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 happy or calm then someone is not kind and vice versa. If fred is not humble or rich then alice is either wise or not kind and vice versa. Everyone who is either not curious or curious is both not happy and curious and vice versa. Everyone who is generous or kind is both strong and not curious. Everyone who is humble is either rich or not humble. If someone is either not curious or not old then someone is not patient. Everyone who is not brave is either tall or curious. Everyone who is not old or not wise is not wise. Everyone who is not calm is both creative and not kind and vice versa. Everyone who is wise is either calm or old. Everyone who is either not funny or kind is either not curious or not brave. Everyone who is not tall is not rich and vice versa. Everyone who is both tall and brave is either not generous or creative and vice versa. Everyone who is either rich or not generous is both not happy and not old and vice versa. If fred is not brave or not patient then someone is either patient or not strong and vice versa. Everyone who is kind is both not calm and not old. Someone is not old. Someone is creative or not calm. Someone is kind or not funny. Lucy is either calm or not brave. Alice is tall or not quiet. Someone is either not brave or curious. Fred is wise or not patient. | Fred is patient. | contradiction | ((?[X]:((happy(X)|calm(X))))<=>(?[X]:(~kind(X))))&
(((~humble(fred)|rich(fred)))<=>((wise(alice)<~>~kind(alice))))&
(![X]:((~curious(X)<~>curious(X))<=>(~happy(X)&curious(X))))&
(![X]:((generous(X)|kind(X))=>(strong(X)&~curious(X))))&
(![X]:(humble(X)=>(rich(X)<~>~humble(X))))&
((?[X]:((~curious(X)<~>~old(X))))=>(?[X]:(~patient(X))))&
(![X]:(~brave(X)=>(tall(X)<~>curious(X))))&
(![X]:((~old(X)|~wise(X))=>~wise(X)))&
(![X]:(~calm(X)<=>(creative(X)&~kind(X))))&
(![X]:(wise(X)=>(calm(X)<~>old(X))))&
(![X]:((~funny(X)<~>kind(X))=>(~curious(X)<~>~brave(X))))&
(![X]:(~tall(X)<=>~rich(X)))&
(![X]:((tall(X)&brave(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(~happy(X)&~old(X))))&
(((~brave(fred)|~patient(fred)))<=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:(kind(X)=>(~calm(X)&~old(X))))&
(?[X]:(~old(X)))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((kind(X)|~funny(X))))&
((calm(lucy)<~>~brave(lucy)))&
((tall(alice)|~quiet(alice)))&
(?[X]:((~brave(X)<~>curious(X))))&
((wise(fred)|~patient(fred))) | patient(fred) | [
"p2",
"p3",
"p6",
"p7",
"p8",
"p9",
"p11",
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5146352336918132171946388
% SZS output start Proof for 5146352336918132171946388
3. ! [X0] : ((~curious(X0) <~> curious(X0)) <=> (curious(X0) & ~happy(X0))) [input p2]
4. ! [X0] : ((kind(X0) | generous(X0)) => (~curious(X0) & strong(X0))) [input p3]
7. ! [X0] : (~brave(X0) => (tall(X0) <~> curious(X0))) [input p6]
8. ! [X0] : ((~wise(X0) | ~old(X0)) => ~wise(X0)) [input p7]
9. ! [X0] : (~calm(X0) <=> (~kind(X0) & creative(X0))) [input p8]
10. ! [X0] : (wise(X0) => (calm(X0) <~> old(X0))) [input p9]
12. ! [X0] : (~tall(X0) <=> ~rich(X0)) [input p11]
13. ! [X0] : ((brave(X0) & tall(X0)) <=> (~generous(X0) <~> creative(X0))) [input p12]
14. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (~old(X0) & ~happy(X0))) [input p13]
23. ~patient(fred) | wise(fred) [input p22]
24. patient(fred) [input hypothesis]
28. ! [X0] : ((~curious(X0) & strong(X0)) | (~kind(X0) & ~generous(X0))) [ennf transformation 4]
31. ! [X0] : ((tall(X0) <~> curious(X0)) | brave(X0)) [ennf transformation 7]
32. ! [X0] : (~wise(X0) | (wise(X0) & old(X0))) [ennf transformation 8]
33. ! [X0] : ((calm(X0) <~> old(X0)) | ~wise(X0)) [ennf transformation 10]
43. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | (~curious(X0) | happy(X0))) & ((curious(X0) & ~happy(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [nnf transformation 3]
44. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | ~curious(X0) | happy(X0)) & ((curious(X0) & ~happy(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [flattening 43]
50. ! [X0] : (((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | brave(X0)) [nnf transformation 31]
51. ! [X0] : ((~calm(X0) | (kind(X0) | ~creative(X0))) & ((~kind(X0) & creative(X0)) | calm(X0))) [nnf transformation 9]
52. ! [X0] : ((~calm(X0) | kind(X0) | ~creative(X0)) & ((~kind(X0) & creative(X0)) | calm(X0))) [flattening 51]
53. ! [X0] : (((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | ~wise(X0)) [nnf transformation 33]
55. ! [X0] : ((~tall(X0) | rich(X0)) & (~rich(X0) | tall(X0))) [nnf transformation 12]
56. ! [X0] : (((brave(X0) & tall(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | (~brave(X0) | ~tall(X0)))) [nnf transformation 13]
57. ! [X0] : (((brave(X0) & tall(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | ~brave(X0) | ~tall(X0))) [flattening 56]
58. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 14]
59. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [flattening 58]
86. curious(X0) | curious(X0) | curious(X0) [cnf transformation 44]
92. ~curious(X0) | ~generous(X0) [cnf transformation 28]
99. ~curious(X0) | ~tall(X0) | brave(X0) [cnf transformation 50]
100. ~wise(X0) | old(X0) [cnf transformation 32]
102. creative(X0) | calm(X0) [cnf transformation 52]
106. ~old(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 53]
111. ~rich(X0) | tall(X0) [cnf transformation 55]
114. ~creative(X0) | generous(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 57]
122. ~old(X0) | rich(X0) | generous(X0) [cnf transformation 59]
140. ~patient(fred) | wise(fred) [cnf transformation 23]
141. patient(fred) [cnf transformation 24]
145. curious(X0) [duplicate literal removal 86]
186. 10 <=> rich(fred) [avatar definition]
188. rich(fred) <- (10) [avatar component clause 186]
198. ~generous(X0) [subsumption resolution 92,145]
208. ~tall(X0) | brave(X0) [subsumption resolution 99,145]
210. ~wise(X0) | ~calm(X0) [subsumption resolution 106,100]
215. ~creative(X0) | ~brave(X0) | ~tall(X0) [subsumption resolution 114,198]
216. ~creative(X0) | ~tall(X0) [subsumption resolution 215,208]
218. ~old(X0) | rich(X0) [subsumption resolution 122,198]
228. 15 <=> patient(fred) [avatar definition]
262. 21 <=> wise(fred) [avatar definition]
264. wise(fred) <- (21) [avatar component clause 262]
265. 21 | ~15 [avatar split clause 140,228,262]
266. 15 [avatar split clause 141,228]
269. old(fred) <- (21) [resolution 100,264]
272. ~calm(fred) <- (21) [resolution 210,264]
279. ~tall(X2) | calm(X2) [resolution 216,102]
280. rich(fred) <- (21) [resolution 218,269]
281. 10 | ~21 [avatar split clause 280,262,186]
282. tall(fred) <- (10) [resolution 188,111]
300. calm(fred) <- (10) [resolution 279,282]
301. $false <- (10, 21) [subsumption resolution 300,272]
302. ~10 | ~21 [avatar contradiction clause 301]
303. $false [avatar sat refutation 265,266,281,302]
% SZS output end Proof for 5146352336918132171946388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not generous is not happy or curious.
Everyone who is not curious is either not curious or not strong.
If someone is either funny or not brave then someone is not creative or not old and vice versa.
Everyone who is both wise and not creative is strong or creative.
Everyone who is not funny or funny is both happy and humble and vice versa.
If someone is not calm or quiet then someone is curious or not curious.
Everyone who is either brave or calm is calm or humble and vice versa.
If john is not patient or creative then paul is humble or not calm.
If mary is not old or not happy then someone is not funny and vice versa.
Everyone who is both old and not strong is either kind or not funny.
Everyone who is not strong is both tall and quiet and vice versa.
Everyone who is both wise and quiet is both wise and curious and vice versa.
Everyone who is either happy or not patient is both tall and not funny and vice versa.
If someone is not generous then paul is either not rich or generous.
Everyone who is not tall or quiet is both funny and curious and vice versa.
Everyone who is either quiet or strong is both happy and not calm.
Mary is not creative or calm.
Someone is either happy or not strong.
Someone is either not curious or not quiet.
Someone is both not kind and not generous.
Susan is not creative or generous.
Susan is both not wise and not calm.
Mary is both not strong and curious. | Mary is not tall. | contradiction | (![X]:((funny(X)|~generous(X))=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~curious(X)<~>~strong(X))))&
((?[X]:((funny(X)<~>~brave(X))))<=>(?[X]:((~creative(X)|~old(X)))))&
(![X]:((wise(X)&~creative(X))=>(strong(X)|creative(X))))&
(![X]:((~funny(X)|funny(X))<=>(happy(X)&humble(X))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((curious(X)|~curious(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(calm(X)|humble(X))))&
(((~patient(john)|creative(john)))=>((humble(paul)|~calm(paul))))&
(((~old(mary)|~happy(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((old(X)&~strong(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~strong(X)<=>(tall(X)&quiet(X))))&
(![X]:((wise(X)&quiet(X))<=>(wise(X)&curious(X))))&
(![X]:((happy(X)<~>~patient(X))<=>(tall(X)&~funny(X))))&
((?[X]:(~generous(X)))=>((~rich(paul)<~>generous(paul))))&
(![X]:((~tall(X)|quiet(X))<=>(funny(X)&curious(X))))&
(![X]:((quiet(X)<~>strong(X))=>(happy(X)&~calm(X))))&
((~creative(mary)|calm(mary)))&
(?[X]:((happy(X)<~>~strong(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((~kind(X)&~generous(X))))&
((~creative(susan)|generous(susan)))&
((~wise(susan)&~calm(susan)))&
((~strong(mary)&curious(mary))) | ~tall(mary) | [
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3928423659944673376258254
% SZS output start Proof for 3928423659944673376258254
11. ! [X0] : (~strong(X0) <=> (quiet(X0) & tall(X0))) [input p10]
23. curious(mary) & ~strong(mary) [input p22]
24. ~tall(mary) [input hypothesis]
58. ! [X0] : ((~strong(X0) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | strong(X0))) [nnf transformation 11]
59. ! [X0] : ((~strong(X0) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | strong(X0))) [flattening 58]
107. tall(X0) | strong(X0) [cnf transformation 59]
141. ~strong(mary) [cnf transformation 23]
143. ~tall(mary) [cnf transformation 24]
239. strong(mary) [resolution 107,143]
240. $false [subsumption resolution 239,141]
% SZS output end Proof for 3928423659944673376258254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not old is funny.
Everyone who is curious or funny is both not tall and not calm and vice versa.
Everyone who is both strong and not strong is curious and vice versa.
Everyone who is curious or not old is not tall.
If fred is not wise then someone is both kind and not old and vice versa.
Everyone who is either not rich or not happy is tall or curious and vice versa.
If alice is both brave and wise then fred is not rich or kind and vice versa.
Everyone who is either humble or kind is either not funny or not patient and vice versa.
If alice is not brave then someone is strong.
Everyone who is not wise or not funny is both not wise and not generous and vice versa.
Everyone who is not brave or quiet is creative and vice versa.
If alice is either not strong or rich then someone is curious and vice versa.
If someone is both not humble and not tall then alice is kind and vice versa.
Everyone who is either generous or not wise is either generous or not humble and vice versa.
Everyone who is calm is both kind and quiet.
Everyone who is either kind or not tall is both strong and brave.
Someone is not funny.
Someone is quiet or not curious.
Paul is both not quiet and kind.
Someone is not quiet.
Susan is humble or generous.
John is both not wise and not kind.
Mary is either not wise or not creative.
John is either not patient or patient. | Mary is not calm. | entailment | (![X]:((calm(X)|~old(X))=>funny(X)))&
(![X]:((curious(X)|funny(X))<=>(~tall(X)&~calm(X))))&
(![X]:((strong(X)&~strong(X))<=>curious(X)))&
(![X]:((curious(X)|~old(X))=>~tall(X)))&
((~wise(fred))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((~rich(X)<~>~happy(X))<=>(tall(X)|curious(X))))&
(((brave(alice)&wise(alice)))<=>((~rich(fred)|kind(fred))))&
(![X]:((humble(X)<~>kind(X))<=>(~funny(X)<~>~patient(X))))&
((~brave(alice))=>(?[X]:(strong(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~wise(X)&~generous(X))))&
(![X]:((~brave(X)|quiet(X))<=>creative(X)))&
(((~strong(alice)<~>rich(alice)))<=>(?[X]:(curious(X))))&
((?[X]:((~humble(X)&~tall(X))))<=>(kind(alice)))&
(![X]:((generous(X)<~>~wise(X))<=>(generous(X)<~>~humble(X))))&
(![X]:(calm(X)=>(kind(X)&quiet(X))))&
(![X]:((kind(X)<~>~tall(X))=>(strong(X)&brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((quiet(X)|~curious(X))))&
((~quiet(paul)&kind(paul)))&
(?[X]:(~quiet(X)))&
((humble(susan)|generous(susan)))&
((~wise(john)&~kind(john)))&
((~wise(mary)<~>~creative(mary)))&
((~patient(john)<~>patient(john))) | ~calm(mary) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 311344297060540728267116
% SZS output start Proof for 311344297060540728267116
1. ! [X0] : ((~old(X0) | calm(X0)) => funny(X0)) [input p0]
2. ! [X0] : ((funny(X0) | curious(X0)) <=> (~calm(X0) & ~tall(X0))) [input p1]
25. calm(mary) [input hypothesis]
26. ! [X0] : (funny(X0) | (old(X0) & ~calm(X0))) [ennf transformation 1]
31. ! [X0] : (((funny(X0) | curious(X0)) | (calm(X0) | tall(X0))) & ((~calm(X0) & ~tall(X0)) | (~funny(X0) & ~curious(X0)))) [nnf transformation 2]
32. ! [X0] : ((funny(X0) | curious(X0) | calm(X0) | tall(X0)) & ((~calm(X0) & ~tall(X0)) | (~funny(X0) & ~curious(X0)))) [flattening 31]
68. funny(X0) | ~calm(X0) [cnf transformation 26]
73. ~calm(X0) | ~funny(X0) [cnf transformation 32]
144. calm(mary) [cnf transformation 25]
150. ~calm(X0) [subsumption resolution 73,68]
241. $false [subsumption resolution 144,150]
% SZS output end Proof for 311344297060540728267116
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then someone is not tall. If paul is not creative then someone is either brave or not tall and vice versa. If susan is not kind or curious then someone is both not kind and wise. Everyone who is creative is quiet or not humble. Everyone who is not wise is either wise or strong. Everyone who is either not happy or calm is either rich or not humble and vice versa. If lucy is old or calm then fred is either not strong or wise and vice versa. If susan is old or rich then john is rich or not old and vice versa. Everyone who is not wise is not generous and vice versa. If someone is brave or strong then someone is generous. If someone is funny or curious then paul is both not humble and not old and vice versa. If someone is both not tall and not patient then susan is quiet and vice versa. Everyone who is generous or old is either tall or not wise. If lucy is both kind and not humble then fred is not funny or brave. Everyone who is both not generous and wise is both tall and patient. Everyone who is both not creative and quiet is both not curious and quiet. Fred is both curious and quiet. Someone is either tall or patient. Someone is not strong. Someone is not curious or not generous. Someone is not humble. Someone is curious or tall. Susan is both not rich and not curious. Alice is not strong or not humble. | Paul is old. | contradiction | ((?[X]:(tall(X)))=>(?[X]:(~tall(X))))&
((~creative(paul))<=>(?[X]:((brave(X)<~>~tall(X)))))&
(((~kind(susan)|curious(susan)))=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:(creative(X)=>(quiet(X)|~humble(X))))&
(![X]:(~wise(X)=>(wise(X)<~>strong(X))))&
(![X]:((~happy(X)<~>calm(X))<=>(rich(X)<~>~humble(X))))&
(((old(lucy)|calm(lucy)))<=>((~strong(fred)<~>wise(fred))))&
(((old(susan)|rich(susan)))<=>((rich(john)|~old(john))))&
(![X]:(~wise(X)<=>~generous(X)))&
((?[X]:((brave(X)|strong(X))))=>(?[X]:(generous(X))))&
((?[X]:((funny(X)|curious(X))))<=>((~humble(paul)&~old(paul))))&
((?[X]:((~tall(X)&~patient(X))))<=>(quiet(susan)))&
(![X]:((generous(X)|old(X))=>(tall(X)<~>~wise(X))))&
(((kind(lucy)&~humble(lucy)))=>((~funny(fred)|brave(fred))))&
(![X]:((~generous(X)&wise(X))=>(tall(X)&patient(X))))&
(![X]:((~creative(X)&quiet(X))=>(~curious(X)&quiet(X))))&
((curious(fred)&quiet(fred)))&
(?[X]:((tall(X)<~>patient(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~curious(X)|~generous(X))))&
(?[X]:(~humble(X)))&
(?[X]:((curious(X)|tall(X))))&
((~rich(susan)&~curious(susan)))&
((~strong(alice)|~humble(alice))) | old(paul) | [
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2073246924063436922969375
% SZS output start Proof for 2073246924063436922969375
11. ? [X0] : (curious(X0) | funny(X0)) <=> (~old(paul) & ~humble(paul)) [input p10]
17. quiet(fred) & curious(fred) [input p16]
25. old(paul) [input hypothesis]
60. (? [X0] : (curious(X0) | funny(X0)) | (old(paul) | humble(paul))) & ((~old(paul) & ~humble(paul)) | ! [X0] : (~curious(X0) & ~funny(X0))) [nnf transformation 11]
61. (? [X0] : (curious(X0) | funny(X0)) | old(paul) | humble(paul)) & ((~old(paul) & ~humble(paul)) | ! [X0] : (~curious(X0) & ~funny(X0))) [flattening 60]
62. (? [X0] : (curious(X0) | funny(X0)) | old(paul) | humble(paul)) & ((~old(paul) & ~humble(paul)) | ! [X1] : (~curious(X1) & ~funny(X1))) [rectify 61]
63. ? [X0] : (curious(X0) | funny(X0)) => (curious(sK4) | funny(sK4)) [choice axiom]
64. ((curious(sK4) | funny(sK4)) | old(paul) | humble(paul)) & ((~old(paul) & ~humble(paul)) | ! [X1] : (~curious(X1) & ~funny(X1))) [skolemisation 62,63]
118. ~old(paul) | ~curious(X1) [cnf transformation 64]
132. curious(fred) [cnf transformation 17]
143. old(paul) [cnf transformation 25]
257. 24 <=> old(paul) [avatar definition]
270. 27 <=> ! [X1] : ~curious(X1) [avatar definition]
271. ~curious(X1) <- (27) [avatar component clause 270]
272. 27 | ~24 [avatar split clause 118,257,270]
354. 24 [avatar split clause 143,257]
355. $false <- (27) [resolution 271,132]
356. ~27 [avatar contradiction clause 355]
357. $false [avatar sat refutation 272,354,356]
% SZS output end Proof for 2073246924063436922969375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and kind then someone is both not humble and funny and vice versa.
Everyone who is not curious is not happy.
Everyone who is both not tall and quiet is either strong or not brave.
Everyone who is strong is happy and vice versa.
If fred is tall then someone is both not creative and strong and vice versa.
If mary is both kind and generous then someone is not patient or tall and vice versa.
If someone is not strong then someone is either generous or not quiet and vice versa.
Everyone who is not patient or not generous is old and vice versa.
If susan is both humble and not happy then lucy is both curious and not funny and vice versa.
Everyone who is not kind or not funny is either curious or generous.
If fred is both not creative and old then someone is either generous or not generous.
Everyone who is old is both not strong and not rich and vice versa.
Everyone who is either not old or not funny is both patient and not generous and vice versa.
Everyone who is either not kind or not creative is both not humble and not happy and vice versa.
Everyone who is both not quiet and not patient is not funny or wise.
If paul is not funny or patient then someone is both rich and happy and vice versa.
Someone is not strong or not patient.
Paul is happy or wise.
Someone is either quiet or wise.
Someone is generous or creative.
Lucy is both not curious and not strong.
Someone is either humble or not strong.
Someone is not wise. | Paul is not rich. | entailment | ((?[X]:((funny(X)&kind(X))))<=>(?[X]:((~humble(X)&funny(X)))))&
(![X]:(~curious(X)=>~happy(X)))&
(![X]:((~tall(X)&quiet(X))=>(strong(X)<~>~brave(X))))&
(![X]:(strong(X)<=>happy(X)))&
((tall(fred))<=>(?[X]:((~creative(X)&strong(X)))))&
(((kind(mary)&generous(mary)))<=>(?[X]:((~patient(X)|tall(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
(![X]:((~patient(X)|~generous(X))<=>old(X)))&
(((humble(susan)&~happy(susan)))<=>((curious(lucy)&~funny(lucy))))&
(![X]:((~kind(X)|~funny(X))=>(curious(X)<~>generous(X))))&
(((~creative(fred)&old(fred)))=>(?[X]:((generous(X)<~>~generous(X)))))&
(![X]:(old(X)<=>(~strong(X)&~rich(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(patient(X)&~generous(X))))&
(![X]:((~kind(X)<~>~creative(X))<=>(~humble(X)&~happy(X))))&
(![X]:((~quiet(X)&~patient(X))=>(~funny(X)|wise(X))))&
(((~funny(paul)|patient(paul)))<=>(?[X]:((rich(X)&happy(X)))))&
(?[X]:((~strong(X)|~patient(X))))&
((happy(paul)|wise(paul)))&
(?[X]:((quiet(X)<~>wise(X))))&
(?[X]:((generous(X)|creative(X))))&
((~curious(lucy)&~strong(lucy)))&
(?[X]:((humble(X)<~>~strong(X))))&
(?[X]:(~wise(X))) | ~rich(paul) | [
"p1",
"p7",
"p9",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4157771723157296741448531
% SZS output start Proof for 4157771723157296741448531
2. ! [X0] : (~curious(X0) => ~happy(X0)) [input p1]
8. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> old(X0)) [input p7]
10. ! [X0] : ((~funny(X0) | ~kind(X0)) => (curious(X0) <~> generous(X0))) [input p9]
12. ! [X0] : (old(X0) <=> (~rich(X0) & ~strong(X0))) [input p11]
13. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> (~generous(X0) & patient(X0))) [input p12]
16. (patient(paul) | ~funny(paul)) <=> ? [X0] : (happy(X0) & rich(X0)) [input p15]
24. rich(paul) [input hypothesis]
27. ! [X0] : (~happy(X0) | curious(X0)) [ennf transformation 2]
30. ! [X0] : ((curious(X0) <~> generous(X0)) | (funny(X0) & kind(X0))) [ennf transformation 10]
56. ! [X0] : (((~generous(X0) | ~patient(X0)) | ~old(X0)) & (old(X0) | (generous(X0) & patient(X0)))) [nnf transformation 8]
57. ! [X0] : ((~generous(X0) | ~patient(X0) | ~old(X0)) & (old(X0) | (generous(X0) & patient(X0)))) [flattening 56]
60. ! [X0] : (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | (funny(X0) & kind(X0))) [nnf transformation 30]
64. ! [X0] : ((old(X0) | (rich(X0) | strong(X0))) & ((~rich(X0) & ~strong(X0)) | ~old(X0))) [nnf transformation 12]
65. ! [X0] : ((old(X0) | rich(X0) | strong(X0)) & ((~rich(X0) & ~strong(X0)) | ~old(X0))) [flattening 64]
66. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | (generous(X0) | ~patient(X0))) & ((~generous(X0) & patient(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 13]
67. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | generous(X0) | ~patient(X0)) & ((~generous(X0) & patient(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [flattening 66]
70. ((patient(paul) | ~funny(paul)) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X0] : (happy(X0) & rich(X0)) | (~patient(paul) & funny(paul))) [nnf transformation 16]
71. (patient(paul) | ~funny(paul) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X0] : (happy(X0) & rich(X0)) | (~patient(paul) & funny(paul))) [flattening 70]
72. (patient(paul) | ~funny(paul) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X1] : (happy(X1) & rich(X1)) | (~patient(paul) & funny(paul))) [rectify 71]
73. ? [X1] : (happy(X1) & rich(X1)) => (happy(sK7) & rich(sK7)) [choice axiom]
74. (patient(paul) | ~funny(paul) | ! [X0] : (~happy(X0) | ~rich(X0))) & ((happy(sK7) & rich(sK7)) | (~patient(paul) & funny(paul))) [skolemisation 72,73]
91. ~happy(X0) | curious(X0) [cnf transformation 27]
109. old(X0) | generous(X0) [cnf transformation 57]
118. ~generous(X0) | ~curious(X0) | funny(X0) [cnf transformation 60]
122. ~rich(X0) | ~old(X0) [cnf transformation 65]
126. ~generous(X0) | ~funny(X0) | old(X0) [cnf transformation 67]
137. rich(sK7) | funny(paul) [cnf transformation 74]
139. happy(sK7) | funny(paul) [cnf transformation 74]
152. rich(paul) [cnf transformation 24]
270. ~funny(X0) | old(X0) [subsumption resolution 126,109]
283. 29 <=> happy(sK7) [avatar definition]
285. happy(sK7) <- (29) [avatar component clause 283]
288. 30 <=> funny(paul) [avatar definition]
290. funny(paul) <- (30) [avatar component clause 288]
291. 30 | 29 [avatar split clause 139,283,288]
293. 31 <=> rich(sK7) [avatar definition]
295. rich(sK7) <- (31) [avatar component clause 293]
297. 30 | 31 [avatar split clause 137,293,288]
353. ~old(paul) [resolution 122,152]
360. curious(sK7) <- (29) [resolution 285,91]
361. ~old(sK7) <- (31) [resolution 295,122]
371. generous(sK7) <- (31) [resolution 361,109]
374. old(paul) <- (30) [resolution 270,290]
375. $false <- (30) [subsumption resolution 374,353]
376. ~30 [avatar contradiction clause 375]
490. ~curious(sK7) | funny(sK7) <- (31) [resolution 371,118]
492. funny(sK7) <- (29, 31) [subsumption resolution 490,360]
621. old(sK7) <- (29, 31) [resolution 492,270]
622. $false <- (29, 31) [subsumption resolution 621,361]
623. ~29 | ~31 [avatar contradiction clause 622]
624. $false [avatar sat refutation 291,297,376,623]
% SZS output end Proof for 4157771723157296741448531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not humble is rich.
Everyone who is happy is both quiet and not calm and vice versa.
If someone is kind then john is both creative and not patient and vice versa.
Everyone who is not old is brave or not tall.
If john is generous then paul is not tall or not kind.
If someone is both wise and not curious then susan is not funny or funny and vice versa.
If mary is not wise or not patient then someone is funny.
Everyone who is not wise or not old is both not old and not happy and vice versa.
If someone is both not kind and old then someone is either curious or humble and vice versa.
Everyone who is not calm or not funny is both humble and old and vice versa.
Everyone who is not kind or not quiet is either not quiet or rich.
Everyone who is not creative or calm is both not rich and not humble.
If fred is generous then alice is not happy.
Everyone who is either brave or patient is both brave and rich.
Everyone who is not humble is both happy and strong and vice versa.
Someone is either not funny or not humble.
Someone is both generous and not patient.
Someone is quiet or generous.
Fred is not kind or patient.
Mary is humble.
Lucy is wise or strong. | Lucy is funny. | neutral | (![X]:((~kind(X)|~humble(X))=>rich(X)))&
(![X]:(happy(X)<=>(quiet(X)&~calm(X))))&
((?[X]:(kind(X)))<=>((creative(john)&~patient(john))))&
(![X]:(~old(X)=>(brave(X)|~tall(X))))&
((generous(john))=>((~tall(paul)|~kind(paul))))&
((?[X]:((wise(X)&~curious(X))))<=>((~funny(susan)|funny(susan))))&
(((~wise(mary)|~patient(mary)))=>(?[X]:(funny(X))))&
(![X]:((~wise(X)|~old(X))<=>(~old(X)&~happy(X))))&
((?[X]:((~kind(X)&old(X))))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((~calm(X)|~funny(X))<=>(humble(X)&old(X))))&
(![X]:((~kind(X)|~quiet(X))=>(~quiet(X)<~>rich(X))))&
(![X]:((~creative(X)|calm(X))=>(~rich(X)&~humble(X))))&
((generous(fred))=>(~happy(alice)))&
(![X]:((brave(X)<~>patient(X))=>(brave(X)&rich(X))))&
(![X]:(~humble(X)<=>(happy(X)&strong(X))))&
(?[X]:((~funny(X)<~>~humble(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((quiet(X)|generous(X))))&
((~kind(fred)|patient(fred)))&
(humble(mary))&
((wise(lucy)|strong(lucy))) | funny(lucy) | [] | null | 0 |
If someone is not quiet then someone is not strong and vice versa.
If fred is either rich or not old then john is not quiet.
Everyone who is both quiet and not old is not patient or calm.
If someone is either not brave or not patient then alice is either rich or not humble and vice versa.
Everyone who is either not brave or happy is both not humble and patient and vice versa.
If lucy is not wise or not tall then alice is kind.
Everyone who is wise or tall is humble and vice versa.
Everyone who is both not curious and tall is either not curious or tall.
Everyone who is either generous or calm is either rich or humble.
Everyone who is either not quiet or not tall is either creative or not humble and vice versa.
If someone is both not calm and not old then paul is generous and vice versa.
Everyone who is not strong is funny or not calm.
If john is both brave and creative then someone is not old or generous.
Everyone who is both old and generous is either tall or not quiet.
If someone is either not brave or funny then alice is either not rich or not old and vice versa.
If someone is both brave and patient then susan is generous and vice versa.
Someone is funny.
John is not quiet.
Someone is both not humble and not funny.
Someone is either not old or humble.
Mary is both not creative and not calm.
Mary is either quiet or not calm.
Lucy is either not wise or not curious.
Someone is not patient. | Mary is tall. | contradiction | ((?[X]:(~quiet(X)))<=>(?[X]:(~strong(X))))&
(((rich(fred)<~>~old(fred)))=>(~quiet(john)))&
(![X]:((quiet(X)&~old(X))=>(~patient(X)|calm(X))))&
((?[X]:((~brave(X)<~>~patient(X))))<=>((rich(alice)<~>~humble(alice))))&
(![X]:((~brave(X)<~>happy(X))<=>(~humble(X)&patient(X))))&
(((~wise(lucy)|~tall(lucy)))=>(kind(alice)))&
(![X]:((wise(X)|tall(X))<=>humble(X)))&
(![X]:((~curious(X)&tall(X))=>(~curious(X)<~>tall(X))))&
(![X]:((generous(X)<~>calm(X))=>(rich(X)<~>humble(X))))&
(![X]:((~quiet(X)<~>~tall(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((~calm(X)&~old(X))))<=>(generous(paul)))&
(![X]:(~strong(X)=>(funny(X)|~calm(X))))&
(((brave(john)&creative(john)))=>(?[X]:((~old(X)|generous(X)))))&
(![X]:((old(X)&generous(X))=>(tall(X)<~>~quiet(X))))&
((?[X]:((~brave(X)<~>funny(X))))<=>((~rich(alice)<~>~old(alice))))&
((?[X]:((brave(X)&patient(X))))<=>(generous(susan)))&
(?[X]:(funny(X)))&
(~quiet(john))&
(?[X]:((~humble(X)&~funny(X))))&
(?[X]:((~old(X)<~>humble(X))))&
((~creative(mary)&~calm(mary)))&
((quiet(mary)<~>~calm(mary)))&
((~wise(lucy)<~>~curious(lucy)))&
(?[X]:(~patient(X))) | tall(mary) | [
"p6",
"p9",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4455202137878620493513069
% SZS output start Proof for 4455202137878620493513069
7. ! [X0] : ((tall(X0) | wise(X0)) <=> humble(X0)) [input p6]
10. ! [X0] : ((~quiet(X0) <~> ~tall(X0)) <=> (creative(X0) <~> ~humble(X0))) [input p9]
21. ~calm(mary) & ~creative(mary) [input p20]
22. quiet(mary) <~> ~calm(mary) [input p21]
25. tall(mary) [input hypothesis]
52. ! [X0] : (((tall(X0) | wise(X0)) | ~humble(X0)) & (humble(X0) | (~tall(X0) & ~wise(X0)))) [nnf transformation 7]
53. ! [X0] : ((tall(X0) | wise(X0) | ~humble(X0)) & (humble(X0) | (~tall(X0) & ~wise(X0)))) [flattening 52]
56. ! [X0] : ((((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))))) [nnf transformation 10]
79. (calm(mary) | ~quiet(mary)) & (~calm(mary) | quiet(mary)) [nnf transformation 22]
103. ~tall(X0) | humble(X0) [cnf transformation 53]
111. ~humble(X0) | creative(X0) | ~tall(X0) | quiet(X0) [cnf transformation 56]
143. ~creative(mary) [cnf transformation 21]
144. ~calm(mary) [cnf transformation 21]
146. calm(mary) | ~quiet(mary) [cnf transformation 79]
150. tall(mary) [cnf transformation 25]
215. ~tall(X0) | creative(X0) | quiet(X0) [subsumption resolution 111,103]
306. ~quiet(mary) [subsumption resolution 146,144]
365. creative(mary) | quiet(mary) [resolution 215,150]
366. quiet(mary) [subsumption resolution 365,143]
367. $false [subsumption resolution 366,306]
% SZS output end Proof for 4455202137878620493513069
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If mary is creative or not curious then someone is both not brave and creative.
If lucy is either humble or old then fred is not brave.
If someone is not kind then john is both wise and old.
Everyone who is not quiet or strong is quiet or not creative and vice versa.
Everyone who is not humble is strong and vice versa.
Everyone who is not strong or old is not kind and vice versa.
Everyone who is not patient or not brave is either funny or happy and vice versa.
Everyone who is both not humble and kind is both kind and rich and vice versa.
If john is strong or quiet then someone is not patient.
Everyone who is creative is both not rich and wise and vice versa.
Everyone who is funny or tall is tall and vice versa.
Everyone who is not old or not funny is both not humble and not quiet.
If lucy is humble then alice is either not generous or tall and vice versa.
If someone is both not calm and funny then someone is not funny or brave and vice versa.
If mary is tall or not humble then someone is either wise or funny.
If someone is both wise and funny then alice is old and vice versa.
Fred is either not curious or brave.
Someone is both patient and not old.
Alice is either not strong or strong.
Lucy is either generous or rich.
Mary is not curious.
Mary is not old.
Fred is both not kind and rich.
Paul is not old. | Paul is quiet. | contradiction | (((creative(mary)|~curious(mary)))=>(?[X]:((~brave(X)&creative(X)))))&
(((humble(lucy)<~>old(lucy)))=>(~brave(fred)))&
((?[X]:(~kind(X)))=>((wise(john)&old(john))))&
(![X]:((~quiet(X)|strong(X))<=>(quiet(X)|~creative(X))))&
(![X]:(~humble(X)<=>strong(X)))&
(![X]:((~strong(X)|old(X))<=>~kind(X)))&
(![X]:((~patient(X)|~brave(X))<=>(funny(X)<~>happy(X))))&
(![X]:((~humble(X)&kind(X))<=>(kind(X)&rich(X))))&
(((strong(john)|quiet(john)))=>(?[X]:(~patient(X))))&
(![X]:(creative(X)<=>(~rich(X)&wise(X))))&
(![X]:((funny(X)|tall(X))<=>tall(X)))&
(![X]:((~old(X)|~funny(X))=>(~humble(X)&~quiet(X))))&
((humble(lucy))<=>((~generous(alice)<~>tall(alice))))&
((?[X]:((~calm(X)&funny(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(((tall(mary)|~humble(mary)))=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((wise(X)&funny(X))))<=>(old(alice)))&
((~curious(fred)<~>brave(fred)))&
(?[X]:((patient(X)&~old(X))))&
((~strong(alice)<~>strong(alice)))&
((generous(lucy)<~>rich(lucy)))&
(~curious(mary))&
(~old(mary))&
((~kind(fred)&rich(fred)))&
(~old(paul)) | quiet(paul) | [
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 868539017449646175661341
% SZS output start Proof for 868539017449646175661341
12. ! [X0] : ((~funny(X0) | ~old(X0)) => (~quiet(X0) & ~humble(X0))) [input p11]
24. ~old(paul) [input p23]
25. quiet(paul) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & ~humble(X0)) | (funny(X0) & old(X0))) [ennf transformation 12]
106. ~quiet(X0) | old(X0) [cnf transformation 31]
136. ~old(paul) [cnf transformation 24]
137. quiet(paul) [cnf transformation 25]
310. old(paul) [resolution 106,137]
311. $false [subsumption resolution 310,136]
% SZS output end Proof for 868539017449646175661341
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and curious is either not humble or tall. Everyone who is either not old or not strong is either wise or tall. Everyone who is either not humble or strong is both kind and wise. Everyone who is both curious and not strong is both rich and generous. Everyone who is both not kind and not tall is both not kind and wise. If someone is not creative or not quiet then mary is both not generous and patient. If someone is not patient or not old then someone is both not wise and not kind and vice versa. Everyone who is humble is both humble and not strong. Everyone who is tall is not funny. Everyone who is either generous or wise is quiet or not kind and vice versa. Everyone who is strong is humble and vice versa. Everyone who is both quiet and not patient is either brave or old and vice versa. Everyone who is not generous is quiet or creative and vice versa. If someone is both happy and not tall then someone is either old or creative and vice versa. Someone is either curious or tall. Paul is not calm or old. Fred is happy. Paul is not creative or kind. | Fred is not rich. | neutral | (![X]:((strong(X)&curious(X))=>(~humble(X)<~>tall(X))))&
(![X]:((~old(X)<~>~strong(X))=>(wise(X)<~>tall(X))))&
(![X]:((~humble(X)<~>strong(X))=>(kind(X)&wise(X))))&
(![X]:((curious(X)&~strong(X))=>(rich(X)&generous(X))))&
(![X]:((~kind(X)&~tall(X))=>(~kind(X)&wise(X))))&
((?[X]:((~creative(X)|~quiet(X))))=>((~generous(mary)&patient(mary))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(humble(X)=>(humble(X)&~strong(X))))&
(![X]:(tall(X)=>~funny(X)))&
(![X]:((generous(X)<~>wise(X))<=>(quiet(X)|~kind(X))))&
(![X]:(strong(X)<=>humble(X)))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>old(X))))&
(![X]:(~generous(X)<=>(quiet(X)|creative(X))))&
((?[X]:((happy(X)&~tall(X))))<=>(?[X]:((old(X)<~>creative(X)))))&
(?[X]:((curious(X)<~>tall(X))))&
((~calm(paul)|old(paul)))&
(happy(fred))&
((~creative(paul)|kind(paul))) | ~rich(fred) | [] | null | 0 |
If someone is tall then someone is not quiet or brave and vice versa.
If mary is not patient then lucy is not wise.
Everyone who is quiet is either creative or not tall and vice versa.
Everyone who is not creative or not quiet is either not tall or not patient.
If fred is both humble and not quiet then alice is either happy or not rich.
If someone is both quiet and happy then someone is brave or generous.
Everyone who is both not tall and not happy is not patient or wise and vice versa.
If someone is rich or not patient then someone is not rich or not old.
If susan is strong or not wise then someone is both not kind and brave.
Everyone who is either not happy or creative is either not creative or not funny.
Everyone who is both patient and not funny is both not tall and not funny.
Everyone who is not creative or not tall is generous or patient and vice versa.
Everyone who is both kind and generous is not tall and vice versa.
Everyone who is both tall and not generous is either generous or not generous.
Everyone who is both not strong and tall is either strong or tall and vice versa.
Someone is kind.
Mary is either calm or not curious.
Someone is not creative.
Someone is not wise.
Alice is not generous or not tall. | Lucy is not generous. | contradiction | ((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)|brave(X)))))&
((~patient(mary))=>(~wise(lucy)))&
(![X]:(quiet(X)<=>(creative(X)<~>~tall(X))))&
(![X]:((~creative(X)|~quiet(X))=>(~tall(X)<~>~patient(X))))&
(((humble(fred)&~quiet(fred)))=>((happy(alice)<~>~rich(alice))))&
((?[X]:((quiet(X)&happy(X))))=>(?[X]:((brave(X)|generous(X)))))&
(![X]:((~tall(X)&~happy(X))<=>(~patient(X)|wise(X))))&
((?[X]:((rich(X)|~patient(X))))=>(?[X]:((~rich(X)|~old(X)))))&
(((strong(susan)|~wise(susan)))=>(?[X]:((~kind(X)&brave(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((patient(X)&~funny(X))=>(~tall(X)&~funny(X))))&
(![X]:((~creative(X)|~tall(X))<=>(generous(X)|patient(X))))&
(![X]:((kind(X)&generous(X))<=>~tall(X)))&
(![X]:((tall(X)&~generous(X))=>(generous(X)<~>~generous(X))))&
(![X]:((~strong(X)&tall(X))<=>(strong(X)<~>tall(X))))&
(?[X]:(kind(X)))&
((calm(mary)<~>~curious(mary)))&
(?[X]:(~creative(X)))&
(?[X]:(~wise(X)))&
((~generous(alice)|~tall(alice))) | ~generous(lucy) | [
"p3",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1401400845573695377702637
% SZS output start Proof for 1401400845573695377702637
4. ! [X0] : ((~quiet(X0) | ~creative(X0)) => (~tall(X0) <~> ~patient(X0))) [input p3]
7. ! [X0] : ((~happy(X0) & ~tall(X0)) <=> (wise(X0) | ~patient(X0))) [input p6]
12. ! [X0] : ((~tall(X0) | ~creative(X0)) <=> (patient(X0) | generous(X0))) [input p11]
13. ! [X0] : ((generous(X0) & kind(X0)) <=> ~tall(X0)) [input p12]
21. ~generous(lucy) [input hypothesis]
28. ! [X0] : ((~tall(X0) <~> ~patient(X0)) | (quiet(X0) & creative(X0))) [ennf transformation 4]
42. ! [X0] : (((patient(X0) | tall(X0)) & (~patient(X0) | ~tall(X0))) | (quiet(X0) & creative(X0))) [nnf transformation 28]
46. ! [X0] : (((~happy(X0) & ~tall(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (happy(X0) | tall(X0)))) [nnf transformation 7]
47. ! [X0] : (((~happy(X0) & ~tall(X0)) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | happy(X0) | tall(X0))) [flattening 46]
51. ! [X0] : (((~tall(X0) | ~creative(X0)) | (~patient(X0) & ~generous(X0))) & ((patient(X0) | generous(X0)) | (tall(X0) & creative(X0)))) [nnf transformation 12]
52. ! [X0] : ((~tall(X0) | ~creative(X0) | (~patient(X0) & ~generous(X0))) & (patient(X0) | generous(X0) | (tall(X0) & creative(X0)))) [flattening 51]
53. ! [X0] : (((generous(X0) & kind(X0)) | tall(X0)) & (~tall(X0) | (~generous(X0) | ~kind(X0)))) [nnf transformation 13]
54. ! [X0] : (((generous(X0) & kind(X0)) | tall(X0)) & (~tall(X0) | ~generous(X0) | ~kind(X0))) [flattening 53]
73. ~patient(X0) | ~tall(X0) | creative(X0) [cnf transformation 42]
79. ~tall(X0) | patient(X0) [cnf transformation 47]
96. ~tall(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 52]
99. generous(X0) | tall(X0) [cnf transformation 54]
114. ~generous(lucy) [cnf transformation 21]
136. 4 <=> ! [X3] : ~tall(X3) [avatar definition]
137. ~tall(X3) <- (4) [avatar component clause 136]
189. ~tall(X0) | ~patient(X0) [subsumption resolution 96,73]
190. ~tall(X0) [subsumption resolution 189,79]
191. 4 [avatar split clause 190,136]
215. tall(lucy) [resolution 99,114]
217. $false <- (4) [subsumption resolution 215,137]
218. ~4 [avatar contradiction clause 217]
221. $false [avatar sat refutation 191,218]
% SZS output end Proof for 1401400845573695377702637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not old then someone is both not generous and happy.
Everyone who is not brave or creative is both not rich and not wise and vice versa.
If someone is either not patient or calm then someone is both happy and not calm.
Everyone who is kind or not happy is both wise and not old and vice versa.
If someone is not kind then alice is patient or not brave and vice versa.
Everyone who is not creative or old is kind or not strong and vice versa.
If mary is brave or not curious then lucy is not funny.
If paul is tall or not creative then paul is not quiet or wise.
Everyone who is not humble or quiet is curious and vice versa.
Everyone who is either not strong or not calm is not happy and vice versa.
Everyone who is not happy or calm is not calm or curious.
Everyone who is not funny or patient is both brave and creative.
Everyone who is both not tall and wise is kind or not creative and vice versa.
If john is both not old and not strong then paul is happy.
Everyone who is not happy or not kind is either happy or not brave and vice versa.
Everyone who is not humble is not kind and vice versa.
Someone is rich or calm.
Fred is not rich or tall.
John is not patient.
Someone is either not wise or old.
Someone is not patient.
Someone is quiet or not patient.
Someone is funny or wise. | Lucy is brave. | entailment | ((?[X]:((kind(X)|~old(X))))=>(?[X]:((~generous(X)&happy(X)))))&
(![X]:((~brave(X)|creative(X))<=>(~rich(X)&~wise(X))))&
((?[X]:((~patient(X)<~>calm(X))))=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((kind(X)|~happy(X))<=>(wise(X)&~old(X))))&
((?[X]:(~kind(X)))<=>((patient(alice)|~brave(alice))))&
(![X]:((~creative(X)|old(X))<=>(kind(X)|~strong(X))))&
(((brave(mary)|~curious(mary)))=>(~funny(lucy)))&
(((tall(paul)|~creative(paul)))=>((~quiet(paul)|wise(paul))))&
(![X]:((~humble(X)|quiet(X))<=>curious(X)))&
(![X]:((~strong(X)<~>~calm(X))<=>~happy(X)))&
(![X]:((~happy(X)|calm(X))=>(~calm(X)|curious(X))))&
(![X]:((~funny(X)|patient(X))=>(brave(X)&creative(X))))&
(![X]:((~tall(X)&wise(X))<=>(kind(X)|~creative(X))))&
(((~old(john)&~strong(john)))=>(happy(paul)))&
(![X]:((~happy(X)|~kind(X))<=>(happy(X)<~>~brave(X))))&
(![X]:(~humble(X)<=>~kind(X)))&
(?[X]:((rich(X)|calm(X))))&
((~rich(fred)|tall(fred)))&
(~patient(john))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:(~patient(X)))&
(?[X]:((quiet(X)|~patient(X))))&
(?[X]:((funny(X)|wise(X)))) | brave(lucy) | [
"p1",
"p3",
"p5",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6883865583371718093346887
% SZS output start Proof for 6883865583371718093346887
2. ! [X0] : ((creative(X0) | ~brave(X0)) <=> (~wise(X0) & ~rich(X0))) [input p1]
4. ! [X0] : ((~happy(X0) | kind(X0)) <=> (~old(X0) & wise(X0))) [input p3]
6. ! [X0] : ((old(X0) | ~creative(X0)) <=> (~strong(X0) | kind(X0))) [input p5]
13. ! [X0] : ((wise(X0) & ~tall(X0)) <=> (~creative(X0) | kind(X0))) [input p12]
15. ! [X0] : ((~kind(X0) | ~happy(X0)) <=> (happy(X0) <~> ~brave(X0))) [input p14]
24. ~brave(lucy) [input hypothesis]
46. ! [X0] : (((creative(X0) | ~brave(X0)) | (wise(X0) | rich(X0))) & ((~wise(X0) & ~rich(X0)) | (~creative(X0) & brave(X0)))) [nnf transformation 2]
47. ! [X0] : ((creative(X0) | ~brave(X0) | wise(X0) | rich(X0)) & ((~wise(X0) & ~rich(X0)) | (~creative(X0) & brave(X0)))) [flattening 46]
52. ! [X0] : (((~happy(X0) | kind(X0)) | (old(X0) | ~wise(X0))) & ((~old(X0) & wise(X0)) | (happy(X0) & ~kind(X0)))) [nnf transformation 4]
53. ! [X0] : ((~happy(X0) | kind(X0) | old(X0) | ~wise(X0)) & ((~old(X0) & wise(X0)) | (happy(X0) & ~kind(X0)))) [flattening 52]
59. ! [X0] : (((old(X0) | ~creative(X0)) | (strong(X0) & ~kind(X0))) & ((~strong(X0) | kind(X0)) | (~old(X0) & creative(X0)))) [nnf transformation 6]
60. ! [X0] : ((old(X0) | ~creative(X0) | (strong(X0) & ~kind(X0))) & (~strong(X0) | kind(X0) | (~old(X0) & creative(X0)))) [flattening 59]
62. ! [X0] : (((wise(X0) & ~tall(X0)) | (creative(X0) & ~kind(X0))) & ((~creative(X0) | kind(X0)) | (~wise(X0) | tall(X0)))) [nnf transformation 13]
63. ! [X0] : (((wise(X0) & ~tall(X0)) | (creative(X0) & ~kind(X0))) & (~creative(X0) | kind(X0) | ~wise(X0) | tall(X0))) [flattening 62]
64. ! [X0] : (((~kind(X0) | ~happy(X0)) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) & (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (kind(X0) & happy(X0)))) [nnf transformation 15]
65. ! [X0] : ((~kind(X0) | ~happy(X0) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) & (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (kind(X0) & happy(X0)))) [flattening 64]
81. ~wise(X0) | brave(X0) [cnf transformation 47]
89. wise(X0) | happy(X0) [cnf transformation 53]
90. ~old(X0) | ~kind(X0) [cnf transformation 53]
98. old(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 60]
119. wise(X0) | creative(X0) [cnf transformation 63]
121. ~brave(X0) | happy(X0) | happy(X0) [cnf transformation 65]
124. ~happy(X0) | brave(X0) | kind(X0) [cnf transformation 65]
136. ~brave(lucy) [cnf transformation 24]
137. ~brave(X0) | happy(X0) [duplicate literal removal 121]
188. ~creative(X0) | ~kind(X0) [subsumption resolution 98,90]
285. happy(X1) | brave(X1) [resolution 89,81]
286. happy(X1) [subsumption resolution 285,137]
294. creative(X1) | brave(X1) [resolution 119,81]
307. brave(X2) | ~kind(X2) [resolution 294,188]
330. brave(X0) | kind(X0) [resolution 124,286]
333. brave(X0) [subsumption resolution 330,307]
352. $false [resolution 333,136]
% SZS output end Proof for 6883865583371718093346887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or generous is creative and vice versa.
Everyone who is not strong is generous or not funny.
If someone is both not patient and not funny then someone is calm or curious and vice versa.
Everyone who is either not old or not funny is calm or wise.
If someone is not funny then alice is either not quiet or generous.
Everyone who is both not patient and quiet is either rich or not humble and vice versa.
If lucy is both wise and not brave then someone is strong or not generous.
Everyone who is either happy or not generous is either tall or curious.
Everyone who is wise is either kind or happy and vice versa.
Everyone who is either not funny or not old is wise or old and vice versa.
Everyone who is both calm and not calm is happy or not humble and vice versa.
If someone is humble then mary is not happy and vice versa.
Everyone who is either old or not humble is both kind and not humble.
If alice is not funny then someone is not wise or not calm and vice versa.
Everyone who is funny is both funny and brave and vice versa.
Everyone who is both not brave and not calm is both old and funny.
Paul is either rich or calm.
Someone is not generous.
Lucy is not old.
Someone is rich or not old.
Someone is both not happy and not strong.
