption resolution 110,177]
285. 31 <=> funny(john) [avatar definition]
289. funny(john) | ~quiet(X0) [subsumption resolution 123,278]
291. 32 <=> ! [X0] : ~quiet(X0) [avatar definition]
292. ~quiet(X0) <- (32) [avatar component clause 291]
293. 32 | 31 [avatar split clause 289,285,291]
312. 36 <=> brave(paul) [avatar definition]
316. 37 <=> kind(paul) [avatar definition]
318. kind(paul) <- (37) [avatar component clause 316]
319. ~36 | 37 [avatar split clause 128,316,312]
332. ~31 [avatar split clause 134,285]
342. 36 [avatar split clause 139,312]
384. humble(paul) | tall(paul) [resolution 126,131]
386. 47 <=> tall(paul) [avatar definition]
388. tall(paul) <- (47) [avatar component clause 386]
390. 48 <=> humble(paul) [avatar definition]
392. humble(paul) <- (48) [avatar component clause 390]
393. 47 | 48 [avatar split clause 384,390,386]
423. quiet(paul) | ~kind(paul) <- (47) [resolution 388,107]
424. ~kind(paul) <- (32, 47) [subsumption resolution 423,292]
425. $false <- (32, 37, 47) [subsumption resolution 424,318]
426. ~32 | ~37 | ~47 [avatar contradiction clause 425]
428. quiet(paul) | ~curious(paul) <- (48) [resolution 392,84]
429. ~curious(paul) <- (32, 48) [subsumption resolution 428,292]
430. $false <- (32, 48) [subsumption resolution 429,131]
431. ~32 | ~48 [avatar contradiction clause 430]
432. $false [avatar sat refutation 293,319,332,342,393,426,431]
% SZS output end Proof for 8169110592620001764234287
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both brave and kind then someone is patient and vice versa.
Everyone who is both wise and generous is strong or not strong.
Everyone who is either not funny or quiet is generous.
If someone is not funny or not humble then someone is not happy and vice versa.
Everyone who is not kind or old is both not tall and curious.
If alice is either generous or not patient then someone is either tall or not wise.
Everyone who is not curious is not generous or creative and vice versa.
Everyone who is both patient and not old is not kind.
Everyone who is both not patient and not calm is both calm and not tall.
Everyone who is both not old and kind is happy or not generous and vice versa.
If someone is both not patient and not quiet then someone is old and vice versa.
If someone is either not generous or not calm then someone is not rich or calm.
Everyone who is strong or not old is kind.
Everyone who is creative or kind is not old or not creative.
Everyone who is generous or not tall is not generous and vice versa.
If someone is both generous and not creative then someone is not quiet and vice versa.
Susan is not tall or rich.
Alice is not tall.
Fred is both not generous and not strong.
Someone is quiet.
Someone is brave. | Alice is not patient. | entailment | (((brave(alice)&kind(alice)))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)&generous(X))=>(strong(X)|~strong(X))))&
(![X]:((~funny(X)<~>quiet(X))=>generous(X)))&
((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)|old(X))=>(~tall(X)&curious(X))))&
(((generous(alice)<~>~patient(alice)))=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:(~curious(X)<=>(~generous(X)|creative(X))))&
(![X]:((patient(X)&~old(X))=>~kind(X)))&
(![X]:((~patient(X)&~calm(X))=>(calm(X)&~tall(X))))&
(![X]:((~old(X)&kind(X))<=>(happy(X)|~generous(X))))&
((?[X]:((~patient(X)&~quiet(X))))<=>(?[X]:(old(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:((strong(X)|~old(X))=>kind(X)))&
(![X]:((creative(X)|kind(X))=>(~old(X)|~creative(X))))&
(![X]:((generous(X)|~tall(X))<=>~generous(X)))&
((?[X]:((generous(X)&~creative(X))))<=>(?[X]:(~quiet(X))))&
((~tall(susan)|rich(susan)))&
(~tall(alice))&
((~generous(fred)&~strong(fred)))&
(?[X]:(quiet(X)))&
(?[X]:(brave(X))) | ~patient(alice) | [
"p7",
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7602670608964612403685445
% SZS output start Proof for 7602670608964612403685445
8. ! [X0] : ((~old(X0) & patient(X0)) => ~kind(X0)) [input p7]
10. ! [X0] : ((kind(X0) & ~old(X0)) <=> (~generous(X0) | happy(X0))) [input p9]
11. ? [X0] : (~quiet(X0) & ~patient(X0)) <=> ? [X0] : old(X0) [input p10]
15. ! [X0] : ((~tall(X0) | generous(X0)) <=> ~generous(X0)) [input p14]
16. ? [X0] : (~creative(X0) & generous(X0)) <=> ? [X0] : ~quiet(X0) [input p15]
22. patient(alice) [input hypothesis]
24. ? [X0] : (~quiet(X0) & ~patient(X0)) <=> ? [X1] : old(X1) [rectify 11]
26. ? [X0] : (~creative(X0) & generous(X0)) <=> ? [X1] : ~quiet(X1) [rectify 16]
34. ! [X0] : (~kind(X0) | (old(X0) | ~patient(X0))) [ennf transformation 8]
35. ! [X0] : (~kind(X0) | old(X0) | ~patient(X0)) [flattening 34]
56. ! [X0] : (((kind(X0) & ~old(X0)) | (generous(X0) & ~happy(X0))) & ((~generous(X0) | happy(X0)) | (~kind(X0) | old(X0)))) [nnf transformation 10]
57. ! [X0] : (((kind(X0) & ~old(X0)) | (generous(X0) & ~happy(X0))) & (~generous(X0) | happy(X0) | ~kind(X0) | old(X0))) [flattening 56]
58. (? [X0] : (~quiet(X0) & ~patient(X0)) | ! [X1] : ~old(X1)) & (? [X1] : old(X1) | ! [X0] : (quiet(X0) | patient(X0))) [nnf transformation 24]
59. (? [X0] : (~quiet(X0) & ~patient(X0)) | ! [X1] : ~old(X1)) & (? [X2] : old(X2) | ! [X3] : (quiet(X3) | patient(X3))) [rectify 58]
60. ? [X0] : (~quiet(X0) & ~patient(X0)) => (~quiet(sK4) & ~patient(sK4)) [choice axiom]
61. ? [X2] : old(X2) => old(sK5) [choice axiom]
62. ((~quiet(sK4) & ~patient(sK4)) | ! [X1] : ~old(X1)) & (old(sK5) | ! [X3] : (quiet(X3) | patient(X3))) [skolemisation 59,61,60]
67. ! [X0] : (((~tall(X0) | generous(X0)) | generous(X0)) & (~generous(X0) | (tall(X0) & ~generous(X0)))) [nnf transformation 15]
68. ! [X0] : ((~tall(X0) | generous(X0) | generous(X0)) & (~generous(X0) | (tall(X0) & ~generous(X0)))) [flattening 67]
69. (? [X0] : (~creative(X0) & generous(X0)) | ! [X1] : quiet(X1)) & (? [X1] : ~quiet(X1) | ! [X0] : (creative(X0) | ~generous(X0))) [nnf transformation 26]
70. (? [X0] : (~creative(X0) & generous(X0)) | ! [X1] : quiet(X1)) & (? [X2] : ~quiet(X2) | ! [X3] : (creative(X3) | ~generous(X3))) [rectify 69]
71. ? [X0] : (~creative(X0) & generous(X0)) => (~creative(sK7) & generous(sK7)) [choice axiom]
72. ? [X2] : ~quiet(X2) => ~quiet(sK8) [choice axiom]
73. ((~creative(sK7) & generous(sK7)) | ! [X1] : quiet(X1)) & (~quiet(sK8) | ! [X3] : (creative(X3) | ~generous(X3))) [skolemisation 70,72,71]
97. ~patient(X0) | old(X0) | ~kind(X0) [cnf transformation 35]
104. generous(X0) | kind(X0) [cnf transformation 57]
107. ~quiet(sK4) | ~old(X1) [cnf transformation 62]
114. ~generous(X0) | ~generous(X0) [cnf transformation 68]
118. generous(sK7) | quiet(X1) [cnf transformation 73]
126. patient(alice) [cnf transformation 22]
127. ~generous(X0) [duplicate literal removal 114]
174. 11 <=> patient(alice) [avatar definition]
176. patient(alice) <- (11) [avatar component clause 174]
194. 15 <=> ! [X1] : ~old(X1) [avatar definition]
195. ~old(X1) <- (15) [avatar component clause 194]
197. 16 <=> quiet(sK4) [avatar definition]
199. ~quiet(sK4) <- (~16) [avatar component clause 197]
200. 15 | ~16 [avatar split clause 107,197,194]
231. 24 <=> ! [X1] : quiet(X1) [avatar definition]
232. quiet(X1) <- (24) [avatar component clause 231]
238. quiet(X1) [subsumption resolution 118,127]
239. 24 [avatar split clause 238,231]
249. 11 [avatar split clause 126,174]
250. $false <- (~16, 24) [subsumption resolution 199,232]
251. 16 | ~24 [avatar contradiction clause 250]
253. kind(X0) [resolution 104,127]
266. old(alice) | ~kind(alice) <- (11) [resolution 97,176]
270. ~kind(alice) <- (11, 15) [subsumption resolution 266,195]
273. $false <- (11, 15) [subsumption resolution 270,253]
274. ~11 | ~15 [avatar contradiction clause 273]
277. $false [avatar sat refutation 200,239,249,251,274]
% SZS output end Proof for 7602670608964612403685445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or curious is either happy or not humble.
If john is curious then someone is both curious and not tall and vice versa.
Everyone who is both humble and not curious is not tall.
If mary is curious then someone is calm.
Everyone who is not funny is either not kind or not wise and vice versa.
If someone is not patient or not wise then someone is funny and vice versa.
Everyone who is not humble or happy is tall or not quiet.
If fred is either not strong or generous then someone is both wise and not humble.
Everyone who is brave or not humble is calm or not patient and vice versa.
If someone is not strong then lucy is both not rich and tall.
If alice is not calm then someone is both old and humble and vice versa.
If someone is both not curious and not old then someone is not calm.
Everyone who is both not happy and not quiet is not old or funny and vice versa.
Everyone who is curious or not calm is creative or quiet and vice versa.
Everyone who is both kind and calm is not creative and vice versa.
Everyone who is both not strong and not kind is patient or not kind and vice versa.
Someone is both not generous and brave.
Mary is both not kind and not patient.
Paul is calm or not patient.
Alice is both creative and not kind.
Alice is both not humble and not patient.
Susan is either funny or patient.
Someone is either happy or curious.
Paul is both patient and tall. | Mary is strong. | contradiction | (![X]:((rich(X)<~>curious(X))=>(happy(X)<~>~humble(X))))&
((curious(john))<=>(?[X]:((curious(X)&~tall(X)))))&
(![X]:((humble(X)&~curious(X))=>~tall(X)))&
((curious(mary))=>(?[X]:(calm(X))))&
(![X]:(~funny(X)<=>(~kind(X)<~>~wise(X))))&
((?[X]:((~patient(X)|~wise(X))))<=>(?[X]:(funny(X))))&
(![X]:((~humble(X)|happy(X))=>(tall(X)|~quiet(X))))&
(((~strong(fred)<~>generous(fred)))=>(?[X]:((wise(X)&~humble(X)))))&
(![X]:((brave(X)|~humble(X))<=>(calm(X)|~patient(X))))&
((?[X]:(~strong(X)))=>((~rich(lucy)&tall(lucy))))&
((~calm(alice))<=>(?[X]:((old(X)&humble(X)))))&
((?[X]:((~curious(X)&~old(X))))=>(?[X]:(~calm(X))))&
(![X]:((~happy(X)&~quiet(X))<=>(~old(X)|funny(X))))&
(![X]:((curious(X)|~calm(X))<=>(creative(X)|quiet(X))))&
(![X]:((kind(X)&calm(X))<=>~creative(X)))&
(![X]:((~strong(X)&~kind(X))<=>(patient(X)|~kind(X))))&
(?[X]:((~generous(X)&brave(X))))&
((~kind(mary)&~patient(mary)))&
((calm(paul)|~patient(paul)))&
((creative(alice)&~kind(alice)))&
((~humble(alice)&~patient(alice)))&
((funny(susan)<~>patient(susan)))&
(?[X]:((happy(X)<~>curious(X))))&
((patient(paul)&tall(paul))) | strong(mary) | [
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7340044835871924985117667
% SZS output start Proof for 7340044835871924985117667
16. ! [X0] : ((~kind(X0) & ~strong(X0)) <=> (~kind(X0) | patient(X0))) [input p15]
18. ~patient(mary) & ~kind(mary) [input p17]
25. strong(mary) [input hypothesis]
68. ! [X0] : (((~kind(X0) & ~strong(X0)) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | (kind(X0) | strong(X0)))) [nnf transformation 16]
69. ! [X0] : (((~kind(X0) & ~strong(X0)) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | kind(X0) | strong(X0))) [flattening 68]
122. ~strong(X0) | kind(X0) [cnf transformation 69]
127. ~kind(mary) [cnf transformation 18]
140. strong(mary) [cnf transformation 25]
291. kind(mary) [resolution 122,140]
293. $false [subsumption resolution 291,127]
% SZS output end Proof for 7340044835871924985117667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then mary is patient.
Everyone who is both not quiet and not old is either rich or wise.
Everyone who is both wise and curious is not creative or creative and vice versa.
If alice is strong then someone is not wise.
Everyone who is either not wise or not tall is not kind or kind.
Everyone who is both creative and not kind is either not kind or patient and vice versa.
Everyone who is both curious and not tall is brave and vice versa.
Everyone who is either curious or not curious is both kind and wise and vice versa.
Everyone who is not strong is not rich and vice versa.
If someone is not generous then someone is not generous or calm and vice versa.
If john is either not brave or creative then someone is not wise.
Everyone who is both not brave and not curious is not happy or tall.
Everyone who is not quiet is kind.
Everyone who is not rich is not brave or generous.
Everyone who is happy or not rich is not quiet and vice versa.
Mary is not happy or wise.
Susan is either brave or not happy.
Someone is strong.
Fred is not generous.
Fred is happy.
Paul is either humble or wise.
Lucy is not calm or not kind.
