premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either happy or rich is tall or not wise and vice versa.
Everyone who is not kind is not tall or generous and vice versa.
Everyone who is not strong or not brave is both curious and kind.
Everyone who is tall or patient is either humble or quiet and vice versa.
Everyone who is wise or not curious is either not wise or humble and vice versa.
Everyone who is wise is both not strong and rich.
If someone is not calm then john is both creative and funny and vice versa.
Everyone who is old or not generous is both brave and quiet.
If paul is either curious or patient then fred is either not patient or not strong.
If lucy is both not rich and not funny then someone is humble and vice versa.
Everyone who is happy or brave is not patient.
Everyone who is both wise and not strong is not strong or old and vice versa.
If lucy is either not wise or generous then someone is both generous and not curious and vice versa.
If someone is not old then someone is not happy and vice versa.
Everyone who is kind or not strong is kind or not happy and vice versa.
Everyone who is not rich or strong is not curious and vice versa.
Someone is old or not happy.
Someone is either kind or humble.
Lucy is not happy or old.
Lucy is either not humble or patient.
Someone is strong or not quiet.
Someone is not curious or not kind. | Lucy is not generous. | entailment | (![X]:((happy(X)<~>rich(X))<=>(tall(X)|~wise(X))))&
(![X]:(~kind(X)<=>(~tall(X)|generous(X))))&
(![X]:((~strong(X)|~brave(X))=>(curious(X)&kind(X))))&
(![X]:((tall(X)|patient(X))<=>(humble(X)<~>quiet(X))))&
(![X]:((wise(X)|~curious(X))<=>(~wise(X)<~>humble(X))))&
(![X]:(wise(X)=>(~strong(X)&rich(X))))&
((?[X]:(~calm(X)))<=>((creative(john)&funny(john))))&
(![X]:((old(X)|~generous(X))=>(brave(X)&quiet(X))))&
(((curious(paul)<~>patient(paul)))=>((~patient(fred)<~>~strong(fred))))&
(((~rich(lucy)&~funny(lucy)))<=>(?[X]:(humble(X))))&
(![X]:((happy(X)|brave(X))=>~patient(X)))&
(![X]:((wise(X)&~strong(X))<=>(~strong(X)|old(X))))&
(((~wise(lucy)<~>generous(lucy)))<=>(?[X]:((generous(X)&~curious(X)))))&
((?[X]:(~old(X)))<=>(?[X]:(~happy(X))))&
(![X]:((kind(X)|~strong(X))<=>(kind(X)|~happy(X))))&
(![X]:((~rich(X)|strong(X))<=>~curious(X)))&
(?[X]:((old(X)|~happy(X))))&
(?[X]:((kind(X)<~>humble(X))))&
((~happy(lucy)|old(lucy)))&
((~humble(lucy)<~>patient(lucy)))&
(?[X]:((strong(X)|~quiet(X))))&
(?[X]:((~curious(X)|~kind(X)))) | ~generous(lucy) | [
"p1",
"p2",
"p4",
"p5",
"p9",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 549003090926678442753281
% SZS output start Proof for 549003090926678442753281
2. ! [X0] : (~kind(X0) <=> (generous(X0) | ~tall(X0))) [input p1]
3. ! [X0] : ((~brave(X0) | ~strong(X0)) => (kind(X0) & curious(X0))) [input p2]
5. ! [X0] : ((~curious(X0) | wise(X0)) <=> (~wise(X0) <~> humble(X0))) [input p4]
6. ! [X0] : (wise(X0) => (rich(X0) & ~strong(X0))) [input p5]
10. (~funny(lucy) & ~rich(lucy)) <=> ? [X0] : humble(X0) [input p9]
12. ! [X0] : ((~strong(X0) & wise(X0)) <=> (old(X0) | ~strong(X0))) [input p11]
15. ! [X0] : ((~strong(X0) | kind(X0)) <=> (~happy(X0) | kind(X0))) [input p14]
19. old(lucy) | ~happy(lucy) [input p18]
23. generous(lucy) [input hypothesis]
25. ! [X0] : ((kind(X0) & curious(X0)) | (brave(X0) & strong(X0))) [ennf transformation 3]
26. ! [X0] : ((rich(X0) & ~strong(X0)) | ~wise(X0)) [ennf transformation 6]
32. ! [X0] : ((~kind(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | kind(X0))) [nnf transformation 2]
33. ! [X0] : ((~kind(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | kind(X0))) [flattening 32]
36. ! [X0] : (((~curious(X0) | wise(X0)) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0)))) & (((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | (curious(X0) & ~wise(X0)))) [nnf transformation 5]
37. ! [X0] : ((~curious(X0) | wise(X0) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0)))) & (((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | (curious(X0) & ~wise(X0)))) [flattening 36]
44. ((~funny(lucy) & ~rich(lucy)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (funny(lucy) | rich(lucy))) [nnf transformation 10]
45. ((~funny(lucy) & ~rich(lucy)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | funny(lucy) | rich(lucy)) [flattening 44]
46. ((~funny(lucy) & ~rich(lucy)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | funny(lucy) | rich(lucy)) [rectify 45]
47. ? [X1] : humble(X1) => humble(sK1) [choice axiom]
48. ((~funny(lucy) & ~rich(lucy)) | ! [X0] : ~humble(X0)) & (humble(sK1) | funny(lucy) | rich(lucy)) [skolemisation 46,47]
49. ! [X0] : (((~strong(X0) & wise(X0)) | (~old(X0) & strong(X0))) & ((old(X0) | ~strong(X0)) | (strong(X0) | ~wise(X0)))) [nnf transformation 12]
50. ! [X0] : (((~strong(X0) & wise(X0)) | (~old(X0) & strong(X0))) & (old(X0) | ~strong(X0) | strong(X0) | ~wise(X0))) [flattening 49]
60. ! [X0] : (((~strong(X0) | kind(X0)) | (happy(X0) & ~kind(X0))) & ((~happy(X0) | kind(X0)) | (strong(X0) & ~kind(X0)))) [nnf transformation 15]
61. ! [X0] : ((~strong(X0) | kind(X0) | (happy(X0) & ~kind(X0))) & (~happy(X0) | kind(X0) | (strong(X0) & ~kind(X0)))) [flattening 60]
82. ~generous(X0) | ~kind(X0) [cnf transformation 33]
85. strong(X0) | kind(X0) [cnf transformation 25]
93. humble(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 37]
100. ~wise(X0) | rich(X0) [cnf transformation 26]
113. ~rich(lucy) | ~humble(X0) [cnf transformation 48]
119. ~old(X0) | wise(X0) [cnf transformation 50]
133. ~strong(X0) | kind(X0) | happy(X0) [cnf transformation 61]
140. old(lucy) | ~happy(lucy) [cnf transformation 19]
145. generous(lucy) [cnf transformation 23]
146. ~wise(X0) | humble(X0) [duplicate literal removal 93]
187. 9 <=> ! [X0] : ~humble(X0) [avatar definition]
188. ~humble(X0) <- (9) [avatar component clause 187]
195. 11 <=> rich(lucy) [avatar definition]
198. 9 | ~11 [avatar split clause 113,195,187]
208. 14 <=> wise(lucy) [avatar definition]
210. wise(lucy) <- (14) [avatar component clause 208]
212. 15 <=> generous(lucy) [avatar definition]
213. generous(lucy) <- (15) [avatar component clause 212]
245. kind(X0) | happy(X0) [subsumption resolution 133,85]
266. 26 <=> happy(lucy) [avatar definition]
270. 27 <=> old(lucy) [avatar definition]
272. old(lucy) <- (27) [avatar component clause 270]
273. ~26 | 27 [avatar split clause 140,270,266]
302. 15 [avatar split clause 145,212]
304. ~kind(lucy) <- (15) [resolution 82,213]
327. happy(lucy) <- (15) [resolution 245,304]
332. 26 | ~15 [avatar split clause 327,212,266]
334. wise(lucy) <- (27) [resolution 272,119]
339. 14 | ~27 [avatar split clause 334,270,208]
340. humble(lucy) <- (14) [resolution 210,146]
341. rich(lucy) <- (14) [resolution 210,100]
344. 11 | ~14 [avatar split clause 341,208,195]
345. $false <- (9, 14) [subsumption resolution 340,188]
346. ~9 | ~14 [avatar contradiction clause 345]
349. $false [avatar sat refutation 198,273,302,332,339,344,346]
% SZS output end Proof for 549003090926678442753281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either tall or not generous then someone is tall or not happy.
Everyone who is both not calm and not rich is either old or not old and vice versa.
Everyone who is patient is both not curious and curious and vice versa.
If someone is calm or happy then susan is both old and not tall.
If john is not generous or not calm then someone is either strong or tall and vice versa.
Everyone who is both calm and not tall is not curious and vice versa.
Everyone who is rich or happy is not old.
If someone is both calm and not humble then someone is funny or happy and vice versa.
Everyone who is not old or not brave is both not quiet and humble and vice versa.
If lucy is humble or happy then fred is not rich and vice versa.
If paul is not curious then mary is either funny or not kind and vice versa.
If paul is generous or wise then alice is either not curious or not quiet and vice versa.
If someone is either brave or not curious then alice is not old and vice versa.
Everyone who is either not patient or kind is either kind or curious.
Everyone who is both not wise and not old is both strong and rich and vice versa.
Everyone who is either humble or funny is either not kind or kind.
Someone is both not humble and kind.
Mary is calm or not calm.
Fred is not quiet.
Mary is either not generous or tall.
Lucy is not old or humble.
Someone is either strong or not calm.
Someone is both not patient and not strong. | John is not generous. | neutral | (((tall(john)<~>~generous(john)))=>(?[X]:((tall(X)|~happy(X)))))&
(![X]:((~calm(X)&~rich(X))<=>(old(X)<~>~old(X))))&
(![X]:(patient(X)<=>(~curious(X)&curious(X))))&
((?[X]:((calm(X)|happy(X))))=>((old(susan)&~tall(susan))))&
(((~generous(john)|~calm(john)))<=>(?[X]:((strong(X)<~>tall(X)))))&
(![X]:((calm(X)&~tall(X))<=>~curious(X)))&
(![X]:((rich(X)|happy(X))=>~old(X)))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~old(X)|~brave(X))<=>(~quiet(X)&humble(X))))&
(((humble(lucy)|happy(lucy)))<=>(~rich(fred)))&
((~curious(paul))<=>((funny(mary)<~>~kind(mary))))&
(((generous(paul)|wise(paul)))<=>((~curious(alice)<~>~quiet(alice))))&
((?[X]:((brave(X)<~>~curious(X))))<=>(~old(alice)))&
(![X]:((~patient(X)<~>kind(X))=>(kind(X)<~>curious(X))))&
(![X]:((~wise(X)&~old(X))<=>(strong(X)&rich(X))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)<~>kind(X))))&
(?[X]:((~humble(X)&kind(X))))&
((calm(mary)|~calm(mary)))&
(~quiet(fred))&
((~generous(mary)<~>tall(mary)))&
((~old(lucy)|humble(lucy)))&
(?[X]:((strong(X)<~>~calm(X))))&
(?[X]:((~patient(X)&~strong(X)))) | ~generous(john) | [] | null | 0 |
If mary is not creative or curious then paul is either not kind or not curious.
Everyone who is not quiet or generous is both not creative and not wise and vice versa.
Everyone who is not quiet is calm.
Everyone who is either not patient or funny is both not old and humble and vice versa.
If alice is not kind or funny then susan is creative.
Everyone who is both generous and not wise is both not tall and brave and vice versa.
Everyone who is either not creative or not kind is not calm or patient.
If someone is not generous or wise then paul is old and vice versa.
If someone is both not rich and not calm then someone is both not rich and happy.
If someone is both kind and not humble then someone is brave or calm.
Everyone who is generous is both not patient and funny and vice versa.
Everyone who is either not rich or curious is curious or not generous.
Everyone who is not curious or not generous is both not tall and not kind.
Everyone who is both not strong and not humble is not kind.
Everyone who is not old or brave is curious.
Everyone who is both not calm and brave is patient and vice versa.
Alice is not wise or not funny.
Someone is not generous or not brave.
Alice is old.
Someone is not old or not humble.
Alice is either kind or old.
Someone is not kind.
John is either wise or creative. | Paul is old. | entailment | (((~creative(mary)|curious(mary)))=>((~kind(paul)<~>~curious(paul))))&
(![X]:((~quiet(X)|generous(X))<=>(~creative(X)&~wise(X))))&
(![X]:(~quiet(X)=>calm(X)))&
(![X]:((~patient(X)<~>funny(X))<=>(~old(X)&humble(X))))&
(((~kind(alice)|funny(alice)))=>(creative(susan)))&
(![X]:((generous(X)&~wise(X))<=>(~tall(X)&brave(X))))&
(![X]:((~creative(X)<~>~kind(X))=>(~calm(X)|patient(X))))&
((?[X]:((~generous(X)|wise(X))))<=>(old(paul)))&
((?[X]:((~rich(X)&~calm(X))))=>(?[X]:((~rich(X)&happy(X)))))&
((?[X]:((kind(X)&~humble(X))))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:(generous(X)<=>(~patient(X)&funny(X))))&
(![X]:((~rich(X)<~>curious(X))=>(curious(X)|~generous(X))))&
(![X]:((~curious(X)|~generous(X))=>(~tall(X)&~kind(X))))&
(![X]:((~strong(X)&~humble(X))=>~kind(X)))&
(![X]:((~old(X)|brave(X))=>curious(X)))&
(![X]:((~calm(X)&brave(X))<=>patient(X)))&
((~wise(alice)|~funny(alice)))&
(?[X]:((~generous(X)|~brave(X))))&
(old(alice))&
(?[X]:((~old(X)|~humble(X))))&
((kind(alice)<~>old(alice)))&
(?[X]:(~kind(X)))&
((wise(john)<~>creative(john))) | old(paul) | [
"p1",
"p5",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7389944409940272681807739
% SZS output start Proof for 7389944409940272681807739
2. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (~wise(X0) & ~creative(X0))) [input p1]
6. ! [X0] : ((~wise(X0) & generous(X0)) <=> (brave(X0) & ~tall(X0))) [input p5]
8. ? [X0] : (wise(X0) | ~generous(X0)) <=> old(paul) [input p7]
18. ? [X0] : (~brave(X0) | ~generous(X0)) [input p17]
24. ~old(paul) [input hypothesis]
41. ! [X0] : (((generous(X0) | ~quiet(X0)) | (wise(X0) | creative(X0))) & ((~wise(X0) & ~creative(X0)) | (~generous(X0) & quiet(X0)))) [nnf transformation 2]
42. ! [X0] : ((generous(X0) | ~quiet(X0) | wise(X0) | creative(X0)) & ((~wise(X0) & ~creative(X0)) | (~generous(X0) & quiet(X0)))) [flattening 41]
45. ! [X0] : (((~wise(X0) & generous(X0)) | (~brave(X0) | tall(X0))) & ((brave(X0) & ~tall(X0)) | (wise(X0) | ~generous(X0)))) [nnf transformation 6]
46. ! [X0] : (((~wise(X0) & generous(X0)) | ~brave(X0) | tall(X0)) & ((brave(X0) & ~tall(X0)) | wise(X0) | ~generous(X0))) [flattening 45]
48. (? [X0] : (wise(X0) | ~generous(X0)) | ~old(paul)) & (old(paul) | ! [X0] : (~wise(X0) & generous(X0))) [nnf transformation 8]
49. (? [X0] : (wise(X0) | ~generous(X0)) | ~old(paul)) & (old(paul) | ! [X1] : (~wise(X1) & generous(X1))) [rectify 48]
50. ? [X0] : (wise(X0) | ~generous(X0)) => (wise(sK0) | ~generous(sK0)) [choice axiom]
51. ((wise(sK0) | ~generous(sK0)) | ~old(paul)) & (old(paul) | ! [X1] : (~wise(X1) & generous(X1))) [skolemisation 49,50]
63. ? [X0] : (~brave(X0) | ~generous(X0)) => (~brave(sK3) | ~generous(sK3)) [choice axiom]
64. ~brave(sK3) | ~generous(sK3) [skolemisation 18,63]
78. ~wise(X0) | ~generous(X0) [cnf transformation 42]
90. brave(X0) | wise(X0) | ~generous(X0) [cnf transformation 46]
95. old(paul) | generous(X1) [cnf transformation 51]
115. ~brave(sK3) | ~generous(sK3) [cnf transformation 64]
123. ~old(paul) [cnf transformation 24]
159. brave(X0) | ~generous(X0) [subsumption resolution 90,78]
163. 8 <=> old(paul) [avatar definition]
176. 11 <=> ! [X1] : generous(X1) [avatar definition]
177. generous(X1) <- (11) [avatar component clause 176]
178. 11 | 8 [avatar split clause 95,163,176]
205. ~generous(sK3) [subsumption resolution 115,159]
227. ~8 [avatar split clause 123,163]
228. $false <- (11) [resolution 205,177]
229. ~11 [avatar contradiction clause 228]
230. $false [avatar sat refutation 178,227,229]
% SZS output end Proof for 7389944409940272681807739
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and kind is rich and vice versa. Everyone who is both not rich and not quiet is not tall or patient. If someone is both not kind and generous then mary is both not happy and not generous and vice versa. If lucy is not generous then mary is calm and vice versa. Everyone who is funny is rich or not calm and vice versa. If mary is not rich or not strong then alice is both not wise and brave. Everyone who is not kind or not strong is either funny or quiet and vice versa. If fred is both not generous and not tall then paul is not strong. Everyone who is both old and rich is both not old and not curious. Everyone who is both calm and kind is old or not rich and vice versa. If someone is both not generous and strong then fred is strong. Everyone who is either not humble or not old is either wise or patient. Everyone who is happy or not rich is either not calm or not quiet and vice versa. Everyone who is either not brave or not wise is both not happy and funny and vice versa. If alice is both curious and not humble then mary is brave and vice versa. If someone is both curious and rich then john is humble. Someone is brave or not tall. Someone is either kind or not wise. Someone is both not curious and funny. Someone is quiet. Someone is not happy. Someone is rich. Someone is either not brave or not humble. | John is not funny. | neutral | (![X]:((wise(X)&kind(X))<=>rich(X)))&
(![X]:((~rich(X)&~quiet(X))=>(~tall(X)|patient(X))))&
((?[X]:((~kind(X)&generous(X))))<=>((~happy(mary)&~generous(mary))))&
((~generous(lucy))<=>(calm(mary)))&
(![X]:(funny(X)<=>(rich(X)|~calm(X))))&
(((~rich(mary)|~strong(mary)))=>((~wise(alice)&brave(alice))))&
(![X]:((~kind(X)|~strong(X))<=>(funny(X)<~>quiet(X))))&
(((~generous(fred)&~tall(fred)))=>(~strong(paul)))&
(![X]:((old(X)&rich(X))=>(~old(X)&~curious(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)|~rich(X))))&
((?[X]:((~generous(X)&strong(X))))=>(strong(fred)))&
(![X]:((~humble(X)<~>~old(X))=>(wise(X)<~>patient(X))))&
(![X]:((happy(X)|~rich(X))<=>(~calm(X)<~>~quiet(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(~happy(X)&funny(X))))&
(((curious(alice)&~humble(alice)))<=>(brave(mary)))&
((?[X]:((curious(X)&rich(X))))=>(humble(john)))&
(?[X]:((brave(X)|~tall(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:(quiet(X)))&
(?[X]:(~happy(X)))&
(?[X]:(rich(X)))&
(?[X]:((~brave(X)<~>~humble(X)))) | ~funny(john) | [] | null | 0 |
Everyone who is both patient and humble is tall or brave. Everyone who is wise or not curious is either curious or wise and vice versa. If john is patient then someone is both not happy and generous. Everyone who is old is either not wise or not tall and vice versa. If john is both wise and generous then someone is not rich and vice versa. If someone is not brave or not strong then someone is either not happy or not funny and vice versa. If susan is not patient then alice is strong or curious and vice versa. Everyone who is not rich or not creative is rich or not calm. Everyone who is happy is not brave and vice versa. Everyone who is both not humble and rich is either not quiet or not creative and vice versa. Everyone who is either not calm or happy is either curious or happy. If susan is both creative and happy then someone is either not brave or humble. If alice is either curious or generous then someone is old or happy and vice versa. If susan is quiet or old then paul is both not old and curious and vice versa. Everyone who is not creative is either wise or creative. Everyone who is tall or not kind is both happy and wise. John is not generous or generous. Lucy is either wise or generous. Someone is either not wise or not rich. Someone is funny. Paul is both patient and rich. Someone is not tall. Lucy is not strong or creative. | Alice is generous. | entailment | (![X]:((patient(X)&humble(X))=>(tall(X)|brave(X))))&
(![X]:((wise(X)|~curious(X))<=>(curious(X)<~>wise(X))))&
((patient(john))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:(old(X)<=>(~wise(X)<~>~tall(X))))&
(((wise(john)&generous(john)))<=>(?[X]:(~rich(X))))&
((?[X]:((~brave(X)|~strong(X))))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
((~patient(susan))<=>((strong(alice)|curious(alice))))&
(![X]:((~rich(X)|~creative(X))=>(rich(X)|~calm(X))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:((~humble(X)&rich(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)<~>happy(X))=>(curious(X)<~>happy(X))))&
(((creative(susan)&happy(susan)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
((~generous(john)|generous(john)))&
((wise(lucy)<~>generous(lucy)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(?[X]:(funny(X)))&
((patient(paul)&rich(paul)))&
(?[X]:(~tall(X)))&
((~strong(lucy)|creative(lucy))) | generous(alice) | [
"p1",
"p3",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3369852844509976727369377
% SZS output start Proof for 3369852844509976727369377
2. ! [X0] : ((~curious(X0) | wise(X0)) <=> (curious(X0) <~> wise(X0))) [input p1]
4. ! [X0] : (old(X0) <=> (~wise(X0) <~> ~tall(X0))) [input p3]
13. (curious(alice) <~> generous(alice)) <=> ? [X0] : (happy(X0) | old(X0)) [input p12]
22. ? [X0] : ~tall(X0) [input p21]
24. ~generous(alice) [input hypothesis]
37. ! [X0] : (((~curious(X0) | wise(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (curious(X0) & ~wise(X0)))) [nnf transformation 2]
38. ! [X0] : ((~curious(X0) | wise(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (curious(X0) & ~wise(X0)))) [flattening 37]
41. ! [X0] : ((old(X0) | ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0)))) & (((tall(X0) | wise(X0)) & (~tall(X0) | ~wise(X0))) | ~old(X0))) [nnf transformation 4]
61. (((~generous(alice) | ~curious(alice)) & (generous(alice) | curious(alice))) | ! [X0] : (~happy(X0) & ~old(X0))) & (? [X0] : (happy(X0) | old(X0)) | ((curious(alice) | ~generous(alice)) & (generous(alice) | ~curious(alice)))) [nnf transformation 13]
62. (((~generous(alice) | ~curious(alice)) & (generous(alice) | curious(alice))) | ! [X0] : (~happy(X0) & ~old(X0))) & (? [X1] : (happy(X1) | old(X1)) | ((curious(alice) | ~generous(alice)) & (generous(alice) | ~curious(alice)))) [rectify 61]
63. ? [X1] : (happy(X1) | old(X1)) => (happy(sK5) | old(sK5)) [choice axiom]
64. (((~generous(alice) | ~curious(alice)) & (generous(alice) | curious(alice))) | ! [X0] : (~happy(X0) & ~old(X0))) & ((happy(sK5) | old(sK5)) | ((curious(alice) | ~generous(alice)) & (generous(alice) | ~curious(alice)))) [skolemisation 62,63]
74. ? [X0] : ~tall(X0) => ~tall(sK8) [choice axiom]
75. ~tall(sK8) [skolemisation 22,74]
78. wise(X0) | curious(X0) | curious(X0) [cnf transformation 38]
79. ~wise(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 38]
81. ~curious(X0) | wise(X0) | wise(X0) | ~curious(X0) [cnf transformation 38]
88. old(X0) | ~wise(X0) | tall(X0) [cnf transformation 41]
119. generous(alice) | curious(alice) | ~old(X0) [cnf transformation 64]
140. ~tall(sK8) [cnf transformation 75]
142. ~generous(alice) [cnf transformation 24]
147. wise(X0) | curious(X0) [duplicate literal removal 78]
148. ~wise(X0) | ~curious(X0) [duplicate literal removal 79]
149. ~curious(X0) | wise(X0) [duplicate literal removal 81]
150. ~curious(X0) [subsumption resolution 148,149]
151. wise(X0) [subsumption resolution 147,150]
166. old(X0) | tall(X0) [subsumption resolution 88,151]
251. 22 <=> generous(alice) [avatar definition]
255. generous(alice) | ~old(X0) [subsumption resolution 119,150]
257. 23 <=> ! [X0] : ~old(X0) [avatar definition]
258. ~old(X0) <- (23) [avatar component clause 257]
259. 23 | 22 [avatar split clause 255,251,257]
283. ~22 [avatar split clause 142,251]
293. tall(X0) <- (23) [resolution 166,258]
295. $false <- (23) [resolution 293,140]
297. ~23 [avatar contradiction clause 295]
300. $false [avatar sat refutation 259,283,297]
% SZS output end Proof for 3369852844509976727369377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is either not rich or rich and vice versa. If someone is not curious or not tall then john is patient. Everyone who is both not kind and not quiet is not happy. If someone is either not wise or wise then alice is either not quiet or calm and vice versa. Everyone who is brave is either patient or funny. Everyone who is either not wise or not rich is wise. Everyone who is both not creative and not curious is not tall or not creative and vice versa. If john is either not creative or not kind then paul is both kind and calm and vice versa. Everyone who is both not wise and not humble is both not generous and quiet. Everyone who is old or not kind is not strong. If someone is both brave and kind then someone is both not funny and not creative. Everyone who is not funny or calm is tall. If someone is rich or not patient then lucy is both not humble and humble. Everyone who is both not generous and tall is both curious and not strong and vice versa. Everyone who is both patient and kind is not happy or generous and vice versa. Everyone who is not tall or not patient is both happy and brave. Paul is not happy. Someone is either not funny or not generous. Someone is both not kind and quiet. Mary is not kind. Someone is either strong or calm. | John is not happy. | neutral | (![X]:(~generous(X)<=>(~rich(X)<~>rich(X))))&
((?[X]:((~curious(X)|~tall(X))))=>(patient(john)))&
(![X]:((~kind(X)&~quiet(X))=>~happy(X)))&
((?[X]:((~wise(X)<~>wise(X))))<=>((~quiet(alice)<~>calm(alice))))&
(![X]:(brave(X)=>(patient(X)<~>funny(X))))&
(![X]:((~wise(X)<~>~rich(X))=>wise(X)))&
(![X]:((~creative(X)&~curious(X))<=>(~tall(X)|~creative(X))))&
(((~creative(john)<~>~kind(john)))<=>((kind(paul)&calm(paul))))&
(![X]:((~wise(X)&~humble(X))=>(~generous(X)&quiet(X))))&
(![X]:((old(X)|~kind(X))=>~strong(X)))&
((?[X]:((brave(X)&kind(X))))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:((~funny(X)|calm(X))=>tall(X)))&
((?[X]:((rich(X)|~patient(X))))=>((~humble(lucy)&humble(lucy))))&
(![X]:((~generous(X)&tall(X))<=>(curious(X)&~strong(X))))&
(![X]:((patient(X)&kind(X))<=>(~happy(X)|generous(X))))&
(![X]:((~tall(X)|~patient(X))=>(happy(X)&brave(X))))&
(~happy(paul))&
(?[X]:((~funny(X)<~>~generous(X))))&
(?[X]:((~kind(X)&quiet(X))))&
(~kind(mary))&
(?[X]:((strong(X)<~>calm(X)))) | ~happy(john) | [] | null | 0 |
Everyone who is either not calm or not strong is not old or happy.
Everyone who is old is not brave or not happy.
If paul is either funny or not tall then john is either not patient or quiet and vice versa.
Everyone who is not kind is not calm and vice versa.
Everyone who is both strong and not curious is both generous and kind and vice versa.
If someone is old then lucy is not wise.
If someone is either kind or happy then alice is either not creative or not humble and vice versa.
If someone is creative then susan is not strong and vice versa.
If someone is not happy or not curious then john is not humble.
If someone is not rich then someone is either tall or not wise.
Everyone who is either happy or curious is creative and vice versa.
Everyone who is both not creative and humble is both not old and curious and vice versa.
If someone is not happy or not kind then john is both generous and not quiet.
Everyone who is not wise is not patient or happy.
Everyone who is curious or not strong is either not old or wise.
Everyone who is wise or not wise is both not curious and not wise.
Mary is curious or brave.
Someone is generous.
Someone is old or rich.
Alice is both not curious and not strong.
John is creative or wise.
Lucy is not quiet or not wise.
John is either not kind or not humble. | Mary is brave. | entailment | (![X]:((~calm(X)<~>~strong(X))=>(~old(X)|happy(X))))&
(![X]:(old(X)=>(~brave(X)|~happy(X))))&
(((funny(paul)<~>~tall(paul)))<=>((~patient(john)<~>quiet(john))))&
(![X]:(~kind(X)<=>~calm(X)))&
(![X]:((strong(X)&~curious(X))<=>(generous(X)&kind(X))))&
((?[X]:(old(X)))=>(~wise(lucy)))&
((?[X]:((kind(X)<~>happy(X))))<=>((~creative(alice)<~>~humble(alice))))&
((?[X]:(creative(X)))<=>(~strong(susan)))&
((?[X]:((~happy(X)|~curious(X))))=>(~humble(john)))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>curious(X))<=>creative(X)))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
((curious(mary)|brave(mary)))&
(?[X]:(generous(X)))&
(?[X]:((old(X)|rich(X))))&
((~curious(alice)&~strong(alice)))&
((creative(john)|wise(john)))&
((~quiet(lucy)|~wise(lucy)))&
((~kind(john)<~>~humble(john))) | brave(mary) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7704964865184630113938768
% SZS output start Proof for 7704964865184630113938768
16. ! [X0] : ((~wise(X0) | wise(X0)) => (~wise(X0) & ~curious(X0))) [input p15]
17. brave(mary) | curious(mary) [input p16]
24. ~brave(mary) [input hypothesis]
38. ! [X0] : ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 16]
107. ~curious(X0) | wise(X0) [cnf transformation 38]
108. ~wise(X0) | ~wise(X0) [cnf transformation 38]
110. brave(mary) | curious(mary) [cnf transformation 17]
118. ~brave(mary) [cnf transformation 24]
119. ~wise(X0) [duplicate literal removal 108]
218. ~curious(X0) [subsumption resolution 107,119]
219. brave(mary) [subsumption resolution 110,218]
227. $false [subsumption resolution 118,219]
% SZS output end Proof for 7704964865184630113938768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is both not curious and funny.
If someone is both not brave and not strong then fred is patient or not quiet and vice versa.
Everyone who is creative is both not old and creative and vice versa.
Everyone who is both happy and not quiet is either not quiet or not creative and vice versa.
Everyone who is both funny and happy is happy or patient and vice versa.
Everyone who is calm is either not brave or wise and vice versa.
If mary is both not generous and not calm then john is not kind or not brave.
If someone is either humble or funny then alice is humble.
If susan is happy or funny then someone is either funny or brave and vice versa.
Everyone who is not tall is not old and vice versa.
Everyone who is either tall or not kind is not kind or not creative.
If someone is creative then someone is not kind.
If john is not curious then someone is wise or happy.
Everyone who is funny or not humble is quiet and vice versa.
Everyone who is kind is either not brave or patient and vice versa.
If someone is both not creative and old then someone is both not generous and creative and vice versa.
Alice is rich.
Someone is not tall or calm.
John is not quiet or not creative.
Someone is tall or not rich.
Alice is both not tall and generous.
Paul is humble or not tall.
Alice is either funny or brave. | Paul is not calm. | neutral | (![X]:((wise(X)&~quiet(X))=>(~curious(X)&funny(X))))&
((?[X]:((~brave(X)&~strong(X))))<=>((patient(fred)|~quiet(fred))))&
(![X]:(creative(X)<=>(~old(X)&creative(X))))&
(![X]:((happy(X)&~quiet(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((funny(X)&happy(X))<=>(happy(X)|patient(X))))&
(![X]:(calm(X)<=>(~brave(X)<~>wise(X))))&
(((~generous(mary)&~calm(mary)))=>((~kind(john)|~brave(john))))&
((?[X]:((humble(X)<~>funny(X))))=>(humble(alice)))&
(((happy(susan)|funny(susan)))<=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:(~tall(X)<=>~old(X)))&
(![X]:((tall(X)<~>~kind(X))=>(~kind(X)|~creative(X))))&
((?[X]:(creative(X)))=>(?[X]:(~kind(X))))&
((~curious(john))=>(?[X]:((wise(X)|happy(X)))))&
(![X]:((funny(X)|~humble(X))<=>quiet(X)))&
(![X]:(kind(X)<=>(~brave(X)<~>patient(X))))&
((?[X]:((~creative(X)&old(X))))<=>(?[X]:((~generous(X)&creative(X)))))&
(rich(alice))&
(?[X]:((~tall(X)|calm(X))))&
((~quiet(john)|~creative(john)))&
(?[X]:((tall(X)|~rich(X))))&
((~tall(alice)&generous(alice)))&
((humble(paul)|~tall(paul)))&
((funny(alice)<~>brave(alice))) | ~calm(paul) | [] | null | 0 |
Everyone who is patient or old is both not quiet and not kind. Everyone who is creative is rich and vice versa. Everyone who is not old is not kind and vice versa. Everyone who is not funny is kind and vice versa. If someone is wise or not generous then john is both kind and not brave and vice versa. If someone is both funny and not quiet then alice is not curious or not patient and vice versa. If fred is wise then lucy is not happy. If john is not humble or not quiet then paul is both not old and not creative and vice versa. If lucy is quiet then someone is both quiet and not happy. Everyone who is either not strong or strong is funny. Everyone who is creative or wise is both brave and not generous and vice versa. If mary is both curious and not quiet then someone is old or not strong. If lucy is either not tall or tall then mary is either calm or strong and vice versa. If paul is both happy and not kind then someone is both creative and wise and vice versa. Someone is quiet or kind. Paul is strong. Someone is calm or not old. Susan is both not strong and patient. Mary is humble or strong. Someone is not strong. Someone is happy. | Lucy is not wise. | entailment | (![X]:((patient(X)|old(X))=>(~quiet(X)&~kind(X))))&
(![X]:(creative(X)<=>rich(X)))&
(![X]:(~old(X)<=>~kind(X)))&
(![X]:(~funny(X)<=>kind(X)))&
((?[X]:((wise(X)|~generous(X))))<=>((kind(john)&~brave(john))))&
((?[X]:((funny(X)&~quiet(X))))<=>((~curious(alice)|~patient(alice))))&
((wise(fred))=>(~happy(lucy)))&
(((~humble(john)|~quiet(john)))<=>((~old(paul)&~creative(paul))))&
((quiet(lucy))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((~strong(X)<~>strong(X))=>funny(X)))&
(![X]:((creative(X)|wise(X))<=>(brave(X)&~generous(X))))&
(((curious(mary)&~quiet(mary)))=>(?[X]:((old(X)|~strong(X)))))&
(((~tall(lucy)<~>tall(lucy)))<=>((calm(mary)<~>strong(mary))))&
(((happy(paul)&~kind(paul)))<=>(?[X]:((creative(X)&wise(X)))))&
(?[X]:((quiet(X)|kind(X))))&
(strong(paul))&
(?[X]:((calm(X)|~old(X))))&
((~strong(susan)&patient(susan)))&
((humble(mary)|strong(mary)))&
(?[X]:(~strong(X)))&
(?[X]:(happy(X))) | ~wise(lucy) | [
"p0",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6721868792997770221919280
% SZS output start Proof for 6721868792997770221919280
1. ! [X0] : ((old(X0) | patient(X0)) => (~kind(X0) & ~quiet(X0))) [input p0]
3. ! [X0] : (~old(X0) <=> ~kind(X0)) [input p2]
5. ? [X0] : (~generous(X0) | wise(X0)) <=> (~brave(john) & kind(john)) [input p4]
22. wise(lucy) [input hypothesis]
23. ! [X0] : ((~kind(X0) & ~quiet(X0)) | (~old(X0) & ~patient(X0))) [ennf transformation 1]
30. ! [X0] : ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0))) [nnf transformation 3]
32. (? [X0] : (~generous(X0) | wise(X0)) | (brave(john) | ~kind(john))) & ((~brave(john) & kind(john)) | ! [X0] : (generous(X0) & ~wise(X0))) [nnf transformation 5]
33. (? [X0] : (~generous(X0) | wise(X0)) | brave(john) | ~kind(john)) & ((~brave(john) & kind(john)) | ! [X0] : (generous(X0) & ~wise(X0))) [flattening 32]
34. (? [X0] : (~generous(X0) | wise(X0)) | brave(john) | ~kind(john)) & ((~brave(john) & kind(john)) | ! [X1] : (generous(X1) & ~wise(X1))) [rectify 33]
35. ? [X0] : (~generous(X0) | wise(X0)) => (~generous(sK0) | wise(sK0)) [choice axiom]
36. ((~generous(sK0) | wise(sK0)) | brave(john) | ~kind(john)) & ((~brave(john) & kind(john)) | ! [X1] : (generous(X1) & ~wise(X1))) [skolemisation 34,35]
68. ~kind(X0) | ~old(X0) [cnf transformation 23]
71. ~kind(X0) | old(X0) [cnf transformation 30]
72. ~old(X0) | kind(X0) [cnf transformation 30]
75. kind(john) | ~wise(X1) [cnf transformation 36]
121. wise(lucy) [cnf transformation 22]
128. ~old(X0) [subsumption resolution 72,68]
129. ~kind(X0) [subsumption resolution 71,128]
140. 3 <=> ! [X1] : ~wise(X1) [avatar definition]
141. ~wise(X1) <- (3) [avatar component clause 140]
145. ~wise(X1) [subsumption resolution 75,129]
146. 3 [avatar split clause 145,140]
261. $false <- (3) [resolution 141,121]
262. ~3 [avatar contradiction clause 261]
263. $false [avatar sat refutation 146,262]
% SZS output end Proof for 6721868792997770221919280
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is both not kind and funny.
If someone is not creative then someone is not rich and vice versa.
Everyone who is not quiet is not tall and vice versa.
If someone is both not quiet and not rich then fred is both humble and not patient and vice versa.
Everyone who is not generous or strong is brave.
Everyone who is either old or kind is old.
Everyone who is not wise or not generous is happy.
If susan is either funny or happy then susan is not quiet and vice versa.
Everyone who is either curious or not tall is both humble and not kind and vice versa.
Everyone who is either humble or old is not quiet and vice versa.
Everyone who is either not old or tall is not tall and vice versa.
Everyone who is both happy and not happy is patient or happy and vice versa.
If susan is not happy then fred is curious or calm.
Everyone who is not quiet is both curious and not brave and vice versa.
If alice is either old or not creative then someone is either strong or not curious.
Everyone who is either wise or creative is both creative and not quiet.
John is not creative or not brave.
Someone is not strong.
Someone is rich.
Someone is either not kind or humble.
Someone is calm or not creative.
Fred is either not strong or calm.
Alice is both quiet and not happy. | Susan is generous. | entailment | (![X]:(~brave(X)=>(~kind(X)&funny(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~rich(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
((?[X]:((~quiet(X)&~rich(X))))<=>((humble(fred)&~patient(fred))))&
(![X]:((~generous(X)|strong(X))=>brave(X)))&
(![X]:((old(X)<~>kind(X))=>old(X)))&
(![X]:((~wise(X)|~generous(X))=>happy(X)))&
(((funny(susan)<~>happy(susan)))<=>(~quiet(susan)))&
(![X]:((curious(X)<~>~tall(X))<=>(humble(X)&~kind(X))))&
(![X]:((humble(X)<~>old(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>tall(X))<=>~tall(X)))&
(![X]:((happy(X)&~happy(X))<=>(patient(X)|happy(X))))&
((~happy(susan))=>((curious(fred)|calm(fred))))&
(![X]:(~quiet(X)<=>(curious(X)&~brave(X))))&
(((old(alice)<~>~creative(alice)))=>(?[X]:((strong(X)<~>~curious(X)))))&
(![X]:((wise(X)<~>creative(X))=>(creative(X)&~quiet(X))))&
((~creative(john)|~brave(john)))&
(?[X]:(~strong(X)))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)<~>humble(X))))&
(?[X]:((calm(X)|~creative(X))))&
((~strong(fred)<~>calm(fred)))&
((quiet(alice)&~happy(alice))) | generous(susan) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 627089233858108757673479
% SZS output start Proof for 627089233858108757673479
7. ! [X0] : ((~generous(X0) | ~wise(X0)) => happy(X0)) [input p6]
12. ! [X0] : ((~happy(X0) & happy(X0)) <=> (happy(X0) | patient(X0))) [input p11]
24. ~generous(susan) [input hypothesis]
29. ! [X0] : (happy(X0) | (generous(X0) & wise(X0))) [ennf transformation 7]
51. ! [X0] : (((~happy(X0) & happy(X0)) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 12]
52. ! [X0] : (((~happy(X0) & happy(X0)) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | happy(X0) | ~happy(X0))) [flattening 51]
84. happy(X0) | generous(X0) [cnf transformation 29]
107. ~happy(X0) | ~happy(X0) [cnf transformation 52]
130. ~generous(susan) [cnf transformation 24]
133. ~happy(X0) [duplicate literal removal 107]
261. generous(X0) [resolution 84,133]
263. $false [resolution 261,130]
% SZS output end Proof for 627089233858108757673479
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or wise is funny or kind and vice versa.
Everyone who is either not funny or old is both not funny and not tall.
If paul is either calm or not funny then fred is not humble or not generous.
If someone is both not generous and patient then someone is happy or strong.
Everyone who is humble is either patient or not kind and vice versa.
If alice is either creative or wise then someone is both not patient and not strong.
If someone is either not curious or calm then someone is both creative and strong.
Everyone who is both old and patient is not funny.
Everyone who is either not quiet or not curious is rich.
Everyone who is either tall or not curious is both rich and not old and vice versa.
Everyone who is not strong is either not creative or rich.
If someone is not brave or not calm then paul is not funny or not quiet.
Everyone who is either not generous or not strong is both not wise and not old and vice versa.
If someone is not happy then someone is not generous or not funny and vice versa.
Everyone who is wise is not patient or not rich and vice versa.
Everyone who is creative or funny is not patient.
Lucy is not brave.
Someone is not old or creative.
Lucy is creative.
Someone is wise.
Mary is either happy or humble.
Fred is rich.
Fred is not tall or not old. | Alice is wise. | neutral | (![X]:((~curious(X)<~>wise(X))<=>(funny(X)|kind(X))))&
(![X]:((~funny(X)<~>old(X))=>(~funny(X)&~tall(X))))&
(((calm(paul)<~>~funny(paul)))=>((~humble(fred)|~generous(fred))))&
((?[X]:((~generous(X)&patient(X))))=>(?[X]:((happy(X)|strong(X)))))&
(![X]:(humble(X)<=>(patient(X)<~>~kind(X))))&
(((creative(alice)<~>wise(alice)))=>(?[X]:((~patient(X)&~strong(X)))))&
((?[X]:((~curious(X)<~>calm(X))))=>(?[X]:((creative(X)&strong(X)))))&
(![X]:((old(X)&patient(X))=>~funny(X)))&
(![X]:((~quiet(X)<~>~curious(X))=>rich(X)))&
(![X]:((tall(X)<~>~curious(X))<=>(rich(X)&~old(X))))&
(![X]:(~strong(X)=>(~creative(X)<~>rich(X))))&
((?[X]:((~brave(X)|~calm(X))))=>((~funny(paul)|~quiet(paul))))&
(![X]:((~generous(X)<~>~strong(X))<=>(~wise(X)&~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~generous(X)|~funny(X)))))&
(![X]:(wise(X)<=>(~patient(X)|~rich(X))))&
(![X]:((creative(X)|funny(X))=>~patient(X)))&
(~brave(lucy))&
(?[X]:((~old(X)|creative(X))))&
(creative(lucy))&
(?[X]:(wise(X)))&
((happy(mary)<~>humble(mary)))&
(rich(fred))&
((~tall(fred)|~old(fred))) | wise(alice) | [] | null | 0 |
Everyone who is not kind is either humble or happy. If someone is either quiet or curious then john is curious. If susan is either not humble or not wise then john is old or not brave. Everyone who is both not curious and patient is curious or not wise and vice versa. If fred is both not creative and brave then fred is humble or curious. Everyone who is either old or wise is either happy or brave and vice versa. Everyone who is both not funny and not curious is either not funny or strong and vice versa. Everyone who is either not humble or happy is both creative and not wise and vice versa. Everyone who is old or not generous is either brave or rich. If john is both old and not humble then someone is not humble or quiet. If someone is either not funny or happy then someone is not strong or creative. Everyone who is happy or funny is patient. Everyone who is both not calm and strong is patient or not tall. If lucy is patient then lucy is curious. If paul is either happy or not happy then someone is not quiet or not old. Everyone who is brave is either calm or not quiet and vice versa. Someone is either not wise or calm. Someone is creative. Susan is not brave or not strong. Alice is both not curious and happy. Mary is either wise or not humble. Mary is quiet or funny. John is either funny or not generous. | Paul is not curious. | entailment | (![X]:(~kind(X)=>(humble(X)<~>happy(X))))&
((?[X]:((quiet(X)<~>curious(X))))=>(curious(john)))&
(((~humble(susan)<~>~wise(susan)))=>((old(john)|~brave(john))))&
(![X]:((~curious(X)&patient(X))<=>(curious(X)|~wise(X))))&
(((~creative(fred)&brave(fred)))=>((humble(fred)|curious(fred))))&
(![X]:((old(X)<~>wise(X))<=>(happy(X)<~>brave(X))))&
(![X]:((~funny(X)&~curious(X))<=>(~funny(X)<~>strong(X))))&
(![X]:((~humble(X)<~>happy(X))<=>(creative(X)&~wise(X))))&
(![X]:((old(X)|~generous(X))=>(brave(X)<~>rich(X))))&
(((old(john)&~humble(john)))=>(?[X]:((~humble(X)|quiet(X)))))&
((?[X]:((~funny(X)<~>happy(X))))=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:((happy(X)|funny(X))=>patient(X)))&
(![X]:((~calm(X)&strong(X))=>(patient(X)|~tall(X))))&
((patient(lucy))=>(curious(lucy)))&
(((happy(paul)<~>~happy(paul)))=>(?[X]:((~quiet(X)|~old(X)))))&
(![X]:(brave(X)<=>(calm(X)<~>~quiet(X))))&
(?[X]:((~wise(X)<~>calm(X))))&
(?[X]:(creative(X)))&
((~brave(susan)|~strong(susan)))&
((~curious(alice)&happy(alice)))&
((wise(mary)<~>~humble(mary)))&
((quiet(mary)|funny(mary)))&
((funny(john)<~>~generous(john))) | ~curious(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 4449689307781808612420363
% SZS output start Proof for 4449689307781808612420363
4. ! [X0] : ((patient(X0) & ~curious(X0)) <=> (~wise(X0) | curious(X0))) [input p3]
24. curious(paul) [input hypothesis]
42. ! [X0] : (((patient(X0) & ~curious(X0)) | (wise(X0) & ~curious(X0))) & ((~wise(X0) | curious(X0)) | (~patient(X0) | curious(X0)))) [nnf transformation 4]
43. ! [X0] : (((patient(X0) & ~curious(X0)) | (wise(X0) & ~curious(X0))) & (~wise(X0) | curious(X0) | ~patient(X0) | curious(X0))) [flattening 42]
72. ~curious(X0) | ~curious(X0) [cnf transformation 43]
124. curious(paul) [cnf transformation 24]
130. ~curious(X0) [duplicate literal removal 72]
245. $false [subsumption resolution 124,130]
% SZS output end Proof for 4449689307781808612420363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then john is either old or funny and vice versa.
If fred is not humble or creative then someone is both patient and quiet and vice versa.
Everyone who is not patient or not generous is happy or humble.
If someone is brave or humble then mary is not generous.
Everyone who is funny is not quiet and vice versa.
If lucy is generous then someone is either not old or tall and vice versa.
If paul is kind or strong then lucy is either not creative or funny and vice versa.
If john is either not funny or strong then someone is either wise or happy and vice versa.
Everyone who is both not funny and patient is both quiet and not strong.
Everyone who is not quiet or not curious is both not strong and tall.
Everyone who is not funny is both not strong and wise and vice versa.
If paul is both wise and not humble then someone is either not tall or curious and vice versa.
Everyone who is either brave or tall is not funny.
If someone is curious then mary is not happy.
Everyone who is quiet is either not funny or not creative and vice versa.
If someone is both old and kind then someone is humble and vice versa.
Someone is funny.
Someone is either not old or not funny.
Mary is both not curious and kind.
Fred is both not quiet and not kind.
Someone is not patient or strong.
Someone is generous or not happy.
Someone is either humble or not patient.
Mary is not happy or not wise. | Fred is wise. | contradiction | ((?[X]:(~tall(X)))<=>((old(john)<~>funny(john))))&
(((~humble(fred)|creative(fred)))<=>(?[X]:((patient(X)&quiet(X)))))&
(![X]:((~patient(X)|~generous(X))=>(happy(X)|humble(X))))&
((?[X]:((brave(X)|humble(X))))=>(~generous(mary)))&
(![X]:(funny(X)<=>~quiet(X)))&
((generous(lucy))<=>(?[X]:((~old(X)<~>tall(X)))))&
(((kind(paul)|strong(paul)))<=>((~creative(lucy)<~>funny(lucy))))&
(((~funny(john)<~>strong(john)))<=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((~funny(X)&patient(X))=>(quiet(X)&~strong(X))))&
(![X]:((~quiet(X)|~curious(X))=>(~strong(X)&tall(X))))&
(![X]:(~funny(X)<=>(~strong(X)&wise(X))))&
(((wise(paul)&~humble(paul)))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:((brave(X)<~>tall(X))=>~funny(X)))&
((?[X]:(curious(X)))=>(~happy(mary)))&
(![X]:(quiet(X)<=>(~funny(X)<~>~creative(X))))&
((?[X]:((old(X)&kind(X))))<=>(?[X]:(humble(X))))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)<~>~funny(X))))&
((~curious(mary)&kind(mary)))&
((~quiet(fred)&~kind(fred)))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
((~happy(mary)|~wise(mary))) | wise(fred) | [
"p4",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8613510457895053764487549
% SZS output start Proof for 8613510457895053764487549
5. ! [X0] : (funny(X0) <=> ~quiet(X0)) [input p4]
10. ! [X0] : ((~curious(X0) | ~quiet(X0)) => (tall(X0) & ~strong(X0))) [input p9]
11. ! [X0] : (~funny(X0) <=> (wise(X0) & ~strong(X0))) [input p10]
20. ~kind(fred) & ~quiet(fred) [input p19]
25. wise(fred) [input hypothesis]
32. ! [X0] : ((tall(X0) & ~strong(X0)) | (curious(X0) & quiet(X0))) [ennf transformation 10]
44. ! [X0] : ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))) [nnf transformation 5]
55. ! [X0] : ((~funny(X0) | (~wise(X0) | strong(X0))) & ((wise(X0) & ~strong(X0)) | funny(X0))) [nnf transformation 11]
56. ! [X0] : ((~funny(X0) | ~wise(X0) | strong(X0)) & ((wise(X0) & ~strong(X0)) | funny(X0))) [flattening 55]
95. quiet(X0) | funny(X0) [cnf transformation 44]
116. ~strong(X0) | quiet(X0) [cnf transformation 32]
122. ~wise(X0) | ~funny(X0) | strong(X0) [cnf transformation 56]
144. ~quiet(fred) [cnf transformation 20]
151. wise(fred) [cnf transformation 25]
381. funny(fred) [resolution 95,144]
460. ~funny(fred) | strong(fred) [resolution 122,151]
462. strong(fred) [subsumption resolution 460,381]
466. quiet(fred) [resolution 462,116]
467. $false [subsumption resolution 466,144]
% SZS output end Proof for 8613510457895053764487549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not tall is curious. If john is both not quiet and not patient then lucy is not generous and vice versa. Everyone who is both not tall and not patient is not wise and vice versa. Everyone who is tall is funny. If john is not kind or not brave then john is both brave and not old and vice versa. Everyone who is humble is both not old and calm. Everyone who is both not tall and rich is not calm or brave and vice versa. If someone is both humble and not rich then paul is kind or not patient. If someone is both not calm and not curious then alice is rich and vice versa. If fred is either rich or not funny then fred is not curious or not wise and vice versa. If john is quiet then fred is either not creative or not humble and vice versa. If paul is brave or kind then susan is old or not quiet and vice versa. Everyone who is not curious is not funny or brave. Everyone who is curious or old is not curious or not creative and vice versa. Everyone who is both wise and happy is both calm and wise. If susan is either not humble or not kind then someone is both not funny and creative. Paul is either brave or humble. Mary is strong or not generous. Lucy is either not creative or kind. Paul is not wise or brave. John is either not rich or not creative. Mary is strong. Fred is not tall. | Lucy is not old. | neutral | (![X]:((kind(X)|~tall(X))=>curious(X)))&
(((~quiet(john)&~patient(john)))<=>(~generous(lucy)))&
(![X]:((~tall(X)&~patient(X))<=>~wise(X)))&
(![X]:(tall(X)=>funny(X)))&
(((~kind(john)|~brave(john)))<=>((brave(john)&~old(john))))&
(![X]:(humble(X)=>(~old(X)&calm(X))))&
(![X]:((~tall(X)&rich(X))<=>(~calm(X)|brave(X))))&
((?[X]:((humble(X)&~rich(X))))=>((kind(paul)|~patient(paul))))&
((?[X]:((~calm(X)&~curious(X))))<=>(rich(alice)))&
(((rich(fred)<~>~funny(fred)))<=>((~curious(fred)|~wise(fred))))&
((quiet(john))<=>((~creative(fred)<~>~humble(fred))))&
(((brave(paul)|kind(paul)))<=>((old(susan)|~quiet(susan))))&
(![X]:(~curious(X)=>(~funny(X)|brave(X))))&
(![X]:((curious(X)|old(X))<=>(~curious(X)|~creative(X))))&
(![X]:((wise(X)&happy(X))=>(calm(X)&wise(X))))&
(((~humble(susan)<~>~kind(susan)))=>(?[X]:((~funny(X)&creative(X)))))&
((brave(paul)<~>humble(paul)))&
((strong(mary)|~generous(mary)))&
((~creative(lucy)<~>kind(lucy)))&
((~wise(paul)|brave(paul)))&
((~rich(john)<~>~creative(john)))&
(strong(mary))&
(~tall(fred)) | ~old(lucy) | [] | null | 0 |
Everyone who is either not happy or not curious is curious.
If someone is either rich or funny then someone is both humble and creative and vice versa.
If john is both not generous and generous then someone is either humble or tall.
Everyone who is not kind or creative is not calm or old and vice versa.
If alice is funny or kind then alice is not quiet or quiet and vice versa.
Everyone who is both quiet and rich is both curious and kind.
Everyone who is not tall or creative is creative and vice versa.
If paul is either happy or not wise then someone is humble and vice versa.
If lucy is either not funny or not strong then someone is either not curious or not rich and vice versa.
Everyone who is curious is both not patient and not curious and vice versa.
If someone is not happy then someone is wise or creative and vice versa.
Everyone who is both wise and not funny is rich or not happy and vice versa.
If someone is old or not brave then susan is both humble and not quiet and vice versa.
If mary is not calm or humble then someone is brave or not funny and vice versa.
Everyone who is either not tall or quiet is either not curious or not quiet and vice versa.
Fred is either curious or not calm.
Someone is calm or tall.
Fred is either quiet or not patient.
Someone is either not brave or not calm.