Lucy is either wise or happy. | Alice is not kind. | entailment | (![X]:((~strong(X)<~>generous(X))<=>creative(X)))&
(![X]:(~strong(X)=>(generous(X)|~funny(X))))&
((?[X]:((~patient(X)&~funny(X))))<=>(?[X]:((calm(X)|curious(X)))))&
(![X]:((~old(X)<~>~funny(X))=>(calm(X)|wise(X))))&
((?[X]:(~funny(X)))=>((~quiet(alice)<~>generous(alice))))&
(![X]:((~patient(X)&quiet(X))<=>(rich(X)<~>~humble(X))))&
(((wise(lucy)&~brave(lucy)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((happy(X)<~>~generous(X))=>(tall(X)<~>curious(X))))&
(![X]:(wise(X)<=>(kind(X)<~>happy(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(wise(X)|old(X))))&
(![X]:((calm(X)&~calm(X))<=>(happy(X)|~humble(X))))&
((?[X]:(humble(X)))<=>(~happy(mary)))&
(![X]:((old(X)<~>~humble(X))=>(kind(X)&~humble(X))))&
((~funny(alice))<=>(?[X]:((~wise(X)|~calm(X)))))&
(![X]:(funny(X)<=>(funny(X)&brave(X))))&
(![X]:((~brave(X)&~calm(X))=>(old(X)&funny(X))))&
((rich(paul)<~>calm(paul)))&
(?[X]:(~generous(X)))&
(~old(lucy))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((~happy(X)&~strong(X))))&
((wise(lucy)<~>happy(lucy))) | ~kind(alice) | [
"p2",
"p8",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2224099618857634835929347
% SZS output start Proof for 2224099618857634835929347
3. ? [X0] : (~funny(X0) & ~patient(X0)) <=> ? [X0] : (curious(X0) | calm(X0)) [input p2]
9. ! [X0] : (wise(X0) <=> (kind(X0) <~> happy(X0))) [input p8]
10. ! [X0] : ((~funny(X0) <~> ~old(X0)) <=> (old(X0) | wise(X0))) [input p9]
11. ! [X0] : ((~calm(X0) & calm(X0)) <=> (~humble(X0) | happy(X0))) [input p10]
13. ! [X0] : ((old(X0) <~> ~humble(X0)) => (~humble(X0) & kind(X0))) [input p12]
14. ~funny(alice) <=> ? [X0] : (~calm(X0) | ~wise(X0)) [input p13]
23. kind(alice) [input hypothesis]
24. ? [X0] : (~funny(X0) & ~patient(X0)) <=> ? [X1] : (curious(X1) | calm(X1)) [rectify 3]
33. ! [X0] : ((~humble(X0) & kind(X0)) | (old(X0) <=> ~humble(X0))) [ennf transformation 13]
36. (? [X0] : (~funny(X0) & ~patient(X0)) | ! [X1] : (~curious(X1) & ~calm(X1))) & (? [X1] : (curious(X1) | calm(X1)) | ! [X0] : (funny(X0) | patient(X0))) [nnf transformation 24]
37. (? [X0] : (~funny(X0) & ~patient(X0)) | ! [X1] : (~curious(X1) & ~calm(X1))) & (? [X2] : (curious(X2) | calm(X2)) | ! [X3] : (funny(X3) | patient(X3))) [rectify 36]
38. ? [X0] : (~funny(X0) & ~patient(X0)) => (~funny(sK0) & ~patient(sK0)) [choice axiom]
39. ? [X2] : (curious(X2) | calm(X2)) => (curious(sK1) | calm(sK1)) [choice axiom]
40. ((~funny(sK0) & ~patient(sK0)) | ! [X1] : (~curious(X1) & ~calm(X1))) & ((curious(sK1) | calm(sK1)) | ! [X3] : (funny(X3) | patient(X3))) [skolemisation 37,39,38]
48. ! [X0] : ((wise(X0) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ~wise(X0))) [nnf transformation 9]
49. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (~old(X0) & ~wise(X0))) & ((old(X0) | wise(X0)) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [nnf transformation 10]
50. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (~old(X0) & ~wise(X0))) & (old(X0) | wise(X0) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [flattening 49]
51. ! [X0] : (((~calm(X0) & calm(X0)) | (humble(X0) & ~happy(X0))) & ((~humble(X0) | happy(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 11]
52. ! [X0] : (((~calm(X0) & calm(X0)) | (humble(X0) & ~happy(X0))) & (~humble(X0) | happy(X0) | calm(X0) | ~calm(X0))) [flattening 51]
57. ! [X0] : ((~humble(X0) & kind(X0)) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0)))) [nnf transformation 33]
58. (~funny(alice) | ! [X0] : (calm(X0) & wise(X0))) & (? [X0] : (~calm(X0) | ~wise(X0)) | funny(alice)) [nnf transformation 14]
59. (~funny(alice) | ! [X0] : (calm(X0) & wise(X0))) & (? [X1] : (~calm(X1) | ~wise(X1)) | funny(alice)) [rectify 58]
60. ? [X1] : (~calm(X1) | ~wise(X1)) => (~calm(sK4) | ~wise(sK4)) [choice axiom]
61. (~funny(alice) | ! [X0] : (calm(X0) & wise(X0))) & ((~calm(sK4) | ~wise(sK4)) | funny(alice)) [skolemisation 59,60]
76. ~funny(sK0) | ~calm(X1) [cnf transformation 40]
95. ~kind(X0) | happy(X0) | wise(X0) [cnf transformation 48]
101. ~wise(X0) | funny(X0) | old(X0) [cnf transformation 50]
104. calm(X0) | ~happy(X0) [cnf transformation 52]
105. calm(X0) | humble(X0) [cnf transformation 52]
106. ~happy(X0) | ~calm(X0) [cnf transformation 52]
107. ~calm(X0) | humble(X0) [cnf transformation 52]
112. ~humble(X0) | ~humble(X0) | ~old(X0) [cnf transformation 57]
115. ~funny(alice) | wise(X0) [cnf transformation 61]
116. ~funny(alice) | calm(X0) [cnf transformation 61]
131. kind(alice) [cnf transformation 23]
132. ~humble(X0) | ~old(X0) [duplicate literal removal 112]
139. 2 <=> funny(sK0) [avatar definition]
141. ~funny(sK0) <- (~2) [avatar component clause 139]
144. 3 <=> ! [X1] : ~calm(X1) [avatar definition]
145. ~calm(X1) <- (3) [avatar component clause 144]
146. 3 | ~2 [avatar split clause 76,139,144]
166. 8 <=> ! [X0] : funny(X0) [avatar definition]
167. funny(X0) <- (8) [avatar component clause 166]
196. humble(X0) [subsumption resolution 105,107]
197. ~happy(X0) [subsumption resolution 104,106]
198. ~old(X0) [subsumption resolution 132,196]
200. 15 <=> ! [X0] : calm(X0) [avatar definition]
201. calm(X0) <- (15) [avatar component clause 200]
203. 16 <=> funny(alice) [avatar definition]
206. 15 | ~16 [avatar split clause 116,203,200]
208. 17 <=> ! [X0] : wise(X0) [avatar definition]
209. wise(X0) <- (17) [avatar component clause 208]
210. 17 | ~16 [avatar split clause 115,203,208]
248. happy(alice) | wise(alice) [resolution 95,131]
250. wise(alice) [subsumption resolution 248,197]
253. funny(alice) | old(alice) [resolution 101,250]
258. funny(alice) [subsumption resolution 253,198]
259. 16 [avatar split clause 258,203]
269. funny(X0) | old(X0) <- (17) [resolution 209,101]
271. funny(X0) <- (17) [subsumption resolution 269,198]
272. 8 | ~17 [avatar split clause 271,208,166]
274. $false <- (~2, 8) [resolution 167,141]
278. 2 | ~8 [avatar contradiction clause 274]
279. $false <- (3, 15) [subsumption resolution 145,201]
280. ~3 | ~15 [avatar contradiction clause 279]
281. $false [avatar sat refutation 146,206,210,259,272,278,280]
% SZS output end Proof for 2224099618857634835929347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not strong is rich or not wise. If mary is generous then susan is calm or strong and vice versa. Everyone who is either happy or not generous is not calm or humble. Everyone who is not curious or not tall is old or not strong and vice versa. Everyone who is humble is both not calm and not quiet and vice versa. Everyone who is generous or not humble is either kind or not old and vice versa. If someone is not brave or not rich then alice is not wise or not patient. Everyone who is either generous or not strong is both not calm and patient and vice versa. Everyone who is both happy and not brave is either rich or not patient and vice versa. If paul is either not kind or brave then fred is both not brave and not creative and vice versa. If susan is both curious and kind then susan is either creative or not strong. If mary is either not generous or quiet then someone is kind or not humble. Everyone who is either wise or not funny is not curious. If john is either not old or kind then someone is not generous or not brave and vice versa. If someone is not strong then someone is both tall and not curious. If someone is not patient or not old then someone is both not kind and not strong and vice versa. Someone is both happy and not old. Someone is creative. Alice is either not rich or not strong. Someone is not creative. Someone is either strong or not brave. Fred is both not curious and not wise. Someone is both curious and wise. | Alice is tall. | neutral | (![X]:((~generous(X)<~>~strong(X))=>(rich(X)|~wise(X))))&
((generous(mary))<=>((calm(susan)|strong(susan))))&
(![X]:((happy(X)<~>~generous(X))=>(~calm(X)|humble(X))))&
(![X]:((~curious(X)|~tall(X))<=>(old(X)|~strong(X))))&
(![X]:(humble(X)<=>(~calm(X)&~quiet(X))))&
(![X]:((generous(X)|~humble(X))<=>(kind(X)<~>~old(X))))&
((?[X]:((~brave(X)|~rich(X))))=>((~wise(alice)|~patient(alice))))&
(![X]:((generous(X)<~>~strong(X))<=>(~calm(X)&patient(X))))&
(![X]:((happy(X)&~brave(X))<=>(rich(X)<~>~patient(X))))&
(((~kind(paul)<~>brave(paul)))<=>((~brave(fred)&~creative(fred))))&
(((curious(susan)&kind(susan)))=>((creative(susan)<~>~strong(susan))))&
(((~generous(mary)<~>quiet(mary)))=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:((wise(X)<~>~funny(X))=>~curious(X)))&
(((~old(john)<~>kind(john)))<=>(?[X]:((~generous(X)|~brave(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((tall(X)&~curious(X)))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((~kind(X)&~strong(X)))))&
(?[X]:((happy(X)&~old(X))))&
(?[X]:(creative(X)))&
((~rich(alice)<~>~strong(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((strong(X)<~>~brave(X))))&
((~curious(fred)&~wise(fred)))&
(?[X]:((curious(X)&wise(X)))) | tall(alice) | [] | null | 0 |
Everyone who is not kind is both not funny and not quiet and vice versa. Everyone who is not happy or not wise is both wise and not funny. If alice is both not patient and quiet then someone is not strong and vice versa. Everyone who is not old is either not calm or not rich. If fred is curious or not strong then fred is both not happy and calm and vice versa. Everyone who is either happy or old is not old or rich and vice versa. Everyone who is either not creative or kind is not old and vice versa. Everyone who is either old or not curious is both funny and quiet. Everyone who is either patient or kind is not funny. If john is either generous or not happy then someone is either funny or not generous and vice versa. If someone is not calm or generous then someone is either not old or not funny. If alice is happy or not kind then someone is either not strong or patient. If someone is generous then someone is creative or not old. If someone is either not kind or not happy then susan is not happy and vice versa. Everyone who is strong is either generous or not creative and vice versa. Everyone who is brave is either patient or not humble and vice versa. Someone is both wise and quiet. Alice is patient or quiet. Alice is either old or not old. Lucy is not creative or patient. John is not strong. Fred is either not rich or curious. Alice is wise or not strong. Someone is not creative. | Fred is not happy. | contradiction | (![X]:(~kind(X)<=>(~funny(X)&~quiet(X))))&
(![X]:((~happy(X)|~wise(X))=>(wise(X)&~funny(X))))&
(((~patient(alice)&quiet(alice)))<=>(?[X]:(~strong(X))))&
(![X]:(~old(X)=>(~calm(X)<~>~rich(X))))&
(((curious(fred)|~strong(fred)))<=>((~happy(fred)&calm(fred))))&
(![X]:((happy(X)<~>old(X))<=>(~old(X)|rich(X))))&
(![X]:((~creative(X)<~>kind(X))<=>~old(X)))&
(![X]:((old(X)<~>~curious(X))=>(funny(X)&quiet(X))))&
(![X]:((patient(X)<~>kind(X))=>~funny(X)))&
(((generous(john)<~>~happy(john)))<=>(?[X]:((funny(X)<~>~generous(X)))))&
((?[X]:((~calm(X)|generous(X))))=>(?[X]:((~old(X)<~>~funny(X)))))&
(((happy(alice)|~kind(alice)))=>(?[X]:((~strong(X)<~>patient(X)))))&
((?[X]:(generous(X)))=>(?[X]:((creative(X)|~old(X)))))&
((?[X]:((~kind(X)<~>~happy(X))))<=>(~happy(susan)))&
(![X]:(strong(X)<=>(generous(X)<~>~creative(X))))&
(![X]:(brave(X)<=>(patient(X)<~>~humble(X))))&
(?[X]:((wise(X)&quiet(X))))&
((patient(alice)|quiet(alice)))&
((old(alice)<~>~old(alice)))&
((~creative(lucy)|patient(lucy)))&
(~strong(john))&
((~rich(fred)<~>curious(fred)))&
((wise(alice)|~strong(alice)))&
(?[X]:(~creative(X))) | ~happy(fred) | [
"p1",
"p3",
"p4",
"p5",
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1664444315893223435389847
% SZS output start Proof for 1664444315893223435389847
2. ! [X0] : ((~wise(X0) | ~happy(X0)) => (~funny(X0) & wise(X0))) [input p1]
4. ! [X0] : (~old(X0) => (~calm(X0) <~> ~rich(X0))) [input p3]
5. (~strong(fred) | curious(fred)) <=> (calm(fred) & ~happy(fred)) [input p4]
6. ! [X0] : ((happy(X0) <~> old(X0)) <=> (rich(X0) | ~old(X0))) [input p5]
8. ! [X0] : ((old(X0) <~> ~curious(X0)) => (quiet(X0) & funny(X0))) [input p7]
22. ~rich(fred) <~> curious(fred) [input p21]
25. ~happy(fred) [input hypothesis]
28. ! [X0] : (~happy(X0) => ~funny(X0)) [pure predicate removal 2]
31. ! [X0] : (~funny(X0) | happy(X0)) [ennf transformation 28]
32. ! [X0] : ((~calm(X0) <~> ~rich(X0)) | old(X0)) [ennf transformation 4]
33. ! [X0] : ((quiet(X0) & funny(X0)) | (old(X0) <=> ~curious(X0))) [ennf transformation 8]
45. ! [X0] : (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | old(X0)) [nnf transformation 32]
46. ((~strong(fred) | curious(fred)) | (~calm(fred) | happy(fred))) & ((calm(fred) & ~happy(fred)) | (strong(fred) & ~curious(fred))) [nnf transformation 5]
47. (~strong(fred) | curious(fred) | ~calm(fred) | happy(fred)) & ((calm(fred) & ~happy(fred)) | (strong(fred) & ~curious(fred))) [flattening 46]
48. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [nnf transformation 6]
49. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [flattening 48]
51. ! [X0] : ((quiet(X0) & funny(X0)) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0)))) [nnf transformation 33]
75. (~curious(fred) | rich(fred)) & (curious(fred) | ~rich(fred)) [nnf transformation 22]
81. ~funny(X0) | happy(X0) [cnf transformation 31]
85. ~rich(X0) | ~calm(X0) | old(X0) [cnf transformation 45]
89. calm(fred) | ~curious(fred) [cnf transformation 47]
93. rich(X0) | ~old(X0) | happy(X0) | ~old(X0) [cnf transformation 49]
94. old(X0) | happy(X0) | old(X0) [cnf transformation 49]
102. ~curious(X0) | funny(X0) | ~old(X0) [cnf transformation 51]
139. curious(fred) | ~rich(fred) [cnf transformation 75]
142. ~happy(fred) [cnf transformation 25]
143. rich(X0) | ~old(X0) | happy(X0) [duplicate literal removal 93]
144. old(X0) | happy(X0) [duplicate literal removal 94]
164. 5 <=> happy(fred) [avatar definition]
165. ~happy(fred) <- (~5) [avatar component clause 164]
168. 6 <=> calm(fred) [avatar definition]
169. calm(fred) <- (6) [avatar component clause 168]
172. 7 <=> curious(fred) [avatar definition]
174. curious(fred) <- (7) [avatar component clause 172]
181. ~7 | 6 [avatar split clause 89,168,172]
184. rich(X0) | happy(X0) [subsumption resolution 143,144]
296. 32 <=> rich(fred) [avatar definition]
297. ~rich(fred) <- (~32) [avatar component clause 296]
298. rich(fred) <- (32) [avatar component clause 296]
300. ~32 | 7 [avatar split clause 139,172,296]
301. ~5 [avatar split clause 142,164]
306. happy(fred) <- (~32) [resolution 184,297]
307. $false <- (~5, ~32) [subsumption resolution 306,165]
308. 5 | 32 [avatar contradiction clause 307]
322. ~calm(fred) | old(fred) <- (32) [resolution 85,298]
323. old(fred) <- (6, 32) [subsumption resolution 322,169]
396. funny(fred) | ~old(fred) <- (7) [resolution 102,174]
397. funny(fred) <- (6, 7, 32) [subsumption resolution 396,323]
399. happy(fred) <- (6, 7, 32) [resolution 397,81]
401. $false <- (~5, 6, 7, 32) [subsumption resolution 399,165]
402. 5 | ~6 | ~7 | ~32 [avatar contradiction clause 401]
405. $false [avatar sat refutation 181,300,301,308,402]
% SZS output end Proof for 1664444315893223435389847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then someone is not brave or kind and vice versa. If someone is both not generous and patient then someone is patient and vice versa. Everyone who is both humble and not kind is either not wise or not quiet and vice versa. If alice is both happy and not strong then someone is rich or not brave. Everyone who is quiet is both creative and not creative. Everyone who is humble or wise is rich or not quiet and vice versa. If john is either not funny or not calm then someone is old and vice versa. Everyone who is brave is either humble or rich and vice versa. If someone is not humble then mary is not old or generous. Everyone who is happy or not strong is kind. Everyone who is both not brave and not creative is not creative or wise. If paul is not wise or strong then someone is either not funny or strong. If alice is creative or not wise then someone is not patient or kind. If paul is both patient and generous then someone is not wise and vice versa. If someone is both not tall and tall then susan is strong or old. Everyone who is either wise or creative is wise or not generous. Alice is both not old and patient. Someone is both not happy and creative. Someone is not rich or happy. Alice is both not calm and not wise. Alice is calm or not calm. Susan is either not tall or not brave. Susan is humble or not happy. Someone is both not creative and happy. | Paul is humble. | entailment | ((?[X]:(generous(X)))<=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:(patient(X))))&
(![X]:((humble(X)&~kind(X))<=>(~wise(X)<~>~quiet(X))))&
(((happy(alice)&~strong(alice)))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:(quiet(X)=>(creative(X)&~creative(X))))&
(![X]:((humble(X)|wise(X))<=>(rich(X)|~quiet(X))))&
(((~funny(john)<~>~calm(john)))<=>(?[X]:(old(X))))&
(![X]:(brave(X)<=>(humble(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>((~old(mary)|generous(mary))))&
(![X]:((happy(X)|~strong(X))=>kind(X)))&
(![X]:((~brave(X)&~creative(X))=>(~creative(X)|wise(X))))&
(((~wise(paul)|strong(paul)))=>(?[X]:((~funny(X)<~>strong(X)))))&
(((creative(alice)|~wise(alice)))=>(?[X]:((~patient(X)|kind(X)))))&
(((patient(paul)&generous(paul)))<=>(?[X]:(~wise(X))))&
((?[X]:((~tall(X)&tall(X))))=>((strong(susan)|old(susan))))&
(![X]:((wise(X)<~>creative(X))=>(wise(X)|~generous(X))))&
((~old(alice)&patient(alice)))&
(?[X]:((~happy(X)&creative(X))))&
(?[X]:((~rich(X)|happy(X))))&
((~calm(alice)&~wise(alice)))&
((calm(alice)|~calm(alice)))&
((~tall(susan)<~>~brave(susan)))&
((humble(susan)|~happy(susan)))&
(?[X]:((~creative(X)&happy(X)))) | humble(paul) | [
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5731916194164868729165327
% SZS output start Proof for 5731916194164868729165327
3. ! [X0] : ((~kind(X0) & humble(X0)) <=> (~wise(X0) <~> ~quiet(X0))) [input p2]
5. ! [X0] : (quiet(X0) => (~creative(X0) & creative(X0))) [input p4]
6. ! [X0] : ((wise(X0) | humble(X0)) <=> (~quiet(X0) | rich(X0))) [input p5]
25. ~humble(paul) [input hypothesis]
30. ! [X0] : ((~creative(X0) & creative(X0)) | ~quiet(X0)) [ennf transformation 5]
52. ! [X0] : (((~kind(X0) & humble(X0)) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | (kind(X0) | ~humble(X0)))) [nnf transformation 3]
53. ! [X0] : (((~kind(X0) & humble(X0)) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | kind(X0) | ~humble(X0))) [flattening 52]
56. ! [X0] : (((wise(X0) | humble(X0)) | (quiet(X0) & ~rich(X0))) & ((~quiet(X0) | rich(X0)) | (~wise(X0) & ~humble(X0)))) [nnf transformation 6]
57. ! [X0] : ((wise(X0) | humble(X0) | (quiet(X0) & ~rich(X0))) & (~quiet(X0) | rich(X0) | (~wise(X0) & ~humble(X0)))) [flattening 56]
90. ~wise(X0) | humble(X0) | quiet(X0) [cnf transformation 53]
94. creative(X0) | ~quiet(X0) [cnf transformation 30]
95. ~creative(X0) | ~quiet(X0) [cnf transformation 30]
99. wise(X0) | humble(X0) | quiet(X0) [cnf transformation 57]
137. ~humble(paul) [cnf transformation 25]
201. ~quiet(X0) [subsumption resolution 94,95]
202. wise(X0) | humble(X0) [subsumption resolution 99,201]
223. 20 <=> ! [X0] : humble(X0) [avatar definition]
224. humble(X0) <- (20) [avatar component clause 223]
334. humble(X0) | quiet(X0) | humble(X0) [resolution 90,202]
335. humble(X0) | quiet(X0) [duplicate literal removal 334]
336. humble(X0) [subsumption resolution 335,201]
337. 20 [avatar split clause 336,223]
338. $false <- (20) [resolution 224,137]
339. ~20 [avatar contradiction clause 338]
340. $false [avatar sat refutation 337,339]
% SZS output end Proof for 5731916194164868729165327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or strong is both not rich and funny and vice versa.
If paul is not old then someone is brave.
Everyone who is either not happy or not creative is both generous and not rich and vice versa.
If john is either not strong or calm then john is both creative and not humble and vice versa.
Everyone who is either quiet or kind is tall and vice versa.
Everyone who is either quiet or not calm is either old or not generous and vice versa.
If someone is not patient or funny then someone is wise and vice versa.
Everyone who is both rich and tall is either old or happy and vice versa.
Everyone who is generous or quiet is both not quiet and funny.
Everyone who is either strong or happy is not old or not calm.
If fred is either not patient or wise then paul is both generous and not curious and vice versa.
Everyone who is either not generous or funny is either not rich or creative.
If someone is both not brave and not patient then someone is both not calm and not wise.
If lucy is calm or funny then lucy is brave or funny.
If mary is not rich or brave then paul is both kind and old.
If someone is creative or calm then someone is not wise and vice versa.
Mary is not quiet or not brave.
Paul is either brave or not wise.
Someone is either old or brave.
Mary is either happy or not old.
Alice is not wise or not happy.
Someone is both rich and wise.
Someone is patient.
Mary is rich or creative. | Paul is not curious. | neutral | (![X]:((quiet(X)<~>strong(X))<=>(~rich(X)&funny(X))))&
((~old(paul))=>(?[X]:(brave(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(generous(X)&~rich(X))))&
(((~strong(john)<~>calm(john)))<=>((creative(john)&~humble(john))))&
(![X]:((quiet(X)<~>kind(X))<=>tall(X)))&
(![X]:((quiet(X)<~>~calm(X))<=>(old(X)<~>~generous(X))))&
((?[X]:((~patient(X)|funny(X))))<=>(?[X]:(wise(X))))&
(![X]:((rich(X)&tall(X))<=>(old(X)<~>happy(X))))&
(![X]:((generous(X)|quiet(X))=>(~quiet(X)&funny(X))))&
(![X]:((strong(X)<~>happy(X))=>(~old(X)|~calm(X))))&
(((~patient(fred)<~>wise(fred)))<=>((generous(paul)&~curious(paul))))&
(![X]:((~generous(X)<~>funny(X))=>(~rich(X)<~>creative(X))))&
((?[X]:((~brave(X)&~patient(X))))=>(?[X]:((~calm(X)&~wise(X)))))&
(((calm(lucy)|funny(lucy)))=>((brave(lucy)|funny(lucy))))&
(((~rich(mary)|brave(mary)))=>((kind(paul)&old(paul))))&
((?[X]:((creative(X)|calm(X))))<=>(?[X]:(~wise(X))))&
((~quiet(mary)|~brave(mary)))&
((brave(paul)<~>~wise(paul)))&
(?[X]:((old(X)<~>brave(X))))&
((happy(mary)<~>~old(mary)))&
((~wise(alice)|~happy(alice)))&
(?[X]:((rich(X)&wise(X))))&
(?[X]:(patient(X)))&
((rich(mary)|creative(mary))) | ~curious(paul) | [] | null | 0 |
If someone is strong or humble then someone is both not kind and brave.
If someone is either not humble or strong then someone is not kind or happy and vice versa.
If someone is not kind then fred is both humble and brave and vice versa.
Everyone who is not funny or curious is not calm and vice versa.
Everyone who is not calm is not curious and vice versa.
Everyone who is either not wise or kind is both not brave and not humble.
Everyone who is both not kind and rich is funny and vice versa.
Everyone who is both not quiet and rich is either not old or kind and vice versa.
Everyone who is both humble and brave is not tall and vice versa.
If mary is either not rich or wise then susan is happy and vice versa.
If lucy is both not strong and strong then someone is both not brave and calm and vice versa.
Everyone who is not strong or calm is either not happy or calm.
If someone is not rich or strong then paul is quiet and vice versa.
Everyone who is not wise is both not quiet and not rich and vice versa.
If susan is either not calm or not patient then someone is humble or not quiet.
Everyone who is creative is both not brave and not quiet and vice versa.
Fred is either rich or patient.
Someone is creative or wise.
John is either funny or old.
John is wise or not kind.
Someone is both not strong and generous.
Someone is not humble or kind.
Mary is either not strong or not old. | Fred is not patient. | contradiction | ((?[X]:((strong(X)|humble(X))))=>(?[X]:((~kind(X)&brave(X)))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:((~kind(X)|happy(X)))))&
((?[X]:(~kind(X)))<=>((humble(fred)&brave(fred))))&
(![X]:((~funny(X)|curious(X))<=>~calm(X)))&
(![X]:(~calm(X)<=>~curious(X)))&
(![X]:((~wise(X)<~>kind(X))=>(~brave(X)&~humble(X))))&
(![X]:((~kind(X)&rich(X))<=>funny(X)))&
(![X]:((~quiet(X)&rich(X))<=>(~old(X)<~>kind(X))))&
(![X]:((humble(X)&brave(X))<=>~tall(X)))&
(((~rich(mary)<~>wise(mary)))<=>(happy(susan)))&
(((~strong(lucy)&strong(lucy)))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~strong(X)|calm(X))=>(~happy(X)<~>calm(X))))&
((?[X]:((~rich(X)|strong(X))))<=>(quiet(paul)))&
(![X]:(~wise(X)<=>(~quiet(X)&~rich(X))))&
(((~calm(susan)<~>~patient(susan)))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:(creative(X)<=>(~brave(X)&~quiet(X))))&
((rich(fred)<~>patient(fred)))&
(?[X]:((creative(X)|wise(X))))&
((funny(john)<~>old(john)))&
((wise(john)|~kind(john)))&
(?[X]:((~strong(X)&generous(X))))&
(?[X]:((~humble(X)|kind(X))))&
((~strong(mary)<~>~old(mary))) | ~patient(fred) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1448156627448185214916018
% SZS output start Proof for 1448156627448185214916018
1. ? [X0] : (humble(X0) | strong(X0)) => ? [X0] : (brave(X0) & ~kind(X0)) [input p0]
2. ? [X0] : (~humble(X0) <~> strong(X0)) <=> ? [X0] : (happy(X0) | ~kind(X0)) [input p1]
3. ? [X0] : ~kind(X0) <=> (brave(fred) & humble(fred)) [input p2]
4. ! [X0] : ((curious(X0) | ~funny(X0)) <=> ~calm(X0)) [input p3]
5. ! [X0] : (~calm(X0) <=> ~curious(X0)) [input p4]
6. ! [X0] : ((~wise(X0) <~> kind(X0)) => (~humble(X0) & ~brave(X0))) [input p5]
7. ! [X0] : ((rich(X0) & ~kind(X0)) <=> funny(X0)) [input p6]
12. ! [X0] : ((calm(X0) | ~strong(X0)) => (~happy(X0) <~> calm(X0))) [input p11]
14. ! [X0] : (~wise(X0) <=> (~rich(X0) & ~quiet(X0))) [input p13]
17. rich(fred) <~> patient(fred) [input p16]
24. ~patient(fred) [input hypothesis]
25. ? [X0] : (humble(X0) | strong(X0)) => ? [X1] : (brave(X1) & ~kind(X1)) [rectify 1]
26. ? [X0] : (~humble(X0) <~> strong(X0)) <=> ? [X1] : (happy(X1) | ~kind(X1)) [rectify 2]
29. ? [X1] : (brave(X1) & ~kind(X1)) | ! [X0] : (~humble(X0) & ~strong(X0)) [ennf transformation 25]
30. ! [X0] : ((~humble(X0) & ~brave(X0)) | (~wise(X0) <=> kind(X0))) [ennf transformation 6]
31. ! [X0] : ((~happy(X0) <~> calm(X0)) | (~calm(X0) & strong(X0))) [ennf transformation 12]
34. ? [X0] : (brave(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~strong(X1)) [rectify 29]
35. ? [X0] : (brave(X0) & ~kind(X0)) => (brave(sK0) & ~kind(sK0)) [choice axiom]
36. (brave(sK0) & ~kind(sK0)) | ! [X1] : (~humble(X1) & ~strong(X1)) [skolemisation 34,35]
37. (? [X0] : ((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | ! [X1] : (~happy(X1) & kind(X1))) & (? [X1] : (happy(X1) | ~kind(X1)) | ! [X0] : ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0)))) [nnf transformation 26]
38. (? [X0] : ((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | ! [X1] : (~happy(X1) & kind(X1))) & (? [X2] : (happy(X2) | ~kind(X2)) | ! [X3] : ((~humble(X3) | ~strong(X3)) & (strong(X3) | humble(X3)))) [rectify 37]
39. ? [X0] : ((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) => ((~strong(sK1) | humble(sK1)) & (strong(sK1) | ~humble(sK1))) [choice axiom]
40. ? [X2] : (happy(X2) | ~kind(X2)) => (happy(sK2) | ~kind(sK2)) [choice axiom]
41. (((~strong(sK1) | humble(sK1)) & (strong(sK1) | ~humble(sK1))) | ! [X1] : (~happy(X1) & kind(X1))) & ((happy(sK2) | ~kind(sK2)) | ! [X3] : ((~humble(X3) | ~strong(X3)) & (strong(X3) | humble(X3)))) [skolemisation 38,40,39]
42. (? [X0] : ~kind(X0) | (~brave(fred) | ~humble(fred))) & ((brave(fred) & humble(fred)) | ! [X0] : kind(X0)) [nnf transformation 3]
43. (? [X0] : ~kind(X0) | ~brave(fred) | ~humble(fred)) & ((brave(fred) & humble(fred)) | ! [X0] : kind(X0)) [flattening 42]
44. (? [X0] : ~kind(X0) | ~brave(fred) | ~humble(fred)) & ((brave(fred) & humble(fred)) | ! [X1] : kind(X1)) [rectify 43]
45. ? [X0] : ~kind(X0) => ~kind(sK3) [choice axiom]
46. (~kind(sK3) | ~brave(fred) | ~humble(fred)) & ((brave(fred) & humble(fred)) | ! [X1] : kind(X1)) [skolemisation 44,45]
47. ! [X0] : (((curious(X0) | ~funny(X0)) | calm(X0)) & (~calm(X0) | (~curious(X0) & funny(X0)))) [nnf transformation 4]
48. ! [X0] : ((curious(X0) | ~funny(X0) | calm(X0)) & (~calm(X0) | (~curious(X0) & funny(X0)))) [flattening 47]
49. ! [X0] : ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))) [nnf transformation 5]
50. ! [X0] : ((~humble(X0) & ~brave(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0)))) [nnf transformation 30]
51. ! [X0] : (((rich(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | (~rich(X0) | kind(X0)))) [nnf transformation 7]
52. ! [X0] : (((rich(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | ~rich(X0) | kind(X0))) [flattening 51]
61. ! [X0] : (((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | (~calm(X0) & strong(X0))) [nnf transformation 31]
66. ! [X0] : ((~wise(X0) | (rich(X0) | quiet(X0))) & ((~rich(X0) & ~quiet(X0)) | wise(X0))) [nnf transformation 14]
67. ! [X0] : ((~wise(X0) | rich(X0) | quiet(X0)) & ((~rich(X0) & ~quiet(X0)) | wise(X0))) [flattening 66]
71. (~patient(fred) | ~rich(fred)) & (patient(fred) | rich(fred)) [nnf transformation 17]
80. ~kind(sK0) | ~strong(X1) [cnf transformation 36]
81. ~kind(sK0) | ~humble(X1) [cnf transformation 36]
84. happy(sK2) | ~kind(sK2) | strong(X3) | humble(X3) [cnf transformation 41]
91. brave(fred) | kind(X1) [cnf transformation 46]
94. ~calm(X0) | ~curious(X0) [cnf transformation 48]
95. ~funny(X0) | curious(X0) | calm(X0) [cnf transformation 48]
96. ~curious(X0) | calm(X0) [cnf transformation 49]
97. ~calm(X0) | curious(X0) [cnf transformation 49]
99. ~wise(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 50]
102. ~rich(X0) | funny(X0) | kind(X0) [cnf transformation 52]
119. calm(X0) | ~happy(X0) | strong(X0) [cnf transformation 61]
127. ~rich(X0) | wise(X0) [cnf transformation 67]
133. patient(fred) | rich(fred) [cnf transformation 71]
143. ~patient(fred) [cnf transformation 24]
146. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
147. ~humble(X1) <- (1) [avatar component clause 146]
154. 3 <=> ! [X1] : ~strong(X1) [avatar definition]
155. ~strong(X1) <- (3) [avatar component clause 154]
158. 4 <=> kind(sK0) [avatar definition]
160. ~kind(sK0) <- (~4) [avatar component clause 158]
161. 1 | ~4 [avatar split clause 81,158,146]
162. 3 | ~4 [avatar split clause 80,158,154]
176. 8 <=> ! [X1] : kind(X1) [avatar definition]
177. kind(X1) <- (8) [avatar component clause 176]
185. 10 <=> kind(sK2) [avatar definition]
187. ~kind(sK2) <- (~10) [avatar component clause 185]
189. 11 <=> happy(sK2) [avatar definition]
191. happy(sK2) <- (11) [avatar component clause 189]
194. 12 <=> ! [X3] : (strong(X3) | humble(X3)) [avatar definition]
195. strong(X3) | humble(X3) <- (12) [avatar component clause 194]
196. 12 | ~10 | 11 [avatar split clause 84,189,185,194]
202. 14 <=> brave(fred) [avatar definition]
203. brave(fred) <- (14) [avatar component clause 202]
210. 8 | 14 [avatar split clause 91,202,176]
212. ~calm(X0) [subsumption resolution 97,94]
213. ~curious(X0) [subsumption resolution 96,212]
230. ~happy(X0) | strong(X0) [subsumption resolution 119,212]
264. 26 <=> rich(fred) [avatar definition]
265. rich(fred) <- (26) [avatar component clause 264]
268. 27 <=> patient(fred) [avatar definition]
272. 26 | 27 [avatar split clause 133,268,264]
320. ~27 [avatar split clause 143,268]
321. $false <- (~4, 8) [subsumption resolution 160,177]
322. 4 | ~8 [avatar contradiction clause 321]
326. wise(fred) <- (26) [resolution 127,265]
336. ~brave(fred) | ~kind(fred) <- (26) [resolution 99,326]
346. ~kind(fred) <- (14, 26) [subsumption resolution 336,203]
352. funny(fred) | kind(fred) <- (26) [resolution 102,265]
353. funny(fred) <- (14, 26) [subsumption resolution 352,346]
354. curious(fred) | calm(fred) <- (14, 26) [resolution 353,95]
357. calm(fred) <- (14, 26) [subsumption resolution 354,213]
358. $false <- (14, 26) [subsumption resolution 357,212]
359. ~14 | ~26 [avatar contradiction clause 358]
383. $false <- (8, ~10) [resolution 177,187]
386. ~8 | 10 [avatar contradiction clause 383]
389. strong(sK2) <- (11) [resolution 191,230]
390. $false <- (3, 11) [subsumption resolution 389,155]
391. ~3 | ~11 [avatar contradiction clause 390]
392. humble(X3) <- (3, 12) [subsumption resolution 195,155]
393. $false <- (1, 3, 12) [subsumption resolution 392,147]
394. ~1 | ~3 | ~12 [avatar contradiction clause 393]
395. $false [avatar sat refutation 161,162,196,210,272,320,322,359,386,391,394]
% SZS output end Proof for 1448156627448185214916018
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not rich and not patient then someone is either not rich or not kind. Everyone who is both humble and not funny is wise or not calm and vice versa. Everyone who is either not generous or not curious is patient and vice versa. Everyone who is either not generous or curious is not brave and vice versa. If someone is kind then paul is creative and vice versa. Everyone who is both wise and brave is either funny or not patient and vice versa. If someone is either not quiet or not generous then someone is either generous or quiet. Everyone who is both kind and not curious is humble or calm and vice versa. Everyone who is brave is kind or not generous. If someone is funny or not creative then susan is not generous and vice versa. Everyone who is both rich and patient is either not funny or kind. If susan is happy or not rich then someone is brave or humble. If alice is humble then john is not old. If lucy is rich or calm then someone is curious and vice versa. Everyone who is either not calm or old is either not creative or not calm and vice versa. If someone is not wise then someone is not patient and vice versa. Someone is brave. Someone is either generous or calm. Mary is strong. John is either creative or not funny. Mary is not calm. Susan is tall. Someone is not quiet or humble. Someone is tall. | John is wise. | contradiction | ((?[X]:((~rich(X)&~patient(X))))=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((humble(X)&~funny(X))<=>(wise(X)|~calm(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>patient(X)))&
(![X]:((~generous(X)<~>curious(X))<=>~brave(X)))&
((?[X]:(kind(X)))<=>(creative(paul)))&
(![X]:((wise(X)&brave(X))<=>(funny(X)<~>~patient(X))))&
((?[X]:((~quiet(X)<~>~generous(X))))=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:((kind(X)&~curious(X))<=>(humble(X)|calm(X))))&
(![X]:(brave(X)=>(kind(X)|~generous(X))))&
((?[X]:((funny(X)|~creative(X))))<=>(~generous(susan)))&
(![X]:((rich(X)&patient(X))=>(~funny(X)<~>kind(X))))&
(((happy(susan)|~rich(susan)))=>(?[X]:((brave(X)|humble(X)))))&
((humble(alice))=>(~old(john)))&
(((rich(lucy)|calm(lucy)))<=>(?[X]:(curious(X))))&
(![X]:((~calm(X)<~>old(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~patient(X))))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)<~>calm(X))))&
(strong(mary))&
((creative(john)<~>~funny(john)))&
(~calm(mary))&
(tall(susan))&
(?[X]:((~quiet(X)|humble(X))))&
(?[X]:(tall(X))) | wise(john) | [
"p1",
"p2",
"p3",
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6919026392917242308942257
% SZS output start Proof for 6919026392917242308942257
2. ! [X0] : ((~funny(X0) & humble(X0)) <=> (~calm(X0) | wise(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> ~curious(X0)) <=> patient(X0)) [input p2]
4. ! [X0] : ((~generous(X0) <~> curious(X0)) <=> ~brave(X0)) [input p3]
6. ! [X0] : ((brave(X0) & wise(X0)) <=> (funny(X0) <~> ~patient(X0))) [input p5]
8. ! [X0] : ((~curious(X0) & kind(X0)) <=> (calm(X0) | humble(X0))) [input p7]
14. (calm(lucy) | rich(lucy)) <=> ? [X0] : curious(X0) [input p13]
25. wise(john) [input hypothesis]
45. ! [X0] : (((~funny(X0) & humble(X0)) | (calm(X0) & ~wise(X0))) & ((~calm(X0) | wise(X0)) | (funny(X0) | ~humble(X0)))) [nnf transformation 2]
46. ! [X0] : (((~funny(X0) & humble(X0)) | (calm(X0) & ~wise(X0))) & (~calm(X0) | wise(X0) | funny(X0) | ~humble(X0))) [flattening 45]
47. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | ~patient(X0)) & (patient(X0) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [nnf transformation 3]
48. ! [X0] : ((((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | brave(X0)) & (~brave(X0) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0))))) [nnf transformation 4]
53. ! [X0] : (((brave(X0) & wise(X0)) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~brave(X0) | ~wise(X0)))) [nnf transformation 6]
54. ! [X0] : (((brave(X0) & wise(X0)) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | ~brave(X0) | ~wise(X0))) [flattening 53]
59. ! [X0] : (((~curious(X0) & kind(X0)) | (~calm(X0) & ~humble(X0))) & ((calm(X0) | humble(X0)) | (curious(X0) | ~kind(X0)))) [nnf transformation 8]
60. ! [X0] : (((~curious(X0) & kind(X0)) | (~calm(X0) & ~humble(X0))) & (calm(X0) | humble(X0) | curious(X0) | ~kind(X0))) [flattening 59]
68. ((calm(lucy) | rich(lucy)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~calm(lucy) & ~rich(lucy))) [nnf transformation 14]
69. (calm(lucy) | rich(lucy) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~calm(lucy) & ~rich(lucy))) [flattening 68]
70. (calm(lucy) | rich(lucy) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | (~calm(lucy) & ~rich(lucy))) [rectify 69]
71. ? [X1] : curious(X1) => curious(sK5) [choice axiom]
72. (calm(lucy) | rich(lucy) | ! [X0] : ~curious(X0)) & (curious(sK5) | (~calm(lucy) & ~rich(lucy))) [skolemisation 70,71]
91. calm(X0) | humble(X0) [cnf transformation 46]
92. ~wise(X0) | ~funny(X0) [cnf transformation 46]
95. ~generous(X0) | patient(X0) | curious(X0) [cnf transformation 47]
97. ~patient(X0) | generous(X0) | curious(X0) [cnf transformation 47]
98. ~brave(X0) | curious(X0) | generous(X0) [cnf transformation 48]
100. ~generous(X0) | curious(X0) | brave(X0) [cnf transformation 48]
104. ~patient(X0) | funny(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 54]
109. brave(X0) | funny(X0) | patient(X0) [cnf transformation 54]
117. ~curious(X0) | ~humble(X0) [cnf transformation 60]
118. ~curious(X0) | ~calm(X0) [cnf transformation 60]
127. curious(sK5) | ~rich(lucy) [cnf transformation 72]
128. curious(sK5) | ~calm(lucy) [cnf transformation 72]
129. calm(lucy) | rich(lucy) | ~curious(X0) [cnf transformation 72]
147. wise(john) [cnf transformation 25]
179. ~brave(X0) | ~patient(X0) | ~wise(X0) [subsumption resolution 104,92]
243. 21 <=> ! [X0] : ~curious(X0) [avatar definition]
244. ~curious(X0) <- (21) [avatar component clause 243]
246. 22 <=> rich(lucy) [avatar definition]
250. 23 <=> calm(lucy) [avatar definition]
253. 21 | 22 | 23 [avatar split clause 129,250,246,243]
255. 24 <=> curious(sK5) [avatar definition]
257. curious(sK5) <- (24) [avatar component clause 255]
258. ~23 | 24 [avatar split clause 128,255,250]
259. ~22 | 24 [avatar split clause 127,255,246]
293. 32 <=> funny(john) [avatar definition]
294. ~funny(john) <- (~32) [avatar component clause 293]
311. ~funny(john) [resolution 92,147]
411. ~calm(sK5) <- (24) [resolution 257,118]
412. ~humble(sK5) <- (24) [resolution 257,117]
439. funny(X1) | patient(X1) | curious(X1) | generous(X1) [resolution 109,98]
464. humble(sK5) <- (24) [resolution 411,91]
465. $false <- (24) [subsumption resolution 464,412]
466. ~24 [avatar contradiction clause 465]
527. generous(X1) | patient(X1) | funny(X1) <- (21) [subsumption resolution 439,244]
556. patient(X1) | funny(X1) | patient(X1) | curious(X1) <- (21) [resolution 527,95]
561. patient(X1) | funny(X1) | curious(X1) <- (21) [duplicate literal removal 556]
562. funny(X1) | patient(X1) <- (21) [subsumption resolution 561,244]
631. ~32 [avatar split clause 311,293]
632. patient(john) <- (21, ~32) [resolution 294,562]
635. generous(john) | curious(john) <- (21, ~32) [resolution 632,97]
636. generous(john) <- (21, ~32) [subsumption resolution 635,244]
637. curious(john) | brave(john) <- (21, ~32) [resolution 636,100]
639. brave(john) <- (21, ~32) [subsumption resolution 637,244]
646. ~patient(john) | ~wise(john) <- (21, ~32) [resolution 639,179]
650. ~wise(john) <- (21, ~32) [subsumption resolution 646,632]
651. $false <- (21, ~32) [subsumption resolution 650,147]
652. ~21 | 32 [avatar contradiction clause 651]
653. $false [avatar sat refutation 253,258,259,466,631,652]
% SZS output end Proof for 6919026392917242308942257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or patient then alice is not kind. Everyone who is either not creative or wise is both not calm and not happy and vice versa. Everyone who is wise or brave is either not funny or generous. Everyone who is not happy is quiet or not strong and vice versa. If fred is both not creative and old then john is either not old or not quiet and vice versa. Everyone who is not rich or tall is both not wise and not kind and vice versa. If someone is generous or not humble then susan is both happy and strong and vice versa. Everyone who is either wise or not wise is both not strong and not rich. If paul is calm then someone is both creative and happy and vice versa. Everyone who is both brave and not rich is brave or wise and vice versa. Everyone who is either not humble or strong is not patient and vice versa. If someone is both not brave and funny then someone is either happy or not curious and vice versa. If fred is both not generous and kind then someone is generous or wise and vice versa. Everyone who is not generous is either calm or not tall and vice versa. Someone is generous or humble. Mary is either not generous or calm. Someone is either not humble or quiet. Someone is both quiet and old. Someone is not brave or quiet. | Paul is kind. | contradiction | ((?[X]:((~rich(X)|patient(X))))=>(~kind(alice)))&
(![X]:((~creative(X)<~>wise(X))<=>(~calm(X)&~happy(X))))&
(![X]:((wise(X)|brave(X))=>(~funny(X)<~>generous(X))))&
(![X]:(~happy(X)<=>(quiet(X)|~strong(X))))&
(((~creative(fred)&old(fred)))<=>((~old(john)<~>~quiet(john))))&
(![X]:((~rich(X)|tall(X))<=>(~wise(X)&~kind(X))))&
((?[X]:((generous(X)|~humble(X))))<=>((happy(susan)&strong(susan))))&
(![X]:((wise(X)<~>~wise(X))=>(~strong(X)&~rich(X))))&
((calm(paul))<=>(?[X]:((creative(X)&happy(X)))))&
(![X]:((brave(X)&~rich(X))<=>(brave(X)|wise(X))))&
(![X]:((~humble(X)<~>strong(X))<=>~patient(X)))&
((?[X]:((~brave(X)&funny(X))))<=>(?[X]:((happy(X)<~>~curious(X)))))&
(((~generous(fred)&kind(fred)))<=>(?[X]:((generous(X)|wise(X)))))&
(![X]:(~generous(X)<=>(calm(X)<~>~tall(X))))&
(?[X]:((generous(X)|humble(X))))&
((~generous(mary)<~>calm(mary)))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((quiet(X)&old(X))))&
(?[X]:((~brave(X)|quiet(X)))) | kind(paul) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 195986611395636542805213
% SZS output start Proof for 195986611395636542805213
6. ! [X0] : ((tall(X0) | ~rich(X0)) <=> (~kind(X0) & ~wise(X0))) [input p5]
8. ! [X0] : ((wise(X0) <~> ~wise(X0)) => (~rich(X0) & ~strong(X0))) [input p7]
20. kind(paul) [input hypothesis]
25. ! [X0] : ((~rich(X0) & ~strong(X0)) | (wise(X0) <=> ~wise(X0))) [ennf transformation 8]
34. ! [X0] : (((tall(X0) | ~rich(X0)) | (kind(X0) | wise(X0))) & ((~kind(X0) & ~wise(X0)) | (~tall(X0) & rich(X0)))) [nnf transformation 6]
35. ! [X0] : ((tall(X0) | ~rich(X0) | kind(X0) | wise(X0)) & ((~kind(X0) & ~wise(X0)) | (~tall(X0) & rich(X0)))) [flattening 34]
41. ! [X0] : ((~rich(X0) & ~strong(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) [nnf transformation 25]
91. ~wise(X0) | rich(X0) [cnf transformation 35]
93. ~kind(X0) | rich(X0) [cnf transformation 35]
103. ~rich(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 41]
104. ~rich(X0) | wise(X0) | wise(X0) [cnf transformation 41]
138. kind(paul) [cnf transformation 20]
141. ~rich(X0) | ~wise(X0) [duplicate literal removal 103]
142. ~rich(X0) | wise(X0) [duplicate literal removal 104]
205. ~wise(X0) [subsumption resolution 141,91]
325. rich(paul) [resolution 93,138]
326. wise(paul) [resolution 142,325]
327. $false [subsumption resolution 326,205]
% SZS output end Proof for 195986611395636542805213
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny or not curious then someone is either tall or kind.
If susan is old or strong then mary is curious or not wise.
If someone is both brave and creative then someone is not rich or not curious.
If someone is not rich then lucy is either strong or calm and vice versa.
If alice is both not quiet and curious then someone is both not patient and not strong.
If someone is generous or not creative then someone is both not quiet and not happy and vice versa.
Everyone who is both rich and not quiet is either tall or not quiet.
Everyone who is tall is both rich and old.
Everyone who is calm or not calm is both brave and wise.
If john is both not happy and funny then someone is either quiet or wise and vice versa.
Everyone who is both not patient and creative is both old and wise and vice versa.
Everyone who is both not funny and calm is both not wise and creative.
Everyone who is not generous is both creative and generous and vice versa.
If someone is both not tall and generous then someone is not humble.
If someone is both rich and tall then alice is not quiet or creative.
Everyone who is both not happy and humble is either not calm or funny and vice versa.
Someone is calm.
Lucy is not humble or not old.
Mary is either funny or creative.
Susan is either not curious or brave.
Someone is not old.
Mary is either not happy or not strong. | Alice is not tall. | entailment | (((~funny(lucy)|~curious(lucy)))=>(?[X]:((tall(X)<~>kind(X)))))&
(((old(susan)|strong(susan)))=>((curious(mary)|~wise(mary))))&
((?[X]:((brave(X)&creative(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:(~rich(X)))<=>((strong(lucy)<~>calm(lucy))))&
(((~quiet(alice)&curious(alice)))=>(?[X]:((~patient(X)&~strong(X)))))&
((?[X]:((generous(X)|~creative(X))))<=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:((rich(X)&~quiet(X))=>(tall(X)<~>~quiet(X))))&
(![X]:(tall(X)=>(rich(X)&old(X))))&
(![X]:((calm(X)|~calm(X))=>(brave(X)&wise(X))))&
(((~happy(john)&funny(john)))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:((~patient(X)&creative(X))<=>(old(X)&wise(X))))&
(![X]:((~funny(X)&calm(X))=>(~wise(X)&creative(X))))&
(![X]:(~generous(X)<=>(creative(X)&generous(X))))&
((?[X]:((~tall(X)&generous(X))))=>(?[X]:(~humble(X))))&
((?[X]:((rich(X)&tall(X))))=>((~quiet(alice)|creative(alice))))&
(![X]:((~happy(X)&humble(X))<=>(~calm(X)<~>funny(X))))&
(?[X]:(calm(X)))&
((~humble(lucy)|~old(lucy)))&
((funny(mary)<~>creative(mary)))&
((~curious(susan)<~>brave(susan)))&
(?[X]:(~old(X)))&
((~happy(mary)<~>~strong(mary))) | ~tall(alice) | [
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8647677210602149307134828
% SZS output start Proof for 8647677210602149307134828
8. ! [X0] : (tall(X0) => (old(X0) & rich(X0))) [input p7]
9. ! [X0] : ((~calm(X0) | calm(X0)) => (wise(X0) & brave(X0))) [input p8]
11. ! [X0] : ((creative(X0) & ~patient(X0)) <=> (wise(X0) & old(X0))) [input p10]
13. ! [X0] : (~generous(X0) <=> (generous(X0) & creative(X0))) [input p12]
23. tall(alice) [input hypothesis]
35. ! [X0] : ((old(X0) & rich(X0)) | ~tall(X0)) [ennf transformation 8]
36. ! [X0] : ((wise(X0) & brave(X0)) | (calm(X0) & ~calm(X0))) [ennf transformation 9]
65. ! [X0] : (((creative(X0) & ~patient(X0)) | (~wise(X0) | ~old(X0))) & ((wise(X0) & old(X0)) | (~creative(X0) | patient(X0)))) [nnf transformation 11]
66. ! [X0] : (((creative(X0) & ~patient(X0)) | ~wise(X0) | ~old(X0)) & ((wise(X0) & old(X0)) | ~creative(X0) | patient(X0))) [flattening 65]
67. ! [X0] : ((~generous(X0) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | generous(X0))) [nnf transformation 13]
68. ! [X0] : ((~generous(X0) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | generous(X0))) [flattening 67]
102. ~tall(X0) | old(X0) [cnf transformation 35]
105. wise(X0) | ~calm(X0) [cnf transformation 36]
106. calm(X0) | wise(X0) [cnf transformation 36]
116. creative(X0) | ~wise(X0) | ~old(X0) [cnf transformation 66]
120. generous(X0) | generous(X0) [cnf transformation 68]
121. ~generous(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 68]
139. tall(alice) [cnf transformation 23]
140. generous(X0) [duplicate literal removal 120]
141. ~generous(X0) | ~creative(X0) [duplicate literal removal 121]
260. wise(X0) [subsumption resolution 105,106]
283. ~old(X0) | creative(X0) [subsumption resolution 116,260]
346. old(alice) [resolution 102,139]
348. ~creative(X0) [resolution 141,140]
349. creative(alice) [resolution 283,346]
351. $false [subsumption resolution 349,348]
% SZS output end Proof for 8647677210602149307134828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not wise then paul is either patient or generous and vice versa. If mary is old then lucy is not happy or brave. Everyone who is tall or not old is not generous. Everyone who is both not curious and not wise is quiet or generous and vice versa. If fred is both patient and curious then someone is not funny. Everyone who is either brave or not kind is both not tall and generous. Everyone who is quiet or not generous is both rich and not kind. Everyone who is not funny is wise. If john is not brave or not generous then susan is both not creative and not funny and vice versa. Everyone who is both tall and not happy is rich and vice versa. If someone is not funny then fred is both not wise and not old. Everyone who is both curious and happy is both not tall and calm. If someone is not old then someone is either calm or happy and vice versa. If mary is not brave or not patient then alice is both tall and kind. Everyone who is not tall or happy is either tall or not wise. Everyone who is funny is both not calm and generous and vice versa. Lucy is either humble or rich. Someone is both not happy and not humble. Someone is generous. Someone is either wise or not creative. Someone is not brave or not rich. Someone is not tall or not happy. | Mary is not funny. | contradiction | ((?[X]:((~happy(X)|~wise(X))))<=>((patient(paul)<~>generous(paul))))&
((old(mary))=>((~happy(lucy)|brave(lucy))))&
(![X]:((tall(X)|~old(X))=>~generous(X)))&
(![X]:((~curious(X)&~wise(X))<=>(quiet(X)|generous(X))))&
(((patient(fred)&curious(fred)))=>(?[X]:(~funny(X))))&
(![X]:((brave(X)<~>~kind(X))=>(~tall(X)&generous(X))))&
(![X]:((quiet(X)|~generous(X))=>(rich(X)&~kind(X))))&
(![X]:(~funny(X)=>wise(X)))&
(((~brave(john)|~generous(john)))<=>((~creative(susan)&~funny(susan))))&
(![X]:((tall(X)&~happy(X))<=>rich(X)))&
((?[X]:(~funny(X)))=>((~wise(fred)&~old(fred))))&
(![X]:((curious(X)&happy(X))=>(~tall(X)&calm(X))))&
((?[X]:(~old(X)))<=>(?[X]:((calm(X)<~>happy(X)))))&
(((~brave(mary)|~patient(mary)))=>((tall(alice)&kind(alice))))&
(![X]:((~tall(X)|happy(X))=>(tall(X)<~>~wise(X))))&
(![X]:(funny(X)<=>(~calm(X)&generous(X))))&
((humble(lucy)<~>rich(lucy)))&
(?[X]:((~happy(X)&~humble(X))))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~tall(X)|~happy(X)))) | ~funny(mary) | [
"p2",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1336155681314304515444971
% SZS output start Proof for 1336155681314304515444971
3. ! [X0] : ((~old(X0) | tall(X0)) => ~generous(X0)) [input p2]
8. ! [X0] : (~funny(X0) => wise(X0)) [input p7]
11. ? [X0] : ~funny(X0) => (~old(fred) & ~wise(fred)) [input p10]
16. ! [X0] : (funny(X0) <=> (generous(X0) & ~calm(X0))) [input p15]
23. ~funny(mary) [input hypothesis]
27. ! [X0] : (~generous(X0) | (old(X0) & ~tall(X0))) [ennf transformation 3]
32. ! [X0] : (wise(X0) | funny(X0)) [ennf transformation 8]
33. (~old(fred) & ~wise(fred)) | ! [X0] : funny(X0) [ennf transformation 11]
57. ! [X0] : ((funny(X0) | (~generous(X0) | calm(X0))) & ((generous(X0) & ~calm(X0)) | ~funny(X0))) [nnf transformation 16]
58. ! [X0] : ((funny(X0) | ~generous(X0) | calm(X0)) & ((generous(X0) & ~calm(X0)) | ~funny(X0))) [flattening 57]
79. ~generous(X0) | old(X0) [cnf transformation 27]
94. funny(X0) | wise(X0) [cnf transformation 32]
103. ~wise(fred) | funny(X0) [cnf transformation 33]
104. ~old(fred) | funny(X0) [cnf transformation 33]
120. ~funny(X0) | generous(X0) [cnf transformation 58]
131. ~funny(mary) [cnf transformation 23]
209. 17 <=> ! [X0] : funny(X0) [avatar definition]
210. funny(X0) <- (17) [avatar component clause 209]
212. 18 <=> old(fred) [avatar definition]
214. ~old(fred) <- (~18) [avatar component clause 212]
215. 17 | ~18 [avatar split clause 104,212,209]
217. 19 <=> wise(fred) [avatar definition]
219. ~wise(fred) <- (~19) [avatar component clause 217]
220. 17 | ~19 [avatar split clause 103,217,209]
310. $false <- (17) [resolution 210,131]
313. ~17 [avatar contradiction clause 310]
328. generous(X0) | wise(X0) [resolution 120,94]
491. old(X2) | wise(X2) [resolution 328,79]
602. wise(fred) <- (~18) [resolution 491,214]
604. $false <- (~18, ~19) [subsumption resolution 602,219]
605. 18 | 19 [avatar contradiction clause 604]
606. $false [avatar sat refutation 215,220,313,605]
% SZS output end Proof for 1336155681314304515444971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not quiet then someone is either calm or strong. Everyone who is both not brave and brave is either tall or not generous. Everyone who is brave or not wise is not generous. If alice is not patient or not calm then someone is either creative or not strong. Everyone who is both not generous and not kind is both rich and quiet and vice versa. Everyone who is not brave is old. Everyone who is both strong and not funny is both old and not rich and vice versa. Everyone who is kind is curious and vice versa. If susan is either patient or strong then someone is happy and vice versa. If mary is either happy or old then paul is both rich and not curious and vice versa. If susan is rich or not curious then someone is either quiet or not brave and vice versa. If someone is either not creative or not strong then susan is either wise or not generous. Everyone who is either rich or not quiet is both curious and not calm and vice versa. Everyone who is either funny or not calm is both patient and not old. Everyone who is happy is not funny and vice versa. Everyone who is both not generous and quiet is calm or not wise and vice versa. Alice is both not humble and not generous. Susan is not kind or not calm. Someone is both strong and not wise. Lucy is not curious. Paul is wise. Someone is generous. Lucy is generous or humble. Alice is not wise. | Susan is kind. | contradiction | ((?[X]:((creative(X)<~>~quiet(X))))=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((~brave(X)&brave(X))=>(tall(X)<~>~generous(X))))&
(![X]:((brave(X)|~wise(X))=>~generous(X)))&
(((~patient(alice)|~calm(alice)))=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((~generous(X)&~kind(X))<=>(rich(X)&quiet(X))))&
(![X]:(~brave(X)=>old(X)))&
(![X]:((strong(X)&~funny(X))<=>(old(X)&~rich(X))))&
(![X]:(kind(X)<=>curious(X)))&
(((patient(susan)<~>strong(susan)))<=>(?[X]:(happy(X))))&
(((happy(mary)<~>old(mary)))<=>((rich(paul)&~curious(paul))))&
(((rich(susan)|~curious(susan)))<=>(?[X]:((quiet(X)<~>~brave(X)))))&
((?[X]:((~creative(X)<~>~strong(X))))=>((wise(susan)<~>~generous(susan))))&
(![X]:((rich(X)<~>~quiet(X))<=>(curious(X)&~calm(X))))&
(![X]:((funny(X)<~>~calm(X))=>(patient(X)&~old(X))))&
(![X]:(happy(X)<=>~funny(X)))&
(![X]:((~generous(X)&quiet(X))<=>(calm(X)|~wise(X))))&
((~humble(alice)&~generous(alice)))&
((~kind(susan)|~calm(susan)))&
(?[X]:((strong(X)&~wise(X))))&
(~curious(lucy))&
(wise(paul))&
(?[X]:(generous(X)))&
((generous(lucy)|humble(lucy)))&
(~wise(alice)) | kind(susan) | [
"p2",
"p4",
"p5",
"p6",
"p7",
"p10",
"p12",
"p13",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8945870744008952223859069
% SZS output start Proof for 8945870744008952223859069
3. ! [X0] : ((~wise(X0) | brave(X0)) => ~generous(X0)) [input p2]
5. ! [X0] : ((~kind(X0) & ~generous(X0)) <=> (quiet(X0) & rich(X0))) [input p4]
6. ! [X0] : (~brave(X0) => old(X0)) [input p5]
7. ! [X0] : ((~funny(X0) & strong(X0)) <=> (~rich(X0) & old(X0))) [input p6]
8. ! [X0] : (kind(X0) <=> curious(X0)) [input p7]
11. (~curious(susan) | rich(susan)) <=> ? [X0] : (quiet(X0) <~> ~brave(X0)) [input p10]
13. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (~calm(X0) & curious(X0))) [input p12]
14. ! [X0] : ((funny(X0) <~> ~calm(X0)) => (~old(X0) & patient(X0))) [input p13]
16. ! [X0] : ((quiet(X0) & ~generous(X0)) <=> (~wise(X0) | calm(X0))) [input p15]
18. ~calm(susan) | ~kind(susan) [input p17]
22. ? [X0] : generous(X0) [input p21]
25. kind(susan) [input hypothesis]
30. ! [X0] : (~generous(X0) | (wise(X0) & ~brave(X0))) [ennf transformation 3]
32. ! [X0] : (old(X0) | brave(X0)) [ennf transformation 6]
34. ! [X0] : ((~old(X0) & patient(X0)) | (funny(X0) <=> ~calm(X0))) [ennf transformation 14]
43. ! [X0] : (((~kind(X0) & ~generous(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (kind(X0) | generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((~kind(X0) & ~generous(X0)) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | kind(X0) | generous(X0))) [flattening 43]
45. ! [X0] : (((~funny(X0) & strong(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (funny(X0) | ~strong(X0)))) [nnf transformation 7]
46. ! [X0] : (((~funny(X0) & strong(X0)) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | funny(X0) | ~strong(X0))) [flattening 45]
47. ! [X0] : ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))) [nnf transformation 8]
54. ((~curious(susan) | rich(susan)) | ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (? [X0] : ((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (curious(susan) & ~rich(susan))) [nnf transformation 11]
55. (~curious(susan) | rich(susan) | ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (? [X0] : ((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (curious(susan) & ~rich(susan))) [flattening 54]
56. (~curious(susan) | rich(susan) | ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (? [X1] : ((brave(X1) | ~quiet(X1)) & (~brave(X1) | quiet(X1))) | (curious(susan) & ~rich(susan))) [rectify 55]
57. ? [X1] : ((brave(X1) | ~quiet(X1)) & (~brave(X1) | quiet(X1))) => ((brave(sK3) | ~quiet(sK3)) & (~brave(sK3) | quiet(sK3))) [choice axiom]
58. (~curious(susan) | rich(susan) | ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(sK3) | ~quiet(sK3)) & (~brave(sK3) | quiet(sK3))) | (curious(susan) & ~rich(susan))) [skolemisation 56,57]
60. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (calm(X0) | ~curious(X0))) & ((~calm(X0) & curious(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 13]
61. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | calm(X0) | ~curious(X0)) & ((~calm(X0) & curious(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [flattening 60]
62. ! [X0] : ((~old(X0) & patient(X0)) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0)))) [nnf transformation 34]
64. ! [X0] : (((quiet(X0) & ~generous(X0)) | (wise(X0) & ~calm(X0))) & ((~wise(X0) | calm(X0)) | (~quiet(X0) | generous(X0)))) [nnf transformation 16]
65. ! [X0] : (((quiet(X0) & ~generous(X0)) | (wise(X0) & ~calm(X0))) & (~wise(X0) | calm(X0) | ~quiet(X0) | generous(X0))) [flattening 64]
68. ? [X0] : generous(X0) => generous(sK5) [choice axiom]
69. generous(sK5) [skolemisation 22,68]
76. ~generous(X0) | ~brave(X0) [cnf transformation 30]
84. ~rich(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 44]
85. ~rich(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 44]
86. old(X0) | brave(X0) [cnf transformation 32]
90. ~funny(X0) | rich(X0) | ~old(X0) [cnf transformation 46]
91. ~kind(X0) | curious(X0) [cnf transformation 47]
108. ~curious(susan) | rich(susan) | quiet(X0) | brave(X0) [cnf transformation 58]
118. ~curious(X0) | ~rich(X0) | calm(X0) | quiet(X0) [cnf transformation 61]
122. ~old(X0) | funny(X0) | calm(X0) [cnf transformation 62]
126. ~generous(X0) | ~calm(X0) [cnf transformation 65]
132. ~calm(susan) | ~kind(susan) [cnf transformation 18]
137. generous(sK5) [cnf transformation 69]
140. kind(susan) [cnf transformation 25]
221. 17 <=> ! [X0] : (quiet(X0) | brave(X0)) [avatar definition]
222. brave(X0) | quiet(X0) <- (17) [avatar component clause 221]
224. 18 <=> rich(susan) [avatar definition]
226. rich(susan) <- (18) [avatar component clause 224]
228. 19 <=> curious(susan) [avatar definition]
229. curious(susan) <- (19) [avatar component clause 228]
231. 17 | 18 | ~19 [avatar split clause 108,228,224,221]
265. 27 <=> kind(susan) [avatar definition]
266. kind(susan) <- (27) [avatar component clause 265]
269. 28 <=> calm(susan) [avatar definition]
271. ~calm(susan) <- (~28) [avatar component clause 269]
272. ~27 | ~28 [avatar split clause 132,269,265]
282. 27 [avatar split clause 140,265]
283. ~brave(sK5) [resolution 76,137]
288. curious(susan) <- (27) [resolution 91,266]
291. 19 | ~27 [avatar split clause 288,265,228]
408. funny(X0) | calm(X0) | brave(X0) [resolution 122,86]
424. ~rich(susan) | calm(susan) | quiet(susan) <- (19) [resolution 118,229]
466. ~rich(susan) | quiet(susan) <- (19, ~28) [subsumption resolution 424,271]
479. quiet(sK5) <- (17) [resolution 222,283]
531. calm(X2) | brave(X2) | rich(X2) | ~old(X2) [resolution 408,90]
537. rich(X2) | brave(X2) | calm(X2) [subsumption resolution 531,86]
616. 52 <=> quiet(susan) [avatar definition]
617. quiet(susan) <- (52) [avatar component clause 616]
620. 52 | ~18 | ~19 | 28 [avatar split clause 466,269,228,224,616]
626. ~quiet(susan) | ~kind(susan) <- (18) [resolution 226,85]
628. ~kind(susan) <- (18, 52) [subsumption resolution 626,617]
629. $false <- (18, 27, 52) [subsumption resolution 628,266]
630. ~18 | ~27 | ~52 [avatar contradiction clause 629]
756. brave(X5) | calm(X5) | ~quiet(X5) | ~generous(X5) [resolution 537,84]
761. calm(X5) | ~quiet(X5) | ~generous(X5) [subsumption resolution 756,76]
762. ~generous(X5) | ~quiet(X5) [subsumption resolution 761,126]
834. ~quiet(sK5) [resolution 762,137]
837. $false <- (17) [subsumption resolution 834,479]
838. ~17 [avatar contradiction clause 837]
841. $false [avatar sat refutation 231,272,282,291,620,630,838]
% SZS output end Proof for 8945870744008952223859069
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and happy is strong or rich.
If john is not curious then lucy is both not generous and wise and vice versa.
If someone is both not kind and not humble then someone is generous and vice versa.
Everyone who is both curious and calm is not brave or not funny.
If someone is either not calm or not patient then john is curious.
Everyone who is funny is either not curious or not calm.
Everyone who is happy is both not calm and not funny and vice versa.
If someone is either not happy or not wise then john is either not humble or not patient.
If someone is calm or curious then someone is not quiet or quiet and vice versa.
Everyone who is either patient or not rich is wise or not curious and vice versa.
If mary is either not kind or kind then someone is humble or calm and vice versa.
Everyone who is both not quiet and not generous is not funny or creative and vice versa.
If someone is not patient then lucy is tall or kind.
Everyone who is not creative or not kind is either not generous or not funny.
Everyone who is either funny or brave is both not old and not quiet and vice versa.
Everyone who is not calm is both generous and not tall.
Fred is not patient or old.
Susan is not calm or not happy.
Someone is either curious or humble.
Fred is not strong.
Paul is either not calm or not tall.
Fred is both not rich and not strong.
Alice is not patient.
Lucy is both not tall and patient. | Paul is tall. | contradiction | (![X]:((wise(X)&happy(X))=>(strong(X)|rich(X))))&
((~curious(john))<=>((~generous(lucy)&wise(lucy))))&
((?[X]:((~kind(X)&~humble(X))))<=>(?[X]:(generous(X))))&
(![X]:((curious(X)&calm(X))=>(~brave(X)|~funny(X))))&
((?[X]:((~calm(X)<~>~patient(X))))=>(curious(john)))&
(![X]:(funny(X)=>(~curious(X)<~>~calm(X))))&
(![X]:(happy(X)<=>(~calm(X)&~funny(X))))&
((?[X]:((~happy(X)<~>~wise(X))))=>((~humble(john)<~>~patient(john))))&
((?[X]:((calm(X)|curious(X))))<=>(?[X]:((~quiet(X)|quiet(X)))))&
(![X]:((patient(X)<~>~rich(X))<=>(wise(X)|~curious(X))))&
(((~kind(mary)<~>kind(mary)))<=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((~quiet(X)&~generous(X))<=>(~funny(X)|creative(X))))&
((?[X]:(~patient(X)))=>((tall(lucy)|kind(lucy))))&
(![X]:((~creative(X)|~kind(X))=>(~generous(X)<~>~funny(X))))&
(![X]:((funny(X)<~>brave(X))<=>(~old(X)&~quiet(X))))&
(![X]:(~calm(X)=>(generous(X)&~tall(X))))&
((~patient(fred)|old(fred)))&
((~calm(susan)|~happy(susan)))&
(?[X]:((curious(X)<~>humble(X))))&
(~strong(fred))&
((~calm(paul)<~>~tall(paul)))&
((~rich(fred)&~strong(fred)))&
(~patient(alice))&
((~tall(lucy)&patient(lucy))) | tall(paul) | [
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1616910535922961644932551
% SZS output start Proof for 1616910535922961644932551
16. ! [X0] : (~calm(X0) => (~tall(X0) & generous(X0))) [input p15]
21. ~calm(paul) <~> ~tall(paul) [input p20]
25. tall(paul) [input hypothesis]
38. ! [X0] : ((~tall(X0) & generous(X0)) | calm(X0)) [ennf transformation 16]
70. (tall(paul) | calm(paul)) & (~tall(paul) | ~calm(paul)) [nnf transformation 21]
123. ~tall(X0) | calm(X0) [cnf transformation 38]
129. ~tall(paul) | ~calm(paul) [cnf transformation 70]
130. tall(paul) | calm(paul) [cnf transformation 70]
136. tall(paul) [cnf transformation 25]
270. calm(paul) [subsumption resolution 130,123]
271. ~tall(paul) [subsumption resolution 129,270]
273. $false [subsumption resolution 136,271]
% SZS output end Proof for 1616910535922961644932551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not calm is either not humble or wise.