Someone is both humble and not strong. | Mary is old. | neutral | ((?[X]:(creative(X)))=>(patient(mary)))&
(![X]:((~quiet(X)&~old(X))=>(rich(X)<~>wise(X))))&
(![X]:((wise(X)&curious(X))<=>(~creative(X)|creative(X))))&
((strong(alice))=>(?[X]:(~wise(X))))&
(![X]:((~wise(X)<~>~tall(X))=>(~kind(X)|kind(X))))&
(![X]:((creative(X)&~kind(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((curious(X)&~tall(X))<=>brave(X)))&
(![X]:((curious(X)<~>~curious(X))<=>(kind(X)&wise(X))))&
(![X]:(~strong(X)<=>~rich(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)|calm(X)))))&
(((~brave(john)<~>creative(john)))=>(?[X]:(~wise(X))))&
(![X]:((~brave(X)&~curious(X))=>(~happy(X)|tall(X))))&
(![X]:(~quiet(X)=>kind(X)))&
(![X]:(~rich(X)=>(~brave(X)|generous(X))))&
(![X]:((happy(X)|~rich(X))<=>~quiet(X)))&
((~happy(mary)|wise(mary)))&
((brave(susan)<~>~happy(susan)))&
(?[X]:(strong(X)))&
(~generous(fred))&
(happy(fred))&
((humble(paul)<~>wise(paul)))&
((~calm(lucy)|~kind(lucy)))&
(?[X]:((humble(X)&~strong(X)))) | old(mary) | [] | null | 0 |
If someone is not happy then someone is either not humble or quiet and vice versa. Everyone who is either quiet or not strong is rich or not generous. If someone is either not generous or not kind then susan is either not old or patient and vice versa. If mary is patient or humble then someone is not generous and vice versa. Everyone who is not funny or strong is not patient or not humble and vice versa. Everyone who is both patient and not tall is both happy and not tall and vice versa. If someone is generous then someone is both not creative and creative and vice versa. Everyone who is tall is calm and vice versa. If susan is both generous and patient then alice is both not patient and not funny and vice versa. If someone is funny then someone is funny or not strong. If someone is wise then someone is not calm or curious. If alice is either not old or not patient then fred is old or not generous and vice versa. If john is not calm or kind then paul is old or calm. Everyone who is happy is both funny and not old. Everyone who is humble is either strong or not patient. Everyone who is either not happy or brave is not old or funny and vice versa. Fred is either tall or not old. Someone is kind. Someone is happy or patient. Someone is brave or not strong. Someone is both not humble and funny. Susan is both creative and not strong. Someone is not calm. Someone is not old. | Alice is humble. | contradiction | ((?[X]:(~happy(X)))<=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:((quiet(X)<~>~strong(X))=>(rich(X)|~generous(X))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>((~old(susan)<~>patient(susan))))&
(((patient(mary)|humble(mary)))<=>(?[X]:(~generous(X))))&
(![X]:((~funny(X)|strong(X))<=>(~patient(X)|~humble(X))))&
(![X]:((patient(X)&~tall(X))<=>(happy(X)&~tall(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:(tall(X)<=>calm(X)))&
(((generous(susan)&patient(susan)))<=>((~patient(alice)&~funny(alice))))&
((?[X]:(funny(X)))=>(?[X]:((funny(X)|~strong(X)))))&
((?[X]:(wise(X)))=>(?[X]:((~calm(X)|curious(X)))))&
(((~old(alice)<~>~patient(alice)))<=>((old(fred)|~generous(fred))))&
(((~calm(john)|kind(john)))=>((old(paul)|calm(paul))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
((tall(fred)<~>~old(fred)))&
(?[X]:(kind(X)))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:((brave(X)|~strong(X))))&
(?[X]:((~humble(X)&funny(X))))&
((creative(susan)&~strong(susan)))&
(?[X]:(~calm(X)))&
(?[X]:(~old(X))) | humble(alice) | [
"p4",
"p6",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6065223627809830063721395
% SZS output start Proof for 6065223627809830063721395
5. ! [X0] : ((strong(X0) | ~funny(X0)) <=> (~humble(X0) | ~patient(X0))) [input p4]
7. ? [X0] : generous(X0) <=> ? [X0] : (creative(X0) & ~creative(X0)) [input p6]
9. (patient(susan) & generous(susan)) <=> (~funny(alice) & ~patient(alice)) [input p8]
15. ! [X0] : (humble(X0) => (strong(X0) <~> ~patient(X0))) [input p14]
25. humble(alice) [input hypothesis]
27. ? [X0] : generous(X0) <=> ? [X1] : (creative(X1) & ~creative(X1)) [rectify 7]
36. ! [X0] : ((strong(X0) <~> ~patient(X0)) | ~humble(X0)) [ennf transformation 15]
51. ! [X0] : (((strong(X0) | ~funny(X0)) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | (~strong(X0) & funny(X0)))) [nnf transformation 5]
52. ! [X0] : ((strong(X0) | ~funny(X0) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | (~strong(X0) & funny(X0)))) [flattening 51]
55. (? [X0] : generous(X0) | ! [X1] : (~creative(X1) | creative(X1))) & (? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : ~generous(X0)) [nnf transformation 27]
56. (? [X0] : generous(X0) | ! [X1] : (~creative(X1) | creative(X1))) & (? [X2] : (creative(X2) & ~creative(X2)) | ! [X3] : ~generous(X3)) [rectify 55]
57. ? [X0] : generous(X0) => generous(sK4) [choice axiom]
58. ? [X2] : (creative(X2) & ~creative(X2)) => (creative(sK5) & ~creative(sK5)) [choice axiom]
59. (generous(sK4) | ! [X1] : (~creative(X1) | creative(X1))) & ((creative(sK5) & ~creative(sK5)) | ! [X3] : ~generous(X3)) [skolemisation 56,58,57]
61. ((patient(susan) & generous(susan)) | (funny(alice) | patient(alice))) & ((~funny(alice) & ~patient(alice)) | (~patient(susan) | ~generous(susan))) [nnf transformation 9]
62. ((patient(susan) & generous(susan)) | funny(alice) | patient(alice)) & ((~funny(alice) & ~patient(alice)) | ~patient(susan) | ~generous(susan)) [flattening 61]
68. ! [X0] : (((patient(X0) | ~strong(X0)) & (~patient(X0) | strong(X0))) | ~humble(X0)) [nnf transformation 36]
100. ~patient(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 52]
101. ~funny(X0) | strong(X0) | patient(X0) [cnf transformation 52]
107. ~creative(sK5) | ~generous(X3) [cnf transformation 59]
108. creative(sK5) | ~generous(X3) [cnf transformation 59]
114. generous(susan) | funny(alice) | patient(alice) [cnf transformation 62]
127. ~patient(X0) | strong(X0) | ~humble(X0) [cnf transformation 68]
128. patient(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 68]
146. humble(alice) [cnf transformation 25]
221. 17 <=> ! [X3] : ~generous(X3) [avatar definition]
222. ~generous(X3) <- (17) [avatar component clause 221]
224. 18 <=> creative(sK5) [avatar definition]
227. 17 | 18 [avatar split clause 108,224,221]
228. 17 | ~18 [avatar split clause 107,224,221]
230. 19 <=> patient(alice) [avatar definition]
231. ~patient(alice) <- (~19) [avatar component clause 230]
232. patient(alice) <- (19) [avatar component clause 230]
234. 20 <=> funny(alice) [avatar definition]
236. funny(alice) <- (20) [avatar component clause 234]
239. 21 <=> generous(susan) [avatar definition]
241. generous(susan) <- (21) [avatar component clause 239]
242. 19 | 20 | 21 [avatar split clause 114,239,234,230]
293. ~strong(X0) | ~humble(X0) [subsumption resolution 128,100]
294. ~patient(X0) | ~humble(X0) [subsumption resolution 127,100]
328. ~humble(alice) <- (19) [resolution 294,232]
330. $false <- (19) [subsumption resolution 328,146]
331. ~19 [avatar contradiction clause 330]
340. strong(alice) | patient(alice) <- (20) [resolution 101,236]
355. strong(alice) <- (~19, 20) [subsumption resolution 340,231]
392. ~humble(alice) <- (~19, 20) [resolution 355,293]
393. $false <- (~19, 20) [subsumption resolution 392,146]
394. 19 | ~20 [avatar contradiction clause 393]
395. $false <- (17, 21) [subsumption resolution 241,222]
396. ~17 | ~21 [avatar contradiction clause 395]
397. $false [avatar sat refutation 227,228,242,331,394,396]
% SZS output end Proof for 6065223627809830063721395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or happy is either rich or patient.
Everyone who is both not generous and curious is humble.
Everyone who is quiet is humble.
Everyone who is not funny or not patient is not patient or not curious and vice versa.
Everyone who is strong is either old or rich and vice versa.
If susan is not calm then john is brave.
Everyone who is not quiet or creative is either not tall or not creative and vice versa.
If someone is not funny then alice is calm and vice versa.
Everyone who is both creative and old is both not calm and not curious.
If john is either not old or not tall then someone is not curious or old.
Everyone who is both not brave and curious is not tall and vice versa.
If fred is creative then mary is generous and vice versa.
Everyone who is not tall or not quiet is either happy or not calm and vice versa.
Everyone who is either patient or curious is generous or wise.
If someone is both kind and rich then someone is both rich and not generous and vice versa.
Everyone who is strong or not strong is patient or not tall and vice versa.
Lucy is both not patient and not generous.
Fred is calm or tall.
Someone is either not brave or not wise.
Alice is either quiet or not calm.
Mary is either old or brave.
Someone is either not old or not generous.
Someone is not old or not strong. | Lucy is not humble. | contradiction | (![X]:((creative(X)<~>happy(X))=>(rich(X)<~>patient(X))))&
(![X]:((~generous(X)&curious(X))=>humble(X)))&
(![X]:(quiet(X)=>humble(X)))&
(![X]:((~funny(X)|~patient(X))<=>(~patient(X)|~curious(X))))&
(![X]:(strong(X)<=>(old(X)<~>rich(X))))&
((~calm(susan))=>(brave(john)))&
(![X]:((~quiet(X)|creative(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:(~funny(X)))<=>(calm(alice)))&
(![X]:((creative(X)&old(X))=>(~calm(X)&~curious(X))))&
(((~old(john)<~>~tall(john)))=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((~brave(X)&curious(X))<=>~tall(X)))&
((creative(fred))<=>(generous(mary)))&
(![X]:((~tall(X)|~quiet(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((patient(X)<~>curious(X))=>(generous(X)|wise(X))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((strong(X)|~strong(X))<=>(patient(X)|~tall(X))))&
((~patient(lucy)&~generous(lucy)))&
((calm(fred)|tall(fred)))&
(?[X]:((~brave(X)<~>~wise(X))))&
((quiet(alice)<~>~calm(alice)))&
((old(mary)<~>brave(mary)))&
(?[X]:((~old(X)<~>~generous(X))))&
(?[X]:((~old(X)|~strong(X)))) | ~humble(lucy) | [
"p1",
"p10",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7185840070436971719984403
% SZS output start Proof for 7185840070436971719984403
2. ! [X0] : ((curious(X0) & ~generous(X0)) => humble(X0)) [input p1]
11. ! [X0] : ((curious(X0) & ~brave(X0)) <=> ~tall(X0)) [input p10]
16. ! [X0] : ((~strong(X0) | strong(X0)) <=> (~tall(X0) | patient(X0))) [input p15]
17. ~generous(lucy) & ~patient(lucy) [input p16]
24. ~humble(lucy) [input hypothesis]
27. ! [X0] : (humble(X0) | (~curious(X0) | generous(X0))) [ennf transformation 2]
28. ! [X0] : (humble(X0) | ~curious(X0) | generous(X0)) [flattening 27]
49. ! [X0] : (((curious(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | (~curious(X0) | brave(X0)))) [nnf transformation 11]
50. ! [X0] : (((curious(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | ~curious(X0) | brave(X0))) [flattening 49]
60. ! [X0] : (((~strong(X0) | strong(X0)) | (tall(X0) & ~patient(X0))) & ((~tall(X0) | patient(X0)) | (strong(X0) & ~strong(X0)))) [nnf transformation 16]
61. ! [X0] : ((~strong(X0) | strong(X0) | (tall(X0) & ~patient(X0))) & (~tall(X0) | patient(X0) | (strong(X0) & ~strong(X0)))) [flattening 60]
76. ~curious(X0) | humble(X0) | generous(X0) [cnf transformation 28]
101. tall(X0) | curious(X0) [cnf transformation 50]
116. ~tall(X0) | patient(X0) | ~strong(X0) [cnf transformation 61]
117. ~tall(X0) | patient(X0) | strong(X0) [cnf transformation 61]
120. ~patient(lucy) [cnf transformation 17]
121. ~generous(lucy) [cnf transformation 17]
132. ~humble(lucy) [cnf transformation 24]
211. ~tall(X0) | patient(X0) [subsumption resolution 116,117]
273. curious(X0) | patient(X0) [resolution 211,101]
282. humble(X1) | patient(X1) | generous(X1) [resolution 273,76]
671. patient(lucy) | generous(lucy) [resolution 282,132]
672. generous(lucy) [subsumption resolution 671,120]
673. $false [subsumption resolution 672,121]
% SZS output end Proof for 7185840070436971719984403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then john is not calm and vice versa.
Everyone who is both generous and quiet is old and vice versa.
Everyone who is not kind is not strong and vice versa.
If someone is not generous then lucy is happy or not quiet and vice versa.
If susan is both not old and creative then john is humble or not old and vice versa.
Everyone who is either curious or wise is wise or not patient.
Everyone who is not creative or not humble is both humble and not patient.
If mary is both generous and funny then mary is humble or calm.
Everyone who is tall is either not calm or quiet and vice versa.
If fred is happy or not curious then someone is not old or tall and vice versa.
Everyone who is wise or not brave is both wise and not quiet and vice versa.
Everyone who is either patient or tall is curious or not curious.
If someone is happy then someone is both patient and creative.
Everyone who is both not brave and curious is not kind and vice versa.
If lucy is either not rich or brave then someone is not creative or strong and vice versa.
Everyone who is tall is not creative.
Paul is either not funny or quiet.
Someone is quiet.
Mary is not old.
Mary is old or tall.
Someone is both calm and creative.
Someone is not wise.
Someone is not happy.
