premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either generous or not strong is both generous and not generous and vice versa.
If john is both quiet and calm then alice is both curious and humble.
Everyone who is either not quiet or not calm is either rich or strong and vice versa.
Everyone who is not strong or not generous is not quiet and vice versa.
Everyone who is not patient or brave is happy or funny.
Everyone who is not rich or brave is either not calm or humble.
If someone is funny or not generous then susan is both brave and not wise.
If lucy is calm or not patient then someone is humble.
If someone is both rich and old then john is either not quiet or curious.
Everyone who is both quiet and not brave is either not rich or not happy and vice versa.
Everyone who is both not rich and strong is not rich or not brave and vice versa.
If someone is happy then paul is either not creative or happy.
Everyone who is creative or happy is not generous.
If someone is not tall then fred is both not funny and quiet and vice versa.
Everyone who is both humble and not curious is either not curious or not brave.
Fred is not quiet or wise.
Someone is both brave and not curious.
Someone is not funny or wise.
Lucy is both calm and not quiet.
Someone is strong or not quiet.
Paul is not kind or humble.
John is either not kind or calm.
Alice is patient or not humble. | Susan is not wise. | entailment | (![X]:((generous(X)<~>~strong(X))<=>(generous(X)&~generous(X))))&
(((quiet(john)&calm(john)))=>((curious(alice)&humble(alice))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(rich(X)<~>strong(X))))&
(![X]:((~strong(X)|~generous(X))<=>~quiet(X)))&
(![X]:((~patient(X)|brave(X))=>(happy(X)|funny(X))))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((funny(X)|~generous(X))))=>((brave(susan)&~wise(susan))))&
(((calm(lucy)|~patient(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((rich(X)&old(X))))=>((~quiet(john)<~>curious(john))))&
(![X]:((quiet(X)&~brave(X))<=>(~rich(X)<~>~happy(X))))&
(![X]:((~rich(X)&strong(X))<=>(~rich(X)|~brave(X))))&
((?[X]:(happy(X)))=>((~creative(paul)<~>happy(paul))))&
(![X]:((creative(X)|happy(X))=>~generous(X)))&
((?[X]:(~tall(X)))<=>((~funny(fred)&quiet(fred))))&
(![X]:((humble(X)&~curious(X))=>(~curious(X)<~>~brave(X))))&
((~quiet(fred)|wise(fred)))&
(?[X]:((brave(X)&~curious(X))))&
(?[X]:((~funny(X)|wise(X))))&
((calm(lucy)&~quiet(lucy)))&
(?[X]:((strong(X)|~quiet(X))))&
((~kind(paul)|humble(paul)))&
((~kind(john)<~>calm(john)))&
((patient(alice)|~humble(alice))) | ~wise(susan) | [
"p4",
"p6",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7353846704836426628956408
% SZS output start Proof for 7353846704836426628956408
5. ! [X0] : ((brave(X0) | ~patient(X0)) => (funny(X0) | happy(X0))) [input p4]
7. ? [X0] : (~generous(X0) | funny(X0)) => (~wise(susan) & brave(susan)) [input p6]
13. ! [X0] : ((happy(X0) | creative(X0)) => ~generous(X0)) [input p12]
17. ? [X0] : (~curious(X0) & brave(X0)) [input p16]
24. wise(susan) [input hypothesis]
27. ! [X0] : (brave(X0) => (funny(X0) | happy(X0))) [pure predicate removal 5]
31. ! [X0] : ((funny(X0) | happy(X0)) | ~brave(X0)) [ennf transformation 27]
32. ! [X0] : (funny(X0) | happy(X0) | ~brave(X0)) [flattening 31]
34. (~wise(susan) & brave(susan)) | ! [X0] : (generous(X0) & ~funny(X0)) [ennf transformation 7]
37. ! [X0] : (~generous(X0) | (~happy(X0) & ~creative(X0))) [ennf transformation 13]
59. ? [X0] : (~curious(X0) & brave(X0)) => (~curious(sK2) & brave(sK2)) [choice axiom]
60. ~curious(sK2) & brave(sK2) [skolemisation 17,59]
85. ~brave(X0) | happy(X0) | funny(X0) [cnf transformation 32]
92. ~wise(susan) | ~funny(X0) [cnf transformation 34]
93. ~wise(susan) | generous(X0) [cnf transformation 34]
109. ~happy(X0) | ~generous(X0) [cnf transformation 37]
116. brave(sK2) [cnf transformation 60]
125. wise(susan) [cnf transformation 24]
150. 5 <=> ! [X0] : generous(X0) [avatar definition]
151. generous(X0) <- (5) [avatar component clause 150]
153. 6 <=> wise(susan) [avatar definition]
156. 5 | ~6 [avatar split clause 93,153,150]
158. 7 <=> ! [X0] : ~funny(X0) [avatar definition]
159. ~funny(X0) <- (7) [avatar component clause 158]
160. 7 | ~6 [avatar split clause 92,153,158]
237. 6 [avatar split clause 125,153]
240. happy(sK2) | funny(sK2) [resolution 85,116]
242. happy(sK2) <- (7) [subsumption resolution 240,159]
244. ~generous(sK2) <- (7) [resolution 242,109]
245. $false <- (5, 7) [subsumption resolution 244,151]
246. ~5 | ~7 [avatar contradiction clause 245]
247. $false [avatar sat refutation 156,160,237,246]
% SZS output end Proof for 7353846704836426628956408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then someone is either patient or happy and vice versa.
If someone is both not wise and brave then someone is either strong or not curious and vice versa.
If someone is either not brave or calm then someone is funny or strong and vice versa.
Everyone who is not kind is not happy and vice versa.
Everyone who is either not wise or not old is happy or kind.
Everyone who is creative is both not creative and not happy.
Everyone who is humble or not wise is not curious or strong and vice versa.
Everyone who is not kind or not tall is either not creative or not happy and vice versa.
Everyone who is not patient is either not curious or humble and vice versa.
Everyone who is both tall and not generous is either not brave or brave.
Everyone who is creative is not kind or not patient.
Everyone who is either not funny or creative is both not rich and wise and vice versa.
If someone is both not wise and not calm then someone is humble or not kind and vice versa.
Everyone who is either not brave or quiet is either tall or not happy.
Everyone who is either curious or tall is rich or not strong.
If alice is both rich and not patient then mary is both brave and strong.
Fred is kind or happy.
Someone is not strong or generous.
Someone is not calm.
Someone is not generous or not funny.
Someone is either not happy or not curious.
Paul is both wise and calm.
Someone is either curious or not humble. | Alice is rich. | neutral | ((?[X]:(~tall(X)))<=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((~wise(X)&brave(X))))<=>(?[X]:((strong(X)<~>~curious(X)))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((funny(X)|strong(X)))))&
(![X]:(~kind(X)<=>~happy(X)))&
(![X]:((~wise(X)<~>~old(X))=>(happy(X)|kind(X))))&
(![X]:(creative(X)=>(~creative(X)&~happy(X))))&
(![X]:((humble(X)|~wise(X))<=>(~curious(X)|strong(X))))&
(![X]:((~kind(X)|~tall(X))<=>(~creative(X)<~>~happy(X))))&
(![X]:(~patient(X)<=>(~curious(X)<~>humble(X))))&
(![X]:((tall(X)&~generous(X))=>(~brave(X)<~>brave(X))))&
(![X]:(creative(X)=>(~kind(X)|~patient(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(~rich(X)&wise(X))))&
((?[X]:((~wise(X)&~calm(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~brave(X)<~>quiet(X))=>(tall(X)<~>~happy(X))))&
(![X]:((curious(X)<~>tall(X))=>(rich(X)|~strong(X))))&
(((rich(alice)&~patient(alice)))=>((brave(mary)&strong(mary))))&
((kind(fred)|happy(fred)))&
(?[X]:((~strong(X)|generous(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~generous(X)|~funny(X))))&
(?[X]:((~happy(X)<~>~curious(X))))&
((wise(paul)&calm(paul)))&
(?[X]:((curious(X)<~>~humble(X)))) | rich(alice) | [] | null | 0 |
Everyone who is strong is both curious and not quiet and vice versa.
If someone is old or not old then someone is quiet and vice versa.
Everyone who is not funny or not rich is both humble and not curious and vice versa.
If someone is not creative or strong then mary is not strong or not funny and vice versa.
Everyone who is either happy or wise is both kind and not patient and vice versa.
Everyone who is either not happy or not creative is not funny and vice versa.
Everyone who is not strong is both creative and kind and vice versa.
Everyone who is both not patient and not creative is curious or not curious.
If mary is either not strong or not wise then fred is not wise or strong and vice versa.
If mary is strong or not strong then paul is either not tall or brave and vice versa.
Everyone who is kind is both not patient and quiet and vice versa.
If someone is either not calm or quiet then someone is wise.
If lucy is both not calm and happy then fred is both not patient and funny.
If paul is not funny then someone is either not kind or not funny and vice versa.
John is either quiet or not wise.
Someone is not patient.
Fred is both not calm and not generous.
Someone is either rich or old.
Someone is both not generous and not brave.
Someone is patient or old.
Someone is creative. | John is not happy. | entailment | (![X]:(strong(X)<=>(curious(X)&~quiet(X))))&
((?[X]:((old(X)|~old(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~funny(X)|~rich(X))<=>(humble(X)&~curious(X))))&
((?[X]:((~creative(X)|strong(X))))<=>((~strong(mary)|~funny(mary))))&
(![X]:((happy(X)<~>wise(X))<=>(kind(X)&~patient(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>~funny(X)))&
(![X]:(~strong(X)<=>(creative(X)&kind(X))))&
(![X]:((~patient(X)&~creative(X))=>(curious(X)|~curious(X))))&
(((~strong(mary)<~>~wise(mary)))<=>((~wise(fred)|strong(fred))))&
(((strong(mary)|~strong(mary)))<=>((~tall(paul)<~>brave(paul))))&
(![X]:(kind(X)<=>(~patient(X)&quiet(X))))&
((?[X]:((~calm(X)<~>quiet(X))))=>(?[X]:(wise(X))))&
(((~calm(lucy)&happy(lucy)))=>((~patient(fred)&funny(fred))))&
((~funny(paul))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
((quiet(john)<~>~wise(john)))&
(?[X]:(~patient(X)))&
((~calm(fred)&~generous(fred)))&
(?[X]:((rich(X)<~>old(X))))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:(creative(X))) | ~happy(john) | [
"p0",
"p4",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6816297760936244545370445
% SZS output start Proof for 6816297760936244545370445
1. ! [X0] : (strong(X0) <=> (~quiet(X0) & curious(X0))) [input p0]
5. ! [X0] : ((happy(X0) <~> wise(X0)) <=> (~patient(X0) & kind(X0))) [input p4]
7. ! [X0] : (~strong(X0) <=> (kind(X0) & creative(X0))) [input p6]
11. ! [X0] : (kind(X0) <=> (quiet(X0) & ~patient(X0))) [input p10]
15. quiet(john) <~> ~wise(john) [input p14]
22. happy(john) [input hypothesis]
32. ! [X0] : ((strong(X0) | (quiet(X0) | ~curious(X0))) & ((~quiet(X0) & curious(X0)) | ~strong(X0))) [nnf transformation 1]
33. ! [X0] : ((strong(X0) | quiet(X0) | ~curious(X0)) & ((~quiet(X0) & curious(X0)) | ~strong(X0))) [flattening 32]
46. ! [X0] : ((((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0))))) [nnf transformation 5]
47. ! [X0] : ((((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0))))) [flattening 46]
49. ! [X0] : ((~strong(X0) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | strong(X0))) [nnf transformation 7]
50. ! [X0] : ((~strong(X0) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | strong(X0))) [flattening 49]
55. ! [X0] : ((kind(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~kind(X0))) [nnf transformation 11]
56. ! [X0] : ((kind(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~kind(X0))) [flattening 55]
65. (wise(john) | ~quiet(john)) & (~wise(john) | quiet(john)) [nnf transformation 15]
78. ~quiet(X0) | ~strong(X0) [cnf transformation 33]
92. ~happy(X0) | wise(X0) | kind(X0) [cnf transformation 47]
97. ~kind(X0) | ~happy(X0) | patient(X0) | ~wise(X0) [cnf transformation 47]
103. kind(X0) | strong(X0) [cnf transformation 50]
118. ~patient(X0) | ~kind(X0) [cnf transformation 56]
119. ~kind(X0) | quiet(X0) [cnf transformation 56]
129. ~wise(john) | quiet(john) [cnf transformation 65]
130. wise(john) | ~quiet(john) [cnf transformation 65]
138. happy(john) [cnf transformation 22]
260. 27 <=> quiet(john) [avatar definition]
261. quiet(john) <- (27) [avatar component clause 260]
262. ~quiet(john) <- (~27) [avatar component clause 260]
264. 28 <=> wise(john) [avatar definition]
265. ~wise(john) <- (~28) [avatar component clause 264]
266. wise(john) <- (28) [avatar component clause 264]
267. ~27 | 28 [avatar split clause 130,264,260]
268. 27 | ~28 [avatar split clause 129,264,260]
316. wise(john) | kind(john) [resolution 92,138]
317. kind(john) <- (~28) [subsumption resolution 316,265]
319. quiet(john) <- (~28) [resolution 317,119]
320. $false <- (~27, ~28) [subsumption resolution 319,262]
321. 27 | 28 [avatar contradiction clause 320]
323. 33 <=> kind(john) [avatar definition]
324. ~kind(john) <- (~33) [avatar component clause 323]
325. kind(john) <- (33) [avatar component clause 323]
327. ~strong(john) <- (27) [resolution 261,78]
489. 58 <=> patient(john) [avatar definition]
490. ~patient(john) <- (~58) [avatar component clause 489]
491. patient(john) <- (58) [avatar component clause 489]
540. ~kind(john) <- (58) [resolution 491,118]
541. ~33 | ~58 [avatar split clause 540,489,323]
542. strong(john) <- (~33) [resolution 324,103]
543. $false <- (27, ~33) [subsumption resolution 542,327]
544. ~27 | 33 [avatar contradiction clause 543]
545. ~happy(john) | patient(john) | ~wise(john) <- (33) [resolution 325,97]
550. patient(john) | ~wise(john) <- (33) [subsumption resolution 545,138]
551. ~wise(john) <- (33, ~58) [subsumption resolution 550,490]
552. $false <- (28, 33, ~58) [subsumption resolution 551,266]
553. ~28 | ~33 | 58 [avatar contradiction clause 552]
554. $false [avatar sat refutation 267,268,321,541,544,553]
% SZS output end Proof for 6816297760936244545370445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or kind is not kind and vice versa.
If john is not old then john is either not tall or not curious and vice versa.
If someone is not tall then someone is both not generous and patient and vice versa.
If lucy is strong or not wise then fred is brave or not strong.
If someone is both not curious and not quiet then susan is either rich or not happy and vice versa.
Everyone who is not quiet is both not wise and funny.
If someone is both not kind and calm then susan is both not generous and tall.
If someone is either creative or not humble then someone is quiet and vice versa.
If susan is not tall or not funny then someone is quiet.
Everyone who is not calm is either happy or not curious and vice versa.
Everyone who is both kind and not happy is not tall or patient.
If someone is brave or not quiet then someone is kind and vice versa.
If mary is both not curious and not old then someone is creative or curious.
If fred is both old and not happy then someone is either generous or not quiet.
Everyone who is not funny or happy is humble and vice versa.
If someone is both curious and not humble then someone is rich or happy.
Alice is either not kind or strong.
Susan is not creative.
Alice is not wise.
Alice is brave or not wise.
Someone is not funny or not humble.
Someone is both curious and rich.
John is happy. | Mary is tall. | entailment | (![X]:((generous(X)|kind(X))<=>~kind(X)))&
((~old(john))<=>((~tall(john)<~>~curious(john))))&
((?[X]:(~tall(X)))<=>(?[X]:((~generous(X)&patient(X)))))&
(((strong(lucy)|~wise(lucy)))=>((brave(fred)|~strong(fred))))&
((?[X]:((~curious(X)&~quiet(X))))<=>((rich(susan)<~>~happy(susan))))&
(![X]:(~quiet(X)=>(~wise(X)&funny(X))))&
((?[X]:((~kind(X)&calm(X))))=>((~generous(susan)&tall(susan))))&
((?[X]:((creative(X)<~>~humble(X))))<=>(?[X]:(quiet(X))))&
(((~tall(susan)|~funny(susan)))=>(?[X]:(quiet(X))))&
(![X]:(~calm(X)<=>(happy(X)<~>~curious(X))))&
(![X]:((kind(X)&~happy(X))=>(~tall(X)|patient(X))))&
((?[X]:((brave(X)|~quiet(X))))<=>(?[X]:(kind(X))))&
(((~curious(mary)&~old(mary)))=>(?[X]:((creative(X)|curious(X)))))&
(((old(fred)&~happy(fred)))=>(?[X]:((generous(X)<~>~quiet(X)))))&
(![X]:((~funny(X)|happy(X))<=>humble(X)))&
((?[X]:((curious(X)&~humble(X))))=>(?[X]:((rich(X)|happy(X)))))&
((~kind(alice)<~>strong(alice)))&
(~creative(susan))&
(~wise(alice))&
((brave(alice)|~wise(alice)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((curious(X)&rich(X))))&
(happy(john)) | tall(mary) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 248382311910722288417169
% SZS output start Proof for 248382311910722288417169
1. ! [X0] : ((kind(X0) | generous(X0)) <=> ~kind(X0)) [input p0]
3. ? [X0] : ~tall(X0) <=> ? [X0] : (patient(X0) & ~generous(X0)) [input p2]
24. ~tall(mary) [input hypothesis]
25. ? [X0] : ~tall(X0) <=> ? [X1] : (patient(X1) & ~generous(X1)) [rectify 3]
43. ! [X0] : (((kind(X0) | generous(X0)) | kind(X0)) & (~kind(X0) | (~kind(X0) & ~generous(X0)))) [nnf transformation 1]
44. ! [X0] : ((kind(X0) | generous(X0) | kind(X0)) & (~kind(X0) | (~kind(X0) & ~generous(X0)))) [flattening 43]
46. (? [X0] : ~tall(X0) | ! [X1] : (~patient(X1) | generous(X1))) & (? [X1] : (patient(X1) & ~generous(X1)) | ! [X0] : tall(X0)) [nnf transformation 25]
47. (? [X0] : ~tall(X0) | ! [X1] : (~patient(X1) | generous(X1))) & (? [X2] : (patient(X2) & ~generous(X2)) | ! [X3] : tall(X3)) [rectify 46]
48. ? [X0] : ~tall(X0) => ~tall(sK0) [choice axiom]
49. ? [X2] : (patient(X2) & ~generous(X2)) => (patient(sK1) & ~generous(sK1)) [choice axiom]
50. (~tall(sK0) | ! [X1] : (~patient(X1) | generous(X1))) & ((patient(sK1) & ~generous(sK1)) | ! [X3] : tall(X3)) [skolemisation 47,49,48]
84. ~kind(X0) | ~kind(X0) [cnf transformation 44]
85. kind(X0) | generous(X0) | kind(X0) [cnf transformation 44]
90. ~generous(sK1) | tall(X3) [cnf transformation 50]
133. ~tall(mary) [cnf transformation 24]
134. ~kind(X0) [duplicate literal removal 84]
135. kind(X0) | generous(X0) [duplicate literal removal 85]
161. 6 <=> ! [X3] : tall(X3) [avatar definition]
162. tall(X3) <- (6) [avatar component clause 161]
169. 8 <=> generous(sK1) [avatar definition]
171. ~generous(sK1) <- (~8) [avatar component clause 169]
172. 6 | ~8 [avatar split clause 90,169,161]
325. $false <- (6) [resolution 162,133]
326. ~6 [avatar contradiction clause 325]
332. generous(X0) [resolution 135,134]
333. $false <- (~8) [resolution 332,171]
336. 8 [avatar contradiction clause 333]
337. $false [avatar sat refutation 172,326,336]
% SZS output end Proof for 248382311910722288417169
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not tall and not brave and vice versa. If someone is either brave or not wise then someone is not patient and vice versa. Everyone who is not funny or funny is either wise or strong and vice versa. Everyone who is both tall and strong is either not calm or tall and vice versa. If someone is either funny or old then susan is brave or happy. Everyone who is either brave or tall is either quiet or not kind and vice versa. Everyone who is happy is both not wise and patient. Everyone who is either not old or not quiet is either not old or not curious and vice versa. If paul is both kind and not kind then someone is not generous or not tall. Everyone who is either not rich or not curious is old or not old and vice versa. Everyone who is either kind or brave is generous and vice versa. Everyone who is rich or funny is humble and vice versa. If someone is both happy and not patient then john is both generous and not funny. If someone is both not rich and happy then alice is both patient and calm. Everyone who is both not wise and not strong is both creative and not tall. If paul is strong or not kind then someone is either brave or not curious. Lucy is both tall and not kind. Mary is either not generous or tall. Fred is either not humble or wise. Someone is both not generous and not wise. Someone is quiet. Someone is both quiet and not old. Mary is not wise or curious. | Lucy is calm. | neutral | (![X]:((kind(X)&~kind(X))<=>(~tall(X)&~brave(X))))&
((?[X]:((brave(X)<~>~wise(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~funny(X)|funny(X))<=>(wise(X)<~>strong(X))))&
(![X]:((tall(X)&strong(X))<=>(~calm(X)<~>tall(X))))&
((?[X]:((funny(X)<~>old(X))))=>((brave(susan)|happy(susan))))&
(![X]:((brave(X)<~>tall(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:(happy(X)=>(~wise(X)&patient(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(~old(X)<~>~curious(X))))&
(((kind(paul)&~kind(paul)))=>(?[X]:((~generous(X)|~tall(X)))))&
(![X]:((~rich(X)<~>~curious(X))<=>(old(X)|~old(X))))&
(![X]:((kind(X)<~>brave(X))<=>generous(X)))&
(![X]:((rich(X)|funny(X))<=>humble(X)))&
((?[X]:((happy(X)&~patient(X))))=>((generous(john)&~funny(john))))&
((?[X]:((~rich(X)&happy(X))))=>((patient(alice)&calm(alice))))&
(![X]:((~wise(X)&~strong(X))=>(creative(X)&~tall(X))))&
(((strong(paul)|~kind(paul)))=>(?[X]:((brave(X)<~>~curious(X)))))&
((tall(lucy)&~kind(lucy)))&
((~generous(mary)<~>tall(mary)))&
((~humble(fred)<~>wise(fred)))&
(?[X]:((~generous(X)&~wise(X))))&
(?[X]:(quiet(X)))&
(?[X]:((quiet(X)&~old(X))))&
((~wise(mary)|curious(mary))) | calm(lucy) | [] | null | 0 |
Everyone who is either not wise or not brave is not old or not brave and vice versa. If someone is either generous or curious then someone is strong or not tall. Everyone who is both calm and happy is both strong and not tall and vice versa. Everyone who is rich is both wise and kind and vice versa. Everyone who is not creative or not humble is funny and vice versa. Everyone who is either curious or kind is brave and vice versa. Everyone who is wise or curious is humble or not calm. If lucy is quiet or brave then someone is funny. If someone is both not funny and not curious then alice is funny and vice versa. Everyone who is not wise or quiet is both curious and not humble and vice versa. If john is both calm and not tall then paul is both calm and happy. If mary is both not strong and old then fred is both funny and not brave and vice versa. If someone is patient or not humble then paul is happy or wise. Everyone who is either humble or funny is not kind or not strong. If susan is not kind then susan is both generous and not old and vice versa. Everyone who is funny or tall is patient and vice versa. Someone is either not calm or humble. John is both humble and patient. Susan is both not rich and funny. Someone is both not quiet and funny. John is both not brave and not quiet. Someone is either patient or curious. Alice is creative or curious. Someone is both not wise and not creative. | Mary is not creative. | neutral | (![X]:((~wise(X)<~>~brave(X))<=>(~old(X)|~brave(X))))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((calm(X)&happy(X))<=>(strong(X)&~tall(X))))&
(![X]:(rich(X)<=>(wise(X)&kind(X))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(funny(alice)))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
((~kind(susan))<=>((generous(susan)&~old(susan))))&
(![X]:((funny(X)|tall(X))<=>patient(X)))&
(?[X]:((~calm(X)<~>humble(X))))&
((humble(john)&patient(john)))&
((~rich(susan)&funny(susan)))&
(?[X]:((~quiet(X)&funny(X))))&
((~brave(john)&~quiet(john)))&
(?[X]:((patient(X)<~>curious(X))))&
((creative(alice)|curious(alice)))&
(?[X]:((~wise(X)&~creative(X)))) | ~creative(mary) | [] | null | 0 |
If mary is either not strong or not kind then mary is not patient.
Everyone who is not funny or creative is either calm or not patient.
Everyone who is not strong is both not generous and not strong.
Everyone who is patient is not happy and vice versa.
If someone is both not rich and creative then paul is both not humble and kind.
Everyone who is either creative or not creative is either tall or kind.
Everyone who is calm or not calm is calm.
Everyone who is either not old or not tall is either not humble or happy.
If susan is not old or old then alice is not wise or rich.
Everyone who is happy or not rich is strong and vice versa.
If mary is both calm and not wise then fred is either not rich or not strong and vice versa.
If fred is humble or not happy then mary is both not calm and not brave and vice versa.
If someone is either not rich or not humble then alice is both rich and strong and vice versa.
Everyone who is either strong or funny is both curious and quiet and vice versa.
Everyone who is funny or not wise is either not strong or not kind and vice versa.
Everyone who is patient is both not wise and not quiet.
Mary is calm or brave.
Paul is creative.
Paul is both patient and not happy.
Alice is both tall and not humble.
Someone is not happy.
Someone is not creative or not curious.
