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 calm or not happy is both not generous and humble and vice versa.
If someone is not creative then mary is either old or tall.
Everyone who is both curious and not creative is either not brave or not quiet.
Everyone who is either not old or not kind is both not rich and brave and vice versa.
If someone is either not creative or quiet then someone is not generous and vice versa.
Everyone who is either not quiet or kind is either not strong or brave.
If someone is old then paul is both funny and rich.
If paul is not brave then someone is not happy or old and vice versa.
If someone is not tall or creative then paul is both not brave and strong and vice versa.
Everyone who is patient or calm is kind or brave and vice versa.
Everyone who is not curious or not tall is both generous and not strong.
If someone is both not calm and humble then someone is not happy and vice versa.
Everyone who is kind or not brave is not tall.
Everyone who is both creative and patient is either old or not old.
If someone is both not wise and not humble then someone is both strong and not generous.
If mary is not patient or old then someone is brave and vice versa.
Susan is not curious or quiet.
Mary is not rich or wise.
Someone is generous.
Mary is either creative or not patient. | Mary is curious. | entailment | (![X]:((calm(X)<~>~happy(X))<=>(~generous(X)&humble(X))))&
((?[X]:(~creative(X)))=>((old(mary)<~>tall(mary))))&
(![X]:((curious(X)&~creative(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(~rich(X)&brave(X))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)<~>kind(X))=>(~strong(X)<~>brave(X))))&
((?[X]:(old(X)))=>((funny(paul)&rich(paul))))&
((~brave(paul))<=>(?[X]:((~happy(X)|old(X)))))&
((?[X]:((~tall(X)|creative(X))))<=>((~brave(paul)&strong(paul))))&
(![X]:((patient(X)|calm(X))<=>(kind(X)|brave(X))))&
(![X]:((~curious(X)|~tall(X))=>(generous(X)&~strong(X))))&
((?[X]:((~calm(X)&humble(X))))<=>(?[X]:(~happy(X))))&
(![X]:((kind(X)|~brave(X))=>~tall(X)))&
(![X]:((creative(X)&patient(X))=>(old(X)<~>~old(X))))&
((?[X]:((~wise(X)&~humble(X))))=>(?[X]:((strong(X)&~generous(X)))))&
(((~patient(mary)|old(mary)))<=>(?[X]:(brave(X))))&
((~curious(susan)|quiet(susan)))&
((~rich(mary)|wise(mary)))&
(?[X]:(generous(X)))&
((creative(mary)<~>~patient(mary))) | curious(mary) | [
"p0",
"p7",
"p8",
"p9",
"p10",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1832889628613597963648103
% SZS output start Proof for 1832889628613597963648103
1. ! [X0] : ((calm(X0) <~> ~happy(X0)) <=> (humble(X0) & ~generous(X0))) [input p0]
8. ~brave(paul) <=> ? [X0] : (old(X0) | ~happy(X0)) [input p7]
9. ? [X0] : (creative(X0) | ~tall(X0)) <=> (strong(paul) & ~brave(paul)) [input p8]
10. ! [X0] : ((calm(X0) | patient(X0)) <=> (brave(X0) | kind(X0))) [input p9]
11. ! [X0] : ((~tall(X0) | ~curious(X0)) => (~strong(X0) & generous(X0))) [input p10]
13. ! [X0] : ((~brave(X0) | kind(X0)) => ~tall(X0)) [input p12]
20. creative(mary) <~> ~patient(mary) [input p19]
21. ~curious(mary) [input hypothesis]
33. ! [X0] : ((~strong(X0) & generous(X0)) | (tall(X0) & curious(X0))) [ennf transformation 11]
34. ! [X0] : (~tall(X0) | (brave(X0) & ~kind(X0))) [ennf transformation 13]
37. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (~humble(X0) | generous(X0))) & ((humble(X0) & ~generous(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [nnf transformation 1]
38. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | ~humble(X0) | generous(X0)) & ((humble(X0) & ~generous(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [flattening 37]
49. (~brave(paul) | ! [X0] : (~old(X0) & happy(X0))) & (? [X0] : (old(X0) | ~happy(X0)) | brave(paul)) [nnf transformation 8]
50. (~brave(paul) | ! [X0] : (~old(X0) & happy(X0))) & (? [X1] : (old(X1) | ~happy(X1)) | brave(paul)) [rectify 49]
51. ? [X1] : (old(X1) | ~happy(X1)) => (old(sK2) | ~happy(sK2)) [choice axiom]
52. (~brave(paul) | ! [X0] : (~old(X0) & happy(X0))) & ((old(sK2) | ~happy(sK2)) | brave(paul)) [skolemisation 50,51]
53. (? [X0] : (creative(X0) | ~tall(X0)) | (~strong(paul) | brave(paul))) & ((strong(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & tall(X0))) [nnf transformation 9]
54. (? [X0] : (creative(X0) | ~tall(X0)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & tall(X0))) [flattening 53]
55. (? [X0] : (creative(X0) | ~tall(X0)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : (~creative(X1) & tall(X1))) [rectify 54]
56. ? [X0] : (creative(X0) | ~tall(X0)) => (creative(sK3) | ~tall(sK3)) [choice axiom]
57. ((creative(sK3) | ~tall(sK3)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : (~creative(X1) & tall(X1))) [skolemisation 55,56]
58. ! [X0] : (((calm(X0) | patient(X0)) | (~brave(X0) & ~kind(X0))) & ((brave(X0) | kind(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 10]
59. ! [X0] : ((calm(X0) | patient(X0) | (~brave(X0) & ~kind(X0))) & (brave(X0) | kind(X0) | (~calm(X0) & ~patient(X0)))) [flattening 58]
73. (patient(mary) | ~creative(mary)) & (~patient(mary) | creative(mary)) [nnf transformation 20]
74. ~generous(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 38]
100. ~brave(paul) | happy(X0) [cnf transformation 52]
102. ~brave(paul) | tall(X1) [cnf transformation 57]
103. ~brave(paul) | ~creative(X1) [cnf transformation 57]
104. strong(paul) | tall(X1) [cnf transformation 57]
110. ~brave(X0) | patient(X0) | calm(X0) [cnf transformation 59]
111. curious(X0) | generous(X0) [cnf transformation 33]
114. ~strong(X0) | tall(X0) [cnf transformation 33]
119. ~tall(X0) | brave(X0) [cnf transformation 34]
127. ~patient(mary) | creative(mary) [cnf transformation 73]
129. ~curious(mary) [cnf transformation 21]
177. 12 <=> brave(paul) [avatar definition]
179. ~brave(paul) <- (~12) [avatar component clause 177]
182. 13 <=> ! [X0] : happy(X0) [avatar definition]
183. happy(X0) <- (13) [avatar component clause 182]
184. 13 | ~12 [avatar split clause 100,177,182]
195. 16 <=> strong(paul) [avatar definition]
196. strong(paul) <- (16) [avatar component clause 195]
208. 19 <=> ! [X1] : ~creative(X1) [avatar definition]
209. ~creative(X1) <- (19) [avatar component clause 208]
212. 20 <=> ! [X1] : tall(X1) [avatar definition]
213. tall(X1) <- (20) [avatar component clause 212]
214. 20 | 16 [avatar split clause 104,195,212]
215. 19 | ~12 [avatar split clause 103,177,208]
216. 20 | ~12 [avatar split clause 102,177,212]
239. 26 <=> patient(mary) [avatar definition]
241. ~patient(mary) <- (~26) [avatar component clause 239]
259. 30 <=> creative(mary) [avatar definition]
260. creative(mary) <- (30) [avatar component clause 259]
263. 30 | ~26 [avatar split clause 127,239,259]
270. generous(mary) [resolution 111,129]
275. tall(paul) <- (16) [resolution 114,196]
277. brave(paul) <- (16) [resolution 275,119]
278. $false <- (~12, 16) [subsumption resolution 277,179]
279. 12 | ~16 [avatar contradiction clause 278]
282. brave(X0) <- (20) [resolution 213,119]
287. ~happy(mary) | ~calm(mary) [resolution 74,270]
291. 31 <=> calm(mary) [avatar definition]
295. 32 <=> happy(mary) [avatar definition]
297. ~happy(mary) <- (~32) [avatar component clause 295]
298. ~31 | ~32 [avatar split clause 287,295,291]
317. $false <- (~12, 20) [resolution 282,179]
318. 12 | ~20 [avatar contradiction clause 317]
351. patient(X1) | calm(X1) <- (20) [resolution 110,282]
361. $false <- (19, 30) [subsumption resolution 260,209]
362. ~19 | ~30 [avatar contradiction clause 361]
377. calm(mary) <- (20, ~26) [resolution 351,241]
380. 31 | ~20 | 26 [avatar split clause 377,239,212,291]
381. $false <- (13, ~32) [subsumption resolution 297,183]
382. ~13 | 32 [avatar contradiction clause 381]
383. $false [avatar sat refutation 184,214,215,216,263,279,298,318,362,380,382]
% SZS output end Proof for 1832889628613597963648103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not tall or not rich then susan is kind and vice versa.
If someone is not humble then someone is not tall or curious and vice versa.
Everyone who is both not generous and brave is either not happy or quiet.
Everyone who is both not rich and strong is tall and vice versa.
If john is either funny or not curious then paul is not kind or not calm.
If paul is strong then someone is old.
Everyone who is happy or not old is patient or not strong and vice versa.
Everyone who is both tall and not tall is rich or not strong and vice versa.
If paul is both not calm and not humble then mary is either brave or creative.
Everyone who is tall or rich is either not wise or brave.
Everyone who is both not humble and funny is either not quiet or not generous and vice versa.
Everyone who is not generous is funny or creative and vice versa.
If alice is either not wise or patient then mary is not quiet or happy and vice versa.
Everyone who is both curious and happy is curious or old and vice versa.
If someone is either not old or not strong then someone is either funny or not happy.
Everyone who is not wise or not rich is both strong and not creative.
Someone is brave or not tall.
Someone is not old or not brave.
Someone is either not generous or not wise.
Fred is quiet or not curious.
Someone is either brave or not quiet.
Fred is not wise. | Alice is tall. | entailment | ((?[X]:((~tall(X)<~>~rich(X))))<=>(kind(susan)))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)|curious(X)))))&
(![X]:((~generous(X)&brave(X))=>(~happy(X)<~>quiet(X))))&
(![X]:((~rich(X)&strong(X))<=>tall(X)))&
(((funny(john)<~>~curious(john)))=>((~kind(paul)|~calm(paul))))&
((strong(paul))=>(?[X]:(old(X))))&
(![X]:((happy(X)|~old(X))<=>(patient(X)|~strong(X))))&
(![X]:((tall(X)&~tall(X))<=>(rich(X)|~strong(X))))&
(((~calm(paul)&~humble(paul)))=>((brave(mary)<~>creative(mary))))&
(![X]:((tall(X)|rich(X))=>(~wise(X)<~>brave(X))))&
(![X]:((~humble(X)&funny(X))<=>(~quiet(X)<~>~generous(X))))&
(![X]:(~generous(X)<=>(funny(X)|creative(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~quiet(mary)|happy(mary))))&
(![X]:((curious(X)&happy(X))<=>(curious(X)|old(X))))&
((?[X]:((~old(X)<~>~strong(X))))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:((~wise(X)|~rich(X))=>(strong(X)&~creative(X))))&
(?[X]:((brave(X)|~tall(X))))&
(?[X]:((~old(X)|~brave(X))))&
(?[X]:((~generous(X)<~>~wise(X))))&
((quiet(fred)|~curious(fred)))&
(?[X]:((brave(X)<~>~quiet(X))))&
(~wise(fred)) | tall(alice) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5545243096859904775379584
% SZS output start Proof for 5545243096859904775379584
4. ! [X0] : ((strong(X0) & ~rich(X0)) <=> tall(X0)) [input p3]
8. ! [X0] : ((~tall(X0) & tall(X0)) <=> (~strong(X0) | rich(X0))) [input p7]
23. ~tall(alice) [input hypothesis]
46. ! [X0] : (((strong(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | (~strong(X0) | rich(X0)))) [nnf transformation 4]
47. ! [X0] : (((strong(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | ~strong(X0) | rich(X0))) [flattening 46]
53. ! [X0] : (((~tall(X0) & tall(X0)) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | (tall(X0) | ~tall(X0)))) [nnf transformation 8]
54. ! [X0] : (((~tall(X0) & tall(X0)) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | tall(X0) | ~tall(X0))) [flattening 53]
88. ~strong(X0) | tall(X0) | rich(X0) [cnf transformation 47]
89. ~rich(X0) | ~tall(X0) [cnf transformation 47]
90. ~tall(X0) | strong(X0) [cnf transformation 47]
99. tall(X0) | ~rich(X0) [cnf transformation 54]
100. tall(X0) | strong(X0) [cnf transformation 54]
145. ~tall(alice) [cnf transformation 23]
177. 8 <=> ! [X1] : tall(X1) [avatar definition]
178. tall(X1) <- (8) [avatar component clause 177]
219. strong(X0) [subsumption resolution 100,90]
220. ~rich(X0) [subsumption resolution 99,89]
326. tall(X0) | rich(X0) [resolution 88,219]
330. tall(X0) [subsumption resolution 326,220]
331. 8 [avatar split clause 330,177]
335. $false <- (8) [resolution 178,145]
340. ~8 [avatar contradiction clause 335]
341. $false [avatar sat refutation 331,340]
% SZS output end Proof for 5545243096859904775379584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not strong and not creative and vice versa.
Everyone who is tall is both not rich and not kind and vice versa.
Everyone who is both strong and old is strong or patient.
If someone is both not funny and not tall then someone is both not calm and quiet.
If susan is both generous and patient then lucy is quiet or funny and vice versa.
Everyone who is either not wise or not funny is either funny or not tall and vice versa.
Everyone who is funny is strong or not quiet and vice versa.
If paul is either creative or rich then susan is both not creative and rich and vice versa.
Everyone who is happy is both rich and happy.
If alice is not wise or old then someone is either patient or not curious and vice versa.
If paul is both rich and not tall then someone is not generous.
Everyone who is not curious or not quiet is both not tall and brave.
If fred is creative then someone is not old or quiet and vice versa.
If alice is strong or kind then fred is either humble or not quiet.
Everyone who is both curious and patient is not tall and vice versa.
Everyone who is both curious and not patient is either not humble or happy.
Someone is old or not happy.
Alice is either tall or wise.
Mary is both not wise and old.
Someone is curious or not curious.
Someone is both not humble and curious.
Susan is tall or not humble. | Fred is not wise. | neutral | (![X]:(kind(X)<=>(~strong(X)&~creative(X))))&
(![X]:(tall(X)<=>(~rich(X)&~kind(X))))&
(![X]:((strong(X)&old(X))=>(strong(X)|patient(X))))&
((?[X]:((~funny(X)&~tall(X))))=>(?[X]:((~calm(X)&quiet(X)))))&
(((generous(susan)&patient(susan)))<=>((quiet(lucy)|funny(lucy))))&
(![X]:((~wise(X)<~>~funny(X))<=>(funny(X)<~>~tall(X))))&
(![X]:(funny(X)<=>(strong(X)|~quiet(X))))&
(((creative(paul)<~>rich(paul)))<=>((~creative(susan)&rich(susan))))&
(![X]:(happy(X)=>(rich(X)&happy(X))))&
(((~wise(alice)|old(alice)))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(((rich(paul)&~tall(paul)))=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~tall(X)&brave(X))))&
((creative(fred))<=>(?[X]:((~old(X)|quiet(X)))))&
(((strong(alice)|kind(alice)))=>((humble(fred)<~>~quiet(fred))))&
(![X]:((curious(X)&patient(X))<=>~tall(X)))&
(![X]:((curious(X)&~patient(X))=>(~humble(X)<~>happy(X))))&
(?[X]:((old(X)|~happy(X))))&
((tall(alice)<~>wise(alice)))&
((~wise(mary)&old(mary)))&
(?[X]:((curious(X)|~curious(X))))&
(?[X]:((~humble(X)&curious(X))))&
((tall(susan)|~humble(susan))) | ~wise(fred) | [] | null | 0 |
Everyone who is both not calm and not humble is quiet. If someone is humble or not happy then someone is either not quiet or wise. If someone is creative then mary is strong or quiet. Everyone who is funny or not wise is happy or not kind. If someone is both not happy and wise then paul is rich or funny and vice versa. Everyone who is both tall and funny is both not generous and patient and vice versa. If fred is not quiet or humble then someone is both brave and kind and vice versa. Everyone who is humble or not brave is both quiet and wise. Everyone who is not wise or calm is not patient or humble and vice versa. Everyone who is old is either not humble or not old and vice versa. Everyone who is both kind and old is strong or happy. Everyone who is either creative or not quiet is both not happy and creative. If someone is brave or not quiet then someone is either not rich or not humble. If someone is both not curious and quiet then someone is strong and vice versa. If someone is not strong then someone is kind. Everyone who is both rich and humble is brave or not wise and vice versa. Paul is either not wise or not calm. Someone is not funny. Someone is either not curious or not brave. Someone is both not calm and curious. | Mary is strong. | neutral | (![X]:((~calm(X)&~humble(X))=>quiet(X)))&
((?[X]:((humble(X)|~happy(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:(creative(X)))=>((strong(mary)|quiet(mary))))&
(![X]:((funny(X)|~wise(X))=>(happy(X)|~kind(X))))&
((?[X]:((~happy(X)&wise(X))))<=>((rich(paul)|funny(paul))))&
(![X]:((tall(X)&funny(X))<=>(~generous(X)&patient(X))))&
(((~quiet(fred)|humble(fred)))<=>(?[X]:((brave(X)&kind(X)))))&
(![X]:((humble(X)|~brave(X))=>(quiet(X)&wise(X))))&
(![X]:((~wise(X)|calm(X))<=>(~patient(X)|humble(X))))&
(![X]:(old(X)<=>(~humble(X)<~>~old(X))))&
(![X]:((kind(X)&old(X))=>(strong(X)|happy(X))))&
(![X]:((creative(X)<~>~quiet(X))=>(~happy(X)&creative(X))))&
((?[X]:((brave(X)|~quiet(X))))=>(?[X]:((~rich(X)<~>~humble(X)))))&
((?[X]:((~curious(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:(~strong(X)))=>(?[X]:(kind(X))))&
(![X]:((rich(X)&humble(X))<=>(brave(X)|~wise(X))))&
((~wise(paul)<~>~calm(paul)))&
(?[X]:(~funny(X)))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((~calm(X)&curious(X)))) | strong(mary) | [] | null | 0 |
If fred is not quiet then mary is either creative or happy and vice versa.
Everyone who is not quiet is either not brave or not humble and vice versa.
Everyone who is either quiet or not patient is not generous and vice versa.
If someone is brave then someone is either not tall or not wise.
Everyone who is both happy and not creative is either not tall or funny and vice versa.
Everyone who is both not curious and patient is not wise.
If alice is not calm then someone is either quiet or not curious.
Everyone who is tall or patient is generous or not funny.
If john is both not calm and strong then someone is both creative and not brave and vice versa.
If alice is either generous or not calm then someone is old or quiet.
Everyone who is either not calm or not tall is happy and vice versa.
If someone is not happy or wise then someone is not calm and vice versa.
Everyone who is not tall is calm.
Everyone who is old is generous and vice versa.
Everyone who is both not old and calm is old or patient and vice versa.
If lucy is either not calm or not curious then mary is either rich or not calm and vice versa.
Susan is old or not strong.
Mary is old or not tall.
Someone is either calm or not old.
Someone is either not kind or strong.
Alice is tall or patient.
Someone is either patient or not calm.
Someone is not calm. | Susan is strong. | contradiction | ((~quiet(fred))<=>((creative(mary)<~>happy(mary))))&
(![X]:(~quiet(X)<=>(~brave(X)<~>~humble(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>~generous(X)))&
((?[X]:(brave(X)))=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:((happy(X)&~creative(X))<=>(~tall(X)<~>funny(X))))&
(![X]:((~curious(X)&patient(X))=>~wise(X)))&
((~calm(alice))=>(?[X]:((quiet(X)<~>~curious(X)))))&
(![X]:((tall(X)|patient(X))=>(generous(X)|~funny(X))))&
(((~calm(john)&strong(john)))<=>(?[X]:((creative(X)&~brave(X)))))&
(((generous(alice)<~>~calm(alice)))=>(?[X]:((old(X)|quiet(X)))))&
(![X]:((~calm(X)<~>~tall(X))<=>happy(X)))&
((?[X]:((~happy(X)|wise(X))))<=>(?[X]:(~calm(X))))&
(![X]:(~tall(X)=>calm(X)))&
(![X]:(old(X)<=>generous(X)))&
(![X]:((~old(X)&calm(X))<=>(old(X)|patient(X))))&
(((~calm(lucy)<~>~curious(lucy)))<=>((rich(mary)<~>~calm(mary))))&
((old(susan)|~strong(susan)))&
((old(mary)|~tall(mary)))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((~kind(X)<~>strong(X))))&
((tall(alice)|patient(alice)))&
(?[X]:((patient(X)<~>~calm(X))))&
(?[X]:(~calm(X))) | strong(susan) | [
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6880209836771582930864374
% SZS output start Proof for 6880209836771582930864374
15. ! [X0] : ((calm(X0) & ~old(X0)) <=> (patient(X0) | old(X0))) [input p14]
17. ~strong(susan) | old(susan) [input p16]
24. strong(susan) [input hypothesis]
62. ! [X0] : (((calm(X0) & ~old(X0)) | (~patient(X0) & ~old(X0))) & ((patient(X0) | old(X0)) | (~calm(X0) | old(X0)))) [nnf transformation 15]
63. ! [X0] : (((calm(X0) & ~old(X0)) | (~patient(X0) & ~old(X0))) & (patient(X0) | old(X0) | ~calm(X0) | old(X0))) [flattening 62]
118. ~old(X0) | ~old(X0) [cnf transformation 63]
130. ~strong(susan) | old(susan) [cnf transformation 17]
140. strong(susan) [cnf transformation 24]
142. ~old(X0) [duplicate literal removal 118]
272. ~strong(susan) [subsumption resolution 130,142]
294. $false [subsumption resolution 140,272]
% SZS output end Proof for 6880209836771582930864374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is calm or old then someone is both humble and not kind.
If someone is both not strong and not kind then someone is either not happy or patient and vice versa.
Everyone who is both quiet and generous is either not curious or rich and vice versa.
If lucy is both not generous and old then someone is either tall or patient and vice versa.
Everyone who is either not generous or not kind is strong or not kind and vice versa.
Everyone who is either calm or not creative is strong or not quiet and vice versa.
Everyone who is not brave is wise.
If someone is rich then john is not curious or not patient.
If mary is tall or not patient then mary is not rich.
Everyone who is either not old or not brave is calm or not generous.
Everyone who is old is happy.
Everyone who is either not wise or not brave is brave or not happy and vice versa.
Everyone who is strong or old is not generous or wise and vice versa.
Everyone who is humble or not happy is not rich or old and vice versa.
Everyone who is not strong or not humble is not calm or curious and vice versa.
If someone is both not old and happy then lucy is wise.
Alice is either humble or calm.
Mary is both not curious and kind.
Fred is patient.
Someone is not brave.
Someone is not old.
Someone is both wise and patient.
Someone is either not calm or not funny.
Fred is both not quiet and patient. | Mary is strong. | entailment | (((calm(john)|old(john)))=>(?[X]:((humble(X)&~kind(X)))))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((quiet(X)&generous(X))<=>(~curious(X)<~>rich(X))))&
(((~generous(lucy)&old(lucy)))<=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:((~generous(X)<~>~kind(X))<=>(strong(X)|~kind(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(strong(X)|~quiet(X))))&
(![X]:(~brave(X)=>wise(X)))&
((?[X]:(rich(X)))=>((~curious(john)|~patient(john))))&
(((tall(mary)|~patient(mary)))=>(~rich(mary)))&
(![X]:((~old(X)<~>~brave(X))=>(calm(X)|~generous(X))))&
(![X]:(old(X)=>happy(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(brave(X)|~happy(X))))&
(![X]:((strong(X)|old(X))<=>(~generous(X)|wise(X))))&
(![X]:((humble(X)|~happy(X))<=>(~rich(X)|old(X))))&
(![X]:((~strong(X)|~humble(X))<=>(~calm(X)|curious(X))))&
((?[X]:((~old(X)&happy(X))))=>(wise(lucy)))&
((humble(alice)<~>calm(alice)))&
((~curious(mary)&kind(mary)))&
(patient(fred))&
(?[X]:(~brave(X)))&
(?[X]:(~old(X)))&
(?[X]:((wise(X)&patient(X))))&
(?[X]:((~calm(X)<~>~funny(X))))&
((~quiet(fred)&patient(fred))) | strong(mary) | [
"p4",
"p6",
"p9",
"p10",
"p11",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3708746162015901817328514
% SZS output start Proof for 3708746162015901817328514
5. ! [X0] : ((~generous(X0) <~> ~kind(X0)) <=> (~kind(X0) | strong(X0))) [input p4]
7. ! [X0] : (~brave(X0) => wise(X0)) [input p6]
10. ! [X0] : ((~old(X0) <~> ~brave(X0)) => (~generous(X0) | calm(X0))) [input p9]
11. ! [X0] : (old(X0) => happy(X0)) [input p10]
12. ! [X0] : ((~wise(X0) <~> ~brave(X0)) <=> (~happy(X0) | brave(X0))) [input p11]
13. ! [X0] : ((old(X0) | strong(X0)) <=> (wise(X0) | ~generous(X0))) [input p12]
15. ! [X0] : ((~humble(X0) | ~strong(X0)) <=> (curious(X0) | ~calm(X0))) [input p14]
18. kind(mary) & ~curious(mary) [input p17]
25. ~strong(mary) [input hypothesis]
28. ! [X0] : (wise(X0) | brave(X0)) [ennf transformation 7]
32. ! [X0] : ((~generous(X0) | calm(X0)) | (~old(X0) <=> ~brave(X0))) [ennf transformation 10]
33. ! [X0] : (~generous(X0) | calm(X0) | (~old(X0) <=> ~brave(X0))) [flattening 32]
34. ! [X0] : (happy(X0) | ~old(X0)) [ennf transformation 11]
50. ! [X0] : ((((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (kind(X0) & ~strong(X0))) & ((~kind(X0) | strong(X0)) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))))) [nnf transformation 5]
51. ! [X0] : ((((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (kind(X0) & ~strong(X0))) & (~kind(X0) | strong(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))))) [flattening 50]
54. ! [X0] : (~generous(X0) | calm(X0) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) [nnf transformation 33]
55. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [nnf transformation 12]
56. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [flattening 55]
57. ! [X0] : (((old(X0) | strong(X0)) | (~wise(X0) & generous(X0))) & ((wise(X0) | ~generous(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 13]
58. ! [X0] : ((old(X0) | strong(X0) | (~wise(X0) & generous(X0))) & (wise(X0) | ~generous(X0) | (~old(X0) & ~strong(X0)))) [flattening 57]
61. ! [X0] : (((~humble(X0) | ~strong(X0)) | (~curious(X0) & calm(X0))) & ((curious(X0) | ~calm(X0)) | (humble(X0) & strong(X0)))) [nnf transformation 15]
62. ! [X0] : ((~humble(X0) | ~strong(X0) | (~curious(X0) & calm(X0))) & (curious(X0) | ~calm(X0) | (humble(X0) & strong(X0)))) [flattening 61]
95. ~kind(X0) | strong(X0) | ~kind(X0) | generous(X0) [cnf transformation 51]
100. kind(X0) | generous(X0) | kind(X0) [cnf transformation 51]
107. wise(X0) | brave(X0) [cnf transformation 28]
111. ~brave(X0) | calm(X0) | ~generous(X0) | old(X0) [cnf transformation 54]
113. ~old(X0) | happy(X0) [cnf transformation 34]
115. ~happy(X0) | brave(X0) | ~wise(X0) | brave(X0) [cnf transformation 56]
116. ~brave(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 56]
121. ~generous(X0) | wise(X0) | ~old(X0) [cnf transformation 58]
123. ~wise(X0) | strong(X0) | old(X0) [cnf transformation 58]
128. ~calm(X0) | curious(X0) | strong(X0) [cnf transformation 62]
135. ~curious(mary) [cnf transformation 18]
146. ~strong(mary) [cnf transformation 25]
147. ~happy(X0) | brave(X0) | ~wise(X0) [duplicate literal removal 115]
148. ~wise(X0) | ~brave(X0) [duplicate literal removal 116]
149. ~kind(X0) | strong(X0) | generous(X0) [duplicate literal removal 95]
150. generous(X0) | kind(X0) [duplicate literal removal 100]
230. generous(X0) | strong(X0) [subsumption resolution 149,150]
257. ~wise(X0) | ~happy(X0) [subsumption resolution 147,148]
326. ~old(X0) | wise(X0) | strong(X0) [resolution 121,230]
330. 32 <=> old(mary) [avatar definition]
331. old(mary) <- (32) [avatar component clause 330]
334. 33 <=> wise(mary) [avatar definition]
336. wise(mary) <- (33) [avatar component clause 334]
339. brave(X0) | old(X0) | strong(X0) [resolution 123,107]
386. 39 <=> calm(mary) [avatar definition]
388. calm(mary) <- (39) [avatar component clause 386]
391. 40 <=> happy(mary) [avatar definition]
393. happy(mary) <- (40) [avatar component clause 391]
469. old(X0) | strong(X0) | calm(X0) | ~generous(X0) | old(X0) [resolution 339,111]
470. old(X0) | strong(X0) | calm(X0) | ~generous(X0) [duplicate literal removal 469]
480. strong(X0) | old(X0) | calm(X0) [subsumption resolution 470,230]
585. old(mary) | calm(mary) [resolution 480,146]
608. curious(mary) | strong(mary) <- (39) [resolution 388,128]
612. strong(mary) <- (39) [subsumption resolution 608,135]
613. $false <- (39) [subsumption resolution 612,146]
614. ~39 [avatar contradiction clause 613]
615. 39 | 32 [avatar split clause 585,330,386]
627. wise(mary) | strong(mary) <- (32) [resolution 331,326]
629. happy(mary) <- (32) [resolution 331,113]
632. 40 | ~32 [avatar split clause 629,330,391]
635. ~happy(mary) <- (33) [resolution 336,257]
637. $false <- (33, 40) [subsumption resolution 635,393]
638. ~33 | ~40 [avatar contradiction clause 637]
641. wise(mary) <- (32) [subsumption resolution 627,146]
642. 33 | ~32 [avatar split clause 641,330,334]
643. $false [avatar sat refutation 614,615,632,638,642]
% SZS output end Proof for 3708746162015901817328514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and humble is patient.
If paul is both calm and not old then mary is either not humble or not patient.
Everyone who is old is both patient and humble and vice versa.
Everyone who is not strong is happy and vice versa.
Everyone who is creative or not wise is kind and vice versa.
Everyone who is both not happy and not tall is both wise and quiet.
If someone is not strong or not patient then john is both generous and old.
If someone is not wise or not rich then alice is quiet and vice versa.
Everyone who is not happy is either not rich or curious.
If someone is either humble or quiet then someone is either curious or humble and vice versa.
Everyone who is humble or not creative is both not happy and not humble and vice versa.
If alice is not funny or funny then someone is either not rich or not patient.
If alice is both brave and funny then someone is either not humble or not rich.
If fred is either wise or creative then mary is tall or not calm and vice versa.
If lucy is both not patient and tall then john is both not strong and not old and vice versa.
Fred is either rich or not generous.
Someone is not humble.
Someone is calm or happy.
Mary is quiet or not tall.
Someone is calm. | Alice is quiet. | entailment | (![X]:((~wise(X)&humble(X))=>patient(X)))&
(((calm(paul)&~old(paul)))=>((~humble(mary)<~>~patient(mary))))&
(![X]:(old(X)<=>(patient(X)&humble(X))))&
(![X]:(~strong(X)<=>happy(X)))&
(![X]:((creative(X)|~wise(X))<=>kind(X)))&
(![X]:((~happy(X)&~tall(X))=>(wise(X)&quiet(X))))&
((?[X]:((~strong(X)|~patient(X))))=>((generous(john)&old(john))))&
((?[X]:((~wise(X)|~rich(X))))<=>(quiet(alice)))&
(![X]:(~happy(X)=>(~rich(X)<~>curious(X))))&
((?[X]:((humble(X)<~>quiet(X))))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((humble(X)|~creative(X))<=>(~happy(X)&~humble(X))))&
(((~funny(alice)|funny(alice)))=>(?[X]:((~rich(X)<~>~patient(X)))))&
(((brave(alice)&funny(alice)))=>(?[X]:((~humble(X)<~>~rich(X)))))&
(((wise(fred)<~>creative(fred)))<=>((tall(mary)|~calm(mary))))&
(((~patient(lucy)&tall(lucy)))<=>((~strong(john)&~old(john))))&
((rich(fred)<~>~generous(fred)))&
(?[X]:(~humble(X)))&
(?[X]:((calm(X)|happy(X))))&
((quiet(mary)|~tall(mary)))&
(?[X]:(calm(X))) | quiet(alice) | [
"p2",
"p6",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4393115124354930228593935
% SZS output start Proof for 4393115124354930228593935
3. ! [X0] : (old(X0) <=> (humble(X0) & patient(X0))) [input p2]
7. ? [X0] : (~patient(X0) | ~strong(X0)) => (old(john) & generous(john)) [input p6]
8. ? [X0] : (~rich(X0) | ~wise(X0)) <=> quiet(alice) [input p7]
11. ! [X0] : ((~creative(X0) | humble(X0)) <=> (~humble(X0) & ~happy(X0))) [input p10]
12. (funny(alice) | ~funny(alice)) => ? [X0] : (~rich(X0) <~> ~patient(X0)) [input p11]
21. ~quiet(alice) [input hypothesis]
30. (old(john) & generous(john)) | ! [X0] : (patient(X0) & strong(X0)) [ennf transformation 7]
32. ? [X0] : (~rich(X0) <~> ~patient(X0)) | (~funny(alice) & funny(alice)) [ennf transformation 12]
34. ! [X0] : ((old(X0) | (~humble(X0) | ~patient(X0))) & ((humble(X0) & patient(X0)) | ~old(X0))) [nnf transformation 3]
35. ! [X0] : ((old(X0) | ~humble(X0) | ~patient(X0)) & ((humble(X0) & patient(X0)) | ~old(X0))) [flattening 34]
37. (? [X0] : (~rich(X0) | ~wise(X0)) | ~quiet(alice)) & (quiet(alice) | ! [X0] : (rich(X0) & wise(X0))) [nnf transformation 8]
38. (? [X0] : (~rich(X0) | ~wise(X0)) | ~quiet(alice)) & (quiet(alice) | ! [X1] : (rich(X1) & wise(X1))) [rectify 37]
39. ? [X0] : (~rich(X0) | ~wise(X0)) => (~rich(sK0) | ~wise(sK0)) [choice axiom]
40. ((~rich(sK0) | ~wise(sK0)) | ~quiet(alice)) & (quiet(alice) | ! [X1] : (rich(X1) & wise(X1))) [skolemisation 38,39]
47. ! [X0] : (((~creative(X0) | humble(X0)) | (humble(X0) | happy(X0))) & ((~humble(X0) & ~happy(X0)) | (creative(X0) & ~humble(X0)))) [nnf transformation 11]
48. ! [X0] : ((~creative(X0) | humble(X0) | humble(X0) | happy(X0)) & ((~humble(X0) & ~happy(X0)) | (creative(X0) & ~humble(X0)))) [flattening 47]
49. ? [X0] : ((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (~funny(alice) & funny(alice)) [nnf transformation 32]
50. ? [X0] : ((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) => ((patient(sK3) | rich(sK3)) & (~patient(sK3) | ~rich(sK3))) [choice axiom]
51. ((patient(sK3) | rich(sK3)) & (~patient(sK3) | ~rich(sK3))) | (~funny(alice) & funny(alice)) [skolemisation 49,50]
67. ~old(X0) | humble(X0) [cnf transformation 35]
76. old(john) | patient(X0) [cnf transformation 30]
78. quiet(alice) | rich(X1) [cnf transformation 40]
92. ~humble(X0) | ~humble(X0) [cnf transformation 48]
95. ~patient(sK3) | ~rich(sK3) | funny(alice) [cnf transformation 51]
96. ~patient(sK3) | ~rich(sK3) | ~funny(alice) [cnf transformation 51]
115. ~quiet(alice) [cnf transformation 21]
116. ~humble(X0) [duplicate literal removal 92]
137. 5 <=> ! [X0] : patient(X0) [avatar definition]
138. patient(X0) <- (5) [avatar component clause 137]
140. 6 <=> old(john) [avatar definition]
142. old(john) <- (6) [avatar component clause 140]
143. 5 | 6 [avatar split clause 76,140,137]
155. 9 <=> quiet(alice) [avatar definition]
168. 12 <=> ! [X1] : rich(X1) [avatar definition]
169. rich(X1) <- (12) [avatar component clause 168]
170. 12 | 9 [avatar split clause 78,155,168]
212. 22 <=> funny(alice) [avatar definition]
216. 23 <=> rich(sK3) [avatar definition]
217. ~rich(sK3) <- (~23) [avatar component clause 216]
220. 24 <=> patient(sK3) [avatar definition]
221. ~patient(sK3) <- (~24) [avatar component clause 220]
225. ~22 | ~23 | ~24 [avatar split clause 96,220,216,212]
226. 22 | ~23 | ~24 [avatar split clause 95,220,216,212]
289. ~9 [avatar split clause 115,155]
292. $false <- (5, ~24) [resolution 221,138]
293. ~5 | 24 [avatar contradiction clause 292]
299. humble(john) <- (6) [resolution 67,142]
300. $false <- (6) [subsumption resolution 299,116]
301. ~6 [avatar contradiction clause 300]
302. $false <- (12, ~23) [subsumption resolution 217,169]
303. ~12 | 23 [avatar contradiction clause 302]
304. $false [avatar sat refutation 143,170,225,226,289,293,301,303]
% SZS output end Proof for 4393115124354930228593935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or happy is kind.
Everyone who is both not rich and old is both not calm and old and vice versa.
Everyone who is patient is either not patient or patient and vice versa.
Everyone who is either not old or not happy is old or not calm and vice versa.
Everyone who is both strong and not rich is both kind and quiet and vice versa.
Everyone who is either not happy or not tall is either not old or creative.
If paul is either not quiet or not happy then someone is both not strong and tall.
Everyone who is either not humble or not old is both patient and humble.
Everyone who is happy or not creative is both creative and quiet.
Everyone who is either not creative or not old is both patient and not old.
If mary is either patient or old then someone is happy and vice versa.
If someone is both not wise and not funny then someone is either wise or generous.
Everyone who is not generous or old is brave.
Everyone who is both not happy and generous is either not humble or not strong and vice versa.
Everyone who is not creative is either not calm or not quiet.
Someone is either not happy or strong.
Alice is not happy or not tall.
John is either not rich or not kind.
Lucy is either not creative or not quiet.
Someone is brave.
Susan is strong. | Paul is not calm. | neutral | (![X]:((strong(X)<~>happy(X))=>kind(X)))&
(![X]:((~rich(X)&old(X))<=>(~calm(X)&old(X))))&
(![X]:(patient(X)<=>(~patient(X)<~>patient(X))))&
(![X]:((~old(X)<~>~happy(X))<=>(old(X)|~calm(X))))&
(![X]:((strong(X)&~rich(X))<=>(kind(X)&quiet(X))))&
(![X]:((~happy(X)<~>~tall(X))=>(~old(X)<~>creative(X))))&
(((~quiet(paul)<~>~happy(paul)))=>(?[X]:((~strong(X)&tall(X)))))&
(![X]:((~humble(X)<~>~old(X))=>(patient(X)&humble(X))))&
(![X]:((happy(X)|~creative(X))=>(creative(X)&quiet(X))))&
(![X]:((~creative(X)<~>~old(X))=>(patient(X)&~old(X))))&
(((patient(mary)<~>old(mary)))<=>(?[X]:(happy(X))))&
((?[X]:((~wise(X)&~funny(X))))=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((~generous(X)|old(X))=>brave(X)))&
(![X]:((~happy(X)&generous(X))<=>(~humble(X)<~>~strong(X))))&
(![X]:(~creative(X)=>(~calm(X)<~>~quiet(X))))&
(?[X]:((~happy(X)<~>strong(X))))&
((~happy(alice)|~tall(alice)))&
((~rich(john)<~>~kind(john)))&
((~creative(lucy)<~>~quiet(lucy)))&
(?[X]:(brave(X)))&
(strong(susan)) | ~calm(paul) | [] | null | 0 |
Everyone who is both not generous and not creative is brave or not wise and vice versa. If someone is happy or quiet then someone is both patient and not patient and vice versa. If someone is brave or not patient then someone is curious or creative and vice versa. Everyone who is not wise or not kind is both not funny and generous and vice versa. If john is both old and kind then alice is either brave or wise. Everyone who is not happy is not creative. Everyone who is strong is either brave or happy. If someone is not tall then paul is brave or wise. Everyone who is creative or wise is either quiet or not old. If mary is either kind or quiet then someone is not calm and vice versa. Everyone who is either calm or rich is both not funny and not old and vice versa. Everyone who is both not tall and not strong is either humble or tall. Everyone who is funny or curious is wise or kind and vice versa. If john is brave then lucy is happy or not patient. If susan is not quiet then mary is both not quiet and not tall and vice versa. Someone is either not strong or not wise. Someone is curious. Susan is both not humble and calm. Susan is not brave or not generous. John is humble or not generous. | Susan is not rich. | neutral | (![X]:((~generous(X)&~creative(X))<=>(brave(X)|~wise(X))))&
((?[X]:((happy(X)|quiet(X))))<=>(?[X]:((patient(X)&~patient(X)))))&
((?[X]:((brave(X)|~patient(X))))<=>(?[X]:((curious(X)|creative(X)))))&
(![X]:((~wise(X)|~kind(X))<=>(~funny(X)&generous(X))))&
(((old(john)&kind(john)))=>((brave(alice)<~>wise(alice))))&
(![X]:(~happy(X)=>~creative(X)))&
(![X]:(strong(X)=>(brave(X)<~>happy(X))))&
((?[X]:(~tall(X)))=>((brave(paul)|wise(paul))))&
(![X]:((creative(X)|wise(X))=>(quiet(X)<~>~old(X))))&
(((kind(mary)<~>quiet(mary)))<=>(?[X]:(~calm(X))))&
(![X]:((calm(X)<~>rich(X))<=>(~funny(X)&~old(X))))&
(![X]:((~tall(X)&~strong(X))=>(humble(X)<~>tall(X))))&
(![X]:((funny(X)|curious(X))<=>(wise(X)|kind(X))))&
((brave(john))=>((happy(lucy)|~patient(lucy))))&
((~quiet(susan))<=>((~quiet(mary)&~tall(mary))))&
(?[X]:((~strong(X)<~>~wise(X))))&
(?[X]:(curious(X)))&
((~humble(susan)&calm(susan)))&
((~brave(susan)|~generous(susan)))&
((humble(john)|~generous(john))) | ~rich(susan) | [] | null | 0 |
Everyone who is not tall or not happy is either tall or creative and vice versa.
If lucy is not tall or not wise then someone is both quiet and brave.
Everyone who is both brave and tall is generous or funny and vice versa.
Everyone who is not wise or creative is both quiet and not old and vice versa.
If someone is not old or not rich then john is either not creative or not curious.
Everyone who is either tall or not kind is wise.
Everyone who is brave is both old and creative.
If someone is either not patient or happy then susan is not tall or old and vice versa.
Everyone who is either not wise or not calm is rich and vice versa.
Everyone who is both not generous and not brave is not quiet.
If paul is not humble then susan is not generous or not wise.
If fred is both not quiet and calm then mary is either not old or rich and vice versa.
Everyone who is creative or old is brave and vice versa.
If lucy is not tall then paul is humble.
Everyone who is brave or not rich is either creative or old.
Someone is not calm.
Alice is not calm.
Fred is not strong or not patient. | John is not curious. | contradiction | (![X]:((~tall(X)|~happy(X))<=>(tall(X)<~>creative(X))))&
(((~tall(lucy)|~wise(lucy)))=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((brave(X)&tall(X))<=>(generous(X)|funny(X))))&
(![X]:((~wise(X)|creative(X))<=>(quiet(X)&~old(X))))&
((?[X]:((~old(X)|~rich(X))))=>((~creative(john)<~>~curious(john))))&
(![X]:((tall(X)<~>~kind(X))=>wise(X)))&
(![X]:(brave(X)=>(old(X)&creative(X))))&
((?[X]:((~patient(X)<~>happy(X))))<=>((~tall(susan)|old(susan))))&
(![X]:((~wise(X)<~>~calm(X))<=>rich(X)))&
(![X]:((~generous(X)&~brave(X))=>~quiet(X)))&
((~humble(paul))=>((~generous(susan)|~wise(susan))))&
(((~quiet(fred)&calm(fred)))<=>((~old(mary)<~>rich(mary))))&
(![X]:((creative(X)|old(X))<=>brave(X)))&
((~tall(lucy))=>(humble(paul)))&
(![X]:((brave(X)|~rich(X))=>(creative(X)<~>old(X))))&
(?[X]:(~calm(X)))&
(~calm(alice))&
((~strong(fred)|~patient(fred))) | ~curious(john) | [
"p3",
"p4",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 687529214798136539223378
% SZS output start Proof for 687529214798136539223378
4. ! [X0] : ((creative(X0) | ~wise(X0)) <=> (~old(X0) & quiet(X0))) [input p3]
5. ? [X0] : (~rich(X0) | ~old(X0)) => (~creative(john) <~> ~curious(john)) [input p4]
7. ! [X0] : (brave(X0) => (creative(X0) & old(X0))) [input p6]
13. ! [X0] : ((old(X0) | creative(X0)) <=> brave(X0)) [input p12]
19. ~curious(john) [input hypothesis]
24. (~creative(john) <~> ~curious(john)) | ! [X0] : (rich(X0) & old(X0)) [ennf transformation 5]
26. ! [X0] : ((creative(X0) & old(X0)) | ~brave(X0)) [ennf transformation 7]
36. ! [X0] : (((creative(X0) | ~wise(X0)) | (old(X0) | ~quiet(X0))) & ((~old(X0) & quiet(X0)) | (~creative(X0) & wise(X0)))) [nnf transformation 4]
37. ! [X0] : ((creative(X0) | ~wise(X0) | old(X0) | ~quiet(X0)) & ((~old(X0) & quiet(X0)) | (~creative(X0) & wise(X0)))) [flattening 36]
38. ((curious(john) | creative(john)) & (~curious(john) | ~creative(john))) | ! [X0] : (rich(X0) & old(X0)) [nnf transformation 24]
48. ! [X0] : (((old(X0) | creative(X0)) | ~brave(X0)) & (brave(X0) | (~old(X0) & ~creative(X0)))) [nnf transformation 13]
49. ! [X0] : ((old(X0) | creative(X0) | ~brave(X0)) & (brave(X0) | (~old(X0) & ~creative(X0)))) [flattening 48]
71. ~old(X0) | ~creative(X0) [cnf transformation 37]
75. curious(john) | creative(john) | old(X0) [cnf transformation 38]
79. ~brave(X0) | old(X0) [cnf transformation 26]
80. ~brave(X0) | creative(X0) [cnf transformation 26]
98. ~creative(X0) | brave(X0) [cnf transformation 49]
99. ~old(X0) | brave(X0) [cnf transformation 49]
107. ~curious(john) [cnf transformation 19]
134. 6 <=> creative(john) [avatar definition]
136. creative(john) <- (6) [avatar component clause 134]
138. 7 <=> curious(john) [avatar definition]
143. 8 <=> ! [X0] : old(X0) [avatar definition]
144. old(X0) <- (8) [avatar component clause 143]
145. 8 | 6 | 7 [avatar split clause 75,138,134,143]
199. ~7 [avatar split clause 107,138]
207. brave(john) <- (6) [resolution 98,136]
209. old(john) <- (6) [resolution 207,79]
213. ~creative(john) <- (6) [resolution 209,71]
215. $false <- (6) [subsumption resolution 213,136]
216. ~6 [avatar contradiction clause 215]
220. brave(X0) <- (8) [resolution 144,99]
221. ~creative(X1) <- (8) [resolution 144,71]
230. creative(X0) <- (8) [resolution 220,80]
234. $false <- (8) [subsumption resolution 230,221]
235. ~8 [avatar contradiction clause 234]
236. $false [avatar sat refutation 145,199,216,235]
% SZS output end Proof for 687529214798136539223378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or not generous then john is not funny and vice versa. Everyone who is either quiet or patient is either generous or not rich. If someone is kind or not strong then someone is not old or generous. If someone is generous or not calm then someone is not calm. Everyone who is funny is not curious or tall and vice versa. If mary is not calm then john is either curious or calm. Everyone who is not calm is not rich. If someone is either old or not rich then mary is both generous and tall and vice versa. If someone is funny then someone is either not kind or not brave. If someone is not brave or happy then john is either quiet or not brave. Everyone who is happy is not tall or not patient. If someone is not curious or old then someone is not rich and vice versa. Everyone who is either not funny or tall is either calm or kind and vice versa. Everyone who is not strong is either not tall or not rich. Everyone who is curious or not funny is both generous and rich and vice versa. Everyone who is humble or strong is not creative. Alice is not happy. Mary is not rich. John is quiet or curious. Someone is rich. Someone is both creative and curious. Lucy is not patient. Someone is both not kind and generous. Paul is brave or not calm. | Mary is not curious. | entailment | ((?[X]:((wise(X)<~>~generous(X))))<=>(~funny(john)))&
(![X]:((quiet(X)<~>patient(X))=>(generous(X)<~>~rich(X))))&
((?[X]:((kind(X)|~strong(X))))=>(?[X]:((~old(X)|generous(X)))))&
((?[X]:((generous(X)|~calm(X))))=>(?[X]:(~calm(X))))&
(![X]:(funny(X)<=>(~curious(X)|tall(X))))&
((~calm(mary))=>((curious(john)<~>calm(john))))&
(![X]:(~calm(X)=>~rich(X)))&
((?[X]:((old(X)<~>~rich(X))))<=>((generous(mary)&tall(mary))))&
((?[X]:(funny(X)))=>(?[X]:((~kind(X)<~>~brave(X)))))&
((?[X]:((~brave(X)|happy(X))))=>((quiet(john)<~>~brave(john))))&
(![X]:(happy(X)=>(~tall(X)|~patient(X))))&
((?[X]:((~curious(X)|old(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~funny(X)<~>tall(X))<=>(calm(X)<~>kind(X))))&
(![X]:(~strong(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((curious(X)|~funny(X))<=>(generous(X)&rich(X))))&
(![X]:((humble(X)|strong(X))=>~creative(X)))&
(~happy(alice))&
(~rich(mary))&
((quiet(john)|curious(john)))&
(?[X]:(rich(X)))&
(?[X]:((creative(X)&curious(X))))&
(~patient(lucy))&
(?[X]:((~kind(X)&generous(X))))&
((brave(paul)|~calm(paul))) | ~curious(mary) | [
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3902152610538496572420369
% SZS output start Proof for 3902152610538496572420369
15. ! [X0] : ((~funny(X0) | curious(X0)) <=> (rich(X0) & generous(X0))) [input p14]
18. ~rich(mary) [input p17]
25. curious(mary) [input hypothesis]
74. ! [X0] : (((~funny(X0) | curious(X0)) | (~rich(X0) | ~generous(X0))) & ((rich(X0) & generous(X0)) | (funny(X0) & ~curious(X0)))) [nnf transformation 15]
75. ! [X0] : ((~funny(X0) | curious(X0) | ~rich(X0) | ~generous(X0)) & ((rich(X0) & generous(X0)) | (funny(X0) & ~curious(X0)))) [flattening 74]
125. ~curious(X0) | rich(X0) [cnf transformation 75]
129. ~rich(mary) [cnf transformation 18]
138. curious(mary) [cnf transformation 25]
308. rich(mary) [resolution 125,138]
310. $false [subsumption resolution 308,129]
% SZS output end Proof for 3902152610538496572420369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either creative or funny is both not patient and humble and vice versa.
Everyone who is both quiet and tall is rich.
If paul is either not strong or not wise then john is either not humble or not calm and vice versa.
If someone is not kind or generous then john is rich and vice versa.
If someone is not generous then lucy is either patient or tall and vice versa.
If john is both not creative and not old then alice is not kind or humble and vice versa.
If someone is either wise or not strong then someone is calm or rich.
Everyone who is not rich is not rich or happy and vice versa.
Everyone who is not generous is either curious or not curious and vice versa.
Everyone who is either rich or not calm is not old or happy and vice versa.
Everyone who is humble or not happy is not humble.
If alice is not curious then someone is both creative and not old.
Everyone who is not happy or not tall is not wise or wise and vice versa.
Everyone who is either not funny or patient is either not calm or not rich.
If susan is either not happy or not brave then fred is either humble or not tall and vice versa.
Everyone who is either not rich or tall is both not brave and generous.
Someone is not brave or rich.
Someone is not brave.
Lucy is either not generous or rich.
Susan is not tall or not patient.
Someone is humble or wise.
Someone is both not wise and not happy.
Mary is not funny or not creative. | John is not strong. | neutral | (![X]:((creative(X)<~>funny(X))<=>(~patient(X)&humble(X))))&
(![X]:((quiet(X)&tall(X))=>rich(X)))&
(((~strong(paul)<~>~wise(paul)))<=>((~humble(john)<~>~calm(john))))&
((?[X]:((~kind(X)|generous(X))))<=>(rich(john)))&
((?[X]:(~generous(X)))<=>((patient(lucy)<~>tall(lucy))))&
(((~creative(john)&~old(john)))<=>((~kind(alice)|humble(alice))))&
((?[X]:((wise(X)<~>~strong(X))))=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~rich(X)|happy(X))))&
(![X]:(~generous(X)<=>(curious(X)<~>~curious(X))))&
(![X]:((rich(X)<~>~calm(X))<=>(~old(X)|happy(X))))&
(![X]:((humble(X)|~happy(X))=>~humble(X)))&
((~curious(alice))=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((~happy(X)|~tall(X))<=>(~wise(X)|wise(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~calm(X)<~>~rich(X))))&
(((~happy(susan)<~>~brave(susan)))<=>((humble(fred)<~>~tall(fred))))&
(![X]:((~rich(X)<~>tall(X))=>(~brave(X)&generous(X))))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:(~brave(X)))&
((~generous(lucy)<~>rich(lucy)))&
((~tall(susan)|~patient(susan)))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:((~wise(X)&~happy(X))))&
((~funny(mary)|~creative(mary))) | ~strong(john) | [] | null | 0 |
Everyone who is either rich or old is either not wise or wise.