Susan is both not generous and not wise. | Lucy is quiet. | neutral | ((?[X]:(generous(X)))<=>(~calm(john)))&
(![X]:((generous(X)&quiet(X))<=>old(X)))&
(![X]:(~kind(X)<=>~strong(X)))&
((?[X]:(~generous(X)))<=>((happy(lucy)|~quiet(lucy))))&
(((~old(susan)&creative(susan)))<=>((humble(john)|~old(john))))&
(![X]:((curious(X)<~>wise(X))=>(wise(X)|~patient(X))))&
(![X]:((~creative(X)|~humble(X))=>(humble(X)&~patient(X))))&
(((generous(mary)&funny(mary)))=>((humble(mary)|calm(mary))))&
(![X]:(tall(X)<=>(~calm(X)<~>quiet(X))))&
(((happy(fred)|~curious(fred)))<=>(?[X]:((~old(X)|tall(X)))))&
(![X]:((wise(X)|~brave(X))<=>(wise(X)&~quiet(X))))&
(![X]:((patient(X)<~>tall(X))=>(curious(X)|~curious(X))))&
((?[X]:(happy(X)))=>(?[X]:((patient(X)&creative(X)))))&
(![X]:((~brave(X)&curious(X))<=>~kind(X)))&
(((~rich(lucy)<~>brave(lucy)))<=>(?[X]:((~creative(X)|strong(X)))))&
(![X]:(tall(X)=>~creative(X)))&
((~funny(paul)<~>quiet(paul)))&
(?[X]:(quiet(X)))&
(~old(mary))&
((old(mary)|tall(mary)))&
(?[X]:((calm(X)&creative(X))))&
(?[X]:(~wise(X)))&
(?[X]:(~happy(X)))&
((~generous(susan)&~wise(susan))) | quiet(lucy) | [] | null | 0 |
Everyone who is either not curious or rich is calm and vice versa.
If someone is not creative then someone is either patient or not humble.
Everyone who is rich is both not rich and not creative.
If someone is both not rich and wise then someone is brave or happy.
If someone is generous or rich then someone is both not old and tall.
If someone is generous then lucy is both not generous and not funny.
Everyone who is either kind or curious is generous or strong and vice versa.
If someone is calm then someone is not calm or not humble and vice versa.
Everyone who is not patient is both curious and not quiet.
Everyone who is both not curious and not quiet is not tall.
Everyone who is both not quiet and kind is both strong and tall.
Everyone who is not happy or not old is either old or not calm.
Everyone who is either funny or tall is either quiet or generous and vice versa.
Everyone who is both calm and not brave is patient or not tall and vice versa.
Everyone who is humble or wise is generous and vice versa.
If someone is not quiet or not kind then someone is not happy.
Someone is quiet or funny.
Someone is not tall or not kind.
Paul is curious.
Alice is wise or old.
Alice is not strong or curious.
John is creative.
Someone is either not patient or not funny. | Lucy is not quiet. | neutral | (![X]:((~curious(X)<~>rich(X))<=>calm(X)))&
((?[X]:(~creative(X)))=>(?[X]:((patient(X)<~>~humble(X)))))&
(![X]:(rich(X)=>(~rich(X)&~creative(X))))&
((?[X]:((~rich(X)&wise(X))))=>(?[X]:((brave(X)|happy(X)))))&
((?[X]:((generous(X)|rich(X))))=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(generous(X)))=>((~generous(lucy)&~funny(lucy))))&
(![X]:((kind(X)<~>curious(X))<=>(generous(X)|strong(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:(~patient(X)=>(curious(X)&~quiet(X))))&
(![X]:((~curious(X)&~quiet(X))=>~tall(X)))&
(![X]:((~quiet(X)&kind(X))=>(strong(X)&tall(X))))&
(![X]:((~happy(X)|~old(X))=>(old(X)<~>~calm(X))))&
(![X]:((funny(X)<~>tall(X))<=>(quiet(X)<~>generous(X))))&
(![X]:((calm(X)&~brave(X))<=>(patient(X)|~tall(X))))&
(![X]:((humble(X)|wise(X))<=>generous(X)))&
((?[X]:((~quiet(X)|~kind(X))))=>(?[X]:(~happy(X))))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:((~tall(X)|~kind(X))))&
(curious(paul))&
((wise(alice)|old(alice)))&
((~strong(alice)|curious(alice)))&
(creative(john))&
(?[X]:((~patient(X)<~>~funny(X)))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is both not tall and generous is either not calm or not quiet. If someone is either not humble or not tall then someone is either not creative or not old. If paul is either old or wise then someone is wise or humble. Everyone who is not brave or not wise is both not rich and generous and vice versa. If someone is generous or not wise then someone is rich and vice versa. If someone is both not patient and not strong then someone is not patient and vice versa. Everyone who is kind is not wise or brave and vice versa. If someone is not creative then john is either quiet or kind. Everyone who is both curious and happy is either not curious or not humble. Everyone who is both creative and not humble is either rich or happy and vice versa. Everyone who is either kind or creative is strong and vice versa. If someone is both not strong and generous then susan is quiet or wise. If someone is either not brave or calm then someone is both not patient and not curious. If someone is both kind and not old then mary is not patient or calm. Everyone who is not happy or generous is both happy and not curious and vice versa. If someone is not strong or not funny then someone is either quiet or not tall. Lucy is either not quiet or quiet. Alice is funny or not creative. Someone is either not patient or not humble. Someone is not quiet. John is generous or creative. Someone is not generous. | Lucy is curious. | neutral | (![X]:((~tall(X)&generous(X))=>(~calm(X)<~>~quiet(X))))&
((?[X]:((~humble(X)<~>~tall(X))))=>(?[X]:((~creative(X)<~>~old(X)))))&
(((old(paul)<~>wise(paul)))=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((~brave(X)|~wise(X))<=>(~rich(X)&generous(X))))&
((?[X]:((generous(X)|~wise(X))))<=>(?[X]:(rich(X))))&
((?[X]:((~patient(X)&~strong(X))))<=>(?[X]:(~patient(X))))&
(![X]:(kind(X)<=>(~wise(X)|brave(X))))&
((?[X]:(~creative(X)))=>((quiet(john)<~>kind(john))))&
(![X]:((curious(X)&happy(X))=>(~curious(X)<~>~humble(X))))&
(![X]:((creative(X)&~humble(X))<=>(rich(X)<~>happy(X))))&
(![X]:((kind(X)<~>creative(X))<=>strong(X)))&
((?[X]:((~strong(X)&generous(X))))=>((quiet(susan)|wise(susan))))&
((?[X]:((~brave(X)<~>calm(X))))=>(?[X]:((~patient(X)&~curious(X)))))&
((?[X]:((kind(X)&~old(X))))=>((~patient(mary)|calm(mary))))&
(![X]:((~happy(X)|generous(X))<=>(happy(X)&~curious(X))))&
((?[X]:((~strong(X)|~funny(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
((~quiet(lucy)<~>quiet(lucy)))&
((funny(alice)|~creative(alice)))&
(?[X]:((~patient(X)<~>~humble(X))))&
(?[X]:(~quiet(X)))&
((generous(john)|creative(john)))&
(?[X]:(~generous(X))) | curious(lucy) | [] | null | 0 |
Everyone who is not generous is both not tall and not funny and vice versa.
Everyone who is not tall is not patient or not tall.
Everyone who is brave is kind or not kind and vice versa.
If mary is not patient then someone is happy or not old and vice versa.
Everyone who is both not tall and happy is not tall and vice versa.
Everyone who is not curious is either tall or curious.
Everyone who is both curious and not old is happy.
Everyone who is not tall is not patient.
If lucy is not strong then mary is funny and vice versa.
Everyone who is kind or not quiet is not brave or happy and vice versa.
Everyone who is either not curious or happy is either humble or not happy.
If someone is tall or curious then alice is either not quiet or calm.
Everyone who is both patient and not happy is either kind or humble and vice versa.
Everyone who is both not funny and not strong is not kind and vice versa.
Everyone who is both not old and not kind is generous or not wise and vice versa.
If someone is not calm or not kind then paul is both humble and generous.
Someone is either old or strong.
Paul is either brave or creative.
Mary is brave.
Alice is wise or not humble. | Paul is kind. | entailment | (![X]:(~generous(X)<=>(~tall(X)&~funny(X))))&
(![X]:(~tall(X)=>(~patient(X)|~tall(X))))&
(![X]:(brave(X)<=>(kind(X)|~kind(X))))&
((~patient(mary))<=>(?[X]:((happy(X)|~old(X)))))&
(![X]:((~tall(X)&happy(X))<=>~tall(X)))&
(![X]:(~curious(X)=>(tall(X)<~>curious(X))))&
(![X]:((curious(X)&~old(X))=>happy(X)))&
(![X]:(~tall(X)=>~patient(X)))&
((~strong(lucy))<=>(funny(mary)))&
(![X]:((kind(X)|~quiet(X))<=>(~brave(X)|happy(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~happy(X))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((patient(X)&~happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~funny(X)&~strong(X))<=>~kind(X)))&
(![X]:((~old(X)&~kind(X))<=>(generous(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))=>((humble(paul)&generous(paul))))&
(?[X]:((old(X)<~>strong(X))))&
((brave(paul)<~>creative(paul)))&
(brave(mary))&
((wise(alice)|~humble(alice))) | kind(paul) | [
"p6",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 702088461218787207778063
% SZS output start Proof for 702088461218787207778063
7. ! [X0] : ((~old(X0) & curious(X0)) => happy(X0)) [input p6]
11. ! [X0] : ((~curious(X0) <~> happy(X0)) => (humble(X0) <~> ~happy(X0))) [input p10]
13. ! [X0] : ((~happy(X0) & patient(X0)) <=> (kind(X0) <~> humble(X0))) [input p12]
15. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~wise(X0) | generous(X0))) [input p14]
16. ? [X0] : (~kind(X0) | ~calm(X0)) => (generous(paul) & humble(paul)) [input p15]
21. ~kind(paul) [input hypothesis]
25. ! [X0] : (happy(X0) | (old(X0) | ~curious(X0))) [ennf transformation 7]
26. ! [X0] : (happy(X0) | old(X0) | ~curious(X0)) [flattening 25]
28. ! [X0] : ((humble(X0) <~> ~happy(X0)) | (~curious(X0) <=> happy(X0))) [ennf transformation 11]
30. (generous(paul) & humble(paul)) | ! [X0] : (kind(X0) & calm(X0)) [ennf transformation 16]
45. ! [X0] : (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) [nnf transformation 28]
47. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (happy(X0) | ~patient(X0)))) [nnf transformation 13]
48. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | happy(X0) | ~patient(X0))) [flattening 47]
51. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (kind(X0) | old(X0)))) [nnf transformation 15]
52. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | kind(X0) | old(X0))) [flattening 51]
72. ~curious(X0) | old(X0) | happy(X0) [cnf transformation 26]
82. happy(X0) | ~humble(X0) | happy(X0) | curious(X0) [cnf transformation 45]
93. ~humble(X0) | kind(X0) | ~happy(X0) [cnf transformation 48]
98. ~old(X0) | ~generous(X0) [cnf transformation 52]
103. humble(paul) | kind(X0) [cnf transformation 30]
105. generous(paul) | kind(X0) [cnf transformation 30]
112. ~kind(paul) [cnf transformation 21]
114. ~humble(X0) | happy(X0) | curious(X0) [duplicate literal removal 82]
171. 12 <=> ! [X0] : kind(X0) [avatar definition]
172. kind(X0) <- (12) [avatar component clause 171]
174. 13 <=> generous(paul) [avatar definition]
176. generous(paul) <- (13) [avatar component clause 174]
177. 12 | 13 [avatar split clause 105,174,171]
183. 15 <=> humble(paul) [avatar definition]
185. humble(paul) <- (15) [avatar component clause 183]
186. 12 | 15 [avatar split clause 103,183,171]
210. $false <- (12) [resolution 172,112]
211. ~12 [avatar contradiction clause 210]
256. kind(paul) | ~happy(paul) <- (15) [resolution 93,185]
258. ~happy(paul) <- (15) [subsumption resolution 256,112]
266. happy(paul) | curious(paul) <- (15) [resolution 114,185]
268. curious(paul) <- (15) [subsumption resolution 266,258]
270. old(paul) | happy(paul) <- (15) [resolution 268,72]
271. old(paul) <- (15) [subsumption resolution 270,258]
274. ~generous(paul) <- (15) [resolution 271,98]
275. $false <- (13, 15) [subsumption resolution 274,176]
276. ~13 | ~15 [avatar contradiction clause 275]
277. $false [avatar sat refutation 177,186,211,276]
% SZS output end Proof for 702088461218787207778063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not creative is not humble.
Everyone who is either patient or wise is not tall.
Everyone who is both brave and not brave is either not rich or not creative and vice versa.
Everyone who is either quiet or not humble is not brave.
If alice is not curious then mary is not tall and vice versa.
Everyone who is either kind or funny is not humble or wise and vice versa.
Everyone who is not brave is both quiet and wise.
If someone is either creative or rich then someone is not brave or generous.
Everyone who is both quiet and humble is either not wise or not strong and vice versa.
If someone is both not brave and not wise then someone is strong or creative.
Everyone who is either not creative or not curious is funny and vice versa.
Everyone who is not happy is brave.
If someone is curious then someone is either not brave or old and vice versa.
Everyone who is both not wise and tall is either curious or not humble.
If someone is not tall then someone is both not happy and not calm and vice versa.
If mary is strong or not rich then alice is not calm.
Paul is not wise or rich.
Someone is both rich and generous.
Susan is rich or not rich.
Alice is both creative and tall.
Someone is brave or not curious.
Someone is not quiet.