Everyone who is either not tall or not patient is not rich.
If someone is not curious then mary is funny and vice versa.
Everyone who is both happy and not quiet is both wise and not patient and vice versa.
Everyone who is quiet is either humble or strong.
If john is either not funny or curious then alice is patient or funny and vice versa.
Everyone who is creative or not calm is curious or rich.
If susan is funny or patient then alice is funny or not happy.
Everyone who is not generous is not calm or quiet.
Everyone who is both not generous and humble is patient and vice versa.
Everyone who is curious is not strong.
Everyone who is both not calm and funny is not patient or not happy and vice versa.
Everyone who is both generous and not generous is calm or kind and vice versa.
Everyone who is not calm or not humble is not calm and vice versa.
Everyone who is either strong or creative is not curious and vice versa.
If someone is both not calm and strong then someone is not old and vice versa.
Someone is either rich or funny.
Someone is either generous or old.
Mary is both not strong and humble.
Someone is either not humble or not happy.
Someone is either creative or calm.
Someone is both not tall and curious.
Paul is either not rich or not wise.
Someone is both patient and brave. | John is not strong. | entailment | (![X]:((~strong(X)|~calm(X))=>(~humble(X)<~>wise(X))))&
(![X]:((~tall(X)<~>~patient(X))=>~rich(X)))&
((?[X]:(~curious(X)))<=>(funny(mary)))&
(![X]:((happy(X)&~quiet(X))<=>(wise(X)&~patient(X))))&
(![X]:(quiet(X)=>(humble(X)<~>strong(X))))&
(((~funny(john)<~>curious(john)))<=>((patient(alice)|funny(alice))))&
(![X]:((creative(X)|~calm(X))=>(curious(X)|rich(X))))&
(((funny(susan)|patient(susan)))=>((funny(alice)|~happy(alice))))&
(![X]:(~generous(X)=>(~calm(X)|quiet(X))))&
(![X]:((~generous(X)&humble(X))<=>patient(X)))&
(![X]:(curious(X)=>~strong(X)))&
(![X]:((~calm(X)&funny(X))<=>(~patient(X)|~happy(X))))&
(![X]:((generous(X)&~generous(X))<=>(calm(X)|kind(X))))&
(![X]:((~calm(X)|~humble(X))<=>~calm(X)))&
(![X]:((strong(X)<~>creative(X))<=>~curious(X)))&
((?[X]:((~calm(X)&strong(X))))<=>(?[X]:(~old(X))))&
(?[X]:((rich(X)<~>funny(X))))&
(?[X]:((generous(X)<~>old(X))))&
((~strong(mary)&humble(mary)))&
(?[X]:((~humble(X)<~>~happy(X))))&
(?[X]:((creative(X)<~>calm(X))))&
(?[X]:((~tall(X)&curious(X))))&
((~rich(paul)<~>~wise(paul)))&
(?[X]:((patient(X)&brave(X)))) | ~strong(john) | [
"p3",
"p4",
"p5",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4515304446535516381791523
% SZS output start Proof for 4515304446535516381791523
4. ! [X0] : ((~quiet(X0) & happy(X0)) <=> (~patient(X0) & wise(X0))) [input p3]
5. ! [X0] : (quiet(X0) => (humble(X0) <~> strong(X0))) [input p4]
6. (~funny(john) <~> curious(john)) <=> (funny(alice) | patient(alice)) [input p5]
10. ! [X0] : ((humble(X0) & ~generous(X0)) <=> patient(X0)) [input p9]
11. ! [X0] : (curious(X0) => ~strong(X0)) [input p10]
12. ! [X0] : ((funny(X0) & ~calm(X0)) <=> (~happy(X0) | ~patient(X0))) [input p11]
25. strong(john) [input hypothesis]
30. ! [X0] : ((humble(X0) <~> strong(X0)) | ~quiet(X0)) [ennf transformation 5]
37. ! [X0] : (~strong(X0) | ~curious(X0)) [ennf transformation 11]
44. ! [X0] : (((~quiet(X0) & happy(X0)) | (patient(X0) | ~wise(X0))) & ((~patient(X0) & wise(X0)) | (quiet(X0) | ~happy(X0)))) [nnf transformation 4]
45. ! [X0] : (((~quiet(X0) & happy(X0)) | patient(X0) | ~wise(X0)) & ((~patient(X0) & wise(X0)) | quiet(X0) | ~happy(X0))) [flattening 44]
46. ! [X0] : (((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | ~quiet(X0)) [nnf transformation 30]
47. (((~curious(john) | funny(john)) & (curious(john) | ~funny(john))) | (~funny(alice) & ~patient(alice))) & ((funny(alice) | patient(alice)) | ((~funny(john) | ~curious(john)) & (curious(john) | funny(john)))) [nnf transformation 6]
48. (((~curious(john) | funny(john)) & (curious(john) | ~funny(john))) | (~funny(alice) & ~patient(alice))) & (funny(alice) | patient(alice) | ((~funny(john) | ~curious(john)) & (curious(john) | funny(john)))) [flattening 47]
49. ! [X0] : (((humble(X0) & ~generous(X0)) | ~patient(X0)) & (patient(X0) | (~humble(X0) | generous(X0)))) [nnf transformation 10]
50. ! [X0] : (((humble(X0) & ~generous(X0)) | ~patient(X0)) & (patient(X0) | ~humble(X0) | generous(X0))) [flattening 49]
51. ! [X0] : (((funny(X0) & ~calm(X0)) | (happy(X0) & patient(X0))) & ((~happy(X0) | ~patient(X0)) | (~funny(X0) | calm(X0)))) [nnf transformation 12]
52. ! [X0] : (((funny(X0) & ~calm(X0)) | (happy(X0) & patient(X0))) & (~happy(X0) | ~patient(X0) | ~funny(X0) | calm(X0))) [flattening 51]
89. ~happy(X0) | quiet(X0) | ~patient(X0) [cnf transformation 45]
93. ~quiet(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 46]
96. curious(john) | ~funny(john) | ~patient(alice) [cnf transformation 48]
97. curious(john) | ~funny(john) | ~funny(alice) [cnf transformation 48]
107. ~patient(X0) | humble(X0) [cnf transformation 50]
108. ~curious(X0) | ~strong(X0) [cnf transformation 37]
112. funny(X0) | patient(X0) [cnf transformation 52]
113. happy(X0) | funny(X0) [cnf transformation 52]
144. strong(john) [cnf transformation 25]
159. 4 <=> funny(alice) [avatar definition]
161. ~funny(alice) <- (~4) [avatar component clause 159]
163. 5 <=> funny(john) [avatar definition]
164. ~funny(john) <- (~5) [avatar component clause 163]
167. 6 <=> curious(john) [avatar definition]
168. curious(john) <- (6) [avatar component clause 167]
172. 7 <=> patient(alice) [avatar definition]
174. ~patient(alice) <- (~7) [avatar component clause 172]
176. ~4 | ~5 | 6 [avatar split clause 97,167,163,159]
177. ~7 | ~5 | 6 [avatar split clause 96,167,163,172]
263. patient(john) <- (~5) [resolution 112,164]
265. humble(john) <- (~5) [resolution 263,107]
335. quiet(X0) | ~patient(X0) | funny(X0) [resolution 89,113]
337. quiet(X0) | funny(X0) [subsumption resolution 335,112]
422. ~humble(X0) | funny(X0) | ~strong(X0) [resolution 337,93]
452. funny(john) | ~strong(john) <- (~5) [resolution 422,265]
455. ~strong(john) <- (~5) [subsumption resolution 452,164]
456. $false <- (~5) [subsumption resolution 455,144]
457. 5 [avatar contradiction clause 456]
460. ~strong(john) <- (6) [resolution 168,108]
461. $false <- (6) [subsumption resolution 460,144]
462. ~6 [avatar contradiction clause 461]
463. patient(alice) <- (~4) [resolution 161,112]
464. $false <- (~4, ~7) [subsumption resolution 463,174]
465. 4 | 7 [avatar contradiction clause 464]
466. $false [avatar sat refutation 176,177,457,462,465]
% SZS output end Proof for 4515304446535516381791523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both generous and not patient then someone is both not patient and rich.
Everyone who is not patient is both not wise and happy and vice versa.
Everyone who is funny or not quiet is not calm or not brave and vice versa.
Everyone who is either not rich or not generous is both not tall and not brave.
If fred is both humble and not wise then paul is not calm or calm.
Everyone who is both not tall and not funny is both kind and not happy.
If someone is humble or wise then john is not patient or patient and vice versa.
If paul is not old then lucy is not strong and vice versa.
If someone is tall or not kind then alice is either not creative or humble and vice versa.
If someone is tall then alice is both strong and curious and vice versa.
If john is either kind or not creative then someone is both kind and not strong and vice versa.
If someone is funny or not happy then someone is both quiet and not quiet and vice versa.
Everyone who is either not wise or not calm is humble and vice versa.
If someone is not humble or not tall then susan is not rich.
Everyone who is not old or wise is both happy and not rich.
Everyone who is either generous or kind is patient.
Susan is either old or not patient.
Someone is wise or rich.
Someone is not humble.
Lucy is not old or quiet.
Paul is not curious.
Someone is brave or not brave.
Someone is generous.
Lucy is either rich or not creative. | Susan is not creative. | neutral | (((generous(alice)&~patient(alice)))=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:(~patient(X)<=>(~wise(X)&happy(X))))&
(![X]:((funny(X)|~quiet(X))<=>(~calm(X)|~brave(X))))&
(![X]:((~rich(X)<~>~generous(X))=>(~tall(X)&~brave(X))))&
(((humble(fred)&~wise(fred)))=>((~calm(paul)|calm(paul))))&
(![X]:((~tall(X)&~funny(X))=>(kind(X)&~happy(X))))&
((?[X]:((humble(X)|wise(X))))<=>((~patient(john)|patient(john))))&
((~old(paul))<=>(~strong(lucy)))&
((?[X]:((tall(X)|~kind(X))))<=>((~creative(alice)<~>humble(alice))))&
((?[X]:(tall(X)))<=>((strong(alice)&curious(alice))))&
(((kind(john)<~>~creative(john)))<=>(?[X]:((kind(X)&~strong(X)))))&
((?[X]:((funny(X)|~happy(X))))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((~wise(X)<~>~calm(X))<=>humble(X)))&
((?[X]:((~humble(X)|~tall(X))))=>(~rich(susan)))&
(![X]:((~old(X)|wise(X))=>(happy(X)&~rich(X))))&
(![X]:((generous(X)<~>kind(X))=>patient(X)))&
((old(susan)<~>~patient(susan)))&
(?[X]:((wise(X)|rich(X))))&
(?[X]:(~humble(X)))&
((~old(lucy)|quiet(lucy)))&
(~curious(paul))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:(generous(X)))&
((rich(lucy)<~>~creative(lucy))) | ~creative(susan) | [] | null | 0 |
Everyone who is not old is either kind or humble and vice versa.
Everyone who is either not tall or rich is not wise or humble and vice versa.
Everyone who is creative or calm is funny.
Everyone who is brave or not strong is either not patient or kind.
If john is not tall or strong then alice is both wise and brave.
Everyone who is both not funny and patient is both quiet and kind.
If someone is either not patient or not calm then mary is either quiet or not patient and vice versa.
If someone is both not brave and not generous then mary is patient and vice versa.
Everyone who is not patient is not funny or curious and vice versa.
Everyone who is not funny or tall is not rich and vice versa.
If someone is not humble then alice is both happy and not brave.
Everyone who is happy or patient is rich.
If mary is not tall then someone is happy and vice versa.
Everyone who is both patient and not quiet is either creative or calm.
If someone is either kind or not calm then mary is not creative.
If someone is both not funny and not quiet then mary is either not kind or kind.
Someone is either curious or not calm.
Someone is either rich or strong.
Someone is both not quiet and not generous.
Someone is both not curious and happy.
Fred is either not calm or not strong.
Susan is either calm or happy.
Fred is not kind.
Lucy is humble. | John is not tall. | contradiction | (![X]:(~old(X)<=>(kind(X)<~>humble(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(~wise(X)|humble(X))))&
(![X]:((creative(X)|calm(X))=>funny(X)))&
(![X]:((brave(X)|~strong(X))=>(~patient(X)<~>kind(X))))&
(((~tall(john)|strong(john)))=>((wise(alice)&brave(alice))))&
(![X]:((~funny(X)&patient(X))=>(quiet(X)&kind(X))))&
((?[X]:((~patient(X)<~>~calm(X))))<=>((quiet(mary)<~>~patient(mary))))&
((?[X]:((~brave(X)&~generous(X))))<=>(patient(mary)))&
(![X]:(~patient(X)<=>(~funny(X)|curious(X))))&
(![X]:((~funny(X)|tall(X))<=>~rich(X)))&
((?[X]:(~humble(X)))=>((happy(alice)&~brave(alice))))&
(![X]:((happy(X)|patient(X))=>rich(X)))&
((~tall(mary))<=>(?[X]:(happy(X))))&
(![X]:((patient(X)&~quiet(X))=>(creative(X)<~>calm(X))))&
((?[X]:((kind(X)<~>~calm(X))))=>(~creative(mary)))&
((?[X]:((~funny(X)&~quiet(X))))=>((~kind(mary)<~>kind(mary))))&
(?[X]:((curious(X)<~>~calm(X))))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((~quiet(X)&~generous(X))))&
(?[X]:((~curious(X)&happy(X))))&
((~calm(fred)<~>~strong(fred)))&
((calm(susan)<~>happy(susan)))&
(~kind(fred))&
(humble(lucy)) | ~tall(john) | [
"p1",
"p4",
"p9",
"p10",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2778869368616279685586054
% SZS output start Proof for 2778869368616279685586054
2. ! [X0] : ((~tall(X0) <~> rich(X0)) <=> (humble(X0) | ~wise(X0))) [input p1]
5. (strong(john) | ~tall(john)) => (brave(alice) & wise(alice)) [input p4]
10. ! [X0] : ((tall(X0) | ~funny(X0)) <=> ~rich(X0)) [input p9]
11. ? [X0] : ~humble(X0) => (~brave(alice) & happy(alice)) [input p10]
12. ! [X0] : ((patient(X0) | happy(X0)) => rich(X0)) [input p11]
20. ? [X0] : (happy(X0) & ~curious(X0)) [input p19]
25. ~tall(john) [input hypothesis]
28. (brave(alice) & wise(alice)) | (~strong(john) & tall(john)) [ennf transformation 5]
31. (~brave(alice) & happy(alice)) | ! [X0] : humble(X0) [ennf transformation 11]
32. ! [X0] : (rich(X0) | (~patient(X0) & ~happy(X0))) [ennf transformation 12]
37. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (~humble(X0) & wise(X0))) & ((humble(X0) | ~wise(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (~humble(X0) & wise(X0))) & (humble(X0) | ~wise(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [flattening 37]
50. ! [X0] : (((tall(X0) | ~funny(X0)) | rich(X0)) & (~rich(X0) | (~tall(X0) & funny(X0)))) [nnf transformation 10]
51. ! [X0] : ((tall(X0) | ~funny(X0) | rich(X0)) & (~rich(X0) | (~tall(X0) & funny(X0)))) [flattening 50]
67. ? [X0] : (happy(X0) & ~curious(X0)) => (happy(sK6) & ~curious(sK6)) [choice axiom]
68. happy(sK6) & ~curious(sK6) [skolemisation 20,67]
76. ~rich(X0) | tall(X0) | ~humble(X0) [cnf transformation 38]
85. brave(alice) | tall(john) [cnf transformation 28]
104. ~rich(X0) | ~tall(X0) [cnf transformation 51]
107. ~brave(alice) | humble(X0) [cnf transformation 31]
108. ~happy(X0) | rich(X0) [cnf transformation 32]
125. happy(sK6) [cnf transformation 68]
132. ~tall(john) [cnf transformation 25]
138. 2 <=> brave(alice) [avatar definition]
143. 3 <=> tall(john) [avatar definition]
146. 3 | 2 [avatar split clause 85,138,143]
198. 14 <=> ! [X0] : humble(X0) [avatar definition]
199. humble(X0) <- (14) [avatar component clause 198]
200. 14 | ~2 [avatar split clause 107,138,198]
271. ~3 [avatar split clause 132,143]
280. rich(sK6) [resolution 108,125]
284. ~tall(sK6) [resolution 280,104]
315. tall(sK6) | ~humble(sK6) [resolution 76,280]
325. ~humble(sK6) [subsumption resolution 315,284]
326. $false <- (14) [subsumption resolution 325,199]
327. ~14 [avatar contradiction clause 326]
328. $false [avatar sat refutation 146,200,271,327]
% SZS output end Proof for 2778869368616279685586054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both brave and old then paul is both not brave and not quiet.
If susan is not rich or tall then someone is calm and vice versa.
If susan is either not quiet or not happy then someone is either brave or quiet and vice versa.
Everyone who is not generous or not rich is both funny and not old and vice versa.
Everyone who is either wise or rich is both kind and not rich.
Everyone who is either kind or tall is either funny or rich and vice versa.
Everyone who is brave or not calm is patient.
Everyone who is not generous or not old is both not generous and happy.
If someone is either tall or calm then alice is either not patient or quiet and vice versa.
If mary is not quiet then john is both not curious and creative and vice versa.
Everyone who is not old or not kind is not creative.
Everyone who is both generous and not tall is not curious or not quiet and vice versa.
Everyone who is kind or not rich is both not old and not generous.
Everyone who is not tall or quiet is not calm and vice versa.
Everyone who is quiet is generous or old.
If someone is not strong or patient then lucy is strong or patient and vice versa.
Mary is either wise or not curious.
Paul is both strong and humble.
Mary is not kind or not curious.
Lucy is either curious or old.
Someone is either not humble or curious.
Someone is humble.
Someone is wise. | Susan is not happy. | neutral | ((?[X]:((brave(X)&old(X))))=>((~brave(paul)&~quiet(paul))))&
(((~rich(susan)|tall(susan)))<=>(?[X]:(calm(X))))&
(((~quiet(susan)<~>~happy(susan)))<=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((~generous(X)|~rich(X))<=>(funny(X)&~old(X))))&
(![X]:((wise(X)<~>rich(X))=>(kind(X)&~rich(X))))&
(![X]:((kind(X)<~>tall(X))<=>(funny(X)<~>rich(X))))&
(![X]:((brave(X)|~calm(X))=>patient(X)))&
(![X]:((~generous(X)|~old(X))=>(~generous(X)&happy(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((~patient(alice)<~>quiet(alice))))&
((~quiet(mary))<=>((~curious(john)&creative(john))))&
(![X]:((~old(X)|~kind(X))=>~creative(X)))&
(![X]:((generous(X)&~tall(X))<=>(~curious(X)|~quiet(X))))&
(![X]:((kind(X)|~rich(X))=>(~old(X)&~generous(X))))&
(![X]:((~tall(X)|quiet(X))<=>~calm(X)))&
(![X]:(quiet(X)=>(generous(X)|old(X))))&
((?[X]:((~strong(X)|patient(X))))<=>((strong(lucy)|patient(lucy))))&
((wise(mary)<~>~curious(mary)))&
((strong(paul)&humble(paul)))&
((~kind(mary)|~curious(mary)))&
((curious(lucy)<~>old(lucy)))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:(humble(X)))&
(?[X]:(wise(X))) | ~happy(susan) | [] | null | 0 |
Everyone who is humble is not generous or not humble and vice versa.
Everyone who is either not wise or old is not funny or not rich.
If someone is either not humble or not tall then someone is both old and kind and vice versa.
If mary is funny or not calm then fred is both not patient and not wise and vice versa.
If someone is not strong then someone is both not wise and not old and vice versa.
Everyone who is either kind or not funny is either not humble or brave.
If mary is not creative then someone is either kind or not curious and vice versa.
Everyone who is not calm is not humble.
If susan is quiet then alice is not strong or kind.
Everyone who is not tall is either old or kind and vice versa.
If someone is creative then susan is both not tall and not patient.
If fred is both not brave and not kind then paul is quiet.
If someone is both patient and funny then fred is wise and vice versa.
If someone is not patient then someone is either wise or calm.
If lucy is both not happy and generous then someone is not calm or not funny.
If someone is both rich and not happy then someone is either not wise or patient and vice versa.
Someone is either old or wise.
John is both not curious and not generous.
Someone is both wise and funny.
Lucy is not calm or not funny.
Someone is both creative and brave.
Lucy is both not strong and not creative.
Someone is curious or funny. | Fred is not humble. | contradiction | (![X]:(humble(X)<=>(~generous(X)|~humble(X))))&
(![X]:((~wise(X)<~>old(X))=>(~funny(X)|~rich(X))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(?[X]:((old(X)&kind(X)))))&
(((funny(mary)|~calm(mary)))<=>((~patient(fred)&~wise(fred))))&
((?[X]:(~strong(X)))<=>(?[X]:((~wise(X)&~old(X)))))&
(![X]:((kind(X)<~>~funny(X))=>(~humble(X)<~>brave(X))))&
((~creative(mary))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:(~calm(X)=>~humble(X)))&
((quiet(susan))=>((~strong(alice)|kind(alice))))&
(![X]:(~tall(X)<=>(old(X)<~>kind(X))))&
((?[X]:(creative(X)))=>((~tall(susan)&~patient(susan))))&
(((~brave(fred)&~kind(fred)))=>(quiet(paul)))&
((?[X]:((patient(X)&funny(X))))<=>(wise(fred)))&
((?[X]:(~patient(X)))=>(?[X]:((wise(X)<~>calm(X)))))&
(((~happy(lucy)&generous(lucy)))=>(?[X]:((~calm(X)|~funny(X)))))&
((?[X]:((rich(X)&~happy(X))))<=>(?[X]:((~wise(X)<~>patient(X)))))&
(?[X]:((old(X)<~>wise(X))))&
((~curious(john)&~generous(john)))&
(?[X]:((wise(X)&funny(X))))&
((~calm(lucy)|~funny(lucy)))&
(?[X]:((creative(X)&brave(X))))&
((~strong(lucy)&~creative(lucy)))&
(?[X]:((curious(X)|funny(X)))) | ~humble(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 47054181708635698357382
% SZS output start Proof for 47054181708635698357382
1. ! [X0] : (humble(X0) <=> (~humble(X0) | ~generous(X0))) [input p0]
24. ~humble(fred) [input hypothesis]
41. ! [X0] : ((humble(X0) | (humble(X0) & generous(X0))) & ((~humble(X0) | ~generous(X0)) | ~humble(X0))) [nnf transformation 1]
42. ! [X0] : ((humble(X0) | (humble(X0) & generous(X0))) & (~humble(X0) | ~generous(X0) | ~humble(X0))) [flattening 41]
88. humble(X0) | humble(X0) [cnf transformation 42]
146. ~humble(fred) [cnf transformation 24]
148. humble(X0) [duplicate literal removal 88]
354. $false [subsumption resolution 146,148]
% SZS output end Proof for 47054181708635698357382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and quiet is rich or generous and vice versa.
If fred is either brave or old then someone is brave or generous and vice versa.
Everyone who is brave is wise or quiet.
If someone is either not rich or patient then paul is not old.
Everyone who is not wise or quiet is brave and vice versa.
Everyone who is both not strong and not calm is both tall and calm.
If lucy is not brave then someone is either patient or not creative.
If someone is both not old and strong then mary is either not strong or not calm and vice versa.
Everyone who is either not rich or creative is either not old or patient.
If someone is either kind or generous then someone is creative or funny.
If paul is not happy then someone is either not rich or brave and vice versa.
If someone is not wise then paul is not creative.
Everyone who is not quiet or quiet is not curious.
If fred is either not patient or calm then someone is both wise and curious.
If someone is either happy or curious then someone is humble and vice versa.
If someone is not quiet or not brave then paul is not quiet and vice versa.
Paul is both not strong and brave.
Someone is brave or wise.
Paul is rich or patient.
Paul is quiet.
John is not curious or not kind.
Alice is not rich.
Susan is either not curious or creative.
Someone is patient or rich. | Lucy is curious. | contradiction | (![X]:((~old(X)&quiet(X))<=>(rich(X)|generous(X))))&
(((brave(fred)<~>old(fred)))<=>(?[X]:((brave(X)|generous(X)))))&
(![X]:(brave(X)=>(wise(X)|quiet(X))))&
((?[X]:((~rich(X)<~>patient(X))))=>(~old(paul)))&
(![X]:((~wise(X)|quiet(X))<=>brave(X)))&
(![X]:((~strong(X)&~calm(X))=>(tall(X)&calm(X))))&
((~brave(lucy))=>(?[X]:((patient(X)<~>~creative(X)))))&
((?[X]:((~old(X)&strong(X))))<=>((~strong(mary)<~>~calm(mary))))&
(![X]:((~rich(X)<~>creative(X))=>(~old(X)<~>patient(X))))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:((creative(X)|funny(X)))))&
((~happy(paul))<=>(?[X]:((~rich(X)<~>brave(X)))))&
((?[X]:(~wise(X)))=>(~creative(paul)))&
(![X]:((~quiet(X)|quiet(X))=>~curious(X)))&
(((~patient(fred)<~>calm(fred)))=>(?[X]:((wise(X)&curious(X)))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(~quiet(paul)))&
((~strong(paul)&brave(paul)))&
(?[X]:((brave(X)|wise(X))))&
((rich(paul)|patient(paul)))&
(quiet(paul))&
((~curious(john)|~kind(john)))&
(~rich(alice))&
((~curious(susan)<~>creative(susan)))&
(?[X]:((patient(X)|rich(X)))) | curious(lucy) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1772014616345201146979290
% SZS output start Proof for 1772014616345201146979290
13. ! [X0] : ((quiet(X0) | ~quiet(X0)) => ~curious(X0)) [input p12]
25. curious(lucy) [input hypothesis]
39. ! [X0] : (~curious(X0) | (~quiet(X0) & quiet(X0))) [ennf transformation 13]
114. ~curious(X0) | quiet(X0) [cnf transformation 39]
115. ~curious(X0) | ~quiet(X0) [cnf transformation 39]
136. curious(lucy) [cnf transformation 25]
253. ~curious(X0) [subsumption resolution 114,115]
328. $false [subsumption resolution 136,253]
% SZS output end Proof for 1772014616345201146979290
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is generous or not rich and vice versa.
If john is not quiet then paul is curious and vice versa.
If someone is both not patient and not quiet then someone is either not kind or not calm and vice versa.
Everyone who is not generous is not humble.
If someone is rich or not funny then alice is not happy.
Everyone who is both patient and not humble is not curious or not creative.
Everyone who is both not tall and not happy is both old and not happy and vice versa.
Everyone who is both not old and not calm is calm and vice versa.
If susan is strong then alice is not patient and vice versa.
Everyone who is either not humble or not patient is quiet or tall and vice versa.
If susan is not quiet then someone is both not funny and not creative.
Everyone who is old is both funny and brave and vice versa.
If someone is either patient or not calm then mary is both creative and not brave and vice versa.
Everyone who is both not generous and rich is not brave.
Everyone who is not old is both not rich and happy.
If john is strong or quiet then mary is both kind and old and vice versa.
Someone is either creative or strong.
Someone is either funny or not patient.
Paul is not creative.
Paul is rich.
Someone is both not wise and generous. | John is calm. | contradiction | (![X]:(~creative(X)<=>(generous(X)|~rich(X))))&
((~quiet(john))<=>(curious(paul)))&
((?[X]:((~patient(X)&~quiet(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:(~generous(X)=>~humble(X)))&
((?[X]:((rich(X)|~funny(X))))=>(~happy(alice)))&
(![X]:((patient(X)&~humble(X))=>(~curious(X)|~creative(X))))&
(![X]:((~tall(X)&~happy(X))<=>(old(X)&~happy(X))))&
(![X]:((~old(X)&~calm(X))<=>calm(X)))&
((strong(susan))<=>(~patient(alice)))&
(![X]:((~humble(X)<~>~patient(X))<=>(quiet(X)|tall(X))))&
((~quiet(susan))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:(old(X)<=>(funny(X)&brave(X))))&
((?[X]:((patient(X)<~>~calm(X))))<=>((creative(mary)&~brave(mary))))&
(![X]:((~generous(X)&rich(X))=>~brave(X)))&
(![X]:(~old(X)=>(~rich(X)&happy(X))))&
(((strong(john)|quiet(john)))<=>((kind(mary)&old(mary))))&
(?[X]:((creative(X)<~>strong(X))))&
(?[X]:((funny(X)<~>~patient(X))))&
(~creative(paul))&
(rich(paul))&
(?[X]:((~wise(X)&generous(X)))) | calm(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1951561367312549515353659
% SZS output start Proof for 1951561367312549515353659
8. ! [X0] : ((~calm(X0) & ~old(X0)) <=> calm(X0)) [input p7]
22. calm(john) [input hypothesis]
43. ! [X0] : (((~calm(X0) & ~old(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) | old(X0)))) [nnf transformation 8]
44. ! [X0] : (((~calm(X0) & ~old(X0)) | ~calm(X0)) & (calm(X0) | calm(X0) | old(X0))) [flattening 43]
88. ~calm(X0) | ~calm(X0) [cnf transformation 44]
123. calm(john) [cnf transformation 22]
125. ~calm(X0) [duplicate literal removal 88]
233. $false [subsumption resolution 123,125]
% SZS output end Proof for 1951561367312549515353659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not patient is not kind or not brave and vice versa.
If someone is both generous and creative then fred is either not old or not funny.
Everyone who is patient is either strong or generous.
Everyone who is both curious and patient is both wise and patient and vice versa.
Everyone who is brave is either old or not generous.
If someone is brave then susan is both generous and not wise and vice versa.
Everyone who is not patient or creative is both not tall and not wise and vice versa.
If someone is either brave or calm then someone is either not happy or not rich.
If someone is humble or not wise then someone is not patient.
If susan is both strong and not generous then someone is brave.
If someone is brave or kind then someone is not humble or not curious.
If fred is either not kind or wise then susan is both patient and not humble.
Everyone who is both not old and wise is both not happy and not curious and vice versa.
Everyone who is either not rich or not patient is either not quiet or not curious.
If someone is tall then someone is old and vice versa.
Everyone who is both not calm and not humble is either curious or not wise and vice versa.
Someone is kind or creative.
Someone is both not funny and happy.
Someone is not happy.
Mary is both brave and tall.
Someone is not patient.
Someone is generous.
Mary is either not rich or not calm.
Susan is either generous or happy. | Susan is tall. | contradiction | (![X]:((wise(X)&~patient(X))<=>(~kind(X)|~brave(X))))&
((?[X]:((generous(X)&creative(X))))=>((~old(fred)<~>~funny(fred))))&
(![X]:(patient(X)=>(strong(X)<~>generous(X))))&
(![X]:((curious(X)&patient(X))<=>(wise(X)&patient(X))))&
(![X]:(brave(X)=>(old(X)<~>~generous(X))))&
((?[X]:(brave(X)))<=>((generous(susan)&~wise(susan))))&
(![X]:((~patient(X)|creative(X))<=>(~tall(X)&~wise(X))))&
((?[X]:((brave(X)<~>calm(X))))=>(?[X]:((~happy(X)<~>~rich(X)))))&
((?[X]:((humble(X)|~wise(X))))=>(?[X]:(~patient(X))))&
(((strong(susan)&~generous(susan)))=>(?[X]:(brave(X))))&
((?[X]:((brave(X)|kind(X))))=>(?[X]:((~humble(X)|~curious(X)))))&
(((~kind(fred)<~>wise(fred)))=>((patient(susan)&~humble(susan))))&
(![X]:((~old(X)&wise(X))<=>(~happy(X)&~curious(X))))&
(![X]:((~rich(X)<~>~patient(X))=>(~quiet(X)<~>~curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:(old(X))))&
(![X]:((~calm(X)&~humble(X))<=>(curious(X)<~>~wise(X))))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((~funny(X)&happy(X))))&
(?[X]:(~happy(X)))&
((brave(mary)&tall(mary)))&
(?[X]:(~patient(X)))&
(?[X]:(generous(X)))&
((~rich(mary)<~>~calm(mary)))&
((generous(susan)<~>happy(susan))) | tall(susan) | [
"p3",
"p5",
"p6",
"p12",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6258733178076221771372404
% SZS output start Proof for 6258733178076221771372404
4. ! [X0] : ((patient(X0) & curious(X0)) <=> (patient(X0) & wise(X0))) [input p3]
6. ? [X0] : brave(X0) <=> (~wise(susan) & generous(susan)) [input p5]
7. ! [X0] : ((creative(X0) | ~patient(X0)) <=> (~wise(X0) & ~tall(X0))) [input p6]
13. ! [X0] : ((wise(X0) & ~old(X0)) <=> (~curious(X0) & ~happy(X0))) [input p12]
20. tall(mary) & brave(mary) [input p19]
24. generous(susan) <~> happy(susan) [input p23]
25. tall(susan) [input hypothesis]
44. ! [X0] : (((patient(X0) & curious(X0)) | (~patient(X0) | ~wise(X0))) & ((patient(X0) & wise(X0)) | (~patient(X0) | ~curious(X0)))) [nnf transformation 4]
45. ! [X0] : (((patient(X0) & curious(X0)) | ~patient(X0) | ~wise(X0)) & ((patient(X0) & wise(X0)) | ~patient(X0) | ~curious(X0))) [flattening 44]
47. (? [X0] : brave(X0) | (wise(susan) | ~generous(susan))) & ((~wise(susan) & generous(susan)) | ! [X0] : ~brave(X0)) [nnf transformation 6]
48. (? [X0] : brave(X0) | wise(susan) | ~generous(susan)) & ((~wise(susan) & generous(susan)) | ! [X0] : ~brave(X0)) [flattening 47]
49. (? [X0] : brave(X0) | wise(susan) | ~generous(susan)) & ((~wise(susan) & generous(susan)) | ! [X1] : ~brave(X1)) [rectify 48]
50. ? [X0] : brave(X0) => brave(sK0) [choice axiom]
51. (brave(sK0) | wise(susan) | ~generous(susan)) & ((~wise(susan) & generous(susan)) | ! [X1] : ~brave(X1)) [skolemisation 49,50]
52. ! [X0] : (((creative(X0) | ~patient(X0)) | (wise(X0) | tall(X0))) & ((~wise(X0) & ~tall(X0)) | (~creative(X0) & patient(X0)))) [nnf transformation 7]
53. ! [X0] : ((creative(X0) | ~patient(X0) | wise(X0) | tall(X0)) & ((~wise(X0) & ~tall(X0)) | (~creative(X0) & patient(X0)))) [flattening 52]
67. ! [X0] : (((wise(X0) & ~old(X0)) | (curious(X0) | happy(X0))) & ((~curious(X0) & ~happy(X0)) | (~wise(X0) | old(X0)))) [nnf transformation 13]
68. ! [X0] : (((wise(X0) & ~old(X0)) | curious(X0) | happy(X0)) & ((~curious(X0) & ~happy(X0)) | ~wise(X0) | old(X0))) [flattening 67]
88. (~happy(susan) | ~generous(susan)) & (happy(susan) | generous(susan)) [nnf transformation 24]
98. ~curious(X0) | ~patient(X0) | wise(X0) [cnf transformation 45]
104. generous(susan) | ~brave(X1) [cnf transformation 51]
105. ~wise(susan) | ~brave(X1) [cnf transformation 51]
107. ~tall(X0) | patient(X0) [cnf transformation 53]
128. happy(X0) | curious(X0) | wise(X0) [cnf transformation 68]
145. brave(mary) [cnf transformation 20]
152. ~happy(susan) | ~generous(susan) [cnf transformation 88]
153. tall(susan) [cnf transformation 25]
168. 4 <=> generous(susan) [avatar definition]
172. 5 <=> wise(susan) [avatar definition]
173. ~wise(susan) <- (~5) [avatar component clause 172]
181. 7 <=> ! [X1] : ~brave(X1) [avatar definition]
182. ~brave(X1) <- (7) [avatar component clause 181]
183. 7 | ~5 [avatar split clause 105,172,181]
184. 7 | 4 [avatar split clause 104,168,181]
251. 23 <=> patient(susan) [avatar definition]
253. patient(susan) <- (23) [avatar component clause 251]
291. 32 <=> happy(susan) [avatar definition]
293. ~happy(susan) <- (~32) [avatar component clause 291]
294. ~4 | ~32 [avatar split clause 152,291,168]
301. patient(susan) [resolution 107,153]
303. 23 [avatar split clause 301,251]
443. $false <- (7) [resolution 182,145]
446. ~7 [avatar contradiction clause 443]
456. curious(susan) | wise(susan) <- (~32) [resolution 128,293]
466. curious(susan) <- (~5, ~32) [subsumption resolution 456,173]
498. ~patient(susan) | wise(susan) <- (~5, ~32) [resolution 466,98]
499. wise(susan) <- (~5, 23, ~32) [subsumption resolution 498,253]
500. $false <- (~5, 23, ~32) [subsumption resolution 499,173]
501. 5 | ~23 | 32 [avatar contradiction clause 500]
502. $false [avatar sat refutation 183,184,294,303,446,501]
% SZS output end Proof for 6258733178076221771372404
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not funny is funny and vice versa.
Everyone who is happy or quiet is happy or not rich.
If lucy is not funny or kind then john is either not humble or not old.
Everyone who is either not rich or not strong is both humble and funny and vice versa.
Everyone who is quiet or not brave is not old or not patient and vice versa.
If paul is brave then someone is either quiet or creative and vice versa.
Everyone who is not wise or not old is both not funny and patient.
Everyone who is both quiet and old is either not curious or rich and vice versa.
Everyone who is curious or not generous is both curious and strong and vice versa.
If mary is both not kind and happy then lucy is either not tall or quiet.
Everyone who is strong or not kind is not humble and vice versa.
If paul is either rich or strong then someone is either not wise or not happy and vice versa.
Everyone who is humble or patient is not humble.
If someone is generous then mary is either not funny or not wise.
If someone is both not funny and rich then john is both calm and quiet and vice versa.
Everyone who is either funny or patient is not patient or quiet and vice versa.
Fred is either generous or creative.
Alice is rich.
Someone is either rich or not quiet.
Mary is not curious.
Someone is both not creative and patient.
Lucy is kind.
Fred is either not tall or humble.
Fred is both not brave and generous. | Alice is happy. | entailment | (![X]:((kind(X)<~>~funny(X))<=>funny(X)))&
(![X]:((happy(X)|quiet(X))=>(happy(X)|~rich(X))))&
(((~funny(lucy)|kind(lucy)))=>((~humble(john)<~>~old(john))))&
(![X]:((~rich(X)<~>~strong(X))<=>(humble(X)&funny(X))))&
(![X]:((quiet(X)|~brave(X))<=>(~old(X)|~patient(X))))&
((brave(paul))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((~wise(X)|~old(X))=>(~funny(X)&patient(X))))&
(![X]:((quiet(X)&old(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((curious(X)|~generous(X))<=>(curious(X)&strong(X))))&
(((~kind(mary)&happy(mary)))=>((~tall(lucy)<~>quiet(lucy))))&
(![X]:((strong(X)|~kind(X))<=>~humble(X)))&
(((rich(paul)<~>strong(paul)))<=>(?[X]:((~wise(X)<~>~happy(X)))))&
(![X]:((humble(X)|patient(X))=>~humble(X)))&
((?[X]:(generous(X)))=>((~funny(mary)<~>~wise(mary))))&
((?[X]:((~funny(X)&rich(X))))<=>((calm(john)&quiet(john))))&
(![X]:((funny(X)<~>patient(X))<=>(~patient(X)|quiet(X))))&
((generous(fred)<~>creative(fred)))&
(rich(alice))&
(?[X]:((rich(X)<~>~quiet(X))))&
(~curious(mary))&
(?[X]:((~creative(X)&patient(X))))&
(kind(lucy))&
((~tall(fred)<~>humble(fred)))&
((~brave(fred)&generous(fred))) | happy(alice) | [
"p0",
"p1",
"p3",
"p6",
"p10",
"p11",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 777262535029399171352163
% SZS output start Proof for 777262535029399171352163
1. ! [X0] : ((kind(X0) <~> ~funny(X0)) <=> funny(X0)) [input p0]
2. ! [X0] : ((quiet(X0) | happy(X0)) => (~rich(X0) | happy(X0))) [input p1]
4. ! [X0] : ((~rich(X0) <~> ~strong(X0)) <=> (funny(X0) & humble(X0))) [input p3]
7. ! [X0] : ((~old(X0) | ~wise(X0)) => (patient(X0) & ~funny(X0))) [input p6]
11. ! [X0] : ((~kind(X0) | strong(X0)) <=> ~humble(X0)) [input p10]
12. (rich(paul) <~> strong(paul)) <=> ? [X0] : (~wise(X0) <~> ~happy(X0)) [input p11]
13. ! [X0] : ((patient(X0) | humble(X0)) => ~humble(X0)) [input p12]
16. ! [X0] : ((funny(X0) <~> patient(X0)) <=> (quiet(X0) | ~patient(X0))) [input p15]
18. rich(alice) [input p17]
25. ~happy(alice) [input hypothesis]
26. ! [X0] : ((~rich(X0) | happy(X0)) | (~quiet(X0) & ~happy(X0))) [ennf transformation 2]
27. ! [X0] : (~rich(X0) | happy(X0) | (~quiet(X0) & ~happy(X0))) [flattening 26]
29. ! [X0] : ((patient(X0) & ~funny(X0)) | (old(X0) & wise(X0))) [ennf transformation 7]
32. ! [X0] : (~humble(X0) | (~patient(X0) & ~humble(X0))) [ennf transformation 13]
34. ! [X0] : ((((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | ~funny(X0)) & (funny(X0) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0))))) [nnf transformation 1]
36. ! [X0] : ((((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))))) [nnf transformation 4]
37. ! [X0] : ((((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))))) [flattening 36]
49. ! [X0] : (((~kind(X0) | strong(X0)) | humble(X0)) & (~humble(X0) | (kind(X0) & ~strong(X0)))) [nnf transformation 11]
50. ! [X0] : ((~kind(X0) | strong(X0) | humble(X0)) & (~humble(X0) | (kind(X0) & ~strong(X0)))) [flattening 49]
51. (((~strong(paul) | ~rich(paul)) & (strong(paul) | rich(paul))) | ! [X0] : ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (? [X0] : ((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ((rich(paul) | ~strong(paul)) & (strong(paul) | ~rich(paul)))) [nnf transformation 12]
52. (((~strong(paul) | ~rich(paul)) & (strong(paul) | rich(paul))) | ! [X0] : ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (? [X1] : ((happy(X1) | wise(X1)) & (~happy(X1) | ~wise(X1))) | ((rich(paul) | ~strong(paul)) & (strong(paul) | ~rich(paul)))) [rectify 51]
53. ? [X1] : ((happy(X1) | wise(X1)) & (~happy(X1) | ~wise(X1))) => ((happy(sK1) | wise(sK1)) & (~happy(sK1) | ~wise(sK1))) [choice axiom]
54. (((~strong(paul) | ~rich(paul)) & (strong(paul) | rich(paul))) | ! [X0] : ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(sK1) | wise(sK1)) & (~happy(sK1) | ~wise(sK1))) | ((rich(paul) | ~strong(paul)) & (strong(paul) | ~rich(paul)))) [skolemisation 52,53]
61. ! [X0] : ((((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (~quiet(X0) & patient(X0))) & ((quiet(X0) | ~patient(X0)) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0))))) [nnf transformation 16]
62. ! [X0] : ((((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (~quiet(X0) & patient(X0))) & (quiet(X0) | ~patient(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0))))) [flattening 61]
71. funny(X0) | kind(X0) | funny(X0) [cnf transformation 34]
72. ~funny(X0) | kind(X0) | ~funny(X0) [cnf transformation 34]
75. ~rich(X0) | happy(X0) | ~quiet(X0) [cnf transformation 27]
80. ~strong(X0) | humble(X0) | rich(X0) [cnf transformation 37]
94. ~funny(X0) | wise(X0) [cnf transformation 29]
113. ~kind(X0) | strong(X0) | humble(X0) [cnf transformation 50]
121. ~strong(paul) | ~rich(paul) | ~wise(X0) | happy(X0) [cnf transformation 54]
122. ~humble(X0) | ~humble(X0) [cnf transformation 32]
131. quiet(X0) | ~patient(X0) | funny(X0) | ~patient(X0) [cnf transformation 62]
132. patient(X0) | funny(X0) | patient(X0) [cnf transformation 62]
138. rich(alice) [cnf transformation 18]
149. ~happy(alice) [cnf transformation 25]
150. quiet(X0) | ~patient(X0) | funny(X0) [duplicate literal removal 131]
151. patient(X0) | funny(X0) [duplicate literal removal 132]
152. ~humble(X0) [duplicate literal removal 122]
153. funny(X0) | kind(X0) [duplicate literal removal 71]
154. ~funny(X0) | kind(X0) [duplicate literal removal 72]
155. kind(X0) [subsumption resolution 153,154]
196. strong(X0) | humble(X0) [subsumption resolution 113,155]
198. 9 <=> ! [X0] : (~wise(X0) | happy(X0)) [avatar definition]
199. ~wise(X0) | happy(X0) <- (9) [avatar component clause 198]
201. 10 <=> rich(paul) [avatar definition]
203. ~rich(paul) <- (~10) [avatar component clause 201]
205. 11 <=> strong(paul) [avatar definition]
207. ~strong(paul) <- (~11) [avatar component clause 205]
208. 9 | ~10 | ~11 [avatar split clause 121,205,201,198]
265. quiet(X0) | funny(X0) [subsumption resolution 150,151]
294. humble(paul) <- (~11) [resolution 196,207]
296. $false <- (~11) [subsumption resolution 294,152]
297. 11 [avatar contradiction clause 296]
305. happy(alice) | ~quiet(alice) [resolution 75,138]
308. ~quiet(alice) [subsumption resolution 305,149]
330. humble(X0) | rich(X0) | humble(X0) [resolution 80,196]
332. humble(X0) | rich(X0) [duplicate literal removal 330]
333. rich(X0) [subsumption resolution 332,152]
334. funny(alice) [resolution 308,265]
401. wise(alice) [resolution 334,94]
488. happy(alice) <- (9) [resolution 401,199]
489. $false <- (9) [subsumption resolution 488,149]
490. ~9 [avatar contradiction clause 489]
491. $false <- (~10) [subsumption resolution 203,333]
492. 10 [avatar contradiction clause 491]
493. $false [avatar sat refutation 208,297,490,492]
% SZS output end Proof for 777262535029399171352163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and happy then lucy is wise and vice versa.
If john is not funny or funny then john is wise.
Everyone who is both not tall and humble is both not funny and not rich.
If someone is either not patient or not happy then someone is tall and vice versa.
Everyone who is not patient or kind is not quiet or happy and vice versa.
Everyone who is not brave is not funny and vice versa.
Everyone who is strong is curious.
Everyone who is curious or strong is both happy and not creative.
If alice is happy or wise then fred is both not calm and patient.
If paul is both not curious and not rich then paul is generous or strong.
If fred is patient or rich then someone is both not tall and rich.
Everyone who is not generous or tall is both not curious and not generous.
Everyone who is either not happy or not tall is both quiet and not curious and vice versa.
Everyone who is both funny and not rich is not kind and vice versa.
Everyone who is curious is both not humble and not curious and vice versa.
Everyone who is generous or not patient is both kind and not generous.
Someone is kind or calm.
Lucy is calm or not funny.
Someone is rich.
Susan is quiet or not calm.
Alice is both quiet and not curious.
Someone is not wise. | Paul is not happy. | contradiction | ((?[X]:((~humble(X)&happy(X))))<=>(wise(lucy)))&
(((~funny(john)|funny(john)))=>(wise(john)))&
(![X]:((~tall(X)&humble(X))=>(~funny(X)&~rich(X))))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(?[X]:(tall(X))))&
(![X]:((~patient(X)|kind(X))<=>(~quiet(X)|happy(X))))&
(![X]:(~brave(X)<=>~funny(X)))&
(![X]:(strong(X)=>curious(X)))&
(![X]:((curious(X)|strong(X))=>(happy(X)&~creative(X))))&
(((happy(alice)|wise(alice)))=>((~calm(fred)&patient(fred))))&
(((~curious(paul)&~rich(paul)))=>((generous(paul)|strong(paul))))&
(((patient(fred)|rich(fred)))=>(?[X]:((~tall(X)&rich(X)))))&
(![X]:((~generous(X)|tall(X))=>(~curious(X)&~generous(X))))&
(![X]:((~happy(X)<~>~tall(X))<=>(quiet(X)&~curious(X))))&
(![X]:((funny(X)&~rich(X))<=>~kind(X)))&
(![X]:(curious(X)<=>(~humble(X)&~curious(X))))&
(![X]:((generous(X)|~patient(X))=>(kind(X)&~generous(X))))&
(?[X]:((kind(X)|calm(X))))&
((calm(lucy)|~funny(lucy)))&
(?[X]:(rich(X)))&
((quiet(susan)|~calm(susan)))&
((quiet(alice)&~curious(alice)))&
(?[X]:(~wise(X))) | ~happy(paul) | [
"p2",
"p4",
"p6",
"p7",
"p9",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1510346209631788320896396
% SZS output start Proof for 1510346209631788320896396
3. ! [X0] : ((humble(X0) & ~tall(X0)) => (~rich(X0) & ~funny(X0))) [input p2]
5. ! [X0] : ((kind(X0) | ~patient(X0)) <=> (happy(X0) | ~quiet(X0))) [input p4]
7. ! [X0] : (strong(X0) => curious(X0)) [input p6]
8. ! [X0] : ((strong(X0) | curious(X0)) => (~creative(X0) & happy(X0))) [input p7]
10. (~rich(paul) & ~curious(paul)) => (strong(paul) | generous(paul)) [input p9]
12. ! [X0] : ((tall(X0) | ~generous(X0)) => (~generous(X0) & ~curious(X0))) [input p11]
13. ! [X0] : ((~happy(X0) <~> ~tall(X0)) <=> (~curious(X0) & quiet(X0))) [input p12]
14. ! [X0] : ((~rich(X0) & funny(X0)) <=> ~kind(X0)) [input p13]
15. ! [X0] : (curious(X0) <=> (~curious(X0) & ~humble(X0))) [input p14]
16. ! [X0] : ((~patient(X0) | generous(X0)) => (~generous(X0) & kind(X0))) [input p15]
23. ~happy(paul) [input hypothesis]
25. ! [X0] : ((strong(X0) | curious(X0)) => happy(X0)) [pure predicate removal 8]
27. ! [X0] : ((~rich(X0) & ~funny(X0)) | (~humble(X0) | tall(X0))) [ennf transformation 3]
28. ! [X0] : ((~rich(X0) & ~funny(X0)) | ~humble(X0) | tall(X0)) [flattening 27]
29. ! [X0] : (curious(X0) | ~strong(X0)) [ennf transformation 7]
30. ! [X0] : (happy(X0) | (~strong(X0) & ~curious(X0))) [ennf transformation 25]
32. (strong(paul) | generous(paul)) | (rich(paul) | curious(paul)) [ennf transformation 10]
33. strong(paul) | generous(paul) | rich(paul) | curious(paul) [flattening 32]
35. ! [X0] : ((~generous(X0) & ~curious(X0)) | (~tall(X0) & generous(X0))) [ennf transformation 12]
36. ! [X0] : ((~generous(X0) & kind(X0)) | (patient(X0) & ~generous(X0))) [ennf transformation 16]
46. ! [X0] : (((kind(X0) | ~patient(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~kind(X0) & patient(X0)))) [nnf transformation 5]
47. ! [X0] : ((kind(X0) | ~patient(X0) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | (~kind(X0) & patient(X0)))) [flattening 46]
50. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [nnf transformation 13]
51. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [flattening 50]
52. ! [X0] : (((~rich(X0) & funny(X0)) | kind(X0)) & (~kind(X0) | (rich(X0) | ~funny(X0)))) [nnf transformation 14]
53. ! [X0] : (((~rich(X0) & funny(X0)) | kind(X0)) & (~kind(X0) | rich(X0) | ~funny(X0))) [flattening 52]
54. ! [X0] : ((curious(X0) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | ~curious(X0))) [nnf transformation 15]
55. ! [X0] : ((curious(X0) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | ~curious(X0))) [flattening 54]
68. ~rich(X0) | ~humble(X0) | tall(X0) [cnf transformation 28]
74. ~quiet(X0) | happy(X0) | ~kind(X0) [cnf transformation 47]
77. ~strong(X0) | curious(X0) [cnf transformation 29]
78. ~curious(X0) | happy(X0) [cnf transformation 30]
84. strong(paul) | generous(paul) | rich(paul) | curious(paul) [cnf transformation 33]
90. ~curious(X0) | ~tall(X0) [cnf transformation 35]
93. ~tall(X0) | quiet(X0) | happy(X0) [cnf transformation 51]
96. ~curious(X0) | ~happy(X0) | tall(X0) [cnf transformation 51]
101. ~rich(X0) | kind(X0) [cnf transformation 53]
104. curious(X0) | curious(X0) | humble(X0) [cnf transformation 55]
107. ~generous(X0) | ~generous(X0) [cnf transformation 36]
116. ~happy(paul) [cnf transformation 23]
117. ~generous(X0) [duplicate literal removal 107]
119. curious(X0) | humble(X0) [duplicate literal removal 104]
193. generous(paul) | rich(paul) | curious(paul) [subsumption resolution 84,77]
195. 17 <=> curious(paul) [avatar definition]
197. curious(paul) <- (17) [avatar component clause 195]
199. 18 <=> rich(paul) [avatar definition]
201. rich(paul) <- (18) [avatar component clause 199]
203. 19 <=> generous(paul) [avatar definition]
205. generous(paul) <- (19) [avatar component clause 203]
206. 17 | 18 | 19 [avatar split clause 193,203,199,195]
225. ~curious(X0) | tall(X0) [subsumption resolution 96,78]
226. ~curious(X0) [subsumption resolution 225,90]
227. humble(X0) [subsumption resolution 119,226]
255. $false <- (17) [subsumption resolution 197,226]
256. ~17 [avatar contradiction clause 255]
260. kind(paul) <- (18) [resolution 101,201]
262. ~humble(paul) | tall(paul) <- (18) [resolution 68,201]
264. tall(paul) <- (18) [subsumption resolution 262,227]
275. quiet(paul) | happy(paul) <- (18) [resolution 93,264]
294. quiet(paul) <- (18) [subsumption resolution 275,116]
365. happy(paul) | ~kind(paul) <- (18) [resolution 294,74]
367. ~kind(paul) <- (18) [subsumption resolution 365,116]
368. $false <- (18) [subsumption resolution 367,260]
369. ~18 [avatar contradiction clause 368]
371. $false <- (19) [subsumption resolution 205,117]
372. ~19 [avatar contradiction clause 371]
373. $false [avatar sat refutation 206,256,369,372]
% SZS output end Proof for 1510346209631788320896396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not calm is not happy or not wise.
Everyone who is not humble is rich and vice versa.
If alice is rich then susan is wise or not quiet.
If alice is both not funny and quiet then someone is either funny or wise.
If susan is not wise then mary is kind and vice versa.
Everyone who is both not wise and calm is not old and vice versa.
If someone is either humble or not patient then someone is both happy and not calm and vice versa.
If john is either curious or calm then someone is quiet or old.
Everyone who is both strong and curious is not humble.
If paul is either rich or not humble then someone is curious.
If mary is not creative or not generous then john is curious.
Everyone who is not strong or happy is either not tall or rich and vice versa.
If john is not rich then lucy is both not generous and brave and vice versa.
Everyone who is either kind or humble is both not creative and kind.
Everyone who is both curious and not calm is either calm or kind.
Paul is both old and not quiet.
John is either not brave or quiet.
Paul is either not strong or not calm.
Someone is either not old or not generous.
John is either not humble or old.
Mary is either not patient or kind.