Someone is either funny or quiet. | Fred is not tall. | contradiction | (((~strong(mary)<~>~kind(mary)))=>(~patient(mary)))&
(![X]:((~funny(X)|creative(X))=>(calm(X)<~>~patient(X))))&
(![X]:(~strong(X)=>(~generous(X)&~strong(X))))&
(![X]:(patient(X)<=>~happy(X)))&
((?[X]:((~rich(X)&creative(X))))=>((~humble(paul)&kind(paul))))&
(![X]:((creative(X)<~>~creative(X))=>(tall(X)<~>kind(X))))&
(![X]:((calm(X)|~calm(X))=>calm(X)))&
(![X]:((~old(X)<~>~tall(X))=>(~humble(X)<~>happy(X))))&
(((~old(susan)|old(susan)))=>((~wise(alice)|rich(alice))))&
(![X]:((happy(X)|~rich(X))<=>strong(X)))&
(((calm(mary)&~wise(mary)))<=>((~rich(fred)<~>~strong(fred))))&
(((humble(fred)|~happy(fred)))<=>((~calm(mary)&~brave(mary))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((rich(alice)&strong(alice))))&
(![X]:((strong(X)<~>funny(X))<=>(curious(X)&quiet(X))))&
(![X]:((funny(X)|~wise(X))<=>(~strong(X)<~>~kind(X))))&
(![X]:(patient(X)=>(~wise(X)&~quiet(X))))&
((calm(mary)|brave(mary)))&
(creative(paul))&
((patient(paul)&~happy(paul)))&
((tall(alice)&~humble(alice)))&
(?[X]:(~happy(X)))&
(?[X]:((~creative(X)|~curious(X))))&
(?[X]:((funny(X)<~>quiet(X)))) | ~tall(fred) | [
"p1",
"p3",
"p5",
"p6",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4584624354595998707178019
% SZS output start Proof for 4584624354595998707178019
2. ! [X0] : ((creative(X0) | ~funny(X0)) => (calm(X0) <~> ~patient(X0))) [input p1]
4. ! [X0] : (patient(X0) <=> ~happy(X0)) [input p3]
6. ! [X0] : ((creative(X0) <~> ~creative(X0)) => (tall(X0) <~> kind(X0))) [input p5]
7. ! [X0] : ((~calm(X0) | calm(X0)) => calm(X0)) [input p6]
10. ! [X0] : ((~rich(X0) | happy(X0)) <=> strong(X0)) [input p9]
12. (~happy(fred) | humble(fred)) <=> (~brave(mary) & ~calm(mary)) [input p11]
15. ! [X0] : ((~wise(X0) | funny(X0)) <=> (~strong(X0) <~> ~kind(X0))) [input p14]
24. ~tall(fred) [input hypothesis]
27. ! [X0] : ((calm(X0) <~> ~patient(X0)) | (~creative(X0) & funny(X0))) [ennf transformation 2]
30. ! [X0] : ((tall(X0) <~> kind(X0)) | (creative(X0) <=> ~creative(X0))) [ennf transformation 6]
31. ! [X0] : (calm(X0) | (calm(X0) & ~calm(X0))) [ennf transformation 7]
37. ! [X0] : (((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | (~creative(X0) & funny(X0))) [nnf transformation 27]
38. ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))) [nnf transformation 4]
39. ! [X0] : (((~kind(X0) | ~tall(X0)) & (kind(X0) | tall(X0))) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) [nnf transformation 30]
41. ! [X0] : (((~rich(X0) | happy(X0)) | ~strong(X0)) & (strong(X0) | (rich(X0) & ~happy(X0)))) [nnf transformation 10]
42. ! [X0] : ((~rich(X0) | happy(X0) | ~strong(X0)) & (strong(X0) | (rich(X0) & ~happy(X0)))) [flattening 41]
45. ((~happy(fred) | humble(fred)) | (brave(mary) | calm(mary))) & ((~brave(mary) & ~calm(mary)) | (happy(fred) & ~humble(fred))) [nnf transformation 12]
46. (~happy(fred) | humble(fred) | brave(mary) | calm(mary)) & ((~brave(mary) & ~calm(mary)) | (happy(fred) & ~humble(fred))) [flattening 45]
54. ! [X0] : (((~wise(X0) | funny(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (wise(X0) & ~funny(X0)))) [nnf transformation 15]
55. ! [X0] : ((~wise(X0) | funny(X0) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (wise(X0) & ~funny(X0)))) [flattening 54]
67. ~calm(X0) | patient(X0) | funny(X0) [cnf transformation 37]
70. ~happy(X0) | ~patient(X0) [cnf transformation 38]
74. kind(X0) | tall(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 39]
75. kind(X0) | tall(X0) | creative(X0) | creative(X0) [cnf transformation 39]
79. calm(X0) | calm(X0) [cnf transformation 31]
86. ~happy(X0) | strong(X0) [cnf transformation 42]
96. ~calm(mary) | happy(fred) [cnf transformation 46]
112. ~funny(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 55]
130. ~tall(fred) [cnf transformation 24]
131. calm(X0) [duplicate literal removal 79]
132. kind(X0) | tall(X0) | ~creative(X0) [duplicate literal removal 74]
133. kind(X0) | tall(X0) | creative(X0) [duplicate literal removal 75]
164. tall(X0) | kind(X0) [subsumption resolution 132,133]
181. 10 <=> strong(fred) [avatar definition]
183. strong(fred) <- (10) [avatar component clause 181]
198. 13 <=> happy(fred) [avatar definition]
200. happy(fred) <- (13) [avatar component clause 198]
211. happy(fred) [subsumption resolution 96,131]
212. 13 [avatar split clause 211,198]
258. ~patient(fred) <- (13) [resolution 70,200]
262. strong(fred) <- (13) [resolution 86,200]
266. 10 | ~13 [avatar split clause 262,198,181]
270. kind(fred) [resolution 164,130]
279. funny(X0) | patient(X0) [resolution 67,131]
315. 30 <=> funny(fred) [avatar definition]
316. ~funny(fred) <- (~30) [avatar component clause 315]
317. funny(fred) <- (30) [avatar component clause 315]
390. ~strong(fred) | ~kind(fred) <- (30) [resolution 112,317]
393. ~kind(fred) <- (10, 30) [subsumption resolution 390,183]
394. $false <- (10, 30) [subsumption resolution 393,270]
395. ~10 | ~30 [avatar contradiction clause 394]
396. patient(fred) <- (~30) [resolution 316,279]
397. $false <- (13, ~30) [subsumption resolution 396,258]
398. ~13 | 30 [avatar contradiction clause 397]
399. $false [avatar sat refutation 212,266,395,398]
% SZS output end Proof for 4584624354595998707178019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or strong is calm and vice versa.
Everyone who is both not quiet and quiet is calm.
Everyone who is not kind is brave.
Everyone who is both not calm and rich is not happy or old and vice versa.
If someone is not tall then someone is creative or not rich.
Everyone who is either generous or not funny is both not quiet and curious.
Everyone who is either not old or not curious is patient and vice versa.
If someone is patient then someone is not old or not patient and vice versa.
Everyone who is curious or strong is patient and vice versa.
Everyone who is either not tall or not calm is both not calm and not tall.
Everyone who is either not funny or not patient is wise or not humble.
If alice is not wise or not strong then someone is both not strong and not quiet.
Everyone who is not calm or not kind is not funny and vice versa.
Everyone who is happy is wise.
If someone is not kind or not patient then someone is either not generous or not brave and vice versa.
Everyone who is either not rich or creative is humble or not calm and vice versa.
Fred is both creative and funny.
Susan is either brave or not happy.
Alice is not generous.
Alice is not calm.
Lucy is either humble or not rich.
Someone is quiet.
Someone is either not calm or generous. | Fred is not old. | entailment | (![X]:((humble(X)<~>strong(X))<=>calm(X)))&
(![X]:((~quiet(X)&quiet(X))=>calm(X)))&
(![X]:(~kind(X)=>brave(X)))&
(![X]:((~calm(X)&rich(X))<=>(~happy(X)|old(X))))&
((?[X]:(~tall(X)))=>(?[X]:((creative(X)|~rich(X)))))&
(![X]:((generous(X)<~>~funny(X))=>(~quiet(X)&curious(X))))&
(![X]:((~old(X)<~>~curious(X))<=>patient(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((curious(X)|strong(X))<=>patient(X)))&
(![X]:((~tall(X)<~>~calm(X))=>(~calm(X)&~tall(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(wise(X)|~humble(X))))&
(((~wise(alice)|~strong(alice)))=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:((~calm(X)|~kind(X))<=>~funny(X)))&
(![X]:(happy(X)=>wise(X)))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(humble(X)|~calm(X))))&
((creative(fred)&funny(fred)))&
((brave(susan)<~>~happy(susan)))&
(~generous(alice))&
(~calm(alice))&
((humble(lucy)<~>~rich(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:((~calm(X)<~>generous(X)))) | ~old(fred) | [
"p3",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8870228582650284954861753
% SZS output start Proof for 8870228582650284954861753
4. ! [X0] : ((rich(X0) & ~calm(X0)) <=> (old(X0) | ~happy(X0))) [input p3]
13. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> ~funny(X0)) [input p12]
17. funny(fred) & creative(fred) [input p16]
24. old(fred) [input hypothesis]
39. ! [X0] : (((rich(X0) & ~calm(X0)) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | (~rich(X0) | calm(X0)))) [nnf transformation 4]
40. ! [X0] : (((rich(X0) & ~calm(X0)) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | ~rich(X0) | calm(X0))) [flattening 39]
56. ! [X0] : (((~kind(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (kind(X0) & calm(X0)))) [nnf transformation 13]
57. ! [X0] : ((~kind(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (kind(X0) & calm(X0)))) [flattening 56]
80. ~old(X0) | ~calm(X0) [cnf transformation 40]
104. ~funny(X0) | calm(X0) [cnf transformation 57]
120. funny(fred) [cnf transformation 17]
130. old(fred) [cnf transformation 24]
246. ~calm(fred) [resolution 80,130]
249. calm(fred) [resolution 104,120]
250. $false [subsumption resolution 249,246]
% SZS output end Proof for 8870228582650284954861753
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is creative then someone is either not calm or funny.
If alice is quiet or strong then someone is either not generous or humble.
Everyone who is not creative or patient is both curious and generous.
If mary is not humble or kind then fred is not rich or not calm.
If someone is funny then mary is quiet or curious and vice versa.
Everyone who is kind is not old or humble.
Everyone who is both strong and tall is either creative or not funny and vice versa.
If someone is patient or not brave then alice is either not generous or not wise and vice versa.
Everyone who is quiet or not tall is both kind and wise.
Everyone who is curious is not patient and vice versa.
Everyone who is both not calm and brave is not calm or not tall and vice versa.
Everyone who is wise or not kind is not humble or funny.
If alice is not creative or humble then someone is both tall and rich and vice versa.
Everyone who is either not brave or patient is either not brave or wise and vice versa.
If john is both not old and not funny then paul is either tall or quiet and vice versa.
Everyone who is creative is not quiet or not patient and vice versa.
Someone is either creative or not old.
Someone is not old.
John is not rich or not humble.
Someone is either not patient or not generous.
Someone is either happy or not generous.
Fred is both strong and old.
John is both kind and brave. | John is not funny. | entailment | ((creative(mary))=>(?[X]:((~calm(X)<~>funny(X)))))&
(((quiet(alice)|strong(alice)))=>(?[X]:((~generous(X)<~>humble(X)))))&
(![X]:((~creative(X)|patient(X))=>(curious(X)&generous(X))))&
(((~humble(mary)|kind(mary)))=>((~rich(fred)|~calm(fred))))&
((?[X]:(funny(X)))<=>((quiet(mary)|curious(mary))))&
(![X]:(kind(X)=>(~old(X)|humble(X))))&
(![X]:((strong(X)&tall(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:((patient(X)|~brave(X))))<=>((~generous(alice)<~>~wise(alice))))&
(![X]:((quiet(X)|~tall(X))=>(kind(X)&wise(X))))&
(![X]:(curious(X)<=>~patient(X)))&
(![X]:((~calm(X)&brave(X))<=>(~calm(X)|~tall(X))))&
(![X]:((wise(X)|~kind(X))=>(~humble(X)|funny(X))))&
(((~creative(alice)|humble(alice)))<=>(?[X]:((tall(X)&rich(X)))))&
(![X]:((~brave(X)<~>patient(X))<=>(~brave(X)<~>wise(X))))&
(((~old(john)&~funny(john)))<=>((tall(paul)<~>quiet(paul))))&
(![X]:(creative(X)<=>(~quiet(X)|~patient(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:(~old(X)))&
((~rich(john)|~humble(john)))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
((strong(fred)&old(fred)))&
((kind(john)&brave(john))) | ~funny(john) | [
"p2",
"p8",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 574734862560294684735944
% SZS output start Proof for 574734862560294684735944
3. ! [X0] : ((patient(X0) | ~creative(X0)) => (generous(X0) & curious(X0))) [input p2]
9. ! [X0] : ((~tall(X0) | quiet(X0)) => (wise(X0) & kind(X0))) [input p8]
10. ! [X0] : (curious(X0) <=> ~patient(X0)) [input p9]
14. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> (~brave(X0) <~> wise(X0))) [input p13]
15. (~funny(john) & ~old(john)) <=> (tall(paul) <~> quiet(paul)) [input p14]
24. funny(john) [input hypothesis]
27. ! [X0] : ((generous(X0) & curious(X0)) | (~patient(X0) & creative(X0))) [ennf transformation 3]
32. ! [X0] : ((wise(X0) & kind(X0)) | (tall(X0) & ~quiet(X0))) [ennf transformation 9]
52. ! [X0] : ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0))) [nnf transformation 10]
60. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 14]
61. ((~funny(john) & ~old(john)) | ((tall(paul) | ~quiet(paul)) & (quiet(paul) | ~tall(paul)))) & (((~quiet(paul) | ~tall(paul)) & (quiet(paul) | tall(paul))) | (funny(john) | old(john))) [nnf transformation 15]
62. ((~funny(john) & ~old(john)) | ((tall(paul) | ~quiet(paul)) & (quiet(paul) | ~tall(paul)))) & (((~quiet(paul) | ~tall(paul)) & (quiet(paul) | tall(paul))) | funny(john) | old(john)) [flattening 61]
83. ~patient(X0) | curious(X0) [cnf transformation 27]
106. ~quiet(X0) | wise(X0) [cnf transformation 32]
107. wise(X0) | tall(X0) [cnf transformation 32]
108. ~patient(X0) | ~curious(X0) [cnf transformation 52]
109. curious(X0) | patient(X0) [cnf transformation 52]
124. ~wise(X0) | brave(X0) | patient(X0) | brave(X0) [cnf transformation 60]
127. patient(X0) | ~brave(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 60]
134. ~funny(john) | quiet(paul) | ~tall(paul) [cnf transformation 62]
151. funny(john) [cnf transformation 24]
153. ~wise(X0) | brave(X0) | patient(X0) [duplicate literal removal 124]
154. patient(X0) | ~brave(X0) | ~wise(X0) [duplicate literal removal 127]
249. 21 <=> ! [X1] : ~patient(X1) [avatar definition]
250. ~patient(X1) <- (21) [avatar component clause 249]
254. curious(X0) [subsumption resolution 109,83]
255. ~patient(X0) [subsumption resolution 108,254]
256. 21 [avatar split clause 255,249]
281. ~wise(X0) | patient(X0) [subsumption resolution 153,154]
284. 27 <=> quiet(paul) [avatar definition]
285. quiet(paul) <- (27) [avatar component clause 284]
288. 28 <=> tall(paul) [avatar definition]
289. ~tall(paul) <- (~28) [avatar component clause 288]
292. 29 <=> funny(john) [avatar definition]
296. ~28 | 27 | ~29 [avatar split clause 134,292,284,288]
336. 29 [avatar split clause 151,292]
358. patient(X0) | tall(X0) [resolution 281,107]
361. tall(X0) <- (21) [subsumption resolution 358,250]
363. $false <- (21, ~28) [resolution 361,289]
365. ~21 | 28 [avatar contradiction clause 363]
366. wise(paul) <- (27) [resolution 285,106]
368. patient(paul) <- (27) [resolution 366,281]
369. $false <- (21, 27) [subsumption resolution 368,250]
370. ~21 | ~27 [avatar contradiction clause 369]
371. $false [avatar sat refutation 256,296,336,365,370]
% SZS output end Proof for 574734862560294684735944
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not rich.
Everyone who is quiet or old is either happy or not strong and vice versa.
Everyone who is both not patient and not creative is not rich and vice versa.
If lucy is either happy or generous then someone is patient or not curious.
Everyone who is strong or tall is old.
If lucy is either not funny or kind then fred is calm and vice versa.
Everyone who is both calm and happy is either not old or not quiet.
Everyone who is not patient or tall is either not old or not rich and vice versa.
Everyone who is not old is strong and vice versa.
If mary is either not happy or not wise then someone is not tall and vice versa.
Everyone who is either not creative or old is generous or brave.
Everyone who is funny or not creative is both generous and quiet.
If susan is both brave and generous then fred is not curious or tall and vice versa.
If john is not patient or creative then mary is both strong and curious and vice versa.
If mary is both not patient and rich then susan is either not kind or not tall.
Everyone who is either not brave or not curious is humble.
Lucy is both brave and creative.
Someone is both not tall and not rich.
Fred is brave.
Susan is either not happy or not patient.
Alice is funny.
Paul is both not kind and not brave.
Someone is wise or happy. | Alice is rich. | neutral | (![X]:(tall(X)=>~rich(X)))&
(![X]:((quiet(X)|old(X))<=>(happy(X)<~>~strong(X))))&
(![X]:((~patient(X)&~creative(X))<=>~rich(X)))&
(((happy(lucy)<~>generous(lucy)))=>(?[X]:((patient(X)|~curious(X)))))&
(![X]:((strong(X)|tall(X))=>old(X)))&
(((~funny(lucy)<~>kind(lucy)))<=>(calm(fred)))&
(![X]:((calm(X)&happy(X))=>(~old(X)<~>~quiet(X))))&
(![X]:((~patient(X)|tall(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(~old(X)<=>strong(X)))&
(((~happy(mary)<~>~wise(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((~creative(X)<~>old(X))=>(generous(X)|brave(X))))&
(![X]:((funny(X)|~creative(X))=>(generous(X)&quiet(X))))&
(((brave(susan)&generous(susan)))<=>((~curious(fred)|tall(fred))))&
(((~patient(john)|creative(john)))<=>((strong(mary)&curious(mary))))&
(((~patient(mary)&rich(mary)))=>((~kind(susan)<~>~tall(susan))))&
(![X]:((~brave(X)<~>~curious(X))=>humble(X)))&
((brave(lucy)&creative(lucy)))&
(?[X]:((~tall(X)&~rich(X))))&
(brave(fred))&
((~happy(susan)<~>~patient(susan)))&
(funny(alice))&
((~kind(paul)&~brave(paul)))&
(?[X]:((wise(X)|happy(X)))) | rich(alice) | [] | null | 0 |
If someone is not funny or curious then susan is either not wise or not kind and vice versa.
If paul is either rich or not quiet then paul is not kind or not old and vice versa.
Everyone who is quiet or funny is either not kind or not funny.
Everyone who is tall or not generous is either humble or curious and vice versa.
If fred is humble then mary is funny or curious and vice versa.
Everyone who is humble is not old.
If someone is either not funny or funny then someone is tall and vice versa.
If someone is quiet or old then someone is curious.
Everyone who is both not calm and generous is not patient.
Everyone who is both happy and not creative is not generous and vice versa.
Everyone who is both funny and not old is either tall or quiet.
Everyone who is either not curious or old is not brave or not funny and vice versa.
If mary is either happy or quiet then lucy is quiet or not creative.
If someone is both not rich and not strong then someone is either not calm or happy and vice versa.
If paul is both quiet and curious then someone is both not old and calm.
Everyone who is both not patient and not happy is not wise or rich.
Lucy is strong.
Someone is rich.
Lucy is both not generous and not rich.
Someone is wise.
Alice is not rich or not happy.
Lucy is not creative.
Fred is not quiet.
Mary is tall. | Alice is rich. | neutral | ((?[X]:((~funny(X)|curious(X))))<=>((~wise(susan)<~>~kind(susan))))&
(((rich(paul)<~>~quiet(paul)))<=>((~kind(paul)|~old(paul))))&
(![X]:((quiet(X)|funny(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((tall(X)|~generous(X))<=>(humble(X)<~>curious(X))))&
((humble(fred))<=>((funny(mary)|curious(mary))))&
(![X]:(humble(X)=>~old(X)))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:(tall(X))))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:(curious(X))))&
(![X]:((~calm(X)&generous(X))=>~patient(X)))&
(![X]:((happy(X)&~creative(X))<=>~generous(X)))&
(![X]:((funny(X)&~old(X))=>(tall(X)<~>quiet(X))))&
(![X]:((~curious(X)<~>old(X))<=>(~brave(X)|~funny(X))))&
(((happy(mary)<~>quiet(mary)))=>((quiet(lucy)|~creative(lucy))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((~calm(X)<~>happy(X)))))&
(((quiet(paul)&curious(paul)))=>(?[X]:((~old(X)&calm(X)))))&
(![X]:((~patient(X)&~happy(X))=>(~wise(X)|rich(X))))&
(strong(lucy))&
(?[X]:(rich(X)))&
((~generous(lucy)&~rich(lucy)))&
(?[X]:(wise(X)))&
((~rich(alice)|~happy(alice)))&
(~creative(lucy))&
(~quiet(fred))&
(tall(mary)) | rich(alice) | [] | null | 0 |
If someone is creative then someone is strong or not funny.
If someone is old then someone is either humble or tall.
If fred is not rich or not quiet then someone is either not rich or not creative.
If paul is not old or not kind then someone is not tall.
If someone is not brave then fred is not patient or not happy and vice versa.
Everyone who is either not strong or tall is funny or not quiet and vice versa.
If fred is curious or kind then john is humble.
If john is both curious and not quiet then fred is both rich and not generous.
If someone is either patient or happy then mary is tall or not strong.
If someone is both patient and not generous then lucy is both not kind and calm.
Everyone who is not patient or brave is not calm or curious and vice versa.
Everyone who is not old is either tall or kind.
Everyone who is not humble or calm is quiet and vice versa.
If lucy is either kind or not generous then fred is happy and vice versa.
Everyone who is either not rich or not curious is wise or not tall.
If mary is either not happy or not creative then lucy is not calm and vice versa.
John is not creative.
Someone is either not old or happy.
Fred is tall or not curious.
John is brave.
Someone is not curious.
Someone is either patient or kind.
Someone is patient or creative.
Lucy is not brave or not calm. | John is not brave. | contradiction | ((?[X]:(creative(X)))=>(?[X]:((strong(X)|~funny(X)))))&
((?[X]:(old(X)))=>(?[X]:((humble(X)<~>tall(X)))))&
(((~rich(fred)|~quiet(fred)))=>(?[X]:((~rich(X)<~>~creative(X)))))&
(((~old(paul)|~kind(paul)))=>(?[X]:(~tall(X))))&
((?[X]:(~brave(X)))<=>((~patient(fred)|~happy(fred))))&
(![X]:((~strong(X)<~>tall(X))<=>(funny(X)|~quiet(X))))&
(((curious(fred)|kind(fred)))=>(humble(john)))&
(((curious(john)&~quiet(john)))=>((rich(fred)&~generous(fred))))&
((?[X]:((patient(X)<~>happy(X))))=>((tall(mary)|~strong(mary))))&
((?[X]:((patient(X)&~generous(X))))=>((~kind(lucy)&calm(lucy))))&
(![X]:((~patient(X)|brave(X))<=>(~calm(X)|curious(X))))&
(![X]:(~old(X)=>(tall(X)<~>kind(X))))&
(![X]:((~humble(X)|calm(X))<=>quiet(X)))&
(((kind(lucy)<~>~generous(lucy)))<=>(happy(fred)))&
(![X]:((~rich(X)<~>~curious(X))=>(wise(X)|~tall(X))))&
(((~happy(mary)<~>~creative(mary)))<=>(~calm(lucy)))&
(~creative(john))&
(?[X]:((~old(X)<~>happy(X))))&
((tall(fred)|~curious(fred)))&
(brave(john))&
(?[X]:(~curious(X)))&
(?[X]:((patient(X)<~>kind(X))))&
(?[X]:((patient(X)|creative(X))))&
((~brave(lucy)|~calm(lucy))) | ~brave(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9128376908012336853862145
% SZS output start Proof for 9128376908012336853862145
20. brave(john) [input p19]
25. ~brave(john) [input hypothesis]
124. brave(john) [cnf transformation 20]
130. ~brave(john) [cnf transformation 25]
324. $false [subsumption resolution 130,124]
% SZS output end Proof for 9128376908012336853862145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and curious is calm or not calm and vice versa.
Everyone who is happy or tall is both not tall and rich.
If fred is both not old and not quiet then alice is either wise or kind.
Everyone who is both not patient and not humble is not creative.
Everyone who is both not humble and brave is either old or brave and vice versa.
Everyone who is patient is brave.
If fred is either not wise or not strong then someone is both strong and happy and vice versa.
If susan is creative or not brave then mary is tall or quiet.
If mary is not old then someone is not funny and vice versa.
Everyone who is not wise or quiet is not creative or not wise.
Everyone who is curious is both calm and not kind and vice versa.
If someone is both not funny and not old then someone is strong or not tall.
If someone is both not wise and funny then lucy is either humble or wise.
If fred is not calm or strong then john is not quiet and vice versa.
Everyone who is either not calm or not brave is either not tall or wise.
Everyone who is both not tall and curious is not kind and vice versa.
Someone is old or wise.
John is generous.
Susan is either calm or not funny.
Mary is either not funny or not wise.
Someone is humble.
Alice is not quiet or happy. | Susan is not generous. | neutral | (![X]:((old(X)&curious(X))<=>(calm(X)|~calm(X))))&
(![X]:((happy(X)|tall(X))=>(~tall(X)&rich(X))))&
(((~old(fred)&~quiet(fred)))=>((wise(alice)<~>kind(alice))))&
(![X]:((~patient(X)&~humble(X))=>~creative(X)))&
(![X]:((~humble(X)&brave(X))<=>(old(X)<~>brave(X))))&
(![X]:(patient(X)=>brave(X)))&
(((~wise(fred)<~>~strong(fred)))<=>(?[X]:((strong(X)&happy(X)))))&
(((creative(susan)|~brave(susan)))=>((tall(mary)|quiet(mary))))&
((~old(mary))<=>(?[X]:(~funny(X))))&
(![X]:((~wise(X)|quiet(X))=>(~creative(X)|~wise(X))))&
(![X]:(curious(X)<=>(calm(X)&~kind(X))))&
((?[X]:((~funny(X)&~old(X))))=>(?[X]:((strong(X)|~tall(X)))))&
((?[X]:((~wise(X)&funny(X))))=>((humble(lucy)<~>wise(lucy))))&
(((~calm(fred)|strong(fred)))<=>(~quiet(john)))&
(![X]:((~calm(X)<~>~brave(X))=>(~tall(X)<~>wise(X))))&
(![X]:((~tall(X)&curious(X))<=>~kind(X)))&
(?[X]:((old(X)|wise(X))))&
(generous(john))&
((calm(susan)<~>~funny(susan)))&
((~funny(mary)<~>~wise(mary)))&
(?[X]:(humble(X)))&
((~quiet(alice)|happy(alice))) | ~generous(susan) | [] | null | 0 |
If lucy is creative or not curious then susan is both not patient and not calm.
Everyone who is either brave or not happy is both not patient and not funny and vice versa.
Everyone who is patient is both not humble and not calm.
If someone is humble then lucy is not rich or not generous.
Everyone who is both brave and wise is either kind or not curious and vice versa.
If someone is either curious or kind then john is both calm and not creative.
Everyone who is either not strong or not humble is both not calm and humble and vice versa.
If someone is happy or not quiet then someone is patient or kind and vice versa.
Everyone who is not rich is both not wise and humble.
If john is not curious or happy then someone is both humble and generous and vice versa.
Everyone who is either not kind or patient is either not kind or rich and vice versa.
If john is quiet then paul is either rich or not funny.
Everyone who is either not quiet or humble is either creative or calm.
Everyone who is not patient is either not curious or curious.
Everyone who is both old and not humble is either not quiet or generous.
Everyone who is either not funny or not calm is either strong or creative.
Paul is both old and strong.
Someone is tall.
Alice is either not happy or not humble.
Someone is happy.
Susan is either kind or humble.
Someone is not strong or not quiet.
Alice is calm.
Someone is not humble. | Paul is patient. | contradiction | (((creative(lucy)|~curious(lucy)))=>((~patient(susan)&~calm(susan))))&
(![X]:((brave(X)<~>~happy(X))<=>(~patient(X)&~funny(X))))&
(![X]:(patient(X)=>(~humble(X)&~calm(X))))&
((?[X]:(humble(X)))=>((~rich(lucy)|~generous(lucy))))&
(![X]:((brave(X)&wise(X))<=>(kind(X)<~>~curious(X))))&
((?[X]:((curious(X)<~>kind(X))))=>((calm(john)&~creative(john))))&
(![X]:((~strong(X)<~>~humble(X))<=>(~calm(X)&humble(X))))&
((?[X]:((happy(X)|~quiet(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:(~rich(X)=>(~wise(X)&humble(X))))&
(((~curious(john)|happy(john)))<=>(?[X]:((humble(X)&generous(X)))))&
(![X]:((~kind(X)<~>patient(X))<=>(~kind(X)<~>rich(X))))&
((quiet(john))=>((rich(paul)<~>~funny(paul))))&
(![X]:((~quiet(X)<~>humble(X))=>(creative(X)<~>calm(X))))&
(![X]:(~patient(X)=>(~curious(X)<~>curious(X))))&
(![X]:((old(X)&~humble(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((~funny(X)<~>~calm(X))=>(strong(X)<~>creative(X))))&
((old(paul)&strong(paul)))&
(?[X]:(tall(X)))&
((~happy(alice)<~>~humble(alice)))&
(?[X]:(happy(X)))&
((kind(susan)<~>humble(susan)))&
(?[X]:((~strong(X)|~quiet(X))))&
(calm(alice))&
(?[X]:(~humble(X))) | patient(paul) | [
"p2",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8072706810974933252560592
% SZS output start Proof for 8072706810974933252560592
3. ! [X0] : (patient(X0) => (~calm(X0) & ~humble(X0))) [input p2]
7. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> (humble(X0) & ~calm(X0))) [input p6]
17. strong(paul) & old(paul) [input p16]
25. patient(paul) [input hypothesis]
29. ! [X0] : ((~calm(X0) & ~humble(X0)) | ~patient(X0)) [ennf transformation 3]
45. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 7]
46. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [flattening 45]
81. ~humble(X0) | ~patient(X0) [cnf transformation 29]
97. humble(X0) | ~strong(X0) | humble(X0) [cnf transformation 46]
134. strong(paul) [cnf transformation 17]
143. patient(paul) [cnf transformation 25]
148. ~strong(X0) | humble(X0) [duplicate literal removal 97]
304. humble(paul) [resolution 148,134]
305. ~patient(paul) [resolution 304,81]
306. $false [subsumption resolution 305,143]
% SZS output end Proof for 8072706810974933252560592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and curious and vice versa.
Everyone who is both not rich and not strong is both not rich and humble.
If paul is both not brave and not calm then someone is both creative and not wise.
If mary is either creative or not strong then someone is not quiet or not wise and vice versa.
Everyone who is not quiet is not generous or not creative and vice versa.
If someone is either not calm or not rich then paul is both kind and brave and vice versa.
If someone is happy then someone is old or tall and vice versa.
Everyone who is not patient or not quiet is not humble and vice versa.
If john is both not rich and tall then someone is patient or calm.
If fred is kind then someone is not humble or funny.
Everyone who is either generous or calm is both calm and not quiet.