Fred is not curious. | Alice is calm. | neutral | (![X]:((humble(X)<~>~creative(X))=>~humble(X)))&
(![X]:((patient(X)<~>wise(X))=>~tall(X)))&
(![X]:((brave(X)&~brave(X))<=>(~rich(X)<~>~creative(X))))&
(![X]:((quiet(X)<~>~humble(X))=>~brave(X)))&
((~curious(alice))<=>(~tall(mary)))&
(![X]:((kind(X)<~>funny(X))<=>(~humble(X)|wise(X))))&
(![X]:(~brave(X)=>(quiet(X)&wise(X))))&
((?[X]:((creative(X)<~>rich(X))))=>(?[X]:((~brave(X)|generous(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~wise(X)<~>~strong(X))))&
((?[X]:((~brave(X)&~wise(X))))=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((~creative(X)<~>~curious(X))<=>funny(X)))&
(![X]:(~happy(X)=>brave(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((~wise(X)&tall(X))=>(curious(X)<~>~humble(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)&~calm(X)))))&
(((strong(mary)|~rich(mary)))=>(~calm(alice)))&
((~wise(paul)|rich(paul)))&
(?[X]:((rich(X)&generous(X))))&
((rich(susan)|~rich(susan)))&
((creative(alice)&tall(alice)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:(~quiet(X)))&
(~curious(fred)) | calm(alice) | [] | null | 0 |
If paul is either happy or not humble then someone is either kind or not curious. Everyone who is either tall or not patient is strong or tall and vice versa. If mary is both not brave and humble then john is both funny and not old and vice versa. If lucy is both tall and wise then someone is both calm and creative and vice versa. If someone is either kind or wise then paul is either curious or not creative. If alice is either wise or strong then alice is both not generous and calm and vice versa. If someone is both wise and curious then fred is not generous. Everyone who is not happy is both not tall and not calm. Everyone who is either rich or humble is quiet or creative. Everyone who is both not quiet and not generous is either strong or not brave and vice versa. Everyone who is either not generous or not wise is both rich and calm. If john is not creative then someone is both not patient and not brave and vice versa. Everyone who is both not tall and not happy is funny or curious and vice versa. Everyone who is both not quiet and happy is either not old or old and vice versa. Everyone who is both not curious and generous is old and vice versa. Everyone who is not funny is either not quiet or not generous and vice versa. Someone is not humble. Someone is either not tall or not happy. Someone is not curious or not calm. Someone is either not happy or wise. Someone is creative or kind. | Paul is not tall. | neutral | (((happy(paul)<~>~humble(paul)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((tall(X)<~>~patient(X))<=>(strong(X)|tall(X))))&
(((~brave(mary)&humble(mary)))<=>((funny(john)&~old(john))))&
(((tall(lucy)&wise(lucy)))<=>(?[X]:((calm(X)&creative(X)))))&
((?[X]:((kind(X)<~>wise(X))))=>((curious(paul)<~>~creative(paul))))&
(((wise(alice)<~>strong(alice)))<=>((~generous(alice)&calm(alice))))&
((?[X]:((wise(X)&curious(X))))=>(~generous(fred)))&
(![X]:(~happy(X)=>(~tall(X)&~calm(X))))&
(![X]:((rich(X)<~>humble(X))=>(quiet(X)|creative(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((~generous(X)<~>~wise(X))=>(rich(X)&calm(X))))&
((~creative(john))<=>(?[X]:((~patient(X)&~brave(X)))))&
(![X]:((~tall(X)&~happy(X))<=>(funny(X)|curious(X))))&
(![X]:((~quiet(X)&happy(X))<=>(~old(X)<~>old(X))))&
(![X]:((~curious(X)&generous(X))<=>old(X)))&
(![X]:(~funny(X)<=>(~quiet(X)<~>~generous(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(?[X]:((~curious(X)|~calm(X))))&
(?[X]:((~happy(X)<~>wise(X))))&
(?[X]:((creative(X)|kind(X)))) | ~tall(paul) | [] | null | 0 |
If someone is either not kind or not rich then mary is both not brave and not humble.
Everyone who is both humble and not curious is not generous or not calm and vice versa.
Everyone who is not curious is old or not kind and vice versa.
Everyone who is not humble is strong.
If john is either not creative or not kind then fred is both not quiet and old.
Everyone who is not happy or patient is generous.
Everyone who is both rich and patient is not kind or not wise and vice versa.
Everyone who is not strong or not brave is both funny and wise.
If someone is brave then susan is not wise and vice versa.
Everyone who is not curious is both not brave and not funny and vice versa.
Everyone who is quiet or funny is both not creative and happy and vice versa.
Everyone who is creative or not humble is either not patient or rich and vice versa.
Everyone who is not wise is brave and vice versa.
Everyone who is both not wise and not calm is not kind or not calm.
Someone is both patient and happy.
Fred is old or curious.
Mary is old or not creative.
Someone is either not old or humble. | John is not brave. | contradiction | ((?[X]:((~kind(X)<~>~rich(X))))=>((~brave(mary)&~humble(mary))))&
(![X]:((humble(X)&~curious(X))<=>(~generous(X)|~calm(X))))&
(![X]:(~curious(X)<=>(old(X)|~kind(X))))&
(![X]:(~humble(X)=>strong(X)))&
(((~creative(john)<~>~kind(john)))=>((~quiet(fred)&old(fred))))&
(![X]:((~happy(X)|patient(X))=>generous(X)))&
(![X]:((rich(X)&patient(X))<=>(~kind(X)|~wise(X))))&
(![X]:((~strong(X)|~brave(X))=>(funny(X)&wise(X))))&
((?[X]:(brave(X)))<=>(~wise(susan)))&
(![X]:(~curious(X)<=>(~brave(X)&~funny(X))))&
(![X]:((quiet(X)|funny(X))<=>(~creative(X)&happy(X))))&
(![X]:((creative(X)|~humble(X))<=>(~patient(X)<~>rich(X))))&
(![X]:(~wise(X)<=>brave(X)))&
(![X]:((~wise(X)&~calm(X))=>(~kind(X)|~calm(X))))&
(?[X]:((patient(X)&happy(X))))&
((old(fred)|curious(fred)))&
((old(mary)|~creative(mary)))&
(?[X]:((~old(X)<~>humble(X)))) | ~brave(john) | [
"p2",
"p4",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4840553238848426553741246
% SZS output start Proof for 4840553238848426553741246
3. ! [X0] : (~curious(X0) <=> (~kind(X0) | old(X0))) [input p2]
5. (~creative(john) <~> ~kind(john)) => (old(fred) & ~quiet(fred)) [input p4]
8. ! [X0] : ((~brave(X0) | ~strong(X0)) => (wise(X0) & funny(X0))) [input p7]
10. ! [X0] : (~curious(X0) <=> (~funny(X0) & ~brave(X0))) [input p9]
11. ! [X0] : ((funny(X0) | quiet(X0)) <=> (happy(X0) & ~creative(X0))) [input p10]
19. ~brave(john) [input hypothesis]
20. ! [X0] : (~brave(X0) => (wise(X0) & funny(X0))) [pure predicate removal 8]
23. (old(fred) & ~quiet(fred)) | (~creative(john) <=> ~kind(john)) [ennf transformation 5]
25. ! [X0] : ((wise(X0) & funny(X0)) | brave(X0)) [ennf transformation 20]
31. ! [X0] : ((~curious(X0) | (kind(X0) & ~old(X0))) & ((~kind(X0) | old(X0)) | curious(X0))) [nnf transformation 3]
32. ! [X0] : ((~curious(X0) | (kind(X0) & ~old(X0))) & (~kind(X0) | old(X0) | curious(X0))) [flattening 31]
33. (old(fred) & ~quiet(fred)) | ((~creative(john) | kind(john)) & (~kind(john) | creative(john))) [nnf transformation 23]
40. ! [X0] : ((~curious(X0) | (funny(X0) | brave(X0))) & ((~funny(X0) & ~brave(X0)) | curious(X0))) [nnf transformation 10]
41. ! [X0] : ((~curious(X0) | funny(X0) | brave(X0)) & ((~funny(X0) & ~brave(X0)) | curious(X0))) [flattening 40]
42. ! [X0] : (((funny(X0) | quiet(X0)) | (~happy(X0) | creative(X0))) & ((happy(X0) & ~creative(X0)) | (~funny(X0) & ~quiet(X0)))) [nnf transformation 11]
43. ! [X0] : ((funny(X0) | quiet(X0) | ~happy(X0) | creative(X0)) & ((happy(X0) & ~creative(X0)) | (~funny(X0) & ~quiet(X0)))) [flattening 42]
62. ~old(X0) | ~curious(X0) [cnf transformation 32]
63. ~curious(X0) | kind(X0) [cnf transformation 32]
66. old(fred) | ~kind(john) | creative(john) [cnf transformation 33]
75. funny(X0) | brave(X0) [cnf transformation 25]
79. ~brave(X0) | curious(X0) [cnf transformation 41]
80. ~funny(X0) | curious(X0) [cnf transformation 41]
83. ~funny(X0) | ~creative(X0) [cnf transformation 43]
102. ~brave(john) [cnf transformation 19]
122. 5 <=> kind(john) [avatar definition]
123. ~kind(john) <- (~5) [avatar component clause 122]
126. 6 <=> creative(john) [avatar definition]
127. creative(john) <- (6) [avatar component clause 126]
130. 7 <=> old(fred) [avatar definition]
132. old(fred) <- (7) [avatar component clause 130]
134. 6 | ~5 | 7 [avatar split clause 66,130,122,126]
155. 12 <=> curious(fred) [avatar definition]
156. ~curious(fred) <- (~12) [avatar component clause 155]
178. ~curious(fred) <- (7) [resolution 62,132]
179. ~12 | ~7 [avatar split clause 178,130,155]
191. curious(X0) | brave(X0) [resolution 80,75]
192. curious(X0) [subsumption resolution 191,79]
193. kind(X0) [resolution 192,63]
196. $false <- (~12) [resolution 192,156]
197. 12 [avatar contradiction clause 196]
198. $false <- (~5) [subsumption resolution 123,193]
199. 5 [avatar contradiction clause 198]
200. ~creative(X0) | brave(X0) [resolution 83,75]
265. brave(john) <- (6) [resolution 200,127]
267. $false <- (6) [subsumption resolution 265,102]
268. ~6 [avatar contradiction clause 267]
269. $false [avatar sat refutation 134,179,197,199,268]
% SZS output end Proof for 4840553238848426553741246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or not quiet then john is not kind and vice versa.
Everyone who is either not brave or not funny is either not kind or not humble and vice versa.
If someone is not creative or not tall then lucy is not funny or not old.
Everyone who is not creative is either not curious or generous and vice versa.
If mary is wise or not creative then mary is either not curious or not old.
If john is both humble and patient then someone is both tall and not brave and vice versa.
Everyone who is not rich or tall is both not quiet and funny.
Everyone who is both not creative and not quiet is either not curious or quiet and vice versa.
If someone is not calm or not happy then john is not funny or not wise.
Everyone who is rich is both not kind and not wise.
Everyone who is both not curious and not humble is either not humble or wise and vice versa.
Everyone who is strong or funny is kind and vice versa.
Everyone who is not old is either not kind or quiet.
If someone is not tall or not brave then someone is creative.
If someone is either not curious or not wise then paul is either not quiet or not happy.
If paul is rich or not kind then someone is funny or not kind and vice versa.
John is not funny or wise.
Someone is either not rich or brave.
Susan is wise or kind.
Someone is both funny and curious.
Alice is either not strong or not rich.
Someone is either not old or not generous.
Someone is not old.
Susan is not patient or wise. | Susan is not old. | contradiction | ((?[X]:((calm(X)<~>~quiet(X))))<=>(~kind(john)))&
(![X]:((~brave(X)<~>~funny(X))<=>(~kind(X)<~>~humble(X))))&
((?[X]:((~creative(X)|~tall(X))))=>((~funny(lucy)|~old(lucy))))&
(![X]:(~creative(X)<=>(~curious(X)<~>generous(X))))&
(((wise(mary)|~creative(mary)))=>((~curious(mary)<~>~old(mary))))&
(((humble(john)&patient(john)))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~rich(X)|tall(X))=>(~quiet(X)&funny(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(~curious(X)<~>quiet(X))))&
((?[X]:((~calm(X)|~happy(X))))=>((~funny(john)|~wise(john))))&
(![X]:(rich(X)=>(~kind(X)&~wise(X))))&
(![X]:((~curious(X)&~humble(X))<=>(~humble(X)<~>wise(X))))&
(![X]:((strong(X)|funny(X))<=>kind(X)))&
(![X]:(~old(X)=>(~kind(X)<~>quiet(X))))&
((?[X]:((~tall(X)|~brave(X))))=>(?[X]:(creative(X))))&
((?[X]:((~curious(X)<~>~wise(X))))=>((~quiet(paul)<~>~happy(paul))))&
(((rich(paul)|~kind(paul)))<=>(?[X]:((funny(X)|~kind(X)))))&
((~funny(john)|wise(john)))&
(?[X]:((~rich(X)<~>brave(X))))&
((wise(susan)|kind(susan)))&
(?[X]:((funny(X)&curious(X))))&
((~strong(alice)<~>~rich(alice)))&
(?[X]:((~old(X)<~>~generous(X))))&
(?[X]:(~old(X)))&
((~patient(susan)|wise(susan))) | ~old(susan) | [
"p6",
"p9",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 865308782194735764496548
% SZS output start Proof for 865308782194735764496548
7. ! [X0] : ((tall(X0) | ~rich(X0)) => (funny(X0) & ~quiet(X0))) [input p6]
10. ! [X0] : (rich(X0) => (~wise(X0) & ~kind(X0))) [input p9]
12. ! [X0] : ((funny(X0) | strong(X0)) <=> kind(X0)) [input p11]
13. ! [X0] : (~old(X0) => (~kind(X0) <~> quiet(X0))) [input p12]
19. kind(susan) | wise(susan) [input p18]
25. ~old(susan) [input hypothesis]
30. ! [X0] : ((funny(X0) & ~quiet(X0)) | (~tall(X0) & rich(X0))) [ennf transformation 7]
33. ! [X0] : ((~wise(X0) & ~kind(X0)) | ~rich(X0)) [ennf transformation 10]
34. ! [X0] : ((~kind(X0) <~> quiet(X0)) | old(X0)) [ennf transformation 13]
53. ! [X0] : (((funny(X0) | strong(X0)) | ~kind(X0)) & (kind(X0) | (~funny(X0) & ~strong(X0)))) [nnf transformation 12]
54. ! [X0] : ((funny(X0) | strong(X0) | ~kind(X0)) & (kind(X0) | (~funny(X0) & ~strong(X0)))) [flattening 53]
55. ! [X0] : (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | old(X0)) [nnf transformation 34]
102. ~quiet(X0) | rich(X0) [cnf transformation 30]
104. rich(X0) | funny(X0) [cnf transformation 30]
114. ~rich(X0) | ~kind(X0) [cnf transformation 33]
115. ~rich(X0) | ~wise(X0) [cnf transformation 33]
123. ~funny(X0) | kind(X0) [cnf transformation 54]
125. ~kind(X0) | quiet(X0) | old(X0) [cnf transformation 55]
140. kind(susan) | wise(susan) [cnf transformation 19]
149. ~old(susan) [cnf transformation 25]
315. 36 <=> wise(susan) [avatar definition]
317. wise(susan) <- (36) [avatar component clause 315]
319. 37 <=> kind(susan) [avatar definition]
321. kind(susan) <- (37) [avatar component clause 319]
322. 36 | 37 [avatar split clause 140,319,315]
365. ~wise(X0) | funny(X0) [resolution 115,104]
541. funny(susan) <- (36) [resolution 365,317]
577. kind(susan) <- (36) [resolution 541,123]
586. 37 | ~36 [avatar split clause 577,315,319]
589. quiet(susan) | old(susan) <- (37) [resolution 321,125]
603. quiet(susan) <- (37) [subsumption resolution 589,149]
620. rich(susan) <- (37) [resolution 603,102]
622. ~kind(susan) <- (37) [resolution 620,114]
623. $false <- (37) [subsumption resolution 622,321]
624. ~37 [avatar contradiction clause 623]
625. $false [avatar sat refutation 322,586,624]
% SZS output end Proof for 865308782194735764496548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa.