Someone is not funny. | John is not brave. | neutral | (![X]:((funny(X)|~calm(X))=>(~happy(X)|~wise(X))))&
(![X]:(~humble(X)<=>rich(X)))&
((rich(alice))=>((wise(susan)|~quiet(susan))))&
(((~funny(alice)&quiet(alice)))=>(?[X]:((funny(X)<~>wise(X)))))&
((~wise(susan))<=>(kind(mary)))&
(![X]:((~wise(X)&calm(X))<=>~old(X)))&
((?[X]:((humble(X)<~>~patient(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(((curious(john)<~>calm(john)))=>(?[X]:((quiet(X)|old(X)))))&
(![X]:((strong(X)&curious(X))=>~humble(X)))&
(((rich(paul)<~>~humble(paul)))=>(?[X]:(curious(X))))&
(((~creative(mary)|~generous(mary)))=>(curious(john)))&
(![X]:((~strong(X)|happy(X))<=>(~tall(X)<~>rich(X))))&
((~rich(john))<=>((~generous(lucy)&brave(lucy))))&
(![X]:((kind(X)<~>humble(X))=>(~creative(X)&kind(X))))&
(![X]:((curious(X)&~calm(X))=>(calm(X)<~>kind(X))))&
((old(paul)&~quiet(paul)))&
((~brave(john)<~>quiet(john)))&
((~strong(paul)<~>~calm(paul)))&
(?[X]:((~old(X)<~>~generous(X))))&
((~humble(john)<~>old(john)))&
((~patient(mary)<~>kind(mary)))&
(?[X]:(~funny(X))) | ~brave(john) | [] | null | 0 |
Everyone who is either not rich or not happy is both not brave and not rich. Everyone who is not kind or wise is both not calm and wise. Everyone who is humble is both quiet and not patient. If alice is both not patient and brave then lucy is humble and vice versa. If someone is creative or not happy then mary is not quiet or patient and vice versa. Everyone who is both strong and generous is not tall. If paul is not creative or humble then someone is not happy or wise. If lucy is either not old or wise then paul is either not brave or calm and vice versa. Everyone who is either not happy or not wise is not patient or not funny and vice versa. If john is brave or strong then mary is old or not rich and vice versa. If someone is either tall or old then lucy is wise. If lucy is funny or not funny then someone is not wise or not old and vice versa. Everyone who is both not happy and wise is not calm or not patient and vice versa. If someone is brave then mary is both generous and not kind. Everyone who is tall or strong is both rich and generous and vice versa. Everyone who is both not humble and rich is either not kind or not rich and vice versa. Someone is patient or strong. Paul is not old or creative. Someone is not calm or happy. Someone is either kind or not humble. Paul is either old or humble. Susan is calm or generous. Someone is either not kind or patient. Lucy is not humble. | John is not calm. | entailment | (![X]:((~rich(X)<~>~happy(X))=>(~brave(X)&~rich(X))))&
(![X]:((~kind(X)|wise(X))=>(~calm(X)&wise(X))))&
(![X]:(humble(X)=>(quiet(X)&~patient(X))))&
(((~patient(alice)&brave(alice)))<=>(humble(lucy)))&
((?[X]:((creative(X)|~happy(X))))<=>((~quiet(mary)|patient(mary))))&
(![X]:((strong(X)&generous(X))=>~tall(X)))&
(((~creative(paul)|humble(paul)))=>(?[X]:((~happy(X)|wise(X)))))&
(((~old(lucy)<~>wise(lucy)))<=>((~brave(paul)<~>calm(paul))))&
(![X]:((~happy(X)<~>~wise(X))<=>(~patient(X)|~funny(X))))&
(((brave(john)|strong(john)))<=>((old(mary)|~rich(mary))))&
((?[X]:((tall(X)<~>old(X))))=>(wise(lucy)))&
(((funny(lucy)|~funny(lucy)))<=>(?[X]:((~wise(X)|~old(X)))))&
(![X]:((~happy(X)&wise(X))<=>(~calm(X)|~patient(X))))&
((?[X]:(brave(X)))=>((generous(mary)&~kind(mary))))&
(![X]:((tall(X)|strong(X))<=>(rich(X)&generous(X))))&
(![X]:((~humble(X)&rich(X))<=>(~kind(X)<~>~rich(X))))&
(?[X]:((patient(X)|strong(X))))&
((~old(paul)|creative(paul)))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:((kind(X)<~>~humble(X))))&
((old(paul)<~>humble(paul)))&
((calm(susan)|generous(susan)))&
(?[X]:((~kind(X)<~>patient(X))))&
(~humble(lucy)) | ~calm(john) | [
"p1",
"p2",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4463118873654291804529255
% SZS output start Proof for 4463118873654291804529255
2. ! [X0] : ((wise(X0) | ~kind(X0)) => (wise(X0) & ~calm(X0))) [input p1]
3. ! [X0] : (humble(X0) => (~patient(X0) & quiet(X0))) [input p2]
13. ! [X0] : ((wise(X0) & ~happy(X0)) <=> (~patient(X0) | ~calm(X0))) [input p12]
16. ! [X0] : ((rich(X0) & ~humble(X0)) <=> (~kind(X0) <~> ~rich(X0))) [input p15]
25. calm(john) [input hypothesis]
27. ! [X0] : ((wise(X0) & ~calm(X0)) | (~wise(X0) & kind(X0))) [ennf transformation 2]
28. ! [X0] : ((~patient(X0) & quiet(X0)) | ~humble(X0)) [ennf transformation 3]
55. ! [X0] : (((wise(X0) & ~happy(X0)) | (patient(X0) & calm(X0))) & ((~patient(X0) | ~calm(X0)) | (~wise(X0) | happy(X0)))) [nnf transformation 13]
56. ! [X0] : (((wise(X0) & ~happy(X0)) | (patient(X0) & calm(X0))) & (~patient(X0) | ~calm(X0) | ~wise(X0) | happy(X0))) [flattening 55]
59. ! [X0] : (((rich(X0) & ~humble(X0)) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | (~rich(X0) | humble(X0)))) [nnf transformation 16]
60. ! [X0] : (((rich(X0) & ~humble(X0)) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | ~rich(X0) | humble(X0))) [flattening 59]
76. ~calm(X0) | kind(X0) [cnf transformation 27]
77. ~calm(X0) | ~wise(X0) [cnf transformation 27]
81. ~patient(X0) | ~humble(X0) [cnf transformation 28]
120. patient(X0) | wise(X0) [cnf transformation 56]
128. ~rich(X0) | ~kind(X0) | ~rich(X0) | humble(X0) [cnf transformation 60]
133. rich(X0) | ~kind(X0) | rich(X0) [cnf transformation 60]
145. calm(john) [cnf transformation 25]
146. ~rich(X0) | ~kind(X0) | humble(X0) [duplicate literal removal 128]
147. ~kind(X0) | rich(X0) [duplicate literal removal 133]
287. ~kind(X0) | humble(X0) [subsumption resolution 146,147]
342. kind(john) [resolution 76,145]
345. ~wise(john) [resolution 77,145]
358. ~humble(X0) | wise(X0) [resolution 120,81]
370. humble(john) [resolution 287,342]
425. wise(john) [resolution 358,370]
430. $false [subsumption resolution 425,345]
% SZS output end Proof for 4463118873654291804529255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not calm or not kind then mary is not creative or calm. Everyone who is patient or not creative is strong or not quiet. Everyone who is not brave is wise. If someone is rich then john is not curious or not patient. If mary is tall or not patient then mary is not rich. Everyone who is either not old or not brave is calm or not generous. Everyone who is old is happy. Everyone who is either not wise or not brave is brave or not happy and vice versa. Everyone who is strong or old is not generous or wise and vice versa. Everyone who is humble or not happy is not rich or old and vice versa. Everyone who is not strong or not humble is not calm or curious and vice versa. If someone is both not old and happy then lucy is wise. If someone is tall then alice is not wise. Everyone who is both calm and kind is either strong or tall. If someone is either generous or strong then fred is either not happy or wise. Everyone who is both old and patient is not quiet and vice versa. Alice is either calm or generous. Someone is not creative or not tall. Someone is quiet or patient. Someone is both creative and curious. Mary is either not strong or kind. Someone is both wise and not happy. Someone is not calm. Someone is not curious or humble. | Alice is calm. | neutral | (((~calm(paul)<~>~kind(paul)))=>((~creative(mary)|calm(mary))))&
(![X]:((patient(X)|~creative(X))=>(strong(X)|~quiet(X))))&
(![X]:(~brave(X)=>wise(X)))&
((?[X]:(rich(X)))=>((~curious(john)|~patient(john))))&
(((tall(mary)|~patient(mary)))=>(~rich(mary)))&
(![X]:((~old(X)<~>~brave(X))=>(calm(X)|~generous(X))))&
(![X]:(old(X)=>happy(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(brave(X)|~happy(X))))&
(![X]:((strong(X)|old(X))<=>(~generous(X)|wise(X))))&
(![X]:((humble(X)|~happy(X))<=>(~rich(X)|old(X))))&
(![X]:((~strong(X)|~humble(X))<=>(~calm(X)|curious(X))))&
((?[X]:((~old(X)&happy(X))))=>(wise(lucy)))&
((?[X]:(tall(X)))=>(~wise(alice)))&
(![X]:((calm(X)&kind(X))=>(strong(X)<~>tall(X))))&
((?[X]:((generous(X)<~>strong(X))))=>((~happy(fred)<~>wise(fred))))&
(![X]:((old(X)&patient(X))<=>~quiet(X)))&
((calm(alice)<~>generous(alice)))&
(?[X]:((~creative(X)|~tall(X))))&
(?[X]:((quiet(X)|patient(X))))&
(?[X]:((creative(X)&curious(X))))&
((~strong(mary)<~>kind(mary)))&
(?[X]:((wise(X)&~happy(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~curious(X)|humble(X)))) | calm(alice) | [] | null | 0 |
If someone is both not happy and not kind then someone is either not happy or brave and vice versa. If alice is either not rich or strong then alice is happy. If paul is both not funny and not kind then susan is not old and vice versa. Everyone who is kind or not funny is both not rich and humble and vice versa. Everyone who is not calm or not creative is either not calm or wise. Everyone who is tall or calm is either not tall or not creative. If john is wise then someone is both not strong and wise. Everyone who is both creative and wise is strong or not wise. Everyone who is both not rich and not old is not strong or strong and vice versa. If someone is not old then alice is calm or not brave and vice versa. Everyone who is not creative or not rich is either happy or not calm and vice versa. If someone is both happy and tall then someone is either not humble or patient. Everyone who is happy is not funny or not old. If john is both funny and strong then someone is not strong and vice versa. Everyone who is brave is both not quiet and not strong and vice versa. Everyone who is not patient is both wise and tall and vice versa. Someone is not funny. Susan is either tall or old. Someone is not generous. Someone is not generous or not brave. Someone is not calm or wise. Paul is rich or calm. Someone is not kind. Paul is either not wise or generous. | Susan is tall. | entailment | ((?[X]:((~happy(X)&~kind(X))))<=>(?[X]:((~happy(X)<~>brave(X)))))&
(((~rich(alice)<~>strong(alice)))=>(happy(alice)))&
(((~funny(paul)&~kind(paul)))<=>(~old(susan)))&
(![X]:((kind(X)|~funny(X))<=>(~rich(X)&humble(X))))&
(![X]:((~calm(X)|~creative(X))=>(~calm(X)<~>wise(X))))&
(![X]:((tall(X)|calm(X))=>(~tall(X)<~>~creative(X))))&
((wise(john))=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:((creative(X)&wise(X))=>(strong(X)|~wise(X))))&
(![X]:((~rich(X)&~old(X))<=>(~strong(X)|strong(X))))&
((?[X]:(~old(X)))<=>((calm(alice)|~brave(alice))))&
(![X]:((~creative(X)|~rich(X))<=>(happy(X)<~>~calm(X))))&
((?[X]:((happy(X)&tall(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:(happy(X)=>(~funny(X)|~old(X))))&
(((funny(john)&strong(john)))<=>(?[X]:(~strong(X))))&
(![X]:(brave(X)<=>(~quiet(X)&~strong(X))))&
(![X]:(~patient(X)<=>(wise(X)&tall(X))))&
(?[X]:(~funny(X)))&
((tall(susan)<~>old(susan)))&
(?[X]:(~generous(X)))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((~calm(X)|wise(X))))&
((rich(paul)|calm(paul)))&
(?[X]:(~kind(X)))&
((~wise(paul)<~>generous(paul))) | tall(susan) | [
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1123916182701033819780258
% SZS output start Proof for 1123916182701033819780258
9. ! [X0] : ((~old(X0) & ~rich(X0)) <=> (strong(X0) | ~strong(X0))) [input p8]
18. tall(susan) <~> old(susan) [input p17]
25. ~tall(susan) [input hypothesis]
51. ! [X0] : (((~old(X0) & ~rich(X0)) | (~strong(X0) & strong(X0))) & ((strong(X0) | ~strong(X0)) | (old(X0) | rich(X0)))) [nnf transformation 9]
52. ! [X0] : (((~old(X0) & ~rich(X0)) | (~strong(X0) & strong(X0))) & (strong(X0) | ~strong(X0) | old(X0) | rich(X0))) [flattening 51]
75. (~old(susan) | ~tall(susan)) & (old(susan) | tall(susan)) [nnf transformation 18]
115. ~old(X0) | strong(X0) [cnf transformation 52]
116. ~old(X0) | ~strong(X0) [cnf transformation 52]
139. old(susan) | tall(susan) [cnf transformation 75]
148. ~tall(susan) [cnf transformation 25]
226. ~old(X0) [subsumption resolution 115,116]
271. tall(susan) [subsumption resolution 139,226]
301. $false [subsumption resolution 148,271]
% SZS output end Proof for 1123916182701033819780258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not generous or calm.
If someone is happy or tall then fred is not generous or brave.
Everyone who is not calm is happy and vice versa.
If someone is creative or not calm then susan is both humble and not wise and vice versa.
Everyone who is either not patient or not calm is both old and calm and vice versa.
If someone is both quiet and strong then john is both calm and strong and vice versa.
Everyone who is either rich or not old is both funny and happy.
Everyone who is happy is calm.
Everyone who is funny or generous is patient or strong.
Everyone who is not patient is both not tall and funny.
Everyone who is either old or patient is both funny and not quiet.
If mary is both not funny and quiet then someone is not brave.
Everyone who is both wise and not generous is not rich or creative.
If paul is strong or generous then mary is either happy or humble.
If someone is both quiet and funny then someone is not strong.
Lucy is tall.
Alice is either curious or strong.
Someone is not strong.
Someone is old.
Mary is generous or not quiet.
Someone is either not happy or not rich.
Someone is either generous or not tall.
Someone is not brave or patient. | John is not happy. | entailment | (![X]:(funny(X)=>(~generous(X)|calm(X))))&
((?[X]:((happy(X)|tall(X))))=>((~generous(fred)|brave(fred))))&
(![X]:(~calm(X)<=>happy(X)))&
((?[X]:((creative(X)|~calm(X))))<=>((humble(susan)&~wise(susan))))&
(![X]:((~patient(X)<~>~calm(X))<=>(old(X)&calm(X))))&
((?[X]:((quiet(X)&strong(X))))<=>((calm(john)&strong(john))))&
(![X]:((rich(X)<~>~old(X))=>(funny(X)&happy(X))))&
(![X]:(happy(X)=>calm(X)))&
(![X]:((funny(X)|generous(X))=>(patient(X)|strong(X))))&
(![X]:(~patient(X)=>(~tall(X)&funny(X))))&
(![X]:((old(X)<~>patient(X))=>(funny(X)&~quiet(X))))&
(((~funny(mary)&quiet(mary)))=>(?[X]:(~brave(X))))&
(![X]:((wise(X)&~generous(X))=>(~rich(X)|creative(X))))&
(((strong(paul)|generous(paul)))=>((happy(mary)<~>humble(mary))))&
((?[X]:((quiet(X)&funny(X))))=>(?[X]:(~strong(X))))&
(tall(lucy))&
((curious(alice)<~>strong(alice)))&
(?[X]:(~strong(X)))&
(?[X]:(old(X)))&
((generous(mary)|~quiet(mary)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(?[X]:((generous(X)<~>~tall(X))))&
(?[X]:((~brave(X)|patient(X)))) | ~happy(john) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8033362598387979069347765
% SZS output start Proof for 8033362598387979069347765
3. ! [X0] : (~calm(X0) <=> happy(X0)) [input p2]
8. ! [X0] : (happy(X0) => calm(X0)) [input p7]
24. happy(john) [input hypothesis]
31. ! [X0] : (calm(X0) | ~happy(X0)) [ennf transformation 8]
42. ! [X0] : ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))) [nnf transformation 3]
80. ~calm(X0) | ~happy(X0) [cnf transformation 42]
100. calm(X0) | ~happy(X0) [cnf transformation 31]
127. happy(john) [cnf transformation 24]
143. 4 <=> ! [X0] : ~happy(X0) [avatar definition]
144. ~happy(X0) <- (4) [avatar component clause 143]
196. ~happy(X0) [subsumption resolution 100,80]
197. 4 [avatar split clause 196,143]
284. $false <- (4) [resolution 144,127]
285. ~4 [avatar contradiction clause 284]
286. $false [avatar sat refutation 197,285]
% SZS output end Proof for 8033362598387979069347765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and calm then someone is patient.
Everyone who is not kind is both not rich and not funny.
Everyone who is not tall is not creative.
If someone is either calm or tall then someone is both wise and old and vice versa.
If someone is either not creative or not kind then fred is both not curious and not rich and vice versa.
If mary is happy then someone is both happy and not old.
Everyone who is calm is either not old or humble.
If someone is either not funny or not quiet then someone is both wise and happy.
If fred is either not creative or tall then someone is both strong and not kind and vice versa.
Everyone who is either not humble or rich is both wise and not funny.
Everyone who is generous or old is both not rich and not humble and vice versa.
If fred is both quiet and humble then mary is old or not humble.
Everyone who is creative is not kind and vice versa.
If someone is not humble then paul is either not humble or curious.
If alice is either generous or not kind then paul is either not happy or brave and vice versa.
Everyone who is either not generous or brave is both funny and not curious.
Someone is either humble or not creative.
John is not rich.
Someone is both not curious and tall.
Someone is both not wise and brave.
Susan is either humble or old.
Someone is both not creative and rich.
Someone is either not tall or not wise.
Someone is not generous or not calm. | John is generous. | neutral | ((?[X]:((~humble(X)&calm(X))))=>(?[X]:(patient(X))))&
(![X]:(~kind(X)=>(~rich(X)&~funny(X))))&
(![X]:(~tall(X)=>~creative(X)))&
((?[X]:((calm(X)<~>tall(X))))<=>(?[X]:((wise(X)&old(X)))))&
((?[X]:((~creative(X)<~>~kind(X))))<=>((~curious(fred)&~rich(fred))))&
((happy(mary))=>(?[X]:((happy(X)&~old(X)))))&
(![X]:(calm(X)=>(~old(X)<~>humble(X))))&
((?[X]:((~funny(X)<~>~quiet(X))))=>(?[X]:((wise(X)&happy(X)))))&
(((~creative(fred)<~>tall(fred)))<=>(?[X]:((strong(X)&~kind(X)))))&
(![X]:((~humble(X)<~>rich(X))=>(wise(X)&~funny(X))))&
(![X]:((generous(X)|old(X))<=>(~rich(X)&~humble(X))))&
(((quiet(fred)&humble(fred)))=>((old(mary)|~humble(mary))))&
(![X]:(creative(X)<=>~kind(X)))&
((?[X]:(~humble(X)))=>((~humble(paul)<~>curious(paul))))&
(((generous(alice)<~>~kind(alice)))<=>((~happy(paul)<~>brave(paul))))&
(![X]:((~generous(X)<~>brave(X))=>(funny(X)&~curious(X))))&
(?[X]:((humble(X)<~>~creative(X))))&
(~rich(john))&
(?[X]:((~curious(X)&tall(X))))&
(?[X]:((~wise(X)&brave(X))))&
((humble(susan)<~>old(susan)))&
(?[X]:((~creative(X)&rich(X))))&
(?[X]:((~tall(X)<~>~wise(X))))&
(?[X]:((~generous(X)|~calm(X)))) | generous(john) | [] | null | 0 |
Everyone who is not old or tall is either happy or curious and vice versa. Everyone who is both funny and old is not rich and vice versa. If someone is not humble or calm then alice is not strong and vice versa. If someone is either not kind or tall then someone is not humble. Everyone who is both humble and not funny is either not strong or not happy and vice versa. Everyone who is both not kind and creative is calm. If someone is both patient and calm then lucy is brave or quiet. If someone is both not creative and wise then mary is both wise and not old and vice versa. Everyone who is not strong or not calm is curious or not strong and vice versa. If susan is not generous then someone is not funny. Everyone who is generous or not generous is both not brave and not wise and vice versa. Everyone who is funny is both not strong and not kind and vice versa. If someone is either happy or not old then paul is both not quiet and not kind. Everyone who is kind or not strong is both not funny and not humble. Everyone who is either not patient or not brave is not patient or strong and vice versa. If mary is not generous or brave then alice is rich or calm. Mary is happy or not creative. Fred is strong or not generous. Someone is either humble or not curious. Someone is not kind or humble. | Susan is not creative. | entailment | (![X]:((~old(X)|tall(X))<=>(happy(X)<~>curious(X))))&
(![X]:((funny(X)&old(X))<=>~rich(X)))&
((?[X]:((~humble(X)|calm(X))))<=>(~strong(alice)))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~humble(X))))&
(![X]:((humble(X)&~funny(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((~kind(X)&creative(X))=>calm(X)))&
((?[X]:((patient(X)&calm(X))))=>((brave(lucy)|quiet(lucy))))&
((?[X]:((~creative(X)&wise(X))))<=>((wise(mary)&~old(mary))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|~generous(X))<=>(~brave(X)&~wise(X))))&
(![X]:(funny(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((happy(X)<~>~old(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&~humble(X))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~patient(X)|strong(X))))&
(((~generous(mary)|brave(mary)))=>((rich(alice)|calm(alice))))&
((happy(mary)|~creative(mary)))&
((strong(fred)|~generous(fred)))&
(?[X]:((humble(X)<~>~curious(X))))&
(?[X]:((~kind(X)|humble(X)))) | ~creative(susan) | [
"p2",
"p5",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8065246673640192193129869
% SZS output start Proof for 8065246673640192193129869
3. ? [X0] : (calm(X0) | ~humble(X0)) <=> ~strong(alice) [input p2]
6. ! [X0] : ((creative(X0) & ~kind(X0)) => calm(X0)) [input p5]
11. ! [X0] : ((~generous(X0) | generous(X0)) <=> (~wise(X0) & ~brave(X0))) [input p10]
14. ! [X0] : ((~strong(X0) | kind(X0)) => (~humble(X0) & ~funny(X0))) [input p13]
15. ! [X0] : ((~patient(X0) <~> ~brave(X0)) <=> (strong(X0) | ~patient(X0))) [input p14]
21. creative(susan) [input hypothesis]
27. ! [X0] : (calm(X0) | (~creative(X0) | kind(X0))) [ennf transformation 6]
28. ! [X0] : (calm(X0) | ~creative(X0) | kind(X0)) [flattening 27]
33. ! [X0] : ((~humble(X0) & ~funny(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 14]
38. (? [X0] : (calm(X0) | ~humble(X0)) | strong(alice)) & (~strong(alice) | ! [X0] : (~calm(X0) & humble(X0))) [nnf transformation 3]
39. (? [X0] : (calm(X0) | ~humble(X0)) | strong(alice)) & (~strong(alice) | ! [X1] : (~calm(X1) & humble(X1))) [rectify 38]
40. ? [X0] : (calm(X0) | ~humble(X0)) => (calm(sK0) | ~humble(sK0)) [choice axiom]
41. ((calm(sK0) | ~humble(sK0)) | strong(alice)) & (~strong(alice) | ! [X1] : (~calm(X1) & humble(X1))) [skolemisation 39,40]
57. ! [X0] : (((~generous(X0) | generous(X0)) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | (generous(X0) & ~generous(X0)))) [nnf transformation 11]
58. ! [X0] : ((~generous(X0) | generous(X0) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | (generous(X0) & ~generous(X0)))) [flattening 57]
62. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (~strong(X0) & patient(X0))) & ((strong(X0) | ~patient(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [nnf transformation 15]
63. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (~strong(X0) & patient(X0))) & (strong(X0) | ~patient(X0) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [flattening 62]
76. ~strong(alice) | humble(X1) [cnf transformation 41]
77. ~strong(alice) | ~calm(X1) [cnf transformation 41]
87. ~creative(X0) | calm(X0) | kind(X0) [cnf transformation 28]
98. ~brave(X0) | ~generous(X0) [cnf transformation 58]
99. ~brave(X0) | generous(X0) [cnf transformation 58]
112. ~kind(X0) | ~humble(X0) [cnf transformation 33]
115. strong(X0) | ~patient(X0) | ~patient(X0) | brave(X0) [cnf transformation 63]
118. brave(X0) | patient(X0) | patient(X0) [cnf transformation 63]
127. creative(susan) [cnf transformation 21]
128. strong(X0) | ~patient(X0) | brave(X0) [duplicate literal removal 115]
129. brave(X0) | patient(X0) [duplicate literal removal 118]
131. 1 <=> strong(alice) [avatar definition]
132. ~strong(alice) <- (~1) [avatar component clause 131]
144. 4 <=> ! [X1] : ~calm(X1) [avatar definition]
145. ~calm(X1) <- (4) [avatar component clause 144]
146. 4 | ~1 [avatar split clause 77,131,144]
148. 5 <=> ! [X1] : humble(X1) [avatar definition]
149. humble(X1) <- (5) [avatar component clause 148]
150. 5 | ~1 [avatar split clause 76,131,148]
208. ~brave(X0) [subsumption resolution 98,99]
229. patient(X0) [subsumption resolution 129,208]
230. strong(X0) | brave(X0) [subsumption resolution 128,229]
231. strong(X0) [subsumption resolution 230,208]
271. $false <- (~1) [subsumption resolution 132,231]
272. 1 [avatar contradiction clause 271]
340. calm(susan) | kind(susan) [resolution 87,127]
341. kind(susan) <- (4) [subsumption resolution 340,145]
343. ~humble(susan) <- (4) [resolution 341,112]
347. $false <- (4, 5) [subsumption resolution 343,149]
348. ~4 | ~5 [avatar contradiction clause 347]
349. $false [avatar sat refutation 146,150,272,348]
% SZS output end Proof for 8065246673640192193129869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If alice is brave then someone is tall or happy.
If fred is both generous and tall then fred is both not tall and strong.
Everyone who is either generous or not patient is tall and vice versa.
If someone is either calm or not tall then john is not brave and vice versa.
Everyone who is either not happy or not humble is either tall or curious and vice versa.
Everyone who is both not brave and not quiet is either not quiet or funny and vice versa.
Everyone who is both creative and curious is either not patient or not rich and vice versa.
Everyone who is both not brave and funny is both not happy and happy and vice versa.
If someone is both quiet and not old then someone is either kind or funny.
Everyone who is not generous is not quiet and vice versa.
Everyone who is not happy is either not old or generous.
Everyone who is not calm is calm.
If lucy is not calm then someone is not wise or tall and vice versa.
Everyone who is not funny is not quiet.
Everyone who is not patient is either old or not strong.
If someone is generous or happy then alice is generous.
Fred is both not creative and not generous.
John is either brave or not kind.
Someone is either not humble or not quiet.
Alice is either humble or not generous.
Mary is either not humble or not calm.
Someone is not old or not kind.
Someone is either strong or generous. | John is not brave. | contradiction | ((brave(alice))=>(?[X]:((tall(X)|happy(X)))))&
(((generous(fred)&tall(fred)))=>((~tall(fred)&strong(fred))))&
(![X]:((generous(X)<~>~patient(X))<=>tall(X)))&
((?[X]:((calm(X)<~>~tall(X))))<=>(~brave(john)))&
(![X]:((~happy(X)<~>~humble(X))<=>(tall(X)<~>curious(X))))&
(![X]:((~brave(X)&~quiet(X))<=>(~quiet(X)<~>funny(X))))&
(![X]:((creative(X)&curious(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((~brave(X)&funny(X))<=>(~happy(X)&happy(X))))&
((?[X]:((quiet(X)&~old(X))))=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:(~generous(X)<=>~quiet(X)))&
(![X]:(~happy(X)=>(~old(X)<~>generous(X))))&
(![X]:(~calm(X)=>calm(X)))&
((~calm(lucy))<=>(?[X]:((~wise(X)|tall(X)))))&
(![X]:(~funny(X)=>~quiet(X)))&
(![X]:(~patient(X)=>(old(X)<~>~strong(X))))&
((?[X]:((generous(X)|happy(X))))=>(generous(alice)))&
((~creative(fred)&~generous(fred)))&
((brave(john)<~>~kind(john)))&
(?[X]:((~humble(X)<~>~quiet(X))))&
((humble(alice)<~>~generous(alice)))&
((~humble(mary)<~>~calm(mary)))&
(?[X]:((~old(X)|~kind(X))))&
(?[X]:((strong(X)<~>generous(X)))) | ~brave(john) | [
"p3",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 513462055533253034741518
% SZS output start Proof for 513462055533253034741518
4. ? [X0] : (calm(X0) <~> ~tall(X0)) <=> ~brave(john) [input p3]
12. ! [X0] : (~calm(X0) => calm(X0)) [input p11]
13. ~calm(lucy) <=> ? [X0] : (tall(X0) | ~wise(X0)) [input p12]
24. ~brave(john) [input hypothesis]
31. ! [X0] : (calm(X0) | calm(X0)) [ennf transformation 12]
38. (? [X0] : ((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | brave(john)) & (~brave(john) | ! [X0] : ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) [nnf transformation 4]
39. (? [X0] : ((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | brave(john)) & (~brave(john) | ! [X1] : ((calm(X1) | tall(X1)) & (~tall(X1) | ~calm(X1)))) [rectify 38]
40. ? [X0] : ((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) => ((tall(sK1) | ~calm(sK1)) & (~tall(sK1) | calm(sK1))) [choice axiom]
41. (((tall(sK1) | ~calm(sK1)) & (~tall(sK1) | calm(sK1))) | brave(john)) & (~brave(john) | ! [X1] : ((calm(X1) | tall(X1)) & (~tall(X1) | ~calm(X1)))) [skolemisation 39,40]
55. (~calm(lucy) | ! [X0] : (~tall(X0) & wise(X0))) & (? [X0] : (tall(X0) | ~wise(X0)) | calm(lucy)) [nnf transformation 13]
56. (~calm(lucy) | ! [X0] : (~tall(X0) & wise(X0))) & (? [X1] : (tall(X1) | ~wise(X1)) | calm(lucy)) [rectify 55]
57. ? [X1] : (tall(X1) | ~wise(X1)) => (tall(sK3) | ~wise(sK3)) [choice axiom]
58. (~calm(lucy) | ! [X0] : (~tall(X0) & wise(X0))) & ((tall(sK3) | ~wise(sK3)) | calm(lucy)) [skolemisation 56,57]
81. tall(sK1) | ~calm(sK1) | brave(john) [cnf transformation 41]
112. calm(X0) | calm(X0) [cnf transformation 31]
115. ~calm(lucy) | ~tall(X0) [cnf transformation 58]
134. ~brave(john) [cnf transformation 24]
135. calm(X0) [duplicate literal removal 112]
167. 7 <=> brave(john) [avatar definition]
171. 8 <=> calm(sK1) [avatar definition]
173. ~calm(sK1) <- (~8) [avatar component clause 171]
175. 9 <=> tall(sK1) [avatar definition]
177. tall(sK1) <- (9) [avatar component clause 175]
178. 7 | ~8 | 9 [avatar split clause 81,175,171,167]
202. ~tall(X0) [subsumption resolution 115,135]
251. ~7 [avatar split clause 134,167]
252. $false <- (~8) [subsumption resolution 173,135]
253. 8 [avatar contradiction clause 252]
254. $false <- (9) [subsumption resolution 177,202]
255. ~9 [avatar contradiction clause 254]
256. $false [avatar sat refutation 178,251,253,255]
% SZS output end Proof for 513462055533253034741518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or not rich then alice is not happy and vice versa.
Everyone who is either kind or tall is not wise and vice versa.
Everyone who is patient or strong is humble or patient.
If someone is not funny then paul is tall or not funny.
Everyone who is brave is not brave or not kind.
If someone is both tall and quiet then mary is brave.
Everyone who is both funny and not strong is both generous and not humble.
Everyone who is calm is either not strong or humble and vice versa.
Everyone who is either generous or not rich is both old and kind and vice versa.
Everyone who is generous or kind is strong and vice versa.
Everyone who is not patient or humble is funny and vice versa.
If someone is both creative and old then someone is both old and creative.
Everyone who is generous or happy is either not tall or rich and vice versa.
Everyone who is either not generous or happy is creative.
Everyone who is either not wise or quiet is not rich or creative.
Everyone who is both not patient and creative is wise and vice versa.
Someone is both wise and not old.
Susan is both brave and rich.
Someone is either not strong or not generous.
Susan is both not humble and not curious.
Alice is either quiet or strong.
Someone is brave.
Paul is not creative or strong.
Someone is either wise or not funny. | Susan is not happy. | contradiction | ((?[X]:((~happy(X)|~rich(X))))<=>(~happy(alice)))&
(![X]:((kind(X)<~>tall(X))<=>~wise(X)))&
(![X]:((patient(X)|strong(X))=>(humble(X)|patient(X))))&
((?[X]:(~funny(X)))=>((tall(paul)|~funny(paul))))&
(![X]:(brave(X)=>(~brave(X)|~kind(X))))&
((?[X]:((tall(X)&quiet(X))))=>(brave(mary)))&
(![X]:((funny(X)&~strong(X))=>(generous(X)&~humble(X))))&
(![X]:(calm(X)<=>(~strong(X)<~>humble(X))))&
(![X]:((generous(X)<~>~rich(X))<=>(old(X)&kind(X))))&
(![X]:((generous(X)|kind(X))<=>strong(X)))&
(![X]:((~patient(X)|humble(X))<=>funny(X)))&
((?[X]:((creative(X)&old(X))))=>(?[X]:((old(X)&creative(X)))))&
(![X]:((generous(X)|happy(X))<=>(~tall(X)<~>rich(X))))&
(![X]:((~generous(X)<~>happy(X))=>creative(X)))&
(![X]:((~wise(X)<~>quiet(X))=>(~rich(X)|creative(X))))&
(![X]:((~patient(X)&creative(X))<=>wise(X)))&
(?[X]:((wise(X)&~old(X))))&
((brave(susan)&rich(susan)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((~humble(susan)&~curious(susan)))&
((quiet(alice)<~>strong(alice)))&
(?[X]:(brave(X)))&
((~creative(paul)|strong(paul)))&
(?[X]:((wise(X)<~>~funny(X)))) | ~happy(susan) | [
"p1",
"p2",
"p4",
"p6",
"p8",
"p9",
"p10",
"p12",
"p15",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6076819821087081640561866
% SZS output start Proof for 6076819821087081640561866
2. ! [X0] : ((kind(X0) <~> tall(X0)) <=> ~wise(X0)) [input p1]
3. ! [X0] : ((strong(X0) | patient(X0)) => (patient(X0) | humble(X0))) [input p2]
5. ! [X0] : (brave(X0) => (~kind(X0) | ~brave(X0))) [input p4]
7. ! [X0] : ((~strong(X0) & funny(X0)) => (~humble(X0) & generous(X0))) [input p6]
9. ! [X0] : ((generous(X0) <~> ~rich(X0)) <=> (kind(X0) & old(X0))) [input p8]
10. ! [X0] : ((kind(X0) | generous(X0)) <=> strong(X0)) [input p9]
11. ! [X0] : ((humble(X0) | ~patient(X0)) <=> funny(X0)) [input p10]
13. ! [X0] : ((happy(X0) | generous(X0)) <=> (~tall(X0) <~> rich(X0))) [input p12]
16. ! [X0] : ((creative(X0) & ~patient(X0)) <=> wise(X0)) [input p15]
18. rich(susan) & brave(susan) [input p17]
20. ~curious(susan) & ~humble(susan) [input p19]
25. ~happy(susan) [input hypothesis]
27. ~humble(susan) [pure predicate removal 20]
28. ! [X0] : ((patient(X0) | humble(X0)) | (~strong(X0) & ~patient(X0))) [ennf transformation 3]
29. ! [X0] : (patient(X0) | humble(X0) | (~strong(X0) & ~patient(X0))) [flattening 28]
32. ! [X0] : ((~kind(X0) | ~brave(X0)) | ~brave(X0)) [ennf transformation 5]
33. ! [X0] : (~kind(X0) | ~brave(X0) | ~brave(X0)) [flattening 32]
35. ! [X0] : ((~humble(X0) & generous(X0)) | (strong(X0) | ~funny(X0))) [ennf transformation 7]
36. ! [X0] : ((~humble(X0) & generous(X0)) | strong(X0) | ~funny(X0)) [flattening 35]
45. ! [X0] : ((((~tall(X0) | ~kind(X0)) & (tall(X0) | kind(X0))) | wise(X0)) & (~wise(X0) | ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0))))) [nnf transformation 2]
46. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | (~kind(X0) | ~old(X0))) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [nnf transformation 9]
47. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ~kind(X0) | ~old(X0)) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [flattening 46]
48. ! [X0] : (((kind(X0) | generous(X0)) | ~strong(X0)) & (strong(X0) | (~kind(X0) & ~generous(X0)))) [nnf transformation 10]
49. ! [X0] : ((kind(X0) | generous(X0) | ~strong(X0)) & (strong(X0) | (~kind(X0) & ~generous(X0)))) [flattening 48]
50. ! [X0] : (((humble(X0) | ~patient(X0)) | ~funny(X0)) & (funny(X0) | (~humble(X0) & patient(X0)))) [nnf transformation 11]
51. ! [X0] : ((humble(X0) | ~patient(X0) | ~funny(X0)) & (funny(X0) | (~humble(X0) & patient(X0)))) [flattening 50]
55. ! [X0] : (((happy(X0) | generous(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (~happy(X0) & ~generous(X0)))) [nnf transformation 13]
56. ! [X0] : ((happy(X0) | generous(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (~happy(X0) & ~generous(X0)))) [flattening 55]
59. ! [X0] : (((creative(X0) & ~patient(X0)) | ~wise(X0)) & (wise(X0) | (~creative(X0) | patient(X0)))) [nnf transformation 16]
60. ! [X0] : (((creative(X0) & ~patient(X0)) | ~wise(X0)) & (wise(X0) | ~creative(X0) | patient(X0))) [flattening 59]
77. wise(X0) | kind(X0) | tall(X0) [cnf transformation 45]
80. ~strong(X0) | humble(X0) | patient(X0) [cnf transformation 29]
82. ~kind(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 33]
84. ~funny(X0) | strong(X0) | generous(X0) [cnf transformation 36]
88. ~generous(X0) | ~rich(X0) | kind(X0) [cnf transformation 47]
92. ~generous(X0) | strong(X0) [cnf transformation 49]
95. funny(X0) | patient(X0) [cnf transformation 51]
105. ~tall(X0) | generous(X0) | happy(X0) | ~rich(X0) [cnf transformation 56]
111. ~patient(X0) | ~wise(X0) [cnf transformation 60]
115. brave(susan) [cnf transformation 18]
116. rich(susan) [cnf transformation 18]
119. ~humble(susan) [cnf transformation 27]
126. ~happy(susan) [cnf transformation 25]
127. ~brave(X0) | ~kind(X0) [duplicate literal removal 82]
218. ~kind(susan) [resolution 127,115]
274. strong(X0) | generous(X0) | patient(X0) [resolution 84,95]
276. strong(X0) | patient(X0) [subsumption resolution 274,92]
462. patient(X1) | humble(X1) | patient(X1) [resolution 276,80]
464. humble(X1) | patient(X1) [duplicate literal removal 462]
546. patient(susan) [resolution 464,119]
566. ~wise(susan) [resolution 546,111]
588. kind(susan) | tall(susan) [resolution 566,77]
589. tall(susan) [subsumption resolution 588,218]
650. generous(susan) | happy(susan) | ~rich(susan) [resolution 589,105]
653. generous(susan) | ~rich(susan) [subsumption resolution 650,126]
654. generous(susan) [subsumption resolution 653,116]
676. ~rich(susan) | kind(susan) [resolution 654,88]
679. kind(susan) [subsumption resolution 676,116]
680. $false [subsumption resolution 679,218]
% SZS output end Proof for 6076819821087081640561866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and generous is generous or not funny and vice versa.
Everyone who is both not brave and not quiet is not funny.
Everyone who is either not tall or funny is old or happy and vice versa.
If alice is not calm or rich then someone is not rich or not humble.
Everyone who is both humble and not strong is either happy or brave and vice versa.
Everyone who is not humble or not old is not strong and vice versa.
Everyone who is both rich and not brave is either not happy or humble and vice versa.
Everyone who is either not humble or not funny is happy and vice versa.
Everyone who is not wise is generous and vice versa.
If someone is either calm or not patient then lucy is not humble or not rich and vice versa.
If someone is either not wise or not curious then someone is happy or not creative.
Everyone who is both kind and not funny is not kind.
Everyone who is not curious or not calm is humble.
If someone is either generous or brave then alice is both not generous and brave and vice versa.
Everyone who is not funny or happy is both not creative and brave and vice versa.
Someone is not creative.
Someone is both wise and strong.
Alice is either not tall or patient.
Someone is either strong or funny.
Someone is both not humble and not kind.
Someone is either brave or not generous.
Alice is either not humble or not wise. | Alice is calm. | entailment | (![X]:((~generous(X)&generous(X))<=>(generous(X)|~funny(X))))&
(![X]:((~brave(X)&~quiet(X))=>~funny(X)))&
(![X]:((~tall(X)<~>funny(X))<=>(old(X)|happy(X))))&
(((~calm(alice)|rich(alice)))=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:((humble(X)&~strong(X))<=>(happy(X)<~>brave(X))))&
(![X]:((~humble(X)|~old(X))<=>~strong(X)))&
(![X]:((rich(X)&~brave(X))<=>(~happy(X)<~>humble(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>happy(X)))&
(![X]:(~wise(X)<=>generous(X)))&
((?[X]:((calm(X)<~>~patient(X))))<=>((~humble(lucy)|~rich(lucy))))&
((?[X]:((~wise(X)<~>~curious(X))))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:((kind(X)&~funny(X))=>~kind(X)))&
(![X]:((~curious(X)|~calm(X))=>humble(X)))&
((?[X]:((generous(X)<~>brave(X))))<=>((~generous(alice)&brave(alice))))&
(![X]:((~funny(X)|happy(X))<=>(~creative(X)&brave(X))))&
(?[X]:(~creative(X)))&
(?[X]:((wise(X)&strong(X))))&
((~tall(alice)<~>patient(alice)))&
(?[X]:((strong(X)<~>funny(X))))&
(?[X]:((~humble(X)&~kind(X))))&
(?[X]:((brave(X)<~>~generous(X))))&
((~humble(alice)<~>~wise(alice))) | calm(alice) | [
"p0",
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 84865669842885143268283
% SZS output start Proof for 84865669842885143268283
1. ! [X0] : ((generous(X0) & ~generous(X0)) <=> (~funny(X0) | generous(X0))) [input p0]
9. ! [X0] : (~wise(X0) <=> generous(X0)) [input p8]
13. ! [X0] : ((~calm(X0) | ~curious(X0)) => humble(X0)) [input p12]
22. ~humble(alice) <~> ~wise(alice) [input p21]
23. ~calm(alice) [input hypothesis]
30. ! [X0] : (humble(X0) | (calm(X0) & curious(X0))) [ennf transformation 13]
31. ! [X0] : (((generous(X0) & ~generous(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (~generous(X0) | generous(X0)))) [nnf transformation 1]
32. ! [X0] : (((generous(X0) & ~generous(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | ~generous(X0) | generous(X0))) [flattening 31]
44. ! [X0] : ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0))) [nnf transformation 9]
74. (wise(alice) | humble(alice)) & (~wise(alice) | ~humble(alice)) [nnf transformation 22]
76. ~generous(X0) | ~generous(X0) [cnf transformation 32]
107. generous(X0) | wise(X0) [cnf transformation 44]
118. humble(X0) | calm(X0) [cnf transformation 30]
140. ~wise(alice) | ~humble(alice) [cnf transformation 74]
142. ~calm(alice) [cnf transformation 23]
144. ~generous(X0) [duplicate literal removal 76]
163. 4 <=> calm(alice) [avatar definition]
164. ~calm(alice) <- (~4) [avatar component clause 163]
169. wise(X0) [subsumption resolution 107,144]
240. ~humble(alice) [subsumption resolution 140,169]
241. ~4 [avatar split clause 142,163]
245. calm(alice) [resolution 118,240]
246. $false <- (~4) [subsumption resolution 245,164]
247. 4 [avatar contradiction clause 246]
248. $false [avatar sat refutation 241,247]
% SZS output end Proof for 84865669842885143268283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is not old or funny.
Everyone who is either not brave or not wise is not tall.
If someone is funny then mary is either tall or quiet and vice versa.
If lucy is quiet then alice is either funny or not calm and vice versa.
If someone is not rich then someone is brave and vice versa.
If fred is not brave then john is either wise or not kind and vice versa.
Everyone who is either curious or not brave is both not patient and not calm.
If john is not happy or tall then mary is not brave or happy.
If lucy is old or humble then someone is funny or not rich and vice versa.
Everyone who is not curious is humble and vice versa.
Everyone who is kind or not patient is either rich or not quiet and vice versa.
Everyone who is both humble and not happy is both not wise and brave.
If someone is either not curious or brave then someone is either not brave or quiet and vice versa.
If paul is both patient and not wise then someone is not rich or quiet and vice versa.
Everyone who is both funny and not funny is both kind and calm.
If someone is both not brave and not wise then someone is either not humble or rich.
Someone is either not creative or not calm.
Lucy is both not kind and not curious.
Someone is either not patient or not rich.
Someone is both not tall and not strong.
Someone is either not calm or not funny.
Fred is not strong or not happy.
Someone is not funny. | Lucy is curious. | contradiction | (![X]:(~humble(X)=>(~old(X)|funny(X))))&
(![X]:((~brave(X)<~>~wise(X))=>~tall(X)))&
((?[X]:(funny(X)))<=>((tall(mary)<~>quiet(mary))))&
((quiet(lucy))<=>((funny(alice)<~>~calm(alice))))&
((?[X]:(~rich(X)))<=>(?[X]:(brave(X))))&
((~brave(fred))<=>((wise(john)<~>~kind(john))))&
(![X]:((curious(X)<~>~brave(X))=>(~patient(X)&~calm(X))))&
(((~happy(john)|tall(john)))=>((~brave(mary)|happy(mary))))&
(((old(lucy)|humble(lucy)))<=>(?[X]:((funny(X)|~rich(X)))))&
(![X]:(~curious(X)<=>humble(X)))&
(![X]:((kind(X)|~patient(X))<=>(rich(X)<~>~quiet(X))))&
(![X]:((humble(X)&~happy(X))=>(~wise(X)&brave(X))))&
((?[X]:((~curious(X)<~>brave(X))))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((patient(paul)&~wise(paul)))<=>(?[X]:((~rich(X)|quiet(X)))))&
(![X]:((funny(X)&~funny(X))=>(kind(X)&calm(X))))&
((?[X]:((~brave(X)&~wise(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
(?[X]:((~creative(X)<~>~calm(X))))&
((~kind(lucy)&~curious(lucy)))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:((~tall(X)&~strong(X))))&
(?[X]:((~calm(X)<~>~funny(X))))&
((~strong(fred)|~happy(fred)))&
(?[X]:(~funny(X))) | curious(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4530394378471354836736127
% SZS output start Proof for 4530394378471354836736127
18. ~curious(lucy) & ~kind(lucy) [input p17]
24. curious(lucy) [input hypothesis]
140. ~curious(lucy) [cnf transformation 18]
147. curious(lucy) [cnf transformation 24]
338. $false [subsumption resolution 147,140]
% SZS output end Proof for 4530394378471354836736127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and brave then john is wise and vice versa. If susan is creative then someone is old and vice versa. Everyone who is either patient or not generous is kind or not brave. Everyone who is not generous is both not patient and strong. Everyone who is both not patient and not humble is either wise or happy and vice versa. If someone is either not happy or not kind then someone is either not kind or creative and vice versa. Everyone who is both curious and funny is generous or not quiet. Everyone who is rich or not quiet is both strong and not quiet. If susan is both not tall and not curious then alice is both not rich and strong and vice versa. If john is humble or not tall then mary is either not funny or not tall. Everyone who is curious or happy is either funny or patient. Everyone who is funny or not patient is not patient or tall and vice versa. Everyone who is both creative and rich is wise or patient. Everyone who is either not tall or not strong is either not calm or brave. Everyone who is both tall and not calm is both not funny and not strong. Everyone who is both not curious and old is not creative or not patient and vice versa. Someone is either not humble or not generous. Mary is not generous. Lucy is either not funny or wise. Susan is not kind or not patient. Mary is both not quiet and humble. Someone is not patient or curious. | Mary is quiet. | contradiction | ((?[X]:((funny(X)&brave(X))))<=>(wise(john)))&
((creative(susan))<=>(?[X]:(old(X))))&
(![X]:((patient(X)<~>~generous(X))=>(kind(X)|~brave(X))))&
(![X]:(~generous(X)=>(~patient(X)&strong(X))))&
(![X]:((~patient(X)&~humble(X))<=>(wise(X)<~>happy(X))))&
((?[X]:((~happy(X)<~>~kind(X))))<=>(?[X]:((~kind(X)<~>creative(X)))))&
(![X]:((curious(X)&funny(X))=>(generous(X)|~quiet(X))))&
(![X]:((rich(X)|~quiet(X))=>(strong(X)&~quiet(X))))&
(((~tall(susan)&~curious(susan)))<=>((~rich(alice)&strong(alice))))&
(((humble(john)|~tall(john)))=>((~funny(mary)<~>~tall(mary))))&
(![X]:((curious(X)|happy(X))=>(funny(X)<~>patient(X))))&
(![X]:((funny(X)|~patient(X))<=>(~patient(X)|tall(X))))&
(![X]:((creative(X)&rich(X))=>(wise(X)|patient(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~calm(X)<~>brave(X))))&
(![X]:((tall(X)&~calm(X))=>(~funny(X)&~strong(X))))&
(![X]:((~curious(X)&old(X))<=>(~creative(X)|~patient(X))))&
(?[X]:((~humble(X)<~>~generous(X))))&
(~generous(mary))&
((~funny(lucy)<~>wise(lucy)))&
((~kind(susan)|~patient(susan)))&
((~quiet(mary)&humble(mary)))&
(?[X]:((~patient(X)|curious(X)))) | quiet(mary) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6290752373822229939204212
% SZS output start Proof for 6290752373822229939204212
21. humble(mary) & ~quiet(mary) [input p20]
23. quiet(mary) [input hypothesis]
131. ~quiet(mary) [cnf transformation 21]
134. quiet(mary) [cnf transformation 23]
280. $false [subsumption resolution 134,131]
% SZS output end Proof for 6290752373822229939204212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not brave is either quiet or not generous and vice versa. Everyone who is not generous or not old is brave and vice versa. If someone is not tall or tall then someone is either not quiet or humble. Everyone who is not happy or patient is not funny or not humble and vice versa. Everyone who is either not generous or humble is wise or not quiet. Everyone who is not old or humble is either not kind or old and vice versa. If someone is either not curious or funny then someone is either not brave or old. Everyone who is not patient or happy is either not old or not generous. Everyone who is both not generous and happy is curious or not happy and vice versa. If someone is not calm then alice is either curious or not strong. Everyone who is not calm is either patient or old and vice versa. Everyone who is either rich or tall is both not patient and calm. If mary is not generous then someone is either calm or patient. Everyone who is either brave or not old is either old or wise and vice versa. If mary is either old or funny then someone is not kind. Everyone who is happy is wise or not tall. Susan is both calm and funny. John is both not old and humble. Someone is not kind or generous. Lucy is not creative or old. Someone is happy. Someone is creative or not old. Someone is either not happy or not humble. | John is not quiet. | entailment | (![X]:((old(X)|~brave(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((~generous(X)|~old(X))<=>brave(X)))&
((?[X]:((~tall(X)|tall(X))))=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:((~happy(X)|patient(X))<=>(~funny(X)|~humble(X))))&
(![X]:((~generous(X)<~>humble(X))=>(wise(X)|~quiet(X))))&
(![X]:((~old(X)|humble(X))<=>(~kind(X)<~>old(X))))&
((?[X]:((~curious(X)<~>funny(X))))=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((~patient(X)|happy(X))=>(~old(X)<~>~generous(X))))&
(![X]:((~generous(X)&happy(X))<=>(curious(X)|~happy(X))))&
((?[X]:(~calm(X)))=>((curious(alice)<~>~strong(alice))))&
(![X]:(~calm(X)<=>(patient(X)<~>old(X))))&
(![X]:((rich(X)<~>tall(X))=>(~patient(X)&calm(X))))&
((~generous(mary))=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:((brave(X)<~>~old(X))<=>(old(X)<~>wise(X))))&
(((old(mary)<~>funny(mary)))=>(?[X]:(~kind(X))))&
(![X]:(happy(X)=>(wise(X)|~tall(X))))&
((calm(susan)&funny(susan)))&
((~old(john)&humble(john)))&
(?[X]:((~kind(X)|generous(X))))&
((~creative(lucy)|old(lucy)))&
(?[X]:(happy(X)))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((~happy(X)<~>~humble(X)))) | ~quiet(john) | [
"p0",
"p1",
"p7",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2995574693108628872173870
% SZS output start Proof for 2995574693108628872173870
1. ! [X0] : ((~brave(X0) | old(X0)) <=> (quiet(X0) <~> ~generous(X0))) [input p0]
2. ! [X0] : ((~old(X0) | ~generous(X0)) <=> brave(X0)) [input p1]
8. ! [X0] : ((happy(X0) | ~patient(X0)) => (~old(X0) <~> ~generous(X0))) [input p7]
9. ! [X0] : ((happy(X0) & ~generous(X0)) <=> (~happy(X0) | curious(X0))) [input p8]
18. humble(john) & ~old(john) [input p17]
24. quiet(john) [input hypothesis]
31. ! [X0] : ((~old(X0) <~> ~generous(X0)) | (~happy(X0) & patient(X0))) [ennf transformation 8]
38. ! [X0] : (((~brave(X0) | old(X0)) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | (brave(X0) & ~old(X0)))) [nnf transformation 1]
39. ! [X0] : ((~brave(X0) | old(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | (brave(X0) & ~old(X0)))) [flattening 38]
40. ! [X0] : (((~old(X0) | ~generous(X0)) | ~brave(X0)) & (brave(X0) | (old(X0) & generous(X0)))) [nnf transformation 2]
41. ! [X0] : ((~old(X0) | ~generous(X0) | ~brave(X0)) & (brave(X0) | (old(X0) & generous(X0)))) [flattening 40]
55. ! [X0] : (((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | (~happy(X0) & patient(X0))) [nnf transformation 31]
56. ! [X0] : (((happy(X0) & ~generous(X0)) | (happy(X0) & ~curious(X0))) & ((~happy(X0) | curious(X0)) | (~happy(X0) | generous(X0)))) [nnf transformation 9]
57. ! [X0] : (((happy(X0) & ~generous(X0)) | (happy(X0) & ~curious(X0))) & (~happy(X0) | curious(X0) | ~happy(X0) | generous(X0))) [flattening 56]
81. ~generous(X0) | old(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 39]
83. generous(X0) | brave(X0) [cnf transformation 41]
84. brave(X0) | old(X0) [cnf transformation 41]
107. ~happy(X0) | ~old(X0) | ~generous(X0) [cnf transformation 55]
109. ~happy(X0) | old(X0) | generous(X0) [cnf transformation 55]
114. happy(X0) | happy(X0) [cnf transformation 57]
140. ~old(john) [cnf transformation 18]
148. quiet(john) [cnf transformation 24]
154. happy(X0) [duplicate literal removal 114]
356. ~generous(X0) | ~old(X0) [resolution 107,154]
357. generous(X0) | old(X0) [resolution 109,154]
358. ~old(X0) | brave(X0) [resolution 356,83]
362. brave(X0) [subsumption resolution 358,84]
413. old(X0) | ~brave(X0) | ~quiet(X0) | old(X0) [resolution 81,357]
417. old(X0) | ~brave(X0) | ~quiet(X0) [duplicate literal removal 413]
418. ~quiet(X0) | old(X0) [subsumption resolution 417,362]
419. old(john) [resolution 418,148]
421. $false [subsumption resolution 419,140]
% SZS output end Proof for 2995574693108628872173870
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either not humble or not kind and vice versa.
Everyone who is either not rich or curious is both not humble and not curious and vice versa.
If susan is wise or creative then lucy is either not tall or not patient and vice versa.
Everyone who is creative is either not kind or not patient and vice versa.
Everyone who is either not old or not kind is either rich or brave.
Everyone who is either not quiet or brave is not quiet or creative and vice versa.
If alice is rich then susan is either wise or generous.
Everyone who is calm or not patient is both rich and not happy and vice versa.
Everyone who is not calm is not wise or not humble.
Everyone who is not rich or rich is either not tall or brave and vice versa.
If mary is both not patient and curious then someone is brave or not old.
Everyone who is both funny and not creative is both not curious and not humble and vice versa.
Everyone who is not wise is either calm or not tall and vice versa.
If someone is brave or rich then fred is strong and vice versa.
Everyone who is either not rich or not patient is either patient or not calm and vice versa.
If someone is not patient then alice is humble or not humble and vice versa.
Paul is either curious or not brave.
Someone is not generous.
Someone is either not old or not wise.
Someone is happy or not old.
Someone is not wise or not humble.
Someone is either not kind or not brave.
Alice is tall or humble. | Lucy is not patient. | entailment | (![X]:(~happy(X)<=>(~humble(X)<~>~kind(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~humble(X)&~curious(X))))&
(((wise(susan)|creative(susan)))<=>((~tall(lucy)<~>~patient(lucy))))&
(![X]:(creative(X)<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)<~>~kind(X))=>(rich(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>brave(X))<=>(~quiet(X)|creative(X))))&
((rich(alice))=>((wise(susan)<~>generous(susan))))&
(![X]:((calm(X)|~patient(X))<=>(rich(X)&~happy(X))))&
(![X]:(~calm(X)=>(~wise(X)|~humble(X))))&
(![X]:((~rich(X)|rich(X))<=>(~tall(X)<~>brave(X))))&
(((~patient(mary)&curious(mary)))=>(?[X]:((brave(X)|~old(X)))))&
(![X]:((funny(X)&~creative(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~wise(X)<=>(calm(X)<~>~tall(X))))&
((?[X]:((brave(X)|rich(X))))<=>(strong(fred)))&
(![X]:((~rich(X)<~>~patient(X))<=>(patient(X)<~>~calm(X))))&
((?[X]:(~patient(X)))<=>((humble(alice)|~humble(alice))))&
((curious(paul)<~>~brave(paul)))&
(?[X]:(~generous(X)))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((happy(X)|~old(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((~kind(X)<~>~brave(X))))&
((tall(alice)|humble(alice))) | ~patient(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p7",
"p8",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 966877863844108626856451
% SZS output start Proof for 966877863844108626856451
1. ! [X0] : (~happy(X0) <=> (~humble(X0) <~> ~kind(X0))) [input p0]
2. ! [X0] : ((~rich(X0) <~> curious(X0)) <=> (~curious(X0) & ~humble(X0))) [input p1]
3. (creative(susan) | wise(susan)) <=> (~tall(lucy) <~> ~patient(lucy)) [input p2]
4. ! [X0] : (creative(X0) <=> (~kind(X0) <~> ~patient(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) <~> brave(X0)) <=> (creative(X0) | ~quiet(X0))) [input p5]
8. ! [X0] : ((~patient(X0) | calm(X0)) <=> (~happy(X0) & rich(X0))) [input p7]
9. ! [X0] : (~calm(X0) => (~humble(X0) | ~wise(X0))) [input p8]
10. ! [X0] : ((rich(X0) | ~rich(X0)) <=> (~tall(X0) <~> brave(X0))) [input p9]
13. ! [X0] : (~wise(X0) <=> (calm(X0) <~> ~tall(X0))) [input p12]
15. ! [X0] : ((~rich(X0) <~> ~patient(X0)) <=> (patient(X0) <~> ~calm(X0))) [input p14]
24. patient(lucy) [input hypothesis]
27. ! [X0] : ((~humble(X0) | ~wise(X0)) | calm(X0)) [ennf transformation 9]
28. ! [X0] : (~humble(X0) | ~wise(X0) | calm(X0)) [flattening 27]
31. ! [X0] : ((~happy(X0) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0)))) & (((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | happy(X0))) [nnf transformation 1]
32. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [nnf transformation 2]
33. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [flattening 32]
34. ((creative(susan) | wise(susan)) | ((~tall(lucy) | patient(lucy)) & (~patient(lucy) | tall(lucy)))) & (((patient(lucy) | tall(lucy)) & (~patient(lucy) | ~tall(lucy))) | (~creative(susan) & ~wise(susan))) [nnf transformation 3]
35. (creative(susan) | wise(susan) | ((~tall(lucy) | patient(lucy)) & (~patient(lucy) | tall(lucy)))) & (((patient(lucy) | tall(lucy)) & (~patient(lucy) | ~tall(lucy))) | (~creative(susan) & ~wise(susan))) [flattening 34]
36. ! [X0] : ((creative(X0) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | ~creative(X0))) [nnf transformation 4]
38. ! [X0] : ((((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0))))) [nnf transformation 6]
39. ! [X0] : ((((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0))))) [flattening 38]
41. ! [X0] : (((~patient(X0) | calm(X0)) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | (patient(X0) & ~calm(X0)))) [nnf transformation 8]
42. ! [X0] : ((~patient(X0) | calm(X0) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | (patient(X0) & ~calm(X0)))) [flattening 41]
43. ! [X0] : (((rich(X0) | ~rich(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (~rich(X0) & rich(X0)))) [nnf transformation 10]
44. ! [X0] : ((rich(X0) | ~rich(X0) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (~rich(X0) & rich(X0)))) [flattening 43]
49. ! [X0] : ((~wise(X0) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | wise(X0))) [nnf transformation 13]
54. ! [X0] : ((((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0)))) & (((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))))) [nnf transformation 15]
73. ~kind(X0) | ~humble(X0) | happy(X0) [cnf transformation 31]
76. ~humble(X0) | ~happy(X0) | kind(X0) [cnf transformation 31]
80. ~curious(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 33]
81. curious(X0) | ~rich(X0) | curious(X0) | humble(X0) [cnf transformation 33]
87. creative(susan) | wise(susan) | ~patient(lucy) | tall(lucy) [cnf transformation 35]
89. ~patient(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 36]
90. ~creative(X0) | kind(X0) | patient(X0) [cnf transformation 36]
98. creative(X0) | ~quiet(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 39]
101. ~brave(X0) | quiet(X0) | quiet(X0) [cnf transformation 39]
105. ~calm(X0) | rich(X0) [cnf transformation 42]
106. patient(X0) | rich(X0) [cnf transformation 42]
108. ~happy(X0) | patient(X0) [cnf transformation 42]
109. ~patient(X0) | calm(X0) | happy(X0) | ~rich(X0) [cnf transformation 42]
110. ~wise(X0) | ~humble(X0) | calm(X0) [cnf transformation 28]
112. ~tall(X0) | brave(X0) | ~rich(X0) [cnf transformation 44]
122. ~tall(X0) | calm(X0) | wise(X0) [cnf transformation 49]
125. ~wise(X0) | calm(X0) | tall(X0) [cnf transformation 49]
130. ~calm(X0) | patient(X0) | ~rich(X0) | patient(X0) [cnf transformation 54]
131. calm(X0) | ~patient(X0) | ~patient(X0) | rich(X0) [cnf transformation 54]
133. ~patient(X0) | ~rich(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 54]
150. patient(lucy) [cnf transformation 24]
151. ~calm(X0) | patient(X0) | ~rich(X0) [duplicate literal removal 130]
152. calm(X0) | ~patient(X0) | rich(X0) [duplicate literal removal 131]
153. ~patient(X0) | ~rich(X0) | ~calm(X0) [duplicate literal removal 133]
155. creative(X0) | ~quiet(X0) | ~brave(X0) [duplicate literal removal 98]
156. ~brave(X0) | quiet(X0) [duplicate literal removal 101]
157. ~curious(X0) | ~rich(X0) [duplicate literal removal 80]
158. ~rich(X0) | curious(X0) | humble(X0) [duplicate literal removal 81]
160. 1 <=> patient(lucy) [avatar definition]
164. 2 <=> tall(lucy) [avatar definition]
165. tall(lucy) <- (2) [avatar component clause 164]
168. 3 <=> wise(susan) [avatar definition]
170. wise(susan) <- (3) [avatar component clause 168]
172. 4 <=> creative(susan) [avatar definition]
174. creative(susan) <- (4) [avatar component clause 172]
176. 2 | ~1 | 3 | 4 [avatar split clause 87,172,168,160,164]
181. ~brave(X0) | creative(X0) [subsumption resolution 155,156]
232. ~calm(X0) | ~patient(X0) [subsumption resolution 153,105]
233. ~patient(X0) | rich(X0) [subsumption resolution 152,232]
234. rich(X0) [subsumption resolution 233,106]
235. ~calm(X0) | patient(X0) [subsumption resolution 151,234]
236. ~calm(X0) [subsumption resolution 235,232]
300. 1 [avatar split clause 150,160]
410. calm(susan) | tall(susan) <- (3) [resolution 125,170]
411. tall(susan) <- (3) [subsumption resolution 410,236]
413. brave(susan) | ~rich(susan) <- (3) [resolution 411,112]
415. brave(susan) <- (3) [subsumption resolution 413,234]
416. curious(X0) | humble(X0) [resolution 158,234]
420. creative(susan) <- (3) [resolution 415,181]
427. 4 | ~3 [avatar split clause 420,168,172]
450. 42 <=> patient(susan) [avatar definition]
452. patient(susan) <- (42) [avatar component clause 450]
454. 43 <=> kind(susan) [avatar definition]
455. ~kind(susan) <- (~43) [avatar component clause 454]
456. kind(susan) <- (43) [avatar component clause 454]
458. calm(lucy) | wise(lucy) <- (2) [resolution 165,122]
461. wise(lucy) <- (2) [subsumption resolution 458,236]
501. ~humble(lucy) | calm(lucy) <- (2) [resolution 461,110]
518. humble(X0) | ~rich(X0) [resolution 416,157]
519. humble(X0) [subsumption resolution 518,234]
541. ~happy(X1) | kind(X1) [resolution 519,76]
548. calm(lucy) <- (2) [subsumption resolution 501,519]
549. $false <- (2) [subsumption resolution 548,236]
550. ~2 [avatar contradiction clause 549]
552. kind(susan) | patient(susan) <- (4) [resolution 174,90]
560. ~humble(susan) | happy(susan) <- (43) [resolution 456,73]
561. happy(susan) <- (43) [subsumption resolution 560,519]
562. patient(susan) <- (43) [resolution 561,108]
563. 42 | ~43 [avatar split clause 562,454,450]
564. 42 | 43 | ~4 [avatar split clause 552,172,454,450]
565. calm(susan) | happy(susan) | ~rich(susan) <- (42) [resolution 452,109]
567. ~kind(susan) | ~creative(susan) <- (42) [resolution 452,89]
568. happy(susan) | ~rich(susan) <- (42) [subsumption resolution 565,236]
569. happy(susan) <- (42) [subsumption resolution 568,234]
570. ~kind(susan) <- (4, 42) [subsumption resolution 567,174]
571. ~43 | ~4 | ~42 [avatar split clause 570,450,172,454]
576. kind(susan) <- (42) [resolution 541,569]
579. $false <- (42, ~43) [subsumption resolution 576,455]
580. ~42 | 43 [avatar contradiction clause 579]
581. $false [avatar sat refutation 176,300,427,550,563,564,571,580]
% SZS output end Proof for 966877863844108626856451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is patient or not kind then someone is either curious or not wise and vice versa. If john is both quiet and wise then alice is either creative or curious and vice versa. Everyone who is either patient or generous is both not old and wise and vice versa. Everyone who is not calm or creative is both wise and not tall and vice versa. Everyone who is both rich and creative is not brave and vice versa. Everyone who is not humble or happy is not strong. Everyone who is creative or brave is both brave and generous and vice versa. Everyone who is not happy or not tall is both not rich and not tall and vice versa. If susan is not strong then someone is both happy and quiet and vice versa. If someone is not patient then fred is either calm or not creative. Everyone who is either humble or kind is either not tall or not generous. Everyone who is brave or not patient is not curious and vice versa. Everyone who is both curious and tall is patient or curious. Everyone who is either kind or not quiet is both funny and patient and vice versa. If someone is either not happy or patient then someone is both happy and not kind. If someone is either not old or old then john is both not happy and calm and vice versa. John is tall or not kind. Someone is either tall or curious. Paul is either not happy or humble. Someone is kind. Lucy is both not quiet and strong. Paul is either wise or not calm. Someone is not happy. | Lucy is not brave. | contradiction | (((patient(susan)|~kind(susan)))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(((quiet(john)&wise(john)))<=>((creative(alice)<~>curious(alice))))&
(![X]:((patient(X)<~>generous(X))<=>(~old(X)&wise(X))))&
(![X]:((~calm(X)|creative(X))<=>(wise(X)&~tall(X))))&
(![X]:((rich(X)&creative(X))<=>~brave(X)))&
(![X]:((~humble(X)|happy(X))=>~strong(X)))&
(![X]:((creative(X)|brave(X))<=>(brave(X)&generous(X))))&
(![X]:((~happy(X)|~tall(X))<=>(~rich(X)&~tall(X))))&
((~strong(susan))<=>(?[X]:((happy(X)&quiet(X)))))&
((?[X]:(~patient(X)))=>((calm(fred)<~>~creative(fred))))&
(![X]:((humble(X)<~>kind(X))=>(~tall(X)<~>~generous(X))))&
(![X]:((brave(X)|~patient(X))<=>~curious(X)))&
(![X]:((curious(X)&tall(X))=>(patient(X)|curious(X))))&
(![X]:((kind(X)<~>~quiet(X))<=>(funny(X)&patient(X))))&
((?[X]:((~happy(X)<~>patient(X))))=>(?[X]:((happy(X)&~kind(X)))))&
((?[X]:((~old(X)<~>old(X))))<=>((~happy(john)&calm(john))))&
((tall(john)|~kind(john)))&
(?[X]:((tall(X)<~>curious(X))))&
((~happy(paul)<~>humble(paul)))&
(?[X]:(kind(X)))&
((~quiet(lucy)&strong(lucy)))&
((wise(paul)<~>~calm(paul)))&
(?[X]:(~happy(X))) | ~brave(lucy) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1303250603168857896120283
% SZS output start Proof for 1303250603168857896120283
5. ! [X0] : ((creative(X0) & rich(X0)) <=> ~brave(X0)) [input p4]
7. ! [X0] : ((brave(X0) | creative(X0)) <=> (generous(X0) & brave(X0))) [input p6]
24. ~brave(lucy) [input hypothesis]
43. ! [X0] : (((creative(X0) & rich(X0)) | brave(X0)) & (~brave(X0) | (~creative(X0) | ~rich(X0)))) [nnf transformation 5]
44. ! [X0] : (((creative(X0) & rich(X0)) | brave(X0)) & (~brave(X0) | ~creative(X0) | ~rich(X0))) [flattening 43]
45. ! [X0] : (((brave(X0) | creative(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~brave(X0) & ~creative(X0)))) [nnf transformation 7]
46. ! [X0] : ((brave(X0) | creative(X0) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | (~brave(X0) & ~creative(X0)))) [flattening 45]
102. creative(X0) | brave(X0) [cnf transformation 44]
105. brave(X0) | ~creative(X0) [cnf transformation 46]
155. ~brave(lucy) [cnf transformation 24]
210. brave(X0) [subsumption resolution 105,102]
301. $false [subsumption resolution 155,210]
% SZS output end Proof for 1303250603168857896120283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not rich is both old and generous. If alice is not patient then alice is both not wise and quiet and vice versa. If someone is not rich or creative then john is patient and vice versa. Everyone who is not quiet or not creative is not patient or generous. If someone is not happy then paul is rich. Everyone who is not quiet is both not strong and not funny. Everyone who is both not funny and not kind is creative or patient. Everyone who is not brave is not generous. If susan is rich then fred is calm or creative and vice versa. If someone is not strong then someone is both not funny and not quiet. If susan is not humble or old then susan is both not kind and not patient and vice versa. If someone is both not generous and not creative then susan is generous or not funny and vice versa. Everyone who is funny is either not kind or not curious and vice versa. Everyone who is not creative is either happy or calm. If someone is not wise then someone is funny. If paul is not creative or not quiet then alice is not rich and vice versa. Fred is tall. Someone is wise or kind. Susan is either generous or quiet. Susan is funny. Fred is not funny. Alice is not brave. Someone is kind or not old. John is not humble or curious. | John is patient. | entailment | (![X]:((~generous(X)&~rich(X))=>(old(X)&generous(X))))&
((~patient(alice))<=>((~wise(alice)&quiet(alice))))&
((?[X]:((~rich(X)|creative(X))))<=>(patient(john)))&
(![X]:((~quiet(X)|~creative(X))=>(~patient(X)|generous(X))))&
((?[X]:(~happy(X)))=>(rich(paul)))&
(![X]:(~quiet(X)=>(~strong(X)&~funny(X))))&
(![X]:((~funny(X)&~kind(X))=>(creative(X)|patient(X))))&
(![X]:(~brave(X)=>~generous(X)))&
((rich(susan))<=>((calm(fred)|creative(fred))))&
((?[X]:(~strong(X)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(((~humble(susan)|old(susan)))<=>((~kind(susan)&~patient(susan))))&
((?[X]:((~generous(X)&~creative(X))))<=>((generous(susan)|~funny(susan))))&
(![X]:(funny(X)<=>(~kind(X)<~>~curious(X))))&
(![X]:(~creative(X)=>(happy(X)<~>calm(X))))&
((?[X]:(~wise(X)))=>(?[X]:(funny(X))))&
(((~creative(paul)|~quiet(paul)))<=>(~rich(alice)))&
(tall(fred))&
(?[X]:((wise(X)|kind(X))))&
((generous(susan)<~>quiet(susan)))&
(funny(susan))&
(~funny(fred))&
(~brave(alice))&
(?[X]:((kind(X)|~old(X))))&
((~humble(john)|curious(john))) | patient(john) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6672782745405651373854714
% SZS output start Proof for 6672782745405651373854714
3. ? [X0] : (creative(X0) | ~rich(X0)) <=> patient(john) [input p2]
16. (~quiet(paul) | ~creative(paul)) <=> ~rich(alice) [input p15]
25. ~patient(john) [input hypothesis]
43. (? [X0] : (creative(X0) | ~rich(X0)) | ~patient(john)) & (patient(john) | ! [X0] : (~creative(X0) & rich(X0))) [nnf transformation 3]
44. (? [X0] : (creative(X0) | ~rich(X0)) | ~patient(john)) & (patient(john) | ! [X1] : (~creative(X1) & rich(X1))) [rectify 43]
45. ? [X0] : (creative(X0) | ~rich(X0)) => (creative(sK0) | ~rich(sK0)) [choice axiom]
46. ((creative(sK0) | ~rich(sK0)) | ~patient(john)) & (patient(john) | ! [X1] : (~creative(X1) & rich(X1))) [skolemisation 44,45]
64. ((~quiet(paul) | ~creative(paul)) | rich(alice)) & (~rich(alice) | (quiet(paul) & creative(paul))) [nnf transformation 16]
65. (~quiet(paul) | ~creative(paul) | rich(alice)) & (~rich(alice) | (quiet(paul) & creative(paul))) [flattening 64]
76. patient(john) | rich(X1) [cnf transformation 46]
77. patient(john) | ~creative(X1) [cnf transformation 46]
108. ~rich(alice) | creative(paul) [cnf transformation 65]
119. ~patient(john) [cnf transformation 25]
137. 4 <=> patient(john) [avatar definition]
150. 7 <=> ! [X1] : ~creative(X1) [avatar definition]
151. ~creative(X1) <- (7) [avatar component clause 150]
152. 7 | 4 [avatar split clause 77,137,150]
154. 8 <=> ! [X1] : rich(X1) [avatar definition]
155. rich(X1) <- (8) [avatar component clause 154]
156. 8 | 4 [avatar split clause 76,137,154]
247. 28 <=> rich(alice) [avatar definition]
248. ~rich(alice) <- (~28) [avatar component clause 247]
251. 29 <=> creative(paul) [avatar definition]
252. creative(paul) <- (29) [avatar component clause 251]
260. 29 | ~28 [avatar split clause 108,247,251]
295. ~4 [avatar split clause 119,137]
302. $false <- (8, ~28) [resolution 248,155]
303. ~8 | 28 [avatar contradiction clause 302]
304. $false <- (7, 29) [subsumption resolution 252,151]
305. ~7 | ~29 [avatar contradiction clause 304]
306. $false [avatar sat refutation 152,156,260,295,303,305]
% SZS output end Proof for 6672782745405651373854714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not creative is both not wise and not generous and vice versa.