Someone is brave or creative. | John is not curious. | entailment | (![X]:((~happy(X)<~>~curious(X))=>curious(X)))&
((?[X]:((rich(X)<~>funny(X))))<=>(?[X]:((humble(X)&creative(X)))))&
(((~generous(john)&generous(john)))=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:((~kind(X)|creative(X))<=>(~calm(X)|old(X))))&
(((funny(alice)|kind(alice)))<=>((~quiet(alice)|quiet(alice))))&
(![X]:((quiet(X)&rich(X))=>(curious(X)&kind(X))))&
(![X]:((~tall(X)|creative(X))<=>creative(X)))&
(((happy(paul)<~>~wise(paul)))<=>(?[X]:(humble(X))))&
(((~funny(lucy)<~>~strong(lucy)))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:(curious(X)<=>(~patient(X)&~curious(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((wise(X)&~funny(X))<=>(rich(X)|~happy(X))))&
((?[X]:((old(X)|~brave(X))))<=>((humble(susan)&~quiet(susan))))&
(((~calm(mary)|humble(mary)))<=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~curious(X)<~>~quiet(X))))&
((curious(fred)<~>~calm(fred)))&
(?[X]:((calm(X)|tall(X))))&
((quiet(fred)<~>~patient(fred)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((brave(X)|creative(X)))) | ~curious(john) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7678405852464783616157872
% SZS output start Proof for 7678405852464783616157872
10. ! [X0] : (curious(X0) <=> (~curious(X0) & ~patient(X0))) [input p9]
21. curious(john) [input hypothesis]
52. ! [X0] : ((curious(X0) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [nnf transformation 10]
53. ! [X0] : ((curious(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [flattening 52]
117. ~curious(X0) | ~curious(X0) [cnf transformation 53]
152. curious(john) [cnf transformation 21]
157. ~curious(X0) [duplicate literal removal 117]
364. $false [subsumption resolution 152,157]
% SZS output end Proof for 7678405852464783616157872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If alice is old then someone is generous or tall. Everyone who is patient or not quiet is both wise and kind. Everyone who is creative or patient is both not generous and generous. If someone is either creative or quiet then susan is both not happy and curious and vice versa. Everyone who is both generous and not calm is not happy and vice versa. If someone is both not curious and strong then john is either not quiet or rich and vice versa. Everyone who is both curious and not creative is either curious or not calm. Everyone who is either not patient or not rich is both not calm and not curious and vice versa. Everyone who is both not tall and not calm is wise and vice versa. If someone is not kind or not creative then someone is both old and not creative. Everyone who is happy is not happy or old. If someone is both calm and not rich then someone is happy. If lucy is not funny then mary is both kind and not kind. If lucy is either not happy or not generous then susan is not curious. Everyone who is old or brave is not quiet. Someone is not old. Someone is either not rich or not funny. Mary is both generous and not funny. Mary is not quiet or curious. Mary is either tall or brave. | Lucy is not wise. | contradiction | ((old(alice))=>(?[X]:((generous(X)|tall(X)))))&
(![X]:((patient(X)|~quiet(X))=>(wise(X)&kind(X))))&
(![X]:((creative(X)|patient(X))=>(~generous(X)&generous(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>((~happy(susan)&curious(susan))))&
(![X]:((generous(X)&~calm(X))<=>~happy(X)))&
((?[X]:((~curious(X)&strong(X))))<=>((~quiet(john)<~>rich(john))))&
(![X]:((curious(X)&~creative(X))=>(curious(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>~rich(X))<=>(~calm(X)&~curious(X))))&
(![X]:((~tall(X)&~calm(X))<=>wise(X)))&
((?[X]:((~kind(X)|~creative(X))))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:(happy(X)=>(~happy(X)|old(X))))&
((?[X]:((calm(X)&~rich(X))))=>(?[X]:(happy(X))))&
((~funny(lucy))=>((kind(mary)&~kind(mary))))&
(((~happy(lucy)<~>~generous(lucy)))=>(~curious(susan)))&
(![X]:((old(X)|brave(X))=>~quiet(X)))&
(?[X]:(~old(X)))&
(?[X]:((~rich(X)<~>~funny(X))))&
((generous(mary)&~funny(mary)))&
((~quiet(mary)|curious(mary)))&
((tall(mary)<~>brave(mary))) | ~wise(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 657157931200800950143890
% SZS output start Proof for 657157931200800950143890
2. ! [X0] : ((~quiet(X0) | patient(X0)) => (kind(X0) & wise(X0))) [input p1]
3. ! [X0] : ((patient(X0) | creative(X0)) => (generous(X0) & ~generous(X0))) [input p2]
4. ? [X0] : (creative(X0) <~> quiet(X0)) <=> (curious(susan) & ~happy(susan)) [input p3]
5. ! [X0] : ((~calm(X0) & generous(X0)) <=> ~happy(X0)) [input p4]
11. ! [X0] : (happy(X0) => (old(X0) | ~happy(X0))) [input p10]
14. (~happy(lucy) <~> ~generous(lucy)) => ~curious(susan) [input p13]
15. ! [X0] : ((brave(X0) | old(X0)) => ~quiet(X0)) [input p14]
21. ~wise(lucy) [input hypothesis]
25. ! [X0] : ((kind(X0) & wise(X0)) | (quiet(X0) & ~patient(X0))) [ennf transformation 2]
26. ! [X0] : ((generous(X0) & ~generous(X0)) | (~patient(X0) & ~creative(X0))) [ennf transformation 3]
30. ! [X0] : ((old(X0) | ~happy(X0)) | ~happy(X0)) [ennf transformation 11]
31. ! [X0] : (old(X0) | ~happy(X0) | ~happy(X0)) [flattening 30]
34. ~curious(susan) | (~happy(lucy) <=> ~generous(lucy)) [ennf transformation 14]
35. ! [X0] : (~quiet(X0) | (~brave(X0) & ~old(X0))) [ennf transformation 15]
38. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | (~curious(susan) | happy(susan))) & ((curious(susan) & ~happy(susan)) | ! [X0] : ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) [nnf transformation 4]
39. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ~curious(susan) | happy(susan)) & ((curious(susan) & ~happy(susan)) | ! [X0] : ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) [flattening 38]
40. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ~curious(susan) | happy(susan)) & ((curious(susan) & ~happy(susan)) | ! [X1] : ((creative(X1) | ~quiet(X1)) & (quiet(X1) | ~creative(X1)))) [rectify 39]
41. ? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) => ((~quiet(sK1) | ~creative(sK1)) & (quiet(sK1) | creative(sK1))) [choice axiom]
42. (((~quiet(sK1) | ~creative(sK1)) & (quiet(sK1) | creative(sK1))) | ~curious(susan) | happy(susan)) & ((curious(susan) & ~happy(susan)) | ! [X1] : ((creative(X1) | ~quiet(X1)) & (quiet(X1) | ~creative(X1)))) [skolemisation 40,41]
43. ! [X0] : (((~calm(X0) & generous(X0)) | happy(X0)) & (~happy(X0) | (calm(X0) | ~generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((~calm(X0) & generous(X0)) | happy(X0)) & (~happy(X0) | calm(X0) | ~generous(X0))) [flattening 43]
60. ~curious(susan) | ((~happy(lucy) | generous(lucy)) & (~generous(lucy) | happy(lucy))) [nnf transformation 34]
69. wise(X0) | quiet(X0) [cnf transformation 25]
72. ~generous(X0) | ~creative(X0) [cnf transformation 26]
74. ~creative(X0) | generous(X0) [cnf transformation 26]
79. curious(susan) | creative(X1) | ~quiet(X1) [cnf transformation 42]
83. happy(X0) | generous(X0) [cnf transformation 44]
106. old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 31]
110. ~curious(susan) | ~generous(lucy) | happy(lucy) [cnf transformation 60]
112. ~quiet(X0) | ~old(X0) [cnf transformation 35]
122. ~wise(lucy) [cnf transformation 21]
123. ~happy(X0) | old(X0) [duplicate literal removal 106]
139. ~creative(X0) [subsumption resolution 72,74]
146. 5 <=> curious(susan) [avatar definition]
154. curious(susan) | ~quiet(X1) [subsumption resolution 79,139]
156. 7 <=> ! [X1] : ~quiet(X1) [avatar definition]
157. ~quiet(X1) <- (7) [avatar component clause 156]
158. 7 | 5 [avatar split clause 154,146,156]
217. ~curious(susan) | happy(lucy) [subsumption resolution 110,83]
219. 18 <=> happy(lucy) [avatar definition]
221. happy(lucy) <- (18) [avatar component clause 219]
222. 18 | ~5 [avatar split clause 217,146,219]
254. quiet(lucy) [resolution 69,122]
255. $false <- (7) [subsumption resolution 254,157]
256. ~7 [avatar contradiction clause 255]
260. ~old(lucy) [resolution 112,254]
262. old(lucy) <- (18) [resolution 123,221]
264. $false <- (18) [subsumption resolution 262,260]
265. ~18 [avatar contradiction clause 264]
266. $false [avatar sat refutation 158,222,256,265]
% SZS output end Proof for 657157931200800950143890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either not funny or not kind then john is calm and vice versa.
Everyone who is not old or not happy is not quiet and vice versa.
Everyone who is not curious or humble is either funny or not funny.
Everyone who is not kind is rich or not calm.
If lucy is both not curious and not tall then paul is either not rich or rich and vice versa.
Everyone who is either rich or funny is not rich or not kind.
If fred is both old and not brave then paul is both not brave and creative and vice versa.
Everyone who is either humble or funny is old or not tall and vice versa.
Everyone who is patient is not generous.
Everyone who is both not wise and not funny is funny or not brave.
If susan is not happy then someone is either kind or not generous.
If mary is creative or patient then mary is not brave and vice versa.
Everyone who is either not happy or not strong is not happy or quiet and vice versa.
If someone is humble then someone is either funny or not wise and vice versa.
If lucy is kind or rich then mary is curious and vice versa.
Everyone who is tall or brave is either wise or not quiet and vice versa.
Alice is both not kind and not calm.
Someone is both calm and wise.
Fred is either rich or not brave.
Paul is not funny.
Lucy is either not creative or not rich.
Alice is both not rich and not humble.
Paul is either strong or happy.
Someone is either curious or not quiet. | Paul is strong. | neutral | (((~funny(susan)<~>~kind(susan)))<=>(calm(john)))&
(![X]:((~old(X)|~happy(X))<=>~quiet(X)))&
(![X]:((~curious(X)|humble(X))=>(funny(X)<~>~funny(X))))&
(![X]:(~kind(X)=>(rich(X)|~calm(X))))&
(((~curious(lucy)&~tall(lucy)))<=>((~rich(paul)<~>rich(paul))))&
(![X]:((rich(X)<~>funny(X))=>(~rich(X)|~kind(X))))&
(((old(fred)&~brave(fred)))<=>((~brave(paul)&creative(paul))))&
(![X]:((humble(X)<~>funny(X))<=>(old(X)|~tall(X))))&
(![X]:(patient(X)=>~generous(X)))&
(![X]:((~wise(X)&~funny(X))=>(funny(X)|~brave(X))))&
((~happy(susan))=>(?[X]:((kind(X)<~>~generous(X)))))&
(((creative(mary)|patient(mary)))<=>(~brave(mary)))&
(![X]:((~happy(X)<~>~strong(X))<=>(~happy(X)|quiet(X))))&
((?[X]:(humble(X)))<=>(?[X]:((funny(X)<~>~wise(X)))))&
(((kind(lucy)|rich(lucy)))<=>(curious(mary)))&
(![X]:((tall(X)|brave(X))<=>(wise(X)<~>~quiet(X))))&
((~kind(alice)&~calm(alice)))&
(?[X]:((calm(X)&wise(X))))&
((rich(fred)<~>~brave(fred)))&
(~funny(paul))&
((~creative(lucy)<~>~rich(lucy)))&
((~rich(alice)&~humble(alice)))&
((strong(paul)<~>happy(paul)))&
(?[X]:((curious(X)<~>~quiet(X)))) | strong(paul) | [] | null | 0 |
If someone is not curious or rich then someone is both quiet and not curious and vice versa. If someone is either not humble or not curious then susan is both not creative and not old. Everyone who is not rich or not happy is wise and vice versa. Everyone who is not kind or not funny is either quiet or calm and vice versa. Everyone who is not creative or patient is either not strong or old. If paul is both rich and not creative then someone is both curious and not humble. Everyone who is both not curious and generous is both strong and kind. Everyone who is either not creative or patient is both creative and brave and vice versa. If someone is not calm or not humble then susan is kind. Everyone who is not kind or quiet is both not patient and not funny and vice versa. Everyone who is either not strong or not patient is not brave and vice versa. If mary is not generous then someone is happy and vice versa. Everyone who is not happy or not tall is humble or happy and vice versa. Everyone who is creative or not old is both not creative and tall. Everyone who is both wise and humble is either old or wise. If john is both not generous and strong then someone is either calm or not patient. John is not strong or not kind. Fred is both generous and old. Lucy is not old. Someone is funny. Paul is both curious and not tall. Someone is both funny and not tall. | Lucy is not rich. | entailment | ((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((quiet(X)&~curious(X)))))&
((?[X]:((~humble(X)<~>~curious(X))))=>((~creative(susan)&~old(susan))))&
(![X]:((~rich(X)|~happy(X))<=>wise(X)))&
(![X]:((~kind(X)|~funny(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~creative(X)|patient(X))=>(~strong(X)<~>old(X))))&
(((rich(paul)&~creative(paul)))=>(?[X]:((curious(X)&~humble(X)))))&
(![X]:((~curious(X)&generous(X))=>(strong(X)&kind(X))))&
(![X]:((~creative(X)<~>patient(X))<=>(creative(X)&brave(X))))&
((?[X]:((~calm(X)|~humble(X))))=>(kind(susan)))&
(![X]:((~kind(X)|quiet(X))<=>(~patient(X)&~funny(X))))&
(![X]:((~strong(X)<~>~patient(X))<=>~brave(X)))&
((~generous(mary))<=>(?[X]:(happy(X))))&
(![X]:((~happy(X)|~tall(X))<=>(humble(X)|happy(X))))&
(![X]:((creative(X)|~old(X))=>(~creative(X)&tall(X))))&
(![X]:((wise(X)&humble(X))=>(old(X)<~>wise(X))))&
(((~generous(john)&strong(john)))=>(?[X]:((calm(X)<~>~patient(X)))))&
((~strong(john)|~kind(john)))&
((generous(fred)&old(fred)))&
(~old(lucy))&
(?[X]:(funny(X)))&
((curious(paul)&~tall(paul)))&
(?[X]:((funny(X)&~tall(X)))) | ~rich(lucy) | [
"p0",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8722236179434657133629564
% SZS output start Proof for 8722236179434657133629564
1. ? [X0] : (rich(X0) | ~curious(X0)) <=> ? [X0] : (~curious(X0) & quiet(X0)) [input p0]
8. ! [X0] : ((~creative(X0) <~> patient(X0)) <=> (brave(X0) & creative(X0))) [input p7]
10. ! [X0] : ((quiet(X0) | ~kind(X0)) <=> (~funny(X0) & ~patient(X0))) [input p9]
14. ! [X0] : ((~old(X0) | creative(X0)) => (tall(X0) & ~creative(X0))) [input p13]
23. rich(lucy) [input hypothesis]
24. ? [X0] : (rich(X0) | ~curious(X0)) <=> ? [X1] : (~curious(X1) & quiet(X1)) [rectify 1]
32. ! [X0] : ((tall(X0) & ~creative(X0)) | (old(X0) & ~creative(X0))) [ennf transformation 14]
37. (? [X0] : (rich(X0) | ~curious(X0)) | ! [X1] : (curious(X1) | ~quiet(X1))) & (? [X1] : (~curious(X1) & quiet(X1)) | ! [X0] : (~rich(X0) & curious(X0))) [nnf transformation 24]
38. (? [X0] : (rich(X0) | ~curious(X0)) | ! [X1] : (curious(X1) | ~quiet(X1))) & (? [X2] : (~curious(X2) & quiet(X2)) | ! [X3] : (~rich(X3) & curious(X3))) [rectify 37]
39. ? [X0] : (rich(X0) | ~curious(X0)) => (rich(sK0) | ~curious(sK0)) [choice axiom]
40. ? [X2] : (~curious(X2) & quiet(X2)) => (~curious(sK1) & quiet(sK1)) [choice axiom]
41. ((rich(sK0) | ~curious(sK0)) | ! [X1] : (curious(X1) | ~quiet(X1))) & ((~curious(sK1) & quiet(sK1)) | ! [X3] : (~rich(X3) & curious(X3))) [skolemisation 38,40,39]
50. ! [X0] : ((((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | (~brave(X0) | ~creative(X0))) & ((brave(X0) & creative(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0))))) [nnf transformation 8]
51. ! [X0] : ((((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | ~brave(X0) | ~creative(X0)) & ((brave(X0) & creative(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0))))) [flattening 50]
52. ! [X0] : (((quiet(X0) | ~kind(X0)) | (funny(X0) | patient(X0))) & ((~funny(X0) & ~patient(X0)) | (~quiet(X0) & kind(X0)))) [nnf transformation 10]
53. ! [X0] : ((quiet(X0) | ~kind(X0) | funny(X0) | patient(X0)) & ((~funny(X0) & ~patient(X0)) | (~quiet(X0) & kind(X0)))) [flattening 52]
70. quiet(sK1) | ~rich(X3) [cnf transformation 41]
95. creative(X0) | patient(X0) | creative(X0) [cnf transformation 51]
104. ~patient(X0) | ~quiet(X0) [cnf transformation 53]
118. ~creative(X0) | ~creative(X0) [cnf transformation 32]
135. rich(lucy) [cnf transformation 23]
137. ~creative(X0) [duplicate literal removal 118]
140. patient(X0) | creative(X0) [duplicate literal removal 95]
155. 4 <=> ! [X3] : ~rich(X3) [avatar definition]
156. ~rich(X3) <- (4) [avatar component clause 155]
167. 7 <=> quiet(sK1) [avatar definition]
169. quiet(sK1) <- (7) [avatar component clause 167]
170. 4 | 7 [avatar split clause 70,167,155]
258. $false <- (4) [resolution 156,135]
259. ~4 [avatar contradiction clause 258]
269. creative(X0) | ~quiet(X0) [resolution 140,104]
271. ~quiet(X0) [subsumption resolution 269,137]
275. $false <- (7) [resolution 271,169]
276. ~7 [avatar contradiction clause 275]
277. $false [avatar sat refutation 170,259,276]
% SZS output end Proof for 8722236179434657133629564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both calm and not patient then someone is either not creative or rich.
Everyone who is either not generous or not quiet is calm and vice versa.
Everyone who is old is both not quiet and not generous and vice versa.
If someone is either not strong or calm then someone is creative or wise.
Everyone who is either not generous or not tall is both not happy and kind.
Everyone who is either tall or not happy is both brave and old and vice versa.
Everyone who is both rich and not rich is both rich and old and vice versa.
Everyone who is generous or funny is not rich and vice versa.
If someone is not calm then alice is both not calm and not old.
Everyone who is creative is not calm.
If someone is either wise or not strong then john is not old or wise.
Everyone who is both wise and humble is not kind and vice versa.
If fred is both not tall and wise then someone is both not funny and funny.
If someone is both not creative and not patient then alice is both old and not funny and vice versa.
Everyone who is generous is either not strong or generous and vice versa.
If someone is not funny then someone is not rich or patient and vice versa.
Someone is both wise and not patient.
Someone is both happy and rich.
Someone is both tall and not quiet.
Someone is brave or not creative.
Fred is both not kind and strong.
Someone is calm.
Someone is strong.
Susan is either not old or generous. | Susan is patient. | entailment | ((?[X]:((calm(X)&~patient(X))))=>(?[X]:((~creative(X)<~>rich(X)))))&
(![X]:((~generous(X)<~>~quiet(X))<=>calm(X)))&
(![X]:(old(X)<=>(~quiet(X)&~generous(X))))&
((?[X]:((~strong(X)<~>calm(X))))=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((~generous(X)<~>~tall(X))=>(~happy(X)&kind(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(brave(X)&old(X))))&
(![X]:((rich(X)&~rich(X))<=>(rich(X)&old(X))))&
(![X]:((generous(X)|funny(X))<=>~rich(X)))&
((?[X]:(~calm(X)))=>((~calm(alice)&~old(alice))))&
(![X]:(creative(X)=>~calm(X)))&
((?[X]:((wise(X)<~>~strong(X))))=>((~old(john)|wise(john))))&
(![X]:((wise(X)&humble(X))<=>~kind(X)))&
(((~tall(fred)&wise(fred)))=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((~creative(X)&~patient(X))))<=>((old(alice)&~funny(alice))))&
(![X]:(generous(X)<=>(~strong(X)<~>generous(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~rich(X)|patient(X)))))&
(?[X]:((wise(X)&~patient(X))))&
(?[X]:((happy(X)&rich(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(?[X]:((brave(X)|~creative(X))))&
((~kind(fred)&strong(fred)))&
(?[X]:(calm(X)))&
(?[X]:(strong(X)))&
((~old(susan)<~>generous(susan))) | patient(susan) | [
"p1",
"p2",
"p8",
"p9",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3711326374369405449535485
% SZS output start Proof for 3711326374369405449535485
2. ! [X0] : ((~generous(X0) <~> ~quiet(X0)) <=> calm(X0)) [input p1]
3. ! [X0] : (old(X0) <=> (~generous(X0) & ~quiet(X0))) [input p2]
9. ? [X0] : ~calm(X0) => (~old(alice) & ~calm(alice)) [input p8]
10. ! [X0] : (creative(X0) => ~calm(X0)) [input p9]
14. ? [X0] : (~patient(X0) & ~creative(X0)) <=> (~funny(alice) & old(alice)) [input p13]
24. ~old(susan) <~> generous(susan) [input p23]
25. ~patient(susan) [input hypothesis]
32. (~old(alice) & ~calm(alice)) | ! [X0] : calm(X0) [ennf transformation 9]
33. ! [X0] : (~calm(X0) | ~creative(X0)) [ennf transformation 10]
42. ! [X0] : ((((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | ~calm(X0)) & (calm(X0) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0))))) [nnf transformation 2]
43. ! [X0] : ((old(X0) | (generous(X0) | quiet(X0))) & ((~generous(X0) & ~quiet(X0)) | ~old(X0))) [nnf transformation 3]
44. ! [X0] : ((old(X0) | generous(X0) | quiet(X0)) & ((~generous(X0) & ~quiet(X0)) | ~old(X0))) [flattening 43]
61. (? [X0] : (~patient(X0) & ~creative(X0)) | (funny(alice) | ~old(alice))) & ((~funny(alice) & old(alice)) | ! [X0] : (patient(X0) | creative(X0))) [nnf transformation 14]
62. (? [X0] : (~patient(X0) & ~creative(X0)) | funny(alice) | ~old(alice)) & ((~funny(alice) & old(alice)) | ! [X0] : (patient(X0) | creative(X0))) [flattening 61]
63. (? [X0] : (~patient(X0) & ~creative(X0)) | funny(alice) | ~old(alice)) & ((~funny(alice) & old(alice)) | ! [X1] : (patient(X1) | creative(X1))) [rectify 62]
64. ? [X0] : (~patient(X0) & ~creative(X0)) => (~patient(sK3) & ~creative(sK3)) [choice axiom]
65. ((~patient(sK3) & ~creative(sK3)) | funny(alice) | ~old(alice)) & ((~funny(alice) & old(alice)) | ! [X1] : (patient(X1) | creative(X1))) [skolemisation 63,64]
84. (~generous(susan) | old(susan)) & (generous(susan) | ~old(susan)) [nnf transformation 24]
87. ~quiet(X0) | calm(X0) | generous(X0) [cnf transformation 42]
90. ~calm(X0) | generous(X0) | quiet(X0) [cnf transformation 42]
91. ~old(X0) | ~quiet(X0) [cnf transformation 44]
92. ~old(X0) | ~generous(X0) [cnf transformation 44]
93. old(X0) | generous(X0) | quiet(X0) [cnf transformation 44]
114. ~old(alice) | calm(X0) [cnf transformation 32]
115. ~creative(X0) | ~calm(X0) [cnf transformation 33]
123. old(alice) | patient(X1) | creative(X1) [cnf transformation 65]
145. generous(susan) | ~old(susan) [cnf transformation 84]
146. ~generous(susan) | old(susan) [cnf transformation 84]
147. ~patient(susan) [cnf transformation 25]
153. 1 <=> ! [X1] : (patient(X1) | ~calm(X1)) [avatar definition]
154. ~calm(X1) | patient(X1) <- (1) [avatar component clause 153]
182. 8 <=> ! [X0] : calm(X0) [avatar definition]
183. calm(X0) <- (8) [avatar component clause 182]
185. 9 <=> old(alice) [avatar definition]
186. old(alice) <- (9) [avatar component clause 185]
188. 8 | ~9 [avatar split clause 114,185,182]
239. 21 <=> ! [X1] : (patient(X1) | creative(X1)) [avatar definition]
240. creative(X1) | patient(X1) <- (21) [avatar component clause 239]
242. 21 | 9 [avatar split clause 123,185,239]
277. ~generous(susan) [subsumption resolution 146,92]
278. ~old(susan) [subsumption resolution 145,277]
279. ~quiet(alice) <- (9) [resolution 91,186]
280. ~generous(alice) <- (9) [resolution 92,186]
290. quiet(X0) | generous(X0) <- (8) [resolution 90,183]
301. generous(susan) | quiet(susan) [resolution 93,278]
350. generous(alice) <- (8, 9) [resolution 290,279]
354. $false <- (8, 9) [subsumption resolution 350,280]
355. ~8 | ~9 [avatar contradiction clause 354]
357. patient(X0) | ~calm(X0) <- (21) [resolution 240,115]
437. quiet(susan) [subsumption resolution 301,277]
482. calm(susan) | generous(susan) [resolution 437,87]
483. calm(susan) [subsumption resolution 482,277]
496. patient(susan) <- (1) [resolution 483,154]
498. $false <- (1) [subsumption resolution 496,147]
499. ~1 [avatar contradiction clause 498]
500. 1 | ~21 [avatar split clause 357,239,153]
501. $false [avatar sat refutation 188,242,355,499,500]
% SZS output end Proof for 3711326374369405449535485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and generous is not happy and vice versa.
Everyone who is either not creative or quiet is either not wise or humble and vice versa.
Everyone who is not quiet or not generous is either curious or not old and vice versa.
Everyone who is either not quiet or not patient is both not curious and quiet.
Everyone who is either not old or not rich is both not quiet and calm and vice versa.
If someone is either not wise or not brave then someone is not wise.
If alice is tall or not rich then someone is both calm and not happy and vice versa.
Everyone who is both not brave and not kind is not strong or quiet.
If someone is not humble then john is either brave or rich and vice versa.
If paul is not humble or old then someone is either not creative or not strong.
If alice is both creative and tall then someone is funny and vice versa.
If someone is both not curious and not tall then someone is either curious or not old and vice versa.
Everyone who is not tall or not brave is both kind and curious.
Everyone who is tall or happy is not brave or humble.
If alice is not patient then mary is either not creative or brave and vice versa.
Everyone who is not strong or not wise is both calm and not humble and vice versa.
Someone is both funny and patient.
Fred is quiet.
Someone is either not calm or not kind.
Someone is tall.
Someone is creative.
Mary is either not rich or rich.
Paul is either quiet or old.
Lucy is funny or generous. | Paul is rich. | contradiction | (![X]:((brave(X)&generous(X))<=>~happy(X)))&
(![X]:((~creative(X)<~>quiet(X))<=>(~wise(X)<~>humble(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(curious(X)<~>~old(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(~curious(X)&quiet(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~quiet(X)&calm(X))))&
((?[X]:((~wise(X)<~>~brave(X))))=>(?[X]:(~wise(X))))&
(((tall(alice)|~rich(alice)))<=>(?[X]:((calm(X)&~happy(X)))))&
(![X]:((~brave(X)&~kind(X))=>(~strong(X)|quiet(X))))&
((?[X]:(~humble(X)))<=>((brave(john)<~>rich(john))))&
(((~humble(paul)|old(paul)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(((creative(alice)&tall(alice)))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~tall(X)|~brave(X))=>(kind(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(~brave(X)|humble(X))))&
((~patient(alice))<=>((~creative(mary)<~>brave(mary))))&
(![X]:((~strong(X)|~wise(X))<=>(calm(X)&~humble(X))))&
(?[X]:((funny(X)&patient(X))))&
(quiet(fred))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:(tall(X)))&
(?[X]:(creative(X)))&
((~rich(mary)<~>rich(mary)))&
((quiet(paul)<~>old(paul)))&
((funny(lucy)|generous(lucy))) | rich(paul) | [
"p2",
"p4",
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 393227149884910468558978
% SZS output start Proof for 393227149884910468558978
3. ! [X0] : ((~generous(X0) | ~quiet(X0)) <=> (curious(X0) <~> ~old(X0))) [input p2]
5. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (calm(X0) & ~quiet(X0))) [input p4]
12. ? [X0] : (~tall(X0) & ~curious(X0)) <=> ? [X0] : (curious(X0) <~> ~old(X0)) [input p11]
13. ! [X0] : ((~brave(X0) | ~tall(X0)) => (curious(X0) & kind(X0))) [input p12]
23. quiet(paul) <~> old(paul) [input p22]
25. rich(paul) [input hypothesis]
27. ? [X0] : (~tall(X0) & ~curious(X0)) <=> ? [X1] : (curious(X1) <~> ~old(X1)) [rectify 12]
33. ! [X0] : ((curious(X0) & kind(X0)) | (brave(X0) & tall(X0))) [ennf transformation 13]
39. ! [X0] : (((~generous(X0) | ~quiet(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (generous(X0) & quiet(X0)))) [nnf transformation 3]
40. ! [X0] : ((~generous(X0) | ~quiet(X0) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (generous(X0) & quiet(X0)))) [flattening 39]
42. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 5]
43. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 42]
65. (? [X0] : (~tall(X0) & ~curious(X0)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (? [X1] : ((old(X1) | ~curious(X1)) & (~old(X1) | curious(X1))) | ! [X0] : (tall(X0) | curious(X0))) [nnf transformation 27]
66. (? [X0] : (~tall(X0) & ~curious(X0)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (? [X2] : ((old(X2) | ~curious(X2)) & (~old(X2) | curious(X2))) | ! [X3] : (tall(X3) | curious(X3))) [rectify 65]
67. ? [X0] : (~tall(X0) & ~curious(X0)) => (~tall(sK5) & ~curious(sK5)) [choice axiom]
68. ? [X2] : ((old(X2) | ~curious(X2)) & (~old(X2) | curious(X2))) => ((old(sK6) | ~curious(sK6)) & (~old(sK6) | curious(sK6))) [choice axiom]
69. ((~tall(sK5) & ~curious(sK5)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (((old(sK6) | ~curious(sK6)) & (~old(sK6) | curious(sK6))) | ! [X3] : (tall(X3) | curious(X3))) [skolemisation 66,68,67]
83. (~old(paul) | ~quiet(paul)) & (old(paul) | quiet(paul)) [nnf transformation 23]
95. ~old(X0) | curious(X0) | quiet(X0) [cnf transformation 40]
105. ~rich(X0) | ~quiet(X0) | old(X0) [cnf transformation 43]
132. ~curious(sK5) | ~old(X1) | ~curious(X1) [cnf transformation 69]
134. ~tall(sK5) | ~old(X1) | ~curious(X1) [cnf transformation 69]
138. curious(X0) | tall(X0) [cnf transformation 33]
160. old(paul) | quiet(paul) [cnf transformation 83]
161. ~old(paul) | ~quiet(paul) [cnf transformation 83]
163. rich(paul) [cnf transformation 25]
221. 13 <=> old(paul) [avatar definition]
222. old(paul) <- (13) [avatar component clause 221]
223. ~old(paul) <- (~13) [avatar component clause 221]
258. 21 <=> tall(sK5) [avatar definition]
260. ~tall(sK5) <- (~21) [avatar component clause 258]
263. 22 <=> ! [X1] : (~old(X1) | ~curious(X1)) [avatar definition]
264. ~old(X1) | ~curious(X1) <- (22) [avatar component clause 263]
265. 22 | ~21 [avatar split clause 134,258,263]
267. 23 <=> curious(sK5) [avatar definition]
269. ~curious(sK5) <- (~23) [avatar component clause 267]
271. 22 | ~23 [avatar split clause 132,267,263]
273. 24 <=> ! [X3] : (tall(X3) | curious(X3)) [avatar definition]
274. tall(X3) | curious(X3) <- (24) [avatar component clause 273]
285. 24 [avatar split clause 138,273]
313. 32 <=> quiet(paul) [avatar definition]
314. quiet(paul) <- (32) [avatar component clause 313]
315. ~quiet(paul) <- (~32) [avatar component clause 313]
316. ~32 | ~13 [avatar split clause 161,221,313]
317. 32 | 13 [avatar split clause 160,221,313]
342. curious(sK5) <- (~21, 24) [resolution 274,260]
343. $false <- (~21, ~23, 24) [subsumption resolution 342,269]
344. 21 | 23 | ~24 [avatar contradiction clause 343]
345. ~curious(paul) <- (13, 22) [resolution 264,222]
350. curious(paul) | quiet(paul) <- (13) [resolution 95,222]
353. quiet(paul) <- (13, 22) [subsumption resolution 350,345]
354. $false <- (13, 22, ~32) [subsumption resolution 353,315]
355. ~13 | ~22 | 32 [avatar contradiction clause 354]
373. ~quiet(paul) | old(paul) [resolution 105,163]
376. old(paul) <- (32) [subsumption resolution 373,314]
377. $false <- (~13, 32) [subsumption resolution 376,223]
378. 13 | ~32 [avatar contradiction clause 377]
381. $false [avatar sat refutation 265,271,285,316,317,344,355,378]
% SZS output end Proof for 393227149884910468558978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either strong or not funny is either quiet or patient and vice versa.
Everyone who is not calm or not quiet is both not wise and not patient and vice versa.
Everyone who is not curious is either wise or generous and vice versa.
Everyone who is not happy or not kind is not calm.
Everyone who is old or not generous is not strong or not brave and vice versa.
Everyone who is either tall or not curious is old or tall and vice versa.
Everyone who is kind or not happy is both not wise and funny.
If someone is not quiet then mary is creative or not calm and vice versa.
Everyone who is both calm and tall is brave.
If lucy is generous then someone is curious.
Everyone who is patient or creative is generous or not kind.
Everyone who is wise or not generous is calm.
If lucy is kind or humble then someone is both kind and patient and vice versa.
If someone is either not strong or funny then someone is either creative or patient and vice versa.
Someone is not kind.
Someone is either curious or patient.
Someone is not patient.
Someone is both not happy and funny.
Mary is not patient or not calm.
Someone is either not humble or not wise.
Someone is both humble and quiet. | Mary is happy. | neutral | (![X]:((strong(X)<~>~funny(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((~calm(X)|~quiet(X))<=>(~wise(X)&~patient(X))))&
(![X]:(~curious(X)<=>(wise(X)<~>generous(X))))&
(![X]:((~happy(X)|~kind(X))=>~calm(X)))&
(![X]:((old(X)|~generous(X))<=>(~strong(X)|~brave(X))))&
(![X]:((tall(X)<~>~curious(X))<=>(old(X)|tall(X))))&
(![X]:((kind(X)|~happy(X))=>(~wise(X)&funny(X))))&
((?[X]:(~quiet(X)))<=>((creative(mary)|~calm(mary))))&
(![X]:((calm(X)&tall(X))=>brave(X)))&
((generous(lucy))=>(?[X]:(curious(X))))&
(![X]:((patient(X)|creative(X))=>(generous(X)|~kind(X))))&
(![X]:((wise(X)|~generous(X))=>calm(X)))&
(((kind(lucy)|humble(lucy)))<=>(?[X]:((kind(X)&patient(X)))))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:((creative(X)<~>patient(X)))))&
(?[X]:(~kind(X)))&
(?[X]:((curious(X)<~>patient(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~happy(X)&funny(X))))&
((~patient(mary)|~calm(mary)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(?[X]:((humble(X)&quiet(X)))) | happy(mary) | [] | null | 0 |
If mary is not generous then someone is both not brave and calm. If someone is curious or quiet then someone is curious and vice versa. If lucy is either brave or quiet then someone is both funny and rich and vice versa. Everyone who is either not wise or curious is not wise or not strong and vice versa. Everyone who is calm or rich is not creative or not rich and vice versa. Everyone who is happy or creative is curious or not creative. Everyone who is not old or calm is not humble or not wise. If someone is both creative and not quiet then someone is either creative or wise and vice versa. Everyone who is either not calm or not curious is both not funny and calm. If someone is not funny then someone is kind and vice versa. Everyone who is wise or not creative is not strong and vice versa. Everyone who is calm or not funny is either calm or not strong and vice versa. If someone is either tall or not curious then alice is not old and vice versa. Everyone who is both tall and rich is either not creative or not rich and vice versa. Everyone who is calm is tall. Alice is either not strong or not tall. Alice is calm or not brave. John is either not brave or not creative. Someone is not strong. Someone is not patient. Alice is generous. | Alice is funny. | contradiction | ((~generous(mary))=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((curious(X)|quiet(X))))<=>(?[X]:(curious(X))))&
(((brave(lucy)<~>quiet(lucy)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~wise(X)|~strong(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)|~rich(X))))&
(![X]:((happy(X)|creative(X))=>(curious(X)|~creative(X))))&
(![X]:((~old(X)|calm(X))=>(~humble(X)|~wise(X))))&
((?[X]:((creative(X)&~quiet(X))))<=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:((~calm(X)<~>~curious(X))=>(~funny(X)&calm(X))))&
((?[X]:(~funny(X)))<=>(?[X]:(kind(X))))&
(![X]:((wise(X)|~creative(X))<=>~strong(X)))&
(![X]:((calm(X)|~funny(X))<=>(calm(X)<~>~strong(X))))&
((?[X]:((tall(X)<~>~curious(X))))<=>(~old(alice)))&
(![X]:((tall(X)&rich(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:(calm(X)=>tall(X)))&
((~strong(alice)<~>~tall(alice)))&
((calm(alice)|~brave(alice)))&
((~brave(john)<~>~creative(john)))&
(?[X]:(~strong(X)))&
(?[X]:(~patient(X)))&
(generous(alice)) | funny(alice) | [
"p4",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1732099517851284795218245
% SZS output start Proof for 1732099517851284795218245
5. ! [X0] : ((rich(X0) | calm(X0)) <=> (~rich(X0) | ~creative(X0))) [input p4]
11. ! [X0] : ((~creative(X0) | wise(X0)) <=> ~strong(X0)) [input p10]
12. ! [X0] : ((~funny(X0) | calm(X0)) <=> (calm(X0) <~> ~strong(X0))) [input p11]
14. ! [X0] : ((rich(X0) & tall(X0)) <=> (~creative(X0) <~> ~rich(X0))) [input p13]
22. funny(alice) [input hypothesis]
46. ! [X0] : (((rich(X0) | calm(X0)) | (rich(X0) & creative(X0))) & ((~rich(X0) | ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 5]
47. ! [X0] : ((rich(X0) | calm(X0) | (rich(X0) & creative(X0))) & (~rich(X0) | ~creative(X0) | (~rich(X0) & ~calm(X0)))) [flattening 46]
59. ! [X0] : (((~creative(X0) | wise(X0)) | strong(X0)) & (~strong(X0) | (creative(X0) & ~wise(X0)))) [nnf transformation 11]
60. ! [X0] : ((~creative(X0) | wise(X0) | strong(X0)) & (~strong(X0) | (creative(X0) & ~wise(X0)))) [flattening 59]
61. ! [X0] : (((~funny(X0) | calm(X0)) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | (funny(X0) & ~calm(X0)))) [nnf transformation 12]
62. ! [X0] : ((~funny(X0) | calm(X0) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | (funny(X0) & ~calm(X0)))) [flattening 61]
67. ! [X0] : (((rich(X0) & tall(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | (~rich(X0) | ~tall(X0)))) [nnf transformation 14]
68. ! [X0] : (((rich(X0) & tall(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ~rich(X0) | ~tall(X0))) [flattening 67]
89. ~rich(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 47]
106. ~strong(X0) | creative(X0) [cnf transformation 60]
110. strong(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 62]
113. ~funny(X0) | calm(X0) | calm(X0) | strong(X0) [cnf transformation 62]
123. rich(X0) | ~creative(X0) | rich(X0) [cnf transformation 68]
131. funny(alice) [cnf transformation 22]
133. rich(X0) | ~creative(X0) [duplicate literal removal 123]
134. ~calm(X0) | strong(X0) [duplicate literal removal 110]
135. ~funny(X0) | calm(X0) | strong(X0) [duplicate literal removal 113]
138. ~creative(X0) | ~rich(X0) [duplicate literal removal 89]
258. ~creative(X0) [subsumption resolution 133,138]
261. 27 <=> strong(alice) [avatar definition]
262. ~strong(alice) <- (~27) [avatar component clause 261]
263. strong(alice) <- (27) [avatar component clause 261]
271. 29 <=> calm(alice) [avatar definition]
272. ~calm(alice) <- (~29) [avatar component clause 271]
273. calm(alice) <- (29) [avatar component clause 271]
285. creative(alice) <- (27) [resolution 106,263]
286. $false <- (27) [subsumption resolution 285,258]
287. ~27 [avatar contradiction clause 286]
325. strong(alice) <- (29) [resolution 273,134]
327. $false <- (~27, 29) [subsumption resolution 325,262]
328. 27 | ~29 [avatar contradiction clause 327]
333. calm(alice) | strong(alice) [resolution 135,131]
335. strong(alice) <- (~29) [subsumption resolution 333,272]
336. $false <- (~27, ~29) [subsumption resolution 335,262]
337. 27 | 29 [avatar contradiction clause 336]
339. $false [avatar sat refutation 287,328,337]
% SZS output end Proof for 1732099517851284795218245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not tall is both not wise and not happy and vice versa.
Everyone who is either not humble or humble is both kind and not patient and vice versa.
Everyone who is both creative and not calm is both not rich and calm.
Everyone who is not funny is not tall or humble and vice versa.
Everyone who is patient or curious is either not kind or rich and vice versa.
If fred is not funny or creative then susan is both brave and wise and vice versa.
If someone is either not calm or funny then mary is either not generous or wise and vice versa.
If someone is either not rich or patient then someone is either not rich or humble.
Everyone who is both curious and not creative is both strong and humble and vice versa.
Everyone who is not happy or not patient is both not calm and strong.
Everyone who is not kind is wise or funny.
Everyone who is calm or brave is calm or rich and vice versa.
Everyone who is kind or not wise is either not quiet or patient and vice versa.
Everyone who is both funny and not kind is both not rich and not curious.
Everyone who is either not wise or kind is both not happy and old and vice versa.
Lucy is calm or generous.
Lucy is generous or not rich.
Someone is not creative.
John is not wise.
Someone is not creative or not kind. | Fred is not brave. | entailment | (![X]:((kind(X)|~tall(X))<=>(~wise(X)&~happy(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(kind(X)&~patient(X))))&
(![X]:((creative(X)&~calm(X))=>(~rich(X)&calm(X))))&
(![X]:(~funny(X)<=>(~tall(X)|humble(X))))&
(![X]:((patient(X)|curious(X))<=>(~kind(X)<~>rich(X))))&
(((~funny(fred)|creative(fred)))<=>((brave(susan)&wise(susan))))&
((?[X]:((~calm(X)<~>funny(X))))<=>((~generous(mary)<~>wise(mary))))&
((?[X]:((~rich(X)<~>patient(X))))=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((curious(X)&~creative(X))<=>(strong(X)&humble(X))))&
(![X]:((~happy(X)|~patient(X))=>(~calm(X)&strong(X))))&
(![X]:(~kind(X)=>(wise(X)|funny(X))))&
(![X]:((calm(X)|brave(X))<=>(calm(X)|rich(X))))&
(![X]:((kind(X)|~wise(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((funny(X)&~kind(X))=>(~rich(X)&~curious(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~happy(X)&old(X))))&
((calm(lucy)|generous(lucy)))&
((generous(lucy)|~rich(lucy)))&
(?[X]:(~creative(X)))&
(~wise(john))&
(?[X]:((~creative(X)|~kind(X)))) | ~brave(fred) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 248577197655391750522014
% SZS output start Proof for 248577197655391750522014
1. ! [X0] : ((~tall(X0) | kind(X0)) <=> (~happy(X0) & ~wise(X0))) [input p0]
2. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~patient(X0) & kind(X0))) [input p1]
4. ! [X0] : (~funny(X0) <=> (humble(X0) | ~tall(X0))) [input p3]
5. ! [X0] : ((curious(X0) | patient(X0)) <=> (~kind(X0) <~> rich(X0))) [input p4]
6. (creative(fred) | ~funny(fred)) <=> (wise(susan) & brave(susan)) [input p5]
9. ! [X0] : ((~creative(X0) & curious(X0)) <=> (humble(X0) & strong(X0))) [input p8]
10. ! [X0] : ((~patient(X0) | ~happy(X0)) => (strong(X0) & ~calm(X0))) [input p9]
12. ! [X0] : ((brave(X0) | calm(X0)) <=> (rich(X0) | calm(X0))) [input p11]
21. brave(fred) [input hypothesis]
26. ! [X0] : ((strong(X0) & ~calm(X0)) | (patient(X0) & happy(X0))) [ennf transformation 10]
31. ! [X0] : (((~tall(X0) | kind(X0)) | (happy(X0) | wise(X0))) & ((~happy(X0) & ~wise(X0)) | (tall(X0) & ~kind(X0)))) [nnf transformation 1]
32. ! [X0] : ((~tall(X0) | kind(X0) | happy(X0) | wise(X0)) & ((~happy(X0) & ~wise(X0)) | (tall(X0) & ~kind(X0)))) [flattening 31]
33. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 2]
34. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 33]
35. ! [X0] : ((~funny(X0) | (~humble(X0) & tall(X0))) & ((humble(X0) | ~tall(X0)) | funny(X0))) [nnf transformation 4]
36. ! [X0] : ((~funny(X0) | (~humble(X0) & tall(X0))) & (humble(X0) | ~tall(X0) | funny(X0))) [flattening 35]
37. ! [X0] : (((curious(X0) | patient(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (~curious(X0) & ~patient(X0)))) [nnf transformation 5]
38. ! [X0] : ((curious(X0) | patient(X0) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (~curious(X0) & ~patient(X0)))) [flattening 37]
39. ((creative(fred) | ~funny(fred)) | (~wise(susan) | ~brave(susan))) & ((wise(susan) & brave(susan)) | (~creative(fred) & funny(fred))) [nnf transformation 6]
40. (creative(fred) | ~funny(fred) | ~wise(susan) | ~brave(susan)) & ((wise(susan) & brave(susan)) | (~creative(fred) & funny(fred))) [flattening 39]
49. ! [X0] : (((~creative(X0) & curious(X0)) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | (creative(X0) | ~curious(X0)))) [nnf transformation 9]
50. ! [X0] : (((~creative(X0) & curious(X0)) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | creative(X0) | ~curious(X0))) [flattening 49]
51. ! [X0] : (((brave(X0) | calm(X0)) | (~rich(X0) & ~calm(X0))) & ((rich(X0) | calm(X0)) | (~brave(X0) & ~calm(X0)))) [nnf transformation 12]
52. ! [X0] : ((brave(X0) | calm(X0) | (~rich(X0) & ~calm(X0))) & (rich(X0) | calm(X0) | (~brave(X0) & ~calm(X0)))) [flattening 51]
61. ~wise(X0) | ~kind(X0) [cnf transformation 32]
66. kind(X0) | humble(X0) | humble(X0) [cnf transformation 34]
67. kind(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 34]
68. ~patient(X0) | humble(X0) | humble(X0) [cnf transformation 34]
69. ~patient(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 34]
76. ~funny(X0) | ~humble(X0) [cnf transformation 36]
82. curious(X0) | patient(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 38]
85. wise(susan) | funny(fred) [cnf transformation 40]
86. wise(susan) | ~creative(fred) [cnf transformation 40]
101. ~curious(X0) | creative(X0) | humble(X0) [cnf transformation 50]
105. ~calm(X0) | patient(X0) [cnf transformation 26]
110. rich(X0) | calm(X0) | ~brave(X0) [cnf transformation 52]
132. brave(fred) [cnf transformation 21]
134. kind(X0) | humble(X0) [duplicate literal removal 66]
135. ~humble(X0) | kind(X0) [duplicate literal removal 67]
136. ~patient(X0) | humble(X0) [duplicate literal removal 68]
137. ~patient(X0) | ~humble(X0) [duplicate literal removal 69]
138. ~patient(X0) [subsumption resolution 136,137]
139. kind(X0) [subsumption resolution 134,135]
140. curious(X0) | ~kind(X0) | ~rich(X0) [subsumption resolution 82,138]
141. ~rich(X0) | curious(X0) [subsumption resolution 140,139]
148. 2 <=> wise(susan) [avatar definition]
149. wise(susan) <- (2) [avatar component clause 148]
152. 3 <=> funny(fred) [avatar definition]
153. funny(fred) <- (3) [avatar component clause 152]
156. 4 <=> creative(fred) [avatar definition]
160. ~4 | 2 [avatar split clause 86,148,156]
161. 3 | 2 [avatar split clause 85,148,152]
210. ~calm(X0) [subsumption resolution 105,138]
212. ~brave(X0) | rich(X0) [subsumption resolution 110,210]
220. ~humble(fred) <- (3) [resolution 76,153]
221. rich(fred) [resolution 212,132]
223. curious(fred) [resolution 221,141]
227. creative(fred) | humble(fred) [resolution 101,223]
231. creative(fred) <- (3) [subsumption resolution 227,220]
232. 4 | ~3 [avatar split clause 231,152,156]
235. ~kind(susan) <- (2) [resolution 149,61]
236. $false <- (2) [subsumption resolution 235,139]
237. ~2 [avatar contradiction clause 236]
238. $false [avatar sat refutation 160,161,232,237]
% SZS output end Proof for 248577197655391750522014
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is either calm or not wise and vice versa.
Everyone who is humble is not old.
Everyone who is both not kind and quiet is not rich.
Everyone who is old is either kind or quiet.
Everyone who is tall is creative and vice versa.
If paul is either patient or kind then someone is both not rich and not brave.
If fred is either humble or not tall then someone is either not generous or happy.
If lucy is not strong or strong then lucy is not rich or creative and vice versa.
Everyone who is either not creative or not generous is both not humble and not calm.
Everyone who is generous is not rich and vice versa.
Everyone who is either not humble or generous is kind or humble.
If john is not patient or not curious then someone is both not quiet and not patient and vice versa.
Everyone who is either humble or not humble is either tall or rich and vice versa.
If someone is not generous or not patient then fred is either humble or generous.
If mary is both not brave and creative then someone is generous.
Everyone who is not quiet is not rich or brave and vice versa.
Lucy is brave or not strong.
Someone is both not creative and not humble.
Someone is not quiet or wise.
Paul is old.
Susan is creative or kind.
Someone is humble or not tall.
Susan is happy or curious.
John is both not kind and rich. | John is rich. | entailment | (![X]:(~generous(X)<=>(calm(X)<~>~wise(X))))&
(![X]:(humble(X)=>~old(X)))&
(![X]:((~kind(X)&quiet(X))=>~rich(X)))&
(![X]:(old(X)=>(kind(X)<~>quiet(X))))&
(![X]:(tall(X)<=>creative(X)))&
(((patient(paul)<~>kind(paul)))=>(?[X]:((~rich(X)&~brave(X)))))&
(((humble(fred)<~>~tall(fred)))=>(?[X]:((~generous(X)<~>happy(X)))))&
(((~strong(lucy)|strong(lucy)))<=>((~rich(lucy)|creative(lucy))))&
(![X]:((~creative(X)<~>~generous(X))=>(~humble(X)&~calm(X))))&
(![X]:(generous(X)<=>~rich(X)))&
(![X]:((~humble(X)<~>generous(X))=>(kind(X)|humble(X))))&
(((~patient(john)|~curious(john)))<=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:((humble(X)<~>~humble(X))<=>(tall(X)<~>rich(X))))&
((?[X]:((~generous(X)|~patient(X))))=>((humble(fred)<~>generous(fred))))&
(((~brave(mary)&creative(mary)))=>(?[X]:(generous(X))))&
(![X]:(~quiet(X)<=>(~rich(X)|brave(X))))&
((brave(lucy)|~strong(lucy)))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:((~quiet(X)|wise(X))))&
(old(paul))&
((creative(susan)|kind(susan)))&
(?[X]:((humble(X)|~tall(X))))&
((happy(susan)|curious(susan)))&
((~kind(john)&rich(john))) | rich(john) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2828925145318304771850110
% SZS output start Proof for 2828925145318304771850110
24. rich(john) & ~kind(john) [input p23]
25. ~rich(john) [input hypothesis]
129. rich(john) [cnf transformation 24]
130. ~rich(john) [cnf transformation 25]
284. $false [subsumption resolution 130,129]
% SZS output end Proof for 2828925145318304771850110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then fred is both not quiet and not wise. If susan is both not kind and not curious then someone is both old and patient. Everyone who is either funny or curious is both not old and not strong and vice versa. Everyone who is not strong or brave is either not old or not generous and vice versa. Everyone who is either kind or not tall is both quiet and not patient and vice versa. Everyone who is either not patient or not kind is curious or rich. If someone is either humble or not generous then lucy is kind and vice versa. Everyone who is patient is old or not brave. Everyone who is either old or not calm is quiet and vice versa. If alice is happy then someone is rich or happy and vice versa. If someone is not humble then someone is not calm and vice versa. Everyone who is creative or not kind is both not generous and not brave. If lucy is either wise or rich then mary is not brave or not rich. Everyone who is either not kind or not curious is either not tall or wise. If someone is both not generous and not calm then someone is not curious or not tall. If mary is not old then lucy is both humble and not rich. Mary is both not quiet and strong. Someone is either kind or calm. Someone is either tall or not curious. Susan is both strong and not creative. Lucy is curious. Susan is both not wise and happy. Someone is kind. | Lucy is not curious. | contradiction | ((old(lucy))=>((~quiet(fred)&~wise(fred))))&
(((~kind(susan)&~curious(susan)))=>(?[X]:((old(X)&patient(X)))))&
(![X]:((funny(X)<~>curious(X))<=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|brave(X))<=>(~old(X)<~>~generous(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(quiet(X)&~patient(X))))&
(![X]:((~patient(X)<~>~kind(X))=>(curious(X)|rich(X))))&
((?[X]:((humble(X)<~>~generous(X))))<=>(kind(lucy)))&
(![X]:(patient(X)=>(old(X)|~brave(X))))&
(![X]:((old(X)<~>~calm(X))<=>quiet(X)))&
((happy(alice))<=>(?[X]:((rich(X)|happy(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)|~kind(X))=>(~generous(X)&~brave(X))))&
(((wise(lucy)<~>rich(lucy)))=>((~brave(mary)|~rich(mary))))&
(![X]:((~kind(X)<~>~curious(X))=>(~tall(X)<~>wise(X))))&
((?[X]:((~generous(X)&~calm(X))))=>(?[X]:((~curious(X)|~tall(X)))))&
((~old(mary))=>((humble(lucy)&~rich(lucy))))&
((~quiet(mary)&strong(mary)))&
(?[X]:((kind(X)<~>calm(X))))&
(?[X]:((tall(X)<~>~curious(X))))&
((strong(susan)&~creative(susan)))&
(curious(lucy))&
((~wise(susan)&happy(susan)))&
(?[X]:(kind(X))) | ~curious(lucy) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 328564309230867835283909
% SZS output start Proof for 328564309230867835283909
21. curious(lucy) [input p20]
24. ~curious(lucy) [input hypothesis]
134. curious(lucy) [cnf transformation 21]
138. ~curious(lucy) [cnf transformation 24]
290. $false [subsumption resolution 138,134]
% SZS output end Proof for 328564309230867835283909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not humble and old then john is old.
If lucy is both not old and curious then someone is creative.
Everyone who is both tall and old is both not patient and strong and vice versa.
Everyone who is not patient or humble is either not creative or not generous.
Everyone who is not tall or rich is not humble or not brave.
Everyone who is either humble or not tall is either not generous or not happy.
If someone is happy or creative then someone is either not kind or not wise and vice versa.
If someone is both not kind and not brave then john is either not generous or quiet and vice versa.
If someone is rich then lucy is strong.
Everyone who is not old or rich is both patient and funny.
If susan is both curious and kind then lucy is not generous or generous and vice versa.
Everyone who is not wise is not tall.
Everyone who is both wise and strong is both generous and not patient and vice versa.
Everyone who is not patient is brave and vice versa.
Everyone who is brave or rich is calm and vice versa.
If someone is not calm then someone is kind.
Someone is curious or quiet.
Lucy is either old or funny.
Someone is either not brave or old.
Someone is either not curious or rich.
Alice is both tall and calm.
John is funny or not wise.
Someone is wise.