Everyone who is both kind and not quiet is old or not quiet.
Everyone who is not creative or not kind is generous or creative.
If fred is either not curious or not calm then paul is not old or quiet.
If someone is either wise or humble then mary is tall or not happy.
Everyone who is either not quiet or creative is either funny or old and vice versa.
If someone is either not patient or quiet then alice is either not kind or not patient and vice versa.
Everyone who is old or patient is calm or not happy.
Everyone who is both patient and not wise is calm or humble and vice versa.
If paul is not brave or not tall then lucy is calm or old and vice versa.
If someone is either not generous or rich then someone is not strong and vice versa.
Everyone who is not quiet is happy.
Everyone who is not generous or tall is creative.
Everyone who is both not creative and not wise is both not happy and not curious.
If alice is either not rich or calm then someone is tall.
Everyone who is not curious is both not tall and rich.
Someone is not calm.
Someone is calm.
Someone is not rich.
Someone is strong or kind.
Lucy is tall or humble.
Mary is generous or not old.
Susan is both not kind and rich. | Alice is not kind. | neutral | (![X]:((rich(X)<~>old(X))=>(~wise(X)<~>wise(X))))&
(![X]:((kind(X)&~quiet(X))=>(old(X)|~quiet(X))))&
(![X]:((~creative(X)|~kind(X))=>(generous(X)|creative(X))))&
(((~curious(fred)<~>~calm(fred)))=>((~old(paul)|quiet(paul))))&
((?[X]:((wise(X)<~>humble(X))))=>((tall(mary)|~happy(mary))))&
(![X]:((~quiet(X)<~>creative(X))<=>(funny(X)<~>old(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>((~kind(alice)<~>~patient(alice))))&
(![X]:((old(X)|patient(X))=>(calm(X)|~happy(X))))&
(![X]:((patient(X)&~wise(X))<=>(calm(X)|humble(X))))&
(((~brave(paul)|~tall(paul)))<=>((calm(lucy)|old(lucy))))&
((?[X]:((~generous(X)<~>rich(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~quiet(X)=>happy(X)))&
(![X]:((~generous(X)|tall(X))=>creative(X)))&
(![X]:((~creative(X)&~wise(X))=>(~happy(X)&~curious(X))))&
(((~rich(alice)<~>calm(alice)))=>(?[X]:(tall(X))))&
(![X]:(~curious(X)=>(~tall(X)&rich(X))))&
(?[X]:(~calm(X)))&
(?[X]:(calm(X)))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)|kind(X))))&
((tall(lucy)|humble(lucy)))&
((generous(mary)|~old(mary)))&
((~kind(susan)&rich(susan))) | ~kind(alice) | [] | null | 0 |
If lucy is tall then someone is not calm or not old and vice versa.
If john is either not tall or rich then lucy is old or patient and vice versa.
Everyone who is patient is both humble and rich.
Everyone who is both quiet and not generous is both not rich and curious.
Everyone who is funny is either not happy or not patient.
Everyone who is both calm and not quiet is either not humble or not wise.
If someone is either generous or curious then someone is humble and vice versa.
Everyone who is either tall or kind is wise.
If someone is not calm then john is either funny or not humble.
Everyone who is both not strong and kind is both not humble and brave and vice versa.
Everyone who is creative is generous or not strong and vice versa.
If john is calm then lucy is tall and vice versa.
Everyone who is not humble is either not humble or creative and vice versa.
Everyone who is either not rich or not quiet is creative and vice versa.
If someone is patient or not creative then someone is either old or generous and vice versa.
Everyone who is not brave is strong or not tall and vice versa.
Lucy is tall.
Paul is either wise or not humble.
Someone is either quiet or not rich.
Mary is both not creative and wise.
Lucy is both strong and not rich.
Someone is not brave or not generous. | Paul is wise. | neutral | ((tall(lucy))<=>(?[X]:((~calm(X)|~old(X)))))&
(((~tall(john)<~>rich(john)))<=>((old(lucy)|patient(lucy))))&
(![X]:(patient(X)=>(humble(X)&rich(X))))&
(![X]:((quiet(X)&~generous(X))=>(~rich(X)&curious(X))))&
(![X]:(funny(X)=>(~happy(X)<~>~patient(X))))&
(![X]:((calm(X)&~quiet(X))=>(~humble(X)<~>~wise(X))))&
((?[X]:((generous(X)<~>curious(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)<~>kind(X))=>wise(X)))&
((?[X]:(~calm(X)))=>((funny(john)<~>~humble(john))))&
(![X]:((~strong(X)&kind(X))<=>(~humble(X)&brave(X))))&
(![X]:(creative(X)<=>(generous(X)|~strong(X))))&
((calm(john))<=>(tall(lucy)))&
(![X]:(~humble(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>creative(X)))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:(~brave(X)<=>(strong(X)|~tall(X))))&
(tall(lucy))&
((wise(paul)<~>~humble(paul)))&
(?[X]:((quiet(X)<~>~rich(X))))&
((~creative(mary)&wise(mary)))&
((strong(lucy)&~rich(lucy)))&
(?[X]:((~brave(X)|~generous(X)))) | wise(paul) | [] | null | 0 |
Everyone who is either not strong or not patient is either not old or happy and vice versa.
If someone is both not happy and generous then john is either not kind or not quiet.
If someone is both not kind and curious then someone is creative or not quiet and vice versa.
Everyone who is both calm and funny is generous or not brave and vice versa.
If alice is not wise or kind then lucy is both not rich and kind.
If someone is generous then someone is either kind or not old.
Everyone who is old is either patient or happy and vice versa.
Everyone who is not humble or not strong is quiet or old and vice versa.
If someone is funny or quiet then susan is not brave.
If someone is not curious or rich then someone is either not generous or not strong and vice versa.
Everyone who is either creative or old is not calm or not curious and vice versa.
Everyone who is either wise or not quiet is brave.
Everyone who is not patient is either old or not funny.
If someone is both not strong and not tall then lucy is not generous or not creative and vice versa.
If mary is both not old and not humble then someone is wise and vice versa.
If someone is both not humble and not curious then someone is both kind and not wise and vice versa.
Fred is either not wise or wise.
Someone is either not curious or creative.
John is both generous and not quiet.
Someone is both kind and quiet.
Mary is humble or calm.
Someone is either patient or calm.
Someone is not humble.
Someone is either not happy or not strong. | Susan is calm. | entailment | (![X]:((~strong(X)<~>~patient(X))<=>(~old(X)<~>happy(X))))&
((?[X]:((~happy(X)&generous(X))))=>((~kind(john)<~>~quiet(john))))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((calm(X)&funny(X))<=>(generous(X)|~brave(X))))&
(((~wise(alice)|kind(alice)))=>((~rich(lucy)&kind(lucy))))&
((?[X]:(generous(X)))=>(?[X]:((kind(X)<~>~old(X)))))&
(![X]:(old(X)<=>(patient(X)<~>happy(X))))&
(![X]:((~humble(X)|~strong(X))<=>(quiet(X)|old(X))))&
((?[X]:((funny(X)|quiet(X))))=>(~brave(susan)))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((creative(X)<~>old(X))<=>(~calm(X)|~curious(X))))&
(![X]:((wise(X)<~>~quiet(X))=>brave(X)))&
(![X]:(~patient(X)=>(old(X)<~>~funny(X))))&
((?[X]:((~strong(X)&~tall(X))))<=>((~generous(lucy)|~creative(lucy))))&
(((~old(mary)&~humble(mary)))<=>(?[X]:(wise(X))))&
((?[X]:((~humble(X)&~curious(X))))<=>(?[X]:((kind(X)&~wise(X)))))&
((~wise(fred)<~>wise(fred)))&
(?[X]:((~curious(X)<~>creative(X))))&
((generous(john)&~quiet(john)))&
(?[X]:((kind(X)&quiet(X))))&
((humble(mary)|calm(mary)))&
(?[X]:((patient(X)<~>calm(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)<~>~strong(X)))) | calm(susan) | [
"p3",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2636727787783608770617767
% SZS output start Proof for 2636727787783608770617767
4. ! [X0] : ((funny(X0) & calm(X0)) <=> (~brave(X0) | generous(X0))) [input p3]
9. ? [X0] : (quiet(X0) | funny(X0)) => ~brave(susan) [input p8]
20. ? [X0] : (quiet(X0) & kind(X0)) [input p19]
25. ~calm(susan) [input hypothesis]
33. ~brave(susan) | ! [X0] : (~quiet(X0) & ~funny(X0)) [ennf transformation 9]
43. ! [X0] : (((funny(X0) & calm(X0)) | (brave(X0) & ~generous(X0))) & ((~brave(X0) | generous(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 4]
44. ! [X0] : (((funny(X0) & calm(X0)) | (brave(X0) & ~generous(X0))) & (~brave(X0) | generous(X0) | ~funny(X0) | ~calm(X0))) [flattening 43]
80. ? [X0] : (quiet(X0) & kind(X0)) => (quiet(sK10) & kind(sK10)) [choice axiom]
81. quiet(sK10) & kind(sK10) [skolemisation 20,80]
107. brave(X0) | calm(X0) [cnf transformation 44]
125. ~brave(susan) | ~quiet(X0) [cnf transformation 33]
161. quiet(sK10) [cnf transformation 81]
168. ~calm(susan) [cnf transformation 25]
246. 18 <=> ! [X0] : ~quiet(X0) [avatar definition]
247. ~quiet(X0) <- (18) [avatar component clause 246]
249. 19 <=> brave(susan) [avatar definition]
251. ~brave(susan) <- (~19) [avatar component clause 249]
252. 18 | ~19 [avatar split clause 125,249,246]
397. calm(susan) <- (~19) [resolution 107,251]
398. $false <- (~19) [subsumption resolution 397,168]
399. 19 [avatar contradiction clause 398]
400. $false <- (18) [resolution 247,161]
401. ~18 [avatar contradiction clause 400]
402. $false [avatar sat refutation 252,399,401]
% SZS output end Proof for 2636727787783608770617767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or brave then paul is brave and vice versa. If mary is calm or not patient then alice is calm. If lucy is calm then john is creative or happy and vice versa. Everyone who is not kind or patient is old and vice versa. Everyone who is not quiet or patient is brave or rich and vice versa. If paul is not wise then someone is kind. Everyone who is either not happy or kind is either not generous or not kind. If lucy is either not generous or creative then someone is either humble or not quiet and vice versa. If someone is happy or not humble then alice is not rich or not curious and vice versa. Everyone who is either not tall or quiet is both not tall and not kind and vice versa. Everyone who is either wise or not brave is not old or funny. If someone is not creative or not old then john is both not wise and funny. Everyone who is both old and not patient is creative and vice versa. Everyone who is either not brave or not humble is both not brave and not patient and vice versa. If someone is either not patient or not generous then paul is not brave or curious and vice versa. If susan is not brave or not funny then someone is not curious or not tall and vice versa. John is quiet or generous. Someone is calm or not creative. Alice is not kind or strong. Mary is not wise. Someone is either creative or not rich. John is generous or not humble. John is not tall or curious. John is not funny. | Susan is old. | entailment | ((?[X]:((wise(X)<~>brave(X))))<=>(brave(paul)))&
(((calm(mary)|~patient(mary)))=>(calm(alice)))&
((calm(lucy))<=>((creative(john)|happy(john))))&
(![X]:((~kind(X)|patient(X))<=>old(X)))&
(![X]:((~quiet(X)|patient(X))<=>(brave(X)|rich(X))))&
((~wise(paul))=>(?[X]:(kind(X))))&
(![X]:((~happy(X)<~>kind(X))=>(~generous(X)<~>~kind(X))))&
(((~generous(lucy)<~>creative(lucy)))<=>(?[X]:((humble(X)<~>~quiet(X)))))&
((?[X]:((happy(X)|~humble(X))))<=>((~rich(alice)|~curious(alice))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)&~kind(X))))&
(![X]:((wise(X)<~>~brave(X))=>(~old(X)|funny(X))))&
((?[X]:((~creative(X)|~old(X))))=>((~wise(john)&funny(john))))&
(![X]:((old(X)&~patient(X))<=>creative(X)))&
(![X]:((~brave(X)<~>~humble(X))<=>(~brave(X)&~patient(X))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>((~brave(paul)|curious(paul))))&
(((~brave(susan)|~funny(susan)))<=>(?[X]:((~curious(X)|~tall(X)))))&
((quiet(john)|generous(john)))&
(?[X]:((calm(X)|~creative(X))))&
((~kind(alice)|strong(alice)))&
(~wise(mary))&
(?[X]:((creative(X)<~>~rich(X))))&
((generous(john)|~humble(john)))&
((~tall(john)|curious(john)))&
(~funny(john)) | old(susan) | [
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7849673200754210021647766
% SZS output start Proof for 7849673200754210021647766
12. ? [X0] : (~old(X0) | ~creative(X0)) => (funny(john) & ~wise(john)) [input p11]
24. ~funny(john) [input p23]
25. ~old(susan) [input hypothesis]
32. (funny(john) & ~wise(john)) | ! [X0] : (old(X0) & creative(X0)) [ennf transformation 12]
121. funny(john) | old(X0) [cnf transformation 32]
148. ~funny(john) [cnf transformation 24]
149. ~old(susan) [cnf transformation 25]
273. 26 <=> ! [X0] : old(X0) [avatar definition]
274. old(X0) <- (26) [avatar component clause 273]
276. 27 <=> funny(john) [avatar definition]
279. 26 | 27 [avatar split clause 121,276,273]
382. ~27 [avatar split clause 148,276]
387. $false <- (26) [resolution 274,149]
388. ~26 [avatar contradiction clause 387]
389. $false [avatar sat refutation 279,382,388]
% SZS output end Proof for 7849673200754210021647766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not rich then susan is not patient or curious. Everyone who is not creative or not strong is both not brave and not strong and vice versa. If someone is not tall or curious then someone is both not happy and generous and vice versa. Everyone who is wise or not quiet is either not brave or strong. Everyone who is either not curious or tall is both not patient and not calm and vice versa. If paul is curious or not humble then someone is not brave or funny and vice versa. If someone is not calm then fred is both wise and happy. If someone is not rich then paul is old and vice versa. Everyone who is not kind is not patient or not generous. If someone is kind or not creative then someone is either not happy or not patient and vice versa. Everyone who is not quiet or generous is either patient or curious and vice versa. Everyone who is quiet or humble is either not humble or not brave and vice versa. If someone is not brave then paul is either quiet or curious and vice versa. If someone is either not curious or not calm then someone is both not strong and not brave. Everyone who is not kind or not curious is either not happy or not tall. If mary is generous or not brave then someone is either not strong or not rich and vice versa. Paul is wise or not generous. Someone is both wise and patient. Lucy is happy or kind. Lucy is strong. John is either not kind or rich. Paul is either not calm or not strong. John is either kind or not humble. | John is not quiet. | neutral | ((?[X]:((wise(X)|~rich(X))))=>((~patient(susan)|curious(susan))))&
(![X]:((~creative(X)|~strong(X))<=>(~brave(X)&~strong(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:((wise(X)|~quiet(X))=>(~brave(X)<~>strong(X))))&
(![X]:((~curious(X)<~>tall(X))<=>(~patient(X)&~calm(X))))&
(((curious(paul)|~humble(paul)))<=>(?[X]:((~brave(X)|funny(X)))))&
((?[X]:(~calm(X)))=>((wise(fred)&happy(fred))))&
((?[X]:(~rich(X)))<=>(old(paul)))&
(![X]:(~kind(X)=>(~patient(X)|~generous(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(patient(X)<~>curious(X))))&
(![X]:((quiet(X)|humble(X))<=>(~humble(X)<~>~brave(X))))&
((?[X]:(~brave(X)))<=>((quiet(paul)<~>curious(paul))))&
((?[X]:((~curious(X)<~>~calm(X))))=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((~kind(X)|~curious(X))=>(~happy(X)<~>~tall(X))))&
(((generous(mary)|~brave(mary)))<=>(?[X]:((~strong(X)<~>~rich(X)))))&
((wise(paul)|~generous(paul)))&
(?[X]:((wise(X)&patient(X))))&
((happy(lucy)|kind(lucy)))&
(strong(lucy))&
((~kind(john)<~>rich(john)))&
((~calm(paul)<~>~strong(paul)))&
((kind(john)<~>~humble(john))) | ~quiet(john) | [] | null | 0 |
If someone is either calm or not calm then susan is not generous or strong.
Everyone who is creative or kind is either old or not rich and vice versa.
Everyone who is both strong and not old is both not quiet and creative.
Everyone who is both creative and not tall is either not quiet or funny.
Everyone who is both funny and strong is old and vice versa.
Everyone who is both strong and not creative is either not kind or not strong and vice versa.
Everyone who is both not curious and not funny is either patient or happy and vice versa.
If alice is both old and not kind then someone is curious.
If someone is wise then susan is either quiet or not strong.
If someone is both not old and strong then someone is both not humble and calm.
If someone is not creative then someone is both not old and not rich and vice versa.
Everyone who is not curious is not humble or not patient.
If someone is both not strong and strong then mary is kind and vice versa.
If john is not rich then someone is both not brave and not curious.
If someone is old then mary is both old and creative and vice versa.
Everyone who is brave is creative or not humble.
Paul is both not kind and not rich.
John is both not rich and brave.
Someone is strong.
Someone is not strong.
Someone is not patient.
Lucy is not brave or not happy.
Mary is either not creative or not kind. | Lucy is not calm. | neutral | ((?[X]:((calm(X)<~>~calm(X))))=>((~generous(susan)|strong(susan))))&
(![X]:((creative(X)|kind(X))<=>(old(X)<~>~rich(X))))&
(![X]:((strong(X)&~old(X))=>(~quiet(X)&creative(X))))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)<~>funny(X))))&
(![X]:((funny(X)&strong(X))<=>old(X)))&
(![X]:((strong(X)&~creative(X))<=>(~kind(X)<~>~strong(X))))&
(![X]:((~curious(X)&~funny(X))<=>(patient(X)<~>happy(X))))&
(((old(alice)&~kind(alice)))=>(?[X]:(curious(X))))&
((?[X]:(wise(X)))=>((quiet(susan)<~>~strong(susan))))&
((?[X]:((~old(X)&strong(X))))=>(?[X]:((~humble(X)&calm(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:(~curious(X)=>(~humble(X)|~patient(X))))&
((?[X]:((~strong(X)&strong(X))))<=>(kind(mary)))&
((~rich(john))=>(?[X]:((~brave(X)&~curious(X)))))&
((?[X]:(old(X)))<=>((old(mary)&creative(mary))))&
(![X]:(brave(X)=>(creative(X)|~humble(X))))&
((~kind(paul)&~rich(paul)))&
((~rich(john)&brave(john)))&
(?[X]:(strong(X)))&
(?[X]:(~strong(X)))&
(?[X]:(~patient(X)))&
((~brave(lucy)|~happy(lucy)))&
((~creative(mary)<~>~kind(mary))) | ~calm(lucy) | [] | null | 0 |
If john is generous then someone is not humble and vice versa.
Everyone who is not calm or not strong is old or funny.
If someone is humble then paul is not funny or humble.
Everyone who is both curious and not patient is both not tall and quiet.
Everyone who is either old or not creative is either strong or not patient.
Everyone who is not happy is calm or not generous.
If lucy is old or not patient then alice is humble or quiet and vice versa.
Everyone who is either not old or calm is wise.
If someone is not funny then alice is either not quiet or generous.
Everyone who is both not patient and quiet is either rich or not humble and vice versa.
If lucy is both wise and not brave then someone is strong or not generous.
Everyone who is either happy or not generous is either tall or curious.
Everyone who is wise is either kind or happy and vice versa.
Everyone who is either not funny or not old is wise or old and vice versa.
Everyone who is both calm and not calm is happy or not humble and vice versa.
If someone is humble then mary is not happy and vice versa.
Someone is brave.
Susan is not curious or not generous.
Someone is not curious or happy.
Someone is not patient or funny.
Mary is both funny and generous.
Someone is either brave or not happy. | Mary is curious. | neutral | ((generous(john))<=>(?[X]:(~humble(X))))&
(![X]:((~calm(X)|~strong(X))=>(old(X)|funny(X))))&
((?[X]:(humble(X)))=>((~funny(paul)|humble(paul))))&
(![X]:((curious(X)&~patient(X))=>(~tall(X)&quiet(X))))&
(![X]:((old(X)<~>~creative(X))=>(strong(X)<~>~patient(X))))&
(![X]:(~happy(X)=>(calm(X)|~generous(X))))&
(((old(lucy)|~patient(lucy)))<=>((humble(alice)|quiet(alice))))&
(![X]:((~old(X)<~>calm(X))=>wise(X)))&
((?[X]:(~funny(X)))=>((~quiet(alice)<~>generous(alice))))&
(![X]:((~patient(X)&quiet(X))<=>(rich(X)<~>~humble(X))))&
(((wise(lucy)&~brave(lucy)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((happy(X)<~>~generous(X))=>(tall(X)<~>curious(X))))&
(![X]:(wise(X)<=>(kind(X)<~>happy(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(wise(X)|old(X))))&
(![X]:((calm(X)&~calm(X))<=>(happy(X)|~humble(X))))&
((?[X]:(humble(X)))<=>(~happy(mary)))&
(?[X]:(brave(X)))&
((~curious(susan)|~generous(susan)))&
(?[X]:((~curious(X)|happy(X))))&
(?[X]:((~patient(X)|funny(X))))&
((funny(mary)&generous(mary)))&
(?[X]:((brave(X)<~>~happy(X)))) | curious(mary) | [] | null | 0 |
Everyone who is either not kind or happy is not old or not humble.
If susan is both rich and kind then someone is curious or strong.
If someone is not creative then someone is not happy or tall and vice versa.
Everyone who is wise or not calm is either not wise or creative and vice versa.
If someone is not wise or not patient then someone is brave or not kind.
If lucy is not strong or creative then someone is kind or quiet.
Everyone who is both kind and not calm is brave or not quiet and vice versa.
Everyone who is not kind is both tall and strong.
Everyone who is old or brave is not rich or quiet.
If susan is either humble or not creative then mary is not wise or patient.
Everyone who is either not wise or creative is both rich and not old and vice versa.
Everyone who is not wise or not humble is calm.
If someone is both not strong and generous then someone is not calm or funny and vice versa.
If someone is not curious or strong then susan is not curious or brave.
Everyone who is calm is not brave or calm.
Everyone who is both wise and not tall is both quiet and strong.
Susan is not curious.
John is either not kind or brave.
Fred is both funny and not old.
Paul is quiet.
Lucy is either creative or not generous. | Lucy is not strong. | neutral | (![X]:((~kind(X)<~>happy(X))=>(~old(X)|~humble(X))))&
(((rich(susan)&kind(susan)))=>(?[X]:((curious(X)|strong(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~happy(X)|tall(X)))))&
(![X]:((wise(X)|~calm(X))<=>(~wise(X)<~>creative(X))))&
((?[X]:((~wise(X)|~patient(X))))=>(?[X]:((brave(X)|~kind(X)))))&
(((~strong(lucy)|creative(lucy)))=>(?[X]:((kind(X)|quiet(X)))))&
(![X]:((kind(X)&~calm(X))<=>(brave(X)|~quiet(X))))&
(![X]:(~kind(X)=>(tall(X)&strong(X))))&
(![X]:((old(X)|brave(X))=>(~rich(X)|quiet(X))))&
(((humble(susan)<~>~creative(susan)))=>((~wise(mary)|patient(mary))))&
(![X]:((~wise(X)<~>creative(X))<=>(rich(X)&~old(X))))&
(![X]:((~wise(X)|~humble(X))=>calm(X)))&
((?[X]:((~strong(X)&generous(X))))<=>(?[X]:((~calm(X)|funny(X)))))&
((?[X]:((~curious(X)|strong(X))))=>((~curious(susan)|brave(susan))))&
(![X]:(calm(X)=>(~brave(X)|calm(X))))&
(![X]:((wise(X)&~tall(X))=>(quiet(X)&strong(X))))&
(~curious(susan))&
((~kind(john)<~>brave(john)))&
((funny(fred)&~old(fred)))&
(quiet(paul))&
((creative(lucy)<~>~generous(lucy))) | ~strong(lucy) | [] | null | 0 |
Everyone who is either not brave or happy is both calm and not calm and vice versa.
If someone is strong or not generous then alice is brave or generous.
If someone is not old or creative then paul is kind or not tall and vice versa.
Everyone who is calm is either quiet or not kind.
If lucy is both not creative and not strong then someone is rich or humble.
Everyone who is either not funny or funny is not patient or not old.
Everyone who is tall is either happy or not creative.
Everyone who is both quiet and not calm is either funny or not happy and vice versa.
If john is not rich or not patient then john is both not quiet and not brave.
Everyone who is both not patient and happy is not old and vice versa.
If john is both calm and kind then someone is old and vice versa.
Everyone who is both humble and patient is both not generous and quiet and vice versa.
Everyone who is either happy or not curious is either brave or humble.
If someone is either funny or wise then paul is either not creative or generous and vice versa.
If fred is humble then fred is both not tall and not happy.
Lucy is not kind.
Someone is both not old and tall.
Someone is not strong or not happy.
Mary is both strong and not generous.
Someone is not tall.
Susan is either creative or not creative. | Susan is not happy. | contradiction | (![X]:((~brave(X)<~>happy(X))<=>(calm(X)&~calm(X))))&
((?[X]:((strong(X)|~generous(X))))=>((brave(alice)|generous(alice))))&
((?[X]:((~old(X)|creative(X))))<=>((kind(paul)|~tall(paul))))&
(![X]:(calm(X)=>(quiet(X)<~>~kind(X))))&
(((~creative(lucy)&~strong(lucy)))=>(?[X]:((rich(X)|humble(X)))))&
(![X]:((~funny(X)<~>funny(X))=>(~patient(X)|~old(X))))&
(![X]:(tall(X)=>(happy(X)<~>~creative(X))))&
(![X]:((quiet(X)&~calm(X))<=>(funny(X)<~>~happy(X))))&
(((~rich(john)|~patient(john)))=>((~quiet(john)&~brave(john))))&
(![X]:((~patient(X)&happy(X))<=>~old(X)))&
(((calm(john)&kind(john)))<=>(?[X]:(old(X))))&
(![X]:((humble(X)&patient(X))<=>(~generous(X)&quiet(X))))&
(![X]:((happy(X)<~>~curious(X))=>(brave(X)<~>humble(X))))&
((?[X]:((funny(X)<~>wise(X))))<=>((~creative(paul)<~>generous(paul))))&
((humble(fred))=>((~tall(fred)&~happy(fred))))&
(~kind(lucy))&
(?[X]:((~old(X)&tall(X))))&
(?[X]:((~strong(X)|~happy(X))))&
((strong(mary)&~generous(mary)))&
(?[X]:(~tall(X)))&
((creative(susan)<~>~creative(susan))) | ~happy(susan) | [
"p3",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2499134336506270042181887
% SZS output start Proof for 2499134336506270042181887
4. ! [X0] : (calm(X0) => (quiet(X0) <~> ~kind(X0))) [input p3]
6. ! [X0] : ((~funny(X0) <~> funny(X0)) => (~old(X0) | ~patient(X0))) [input p5]
9. (~patient(john) | ~rich(john)) => (~brave(john) & ~quiet(john)) [input p8]
10. ! [X0] : ((happy(X0) & ~patient(X0)) <=> ~old(X0)) [input p9]
11. (kind(john) & calm(john)) <=> ? [X0] : old(X0) [input p10]
22. ~happy(susan) [input hypothesis]
23. ~patient(john) => (~brave(john) & ~quiet(john)) [pure predicate removal 9]
27. ! [X0] : ((quiet(X0) <~> ~kind(X0)) | ~calm(X0)) [ennf transformation 4]
28. ! [X0] : ((~old(X0) | ~patient(X0)) | (~funny(X0) <=> funny(X0))) [ennf transformation 6]
29. ! [X0] : (~old(X0) | ~patient(X0) | (~funny(X0) <=> funny(X0))) [flattening 28]
31. (~brave(john) & ~quiet(john)) | patient(john) [ennf transformation 23]
41. ! [X0] : (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | ~calm(X0)) [nnf transformation 27]
42. ! [X0] : (~old(X0) | ~patient(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) [nnf transformation 29]
46. ! [X0] : (((happy(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | (~happy(X0) | patient(X0)))) [nnf transformation 10]
47. ! [X0] : (((happy(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | ~happy(X0) | patient(X0))) [flattening 46]
48. ((kind(john) & calm(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (~kind(john) | ~calm(john))) [nnf transformation 11]
49. ((kind(john) & calm(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ~kind(john) | ~calm(john)) [flattening 48]
50. ((kind(john) & calm(john)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ~kind(john) | ~calm(john)) [rectify 49]
51. ? [X1] : old(X1) => old(sK1) [choice axiom]
52. ((kind(john) & calm(john)) | ! [X0] : ~old(X0)) & (old(sK1) | ~kind(john) | ~calm(john)) [skolemisation 50,51]
79. ~kind(X0) | quiet(X0) | ~calm(X0) [cnf transformation 41]
81. ~old(X0) | ~patient(X0) | funny(X0) | funny(X0) [cnf transformation 42]
82. ~old(X0) | ~patient(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 42]
91. ~quiet(john) | patient(john) [cnf transformation 31]
94. ~patient(X0) | old(X0) [cnf transformation 47]
95. old(X0) | happy(X0) [cnf transformation 47]
97. calm(john) | ~old(X0) [cnf transformation 52]
98. kind(john) | ~old(X0) [cnf transformation 52]
126. ~happy(susan) [cnf transformation 22]
127. ~old(X0) | ~patient(X0) | funny(X0) [duplicate literal removal 81]
128. ~old(X0) | ~patient(X0) | ~funny(X0) [duplicate literal removal 82]
173. ~patient(X0) | ~old(X0) [subsumption resolution 127,128]
175. 11 <=> patient(john) [avatar definition]
177. patient(john) <- (11) [avatar component clause 175]
184. 13 <=> quiet(john) [avatar definition]
187. 11 | ~13 [avatar split clause 91,184,175]
188. ~patient(X0) [subsumption resolution 94,173]
191. 14 <=> ! [X0] : ~old(X0) [avatar definition]
192. ~old(X0) <- (14) [avatar component clause 191]
194. 15 <=> kind(john) [avatar definition]
196. kind(john) <- (15) [avatar component clause 194]
197. 14 | 15 [avatar split clause 98,194,191]
199. 16 <=> calm(john) [avatar definition]
201. calm(john) <- (16) [avatar component clause 199]
202. 14 | 16 [avatar split clause 97,199,191]
265. happy(X0) <- (14) [resolution 95,192]
270. $false <- (14) [resolution 265,126]
274. ~14 [avatar contradiction clause 270]
282. quiet(john) | ~calm(john) <- (15) [resolution 79,196]
286. quiet(john) <- (15, 16) [subsumption resolution 282,201]
287. 13 | ~15 | ~16 [avatar split clause 286,199,194,184]
288. $false <- (11) [subsumption resolution 177,188]
289. ~11 [avatar contradiction clause 288]
290. $false [avatar sat refutation 187,197,202,274,287,289]
% SZS output end Proof for 2499134336506270042181887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or not happy then lucy is not humble or old and vice versa. Everyone who is either not curious or generous is either not brave or rich and vice versa. Everyone who is either not happy or curious is either not creative or not tall and vice versa. Everyone who is not wise or not brave is not brave or not generous and vice versa. Everyone who is not tall or patient is either not brave or not kind and vice versa. Everyone who is not funny or rich is strong or tall and vice versa. If paul is both not old and creative then susan is not humble or not rich. If someone is either happy or calm then lucy is not patient and vice versa. If mary is not creative then mary is either not happy or strong. If paul is funny or not humble then someone is both quiet and kind. If paul is both curious and happy then someone is both funny and not happy and vice versa. Everyone who is both quiet and not wise is both not old and brave. Everyone who is not wise is both tall and not generous and vice versa. Everyone who is either not curious or happy is kind or not kind and vice versa. Everyone who is both kind and not kind is both creative and wise and vice versa. If susan is either not kind or not funny then someone is not old or quiet. Someone is both not patient and not funny. Mary is either not kind or curious. Someone is funny. Fred is funny or old. John is both kind and not wise. John is either generous or calm. Someone is either not strong or wise. Lucy is either generous or patient. | John is not generous. | entailment | ((?[X]:((strong(X)<~>~happy(X))))<=>((~humble(lucy)|old(lucy))))&
(![X]:((~curious(X)<~>generous(X))<=>(~brave(X)<~>rich(X))))&
(![X]:((~happy(X)<~>curious(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~brave(X)|~generous(X))))&
(![X]:((~tall(X)|patient(X))<=>(~brave(X)<~>~kind(X))))&
(![X]:((~funny(X)|rich(X))<=>(strong(X)|tall(X))))&
(((~old(paul)&creative(paul)))=>((~humble(susan)|~rich(susan))))&
((?[X]:((happy(X)<~>calm(X))))<=>(~patient(lucy)))&
((~creative(mary))=>((~happy(mary)<~>strong(mary))))&
(((funny(paul)|~humble(paul)))=>(?[X]:((quiet(X)&kind(X)))))&
(((curious(paul)&happy(paul)))<=>(?[X]:((funny(X)&~happy(X)))))&
(![X]:((quiet(X)&~wise(X))=>(~old(X)&brave(X))))&
(![X]:(~wise(X)<=>(tall(X)&~generous(X))))&
(![X]:((~curious(X)<~>happy(X))<=>(kind(X)|~kind(X))))&
(![X]:((kind(X)&~kind(X))<=>(creative(X)&wise(X))))&
(((~kind(susan)<~>~funny(susan)))=>(?[X]:((~old(X)|quiet(X)))))&
(?[X]:((~patient(X)&~funny(X))))&
((~kind(mary)<~>curious(mary)))&
(?[X]:(funny(X)))&
((funny(fred)|old(fred)))&
((kind(john)&~wise(john)))&
((generous(john)<~>calm(john)))&
(?[X]:((~strong(X)<~>wise(X))))&
((generous(lucy)<~>patient(lucy))) | ~generous(john) | [
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4007103441701934323555236
% SZS output start Proof for 4007103441701934323555236
13. ! [X0] : (~wise(X0) <=> (~generous(X0) & tall(X0))) [input p12]
21. ~wise(john) & kind(john) [input p20]
25. generous(john) [input hypothesis]
58. ! [X0] : ((~wise(X0) | (generous(X0) | ~tall(X0))) & ((~generous(X0) & tall(X0)) | wise(X0))) [nnf transformation 13]
59. ! [X0] : ((~wise(X0) | generous(X0) | ~tall(X0)) & ((~generous(X0) & tall(X0)) | wise(X0))) [flattening 58]
131. ~generous(X0) | wise(X0) [cnf transformation 59]
152. ~wise(john) [cnf transformation 21]
159. generous(john) [cnf transformation 25]
325. 36 <=> generous(john) [avatar definition]
326. generous(john) <- (36) [avatar component clause 325]
350. 36 [avatar split clause 159,325]
353. wise(john) <- (36) [resolution 131,326]
354. $false <- (36) [subsumption resolution 353,152]
355. ~36 [avatar contradiction clause 354]
356. $false [avatar sat refutation 350,355]
% SZS output end Proof for 4007103441701934323555236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not kind is either not kind or strong and vice versa. Everyone who is strong or not patient is both curious and not wise and vice versa. Everyone who is both not funny and not tall is either not tall or generous. Everyone who is wise is not quiet. Everyone who is not humble or tall is not creative and vice versa. Everyone who is either not humble or tall is either humble or brave. Everyone who is not creative or not patient is either not curious or quiet. Everyone who is patient is not strong. If susan is both not kind and not old then mary is both creative and not calm. Everyone who is not quiet is both not quiet and not happy. If someone is either not strong or not patient then someone is both not brave and strong. If lucy is not humble or not rich then someone is not humble. Everyone who is both not creative and not wise is calm and vice versa. If john is both not wise and humble then someone is tall or funny. Everyone who is not kind or not strong is both not generous and humble and vice versa. If someone is strong or creative then susan is not patient and vice versa. John is funny. Paul is happy or not old. Someone is either humble or not kind. Paul is not rich. Someone is not rich or not generous. Someone is kind. Someone is not tall or happy. | Paul is wise. | contradiction | (![X]:((humble(X)&~kind(X))<=>(~kind(X)<~>strong(X))))&
(![X]:((strong(X)|~patient(X))<=>(curious(X)&~wise(X))))&
(![X]:((~funny(X)&~tall(X))=>(~tall(X)<~>generous(X))))&
(![X]:(wise(X)=>~quiet(X)))&
(![X]:((~humble(X)|tall(X))<=>~creative(X)))&
(![X]:((~humble(X)<~>tall(X))=>(humble(X)<~>brave(X))))&
(![X]:((~creative(X)|~patient(X))=>(~curious(X)<~>quiet(X))))&
(![X]:(patient(X)=>~strong(X)))&
(((~kind(susan)&~old(susan)))=>((creative(mary)&~calm(mary))))&
(![X]:(~quiet(X)=>(~quiet(X)&~happy(X))))&
((?[X]:((~strong(X)<~>~patient(X))))=>(?[X]:((~brave(X)&strong(X)))))&
(((~humble(lucy)|~rich(lucy)))=>(?[X]:(~humble(X))))&
(![X]:((~creative(X)&~wise(X))<=>calm(X)))&
(((~wise(john)&humble(john)))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:((~kind(X)|~strong(X))<=>(~generous(X)&humble(X))))&
((?[X]:((strong(X)|creative(X))))<=>(~patient(susan)))&
(funny(john))&
((happy(paul)|~old(paul)))&
(?[X]:((humble(X)<~>~kind(X))))&
(~rich(paul))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:(kind(X)))&
(?[X]:((~tall(X)|happy(X)))) | wise(paul) | [
"p0",
"p1",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4083688620692122508835865
% SZS output start Proof for 4083688620692122508835865
1. ! [X0] : ((~kind(X0) & humble(X0)) <=> (~kind(X0) <~> strong(X0))) [input p0]
2. ! [X0] : ((~patient(X0) | strong(X0)) <=> (~wise(X0) & curious(X0))) [input p1]
8. ! [X0] : (patient(X0) => ~strong(X0)) [input p7]
11. ? [X0] : (~strong(X0) <~> ~patient(X0)) => ? [X0] : (strong(X0) & ~brave(X0)) [input p10]
15. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> (humble(X0) & ~generous(X0))) [input p14]
24. wise(paul) [input hypothesis]
25. ? [X0] : (~strong(X0) <~> ~patient(X0)) => ? [X1] : (strong(X1) & ~brave(X1)) [rectify 11]
33. ! [X0] : (~strong(X0) | ~patient(X0)) [ennf transformation 8]
37. ? [X1] : (strong(X1) & ~brave(X1)) | ! [X0] : (~strong(X0) <=> ~patient(X0)) [ennf transformation 25]
41. ! [X0] : (((~kind(X0) & humble(X0)) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) & (((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | (kind(X0) | ~humble(X0)))) [nnf transformation 1]
42. ! [X0] : (((~kind(X0) & humble(X0)) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) & (((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | kind(X0) | ~humble(X0))) [flattening 41]
43. ! [X0] : (((~patient(X0) | strong(X0)) | (wise(X0) | ~curious(X0))) & ((~wise(X0) & curious(X0)) | (patient(X0) & ~strong(X0)))) [nnf transformation 2]
44. ! [X0] : ((~patient(X0) | strong(X0) | wise(X0) | ~curious(X0)) & ((~wise(X0) & curious(X0)) | (patient(X0) & ~strong(X0)))) [flattening 43]
49. ? [X1] : (strong(X1) & ~brave(X1)) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0))) [nnf transformation 37]
50. ? [X0] : (strong(X0) & ~brave(X0)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1))) [rectify 49]
51. ? [X0] : (strong(X0) & ~brave(X0)) => (strong(sK0) & ~brave(sK0)) [choice axiom]
52. (strong(sK0) & ~brave(sK0)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1))) [skolemisation 50,51]
55. ! [X0] : (((~strong(X0) | ~kind(X0)) | (~humble(X0) | generous(X0))) & ((humble(X0) & ~generous(X0)) | (strong(X0) & kind(X0)))) [nnf transformation 15]
56. ! [X0] : ((~strong(X0) | ~kind(X0) | ~humble(X0) | generous(X0)) & ((humble(X0) & ~generous(X0)) | (strong(X0) & kind(X0)))) [flattening 55]
71. ~strong(X0) | kind(X0) | kind(X0) | ~humble(X0) [cnf transformation 42]
75. ~kind(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 42]
79. ~wise(X0) | patient(X0) [cnf transformation 44]
93. ~patient(X0) | ~strong(X0) [cnf transformation 33]
100. strong(sK0) | ~patient(X1) | strong(X1) [cnf transformation 52]
107. kind(X0) | humble(X0) [cnf transformation 56]
108. strong(X0) | humble(X0) [cnf transformation 56]
120. wise(paul) [cnf transformation 24]
123. ~strong(X0) | kind(X0) | ~humble(X0) [duplicate literal removal 71]
124. ~strong(X0) | ~kind(X0) [duplicate literal removal 75]
125. ~strong(X0) | ~humble(X0) [subsumption resolution 123,124]
150. 6 <=> strong(sK0) [avatar definition]
152. strong(sK0) <- (6) [avatar component clause 150]
154. strong(sK0) | ~patient(X1) [subsumption resolution 100,93]
156. 7 <=> ! [X1] : ~patient(X1) [avatar definition]
157. ~patient(X1) <- (7) [avatar component clause 156]
158. 7 | 6 [avatar split clause 154,150,156]
231. patient(paul) [resolution 79,120]
237. ~kind(X0) | humble(X0) [resolution 124,108]
238. humble(X0) [subsumption resolution 237,107]
240. ~humble(sK0) <- (6) [resolution 125,152]
243. $false <- (6) [subsumption resolution 240,238]
244. ~6 [avatar contradiction clause 243]
249. $false <- (7) [resolution 157,231]
250. ~7 [avatar contradiction clause 249]
251. $false [avatar sat refutation 158,244,250]
% SZS output end Proof for 4083688620692122508835865
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient or not strong then susan is both not tall and not creative.
Everyone who is funny is strong or tall.
Everyone who is generous or wise is either not creative or generous.
If someone is not humble or not patient then someone is both not kind and kind.
Everyone who is not quiet or creative is not rich.
Everyone who is either not happy or old is not kind or not humble.
Everyone who is both rich and brave is not creative.
Everyone who is not brave is curious.
Everyone who is patient is rich or not generous and vice versa.
If paul is both brave and kind then susan is both not kind and humble and vice versa.
Everyone who is either tall or not calm is wise and vice versa.
Everyone who is either not tall or humble is either calm or not kind.
Everyone who is both generous and humble is not rich or happy and vice versa.
Everyone who is both not tall and calm is either not generous or not quiet.
Everyone who is not funny is either not brave or not rich.
Paul is not curious or calm.
Alice is calm.
Someone is not curious or not wise.
Someone is quiet or not tall.
Paul is either happy or old.
Someone is patient. | Paul is not happy. | entailment | ((?[X]:((patient(X)|~strong(X))))=>((~tall(susan)&~creative(susan))))&
(![X]:(funny(X)=>(strong(X)|tall(X))))&
(![X]:((generous(X)|wise(X))=>(~creative(X)<~>generous(X))))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((~kind(X)&kind(X)))))&
(![X]:((~quiet(X)|creative(X))=>~rich(X)))&
(![X]:((~happy(X)<~>old(X))=>(~kind(X)|~humble(X))))&
(![X]:((rich(X)&brave(X))=>~creative(X)))&
(![X]:(~brave(X)=>curious(X)))&
(![X]:(patient(X)<=>(rich(X)|~generous(X))))&
(((brave(paul)&kind(paul)))<=>((~kind(susan)&humble(susan))))&
(![X]:((tall(X)<~>~calm(X))<=>wise(X)))&
(![X]:((~tall(X)<~>humble(X))=>(calm(X)<~>~kind(X))))&
(![X]:((generous(X)&humble(X))<=>(~rich(X)|happy(X))))&
(![X]:((~tall(X)&calm(X))=>(~generous(X)<~>~quiet(X))))&
(![X]:(~funny(X)=>(~brave(X)<~>~rich(X))))&
((~curious(paul)|calm(paul)))&
(calm(alice))&
(?[X]:((~curious(X)|~wise(X))))&
(?[X]:((quiet(X)|~tall(X))))&
((happy(paul)<~>old(paul)))&
(?[X]:(patient(X))) | ~happy(paul) | [
"p2",
"p3",
"p4",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 62295447508073368770629
% SZS output start Proof for 62295447508073368770629
3. ! [X0] : ((wise(X0) | generous(X0)) => (~creative(X0) <~> generous(X0))) [input p2]
4. ? [X0] : (~patient(X0) | ~humble(X0)) => ? [X0] : (kind(X0) & ~kind(X0)) [input p3]
5. ! [X0] : ((creative(X0) | ~quiet(X0)) => ~rich(X0)) [input p4]
9. ! [X0] : (patient(X0) <=> (~generous(X0) | rich(X0))) [input p8]
13. ! [X0] : ((humble(X0) & generous(X0)) <=> (happy(X0) | ~rich(X0))) [input p12]
22. happy(paul) [input hypothesis]
23. ? [X0] : (~patient(X0) | ~humble(X0)) => ? [X1] : (kind(X1) & ~kind(X1)) [rectify 4]
29. ! [X0] : ((~creative(X0) <~> generous(X0)) | (~wise(X0) & ~generous(X0))) [ennf transformation 3]
30. ? [X1] : (kind(X1) & ~kind(X1)) | ! [X0] : (patient(X0) & humble(X0)) [ennf transformation 23]
31. ! [X0] : (~rich(X0) | (~creative(X0) & quiet(X0))) [ennf transformation 5]
41. ! [X0] : (((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (~wise(X0) & ~generous(X0))) [nnf transformation 29]
42. ? [X0] : (kind(X0) & ~kind(X0)) | ! [X1] : (patient(X1) & humble(X1)) [rectify 30]
43. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK0) & ~kind(sK0)) [choice axiom]
44. (kind(sK0) & ~kind(sK0)) | ! [X1] : (patient(X1) & humble(X1)) [skolemisation 42,43]
46. ! [X0] : ((patient(X0) | (generous(X0) & ~rich(X0))) & ((~generous(X0) | rich(X0)) | ~patient(X0))) [nnf transformation 9]
47. ! [X0] : ((patient(X0) | (generous(X0) & ~rich(X0))) & (~generous(X0) | rich(X0) | ~patient(X0))) [flattening 46]
52. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | (~humble(X0) | ~generous(X0)))) [nnf transformation 13]
53. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | ~humble(X0) | ~generous(X0))) [flattening 52]
66. ~generous(X0) | creative(X0) | ~generous(X0) [cnf transformation 41]
69. ~kind(sK0) | patient(X1) [cnf transformation 44]
71. kind(sK0) | patient(X1) [cnf transformation 44]
73. ~rich(X0) | ~creative(X0) [cnf transformation 31]
78. ~generous(X0) | rich(X0) | ~patient(X0) [cnf transformation 47]
93. ~happy(X0) | generous(X0) [cnf transformation 53]
105. happy(paul) [cnf transformation 22]
106. ~generous(X0) | creative(X0) [duplicate literal removal 66]
121. 4 <=> ! [X1] : patient(X1) [avatar definition]
122. patient(X1) <- (4) [avatar component clause 121]
124. 5 <=> kind(sK0) [avatar definition]
127. 4 | 5 [avatar split clause 71,124,121]
132. 4 | ~5 [avatar split clause 69,124,121]
182. 17 <=> happy(paul) [avatar definition]
183. happy(paul) <- (17) [avatar component clause 182]
191. 17 [avatar split clause 105,182]
202. generous(paul) <- (17) [resolution 93,183]
208. creative(paul) <- (17) [resolution 106,202]
211. rich(paul) | ~patient(paul) <- (17) [resolution 78,202]
212. rich(paul) <- (4, 17) [subsumption resolution 211,122]
214. ~creative(paul) <- (4, 17) [resolution 212,73]
216. $false <- (4, 17) [subsumption resolution 214,208]
217. ~4 | ~17 [avatar contradiction clause 216]
218. $false [avatar sat refutation 127,132,191,217]
% SZS output end Proof for 62295447508073368770629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both not kind and not humble.
Everyone who is both not generous and brave is not wise.
If fred is not patient then alice is either creative or curious and vice versa.
If someone is either not patient or not humble then mary is both not quiet and quiet and vice versa.
Everyone who is not calm or not rich is either wise or not patient.
Everyone who is wise or calm is not curious or tall and vice versa.
If john is not rich or not wise then mary is brave or calm.
Everyone who is humble or not rich is either calm or rich and vice versa.
Everyone who is not old or not calm is either not patient or old and vice versa.
If susan is rich or creative then someone is both not calm and creative and vice versa.
Everyone who is either tall or not funny is either not old or wise and vice versa.
Everyone who is not old is not brave or wise.
Everyone who is not creative or calm is both not brave and funny and vice versa.
If someone is either not strong or not curious then someone is not humble or creative.
Everyone who is funny is both not calm and strong.
Everyone who is both strong and kind is not happy.
Someone is creative.
Alice is funny.
Someone is not creative or not happy.
Someone is not kind or creative.
Lucy is old. | John is not old. | contradiction | (![X]:(calm(X)=>(~kind(X)&~humble(X))))&
(![X]:((~generous(X)&brave(X))=>~wise(X)))&
((~patient(fred))<=>((creative(alice)<~>curious(alice))))&
((?[X]:((~patient(X)<~>~humble(X))))<=>((~quiet(mary)&quiet(mary))))&
(![X]:((~calm(X)|~rich(X))=>(wise(X)<~>~patient(X))))&
(![X]:((wise(X)|calm(X))<=>(~curious(X)|tall(X))))&
(((~rich(john)|~wise(john)))=>((brave(mary)|calm(mary))))&
(![X]:((humble(X)|~rich(X))<=>(calm(X)<~>rich(X))))&
(![X]:((~old(X)|~calm(X))<=>(~patient(X)<~>old(X))))&
(((rich(susan)|creative(susan)))<=>(?[X]:((~calm(X)&creative(X)))))&
(![X]:((tall(X)<~>~funny(X))<=>(~old(X)<~>wise(X))))&
(![X]:(~old(X)=>(~brave(X)|wise(X))))&
(![X]:((~creative(X)|calm(X))<=>(~brave(X)&funny(X))))&
((?[X]:((~strong(X)<~>~curious(X))))=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:(funny(X)=>(~calm(X)&strong(X))))&
(![X]:((strong(X)&kind(X))=>~happy(X)))&
(?[X]:(creative(X)))&
(funny(alice))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:((~kind(X)|creative(X))))&
(old(lucy)) | ~old(john) | [
"p3",
"p7",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3971597156751387217290076
% SZS output start Proof for 3971597156751387217290076
4. ? [X0] : (~patient(X0) <~> ~humble(X0)) <=> (quiet(mary) & ~quiet(mary)) [input p3]
8. ! [X0] : ((~rich(X0) | humble(X0)) <=> (calm(X0) <~> rich(X0))) [input p7]
9. ! [X0] : ((~calm(X0) | ~old(X0)) <=> (~patient(X0) <~> old(X0))) [input p8]
13. ! [X0] : ((calm(X0) | ~creative(X0)) <=> (funny(X0) & ~brave(X0))) [input p12]
15. ! [X0] : (funny(X0) => (strong(X0) & ~calm(X0))) [input p14]
22. ~old(john) [input hypothesis]
36. ! [X0] : ((strong(X0) & ~calm(X0)) | ~funny(X0)) [ennf transformation 15]
38. (? [X0] : ((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | (~quiet(mary) | quiet(mary))) & ((quiet(mary) & ~quiet(mary)) | ! [X0] : ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0)))) [nnf transformation 4]
39. (? [X0] : ((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ~quiet(mary) | quiet(mary)) & ((quiet(mary) & ~quiet(mary)) | ! [X0] : ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0)))) [flattening 38]
40. (? [X0] : ((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ~quiet(mary) | quiet(mary)) & ((quiet(mary) & ~quiet(mary)) | ! [X1] : ((~patient(X1) | humble(X1)) & (~humble(X1) | patient(X1)))) [rectify 39]
41. ? [X0] : ((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) => ((humble(sK0) | patient(sK0)) & (~humble(sK0) | ~patient(sK0))) [choice axiom]
42. (((humble(sK0) | patient(sK0)) & (~humble(sK0) | ~patient(sK0))) | ~quiet(mary) | quiet(mary)) & ((quiet(mary) & ~quiet(mary)) | ! [X1] : ((~patient(X1) | humble(X1)) & (~humble(X1) | patient(X1)))) [skolemisation 40,41]
46. ! [X0] : (((~rich(X0) | humble(X0)) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) & (((~rich(X0) | ~calm(X0)) & (rich(X0) | calm(X0))) | (rich(X0) & ~humble(X0)))) [nnf transformation 8]
47. ! [X0] : ((~rich(X0) | humble(X0) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) & (((~rich(X0) | ~calm(X0)) & (rich(X0) | calm(X0))) | (rich(X0) & ~humble(X0)))) [flattening 46]
48. ! [X0] : (((~calm(X0) | ~old(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (calm(X0) & old(X0)))) [nnf transformation 9]
49. ! [X0] : ((~calm(X0) | ~old(X0) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (calm(X0) & old(X0)))) [flattening 48]
56. ! [X0] : (((calm(X0) | ~creative(X0)) | (~funny(X0) | brave(X0))) & ((funny(X0) & ~brave(X0)) | (~calm(X0) & creative(X0)))) [nnf transformation 13]
57. ! [X0] : ((calm(X0) | ~creative(X0) | ~funny(X0) | brave(X0)) & ((funny(X0) & ~brave(X0)) | (~calm(X0) & creative(X0)))) [flattening 56]
69. ~quiet(mary) | ~humble(X1) | patient(X1) [cnf transformation 42]
71. quiet(mary) | ~humble(X1) | patient(X1) [cnf transformation 42]
86. rich(X0) | calm(X0) | rich(X0) [cnf transformation 47]
90. ~rich(X0) | humble(X0) | calm(X0) | ~rich(X0) [cnf transformation 47]
92. ~patient(X0) | old(X0) | calm(X0) [cnf transformation 49]
114. ~calm(X0) | funny(X0) [cnf transformation 57]
118. ~calm(X0) | ~funny(X0) [cnf transformation 36]
123. ~old(john) [cnf transformation 22]
126. rich(X0) | calm(X0) [duplicate literal removal 86]
127. ~rich(X0) | humble(X0) | calm(X0) [duplicate literal removal 90]
148. 5 <=> quiet(mary) [avatar definition]
153. 6 <=> ! [X1] : (~humble(X1) | patient(X1)) [avatar definition]
154. ~humble(X1) | patient(X1) <- (6) [avatar component clause 153]
155. 6 | 5 [avatar split clause 71,148,153]
157. 6 | ~5 [avatar split clause 69,148,153]
216. ~calm(X0) [subsumption resolution 118,114]
287. humble(X0) | calm(X0) | calm(X0) [resolution 127,126]
290. humble(X0) | calm(X0) [duplicate literal removal 287]
291. humble(X0) [subsumption resolution 290,216]
320. patient(X0) <- (6) [resolution 291,154]
364. old(X0) | calm(X0) <- (6) [resolution 320,92]
370. old(X0) <- (6) [subsumption resolution 364,216]
379. $false <- (6) [resolution 370,123]
385. ~6 [avatar contradiction clause 379]
387. $false [avatar sat refutation 155,157,385]
% SZS output end Proof for 3971597156751387217290076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then someone is both happy and tall and vice versa.