If fred is wise then john is creative and vice versa.
Everyone who is either not old or humble is not wise or happy.
Everyone who is brave is both old and calm.
Everyone who is both not curious and not wise is not happy or quiet and vice versa.
Everyone who is happy or wise is not patient or kind and vice versa.
Everyone who is not patient is quiet or not generous and vice versa.
If paul is both not quiet and old then someone is either wise or strong and vice versa.
Everyone who is old or rich is brave or not happy and vice versa.
If someone is both generous and not brave then someone is either patient or not happy.
Everyone who is not kind is either kind or wise.
Everyone who is both not kind and happy is kind or not happy.
If paul is kind or not patient then paul is brave or not wise and vice versa.
Everyone who is both humble and not humble is both funny and not humble and vice versa.
If someone is not patient or not quiet then someone is funny or wise.
Everyone who is not strong is humble or not patient.
Mary is not calm or quiet.
John is either calm or not humble.
Someone is both not generous and not rich.
Susan is either generous or not patient.
Alice is both not brave and not strong.
Someone is either brave or not quiet.
Someone is either strong or not calm.
Someone is not brave or not wise. | John is not humble. | neutral | (![X]:((~humble(X)&~creative(X))<=>(~wise(X)&~generous(X))))&
((wise(fred))<=>(creative(john)))&
(![X]:((~old(X)<~>humble(X))=>(~wise(X)|happy(X))))&
(![X]:(brave(X)=>(old(X)&calm(X))))&
(![X]:((~curious(X)&~wise(X))<=>(~happy(X)|quiet(X))))&
(![X]:((happy(X)|wise(X))<=>(~patient(X)|kind(X))))&
(![X]:(~patient(X)<=>(quiet(X)|~generous(X))))&
(((~quiet(paul)&old(paul)))<=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((old(X)|rich(X))<=>(brave(X)|~happy(X))))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:(~kind(X)=>(kind(X)<~>wise(X))))&
(![X]:((~kind(X)&happy(X))=>(kind(X)|~happy(X))))&
(((kind(paul)|~patient(paul)))<=>((brave(paul)|~wise(paul))))&
(![X]:((humble(X)&~humble(X))<=>(funny(X)&~humble(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>(?[X]:((funny(X)|wise(X)))))&
(![X]:(~strong(X)=>(humble(X)|~patient(X))))&
((~calm(mary)|quiet(mary)))&
((calm(john)<~>~humble(john)))&
(?[X]:((~generous(X)&~rich(X))))&
((generous(susan)<~>~patient(susan)))&
((~brave(alice)&~strong(alice)))&
(?[X]:((brave(X)<~>~quiet(X))))&
(?[X]:((strong(X)<~>~calm(X))))&
(?[X]:((~brave(X)|~wise(X)))) | ~humble(john) | [] | null | 0 |
If alice is both not happy and humble then fred is either happy or old.
If someone is not calm or patient then alice is not wise and vice versa.
If fred is not patient or happy then john is not quiet or humble.
Everyone who is happy is both not humble and not brave.
Everyone who is both tall and happy is either brave or generous.
Everyone who is rich is either not calm or not tall and vice versa.
If someone is both old and not happy then someone is either quiet or not curious and vice versa.
If someone is not wise then someone is strong and vice versa.
If someone is either not kind or calm then someone is curious and vice versa.
If someone is happy or not happy then someone is both wise and curious.
Everyone who is brave is quiet.
If mary is quiet then someone is not calm or wise and vice versa.
If someone is both calm and humble then lucy is happy or not quiet and vice versa.
If paul is both patient and generous then someone is happy or curious and vice versa.
Everyone who is strong is either old or calm.
Everyone who is not happy or not brave is not old.
Someone is both humble and not curious.
Someone is both not humble and generous.
John is not generous.
Someone is both tall and not quiet.
Someone is both not wise and not creative.
Someone is either not brave or not humble. | Paul is not generous. | contradiction | (((~happy(alice)&humble(alice)))=>((happy(fred)<~>old(fred))))&
((?[X]:((~calm(X)|patient(X))))<=>(~wise(alice)))&
(((~patient(fred)|happy(fred)))=>((~quiet(john)|humble(john))))&
(![X]:(happy(X)=>(~humble(X)&~brave(X))))&
(![X]:((tall(X)&happy(X))=>(brave(X)<~>generous(X))))&
(![X]:(rich(X)<=>(~calm(X)<~>~tall(X))))&
((?[X]:((old(X)&~happy(X))))<=>(?[X]:((quiet(X)<~>~curious(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~kind(X)<~>calm(X))))<=>(?[X]:(curious(X))))&
((?[X]:((happy(X)|~happy(X))))=>(?[X]:((wise(X)&curious(X)))))&
(![X]:(brave(X)=>quiet(X)))&
((quiet(mary))<=>(?[X]:((~calm(X)|wise(X)))))&
((?[X]:((calm(X)&humble(X))))<=>((happy(lucy)|~quiet(lucy))))&
(((patient(paul)&generous(paul)))<=>(?[X]:((happy(X)|curious(X)))))&
(![X]:(strong(X)=>(old(X)<~>calm(X))))&
(![X]:((~happy(X)|~brave(X))=>~old(X)))&
(?[X]:((humble(X)&~curious(X))))&
(?[X]:((~humble(X)&generous(X))))&
(~generous(john))&
(?[X]:((tall(X)&~quiet(X))))&
(?[X]:((~wise(X)&~creative(X))))&
(?[X]:((~brave(X)<~>~humble(X)))) | ~generous(paul) | [
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4696149012811833109394284
% SZS output start Proof for 4696149012811833109394284
10. ? [X0] : (~happy(X0) | happy(X0)) => ? [X0] : (curious(X0) & wise(X0)) [input p9]
14. (generous(paul) & patient(paul)) <=> ? [X0] : (curious(X0) | happy(X0)) [input p13]
23. ~generous(paul) [input hypothesis]
27. ? [X0] : (~happy(X0) | happy(X0)) => ? [X1] : (curious(X1) & wise(X1)) [rectify 10]
36. ? [X1] : (curious(X1) & wise(X1)) | ! [X0] : (happy(X0) & ~happy(X0)) [ennf transformation 27]
61. ? [X0] : (curious(X0) & wise(X0)) | ! [X1] : (happy(X1) & ~happy(X1)) [rectify 36]
62. ? [X0] : (curious(X0) & wise(X0)) => (curious(sK7) & wise(sK7)) [choice axiom]
63. (curious(sK7) & wise(sK7)) | ! [X1] : (happy(X1) & ~happy(X1)) [skolemisation 61,62]
73. ((generous(paul) & patient(paul)) | ! [X0] : (~curious(X0) & ~happy(X0))) & (? [X0] : (curious(X0) | happy(X0)) | (~generous(paul) | ~patient(paul))) [nnf transformation 14]
74. ((generous(paul) & patient(paul)) | ! [X0] : (~curious(X0) & ~happy(X0))) & (? [X0] : (curious(X0) | happy(X0)) | ~generous(paul) | ~patient(paul)) [flattening 73]
75. ((generous(paul) & patient(paul)) | ! [X0] : (~curious(X0) & ~happy(X0))) & (? [X1] : (curious(X1) | happy(X1)) | ~generous(paul) | ~patient(paul)) [rectify 74]
76. ? [X1] : (curious(X1) | happy(X1)) => (curious(sK10) | happy(sK10)) [choice axiom]
77. ((generous(paul) & patient(paul)) | ! [X0] : (~curious(X0) & ~happy(X0))) & ((curious(sK10) | happy(sK10)) | ~generous(paul) | ~patient(paul)) [skolemisation 75,76]
116. curious(sK7) | happy(X1) [cnf transformation 63]
129. generous(paul) | ~happy(X0) [cnf transformation 77]
130. generous(paul) | ~curious(X0) [cnf transformation 77]
145. ~generous(paul) [cnf transformation 23]
248. 24 <=> ! [X1] : ~curious(X1) [avatar definition]
249. ~curious(X1) <- (24) [avatar component clause 248]
273. 30 <=> ! [X1] : happy(X1) [avatar definition]
274. happy(X1) <- (30) [avatar component clause 273]
276. 31 <=> curious(sK7) [avatar definition]
278. curious(sK7) <- (31) [avatar component clause 276]
279. 30 | 31 [avatar split clause 116,276,273]
281. 32 <=> ! [X1] : ~happy(X1) [avatar definition]
282. ~happy(X1) <- (32) [avatar component clause 281]
333. 43 <=> generous(paul) [avatar definition]
336. 24 | 43 [avatar split clause 130,333,248]
337. 32 | 43 [avatar split clause 129,333,281]
364. ~43 [avatar split clause 145,333]
365. $false <- (30, 32) [subsumption resolution 274,282]
366. ~30 | ~32 [avatar contradiction clause 365]
377. $false <- (24, 31) [subsumption resolution 278,249]
378. ~24 | ~31 [avatar contradiction clause 377]
381. $false [avatar sat refutation 279,336,337,364,366,378]
% SZS output end Proof for 4696149012811833109394284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient then someone is both happy and not patient.
If fred is curious or brave then someone is both quiet and rich.
Everyone who is strong or not patient is both not rich and not funny and vice versa.
If someone is either not wise or curious then someone is calm.
Everyone who is both not generous and tall is either not humble or funny.
If someone is happy or funny then mary is both strong and generous.
If someone is either brave or calm then someone is both wise and not creative and vice versa.
Everyone who is both tall and not funny is both not happy and generous and vice versa.
If someone is either quiet or creative then someone is patient or not calm and vice versa.
Everyone who is patient is both not wise and not calm and vice versa.
If someone is either not creative or not kind then someone is either happy or not kind.
Everyone who is not calm or not generous is either not generous or not tall and vice versa.
If someone is either not kind or wise then someone is both patient and brave.
Everyone who is either not wise or curious is not humble.
Everyone who is kind is quiet or kind and vice versa.
Lucy is both not humble and curious.
Someone is either patient or not quiet.
Lucy is both not happy and curious.
Someone is humble.
Someone is strong.
Paul is patient or not happy.
Alice is not patient. | Paul is funny. | neutral | ((?[X]:(patient(X)))=>(?[X]:((happy(X)&~patient(X)))))&
(((curious(fred)|brave(fred)))=>(?[X]:((quiet(X)&rich(X)))))&
(![X]:((strong(X)|~patient(X))<=>(~rich(X)&~funny(X))))&
((?[X]:((~wise(X)<~>curious(X))))=>(?[X]:(calm(X))))&
(![X]:((~generous(X)&tall(X))=>(~humble(X)<~>funny(X))))&
((?[X]:((happy(X)|funny(X))))=>((strong(mary)&generous(mary))))&
((?[X]:((brave(X)<~>calm(X))))<=>(?[X]:((wise(X)&~creative(X)))))&
(![X]:((tall(X)&~funny(X))<=>(~happy(X)&generous(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:(patient(X)<=>(~wise(X)&~calm(X))))&
((?[X]:((~creative(X)<~>~kind(X))))=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((~calm(X)|~generous(X))<=>(~generous(X)<~>~tall(X))))&
((?[X]:((~kind(X)<~>wise(X))))=>(?[X]:((patient(X)&brave(X)))))&
(![X]:((~wise(X)<~>curious(X))=>~humble(X)))&
(![X]:(kind(X)<=>(quiet(X)|kind(X))))&
((~humble(lucy)&curious(lucy)))&
(?[X]:((patient(X)<~>~quiet(X))))&
((~happy(lucy)&curious(lucy)))&
(?[X]:(humble(X)))&
(?[X]:(strong(X)))&
((patient(paul)|~happy(paul)))&
(~patient(alice)) | funny(paul) | [] | null | 0 |
If alice is quiet then fred is either creative or patient.
Everyone who is either brave or rich is both not curious and not brave and vice versa.
If someone is generous then someone is both humble and brave.
If mary is humble or not happy then someone is not happy.
If someone is not curious then lucy is humble or not kind.
Everyone who is both not creative and old is brave and vice versa.
Everyone who is both funny and not generous is either creative or humble and vice versa.
If fred is both funny and not happy then someone is not tall.
If lucy is either not patient or not generous then mary is either not rich or not humble.
If paul is either curious or wise then someone is creative or patient.
Everyone who is either brave or generous is both rich and generous and vice versa.
If someone is not curious or not generous then paul is both calm and not creative and vice versa.
If fred is either patient or not humble then someone is rich or wise and vice versa.
If lucy is either not happy or not rich then someone is both not wise and not generous.
If someone is both not kind and not patient then john is not strong or not brave and vice versa.
Someone is creative or not quiet.
Lucy is old.
Someone is either curious or funny.
Lucy is not rich or not brave.
Someone is generous or not brave.
Fred is not humble or quiet. | John is not generous. | entailment | ((quiet(alice))=>((creative(fred)<~>patient(fred))))&
(![X]:((brave(X)<~>rich(X))<=>(~curious(X)&~brave(X))))&
((?[X]:(generous(X)))=>(?[X]:((humble(X)&brave(X)))))&
(((humble(mary)|~happy(mary)))=>(?[X]:(~happy(X))))&
((?[X]:(~curious(X)))=>((humble(lucy)|~kind(lucy))))&
(![X]:((~creative(X)&old(X))<=>brave(X)))&
(![X]:((funny(X)&~generous(X))<=>(creative(X)<~>humble(X))))&
(((funny(fred)&~happy(fred)))=>(?[X]:(~tall(X))))&
(((~patient(lucy)<~>~generous(lucy)))=>((~rich(mary)<~>~humble(mary))))&
(((curious(paul)<~>wise(paul)))=>(?[X]:((creative(X)|patient(X)))))&
(![X]:((brave(X)<~>generous(X))<=>(rich(X)&generous(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((calm(paul)&~creative(paul))))&
(((patient(fred)<~>~humble(fred)))<=>(?[X]:((rich(X)|wise(X)))))&
(((~happy(lucy)<~>~rich(lucy)))=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~kind(X)&~patient(X))))<=>((~strong(john)|~brave(john))))&
(?[X]:((creative(X)|~quiet(X))))&
(old(lucy))&
(?[X]:((curious(X)<~>funny(X))))&
((~rich(lucy)|~brave(lucy)))&
(?[X]:((generous(X)|~brave(X))))&
((~humble(fred)|quiet(fred))) | ~generous(john) | [
"p1",
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 9205201255891412721360426
% SZS output start Proof for 9205201255891412721360426
2. ! [X0] : ((brave(X0) <~> rich(X0)) <=> (~brave(X0) & ~curious(X0))) [input p1]
3. ? [X0] : generous(X0) => ? [X0] : (brave(X0) & humble(X0)) [input p2]
11. ! [X0] : ((brave(X0) <~> generous(X0)) <=> (generous(X0) & rich(X0))) [input p10]
22. generous(john) [input hypothesis]
23. ? [X0] : generous(X0) => ? [X1] : (brave(X1) & humble(X1)) [rectify 3]
26. ? [X1] : (brave(X1) & humble(X1)) | ! [X0] : ~generous(X0) [ennf transformation 23]
34. ! [X0] : ((((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0))))) [nnf transformation 2]
35. ! [X0] : ((((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0))))) [flattening 34]
36. ? [X0] : (brave(X0) & humble(X0)) | ! [X1] : ~generous(X1) [rectify 26]
37. ? [X0] : (brave(X0) & humble(X0)) => (brave(sK0) & humble(sK0)) [choice axiom]
38. (brave(sK0) & humble(sK0)) | ! [X1] : ~generous(X1) [skolemisation 36,37]
49. ! [X0] : ((((~generous(X0) | ~brave(X0)) & (generous(X0) | brave(X0))) | (~generous(X0) | ~rich(X0))) & ((generous(X0) & rich(X0)) | ((brave(X0) | ~generous(X0)) & (generous(X0) | ~brave(X0))))) [nnf transformation 11]
50. ! [X0] : ((((~generous(X0) | ~brave(X0)) & (generous(X0) | brave(X0))) | ~generous(X0) | ~rich(X0)) & ((generous(X0) & rich(X0)) | ((brave(X0) | ~generous(X0)) & (generous(X0) | ~brave(X0))))) [flattening 49]
79. ~brave(X0) | rich(X0) | ~brave(X0) [cnf transformation 35]
84. brave(sK0) | ~generous(X1) [cnf transformation 38]
105. generous(X0) | generous(X0) | ~brave(X0) [cnf transformation 50]
108. ~generous(X0) | ~brave(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 50]
136. generous(john) [cnf transformation 22]
137. generous(X0) | ~brave(X0) [duplicate literal removal 105]
138. ~generous(X0) | ~brave(X0) | ~rich(X0) [duplicate literal removal 108]
139. ~brave(X0) | rich(X0) [duplicate literal removal 79]
156. 4 <=> ! [X1] : ~generous(X1) [avatar definition]
157. ~generous(X1) <- (4) [avatar component clause 156]
159. 5 <=> brave(sK0) [avatar definition]
161. brave(sK0) <- (5) [avatar component clause 159]
162. 4 | 5 [avatar split clause 84,159,156]
228. ~generous(X0) | ~brave(X0) [subsumption resolution 138,139]
229. ~brave(X0) [subsumption resolution 137,228]
325. $false <- (4) [resolution 157,136]
326. ~4 [avatar contradiction clause 325]
327. $false <- (5) [subsumption resolution 161,229]
328. ~5 [avatar contradiction clause 327]
329. $false [avatar sat refutation 162,326,328]
% SZS output end Proof for 9205201255891412721360426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is quiet.
Everyone who is not tall or not funny is humble.
Everyone who is not generous or tall is brave.
Everyone who is not humble or not old is either calm or tall.
Everyone who is either not strong or not tall is funny or not rich and vice versa.
Everyone who is either generous or patient is patient and vice versa.
Everyone who is either tall or not generous is both old and wise.
Everyone who is brave or not calm is either funny or quiet and vice versa.
If someone is funny then someone is not generous.
Everyone who is happy or rich is generous and vice versa.
If mary is both patient and generous then someone is not wise.
Everyone who is either not curious or happy is happy and vice versa.
If someone is both happy and not patient then someone is both not humble and strong and vice versa.
Everyone who is either generous or not wise is both curious and quiet.
Everyone who is both not humble and kind is either not patient or not creative and vice versa.
Someone is either not happy or wise.
John is both not kind and not quiet.
Someone is either not humble or not quiet.
Someone is not quiet.
Mary is either not humble or not kind.
Susan is either creative or strong.
Someone is wise or not rich. | John is not brave. | contradiction | (![X]:(~strong(X)=>quiet(X)))&
(![X]:((~tall(X)|~funny(X))=>humble(X)))&
(![X]:((~generous(X)|tall(X))=>brave(X)))&
(![X]:((~humble(X)|~old(X))=>(calm(X)<~>tall(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(funny(X)|~rich(X))))&
(![X]:((generous(X)<~>patient(X))<=>patient(X)))&
(![X]:((tall(X)<~>~generous(X))=>(old(X)&wise(X))))&
(![X]:((brave(X)|~calm(X))<=>(funny(X)<~>quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:(~generous(X))))&
(![X]:((happy(X)|rich(X))<=>generous(X)))&
(((patient(mary)&generous(mary)))=>(?[X]:(~wise(X))))&
(![X]:((~curious(X)<~>happy(X))<=>happy(X)))&
((?[X]:((happy(X)&~patient(X))))<=>(?[X]:((~humble(X)&strong(X)))))&
(![X]:((generous(X)<~>~wise(X))=>(curious(X)&quiet(X))))&
(![X]:((~humble(X)&kind(X))<=>(~patient(X)<~>~creative(X))))&
(?[X]:((~happy(X)<~>wise(X))))&
((~kind(john)&~quiet(john)))&
(?[X]:((~humble(X)<~>~quiet(X))))&
(?[X]:(~quiet(X)))&
((~humble(mary)<~>~kind(mary)))&
((creative(susan)<~>strong(susan)))&
(?[X]:((wise(X)|~rich(X)))) | ~brave(john) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6681769943939516103469319
% SZS output start Proof for 6681769943939516103469319
3. ! [X0] : ((tall(X0) | ~generous(X0)) => brave(X0)) [input p2]
6. ! [X0] : ((generous(X0) <~> patient(X0)) <=> patient(X0)) [input p5]
23. ~brave(john) [input hypothesis]
30. ! [X0] : (brave(X0) | (~tall(X0) & generous(X0))) [ennf transformation 3]
40. ! [X0] : ((((~patient(X0) | ~generous(X0)) & (patient(X0) | generous(X0))) | ~patient(X0)) & (patient(X0) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0))))) [nnf transformation 6]
75. brave(X0) | generous(X0) [cnf transformation 30]
85. patient(X0) | patient(X0) | ~generous(X0) [cnf transformation 40]
88. ~patient(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 40]
132. ~brave(john) [cnf transformation 23]
135. patient(X0) | ~generous(X0) [duplicate literal removal 85]
136. ~patient(X0) | ~generous(X0) [duplicate literal removal 88]
138. ~generous(X0) [subsumption resolution 135,136]
188. generous(john) [resolution 75,132]
189. $false [subsumption resolution 188,138]
% SZS output end Proof for 6681769943939516103469319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not tall then fred is either generous or patient. Everyone who is either patient or not generous is not humble. If lucy is either not brave or not patient then paul is tall or not happy. If alice is both not patient and not quiet then john is not tall and vice versa. Everyone who is generous is not patient or not calm. If paul is both not calm and not wise then someone is happy or generous and vice versa. Everyone who is not tall or patient is not creative or happy. Everyone who is calm or not strong is not patient or funny and vice versa. Everyone who is generous or not creative is both not humble and generous and vice versa. If someone is patient or not quiet then someone is both creative and generous and vice versa. Everyone who is both rich and quiet is not humble or not calm and vice versa. Everyone who is either rich or not calm is calm or not strong. Everyone who is both not old and not creative is either not strong or humble and vice versa. Everyone who is not old or patient is not funny or not old. Everyone who is not wise is happy or old and vice versa. If someone is not old then alice is old or rich. Someone is not creative. John is funny. Mary is either not strong or not rich. Fred is not tall or not patient. Someone is both not old and not patient. Someone is either not old or happy. John is either not strong or not happy. Mary is brave or not generous. | Lucy is quiet. | neutral | ((?[X]:((wise(X)|~tall(X))))=>((generous(fred)<~>patient(fred))))&
(![X]:((patient(X)<~>~generous(X))=>~humble(X)))&
(((~brave(lucy)<~>~patient(lucy)))=>((tall(paul)|~happy(paul))))&
(((~patient(alice)&~quiet(alice)))<=>(~tall(john)))&
(![X]:(generous(X)=>(~patient(X)|~calm(X))))&
(((~calm(paul)&~wise(paul)))<=>(?[X]:((happy(X)|generous(X)))))&
(![X]:((~tall(X)|patient(X))=>(~creative(X)|happy(X))))&
(![X]:((calm(X)|~strong(X))<=>(~patient(X)|funny(X))))&
(![X]:((generous(X)|~creative(X))<=>(~humble(X)&generous(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:((creative(X)&generous(X)))))&
(![X]:((rich(X)&quiet(X))<=>(~humble(X)|~calm(X))))&
(![X]:((rich(X)<~>~calm(X))=>(calm(X)|~strong(X))))&
(![X]:((~old(X)&~creative(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((~old(X)|patient(X))=>(~funny(X)|~old(X))))&
(![X]:(~wise(X)<=>(happy(X)|old(X))))&
((?[X]:(~old(X)))=>((old(alice)|rich(alice))))&
(?[X]:(~creative(X)))&
(funny(john))&
((~strong(mary)<~>~rich(mary)))&
((~tall(fred)|~patient(fred)))&
(?[X]:((~old(X)&~patient(X))))&
(?[X]:((~old(X)<~>happy(X))))&
((~strong(john)<~>~happy(john)))&
((brave(mary)|~generous(mary))) | quiet(lucy) | [] | null | 0 |
If paul is both curious and rich then john is not happy or not humble and vice versa.
Everyone who is calm or not creative is both patient and not kind.
Everyone who is both not funny and not brave is creative or not tall and vice versa.
If fred is both not happy and not tall then someone is either kind or happy and vice versa.
If john is both tall and rich then someone is both not humble and funny and vice versa.
Everyone who is both not calm and old is either happy or calm and vice versa.
If someone is not humble or tall then someone is both strong and not patient and vice versa.
If someone is both not strong and brave then someone is either not quiet or not old.
If susan is both not generous and not patient then john is both quiet and curious.
If someone is both happy and funny then someone is calm.
If fred is both creative and curious then lucy is not strong or not funny and vice versa.
If someone is both happy and not old then mary is not kind or brave and vice versa.
Everyone who is brave is both not quiet and not old and vice versa.
Everyone who is funny or curious is brave or not creative and vice versa.
Everyone who is both curious and creative is not rich and vice versa.
Everyone who is both kind and not curious is old or happy.
Someone is old.
Fred is strong.
Alice is both humble and not happy.
Susan is either not tall or not patient.
John is humble or rich.
John is rich or not brave.
Lucy is either old or creative. | Mary is kind. | neutral | (((curious(paul)&rich(paul)))<=>((~happy(john)|~humble(john))))&
(![X]:((calm(X)|~creative(X))=>(patient(X)&~kind(X))))&
(![X]:((~funny(X)&~brave(X))<=>(creative(X)|~tall(X))))&
(((~happy(fred)&~tall(fred)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(((tall(john)&rich(john)))<=>(?[X]:((~humble(X)&funny(X)))))&
(![X]:((~calm(X)&old(X))<=>(happy(X)<~>calm(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((strong(X)&~patient(X)))))&
((?[X]:((~strong(X)&brave(X))))=>(?[X]:((~quiet(X)<~>~old(X)))))&
(((~generous(susan)&~patient(susan)))=>((quiet(john)&curious(john))))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:(calm(X))))&
(((creative(fred)&curious(fred)))<=>((~strong(lucy)|~funny(lucy))))&
((?[X]:((happy(X)&~old(X))))<=>((~kind(mary)|brave(mary))))&
(![X]:(brave(X)<=>(~quiet(X)&~old(X))))&
(![X]:((funny(X)|curious(X))<=>(brave(X)|~creative(X))))&
(![X]:((curious(X)&creative(X))<=>~rich(X)))&
(![X]:((kind(X)&~curious(X))=>(old(X)|happy(X))))&
(?[X]:(old(X)))&
(strong(fred))&
((humble(alice)&~happy(alice)))&
((~tall(susan)<~>~patient(susan)))&
((humble(john)|rich(john)))&
((rich(john)|~brave(john)))&
((old(lucy)<~>creative(lucy))) | kind(mary) | [] | null | 0 |
Everyone who is quiet or tall is either strong or generous.
If john is both tall and quiet then paul is creative and vice versa.
Everyone who is not generous or strong is both not strong and not quiet.
Everyone who is either funny or not quiet is either not rich or not kind.
Everyone who is not creative or not patient is either not funny or not humble.
Everyone who is not tall is both tall and not kind and vice versa.
Everyone who is both tall and funny is funny or patient and vice versa.
Everyone who is rich is not brave and vice versa.
If someone is wise then paul is both calm and not calm.
Everyone who is both wise and not creative is both not funny and not quiet.
Everyone who is rich is both creative and curious.
If paul is not wise or humble then someone is not old or happy and vice versa.
If someone is both not brave and not happy then someone is either not tall or curious.
If someone is either not quiet or curious then lucy is either happy or not patient and vice versa.
If mary is either not rich or not calm then someone is tall or not calm.
Someone is generous or humble.
Fred is either humble or quiet.
Someone is either tall or not rich.
Someone is wise or curious.
Someone is either curious or happy.
Someone is curious.
Mary is either creative or not creative.
Alice is patient. | Alice is generous. | entailment | (![X]:((quiet(X)|tall(X))=>(strong(X)<~>generous(X))))&
(((tall(john)&quiet(john)))<=>(creative(paul)))&
(![X]:((~generous(X)|strong(X))=>(~strong(X)&~quiet(X))))&
(![X]:((funny(X)<~>~quiet(X))=>(~rich(X)<~>~kind(X))))&
(![X]:((~creative(X)|~patient(X))=>(~funny(X)<~>~humble(X))))&
(![X]:(~tall(X)<=>(tall(X)&~kind(X))))&
(![X]:((tall(X)&funny(X))<=>(funny(X)|patient(X))))&
(![X]:(rich(X)<=>~brave(X)))&
((?[X]:(wise(X)))=>((calm(paul)&~calm(paul))))&
(![X]:((wise(X)&~creative(X))=>(~funny(X)&~quiet(X))))&
(![X]:(rich(X)=>(creative(X)&curious(X))))&
(((~wise(paul)|humble(paul)))<=>(?[X]:((~old(X)|happy(X)))))&
((?[X]:((~brave(X)&~happy(X))))=>(?[X]:((~tall(X)<~>curious(X)))))&
((?[X]:((~quiet(X)<~>curious(X))))<=>((happy(lucy)<~>~patient(lucy))))&
(((~rich(mary)<~>~calm(mary)))=>(?[X]:((tall(X)|~calm(X)))))&
(?[X]:((generous(X)|humble(X))))&
((humble(fred)<~>quiet(fred)))&
(?[X]:((tall(X)<~>~rich(X))))&
(?[X]:((wise(X)|curious(X))))&
(?[X]:((curious(X)<~>happy(X))))&
(?[X]:(curious(X)))&
((creative(mary)<~>~creative(mary)))&
(patient(alice)) | generous(alice) | [
"p0",
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2878742409769269488937358
% SZS output start Proof for 2878742409769269488937358
1. ! [X0] : ((tall(X0) | quiet(X0)) => (strong(X0) <~> generous(X0))) [input p0]
3. ! [X0] : ((strong(X0) | ~generous(X0)) => (~quiet(X0) & ~strong(X0))) [input p2]
6. ! [X0] : (~tall(X0) <=> (~kind(X0) & tall(X0))) [input p5]
24. ~generous(alice) [input hypothesis]
26. ! [X0] : ((strong(X0) <~> generous(X0)) | (~tall(X0) & ~quiet(X0))) [ennf transformation 1]
27. ! [X0] : ((~quiet(X0) & ~strong(X0)) | (~strong(X0) & generous(X0))) [ennf transformation 3]
36. ! [X0] : (((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | (~tall(X0) & ~quiet(X0))) [nnf transformation 26]
41. ! [X0] : ((~tall(X0) | (kind(X0) | ~tall(X0))) & ((~kind(X0) & tall(X0)) | tall(X0))) [nnf transformation 6]
42. ! [X0] : ((~tall(X0) | kind(X0) | ~tall(X0)) & ((~kind(X0) & tall(X0)) | tall(X0))) [flattening 41]
77. ~tall(X0) | strong(X0) | generous(X0) [cnf transformation 36]
84. ~strong(X0) | ~strong(X0) [cnf transformation 27]
95. tall(X0) | tall(X0) [cnf transformation 42]
139. ~generous(alice) [cnf transformation 24]
140. tall(X0) [duplicate literal removal 95]
142. ~strong(X0) [duplicate literal removal 84]
285. strong(X0) | generous(X0) [resolution 77,140]
286. generous(X0) [subsumption resolution 285,142]
287. $false [resolution 286,139]
% SZS output end Proof for 2878742409769269488937358
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not calm is not kind. If mary is not rich then mary is not happy or not patient and vice versa. Everyone who is both quiet and not rich is both not funny and rich. Everyone who is either not strong or patient is both not funny and not strong. If fred is patient or happy then lucy is rich or not tall and vice versa. If paul is quiet then alice is creative and vice versa. If someone is not funny then paul is both not humble and not wise. If alice is not patient then someone is both not generous and not humble. Everyone who is not creative is not kind or not funny and vice versa. If lucy is kind then fred is either not old or not rich and vice versa. If someone is strong then fred is both not patient and quiet and vice versa. Everyone who is either calm or not patient is not rich or happy and vice versa. Everyone who is both tall and generous is both kind and wise. If someone is either not funny or not tall then someone is either creative or not calm. Everyone who is tall or brave is not funny. If someone is both funny and not old then fred is either not brave or tall. Someone is both happy and generous. Someone is both patient and funny. Someone is strong. Someone is not wise. John is not kind or old. Someone is creative or rich. Fred is rich or not quiet. | Paul is old. | neutral | (![X]:((patient(X)|~calm(X))=>~kind(X)))&
((~rich(mary))<=>((~happy(mary)|~patient(mary))))&
(![X]:((quiet(X)&~rich(X))=>(~funny(X)&rich(X))))&
(![X]:((~strong(X)<~>patient(X))=>(~funny(X)&~strong(X))))&
(((patient(fred)|happy(fred)))<=>((rich(lucy)|~tall(lucy))))&
((quiet(paul))<=>(creative(alice)))&
((?[X]:(~funny(X)))=>((~humble(paul)&~wise(paul))))&
((~patient(alice))=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:(~creative(X)<=>(~kind(X)|~funny(X))))&
((kind(lucy))<=>((~old(fred)<~>~rich(fred))))&
((?[X]:(strong(X)))<=>((~patient(fred)&quiet(fred))))&
(![X]:((calm(X)<~>~patient(X))<=>(~rich(X)|happy(X))))&
(![X]:((tall(X)&generous(X))=>(kind(X)&wise(X))))&
((?[X]:((~funny(X)<~>~tall(X))))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((tall(X)|brave(X))=>~funny(X)))&
((?[X]:((funny(X)&~old(X))))=>((~brave(fred)<~>tall(fred))))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:((patient(X)&funny(X))))&
(?[X]:(strong(X)))&
(?[X]:(~wise(X)))&
((~kind(john)|old(john)))&
(?[X]:((creative(X)|rich(X))))&
((rich(fred)|~quiet(fred))) | old(paul) | [] | null | 0 |
If someone is patient or not rich then susan is not old. Everyone who is either not kind or funny is either old or rich and vice versa. Everyone who is both not humble and not quiet is humble or not patient and vice versa. Everyone who is rich or old is not kind and vice versa. If susan is strong then john is both not rich and not generous and vice versa. Everyone who is both tall and not quiet is old or happy and vice versa. Everyone who is curious is both not old and not curious. If someone is both not funny and not happy then susan is not happy or kind and vice versa. Everyone who is not brave is either not strong or not humble and vice versa. If susan is both not curious and calm then someone is both not patient and not rich and vice versa. If someone is both creative and curious then someone is patient or not funny and vice versa. If someone is humble or not quiet then someone is both rich and old and vice versa. If susan is either not funny or not generous then fred is both not calm and not happy. Everyone who is creative or not strong is not creative. Everyone who is creative is tall. Everyone who is both patient and not kind is kind or not generous and vice versa. Someone is generous or brave. Paul is not calm or quiet. Someone is either not curious or not funny. Fred is both not kind and not quiet. Someone is kind or generous. | Susan is rich. | entailment | ((?[X]:((patient(X)|~rich(X))))=>(~old(susan)))&
(![X]:((~kind(X)<~>funny(X))<=>(old(X)<~>rich(X))))&
(![X]:((~humble(X)&~quiet(X))<=>(humble(X)|~patient(X))))&
(![X]:((rich(X)|old(X))<=>~kind(X)))&
((strong(susan))<=>((~rich(john)&~generous(john))))&
(![X]:((tall(X)&~quiet(X))<=>(old(X)|happy(X))))&
(![X]:(curious(X)=>(~old(X)&~curious(X))))&
((?[X]:((~funny(X)&~happy(X))))<=>((~happy(susan)|kind(susan))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~humble(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(?[X]:((generous(X)|brave(X))))&
((~calm(paul)|quiet(paul)))&
(?[X]:((~curious(X)<~>~funny(X))))&
((~kind(fred)&~quiet(fred)))&
(?[X]:((kind(X)|generous(X)))) | rich(susan) | [
"p0",
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7537408465431819008754790
% SZS output start Proof for 7537408465431819008754790
1. ? [X0] : (~rich(X0) | patient(X0)) => ~old(susan) [input p0]
4. ! [X0] : ((old(X0) | rich(X0)) <=> ~kind(X0)) [input p3]
16. ! [X0] : ((~kind(X0) & patient(X0)) <=> (~generous(X0) | kind(X0))) [input p15]
22. ~rich(susan) [input hypothesis]
26. ~old(susan) | ! [X0] : (rich(X0) & ~patient(X0)) [ennf transformation 1]
35. ! [X0] : (((old(X0) | rich(X0)) | kind(X0)) & (~kind(X0) | (~old(X0) & ~rich(X0)))) [nnf transformation 4]
36. ! [X0] : ((old(X0) | rich(X0) | kind(X0)) & (~kind(X0) | (~old(X0) & ~rich(X0)))) [flattening 35]
63. ! [X0] : (((~kind(X0) & patient(X0)) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | (kind(X0) | ~patient(X0)))) [nnf transformation 16]
64. ! [X0] : (((~kind(X0) & patient(X0)) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | kind(X0) | ~patient(X0))) [flattening 63]
73. ~old(susan) | rich(X0) [cnf transformation 26]
89. kind(X0) | rich(X0) | old(X0) [cnf transformation 36]
131. ~kind(X0) | ~kind(X0) [cnf transformation 64]
140. ~rich(susan) [cnf transformation 22]
142. ~kind(X0) [duplicate literal removal 131]
148. 1 <=> ! [X0] : rich(X0) [avatar definition]
149. rich(X0) <- (1) [avatar component clause 148]
151. 2 <=> old(susan) [avatar definition]
153. ~old(susan) <- (~2) [avatar component clause 151]
154. 1 | ~2 [avatar split clause 73,151,148]
311. old(X3) | rich(X3) [resolution 89,142]
312. rich(susan) <- (~2) [resolution 311,153]
314. $false <- (~2) [subsumption resolution 312,140]
315. 2 [avatar contradiction clause 314]
316. $false <- (1) [resolution 149,140]
319. ~1 [avatar contradiction clause 316]
320. $false [avatar sat refutation 154,315,319]
% SZS output end Proof for 7537408465431819008754790
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and tall is either brave or old.
Everyone who is both not creative and not humble is both not strong and not rich and vice versa.
Everyone who is either humble or tall is quiet and vice versa.
If fred is both patient and not curious then lucy is either old or not happy.
Everyone who is both not funny and not tall is creative or not generous.
Everyone who is either not strong or generous is generous or not kind and vice versa.
Everyone who is brave or not brave is not brave and vice versa.
Everyone who is not quiet or not happy is both wise and strong.
Everyone who is not tall or creative is creative or not patient and vice versa.
Everyone who is both not rich and quiet is either not brave or not humble.
Everyone who is not patient is both quiet and not rich.
Everyone who is quiet is both tall and funny.
Everyone who is not patient is funny or generous.
If someone is either happy or wise then paul is either curious or patient and vice versa.
If alice is either not tall or creative then someone is humble and vice versa.
If someone is not rich or not humble then someone is humble or not kind and vice versa.
Someone is either not tall or humble.
Alice is humble or generous.
Mary is not quiet.
Susan is either old or not kind.
Fred is either not funny or kind.
Fred is either not old or strong. | Paul is not creative. | neutral | (![X]:((kind(X)&tall(X))=>(brave(X)<~>old(X))))&
(![X]:((~creative(X)&~humble(X))<=>(~strong(X)&~rich(X))))&
(![X]:((humble(X)<~>tall(X))<=>quiet(X)))&
(((patient(fred)&~curious(fred)))=>((old(lucy)<~>~happy(lucy))))&
(![X]:((~funny(X)&~tall(X))=>(creative(X)|~generous(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(generous(X)|~kind(X))))&
(![X]:((brave(X)|~brave(X))<=>~brave(X)))&
(![X]:((~quiet(X)|~happy(X))=>(wise(X)&strong(X))))&
(![X]:((~tall(X)|creative(X))<=>(creative(X)|~patient(X))))&
(![X]:((~rich(X)&quiet(X))=>(~brave(X)<~>~humble(X))))&
(![X]:(~patient(X)=>(quiet(X)&~rich(X))))&
(![X]:(quiet(X)=>(tall(X)&funny(X))))&
(![X]:(~patient(X)=>(funny(X)|generous(X))))&
((?[X]:((happy(X)<~>wise(X))))<=>((curious(paul)<~>patient(paul))))&
(((~tall(alice)<~>creative(alice)))<=>(?[X]:(humble(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
(?[X]:((~tall(X)<~>humble(X))))&
((humble(alice)|generous(alice)))&
(~quiet(mary))&
((old(susan)<~>~kind(susan)))&
((~funny(fred)<~>kind(fred)))&
((~old(fred)<~>strong(fred))) | ~creative(paul) | [] | null | 0 |
Everyone who is either not creative or not old is not generous.
If someone is old then someone is both not kind and not creative and vice versa.
Everyone who is either old or generous is generous.
Everyone who is not calm or not funny is either creative or generous.
Everyone who is both not creative and old is either patient or brave and vice versa.
Everyone who is quiet is rich.
Everyone who is creative or patient is either calm or patient and vice versa.
Everyone who is happy or tall is either not quiet or funny and vice versa.
Everyone who is not calm is rich and vice versa.
If someone is both not strong and not humble then someone is old and vice versa.
Everyone who is either funny or not patient is either not wise or not calm.
Everyone who is strong or rich is not patient or not quiet and vice versa.
Everyone who is both quiet and not happy is either generous or not patient.
Everyone who is patient or generous is either funny or not patient.
Everyone who is either quiet or strong is either not funny or humble and vice versa.
Everyone who is not quiet or not strong is both brave and not tall.
Paul is either kind or creative.
John is not tall.
Someone is strong or not kind.
Fred is not patient or not quiet.
Paul is humble.
Fred is not kind or tall. | John is not happy. | entailment | (![X]:((~creative(X)<~>~old(X))=>~generous(X)))&
((?[X]:(old(X)))<=>(?[X]:((~kind(X)&~creative(X)))))&
(![X]:((old(X)<~>generous(X))=>generous(X)))&
(![X]:((~calm(X)|~funny(X))=>(creative(X)<~>generous(X))))&
(![X]:((~creative(X)&old(X))<=>(patient(X)<~>brave(X))))&
(![X]:(quiet(X)=>rich(X)))&
(![X]:((creative(X)|patient(X))<=>(calm(X)<~>patient(X))))&
(![X]:((happy(X)|tall(X))<=>(~quiet(X)<~>funny(X))))&
(![X]:(~calm(X)<=>rich(X)))&
((?[X]:((~strong(X)&~humble(X))))<=>(?[X]:(old(X))))&
(![X]:((funny(X)<~>~patient(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((strong(X)|rich(X))<=>(~patient(X)|~quiet(X))))&
(![X]:((quiet(X)&~happy(X))=>(generous(X)<~>~patient(X))))&
(![X]:((patient(X)|generous(X))=>(funny(X)<~>~patient(X))))&
(![X]:((quiet(X)<~>strong(X))<=>(~funny(X)<~>humble(X))))&
(![X]:((~quiet(X)|~strong(X))=>(brave(X)&~tall(X))))&
((kind(paul)<~>creative(paul)))&
(~tall(john))&
(?[X]:((strong(X)|~kind(X))))&
((~patient(fred)|~quiet(fred)))&
(humble(paul))&
((~kind(fred)|tall(fred))) | ~happy(john) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5019170454164701688713384
% SZS output start Proof for 5019170454164701688713384
1. ! [X0] : ((~creative(X0) <~> ~old(X0)) => ~generous(X0)) [input p0]
2. ? [X0] : old(X0) <=> ? [X0] : (~creative(X0) & ~kind(X0)) [input p1]
3. ! [X0] : ((old(X0) <~> generous(X0)) => generous(X0)) [input p2]
4. ! [X0] : ((~funny(X0) | ~calm(X0)) => (creative(X0) <~> generous(X0))) [input p3]
5. ! [X0] : ((old(X0) & ~creative(X0)) <=> (patient(X0) <~> brave(X0))) [input p4]
6. ! [X0] : (quiet(X0) => rich(X0)) [input p5]
7. ! [X0] : ((patient(X0) | creative(X0)) <=> (calm(X0) <~> patient(X0))) [input p6]
8. ! [X0] : ((tall(X0) | happy(X0)) <=> (~quiet(X0) <~> funny(X0))) [input p7]
9. ! [X0] : (~calm(X0) <=> rich(X0)) [input p8]
12. ! [X0] : ((rich(X0) | strong(X0)) <=> (~quiet(X0) | ~patient(X0))) [input p11]
14. ! [X0] : ((generous(X0) | patient(X0)) => (funny(X0) <~> ~patient(X0))) [input p13]
16. ! [X0] : ((~strong(X0) | ~quiet(X0)) => (~tall(X0) & brave(X0))) [input p15]
23. happy(john) [input hypothesis]
24. ? [X0] : old(X0) <=> ? [X1] : (~creative(X1) & ~kind(X1)) [rectify 2]
26. ! [X0] : (~generous(X0) | (~creative(X0) <=> ~old(X0))) [ennf transformation 1]
27. ! [X0] : (generous(X0) | (old(X0) <=> generous(X0))) [ennf transformation 3]
28. ! [X0] : ((creative(X0) <~> generous(X0)) | (funny(X0) & calm(X0))) [ennf transformation 4]
29. ! [X0] : (rich(X0) | ~quiet(X0)) [ennf transformation 6]
33. ! [X0] : ((funny(X0) <~> ~patient(X0)) | (~generous(X0) & ~patient(X0))) [ennf transformation 14]
34. ! [X0] : ((~tall(X0) & brave(X0)) | (strong(X0) & quiet(X0))) [ennf transformation 16]
35. ! [X0] : (~generous(X0) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [nnf transformation 26]
36. (? [X0] : old(X0) | ! [X1] : (creative(X1) | kind(X1))) & (? [X1] : (~creative(X1) & ~kind(X1)) | ! [X0] : ~old(X0)) [nnf transformation 24]
37. (? [X0] : old(X0) | ! [X1] : (creative(X1) | kind(X1))) & (? [X2] : (~creative(X2) & ~kind(X2)) | ! [X3] : ~old(X3)) [rectify 36]
38. ? [X0] : old(X0) => old(sK0) [choice axiom]
39. ? [X2] : (~creative(X2) & ~kind(X2)) => (~creative(sK1) & ~kind(sK1)) [choice axiom]
40. (old(sK0) | ! [X1] : (creative(X1) | kind(X1))) & ((~creative(sK1) & ~kind(sK1)) | ! [X3] : ~old(X3)) [skolemisation 37,39,38]
41. ! [X0] : (generous(X0) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 27]
42. ! [X0] : (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | (funny(X0) & calm(X0))) [nnf transformation 28]
43. ! [X0] : (((old(X0) & ~creative(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~old(X0) | creative(X0)))) [nnf transformation 5]
44. ! [X0] : (((old(X0) & ~creative(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | ~old(X0) | creative(X0))) [flattening 43]
45. ! [X0] : (((patient(X0) | creative(X0)) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0)))) & (((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | (~patient(X0) & ~creative(X0)))) [nnf transformation 7]
46. ! [X0] : ((patient(X0) | creative(X0) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0)))) & (((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | (~patient(X0) & ~creative(X0)))) [flattening 45]
47. ! [X0] : (((tall(X0) | happy(X0)) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0)))) & (((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | (~tall(X0) & ~happy(X0)))) [nnf transformation 8]
48. ! [X0] : ((tall(X0) | happy(X0) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0)))) & (((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | (~tall(X0) & ~happy(X0)))) [flattening 47]
49. ! [X0] : ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0))) [nnf transformation 9]
56. ! [X0] : (((rich(X0) | strong(X0)) | (quiet(X0) & patient(X0))) & ((~quiet(X0) | ~patient(X0)) | (~rich(X0) & ~strong(X0)))) [nnf transformation 12]
57. ! [X0] : ((rich(X0) | strong(X0) | (quiet(X0) & patient(X0))) & (~quiet(X0) | ~patient(X0) | (~rich(X0) & ~strong(X0)))) [flattening 56]
59. ! [X0] : (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~generous(X0) & ~patient(X0))) [nnf transformation 33]
64. ~generous(X0) | ~old(X0) | creative(X0) [cnf transformation 35]
66. ~kind(sK1) | ~old(X3) [cnf transformation 40]
67. ~creative(sK1) | ~old(X3) [cnf transformation 40]
68. old(sK0) | creative(X1) | kind(X1) [cnf transformation 40]
69. generous(X0) | generous(X0) | ~old(X0) [cnf transformation 41]
71. calm(X0) | creative(X0) | generous(X0) [cnf transformation 42]
73. ~generous(X0) | ~creative(X0) | calm(X0) [cnf transformation 42]
74. ~generous(X0) | ~creative(X0) | funny(X0) [cnf transformation 42]
80. ~brave(X0) | patient(X0) | old(X0) [cnf transformation 44]
81. ~quiet(X0) | rich(X0) [cnf transformation 29]
82. ~creative(X0) | calm(X0) | patient(X0) [cnf transformation 46]
85. ~patient(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 46]
86. patient(X0) | creative(X0) | patient(X0) | ~calm(X0) [cnf transformation 46]
88. ~happy(X0) | ~quiet(X0) | funny(X0) [cnf transformation 48]
90. ~happy(X0) | quiet(X0) | ~funny(X0) [cnf transformation 48]
95. ~rich(X0) | ~calm(X0) [cnf transformation 49]
104. ~quiet(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 57]
109. ~patient(X0) | funny(X0) | ~patient(X0) [cnf transformation 59]
112. ~funny(X0) | patient(X0) | ~generous(X0) [cnf transformation 59]
121. quiet(X0) | brave(X0) [cnf transformation 34]
132. happy(john) [cnf transformation 23]
133. ~patient(X0) | funny(X0) [duplicate literal removal 109]
134. ~patient(X0) | ~calm(X0) [duplicate literal removal 85]
135. ~calm(X0) | creative(X0) | patient(X0) [duplicate literal removal 86]
136. ~old(X0) | generous(X0) [duplicate literal removal 69]
138. 1 <=> ! [X1] : (creative(X1) | kind(X1)) [avatar definition]
139. kind(X1) | creative(X1) <- (1) [avatar component clause 138]
141. 2 <=> old(sK0) [avatar definition]
143. old(sK0) <- (2) [avatar component clause 141]
144. 1 | 2 [avatar split clause 68,141,138]
146. 3 <=> ! [X3] : ~old(X3) [avatar definition]
147. ~old(X3) <- (3) [avatar component clause 146]
149. 4 <=> creative(sK1) [avatar definition]
151. ~creative(sK1) <- (~4) [avatar component clause 149]
152. 3 | ~4 [avatar split clause 67,149,146]
154. 5 <=> kind(sK1) [avatar definition]
156. ~kind(sK1) <- (~5) [avatar component clause 154]
157. 3 | ~5 [avatar split clause 66,154,146]
179. ~quiet(X0) | ~patient(X0) [subsumption resolution 104,81]
240. creative(sK1) <- (1, ~5) [resolution 139,156]
243. $false <- (1, ~4, ~5) [subsumption resolution 240,151]
244. ~1 | 4 | 5 [avatar contradiction clause 243]
268. generous(sK0) <- (2) [resolution 143,136]
272. ~creative(sK0) | funny(sK0) <- (2) [resolution 268,74]
273. ~creative(sK0) | calm(sK0) <- (2) [resolution 268,73]
275. ~old(sK0) | creative(sK0) <- (2) [resolution 268,64]
277. 22 <=> funny(sK0) [avatar definition]
279. funny(sK0) <- (22) [avatar component clause 277]
281. 23 <=> creative(sK0) [avatar definition]
284. 22 | ~23 | ~2 [avatar split clause 272,141,281,277]
286. 24 <=> calm(sK0) [avatar definition]
288. calm(sK0) <- (24) [avatar component clause 286]
289. 24 | ~23 | ~2 [avatar split clause 273,141,281,286]
290. creative(sK0) <- (2) [subsumption resolution 275,143]
291. 23 | ~2 [avatar split clause 290,141,281]
308. ~quiet(john) | funny(john) [resolution 88,132]
310. 27 <=> funny(john) [avatar definition]
311. ~funny(john) <- (~27) [avatar component clause 310]
312. funny(john) <- (27) [avatar component clause 310]
314. 28 <=> quiet(john) [avatar definition]
315. quiet(john) <- (28) [avatar component clause 314]
316. ~quiet(john) <- (~28) [avatar component clause 314]
317. 27 | ~28 [avatar split clause 308,314,310]
319. brave(john) <- (~28) [resolution 316,121]
320. quiet(john) | ~funny(john) [resolution 90,132]
325. 29 <=> generous(john) [avatar definition]
326. ~generous(john) <- (~29) [avatar component clause 325]
329. 30 <=> creative(john) [avatar definition]
331. creative(john) <- (30) [avatar component clause 329]
354. creative(X0) | patient(X0) | creative(X0) | generous(X0) [resolution 135,71]
357. patient(X0) | creative(X0) | generous(X0) [duplicate literal removal 354]
358. patient(john) | old(john) <- (~28) [resolution 319,80]
360. patient(john) <- (3, ~28) [subsumption resolution 358,147]
363. calm(john) | patient(john) <- (30) [resolution 331,82]
530. creative(X4) | generous(X4) | ~calm(X4) [resolution 357,134]
533. generous(X4) | creative(X4) [subsumption resolution 530,71]
657. funny(john) <- (3, ~28) [resolution 360,133]
663. $false <- (3, ~27, ~28) [subsumption resolution 657,311]
664. ~3 | 27 | 28 [avatar contradiction clause 663]
666. 56 <=> patient(john) [avatar definition]
668. patient(john) <- (56) [avatar component clause 666]
670. 57 <=> calm(john) [avatar definition]
672. calm(john) <- (57) [avatar component clause 670]
673. 56 | 57 | ~30 [avatar split clause 363,329,670,666]
674. ~27 | 28 [avatar split clause 320,314,310]
678. patient(john) | ~generous(john) <- (27) [resolution 312,112]
680. 58 <=> rich(john) [avatar definition]
682. rich(john) <- (58) [avatar component clause 680]
688. ~29 | 56 | ~27 [avatar split clause 678,310,666,325]
693. ~patient(john) <- (28) [resolution 315,179]
694. rich(john) <- (28) [resolution 315,81]
695. ~56 | ~28 [avatar split clause 693,314,666]
696. creative(john) <- (~29) [resolution 326,533]
697. ~calm(john) <- (58) [resolution 682,95]
698. $false <- (57, 58) [subsumption resolution 697,672]
699. ~57 | ~58 [avatar contradiction clause 698]
700. 58 | ~28 [avatar split clause 694,314,680]
701. 30 | 29 [avatar split clause 696,325,329]
746. generous(sK0) <- (2) [resolution 143,136]
799. patient(sK0) | ~generous(sK0) <- (22) [resolution 279,112]
809. patient(sK0) <- (2, 22) [subsumption resolution 799,746]
898. funny(john) <- (56) [resolution 668,133]
902. $false <- (~27, 56) [subsumption resolution 898,311]
903. 27 | ~56 [avatar contradiction clause 902]
940. ~calm(sK0) <- (2, 22) [resolution 809,134]
943. $false <- (2, 22, 24) [subsumption resolution 940,288]
944. ~2 | ~22 | ~24 [avatar contradiction clause 943]
946. $false [avatar sat refutation 144,152,157,244,284,289,291,317,664,673,674,688,695,699,700,701,903,944]
% SZS output end Proof for 5019170454164701688713384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then alice is both not patient and not curious and vice versa. If paul is not curious or not old then someone is either patient or not creative. Everyone who is either calm or not funny is humble and vice versa. Everyone who is both patient and not generous is not creative or old. Everyone who is either tall or strong is either not brave or not humble and vice versa. If lucy is brave or creative then someone is not happy and vice versa. Everyone who is both not old and strong is both not strong and not tall and vice versa. Everyone who is not old is both humble and not strong and vice versa. If someone is not calm then paul is not funny or not creative and vice versa. Everyone who is either not tall or not creative is not happy. If susan is both not creative and not old then someone is either tall or kind. Everyone who is strong is both kind and strong. If someone is not calm or not funny then someone is not calm or funny and vice versa. Everyone who is not generous is both not patient and not wise and vice versa. If someone is not old then susan is rich and vice versa. Susan is not wise. Someone is rich or not curious. Lucy is not old or not happy. Alice is quiet or not generous. Someone is either creative or humble. Someone is generous. Fred is both not tall and humble. Someone is either creative or not strong. | Paul is not creative. | neutral | ((?[X]:(~calm(X)))<=>((~patient(alice)&~curious(alice))))&
(((~curious(paul)|~old(paul)))=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((calm(X)<~>~funny(X))<=>humble(X)))&
(![X]:((patient(X)&~generous(X))=>(~creative(X)|old(X))))&
(![X]:((tall(X)<~>strong(X))<=>(~brave(X)<~>~humble(X))))&
(((brave(lucy)|creative(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((~old(X)&strong(X))<=>(~strong(X)&~tall(X))))&
(![X]:(~old(X)<=>(humble(X)&~strong(X))))&
((?[X]:(~calm(X)))<=>((~funny(paul)|~creative(paul))))&
(![X]:((~tall(X)<~>~creative(X))=>~happy(X)))&
(((~creative(susan)&~old(susan)))=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(strong(X)=>(kind(X)&strong(X))))&
((?[X]:((~calm(X)|~funny(X))))<=>(?[X]:((~calm(X)|funny(X)))))&
(![X]:(~generous(X)<=>(~patient(X)&~wise(X))))&
((?[X]:(~old(X)))<=>(rich(susan)))&
(~wise(susan))&
(?[X]:((rich(X)|~curious(X))))&
((~old(lucy)|~happy(lucy)))&
((quiet(alice)|~generous(alice)))&
(?[X]:((creative(X)<~>humble(X))))&
(?[X]:(generous(X)))&
((~tall(fred)&humble(fred)))&
(?[X]:((creative(X)<~>~strong(X)))) | ~creative(paul) | [] | null | 0 |
Everyone who is either not rich or not humble is either not funny or tall.