Everyone who is not generous or not calm is not kind or curious and vice versa.
Everyone who is either not quiet or wise is old.
Everyone who is either not creative or not generous is not wise or not humble.
If someone is tall then fred is brave or patient.
If lucy is both not brave and not wise then mary is either strong or not brave and vice versa.
Fred is not old.
Lucy is brave or not quiet.
Someone is either rich or patient.
Someone is both not quiet and rich.
John is not funny.
Paul is funny. | Fred is rich. | neutral | (![X]:(kind(X)<=>(~brave(X)&curious(X))))&
(![X]:((~rich(X)&~strong(X))=>(~rich(X)&humble(X))))&
(((~brave(paul)&~calm(paul)))=>(?[X]:((creative(X)&~wise(X)))))&
(((creative(mary)<~>~strong(mary)))<=>(?[X]:((~quiet(X)|~wise(X)))))&
(![X]:(~quiet(X)<=>(~generous(X)|~creative(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>((kind(paul)&brave(paul))))&
((?[X]:(happy(X)))<=>(?[X]:((old(X)|tall(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>~humble(X)))&
(((~rich(john)&tall(john)))=>(?[X]:((patient(X)|calm(X)))))&
((kind(fred))=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:((generous(X)<~>calm(X))=>(calm(X)&~quiet(X))))&
(![X]:((~generous(X)|~calm(X))<=>(~kind(X)|curious(X))))&
(![X]:((~quiet(X)<~>wise(X))=>old(X)))&
(![X]:((~creative(X)<~>~generous(X))=>(~wise(X)|~humble(X))))&
((?[X]:(tall(X)))=>((brave(fred)|patient(fred))))&
(((~brave(lucy)&~wise(lucy)))<=>((strong(mary)<~>~brave(mary))))&
(~old(fred))&
((brave(lucy)|~quiet(lucy)))&
(?[X]:((rich(X)<~>patient(X))))&
(?[X]:((~quiet(X)&rich(X))))&
(~funny(john))&
(funny(paul)) | rich(fred) | [] | null | 0 |
Everyone who is kind or rich is both not old and not wise.
Everyone who is not happy is wise or not patient and vice versa.
Everyone who is not old or calm is either not kind or calm and vice versa.
Everyone who is calm is either not brave or not humble.
Everyone who is either not humble or not creative is either humble or not patient.
If someone is wise or happy then fred is either calm or not generous and vice versa.
Everyone who is rich or calm is either funny or generous and vice versa.
Everyone who is either creative or not funny is not rich or creative and vice versa.
Everyone who is funny is either not generous or not rich and vice versa.
Everyone who is brave is not curious and vice versa.
Everyone who is calm is both patient and not funny and vice versa.
If someone is either brave or not quiet then someone is both not tall and not happy and vice versa.
Everyone who is quiet is both not wise and happy.
Everyone who is both humble and not calm is tall.
If someone is not patient or calm then susan is happy or not wise.
Everyone who is humble or not patient is happy and vice versa.
Lucy is creative.
Susan is either not generous or not curious.
Lucy is curious or not humble.
Someone is patient or not creative.
Alice is quiet or generous. | Lucy is not kind. | entailment | (![X]:((kind(X)|rich(X))=>(~old(X)&~wise(X))))&
(![X]:(~happy(X)<=>(wise(X)|~patient(X))))&
(![X]:((~old(X)|calm(X))<=>(~kind(X)<~>calm(X))))&
(![X]:(calm(X)=>(~brave(X)<~>~humble(X))))&
(![X]:((~humble(X)<~>~creative(X))=>(humble(X)<~>~patient(X))))&
((?[X]:((wise(X)|happy(X))))<=>((calm(fred)<~>~generous(fred))))&
(![X]:((rich(X)|calm(X))<=>(funny(X)<~>generous(X))))&
(![X]:((creative(X)<~>~funny(X))<=>(~rich(X)|creative(X))))&
(![X]:(funny(X)<=>(~generous(X)<~>~rich(X))))&
(![X]:(brave(X)<=>~curious(X)))&
(![X]:(calm(X)<=>(patient(X)&~funny(X))))&
((?[X]:((brave(X)<~>~quiet(X))))<=>(?[X]:((~tall(X)&~happy(X)))))&
(![X]:(quiet(X)=>(~wise(X)&happy(X))))&
(![X]:((humble(X)&~calm(X))=>tall(X)))&
((?[X]:((~patient(X)|calm(X))))=>((happy(susan)|~wise(susan))))&
(![X]:((humble(X)|~patient(X))<=>happy(X)))&
(creative(lucy))&
((~generous(susan)<~>~curious(susan)))&
((curious(lucy)|~humble(lucy)))&
(?[X]:((patient(X)|~creative(X))))&
((quiet(alice)|generous(alice))) | ~kind(lucy) | [
"p0",
"p2",
"p7",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5587469721941603654994099
% SZS output start Proof for 5587469721941603654994099
1. ! [X0] : ((rich(X0) | kind(X0)) => (~wise(X0) & ~old(X0))) [input p0]
3. ! [X0] : ((calm(X0) | ~old(X0)) <=> (~kind(X0) <~> calm(X0))) [input p2]
8. ! [X0] : ((creative(X0) <~> ~funny(X0)) <=> (creative(X0) | ~rich(X0))) [input p7]
11. ! [X0] : (calm(X0) <=> (~funny(X0) & patient(X0))) [input p10]
17. creative(lucy) [input p16]
22. kind(lucy) [input hypothesis]
24. ! [X0] : ((~wise(X0) & ~old(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 1]
34. ! [X0] : (((calm(X0) | ~old(X0)) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0)))) & (((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~calm(X0) & old(X0)))) [nnf transformation 3]
35. ! [X0] : ((calm(X0) | ~old(X0) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0)))) & (((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~calm(X0) & old(X0)))) [flattening 34]
44. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (~creative(X0) & rich(X0))) & ((creative(X0) | ~rich(X0)) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [nnf transformation 8]
45. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (~creative(X0) & rich(X0))) & (creative(X0) | ~rich(X0) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [flattening 44]
48. ! [X0] : ((calm(X0) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | ~calm(X0))) [nnf transformation 11]
49. ! [X0] : ((calm(X0) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | ~calm(X0))) [flattening 48]
60. ~old(X0) | ~kind(X0) [cnf transformation 24]
67. calm(X0) | ~kind(X0) | old(X0) [cnf transformation 35]
96. funny(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 45]
104. ~funny(X0) | ~calm(X0) [cnf transformation 49]
120. creative(lucy) [cnf transformation 17]
126. kind(lucy) [cnf transformation 22]
128. ~creative(X0) | funny(X0) [duplicate literal removal 96]
134. ~kind(X0) | calm(X0) [subsumption resolution 67,60]
258. funny(lucy) [resolution 128,120]
259. ~calm(lucy) [resolution 258,104]
260. calm(lucy) [resolution 134,126]
261. $false [subsumption resolution 260,259]
% SZS output end Proof for 5587469721941603654994099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is curious and vice versa.
Everyone who is creative is both strong and generous.
Everyone who is not creative or funny is kind or not funny.
Everyone who is either not quiet or old is not quiet or creative and vice versa.
If someone is either kind or not brave then someone is both happy and not rich and vice versa.
Everyone who is either not funny or rich is either not creative or humble and vice versa.
If someone is either not humble or generous then someone is both not brave and calm and vice versa.
Everyone who is either not funny or funny is not creative or strong and vice versa.
Everyone who is both calm and funny is both kind and not kind.
Everyone who is either not old or not kind is both not patient and not wise.
Everyone who is both patient and funny is not creative or not kind and vice versa.
If someone is both creative and happy then someone is either not kind or old.
If mary is both not generous and not funny then lucy is not funny or not tall.
If john is generous or not tall then someone is either not kind or not tall.
Everyone who is either humble or not funny is both not calm and not strong and vice versa.
Everyone who is either calm or wise is brave or strong and vice versa.
Paul is either not wise or old.
Someone is not creative or not rich.
Someone is both not old and not happy.
Fred is kind or not happy.
Fred is patient.
Fred is not calm. | John is not rich. | entailment | (![X]:((happy(X)|~patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(strong(X)&generous(X))))&
(![X]:((~creative(X)|funny(X))=>(kind(X)|~funny(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(~quiet(X)|creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((~funny(X)<~>rich(X))<=>(~creative(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~creative(X)|strong(X))))&
(![X]:((calm(X)&funny(X))=>(kind(X)&~kind(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~patient(X)&~wise(X))))&
(![X]:((patient(X)&funny(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((creative(X)&happy(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(((~generous(mary)&~funny(mary)))=>((~funny(lucy)|~tall(lucy))))&
(((generous(john)|~tall(john)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((humble(X)<~>~funny(X))<=>(~calm(X)&~strong(X))))&
(![X]:((calm(X)<~>wise(X))<=>(brave(X)|strong(X))))&
((~wise(paul)<~>old(paul)))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:((~old(X)&~happy(X))))&
((kind(fred)|~happy(fred)))&
(patient(fred))&
(~calm(fred)) | ~rich(john) | [
"p1",
"p2",
"p3",
"p5",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 16225401019648041305191
% SZS output start Proof for 16225401019648041305191
2. ! [X0] : (creative(X0) => (generous(X0) & strong(X0))) [input p1]
3. ! [X0] : ((funny(X0) | ~creative(X0)) => (~funny(X0) | kind(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> (creative(X0) | ~quiet(X0))) [input p3]
6. ! [X0] : ((~funny(X0) <~> rich(X0)) <=> (~creative(X0) <~> humble(X0))) [input p5]
10. ! [X0] : ((~old(X0) <~> ~kind(X0)) => (~wise(X0) & ~patient(X0))) [input p9]
11. ! [X0] : ((funny(X0) & patient(X0)) <=> (~kind(X0) | ~creative(X0))) [input p10]
15. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (~strong(X0) & ~calm(X0))) [input p14]
23. rich(john) [input hypothesis]
27. ! [X0] : ((generous(X0) & strong(X0)) | ~creative(X0)) [ennf transformation 2]
28. ! [X0] : ((~funny(X0) | kind(X0)) | (~funny(X0) & creative(X0))) [ennf transformation 3]
29. ! [X0] : (~funny(X0) | kind(X0) | (~funny(X0) & creative(X0))) [flattening 28]
32. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~old(X0) <=> ~kind(X0))) [ennf transformation 10]
37. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 4]
38. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [flattening 37]
44. ! [X0] : ((((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0)))) & (((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0))))) [nnf transformation 6]
52. ! [X0] : ((~wise(X0) & ~patient(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 32]
53. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 11]
54. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0))) [flattening 53]
62. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (strong(X0) | calm(X0))) & ((~strong(X0) & ~calm(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 15]
63. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | strong(X0) | calm(X0)) & ((~strong(X0) & ~calm(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [flattening 62]
71. ~creative(X0) | strong(X0) [cnf transformation 27]
74. ~funny(X0) | kind(X0) | ~funny(X0) [cnf transformation 29]
76. creative(X0) | ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 38]
79. ~old(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
88. ~rich(X0) | ~creative(X0) | ~funny(X0) | humble(X0) [cnf transformation 44]
94. ~humble(X0) | funny(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 44]
109. ~kind(X0) | ~patient(X0) | old(X0) [cnf transformation 52]
114. creative(X0) | patient(X0) [cnf transformation 54]
117. funny(X0) | kind(X0) [cnf transformation 54]
127. ~humble(X0) | ~funny(X0) | ~strong(X0) [cnf transformation 63]
128. ~strong(X0) | humble(X0) | funny(X0) [cnf transformation 63]
145. rich(john) [cnf transformation 23]
148. creative(X0) | ~quiet(X0) | ~old(X0) [duplicate literal removal 76]
149. ~old(X0) | quiet(X0) [duplicate literal removal 79]
150. ~funny(X0) | kind(X0) [duplicate literal removal 74]
151. ~old(X0) | creative(X0) [subsumption resolution 148,149]
215. kind(X0) [subsumption resolution 117,150]
296. ~patient(X0) | old(X0) [resolution 109,215]
374. ~creative(john) | ~funny(john) | humble(john) [resolution 88,145]
377. 36 <=> humble(john) [avatar definition]
378. ~humble(john) <- (~36) [avatar component clause 377]
379. humble(john) <- (36) [avatar component clause 377]
381. 37 <=> funny(john) [avatar definition]
383. ~funny(john) <- (~37) [avatar component clause 381]
385. 38 <=> creative(john) [avatar definition]
386. creative(john) <- (38) [avatar component clause 385]
387. ~creative(john) <- (~38) [avatar component clause 385]
388. 36 | ~37 | ~38 [avatar split clause 374,385,381,377]
417. patient(john) <- (~38) [resolution 387,114]
442. old(john) <- (~38) [resolution 417,296]
799. creative(john) <- (~38) [resolution 442,151]
801. $false <- (~38) [subsumption resolution 799,387]
802. 38 [avatar contradiction clause 801]
811. funny(john) | ~creative(john) | ~rich(john) <- (36) [resolution 379,94]
812. ~funny(john) | ~strong(john) <- (36) [resolution 379,127]
817. strong(john) <- (38) [resolution 386,71]
821. ~funny(john) <- (36, 38) [subsumption resolution 812,817]
822. ~37 | ~36 | ~38 [avatar split clause 821,385,377,381]
823. funny(john) | ~rich(john) <- (36, 38) [subsumption resolution 811,386]
824. funny(john) <- (36, 38) [subsumption resolution 823,145]
825. 37 | ~36 | ~38 [avatar split clause 824,385,377,381]
836. humble(john) | funny(john) <- (38) [resolution 817,128]
846. funny(john) <- (~36, 38) [subsumption resolution 836,378]
847. $false <- (~36, ~37, 38) [subsumption resolution 846,383]
848. 36 | 37 | ~38 [avatar contradiction clause 847]
849. $false [avatar sat refutation 388,802,822,825,848]
% SZS output end Proof for 16225401019648041305191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both strong and humble then someone is both brave and rich and vice versa. Everyone who is either not wise or kind is quiet and vice versa. If someone is both humble and rich then someone is both not funny and not calm. Everyone who is either rich or old is both not humble and not old and vice versa. Everyone who is either patient or creative is both not brave and not tall. Everyone who is either not happy or not old is not wise or wise and vice versa. Everyone who is both not generous and not patient is either wise or not kind. If mary is curious then paul is brave or wise. If someone is strong then susan is either funny or curious and vice versa. If paul is not patient then alice is humble or kind and vice versa. Everyone who is not wise or rich is both not patient and humble and vice versa. Everyone who is not tall is both funny and not rich. If lucy is not tall or not strong then someone is not generous or rich and vice versa. Everyone who is generous or not old is either strong or not curious and vice versa. Everyone who is either patient or rich is not funny and vice versa. Everyone who is either not strong or not quiet is either quiet or not humble and vice versa. Someone is patient or tall. John is both not brave and tall. Lucy is not generous. Fred is tall. Susan is not quiet or not old. Fred is either not happy or not funny. | Mary is not generous. | neutral | (((strong(mary)&humble(mary)))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:((~wise(X)<~>kind(X))<=>quiet(X)))&
((?[X]:((humble(X)&rich(X))))=>(?[X]:((~funny(X)&~calm(X)))))&
(![X]:((rich(X)<~>old(X))<=>(~humble(X)&~old(X))))&
(![X]:((patient(X)<~>creative(X))=>(~brave(X)&~tall(X))))&
(![X]:((~happy(X)<~>~old(X))<=>(~wise(X)|wise(X))))&
(![X]:((~generous(X)&~patient(X))=>(wise(X)<~>~kind(X))))&
((curious(mary))=>((brave(paul)|wise(paul))))&
((?[X]:(strong(X)))<=>((funny(susan)<~>curious(susan))))&
((~patient(paul))<=>((humble(alice)|kind(alice))))&
(![X]:((~wise(X)|rich(X))<=>(~patient(X)&humble(X))))&
(![X]:(~tall(X)=>(funny(X)&~rich(X))))&
(((~tall(lucy)|~strong(lucy)))<=>(?[X]:((~generous(X)|rich(X)))))&
(![X]:((generous(X)|~old(X))<=>(strong(X)<~>~curious(X))))&
(![X]:((patient(X)<~>rich(X))<=>~funny(X)))&
(![X]:((~strong(X)<~>~quiet(X))<=>(quiet(X)<~>~humble(X))))&
(?[X]:((patient(X)|tall(X))))&
((~brave(john)&tall(john)))&
(~generous(lucy))&
(tall(fred))&
((~quiet(susan)|~old(susan)))&
((~happy(fred)<~>~funny(fred))) | ~generous(mary) | [] | null | 0 |
If someone is both wise and not wise then someone is humble or not rich.
Everyone who is both tall and strong is either creative or not old.
Everyone who is not humble or not strong is creative or calm and vice versa.
Everyone who is either not brave or not funny is either old or not kind.
Everyone who is either wise or not generous is not generous or curious.
If paul is either not rich or funny then paul is creative and vice versa.
If alice is happy or humble then susan is both not patient and kind.
If paul is both rich and funny then lucy is either funny or patient and vice versa.
If mary is either not humble or rich then someone is both patient and not happy and vice versa.
Everyone who is strong is both not humble and kind and vice versa.
If paul is funny then alice is either not quiet or kind.
Everyone who is not tall is both kind and not old and vice versa.
Everyone who is either not old or curious is patient.
If susan is not happy or not patient then someone is either not old or not creative and vice versa.
Everyone who is not calm or not happy is both wise and not patient.
Everyone who is not generous or strong is both not creative and not rich and vice versa.
Someone is both rich and curious.
Someone is humble or patient.
Someone is both happy and strong.
Lucy is both strong and generous.
Mary is both tall and rich.
Susan is quiet.
Someone is either not brave or not rich.
Someone is either not strong or strong. | Mary is kind. | contradiction | ((?[X]:((wise(X)&~wise(X))))=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:((tall(X)&strong(X))=>(creative(X)<~>~old(X))))&
(![X]:((~humble(X)|~strong(X))<=>(creative(X)|calm(X))))&
(![X]:((~brave(X)<~>~funny(X))=>(old(X)<~>~kind(X))))&
(![X]:((wise(X)<~>~generous(X))=>(~generous(X)|curious(X))))&
(((~rich(paul)<~>funny(paul)))<=>(creative(paul)))&
(((happy(alice)|humble(alice)))=>((~patient(susan)&kind(susan))))&
(((rich(paul)&funny(paul)))<=>((funny(lucy)<~>patient(lucy))))&
(((~humble(mary)<~>rich(mary)))<=>(?[X]:((patient(X)&~happy(X)))))&
(![X]:(strong(X)<=>(~humble(X)&kind(X))))&
((funny(paul))=>((~quiet(alice)<~>kind(alice))))&
(![X]:(~tall(X)<=>(kind(X)&~old(X))))&
(![X]:((~old(X)<~>curious(X))=>patient(X)))&
(((~happy(susan)|~patient(susan)))<=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:((~calm(X)|~happy(X))=>(wise(X)&~patient(X))))&
(![X]:((~generous(X)|strong(X))<=>(~creative(X)&~rich(X))))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((humble(X)|patient(X))))&
(?[X]:((happy(X)&strong(X))))&
((strong(lucy)&generous(lucy)))&
((tall(mary)&rich(mary)))&
(quiet(susan))&
(?[X]:((~brave(X)<~>~rich(X))))&
(?[X]:((~strong(X)<~>strong(X)))) | kind(mary) | [
"p8",
"p9",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2115363054053722507654807
% SZS output start Proof for 2115363054053722507654807
9. (~humble(mary) <~> rich(mary)) <=> ? [X0] : (~happy(X0) & patient(X0)) [input p8]
10. ! [X0] : (strong(X0) <=> (kind(X0) & ~humble(X0))) [input p9]
15. ! [X0] : ((~happy(X0) | ~calm(X0)) => (~patient(X0) & wise(X0))) [input p14]
16. ! [X0] : ((strong(X0) | ~generous(X0)) <=> (~rich(X0) & ~creative(X0))) [input p15]
21. rich(mary) & tall(mary) [input p20]
25. kind(mary) [input hypothesis]
36. ! [X0] : ((~patient(X0) & wise(X0)) | (happy(X0) & calm(X0))) [ennf transformation 15]
48. (((~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary))) | ! [X0] : (happy(X0) | ~patient(X0))) & (? [X0] : (~happy(X0) & patient(X0)) | ((~humble(mary) | ~rich(mary)) & (rich(mary) | humble(mary)))) [nnf transformation 9]
49. (((~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary))) | ! [X0] : (happy(X0) | ~patient(X0))) & (? [X1] : (~happy(X1) & patient(X1)) | ((~humble(mary) | ~rich(mary)) & (rich(mary) | humble(mary)))) [rectify 48]
50. ? [X1] : (~happy(X1) & patient(X1)) => (~happy(sK1) & patient(sK1)) [choice axiom]
51. (((~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary))) | ! [X0] : (happy(X0) | ~patient(X0))) & ((~happy(sK1) & patient(sK1)) | ((~humble(mary) | ~rich(mary)) & (rich(mary) | humble(mary)))) [skolemisation 49,50]
52. ! [X0] : ((strong(X0) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | ~strong(X0))) [nnf transformation 10]
53. ! [X0] : ((strong(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | ~strong(X0))) [flattening 52]
63. ! [X0] : (((strong(X0) | ~generous(X0)) | (rich(X0) | creative(X0))) & ((~rich(X0) & ~creative(X0)) | (~strong(X0) & generous(X0)))) [nnf transformation 16]
64. ! [X0] : ((strong(X0) | ~generous(X0) | rich(X0) | creative(X0)) & ((~rich(X0) & ~creative(X0)) | (~strong(X0) & generous(X0)))) [flattening 63]
105. patient(sK1) | ~humble(mary) | ~rich(mary) [cnf transformation 51]
107. ~happy(sK1) | ~humble(mary) | ~rich(mary) [cnf transformation 51]
112. ~kind(X0) | strong(X0) | humble(X0) [cnf transformation 53]
129. ~patient(X0) | happy(X0) [cnf transformation 36]
133. ~strong(X0) | ~rich(X0) [cnf transformation 64]
143. rich(mary) [cnf transformation 21]
149. kind(mary) [cnf transformation 25]
202. 10 <=> ! [X0] : (happy(X0) | ~patient(X0)) [avatar definition]
203. ~patient(X0) | happy(X0) <- (10) [avatar component clause 202]
205. 11 <=> humble(mary) [avatar definition]
206. ~humble(mary) <- (~11) [avatar component clause 205]
209. 12 <=> rich(mary) [avatar definition]
210. rich(mary) <- (12) [avatar component clause 209]
215. 13 <=> happy(sK1) [avatar definition]
217. ~happy(sK1) <- (~13) [avatar component clause 215]
218. ~12 | ~11 | ~13 [avatar split clause 107,215,205,209]
221. 14 <=> patient(sK1) [avatar definition]
223. patient(sK1) <- (14) [avatar component clause 221]
224. ~12 | ~11 | 14 [avatar split clause 105,221,205,209]
260. 10 [avatar split clause 129,202]
270. 12 [avatar split clause 143,209]
299. strong(mary) | humble(mary) [resolution 112,149]
301. strong(mary) <- (~11) [subsumption resolution 299,206]
302. ~rich(mary) <- (~11) [resolution 301,133]
305. $false <- (~11, 12) [subsumption resolution 302,210]
306. 11 | ~12 [avatar contradiction clause 305]
313. happy(sK1) <- (10, 14) [resolution 223,203]
315. $false <- (10, ~13, 14) [subsumption resolution 313,217]
316. ~10 | 13 | ~14 [avatar contradiction clause 315]
317. $false [avatar sat refutation 218,224,260,270,306,316]
% SZS output end Proof for 2115363054053722507654807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not kind is either quiet or happy and vice versa.
Everyone who is either patient or not calm is not kind or not curious and vice versa.
If alice is not calm or old then someone is either funny or not tall and vice versa.
If someone is calm or humble then someone is both funny and happy.
Everyone who is not generous is both brave and not kind and vice versa.
If lucy is rich or humble then someone is either happy or kind.
If someone is not brave or kind then lucy is either not funny or not strong and vice versa.
If john is not curious or not tall then mary is wise and vice versa.
If someone is generous then lucy is either generous or not strong.
If someone is not patient or not rich then lucy is both not generous and not humble.
Everyone who is either not patient or not kind is not quiet and vice versa.
Everyone who is both not strong and not generous is not happy or not kind and vice versa.
If someone is either not calm or not generous then someone is rich or wise and vice versa.
Everyone who is either kind or humble is either not patient or not old and vice versa.
Everyone who is old is either humble or not generous.
Everyone who is either not calm or kind is not happy and vice versa.
Someone is either tall or not rich.
John is quiet.
Someone is not creative.
Lucy is both happy and humble.
Someone is patient or not strong.
Someone is both not kind and not curious.
Lucy is wise or humble. | Lucy is brave. | neutral | (![X]:((~funny(X)&~kind(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((patient(X)<~>~calm(X))<=>(~kind(X)|~curious(X))))&
(((~calm(alice)|old(alice)))<=>(?[X]:((funny(X)<~>~tall(X)))))&
((?[X]:((calm(X)|humble(X))))=>(?[X]:((funny(X)&happy(X)))))&
(![X]:(~generous(X)<=>(brave(X)&~kind(X))))&
(((rich(lucy)|humble(lucy)))=>(?[X]:((happy(X)<~>kind(X)))))&
((?[X]:((~brave(X)|kind(X))))<=>((~funny(lucy)<~>~strong(lucy))))&
(((~curious(john)|~tall(john)))<=>(wise(mary)))&
((?[X]:(generous(X)))=>((generous(lucy)<~>~strong(lucy))))&
((?[X]:((~patient(X)|~rich(X))))=>((~generous(lucy)&~humble(lucy))))&
(![X]:((~patient(X)<~>~kind(X))<=>~quiet(X)))&
(![X]:((~strong(X)&~generous(X))<=>(~happy(X)|~kind(X))))&
((?[X]:((~calm(X)<~>~generous(X))))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((kind(X)<~>humble(X))<=>(~patient(X)<~>~old(X))))&
(![X]:(old(X)=>(humble(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>kind(X))<=>~happy(X)))&
(?[X]:((tall(X)<~>~rich(X))))&
(quiet(john))&
(?[X]:(~creative(X)))&
((happy(lucy)&humble(lucy)))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:((~kind(X)&~curious(X))))&
((wise(lucy)|humble(lucy))) | brave(lucy) | [] | null | 0 |
Everyone who is funny or not creative is not curious and vice versa. If susan is strong or not quiet then fred is tall and vice versa. Everyone who is not humble is both not brave and rich and vice versa. If alice is tall or creative then someone is both not happy and not curious and vice versa. If mary is both creative and wise then someone is creative or patient and vice versa. Everyone who is not quiet or brave is both calm and not strong. Everyone who is either not generous or not patient is not old or calm and vice versa. Everyone who is either not kind or not quiet is either not happy or not calm and vice versa. Everyone who is either tall or kind is either kind or not curious and vice versa. Everyone who is funny is either humble or calm. If alice is both brave and kind then someone is brave. Everyone who is tall is either not brave or brave. If someone is patient or not funny then john is kind or old and vice versa. Everyone who is funny is not tall. Everyone who is not curious or happy is not rich or not brave and vice versa. If fred is not creative then paul is either funny or not rich and vice versa. Someone is either not curious or not calm. Fred is both strong and old. Someone is generous. Someone is both wise and tall. Lucy is not strong or generous. Someone is old. Someone is not happy. | Fred is not brave. | entailment | (![X]:((funny(X)|~creative(X))<=>~curious(X)))&
(((strong(susan)|~quiet(susan)))<=>(tall(fred)))&
(![X]:(~humble(X)<=>(~brave(X)&rich(X))))&
(((tall(alice)|creative(alice)))<=>(?[X]:((~happy(X)&~curious(X)))))&
(((creative(mary)&wise(mary)))<=>(?[X]:((creative(X)|patient(X)))))&
(![X]:((~quiet(X)|brave(X))=>(calm(X)&~strong(X))))&
(![X]:((~generous(X)<~>~patient(X))<=>(~old(X)|calm(X))))&
(![X]:((~kind(X)<~>~quiet(X))<=>(~happy(X)<~>~calm(X))))&
(![X]:((tall(X)<~>kind(X))<=>(kind(X)<~>~curious(X))))&
(![X]:(funny(X)=>(humble(X)<~>calm(X))))&
(((brave(alice)&kind(alice)))=>(?[X]:(brave(X))))&
(![X]:(tall(X)=>(~brave(X)<~>brave(X))))&
((?[X]:((patient(X)|~funny(X))))<=>((kind(john)|old(john))))&
(![X]:(funny(X)=>~tall(X)))&
(![X]:((~curious(X)|happy(X))<=>(~rich(X)|~brave(X))))&
((~creative(fred))<=>((funny(paul)<~>~rich(paul))))&
(?[X]:((~curious(X)<~>~calm(X))))&
((strong(fred)&old(fred)))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)&tall(X))))&
((~strong(lucy)|generous(lucy)))&
(?[X]:(old(X)))&
(?[X]:(~happy(X))) | ~brave(fred) | [
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8615660462707787979452634
% SZS output start Proof for 8615660462707787979452634
6. ! [X0] : ((brave(X0) | ~quiet(X0)) => (~strong(X0) & calm(X0))) [input p5]
18. old(fred) & strong(fred) [input p17]
24. brave(fred) [input hypothesis]
25. ! [X0] : ((~strong(X0) & calm(X0)) | (~brave(X0) & quiet(X0))) [ennf transformation 6]
96. ~brave(X0) | ~strong(X0) [cnf transformation 25]
139. strong(fred) [cnf transformation 18]
147. brave(fred) [cnf transformation 24]
304. ~strong(fred) [resolution 96,147]
305. $false [subsumption resolution 304,139]
% SZS output end Proof for 8615660462707787979452634
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old is either strong or not creative and vice versa.