Paul is either tall or rich. | Lucy is old. | neutral | (((~humble(susan)&old(susan)))=>(old(john)))&
(((~old(lucy)&curious(lucy)))=>(?[X]:(creative(X))))&
(![X]:((tall(X)&old(X))<=>(~patient(X)&strong(X))))&
(![X]:((~patient(X)|humble(X))=>(~creative(X)<~>~generous(X))))&
(![X]:((~tall(X)|rich(X))=>(~humble(X)|~brave(X))))&
(![X]:((humble(X)<~>~tall(X))=>(~generous(X)<~>~happy(X))))&
((?[X]:((happy(X)|creative(X))))<=>(?[X]:((~kind(X)<~>~wise(X)))))&
((?[X]:((~kind(X)&~brave(X))))<=>((~generous(john)<~>quiet(john))))&
((?[X]:(rich(X)))=>(strong(lucy)))&
(![X]:((~old(X)|rich(X))=>(patient(X)&funny(X))))&
(((curious(susan)&kind(susan)))<=>((~generous(lucy)|generous(lucy))))&
(![X]:(~wise(X)=>~tall(X)))&
(![X]:((wise(X)&strong(X))<=>(generous(X)&~patient(X))))&
(![X]:(~patient(X)<=>brave(X)))&
(![X]:((brave(X)|rich(X))<=>calm(X)))&
((?[X]:(~calm(X)))=>(?[X]:(kind(X))))&
(?[X]:((curious(X)|quiet(X))))&
((old(lucy)<~>funny(lucy)))&
(?[X]:((~brave(X)<~>old(X))))&
(?[X]:((~curious(X)<~>rich(X))))&
((tall(alice)&calm(alice)))&
((funny(john)|~wise(john)))&
(?[X]:(wise(X)))&
((tall(paul)<~>rich(paul))) | old(lucy) | [] | null | 0 |
Everyone who is old is either not humble or not strong. Everyone who is creative or wise is both not generous and not curious and vice versa. Everyone who is both not rich and funny is wise or curious. If someone is either funny or creative then someone is either not kind or rich and vice versa. If mary is either brave or not creative then alice is both not tall and tall. If someone is both not strong and not humble then alice is tall. If someone is both old and not kind then someone is either not creative or not rich. Everyone who is both not calm and not wise is both funny and not quiet. If mary is both not calm and happy then someone is creative or not old. Everyone who is not rich or not quiet is not curious. Everyone who is calm is funny and vice versa. If someone is either not generous or not brave then mary is patient or not generous. Everyone who is either curious or patient is both not rich and not humble. If lucy is not generous or generous then someone is either quiet or not rich and vice versa. If someone is either not tall or old then fred is not funny or strong. If alice is both not funny and not quiet then someone is both old and quiet and vice versa. Paul is not funny. Lucy is not funny. Someone is not creative. Someone is both not rich and strong. Someone is old or not strong. Lucy is either tall or curious. Someone is happy. Alice is not funny or not old. | Lucy is not tall. | contradiction | (![X]:(old(X)=>(~humble(X)<~>~strong(X))))&
(![X]:((creative(X)|wise(X))<=>(~generous(X)&~curious(X))))&
(![X]:((~rich(X)&funny(X))=>(wise(X)|curious(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)<~>rich(X)))))&
(((brave(mary)<~>~creative(mary)))=>((~tall(alice)&tall(alice))))&
((?[X]:((~strong(X)&~humble(X))))=>(tall(alice)))&
((?[X]:((old(X)&~kind(X))))=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((~calm(X)&~wise(X))=>(funny(X)&~quiet(X))))&
(((~calm(mary)&happy(mary)))=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((~rich(X)|~quiet(X))=>~curious(X)))&
(![X]:(calm(X)<=>funny(X)))&
((?[X]:((~generous(X)<~>~brave(X))))=>((patient(mary)|~generous(mary))))&
(![X]:((curious(X)<~>patient(X))=>(~rich(X)&~humble(X))))&
(((~generous(lucy)|generous(lucy)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
((?[X]:((~tall(X)<~>old(X))))=>((~funny(fred)|strong(fred))))&
(((~funny(alice)&~quiet(alice)))<=>(?[X]:((old(X)&quiet(X)))))&
(~funny(paul))&
(~funny(lucy))&
(?[X]:(~creative(X)))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((old(X)|~strong(X))))&
((tall(lucy)<~>curious(lucy)))&
(?[X]:(happy(X)))&
((~funny(alice)|~old(alice))) | ~tall(lucy) | [
"p1",
"p7",
"p10",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5544223523629718694467830
% SZS output start Proof for 5544223523629718694467830
2. ! [X0] : ((wise(X0) | creative(X0)) <=> (~curious(X0) & ~generous(X0))) [input p1]
8. ! [X0] : ((~wise(X0) & ~calm(X0)) => (~quiet(X0) & funny(X0))) [input p7]
11. ! [X0] : (calm(X0) <=> funny(X0)) [input p10]
18. ~funny(lucy) [input p17]
22. tall(lucy) <~> curious(lucy) [input p21]
25. ~tall(lucy) [input hypothesis]
28. ! [X0] : (calm(X0) => funny(X0)) [unused predicate definition removal 11]
35. ! [X0] : ((~quiet(X0) & funny(X0)) | (wise(X0) | calm(X0))) [ennf transformation 8]
36. ! [X0] : ((~quiet(X0) & funny(X0)) | wise(X0) | calm(X0)) [flattening 35]
40. ! [X0] : (funny(X0) | ~calm(X0)) [ennf transformation 28]
47. ! [X0] : (((wise(X0) | creative(X0)) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~creative(X0)))) [nnf transformation 2]
48. ! [X0] : ((wise(X0) | creative(X0) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~creative(X0)))) [flattening 47]
80. (~curious(lucy) | ~tall(lucy)) & (curious(lucy) | tall(lucy)) [nnf transformation 22]
88. ~curious(X0) | ~wise(X0) [cnf transformation 48]
106. calm(X0) | wise(X0) | funny(X0) [cnf transformation 36]
111. ~calm(X0) | funny(X0) [cnf transformation 40]
131. ~funny(lucy) [cnf transformation 18]
136. curious(lucy) | tall(lucy) [cnf transformation 80]
140. ~tall(lucy) [cnf transformation 25]
309. 38 <=> tall(lucy) [avatar definition]
313. 39 <=> curious(lucy) [avatar definition]
314. curious(lucy) <- (39) [avatar component clause 313]
317. 38 | 39 [avatar split clause 136,313,309]
323. ~38 [avatar split clause 140,309]
325. ~wise(lucy) <- (39) [resolution 88,314]
342. wise(X0) | funny(X0) | funny(X0) [resolution 106,111]
343. funny(X0) | wise(X0) [duplicate literal removal 342]
345. wise(lucy) [resolution 343,131]
348. $false <- (39) [subsumption resolution 345,325]
349. ~39 [avatar contradiction clause 348]
350. $false [avatar sat refutation 317,323,349]
% SZS output end Proof for 5544223523629718694467830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or brave is not quiet or not humble.
If paul is both not generous and rich then john is either not kind or calm.
Everyone who is not calm is wise or creative and vice versa.
If someone is either not patient or not kind then fred is tall.
Everyone who is both humble and kind is both not funny and tall and vice versa.
Everyone who is both old and not old is both rich and funny and vice versa.
If someone is either not wise or not funny then mary is both not humble and not happy.
If someone is kind or tall then susan is either not patient or not happy and vice versa.
Everyone who is brave is both kind and not kind and vice versa.
Everyone who is both generous and not creative is quiet or not happy and vice versa.
If susan is not creative then mary is both not strong and patient and vice versa.
If mary is not strong or kind then paul is not tall and vice versa.
Everyone who is either not generous or patient is not brave and vice versa.
Everyone who is both not rich and not patient is either calm or not old and vice versa.
Everyone who is not happy or rich is not patient or rich and vice versa.
Everyone who is happy or not strong is either not curious or not patient.
Lucy is kind or brave.
Someone is not brave.
Someone is both not happy and old.
Alice is either not creative or not curious.
John is either not kind or not patient.
Susan is either not brave or not strong.
John is either old or not humble. | Paul is not curious. | neutral | (![X]:((~humble(X)|brave(X))=>(~quiet(X)|~humble(X))))&
(((~generous(paul)&rich(paul)))=>((~kind(john)<~>calm(john))))&
(![X]:(~calm(X)<=>(wise(X)|creative(X))))&
((?[X]:((~patient(X)<~>~kind(X))))=>(tall(fred)))&
(![X]:((humble(X)&kind(X))<=>(~funny(X)&tall(X))))&
(![X]:((old(X)&~old(X))<=>(rich(X)&funny(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>((~humble(mary)&~happy(mary))))&
((?[X]:((kind(X)|tall(X))))<=>((~patient(susan)<~>~happy(susan))))&
(![X]:(brave(X)<=>(kind(X)&~kind(X))))&
(![X]:((generous(X)&~creative(X))<=>(quiet(X)|~happy(X))))&
((~creative(susan))<=>((~strong(mary)&patient(mary))))&
(((~strong(mary)|kind(mary)))<=>(~tall(paul)))&
(![X]:((~generous(X)<~>patient(X))<=>~brave(X)))&
(![X]:((~rich(X)&~patient(X))<=>(calm(X)<~>~old(X))))&
(![X]:((~happy(X)|rich(X))<=>(~patient(X)|rich(X))))&
(![X]:((happy(X)|~strong(X))=>(~curious(X)<~>~patient(X))))&
((kind(lucy)|brave(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~happy(X)&old(X))))&
((~creative(alice)<~>~curious(alice)))&
((~kind(john)<~>~patient(john)))&
((~brave(susan)<~>~strong(susan)))&
((old(john)<~>~humble(john))) | ~curious(paul) | [] | null | 0 |
If alice is creative then mary is wise or not kind and vice versa.
If someone is happy or wise then john is not old and vice versa.
Everyone who is not kind or wise is both happy and quiet and vice versa.
Everyone who is either not funny or funny is both not patient and wise and vice versa.
If someone is not patient then someone is both not old and not strong.
Everyone who is curious is both generous and brave.
If someone is both not humble and wise then john is not humble or wise and vice versa.
Everyone who is both not quiet and rich is wise or not calm.
If someone is both funny and humble then paul is either curious or not old and vice versa.
Everyone who is both not brave and not rich is wise or old.
Everyone who is not wise is humble.
If alice is both not humble and not brave then paul is both not old and not brave and vice versa.
If someone is tall then someone is curious.
Everyone who is not wise is old.
Everyone who is creative or wise is either generous or quiet.
Everyone who is wise or old is funny and vice versa.
Someone is not creative.
Mary is either not wise or kind.
Susan is both calm and brave.
Someone is either not funny or rich.
Paul is creative. | Susan is happy. | entailment | ((creative(alice))<=>((wise(mary)|~kind(mary))))&
((?[X]:((happy(X)|wise(X))))<=>(~old(john)))&
(![X]:((~kind(X)|wise(X))<=>(happy(X)&quiet(X))))&
(![X]:((~funny(X)<~>funny(X))<=>(~patient(X)&wise(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~old(X)&~strong(X)))))&
(![X]:(curious(X)=>(generous(X)&brave(X))))&
((?[X]:((~humble(X)&wise(X))))<=>((~humble(john)|wise(john))))&
(![X]:((~quiet(X)&rich(X))=>(wise(X)|~calm(X))))&
((?[X]:((funny(X)&humble(X))))<=>((curious(paul)<~>~old(paul))))&
(![X]:((~brave(X)&~rich(X))=>(wise(X)|old(X))))&
(![X]:(~wise(X)=>humble(X)))&
(((~humble(alice)&~brave(alice)))<=>((~old(paul)&~brave(paul))))&
((?[X]:(tall(X)))=>(?[X]:(curious(X))))&
(![X]:(~wise(X)=>old(X)))&
(![X]:((creative(X)|wise(X))=>(generous(X)<~>quiet(X))))&
(![X]:((wise(X)|old(X))<=>funny(X)))&
(?[X]:(~creative(X)))&
((~wise(mary)<~>kind(mary)))&
((calm(susan)&brave(susan)))&
(?[X]:((~funny(X)<~>rich(X))))&
(creative(paul)) | happy(susan) | [
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8206178036656924195217590
% SZS output start Proof for 8206178036656924195217590
3. ! [X0] : ((wise(X0) | ~kind(X0)) <=> (quiet(X0) & happy(X0))) [input p2]
4. ! [X0] : ((~funny(X0) <~> funny(X0)) <=> (wise(X0) & ~patient(X0))) [input p3]
22. ~happy(susan) [input hypothesis]
42. ! [X0] : (((wise(X0) | ~kind(X0)) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | (~wise(X0) & kind(X0)))) [nnf transformation 3]
43. ! [X0] : ((wise(X0) | ~kind(X0) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | (~wise(X0) & kind(X0)))) [flattening 42]
44. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (~wise(X0) | patient(X0))) & ((wise(X0) & ~patient(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [nnf transformation 4]
45. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ~wise(X0) | patient(X0)) & ((wise(X0) & ~patient(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [flattening 44]
76. ~wise(X0) | happy(X0) [cnf transformation 43]
82. wise(X0) | funny(X0) | funny(X0) [cnf transformation 45]
83. wise(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 45]
123. ~happy(susan) [cnf transformation 22]
126. wise(X0) | funny(X0) [duplicate literal removal 82]
127. wise(X0) | ~funny(X0) [duplicate literal removal 83]
164. wise(X0) [subsumption resolution 126,127]
217. happy(X0) [resolution 76,164]
218. $false [resolution 217,123]
% SZS output end Proof for 8206178036656924195217590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is wise then someone is not quiet and vice versa.
Everyone who is either creative or not wise is not funny and vice versa.
Everyone who is both calm and quiet is not quiet.
If alice is old then someone is not wise or not kind and vice versa.
Everyone who is not happy is not rich.
If someone is not patient then someone is not funny or generous.
Everyone who is not generous is generous or happy and vice versa.
Everyone who is both rich and not humble is both funny and quiet.
If someone is both funny and not calm then someone is both not patient and old.
If someone is not tall or generous then alice is not humble or kind and vice versa.
Everyone who is both not quiet and not kind is brave or quiet and vice versa.
If paul is humble then someone is happy or not humble.
If paul is not rich then someone is not tall or calm and vice versa.
If someone is both tall and creative then someone is either not rich or not funny.
Everyone who is both old and happy is both rich and brave and vice versa.
If mary is both calm and not happy then someone is either not humble or generous and vice versa.
Someone is old.
Lucy is not calm or not wise.
Paul is both happy and not creative.
John is both humble and not strong.
Paul is not patient or happy.
Mary is either generous or creative.
Paul is either patient or kind. | John is tall. | entailment | ((?[X]:(wise(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)<~>~wise(X))<=>~funny(X)))&
(![X]:((calm(X)&quiet(X))=>~quiet(X)))&
((old(alice))<=>(?[X]:((~wise(X)|~kind(X)))))&
(![X]:(~happy(X)=>~rich(X)))&
((?[X]:(~patient(X)))=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:(~generous(X)<=>(generous(X)|happy(X))))&
(![X]:((rich(X)&~humble(X))=>(funny(X)&quiet(X))))&
((?[X]:((funny(X)&~calm(X))))=>(?[X]:((~patient(X)&old(X)))))&
((?[X]:((~tall(X)|generous(X))))<=>((~humble(alice)|kind(alice))))&
(![X]:((~quiet(X)&~kind(X))<=>(brave(X)|quiet(X))))&
((humble(paul))=>(?[X]:((happy(X)|~humble(X)))))&
((~rich(paul))<=>(?[X]:((~tall(X)|calm(X)))))&
((?[X]:((tall(X)&creative(X))))=>(?[X]:((~rich(X)<~>~funny(X)))))&
(![X]:((old(X)&happy(X))<=>(rich(X)&brave(X))))&
(((calm(mary)&~happy(mary)))<=>(?[X]:((~humble(X)<~>generous(X)))))&
(?[X]:(old(X)))&
((~calm(lucy)|~wise(lucy)))&
((happy(paul)&~creative(paul)))&
((humble(john)&~strong(john)))&
((~patient(paul)|happy(paul)))&
((generous(mary)<~>creative(mary)))&
((patient(paul)<~>kind(paul))) | tall(john) | [
"p3",
"p6",
"p9",
"p10",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 626221511061730336871645
% SZS output start Proof for 626221511061730336871645
4. old(alice) <=> ? [X0] : (~kind(X0) | ~wise(X0)) [input p3]
7. ! [X0] : (~generous(X0) <=> (happy(X0) | generous(X0))) [input p6]
10. ? [X0] : (generous(X0) | ~tall(X0)) <=> (kind(alice) | ~humble(alice)) [input p9]
11. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> (quiet(X0) | brave(X0))) [input p10]
15. ! [X0] : ((happy(X0) & old(X0)) <=> (brave(X0) & rich(X0))) [input p14]
16. (~happy(mary) & calm(mary)) <=> ? [X0] : (~humble(X0) <~> generous(X0)) [input p15]
17. ? [X0] : old(X0) [input p16]
24. ~tall(john) [input hypothesis]
45. (old(alice) | ! [X0] : (kind(X0) & wise(X0))) & (? [X0] : (~kind(X0) | ~wise(X0)) | ~old(alice)) [nnf transformation 4]
46. (old(alice) | ! [X0] : (kind(X0) & wise(X0))) & (? [X1] : (~kind(X1) | ~wise(X1)) | ~old(alice)) [rectify 45]
47. ? [X1] : (~kind(X1) | ~wise(X1)) => (~kind(sK2) | ~wise(sK2)) [choice axiom]
48. (old(alice) | ! [X0] : (kind(X0) & wise(X0))) & ((~kind(sK2) | ~wise(sK2)) | ~old(alice)) [skolemisation 46,47]
52. ! [X0] : ((~generous(X0) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | generous(X0))) [nnf transformation 7]
53. ! [X0] : ((~generous(X0) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | generous(X0))) [flattening 52]
57. (? [X0] : (generous(X0) | ~tall(X0)) | (~kind(alice) & humble(alice))) & ((kind(alice) | ~humble(alice)) | ! [X0] : (~generous(X0) & tall(X0))) [nnf transformation 10]
58. (? [X0] : (generous(X0) | ~tall(X0)) | (~kind(alice) & humble(alice))) & (kind(alice) | ~humble(alice) | ! [X0] : (~generous(X0) & tall(X0))) [flattening 57]
59. (? [X0] : (generous(X0) | ~tall(X0)) | (~kind(alice) & humble(alice))) & (kind(alice) | ~humble(alice) | ! [X1] : (~generous(X1) & tall(X1))) [rectify 58]
60. ? [X0] : (generous(X0) | ~tall(X0)) => (generous(sK5) | ~tall(sK5)) [choice axiom]
61. ((generous(sK5) | ~tall(sK5)) | (~kind(alice) & humble(alice))) & (kind(alice) | ~humble(alice) | ! [X1] : (~generous(X1) & tall(X1))) [skolemisation 59,60]
62. ! [X0] : (((~kind(X0) & ~quiet(X0)) | (~quiet(X0) & ~brave(X0))) & ((quiet(X0) | brave(X0)) | (kind(X0) | quiet(X0)))) [nnf transformation 11]
63. ! [X0] : (((~kind(X0) & ~quiet(X0)) | (~quiet(X0) & ~brave(X0))) & (quiet(X0) | brave(X0) | kind(X0) | quiet(X0))) [flattening 62]
74. ! [X0] : (((happy(X0) & old(X0)) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | (~happy(X0) | ~old(X0)))) [nnf transformation 15]
75. ! [X0] : (((happy(X0) & old(X0)) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ~happy(X0) | ~old(X0))) [flattening 74]
76. ((~happy(mary) & calm(mary)) | ! [X0] : ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (? [X0] : ((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (happy(mary) | ~calm(mary))) [nnf transformation 16]
77. ((~happy(mary) & calm(mary)) | ! [X0] : ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (? [X0] : ((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | happy(mary) | ~calm(mary)) [flattening 76]
78. ((~happy(mary) & calm(mary)) | ! [X0] : ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (? [X1] : ((~generous(X1) | humble(X1)) & (generous(X1) | ~humble(X1))) | happy(mary) | ~calm(mary)) [rectify 77]
79. ? [X1] : ((~generous(X1) | humble(X1)) & (generous(X1) | ~humble(X1))) => ((~generous(sK9) | humble(sK9)) & (generous(sK9) | ~humble(sK9))) [choice axiom]
80. ((~happy(mary) & calm(mary)) | ! [X0] : ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (((~generous(sK9) | humble(sK9)) & (generous(sK9) | ~humble(sK9))) | happy(mary) | ~calm(mary)) [skolemisation 78,79]
81. ? [X0] : old(X0) => old(sK10) [choice axiom]
82. old(sK10) [skolemisation 17,81]
94. old(alice) | kind(X0) [cnf transformation 48]
97. happy(X0) | generous(X0) | generous(X0) [cnf transformation 53]
98. ~generous(X0) | ~generous(X0) [cnf transformation 53]
104. kind(alice) | ~humble(alice) | tall(X1) [cnf transformation 61]
111. ~brave(X0) | ~kind(X0) [cnf transformation 63]
120. brave(X0) | ~happy(X0) | ~old(X0) [cnf transformation 75]
127. ~happy(mary) | generous(X0) | humble(X0) [cnf transformation 80]
129. old(sK10) [cnf transformation 82]
139. ~tall(john) [cnf transformation 24]
142. happy(X0) | generous(X0) [duplicate literal removal 97]
143. ~generous(X0) [duplicate literal removal 98]
162. 5 <=> ! [X0] : kind(X0) [avatar definition]
163. kind(X0) <- (5) [avatar component clause 162]
165. 6 <=> old(alice) [avatar definition]
167. old(alice) <- (6) [avatar component clause 165]
168. 5 | 6 [avatar split clause 94,165,162]
194. happy(X0) [subsumption resolution 142,143]
210. 16 <=> kind(alice) [avatar definition]
211. kind(alice) <- (16) [avatar component clause 210]
220. 18 <=> humble(alice) [avatar definition]
221. ~humble(alice) <- (~18) [avatar component clause 220]
225. 19 <=> ! [X1] : tall(X1) [avatar definition]
226. tall(X1) <- (19) [avatar component clause 225]
227. 19 | ~18 | 16 [avatar split clause 104,210,220,225]
260. ~old(X0) | brave(X0) [subsumption resolution 120,194]
262. generous(X0) | humble(X0) [subsumption resolution 127,194]
263. humble(X0) [subsumption resolution 262,143]
284. $false <- (~18) [subsumption resolution 221,263]
285. 18 [avatar contradiction clause 284]
288. brave(sK10) [resolution 260,129]
289. brave(alice) <- (6) [resolution 260,167]
290. ~kind(sK10) [resolution 288,111]
293. ~kind(alice) <- (6) [resolution 289,111]
294. $false <- (6, 16) [subsumption resolution 293,211]
295. ~6 | ~16 [avatar contradiction clause 294]
306. $false <- (19) [resolution 226,139]
311. ~19 [avatar contradiction clause 306]
316. $false <- (5) [resolution 290,163]
317. ~5 [avatar contradiction clause 316]
318. $false [avatar sat refutation 168,227,285,295,311,317]
% SZS output end Proof for 626221511061730336871645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not quiet is either old or calm and vice versa.
If someone is not calm or curious then john is not tall or quiet and vice versa.
If alice is both not happy and quiet then someone is either old or funny.
Everyone who is not creative or not quiet is tall and vice versa.
Everyone who is not calm or not strong is generous.
If someone is not kind then fred is both not funny and old.
Everyone who is either calm or not humble is both not quiet and not strong.
If paul is not tall or not humble then someone is both not tall and tall.
If someone is not creative then lucy is either not wise or not humble and vice versa.
Everyone who is both not calm and not curious is either wise or calm and vice versa.
If someone is old then fred is either not tall or not strong.
Everyone who is both not patient and strong is old.
Everyone who is both old and not funny is not wise or humble.
If susan is not humble or not brave then someone is creative and vice versa.
John is either not quiet or not happy.
John is funny.
Mary is either not strong or happy.
Someone is generous or calm.
Lucy is curious or not calm.
John is not rich or calm. | Alice is not generous. | neutral | (![X]:((~patient(X)|~quiet(X))<=>(old(X)<~>calm(X))))&
((?[X]:((~calm(X)|curious(X))))<=>((~tall(john)|quiet(john))))&
(((~happy(alice)&quiet(alice)))=>(?[X]:((old(X)<~>funny(X)))))&
(![X]:((~creative(X)|~quiet(X))<=>tall(X)))&
(![X]:((~calm(X)|~strong(X))=>generous(X)))&
((?[X]:(~kind(X)))=>((~funny(fred)&old(fred))))&
(![X]:((calm(X)<~>~humble(X))=>(~quiet(X)&~strong(X))))&
(((~tall(paul)|~humble(paul)))=>(?[X]:((~tall(X)&tall(X)))))&
((?[X]:(~creative(X)))<=>((~wise(lucy)<~>~humble(lucy))))&
(![X]:((~calm(X)&~curious(X))<=>(wise(X)<~>calm(X))))&
((?[X]:(old(X)))=>((~tall(fred)<~>~strong(fred))))&
(![X]:((~patient(X)&strong(X))=>old(X)))&
(![X]:((old(X)&~funny(X))=>(~wise(X)|humble(X))))&
(((~humble(susan)|~brave(susan)))<=>(?[X]:(creative(X))))&
((~quiet(john)<~>~happy(john)))&
(funny(john))&
((~strong(mary)<~>happy(mary)))&
(?[X]:((generous(X)|calm(X))))&
((curious(lucy)|~calm(lucy)))&
((~rich(john)|calm(john))) | ~generous(alice) | [] | null | 0 |
If someone is either curious or kind then fred is wise or old.
Everyone who is brave or not quiet is quiet and vice versa.
Everyone who is both brave and not old is kind and vice versa.
Everyone who is creative or not wise is not calm.
Everyone who is brave or creative is either brave or curious.
Everyone who is rich or not curious is both not tall and generous and vice versa.
Everyone who is either strong or happy is both tall and not creative.
Everyone who is not kind is both creative and not old.
Everyone who is either not rich or not strong is not tall and vice versa.
If john is not happy or creative then mary is both old and not generous.
Everyone who is not calm or not patient is either creative or kind.
Everyone who is both not calm and not happy is rich or not happy.
If someone is not tall or not brave then susan is either funny or not funny and vice versa.
If someone is either brave or not brave then alice is not curious or not creative.
Everyone who is calm is creative.
Everyone who is calm is either not tall or not happy.
Someone is not strong or not funny.
Someone is both not humble and not creative.
Alice is patient or happy.
Susan is either not tall or not brave.
Someone is both funny and not happy.
Someone is either rich or not wise. | Mary is brave. | entailment | ((?[X]:((curious(X)<~>kind(X))))=>((wise(fred)|old(fred))))&
(![X]:((brave(X)|~quiet(X))<=>quiet(X)))&
(![X]:((brave(X)&~old(X))<=>kind(X)))&
(![X]:((creative(X)|~wise(X))=>~calm(X)))&
(![X]:((brave(X)|creative(X))=>(brave(X)<~>curious(X))))&
(![X]:((rich(X)|~curious(X))<=>(~tall(X)&generous(X))))&
(![X]:((strong(X)<~>happy(X))=>(tall(X)&~creative(X))))&
(![X]:(~kind(X)=>(creative(X)&~old(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>~tall(X)))&
(((~happy(john)|creative(john)))=>((old(mary)&~generous(mary))))&
(![X]:((~calm(X)|~patient(X))=>(creative(X)<~>kind(X))))&
(![X]:((~calm(X)&~happy(X))=>(rich(X)|~happy(X))))&
((?[X]:((~tall(X)|~brave(X))))<=>((funny(susan)<~>~funny(susan))))&
((?[X]:((brave(X)<~>~brave(X))))=>((~curious(alice)|~creative(alice))))&
(![X]:(calm(X)=>creative(X)))&
(![X]:(calm(X)=>(~tall(X)<~>~happy(X))))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:((~humble(X)&~creative(X))))&
((patient(alice)|happy(alice)))&
((~tall(susan)<~>~brave(susan)))&
(?[X]:((funny(X)&~happy(X))))&
(?[X]:((rich(X)<~>~wise(X)))) | brave(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 907157174413481397252082
% SZS output start Proof for 907157174413481397252082
2. ! [X0] : ((~quiet(X0) | brave(X0)) <=> quiet(X0)) [input p1]
23. ~brave(mary) [input hypothesis]
42. ! [X0] : (((~quiet(X0) | brave(X0)) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & ~brave(X0)))) [nnf transformation 2]
43. ! [X0] : ((~quiet(X0) | brave(X0) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & ~brave(X0)))) [flattening 42]
71. quiet(X0) | quiet(X0) [cnf transformation 43]
72. ~quiet(X0) | brave(X0) | ~quiet(X0) [cnf transformation 43]
123. ~brave(mary) [cnf transformation 23]
129. quiet(X0) [duplicate literal removal 71]
130. ~quiet(X0) | brave(X0) [duplicate literal removal 72]
184. 11 <=> ! [X0] : brave(X0) [avatar definition]
185. brave(X0) <- (11) [avatar component clause 184]
235. brave(X0) [resolution 130,129]
236. 11 [avatar split clause 235,184]
238. $false <- (11) [resolution 185,123]
243. ~11 [avatar contradiction clause 238]
244. $false [avatar sat refutation 236,243]
% SZS output end Proof for 907157174413481397252082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not kind is humble or rich and vice versa.
If fred is both not wise and rich then alice is both not generous and not creative and vice versa.
Everyone who is either not tall or not rich is both not generous and not patient and vice versa.
If fred is either not funny or humble then someone is both not patient and quiet and vice versa.
If mary is not patient then paul is both not old and old.
Everyone who is both quiet and not humble is both not generous and old.
Everyone who is both creative and not brave is humble or not wise.
If someone is patient then someone is not brave or calm and vice versa.
Everyone who is strong or old is either strong or not curious and vice versa.
If john is not brave or creative then paul is old.
Everyone who is wise or patient is quiet or curious and vice versa.
If mary is either generous or calm then susan is quiet or calm and vice versa.
Everyone who is either tall or old is both kind and wise.
If someone is either quiet or funny then lucy is not strong and vice versa.
Everyone who is quiet is curious or rich and vice versa.
Everyone who is either tall or rich is both not strong and not generous and vice versa.
Someone is not calm or quiet.
Someone is either curious or humble.
John is either not humble or old.
Fred is either happy or not kind.
Someone is not generous.
Someone is both not funny and not calm.
Someone is both calm and not curious.
Fred is not quiet. | Lucy is not quiet. | neutral | (![X]:((~calm(X)&~kind(X))<=>(humble(X)|rich(X))))&
(((~wise(fred)&rich(fred)))<=>((~generous(alice)&~creative(alice))))&
(![X]:((~tall(X)<~>~rich(X))<=>(~generous(X)&~patient(X))))&
(((~funny(fred)<~>humble(fred)))<=>(?[X]:((~patient(X)&quiet(X)))))&
((~patient(mary))=>((~old(paul)&old(paul))))&
(![X]:((quiet(X)&~humble(X))=>(~generous(X)&old(X))))&
(![X]:((creative(X)&~brave(X))=>(humble(X)|~wise(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)|calm(X)))))&
(![X]:((strong(X)|old(X))<=>(strong(X)<~>~curious(X))))&
(((~brave(john)|creative(john)))=>(old(paul)))&
(![X]:((wise(X)|patient(X))<=>(quiet(X)|curious(X))))&
(((generous(mary)<~>calm(mary)))<=>((quiet(susan)|calm(susan))))&
(![X]:((tall(X)<~>old(X))=>(kind(X)&wise(X))))&
((?[X]:((quiet(X)<~>funny(X))))<=>(~strong(lucy)))&
(![X]:(quiet(X)<=>(curious(X)|rich(X))))&
(![X]:((tall(X)<~>rich(X))<=>(~strong(X)&~generous(X))))&
(?[X]:((~calm(X)|quiet(X))))&
(?[X]:((curious(X)<~>humble(X))))&
((~humble(john)<~>old(john)))&
((happy(fred)<~>~kind(fred)))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((calm(X)&~curious(X))))&
(~quiet(fred)) | ~quiet(lucy) | [] | null | 0 |
If someone is both not funny and quiet then someone is either brave or curious.
Everyone who is creative or rich is both curious and old and vice versa.
If someone is not old or generous then someone is either not old or strong and vice versa.
If lucy is either curious or generous then someone is not tall.
If paul is quiet or not kind then someone is either wise or not kind and vice versa.
Everyone who is both patient and not wise is strong.
Everyone who is both rich and not quiet is not old or creative and vice versa.
Everyone who is both happy and not kind is not humble or not tall and vice versa.
Everyone who is both calm and tall is humble or old and vice versa.
Everyone who is not funny is rich and vice versa.
Everyone who is both not kind and not quiet is both strong and not rich and vice versa.
Everyone who is curious is both rich and not curious.
If someone is both not quiet and wise then fred is not strong or kind and vice versa.
Everyone who is both kind and not humble is not curious or not tall.
Everyone who is either not brave or curious is not happy or strong.
Everyone who is either calm or not funny is either not strong or funny.
Mary is either funny or wise.
Someone is either not humble or not patient.
Someone is not quiet.
Someone is calm or not curious.
Mary is both not kind and humble.
Someone is either wise or not kind. | Lucy is humble. | neutral | ((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:((creative(X)|rich(X))<=>(curious(X)&old(X))))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((~old(X)<~>strong(X)))))&
(((curious(lucy)<~>generous(lucy)))=>(?[X]:(~tall(X))))&
(((quiet(paul)|~kind(paul)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:((patient(X)&~wise(X))=>strong(X)))&
(![X]:((rich(X)&~quiet(X))<=>(~old(X)|creative(X))))&
(![X]:((happy(X)&~kind(X))<=>(~humble(X)|~tall(X))))&
(![X]:((calm(X)&tall(X))<=>(humble(X)|old(X))))&
(![X]:(~funny(X)<=>rich(X)))&
(![X]:((~kind(X)&~quiet(X))<=>(strong(X)&~rich(X))))&
(![X]:(curious(X)=>(rich(X)&~curious(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((~strong(fred)|kind(fred))))&
(![X]:((kind(X)&~humble(X))=>(~curious(X)|~tall(X))))&
(![X]:((~brave(X)<~>curious(X))=>(~happy(X)|strong(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~strong(X)<~>funny(X))))&
((funny(mary)<~>wise(mary)))&
(?[X]:((~humble(X)<~>~patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((calm(X)|~curious(X))))&
((~kind(mary)&humble(mary)))&
(?[X]:((wise(X)<~>~kind(X)))) | humble(lucy) | [] | null | 0 |
If someone is wise then paul is not funny and vice versa.
Everyone who is both not old and tall is either not happy or not rich and vice versa.
Everyone who is wise or not humble is either quiet or not rich and vice versa.
If susan is strong or old then susan is strong or brave and vice versa.
Everyone who is either not curious or old is either old or not funny and vice versa.
Everyone who is both not humble and quiet is calm or not old and vice versa.
If someone is either humble or patient then someone is either not funny or curious.
If lucy is calm or generous then alice is not humble and vice versa.
Everyone who is not calm or tall is calm and vice versa.
Everyone who is not rich or not curious is not tall or not humble.
If someone is not quiet then mary is both happy and not calm and vice versa.
Everyone who is generous is not patient or calm and vice versa.
If someone is not old then fred is not kind.
If mary is not tall or tall then someone is patient and vice versa.
Everyone who is both tall and not curious is rich or not creative.
Everyone who is quiet is not old and vice versa.
Someone is funny or strong.
Susan is not creative.
Someone is either not curious or generous.
Someone is both calm and not funny.
Someone is not creative or not old. | Fred is not kind. | entailment | ((?[X]:(wise(X)))<=>(~funny(paul)))&
(![X]:((~old(X)&tall(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:((wise(X)|~humble(X))<=>(quiet(X)<~>~rich(X))))&
(((strong(susan)|old(susan)))<=>((strong(susan)|brave(susan))))&
(![X]:((~curious(X)<~>old(X))<=>(old(X)<~>~funny(X))))&
(![X]:((~humble(X)&quiet(X))<=>(calm(X)|~old(X))))&
((?[X]:((humble(X)<~>patient(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(((calm(lucy)|generous(lucy)))<=>(~humble(alice)))&
(![X]:((~calm(X)|tall(X))<=>calm(X)))&
(![X]:((~rich(X)|~curious(X))=>(~tall(X)|~humble(X))))&
((?[X]:(~quiet(X)))<=>((happy(mary)&~calm(mary))))&
(![X]:(generous(X)<=>(~patient(X)|calm(X))))&
((?[X]:(~old(X)))=>(~kind(fred)))&
(((~tall(mary)|tall(mary)))<=>(?[X]:(patient(X))))&
(![X]:((tall(X)&~curious(X))=>(rich(X)|~creative(X))))&
(![X]:(quiet(X)<=>~old(X)))&
(?[X]:((funny(X)|strong(X))))&
(~creative(susan))&
(?[X]:((~curious(X)<~>generous(X))))&
(?[X]:((calm(X)&~funny(X))))&
(?[X]:((~creative(X)|~old(X)))) | ~kind(fred) | [
"p8",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 88535110841264542128217
% SZS output start Proof for 88535110841264542128217
9. ! [X0] : ((tall(X0) | ~calm(X0)) <=> calm(X0)) [input p8]
11. ? [X0] : ~quiet(X0) <=> (~calm(mary) & happy(mary)) [input p10]
13. ? [X0] : ~old(X0) => ~kind(fred) [input p12]
16. ! [X0] : (quiet(X0) <=> ~old(X0)) [input p15]
22. kind(fred) [input hypothesis]
30. ~kind(fred) | ! [X0] : old(X0) [ennf transformation 13]
50. ! [X0] : (((tall(X0) | ~calm(X0)) | ~calm(X0)) & (calm(X0) | (~tall(X0) & calm(X0)))) [nnf transformation 9]
51. ! [X0] : ((tall(X0) | ~calm(X0) | ~calm(X0)) & (calm(X0) | (~tall(X0) & calm(X0)))) [flattening 50]
52. (? [X0] : ~quiet(X0) | (calm(mary) | ~happy(mary))) & ((~calm(mary) & happy(mary)) | ! [X0] : quiet(X0)) [nnf transformation 11]
53. (? [X0] : ~quiet(X0) | calm(mary) | ~happy(mary)) & ((~calm(mary) & happy(mary)) | ! [X0] : quiet(X0)) [flattening 52]
54. (? [X0] : ~quiet(X0) | calm(mary) | ~happy(mary)) & ((~calm(mary) & happy(mary)) | ! [X1] : quiet(X1)) [rectify 53]
55. ? [X0] : ~quiet(X0) => ~quiet(sK2) [choice axiom]
56. (~quiet(sK2) | calm(mary) | ~happy(mary)) & ((~calm(mary) & happy(mary)) | ! [X1] : quiet(X1)) [skolemisation 54,55]
64. ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0))) [nnf transformation 16]
110. calm(X0) | calm(X0) [cnf transformation 51]
116. ~calm(mary) | quiet(X1) [cnf transformation 56]
121. ~kind(fred) | old(X0) [cnf transformation 30]
125. ~old(X0) | ~quiet(X0) [cnf transformation 64]
132. kind(fred) [cnf transformation 22]
133. calm(X0) [duplicate literal removal 110]
183. quiet(X1) [subsumption resolution 116,133]
186. 10 <=> ! [X0] : old(X0) [avatar definition]
187. old(X0) <- (10) [avatar component clause 186]
189. 11 <=> kind(fred) [avatar definition]
192. 10 | ~11 [avatar split clause 121,189,186]
203. ~old(X0) [subsumption resolution 125,183]
214. 11 [avatar split clause 132,189]
215. $false <- (10) [subsumption resolution 187,203]
216. ~10 [avatar contradiction clause 215]
221. $false [avatar sat refutation 192,214,216]
% SZS output end Proof for 88535110841264542128217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not brave. If fred is both not kind and not brave then alice is not tall or tall. If someone is both not quiet and kind then someone is strong. Everyone who is not strong or not rich is calm and vice versa. If mary is both not wise and not creative then mary is patient and vice versa. Everyone who is generous or not kind is both not curious and quiet. Everyone who is not brave or kind is strong or kind. Everyone who is not patient is not brave or wise. If someone is either not patient or humble then someone is patient and vice versa. If someone is not calm or kind then someone is either not kind or wise and vice versa. If john is either calm or not rich then lucy is curious and vice versa. Everyone who is either curious or quiet is both not creative and happy and vice versa. Everyone who is both not funny and not old is not rich or quiet and vice versa. Everyone who is not tall or creative is humble and vice versa. Everyone who is both not humble and patient is kind. If someone is not strong then someone is both curious and wise and vice versa. Mary is both quiet and happy. Alice is either not generous or curious. Susan is not happy or not calm. Mary is curious or wise. Someone is either funny or not wise. John is not funny or rich. Paul is either not calm or not patient. | Paul is old. | neutral | (![X]:(~humble(X)=>(calm(X)|~brave(X))))&
(((~kind(fred)&~brave(fred)))=>((~tall(alice)|tall(alice))))&
((?[X]:((~quiet(X)&kind(X))))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)|~rich(X))<=>calm(X)))&
(((~wise(mary)&~creative(mary)))<=>(patient(mary)))&
(![X]:((generous(X)|~kind(X))=>(~curious(X)&quiet(X))))&
(![X]:((~brave(X)|kind(X))=>(strong(X)|kind(X))))&
(![X]:(~patient(X)=>(~brave(X)|wise(X))))&
((?[X]:((~patient(X)<~>humble(X))))<=>(?[X]:(patient(X))))&
((?[X]:((~calm(X)|kind(X))))<=>(?[X]:((~kind(X)<~>wise(X)))))&
(((calm(john)<~>~rich(john)))<=>(curious(lucy)))&
(![X]:((curious(X)<~>quiet(X))<=>(~creative(X)&happy(X))))&
(![X]:((~funny(X)&~old(X))<=>(~rich(X)|quiet(X))))&
(![X]:((~tall(X)|creative(X))<=>humble(X)))&
(![X]:((~humble(X)&patient(X))=>kind(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((curious(X)&wise(X)))))&
((quiet(mary)&happy(mary)))&
((~generous(alice)<~>curious(alice)))&
((~happy(susan)|~calm(susan)))&
((curious(mary)|wise(mary)))&
(?[X]:((funny(X)<~>~wise(X))))&
((~funny(john)|rich(john)))&
((~calm(paul)<~>~patient(paul))) | old(paul) | [] | null | 0 |
Everyone who is not strong or funny is both not tall and creative and vice versa.
Everyone who is both brave and not kind is not generous and vice versa.
If alice is both wise and not happy then alice is quiet or kind.
If fred is curious then someone is both not happy and not brave.
Everyone who is not tall is happy.
Everyone who is either happy or not funny is either rich or not kind and vice versa.
Everyone who is funny is quiet or not curious and vice versa.
Everyone who is not rich is either not happy or rich.
Everyone who is not strong is not strong or generous and vice versa.
If someone is either quiet or not funny then paul is both brave and not humble.
If john is kind or not calm then susan is either happy or not old.
Everyone who is not funny is quiet.
Everyone who is both not rich and humble is both not strong and humble and vice versa.
If paul is both not happy and not generous then fred is both not patient and not happy.
Everyone who is either kind or creative is both brave and not strong.
If john is both creative and happy then alice is old.
Someone is either not tall or not curious.
Someone is not old.
Someone is not kind or not strong.
Someone is old.
Paul is curious.
Alice is not brave or calm. | Susan is kind. | entailment | (![X]:((~strong(X)|funny(X))<=>(~tall(X)&creative(X))))&
(![X]:((brave(X)&~kind(X))<=>~generous(X)))&
(((wise(alice)&~happy(alice)))=>((quiet(alice)|kind(alice))))&
((curious(fred))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(~tall(X)=>happy(X)))&
(![X]:((happy(X)<~>~funny(X))<=>(rich(X)<~>~kind(X))))&
(![X]:(funny(X)<=>(quiet(X)|~curious(X))))&
(![X]:(~rich(X)=>(~happy(X)<~>rich(X))))&
(![X]:(~strong(X)<=>(~strong(X)|generous(X))))&
((?[X]:((quiet(X)<~>~funny(X))))=>((brave(paul)&~humble(paul))))&
(((kind(john)|~calm(john)))=>((happy(susan)<~>~old(susan))))&
(![X]:(~funny(X)=>quiet(X)))&
(![X]:((~rich(X)&humble(X))<=>(~strong(X)&humble(X))))&
(((~happy(paul)&~generous(paul)))=>((~patient(fred)&~happy(fred))))&
(![X]:((kind(X)<~>creative(X))=>(brave(X)&~strong(X))))&
(((creative(john)&happy(john)))=>(old(alice)))&
(?[X]:((~tall(X)<~>~curious(X))))&
(?[X]:(~old(X)))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:(old(X)))&
(curious(paul))&
((~brave(alice)|calm(alice))) | kind(susan) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6601610671746301392343209
% SZS output start Proof for 6601610671746301392343209
1. ! [X0] : ((funny(X0) | ~strong(X0)) <=> (creative(X0) & ~tall(X0))) [input p0]
5. ! [X0] : (~tall(X0) => happy(X0)) [input p4]
6. ! [X0] : ((happy(X0) <~> ~funny(X0)) <=> (rich(X0) <~> ~kind(X0))) [input p5]
7. ! [X0] : (funny(X0) <=> (~curious(X0) | quiet(X0))) [input p6]
8. ! [X0] : (~rich(X0) => (~happy(X0) <~> rich(X0))) [input p7]
12. ! [X0] : (~funny(X0) => quiet(X0)) [input p11]
23. ~kind(susan) [input hypothesis]
29. ! [X0] : (happy(X0) | tall(X0)) [ennf transformation 5]
30. ! [X0] : ((~happy(X0) <~> rich(X0)) | rich(X0)) [ennf transformation 8]
33. ! [X0] : (quiet(X0) | funny(X0)) [ennf transformation 12]
39. ! [X0] : (((funny(X0) | ~strong(X0)) | (~creative(X0) | tall(X0))) & ((creative(X0) & ~tall(X0)) | (~funny(X0) & strong(X0)))) [nnf transformation 1]
40. ! [X0] : ((funny(X0) | ~strong(X0) | ~creative(X0) | tall(X0)) & ((creative(X0) & ~tall(X0)) | (~funny(X0) & strong(X0)))) [flattening 39]
45. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) & (((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [nnf transformation 6]
46. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | ~funny(X0))) [nnf transformation 7]
47. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~funny(X0))) [flattening 46]
48. ! [X0] : (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | rich(X0)) [nnf transformation 30]
66. ~tall(X0) | ~funny(X0) [cnf transformation 40]
75. happy(X0) | tall(X0) [cnf transformation 29]
78. ~rich(X0) | kind(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 45]
85. ~quiet(X0) | funny(X0) [cnf transformation 47]
87. rich(X0) | ~happy(X0) | rich(X0) [cnf transformation 48]
98. quiet(X0) | funny(X0) [cnf transformation 33]
115. ~kind(susan) [cnf transformation 23]
116. ~happy(X0) | rich(X0) [duplicate literal removal 87]
133. 4 <=> ! [X0] : funny(X0) [avatar definition]
134. funny(X0) <- (4) [avatar component clause 133]
158. 9 <=> happy(susan) [avatar definition]
159. happy(susan) <- (9) [avatar component clause 158]
160. ~happy(susan) <- (~9) [avatar component clause 158]
167. funny(X0) [subsumption resolution 98,85]
168. 4 [avatar split clause 167,133]
287. tall(susan) <- (~9) [resolution 160,75]
298. ~funny(susan) <- (~9) [resolution 287,66]
300. $false <- (4, ~9) [subsumption resolution 298,134]
301. ~4 | 9 [avatar contradiction clause 300]
303. rich(susan) <- (9) [resolution 159,116]
308. kind(susan) | ~funny(susan) | ~happy(susan) <- (9) [resolution 303,78]
309. ~funny(susan) | ~happy(susan) <- (9) [subsumption resolution 308,115]
310. ~happy(susan) <- (4, 9) [subsumption resolution 309,134]
311. $false <- (4, 9) [subsumption resolution 310,159]
312. ~4 | ~9 [avatar contradiction clause 311]
313. $false [avatar sat refutation 168,301,312]
% SZS output end Proof for 6601610671746301392343209
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not humble is not kind or not creative and vice versa.
Everyone who is either not rich or not generous is both not kind and not brave.
If john is old or calm then someone is not strong or curious and vice versa.
If someone is strong or wise then fred is not tall or not patient and vice versa.
If someone is funny or quiet then mary is not calm and vice versa.
Everyone who is either kind or not wise is either rich or kind and vice versa.
If mary is both generous and not brave then lucy is wise or quiet.
Everyone who is brave or creative is patient or not strong and vice versa.
Everyone who is both not old and creative is both happy and not old and vice versa.
If susan is either humble or not tall then someone is both wise and not brave and vice versa.
Everyone who is wise is generous and vice versa.
If fred is not quiet then john is rich.
Everyone who is both not calm and not curious is both not kind and happy and vice versa.
If fred is not strong or humble then someone is not funny or not quiet.
If someone is not strong or not old then someone is either not humble or quiet.
Everyone who is patient is not patient.
Someone is either wise or brave.
Alice is rich or not wise.
Someone is either not happy or not kind.
Someone is old or patient.
Someone is creative or humble.
Mary is either kind or happy.
Mary is creative. | Lucy is not kind. | entailment | (![X]:((patient(X)<~>~humble(X))<=>(~kind(X)|~creative(X))))&
(![X]:((~rich(X)<~>~generous(X))=>(~kind(X)&~brave(X))))&
(((old(john)|calm(john)))<=>(?[X]:((~strong(X)|curious(X)))))&
((?[X]:((strong(X)|wise(X))))<=>((~tall(fred)|~patient(fred))))&
((?[X]:((funny(X)|quiet(X))))<=>(~calm(mary)))&
(![X]:((kind(X)<~>~wise(X))<=>(rich(X)<~>kind(X))))&
(((generous(mary)&~brave(mary)))=>((wise(lucy)|quiet(lucy))))&
(![X]:((brave(X)|creative(X))<=>(patient(X)|~strong(X))))&
(![X]:((~old(X)&creative(X))<=>(happy(X)&~old(X))))&
(((humble(susan)<~>~tall(susan)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(wise(X)<=>generous(X)))&
((~quiet(fred))=>(rich(john)))&
(![X]:((~calm(X)&~curious(X))<=>(~kind(X)&happy(X))))&
(((~strong(fred)|humble(fred)))=>(?[X]:((~funny(X)|~quiet(X)))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:(patient(X)=>~patient(X)))&
(?[X]:((wise(X)<~>brave(X))))&
((rich(alice)|~wise(alice)))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((creative(X)|humble(X))))&
((kind(mary)<~>happy(mary)))&
(creative(mary)) | ~kind(lucy) | [
"p1",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4992248580992234267953830
% SZS output start Proof for 4992248580992234267953830
2. ! [X0] : ((~rich(X0) <~> ~generous(X0)) => (~brave(X0) & ~kind(X0))) [input p1]
6. ! [X0] : ((kind(X0) <~> ~wise(X0)) <=> (rich(X0) <~> kind(X0))) [input p5]
11. ! [X0] : (wise(X0) <=> generous(X0)) [input p10]
24. kind(lucy) [input hypothesis]
26. ! [X0] : ((~brave(X0) & ~kind(X0)) | (~rich(X0) <=> ~generous(X0))) [ennf transformation 2]
35. ! [X0] : ((~brave(X0) & ~kind(X0)) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0)))) [nnf transformation 26]
50. ! [X0] : ((((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | ((rich(X0) | ~kind(X0)) & (kind(X0) | ~rich(X0)))) & (((~kind(X0) | ~rich(X0)) & (kind(X0) | rich(X0))) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0))))) [nnf transformation 6]
59. ! [X0] : ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0))) [nnf transformation 11]
85. ~generous(X0) | ~kind(X0) | rich(X0) [cnf transformation 35]
86. ~rich(X0) | ~kind(X0) | generous(X0) [cnf transformation 35]
101. kind(X0) | rich(X0) | kind(X0) | wise(X0) [cnf transformation 50]
102. ~kind(X0) | ~rich(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 50]
104. ~wise(X0) | kind(X0) | kind(X0) | ~rich(X0) [cnf transformation 50]
107. wise(X0) | ~kind(X0) | rich(X0) | ~kind(X0) [cnf transformation 50]
123. ~wise(X0) | generous(X0) [cnf transformation 59]
124. ~generous(X0) | wise(X0) [cnf transformation 59]
147. kind(lucy) [cnf transformation 24]
149. kind(X0) | rich(X0) | wise(X0) [duplicate literal removal 101]
150. ~kind(X0) | ~rich(X0) | ~wise(X0) [duplicate literal removal 102]
151. ~wise(X0) | kind(X0) | ~rich(X0) [duplicate literal removal 104]
152. ~kind(X0) | wise(X0) | rich(X0) [duplicate literal removal 107]
226. ~wise(X0) | ~rich(X0) [subsumption resolution 150,151]
227. wise(X0) | rich(X0) [subsumption resolution 149,152]
237. 20 <=> wise(lucy) [avatar definition]
238. ~wise(lucy) <- (~20) [avatar component clause 237]
239. wise(lucy) <- (20) [avatar component clause 237]
358. generous(X1) | rich(X1) [resolution 227,123]
370. ~kind(X0) | rich(X0) | rich(X0) [resolution 85,358]
371. ~kind(X0) | rich(X0) [duplicate literal removal 370]
396. ~rich(lucy) <- (20) [resolution 239,226]
519. rich(lucy) [resolution 371,147]
521. $false <- (20) [subsumption resolution 519,396]
522. ~20 [avatar contradiction clause 521]
542. ~kind(lucy) | generous(lucy) [resolution 519,86]
543. generous(lucy) [subsumption resolution 542,147]
545. wise(lucy) [resolution 543,124]
546. $false <- (~20) [subsumption resolution 545,238]
547. 20 [avatar contradiction clause 546]
548. $false [avatar sat refutation 522,547]
% SZS output end Proof for 4992248580992234267953830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and brave is calm and vice versa.
Everyone who is both not funny and not happy is both not brave and curious and vice versa.
Everyone who is both not quiet and brave is either calm or funny.
Everyone who is both brave and not quiet is wise and vice versa.
If lucy is not creative then someone is not creative or wise.
If paul is both happy and not wise then someone is both not brave and not calm and vice versa.
Everyone who is either not happy or tall is not calm and vice versa.
Everyone who is tall or not quiet is not creative or not patient.
Everyone who is both not humble and generous is both not tall and not curious and vice versa.
Everyone who is either not creative or kind is both not strong and not old and vice versa.
If john is either not wise or brave then lucy is either not quiet or not humble.
Everyone who is curious or strong is both not tall and not quiet.
Everyone who is not calm or quiet is happy or not wise.
Everyone who is not generous is rich and vice versa.
If paul is not happy or creative then someone is both happy and not brave and vice versa.
If someone is not happy or not quiet then someone is both not patient and not strong.
Fred is both curious and not old.
Someone is either strong or not curious.
Someone is not quiet.
Paul is either not strong or kind.
Someone is not generous or quiet.
John is either not curious or not generous.
Alice is both not rich and brave.