Everyone who is both not happy and not wise is either generous or not generous and vice versa.
Everyone who is not quiet or tall is not funny.
If someone is creative then mary is strong or patient.
If lucy is curious or quiet then paul is not patient or not calm and vice versa.
Everyone who is both rich and not kind is both rich and quiet and vice versa.
Everyone who is not strong or curious is not patient or not brave.
Everyone who is not wise or not calm is either curious or not creative.
If alice is both not quiet and not calm then john is humble or tall.
Everyone who is both generous and not wise is humble and vice versa.
If someone is brave then susan is both quiet and curious.
Everyone who is both not patient and funny is both not patient and curious and vice versa.
Everyone who is either not kind or not curious is not strong and vice versa.
If someone is humble then paul is both kind and not strong and vice versa.
Everyone who is rich is not kind or not quiet.
If someone is either not quiet or not creative then mary is either tall or wise.
Mary is not old.
Mary is not funny.
Someone is not kind or not brave.
Someone is not strong.
Lucy is kind.
Mary is not humble. | Mary is not tall. | neutral | (![X]:((~rich(X)<~>~humble(X))=>(~funny(X)<~>tall(X))))&
(![X]:((~happy(X)&~wise(X))<=>(generous(X)<~>~generous(X))))&
(![X]:((~quiet(X)|tall(X))=>~funny(X)))&
((?[X]:(creative(X)))=>((strong(mary)|patient(mary))))&
(((curious(lucy)|quiet(lucy)))<=>((~patient(paul)|~calm(paul))))&
(![X]:((rich(X)&~kind(X))<=>(rich(X)&quiet(X))))&
(![X]:((~strong(X)|curious(X))=>(~patient(X)|~brave(X))))&
(![X]:((~wise(X)|~calm(X))=>(curious(X)<~>~creative(X))))&
(((~quiet(alice)&~calm(alice)))=>((humble(john)|tall(john))))&
(![X]:((generous(X)&~wise(X))<=>humble(X)))&
((?[X]:(brave(X)))=>((quiet(susan)&curious(susan))))&
(![X]:((~patient(X)&funny(X))<=>(~patient(X)&curious(X))))&
(![X]:((~kind(X)<~>~curious(X))<=>~strong(X)))&
((?[X]:(humble(X)))<=>((kind(paul)&~strong(paul))))&
(![X]:(rich(X)=>(~kind(X)|~quiet(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))=>((tall(mary)<~>wise(mary))))&
(~old(mary))&
(~funny(mary))&
(?[X]:((~kind(X)|~brave(X))))&
(?[X]:(~strong(X)))&
(kind(lucy))&
(~humble(mary)) | ~tall(mary) | [] | null | 0 |
If lucy is kind or not generous then someone is both wise and not brave and vice versa. Everyone who is not curious is funny and vice versa. Everyone who is both generous and kind is both not wise and not old and vice versa. If mary is either tall or quiet then someone is both not old and not quiet. Everyone who is either curious or not curious is not old or kind and vice versa. Everyone who is not brave or curious is not curious and vice versa. If someone is curious or humble then john is creative. If someone is either not kind or not happy then alice is both funny and not humble and vice versa. Everyone who is both generous and not generous is generous. Everyone who is both brave and not patient is either wise or not quiet. Everyone who is either tall or patient is both not quiet and not creative. Everyone who is either not funny or not kind is curious or not patient and vice versa. If someone is either creative or brave then someone is wise or kind. Everyone who is both creative and strong is patient or old and vice versa. If someone is quiet or not strong then fred is both quiet and not strong and vice versa. Everyone who is funny or creative is not tall or not rich and vice versa. Someone is both calm and not brave. Paul is not tall or creative. Alice is both not calm and kind. Someone is either tall or not strong. Someone is either not creative or kind. Paul is not strong. | Fred is not kind. | entailment | (((kind(lucy)|~generous(lucy)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((generous(X)&kind(X))<=>(~wise(X)&~old(X))))&
(((tall(mary)<~>quiet(mary)))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))&
(![X]:((~brave(X)|curious(X))<=>~curious(X)))&
((?[X]:((curious(X)|humble(X))))=>(creative(john)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((generous(X)&~generous(X))=>generous(X)))&
(![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)|old(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((quiet(fred)&~strong(fred))))&
(![X]:((funny(X)|creative(X))<=>(~tall(X)|~rich(X))))&
(?[X]:((calm(X)&~brave(X))))&
((~tall(paul)|creative(paul)))&
((~calm(alice)&kind(alice)))&
(?[X]:((tall(X)<~>~strong(X))))&
(?[X]:((~creative(X)<~>kind(X))))&
(~strong(paul)) | ~kind(fred) | [
"p1",
"p5",
"p11",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6214245381078147010354820
% SZS output start Proof for 6214245381078147010354820
2. ! [X0] : (~curious(X0) <=> funny(X0)) [input p1]
6. ! [X0] : ((curious(X0) | ~brave(X0)) <=> ~curious(X0)) [input p5]
12. ! [X0] : ((~funny(X0) <~> ~kind(X0)) <=> (~patient(X0) | curious(X0))) [input p11]
14. ! [X0] : ((strong(X0) & creative(X0)) <=> (old(X0) | patient(X0))) [input p13]
15. ? [X0] : (~strong(X0) | quiet(X0)) <=> (~strong(fred) & quiet(fred)) [input p14]
22. ~strong(paul) [input p21]
23. kind(fred) [input hypothesis]
38. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 2]
46. ! [X0] : (((curious(X0) | ~brave(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [nnf transformation 6]
47. ! [X0] : ((curious(X0) | ~brave(X0) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [flattening 46]
55. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [nnf transformation 12]
56. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [flattening 55]
61. ! [X0] : (((strong(X0) & creative(X0)) | (~old(X0) & ~patient(X0))) & ((old(X0) | patient(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 14]
62. ! [X0] : (((strong(X0) & creative(X0)) | (~old(X0) & ~patient(X0))) & (old(X0) | patient(X0) | ~strong(X0) | ~creative(X0))) [flattening 61]
63. (? [X0] : (~strong(X0) | quiet(X0)) | (strong(fred) | ~quiet(fred))) & ((~strong(fred) & quiet(fred)) | ! [X0] : (strong(X0) & ~quiet(X0))) [nnf transformation 15]
64. (? [X0] : (~strong(X0) | quiet(X0)) | strong(fred) | ~quiet(fred)) & ((~strong(fred) & quiet(fred)) | ! [X0] : (strong(X0) & ~quiet(X0))) [flattening 63]
65. (? [X0] : (~strong(X0) | quiet(X0)) | strong(fred) | ~quiet(fred)) & ((~strong(fred) & quiet(fred)) | ! [X1] : (strong(X1) & ~quiet(X1))) [rectify 64]
66. ? [X0] : (~strong(X0) | quiet(X0)) => (~strong(sK4) | quiet(sK4)) [choice axiom]
67. ((~strong(sK4) | quiet(sK4)) | strong(fred) | ~quiet(fred)) & ((~strong(fred) & quiet(fred)) | ! [X1] : (strong(X1) & ~quiet(X1))) [skolemisation 65,66]
83. funny(X0) | curious(X0) [cnf transformation 38]
100. ~curious(X0) | ~curious(X0) [cnf transformation 47]
120. ~funny(X0) | ~kind(X0) | patient(X0) [cnf transformation 56]
128. ~patient(X0) | strong(X0) [cnf transformation 62]
133. ~strong(fred) | strong(X1) [cnf transformation 67]
148. ~strong(paul) [cnf transformation 22]
149. kind(fred) [cnf transformation 23]
151. ~curious(X0) [duplicate literal removal 100]
258. 23 <=> strong(fred) [avatar definition]
271. 26 <=> ! [X1] : strong(X1) [avatar definition]
272. strong(X1) <- (26) [avatar component clause 271]
273. 26 | ~23 [avatar split clause 133,258,271]
359. 41 <=> patient(fred) [avatar definition]
361. patient(fred) <- (41) [avatar component clause 359]
365. ~kind(X0) | patient(X0) | curious(X0) [resolution 120,83]
367. ~kind(X0) | patient(X0) [subsumption resolution 365,151]
407. patient(fred) [resolution 367,149]
409. 41 [avatar split clause 407,359]
415. strong(fred) <- (41) [resolution 361,128]
425. 23 | ~41 [avatar split clause 415,359,258]
430. $false <- (26) [resolution 272,148]
435. ~26 [avatar contradiction clause 430]
436. $false [avatar sat refutation 273,409,425,435]
% SZS output end Proof for 6214245381078147010354820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or not creative then someone is quiet or not rich. Everyone who is both not strong and creative is both not funny and not happy. If someone is not quiet or creative then john is patient and vice versa. Everyone who is not rich is wise. Everyone who is either not funny or not strong is not wise. Everyone who is not quiet is either not wise or patient. Everyone who is not rich is funny and vice versa. Everyone who is either brave or generous is not brave or not kind and vice versa. If someone is either patient or not patient then mary is kind and vice versa. If mary is not curious or not calm then paul is funny and vice versa. Everyone who is both strong and rich is either wise or brave and vice versa. Everyone who is not calm or not patient is not creative and vice versa. If someone is either patient or creative then susan is either not old or not quiet. If mary is quiet then lucy is not kind. If someone is not curious or not strong then lucy is either quiet or not curious. If john is not strong or not quiet then someone is patient and vice versa. Someone is either not brave or happy. Susan is brave or not patient. Lucy is not funny or kind. Mary is funny. Someone is either creative or funny. Someone is happy. John is brave. Someone is not old. | Susan is not funny. | neutral | ((?[X]:((~rich(X)|~creative(X))))=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:((~strong(X)&creative(X))=>(~funny(X)&~happy(X))))&
((?[X]:((~quiet(X)|creative(X))))<=>(patient(john)))&
(![X]:(~rich(X)=>wise(X)))&
(![X]:((~funny(X)<~>~strong(X))=>~wise(X)))&
(![X]:(~quiet(X)=>(~wise(X)<~>patient(X))))&
(![X]:(~rich(X)<=>funny(X)))&
(![X]:((brave(X)<~>generous(X))<=>(~brave(X)|~kind(X))))&
((?[X]:((patient(X)<~>~patient(X))))<=>(kind(mary)))&
(((~curious(mary)|~calm(mary)))<=>(funny(paul)))&
(![X]:((strong(X)&rich(X))<=>(wise(X)<~>brave(X))))&
(![X]:((~calm(X)|~patient(X))<=>~creative(X)))&
((?[X]:((patient(X)<~>creative(X))))=>((~old(susan)<~>~quiet(susan))))&
((quiet(mary))=>(~kind(lucy)))&
((?[X]:((~curious(X)|~strong(X))))=>((quiet(lucy)<~>~curious(lucy))))&
(((~strong(john)|~quiet(john)))<=>(?[X]:(patient(X))))&
(?[X]:((~brave(X)<~>happy(X))))&
((brave(susan)|~patient(susan)))&
((~funny(lucy)|kind(lucy)))&
(funny(mary))&
(?[X]:((creative(X)<~>funny(X))))&
(?[X]:(happy(X)))&
(brave(john))&
(?[X]:(~old(X))) | ~funny(susan) | [] | null | 0 |
Everyone who is both humble and strong is not brave or not rich. Everyone who is either not curious or not rich is either not generous or not quiet and vice versa. If alice is both calm and not generous then fred is not tall and vice versa. Everyone who is not brave or not calm is either funny or not rich and vice versa. If fred is quiet then someone is not humble or rich. If mary is either not humble or generous then someone is funny or not kind and vice versa. If alice is either creative or calm then someone is not old or not brave and vice versa. If fred is both not rich and not strong then someone is both calm and funny. Everyone who is both humble and not tall is both not calm and not rich and vice versa. If paul is not generous then mary is either strong or not generous and vice versa. Everyone who is either not patient or not strong is not tall. Everyone who is wise or humble is patient or creative. Everyone who is quiet or not quiet is both not calm and not wise and vice versa. Everyone who is not tall is both not strong and creative and vice versa. If someone is happy or not brave then someone is strong or not wise and vice versa. If someone is wise or not happy then someone is both brave and not happy. Mary is either kind or not strong. Mary is not funny or old. Fred is both not generous and creative. Someone is either not wise or not kind. Someone is not rich or humble. Alice is not quiet. Fred is not generous or not humble. Alice is both patient and generous. | Paul is not rich. | neutral | (![X]:((humble(X)&strong(X))=>(~brave(X)|~rich(X))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~generous(X)<~>~quiet(X))))&
(((calm(alice)&~generous(alice)))<=>(~tall(fred)))&
(![X]:((~brave(X)|~calm(X))<=>(funny(X)<~>~rich(X))))&
((quiet(fred))=>(?[X]:((~humble(X)|rich(X)))))&
(((~humble(mary)<~>generous(mary)))<=>(?[X]:((funny(X)|~kind(X)))))&
(((creative(alice)<~>calm(alice)))<=>(?[X]:((~old(X)|~brave(X)))))&
(((~rich(fred)&~strong(fred)))=>(?[X]:((calm(X)&funny(X)))))&
(![X]:((humble(X)&~tall(X))<=>(~calm(X)&~rich(X))))&
((~generous(paul))<=>((strong(mary)<~>~generous(mary))))&
(![X]:((~patient(X)<~>~strong(X))=>~tall(X)))&
(![X]:((wise(X)|humble(X))=>(patient(X)|creative(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~calm(X)&~wise(X))))&
(![X]:(~tall(X)<=>(~strong(X)&creative(X))))&
((?[X]:((happy(X)|~brave(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
((?[X]:((wise(X)|~happy(X))))=>(?[X]:((brave(X)&~happy(X)))))&
((kind(mary)<~>~strong(mary)))&
((~funny(mary)|old(mary)))&
((~generous(fred)&creative(fred)))&
(?[X]:((~wise(X)<~>~kind(X))))&
(?[X]:((~rich(X)|humble(X))))&
(~quiet(alice))&
((~generous(fred)|~humble(fred)))&
((patient(alice)&generous(alice))) | ~rich(paul) | [] | null | 0 |
Everyone who is either not kind or not calm is creative or not kind and vice versa.
Everyone who is both funny and not calm is generous.
If someone is not strong then john is both not wise and not brave and vice versa.
Everyone who is quiet is both not strong and not brave.
Everyone who is kind or wise is both not brave and not calm.
If someone is not brave then someone is tall and vice versa.
Everyone who is both tall and patient is either not creative or not calm and vice versa.
If susan is both not happy and not calm then susan is both curious and not quiet.
Everyone who is both not patient and not kind is not creative and vice versa.
Everyone who is calm or not calm is either not creative or brave and vice versa.
Everyone who is both tall and not calm is not brave.
Everyone who is not quiet is both creative and strong.
If someone is both not funny and strong then mary is not quiet and vice versa.
Everyone who is both creative and not kind is either not rich or patient.
If someone is quiet or rich then susan is either calm or quiet and vice versa.
John is not quiet.
Someone is either humble or funny.
Susan is not old.
Lucy is not kind or kind.
Mary is both not kind and curious.
Fred is not rich or funny.
Someone is not quiet or calm. | Susan is not tall. | entailment | (![X]:((~kind(X)<~>~calm(X))<=>(creative(X)|~kind(X))))&
(![X]:((funny(X)&~calm(X))=>generous(X)))&
((?[X]:(~strong(X)))<=>((~wise(john)&~brave(john))))&
(![X]:(quiet(X)=>(~strong(X)&~brave(X))))&
(![X]:((kind(X)|wise(X))=>(~brave(X)&~calm(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(tall(X))))&
(![X]:((tall(X)&patient(X))<=>(~creative(X)<~>~calm(X))))&
(((~happy(susan)&~calm(susan)))=>((curious(susan)&~quiet(susan))))&
(![X]:((~patient(X)&~kind(X))<=>~creative(X)))&
(![X]:((calm(X)|~calm(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((tall(X)&~calm(X))=>~brave(X)))&
(![X]:(~quiet(X)=>(creative(X)&strong(X))))&
((?[X]:((~funny(X)&strong(X))))<=>(~quiet(mary)))&
(![X]:((creative(X)&~kind(X))=>(~rich(X)<~>patient(X))))&
((?[X]:((quiet(X)|rich(X))))<=>((calm(susan)<~>quiet(susan))))&
(~quiet(john))&
(?[X]:((humble(X)<~>funny(X))))&
(~old(susan))&
((~kind(lucy)|kind(lucy)))&
((~kind(mary)&curious(mary)))&
((~rich(fred)|funny(fred)))&
(?[X]:((~quiet(X)|calm(X)))) | ~tall(susan) | [
"p0",
"p5",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8780880698565340827743271
% SZS output start Proof for 8780880698565340827743271
1. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> (~kind(X0) | creative(X0))) [input p0]
6. ? [X0] : ~brave(X0) <=> ? [X0] : tall(X0) [input p5]
7. ! [X0] : ((patient(X0) & tall(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p6]
9. ! [X0] : ((~kind(X0) & ~patient(X0)) <=> ~creative(X0)) [input p8]
10. ! [X0] : ((~calm(X0) | calm(X0)) <=> (~creative(X0) <~> brave(X0))) [input p9]
23. tall(susan) [input hypothesis]
24. ? [X0] : ~brave(X0) <=> ? [X1] : tall(X1) [rectify 6]
37. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (kind(X0) & ~creative(X0))) & ((~kind(X0) | creative(X0)) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 1]
38. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (kind(X0) & ~creative(X0))) & (~kind(X0) | creative(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [flattening 37]
44. (? [X0] : ~brave(X0) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : brave(X0)) [nnf transformation 24]
45. (? [X0] : ~brave(X0) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : brave(X3)) [rectify 44]
46. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
47. ? [X2] : tall(X2) => tall(sK2) [choice axiom]
48. (~brave(sK1) | ! [X1] : ~tall(X1)) & (tall(sK2) | ! [X3] : brave(X3)) [skolemisation 45,47,46]
49. ! [X0] : (((patient(X0) & tall(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (~patient(X0) | ~tall(X0)))) [nnf transformation 7]
50. ! [X0] : (((patient(X0) & tall(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ~patient(X0) | ~tall(X0))) [flattening 49]
51. ! [X0] : (((~kind(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | (kind(X0) | patient(X0)))) [nnf transformation 9]
52. ! [X0] : (((~kind(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | kind(X0) | patient(X0))) [flattening 51]
53. ! [X0] : (((~calm(X0) | calm(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (calm(X0) & ~calm(X0)))) [nnf transformation 10]
54. ! [X0] : ((~calm(X0) | calm(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (calm(X0) & ~calm(X0)))) [flattening 53]
70. ~kind(X0) | creative(X0) | ~kind(X0) | calm(X0) [cnf transformation 38]
74. calm(X0) | kind(X0) | kind(X0) [cnf transformation 38]
85. ~brave(sK1) | ~tall(X1) [cnf transformation 48]
90. patient(X0) | ~calm(X0) | creative(X0) [cnf transformation 50]
93. ~patient(X0) | creative(X0) [cnf transformation 52]
95. brave(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 54]
96. brave(X0) | ~creative(X0) | calm(X0) [cnf transformation 54]
122. tall(susan) [cnf transformation 23]
123. ~kind(X0) | creative(X0) | calm(X0) [duplicate literal removal 70]
124. calm(X0) | kind(X0) [duplicate literal removal 74]
125. creative(X0) | calm(X0) [subsumption resolution 123,124]
145. 5 <=> ! [X1] : ~tall(X1) [avatar definition]
146. ~tall(X1) <- (5) [avatar component clause 145]
148. 6 <=> brave(sK1) [avatar definition]
150. ~brave(sK1) <- (~6) [avatar component clause 148]
151. 5 | ~6 [avatar split clause 85,148,145]
153. 7 <=> ! [X3] : brave(X3) [avatar definition]
154. brave(X3) <- (7) [avatar component clause 153]
161. patient(X0) | creative(X0) [subsumption resolution 90,125]
164. creative(X0) [subsumption resolution 93,161]
166. brave(X0) | calm(X0) [subsumption resolution 96,164]
167. brave(X0) | ~calm(X0) [subsumption resolution 95,164]
168. brave(X0) [subsumption resolution 167,166]
169. 7 [avatar split clause 168,153]
235. $false <- (~6, 7) [subsumption resolution 150,154]
236. 6 | ~7 [avatar contradiction clause 235]
241. $false <- (5) [resolution 146,122]
242. ~5 [avatar contradiction clause 241]
243. $false [avatar sat refutation 151,169,236,242]
% SZS output end Proof for 8780880698565340827743271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not tall is either quiet or not generous and vice versa. Everyone who is either wise or not tall is not creative and vice versa. Everyone who is not generous or curious is not brave or not strong and vice versa. If john is both not funny and not wise then someone is humble and vice versa. Everyone who is both not funny and kind is calm. Everyone who is not rich or not tall is not brave or creative and vice versa. Everyone who is either not brave or humble is strong or not quiet and vice versa. If someone is not wise then someone is either not kind or rich and vice versa. Everyone who is not strong is creative. Everyone who is happy is rich. If someone is not rich or happy then lucy is both not funny and not wise and vice versa. Everyone who is happy is either strong or not old and vice versa. If paul is brave or creative then paul is not brave or kind and vice versa. If someone is either old or generous then susan is either calm or patient and vice versa. Everyone who is not rich or not old is old or kind. Everyone who is not generous is happy or generous and vice versa. Someone is not creative or not generous. Someone is either not strong or not quiet. Someone is not old or old. Someone is tall or funny. Susan is kind. John is either quiet or not patient. Fred is not humble. Someone is creative or tall. | Susan is generous. | contradiction | (![X]:((~kind(X)<~>~tall(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((wise(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((~generous(X)|curious(X))<=>(~brave(X)|~strong(X))))&
(((~funny(john)&~wise(john)))<=>(?[X]:(humble(X))))&
(![X]:((~funny(X)&kind(X))=>calm(X)))&
(![X]:((~rich(X)|~tall(X))<=>(~brave(X)|creative(X))))&
(![X]:((~brave(X)<~>humble(X))<=>(strong(X)|~quiet(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~kind(X)<~>rich(X)))))&
(![X]:(~strong(X)=>creative(X)))&
(![X]:(happy(X)=>rich(X)))&
((?[X]:((~rich(X)|happy(X))))<=>((~funny(lucy)&~wise(lucy))))&
(![X]:(happy(X)<=>(strong(X)<~>~old(X))))&
(((brave(paul)|creative(paul)))<=>((~brave(paul)|kind(paul))))&
((?[X]:((old(X)<~>generous(X))))<=>((calm(susan)<~>patient(susan))))&
(![X]:((~rich(X)|~old(X))=>(old(X)|kind(X))))&
(![X]:(~generous(X)<=>(happy(X)|generous(X))))&
(?[X]:((~creative(X)|~generous(X))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
(?[X]:((~old(X)|old(X))))&
(?[X]:((tall(X)|funny(X))))&
(kind(susan))&
((quiet(john)<~>~patient(john)))&
(~humble(fred))&
(?[X]:((creative(X)|tall(X)))) | generous(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1916205767284172435480089
% SZS output start Proof for 1916205767284172435480089
16. ! [X0] : (~generous(X0) <=> (generous(X0) | happy(X0))) [input p15]
25. generous(susan) [input hypothesis]
63. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | generous(X0))) [nnf transformation 16]
64. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | generous(X0))) [flattening 63]
138. ~generous(X0) | ~generous(X0) [cnf transformation 64]
149. generous(susan) [cnf transformation 25]
151. ~generous(X0) [duplicate literal removal 138]
310. $false [subsumption resolution 149,151]
% SZS output end Proof for 1916205767284172435480089
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or rich is not brave. If mary is both quiet and patient then someone is not kind or not generous and vice versa. If mary is either not calm or brave then someone is either kind or not kind. If fred is either not old or not calm then someone is not generous and vice versa. Everyone who is not humble is either not happy or not kind and vice versa. If someone is tall then someone is either not wise or generous. If fred is not creative then john is both not rich and creative. Everyone who is not happy or not brave is rich or not humble. If lucy is not generous then mary is not wise or patient and vice versa. If someone is not patient or not happy then john is either strong or wise and vice versa. Everyone who is quiet or not rich is either not curious or creative and vice versa. Everyone who is calm is both happy and not quiet. Everyone who is both generous and old is both not tall and creative. If fred is not tall or not brave then alice is both quiet and not kind. Everyone who is calm or not kind is humble and vice versa. Everyone who is both curious and strong is both not creative and not wise and vice versa. Paul is either kind or generous. Someone is both not calm and not rich. Someone is old or quiet. Someone is either calm or not funny. John is either not kind or strong. Someone is either not old or not calm. Paul is tall. Someone is both rich and curious. | Alice is happy. | contradiction | (![X]:((~rich(X)|rich(X))=>~brave(X)))&
(((quiet(mary)&patient(mary)))<=>(?[X]:((~kind(X)|~generous(X)))))&
(((~calm(mary)<~>brave(mary)))=>(?[X]:((kind(X)<~>~kind(X)))))&
(((~old(fred)<~>~calm(fred)))<=>(?[X]:(~generous(X))))&
(![X]:(~humble(X)<=>(~happy(X)<~>~kind(X))))&
((?[X]:(tall(X)))=>(?[X]:((~wise(X)<~>generous(X)))))&
((~creative(fred))=>((~rich(john)&creative(john))))&
(![X]:((~happy(X)|~brave(X))=>(rich(X)|~humble(X))))&
((~generous(lucy))<=>((~wise(mary)|patient(mary))))&
((?[X]:((~patient(X)|~happy(X))))<=>((strong(john)<~>wise(john))))&
(![X]:((quiet(X)|~rich(X))<=>(~curious(X)<~>creative(X))))&
(![X]:(calm(X)=>(happy(X)&~quiet(X))))&
(![X]:((generous(X)&old(X))=>(~tall(X)&creative(X))))&
(((~tall(fred)|~brave(fred)))=>((quiet(alice)&~kind(alice))))&
(![X]:((calm(X)|~kind(X))<=>humble(X)))&
(![X]:((curious(X)&strong(X))<=>(~creative(X)&~wise(X))))&
((kind(paul)<~>generous(paul)))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((old(X)|quiet(X))))&
(?[X]:((calm(X)<~>~funny(X))))&
((~kind(john)<~>strong(john)))&
(?[X]:((~old(X)<~>~calm(X))))&
(tall(paul))&
(?[X]:((rich(X)&curious(X)))) | happy(alice) | [
"p0",
"p4",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1316134730094908905432259
% SZS output start Proof for 1316134730094908905432259
1. ! [X0] : ((rich(X0) | ~rich(X0)) => ~brave(X0)) [input p0]
5. ! [X0] : (~humble(X0) <=> (~happy(X0) <~> ~kind(X0))) [input p4]
14. (~brave(fred) | ~tall(fred)) => (~kind(alice) & quiet(alice)) [input p13]
15. ! [X0] : ((~kind(X0) | calm(X0)) <=> humble(X0)) [input p14]
25. happy(alice) [input hypothesis]
27. ! [X0] : (~brave(X0) | (~rich(X0) & rich(X0))) [ennf transformation 1]
36. (~kind(alice) & quiet(alice)) | (brave(fred) & tall(fred)) [ennf transformation 14]
49. ! [X0] : ((~humble(X0) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | humble(X0))) [nnf transformation 5]
62. ! [X0] : (((~kind(X0) | calm(X0)) | ~humble(X0)) & (humble(X0) | (kind(X0) & ~calm(X0)))) [nnf transformation 15]
63. ! [X0] : ((~kind(X0) | calm(X0) | ~humble(X0)) & (humble(X0) | (kind(X0) & ~calm(X0)))) [flattening 62]
80. ~brave(X0) | rich(X0) [cnf transformation 27]
81. ~brave(X0) | ~rich(X0) [cnf transformation 27]
98. ~happy(X0) | ~humble(X0) | kind(X0) [cnf transformation 49]
127. ~kind(alice) | brave(fred) [cnf transformation 36]
129. humble(X0) | kind(X0) [cnf transformation 63]
149. happy(alice) [cnf transformation 25]
150. ~brave(X0) [subsumption resolution 80,81]
261. ~kind(alice) [subsumption resolution 127,150]
316. ~humble(alice) | kind(alice) [resolution 98,149]
319. ~humble(alice) [subsumption resolution 316,261]
330. kind(alice) [resolution 319,129]
331. $false [subsumption resolution 330,261]
% SZS output end Proof for 1316134730094908905432259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and creative is not brave or not funny and vice versa. If someone is either patient or curious then someone is wise or calm and vice versa. If someone is either old or not humble then lucy is not curious or humble. Everyone who is either not patient or creative is not wise and vice versa. Everyone who is both happy and funny is funny and vice versa. Everyone who is either rich or calm is both not tall and not humble and vice versa. If someone is either rich or quiet then fred is both not strong and not generous and vice versa. Everyone who is both not tall and not happy is both brave and not generous and vice versa. Everyone who is both not tall and not strong is either funny or tall. If someone is either not creative or not happy then lucy is both not creative and curious. Everyone who is both patient and quiet is brave. If fred is not curious then alice is either humble or patient and vice versa. If lucy is not creative or funny then susan is both not brave and tall. Everyone who is either curious or rich is kind or not tall and vice versa. Everyone who is both kind and not creative is both not rich and patient. Everyone who is wise is not brave or not generous and vice versa. Susan is either not quiet or not generous. Lucy is either not old or funny. Fred is either funny or not curious. Someone is either not wise or not quiet. Susan is humble or funny. Fred is either curious or not old. John is not rich. | Susan is patient. | contradiction | (![X]:((old(X)&creative(X))<=>(~brave(X)|~funny(X))))&
((?[X]:((patient(X)<~>curious(X))))<=>(?[X]:((wise(X)|calm(X)))))&
((?[X]:((old(X)<~>~humble(X))))=>((~curious(lucy)|humble(lucy))))&
(![X]:((~patient(X)<~>creative(X))<=>~wise(X)))&
(![X]:((happy(X)&funny(X))<=>funny(X)))&
(![X]:((rich(X)<~>calm(X))<=>(~tall(X)&~humble(X))))&
((?[X]:((rich(X)<~>quiet(X))))<=>((~strong(fred)&~generous(fred))))&
(![X]:((~tall(X)&~happy(X))<=>(brave(X)&~generous(X))))&
(![X]:((~tall(X)&~strong(X))=>(funny(X)<~>tall(X))))&
((?[X]:((~creative(X)<~>~happy(X))))=>((~creative(lucy)&curious(lucy))))&
(![X]:((patient(X)&quiet(X))=>brave(X)))&
((~curious(fred))<=>((humble(alice)<~>patient(alice))))&
(((~creative(lucy)|funny(lucy)))=>((~brave(susan)&tall(susan))))&
(![X]:((curious(X)<~>rich(X))<=>(kind(X)|~tall(X))))&
(![X]:((kind(X)&~creative(X))=>(~rich(X)&patient(X))))&
(![X]:(wise(X)<=>(~brave(X)|~generous(X))))&
((~quiet(susan)<~>~generous(susan)))&
((~old(lucy)<~>funny(lucy)))&
((funny(fred)<~>~curious(fred)))&
(?[X]:((~wise(X)<~>~quiet(X))))&
((humble(susan)|funny(susan)))&
((curious(fred)<~>~old(fred)))&
(~rich(john)) | patient(susan) | [
"p0",
"p3",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 329679074276780924637357
% SZS output start Proof for 329679074276780924637357
1. ! [X0] : ((creative(X0) & old(X0)) <=> (~funny(X0) | ~brave(X0))) [input p0]
4. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> ~wise(X0)) [input p3]
13. (funny(lucy) | ~creative(lucy)) => (tall(susan) & ~brave(susan)) [input p12]
16. ! [X0] : (wise(X0) <=> (~generous(X0) | ~brave(X0))) [input p15]
18. ~old(lucy) <~> funny(lucy) [input p17]
24. patient(susan) [input hypothesis]
33. (tall(susan) & ~brave(susan)) | (~funny(lucy) & creative(lucy)) [ennf transformation 13]
36. ! [X0] : (((creative(X0) & old(X0)) | (funny(X0) & brave(X0))) & ((~funny(X0) | ~brave(X0)) | (~creative(X0) | ~old(X0)))) [nnf transformation 1]
37. ! [X0] : (((creative(X0) & old(X0)) | (funny(X0) & brave(X0))) & (~funny(X0) | ~brave(X0) | ~creative(X0) | ~old(X0))) [flattening 36]
44. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | wise(X0)) & (~wise(X0) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 4]
61. ! [X0] : ((wise(X0) | (generous(X0) & brave(X0))) & ((~generous(X0) | ~brave(X0)) | ~wise(X0))) [nnf transformation 16]
62. ! [X0] : ((wise(X0) | (generous(X0) & brave(X0))) & (~generous(X0) | ~brave(X0) | ~wise(X0))) [flattening 61]
64. (~funny(lucy) | old(lucy)) & (funny(lucy) | ~old(lucy)) [nnf transformation 18]
72. funny(X0) | old(X0) [cnf transformation 37]
73. brave(X0) | creative(X0) [cnf transformation 37]
84. ~wise(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 44]
118. ~brave(susan) | ~funny(lucy) [cnf transformation 33]
130. wise(X0) | brave(X0) [cnf transformation 62]
134. funny(lucy) | ~old(lucy) [cnf transformation 64]
135. ~funny(lucy) | old(lucy) [cnf transformation 64]
144. patient(susan) [cnf transformation 24]
255. 25 <=> funny(lucy) [avatar definition]
265. 27 <=> brave(susan) [avatar definition]
267. ~brave(susan) <- (~27) [avatar component clause 265]
268. ~25 | ~27 [avatar split clause 118,265,255]
280. old(lucy) [subsumption resolution 135,72]
281. funny(lucy) [subsumption resolution 134,280]
282. 25 [avatar split clause 281,255]
364. ~patient(X0) | ~creative(X0) | brave(X0) [resolution 84,130]
366. ~patient(X0) | brave(X0) [subsumption resolution 364,73]
422. brave(susan) [resolution 366,144]
423. $false <- (~27) [subsumption resolution 422,267]
424. 27 [avatar contradiction clause 423]
425. $false [avatar sat refutation 268,282,424]
% SZS output end Proof for 329679074276780924637357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not humble then paul is patient and vice versa. Everyone who is either happy or not old is both not happy and not quiet. Everyone who is old is either not kind or not quiet and vice versa. Everyone who is wise is both not strong and not calm. Everyone who is happy is not strong or patient and vice versa. If lucy is both quiet and kind then lucy is not calm or kind. Everyone who is either not quiet or not wise is either not funny or quiet and vice versa. If susan is both brave and not calm then paul is both tall and not creative and vice versa. Everyone who is both not funny and generous is not patient and vice versa. If someone is not calm or brave then someone is both not humble and rich and vice versa. Everyone who is rich is both not old and old and vice versa. Everyone who is both not humble and old is either not old or happy. If lucy is not generous then lucy is both not calm and tall and vice versa. Everyone who is happy or not kind is either creative or not kind and vice versa. If lucy is either not kind or quiet then alice is not rich. Susan is either curious or not generous. Someone is old or generous. Someone is patient or not calm. Someone is both humble and tall. Someone is happy. Lucy is not funny or quiet. | Susan is not strong. | neutral | ((~humble(susan))<=>(patient(paul)))&
(![X]:((happy(X)<~>~old(X))=>(~happy(X)&~quiet(X))))&
(![X]:(old(X)<=>(~kind(X)<~>~quiet(X))))&
(![X]:(wise(X)=>(~strong(X)&~calm(X))))&
(![X]:(happy(X)<=>(~strong(X)|patient(X))))&
(((quiet(lucy)&kind(lucy)))=>((~calm(lucy)|kind(lucy))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~funny(X)<~>quiet(X))))&
(((brave(susan)&~calm(susan)))<=>((tall(paul)&~creative(paul))))&
(![X]:((~funny(X)&generous(X))<=>~patient(X)))&
((?[X]:((~calm(X)|brave(X))))<=>(?[X]:((~humble(X)&rich(X)))))&
(![X]:(rich(X)<=>(~old(X)&old(X))))&
(![X]:((~humble(X)&old(X))=>(~old(X)<~>happy(X))))&
((~generous(lucy))<=>((~calm(lucy)&tall(lucy))))&
(![X]:((happy(X)|~kind(X))<=>(creative(X)<~>~kind(X))))&
(((~kind(lucy)<~>quiet(lucy)))=>(~rich(alice)))&
((curious(susan)<~>~generous(susan)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((patient(X)|~calm(X))))&
(?[X]:((humble(X)&tall(X))))&
(?[X]:(happy(X)))&
((~funny(lucy)|quiet(lucy))) | ~strong(susan) | [] | null | 0 |
Everyone who is strong is both humble and generous. If someone is both patient and quiet then someone is not funny. If someone is both not kind and creative then paul is either rich or not creative and vice versa. If someone is either not old or not kind then someone is strong or generous. If john is either not patient or not funny then someone is either kind or patient. If someone is both tall and not curious then susan is not old or strong and vice versa. Everyone who is not brave or not quiet is either not humble or funny. Everyone who is happy or not creative is either curious or generous and vice versa. Everyone who is either tall or not tall is brave and vice versa. If someone is strong then someone is either not creative or old and vice versa. If susan is both not calm and not wise then lucy is not brave and vice versa. Everyone who is not funny is not brave. Everyone who is calm is curious. Everyone who is either not patient or patient is strong or quiet. If someone is either not tall or not happy then someone is brave and vice versa. Everyone who is old or not strong is either humble or happy and vice versa. Someone is not tall. Someone is either not happy or not patient. Mary is either not kind or kind. Susan is not funny or patient. Susan is calm. Fred is curious or not funny. Someone is not creative. Someone is patient or not calm. | Susan is old. | entailment | (![X]:(strong(X)=>(humble(X)&generous(X))))&
((?[X]:((patient(X)&quiet(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~kind(X)&creative(X))))<=>((rich(paul)<~>~creative(paul))))&
((?[X]:((~old(X)<~>~kind(X))))=>(?[X]:((strong(X)|generous(X)))))&
(((~patient(john)<~>~funny(john)))=>(?[X]:((kind(X)<~>patient(X)))))&
((?[X]:((tall(X)&~curious(X))))<=>((~old(susan)|strong(susan))))&
(![X]:((~brave(X)|~quiet(X))=>(~humble(X)<~>funny(X))))&
(![X]:((happy(X)|~creative(X))<=>(curious(X)<~>generous(X))))&
(![X]:((tall(X)<~>~tall(X))<=>brave(X)))&
((?[X]:(strong(X)))<=>(?[X]:((~creative(X)<~>old(X)))))&
(((~calm(susan)&~wise(susan)))<=>(~brave(lucy)))&
(![X]:(~funny(X)=>~brave(X)))&
(![X]:(calm(X)=>curious(X)))&
(![X]:((~patient(X)<~>patient(X))=>(strong(X)|quiet(X))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:(brave(X))))&
(![X]:((old(X)|~strong(X))<=>(humble(X)<~>happy(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~happy(X)<~>~patient(X))))&
((~kind(mary)<~>kind(mary)))&
((~funny(susan)|patient(susan)))&
(calm(susan))&
((curious(fred)|~funny(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((patient(X)|~calm(X)))) | old(susan) | [
"p0",
"p1",
"p7",
"p8",
"p11",
"p12",
"p13",
"p15",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7514137169357115802777347
% SZS output start Proof for 7514137169357115802777347
1. ! [X0] : (strong(X0) => (generous(X0) & humble(X0))) [input p0]
2. ? [X0] : (quiet(X0) & patient(X0)) => ? [X0] : ~funny(X0) [input p1]
8. ! [X0] : ((~creative(X0) | happy(X0)) <=> (curious(X0) <~> generous(X0))) [input p7]
9. ! [X0] : ((tall(X0) <~> ~tall(X0)) <=> brave(X0)) [input p8]
12. ! [X0] : (~funny(X0) => ~brave(X0)) [input p11]
13. ! [X0] : (calm(X0) => curious(X0)) [input p12]
14. ! [X0] : ((~patient(X0) <~> patient(X0)) => (quiet(X0) | strong(X0))) [input p13]
16. ! [X0] : ((~strong(X0) | old(X0)) <=> (humble(X0) <~> happy(X0))) [input p15]
20. patient(susan) | ~funny(susan) [input p19]
21. calm(susan) [input p20]
25. ~old(susan) [input hypothesis]
26. ? [X0] : (quiet(X0) & patient(X0)) => ? [X1] : ~funny(X1) [rectify 2]
30. ! [X0] : ((generous(X0) & humble(X0)) | ~strong(X0)) [ennf transformation 1]
31. ? [X1] : ~funny(X1) | ! [X0] : (~quiet(X0) | ~patient(X0)) [ennf transformation 26]
35. ! [X0] : (~brave(X0) | funny(X0)) [ennf transformation 12]
36. ! [X0] : (curious(X0) | ~calm(X0)) [ennf transformation 13]
37. ! [X0] : ((quiet(X0) | strong(X0)) | (~patient(X0) <=> patient(X0))) [ennf transformation 14]
38. ! [X0] : (quiet(X0) | strong(X0) | (~patient(X0) <=> patient(X0))) [flattening 37]
39. ? [X0] : ~funny(X0) | ! [X1] : (~quiet(X1) | ~patient(X1)) [rectify 31]
40. ? [X0] : ~funny(X0) => ~funny(sK0) [choice axiom]
41. ~funny(sK0) | ! [X1] : (~quiet(X1) | ~patient(X1)) [skolemisation 39,40]
59. ! [X0] : (((~creative(X0) | happy(X0)) | ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0)))) & (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | (creative(X0) & ~happy(X0)))) [nnf transformation 8]
60. ! [X0] : ((~creative(X0) | happy(X0) | ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0)))) & (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | (creative(X0) & ~happy(X0)))) [flattening 59]
61. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ~brave(X0)) & (brave(X0) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [nnf transformation 9]
69. ! [X0] : (quiet(X0) | strong(X0) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 38]
75. ! [X0] : (((~strong(X0) | old(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) & (((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (strong(X0) & ~old(X0)))) [nnf transformation 16]
76. ! [X0] : ((~strong(X0) | old(X0) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) & (((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (strong(X0) & ~old(X0)))) [flattening 75]
87. ~strong(X0) | humble(X0) [cnf transformation 30]
88. ~strong(X0) | generous(X0) [cnf transformation 30]
89. ~funny(sK0) | ~quiet(X1) | ~patient(X1) [cnf transformation 41]
113. ~happy(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 60]
117. brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 61]
118. brave(X0) | tall(X0) | tall(X0) [cnf transformation 61]
128. ~brave(X0) | funny(X0) [cnf transformation 35]
129. ~calm(X0) | curious(X0) [cnf transformation 36]
130. quiet(X0) | strong(X0) | patient(X0) | patient(X0) [cnf transformation 69]
131. quiet(X0) | strong(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 69]
140. ~strong(X0) | old(X0) | happy(X0) | ~humble(X0) [cnf transformation 76]
147. patient(susan) | ~funny(susan) [cnf transformation 20]
148. calm(susan) [cnf transformation 21]
152. ~old(susan) [cnf transformation 25]
153. quiet(X0) | strong(X0) | patient(X0) [duplicate literal removal 130]
154. ~patient(X0) | strong(X0) | quiet(X0) [duplicate literal removal 131]
155. brave(X0) | ~tall(X0) [duplicate literal removal 117]
156. brave(X0) | tall(X0) [duplicate literal removal 118]
158. 1 <=> ! [X1] : (~quiet(X1) | ~patient(X1)) [avatar definition]
159. ~quiet(X1) | ~patient(X1) <- (1) [avatar component clause 158]
161. 2 <=> funny(sK0) [avatar definition]
163. ~funny(sK0) <- (~2) [avatar component clause 161]
164. 1 | ~2 [avatar split clause 89,161,158]
225. 15 <=> strong(susan) [avatar definition]
226. strong(susan) <- (15) [avatar component clause 225]
234. 17 <=> old(susan) [avatar definition]
235. ~old(susan) <- (~17) [avatar component clause 234]
248. brave(X0) [subsumption resolution 155,156]
276. 26 <=> calm(susan) [avatar definition]
278. calm(susan) <- (26) [avatar component clause 276]
284. funny(X0) [subsumption resolution 128,248]
285. quiet(X0) | strong(X0) [subsumption resolution 153,154]
298. ~strong(X0) | old(X0) | happy(X0) [subsumption resolution 140,87]
310. patient(susan) [subsumption resolution 147,284]
311. 26 [avatar split clause 148,276]
322. ~17 [avatar split clause 152,234]
325. $false <- (~2) [subsumption resolution 163,284]
326. 2 [avatar contradiction clause 325]
329. curious(susan) <- (26) [resolution 129,278]
330. ~patient(X0) | strong(X0) <- (1) [resolution 285,159]
335. strong(susan) <- (1) [resolution 330,310]
336. 15 | ~1 [avatar split clause 335,158,225]
337. generous(susan) <- (15) [resolution 226,88]
408. old(susan) | happy(susan) <- (15) [resolution 298,226]
419. happy(susan) <- (15, ~17) [subsumption resolution 408,235]
464. ~curious(susan) | ~generous(susan) <- (15, ~17) [resolution 419,113]
466. ~generous(susan) <- (15, ~17, 26) [subsumption resolution 464,329]
467. $false <- (15, ~17, 26) [subsumption resolution 466,337]
468. ~15 | 17 | ~26 [avatar contradiction clause 467]
469. $false [avatar sat refutation 164,311,322,326,336,468]
% SZS output end Proof for 7514137169357115802777347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious and funny then someone is both brave and not happy. Everyone who is not generous or not quiet is not creative or creative. Everyone who is both rich and not strong is funny and vice versa. Everyone who is both not funny and quiet is both not old and kind and vice versa. If mary is both wise and not humble then someone is old and vice versa. Everyone who is happy is both patient and not curious. If alice is not strong or humble then someone is not creative. Everyone who is both not old and not patient is both tall and kind. If paul is funny then alice is either funny or not generous. Everyone who is both not happy and calm is both not curious and old. If someone is either not curious or not rich then susan is not brave. If paul is either calm or patient then fred is both generous and funny. Everyone who is either creative or humble is not humble and vice versa. Everyone who is either brave or not creative is not funny and vice versa. Everyone who is either strong or curious is calm or wise. Everyone who is both calm and funny is not quiet or not calm and vice versa. Someone is not tall. Someone is curious or humble. Someone is either not creative or quiet. | Mary is not happy. | contradiction | ((?[X]:((~curious(X)&funny(X))))=>(?[X]:((brave(X)&~happy(X)))))&
(![X]:((~generous(X)|~quiet(X))=>(~creative(X)|creative(X))))&
(![X]:((rich(X)&~strong(X))<=>funny(X)))&
(![X]:((~funny(X)&quiet(X))<=>(~old(X)&kind(X))))&
(((wise(mary)&~humble(mary)))<=>(?[X]:(old(X))))&
(![X]:(happy(X)=>(patient(X)&~curious(X))))&
(((~strong(alice)|humble(alice)))=>(?[X]:(~creative(X))))&
(![X]:((~old(X)&~patient(X))=>(tall(X)&kind(X))))&
((funny(paul))=>((funny(alice)<~>~generous(alice))))&
(![X]:((~happy(X)&calm(X))=>(~curious(X)&old(X))))&
((?[X]:((~curious(X)<~>~rich(X))))=>(~brave(susan)))&
(((calm(paul)<~>patient(paul)))=>((generous(fred)&funny(fred))))&
(![X]:((creative(X)<~>humble(X))<=>~humble(X)))&
(![X]:((brave(X)<~>~creative(X))<=>~funny(X)))&
(![X]:((strong(X)<~>curious(X))=>(calm(X)|wise(X))))&
(![X]:((calm(X)&funny(X))<=>(~quiet(X)|~calm(X))))&
(?[X]:(~tall(X)))&
(?[X]:((curious(X)|humble(X))))&
(?[X]:((~creative(X)<~>quiet(X)))) | ~happy(mary) | [
"p0",
"p3",
"p4",
"p5",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 768724426846430763629087
% SZS output start Proof for 768724426846430763629087
1. ? [X0] : (funny(X0) & ~curious(X0)) => ? [X0] : (~happy(X0) & brave(X0)) [input p0]
4. ! [X0] : ((quiet(X0) & ~funny(X0)) <=> (kind(X0) & ~old(X0))) [input p3]
5. (~humble(mary) & wise(mary)) <=> ? [X0] : old(X0) [input p4]
6. ! [X0] : (happy(X0) => (~curious(X0) & patient(X0))) [input p5]
10. ! [X0] : ((calm(X0) & ~happy(X0)) => (old(X0) & ~curious(X0))) [input p9]
13. ! [X0] : ((creative(X0) <~> humble(X0)) <=> ~humble(X0)) [input p12]
14. ! [X0] : ((brave(X0) <~> ~creative(X0)) <=> ~funny(X0)) [input p13]
16. ! [X0] : ((funny(X0) & calm(X0)) <=> (~calm(X0) | ~quiet(X0))) [input p15]
20. ~happy(mary) [input hypothesis]
21. ? [X0] : (funny(X0) & ~curious(X0)) => ? [X1] : (~happy(X1) & brave(X1)) [rectify 1]
22. ? [X1] : (~happy(X1) & brave(X1)) | ! [X0] : (~funny(X0) | curious(X0)) [ennf transformation 21]
25. ! [X0] : ((~curious(X0) & patient(X0)) | ~happy(X0)) [ennf transformation 6]
30. ! [X0] : ((old(X0) & ~curious(X0)) | (~calm(X0) | happy(X0))) [ennf transformation 10]
31. ! [X0] : ((old(X0) & ~curious(X0)) | ~calm(X0) | happy(X0)) [flattening 30]
36. ? [X0] : (~happy(X0) & brave(X0)) | ! [X1] : (~funny(X1) | curious(X1)) [rectify 22]
37. ? [X0] : (~happy(X0) & brave(X0)) => (~happy(sK0) & brave(sK0)) [choice axiom]
38. (~happy(sK0) & brave(sK0)) | ! [X1] : (~funny(X1) | curious(X1)) [skolemisation 36,37]
41. ! [X0] : (((quiet(X0) & ~funny(X0)) | (~kind(X0) | old(X0))) & ((kind(X0) & ~old(X0)) | (~quiet(X0) | funny(X0)))) [nnf transformation 4]
42. ! [X0] : (((quiet(X0) & ~funny(X0)) | ~kind(X0) | old(X0)) & ((kind(X0) & ~old(X0)) | ~quiet(X0) | funny(X0))) [flattening 41]
43. ((~humble(mary) & wise(mary)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (humble(mary) | ~wise(mary))) [nnf transformation 5]
44. ((~humble(mary) & wise(mary)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | humble(mary) | ~wise(mary)) [flattening 43]
45. ((~humble(mary) & wise(mary)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | humble(mary) | ~wise(mary)) [rectify 44]
46. ? [X1] : old(X1) => old(sK1) [choice axiom]
47. ((~humble(mary) & wise(mary)) | ! [X0] : ~old(X0)) & (old(sK1) | humble(mary) | ~wise(mary)) [skolemisation 45,46]
53. ! [X0] : ((((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | humble(X0)) & (~humble(X0) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0))))) [nnf transformation 13]
54. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | funny(X0)) & (~funny(X0) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [nnf transformation 14]
56. ! [X0] : (((funny(X0) & calm(X0)) | (calm(X0) & quiet(X0))) & ((~calm(X0) | ~quiet(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 16]
57. ! [X0] : (((funny(X0) & calm(X0)) | (calm(X0) & quiet(X0))) & (~calm(X0) | ~quiet(X0) | ~funny(X0) | ~calm(X0))) [flattening 56]
65. brave(sK0) | ~funny(X1) | curious(X1) [cnf transformation 38]
66. ~happy(sK0) | ~funny(X1) | curious(X1) [cnf transformation 38]
72. ~old(X0) | ~quiet(X0) | funny(X0) [cnf transformation 42]
76. old(sK1) | humble(mary) | ~wise(mary) [cnf transformation 47]
77. wise(mary) | ~old(X0) [cnf transformation 47]
78. ~humble(mary) | ~old(X0) [cnf transformation 47]
80. ~happy(X0) | ~curious(X0) [cnf transformation 25]
87. ~curious(X0) | ~calm(X0) | happy(X0) [cnf transformation 31]
88. ~calm(X0) | old(X0) | happy(X0) [cnf transformation 31]
96. ~humble(X0) | creative(X0) | ~humble(X0) [cnf transformation 53]
97. humble(X0) | creative(X0) | humble(X0) [cnf transformation 53]
99. ~funny(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 54]
107. calm(X0) | calm(X0) [cnf transformation 57]
108. quiet(X0) | funny(X0) [cnf transformation 57]
114. ~happy(mary) [cnf transformation 20]
116. calm(X0) [duplicate literal removal 107]
117. ~humble(X0) | creative(X0) [duplicate literal removal 96]
118. humble(X0) | creative(X0) [duplicate literal removal 97]
120. 1 <=> ! [X1] : (~funny(X1) | curious(X1)) [avatar definition]
121. ~funny(X1) | curious(X1) <- (1) [avatar component clause 120]
123. 2 <=> happy(sK0) [avatar definition]
125. ~happy(sK0) <- (~2) [avatar component clause 123]
126. 1 | ~2 [avatar split clause 66,123,120]
128. 3 <=> brave(sK0) [avatar definition]
130. brave(sK0) <- (3) [avatar component clause 128]
131. 1 | 3 [avatar split clause 65,128,120]
133. 4 <=> ! [X0] : ~old(X0) [avatar definition]
134. ~old(X0) <- (4) [avatar component clause 133]
136. 5 <=> humble(mary) [avatar definition]
139. 4 | ~5 [avatar split clause 78,136,133]
141. 6 <=> wise(mary) [avatar definition]
144. 4 | 6 [avatar split clause 77,141,133]
146. 7 <=> old(sK1) [avatar definition]
148. old(sK1) <- (7) [avatar component clause 146]
149. ~6 | 5 | 7 [avatar split clause 76,146,136,141]
178. ~calm(X0) | ~curious(X0) [subsumption resolution 87,80]
211. creative(X0) [subsumption resolution 117,118]
213. ~brave(X0) | ~funny(X0) [subsumption resolution 99,211]
234. ~curious(X1) [resolution 178,116]
238. ~funny(sK0) <- (3) [resolution 213,130]
255. old(X1) | happy(X1) [resolution 88,116]
257. happy(X1) <- (4) [subsumption resolution 255,134]
258. $false <- (4) [resolution 257,114]
263. ~4 [avatar contradiction clause 258]
274. ~quiet(sK1) | funny(sK1) <- (7) [resolution 148,72]
275. funny(sK1) <- (7) [subsumption resolution 274,108]
280. happy(X0) | ~quiet(X0) | funny(X0) [resolution 255,72]
281. happy(X0) | funny(X0) [subsumption resolution 280,108]
286. funny(sK0) <- (~2) [resolution 281,125]
289. $false <- (~2, 3) [subsumption resolution 286,238]
290. 2 | ~3 [avatar contradiction clause 289]
291. ~funny(X1) <- (1) [subsumption resolution 121,234]
294. $false <- (1, 7) [resolution 291,275]
297. ~1 | ~7 [avatar contradiction clause 294]
299. $false [avatar sat refutation 126,131,139,144,149,263,290,297]
% SZS output end Proof for 768724426846430763629087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both creative and generous is rich or kind and vice versa.
Everyone who is both not strong and happy is patient or rich.
If lucy is not curious or not happy then susan is either patient or not kind.
If someone is either not tall or wise then alice is not happy or wise.
If someone is both not tall and creative then someone is both patient and wise and vice versa.
Everyone who is not humble or not rich is creative or strong and vice versa.
Everyone who is not rich is tall or not calm and vice versa.
Everyone who is not happy or not strong is both not funny and strong.
Everyone who is not curious is strong or quiet and vice versa.
Everyone who is not patient is either kind or creative and vice versa.
If paul is not generous or not tall then paul is not wise or humble and vice versa.
Everyone who is both kind and not wise is not wise or generous and vice versa.
Everyone who is both not rich and not calm is both not creative and humble.
If someone is old then someone is either not quiet or not tall.
If mary is either not rich or funny then someone is either generous or strong.
Everyone who is brave is not patient.
Lucy is not old.
Someone is strong or not happy.
Lucy is not generous.
Someone is humble.
Someone is not old.
Someone is strong or tall.