If john is not funny or not humble then someone is either strong or quiet and vice versa.
If paul is kind then mary is either not quiet or not strong.
Everyone who is either not patient or not tall is not tall or not wise and vice versa.
If fred is tall then john is either wise or tall and vice versa.
If someone is not humble or old then someone is either humble or not strong.
If fred is humble then someone is either generous or humble and vice versa.
If someone is both patient and not creative then someone is generous or brave and vice versa.
Everyone who is either not generous or strong is brave.
Everyone who is rich or strong is either humble or curious and vice versa.
If someone is old then someone is both not wise and not kind.
Everyone who is either generous or humble is not calm and vice versa.
Everyone who is both not strong and humble is either not funny or old.
If someone is either happy or not humble then fred is either not generous or not humble.
If fred is tall or not strong then paul is not calm.
Paul is kind.
Lucy is both not humble and strong.
Paul is both not tall and not rich.
Fred is not calm or not happy.
Someone is both rich and not funny.
Someone is not calm or old.
Fred is kind or creative. | Mary is not curious. | neutral | (![X]:((strong(X)<~>~old(X))<=>(strong(X)<~>~creative(X))))&
(((~funny(john)|~humble(john)))<=>(?[X]:((strong(X)<~>quiet(X)))))&
((kind(paul))=>((~quiet(mary)<~>~strong(mary))))&
(![X]:((~patient(X)<~>~tall(X))<=>(~tall(X)|~wise(X))))&
((tall(fred))<=>((wise(john)<~>tall(john))))&
((?[X]:((~humble(X)|old(X))))=>(?[X]:((humble(X)<~>~strong(X)))))&
((humble(fred))<=>(?[X]:((generous(X)<~>humble(X)))))&
((?[X]:((patient(X)&~creative(X))))<=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~generous(X)<~>strong(X))=>brave(X)))&
(![X]:((rich(X)|strong(X))<=>(humble(X)<~>curious(X))))&
((?[X]:(old(X)))=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:((generous(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~strong(X)&humble(X))=>(~funny(X)<~>old(X))))&
((?[X]:((happy(X)<~>~humble(X))))=>((~generous(fred)<~>~humble(fred))))&
(((tall(fred)|~strong(fred)))=>(~calm(paul)))&
(kind(paul))&
((~humble(lucy)&strong(lucy)))&
((~tall(paul)&~rich(paul)))&
((~calm(fred)|~happy(fred)))&
(?[X]:((rich(X)&~funny(X))))&
(?[X]:((~calm(X)|old(X))))&
((kind(fred)|creative(fred))) | ~curious(mary) | [] | null | 0 |
Everyone who is either not brave or generous is both old and not generous.
Everyone who is happy is either generous or kind.
If alice is either not curious or not creative then lucy is not generous or tall.
If someone is both brave and wise then alice is old or not quiet and vice versa.
Everyone who is brave or not calm is not happy and vice versa.
If someone is both happy and patient then someone is both not strong and tall.
If mary is not creative then someone is calm.
If paul is not brave or not calm then mary is either not rich or generous and vice versa.
Everyone who is calm or not strong is happy and vice versa.
Everyone who is both brave and not brave is both wise and brave and vice versa.
Everyone who is not generous or humble is either strong or not patient.
If someone is both humble and patient then mary is not patient and vice versa.
Everyone who is either not tall or happy is not kind or strong.
Everyone who is patient is quiet.
If paul is not generous then john is not quiet or wise and vice versa.
Someone is both funny and not wise.
Someone is either not calm or rich.
Lucy is not funny.
John is either not calm or strong.
Someone is both humble and not calm.
Someone is tall.
Lucy is either not funny or not quiet.
Alice is either not creative or rich. | Alice is not old. | entailment | (![X]:((~brave(X)<~>generous(X))=>(old(X)&~generous(X))))&
(![X]:(happy(X)=>(generous(X)<~>kind(X))))&
(((~curious(alice)<~>~creative(alice)))=>((~generous(lucy)|tall(lucy))))&
((?[X]:((brave(X)&wise(X))))<=>((old(alice)|~quiet(alice))))&
(![X]:((brave(X)|~calm(X))<=>~happy(X)))&
((?[X]:((happy(X)&patient(X))))=>(?[X]:((~strong(X)&tall(X)))))&
((~creative(mary))=>(?[X]:(calm(X))))&
(((~brave(paul)|~calm(paul)))<=>((~rich(mary)<~>generous(mary))))&
(![X]:((calm(X)|~strong(X))<=>happy(X)))&
(![X]:((brave(X)&~brave(X))<=>(wise(X)&brave(X))))&
(![X]:((~generous(X)|humble(X))=>(strong(X)<~>~patient(X))))&
((?[X]:((humble(X)&patient(X))))<=>(~patient(mary)))&
(![X]:((~tall(X)<~>happy(X))=>(~kind(X)|strong(X))))&
(![X]:(patient(X)=>quiet(X)))&
((~generous(paul))<=>((~quiet(john)|wise(john))))&
(?[X]:((funny(X)&~wise(X))))&
(?[X]:((~calm(X)<~>rich(X))))&
(~funny(lucy))&
((~calm(john)<~>strong(john)))&
(?[X]:((humble(X)&~calm(X))))&
(?[X]:(tall(X)))&
((~funny(lucy)<~>~quiet(lucy)))&
((~creative(alice)<~>rich(alice))) | ~old(alice) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7514683354203841281271943
% SZS output start Proof for 7514683354203841281271943
4. ? [X0] : (wise(X0) & brave(X0)) <=> (~quiet(alice) | old(alice)) [input p3]
10. ! [X0] : ((~brave(X0) & brave(X0)) <=> (brave(X0) & wise(X0))) [input p9]
24. old(alice) [input hypothesis]
39. (? [X0] : (wise(X0) & brave(X0)) | (quiet(alice) & ~old(alice))) & ((~quiet(alice) | old(alice)) | ! [X0] : (~wise(X0) | ~brave(X0))) [nnf transformation 4]
40. (? [X0] : (wise(X0) & brave(X0)) | (quiet(alice) & ~old(alice))) & (~quiet(alice) | old(alice) | ! [X0] : (~wise(X0) | ~brave(X0))) [flattening 39]
41. (? [X0] : (wise(X0) & brave(X0)) | (quiet(alice) & ~old(alice))) & (~quiet(alice) | old(alice) | ! [X1] : (~wise(X1) | ~brave(X1))) [rectify 40]
42. ? [X0] : (wise(X0) & brave(X0)) => (wise(sK0) & brave(sK0)) [choice axiom]
43. ((wise(sK0) & brave(sK0)) | (quiet(alice) & ~old(alice))) & (~quiet(alice) | old(alice) | ! [X1] : (~wise(X1) | ~brave(X1))) [skolemisation 41,42]
55. ! [X0] : (((~brave(X0) & brave(X0)) | (~brave(X0) | ~wise(X0))) & ((brave(X0) & wise(X0)) | (brave(X0) | ~brave(X0)))) [nnf transformation 10]
56. ! [X0] : (((~brave(X0) & brave(X0)) | ~brave(X0) | ~wise(X0)) & ((brave(X0) & wise(X0)) | brave(X0) | ~brave(X0))) [flattening 55]
86. brave(sK0) | ~old(alice) [cnf transformation 43]
88. wise(sK0) | ~old(alice) [cnf transformation 43]
108. ~brave(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 56]
136. old(alice) [cnf transformation 24]
138. ~brave(X0) | ~wise(X0) [duplicate literal removal 108]
163. 6 <=> wise(sK0) [avatar definition]
165. wise(sK0) <- (6) [avatar component clause 163]
168. 7 <=> old(alice) [avatar definition]
171. ~7 | 6 [avatar split clause 88,163,168]
173. 8 <=> brave(sK0) [avatar definition]
175. brave(sK0) <- (8) [avatar component clause 173]
177. ~7 | 8 [avatar split clause 86,173,168]
179. 9 <=> ! [X1] : (~wise(X1) | ~brave(X1)) [avatar definition]
180. ~wise(X1) | ~brave(X1) <- (9) [avatar component clause 179]
226. 9 [avatar split clause 138,179]
288. 7 [avatar split clause 136,168]
298. ~brave(sK0) <- (6, 9) [resolution 180,165]
299. $false <- (6, 8, 9) [subsumption resolution 298,175]
300. ~6 | ~8 | ~9 [avatar contradiction clause 299]
301. $false [avatar sat refutation 171,177,226,288,300]
% SZS output end Proof for 7514683354203841281271943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and generous is curious.
Everyone who is kind or not old is either wise or not wise and vice versa.
Everyone who is either not brave or not curious is not calm or rich and vice versa.
If susan is not wise or creative then fred is either humble or happy.
Everyone who is both not kind and quiet is both not happy and not curious and vice versa.
Everyone who is both strong and funny is quiet.
If someone is either not curious or not funny then someone is humble.
Everyone who is not tall or not happy is brave.
If someone is either not generous or quiet then fred is both not humble and old.
If susan is either quiet or not rich then fred is generous or not happy and vice versa.
If someone is both not rich and not kind then someone is not brave or not generous.
If susan is both not wise and not curious then someone is either not brave or not calm and vice versa.
If someone is patient then john is both rich and not tall and vice versa.
Everyone who is both rich and humble is kind and vice versa.
Everyone who is both not wise and not tall is curious or tall and vice versa.
Everyone who is either not happy or happy is both brave and strong and vice versa.
Susan is both creative and not funny.
John is wise or brave.
John is humble or not brave.
Someone is either curious or not old.
Someone is not creative.
Someone is either humble or quiet.
Fred is not curious or not quiet.
Someone is kind or not quiet. | Susan is not calm. | contradiction | (![X]:((~patient(X)&generous(X))=>curious(X)))&
(![X]:((kind(X)|~old(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((~brave(X)<~>~curious(X))<=>(~calm(X)|rich(X))))&
(((~wise(susan)|creative(susan)))=>((humble(fred)<~>happy(fred))))&
(![X]:((~kind(X)&quiet(X))<=>(~happy(X)&~curious(X))))&
(![X]:((strong(X)&funny(X))=>quiet(X)))&
((?[X]:((~curious(X)<~>~funny(X))))=>(?[X]:(humble(X))))&
(![X]:((~tall(X)|~happy(X))=>brave(X)))&
((?[X]:((~generous(X)<~>quiet(X))))=>((~humble(fred)&old(fred))))&
(((quiet(susan)<~>~rich(susan)))<=>((generous(fred)|~happy(fred))))&
((?[X]:((~rich(X)&~kind(X))))=>(?[X]:((~brave(X)|~generous(X)))))&
(((~wise(susan)&~curious(susan)))<=>(?[X]:((~brave(X)<~>~calm(X)))))&
((?[X]:(patient(X)))<=>((rich(john)&~tall(john))))&
(![X]:((rich(X)&humble(X))<=>kind(X)))&
(![X]:((~wise(X)&~tall(X))<=>(curious(X)|tall(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(brave(X)&strong(X))))&
((creative(susan)&~funny(susan)))&
((wise(john)|brave(john)))&
((humble(john)|~brave(john)))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:(~creative(X)))&
(?[X]:((humble(X)<~>quiet(X))))&
((~curious(fred)|~quiet(fred)))&
(?[X]:((kind(X)|~quiet(X)))) | ~calm(susan) | [
"p7",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3262580570108875294173917
% SZS output start Proof for 3262580570108875294173917
8. ! [X0] : ((~happy(X0) | ~tall(X0)) => brave(X0)) [input p7]
12. (~curious(susan) & ~wise(susan)) <=> ? [X0] : (~brave(X0) <~> ~calm(X0)) [input p11]
15. ! [X0] : ((~tall(X0) & ~wise(X0)) <=> (tall(X0) | curious(X0))) [input p14]
16. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> (strong(X0) & brave(X0))) [input p15]
25. ~calm(susan) [input hypothesis]
34. ! [X0] : (brave(X0) | (happy(X0) & tall(X0))) [ennf transformation 8]
54. ((~curious(susan) & ~wise(susan)) | ! [X0] : ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0)))) & (? [X0] : ((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (curious(susan) | wise(susan))) [nnf transformation 12]
55. ((~curious(susan) & ~wise(susan)) | ! [X0] : ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0)))) & (? [X0] : ((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | curious(susan) | wise(susan)) [flattening 54]
56. ((~curious(susan) & ~wise(susan)) | ! [X0] : ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0)))) & (? [X1] : ((calm(X1) | brave(X1)) & (~calm(X1) | ~brave(X1))) | curious(susan) | wise(susan)) [rectify 55]
57. ? [X1] : ((calm(X1) | brave(X1)) & (~calm(X1) | ~brave(X1))) => ((calm(sK2) | brave(sK2)) & (~calm(sK2) | ~brave(sK2))) [choice axiom]
58. ((~curious(susan) & ~wise(susan)) | ! [X0] : ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0)))) & (((calm(sK2) | brave(sK2)) & (~calm(sK2) | ~brave(sK2))) | curious(susan) | wise(susan)) [skolemisation 56,57]
66. ! [X0] : (((~tall(X0) & ~wise(X0)) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | (tall(X0) | wise(X0)))) [nnf transformation 15]
67. ! [X0] : (((~tall(X0) & ~wise(X0)) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | tall(X0) | wise(X0))) [flattening 66]
68. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (~strong(X0) | ~brave(X0))) & ((strong(X0) & brave(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 16]
69. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~strong(X0) | ~brave(X0)) & ((strong(X0) & brave(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [flattening 68]
105. happy(X0) | brave(X0) [cnf transformation 34]
120. ~wise(susan) | ~brave(X0) | calm(X0) [cnf transformation 58]
122. ~curious(susan) | ~brave(X0) | calm(X0) [cnf transformation 58]
129. tall(X0) | curious(X0) | tall(X0) | wise(X0) [cnf transformation 67]
133. ~tall(X0) | ~tall(X0) [cnf transformation 67]
135. brave(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 69]
151. ~calm(susan) [cnf transformation 25]
153. brave(X0) | ~happy(X0) [duplicate literal removal 135]
156. tall(X0) | curious(X0) | wise(X0) [duplicate literal removal 129]
157. ~tall(X0) [duplicate literal removal 133]
175. 4 <=> wise(susan) [avatar definition]
176. ~wise(susan) <- (~4) [avatar component clause 175]
238. 17 <=> ! [X0] : (~brave(X0) | calm(X0)) [avatar definition]
239. ~brave(X0) | calm(X0) <- (17) [avatar component clause 238]
241. 18 <=> curious(susan) [avatar definition]
243. ~curious(susan) <- (~18) [avatar component clause 241]
244. 17 | ~18 [avatar split clause 122,241,238]
249. 17 | ~4 [avatar split clause 120,175,238]
279. wise(X0) | curious(X0) [subsumption resolution 156,157]
281. brave(X0) [subsumption resolution 153,105]
322. calm(X0) <- (17) [subsumption resolution 239,281]
323. $false <- (17) [resolution 322,151]
324. ~17 [avatar contradiction clause 323]
341. curious(susan) <- (~4) [resolution 279,176]
343. $false <- (~4, ~18) [subsumption resolution 341,243]
344. 4 | 18 [avatar contradiction clause 343]
345. $false [avatar sat refutation 244,249,324,344]
% SZS output end Proof for 3262580570108875294173917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If alice is calm or wise then someone is both curious and not kind and vice versa.
Everyone who is not calm is not quiet.
Everyone who is either not curious or not tall is either not creative or curious and vice versa.
If someone is either patient or curious then paul is not strong or not wise.
Everyone who is either not curious or brave is tall.
Everyone who is both not rich and quiet is not brave or wise.
Everyone who is either not quiet or not generous is old or quiet and vice versa.
Everyone who is not humble or kind is either not patient or not rich.
If someone is not quiet then someone is not patient or not happy.
Everyone who is not quiet is both not humble and strong and vice versa.
Everyone who is not quiet is curious or not wise and vice versa.
Everyone who is both not kind and not wise is curious or old and vice versa.
Everyone who is both not patient and not tall is both happy and not creative and vice versa.
Everyone who is tall or not tall is old or not tall.
Everyone who is either humble or creative is creative or kind.
If mary is tall or not curious then john is tall.
Someone is both strong and not kind.
Fred is either not strong or rich.
Mary is either happy or not tall.
Mary is either not creative or quiet.
Someone is both brave and happy.
Alice is wise.
Someone is not strong. | Mary is not curious. | entailment | (((calm(alice)|wise(alice)))<=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:(~calm(X)=>~quiet(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~creative(X)<~>curious(X))))&
((?[X]:((patient(X)<~>curious(X))))=>((~strong(paul)|~wise(paul))))&
(![X]:((~curious(X)<~>brave(X))=>tall(X)))&
(![X]:((~rich(X)&quiet(X))=>(~brave(X)|wise(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(old(X)|quiet(X))))&
(![X]:((~humble(X)|kind(X))=>(~patient(X)<~>~rich(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~patient(X)|~happy(X)))))&
(![X]:(~quiet(X)<=>(~humble(X)&strong(X))))&
(![X]:(~quiet(X)<=>(curious(X)|~wise(X))))&
(![X]:((~kind(X)&~wise(X))<=>(curious(X)|old(X))))&
(![X]:((~patient(X)&~tall(X))<=>(happy(X)&~creative(X))))&
(![X]:((tall(X)|~tall(X))=>(old(X)|~tall(X))))&
(![X]:((humble(X)<~>creative(X))=>(creative(X)|kind(X))))&
(((tall(mary)|~curious(mary)))=>(tall(john)))&
(?[X]:((strong(X)&~kind(X))))&
((~strong(fred)<~>rich(fred)))&
((happy(mary)<~>~tall(mary)))&
((~creative(mary)<~>quiet(mary)))&
(?[X]:((brave(X)&happy(X))))&
(wise(alice))&
(?[X]:(~strong(X))) | ~curious(mary) | [
"p2",
"p10",
"p12",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8575911536060401428605726
% SZS output start Proof for 8575911536060401428605726
3. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> (~creative(X0) <~> curious(X0))) [input p2]
11. ! [X0] : (~quiet(X0) <=> (~wise(X0) | curious(X0))) [input p10]
13. ! [X0] : ((~tall(X0) & ~patient(X0)) <=> (~creative(X0) & happy(X0))) [input p12]
19. happy(mary) <~> ~tall(mary) [input p18]
20. ~creative(mary) <~> quiet(mary) [input p19]
24. curious(mary) [input hypothesis]
44. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 3]
55. ! [X0] : ((~quiet(X0) | (wise(X0) & ~curious(X0))) & ((~wise(X0) | curious(X0)) | quiet(X0))) [nnf transformation 11]
56. ! [X0] : ((~quiet(X0) | (wise(X0) & ~curious(X0))) & (~wise(X0) | curious(X0) | quiet(X0))) [flattening 55]
59. ! [X0] : (((~tall(X0) & ~patient(X0)) | (creative(X0) | ~happy(X0))) & ((~creative(X0) & happy(X0)) | (tall(X0) | patient(X0)))) [nnf transformation 13]
60. ! [X0] : (((~tall(X0) & ~patient(X0)) | creative(X0) | ~happy(X0)) & ((~creative(X0) & happy(X0)) | tall(X0) | patient(X0))) [flattening 59]
65. (tall(mary) | ~happy(mary)) & (~tall(mary) | happy(mary)) [nnf transformation 19]
66. (~quiet(mary) | creative(mary)) & (quiet(mary) | ~creative(mary)) [nnf transformation 20]
80. ~curious(X0) | creative(X0) | ~curious(X0) | tall(X0) [cnf transformation 44]
83. tall(X0) | curious(X0) | curious(X0) | creative(X0) [cnf transformation 44]
105. ~quiet(X0) | ~curious(X0) [cnf transformation 56]
115. ~tall(X0) | creative(X0) | ~happy(X0) [cnf transformation 60]
126. ~tall(mary) | happy(mary) [cnf transformation 65]
128. quiet(mary) | ~creative(mary) [cnf transformation 66]
134. curious(mary) [cnf transformation 24]
140. ~curious(X0) | creative(X0) | tall(X0) [duplicate literal removal 80]
142. tall(X0) | curious(X0) | creative(X0) [duplicate literal removal 83]
167. creative(X0) | tall(X0) [subsumption resolution 140,142]
198. ~happy(X0) | creative(X0) [subsumption resolution 115,167]
201. 13 <=> curious(mary) [avatar definition]
203. curious(mary) <- (13) [avatar component clause 201]
210. 15 <=> tall(mary) [avatar definition]
225. 18 <=> happy(mary) [avatar definition]
226. happy(mary) <- (18) [avatar component clause 225]
229. 18 | ~15 [avatar split clause 126,210,225]
231. 19 <=> creative(mary) [avatar definition]
232. ~creative(mary) <- (~19) [avatar component clause 231]
235. 20 <=> quiet(mary) [avatar definition]
236. quiet(mary) <- (20) [avatar component clause 235]
239. ~19 | 20 [avatar split clause 128,235,231]
241. 13 [avatar split clause 134,201]
257. tall(mary) <- (~19) [resolution 167,232]
260. 15 | 19 [avatar split clause 257,231,210]
269. creative(mary) <- (18) [resolution 198,226]
272. 19 | ~18 [avatar split clause 269,225,231]
278. ~curious(mary) <- (20) [resolution 236,105]
282. $false <- (13, 20) [subsumption resolution 278,203]
283. ~13 | ~20 [avatar contradiction clause 282]
284. $false [avatar sat refutation 229,239,241,260,272,283]
% SZS output end Proof for 8575911536060401428605726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or not creative then fred is either strong or not curious.
Everyone who is humble or generous is not rich or patient.
If paul is both not calm and kind then mary is either not strong or not old and vice versa.
Everyone who is happy is quiet.
If someone is either not quiet or funny then john is either not humble or generous and vice versa.
If alice is not kind or strong then someone is both not strong and not creative.
Everyone who is either not quiet or old is not rich and vice versa.
If mary is not kind or brave then someone is both not old and kind.
If lucy is either humble or kind then lucy is both old and not strong and vice versa.
Everyone who is both creative and brave is both strong and wise and vice versa.
If mary is not wise then someone is kind.
If lucy is either not funny or kind then someone is not generous and vice versa.
Everyone who is both old and rich is not old and vice versa.
Everyone who is not old is humble.
Everyone who is either rich or brave is both happy and not kind.
Everyone who is either not curious or not creative is curious or not wise.
Someone is both not curious and strong.
Someone is funny.
Fred is funny.
Someone is not calm.
Susan is either patient or rich.
Paul is either not rich or not kind.
Someone is either not brave or happy. | Mary is kind. | entailment | ((?[X]:((~wise(X)<~>~creative(X))))=>((strong(fred)<~>~curious(fred))))&
(![X]:((humble(X)|generous(X))=>(~rich(X)|patient(X))))&
(((~calm(paul)&kind(paul)))<=>((~strong(mary)<~>~old(mary))))&
(![X]:(happy(X)=>quiet(X)))&
((?[X]:((~quiet(X)<~>funny(X))))<=>((~humble(john)<~>generous(john))))&
(((~kind(alice)|strong(alice)))=>(?[X]:((~strong(X)&~creative(X)))))&
(![X]:((~quiet(X)<~>old(X))<=>~rich(X)))&
(((~kind(mary)|brave(mary)))=>(?[X]:((~old(X)&kind(X)))))&
(((humble(lucy)<~>kind(lucy)))<=>((old(lucy)&~strong(lucy))))&
(![X]:((creative(X)&brave(X))<=>(strong(X)&wise(X))))&
((~wise(mary))=>(?[X]:(kind(X))))&
(((~funny(lucy)<~>kind(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:((old(X)&rich(X))<=>~old(X)))&
(![X]:(~old(X)=>humble(X)))&
(![X]:((rich(X)<~>brave(X))=>(happy(X)&~kind(X))))&
(![X]:((~curious(X)<~>~creative(X))=>(curious(X)|~wise(X))))&
(?[X]:((~curious(X)&strong(X))))&
(?[X]:(funny(X)))&
(funny(fred))&
(?[X]:(~calm(X)))&
((patient(susan)<~>rich(susan)))&
((~rich(paul)<~>~kind(paul)))&
(?[X]:((~brave(X)<~>happy(X)))) | kind(mary) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1732783960092331006560463
% SZS output start Proof for 1732783960092331006560463
8. (brave(mary) | ~kind(mary)) => ? [X0] : (kind(X0) & ~old(X0)) [input p7]
13. ! [X0] : ((rich(X0) & old(X0)) <=> ~old(X0)) [input p12]
24. ~kind(mary) [input hypothesis]
30. ? [X0] : (kind(X0) & ~old(X0)) | (~brave(mary) & kind(mary)) [ennf transformation 8]
46. ? [X0] : (kind(X0) & ~old(X0)) => (kind(sK2) & ~old(sK2)) [choice axiom]
47. (kind(sK2) & ~old(sK2)) | (~brave(mary) & kind(mary)) [skolemisation 30,46]
58. ! [X0] : (((rich(X0) & old(X0)) | old(X0)) & (~old(X0) | (~rich(X0) | ~old(X0)))) [nnf transformation 13]
59. ! [X0] : (((rich(X0) & old(X0)) | old(X0)) & (~old(X0) | ~rich(X0) | ~old(X0))) [flattening 58]
102. ~old(sK2) | kind(mary) [cnf transformation 47]
122. old(X0) | old(X0) [cnf transformation 59]
142. ~kind(mary) [cnf transformation 24]
145. old(X0) [duplicate literal removal 122]
246. 21 <=> kind(mary) [avatar definition]
251. 22 <=> old(sK2) [avatar definition]
253. ~old(sK2) <- (~22) [avatar component clause 251]
255. 21 | ~22 [avatar split clause 102,251,246]
317. ~21 [avatar split clause 142,246]
320. $false <- (~22) [subsumption resolution 253,145]
321. 22 [avatar contradiction clause 320]
322. $false [avatar sat refutation 255,317,321]
% SZS output end Proof for 1732783960092331006560463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If john is not strong or not kind then fred is either curious or not kind and vice versa.
Everyone who is both calm and kind is both kind and not happy and vice versa.
Everyone who is both not old and not creative is not patient or not strong and vice versa.
Everyone who is either not generous or kind is both creative and not generous and vice versa.
Everyone who is not calm or wise is calm and vice versa.
Everyone who is patient is rich and vice versa.
Everyone who is happy or not happy is funny or quiet.
If someone is either strong or not calm then alice is either not kind or rich.
If mary is either not patient or wise then someone is either not wise or humble.
Everyone who is brave or not wise is both brave and creative.
Everyone who is not humble or kind is not old and vice versa.
If someone is both humble and not old then mary is humble or curious and vice versa.
Everyone who is not calm or brave is not strong or brave and vice versa.
If someone is both not brave and quiet then lucy is not kind.
Everyone who is either generous or funny is both humble and not generous and vice versa.
If fred is not calm then alice is either not wise or not quiet.
Someone is not brave or not humble.
Someone is curious or wise.
John is funny.
Lucy is both rich and not tall.
Fred is not tall.
Someone is either not old or old. | Lucy is not creative. | neutral | (((~strong(john)|~kind(john)))<=>((curious(fred)<~>~kind(fred))))&
(![X]:((calm(X)&kind(X))<=>(kind(X)&~happy(X))))&
(![X]:((~old(X)&~creative(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(creative(X)&~generous(X))))&
(![X]:((~calm(X)|wise(X))<=>calm(X)))&
(![X]:(patient(X)<=>rich(X)))&
(![X]:((happy(X)|~happy(X))=>(funny(X)|quiet(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>((~kind(alice)<~>rich(alice))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((brave(X)|~wise(X))=>(brave(X)&creative(X))))&
(![X]:((~humble(X)|kind(X))<=>~old(X)))&
((?[X]:((humble(X)&~old(X))))<=>((humble(mary)|curious(mary))))&
(![X]:((~calm(X)|brave(X))<=>(~strong(X)|brave(X))))&
((?[X]:((~brave(X)&quiet(X))))=>(~kind(lucy)))&
(![X]:((generous(X)<~>funny(X))<=>(humble(X)&~generous(X))))&
((~calm(fred))=>((~wise(alice)<~>~quiet(alice))))&
(?[X]:((~brave(X)|~humble(X))))&
(?[X]:((curious(X)|wise(X))))&
(funny(john))&
((rich(lucy)&~tall(lucy)))&
(~tall(fred))&
(?[X]:((~old(X)<~>old(X)))) | ~creative(lucy) | [] | null | 0 |
If paul is either not wise or patient then someone is not creative.