Everyone who is both not wise and wise is both not old and not rich.
If someone is either not curious or generous then someone is not brave and vice versa.
Everyone who is both not rich and not happy is both brave and kind and vice versa.
If someone is either not wise or brave then someone is not happy and vice versa.
Everyone who is either not generous or not creative is calm or generous.
If someone is quiet then someone is both happy and generous.
Everyone who is both not happy and not curious is either calm or creative.
Everyone who is not generous is both not quiet and not calm.
If susan is both not quiet and funny then john is not happy or not quiet and vice versa.
Everyone who is either not curious or funny is both strong and not rich and vice versa.
Everyone who is both creative and patient is not kind and vice versa.
If someone is not old then paul is patient and vice versa.
Everyone who is either wise or brave is either not quiet or not calm and vice versa.
Everyone who is both humble and not kind is either not brave or old.
If susan is both calm and not tall then someone is either tall or humble and vice versa.
Someone is not brave or funny.
Someone is both brave and quiet.
Mary is either calm or not brave.
Someone is both curious and not old.
Someone is both not funny and not creative.
Someone is both happy and old.
Lucy is both tall and patient.
Someone is either happy or not funny. | Susan is kind. | neutral | ((?[X]:(~wise(X)))<=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((~wise(X)&wise(X))=>(~old(X)&~rich(X))))&
((?[X]:((~curious(X)<~>generous(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~rich(X)&~happy(X))<=>(brave(X)&kind(X))))&
((?[X]:((~wise(X)<~>brave(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(calm(X)|generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((happy(X)&generous(X)))))&
(![X]:((~happy(X)&~curious(X))=>(calm(X)<~>creative(X))))&
(![X]:(~generous(X)=>(~quiet(X)&~calm(X))))&
(((~quiet(susan)&funny(susan)))<=>((~happy(john)|~quiet(john))))&
(![X]:((~curious(X)<~>funny(X))<=>(strong(X)&~rich(X))))&
(![X]:((creative(X)&patient(X))<=>~kind(X)))&
((?[X]:(~old(X)))<=>(patient(paul)))&
(![X]:((wise(X)<~>brave(X))<=>(~quiet(X)<~>~calm(X))))&
(![X]:((humble(X)&~kind(X))=>(~brave(X)<~>old(X))))&
(((calm(susan)&~tall(susan)))<=>(?[X]:((tall(X)<~>humble(X)))))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((brave(X)&quiet(X))))&
((calm(mary)<~>~brave(mary)))&
(?[X]:((curious(X)&~old(X))))&
(?[X]:((~funny(X)&~creative(X))))&
(?[X]:((happy(X)&old(X))))&
((tall(lucy)&patient(lucy)))&
(?[X]:((happy(X)<~>~funny(X)))) | kind(susan) | [] | null | 0 |
Everyone who is rich or curious is wise. If mary is not old or not humble then fred is both patient and not curious and vice versa. If lucy is both not quiet and humble then susan is either not patient or not calm. If someone is not wise then someone is either creative or wise. If someone is not wise or not funny then lucy is either kind or not rich and vice versa. Everyone who is either creative or calm is both not strong and not rich and vice versa. If susan is strong or kind then mary is not humble or not funny. Everyone who is both not curious and patient is both happy and not humble. Everyone who is happy or tall is not rich or funny and vice versa. If someone is either quiet or happy then someone is humble and vice versa. Everyone who is not strong or not calm is both brave and calm and vice versa. If mary is both humble and not brave then john is tall. If someone is happy or quiet then someone is either not funny or not humble and vice versa. If susan is both not tall and not curious then alice is funny or not brave and vice versa. If someone is both not quiet and not creative then someone is either generous or curious and vice versa. Everyone who is both not strong and not quiet is both patient and not quiet. Alice is either not generous or not creative. Paul is either not rich or not humble. Susan is strong. John is both not happy and not quiet. Someone is not humble or kind. Someone is not quiet or not rich. Someone is either not patient or curious. Someone is either not tall or tall. | Lucy is calm. | entailment | (![X]:((rich(X)|curious(X))=>wise(X)))&
(((~old(mary)|~humble(mary)))<=>((patient(fred)&~curious(fred))))&
(((~quiet(lucy)&humble(lucy)))=>((~patient(susan)<~>~calm(susan))))&
((?[X]:(~wise(X)))=>(?[X]:((creative(X)<~>wise(X)))))&
((?[X]:((~wise(X)|~funny(X))))<=>((kind(lucy)<~>~rich(lucy))))&
(![X]:((creative(X)<~>calm(X))<=>(~strong(X)&~rich(X))))&
(((strong(susan)|kind(susan)))=>((~humble(mary)|~funny(mary))))&
(![X]:((~curious(X)&patient(X))=>(happy(X)&~humble(X))))&
(![X]:((happy(X)|tall(X))<=>(~rich(X)|funny(X))))&
((?[X]:((quiet(X)<~>happy(X))))<=>(?[X]:(humble(X))))&
(![X]:((~strong(X)|~calm(X))<=>(brave(X)&calm(X))))&
(((humble(mary)&~brave(mary)))=>(tall(john)))&
((?[X]:((happy(X)|quiet(X))))<=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((~tall(susan)&~curious(susan)))<=>((funny(alice)|~brave(alice))))&
((?[X]:((~quiet(X)&~creative(X))))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~strong(X)&~quiet(X))=>(patient(X)&~quiet(X))))&
((~generous(alice)<~>~creative(alice)))&
((~rich(paul)<~>~humble(paul)))&
(strong(susan))&
((~happy(john)&~quiet(john)))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:((~quiet(X)|~rich(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((~tall(X)<~>tall(X)))) | calm(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5156117783412816732871071
% SZS output start Proof for 5156117783412816732871071
11. ! [X0] : ((~calm(X0) | ~strong(X0)) <=> (calm(X0) & brave(X0))) [input p10]
25. ~calm(lucy) [input hypothesis]
62. ! [X0] : (((~calm(X0) | ~strong(X0)) | (~calm(X0) | ~brave(X0))) & ((calm(X0) & brave(X0)) | (calm(X0) & strong(X0)))) [nnf transformation 11]
63. ! [X0] : ((~calm(X0) | ~strong(X0) | ~calm(X0) | ~brave(X0)) & ((calm(X0) & brave(X0)) | (calm(X0) & strong(X0)))) [flattening 62]
126. calm(X0) | calm(X0) [cnf transformation 63]
161. ~calm(lucy) [cnf transformation 25]
162. calm(X0) [duplicate literal removal 126]
424. $false [subsumption resolution 161,162]
% SZS output end Proof for 5156117783412816732871071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or humble then someone is not tall and vice versa.
If someone is generous then alice is both not generous and not wise.
If john is patient or wise then someone is not quiet or not generous and vice versa.
If fred is either not patient or not creative then someone is old.
Everyone who is both not patient and not creative is both not wise and brave and vice versa.
Everyone who is not rich or not wise is either wise or generous and vice versa.
If paul is both rich and not strong then alice is both not strong and quiet.
Everyone who is not old or not brave is happy or rich and vice versa.
Everyone who is old or brave is not happy.
Everyone who is both not patient and not funny is either strong or not quiet.
Everyone who is not tall or wise is not creative.
If mary is either quiet or not humble then someone is both not humble and strong and vice versa.
If susan is not tall then someone is strong or not patient and vice versa.
Everyone who is not rich or not brave is funny and vice versa.
If someone is not generous then mary is both curious and not happy and vice versa.
Mary is either not funny or not tall.
Someone is both not curious and not happy.
Someone is brave.
Someone is either wise or not kind.
John is both not creative and not generous. | Mary is curious. | entailment | ((?[X]:((quiet(X)|humble(X))))<=>(?[X]:(~tall(X))))&
((?[X]:(generous(X)))=>((~generous(alice)&~wise(alice))))&
(((patient(john)|wise(john)))<=>(?[X]:((~quiet(X)|~generous(X)))))&
(((~patient(fred)<~>~creative(fred)))=>(?[X]:(old(X))))&
(![X]:((~patient(X)&~creative(X))<=>(~wise(X)&brave(X))))&
(![X]:((~rich(X)|~wise(X))<=>(wise(X)<~>generous(X))))&
(((rich(paul)&~strong(paul)))=>((~strong(alice)&quiet(alice))))&
(![X]:((~old(X)|~brave(X))<=>(happy(X)|rich(X))))&
(![X]:((old(X)|brave(X))=>~happy(X)))&
(![X]:((~patient(X)&~funny(X))=>(strong(X)<~>~quiet(X))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
(((quiet(mary)<~>~humble(mary)))<=>(?[X]:((~humble(X)&strong(X)))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
((~funny(mary)<~>~tall(mary)))&
(?[X]:((~curious(X)&~happy(X))))&
(?[X]:(brave(X)))&
(?[X]:((wise(X)<~>~kind(X))))&
((~creative(john)&~generous(john))) | curious(mary) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6663126880129805000201856
% SZS output start Proof for 6663126880129805000201856
2. ? [X0] : generous(X0) => (~wise(alice) & ~generous(alice)) [input p1]
15. ? [X0] : ~generous(X0) <=> (~happy(mary) & curious(mary)) [input p14]
21. ~curious(mary) [input hypothesis]
23. (~wise(alice) & ~generous(alice)) | ! [X0] : ~generous(X0) [ennf transformation 2]
61. (? [X0] : ~generous(X0) | (happy(mary) | ~curious(mary))) & ((~happy(mary) & curious(mary)) | ! [X0] : generous(X0)) [nnf transformation 15]
62. (? [X0] : ~generous(X0) | happy(mary) | ~curious(mary)) & ((~happy(mary) & curious(mary)) | ! [X0] : generous(X0)) [flattening 61]
63. (? [X0] : ~generous(X0) | happy(mary) | ~curious(mary)) & ((~happy(mary) & curious(mary)) | ! [X1] : generous(X1)) [rectify 62]
64. ? [X0] : ~generous(X0) => ~generous(sK6) [choice axiom]
65. (~generous(sK6) | happy(mary) | ~curious(mary)) & ((~happy(mary) & curious(mary)) | ! [X1] : generous(X1)) [skolemisation 63,64]
77. ~generous(alice) | ~generous(X0) [cnf transformation 23]
119. curious(mary) | generous(X1) [cnf transformation 65]
131. ~curious(mary) [cnf transformation 21]
159. 7 <=> ! [X0] : ~generous(X0) [avatar definition]
160. ~generous(X0) <- (7) [avatar component clause 159]
167. 9 <=> generous(alice) [avatar definition]
169. ~generous(alice) <- (~9) [avatar component clause 167]
170. 7 | ~9 [avatar split clause 77,167,159]
172. 10 <=> ! [X0] : generous(X0) [avatar definition]
173. generous(X0) <- (10) [avatar component clause 172]
276. 33 <=> curious(mary) [avatar definition]
289. 10 | 33 [avatar split clause 119,276,172]
310. ~33 [avatar split clause 131,276]
311. $false <- (~9, 10) [subsumption resolution 169,173]
312. 9 | ~10 [avatar contradiction clause 311]
313. $false <- (7, 10) [subsumption resolution 160,173]
314. ~7 | ~10 [avatar contradiction clause 313]
315. $false [avatar sat refutation 170,289,310,312,314]
% SZS output end Proof for 6663126880129805000201856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not curious is patient and vice versa.
Everyone who is not patient is happy and vice versa.
Everyone who is either brave or not patient is either tall or not humble.
If fred is not patient then someone is either not brave or not wise and vice versa.
Everyone who is either not brave or not patient is both happy and rich and vice versa.
Everyone who is generous is either not kind or tall.
Everyone who is either tall or not tall is either not generous or not humble and vice versa.
Everyone who is either rich or wise is not kind or strong.
If someone is either not old or kind then alice is either rich or quiet and vice versa.
Everyone who is tall is both strong and funny and vice versa.
Everyone who is not rich is not funny or strong.
Everyone who is either not curious or rich is both not patient and quiet.
If paul is either quiet or generous then lucy is both creative and happy and vice versa.
Everyone who is either strong or old is both brave and old and vice versa.
Everyone who is humble is wise.
Everyone who is humble or not strong is both not rich and brave and vice versa.
Mary is strong or old.
Someone is both old and strong.
Someone is not humble.
Mary is not quiet or funny.
Someone is generous or not wise. | Mary is not quiet. | entailment | (![X]:((funny(X)&~curious(X))<=>patient(X)))&
(![X]:(~patient(X)<=>happy(X)))&
(![X]:((brave(X)<~>~patient(X))=>(tall(X)<~>~humble(X))))&
((~patient(fred))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(![X]:((~brave(X)<~>~patient(X))<=>(happy(X)&rich(X))))&
(![X]:(generous(X)=>(~kind(X)<~>tall(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((rich(X)<~>wise(X))=>(~kind(X)|strong(X))))&
((?[X]:((~old(X)<~>kind(X))))<=>((rich(alice)<~>quiet(alice))))&
(![X]:(tall(X)<=>(strong(X)&funny(X))))&
(![X]:(~rich(X)=>(~funny(X)|strong(X))))&
(![X]:((~curious(X)<~>rich(X))=>(~patient(X)&quiet(X))))&
(((quiet(paul)<~>generous(paul)))<=>((creative(lucy)&happy(lucy))))&
(![X]:((strong(X)<~>old(X))<=>(brave(X)&old(X))))&
(![X]:(humble(X)=>wise(X)))&
(![X]:((humble(X)|~strong(X))<=>(~rich(X)&brave(X))))&
((strong(mary)|old(mary)))&
(?[X]:((old(X)&strong(X))))&
(?[X]:(~humble(X)))&
((~quiet(mary)|funny(mary)))&
(?[X]:((generous(X)|~wise(X)))) | ~quiet(mary) | [
"p0",
"p1",
"p2",
"p4",
"p9",
"p10",
"p11",
"p13",
"p15",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7182958143888999509974697
% SZS output start Proof for 7182958143888999509974697
1. ! [X0] : ((~curious(X0) & funny(X0)) <=> patient(X0)) [input p0]
2. ! [X0] : (~patient(X0) <=> happy(X0)) [input p1]
3. ! [X0] : ((brave(X0) <~> ~patient(X0)) => (tall(X0) <~> ~humble(X0))) [input p2]
5. ! [X0] : ((~brave(X0) <~> ~patient(X0)) <=> (rich(X0) & happy(X0))) [input p4]
10. ! [X0] : (tall(X0) <=> (funny(X0) & strong(X0))) [input p9]
11. ! [X0] : (~rich(X0) => (strong(X0) | ~funny(X0))) [input p10]
12. ! [X0] : ((~curious(X0) <~> rich(X0)) => (quiet(X0) & ~patient(X0))) [input p11]
14. ! [X0] : ((strong(X0) <~> old(X0)) <=> (old(X0) & brave(X0))) [input p13]
16. ! [X0] : ((~strong(X0) | humble(X0)) <=> (brave(X0) & ~rich(X0))) [input p15]
17. old(mary) | strong(mary) [input p16]
20. funny(mary) | ~quiet(mary) [input p19]
22. quiet(mary) [input hypothesis]
23. ! [X0] : ((tall(X0) <~> ~humble(X0)) | (brave(X0) <=> ~patient(X0))) [ennf transformation 3]
27. ! [X0] : ((strong(X0) | ~funny(X0)) | rich(X0)) [ennf transformation 11]
28. ! [X0] : (strong(X0) | ~funny(X0) | rich(X0)) [flattening 27]
29. ! [X0] : ((quiet(X0) & ~patient(X0)) | (~curious(X0) <=> rich(X0))) [ennf transformation 12]
31. ! [X0] : (((~curious(X0) & funny(X0)) | ~patient(X0)) & (patient(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 1]
32. ! [X0] : (((~curious(X0) & funny(X0)) | ~patient(X0)) & (patient(X0) | curious(X0) | ~funny(X0))) [flattening 31]
33. ! [X0] : ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0))) [nnf transformation 2]
34. ! [X0] : (((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) [nnf transformation 23]
39. ! [X0] : ((((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0))))) [nnf transformation 5]
40. ! [X0] : ((((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0))))) [flattening 39]
48. ! [X0] : ((tall(X0) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | ~tall(X0))) [nnf transformation 10]
49. ! [X0] : ((tall(X0) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | ~tall(X0))) [flattening 48]
50. ! [X0] : ((quiet(X0) & ~patient(X0)) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) [nnf transformation 29]
53. ! [X0] : ((((~old(X0) | ~strong(X0)) & (old(X0) | strong(X0))) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0))))) [nnf transformation 14]
54. ! [X0] : ((((~old(X0) | ~strong(X0)) & (old(X0) | strong(X0))) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0))))) [flattening 53]
55. ! [X0] : (((~strong(X0) | humble(X0)) | (~brave(X0) | rich(X0))) & ((brave(X0) & ~rich(X0)) | (strong(X0) & ~humble(X0)))) [nnf transformation 16]
56. ! [X0] : ((~strong(X0) | humble(X0) | ~brave(X0) | rich(X0)) & ((brave(X0) & ~rich(X0)) | (strong(X0) & ~humble(X0)))) [flattening 55]
65. ~patient(X0) | ~curious(X0) [cnf transformation 32]
66. happy(X0) | patient(X0) [cnf transformation 33]
67. ~happy(X0) | ~patient(X0) [cnf transformation 33]
71. ~tall(X0) | humble(X0) | brave(X0) | patient(X0) [cnf transformation 34]
76. happy(X0) | ~patient(X0) | brave(X0) [cnf transformation 40]
81. patient(X0) | brave(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 40]
104. ~strong(X0) | ~funny(X0) | tall(X0) [cnf transformation 49]
105. ~funny(X0) | strong(X0) | rich(X0) [cnf transformation 28]
106. ~patient(X0) | rich(X0) | curious(X0) [cnf transformation 50]
118. old(X0) | old(X0) | ~strong(X0) [cnf transformation 54]
121. ~old(X0) | ~strong(X0) | ~old(X0) | ~brave(X0) [cnf transformation 54]
124. ~rich(X0) | strong(X0) [cnf transformation 56]
125. ~humble(X0) | brave(X0) [cnf transformation 56]
128. old(mary) | strong(mary) [cnf transformation 17]
132. funny(mary) | ~quiet(mary) [cnf transformation 20]
134. quiet(mary) [cnf transformation 22]
135. ~strong(X0) | old(X0) [duplicate literal removal 118]
136. ~old(X0) | ~strong(X0) | ~brave(X0) [duplicate literal removal 121]
163. ~rich(X0) | brave(X0) | ~happy(X0) [subsumption resolution 81,67]
164. brave(X0) | happy(X0) [subsumption resolution 76,66]
197. ~patient(X0) | rich(X0) [subsumption resolution 106,65]
220. old(mary) [subsumption resolution 128,135]
222. 16 <=> quiet(mary) [avatar definition]
226. 17 <=> funny(mary) [avatar definition]
228. funny(mary) <- (17) [avatar component clause 226]
229. ~16 | 17 [avatar split clause 132,226,222]
239. 16 [avatar split clause 134,222]
249. 20 <=> patient(mary) [avatar definition]
250. ~patient(mary) <- (~20) [avatar component clause 249]
251. patient(mary) <- (20) [avatar component clause 249]
257. rich(mary) <- (20) [resolution 251,197]
270. strong(mary) <- (20) [resolution 257,124]
283. strong(mary) | rich(mary) <- (17) [resolution 105,228]
337. ~strong(mary) | ~brave(mary) [resolution 136,220]
339. ~brave(mary) <- (20) [subsumption resolution 337,270]
347. brave(mary) | ~happy(mary) <- (20) [resolution 163,257]
348. ~happy(mary) <- (20) [subsumption resolution 347,339]
350. happy(mary) <- (20) [resolution 339,164]
351. $false <- (20) [subsumption resolution 350,348]
352. ~20 [avatar contradiction clause 351]
354. 32 <=> brave(mary) [avatar definition]
356. ~brave(mary) <- (~32) [avatar component clause 354]
358. 33 <=> strong(mary) [avatar definition]
359. strong(mary) <- (33) [avatar component clause 358]
361. ~32 | ~33 [avatar split clause 337,358,354]
362. strong(mary) <- (17) [subsumption resolution 283,124]
363. 33 | ~17 [avatar split clause 362,226,358]
365. ~funny(mary) | tall(mary) <- (33) [resolution 359,104]
367. tall(mary) <- (17, 33) [subsumption resolution 365,228]
378. humble(mary) | brave(mary) | patient(mary) <- (17, 33) [resolution 367,71]
382. humble(mary) | patient(mary) <- (17, ~32, 33) [subsumption resolution 378,356]
383. humble(mary) <- (17, ~20, ~32, 33) [subsumption resolution 382,250]
397. brave(mary) <- (17, ~20, ~32, 33) [resolution 383,125]
399. $false <- (17, ~20, ~32, 33) [subsumption resolution 397,356]
400. ~17 | 20 | 32 | ~33 [avatar contradiction clause 399]
401. $false [avatar sat refutation 229,239,352,361,363,400]
% SZS output end Proof for 7182958143888999509974697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise or brave is not tall or happy. If someone is not creative or not rich then someone is either not generous or kind and vice versa. Everyone who is both curious and not old is old and vice versa. Everyone who is not old or brave is either generous or not creative and vice versa. Everyone who is both generous and not brave is either funny or kind and vice versa. Everyone who is either curious or rich is strong. Everyone who is not funny or funny is curious or not humble. Everyone who is kind is both not humble and funny. If someone is both quiet and curious then someone is either happy or brave and vice versa. Everyone who is rich or not strong is strong or not humble. If someone is brave or curious then paul is either not curious or not generous. Everyone who is either humble or not funny is not wise. If alice is not funny then alice is either happy or not quiet. If susan is not generous or patient then someone is both kind and not funny. If someone is either rich or kind then someone is not wise. Everyone who is both not tall and tall is tall and vice versa. Someone is either not calm or not tall. Someone is either creative or not old. Mary is not tall. John is wise. Someone is calm. Someone is not tall. Lucy is both not strong and not brave. Lucy is patient. | Lucy is humble. | contradiction | (![X]:((~wise(X)<~>brave(X))=>(~tall(X)|happy(X))))&
((?[X]:((~creative(X)|~rich(X))))<=>(?[X]:((~generous(X)<~>kind(X)))))&
(![X]:((curious(X)&~old(X))<=>old(X)))&
(![X]:((~old(X)|brave(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((generous(X)&~brave(X))<=>(funny(X)<~>kind(X))))&
(![X]:((curious(X)<~>rich(X))=>strong(X)))&
(![X]:((~funny(X)|funny(X))=>(curious(X)|~humble(X))))&
(![X]:(kind(X)=>(~humble(X)&funny(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((rich(X)|~strong(X))=>(strong(X)|~humble(X))))&
((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((humble(X)<~>~funny(X))=>~wise(X)))&
((~funny(alice))=>((happy(alice)<~>~quiet(alice))))&
(((~generous(susan)|patient(susan)))=>(?[X]:((kind(X)&~funny(X)))))&
((?[X]:((rich(X)<~>kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>tall(X)))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(~tall(mary))&
(wise(john))&
(?[X]:(calm(X)))&
(?[X]:(~tall(X)))&
((~strong(lucy)&~brave(lucy)))&
(patient(lucy)) | humble(lucy) | [
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5941122005983658984466344
% SZS output start Proof for 5941122005983658984466344
3. ! [X0] : ((~old(X0) & curious(X0)) <=> old(X0)) [input p2]
7. ! [X0] : ((funny(X0) | ~funny(X0)) => (~humble(X0) | curious(X0))) [input p6]
25. humble(lucy) [input hypothesis]
32. ! [X0] : ((~humble(X0) | curious(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 7]
33. ! [X0] : (~humble(X0) | curious(X0) | (~funny(X0) & funny(X0))) [flattening 32]
48. ! [X0] : (((~old(X0) & curious(X0)) | ~old(X0)) & (old(X0) | (old(X0) | ~curious(X0)))) [nnf transformation 3]
49. ! [X0] : (((~old(X0) & curious(X0)) | ~old(X0)) & (old(X0) | old(X0) | ~curious(X0))) [flattening 48]
89. old(X0) | old(X0) | ~curious(X0) [cnf transformation 49]
91. ~old(X0) | ~old(X0) [cnf transformation 49]
106. ~humble(X0) | curious(X0) | funny(X0) [cnf transformation 33]
107. ~humble(X0) | curious(X0) | ~funny(X0) [cnf transformation 33]
146. humble(lucy) [cnf transformation 25]
150. old(X0) | ~curious(X0) [duplicate literal removal 89]
151. ~old(X0) [duplicate literal removal 91]
186. ~curious(X0) [subsumption resolution 150,151]
190. ~humble(X0) | ~funny(X0) [subsumption resolution 107,186]
191. ~humble(X0) | funny(X0) [subsumption resolution 106,186]
192. ~humble(X0) [subsumption resolution 191,190]
253. $false [subsumption resolution 146,192]
% SZS output end Proof for 5941122005983658984466344
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not rich is patient or kind. Everyone who is both not wise and patient is not happy or not kind and vice versa. If someone is rich then lucy is not brave or patient. If alice is rich then someone is strong. If someone is either not quiet or not brave then someone is not curious or curious and vice versa. If someone is not rich or quiet then paul is curious or patient. If lucy is both not happy and not creative then someone is funny or humble and vice versa. If susan is old then someone is not kind or not calm and vice versa. Everyone who is both not brave and not generous is both not patient and not generous and vice versa. If someone is both strong and old then fred is either strong or old. If mary is not generous then alice is not funny. If alice is both brave and calm then someone is either creative or funny. Everyone who is rich or happy is either not rich or funny and vice versa. If fred is both rich and not old then john is not quiet and vice versa. If someone is both not creative and not wise then alice is both not happy and not tall and vice versa. Everyone who is either not patient or old is both not tall and not happy and vice versa. Someone is both not humble and not generous. Alice is both not humble and calm. Susan is either not strong or not curious. Mary is not humble. Lucy is both creative and strong. John is funny or not brave. Someone is either not humble or not generous. Someone is either generous or not funny. | Fred is not happy. | contradiction | (![X]:((~generous(X)&~rich(X))=>(patient(X)|kind(X))))&
(![X]:((~wise(X)&patient(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(rich(X)))=>((~brave(lucy)|patient(lucy))))&
((rich(alice))=>(?[X]:(strong(X))))&
((?[X]:((~quiet(X)<~>~brave(X))))<=>(?[X]:((~curious(X)|curious(X)))))&
((?[X]:((~rich(X)|quiet(X))))=>((curious(paul)|patient(paul))))&
(((~happy(lucy)&~creative(lucy)))<=>(?[X]:((funny(X)|humble(X)))))&
((old(susan))<=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:((~brave(X)&~generous(X))<=>(~patient(X)&~generous(X))))&
((?[X]:((strong(X)&old(X))))=>((strong(fred)<~>old(fred))))&
((~generous(mary))=>(~funny(alice)))&
(((brave(alice)&calm(alice)))=>(?[X]:((creative(X)<~>funny(X)))))&
(![X]:((rich(X)|happy(X))<=>(~rich(X)<~>funny(X))))&
(((rich(fred)&~old(fred)))<=>(~quiet(john)))&
((?[X]:((~creative(X)&~wise(X))))<=>((~happy(alice)&~tall(alice))))&
(![X]:((~patient(X)<~>old(X))<=>(~tall(X)&~happy(X))))&
(?[X]:((~humble(X)&~generous(X))))&
((~humble(alice)&calm(alice)))&
((~strong(susan)<~>~curious(susan)))&
(~humble(mary))&
((creative(lucy)&strong(lucy)))&
((funny(john)|~brave(john)))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:((generous(X)<~>~funny(X)))) | ~happy(fred) | [
"p6",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2695429122335162936964015
% SZS output start Proof for 2695429122335162936964015
7. (~creative(lucy) & ~happy(lucy)) <=> ? [X0] : (humble(X0) | funny(X0)) [input p6]
13. ! [X0] : ((happy(X0) | rich(X0)) <=> (~rich(X0) <~> funny(X0))) [input p12]
21. strong(lucy) & creative(lucy) [input p20]
25. ~happy(fred) [input hypothesis]
47. ((~creative(lucy) & ~happy(lucy)) | ! [X0] : (~humble(X0) & ~funny(X0))) & (? [X0] : (humble(X0) | funny(X0)) | (creative(lucy) | happy(lucy))) [nnf transformation 7]
48. ((~creative(lucy) & ~happy(lucy)) | ! [X0] : (~humble(X0) & ~funny(X0))) & (? [X0] : (humble(X0) | funny(X0)) | creative(lucy) | happy(lucy)) [flattening 47]
49. ((~creative(lucy) & ~happy(lucy)) | ! [X0] : (~humble(X0) & ~funny(X0))) & (? [X1] : (humble(X1) | funny(X1)) | creative(lucy) | happy(lucy)) [rectify 48]
50. ? [X1] : (humble(X1) | funny(X1)) => (humble(sK3) | funny(sK3)) [choice axiom]
51. ((~creative(lucy) & ~happy(lucy)) | ! [X0] : (~humble(X0) & ~funny(X0))) & ((humble(sK3) | funny(sK3)) | creative(lucy) | happy(lucy)) [skolemisation 49,50]
62. ! [X0] : (((happy(X0) | rich(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~happy(X0) & ~rich(X0)))) [nnf transformation 13]
63. ! [X0] : ((happy(X0) | rich(X0) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~happy(X0) & ~rich(X0)))) [flattening 62]
101. ~creative(lucy) | ~funny(X0) [cnf transformation 51]
115. funny(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
119. happy(X0) | rich(X0) | funny(X0) | rich(X0) [cnf transformation 63]
141. creative(lucy) [cnf transformation 21]
148. ~happy(fred) [cnf transformation 25]
149. ~rich(X0) | funny(X0) [duplicate literal removal 115]
150. funny(X0) | rich(X0) | happy(X0) [duplicate literal removal 119]
210. 15 <=> creative(lucy) [avatar definition]
215. 16 <=> ! [X0] : ~funny(X0) [avatar definition]
216. ~funny(X0) <- (16) [avatar component clause 215]
217. 16 | ~15 [avatar split clause 101,210,215]
300. 35 <=> rich(fred) [avatar definition]
302. rich(fred) <- (35) [avatar component clause 300]
341. 15 [avatar split clause 141,210]
434. happy(X1) | rich(X1) <- (16) [resolution 150,216]
448. rich(fred) <- (16) [resolution 434,148]
454. 35 | ~16 [avatar split clause 448,215,300]
468. funny(fred) <- (35) [resolution 302,149]
469. $false <- (16, 35) [subsumption resolution 468,216]
470. ~16 | ~35 [avatar contradiction clause 469]
471. $false [avatar sat refutation 217,341,454,470]
% SZS output end Proof for 2695429122335162936964015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not tall or quiet then someone is creative or quiet and vice versa. Everyone who is not happy is both curious and rich and vice versa. If someone is patient then someone is both happy and strong. Everyone who is either not humble or not creative is both generous and wise. If susan is not rich then someone is either not patient or not tall and vice versa. If mary is not tall then fred is either generous or patient and vice versa. Everyone who is either not quiet or not creative is either not funny or happy and vice versa. Everyone who is both brave and not curious is either not humble or creative and vice versa. If paul is not rich then paul is brave or not wise and vice versa. Everyone who is not old or happy is both strong and happy. Everyone who is not brave or curious is both not brave and not wise and vice versa. If susan is either humble or wise then someone is either not kind or old and vice versa. Everyone who is both rich and calm is both funny and rich. If someone is either not rich or not quiet then someone is not funny and vice versa. If susan is both rich and not rich then mary is either not kind or not happy and vice versa. Lucy is not rich or not patient. Someone is both patient and calm. Someone is not rich or not calm. Someone is both quiet and not creative. Someone is quiet or not patient. | Fred is not happy. | contradiction | (((~tall(susan)<~>quiet(susan)))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:(~happy(X)<=>(curious(X)&rich(X))))&
((?[X]:(patient(X)))=>(?[X]:((happy(X)&strong(X)))))&
(![X]:((~humble(X)<~>~creative(X))=>(generous(X)&wise(X))))&
((~rich(susan))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
((~tall(mary))<=>((generous(fred)<~>patient(fred))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(~funny(X)<~>happy(X))))&
(![X]:((brave(X)&~curious(X))<=>(~humble(X)<~>creative(X))))&
((~rich(paul))<=>((brave(paul)|~wise(paul))))&
(![X]:((~old(X)|happy(X))=>(strong(X)&happy(X))))&
(![X]:((~brave(X)|curious(X))<=>(~brave(X)&~wise(X))))&
(((humble(susan)<~>wise(susan)))<=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((rich(X)&calm(X))=>(funny(X)&rich(X))))&
((?[X]:((~rich(X)<~>~quiet(X))))<=>(?[X]:(~funny(X))))&
(((rich(susan)&~rich(susan)))<=>((~kind(mary)<~>~happy(mary))))&
((~rich(lucy)|~patient(lucy)))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:((quiet(X)&~creative(X))))&
(?[X]:((quiet(X)|~patient(X)))) | ~happy(fred) | [
"p1",
"p3",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5602039507671659511340283
% SZS output start Proof for 5602039507671659511340283
2. ! [X0] : (~happy(X0) <=> (rich(X0) & curious(X0))) [input p1]
4. ! [X0] : ((~humble(X0) <~> ~creative(X0)) => (wise(X0) & generous(X0))) [input p3]
8. ! [X0] : ((~curious(X0) & brave(X0)) <=> (~humble(X0) <~> creative(X0))) [input p7]
11. ! [X0] : ((curious(X0) | ~brave(X0)) <=> (~wise(X0) & ~brave(X0))) [input p10]
21. ~happy(fred) [input hypothesis]
27. ! [X0] : ((wise(X0) & generous(X0)) | (~humble(X0) <=> ~creative(X0))) [ennf transformation 4]
35. ! [X0] : ((~happy(X0) | (~rich(X0) | ~curious(X0))) & ((rich(X0) & curious(X0)) | happy(X0))) [nnf transformation 2]
36. ! [X0] : ((~happy(X0) | ~rich(X0) | ~curious(X0)) & ((rich(X0) & curious(X0)) | happy(X0))) [flattening 35]
40. ! [X0] : ((wise(X0) & generous(X0)) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0)))) [nnf transformation 27]
47. ! [X0] : (((~curious(X0) & brave(X0)) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0)))) & (((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | (curious(X0) | ~brave(X0)))) [nnf transformation 8]
48. ! [X0] : (((~curious(X0) & brave(X0)) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0)))) & (((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | curious(X0) | ~brave(X0))) [flattening 47]
51. ! [X0] : (((curious(X0) | ~brave(X0)) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | (~curious(X0) & brave(X0)))) [nnf transformation 11]
52. ! [X0] : ((curious(X0) | ~brave(X0) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | (~curious(X0) & brave(X0)))) [flattening 51]
78. curious(X0) | happy(X0) [cnf transformation 36]
84. ~creative(X0) | wise(X0) | humble(X0) [cnf transformation 40]
85. ~humble(X0) | wise(X0) | creative(X0) [cnf transformation 40]
106. ~curious(X0) | creative(X0) | humble(X0) [cnf transformation 48]
107. ~humble(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 48]
116. ~wise(X0) | ~curious(X0) [cnf transformation 52]
145. ~happy(fred) [cnf transformation 21]
399. humble(X0) | creative(X0) | happy(X0) [resolution 106,78]
576. creative(X2) | happy(X2) | wise(X2) | creative(X2) [resolution 399,85]
581. wise(X2) | happy(X2) | creative(X2) [duplicate literal removal 576]
616. happy(X0) | creative(X0) | ~curious(X0) [resolution 581,116]
619. happy(X0) | creative(X0) [subsumption resolution 616,78]
634. 76 <=> humble(fred) [avatar definition]
636. humble(fred) <- (76) [avatar component clause 634]
638. 77 <=> wise(fred) [avatar definition]
640. wise(fred) <- (77) [avatar component clause 638]
649. creative(fred) [resolution 619,145]
680. wise(fred) | humble(fred) [resolution 649,84]
684. 76 | 77 [avatar split clause 680,638,634]
685. ~curious(fred) <- (77) [resolution 640,116]
712. happy(fred) <- (77) [resolution 685,78]
713. $false <- (77) [subsumption resolution 712,145]
714. ~77 [avatar contradiction clause 713]
715. ~curious(fred) | ~creative(fred) <- (76) [resolution 636,107]
719. ~curious(fred) <- (76) [subsumption resolution 715,649]
757. happy(fred) <- (76) [resolution 719,78]
758. $false <- (76) [subsumption resolution 757,145]
759. ~76 [avatar contradiction clause 758]
760. $false [avatar sat refutation 684,714,759]
% SZS output end Proof for 5602039507671659511340283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or kind then john is not generous. Everyone who is either curious or not brave is both quiet and tall. If fred is either not wise or not creative then mary is rich or creative and vice versa. If susan is either not old or old then someone is both not kind and not wise and vice versa. Everyone who is happy is not brave or happy and vice versa. Everyone who is rich is curious and vice versa. If susan is humble or not rich then lucy is both not creative and patient. Everyone who is not strong or kind is not rich and vice versa. If susan is not calm or humble then someone is both not tall and not creative. Everyone who is not strong or rich is tall or happy. If someone is not wise then someone is brave or creative. Everyone who is strong is either calm or wise and vice versa. Everyone who is creative is not funny. Everyone who is both curious and not humble is both calm and curious and vice versa. Everyone who is either not patient or not wise is either old or not calm and vice versa. Everyone who is humble is either quiet or old. Susan is both not calm and not old. Someone is not curious or tall. Paul is happy or old. John is both not rich and not old. Alice is both not brave and happy. Paul is both calm and not wise. Paul is both humble and not creative. | John is tall. | neutral | ((?[X]:((~brave(X)<~>kind(X))))=>(~generous(john)))&
(![X]:((curious(X)<~>~brave(X))=>(quiet(X)&tall(X))))&
(((~wise(fred)<~>~creative(fred)))<=>((rich(mary)|creative(mary))))&
(((~old(susan)<~>old(susan)))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:(happy(X)<=>(~brave(X)|happy(X))))&
(![X]:(rich(X)<=>curious(X)))&
(((humble(susan)|~rich(susan)))=>((~creative(lucy)&patient(lucy))))&
(![X]:((~strong(X)|kind(X))<=>~rich(X)))&
(((~calm(susan)|humble(susan)))=>(?[X]:((~tall(X)&~creative(X)))))&
(![X]:((~strong(X)|rich(X))=>(tall(X)|happy(X))))&
((?[X]:(~wise(X)))=>(?[X]:((brave(X)|creative(X)))))&
(![X]:(strong(X)<=>(calm(X)<~>wise(X))))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:((curious(X)&~humble(X))<=>(calm(X)&curious(X))))&
(![X]:((~patient(X)<~>~wise(X))<=>(old(X)<~>~calm(X))))&
(![X]:(humble(X)=>(quiet(X)<~>old(X))))&
((~calm(susan)&~old(susan)))&
(?[X]:((~curious(X)|tall(X))))&
((happy(paul)|old(paul)))&
((~rich(john)&~old(john)))&
((~brave(alice)&happy(alice)))&
((calm(paul)&~wise(paul)))&
((humble(paul)&~creative(paul))) | tall(john) | [] | null | 0 |
Everyone who is both not rich and not brave is both humble and not old. Everyone who is calm is either not generous or kind. Everyone who is either kind or not curious is both not generous and kind. Everyone who is either happy or not generous is not humble or not wise. Everyone who is not brave or not rich is not funny and vice versa. If someone is not curious then someone is both funny and calm and vice versa. Everyone who is either not funny or not strong is not rich. Everyone who is both not generous and humble is not patient and vice versa. If fred is humble or not funny then someone is creative. If mary is brave or tall then someone is both not curious and not old and vice versa. If john is either tall or not wise then alice is not old and vice versa. If someone is both not curious and patient then fred is funny. If someone is rich then alice is kind or strong. Everyone who is strong or not old is either rich or brave and vice versa. If lucy is both humble and calm then lucy is patient or old. If alice is both funny and happy then lucy is both humble and brave. Lucy is either patient or not happy. Someone is not quiet or not brave. Paul is not happy or not curious. Paul is generous. Alice is not happy. Paul is not tall. | Lucy is happy. | neutral | (![X]:((~rich(X)&~brave(X))=>(humble(X)&~old(X))))&
(![X]:(calm(X)=>(~generous(X)<~>kind(X))))&
(![X]:((kind(X)<~>~curious(X))=>(~generous(X)&kind(X))))&
(![X]:((happy(X)<~>~generous(X))=>(~humble(X)|~wise(X))))&
(![X]:((~brave(X)|~rich(X))<=>~funny(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((funny(X)&calm(X)))))&
(![X]:((~funny(X)<~>~strong(X))=>~rich(X)))&
(![X]:((~generous(X)&humble(X))<=>~patient(X)))&
(((humble(fred)|~funny(fred)))=>(?[X]:(creative(X))))&
(((brave(mary)|tall(mary)))<=>(?[X]:((~curious(X)&~old(X)))))&
(((tall(john)<~>~wise(john)))<=>(~old(alice)))&
((?[X]:((~curious(X)&patient(X))))=>(funny(fred)))&
((?[X]:(rich(X)))=>((kind(alice)|strong(alice))))&
(![X]:((strong(X)|~old(X))<=>(rich(X)<~>brave(X))))&
(((humble(lucy)&calm(lucy)))=>((patient(lucy)|old(lucy))))&
(((funny(alice)&happy(alice)))=>((humble(lucy)&brave(lucy))))&
((patient(lucy)<~>~happy(lucy)))&
(?[X]:((~quiet(X)|~brave(X))))&
((~happy(paul)|~curious(paul)))&
(generous(paul))&
(~happy(alice))&
(~tall(paul)) | happy(lucy) | [] | null | 0 |
Everyone who is either happy or not funny is both humble and not tall and vice versa.
Everyone who is creative or not generous is both not strong and wise.
Everyone who is rich or not strong is humble.
If john is either not rich or not curious then john is old and vice versa.
If fred is both not wise and not strong then someone is patient.
Everyone who is not curious is tall and vice versa.
If mary is not kind or old then someone is both not rich and not happy.
If alice is not funny then susan is both kind and not old and vice versa.
If alice is not quiet or quiet then someone is strong or not happy and vice versa.
If someone is either not old or humble then paul is not strong.
Everyone who is brave or not generous is either brave or not creative and vice versa.
Everyone who is both not brave and not kind is not kind or not old.
Everyone who is not old is both humble and not old.
If paul is both not strong and not calm then someone is both rich and calm.
John is curious or not quiet.
Someone is not kind or humble.
Paul is humble.
Someone is either not funny or creative.
Mary is either not tall or not quiet.
Susan is either not curious or old. | Fred is kind. | neutral | (![X]:((happy(X)<~>~funny(X))<=>(humble(X)&~tall(X))))&
(![X]:((creative(X)|~generous(X))=>(~strong(X)&wise(X))))&
(![X]:((rich(X)|~strong(X))=>humble(X)))&
(((~rich(john)<~>~curious(john)))<=>(old(john)))&
(((~wise(fred)&~strong(fred)))=>(?[X]:(patient(X))))&
(![X]:(~curious(X)<=>tall(X)))&
(((~kind(mary)|old(mary)))=>(?[X]:((~rich(X)&~happy(X)))))&
((~funny(alice))<=>((kind(susan)&~old(susan))))&
(((~quiet(alice)|quiet(alice)))<=>(?[X]:((strong(X)|~happy(X)))))&
((?[X]:((~old(X)<~>humble(X))))=>(~strong(paul)))&
(![X]:((brave(X)|~generous(X))<=>(brave(X)<~>~creative(X))))&
(![X]:((~brave(X)&~kind(X))=>(~kind(X)|~old(X))))&
(![X]:(~old(X)=>(humble(X)&~old(X))))&
(((~strong(paul)&~calm(paul)))=>(?[X]:((rich(X)&calm(X)))))&
((curious(john)|~quiet(john)))&
(?[X]:((~kind(X)|humble(X))))&
(humble(paul))&
(?[X]:((~funny(X)<~>creative(X))))&
((~tall(mary)<~>~quiet(mary)))&
((~curious(susan)<~>old(susan))) | kind(fred) | [] | null | 0 |
Everyone who is either rich or tall is either not creative or creative and vice versa.
Everyone who is not kind or not humble is rich.
Everyone who is happy is both quiet and not calm and vice versa.
If someone is kind then john is both creative and not patient and vice versa.
Everyone who is not old is brave or not tall.
If john is generous then paul is not tall or not kind.
If someone is both wise and not curious then susan is not funny or funny and vice versa.
If mary is not wise or not patient then someone is funny.
Everyone who is not wise or not old is both not old and not happy and vice versa.
If someone is both not kind and old then someone is either curious or humble and vice versa.
Everyone who is not calm or not funny is both humble and old and vice versa.
Everyone who is not kind or not quiet is either not quiet or rich.
Everyone who is not creative or calm is both not rich and not humble.
If fred is generous then alice is not happy.
Everyone who is either brave or patient is both brave and rich.
Someone is either not calm or happy.
Someone is either not funny or not humble.
Someone is both generous and not patient.
Someone is quiet or generous.
Fred is not kind or patient.
Mary is humble. | Alice is not funny. | neutral | (![X]:((rich(X)<~>tall(X))<=>(~creative(X)<~>creative(X))))&
(![X]:((~kind(X)|~humble(X))=>rich(X)))&
(![X]:(happy(X)<=>(quiet(X)&~calm(X))))&
((?[X]:(kind(X)))<=>((creative(john)&~patient(john))))&
(![X]:(~old(X)=>(brave(X)|~tall(X))))&
((generous(john))=>((~tall(paul)|~kind(paul))))&
((?[X]:((wise(X)&~curious(X))))<=>((~funny(susan)|funny(susan))))&
(((~wise(mary)|~patient(mary)))=>(?[X]:(funny(X))))&
(![X]:((~wise(X)|~old(X))<=>(~old(X)&~happy(X))))&
((?[X]:((~kind(X)&old(X))))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((~calm(X)|~funny(X))<=>(humble(X)&old(X))))&
(![X]:((~kind(X)|~quiet(X))=>(~quiet(X)<~>rich(X))))&
(![X]:((~creative(X)|calm(X))=>(~rich(X)&~humble(X))))&
((generous(fred))=>(~happy(alice)))&
(![X]:((brave(X)<~>patient(X))=>(brave(X)&rich(X))))&
(?[X]:((~calm(X)<~>happy(X))))&
(?[X]:((~funny(X)<~>~humble(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((quiet(X)|generous(X))))&
((~kind(fred)|patient(fred)))&
(humble(mary)) | ~funny(alice) | [] | null | 0 |
Everyone who is both rich and funny is either not rich or patient and vice versa.
Everyone who is either humble or not kind is calm or not generous.
Everyone who is not old is both not wise and not rich and vice versa.
Everyone who is not funny or not curious is not generous or not brave.
If someone is not tall then paul is not calm or not patient and vice versa.
Everyone who is both not wise and not kind is either not happy or not brave and vice versa.
Everyone who is not happy is humble or not creative.
If someone is either happy or not old then someone is not rich and vice versa.
Everyone who is both not brave and kind is either not funny or not kind.
If someone is both quiet and happy then someone is both calm and not strong.
If someone is tall or strong then someone is calm and vice versa.
Everyone who is not humble is both not tall and not brave and vice versa.
If paul is both not kind and not quiet then someone is either not strong or not calm and vice versa.
Everyone who is both not happy and not curious is kind and vice versa.
Everyone who is generous or not rich is either not generous or not kind.
Everyone who is calm is both generous and humble and vice versa.
Fred is both not patient and creative.
Susan is not wise or kind.
Someone is not funny.
Someone is either wise or not strong.
Susan is either not funny or humble.
Someone is either not rich or not creative.
Someone is either not kind or wise.
Someone is not happy. | Fred is humble. | neutral | (![X]:((rich(X)&funny(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((humble(X)<~>~kind(X))=>(calm(X)|~generous(X))))&
(![X]:(~old(X)<=>(~wise(X)&~rich(X))))&
(![X]:((~funny(X)|~curious(X))=>(~generous(X)|~brave(X))))&
((?[X]:(~tall(X)))<=>((~calm(paul)|~patient(paul))))&
(![X]:((~wise(X)&~kind(X))<=>(~happy(X)<~>~brave(X))))&
(![X]:(~happy(X)=>(humble(X)|~creative(X))))&
((?[X]:((happy(X)<~>~old(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)&kind(X))=>(~funny(X)<~>~kind(X))))&
((?[X]:((quiet(X)&happy(X))))=>(?[X]:((calm(X)&~strong(X)))))&
((?[X]:((tall(X)|strong(X))))<=>(?[X]:(calm(X))))&
(![X]:(~humble(X)<=>(~tall(X)&~brave(X))))&
(((~kind(paul)&~quiet(paul)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((~happy(X)&~curious(X))<=>kind(X)))&
(![X]:((generous(X)|~rich(X))=>(~generous(X)<~>~kind(X))))&
(![X]:(calm(X)<=>(generous(X)&humble(X))))&
((~patient(fred)&creative(fred)))&
((~wise(susan)|kind(susan)))&
(?[X]:(~funny(X)))&
(?[X]:((wise(X)<~>~strong(X))))&
((~funny(susan)<~>humble(susan)))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:((~kind(X)<~>wise(X))))&
(?[X]:(~happy(X))) | humble(fred) | [] | null | 0 |
If someone is either not old or tall then someone is old or calm and vice versa. Everyone who is either not tall or happy is both happy and not patient and vice versa. Everyone who is not generous is not happy. Everyone who is either creative or not calm is both not happy and happy. Everyone who is both quiet and calm is funny or not calm and vice versa. If someone is wise then someone is either creative or kind. If someone is not humble then someone is happy or funny. If mary is both kind and quiet then someone is either not patient or strong. Everyone who is both quiet and strong is either not creative or not happy. Everyone who is generous is not generous or patient and vice versa. Everyone who is strong is not generous. If someone is either humble or calm then paul is both not curious and old and vice versa. Everyone who is not strong or calm is not curious or not generous. Everyone who is not rich is both not curious and strong and vice versa. If paul is either old or not calm then someone is either not patient or strong. If lucy is both curious and not calm then fred is wise or not wise. Fred is funny or quiet. Someone is either not kind or creative. Someone is either kind or not wise. Mary is both not kind and humble. Fred is not quiet or not old. Lucy is either not wise or old. | Paul is not wise. | neutral | ((?[X]:((~old(X)<~>tall(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~tall(X)<~>happy(X))<=>(happy(X)&~patient(X))))&
(![X]:(~generous(X)=>~happy(X)))&
(![X]:((creative(X)<~>~calm(X))=>(~happy(X)&happy(X))))&
(![X]:((quiet(X)&calm(X))<=>(funny(X)|~calm(X))))&
((?[X]:(wise(X)))=>(?[X]:((creative(X)<~>kind(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((happy(X)|funny(X)))))&
(((kind(mary)&quiet(mary)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((quiet(X)&strong(X))=>(~creative(X)<~>~happy(X))))&
(![X]:(generous(X)<=>(~generous(X)|patient(X))))&
(![X]:(strong(X)=>~generous(X)))&
((?[X]:((humble(X)<~>calm(X))))<=>((~curious(paul)&old(paul))))&
(![X]:((~strong(X)|calm(X))=>(~curious(X)|~generous(X))))&
(![X]:(~rich(X)<=>(~curious(X)&strong(X))))&
(((old(paul)<~>~calm(paul)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(((curious(lucy)&~calm(lucy)))=>((wise(fred)|~wise(fred))))&
((funny(fred)|quiet(fred)))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
((~kind(mary)&humble(mary)))&
((~quiet(fred)|~old(fred)))&
((~wise(lucy)<~>old(lucy))) | ~wise(paul) | [] | null | 0 |
If lucy is both strong and not generous then someone is both not generous and kind and vice versa.
Everyone who is funny or not tall is either rich or not creative.
Everyone who is not humble or not rich is either old or wise and vice versa.
Everyone who is either generous or happy is both old and curious and vice versa.
If mary is either old or funny then alice is not generous or old and vice versa.
If mary is strong or generous then someone is creative or not curious and vice versa.
If someone is both tall and not strong then someone is not kind or curious and vice versa.
Everyone who is calm is both not patient and kind.
If someone is generous then paul is either not quiet or curious.
If alice is not quiet or happy then alice is both strong and patient.
Everyone who is not humble or not happy is both not funny and not brave and vice versa.
If someone is not strong or curious then someone is either not strong or funny and vice versa.
Everyone who is strong or not tall is not humble or not quiet and vice versa.
Everyone who is not creative is both tall and brave.
Everyone who is curious is not creative and vice versa.