Alice is both not funny and happy. | Paul is strong. | entailment | (![X]:((creative(X)&generous(X))<=>(rich(X)|kind(X))))&
(![X]:((~strong(X)&happy(X))=>(patient(X)|rich(X))))&
(((~curious(lucy)|~happy(lucy)))=>((patient(susan)<~>~kind(susan))))&
((?[X]:((~tall(X)<~>wise(X))))=>((~happy(alice)|wise(alice))))&
((?[X]:((~tall(X)&creative(X))))<=>(?[X]:((patient(X)&wise(X)))))&
(![X]:((~humble(X)|~rich(X))<=>(creative(X)|strong(X))))&
(![X]:(~rich(X)<=>(tall(X)|~calm(X))))&
(![X]:((~happy(X)|~strong(X))=>(~funny(X)&strong(X))))&
(![X]:(~curious(X)<=>(strong(X)|quiet(X))))&
(![X]:(~patient(X)<=>(kind(X)<~>creative(X))))&
(((~generous(paul)|~tall(paul)))<=>((~wise(paul)|humble(paul))))&
(![X]:((kind(X)&~wise(X))<=>(~wise(X)|generous(X))))&
(![X]:((~rich(X)&~calm(X))=>(~creative(X)&humble(X))))&
((?[X]:(old(X)))=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(((~rich(mary)<~>funny(mary)))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:(brave(X)=>~patient(X)))&
(~old(lucy))&
(?[X]:((strong(X)|~happy(X))))&
(~generous(lucy))&
(?[X]:(humble(X)))&
(?[X]:(~old(X)))&
(?[X]:((strong(X)|tall(X))))&
((~funny(alice)&happy(alice))) | strong(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 290423029596412658398302
% SZS output start Proof for 290423029596412658398302
8. ! [X0] : ((~strong(X0) | ~happy(X0)) => (strong(X0) & ~funny(X0))) [input p7]
24. ~strong(paul) [input hypothesis]
38. ! [X0] : ((strong(X0) & ~funny(X0)) | (strong(X0) & happy(X0))) [ennf transformation 8]
96. strong(X0) | strong(X0) [cnf transformation 38]
123. ~strong(paul) [cnf transformation 24]
124. strong(X0) [duplicate literal removal 96]
231. $false [subsumption resolution 123,124]
% SZS output end Proof for 290423029596412658398302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not rich then lucy is both wise and generous. Everyone who is not humble is not quiet and vice versa. Everyone who is either not strong or wise is either not humble or not calm. Everyone who is quiet is not kind or humble and vice versa. Everyone who is quiet or not rich is old or not humble. Everyone who is not funny or kind is both quiet and not creative. Everyone who is not kind is wise and vice versa. Everyone who is either funny or calm is not brave or quiet. If someone is not happy then alice is either not rich or not quiet. Everyone who is both not humble and not generous is either not rich or not old and vice versa. If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa. If someone is generous or tall then alice is strong and vice versa. Everyone who is not happy is brave or humble. Everyone who is not happy or not funny is both creative and quiet. Everyone who is not patient is both not kind and happy and vice versa. Someone is brave or wise. Susan is both brave and not strong. Someone is kind or happy. Someone is both not kind and not creative. Alice is not tall or not old. Someone is not calm or funny. Mary is not rich or curious. | Susan is happy. | entailment | ((~rich(susan))=>((wise(lucy)&generous(lucy))))&
(![X]:(~humble(X)<=>~quiet(X)))&
(![X]:((~strong(X)<~>wise(X))=>(~humble(X)<~>~calm(X))))&
(![X]:(quiet(X)<=>(~kind(X)|humble(X))))&
(![X]:((quiet(X)|~rich(X))=>(old(X)|~humble(X))))&
(![X]:((~funny(X)|kind(X))=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(![X]:((funny(X)<~>calm(X))=>(~brave(X)|quiet(X))))&
((?[X]:(~happy(X)))=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
(?[X]:((brave(X)|wise(X))))&
((brave(susan)&~strong(susan)))&
(?[X]:((kind(X)|happy(X))))&
(?[X]:((~kind(X)&~creative(X))))&
((~tall(alice)|~old(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(mary)|curious(mary))) | happy(susan) | [
"p1",
"p3",
"p4",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4475717802690002910759655
% SZS output start Proof for 4475717802690002910759655
2. ! [X0] : (~humble(X0) <=> ~quiet(X0)) [input p1]
4. ! [X0] : (quiet(X0) <=> (humble(X0) | ~kind(X0))) [input p3]
5. ! [X0] : ((~rich(X0) | quiet(X0)) => (~humble(X0) | old(X0))) [input p4]
6. ! [X0] : ((kind(X0) | ~funny(X0)) => (~creative(X0) & quiet(X0))) [input p5]
9. ? [X0] : ~happy(X0) => (~rich(alice) <~> ~quiet(alice)) [input p8]
10. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> (~rich(X0) <~> ~old(X0))) [input p9]
23. ~happy(susan) [input hypothesis]
28. ! [X0] : ((~humble(X0) | old(X0)) | (rich(X0) & ~quiet(X0))) [ennf transformation 5]
29. ! [X0] : (~humble(X0) | old(X0) | (rich(X0) & ~quiet(X0))) [flattening 28]
30. ! [X0] : ((~creative(X0) & quiet(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 6]
33. (~rich(alice) <~> ~quiet(alice)) | ! [X0] : happy(X0) [ennf transformation 9]
37. ! [X0] : ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))) [nnf transformation 2]
39. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ~quiet(X0))) [nnf transformation 4]
40. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ~quiet(X0))) [flattening 39]
43. ((quiet(alice) | rich(alice)) & (~quiet(alice) | ~rich(alice))) | ! [X0] : happy(X0) [nnf transformation 33]
44. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (generous(X0) | humble(X0)))) [nnf transformation 10]
45. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | generous(X0) | humble(X0))) [flattening 44]
65. ~quiet(X0) | humble(X0) [cnf transformation 37]
72. kind(X0) | quiet(X0) [cnf transformation 40]
75. ~humble(X0) | old(X0) | rich(X0) [cnf transformation 29]
77. quiet(X0) | ~kind(X0) [cnf transformation 30]
84. ~quiet(alice) | ~rich(alice) | happy(X0) [cnf transformation 43]
88. ~humble(X0) | ~old(X0) | rich(X0) [cnf transformation 45]
89. ~humble(X0) | ~rich(X0) | old(X0) [cnf transformation 45]
112. ~happy(susan) [cnf transformation 23]
128. quiet(X0) [subsumption resolution 77,72]
129. ~rich(alice) | happy(X0) [subsumption resolution 84,128]
131. 4 <=> ! [X0] : happy(X0) [avatar definition]
132. happy(X0) <- (4) [avatar component clause 131]
134. 5 <=> rich(alice) [avatar definition]
136. ~rich(alice) <- (~5) [avatar component clause 134]
137. 4 | ~5 [avatar split clause 129,134,131]
138. ~humble(X0) | old(X0) [subsumption resolution 89,75]
139. ~humble(X0) | rich(X0) [subsumption resolution 88,138]
190. humble(X0) [resolution 65,128]
206. rich(X0) [resolution 139,190]
207. $false <- (~5) [resolution 206,136]
208. 5 [avatar contradiction clause 207]
209. $false <- (4) [resolution 132,112]
210. ~4 [avatar contradiction clause 209]
211. $false [avatar sat refutation 137,208,210]
% SZS output end Proof for 4475717802690002910759655
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not brave then mary is both kind and not humble and vice versa. Everyone who is not happy or rich is both not calm and not rich and vice versa. If lucy is either kind or not quiet then lucy is either generous or not calm. Everyone who is either strong or not quiet is either not calm or not curious. Everyone who is not humble is not happy or curious and vice versa. If someone is not calm then someone is kind or generous. Everyone who is either not curious or not generous is not patient. Everyone who is not generous is calm or generous and vice versa. Everyone who is not kind is brave or not tall and vice versa. If john is both not strong and not tall then alice is not old. Everyone who is both old and generous is both not quiet and not brave and vice versa. Everyone who is not patient is both kind and not funny and vice versa. Everyone who is not brave or not strong is old. Everyone who is both quiet and not wise is not strong or quiet and vice versa. Everyone who is either old or not generous is either patient or generous and vice versa. Susan is both calm and not strong. Someone is not calm or tall. Fred is either not strong or not curious. Susan is quiet or calm. Someone is either not rich or not curious. Mary is either tall or not wise. | Mary is patient. | entailment | ((?[X]:((humble(X)&~brave(X))))<=>((kind(mary)&~humble(mary))))&
(![X]:((~happy(X)|rich(X))<=>(~calm(X)&~rich(X))))&
(((kind(lucy)<~>~quiet(lucy)))=>((generous(lucy)<~>~calm(lucy))))&
(![X]:((strong(X)<~>~quiet(X))=>(~calm(X)<~>~curious(X))))&
(![X]:(~humble(X)<=>(~happy(X)|curious(X))))&
((?[X]:(~calm(X)))=>(?[X]:((kind(X)|generous(X)))))&
(![X]:((~curious(X)<~>~generous(X))=>~patient(X)))&
(![X]:(~generous(X)<=>(calm(X)|generous(X))))&
(![X]:(~kind(X)<=>(brave(X)|~tall(X))))&
(((~strong(john)&~tall(john)))=>(~old(alice)))&
(![X]:((old(X)&generous(X))<=>(~quiet(X)&~brave(X))))&
(![X]:(~patient(X)<=>(kind(X)&~funny(X))))&
(![X]:((~brave(X)|~strong(X))=>old(X)))&
(![X]:((quiet(X)&~wise(X))<=>(~strong(X)|quiet(X))))&
(![X]:((old(X)<~>~generous(X))<=>(patient(X)<~>generous(X))))&
((calm(susan)&~strong(susan)))&
(?[X]:((~calm(X)|tall(X))))&
((~strong(fred)<~>~curious(fred)))&
((quiet(susan)|calm(susan)))&
(?[X]:((~rich(X)<~>~curious(X))))&
((tall(mary)<~>~wise(mary))) | patient(mary) | [
"p7",
"p8",
"p10",
"p11",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4908280637478922532311366
% SZS output start Proof for 4908280637478922532311366
8. ! [X0] : (~generous(X0) <=> (generous(X0) | calm(X0))) [input p7]
9. ! [X0] : (~kind(X0) <=> (~tall(X0) | brave(X0))) [input p8]
11. ! [X0] : ((generous(X0) & old(X0)) <=> (~brave(X0) & ~quiet(X0))) [input p10]
12. ! [X0] : (~patient(X0) <=> (~funny(X0) & kind(X0))) [input p11]
14. ! [X0] : ((~wise(X0) & quiet(X0)) <=> (quiet(X0) | ~strong(X0))) [input p13]
21. tall(mary) <~> ~wise(mary) [input p20]
22. ~patient(mary) [input hypothesis]
46. ! [X0] : ((~generous(X0) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | generous(X0))) [nnf transformation 8]
47. ! [X0] : ((~generous(X0) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | generous(X0))) [flattening 46]
48. ! [X0] : ((~kind(X0) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | kind(X0))) [nnf transformation 9]
49. ! [X0] : ((~kind(X0) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | kind(X0))) [flattening 48]
50. ! [X0] : (((generous(X0) & old(X0)) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | (~generous(X0) | ~old(X0)))) [nnf transformation 11]
51. ! [X0] : (((generous(X0) & old(X0)) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | ~generous(X0) | ~old(X0))) [flattening 50]
52. ! [X0] : ((~patient(X0) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | patient(X0))) [nnf transformation 12]
53. ! [X0] : ((~patient(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | patient(X0))) [flattening 52]
54. ! [X0] : (((~wise(X0) & quiet(X0)) | (~quiet(X0) & strong(X0))) & ((quiet(X0) | ~strong(X0)) | (wise(X0) | ~quiet(X0)))) [nnf transformation 14]
55. ! [X0] : (((~wise(X0) & quiet(X0)) | (~quiet(X0) & strong(X0))) & (quiet(X0) | ~strong(X0) | wise(X0) | ~quiet(X0))) [flattening 54]
63. (wise(mary) | ~tall(mary)) & (~wise(mary) | tall(mary)) [nnf transformation 21]
89. ~generous(X0) | ~generous(X0) [cnf transformation 47]
91. ~kind(X0) | ~brave(X0) [cnf transformation 49]
92. ~kind(X0) | tall(X0) [cnf transformation 49]
97. generous(X0) | brave(X0) | quiet(X0) [cnf transformation 51]
98. patient(X0) | kind(X0) [cnf transformation 53]
107. ~wise(X0) | ~quiet(X0) [cnf transformation 55]
125. wise(mary) | ~tall(mary) [cnf transformation 63]
126. ~patient(mary) [cnf transformation 22]
132. ~generous(X0) [duplicate literal removal 89]
136. 1 <=> kind(mary) [avatar definition]
137. kind(mary) <- (1) [avatar component clause 136]
205. quiet(X0) | brave(X0) [subsumption resolution 97,132]
229. 20 <=> tall(mary) [avatar definition]
233. 21 <=> wise(mary) [avatar definition]
235. wise(mary) <- (21) [avatar component clause 233]
236. ~20 | 21 [avatar split clause 125,233,229]
245. kind(mary) [resolution 98,126]
248. 1 [avatar split clause 245,136]
249. tall(mary) <- (1) [resolution 137,92]
250. ~brave(mary) <- (1) [resolution 137,91]
253. 20 | ~1 [avatar split clause 249,136,229]
259. ~quiet(mary) <- (21) [resolution 107,235]
268. brave(mary) <- (21) [resolution 205,259]
269. $false <- (1, 21) [subsumption resolution 268,250]
270. ~1 | ~21 [avatar contradiction clause 269]
271. $false [avatar sat refutation 236,248,253,270]
% SZS output end Proof for 4908280637478922532311366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or humble is both not creative and not tall.
If fred is curious then lucy is not strong or not quiet and vice versa.
If someone is not quiet or curious then someone is wise.
Everyone who is both not old and generous is not brave or brave and vice versa.
Everyone who is both calm and humble is either happy or not rich.
Everyone who is not kind is calm.
Everyone who is calm is either not creative or kind and vice versa.
If lucy is not quiet then someone is either not happy or humble.
If alice is creative or generous then someone is creative or curious and vice versa.
If paul is either not wise or not strong then someone is curious and vice versa.
If john is not curious then someone is both funny and curious.
Everyone who is funny or not happy is not generous and vice versa.
If someone is strong or creative then fred is both not happy and strong.
If john is either not rich or not tall then someone is either humble or not tall.
Everyone who is creative or humble is either happy or not rich and vice versa.
Someone is both calm and brave.
Alice is either wise or not wise.
Someone is not funny.
Someone is both rich and curious.
Someone is curious or tall. | Paul is wise. | entailment | (![X]:((~brave(X)|humble(X))=>(~creative(X)&~tall(X))))&
((curious(fred))<=>((~strong(lucy)|~quiet(lucy))))&
((?[X]:((~quiet(X)|curious(X))))=>(?[X]:(wise(X))))&
(![X]:((~old(X)&generous(X))<=>(~brave(X)|brave(X))))&
(![X]:((calm(X)&humble(X))=>(happy(X)<~>~rich(X))))&
(![X]:(~kind(X)=>calm(X)))&
(![X]:(calm(X)<=>(~creative(X)<~>kind(X))))&
((~quiet(lucy))=>(?[X]:((~happy(X)<~>humble(X)))))&
(((creative(alice)|generous(alice)))<=>(?[X]:((creative(X)|curious(X)))))&
(((~wise(paul)<~>~strong(paul)))<=>(?[X]:(curious(X))))&
((~curious(john))=>(?[X]:((funny(X)&curious(X)))))&
(![X]:((funny(X)|~happy(X))<=>~generous(X)))&
((?[X]:((strong(X)|creative(X))))=>((~happy(fred)&strong(fred))))&
(((~rich(john)<~>~tall(john)))=>(?[X]:((humble(X)<~>~tall(X)))))&
(![X]:((creative(X)|humble(X))<=>(happy(X)<~>~rich(X))))&
(?[X]:((calm(X)&brave(X))))&
((wise(alice)<~>~wise(alice)))&
(?[X]:(~funny(X)))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((curious(X)|tall(X)))) | wise(paul) | [
"p1",
"p3",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3763342880461778602397413
% SZS output start Proof for 3763342880461778602397413
2. curious(fred) <=> (~quiet(lucy) | ~strong(lucy)) [input p1]
4. ! [X0] : ((generous(X0) & ~old(X0)) <=> (brave(X0) | ~brave(X0))) [input p3]
10. (~wise(paul) <~> ~strong(paul)) <=> ? [X0] : curious(X0) [input p9]
12. ! [X0] : ((~happy(X0) | funny(X0)) <=> ~generous(X0)) [input p11]
13. ? [X0] : (creative(X0) | strong(X0)) => (strong(fred) & ~happy(fred)) [input p12]
21. ~wise(paul) [input hypothesis]
30. (strong(fred) & ~happy(fred)) | ! [X0] : (~creative(X0) & ~strong(X0)) [ennf transformation 13]
32. (curious(fred) | (quiet(lucy) & strong(lucy))) & ((~quiet(lucy) | ~strong(lucy)) | ~curious(fred)) [nnf transformation 2]
33. (curious(fred) | (quiet(lucy) & strong(lucy))) & (~quiet(lucy) | ~strong(lucy) | ~curious(fred)) [flattening 32]
37. ! [X0] : (((generous(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) & ((brave(X0) | ~brave(X0)) | (~generous(X0) | old(X0)))) [nnf transformation 4]
38. ! [X0] : (((generous(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) & (brave(X0) | ~brave(X0) | ~generous(X0) | old(X0))) [flattening 37]
49. (((strong(paul) | wise(paul)) & (~strong(paul) | ~wise(paul))) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ((~wise(paul) | strong(paul)) & (~strong(paul) | wise(paul)))) [nnf transformation 10]
50. (((strong(paul) | wise(paul)) & (~strong(paul) | ~wise(paul))) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ((~wise(paul) | strong(paul)) & (~strong(paul) | wise(paul)))) [rectify 49]
51. ? [X1] : curious(X1) => curious(sK3) [choice axiom]
52. (((strong(paul) | wise(paul)) & (~strong(paul) | ~wise(paul))) | ! [X0] : ~curious(X0)) & (curious(sK3) | ((~wise(paul) | strong(paul)) & (~strong(paul) | wise(paul)))) [skolemisation 50,51]
55. ! [X0] : (((~happy(X0) | funny(X0)) | generous(X0)) & (~generous(X0) | (happy(X0) & ~funny(X0)))) [nnf transformation 12]
56. ! [X0] : ((~happy(X0) | funny(X0) | generous(X0)) & (~generous(X0) | (happy(X0) & ~funny(X0)))) [flattening 55]
76. curious(fred) | strong(lucy) [cnf transformation 33]
83. generous(X0) | brave(X0) [cnf transformation 38]
84. generous(X0) | ~brave(X0) [cnf transformation 38]
101. strong(paul) | wise(paul) | ~curious(X0) [cnf transformation 52]
105. ~generous(X0) | happy(X0) [cnf transformation 56]
107. ~happy(fred) | ~strong(X0) [cnf transformation 30]
129. ~wise(paul) [cnf transformation 21]
135. 2 <=> curious(fred) [avatar definition]
137. curious(fred) <- (2) [avatar component clause 135]
140. 3 <=> strong(lucy) [avatar definition]
142. strong(lucy) <- (3) [avatar component clause 140]
143. 3 | 2 [avatar split clause 76,135,140]
146. 4 <=> ! [X1] : ~curious(X1) [avatar definition]
147. ~curious(X1) <- (4) [avatar component clause 146]
157. generous(X0) [subsumption resolution 83,84]
187. 12 <=> wise(paul) [avatar definition]
191. 13 <=> strong(paul) [avatar definition]
193. strong(paul) <- (13) [avatar component clause 191]
194. 4 | 12 | 13 [avatar split clause 101,191,187,146]
216. happy(X0) [subsumption resolution 105,157]
227. 20 <=> ! [X0] : ~strong(X0) [avatar definition]
228. ~strong(X0) <- (20) [avatar component clause 227]
232. ~strong(X0) [subsumption resolution 107,216]
233. 20 [avatar split clause 232,227]
270. ~12 [avatar split clause 129,187]
275. $false <- (2, 4) [subsumption resolution 137,147]
276. ~2 | ~4 [avatar contradiction clause 275]
277. $false <- (13, 20) [subsumption resolution 193,228]
278. ~13 | ~20 [avatar contradiction clause 277]
279. $false <- (3, 20) [subsumption resolution 142,228]
280. ~3 | ~20 [avatar contradiction clause 279]
281. $false [avatar sat refutation 143,194,233,270,276,278,280]
% SZS output end Proof for 3763342880461778602397413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or kind is both curious and not brave.
Everyone who is funny or quiet is not quiet and vice versa.
If someone is calm or generous then paul is quiet and vice versa.
If someone is not generous or brave then john is either kind or not quiet and vice versa.
Everyone who is both humble and happy is not rich.
Everyone who is old is not strong or not happy.
Everyone who is not happy is either rich or happy and vice versa.
Everyone who is creative or humble is not old or not creative and vice versa.
Everyone who is both old and funny is both not strong and rich.
If lucy is either happy or not wise then someone is wise or not curious and vice versa.
Everyone who is wise is both happy and not creative.
If paul is not strong or brave then someone is humble or tall.
If susan is patient or strong then someone is not strong and vice versa.
Everyone who is either not old or not funny is either not humble or funny.
Everyone who is either not generous or brave is patient and vice versa.
Mary is either not tall or curious.
Alice is either not humble or not patient.
Someone is not funny or humble.
Lucy is either patient or not calm. | Alice is kind. | contradiction | (![X]:((curious(X)|kind(X))=>(curious(X)&~brave(X))))&
(![X]:((funny(X)|quiet(X))<=>~quiet(X)))&
((?[X]:((calm(X)|generous(X))))<=>(quiet(paul)))&
((?[X]:((~generous(X)|brave(X))))<=>((kind(john)<~>~quiet(john))))&
(![X]:((humble(X)&happy(X))=>~rich(X)))&
(![X]:(old(X)=>(~strong(X)|~happy(X))))&
(![X]:(~happy(X)<=>(rich(X)<~>happy(X))))&
(![X]:((creative(X)|humble(X))<=>(~old(X)|~creative(X))))&
(![X]:((old(X)&funny(X))=>(~strong(X)&rich(X))))&
(((happy(lucy)<~>~wise(lucy)))<=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:(wise(X)=>(happy(X)&~creative(X))))&
(((~strong(paul)|brave(paul)))=>(?[X]:((humble(X)|tall(X)))))&
(((patient(susan)|strong(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~old(X)<~>~funny(X))=>(~humble(X)<~>funny(X))))&
(![X]:((~generous(X)<~>brave(X))<=>patient(X)))&
((~tall(mary)<~>curious(mary)))&
((~humble(alice)<~>~patient(alice)))&
(?[X]:((~funny(X)|humble(X))))&
((patient(lucy)<~>~calm(lucy))) | kind(alice) | [
"p0",
"p1",
"p2",
"p7",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5917014405350395185255120
% SZS output start Proof for 5917014405350395185255120
1. ! [X0] : ((kind(X0) | curious(X0)) => (~brave(X0) & curious(X0))) [input p0]
2. ! [X0] : ((quiet(X0) | funny(X0)) <=> ~quiet(X0)) [input p1]
3. ? [X0] : (generous(X0) | calm(X0)) <=> quiet(paul) [input p2]
8. ! [X0] : ((humble(X0) | creative(X0)) <=> (~creative(X0) | ~old(X0))) [input p7]
14. ! [X0] : ((~old(X0) <~> ~funny(X0)) => (~humble(X0) <~> funny(X0))) [input p13]
15. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> patient(X0)) [input p14]
17. ~humble(alice) <~> ~patient(alice) [input p16]
20. kind(alice) [input hypothesis]
21. ! [X0] : ((~brave(X0) & curious(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 1]
30. ! [X0] : ((~humble(X0) <~> funny(X0)) | (~old(X0) <=> ~funny(X0))) [ennf transformation 14]
31. ! [X0] : (((quiet(X0) | funny(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [nnf transformation 2]
32. ! [X0] : ((quiet(X0) | funny(X0) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [flattening 31]
33. (? [X0] : (generous(X0) | calm(X0)) | ~quiet(paul)) & (quiet(paul) | ! [X0] : (~generous(X0) & ~calm(X0))) [nnf transformation 3]
34. (? [X0] : (generous(X0) | calm(X0)) | ~quiet(paul)) & (quiet(paul) | ! [X1] : (~generous(X1) & ~calm(X1))) [rectify 33]
35. ? [X0] : (generous(X0) | calm(X0)) => (generous(sK0) | calm(sK0)) [choice axiom]
36. ((generous(sK0) | calm(sK0)) | ~quiet(paul)) & (quiet(paul) | ! [X1] : (~generous(X1) & ~calm(X1))) [skolemisation 34,35]
42. ! [X0] : (((humble(X0) | creative(X0)) | (creative(X0) & old(X0))) & ((~creative(X0) | ~old(X0)) | (~humble(X0) & ~creative(X0)))) [nnf transformation 8]
43. ! [X0] : ((humble(X0) | creative(X0) | (creative(X0) & old(X0))) & (~creative(X0) | ~old(X0) | (~humble(X0) & ~creative(X0)))) [flattening 42]
55. ! [X0] : (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0)))) [nnf transformation 30]
56. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | ~patient(X0)) & (patient(X0) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 15]
58. (patient(alice) | humble(alice)) & (~patient(alice) | ~humble(alice)) [nnf transformation 17]
63. ~kind(X0) | curious(X0) [cnf transformation 21]
64. ~brave(X0) | ~curious(X0) [cnf transformation 21]
67. ~quiet(X0) | ~quiet(X0) [cnf transformation 32]
68. quiet(X0) | funny(X0) | quiet(X0) [cnf transformation 32]
70. quiet(paul) | ~generous(X1) [cnf transformation 36]
84. ~creative(X0) | ~old(X0) | ~creative(X0) [cnf transformation 43]
87. humble(X0) | creative(X0) | creative(X0) [cnf transformation 43]
105. ~funny(X0) | humble(X0) | ~funny(X0) | old(X0) [cnf transformation 55]
107. patient(X0) | brave(X0) | generous(X0) [cnf transformation 56]
113. ~patient(alice) | ~humble(alice) [cnf transformation 58]
118. kind(alice) [cnf transformation 20]
120. ~funny(X0) | humble(X0) | old(X0) [duplicate literal removal 105]
121. ~creative(X0) | ~old(X0) [duplicate literal removal 84]
122. creative(X0) | humble(X0) [duplicate literal removal 87]
125. ~quiet(X0) [duplicate literal removal 67]
126. quiet(X0) | funny(X0) [duplicate literal removal 68]
127. ~generous(X1) [subsumption resolution 70,125]
207. patient(X0) | brave(X0) [subsumption resolution 107,127]
219. 19 <=> humble(alice) [avatar definition]
220. ~humble(alice) <- (~19) [avatar component clause 219]
223. 20 <=> patient(alice) [avatar definition]
224. ~patient(alice) <- (~20) [avatar component clause 223]
227. ~19 | ~20 [avatar split clause 113,223,219]
240. curious(alice) [resolution 63,118]
241. ~old(X0) | humble(X0) [resolution 122,121]
242. funny(X0) [resolution 126,125]
246. brave(alice) <- (~20) [resolution 207,224]
250. ~curious(alice) <- (~20) [resolution 246,64]
253. $false <- (~20) [subsumption resolution 250,240]
254. 20 [avatar contradiction clause 253]
260. humble(X0) | old(X0) [resolution 120,242]
261. humble(X0) [subsumption resolution 260,241]
262. $false <- (~19) [resolution 261,220]
263. 19 [avatar contradiction clause 262]
264. $false [avatar sat refutation 227,254,263]
% SZS output end Proof for 5917014405350395185255120
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or not curious then john is both not brave and brave and vice versa.
Everyone who is both brave and rich is both not calm and not brave.
If someone is not generous or brave then someone is not tall or not wise and vice versa.
Everyone who is not curious or humble is not curious.
If someone is either not kind or not rich then someone is brave or kind.
Everyone who is generous or not patient is either patient or not humble.
Everyone who is both not rich and brave is not creative or happy.
Everyone who is either calm or not wise is brave or rich and vice versa.
If someone is both not old and not humble then someone is either not calm or not patient.
If alice is rich then alice is both not funny and creative.
Everyone who is both not strong and strong is either calm or not generous and vice versa.
Everyone who is both not wise and calm is both strong and happy and vice versa.
If alice is both not wise and not patient then someone is either not brave or not curious.
If mary is either not patient or kind then paul is not old or not funny.
If someone is both not funny and not quiet then someone is either strong or kind and vice versa.
Everyone who is both brave and strong is not humble.
Someone is both not funny and tall.
Mary is both patient and strong.
Mary is either not kind or not old.
Someone is not funny.
Mary is either not funny or not tall.
Fred is not generous.
John is either not generous or not calm.
Someone is both rich and not humble. | Mary is old. | neutral | (((~rich(lucy)|~curious(lucy)))<=>((~brave(john)&brave(john))))&
(![X]:((brave(X)&rich(X))=>(~calm(X)&~brave(X))))&
((?[X]:((~generous(X)|brave(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
(![X]:((~curious(X)|humble(X))=>~curious(X)))&
((?[X]:((~kind(X)<~>~rich(X))))=>(?[X]:((brave(X)|kind(X)))))&
(![X]:((generous(X)|~patient(X))=>(patient(X)<~>~humble(X))))&
(![X]:((~rich(X)&brave(X))=>(~creative(X)|happy(X))))&
(![X]:((calm(X)<~>~wise(X))<=>(brave(X)|rich(X))))&
((?[X]:((~old(X)&~humble(X))))=>(?[X]:((~calm(X)<~>~patient(X)))))&
((rich(alice))=>((~funny(alice)&creative(alice))))&
(![X]:((~strong(X)&strong(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((~wise(X)&calm(X))<=>(strong(X)&happy(X))))&
(((~wise(alice)&~patient(alice)))=>(?[X]:((~brave(X)<~>~curious(X)))))&
(((~patient(mary)<~>kind(mary)))=>((~old(paul)|~funny(paul))))&
((?[X]:((~funny(X)&~quiet(X))))<=>(?[X]:((strong(X)<~>kind(X)))))&
(![X]:((brave(X)&strong(X))=>~humble(X)))&
(?[X]:((~funny(X)&tall(X))))&
((patient(mary)&strong(mary)))&
((~kind(mary)<~>~old(mary)))&
(?[X]:(~funny(X)))&
((~funny(mary)<~>~tall(mary)))&
(~generous(fred))&
((~generous(john)<~>~calm(john)))&
(?[X]:((rich(X)&~humble(X)))) | old(mary) | [] | null | 0 |
If someone is both not rich and not patient then alice is not brave and vice versa.
If someone is either strong or not old then someone is not funny or not strong and vice versa.
Everyone who is not old is not wise and vice versa.
Everyone who is both calm and not funny is both not brave and calm.
Everyone who is brave is either rich or curious.
Everyone who is generous is not curious or wise and vice versa.
If someone is not quiet then someone is rich or generous and vice versa.
Everyone who is not kind or not old is not creative or not happy and vice versa.
Everyone who is either strong or not generous is either not rich or not humble and vice versa.
If someone is both creative and quiet then someone is either wise or strong and vice versa.
Everyone who is not generous or not quiet is not creative.
If someone is old then someone is both not funny and old.
Everyone who is both curious and brave is old or generous.
Everyone who is both not happy and not creative is both not rich and creative and vice versa.
Everyone who is both not brave and not patient is either not patient or wise and vice versa.
Everyone who is not tall is not kind or not quiet and vice versa.
Alice is not strong.
Lucy is either not old or not funny.
Someone is either not brave or not generous.
Alice is both not funny and not strong.
Someone is either not wise or not patient.
Susan is either tall or rich.
Mary is not creative.
Someone is either creative or not rich. | Alice is not brave. | neutral | ((?[X]:((~rich(X)&~patient(X))))<=>(~brave(alice)))&
((?[X]:((strong(X)<~>~old(X))))<=>(?[X]:((~funny(X)|~strong(X)))))&
(![X]:(~old(X)<=>~wise(X)))&
(![X]:((calm(X)&~funny(X))=>(~brave(X)&calm(X))))&
(![X]:(brave(X)=>(rich(X)<~>curious(X))))&
(![X]:(generous(X)<=>(~curious(X)|wise(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((rich(X)|generous(X)))))&
(![X]:((~kind(X)|~old(X))<=>(~creative(X)|~happy(X))))&
(![X]:((strong(X)<~>~generous(X))<=>(~rich(X)<~>~humble(X))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((~generous(X)|~quiet(X))=>~creative(X)))&
((?[X]:(old(X)))=>(?[X]:((~funny(X)&old(X)))))&
(![X]:((curious(X)&brave(X))=>(old(X)|generous(X))))&
(![X]:((~happy(X)&~creative(X))<=>(~rich(X)&creative(X))))&
(![X]:((~brave(X)&~patient(X))<=>(~patient(X)<~>wise(X))))&
(![X]:(~tall(X)<=>(~kind(X)|~quiet(X))))&
(~strong(alice))&
((~old(lucy)<~>~funny(lucy)))&
(?[X]:((~brave(X)<~>~generous(X))))&
((~funny(alice)&~strong(alice)))&
(?[X]:((~wise(X)<~>~patient(X))))&
((tall(susan)<~>rich(susan)))&
(~creative(mary))&
(?[X]:((creative(X)<~>~rich(X)))) | ~brave(alice) | [] | null | 0 |
Everyone who is humble is rich and vice versa.
If someone is either not kind or not quiet then paul is not rich and vice versa.
Everyone who is either happy or not curious is both not wise and not strong and vice versa.
Everyone who is tall or not generous is not brave or generous and vice versa.
If someone is quiet or calm then someone is patient or not quiet.
Everyone who is kind is not old or not curious.
Everyone who is both quiet and not old is both old and not happy.
If fred is either kind or not happy then mary is both not humble and not calm and vice versa.
Everyone who is both tall and old is both curious and kind and vice versa.
If mary is not funny then fred is both not rich and kind.
If alice is funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
If alice is quiet or not generous then someone is strong or not tall.
Everyone who is rich is brave or not rich and vice versa.
If someone is old then lucy is either rich or not happy and vice versa.
Lucy is not kind.
Someone is not curious or not kind.
Someone is both humble and wise.
Someone is curious or not tall.
John is not quiet. | Paul is tall. | entailment | (![X]:(humble(X)<=>rich(X)))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(~rich(paul)))&
(![X]:((happy(X)<~>~curious(X))<=>(~wise(X)&~strong(X))))&
(![X]:((tall(X)|~generous(X))<=>(~brave(X)|generous(X))))&
((?[X]:((quiet(X)|calm(X))))=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:(kind(X)=>(~old(X)|~curious(X))))&
(![X]:((quiet(X)&~old(X))=>(old(X)&~happy(X))))&
(((kind(fred)<~>~happy(fred)))<=>((~humble(mary)&~calm(mary))))&
(![X]:((tall(X)&old(X))<=>(curious(X)&kind(X))))&
((~funny(mary))=>((~rich(fred)&kind(fred))))&
((funny(alice))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(((quiet(alice)|~generous(alice)))=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:(rich(X)<=>(brave(X)|~rich(X))))&
((?[X]:(old(X)))<=>((rich(lucy)<~>~happy(lucy))))&
(~kind(lucy))&
(?[X]:((~curious(X)|~kind(X))))&
(?[X]:((humble(X)&wise(X))))&
(?[X]:((curious(X)|~tall(X))))&
(~quiet(john)) | tall(paul) | [
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3103796514993455593867537
% SZS output start Proof for 3103796514993455593867537
4. ! [X0] : ((~generous(X0) | tall(X0)) <=> (generous(X0) | ~brave(X0))) [input p3]
15. ! [X0] : (rich(X0) <=> (~rich(X0) | brave(X0))) [input p14]
22. ~tall(paul) [input hypothesis]
40. ! [X0] : (((~generous(X0) | tall(X0)) | (~generous(X0) & brave(X0))) & ((generous(X0) | ~brave(X0)) | (generous(X0) & ~tall(X0)))) [nnf transformation 4]
41. ! [X0] : ((~generous(X0) | tall(X0) | (~generous(X0) & brave(X0))) & (generous(X0) | ~brave(X0) | (generous(X0) & ~tall(X0)))) [flattening 40]
56. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | ~rich(X0))) [nnf transformation 15]
57. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | ~rich(X0))) [flattening 56]
81. generous(X0) | ~brave(X0) | generous(X0) [cnf transformation 41]
83. ~generous(X0) | tall(X0) | ~generous(X0) [cnf transformation 41]
111. ~rich(X0) | brave(X0) | ~rich(X0) [cnf transformation 57]
113. rich(X0) | rich(X0) [cnf transformation 57]
124. ~tall(paul) [cnf transformation 22]
125. ~rich(X0) | brave(X0) [duplicate literal removal 111]
126. rich(X0) [duplicate literal removal 113]
128. ~brave(X0) | generous(X0) [duplicate literal removal 81]
129. ~generous(X0) | tall(X0) [duplicate literal removal 83]
241. brave(X0) [subsumption resolution 125,126]
275. generous(X0) [resolution 128,241]
276. tall(X0) [resolution 129,275]
277. $false [resolution 276,124]
% SZS output end Proof for 3103796514993455593867537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not patient is both generous and patient and vice versa.
Everyone who is not curious or rich is either not rich or tall.
Everyone who is not wise or not patient is either kind or humble and vice versa.
Everyone who is happy is either not curious or not old and vice versa.
Everyone who is both not humble and happy is humble or curious and vice versa.
Everyone who is not wise is not curious.
If fred is either calm or not quiet then lucy is both not patient and wise.
Everyone who is not wise is either not kind or not creative and vice versa.
If john is rich then someone is not brave and vice versa.
If mary is either not humble or strong then john is not wise.
Everyone who is both not calm and not quiet is either not happy or not funny.
Everyone who is not patient is not calm or not brave.
Everyone who is not rich or tall is rich or not kind and vice versa.
Everyone who is both happy and not old is not creative and vice versa.
If john is tall then someone is either not rich or patient and vice versa.
If someone is either calm or rich then someone is either curious or not rich.
Someone is not humble.
Susan is quiet.
Someone is wise.
Someone is both curious and not quiet.
Someone is both tall and patient. | Mary is calm. | neutral | (![X]:((~quiet(X)<~>~patient(X))<=>(generous(X)&patient(X))))&
(![X]:((~curious(X)|rich(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|~patient(X))<=>(kind(X)<~>humble(X))))&
(![X]:(happy(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~humble(X)&happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~wise(X)=>~curious(X)))&
(((calm(fred)<~>~quiet(fred)))=>((~patient(lucy)&wise(lucy))))&
(![X]:(~wise(X)<=>(~kind(X)<~>~creative(X))))&
((rich(john))<=>(?[X]:(~brave(X))))&
(((~humble(mary)<~>strong(mary)))=>(~wise(john)))&
(![X]:((~calm(X)&~quiet(X))=>(~happy(X)<~>~funny(X))))&
(![X]:(~patient(X)=>(~calm(X)|~brave(X))))&
(![X]:((~rich(X)|tall(X))<=>(rich(X)|~kind(X))))&
(![X]:((happy(X)&~old(X))<=>~creative(X)))&
((tall(john))<=>(?[X]:((~rich(X)<~>patient(X)))))&
((?[X]:((calm(X)<~>rich(X))))=>(?[X]:((curious(X)<~>~rich(X)))))&
(?[X]:(~humble(X)))&
(quiet(susan))&
(?[X]:(wise(X)))&
(?[X]:((curious(X)&~quiet(X))))&
(?[X]:((tall(X)&patient(X)))) | calm(mary) | [] | null | 0 |
Everyone who is both not happy and calm is both not kind and humble and vice versa.
Everyone who is both not tall and curious is either wise or old and vice versa.
Everyone who is rich or creative is kind.
Everyone who is both not funny and humble is either creative or not strong.
Everyone who is either not creative or tall is not rich or not curious.
If someone is either not kind or not humble then mary is old or not kind.
Everyone who is patient is either not tall or not strong and vice versa.
If alice is not calm then alice is either old or rich and vice versa.
Everyone who is both kind and not curious is both old and not calm and vice versa.
If fred is not tall then someone is both not old and strong.
Everyone who is brave is either not patient or funny.
Everyone who is both wise and not curious is not curious or old.
If mary is both not happy and humble then paul is not brave and vice versa.
Everyone who is either not wise or strong is wise and vice versa.
If alice is brave or tall then someone is either not tall or patient and vice versa.
Everyone who is both happy and calm is both not kind and wise and vice versa.
Alice is kind.
Fred is not patient.
Lucy is either curious or old.
Susan is not curious or not happy.
Someone is either generous or not strong.
Someone is not patient or strong.
Someone is both tall and not funny. | Alice is not generous. | neutral | (![X]:((~happy(X)&calm(X))<=>(~kind(X)&humble(X))))&
(![X]:((~tall(X)&curious(X))<=>(wise(X)<~>old(X))))&
(![X]:((rich(X)|creative(X))=>kind(X)))&
(![X]:((~funny(X)&humble(X))=>(creative(X)<~>~strong(X))))&
(![X]:((~creative(X)<~>tall(X))=>(~rich(X)|~curious(X))))&
((?[X]:((~kind(X)<~>~humble(X))))=>((old(mary)|~kind(mary))))&
(![X]:(patient(X)<=>(~tall(X)<~>~strong(X))))&
((~calm(alice))<=>((old(alice)<~>rich(alice))))&
(![X]:((kind(X)&~curious(X))<=>(old(X)&~calm(X))))&
((~tall(fred))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(brave(X)=>(~patient(X)<~>funny(X))))&
(![X]:((wise(X)&~curious(X))=>(~curious(X)|old(X))))&
(((~happy(mary)&humble(mary)))<=>(~brave(paul)))&
(![X]:((~wise(X)<~>strong(X))<=>wise(X)))&
(((brave(alice)|tall(alice)))<=>(?[X]:((~tall(X)<~>patient(X)))))&
(![X]:((happy(X)&calm(X))<=>(~kind(X)&wise(X))))&
(kind(alice))&
(~patient(fred))&
((curious(lucy)<~>old(lucy)))&
((~curious(susan)|~happy(susan)))&
(?[X]:((generous(X)<~>~strong(X))))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((tall(X)&~funny(X)))) | ~generous(alice) | [] | null | 0 |
If someone is either not calm or not curious then someone is either strong or not old and vice versa. If someone is not humble or not creative then lucy is both not creative and rich. Everyone who is funny or kind is both not quiet and old. If someone is happy or not calm then someone is not quiet. Everyone who is creative is not wise or not happy. If someone is both not quiet and kind then lucy is either happy or not patient. Everyone who is funny or not humble is humble and vice versa. Everyone who is either quiet or calm is brave or not patient. Everyone who is either not strong or funny is kind and vice versa. Everyone who is both happy and creative is both not rich and brave. Everyone who is not creative or humble is not old or not creative and vice versa. If someone is quiet then someone is both funny and not quiet. If fred is not generous then someone is not strong or not curious. Everyone who is both not happy and not creative is either not quiet or creative. If someone is not old then fred is not quiet or wise. Everyone who is wise is funny or humble. Someone is not strong or not humble. Someone is both generous and not wise. Someone is not wise. Lucy is not quiet. Someone is funny. | Lucy is not creative. | entailment | ((?[X]:((~calm(X)<~>~curious(X))))<=>(?[X]:((strong(X)<~>~old(X)))))&
((?[X]:((~humble(X)|~creative(X))))=>((~creative(lucy)&rich(lucy))))&
(![X]:((funny(X)|kind(X))=>(~quiet(X)&old(X))))&
((?[X]:((happy(X)|~calm(X))))=>(?[X]:(~quiet(X))))&
(![X]:(creative(X)=>(~wise(X)|~happy(X))))&
((?[X]:((~quiet(X)&kind(X))))=>((happy(lucy)<~>~patient(lucy))))&
(![X]:((funny(X)|~humble(X))<=>humble(X)))&
(![X]:((quiet(X)<~>calm(X))=>(brave(X)|~patient(X))))&
(![X]:((~strong(X)<~>funny(X))<=>kind(X)))&
(![X]:((happy(X)&creative(X))=>(~rich(X)&brave(X))))&
(![X]:((~creative(X)|humble(X))<=>(~old(X)|~creative(X))))&
((?[X]:(quiet(X)))=>(?[X]:((funny(X)&~quiet(X)))))&
((~generous(fred))=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((~happy(X)&~creative(X))=>(~quiet(X)<~>creative(X))))&
((?[X]:(~old(X)))=>((~quiet(fred)|wise(fred))))&
(![X]:(wise(X)=>(funny(X)|humble(X))))&
(?[X]:((~strong(X)|~humble(X))))&
(?[X]:((generous(X)&~wise(X))))&
(?[X]:(~wise(X)))&
(~quiet(lucy))&
(?[X]:(funny(X))) | ~creative(lucy) | [
"p2",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8736918998333958411406756
% SZS output start Proof for 8736918998333958411406756
3. ! [X0] : ((kind(X0) | funny(X0)) => (old(X0) & ~quiet(X0))) [input p2]
7. ! [X0] : ((~humble(X0) | funny(X0)) <=> humble(X0)) [input p6]
11. ! [X0] : ((humble(X0) | ~creative(X0)) <=> (~creative(X0) | ~old(X0))) [input p10]
22. creative(lucy) [input hypothesis]
32. ! [X0] : ((old(X0) & ~quiet(X0)) | (~kind(X0) & ~funny(X0))) [ennf transformation 3]
56. ! [X0] : (((~humble(X0) | funny(X0)) | ~humble(X0)) & (humble(X0) | (humble(X0) & ~funny(X0)))) [nnf transformation 7]
57. ! [X0] : ((~humble(X0) | funny(X0) | ~humble(X0)) & (humble(X0) | (humble(X0) & ~funny(X0)))) [flattening 56]
59. ! [X0] : (((humble(X0) | ~creative(X0)) | (creative(X0) & old(X0))) & ((~creative(X0) | ~old(X0)) | (~humble(X0) & creative(X0)))) [nnf transformation 11]
60. ! [X0] : ((humble(X0) | ~creative(X0) | (creative(X0) & old(X0))) & (~creative(X0) | ~old(X0) | (~humble(X0) & creative(X0)))) [flattening 59]
87. ~funny(X0) | old(X0) [cnf transformation 32]
95. humble(X0) | humble(X0) [cnf transformation 57]
96. ~humble(X0) | funny(X0) | ~humble(X0) [cnf transformation 57]
101. ~creative(X0) | ~old(X0) | ~humble(X0) [cnf transformation 60]
115. creative(lucy) [cnf transformation 22]
117. humble(X0) [duplicate literal removal 95]
118. ~humble(X0) | funny(X0) [duplicate literal removal 96]
164. 11 <=> ! [X0] : humble(X0) [avatar definition]
165. humble(X0) <- (11) [avatar component clause 164]
168. 12 <=> creative(lucy) [avatar definition]
169. creative(lucy) <- (12) [avatar component clause 168]
200. 11 [avatar split clause 117,164]
215. 22 <=> ! [X0] : old(X0) [avatar definition]
216. old(X0) <- (22) [avatar component clause 215]
236. 12 [avatar split clause 115,168]
239. funny(X0) <- (11) [resolution 118,165]
241. old(X1) <- (11) [resolution 239,87]
242. 22 | ~11 [avatar split clause 241,164,215]
259. ~old(lucy) | ~humble(lucy) <- (12) [resolution 101,169]
263. ~humble(lucy) <- (12, 22) [subsumption resolution 259,216]
264. $false <- (11, 12, 22) [subsumption resolution 263,165]
265. ~11 | ~12 | ~22 [avatar contradiction clause 264]
266. $false [avatar sat refutation 200,236,242,265]
% SZS output end Proof for 8736918998333958411406756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is calm then susan is either not humble or quiet and vice versa.
Everyone who is happy is both old and happy.
Everyone who is not tall or not strong is not strong or not quiet and vice versa.
If someone is both patient and generous then someone is not rich.
If susan is both not generous and quiet then lucy is not patient and vice versa.
Everyone who is strong or tall is not kind or kind and vice versa.
Everyone who is either funny or wise is not kind or not old.
If someone is not wise then someone is creative or curious.
If someone is either strong or happy then someone is either not wise or not brave and vice versa.
Everyone who is both happy and tall is not wise or not humble and vice versa.
If someone is either not tall or rich then john is generous or not calm.
Everyone who is both not brave and not quiet is wise or not kind.
Everyone who is both not quiet and wise is not kind or not quiet and vice versa.
Everyone who is strong is generous or wise and vice versa.
Everyone who is not kind is either humble or creative and vice versa.
If someone is both happy and not old then someone is humble or not wise.
Someone is not old or not curious.
Someone is not happy or old.
Mary is either creative or not curious.
Mary is not kind.
Lucy is either old or not funny.
Fred is creative or brave.
Alice is both quiet and not strong.
Someone is not old or wise. | Mary is not creative. | entailment | ((calm(fred))<=>((~humble(susan)<~>quiet(susan))))&
(![X]:(happy(X)=>(old(X)&happy(X))))&
(![X]:((~tall(X)|~strong(X))<=>(~strong(X)|~quiet(X))))&
((?[X]:((patient(X)&generous(X))))=>(?[X]:(~rich(X))))&
(((~generous(susan)&quiet(susan)))<=>(~patient(lucy)))&
(![X]:((strong(X)|tall(X))<=>(~kind(X)|kind(X))))&
(![X]:((funny(X)<~>wise(X))=>(~kind(X)|~old(X))))&
((?[X]:(~wise(X)))=>(?[X]:((creative(X)|curious(X)))))&
((?[X]:((strong(X)<~>happy(X))))<=>(?[X]:((~wise(X)<~>~brave(X)))))&
(![X]:((happy(X)&tall(X))<=>(~wise(X)|~humble(X))))&
((?[X]:((~tall(X)<~>rich(X))))=>((generous(john)|~calm(john))))&
(![X]:((~brave(X)&~quiet(X))=>(wise(X)|~kind(X))))&
(![X]:((~quiet(X)&wise(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(strong(X)<=>(generous(X)|wise(X))))&
(![X]:(~kind(X)<=>(humble(X)<~>creative(X))))&
((?[X]:((happy(X)&~old(X))))=>(?[X]:((humble(X)|~wise(X)))))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((~happy(X)|old(X))))&
((creative(mary)<~>~curious(mary)))&
(~kind(mary))&
((old(lucy)<~>~funny(lucy)))&
((creative(fred)|brave(fred)))&
((quiet(alice)&~strong(alice)))&
(?[X]:((~old(X)|wise(X)))) | ~creative(mary) | [
"p2",
"p9",
"p12",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5071726133240160402203445
% SZS output start Proof for 5071726133240160402203445
3. ! [X0] : ((~strong(X0) | ~tall(X0)) <=> (~quiet(X0) | ~strong(X0))) [input p2]
10. ! [X0] : ((tall(X0) & happy(X0)) <=> (~humble(X0) | ~wise(X0))) [input p9]
13. ! [X0] : ((wise(X0) & ~quiet(X0)) <=> (~quiet(X0) | ~kind(X0))) [input p12]
14. ! [X0] : (strong(X0) <=> (wise(X0) | generous(X0))) [input p13]
15. ! [X0] : (~kind(X0) <=> (humble(X0) <~> creative(X0))) [input p14]
20. ~kind(mary) [input p19]
25. creative(mary) [input hypothesis]
41. ! [X0] : (((~strong(X0) | ~tall(X0)) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | (strong(X0) & tall(X0)))) [nnf transformation 3]
42. ! [X0] : ((~strong(X0) | ~tall(X0) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | (strong(X0) & tall(X0)))) [flattening 41]
59. ! [X0] : (((tall(X0) & happy(X0)) | (humble(X0) & wise(X0))) & ((~humble(X0) | ~wise(X0)) | (~tall(X0) | ~happy(X0)))) [nnf transformation 10]
60. ! [X0] : (((tall(X0) & happy(X0)) | (humble(X0) & wise(X0))) & (~humble(X0) | ~wise(X0) | ~tall(X0) | ~happy(X0))) [flattening 59]
62. ! [X0] : (((wise(X0) & ~quiet(X0)) | (quiet(X0) & kind(X0))) & ((~quiet(X0) | ~kind(X0)) | (~wise(X0) | quiet(X0)))) [nnf transformation 13]
63. ! [X0] : (((wise(X0) & ~quiet(X0)) | (quiet(X0) & kind(X0))) & (~quiet(X0) | ~kind(X0) | ~wise(X0) | quiet(X0))) [flattening 62]
64. ! [X0] : ((strong(X0) | (~wise(X0) & ~generous(X0))) & ((wise(X0) | generous(X0)) | ~strong(X0))) [nnf transformation 14]
65. ! [X0] : ((strong(X0) | (~wise(X0) & ~generous(X0))) & (wise(X0) | generous(X0) | ~strong(X0))) [flattening 64]
66. ! [X0] : ((~kind(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) & (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | kind(X0))) [nnf transformation 15]
87. ~strong(X0) | ~tall(X0) | quiet(X0) [cnf transformation 42]
111. tall(X0) | humble(X0) [cnf transformation 60]
116. ~quiet(X0) | kind(X0) [cnf transformation 63]
119. wise(X0) | quiet(X0) [cnf transformation 63]
122. ~wise(X0) | strong(X0) [cnf transformation 65]
124. ~creative(X0) | ~humble(X0) | kind(X0) [cnf transformation 66]
132. ~kind(mary) [cnf transformation 20]
139. creative(mary) [cnf transformation 25]
250. 25 <=> creative(mary) [avatar definition]
251. creative(mary) <- (25) [avatar component clause 250]
287. 25 [avatar split clause 139,250]
291. strong(X0) | quiet(X0) [resolution 122,119]
348. ~humble(mary) | kind(mary) <- (25) [resolution 124,251]
360. ~humble(mary) <- (25) [subsumption resolution 348,132]
419. quiet(X1) | ~tall(X1) | quiet(X1) [resolution 291,87]
422. ~tall(X1) | quiet(X1) [duplicate literal removal 419]
561. quiet(X0) | humble(X0) [resolution 422,111]
721. kind(X1) | humble(X1) [resolution 561,116]
739. humble(mary) [resolution 721,132]
741. $false <- (25) [subsumption resolution 739,360]
742. ~25 [avatar contradiction clause 741]
743. $false [avatar sat refutation 287,742]
% SZS output end Proof for 5071726133240160402203445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then alice is either not happy or rich and vice versa.
If alice is brave or calm then susan is both wise and not generous.
If someone is not rich then someone is wise.
If john is not brave or generous then john is brave.
Everyone who is not curious is both not humble and not wise and vice versa.
If someone is either calm or rich then lucy is not wise or tall.
If someone is both not strong and kind then john is either wise or funny.
If lucy is both not tall and not humble then someone is not quiet.
If john is kind or wise then lucy is not brave and vice versa.
If fred is not patient then someone is old and vice versa.
If someone is not strong or not humble then someone is not quiet or happy.
Everyone who is both generous and not happy is not patient and vice versa.
Everyone who is not kind is wise or rich and vice versa.
Everyone who is both kind and wise is not generous.
If someone is either brave or wise then fred is not humble and vice versa.
Everyone who is either brave or creative is strong or not strong.
Someone is both not curious and patient.
Fred is either not happy or not funny.
Mary is both not wise and tall.
Someone is not patient or humble.
Someone is both not calm and old.
Someone is not quiet.
Fred is not old or not generous.
Lucy is both not brave and not rich. | Fred is funny. | entailment | ((?[X]:(~brave(X)))<=>((~happy(alice)<~>rich(alice))))&
(((brave(alice)|calm(alice)))=>((wise(susan)&~generous(susan))))&
((?[X]:(~rich(X)))=>(?[X]:(wise(X))))&
(((~brave(john)|generous(john)))=>(brave(john)))&
(![X]:(~curious(X)<=>(~humble(X)&~wise(X))))&
((?[X]:((calm(X)<~>rich(X))))=>((~wise(lucy)|tall(lucy))))&
((?[X]:((~strong(X)&kind(X))))=>((wise(john)<~>funny(john))))&
(((~tall(lucy)&~humble(lucy)))=>(?[X]:(~quiet(X))))&
(((kind(john)|wise(john)))<=>(~brave(lucy)))&
((~patient(fred))<=>(?[X]:(old(X))))&
((?[X]:((~strong(X)|~humble(X))))=>(?[X]:((~quiet(X)|happy(X)))))&
(![X]:((generous(X)&~happy(X))<=>~patient(X)))&
(![X]:(~kind(X)<=>(wise(X)|rich(X))))&
(![X]:((kind(X)&wise(X))=>~generous(X)))&
((?[X]:((brave(X)<~>wise(X))))<=>(~humble(fred)))&
(![X]:((brave(X)<~>creative(X))=>(strong(X)|~strong(X))))&
(?[X]:((~curious(X)&patient(X))))&
((~happy(fred)<~>~funny(fred)))&
((~wise(mary)&tall(mary)))&
(?[X]:((~patient(X)|humble(X))))&
(?[X]:((~calm(X)&old(X))))&
(?[X]:(~quiet(X)))&
((~old(fred)|~generous(fred)))&
((~brave(lucy)&~rich(lucy))) | funny(fred) | [
"p9",
"p11",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 121120275998054090182131
% SZS output start Proof for 121120275998054090182131
10. ~patient(fred) <=> ? [X0] : old(X0) [input p9]
12. ! [X0] : ((~happy(X0) & generous(X0)) <=> ~patient(X0)) [input p11]
18. ~happy(fred) <~> ~funny(fred) [input p17]
21. ? [X0] : (old(X0) & ~calm(X0)) [input p20]
25. ~funny(fred) [input hypothesis]
35. ? [X0] : old(X0) [pure predicate removal 21]
55. (~patient(fred) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | patient(fred)) [nnf transformation 10]
56. (~patient(fred) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | patient(fred)) [rectify 55]
57. ? [X1] : old(X1) => old(sK2) [choice axiom]
58. (~patient(fred) | ! [X0] : ~old(X0)) & (old(sK2) | patient(fred)) [skolemisation 56,57]
59. ! [X0] : (((~happy(X0) & generous(X0)) | patient(X0)) & (~patient(X0) | (happy(X0) | ~generous(X0)))) [nnf transformation 12]
60. ! [X0] : (((~happy(X0) & generous(X0)) | patient(X0)) & (~patient(X0) | happy(X0) | ~generous(X0))) [flattening 59]
70. (funny(fred) | happy(fred)) & (~funny(fred) | ~happy(fred)) [nnf transformation 18]
73. ? [X0] : old(X0) => old(sK6) [choice axiom]
74. old(sK6) [skolemisation 35,73]
92. ~patient(fred) | ~old(X0) [cnf transformation 58]
95. ~happy(X0) | patient(X0) [cnf transformation 60]
109. funny(fred) | happy(fred) [cnf transformation 70]
112. old(sK6) [cnf transformation 74]
116. ~funny(fred) [cnf transformation 25]
194. 17 <=> ! [X0] : ~old(X0) [avatar definition]
195. ~old(X0) <- (17) [avatar component clause 194]
197. 18 <=> patient(fred) [avatar definition]
199. ~patient(fred) <- (~18) [avatar component clause 197]
200. 17 | ~18 [avatar split clause 92,197,194]
229. 25 <=> happy(fred) [avatar definition]
231. happy(fred) <- (25) [avatar component clause 229]
233. 26 <=> funny(fred) [avatar definition]
236. 25 | 26 [avatar split clause 109,233,229]
257. ~26 [avatar split clause 116,233]
260. $false <- (17) [resolution 195,112]
261. ~17 [avatar contradiction clause 260]
267. patient(fred) <- (25) [resolution 95,231]
268. $false <- (~18, 25) [subsumption resolution 267,199]
269. 18 | ~25 [avatar contradiction clause 268]
270. $false [avatar sat refutation 200,236,257,261,269]
% SZS output end Proof for 121120275998054090182131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious then paul is not patient or happy and vice versa.
If someone is either not strong or not wise then john is both not patient and funny.
Everyone who is both calm and creative is strong and vice versa.
Everyone who is not calm or patient is not kind and vice versa.
Everyone who is both not rich and not funny is not tall.
If john is either not funny or calm then paul is calm or creative and vice versa.
Everyone who is humble or not funny is both not calm and curious.
If alice is not happy then fred is both not generous and not happy.
If susan is not brave then someone is either rich or not strong and vice versa.
If someone is creative then paul is either not quiet or not funny.
Everyone who is not old is strong or not patient and vice versa.
If someone is generous then someone is either calm or rich.
If mary is both humble and funny then someone is both humble and quiet and vice versa.
Everyone who is either wise or not strong is humble or wise and vice versa.
If john is either not strong or creative then someone is both not strong and quiet and vice versa.
Everyone who is kind is not brave and vice versa.
Lucy is either not wise or creative.
Alice is either patient or rich.
Paul is kind or happy.
Alice is either patient or strong.
Alice is either not strong or not funny.
Someone is both not kind and not generous.
Someone is creative or quiet. | Susan is old. | contradiction | ((?[X]:(~curious(X)))<=>((~patient(paul)|happy(paul))))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~patient(john)&funny(john))))&
(![X]:((calm(X)&creative(X))<=>strong(X)))&
(![X]:((~calm(X)|patient(X))<=>~kind(X)))&
(![X]:((~rich(X)&~funny(X))=>~tall(X)))&
(((~funny(john)<~>calm(john)))<=>((calm(paul)|creative(paul))))&
(![X]:((humble(X)|~funny(X))=>(~calm(X)&curious(X))))&
((~happy(alice))=>((~generous(fred)&~happy(fred))))&
((~brave(susan))<=>(?[X]:((rich(X)<~>~strong(X)))))&
((?[X]:(creative(X)))=>((~quiet(paul)<~>~funny(paul))))&
(![X]:(~old(X)<=>(strong(X)|~patient(X))))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(((humble(mary)&funny(mary)))<=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:((wise(X)<~>~strong(X))<=>(humble(X)|wise(X))))&
(((~strong(john)<~>creative(john)))<=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:(kind(X)<=>~brave(X)))&
((~wise(lucy)<~>creative(lucy)))&
((patient(alice)<~>rich(alice)))&
((kind(paul)|happy(paul)))&
((patient(alice)<~>strong(alice)))&
((~strong(alice)<~>~funny(alice)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((creative(X)|quiet(X)))) | old(susan) | [
"p2",
"p3",
"p6",
"p8",
"p10",
"p15",
"p17",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4106119535333550228361625
% SZS output start Proof for 4106119535333550228361625
3. ! [X0] : ((creative(X0) & calm(X0)) <=> strong(X0)) [input p2]
4. ! [X0] : ((patient(X0) | ~calm(X0)) <=> ~kind(X0)) [input p3]
7. ! [X0] : ((~funny(X0) | humble(X0)) => (curious(X0) & ~calm(X0))) [input p6]
9. ~brave(susan) <=> ? [X0] : (rich(X0) <~> ~strong(X0)) [input p8]
11. ! [X0] : (~old(X0) <=> (~patient(X0) | strong(X0))) [input p10]
16. ! [X0] : (kind(X0) <=> ~brave(X0)) [input p15]
18. patient(alice) <~> rich(alice) [input p17]
20. patient(alice) <~> strong(alice) [input p19]
21. ~strong(alice) <~> ~funny(alice) [input p20]
24. old(susan) [input hypothesis]
26. ! [X0] : ((~patient(X0) | strong(X0)) => ~old(X0)) [unused predicate definition removal 11]
32. ! [X0] : ((curious(X0) & ~calm(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 7]
35. ! [X0] : (~old(X0) | (patient(X0) & ~strong(X0))) [ennf transformation 26]
42. ! [X0] : (((creative(X0) & calm(X0)) | ~strong(X0)) & (strong(X0) | (~creative(X0) | ~calm(X0)))) [nnf transformation 3]
43. ! [X0] : (((creative(X0) & calm(X0)) | ~strong(X0)) & (strong(X0) | ~creative(X0) | ~calm(X0))) [flattening 42]
44. ! [X0] : (((patient(X0) | ~calm(X0)) | kind(X0)) & (~kind(X0) | (~patient(X0) & calm(X0)))) [nnf transformation 4]
45. ! [X0] : ((patient(X0) | ~calm(X0) | kind(X0)) & (~kind(X0) | (~patient(X0) & calm(X0)))) [flattening 44]
48. (~brave(susan) | ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (? [X0] : ((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | brave(susan)) [nnf transformation 9]
49. (~brave(susan) | ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (? [X1] : ((strong(X1) | ~rich(X1)) & (~strong(X1) | rich(X1))) | brave(susan)) [rectify 48]
50. ? [X1] : ((strong(X1) | ~rich(X1)) & (~strong(X1) | rich(X1))) => ((strong(sK1) | ~rich(sK1)) & (~strong(sK1) | rich(sK1))) [choice axiom]
51. (~brave(susan) | ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(sK1) | ~rich(sK1)) & (~strong(sK1) | rich(sK1))) | brave(susan)) [skolemisation 49,50]
64. ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0))) [nnf transformation 16]
66. (~rich(alice) | ~patient(alice)) & (rich(alice) | patient(alice)) [nnf transformation 18]
67. (~strong(alice) | ~patient(alice)) & (strong(alice) | patient(alice)) [nnf transformation 20]
68. (funny(alice) | strong(alice)) & (~funny(alice) | ~strong(alice)) [nnf transformation 21]
81. ~strong(X0) | calm(X0) [cnf transformation 43]
84. ~kind(X0) | ~patient(X0) [cnf transformation 45]
93. ~calm(X0) | funny(X0) [cnf transformation 32]
100. ~brave(susan) | rich(X0) | strong(X0) [cnf transformation 51]
104. ~old(X0) | patient(X0) [cnf transformation 35]
122. brave(X0) | kind(X0) [cnf transformation 64]
126. ~rich(alice) | ~patient(alice) [cnf transformation 66]
128. strong(alice) | patient(alice) [cnf transformation 67]
130. ~funny(alice) | ~strong(alice) [cnf transformation 68]
131. funny(alice) | strong(alice) [cnf transformation 68]
134. old(susan) [cnf transformation 24]
201. 14 <=> ! [X0] : (rich(X0) | strong(X0)) [avatar definition]
202. rich(X0) | strong(X0) <- (14) [avatar component clause 201]
204. 15 <=> brave(susan) [avatar definition]
206. ~brave(susan) <- (~15) [avatar component clause 204]
207. 14 | ~15 [avatar split clause 100,204,201]
298. 34 <=> patient(alice) [avatar definition]
302. 35 <=> rich(alice) [avatar definition]
304. ~rich(alice) <- (~35) [avatar component clause 302]
305. ~34 | ~35 [avatar split clause 126,302,298]
313. 37 <=> strong(alice) [avatar definition]
314. strong(alice) <- (37) [avatar component clause 313]
315. ~strong(alice) <- (~37) [avatar component clause 313]
317. 34 | 37 [avatar split clause 128,313,298]
319. 38 <=> funny(alice) [avatar definition]
320. ~funny(alice) <- (~38) [avatar component clause 319]
322. 37 | 38 [avatar split clause 131,319,313]
323. ~37 | ~38 [avatar split clause 130,319,313]
335. calm(alice) <- (37) [resolution 81,314]
342. funny(alice) <- (37) [resolution 93,335]
344. $false <- (37, ~38) [subsumption resolution 342,320]
345. ~37 | 38 [avatar contradiction clause 344]
352. patient(susan) [resolution 104,134]
353. kind(susan) <- (~15) [resolution 122,206]
355. ~patient(susan) <- (~15) [resolution 353,84]
357. $false <- (~15) [subsumption resolution 355,352]
358. 15 [avatar contradiction clause 357]
361. strong(alice) <- (14, ~35) [resolution 202,304]
364. $false <- (14, ~35, ~37) [subsumption resolution 361,315]
365. ~14 | 35 | 37 [avatar contradiction clause 364]
366. $false [avatar sat refutation 207,305,317,322,323,345,358,365]
% SZS output end Proof for 4106119535333550228361625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or humble is not funny or kind and vice versa.