Everyone who is not old or not funny is either not strong or patient.
If mary is both not happy and happy then paul is both brave and quiet.
Everyone who is both tall and curious is not calm or not humble and vice versa.
Everyone who is either wise or not quiet is not creative or not brave and vice versa.
Everyone who is strong or not humble is humble.
Everyone who is calm is curious or not funny and vice versa.
Everyone who is rich or funny is both strong and tall.
If someone is both not rich and not calm then someone is both quiet and not strong and vice versa.
If lucy is generous or not generous then lucy is both not old and humble and vice versa.
Everyone who is kind is generous and vice versa.
If susan is not quiet or tall then paul is not patient and vice versa.
If mary is not quiet then someone is either tall or not funny and vice versa.
If someone is not wise or not tall then someone is strong or creative.
If someone is not strong then someone is curious or patient.
Someone is not kind.
Fred is either not generous or generous.
Someone is not old or not wise.
Alice is not patient or not creative.
Lucy is both curious and not quiet.
Susan is not tall or curious. | Lucy is funny. | contradiction | (((~wise(paul)<~>patient(paul)))=>(?[X]:(~creative(X))))&
(![X]:((~old(X)|~funny(X))=>(~strong(X)<~>patient(X))))&
(((~happy(mary)&happy(mary)))=>((brave(paul)&quiet(paul))))&
(![X]:((tall(X)&curious(X))<=>(~calm(X)|~humble(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~creative(X)|~brave(X))))&
(![X]:((strong(X)|~humble(X))=>humble(X)))&
(![X]:(calm(X)<=>(curious(X)|~funny(X))))&
(![X]:((rich(X)|funny(X))=>(strong(X)&tall(X))))&
((?[X]:((~rich(X)&~calm(X))))<=>(?[X]:((quiet(X)&~strong(X)))))&
(((generous(lucy)|~generous(lucy)))<=>((~old(lucy)&humble(lucy))))&
(![X]:(kind(X)<=>generous(X)))&
(((~quiet(susan)|tall(susan)))<=>(~patient(paul)))&
((~quiet(mary))<=>(?[X]:((tall(X)<~>~funny(X)))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((strong(X)|creative(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((curious(X)|patient(X)))))&
(?[X]:(~kind(X)))&
((~generous(fred)<~>generous(fred)))&
(?[X]:((~old(X)|~wise(X))))&
((~patient(alice)|~creative(alice)))&
((curious(lucy)&~quiet(lucy)))&
((~tall(susan)|curious(susan))) | funny(lucy) | [
"p3",
"p5",
"p6",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6624343177880039414128728
% SZS output start Proof for 6624343177880039414128728
4. ! [X0] : ((curious(X0) & tall(X0)) <=> (~humble(X0) | ~calm(X0))) [input p3]
6. ! [X0] : ((~humble(X0) | strong(X0)) => humble(X0)) [input p5]
7. ! [X0] : (calm(X0) <=> (~funny(X0) | curious(X0))) [input p6]
8. ! [X0] : ((funny(X0) | rich(X0)) => (tall(X0) & strong(X0))) [input p7]
20. ~quiet(lucy) & curious(lucy) [input p19]
22. funny(lucy) [input hypothesis]
31. ! [X0] : (humble(X0) | (humble(X0) & ~strong(X0))) [ennf transformation 6]
32. ! [X0] : ((tall(X0) & strong(X0)) | (~funny(X0) & ~rich(X0))) [ennf transformation 8]
40. ! [X0] : (((curious(X0) & tall(X0)) | (humble(X0) & calm(X0))) & ((~humble(X0) | ~calm(X0)) | (~curious(X0) | ~tall(X0)))) [nnf transformation 4]
41. ! [X0] : (((curious(X0) & tall(X0)) | (humble(X0) & calm(X0))) & (~humble(X0) | ~calm(X0) | ~curious(X0) | ~tall(X0))) [flattening 40]
44. ! [X0] : ((calm(X0) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | ~calm(X0))) [nnf transformation 7]
45. ! [X0] : ((calm(X0) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | ~calm(X0))) [flattening 44]
78. ~humble(X0) | ~calm(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 41]
81. calm(X0) | curious(X0) [cnf transformation 41]
90. humble(X0) | humble(X0) [cnf transformation 31]
92. calm(X0) | ~curious(X0) [cnf transformation 45]
97. ~funny(X0) | tall(X0) [cnf transformation 32]
123. curious(lucy) [cnf transformation 20]
126. funny(lucy) [cnf transformation 22]
127. humble(X0) [duplicate literal removal 90]
142. calm(X0) [subsumption resolution 92,81]
238. tall(lucy) [resolution 97,126]
259. ~calm(X2) | ~curious(X2) | ~tall(X2) [resolution 78,127]
260. ~curious(X2) | ~tall(X2) [subsumption resolution 259,142]
261. ~tall(lucy) [resolution 260,123]
263. $false [subsumption resolution 261,238]
% SZS output end Proof for 6624343177880039414128728
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not tall then someone is either calm or generous and vice versa. If someone is both not quiet and funny then someone is calm and vice versa. If someone is creative or not happy then fred is not calm and vice versa. If someone is not wise then mary is either not kind or funny and vice versa. If john is either humble or not funny then someone is not patient or patient. Everyone who is curious or quiet is not old or not brave and vice versa. Everyone who is not brave or patient is not quiet. If someone is not old then fred is both creative and not happy. If mary is funny or calm then mary is both not calm and not humble. If someone is either generous or curious then mary is not generous or not old and vice versa. If someone is not tall then john is curious or rich. If fred is quiet or not curious then someone is both brave and not calm and vice versa. Everyone who is either not strong or not funny is either not creative or funny and vice versa. Everyone who is not generous is quiet. If john is either not generous or quiet then fred is not humble and vice versa. If mary is not humble then alice is both old and not funny. Someone is both not tall and not curious. Someone is patient. Fred is either rich or not kind. Someone is either kind or creative. Someone is either not rich or not wise. Someone is not funny. Alice is not calm or not kind. Someone is wise or not rich. | Fred is strong. | contradiction | ((?[X]:(~tall(X)))<=>(?[X]:((calm(X)<~>generous(X)))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:(calm(X))))&
((?[X]:((creative(X)|~happy(X))))<=>(~calm(fred)))&
((?[X]:(~wise(X)))<=>((~kind(mary)<~>funny(mary))))&
(((humble(john)<~>~funny(john)))=>(?[X]:((~patient(X)|patient(X)))))&
(![X]:((curious(X)|quiet(X))<=>(~old(X)|~brave(X))))&
(![X]:((~brave(X)|patient(X))=>~quiet(X)))&
((?[X]:(~old(X)))=>((creative(fred)&~happy(fred))))&
(((funny(mary)|calm(mary)))=>((~calm(mary)&~humble(mary))))&
((?[X]:((generous(X)<~>curious(X))))<=>((~generous(mary)|~old(mary))))&
((?[X]:(~tall(X)))=>((curious(john)|rich(john))))&
(((quiet(fred)|~curious(fred)))<=>(?[X]:((brave(X)&~calm(X)))))&
(![X]:((~strong(X)<~>~funny(X))<=>(~creative(X)<~>funny(X))))&
(![X]:(~generous(X)=>quiet(X)))&
(((~generous(john)<~>quiet(john)))<=>(~humble(fred)))&
((~humble(mary))=>((old(alice)&~funny(alice))))&
(?[X]:((~tall(X)&~curious(X))))&
(?[X]:(patient(X)))&
((rich(fred)<~>~kind(fred)))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:(~funny(X)))&
((~calm(alice)|~kind(alice)))&
(?[X]:((wise(X)|~rich(X)))) | strong(fred) | [
"p5",
"p6",
"p7",
"p9",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5218249087876767482743893
% SZS output start Proof for 5218249087876767482743893
6. ! [X0] : ((quiet(X0) | curious(X0)) <=> (~brave(X0) | ~old(X0))) [input p5]
7. ! [X0] : ((patient(X0) | ~brave(X0)) => ~quiet(X0)) [input p6]
8. ? [X0] : ~old(X0) => (~happy(fred) & creative(fred)) [input p7]
10. ? [X0] : (generous(X0) <~> curious(X0)) <=> (~old(mary) | ~generous(mary)) [input p9]
13. ! [X0] : ((~strong(X0) <~> ~funny(X0)) <=> (~creative(X0) <~> funny(X0))) [input p12]
14. ! [X0] : (~generous(X0) => quiet(X0)) [input p13]
17. ? [X0] : (~curious(X0) & ~tall(X0)) [input p16]
25. strong(fred) [input hypothesis]
29. ! [X0] : (~quiet(X0) | (~patient(X0) & brave(X0))) [ennf transformation 7]
30. (~happy(fred) & creative(fred)) | ! [X0] : old(X0) [ennf transformation 8]
34. ! [X0] : (quiet(X0) | generous(X0)) [ennf transformation 14]
57. ! [X0] : (((quiet(X0) | curious(X0)) | (brave(X0) & old(X0))) & ((~brave(X0) | ~old(X0)) | (~quiet(X0) & ~curious(X0)))) [nnf transformation 6]
58. ! [X0] : ((quiet(X0) | curious(X0) | (brave(X0) & old(X0))) & (~brave(X0) | ~old(X0) | (~quiet(X0) & ~curious(X0)))) [flattening 57]
59. (? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (old(mary) & generous(mary))) & ((~old(mary) | ~generous(mary)) | ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) [nnf transformation 10]
60. (? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (old(mary) & generous(mary))) & (~old(mary) | ~generous(mary) | ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) [flattening 59]
61. (? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (old(mary) & generous(mary))) & (~old(mary) | ~generous(mary) | ! [X1] : ((generous(X1) | ~curious(X1)) & (curious(X1) | ~generous(X1)))) [rectify 60]
62. ? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) => ((~curious(sK7) | ~generous(sK7)) & (curious(sK7) | generous(sK7))) [choice axiom]
63. (((~curious(sK7) | ~generous(sK7)) & (curious(sK7) | generous(sK7))) | (old(mary) & generous(mary))) & (~old(mary) | ~generous(mary) | ! [X1] : ((generous(X1) | ~curious(X1)) & (curious(X1) | ~generous(X1)))) [skolemisation 61,62]
69. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [nnf transformation 13]
71. ? [X0] : (~curious(X0) & ~tall(X0)) => (~curious(sK9) & ~tall(sK9)) [choice axiom]
72. ~curious(sK9) & ~tall(sK9) [skolemisation 17,71]
103. ~brave(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 58]
106. ~quiet(X0) | brave(X0) [cnf transformation 29]
108. creative(fred) | old(X0) [cnf transformation 30]
114. ~old(mary) | ~generous(mary) | curious(X1) | ~generous(X1) [cnf transformation 63]
127. funny(X0) | ~creative(X0) | ~strong(X0) | funny(X0) [cnf transformation 69]
131. ~funny(X0) | ~strong(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 69]
134. quiet(X0) | generous(X0) [cnf transformation 34]
142. ~curious(sK9) [cnf transformation 72]
153. strong(fred) [cnf transformation 25]
154. funny(X0) | ~creative(X0) | ~strong(X0) [duplicate literal removal 127]
156. ~funny(X0) | ~strong(X0) | ~creative(X0) [duplicate literal removal 131]
246. 21 <=> ! [X0] : old(X0) [avatar definition]
247. old(X0) <- (21) [avatar component clause 246]
254. 23 <=> creative(fred) [avatar definition]
257. 21 | 23 [avatar split clause 108,254,246]
271. 26 <=> old(mary) [avatar definition]
272. ~old(mary) <- (~26) [avatar component clause 271]
284. 29 <=> generous(mary) [avatar definition]
285. ~generous(mary) <- (~29) [avatar component clause 284]
295. 31 <=> ! [X1] : (curious(X1) | ~generous(X1)) [avatar definition]
296. curious(X1) | ~generous(X1) <- (31) [avatar component clause 295]
297. 31 | ~29 | ~26 [avatar split clause 114,271,284,295]
332. ~strong(X0) | ~creative(X0) [subsumption resolution 154,156]
412. $false <- (21, ~26) [resolution 272,247]
413. ~21 | 26 [avatar contradiction clause 412]
415. brave(X0) | generous(X0) [resolution 134,106]
422. ~creative(fred) [resolution 332,153]
426. ~23 [avatar split clause 422,254]
448. ~old(X0) | ~quiet(X0) | generous(X0) [resolution 103,415]
450. ~quiet(X0) | generous(X0) <- (21) [subsumption resolution 448,247]
451. generous(X0) <- (21) [subsumption resolution 450,134]
456. $false <- (21, ~29) [resolution 451,285]
457. ~21 | 29 [avatar contradiction clause 456]
458. curious(X1) <- (21, 31) [subsumption resolution 296,451]
463. $false <- (21, 31) [resolution 458,142]
464. ~21 | ~31 [avatar contradiction clause 463]
468. $false [avatar sat refutation 257,297,413,426,457,464]
% SZS output end Proof for 5218249087876767482743893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is curious.
Everyone who is not tall is humble and vice versa.
If someone is both not calm and not funny then paul is not old and vice versa.
If fred is not creative then someone is either kind or not quiet and vice versa.
Everyone who is creative or not wise is either not rich or calm.
If susan is not curious then someone is generous or not funny.
Everyone who is either not curious or happy is not strong or quiet.
If someone is both not tall and not generous then someone is not quiet or curious.
If mary is not funny or not happy then someone is generous or not calm and vice versa.
Everyone who is happy or not patient is both not strong and not humble and vice versa.
If someone is rich then someone is either kind or patient and vice versa.
Everyone who is wise is not rich and vice versa.
If susan is funny or happy then paul is not patient or funny.
Everyone who is both not rich and old is both creative and not humble and vice versa.
Everyone who is wise or happy is either patient or not kind and vice versa.
If someone is either not calm or curious then someone is not strong.
Someone is both humble and funny.
Someone is either not quiet or not strong.
Someone is both not brave and old.
Paul is both not strong and not creative.
Someone is quiet.
Someone is both funny and quiet.
Someone is both curious and patient. | Susan is strong. | neutral | (![X]:(creative(X)=>curious(X)))&
(![X]:(~tall(X)<=>humble(X)))&
((?[X]:((~calm(X)&~funny(X))))<=>(~old(paul)))&
((~creative(fred))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:((creative(X)|~wise(X))=>(~rich(X)<~>calm(X))))&
((~curious(susan))=>(?[X]:((generous(X)|~funny(X)))))&
(![X]:((~curious(X)<~>happy(X))=>(~strong(X)|quiet(X))))&
((?[X]:((~tall(X)&~generous(X))))=>(?[X]:((~quiet(X)|curious(X)))))&
(((~funny(mary)|~happy(mary)))<=>(?[X]:((generous(X)|~calm(X)))))&
(![X]:((happy(X)|~patient(X))<=>(~strong(X)&~humble(X))))&
((?[X]:(rich(X)))<=>(?[X]:((kind(X)<~>patient(X)))))&
(![X]:(wise(X)<=>~rich(X)))&
(((funny(susan)|happy(susan)))=>((~patient(paul)|funny(paul))))&
(![X]:((~rich(X)&old(X))<=>(creative(X)&~humble(X))))&
(![X]:((wise(X)|happy(X))<=>(patient(X)<~>~kind(X))))&
((?[X]:((~calm(X)<~>curious(X))))=>(?[X]:(~strong(X))))&
(?[X]:((humble(X)&funny(X))))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~brave(X)&old(X))))&
((~strong(paul)&~creative(paul)))&
(?[X]:(quiet(X)))&
(?[X]:((funny(X)&quiet(X))))&
(?[X]:((curious(X)&patient(X)))) | strong(susan) | [] | null | 0 |
If fred is not rich then someone is both not humble and not strong. Everyone who is either not tall or not quiet is tall and vice versa. If paul is not tall or old then someone is not curious. If mary is both not creative and generous then alice is curious or happy. Everyone who is wise or not curious is either not old or not patient. Everyone who is not rich or strong is old or not strong and vice versa. If someone is strong or wise then someone is quiet. Everyone who is either tall or brave is either patient or curious and vice versa. If someone is rich or not quiet then paul is not patient and vice versa. Everyone who is not rich is not humble and vice versa. If john is not calm then susan is rich or funny. Everyone who is brave or humble is not humble or not curious. If susan is both funny and not calm then someone is both kind and not happy. If susan is not humble then someone is curious and vice versa. Everyone who is patient is not calm and vice versa. Everyone who is both not old and not wise is either not generous or not strong. Someone is not happy. Mary is either tall or not kind. Someone is either old or not calm. Paul is both generous and not humble. Someone is either generous or old. | Susan is not creative. | neutral | ((~rich(fred))=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>tall(X)))&
(((~tall(paul)|old(paul)))=>(?[X]:(~curious(X))))&
(((~creative(mary)&generous(mary)))=>((curious(alice)|happy(alice))))&
(![X]:((wise(X)|~curious(X))=>(~old(X)<~>~patient(X))))&
(![X]:((~rich(X)|strong(X))<=>(old(X)|~strong(X))))&
((?[X]:((strong(X)|wise(X))))=>(?[X]:(quiet(X))))&
(![X]:((tall(X)<~>brave(X))<=>(patient(X)<~>curious(X))))&
((?[X]:((rich(X)|~quiet(X))))<=>(~patient(paul)))&
(![X]:(~rich(X)<=>~humble(X)))&
((~calm(john))=>((rich(susan)|funny(susan))))&
(![X]:((brave(X)|humble(X))=>(~humble(X)|~curious(X))))&
(((funny(susan)&~calm(susan)))=>(?[X]:((kind(X)&~happy(X)))))&
((~humble(susan))<=>(?[X]:(curious(X))))&
(![X]:(patient(X)<=>~calm(X)))&
(![X]:((~old(X)&~wise(X))=>(~generous(X)<~>~strong(X))))&
(?[X]:(~happy(X)))&
((tall(mary)<~>~kind(mary)))&
(?[X]:((old(X)<~>~calm(X))))&
((generous(paul)&~humble(paul)))&
(?[X]:((generous(X)<~>old(X)))) | ~creative(susan) | [] | 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 913664976450233761125385
% SZS output start Proof for 913664976450233761125385
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 913664976450233761125385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either not creative or calm then someone is both not funny and funny.
Everyone who is either not calm or not funny is not calm and vice versa.
Everyone who is either brave or not curious is either calm or kind.
Everyone who is either not old or rich is curious or not tall.
If mary is not brave or not calm then mary is both curious and rich.
Everyone who is funny is tall or not tall.
Everyone who is both brave and not wise is not humble or tall and vice versa.
If someone is both strong and not generous then someone is wise.
Everyone who is not quiet or happy is both rich and not tall.
Everyone who is both not generous and not calm is not strong or wise.
Everyone who is both not quiet and old is humble or not wise.
Everyone who is either tall or not patient is tall or generous.
Everyone who is brave is either wise or not creative.
Everyone who is both not kind and brave is not generous or not happy and vice versa.
If someone is both not happy and not tall then fred is not strong or not curious.
Everyone who is rich or not brave is either strong or quiet and vice versa.
Mary is not old.
Someone is both not humble and not generous.
Alice is humble or not happy.
Someone is not rich.
Alice is old.
Someone is not funny or humble.
Fred is both not generous and not curious. | Fred is not funny. | contradiction | (((~creative(susan)<~>calm(susan)))=>(?[X]:((~funny(X)&funny(X)))))&
(![X]:((~calm(X)<~>~funny(X))<=>~calm(X)))&
(![X]:((brave(X)<~>~curious(X))=>(calm(X)<~>kind(X))))&
(![X]:((~old(X)<~>rich(X))=>(curious(X)|~tall(X))))&
(((~brave(mary)|~calm(mary)))=>((curious(mary)&rich(mary))))&
(![X]:(funny(X)=>(tall(X)|~tall(X))))&
(![X]:((brave(X)&~wise(X))<=>(~humble(X)|tall(X))))&
((?[X]:((strong(X)&~generous(X))))=>(?[X]:(wise(X))))&
(![X]:((~quiet(X)|happy(X))=>(rich(X)&~tall(X))))&
(![X]:((~generous(X)&~calm(X))=>(~strong(X)|wise(X))))&
(![X]:((~quiet(X)&old(X))=>(humble(X)|~wise(X))))&
(![X]:((tall(X)<~>~patient(X))=>(tall(X)|generous(X))))&
(![X]:(brave(X)=>(wise(X)<~>~creative(X))))&
(![X]:((~kind(X)&brave(X))<=>(~generous(X)|~happy(X))))&
((?[X]:((~happy(X)&~tall(X))))=>((~strong(fred)|~curious(fred))))&
(![X]:((rich(X)|~brave(X))<=>(strong(X)<~>quiet(X))))&
(~old(mary))&
(?[X]:((~humble(X)&~generous(X))))&
((humble(alice)|~happy(alice)))&
(?[X]:(~rich(X)))&
(old(alice))&
(?[X]:((~funny(X)|humble(X))))&
((~generous(fred)&~curious(fred))) | ~funny(fred) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 7060050602568425917534872
% SZS output start Proof for 7060050602568425917534872
2. ! [X0] : ((~calm(X0) <~> ~funny(X0)) <=> ~calm(X0)) [input p1]
24. ~funny(fred) [input hypothesis]
47. ! [X0] : ((((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0))))) [nnf transformation 2]
72. ~calm(X0) | ~calm(X0) | funny(X0) [cnf transformation 47]
74. funny(X0) | calm(X0) | calm(X0) [cnf transformation 47]
123. ~funny(fred) [cnf transformation 24]
125. ~calm(X0) | funny(X0) [duplicate literal removal 72]
126. funny(X0) | calm(X0) [duplicate literal removal 74]
143. funny(X0) [subsumption resolution 125,126]
197. $false [subsumption resolution 123,143]
% SZS output end Proof for 7060050602568425917534872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either not tall or generous. Everyone who is either not strong or brave is not kind or not tall. If alice is both not wise and not generous then fred is both happy and not funny and vice versa. Everyone who is either generous or tall is not tall and vice versa. Everyone who is both not quiet and not patient is either not funny or old and vice versa. Everyone who is both not rich and curious is not calm or humble. Everyone who is both strong and brave is both patient and not tall. If fred is not tall then lucy is either not brave or humble. If susan is either happy or not tall then someone is both not wise and not creative and vice versa. If fred is both calm and not strong then someone is either strong or not patient. If fred is funny or not strong then alice is both not old and not funny. Everyone who is either not funny or creative is not creative and vice versa. If someone is generous or old then paul is either not calm or calm and vice versa. Everyone who is both brave and not tall is either not curious or funny and vice versa. Everyone who is both not calm and not happy is quiet or not kind and vice versa. Everyone who is not brave is either not happy or not tall and vice versa. Someone is curious or not patient. Someone is either generous or creative. Susan is not brave or humble. Paul is both not brave and not quiet. John is both patient and not calm. Susan is both not calm and strong. Someone is either not strong or not quiet. | John is curious. | entailment | (![X]:(~funny(X)=>(~tall(X)<~>generous(X))))&
(![X]:((~strong(X)<~>brave(X))=>(~kind(X)|~tall(X))))&
(((~wise(alice)&~generous(alice)))<=>((happy(fred)&~funny(fred))))&
(![X]:((generous(X)<~>tall(X))<=>~tall(X)))&
(![X]:((~quiet(X)&~patient(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~rich(X)&curious(X))=>(~calm(X)|humble(X))))&
(![X]:((strong(X)&brave(X))=>(patient(X)&~tall(X))))&
((~tall(fred))=>((~brave(lucy)<~>humble(lucy))))&
(((happy(susan)<~>~tall(susan)))<=>(?[X]:((~wise(X)&~creative(X)))))&
(((calm(fred)&~strong(fred)))=>(?[X]:((strong(X)<~>~patient(X)))))&
(((funny(fred)|~strong(fred)))=>((~old(alice)&~funny(alice))))&
(![X]:((~funny(X)<~>creative(X))<=>~creative(X)))&
((?[X]:((generous(X)|old(X))))<=>((~calm(paul)<~>calm(paul))))&
(![X]:((brave(X)&~tall(X))<=>(~curious(X)<~>funny(X))))&
(![X]:((~calm(X)&~happy(X))<=>(quiet(X)|~kind(X))))&
(![X]:(~brave(X)<=>(~happy(X)<~>~tall(X))))&
(?[X]:((curious(X)|~patient(X))))&
(?[X]:((generous(X)<~>creative(X))))&
((~brave(susan)|humble(susan)))&
((~brave(paul)&~quiet(paul)))&
((patient(john)&~calm(john)))&
((~calm(susan)&strong(susan)))&
(?[X]:((~strong(X)<~>~quiet(X)))) | curious(john) | [
"p0",
"p3",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2258988507355640320308525
% SZS output start Proof for 2258988507355640320308525
1. ! [X0] : (~funny(X0) => (~tall(X0) <~> generous(X0))) [input p0]
4. ! [X0] : ((generous(X0) <~> tall(X0)) <=> ~tall(X0)) [input p3]
12. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> ~creative(X0)) [input p11]
14. ! [X0] : ((~tall(X0) & brave(X0)) <=> (~curious(X0) <~> funny(X0))) [input p13]
24. ~curious(john) [input hypothesis]
26. ! [X0] : ((~tall(X0) <~> generous(X0)) | funny(X0)) [ennf transformation 1]
35. ! [X0] : (((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | funny(X0)) [nnf transformation 26]
39. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | tall(X0)) & (~tall(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [nnf transformation 4]
50. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | creative(X0)) & (~creative(X0) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [nnf transformation 12]
55. ! [X0] : (((~tall(X0) & brave(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | (tall(X0) | ~brave(X0)))) [nnf transformation 14]
56. ! [X0] : (((~tall(X0) & brave(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | tall(X0) | ~brave(X0))) [flattening 55]
69. ~generous(X0) | tall(X0) | funny(X0) [cnf transformation 35]
78. tall(X0) | generous(X0) | tall(X0) [cnf transformation 39]
103. ~creative(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 50]
104. creative(X0) | ~funny(X0) | creative(X0) [cnf transformation 50]
116. ~tall(X0) | funny(X0) | curious(X0) [cnf transformation 56]
139. ~curious(john) [cnf transformation 24]
142. ~creative(X0) | ~funny(X0) [duplicate literal removal 103]
143. ~funny(X0) | creative(X0) [duplicate literal removal 104]
145. generous(X0) | tall(X0) [duplicate literal removal 78]
236. ~funny(X0) [subsumption resolution 142,143]
237. ~tall(X0) | curious(X0) [subsumption resolution 116,236]
270. tall(X0) | funny(X0) | tall(X0) [resolution 69,145]
272. tall(X0) | funny(X0) [duplicate literal removal 270]
273. tall(X0) [subsumption resolution 272,236]
276. curious(X1) [resolution 273,237]
283. $false [resolution 276,139]
% SZS output end Proof for 2258988507355640320308525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is creative. Everyone who is either patient or quiet is both not humble and calm and vice versa. If someone is both happy and rich then someone is creative or happy and vice versa. If alice is not quiet or not calm then someone is happy. If someone is not calm or not patient then someone is strong. If someone is both not brave and not tall then mary is not happy. If alice is not creative then fred is not happy or not funny and vice versa. If susan is curious or not quiet then fred is not curious and vice versa. Everyone who is either not quiet or not creative is strong and vice versa. If paul is either not funny or curious then someone is either not strong or strong and vice versa. If paul is either happy or not kind then someone is both not creative and not quiet and vice versa. If someone is not wise or not creative then fred is happy or calm and vice versa. Everyone who is wise or not tall is either creative or not creative. If someone is not happy then someone is either not happy or not humble and vice versa. Everyone who is either tall or not creative is either not quiet or not strong and vice versa. Everyone who is both not funny and calm is either funny or not wise and vice versa. Someone is either generous or humble. Mary is both happy and wise. Someone is either old or patient. Someone is generous. Alice is quiet. Someone is either funny or happy. Mary is either humble or not funny. Susan is not kind. | Mary is tall. | entailment | (![X]:(~humble(X)=>creative(X)))&
(![X]:((patient(X)<~>quiet(X))<=>(~humble(X)&calm(X))))&
((?[X]:((happy(X)&rich(X))))<=>(?[X]:((creative(X)|happy(X)))))&