If someone is both strong and not brave then someone is either not generous or not old.
Someone is happy.
Susan is either patient or not calm.
Lucy is creative.
Mary is either humble or happy.
Alice is not calm.
Someone is not happy or tall.
Lucy is generous or old.
John is brave. | John is creative. | neutral | (((strong(lucy)&~generous(lucy)))<=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:((funny(X)|~tall(X))=>(rich(X)<~>~creative(X))))&
(![X]:((~humble(X)|~rich(X))<=>(old(X)<~>wise(X))))&
(![X]:((generous(X)<~>happy(X))<=>(old(X)&curious(X))))&
(((old(mary)<~>funny(mary)))<=>((~generous(alice)|old(alice))))&
(((strong(mary)|generous(mary)))<=>(?[X]:((creative(X)|~curious(X)))))&
((?[X]:((tall(X)&~strong(X))))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:(calm(X)=>(~patient(X)&kind(X))))&
((?[X]:(generous(X)))=>((~quiet(paul)<~>curious(paul))))&
(((~quiet(alice)|happy(alice)))=>((strong(alice)&patient(alice))))&
(![X]:((~humble(X)|~happy(X))<=>(~funny(X)&~brave(X))))&
((?[X]:((~strong(X)|curious(X))))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((strong(X)|~tall(X))<=>(~humble(X)|~quiet(X))))&
(![X]:(~creative(X)=>(tall(X)&brave(X))))&
(![X]:(curious(X)<=>~creative(X)))&
((?[X]:((strong(X)&~brave(X))))=>(?[X]:((~generous(X)<~>~old(X)))))&
(?[X]:(happy(X)))&
((patient(susan)<~>~calm(susan)))&
(creative(lucy))&
((humble(mary)<~>happy(mary)))&
(~calm(alice))&
(?[X]:((~happy(X)|tall(X))))&
((generous(lucy)|old(lucy)))&
(brave(john)) | creative(john) | [] | null | 0 |
If mary is not kind or calm then someone is not funny.
Everyone who is either wise or not quiet is quiet or not humble and vice versa.
Everyone who is both not quiet and not tall is both not patient and curious.
If fred is strong then susan is not quiet.
If someone is both not rich and humble then someone is either kind or not brave and vice versa.
Everyone who is either not rich or not quiet is tall or not kind and vice versa.
Everyone who is either not kind or kind is calm.
If fred is either funny or not strong then lucy is not strong.
Everyone who is either not brave or quiet is not generous or not strong and vice versa.
If susan is not brave then john is both rich and not funny and vice versa.
Everyone who is either not tall or happy is either not funny or creative.
Everyone who is both not funny and not kind is funny and vice versa.
If fred is either quiet or old then someone is generous and vice versa.
If someone is either happy or not funny then someone is both happy and wise.
If paul is both not old and old then alice is either not kind or tall and vice versa.
If someone is both not brave and tall then paul is either wise or calm and vice versa.
Someone is either not generous or not curious.
Someone is both humble and not happy.
Susan is either not rich or not humble.
Someone is both patient and creative.
Someone is either not quiet or generous.
Someone is either kind or not calm.
Mary is both curious and not strong. | Fred is not generous. | neutral | (((~kind(mary)|calm(mary)))=>(?[X]:(~funny(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(quiet(X)|~humble(X))))&
(![X]:((~quiet(X)&~tall(X))=>(~patient(X)&curious(X))))&
((strong(fred))=>(~quiet(susan)))&
((?[X]:((~rich(X)&humble(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(tall(X)|~kind(X))))&
(![X]:((~kind(X)<~>kind(X))=>calm(X)))&
(((funny(fred)<~>~strong(fred)))=>(~strong(lucy)))&
(![X]:((~brave(X)<~>quiet(X))<=>(~generous(X)|~strong(X))))&
((~brave(susan))<=>((rich(john)&~funny(john))))&
(![X]:((~tall(X)<~>happy(X))=>(~funny(X)<~>creative(X))))&
(![X]:((~funny(X)&~kind(X))<=>funny(X)))&
(((quiet(fred)<~>old(fred)))<=>(?[X]:(generous(X))))&
((?[X]:((happy(X)<~>~funny(X))))=>(?[X]:((happy(X)&wise(X)))))&
(((~old(paul)&old(paul)))<=>((~kind(alice)<~>tall(alice))))&
((?[X]:((~brave(X)&tall(X))))<=>((wise(paul)<~>calm(paul))))&
(?[X]:((~generous(X)<~>~curious(X))))&
(?[X]:((humble(X)&~happy(X))))&
((~rich(susan)<~>~humble(susan)))&
(?[X]:((patient(X)&creative(X))))&
(?[X]:((~quiet(X)<~>generous(X))))&
(?[X]:((kind(X)<~>~calm(X))))&
((curious(mary)&~strong(mary))) | ~generous(fred) | [] | null | 0 |
Everyone who is wise is either creative or not funny.
Everyone who is wise is either not calm or not strong and vice versa.
If someone is both funny and not rich then someone is not wise.
Everyone who is not quiet is either calm or funny and vice versa.
If mary is either happy or quiet then someone is not quiet or calm and vice versa.
Everyone who is both happy and not old is both not funny and humble.
Everyone who is not calm is curious or not patient and vice versa.
Everyone who is kind or not quiet is not quiet or not kind.
If someone is not calm or not creative then someone is not old or happy and vice versa.
If fred is not kind or funny then susan is both not brave and tall.
Everyone who is not tall or not generous is both not happy and curious.
Everyone who is either not humble or not generous is not patient or not kind and vice versa.
Everyone who is both patient and kind is not tall or not kind and vice versa.
If susan is either patient or calm then someone is both not kind and not patient.
Everyone who is not wise or generous is not calm or not rich and vice versa.
If susan is both patient and not rich then john is not creative.
Someone is not humble or funny.
Someone is strong.
Alice is humble.
Someone is curious.
Mary is not creative or funny.
Lucy is creative or old. | Fred is calm. | contradiction | (![X]:(wise(X)=>(creative(X)<~>~funny(X))))&
(![X]:(wise(X)<=>(~calm(X)<~>~strong(X))))&
((?[X]:((funny(X)&~rich(X))))=>(?[X]:(~wise(X))))&
(![X]:(~quiet(X)<=>(calm(X)<~>funny(X))))&
(((happy(mary)<~>quiet(mary)))<=>(?[X]:((~quiet(X)|calm(X)))))&
(![X]:((happy(X)&~old(X))=>(~funny(X)&humble(X))))&
(![X]:(~calm(X)<=>(curious(X)|~patient(X))))&
(![X]:((kind(X)|~quiet(X))=>(~quiet(X)|~kind(X))))&
((?[X]:((~calm(X)|~creative(X))))<=>(?[X]:((~old(X)|happy(X)))))&
(((~kind(fred)|funny(fred)))=>((~brave(susan)&tall(susan))))&
(![X]:((~tall(X)|~generous(X))=>(~happy(X)&curious(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~patient(X)|~kind(X))))&
(![X]:((patient(X)&kind(X))<=>(~tall(X)|~kind(X))))&
(((patient(susan)<~>calm(susan)))=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~calm(X)|~rich(X))))&
(((patient(susan)&~rich(susan)))=>(~creative(john)))&
(?[X]:((~humble(X)|funny(X))))&
(?[X]:(strong(X)))&
(humble(alice))&
(?[X]:(curious(X)))&
((~creative(mary)|funny(mary)))&
((creative(lucy)|old(lucy))) | calm(fred) | [
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4383897509216867891894093
% SZS output start Proof for 4383897509216867891894093
7. ! [X0] : (~calm(X0) <=> (~patient(X0) | curious(X0))) [input p6]
11. ! [X0] : ((~generous(X0) | ~tall(X0)) => (curious(X0) & ~happy(X0))) [input p10]
13. ! [X0] : ((kind(X0) & patient(X0)) <=> (~kind(X0) | ~tall(X0))) [input p12]
23. calm(fred) [input hypothesis]
34. ! [X0] : ((curious(X0) & ~happy(X0)) | (generous(X0) & tall(X0))) [ennf transformation 11]
48. ! [X0] : ((~calm(X0) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | calm(X0))) [nnf transformation 7]
49. ! [X0] : ((~calm(X0) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | calm(X0))) [flattening 48]
57. ! [X0] : (((kind(X0) & patient(X0)) | (kind(X0) & tall(X0))) & ((~kind(X0) | ~tall(X0)) | (~kind(X0) | ~patient(X0)))) [nnf transformation 13]
58. ! [X0] : (((kind(X0) & patient(X0)) | (kind(X0) & tall(X0))) & (~kind(X0) | ~tall(X0) | ~kind(X0) | ~patient(X0))) [flattening 57]
90. ~curious(X0) | ~calm(X0) [cnf transformation 49]
91. ~calm(X0) | patient(X0) [cnf transformation 49]
102. tall(X0) | curious(X0) [cnf transformation 34]
110. ~kind(X0) | ~tall(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 58]
114. kind(X0) | kind(X0) [cnf transformation 58]
130. calm(fred) [cnf transformation 23]
131. ~kind(X0) | ~tall(X0) | ~patient(X0) [duplicate literal removal 110]
132. kind(X0) [duplicate literal removal 114]
216. ~tall(X0) | ~patient(X0) [subsumption resolution 131,132]
269. patient(fred) [resolution 91,130]
276. ~patient(X1) | curious(X1) [resolution 216,102]
277. curious(fred) [resolution 276,269]
298. ~calm(fred) [resolution 277,90]
299. $false [subsumption resolution 298,130]
% SZS output end Proof for 4383897509216867891894093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not wise and not patient then alice is either brave or happy and vice versa.
If mary is not humble then someone is both not wise and tall.
Everyone who is not generous or strong is either brave or rich.
Everyone who is happy or not funny is both happy and rich.
Everyone who is happy or curious is not patient and vice versa.
If mary is either strong or creative then mary is not tall or wise.
Everyone who is rich is generous.
If mary is both not patient and not brave then someone is both not quiet and not strong and vice versa.
Everyone who is creative or not quiet is either not wise or not happy.
If someone is not rich or humble then someone is not calm.
Everyone who is creative is not patient.
Everyone who is wise is old.
Everyone who is both not kind and wise is rich and vice versa.
Everyone who is not funny or not tall is either not calm or strong and vice versa.
If paul is either not wise or not funny then someone is not brave or wise and vice versa.
If someone is not tall or curious then lucy is not tall or not strong.
Mary is rich.
John is both not rich and old.
Someone is either not calm or brave.
Susan is kind or not kind.
Someone is either not strong or funny.
Someone is both not tall and patient.
Mary is both wise and not calm.
Paul is not wise or patient. | Paul is not rich. | entailment | (((~wise(alice)&~patient(alice)))<=>((brave(alice)<~>happy(alice))))&
((~humble(mary))=>(?[X]:((~wise(X)&tall(X)))))&
(![X]:((~generous(X)|strong(X))=>(brave(X)<~>rich(X))))&
(![X]:((happy(X)|~funny(X))=>(happy(X)&rich(X))))&
(![X]:((happy(X)|curious(X))<=>~patient(X)))&
(((strong(mary)<~>creative(mary)))=>((~tall(mary)|wise(mary))))&
(![X]:(rich(X)=>generous(X)))&
(((~patient(mary)&~brave(mary)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((creative(X)|~quiet(X))=>(~wise(X)<~>~happy(X))))&
((?[X]:((~rich(X)|humble(X))))=>(?[X]:(~calm(X))))&
(![X]:(creative(X)=>~patient(X)))&
(![X]:(wise(X)=>old(X)))&
(![X]:((~kind(X)&wise(X))<=>rich(X)))&
(![X]:((~funny(X)|~tall(X))<=>(~calm(X)<~>strong(X))))&
(((~wise(paul)<~>~funny(paul)))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((~tall(X)|curious(X))))=>((~tall(lucy)|~strong(lucy))))&
(rich(mary))&
((~rich(john)&old(john)))&
(?[X]:((~calm(X)<~>brave(X))))&
((kind(susan)|~kind(susan)))&
(?[X]:((~strong(X)<~>funny(X))))&
(?[X]:((~tall(X)&patient(X))))&
((wise(mary)&~calm(mary)))&
((~wise(paul)|patient(paul))) | ~rich(paul) | [
"p3",
"p4",
"p12",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6149548407513567231116977
% SZS output start Proof for 6149548407513567231116977
4. ! [X0] : ((~funny(X0) | happy(X0)) => (rich(X0) & happy(X0))) [input p3]
5. ! [X0] : ((curious(X0) | happy(X0)) <=> ~patient(X0)) [input p4]
13. ! [X0] : ((wise(X0) & ~kind(X0)) <=> rich(X0)) [input p12]
15. (~wise(paul) <~> ~funny(paul)) <=> ? [X0] : (wise(X0) | ~brave(X0)) [input p14]
24. patient(paul) | ~wise(paul) [input p23]
25. rich(paul) [input hypothesis]
33. ! [X0] : ((rich(X0) & happy(X0)) | (funny(X0) & ~happy(X0))) [ennf transformation 4]
46. ! [X0] : (((curious(X0) | happy(X0)) | patient(X0)) & (~patient(X0) | (~curious(X0) & ~happy(X0)))) [nnf transformation 5]
47. ! [X0] : ((curious(X0) | happy(X0) | patient(X0)) & (~patient(X0) | (~curious(X0) & ~happy(X0)))) [flattening 46]
58. ! [X0] : (((wise(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 13]
59. ! [X0] : (((wise(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | ~wise(X0) | kind(X0))) [flattening 58]
62. (((funny(paul) | wise(paul)) & (~funny(paul) | ~wise(paul))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X0] : (wise(X0) | ~brave(X0)) | ((~wise(paul) | funny(paul)) & (~funny(paul) | wise(paul)))) [nnf transformation 15]
63. (((funny(paul) | wise(paul)) & (~funny(paul) | ~wise(paul))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X1] : (wise(X1) | ~brave(X1)) | ((~wise(paul) | funny(paul)) & (~funny(paul) | wise(paul)))) [rectify 62]
64. ? [X1] : (wise(X1) | ~brave(X1)) => (wise(sK3) | ~brave(sK3)) [choice axiom]
65. (((funny(paul) | wise(paul)) & (~funny(paul) | ~wise(paul))) | ! [X0] : (~wise(X0) & brave(X0))) & ((wise(sK3) | ~brave(sK3)) | ((~wise(paul) | funny(paul)) & (~funny(paul) | wise(paul)))) [skolemisation 63,64]
85. funny(X0) | happy(X0) [cnf transformation 33]
88. ~happy(X0) | ~patient(X0) [cnf transformation 47]
106. ~rich(X0) | wise(X0) [cnf transformation 59]
116. ~funny(paul) | ~wise(paul) | ~wise(X0) [cnf transformation 65]
132. patient(paul) | ~wise(paul) [cnf transformation 24]
133. rich(paul) [cnf transformation 25]
224. 20 <=> ! [X0] : ~wise(X0) [avatar definition]
225. ~wise(X0) <- (20) [avatar component clause 224]
227. 21 <=> wise(paul) [avatar definition]
229. wise(paul) <- (21) [avatar component clause 227]
231. 22 <=> funny(paul) [avatar definition]
232. ~funny(paul) <- (~22) [avatar component clause 231]
239. 20 | ~21 | ~22 [avatar split clause 116,231,227,224]
289. 34 <=> patient(paul) [avatar definition]
291. patient(paul) <- (34) [avatar component clause 289]
292. ~21 | 34 [avatar split clause 132,289,227]
298. wise(paul) [resolution 106,133]
302. 21 [avatar split clause 298,227]
304. happy(paul) <- (~22) [resolution 232,85]
305. ~patient(paul) <- (~22) [resolution 304,88]
307. $false <- (~22, 34) [subsumption resolution 305,291]
308. 22 | ~34 [avatar contradiction clause 307]
310. $false <- (20, 21) [resolution 225,229]
311. ~20 | ~21 [avatar contradiction clause 310]
313. $false [avatar sat refutation 239,292,302,308,311]
% SZS output end Proof for 6149548407513567231116977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not curious is either strong or not strong and vice versa.
Everyone who is both kind and not calm is both quiet and not curious and vice versa.
Everyone who is both not kind and calm is both not curious and not strong.
Everyone who is both humble and generous is not tall or not generous.
Everyone who is not curious or brave is either not wise or patient.
Everyone who is either creative or kind is not generous and vice versa.
Everyone who is not tall is either not quiet or calm.
If susan is both brave and not quiet then susan is either not calm or not funny and vice versa.
If alice is not brave then someone is old or humble and vice versa.
Everyone who is both brave and generous is both old and patient.
If someone is either not humble or generous then mary is both strong and not calm and vice versa.
Everyone who is either strong or patient is either wise or creative and vice versa.
Everyone who is either not patient or brave is not tall and vice versa.
If mary is both not kind and old then someone is both humble and not humble and vice versa.
Everyone who is either quiet or tall is both wise and strong.
Everyone who is not generous is curious and vice versa.
Susan is either not patient or not humble.
Someone is either not brave or brave.
Someone is both old and creative.
Mary is either rich or not humble.
Fred is both not strong and not kind.
Someone is either funny or tall.
Someone is not kind.
Someone is not brave. | Fred is not old. | neutral | (![X]:((happy(X)|~curious(X))<=>(strong(X)<~>~strong(X))))&
(![X]:((kind(X)&~calm(X))<=>(quiet(X)&~curious(X))))&
(![X]:((~kind(X)&calm(X))=>(~curious(X)&~strong(X))))&
(![X]:((humble(X)&generous(X))=>(~tall(X)|~generous(X))))&
(![X]:((~curious(X)|brave(X))=>(~wise(X)<~>patient(X))))&
(![X]:((creative(X)<~>kind(X))<=>~generous(X)))&
(![X]:(~tall(X)=>(~quiet(X)<~>calm(X))))&
(((brave(susan)&~quiet(susan)))<=>((~calm(susan)<~>~funny(susan))))&
((~brave(alice))<=>(?[X]:((old(X)|humble(X)))))&
(![X]:((brave(X)&generous(X))=>(old(X)&patient(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>((strong(mary)&~calm(mary))))&
(![X]:((strong(X)<~>patient(X))<=>(wise(X)<~>creative(X))))&
(![X]:((~patient(X)<~>brave(X))<=>~tall(X)))&
(((~kind(mary)&old(mary)))<=>(?[X]:((humble(X)&~humble(X)))))&
(![X]:((quiet(X)<~>tall(X))=>(wise(X)&strong(X))))&
(![X]:(~generous(X)<=>curious(X)))&
((~patient(susan)<~>~humble(susan)))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:((old(X)&creative(X))))&
((rich(mary)<~>~humble(mary)))&
((~strong(fred)&~kind(fred)))&
(?[X]:((funny(X)<~>tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~brave(X))) | ~old(fred) | [] | null | 0 |
If susan is either not quiet or not tall then someone is rich or humble and vice versa.
If fred is either not brave or not kind then someone is both not tall and kind and vice versa.
If mary is not tall then paul is not strong and vice versa.
Everyone who is both not rich and not generous is either not kind or patient and vice versa.
Everyone who is both calm and humble is not humble or not wise and vice versa.
Everyone who is either old or not old is both funny and wise.
Everyone who is wise or not kind is not strong.
Everyone who is tall is strong or old and vice versa.
If fred is either creative or not patient then someone is strong or creative and vice versa.
Everyone who is either curious or not quiet is not kind or not happy and vice versa.
Everyone who is either not funny or not happy is both not creative and generous and vice versa.
Everyone who is not curious or not quiet is both not old and not kind.
If lucy is either not patient or brave then susan is tall or not rich and vice versa.
Everyone who is not funny is humble.
If fred is either not curious or not quiet then someone is either wise or not old.
Everyone who is not kind is either not calm or quiet.
Fred is not old.
Someone is not patient or humble.
Someone is brave or not happy.
Someone is either humble or not brave.
Someone is both funny and kind.
Alice is not brave. | Lucy is not kind. | neutral | (((~quiet(susan)<~>~tall(susan)))<=>(?[X]:((rich(X)|humble(X)))))&
(((~brave(fred)<~>~kind(fred)))<=>(?[X]:((~tall(X)&kind(X)))))&
((~tall(mary))<=>(~strong(paul)))&
(![X]:((~rich(X)&~generous(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((calm(X)&humble(X))<=>(~humble(X)|~wise(X))))&
(![X]:((old(X)<~>~old(X))=>(funny(X)&wise(X))))&
(![X]:((wise(X)|~kind(X))=>~strong(X)))&
(![X]:(tall(X)<=>(strong(X)|old(X))))&
(((creative(fred)<~>~patient(fred)))<=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~creative(X)&generous(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~old(X)&~kind(X))))&
(((~patient(lucy)<~>brave(lucy)))<=>((tall(susan)|~rich(susan))))&
(![X]:(~funny(X)=>humble(X)))&
(((~curious(fred)<~>~quiet(fred)))=>(?[X]:((wise(X)<~>~old(X)))))&
(![X]:(~kind(X)=>(~calm(X)<~>quiet(X))))&
(~old(fred))&
(?[X]:((~patient(X)|humble(X))))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:((humble(X)<~>~brave(X))))&
(?[X]:((funny(X)&kind(X))))&
(~brave(alice)) | ~kind(lucy) | [] | null | 0 |
Everyone who is either not kind or not wise is not funny.
If alice is not quiet then susan is not brave and vice versa.
Everyone who is not funny or not brave is not rich or not calm and vice versa.
Everyone who is not generous or not creative is not wise or not tall and vice versa.
Everyone who is happy or brave is either not calm or tall.
If susan is not funny then john is not quiet and vice versa.
If someone is both creative and funny then someone is both not creative and not quiet.
Everyone who is not kind or not tall is not curious or creative and vice versa.
Everyone who is both not humble and not happy is old or not strong.
Everyone who is both not happy and humble is both funny and not happy.
Everyone who is either not calm or not wise is old or not generous and vice versa.
If someone is either not rich or kind then someone is not funny or tall and vice versa.
If someone is both kind and not kind then someone is either wise or kind and vice versa.
Everyone who is not rich is both not generous and generous and vice versa.
If someone is both kind and humble then someone is both not rich and not quiet and vice versa.
Everyone who is not creative or not old is both not creative and creative.
Paul is not generous.
Someone is generous or quiet.
Mary is not curious.
Someone is not happy or not brave.
Someone is either strong or not humble.
Someone is strong or quiet.
Someone is either old or generous. | Alice is not wise. | contradiction | (![X]:((~kind(X)<~>~wise(X))=>~funny(X)))&
((~quiet(alice))<=>(~brave(susan)))&
(![X]:((~funny(X)|~brave(X))<=>(~rich(X)|~calm(X))))&
(![X]:((~generous(X)|~creative(X))<=>(~wise(X)|~tall(X))))&
(![X]:((happy(X)|brave(X))=>(~calm(X)<~>tall(X))))&
((~funny(susan))<=>(~quiet(john)))&
((?[X]:((creative(X)&funny(X))))=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:((~kind(X)|~tall(X))<=>(~curious(X)|creative(X))))&
(![X]:((~humble(X)&~happy(X))=>(old(X)|~strong(X))))&
(![X]:((~happy(X)&humble(X))=>(funny(X)&~happy(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>(old(X)|~generous(X))))&
((?[X]:((~rich(X)<~>kind(X))))<=>(?[X]:((~funny(X)|tall(X)))))&
((?[X]:((kind(X)&~kind(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
(![X]:(~rich(X)<=>(~generous(X)&generous(X))))&
((?[X]:((kind(X)&humble(X))))<=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((~creative(X)|~old(X))=>(~creative(X)&creative(X))))&
(~generous(paul))&
(?[X]:((generous(X)|quiet(X))))&
(~curious(mary))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:((strong(X)<~>~humble(X))))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:((old(X)<~>generous(X)))) | ~wise(alice) | [
"p2",
"p6",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9136649764502337611768965
% SZS output start Proof for 9136649764502337611768965
3. ! [X0] : ((~brave(X0) | ~funny(X0)) <=> (~calm(X0) | ~rich(X0))) [input p2]
7. ? [X0] : (funny(X0) & creative(X0)) => ? [X0] : (~quiet(X0) & ~creative(X0)) [input p6]
11. ! [X0] : ((~calm(X0) <~> ~wise(X0)) <=> (~generous(X0) | old(X0))) [input p10]
14. ! [X0] : (~rich(X0) <=> (generous(X0) & ~generous(X0))) [input p13]
16. ! [X0] : ((~old(X0) | ~creative(X0)) => (creative(X0) & ~creative(X0))) [input p15]
24. ~wise(alice) [input hypothesis]
25. ? [X0] : (funny(X0) & creative(X0)) => ? [X1] : (~quiet(X1) & ~creative(X1)) [rectify 7]
31. ? [X1] : (~quiet(X1) & ~creative(X1)) | ! [X0] : (~funny(X0) | ~creative(X0)) [ennf transformation 25]
36. ! [X0] : ((creative(X0) & ~creative(X0)) | (old(X0) & creative(X0))) [ennf transformation 16]
39. ! [X0] : (((~brave(X0) | ~funny(X0)) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | (brave(X0) & funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((~brave(X0) | ~funny(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | (brave(X0) & funny(X0)))) [flattening 39]
45. ? [X0] : (~quiet(X0) & ~creative(X0)) | ! [X1] : (~funny(X1) | ~creative(X1)) [rectify 31]
46. ? [X0] : (~quiet(X0) & ~creative(X0)) => (~quiet(sK0) & ~creative(sK0)) [choice axiom]
47. (~quiet(sK0) & ~creative(sK0)) | ! [X1] : (~funny(X1) | ~creative(X1)) [skolemisation 45,46]
50. ! [X0] : ((((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (generous(X0) & ~old(X0))) & ((~generous(X0) | old(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))))) [nnf transformation 11]
51. ! [X0] : ((((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (generous(X0) & ~old(X0))) & (~generous(X0) | old(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))))) [flattening 50]
62. ! [X0] : ((~rich(X0) | (~generous(X0) | generous(X0))) & ((generous(X0) & ~generous(X0)) | rich(X0))) [nnf transformation 14]
63. ! [X0] : ((~rich(X0) | ~generous(X0) | generous(X0)) & ((generous(X0) & ~generous(X0)) | rich(X0))) [flattening 62]
85. ~calm(X0) | ~rich(X0) | funny(X0) [cnf transformation 40]
99. ~creative(sK0) | ~funny(X1) | ~creative(X1) [cnf transformation 47]
112. ~old(X0) | calm(X0) | wise(X0) [cnf transformation 51]
126. ~generous(X0) | rich(X0) [cnf transformation 63]
127. generous(X0) | rich(X0) [cnf transformation 63]
134. ~creative(X0) | old(X0) [cnf transformation 36]
135. creative(X0) | creative(X0) [cnf transformation 36]
146. ~wise(alice) [cnf transformation 24]
147. creative(X0) [duplicate literal removal 135]
169. 5 <=> ! [X1] : (~funny(X1) | ~creative(X1)) [avatar definition]
170. ~funny(X1) | ~creative(X1) <- (5) [avatar component clause 169]
177. 7 <=> creative(sK0) [avatar definition]
179. ~creative(sK0) <- (~7) [avatar component clause 177]
180. 5 | ~7 [avatar split clause 99,177,169]
229. rich(X0) [subsumption resolution 126,127]
240. old(X0) [subsumption resolution 134,147]
281. $false <- (~7) [subsumption resolution 179,147]
282. 7 [avatar contradiction clause 281]
283. ~funny(X1) <- (5) [subsumption resolution 170,147]
318. calm(X1) | wise(X1) [resolution 112,240]
329. wise(X4) | ~rich(X4) | funny(X4) [resolution 318,85]
331. wise(X4) | funny(X4) [subsumption resolution 329,229]
332. wise(X4) <- (5) [subsumption resolution 331,283]
334. $false <- (5) [resolution 332,146]
336. ~5 [avatar contradiction clause 334]
337. $false [avatar sat refutation 180,282,336]
% SZS output end Proof for 9136649764502337611768965
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is both not curious and not creative and vice versa.
Everyone who is both calm and not rich is either not kind or not brave.
Everyone who is not quiet or brave is both curious and happy.
If paul is either calm or quiet then fred is either patient or humble and vice versa.
Everyone who is not creative or quiet is both not humble and not kind.
If mary is both wise and creative then someone is both not happy and not strong and vice versa.
If someone is creative then paul is funny or not tall and vice versa.
Everyone who is either not kind or not funny is calm or kind and vice versa.
Everyone who is not rich is both not old and tall and vice versa.
If fred is both not old and not tall then someone is either not old or patient and vice versa.
If fred is both not quiet and old then fred is not generous.
Everyone who is both not happy and not humble is both not patient and happy.
Everyone who is both creative and not happy is either generous or not patient.
If paul is both not creative and not funny then fred is not happy.
Everyone who is both not calm and not happy is not curious and vice versa.
Everyone who is not rich is not strong and vice versa.
Fred is either not happy or creative.
Someone is wise.
Someone is wise or patient.
John is quiet.
Someone is either not old or brave.
Someone is funny or not strong.
Alice is either not curious or humble. | Alice is strong. | neutral | (![X]:((kind(X)&~creative(X))<=>(~curious(X)&~creative(X))))&
(![X]:((calm(X)&~rich(X))=>(~kind(X)<~>~brave(X))))&
(![X]:((~quiet(X)|brave(X))=>(curious(X)&happy(X))))&
(((calm(paul)<~>quiet(paul)))<=>((patient(fred)<~>humble(fred))))&
(![X]:((~creative(X)|quiet(X))=>(~humble(X)&~kind(X))))&
(((wise(mary)&creative(mary)))<=>(?[X]:((~happy(X)&~strong(X)))))&
((?[X]:(creative(X)))<=>((funny(paul)|~tall(paul))))&
(![X]:((~kind(X)<~>~funny(X))<=>(calm(X)|kind(X))))&
(![X]:(~rich(X)<=>(~old(X)&tall(X))))&
(((~old(fred)&~tall(fred)))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~quiet(fred)&old(fred)))=>(~generous(fred)))&
(![X]:((~happy(X)&~humble(X))=>(~patient(X)&happy(X))))&
(![X]:((creative(X)&~happy(X))=>(generous(X)<~>~patient(X))))&
(((~creative(paul)&~funny(paul)))=>(~happy(fred)))&
(![X]:((~calm(X)&~happy(X))<=>~curious(X)))&
(![X]:(~rich(X)<=>~strong(X)))&
((~happy(fred)<~>creative(fred)))&
(?[X]:(wise(X)))&
(?[X]:((wise(X)|patient(X))))&
(quiet(john))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((funny(X)|~strong(X))))&
((~curious(alice)<~>humble(alice))) | strong(alice) | [] | null | 0 |
Everyone who is not tall is not old or not happy and vice versa.
Everyone who is quiet is brave or not happy.
Everyone who is both strong and wise is patient.
Everyone who is strong or not generous is curious and vice versa.
Everyone who is tall is not wise or not calm and vice versa.
Everyone who is both quiet and not rich is both not humble and old and vice versa.
If someone is humble or old then lucy is both not wise and funny.
Everyone who is both humble and old is not funny or not quiet.
If mary is both not brave and not funny then someone is both not strong and humble and vice versa.
Everyone who is either strong or old is not humble or not wise and vice versa.
If someone is funny then paul is not brave and vice versa.
If paul is not tall or not generous then someone is both not patient and funny.
If fred is both not kind and not calm then someone is either funny or brave.
If someone is both funny and creative then mary is both not creative and not strong and vice versa.
Everyone who is either quiet or creative is wise.
Someone is kind or not generous.
Susan is both not old and wise.
Fred is not brave.
Alice is not patient.
Someone is either creative or not generous.
Someone is not strong or not tall.
Someone is both strong and quiet.
Mary is both not strong and not curious. | Lucy is not strong. | entailment | (![X]:(~tall(X)<=>(~old(X)|~happy(X))))&
(![X]:(quiet(X)=>(brave(X)|~happy(X))))&
(![X]:((strong(X)&wise(X))=>patient(X)))&
(![X]:((strong(X)|~generous(X))<=>curious(X)))&
(![X]:(tall(X)<=>(~wise(X)|~calm(X))))&
(![X]:((quiet(X)&~rich(X))<=>(~humble(X)&old(X))))&
((?[X]:((humble(X)|old(X))))=>((~wise(lucy)&funny(lucy))))&
(![X]:((humble(X)&old(X))=>(~funny(X)|~quiet(X))))&
(((~brave(mary)&~funny(mary)))<=>(?[X]:((~strong(X)&humble(X)))))&
(![X]:((strong(X)<~>old(X))<=>(~humble(X)|~wise(X))))&
((?[X]:(funny(X)))<=>(~brave(paul)))&
(((~tall(paul)|~generous(paul)))=>(?[X]:((~patient(X)&funny(X)))))&
(((~kind(fred)&~calm(fred)))=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((funny(X)&creative(X))))<=>((~creative(mary)&~strong(mary))))&
(![X]:((quiet(X)<~>creative(X))=>wise(X)))&
(?[X]:((kind(X)|~generous(X))))&
((~old(susan)&wise(susan)))&
(~brave(fred))&
(~patient(alice))&
(?[X]:((creative(X)<~>~generous(X))))&
(?[X]:((~strong(X)|~tall(X))))&
(?[X]:((strong(X)&quiet(X))))&
((~strong(mary)&~curious(mary))) | ~strong(lucy) | [
"p0",
"p4",
"p6",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4769483440610754591644267
% SZS output start Proof for 4769483440610754591644267
1. ! [X0] : (~tall(X0) <=> (~happy(X0) | ~old(X0))) [input p0]
5. ! [X0] : (tall(X0) <=> (~calm(X0) | ~wise(X0))) [input p4]
7. ? [X0] : (old(X0) | humble(X0)) => (funny(lucy) & ~wise(lucy)) [input p6]
10. ! [X0] : ((strong(X0) <~> old(X0)) <=> (~wise(X0) | ~humble(X0))) [input p9]
23. ~curious(mary) & ~strong(mary) [input p22]
24. strong(lucy) [input hypothesis]
33. (funny(lucy) & ~wise(lucy)) | ! [X0] : (~old(X0) & ~humble(X0)) [ennf transformation 7]
38. ! [X0] : ((~tall(X0) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | tall(X0))) [nnf transformation 1]
39. ! [X0] : ((~tall(X0) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | tall(X0))) [flattening 38]
40. ! [X0] : ((tall(X0) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | ~tall(X0))) [nnf transformation 5]
41. ! [X0] : ((tall(X0) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0))) [flattening 40]
49. ! [X0] : ((((~old(X0) | ~strong(X0)) & (old(X0) | strong(X0))) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0))))) [nnf transformation 10]
50. ! [X0] : ((((~old(X0) | ~strong(X0)) & (old(X0) | strong(X0))) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0))))) [flattening 49]
71. ~tall(X0) | old(X0) [cnf transformation 39]
78. wise(X0) | tall(X0) [cnf transformation 41]
84. ~wise(lucy) | ~humble(X0) [cnf transformation 33]
85. ~wise(lucy) | ~old(X0) [cnf transformation 33]
95. humble(X0) | strong(X0) | old(X0) [cnf transformation 50]
98. ~strong(X0) | ~old(X0) | wise(X0) [cnf transformation 50]
120. ~strong(mary) [cnf transformation 23]
122. strong(lucy) [cnf transformation 24]
124. 1 <=> ! [X0] : ~old(X0) [avatar definition]
125. ~old(X0) <- (1) [avatar component clause 124]
132. 3 <=> ! [X0] : ~humble(X0) [avatar definition]
133. ~humble(X0) <- (3) [avatar component clause 132]
136. 4 <=> wise(lucy) [avatar definition]
138. ~wise(lucy) <- (~4) [avatar component clause 136]
139. 1 | ~4 [avatar split clause 85,136,124]
140. 3 | ~4 [avatar split clause 84,136,132]
202. 18 <=> strong(mary) [avatar definition]
203. ~strong(mary) <- (~18) [avatar component clause 202]
239. ~18 [avatar split clause 120,202]
294. strong(X0) | old(X0) <- (3) [resolution 95,133]
298. strong(X0) <- (1, 3) [subsumption resolution 294,125]
305. $false <- (1, 3, ~18) [resolution 298,203]
310. ~1 | ~3 | 18 [avatar contradiction clause 305]
313. tall(lucy) <- (~4) [resolution 138,78]
333. ~old(lucy) | wise(lucy) [resolution 98,122]
335. old(lucy) <- (~4) [resolution 313,71]
338. wise(lucy) <- (~4) [subsumption resolution 333,335]
339. $false <- (~4) [subsumption resolution 338,138]
340. 4 [avatar contradiction clause 339]
354. $false [avatar sat refutation 139,140,239,310,340]
% SZS output end Proof for 4769483440610754591644267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not quiet is wise or not strong.
If someone is not brave then someone is both humble and not quiet and vice versa.
If mary is quiet or not happy then susan is both not curious and not rich and vice versa.
If fred is not funny then someone is both rich and wise and vice versa.
If lucy is not generous then paul is generous or old and vice versa.
If someone is both quiet and not calm then john is either creative or not rich and vice versa.
Everyone who is both tall and not patient is humble and vice versa.
If someone is both not happy and quiet then paul is either not humble or curious and vice versa.
If paul is either creative or not strong then susan is both not curious and not old and vice versa.
If paul is both not calm and not tall then someone is either not calm or quiet and vice versa.
Everyone who is both not old and not curious is either rich or not calm and vice versa.
Everyone who is either not calm or brave is both humble and generous.
If john is both not kind and not humble then john is both old and funny and vice versa.
If fred is both kind and humble then someone is kind or rich and vice versa.
Everyone who is not creative is not tall.
Everyone who is both not tall and humble is not humble or not rich and vice versa.
Someone is both not old and not curious.
John is old.
Someone is brave.
Someone is both not quiet and creative.
Paul is either rich or brave.
Someone is both happy and funny.
Someone is both not strong and curious. | Mary is not curious. | entailment | (![X]:((~creative(X)&~quiet(X))=>(wise(X)|~strong(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((humble(X)&~quiet(X)))))&
(((quiet(mary)|~happy(mary)))<=>((~curious(susan)&~rich(susan))))&
((~funny(fred))<=>(?[X]:((rich(X)&wise(X)))))&
((~generous(lucy))<=>((generous(paul)|old(paul))))&
((?[X]:((quiet(X)&~calm(X))))<=>((creative(john)<~>~rich(john))))&
(![X]:((tall(X)&~patient(X))<=>humble(X)))&
((?[X]:((~happy(X)&quiet(X))))<=>((~humble(paul)<~>curious(paul))))&
(((creative(paul)<~>~strong(paul)))<=>((~curious(susan)&~old(susan))))&
(((~calm(paul)&~tall(paul)))<=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:((~old(X)&~curious(X))<=>(rich(X)<~>~calm(X))))&
(![X]:((~calm(X)<~>brave(X))=>(humble(X)&generous(X))))&
(((~kind(john)&~humble(john)))<=>((old(john)&funny(john))))&
(((kind(fred)&humble(fred)))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:(~creative(X)=>~tall(X)))&
(![X]:((~tall(X)&humble(X))<=>(~humble(X)|~rich(X))))&
(?[X]:((~old(X)&~curious(X))))&
(old(john))&
(?[X]:(brave(X)))&
(?[X]:((~quiet(X)&creative(X))))&
((rich(paul)<~>brave(paul)))&
(?[X]:((happy(X)&funny(X))))&
(?[X]:((~strong(X)&curious(X)))) | ~curious(mary) | [
"p2",
"p6",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2325566501484197436902300
% SZS output start Proof for 2325566501484197436902300
3. (~happy(mary) | quiet(mary)) <=> (~rich(susan) & ~curious(susan)) [input p2]
7. ! [X0] : ((~patient(X0) & tall(X0)) <=> humble(X0)) [input p6]
10. (~tall(paul) & ~calm(paul)) <=> ? [X0] : (~calm(X0) <~> quiet(X0)) [input p9]
11. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (rich(X0) <~> ~calm(X0))) [input p10]
16. ! [X0] : ((humble(X0) & ~tall(X0)) <=> (~rich(X0) | ~humble(X0))) [input p15]
24. curious(mary) [input hypothesis]
35. ((~happy(mary) | quiet(mary)) | (rich(susan) | curious(susan))) & ((~rich(susan) & ~curious(susan)) | (happy(mary) & ~quiet(mary))) [nnf transformation 3]
36. (~happy(mary) | quiet(mary) | rich(susan) | curious(susan)) & ((~rich(susan) & ~curious(susan)) | (happy(mary) & ~quiet(mary))) [flattening 35]
47. ! [X0] : (((~patient(X0) & tall(X0)) | ~humble(X0)) & (humble(X0) | (patient(X0) | ~tall(X0)))) [nnf transformation 7]
48. ! [X0] : (((~patient(X0) & tall(X0)) | ~humble(X0)) & (humble(X0) | patient(X0) | ~tall(X0))) [flattening 47]
55. ((~tall(paul) & ~calm(paul)) | ! [X0] : ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (? [X0] : ((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | (tall(paul) | calm(paul))) [nnf transformation 10]
56. ((~tall(paul) & ~calm(paul)) | ! [X0] : ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (? [X0] : ((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | tall(paul) | calm(paul)) [flattening 55]
57. ((~tall(paul) & ~calm(paul)) | ! [X0] : ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (? [X1] : ((~quiet(X1) | calm(X1)) & (quiet(X1) | ~calm(X1))) | tall(paul) | calm(paul)) [rectify 56]
58. ? [X1] : ((~quiet(X1) | calm(X1)) & (quiet(X1) | ~calm(X1))) => ((~quiet(sK5) | calm(sK5)) & (quiet(sK5) | ~calm(sK5))) [choice axiom]
59. ((~tall(paul) & ~calm(paul)) | ! [X0] : ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (((~quiet(sK5) | calm(sK5)) & (quiet(sK5) | ~calm(sK5))) | tall(paul) | calm(paul)) [skolemisation 57,58]
60. ! [X0] : (((~curious(X0) & ~old(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (curious(X0) | old(X0)))) [nnf transformation 11]
61. ! [X0] : (((~curious(X0) & ~old(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | curious(X0) | old(X0))) [flattening 60]
70. ! [X0] : (((humble(X0) & ~tall(X0)) | (rich(X0) & humble(X0))) & ((~rich(X0) | ~humble(X0)) | (~humble(X0) | tall(X0)))) [nnf transformation 16]
71. ! [X0] : (((humble(X0) & ~tall(X0)) | (rich(X0) & humble(X0))) & (~rich(X0) | ~humble(X0) | ~humble(X0) | tall(X0))) [flattening 70]
89. ~rich(susan) | ~quiet(mary) [cnf transformation 36]
105. ~humble(X0) | tall(X0) [cnf transformation 48]
123. ~tall(paul) | quiet(X0) | calm(X0) [cnf transformation 59]
129. ~calm(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 61]
147. ~tall(X0) | rich(X0) [cnf transformation 71]
148. humble(X0) | humble(X0) [cnf transformation 71]
162. curious(mary) [cnf transformation 24]
164. humble(X0) [duplicate literal removal 148]
191. 7 <=> rich(susan) [avatar definition]
192. ~rich(susan) <- (~7) [avatar component clause 191]
195. 8 <=> quiet(mary) [avatar definition]
196. ~quiet(mary) <- (~8) [avatar component clause 195]
204. ~8 | ~7 [avatar split clause 89,191,195]
312. 31 <=> tall(paul) [avatar definition]
314. ~tall(paul) <- (~31) [avatar component clause 312]
317. 32 <=> ! [X0] : (quiet(X0) | calm(X0)) [avatar definition]
318. calm(X0) | quiet(X0) <- (32) [avatar component clause 317]
319. 32 | ~31 [avatar split clause 123,312,317]
413. tall(X0) [resolution 105,164]
414. $false <- (~31) [resolution 413,314]
415. 31 [avatar contradiction clause 414]
417. rich(X0) [resolution 147,413]
422. $false <- (~7) [resolution 417,192]
425. 7 [avatar contradiction clause 422]
450. ~curious(X0) | ~rich(X0) | quiet(X0) <- (32) [resolution 129,318]
452. ~curious(X0) | quiet(X0) <- (32) [subsumption resolution 450,417]
525. quiet(mary) <- (32) [resolution 452,162]
529. $false <- (~8, 32) [subsumption resolution 525,196]
530. 8 | ~32 [avatar contradiction clause 529]
531. $false [avatar sat refutation 204,319,415,425,530]
% SZS output end Proof for 2325566501484197436902300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not wise is both wise and not funny and vice versa.
Everyone who is both curious and not calm is not calm and vice versa.
Everyone who is not curious is not wise or not strong and vice versa.
Everyone who is both old and creative is either strong or not wise and vice versa.
If paul is not brave then alice is brave and vice versa.
If mary is creative or not calm then lucy is tall or not strong and vice versa.
Everyone who is either creative or not funny is brave and vice versa.
If lucy is both not kind and not humble then fred is both not generous and not curious.
Everyone who is either patient or tall is strong or not tall and vice versa.
Everyone who is not quiet is not wise or not calm.
Everyone who is either not wise or tall is both not rich and not quiet.
If mary is calm or not curious then mary is not old.
Everyone who is either calm or wise is both not patient and not strong.
If fred is both not quiet and not patient then someone is both tall and not happy.
Everyone who is not calm or humble is either not curious or not tall and vice versa.
If mary is not patient or not old then someone is not humble and vice versa.
Someone is either brave or calm.
Paul is brave.
Someone is generous or wise.
Someone is either kind or not rich.
Someone is kind or not wise.
Someone is not patient or funny. | Paul is not generous. | neutral | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&~funny(X))))&
(![X]:((curious(X)&~calm(X))<=>~calm(X)))&
(![X]:(~curious(X)<=>(~wise(X)|~strong(X))))&
(![X]:((old(X)&creative(X))<=>(strong(X)<~>~wise(X))))&
((~brave(paul))<=>(brave(alice)))&
(((creative(mary)|~calm(mary)))<=>((tall(lucy)|~strong(lucy))))&
(![X]:((creative(X)<~>~funny(X))<=>brave(X)))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
(![X]:((calm(X)<~>wise(X))=>(~patient(X)&~strong(X))))&
(((~quiet(fred)&~patient(fred)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
(((~patient(mary)|~old(mary)))<=>(?[X]:(~humble(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~patient(X)|funny(X)))) | ~generous(paul) | [] | null | 0 |
Everyone who is either tall or not generous is not creative or not kind and vice versa.
If paul is either not funny or not creative then someone is either generous or brave.
If fred is not funny then someone is either funny or not strong and vice versa.
If someone is both kind and rich then someone is both brave and not strong and vice versa.
If susan is not rich or not brave then someone is either humble or not happy and vice versa.
Everyone who is quiet or not curious is both not creative and happy and vice versa.
Everyone who is tall or not strong is both not tall and kind.
If someone is not brave then someone is kind and vice versa.
Everyone who is not calm or strong is both not curious and strong.
Everyone who is both not funny and kind is both not calm and not humble.
Everyone who is either not brave or kind is not strong or wise and vice versa.
If john is not curious then fred is not quiet.
If fred is strong then susan is either calm or happy.
If someone is either old or patient then someone is not creative and vice versa.
Everyone who is both not brave and rich is both not calm and creative and vice versa.
Everyone who is both kind and not strong is not kind or brave.
Lucy is not old.
Susan is both not patient and old.
Someone is both generous and not old.
Someone is either not creative or patient.
Someone is either not curious or strong.
Someone is both not curious and funny.
Someone is both wise and quiet.
Lucy is not funny or old. | Susan is not tall. | entailment | (![X]:((tall(X)<~>~generous(X))<=>(~creative(X)|~kind(X))))&
(((~funny(paul)<~>~creative(paul)))=>(?[X]:((generous(X)<~>brave(X)))))&
((~funny(fred))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((brave(X)&~strong(X)))))&
(((~rich(susan)|~brave(susan)))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((quiet(X)|~curious(X))<=>(~creative(X)&happy(X))))&
(![X]:((tall(X)|~strong(X))=>(~tall(X)&kind(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(kind(X))))&
(![X]:((~calm(X)|strong(X))=>(~curious(X)&strong(X))))&
(![X]:((~funny(X)&kind(X))=>(~calm(X)&~humble(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(~strong(X)|wise(X))))&
((~curious(john))=>(~quiet(fred)))&
((strong(fred))=>((calm(susan)<~>happy(susan))))&
((?[X]:((old(X)<~>patient(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~brave(X)&rich(X))<=>(~calm(X)&creative(X))))&
(![X]:((kind(X)&~strong(X))=>(~kind(X)|brave(X))))&
(~old(lucy))&
((~patient(susan)&old(susan)))&
(?[X]:((generous(X)&~old(X))))&
(?[X]:((~creative(X)<~>patient(X))))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:((wise(X)&quiet(X))))&
((~funny(lucy)|old(lucy))) | ~tall(susan) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 441085976936739819368716
% SZS output start Proof for 441085976936739819368716
7. ! [X0] : ((~strong(X0) | tall(X0)) => (kind(X0) & ~tall(X0))) [input p6]
25. tall(susan) [input hypothesis]
30. ! [X0] : ((kind(X0) & ~tall(X0)) | (strong(X0) & ~tall(X0))) [ennf transformation 7]
115. ~tall(X0) | ~tall(X0) [cnf transformation 30]
159. tall(susan) [cnf transformation 25]
161. ~tall(X0) [duplicate literal removal 115]
337. $false [subsumption resolution 159,161]
% SZS output end Proof for 441085976936739819368716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or patient is both not kind and funny and vice versa.
Everyone who is rich or quiet is curious.
If someone is funny then fred is both funny and curious and vice versa.
Everyone who is tall is both curious and not rich and vice versa.
Everyone who is both generous and not wise is either not happy or not humble and vice versa.
Everyone who is both brave and not strong is not wise or not patient and vice versa.
If someone is not calm or not creative then someone is both not kind and patient and vice versa.
Everyone who is not funny or not old is not patient or not wise.
If lucy is kind then someone is both happy and old.
Everyone who is not patient or not old is both humble and calm and vice versa.
If someone is not patient then someone is not creative or not strong.
If paul is not funny or curious then someone is both not funny and not humble.
If mary is both humble and not tall then someone is not brave.
If susan is not strong then someone is either not funny or funny.
If lucy is brave or quiet then mary is patient.
Everyone who is both not rich and rich is either not wise or not generous.
Mary is not wise or old.
Someone is not old.
Someone is funny or not creative.
Fred is not tall or happy.
Mary is either not wise or not humble.
Paul is kind or not strong.
John is either strong or not quiet. | John is strong. | neutral | (![X]:((brave(X)|patient(X))<=>(~kind(X)&funny(X))))&
(![X]:((rich(X)|quiet(X))=>curious(X)))&
((?[X]:(funny(X)))<=>((funny(fred)&curious(fred))))&
(![X]:(tall(X)<=>(curious(X)&~rich(X))))&
(![X]:((generous(X)&~wise(X))<=>(~happy(X)<~>~humble(X))))&
(![X]:((brave(X)&~strong(X))<=>(~wise(X)|~patient(X))))&
((?[X]:((~calm(X)|~creative(X))))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((~funny(X)|~old(X))=>(~patient(X)|~wise(X))))&
((kind(lucy))=>(?[X]:((happy(X)&old(X)))))&
(![X]:((~patient(X)|~old(X))<=>(humble(X)&calm(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~creative(X)|~strong(X)))))&
(((~funny(paul)|curious(paul)))=>(?[X]:((~funny(X)&~humble(X)))))&
(((humble(mary)&~tall(mary)))=>(?[X]:(~brave(X))))&
((~strong(susan))=>(?[X]:((~funny(X)<~>funny(X)))))&
(((brave(lucy)|quiet(lucy)))=>(patient(mary)))&
(![X]:((~rich(X)&rich(X))=>(~wise(X)<~>~generous(X))))&
((~wise(mary)|old(mary)))&
(?[X]:(~old(X)))&
(?[X]:((funny(X)|~creative(X))))&
((~tall(fred)|happy(fred)))&
((~wise(mary)<~>~humble(mary)))&
((kind(paul)|~strong(paul)))&
((strong(john)<~>~quiet(john))) | strong(john) | [] | null | 0 |
Everyone who is either not funny or old is both not happy and quiet and vice versa.
If someone is not funny then someone is both not brave and humble and vice versa.
If someone is patient or not funny then paul is both not rich and not calm and vice versa.
Everyone who is both kind and not generous is tall.
If alice is either patient or not tall then someone is either old or patient and vice versa.
If someone is both tall and curious then someone is either not generous or rich.
Everyone who is both not quiet and not strong is either not rich or old and vice versa.
Everyone who is either humble or rich is humble and vice versa.
If alice is either not rich or not tall then someone is generous.
If someone is not tall then someone is not brave or not happy.
If someone is both not patient and brave then someone is both not happy and not wise and vice versa.
Everyone who is not quiet is funny or humble.
Everyone who is both not calm and not rich is both not patient and not funny.
If alice is both not calm and not creative then someone is curious.
Everyone who is generous is not patient.
If paul is both not old and not generous then paul is either not brave or not humble and vice versa.
Lucy is either not happy or humble.
Someone is either not humble or calm.
Paul is not humble or kind.
John is tall.
Someone is both not kind and patient.
Someone is both calm and patient.
Someone is either not calm or not tall.