Everyone who is not kind or not funny is either wise or not funny and vice versa.
Everyone who is either quiet or not kind is quiet or kind.
If alice is not patient then mary is either creative or not brave.
Everyone who is both tall and strong is both brave and generous and vice versa.
Everyone who is funny or not wise is both tall and rich and vice versa.
Everyone who is happy or not patient is patient.
Everyone who is tall is both strong and humble and vice versa.
If someone is either happy or brave then someone is not patient and vice versa.
If someone is not kind then someone is brave or not creative.
If lucy is brave or old then someone is either not strong or patient and vice versa.
If alice is both not brave and humble then alice is either quiet or calm.
If someone is either happy or not creative then someone is either not humble or patient.
If paul is curious then susan is either not humble or old and vice versa.
Everyone who is both rich and not creative is either not happy or curious.
Everyone who is rich is not curious or creative.
Someone is not rich or calm.
Lucy is funny.
Someone is either not old or brave.
Alice is either tall or kind.
Mary is brave or not quiet.
Someone is tall. | Alice is patient. | entailment | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(quiet(X)|kind(X))))&
((~patient(alice))=>((creative(mary)<~>~brave(mary))))&
(![X]:((tall(X)&strong(X))<=>(brave(X)&generous(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)&rich(X))))&
(![X]:((happy(X)|~patient(X))=>patient(X)))&
(![X]:(tall(X)<=>(strong(X)&humble(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)|~creative(X)))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~brave(alice)&humble(alice)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
((curious(paul))<=>((~humble(susan)<~>old(susan))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)<~>curious(X))))&
(![X]:(rich(X)=>(~curious(X)|creative(X))))&
(?[X]:((~rich(X)|calm(X))))&
(funny(lucy))&
(?[X]:((~old(X)<~>brave(X))))&
((tall(alice)<~>kind(alice)))&
((brave(mary)|~quiet(mary)))&
(?[X]:(tall(X))) | patient(alice) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5821254406960318091697118
% SZS output start Proof for 5821254406960318091697118
7. ! [X0] : ((~patient(X0) | happy(X0)) => patient(X0)) [input p6]
23. ~patient(alice) [input hypothesis]
30. ! [X0] : (patient(X0) | (patient(X0) & ~happy(X0))) [ennf transformation 7]
105. patient(X0) | patient(X0) [cnf transformation 30]
141. ~patient(alice) [cnf transformation 23]
142. patient(X0) [duplicate literal removal 105]
277. $false [subsumption resolution 141,142]
% SZS output end Proof for 5821254406960318091697118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or quiet is either not quiet or generous. Everyone who is either not happy or not calm is either not wise or patient and vice versa. If someone is either not calm or quiet then lucy is not rich. If someone is patient then someone is both not tall and not old. If fred is either not funny or not strong then someone is both patient and not funny. If someone is both not old and creative then alice is not happy. Everyone who is tall is not brave or not tall and vice versa. Everyone who is either humble or not strong is not generous or not humble. If someone is both curious and not curious then someone is not happy or not old and vice versa. If john is both not tall and generous then susan is either not kind or not rich. If susan is humble then someone is both not brave and not strong and vice versa. If paul is not old or not calm then someone is both not humble and quiet. If someone is both not generous and not happy then someone is either patient or not happy. If mary is either not wise or quiet then someone is either not brave or not happy. If fred is both not calm and not humble then someone is tall or not old. Someone is not kind or not wise. Alice is either not curious or quiet. Someone is happy or strong. John is either not old or calm. John is wise. Susan is either old or wise. Fred is happy. | Susan is happy. | entailment | (![X]:((~patient(X)|quiet(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((~happy(X)<~>~calm(X))<=>(~wise(X)<~>patient(X))))&
((?[X]:((~calm(X)<~>quiet(X))))=>(~rich(lucy)))&
((?[X]:(patient(X)))=>(?[X]:((~tall(X)&~old(X)))))&
(((~funny(fred)<~>~strong(fred)))=>(?[X]:((patient(X)&~funny(X)))))&
((?[X]:((~old(X)&creative(X))))=>(~happy(alice)))&
(![X]:(tall(X)<=>(~brave(X)|~tall(X))))&
(![X]:((humble(X)<~>~strong(X))=>(~generous(X)|~humble(X))))&
((?[X]:((curious(X)&~curious(X))))<=>(?[X]:((~happy(X)|~old(X)))))&
(((~tall(john)&generous(john)))=>((~kind(susan)<~>~rich(susan))))&
((humble(susan))<=>(?[X]:((~brave(X)&~strong(X)))))&
(((~old(paul)|~calm(paul)))=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((~generous(X)&~happy(X))))=>(?[X]:((patient(X)<~>~happy(X)))))&
(((~wise(mary)<~>quiet(mary)))=>(?[X]:((~brave(X)<~>~happy(X)))))&
(((~calm(fred)&~humble(fred)))=>(?[X]:((tall(X)|~old(X)))))&
(?[X]:((~kind(X)|~wise(X))))&
((~curious(alice)<~>quiet(alice)))&
(?[X]:((happy(X)|strong(X))))&
((~old(john)<~>calm(john)))&
(wise(john))&
((old(susan)<~>wise(susan)))&
(happy(fred)) | happy(susan) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8944735485880397627642412
% SZS output start Proof for 8944735485880397627642412
9. ? [X0] : (~curious(X0) & curious(X0)) <=> ? [X0] : (~old(X0) | ~happy(X0)) [input p8]
23. ~happy(susan) [input hypothesis]
25. ? [X0] : (~curious(X0) & curious(X0)) <=> ? [X1] : (~old(X1) | ~happy(X1)) [rectify 9]
53. (? [X0] : (~curious(X0) & curious(X0)) | ! [X1] : (old(X1) & happy(X1))) & (? [X1] : (~old(X1) | ~happy(X1)) | ! [X0] : (curious(X0) | ~curious(X0))) [nnf transformation 25]
54. (? [X0] : (~curious(X0) & curious(X0)) | ! [X1] : (old(X1) & happy(X1))) & (? [X2] : (~old(X2) | ~happy(X2)) | ! [X3] : (curious(X3) | ~curious(X3))) [rectify 53]
55. ? [X0] : (~curious(X0) & curious(X0)) => (~curious(sK2) & curious(sK2)) [choice axiom]
56. ? [X2] : (~old(X2) | ~happy(X2)) => (~old(sK3) | ~happy(sK3)) [choice axiom]
57. ((~curious(sK2) & curious(sK2)) | ! [X1] : (old(X1) & happy(X1))) & ((~old(sK3) | ~happy(sK3)) | ! [X3] : (curious(X3) | ~curious(X3))) [skolemisation 54,56,55]
107. curious(sK2) | happy(X1) [cnf transformation 57]
109. ~curious(sK2) | happy(X1) [cnf transformation 57]
137. ~happy(susan) [cnf transformation 23]
192. 12 <=> curious(sK2) [avatar definition]
197. 13 <=> ! [X1] : happy(X1) [avatar definition]
198. happy(X1) <- (13) [avatar component clause 197]
199. 13 | ~12 [avatar split clause 109,192,197]
201. 13 | 12 [avatar split clause 107,192,197]
319. $false <- (13) [resolution 198,137]
320. ~13 [avatar contradiction clause 319]
321. $false [avatar sat refutation 199,201,320]
% SZS output end Proof for 8944735485880397627642412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or calm is not patient or not wise.
If lucy is generous or not strong then someone is both brave and not brave.
Everyone who is either not quiet or not generous is not generous or not happy and vice versa.
If lucy is happy or patient then paul is either calm or not strong.
Everyone who is not calm or tall is either not calm or calm.
If paul is either rich or brave then someone is both not brave and humble and vice versa.
If someone is not strong then lucy is not patient and vice versa.
Everyone who is rich is both not happy and not quiet and vice versa.
If someone is not kind then john is both happy and wise.
Everyone who is both rich and curious is wise or not kind and vice versa.
Everyone who is not old or not generous is not generous or brave and vice versa.
If paul is old then someone is both tall and not quiet and vice versa.
If someone is either not quiet or not happy then john is either kind or not calm and vice versa.
If mary is creative or patient then mary is not funny or rich.
If someone is not brave then someone is patient.
If someone is both not old and not wise then someone is both not creative and brave and vice versa.
Someone is not strong or not funny.
Someone is not rich.
Susan is strong or not brave.
Someone is both strong and not calm.
John is either happy or not strong.
Someone is not calm.
Alice is not happy.
Someone is either strong or creative. | Lucy is not generous. | entailment | (![X]:((kind(X)|calm(X))=>(~patient(X)|~wise(X))))&
(((generous(lucy)|~strong(lucy)))=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~generous(X)|~happy(X))))&
(((happy(lucy)|patient(lucy)))=>((calm(paul)<~>~strong(paul))))&
(![X]:((~calm(X)|tall(X))=>(~calm(X)<~>calm(X))))&
(((rich(paul)<~>brave(paul)))<=>(?[X]:((~brave(X)&humble(X)))))&
((?[X]:(~strong(X)))<=>(~patient(lucy)))&
(![X]:(rich(X)<=>(~happy(X)&~quiet(X))))&
((?[X]:(~kind(X)))=>((happy(john)&wise(john))))&
(![X]:((rich(X)&curious(X))<=>(wise(X)|~kind(X))))&
(![X]:((~old(X)|~generous(X))<=>(~generous(X)|brave(X))))&
((old(paul))<=>(?[X]:((tall(X)&~quiet(X)))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>((kind(john)<~>~calm(john))))&
(((creative(mary)|patient(mary)))=>((~funny(mary)|rich(mary))))&
((?[X]:(~brave(X)))=>(?[X]:(patient(X))))&
((?[X]:((~old(X)&~wise(X))))<=>(?[X]:((~creative(X)&brave(X)))))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:(~rich(X)))&
((strong(susan)|~brave(susan)))&
(?[X]:((strong(X)&~calm(X))))&
((happy(john)<~>~strong(john)))&
(?[X]:(~calm(X)))&
(~happy(alice))&
(?[X]:((strong(X)<~>creative(X)))) | ~generous(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 8858596073967929476974277
% SZS output start Proof for 8858596073967929476974277
2. (~strong(lucy) | generous(lucy)) => ? [X0] : (~brave(X0) & brave(X0)) [input p1]
25. generous(lucy) [input hypothesis]
32. ? [X0] : (~brave(X0) & brave(X0)) | (strong(lucy) & ~generous(lucy)) [ennf transformation 2]
37. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK0) & brave(sK0)) [choice axiom]
38. (~brave(sK0) & brave(sK0)) | (strong(lucy) & ~generous(lucy)) [skolemisation 32,37]
85. brave(sK0) | ~generous(lucy) [cnf transformation 38]
87. ~brave(sK0) | ~generous(lucy) [cnf transformation 38]
151. generous(lucy) [cnf transformation 25]
161. 2 <=> brave(sK0) [avatar definition]
166. 3 <=> generous(lucy) [avatar definition]
169. ~3 | ~2 [avatar split clause 87,161,166]
171. ~3 | 2 [avatar split clause 85,161,166]
347. 3 [avatar split clause 151,166]
348. $false [avatar sat refutation 169,171,347]
% SZS output end Proof for 8858596073967929476974277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is both not rich and not strong and vice versa.
Everyone who is patient or strong is strong and vice versa.
If someone is both creative and not happy then someone is not old and vice versa.
If someone is both not humble and quiet then lucy is rich and vice versa.
Everyone who is old is not tall and vice versa.
If someone is not generous then someone is both old and not brave and vice versa.
If john is patient or curious then someone is either patient or generous and vice versa.
Everyone who is either not patient or humble is both not tall and patient and vice versa.
Everyone who is both strong and calm is curious or not patient.
Everyone who is not wise is either not rich or not happy and vice versa.
If mary is not tall or happy then someone is not old or kind and vice versa.
Everyone who is happy is not humble or not calm.
If lucy is both generous and not funny then paul is wise.
Everyone who is both not happy and tall is both funny and not happy and vice versa.
Everyone who is both quiet and not old is either not humble or rich.
If paul is patient then fred is either not quiet or wise.
Someone is not brave.
Fred is generous or tall.
Someone is both funny and old.
Mary is both not curious and not creative.
Susan is happy.
Lucy is humble.
Someone is both humble and happy.
Paul is both not curious and not quiet. | Susan is not happy. | contradiction | (![X]:(~quiet(X)<=>(~rich(X)&~strong(X))))&
(![X]:((patient(X)|strong(X))<=>strong(X)))&
((?[X]:((creative(X)&~happy(X))))<=>(?[X]:(~old(X))))&
((?[X]:((~humble(X)&quiet(X))))<=>(rich(lucy)))&
(![X]:(old(X)<=>~tall(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((old(X)&~brave(X)))))&
(((patient(john)|curious(john)))<=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(~tall(X)&patient(X))))&
(![X]:((strong(X)&calm(X))=>(curious(X)|~patient(X))))&
(![X]:(~wise(X)<=>(~rich(X)<~>~happy(X))))&
(((~tall(mary)|happy(mary)))<=>(?[X]:((~old(X)|kind(X)))))&
(![X]:(happy(X)=>(~humble(X)|~calm(X))))&
(((generous(lucy)&~funny(lucy)))=>(wise(paul)))&
(![X]:((~happy(X)&tall(X))<=>(funny(X)&~happy(X))))&
(![X]:((quiet(X)&~old(X))=>(~humble(X)<~>rich(X))))&
((patient(paul))=>((~quiet(fred)<~>wise(fred))))&
(?[X]:(~brave(X)))&
((generous(fred)|tall(fred)))&
(?[X]:((funny(X)&old(X))))&
((~curious(mary)&~creative(mary)))&
(happy(susan))&
(humble(lucy))&
(?[X]:((humble(X)&happy(X))))&
((~curious(paul)&~quiet(paul))) | ~happy(susan) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7915084887485614937177973
% SZS output start Proof for 7915084887485614937177973
21. happy(susan) [input p20]
25. ~happy(susan) [input hypothesis]
129. happy(susan) [cnf transformation 21]
135. ~happy(susan) [cnf transformation 25]
286. $false [subsumption resolution 135,129]
% SZS output end Proof for 7915084887485614937177973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet or humble then someone is kind or happy.