(((~quiet(alice)|~calm(alice)))=>(?[X]:(happy(X))))&
((?[X]:((~calm(X)|~patient(X))))=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)&~tall(X))))=>(~happy(mary)))&
((~creative(alice))<=>((~happy(fred)|~funny(fred))))&
(((curious(susan)|~quiet(susan)))<=>(~curious(fred)))&
(![X]:((~quiet(X)<~>~creative(X))<=>strong(X)))&
(((~funny(paul)<~>curious(paul)))<=>(?[X]:((~strong(X)<~>strong(X)))))&
(((happy(paul)<~>~kind(paul)))<=>(?[X]:((~creative(X)&~quiet(X)))))&
((?[X]:((~wise(X)|~creative(X))))<=>((happy(fred)|calm(fred))))&
(![X]:((wise(X)|~tall(X))=>(creative(X)<~>~creative(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~happy(X)<~>~humble(X)))))&
(![X]:((tall(X)<~>~creative(X))<=>(~quiet(X)<~>~strong(X))))&
(![X]:((~funny(X)&calm(X))<=>(funny(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>humble(X))))&
((happy(mary)&wise(mary)))&
(?[X]:((old(X)<~>patient(X))))&
(?[X]:(generous(X)))&
(quiet(alice))&
(?[X]:((funny(X)<~>happy(X))))&
((humble(mary)<~>~funny(mary)))&
(~kind(susan)) | tall(mary) | [
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 872565902105675473530381
% SZS output start Proof for 872565902105675473530381
9. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) <=> strong(X0)) [input p8]
15. ! [X0] : ((tall(X0) <~> ~creative(X0)) <=> (~quiet(X0) <~> ~strong(X0))) [input p14]
25. ~tall(mary) [input hypothesis]
50. ! [X0] : ((((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ~strong(X0)) & (strong(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0))))) [nnf transformation 9]
70. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) & (((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [nnf transformation 15]
107. ~creative(X0) | strong(X0) | quiet(X0) [cnf transformation 50]
108. ~quiet(X0) | strong(X0) | creative(X0) [cnf transformation 50]
109. ~strong(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 50]
110. ~strong(X0) | quiet(X0) | creative(X0) [cnf transformation 50]
138. ~strong(X0) | ~quiet(X0) | tall(X0) | creative(X0) [cnf transformation 70]
140. strong(X0) | quiet(X0) | tall(X0) | creative(X0) [cnf transformation 70]
141. ~creative(X0) | tall(X0) | ~strong(X0) | quiet(X0) [cnf transformation 70]
142. ~creative(X0) | tall(X0) | ~quiet(X0) | strong(X0) [cnf transformation 70]
164. ~tall(mary) [cnf transformation 25]
347. ~quiet(X0) | tall(X0) | strong(X0) [subsumption resolution 142,108]
348. ~strong(X0) | tall(X0) | quiet(X0) [subsumption resolution 141,110]
349. tall(X0) | quiet(X0) | creative(X0) [subsumption resolution 140,348]
350. ~strong(X0) | tall(X0) | creative(X0) [subsumption resolution 138,349]
520. quiet(mary) | creative(mary) [resolution 349,164]
522. 54 <=> creative(mary) [avatar definition]
524. creative(mary) <- (54) [avatar component clause 522]
526. 55 <=> quiet(mary) [avatar definition]
528. quiet(mary) <- (55) [avatar component clause 526]
529. 54 | 55 [avatar split clause 520,526,522]
534. strong(mary) | quiet(mary) <- (54) [resolution 524,107]
536. 56 <=> strong(mary) [avatar definition]
538. strong(mary) <- (56) [avatar component clause 536]
539. 55 | 56 | ~54 [avatar split clause 534,522,536,526]
541. tall(mary) | strong(mary) <- (55) [resolution 528,347]
545. strong(mary) <- (55) [subsumption resolution 541,164]
546. 56 | ~55 [avatar split clause 545,526,536]
596. tall(mary) | creative(mary) <- (56) [resolution 538,350]
597. tall(mary) | quiet(mary) <- (56) [resolution 538,348]
599. ~quiet(mary) | ~creative(mary) <- (56) [resolution 538,109]
605. quiet(mary) <- (56) [subsumption resolution 597,164]
606. 55 | ~56 [avatar split clause 605,536,526]
608. ~54 | ~55 | ~56 [avatar split clause 599,536,526,522]
609. creative(mary) <- (56) [subsumption resolution 596,164]
610. 54 | ~56 [avatar split clause 609,536,522]
611. $false [avatar sat refutation 529,539,546,606,608,610]
% SZS output end Proof for 872565902105675473530381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not curious is not calm. If someone is either not strong or brave then someone is not creative or not rich and vice versa. If mary is both humble and not generous then alice is not wise and vice versa. If someone is patient or not wise then paul is both not kind and curious and vice versa. Everyone who is calm or not calm is creative or not curious. Everyone who is both not kind and creative is not rich. Everyone who is both not patient and quiet is not happy or old and vice versa. Everyone who is not generous is humble or not strong and vice versa. Everyone who is both rich and not quiet is happy or not wise. If someone is both funny and tall then alice is not creative and vice versa. Everyone who is either curious or old is both not humble and rich and vice versa. Everyone who is not kind or not humble is either not creative or not humble and vice versa. If paul is either not humble or wise then alice is both not quiet and strong and vice versa. If someone is curious then lucy is both funny and humble. Everyone who is patient or not creative is either patient or wise and vice versa. Everyone who is both creative and not patient is both not kind and not rich. Mary is either not strong or not humble. Someone is both not strong and calm. Someone is old. Someone is creative. Alice is not funny. Susan is either not quiet or not funny. Someone is both not brave and strong. Someone is either rich or not old. | Paul is not quiet. | contradiction | (![X]:((~humble(X)<~>~curious(X))=>~calm(X)))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((~creative(X)|~rich(X)))))&
(((humble(mary)&~generous(mary)))<=>(~wise(alice)))&
((?[X]:((patient(X)|~wise(X))))<=>((~kind(paul)&curious(paul))))&
(![X]:((calm(X)|~calm(X))=>(creative(X)|~curious(X))))&
(![X]:((~kind(X)&creative(X))=>~rich(X)))&
(![X]:((~patient(X)&quiet(X))<=>(~happy(X)|old(X))))&
(![X]:(~generous(X)<=>(humble(X)|~strong(X))))&
(![X]:((rich(X)&~quiet(X))=>(happy(X)|~wise(X))))&
((?[X]:((funny(X)&tall(X))))<=>(~creative(alice)))&
(![X]:((curious(X)<~>old(X))<=>(~humble(X)&rich(X))))&
(![X]:((~kind(X)|~humble(X))<=>(~creative(X)<~>~humble(X))))&
(((~humble(paul)<~>wise(paul)))<=>((~quiet(alice)&strong(alice))))&
((?[X]:(curious(X)))=>((funny(lucy)&humble(lucy))))&
(![X]:((patient(X)|~creative(X))<=>(patient(X)<~>wise(X))))&
(![X]:((creative(X)&~patient(X))=>(~kind(X)&~rich(X))))&
((~strong(mary)<~>~humble(mary)))&
(?[X]:((~strong(X)&calm(X))))&
(?[X]:(old(X)))&
(?[X]:(creative(X)))&
(~funny(alice))&
((~quiet(susan)<~>~funny(susan)))&
(?[X]:((~brave(X)&strong(X))))&
(?[X]:((rich(X)<~>~old(X)))) | ~quiet(paul) | [
"p3",
"p4",
"p5",
"p6",
"p10",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4482837417350219967125785
% SZS output start Proof for 4482837417350219967125785
4. ? [X0] : (~wise(X0) | patient(X0)) <=> (curious(paul) & ~kind(paul)) [input p3]
5. ! [X0] : ((~calm(X0) | calm(X0)) => (~curious(X0) | creative(X0))) [input p4]
6. ! [X0] : ((creative(X0) & ~kind(X0)) => ~rich(X0)) [input p5]
7. ! [X0] : ((quiet(X0) & ~patient(X0)) <=> (old(X0) | ~happy(X0))) [input p6]
11. ! [X0] : ((curious(X0) <~> old(X0)) <=> (rich(X0) & ~humble(X0))) [input p10]
15. ! [X0] : ((~creative(X0) | patient(X0)) <=> (patient(X0) <~> wise(X0))) [input p14]
16. ! [X0] : ((~patient(X0) & creative(X0)) => (~rich(X0) & ~kind(X0))) [input p15]
20. ? [X0] : creative(X0) [input p19]
25. ~quiet(paul) [input hypothesis]
28. ! [X0] : ((~curious(X0) | creative(X0)) | (calm(X0) & ~calm(X0))) [ennf transformation 5]
29. ! [X0] : (~curious(X0) | creative(X0) | (calm(X0) & ~calm(X0))) [flattening 28]
30. ! [X0] : (~rich(X0) | (~creative(X0) | kind(X0))) [ennf transformation 6]
31. ! [X0] : (~rich(X0) | ~creative(X0) | kind(X0)) [flattening 30]
35. ! [X0] : ((~rich(X0) & ~kind(X0)) | (patient(X0) | ~creative(X0))) [ennf transformation 16]
36. ! [X0] : ((~rich(X0) & ~kind(X0)) | patient(X0) | ~creative(X0)) [flattening 35]
45. (? [X0] : (~wise(X0) | patient(X0)) | (~curious(paul) | kind(paul))) & ((curious(paul) & ~kind(paul)) | ! [X0] : (wise(X0) & ~patient(X0))) [nnf transformation 4]
46. (? [X0] : (~wise(X0) | patient(X0)) | ~curious(paul) | kind(paul)) & ((curious(paul) & ~kind(paul)) | ! [X0] : (wise(X0) & ~patient(X0))) [flattening 45]
47. (? [X0] : (~wise(X0) | patient(X0)) | ~curious(paul) | kind(paul)) & ((curious(paul) & ~kind(paul)) | ! [X1] : (wise(X1) & ~patient(X1))) [rectify 46]
48. ? [X0] : (~wise(X0) | patient(X0)) => (~wise(sK2) | patient(sK2)) [choice axiom]
49. ((~wise(sK2) | patient(sK2)) | ~curious(paul) | kind(paul)) & ((curious(paul) & ~kind(paul)) | ! [X1] : (wise(X1) & ~patient(X1))) [skolemisation 47,48]
50. ! [X0] : (((quiet(X0) & ~patient(X0)) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | (~quiet(X0) | patient(X0)))) [nnf transformation 7]
51. ! [X0] : (((quiet(X0) & ~patient(X0)) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | ~quiet(X0) | patient(X0))) [flattening 50]
58. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | (~rich(X0) | humble(X0))) & ((rich(X0) & ~humble(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 11]
59. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | ~rich(X0) | humble(X0)) & ((rich(X0) & ~humble(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [flattening 58]
64. ! [X0] : (((~creative(X0) | patient(X0)) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) & (((~wise(X0) | ~patient(X0)) & (wise(X0) | patient(X0))) | (creative(X0) & ~patient(X0)))) [nnf transformation 15]
65. ! [X0] : ((~creative(X0) | patient(X0) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) & (((~wise(X0) | ~patient(X0)) & (wise(X0) | patient(X0))) | (creative(X0) & ~patient(X0)))) [flattening 64]
71. ? [X0] : creative(X0) => creative(sK6) [choice axiom]
72. creative(sK6) [skolemisation 20,71]
90. ~kind(paul) | ~patient(X1) [cnf transformation 49]
92. curious(paul) | ~patient(X1) [cnf transformation 49]
93. curious(paul) | wise(X1) [cnf transformation 49]
95. ~curious(X0) | creative(X0) | ~calm(X0) [cnf transformation 29]
96. ~curious(X0) | creative(X0) | calm(X0) [cnf transformation 29]
97. ~rich(X0) | ~creative(X0) | kind(X0) [cnf transformation 31]
102. ~old(X0) | quiet(X0) [cnf transformation 51]
112. ~curious(X0) | old(X0) | rich(X0) [cnf transformation 59]
135. ~creative(X0) | patient(X0) | patient(X0) | ~wise(X0) [cnf transformation 65]
136. ~kind(X0) | patient(X0) | ~creative(X0) [cnf transformation 36]
143. creative(sK6) [cnf transformation 72]
151. ~quiet(paul) [cnf transformation 25]
153. ~wise(X0) | patient(X0) | ~creative(X0) [duplicate literal removal 135]
206. 12 <=> kind(paul) [avatar definition]
207. ~kind(paul) <- (~12) [avatar component clause 206]
208. kind(paul) <- (12) [avatar component clause 206]
210. 13 <=> curious(paul) [avatar definition]
211. curious(paul) <- (13) [avatar component clause 210]
223. 16 <=> ! [X1] : wise(X1) [avatar definition]
224. wise(X1) <- (16) [avatar component clause 223]
225. 16 | 13 [avatar split clause 93,210,223]
227. 17 <=> ! [X1] : ~patient(X1) [avatar definition]
228. ~patient(X1) <- (17) [avatar component clause 227]
229. 17 | 13 [avatar split clause 92,210,227]
231. 17 | ~12 [avatar split clause 90,206,227]
232. ~curious(X0) | creative(X0) [subsumption resolution 95,96]
370. 40 <=> rich(paul) [avatar definition]
372. rich(paul) <- (40) [avatar component clause 370]
374. 41 <=> old(paul) [avatar definition]
376. old(paul) <- (41) [avatar component clause 374]
382. old(paul) | rich(paul) <- (13) [resolution 211,112]
385. creative(paul) <- (13) [resolution 211,232]
391. 43 <=> creative(paul) [avatar definition]
393. creative(paul) <- (43) [avatar component clause 391]
395. 43 | ~13 [avatar split clause 385,210,391]
413. ~creative(paul) | kind(paul) <- (40) [resolution 372,97]
414. kind(paul) <- (40, 43) [subsumption resolution 413,393]
415. $false <- (~12, 40, 43) [subsumption resolution 414,207]
416. 12 | ~40 | ~43 [avatar contradiction clause 415]
417. 40 | 41 | ~13 [avatar split clause 382,210,374,370]
425. quiet(paul) <- (41) [resolution 376,102]
427. $false <- (41) [subsumption resolution 425,151]
428. ~41 [avatar contradiction clause 427]
433. patient(paul) | ~creative(paul) <- (12) [resolution 136,208]
434. ~creative(paul) <- (12, 17) [subsumption resolution 433,228]
437. ~43 | ~12 | ~17 [avatar split clause 434,227,206,391]
440. patient(X0) | ~creative(X0) <- (16) [resolution 153,224]
441. ~creative(X0) <- (16, 17) [subsumption resolution 440,228]
459. $false <- (16, 17) [resolution 441,143]
461. ~16 | ~17 [avatar contradiction clause 459]
462. $false [avatar sat refutation 225,229,231,395,416,417,428,437,461]
% SZS output end Proof for 4482837417350219967125785
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is generous or kind then someone is not rich or not old.
Everyone who is strong is either not tall or not creative and vice versa.
Everyone who is wise is both generous and not brave and vice versa.
If lucy is generous or not curious then someone is either not curious or not creative and vice versa.
Everyone who is calm or not kind is rich or not strong and vice versa.
If fred is either brave or kind then alice is both tall and not wise and vice versa.
If someone is either not humble or patient then someone is either funny or not happy and vice versa.
If someone is both not tall and creative then fred is patient or happy and vice versa.
If someone is both not old and not creative then susan is both patient and old.
Everyone who is either not happy or kind is creative or happy and vice versa.
Everyone who is not funny or quiet is both not calm and curious and vice versa.
Everyone who is wise is either not old or humble.
If someone is either tall or not humble then fred is both not calm and funny and vice versa.
Everyone who is wise is not generous and vice versa.
Everyone who is quiet or not old is not calm or patient.
Everyone who is not kind or not happy is both not kind and not tall and vice versa.
Someone is both generous and not tall.
Someone is not humble.
Mary is old.
Alice is both not quiet and brave.
Lucy is not strong.
Someone is either rich or old. | Mary is brave. | entailment | (((generous(susan)|kind(susan)))=>(?[X]:((~rich(X)|~old(X)))))&
(![X]:(strong(X)<=>(~tall(X)<~>~creative(X))))&
(![X]:(wise(X)<=>(generous(X)&~brave(X))))&
(((generous(lucy)|~curious(lucy)))<=>(?[X]:((~curious(X)<~>~creative(X)))))&
(![X]:((calm(X)|~kind(X))<=>(rich(X)|~strong(X))))&
(((brave(fred)<~>kind(fred)))<=>((tall(alice)&~wise(alice))))&
((?[X]:((~humble(X)<~>patient(X))))<=>(?[X]:((funny(X)<~>~happy(X)))))&
((?[X]:((~tall(X)&creative(X))))<=>((patient(fred)|happy(fred))))&
((?[X]:((~old(X)&~creative(X))))=>((patient(susan)&old(susan))))&
(![X]:((~happy(X)<~>kind(X))<=>(creative(X)|happy(X))))&
(![X]:((~funny(X)|quiet(X))<=>(~calm(X)&curious(X))))&
(![X]:(wise(X)=>(~old(X)<~>humble(X))))&
((?[X]:((tall(X)<~>~humble(X))))<=>((~calm(fred)&funny(fred))))&
(![X]:(wise(X)<=>~generous(X)))&
(![X]:((quiet(X)|~old(X))=>(~calm(X)|patient(X))))&
(![X]:((~kind(X)|~happy(X))<=>(~kind(X)&~tall(X))))&
(?[X]:((generous(X)&~tall(X))))&
(?[X]:(~humble(X)))&
(old(mary))&
((~quiet(alice)&brave(alice)))&
(~strong(lucy))&
(?[X]:((rich(X)<~>old(X)))) | brave(mary) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6402832199833784096789147
% SZS output start Proof for 6402832199833784096789147
3. ! [X0] : (wise(X0) <=> (~brave(X0) & generous(X0))) [input p2]
14. ! [X0] : (wise(X0) <=> ~generous(X0)) [input p13]
23. ~brave(mary) [input hypothesis]
33. ! [X0] : ((wise(X0) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | ~wise(X0))) [nnf transformation 3]
34. ! [X0] : ((wise(X0) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | ~wise(X0))) [flattening 33]
64. ! [X0] : ((wise(X0) | generous(X0)) & (~generous(X0) | ~wise(X0))) [nnf transformation 14]
80. ~wise(X0) | generous(X0) [cnf transformation 34]
82. ~generous(X0) | brave(X0) | wise(X0) [cnf transformation 34]
133. ~generous(X0) | ~wise(X0) [cnf transformation 64]
134. wise(X0) | generous(X0) [cnf transformation 64]
151. ~brave(mary) [cnf transformation 23]
324. generous(X0) [subsumption resolution 134,80]
325. ~wise(X0) [subsumption resolution 133,324]
381. brave(X0) | wise(X0) [resolution 82,324]
382. brave(X0) [subsumption resolution 381,325]
383. $false [resolution 382,151]
% SZS output end Proof for 6402832199833784096789147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is tall or creative then someone is either not generous or not curious and vice versa. If john is both not patient and strong then paul is not funny or humble. Everyone who is funny or quiet is either not humble or not rich. If lucy is either funny or not humble then alice is either humble or not kind. If mary is both wise and not humble then someone is not rich and vice versa. If someone is not old then paul is strong. Everyone who is either rich or generous is either not tall or wise. If someone is not rich then someone is not creative or happy and vice versa. If susan is not wise then paul is rich and vice versa. If alice is both calm and not wise then someone is not wise or not humble. Everyone who is patient or creative is brave. Everyone who is not curious is both tall and wise. Everyone who is either not quiet or tall is not quiet or not old. Everyone who is both creative and wise is either creative or not generous and vice versa. Everyone who is generous or curious is both humble and not tall. Everyone who is not tall or humble is funny or humble and vice versa. Paul is not funny or not strong. Someone is not patient. John is rich or creative. John is quiet or old. Someone is either not rich or not calm. | Lucy is wise. | neutral | (((tall(alice)|creative(alice)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(((~patient(john)&strong(john)))=>((~funny(paul)|humble(paul))))&
(![X]:((funny(X)|quiet(X))=>(~humble(X)<~>~rich(X))))&
(((funny(lucy)<~>~humble(lucy)))=>((humble(alice)<~>~kind(alice))))&
(((wise(mary)&~humble(mary)))<=>(?[X]:(~rich(X))))&
((?[X]:(~old(X)))=>(strong(paul)))&
(![X]:((rich(X)<~>generous(X))=>(~tall(X)<~>wise(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)|happy(X)))))&
((~wise(susan))<=>(rich(paul)))&
(((calm(alice)&~wise(alice)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((patient(X)|creative(X))=>brave(X)))&
(![X]:(~curious(X)=>(tall(X)&wise(X))))&
(![X]:((~quiet(X)<~>tall(X))=>(~quiet(X)|~old(X))))&
(![X]:((creative(X)&wise(X))<=>(creative(X)<~>~generous(X))))&
(![X]:((generous(X)|curious(X))=>(humble(X)&~tall(X))))&
(![X]:((~tall(X)|humble(X))<=>(funny(X)|humble(X))))&
((~funny(paul)|~strong(paul)))&
(?[X]:(~patient(X)))&
((rich(john)|creative(john)))&
((quiet(john)|old(john)))&
(?[X]:((~rich(X)<~>~calm(X)))) | wise(lucy) | [] | null | 0 |
Everyone who is not calm or kind is either not brave or not quiet. Everyone who is not humble is either not calm or humble and vice versa. If susan is not brave or not rich then someone is old and vice versa. Everyone who is quiet or not rich is happy and vice versa. Everyone who is both funny and not kind is both rich and not kind. If someone is either brave or kind then someone is either tall or patient and vice versa. Everyone who is not curious is not generous and vice versa. If john is either kind or not generous then someone is not tall or happy. Everyone who is both happy and patient is either not strong or quiet. If someone is kind or brave then paul is not quiet. If someone is happy then someone is both not humble and curious. Everyone who is both not curious and happy is not quiet. Everyone who is not happy is either funny or kind. If someone is both not happy and not brave then someone is creative or happy and vice versa. If susan is either curious or not generous then someone is not wise or patient and vice versa. Everyone who is both wise and not calm is either not strong or curious. Lucy is both not strong and not generous. Someone is kind or happy. John is either creative or not wise. Susan is either quiet or not calm. Susan is both not calm and not wise. | Paul is not humble. | neutral | (![X]:((~calm(X)|kind(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:(~humble(X)<=>(~calm(X)<~>humble(X))))&
(((~brave(susan)|~rich(susan)))<=>(?[X]:(old(X))))&
(![X]:((quiet(X)|~rich(X))<=>happy(X)))&
(![X]:((funny(X)&~kind(X))=>(rich(X)&~kind(X))))&
((?[X]:((brave(X)<~>kind(X))))<=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:(~curious(X)<=>~generous(X)))&
(((kind(john)<~>~generous(john)))=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:((happy(X)&patient(X))=>(~strong(X)<~>quiet(X))))&
((?[X]:((kind(X)|brave(X))))=>(~quiet(paul)))&
((?[X]:(happy(X)))=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((~curious(X)&happy(X))=>~quiet(X)))&
(![X]:(~happy(X)=>(funny(X)<~>kind(X))))&
((?[X]:((~happy(X)&~brave(X))))<=>(?[X]:((creative(X)|happy(X)))))&
(((curious(susan)<~>~generous(susan)))<=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((wise(X)&~calm(X))=>(~strong(X)<~>curious(X))))&
((~strong(lucy)&~generous(lucy)))&
(?[X]:((kind(X)|happy(X))))&
((creative(john)<~>~wise(john)))&
((quiet(susan)<~>~calm(susan)))&
((~calm(susan)&~wise(susan))) | ~humble(paul) | [] | null | 0 |
Everyone who is either not curious or not wise is both not rich and not old and vice versa. Everyone who is both strong and kind is either not calm or brave and vice versa. If mary is both not patient and curious then someone is either not old or not rich. If alice is not creative then susan is curious or not calm. If someone is both not kind and creative then john is calm and vice versa. If mary is not rich or creative then alice is not funny. If paul is patient or strong then someone is both happy and kind. Everyone who is funny or not strong is both not rich and not funny and vice versa. If someone is both not quiet and not patient then mary is either not humble or not strong and vice versa. Everyone who is brave or not patient is either creative or not humble. If fred is either kind or not strong then someone is not happy and vice versa. If alice is both generous and not funny then susan is curious or not creative. If someone is not tall or old then someone is either not strong or not kind. Everyone who is either not rich or not happy is not funny or rich. If fred is quiet then someone is not rich or not quiet. Everyone who is both happy and not happy is not rich or curious and vice versa. John is happy or not old. Someone is tall. Alice is either patient or not happy. Someone is either humble or not kind. Someone is both not quiet and calm. Someone is not wise or not old. | John is not quiet. | neutral | (![X]:((~curious(X)<~>~wise(X))<=>(~rich(X)&~old(X))))&
(![X]:((strong(X)&kind(X))<=>(~calm(X)<~>brave(X))))&
(((~patient(mary)&curious(mary)))=>(?[X]:((~old(X)<~>~rich(X)))))&
((~creative(alice))=>((curious(susan)|~calm(susan))))&
((?[X]:((~kind(X)&creative(X))))<=>(calm(john)))&
(((~rich(mary)|creative(mary)))=>(~funny(alice)))&
(((patient(paul)|strong(paul)))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((funny(X)|~strong(X))<=>(~rich(X)&~funny(X))))&
((?[X]:((~quiet(X)&~patient(X))))<=>((~humble(mary)<~>~strong(mary))))&
(![X]:((brave(X)|~patient(X))=>(creative(X)<~>~humble(X))))&
(((kind(fred)<~>~strong(fred)))<=>(?[X]:(~happy(X))))&
(((generous(alice)&~funny(alice)))=>((curious(susan)|~creative(susan))))&
((?[X]:((~tall(X)|old(X))))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~rich(X)<~>~happy(X))=>(~funny(X)|rich(X))))&
((quiet(fred))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((happy(X)&~happy(X))<=>(~rich(X)|curious(X))))&
((happy(john)|~old(john)))&
(?[X]:(tall(X)))&
((patient(alice)<~>~happy(alice)))&
(?[X]:((humble(X)<~>~kind(X))))&
(?[X]:((~quiet(X)&calm(X))))&
(?[X]:((~wise(X)|~old(X)))) | ~quiet(john) | [] | null | 0 |
Everyone who is either humble or not happy is both wise and not kind and vice versa.
Everyone who is not strong is not funny or humble and vice versa.
Everyone who is not happy is either curious or humble.
Everyone who is either not funny or not kind is either brave or humble.
Everyone who is brave is either not patient or not tall.
If alice is not happy or not old then someone is both quiet and not brave and vice versa.
Everyone who is funny is not humble or not calm and vice versa.
Everyone who is not kind is either calm or not creative.
Everyone who is both generous and not brave is both happy and brave and vice versa.
Everyone who is calm or kind is both not brave and calm.
If someone is not wise then someone is either humble or not quiet and vice versa.
Everyone who is rich is not old and vice versa.
If john is either not wise or not happy then alice is both not calm and patient.
If susan is not creative or generous then someone is either old or strong and vice versa.
If someone is either wise or not brave then susan is both strong and creative and vice versa.
Everyone who is not old or funny is not calm or not old.
Someone is both rich and not strong.
Mary is either not calm or not brave.
Fred is both not curious and not tall.
Paul is either strong or old.
Someone is both not tall and not funny.
Someone is either old or not kind. | Susan is calm. | neutral | (![X]:((humble(X)<~>~happy(X))<=>(wise(X)&~kind(X))))&
(![X]:(~strong(X)<=>(~funny(X)|humble(X))))&
(![X]:(~happy(X)=>(curious(X)<~>humble(X))))&
(![X]:((~funny(X)<~>~kind(X))=>(brave(X)<~>humble(X))))&
(![X]:(brave(X)=>(~patient(X)<~>~tall(X))))&
(((~happy(alice)|~old(alice)))<=>(?[X]:((quiet(X)&~brave(X)))))&
(![X]:(funny(X)<=>(~humble(X)|~calm(X))))&
(![X]:(~kind(X)=>(calm(X)<~>~creative(X))))&
(![X]:((generous(X)&~brave(X))<=>(happy(X)&brave(X))))&
(![X]:((calm(X)|kind(X))=>(~brave(X)&calm(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:(rich(X)<=>~old(X)))&
(((~wise(john)<~>~happy(john)))=>((~calm(alice)&patient(alice))))&
(((~creative(susan)|generous(susan)))<=>(?[X]:((old(X)<~>strong(X)))))&
((?[X]:((wise(X)<~>~brave(X))))<=>((strong(susan)&creative(susan))))&
(![X]:((~old(X)|funny(X))=>(~calm(X)|~old(X))))&
(?[X]:((rich(X)&~strong(X))))&
((~calm(mary)<~>~brave(mary)))&
((~curious(fred)&~tall(fred)))&
((strong(paul)<~>old(paul)))&
(?[X]:((~tall(X)&~funny(X))))&
(?[X]:((old(X)<~>~kind(X)))) | calm(susan) | [] | null | 0 |
If paul is both tall and generous then someone is not creative and vice versa.