Paul is calm or not humble. | Alice is not brave. | contradiction | (![X]:((old(X)&brave(X))<=>calm(X)))&
(![X]:((~funny(X)&~happy(X))<=>(~brave(X)&curious(X))))&
(![X]:((~quiet(X)&brave(X))=>(calm(X)<~>funny(X))))&
(![X]:((brave(X)&~quiet(X))<=>wise(X)))&
((~creative(lucy))=>(?[X]:((~creative(X)|wise(X)))))&
(((happy(paul)&~wise(paul)))<=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>~calm(X)))&
(![X]:((tall(X)|~quiet(X))=>(~creative(X)|~patient(X))))&
(![X]:((~humble(X)&generous(X))<=>(~tall(X)&~curious(X))))&
(![X]:((~creative(X)<~>kind(X))<=>(~strong(X)&~old(X))))&
(((~wise(john)<~>brave(john)))=>((~quiet(lucy)<~>~humble(lucy))))&
(![X]:((curious(X)|strong(X))=>(~tall(X)&~quiet(X))))&
(![X]:((~calm(X)|quiet(X))=>(happy(X)|~wise(X))))&
(![X]:(~generous(X)<=>rich(X)))&
(((~happy(paul)|creative(paul)))<=>(?[X]:((happy(X)&~brave(X)))))&
((?[X]:((~happy(X)|~quiet(X))))=>(?[X]:((~patient(X)&~strong(X)))))&
((curious(fred)&~old(fred)))&
(?[X]:((strong(X)<~>~curious(X))))&
(?[X]:(~quiet(X)))&
((~strong(paul)<~>kind(paul)))&
(?[X]:((~generous(X)|quiet(X))))&
((~curious(john)<~>~generous(john)))&
((~rich(alice)&brave(alice)))&
((calm(paul)|~humble(paul))) | ~brave(alice) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 694429300940837700872964
% SZS output start Proof for 694429300940837700872964
23. brave(alice) & ~rich(alice) [input p22]
25. ~brave(alice) [input hypothesis]
136. brave(alice) [cnf transformation 23]
138. ~brave(alice) [cnf transformation 25]
282. $false [subsumption resolution 138,136]
% SZS output end Proof for 694429300940837700872964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or not patient then mary is not creative. If someone is not curious or not kind then paul is both creative and not generous. Everyone who is not funny or not quiet is not funny or creative and vice versa. If someone is not brave or not generous then susan is not patient. Everyone who is either not happy or not brave is both funny and not generous. Everyone who is either rich or not wise is not patient. If lucy is either not brave or not generous then alice is either not tall or funny and vice versa. Everyone who is both generous and not wise is both brave and strong. Everyone who is either not happy or happy is funny or humble and vice versa. If someone is either not kind or not brave then susan is happy or not kind and vice versa. Everyone who is not calm is not strong and vice versa. Everyone who is either not generous or not quiet is kind or rich and vice versa. Everyone who is not creative is either quiet or not quiet. If paul is either not strong or strong then someone is not wise or creative. Everyone who is not kind is old or not brave and vice versa. If lucy is either tall or not curious then someone is either not generous or not funny and vice versa. John is both not patient and not creative. Someone is either kind or creative. Someone is either wise or funny. John is both not rich and not funny. Paul is both brave and generous. Paul is either not old or not humble. | Alice is not patient. | neutral | ((?[X]:((~happy(X)<~>~patient(X))))=>(~creative(mary)))&
((?[X]:((~curious(X)|~kind(X))))=>((creative(paul)&~generous(paul))))&
(![X]:((~funny(X)|~quiet(X))<=>(~funny(X)|creative(X))))&
((?[X]:((~brave(X)|~generous(X))))=>(~patient(susan)))&
(![X]:((~happy(X)<~>~brave(X))=>(funny(X)&~generous(X))))&
(![X]:((rich(X)<~>~wise(X))=>~patient(X)))&
(((~brave(lucy)<~>~generous(lucy)))<=>((~tall(alice)<~>funny(alice))))&
(![X]:((generous(X)&~wise(X))=>(brave(X)&strong(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(funny(X)|humble(X))))&
((?[X]:((~kind(X)<~>~brave(X))))<=>((happy(susan)|~kind(susan))))&
(![X]:(~calm(X)<=>~strong(X)))&
(![X]:((~generous(X)<~>~quiet(X))<=>(kind(X)|rich(X))))&
(![X]:(~creative(X)=>(quiet(X)<~>~quiet(X))))&
(((~strong(paul)<~>strong(paul)))=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:(~kind(X)<=>(old(X)|~brave(X))))&
(((tall(lucy)<~>~curious(lucy)))<=>(?[X]:((~generous(X)<~>~funny(X)))))&
((~patient(john)&~creative(john)))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((~rich(john)&~funny(john)))&
((brave(paul)&generous(paul)))&
((~old(paul)<~>~humble(paul))) | ~patient(alice) | [] | null | 0 |
Everyone who is both not old and patient is either creative or brave. Everyone who is wise is not old or not calm. If someone is both not brave and old then alice is not rich. Everyone who is both not funny and brave is not brave. Everyone who is curious is both curious and not happy and vice versa. Everyone who is not generous or curious is not patient. Everyone who is not old is both not wise and happy and vice versa. Everyone who is both not brave and old is both funny and not brave and vice versa. If susan is either curious or wise then paul is curious and vice versa. Everyone who is funny or not patient is both brave and not old. If alice is not old or not calm then paul is either tall or not kind. Everyone who is not rich is old or quiet. Everyone who is tall is not funny or not quiet and vice versa. If someone is brave or quiet then someone is either calm or wise. Everyone who is curious is either patient or not humble and vice versa. If lucy is generous or not tall then someone is either not creative or not generous. Someone is quiet. Someone is not tall or generous. Someone is both not generous and not curious. Alice is calm or funny. Someone is either not wise or not tall. Alice is not tall. Someone is humble. | Paul is not curious. | entailment | (![X]:((~old(X)&patient(X))=>(creative(X)<~>brave(X))))&
(![X]:(wise(X)=>(~old(X)|~calm(X))))&
((?[X]:((~brave(X)&old(X))))=>(~rich(alice)))&
(![X]:((~funny(X)&brave(X))=>~brave(X)))&
(![X]:(curious(X)<=>(curious(X)&~happy(X))))&
(![X]:((~generous(X)|curious(X))=>~patient(X)))&
(![X]:(~old(X)<=>(~wise(X)&happy(X))))&
(![X]:((~brave(X)&old(X))<=>(funny(X)&~brave(X))))&
(((curious(susan)<~>wise(susan)))<=>(curious(paul)))&
(![X]:((funny(X)|~patient(X))=>(brave(X)&~old(X))))&
(((~old(alice)|~calm(alice)))=>((tall(paul)<~>~kind(paul))))&
(![X]:(~rich(X)=>(old(X)|quiet(X))))&
(![X]:(tall(X)<=>(~funny(X)|~quiet(X))))&
((?[X]:((brave(X)|quiet(X))))=>(?[X]:((calm(X)<~>wise(X)))))&
(![X]:(curious(X)<=>(patient(X)<~>~humble(X))))&
(((generous(lucy)|~tall(lucy)))=>(?[X]:((~creative(X)<~>~generous(X)))))&
(?[X]:(quiet(X)))&
(?[X]:((~tall(X)|generous(X))))&
(?[X]:((~generous(X)&~curious(X))))&
((calm(alice)|funny(alice)))&
(?[X]:((~wise(X)<~>~tall(X))))&
(~tall(alice))&
(?[X]:(humble(X))) | ~curious(paul) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 686051602978559929918822
% SZS output start Proof for 686051602978559929918822
4. ! [X0] : ((brave(X0) & ~funny(X0)) => ~brave(X0)) [input p3]
5. ! [X0] : (curious(X0) <=> (~happy(X0) & curious(X0))) [input p4]
7. ! [X0] : (~old(X0) <=> (happy(X0) & ~wise(X0))) [input p6]
8. ! [X0] : ((old(X0) & ~brave(X0)) <=> (~brave(X0) & funny(X0))) [input p7]
10. ! [X0] : ((~patient(X0) | funny(X0)) => (~old(X0) & brave(X0))) [input p9]
24. curious(paul) [input hypothesis]
31. ! [X0] : (~brave(X0) | (~brave(X0) | funny(X0))) [ennf transformation 4]
32. ! [X0] : (~brave(X0) | ~brave(X0) | funny(X0)) [flattening 31]
34. ! [X0] : ((~old(X0) & brave(X0)) | (patient(X0) & ~funny(X0))) [ennf transformation 10]
41. ! [X0] : ((curious(X0) | (happy(X0) | ~curious(X0))) & ((~happy(X0) & curious(X0)) | ~curious(X0))) [nnf transformation 5]
42. ! [X0] : ((curious(X0) | happy(X0) | ~curious(X0)) & ((~happy(X0) & curious(X0)) | ~curious(X0))) [flattening 41]
43. ! [X0] : ((~old(X0) | (~happy(X0) | wise(X0))) & ((happy(X0) & ~wise(X0)) | old(X0))) [nnf transformation 7]
44. ! [X0] : ((~old(X0) | ~happy(X0) | wise(X0)) & ((happy(X0) & ~wise(X0)) | old(X0))) [flattening 43]
45. ! [X0] : (((old(X0) & ~brave(X0)) | (brave(X0) | ~funny(X0))) & ((~brave(X0) & funny(X0)) | (~old(X0) | brave(X0)))) [nnf transformation 8]
46. ! [X0] : (((old(X0) & ~brave(X0)) | brave(X0) | ~funny(X0)) & ((~brave(X0) & funny(X0)) | ~old(X0) | brave(X0))) [flattening 45]
74. ~brave(X0) | ~brave(X0) | funny(X0) [cnf transformation 32]
76. ~happy(X0) | ~curious(X0) [cnf transformation 42]
81. happy(X0) | old(X0) [cnf transformation 44]
83. funny(X0) | ~old(X0) | brave(X0) [cnf transformation 46]
93. ~old(X0) | ~funny(X0) [cnf transformation 34]
124. curious(paul) [cnf transformation 24]
125. ~brave(X0) | funny(X0) [duplicate literal removal 74]
134. funny(X0) | ~old(X0) [subsumption resolution 83,125]
136. 3 <=> curious(paul) [avatar definition]
137. curious(paul) <- (3) [avatar component clause 136]
151. ~old(X0) [subsumption resolution 93,134]
235. 3 [avatar split clause 124,136]
241. old(X0) | ~curious(X0) [resolution 81,76]
242. ~curious(X0) [subsumption resolution 241,151]
243. $false <- (3) [resolution 242,137]
246. ~3 [avatar contradiction clause 243]
247. $false [avatar sat refutation 235,246]
% SZS output end Proof for 686051602978559929918822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is wise or not tall. Everyone who is both kind and quiet is not patient or not creative and vice versa. If someone is both not curious and not humble then susan is not creative. If someone is not brave then someone is not funny. Everyone who is both calm and not old is tall or not strong. Everyone who is calm is not old and vice versa. If alice is kind or not tall then someone is strong and vice versa. Everyone who is funny or not happy is not quiet or not strong and vice versa. Everyone who is both not creative and not old is either not curious or brave. Everyone who is rich is not curious and vice versa. Everyone who is wise is both not funny and not patient. If someone is either rich or not brave then someone is either patient or not brave and vice versa. Everyone who is not calm is not curious or kind and vice versa. If someone is either tall or not strong then fred is either not rich or humble. Everyone who is both brave and not quiet is creative or kind. If lucy is both not strong and kind then mary is not happy and vice versa. Alice is both rich and not funny. Paul is both humble and not quiet. Someone is either not brave or not funny. Someone is either not kind or not humble. John is patient or not generous. Paul is either calm or not happy. Paul is either funny or not creative. | Paul is not tall. | entailment | (![X]:(patient(X)=>(wise(X)|~tall(X))))&
(![X]:((kind(X)&quiet(X))<=>(~patient(X)|~creative(X))))&
((?[X]:((~curious(X)&~humble(X))))=>(~creative(susan)))&
((?[X]:(~brave(X)))=>(?[X]:(~funny(X))))&
(![X]:((calm(X)&~old(X))=>(tall(X)|~strong(X))))&
(![X]:(calm(X)<=>~old(X)))&
(((kind(alice)|~tall(alice)))<=>(?[X]:(strong(X))))&
(![X]:((funny(X)|~happy(X))<=>(~quiet(X)|~strong(X))))&
(![X]:((~creative(X)&~old(X))=>(~curious(X)<~>brave(X))))&
(![X]:(rich(X)<=>~curious(X)))&
(![X]:(wise(X)=>(~funny(X)&~patient(X))))&
((?[X]:((rich(X)<~>~brave(X))))<=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:(~calm(X)<=>(~curious(X)|kind(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>((~rich(fred)<~>humble(fred))))&
(![X]:((brave(X)&~quiet(X))=>(creative(X)|kind(X))))&
(((~strong(lucy)&kind(lucy)))<=>(~happy(mary)))&
((rich(alice)&~funny(alice)))&
((humble(paul)&~quiet(paul)))&
(?[X]:((~brave(X)<~>~funny(X))))&
(?[X]:((~kind(X)<~>~humble(X))))&
((patient(john)|~generous(john)))&
((calm(paul)<~>~happy(paul)))&
((funny(paul)<~>~creative(paul))) | ~tall(paul) | [
"p0",
"p1",
"p10",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3729177484973882548296400
% SZS output start Proof for 3729177484973882548296400
1. ! [X0] : (patient(X0) => (~tall(X0) | wise(X0))) [input p0]
2. ! [X0] : ((quiet(X0) & kind(X0)) <=> (~creative(X0) | ~patient(X0))) [input p1]
11. ! [X0] : (wise(X0) => (~patient(X0) & ~funny(X0))) [input p10]
18. ~quiet(paul) & humble(paul) [input p17]
23. funny(paul) <~> ~creative(paul) [input p22]
24. tall(paul) [input hypothesis]
28. ! [X0] : ((~tall(X0) | wise(X0)) | ~patient(X0)) [ennf transformation 1]
29. ! [X0] : (~tall(X0) | wise(X0) | ~patient(X0)) [flattening 28]
36. ! [X0] : ((~patient(X0) & ~funny(X0)) | ~wise(X0)) [ennf transformation 11]
40. ! [X0] : (((quiet(X0) & kind(X0)) | (creative(X0) & patient(X0))) & ((~creative(X0) | ~patient(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 2]
41. ! [X0] : (((quiet(X0) & kind(X0)) | (creative(X0) & patient(X0))) & (~creative(X0) | ~patient(X0) | ~quiet(X0) | ~kind(X0))) [flattening 40]
72. (creative(paul) | ~funny(paul)) & (~creative(paul) | funny(paul)) [nnf transformation 23]
73. ~tall(X0) | wise(X0) | ~patient(X0) [cnf transformation 29]
77. quiet(X0) | patient(X0) [cnf transformation 41]
78. creative(X0) | quiet(X0) [cnf transformation 41]
95. ~funny(X0) | ~wise(X0) [cnf transformation 36]
119. ~quiet(paul) [cnf transformation 18]
126. ~creative(paul) | funny(paul) [cnf transformation 72]
128. tall(paul) [cnf transformation 24]
263. 30 <=> funny(paul) [avatar definition]
264. funny(paul) <- (30) [avatar component clause 263]
267. 31 <=> creative(paul) [avatar definition]
268. ~creative(paul) <- (~31) [avatar component clause 267]
271. 30 | ~31 [avatar split clause 126,267,263]
276. patient(paul) [resolution 77,119]
278. quiet(paul) <- (~31) [resolution 78,268]
279. $false <- (~31) [subsumption resolution 278,119]
280. 31 [avatar contradiction clause 279]
286. ~wise(paul) <- (30) [resolution 95,264]
287. wise(paul) | ~patient(paul) [resolution 73,128]
289. ~patient(paul) <- (30) [subsumption resolution 287,286]
290. $false <- (30) [subsumption resolution 289,276]
291. ~30 [avatar contradiction clause 290]
293. $false [avatar sat refutation 271,280,291]
% SZS output end Proof for 3729177484973882548296400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or not humble then someone is calm or not rich and vice versa.
Everyone who is generous or not happy is both calm and not creative and vice versa.
Everyone who is either quiet or not calm is both funny and creative and vice versa.
If fred is both funny and humble then fred is creative.
Everyone who is old is either not happy or not strong and vice versa.
If someone is either generous or not rich then susan is both not creative and not happy.
If fred is not brave or wise then susan is humble or generous and vice versa.
Everyone who is not quiet or tall is generous and vice versa.
If someone is tall then someone is not funny and vice versa.
If mary is brave then john is not generous and vice versa.
If someone is either not generous or not patient then someone is not old.
Everyone who is quiet or generous is either generous or calm and vice versa.
Everyone who is either not calm or old is both tall and curious.
Everyone who is both curious and rich is generous and vice versa.
Everyone who is both not quiet and not curious is not patient or not quiet.
If paul is both not old and not quiet then someone is calm or not wise.
Paul is either generous or wise.
Someone is not patient or not tall.
Mary is not humble.
Someone is not tall.
Someone is not patient.
Lucy is not curious. | John is not strong. | contradiction | ((?[X]:((~kind(X)<~>~humble(X))))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:((generous(X)|~happy(X))<=>(calm(X)&~creative(X))))&
(![X]:((quiet(X)<~>~calm(X))<=>(funny(X)&creative(X))))&
(((funny(fred)&humble(fred)))=>(creative(fred)))&
(![X]:(old(X)<=>(~happy(X)<~>~strong(X))))&
((?[X]:((generous(X)<~>~rich(X))))=>((~creative(susan)&~happy(susan))))&
(((~brave(fred)|wise(fred)))<=>((humble(susan)|generous(susan))))&
(![X]:((~quiet(X)|tall(X))<=>generous(X)))&
((?[X]:(tall(X)))<=>(?[X]:(~funny(X))))&
((brave(mary))<=>(~generous(john)))&
((?[X]:((~generous(X)<~>~patient(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|generous(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~calm(X)<~>old(X))=>(tall(X)&curious(X))))&
(![X]:((curious(X)&rich(X))<=>generous(X)))&
(![X]:((~quiet(X)&~curious(X))=>(~patient(X)|~quiet(X))))&
(((~old(paul)&~quiet(paul)))=>(?[X]:((calm(X)|~wise(X)))))&
((generous(paul)<~>wise(paul)))&
(?[X]:((~patient(X)|~tall(X))))&
(~humble(mary))&
(?[X]:(~tall(X)))&
(?[X]:(~patient(X)))&
(~curious(lucy)) | ~strong(john) | [
"p1",
"p2",
"p4",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4950862437050247639513300
% SZS output start Proof for 4950862437050247639513300
2. ! [X0] : ((~happy(X0) | generous(X0)) <=> (~creative(X0) & calm(X0))) [input p1]
3. ! [X0] : ((quiet(X0) <~> ~calm(X0)) <=> (creative(X0) & funny(X0))) [input p2]
5. ! [X0] : (old(X0) <=> (~happy(X0) <~> ~strong(X0))) [input p4]
8. ! [X0] : ((tall(X0) | ~quiet(X0)) <=> generous(X0)) [input p7]
9. ? [X0] : tall(X0) <=> ? [X0] : ~funny(X0) [input p8]
12. ! [X0] : ((generous(X0) | quiet(X0)) <=> (generous(X0) <~> calm(X0))) [input p11]
13. ! [X0] : ((~calm(X0) <~> old(X0)) => (curious(X0) & tall(X0))) [input p12]
23. ~strong(john) [input hypothesis]
25. ? [X0] : tall(X0) <=> ? [X1] : ~funny(X1) [rectify 9]
31. ! [X0] : ((curious(X0) & tall(X0)) | (~calm(X0) <=> old(X0))) [ennf transformation 13]
41. ! [X0] : (((~happy(X0) | generous(X0)) | (creative(X0) | ~calm(X0))) & ((~creative(X0) & calm(X0)) | (happy(X0) & ~generous(X0)))) [nnf transformation 2]
42. ! [X0] : ((~happy(X0) | generous(X0) | creative(X0) | ~calm(X0)) & ((~creative(X0) & calm(X0)) | (happy(X0) & ~generous(X0)))) [flattening 41]
43. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | (~creative(X0) | ~funny(X0))) & ((creative(X0) & funny(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [nnf transformation 3]
44. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | ~creative(X0) | ~funny(X0)) & ((creative(X0) & funny(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [flattening 43]
45. ! [X0] : ((old(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) & (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | ~old(X0))) [nnf transformation 5]
49. ! [X0] : (((tall(X0) | ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (~tall(X0) & quiet(X0)))) [nnf transformation 8]
50. ! [X0] : ((tall(X0) | ~quiet(X0) | ~generous(X0)) & (generous(X0) | (~tall(X0) & quiet(X0)))) [flattening 49]
51. (? [X0] : tall(X0) | ! [X1] : funny(X1)) & (? [X1] : ~funny(X1) | ! [X0] : ~tall(X0)) [nnf transformation 25]
52. (? [X0] : tall(X0) | ! [X1] : funny(X1)) & (? [X2] : ~funny(X2) | ! [X3] : ~tall(X3)) [rectify 51]
53. ? [X0] : tall(X0) => tall(sK2) [choice axiom]
54. ? [X2] : ~funny(X2) => ~funny(sK3) [choice axiom]
55. (tall(sK2) | ! [X1] : funny(X1)) & (~funny(sK3) | ! [X3] : ~tall(X3)) [skolemisation 52,54,53]
61. ! [X0] : (((generous(X0) | quiet(X0)) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (~generous(X0) & ~quiet(X0)))) [nnf transformation 12]
62. ! [X0] : ((generous(X0) | quiet(X0) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (~generous(X0) & ~quiet(X0)))) [flattening 61]
63. ! [X0] : ((curious(X0) & tall(X0)) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) [nnf transformation 31]
81. ~generous(X0) | calm(X0) [cnf transformation 42]
84. ~creative(X0) | happy(X0) [cnf transformation 42]
88. ~quiet(X0) | ~calm(X0) | creative(X0) [cnf transformation 44]
96. ~happy(X0) | old(X0) | strong(X0) [cnf transformation 45]
105. quiet(X0) | generous(X0) [cnf transformation 50]
106. ~tall(X0) | generous(X0) [cnf transformation 50]
108. ~funny(sK3) | ~tall(X3) [cnf transformation 55]
109. tall(sK2) | funny(X1) [cnf transformation 55]
114. calm(X0) | generous(X0) | ~quiet(X0) [cnf transformation 62]
117. ~calm(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 62]
121. ~old(X0) | ~calm(X0) | tall(X0) [cnf transformation 63]
136. ~strong(john) [cnf transformation 23]
137. ~calm(X0) | ~generous(X0) [duplicate literal removal 117]
225. 20 <=> ! [X1] : funny(X1) [avatar definition]
226. funny(X1) <- (20) [avatar component clause 225]
228. 21 <=> tall(sK2) [avatar definition]
230. tall(sK2) <- (21) [avatar component clause 228]
231. 20 | 21 [avatar split clause 109,228,225]
233. 22 <=> ! [X3] : ~tall(X3) [avatar definition]
234. ~tall(X3) <- (22) [avatar component clause 233]
236. 23 <=> funny(sK3) [avatar definition]
238. ~funny(sK3) <- (~23) [avatar component clause 236]
239. 22 | ~23 [avatar split clause 108,236,233]
262. ~generous(X0) [subsumption resolution 137,81]
263. ~quiet(X0) | calm(X0) [subsumption resolution 114,262]
298. $false <- (20, ~23) [resolution 238,226]
299. ~20 | 23 [avatar contradiction clause 298]
301. generous(sK2) <- (21) [resolution 106,230]
302. $false <- (21) [subsumption resolution 301,262]
303. ~21 [avatar contradiction clause 302]
304. calm(X0) | generous(X0) [resolution 263,105]
305. calm(X0) [subsumption resolution 304,262]
307. ~calm(X0) | creative(X0) | generous(X0) [resolution 88,105]
308. creative(X0) | generous(X0) [subsumption resolution 307,305]
309. creative(X0) [subsumption resolution 308,262]
311. happy(X0) [resolution 309,84]
325. strong(X0) | old(X0) [resolution 96,311]
327. old(john) [resolution 325,136]
338. ~calm(john) | tall(john) [resolution 121,327]
339. tall(john) [subsumption resolution 338,305]
340. $false <- (22) [subsumption resolution 339,234]
341. ~22 [avatar contradiction clause 340]
342. $false [avatar sat refutation 231,239,299,303,341]
% SZS output end Proof for 4950862437050247639513300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and rich is not generous. Everyone who is kind or happy is not quiet or wise. Everyone who is happy or not old is not tall or not calm and vice versa. Everyone who is tall or not strong is either not generous or not humble and vice versa. Everyone who is generous is not calm or quiet. If someone is either not patient or rich then mary is both funny and generous and vice versa. If someone is kind then mary is either generous or not kind. Everyone who is both tall and not rich is either generous or not funny and vice versa. If fred is either brave or not curious then someone is not quiet. Everyone who is either wise or not tall is wise or strong and vice versa. If alice is not funny or happy then someone is either not quiet or not curious and vice versa. Everyone who is either strong or not generous is both not tall and happy. If someone is both brave and creative then john is not brave or not humble and vice versa. If mary is both funny and humble then someone is brave and vice versa. Everyone who is tall or strong is either quiet or not calm and vice versa. Everyone who is either not creative or not tall is curious. Someone is not tall. Mary is not brave or funny. John is not patient. Fred is both strong and happy. Someone is not generous. Someone is humble. Alice is either not strong or not patient. Someone is not rich. | Mary is generous. | contradiction | (![X]:((kind(X)&rich(X))=>~generous(X)))&
(![X]:((kind(X)|happy(X))=>(~quiet(X)|wise(X))))&
(![X]:((happy(X)|~old(X))<=>(~tall(X)|~calm(X))))&
(![X]:((tall(X)|~strong(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:(generous(X)=>(~calm(X)|quiet(X))))&
((?[X]:((~patient(X)<~>rich(X))))<=>((funny(mary)&generous(mary))))&
((?[X]:(kind(X)))=>((generous(mary)<~>~kind(mary))))&
(![X]:((tall(X)&~rich(X))<=>(generous(X)<~>~funny(X))))&
(((brave(fred)<~>~curious(fred)))=>(?[X]:(~quiet(X))))&
(![X]:((wise(X)<~>~tall(X))<=>(wise(X)|strong(X))))&
(((~funny(alice)|happy(alice)))<=>(?[X]:((~quiet(X)<~>~curious(X)))))&
(![X]:((strong(X)<~>~generous(X))=>(~tall(X)&happy(X))))&
((?[X]:((brave(X)&creative(X))))<=>((~brave(john)|~humble(john))))&
(((funny(mary)&humble(mary)))<=>(?[X]:(brave(X))))&
(![X]:((tall(X)|strong(X))<=>(quiet(X)<~>~calm(X))))&
(![X]:((~creative(X)<~>~tall(X))=>curious(X)))&
(?[X]:(~tall(X)))&
((~brave(mary)|funny(mary)))&
(~patient(john))&
((strong(fred)&happy(fred)))&
(?[X]:(~generous(X)))&
(?[X]:(humble(X)))&
((~strong(alice)<~>~patient(alice)))&
(?[X]:(~rich(X))) | generous(mary) | [
"p3",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8822413731792452669687317
% SZS output start Proof for 8822413731792452669687317
4. ! [X0] : ((~strong(X0) | tall(X0)) <=> (~generous(X0) <~> ~humble(X0))) [input p3]
8. ! [X0] : ((~rich(X0) & tall(X0)) <=> (generous(X0) <~> ~funny(X0))) [input p7]
13. ? [X0] : (creative(X0) & brave(X0)) <=> (~humble(john) | ~brave(john)) [input p12]
14. (humble(mary) & funny(mary)) <=> ? [X0] : brave(X0) [input p13]
25. generous(mary) [input hypothesis]
38. ! [X0] : (((~strong(X0) | tall(X0)) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) & (((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | (strong(X0) & ~tall(X0)))) [nnf transformation 4]
39. ! [X0] : ((~strong(X0) | tall(X0) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) & (((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | (strong(X0) & ~tall(X0)))) [flattening 38]
46. ! [X0] : (((~rich(X0) & tall(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (rich(X0) | ~tall(X0)))) [nnf transformation 8]
47. ! [X0] : (((~rich(X0) & tall(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | rich(X0) | ~tall(X0))) [flattening 46]
59. (? [X0] : (creative(X0) & brave(X0)) | (humble(john) & brave(john))) & ((~humble(john) | ~brave(john)) | ! [X0] : (~creative(X0) | ~brave(X0))) [nnf transformation 13]
60. (? [X0] : (creative(X0) & brave(X0)) | (humble(john) & brave(john))) & (~humble(john) | ~brave(john) | ! [X0] : (~creative(X0) | ~brave(X0))) [flattening 59]
61. (? [X0] : (creative(X0) & brave(X0)) | (humble(john) & brave(john))) & (~humble(john) | ~brave(john) | ! [X1] : (~creative(X1) | ~brave(X1))) [rectify 60]
62. ? [X0] : (creative(X0) & brave(X0)) => (creative(sK3) & brave(sK3)) [choice axiom]
63. ((creative(sK3) & brave(sK3)) | (humble(john) & brave(john))) & (~humble(john) | ~brave(john) | ! [X1] : (~creative(X1) | ~brave(X1))) [skolemisation 61,62]
64. ((humble(mary) & funny(mary)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~humble(mary) | ~funny(mary))) [nnf transformation 14]
65. ((humble(mary) & funny(mary)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~humble(mary) | ~funny(mary)) [flattening 64]
66. ((humble(mary) & funny(mary)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~humble(mary) | ~funny(mary)) [rectify 65]
67. ? [X1] : brave(X1) => brave(sK4) [choice axiom]
68. ((humble(mary) & funny(mary)) | ! [X0] : ~brave(X0)) & (brave(sK4) | ~humble(mary) | ~funny(mary)) [skolemisation 66,67]
88. ~humble(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 39]
105. ~funny(X0) | tall(X0) | ~generous(X0) [cnf transformation 47]
128. brave(sK3) | brave(john) [cnf transformation 63]
133. funny(mary) | ~brave(X0) [cnf transformation 68]
134. humble(mary) | ~brave(X0) [cnf transformation 68]
153. generous(mary) [cnf transformation 25]
157. 1 <=> funny(mary) [avatar definition]
158. funny(mary) <- (1) [avatar component clause 157]
161. 2 <=> generous(mary) [avatar definition]
162. generous(mary) <- (2) [avatar component clause 161]
247. 20 <=> brave(john) [avatar definition]
249. brave(john) <- (20) [avatar component clause 247]
252. 21 <=> brave(sK3) [avatar definition]
254. brave(sK3) <- (21) [avatar component clause 252]
256. 20 | 21 [avatar split clause 128,252,247]
262. 23 <=> ! [X0] : ~brave(X0) [avatar definition]
263. ~brave(X0) <- (23) [avatar component clause 262]
265. 24 <=> humble(mary) [avatar definition]
267. humble(mary) <- (24) [avatar component clause 265]
268. 23 | 24 [avatar split clause 134,265,262]
269. 23 | 1 [avatar split clause 133,157,262]
290. 2 [avatar split clause 153,161]
291. $false <- (21, 23) [subsumption resolution 254,263]
292. ~21 | ~23 [avatar contradiction clause 291]
301. ~generous(mary) | ~tall(mary) <- (24) [resolution 88,267]
311. ~tall(mary) <- (2, 24) [subsumption resolution 301,162]
320. tall(mary) | ~generous(mary) <- (1) [resolution 105,158]
322. ~generous(mary) <- (1, 2, 24) [subsumption resolution 320,311]
323. $false <- (1, 2, 24) [subsumption resolution 322,162]
324. ~1 | ~2 | ~24 [avatar contradiction clause 323]
335. $false <- (20, 23) [subsumption resolution 249,263]
336. ~20 | ~23 [avatar contradiction clause 335]
337. $false [avatar sat refutation 256,268,269,290,292,324,336]
% SZS output end Proof for 8822413731792452669687317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or humble is either old or not curious.
Everyone who is either tall or not strong is creative or strong.
Everyone who is generous is either patient or funny.
Everyone who is not patient or not brave is either not funny or brave.
Everyone who is either funny or not quiet is both humble and not tall and vice versa.
Everyone who is not old or kind is not quiet or brave.
Everyone who is either not old or brave is not kind.
If fred is not patient then someone is both quiet and kind and vice versa.
If someone is either not happy or not old then someone is both not calm and not quiet and vice versa.
Everyone who is generous or happy is either rich or old and vice versa.
If someone is either not tall or humble then lucy is rich and vice versa.
If someone is brave then someone is either not calm or tall.
Everyone who is creative or happy is generous or not creative and vice versa.
Everyone who is not curious or rich is both curious and not patient.
If someone is humble then someone is either not wise or not old.
Everyone who is happy is not rich.
Someone is either not old or not kind.
Someone is not calm.
Someone is rich or not wise.
Lucy is tall or happy.
Susan is either not kind or not brave.
Lucy is strong or calm.
Lucy is either not wise or happy. | Fred is rich. | contradiction | (![X]:((~generous(X)|humble(X))=>(old(X)<~>~curious(X))))&
(![X]:((tall(X)<~>~strong(X))=>(creative(X)|strong(X))))&
(![X]:(generous(X)=>(patient(X)<~>funny(X))))&
(![X]:((~patient(X)|~brave(X))=>(~funny(X)<~>brave(X))))&
(![X]:((funny(X)<~>~quiet(X))<=>(humble(X)&~tall(X))))&
(![X]:((~old(X)|kind(X))=>(~quiet(X)|brave(X))))&
(![X]:((~old(X)<~>brave(X))=>~kind(X)))&
((~patient(fred))<=>(?[X]:((quiet(X)&kind(X)))))&
((?[X]:((~happy(X)<~>~old(X))))<=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:((generous(X)|happy(X))<=>(rich(X)<~>old(X))))&
((?[X]:((~tall(X)<~>humble(X))))<=>(rich(lucy)))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:((creative(X)|happy(X))<=>(generous(X)|~creative(X))))&
(![X]:((~curious(X)|rich(X))=>(curious(X)&~patient(X))))&
((?[X]:(humble(X)))=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:(happy(X)=>~rich(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(?[X]:(~calm(X)))&
(?[X]:((rich(X)|~wise(X))))&
((tall(lucy)|happy(lucy)))&
((~kind(susan)<~>~brave(susan)))&
((strong(lucy)|calm(lucy)))&
((~wise(lucy)<~>happy(lucy))) | rich(fred) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8065755979444461169711109
% SZS output start Proof for 8065755979444461169711109
1. ! [X0] : ((humble(X0) | ~generous(X0)) => (old(X0) <~> ~curious(X0))) [input p0]
4. ! [X0] : ((~brave(X0) | ~patient(X0)) => (~funny(X0) <~> brave(X0))) [input p3]
5. ! [X0] : ((funny(X0) <~> ~quiet(X0)) <=> (~tall(X0) & humble(X0))) [input p4]
6. ! [X0] : ((kind(X0) | ~old(X0)) => (brave(X0) | ~quiet(X0))) [input p5]
7. ! [X0] : ((~old(X0) <~> brave(X0)) => ~kind(X0)) [input p6]
8. ~patient(fred) <=> ? [X0] : (kind(X0) & quiet(X0)) [input p7]
10. ! [X0] : ((happy(X0) | generous(X0)) <=> (rich(X0) <~> old(X0))) [input p9]
14. ! [X0] : ((rich(X0) | ~curious(X0)) => (~patient(X0) & curious(X0))) [input p13]
24. rich(fred) [input hypothesis]
28. ! [X0] : ((old(X0) <~> ~curious(X0)) | (~humble(X0) & generous(X0))) [ennf transformation 1]
32. ! [X0] : ((~funny(X0) <~> brave(X0)) | (brave(X0) & patient(X0))) [ennf transformation 4]
33. ! [X0] : ((brave(X0) | ~quiet(X0)) | (~kind(X0) & old(X0))) [ennf transformation 6]
34. ! [X0] : (brave(X0) | ~quiet(X0) | (~kind(X0) & old(X0))) [flattening 33]
35. ! [X0] : (~kind(X0) | (~old(X0) <=> brave(X0))) [ennf transformation 7]
37. ! [X0] : ((~patient(X0) & curious(X0)) | (~rich(X0) & curious(X0))) [ennf transformation 14]
40. ! [X0] : (((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~humble(X0) & generous(X0))) [nnf transformation 28]
43. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (brave(X0) & patient(X0))) [nnf transformation 32]
44. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (tall(X0) | ~humble(X0))) & ((~tall(X0) & humble(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [nnf transformation 5]
45. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | tall(X0) | ~humble(X0)) & ((~tall(X0) & humble(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [flattening 44]
46. ! [X0] : (~kind(X0) | ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0)))) [nnf transformation 35]
47. (~patient(fred) | ! [X0] : (~kind(X0) | ~quiet(X0))) & (? [X0] : (kind(X0) & quiet(X0)) | patient(fred)) [nnf transformation 8]
48. (~patient(fred) | ! [X0] : (~kind(X0) | ~quiet(X0))) & (? [X1] : (kind(X1) & quiet(X1)) | patient(fred)) [rectify 47]
49. ? [X1] : (kind(X1) & quiet(X1)) => (kind(sK0) & quiet(sK0)) [choice axiom]
50. (~patient(fred) | ! [X0] : (~kind(X0) | ~quiet(X0))) & ((kind(sK0) & quiet(sK0)) | patient(fred)) [skolemisation 48,49]
56. ! [X0] : (((happy(X0) | generous(X0)) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (~happy(X0) & ~generous(X0)))) [nnf transformation 10]
57. ! [X0] : ((happy(X0) | generous(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (~happy(X0) & ~generous(X0)))) [flattening 56]
81. ~curious(X0) | old(X0) | generous(X0) [cnf transformation 40]
82. ~curious(X0) | old(X0) | ~humble(X0) [cnf transformation 40]
91. ~brave(X0) | funny(X0) | patient(X0) [cnf transformation 43]
93. ~quiet(X0) | humble(X0) | ~funny(X0) [cnf transformation 45]
100. ~kind(X0) | ~quiet(X0) | brave(X0) [cnf transformation 34]
102. ~kind(X0) | ~old(X0) | ~brave(X0) [cnf transformation 46]
103. quiet(sK0) | patient(fred) [cnf transformation 50]
104. kind(sK0) | patient(fred) [cnf transformation 50]
112. ~generous(X0) | rich(X0) | old(X0) [cnf transformation 57]
128. curious(X0) | curious(X0) [cnf transformation 37]
131. ~rich(X0) | ~patient(X0) [cnf transformation 37]
145. rich(fred) [cnf transformation 24]
146. curious(X0) [duplicate literal removal 128]
155. 2 <=> patient(fred) [avatar definition]
160. 3 <=> kind(sK0) [avatar definition]
162. kind(sK0) <- (3) [avatar component clause 160]
163. 2 | 3 [avatar split clause 104,160,155]
165. 4 <=> quiet(sK0) [avatar definition]
167. quiet(sK0) <- (4) [avatar component clause 165]
168. 2 | 4 [avatar split clause 103,165,155]
303. ~patient(fred) [resolution 131,145]
319. old(X0) | generous(X0) [resolution 81,146]
321. ~humble(X0) | old(X0) [resolution 82,146]
334. humble(sK0) | ~funny(sK0) <- (4) [resolution 93,167]
358. ~quiet(sK0) | brave(sK0) <- (3) [resolution 100,162]
360. brave(sK0) <- (3, 4) [subsumption resolution 358,167]
362. funny(sK0) | patient(sK0) <- (3, 4) [resolution 360,91]
400. 38 <=> patient(sK0) [avatar definition]
402. patient(sK0) <- (38) [avatar component clause 400]
404. 39 <=> funny(sK0) [avatar definition]
407. 38 | 39 | ~3 | ~4 [avatar split clause 362,165,160,404,400]
479. 55 <=> humble(sK0) [avatar definition]
481. humble(sK0) <- (55) [avatar component clause 479]
482. ~39 | 55 | ~4 [avatar split clause 334,165,479,404]
488. ~2 [avatar split clause 303,155]
490. 57 <=> old(sK0) [avatar definition]
491. ~old(sK0) <- (~57) [avatar component clause 490]
494. 58 <=> brave(sK0) [avatar definition]
496. brave(sK0) <- (58) [avatar component clause 494]
498. ~old(sK0) | ~brave(sK0) <- (3) [resolution 162,102]
500. ~quiet(sK0) | brave(sK0) <- (3) [resolution 162,100]
501. ~old(sK0) <- (3, 58) [subsumption resolution 498,496]
502. ~57 | ~3 | ~58 [avatar split clause 501,494,160,490]
605. old(sK0) <- (55) [resolution 321,481]
609. 57 | ~55 [avatar split clause 605,479,490]
610. brave(sK0) <- (3, 4) [subsumption resolution 500,167]
611. 58 | ~3 | ~4 [avatar split clause 610,165,160,494]
616. generous(sK0) <- (~57) [resolution 491,319]
656. rich(sK0) | old(sK0) <- (~57) [resolution 616,112]
658. rich(sK0) <- (~57) [subsumption resolution 656,491]
719. ~patient(sK0) <- (~57) [resolution 658,131]
721. $false <- (38, ~57) [subsumption resolution 719,402]
722. ~38 | 57 [avatar contradiction clause 721]
723. $false [avatar sat refutation 163,168,407,482,488,502,609,611,722]
% SZS output end Proof for 8065755979444461169711109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient is either not calm or old and vice versa.
If fred is both not tall and kind then someone is funny and vice versa.
Everyone who is both not tall and kind is happy or not kind.
Everyone who is not old or not kind is both not old and not calm and vice versa.
Everyone who is not wise or not strong is both old and not patient.
If susan is happy then susan is calm or not wise and vice versa.
If lucy is either not calm or calm then someone is not curious.
Everyone who is not generous or not calm is both not creative and funny.
Everyone who is not calm or not funny is either not rich or not patient.
If someone is both not tall and strong then someone is both brave and calm.
If someone is wise or quiet then fred is not brave.
If john is either not brave or strong then john is either kind or curious and vice versa.
Everyone who is either not calm or not quiet is not kind or not patient and vice versa.
Everyone who is either old or not patient is not funny or not curious.
If mary is not brave or not curious then someone is either happy or not happy.
Everyone who is not funny is old or rich and vice versa.
Someone is either not generous or strong.
John is humble.
Fred is quiet or kind.
Someone is not brave or humble.
Someone is either wise or not patient.
Someone is either not quiet or quiet.
Someone is not tall. | Fred is calm. | entailment | (![X]:(~patient(X)<=>(~calm(X)<~>old(X))))&
(((~tall(fred)&kind(fred)))<=>(?[X]:(funny(X))))&
(![X]:((~tall(X)&kind(X))=>(happy(X)|~kind(X))))&
(![X]:((~old(X)|~kind(X))<=>(~old(X)&~calm(X))))&
(![X]:((~wise(X)|~strong(X))=>(old(X)&~patient(X))))&
((happy(susan))<=>((calm(susan)|~wise(susan))))&
(((~calm(lucy)<~>calm(lucy)))=>(?[X]:(~curious(X))))&
(![X]:((~generous(X)|~calm(X))=>(~creative(X)&funny(X))))&
(![X]:((~calm(X)|~funny(X))=>(~rich(X)<~>~patient(X))))&
((?[X]:((~tall(X)&strong(X))))=>(?[X]:((brave(X)&calm(X)))))&
((?[X]:((wise(X)|quiet(X))))=>(~brave(fred)))&
(((~brave(john)<~>strong(john)))<=>((kind(john)<~>curious(john))))&
(![X]:((~calm(X)<~>~quiet(X))<=>(~kind(X)|~patient(X))))&
(![X]:((old(X)<~>~patient(X))=>(~funny(X)|~curious(X))))&
(((~brave(mary)|~curious(mary)))=>(?[X]:((happy(X)<~>~happy(X)))))&
(![X]:(~funny(X)<=>(old(X)|rich(X))))&
(?[X]:((~generous(X)<~>strong(X))))&
(humble(john))&
((quiet(fred)|kind(fred)))&
(?[X]:((~brave(X)|humble(X))))&
(?[X]:((wise(X)<~>~patient(X))))&
(?[X]:((~quiet(X)<~>quiet(X))))&
(?[X]:(~tall(X))) | calm(fred) | [
"p0",
"p7",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5766672642454290939410040
% SZS output start Proof for 5766672642454290939410040
1. ! [X0] : (~patient(X0) <=> (~calm(X0) <~> old(X0))) [input p0]
8. ! [X0] : ((~calm(X0) | ~generous(X0)) => (funny(X0) & ~creative(X0))) [input p7]
9. ! [X0] : ((~funny(X0) | ~calm(X0)) => (~rich(X0) <~> ~patient(X0))) [input p8]
16. ! [X0] : (~funny(X0) <=> (rich(X0) | old(X0))) [input p15]
24. ~calm(fred) [input hypothesis]
28. ! [X0] : ((~calm(X0) | ~generous(X0)) => funny(X0)) [pure predicate removal 8]
33. ! [X0] : (funny(X0) | (calm(X0) & generous(X0))) [ennf transformation 28]
34. ! [X0] : ((~rich(X0) <~> ~patient(X0)) | (funny(X0) & calm(X0))) [ennf transformation 9]
40. ! [X0] : ((~patient(X0) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | patient(X0))) [nnf transformation 1]
53. ! [X0] : (((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (funny(X0) & calm(X0))) [nnf transformation 34]
64. ! [X0] : ((~funny(X0) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | funny(X0))) [nnf transformation 16]
65. ! [X0] : ((~funny(X0) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | funny(X0))) [flattening 64]
79. ~patient(X0) | old(X0) | calm(X0) [cnf transformation 40]
100. funny(X0) | calm(X0) [cnf transformation 33]
103. rich(X0) | patient(X0) | calm(X0) [cnf transformation 53]
130. ~funny(X0) | ~old(X0) [cnf transformation 65]
131. ~rich(X0) | ~funny(X0) [cnf transformation 65]
140. ~calm(fred) [cnf transformation 24]
269. ~old(X0) | calm(X0) [resolution 130,100]
293. patient(X2) | calm(X2) | ~funny(X2) [resolution 103,131]
295. calm(X2) | patient(X2) [subsumption resolution 293,100]
347. patient(fred) [resolution 295,140]
461. old(fred) | calm(fred) [resolution 347,79]
464. old(fred) [subsumption resolution 461,140]
513. calm(fred) [resolution 464,269]
515. $false [subsumption resolution 513,140]
% SZS output end Proof for 5766672642454290939410040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both curious and not happy is both not wise and quiet and vice versa. Everyone who is both creative and not humble is both funny and curious and vice versa. If alice is happy then lucy is either not old or generous. If lucy is either not happy or not generous then susan is not old or patient and vice versa. Everyone who is both brave and not patient is creative. Everyone who is both not kind and humble is either strong or not patient. Everyone who is either strong or not calm is strong. Everyone who is either not humble or calm is not curious or calm. If susan is either not quiet or not humble then susan is either not strong or not generous and vice versa. Everyone who is not kind or not old is both not funny and old and vice versa. Everyone who is not quiet is not rich and vice versa. Everyone who is not strong is not funny and vice versa. Everyone who is either generous or rich is both funny and old and vice versa. If fred is not patient or not happy then paul is either kind or humble and vice versa. If someone is either not creative or happy then someone is either kind or not brave. Everyone who is not generous or kind is kind and vice versa. Someone is either strong or tall. Fred is both not patient and calm. Someone is either not kind or not creative. Paul is both not curious and happy. Susan is either generous or not funny. Mary is both curious and quiet. Someone is humble or generous. Mary is patient or not strong. | Susan is humble. | contradiction | (![X]:((curious(X)&~happy(X))<=>(~wise(X)&quiet(X))))&
(![X]:((creative(X)&~humble(X))<=>(funny(X)&curious(X))))&
((happy(alice))=>((~old(lucy)<~>generous(lucy))))&
(((~happy(lucy)<~>~generous(lucy)))<=>((~old(susan)|patient(susan))))&
(![X]:((brave(X)&~patient(X))=>creative(X)))&
(![X]:((~kind(X)&humble(X))=>(strong(X)<~>~patient(X))))&
(![X]:((strong(X)<~>~calm(X))=>strong(X)))&
(![X]:((~humble(X)<~>calm(X))=>(~curious(X)|calm(X))))&
(((~quiet(susan)<~>~humble(susan)))<=>((~strong(susan)<~>~generous(susan))))&
(![X]:((~kind(X)|~old(X))<=>(~funny(X)&old(X))))&
(![X]:(~quiet(X)<=>~rich(X)))&
(![X]:(~strong(X)<=>~funny(X)))&
(![X]:((generous(X)<~>rich(X))<=>(funny(X)&old(X))))&
(((~patient(fred)|~happy(fred)))<=>((kind(paul)<~>humble(paul))))&
((?[X]:((~creative(X)<~>happy(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((~generous(X)|kind(X))<=>kind(X)))&
(?[X]:((strong(X)<~>tall(X))))&
((~patient(fred)&calm(fred)))&
(?[X]:((~kind(X)<~>~creative(X))))&
((~curious(paul)&happy(paul)))&
((generous(susan)<~>~funny(susan)))&
((curious(mary)&quiet(mary)))&
(?[X]:((humble(X)|generous(X))))&
((patient(mary)|~strong(mary))) | humble(susan) | [
"p8",
"p9",
"p10",
"p11",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7841862422490402893909542
% SZS output start Proof for 7841862422490402893909542
9. (~quiet(susan) <~> ~humble(susan)) <=> (~strong(susan) <~> ~generous(susan)) [input p8]
10. ! [X0] : ((~old(X0) | ~kind(X0)) <=> (old(X0) & ~funny(X0))) [input p9]
11. ! [X0] : (~quiet(X0) <=> ~rich(X0)) [input p10]
12. ! [X0] : (~strong(X0) <=> ~funny(X0)) [input p11]
13. ! [X0] : ((generous(X0) <~> rich(X0)) <=> (old(X0) & funny(X0))) [input p12]
16. ! [X0] : ((kind(X0) | ~generous(X0)) <=> kind(X0)) [input p15]
21. generous(susan) <~> ~funny(susan) [input p20]
25. humble(susan) [input hypothesis]
46. (((humble(susan) | quiet(susan)) & (~humble(susan) | ~quiet(susan))) | ((~strong(susan) | generous(susan)) & (~generous(susan) | strong(susan)))) & (((generous(susan) | strong(susan)) & (~generous(susan) | ~strong(susan))) | ((~quiet(susan) | humble(susan)) & (~humble(susan) | quiet(susan)))) [nnf transformation 9]
47. ! [X0] : (((~old(X0) | ~kind(X0)) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | (old(X0) & kind(X0)))) [nnf transformation 10]
48. ! [X0] : ((~old(X0) | ~kind(X0) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | (old(X0) & kind(X0)))) [flattening 47]
49. ! [X0] : ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0))) [nnf transformation 11]
50. ! [X0] : ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))) [nnf transformation 12]
51. ! [X0] : ((((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0))))) [nnf transformation 13]
52. ! [X0] : ((((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0))))) [flattening 51]
59. ! [X0] : (((kind(X0) | ~generous(X0)) | ~kind(X0)) & (kind(X0) | (~kind(X0) & generous(X0)))) [nnf transformation 16]
60. ! [X0] : ((kind(X0) | ~generous(X0) | ~kind(X0)) & (kind(X0) | (~kind(X0) & generous(X0)))) [flattening 59]
67. (funny(susan) | ~generous(susan)) & (~funny(susan) | generous(susan)) [nnf transformation 21]
93. ~generous(susan) | ~strong(susan) | ~humble(susan) | quiet(susan) [cnf transformation 46]
104. old(X0) | old(X0) [cnf transformation 48]
105. ~old(X0) | ~kind(X0) | ~old(X0) | funny(X0) [cnf transformation 48]
107. ~quiet(X0) | rich(X0) [cnf transformation 49]
108. ~funny(X0) | strong(X0) [cnf transformation 50]
115. ~rich(X0) | ~generous(X0) | ~old(X0) | ~funny(X0) [cnf transformation 52]
126. kind(X0) | generous(X0) [cnf transformation 60]
137. ~funny(susan) | generous(susan) [cnf transformation 67]
138. funny(susan) | ~generous(susan) [cnf transformation 67]
143. humble(susan) [cnf transformation 25]
144. old(X0) [duplicate literal removal 104]
145. ~kind(X0) | ~old(X0) | funny(X0) [duplicate literal removal 105]
181. 7 <=> generous(susan) [avatar definition]
182. ~generous(susan) <- (~7) [avatar component clause 181]
185. 8 <=> strong(susan) [avatar definition]
189. 9 <=> quiet(susan) [avatar definition]
191. quiet(susan) <- (9) [avatar component clause 189]
193. 10 <=> humble(susan) [avatar definition]
203. 9 | ~10 | ~8 | ~7 [avatar split clause 93,181,185,193,189]
204. ~rich(X0) | ~generous(X0) | ~funny(X0) [subsumption resolution 115,144]
268. 23 <=> funny(susan) [avatar definition]
269. ~funny(susan) <- (~23) [avatar component clause 268]
270. funny(susan) <- (23) [avatar component clause 268]
271. ~7 | 23 [avatar split clause 138,268,181]
272. 7 | ~23 [avatar split clause 137,268,181]
291. 10 [avatar split clause 143,193]
318. strong(susan) <- (23) [resolution 270,108]
322. 8 | ~23 [avatar split clause 318,268,185]
325. rich(susan) <- (9) [resolution 191,107]
412. ~old(X0) | funny(X0) | generous(X0) [resolution 145,126]
417. generous(X0) | funny(X0) [subsumption resolution 412,144]
447. ~generous(susan) | ~funny(susan) <- (9) [resolution 204,325]
453. ~23 | ~7 | ~9 [avatar split clause 447,189,181,268]
537. funny(susan) <- (~7) [resolution 417,182]
540. $false <- (~7, ~23) [subsumption resolution 537,269]
541. 7 | 23 [avatar contradiction clause 540]
542. $false [avatar sat refutation 203,271,272,291,322,453,541]
% SZS output end Proof for 7841862422490402893909542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is not funny and vice versa. Everyone who is creative is either curious or not wise. Everyone who is tall is both not wise and not quiet and vice versa. Everyone who is not wise or not kind is both not generous and not calm. If john is humble then lucy is humble and vice versa. Everyone who is calm is tall. If paul is brave then someone is both not rich and not funny and vice versa. Everyone who is brave or not humble is both not strong and not creative and vice versa. If someone is either happy or not quiet then someone is both humble and calm. If someone is generous then someone is creative. If lucy is either not generous or not wise then paul is either not happy or strong and vice versa. Everyone who is not humble is creative or not old and vice versa. If someone is not rich then someone is either happy or not old. Everyone who is not strong is either tall or not calm and vice versa. If fred is either old or rich then paul is either happy or not calm. If paul is strong then alice is either creative or patient and vice versa. Someone is curious. Alice is either calm or not calm. Someone is not old or not patient. Paul is not rich or not old. John is either not rich or humble. Fred is kind or generous. Alice is both not happy and not brave. Someone is both not generous and not calm. | Alice is not patient. | entailment | (![X]:(~creative(X)<=>~funny(X)))&
(![X]:(creative(X)=>(curious(X)<~>~wise(X))))&
(![X]:(tall(X)<=>(~wise(X)&~quiet(X))))&
(![X]:((~wise(X)|~kind(X))=>(~generous(X)&~calm(X))))&
((humble(john))<=>(humble(lucy)))&
(![X]:(calm(X)=>tall(X)))&
((brave(paul))<=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((brave(X)|~humble(X))<=>(~strong(X)&~creative(X))))&
((?[X]:((happy(X)<~>~quiet(X))))=>(?[X]:((humble(X)&calm(X)))))&
((?[X]:(generous(X)))=>(?[X]:(creative(X))))&
(((~generous(lucy)<~>~wise(lucy)))<=>((~happy(paul)<~>strong(paul))))&
(![X]:(~humble(X)<=>(creative(X)|~old(X))))&
((?[X]:(~rich(X)))=>(?[X]:((happy(X)<~>~old(X)))))&
(![X]:(~strong(X)<=>(tall(X)<~>~calm(X))))&
(((old(fred)<~>rich(fred)))=>((happy(paul)<~>~calm(paul))))&
((strong(paul))<=>((creative(alice)<~>patient(alice))))&
(?[X]:(curious(X)))&
((calm(alice)<~>~calm(alice)))&
(?[X]:((~old(X)|~patient(X))))&
((~rich(paul)|~old(paul)))&
((~rich(john)<~>humble(john)))&
((kind(fred)|generous(fred)))&
((~happy(alice)&~brave(alice)))&
(?[X]:((~generous(X)&~calm(X)))) | ~patient(alice) | [
"p0",
"p6",
"p7",
"p11",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 572900433239520798829802
% SZS output start Proof for 572900433239520798829802
1. ! [X0] : (~creative(X0) <=> ~funny(X0)) [input p0]
7. brave(paul) <=> ? [X0] : (~funny(X0) & ~rich(X0)) [input p6]
8. ! [X0] : ((~humble(X0) | brave(X0)) <=> (~creative(X0) & ~strong(X0))) [input p7]
12. ! [X0] : (~humble(X0) <=> (~old(X0) | creative(X0))) [input p11]
16. strong(paul) <=> (creative(alice) <~> patient(alice)) [input p15]
20. ~old(paul) | ~rich(paul) [input p19]
25. patient(alice) [input hypothesis]
38. ! [X0] : ((~creative(X0) | funny(X0)) & (~funny(X0) | creative(X0))) [nnf transformation 1]
43. (brave(paul) | ! [X0] : (funny(X0) | rich(X0))) & (? [X0] : (~funny(X0) & ~rich(X0)) | ~brave(paul)) [nnf transformation 7]
44. (brave(paul) | ! [X0] : (funny(X0) | rich(X0))) & (? [X1] : (~funny(X1) & ~rich(X1)) | ~brave(paul)) [rectify 43]
45. ? [X1] : (~funny(X1) & ~rich(X1)) => (~funny(sK0) & ~rich(sK0)) [choice axiom]
46. (brave(paul) | ! [X0] : (funny(X0) | rich(X0))) & ((~funny(sK0) & ~rich(sK0)) | ~brave(paul)) [skolemisation 44,45]
47. ! [X0] : (((~humble(X0) | brave(X0)) | (creative(X0) | strong(X0))) & ((~creative(X0) & ~strong(X0)) | (humble(X0) & ~brave(X0)))) [nnf transformation 8]
48. ! [X0] : ((~humble(X0) | brave(X0) | creative(X0) | strong(X0)) & ((~creative(X0) & ~strong(X0)) | (humble(X0) & ~brave(X0)))) [flattening 47]
57. ! [X0] : ((~humble(X0) | (old(X0) & ~creative(X0))) & ((~old(X0) | creative(X0)) | humble(X0))) [nnf transformation 12]
58. ! [X0] : ((~humble(X0) | (old(X0) & ~creative(X0))) & (~old(X0) | creative(X0) | humble(X0))) [flattening 57]
65. (strong(paul) | ((creative(alice) | ~patient(alice)) & (patient(alice) | ~creative(alice)))) & (((~patient(alice) | ~creative(alice)) & (patient(alice) | creative(alice))) | ~strong(paul)) [nnf transformation 16]
74. ~funny(X0) | creative(X0) [cnf transformation 38]
88. brave(paul) | funny(X0) | rich(X0) [cnf transformation 46]
89. ~strong(X0) | ~brave(X0) [cnf transformation 48]
90. ~strong(X0) | humble(X0) [cnf transformation 48]
92. ~creative(X0) | humble(X0) [cnf transformation 48]
108. ~humble(X0) | ~creative(X0) [cnf transformation 58]
109. ~humble(X0) | old(X0) [cnf transformation 58]
123. strong(paul) | creative(alice) | ~patient(alice) [cnf transformation 65]
128. ~old(paul) | ~rich(paul) [cnf transformation 20]
135. patient(alice) [cnf transformation 25]
147. 3 <=> ! [X0] : (funny(X0) | rich(X0)) [avatar definition]
148. rich(X0) | funny(X0) <- (3) [avatar component clause 147]
150. 4 <=> brave(paul) [avatar definition]
153. 3 | 4 [avatar split clause 88,150,147]
192. 13 <=> strong(paul) [avatar definition]
193. strong(paul) <- (13) [avatar component clause 192]
216. ~creative(X0) [subsumption resolution 108,92]
249. strong(paul) | ~patient(alice) [subsumption resolution 123,216]
251. 23 <=> patient(alice) [avatar definition]
254. ~23 | 13 [avatar split clause 249,192,251]
267. 26 <=> rich(paul) [avatar definition]
269. ~rich(paul) <- (~26) [avatar component clause 267]
271. 27 <=> old(paul) [avatar definition]
274. ~26 | ~27 [avatar split clause 128,271,267]
281. 23 [avatar split clause 135,251]
282. ~brave(paul) <- (13) [resolution 89,193]
283. humble(paul) <- (13) [resolution 90,193]
284. old(paul) <- (13) [resolution 109,283]
287. 27 | ~13 [avatar split clause 284,192,271]
293. ~4 | ~13 [avatar split clause 282,192,150]
296. funny(paul) <- (3, ~26) [resolution 148,269]
307. creative(paul) <- (3, ~26) [resolution 296,74]
308. $false <- (3, ~26) [subsumption resolution 307,216]
309. ~3 | 26 [avatar contradiction clause 308]
310. $false [avatar sat refutation 153,254,274,281,287,293,309]
% SZS output end Proof for 572900433239520798829802
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or quiet is either rich or not calm and vice versa.