Everyone who is not tall or not brave is either wise or not generous.
Everyone who is tall or wise is not happy.
If someone is either wise or happy then fred is not curious.
Everyone who is both not tall and not kind is not funny.
Everyone who is curious is wise or happy.
Everyone who is either not strong or tall is not rich or not happy and vice versa.
Everyone who is either calm or curious is both old and not curious and vice versa.
If fred is rich or wise then mary is not generous.
Everyone who is both not strong and not happy is funny or generous and vice versa.
If someone is old then someone is both patient and rich and vice versa.
If someone is either not strong or not generous then someone is both not creative and creative.
If someone is not tall then fred is both patient and not quiet and vice versa.
If someone is not wise or not tall then lucy is not curious or old and vice versa.
Everyone who is either not funny or not quiet is both rich and not creative.
Everyone who is both wise and curious is both strong and not kind and vice versa.
Fred is either not wise or not funny.
Someone is either not quiet or kind.
Alice is rich or patient.
Someone is strong or not tall.
John is either creative or rich.
Susan is not funny or calm.
Someone is both not tall and old.
Someone is calm. | Lucy is not wise. | entailment | ((?[X]:((~quiet(X)|humble(X))))=>(?[X]:((kind(X)|happy(X)))))&
(![X]:((~tall(X)|~brave(X))=>(wise(X)<~>~generous(X))))&
(![X]:((tall(X)|wise(X))=>~happy(X)))&
((?[X]:((wise(X)<~>happy(X))))=>(~curious(fred)))&
(![X]:((~tall(X)&~kind(X))=>~funny(X)))&
(![X]:(curious(X)=>(wise(X)|happy(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~rich(X)|~happy(X))))&
(![X]:((calm(X)<~>curious(X))<=>(old(X)&~curious(X))))&
(((rich(fred)|wise(fred)))=>(~generous(mary)))&
(![X]:((~strong(X)&~happy(X))<=>(funny(X)|generous(X))))&
((?[X]:(old(X)))<=>(?[X]:((patient(X)&rich(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))=>(?[X]:((~creative(X)&creative(X)))))&
((?[X]:(~tall(X)))<=>((patient(fred)&~quiet(fred))))&
((?[X]:((~wise(X)|~tall(X))))<=>((~curious(lucy)|old(lucy))))&
(![X]:((~funny(X)<~>~quiet(X))=>(rich(X)&~creative(X))))&
(![X]:((wise(X)&curious(X))<=>(strong(X)&~kind(X))))&
((~wise(fred)<~>~funny(fred)))&
(?[X]:((~quiet(X)<~>kind(X))))&
((rich(alice)|patient(alice)))&
(?[X]:((strong(X)|~tall(X))))&
((creative(john)<~>rich(john)))&
((~funny(susan)|calm(susan)))&
(?[X]:((~tall(X)&old(X))))&
(?[X]:(calm(X))) | ~wise(lucy) | [
"p1",
"p2",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6362768066026008602142161
% SZS output start Proof for 6362768066026008602142161
2. ! [X0] : ((~brave(X0) | ~tall(X0)) => (wise(X0) <~> ~generous(X0))) [input p1]
3. ! [X0] : ((wise(X0) | tall(X0)) => ~happy(X0)) [input p2]
7. ! [X0] : ((~strong(X0) <~> tall(X0)) <=> (~happy(X0) | ~rich(X0))) [input p6]
10. ! [X0] : ((~happy(X0) & ~strong(X0)) <=> (generous(X0) | funny(X0))) [input p9]
12. ? [X0] : (~strong(X0) <~> ~generous(X0)) => ? [X0] : (creative(X0) & ~creative(X0)) [input p11]
25. wise(lucy) [input hypothesis]
28. ? [X0] : (~strong(X0) <~> ~generous(X0)) => ? [X1] : (creative(X1) & ~creative(X1)) [rectify 12]
29. ! [X0] : (~tall(X0) => (wise(X0) <~> ~generous(X0))) [pure predicate removal 2]
32. ! [X0] : ((wise(X0) <~> ~generous(X0)) | tall(X0)) [ennf transformation 29]
33. ! [X0] : (~happy(X0) | (~wise(X0) & ~tall(X0))) [ennf transformation 3]
40. ? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : (~strong(X0) <=> ~generous(X0)) [ennf transformation 28]
45. ! [X0] : (((generous(X0) | ~wise(X0)) & (~generous(X0) | wise(X0))) | tall(X0)) [nnf transformation 32]
47. ! [X0] : ((((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))))) [flattening 47]
51. ! [X0] : (((~happy(X0) & ~strong(X0)) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | (happy(X0) | strong(X0)))) [nnf transformation 10]
52. ! [X0] : (((~happy(X0) & ~strong(X0)) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | happy(X0) | strong(X0))) [flattening 51]
58. ? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))) [nnf transformation 40]
59. ? [X0] : (creative(X0) & ~creative(X0)) | ! [X1] : ((~strong(X1) | generous(X1)) & (~generous(X1) | strong(X1))) [rectify 58]
60. ? [X0] : (creative(X0) & ~creative(X0)) => (creative(sK3) & ~creative(sK3)) [choice axiom]
61. (creative(sK3) & ~creative(sK3)) | ! [X1] : ((~strong(X1) | generous(X1)) & (~generous(X1) | strong(X1))) [skolemisation 59,60]
88. ~wise(X0) | generous(X0) | tall(X0) [cnf transformation 45]
89. ~tall(X0) | ~happy(X0) [cnf transformation 33]
100. ~tall(X0) | strong(X0) | happy(X0) [cnf transformation 48]
111. ~strong(X0) | ~generous(X0) [cnf transformation 52]
117. ~creative(sK3) | ~generous(X1) | strong(X1) [cnf transformation 61]
118. ~creative(sK3) | ~strong(X1) | generous(X1) [cnf transformation 61]
119. creative(sK3) | ~generous(X1) | strong(X1) [cnf transformation 61]
120. creative(sK3) | ~strong(X1) | generous(X1) [cnf transformation 61]
148. wise(lucy) [cnf transformation 25]
177. ~tall(X0) | strong(X0) [subsumption resolution 100,89]
214. creative(sK3) | ~strong(X1) [subsumption resolution 120,111]
216. 15 <=> ! [X1] : ~strong(X1) [avatar definition]
217. ~strong(X1) <- (15) [avatar component clause 216]
219. 16 <=> creative(sK3) [avatar definition]
222. 15 | 16 [avatar split clause 214,219,216]
223. creative(sK3) | ~generous(X1) [subsumption resolution 119,111]
225. 17 <=> ! [X1] : ~generous(X1) [avatar definition]
226. ~generous(X1) <- (17) [avatar component clause 225]
227. 17 | 16 [avatar split clause 223,219,225]
228. ~creative(sK3) | ~strong(X1) [subsumption resolution 118,111]
229. 15 | ~16 [avatar split clause 228,219,216]
230. ~creative(sK3) | ~generous(X1) [subsumption resolution 117,111]
231. 17 | ~16 [avatar split clause 230,219,225]
328. generous(lucy) | tall(lucy) [resolution 88,148]
330. tall(lucy) <- (17) [subsumption resolution 328,226]
332. strong(lucy) <- (17) [resolution 330,177]
334. $false <- (15, 17) [subsumption resolution 332,217]
335. ~15 | ~17 [avatar contradiction clause 334]
336. $false [avatar sat refutation 222,227,229,231,335]
% SZS output end Proof for 6362768066026008602142161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is either rich or funny and vice versa.
If paul is funny then someone is rich or not rich and vice versa.
Everyone who is either strong or not strong is both not old and generous and vice versa.
Everyone who is either not funny or not calm is either not tall or generous and vice versa.
Everyone who is not strong is not old or strong.
Everyone who is either not wise or old is strong or not calm.
Everyone who is not wise is not funny or strong.
Everyone who is quiet is not funny and vice versa.
Everyone who is not creative is either strong or patient and vice versa.
Everyone who is both not wise and not brave is brave and vice versa.
Everyone who is both kind and not old is both not kind and humble.
If lucy is both not patient and creative then someone is tall or brave and vice versa.
Everyone who is not brave or not kind is curious or not rich and vice versa.
Everyone who is not calm or creative is not wise or brave and vice versa.
If someone is either rich or brave then lucy is both humble and calm and vice versa.
Someone is not kind.
Paul is not patient or not generous.
Someone is either humble or not wise.
Fred is creative or not old. | Lucy is not patient. | neutral | (![X]:(old(X)<=>(rich(X)<~>funny(X))))&
((funny(paul))<=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:((strong(X)<~>~strong(X))<=>(~old(X)&generous(X))))&
(![X]:((~funny(X)<~>~calm(X))<=>(~tall(X)<~>generous(X))))&
(![X]:(~strong(X)=>(~old(X)|strong(X))))&
(![X]:((~wise(X)<~>old(X))=>(strong(X)|~calm(X))))&
(![X]:(~wise(X)=>(~funny(X)|strong(X))))&
(![X]:(quiet(X)<=>~funny(X)))&
(![X]:(~creative(X)<=>(strong(X)<~>patient(X))))&
(![X]:((~wise(X)&~brave(X))<=>brave(X)))&
(![X]:((kind(X)&~old(X))=>(~kind(X)&humble(X))))&
(((~patient(lucy)&creative(lucy)))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~brave(X)|~kind(X))<=>(curious(X)|~rich(X))))&
(![X]:((~calm(X)|creative(X))<=>(~wise(X)|brave(X))))&
((?[X]:((rich(X)<~>brave(X))))<=>((humble(lucy)&calm(lucy))))&
(?[X]:(~kind(X)))&
((~patient(paul)|~generous(paul)))&
(?[X]:((humble(X)<~>~wise(X))))&
((creative(fred)|~old(fred))) | ~patient(lucy) | [] | null | 0 |
If lucy is both not quiet and not curious then susan is both kind and not brave. If someone is either strong or happy then lucy is not happy and vice versa. Everyone who is both kind and not rich is either wise or quiet. Everyone who is creative or not rich is kind or not humble. If alice is either not generous or wise then someone is either old or not brave. If someone is creative then susan is either humble or not humble. Everyone who is not brave is not quiet or not calm and vice versa. If someone is both patient and wise then fred is quiet or not humble. If someone is either not wise or patient then someone is not kind or happy. Everyone who is not creative or generous is wise. Everyone who is not strong is both old and happy. If someone is not kind then lucy is either rich or generous and vice versa. If paul is not happy then someone is both generous and not humble and vice versa. If lucy is either quiet or not curious then someone is happy or tall. If someone is not old or kind then someone is both not kind and kind. If mary is either tall or not generous then fred is not rich or strong and vice versa. Someone is either not humble or not generous. Someone is both generous and not curious. John is either not funny or not patient. Someone is either rich or not happy. Mary is both not tall and wise. Paul is either not curious or rich. Someone is both not calm and not strong. Someone is not creative. | Mary is kind. | contradiction | (((~quiet(lucy)&~curious(lucy)))=>((kind(susan)&~brave(susan))))&
((?[X]:((strong(X)<~>happy(X))))<=>(~happy(lucy)))&
(![X]:((kind(X)&~rich(X))=>(wise(X)<~>quiet(X))))&
(![X]:((creative(X)|~rich(X))=>(kind(X)|~humble(X))))&
(((~generous(alice)<~>wise(alice)))=>(?[X]:((old(X)<~>~brave(X)))))&
((?[X]:(creative(X)))=>((humble(susan)<~>~humble(susan))))&
(![X]:(~brave(X)<=>(~quiet(X)|~calm(X))))&
((?[X]:((patient(X)&wise(X))))=>((quiet(fred)|~humble(fred))))&
((?[X]:((~wise(X)<~>patient(X))))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((~creative(X)|generous(X))=>wise(X)))&
(![X]:(~strong(X)=>(old(X)&happy(X))))&
((?[X]:(~kind(X)))<=>((rich(lucy)<~>generous(lucy))))&
((~happy(paul))<=>(?[X]:((generous(X)&~humble(X)))))&
(((quiet(lucy)<~>~curious(lucy)))=>(?[X]:((happy(X)|tall(X)))))&
((?[X]:((~old(X)|kind(X))))=>(?[X]:((~kind(X)&kind(X)))))&
(((tall(mary)<~>~generous(mary)))<=>((~rich(fred)|strong(fred))))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:((generous(X)&~curious(X))))&
((~funny(john)<~>~patient(john)))&
(?[X]:((rich(X)<~>~happy(X))))&
((~tall(mary)&wise(mary)))&
((~curious(paul)<~>rich(paul)))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:(~creative(X))) | kind(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 630733221550077791261589
% SZS output start Proof for 630733221550077791261589
15. ? [X0] : (kind(X0) | ~old(X0)) => ? [X0] : (kind(X0) & ~kind(X0)) [input p14]
25. kind(mary) [input hypothesis]
27. ? [X0] : (kind(X0) | ~old(X0)) => ? [X1] : (kind(X1) & ~kind(X1)) [rectify 15]
42. ? [X1] : (kind(X1) & ~kind(X1)) | ! [X0] : (~kind(X0) & old(X0)) [ennf transformation 27]
69. ? [X0] : (kind(X0) & ~kind(X0)) | ! [X1] : (~kind(X1) & old(X1)) [rectify 42]
70. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK6) & ~kind(sK6)) [choice axiom]
71. (kind(sK6) & ~kind(sK6)) | ! [X1] : (~kind(X1) & old(X1)) [skolemisation 69,70]
124. ~kind(sK6) | ~kind(X1) [cnf transformation 71]
126. kind(sK6) | ~kind(X1) [cnf transformation 71]
148. kind(mary) [cnf transformation 25]
282. 30 <=> ! [X1] : ~kind(X1) [avatar definition]
283. ~kind(X1) <- (30) [avatar component clause 282]
285. 31 <=> kind(sK6) [avatar definition]
288. 30 | 31 [avatar split clause 126,285,282]
293. 30 | ~31 [avatar split clause 124,285,282]
360. $false <- (30) [resolution 283,148]
361. ~30 [avatar contradiction clause 360]
362. $false [avatar sat refutation 288,293,361]
% SZS output end Proof for 630733221550077791261589
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.015 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or kind is rich and vice versa. Everyone who is either not humble or not calm is both quiet and patient. If john is rich then lucy is either old or brave. If someone is both not tall and not old then lucy is not generous or wise. Everyone who is wise is both old and kind and vice versa. Everyone who is not strong is both not rich and brave and vice versa. Everyone who is either brave or not happy is tall. If fred is not generous or calm then mary is happy and vice versa. Everyone who is either not patient or brave is not kind and vice versa. If john is either not humble or old then someone is both funny and calm and vice versa. Everyone who is not kind or kind is either not brave or rich. Everyone who is either humble or curious is both creative and not rich. Everyone who is either kind or not generous is both calm and not quiet and vice versa. If mary is either wise or strong then someone is wise or not calm and vice versa. Everyone who is not rich or not quiet is strong or generous and vice versa. Everyone who is both old and kind is either not tall or not patient and vice versa. Someone is not generous or quiet. Someone is either not humble or not tall. Someone is quiet. Lucy is both not quiet and not tall. Fred is not brave or funny. Susan is strong or not old. | Susan is rich. | neutral | (![X]:((humble(X)|kind(X))<=>rich(X)))&
(![X]:((~humble(X)<~>~calm(X))=>(quiet(X)&patient(X))))&
((rich(john))=>((old(lucy)<~>brave(lucy))))&
((?[X]:((~tall(X)&~old(X))))=>((~generous(lucy)|wise(lucy))))&
(![X]:(wise(X)<=>(old(X)&kind(X))))&
(![X]:(~strong(X)<=>(~rich(X)&brave(X))))&
(![X]:((brave(X)<~>~happy(X))=>tall(X)))&
(((~generous(fred)|calm(fred)))<=>(happy(mary)))&