If someone is brave then mary is brave or wise and vice versa.
Everyone who is not old or funny is either strong or wise and vice versa.
Everyone who is both not rich and not tall is both wise and not strong and vice versa.
Everyone who is either not generous or not happy is both not quiet and not tall and vice versa.
Everyone who is not rich is not strong or patient.
Everyone who is not strong or not old is either not funny or not brave and vice versa.
If someone is both brave and wise then lucy is strong.
Everyone who is not rich or not kind is either not brave or not funny and vice versa.
Everyone who is not kind or not funny is old or funny and vice versa.
If someone is funny then someone is either curious or not kind.
Everyone who is not strong or not funny is either not creative or tall and vice versa.
Everyone who is not tall or patient is both tall and not calm and vice versa.
Everyone who is either not strong or old is either not tall or kind and vice versa.
If john is both strong and not patient then lucy is either not tall or not kind.
Everyone who is not old is both tall and curious and vice versa.
Someone is either not old or not funny.
Someone is both rich and not strong.
Fred is not curious.
Someone is both curious and not old.
Someone is brave.
Someone is old or not old.
Someone is either not creative or not rich.
Lucy is creative or not strong. | John is patient. | neutral | (![X]:((curious(X)<~>humble(X))<=>(~funny(X)|kind(X))))&
((?[X]:(brave(X)))<=>((brave(mary)|wise(mary))))&
(![X]:((~old(X)|funny(X))<=>(strong(X)<~>wise(X))))&
(![X]:((~rich(X)&~tall(X))<=>(wise(X)&~strong(X))))&
(![X]:((~generous(X)<~>~happy(X))<=>(~quiet(X)&~tall(X))))&
(![X]:(~rich(X)=>(~strong(X)|patient(X))))&
(![X]:((~strong(X)|~old(X))<=>(~funny(X)<~>~brave(X))))&
((?[X]:((brave(X)&wise(X))))=>(strong(lucy)))&
(![X]:((~rich(X)|~kind(X))<=>(~brave(X)<~>~funny(X))))&
(![X]:((~kind(X)|~funny(X))<=>(old(X)|funny(X))))&
((?[X]:(funny(X)))=>(?[X]:((curious(X)<~>~kind(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~creative(X)<~>tall(X))))&
(![X]:((~tall(X)|patient(X))<=>(tall(X)&~calm(X))))&
(![X]:((~strong(X)<~>old(X))<=>(~tall(X)<~>kind(X))))&
(((strong(john)&~patient(john)))=>((~tall(lucy)<~>~kind(lucy))))&
(![X]:(~old(X)<=>(tall(X)&curious(X))))&
(?[X]:((~old(X)<~>~funny(X))))&
(?[X]:((rich(X)&~strong(X))))&
(~curious(fred))&
(?[X]:((curious(X)&~old(X))))&
(?[X]:(brave(X)))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~creative(X)<~>~rich(X))))&
((creative(lucy)|~strong(lucy))) | patient(john) | [] | null | 0 |
Everyone who is not patient is not quiet and vice versa. Everyone who is both not happy and curious is either not funny or not patient and vice versa. Everyone who is both not calm and not tall is both kind and not quiet. Everyone who is either not happy or rich is both not curious and curious. Everyone who is either not rich or tall is funny or not happy and vice versa. Everyone who is either not kind or not humble is strong and vice versa. If someone is not old or not funny then lucy is either calm or not creative and vice versa. Everyone who is both not wise and generous is either not brave or not humble. If someone is not humble or not creative then mary is both not brave and not generous and vice versa. If someone is both not funny and not old then susan is both not generous and not quiet and vice versa. If someone is either tall or quiet then paul is both happy and not old and vice versa. If someone is not quiet or strong then someone is both kind and not kind. Everyone who is both not calm and not rich is not funny or not kind. Everyone who is either not rich or generous is both humble and not generous. Everyone who is both quiet and generous is both not generous and not patient and vice versa. If someone is calm or not kind then mary is brave and vice versa. Someone is either kind or not funny. Lucy is tall. Someone is both not happy and not generous. Mary is either not calm or quiet. | Paul is not brave. | neutral | (![X]:(~patient(X)<=>~quiet(X)))&
(![X]:((~happy(X)&curious(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:((~calm(X)&~tall(X))=>(kind(X)&~quiet(X))))&
(![X]:((~happy(X)<~>rich(X))=>(~curious(X)&curious(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(funny(X)|~happy(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>strong(X)))&
((?[X]:((~old(X)|~funny(X))))<=>((calm(lucy)<~>~creative(lucy))))&
(![X]:((~wise(X)&generous(X))=>(~brave(X)<~>~humble(X))))&
((?[X]:((~humble(X)|~creative(X))))<=>((~brave(mary)&~generous(mary))))&
((?[X]:((~funny(X)&~old(X))))<=>((~generous(susan)&~quiet(susan))))&
((?[X]:((tall(X)<~>quiet(X))))<=>((happy(paul)&~old(paul))))&
((?[X]:((~quiet(X)|strong(X))))=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((~calm(X)&~rich(X))=>(~funny(X)|~kind(X))))&
(![X]:((~rich(X)<~>generous(X))=>(humble(X)&~generous(X))))&
(![X]:((quiet(X)&generous(X))<=>(~generous(X)&~patient(X))))&
((?[X]:((calm(X)|~kind(X))))<=>(brave(mary)))&
(?[X]:((kind(X)<~>~funny(X))))&
(tall(lucy))&
(?[X]:((~happy(X)&~generous(X))))&
((~calm(mary)<~>quiet(mary))) | ~brave(paul) | [] | null | 0 |
Everyone who is funny is either not wise or calm and vice versa. If someone is kind or not strong then paul is happy or brave. If susan is either creative or tall then fred is not strong. If fred is quiet or not rich then susan is not happy or not old. Everyone who is rich or not wise is not brave. Everyone who is not strong or not generous is strong. If fred is either not old or kind then someone is strong and vice versa. Everyone who is not brave is both happy and not wise and vice versa. Everyone who is both not wise and rich is either generous or brave and vice versa. If susan is either strong or happy then paul is either patient or not tall and vice versa. Everyone who is brave is either tall or not brave and vice versa. Everyone who is either not humble or not old is both tall and old and vice versa. Everyone who is both patient and calm is humble or not happy. If someone is not creative then susan is not rich or happy. Everyone who is either patient or not wise is rich. If someone is both not curious and not kind then someone is patient and vice versa. Someone is not kind. Someone is both not wise and not creative. John is either tall or generous. Someone is quiet or not kind. Paul is either wise or funny. Lucy is both not creative and not generous. Alice is not funny. Someone is not humble. | Alice is patient. | contradiction | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((kind(X)|~strong(X))))=>((happy(paul)|brave(paul))))&
(((creative(susan)<~>tall(susan)))=>(~strong(fred)))&
(((quiet(fred)|~rich(fred)))=>((~happy(susan)|~old(susan))))&
(![X]:((rich(X)|~wise(X))=>~brave(X)))&
(![X]:((~strong(X)|~generous(X))=>strong(X)))&
(((~old(fred)<~>kind(fred)))<=>(?[X]:(strong(X))))&
(![X]:(~brave(X)<=>(happy(X)&~wise(X))))&
(![X]:((~wise(X)&rich(X))<=>(generous(X)<~>brave(X))))&
(((strong(susan)<~>happy(susan)))<=>((patient(paul)<~>~tall(paul))))&
(![X]:(brave(X)<=>(tall(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(john)<~>generous(john)))&
(?[X]:((quiet(X)|~kind(X))))&
((wise(paul)<~>funny(paul)))&
((~creative(lucy)&~generous(lucy)))&
(~funny(alice))&
(?[X]:(~humble(X))) | patient(alice) | [
"p0",
"p4",
"p7",
"p10",
"p11",
"p12",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 681893205883942903770246
% SZS output start Proof for 681893205883942903770246
1. ! [X0] : (funny(X0) <=> (~wise(X0) <~> calm(X0))) [input p0]
5. ! [X0] : ((~wise(X0) | rich(X0)) => ~brave(X0)) [input p4]
8. ! [X0] : (~brave(X0) <=> (~wise(X0) & happy(X0))) [input p7]
11. ! [X0] : (brave(X0) <=> (tall(X0) <~> ~brave(X0))) [input p10]
12. ! [X0] : ((~humble(X0) <~> ~old(X0)) <=> (old(X0) & tall(X0))) [input p11]
13. ! [X0] : ((calm(X0) & patient(X0)) => (~happy(X0) | humble(X0))) [input p12]
15. ! [X0] : ((patient(X0) <~> ~wise(X0)) => rich(X0)) [input p14]
23. ~funny(alice) [input p22]
25. patient(alice) [input hypothesis]
32. ! [X0] : (~brave(X0) | (wise(X0) & ~rich(X0))) [ennf transformation 5]
34. ! [X0] : ((~happy(X0) | humble(X0)) | (~calm(X0) | ~patient(X0))) [ennf transformation 13]
35. ! [X0] : (~happy(X0) | humble(X0) | ~calm(X0) | ~patient(X0)) [flattening 34]
38. ! [X0] : (rich(X0) | (patient(X0) <=> ~wise(X0))) [ennf transformation 15]
39. ! [X0] : ((funny(X0) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ~funny(X0))) [nnf transformation 1]
45. ! [X0] : ((~brave(X0) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | brave(X0))) [nnf transformation 8]
46. ! [X0] : ((~brave(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | brave(X0))) [flattening 45]
50. ! [X0] : ((brave(X0) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) & (((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | ~brave(X0))) [nnf transformation 11]
51. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (~old(X0) | ~tall(X0))) & ((old(X0) & tall(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [nnf transformation 12]
52. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ~old(X0) | ~tall(X0)) & ((old(X0) & tall(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [flattening 51]
53. ! [X0] : (rich(X0) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0)))) [nnf transformation 38]
71. calm(X0) | funny(X0) | wise(X0) [cnf transformation 39]
79. ~rich(X0) | ~brave(X0) [cnf transformation 32]
80. ~brave(X0) | wise(X0) [cnf transformation 32]
87. brave(X0) | happy(X0) [cnf transformation 46]
88. ~wise(X0) | brave(X0) [cnf transformation 46]
104. ~brave(X0) | tall(X0) | ~brave(X0) [cnf transformation 50]
107. brave(X0) | tall(X0) | brave(X0) [cnf transformation 50]
111. old(X0) | ~humble(X0) | old(X0) [cnf transformation 52]
112. ~old(X0) | ~humble(X0) | ~old(X0) | ~tall(X0) [cnf transformation 52]
114. ~happy(X0) | humble(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 35]
116. ~patient(X0) | ~wise(X0) | rich(X0) [cnf transformation 53]
131. ~funny(alice) [cnf transformation 23]
133. patient(alice) [cnf transformation 25]
134. old(X0) | ~humble(X0) [duplicate literal removal 111]
135. ~old(X0) | ~humble(X0) | ~tall(X0) [duplicate literal removal 112]
136. ~brave(X0) | tall(X0) [duplicate literal removal 104]
137. tall(X0) | brave(X0) [duplicate literal removal 107]
229. tall(X0) [subsumption resolution 136,137]
230. ~humble(X0) | ~old(X0) [subsumption resolution 135,229]
231. ~humble(X0) [subsumption resolution 134,230]
232. ~patient(X0) | ~calm(X0) | ~happy(X0) [subsumption resolution 114,231]
295. happy(X0) | wise(X0) [resolution 87,80]
315. ~wise(alice) | rich(alice) [resolution 116,133]
318. 30 <=> rich(alice) [avatar definition]
320. rich(alice) <- (30) [avatar component clause 318]
322. 31 <=> wise(alice) [avatar definition]
323. wise(alice) <- (31) [avatar component clause 322]
324. ~wise(alice) <- (~31) [avatar component clause 322]
325. 30 | ~31 [avatar split clause 315,322,318]
338. ~calm(alice) | ~happy(alice) [resolution 232,133]
342. 34 <=> happy(alice) [avatar definition]
344. ~happy(alice) <- (~34) [avatar component clause 342]
346. 35 <=> calm(alice) [avatar definition]
348. ~calm(alice) <- (~35) [avatar component clause 346]
349. ~34 | ~35 [avatar split clause 338,346,342]
360. wise(alice) <- (~34) [resolution 344,295]
363. 31 | 34 [avatar split clause 360,342,322]
365. ~brave(alice) <- (30) [resolution 320,79]
367. brave(alice) <- (31) [resolution 323,88]
368. $false <- (30, 31) [subsumption resolution 367,365]
369. ~30 | ~31 [avatar contradiction clause 368]
375. funny(alice) | wise(alice) <- (~35) [resolution 348,71]
376. wise(alice) <- (~35) [subsumption resolution 375,131]
377. $false <- (~31, ~35) [subsumption resolution 376,324]
378. 31 | 35 [avatar contradiction clause 377]
379. $false [avatar sat refutation 325,349,363,369,378]
% SZS output end Proof for 681893205883942903770246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either not quiet or calm and vice versa. If someone is both not tall and not strong then someone is both creative and not tall and vice versa. If someone is both brave and not generous then someone is not brave or not patient. If someone is either funny or not creative then susan is both kind and not rich and vice versa. If someone is not brave then alice is quiet or not calm and vice versa. If someone is both tall and patient then fred is not creative. If paul is not kind or not funny then alice is not strong or brave. If someone is both not funny and not curious then someone is not curious. Everyone who is both not calm and not curious is curious or not old and vice versa. If fred is either curious or generous then someone is either not wise or not quiet. Everyone who is both not happy and happy is not happy or not humble and vice versa. If someone is not old or not wise then someone is not calm or wise and vice versa. Everyone who is curious or kind is both not generous and not calm. If someone is both not creative and calm then someone is both happy and patient and vice versa. If someone is either not calm or funny then someone is rich and vice versa. If paul is either not wise or tall then lucy is not strong or not happy and vice versa. Someone is brave. Alice is not calm. Someone is either brave or strong. Lucy is either not generous or not patient. Mary is quiet. | Lucy is calm. | contradiction | (![X]:(~quiet(X)<=>(~quiet(X)<~>calm(X))))&
((?[X]:((~tall(X)&~strong(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:((brave(X)&~generous(X))))=>(?[X]:((~brave(X)|~patient(X)))))&
((?[X]:((funny(X)<~>~creative(X))))<=>((kind(susan)&~rich(susan))))&
((?[X]:(~brave(X)))<=>((quiet(alice)|~calm(alice))))&
((?[X]:((tall(X)&patient(X))))=>(~creative(fred)))&
(((~kind(paul)|~funny(paul)))=>((~strong(alice)|brave(alice))))&
((?[X]:((~funny(X)&~curious(X))))=>(?[X]:(~curious(X))))&
(![X]:((~calm(X)&~curious(X))<=>(curious(X)|~old(X))))&
(((curious(fred)<~>generous(fred)))=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:((~happy(X)&happy(X))<=>(~happy(X)|~humble(X))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:((~calm(X)|wise(X)))))&
(![X]:((curious(X)|kind(X))=>(~generous(X)&~calm(X))))&
((?[X]:((~creative(X)&calm(X))))<=>(?[X]:((happy(X)&patient(X)))))&
((?[X]:((~calm(X)<~>funny(X))))<=>(?[X]:(rich(X))))&
(((~wise(paul)<~>tall(paul)))<=>((~strong(lucy)|~happy(lucy))))&
(?[X]:(brave(X)))&
(~calm(alice))&
(?[X]:((brave(X)<~>strong(X))))&
((~generous(lucy)<~>~patient(lucy)))&
(quiet(mary)) | calm(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 4054271845260059467891007
% SZS output start Proof for 4054271845260059467891007
1. ! [X0] : (~quiet(X0) <=> (~quiet(X0) <~> calm(X0))) [input p0]
22. calm(lucy) [input hypothesis]
36. ! [X0] : ((~quiet(X0) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) & (((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | quiet(X0))) [nnf transformation 1]
89. ~calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 36]
91. ~quiet(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 36]
153. calm(lucy) [cnf transformation 22]
158. ~calm(X0) | quiet(X0) [duplicate literal removal 89]
159. ~quiet(X0) | ~calm(X0) [duplicate literal removal 91]
160. ~calm(X0) [subsumption resolution 158,159]
330. $false [subsumption resolution 153,160]
% SZS output end Proof for 4054271845260059467891007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or generous is both strong and patient. Everyone who is both tall and not creative is either not strong or wise. Everyone who is brave is quiet and vice versa. Everyone who is humble is not wise. If paul is either tall or curious then paul is not strong and vice versa. If alice is either humble or not kind then alice is not patient. If someone is either curious or happy then mary is both not strong and kind. Everyone who is either funny or wise is not rich. Everyone who is tall is either wise or not funny and vice versa. Everyone who is both brave and kind is both not curious and wise. If someone is either rich or not wise then someone is wise and vice versa. If john is not creative or not generous then someone is either wise or old and vice versa. If someone is either kind or curious then lucy is either wise or not rich and vice versa. Everyone who is not happy or humble is both not strong and not wise and vice versa. Everyone who is either brave or creative is either not rich or rich and vice versa. Everyone who is humble is either not wise or not curious and vice versa. John is humble. Lucy is not calm or humble. Someone is both not rich and tall. Lucy is either creative or generous. John is either not funny or not strong. Mary is both rich and not calm. Someone is not happy. | Paul is not calm. | neutral | (![X]:((brave(X)|generous(X))=>(strong(X)&patient(X))))&
(![X]:((tall(X)&~creative(X))=>(~strong(X)<~>wise(X))))&
(![X]:(brave(X)<=>quiet(X)))&
(![X]:(humble(X)=>~wise(X)))&
(((tall(paul)<~>curious(paul)))<=>(~strong(paul)))&
(((humble(alice)<~>~kind(alice)))=>(~patient(alice)))&
((?[X]:((curious(X)<~>happy(X))))=>((~strong(mary)&kind(mary))))&
(![X]:((funny(X)<~>wise(X))=>~rich(X)))&
(![X]:(tall(X)<=>(wise(X)<~>~funny(X))))&
(![X]:((brave(X)&kind(X))=>(~curious(X)&wise(X))))&
((?[X]:((rich(X)<~>~wise(X))))<=>(?[X]:(wise(X))))&
(((~creative(john)|~generous(john)))<=>(?[X]:((wise(X)<~>old(X)))))&
((?[X]:((kind(X)<~>curious(X))))<=>((wise(lucy)<~>~rich(lucy))))&
(![X]:((~happy(X)|humble(X))<=>(~strong(X)&~wise(X))))&
(![X]:((brave(X)<~>creative(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(humble(X)<=>(~wise(X)<~>~curious(X))))&
(humble(john))&
((~calm(lucy)|humble(lucy)))&
(?[X]:((~rich(X)&tall(X))))&
((creative(lucy)<~>generous(lucy)))&
((~funny(john)<~>~strong(john)))&
((rich(mary)&~calm(mary)))&
(?[X]:(~happy(X))) | ~calm(paul) | [] | null | 0 |
If someone is humble or rich then someone is both old and not wise. If susan is either not quiet or not calm then john is brave. Everyone who is both not curious and quiet is both not generous and happy and vice versa. Everyone who is not old or not wise is not old and vice versa. Everyone who is both not patient and not humble is both not creative and not happy and vice versa. If fred is either kind or patient then alice is creative and vice versa. If paul is either not calm or calm then mary is either not old or generous. Everyone who is both not rich and old is either not tall or calm and vice versa. If someone is not generous then alice is happy or curious. If fred is either not funny or funny then someone is old or funny and vice versa. If fred is patient then someone is either not rich or not calm and vice versa. If alice is not kind or not happy then susan is quiet. Everyone who is both happy and humble is creative or not old. Everyone who is kind or patient is rich. Everyone who is not curious is either funny or not patient and vice versa. Everyone who is either not generous or not creative is quiet and vice versa. Lucy is either creative or generous. Someone is either not happy or not curious. Someone is both not generous and not brave. Fred is either not tall or humble. Someone is not strong. | Paul is rich. | contradiction | ((?[X]:((humble(X)|rich(X))))=>(?[X]:((old(X)&~wise(X)))))&
(((~quiet(susan)<~>~calm(susan)))=>(brave(john)))&
(![X]:((~curious(X)&quiet(X))<=>(~generous(X)&happy(X))))&
(![X]:((~old(X)|~wise(X))<=>~old(X)))&
(![X]:((~patient(X)&~humble(X))<=>(~creative(X)&~happy(X))))&
(((kind(fred)<~>patient(fred)))<=>(creative(alice)))&
(((~calm(paul)<~>calm(paul)))=>((~old(mary)<~>generous(mary))))&
(![X]:((~rich(X)&old(X))<=>(~tall(X)<~>calm(X))))&
((?[X]:(~generous(X)))=>((happy(alice)|curious(alice))))&
(((~funny(fred)<~>funny(fred)))<=>(?[X]:((old(X)|funny(X)))))&
((patient(fred))<=>(?[X]:((~rich(X)<~>~calm(X)))))&
(((~kind(alice)|~happy(alice)))=>(quiet(susan)))&
(![X]:((happy(X)&humble(X))=>(creative(X)|~old(X))))&
(![X]:((kind(X)|patient(X))=>rich(X)))&
(![X]:(~curious(X)<=>(funny(X)<~>~patient(X))))&
(![X]:((~generous(X)<~>~creative(X))<=>quiet(X)))&
((creative(lucy)<~>generous(lucy)))&
(?[X]:((~happy(X)<~>~curious(X))))&
(?[X]:((~generous(X)&~brave(X))))&
((~tall(fred)<~>humble(fred)))&
(?[X]:(~strong(X))) | rich(paul) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 790293372406256823094848
% SZS output start Proof for 790293372406256823094848
1. ? [X0] : (rich(X0) | humble(X0)) => ? [X0] : (~wise(X0) & old(X0)) [input p0]
4. ! [X0] : ((~wise(X0) | ~old(X0)) <=> ~old(X0)) [input p3]
22. rich(paul) [input hypothesis]
23. ? [X0] : (rich(X0) | humble(X0)) => ? [X1] : (~wise(X1) & old(X1)) [rectify 1]
25. ? [X1] : (~wise(X1) & old(X1)) | ! [X0] : (~rich(X0) & ~humble(X0)) [ennf transformation 23]
34. ? [X0] : (~wise(X0) & old(X0)) | ! [X1] : (~rich(X1) & ~humble(X1)) [rectify 25]
35. ? [X0] : (~wise(X0) & old(X0)) => (~wise(sK0) & old(sK0)) [choice axiom]
36. (~wise(sK0) & old(sK0)) | ! [X1] : (~rich(X1) & ~humble(X1)) [skolemisation 34,35]
40. ! [X0] : (((~wise(X0) | ~old(X0)) | old(X0)) & (~old(X0) | (wise(X0) & old(X0)))) [nnf transformation 4]
41. ! [X0] : ((~wise(X0) | ~old(X0) | old(X0)) & (~old(X0) | (wise(X0) & old(X0)))) [flattening 40]
66. old(sK0) | ~rich(X1) [cnf transformation 36]
68. ~wise(sK0) | ~rich(X1) [cnf transformation 36]
76. ~old(X0) | wise(X0) [cnf transformation 41]
128. rich(paul) [cnf transformation 22]
136. 1 <=> ! [X1] : ~rich(X1) [avatar definition]
137. ~rich(X1) <- (1) [avatar component clause 136]
139. 2 <=> wise(sK0) [avatar definition]
142. 1 | ~2 [avatar split clause 68,139,136]
148. 4 <=> old(sK0) [avatar definition]
150. old(sK0) <- (4) [avatar component clause 148]
151. 1 | 4 [avatar split clause 66,148,136]
282. wise(sK0) <- (4) [resolution 76,150]
286. 2 | ~4 [avatar split clause 282,148,139]
287. $false <- (1) [resolution 137,128]
288. ~1 [avatar contradiction clause 287]
289. $false [avatar sat refutation 142,151,286,288]
% SZS output end Proof for 790293372406256823094848
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is both not humble and tall and vice versa.
If john is both not creative and quiet then paul is strong or brave.
If lucy is either strong or not quiet then mary is not happy or not rich and vice versa.
If someone is both not generous and rich then paul is not tall or not creative and vice versa.
Everyone who is either not creative or calm is both not happy and happy and vice versa.
If john is not wise or not calm then fred is both not creative and not rich and vice versa.
Everyone who is old or not tall is not generous or not brave.
Everyone who is either not tall or not patient is either strong or not strong and vice versa.
If someone is either not kind or not rich then mary is either not generous or tall.
Everyone who is either strong or not curious is both not happy and creative and vice versa.
Everyone who is either not quiet or strong is wise or curious.
Everyone who is happy or not humble is either not curious or not patient.
Everyone who is kind is either not generous or brave and vice versa.
If fred is either strong or happy then alice is both strong and rich and vice versa.
Everyone who is both not generous and not kind is happy.
If john is not brave then someone is either strong or not funny.
Fred is either curious or happy.
Someone is either not strong or creative.
Someone is either strong or not kind.
Fred is either not funny or not rich.
Someone is both not patient and rich. | John is humble. | entailment | (![X]:(patient(X)<=>(~humble(X)&tall(X))))&
(((~creative(john)&quiet(john)))=>((strong(paul)|brave(paul))))&
(((strong(lucy)<~>~quiet(lucy)))<=>((~happy(mary)|~rich(mary))))&
((?[X]:((~generous(X)&rich(X))))<=>((~tall(paul)|~creative(paul))))&
(![X]:((~creative(X)<~>calm(X))<=>(~happy(X)&happy(X))))&
(((~wise(john)|~calm(john)))<=>((~creative(fred)&~rich(fred))))&
(![X]:((old(X)|~tall(X))=>(~generous(X)|~brave(X))))&
(![X]:((~tall(X)<~>~patient(X))<=>(strong(X)<~>~strong(X))))&
((?[X]:((~kind(X)<~>~rich(X))))=>((~generous(mary)<~>tall(mary))))&
(![X]:((strong(X)<~>~curious(X))<=>(~happy(X)&creative(X))))&
(![X]:((~quiet(X)<~>strong(X))=>(wise(X)|curious(X))))&
(![X]:((happy(X)|~humble(X))=>(~curious(X)<~>~patient(X))))&
(![X]:(kind(X)<=>(~generous(X)<~>brave(X))))&
(((strong(fred)<~>happy(fred)))<=>((strong(alice)&rich(alice))))&
(![X]:((~generous(X)&~kind(X))=>happy(X)))&
((~brave(john))=>(?[X]:((strong(X)<~>~funny(X)))))&
((curious(fred)<~>happy(fred)))&
(?[X]:((~strong(X)<~>creative(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
((~funny(fred)<~>~rich(fred)))&
(?[X]:((~patient(X)&rich(X)))) | humble(john) | [
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6541103302935906245543372
% SZS output start Proof for 6541103302935906245543372
1. ! [X0] : (patient(X0) <=> (tall(X0) & ~humble(X0))) [input p0]
8. ! [X0] : ((~tall(X0) <~> ~patient(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p7]
22. ~humble(john) [input hypothesis]
35. ! [X0] : ((patient(X0) | (~tall(X0) | humble(X0))) & ((tall(X0) & ~humble(X0)) | ~patient(X0))) [nnf transformation 1]
36. ! [X0] : ((patient(X0) | ~tall(X0) | humble(X0)) & ((tall(X0) & ~humble(X0)) | ~patient(X0))) [flattening 35]
48. ! [X0] : ((((patient(X0) | tall(X0)) & (~patient(X0) | ~tall(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0))))) [nnf transformation 8]
71. ~patient(X0) | tall(X0) [cnf transformation 36]
72. ~tall(X0) | patient(X0) | humble(X0) [cnf transformation 36]
101. ~patient(X0) | ~tall(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 48]
102. ~patient(X0) | ~tall(X0) | strong(X0) | strong(X0) [cnf transformation 48]
103. patient(X0) | tall(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 48]
104. patient(X0) | tall(X0) | strong(X0) | strong(X0) [cnf transformation 48]
144. ~humble(john) [cnf transformation 22]
145. ~patient(X0) | ~tall(X0) | ~strong(X0) [duplicate literal removal 101]
146. ~patient(X0) | ~tall(X0) | strong(X0) [duplicate literal removal 102]
147. patient(X0) | tall(X0) | ~strong(X0) [duplicate literal removal 103]
148. patient(X0) | tall(X0) | strong(X0) [duplicate literal removal 104]
235. strong(X0) | tall(X0) [subsumption resolution 148,71]
236. tall(X0) | ~strong(X0) [subsumption resolution 147,71]
237. tall(X0) [subsumption resolution 236,235]
238. ~patient(X0) | strong(X0) [subsumption resolution 146,237]
239. ~patient(X0) | ~strong(X0) [subsumption resolution 145,237]
240. ~patient(X0) [subsumption resolution 239,238]
332. patient(X0) | humble(X0) [resolution 72,237]
333. humble(X0) [subsumption resolution 332,240]
335. $false [resolution 333,144]
% SZS output end Proof for 6541103302935906245543372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or brave is not brave.
Everyone who is not wise or not happy is not kind or not funny.
Everyone who is either generous or not wise is either humble or not tall and vice versa.
If susan is both not strong and not brave then lucy is both not kind and brave and vice versa.
If mary is not rich or kind then someone is not funny or wise.
If someone is not humble or patient then lucy is tall or happy.
Everyone who is both creative and not old is creative and vice versa.
Everyone who is both funny and not generous is calm and vice versa.
If alice is funny then someone is rich and vice versa.
Everyone who is generous or happy is both generous and kind.
Everyone who is either not kind or generous is both quiet and not strong and vice versa.
Everyone who is not humble or funny is either creative or funny.
If susan is not rich or not creative then john is either not calm or not brave and vice versa.
Everyone who is both not kind and not rich is happy or not patient and vice versa.
Someone is both tall and patient.
Alice is patient or not creative.
Alice is either not patient or tall.
Someone is not funny or not tall.
Someone is both creative and not brave.
Susan is not quiet. | Susan is funny. | contradiction | (![X]:((~tall(X)|brave(X))=>~brave(X)))&
(![X]:((~wise(X)|~happy(X))=>(~kind(X)|~funny(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(humble(X)<~>~tall(X))))&
(((~strong(susan)&~brave(susan)))<=>((~kind(lucy)&brave(lucy))))&
(((~rich(mary)|kind(mary)))=>(?[X]:((~funny(X)|wise(X)))))&
((?[X]:((~humble(X)|patient(X))))=>((tall(lucy)|happy(lucy))))&
(![X]:((creative(X)&~old(X))<=>creative(X)))&
(![X]:((funny(X)&~generous(X))<=>calm(X)))&
((funny(alice))<=>(?[X]:(rich(X))))&
(![X]:((generous(X)|happy(X))=>(generous(X)&kind(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(quiet(X)&~strong(X))))&
(![X]:((~humble(X)|funny(X))=>(creative(X)<~>funny(X))))&
(((~rich(susan)|~creative(susan)))<=>((~calm(john)<~>~brave(john))))&
(![X]:((~kind(X)&~rich(X))<=>(happy(X)|~patient(X))))&
(?[X]:((tall(X)&patient(X))))&
((patient(alice)|~creative(alice)))&
((~patient(alice)<~>tall(alice)))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((creative(X)&~brave(X))))&
(~quiet(susan)) | funny(susan) | [
"p0",
"p1",
"p3",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6003313122840853414521700
% SZS output start Proof for 6003313122840853414521700
1. ! [X0] : ((brave(X0) | ~tall(X0)) => ~brave(X0)) [input p0]
2. ! [X0] : ((~happy(X0) | ~wise(X0)) => (~funny(X0) | ~kind(X0))) [input p1]
4. (~brave(susan) & ~strong(susan)) <=> (brave(lucy) & ~kind(lucy)) [input p3]
10. ! [X0] : ((happy(X0) | generous(X0)) => (kind(X0) & generous(X0))) [input p9]
11. ! [X0] : ((~kind(X0) <~> generous(X0)) <=> (~strong(X0) & quiet(X0))) [input p10]
14. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (~patient(X0) | happy(X0))) [input p13]
21. funny(susan) [input hypothesis]
22. ! [X0] : (~brave(X0) | (~brave(X0) & tall(X0))) [ennf transformation 1]
23. ! [X0] : ((~funny(X0) | ~kind(X0)) | (happy(X0) & wise(X0))) [ennf transformation 2]
24. ! [X0] : (~funny(X0) | ~kind(X0) | (happy(X0) & wise(X0))) [flattening 23]
28. ! [X0] : ((kind(X0) & generous(X0)) | (~happy(X0) & ~generous(X0))) [ennf transformation 10]
31. ((~brave(susan) & ~strong(susan)) | (~brave(lucy) | kind(lucy))) & ((brave(lucy) & ~kind(lucy)) | (brave(susan) | strong(susan))) [nnf transformation 4]
32. ((~brave(susan) & ~strong(susan)) | ~brave(lucy) | kind(lucy)) & ((brave(lucy) & ~kind(lucy)) | brave(susan) | strong(susan)) [flattening 31]
43. ! [X0] : ((((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (strong(X0) | ~quiet(X0))) & ((~strong(X0) & quiet(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))))) [nnf transformation 11]
44. ! [X0] : ((((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | strong(X0) | ~quiet(X0)) & ((~strong(X0) & quiet(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))))) [flattening 43]
48. ! [X0] : (((~rich(X0) & ~kind(X0)) | (patient(X0) & ~happy(X0))) & ((~patient(X0) | happy(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 14]
49. ! [X0] : (((~rich(X0) & ~kind(X0)) | (patient(X0) & ~happy(X0))) & (~patient(X0) | happy(X0) | rich(X0) | kind(X0))) [flattening 48]
58. ~brave(X0) | ~brave(X0) [cnf transformation 22]
60. ~funny(X0) | ~kind(X0) | happy(X0) [cnf transformation 24]
70. brave(lucy) | brave(susan) | strong(susan) [cnf transformation 32]
87. ~generous(X0) | kind(X0) [cnf transformation 28]
88. ~happy(X0) | kind(X0) [cnf transformation 28]
91. ~strong(X0) | generous(X0) | kind(X0) [cnf transformation 44]
92. ~strong(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 44]
106. ~kind(X0) | ~happy(X0) [cnf transformation 49]
119. funny(susan) [cnf transformation 21]
121. ~brave(X0) [duplicate literal removal 58]
122. brave(susan) | strong(susan) [subsumption resolution 70,121]
123. strong(susan) [subsumption resolution 122,121]
171. ~strong(X0) | ~generous(X0) [subsumption resolution 92,87]
172. ~strong(X0) | kind(X0) [subsumption resolution 91,171]
193. ~happy(X0) [subsumption resolution 106,88]
223. kind(susan) [resolution 172,123]
238. ~kind(susan) | happy(susan) [resolution 60,119]
240. happy(susan) [subsumption resolution 238,223]
241. $false [subsumption resolution 240,193]
% SZS output end Proof for 6003313122840853414521700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both generous and not wise then someone is either rich or funny and vice versa. Everyone who is kind is wise or calm and vice versa. Everyone who is not patient or not wise is both funny and not rich and vice versa. Everyone who is either happy or tall is both not kind and strong. Everyone who is either kind or old is either tall or not creative and vice versa. Everyone who is both not humble and wise is both not curious and not old and vice versa. If fred is kind then someone is either not strong or funny. If someone is not curious then someone is either rich or not tall and vice versa. If someone is both not quiet and creative then susan is both not curious and strong. If paul is not curious then someone is not calm and vice versa. If susan is not quiet or not kind then lucy is both funny and rich. Everyone who is either happy or old is either not patient or rich. Everyone who is tall or not curious is both brave and patient and vice versa. Everyone who is both not happy and creative is old or not curious. If susan is not wise then someone is both kind and not wise and vice versa. If mary is both not kind and not funny then someone is both generous and not old. Someone is old. Mary is calm or brave. Someone is either patient or not happy. Someone is not calm. Paul is both not generous and not funny. Someone is either not creative or humble. Susan is patient. Someone is both not strong and curious. | Lucy is funny. | neutral | ((?[X]:((generous(X)&~wise(X))))<=>(?[X]:((rich(X)<~>funny(X)))))&
(![X]:(kind(X)<=>(wise(X)|calm(X))))&
(![X]:((~patient(X)|~wise(X))<=>(funny(X)&~rich(X))))&
(![X]:((happy(X)<~>tall(X))=>(~kind(X)&strong(X))))&
(![X]:((kind(X)<~>old(X))<=>(tall(X)<~>~creative(X))))&
(![X]:((~humble(X)&wise(X))<=>(~curious(X)&~old(X))))&
((kind(fred))=>(?[X]:((~strong(X)<~>funny(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((rich(X)<~>~tall(X)))))&
((?[X]:((~quiet(X)&creative(X))))=>((~curious(susan)&strong(susan))))&
((~curious(paul))<=>(?[X]:(~calm(X))))&
(((~quiet(susan)|~kind(susan)))=>((funny(lucy)&rich(lucy))))&
(![X]:((happy(X)<~>old(X))=>(~patient(X)<~>rich(X))))&
(![X]:((tall(X)|~curious(X))<=>(brave(X)&patient(X))))&
(![X]:((~happy(X)&creative(X))=>(old(X)|~curious(X))))&
((~wise(susan))<=>(?[X]:((kind(X)&~wise(X)))))&
(((~kind(mary)&~funny(mary)))=>(?[X]:((generous(X)&~old(X)))))&
(?[X]:(old(X)))&
((calm(mary)|brave(mary)))&
(?[X]:((patient(X)<~>~happy(X))))&
(?[X]:(~calm(X)))&
((~generous(paul)&~funny(paul)))&
(?[X]:((~creative(X)<~>humble(X))))&
(patient(susan))&
(?[X]:((~strong(X)&curious(X)))) | funny(lucy) | [] | null | 0 |
Everyone who is either generous or wise is either not humble or not brave.
Everyone who is either not funny or strong is either not patient or rich and vice versa.
Everyone who is either funny or humble is brave or happy and vice versa.
Everyone who is brave is not funny and vice versa.
If someone is both not rich and not creative then someone is both curious and old and vice versa.
Everyone who is either not rich or funny is calm or not curious.
If someone is both not curious and not generous then someone is not generous or old.
If someone is either wise or not old then mary is either not humble or patient and vice versa.
Everyone who is curious is either quiet or not calm and vice versa.
If someone is either not curious or tall then someone is curious.
Everyone who is both happy and calm is humble or tall and vice versa.
Everyone who is rich is both quiet and wise and vice versa.
Everyone who is humble is not generous or not creative and vice versa.
If fred is both humble and not brave then someone is not curious or not patient and vice versa.
Everyone who is not funny is both not generous and not strong and vice versa.
If someone is both brave and creative then someone is patient or not patient.
Someone is not funny or quiet.
Someone is both not kind and wise.
Fred is not strong.
Paul is not quiet.
Someone is not quiet.
Someone is calm.
Someone is not happy or not humble. | Mary is not brave. | entailment | (![X]:((generous(X)<~>wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((~funny(X)<~>strong(X))<=>(~patient(X)<~>rich(X))))&
(![X]:((funny(X)<~>humble(X))<=>(brave(X)|happy(X))))&
(![X]:(brave(X)<=>~funny(X)))&
((?[X]:((~rich(X)&~creative(X))))<=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~rich(X)<~>funny(X))=>(calm(X)|~curious(X))))&
((?[X]:((~curious(X)&~generous(X))))=>(?[X]:((~generous(X)|old(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>((~humble(mary)<~>patient(mary))))&
(![X]:(curious(X)<=>(quiet(X)<~>~calm(X))))&
((?[X]:((~curious(X)<~>tall(X))))=>(?[X]:(curious(X))))&
(![X]:((happy(X)&calm(X))<=>(humble(X)|tall(X))))&
(![X]:(rich(X)<=>(quiet(X)&wise(X))))&
(![X]:(humble(X)<=>(~generous(X)|~creative(X))))&
(((humble(fred)&~brave(fred)))<=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:(~funny(X)<=>(~generous(X)&~strong(X))))&
((?[X]:((brave(X)&creative(X))))=>(?[X]:((patient(X)|~patient(X)))))&
(?[X]:((~funny(X)|quiet(X))))&
(?[X]:((~kind(X)&wise(X))))&
(~strong(fred))&
(~quiet(paul))&
(?[X]:(~quiet(X)))&
(?[X]:(calm(X)))&
(?[X]:((~happy(X)|~humble(X)))) | ~brave(mary) | [
"p0",
"p1",
"p2",
"p3",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 111957779264235096457434
% SZS output start Proof for 111957779264235096457434
1. ! [X0] : ((generous(X0) <~> wise(X0)) => (~humble(X0) <~> ~brave(X0))) [input p0]
2. ! [X0] : ((~funny(X0) <~> strong(X0)) <=> (~patient(X0) <~> rich(X0))) [input p1]
3. ! [X0] : ((funny(X0) <~> humble(X0)) <=> (happy(X0) | brave(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> ~funny(X0)) [input p3]
11. ! [X0] : ((calm(X0) & happy(X0)) <=> (tall(X0) | humble(X0))) [input p10]
12. ! [X0] : (rich(X0) <=> (wise(X0) & quiet(X0))) [input p11]
13. ! [X0] : (humble(X0) <=> (~creative(X0) | ~generous(X0))) [input p12]
14. (~brave(fred) & humble(fred)) <=> ? [X0] : (~patient(X0) | ~curious(X0)) [input p13]
15. ! [X0] : (~funny(X0) <=> (~strong(X0) & ~generous(X0))) [input p14]
24. brave(mary) [input hypothesis]
30. ! [X0] : ((~humble(X0) <~> ~brave(X0)) | (generous(X0) <=> wise(X0))) [ennf transformation 1]
36. ! [X0] : (((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0)))) [nnf transformation 30]
37. ! [X0] : ((((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) & (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | ((~funny(X0) | ~strong(X0)) & (strong(X0) | funny(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [nnf transformation 3]
39. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [flattening 38]
40. ! [X0] : ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))) [nnf transformation 4]
59. ! [X0] : (((calm(X0) & happy(X0)) | (~tall(X0) & ~humble(X0))) & ((tall(X0) | humble(X0)) | (~calm(X0) | ~happy(X0)))) [nnf transformation 11]
60. ! [X0] : (((calm(X0) & happy(X0)) | (~tall(X0) & ~humble(X0))) & (tall(X0) | humble(X0) | ~calm(X0) | ~happy(X0))) [flattening 59]
61. ! [X0] : ((rich(X0) | (~wise(X0) | ~quiet(X0))) & ((wise(X0) & quiet(X0)) | ~rich(X0))) [nnf transformation 12]
62. ! [X0] : ((rich(X0) | ~wise(X0) | ~quiet(X0)) & ((wise(X0) & quiet(X0)) | ~rich(X0))) [flattening 61]
63. ! [X0] : ((humble(X0) | (creative(X0) & generous(X0))) & ((~creative(X0) | ~generous(X0)) | ~humble(X0))) [nnf transformation 13]
64. ! [X0] : ((humble(X0) | (creative(X0) & generous(X0))) & (~creative(X0) | ~generous(X0) | ~humble(X0))) [flattening 63]
65. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X0] : (~patient(X0) | ~curious(X0)) | (brave(fred) | ~humble(fred))) [nnf transformation 14]
66. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X0] : (~patient(X0) | ~curious(X0)) | brave(fred) | ~humble(fred)) [flattening 65]
67. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X1] : (~patient(X1) | ~curious(X1)) | brave(fred) | ~humble(fred)) [rectify 66]
68. ? [X1] : (~patient(X1) | ~curious(X1)) => (~patient(sK5) | ~curious(sK5)) [choice axiom]
69. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & ((~patient(sK5) | ~curious(sK5)) | brave(fred) | ~humble(fred)) [skolemisation 67,68]
70. ! [X0] : ((~funny(X0) | (strong(X0) | generous(X0))) & ((~strong(X0) & ~generous(X0)) | funny(X0))) [nnf transformation 15]
71. ! [X0] : ((~funny(X0) | strong(X0) | generous(X0)) & ((~strong(X0) & ~generous(X0)) | funny(X0))) [flattening 70]
86. ~brave(X0) | ~humble(X0) | generous(X0) | ~wise(X0) [cnf transformation 36]
89. ~patient(X0) | rich(X0) | strong(X0) | funny(X0) [cnf transformation 37]
102. ~happy(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 39]
103. ~funny(X0) | ~brave(X0) [cnf transformation 40]
104. funny(X0) | brave(X0) [cnf transformation 40]
127. ~humble(X0) | happy(X0) [cnf transformation 60]
132. ~rich(X0) | wise(X0) [cnf transformation 62]
135. humble(X0) | generous(X0) [cnf transformation 64]
139. humble(fred) | patient(X0) [cnf transformation 69]
141. ~brave(fred) | patient(X0) [cnf transformation 69]
142. ~generous(X0) | funny(X0) [cnf transformation 71]
143. ~strong(X0) | funny(X0) [cnf transformation 71]
153. brave(mary) [cnf transformation 24]
193. 10 <=> patient(mary) [avatar definition]
194. patient(mary) <- (10) [avatar component clause 193]
195. ~patient(mary) <- (~10) [avatar component clause 193]
197. 11 <=> humble(mary) [avatar definition]
198. humble(mary) <- (11) [avatar component clause 197]
199. ~humble(mary) <- (~11) [avatar component clause 197]
235. 19 <=> ! [X0] : patient(X0) [avatar definition]
236. patient(X0) <- (19) [avatar component clause 235]
238. 20 <=> brave(fred) [avatar definition]
240. ~brave(fred) <- (~20) [avatar component clause 238]
241. 19 | ~20 [avatar split clause 141,238,235]
247. 22 <=> humble(fred) [avatar definition]
249. humble(fred) <- (22) [avatar component clause 247]
250. 19 | 22 [avatar split clause 139,247,235]
271. $false <- (~10, 19) [subsumption resolution 195,236]
272. 10 | ~19 [avatar contradiction clause 271]
278. happy(fred) <- (22) [resolution 127,249]
303. ~funny(fred) | ~humble(fred) <- (22) [resolution 102,278]
305. ~funny(fred) <- (22) [subsumption resolution 303,249]
348. brave(fred) <- (22) [resolution 305,104]
349. $false <- (~20, 22) [subsumption resolution 348,240]
350. 20 | ~22 [avatar contradiction clause 349]
410. 40 <=> generous(mary) [avatar definition]
411. generous(mary) <- (40) [avatar component clause 410]
412. ~generous(mary) <- (~40) [avatar component clause 410]
414. 41 <=> wise(mary) [avatar definition]
420. ~humble(mary) | generous(mary) | ~wise(mary) [resolution 86,153]
435. 42 <=> funny(mary) [avatar definition]
436. ~funny(mary) <- (~42) [avatar component clause 435]
437. funny(mary) <- (42) [avatar component clause 435]
439. generous(mary) <- (~11) [resolution 199,135]
440. $false <- (~11, ~40) [subsumption resolution 439,412]
441. 11 | 40 [avatar contradiction clause 440]
451. ~brave(mary) <- (42) [resolution 437,103]
456. $false <- (42) [subsumption resolution 451,153]
457. ~42 [avatar contradiction clause 456]
459. rich(mary) | strong(mary) | funny(mary) <- (10) [resolution 89,194]
462. rich(mary) | strong(mary) <- (10, ~42) [subsumption resolution 459,436]
464. 43 <=> strong(mary) [avatar definition]
466. strong(mary) <- (43) [avatar component clause 464]
468. 44 <=> rich(mary) [avatar definition]
470. rich(mary) <- (44) [avatar component clause 468]
471. 43 | 44 | ~10 | 42 [avatar split clause 462,435,193,468,464]
480. funny(mary) <- (43) [resolution 466,143]
481. $false <- (~42, 43) [subsumption resolution 480,436]
482. 42 | ~43 [avatar contradiction clause 481]
487. wise(mary) <- (44) [resolution 470,132]
493. 41 | ~44 [avatar split clause 487,468,414]
494. generous(mary) | ~wise(mary) <- (11) [subsumption resolution 420,198]
495. ~41 | 40 | ~11 [avatar split clause 494,197,410,414]
498. funny(mary) <- (40) [resolution 411,142]
499. $false <- (40, ~42) [subsumption resolution 498,436]
500. ~40 | 42 [avatar contradiction clause 499]
501. $false [avatar sat refutation 241,250,272,350,441,457,471,482,493,495,500]
% SZS output end Proof for 111957779264235096457434
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not tall is not patient.
Everyone who is calm or curious is both not old and not happy.
Everyone who is not wise is funny or not strong.
If fred is quiet then someone is wise or not brave.
If someone is not brave then someone is not old.
If susan is curious or not tall then someone is not humble.
Everyone who is both not curious and quiet is not funny and vice versa.
Everyone who is both rich and patient is both not rich and not funny and vice versa.
Everyone who is either not old or humble is curious or not tall and vice versa.
Everyone who is both not happy and funny is not calm and vice versa.
Everyone who is either not happy or happy is curious and vice versa.
Everyone who is brave is generous and vice versa.
If fred is calm or creative then someone is both not tall and generous and vice versa.
Everyone who is both strong and happy is both creative and calm and vice versa.
If someone is both not old and not rich then someone is not patient or humble and vice versa.
Everyone who is either strong or not funny is not tall.
John is not old.
John is not kind or not humble.
Someone is not humble.
John is either patient or not curious.
Paul is either wise or old.
Someone is both quiet and not creative.
Someone is both not strong and not creative. | Paul is old. | contradiction | (![X]:((~wise(X)|~tall(X))=>~patient(X)))&
(![X]:((calm(X)|curious(X))=>(~old(X)&~happy(X))))&
(![X]:(~wise(X)=>(funny(X)|~strong(X))))&
((quiet(fred))=>(?[X]:((wise(X)|~brave(X)))))&
((?[X]:(~brave(X)))=>(?[X]:(~old(X))))&
(((curious(susan)|~tall(susan)))=>(?[X]:(~humble(X))))&
(![X]:((~curious(X)&quiet(X))<=>~funny(X)))&
(![X]:((rich(X)&patient(X))<=>(~rich(X)&~funny(X))))&
(![X]:((~old(X)<~>humble(X))<=>(curious(X)|~tall(X))))&
(![X]:((~happy(X)&funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>happy(X))<=>curious(X)))&
(![X]:(brave(X)<=>generous(X)))&
(((calm(fred)|creative(fred)))<=>(?[X]:((~tall(X)&generous(X)))))&
(![X]:((strong(X)&happy(X))<=>(creative(X)&calm(X))))&
((?[X]:((~old(X)&~rich(X))))<=>(?[X]:((~patient(X)|humble(X)))))&
(![X]:((strong(X)<~>~funny(X))=>~tall(X)))&
(~old(john))&
((~kind(john)|~humble(john)))&
(?[X]:(~humble(X)))&
((patient(john)<~>~curious(john)))&
((wise(paul)<~>old(paul)))&
(?[X]:((quiet(X)&~creative(X))))&
(?[X]:((~strong(X)&~creative(X)))) | old(paul) | [
"p1",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6066170632739977413352696
% SZS output start Proof for 6066170632739977413352696
2. ! [X0] : ((curious(X0) | calm(X0)) => (~happy(X0) & ~old(X0))) [input p1]
10. ! [X0] : ((funny(X0) & ~happy(X0)) <=> ~calm(X0)) [input p9]
11. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> curious(X0)) [input p10]
24. old(paul) [input hypothesis]
29. ! [X0] : ((~happy(X0) & ~old(X0)) | (~curious(X0) & ~calm(X0))) [ennf transformation 2]
49. ! [X0] : (((funny(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | (~funny(X0) | happy(X0)))) [nnf transformation 10]
50. ! [X0] : (((funny(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | ~funny(X0) | happy(X0))) [flattening 49]
51. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~curious(X0)) & (curious(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 11]
77. ~old(X0) | ~curious(X0) [cnf transformation 29]
78. ~happy(X0) | ~calm(X0) [cnf transformation 29]
99. ~happy(X0) | calm(X0) [cnf transformation 50]
101. curious(X0) | happy(X0) | happy(X0) [cnf transformation 51]
133. old(paul) [cnf transformation 24]
134. curious(X0) | happy(X0) [duplicate literal removal 101]
175. ~happy(X0) [subsumption resolution 99,78]
177. curious(X0) [subsumption resolution 134,175]
239. 22 <=> old(paul) [avatar definition]
240. old(paul) <- (22) [avatar component clause 239]
244. 22 [avatar split clause 133,239]
248. ~curious(paul) <- (22) [resolution 77,240]
249. $false <- (22) [subsumption resolution 248,177]
250. ~22 [avatar contradiction clause 249]
251. $false [avatar sat refutation 244,250]
% SZS output end Proof for 6066170632739977413352696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and generous then paul is not tall.
Everyone who is tall or wise is both old and not creative.
Everyone who is both not curious and not rich is not calm or not creative.
Everyone who is either tall or patient is both not quiet and old and vice versa.
Everyone who is either happy or not generous is not kind and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is quiet or funny is calm or kind and vice versa.
Everyone who is brave or not brave is either rich or wise.
If fred is calm or tall then john is both not brave and not tall and vice versa.
Everyone who is brave or strong is not creative and vice versa.
If alice is rich then someone is both not brave and not humble and vice versa.
Everyone who is not kind or not quiet is both tall and not wise and vice versa.
Everyone who is patient or not kind is not happy.
If someone is either wise or not kind then john is not kind.
Everyone who is either not rich or creative is not patient or old and vice versa.
If fred is both quiet and funny then someone is either creative or not generous.
Fred is both calm and kind.
Alice is either not old or not generous.
John is funny.
Susan is either not brave or humble.
Someone is either not creative or happy.
Someone is calm or not brave. | Alice is not brave. | entailment | ((?[X]:((~tall(X)&generous(X))))=>(~tall(paul)))&
(![X]:((tall(X)|wise(X))=>(old(X)&~creative(X))))&
(![X]:((~curious(X)&~rich(X))=>(~calm(X)|~creative(X))))&
(![X]:((tall(X)<~>patient(X))<=>(~quiet(X)&old(X))))&
(![X]:((happy(X)<~>~generous(X))<=>~kind(X)))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((quiet(X)|funny(X))<=>(calm(X)|kind(X))))&
(![X]:((brave(X)|~brave(X))=>(rich(X)<~>wise(X))))&
(((calm(fred)|tall(fred)))<=>((~brave(john)&~tall(john))))&
(![X]:((brave(X)|strong(X))<=>~creative(X)))&
((rich(alice))<=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((~kind(X)|~quiet(X))<=>(tall(X)&~wise(X))))&
(![X]:((patient(X)|~kind(X))=>~happy(X)))&
((?[X]:((wise(X)<~>~kind(X))))=>(~kind(john)))&
(![X]:((~rich(X)<~>creative(X))<=>(~patient(X)|old(X))))&
(((quiet(fred)&funny(fred)))=>(?[X]:((creative(X)<~>~generous(X)))))&
((calm(fred)&kind(fred)))&
((~old(alice)<~>~generous(alice)))&
(funny(john))&
((~brave(susan)<~>humble(susan)))&
(?[X]:((~creative(X)<~>happy(X))))&
(?[X]:((calm(X)|~brave(X)))) | ~brave(alice) | [
"p1",
"p5",
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1349376742010868301260470
% SZS output start Proof for 1349376742010868301260470
2. ! [X0] : ((wise(X0) | tall(X0)) => (~creative(X0) & old(X0))) [input p1]
6. ! [X0] : (~old(X0) <=> wise(X0)) [input p5]
8. ! [X0] : ((~brave(X0) | brave(X0)) => (rich(X0) <~> wise(X0))) [input p7]
10. ! [X0] : ((strong(X0) | brave(X0)) <=> ~creative(X0)) [input p9]
15. ! [X0] : ((~rich(X0) <~> creative(X0)) <=> (old(X0) | ~patient(X0))) [input p14]
23. brave(alice) [input hypothesis]
26. ! [X0] : ((~creative(X0) & old(X0)) | (~wise(X0) & ~tall(X0))) [ennf transformation 2]
27. ! [X0] : ((rich(X0) <~> wise(X0)) | (brave(X0) & ~brave(X0))) [ennf transformation 8]
35. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 6]
38. ! [X0] : (((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | (brave(X0) & ~brave(X0))) [nnf transformation 27]
41. ! [X0] : (((strong(X0) | brave(X0)) | creative(X0)) & (~creative(X0) | (~strong(X0) & ~brave(X0)))) [nnf transformation 10]
42. ! [X0] : ((strong(X0) | brave(X0) | creative(X0)) & (~creative(X0) | (~strong(X0) & ~brave(X0)))) [flattening 41]
50. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [nnf transformation 15]
51. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [flattening 50]
64. ~wise(X0) | old(X0) [cnf transformation 26]
77. wise(X0) | old(X0) [cnf transformation 35]
78. ~old(X0) | ~wise(X0) [cnf transformation 35]
83. wise(X0) | rich(X0) | ~brave(X0) [cnf transformation 38]
84. wise(X0) | rich(X0) | brave(X0) [cnf transformation 38]
92. ~brave(X0) | ~creative(X0) [cnf transformation 42]
110. creative(X0) | ~rich(X0) | ~old(X0) [cnf transformation 51]
125. brave(alice) [cnf transformation 23]
136. ~wise(X0) [subsumption resolution 78,64]
137. old(X0) [subsumption resolution 77,136]
138. rich(X0) | brave(X0) [subsumption resolution 84,136]
139. rich(X0) | ~brave(X0) [subsumption resolution 83,136]
140. rich(X0) [subsumption resolution 139,138]
174. creative(X0) | ~old(X0) [subsumption resolution 110,140]
175. creative(X0) [subsumption resolution 174,137]
214. ~creative(alice) [resolution 92,125]
215. $false [subsumption resolution 214,175]
% SZS output end Proof for 1349376742010868301260470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both humble and funny then someone is both not creative and not kind.
If john is quiet then paul is creative and vice versa.
If paul is old or rich then someone is not brave or happy.
Everyone who is rich or not curious is both kind and calm and vice versa.
Everyone who is not funny or curious is strong and vice versa.
If alice is either generous or not happy then lucy is rich.
If someone is not rich or not funny then john is both happy and not kind and vice versa.
Everyone who is both not tall and kind is either calm or creative.
If john is both funny and generous then someone is both kind and tall.
Everyone who is curious or not brave is not calm or creative.
Everyone who is not wise is both brave and curious and vice versa.
If someone is not strong or not humble then someone is both quiet and generous and vice versa.
If alice is not quiet or not wise then alice is not calm or generous.
If lucy is not rich then mary is brave or creative and vice versa.
If someone is both not humble and tall then someone is not creative and vice versa.
If lucy is happy then paul is both happy and not rich and vice versa.
Someone is rich.
Alice is not creative.
Someone is not old.
John is either wise or strong.
Someone is calm or tall.
Mary is both wise and calm.
Someone is not strong or brave.
Mary is not tall. | Paul is not creative. | neutral | (((humble(lucy)&funny(lucy)))=>(?[X]:((~creative(X)&~kind(X)))))&
((quiet(john))<=>(creative(paul)))&
(((old(paul)|rich(paul)))=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:((rich(X)|~curious(X))<=>(kind(X)&calm(X))))&
(![X]:((~funny(X)|curious(X))<=>strong(X)))&
(((generous(alice)<~>~happy(alice)))=>(rich(lucy)))&
((?[X]:((~rich(X)|~funny(X))))<=>((happy(john)&~kind(john))))&
(![X]:((~tall(X)&kind(X))=>(calm(X)<~>creative(X))))&
(((funny(john)&generous(john)))=>(?[X]:((kind(X)&tall(X)))))&
(![X]:((curious(X)|~brave(X))=>(~calm(X)|creative(X))))&
(![X]:(~wise(X)<=>(brave(X)&curious(X))))&
((?[X]:((~strong(X)|~humble(X))))<=>(?[X]:((quiet(X)&generous(X)))))&
(((~quiet(alice)|~wise(alice)))=>((~calm(alice)|generous(alice))))&
((~rich(lucy))<=>((brave(mary)|creative(mary))))&
((?[X]:((~humble(X)&tall(X))))<=>(?[X]:(~creative(X))))&
((happy(lucy))<=>((happy(paul)&~rich(paul))))&
(?[X]:(rich(X)))&
(~creative(alice))&
(?[X]:(~old(X)))&
((wise(john)<~>strong(john)))&
(?[X]:((calm(X)|tall(X))))&
((wise(mary)&calm(mary)))&
(?[X]:((~strong(X)|brave(X))))&
(~tall(mary)) | ~creative(paul) | [] | null | 0 |
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