If someone is brave or curious then someone is either not quiet or not creative and vice versa.
Everyone who is humble is either tall or happy.
If john is either not strong or not brave then someone is both brave and curious and vice versa.
If someone is either not wise or brave then someone is both not patient and brave and vice versa.
Everyone who is not generous or not happy is not old or old.
Everyone who is not funny or not calm is funny.
Everyone who is old is old or not creative.
If someone is curious or not wise then someone is either not rich or not generous and vice versa.
Everyone who is both not creative and not humble is both wise and old.
Everyone who is not funny or not calm is both not brave and brave and vice versa.
If someone is either not creative or not wise then john is brave.
Everyone who is rich is either wise or not generous.
Everyone who is both not old and old is either quiet or patient.
If someone is curious then lucy is both curious and not tall.
Everyone who is both calm and not calm is not old or creative and vice versa.
John is quiet.
Susan is old or generous.
Someone is tall or quiet.
Someone is not quiet or brave.
John is not generous.
Someone is not generous or wise.
John is either not old or not kind.
Mary is both not patient and not quiet. | Susan is funny. | entailment | (![X]:((wise(X)<~>quiet(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((brave(X)|curious(X))))<=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(![X]:(humble(X)=>(tall(X)<~>happy(X))))&
(((~strong(john)<~>~brave(john)))<=>(?[X]:((brave(X)&curious(X)))))&
((?[X]:((~wise(X)<~>brave(X))))<=>(?[X]:((~patient(X)&brave(X)))))&
(![X]:((~generous(X)|~happy(X))=>(~old(X)|old(X))))&
(![X]:((~funny(X)|~calm(X))=>funny(X)))&
(![X]:(old(X)=>(old(X)|~creative(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((~creative(X)&~humble(X))=>(wise(X)&old(X))))&
(![X]:((~funny(X)|~calm(X))<=>(~brave(X)&brave(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>(brave(john)))&
(![X]:(rich(X)=>(wise(X)<~>~generous(X))))&
(![X]:((~old(X)&old(X))=>(quiet(X)<~>patient(X))))&
((?[X]:(curious(X)))=>((curious(lucy)&~tall(lucy))))&
(![X]:((calm(X)&~calm(X))<=>(~old(X)|creative(X))))&
(quiet(john))&
((old(susan)|generous(susan)))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:((~quiet(X)|brave(X))))&
(~generous(john))&
(?[X]:((~generous(X)|wise(X))))&
((~old(john)<~>~kind(john)))&
((~patient(mary)&~quiet(mary))) | funny(susan) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8758745192332638621632943
% SZS output start Proof for 8758745192332638621632943
7. ! [X0] : ((~calm(X0) | ~funny(X0)) => funny(X0)) [input p6]
25. ~funny(susan) [input hypothesis]
32. ! [X0] : (funny(X0) | (calm(X0) & funny(X0))) [ennf transformation 7]
107. funny(X0) | funny(X0) [cnf transformation 32]
146. ~funny(susan) [cnf transformation 25]
147. funny(X0) [duplicate literal removal 107]
318. $false [subsumption resolution 146,147]
% SZS output end Proof for 8758745192332638621632943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not quiet is both not generous and humble and vice versa. If mary is rich then lucy is not old. Everyone who is not happy or creative is either calm or old. Everyone who is creative or not creative is both not brave and not calm. If someone is either not quiet or tall then someone is either humble or not kind and vice versa. If someone is brave or funny then fred is either brave or not funny. If someone is happy or humble then paul is tall and vice versa. Everyone who is calm or not generous is creative and vice versa. If someone is either not patient or funny then someone is kind. If susan is not old or strong then lucy is not curious or rich and vice versa. If someone is either wise or not humble then someone is not funny or not patient. If someone is both brave and not creative then fred is wise and vice versa. Everyone who is not funny or not quiet is either funny or not generous. Everyone who is both not happy and funny is quiet or rich and vice versa. If alice is generous then someone is either quiet or not happy. Someone is both not patient and wise. Alice is creative. Susan is funny or curious. Someone is both not patient and not rich. Lucy is not happy. Alice is either not wise or wise. | Lucy is not generous. | entailment | (![X]:((quiet(X)|~quiet(X))<=>(~generous(X)&humble(X))))&
((rich(mary))=>(~old(lucy)))&
(![X]:((~happy(X)|creative(X))=>(calm(X)<~>old(X))))&
(![X]:((creative(X)|~creative(X))=>(~brave(X)&~calm(X))))&
((?[X]:((~quiet(X)<~>tall(X))))<=>(?[X]:((humble(X)<~>~kind(X)))))&
((?[X]:((brave(X)|funny(X))))=>((brave(fred)<~>~funny(fred))))&
((?[X]:((happy(X)|humble(X))))<=>(tall(paul)))&
(![X]:((calm(X)|~generous(X))<=>creative(X)))&
((?[X]:((~patient(X)<~>funny(X))))=>(?[X]:(kind(X))))&
(((~old(susan)|strong(susan)))<=>((~curious(lucy)|rich(lucy))))&
((?[X]:((wise(X)<~>~humble(X))))=>(?[X]:((~funny(X)|~patient(X)))))&
((?[X]:((brave(X)&~creative(X))))<=>(wise(fred)))&
(![X]:((~funny(X)|~quiet(X))=>(funny(X)<~>~generous(X))))&
(![X]:((~happy(X)&funny(X))<=>(quiet(X)|rich(X))))&
((generous(alice))=>(?[X]:((quiet(X)<~>~happy(X)))))&
(?[X]:((~patient(X)&wise(X))))&
(creative(alice))&
((funny(susan)|curious(susan)))&
(?[X]:((~patient(X)&~rich(X))))&
(~happy(lucy))&
((~wise(alice)<~>wise(alice))) | ~generous(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 701316208887936943424382
% SZS output start Proof for 701316208887936943424382
1. ! [X0] : ((~quiet(X0) | quiet(X0)) <=> (humble(X0) & ~generous(X0))) [input p0]
22. generous(lucy) [input hypothesis]
34. ! [X0] : (((~quiet(X0) | quiet(X0)) | (~humble(X0) | generous(X0))) & ((humble(X0) & ~generous(X0)) | (quiet(X0) & ~quiet(X0)))) [nnf transformation 1]
35. ! [X0] : ((~quiet(X0) | quiet(X0) | ~humble(X0) | generous(X0)) & ((humble(X0) & ~generous(X0)) | (quiet(X0) & ~quiet(X0)))) [flattening 34]
74. ~generous(X0) | ~quiet(X0) [cnf transformation 35]
75. ~generous(X0) | quiet(X0) [cnf transformation 35]
137. generous(lucy) [cnf transformation 22]
140. ~generous(X0) [subsumption resolution 74,75]
248. $false [subsumption resolution 137,140]
% SZS output end Proof for 701316208887936943424382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and not wise is not tall or not strong and vice versa.
If paul is not wise or tall then fred is not strong.
Everyone who is rich or not strong is not brave or not kind and vice versa.
Everyone who is not kind or patient is both not brave and not tall.
Everyone who is creative is rich and vice versa.
If alice is rich then mary is both patient and not happy and vice versa.
Everyone who is not kind is funny or creative.
If susan is not happy then someone is both not happy and not kind.
Everyone who is not generous or not calm is either funny or patient and vice versa.
Everyone who is both quiet and not tall is both generous and not wise and vice versa.
Everyone who is not curious or not generous is generous.
Everyone who is either creative or not happy is old or happy.
Everyone who is both not curious and not funny is not patient or happy and vice versa.
Everyone who is either not old or not funny is both kind and not strong and vice versa.
Everyone who is quiet is generous and vice versa.
If fred is either creative or not wise then someone is both brave and not patient.
Susan is not humble.
Someone is humble or brave.
Someone is wise.
Someone is either not rich or rich.
Paul is both strong and not kind.
Someone is not brave or calm. | Paul is creative. | entailment | (![X]:((~patient(X)&~wise(X))<=>(~tall(X)|~strong(X))))&
(((~wise(paul)|tall(paul)))=>(~strong(fred)))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(![X]:(quiet(X)<=>generous(X)))&
(((creative(fred)<~>~wise(fred)))=>(?[X]:((brave(X)&~patient(X)))))&
(~humble(susan))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:(wise(X)))&
(?[X]:((~rich(X)<~>rich(X))))&
((strong(paul)&~kind(paul)))&
(?[X]:((~brave(X)|calm(X)))) | creative(paul) | [
"p2",
"p3",
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7730342922994834018732334
% SZS output start Proof for 7730342922994834018732334
3. ! [X0] : ((~strong(X0) | rich(X0)) <=> (~kind(X0) | ~brave(X0))) [input p2]
4. ! [X0] : ((patient(X0) | ~kind(X0)) => (~tall(X0) & ~brave(X0))) [input p3]
5. ! [X0] : (creative(X0) <=> rich(X0)) [input p4]
21. ~kind(paul) & strong(paul) [input p20]
23. ~creative(paul) [input hypothesis]
25. ! [X0] : ((~tall(X0) & ~brave(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 4]
35. ! [X0] : (((~strong(X0) | rich(X0)) | (kind(X0) & brave(X0))) & ((~kind(X0) | ~brave(X0)) | (strong(X0) & ~rich(X0)))) [nnf transformation 3]
36. ! [X0] : ((~strong(X0) | rich(X0) | (kind(X0) & brave(X0))) & (~kind(X0) | ~brave(X0) | (strong(X0) & ~rich(X0)))) [flattening 35]
37. ! [X0] : ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))) [nnf transformation 5]
73. ~strong(X0) | rich(X0) | brave(X0) [cnf transformation 36]
75. ~brave(X0) | kind(X0) [cnf transformation 25]
80. ~rich(X0) | creative(X0) [cnf transformation 37]
123. strong(paul) [cnf transformation 21]
124. ~kind(paul) [cnf transformation 21]
126. ~creative(paul) [cnf transformation 23]
230. rich(paul) | brave(paul) [resolution 73,123]
233. 18 <=> brave(paul) [avatar definition]
235. brave(paul) <- (18) [avatar component clause 233]
237. 19 <=> rich(paul) [avatar definition]
239. rich(paul) <- (19) [avatar component clause 237]
240. 18 | 19 [avatar split clause 230,237,233]
244. kind(paul) <- (18) [resolution 235,75]
245. $false <- (18) [subsumption resolution 244,124]
246. ~18 [avatar contradiction clause 245]
251. creative(paul) <- (19) [resolution 239,80]
252. $false <- (19) [subsumption resolution 251,126]
253. ~19 [avatar contradiction clause 252]
254. $false [avatar sat refutation 240,246,253]
% SZS output end Proof for 7730342922994834018732334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or patient is both not wise and happy and vice versa.
If mary is both creative and not patient then someone is either creative or not patient and vice versa.
If mary is not calm then susan is kind and vice versa.
Everyone who is not kind or not calm is both brave and not old.
If someone is either brave or strong then someone is brave.
If susan is either rich or old then someone is both happy and patient.
If someone is both not calm and tall then someone is not patient.
If someone is both calm and tall then someone is both not curious and humble.
Everyone who is not generous or humble is either humble or not wise and vice versa.
If john is not brave then someone is not old.
Everyone who is both strong and kind is not strong and vice versa.
Everyone who is generous or not kind is curious.
If someone is either not patient or kind then someone is wise or not happy.
If someone is both not happy and strong then someone is generous or not patient.
Everyone who is not patient is both wise and not patient.
Someone is either quiet or wise.
Lucy is both not funny and not wise.
Someone is either not brave or not tall.
Someone is quiet. | Lucy is strong. | entailment | (![X]:((~patient(X)<~>patient(X))<=>(~wise(X)&happy(X))))&
(((creative(mary)&~patient(mary)))<=>(?[X]:((creative(X)<~>~patient(X)))))&
((~calm(mary))<=>(kind(susan)))&
(![X]:((~kind(X)|~calm(X))=>(brave(X)&~old(X))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:(brave(X))))&
(((rich(susan)<~>old(susan)))=>(?[X]:((happy(X)&patient(X)))))&
((?[X]:((~calm(X)&tall(X))))=>(?[X]:(~patient(X))))&
((?[X]:((calm(X)&tall(X))))=>(?[X]:((~curious(X)&humble(X)))))&
(![X]:((~generous(X)|humble(X))<=>(humble(X)<~>~wise(X))))&
((~brave(john))=>(?[X]:(~old(X))))&
(![X]:((strong(X)&kind(X))<=>~strong(X)))&
(![X]:((generous(X)|~kind(X))=>curious(X)))&
((?[X]:((~patient(X)<~>kind(X))))=>(?[X]:((wise(X)|~happy(X)))))&
((?[X]:((~happy(X)&strong(X))))=>(?[X]:((generous(X)|~patient(X)))))&
(![X]:(~patient(X)=>(wise(X)&~patient(X))))&
(?[X]:((quiet(X)<~>wise(X))))&
((~funny(lucy)&~wise(lucy)))&
(?[X]:((~brave(X)<~>~tall(X))))&
(?[X]:(quiet(X))) | strong(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1878656194333667393380615
% SZS output start Proof for 1878656194333667393380615
11. ! [X0] : ((kind(X0) & strong(X0)) <=> ~strong(X0)) [input p10]
20. ~strong(lucy) [input hypothesis]
62. ! [X0] : (((kind(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) | ~strong(X0)))) [nnf transformation 11]
63. ! [X0] : (((kind(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | ~kind(X0) | ~strong(X0))) [flattening 62]
114. strong(X0) | strong(X0) [cnf transformation 63]
129. ~strong(lucy) [cnf transformation 20]
131. strong(X0) [duplicate literal removal 114]
252. $false [subsumption resolution 129,131]
% SZS output end Proof for 1878656194333667393380615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not brave is both not kind and funny and vice versa. Everyone who is either brave or old is curious or calm and vice versa. Everyone who is either not tall or generous is either not funny or calm. If someone is both not rich and not kind then someone is rich. Everyone who is not curious or patient is wise or not patient. If someone is either patient or not brave then john is both generous and kind. If susan is both not kind and funny then someone is either tall or not patient and vice versa. If someone is both not quiet and not calm then someone is both humble and tall. If someone is either not calm or tall then someone is either brave or quiet and vice versa. Everyone who is either old or not funny is both not generous and funny and vice versa. Everyone who is either curious or funny is not wise or old and vice versa. If someone is either curious or funny then someone is either kind or not rich and vice versa. Everyone who is not wise is either not brave or not patient and vice versa. Everyone who is both not rich and humble is both humble and not funny and vice versa. If someone is both not creative and not generous then someone is both not funny and wise and vice versa. If someone is either not generous or tall then someone is both not creative and not rich. Someone is old. Someone is not funny. Someone is both not brave and funny. Someone is curious or not funny. Mary is both creative and curious. Someone is not kind. Someone is not quiet or wise. Someone is happy or not brave. | John is generous. | entailment | (![X]:((creative(X)&~brave(X))<=>(~kind(X)&funny(X))))&
(![X]:((brave(X)<~>old(X))<=>(curious(X)|calm(X))))&
(![X]:((~tall(X)<~>generous(X))=>(~funny(X)<~>calm(X))))&
((?[X]:((~rich(X)&~kind(X))))=>(?[X]:(rich(X))))&
(![X]:((~curious(X)|patient(X))=>(wise(X)|~patient(X))))&
((?[X]:((patient(X)<~>~brave(X))))=>((generous(john)&kind(john))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:((tall(X)<~>~patient(X)))))&
((?[X]:((~quiet(X)&~calm(X))))=>(?[X]:((humble(X)&tall(X)))))&
((?[X]:((~calm(X)<~>tall(X))))<=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((old(X)<~>~funny(X))<=>(~generous(X)&funny(X))))&
(![X]:((curious(X)<~>funny(X))<=>(~wise(X)|old(X))))&
((?[X]:((curious(X)<~>funny(X))))<=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:(~wise(X)<=>(~brave(X)<~>~patient(X))))&
(![X]:((~rich(X)&humble(X))<=>(humble(X)&~funny(X))))&
((?[X]:((~creative(X)&~generous(X))))<=>(?[X]:((~funny(X)&wise(X)))))&
((?[X]:((~generous(X)<~>tall(X))))=>(?[X]:((~creative(X)&~rich(X)))))&
(?[X]:(old(X)))&
(?[X]:(~funny(X)))&
(?[X]:((~brave(X)&funny(X))))&
(?[X]:((curious(X)|~funny(X))))&
((creative(mary)&curious(mary)))&
(?[X]:(~kind(X)))&
(?[X]:((~quiet(X)|wise(X))))&
(?[X]:((happy(X)|~brave(X)))) | generous(john) | [
"p4",
"p5",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1891833519509927139604405
% SZS output start Proof for 1891833519509927139604405
5. ! [X0] : ((patient(X0) | ~curious(X0)) => (~patient(X0) | wise(X0))) [input p4]
6. ? [X0] : (patient(X0) <~> ~brave(X0)) => (kind(john) & generous(john)) [input p5]
13. ! [X0] : (~wise(X0) <=> (~brave(X0) <~> ~patient(X0))) [input p12]
19. ? [X0] : (funny(X0) & ~brave(X0)) [input p18]
25. ~generous(john) [input hypothesis]
35. ! [X0] : ((~patient(X0) | wise(X0)) | (~patient(X0) & curious(X0))) [ennf transformation 5]
36. ! [X0] : (~patient(X0) | wise(X0) | (~patient(X0) & curious(X0))) [flattening 35]
37. (kind(john) & generous(john)) | ! [X0] : (patient(X0) <=> ~brave(X0)) [ennf transformation 6]
48. (kind(john) & generous(john)) | ! [X0] : ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))) [nnf transformation 37]
71. ! [X0] : ((~wise(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) & (((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | wise(X0))) [nnf transformation 13]
87. ? [X0] : (funny(X0) & ~brave(X0)) => (funny(sK12) & ~brave(sK12)) [choice axiom]
88. funny(sK12) & ~brave(sK12) [skolemisation 19,87]
111. ~patient(X0) | wise(X0) | ~patient(X0) [cnf transformation 36]
112. generous(john) | ~brave(X0) | ~patient(X0) [cnf transformation 48]
113. generous(john) | patient(X0) | brave(X0) [cnf transformation 48]
154. ~wise(X0) | ~patient(X0) | brave(X0) [cnf transformation 71]
170. ~brave(sK12) [cnf transformation 88]
177. ~generous(john) [cnf transformation 25]
180. ~patient(X0) | wise(X0) [duplicate literal removal 111]
190. 3 <=> ! [X0] : (patient(X0) | brave(X0)) [avatar definition]
191. patient(X0) | brave(X0) <- (3) [avatar component clause 190]
198. 5 <=> ! [X0] : (~brave(X0) | ~patient(X0)) [avatar definition]
199. ~brave(X0) | ~patient(X0) <- (5) [avatar component clause 198]
202. 6 <=> generous(john) [avatar definition]
205. 3 | 6 [avatar split clause 113,202,190]
206. 5 | 6 [avatar split clause 112,202,198]
321. ~patient(X0) | brave(X0) [subsumption resolution 154,180]
377. ~6 [avatar split clause 177,202]
378. ~patient(X0) <- (5) [subsumption resolution 199,321]
379. brave(X0) <- (3, 5) [subsumption resolution 191,378]
380. $false <- (3, 5) [resolution 379,170]
381. ~3 | ~5 [avatar contradiction clause 380]
382. $false [avatar sat refutation 205,206,377,381]
% SZS output end Proof for 1891833519509927139604405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and tall is both not kind and quiet and vice versa.
If someone is not rich then someone is not old or happy.
Everyone who is either not funny or not tall is both wise and humble.
Everyone who is either not strong or brave is either generous or not funny.
If someone is either not patient or happy then mary is either tall or not curious and vice versa.
If someone is curious then someone is both not wise and old.
If mary is both not happy and not calm then someone is curious or creative.
If paul is both generous and not funny then someone is either not generous or rich and vice versa.
If paul is either rich or not tall then mary is not brave or brave.
If john is both not curious and happy then lucy is not tall or humble.
Everyone who is either not rich or not strong is brave or funny and vice versa.
If someone is both quiet and not funny then alice is old or calm and vice versa.
Everyone who is both not calm and curious is either humble or not humble and vice versa.
If someone is both tall and kind then john is not strong or not old.
If someone is both generous and not quiet then paul is not generous or creative and vice versa.
Lucy is either happy or not strong.
Lucy is both not old and not kind.
Alice is not creative or not rich.
Someone is happy or not old.
Mary is either brave or funny.
Someone is not rich or old.
Someone is either kind or not tall.
Someone is not old. | Lucy is calm. | contradiction | (![X]:((~rich(X)&tall(X))<=>(~kind(X)&quiet(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~old(X)|happy(X)))))&
(![X]:((~funny(X)<~>~tall(X))=>(wise(X)&humble(X))))&
(![X]:((~strong(X)<~>brave(X))=>(generous(X)<~>~funny(X))))&
((?[X]:((~patient(X)<~>happy(X))))<=>((tall(mary)<~>~curious(mary))))&
((?[X]:(curious(X)))=>(?[X]:((~wise(X)&old(X)))))&
(((~happy(mary)&~calm(mary)))=>(?[X]:((curious(X)|creative(X)))))&
(((generous(paul)&~funny(paul)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((rich(paul)<~>~tall(paul)))=>((~brave(mary)|brave(mary))))&
(((~curious(john)&happy(john)))=>((~tall(lucy)|humble(lucy))))&
(![X]:((~rich(X)<~>~strong(X))<=>(brave(X)|funny(X))))&
((?[X]:((quiet(X)&~funny(X))))<=>((old(alice)|calm(alice))))&
(![X]:((~calm(X)&curious(X))<=>(humble(X)<~>~humble(X))))&
((?[X]:((tall(X)&kind(X))))=>((~strong(john)|~old(john))))&
((?[X]:((generous(X)&~quiet(X))))<=>((~generous(paul)|creative(paul))))&
((happy(lucy)<~>~strong(lucy)))&
((~old(lucy)&~kind(lucy)))&
((~creative(alice)|~rich(alice)))&
(?[X]:((happy(X)|~old(X))))&
((brave(mary)<~>funny(mary)))&
(?[X]:((~rich(X)|old(X))))&
(?[X]:((kind(X)<~>~tall(X))))&
(?[X]:(~old(X))) | calm(lucy) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5249967185517230851294712
% SZS output start Proof for 5249967185517230851294712
13. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (humble(X0) <~> ~humble(X0))) [input p12]
24. calm(lucy) [input hypothesis]
68. ! [X0] : (((curious(X0) & ~calm(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) & (((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | (~curious(X0) | calm(X0)))) [nnf transformation 13]
69. ! [X0] : (((curious(X0) & ~calm(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) & (((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | ~curious(X0) | calm(X0))) [flattening 68]
132. ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 69]
133. ~calm(X0) | humble(X0) | humble(X0) [cnf transformation 69]
154. calm(lucy) [cnf transformation 24]
155. ~calm(X0) | ~humble(X0) [duplicate literal removal 132]
156. ~calm(X0) | humble(X0) [duplicate literal removal 133]
301. ~calm(X0) [subsumption resolution 155,156]
391. $false [subsumption resolution 154,301]
% SZS output end Proof for 5249967185517230851294712
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not curious is kind and vice versa.
If someone is not brave or calm then someone is not brave or kind and vice versa.
Everyone who is either not calm or not kind is calm and vice versa.
If someone is happy or not calm then john is either not generous or old and vice versa.
Everyone who is not funny is not tall.
If someone is both kind and not tall then someone is not curious or generous and vice versa.
Everyone who is not strong is happy and vice versa.
If someone is either not patient or not strong then lucy is either not rich or not wise and vice versa.
Everyone who is happy is quiet or happy and vice versa.
Everyone who is either not creative or rich is both not strong and quiet.
If lucy is either not curious or happy then susan is not patient or not brave.
If someone is not quiet or not happy then susan is humble or rich and vice versa.
Everyone who is either not strong or happy is brave.
Everyone who is either not wise or generous is either not curious or not old and vice versa.
If susan is either wise or quiet then lucy is not quiet and vice versa.
If someone is both happy and not patient then someone is either not happy or not quiet.
Someone is both not quiet and rich.
Someone is either patient or old.
Lucy is both not wise and quiet.
Someone is happy or strong.
Susan is patient or not happy.
Someone is either wise or not curious.
Mary is either not quiet or not kind.
Someone is both not calm and not quiet. | John is curious. | entailment | (![X]:((brave(X)&~curious(X))<=>kind(X)))&
((?[X]:((~brave(X)|calm(X))))<=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((~calm(X)<~>~kind(X))<=>calm(X)))&
((?[X]:((happy(X)|~calm(X))))<=>((~generous(john)<~>old(john))))&
(![X]:(~funny(X)=>~tall(X)))&
((?[X]:((kind(X)&~tall(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:(~strong(X)<=>happy(X)))&
((?[X]:((~patient(X)<~>~strong(X))))<=>((~rich(lucy)<~>~wise(lucy))))&
(![X]:(happy(X)<=>(quiet(X)|happy(X))))&
(![X]:((~creative(X)<~>rich(X))=>(~strong(X)&quiet(X))))&
(((~curious(lucy)<~>happy(lucy)))=>((~patient(susan)|~brave(susan))))&
((?[X]:((~quiet(X)|~happy(X))))<=>((humble(susan)|rich(susan))))&
(![X]:((~strong(X)<~>happy(X))=>brave(X)))&
(![X]:((~wise(X)<~>generous(X))<=>(~curious(X)<~>~old(X))))&
(((wise(susan)<~>quiet(susan)))<=>(~quiet(lucy)))&
((?[X]:((happy(X)&~patient(X))))=>(?[X]:((~happy(X)<~>~quiet(X)))))&
(?[X]:((~quiet(X)&rich(X))))&
(?[X]:((patient(X)<~>old(X))))&
((~wise(lucy)&quiet(lucy)))&
(?[X]:((happy(X)|strong(X))))&
((patient(susan)|~happy(susan)))&
(?[X]:((wise(X)<~>~curious(X))))&
((~quiet(mary)<~>~kind(mary)))&
(?[X]:((~calm(X)&~quiet(X)))) | curious(john) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5498864719255919891340557
% SZS output start Proof for 5498864719255919891340557
3. ! [X0] : ((~calm(X0) <~> ~kind(X0)) <=> calm(X0)) [input p2]
6. ? [X0] : (~tall(X0) & kind(X0)) <=> ? [X0] : (generous(X0) | ~curious(X0)) [input p5]
25. ~curious(john) [input hypothesis]
27. ? [X0] : (~tall(X0) & kind(X0)) <=> ? [X1] : (generous(X1) | ~curious(X1)) [rectify 6]
42. ! [X0] : ((((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | ~calm(X0)) & (calm(X0) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0))))) [nnf transformation 3]
47. (? [X0] : (~tall(X0) & kind(X0)) | ! [X1] : (~generous(X1) & curious(X1))) & (? [X1] : (generous(X1) | ~curious(X1)) | ! [X0] : (tall(X0) | ~kind(X0))) [nnf transformation 27]
48. (? [X0] : (~tall(X0) & kind(X0)) | ! [X1] : (~generous(X1) & curious(X1))) & (? [X2] : (generous(X2) | ~curious(X2)) | ! [X3] : (tall(X3) | ~kind(X3))) [rectify 47]
49. ? [X0] : (~tall(X0) & kind(X0)) => (~tall(sK3) & kind(sK3)) [choice axiom]
50. ? [X2] : (generous(X2) | ~curious(X2)) => (generous(sK4) | ~curious(sK4)) [choice axiom]
51. ((~tall(sK3) & kind(sK3)) | ! [X1] : (~generous(X1) & curious(X1))) & ((generous(sK4) | ~curious(sK4)) | ! [X3] : (tall(X3) | ~kind(X3))) [skolemisation 48,50,49]
93. calm(X0) | ~kind(X0) | calm(X0) [cnf transformation 42]
95. ~kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 42]
104. kind(sK3) | curious(X1) [cnf transformation 51]
161. ~curious(john) [cnf transformation 25]
162. calm(X0) | ~kind(X0) [duplicate literal removal 93]
163. ~kind(X0) | ~calm(X0) [duplicate literal removal 95]
165. 1 <=> ! [X1] : ~kind(X1) [avatar definition]
166. ~kind(X1) <- (1) [avatar component clause 165]
193. ~kind(X0) [subsumption resolution 162,163]
194. 1 [avatar split clause 193,165]
232. 16 <=> ! [X1] : curious(X1) [avatar definition]
233. curious(X1) <- (16) [avatar component clause 232]
236. 17 <=> kind(sK3) [avatar definition]
238. kind(sK3) <- (17) [avatar component clause 236]
240. 16 | 17 [avatar split clause 104,236,232]
393. $false <- (16) [resolution 233,161]
394. ~16 [avatar contradiction clause 393]
395. $false <- (1, 17) [subsumption resolution 238,166]
396. ~1 | ~17 [avatar contradiction clause 395]
397. $false [avatar sat refutation 194,240,394,396]
% SZS output end Proof for 5498864719255919891340557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or creative is either wise or creative and vice versa.
Everyone who is both not patient and not calm is not kind.
Everyone who is brave is not patient or generous and vice versa.
If john is not funny then someone is either not brave or not happy.
Everyone who is not kind or calm is not curious or humble.
Everyone who is not patient is not tall or not kind and vice versa.
If someone is both not patient and kind then someone is both not curious and funny and vice versa.
Everyone who is either generous or old is both not rich and not wise.
If someone is curious then someone is not curious or not rich.
Everyone who is rich is old and vice versa.
Everyone who is either happy or not happy is not curious or not wise and vice versa.
If alice is old or calm then lucy is both not wise and not strong and vice versa.
Everyone who is both not brave and wise is either not curious or not creative and vice versa.
If someone is both funny and not creative then someone is either curious or not tall.
Everyone who is not rich is both funny and not creative and vice versa.
John is tall or quiet.
Someone is both not kind and rich.
Someone is calm.
Mary is strong.
Paul is either not humble or generous.
Susan is tall or patient.
Someone is happy.
Someone is old or not creative. | Lucy is not strong. | neutral | (![X]:((~rich(X)<~>creative(X))<=>(wise(X)<~>creative(X))))&
(![X]:((~patient(X)&~calm(X))=>~kind(X)))&
(![X]:(brave(X)<=>(~patient(X)|generous(X))))&
((~funny(john))=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:((~kind(X)|calm(X))=>(~curious(X)|humble(X))))&
(![X]:(~patient(X)<=>(~tall(X)|~kind(X))))&
((?[X]:((~patient(X)&kind(X))))<=>(?[X]:((~curious(X)&funny(X)))))&
(![X]:((generous(X)<~>old(X))=>(~rich(X)&~wise(X))))&
((?[X]:(curious(X)))=>(?[X]:((~curious(X)|~rich(X)))))&
(![X]:(rich(X)<=>old(X)))&
(![X]:((happy(X)<~>~happy(X))<=>(~curious(X)|~wise(X))))&
(((old(alice)|calm(alice)))<=>((~wise(lucy)&~strong(lucy))))&
(![X]:((~brave(X)&wise(X))<=>(~curious(X)<~>~creative(X))))&
((?[X]:((funny(X)&~creative(X))))=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:(~rich(X)<=>(funny(X)&~creative(X))))&
((tall(john)|quiet(john)))&
(?[X]:((~kind(X)&rich(X))))&
(?[X]:(calm(X)))&
(strong(mary))&
((~humble(paul)<~>generous(paul)))&
((tall(susan)|patient(susan)))&
(?[X]:(happy(X)))&
(?[X]:((old(X)|~creative(X)))) | ~strong(lucy) | [] | null | 0 |
Everyone who is not tall is rich.
If john is funny or not strong then someone is not old or patient.
If paul is not wise then alice is both not curious and not calm and vice versa.
Everyone who is not humble is both not calm and brave.
If paul is either patient or not humble then fred is wise or strong.
Everyone who is funny or not wise is rich and vice versa.
Everyone who is either kind or not kind is either not rich or not tall.
Everyone who is tall is both not patient and not wise and vice versa.
Everyone who is either brave or humble is strong or generous.
If paul is not happy then john is both brave and quiet and vice versa.
Everyone who is both not patient and not quiet is both humble and not brave.
Everyone who is not patient or not funny is either not wise or not patient and vice versa.
Everyone who is either not kind or tall is not generous.
Everyone who is not quiet is either rich or not old and vice versa.
Everyone who is both funny and calm is not wise or humble and vice versa.
Mary is not happy or patient.
Susan is both not generous and brave.
Alice is kind.
Fred is both patient and kind.
Fred is either humble or creative.
John is either calm or not tall.
Fred is either strong or not patient. | Susan is not humble. | neutral | (![X]:(~tall(X)=>rich(X)))&
(((funny(john)|~strong(john)))=>(?[X]:((~old(X)|patient(X)))))&
((~wise(paul))<=>((~curious(alice)&~calm(alice))))&
(![X]:(~humble(X)=>(~calm(X)&brave(X))))&
(((patient(paul)<~>~humble(paul)))=>((wise(fred)|strong(fred))))&
(![X]:((funny(X)|~wise(X))<=>rich(X)))&
(![X]:((kind(X)<~>~kind(X))=>(~rich(X)<~>~tall(X))))&
(![X]:(tall(X)<=>(~patient(X)&~wise(X))))&
(![X]:((brave(X)<~>humble(X))=>(strong(X)|generous(X))))&
((~happy(paul))<=>((brave(john)&quiet(john))))&
(![X]:((~patient(X)&~quiet(X))=>(humble(X)&~brave(X))))&
(![X]:((~patient(X)|~funny(X))<=>(~wise(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>tall(X))=>~generous(X)))&
(![X]:(~quiet(X)<=>(rich(X)<~>~old(X))))&
(![X]:((funny(X)&calm(X))<=>(~wise(X)|humble(X))))&
((~happy(mary)|patient(mary)))&
((~generous(susan)&brave(susan)))&
(kind(alice))&
((patient(fred)&kind(fred)))&
((humble(fred)<~>creative(fred)))&
((calm(john)<~>~tall(john)))&
((strong(fred)<~>~patient(fred))) | ~humble(susan) | [] | null | 0 |
Everyone who is both not calm and brave is both not rich and not brave and vice versa.
If lucy is not quiet or rich then alice is not rich or not funny.
Everyone who is either not kind or not humble is not brave or creative and vice versa.
If susan is both not wise and calm then someone is either generous or humble and vice versa.
Everyone who is not calm is creative.
Everyone who is brave is either not brave or funny.
Everyone who is either creative or curious is not humble and vice versa.
If someone is not rich or not creative then someone is both kind and happy.
Everyone who is not quiet or not kind is not strong and vice versa.
Everyone who is generous or not curious is both not quiet and creative and vice versa.
Everyone who is either not happy or wise is generous and vice versa.
If lucy is either not rich or not tall then someone is either generous or not funny and vice versa.
Everyone who is either not generous or not creative is both kind and not brave and vice versa.
Everyone who is both not rich and calm is both not wise and happy and vice versa.
If someone is both curious and creative then fred is not patient or not old.
If paul is both strong and not old then someone is patient and vice versa.
Alice is not kind or not wise.
Mary is either not kind or not happy.
Someone is not rich or not patient.
Susan is not calm or rich.
Lucy is brave.
Lucy is either not kind or patient.
John is both not tall and curious. | Lucy is not rich. | neutral | (![X]:((~calm(X)&brave(X))<=>(~rich(X)&~brave(X))))&
(((~quiet(lucy)|rich(lucy)))=>((~rich(alice)|~funny(alice))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~brave(X)|creative(X))))&
(((~wise(susan)&calm(susan)))<=>(?[X]:((generous(X)<~>humble(X)))))&
(![X]:(~calm(X)=>creative(X)))&
(![X]:(brave(X)=>(~brave(X)<~>funny(X))))&
(![X]:((creative(X)<~>curious(X))<=>~humble(X)))&
((?[X]:((~rich(X)|~creative(X))))=>(?[X]:((kind(X)&happy(X)))))&
(![X]:((~quiet(X)|~kind(X))<=>~strong(X)))&
(![X]:((generous(X)|~curious(X))<=>(~quiet(X)&creative(X))))&
(![X]:((~happy(X)<~>wise(X))<=>generous(X)))&
(((~rich(lucy)<~>~tall(lucy)))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:((~generous(X)<~>~creative(X))<=>(kind(X)&~brave(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&happy(X))))&
((?[X]:((curious(X)&creative(X))))=>((~patient(fred)|~old(fred))))&
(((strong(paul)&~old(paul)))<=>(?[X]:(patient(X))))&
((~kind(alice)|~wise(alice)))&
((~kind(mary)<~>~happy(mary)))&
(?[X]:((~rich(X)|~patient(X))))&
((~calm(susan)|rich(susan)))&
(brave(lucy))&
((~kind(lucy)<~>patient(lucy)))&
((~tall(john)&curious(john))) | ~rich(lucy) | [] | null | 0 |
Everyone who is wise or patient is both patient and not brave and vice versa.
If mary is either not creative or not generous then someone is both kind and patient.
Everyone who is funny or not old is both not rich and patient.
Everyone who is funny or not curious is patient or quiet and vice versa.
Everyone who is either not patient or happy is old and vice versa.
If someone is both not kind and not brave then someone is both not strong and not old.
If lucy is either not kind or not calm then someone is old or rich and vice versa.
Everyone who is either happy or generous is both calm and not happy.
If someone is both funny and not calm then someone is not calm and vice versa.
Everyone who is creative or humble is both brave and not old and vice versa.
Everyone who is either not funny or tall is either not tall or not humble and vice versa.
If someone is not kind then mary is either not kind or not generous and vice versa.
If lucy is kind then alice is wise or patient and vice versa.
Everyone who is not old is both not strong and not creative.
If someone is humble then susan is not calm.
If paul is creative then someone is curious.
Someone is either creative or strong.
Someone is not humble.
Lucy is not curious.
Lucy is funny or not happy.
John is not kind or funny.
Someone is not quiet.
Someone is not generous or generous. | Lucy is humble. | contradiction | (![X]:((wise(X)|patient(X))<=>(patient(X)&~brave(X))))&
(((~creative(mary)<~>~generous(mary)))=>(?[X]:((kind(X)&patient(X)))))&
(![X]:((funny(X)|~old(X))=>(~rich(X)&patient(X))))&
(![X]:((funny(X)|~curious(X))<=>(patient(X)|quiet(X))))&
(![X]:((~patient(X)<~>happy(X))<=>old(X)))&
((?[X]:((~kind(X)&~brave(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(((~kind(lucy)<~>~calm(lucy)))<=>(?[X]:((old(X)|rich(X)))))&
(![X]:((happy(X)<~>generous(X))=>(calm(X)&~happy(X))))&
((?[X]:((funny(X)&~calm(X))))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)|humble(X))<=>(brave(X)&~old(X))))&
(![X]:((~funny(X)<~>tall(X))<=>(~tall(X)<~>~humble(X))))&
((?[X]:(~kind(X)))<=>((~kind(mary)<~>~generous(mary))))&
((kind(lucy))<=>((wise(alice)|patient(alice))))&
(![X]:(~old(X)=>(~strong(X)&~creative(X))))&
((?[X]:(humble(X)))=>(~calm(susan)))&
((creative(paul))=>(?[X]:(curious(X))))&
(?[X]:((creative(X)<~>strong(X))))&
(?[X]:(~humble(X)))&
(~curious(lucy))&
((funny(lucy)|~happy(lucy)))&
((~kind(john)|funny(john)))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)|generous(X)))) | humble(lucy) | [
"p0",
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4001577247247892584685680
% SZS output start Proof for 4001577247247892584685680
1. ! [X0] : ((patient(X0) | wise(X0)) <=> (~brave(X0) & patient(X0))) [input p0]
3. ! [X0] : ((~old(X0) | funny(X0)) => (patient(X0) & ~rich(X0))) [input p2]
10. ! [X0] : ((humble(X0) | creative(X0)) <=> (~old(X0) & brave(X0))) [input p9]
24. humble(lucy) [input hypothesis]
28. ! [X0] : ((patient(X0) & ~rich(X0)) | (old(X0) & ~funny(X0))) [ennf transformation 3]
34. ! [X0] : (((patient(X0) | wise(X0)) | (brave(X0) | ~patient(X0))) & ((~brave(X0) & patient(X0)) | (~patient(X0) & ~wise(X0)))) [nnf transformation 1]
35. ! [X0] : ((patient(X0) | wise(X0) | brave(X0) | ~patient(X0)) & ((~brave(X0) & patient(X0)) | (~patient(X0) & ~wise(X0)))) [flattening 34]
55. ! [X0] : (((humble(X0) | creative(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (~humble(X0) & ~creative(X0)))) [nnf transformation 10]
56. ! [X0] : ((humble(X0) | creative(X0) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | (~humble(X0) & ~creative(X0)))) [flattening 55]
78. ~brave(X0) | ~patient(X0) [cnf transformation 35]
87. old(X0) | patient(X0) [cnf transformation 28]
112. ~humble(X0) | brave(X0) [cnf transformation 56]
114. ~humble(X0) | ~old(X0) [cnf transformation 56]
143. humble(lucy) [cnf transformation 24]
296. brave(lucy) [resolution 112,143]
299. ~patient(lucy) [resolution 296,78]
301. ~old(lucy) [resolution 114,143]
302. patient(lucy) [resolution 301,87]
303. $false [subsumption resolution 302,299]
% SZS output end Proof for 4001577247247892584685680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and generous is wise and vice versa.
Everyone who is not brave or generous is both not rich and rich.
If john is old or calm then someone is rich or not curious and vice versa.
Everyone who is both humble and not funny is both not happy and not generous and vice versa.
If someone is both strong and not creative then mary is wise or not happy.
Everyone who is either not creative or not rich is either not happy or not generous and vice versa.
Everyone who is not humble is either not humble or happy and vice versa.
Everyone who is not wise is quiet or not wise and vice versa.
If someone is calm or kind then someone is happy and vice versa.
If lucy is either not calm or not old then someone is both not tall and not strong and vice versa.
Everyone who is either not strong or strong is both quiet and not tall.
If fred is either tall or not tall then paul is not rich or not curious and vice versa.
If alice is curious or not wise then lucy is not kind.
If someone is not strong or quiet then someone is either not creative or patient.
If someone is funny then mary is happy.
Everyone who is either brave or tall is not rich and vice versa.
Someone is either not rich or not quiet.
Alice is not wise.
Someone is both not creative and brave. | Paul is not happy. | entailment | (![X]:((brave(X)&generous(X))<=>wise(X)))&
(![X]:((~brave(X)|generous(X))=>(~rich(X)&rich(X))))&
(((old(john)|calm(john)))<=>(?[X]:((rich(X)|~curious(X)))))&
(![X]:((humble(X)&~funny(X))<=>(~happy(X)&~generous(X))))&
((?[X]:((strong(X)&~creative(X))))=>((wise(mary)|~happy(mary))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:(~humble(X)<=>(~humble(X)<~>happy(X))))&
(![X]:(~wise(X)<=>(quiet(X)|~wise(X))))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:(happy(X))))&
(((~calm(lucy)<~>~old(lucy)))<=>(?[X]:((~tall(X)&~strong(X)))))&
(![X]:((~strong(X)<~>strong(X))=>(quiet(X)&~tall(X))))&
(((tall(fred)<~>~tall(fred)))<=>((~rich(paul)|~curious(paul))))&
(((curious(alice)|~wise(alice)))=>(~kind(lucy)))&
((?[X]:((~strong(X)|quiet(X))))=>(?[X]:((~creative(X)<~>patient(X)))))&
((?[X]:(funny(X)))=>(happy(mary)))&
(![X]:((brave(X)<~>tall(X))<=>~rich(X)))&
(?[X]:((~rich(X)<~>~quiet(X))))&
(~wise(alice))&
(?[X]:((~creative(X)&brave(X)))) | ~happy(paul) | [
"p1",
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8002676349235038693817779
% SZS output start Proof for 8002676349235038693817779
2. ! [X0] : ((generous(X0) | ~brave(X0)) => (rich(X0) & ~rich(X0))) [input p1]
4. ! [X0] : ((~funny(X0) & humble(X0)) <=> (~generous(X0) & ~happy(X0))) [input p3]
7. ! [X0] : (~humble(X0) <=> (~humble(X0) <~> happy(X0))) [input p6]
20. happy(paul) [input hypothesis]
23. ! [X0] : ((rich(X0) & ~rich(X0)) | (~generous(X0) & brave(X0))) [ennf transformation 2]
37. ! [X0] : (((~funny(X0) & humble(X0)) | (generous(X0) | happy(X0))) & ((~generous(X0) & ~happy(X0)) | (funny(X0) | ~humble(X0)))) [nnf transformation 4]
38. ! [X0] : (((~funny(X0) & humble(X0)) | generous(X0) | happy(X0)) & ((~generous(X0) & ~happy(X0)) | funny(X0) | ~humble(X0))) [flattening 37]
40. ! [X0] : ((~humble(X0) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0)))) & (((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | humble(X0))) [nnf transformation 7]
69. ~rich(X0) | ~generous(X0) [cnf transformation 23]
71. ~generous(X0) | rich(X0) [cnf transformation 23]
78. humble(X0) | generous(X0) | happy(X0) [cnf transformation 38]
90. ~happy(X0) | humble(X0) | humble(X0) [cnf transformation 40]
92. ~humble(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 40]
131. happy(paul) [cnf transformation 20]
138. ~happy(X0) | humble(X0) [duplicate literal removal 90]
139. ~happy(X0) | ~humble(X0) [duplicate literal removal 92]
140. ~generous(X0) [subsumption resolution 69,71]
169. humble(X0) | happy(X0) [subsumption resolution 78,140]
186. humble(X0) [subsumption resolution 138,169]
295. ~humble(paul) [resolution 139,131]
298. $false [subsumption resolution 295,186]
% SZS output end Proof for 8002676349235038693817779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not wise is quiet.
Everyone who is both not generous and not creative is not creative and vice versa.
If john is either curious or happy then someone is not humble and vice versa.
Everyone who is both not happy and not curious is not tall and vice versa.
If susan is both happy and not strong then fred is either funny or not humble.
If someone is both not calm and not wise then someone is not creative or not generous and vice versa.
If someone is both generous and kind then someone is not wise.
Everyone who is either not quiet or curious is rich.
Everyone who is not creative is either kind or funny and vice versa.
If someone is either not tall or not patient then mary is not old.
If paul is not tall or patient then lucy is generous and vice versa.
If lucy is both not strong and not tall then alice is both calm and patient and vice versa.
If susan is both generous and wise then someone is not strong or humble and vice versa.
If someone is wise then someone is either humble or not rich.
If someone is both not calm and old then lucy is strong.
Everyone who is brave is both not curious and not strong.
Susan is both patient and tall.
Someone is not old or not humble.
Someone is creative.
Lucy is not humble.
Someone is not curious.
Susan is funny or not creative.
Someone is not old or not tall.
Susan is either quiet or generous. | Mary is not humble. | entailment | (![X]:((wise(X)<~>~wise(X))=>quiet(X)))&
(![X]:((~generous(X)&~creative(X))<=>~creative(X)))&
(((curious(john)<~>happy(john)))<=>(?[X]:(~humble(X))))&
(![X]:((~happy(X)&~curious(X))<=>~tall(X)))&
(((happy(susan)&~strong(susan)))=>((funny(fred)<~>~humble(fred))))&
((?[X]:((~calm(X)&~wise(X))))<=>(?[X]:((~creative(X)|~generous(X)))))&
((?[X]:((generous(X)&kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~quiet(X)<~>curious(X))=>rich(X)))&
(![X]:(~creative(X)<=>(kind(X)<~>funny(X))))&
((?[X]:((~tall(X)<~>~patient(X))))=>(~old(mary)))&
(((~tall(paul)|patient(paul)))<=>(generous(lucy)))&
(((~strong(lucy)&~tall(lucy)))<=>((calm(alice)&patient(alice))))&
(((generous(susan)&wise(susan)))<=>(?[X]:((~strong(X)|humble(X)))))&
((?[X]:(wise(X)))=>(?[X]:((humble(X)<~>~rich(X)))))&
((?[X]:((~calm(X)&old(X))))=>(strong(lucy)))&
(![X]:(brave(X)=>(~curious(X)&~strong(X))))&
((patient(susan)&tall(susan)))&
(?[X]:((~old(X)|~humble(X))))&
(?[X]:(creative(X)))&
(~humble(lucy))&
(?[X]:(~curious(X)))&
((funny(susan)|~creative(susan)))&
(?[X]:((~old(X)|~tall(X))))&
((quiet(susan)<~>generous(susan))) | ~humble(mary) | [
"p0",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 940850790739948294459618
% SZS output start Proof for 940850790739948294459618
1. ! [X0] : ((wise(X0) <~> ~wise(X0)) => quiet(X0)) [input p0]
13. (wise(susan) & generous(susan)) <=> ? [X0] : (humble(X0) | ~strong(X0)) [input p12]
24. quiet(susan) <~> generous(susan) [input p23]
25. humble(mary) [input hypothesis]
34. ! [X0] : (quiet(X0) | (wise(X0) <=> ~wise(X0))) [ennf transformation 1]
40. ! [X0] : (quiet(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) [nnf transformation 34]
64. ((wise(susan) & generous(susan)) | ! [X0] : (~humble(X0) & strong(X0))) & (? [X0] : (humble(X0) | ~strong(X0)) | (~wise(susan) | ~generous(susan))) [nnf transformation 13]
65. ((wise(susan) & generous(susan)) | ! [X0] : (~humble(X0) & strong(X0))) & (? [X0] : (humble(X0) | ~strong(X0)) | ~wise(susan) | ~generous(susan)) [flattening 64]
66. ((wise(susan) & generous(susan)) | ! [X0] : (~humble(X0) & strong(X0))) & (? [X1] : (humble(X1) | ~strong(X1)) | ~wise(susan) | ~generous(susan)) [rectify 65]
67. ? [X1] : (humble(X1) | ~strong(X1)) => (humble(sK4) | ~strong(sK4)) [choice axiom]
68. ((wise(susan) & generous(susan)) | ! [X0] : (~humble(X0) & strong(X0))) & ((humble(sK4) | ~strong(sK4)) | ~wise(susan) | ~generous(susan)) [skolemisation 66,67]
77. (~generous(susan) | ~quiet(susan)) & (generous(susan) | quiet(susan)) [nnf transformation 24]
78. quiet(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 40]
79. quiet(X0) | wise(X0) | wise(X0) [cnf transformation 40]
113. generous(susan) | ~humble(X0) [cnf transformation 68]
125. ~generous(susan) | ~quiet(susan) [cnf transformation 77]
126. humble(mary) [cnf transformation 25]
127. quiet(X0) | ~wise(X0) [duplicate literal removal 78]
128. quiet(X0) | wise(X0) [duplicate literal removal 79]
129. quiet(X0) [subsumption resolution 127,128]
239. 24 <=> ! [X0] : ~humble(X0) [avatar definition]
240. ~humble(X0) <- (24) [avatar component clause 239]
251. 27 <=> generous(susan) [avatar definition]
254. 24 | 27 [avatar split clause 113,251,239]
287. ~generous(susan) [subsumption resolution 125,129]
288. ~27 [avatar split clause 287,251]
291. $false <- (24) [resolution 240,126]
292. ~24 [avatar contradiction clause 291]
293. $false [avatar sat refutation 254,288,292]
% SZS output end Proof for 940850790739948294459618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or quiet is both not calm and not kind and vice versa.
Everyone who is funny or not patient is not creative or wise and vice versa.
If someone is strong then someone is not tall and vice versa.
Everyone who is not brave or not humble is either not generous or not calm and vice versa.
Everyone who is not calm is humble.
Everyone who is either quiet or not kind is both patient and not funny and vice versa.
Everyone who is either brave or old is patient and vice versa.
If someone is either old or not tall then someone is kind and vice versa.
Everyone who is either creative or curious is rich and vice versa.
If someone is both patient and not creative then someone is not curious.
Everyone who is either not curious or strong is either not rich or patient and vice versa.
Everyone who is both rich and humble is both brave and tall.
If lucy is strong then lucy is both old and calm and vice versa.
If someone is either wise or rich then someone is not generous or curious.
Everyone who is not happy or not rich is brave or kind.
Everyone who is not quiet or tall is not strong or humble and vice versa.
Someone is not brave or happy.
Alice is both strong and not wise.
Someone is either calm or generous.
Alice is not humble.
Someone is both happy and not old.
Someone is not tall.
Someone is either curious or not rich.