Someone is old. | John is quiet. | neutral | (![X]:((~funny(X)<~>old(X))<=>(~happy(X)&quiet(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~brave(X)&humble(X)))))&
((?[X]:((patient(X)|~funny(X))))<=>((~rich(paul)&~calm(paul))))&
(![X]:((kind(X)&~generous(X))=>tall(X)))&
(((patient(alice)<~>~tall(alice)))<=>(?[X]:((old(X)<~>patient(X)))))&
((?[X]:((tall(X)&curious(X))))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:((~quiet(X)&~strong(X))<=>(~rich(X)<~>old(X))))&
(![X]:((humble(X)<~>rich(X))<=>humble(X)))&
(((~rich(alice)<~>~tall(alice)))=>(?[X]:(generous(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~patient(X)&brave(X))))<=>(?[X]:((~happy(X)&~wise(X)))))&
(![X]:(~quiet(X)=>(funny(X)|humble(X))))&
(![X]:((~calm(X)&~rich(X))=>(~patient(X)&~funny(X))))&
(((~calm(alice)&~creative(alice)))=>(?[X]:(curious(X))))&
(![X]:(generous(X)=>~patient(X)))&
(((~old(paul)&~generous(paul)))<=>((~brave(paul)<~>~humble(paul))))&
((~happy(lucy)<~>humble(lucy)))&
(?[X]:((~humble(X)<~>calm(X))))&
((~humble(paul)|kind(paul)))&
(tall(john))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:((calm(X)&patient(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:(old(X))) | quiet(john) | [] | null | 0 |
If someone is either not calm or wise then lucy is quiet. Everyone who is both not calm and not brave is not quiet or quiet. If someone is rich then someone is either quiet or not wise and vice versa. Everyone who is rich or not quiet is both quiet and strong. If alice is not kind or rich then someone is either not quiet or not kind. Everyone who is old is both not humble and not brave. Everyone who is not generous or kind is brave or not tall and vice versa. Everyone who is either not rich or not curious is both tall and brave. Everyone who is both not calm and not humble is creative or not old. Everyone who is both calm and not kind is both not rich and not patient and vice versa. Everyone who is both strong and not rich is either wise or old and vice versa. If someone is kind then someone is both not patient and rich. Everyone who is curious or not wise is both not tall and not strong. Everyone who is both not calm and old is either not curious or not rich. Everyone who is either brave or not strong is either not patient or strong and vice versa. Someone is strong or not rich. Someone is not curious. Susan is funny. Mary is either not curious or not humble. Someone is not generous or brave. Fred is not brave or brave. Alice is both creative and quiet. | Fred is kind. | contradiction | ((?[X]:((~calm(X)<~>wise(X))))=>(quiet(lucy)))&
(![X]:((~calm(X)&~brave(X))=>(~quiet(X)|quiet(X))))&
((?[X]:(rich(X)))<=>(?[X]:((quiet(X)<~>~wise(X)))))&
(![X]:((rich(X)|~quiet(X))=>(quiet(X)&strong(X))))&
(((~kind(alice)|rich(alice)))=>(?[X]:((~quiet(X)<~>~kind(X)))))&
(![X]:(old(X)=>(~humble(X)&~brave(X))))&
(![X]:((~generous(X)|kind(X))<=>(brave(X)|~tall(X))))&
(![X]:((~rich(X)<~>~curious(X))=>(tall(X)&brave(X))))&
(![X]:((~calm(X)&~humble(X))=>(creative(X)|~old(X))))&
(![X]:((calm(X)&~kind(X))<=>(~rich(X)&~patient(X))))&
(![X]:((strong(X)&~rich(X))<=>(wise(X)<~>old(X))))&
((?[X]:(kind(X)))=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:((curious(X)|~wise(X))=>(~tall(X)&~strong(X))))&
(![X]:((~calm(X)&old(X))=>(~curious(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~strong(X))<=>(~patient(X)<~>strong(X))))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:(~curious(X)))&
(funny(susan))&
((~curious(mary)<~>~humble(mary)))&
(?[X]:((~generous(X)|brave(X))))&
((~brave(fred)|brave(fred)))&
((creative(alice)&quiet(alice))) | kind(fred) | [
"p3",
"p7",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7204535155196033208196947
% SZS output start Proof for 7204535155196033208196947
4. ! [X0] : ((~quiet(X0) | rich(X0)) => (strong(X0) & quiet(X0))) [input p3]
8. ! [X0] : ((~rich(X0) <~> ~curious(X0)) => (brave(X0) & tall(X0))) [input p7]
12. ? [X0] : kind(X0) => ? [X0] : (rich(X0) & ~patient(X0)) [input p11]
13. ! [X0] : ((~wise(X0) | curious(X0)) => (~strong(X0) & ~tall(X0))) [input p12]
15. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (~patient(X0) <~> strong(X0))) [input p14]
23. kind(fred) [input hypothesis]
25. ? [X0] : kind(X0) => ? [X1] : (rich(X1) & ~patient(X1)) [rectify 12]
32. ! [X0] : ((strong(X0) & quiet(X0)) | (quiet(X0) & ~rich(X0))) [ennf transformation 4]
35. ! [X0] : ((brave(X0) & tall(X0)) | (~rich(X0) <=> ~curious(X0))) [ennf transformation 8]
36. ? [X1] : (rich(X1) & ~patient(X1)) | ! [X0] : ~kind(X0) [ennf transformation 25]
37. ! [X0] : ((~strong(X0) & ~tall(X0)) | (wise(X0) & ~curious(X0))) [ennf transformation 13]
51. ! [X0] : ((brave(X0) & tall(X0)) | ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) [nnf transformation 35]
56. ? [X0] : (rich(X0) & ~patient(X0)) | ! [X1] : ~kind(X1) [rectify 36]
57. ? [X0] : (rich(X0) & ~patient(X0)) => (rich(sK3) & ~patient(sK3)) [choice axiom]
58. (rich(sK3) & ~patient(sK3)) | ! [X1] : ~kind(X1) [skolemisation 56,57]
60. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0)))) & (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 15]
77. ~rich(X0) | strong(X0) [cnf transformation 32]
92. ~rich(X0) | brave(X0) | curious(X0) [cnf transformation 51]
103. ~patient(sK3) | ~kind(X1) [cnf transformation 58]
104. rich(sK3) | ~kind(X1) [cnf transformation 58]
107. ~curious(X0) | ~strong(X0) [cnf transformation 37]
113. ~strong(X0) | patient(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 60]
117. strong(X0) | ~brave(X0) | strong(X0) | patient(X0) [cnf transformation 60]
126. kind(fred) [cnf transformation 23]
128. ~strong(X0) | patient(X0) | ~brave(X0) [duplicate literal removal 113]
130. strong(X0) | ~brave(X0) | patient(X0) [duplicate literal removal 117]
186. 13 <=> ! [X1] : ~kind(X1) [avatar definition]
187. ~kind(X1) <- (13) [avatar component clause 186]
189. 14 <=> rich(sK3) [avatar definition]
191. rich(sK3) <- (14) [avatar component clause 189]
192. 13 | 14 [avatar split clause 104,189,186]
194. 15 <=> patient(sK3) [avatar definition]
196. ~patient(sK3) <- (~15) [avatar component clause 194]
197. 13 | ~15 [avatar split clause 103,194,186]
198. ~brave(X0) | patient(X0) [subsumption resolution 128,130]
224. $false <- (13) [resolution 187,126]
225. ~13 [avatar contradiction clause 224]
231. strong(sK3) <- (14) [resolution 77,191]
256. 22 <=> curious(sK3) [avatar definition]
258. curious(sK3) <- (22) [avatar component clause 256]
272. brave(sK3) | curious(sK3) <- (14) [resolution 92,191]
299. ~strong(sK3) <- (22) [resolution 258,107]
301. $false <- (14, 22) [subsumption resolution 299,231]
302. ~14 | ~22 [avatar contradiction clause 301]
305. 28 <=> brave(sK3) [avatar definition]
307. brave(sK3) <- (28) [avatar component clause 305]
308. 22 | 28 | ~14 [avatar split clause 272,189,305,256]
342. patient(sK3) <- (28) [resolution 307,198]
343. $false <- (~15, 28) [subsumption resolution 342,196]
344. 15 | ~28 [avatar contradiction clause 343]
345. $false [avatar sat refutation 192,197,225,302,308,344]
% SZS output end Proof for 7204535155196033208196947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not generous is not curious and vice versa. Everyone who is not tall is not quiet and vice versa. If paul is brave then someone is old. Everyone who is either old or humble is both funny and not quiet. Everyone who is not curious or generous is either generous or brave. If someone is either old or not brave then susan is not quiet or not tall and vice versa. Everyone who is patient is both not curious and funny. If fred is either not wise or not quiet then someone is not humble or happy and vice versa. If john is not humble or calm then someone is humble. If susan is tall then someone is not happy. Everyone who is humble is calm or generous and vice versa. If lucy is rich or funny then john is either not happy or not kind and vice versa. Everyone who is not wise is both generous and wise and vice versa. Everyone who is both rich and not humble is curious. If lucy is both funny and not funny then mary is both not old and not quiet. Everyone who is either not strong or wise is both strong and not calm. Alice is not creative or curious. Alice is either old or not strong. Lucy is not kind or not patient. Paul is not humble. Someone is kind or generous. Lucy is not creative or not humble. | Mary is funny. | neutral | (![X]:((wise(X)|~generous(X))<=>~curious(X)))&
(![X]:(~tall(X)<=>~quiet(X)))&
((brave(paul))=>(?[X]:(old(X))))&
(![X]:((old(X)<~>humble(X))=>(funny(X)&~quiet(X))))&
(![X]:((~curious(X)|generous(X))=>(generous(X)<~>brave(X))))&
((?[X]:((old(X)<~>~brave(X))))<=>((~quiet(susan)|~tall(susan))))&
(![X]:(patient(X)=>(~curious(X)&funny(X))))&
(((~wise(fred)<~>~quiet(fred)))<=>(?[X]:((~humble(X)|happy(X)))))&
(((~humble(john)|calm(john)))=>(?[X]:(humble(X))))&
((tall(susan))=>(?[X]:(~happy(X))))&
(![X]:(humble(X)<=>(calm(X)|generous(X))))&
(((rich(lucy)|funny(lucy)))<=>((~happy(john)<~>~kind(john))))&
(![X]:(~wise(X)<=>(generous(X)&wise(X))))&
(![X]:((rich(X)&~humble(X))=>curious(X)))&
(((funny(lucy)&~funny(lucy)))=>((~old(mary)&~quiet(mary))))&
(![X]:((~strong(X)<~>wise(X))=>(strong(X)&~calm(X))))&
((~creative(alice)|curious(alice)))&
((old(alice)<~>~strong(alice)))&
((~kind(lucy)|~patient(lucy)))&
(~humble(paul))&
(?[X]:((kind(X)|generous(X))))&
((~creative(lucy)|~humble(lucy))) | funny(mary) | [] | null | 0 |
If susan is not generous then alice is not quiet. If alice is both curious and not generous then someone is patient and vice versa. Everyone who is either funny or not old is not funny and vice versa. Everyone who is both not generous and curious is both not kind and quiet. If susan is both not strong and not wise then someone is both not patient and not humble. Everyone who is creative is not happy. Everyone who is both not brave and not kind is either calm or generous and vice versa. Everyone who is both not happy and not wise is wise or curious. Everyone who is both not humble and strong is either funny or happy and vice versa. Everyone who is funny is both quiet and brave and vice versa. If someone is happy then someone is not creative and vice versa. If alice is curious then someone is patient or not creative. If fred is not humble then someone is either not calm or not patient. If john is happy or kind then someone is creative and vice versa. If fred is brave or not curious then someone is both happy and not kind and vice versa. Everyone who is either not kind or not strong is both not tall and creative. Someone is both rich and tall. Lucy is either quiet or not happy. Fred is both creative and curious. Someone is either patient or humble. John is either quiet or not happy. Someone is both happy and not funny. Lucy is not kind. Someone is either not quiet or rich. | Alice is not old. | entailment | ((~generous(susan))=>(~quiet(alice)))&
(((curious(alice)&~generous(alice)))<=>(?[X]:(patient(X))))&
(![X]:((funny(X)<~>~old(X))<=>~funny(X)))&
(![X]:((~generous(X)&curious(X))=>(~kind(X)&quiet(X))))&
(((~strong(susan)&~wise(susan)))=>(?[X]:((~patient(X)&~humble(X)))))&
(![X]:(creative(X)=>~happy(X)))&
(![X]:((~brave(X)&~kind(X))<=>(calm(X)<~>generous(X))))&
(![X]:((~happy(X)&~wise(X))=>(wise(X)|curious(X))))&
(![X]:((~humble(X)&strong(X))<=>(funny(X)<~>happy(X))))&
(![X]:(funny(X)<=>(quiet(X)&brave(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((curious(alice))=>(?[X]:((patient(X)|~creative(X)))))&
((~humble(fred))=>(?[X]:((~calm(X)<~>~patient(X)))))&
(((happy(john)|kind(john)))<=>(?[X]:(creative(X))))&
(((brave(fred)|~curious(fred)))<=>(?[X]:((happy(X)&~kind(X)))))&
(![X]:((~kind(X)<~>~strong(X))=>(~tall(X)&creative(X))))&
(?[X]:((rich(X)&tall(X))))&
((quiet(lucy)<~>~happy(lucy)))&
((creative(fred)&curious(fred)))&
(?[X]:((patient(X)<~>humble(X))))&
((quiet(john)<~>~happy(john)))&
(?[X]:((happy(X)&~funny(X))))&
(~kind(lucy))&
(?[X]:((~quiet(X)<~>rich(X)))) | ~old(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8342254315024035595813147
% SZS output start Proof for 8342254315024035595813147
3. ! [X0] : ((funny(X0) <~> ~old(X0)) <=> ~funny(X0)) [input p2]
25. old(alice) [input hypothesis]
41. ! [X0] : ((((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | funny(X0)) & (~funny(X0) | ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0))))) [nnf transformation 3]
85. ~funny(X0) | ~old(X0) | ~funny(X0) [cnf transformation 41]
87. ~old(X0) | funny(X0) | funny(X0) [cnf transformation 41]
139. old(alice) [cnf transformation 25]
140. ~funny(X0) | ~old(X0) [duplicate literal removal 85]
141. ~old(X0) | funny(X0) [duplicate literal removal 87]
169. ~old(X0) [subsumption resolution 140,141]
288. $false [subsumption resolution 139,169]
% SZS output end Proof for 8342254315024035595813147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or wise is either kind or rich and vice versa.
If someone is either not kind or wise then someone is calm and vice versa.
If someone is not happy then someone is creative or brave and vice versa.
If john is both happy and creative then fred is not humble or not calm and vice versa.
If mary is not generous then john is not patient.
If someone is both not calm and rich then someone is not generous or tall.
Everyone who is both brave and wise is not wise and vice versa.
Everyone who is calm is quiet or kind and vice versa.
Everyone who is both not strong and kind is both rich and tall and vice versa.
Everyone who is both not kind and tall is both not curious and creative.
Everyone who is both not curious and not kind is not brave or humble and vice versa.
Everyone who is rich or not patient is either wise or kind and vice versa.
If someone is curious then fred is not funny.
If fred is both not quiet and not old then someone is either not quiet or not happy and vice versa.
Everyone who is not tall is not funny or funny and vice versa.
Everyone who is either not patient or not kind is rich.
Someone is not curious.
Someone is both strong and not rich.
Alice is either not generous or not creative.
John is not curious or brave.
Alice is both not quiet and not calm.
Someone is either kind or not quiet.
Alice is generous. | Mary is not creative. | neutral | (![X]:((~curious(X)<~>wise(X))<=>(kind(X)<~>rich(X))))&
((?[X]:((~kind(X)<~>wise(X))))<=>(?[X]:(calm(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((creative(X)|brave(X)))))&
(((happy(john)&creative(john)))<=>((~humble(fred)|~calm(fred))))&
((~generous(mary))=>(~patient(john)))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:((~generous(X)|tall(X)))))&
(![X]:((brave(X)&wise(X))<=>~wise(X)))&
(![X]:(calm(X)<=>(quiet(X)|kind(X))))&
(![X]:((~strong(X)&kind(X))<=>(rich(X)&tall(X))))&
(![X]:((~kind(X)&tall(X))=>(~curious(X)&creative(X))))&
(![X]:((~curious(X)&~kind(X))<=>(~brave(X)|humble(X))))&
(![X]:((rich(X)|~patient(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(curious(X)))=>(~funny(fred)))&
(((~quiet(fred)&~old(fred)))<=>(?[X]:((~quiet(X)<~>~happy(X)))))&
(![X]:(~tall(X)<=>(~funny(X)|funny(X))))&
(![X]:((~patient(X)<~>~kind(X))=>rich(X)))&
(?[X]:(~curious(X)))&
(?[X]:((strong(X)&~rich(X))))&
((~generous(alice)<~>~creative(alice)))&
((~curious(john)|brave(john)))&
((~quiet(alice)&~calm(alice)))&
(?[X]:((kind(X)<~>~quiet(X))))&
(generous(alice)) | ~creative(mary) | [] | null | 0 |
Everyone who is not wise or patient is happy and vice versa.
Everyone who is not old or not quiet is both old and not humble and vice versa.
Everyone who is either not quiet or wise is both curious and generous.
Everyone who is kind or happy is not rich or curious and vice versa.
Everyone who is not patient or funny is rich or strong and vice versa.
Everyone who is either funny or wise is both not old and quiet.
Everyone who is both old and not strong is both not calm and not funny.
Everyone who is rich is both funny and creative.
If alice is not patient then mary is both not generous and quiet.
Everyone who is either creative or patient is not calm or not old.
Everyone who is not quiet is both rich and not strong and vice versa.
Everyone who is generous is either not old or quiet.
If mary is rich or humble then someone is humble and vice versa.
If someone is either not generous or not kind then someone is funny or tall and vice versa.
Everyone who is either not rich or not brave is both generous and not humble and vice versa.
Everyone who is kind or not creative is both not patient and not rich.
Susan is funny.
Alice is either quiet or not funny.
Mary is curious.
Fred is not kind.
Fred is rich or not curious.
Someone is tall. | Alice is generous. | entailment | (![X]:((~wise(X)|patient(X))<=>happy(X)))&
(![X]:((~old(X)|~quiet(X))<=>(old(X)&~humble(X))))&
(![X]:((~quiet(X)<~>wise(X))=>(curious(X)&generous(X))))&
(![X]:((kind(X)|happy(X))<=>(~rich(X)|curious(X))))&
(![X]:((~patient(X)|funny(X))<=>(rich(X)|strong(X))))&
(![X]:((funny(X)<~>wise(X))=>(~old(X)&quiet(X))))&
(![X]:((old(X)&~strong(X))=>(~calm(X)&~funny(X))))&
(![X]:(rich(X)=>(funny(X)&creative(X))))&
((~patient(alice))=>((~generous(mary)&quiet(mary))))&
(![X]:((creative(X)<~>patient(X))=>(~calm(X)|~old(X))))&
(![X]:(~quiet(X)<=>(rich(X)&~strong(X))))&
(![X]:(generous(X)=>(~old(X)<~>quiet(X))))&
(((rich(mary)|humble(mary)))<=>(?[X]:(humble(X))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>(?[X]:((funny(X)|tall(X)))))&
(![X]:((~rich(X)<~>~brave(X))<=>(generous(X)&~humble(X))))&
(![X]:((kind(X)|~creative(X))=>(~patient(X)&~rich(X))))&
(funny(susan))&
((quiet(alice)<~>~funny(alice)))&
(curious(mary))&
(~kind(fred))&
((rich(fred)|~curious(fred)))&
(?[X]:(tall(X))) | generous(alice) | [
"p1",
"p2",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3831876733958423387165353
% SZS output start Proof for 3831876733958423387165353
2. ! [X0] : ((~quiet(X0) | ~old(X0)) <=> (~humble(X0) & old(X0))) [input p1]
3. ! [X0] : ((~quiet(X0) <~> wise(X0)) => (generous(X0) & curious(X0))) [input p2]
6. ! [X0] : ((funny(X0) <~> wise(X0)) => (quiet(X0) & ~old(X0))) [input p5]
18. quiet(alice) <~> ~funny(alice) [input p17]
23. ~generous(alice) [input hypothesis]
29. ! [X0] : ((generous(X0) & curious(X0)) | (~quiet(X0) <=> wise(X0))) [ennf transformation 3]
30. ! [X0] : ((quiet(X0) & ~old(X0)) | (funny(X0) <=> wise(X0))) [ennf transformation 6]
39. ! [X0] : (((~quiet(X0) | ~old(X0)) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | (quiet(X0) & old(X0)))) [nnf transformation 2]
40. ! [X0] : ((~quiet(X0) | ~old(X0) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | (quiet(X0) & old(X0)))) [flattening 39]
41. ! [X0] : ((generous(X0) & curious(X0)) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) [nnf transformation 29]
46. ! [X0] : ((quiet(X0) & ~old(X0)) | ((funny(X0) | ~wise(X0)) & (wise(X0) | ~funny(X0)))) [nnf transformation 30]
62. (funny(alice) | ~quiet(alice)) & (~funny(alice) | quiet(alice)) [nnf transformation 18]
68. old(X0) | old(X0) [cnf transformation 40]
75. generous(X0) | wise(X0) | quiet(X0) [cnf transformation 41]
76. ~quiet(X0) | generous(X0) | ~wise(X0) [cnf transformation 41]
85. ~old(X0) | wise(X0) | ~funny(X0) [cnf transformation 46]
86. ~old(X0) | funny(X0) | ~wise(X0) [cnf transformation 46]
116. ~funny(alice) | quiet(alice) [cnf transformation 62]
117. funny(alice) | ~quiet(alice) [cnf transformation 62]
122. ~generous(alice) [cnf transformation 23]
123. old(X0) [duplicate literal removal 68]
125. ~wise(X0) | funny(X0) [subsumption resolution 86,123]
126. ~funny(X0) | wise(X0) [subsumption resolution 85,123]
196. 16 <=> quiet(alice) [avatar definition]
197. quiet(alice) <- (16) [avatar component clause 196]
198. ~quiet(alice) <- (~16) [avatar component clause 196]
200. 17 <=> funny(alice) [avatar definition]
201. ~funny(alice) <- (~17) [avatar component clause 200]
202. funny(alice) <- (17) [avatar component clause 200]
203. ~16 | 17 [avatar split clause 117,200,196]
204. 16 | ~17 [avatar split clause 116,200,196]
252. wise(alice) | quiet(alice) [resolution 75,122]
256. wise(alice) <- (~16) [subsumption resolution 252,198]
277. funny(alice) <- (~16) [resolution 256,125]
278. $false <- (~16, ~17) [subsumption resolution 277,201]
279. 16 | 17 [avatar contradiction clause 278]
280. generous(alice) | ~wise(alice) <- (16) [resolution 197,76]
282. ~wise(alice) <- (16) [subsumption resolution 280,122]
284. wise(alice) <- (17) [resolution 202,126]
285. $false <- (16, 17) [subsumption resolution 284,282]
286. ~16 | ~17 [avatar contradiction clause 285]
287. $false [avatar sat refutation 203,204,279,286]
% SZS output end Proof for 3831876733958423387165353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then paul is not strong and vice versa.
If john is brave then lucy is either not rich or generous and vice versa.
If someone is not old then someone is either happy or not wise and vice versa.
If mary is both creative and not curious then someone is either not rich or not brave.
Everyone who is not patient or not quiet is quiet or calm and vice versa.
If someone is rich or not kind then someone is old.
Everyone who is wise is not humble and vice versa.
Everyone who is not strong or not wise is both funny and patient.
Everyone who is both funny and not creative is not wise or not old and vice versa.
If mary is creative then someone is not brave and vice versa.
Everyone who is tall is both not happy and happy and vice versa.
Everyone who is quiet is either not creative or patient.
Everyone who is not old is either not strong or not happy.
Everyone who is not old is either happy or humble.
Everyone who is not generous or not rich is quiet and vice versa.
Everyone who is quiet or not creative is either not creative or happy and vice versa.
Someone is not rich or not kind.
Alice is both quiet and not patient.
Someone is calm or not old.
Lucy is either kind or not kind.
Someone is wise or funny.
Someone is either patient or funny. | Alice is funny. | contradiction | ((?[X]:(old(X)))<=>(~strong(paul)))&
((brave(john))<=>((~rich(lucy)<~>generous(lucy))))&
((?[X]:(~old(X)))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(((creative(mary)&~curious(mary)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(quiet(X)|calm(X))))&
((?[X]:((rich(X)|~kind(X))))=>(?[X]:(old(X))))&
(![X]:(wise(X)<=>~humble(X)))&
(![X]:((~strong(X)|~wise(X))=>(funny(X)&patient(X))))&
(![X]:((funny(X)&~creative(X))<=>(~wise(X)|~old(X))))&
((creative(mary))<=>(?[X]:(~brave(X))))&
(![X]:(tall(X)<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~creative(X)<~>patient(X))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|~rich(X))<=>quiet(X)))&
(![X]:((quiet(X)|~creative(X))<=>(~creative(X)<~>happy(X))))&
(?[X]:((~rich(X)|~kind(X))))&
((quiet(alice)&~patient(alice)))&
(?[X]:((calm(X)|~old(X))))&
((kind(lucy)<~>~kind(lucy)))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:((patient(X)<~>funny(X)))) | funny(alice) | [
"p4",
"p6",
"p7",
"p8",
"p11",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5657914958529655767749093
% SZS output start Proof for 5657914958529655767749093
5. ! [X0] : ((~quiet(X0) | ~patient(X0)) <=> (calm(X0) | quiet(X0))) [input p4]
7. ! [X0] : (wise(X0) <=> ~humble(X0)) [input p6]
8. ! [X0] : ((~wise(X0) | ~strong(X0)) => (patient(X0) & funny(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~old(X0) | ~wise(X0))) [input p8]
12. ! [X0] : (quiet(X0) => (~creative(X0) <~> patient(X0))) [input p11]
14. ! [X0] : (~old(X0) => (happy(X0) <~> humble(X0))) [input p13]
16. ! [X0] : ((~creative(X0) | quiet(X0)) <=> (~creative(X0) <~> happy(X0))) [input p15]
18. ~patient(alice) & quiet(alice) [input p17]
23. funny(alice) [input hypothesis]
28. ! [X0] : ((patient(X0) & funny(X0)) | (wise(X0) & strong(X0))) [ennf transformation 8]
29. ! [X0] : ((~creative(X0) <~> patient(X0)) | ~quiet(X0)) [ennf transformation 12]
31. ! [X0] : ((happy(X0) <~> humble(X0)) | old(X0)) [ennf transformation 14]
42. ! [X0] : (((~quiet(X0) | ~patient(X0)) | (~calm(X0) & ~quiet(X0))) & ((calm(X0) | quiet(X0)) | (quiet(X0) & patient(X0)))) [nnf transformation 5]
43. ! [X0] : ((~quiet(X0) | ~patient(X0) | (~calm(X0) & ~quiet(X0))) & (calm(X0) | quiet(X0) | (quiet(X0) & patient(X0)))) [flattening 42]
47. ! [X0] : ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0))) [nnf transformation 7]
48. ! [X0] : (((~creative(X0) & funny(X0)) | (old(X0) & wise(X0))) & ((~old(X0) | ~wise(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 9]
49. ! [X0] : (((~creative(X0) & funny(X0)) | (old(X0) & wise(X0))) & (~old(X0) | ~wise(X0) | creative(X0) | ~funny(X0))) [flattening 48]
54. ! [X0] : (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | ~quiet(X0)) [nnf transformation 29]
56. ! [X0] : (((~humble(X0) | ~happy(X0)) & (humble(X0) | happy(X0))) | old(X0)) [nnf transformation 31]
59. ! [X0] : (((~creative(X0) | quiet(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [nnf transformation 16]
60. ! [X0] : ((~creative(X0) | quiet(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [flattening 59]
83. ~quiet(X0) | ~patient(X0) | ~quiet(X0) [cnf transformation 43]
87. ~humble(X0) | ~wise(X0) [cnf transformation 47]
92. patient(X0) | wise(X0) [cnf transformation 28]
93. ~funny(X0) | ~wise(X0) | creative(X0) | ~old(X0) [cnf transformation 49]
100. patient(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 54]
104. humble(X0) | happy(X0) | old(X0) [cnf transformation 56]
112. ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 60]
114. ~creative(X0) | quiet(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 60]
116. quiet(alice) [cnf transformation 18]
117. ~patient(alice) [cnf transformation 18]
124. funny(alice) [cnf transformation 23]
125. ~happy(X0) | creative(X0) [duplicate literal removal 112]
126. ~creative(X0) | quiet(X0) | ~happy(X0) [duplicate literal removal 114]
128. ~quiet(X0) | ~patient(X0) [duplicate literal removal 83]
208. ~quiet(X0) | ~creative(X0) [subsumption resolution 100,128]
209. ~creative(X0) | ~happy(X0) [subsumption resolution 126,208]
210. ~happy(X0) [subsumption resolution 125,209]
247. wise(alice) [resolution 92,117]
254. ~creative(alice) [resolution 208,116]
268. happy(X0) | old(X0) | ~wise(X0) [resolution 104,87]
269. ~wise(X0) | old(X0) [subsumption resolution 268,210]
286. ~wise(alice) | creative(alice) | ~old(alice) [resolution 93,124]
290. creative(alice) | ~old(alice) [subsumption resolution 286,247]
291. ~old(alice) [subsumption resolution 290,254]
296. old(alice) [resolution 269,247]
298. $false [subsumption resolution 296,291]
% SZS output end Proof for 5657914958529655767749093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and humble is brave or patient.
If someone is both happy and not kind then someone is not brave.
If alice is either not curious or funny then mary is not kind or not brave.
If lucy is strong or kind then someone is either strong or humble and vice versa.
If someone is both calm and quiet then mary is either not old or not curious and vice versa.
If someone is both not strong and not humble then someone is either not calm or not wise and vice versa.
If someone is both calm and not brave then someone is not curious or quiet.
If paul is rich or old then alice is either not brave or not kind and vice versa.
If someone is generous or not tall then fred is either calm or not strong and vice versa.
Everyone who is not wise or calm is wise and vice versa.
If someone is both brave and not strong then someone is either not happy or tall and vice versa.
Everyone who is either not brave or not patient is quiet.
Everyone who is wise is either not curious or tall and vice versa.
Everyone who is not wise is happy and vice versa.
Everyone who is happy is not quiet and vice versa.
If someone is brave or old then lucy is not old or wise and vice versa.
Someone is both creative and brave.
Someone is both not happy and strong.
Fred is wise.
Paul is both tall and humble.
Someone is either brave or curious. | Lucy is not calm. | contradiction | (![X]:((~humble(X)&humble(X))=>(brave(X)|patient(X))))&
((?[X]:((happy(X)&~kind(X))))=>(?[X]:(~brave(X))))&
(((~curious(alice)<~>funny(alice)))=>((~kind(mary)|~brave(mary))))&
(((strong(lucy)|kind(lucy)))<=>(?[X]:((strong(X)<~>humble(X)))))&
((?[X]:((calm(X)&quiet(X))))<=>((~old(mary)<~>~curious(mary))))&
((?[X]:((~strong(X)&~humble(X))))<=>(?[X]:((~calm(X)<~>~wise(X)))))&
((?[X]:((calm(X)&~brave(X))))=>(?[X]:((~curious(X)|quiet(X)))))&
(((rich(paul)|old(paul)))<=>((~brave(alice)<~>~kind(alice))))&
((?[X]:((generous(X)|~tall(X))))<=>((calm(fred)<~>~strong(fred))))&
(![X]:((~wise(X)|calm(X))<=>wise(X)))&
((?[X]:((brave(X)&~strong(X))))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:((~brave(X)<~>~patient(X))=>quiet(X)))&
(![X]:(wise(X)<=>(~curious(X)<~>tall(X))))&
(![X]:(~wise(X)<=>happy(X)))&
(![X]:(happy(X)<=>~quiet(X)))&
((?[X]:((brave(X)|old(X))))<=>((~old(lucy)|wise(lucy))))&
(?[X]:((creative(X)&brave(X))))&
(?[X]:((~happy(X)&strong(X))))&
(wise(fred))&
((tall(paul)&humble(paul)))&
(?[X]:((brave(X)<~>curious(X)))) | ~calm(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1667141663554386704945543
% SZS output start Proof for 1667141663554386704945543
10. ! [X0] : ((calm(X0) | ~wise(X0)) <=> wise(X0)) [input p9]
22. ~calm(lucy) [input hypothesis]
62. ! [X0] : (((calm(X0) | ~wise(X0)) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [nnf transformation 10]
63. ! [X0] : ((calm(X0) | ~wise(X0) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [flattening 62]
120. wise(X0) | wise(X0) [cnf transformation 63]
122. calm(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 63]
151. ~calm(lucy) [cnf transformation 22]
152. wise(X0) [duplicate literal removal 120]
153. calm(X0) | ~wise(X0) [duplicate literal removal 122]
242. 20 <=> ! [X1] : (~wise(X1) | calm(X1)) [avatar definition]
243. ~wise(X1) | calm(X1) <- (20) [avatar component clause 242]
326. 20 [avatar split clause 153,242]
390. calm(X1) <- (20) [subsumption resolution 243,152]
401. $false <- (20) [resolution 390,151]
404. ~20 [avatar contradiction clause 401]
405. $false [avatar sat refutation 326,404]
% SZS output end Proof for 1667141663554386704945543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is happy then mary is wise and vice versa. Everyone who is curious is either happy or not patient. If someone is both strong and not quiet then someone is either not brave or not old. Everyone who is both kind and not strong is kind. Everyone who is old is creative or patient. If paul is not quiet or quiet then someone is happy and vice versa. Everyone who is either not wise or patient is funny or not brave and vice versa. Everyone who is not calm is both not creative and humble. Everyone who is either not wise or not happy is humble or rich and vice versa. Everyone who is wise is either curious or not rich. If someone is kind then lucy is either creative or not brave. If susan is not brave then susan is funny and vice versa. Everyone who is not kind is either brave or not patient. If fred is not generous then mary is kind or creative. Everyone who is not funny or wise is funny and vice versa. Everyone who is not humble is either not tall or not calm and vice versa. Paul is either happy or not happy. Someone is both not rich and patient. Paul is either not creative or not rich. Someone is either quiet or creative. Someone is not kind. John is both not brave and kind. Someone is either not strong or not brave. | Fred is rich. | contradiction | ((happy(john))<=>(wise(mary)))&
(![X]:(curious(X)=>(happy(X)<~>~patient(X))))&
((?[X]:((strong(X)&~quiet(X))))=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((kind(X)&~strong(X))=>kind(X)))&
(![X]:(old(X)=>(creative(X)|patient(X))))&
(((~quiet(paul)|quiet(paul)))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)<~>patient(X))<=>(funny(X)|~brave(X))))&
(![X]:(~calm(X)=>(~creative(X)&humble(X))))&
(![X]:((~wise(X)<~>~happy(X))<=>(humble(X)|rich(X))))&
(![X]:(wise(X)=>(curious(X)<~>~rich(X))))&
((?[X]:(kind(X)))=>((creative(lucy)<~>~brave(lucy))))&
((~brave(susan))<=>(funny(susan)))&
(![X]:(~kind(X)=>(brave(X)<~>~patient(X))))&
((~generous(fred))=>((kind(mary)|creative(mary))))&
(![X]:((~funny(X)|wise(X))<=>funny(X)))&
(![X]:(~humble(X)<=>(~tall(X)<~>~calm(X))))&
((happy(paul)<~>~happy(paul)))&
(?[X]:((~rich(X)&patient(X))))&
((~creative(paul)<~>~rich(paul)))&
(?[X]:((quiet(X)<~>creative(X))))&
(?[X]:(~kind(X)))&
((~brave(john)&kind(john)))&
(?[X]:((~strong(X)<~>~brave(X)))) | rich(fred) | [
"p1",
"p6",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5546971127083996262157605
% SZS output start Proof for 5546971127083996262157605
2. ! [X0] : (curious(X0) => (happy(X0) <~> ~patient(X0))) [input p1]
7. ! [X0] : ((~wise(X0) <~> patient(X0)) <=> (~brave(X0) | funny(X0))) [input p6]
9. ! [X0] : ((~wise(X0) <~> ~happy(X0)) <=> (rich(X0) | humble(X0))) [input p8]
10. ! [X0] : (wise(X0) => (curious(X0) <~> ~rich(X0))) [input p9]
15. ! [X0] : ((wise(X0) | ~funny(X0)) <=> funny(X0)) [input p14]
24. rich(fred) [input hypothesis]
27. ! [X0] : ((happy(X0) <~> ~patient(X0)) | ~curious(X0)) [ennf transformation 2]
34. ! [X0] : ((curious(X0) <~> ~rich(X0)) | ~wise(X0)) [ennf transformation 10]
38. ! [X0] : (((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | ~curious(X0)) [nnf transformation 27]
48. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (brave(X0) & ~funny(X0))) & ((~brave(X0) | funny(X0)) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [nnf transformation 7]
49. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (brave(X0) & ~funny(X0))) & (~brave(X0) | funny(X0) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [flattening 48]
50. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (~rich(X0) & ~humble(X0))) & ((rich(X0) | humble(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [nnf transformation 9]
51. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (~rich(X0) & ~humble(X0))) & (rich(X0) | humble(X0) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [flattening 50]
52. ! [X0] : (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | ~wise(X0)) [nnf transformation 34]
56. ! [X0] : (((wise(X0) | ~funny(X0)) | ~funny(X0)) & (funny(X0) | (~wise(X0) & funny(X0)))) [nnf transformation 15]
57. ! [X0] : ((wise(X0) | ~funny(X0) | ~funny(X0)) & (funny(X0) | (~wise(X0) & funny(X0)))) [flattening 56]
73. ~patient(X0) | happy(X0) | ~curious(X0) [cnf transformation 38]
84. ~funny(X0) | ~wise(X0) | patient(X0) [cnf transformation 49]
93. ~rich(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 51]
96. ~rich(X0) | curious(X0) | ~wise(X0) [cnf transformation 52]
104. funny(X0) | funny(X0) [cnf transformation 57]
106. wise(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 57]
124. rich(fred) [cnf transformation 24]
125. funny(X0) [duplicate literal removal 104]
126. ~funny(X0) | wise(X0) [duplicate literal removal 106]
216. wise(X0) [resolution 126,125]
230. ~wise(X0) | patient(X0) [resolution 84,125]
231. patient(X0) [subsumption resolution 230,216]
233. ~curious(X0) | happy(X0) [resolution 231,73]
239. ~wise(fred) | ~happy(fred) [resolution 93,124]
240. ~happy(fred) [subsumption resolution 239,216]
245. curious(fred) | ~wise(fred) [resolution 96,124]
246. curious(fred) [subsumption resolution 245,216]
247. happy(fred) [resolution 246,233]
249. $false [subsumption resolution 247,240]
% SZS output end Proof for 5546971127083996262157605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.014 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not tall is tall and vice versa.
If someone is both not strong and not kind then susan is either not generous or happy and vice versa.
If susan is either not curious or not creative then paul is either not generous or brave and vice versa.
Everyone who is both quiet and not happy is not tall and vice versa.
Everyone who is either brave or quiet is not happy.
If someone is not kind or curious then someone is quiet and vice versa.
Everyone who is generous or wise is both humble and not creative and vice versa.
If someone is both not creative and patient then lucy is both not strong and rich and vice versa.
If paul is not kind or funny then paul is either not curious or not old and vice versa.
Everyone who is happy or quiet is rich.
Everyone who is both not kind and calm is both funny and not patient and vice versa.
If someone is both tall and patient then alice is tall or humble.
If mary is both strong and creative then someone is either not quiet or generous.
If someone is not generous or creative then someone is both not brave and not curious and vice versa.
If john is both not rich and not generous then mary is either not tall or not strong.
If fred is happy or not funny then john is not kind and vice versa.
Someone is rich or not rich.
Mary is not strong.
Alice is not creative.
Someone is patient.
Someone is both patient and not happy.
Paul is happy.
Someone is strong. | John is not calm. | neutral | (![X]:((~generous(X)|~tall(X))<=>tall(X)))&
((?[X]:((~strong(X)&~kind(X))))<=>((~generous(susan)<~>happy(susan))))&
(((~curious(susan)<~>~creative(susan)))<=>((~generous(paul)<~>brave(paul))))&
(![X]:((quiet(X)&~happy(X))<=>~tall(X)))&
(![X]:((brave(X)<~>quiet(X))=>~happy(X)))&
((?[X]:((~kind(X)|curious(X))))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)|wise(X))<=>(humble(X)&~creative(X))))&
((?[X]:((~creative(X)&patient(X))))<=>((~strong(lucy)&rich(lucy))))&
(((~kind(paul)|funny(paul)))<=>((~curious(paul)<~>~old(paul))))&
(![X]:((happy(X)|quiet(X))=>rich(X)))&
(![X]:((~kind(X)&calm(X))<=>(funny(X)&~patient(X))))&
((?[X]:((tall(X)&patient(X))))=>((tall(alice)|humble(alice))))&
(((strong(mary)&creative(mary)))=>(?[X]:((~quiet(X)<~>generous(X)))))&
((?[X]:((~generous(X)|creative(X))))<=>(?[X]:((~brave(X)&~curious(X)))))&
(((~rich(john)&~generous(john)))=>((~tall(mary)<~>~strong(mary))))&
(((happy(fred)|~funny(fred)))<=>(~kind(john)))&
(?[X]:((rich(X)|~rich(X))))&
(~strong(mary))&
(~creative(alice))&
(?[X]:(patient(X)))&
(?[X]:((patient(X)&~happy(X))))&
(happy(paul))&
(?[X]:(strong(X))) | ~calm(john) | [] | null | 0 |
If someone is both not calm and not creative then susan is tall and vice versa.
Everyone who is both curious and kind is patient or happy.
Everyone who is either quiet or humble is happy.
If someone is both quiet and not rich then mary is either patient or not quiet and vice versa.
If someone is either not strong or wise then susan is both not happy and generous.
Everyone who is not generous or not wise is both not happy and brave.
Everyone who is either generous or funny is both not rich and not curious and vice versa.
If someone is funny then someone is both strong and not creative.
Everyone who is either not rich or funny is both creative and not tall.
Everyone who is not kind or happy is not funny or not curious.
Everyone who is either tall or kind is not patient.
Everyone who is either kind or not humble is either kind or patient.
Everyone who is either not strong or old is both not patient and wise and vice versa.
Everyone who is humble is both kind and curious.
If alice is not funny then someone is both not funny and not rich and vice versa.
Everyone who is both generous and not brave is either happy or curious.
Someone is both happy and not curious.
John is not old or wise.
Someone is curious or not calm.
Susan is not creative or rich.
Alice is rich or not happy.
John is rich or not tall.
Someone is rich. | Mary is not humble. | entailment | ((?[X]:((~calm(X)&~creative(X))))<=>(tall(susan)))&
(![X]:((curious(X)&kind(X))=>(patient(X)|happy(X))))&
(![X]:((quiet(X)<~>humble(X))=>happy(X)))&
((?[X]:((quiet(X)&~rich(X))))<=>((patient(mary)<~>~quiet(mary))))&
((?[X]:((~strong(X)<~>wise(X))))=>((~happy(susan)&generous(susan))))&
(![X]:((~generous(X)|~wise(X))=>(~happy(X)&brave(X))))&
(![X]:((generous(X)<~>funny(X))<=>(~rich(X)&~curious(X))))&
((?[X]:(funny(X)))=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~rich(X)<~>funny(X))=>(creative(X)&~tall(X))))&
(![X]:((~kind(X)|happy(X))=>(~funny(X)|~curious(X))))&
(![X]:((tall(X)<~>kind(X))=>~patient(X)))&
(![X]:((kind(X)<~>~humble(X))=>(kind(X)<~>patient(X))))&
(![X]:((~strong(X)<~>old(X))<=>(~patient(X)&wise(X))))&
(![X]:(humble(X)=>(kind(X)&curious(X))))&
((~funny(alice))<=>(?[X]:((~funny(X)&~rich(X)))))&
(![X]:((generous(X)&~brave(X))=>(happy(X)<~>curious(X))))&
(?[X]:((happy(X)&~curious(X))))&
((~old(john)|wise(john)))&
(?[X]:((curious(X)|~calm(X))))&
((~creative(susan)|rich(susan)))&
((rich(alice)|~happy(alice)))&
((rich(john)|~tall(john)))&
(?[X]:(rich(X))) | ~humble(mary) | [
"p1",
"p5",
"p6",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1702633079104900595447273
% SZS output start Proof for 1702633079104900595447273
2. ! [X0] : ((kind(X0) & curious(X0)) => (happy(X0) | patient(X0))) [input p1]
6. ! [X0] : ((~wise(X0) | ~generous(X0)) => (brave(X0) & ~happy(X0))) [input p5]
7. ! [X0] : ((generous(X0) <~> funny(X0)) <=> (~curious(X0) & ~rich(X0))) [input p6]
10. ! [X0] : ((happy(X0) | ~kind(X0)) => (~curious(X0) | ~funny(X0))) [input p9]
12. ! [X0] : ((kind(X0) <~> ~humble(X0)) => (kind(X0) <~> patient(X0))) [input p11]
14. ! [X0] : (humble(X0) => (curious(X0) & kind(X0))) [input p13]
24. humble(mary) [input hypothesis]
26. ! [X0] : ((~wise(X0) | ~generous(X0)) => ~happy(X0)) [pure predicate removal 6]
28. ! [X0] : ((happy(X0) | patient(X0)) | (~kind(X0) | ~curious(X0))) [ennf transformation 2]
29. ! [X0] : (happy(X0) | patient(X0) | ~kind(X0) | ~curious(X0)) [flattening 28]
32. ! [X0] : (~happy(X0) | (wise(X0) & generous(X0))) [ennf transformation 26]
35. ! [X0] : ((~curious(X0) | ~funny(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 10]
36. ! [X0] : (~curious(X0) | ~funny(X0) | (~happy(X0) & kind(X0))) [flattening 35]
38. ! [X0] : ((kind(X0) <~> patient(X0)) | (kind(X0) <=> ~humble(X0))) [ennf transformation 12]
39. ! [X0] : ((curious(X0) & kind(X0)) | ~humble(X0)) [ennf transformation 14]
50. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (curious(X0) | rich(X0))) & ((~curious(X0) & ~rich(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [nnf transformation 7]
51. ! [X0] : ((((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | curious(X0) | rich(X0)) & ((~curious(X0) & ~rich(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0))))) [flattening 50]
57. ! [X0] : (((~patient(X0) | ~kind(X0)) & (patient(X0) | kind(X0))) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) [nnf transformation 38]
73. ~kind(X0) | patient(X0) | happy(X0) | ~curious(X0) [cnf transformation 29]
86. ~happy(X0) | generous(X0) [cnf transformation 32]
90. ~generous(X0) | funny(X0) | ~curious(X0) [cnf transformation 51]
101. ~funny(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 36]
106. ~patient(X0) | ~kind(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 57]
114. ~humble(X0) | kind(X0) [cnf transformation 39]
115. ~humble(X0) | curious(X0) [cnf transformation 39]
127. humble(mary) [cnf transformation 24]
129. ~humble(X0) | ~kind(X0) | ~patient(X0) [duplicate literal removal 106]
153. 6 <=> patient(mary) [avatar definition]
154. ~patient(mary) <- (~6) [avatar component clause 153]
269. kind(mary) [resolution 114,127]
270. curious(mary) [resolution 115,127]
316. 34 <=> funny(mary) [avatar definition]
317. ~funny(mary) <- (~34) [avatar component clause 316]
318. funny(mary) <- (34) [avatar component clause 316]
395. ~curious(mary) | ~happy(mary) <- (34) [resolution 318,101]
401. ~happy(mary) <- (34) [subsumption resolution 395,270]
415. 47 <=> generous(mary) [avatar definition]
417. generous(mary) <- (47) [avatar component clause 415]
451. ~kind(mary) | ~patient(mary) [resolution 129,127]
454. ~patient(mary) [subsumption resolution 451,269]
458. ~6 [avatar split clause 454,153]
467. patient(mary) | happy(mary) | ~curious(mary) [resolution 73,269]
469. happy(mary) | ~curious(mary) <- (~6) [subsumption resolution 467,154]
470. ~curious(mary) <- (~6, 34) [subsumption resolution 469,401]
471. $false <- (~6, 34) [subsumption resolution 470,270]
472. 6 | ~34 [avatar contradiction clause 471]
476. happy(mary) <- (~6) [subsumption resolution 469,270]
496. generous(mary) <- (~6) [resolution 476,86]
615. funny(mary) | ~curious(mary) <- (47) [resolution 417,90]
617. ~curious(mary) <- (~34, 47) [subsumption resolution 615,317]
618. $false <- (~34, 47) [subsumption resolution 617,270]
619. 34 | ~47 [avatar contradiction clause 618]
623. 47 | 6 [avatar split clause 496,153,415]
624. $false [avatar sat refutation 458,472,619,623]
% SZS output end Proof for 1702633079104900595447273
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and creative then fred is either quiet or kind and vice versa.
If someone is either quiet or not calm then someone is wise.
Everyone who is either generous or humble is rich or curious.
Everyone who is either creative or generous is not humble.
If someone is either strong or generous then fred is either not happy or creative and vice versa.
If someone is kind or generous then someone is both not humble and not brave.
Everyone who is old or not brave is both patient and happy.
Everyone who is either not old or not quiet is either creative or humble.
If someone is both rich and not old then someone is both not patient and rich and vice versa.
Everyone who is happy is either strong or quiet.
Everyone who is both humble and not strong is both not strong and tall and vice versa.
If someone is not funny or funny then someone is both not kind and brave.
Everyone who is either not wise or generous is patient and vice versa.
Everyone who is either not creative or not generous is both old and strong.
Everyone who is not humble or not quiet is either rich or not curious.
If alice is curious then someone is either kind or funny and vice versa.
Someone is old.
Someone is creative.
Someone is both not wise and not quiet.
Someone is funny or calm.
Fred is not happy or not old.
Susan is either patient or curious.
Someone is strong or calm. | Fred is happy. | neutral | ((?[X]:((~tall(X)&creative(X))))<=>((quiet(fred)<~>kind(fred))))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:(wise(X))))&
(![X]:((generous(X)<~>humble(X))=>(rich(X)|curious(X))))&
(![X]:((creative(X)<~>generous(X))=>~humble(X)))&
((?[X]:((strong(X)<~>generous(X))))<=>((~happy(fred)<~>creative(fred))))&
((?[X]:((kind(X)|generous(X))))=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:((old(X)|~brave(X))=>(patient(X)&happy(X))))&
(![X]:((~old(X)<~>~quiet(X))=>(creative(X)<~>humble(X))))&
((?[X]:((rich(X)&~old(X))))<=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:(happy(X)=>(strong(X)<~>quiet(X))))&
(![X]:((humble(X)&~strong(X))<=>(~strong(X)&tall(X))))&
((?[X]:((~funny(X)|funny(X))))=>(?[X]:((~kind(X)&brave(X)))))&
(![X]:((~wise(X)<~>generous(X))<=>patient(X)))&
(![X]:((~creative(X)<~>~generous(X))=>(old(X)&strong(X))))&
(![X]:((~humble(X)|~quiet(X))=>(rich(X)<~>~curious(X))))&
((curious(alice))<=>(?[X]:((kind(X)<~>funny(X)))))&
(?[X]:(old(X)))&
(?[X]:(creative(X)))&
(?[X]:((~wise(X)&~quiet(X))))&
(?[X]:((funny(X)|calm(X))))&
((~happy(fred)|~old(fred)))&
((patient(susan)<~>curious(susan)))&
(?[X]:((strong(X)|calm(X)))) | happy(fred) | [] | null | 0 |
If someone is either quiet or rich then someone is both creative and not calm.
Everyone who is either not brave or not strong is either not generous or not rich and vice versa.
Everyone who is either quiet or not wise is not curious or not quiet and vice versa.
Everyone who is calm or patient is both old and not creative.
Everyone who is not quiet or patient is not patient.
Everyone who is funny is wise.
If someone is either not patient or wise then someone is both not quiet and not old.
If mary is both not curious and tall then someone is old or wise and vice versa.
Everyone who is not curious is funny and vice versa.
If someone is both not tall and wise then lucy is either patient or not curious and vice versa.
If someone is both wise and not curious then someone is both not humble and patient.
If someone is generous or wise then someone is either not quiet or wise and vice versa.
If someone is either not creative or patient then mary is both strong and not strong and vice versa.
If someone is not rich then someone is both generous and not wise and vice versa.
Everyone who is not strong or creative is strong and vice versa.
Susan is either brave or tall.
Someone is generous.
Mary is strong.
Someone is either not patient or brave.
Mary is generous or not tall.
Someone is either not tall or calm. | Mary is not creative. | contradiction | ((?[X]:((quiet(X)<~>rich(X))))=>(?[X]:((creative(X)&~calm(X)))))&
(![X]:((~brave(X)<~>~strong(X))<=>(~generous(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>(~curious(X)|~quiet(X))))&
(![X]:((calm(X)|patient(X))=>(old(X)&~creative(X))))&
(![X]:((~quiet(X)|patient(X))=>~patient(X)))&
(![X]:(funny(X)=>wise(X)))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:((~quiet(X)&~old(X)))))&
(((~curious(mary)&tall(mary)))<=>(?[X]:((old(X)|wise(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
((?[X]:((~tall(X)&wise(X))))<=>((patient(lucy)<~>~curious(lucy))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((~creative(X)<~>patient(X))))<=>((strong(mary)&~strong(mary))))&
((?[X]:(~rich(X)))<=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~strong(X)|creative(X))<=>strong(X)))&
((brave(susan)<~>tall(susan)))&
(?[X]:(generous(X)))&
(strong(mary))&
(?[X]:((~patient(X)<~>brave(X))))&
((generous(mary)|~tall(mary)))&
(?[X]:((~tall(X)<~>calm(X)))) | ~creative(mary) | [
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 418478478938967585668951
% SZS output start Proof for 418478478938967585668951
5. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~patient(X0)) [input p4]
13. ? [X0] : (~creative(X0) <~> patient(X0)) <=> (~strong(mary) & strong(mary)) [input p12]
22. ~creative(mary) [input hypothesis]
31. ! [X0] : (~patient(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 5]
64. (? [X0] : ((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | (strong(mary) | ~strong(mary))) & ((~strong(mary) & strong(mary)) | ! [X0] : ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) [nnf transformation 13]
65. (? [X0] : ((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | strong(mary) | ~strong(mary)) & ((~strong(mary) & strong(mary)) | ! [X0] : ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) [flattening 64]
66. (? [X0] : ((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | strong(mary) | ~strong(mary)) & ((~strong(mary) & strong(mary)) | ! [X1] : ((~creative(X1) | ~patient(X1)) & (patient(X1) | creative(X1)))) [rectify 65]
67. ? [X0] : ((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) => ((~patient(sK7) | creative(sK7)) & (patient(sK7) | ~creative(sK7))) [choice axiom]
68. (((~patient(sK7) | creative(sK7)) & (patient(sK7) | ~creative(sK7))) | strong(mary) | ~strong(mary)) & ((~strong(mary) & strong(mary)) | ! [X1] : ((~creative(X1) | ~patient(X1)) & (patient(X1) | creative(X1)))) [skolemisation 66,67]
108. ~patient(X0) | ~patient(X0) [cnf transformation 31]
134. strong(mary) | patient(X1) | creative(X1) [cnf transformation 68]
136. ~strong(mary) | patient(X1) | creative(X1) [cnf transformation 68]
155. ~creative(mary) [cnf transformation 22]
158. ~patient(X0) [duplicate literal removal 108]
274. ~strong(mary) | creative(X1) [subsumption resolution 136,158]
276. 24 <=> ! [X1] : creative(X1) [avatar definition]
277. creative(X1) <- (24) [avatar component clause 276]
279. 25 <=> strong(mary) [avatar definition]
282. 24 | ~25 [avatar split clause 274,279,276]
283. strong(mary) | creative(X1) [subsumption resolution 134,158]
284. 24 | 25 [avatar split clause 283,279,276]
342. $false <- (24) [resolution 277,155]
343. ~24 [avatar contradiction clause 342]
344. $false [avatar sat refutation 282,284,343]
% SZS output end Proof for 418478478938967585668951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not old or humble then someone is both tall and not curious.