(![X]:((~patient(X)<~>brave(X))<=>~kind(X)))&
(((~humble(john)<~>old(john)))<=>(?[X]:((funny(X)&calm(X)))))&
(![X]:((~kind(X)|kind(X))=>(~brave(X)<~>rich(X))))&
(![X]:((humble(X)<~>curious(X))=>(creative(X)&~rich(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(calm(X)&~quiet(X))))&
(((wise(mary)<~>strong(mary)))<=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:((~rich(X)|~quiet(X))<=>(strong(X)|generous(X))))&
(![X]:((old(X)&kind(X))<=>(~tall(X)<~>~patient(X))))&
(?[X]:((~generous(X)|quiet(X))))&
(?[X]:((~humble(X)<~>~tall(X))))&
(?[X]:(quiet(X)))&
((~quiet(lucy)&~tall(lucy)))&
((~brave(fred)|funny(fred)))&
((strong(susan)|~old(susan))) | rich(susan) | [] | null | 0 |
Everyone who is humble is either wise or not creative and vice versa. If someone is either not humble or calm then someone is happy or not creative. If someone is not strong then susan is not funny or kind and vice versa. If someone is both old and not humble then mary is not tall or happy. Everyone who is old or kind is either not curious or patient and vice versa. Everyone who is not patient or not wise is not happy. Everyone who is both curious and patient is old or not curious. If susan is not tall then susan is generous or old. Everyone who is both patient and not brave is kind or quiet and vice versa. If fred is both curious and calm then john is both humble and not happy. If mary is either not funny or humble then mary is both not humble and curious. Everyone who is not wise or not rich is generous or creative. If someone is brave or old then fred is either not curious or brave. Everyone who is either not curious or not patient is either not curious or not kind and vice versa. If someone is either not strong or funny then someone is humble or not quiet. Someone is either happy or patient. Someone is either not calm or not patient. Someone is not kind or not wise. John is both not rich and funny. Paul is not kind or not humble. Mary is not old. | Fred is not kind. | entailment | (![X]:(humble(X)<=>(wise(X)<~>~creative(X))))&
((?[X]:((~humble(X)<~>calm(X))))=>(?[X]:((happy(X)|~creative(X)))))&
((?[X]:(~strong(X)))<=>((~funny(susan)|kind(susan))))&
((?[X]:((old(X)&~humble(X))))=>((~tall(mary)|happy(mary))))&
(![X]:((old(X)|kind(X))<=>(~curious(X)<~>patient(X))))&
(![X]:((~patient(X)|~wise(X))=>~happy(X)))&
(![X]:((curious(X)&patient(X))=>(old(X)|~curious(X))))&
((~tall(susan))=>((generous(susan)|old(susan))))&
(![X]:((patient(X)&~brave(X))<=>(kind(X)|quiet(X))))&
(((curious(fred)&calm(fred)))=>((humble(john)&~happy(john))))&
(((~funny(mary)<~>humble(mary)))=>((~humble(mary)&curious(mary))))&
(![X]:((~wise(X)|~rich(X))=>(generous(X)|creative(X))))&
((?[X]:((brave(X)|old(X))))=>((~curious(fred)<~>brave(fred))))&
(![X]:((~curious(X)<~>~patient(X))<=>(~curious(X)<~>~kind(X))))&
((?[X]:((~strong(X)<~>funny(X))))=>(?[X]:((humble(X)|~quiet(X)))))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((~calm(X)<~>~patient(X))))&
(?[X]:((~kind(X)|~wise(X))))&
((~rich(john)&funny(john)))&
((~kind(paul)|~humble(paul)))&
(~old(mary)) | ~kind(fred) | [
"p4",
"p6",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 23987679150004805307354
% SZS output start Proof for 23987679150004805307354
5. ! [X0] : ((kind(X0) | old(X0)) <=> (~curious(X0) <~> patient(X0))) [input p4]
7. ! [X0] : ((patient(X0) & curious(X0)) => (~curious(X0) | old(X0))) [input p6]
9. ! [X0] : ((~brave(X0) & patient(X0)) <=> (quiet(X0) | kind(X0))) [input p8]
13. ? [X0] : (old(X0) | brave(X0)) => (~curious(fred) <~> brave(fred)) [input p12]
22. kind(fred) [input hypothesis]
31. ! [X0] : ((~curious(X0) | old(X0)) | (~patient(X0) | ~curious(X0))) [ennf transformation 7]
32. ! [X0] : (~curious(X0) | old(X0) | ~patient(X0) | ~curious(X0)) [flattening 31]
36. (~curious(fred) <~> brave(fred)) | ! [X0] : (~old(X0) & ~brave(X0)) [ennf transformation 13]
48. ! [X0] : (((kind(X0) | old(X0)) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0)))) & (((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~kind(X0) & ~old(X0)))) [nnf transformation 5]
49. ! [X0] : ((kind(X0) | old(X0) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0)))) & (((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~kind(X0) & ~old(X0)))) [flattening 48]
50. ! [X0] : (((~brave(X0) & patient(X0)) | (~quiet(X0) & ~kind(X0))) & ((quiet(X0) | kind(X0)) | (brave(X0) | ~patient(X0)))) [nnf transformation 9]
51. ! [X0] : (((~brave(X0) & patient(X0)) | (~quiet(X0) & ~kind(X0))) & (quiet(X0) | kind(X0) | brave(X0) | ~patient(X0))) [flattening 50]
53. ((~brave(fred) | curious(fred)) & (brave(fred) | ~curious(fred))) | ! [X0] : (~old(X0) & ~brave(X0)) [nnf transformation 36]
79. ~patient(X0) | curious(X0) | ~kind(X0) [cnf transformation 49]
84. ~curious(X0) | old(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 32]
86. ~kind(X0) | patient(X0) [cnf transformation 51]
88. ~brave(X0) | ~kind(X0) [cnf transformation 51]
97. brave(fred) | ~curious(fred) | ~old(X0) [cnf transformation 53]
118. kind(fred) [cnf transformation 22]
124. ~patient(X0) | old(X0) | ~curious(X0) [duplicate literal removal 84]
160. 9 <=> curious(fred) [avatar definition]
161. curious(fred) <- (9) [avatar component clause 160]
193. 16 <=> ! [X0] : ~old(X0) [avatar definition]
194. ~old(X0) <- (16) [avatar component clause 193]
196. 17 <=> brave(fred) [avatar definition]
197. brave(fred) <- (17) [avatar component clause 196]
204. 16 | ~9 | 17 [avatar split clause 97,196,160,193]
253. patient(fred) [resolution 86,118]
290. curious(fred) | ~kind(fred) [resolution 79,253]
296. curious(fred) [subsumption resolution 290,118]
297. 9 [avatar split clause 296,160]
306. ~kind(fred) <- (17) [resolution 197,88]
307. $false <- (17) [subsumption resolution 306,118]
308. ~17 [avatar contradiction clause 307]
312. old(fred) | ~curious(fred) [resolution 124,253]
316. ~curious(fred) <- (16) [subsumption resolution 312,194]
317. $false <- (9, 16) [subsumption resolution 316,161]
318. ~9 | ~16 [avatar contradiction clause 317]
319. $false [avatar sat refutation 204,297,308,318]
% SZS output end Proof for 23987679150004805307354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not funny is not strong and vice versa. Everyone who is not rich or not creative is both generous and patient and vice versa. Everyone who is either not happy or not brave is both not curious and old. Everyone who is funny is rich and vice versa. Everyone who is not happy is not wise. Everyone who is not happy or not quiet is both brave and not old and vice versa. If someone is not tall then lucy is either not generous or not rich and vice versa. Everyone who is both not strong and not curious is both not calm and not funny and vice versa. If alice is both quiet and strong then someone is both not strong and not funny. If someone is both not calm and generous then someone is both not wise and brave and vice versa. Everyone who is funny or patient is both not strong and curious. If someone is both funny and calm then paul is not humble or calm and vice versa. If susan is old then susan is either strong or not creative. Everyone who is wise is both not patient and not generous. If someone is either generous or funny then lucy is funny. Everyone who is both wise and funny is not humble or quiet and vice versa. Alice is both old and creative. Someone is either not generous or not old. Alice is not patient. Lucy is not patient or strong. Someone is either funny or not calm. | Paul is not patient. | entailment | (![X]:((~humble(X)|~funny(X))<=>~strong(X)))&
(![X]:((~rich(X)|~creative(X))<=>(generous(X)&patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~curious(X)&old(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:(~happy(X)=>~wise(X)))&
(![X]:((~happy(X)|~quiet(X))<=>(brave(X)&~old(X))))&
((?[X]:(~tall(X)))<=>((~generous(lucy)<~>~rich(lucy))))&
(![X]:((~strong(X)&~curious(X))<=>(~calm(X)&~funny(X))))&
(((quiet(alice)&strong(alice)))=>(?[X]:((~strong(X)&~funny(X)))))&
((?[X]:((~calm(X)&generous(X))))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((funny(X)|patient(X))=>(~strong(X)&curious(X))))&
((?[X]:((funny(X)&calm(X))))<=>((~humble(paul)|calm(paul))))&
((old(susan))=>((strong(susan)<~>~creative(susan))))&
(![X]:(wise(X)=>(~patient(X)&~generous(X))))&
((?[X]:((generous(X)<~>funny(X))))=>(funny(lucy)))&
(![X]:((wise(X)&funny(X))<=>(~humble(X)|quiet(X))))&
((old(alice)&creative(alice)))&
(?[X]:((~generous(X)<~>~old(X))))&
(~patient(alice))&
((~patient(lucy)|strong(lucy)))&
(?[X]:((funny(X)<~>~calm(X)))) | ~patient(paul) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5111305838169937934379011
% SZS output start Proof for 5111305838169937934379011
1. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> ~strong(X0)) [input p0]
2. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (patient(X0) & generous(X0))) [input p1]
4. ! [X0] : (funny(X0) <=> rich(X0)) [input p3]
6. ! [X0] : ((~quiet(X0) | ~happy(X0)) <=> (~old(X0) & brave(X0))) [input p5]
8. ! [X0] : ((~curious(X0) & ~strong(X0)) <=> (~funny(X0) & ~calm(X0))) [input p7]
10. ? [X0] : (generous(X0) & ~calm(X0)) <=> ? [X0] : (brave(X0) & ~wise(X0)) [input p9]
11. ! [X0] : ((patient(X0) | funny(X0)) => (curious(X0) & ~strong(X0))) [input p10]
14. ! [X0] : (wise(X0) => (~generous(X0) & ~patient(X0))) [input p13]
16. ! [X0] : ((funny(X0) & wise(X0)) <=> (quiet(X0) | ~humble(X0))) [input p15]
22. patient(paul) [input hypothesis]
23. ? [X0] : (generous(X0) & ~calm(X0)) <=> ? [X1] : (brave(X1) & ~wise(X1)) [rectify 10]
28. ! [X0] : ((curious(X0) & ~strong(X0)) | (~patient(X0) & ~funny(X0))) [ennf transformation 11]
30. ! [X0] : ((~generous(X0) & ~patient(X0)) | ~wise(X0)) [ennf transformation 14]
32. ! [X0] : (((~funny(X0) | ~humble(X0)) | strong(X0)) & (~strong(X0) | (funny(X0) & humble(X0)))) [nnf transformation 1]
33. ! [X0] : ((~funny(X0) | ~humble(X0) | strong(X0)) & (~strong(X0) | (funny(X0) & humble(X0)))) [flattening 32]
34. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 2]
35. ! [X0] : ((~creative(X0) | ~rich(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [flattening 34]
37. ! [X0] : ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))) [nnf transformation 4]
38. ! [X0] : (((~quiet(X0) | ~happy(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (quiet(X0) & happy(X0)))) [nnf transformation 6]
39. ! [X0] : ((~quiet(X0) | ~happy(X0) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | (quiet(X0) & happy(X0)))) [flattening 38]
44. ! [X0] : (((~curious(X0) & ~strong(X0)) | (funny(X0) | calm(X0))) & ((~funny(X0) & ~calm(X0)) | (curious(X0) | strong(X0)))) [nnf transformation 8]
45. ! [X0] : (((~curious(X0) & ~strong(X0)) | funny(X0) | calm(X0)) & ((~funny(X0) & ~calm(X0)) | curious(X0) | strong(X0))) [flattening 44]
48. (? [X0] : (generous(X0) & ~calm(X0)) | ! [X1] : (~brave(X1) | wise(X1))) & (? [X1] : (brave(X1) & ~wise(X1)) | ! [X0] : (~generous(X0) | calm(X0))) [nnf transformation 23]
49. (? [X0] : (generous(X0) & ~calm(X0)) | ! [X1] : (~brave(X1) | wise(X1))) & (? [X2] : (brave(X2) & ~wise(X2)) | ! [X3] : (~generous(X3) | calm(X3))) [rectify 48]
50. ? [X0] : (generous(X0) & ~calm(X0)) => (generous(sK2) & ~calm(sK2)) [choice axiom]
51. ? [X2] : (brave(X2) & ~wise(X2)) => (brave(sK3) & ~wise(sK3)) [choice axiom]
52. ((generous(sK2) & ~calm(sK2)) | ! [X1] : (~brave(X1) | wise(X1))) & ((brave(sK3) & ~wise(sK3)) | ! [X3] : (~generous(X3) | calm(X3))) [skolemisation 49,51,50]
60. ! [X0] : (((funny(X0) & wise(X0)) | (~quiet(X0) & humble(X0))) & ((quiet(X0) | ~humble(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 16]
61. ! [X0] : (((funny(X0) & wise(X0)) | (~quiet(X0) & humble(X0))) & (quiet(X0) | ~humble(X0) | ~funny(X0) | ~wise(X0))) [flattening 60]
69. ~strong(X0) | funny(X0) [cnf transformation 33]
70. ~funny(X0) | ~humble(X0) | strong(X0) [cnf transformation 33]
73. patient(X0) | rich(X0) [cnf transformation 35]
80. ~funny(X0) | rich(X0) [cnf transformation 37]
81. ~rich(X0) | funny(X0) [cnf transformation 37]
84. quiet(X0) | brave(X0) [cnf transformation 39]
95. ~curious(X0) | funny(X0) | calm(X0) [cnf transformation 45]
100. ~calm(sK2) | ~brave(X1) | wise(X1) [cnf transformation 52]
101. generous(sK2) | ~brave(X1) | wise(X1) [cnf transformation 52]
102. ~strong(X0) | ~funny(X0) [cnf transformation 28]
105. ~patient(X0) | curious(X0) [cnf transformation 28]
113. ~wise(X0) | ~patient(X0) [cnf transformation 30]
114. ~wise(X0) | ~generous(X0) [cnf transformation 30]
118. wise(X0) | humble(X0) [cnf transformation 61]
119. ~quiet(X0) | wise(X0) [cnf transformation 61]
130. patient(paul) [cnf transformation 22]
171. 9 <=> ! [X1] : (~brave(X1) | wise(X1)) [avatar definition]
172. ~brave(X1) | wise(X1) <- (9) [avatar component clause 171]
174. 10 <=> generous(sK2) [avatar definition]
176. generous(sK2) <- (10) [avatar component clause 174]
177. 9 | 10 [avatar split clause 101,174,171]
179. 11 <=> calm(sK2) [avatar definition]
181. ~calm(sK2) <- (~11) [avatar component clause 179]
182. 9 | ~11 [avatar split clause 100,179,171]
196. ~strong(X0) [subsumption resolution 102,69]
293. curious(X1) | rich(X1) [resolution 105,73]
294. ~generous(X0) | humble(X0) [resolution 118,114]
297. wise(X0) | brave(X0) [resolution 119,84]
319. wise(X1) <- (9) [subsumption resolution 172,297]
327. ~patient(X1) <- (9) [resolution 319,113]
371. $false <- (9) [resolution 327,130]
374. ~9 [avatar contradiction clause 371]
420. rich(X0) | funny(X0) | calm(X0) [resolution 293,95]
423. calm(X0) | rich(X0) [subsumption resolution 420,80]
431. humble(sK2) <- (10) [resolution 294,176]
469. rich(sK2) <- (~11) [resolution 423,181]
495. funny(sK2) <- (~11) [resolution 469,81]
506. ~humble(sK2) | strong(sK2) <- (~11) [resolution 495,70]
510. strong(sK2) <- (10, ~11) [subsumption resolution 506,431]
511. $false <- (10, ~11) [subsumption resolution 510,196]
512. ~10 | 11 [avatar contradiction clause 511]
513. $false [avatar sat refutation 177,182,374,512]
% SZS output end Proof for 5111305838169937934379011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is calm or kind then someone is either not patient or not humble.