Paul is either happy or tall. | Alice is funny. | entailment | (![X]:((~wise(X)<~>quiet(X))<=>(~calm(X)&~kind(X))))&
(![X]:((funny(X)|~patient(X))<=>(~creative(X)|wise(X))))&
((?[X]:(strong(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~brave(X)|~humble(X))<=>(~generous(X)<~>~calm(X))))&
(![X]:(~calm(X)=>humble(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>(patient(X)&~funny(X))))&
(![X]:((brave(X)<~>old(X))<=>patient(X)))&
((?[X]:((old(X)<~>~tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((creative(X)<~>curious(X))<=>rich(X)))&
((?[X]:((patient(X)&~creative(X))))=>(?[X]:(~curious(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((rich(X)&humble(X))=>(brave(X)&tall(X))))&
((strong(lucy))<=>((old(lucy)&calm(lucy))))&
((?[X]:((wise(X)<~>rich(X))))=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((~happy(X)|~rich(X))=>(brave(X)|kind(X))))&
(![X]:((~quiet(X)|tall(X))<=>(~strong(X)|humble(X))))&
(?[X]:((~brave(X)|happy(X))))&
((strong(alice)&~wise(alice)))&
(?[X]:((calm(X)<~>generous(X))))&
(~humble(alice))&
(?[X]:((happy(X)&~old(X))))&
(?[X]:(~tall(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
((happy(paul)<~>tall(paul))) | funny(alice) | [
"p1",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5545217392087091510445946
% SZS output start Proof for 5545217392087091510445946
2. ! [X0] : ((~patient(X0) | funny(X0)) <=> (wise(X0) | ~creative(X0))) [input p1]
9. ! [X0] : ((creative(X0) <~> curious(X0)) <=> rich(X0)) [input p8]
11. ! [X0] : ((~curious(X0) <~> strong(X0)) <=> (~rich(X0) <~> patient(X0))) [input p10]
18. ~wise(alice) & strong(alice) [input p17]
25. ~funny(alice) [input hypothesis]
39. ! [X0] : (((~patient(X0) | funny(X0)) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | (patient(X0) & ~funny(X0)))) [nnf transformation 2]
40. ! [X0] : ((~patient(X0) | funny(X0) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | (patient(X0) & ~funny(X0)))) [flattening 39]
56. ! [X0] : ((((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | ~rich(X0)) & (rich(X0) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))))) [nnf transformation 9]
60. ! [X0] : ((((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0)))) & (((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0))))) [nnf transformation 11]
89. ~creative(X0) | wise(X0) | patient(X0) [cnf transformation 40]
90. ~patient(X0) | funny(X0) | creative(X0) [cnf transformation 40]
115. ~creative(X0) | curious(X0) | rich(X0) [cnf transformation 56]
116. ~curious(X0) | creative(X0) | rich(X0) [cnf transformation 56]
117. ~rich(X0) | creative(X0) | curious(X0) [cnf transformation 56]
118. ~rich(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 56]
121. ~rich(X0) | patient(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 60]
123. ~curious(X0) | rich(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 60]
126. ~strong(X0) | curious(X0) | patient(X0) | rich(X0) [cnf transformation 60]
127. ~rich(X0) | curious(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 60]
142. strong(alice) [cnf transformation 18]
143. ~wise(alice) [cnf transformation 18]
154. ~funny(alice) [cnf transformation 25]
562. curious(alice) | patient(alice) | rich(alice) [resolution 126,142]
565. 61 <=> rich(alice) [avatar definition]
566. ~rich(alice) <- (~61) [avatar component clause 565]
567. rich(alice) <- (61) [avatar component clause 565]
569. 62 <=> patient(alice) [avatar definition]
570. ~patient(alice) <- (~62) [avatar component clause 569]
571. patient(alice) <- (62) [avatar component clause 569]
573. 63 <=> curious(alice) [avatar definition]
575. curious(alice) <- (63) [avatar component clause 573]
576. 61 | 62 | 63 [avatar split clause 562,573,569,565]
629. creative(alice) | curious(alice) <- (61) [resolution 567,117]
630. ~creative(alice) | ~curious(alice) <- (61) [resolution 567,118]
632. patient(alice) | ~curious(alice) | ~strong(alice) <- (61) [resolution 567,121]
634. curious(alice) | ~strong(alice) | ~patient(alice) <- (61) [resolution 567,127]
638. 71 <=> creative(alice) [avatar definition]
640. creative(alice) <- (71) [avatar component clause 638]
641. 63 | 71 | ~61 [avatar split clause 629,565,638,573]
642. ~63 | ~71 | ~61 [avatar split clause 630,565,638,573]
643. patient(alice) | ~curious(alice) <- (61) [subsumption resolution 632,142]
644. ~63 | 62 | ~61 [avatar split clause 643,565,569,573]
645. curious(alice) | ~patient(alice) <- (61) [subsumption resolution 634,142]
646. ~62 | 63 | ~61 [avatar split clause 645,565,573,569]
706. wise(alice) | patient(alice) <- (71) [resolution 640,89]
708. patient(alice) <- (71) [subsumption resolution 706,143]
709. $false <- (~62, 71) [subsumption resolution 708,570]
710. 62 | ~71 [avatar contradiction clause 709]
726. funny(alice) | creative(alice) <- (62) [resolution 571,90]
732. creative(alice) <- (62) [subsumption resolution 726,154]
733. 71 | ~62 [avatar split clause 732,569,638]
766. curious(alice) | rich(alice) <- (71) [resolution 640,115]
772. curious(alice) <- (~61, 71) [subsumption resolution 766,566]
773. 63 | 61 | ~71 [avatar split clause 772,638,565,573]
775. rich(alice) | ~patient(alice) | ~strong(alice) <- (63) [resolution 575,123]
776. creative(alice) | rich(alice) <- (63) [resolution 575,116]
777. ~patient(alice) | ~strong(alice) <- (~61, 63) [subsumption resolution 775,566]
781. ~patient(alice) <- (~61, 63) [subsumption resolution 777,142]
782. ~62 | 61 | ~63 [avatar split clause 781,573,565,569]
783. creative(alice) <- (~61, 63) [subsumption resolution 776,566]
784. 71 | 61 | ~63 [avatar split clause 783,573,565,638]
785. $false [avatar sat refutation 576,641,642,644,646,710,733,773,782,784]
% SZS output end Proof for 5545217392087091510445946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not quiet or creative is old and vice versa. Everyone who is both tall and patient is brave or not generous and vice versa. Everyone who is either not calm or wise is calm and vice versa. If fred is either brave or curious then someone is funny or not strong and vice versa. Everyone who is not patient or happy is wise. If john is humble then someone is both not tall and rich and vice versa. Everyone who is both happy and not patient is either not creative or not generous and vice versa. If someone is patient then someone is either generous or not rich and vice versa. If someone is not brave then paul is both funny and generous and vice versa. If someone is either tall or rich then someone is patient and vice versa. Everyone who is not brave or not quiet is both tall and calm and vice versa. If fred is both not quiet and not kind then paul is either tall or not brave. Everyone who is not kind is not patient. If someone is quiet or generous then paul is strong or happy. Everyone who is patient or not generous is not strong or happy and vice versa. If john is both not strong and not old then lucy is not creative and vice versa. Someone is not curious or not generous. Alice is not calm or quiet. Someone is both curious and strong. Someone is wise. Alice is tall. Someone is not calm. Someone is either curious or humble. Someone is both happy and rich. | Fred is not tall. | contradiction | (![X]:((~quiet(X)<~>creative(X))<=>old(X)))&
(![X]:((tall(X)&patient(X))<=>(brave(X)|~generous(X))))&
(![X]:((~calm(X)<~>wise(X))<=>calm(X)))&
(((brave(fred)<~>curious(fred)))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:((~patient(X)|happy(X))=>wise(X)))&
((humble(john))<=>(?[X]:((~tall(X)&rich(X)))))&
(![X]:((happy(X)&~patient(X))<=>(~creative(X)<~>~generous(X))))&
((?[X]:(patient(X)))<=>(?[X]:((generous(X)<~>~rich(X)))))&
((?[X]:(~brave(X)))<=>((funny(paul)&generous(paul))))&
((?[X]:((tall(X)<~>rich(X))))<=>(?[X]:(patient(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(tall(X)&calm(X))))&
(((~quiet(fred)&~kind(fred)))=>((tall(paul)<~>~brave(paul))))&
(![X]:(~kind(X)=>~patient(X)))&
((?[X]:((quiet(X)|generous(X))))=>((strong(paul)|happy(paul))))&
(![X]:((patient(X)|~generous(X))<=>(~strong(X)|happy(X))))&
(((~strong(john)&~old(john)))<=>(~creative(lucy)))&
(?[X]:((~curious(X)|~generous(X))))&
((~calm(alice)|quiet(alice)))&
(?[X]:((curious(X)&strong(X))))&
(?[X]:(wise(X)))&
(tall(alice))&
(?[X]:(~calm(X)))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((happy(X)&rich(X)))) | ~tall(fred) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2209305898480241902197180
% SZS output start Proof for 2209305898480241902197180
2. ! [X0] : ((patient(X0) & tall(X0)) <=> (~generous(X0) | brave(X0))) [input p1]
11. ! [X0] : ((~quiet(X0) | ~brave(X0)) <=> (calm(X0) & tall(X0))) [input p10]
25. ~tall(fred) [input hypothesis]
34. ! [X0] : (((patient(X0) & tall(X0)) | (generous(X0) & ~brave(X0))) & ((~generous(X0) | brave(X0)) | (~patient(X0) | ~tall(X0)))) [nnf transformation 2]
35. ! [X0] : (((patient(X0) & tall(X0)) | (generous(X0) & ~brave(X0))) & (~generous(X0) | brave(X0) | ~patient(X0) | ~tall(X0))) [flattening 34]
62. ! [X0] : (((~quiet(X0) | ~brave(X0)) | (~calm(X0) | ~tall(X0))) & ((calm(X0) & tall(X0)) | (quiet(X0) & brave(X0)))) [nnf transformation 11]
63. ! [X0] : ((~quiet(X0) | ~brave(X0) | ~calm(X0) | ~tall(X0)) & ((calm(X0) & tall(X0)) | (quiet(X0) & brave(X0)))) [flattening 62]
86. tall(X0) | ~brave(X0) [cnf transformation 35]
122. tall(X0) | brave(X0) [cnf transformation 63]
147. ~tall(fred) [cnf transformation 25]
262. tall(X0) [subsumption resolution 122,86]
316. $false [subsumption resolution 147,262]
% SZS output end Proof for 2209305898480241902197180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not wise or tall and vice versa.
Everyone who is not funny is both wise and quiet and vice versa.
Everyone who is not tall or not funny is either not creative or old.
If lucy is not humble then someone is creative or strong.
If someone is both not rich and old then someone is tall.
Everyone who is funny is both not curious and old.
If paul is not funny or old then someone is either not kind or brave.
If someone is either brave or quiet then someone is both strong and not rich and vice versa.
Everyone who is not tall is not curious or not old and vice versa.
If john is happy or not brave then paul is strong or not brave.
Everyone who is either kind or not tall is both not wise and not strong.
Everyone who is either wise or quiet is patient and vice versa.
If john is happy then john is either not tall or generous and vice versa.
Everyone who is not wise is both not tall and not curious.
If alice is both old and not rich then someone is old.
If someone is both not creative and not kind then someone is both quiet and humble and vice versa.
Someone is both brave and quiet.
Paul is not wise.
Someone is either not wise or not generous.
Susan is both not old and not patient.
Mary is either not happy or wise.
Someone is either tall or brave.
Someone is not quiet.
Alice is both wise and quiet. | Alice is not funny. | entailment | (![X]:(generous(X)<=>(~wise(X)|tall(X))))&
(![X]:(~funny(X)<=>(wise(X)&quiet(X))))&
(![X]:((~tall(X)|~funny(X))=>(~creative(X)<~>old(X))))&
((~humble(lucy))=>(?[X]:((creative(X)|strong(X)))))&
((?[X]:((~rich(X)&old(X))))=>(?[X]:(tall(X))))&
(![X]:(funny(X)=>(~curious(X)&old(X))))&
(((~funny(paul)|old(paul)))=>(?[X]:((~kind(X)<~>brave(X)))))&
((?[X]:((brave(X)<~>quiet(X))))<=>(?[X]:((strong(X)&~rich(X)))))&
(![X]:(~tall(X)<=>(~curious(X)|~old(X))))&
(((happy(john)|~brave(john)))=>((strong(paul)|~brave(paul))))&
(![X]:((kind(X)<~>~tall(X))=>(~wise(X)&~strong(X))))&
(![X]:((wise(X)<~>quiet(X))<=>patient(X)))&
((happy(john))<=>((~tall(john)<~>generous(john))))&
(![X]:(~wise(X)=>(~tall(X)&~curious(X))))&
(((old(alice)&~rich(alice)))=>(?[X]:(old(X))))&
((?[X]:((~creative(X)&~kind(X))))<=>(?[X]:((quiet(X)&humble(X)))))&
(?[X]:((brave(X)&quiet(X))))&
(~wise(paul))&
(?[X]:((~wise(X)<~>~generous(X))))&
((~old(susan)&~patient(susan)))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((tall(X)<~>brave(X))))&
(?[X]:(~quiet(X)))&
((wise(alice)&quiet(alice))) | ~funny(alice) | [
"p1",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3803007813396601989397320
% SZS output start Proof for 3803007813396601989397320
2. ! [X0] : (~funny(X0) <=> (quiet(X0) & wise(X0))) [input p1]
24. quiet(alice) & wise(alice) [input p23]
25. funny(alice) [input hypothesis]
44. ! [X0] : ((~funny(X0) | (~quiet(X0) | ~wise(X0))) & ((quiet(X0) & wise(X0)) | funny(X0))) [nnf transformation 2]
45. ! [X0] : ((~funny(X0) | ~quiet(X0) | ~wise(X0)) & ((quiet(X0) & wise(X0)) | funny(X0))) [flattening 44]
88. ~quiet(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 45]
141. wise(alice) [cnf transformation 24]
142. quiet(alice) [cnf transformation 24]
143. funny(alice) [cnf transformation 25]
356. ~funny(alice) | ~wise(alice) [resolution 88,142]
367. ~wise(alice) [subsumption resolution 356,143]
368. $false [subsumption resolution 367,141]
% SZS output end Proof for 3803007813396601989397320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or humble is both happy and patient.
If someone is either not calm or curious then fred is either not curious or not quiet and vice versa.
Everyone who is either kind or not rich is tall or not funny and vice versa.
If someone is both strong and tall then paul is either brave or curious and vice versa.
Everyone who is not old or creative is not calm or rich.
Everyone who is kind or not brave is either not quiet or kind and vice versa.
Everyone who is humble or funny is both not humble and not quiet.
If john is either not curious or not generous then someone is happy.
Everyone who is both curious and not curious is either rich or not creative.
Everyone who is rich is humble.
If john is calm or not strong then someone is either not rich or not quiet and vice versa.
If someone is both not kind and not happy then someone is strong or not kind.
Everyone who is both not old and curious is both not brave and curious and vice versa.
Everyone who is not old or happy is rich or not rich.
If paul is both funny and generous then someone is both not calm and kind and vice versa.
If john is not calm then mary is either funny or not creative and vice versa.
Paul is generous.
John is not patient or not creative.
Someone is either calm or not creative.
Someone is old or brave.
Someone is generous.
Lucy is not old.
Someone is either strong or not brave. | John is strong. | neutral | (![X]:((~tall(X)<~>humble(X))=>(happy(X)&patient(X))))&
((?[X]:((~calm(X)<~>curious(X))))<=>((~curious(fred)<~>~quiet(fred))))&
(![X]:((kind(X)<~>~rich(X))<=>(tall(X)|~funny(X))))&
((?[X]:((strong(X)&tall(X))))<=>((brave(paul)<~>curious(paul))))&
(![X]:((~old(X)|creative(X))=>(~calm(X)|rich(X))))&
(![X]:((kind(X)|~brave(X))<=>(~quiet(X)<~>kind(X))))&
(![X]:((humble(X)|funny(X))=>(~humble(X)&~quiet(X))))&
(((~curious(john)<~>~generous(john)))=>(?[X]:(happy(X))))&
(![X]:((curious(X)&~curious(X))=>(rich(X)<~>~creative(X))))&
(![X]:(rich(X)=>humble(X)))&
(((calm(john)|~strong(john)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
((?[X]:((~kind(X)&~happy(X))))=>(?[X]:((strong(X)|~kind(X)))))&
(![X]:((~old(X)&curious(X))<=>(~brave(X)&curious(X))))&
(![X]:((~old(X)|happy(X))=>(rich(X)|~rich(X))))&
(((funny(paul)&generous(paul)))<=>(?[X]:((~calm(X)&kind(X)))))&
((~calm(john))<=>((funny(mary)<~>~creative(mary))))&
(generous(paul))&
((~patient(john)|~creative(john)))&
(?[X]:((calm(X)<~>~creative(X))))&
(?[X]:((old(X)|brave(X))))&
(?[X]:(generous(X)))&
(~old(lucy))&
(?[X]:((strong(X)<~>~brave(X)))) | strong(john) | [] | null | 0 |
Everyone who is either not creative or patient is quiet and vice versa.
Everyone who is either happy or not quiet is not wise or quiet and vice versa.
If someone is rich then lucy is either strong or not humble.
Everyone who is both quiet and not happy is either strong or not curious.
Everyone who is not quiet is both humble and not strong and vice versa.
Everyone who is either creative or not calm is either generous or not rich.
Everyone who is either brave or not brave is both happy and not creative.
If someone is both old and patient then lucy is not generous and vice versa.
If someone is not brave or not happy then susan is not wise or patient.
Everyone who is patient or strong is either not happy or not wise.
If someone is either brave or not rich then alice is both kind and funny.
Everyone who is strong is either patient or curious and vice versa.
Everyone who is both wise and not creative is not brave.
If someone is humble then someone is not tall or old.
Everyone who is either not generous or happy is both rich and not curious.
Someone is either quiet or kind.
Someone is funny or not patient.
Mary is not generous.
Someone is curious or generous.
Fred is either brave or kind.
Someone is not old or brave.
Mary is strong.
Someone is both calm and quiet. | Mary is not quiet. | contradiction | (![X]:((~creative(X)<~>patient(X))<=>quiet(X)))&
(![X]:((happy(X)<~>~quiet(X))<=>(~wise(X)|quiet(X))))&
((?[X]:(rich(X)))=>((strong(lucy)<~>~humble(lucy))))&
(![X]:((quiet(X)&~happy(X))=>(strong(X)<~>~curious(X))))&
(![X]:(~quiet(X)<=>(humble(X)&~strong(X))))&
(![X]:((creative(X)<~>~calm(X))=>(generous(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~brave(X))=>(happy(X)&~creative(X))))&
((?[X]:((old(X)&patient(X))))<=>(~generous(lucy)))&
((?[X]:((~brave(X)|~happy(X))))=>((~wise(susan)|patient(susan))))&
(![X]:((patient(X)|strong(X))=>(~happy(X)<~>~wise(X))))&
((?[X]:((brave(X)<~>~rich(X))))=>((kind(alice)&funny(alice))))&
(![X]:(strong(X)<=>(patient(X)<~>curious(X))))&
(![X]:((wise(X)&~creative(X))=>~brave(X)))&
((?[X]:(humble(X)))=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((~generous(X)<~>happy(X))=>(rich(X)&~curious(X))))&
(?[X]:((quiet(X)<~>kind(X))))&
(?[X]:((funny(X)|~patient(X))))&
(~generous(mary))&
(?[X]:((curious(X)|generous(X))))&
((brave(fred)<~>kind(fred)))&
(?[X]:((~old(X)|brave(X))))&
(strong(mary))&
(?[X]:((calm(X)&quiet(X)))) | ~quiet(mary) | [
"p4",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1085336700586735891348223
% SZS output start Proof for 1085336700586735891348223
5. ! [X0] : (~quiet(X0) <=> (~strong(X0) & humble(X0))) [input p4]
22. strong(mary) [input p21]
24. ~quiet(mary) [input hypothesis]
46. ! [X0] : ((~quiet(X0) | (strong(X0) | ~humble(X0))) & ((~strong(X0) & humble(X0)) | quiet(X0))) [nnf transformation 5]
47. ! [X0] : ((~quiet(X0) | strong(X0) | ~humble(X0)) & ((~strong(X0) & humble(X0)) | quiet(X0))) [flattening 46]
83. ~strong(X0) | quiet(X0) [cnf transformation 47]
120. strong(mary) [cnf transformation 22]
123. ~quiet(mary) [cnf transformation 24]
232. quiet(mary) [resolution 83,120]
233. $false [subsumption resolution 232,123]
% SZS output end Proof for 1085336700586735891348223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and strong is either rich or not wise.
Everyone who is strong or not humble is both humble and calm.
If someone is both generous and funny then someone is either funny or quiet and vice versa.
Everyone who is both not funny and not quiet is calm and vice versa.
If lucy is not rich or strong then paul is either not creative or kind and vice versa.
If someone is either not tall or rich then someone is patient or kind and vice versa.
Everyone who is creative or not funny is both patient and not old and vice versa.
Everyone who is curious or funny is either rich or quiet.
If someone is either rich or not happy then john is not patient.
Everyone who is either brave or patient is both quiet and not old.
Everyone who is generous or not strong is either old or strong.
If someone is not curious or not quiet then fred is rich.
Everyone who is not brave or generous is either tall or curious and vice versa.
If fred is not brave or calm then someone is not funny.
Everyone who is funny is either brave or patient.
If susan is either tall or curious then someone is either strong or not funny and vice versa.
Mary is creative or not creative.
Someone is not quiet or wise.
Mary is generous.
Someone is either not humble or kind.
Alice is both tall and not old.
Alice is both not wise and not old. | Susan is calm. | entailment | (![X]:((~generous(X)&strong(X))=>(rich(X)<~>~wise(X))))&
(![X]:((strong(X)|~humble(X))=>(humble(X)&calm(X))))&
((?[X]:((generous(X)&funny(X))))<=>(?[X]:((funny(X)<~>quiet(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>calm(X)))&
(((~rich(lucy)|strong(lucy)))<=>((~creative(paul)<~>kind(paul))))&
((?[X]:((~tall(X)<~>rich(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:((creative(X)|~funny(X))<=>(patient(X)&~old(X))))&
(![X]:((curious(X)|funny(X))=>(rich(X)<~>quiet(X))))&
((?[X]:((rich(X)<~>~happy(X))))=>(~patient(john)))&
(![X]:((brave(X)<~>patient(X))=>(quiet(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))=>(old(X)<~>strong(X))))&
((?[X]:((~curious(X)|~quiet(X))))=>(rich(fred)))&
(![X]:((~brave(X)|generous(X))<=>(tall(X)<~>curious(X))))&
(((~brave(fred)|calm(fred)))=>(?[X]:(~funny(X))))&
(![X]:(funny(X)=>(brave(X)<~>patient(X))))&
(((tall(susan)<~>curious(susan)))<=>(?[X]:((strong(X)<~>~funny(X)))))&
((creative(mary)|~creative(mary)))&
(?[X]:((~quiet(X)|wise(X))))&
(generous(mary))&
(?[X]:((~humble(X)<~>kind(X))))&
((tall(alice)&~old(alice)))&
((~wise(alice)&~old(alice))) | calm(susan) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 853076115818725646170428
% SZS output start Proof for 853076115818725646170428
2. ! [X0] : ((~humble(X0) | strong(X0)) => (calm(X0) & humble(X0))) [input p1]
4. ! [X0] : ((~quiet(X0) & ~funny(X0)) <=> calm(X0)) [input p3]
7. ! [X0] : ((~funny(X0) | creative(X0)) <=> (~old(X0) & patient(X0))) [input p6]
10. ! [X0] : ((brave(X0) <~> patient(X0)) => (~old(X0) & quiet(X0))) [input p9]
11. ! [X0] : ((~strong(X0) | generous(X0)) => (old(X0) <~> strong(X0))) [input p10]
15. ! [X0] : (funny(X0) => (brave(X0) <~> patient(X0))) [input p14]
16. (tall(susan) <~> curious(susan)) <=> ? [X0] : (strong(X0) <~> ~funny(X0)) [input p15]
23. ~calm(susan) [input hypothesis]
28. ! [X0] : ((calm(X0) & humble(X0)) | (humble(X0) & ~strong(X0))) [ennf transformation 2]
31. ! [X0] : ((~old(X0) & quiet(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 10]
32. ! [X0] : ((old(X0) <~> strong(X0)) | (strong(X0) & ~generous(X0))) [ennf transformation 11]
35. ! [X0] : ((brave(X0) <~> patient(X0)) | ~funny(X0)) [ennf transformation 15]
42. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) | funny(X0)))) [nnf transformation 4]
43. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | quiet(X0) | funny(X0))) [flattening 42]
51. ! [X0] : (((~funny(X0) | creative(X0)) | (old(X0) | ~patient(X0))) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [nnf transformation 7]
52. ! [X0] : ((~funny(X0) | creative(X0) | old(X0) | ~patient(X0)) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [flattening 51]
55. ! [X0] : ((~old(X0) & quiet(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 31]
56. ! [X0] : (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (strong(X0) & ~generous(X0))) [nnf transformation 32]
61. ! [X0] : (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~funny(X0)) [nnf transformation 35]
62. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (? [X0] : ((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [nnf transformation 16]
63. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (? [X1] : ((funny(X1) | ~strong(X1)) & (~funny(X1) | strong(X1))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [rectify 62]
64. ? [X1] : ((funny(X1) | ~strong(X1)) & (~funny(X1) | strong(X1))) => ((funny(sK5) | ~strong(sK5)) & (~funny(sK5) | strong(sK5))) [choice axiom]
65. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (((funny(sK5) | ~strong(sK5)) & (~funny(sK5) | strong(sK5))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [skolemisation 63,64]
75. ~strong(X0) | calm(X0) [cnf transformation 28]
84. ~funny(X0) | ~calm(X0) [cnf transformation 43]
99. patient(X0) | funny(X0) [cnf transformation 52]
101. ~old(X0) | funny(X0) [cnf transformation 52]
111. ~brave(X0) | patient(X0) | ~old(X0) [cnf transformation 55]
112. ~old(X0) | brave(X0) | ~patient(X0) [cnf transformation 55]
114. strong(X0) | old(X0) | strong(X0) [cnf transformation 56]
127. patient(X0) | brave(X0) | ~funny(X0) [cnf transformation 61]
128. ~brave(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 61]
129. ~funny(sK5) | strong(sK5) | curious(susan) | ~tall(susan) [cnf transformation 65]
130. ~funny(sK5) | strong(sK5) | tall(susan) | ~curious(susan) [cnf transformation 65]
131. funny(sK5) | ~strong(sK5) | curious(susan) | ~tall(susan) [cnf transformation 65]
132. funny(sK5) | ~strong(sK5) | tall(susan) | ~curious(susan) [cnf transformation 65]
133. curious(susan) | tall(susan) | ~funny(X0) | ~strong(X0) [cnf transformation 65]
135. ~curious(susan) | ~tall(susan) | ~funny(X0) | ~strong(X0) [cnf transformation 65]
146. ~calm(susan) [cnf transformation 23]
147. old(X0) | strong(X0) [duplicate literal removal 114]
274. brave(X0) | patient(X0) [subsumption resolution 127,99]
276. 29 <=> ! [X0] : (strong(X0) | funny(X0)) [avatar definition]
277. funny(X0) | strong(X0) <- (29) [avatar component clause 276]
279. 30 <=> tall(susan) [avatar definition]
283. 31 <=> curious(susan) [avatar definition]
288. 32 <=> ! [X0] : (~funny(X0) | ~strong(X0)) [avatar definition]
289. ~funny(X0) | ~strong(X0) <- (32) [avatar component clause 288]
290. 32 | ~30 | ~31 [avatar split clause 135,283,279,288]
292. 32 | 30 | 31 [avatar split clause 133,283,279,288]
294. 33 <=> strong(sK5) [avatar definition]
295. strong(sK5) <- (33) [avatar component clause 294]
296. ~strong(sK5) <- (~33) [avatar component clause 294]
298. 34 <=> funny(sK5) [avatar definition]
299. ~funny(sK5) <- (~34) [avatar component clause 298]
300. funny(sK5) <- (34) [avatar component clause 298]
301. ~31 | 30 | ~33 | 34 [avatar split clause 132,298,294,279,283]
302. ~30 | 31 | ~33 | 34 [avatar split clause 131,298,294,283,279]
303. ~31 | 30 | 33 | ~34 [avatar split clause 130,298,294,279,283]
304. ~30 | 31 | 33 | ~34 [avatar split clause 129,298,294,283,279]
322. strong(X0) | funny(X0) [resolution 147,101]
324. 29 [avatar split clause 322,276]
336. strong(sK5) <- (29, ~34) [resolution 277,299]
337. $false <- (29, ~33, ~34) [subsumption resolution 336,296]
338. ~29 | 33 | 34 [avatar contradiction clause 337]
406. patient(X0) | ~old(X0) | patient(X0) [resolution 111,274]
407. ~old(X0) | patient(X0) [duplicate literal removal 406]
412. brave(X0) | ~patient(X0) | strong(X0) [resolution 112,147]
413. brave(X0) | strong(X0) [subsumption resolution 412,274]
558. patient(X0) | strong(X0) [resolution 407,147]
561. strong(X2) | ~patient(X2) | ~funny(X2) [resolution 413,128]
566. ~patient(X2) | ~funny(X2) <- (32) [subsumption resolution 561,289]
678. ~funny(X0) | strong(X0) <- (32) [resolution 566,558]
684. strong(X0) <- (29, 32) [subsumption resolution 678,277]
702. calm(X0) <- (29, 32) [resolution 684,75]
727. $false <- (29, 32) [resolution 702,146]
728. ~29 | ~32 [avatar contradiction clause 727]
763. calm(sK5) <- (33) [resolution 295,75]
767. ~calm(sK5) <- (34) [resolution 300,84]
778. $false <- (33, 34) [subsumption resolution 767,763]
779. ~33 | ~34 [avatar contradiction clause 778]
780. $false [avatar sat refutation 290,292,301,302,303,304,324,338,728,779]
% SZS output end Proof for 853076115818725646170428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and curious is wise or happy. If someone is both not calm and quiet then someone is not brave or not tall and vice versa. Everyone who is both not generous and kind is either not kind or not funny and vice versa. Everyone who is wise or quiet is both not curious and brave and vice versa. If someone is either creative or old then someone is both calm and kind. Everyone who is both not curious and not old is brave or rich. Everyone who is either not creative or funny is either not curious or not rich. Everyone who is either not generous or generous is either not wise or happy. Everyone who is both brave and calm is not quiet and vice versa. If someone is either generous or not old then someone is both not curious and happy and vice versa. Everyone who is humble is either not quiet or not calm. Everyone who is not kind or not old is not patient. Everyone who is tall or not calm is both not humble and old and vice versa. If john is humble then someone is either not humble or not calm and vice versa. If someone is not generous then someone is either not old or not calm and vice versa. If someone is funny or not patient then john is either wise or happy and vice versa. Alice is either tall or rich. Fred is either old or not creative. Someone is rich. Mary is not humble. John is funny or tall. | Fred is not humble. | entailment | (![X]:((calm(X)&curious(X))=>(wise(X)|happy(X))))&
((?[X]:((~calm(X)&quiet(X))))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~generous(X)&kind(X))<=>(~kind(X)<~>~funny(X))))&
(![X]:((wise(X)|quiet(X))<=>(~curious(X)&brave(X))))&
((?[X]:((creative(X)<~>old(X))))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:((~curious(X)&~old(X))=>(brave(X)|rich(X))))&
(![X]:((~creative(X)<~>funny(X))=>(~curious(X)<~>~rich(X))))&
(![X]:((~generous(X)<~>generous(X))=>(~wise(X)<~>happy(X))))&
(![X]:((brave(X)&calm(X))<=>~quiet(X)))&
((?[X]:((generous(X)<~>~old(X))))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(humble(X)=>(~quiet(X)<~>~calm(X))))&
(![X]:((~kind(X)|~old(X))=>~patient(X)))&
(![X]:((tall(X)|~calm(X))<=>(~humble(X)&old(X))))&
((humble(john))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
((?[X]:((funny(X)|~patient(X))))<=>((wise(john)<~>happy(john))))&
((tall(alice)<~>rich(alice)))&
((old(fred)<~>~creative(fred)))&
(?[X]:(rich(X)))&
(~humble(mary))&
((funny(john)|tall(john))) | ~humble(fred) | [
"p0",
"p2",
"p3",
"p7",
"p8",
"p9",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5792642128876559975259145
% SZS output start Proof for 5792642128876559975259145
1. ! [X0] : ((curious(X0) & calm(X0)) => (happy(X0) | wise(X0))) [input p0]
3. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (~kind(X0) <~> ~funny(X0))) [input p2]
4. ! [X0] : ((quiet(X0) | wise(X0)) <=> (brave(X0) & ~curious(X0))) [input p3]
8. ! [X0] : ((~generous(X0) <~> generous(X0)) => (~wise(X0) <~> happy(X0))) [input p7]
9. ! [X0] : ((calm(X0) & brave(X0)) <=> ~quiet(X0)) [input p8]
10. ? [X0] : (generous(X0) <~> ~old(X0)) <=> ? [X0] : (happy(X0) & ~curious(X0)) [input p9]
12. ! [X0] : ((~old(X0) | ~kind(X0)) => ~patient(X0)) [input p11]
13. ! [X0] : ((~calm(X0) | tall(X0)) <=> (old(X0) & ~humble(X0))) [input p12]
16. ? [X0] : (~patient(X0) | funny(X0)) <=> (wise(john) <~> happy(john)) [input p15]
22. humble(fred) [input hypothesis]
25. ? [X0] : (generous(X0) <~> ~old(X0)) <=> ? [X1] : (happy(X1) & ~curious(X1)) [rectify 10]
27. ! [X0] : ((happy(X0) | wise(X0)) | (~curious(X0) | ~calm(X0))) [ennf transformation 1]
28. ! [X0] : (happy(X0) | wise(X0) | ~curious(X0) | ~calm(X0)) [flattening 27]
33. ! [X0] : ((~wise(X0) <~> happy(X0)) | (~generous(X0) <=> generous(X0))) [ennf transformation 8]
35. ! [X0] : (~patient(X0) | (old(X0) & kind(X0))) [ennf transformation 12]
41. ! [X0] : (((kind(X0) & ~generous(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~kind(X0) | generous(X0)))) [nnf transformation 3]
42. ! [X0] : (((kind(X0) & ~generous(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~kind(X0) | generous(X0))) [flattening 41]
43. ! [X0] : (((quiet(X0) | wise(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (~quiet(X0) & ~wise(X0)))) [nnf transformation 4]
44. ! [X0] : ((quiet(X0) | wise(X0) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | (~quiet(X0) & ~wise(X0)))) [flattening 43]
50. ! [X0] : (((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 33]
51. ! [X0] : (((calm(X0) & brave(X0)) | quiet(X0)) & (~quiet(X0) | (~calm(X0) | ~brave(X0)))) [nnf transformation 9]
52. ! [X0] : (((calm(X0) & brave(X0)) | quiet(X0)) & (~quiet(X0) | ~calm(X0) | ~brave(X0))) [flattening 51]
53. (? [X0] : ((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | ! [X1] : (~happy(X1) | curious(X1))) & (? [X1] : (happy(X1) & ~curious(X1)) | ! [X0] : ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) [nnf transformation 25]
54. (? [X0] : ((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | ! [X1] : (~happy(X1) | curious(X1))) & (? [X2] : (happy(X2) & ~curious(X2)) | ! [X3] : ((generous(X3) | old(X3)) & (~old(X3) | ~generous(X3)))) [rectify 53]
55. ? [X0] : ((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) => ((old(sK3) | ~generous(sK3)) & (~old(sK3) | generous(sK3))) [choice axiom]
56. ? [X2] : (happy(X2) & ~curious(X2)) => (happy(sK4) & ~curious(sK4)) [choice axiom]
57. (((old(sK3) | ~generous(sK3)) & (~old(sK3) | generous(sK3))) | ! [X1] : (~happy(X1) | curious(X1))) & ((happy(sK4) & ~curious(sK4)) | ! [X3] : ((generous(X3) | old(X3)) & (~old(X3) | ~generous(X3)))) [skolemisation 54,56,55]
59. ! [X0] : (((~calm(X0) | tall(X0)) | (~old(X0) | humble(X0))) & ((old(X0) & ~humble(X0)) | (calm(X0) & ~tall(X0)))) [nnf transformation 13]
60. ! [X0] : ((~calm(X0) | tall(X0) | ~old(X0) | humble(X0)) & ((old(X0) & ~humble(X0)) | (calm(X0) & ~tall(X0)))) [flattening 59]
70. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X0] : (patient(X0) & ~funny(X0))) [nnf transformation 16]
71. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [rectify 70]
72. ? [X0] : (~patient(X0) | funny(X0)) => (~patient(sK8) | funny(sK8)) [choice axiom]
73. ((~patient(sK8) | funny(sK8)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [skolemisation 71,72]
78. ~curious(X0) | wise(X0) | happy(X0) | ~calm(X0) [cnf transformation 28]
87. ~kind(X0) | ~generous(X0) | funny(X0) [cnf transformation 42]
90. ~wise(X0) | ~curious(X0) [cnf transformation 44]
93. ~quiet(X0) | brave(X0) [cnf transformation 44]
94. ~brave(X0) | wise(X0) | quiet(X0) | curious(X0) [cnf transformation 44]
104. happy(X0) | ~wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
105. happy(X0) | ~wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
106. ~happy(X0) | wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
107. ~happy(X0) | wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
108. ~quiet(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 52]
109. brave(X0) | quiet(X0) [cnf transformation 52]
115. ~old(sK3) | generous(sK3) | ~happy(X1) | curious(X1) [cnf transformation 57]
119. ~patient(X0) | kind(X0) [cnf transformation 35]
120. ~patient(X0) | old(X0) [cnf transformation 35]
122. ~humble(X0) | calm(X0) [cnf transformation 60]
134. happy(john) | wise(john) | ~funny(X1) [cnf transformation 73]
135. happy(john) | wise(john) | patient(X1) [cnf transformation 73]
136. ~happy(john) | ~wise(john) | ~funny(X1) [cnf transformation 73]
137. ~happy(john) | ~wise(john) | patient(X1) [cnf transformation 73]
147. humble(fred) [cnf transformation 22]
148. happy(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 104]
149. ~generous(X0) | ~wise(X0) | happy(X0) [duplicate literal removal 105]
150. ~happy(X0) | wise(X0) | generous(X0) [duplicate literal removal 106]
151. ~generous(X0) | wise(X0) | ~happy(X0) [duplicate literal removal 107]
163. 3 <=> ! [X1] : brave(X1) [avatar definition]
164. brave(X1) <- (3) [avatar component clause 163]
203. ~happy(X0) | wise(X0) [subsumption resolution 150,151]
204. ~wise(X0) | happy(X0) [subsumption resolution 148,149]
205. brave(X0) [subsumption resolution 109,93]
206. 3 [avatar split clause 205,163]
207. ~quiet(X0) | ~calm(X0) [subsumption resolution 108,93]
209. 12 <=> ! [X1] : (~happy(X1) | curious(X1)) [avatar definition]
210. ~happy(X1) | curious(X1) <- (12) [avatar component clause 209]
212. 13 <=> generous(sK3) [avatar definition]
213. generous(sK3) <- (13) [avatar component clause 212]
216. 14 <=> old(sK3) [avatar definition]
217. ~old(sK3) <- (~14) [avatar component clause 216]
220. 12 | 13 | ~14 [avatar split clause 115,216,212,209]
270. 25 <=> ! [X1] : old(X1) [avatar definition]
271. old(X1) <- (25) [avatar component clause 270]
285. ~wise(john) | patient(X1) [subsumption resolution 137,204]
287. 29 <=> ! [X1] : patient(X1) [avatar definition]
288. patient(X1) <- (29) [avatar component clause 287]
290. 30 <=> wise(john) [avatar definition]
293. 29 | ~30 [avatar split clause 285,290,287]
294. ~wise(john) | ~funny(X1) [subsumption resolution 136,204]
296. 31 <=> ! [X1] : ~funny(X1) [avatar definition]
297. ~funny(X1) <- (31) [avatar component clause 296]
298. 31 | ~30 [avatar split clause 294,290,296]
299. wise(john) | patient(X1) [subsumption resolution 135,203]
300. 29 | 30 [avatar split clause 299,290,287]
301. wise(john) | ~funny(X1) [subsumption resolution 134,203]
302. 31 | 30 [avatar split clause 301,290,296]
338. kind(X0) <- (29) [resolution 119,288]
339. old(X0) <- (29) [resolution 120,288]
340. 25 | ~29 [avatar split clause 339,287,270]
341. $false <- (~14, 25) [resolution 271,217]
344. 14 | ~25 [avatar contradiction clause 341]
346. calm(fred) [resolution 122,147]
358. ~generous(X0) | funny(X0) <- (29) [resolution 87,338]
360. ~generous(X0) <- (29, 31) [subsumption resolution 358,297]
365. $false <- (13, 29, 31) [resolution 360,213]
366. ~13 | ~29 | ~31 [avatar contradiction clause 365]
370. quiet(X0) | wise(X0) | curious(X0) <- (3) [resolution 94,164]
372. ~calm(X0) | curious(X0) | wise(X0) <- (3) [resolution 370,207]
390. curious(fred) | wise(fred) <- (3) [resolution 372,346]
401. 42 <=> wise(fred) [avatar definition]
402. ~wise(fred) <- (~42) [avatar component clause 401]
403. wise(fred) <- (42) [avatar component clause 401]
405. 43 <=> curious(fred) [avatar definition]
406. ~curious(fred) <- (~43) [avatar component clause 405]
407. curious(fred) <- (43) [avatar component clause 405]
408. 42 | 43 | ~3 [avatar split clause 390,163,405,401]
431. happy(fred) <- (42) [resolution 403,204]
433. ~curious(fred) <- (42) [resolution 403,90]
434. ~43 | ~42 [avatar split clause 433,401,405]
444. curious(fred) <- (12, 42) [resolution 431,210]
446. $false <- (12, 42, ~43) [subsumption resolution 444,406]
447. ~12 | ~42 | 43 [avatar contradiction clause 446]
449. wise(fred) | happy(fred) | ~calm(fred) <- (43) [resolution 407,78]
450. happy(fred) | ~calm(fred) <- (~42, 43) [subsumption resolution 449,402]
451. happy(fred) <- (~42, 43) [subsumption resolution 450,346]
459. wise(fred) <- (~42, 43) [resolution 451,203]
460. $false <- (~42, 43) [subsumption resolution 459,402]
461. 42 | ~43 [avatar contradiction clause 460]
462. $false [avatar sat refutation 206,220,293,298,300,302,340,344,366,408,434,447,461]
% SZS output end Proof for 5792642128876559975259145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not rich or curious then john is kind or tall and vice versa.
Everyone who is wise or kind is not tall or not kind and vice versa.
If fred is both not wise and not funny then mary is either not funny or not quiet and vice versa.
Everyone who is both rich and wise is either not rich or tall and vice versa.
Everyone who is both not quiet and not patient is not old.
Everyone who is not rich is both curious and not kind and vice versa.
Everyone who is either not strong or not quiet is either old or brave.
If someone is kind then susan is not quiet and vice versa.
If someone is patient then someone is either old or not humble and vice versa.
Everyone who is not funny or not patient is either strong or tall and vice versa.
If someone is not funny or not kind then someone is not patient or calm and vice versa.
If alice is either not rich or not tall then fred is both kind and not calm.
Everyone who is not patient or calm is both rich and not old.
Everyone who is happy is humble or not patient and vice versa.
Everyone who is not rich or not funny is not quiet or rich and vice versa.
Everyone who is either kind or wise is not strong or old.
Someone is kind.
Mary is either not quiet or not humble.
Alice is not quiet or creative.
Someone is either not humble or not funny.
Paul is both not curious and kind.
Someone is calm or patient.
Someone is not kind or strong. | Alice is quiet. | neutral | (((~rich(mary)|curious(mary)))<=>((kind(john)|tall(john))))&
(![X]:((wise(X)|kind(X))<=>(~tall(X)|~kind(X))))&
(((~wise(fred)&~funny(fred)))<=>((~funny(mary)<~>~quiet(mary))))&
(![X]:((rich(X)&wise(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((~quiet(X)&~patient(X))=>~old(X)))&
(![X]:(~rich(X)<=>(curious(X)&~kind(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>(old(X)<~>brave(X))))&
((?[X]:(kind(X)))<=>(~quiet(susan)))&
((?[X]:(patient(X)))<=>(?[X]:((old(X)<~>~humble(X)))))&
(![X]:((~funny(X)|~patient(X))<=>(strong(X)<~>tall(X))))&
((?[X]:((~funny(X)|~kind(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
(((~rich(alice)<~>~tall(alice)))=>((kind(fred)&~calm(fred))))&
(![X]:((~patient(X)|calm(X))=>(rich(X)&~old(X))))&
(![X]:(happy(X)<=>(humble(X)|~patient(X))))&
(![X]:((~rich(X)|~funny(X))<=>(~quiet(X)|rich(X))))&
(![X]:((kind(X)<~>wise(X))=>(~strong(X)|old(X))))&
(?[X]:(kind(X)))&
((~quiet(mary)<~>~humble(mary)))&
((~quiet(alice)|creative(alice)))&
(?[X]:((~humble(X)<~>~funny(X))))&
((~curious(paul)&kind(paul)))&
(?[X]:((calm(X)|patient(X))))&
(?[X]:((~kind(X)|strong(X)))) | quiet(alice) | [] | null | 0 |
If someone is both tall and creative then someone is both not old and strong. Everyone who is not calm is not rich or funny. If john is either not creative or not patient then someone is not rich and vice versa. Everyone who is either brave or not wise is either brave or not quiet. Everyone who is creative or tall is not tall. If lucy is curious then john is not curious or not humble. Everyone who is either brave or not humble is either quiet or tall. Everyone who is not funny or not brave is both brave and kind. Everyone who is not tall or not brave is both brave and not tall and vice versa. If someone is either kind or not calm then susan is both curious and rich and vice versa. If lucy is either not wise or funny then fred is not calm and vice versa. Everyone who is calm is both not creative and not quiet. Everyone who is both not curious and not humble is both not humble and not strong and vice versa. If someone is either not rich or calm then alice is either not happy or not patient. If lucy is both not calm and not quiet then susan is both not curious and strong and vice versa. If someone is not kind then someone is not curious. Someone is both creative and humble. Alice is funny or not tall. Someone is both not happy and humble. Someone is either not patient or tall. Alice is both strong and rich. Someone is not rich or happy. Fred is not strong or strong. | Susan is curious. | neutral | ((?[X]:((tall(X)&creative(X))))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(~calm(X)=>(~rich(X)|funny(X))))&
(((~creative(john)<~>~patient(john)))<=>(?[X]:(~rich(X))))&
(![X]:((brave(X)<~>~wise(X))=>(brave(X)<~>~quiet(X))))&
(![X]:((creative(X)|tall(X))=>~tall(X)))&
((curious(lucy))=>((~curious(john)|~humble(john))))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)<~>tall(X))))&
(![X]:((~funny(X)|~brave(X))=>(brave(X)&kind(X))))&
(![X]:((~tall(X)|~brave(X))<=>(brave(X)&~tall(X))))&
((?[X]:((kind(X)<~>~calm(X))))<=>((curious(susan)&rich(susan))))&
(((~wise(lucy)<~>funny(lucy)))<=>(~calm(fred)))&
(![X]:(calm(X)=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)&~humble(X))<=>(~humble(X)&~strong(X))))&
((?[X]:((~rich(X)<~>calm(X))))=>((~happy(alice)<~>~patient(alice))))&
(((~calm(lucy)&~quiet(lucy)))<=>((~curious(susan)&strong(susan))))&
((?[X]:(~kind(X)))=>(?[X]:(~curious(X))))&
(?[X]:((creative(X)&humble(X))))&
((funny(alice)|~tall(alice)))&
(?[X]:((~happy(X)&humble(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((strong(alice)&rich(alice)))&
(?[X]:((~rich(X)|happy(X))))&
((~strong(fred)|strong(fred))) | curious(susan) | [] | null | 0 |
Everyone who is not calm or not tall is calm or not funny.
Everyone who is funny or brave is not kind or not happy and vice versa.
Everyone who is either curious or rich is either not wise or not generous.
Everyone who is not calm or not patient is both not generous and wise.
If someone is old then susan is wise or not brave.
If someone is both funny and not rich then fred is either generous or kind and vice versa.
Everyone who is not rich is either not humble or not generous.
If john is either not humble or rich then mary is generous.
Everyone who is not curious or funny is kind or not curious and vice versa.
Everyone who is either not creative or not funny is not kind or tall and vice versa.
If lucy is either brave or not generous then someone is creative or calm and vice versa.
If paul is either not tall or not generous then someone is curious or brave and vice versa.
If susan is quiet then someone is not tall.
Everyone who is both kind and old is either not patient or not tall and vice versa.
If someone is wise or rich then someone is not wise or not tall and vice versa.
If someone is either not creative or not kind then john is brave or calm and vice versa.
Alice is either not quiet or not generous.
Someone is not creative.
Someone is either humble or kind.
Lucy is both happy and not calm.
Susan is kind.
Alice is wise or kind.
Someone is both not old and humble. | Susan is not brave. | neutral | (![X]:((~calm(X)|~tall(X))=>(calm(X)|~funny(X))))&
(![X]:((funny(X)|brave(X))<=>(~kind(X)|~happy(X))))&
(![X]:((curious(X)<~>rich(X))=>(~wise(X)<~>~generous(X))))&
(![X]:((~calm(X)|~patient(X))=>(~generous(X)&wise(X))))&
((?[X]:(old(X)))=>((wise(susan)|~brave(susan))))&
((?[X]:((funny(X)&~rich(X))))<=>((generous(fred)<~>kind(fred))))&
(![X]:(~rich(X)=>(~humble(X)<~>~generous(X))))&
(((~humble(john)<~>rich(john)))=>(generous(mary)))&
(![X]:((~curious(X)|funny(X))<=>(kind(X)|~curious(X))))&
(![X]:((~creative(X)<~>~funny(X))<=>(~kind(X)|tall(X))))&
(((brave(lucy)<~>~generous(lucy)))<=>(?[X]:((creative(X)|calm(X)))))&
(((~tall(paul)<~>~generous(paul)))<=>(?[X]:((curious(X)|brave(X)))))&
((quiet(susan))=>(?[X]:(~tall(X))))&
(![X]:((kind(X)&old(X))<=>(~patient(X)<~>~tall(X))))&
((?[X]:((wise(X)|rich(X))))<=>(?[X]:((~wise(X)|~tall(X)))))&
((?[X]:((~creative(X)<~>~kind(X))))<=>((brave(john)|calm(john))))&
((~quiet(alice)<~>~generous(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((humble(X)<~>kind(X))))&
((happy(lucy)&~calm(lucy)))&
(kind(susan))&
((wise(alice)|kind(alice)))&
(?[X]:((~old(X)&humble(X)))) | ~brave(susan) | [] | null | 0 |
If someone is either patient or not brave then alice is not patient. If someone is both not generous and not kind then someone is old or happy and vice versa. If someone is either not happy or calm then fred is both rich and not brave. Everyone who is generous is not tall or humble and vice versa. If mary is happy then someone is both not rich and brave and vice versa. Everyone who is both not humble and wise is both creative and quiet and vice versa. If someone is either brave or not rich then susan is both calm and not funny and vice versa. Everyone who is not funny is curious. If someone is either calm or patient then someone is not funny. Everyone who is not tall or old is not curious and vice versa. If someone is wise or not creative then someone is either not quiet or kind. If alice is both tall and generous then someone is either not happy or strong and vice versa. Everyone who is not happy is both not curious and not old. Everyone who is both not kind and rich is either not kind or patient and vice versa. If alice is either generous or not curious then someone is patient and vice versa. Everyone who is not old or not happy is wise. John is either not creative or curious. Someone is both humble and not brave. Someone is generous. Someone is brave or not calm. Someone is strong. Susan is generous or strong. Mary is generous. Mary is both not tall and calm. | Fred is brave. | contradiction | ((?[X]:((patient(X)<~>~brave(X))))=>(~patient(alice)))&
((?[X]:((~generous(X)&~kind(X))))<=>(?[X]:((old(X)|happy(X)))))&
((?[X]:((~happy(X)<~>calm(X))))=>((rich(fred)&~brave(fred))))&
(![X]:(generous(X)<=>(~tall(X)|humble(X))))&
((happy(mary))<=>(?[X]:((~rich(X)&brave(X)))))&
(![X]:((~humble(X)&wise(X))<=>(creative(X)&quiet(X))))&
((?[X]:((brave(X)<~>~rich(X))))<=>((calm(susan)&~funny(susan))))&
(![X]:(~funny(X)=>curious(X)))&
((?[X]:((calm(X)<~>patient(X))))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)|old(X))<=>~curious(X)))&
((?[X]:((wise(X)|~creative(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(((tall(alice)&generous(alice)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:(~happy(X)=>(~curious(X)&~old(X))))&
(![X]:((~kind(X)&rich(X))<=>(~kind(X)<~>patient(X))))&
(((generous(alice)<~>~curious(alice)))<=>(?[X]:(patient(X))))&
(![X]:((~old(X)|~happy(X))=>wise(X)))&
((~creative(john)<~>curious(john)))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:(generous(X)))&
(?[X]:((brave(X)|~calm(X))))&
(?[X]:(strong(X)))&
((generous(susan)|strong(susan)))&
(generous(mary))&
((~tall(mary)&calm(mary))) | brave(fred) | [
"p2",
"p4",
"p6",
"p7",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1003013059901348693413900
% SZS output start Proof for 1003013059901348693413900
3. ? [X0] : (~happy(X0) <~> calm(X0)) => (~brave(fred) & rich(fred)) [input p2]
5. happy(mary) <=> ? [X0] : (brave(X0) & ~rich(X0)) [input p4]
7. ? [X0] : (brave(X0) <~> ~rich(X0)) <=> (~funny(susan) & calm(susan)) [input p6]
8. ! [X0] : (~funny(X0) => curious(X0)) [input p7]
13. ! [X0] : (~happy(X0) => (~old(X0) & ~curious(X0))) [input p12]
24. calm(mary) & ~tall(mary) [input p23]
25. brave(fred) [input hypothesis]
30. (~brave(fred) & rich(fred)) | ! [X0] : (~happy(X0) <=> calm(X0)) [ennf transformation 3]
31. ! [X0] : (curious(X0) | funny(X0)) [ennf transformation 8]
34. ! [X0] : ((~old(X0) & ~curious(X0)) | happy(X0)) [ennf transformation 13]
42. (~brave(fred) & rich(fred)) | ! [X0] : ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))) [nnf transformation 30]
45. (happy(mary) | ! [X0] : (~brave(X0) | rich(X0))) & (? [X0] : (brave(X0) & ~rich(X0)) | ~happy(mary)) [nnf transformation 5]
46. (happy(mary) | ! [X0] : (~brave(X0) | rich(X0))) & (? [X1] : (brave(X1) & ~rich(X1)) | ~happy(mary)) [rectify 45]
47. ? [X1] : (brave(X1) & ~rich(X1)) => (brave(sK2) & ~rich(sK2)) [choice axiom]
48. (happy(mary) | ! [X0] : (~brave(X0) | rich(X0))) & ((brave(sK2) & ~rich(sK2)) | ~happy(mary)) [skolemisation 46,47]
51. (? [X0] : ((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | (funny(susan) | ~calm(susan))) & ((~funny(susan) & calm(susan)) | ! [X0] : ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) [nnf transformation 7]
52. (? [X0] : ((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | funny(susan) | ~calm(susan)) & ((~funny(susan) & calm(susan)) | ! [X0] : ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) [flattening 51]
53. (? [X0] : ((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | funny(susan) | ~calm(susan)) & ((~funny(susan) & calm(susan)) | ! [X1] : ((brave(X1) | rich(X1)) & (~rich(X1) | ~brave(X1)))) [rectify 52]
54. ? [X0] : ((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) => ((rich(sK3) | ~brave(sK3)) & (~rich(sK3) | brave(sK3))) [choice axiom]
55. (((rich(sK3) | ~brave(sK3)) & (~rich(sK3) | brave(sK3))) | funny(susan) | ~calm(susan)) & ((~funny(susan) & calm(susan)) | ! [X1] : ((brave(X1) | rich(X1)) & (~rich(X1) | ~brave(X1)))) [skolemisation 53,54]
96. ~brave(fred) | ~happy(X0) | ~calm(X0) [cnf transformation 42]
102. happy(mary) | ~brave(X0) | rich(X0) [cnf transformation 48]
107. calm(susan) | ~rich(X1) | ~brave(X1) [cnf transformation 55]
109. ~funny(susan) | ~rich(X1) | ~brave(X1) [cnf transformation 55]
113. curious(X0) | funny(X0) [cnf transformation 31]
129. ~curious(X0) | happy(X0) [cnf transformation 34]
153. calm(mary) [cnf transformation 24]
154. brave(fred) [cnf transformation 25]
200. 11 <=> ! [X0] : (~happy(X0) | ~calm(X0)) [avatar definition]
201. ~calm(X0) | ~happy(X0) <- (11) [avatar component clause 200]
203. 12 <=> brave(fred) [avatar definition]
204. brave(fred) <- (12) [avatar component clause 203]
206. 11 | ~12 [avatar split clause 96,203,200]
218. 15 <=> ! [X0] : (~brave(X0) | rich(X0)) [avatar definition]
219. ~brave(X0) | rich(X0) <- (15) [avatar component clause 218]
221. 16 <=> happy(mary) [avatar definition]
224. 15 | 16 [avatar split clause 102,221,218]
236. 19 <=> calm(susan) [avatar definition]
237. calm(susan) <- (19) [avatar component clause 236]
240. 20 <=> funny(susan) [avatar definition]
241. ~funny(susan) <- (~20) [avatar component clause 240]
258. 24 <=> ! [X1] : (~rich(X1) | ~brave(X1)) [avatar definition]
259. ~rich(X1) | ~brave(X1) <- (24) [avatar component clause 258]
260. 24 | ~20 [avatar split clause 109,240,258]
262. 24 | 19 [avatar split clause 107,236,258]
365. 12 [avatar split clause 154,203]
373. funny(X0) | happy(X0) [resolution 129,113]
380. ~happy(mary) <- (11) [resolution 201,153]
441. ~brave(X1) <- (15, 24) [subsumption resolution 259,219]
443. $false <- (12, 15, 24) [resolution 441,204]
446. ~12 | ~15 | ~24 [avatar contradiction clause 443]
449. ~16 | ~11 [avatar split clause 380,200,221]
462. ~happy(susan) <- (11, 19) [resolution 237,201]
512. happy(susan) <- (~20) [resolution 373,241]
513. $false <- (11, 19, ~20) [subsumption resolution 512,462]
514. ~11 | ~19 | 20 [avatar contradiction clause 513]
515. $false [avatar sat refutation 206,224,260,262,365,446,449,514]
% SZS output end Proof for 1003013059901348693413900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not curious is not calm and vice versa.
Everyone who is not generous is rich and vice versa.
If susan is either not wise or not kind then lucy is both brave and rich.
If susan is either generous or not strong then fred is not tall or happy and vice versa.
Everyone who is not generous is calm.
If someone is either generous or rich then someone is either not funny or not humble and vice versa.
Everyone who is either rich or not curious is both not patient and generous.
If susan is brave or quiet then someone is either not tall or not humble and vice versa.
Everyone who is either not rich or rich is both not happy and not creative.
If someone is not tall or humble then someone is funny or not calm and vice versa.
Everyone who is both funny and creative is both not humble and brave and vice versa.
Everyone who is not brave is either funny or humble.
If paul is both not happy and not wise then fred is kind and vice versa.
Everyone who is both not curious and old is either not calm or humble and vice versa.
Everyone who is either generous or old is happy or not happy and vice versa.
Everyone who is brave is quiet or kind and vice versa.
Someone is rich or not rich.
Someone is either brave or kind.
Lucy is both not patient and not generous.
Someone is not creative or not funny.
Someone is either not creative or quiet.
Someone is either not wise or not strong.
Fred is not patient or not old.