Everyone who is both tall and not patient is either not creative or funny.
If mary is quiet or not happy then susan is either not humble or not generous.
Everyone who is either not calm or funny is not old.
Everyone who is curious or humble is both not old and not creative.
If fred is not creative then fred is calm or not quiet.
If fred is rich then someone is both happy and not tall and vice versa.
Everyone who is creative is both creative and not rich.
If lucy is not kind or not creative then someone is both not quiet and not brave and vice versa.
Everyone who is not brave is both not rich and not creative and vice versa.
Everyone who is either rich or not strong is either generous or strong and vice versa.
Everyone who is either not creative or not quiet is both old and calm.
If susan is both not brave and creative then lucy is either not humble or brave.
Everyone who is tall or calm is both tall and not kind and vice versa.
If alice is both funny and not funny then fred is both not patient and creative and vice versa.
If fred is not kind then john is either old or patient and vice versa.
Someone is kind or not quiet.
John is both not old and tall.
John is happy.
Someone is rich or funny.
Someone is quiet.
Fred is either not old or not humble.
Fred is creative.
Someone is kind. | Fred is generous. | entailment | (((~old(susan)<~>humble(susan)))=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:((tall(X)&~patient(X))=>(~creative(X)<~>funny(X))))&
(((quiet(mary)|~happy(mary)))=>((~humble(susan)<~>~generous(susan))))&
(![X]:((~calm(X)<~>funny(X))=>~old(X)))&
(![X]:((curious(X)|humble(X))=>(~old(X)&~creative(X))))&
((~creative(fred))=>((calm(fred)|~quiet(fred))))&
((rich(fred))<=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:(creative(X)=>(creative(X)&~rich(X))))&
(((~kind(lucy)|~creative(lucy)))<=>(?[X]:((~quiet(X)&~brave(X)))))&
(![X]:(~brave(X)<=>(~rich(X)&~creative(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(generous(X)<~>strong(X))))&
(![X]:((~creative(X)<~>~quiet(X))=>(old(X)&calm(X))))&
(((~brave(susan)&creative(susan)))=>((~humble(lucy)<~>brave(lucy))))&
(![X]:((tall(X)|calm(X))<=>(tall(X)&~kind(X))))&
(((funny(alice)&~funny(alice)))<=>((~patient(fred)&creative(fred))))&
((~kind(fred))<=>((old(john)<~>patient(john))))&
(?[X]:((kind(X)|~quiet(X))))&
((~old(john)&tall(john)))&
(happy(john))&
(?[X]:((rich(X)|funny(X))))&
(?[X]:(quiet(X)))&
((~old(fred)<~>~humble(fred)))&
(creative(fred))&
(?[X]:(kind(X))) | generous(fred) | [
"p7",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 137155481086308290880209
% SZS output start Proof for 137155481086308290880209
8. ! [X0] : (creative(X0) => (~rich(X0) & creative(X0))) [input p7]
11. ! [X0] : ((rich(X0) <~> ~strong(X0)) <=> (generous(X0) <~> strong(X0))) [input p10]
23. creative(fred) [input p22]
25. ~generous(fred) [input hypothesis]
36. ! [X0] : ((~rich(X0) & creative(X0)) | ~creative(X0)) [ennf transformation 8]
57. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0)))) & (((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [nnf transformation 11]
91. ~rich(X0) | ~creative(X0) [cnf transformation 36]
101. strong(X0) | generous(X0) | rich(X0) | strong(X0) [cnf transformation 57]
105. ~strong(X0) | rich(X0) | generous(X0) | ~strong(X0) [cnf transformation 57]
135. creative(fred) [cnf transformation 23]
137. ~generous(fred) [cnf transformation 25]
138. strong(X0) | generous(X0) | rich(X0) [duplicate literal removal 101]
140. ~strong(X0) | rich(X0) | generous(X0) [duplicate literal removal 105]
173. 7 <=> creative(fred) [avatar definition]
175. creative(fred) <- (7) [avatar component clause 173]
189. 11 <=> rich(fred) [avatar definition]
190. ~rich(fred) <- (~11) [avatar component clause 189]
191. rich(fred) <- (11) [avatar component clause 189]
228. rich(X0) | generous(X0) [subsumption resolution 138,140]
283. 7 [avatar split clause 135,173]
294. generous(fred) <- (~11) [resolution 228,190]
298. $false <- (~11) [subsumption resolution 294,137]
299. 11 [avatar contradiction clause 298]
302. ~creative(fred) <- (11) [resolution 191,91]
303. $false <- (7, 11) [subsumption resolution 302,175]
304. ~7 | ~11 [avatar contradiction clause 303]
305. $false [avatar sat refutation 283,299,304]
% SZS output end Proof for 137155481086308290880209
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not funny then mary is curious.
If someone is not funny or not curious then alice is either not curious or not brave.
If someone is patient or creative then mary is either curious or not calm.
Everyone who is calm or old is either not strong or generous.
If john is either humble or strong then someone is funny.
Everyone who is not tall or wise is not wise.
If fred is wise or not strong then paul is strong.
If someone is creative or rich then someone is either calm or not happy and vice versa.
Everyone who is either not tall or not patient is both creative and brave.
If fred is funny or curious then alice is not strong or kind and vice versa.
If someone is humble then someone is either not tall or strong and vice versa.
If someone is brave or tall then alice is both not rich and calm.
If someone is both wise and not patient then someone is not rich or not calm and vice versa.
Everyone who is either not generous or not wise is funny.
Someone is rich or not wise.
John is both not quiet and generous.
Someone is not tall or not quiet.
Alice is either not curious or not old.
Someone is not funny.
Fred is either not curious or not quiet.
Mary is not calm or rich. | Mary is tall. | contradiction | ((?[X]:((brave(X)&~funny(X))))=>(curious(mary)))&
((?[X]:((~funny(X)|~curious(X))))=>((~curious(alice)<~>~brave(alice))))&
((?[X]:((patient(X)|creative(X))))=>((curious(mary)<~>~calm(mary))))&
(![X]:((calm(X)|old(X))=>(~strong(X)<~>generous(X))))&
(((humble(john)<~>strong(john)))=>(?[X]:(funny(X))))&
(![X]:((~tall(X)|wise(X))=>~wise(X)))&
(((wise(fred)|~strong(fred)))=>(strong(paul)))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((calm(X)<~>~happy(X)))))&
(![X]:((~tall(X)<~>~patient(X))=>(creative(X)&brave(X))))&
(((funny(fred)|curious(fred)))<=>((~strong(alice)|kind(alice))))&
((?[X]:(humble(X)))<=>(?[X]:((~tall(X)<~>strong(X)))))&
((?[X]:((brave(X)|tall(X))))=>((~rich(alice)&calm(alice))))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((~rich(X)|~calm(X)))))&
(![X]:((~generous(X)<~>~wise(X))=>funny(X)))&
(?[X]:((rich(X)|~wise(X))))&
((~quiet(john)&generous(john)))&
(?[X]:((~tall(X)|~quiet(X))))&
((~curious(alice)<~>~old(alice)))&
(?[X]:(~funny(X)))&
((~curious(fred)<~>~quiet(fred)))&
((~calm(mary)|rich(mary))) | tall(mary) | [
"p5",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2683670932919322268447721
% SZS output start Proof for 2683670932919322268447721
6. ! [X0] : ((wise(X0) | ~tall(X0)) => ~wise(X0)) [input p5]
12. ? [X0] : (tall(X0) | brave(X0)) => (calm(alice) & ~rich(alice)) [input p11]
13. ? [X0] : (~patient(X0) & wise(X0)) <=> ? [X0] : (~calm(X0) | ~rich(X0)) [input p12]
22. tall(mary) [input hypothesis]
25. ? [X0] : (~patient(X0) & wise(X0)) <=> ? [X1] : (~calm(X1) | ~rich(X1)) [rectify 13]
31. ! [X0] : (~wise(X0) | (~wise(X0) & tall(X0))) [ennf transformation 6]
34. (calm(alice) & ~rich(alice)) | ! [X0] : (~tall(X0) & ~brave(X0)) [ennf transformation 12]
55. (? [X0] : (~patient(X0) & wise(X0)) | ! [X1] : (calm(X1) & rich(X1))) & (? [X1] : (~calm(X1) | ~rich(X1)) | ! [X0] : (patient(X0) | ~wise(X0))) [nnf transformation 25]
56. (? [X0] : (~patient(X0) & wise(X0)) | ! [X1] : (calm(X1) & rich(X1))) & (? [X2] : (~calm(X2) | ~rich(X2)) | ! [X3] : (patient(X3) | ~wise(X3))) [rectify 55]
57. ? [X0] : (~patient(X0) & wise(X0)) => (~patient(sK5) & wise(sK5)) [choice axiom]
58. ? [X2] : (~calm(X2) | ~rich(X2)) => (~calm(sK6) | ~rich(sK6)) [choice axiom]
59. ((~patient(sK5) & wise(sK5)) | ! [X1] : (calm(X1) & rich(X1))) & ((~calm(sK6) | ~rich(sK6)) | ! [X3] : (patient(X3) | ~wise(X3))) [skolemisation 56,58,57]
85. ~wise(X0) | ~wise(X0) [cnf transformation 31]
107. ~rich(alice) | ~tall(X0) [cnf transformation 34]
111. wise(sK5) | rich(X1) [cnf transformation 59]
127. tall(mary) [cnf transformation 22]
128. ~wise(X0) [duplicate literal removal 85]
269. 32 <=> ! [X0] : ~tall(X0) [avatar definition]
270. ~tall(X0) <- (32) [avatar component clause 269]
281. 35 <=> rich(alice) [avatar definition]
283. ~rich(alice) <- (~35) [avatar component clause 281]
284. 32 | ~35 [avatar split clause 107,281,269]
295. 38 <=> ! [X1] : rich(X1) [avatar definition]
296. rich(X1) <- (38) [avatar component clause 295]
300. rich(X1) [subsumption resolution 111,128]
301. 38 [avatar split clause 300,295]
329. $false <- (~35, 38) [subsumption resolution 283,296]
330. 35 | ~38 [avatar contradiction clause 329]
339. $false <- (32) [resolution 270,127]
340. ~32 [avatar contradiction clause 339]
341. $false [avatar sat refutation 284,301,330,340]
% SZS output end Proof for 2683670932919322268447721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not patient or quiet is not kind or not patient and vice versa.
If someone is not quiet then john is both quiet and curious and vice versa.
If someone is either quiet or not strong then mary is either wise or rich.
If fred is not brave then alice is either quiet or not curious.
Everyone who is either not creative or not happy is either happy or not calm.
If lucy is not creative then susan is not happy.
Everyone who is not strong or happy is not happy and vice versa.
Everyone who is brave or not patient is old and vice versa.
Everyone who is not happy is both not curious and not happy and vice versa.
If someone is both funny and not happy then fred is kind or strong and vice versa.
If fred is funny or wise then someone is both not humble and strong.
Everyone who is not brave or rich is not quiet or brave and vice versa.
If mary is either not creative or not brave then someone is generous.
Everyone who is either not wise or generous is either not old or patient and vice versa.
Everyone who is not humble is creative and vice versa.
Mary is not tall.
Someone is both generous and not strong.
Someone is not funny or curious.
Someone is either generous or not quiet.
Susan is either wise or calm. | John is not old. | contradiction | (![X]:((~patient(X)<~>quiet(X))<=>(~kind(X)|~patient(X))))&
((?[X]:(~quiet(X)))<=>((quiet(john)&curious(john))))&
((?[X]:((quiet(X)<~>~strong(X))))=>((wise(mary)<~>rich(mary))))&
((~brave(fred))=>((quiet(alice)<~>~curious(alice))))&
(![X]:((~creative(X)<~>~happy(X))=>(happy(X)<~>~calm(X))))&
((~creative(lucy))=>(~happy(susan)))&
(![X]:((~strong(X)|happy(X))<=>~happy(X)))&
(![X]:((brave(X)|~patient(X))<=>old(X)))&
(![X]:(~happy(X)<=>(~curious(X)&~happy(X))))&
((?[X]:((funny(X)&~happy(X))))<=>((kind(fred)|strong(fred))))&
(((funny(fred)|wise(fred)))=>(?[X]:((~humble(X)&strong(X)))))&
(![X]:((~brave(X)|rich(X))<=>(~quiet(X)|brave(X))))&
(((~creative(mary)<~>~brave(mary)))=>(?[X]:(generous(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(~old(X)<~>patient(X))))&
(![X]:(~humble(X)<=>creative(X)))&
(~tall(mary))&
(?[X]:((generous(X)&~strong(X))))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((wise(susan)<~>calm(susan))) | ~old(john) | [
"p1",
"p6",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 738546641497812351311603
% SZS output start Proof for 738546641497812351311603
2. ? [X0] : ~quiet(X0) <=> (curious(john) & quiet(john)) [input p1]
7. ! [X0] : ((happy(X0) | ~strong(X0)) <=> ~happy(X0)) [input p6]
8. ! [X0] : ((~patient(X0) | brave(X0)) <=> old(X0)) [input p7]
9. ! [X0] : (~happy(X0) <=> (~happy(X0) & ~curious(X0))) [input p8]
12. ! [X0] : ((rich(X0) | ~brave(X0)) <=> (brave(X0) | ~quiet(X0))) [input p11]
21. ~old(john) [input hypothesis]
33. (? [X0] : ~quiet(X0) | (~curious(john) | ~quiet(john))) & ((curious(john) & quiet(john)) | ! [X0] : quiet(X0)) [nnf transformation 2]
34. (? [X0] : ~quiet(X0) | ~curious(john) | ~quiet(john)) & ((curious(john) & quiet(john)) | ! [X0] : quiet(X0)) [flattening 33]
35. (? [X0] : ~quiet(X0) | ~curious(john) | ~quiet(john)) & ((curious(john) & quiet(john)) | ! [X1] : quiet(X1)) [rectify 34]
36. ? [X0] : ~quiet(X0) => ~quiet(sK0) [choice axiom]
37. (~quiet(sK0) | ~curious(john) | ~quiet(john)) & ((curious(john) & quiet(john)) | ! [X1] : quiet(X1)) [skolemisation 35,36]
41. ! [X0] : (((happy(X0) | ~strong(X0)) | happy(X0)) & (~happy(X0) | (~happy(X0) & strong(X0)))) [nnf transformation 7]
42. ! [X0] : ((happy(X0) | ~strong(X0) | happy(X0)) & (~happy(X0) | (~happy(X0) & strong(X0)))) [flattening 41]
43. ! [X0] : (((~patient(X0) | brave(X0)) | ~old(X0)) & (old(X0) | (patient(X0) & ~brave(X0)))) [nnf transformation 8]
44. ! [X0] : ((~patient(X0) | brave(X0) | ~old(X0)) & (old(X0) | (patient(X0) & ~brave(X0)))) [flattening 43]
45. ! [X0] : ((~happy(X0) | (happy(X0) | curious(X0))) & ((~happy(X0) & ~curious(X0)) | happy(X0))) [nnf transformation 9]
46. ! [X0] : ((~happy(X0) | happy(X0) | curious(X0)) & ((~happy(X0) & ~curious(X0)) | happy(X0))) [flattening 45]
54. ! [X0] : (((rich(X0) | ~brave(X0)) | (~brave(X0) & quiet(X0))) & ((brave(X0) | ~quiet(X0)) | (~rich(X0) & brave(X0)))) [nnf transformation 12]
55. ! [X0] : ((rich(X0) | ~brave(X0) | (~brave(X0) & quiet(X0))) & (brave(X0) | ~quiet(X0) | (~rich(X0) & brave(X0)))) [flattening 54]
75. curious(john) | quiet(X1) [cnf transformation 37]
89. ~happy(X0) | ~happy(X0) [cnf transformation 42]
91. ~brave(X0) | old(X0) [cnf transformation 44]
94. ~curious(X0) | happy(X0) [cnf transformation 46]
106. brave(X0) | ~quiet(X0) | brave(X0) [cnf transformation 55]
128. ~old(john) [cnf transformation 21]
129. ~quiet(X0) | brave(X0) [duplicate literal removal 106]
131. ~happy(X0) [duplicate literal removal 89]
143. 2 <=> curious(john) [avatar definition]
144. curious(john) <- (2) [avatar component clause 143]
152. 4 <=> ! [X1] : quiet(X1) [avatar definition]
153. quiet(X1) <- (4) [avatar component clause 152]
154. 4 | 2 [avatar split clause 75,143,152]
197. ~curious(X0) [subsumption resolution 94,131]
282. brave(X0) <- (4) [resolution 129,153]
284. old(X0) <- (4) [resolution 282,91]
286. $false <- (4) [resolution 284,128]
287. ~4 [avatar contradiction clause 286]
288. $false <- (2) [subsumption resolution 144,197]
289. ~2 [avatar contradiction clause 288]
290. $false [avatar sat refutation 154,287,289]
% SZS output end Proof for 738546641497812351311603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both generous and not curious then lucy is not tall and vice versa.
If john is not brave then john is not kind or happy and vice versa.
Everyone who is kind or not tall is not strong or funny and vice versa.
Everyone who is both humble and not kind is kind and vice versa.
Everyone who is patient is creative or not generous.
Everyone who is brave or old is either not brave or not rich and vice versa.
Everyone who is not kind is both not funny and not old and vice versa.
Everyone who is not quiet is not patient or not kind.
Everyone who is both not calm and not brave is both wise and rich and vice versa.
Everyone who is both wise and happy is not creative.
Everyone who is either strong or not old is either brave or strong.
Everyone who is tall is not creative or wise.
Everyone who is not happy or creative is not curious or wise.
Everyone who is either not creative or calm is either patient or not generous and vice versa.
If fred is not generous or creative then alice is old and vice versa.
Fred is either tall or generous.
John is both quiet and creative.
Someone is either curious or strong.
Susan is patient or not creative.
Fred is either not old or quiet.
Lucy is curious or strong.
Someone is both patient and not rich. | Alice is calm. | neutral | (((generous(alice)&~curious(alice)))<=>(~tall(lucy)))&
((~brave(john))<=>((~kind(john)|happy(john))))&
(![X]:((kind(X)|~tall(X))<=>(~strong(X)|funny(X))))&
(![X]:((humble(X)&~kind(X))<=>kind(X)))&
(![X]:(patient(X)=>(creative(X)|~generous(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:(~kind(X)<=>(~funny(X)&~old(X))))&
(![X]:(~quiet(X)=>(~patient(X)|~kind(X))))&
(![X]:((~calm(X)&~brave(X))<=>(wise(X)&rich(X))))&
(![X]:((wise(X)&happy(X))=>~creative(X)))&
(![X]:((strong(X)<~>~old(X))=>(brave(X)<~>strong(X))))&
(![X]:(tall(X)=>(~creative(X)|wise(X))))&
(![X]:((~happy(X)|creative(X))=>(~curious(X)|wise(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(patient(X)<~>~generous(X))))&
(((~generous(fred)|creative(fred)))<=>(old(alice)))&
((tall(fred)<~>generous(fred)))&
((quiet(john)&creative(john)))&
(?[X]:((curious(X)<~>strong(X))))&
((patient(susan)|~creative(susan)))&
((~old(fred)<~>quiet(fred)))&
((curious(lucy)|strong(lucy)))&
(?[X]:((patient(X)&~rich(X)))) | calm(alice) | [] | null | 0 |
If fred is patient then someone is not old and vice versa.
Everyone who is not old or generous is not curious and vice versa.
Everyone who is calm or funny is calm and vice versa.
Everyone who is not tall is either funny or strong and vice versa.
If john is not creative then someone is patient and vice versa.
Everyone who is not calm is both not rich and tall and vice versa.
Everyone who is not generous or not funny is not brave or not strong and vice versa.
If someone is old or creative then fred is not patient.
If someone is tall or strong then susan is either wise or not tall.
If lucy is either not rich or not old then someone is both not strong and wise and vice versa.
If mary is old then fred is rich or kind and vice versa.
If someone is patient or old then someone is wise and vice versa.
If someone is not old or not wise then someone is either not old or not brave.
If someone is patient or creative then mary is not curious or quiet.
Everyone who is not generous is not happy and vice versa.
If someone is both not brave and not strong then lucy is either not tall or rich and vice versa.
Someone is tall.
Paul is not wise or tall.
Mary is both funny and not brave.
Someone is old or humble.
Someone is curious.
Paul is not tall.
Susan is not wise or wise.
Someone is not quiet. | Lucy is old. | entailment | ((patient(fred))<=>(?[X]:(~old(X))))&
(![X]:((~old(X)|generous(X))<=>~curious(X)))&
(![X]:((calm(X)|funny(X))<=>calm(X)))&
(![X]:(~tall(X)<=>(funny(X)<~>strong(X))))&
((~creative(john))<=>(?[X]:(patient(X))))&
(![X]:(~calm(X)<=>(~rich(X)&tall(X))))&
(![X]:((~generous(X)|~funny(X))<=>(~brave(X)|~strong(X))))&
((?[X]:((old(X)|creative(X))))=>(~patient(fred)))&
((?[X]:((tall(X)|strong(X))))=>((wise(susan)<~>~tall(susan))))&
(((~rich(lucy)<~>~old(lucy)))<=>(?[X]:((~strong(X)&wise(X)))))&
((old(mary))<=>((rich(fred)|kind(fred))))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:(wise(X))))&
((?[X]:((~old(X)|~wise(X))))=>(?[X]:((~old(X)<~>~brave(X)))))&
((?[X]:((patient(X)|creative(X))))=>((~curious(mary)|quiet(mary))))&
(![X]:(~generous(X)<=>~happy(X)))&
((?[X]:((~brave(X)&~strong(X))))<=>((~tall(lucy)<~>rich(lucy))))&
(?[X]:(tall(X)))&
((~wise(paul)|tall(paul)))&
((funny(mary)&~brave(mary)))&
(?[X]:((old(X)|humble(X))))&
(?[X]:(curious(X)))&
(~tall(paul))&
((~wise(susan)|wise(susan)))&
(?[X]:(~quiet(X))) | old(lucy) | [
"p0",
"p1",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8866438770465535996486682
% SZS output start Proof for 8866438770465535996486682
1. patient(fred) <=> ? [X0] : ~old(X0) [input p0]
2. ! [X0] : ((generous(X0) | ~old(X0)) <=> ~curious(X0)) [input p1]
8. ? [X0] : (creative(X0) | old(X0)) => ~patient(fred) [input p7]
21. ? [X0] : curious(X0) [input p20]
25. ~old(lucy) [input hypothesis]
29. ~patient(fred) | ! [X0] : (~creative(X0) & ~old(X0)) [ennf transformation 8]
34. (patient(fred) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~patient(fred)) [nnf transformation 1]
35. (patient(fred) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~patient(fred)) [rectify 34]
36. ? [X1] : ~old(X1) => ~old(sK0) [choice axiom]
37. (patient(fred) | ! [X0] : old(X0)) & (~old(sK0) | ~patient(fred)) [skolemisation 35,36]
38. ! [X0] : (((generous(X0) | ~old(X0)) | curious(X0)) & (~curious(X0) | (~generous(X0) & old(X0)))) [nnf transformation 2]
39. ! [X0] : ((generous(X0) | ~old(X0) | curious(X0)) & (~curious(X0) | (~generous(X0) & old(X0)))) [flattening 38]
74. ? [X0] : curious(X0) => curious(sK8) [choice axiom]
75. curious(sK8) [skolemisation 21,74]
79. patient(fred) | old(X0) [cnf transformation 37]
80. ~curious(X0) | old(X0) [cnf transformation 39]
99. ~patient(fred) | ~old(X0) [cnf transformation 29]
135. curious(sK8) [cnf transformation 75]
139. ~old(lucy) [cnf transformation 25]
141. 1 <=> ! [X0] : old(X0) [avatar definition]
142. old(X0) <- (1) [avatar component clause 141]
144. 2 <=> patient(fred) [avatar definition]
147. 1 | 2 [avatar split clause 79,144,141]
171. 8 <=> ! [X0] : ~old(X0) [avatar definition]
172. ~old(X0) <- (8) [avatar component clause 171]
173. 8 | ~2 [avatar split clause 99,144,171]
200. 15 <=> old(lucy) [avatar definition]
201. ~old(lucy) <- (~15) [avatar component clause 200]
306. ~15 [avatar split clause 139,200]
319. $false <- (1, ~15) [resolution 201,142]
320. ~1 | 15 [avatar contradiction clause 319]
325. old(sK8) [resolution 80,135]
326. $false <- (8) [subsumption resolution 325,172]
327. ~8 [avatar contradiction clause 326]
328. $false [avatar sat refutation 147,173,306,320,327]
% SZS output end Proof for 8866438770465535996486682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is wise or not old then fred is both quiet and not quiet and vice versa. Everyone who is either kind or generous is both not curious and not funny and vice versa. Everyone who is both not old and not quiet is either not old or not quiet and vice versa. Everyone who is generous is curious or old and vice versa. Everyone who is strong or not curious is either not kind or patient and vice versa. Everyone who is both funny and not patient is both old and not patient and vice versa. Everyone who is both quiet and not quiet is strong or calm and vice versa. If alice is happy then someone is both old and not quiet and vice versa. Everyone who is either rich or not curious is either not wise or not old and vice versa. Everyone who is either not patient or calm is either not tall or generous. Everyone who is both tall and not humble is both not patient and funny and vice versa. Everyone who is funny is not wise and vice versa. If fred is curious or brave then someone is either creative or not strong and vice versa. If mary is not wise or curious then fred is humble or not patient and vice versa. Everyone who is either funny or not brave is calm and vice versa. Fred is not kind or not curious. Someone is both generous and patient. Paul is humble. Someone is generous or not old. Mary is not brave. | Fred is not calm. | entailment | (((wise(paul)|~old(paul)))<=>((quiet(fred)&~quiet(fred))))&
(![X]:((kind(X)<~>generous(X))<=>(~curious(X)&~funny(X))))&
(![X]:((~old(X)&~quiet(X))<=>(~old(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>(curious(X)|old(X))))&
(![X]:((strong(X)|~curious(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((funny(X)&~patient(X))<=>(old(X)&~patient(X))))&
(![X]:((quiet(X)&~quiet(X))<=>(strong(X)|calm(X))))&
((happy(alice))<=>(?[X]:((old(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~curious(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((~patient(X)<~>calm(X))=>(~tall(X)<~>generous(X))))&
(![X]:((tall(X)&~humble(X))<=>(~patient(X)&funny(X))))&
(![X]:(funny(X)<=>~wise(X)))&
(((curious(fred)|brave(fred)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(((~wise(mary)|curious(mary)))<=>((humble(fred)|~patient(fred))))&
(![X]:((funny(X)<~>~brave(X))<=>calm(X)))&
((~kind(fred)|~curious(fred)))&
(?[X]:((generous(X)&patient(X))))&
(humble(paul))&
(?[X]:((generous(X)|~old(X))))&
(~brave(mary)) | ~calm(fred) | [
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3742020152726688611544802
% SZS output start Proof for 3742020152726688611544802
3. ! [X0] : ((~quiet(X0) & ~old(X0)) <=> (~old(X0) <~> ~quiet(X0))) [input p2]
7. ! [X0] : ((~quiet(X0) & quiet(X0)) <=> (calm(X0) | strong(X0))) [input p6]
21. calm(fred) [input hypothesis]
27. ! [X0] : (((~quiet(X0) & ~old(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0)))) & (((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (quiet(X0) | old(X0)))) [nnf transformation 3]
28. ! [X0] : (((~quiet(X0) & ~old(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0)))) & (((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | quiet(X0) | old(X0))) [flattening 27]
35. ! [X0] : (((~quiet(X0) & quiet(X0)) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | (quiet(X0) | ~quiet(X0)))) [nnf transformation 7]
36. ! [X0] : (((~quiet(X0) & quiet(X0)) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | quiet(X0) | ~quiet(X0))) [flattening 35]
70. quiet(X0) | old(X0) | quiet(X0) | old(X0) [cnf transformation 28]
72. ~old(X0) | ~old(X0) | quiet(X0) [cnf transformation 28]
92. ~quiet(X0) | ~calm(X0) [cnf transformation 36]
134. calm(fred) [cnf transformation 21]
135. quiet(X0) | old(X0) [duplicate literal removal 70]
136. ~old(X0) | quiet(X0) [duplicate literal removal 72]
154. quiet(X0) [subsumption resolution 135,136]
155. ~calm(X0) [subsumption resolution 92,154]
208. $false [subsumption resolution 134,155]
% SZS output end Proof for 3742020152726688611544802
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or tall is both not wise and curious.
Everyone who is either brave or happy is not patient or not funny and vice versa.
Everyone who is old or not creative is patient or creative.
If someone is wise then someone is both not humble and brave.
If susan is old or creative then someone is not generous or happy and vice versa.
Everyone who is both not patient and kind is either curious or brave.
Everyone who is not kind or not generous is not humble and vice versa.
Everyone who is both quiet and not patient is either not happy or tall and vice versa.
If alice is not curious then lucy is either wise or patient.
Everyone who is either funny or tall is curious or tall and vice versa.
If lucy is not wise or not old then someone is not strong or funny.
Everyone who is either not happy or brave is not old or quiet and vice versa.
If someone is wise or patient then alice is funny or not old and vice versa.
Everyone who is both not humble and tall is not humble or patient.
Everyone who is either rich or not happy is humble and vice versa.
Everyone who is either kind or not curious is not strong.
Someone is creative.
John is humble or not old.
Someone is kind or not patient.
Lucy is either not curious or not brave.
Alice is rich.
Someone is either old or happy.
John is not creative or brave.
Someone is both not tall and quiet. | Alice is not generous. | contradiction | (![X]:((happy(X)<~>tall(X))=>(~wise(X)&curious(X))))&
(![X]:((brave(X)<~>happy(X))<=>(~patient(X)|~funny(X))))&
(![X]:((old(X)|~creative(X))=>(patient(X)|creative(X))))&
((?[X]:(wise(X)))=>(?[X]:((~humble(X)&brave(X)))))&
(((old(susan)|creative(susan)))<=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~patient(X)&kind(X))=>(curious(X)<~>brave(X))))&
(![X]:((~kind(X)|~generous(X))<=>~humble(X)))&
(![X]:((quiet(X)&~patient(X))<=>(~happy(X)<~>tall(X))))&
((~curious(alice))=>((wise(lucy)<~>patient(lucy))))&
(![X]:((funny(X)<~>tall(X))<=>(curious(X)|tall(X))))&
(((~wise(lucy)|~old(lucy)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|quiet(X))))&
((?[X]:((wise(X)|patient(X))))<=>((funny(alice)|~old(alice))))&
(![X]:((~humble(X)&tall(X))=>(~humble(X)|patient(X))))&
(![X]:((rich(X)<~>~happy(X))<=>humble(X)))&
(![X]:((kind(X)<~>~curious(X))=>~strong(X)))&
(?[X]:(creative(X)))&
((humble(john)|~old(john)))&
(?[X]:((kind(X)|~patient(X))))&
((~curious(lucy)<~>~brave(lucy)))&
(rich(alice))&
(?[X]:((old(X)<~>happy(X))))&
((~creative(john)|brave(john)))&
(?[X]:((~tall(X)&quiet(X)))) | ~generous(alice) | [
"p1",
"p6",
"p7",
"p9",
"p11",
"p12",
"p14",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4634818609628467725546084
% SZS output start Proof for 4634818609628467725546084
2. ! [X0] : ((brave(X0) <~> happy(X0)) <=> (~funny(X0) | ~patient(X0))) [input p1]
7. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> ~humble(X0)) [input p6]
8. ! [X0] : ((~patient(X0) & quiet(X0)) <=> (~happy(X0) <~> tall(X0))) [input p7]
10. ! [X0] : ((funny(X0) <~> tall(X0)) <=> (tall(X0) | curious(X0))) [input p9]
12. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (quiet(X0) | ~old(X0))) [input p11]
13. ? [X0] : (patient(X0) | wise(X0)) <=> (~old(alice) | funny(alice)) [input p12]
15. ! [X0] : ((rich(X0) <~> ~happy(X0)) <=> humble(X0)) [input p14]
21. rich(alice) [input p20]
24. ? [X0] : (quiet(X0) & ~tall(X0)) [input p23]
25. ~generous(alice) [input hypothesis]
39. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [flattening 39]
50. ! [X0] : (((~generous(X0) | ~kind(X0)) | humble(X0)) & (~humble(X0) | (generous(X0) & kind(X0)))) [nnf transformation 7]
51. ! [X0] : ((~generous(X0) | ~kind(X0) | humble(X0)) & (~humble(X0) | (generous(X0) & kind(X0)))) [flattening 50]
52. ! [X0] : (((~patient(X0) & quiet(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (patient(X0) | ~quiet(X0)))) [nnf transformation 8]
53. ! [X0] : (((~patient(X0) & quiet(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | patient(X0) | ~quiet(X0))) [flattening 52]
55. ! [X0] : ((((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))))) [nnf transformation 10]
56. ! [X0] : ((((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))))) [flattening 55]
57. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 12]
58. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 57]
59. (? [X0] : (patient(X0) | wise(X0)) | (old(alice) & ~funny(alice))) & ((~old(alice) | funny(alice)) | ! [X0] : (~patient(X0) & ~wise(X0))) [nnf transformation 13]
60. (? [X0] : (patient(X0) | wise(X0)) | (old(alice) & ~funny(alice))) & (~old(alice) | funny(alice) | ! [X0] : (~patient(X0) & ~wise(X0))) [flattening 59]
61. (? [X0] : (patient(X0) | wise(X0)) | (old(alice) & ~funny(alice))) & (~old(alice) | funny(alice) | ! [X1] : (~patient(X1) & ~wise(X1))) [rectify 60]
62. ? [X0] : (patient(X0) | wise(X0)) => (patient(sK2) | wise(sK2)) [choice axiom]
63. ((patient(sK2) | wise(sK2)) | (old(alice) & ~funny(alice))) & (~old(alice) | funny(alice) | ! [X1] : (~patient(X1) & ~wise(X1))) [skolemisation 61,62]
64. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | ~humble(X0)) & (humble(X0) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [nnf transformation 15]
73. ? [X0] : (quiet(X0) & ~tall(X0)) => (quiet(sK6) & ~tall(sK6)) [choice axiom]
74. quiet(sK6) & ~tall(sK6) [skolemisation 24,73]
81. patient(X0) | brave(X0) | happy(X0) [cnf transformation 40]
82. funny(X0) | brave(X0) | happy(X0) [cnf transformation 40]
83. ~brave(X0) | ~happy(X0) | patient(X0) [cnf transformation 40]
96. ~humble(X0) | generous(X0) [cnf transformation 51]
100. quiet(X0) | tall(X0) | happy(X0) [cnf transformation 53]
102. ~patient(X0) | tall(X0) | happy(X0) [cnf transformation 53]
111. ~tall(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 56]
115. ~quiet(X0) | ~happy(X0) | brave(X0) [cnf transformation 58]
116. ~brave(X0) | happy(X0) | old(X0) [cnf transformation 58]
117. ~quiet(X0) | happy(X0) | ~brave(X0) [cnf transformation 58]
119. ~old(alice) | funny(alice) | ~patient(X1) [cnf transformation 63]
123. ~rich(X0) | ~happy(X0) | humble(X0) [cnf transformation 64]
132. rich(alice) [cnf transformation 21]
137. quiet(sK6) [cnf transformation 74]
138. ~generous(alice) [cnf transformation 25]
140. ~funny(X0) | ~tall(X0) [duplicate literal removal 111]
197. 13 <=> old(alice) [avatar definition]
198. ~old(alice) <- (~13) [avatar component clause 197]
210. 16 <=> funny(alice) [avatar definition]
211. funny(alice) <- (16) [avatar component clause 210]
215. 17 <=> ! [X1] : ~patient(X1) [avatar definition]
216. ~patient(X1) <- (17) [avatar component clause 215]
217. 17 | 16 | ~13 [avatar split clause 119,197,210,215]
291. ~tall(X1) | happy(X1) | brave(X1) [resolution 82,140]
314. tall(X0) | happy(X0) | brave(X0) | happy(X0) [resolution 102,81]
316. tall(X0) | happy(X0) | brave(X0) [duplicate literal removal 314]
326. brave(X0) | happy(X0) [subsumption resolution 316,291]
353. 41 <=> tall(alice) [avatar definition]
354. ~tall(alice) <- (~41) [avatar component clause 353]
355. tall(alice) <- (41) [avatar component clause 353]
379. 46 <=> happy(alice) [avatar definition]
383. ~happy(sK6) | brave(sK6) [resolution 115,137]
385. brave(sK6) [subsumption resolution 383,326]
398. happy(sK6) | ~brave(sK6) [resolution 117,137]
399. happy(X0) | ~brave(X0) | tall(X0) | happy(X0) [resolution 117,100]
400. happy(X0) | ~brave(X0) | tall(X0) [duplicate literal removal 399]
401. happy(sK6) [subsumption resolution 398,385]
402. tall(X0) | happy(X0) [subsumption resolution 400,326]
405. ~happy(sK6) | patient(sK6) [resolution 385,83]
407. patient(sK6) [subsumption resolution 405,401]
408. ~happy(alice) | humble(alice) [resolution 123,132]
487. happy(X0) | happy(X0) | old(X0) [resolution 326,116]
491. old(X0) | happy(X0) [duplicate literal removal 487]
508. $false <- (17) [resolution 216,407]
509. ~17 [avatar contradiction clause 508]
590. happy(alice) <- (~13) [resolution 491,198]
594. 46 | 13 [avatar split clause 590,197,379]
596. 56 <=> humble(alice) [avatar definition]
597. humble(alice) <- (56) [avatar component clause 596]
600. 56 | ~46 [avatar split clause 408,379,596]
608. happy(alice) <- (~41) [resolution 354,402]
615. generous(alice) <- (56) [resolution 597,96]
617. $false <- (56) [subsumption resolution 615,138]
618. ~56 [avatar contradiction clause 617]
619. 46 | 41 [avatar split clause 608,353,379]
625. ~tall(alice) <- (16) [resolution 211,140]
638. $false <- (16, 41) [subsumption resolution 625,355]
639. ~16 | ~41 [avatar contradiction clause 638]
640. $false [avatar sat refutation 217,509,594,600,618,619,639]
% SZS output end Proof for 4634818609628467725546084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and old then alice is not generous and vice versa. Everyone who is both not generous and generous is either not tall or not strong and vice versa. If mary is either humble or creative then susan is not generous or creative and vice versa. If lucy is not wise then susan is wise and vice versa. Everyone who is both old and not wise is rich or not kind and vice versa. If someone is calm or not creative then someone is both brave and patient and vice versa. If paul is not kind then someone is both not old and kind and vice versa. Everyone who is both creative and old is both not wise and humble. Everyone who is not curious is both old and not old and vice versa. Everyone who is patient is either not brave or strong and vice versa. If someone is not tall or not humble then lucy is both funny and not wise. If fred is wise then someone is wise or generous. If alice is either not brave or not quiet then someone is both patient and not happy and vice versa. Everyone who is not rich or not patient is not calm. Everyone who is either not quiet or happy is both curious and strong and vice versa. Everyone who is both not calm and not generous is calm. Someone is not strong or strong. Lucy is strong. Mary is not patient or strong. Someone is old. John is both generous and not calm. Someone is both happy and brave. Someone is both not brave and not wise. Someone is not patient. | John is strong. | neutral | ((?[X]:((~humble(X)&old(X))))<=>(~generous(alice)))&
(![X]:((~generous(X)&generous(X))<=>(~tall(X)<~>~strong(X))))&
(((humble(mary)<~>creative(mary)))<=>((~generous(susan)|creative(susan))))&
((~wise(lucy))<=>(wise(susan)))&
(![X]:((old(X)&~wise(X))<=>(rich(X)|~kind(X))))&
((?[X]:((calm(X)|~creative(X))))<=>(?[X]:((brave(X)&patient(X)))))&
((~kind(paul))<=>(?[X]:((~old(X)&kind(X)))))&
(![X]:((creative(X)&old(X))=>(~wise(X)&humble(X))))&
(![X]:(~curious(X)<=>(old(X)&~old(X))))&
(![X]:(patient(X)<=>(~brave(X)<~>strong(X))))&
((?[X]:((~tall(X)|~humble(X))))=>((funny(lucy)&~wise(lucy))))&
((wise(fred))=>(?[X]:((wise(X)|generous(X)))))&
(((~brave(alice)<~>~quiet(alice)))<=>(?[X]:((patient(X)&~happy(X)))))&
(![X]:((~rich(X)|~patient(X))=>~calm(X)))&
(![X]:((~quiet(X)<~>happy(X))<=>(curious(X)&strong(X))))&
(![X]:((~calm(X)&~generous(X))=>calm(X)))&
(?[X]:((~strong(X)|strong(X))))&
(strong(lucy))&
((~patient(mary)|strong(mary)))&
(?[X]:(old(X)))&
((generous(john)&~calm(john)))&
(?[X]:((happy(X)&brave(X))))&
(?[X]:((~brave(X)&~wise(X))))&
(?[X]:(~patient(X))) | strong(john) | [] | null | 0 |
Everyone who is not old is not wise and vice versa. Everyone who is both strong and not quiet is both generous and not curious and vice versa. If alice is not quiet or happy then someone is both creative and quiet and vice versa. Everyone who is generous is not rich. Everyone who is either not patient or wise is both wise and rich. If someone is humble or not brave then lucy is patient and vice versa. If someone is generous then fred is curious or quiet and vice versa. If someone is not rich or not brave then lucy is not rich or brave and vice versa. Everyone who is curious or not humble is both kind and quiet and vice versa. Everyone who is not humble or not happy is not curious or not patient and vice versa. Everyone who is not creative is not old. If mary is both funny and kind then someone is not kind or not old and vice versa. If lucy is calm then john is not humble. Everyone who is not curious or strong is not rich or old. Everyone who is curious or rich is either funny or not tall. If someone is both not curious and not rich then lucy is either not strong or not tall. John is humble or not patient. John is both not patient and not happy. Susan is generous. Mary is not patient. Alice is both not kind and not funny. Someone is curious or not brave. Someone is both kind and not happy. Susan is both not humble and not happy. | Fred is wise. | neutral | (![X]:(~old(X)<=>~wise(X)))&
(![X]:((strong(X)&~quiet(X))<=>(generous(X)&~curious(X))))&
(((~quiet(alice)|happy(alice)))<=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:(generous(X)=>~rich(X)))&
(![X]:((~patient(X)<~>wise(X))=>(wise(X)&rich(X))))&
((?[X]:((humble(X)|~brave(X))))<=>(patient(lucy)))&
((?[X]:(generous(X)))<=>((curious(fred)|quiet(fred))))&
((?[X]:((~rich(X)|~brave(X))))<=>((~rich(lucy)|brave(lucy))))&
(![X]:((curious(X)|~humble(X))<=>(kind(X)&quiet(X))))&
(![X]:((~humble(X)|~happy(X))<=>(~curious(X)|~patient(X))))&
(![X]:(~creative(X)=>~old(X)))&
(((funny(mary)&kind(mary)))<=>(?[X]:((~kind(X)|~old(X)))))&
((calm(lucy))=>(~humble(john)))&
(![X]:((~curious(X)|strong(X))=>(~rich(X)|old(X))))&
(![X]:((curious(X)|rich(X))=>(funny(X)<~>~tall(X))))&
((?[X]:((~curious(X)&~rich(X))))=>((~strong(lucy)<~>~tall(lucy))))&
((humble(john)|~patient(john)))&
((~patient(john)&~happy(john)))&
(generous(susan))&
(~patient(mary))&
((~kind(alice)&~funny(alice)))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((kind(X)&~happy(X))))&
((~humble(susan)&~happy(susan))) | wise(fred) | [] | null | 0 |
Everyone who is rich or brave is creative. Everyone who is not calm or not creative is either strong or not tall. If someone is either kind or humble then paul is funny or not curious. Everyone who is humble is not old or strong and vice versa. Everyone who is both not calm and not creative is not quiet and vice versa. Everyone who is both creative and not generous is either not kind or not wise and vice versa. If someone is either rich or not quiet then alice is either tall or not quiet and vice versa. Everyone who is either not rich or calm is not creative or not generous. If john is either happy or not calm then someone is not curious or not wise. Everyone who is strong is both funny and creative and vice versa. Everyone who is both happy and quiet is funny or not humble and vice versa. If someone is both old and not tall then someone is generous and vice versa. If paul is both patient and not humble then alice is both strong and not tall. If someone is not strong or brave then lucy is not generous and vice versa. If lucy is either generous or not humble then someone is kind or creative and vice versa. Everyone who is both kind and not generous is either generous or not generous and vice versa. Someone is rich or not calm. Alice is not creative or not wise. Someone is not patient or creative. Someone is either not calm or not kind. Someone is humble or not quiet. Mary is not funny or curious. | Paul is not brave. | neutral | (![X]:((rich(X)|brave(X))=>creative(X)))&
(![X]:((~calm(X)|~creative(X))=>(strong(X)<~>~tall(X))))&
((?[X]:((kind(X)<~>humble(X))))=>((funny(paul)|~curious(paul))))&
(![X]:(humble(X)<=>(~old(X)|strong(X))))&
(![X]:((~calm(X)&~creative(X))<=>~quiet(X)))&
(![X]:((creative(X)&~generous(X))<=>(~kind(X)<~>~wise(X))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>((tall(alice)<~>~quiet(alice))))&
(![X]:((~rich(X)<~>calm(X))=>(~creative(X)|~generous(X))))&
(((happy(john)<~>~calm(john)))=>(?[X]:((~curious(X)|~wise(X)))))&
(![X]:(strong(X)<=>(funny(X)&creative(X))))&
(![X]:((happy(X)&quiet(X))<=>(funny(X)|~humble(X))))&
((?[X]:((old(X)&~tall(X))))<=>(?[X]:(generous(X))))&
(((patient(paul)&~humble(paul)))=>((strong(alice)&~tall(alice))))&
((?[X]:((~strong(X)|brave(X))))<=>(~generous(lucy)))&
(((generous(lucy)<~>~humble(lucy)))<=>(?[X]:((kind(X)|creative(X)))))&
(![X]:((kind(X)&~generous(X))<=>(generous(X)<~>~generous(X))))&
(?[X]:((rich(X)|~calm(X))))&
((~creative(alice)|~wise(alice)))&
(?[X]:((~patient(X)|creative(X))))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:((humble(X)|~quiet(X))))&
((~funny(mary)|curious(mary))) | ~brave(paul) | [] | null | 0 |
Everyone who is not creative or not funny is both patient and not patient and vice versa.
Everyone who is both calm and not old is either old or wise and vice versa.
Everyone who is not happy or not funny is rich or happy.
If someone is not rich or humble then someone is either not quiet or kind.
If paul is both not creative and generous then someone is both old and not creative.
If someone is rich or wise then mary is both not old and kind.
If someone is not brave then mary is either old or not tall.
If someone is both quiet and not humble then someone is either not funny or not brave and vice versa.
If paul is not humble then john is both not old and not strong and vice versa.
If mary is not humble then lucy is both not tall and humble and vice versa.
If mary is not strong or funny then lucy is both curious and not tall.
If someone is either not creative or wise then someone is either not old or not tall and vice versa.
Everyone who is both patient and not happy is both not tall and not curious.
If someone is either funny or generous then someone is humble or not tall.
If mary is either not creative or calm then someone is not calm.
Someone is kind or humble.
Someone is both not humble and not kind.
Mary is not happy.
Someone is happy.
Someone is not kind or not generous.
Fred is not wise.
John is both creative and not happy.
Alice is either not generous or patient. | Lucy is creative. | entailment | (![X]:((~creative(X)|~funny(X))<=>(patient(X)&~patient(X))))&
(![X]:((calm(X)&~old(X))<=>(old(X)<~>wise(X))))&
(![X]:((~happy(X)|~funny(X))=>(rich(X)|happy(X))))&
((?[X]:((~rich(X)|humble(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(((~creative(paul)&generous(paul)))=>(?[X]:((old(X)&~creative(X)))))&
((?[X]:((rich(X)|wise(X))))=>((~old(mary)&kind(mary))))&
((?[X]:(~brave(X)))=>((old(mary)<~>~tall(mary))))&
((?[X]:((quiet(X)&~humble(X))))<=>(?[X]:((~funny(X)<~>~brave(X)))))&
((~humble(paul))<=>((~old(john)&~strong(john))))&
((~humble(mary))<=>((~tall(lucy)&humble(lucy))))&
(((~strong(mary)|funny(mary)))=>((curious(lucy)&~tall(lucy))))&
((?[X]:((~creative(X)<~>wise(X))))<=>(?[X]:((~old(X)<~>~tall(X)))))&
(![X]:((patient(X)&~happy(X))=>(~tall(X)&~curious(X))))&
((?[X]:((funny(X)<~>generous(X))))=>(?[X]:((humble(X)|~tall(X)))))&
(((~creative(mary)<~>calm(mary)))=>(?[X]:(~calm(X))))&
(?[X]:((kind(X)|humble(X))))&
(?[X]:((~humble(X)&~kind(X))))&
(~happy(mary))&
(?[X]:(happy(X)))&
(?[X]:((~kind(X)|~generous(X))))&
(~wise(fred))&
((creative(john)&~happy(john)))&
((~generous(alice)<~>patient(alice))) | creative(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 957106005483590814735857
% SZS output start Proof for 957106005483590814735857
1. ! [X0] : ((~funny(X0) | ~creative(X0)) <=> (~patient(X0) & patient(X0))) [input p0]
24. ~creative(lucy) [input hypothesis]
41. ! [X0] : (((~funny(X0) | ~creative(X0)) | (patient(X0) | ~patient(X0))) & ((~patient(X0) & patient(X0)) | (funny(X0) & creative(X0)))) [nnf transformation 1]
42. ! [X0] : ((~funny(X0) | ~creative(X0) | patient(X0) | ~patient(X0)) & ((~patient(X0) & patient(X0)) | (funny(X0) & creative(X0)))) [flattening 41]
82. patient(X0) | creative(X0) [cnf transformation 42]
84. ~patient(X0) | creative(X0) [cnf transformation 42]
148. ~creative(lucy) [cnf transformation 24]
153. creative(X0) [subsumption resolution 82,84]
336. $false [subsumption resolution 148,153]
% SZS output end Proof for 957106005483590814735857
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not humble then alice is both not calm and not strong.
Everyone who is either not funny or not patient is either not quiet or creative.
If mary is both not kind and not happy then alice is generous or not rich and vice versa.
Everyone who is either brave or not creative is calm and vice versa.
If mary is both not creative and not old then john is not rich or creative and vice versa.
Everyone who is either patient or not humble is wise and vice versa.
Everyone who is either curious or not old is calm or kind and vice versa.
Everyone who is both not funny and old is either creative or old and vice versa.
Everyone who is both brave and quiet is either not humble or not creative and vice versa.
Everyone who is calm is not old.
Everyone who is either patient or funny is both not happy and brave and vice versa.
Everyone who is both not happy and not creative is either not generous or rich and vice versa.
If fred is not rich then someone is calm or funny and vice versa.
If someone is both not patient and funny then susan is both humble and not generous.
Everyone who is not old is not patient.
Everyone who is both funny and not patient is quiet or not patient and vice versa.
Someone is not kind.
John is either patient or humble.
Someone is both not old and tall.
Someone is not happy.
Mary is both rich and funny.
Someone is strong.
Someone is brave or not strong.