Everyone who is quiet or brave is wise.
If someone is both rich and tall then someone is either not quiet or not strong.
Everyone who is not old is kind or creative.
Everyone who is humble or patient is not tall.
If someone is not brave then someone is not tall or funny and vice versa.
Everyone who is generous or not generous is both old and patient.
If someone is calm then someone is not creative and vice versa.
If mary is either curious or not wise then susan is not humble or not funny.
If fred is tall then susan is either kind or not humble and vice versa.
If fred is not tall then lucy is not wise or not strong.
Everyone who is not humble or generous is not funny or not humble and vice versa.
Everyone who is either not humble or not curious is calm.
Everyone who is either funny or old is either calm or curious.
Everyone who is both quiet and not old is both calm and patient.
Everyone who is calm or rich is either not brave or not humble.
Someone is either curious or not kind.
John is either not funny or old.
Someone is funny or not patient.
Alice is creative or patient.
Susan is both creative and not humble.
Someone is either not kind or not tall. | Alice is not wise. | neutral | (((tall(paul)&generous(paul)))<=>(?[X]:(~creative(X))))&
(![X]:((quiet(X)|brave(X))=>wise(X)))&
((?[X]:((rich(X)&tall(X))))=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:(~old(X)=>(kind(X)|creative(X))))&
(![X]:((humble(X)|patient(X))=>~tall(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~tall(X)|funny(X)))))&
(![X]:((generous(X)|~generous(X))=>(old(X)&patient(X))))&
((?[X]:(calm(X)))<=>(?[X]:(~creative(X))))&
(((curious(mary)<~>~wise(mary)))=>((~humble(susan)|~funny(susan))))&
((tall(fred))<=>((kind(susan)<~>~humble(susan))))&
((~tall(fred))=>((~wise(lucy)|~strong(lucy))))&
(![X]:((~humble(X)|generous(X))<=>(~funny(X)|~humble(X))))&
(![X]:((~humble(X)<~>~curious(X))=>calm(X)))&
(![X]:((funny(X)<~>old(X))=>(calm(X)<~>curious(X))))&
(![X]:((quiet(X)&~old(X))=>(calm(X)&patient(X))))&
(![X]:((calm(X)|rich(X))=>(~brave(X)<~>~humble(X))))&
(?[X]:((curious(X)<~>~kind(X))))&
((~funny(john)<~>old(john)))&
(?[X]:((funny(X)|~patient(X))))&
((creative(alice)|patient(alice)))&
((creative(susan)&~humble(susan)))&
(?[X]:((~kind(X)<~>~tall(X)))) | ~wise(alice) | [] | null | 0 |
If someone is not tall then someone is either patient or happy and vice versa.
If someone is both not wise and brave then someone is either strong or not curious and vice versa.
If someone is either not brave or calm then someone is funny or strong and vice versa.
Everyone who is not kind is not happy and vice versa.
Everyone who is either not wise or not old is happy or kind.
Everyone who is creative is both not creative and not happy.
Everyone who is humble or not wise is not curious or strong and vice versa.
Everyone who is not kind or not tall is either not creative or not happy and vice versa.
Everyone who is not patient is either not curious or humble and vice versa.
Everyone who is both tall and not generous is either not brave or brave.
Everyone who is creative is not kind or not patient.
Everyone who is either not funny or creative is both not rich and wise and vice versa.
If someone is both not wise and not calm then someone is humble or not kind and vice versa.
Everyone who is either not brave or quiet is either tall or not happy.
Everyone who is either curious or tall is rich or not strong.
If alice is both rich and not patient then mary is both brave and strong.
Fred is kind or happy.
Someone is not strong or generous.
Someone is not calm.
Someone is not generous or not funny.
Someone is either not happy or not curious.
Paul is both wise and calm.
Someone is either curious or not humble. | Paul is not generous. | neutral | ((?[X]:(~tall(X)))<=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((~wise(X)&brave(X))))<=>(?[X]:((strong(X)<~>~curious(X)))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((funny(X)|strong(X)))))&
(![X]:(~kind(X)<=>~happy(X)))&
(![X]:((~wise(X)<~>~old(X))=>(happy(X)|kind(X))))&
(![X]:(creative(X)=>(~creative(X)&~happy(X))))&
(![X]:((humble(X)|~wise(X))<=>(~curious(X)|strong(X))))&
(![X]:((~kind(X)|~tall(X))<=>(~creative(X)<~>~happy(X))))&
(![X]:(~patient(X)<=>(~curious(X)<~>humble(X))))&
(![X]:((tall(X)&~generous(X))=>(~brave(X)<~>brave(X))))&
(![X]:(creative(X)=>(~kind(X)|~patient(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(~rich(X)&wise(X))))&
((?[X]:((~wise(X)&~calm(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~brave(X)<~>quiet(X))=>(tall(X)<~>~happy(X))))&
(![X]:((curious(X)<~>tall(X))=>(rich(X)|~strong(X))))&
(((rich(alice)&~patient(alice)))=>((brave(mary)&strong(mary))))&
((kind(fred)|happy(fred)))&
(?[X]:((~strong(X)|generous(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~generous(X)|~funny(X))))&
(?[X]:((~happy(X)<~>~curious(X))))&
((wise(paul)&calm(paul)))&
(?[X]:((curious(X)<~>~humble(X)))) | ~generous(paul) | [] | null | 0 |
Everyone who is strong or not creative is generous or not patient and vice versa.
Everyone who is not wise is not quiet or calm.
Everyone who is both humble and funny is rich or not generous and vice versa.
Everyone who is not strong is both not wise and not quiet and vice versa.
Everyone who is either curious or calm is old or creative.
Everyone who is both humble and generous is wise or brave and vice versa.
If susan is rich or curious then paul is kind or humble and vice versa.
If fred is both rich and creative then paul is both brave and not patient and vice versa.
If someone is either not brave or kind then lucy is not wise or quiet and vice versa.
If john is strong then someone is either brave or not humble and vice versa.
If someone is either not tall or humble then someone is not patient or brave and vice versa.
Everyone who is both not curious and funny is brave.
Everyone who is both not quiet and not humble is both not humble and humble.
Everyone who is either generous or happy is not strong or not happy and vice versa.
If alice is not kind or tall then susan is brave or not funny and vice versa.
If lucy is not patient then someone is creative or generous and vice versa.
Someone is either kind or not happy.
Someone is not happy.
Someone is either calm or old.
Someone is either not kind or not humble.
Someone is either brave or strong.
Paul is either calm or strong.
Someone is old.
Susan is both creative and not strong. | Paul is not humble. | contradiction | (![X]:((strong(X)|~creative(X))<=>(generous(X)|~patient(X))))&
(![X]:(~wise(X)=>(~quiet(X)|calm(X))))&
(![X]:((humble(X)&funny(X))<=>(rich(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~wise(X)&~quiet(X))))&
(![X]:((curious(X)<~>calm(X))=>(old(X)|creative(X))))&
(![X]:((humble(X)&generous(X))<=>(wise(X)|brave(X))))&
(((rich(susan)|curious(susan)))<=>((kind(paul)|humble(paul))))&
(((rich(fred)&creative(fred)))<=>((brave(paul)&~patient(paul))))&
((?[X]:((~brave(X)<~>kind(X))))<=>((~wise(lucy)|quiet(lucy))))&
((strong(john))<=>(?[X]:((brave(X)<~>~humble(X)))))&
((?[X]:((~tall(X)<~>humble(X))))<=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:((~curious(X)&funny(X))=>brave(X)))&
(![X]:((~quiet(X)&~humble(X))=>(~humble(X)&humble(X))))&
(![X]:((generous(X)<~>happy(X))<=>(~strong(X)|~happy(X))))&
(((~kind(alice)|tall(alice)))<=>((brave(susan)|~funny(susan))))&
((~patient(lucy))<=>(?[X]:((creative(X)|generous(X)))))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)<~>old(X))))&
(?[X]:((~kind(X)<~>~humble(X))))&
(?[X]:((brave(X)<~>strong(X))))&
((calm(paul)<~>strong(paul)))&
(?[X]:(old(X)))&
((creative(susan)&~strong(susan))) | ~humble(paul) | [
"p1",
"p3",
"p5",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8795384187606889708263386
% SZS output start Proof for 8795384187606889708263386
2. ! [X0] : (~wise(X0) => (calm(X0) | ~quiet(X0))) [input p1]
4. ! [X0] : (~strong(X0) <=> (~quiet(X0) & ~wise(X0))) [input p3]
6. ! [X0] : ((generous(X0) & humble(X0)) <=> (brave(X0) | wise(X0))) [input p5]
13. ! [X0] : ((~humble(X0) & ~quiet(X0)) => (humble(X0) & ~humble(X0))) [input p12]
22. calm(paul) <~> strong(paul) [input p21]
25. ~humble(paul) [input hypothesis]
27. ! [X0] : ((calm(X0) | ~quiet(X0)) | wise(X0)) [ennf transformation 2]
28. ! [X0] : (calm(X0) | ~quiet(X0) | wise(X0)) [flattening 27]
33. ! [X0] : ((humble(X0) & ~humble(X0)) | (humble(X0) | quiet(X0))) [ennf transformation 13]
34. ! [X0] : ((humble(X0) & ~humble(X0)) | humble(X0) | quiet(X0)) [flattening 33]
39. ! [X0] : ((~strong(X0) | (quiet(X0) | wise(X0))) & ((~quiet(X0) & ~wise(X0)) | strong(X0))) [nnf transformation 4]
40. ! [X0] : ((~strong(X0) | quiet(X0) | wise(X0)) & ((~quiet(X0) & ~wise(X0)) | strong(X0))) [flattening 39]
42. ! [X0] : (((generous(X0) & humble(X0)) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | (~generous(X0) | ~humble(X0)))) [nnf transformation 6]
43. ! [X0] : (((generous(X0) & humble(X0)) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | ~generous(X0) | ~humble(X0))) [flattening 42]
84. (~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul)) [nnf transformation 22]
91. ~quiet(X0) | calm(X0) | wise(X0) [cnf transformation 28]
98. ~quiet(X0) | strong(X0) [cnf transformation 40]
103. ~wise(X0) | humble(X0) [cnf transformation 43]
133. humble(X0) | humble(X0) | quiet(X0) [cnf transformation 34]
157. ~strong(paul) | ~calm(paul) [cnf transformation 84]
161. ~humble(paul) [cnf transformation 25]
164. humble(X0) | quiet(X0) [duplicate literal removal 133]
166. 1 <=> humble(paul) [avatar definition]
168. ~humble(paul) <- (~1) [avatar component clause 166]
370. 44 <=> calm(paul) [avatar definition]
372. ~calm(paul) <- (~44) [avatar component clause 370]
374. 45 <=> strong(paul) [avatar definition]
377. ~44 | ~45 [avatar split clause 157,374,370]
379. ~1 [avatar split clause 161,166]
399. quiet(paul) <- (~1) [resolution 164,168]
404. strong(paul) <- (~1) [resolution 399,98]
407. 45 | 1 [avatar split clause 404,166,374]
466. calm(paul) | wise(paul) <- (~1) [resolution 91,399]
469. wise(paul) <- (~1, ~44) [subsumption resolution 466,372]
657. humble(paul) <- (~1, ~44) [resolution 469,103]
659. $false <- (~1, ~44) [subsumption resolution 657,168]
660. 1 | 44 [avatar contradiction clause 659]
661. $false [avatar sat refutation 377,379,407,660]
% SZS output end Proof for 8795384187606889708263386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not calm is not old. Everyone who is both old and rich is both not curious and rich and vice versa. If john is both not patient and strong then someone is not tall. If someone is not quiet then someone is not calm or not old and vice versa. Everyone who is not generous or not calm is either not humble or patient. If mary is happy or not calm then lucy is not kind or not happy. Everyone who is wise or not generous is both generous and not tall and vice versa. Everyone who is not patient is curious. Everyone who is not brave is not curious or not old and vice versa. Everyone who is happy or wise is not calm or kind and vice versa. If someone is not calm then someone is either calm or rich. Everyone who is either patient or not creative is not old and vice versa. Everyone who is either creative or happy is either brave or not kind and vice versa. If someone is both brave and creative then someone is both patient and not old and vice versa. Everyone who is both rich and not happy is rich. Everyone who is funny or not generous is kind and vice versa. Someone is humble. Fred is not kind. Someone is generous or curious. Someone is both strong and not creative. Someone is both funny and patient. Someone is quiet. | Mary is not happy. | neutral | (![X]:((curious(X)&~calm(X))=>~old(X)))&
(![X]:((old(X)&rich(X))<=>(~curious(X)&rich(X))))&
(((~patient(john)&strong(john)))=>(?[X]:(~tall(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~calm(X)|~old(X)))))&
(![X]:((~generous(X)|~calm(X))=>(~humble(X)<~>patient(X))))&
(((happy(mary)|~calm(mary)))=>((~kind(lucy)|~happy(lucy))))&
(![X]:((wise(X)|~generous(X))<=>(generous(X)&~tall(X))))&
(![X]:(~patient(X)=>curious(X)))&
(![X]:(~brave(X)<=>(~curious(X)|~old(X))))&
(![X]:((happy(X)|wise(X))<=>(~calm(X)|kind(X))))&
((?[X]:(~calm(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((patient(X)<~>~creative(X))<=>~old(X)))&
(![X]:((creative(X)<~>happy(X))<=>(brave(X)<~>~kind(X))))&
((?[X]:((brave(X)&creative(X))))<=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((rich(X)&~happy(X))=>rich(X)))&
(![X]:((funny(X)|~generous(X))<=>kind(X)))&
(?[X]:(humble(X)))&
(~kind(fred))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((funny(X)&patient(X))))&
(?[X]:(quiet(X))) | ~happy(mary) | [] | null | 0 |
Everyone who is funny is either not brave or not old and vice versa.
If mary is not wise then john is not kind and vice versa.
If john is both quiet and happy then fred is either wise or generous and vice versa.
Everyone who is both not humble and not generous is both not kind and not patient and vice versa.
Everyone who is tall is both not humble and humble.
If someone is both not strong and strong then lucy is either not creative or funny and vice versa.
Everyone who is rich is patient.
Everyone who is either not tall or tall is either not humble or quiet.
If fred is both happy and funny then lucy is both rich and old and vice versa.
Everyone who is either not kind or not calm is both not generous and quiet and vice versa.
Everyone who is kind or not calm is both not patient and quiet and vice versa.
If susan is not calm then fred is not kind or patient.
If someone is either not patient or curious then alice is both not tall and quiet and vice versa.
Everyone who is either curious or kind is either humble or not creative and vice versa.
If someone is not creative then someone is not calm and vice versa.
If fred is either not wise or not humble then susan is brave and vice versa.
Someone is either not calm or not rich.
Someone is not quiet or calm.
Fred is both humble and not generous.
Susan is both creative and wise.
Someone is humble.
Paul is creative or not patient.
Someone is either not calm or kind.
Alice is either not curious or not calm. | Susan is not calm. | neutral | (![X]:(funny(X)<=>(~brave(X)<~>~old(X))))&
((~wise(mary))<=>(~kind(john)))&
(((quiet(john)&happy(john)))<=>((wise(fred)<~>generous(fred))))&
(![X]:((~humble(X)&~generous(X))<=>(~kind(X)&~patient(X))))&
(![X]:(tall(X)=>(~humble(X)&humble(X))))&
((?[X]:((~strong(X)&strong(X))))<=>((~creative(lucy)<~>funny(lucy))))&
(![X]:(rich(X)=>patient(X)))&
(![X]:((~tall(X)<~>tall(X))=>(~humble(X)<~>quiet(X))))&
(((happy(fred)&funny(fred)))<=>((rich(lucy)&old(lucy))))&
(![X]:((~kind(X)<~>~calm(X))<=>(~generous(X)&quiet(X))))&
(![X]:((kind(X)|~calm(X))<=>(~patient(X)&quiet(X))))&
((~calm(susan))=>((~kind(fred)|patient(fred))))&
((?[X]:((~patient(X)<~>curious(X))))<=>((~tall(alice)&quiet(alice))))&
(![X]:((curious(X)<~>kind(X))<=>(humble(X)<~>~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~calm(X))))&
(((~wise(fred)<~>~humble(fred)))<=>(brave(susan)))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~quiet(X)|calm(X))))&
((humble(fred)&~generous(fred)))&
((creative(susan)&wise(susan)))&
(?[X]:(humble(X)))&
((creative(paul)|~patient(paul)))&
(?[X]:((~calm(X)<~>kind(X))))&
((~curious(alice)<~>~calm(alice))) | ~calm(susan) | [] | null | 0 |
Everyone who is either not calm or not strong is either wise or funny and vice versa. If someone is tall or wise then someone is either happy or not patient and vice versa. If alice is happy or wise then john is either wise or not funny. Everyone who is not strong is curious or not tall. If someone is not quiet then john is not wise or not creative. If someone is not quiet or happy then someone is not kind. If lucy is both curious and not rich then john is either happy or quiet. If someone is either not patient or not rich then someone is both strong and not generous and vice versa. If susan is either old or not funny then john is both patient and wise and vice versa. If someone is both curious and not calm then alice is creative or rich. If someone is not strong then someone is both creative and not happy. Everyone who is creative or not brave is wise. If someone is not curious then someone is either kind or not generous. Everyone who is both not generous and brave is generous or wise and vice versa. Everyone who is not strong is not creative. If someone is not quiet or calm then someone is strong or not rich. John is tall. Fred is either creative or not funny. Lucy is both not funny and quiet. Mary is creative or not patient. Someone is both curious and not quiet. Someone is either not old or not humble. Someone is either patient or not quiet. Alice is not curious or tall. | John is not generous. | entailment | (![X]:((~calm(X)<~>~strong(X))<=>(wise(X)<~>funny(X))))&
((?[X]:((tall(X)|wise(X))))<=>(?[X]:((happy(X)<~>~patient(X)))))&
(((happy(alice)|wise(alice)))=>((wise(john)<~>~funny(john))))&
(![X]:(~strong(X)=>(curious(X)|~tall(X))))&
((?[X]:(~quiet(X)))=>((~wise(john)|~creative(john))))&
((?[X]:((~quiet(X)|happy(X))))=>(?[X]:(~kind(X))))&
(((curious(lucy)&~rich(lucy)))=>((happy(john)<~>quiet(john))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>(?[X]:((strong(X)&~generous(X)))))&
(((old(susan)<~>~funny(susan)))<=>((patient(john)&wise(john))))&
((?[X]:((curious(X)&~calm(X))))=>((creative(alice)|rich(alice))))&
((?[X]:(~strong(X)))=>(?[X]:((creative(X)&~happy(X)))))&
(![X]:((creative(X)|~brave(X))=>wise(X)))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)<~>~generous(X)))))&
(![X]:((~generous(X)&brave(X))<=>(generous(X)|wise(X))))&
(![X]:(~strong(X)=>~creative(X)))&
((?[X]:((~quiet(X)|calm(X))))=>(?[X]:((strong(X)|~rich(X)))))&
(tall(john))&
((creative(fred)<~>~funny(fred)))&
((~funny(lucy)&quiet(lucy)))&
((creative(mary)|~patient(mary)))&
(?[X]:((curious(X)&~quiet(X))))&
(?[X]:((~old(X)<~>~humble(X))))&
(?[X]:((patient(X)<~>~quiet(X))))&
((~curious(alice)|tall(alice))) | ~generous(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 362107436552450395869276
% SZS output start Proof for 362107436552450395869276
14. ! [X0] : ((brave(X0) & ~generous(X0)) <=> (wise(X0) | generous(X0))) [input p13]
25. generous(john) [input hypothesis]
72. ! [X0] : (((brave(X0) & ~generous(X0)) | (~wise(X0) & ~generous(X0))) & ((wise(X0) | generous(X0)) | (~brave(X0) | generous(X0)))) [nnf transformation 14]
73. ! [X0] : (((brave(X0) & ~generous(X0)) | (~wise(X0) & ~generous(X0))) & (wise(X0) | generous(X0) | ~brave(X0) | generous(X0))) [flattening 72]
130. ~generous(X0) | ~generous(X0) [cnf transformation 73]
150. generous(john) [cnf transformation 25]
152. ~generous(X0) [duplicate literal removal 130]
393. $false [subsumption resolution 150,152]
% SZS output end Proof for 362107436552450395869276
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or kind is both creative and calm and vice versa.
If someone is both wise and calm then someone is not calm.
If alice is both kind and not wise then alice is kind or not brave and vice versa.
Everyone who is not kind or kind is either calm or tall.
Everyone who is both creative and strong is quiet or patient and vice versa.
Everyone who is either quiet or humble is not rich or patient and vice versa.
Everyone who is both not tall and funny is not old or curious and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Someone is humble or not brave.
Someone is not kind.
Susan is not funny or funny.
Someone is both not tall and not wise.
Susan is either not generous or rich.
Someone is either not calm or not quiet. | Fred is not kind. | entailment | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&calm(X))))=>(?[X]:(~calm(X))))&
(((kind(alice)&~wise(alice)))<=>((kind(alice)|~brave(alice))))&
(![X]:((~kind(X)|kind(X))=>(calm(X)<~>tall(X))))&
(![X]:((creative(X)&strong(X))<=>(quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~rich(X)|patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
(?[X]:((humble(X)|~brave(X))))&
(?[X]:(~kind(X)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>~quiet(X)))) | ~kind(fred) | [
"p0",
"p4",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5340059039755868402636127
% SZS output start Proof for 5340059039755868402636127
1. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> (calm(X0) & creative(X0))) [input p0]
5. ! [X0] : ((strong(X0) & creative(X0)) <=> (patient(X0) | quiet(X0))) [input p4]
8. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p7]
9. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p8]
12. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p11]
22. kind(fred) [input hypothesis]
27. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 12]
28. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 1]
29. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [flattening 28]
36. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 5]
37. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~strong(X0) | ~creative(X0))) [flattening 36]
42. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 8]
43. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 42]
44. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 9]
45. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 44]
72. ~kind(X0) | ~wise(X0) | calm(X0) [cnf transformation 29]
89. ~patient(X0) | strong(X0) [cnf transformation 37]
102. ~calm(X0) | patient(X0) | strong(X0) [cnf transformation 43]
104. brave(X0) | patient(X0) | strong(X0) [cnf transformation 43]
108. ~strong(X0) | ~kind(X0) [cnf transformation 45]
109. ~strong(X0) | calm(X0) [cnf transformation 45]
119. ~brave(X0) | wise(X0) [cnf transformation 27]
145. kind(fred) [cnf transformation 22]
173. strong(X0) | brave(X0) [subsumption resolution 104,89]
175. ~calm(X0) | strong(X0) [subsumption resolution 102,89]
272. brave(X0) | calm(X0) [resolution 173,109]
315. ~wise(fred) | calm(fred) [resolution 72,145]
518. calm(X2) | wise(X2) [resolution 272,119]
615. calm(fred) [subsumption resolution 315,518]
618. strong(fred) [resolution 615,175]
647. ~kind(fred) [resolution 618,108]
658. $false [subsumption resolution 647,145]
% SZS output end Proof for 5340059039755868402636127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not funny or not generous then someone is not strong. Everyone who is either generous or not generous is both not humble and not kind. If someone is both not wise and not curious then mary is old or not tall and vice versa. Everyone who is both not kind and not curious is brave or strong and vice versa. Everyone who is not calm is either tall or happy and vice versa. Everyone who is both brave and not humble is not old or wise and vice versa. If paul is happy then susan is strong. Everyone who is either not creative or not rich is either not happy or kind and vice versa. If john is either not wise or not calm then someone is either not patient or creative and vice versa. If lucy is either calm or not kind then lucy is both kind and strong and vice versa. If paul is kind then john is either not old or not humble. Everyone who is strong is not funny or happy. If fred is not funny or quiet then someone is both not curious and tall and vice versa. Everyone who is tall is both happy and not wise. Everyone who is not creative or not kind is either not quiet or not curious. If someone is both not old and not curious then someone is either not strong or not funny. Susan is funny. Susan is patient or humble. Someone is both not funny and quiet. Paul is not quiet. Alice is either funny or quiet. Someone is tall or quiet. Someone is brave. | Lucy is not humble. | entailment | (((~funny(fred)|~generous(fred)))=>(?[X]:(~strong(X))))&
(![X]:((generous(X)<~>~generous(X))=>(~humble(X)&~kind(X))))&
((?[X]:((~wise(X)&~curious(X))))<=>((old(mary)|~tall(mary))))&
(![X]:((~kind(X)&~curious(X))<=>(brave(X)|strong(X))))&
(![X]:(~calm(X)<=>(tall(X)<~>happy(X))))&
(![X]:((brave(X)&~humble(X))<=>(~old(X)|wise(X))))&
((happy(paul))=>(strong(susan)))&
(![X]:((~creative(X)<~>~rich(X))<=>(~happy(X)<~>kind(X))))&
(((~wise(john)<~>~calm(john)))<=>(?[X]:((~patient(X)<~>creative(X)))))&
(((calm(lucy)<~>~kind(lucy)))<=>((kind(lucy)&strong(lucy))))&
((kind(paul))=>((~old(john)<~>~humble(john))))&
(![X]:(strong(X)=>(~funny(X)|happy(X))))&
(((~funny(fred)|quiet(fred)))<=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:(tall(X)=>(happy(X)&~wise(X))))&
(![X]:((~creative(X)|~kind(X))=>(~quiet(X)<~>~curious(X))))&
((?[X]:((~old(X)&~curious(X))))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(funny(susan))&
((patient(susan)|humble(susan)))&
(?[X]:((~funny(X)&quiet(X))))&
(~quiet(paul))&
((funny(alice)<~>quiet(alice)))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:(brave(X))) | ~humble(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1145391767665722133534583
% SZS output start Proof for 1145391767665722133534583
2. ! [X0] : ((generous(X0) <~> ~generous(X0)) => (~kind(X0) & ~humble(X0))) [input p1]
24. humble(lucy) [input hypothesis]
27. ! [X0] : ((~kind(X0) & ~humble(X0)) | (generous(X0) <=> ~generous(X0))) [ennf transformation 2]
37. ! [X0] : ((~kind(X0) & ~humble(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) [nnf transformation 27]
75. ~humble(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 37]
76. ~humble(X0) | generous(X0) | generous(X0) [cnf transformation 37]
146. humble(lucy) [cnf transformation 24]
149. ~humble(X0) | ~generous(X0) [duplicate literal removal 75]
150. ~humble(X0) | generous(X0) [duplicate literal removal 76]
168. ~humble(X0) [subsumption resolution 149,150]
305. $false [subsumption resolution 146,168]
% SZS output end Proof for 1145391767665722133534583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not happy is not calm and vice versa.
If someone is not curious then mary is either not happy or not rich and vice versa.
If someone is either quiet or not calm then someone is both not old and funny.
Everyone who is creative or patient is either not old or happy and vice versa.
Everyone who is both strong and quiet is either not quiet or funny and vice versa.
If alice is not happy or not humble then fred is either wise or generous.
If someone is either not rich or not generous then someone is both curious and not calm and vice versa.
Everyone who is both patient and not wise is either creative or not happy.
Everyone who is both humble and old is not strong.
Everyone who is kind or rich is either not calm or curious.
Everyone who is both humble and generous is not humble.
Everyone who is both not patient and not quiet is not patient or wise and vice versa.
Everyone who is happy or not strong is either not wise or curious and vice versa.
Everyone who is not quiet is either not patient or kind and vice versa.
Everyone who is either happy or generous is not kind or kind.
Everyone who is patient or humble is both not kind and tall.
Someone is wise or brave.
Mary is either funny or not patient.
Alice is either rich or not brave.
Alice is both not patient and not wise.
Someone is happy or not patient.
Fred is humble or funny.