Someone is strong or not generous. | Lucy is humble. | entailment | (![X]:((~strong(X)<~>~curious(X))<=>~calm(X)))&
(![X]:(~generous(X)<=>rich(X)))&
(((~wise(susan)<~>~kind(susan)))=>((brave(lucy)&rich(lucy))))&
(((generous(susan)<~>~strong(susan)))<=>((~tall(fred)|happy(fred))))&
(![X]:(~generous(X)=>calm(X)))&
((?[X]:((generous(X)<~>rich(X))))<=>(?[X]:((~funny(X)<~>~humble(X)))))&
(![X]:((rich(X)<~>~curious(X))=>(~patient(X)&generous(X))))&
(((brave(susan)|quiet(susan)))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((~rich(X)<~>rich(X))=>(~happy(X)&~creative(X))))&
((?[X]:((~tall(X)|humble(X))))<=>(?[X]:((funny(X)|~calm(X)))))&
(![X]:((funny(X)&creative(X))<=>(~humble(X)&brave(X))))&
(![X]:(~brave(X)=>(funny(X)<~>humble(X))))&
(((~happy(paul)&~wise(paul)))<=>(kind(fred)))&
(![X]:((~curious(X)&old(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((generous(X)<~>old(X))<=>(happy(X)|~happy(X))))&
(![X]:(brave(X)<=>(quiet(X)|kind(X))))&
(?[X]:((rich(X)|~rich(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((~patient(lucy)&~generous(lucy)))&
(?[X]:((~creative(X)|~funny(X))))&
(?[X]:((~creative(X)<~>quiet(X))))&
(?[X]:((~wise(X)<~>~strong(X))))&
((~patient(fred)|~old(fred)))&
(?[X]:((strong(X)|~generous(X)))) | humble(lucy) | [
"p1",
"p4",
"p6",
"p8",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7369216845065421957696536
% SZS output start Proof for 7369216845065421957696536
2. ! [X0] : (~generous(X0) <=> rich(X0)) [input p1]
5. ! [X0] : (~generous(X0) => calm(X0)) [input p4]
7. ! [X0] : ((rich(X0) <~> ~curious(X0)) => (generous(X0) & ~patient(X0))) [input p6]
9. ! [X0] : ((~rich(X0) <~> rich(X0)) => (~creative(X0) & ~happy(X0))) [input p8]
14. ! [X0] : ((old(X0) & ~curious(X0)) <=> (~calm(X0) <~> humble(X0))) [input p13]
15. ! [X0] : ((generous(X0) <~> old(X0)) <=> (~happy(X0) | happy(X0))) [input p14]
19. ~generous(lucy) & ~patient(lucy) [input p18]
25. ~humble(lucy) [input hypothesis]
28. ~generous(lucy) [pure predicate removal 19]
29. ! [X0] : ((rich(X0) <~> ~curious(X0)) => generous(X0)) [pure predicate removal 7]
32. ! [X0] : (calm(X0) | generous(X0)) [ennf transformation 5]
33. ! [X0] : (generous(X0) | (rich(X0) <=> ~curious(X0))) [ennf transformation 29]
34. ! [X0] : ((~creative(X0) & ~happy(X0)) | (~rich(X0) <=> rich(X0))) [ennf transformation 9]
37. ! [X0] : ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0))) [nnf transformation 2]
46. ! [X0] : (generous(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) [nnf transformation 33]
52. ! [X0] : ((~creative(X0) & ~happy(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) [nnf transformation 34]
63. ! [X0] : (((old(X0) & ~curious(X0)) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | (~old(X0) | curious(X0)))) [nnf transformation 14]
64. ! [X0] : (((old(X0) & ~curious(X0)) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | ~old(X0) | curious(X0))) [flattening 63]
65. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [nnf transformation 15]
66. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [flattening 65]
88. rich(X0) | generous(X0) [cnf transformation 37]
89. ~rich(X0) | ~generous(X0) [cnf transformation 37]
100. generous(X0) | calm(X0) [cnf transformation 32]
109. generous(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 46]
117. ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 52]
118. ~happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 52]
134. ~old(X0) | ~calm(X0) | humble(X0) | curious(X0) [cnf transformation 64]
143. old(X0) | generous(X0) | happy(X0) [cnf transformation 66]
152. ~generous(lucy) [cnf transformation 28]
159. ~humble(lucy) [cnf transformation 25]
160. ~happy(X0) | rich(X0) [duplicate literal removal 117]
161. ~happy(X0) | ~rich(X0) [duplicate literal removal 118]
228. ~rich(X0) | ~curious(X0) [subsumption resolution 109,89]
258. ~happy(X0) [subsumption resolution 160,161]
305. old(X0) | generous(X0) [subsumption resolution 143,258]
333. ~curious(X0) | generous(X0) [resolution 228,88]
436. ~calm(X1) | humble(X1) | curious(X1) | generous(X1) [resolution 134,305]
438. humble(X1) | curious(X1) | generous(X1) [subsumption resolution 436,100]
439. humble(X1) | generous(X1) [subsumption resolution 438,333]
466. generous(lucy) [resolution 439,159]
472. $false [subsumption resolution 466,152]
% SZS output end Proof for 7369216845065421957696536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is happy or old then someone is creative. Everyone who is not brave is curious or not brave. If someone is creative or brave then alice is both tall and not funny. Everyone who is both brave and old is either not humble or not happy and vice versa. Everyone who is not old is both tall and kind and vice versa. Everyone who is both not calm and creative is either kind or not old and vice versa. Everyone who is either wise or generous is patient. Everyone who is humble or calm is both calm and not quiet. If mary is tall then someone is not tall or not brave and vice versa. If someone is both calm and not old then paul is strong and vice versa. Everyone who is both calm and not old is not curious. If someone is wise then someone is both not calm and not brave and vice versa. Everyone who is generous or rich is calm and vice versa. Everyone who is both not calm and happy is not quiet or happy and vice versa. If lucy is either not quiet or old then john is either not creative or not old and vice versa. Everyone who is both not strong and kind is not patient. Someone is not generous or patient. Mary is both not rich and not quiet. Someone is creative or not tall. Someone is either happy or generous. Someone is both not funny and wise. Lucy is not funny or not kind. Someone is either not tall or patient. | John is not humble. | entailment | (((happy(john)|old(john)))=>(?[X]:(creative(X))))&
(![X]:(~brave(X)=>(curious(X)|~brave(X))))&
((?[X]:((creative(X)|brave(X))))=>((tall(alice)&~funny(alice))))&
(![X]:((brave(X)&old(X))<=>(~humble(X)<~>~happy(X))))&
(![X]:(~old(X)<=>(tall(X)&kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(kind(X)<~>~old(X))))&
(![X]:((wise(X)<~>generous(X))=>patient(X)))&
(![X]:((humble(X)|calm(X))=>(calm(X)&~quiet(X))))&
((tall(mary))<=>(?[X]:((~tall(X)|~brave(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(strong(paul)))&
(![X]:((calm(X)&~old(X))=>~curious(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((generous(X)|rich(X))<=>calm(X)))&
(![X]:((~calm(X)&happy(X))<=>(~quiet(X)|happy(X))))&
(((~quiet(lucy)<~>old(lucy)))<=>((~creative(john)<~>~old(john))))&
(![X]:((~strong(X)&kind(X))=>~patient(X)))&
(?[X]:((~generous(X)|patient(X))))&
((~rich(mary)&~quiet(mary)))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:((~funny(X)&wise(X))))&
((~funny(lucy)|~kind(lucy)))&
(?[X]:((~tall(X)<~>patient(X)))) | ~humble(john) | [
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8495955329722006273335760
% SZS output start Proof for 8495955329722006273335760
8. ! [X0] : ((calm(X0) | humble(X0)) => (~quiet(X0) & calm(X0))) [input p7]
14. ! [X0] : ((happy(X0) & ~calm(X0)) <=> (happy(X0) | ~quiet(X0))) [input p13]
24. humble(john) [input hypothesis]
34. ! [X0] : ((~quiet(X0) & calm(X0)) | (~calm(X0) & ~humble(X0))) [ennf transformation 8]
63. ! [X0] : (((happy(X0) & ~calm(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~happy(X0) | calm(X0)))) [nnf transformation 14]
64. ! [X0] : (((happy(X0) & ~calm(X0)) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~happy(X0) | calm(X0))) [flattening 63]
100. ~humble(X0) | calm(X0) [cnf transformation 34]
103. ~quiet(X0) | ~calm(X0) [cnf transformation 34]
118. ~calm(X0) | quiet(X0) [cnf transformation 64]
140. humble(john) [cnf transformation 24]
229. ~calm(X0) [subsumption resolution 118,103]
299. calm(john) [resolution 100,140]
300. $false [subsumption resolution 299,229]
% SZS output end Proof for 8495955329722006273335760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or curious is both brave and not patient.
Everyone who is not happy is either not strong or not funny and vice versa.
Everyone who is kind or not rich is not strong and vice versa.
Everyone who is both curious and not curious is quiet or not funny.
If someone is not patient then mary is not patient and vice versa.
If john is strong then mary is generous or creative and vice versa.
If lucy is tall then paul is both not patient and brave and vice versa.
If someone is not creative then paul is both not curious and wise.
Everyone who is wise or not curious is both not rich and generous and vice versa.
If someone is either not kind or not patient then someone is either not funny or not calm and vice versa.
If fred is not tall or not humble then someone is creative or quiet and vice versa.
If lucy is not kind or happy then someone is both funny and brave and vice versa.
Everyone who is not happy is kind and vice versa.
If john is calm or not tall then someone is either not curious or not creative and vice versa.
Everyone who is either not wise or wise is not tall and vice versa.
If john is both not curious and not humble then john is tall or humble and vice versa.
Someone is either not patient or not curious.
Someone is not calm.
Lucy is kind.
Fred is either not kind or not quiet.
Lucy is either creative or patient.
Someone is humble.
Fred is both generous and quiet. | Fred is not strong. | entailment | (![X]:((quiet(X)|curious(X))=>(brave(X)&~patient(X))))&
(![X]:(~happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((kind(X)|~rich(X))<=>~strong(X)))&
(![X]:((curious(X)&~curious(X))=>(quiet(X)|~funny(X))))&
((?[X]:(~patient(X)))<=>(~patient(mary)))&
((strong(john))<=>((generous(mary)|creative(mary))))&
((tall(lucy))<=>((~patient(paul)&brave(paul))))&
((?[X]:(~creative(X)))=>((~curious(paul)&wise(paul))))&
(![X]:((wise(X)|~curious(X))<=>(~rich(X)&generous(X))))&
((?[X]:((~kind(X)<~>~patient(X))))<=>(?[X]:((~funny(X)<~>~calm(X)))))&
(((~tall(fred)|~humble(fred)))<=>(?[X]:((creative(X)|quiet(X)))))&
(((~kind(lucy)|happy(lucy)))<=>(?[X]:((funny(X)&brave(X)))))&
(![X]:(~happy(X)<=>kind(X)))&
(((calm(john)|~tall(john)))<=>(?[X]:((~curious(X)<~>~creative(X)))))&
(![X]:((~wise(X)<~>wise(X))<=>~tall(X)))&
(((~curious(john)&~humble(john)))<=>((tall(john)|humble(john))))&
(?[X]:((~patient(X)<~>~curious(X))))&
(?[X]:(~calm(X)))&
(kind(lucy))&
((~kind(fred)<~>~quiet(fred)))&
((creative(lucy)<~>patient(lucy)))&
(?[X]:(humble(X)))&
((generous(fred)&quiet(fred))) | ~strong(fred) | [
"p0",
"p1",
"p11",
"p12",
"p18",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7315129975366846271239661
% SZS output start Proof for 7315129975366846271239661
1. ! [X0] : ((curious(X0) | quiet(X0)) => (~patient(X0) & brave(X0))) [input p0]
2. ! [X0] : (~happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p1]
12. (happy(lucy) | ~kind(lucy)) <=> ? [X0] : (brave(X0) & funny(X0)) [input p11]
13. ! [X0] : (~happy(X0) <=> kind(X0)) [input p12]
19. kind(lucy) [input p18]
20. ~kind(fred) <~> ~quiet(fred) [input p19]
23. quiet(fred) & generous(fred) [input p22]
24. strong(fred) [input hypothesis]
26. ! [X0] : ((~patient(X0) & brave(X0)) | (~curious(X0) & ~quiet(X0))) [ennf transformation 1]
30. ! [X0] : ((~happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | happy(X0))) [nnf transformation 2]
53. ((happy(lucy) | ~kind(lucy)) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X0] : (brave(X0) & funny(X0)) | (~happy(lucy) & kind(lucy))) [nnf transformation 12]
54. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X0] : (brave(X0) & funny(X0)) | (~happy(lucy) & kind(lucy))) [flattening 53]
55. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X1] : (brave(X1) & funny(X1)) | (~happy(lucy) & kind(lucy))) [rectify 54]
56. ? [X1] : (brave(X1) & funny(X1)) => (brave(sK4) & funny(sK4)) [choice axiom]
57. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & ((brave(sK4) & funny(sK4)) | (~happy(lucy) & kind(lucy))) [skolemisation 55,56]
58. ! [X0] : ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))) [nnf transformation 13]
72. (quiet(fred) | kind(fred)) & (~quiet(fred) | ~kind(fred)) [nnf transformation 20]
76. ~quiet(X0) | brave(X0) [cnf transformation 26]
83. ~strong(X0) | ~happy(X0) | funny(X0) [cnf transformation 30]
119. happy(lucy) | ~kind(lucy) | ~brave(X0) | ~funny(X0) [cnf transformation 57]
120. kind(X0) | happy(X0) [cnf transformation 58]
121. ~kind(X0) | ~happy(X0) [cnf transformation 58]
140. kind(lucy) [cnf transformation 19]
141. ~quiet(fred) | ~kind(fred) [cnf transformation 72]
147. quiet(fred) [cnf transformation 23]
148. strong(fred) [cnf transformation 24]
272. 27 <=> ! [X0] : (~brave(X0) | ~funny(X0)) [avatar definition]
273. ~funny(X0) | ~brave(X0) <- (27) [avatar component clause 272]
275. 28 <=> kind(lucy) [avatar definition]
276. kind(lucy) <- (28) [avatar component clause 275]
279. 29 <=> happy(lucy) [avatar definition]
282. 27 | ~28 | 29 [avatar split clause 119,279,275,272]
335. 28 [avatar split clause 140,275]
337. 40 <=> kind(fred) [avatar definition]
338. ~kind(fred) <- (~40) [avatar component clause 337]
341. 41 <=> quiet(fred) [avatar definition]
343. quiet(fred) <- (41) [avatar component clause 341]
345. ~40 | ~41 [avatar split clause 141,341,337]
356. 41 [avatar split clause 147,341]
367. brave(fred) <- (41) [resolution 76,343]
380. happy(fred) <- (~40) [resolution 120,338]
383. ~happy(lucy) <- (28) [resolution 121,276]
417. ~happy(fred) | funny(fred) [resolution 83,148]
418. funny(fred) <- (~40) [subsumption resolution 417,380]
421. ~brave(fred) <- (27, ~40) [resolution 418,273]
422. $false <- (27, ~40, 41) [subsumption resolution 421,367]
423. ~27 | 40 | ~41 [avatar contradiction clause 422]
424. ~29 | ~28 [avatar split clause 383,275,279]
425. $false [avatar sat refutation 282,335,345,356,423,424]
% SZS output end Proof for 7315129975366846271239661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or quiet then susan is either calm or not humble. Everyone who is not calm is either not creative or not rich and vice versa. If someone is not humble or not patient then someone is not rich and vice versa. Everyone who is generous is not humble and vice versa. Everyone who is strong is not strong or not wise and vice versa. If mary is either not strong or quiet then someone is strong or not wise. If john is both not wise and curious then someone is either creative or strong. If lucy is either happy or not calm then someone is not brave or not rich. If paul is both not old and calm then paul is not creative or not tall and vice versa. If susan is not wise then alice is not happy or wise and vice versa. Everyone who is both not patient and not funny is either brave or not creative and vice versa. Everyone who is quiet is not humble and vice versa. If susan is not old then someone is not patient or not tall. Everyone who is both calm and not brave is both not happy and humble and vice versa. Everyone who is curious is both not tall and curious. Fred is both calm and curious. John is both brave and humble. Lucy is not quiet. Susan is both not funny and not humble. Paul is either not rich or wise. Paul is both not calm and not funny. Lucy is both rich and creative. John is both humble and not curious. | Paul is not wise. | entailment | ((?[X]:((~curious(X)<~>quiet(X))))=>((calm(susan)<~>~humble(susan))))&
(![X]:(~calm(X)<=>(~creative(X)<~>~rich(X))))&
((?[X]:((~humble(X)|~patient(X))))<=>(?[X]:(~rich(X))))&
(![X]:(generous(X)<=>~humble(X)))&
(![X]:(strong(X)<=>(~strong(X)|~wise(X))))&
(((~strong(mary)<~>quiet(mary)))=>(?[X]:((strong(X)|~wise(X)))))&
(((~wise(john)&curious(john)))=>(?[X]:((creative(X)<~>strong(X)))))&
(((happy(lucy)<~>~calm(lucy)))=>(?[X]:((~brave(X)|~rich(X)))))&
(((~old(paul)&calm(paul)))<=>((~creative(paul)|~tall(paul))))&
((~wise(susan))<=>((~happy(alice)|wise(alice))))&
(![X]:((~patient(X)&~funny(X))<=>(brave(X)<~>~creative(X))))&
(![X]:(quiet(X)<=>~humble(X)))&
((~old(susan))=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:((calm(X)&~brave(X))<=>(~happy(X)&humble(X))))&
(![X]:(curious(X)=>(~tall(X)&curious(X))))&
((calm(fred)&curious(fred)))&
((brave(john)&humble(john)))&
(~quiet(lucy))&
((~funny(susan)&~humble(susan)))&
((~rich(paul)<~>wise(paul)))&
((~calm(paul)&~funny(paul)))&
((rich(lucy)&creative(lucy)))&
((humble(john)&~curious(john))) | ~wise(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3150109795916716860611771
% SZS output start Proof for 3150109795916716860611771
5. ! [X0] : (strong(X0) <=> (~wise(X0) | ~strong(X0))) [input p4]
24. wise(paul) [input hypothesis]
40. ! [X0] : ((strong(X0) | (wise(X0) & strong(X0))) & ((~wise(X0) | ~strong(X0)) | ~strong(X0))) [nnf transformation 5]
41. ! [X0] : ((strong(X0) | (wise(X0) & strong(X0))) & (~wise(X0) | ~strong(X0) | ~strong(X0))) [flattening 40]
74. ~wise(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 41]
75. strong(X0) | strong(X0) [cnf transformation 41]
121. wise(paul) [cnf transformation 24]
122. ~wise(X0) | ~strong(X0) [duplicate literal removal 74]
123. strong(X0) [duplicate literal removal 75]
166. ~wise(X0) [subsumption resolution 122,123]
236. $false [subsumption resolution 121,166]
% SZS output end Proof for 3150109795916716860611771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is both tall and not happy.
Everyone who is either quiet or not strong is both happy and not old.
Everyone who is both not strong and not humble is not brave or not patient and vice versa.
If john is not curious then someone is quiet.
If fred is either tall or curious then lucy is either not curious or patient and vice versa.
If someone is both not generous and not calm then someone is not curious or not rich and vice versa.
If someone is either not kind or strong then someone is both quiet and not kind and vice versa.
Everyone who is not old is both old and not curious.
Everyone who is kind is either not curious or not funny and vice versa.
If lucy is tall or humble then fred is either not brave or not funny and vice versa.
If fred is both not creative and happy then someone is either brave or humble and vice versa.
If someone is both not brave and not happy then mary is patient.
If fred is not funny then susan is not curious.
If someone is both not calm and patient then fred is both not old and funny and vice versa.
Everyone who is either quiet or not rich is either not tall or not creative and vice versa.
Everyone who is either happy or generous is not creative or tall.
Mary is happy.
Someone is both not rich and tall.
Someone is not strong or old.
Mary is either strong or rich.
Someone is either curious or kind.
Mary is either calm or not brave.
Paul is patient. | Lucy is humble. | neutral | (![X]:(quiet(X)=>(tall(X)&~happy(X))))&
(![X]:((quiet(X)<~>~strong(X))=>(happy(X)&~old(X))))&
(![X]:((~strong(X)&~humble(X))<=>(~brave(X)|~patient(X))))&
((~curious(john))=>(?[X]:(quiet(X))))&
(((tall(fred)<~>curious(fred)))<=>((~curious(lucy)<~>patient(lucy))))&
((?[X]:((~generous(X)&~calm(X))))<=>(?[X]:((~curious(X)|~rich(X)))))&
((?[X]:((~kind(X)<~>strong(X))))<=>(?[X]:((quiet(X)&~kind(X)))))&
(![X]:(~old(X)=>(old(X)&~curious(X))))&
(![X]:(kind(X)<=>(~curious(X)<~>~funny(X))))&
(((tall(lucy)|humble(lucy)))<=>((~brave(fred)<~>~funny(fred))))&
(((~creative(fred)&happy(fred)))<=>(?[X]:((brave(X)<~>humble(X)))))&
((?[X]:((~brave(X)&~happy(X))))=>(patient(mary)))&
((~funny(fred))=>(~curious(susan)))&
((?[X]:((~calm(X)&patient(X))))<=>((~old(fred)&funny(fred))))&
(![X]:((quiet(X)<~>~rich(X))<=>(~tall(X)<~>~creative(X))))&
(![X]:((happy(X)<~>generous(X))=>(~creative(X)|tall(X))))&
(happy(mary))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((~strong(X)|old(X))))&
((strong(mary)<~>rich(mary)))&
(?[X]:((curious(X)<~>kind(X))))&
((calm(mary)<~>~brave(mary)))&
(patient(paul)) | humble(lucy) | [] | null | 0 |
Everyone who is either rich or curious is calm.
Everyone who is not happy or tall is either not strong or rich and vice versa.
If paul is both wise and not creative then alice is either not tall or not brave and vice versa.
Everyone who is not old is generous or not tall and vice versa.
Everyone who is both not wise and not happy is brave and vice versa.
Everyone who is not humble or not happy is not generous or rich and vice versa.
If fred is not rich or not happy then someone is either quiet or patient and vice versa.
Everyone who is either kind or old is tall or not curious.
If someone is both not curious and not calm then someone is either wise or funny.
Everyone who is not brave is not wise.
Everyone who is both quiet and not brave is either not brave or not tall.
Everyone who is funny or not brave is tall and vice versa.
Everyone who is either old or humble is not brave and vice versa.
If someone is not patient or humble then someone is calm or strong and vice versa.
If someone is either tall or patient then fred is not patient and vice versa.
If lucy is either not funny or not quiet then alice is either quiet or tall.
Someone is not wise or brave.
Someone is either not calm or not strong.
Alice is not quiet or not rich.
Lucy is either not quiet or not kind.
Someone is not brave.
Paul is both quiet and kind.
Someone is not curious.
Susan is either not quiet or funny. | Lucy is not curious. | neutral | (![X]:((rich(X)<~>curious(X))=>calm(X)))&
(![X]:((~happy(X)|tall(X))<=>(~strong(X)<~>rich(X))))&
(((wise(paul)&~creative(paul)))<=>((~tall(alice)<~>~brave(alice))))&
(![X]:(~old(X)<=>(generous(X)|~tall(X))))&
(![X]:((~wise(X)&~happy(X))<=>brave(X)))&
(![X]:((~humble(X)|~happy(X))<=>(~generous(X)|rich(X))))&
(((~rich(fred)|~happy(fred)))<=>(?[X]:((quiet(X)<~>patient(X)))))&
(![X]:((kind(X)<~>old(X))=>(tall(X)|~curious(X))))&
((?[X]:((~curious(X)&~calm(X))))=>(?[X]:((wise(X)<~>funny(X)))))&
(![X]:(~brave(X)=>~wise(X)))&
(![X]:((quiet(X)&~brave(X))=>(~brave(X)<~>~tall(X))))&
(![X]:((funny(X)|~brave(X))<=>tall(X)))&
(![X]:((old(X)<~>humble(X))<=>~brave(X)))&
((?[X]:((~patient(X)|humble(X))))<=>(?[X]:((calm(X)|strong(X)))))&
((?[X]:((tall(X)<~>patient(X))))<=>(~patient(fred)))&
(((~funny(lucy)<~>~quiet(lucy)))=>((quiet(alice)<~>tall(alice))))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:((~calm(X)<~>~strong(X))))&
((~quiet(alice)|~rich(alice)))&
((~quiet(lucy)<~>~kind(lucy)))&
(?[X]:(~brave(X)))&
((quiet(paul)&kind(paul)))&
(?[X]:(~curious(X)))&
((~quiet(susan)<~>funny(susan))) | ~curious(lucy) | [] | null | 0 |
Everyone who is both not calm and old is not old and vice versa.
Everyone who is both curious and not wise is either strong or not funny and vice versa.
Everyone who is both funny and not strong is both rich and not happy and vice versa.
If someone is not old or not quiet then susan is wise or not funny.
Everyone who is both not wise and not generous is happy or not tall and vice versa.
Everyone who is both quiet and not kind is both funny and not quiet.
Everyone who is wise is strong or not funny and vice versa.
Everyone who is tall or not creative is generous and vice versa.
If alice is both patient and not kind then someone is not happy or not rich and vice versa.
If someone is not wise or not patient then someone is generous and vice versa.
Everyone who is curious is not tall or not wise and vice versa.
Everyone who is kind or calm is both humble and not funny and vice versa.
If someone is either not tall or not creative then someone is both not creative and quiet and vice versa.
If alice is either happy or not kind then someone is either tall or quiet.
If susan is both not curious and old then someone is either wise or not kind and vice versa.
Everyone who is not patient is both not curious and not funny.
Someone is not quiet.
Someone is either not brave or funny.
Someone is either not brave or not curious.
Susan is either not creative or not kind.
Alice is creative or not funny. | Alice is not curious. | entailment | (![X]:((~calm(X)&old(X))<=>~old(X)))&
(![X]:((curious(X)&~wise(X))<=>(strong(X)<~>~funny(X))))&
(![X]:((funny(X)&~strong(X))<=>(rich(X)&~happy(X))))&
((?[X]:((~old(X)|~quiet(X))))=>((wise(susan)|~funny(susan))))&
(![X]:((~wise(X)&~generous(X))<=>(happy(X)|~tall(X))))&
(![X]:((quiet(X)&~kind(X))=>(funny(X)&~quiet(X))))&
(![X]:(wise(X)<=>(strong(X)|~funny(X))))&
(![X]:((tall(X)|~creative(X))<=>generous(X)))&
(((patient(alice)&~kind(alice)))<=>(?[X]:((~happy(X)|~rich(X)))))&
((?[X]:((~wise(X)|~patient(X))))<=>(?[X]:(generous(X))))&
(![X]:(curious(X)<=>(~tall(X)|~wise(X))))&
(![X]:((kind(X)|calm(X))<=>(humble(X)&~funny(X))))&
((?[X]:((~tall(X)<~>~creative(X))))<=>(?[X]:((~creative(X)&quiet(X)))))&
(((happy(alice)<~>~kind(alice)))=>(?[X]:((tall(X)<~>quiet(X)))))&
(((~curious(susan)&old(susan)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:(~patient(X)=>(~curious(X)&~funny(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:((~brave(X)<~>~curious(X))))&
((~creative(susan)<~>~kind(susan)))&
((creative(alice)|~funny(alice))) | ~curious(alice) | [
"p0",
"p4",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7367178701604253271136602
% SZS output start Proof for 7367178701604253271136602
1. ! [X0] : ((old(X0) & ~calm(X0)) <=> ~old(X0)) [input p0]
5. ! [X0] : ((~generous(X0) & ~wise(X0)) <=> (~tall(X0) | happy(X0))) [input p4]
7. ! [X0] : (wise(X0) <=> (~funny(X0) | strong(X0))) [input p6]
11. ! [X0] : (curious(X0) <=> (~wise(X0) | ~tall(X0))) [input p10]
12. ! [X0] : ((calm(X0) | kind(X0)) <=> (~funny(X0) & humble(X0))) [input p11]
22. curious(alice) [input hypothesis]
31. ! [X0] : (((old(X0) & ~calm(X0)) | old(X0)) & (~old(X0) | (~old(X0) | calm(X0)))) [nnf transformation 1]
32. ! [X0] : (((old(X0) & ~calm(X0)) | old(X0)) & (~old(X0) | ~old(X0) | calm(X0))) [flattening 31]
37. ! [X0] : (((~generous(X0) & ~wise(X0)) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | (generous(X0) | wise(X0)))) [nnf transformation 5]
38. ! [X0] : (((~generous(X0) & ~wise(X0)) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | generous(X0) | wise(X0))) [flattening 37]
39. ! [X0] : ((wise(X0) | (funny(X0) & ~strong(X0))) & ((~funny(X0) | strong(X0)) | ~wise(X0))) [nnf transformation 7]
40. ! [X0] : ((wise(X0) | (funny(X0) & ~strong(X0))) & (~funny(X0) | strong(X0) | ~wise(X0))) [flattening 39]
53. ! [X0] : ((curious(X0) | (wise(X0) & tall(X0))) & ((~wise(X0) | ~tall(X0)) | ~curious(X0))) [nnf transformation 11]
54. ! [X0] : ((curious(X0) | (wise(X0) & tall(X0))) & (~wise(X0) | ~tall(X0) | ~curious(X0))) [flattening 53]
55. ! [X0] : (((calm(X0) | kind(X0)) | (funny(X0) | ~humble(X0))) & ((~funny(X0) & humble(X0)) | (~calm(X0) & ~kind(X0)))) [nnf transformation 12]
56. ! [X0] : ((calm(X0) | kind(X0) | funny(X0) | ~humble(X0)) & ((~funny(X0) & humble(X0)) | (~calm(X0) & ~kind(X0)))) [flattening 55]
79. ~old(X0) | ~old(X0) | calm(X0) [cnf transformation 32]
81. old(X0) | old(X0) [cnf transformation 32]
96. ~wise(X0) | tall(X0) [cnf transformation 38]
103. funny(X0) | wise(X0) [cnf transformation 40]
115. ~wise(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 54]
121. ~funny(X0) | ~calm(X0) [cnf transformation 56]
149. curious(alice) [cnf transformation 22]
151. ~old(X0) | calm(X0) [duplicate literal removal 79]
152. old(X0) [duplicate literal removal 81]
153. calm(X0) [subsumption resolution 151,152]
215. 15 <=> ! [X3] : wise(X3) [avatar definition]
216. wise(X3) <- (15) [avatar component clause 215]
218. ~wise(X0) | ~curious(X0) [subsumption resolution 115,96]
219. ~funny(X0) [subsumption resolution 121,153]
318. wise(X0) [resolution 103,219]
319. 15 [avatar split clause 318,215]
347. ~curious(X1) <- (15) [resolution 218,216]
348. $false <- (15) [resolution 347,149]
351. ~15 [avatar contradiction clause 348]
352. $false [avatar sat refutation 319,351]
% SZS output end Proof for 7367178701604253271136602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or creative is not old and vice versa.
Everyone who is not creative is brave.
Everyone who is not humble or not creative is both not kind and humble and vice versa.
Everyone who is either not tall or happy is both happy and rich and vice versa.
Everyone who is both not happy and generous is either not strong or not calm and vice versa.
If mary is either generous or not old then mary is both humble and not quiet and vice versa.
If john is not creative then lucy is brave or not rich and vice versa.
If someone is not brave or not humble then paul is rich or not old and vice versa.
Everyone who is either not humble or wise is not rich or tall and vice versa.
Everyone who is creative is either not kind or tall and vice versa.
Everyone who is both quiet and not calm is strong or not wise and vice versa.
If susan is not rich or not humble then someone is either not funny or not kind.
Everyone who is not strong is either not kind or curious and vice versa.
Everyone who is either not patient or patient is creative or strong.
If fred is both not tall and strong then someone is both brave and not tall.
Everyone who is generous or not happy is not humble.
Someone is humble or not curious.
Someone is not funny.
Someone is not humble or tall.
Someone is either quiet or not patient. | Mary is not generous. | entailment | (![X]:((humble(X)|creative(X))<=>~old(X)))&
(![X]:(~creative(X)=>brave(X)))&
(![X]:((~humble(X)|~creative(X))<=>(~kind(X)&humble(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(happy(X)&rich(X))))&
(![X]:((~happy(X)&generous(X))<=>(~strong(X)<~>~calm(X))))&
(((generous(mary)<~>~old(mary)))<=>((humble(mary)&~quiet(mary))))&
((~creative(john))<=>((brave(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>((rich(paul)|~old(paul))))&
(![X]:((~humble(X)<~>wise(X))<=>(~rich(X)|tall(X))))&
(![X]:(creative(X)<=>(~kind(X)<~>tall(X))))&
(![X]:((quiet(X)&~calm(X))<=>(strong(X)|~wise(X))))&
(((~rich(susan)|~humble(susan)))=>(?[X]:((~funny(X)<~>~kind(X)))))&
(![X]:(~strong(X)<=>(~kind(X)<~>curious(X))))&
(![X]:((~patient(X)<~>patient(X))=>(creative(X)|strong(X))))&
(((~tall(fred)&strong(fred)))=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((generous(X)|~happy(X))=>~humble(X)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | ~generous(mary) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6474104918774703466287204
% SZS output start Proof for 6474104918774703466287204
3. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (humble(X0) & ~kind(X0))) [input p2]
16. ! [X0] : ((~happy(X0) | generous(X0)) => ~humble(X0)) [input p15]
21. generous(mary) [input hypothesis]
28. ! [X0] : (~humble(X0) | (happy(X0) & ~generous(X0))) [ennf transformation 16]
31. ! [X0] : (((~creative(X0) | ~humble(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [nnf transformation 3]
32. ! [X0] : ((~creative(X0) | ~humble(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [flattening 31]
73. humble(X0) | humble(X0) [cnf transformation 32]
128. ~humble(X0) | ~generous(X0) [cnf transformation 28]
135. generous(mary) [cnf transformation 21]
140. humble(X0) [duplicate literal removal 73]
232. ~generous(X0) [subsumption resolution 128,140]
244. $false [subsumption resolution 135,232]
% SZS output end Proof for 6474104918774703466287204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not happy or not creative and vice versa.
If someone is both kind and old then someone is both happy and old.
Everyone who is not rich is strong and vice versa.
If someone is wise then someone is either tall or not calm and vice versa.
Everyone who is kind is both not wise and calm and vice versa.
Everyone who is both not happy and not wise is both not quiet and tall and vice versa.
Everyone who is either not brave or not old is both quiet and wise.
If someone is both strong and humble then someone is not creative or old and vice versa.
Everyone who is both not patient and not happy is quiet or old and vice versa.
If susan is not generous or creative then mary is not rich or not brave.
Everyone who is both brave and strong is both not curious and brave.
Everyone who is both not curious and not happy is both not kind and not calm.
If someone is either creative or not calm then someone is wise and vice versa.
Everyone who is strong is either happy or brave and vice versa.
Everyone who is not generous or not strong is not curious.
Everyone who is kind or not rich is happy and vice versa.
Paul is both kind and humble.
Someone is not humble.
John is both strong and not rich.
Paul is either quiet or humble.
Paul is either humble or quiet.
Paul is humble. | Mary is not brave. | entailment | (![X]:((funny(X)|~strong(X))<=>(~happy(X)|~creative(X))))&
((?[X]:((kind(X)&old(X))))=>(?[X]:((happy(X)&old(X)))))&
(![X]:(~rich(X)<=>strong(X)))&
((?[X]:(wise(X)))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(![X]:(kind(X)<=>(~wise(X)&calm(X))))&
(![X]:((~happy(X)&~wise(X))<=>(~quiet(X)&tall(X))))&
(![X]:((~brave(X)<~>~old(X))=>(quiet(X)&wise(X))))&
((?[X]:((strong(X)&humble(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((~patient(X)&~happy(X))<=>(quiet(X)|old(X))))&
(((~generous(susan)|creative(susan)))=>((~rich(mary)|~brave(mary))))&
(![X]:((brave(X)&strong(X))=>(~curious(X)&brave(X))))&
(![X]:((~curious(X)&~happy(X))=>(~kind(X)&~calm(X))))&
((?[X]:((creative(X)<~>~calm(X))))<=>(?[X]:(wise(X))))&
(![X]:(strong(X)<=>(happy(X)<~>brave(X))))&
(![X]:((~generous(X)|~strong(X))=>~curious(X)))&
(![X]:((kind(X)|~rich(X))<=>happy(X)))&
((kind(paul)&humble(paul)))&
(?[X]:(~humble(X)))&
((strong(john)&~rich(john)))&
((quiet(paul)<~>humble(paul)))&
((humble(paul)<~>quiet(paul)))&
(humble(paul)) | ~brave(mary) | [
"p2",
"p6",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7116212096173579704254297
% SZS output start Proof for 7116212096173579704254297
3. ! [X0] : (~rich(X0) <=> strong(X0)) [input p2]
7. ! [X0] : ((~brave(X0) <~> ~old(X0)) => (wise(X0) & quiet(X0))) [input p6]
9. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (old(X0) | quiet(X0))) [input p8]
14. ! [X0] : (strong(X0) <=> (happy(X0) <~> brave(X0))) [input p13]
16. ! [X0] : ((~rich(X0) | kind(X0)) <=> happy(X0)) [input p15]
23. brave(mary) [input hypothesis]
31. ! [X0] : ((wise(X0) & quiet(X0)) | (~brave(X0) <=> ~old(X0))) [ennf transformation 7]
44. ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))) [nnf transformation 3]
54. ! [X0] : ((wise(X0) & quiet(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) [nnf transformation 31]
60. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~old(X0) & ~quiet(X0))) & ((old(X0) | quiet(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 9]
61. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~old(X0) & ~quiet(X0))) & (old(X0) | quiet(X0) | happy(X0) | patient(X0))) [flattening 60]
67. ! [X0] : ((strong(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ~strong(X0))) [nnf transformation 14]
68. ! [X0] : (((~rich(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((~rich(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [flattening 68]
81. ~rich(X0) | ~strong(X0) [cnf transformation 44]
94. ~brave(X0) | quiet(X0) | old(X0) [cnf transformation 54]
105. ~quiet(X0) | ~happy(X0) [cnf transformation 61]
106. ~old(X0) | ~happy(X0) [cnf transformation 61]
119. ~brave(X0) | happy(X0) | strong(X0) [cnf transformation 67]
122. rich(X0) | happy(X0) [cnf transformation 69]
134. brave(mary) [cnf transformation 23]
208. 18 <=> rich(mary) [avatar definition]
209. rich(mary) <- (18) [avatar component clause 208]
210. ~rich(mary) <- (~18) [avatar component clause 208]
212. 19 <=> brave(mary) [avatar definition]
213. brave(mary) <- (19) [avatar component clause 212]
239. 19 [avatar split clause 134,212]
256. happy(mary) <- (~18) [resolution 122,210]
324. quiet(mary) | old(mary) <- (19) [resolution 94,213]
326. 35 <=> old(mary) [avatar definition]
328. old(mary) <- (35) [avatar component clause 326]
330. 36 <=> quiet(mary) [avatar definition]
332. quiet(mary) <- (36) [avatar component clause 330]
333. 35 | 36 | ~19 [avatar split clause 324,212,330,326]
339. ~happy(mary) <- (36) [resolution 332,105]
340. $false <- (~18, 36) [subsumption resolution 339,256]
341. 18 | ~36 [avatar contradiction clause 340]
343. ~strong(mary) <- (18) [resolution 209,81]
364. happy(mary) | strong(mary) <- (19) [resolution 119,213]
365. strong(mary) <- (19, 36) [subsumption resolution 364,339]
366. $false <- (18, 19, 36) [subsumption resolution 365,343]
367. ~18 | ~19 | ~36 [avatar contradiction clause 366]
368. happy(mary) <- (18, 19) [subsumption resolution 364,343]
377. ~happy(mary) <- (35) [resolution 328,106]
378. $false <- (18, 19, 35) [subsumption resolution 377,368]
379. ~18 | ~19 | ~35 [avatar contradiction clause 378]
381. happy(mary) <- (~18) [resolution 210,122]
383. $false <- (~18, 35) [subsumption resolution 381,377]
384. 18 | ~35 [avatar contradiction clause 383]
385. $false [avatar sat refutation 239,333,341,367,379,384]
% SZS output end Proof for 7116212096173579704254297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous is both not tall and not quiet.
If fred is strong then lucy is not brave or not curious.
Everyone who is not quiet or generous is not humble and vice versa.
If mary is not quiet then mary is funny or creative.
If someone is either not calm or not kind then susan is both not curious and not generous and vice versa.
If someone is both not old and not kind then someone is either patient or not curious and vice versa.
Everyone who is both not humble and happy is either not strong or humble and vice versa.
If susan is kind or not tall then paul is both tall and not creative.
If someone is not quiet or not creative then someone is either generous or not happy and vice versa.
If john is either patient or not patient then alice is old or not brave and vice versa.
Everyone who is not kind or not curious is not old or rich.
If someone is funny or humble then someone is rich.
Everyone who is both not tall and not old is both calm and generous and vice versa.
If someone is not wise then paul is either not rich or old and vice versa.
If john is either not strong or kind then someone is not curious.
If someone is brave or not funny then lucy is both wise and happy.
Someone is either not tall or calm.
Alice is both funny and old.
Susan is both not old and not quiet.
Someone is either not patient or old.
Someone is both not tall and generous.
Paul is patient.
Someone is quiet or not kind.
Someone is not rich or curious. | Fred is humble. | contradiction | (![X]:(~generous(X)=>(~tall(X)&~quiet(X))))&
((strong(fred))=>((~brave(lucy)|~curious(lucy))))&
(![X]:((~quiet(X)|generous(X))<=>~humble(X)))&
((~quiet(mary))=>((funny(mary)|creative(mary))))&
((?[X]:((~calm(X)<~>~kind(X))))<=>((~curious(susan)&~generous(susan))))&
((?[X]:((~old(X)&~kind(X))))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:((~humble(X)&happy(X))<=>(~strong(X)<~>humble(X))))&
(((kind(susan)|~tall(susan)))=>((tall(paul)&~creative(paul))))&
((?[X]:((~quiet(X)|~creative(X))))<=>(?[X]:((generous(X)<~>~happy(X)))))&
(((patient(john)<~>~patient(john)))<=>((old(alice)|~brave(alice))))&
(![X]:((~kind(X)|~curious(X))=>(~old(X)|rich(X))))&
((?[X]:((funny(X)|humble(X))))=>(?[X]:(rich(X))))&
(![X]:((~tall(X)&~old(X))<=>(calm(X)&generous(X))))&
((?[X]:(~wise(X)))<=>((~rich(paul)<~>old(paul))))&
(((~strong(john)<~>kind(john)))=>(?[X]:(~curious(X))))&
((?[X]:((brave(X)|~funny(X))))=>((wise(lucy)&happy(lucy))))&
(?[X]:((~tall(X)<~>calm(X))))&
((funny(alice)&old(alice)))&
((~old(susan)&~quiet(susan)))&
(?[X]:((~patient(X)<~>old(X))))&
(?[X]:((~tall(X)&generous(X))))&
(patient(paul))&
(?[X]:((quiet(X)|~kind(X))))&
(?[X]:((~rich(X)|curious(X)))) | humble(fred) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 982044774499341806768888
% SZS output start Proof for 982044774499341806768888
1. ! [X0] : (~generous(X0) => (~quiet(X0) & ~tall(X0))) [input p0]
3. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> ~humble(X0)) [input p2]
25. humble(fred) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & ~tall(X0)) | generous(X0)) [ennf transformation 1]
40. ! [X0] : (((generous(X0) | ~quiet(X0)) | humble(X0)) & (~humble(X0) | (~generous(X0) & quiet(X0)))) [nnf transformation 3]
41. ! [X0] : ((generous(X0) | ~quiet(X0) | humble(X0)) & (~humble(X0) | (~generous(X0) & quiet(X0)))) [flattening 40]
86. ~quiet(X0) | generous(X0) [cnf transformation 29]
88. ~humble(X0) | quiet(X0) [cnf transformation 41]
89. ~humble(X0) | ~generous(X0) [cnf transformation 41]
157. humble(fred) [cnf transformation 25]
417. quiet(fred) [resolution 88,157]
418. generous(fred) [resolution 417,86]
419. ~generous(fred) [resolution 89,157]
420. $false [subsumption resolution 419,418]
% SZS output end Proof for 982044774499341806768888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and funny is rich and vice versa.
Everyone who is both strong and quiet is old.
If paul is not kind or not strong then mary is either humble or curious.
Everyone who is not wise is not generous or not kind and vice versa.
Everyone who is quiet is either not funny or not wise.
Everyone who is brave is not wise.
Everyone who is not humble is both not happy and wise.
Everyone who is brave is not rich and vice versa.
If someone is either not rich or old then susan is strong or quiet and vice versa.
If someone is both quiet and not humble then someone is not humble or kind.
Everyone who is both patient and strong is generous or not creative.
If paul is not humble or wise then susan is both wise and not wise and vice versa.
Everyone who is not rich is both kind and not brave.
If someone is generous or not generous then someone is both strong and not kind.
If someone is kind or not strong then lucy is either not generous or not patient.
Everyone who is quiet is quiet or not quiet.
Mary is both humble and quiet.
Someone is not kind or not curious.
Alice is either strong or generous.
Susan is tall or not creative.
John is both not curious and kind.
Someone is not quiet.
Someone is creative. | Alice is not old. | entailment | (![X]:((~old(X)&funny(X))<=>rich(X)))&
(![X]:((strong(X)&quiet(X))=>old(X)))&
(((~kind(paul)|~strong(paul)))=>((humble(mary)<~>curious(mary))))&
(![X]:(~wise(X)<=>(~generous(X)|~kind(X))))&
(![X]:(quiet(X)=>(~funny(X)<~>~wise(X))))&
(![X]:(brave(X)=>~wise(X)))&
(![X]:(~humble(X)=>(~happy(X)&wise(X))))&
(![X]:(brave(X)<=>~rich(X)))&
((?[X]:((~rich(X)<~>old(X))))<=>((strong(susan)|quiet(susan))))&
((?[X]:((quiet(X)&~humble(X))))=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((patient(X)&strong(X))=>(generous(X)|~creative(X))))&
(((~humble(paul)|wise(paul)))<=>((wise(susan)&~wise(susan))))&
(![X]:(~rich(X)=>(kind(X)&~brave(X))))&
((?[X]:((generous(X)|~generous(X))))=>(?[X]:((strong(X)&~kind(X)))))&
((?[X]:((kind(X)|~strong(X))))=>((~generous(lucy)<~>~patient(lucy))))&
(![X]:(quiet(X)=>(quiet(X)|~quiet(X))))&
((humble(mary)&quiet(mary)))&
(?[X]:((~kind(X)|~curious(X))))&
((strong(alice)<~>generous(alice)))&
((tall(susan)|~creative(susan)))&
((~curious(john)&kind(john)))&
(?[X]:(~quiet(X)))&
(?[X]:(creative(X))) | ~old(alice) | [
"p0",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7611606764331531115690952
% SZS output start Proof for 7611606764331531115690952
1. ! [X0] : ((funny(X0) & ~old(X0)) <=> rich(X0)) [input p0]
8. ! [X0] : (brave(X0) <=> ~rich(X0)) [input p7]
13. ! [X0] : (~rich(X0) => (~brave(X0) & kind(X0))) [input p12]
24. old(alice) [input hypothesis]
27. ! [X0] : (~rich(X0) => brave(X0)) [unused predicate definition removal 8]
36. ! [X0] : (brave(X0) | rich(X0)) [ennf transformation 27]
40. ! [X0] : ((~brave(X0) & kind(X0)) | rich(X0)) [ennf transformation 13]
45. ! [X0] : (((funny(X0) & ~old(X0)) | ~rich(X0)) & (rich(X0) | (~funny(X0) | old(X0)))) [nnf transformation 1]
46. ! [X0] : (((funny(X0) & ~old(X0)) | ~rich(X0)) & (rich(X0) | ~funny(X0) | old(X0))) [flattening 45]
73. ~rich(X0) | ~old(X0) [cnf transformation 46]
87. brave(X0) | rich(X0) [cnf transformation 36]
102. ~brave(X0) | rich(X0) [cnf transformation 40]
121. old(alice) [cnf transformation 24]
199. rich(X0) [subsumption resolution 102,87]
262. ~old(X0) [resolution 73,199]
264. $false [resolution 262,121]
% SZS output end Proof for 7611606764331531115690952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and rich then john is either not wise or not kind and vice versa. If john is both kind and generous then someone is either curious or funny and vice versa. Everyone who is not creative or not happy is happy and vice versa. If alice is both tall and not wise then someone is happy or not strong. Everyone who is not strong is quiet and vice versa. If someone is not wise then fred is quiet or not old. Everyone who is either not funny or not happy is happy and vice versa. If someone is either not quiet or rich then someone is not patient or not creative and vice versa. Everyone who is not humble or old is happy. If someone is either not funny or old then someone is not old or strong. Everyone who is kind is not creative or not curious and vice versa. If lucy is creative then fred is wise and vice versa. If alice is curious then john is not humble or not calm. If someone is creative or not generous then someone is not tall or calm and vice versa. Everyone who is either not creative or not happy is both brave and curious. Everyone who is calm or kind is rich or not calm. Someone is patient. Someone is curious or tall. Susan is either not generous or not curious. Someone is not generous. Someone is either not kind or not generous. Someone is humble or patient. | Fred is not old. | neutral | ((?[X]:((~generous(X)&rich(X))))<=>((~wise(john)<~>~kind(john))))&
(((kind(john)&generous(john)))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((~creative(X)|~happy(X))<=>happy(X)))&
(((tall(alice)&~wise(alice)))=>(?[X]:((happy(X)|~strong(X)))))&
(![X]:(~strong(X)<=>quiet(X)))&
((?[X]:(~wise(X)))=>((quiet(fred)|~old(fred))))&
(![X]:((~funny(X)<~>~happy(X))<=>happy(X)))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(?[X]:((~patient(X)|~creative(X)))))&
(![X]:((~humble(X)|old(X))=>happy(X)))&
((?[X]:((~funny(X)<~>old(X))))=>(?[X]:((~old(X)|strong(X)))))&
(![X]:(kind(X)<=>(~creative(X)|~curious(X))))&
((creative(lucy))<=>(wise(fred)))&
((curious(alice))=>((~humble(john)|~calm(john))))&
((?[X]:((creative(X)|~generous(X))))<=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:((~creative(X)<~>~happy(X))=>(brave(X)&curious(X))))&
(![X]:((calm(X)|kind(X))=>(rich(X)|~calm(X))))&
(?[X]:(patient(X)))&
(?[X]:((curious(X)|tall(X))))&
((~generous(susan)<~>~curious(susan)))&
(?[X]:(~generous(X)))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((humble(X)|patient(X)))) | ~old(fred) | [] | null | 0 |
If someone is both calm and not old then someone is not curious and vice versa. If someone is both not kind and curious then someone is happy. If someone is both not wise and not funny then someone is either generous or not curious. If someone is humble or patient then lucy is both curious and strong and vice versa. If someone is not curious or humble then someone is both kind and not happy and vice versa. If alice is not curious then john is wise or old. Everyone who is both old and brave is either not strong or not funny and vice versa. Everyone who is brave is calm or kind and vice versa. Everyone who is happy or creative is not quiet and vice versa. Everyone who is both not humble and not curious is either brave or not humble. If someone is funny then someone is both creative and not humble and vice versa. Everyone who is both generous and not curious is not creative or not rich and vice versa. Everyone who is generous is either patient or rich. If mary is either not quiet or funny then john is either not quiet or old and vice versa. Everyone who is kind is both humble and wise and vice versa. If someone is brave then someone is both not curious and not quiet and vice versa. Mary is patient. Fred is either not funny or strong. Someone is either generous or not old. Someone is both curious and not humble. Fred is both not funny and wise. Lucy is not creative or not generous. John is either not generous or not wise. Paul is both kind and curious. | Fred is not wise. | contradiction | ((?[X]:((calm(X)&~old(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:(happy(X))))&
((?[X]:((~wise(X)&~funny(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
((?[X]:((humble(X)|patient(X))))<=>((curious(lucy)&strong(lucy))))&
((?[X]:((~curious(X)|humble(X))))<=>(?[X]:((kind(X)&~happy(X)))))&
((~curious(alice))=>((wise(john)|old(john))))&
(![X]:((old(X)&brave(X))<=>(~strong(X)<~>~funny(X))))&
(![X]:(brave(X)<=>(calm(X)|kind(X))))&
(![X]:((happy(X)|creative(X))<=>~quiet(X)))&
(![X]:((~humble(X)&~curious(X))=>(brave(X)<~>~humble(X))))&
((?[X]:(funny(X)))<=>(?[X]:((creative(X)&~humble(X)))))&
(![X]:((generous(X)&~curious(X))<=>(~creative(X)|~rich(X))))&
(![X]:(generous(X)=>(patient(X)<~>rich(X))))&
(((~quiet(mary)<~>funny(mary)))<=>((~quiet(john)<~>old(john))))&
(![X]:(kind(X)<=>(humble(X)&wise(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~curious(X)&~quiet(X)))))&
(patient(mary))&
((~funny(fred)<~>strong(fred)))&
(?[X]:((generous(X)<~>~old(X))))&
(?[X]:((curious(X)&~humble(X))))&
((~funny(fred)&wise(fred)))&
((~creative(lucy)|~generous(lucy)))&
((~generous(john)<~>~wise(john)))&
((kind(paul)&curious(paul))) | ~wise(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 569594351257884337720768
% SZS output start Proof for 569594351257884337720768
21. wise(fred) & ~funny(fred) [input p20]
25. ~wise(fred) [input hypothesis]
154. wise(fred) [cnf transformation 21]
160. ~wise(fred) [cnf transformation 25]
367. $false [subsumption resolution 160,154]
% SZS output end Proof for 569594351257884337720768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or creative is either quiet or funny.
Everyone who is both not creative and not rich is tall and vice versa.
Everyone who is not generous or not old is either patient or curious and vice versa.
If someone is both wise and quiet then alice is not happy or not brave and vice versa.
If someone is humble then fred is either not patient or calm and vice versa.
If paul is not calm then someone is not calm.
If paul is both not happy and curious then someone is not strong or generous.
Everyone who is not generous is rich or curious.
Everyone who is generous is kind.
Everyone who is strong is either strong or patient and vice versa.
Everyone who is not rich is not creative or not old.
Everyone who is funny is not generous.
If someone is curious then someone is old or rich.
Everyone who is kind is both not happy and brave.
Everyone who is either humble or quiet is strong or not patient.
Everyone who is both not calm and not humble is both not strong and old.
Someone is not curious or not brave.
Someone is both calm and not tall.
Someone is either old or curious.
Someone is both funny and not tall.
Mary is either calm or not rich.
Someone is either not tall or not curious.
Someone is curious.
Paul is not calm or not quiet. | Fred is calm. | neutral | (![X]:((~creative(X)|creative(X))=>(quiet(X)<~>funny(X))))&
(![X]:((~creative(X)&~rich(X))<=>tall(X)))&
(![X]:((~generous(X)|~old(X))<=>(patient(X)<~>curious(X))))&
((?[X]:((wise(X)&quiet(X))))<=>((~happy(alice)|~brave(alice))))&
((?[X]:(humble(X)))<=>((~patient(fred)<~>calm(fred))))&
((~calm(paul))=>(?[X]:(~calm(X))))&
(((~happy(paul)&curious(paul)))=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:(~generous(X)=>(rich(X)|curious(X))))&
(![X]:(generous(X)=>kind(X)))&
(![X]:(strong(X)<=>(strong(X)<~>patient(X))))&
(![X]:(~rich(X)=>(~creative(X)|~old(X))))&
(![X]:(funny(X)=>~generous(X)))&
((?[X]:(curious(X)))=>(?[X]:((old(X)|rich(X)))))&
(![X]:(kind(X)=>(~happy(X)&brave(X))))&
(![X]:((humble(X)<~>quiet(X))=>(strong(X)|~patient(X))))&
(![X]:((~calm(X)&~humble(X))=>(~strong(X)&old(X))))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:((calm(X)&~tall(X))))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:((funny(X)&~tall(X))))&
((calm(mary)<~>~rich(mary)))&
(?[X]:((~tall(X)<~>~curious(X))))&
(?[X]:(curious(X)))&
((~calm(paul)|~quiet(paul))) | calm(fred) | [] | null | 0 |
Everyone who is not tall is both happy and not happy.
Everyone who is both generous and not creative is rich.
Everyone who is either creative or humble is not calm or not old.
Everyone who is curious is either funny or quiet.
Everyone who is patient is humble or happy and vice versa.
If someone is either brave or funny then someone is not strong or not patient.
Everyone who is either not brave or wise is not strong or not humble and vice versa.
If someone is funny or not patient then mary is both not brave and generous.
Everyone who is not creative or not wise is both brave and not quiet.
If fred is either quiet or not rich then someone is happy or curious.
If someone is not strong or brave then someone is both not brave and not wise and vice versa.
If paul is wise then mary is either not kind or not generous and vice versa.
If someone is not kind or wise then john is both not kind and not brave.
If alice is both rich and not kind then someone is not quiet or not funny.
If susan is creative or not patient then paul is not generous and vice versa.
Everyone who is not generous is either humble or not creative and vice versa.
Someone is not quiet.
Lucy is either old or not happy.
Someone is either calm or quiet.