Susan is patient. | Alice is rich. | neutral | ((~humble(fred))=>((~calm(alice)&~strong(alice))))&
(![X]:((~funny(X)<~>~patient(X))=>(~quiet(X)<~>creative(X))))&
(((~kind(mary)&~happy(mary)))<=>((generous(alice)|~rich(alice))))&
(![X]:((brave(X)<~>~creative(X))<=>calm(X)))&
(((~creative(mary)&~old(mary)))<=>((~rich(john)|creative(john))))&
(![X]:((patient(X)<~>~humble(X))<=>wise(X)))&
(![X]:((curious(X)<~>~old(X))<=>(calm(X)|kind(X))))&
(![X]:((~funny(X)&old(X))<=>(creative(X)<~>old(X))))&
(![X]:((brave(X)&quiet(X))<=>(~humble(X)<~>~creative(X))))&
(![X]:(calm(X)=>~old(X)))&
(![X]:((patient(X)<~>funny(X))<=>(~happy(X)&brave(X))))&
(![X]:((~happy(X)&~creative(X))<=>(~generous(X)<~>rich(X))))&
((~rich(fred))<=>(?[X]:((calm(X)|funny(X)))))&
((?[X]:((~patient(X)&funny(X))))=>((humble(susan)&~generous(susan))))&
(![X]:(~old(X)=>~patient(X)))&
(![X]:((funny(X)&~patient(X))<=>(quiet(X)|~patient(X))))&
(?[X]:(~kind(X)))&
((patient(john)<~>humble(john)))&
(?[X]:((~old(X)&tall(X))))&
(?[X]:(~happy(X)))&
((rich(mary)&funny(mary)))&
(?[X]:(strong(X)))&
(?[X]:((brave(X)|~strong(X))))&
(patient(susan)) | rich(alice) | [] | null | 0 |
Everyone who is not wise is both quiet and not curious and vice versa. Everyone who is both not patient and wise is curious or not old. If someone is both not quiet and patient then john is not happy or not strong. If someone is not brave or not happy then someone is both not kind and happy. If someone is either not kind or not humble then lucy is funny and vice versa. Everyone who is either calm or generous is creative and vice versa. If paul is not creative or wise then lucy is not wise. Everyone who is either funny or calm is wise or not patient. Everyone who is wise or not funny is not kind or not quiet and vice versa. If someone is either generous or strong then someone is not curious or quiet and vice versa. If fred is rich or strong then lucy is brave or wise. Everyone who is either old or not strong is kind. Everyone who is either not rich or humble is either funny or not funny and vice versa. Everyone who is both not calm and not creative is curious or quiet and vice versa. If alice is either not curious or not old then someone is humble or quiet. If someone is not rich or creative then mary is either humble or not creative. Alice is both old and curious. Paul is humble. John is both old and not calm. Someone is both not kind and patient. Alice is curious. Someone is not wise or patient. Mary is both happy and patient. Someone is either not humble or not calm. | Mary is humble. | neutral | (![X]:(~wise(X)<=>(quiet(X)&~curious(X))))&
(![X]:((~patient(X)&wise(X))=>(curious(X)|~old(X))))&
((?[X]:((~quiet(X)&patient(X))))=>((~happy(john)|~strong(john))))&
((?[X]:((~brave(X)|~happy(X))))=>(?[X]:((~kind(X)&happy(X)))))&
((?[X]:((~kind(X)<~>~humble(X))))<=>(funny(lucy)))&
(![X]:((calm(X)<~>generous(X))<=>creative(X)))&
(((~creative(paul)|wise(paul)))=>(~wise(lucy)))&
(![X]:((funny(X)<~>calm(X))=>(wise(X)|~patient(X))))&
(![X]:((wise(X)|~funny(X))<=>(~kind(X)|~quiet(X))))&
((?[X]:((generous(X)<~>strong(X))))<=>(?[X]:((~curious(X)|quiet(X)))))&
(((rich(fred)|strong(fred)))=>((brave(lucy)|wise(lucy))))&
(![X]:((old(X)<~>~strong(X))=>kind(X)))&
(![X]:((~rich(X)<~>humble(X))<=>(funny(X)<~>~funny(X))))&
(![X]:((~calm(X)&~creative(X))<=>(curious(X)|quiet(X))))&
(((~curious(alice)<~>~old(alice)))=>(?[X]:((humble(X)|quiet(X)))))&
((?[X]:((~rich(X)|creative(X))))=>((humble(mary)<~>~creative(mary))))&
((old(alice)&curious(alice)))&
(humble(paul))&
((old(john)&~calm(john)))&
(?[X]:((~kind(X)&patient(X))))&
(curious(alice))&
(?[X]:((~wise(X)|patient(X))))&
((happy(mary)&patient(mary)))&
(?[X]:((~humble(X)<~>~calm(X)))) | humble(mary) | [] | null | 0 |
Everyone who is both not old and not rich is both kind and generous. Everyone who is either strong or not rich is patient or generous and vice versa. Everyone who is old is not curious or brave. Everyone who is creative or not generous is both not creative and not wise. Everyone who is both wise and not old is either humble or happy and vice versa. Everyone who is funny is creative. If someone is either patient or old then someone is tall or generous. Everyone who is not funny is either not strong or patient. Everyone who is both not funny and not strong is both kind and brave and vice versa. Everyone who is not happy or humble is either calm or not creative and vice versa. Everyone who is creative is not patient or not creative. If fred is not happy or calm then someone is brave or not kind. Everyone who is either old or not kind is either rich or not rich and vice versa. Everyone who is both happy and not funny is either not strong or creative. Everyone who is both not quiet and not curious is not kind or old. Everyone who is both patient and not strong is both kind and not tall and vice versa. Susan is not generous or not kind. Someone is both happy and quiet. Paul is either not curious or not funny. Someone is both patient and not kind. Someone is happy. Someone is not wise. Someone is happy or rich. | Susan is not calm. | entailment | (![X]:((~old(X)&~rich(X))=>(kind(X)&generous(X))))&
(![X]:((strong(X)<~>~rich(X))<=>(patient(X)|generous(X))))&
(![X]:(old(X)=>(~curious(X)|brave(X))))&
(![X]:((creative(X)|~generous(X))=>(~creative(X)&~wise(X))))&
(![X]:((wise(X)&~old(X))<=>(humble(X)<~>happy(X))))&
(![X]:(funny(X)=>creative(X)))&
((?[X]:((patient(X)<~>old(X))))=>(?[X]:((tall(X)|generous(X)))))&
(![X]:(~funny(X)=>(~strong(X)<~>patient(X))))&
(![X]:((~funny(X)&~strong(X))<=>(kind(X)&brave(X))))&
(![X]:((~happy(X)|humble(X))<=>(calm(X)<~>~creative(X))))&
(![X]:(creative(X)=>(~patient(X)|~creative(X))))&
(((~happy(fred)|calm(fred)))=>(?[X]:((brave(X)|~kind(X)))))&
(![X]:((old(X)<~>~kind(X))<=>(rich(X)<~>~rich(X))))&
(![X]:((happy(X)&~funny(X))=>(~strong(X)<~>creative(X))))&
(![X]:((~quiet(X)&~curious(X))=>(~kind(X)|old(X))))&
(![X]:((patient(X)&~strong(X))<=>(kind(X)&~tall(X))))&
((~generous(susan)|~kind(susan)))&
(?[X]:((happy(X)&quiet(X))))&
((~curious(paul)<~>~funny(paul)))&
(?[X]:((patient(X)&~kind(X))))&
(?[X]:(happy(X)))&
(?[X]:(~wise(X)))&
(?[X]:((happy(X)|rich(X)))) | ~calm(susan) | [
"p0",
"p3",
"p4",
"p5",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3816661878422817759801615
% SZS output start Proof for 3816661878422817759801615
1. ! [X0] : ((~rich(X0) & ~old(X0)) => (generous(X0) & kind(X0))) [input p0]
4. ! [X0] : ((~generous(X0) | creative(X0)) => (~wise(X0) & ~creative(X0))) [input p3]
5. ! [X0] : ((~old(X0) & wise(X0)) <=> (humble(X0) <~> happy(X0))) [input p4]
6. ! [X0] : (funny(X0) => creative(X0)) [input p5]
9. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (brave(X0) & kind(X0))) [input p8]
10. ! [X0] : ((humble(X0) | ~happy(X0)) <=> (calm(X0) <~> ~creative(X0))) [input p9]
13. ! [X0] : ((old(X0) <~> ~kind(X0)) <=> (rich(X0) <~> ~rich(X0))) [input p12]
14. ! [X0] : ((~funny(X0) & happy(X0)) => (~strong(X0) <~> creative(X0))) [input p13]
24. calm(susan) [input hypothesis]
28. ! [X0] : ((generous(X0) & kind(X0)) | (rich(X0) | old(X0))) [ennf transformation 1]
29. ! [X0] : ((generous(X0) & kind(X0)) | rich(X0) | old(X0)) [flattening 28]
32. ! [X0] : ((~wise(X0) & ~creative(X0)) | (generous(X0) & ~creative(X0))) [ennf transformation 4]
33. ! [X0] : (creative(X0) | ~funny(X0)) [ennf transformation 6]
39. ! [X0] : ((~strong(X0) <~> creative(X0)) | (funny(X0) | ~happy(X0))) [ennf transformation 14]
40. ! [X0] : ((~strong(X0) <~> creative(X0)) | funny(X0) | ~happy(X0)) [flattening 39]
43. ! [X0] : (((~old(X0) & wise(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) & (((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (old(X0) | ~wise(X0)))) [nnf transformation 5]
44. ! [X0] : (((~old(X0) & wise(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) & (((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | old(X0) | ~wise(X0))) [flattening 43]
50. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~brave(X0) | ~kind(X0))) & ((brave(X0) & kind(X0)) | (strong(X0) | funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((~strong(X0) & ~funny(X0)) | ~brave(X0) | ~kind(X0)) & ((brave(X0) & kind(X0)) | strong(X0) | funny(X0))) [flattening 50]
52. ! [X0] : (((humble(X0) | ~happy(X0)) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) & (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | (~humble(X0) & happy(X0)))) [nnf transformation 10]
53. ! [X0] : ((humble(X0) | ~happy(X0) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) & (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | (~humble(X0) & happy(X0)))) [flattening 52]
56. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) & (((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [nnf transformation 13]
57. ! [X0] : (((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | funny(X0) | ~happy(X0)) [nnf transformation 40]
71. kind(X0) | rich(X0) | old(X0) [cnf transformation 29]
80. ~creative(X0) | ~creative(X0) [cnf transformation 32]
89. ~happy(X0) | humble(X0) | ~old(X0) [cnf transformation 44]
90. creative(X0) | ~funny(X0) [cnf transformation 33]
95. kind(X0) | strong(X0) | funny(X0) [cnf transformation 51]
101. creative(X0) | ~calm(X0) | happy(X0) [cnf transformation 53]
102. creative(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 53]
112. ~kind(X0) | old(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 56]
113. ~kind(X0) | old(X0) | rich(X0) | rich(X0) [cnf transformation 56]
115. kind(X0) | ~old(X0) | rich(X0) | rich(X0) [cnf transformation 56]
116. creative(X0) | ~strong(X0) | funny(X0) | ~happy(X0) [cnf transformation 57]
131. calm(susan) [cnf transformation 24]
132. ~kind(X0) | old(X0) | ~rich(X0) [duplicate literal removal 112]
133. ~kind(X0) | old(X0) | rich(X0) [duplicate literal removal 113]
135. kind(X0) | ~old(X0) | rich(X0) [duplicate literal removal 115]
137. ~creative(X0) [duplicate literal removal 80]
138. ~funny(X0) [subsumption resolution 90,137]
158. strong(X0) | kind(X0) [subsumption resolution 95,138]
160. ~calm(X0) | ~humble(X0) [subsumption resolution 102,137]
161. ~calm(X0) | happy(X0) [subsumption resolution 101,137]
180. kind(X0) | rich(X0) [subsumption resolution 135,71]
182. rich(X0) | old(X0) [subsumption resolution 133,180]
183. ~kind(X0) | old(X0) [subsumption resolution 132,182]
184. ~strong(X0) | funny(X0) | ~happy(X0) [subsumption resolution 116,137]
185. ~happy(X0) | ~strong(X0) [subsumption resolution 184,138]
191. 10 <=> kind(susan) [avatar definition]
192. kind(susan) <- (10) [avatar component clause 191]
208. ~humble(susan) [resolution 160,131]
209. happy(susan) [resolution 161,131]
214. ~strong(susan) [resolution 185,209]
228. kind(susan) [resolution 214,158]
231. 10 [avatar split clause 228,191]
233. old(susan) <- (10) [resolution 192,183]
286. humble(susan) | ~old(susan) [resolution 89,209]
289. ~old(susan) [subsumption resolution 286,208]
290. $false <- (10) [subsumption resolution 289,233]
291. ~10 [avatar contradiction clause 290]
296. $false [avatar sat refutation 231,291]
% SZS output end Proof for 3816661878422817759801615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not creative then someone is either happy or brave and vice versa.
Everyone who is happy is both calm and not old and vice versa.
If susan is either generous or quiet then someone is either not old or happy and vice versa.
If someone is humble or not curious then someone is generous or wise.
Everyone who is either not curious or not generous is either not curious or not old and vice versa.
Everyone who is both humble and creative is either creative or not humble and vice versa.
Everyone who is both generous and not rich is either generous or creative.
Everyone who is both creative and curious is both not strong and not calm.
Everyone who is both not quiet and happy is both rich and curious and vice versa.
Everyone who is either not humble or funny is both tall and generous and vice versa.
If paul is either rich or funny then susan is both wise and brave and vice versa.
If someone is humble or calm then lucy is either rich or happy.
Everyone who is either not kind or not curious is both generous and not kind and vice versa.
If mary is kind or not happy then paul is both kind and not funny and vice versa.
Everyone who is both not tall and curious is not rich.
Everyone who is both not creative and quiet is either creative or not rich.
Someone is both wise and not patient.
Mary is either strong or funny.
Someone is both rich and humble.
Someone is not strong.
Paul is either not patient or not generous.
Lucy is not curious.
Susan is funny or not strong.
John is happy. | John is calm. | entailment | ((~creative(paul))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:(happy(X)<=>(calm(X)&~old(X))))&
(((generous(susan)<~>quiet(susan)))<=>(?[X]:((~old(X)<~>happy(X)))))&
((?[X]:((humble(X)|~curious(X))))=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((~curious(X)<~>~generous(X))<=>(~curious(X)<~>~old(X))))&
(![X]:((humble(X)&creative(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((generous(X)&~rich(X))=>(generous(X)<~>creative(X))))&
(![X]:((creative(X)&curious(X))=>(~strong(X)&~calm(X))))&
(![X]:((~quiet(X)&happy(X))<=>(rich(X)&curious(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(tall(X)&generous(X))))&
(((rich(paul)<~>funny(paul)))<=>((wise(susan)&brave(susan))))&
((?[X]:((humble(X)|calm(X))))=>((rich(lucy)<~>happy(lucy))))&
(![X]:((~kind(X)<~>~curious(X))<=>(generous(X)&~kind(X))))&
(((kind(mary)|~happy(mary)))<=>((kind(paul)&~funny(paul))))&
(![X]:((~tall(X)&curious(X))=>~rich(X)))&
(![X]:((~creative(X)&quiet(X))=>(creative(X)<~>~rich(X))))&
(?[X]:((wise(X)&~patient(X))))&
((strong(mary)<~>funny(mary)))&
(?[X]:((rich(X)&humble(X))))&
(?[X]:(~strong(X)))&
((~patient(paul)<~>~generous(paul)))&
(~curious(lucy))&
((funny(susan)|~strong(susan)))&
(happy(john)) | calm(john) | [
"p1",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3064512167101169610211342
% SZS output start Proof for 3064512167101169610211342
2. ! [X0] : (happy(X0) <=> (~old(X0) & calm(X0))) [input p1]
24. happy(john) [input p23]
25. ~calm(john) [input hypothesis]
41. ! [X0] : ((happy(X0) | (old(X0) | ~calm(X0))) & ((~old(X0) & calm(X0)) | ~happy(X0))) [nnf transformation 2]
42. ! [X0] : ((happy(X0) | old(X0) | ~calm(X0)) & ((~old(X0) & calm(X0)) | ~happy(X0))) [flattening 41]
78. ~happy(X0) | calm(X0) [cnf transformation 42]
154. happy(john) [cnf transformation 24]
155. ~calm(john) [cnf transformation 25]
324. calm(john) [resolution 78,154]
326. $false [subsumption resolution 324,155]
% SZS output end Proof for 3064512167101169610211342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is not funny or generous and vice versa. Everyone who is tall is both not kind and wise and vice versa. Everyone who is either not strong or kind is both old and not humble. Everyone who is either humble or generous is happy and vice versa. If someone is funny or kind then fred is either not generous or not humble and vice versa. If fred is strong or not generous then lucy is happy or not quiet. If john is both creative and quiet then susan is curious or patient and vice versa. If paul is not curious or generous then john is both not generous and not rich and vice versa. Everyone who is tall or old is old and vice versa. If mary is both not generous and not patient then paul is wise or generous. Everyone who is funny is either tall or strong and vice versa. Everyone who is not calm is not patient or happy. If john is not calm or quiet then someone is either old or not old. Everyone who is patient is both brave and quiet and vice versa. Everyone who is quiet is funny or rich and vice versa. Everyone who is both not kind and old is either patient or not brave and vice versa. Someone is either creative or not calm. Mary is old or not quiet. Someone is not quiet. John is both not generous and not tall. Someone is either not patient or not generous. Someone is both not brave and not curious. Someone is both not brave and humble. Someone is not patient. | Mary is brave. | neutral | (![X]:(humble(X)<=>(~funny(X)|generous(X))))&
(![X]:(tall(X)<=>(~kind(X)&wise(X))))&
(![X]:((~strong(X)<~>kind(X))=>(old(X)&~humble(X))))&
(![X]:((humble(X)<~>generous(X))<=>happy(X)))&
((?[X]:((funny(X)|kind(X))))<=>((~generous(fred)<~>~humble(fred))))&
(((strong(fred)|~generous(fred)))=>((happy(lucy)|~quiet(lucy))))&
(((creative(john)&quiet(john)))<=>((curious(susan)|patient(susan))))&
(((~curious(paul)|generous(paul)))<=>((~generous(john)&~rich(john))))&
(![X]:((tall(X)|old(X))<=>old(X)))&
(((~generous(mary)&~patient(mary)))=>((wise(paul)|generous(paul))))&
(![X]:(funny(X)<=>(tall(X)<~>strong(X))))&
(![X]:(~calm(X)=>(~patient(X)|happy(X))))&
(((~calm(john)|quiet(john)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:(patient(X)<=>(brave(X)&quiet(X))))&
(![X]:(quiet(X)<=>(funny(X)|rich(X))))&
(![X]:((~kind(X)&old(X))<=>(patient(X)<~>~brave(X))))&
(?[X]:((creative(X)<~>~calm(X))))&
((old(mary)|~quiet(mary)))&
(?[X]:(~quiet(X)))&
((~generous(john)&~tall(john)))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:((~brave(X)&~curious(X))))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:(~patient(X))) | brave(mary) | [] | null | 0 |
Everyone who is either not funny or old is both not happy and quiet and vice versa.
If someone is not funny then someone is both not brave and humble and vice versa.
If someone is patient or not funny then paul is both not rich and not calm and vice versa.
Everyone who is both kind and not generous is tall.
If alice is either patient or not tall then someone is either old or patient and vice versa.
If someone is both tall and curious then someone is either not generous or rich.
Everyone who is both not quiet and not strong is either not rich or old and vice versa.
Everyone who is either humble or rich is humble and vice versa.
If alice is either not rich or not tall then someone is generous.
If someone is not tall then someone is not brave or not happy.
If someone is both not patient and brave then someone is both not happy and not wise and vice versa.
Everyone who is not quiet is funny or humble.
Everyone who is both not calm and not rich is both not patient and not funny.
If alice is both not calm and not creative then someone is curious.
Everyone who is generous is not patient.
If paul is both not old and not generous then paul is either not brave or not humble and vice versa.
Lucy is either not happy or humble.
Someone is either not humble or calm.
Paul is not humble or kind.
John is tall.
Someone is both not kind and patient.
Someone is both calm and patient.
Someone is either not calm or not tall.
Someone is old. | Paul is calm. | contradiction | (![X]:((~funny(X)<~>old(X))<=>(~happy(X)&quiet(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~brave(X)&humble(X)))))&
((?[X]:((patient(X)|~funny(X))))<=>((~rich(paul)&~calm(paul))))&
(![X]:((kind(X)&~generous(X))=>tall(X)))&
(((patient(alice)<~>~tall(alice)))<=>(?[X]:((old(X)<~>patient(X)))))&
((?[X]:((tall(X)&curious(X))))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:((~quiet(X)&~strong(X))<=>(~rich(X)<~>old(X))))&
(![X]:((humble(X)<~>rich(X))<=>humble(X)))&
(((~rich(alice)<~>~tall(alice)))=>(?[X]:(generous(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~patient(X)&brave(X))))<=>(?[X]:((~happy(X)&~wise(X)))))&
(![X]:(~quiet(X)=>(funny(X)|humble(X))))&
(![X]:((~calm(X)&~rich(X))=>(~patient(X)&~funny(X))))&
(((~calm(alice)&~creative(alice)))=>(?[X]:(curious(X))))&
(![X]:(generous(X)=>~patient(X)))&
(((~old(paul)&~generous(paul)))<=>((~brave(paul)<~>~humble(paul))))&
((~happy(lucy)<~>humble(lucy)))&
(?[X]:((~humble(X)<~>calm(X))))&
((~humble(paul)|kind(paul)))&
(tall(john))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:((calm(X)&patient(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:(old(X))) | calm(paul) | [
"p2",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7817221019198883094301643
% SZS output start Proof for 7817221019198883094301643
3. ? [X0] : (~funny(X0) | patient(X0)) <=> (~calm(paul) & ~rich(paul)) [input p2]
21. ? [X0] : (patient(X0) & ~kind(X0)) [input p20]
25. calm(paul) [input hypothesis]
48. (? [X0] : (~funny(X0) | patient(X0)) | (calm(paul) | rich(paul))) & ((~calm(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & ~patient(X0))) [nnf transformation 3]
49. (? [X0] : (~funny(X0) | patient(X0)) | calm(paul) | rich(paul)) & ((~calm(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & ~patient(X0))) [flattening 48]
50. (? [X0] : (~funny(X0) | patient(X0)) | calm(paul) | rich(paul)) & ((~calm(paul) & ~rich(paul)) | ! [X1] : (funny(X1) & ~patient(X1))) [rectify 49]
51. ? [X0] : (~funny(X0) | patient(X0)) => (~funny(sK2) | patient(sK2)) [choice axiom]
52. ((~funny(sK2) | patient(sK2)) | calm(paul) | rich(paul)) & ((~calm(paul) & ~rich(paul)) | ! [X1] : (funny(X1) & ~patient(X1))) [skolemisation 50,51]
77. ? [X0] : (patient(X0) & ~kind(X0)) => (patient(sK9) & ~kind(sK9)) [choice axiom]
78. patient(sK9) & ~kind(sK9) [skolemisation 21,77]
97. ~calm(paul) | ~patient(X1) [cnf transformation 52]
143. patient(sK9) [cnf transformation 78]
149. calm(paul) [cnf transformation 25]
178. 7 <=> calm(paul) [avatar definition]
192. 10 <=> ! [X1] : ~patient(X1) [avatar definition]
193. ~patient(X1) <- (10) [avatar component clause 192]
194. 10 | ~7 [avatar split clause 97,178,192]
331. 7 [avatar split clause 149,178]
334. $false <- (10) [resolution 193,143]
337. ~10 [avatar contradiction clause 334]
338. $false [avatar sat refutation 194,331,337]
% SZS output end Proof for 7817221019198883094301643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If paul is both wise and not humble then lucy is both calm and not old.
Everyone who is both funny and not happy is not old or not kind and vice versa.
If someone is not wise or not calm then someone is wise or not brave.
Everyone who is wise is calm or creative and vice versa.
If someone is not tall or not calm then alice is both not humble and not patient.
If someone is either patient or creative then someone is either not curious or not calm and vice versa.
Everyone who is both generous and calm is generous or rich.
Everyone who is kind is both tall and not wise and vice versa.
If paul is either not rich or patient then someone is either not quiet or old and vice versa.
Everyone who is both not kind and not happy is not funny.
If someone is not calm then alice is both quiet and not curious.
Everyone who is either wise or brave is tall or not rich.
Everyone who is not quiet or not wise is either patient or kind and vice versa.
If someone is wise then someone is happy or rich.
Everyone who is either tall or not funny is patient and vice versa.
If mary is humble or tall then paul is funny or kind and vice versa.
Fred is either not quiet or brave.
Someone is either not wise or not kind. | Mary is calm. | contradiction | (((wise(paul)&~humble(paul)))=>((calm(lucy)&~old(lucy))))&
(![X]:((funny(X)&~happy(X))<=>(~old(X)|~kind(X))))&
((?[X]:((~wise(X)|~calm(X))))=>(?[X]:((wise(X)|~brave(X)))))&
(![X]:(wise(X)<=>(calm(X)|creative(X))))&
((?[X]:((~tall(X)|~calm(X))))=>((~humble(alice)&~patient(alice))))&
((?[X]:((patient(X)<~>creative(X))))<=>(?[X]:((~curious(X)<~>~calm(X)))))&
(![X]:((generous(X)&calm(X))=>(generous(X)|rich(X))))&
(![X]:(kind(X)<=>(tall(X)&~wise(X))))&
(((~rich(paul)<~>patient(paul)))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(![X]:((~kind(X)&~happy(X))=>~funny(X)))&
((?[X]:(~calm(X)))=>((quiet(alice)&~curious(alice))))&
(![X]:((wise(X)<~>brave(X))=>(tall(X)|~rich(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(patient(X)<~>kind(X))))&
((?[X]:(wise(X)))=>(?[X]:((happy(X)|rich(X)))))&
(![X]:((tall(X)<~>~funny(X))<=>patient(X)))&
(((humble(mary)|tall(mary)))<=>((funny(paul)|kind(paul))))&
((~quiet(fred)<~>brave(fred)))&
(?[X]:((~wise(X)<~>~kind(X)))) | calm(mary) | [
"p1",
"p3",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3199635801347447451833242
% SZS output start Proof for 3199635801347447451833242
2. ! [X0] : ((~happy(X0) & funny(X0)) <=> (~kind(X0) | ~old(X0))) [input p1]
4. ! [X0] : (wise(X0) <=> (creative(X0) | calm(X0))) [input p3]
8. ! [X0] : (kind(X0) <=> (~wise(X0) & tall(X0))) [input p7]
10. ! [X0] : ((~happy(X0) & ~kind(X0)) => ~funny(X0)) [input p9]
19. calm(mary) [input hypothesis]
29. ! [X0] : (~funny(X0) | (happy(X0) | kind(X0))) [ennf transformation 10]
30. ! [X0] : (~funny(X0) | happy(X0) | kind(X0)) [flattening 29]
35. ! [X0] : (((~happy(X0) & funny(X0)) | (kind(X0) & old(X0))) & ((~kind(X0) | ~old(X0)) | (happy(X0) | ~funny(X0)))) [nnf transformation 2]
36. ! [X0] : (((~happy(X0) & funny(X0)) | (kind(X0) & old(X0))) & (~kind(X0) | ~old(X0) | happy(X0) | ~funny(X0))) [flattening 35]
40. ! [X0] : ((wise(X0) | (~creative(X0) & ~calm(X0))) & ((creative(X0) | calm(X0)) | ~wise(X0))) [nnf transformation 4]
41. ! [X0] : ((wise(X0) | (~creative(X0) & ~calm(X0))) & (creative(X0) | calm(X0) | ~wise(X0))) [flattening 40]
47. ! [X0] : ((kind(X0) | (wise(X0) | ~tall(X0))) & ((~wise(X0) & tall(X0)) | ~kind(X0))) [nnf transformation 8]
48. ! [X0] : ((kind(X0) | wise(X0) | ~tall(X0)) & ((~wise(X0) & tall(X0)) | ~kind(X0))) [flattening 47]
70. kind(X0) | funny(X0) [cnf transformation 36]
72. ~happy(X0) | kind(X0) [cnf transformation 36]
76. ~calm(X0) | wise(X0) [cnf transformation 41]
92. ~kind(X0) | ~wise(X0) [cnf transformation 48]
102. ~funny(X0) | happy(X0) | kind(X0) [cnf transformation 30]
126. calm(mary) [cnf transformation 19]
242. ~funny(X0) | kind(X0) [subsumption resolution 102,72]
243. kind(X0) [subsumption resolution 242,70]
257. 28 <=> ! [X1] : ~wise(X1) [avatar definition]
258. ~wise(X1) <- (28) [avatar component clause 257]
295. wise(mary) [resolution 76,126]
297. $false <- (28) [subsumption resolution 295,258]
298. ~28 [avatar contradiction clause 297]
311. ~wise(X1) [resolution 92,243]
312. 28 [avatar split clause 311,257]
313. $false [avatar sat refutation 298,312]
% SZS output end Proof for 3199635801347447451833242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is rich then someone is not kind and vice versa.
Everyone who is patient is either wise or not funny.
If someone is either strong or not funny then someone is both rich and funny and vice versa.
If someone is not funny or happy then someone is not tall.
Everyone who is either not calm or brave is not brave.
Everyone who is both not tall and not rich is both patient and rich.
Everyone who is not brave or happy is both not kind and funny.
Everyone who is both not kind and happy is creative or not kind.
Everyone who is either strong or not brave is either not old or not wise and vice versa.
If someone is either old or not tall then someone is both generous and patient and vice versa.
If susan is funny then someone is not rich or not wise and vice versa.
Everyone who is both not patient and rich is happy or humble.
Everyone who is both not strong and quiet is either curious or not strong.
Everyone who is wise is both patient and quiet and vice versa.
If john is quiet then paul is either creative or calm and vice versa.
Everyone who is brave is both not creative and rich and vice versa.
Someone is either not happy or not funny.
John is both not rich and not kind.
Someone is quiet or not quiet.
John is either not rich or quiet.
Someone is either rich or kind.
Mary is curious or not rich.
Someone is not creative or generous. | John is patient. | contradiction | ((rich(fred))<=>(?[X]:(~kind(X))))&
(![X]:(patient(X)=>(wise(X)<~>~funny(X))))&
((?[X]:((strong(X)<~>~funny(X))))<=>(?[X]:((rich(X)&funny(X)))))&
((?[X]:((~funny(X)|happy(X))))=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)<~>brave(X))=>~brave(X)))&
(![X]:((~tall(X)&~rich(X))=>(patient(X)&rich(X))))&
(![X]:((~brave(X)|happy(X))=>(~kind(X)&funny(X))))&
(![X]:((~kind(X)&happy(X))=>(creative(X)|~kind(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~old(X)<~>~wise(X))))&
((?[X]:((old(X)<~>~tall(X))))<=>(?[X]:((generous(X)&patient(X)))))&
((funny(susan))<=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:((~patient(X)&rich(X))=>(happy(X)|humble(X))))&
(![X]:((~strong(X)&quiet(X))=>(curious(X)<~>~strong(X))))&
(![X]:(wise(X)<=>(patient(X)&quiet(X))))&
((quiet(john))<=>((creative(paul)<~>calm(paul))))&
(![X]:(brave(X)<=>(~creative(X)&rich(X))))&
(?[X]:((~happy(X)<~>~funny(X))))&
((~rich(john)&~kind(john)))&
(?[X]:((quiet(X)|~quiet(X))))&
((~rich(john)<~>quiet(john)))&
(?[X]:((rich(X)<~>kind(X))))&
((curious(mary)|~rich(mary)))&
(?[X]:((~creative(X)|generous(X)))) | patient(john) | [
"p1",
"p6",
"p13",
"p15",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1927100684678736819194858
% SZS output start Proof for 1927100684678736819194858
2. ! [X0] : (patient(X0) => (wise(X0) <~> ~funny(X0))) [input p1]
7. ! [X0] : ((happy(X0) | ~brave(X0)) => (funny(X0) & ~kind(X0))) [input p6]
14. ! [X0] : (wise(X0) <=> (quiet(X0) & patient(X0))) [input p13]
16. ! [X0] : (brave(X0) <=> (rich(X0) & ~creative(X0))) [input p15]
18. ~kind(john) & ~rich(john) [input p17]
20. ~rich(john) <~> quiet(john) [input p19]
24. patient(john) [input hypothesis]
29. ! [X0] : ((wise(X0) <~> ~funny(X0)) | ~patient(X0)) [ennf transformation 2]
34. ! [X0] : ((funny(X0) & ~kind(X0)) | (~happy(X0) & brave(X0))) [ennf transformation 7]
43. ! [X0] : (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | ~patient(X0)) [nnf transformation 29]
64. ! [X0] : ((wise(X0) | (~quiet(X0) | ~patient(X0))) & ((quiet(X0) & patient(X0)) | ~wise(X0))) [nnf transformation 14]
65. ! [X0] : ((wise(X0) | ~quiet(X0) | ~patient(X0)) & ((quiet(X0) & patient(X0)) | ~wise(X0))) [flattening 64]
67. ! [X0] : ((brave(X0) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | ~brave(X0))) [nnf transformation 16]
68. ! [X0] : ((brave(X0) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | ~brave(X0))) [flattening 67]
74. (~quiet(john) | rich(john)) & (quiet(john) | ~rich(john)) [nnf transformation 20]
82. ~funny(X0) | wise(X0) | ~patient(X0) [cnf transformation 43]
98. brave(X0) | funny(X0) [cnf transformation 34]
121. ~wise(X0) | quiet(X0) [cnf transformation 65]
128. ~brave(X0) | rich(X0) [cnf transformation 68]
132. ~rich(john) [cnf transformation 18]
136. ~quiet(john) | rich(john) [cnf transformation 74]
141. patient(john) [cnf transformation 24]
262. 28 <=> quiet(john) [avatar definition]
263. ~quiet(john) <- (~28) [avatar component clause 262]
271. ~quiet(john) [subsumption resolution 136,132]
272. ~28 [avatar split clause 271,262]
301. funny(X0) | rich(X0) [resolution 128,98]
473. ~patient(X0) | wise(X0) | rich(X0) [resolution 301,82]
535. wise(john) | rich(john) [resolution 473,141]
537. wise(john) [subsumption resolution 535,132]
552. quiet(john) [resolution 537,121]
574. $false <- (~28) [subsumption resolution 552,263]
575. 28 [avatar contradiction clause 574]
576. $false [avatar sat refutation 272,575]
% SZS output end Proof for 1927100684678736819194858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not funny is either not quiet or brave.
If paul is not rich then someone is either patient or old.
Everyone who is either rich or brave is not brave or not patient and vice versa.
Everyone who is both not calm and creative is not generous and vice versa.
Everyone who is both not strong and quiet is both not wise and patient.
Everyone who is not tall or curious is both not kind and not brave.
If fred is either not rich or strong then someone is quiet or not calm.
Everyone who is both not humble and not tall is not rich or old.
Everyone who is not generous or strong is wise or patient and vice versa.
If someone is brave then someone is either not brave or funny.
Everyone who is not funny is either patient or not tall.
Everyone who is not tall or humble is humble or not generous.
Everyone who is not quiet is tall or rich and vice versa.
Everyone who is not strong is not old or not calm.
If someone is old or not rich then someone is either kind or quiet.
Everyone who is humble is curious and vice versa.
Paul is not brave or old.
Someone is curious.
Someone is not creative.
Fred is both funny and curious.
Someone is either creative or not tall.
Someone is brave or strong.
Someone is both not generous and not patient. | Fred is not generous. | neutral | (![X]:((tall(X)<~>~funny(X))=>(~quiet(X)<~>brave(X))))&
((~rich(paul))=>(?[X]:((patient(X)<~>old(X)))))&
(![X]:((rich(X)<~>brave(X))<=>(~brave(X)|~patient(X))))&
(![X]:((~calm(X)&creative(X))<=>~generous(X)))&
(![X]:((~strong(X)&quiet(X))=>(~wise(X)&patient(X))))&
(![X]:((~tall(X)|curious(X))=>(~kind(X)&~brave(X))))&
(((~rich(fred)<~>strong(fred)))=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((~humble(X)&~tall(X))=>(~rich(X)|old(X))))&
(![X]:((~generous(X)|strong(X))<=>(wise(X)|patient(X))))&
((?[X]:(brave(X)))=>(?[X]:((~brave(X)<~>funny(X)))))&
(![X]:(~funny(X)=>(patient(X)<~>~tall(X))))&
(![X]:((~tall(X)|humble(X))=>(humble(X)|~generous(X))))&
(![X]:(~quiet(X)<=>(tall(X)|rich(X))))&
(![X]:(~strong(X)=>(~old(X)|~calm(X))))&
((?[X]:((old(X)|~rich(X))))=>(?[X]:((kind(X)<~>quiet(X)))))&
(![X]:(humble(X)<=>curious(X)))&
((~brave(paul)|old(paul)))&
(?[X]:(curious(X)))&
(?[X]:(~creative(X)))&
((funny(fred)&curious(fred)))&
(?[X]:((creative(X)<~>~tall(X))))&
(?[X]:((brave(X)|strong(X))))&
(?[X]:((~generous(X)&~patient(X)))) | ~generous(fred) | [] | null | 0 |
If mary is not funny then someone is not rich or not strong and vice versa. Everyone who is quiet or generous is both not wise and generous. Everyone who is funny or not quiet is either wise or not old and vice versa. If someone is generous or not tall then lucy is not quiet. Everyone who is not brave is both not funny and not generous and vice versa. Everyone who is creative is both not curious and curious and vice versa. If someone is tall then fred is both old and not happy. If someone is generous or funny then someone is either funny or not funny and vice versa. If someone is either rich or curious then someone is not curious and vice versa. If paul is patient then someone is not creative. Everyone who is not humble or not generous is not brave and vice versa. Everyone who is both not humble and not creative is happy or rich and vice versa. If paul is either not generous or patient then susan is humble or not tall and vice versa. Everyone who is kind or not brave is both funny and not strong. Everyone who is not tall or not old is not curious and vice versa. If someone is rich then someone is both not calm and not rich and vice versa. Someone is either not funny or patient. John is happy or not wise. Someone is not funny or not humble. Someone is not curious. John is not quiet. Mary is both not kind and not old. Alice is not old or quiet. | Lucy is curious. | contradiction | ((~funny(mary))<=>(?[X]:((~rich(X)|~strong(X)))))&
(![X]:((quiet(X)|generous(X))=>(~wise(X)&generous(X))))&
(![X]:((funny(X)|~quiet(X))<=>(wise(X)<~>~old(X))))&
((?[X]:((generous(X)|~tall(X))))=>(~quiet(lucy)))&
(![X]:(~brave(X)<=>(~funny(X)&~generous(X))))&
(![X]:(creative(X)<=>(~curious(X)&curious(X))))&
((?[X]:(tall(X)))=>((old(fred)&~happy(fred))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
((?[X]:((rich(X)<~>curious(X))))<=>(?[X]:(~curious(X))))&
((patient(paul))=>(?[X]:(~creative(X))))&
(![X]:((~humble(X)|~generous(X))<=>~brave(X)))&
(![X]:((~humble(X)&~creative(X))<=>(happy(X)|rich(X))))&
(((~generous(paul)<~>patient(paul)))<=>((humble(susan)|~tall(susan))))&
(![X]:((kind(X)|~brave(X))=>(funny(X)&~strong(X))))&
(![X]:((~tall(X)|~old(X))<=>~curious(X)))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)&~rich(X)))))&
(?[X]:((~funny(X)<~>patient(X))))&
((happy(john)|~wise(john)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:(~curious(X)))&
(~quiet(john))&
((~kind(mary)&~old(mary)))&
((~old(alice)|quiet(alice))) | curious(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7922471316262410579385242
% SZS output start Proof for 7922471316262410579385242
2. ! [X0] : ((generous(X0) | quiet(X0)) => (generous(X0) & ~wise(X0))) [input p1]
3. ! [X0] : ((~quiet(X0) | funny(X0)) <=> (wise(X0) <~> ~old(X0))) [input p2]
4. ? [X0] : (~tall(X0) | generous(X0)) => ~quiet(lucy) [input p3]
5. ! [X0] : (~brave(X0) <=> (~generous(X0) & ~funny(X0))) [input p4]
11. ! [X0] : ((~generous(X0) | ~humble(X0)) <=> ~brave(X0)) [input p10]
14. ! [X0] : ((~brave(X0) | kind(X0)) => (~strong(X0) & funny(X0))) [input p13]
15. ! [X0] : ((~old(X0) | ~tall(X0)) <=> ~curious(X0)) [input p14]
24. curious(lucy) [input hypothesis]
28. ! [X0] : (~brave(X0) => (~strong(X0) & funny(X0))) [pure predicate removal 14]
30. ! [X0] : ((generous(X0) & ~wise(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 2]
31. ~quiet(lucy) | ! [X0] : (tall(X0) & ~generous(X0)) [ennf transformation 4]
34. ! [X0] : ((~strong(X0) & funny(X0)) | brave(X0)) [ennf transformation 28]
39. ! [X0] : (((~quiet(X0) | funny(X0)) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0)))) & (((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (quiet(X0) & ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((~quiet(X0) | funny(X0) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0)))) & (((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (quiet(X0) & ~funny(X0)))) [flattening 39]
41. ! [X0] : ((~brave(X0) | (generous(X0) | funny(X0))) & ((~generous(X0) & ~funny(X0)) | brave(X0))) [nnf transformation 5]
42. ! [X0] : ((~brave(X0) | generous(X0) | funny(X0)) & ((~generous(X0) & ~funny(X0)) | brave(X0))) [flattening 41]
57. ! [X0] : (((~generous(X0) | ~humble(X0)) | brave(X0)) & (~brave(X0) | (generous(X0) & humble(X0)))) [nnf transformation 11]
58. ! [X0] : ((~generous(X0) | ~humble(X0) | brave(X0)) & (~brave(X0) | (generous(X0) & humble(X0)))) [flattening 57]
63. ! [X0] : (((~old(X0) | ~tall(X0)) | curious(X0)) & (~curious(X0) | (old(X0) & tall(X0)))) [nnf transformation 15]
64. ! [X0] : ((~old(X0) | ~tall(X0) | curious(X0)) & (~curious(X0) | (old(X0) & tall(X0)))) [flattening 63]
81. ~wise(X0) | ~generous(X0) [cnf transformation 30]
85. ~old(X0) | wise(X0) | quiet(X0) [cnf transformation 40]
90. ~quiet(lucy) | ~generous(X0) [cnf transformation 31]
92. ~funny(X0) | brave(X0) [cnf transformation 42]
112. ~brave(X0) | generous(X0) [cnf transformation 58]
125. funny(X0) | brave(X0) [cnf transformation 34]
128. ~curious(X0) | old(X0) [cnf transformation 64]
141. curious(lucy) [cnf transformation 24]
171. 7 <=> quiet(lucy) [avatar definition]
176. 8 <=> ! [X0] : ~generous(X0) [avatar definition]
177. ~generous(X0) <- (8) [avatar component clause 176]
178. 8 | ~7 [avatar split clause 90,171,176]
257. brave(X0) [subsumption resolution 125,92]
322. generous(X0) [resolution 112,257]
337. old(lucy) [resolution 128,141]
363. 42 <=> wise(lucy) [avatar definition]
365. wise(lucy) <- (42) [avatar component clause 363]
378. wise(lucy) | quiet(lucy) [resolution 85,337]
392. 7 | 42 [avatar split clause 378,363,171]
393. $false <- (8) [subsumption resolution 177,322]
394. ~8 [avatar contradiction clause 393]
418. ~generous(lucy) <- (42) [resolution 365,81]
420. $false <- (42) [subsumption resolution 418,322]
421. ~42 [avatar contradiction clause 420]
422. $false [avatar sat refutation 178,392,394,421]
% SZS output end Proof for 7922471316262410579385242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not curious and not wise then someone is not tall or not calm and vice versa. If john is not generous or not wise then someone is not rich. If someone is either not old or tall then john is calm. Everyone who is either strong or calm is not creative and vice versa. Everyone who is quiet is both brave and not tall. Everyone who is funny is not calm or quiet and vice versa. Everyone who is both not kind and generous is funny or not brave and vice versa. If john is not tall then fred is either funny or curious. Everyone who is not quiet or not tall is happy or not tall and vice versa. Everyone who is not quiet or not strong is not happy or strong and vice versa. Everyone who is both kind and not tall is either humble or kind and vice versa. Everyone who is not quiet or funny is not funny or not generous. If someone is both happy and not calm then someone is patient and vice versa. Everyone who is not rich is not tall. Everyone who is not humble is not quiet and vice versa. If someone is both not calm and old then lucy is not curious and vice versa. Someone is not happy or patient. Someone is either creative or not tall. Alice is not humble. Fred is not brave. Fred is both not happy and not kind. Someone is not happy. Alice is not creative. Alice is not funny or not brave. | John is not patient. | entailment | (((~curious(fred)&~wise(fred)))<=>(?[X]:((~tall(X)|~calm(X)))))&
(((~generous(john)|~wise(john)))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)<~>tall(X))))=>(calm(john)))&
(![X]:((strong(X)<~>calm(X))<=>~creative(X)))&
(![X]:(quiet(X)=>(brave(X)&~tall(X))))&
(![X]:(funny(X)<=>(~calm(X)|quiet(X))))&
(![X]:((~kind(X)&generous(X))<=>(funny(X)|~brave(X))))&
((~tall(john))=>((funny(fred)<~>curious(fred))))&
(![X]:((~quiet(X)|~tall(X))<=>(happy(X)|~tall(X))))&
(![X]:((~quiet(X)|~strong(X))<=>(~happy(X)|strong(X))))&
(![X]:((kind(X)&~tall(X))<=>(humble(X)<~>kind(X))))&
(![X]:((~quiet(X)|funny(X))=>(~funny(X)|~generous(X))))&
((?[X]:((happy(X)&~calm(X))))<=>(?[X]:(patient(X))))&
(![X]:(~rich(X)=>~tall(X)))&
(![X]:(~humble(X)<=>~quiet(X)))&
((?[X]:((~calm(X)&old(X))))<=>(~curious(lucy)))&
(?[X]:((~happy(X)|patient(X))))&
(?[X]:((creative(X)<~>~tall(X))))&
(~humble(alice))&
(~brave(fred))&
((~happy(fred)&~kind(fred)))&
(?[X]:(~happy(X)))&
(~creative(alice))&
((~funny(alice)|~brave(alice))) | ~patient(john) | [
"p5",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4330267215904177408949432
% SZS output start Proof for 4330267215904177408949432
6. ! [X0] : (funny(X0) <=> (quiet(X0) | ~calm(X0))) [input p5]
7. ! [X0] : ((generous(X0) & ~kind(X0)) <=> (~brave(X0) | funny(X0))) [input p6]
12. ! [X0] : ((funny(X0) | ~quiet(X0)) => (~generous(X0) | ~funny(X0))) [input p11]
13. ? [X0] : (~calm(X0) & happy(X0)) <=> ? [X0] : patient(X0) [input p12]
25. patient(john) [input hypothesis]
26. ? [X0] : (~calm(X0) & happy(X0)) <=> ? [X1] : patient(X1) [rectify 13]
31. ! [X0] : ((~generous(X0) | ~funny(X0)) | (~funny(X0) & quiet(X0))) [ennf transformation 12]
32. ! [X0] : (~generous(X0) | ~funny(X0) | (~funny(X0) & quiet(X0))) [flattening 31]
43. ! [X0] : ((funny(X0) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | ~funny(X0))) [nnf transformation 6]
44. ! [X0] : ((funny(X0) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ~funny(X0))) [flattening 43]
45. ! [X0] : (((generous(X0) & ~kind(X0)) | (brave(X0) & ~funny(X0))) & ((~brave(X0) | funny(X0)) | (~generous(X0) | kind(X0)))) [nnf transformation 7]
46. ! [X0] : (((generous(X0) & ~kind(X0)) | (brave(X0) & ~funny(X0))) & (~brave(X0) | funny(X0) | ~generous(X0) | kind(X0))) [flattening 45]
54. (? [X0] : (~calm(X0) & happy(X0)) | ! [X1] : ~patient(X1)) & (? [X1] : patient(X1) | ! [X0] : (calm(X0) | ~happy(X0))) [nnf transformation 26]
55. (? [X0] : (~calm(X0) & happy(X0)) | ! [X1] : ~patient(X1)) & (? [X2] : patient(X2) | ! [X3] : (calm(X3) | ~happy(X3))) [rectify 54]
56. ? [X0] : (~calm(X0) & happy(X0)) => (~calm(sK2) & happy(sK2)) [choice axiom]
57. ? [X2] : patient(X2) => patient(sK3) [choice axiom]
58. ((~calm(sK2) & happy(sK2)) | ! [X1] : ~patient(X1)) & (patient(sK3) | ! [X3] : (calm(X3) | ~happy(X3))) [skolemisation 55,57,56]
87. funny(X0) | calm(X0) [cnf transformation 44]
92. generous(X0) | ~funny(X0) [cnf transformation 46]
111. ~generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 32]
114. ~calm(sK2) | ~patient(X1) [cnf transformation 58]
131. patient(john) [cnf transformation 25]
132. ~generous(X0) | ~funny(X0) [duplicate literal removal 111]
138. 1 <=> ! [X0] : calm(X0) [avatar definition]
139. calm(X0) <- (1) [avatar component clause 138]
202. ~funny(X0) [subsumption resolution 132,92]
204. 15 <=> ! [X1] : ~patient(X1) [avatar definition]
205. ~patient(X1) <- (15) [avatar component clause 204]
207. 16 <=> calm(sK2) [avatar definition]
209. ~calm(sK2) <- (~16) [avatar component clause 207]
210. 15 | ~16 [avatar split clause 114,207,204]
261. $false <- (15) [resolution 205,131]
262. ~15 [avatar contradiction clause 261]
263. calm(X0) [resolution 87,202]
264. 1 [avatar split clause 263,138]
266. $false <- (1, ~16) [resolution 139,209]
269. ~1 | 16 [avatar contradiction clause 266]
271. $false [avatar sat refutation 210,262,264,269]
% SZS output end Proof for 4330267215904177408949432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then susan is both not kind and rich and vice versa. If someone is both not creative and wise then someone is not rich or not humble. Everyone who is either not tall or humble is both rich and calm and vice versa. If paul is not brave then john is humble or old and vice versa. Everyone who is either creative or brave is both brave and not creative and vice versa. If alice is curious then susan is not patient. Everyone who is not funny or not wise is both not creative and curious and vice versa. Everyone who is not old is either strong or not funny. Everyone who is not wise or not creative is calm and vice versa. If someone is either rich or funny then someone is either not calm or not strong. Everyone who is not creative is not quiet and vice versa. Everyone who is funny or curious is rich or not rich. Everyone who is either patient or not kind is rich and vice versa. Everyone who is happy is both not funny and creative. If someone is not patient or curious then someone is either kind or not patient and vice versa. If paul is both brave and not quiet then someone is not quiet and vice versa. Someone is either curious or old. Lucy is both not tall and not generous. Someone is creative or happy. Paul is either creative or happy. Paul is happy or creative. Mary is quiet or not kind. | Alice is not curious. | neutral | ((?[X]:(~tall(X)))<=>((~kind(susan)&rich(susan))))&
((?[X]:((~creative(X)&wise(X))))=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:((~tall(X)<~>humble(X))<=>(rich(X)&calm(X))))&
((~brave(paul))<=>((humble(john)|old(john))))&
(![X]:((creative(X)<~>brave(X))<=>(brave(X)&~creative(X))))&
((curious(alice))=>(~patient(susan)))&
(![X]:((~funny(X)|~wise(X))<=>(~creative(X)&curious(X))))&
(![X]:(~old(X)=>(strong(X)<~>~funny(X))))&
(![X]:((~wise(X)|~creative(X))<=>calm(X)))&
((?[X]:((rich(X)<~>funny(X))))=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:(~creative(X)<=>~quiet(X)))&
(![X]:((funny(X)|curious(X))=>(rich(X)|~rich(X))))&
(![X]:((patient(X)<~>~kind(X))<=>rich(X)))&
(![X]:(happy(X)=>(~funny(X)&creative(X))))&
((?[X]:((~patient(X)|curious(X))))<=>(?[X]:((kind(X)<~>~patient(X)))))&
(((brave(paul)&~quiet(paul)))<=>(?[X]:(~quiet(X))))&
(?[X]:((curious(X)<~>old(X))))&
((~tall(lucy)&~generous(lucy)))&
(?[X]:((creative(X)|happy(X))))&
((creative(paul)<~>happy(paul)))&
((happy(paul)|creative(paul)))&
((quiet(mary)|~kind(mary))) | ~curious(alice) | [] | null | 0 |
Everyone who is either not tall or not calm is both not creative and not old. If susan is funny then someone is rich and vice versa. Everyone who is not calm or patient is both creative and old and vice versa. If lucy is not kind then someone is either generous or not strong and vice versa. Everyone who is both not quiet and strong is both not humble and curious and vice versa. If someone is not calm or not strong then someone is both tall and not generous and vice versa. Everyone who is not strong is not wise or quiet and vice versa. If someone is not curious or not old then alice is wise or old and vice versa. Everyone who is generous or rich is either not patient or not brave. If someone is humble then susan is both not quiet and brave and vice versa. Everyone who is not patient or not creative is both humble and not generous and vice versa. Everyone who is either not quiet or not patient is both brave and not calm. If john is both not old and not rich then someone is not kind or happy. Everyone who is either not rich or patient is both not creative and not happy and vice versa. Everyone who is both funny and not kind is either humble or not old. Someone is quiet or not old. Someone is tall or rich. Mary is strong or generous. Alice is either kind or not brave. Someone is strong or happy. Someone is either quiet or not funny. Someone is humble or not creative. Susan is not brave or not funny. | Alice is not rich. | entailment | (![X]:((~tall(X)<~>~calm(X))=>(~creative(X)&~old(X))))&
((funny(susan))<=>(?[X]:(rich(X))))&
(![X]:((~calm(X)|patient(X))<=>(creative(X)&old(X))))&
((~kind(lucy))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~quiet(X)&strong(X))<=>(~humble(X)&curious(X))))&
((?[X]:((~calm(X)|~strong(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(![X]:(~strong(X)<=>(~wise(X)|quiet(X))))&
((?[X]:((~curious(X)|~old(X))))<=>((wise(alice)|old(alice))))&
(![X]:((generous(X)|rich(X))=>(~patient(X)<~>~brave(X))))&
((?[X]:(humble(X)))<=>((~quiet(susan)&brave(susan))))&
(![X]:((~patient(X)|~creative(X))<=>(humble(X)&~generous(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(brave(X)&~calm(X))))&
(((~old(john)&~rich(john)))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((~rich(X)<~>patient(X))<=>(~creative(X)&~happy(X))))&
(![X]:((funny(X)&~kind(X))=>(humble(X)<~>~old(X))))&
(?[X]:((quiet(X)|~old(X))))&
(?[X]:((tall(X)|rich(X))))&
((strong(mary)|generous(mary)))&
((kind(alice)<~>~brave(alice)))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((quiet(X)<~>~funny(X))))&
(?[X]:((humble(X)|~creative(X))))&
((~brave(susan)|~funny(susan))) | ~rich(alice) | [
"p1",
"p9",
"p10",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7880109200814793567403496
% SZS output start Proof for 7880109200814793567403496
2. funny(susan) <=> ? [X0] : rich(X0) [input p1]
10. ? [X0] : humble(X0) <=> (brave(susan) & ~quiet(susan)) [input p9]
11. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (~generous(X0) & humble(X0))) [input p10]
22. ? [X0] : (~creative(X0) | humble(X0)) [input p21]
23. ~funny(susan) | ~brave(susan) [input p22]
24. rich(alice) [input hypothesis]
34. (funny(susan) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | ~funny(susan)) [nnf transformation 2]
35. (funny(susan) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | ~funny(susan)) [rectify 34]
36. ? [X1] : rich(X1) => rich(sK0) [choice axiom]
37. (funny(susan) | ! [X0] : ~rich(X0)) & (rich(sK0) | ~funny(susan)) [skolemisation 35,36]
59. (? [X0] : humble(X0) | (~brave(susan) | quiet(susan))) & ((brave(susan) & ~quiet(susan)) | ! [X0] : ~humble(X0)) [nnf transformation 10]
60. (? [X0] : humble(X0) | ~brave(susan) | quiet(susan)) & ((brave(susan) & ~quiet(susan)) | ! [X0] : ~humble(X0)) [flattening 59]
61. (? [X0] : humble(X0) | ~brave(susan) | quiet(susan)) & ((brave(susan) & ~quiet(susan)) | ! [X1] : ~humble(X1)) [rectify 60]
62. ? [X0] : humble(X0) => humble(sK5) [choice axiom]
63. (humble(sK5) | ~brave(susan) | quiet(susan)) & ((brave(susan) & ~quiet(susan)) | ! [X1] : ~humble(X1)) [skolemisation 61,62]
64. ! [X0] : (((~creative(X0) | ~patient(X0)) | (generous(X0) | ~humble(X0))) & ((~generous(X0) & humble(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 11]
65. ! [X0] : ((~creative(X0) | ~patient(X0) | generous(X0) | ~humble(X0)) & ((~generous(X0) & humble(X0)) | (creative(X0) & patient(X0)))) [flattening 64]
82. ? [X0] : (~creative(X0) | humble(X0)) => (~creative(sK11) | humble(sK11)) [choice axiom]
83. ~creative(sK11) | humble(sK11) [skolemisation 22,82]
89. funny(susan) | ~rich(X0) [cnf transformation 37]
120. brave(susan) | ~humble(X1) [cnf transformation 63]
123. humble(X0) | creative(X0) [cnf transformation 65]
148. ~creative(sK11) | humble(sK11) [cnf transformation 83]
149. ~funny(susan) | ~brave(susan) [cnf transformation 23]
150. rich(alice) [cnf transformation 24]
152. 1 <=> ! [X0] : ~rich(X0) [avatar definition]
153. ~rich(X0) <- (1) [avatar component clause 152]
155. 2 <=> funny(susan) [avatar definition]
158. 1 | 2 [avatar split clause 89,155,152]
247. 23 <=> brave(susan) [avatar definition]
256. 25 <=> ! [X1] : ~humble(X1) [avatar definition]
257. ~humble(X1) <- (25) [avatar component clause 256]
258. 25 | 23 [avatar split clause 120,247,256]
336. humble(sK11) [subsumption resolution 148,123]
337. ~23 | ~2 [avatar split clause 149,155,247]
344. $false <- (25) [resolution 336,257]
345. ~25 [avatar contradiction clause 344]
346. $false <- (1) [resolution 153,150]
349. ~1 [avatar contradiction clause 346]
350. $false [avatar sat refutation 158,258,337,345,349]
% SZS output end Proof for 7880109200814793567403496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not patient is patient and vice versa. Everyone who is strong is tall. If someone is calm then lucy is not patient or not calm. Everyone who is calm is curious and vice versa. If alice is not rich then lucy is not generous. If someone is both not curious and creative then someone is not happy or funny. Everyone who is not creative is funny or not humble and vice versa. If someone is happy or brave then someone is both not generous and funny. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. If someone is both kind and not humble then fred is either not funny or creative. Everyone who is curious or wise is not curious. Everyone who is both humble and rich is not brave and vice versa. If mary is not patient or funny then john is either strong or not patient and vice versa. Everyone who is either patient or kind is either strong or happy. Alice is tall or happy. Someone is either not kind or not rich. Fred is either tall or not generous. Someone is strong. Someone is both not old and tall. Alice is generous or happy. | Lucy is calm. | contradiction | (![X]:((creative(X)<~>~patient(X))<=>patient(X)))&
(![X]:(strong(X)=>tall(X)))&
((?[X]:(calm(X)))=>((~patient(lucy)|~calm(lucy))))&
(![X]:(calm(X)<=>curious(X)))&
((~rich(alice))=>(~generous(lucy)))&
((?[X]:((~curious(X)&creative(X))))=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:(~creative(X)<=>(funny(X)|~humble(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
((tall(alice)|happy(alice)))&
(?[X]:((~kind(X)<~>~rich(X))))&
((tall(fred)<~>~generous(fred)))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)&tall(X))))&
((generous(alice)|happy(alice))) | calm(lucy) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3115368302843065496418991
% SZS output start Proof for 3115368302843065496418991
4. ! [X0] : (calm(X0) <=> curious(X0)) [input p3]
13. ! [X0] : ((wise(X0) | curious(X0)) => ~curious(X0)) [input p12]
23. calm(lucy) [input hypothesis]
36. ! [X0] : (~curious(X0) | (~wise(X0) & ~curious(X0))) [ennf transformation 13]
40. ! [X0] : ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))) [nnf transformation 4]
70. ~calm(X0) | curious(X0) [cnf transformation 40]
93. ~curious(X0) | ~curious(X0) [cnf transformation 36]
115. calm(lucy) [cnf transformation 23]
116. ~curious(X0) [duplicate literal removal 93]
128. 3 <=> calm(lucy) [avatar definition]
129. calm(lucy) <- (3) [avatar component clause 128]
197. 3 [avatar split clause 115,128]
199. curious(lucy) <- (3) [resolution 70,129]
200. $false <- (3) [subsumption resolution 199,116]
201. ~3 [avatar contradiction clause 200]
202. $false [avatar sat refutation 197,201]
% SZS output end Proof for 3115368302843065496418991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then someone is not funny.