Everyone who is not brave or patient is not brave and vice versa.
Everyone who is not old or not quiet is either not brave or not quiet.
Everyone who is either creative or generous is not wise and vice versa.
If susan is either not curious or wise then someone is either creative or tall and vice versa.
If someone is either brave or not brave then someone is creative or not tall.
If paul is not calm then someone is not quiet and vice versa.
Everyone who is both happy and not patient is either rich or not generous and vice versa.
Everyone who is kind is either not quiet or not rich.
If alice is both wise and strong then someone is both tall and not patient.
If mary is either not creative or patient then susan is both humble and brave.
Everyone who is not happy or not curious is not curious and vice versa.
If fred is both not happy and not tall then someone is either patient or not rich.
Everyone who is both not generous and not patient is not happy or happy and vice versa.
If mary is either wise or quiet then alice is curious and vice versa.
If someone is both old and not generous then lucy is not wise and vice versa.
John is quiet.
Someone is either not creative or not happy.
Someone is either funny or not wise.
Someone is not happy.
Someone is either calm or funny.
Someone is either not generous or generous.
Someone is both not funny and not happy.
Alice is both not calm and not curious. | Alice is curious. | contradiction | (((calm(fred)|kind(fred)))=>(?[X]:((~patient(X)<~>~humble(X)))))&
(![X]:((~brave(X)|patient(X))<=>~brave(X)))&
(![X]:((~old(X)|~quiet(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((creative(X)<~>generous(X))<=>~wise(X)))&
(((~curious(susan)<~>wise(susan)))<=>(?[X]:((creative(X)<~>tall(X)))))&
((?[X]:((brave(X)<~>~brave(X))))=>(?[X]:((creative(X)|~tall(X)))))&
((~calm(paul))<=>(?[X]:(~quiet(X))))&
(![X]:((happy(X)&~patient(X))<=>(rich(X)<~>~generous(X))))&
(![X]:(kind(X)=>(~quiet(X)<~>~rich(X))))&
(((wise(alice)&strong(alice)))=>(?[X]:((tall(X)&~patient(X)))))&
(((~creative(mary)<~>patient(mary)))=>((humble(susan)&brave(susan))))&
(![X]:((~happy(X)|~curious(X))<=>~curious(X)))&
(((~happy(fred)&~tall(fred)))=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:((~generous(X)&~patient(X))<=>(~happy(X)|happy(X))))&
(((wise(mary)<~>quiet(mary)))<=>(curious(alice)))&
((?[X]:((old(X)&~generous(X))))<=>(~wise(lucy)))&
(quiet(john))&
(?[X]:((~creative(X)<~>~happy(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~generous(X)<~>generous(X))))&
(?[X]:((~funny(X)&~happy(X))))&
((~calm(alice)&~curious(alice))) | curious(alice) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3783578704421909140492377
% SZS output start Proof for 3783578704421909140492377
24. ~curious(alice) & ~calm(alice) [input p23]
25. curious(alice) [input hypothesis]
151. ~curious(alice) [cnf transformation 24]
152. curious(alice) [cnf transformation 25]
270. 25 <=> curious(alice) [avatar definition]
329. ~25 [avatar split clause 151,270]
330. 25 [avatar split clause 152,270]
331. $false [avatar sat refutation 329,330]
% SZS output end Proof for 3783578704421909140492377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not brave is both not creative and old. Everyone who is either brave or not strong is both not patient and patient and vice versa. Everyone who is not tall or not wise is both happy and not creative and vice versa. If lucy is patient or not generous then alice is not old or wise. Everyone who is not funny or not creative is either old or not quiet. Everyone who is both not calm and not generous is both creative and tall and vice versa. If someone is both tall and not patient then someone is not curious or not old. If mary is both not happy and generous then someone is both curious and quiet. If susan is both not old and quiet then mary is either generous or not humble. If someone is not old then susan is kind. Everyone who is quiet is either not brave or patient. Everyone who is not happy is strong or rich and vice versa. If someone is rich or funny then someone is both not quiet and strong and vice versa. Everyone who is wise is both not quiet and rich and vice versa. Everyone who is either wise or not brave is both not tall and rich. Everyone who is both not tall and not happy is not quiet. Someone is either quiet or not strong. Paul is generous or wise. John is both calm and not tall. Someone is not curious. Someone is either not rich or not humble. Someone is either tall or not happy. | Paul is happy. | entailment | (![X]:((curious(X)|~brave(X))=>(~creative(X)&old(X))))&
(![X]:((brave(X)<~>~strong(X))<=>(~patient(X)&patient(X))))&
(![X]:((~tall(X)|~wise(X))<=>(happy(X)&~creative(X))))&
(((patient(lucy)|~generous(lucy)))=>((~old(alice)|wise(alice))))&
(![X]:((~funny(X)|~creative(X))=>(old(X)<~>~quiet(X))))&
(![X]:((~calm(X)&~generous(X))<=>(creative(X)&tall(X))))&
((?[X]:((tall(X)&~patient(X))))=>(?[X]:((~curious(X)|~old(X)))))&
(((~happy(mary)&generous(mary)))=>(?[X]:((curious(X)&quiet(X)))))&
(((~old(susan)&quiet(susan)))=>((generous(mary)<~>~humble(mary))))&
((?[X]:(~old(X)))=>(kind(susan)))&
(![X]:(quiet(X)=>(~brave(X)<~>patient(X))))&
(![X]:(~happy(X)<=>(strong(X)|rich(X))))&
((?[X]:((rich(X)|funny(X))))<=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:(wise(X)<=>(~quiet(X)&rich(X))))&
(![X]:((wise(X)<~>~brave(X))=>(~tall(X)&rich(X))))&
(![X]:((~tall(X)&~happy(X))=>~quiet(X)))&
(?[X]:((quiet(X)<~>~strong(X))))&
((generous(paul)|wise(paul)))&
((calm(john)&~tall(john)))&
(?[X]:(~curious(X)))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:((tall(X)<~>~happy(X)))) | happy(paul) | [
"p0",
"p1",
"p2",
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 672579663002466608879012
% SZS output start Proof for 672579663002466608879012
1. ! [X0] : ((~brave(X0) | curious(X0)) => (old(X0) & ~creative(X0))) [input p0]
2. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (patient(X0) & ~patient(X0))) [input p1]
3. ! [X0] : ((~wise(X0) | ~tall(X0)) <=> (~creative(X0) & happy(X0))) [input p2]
5. ! [X0] : ((~creative(X0) | ~funny(X0)) => (old(X0) <~> ~quiet(X0))) [input p4]
13. ? [X0] : (funny(X0) | rich(X0)) <=> ? [X0] : (strong(X0) & ~quiet(X0)) [input p12]
14. ! [X0] : (wise(X0) <=> (rich(X0) & ~quiet(X0))) [input p13]
23. ~happy(paul) [input hypothesis]
25. ? [X0] : (funny(X0) | rich(X0)) <=> ? [X1] : (strong(X1) & ~quiet(X1)) [rectify 13]
27. ! [X0] : ((old(X0) & ~creative(X0)) | (brave(X0) & ~curious(X0))) [ennf transformation 1]
30. ! [X0] : ((old(X0) <~> ~quiet(X0)) | (creative(X0) & funny(X0))) [ennf transformation 5]
40. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 2]
41. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 40]
42. ! [X0] : (((~wise(X0) | ~tall(X0)) | (creative(X0) | ~happy(X0))) & ((~creative(X0) & happy(X0)) | (wise(X0) & tall(X0)))) [nnf transformation 3]
43. ! [X0] : ((~wise(X0) | ~tall(X0) | creative(X0) | ~happy(X0)) & ((~creative(X0) & happy(X0)) | (wise(X0) & tall(X0)))) [flattening 42]
44. ! [X0] : (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (creative(X0) & funny(X0))) [nnf transformation 30]
56. (? [X0] : (funny(X0) | rich(X0)) | ! [X1] : (~strong(X1) | quiet(X1))) & (? [X1] : (strong(X1) & ~quiet(X1)) | ! [X0] : (~funny(X0) & ~rich(X0))) [nnf transformation 25]
57. (? [X0] : (funny(X0) | rich(X0)) | ! [X1] : (~strong(X1) | quiet(X1))) & (? [X2] : (strong(X2) & ~quiet(X2)) | ! [X3] : (~funny(X3) & ~rich(X3))) [rectify 56]
58. ? [X0] : (funny(X0) | rich(X0)) => (funny(sK2) | rich(sK2)) [choice axiom]
59. ? [X2] : (strong(X2) & ~quiet(X2)) => (strong(sK3) & ~quiet(sK3)) [choice axiom]
60. ((funny(sK2) | rich(sK2)) | ! [X1] : (~strong(X1) | quiet(X1))) & ((strong(sK3) & ~quiet(sK3)) | ! [X3] : (~funny(X3) & ~rich(X3))) [skolemisation 57,59,58]
61. ! [X0] : ((wise(X0) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | ~wise(X0))) [nnf transformation 14]
62. ! [X0] : ((wise(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | ~wise(X0))) [flattening 61]
76. ~creative(X0) | brave(X0) [cnf transformation 27]
78. old(X0) | brave(X0) [cnf transformation 27]
79. ~patient(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 41]
81. ~strong(X0) | patient(X0) | ~brave(X0) [cnf transformation 41]
86. happy(X0) | wise(X0) [cnf transformation 43]
95. ~old(X0) | quiet(X0) | creative(X0) [cnf transformation 44]
110. ~quiet(sK3) | ~rich(X3) [cnf transformation 60]
112. strong(sK3) | ~rich(X3) [cnf transformation 60]
116. ~wise(X0) | rich(X0) [cnf transformation 62]
133. ~happy(paul) [cnf transformation 23]
135. ~strong(X0) | ~brave(X0) [subsumption resolution 79,81]
213. 18 <=> strong(sK3) [avatar definition]
215. strong(sK3) <- (18) [avatar component clause 213]
218. 19 <=> ! [X3] : ~rich(X3) [avatar definition]
219. ~rich(X3) <- (19) [avatar component clause 218]
220. 19 | 18 [avatar split clause 112,213,218]
222. 20 <=> quiet(sK3) [avatar definition]
224. ~quiet(sK3) <- (~20) [avatar component clause 222]
226. 19 | ~20 [avatar split clause 110,222,218]
243. 24 <=> wise(paul) [avatar definition]
245. wise(paul) <- (24) [avatar component clause 243]
261. wise(paul) [resolution 86,133]
262. 24 [avatar split clause 261,243]
269. rich(paul) <- (24) [resolution 116,245]
273. ~brave(sK3) <- (18) [resolution 135,215]
290. quiet(X0) | creative(X0) | brave(X0) [resolution 95,78]
291. quiet(X0) | brave(X0) [subsumption resolution 290,76]
337. brave(sK3) <- (~20) [resolution 291,224]
345. $false <- (18, ~20) [subsumption resolution 337,273]
346. ~18 | 20 [avatar contradiction clause 345]
351. $false <- (19, 24) [resolution 219,269]
356. ~19 | ~24 [avatar contradiction clause 351]
357. $false [avatar sat refutation 220,226,262,346,356]
% SZS output end Proof for 672579663002466608879012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.