Someone is either not rich or kind. | Fred is not tall. | contradiction | (![X]:(~tall(X)=>(happy(X)&~happy(X))))&
(![X]:((generous(X)&~creative(X))=>rich(X)))&
(![X]:((creative(X)<~>humble(X))=>(~calm(X)|~old(X))))&
(![X]:(curious(X)=>(funny(X)<~>quiet(X))))&
(![X]:(patient(X)<=>(humble(X)|happy(X))))&
((?[X]:((brave(X)<~>funny(X))))=>(?[X]:((~strong(X)|~patient(X)))))&
(![X]:((~brave(X)<~>wise(X))<=>(~strong(X)|~humble(X))))&
((?[X]:((funny(X)|~patient(X))))=>((~brave(mary)&generous(mary))))&
(![X]:((~creative(X)|~wise(X))=>(brave(X)&~quiet(X))))&
(((quiet(fred)<~>~rich(fred)))=>(?[X]:((happy(X)|curious(X)))))&
((?[X]:((~strong(X)|brave(X))))<=>(?[X]:((~brave(X)&~wise(X)))))&
((wise(paul))<=>((~kind(mary)<~>~generous(mary))))&
((?[X]:((~kind(X)|wise(X))))=>((~kind(john)&~brave(john))))&
(((rich(alice)&~kind(alice)))=>(?[X]:((~quiet(X)|~funny(X)))))&
(((creative(susan)|~patient(susan)))<=>(~generous(paul)))&
(![X]:(~generous(X)<=>(humble(X)<~>~creative(X))))&
(?[X]:(~quiet(X)))&
((old(lucy)<~>~happy(lucy)))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((~rich(X)<~>kind(X)))) | ~tall(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7846608038967974150675207
% SZS output start Proof for 7846608038967974150675207
1. ! [X0] : (~tall(X0) => (~happy(X0) & happy(X0))) [input p0]
21. ~tall(fred) [input hypothesis]
24. ! [X0] : ((~happy(X0) & happy(X0)) | tall(X0)) [ennf transformation 1]
70. happy(X0) | tall(X0) [cnf transformation 24]
71. ~happy(X0) | tall(X0) [cnf transformation 24]
126. ~tall(fred) [cnf transformation 21]
127. tall(X0) [subsumption resolution 70,71]
290. $false [subsumption resolution 126,127]
% SZS output end Proof for 7846608038967974150675207
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not old is patient or not funny and vice versa. Everyone who is either not brave or rich is not brave or brave. Everyone who is curious is either wise or generous. If someone is either humble or not tall then someone is either not patient or funny and vice versa. If someone is kind or not strong then someone is either not wise or not humble. If someone is tall then someone is either generous or quiet. If mary is old then fred is not funny. If someone is not patient or humble then someone is kind. Everyone who is both not old and not funny is wise or not kind and vice versa. Everyone who is wise is not curious and vice versa. If lucy is either not generous or kind then someone is not patient or not generous. Everyone who is not tall or patient is both rich and calm and vice versa. Everyone who is not brave or not kind is both not quiet and not brave. If someone is funny then someone is both not happy and quiet. Everyone who is tall is either wise or not generous. Everyone who is not kind is both not calm and kind and vice versa. Someone is either not humble or funny. Fred is either happy or not happy. Susan is either generous or rich. Alice is generous or calm. Someone is either patient or tall. Lucy is not wise or not funny. Someone is either not quiet or not wise. | Susan is not old. | entailment | (![X]:((~wise(X)|~old(X))<=>(patient(X)|~funny(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~brave(X)|brave(X))))&
(![X]:(curious(X)=>(wise(X)<~>generous(X))))&
((?[X]:((humble(X)<~>~tall(X))))<=>(?[X]:((~patient(X)<~>funny(X)))))&
((?[X]:((kind(X)|~strong(X))))=>(?[X]:((~wise(X)<~>~humble(X)))))&
((?[X]:(tall(X)))=>(?[X]:((generous(X)<~>quiet(X)))))&
((old(mary))=>(~funny(fred)))&
((?[X]:((~patient(X)|humble(X))))=>(?[X]:(kind(X))))&
(![X]:((~old(X)&~funny(X))<=>(wise(X)|~kind(X))))&
(![X]:(wise(X)<=>~curious(X)))&
(((~generous(lucy)<~>kind(lucy)))=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((~tall(X)|patient(X))<=>(rich(X)&calm(X))))&
(![X]:((~brave(X)|~kind(X))=>(~quiet(X)&~brave(X))))&
((?[X]:(funny(X)))=>(?[X]:((~happy(X)&quiet(X)))))&
(![X]:(tall(X)=>(wise(X)<~>~generous(X))))&
(![X]:(~kind(X)<=>(~calm(X)&kind(X))))&
(?[X]:((~humble(X)<~>funny(X))))&
((happy(fred)<~>~happy(fred)))&
((generous(susan)<~>rich(susan)))&
((generous(alice)|calm(alice)))&
(?[X]:((patient(X)<~>tall(X))))&
((~wise(lucy)|~funny(lucy)))&
(?[X]:((~quiet(X)<~>~wise(X)))) | ~old(susan) | [
"p2",
"p8",
"p9",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8957435561680062171715109
% SZS output start Proof for 8957435561680062171715109
3. ! [X0] : (curious(X0) => (wise(X0) <~> generous(X0))) [input p2]
9. ! [X0] : ((~funny(X0) & ~old(X0)) <=> (~kind(X0) | wise(X0))) [input p8]
10. ! [X0] : (wise(X0) <=> ~curious(X0)) [input p9]
12. ! [X0] : ((patient(X0) | ~tall(X0)) <=> (calm(X0) & rich(X0))) [input p11]
15. ! [X0] : (tall(X0) => (wise(X0) <~> ~generous(X0))) [input p14]
19. generous(susan) <~> rich(susan) [input p18]
24. old(susan) [input hypothesis]
33. ! [X0] : ((wise(X0) <~> generous(X0)) | ~curious(X0)) [ennf transformation 3]
41. ! [X0] : ((wise(X0) <~> ~generous(X0)) | ~tall(X0)) [ennf transformation 15]
45. ! [X0] : (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | ~curious(X0)) [nnf transformation 33]
62. ! [X0] : (((~funny(X0) & ~old(X0)) | (kind(X0) & ~wise(X0))) & ((~kind(X0) | wise(X0)) | (funny(X0) | old(X0)))) [nnf transformation 9]
63. ! [X0] : (((~funny(X0) & ~old(X0)) | (kind(X0) & ~wise(X0))) & (~kind(X0) | wise(X0) | funny(X0) | old(X0))) [flattening 62]
64. ! [X0] : ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0))) [nnf transformation 10]
68. ! [X0] : (((patient(X0) | ~tall(X0)) | (~calm(X0) | ~rich(X0))) & ((calm(X0) & rich(X0)) | (~patient(X0) & tall(X0)))) [nnf transformation 12]
69. ! [X0] : ((patient(X0) | ~tall(X0) | ~calm(X0) | ~rich(X0)) & ((calm(X0) & rich(X0)) | (~patient(X0) & tall(X0)))) [flattening 68]
73. ! [X0] : (((generous(X0) | ~wise(X0)) & (~generous(X0) | wise(X0))) | ~tall(X0)) [nnf transformation 41]
80. (~rich(susan) | ~generous(susan)) & (rich(susan) | generous(susan)) [nnf transformation 19]
93. ~curious(X0) | wise(X0) | generous(X0) [cnf transformation 45]
111. ~old(X0) | ~wise(X0) [cnf transformation 63]
116. curious(X0) | wise(X0) [cnf transformation 64]
119. tall(X0) | rich(X0) [cnf transformation 69]
130. ~tall(X0) | wise(X0) | ~generous(X0) [cnf transformation 73]
140. ~rich(susan) | ~generous(susan) [cnf transformation 80]
147. old(susan) [cnf transformation 24]
277. 29 <=> generous(susan) [avatar definition]
279. ~generous(susan) <- (~29) [avatar component clause 277]
281. 30 <=> rich(susan) [avatar definition]
283. ~rich(susan) <- (~30) [avatar component clause 281]
284. ~29 | ~30 [avatar split clause 140,281,277]
317. ~wise(susan) [resolution 111,147]
333. wise(X0) | generous(X0) | wise(X0) [resolution 93,116]
334. generous(X0) | wise(X0) [duplicate literal removal 333]
339. wise(X0) | ~generous(X0) | rich(X0) [resolution 130,119]
340. rich(X0) | wise(X0) [subsumption resolution 339,334]
343. wise(susan) <- (~30) [resolution 340,283]
344. $false <- (~30) [subsumption resolution 343,317]
345. 30 [avatar contradiction clause 344]
346. wise(susan) <- (~29) [resolution 279,334]
347. $false <- (~29) [subsumption resolution 346,317]
348. 29 [avatar contradiction clause 347]
349. $false [avatar sat refutation 284,345,348]
% SZS output end Proof for 8957435561680062171715109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and curious is quiet and vice versa.
Everyone who is both not old and not kind is not curious or curious and vice versa.
Everyone who is humble is both not creative and generous.
If someone is both humble and strong then someone is tall or not wise and vice versa.
If fred is not tall then lucy is not tall or not patient and vice versa.
If john is strong then mary is both not quiet and humble.
If susan is not funny then fred is both not brave and not humble.
If paul is both rich and old then lucy is not happy and vice versa.
Everyone who is not funny or humble is not funny or calm and vice versa.
If someone is not wise then lucy is rich or not old.
If john is both creative and not patient then someone is not brave and vice versa.
If john is brave then john is curious or not brave and vice versa.
Everyone who is not patient or not curious is either strong or not humble.
If someone is either not humble or brave then alice is calm.
Everyone who is wise or old is not curious and vice versa.
If mary is not brave then someone is both not rich and patient and vice versa.
Susan is either not calm or not curious.
Someone is both not brave and not generous.
Paul is tall.
Someone is either brave or not brave.
Someone is both not strong and not old.
Someone is either not kind or funny. | Paul is funny. | neutral | (![X]:((old(X)&curious(X))<=>quiet(X)))&
(![X]:((~old(X)&~kind(X))<=>(~curious(X)|curious(X))))&
(![X]:(humble(X)=>(~creative(X)&generous(X))))&
((?[X]:((humble(X)&strong(X))))<=>(?[X]:((tall(X)|~wise(X)))))&
((~tall(fred))<=>((~tall(lucy)|~patient(lucy))))&
((strong(john))=>((~quiet(mary)&humble(mary))))&
((~funny(susan))=>((~brave(fred)&~humble(fred))))&
(((rich(paul)&old(paul)))<=>(~happy(lucy)))&
(![X]:((~funny(X)|humble(X))<=>(~funny(X)|calm(X))))&
((?[X]:(~wise(X)))=>((rich(lucy)|~old(lucy))))&
(((creative(john)&~patient(john)))<=>(?[X]:(~brave(X))))&
((brave(john))<=>((curious(john)|~brave(john))))&
(![X]:((~patient(X)|~curious(X))=>(strong(X)<~>~humble(X))))&
((?[X]:((~humble(X)<~>brave(X))))=>(calm(alice)))&
(![X]:((wise(X)|old(X))<=>~curious(X)))&
((~brave(mary))<=>(?[X]:((~rich(X)&patient(X)))))&
((~calm(susan)<~>~curious(susan)))&
(?[X]:((~brave(X)&~generous(X))))&
(tall(paul))&
(?[X]:((brave(X)<~>~brave(X))))&
(?[X]:((~strong(X)&~old(X))))&
(?[X]:((~kind(X)<~>funny(X)))) | funny(paul) | [] | null | 0 |
If someone is either kind or funny then someone is both not curious and old. If john is not happy or wise then someone is both strong and not tall. If someone is either old or funny then someone is strong. If paul is either not patient or creative then paul is happy or kind and vice versa. If susan is tall or not calm then someone is old. Everyone who is not old is not wise or not generous and vice versa. If mary is wise then someone is both quiet and not wise and vice versa. If someone is both not quiet and quiet then john is brave and vice versa. If john is either not old or patient then fred is old or not happy and vice versa. If lucy is wise then someone is both not wise and not old and vice versa. Everyone who is both old and not quiet is not happy and vice versa. Everyone who is both old and tall is curious. If john is both not tall and brave then fred is not patient or tall and vice versa. If mary is brave then susan is either not old or not brave. Everyone who is not old is both brave and not creative and vice versa. Everyone who is either calm or wise is either funny or not humble. Someone is either not calm or calm. Someone is not strong or not old. Someone is both not strong and not happy. Alice is both humble and patient. Lucy is both not strong and not old. Someone is both generous and happy. Someone is funny. Someone is generous or funny. | John is not generous. | contradiction | ((?[X]:((kind(X)<~>funny(X))))=>(?[X]:((~curious(X)&old(X)))))&
(((~happy(john)|wise(john)))=>(?[X]:((strong(X)&~tall(X)))))&
((?[X]:((old(X)<~>funny(X))))=>(?[X]:(strong(X))))&
(((~patient(paul)<~>creative(paul)))<=>((happy(paul)|kind(paul))))&
(((tall(susan)|~calm(susan)))=>(?[X]:(old(X))))&
(![X]:(~old(X)<=>(~wise(X)|~generous(X))))&
((wise(mary))<=>(?[X]:((quiet(X)&~wise(X)))))&
((?[X]:((~quiet(X)&quiet(X))))<=>(brave(john)))&
(((~old(john)<~>patient(john)))<=>((old(fred)|~happy(fred))))&
((wise(lucy))<=>(?[X]:((~wise(X)&~old(X)))))&
(![X]:((old(X)&~quiet(X))<=>~happy(X)))&
(![X]:((old(X)&tall(X))=>curious(X)))&
(((~tall(john)&brave(john)))<=>((~patient(fred)|tall(fred))))&
((brave(mary))=>((~old(susan)<~>~brave(susan))))&
(![X]:(~old(X)<=>(brave(X)&~creative(X))))&
(![X]:((calm(X)<~>wise(X))=>(funny(X)<~>~humble(X))))&
(?[X]:((~calm(X)<~>calm(X))))&
(?[X]:((~strong(X)|~old(X))))&
(?[X]:((~strong(X)&~happy(X))))&
((humble(alice)&patient(alice)))&
((~strong(lucy)&~old(lucy)))&
(?[X]:((generous(X)&happy(X))))&
(?[X]:(funny(X)))&
(?[X]:((generous(X)|funny(X)))) | ~generous(john) | [
"p5",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7281311784647907724642145
% SZS output start Proof for 7281311784647907724642145
6. ! [X0] : (~old(X0) <=> (~generous(X0) | ~wise(X0))) [input p5]
8. ? [X0] : (quiet(X0) & ~quiet(X0)) <=> brave(john) [input p7]
15. ! [X0] : (~old(X0) <=> (~creative(X0) & brave(X0))) [input p14]
25. ~generous(john) [input hypothesis]
50. ! [X0] : ((~old(X0) | (generous(X0) & wise(X0))) & ((~generous(X0) | ~wise(X0)) | old(X0))) [nnf transformation 6]
51. ! [X0] : ((~old(X0) | (generous(X0) & wise(X0))) & (~generous(X0) | ~wise(X0) | old(X0))) [flattening 50]
56. (? [X0] : (quiet(X0) & ~quiet(X0)) | ~brave(john)) & (brave(john) | ! [X0] : (~quiet(X0) | quiet(X0))) [nnf transformation 8]
57. (? [X0] : (quiet(X0) & ~quiet(X0)) | ~brave(john)) & (brave(john) | ! [X1] : (~quiet(X1) | quiet(X1))) [rectify 56]
58. ? [X0] : (quiet(X0) & ~quiet(X0)) => (quiet(sK5) & ~quiet(sK5)) [choice axiom]
59. ((quiet(sK5) & ~quiet(sK5)) | ~brave(john)) & (brave(john) | ! [X1] : (~quiet(X1) | quiet(X1))) [skolemisation 57,58]
71. ! [X0] : ((~old(X0) | (creative(X0) | ~brave(X0))) & ((~creative(X0) & brave(X0)) | old(X0))) [nnf transformation 15]
72. ! [X0] : ((~old(X0) | creative(X0) | ~brave(X0)) & ((~creative(X0) & brave(X0)) | old(X0))) [flattening 71]
107. ~old(X0) | generous(X0) [cnf transformation 51]
112. ~quiet(sK5) | ~brave(john) [cnf transformation 59]
113. quiet(sK5) | ~brave(john) [cnf transformation 59]
134. brave(X0) | old(X0) [cnf transformation 72]
154. ~generous(john) [cnf transformation 25]
260. 23 <=> brave(john) [avatar definition]
262. ~brave(john) <- (~23) [avatar component clause 260]
264. 24 <=> quiet(sK5) [avatar definition]
267. ~23 | 24 [avatar split clause 113,264,260]
268. ~23 | ~24 [avatar split clause 112,264,260]
274. 26 <=> old(john) [avatar definition]
275. ~old(john) <- (~26) [avatar component clause 274]
276. old(john) <- (26) [avatar component clause 274]
369. generous(john) <- (26) [resolution 276,107]
371. $false <- (26) [subsumption resolution 369,154]
372. ~26 [avatar contradiction clause 371]
377. old(john) <- (~23) [resolution 134,262]
379. $false <- (~23, ~26) [subsumption resolution 377,275]
380. 23 | 26 [avatar contradiction clause 379]
381. $false [avatar sat refutation 267,268,372,380]
% SZS output end Proof for 7281311784647907724642145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then someone is either old or not rich and vice versa.
If mary is generous or strong then alice is both calm and kind and vice versa.
If paul is generous then someone is both not funny and quiet and vice versa.
If someone is not wise or not old then susan is generous and vice versa.
If mary is rich then someone is humble and vice versa.
If someone is not calm then paul is curious.
Everyone who is wise is not old and vice versa.
If someone is brave then mary is either calm or happy.
Everyone who is both not curious and old is funny.
If mary is either strong or quiet then someone is kind or old and vice versa.
If susan is either quiet or not kind then someone is both not wise and not patient.
If someone is not strong then alice is both kind and not rich and vice versa.
If paul is calm then someone is both not curious and kind and vice versa.
Everyone who is calm or strong is both not tall and not humble and vice versa.
If paul is rich then lucy is either not old or not rich.
Someone is old or wise.
Mary is strong or patient.
Lucy is not funny.
Someone is both not rich and brave.
Lucy is not humble or patient.
Someone is either not wise or strong.
Someone is not creative or funny. | Alice is not old. | neutral | ((?[X]:(~creative(X)))<=>(?[X]:((old(X)<~>~rich(X)))))&
(((generous(mary)|strong(mary)))<=>((calm(alice)&kind(alice))))&
((generous(paul))<=>(?[X]:((~funny(X)&quiet(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>(generous(susan)))&
((rich(mary))<=>(?[X]:(humble(X))))&
((?[X]:(~calm(X)))=>(curious(paul)))&
(![X]:(wise(X)<=>~old(X)))&
((?[X]:(brave(X)))=>((calm(mary)<~>happy(mary))))&
(![X]:((~curious(X)&old(X))=>funny(X)))&
(((strong(mary)<~>quiet(mary)))<=>(?[X]:((kind(X)|old(X)))))&
(((quiet(susan)<~>~kind(susan)))=>(?[X]:((~wise(X)&~patient(X)))))&
((?[X]:(~strong(X)))<=>((kind(alice)&~rich(alice))))&
((calm(paul))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((calm(X)|strong(X))<=>(~tall(X)&~humble(X))))&
((rich(paul))=>((~old(lucy)<~>~rich(lucy))))&
(?[X]:((old(X)|wise(X))))&
((strong(mary)|patient(mary)))&
(~funny(lucy))&
(?[X]:((~rich(X)&brave(X))))&
((~humble(lucy)|patient(lucy)))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~creative(X)|funny(X)))) | ~old(alice) | [] | null | 0 |
Everyone who is either kind or happy is either not humble or wise.
If someone is not funny then mary is not patient and vice versa.
Everyone who is both generous and wise is both tall and patient.
Everyone who is funny or not quiet is both not patient and not curious and vice versa.
If someone is both strong and humble then someone is both not wise and not calm.
If mary is generous then fred is both not calm and tall.
Everyone who is either curious or creative is both funny and generous and vice versa.
Everyone who is not tall or kind is patient and vice versa.
Everyone who is both old and tall is both creative and not strong.
Everyone who is not creative is funny.
Everyone who is kind is not curious.
If susan is old then someone is both brave and old.
Everyone who is brave or kind is either not kind or quiet.
Everyone who is both not quiet and not happy is creative or not brave.
Everyone who is either not tall or calm is both not happy and not rich and vice versa.
Everyone who is either not quiet or wise is both rich and calm and vice versa.
Alice is both generous and not curious.
Someone is not rich or not patient.
Fred is either funny or not humble.
Someone is both not wise and funny.
Lucy is not brave.
Someone is old or not humble.
Someone is either tall or not curious. | Fred is old. | neutral | (![X]:((kind(X)<~>happy(X))=>(~humble(X)<~>wise(X))))&
((?[X]:(~funny(X)))<=>(~patient(mary)))&
(![X]:((generous(X)&wise(X))=>(tall(X)&patient(X))))&
(![X]:((funny(X)|~quiet(X))<=>(~patient(X)&~curious(X))))&
((?[X]:((strong(X)&humble(X))))=>(?[X]:((~wise(X)&~calm(X)))))&
((generous(mary))=>((~calm(fred)&tall(fred))))&
(![X]:((curious(X)<~>creative(X))<=>(funny(X)&generous(X))))&
(![X]:((~tall(X)|kind(X))<=>patient(X)))&
(![X]:((old(X)&tall(X))=>(creative(X)&~strong(X))))&
(![X]:(~creative(X)=>funny(X)))&
(![X]:(kind(X)=>~curious(X)))&
((old(susan))=>(?[X]:((brave(X)&old(X)))))&
(![X]:((brave(X)|kind(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((~quiet(X)&~happy(X))=>(creative(X)|~brave(X))))&
(![X]:((~tall(X)<~>calm(X))<=>(~happy(X)&~rich(X))))&
(![X]:((~quiet(X)<~>wise(X))<=>(rich(X)&calm(X))))&
((generous(alice)&~curious(alice)))&
(?[X]:((~rich(X)|~patient(X))))&
((funny(fred)<~>~humble(fred)))&
(?[X]:((~wise(X)&funny(X))))&
(~brave(lucy))&
(?[X]:((old(X)|~humble(X))))&
(?[X]:((tall(X)<~>~curious(X)))) | old(fred) | [] | null | 0 |
If someone is either curious or not rich then john is both tall and not calm and vice versa. Everyone who is either not strong or wise is not kind. If mary is tall or calm then someone is not creative or wise and vice versa. If fred is not creative or not happy then susan is tall or not kind and vice versa. If someone is not brave or tall then someone is either creative or strong. Everyone who is not calm or not rich is either curious or calm and vice versa. If lucy is either not happy or not tall then susan is not rich or not kind. If someone is funny or not patient then someone is both not kind and creative. If fred is either curious or not generous then paul is tall and vice versa. Everyone who is either not patient or curious is either not strong or not calm and vice versa. If someone is not creative then someone is either not rich or not patient and vice versa. If someone is brave or not humble then alice is not kind. If someone is not strong then someone is both brave and rich. If someone is not tall or rich then someone is either not rich or curious and vice versa. Everyone who is both calm and not curious is not funny. Someone is both strong and not kind. John is both not wise and kind. Paul is either brave or not happy. Mary is both quiet and patient. Fred is not humble. Paul is both rich and quiet. Alice is both tall and rich. Someone is tall or not humble. | John is not patient. | contradiction | ((?[X]:((curious(X)<~>~rich(X))))<=>((tall(john)&~calm(john))))&
(![X]:((~strong(X)<~>wise(X))=>~kind(X)))&
(((tall(mary)|calm(mary)))<=>(?[X]:((~creative(X)|wise(X)))))&
(((~creative(fred)|~happy(fred)))<=>((tall(susan)|~kind(susan))))&
((?[X]:((~brave(X)|tall(X))))=>(?[X]:((creative(X)<~>strong(X)))))&
(![X]:((~calm(X)|~rich(X))<=>(curious(X)<~>calm(X))))&
(((~happy(lucy)<~>~tall(lucy)))=>((~rich(susan)|~kind(susan))))&
((?[X]:((funny(X)|~patient(X))))=>(?[X]:((~kind(X)&creative(X)))))&
(((curious(fred)<~>~generous(fred)))<=>(tall(paul)))&
(![X]:((~patient(X)<~>curious(X))<=>(~strong(X)<~>~calm(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
((?[X]:((brave(X)|~humble(X))))=>(~kind(alice)))&
((?[X]:(~strong(X)))=>(?[X]:((brave(X)&rich(X)))))&
((?[X]:((~tall(X)|rich(X))))<=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:((calm(X)&~curious(X))=>~funny(X)))&
(?[X]:((strong(X)&~kind(X))))&
((~wise(john)&kind(john)))&
((brave(paul)<~>~happy(paul)))&
((quiet(mary)&patient(mary)))&
(~humble(fred))&
((rich(paul)&quiet(paul)))&
((tall(alice)&rich(alice)))&
(?[X]:((tall(X)|~humble(X)))) | ~patient(john) | [
"p0",
"p1",
"p5",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8451962629294627364788795
% SZS output start Proof for 8451962629294627364788795
1. ? [X0] : (curious(X0) <~> ~rich(X0)) <=> (~calm(john) & tall(john)) [input p0]
2. ! [X0] : ((~strong(X0) <~> wise(X0)) => ~kind(X0)) [input p1]
6. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> (curious(X0) <~> calm(X0))) [input p5]
10. ! [X0] : ((~patient(X0) <~> curious(X0)) <=> (~strong(X0) <~> ~calm(X0))) [input p9]
17. kind(john) & ~wise(john) [input p16]
24. ~patient(john) [input hypothesis]
34. ! [X0] : (~kind(X0) | (~strong(X0) <=> wise(X0))) [ennf transformation 2]
41. (? [X0] : ((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | (calm(john) | ~tall(john))) & ((~calm(john) & tall(john)) | ! [X0] : ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) [nnf transformation 1]
42. (? [X0] : ((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | calm(john) | ~tall(john)) & ((~calm(john) & tall(john)) | ! [X0] : ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) [flattening 41]
43. (? [X0] : ((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | calm(john) | ~tall(john)) & ((~calm(john) & tall(john)) | ! [X1] : ((curious(X1) | rich(X1)) & (~rich(X1) | ~curious(X1)))) [rectify 42]
44. ? [X0] : ((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) => ((rich(sK0) | ~curious(sK0)) & (~rich(sK0) | curious(sK0))) [choice axiom]
45. (((rich(sK0) | ~curious(sK0)) & (~rich(sK0) | curious(sK0))) | calm(john) | ~tall(john)) & ((~calm(john) & tall(john)) | ! [X1] : ((curious(X1) | rich(X1)) & (~rich(X1) | ~curious(X1)))) [skolemisation 43,44]
46. ! [X0] : (~kind(X0) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) [nnf transformation 34]
58. ! [X0] : (((~rich(X0) | ~calm(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | (rich(X0) & calm(X0)))) [nnf transformation 6]
59. ! [X0] : ((~rich(X0) | ~calm(X0) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | (rich(X0) & calm(X0)))) [flattening 58]
65. ! [X0] : ((((~curious(X0) | patient(X0)) & (curious(X0) | ~patient(X0))) | ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | ((~patient(X0) | ~curious(X0)) & (curious(X0) | patient(X0))))) [nnf transformation 10]
86. ~calm(john) | ~rich(X1) | ~curious(X1) [cnf transformation 45]
90. ~kind(X0) | wise(X0) | strong(X0) [cnf transformation 46]
104. calm(X0) | curious(X0) | calm(X0) [cnf transformation 59]
107. ~calm(X0) | ~curious(X0) | rich(X0) [cnf transformation 59]
109. ~rich(X0) | ~calm(X0) | curious(X0) | ~calm(X0) [cnf transformation 59]
118. ~calm(X0) | ~strong(X0) | curious(X0) | patient(X0) [cnf transformation 65]
125. ~curious(X0) | patient(X0) | ~strong(X0) | calm(X0) [cnf transformation 65]
142. ~wise(john) [cnf transformation 17]
143. kind(john) [cnf transformation 17]
152. ~patient(john) [cnf transformation 24]
153. calm(X0) | curious(X0) [duplicate literal removal 104]
154. ~calm(X0) | ~rich(X0) | curious(X0) [duplicate literal removal 109]
160. 2 <=> calm(john) [avatar definition]
162. calm(john) <- (2) [avatar component clause 160]
178. 6 <=> ! [X1] : (~rich(X1) | ~curious(X1)) [avatar definition]
179. ~rich(X1) | ~curious(X1) <- (6) [avatar component clause 178]
180. 6 | ~2 [avatar split clause 86,160,178]
290. ~strong(X0) | patient(X0) | calm(X0) [subsumption resolution 125,153]
293. ~strong(X0) | curious(X0) | patient(X0) [subsumption resolution 118,290]
352. 43 <=> ! [X3] : ~rich(X3) [avatar definition]
353. ~rich(X3) <- (43) [avatar component clause 352]
409. wise(john) | strong(john) [resolution 90,143]
419. ~rich(X1) | curious(X1) | curious(X1) [resolution 154,153]
420. ~rich(X1) | curious(X1) [duplicate literal removal 419]
423. ~rich(X1) <- (6) [subsumption resolution 420,179]
424. 43 | ~6 [avatar split clause 423,178,352]
482. strong(john) [subsumption resolution 409,142]
502. curious(john) | patient(john) [resolution 482,293]
503. patient(john) | calm(john) [resolution 482,290]
504. calm(john) [subsumption resolution 503,152]
507. 2 [avatar split clause 504,160]
508. curious(john) [subsumption resolution 502,152]
512. ~curious(john) | rich(john) <- (2) [resolution 162,107]
513. rich(john) <- (2) [subsumption resolution 512,508]
514. $false <- (2, 43) [subsumption resolution 513,353]
515. ~2 | ~43 [avatar contradiction clause 514]
516. $false [avatar sat refutation 180,424,507,515]
% SZS output end Proof for 8451962629294627364788795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not curious then mary is either wise or funny.
Everyone who is both not calm and calm is both not strong and quiet and vice versa.
If someone is not humble or happy then someone is either brave or wise and vice versa.
Everyone who is either funny or not happy is not kind.
Everyone who is not funny or brave is either strong or not brave and vice versa.
Everyone who is not creative or wise is funny or not generous and vice versa.
Everyone who is both not generous and kind is both patient and humble.
Everyone who is old or funny is either not brave or not quiet.
If someone is kind then fred is strong or not old.
Everyone who is either strong or not tall is either not rich or not strong.
Everyone who is either quiet or not calm is creative.
If someone is rich or not curious then someone is tall or old.
Everyone who is not kind or curious is either not strong or not humble.
Everyone who is not creative or happy is either not patient or calm and vice versa.
If someone is not humble or creative then someone is both not funny and not brave.
Everyone who is not funny or not creative is old or quiet.
Someone is not patient.
Lucy is both rich and not creative.
Susan is old or not humble.
Paul is either not old or creative.
Susan is both calm and funny. | Mary is kind. | entailment | ((?[X]:((calm(X)|~curious(X))))=>((wise(mary)<~>funny(mary))))&
(![X]:((~calm(X)&calm(X))<=>(~strong(X)&quiet(X))))&
((?[X]:((~humble(X)|happy(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((funny(X)<~>~happy(X))=>~kind(X)))&
(![X]:((~funny(X)|brave(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((~creative(X)|wise(X))<=>(funny(X)|~generous(X))))&
(![X]:((~generous(X)&kind(X))=>(patient(X)&humble(X))))&
(![X]:((old(X)|funny(X))=>(~brave(X)<~>~quiet(X))))&
((?[X]:(kind(X)))=>((strong(fred)|~old(fred))))&
(![X]:((strong(X)<~>~tall(X))=>(~rich(X)<~>~strong(X))))&
(![X]:((quiet(X)<~>~calm(X))=>creative(X)))&
((?[X]:((rich(X)|~curious(X))))=>(?[X]:((tall(X)|old(X)))))&
(![X]:((~kind(X)|curious(X))=>(~strong(X)<~>~humble(X))))&
(![X]:((~creative(X)|happy(X))<=>(~patient(X)<~>calm(X))))&
((?[X]:((~humble(X)|creative(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((~funny(X)|~creative(X))=>(old(X)|quiet(X))))&
(?[X]:(~patient(X)))&
((rich(lucy)&~creative(lucy)))&
((old(susan)|~humble(susan)))&
((~old(paul)<~>creative(paul)))&
((calm(susan)&funny(susan))) | kind(mary) | [
"p1",
"p4",
"p7",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8551479866446599401267991
% SZS output start Proof for 8551479866446599401267991
2. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (quiet(X0) & ~strong(X0))) [input p1]
5. ! [X0] : ((brave(X0) | ~funny(X0)) <=> (strong(X0) <~> ~brave(X0))) [input p4]
8. ! [X0] : ((funny(X0) | old(X0)) => (~brave(X0) <~> ~quiet(X0))) [input p7]
13. ! [X0] : ((curious(X0) | ~kind(X0)) => (~strong(X0) <~> ~humble(X0))) [input p12]
15. ? [X0] : (creative(X0) | ~humble(X0)) => ? [X0] : (~brave(X0) & ~funny(X0)) [input p14]
16. ! [X0] : ((~creative(X0) | ~funny(X0)) => (quiet(X0) | old(X0))) [input p15]
22. ~kind(mary) [input hypothesis]
25. ? [X0] : (creative(X0) | ~humble(X0)) => ? [X1] : (~brave(X1) & ~funny(X1)) [rectify 15]
30. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) | (~funny(X0) & ~old(X0))) [ennf transformation 8]
36. ! [X0] : ((~strong(X0) <~> ~humble(X0)) | (~curious(X0) & kind(X0))) [ennf transformation 13]
37. ? [X1] : (~brave(X1) & ~funny(X1)) | ! [X0] : (~creative(X0) & humble(X0)) [ennf transformation 25]
38. ! [X0] : ((quiet(X0) | old(X0)) | (creative(X0) & funny(X0))) [ennf transformation 16]
39. ! [X0] : (quiet(X0) | old(X0) | (creative(X0) & funny(X0))) [flattening 38]
41. ! [X0] : (((calm(X0) & ~calm(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 2]
42. ! [X0] : (((calm(X0) & ~calm(X0)) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | ~calm(X0) | calm(X0))) [flattening 41]
49. ! [X0] : (((brave(X0) | ~funny(X0)) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (~brave(X0) & funny(X0)))) [nnf transformation 5]
50. ! [X0] : ((brave(X0) | ~funny(X0) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (~brave(X0) & funny(X0)))) [flattening 49]
53. ! [X0] : (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (~funny(X0) & ~old(X0))) [nnf transformation 30]
59. ! [X0] : (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~curious(X0) & kind(X0))) [nnf transformation 36]
62. ? [X0] : (~brave(X0) & ~funny(X0)) | ! [X1] : (~creative(X1) & humble(X1)) [rectify 37]
63. ? [X0] : (~brave(X0) & ~funny(X0)) => (~brave(sK3) & ~funny(sK3)) [choice axiom]
64. (~brave(sK3) & ~funny(sK3)) | ! [X1] : (~creative(X1) & humble(X1)) [skolemisation 62,63]
74. ~calm(X0) | ~quiet(X0) | strong(X0) [cnf transformation 42]
75. ~quiet(X0) | calm(X0) | strong(X0) [cnf transformation 42]
85. ~brave(X0) | strong(X0) | ~brave(X0) [cnf transformation 50]
86. ~strong(X0) | brave(X0) | funny(X0) [cnf transformation 50]
98. ~old(X0) | brave(X0) | quiet(X0) [cnf transformation 53]
99. ~funny(X0) | brave(X0) | quiet(X0) [cnf transformation 53]
109. ~humble(X0) | ~strong(X0) | kind(X0) [cnf transformation 59]
119. ~funny(sK3) | humble(X1) [cnf transformation 64]
121. ~brave(sK3) | humble(X1) [cnf transformation 64]
123. old(X0) | quiet(X0) | funny(X0) [cnf transformation 39]
133. ~kind(mary) [cnf transformation 22]
136. ~brave(X0) | strong(X0) [duplicate literal removal 85]
156. ~quiet(X0) | strong(X0) [subsumption resolution 74,75]
186. 12 <=> ! [X3] : humble(X3) [avatar definition]
187. humble(X3) <- (12) [avatar component clause 186]
220. 20 <=> brave(sK3) [avatar definition]
222. ~brave(sK3) <- (~20) [avatar component clause 220]
224. 12 | ~20 [avatar split clause 121,220,186]
226. 21 <=> funny(sK3) [avatar definition]
228. ~funny(sK3) <- (~21) [avatar component clause 226]
230. 12 | ~21 [avatar split clause 119,226,186]
315. 35 <=> humble(mary) [avatar definition]
316. ~humble(mary) <- (~35) [avatar component clause 315]
317. humble(mary) <- (35) [avatar component clause 315]
319. 36 <=> strong(mary) [avatar definition]
320. ~strong(mary) <- (~36) [avatar component clause 319]
324. ~strong(mary) | kind(mary) <- (35) [resolution 317,109]
330. ~strong(mary) <- (35) [subsumption resolution 324,133]
331. ~36 | ~35 [avatar split clause 330,315,319]
367. quiet(X0) | funny(X0) | brave(X0) | quiet(X0) [resolution 123,98]
370. quiet(X0) | funny(X0) | brave(X0) [duplicate literal removal 367]
380. brave(X0) | quiet(X0) [subsumption resolution 370,99]
431. quiet(X1) | strong(X1) [resolution 380,136]
432. strong(X1) [subsumption resolution 431,156]
455. brave(X0) | funny(X0) [resolution 432,86]
456. $false <- (~36) [resolution 432,320]
457. 36 [avatar contradiction clause 456]
460. funny(sK3) <- (~20) [resolution 455,222]
463. $false <- (~20, ~21) [subsumption resolution 460,228]
464. 20 | 21 [avatar contradiction clause 463]
467. $false <- (12, ~35) [resolution 187,316]
472. ~12 | 35 [avatar contradiction clause 467]
475. $false [avatar sat refutation 224,230,331,457,464,472]
% SZS output end Proof for 8551479866446599401267991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is either not happy or not creative.
Everyone who is both funny and not calm is either not old or not patient and vice versa.
If paul is both quiet and not kind then someone is both not humble and not old.
Everyone who is not patient is not happy.
If someone is old or not tall then someone is funny.
Everyone who is both strong and patient is old or not wise.
Everyone who is either creative or not tall is tall or generous and vice versa.
Everyone who is both tall and not patient is not creative or quiet.
Everyone who is not happy or happy is not funny or calm.
If someone is not humble or not rich then someone is both not humble and brave.
Everyone who is either creative or generous is tall or not happy and vice versa.
If paul is not generous or not tall then lucy is not rich or happy.
If someone is both patient and brave then someone is both curious and not generous and vice versa.
If mary is not humble then fred is happy or not brave.
If paul is both patient and not happy then fred is strong or not kind and vice versa.
Everyone who is both funny and not patient is not rich or not curious.
Someone is not patient.
Someone is not happy.
Someone is tall or brave.
Someone is both not rich and generous.
Someone is not kind.
Lucy is both not creative and not kind.
Fred is not patient or brave.
Someone is both kind and wise. | Lucy is not humble. | entailment | (![X]:(humble(X)=>(~happy(X)<~>~creative(X))))&
(![X]:((funny(X)&~calm(X))<=>(~old(X)<~>~patient(X))))&
(((quiet(paul)&~kind(paul)))=>(?[X]:((~humble(X)&~old(X)))))&
(![X]:(~patient(X)=>~happy(X)))&
((?[X]:((old(X)|~tall(X))))=>(?[X]:(funny(X))))&
(![X]:((strong(X)&patient(X))=>(old(X)|~wise(X))))&
(![X]:((creative(X)<~>~tall(X))<=>(tall(X)|generous(X))))&
(![X]:((tall(X)&~patient(X))=>(~creative(X)|quiet(X))))&
(![X]:((~happy(X)|happy(X))=>(~funny(X)|calm(X))))&
((?[X]:((~humble(X)|~rich(X))))=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((creative(X)<~>generous(X))<=>(tall(X)|~happy(X))))&
(((~generous(paul)|~tall(paul)))=>((~rich(lucy)|happy(lucy))))&
((?[X]:((patient(X)&brave(X))))<=>(?[X]:((curious(X)&~generous(X)))))&
((~humble(mary))=>((happy(fred)|~brave(fred))))&
(((patient(paul)&~happy(paul)))<=>((strong(fred)|~kind(fred))))&
(![X]:((funny(X)&~patient(X))=>(~rich(X)|~curious(X))))&
(?[X]:(~patient(X)))&
(?[X]:(~happy(X)))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((~rich(X)&generous(X))))&
(?[X]:(~kind(X)))&
((~creative(lucy)&~kind(lucy)))&
((~patient(fred)|brave(fred)))&
(?[X]:((kind(X)&wise(X)))) | ~humble(lucy) | [
"p0",
"p6",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 840781146472995251431787
% SZS output start Proof for 840781146472995251431787
1. ! [X0] : (humble(X0) => (~happy(X0) <~> ~creative(X0))) [input p0]
7. ! [X0] : ((creative(X0) <~> ~tall(X0)) <=> (generous(X0) | tall(X0))) [input p6]
11. ! [X0] : ((creative(X0) <~> generous(X0)) <=> (~happy(X0) | tall(X0))) [input p10]
22. ~kind(lucy) & ~creative(lucy) [input p21]
25. humble(lucy) [input hypothesis]
29. ! [X0] : ((~happy(X0) <~> ~creative(X0)) | ~humble(X0)) [ennf transformation 1]
47. ! [X0] : (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | ~humble(X0)) [nnf transformation 29]
55. ! [X0] : ((((tall(X0) | ~creative(X0)) & (~tall(X0) | creative(X0))) | (~generous(X0) & ~tall(X0))) & ((generous(X0) | tall(X0)) | ((creative(X0) | tall(X0)) & (~tall(X0) | ~creative(X0))))) [nnf transformation 7]
56. ! [X0] : ((((tall(X0) | ~creative(X0)) & (~tall(X0) | creative(X0))) | (~generous(X0) & ~tall(X0))) & (generous(X0) | tall(X0) | ((creative(X0) | tall(X0)) & (~tall(X0) | ~creative(X0))))) [flattening 55]
60. ! [X0] : ((((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | (happy(X0) & ~tall(X0))) & ((~happy(X0) | tall(X0)) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0))))) [nnf transformation 11]
61. ! [X0] : ((((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | (happy(X0) & ~tall(X0))) & (~happy(X0) | tall(X0) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0))))) [flattening 60]
82. ~humble(X0) | happy(X0) | creative(X0) [cnf transformation 47]
96. generous(X0) | tall(X0) | creative(X0) | tall(X0) [cnf transformation 56]
97. ~tall(X0) | creative(X0) | ~tall(X0) [cnf transformation 56]
100. tall(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 56]
108. ~happy(X0) | tall(X0) | generous(X0) | ~creative(X0) [cnf transformation 61]
109. ~happy(X0) | tall(X0) | creative(X0) | ~generous(X0) [cnf transformation 61]
112. ~generous(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 61]
133. ~creative(lucy) [cnf transformation 22]
138. humble(lucy) [cnf transformation 25]
139. generous(X0) | tall(X0) | creative(X0) [duplicate literal removal 96]
140. ~tall(X0) | creative(X0) [duplicate literal removal 97]
171. generous(X0) | creative(X0) [subsumption resolution 139,140]
192. ~generous(X0) | ~tall(X0) [subsumption resolution 112,140]
193. ~happy(X0) | tall(X0) | ~generous(X0) [subsumption resolution 109,100]
194. ~generous(X0) | ~happy(X0) [subsumption resolution 193,192]
195. ~happy(X0) | tall(X0) | generous(X0) [subsumption resolution 108,171]
196. ~happy(X0) | tall(X0) [subsumption resolution 195,194]
206. 14 <=> happy(lucy) [avatar definition]
208. happy(lucy) <- (14) [avatar component clause 206]
306. happy(lucy) | creative(lucy) [resolution 82,138]
307. happy(lucy) [subsumption resolution 306,133]
308. 14 [avatar split clause 307,206]
309. tall(lucy) <- (14) [resolution 208,196]
311. creative(lucy) <- (14) [resolution 309,140]
312. $false <- (14) [subsumption resolution 311,133]
313. ~14 [avatar contradiction clause 312]
314. $false [avatar sat refutation 308,313]
% SZS output end Proof for 840781146472995251431787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is generous or rich.
If someone is either patient or not patient then fred is not strong or not old.
Everyone who is not kind is either not kind or generous and vice versa.
If someone is not curious or not kind then someone is either funny or not old and vice versa.
Everyone who is not patient or generous is either strong or not calm and vice versa.
If someone is both creative and not brave then someone is both not calm and calm and vice versa.
If someone is creative then fred is not wise or generous and vice versa.
Everyone who is both not creative and patient is both curious and not funny.
Everyone who is kind or not rich is either not funny or not strong and vice versa.
If john is both not creative and not generous then someone is funny and vice versa.
If someone is rich or strong then someone is both calm and not curious and vice versa.
Everyone who is kind or rich is humble or patient.
If susan is not curious or not old then someone is either not generous or not curious and vice versa.
If someone is both not rich and funny then paul is funny.
Everyone who is not tall or not patient is not happy.
If fred is generous then john is either funny or not patient.
Someone is patient.
Lucy is both wise and quiet.
Lucy is either not brave or not calm.
Someone is both brave and not curious.
Someone is both not generous and calm.
Mary is not quiet or not rich.
Someone is quiet. | Fred is strong. | neutral | (![X]:(happy(X)=>(generous(X)|rich(X))))&
((?[X]:((patient(X)<~>~patient(X))))=>((~strong(fred)|~old(fred))))&
(![X]:(~kind(X)<=>(~kind(X)<~>generous(X))))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((funny(X)<~>~old(X)))))&
(![X]:((~patient(X)|generous(X))<=>(strong(X)<~>~calm(X))))&
((?[X]:((creative(X)&~brave(X))))<=>(?[X]:((~calm(X)&calm(X)))))&
((?[X]:(creative(X)))<=>((~wise(fred)|generous(fred))))&
(![X]:((~creative(X)&patient(X))=>(curious(X)&~funny(X))))&
(![X]:((kind(X)|~rich(X))<=>(~funny(X)<~>~strong(X))))&
(((~creative(john)&~generous(john)))<=>(?[X]:(funny(X))))&
((?[X]:((rich(X)|strong(X))))<=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:((kind(X)|rich(X))=>(humble(X)|patient(X))))&
(((~curious(susan)|~old(susan)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((~rich(X)&funny(X))))=>(funny(paul)))&
(![X]:((~tall(X)|~patient(X))=>~happy(X)))&
((generous(fred))=>((funny(john)<~>~patient(john))))&
(?[X]:(patient(X)))&
((wise(lucy)&quiet(lucy)))&
((~brave(lucy)<~>~calm(lucy)))&
(?[X]:((brave(X)&~curious(X))))&
(?[X]:((~generous(X)&calm(X))))&
((~quiet(mary)|~rich(mary)))&
(?[X]:(quiet(X))) | strong(fred) | [] | null | 0 |
If someone is not brave or not rich then susan is generous and vice versa. Everyone who is both wise and funny is both strong and wise and vice versa. Everyone who is not rich is either not curious or quiet. If someone is calm then alice is both not calm and not quiet. Everyone who is not happy is not rich and vice versa. If mary is either strong or old then someone is not happy. If someone is funny then john is not brave or quiet and vice versa. Everyone who is not brave or not patient is not patient or calm and vice versa. If paul is not creative or not wise then john is rich and vice versa. Everyone who is not old or wise is kind and vice versa. Everyone who is not calm or curious is not funny. Everyone who is either not humble or funny is happy and vice versa. Everyone who is quiet or not brave is not humble or patient. Everyone who is not quiet or not brave is either brave or humble and vice versa. Everyone who is happy is both generous and kind and vice versa. Everyone who is both not generous and not calm is either not happy or not rich. Mary is not patient or humble. Someone is not kind. Someone is not wise. Someone is either old or not rich. Alice is both not curious and happy. Someone is kind. Someone is not funny. | Susan is not happy. | neutral | ((?[X]:((~brave(X)|~rich(X))))<=>(generous(susan)))&
(![X]:((wise(X)&funny(X))<=>(strong(X)&wise(X))))&
(![X]:(~rich(X)=>(~curious(X)<~>quiet(X))))&
((?[X]:(calm(X)))=>((~calm(alice)&~quiet(alice))))&
(![X]:(~happy(X)<=>~rich(X)))&
(((strong(mary)<~>old(mary)))=>(?[X]:(~happy(X))))&
((?[X]:(funny(X)))<=>((~brave(john)|quiet(john))))&
(![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))&
(((~creative(paul)|~wise(paul)))<=>(rich(john)))&
(![X]:((~old(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)|curious(X))=>~funny(X)))&
(![X]:((~humble(X)<~>funny(X))<=>happy(X)))&
(![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))&
(![X]:(happy(X)<=>(generous(X)&kind(X))))&
(![X]:((~generous(X)&~calm(X))=>(~happy(X)<~>~rich(X))))&
((~patient(mary)|humble(mary)))&
(?[X]:(~kind(X)))&
(?[X]:(~wise(X)))&
(?[X]:((old(X)<~>~rich(X))))&
((~curious(alice)&happy(alice)))&
(?[X]:(kind(X)))&
(?[X]:(~funny(X))) | ~happy(susan) | [] | null | 0 |
If someone is both generous and not rich then someone is creative and vice versa.
Everyone who is either quiet or not patient is either not strong or funny and vice versa.
Everyone who is both not curious and tall is both not tall and not generous and vice versa.
Everyone who is not funny or brave is funny or not curious and vice versa.
Everyone who is both humble and generous is both generous and kind and vice versa.
Everyone who is both not curious and old is happy or not kind.
If fred is funny then someone is either kind or calm and vice versa.
Everyone who is kind is either funny or not calm.
If someone is both not curious and not creative then someone is both not curious and not quiet.
Everyone who is both not patient and not strong is wise and vice versa.
If someone is not kind or brave then john is not strong or creative.
Everyone who is humble or patient is old and vice versa.
If someone is not tall or not generous then paul is wise or not tall and vice versa.
If john is kind or not kind then paul is either creative or not humble.
Everyone who is either calm or quiet is not happy or not kind and vice versa.
If lucy is both strong and old then paul is not quiet or brave.
Someone is both not funny and happy.
Someone is both tall and not happy.
John is not old or rich.
Paul is quiet.
Someone is humble or kind.
Someone is both brave and not generous.
Someone is not happy.
John is both not generous and not calm. | John is not curious. | contradiction | ((?[X]:((generous(X)&~rich(X))))<=>(?[X]:(creative(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>(~strong(X)<~>funny(X))))&
(![X]:((~curious(X)&tall(X))<=>(~tall(X)&~generous(X))))&
(![X]:((~funny(X)|brave(X))<=>(funny(X)|~curious(X))))&
(![X]:((humble(X)&generous(X))<=>(generous(X)&kind(X))))&
(![X]:((~curious(X)&old(X))=>(happy(X)|~kind(X))))&
((funny(fred))<=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:(kind(X)=>(funny(X)<~>~calm(X))))&
((?[X]:((~curious(X)&~creative(X))))=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((~patient(X)&~strong(X))<=>wise(X)))&
((?[X]:((~kind(X)|brave(X))))=>((~strong(john)|creative(john))))&
(![X]:((humble(X)|patient(X))<=>old(X)))&
((?[X]:((~tall(X)|~generous(X))))<=>((wise(paul)|~tall(paul))))&
(((kind(john)|~kind(john)))=>((creative(paul)<~>~humble(paul))))&
(![X]:((calm(X)<~>quiet(X))<=>(~happy(X)|~kind(X))))&
(((strong(lucy)&old(lucy)))=>((~quiet(paul)|brave(paul))))&
(?[X]:((~funny(X)&happy(X))))&
(?[X]:((tall(X)&~happy(X))))&
((~old(john)|rich(john)))&
(quiet(paul))&
(?[X]:((humble(X)|kind(X))))&
(?[X]:((brave(X)&~generous(X))))&
(?[X]:(~happy(X)))&
((~generous(john)&~calm(john))) | ~curious(john) | [
"p2",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6935027166676983746922356
% SZS output start Proof for 6935027166676983746922356
3. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~generous(X0) & ~tall(X0))) [input p2]
24. ~calm(john) & ~generous(john) [input p23]
25. ~curious(john) [input hypothesis]
45. ! [X0] : (((tall(X0) & ~curious(X0)) | (generous(X0) | tall(X0))) & ((~generous(X0) & ~tall(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 3]
46. ! [X0] : (((tall(X0) & ~curious(X0)) | generous(X0) | tall(X0)) & ((~generous(X0) & ~tall(X0)) | ~tall(X0) | curious(X0))) [flattening 45]
90. ~tall(X0) | ~tall(X0) | curious(X0) [cnf transformation 46]
93. tall(X0) | generous(X0) | tall(X0) [cnf transformation 46]
143. ~generous(john) [cnf transformation 24]
145. ~curious(john) [cnf transformation 25]
148. ~tall(X0) | curious(X0) [duplicate literal removal 90]
149. tall(X0) | generous(X0) [duplicate literal removal 93]
304. curious(X0) | generous(X0) [resolution 149,148]
330. generous(john) [resolution 304,145]
333. $false [subsumption resolution 330,143]
% SZS output end Proof for 6935027166676983746922356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or curious is not curious and vice versa.
If someone is both generous and not curious then someone is either old or generous and vice versa.
Everyone who is both strong and not curious is either funny or calm and vice versa.
If fred is not strong then someone is both brave and not patient and vice versa.
Everyone who is not strong is both not kind and not patient.
Everyone who is both happy and not quiet is either kind or not tall and vice versa.
Everyone who is either brave or humble is strong or creative.
Everyone who is both not tall and patient is funny or patient.
If alice is tall or old then paul is not old and vice versa.
Everyone who is both wise and generous is strong and vice versa.
If someone is not funny then someone is either humble or happy.
If lucy is both strong and tall then susan is either not funny or not old and vice versa.
Everyone who is funny is not wise.
Everyone who is both creative and tall is old or funny.
If someone is either patient or not humble then someone is either not curious or not kind.
If mary is not brave then alice is patient.
Someone is not brave.
Paul is either not quiet or not curious.
Lucy is both not generous and not funny.
Someone is both wise and not brave.
Lucy is both not brave and not curious.
Someone is both not humble and creative.
Lucy is not generous.
Fred is quiet. | Susan is humble. | neutral | (![X]:((~happy(X)<~>curious(X))<=>~curious(X)))&
((?[X]:((generous(X)&~curious(X))))<=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:((strong(X)&~curious(X))<=>(funny(X)<~>calm(X))))&
((~strong(fred))<=>(?[X]:((brave(X)&~patient(X)))))&
(![X]:(~strong(X)=>(~kind(X)&~patient(X))))&
(![X]:((happy(X)&~quiet(X))<=>(kind(X)<~>~tall(X))))&
(![X]:((brave(X)<~>humble(X))=>(strong(X)|creative(X))))&
(![X]:((~tall(X)&patient(X))=>(funny(X)|patient(X))))&
(((tall(alice)|old(alice)))<=>(~old(paul)))&
(![X]:((wise(X)&generous(X))<=>strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((humble(X)<~>happy(X)))))&
(((strong(lucy)&tall(lucy)))<=>((~funny(susan)<~>~old(susan))))&
(![X]:(funny(X)=>~wise(X)))&
(![X]:((creative(X)&tall(X))=>(old(X)|funny(X))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((~curious(X)<~>~kind(X)))))&
((~brave(mary))=>(patient(alice)))&
(?[X]:(~brave(X)))&
((~quiet(paul)<~>~curious(paul)))&
((~generous(lucy)&~funny(lucy)))&
(?[X]:((wise(X)&~brave(X))))&
((~brave(lucy)&~curious(lucy)))&
(?[X]:((~humble(X)&creative(X))))&
(~generous(lucy))&
(quiet(fred)) | humble(susan) | [] | null | 0 |
If someone is not rich or not strong then someone is both not funny and old.
If someone is both not strong and not brave then john is not wise or not kind.
Everyone who is old or rich is either not humble or not patient and vice versa.
Everyone who is not humble is either generous or not kind.
If someone is not creative or humble then fred is not wise and vice versa.
Everyone who is both rich and humble is not old or tall.
Everyone who is either kind or not happy is not brave.
If lucy is both patient and not old then alice is not kind and vice versa.
Everyone who is either funny or not kind is either not kind or not old and vice versa.
Everyone who is either quiet or not creative is either rich or old and vice versa.
If someone is either not quiet or quiet then fred is not tall or tall and vice versa.
If someone is humble or not funny then someone is not patient or quiet.
Everyone who is brave or curious is not brave.
Everyone who is curious or not old is either wise or not curious and vice versa.
Everyone who is wise or not funny is both brave and not curious.
Everyone who is either not strong or funny is either not wise or not funny and vice versa.
Someone is not generous.
Someone is either quiet or kind.
Paul is happy or not curious.
Fred is humble or not calm.
Paul is both funny and not old.
Someone is strong. | Alice is not brave. | entailment | ((?[X]:((~rich(X)|~strong(X))))=>(?[X]:((~funny(X)&old(X)))))&
((?[X]:((~strong(X)&~brave(X))))=>((~wise(john)|~kind(john))))&
(![X]:((old(X)|rich(X))<=>(~humble(X)<~>~patient(X))))&
(![X]:(~humble(X)=>(generous(X)<~>~kind(X))))&
((?[X]:((~creative(X)|humble(X))))<=>(~wise(fred)))&
(![X]:((rich(X)&humble(X))=>(~old(X)|tall(X))))&
(![X]:((kind(X)<~>~happy(X))=>~brave(X)))&
(((patient(lucy)&~old(lucy)))<=>(~kind(alice)))&
(![X]:((funny(X)<~>~kind(X))<=>(~kind(X)<~>~old(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(rich(X)<~>old(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>((~tall(fred)|tall(fred))))&
((?[X]:((humble(X)|~funny(X))))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((brave(X)|curious(X))=>~brave(X)))&
(![X]:((curious(X)|~old(X))<=>(wise(X)<~>~curious(X))))&
(![X]:((wise(X)|~funny(X))=>(brave(X)&~curious(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(~wise(X)<~>~funny(X))))&
(?[X]:(~generous(X)))&
(?[X]:((quiet(X)<~>kind(X))))&
((happy(paul)|~curious(paul)))&
((humble(fred)|~calm(fred)))&
((funny(paul)&~old(paul)))&
(?[X]:(strong(X))) | ~brave(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4649913138532134237128742
% SZS output start Proof for 4649913138532134237128742
13. ! [X0] : ((curious(X0) | brave(X0)) => ~brave(X0)) [input p12]
23. brave(alice) [input hypothesis]
35. ! [X0] : (~brave(X0) | (~curious(X0) & ~brave(X0))) [ennf transformation 13]
116. ~brave(X0) | ~brave(X0) [cnf transformation 35]
143. brave(alice) [cnf transformation 23]
150. ~brave(X0) [duplicate literal removal 116]
256. $false [subsumption resolution 143,150]
% SZS output end Proof for 4649913138532134237128742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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