If someone is either old or strong then someone is either brave or funny.
Everyone who is not curious or brave is either not curious or not brave and vice versa.
Everyone who is kind or tall is generous and vice versa.
Everyone who is generous is both rich and funny.
Everyone who is both not quiet and not calm is both not strong and not tall.
Everyone who is both brave and old is brave.
If susan is both not tall and not creative then paul is not patient.
If mary is both old and not old then someone is not happy and vice versa.
If someone is creative or not creative then someone is both humble and not strong and vice versa.
Everyone who is not kind is brave or not brave.
If someone is both not strong and humble then fred is either strong or old.
If fred is either generous or wise then someone is either not funny or not old.
If someone is either not strong or not brave then paul is not humble and vice versa.
Everyone who is either kind or tall is either old or happy and vice versa.
If paul is either not calm or happy then alice is either not funny or wise and vice versa.
Mary is not calm.
Someone is either curious or kind.
Someone is wise or not quiet.
Someone is not curious or humble.
Lucy is either not tall or humble.
John is humble or old.
Susan is either strong or not brave. | Mary is not happy. | contradiction | ((?[X]:(quiet(X)))=>(?[X]:(~funny(X))))&
((?[X]:((old(X)<~>strong(X))))=>(?[X]:((brave(X)<~>funny(X)))))&
(![X]:((~curious(X)|brave(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((kind(X)|tall(X))<=>generous(X)))&
(![X]:(generous(X)=>(rich(X)&funny(X))))&
(![X]:((~quiet(X)&~calm(X))=>(~strong(X)&~tall(X))))&
(![X]:((brave(X)&old(X))=>brave(X)))&
(((~tall(susan)&~creative(susan)))=>(~patient(paul)))&
(((old(mary)&~old(mary)))<=>(?[X]:(~happy(X))))&
((?[X]:((creative(X)|~creative(X))))<=>(?[X]:((humble(X)&~strong(X)))))&
(![X]:(~kind(X)=>(brave(X)|~brave(X))))&
((?[X]:((~strong(X)&humble(X))))=>((strong(fred)<~>old(fred))))&
(((generous(fred)<~>wise(fred)))=>(?[X]:((~funny(X)<~>~old(X)))))&
((?[X]:((~strong(X)<~>~brave(X))))<=>(~humble(paul)))&
(![X]:((kind(X)<~>tall(X))<=>(old(X)<~>happy(X))))&
(((~calm(paul)<~>happy(paul)))<=>((~funny(alice)<~>wise(alice))))&
(~calm(mary))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:((~curious(X)|humble(X))))&
((~tall(lucy)<~>humble(lucy)))&
((humble(john)|old(john)))&
((strong(susan)<~>~brave(susan))) | ~happy(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7774578530541936216455453
% SZS output start Proof for 7774578530541936216455453
9. (~old(mary) & old(mary)) <=> ? [X0] : ~happy(X0) [input p8]
24. ~happy(mary) [input hypothesis]
52. ((~old(mary) & old(mary)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (old(mary) | ~old(mary))) [nnf transformation 9]
53. ((~old(mary) & old(mary)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | old(mary) | ~old(mary)) [flattening 52]
54. ((~old(mary) & old(mary)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | old(mary) | ~old(mary)) [rectify 53]
55. ? [X1] : ~happy(X1) => ~happy(sK2) [choice axiom]
56. ((~old(mary) & old(mary)) | ! [X0] : happy(X0)) & (~happy(sK2) | old(mary) | ~old(mary)) [skolemisation 54,55]
100. old(mary) | happy(X0) [cnf transformation 56]
101. ~old(mary) | happy(X0) [cnf transformation 56]
144. ~happy(mary) [cnf transformation 24]
177. 7 <=> ! [X0] : happy(X0) [avatar definition]
178. happy(X0) <- (7) [avatar component clause 177]
180. 8 <=> old(mary) [avatar definition]
183. 7 | ~8 [avatar split clause 101,180,177]
184. 7 | 8 [avatar split clause 100,180,177]
307. $false <- (7) [resolution 178,144]
308. ~7 [avatar contradiction clause 307]
309. $false [avatar sat refutation 183,184,308]
% SZS output end Proof for 7774578530541936216455453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both not wise and patient. Everyone who is both not calm and generous is not creative or not kind and vice versa. Everyone who is either humble or creative is either not rich or generous and vice versa. Everyone who is funny is both not creative and not strong. If someone is not curious or wise then susan is kind and vice versa. Everyone who is both humble and curious is not calm and vice versa. If someone is funny then someone is either not funny or funny and vice versa. If fred is either not creative or not humble then alice is not funny and vice versa. Everyone who is both not quiet and calm is not humble. If paul is tall or not tall then lucy is either not curious or not strong and vice versa. If someone is humble then someone is both not tall and quiet and vice versa. Everyone who is kind is kind or calm and vice versa. Everyone who is either quiet or not quiet is either creative or not wise. Everyone who is both wise and creative is not generous or old and vice versa. Everyone who is not brave or generous is curious or not generous. Everyone who is either funny or quiet is not kind or rich. Paul is tall or not kind. Lucy is both not strong and not creative. Someone is brave or funny. Someone is either not brave or not quiet. Someone is both curious and happy. Alice is tall. | Lucy is rich. | entailment | (![X]:(~funny(X)=>(~wise(X)&patient(X))))&
(![X]:((~calm(X)&generous(X))<=>(~creative(X)|~kind(X))))&
(![X]:((humble(X)<~>creative(X))<=>(~rich(X)<~>generous(X))))&
(![X]:(funny(X)=>(~creative(X)&~strong(X))))&
((?[X]:((~curious(X)|wise(X))))<=>(kind(susan)))&
(![X]:((humble(X)&curious(X))<=>~calm(X)))&
((?[X]:(funny(X)))<=>(?[X]:((~funny(X)<~>funny(X)))))&
(((~creative(fred)<~>~humble(fred)))<=>(~funny(alice)))&
(![X]:((~quiet(X)&calm(X))=>~humble(X)))&
(((tall(paul)|~tall(paul)))<=>((~curious(lucy)<~>~strong(lucy))))&
((?[X]:(humble(X)))<=>(?[X]:((~tall(X)&quiet(X)))))&
(![X]:(kind(X)<=>(kind(X)|calm(X))))&
(![X]:((quiet(X)<~>~quiet(X))=>(creative(X)<~>~wise(X))))&
(![X]:((wise(X)&creative(X))<=>(~generous(X)|old(X))))&
(![X]:((~brave(X)|generous(X))=>(curious(X)|~generous(X))))&
(![X]:((funny(X)<~>quiet(X))=>(~kind(X)|rich(X))))&
((tall(paul)|~kind(paul)))&
((~strong(lucy)&~creative(lucy)))&
(?[X]:((brave(X)|funny(X))))&
(?[X]:((~brave(X)<~>~quiet(X))))&
(?[X]:((curious(X)&happy(X))))&
(tall(alice)) | rich(lucy) | [
"p1",
"p2",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1932795826985487185820335
% SZS output start Proof for 1932795826985487185820335
2. ! [X0] : ((generous(X0) & ~calm(X0)) <=> (~kind(X0) | ~creative(X0))) [input p1]
3. ! [X0] : ((humble(X0) <~> creative(X0)) <=> (~rich(X0) <~> generous(X0))) [input p2]
6. ! [X0] : ((curious(X0) & humble(X0)) <=> ~calm(X0)) [input p5]
18. ~creative(lucy) & ~strong(lucy) [input p17]
23. ~rich(lucy) [input hypothesis]
37. ! [X0] : (((generous(X0) & ~calm(X0)) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | (~generous(X0) | calm(X0)))) [nnf transformation 2]
38. ! [X0] : (((generous(X0) & ~calm(X0)) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ~generous(X0) | calm(X0))) [flattening 37]
39. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [nnf transformation 3]
44. ! [X0] : (((curious(X0) & humble(X0)) | calm(X0)) & (~calm(X0) | (~curious(X0) | ~humble(X0)))) [nnf transformation 6]
45. ! [X0] : (((curious(X0) & humble(X0)) | calm(X0)) & (~calm(X0) | ~curious(X0) | ~humble(X0))) [flattening 44]
74. ~calm(X0) | creative(X0) [cnf transformation 38]
76. creative(X0) | generous(X0) [cnf transformation 38]
80. ~generous(X0) | rich(X0) | creative(X0) | ~humble(X0) [cnf transformation 39]
84. ~creative(X0) | ~humble(X0) | generous(X0) | rich(X0) [cnf transformation 39]
92. humble(X0) | calm(X0) [cnf transformation 45]
130. ~creative(lucy) [cnf transformation 18]
136. ~rich(lucy) [cnf transformation 23]
144. ~humble(X0) | generous(X0) | rich(X0) [subsumption resolution 84,76]
146. ~humble(X0) | creative(X0) | rich(X0) [subsumption resolution 80,144]
369. creative(X0) | rich(X0) | calm(X0) [resolution 146,92]
373. rich(X0) | creative(X0) [subsumption resolution 369,74]
493. creative(lucy) [resolution 373,136]
498. $false [subsumption resolution 493,130]
% SZS output end Proof for 1932795826985487185820335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both not funny and strong then alice is not funny.
If paul is either not tall or not patient then paul is generous or not brave.
If lucy is tall then alice is quiet and vice versa.
If someone is tall then john is both strong and not happy and vice versa.
If susan is not old then someone is either curious or not kind and vice versa.
Everyone who is both not calm and not happy is either not rich or not happy and vice versa.
Everyone who is both not quiet and not curious is both generous and calm and vice versa.
Everyone who is both creative and generous is not tall or not creative and vice versa.
Everyone who is wise is not generous or not creative.
Everyone who is both calm and happy is either kind or old.
If someone is not rich then susan is either tall or not curious and vice versa.
If alice is calm then someone is either not happy or strong.
Everyone who is quiet is either kind or curious.
Everyone who is old or funny is both not happy and not kind and vice versa.
If lucy is both not kind and not brave then susan is either not tall or not rich and vice versa.
Everyone who is either patient or not patient is creative or not quiet and vice versa.
Someone is creative or old.
Paul is old.
Someone is not strong or not patient.
Fred is either generous or funny.
Lucy is not patient or not rich.
Someone is either creative or not humble.
Alice is either rich or quiet. | Fred is creative. | entailment | (((~funny(john)&strong(john)))=>(~funny(alice)))&
(((~tall(paul)<~>~patient(paul)))=>((generous(paul)|~brave(paul))))&
((tall(lucy))<=>(quiet(alice)))&
((?[X]:(tall(X)))<=>((strong(john)&~happy(john))))&
((~old(susan))<=>(?[X]:((curious(X)<~>~kind(X)))))&
(![X]:((~calm(X)&~happy(X))<=>(~rich(X)<~>~happy(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(generous(X)&calm(X))))&
(![X]:((creative(X)&generous(X))<=>(~tall(X)|~creative(X))))&
(![X]:(wise(X)=>(~generous(X)|~creative(X))))&
(![X]:((calm(X)&happy(X))=>(kind(X)<~>old(X))))&
((?[X]:(~rich(X)))<=>((tall(susan)<~>~curious(susan))))&
((calm(alice))=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:(quiet(X)=>(kind(X)<~>curious(X))))&
(![X]:((old(X)|funny(X))<=>(~happy(X)&~kind(X))))&
(((~kind(lucy)&~brave(lucy)))<=>((~tall(susan)<~>~rich(susan))))&
(![X]:((patient(X)<~>~patient(X))<=>(creative(X)|~quiet(X))))&
(?[X]:((creative(X)|old(X))))&
(old(paul))&
(?[X]:((~strong(X)|~patient(X))))&
((generous(fred)<~>funny(fred)))&
((~patient(lucy)|~rich(lucy)))&
(?[X]:((creative(X)<~>~humble(X))))&
((rich(alice)<~>quiet(alice))) | creative(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 512824528723925435336125
% SZS output start Proof for 512824528723925435336125
8. ! [X0] : ((generous(X0) & creative(X0)) <=> (~creative(X0) | ~tall(X0))) [input p7]
24. ~creative(fred) [input hypothesis]
49. ! [X0] : (((generous(X0) & creative(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (~generous(X0) | ~creative(X0)))) [nnf transformation 8]
50. ! [X0] : (((generous(X0) & creative(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | ~generous(X0) | ~creative(X0))) [flattening 49]
99. creative(X0) | creative(X0) [cnf transformation 50]
139. ~creative(fred) [cnf transformation 24]
143. creative(X0) [duplicate literal removal 99]
311. $false [subsumption resolution 139,143]
% SZS output end Proof for 512824528723925435336125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not generous is not old and vice versa.
If susan is not brave or not generous then alice is both not tall and calm.
Everyone who is both patient and brave is patient or not humble and vice versa.
If someone is either happy or quiet then lucy is both not curious and not humble and vice versa.
Everyone who is both kind and not wise is generous or not tall and vice versa.
Everyone who is not funny is both not curious and tall.
If fred is either creative or wise then susan is both not old and curious.
If paul is both not old and not funny then lucy is not creative.
If someone is either not patient or wise then paul is curious or not calm and vice versa.
If someone is either not calm or generous then someone is either not generous or creative.
Everyone who is either patient or rich is happy or not old.
If lucy is not kind or not patient then someone is not happy or not strong.
If fred is not quiet or not patient then paul is either not patient or not quiet and vice versa.
Everyone who is tall is strong.
Everyone who is not calm is not tall or calm and vice versa.
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.
Someone is not old or tall.
Susan is creative or wise. | Susan is funny. | entailment | (![X]:((~patient(X)|~generous(X))<=>~old(X)))&
(((~brave(susan)|~generous(susan)))=>((~tall(alice)&calm(alice))))&
(![X]:((patient(X)&brave(X))<=>(patient(X)|~humble(X))))&
((?[X]:((happy(X)<~>quiet(X))))<=>((~curious(lucy)&~humble(lucy))))&
(![X]:((kind(X)&~wise(X))<=>(generous(X)|~tall(X))))&
(![X]:(~funny(X)=>(~curious(X)&tall(X))))&
(((creative(fred)<~>wise(fred)))=>((~old(susan)&curious(susan))))&
(((~old(paul)&~funny(paul)))=>(~creative(lucy)))&
((?[X]:((~patient(X)<~>wise(X))))<=>((curious(paul)|~calm(paul))))&
((?[X]:((~calm(X)<~>generous(X))))=>(?[X]:((~generous(X)<~>creative(X)))))&
(![X]:((patient(X)<~>rich(X))=>(happy(X)|~old(X))))&
(((~kind(lucy)|~patient(lucy)))=>(?[X]:((~happy(X)|~strong(X)))))&
(((~quiet(fred)|~patient(fred)))<=>((~patient(paul)<~>~quiet(paul))))&
(![X]:(tall(X)=>strong(X)))&
(![X]:(~calm(X)<=>(~tall(X)|calm(X))))&
((generous(susan)<~>rich(susan)))&
((generous(alice)|calm(alice)))&
(?[X]:((patient(X)<~>tall(X))))&
((~wise(lucy)|~funny(lucy)))&
(?[X]:((~quiet(X)<~>~wise(X))))&
(?[X]:((~old(X)|tall(X))))&
((creative(susan)|wise(susan))) | funny(susan) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5078965954100340269658913
% SZS output start Proof for 5078965954100340269658913
6. ! [X0] : (~funny(X0) => (tall(X0) & ~curious(X0))) [input p5]
15. ! [X0] : (~calm(X0) <=> (calm(X0) | ~tall(X0))) [input p14]
23. ~funny(susan) [input hypothesis]
26. ! [X0] : ((tall(X0) & ~curious(X0)) | funny(X0)) [ennf transformation 6]
61. ! [X0] : ((~calm(X0) | (~calm(X0) & tall(X0))) & ((calm(X0) | ~tall(X0)) | calm(X0))) [nnf transformation 15]
62. ! [X0] : ((~calm(X0) | (~calm(X0) & tall(X0))) & (calm(X0) | ~tall(X0) | calm(X0))) [flattening 61]
96. funny(X0) | tall(X0) [cnf transformation 26]
123. calm(X0) | ~tall(X0) | calm(X0) [cnf transformation 62]
125. ~calm(X0) | ~calm(X0) [cnf transformation 62]
136. ~funny(susan) [cnf transformation 23]
137. calm(X0) | ~tall(X0) [duplicate literal removal 123]
138. ~calm(X0) [duplicate literal removal 125]
307. ~tall(X0) [subsumption resolution 137,138]
352. tall(susan) [resolution 96,136]
354. $false [subsumption resolution 352,307]
% SZS output end Proof for 5078965954100340269658913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is tall or not strong then someone is not rich and vice versa.
If someone is not tall or not happy then someone is either not tall or brave.
If paul is not wise or patient then someone is not strong or creative and vice versa.
Everyone who is not kind or not funny is both not rich and not tall.
Everyone who is not happy or happy is both kind and not curious and vice versa.
If someone is both quiet and not happy then alice is both not brave and tall and vice versa.
Everyone who is not brave or not kind is both strong and patient.
If mary is not quiet or patient then someone is either curious or calm and vice versa.
Everyone who is either happy or funny is not old or not brave and vice versa.
Everyone who is not kind or strong is both funny and generous.
Everyone who is not kind or curious is both not happy and kind and vice versa.
Everyone who is humble is either not funny or not kind.
Everyone who is either not funny or not wise is not rich or old and vice versa.
If fred is not calm or creative then susan is both creative and rich.
Everyone who is not old is both not happy and quiet.
Everyone who is both not kind and funny is not wise.
Mary is not strong.
Lucy is not strong or not curious.
Mary is not old or calm.
Someone is kind or not old.
Someone is not rich.
Mary is kind.
Someone is not calm or not brave. | Paul is not curious. | entailment | (((tall(alice)|~strong(alice)))<=>(?[X]:(~rich(X))))&
((?[X]:((~tall(X)|~happy(X))))=>(?[X]:((~tall(X)<~>brave(X)))))&
(((~wise(paul)|patient(paul)))<=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:((~kind(X)|~funny(X))=>(~rich(X)&~tall(X))))&
(![X]:((~happy(X)|happy(X))<=>(kind(X)&~curious(X))))&
((?[X]:((quiet(X)&~happy(X))))<=>((~brave(alice)&tall(alice))))&
(![X]:((~brave(X)|~kind(X))=>(strong(X)&patient(X))))&
(((~quiet(mary)|patient(mary)))<=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((happy(X)<~>funny(X))<=>(~old(X)|~brave(X))))&
(![X]:((~kind(X)|strong(X))=>(funny(X)&generous(X))))&
(![X]:((~kind(X)|curious(X))<=>(~happy(X)&kind(X))))&
(![X]:(humble(X)=>(~funny(X)<~>~kind(X))))&
(![X]:((~funny(X)<~>~wise(X))<=>(~rich(X)|old(X))))&
(((~calm(fred)|creative(fred)))=>((creative(susan)&rich(susan))))&
(![X]:(~old(X)=>(~happy(X)&quiet(X))))&
(![X]:((~kind(X)&funny(X))=>~wise(X)))&
(~strong(mary))&
((~strong(lucy)|~curious(lucy)))&
((~old(mary)|calm(mary)))&
(?[X]:((kind(X)|~old(X))))&
(?[X]:(~rich(X)))&
(kind(mary))&
(?[X]:((~calm(X)|~brave(X)))) | ~curious(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 69575618365570424990401
% SZS output start Proof for 69575618365570424990401
5. ! [X0] : ((happy(X0) | ~happy(X0)) <=> (~curious(X0) & kind(X0))) [input p4]
24. curious(paul) [input hypothesis]
50. ! [X0] : (((happy(X0) | ~happy(X0)) | (curious(X0) | ~kind(X0))) & ((~curious(X0) & kind(X0)) | (~happy(X0) & happy(X0)))) [nnf transformation 5]
51. ! [X0] : ((happy(X0) | ~happy(X0) | curious(X0) | ~kind(X0)) & ((~curious(X0) & kind(X0)) | (~happy(X0) & happy(X0)))) [flattening 50]
91. ~curious(X0) | happy(X0) [cnf transformation 51]
92. ~curious(X0) | ~happy(X0) [cnf transformation 51]
141. curious(paul) [cnf transformation 24]
206. ~curious(X0) [subsumption resolution 91,92]
291. $false [subsumption resolution 141,206]
% SZS output end Proof for 69575618365570424990401
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm then someone is both not funny and curious.
Everyone who is quiet or not creative is not kind or calm.
Everyone who is not old is both generous and calm.
If someone is not curious or not humble then paul is either patient or not quiet.
Everyone who is both not humble and not generous is either not rich or not old and vice versa.
If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa.
If someone is generous or tall then alice is strong and vice versa.
Everyone who is not happy is brave or humble.
Everyone who is not happy or not funny is both creative and quiet.
If someone is not creative or quiet then someone is both wise and not wise.
Everyone who is not patient is both not kind and happy and vice versa.
If someone is either brave or wise then susan is both brave and not strong and vice versa.
If someone is either kind or happy then someone is both not kind and not creative and vice versa.
Everyone who is not wise or humble is creative or not strong and vice versa.
Everyone who is both funny and strong is either funny or curious and vice versa.
Someone is humble.
Mary is either quiet or happy.
John is either not tall or wise.
Alice is not kind or rich. | Alice is not rich. | contradiction | ((?[X]:(calm(X)))=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:((quiet(X)|~creative(X))=>(~kind(X)|calm(X))))&
(![X]:(~old(X)=>(generous(X)&calm(X))))&
((?[X]:((~curious(X)|~humble(X))))=>((patient(paul)<~>~quiet(paul))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
((?[X]:((brave(X)<~>wise(X))))<=>((brave(susan)&~strong(susan))))&
((?[X]:((kind(X)<~>happy(X))))<=>(?[X]:((~kind(X)&~creative(X)))))&
(![X]:((~wise(X)|humble(X))<=>(creative(X)|~strong(X))))&
(![X]:((funny(X)&strong(X))<=>(funny(X)<~>curious(X))))&
(?[X]:(humble(X)))&
((quiet(mary)<~>happy(mary)))&
((~tall(john)<~>wise(john)))&
((~kind(alice)|rich(alice))) | ~rich(alice) | [
"p8",
"p9",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3791047425340726187640418
% SZS output start Proof for 3791047425340726187640418
9. ! [X0] : ((~funny(X0) | ~happy(X0)) => (quiet(X0) & creative(X0))) [input p8]
10. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X0] : (~wise(X0) & wise(X0)) [input p9]
13. ? [X0] : (kind(X0) <~> happy(X0)) <=> ? [X0] : (~creative(X0) & ~kind(X0)) [input p12]
19. rich(alice) | ~kind(alice) [input p18]
20. ~rich(alice) [input hypothesis]
23. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 10]
24. ? [X0] : (kind(X0) <~> happy(X0)) <=> ? [X1] : (~creative(X1) & ~kind(X1)) [rectify 13]
32. ! [X0] : ((quiet(X0) & creative(X0)) | (funny(X0) & happy(X0))) [ennf transformation 9]
33. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~quiet(X0) & creative(X0)) [ennf transformation 23]
49. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : (~quiet(X1) & creative(X1)) [rectify 33]
50. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK4) & wise(sK4)) [choice axiom]
51. (~wise(sK4) & wise(sK4)) | ! [X1] : (~quiet(X1) & creative(X1)) [skolemisation 49,50]
59. (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ! [X1] : (creative(X1) | kind(X1))) & (? [X1] : (~creative(X1) & ~kind(X1)) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) [nnf transformation 24]
60. (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ! [X1] : (creative(X1) | kind(X1))) & (? [X2] : (~creative(X2) & ~kind(X2)) | ! [X3] : ((kind(X3) | ~happy(X3)) & (happy(X3) | ~kind(X3)))) [rectify 59]
61. ? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) => ((~happy(sK6) | ~kind(sK6)) & (happy(sK6) | kind(sK6))) [choice axiom]
62. ? [X2] : (~creative(X2) & ~kind(X2)) => (~creative(sK7) & ~kind(sK7)) [choice axiom]
63. (((~happy(sK6) | ~kind(sK6)) & (happy(sK6) | kind(sK6))) | ! [X1] : (creative(X1) | kind(X1))) & ((~creative(sK7) & ~kind(sK7)) | ! [X3] : ((kind(X3) | ~happy(X3)) & (happy(X3) | ~kind(X3)))) [skolemisation 60,62,61]
98. happy(X0) | quiet(X0) [cnf transformation 32]
100. wise(sK4) | creative(X1) [cnf transformation 51]
101. wise(sK4) | ~quiet(X1) [cnf transformation 51]
102. ~wise(sK4) | creative(X1) [cnf transformation 51]
103. ~wise(sK4) | ~quiet(X1) [cnf transformation 51]
116. ~creative(sK7) | kind(X3) | ~happy(X3) [cnf transformation 63]
134. rich(alice) | ~kind(alice) [cnf transformation 19]
135. ~rich(alice) [cnf transformation 20]
219. 19 <=> ! [X1] : ~quiet(X1) [avatar definition]
220. ~quiet(X1) <- (19) [avatar component clause 219]
222. 20 <=> wise(sK4) [avatar definition]
225. 19 | ~20 [avatar split clause 103,222,219]
227. 21 <=> ! [X1] : creative(X1) [avatar definition]
228. creative(X1) <- (21) [avatar component clause 227]
229. 21 | ~20 [avatar split clause 102,222,227]
230. 19 | 20 [avatar split clause 101,222,219]
231. 21 | 20 [avatar split clause 100,222,227]
274. 31 <=> ! [X3] : (kind(X3) | ~happy(X3)) [avatar definition]
275. ~happy(X3) | kind(X3) <- (31) [avatar component clause 274]
277. 32 <=> creative(sK7) [avatar definition]
279. ~creative(sK7) <- (~32) [avatar component clause 277]
280. 31 | ~32 [avatar split clause 116,277,274]
312. 39 <=> kind(alice) [avatar definition]
314. ~kind(alice) <- (~39) [avatar component clause 312]
316. 40 <=> rich(alice) [avatar definition]
319. ~39 | 40 [avatar split clause 134,316,312]
320. ~40 [avatar split clause 135,316]
321. $false <- (21, ~32) [resolution 279,228]
322. ~21 | 32 [avatar contradiction clause 321]
335. kind(X1) | quiet(X1) <- (31) [resolution 275,98]
339. kind(X1) <- (19, 31) [subsumption resolution 335,220]
347. $false <- (19, 31, ~39) [resolution 339,314]
350. ~19 | ~31 | 39 [avatar contradiction clause 347]
352. $false [avatar sat refutation 225,229,230,231,280,319,320,322,350]
% SZS output end Proof for 3791047425340726187640418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or strong is both wise and rich and vice versa.
If alice is not creative then someone is generous and vice versa.
Everyone who is both curious and not strong is not calm or kind.
If someone is either funny or generous then someone is both not calm and not patient.
Everyone who is both not curious and not wise is not happy.
If paul is both funny and not kind then someone is either tall or not creative and vice versa.
If someone is either curious or not happy then someone is both not creative and creative and vice versa.
Everyone who is not patient is both not humble and rich.
If someone is not old then mary is not wise and vice versa.
Everyone who is either patient or strong is not wise.
Everyone who is both quiet and curious is not creative and vice versa.
If lucy is either not old or not generous then mary is both wise and calm and vice versa.
If fred is brave then someone is either tall or quiet and vice versa.
If someone is not calm then susan is both not brave and not patient and vice versa.
Everyone who is either humble or not happy is rich or not funny.
Everyone who is not tall or not quiet is not old or generous.
John is not funny.
Someone is patient.
Susan is both curious and old.
Someone is both not calm and not kind.
Someone is rich. | Paul is tall. | neutral | (![X]:((~strong(X)|strong(X))<=>(wise(X)&rich(X))))&
((~creative(alice))<=>(?[X]:(generous(X))))&
(![X]:((curious(X)&~strong(X))=>(~calm(X)|kind(X))))&
((?[X]:((funny(X)<~>generous(X))))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~curious(X)&~wise(X))=>~happy(X)))&
(((funny(paul)&~kind(paul)))<=>(?[X]:((tall(X)<~>~creative(X)))))&
((?[X]:((curious(X)<~>~happy(X))))<=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:(~patient(X)=>(~humble(X)&rich(X))))&
((?[X]:(~old(X)))<=>(~wise(mary)))&
(![X]:((patient(X)<~>strong(X))=>~wise(X)))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~old(X)|generous(X))))&
(~funny(john))&
(?[X]:(patient(X)))&
((curious(susan)&old(susan)))&
(?[X]:((~calm(X)&~kind(X))))&
(?[X]:(rich(X))) | tall(paul) | [] | null | 0 |
Everyone who is strong or not curious is either happy or not curious and vice versa.
If alice is not generous then lucy is not wise or curious.
Everyone who is both old and not humble is either not generous or old and vice versa.
If mary is both not strong and not patient then someone is not creative and vice versa.
Everyone who is both kind and not kind is both old and not wise.
If someone is either quiet or not patient then someone is both generous and not brave and vice versa.
If someone is calm or curious then paul is kind or rich.
If someone is not quiet or wise then someone is both strong and brave.
If mary is both happy and curious then susan is not curious.
Everyone who is not patient or not old is either generous or rich and vice versa.
If mary is either creative or humble then someone is patient or not funny.
Everyone who is wise or not humble is either old or not brave and vice versa.
Everyone who is old or not old is both not generous and not curious.
Everyone who is humble or generous is either not generous or not strong.
If someone is either not patient or rich then mary is both not quiet and not strong.
Everyone who is both not curious and not old is not quiet and vice versa.
Someone is both old and kind.
Paul is not patient.
Someone is humble or not wise.
Paul is brave or not strong.
Susan is either rich or not brave.
John is calm or not strong.
Fred is not curious. | Alice is strong. | entailment | (![X]:((strong(X)|~curious(X))<=>(happy(X)<~>~curious(X))))&
((~generous(alice))=>((~wise(lucy)|curious(lucy))))&
(![X]:((old(X)&~humble(X))<=>(~generous(X)<~>old(X))))&
(((~strong(mary)&~patient(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((kind(X)&~kind(X))=>(old(X)&~wise(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((calm(X)|curious(X))))=>((kind(paul)|rich(paul))))&
((?[X]:((~quiet(X)|wise(X))))=>(?[X]:((strong(X)&brave(X)))))&
(((happy(mary)&curious(mary)))=>(~curious(susan)))&
(![X]:((~patient(X)|~old(X))<=>(generous(X)<~>rich(X))))&
(((creative(mary)<~>humble(mary)))=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((wise(X)|~humble(X))<=>(old(X)<~>~brave(X))))&
(![X]:((old(X)|~old(X))=>(~generous(X)&~curious(X))))&
(![X]:((humble(X)|generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(?[X]:((old(X)&kind(X))))&
(~patient(paul))&
(?[X]:((humble(X)|~wise(X))))&
((brave(paul)|~strong(paul)))&
((rich(susan)<~>~brave(susan)))&
((calm(john)|~strong(john)))&
(~curious(fred)) | strong(alice) | [
"p2",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 815331876295787203759083
% SZS output start Proof for 815331876295787203759083
3. ! [X0] : ((~humble(X0) & old(X0)) <=> (~generous(X0) <~> old(X0))) [input p2]
13. ! [X0] : ((~old(X0) | old(X0)) => (~curious(X0) & ~generous(X0))) [input p12]
14. ! [X0] : ((generous(X0) | humble(X0)) => (~generous(X0) <~> ~strong(X0))) [input p13]
24. ~strong(alice) [input hypothesis]
37. ! [X0] : ((~curious(X0) & ~generous(X0)) | (old(X0) & ~old(X0))) [ennf transformation 13]
38. ! [X0] : ((~generous(X0) <~> ~strong(X0)) | (~generous(X0) & ~humble(X0))) [ennf transformation 14]
42. ! [X0] : (((~humble(X0) & old(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) & (((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | (humble(X0) | ~old(X0)))) [nnf transformation 3]
43. ! [X0] : (((~humble(X0) & old(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) & (((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | humble(X0) | ~old(X0))) [flattening 42]
61. ! [X0] : (((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | (~generous(X0) & ~humble(X0))) [nnf transformation 38]
78. ~old(X0) | generous(X0) | humble(X0) | ~old(X0) [cnf transformation 43]
79. old(X0) | old(X0) | generous(X0) [cnf transformation 43]
113. ~generous(X0) | ~old(X0) [cnf transformation 37]
114. ~generous(X0) | old(X0) [cnf transformation 37]
119. strong(X0) | generous(X0) | ~humble(X0) [cnf transformation 61]
137. ~strong(alice) [cnf transformation 24]
139. ~old(X0) | generous(X0) | humble(X0) [duplicate literal removal 78]
140. old(X0) | generous(X0) [duplicate literal removal 79]
156. humble(X0) | generous(X0) [subsumption resolution 139,140]
254. old(X0) [subsumption resolution 114,140]
255. ~generous(X0) [subsumption resolution 113,254]
256. ~humble(X0) | strong(X0) [subsumption resolution 119,255]
322. strong(X0) | generous(X0) [resolution 256,156]
323. strong(X0) [subsumption resolution 322,255]
324. $false [resolution 323,137]
% SZS output end Proof for 815331876295787203759083
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not quiet is not brave and vice versa.
If lucy is both not wise and wise then paul is both quiet and not rich and vice versa.
Everyone who is both not funny and not kind is both not creative and happy.
If susan is patient or generous then someone is kind and vice versa.
If fred is rich or kind then mary is not humble or calm.
If someone is kind then someone is quiet and vice versa.
If someone is not brave or not old then someone is curious.
Everyone who is kind is not kind.
If someone is either not curious or quiet then someone is tall or brave and vice versa.
Everyone who is both not quiet and kind is humble or not curious and vice versa.
If mary is either creative or tall then alice is not creative or rich and vice versa.
If someone is not quiet or quiet then lucy is either not humble or creative.
If someone is either not rich or tall then fred is curious or not happy.
If someone is either not old or humble then someone is either kind or calm.
Everyone who is humble is wise.
Someone is either not funny or not calm.
Someone is either happy or not tall.
Someone is either not wise or not humble.
Someone is either rich or quiet.
Mary is either strong or not wise.
Alice is either not happy or not patient. | Paul is brave. | contradiction | (![X]:((~calm(X)<~>~quiet(X))<=>~brave(X)))&
(((~wise(lucy)&wise(lucy)))<=>((quiet(paul)&~rich(paul))))&
(![X]:((~funny(X)&~kind(X))=>(~creative(X)&happy(X))))&
(((patient(susan)|generous(susan)))<=>(?[X]:(kind(X))))&
(((rich(fred)|kind(fred)))=>((~humble(mary)|calm(mary))))&
((?[X]:(kind(X)))<=>(?[X]:(quiet(X))))&
((?[X]:((~brave(X)|~old(X))))=>(?[X]:(curious(X))))&
(![X]:(kind(X)=>~kind(X)))&
((?[X]:((~curious(X)<~>quiet(X))))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(humble(X)|~curious(X))))&
(((creative(mary)<~>tall(mary)))<=>((~creative(alice)|rich(alice))))&
((?[X]:((~quiet(X)|quiet(X))))=>((~humble(lucy)<~>creative(lucy))))&
((?[X]:((~rich(X)<~>tall(X))))=>((curious(fred)|~happy(fred))))&
((?[X]:((~old(X)<~>humble(X))))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:(humble(X)=>wise(X)))&
(?[X]:((~funny(X)<~>~calm(X))))&
(?[X]:((happy(X)<~>~tall(X))))&
(?[X]:((~wise(X)<~>~humble(X))))&
(?[X]:((rich(X)<~>quiet(X))))&
((strong(mary)<~>~wise(mary)))&
((~happy(alice)<~>~patient(alice))) | brave(paul) | [
"p5",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5704145362043723802138393
% SZS output start Proof for 5704145362043723802138393
6. ? [X0] : kind(X0) <=> ? [X0] : quiet(X0) [input p5]
8. ! [X0] : (kind(X0) => ~kind(X0)) [input p7]
9. ? [X0] : (~curious(X0) <~> quiet(X0)) <=> ? [X0] : (brave(X0) | tall(X0)) [input p8]
10. ! [X0] : ((kind(X0) & ~quiet(X0)) <=> (~curious(X0) | humble(X0))) [input p9]
22. brave(paul) [input hypothesis]
23. ? [X0] : kind(X0) <=> ? [X1] : quiet(X1) [rectify 6]
25. ? [X0] : (~curious(X0) <~> quiet(X0)) <=> ? [X1] : (brave(X1) | tall(X1)) [rectify 9]
32. ! [X0] : (~kind(X0) | ~kind(X0)) [ennf transformation 8]
46. (? [X0] : kind(X0) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : ~kind(X0)) [nnf transformation 23]
47. (? [X0] : kind(X0) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : ~kind(X3)) [rectify 46]
48. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
49. ? [X2] : quiet(X2) => quiet(sK2) [choice axiom]
50. (kind(sK1) | ! [X1] : ~quiet(X1)) & (quiet(sK2) | ! [X3] : ~kind(X3)) [skolemisation 47,49,48]
54. (? [X0] : ((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ! [X1] : (~brave(X1) & ~tall(X1))) & (? [X1] : (brave(X1) | tall(X1)) | ! [X0] : ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0)))) [nnf transformation 25]
55. (? [X0] : ((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ! [X1] : (~brave(X1) & ~tall(X1))) & (? [X2] : (brave(X2) | tall(X2)) | ! [X3] : ((~curious(X3) | ~quiet(X3)) & (quiet(X3) | curious(X3)))) [rectify 54]
56. ? [X0] : ((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) => ((~quiet(sK4) | curious(sK4)) & (quiet(sK4) | ~curious(sK4))) [choice axiom]
57. ? [X2] : (brave(X2) | tall(X2)) => (brave(sK5) | tall(sK5)) [choice axiom]
58. (((~quiet(sK4) | curious(sK4)) & (quiet(sK4) | ~curious(sK4))) | ! [X1] : (~brave(X1) & ~tall(X1))) & ((brave(sK5) | tall(sK5)) | ! [X3] : ((~curious(X3) | ~quiet(X3)) & (quiet(X3) | curious(X3)))) [skolemisation 55,57,56]
59. ! [X0] : (((kind(X0) & ~quiet(X0)) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | (~kind(X0) | quiet(X0)))) [nnf transformation 10]
60. ! [X0] : (((kind(X0) & ~quiet(X0)) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | ~kind(X0) | quiet(X0))) [flattening 59]
99. kind(sK1) | ~quiet(X1) [cnf transformation 50]
102. ~kind(X0) | ~kind(X0) [cnf transformation 32]
106. quiet(sK4) | ~curious(sK4) | ~brave(X1) [cnf transformation 58]
113. curious(X0) | kind(X0) [cnf transformation 60]
143. brave(paul) [cnf transformation 22]
144. ~kind(X0) [duplicate literal removal 102]
160. 4 <=> ! [X0] : ~kind(X0) [avatar definition]
161. ~kind(X0) <- (4) [avatar component clause 160]
196. 12 <=> ! [X1] : ~quiet(X1) [avatar definition]
197. ~quiet(X1) <- (12) [avatar component clause 196]
199. 13 <=> kind(sK1) [avatar definition]
201. kind(sK1) <- (13) [avatar component clause 199]
202. 12 | 13 [avatar split clause 99,199,196]
220. 4 [avatar split clause 144,160]
222. 18 <=> ! [X1] : ~brave(X1) [avatar definition]
223. ~brave(X1) <- (18) [avatar component clause 222]
225. 19 <=> curious(sK4) [avatar definition]
226. ~curious(sK4) <- (~19) [avatar component clause 225]
229. 20 <=> quiet(sK4) [avatar definition]
230. quiet(sK4) <- (20) [avatar component clause 229]
237. 18 | ~19 | 20 [avatar split clause 106,229,225,222]
380. kind(sK4) <- (~19) [resolution 113,226]
381. $false <- (4, ~19) [subsumption resolution 380,161]
382. ~4 | 19 [avatar contradiction clause 381]
383. $false <- (12, 20) [subsumption resolution 230,197]
384. ~12 | ~20 [avatar contradiction clause 383]
385. $false <- (4, 13) [subsumption resolution 201,161]
386. ~4 | ~13 [avatar contradiction clause 385]
387. $false <- (18) [resolution 223,143]
388. ~18 [avatar contradiction clause 387]
389. $false [avatar sat refutation 202,220,237,382,384,386,388]
% SZS output end Proof for 5704145362043723802138393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If fred is calm then someone is either quiet or wise and vice versa. If mary is both brave and not wise then john is creative and vice versa. If someone is not generous then alice is not funny. Everyone who is calm or humble is strong or not tall. Everyone who is not tall is rich. If someone is either not humble or kind then susan is both not generous and not humble. If lucy is either funny or kind then fred is both humble and not wise. Everyone who is both not quiet and not kind is both creative and not tall. If someone is not creative then someone is either funny or strong. Everyone who is both brave and not curious is quiet or wise and vice versa. If someone is both humble and not kind then someone is either not strong or not quiet and vice versa. Everyone who is either not funny or not happy is not wise or happy and vice versa. If paul is both rich and not wise then paul is generous and vice versa. Everyone who is not wise or brave is not generous. Everyone who is old or not rich is either not curious or creative. If john is both not quiet and quiet then someone is brave and vice versa. Someone is either curious or kind. Someone is either not kind or not happy. Lucy is not creative or tall. Paul is both curious and kind. Paul is happy. Someone is not creative. Susan is strong. | John is kind. | entailment | ((calm(fred))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(((brave(mary)&~wise(mary)))<=>(creative(john)))&
((?[X]:(~generous(X)))=>(~funny(alice)))&
(![X]:((calm(X)|humble(X))=>(strong(X)|~tall(X))))&
(![X]:(~tall(X)=>rich(X)))&
((?[X]:((~humble(X)<~>kind(X))))=>((~generous(susan)&~humble(susan))))&
(((funny(lucy)<~>kind(lucy)))=>((humble(fred)&~wise(fred))))&
(![X]:((~quiet(X)&~kind(X))=>(creative(X)&~tall(X))))&
((?[X]:(~creative(X)))=>(?[X]:((funny(X)<~>strong(X)))))&
(![X]:((brave(X)&~curious(X))<=>(quiet(X)|wise(X))))&
((?[X]:((humble(X)&~kind(X))))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~wise(X)|happy(X))))&
(((rich(paul)&~wise(paul)))<=>(generous(paul)))&
(![X]:((~wise(X)|brave(X))=>~generous(X)))&
(![X]:((old(X)|~rich(X))=>(~curious(X)<~>creative(X))))&
(((~quiet(john)&quiet(john)))<=>(?[X]:(brave(X))))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:((~kind(X)<~>~happy(X))))&
((~creative(lucy)|tall(lucy)))&
((curious(paul)&kind(paul)))&
(happy(paul))&
(?[X]:(~creative(X)))&
(strong(susan)) | kind(john) | [
"p1",
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6715639568884921621918380
% SZS output start Proof for 6715639568884921621918380
2. (~wise(mary) & brave(mary)) <=> creative(john) [input p1]
8. ! [X0] : ((~kind(X0) & ~quiet(X0)) => (~tall(X0) & creative(X0))) [input p7]
10. ! [X0] : ((~curious(X0) & brave(X0)) <=> (wise(X0) | quiet(X0))) [input p9]
16. (quiet(john) & ~quiet(john)) <=> ? [X0] : brave(X0) [input p15]
24. ~kind(john) [input hypothesis]
34. ! [X0] : ((~tall(X0) & creative(X0)) | (kind(X0) | quiet(X0))) [ennf transformation 8]
35. ! [X0] : ((~tall(X0) & creative(X0)) | kind(X0) | quiet(X0)) [flattening 34]
43. ((~wise(mary) & brave(mary)) | ~creative(john)) & (creative(john) | (wise(mary) | ~brave(mary))) [nnf transformation 2]
44. ((~wise(mary) & brave(mary)) | ~creative(john)) & (creative(john) | wise(mary) | ~brave(mary)) [flattening 43]
51. ! [X0] : (((~curious(X0) & brave(X0)) | (~wise(X0) & ~quiet(X0))) & ((wise(X0) | quiet(X0)) | (curious(X0) | ~brave(X0)))) [nnf transformation 10]
52. ! [X0] : (((~curious(X0) & brave(X0)) | (~wise(X0) & ~quiet(X0))) & (wise(X0) | quiet(X0) | curious(X0) | ~brave(X0))) [flattening 51]
63. ((quiet(john) & ~quiet(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~quiet(john) | quiet(john))) [nnf transformation 16]
64. ((quiet(john) & ~quiet(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~quiet(john) | quiet(john)) [flattening 63]
65. ((quiet(john) & ~quiet(john)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~quiet(john) | quiet(john)) [rectify 64]
66. ? [X1] : brave(X1) => brave(sK4) [choice axiom]
67. ((quiet(john) & ~quiet(john)) | ! [X0] : ~brave(X0)) & (brave(sK4) | ~quiet(john) | quiet(john)) [skolemisation 65,66]
81. brave(mary) | ~creative(john) [cnf transformation 44]
95. kind(X0) | creative(X0) | quiet(X0) [cnf transformation 35]
100. ~quiet(X0) | brave(X0) [cnf transformation 52]
124. ~quiet(john) | ~brave(X0) [cnf transformation 67]
125. quiet(john) | ~brave(X0) [cnf transformation 67]
136. ~kind(john) [cnf transformation 24]
162. 6 <=> creative(john) [avatar definition]
164. ~creative(john) <- (~6) [avatar component clause 162]
171. 8 <=> brave(mary) [avatar definition]
173. brave(mary) <- (8) [avatar component clause 171]
174. ~6 | 8 [avatar split clause 81,171,162]
283. 32 <=> ! [X0] : ~brave(X0) [avatar definition]
284. ~brave(X0) <- (32) [avatar component clause 283]
286. 33 <=> quiet(john) [avatar definition]
288. quiet(john) <- (33) [avatar component clause 286]
289. 32 | 33 [avatar split clause 125,286,283]
290. 32 | ~33 [avatar split clause 124,286,283]
322. $false <- (8, 32) [subsumption resolution 173,284]
323. ~8 | ~32 [avatar contradiction clause 322]
363. creative(john) | quiet(john) [resolution 95,136]
367. quiet(john) <- (~6) [subsumption resolution 363,164]
368. 33 | 6 [avatar split clause 367,162,286]
382. brave(john) <- (33) [resolution 288,100]
383. $false <- (32, 33) [subsumption resolution 382,284]
384. ~32 | ~33 [avatar contradiction clause 383]
385. $false [avatar sat refutation 174,289,290,323,368,384]
% SZS output end Proof for 6715639568884921621918380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or creative is not quiet or quiet and vice versa. Everyone who is not rich is happy and vice versa. Everyone who is either not happy or not humble is both not kind and not creative. Everyone who is either not calm or tall is both creative and calm and vice versa. Everyone who is either not wise or not generous is either old or not brave and vice versa. Everyone who is both not curious and brave is kind and vice versa. Everyone who is not curious is either not wise or not generous. Everyone who is both not brave and tall is creative or strong. Everyone who is either patient or kind is funny or not brave. If john is both not happy and not brave then someone is not patient or not wise. If lucy is not rich or creative then lucy is rich or not old and vice versa. Everyone who is both calm and tall is both not calm and strong and vice versa. Everyone who is not patient or creative is tall or not strong and vice versa. If john is both not calm and curious then someone is either not creative or not strong and vice versa. Everyone who is curious or calm is not creative and vice versa. Everyone who is curious is either not funny or calm and vice versa. Fred is not kind. Someone is calm or not strong. Someone is not creative. Someone is both not old and not humble. Paul is either not generous or not wise. Someone is both not rich and not quiet. Someone is funny or not calm. | Paul is not patient. | neutral | (![X]:((old(X)|creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~rich(X)<=>happy(X)))&
(![X]:((~happy(X)<~>~humble(X))=>(~kind(X)&~creative(X))))&
(![X]:((~calm(X)<~>tall(X))<=>(creative(X)&calm(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(old(X)<~>~brave(X))))&
(![X]:((~curious(X)&brave(X))<=>kind(X)))&
(![X]:(~curious(X)=>(~wise(X)<~>~generous(X))))&
(![X]:((~brave(X)&tall(X))=>(creative(X)|strong(X))))&
(![X]:((patient(X)<~>kind(X))=>(funny(X)|~brave(X))))&
(((~happy(john)&~brave(john)))=>(?[X]:((~patient(X)|~wise(X)))))&
(((~rich(lucy)|creative(lucy)))<=>((rich(lucy)|~old(lucy))))&
(![X]:((calm(X)&tall(X))<=>(~calm(X)&strong(X))))&
(![X]:((~patient(X)|creative(X))<=>(tall(X)|~strong(X))))&
(((~calm(john)&curious(john)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:((curious(X)|calm(X))<=>~creative(X)))&
(![X]:(curious(X)<=>(~funny(X)<~>calm(X))))&
(~kind(fred))&
(?[X]:((calm(X)|~strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~old(X)&~humble(X))))&
((~generous(paul)<~>~wise(paul)))&
(?[X]:((~rich(X)&~quiet(X))))&
(?[X]:((funny(X)|~calm(X)))) | ~patient(paul) | [] | null | 0 |
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