Someone is either not old or not wise. | Alice is not happy. | neutral | (![X]:((generous(X)&~happy(X))<=>~calm(X)))&
((?[X]:(~curious(X)))<=>((~happy(mary)<~>~rich(mary))))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((creative(X)|patient(X))<=>(~old(X)<~>happy(X))))&
(![X]:((strong(X)&quiet(X))<=>(~quiet(X)<~>funny(X))))&
(((~happy(alice)|~humble(alice)))=>((wise(fred)<~>generous(fred))))&
((?[X]:((~rich(X)<~>~generous(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((patient(X)&~wise(X))=>(creative(X)<~>~happy(X))))&
(![X]:((humble(X)&old(X))=>~strong(X)))&
(![X]:((kind(X)|rich(X))=>(~calm(X)<~>curious(X))))&
(![X]:((humble(X)&generous(X))=>~humble(X)))&
(![X]:((~patient(X)&~quiet(X))<=>(~patient(X)|wise(X))))&
(![X]:((happy(X)|~strong(X))<=>(~wise(X)<~>curious(X))))&
(![X]:(~quiet(X)<=>(~patient(X)<~>kind(X))))&
(![X]:((happy(X)<~>generous(X))=>(~kind(X)|kind(X))))&
(![X]:((patient(X)|humble(X))=>(~kind(X)&tall(X))))&
(?[X]:((wise(X)|brave(X))))&
((funny(mary)<~>~patient(mary)))&
((rich(alice)<~>~brave(alice)))&
((~patient(alice)&~wise(alice)))&
(?[X]:((happy(X)|~patient(X))))&
((humble(fred)|funny(fred)))&
(?[X]:((~old(X)<~>~wise(X)))) | ~happy(alice) | [] | null | 0 |
Everyone who is either not patient or not wise is both wise and calm and vice versa.
If john is rich then someone is not tall and vice versa.
If someone is both tall and not rich then lucy is tall or not brave.
Everyone who is both not calm and wise is both not strong and curious and vice versa.
If alice is both strong and old then susan is calm.
Everyone who is both generous and not calm is not brave.
Everyone who is either not kind or tall is either not strong or tall and vice versa.
If someone is either tall or calm then john is either not creative or wise.
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.
Fred is not creative or not old.
Someone is not humble.
Someone is not patient or tall.
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. | Susan is not kind. | contradiction | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&calm(X))))&
((rich(john))<=>(?[X]:(~tall(X))))&
((?[X]:((tall(X)&~rich(X))))=>((tall(lucy)|~brave(lucy))))&
(![X]:((~calm(X)&wise(X))<=>(~strong(X)&curious(X))))&
(((strong(alice)&old(alice)))=>(calm(susan)))&
(![X]:((generous(X)&~calm(X))=>~brave(X)))&
(![X]:((~kind(X)<~>tall(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~creative(john)<~>wise(john))))&
(((~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))))&
((~creative(fred)|~old(fred)))&
(?[X]:(~humble(X)))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X)))) | ~kind(susan) | [
"p0",
"p6",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 780459585332834736338490
% SZS output start Proof for 780459585332834736338490
1. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> (calm(X0) & wise(X0))) [input p0]
7. ! [X0] : ((~kind(X0) <~> tall(X0)) <=> (~strong(X0) <~> tall(X0))) [input p6]
10. ! [X0] : ((patient(X0) <~> tall(X0)) <=> (~tall(X0) | strong(X0))) [input p9]
14. ! [X0] : ((calm(X0) <~> wise(X0)) => (~strong(X0) & ~patient(X0))) [input p13]
25. ~kind(susan) [input hypothesis]
40. ! [X0] : ((~strong(X0) & ~patient(X0)) | (calm(X0) <=> wise(X0))) [ennf transformation 14]
43. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 1]
44. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [flattening 43]
51. ! [X0] : ((((~tall(X0) | kind(X0)) & (tall(X0) | ~kind(X0))) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0))))) [nnf transformation 7]
53. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [nnf transformation 10]
54. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [flattening 53]
56. ! [X0] : ((~strong(X0) & ~patient(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) [nnf transformation 40]
76. wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 44]
78. ~patient(X0) | calm(X0) | wise(X0) [cnf transformation 44]
79. ~wise(X0) | ~patient(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 44]
89. tall(X0) | ~strong(X0) | tall(X0) | kind(X0) [cnf transformation 51]
96. ~tall(X0) | kind(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 51]
104. ~tall(X0) | strong(X0) | patient(X0) | ~tall(X0) [cnf transformation 54]
106. tall(X0) | patient(X0) | tall(X0) [cnf transformation 54]
115. ~patient(X0) | calm(X0) | ~wise(X0) [cnf transformation 56]
134. ~kind(susan) [cnf transformation 25]
135. ~tall(X0) | strong(X0) | patient(X0) [duplicate literal removal 104]
136. tall(X0) | patient(X0) [duplicate literal removal 106]
137. tall(X0) | ~strong(X0) | kind(X0) [duplicate literal removal 89]
140. ~strong(X0) | kind(X0) | ~tall(X0) [duplicate literal removal 96]
141. ~patient(X0) | wise(X0) [duplicate literal removal 76]
142. ~calm(X0) | ~patient(X0) | ~wise(X0) [duplicate literal removal 79]
169. ~strong(X0) | kind(X0) [subsumption resolution 137,140]
206. strong(X0) | patient(X0) [subsumption resolution 135,136]
207. ~patient(X0) | calm(X0) [subsumption resolution 115,78]
262. kind(X0) | patient(X0) [resolution 206,169]
265. patient(susan) [resolution 262,134]
270. calm(susan) [resolution 265,207]
271. wise(susan) [resolution 265,141]
273. 26 <=> wise(susan) [avatar definition]
275. wise(susan) <- (26) [avatar component clause 273]
277. 27 <=> calm(susan) [avatar definition]
279. calm(susan) <- (27) [avatar component clause 277]
281. 27 [avatar split clause 270,277]
282. 26 [avatar split clause 271,273]
407. ~patient(susan) | ~wise(susan) <- (27) [resolution 142,279]
411. ~wise(susan) <- (27) [subsumption resolution 407,265]
412. $false <- (26, 27) [subsumption resolution 411,275]
413. ~26 | ~27 [avatar contradiction clause 412]
414. $false [avatar sat refutation 281,282,413]
% SZS output end Proof for 780459585332834736338490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or brave is not happy or not strong.
If someone is either brave or creative then someone is either brave or rich.
Everyone who is not funny is either tall or not creative and vice versa.
Everyone who is quiet is old.
If someone is not funny or generous then someone is both not creative and quiet and vice versa.
If paul is either humble or curious then someone is both funny and not quiet and vice versa.
If alice is both kind and not strong then someone is either patient or not creative and vice versa.
If someone is both happy and curious then someone is not creative or not strong.
If someone is either not patient or not brave then lucy is not wise or not generous and vice versa.
Everyone who is tall is tall or happy.
If someone is both not wise and tall then someone is not tall or not strong.
Everyone who is not funny is not creative or brave.
If lucy is wise then john is wise.
If someone is either patient or calm then someone is both not humble and not brave.
If someone is not kind then alice is either funny or strong and vice versa.
Everyone who is either calm or not humble is not strong.
Susan is not strong.
Alice is either not creative or not wise.
Lucy is not strong.
Alice is brave.
Paul is not old.
Someone is calm.
John is not brave. | Lucy is strong. | contradiction | (![X]:((~creative(X)<~>brave(X))=>(~happy(X)|~strong(X))))&
((?[X]:((brave(X)<~>creative(X))))=>(?[X]:((brave(X)<~>rich(X)))))&
(![X]:(~funny(X)<=>(tall(X)<~>~creative(X))))&
(![X]:(quiet(X)=>old(X)))&
((?[X]:((~funny(X)|generous(X))))<=>(?[X]:((~creative(X)&quiet(X)))))&
(((humble(paul)<~>curious(paul)))<=>(?[X]:((funny(X)&~quiet(X)))))&
(((kind(alice)&~strong(alice)))<=>(?[X]:((patient(X)<~>~creative(X)))))&
((?[X]:((happy(X)&curious(X))))=>(?[X]:((~creative(X)|~strong(X)))))&
((?[X]:((~patient(X)<~>~brave(X))))<=>((~wise(lucy)|~generous(lucy))))&
(![X]:(tall(X)=>(tall(X)|happy(X))))&
((?[X]:((~wise(X)&tall(X))))=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:(~funny(X)=>(~creative(X)|brave(X))))&
((wise(lucy))=>(wise(john)))&
((?[X]:((patient(X)<~>calm(X))))=>(?[X]:((~humble(X)&~brave(X)))))&
((?[X]:(~kind(X)))<=>((funny(alice)<~>strong(alice))))&
(![X]:((calm(X)<~>~humble(X))=>~strong(X)))&
(~strong(susan))&
((~creative(alice)<~>~wise(alice)))&
(~strong(lucy))&
(brave(alice))&
(~old(paul))&
(?[X]:(calm(X)))&
(~brave(john)) | strong(lucy) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7612134665467055941776606
% SZS output start Proof for 7612134665467055941776606
19. ~strong(lucy) [input p18]
24. strong(lucy) [input hypothesis]
138. ~strong(lucy) [cnf transformation 19]
143. strong(lucy) [cnf transformation 24]
345. $false [subsumption resolution 143,138]
% SZS output end Proof for 7612134665467055941776606
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or patient then lucy is both old and not curious and vice versa.
Everyone who is both quiet and not patient is not calm.
If someone is either humble or not funny then someone is both old and not kind and vice versa.
If mary is either not humble or quiet then someone is either not rich or not creative.
Everyone who is either strong or not curious is curious or old and vice versa.
Everyone who is brave or not old is either quiet or not rich.
Everyone who is either not humble or calm is tall or wise and vice versa.
Everyone who is either not patient or not kind is not wise and vice versa.
Everyone who is not brave or not generous is both patient and strong.
If someone is old or wise then fred is either not old or not creative and vice versa.
Everyone who is either not kind or brave is not tall or not brave.
If lucy is both not quiet and generous then lucy is both not patient and not wise.
Everyone who is either tall or wise is not patient.
If alice is creative or wise then lucy is both happy and tall and vice versa.
If lucy is either not wise or kind then someone is either not tall or not quiet.
If john is not tall or kind then lucy is both not tall and not old.
Someone is either not calm or not quiet.
John is either not brave or curious.
Someone is generous or not wise.
Someone is rich or not humble.
Someone is either creative or not creative.
Mary is not creative.
Someone is not generous or not happy.
Someone is not humble or quiet. | Lucy is not curious. | neutral | ((?[X]:((rich(X)|patient(X))))<=>((old(lucy)&~curious(lucy))))&
(![X]:((quiet(X)&~patient(X))=>~calm(X)))&
((?[X]:((humble(X)<~>~funny(X))))<=>(?[X]:((old(X)&~kind(X)))))&
(((~humble(mary)<~>quiet(mary)))=>(?[X]:((~rich(X)<~>~creative(X)))))&
(![X]:((strong(X)<~>~curious(X))<=>(curious(X)|old(X))))&
(![X]:((brave(X)|~old(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(tall(X)|wise(X))))&
(![X]:((~patient(X)<~>~kind(X))<=>~wise(X)))&
(![X]:((~brave(X)|~generous(X))=>(patient(X)&strong(X))))&
((?[X]:((old(X)|wise(X))))<=>((~old(fred)<~>~creative(fred))))&
(![X]:((~kind(X)<~>brave(X))=>(~tall(X)|~brave(X))))&
(((~quiet(lucy)&generous(lucy)))=>((~patient(lucy)&~wise(lucy))))&
(![X]:((tall(X)<~>wise(X))=>~patient(X)))&
(((creative(alice)|wise(alice)))<=>((happy(lucy)&tall(lucy))))&
(((~wise(lucy)<~>kind(lucy)))=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(((~tall(john)|kind(john)))=>((~tall(lucy)&~old(lucy))))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((~brave(john)<~>curious(john)))&
(?[X]:((generous(X)|~wise(X))))&
(?[X]:((rich(X)|~humble(X))))&
(?[X]:((creative(X)<~>~creative(X))))&
(~creative(mary))&
(?[X]:((~generous(X)|~happy(X))))&
(?[X]:((~humble(X)|quiet(X)))) | ~curious(lucy) | [] | null | 0 |
If someone is both not patient and not calm then susan is either funny or kind and vice versa.
Everyone who is either not generous or not old is tall and vice versa.
Everyone who is not rich is either strong or wise and vice versa.
Everyone who is either not calm or not creative is brave or funny and vice versa.
If someone is either happy or not curious then someone is both not brave and strong.
Everyone who is both not creative and quiet is not tall and vice versa.
If lucy is not patient then susan is both quiet and creative.
Everyone who is not humble or calm is not tall and vice versa.
Everyone who is not curious is quiet or generous and vice versa.
If fred is wise or not happy then lucy is humble or funny.
If lucy is both not creative and not happy then lucy is not brave and vice versa.
If someone is not strong then lucy is not tall.
Everyone who is either not patient or calm is both humble and not old and vice versa.
Everyone who is calm is strong.
Everyone who is not happy or not curious is both wise and kind and vice versa.
If fred is generous or quiet then someone is happy or patient.
Someone is not creative or not calm.
Someone is creative or curious.
Someone is not humble or not calm.
Someone is either strong or not creative.
Fred is generous or strong.
Someone is either not quiet or not old.
Fred is both not strong and not funny.
John is not wise or calm. | Lucy is wise. | entailment | ((?[X]:((~patient(X)&~calm(X))))<=>((funny(susan)<~>kind(susan))))&
(![X]:((~generous(X)<~>~old(X))<=>tall(X)))&
(![X]:(~rich(X)<=>(strong(X)<~>wise(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(brave(X)|funny(X))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:((~creative(X)&quiet(X))<=>~tall(X)))&
((~patient(lucy))=>((quiet(susan)&creative(susan))))&
(![X]:((~humble(X)|calm(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>(quiet(X)|generous(X))))&
(((wise(fred)|~happy(fred)))=>((humble(lucy)|funny(lucy))))&
(((~creative(lucy)&~happy(lucy)))<=>(~brave(lucy)))&
((?[X]:(~strong(X)))=>(~tall(lucy)))&
(![X]:((~patient(X)<~>calm(X))<=>(humble(X)&~old(X))))&
(![X]:(calm(X)=>strong(X)))&
(![X]:((~happy(X)|~curious(X))<=>(wise(X)&kind(X))))&
(((generous(fred)|quiet(fred)))=>(?[X]:((happy(X)|patient(X)))))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:((creative(X)|curious(X))))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((strong(X)<~>~creative(X))))&
((generous(fred)|strong(fred)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~strong(fred)&~funny(fred)))&
((~wise(john)|calm(john))) | wise(lucy) | [
"p5",
"p8",
"p11",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5888797482439434987950089
% SZS output start Proof for 5888797482439434987950089
6. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> ~tall(X0)) [input p5]
9. ! [X0] : (~curious(X0) <=> (generous(X0) | quiet(X0))) [input p8]
12. ? [X0] : ~strong(X0) => ~tall(lucy) [input p11]
15. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (kind(X0) & wise(X0))) [input p14]
23. ~funny(fred) & ~strong(fred) [input p22]
25. ~wise(lucy) [input hypothesis]
31. ~tall(lucy) | ! [X0] : strong(X0) [ennf transformation 12]
45. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | (~quiet(X0) | creative(X0)))) [nnf transformation 6]
46. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | ~quiet(X0) | creative(X0))) [flattening 45]
49. ! [X0] : ((~curious(X0) | (~generous(X0) & ~quiet(X0))) & ((generous(X0) | quiet(X0)) | curious(X0))) [nnf transformation 9]
50. ! [X0] : ((~curious(X0) | (~generous(X0) & ~quiet(X0))) & (generous(X0) | quiet(X0) | curious(X0))) [flattening 49]
55. ! [X0] : (((~curious(X0) | ~happy(X0)) | (~kind(X0) | ~wise(X0))) & ((kind(X0) & wise(X0)) | (curious(X0) & happy(X0)))) [nnf transformation 15]
56. ! [X0] : ((~curious(X0) | ~happy(X0) | ~kind(X0) | ~wise(X0)) & ((kind(X0) & wise(X0)) | (curious(X0) & happy(X0)))) [flattening 55]
93. quiet(X0) | tall(X0) [cnf transformation 46]
100. ~quiet(X0) | ~curious(X0) [cnf transformation 50]
107. ~tall(lucy) | strong(X0) [cnf transformation 31]
116. curious(X0) | wise(X0) [cnf transformation 56]
130. ~strong(fred) [cnf transformation 23]
133. ~wise(lucy) [cnf transformation 25]
225. 20 <=> ! [X0] : strong(X0) [avatar definition]
226. strong(X0) <- (20) [avatar component clause 225]
228. 21 <=> tall(lucy) [avatar definition]
231. 20 | ~21 [avatar split clause 107,228,225]
288. 34 <=> strong(fred) [avatar definition]
289. ~strong(fred) <- (~34) [avatar component clause 288]
302. ~34 [avatar split clause 130,288]
316. ~curious(X0) | tall(X0) [resolution 100,93]
325. wise(X1) | tall(X1) [resolution 316,116]
530. tall(lucy) [resolution 325,133]
534. 21 [avatar split clause 530,228]
536. $false <- (20, ~34) [resolution 226,289]
537. ~20 | 34 [avatar contradiction clause 536]
539. $false [avatar sat refutation 231,302,534,537]
% SZS output end Proof for 5888797482439434987950089
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or wise is either not curious or quiet and vice versa.
If someone is not old or not calm then someone is both curious and tall and vice versa.
Everyone who is creative or rich is either calm or tall and vice versa.
Everyone who is both not rich and curious is both patient and tall and vice versa.
If lucy is not tall or brave then someone is either not creative or not rich.
If someone is either not funny or happy then paul is both strong and not generous.
If mary is not creative then someone is not rich or kind.
If susan is either quiet or calm then paul is generous or not brave.
Everyone who is either not rich or not wise is both not rich and not wise and vice versa.
If lucy is curious or happy then fred is either old or not curious.
Everyone who is either quiet or not brave is not strong and vice versa.
If someone is either not humble or not generous then paul is both not quiet and generous and vice versa.
If john is either calm or not tall then alice is both not happy and not generous and vice versa.
If lucy is calm or funny then someone is either not curious or not creative and vice versa.
If someone is both tall and quiet then someone is both not brave and not creative.
Everyone who is either not tall or tall is happy or not calm and vice versa.
Someone is either not tall or not brave.
Someone is either not quiet or not calm.
Someone is either not funny or calm.
Mary is not tall.
Someone is both curious and not tall. | Lucy is curious. | neutral | (![X]:((~calm(X)<~>wise(X))<=>(~curious(X)<~>quiet(X))))&
((?[X]:((~old(X)|~calm(X))))<=>(?[X]:((curious(X)&tall(X)))))&
(![X]:((creative(X)|rich(X))<=>(calm(X)<~>tall(X))))&
(![X]:((~rich(X)&curious(X))<=>(patient(X)&tall(X))))&
(((~tall(lucy)|brave(lucy)))=>(?[X]:((~creative(X)<~>~rich(X)))))&
((?[X]:((~funny(X)<~>happy(X))))=>((strong(paul)&~generous(paul))))&
((~creative(mary))=>(?[X]:((~rich(X)|kind(X)))))&
(((quiet(susan)<~>calm(susan)))=>((generous(paul)|~brave(paul))))&
(![X]:((~rich(X)<~>~wise(X))<=>(~rich(X)&~wise(X))))&
(((curious(lucy)|happy(lucy)))=>((old(fred)<~>~curious(fred))))&
(![X]:((quiet(X)<~>~brave(X))<=>~strong(X)))&
((?[X]:((~humble(X)<~>~generous(X))))<=>((~quiet(paul)&generous(paul))))&
(((calm(john)<~>~tall(john)))<=>((~happy(alice)&~generous(alice))))&
(((calm(lucy)|funny(lucy)))<=>(?[X]:((~curious(X)<~>~creative(X)))))&
((?[X]:((tall(X)&quiet(X))))=>(?[X]:((~brave(X)&~creative(X)))))&
(![X]:((~tall(X)<~>tall(X))<=>(happy(X)|~calm(X))))&
(?[X]:((~tall(X)<~>~brave(X))))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
(~tall(mary))&
(?[X]:((curious(X)&~tall(X)))) | curious(lucy) | [] | null | 0 |
If someone is not tall then someone is not patient and vice versa.
Everyone who is not happy is both not humble and not rich.
If paul is strong then lucy is kind and vice versa.
Everyone who is not generous or not creative is not funny.
If someone is both curious and not generous then mary is not happy or brave.
Everyone who is not rich or not funny is happy.
If someone is not patient or wise then someone is not calm.
Everyone who is brave is not curious or not tall.
If mary is not wise or not happy then someone is not funny and vice versa.
Everyone who is not rich is curious or quiet and vice versa.
If fred is both not calm and tall then susan is either not funny or not happy and vice versa.
If mary is either brave or not rich then someone is not rich or patient.
If someone is either not happy or brave then someone is either kind or generous.
Everyone who is both curious and humble is either creative or happy and vice versa.
Everyone who is old is either wise or happy.
Everyone who is both tall and not quiet is both not wise and not patient and vice versa.
Someone is not creative.
Someone is creative.
Susan is both funny and not wise.
Alice is either not curious or not strong.
Lucy is not tall.
Someone is both not brave and not old.
Mary is both humble and not brave. | Fred is happy. | entailment | ((?[X]:(~tall(X)))<=>(?[X]:(~patient(X))))&
(![X]:(~happy(X)=>(~humble(X)&~rich(X))))&
((strong(paul))<=>(kind(lucy)))&
(![X]:((~generous(X)|~creative(X))=>~funny(X)))&
((?[X]:((curious(X)&~generous(X))))=>((~happy(mary)|brave(mary))))&
(![X]:((~rich(X)|~funny(X))=>happy(X)))&
((?[X]:((~patient(X)|wise(X))))=>(?[X]:(~calm(X))))&
(![X]:(brave(X)=>(~curious(X)|~tall(X))))&
(((~wise(mary)|~happy(mary)))<=>(?[X]:(~funny(X))))&
(![X]:(~rich(X)<=>(curious(X)|quiet(X))))&
(((~calm(fred)&tall(fred)))<=>((~funny(susan)<~>~happy(susan))))&
(((brave(mary)<~>~rich(mary)))=>(?[X]:((~rich(X)|patient(X)))))&
((?[X]:((~happy(X)<~>brave(X))))=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:((curious(X)&humble(X))<=>(creative(X)<~>happy(X))))&
(![X]:(old(X)=>(wise(X)<~>happy(X))))&
(![X]:((tall(X)&~quiet(X))<=>(~wise(X)&~patient(X))))&
(?[X]:(~creative(X)))&
(?[X]:(creative(X)))&
((funny(susan)&~wise(susan)))&
((~curious(alice)<~>~strong(alice)))&
(~tall(lucy))&
(?[X]:((~brave(X)&~old(X))))&
((humble(mary)&~brave(mary))) | happy(fred) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 479864596849603027425325
% SZS output start Proof for 479864596849603027425325
2. ! [X0] : (~happy(X0) => (~rich(X0) & ~humble(X0))) [input p1]
6. ! [X0] : ((~funny(X0) | ~rich(X0)) => happy(X0)) [input p5]
24. ~happy(fred) [input hypothesis]
30. ! [X0] : ((~rich(X0) & ~humble(X0)) | happy(X0)) [ennf transformation 2]
34. ! [X0] : (happy(X0) | (funny(X0) & rich(X0))) [ennf transformation 6]
79. ~rich(X0) | happy(X0) [cnf transformation 30]
85. happy(X0) | rich(X0) [cnf transformation 34]
128. ~happy(fred) [cnf transformation 24]
167. happy(X0) [subsumption resolution 85,79]
253. $false [subsumption resolution 128,167]
% SZS output end Proof for 479864596849603027425325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and generous is creative or quiet and vice versa.
If someone is either not brave or not curious then mary is both not funny and happy and vice versa.
If lucy is either brave or humble then someone is both strong and not curious and vice versa.
If susan is both not tall and not curious then lucy is kind and vice versa.
If lucy is either calm or not patient then someone is both not generous and wise and vice versa.
Everyone who is kind or generous is both not calm and funny.
If someone is wise then someone is not strong and vice versa.
Everyone who is either kind or old is not humble or strong.
Everyone who is humble is both not kind and brave and vice versa.
If someone is both not wise and generous then john is either not old or not happy.
If lucy is rich then someone is both not curious and happy and vice versa.
Everyone who is calm is either wise or not funny.
Everyone who is both not patient and not wise is not tall or patient and vice versa.
Everyone who is both not rich and not tall is either not generous or not quiet.
Everyone who is quiet is not strong.
Everyone who is kind is not patient and vice versa.
Mary is happy.
Someone is both not brave and quiet.
Paul is not old or not kind.
Someone is either patient or not calm.
Someone is old or humble.
Someone is not calm or not brave.
Alice is not calm. | Alice is generous. | neutral | (![X]:((tall(X)&generous(X))<=>(creative(X)|quiet(X))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>((~funny(mary)&happy(mary))))&
(((brave(lucy)<~>humble(lucy)))<=>(?[X]:((strong(X)&~curious(X)))))&
(((~tall(susan)&~curious(susan)))<=>(kind(lucy)))&
(((calm(lucy)<~>~patient(lucy)))<=>(?[X]:((~generous(X)&wise(X)))))&
(![X]:((kind(X)|generous(X))=>(~calm(X)&funny(X))))&
((?[X]:(wise(X)))<=>(?[X]:(~strong(X))))&
(![X]:((kind(X)<~>old(X))=>(~humble(X)|strong(X))))&
(![X]:(humble(X)<=>(~kind(X)&brave(X))))&
((?[X]:((~wise(X)&generous(X))))=>((~old(john)<~>~happy(john))))&
((rich(lucy))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(calm(X)=>(wise(X)<~>~funny(X))))&
(![X]:((~patient(X)&~wise(X))<=>(~tall(X)|patient(X))))&
(![X]:((~rich(X)&~tall(X))=>(~generous(X)<~>~quiet(X))))&
(![X]:(quiet(X)=>~strong(X)))&
(![X]:(kind(X)<=>~patient(X)))&
(happy(mary))&
(?[X]:((~brave(X)&quiet(X))))&
((~old(paul)|~kind(paul)))&
(?[X]:((patient(X)<~>~calm(X))))&
(?[X]:((old(X)|humble(X))))&
(?[X]:((~calm(X)|~brave(X))))&
(~calm(alice)) | generous(alice) | [] | null | 0 |
If someone is either brave or not wise then someone is creative and vice versa.
If someone is both creative and not quiet then lucy is either not generous or quiet.
Everyone who is both not rich and curious is not funny or rich and vice versa.
If someone is both old and not brave then alice is strong.
Everyone who is wise or not funny is both not curious and curious.
If susan is not strong or funny then someone is not kind.
If lucy is quiet then someone is either not wise or happy.
Everyone who is creative or quiet is calm or not humble.
Everyone who is quiet or wise is old and vice versa.
Everyone who is not kind or not strong is strong.
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 someone is either happy or curious then someone is either not kind or not happy and vice versa.
Lucy is not creative or tall.
Someone is not creative.
Susan is both quiet and not humble.
Susan is strong.
Paul is not kind or calm.
John is either calm or rich. | Paul is old. | neutral | ((?[X]:((brave(X)<~>~wise(X))))<=>(?[X]:(creative(X))))&
((?[X]:((creative(X)&~quiet(X))))=>((~generous(lucy)<~>quiet(lucy))))&
(![X]:((~rich(X)&curious(X))<=>(~funny(X)|rich(X))))&
((?[X]:((old(X)&~brave(X))))=>(strong(alice)))&
(![X]:((wise(X)|~funny(X))=>(~curious(X)&curious(X))))&
(((~strong(susan)|funny(susan)))=>(?[X]:(~kind(X))))&
((quiet(lucy))=>(?[X]:((~wise(X)<~>happy(X)))))&
(![X]:((creative(X)|quiet(X))=>(calm(X)|~humble(X))))&
(![X]:((quiet(X)|wise(X))<=>old(X)))&
(![X]:((~kind(X)|~strong(X))=>strong(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))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
((~creative(lucy)|tall(lucy)))&
(?[X]:(~creative(X)))&
((quiet(susan)&~humble(susan)))&
(strong(susan))&
((~kind(paul)|calm(paul)))&
((calm(john)<~>rich(john))) | old(paul) | [] | null | 0 |
Everyone who is both not funny and not strong is both creative and not old and vice versa. If alice is not happy or kind then susan is not kind and vice versa. If someone is either funny or generous then susan is patient. If someone is either not creative or not happy then someone is not rich or calm. Everyone who is both not rich and humble is not creative. Everyone who is both funny and not creative is not calm and vice versa. If someone is brave then lucy is both funny and not creative. If mary is brave then paul is not generous. If john is either humble or tall then susan is either not rich or not calm. Everyone who is funny or not quiet is not calm and vice versa. Everyone who is either patient or creative is either patient or happy. If fred is not quiet or patient then someone is either brave or not old. Everyone who is old is either happy or not wise and vice versa. If alice is not funny or calm then alice is either rich or old. If alice is not strong then lucy is not brave or not generous. If someone is not wise then someone is either quiet or not wise and vice versa. Someone is humble. John is quiet. Someone is both rich and not tall. Paul is both kind and not curious. Someone is either not calm or wise. Susan is humble. Someone is both quiet and not generous. Lucy is brave or not old. | Paul is kind. | entailment | (![X]:((~funny(X)&~strong(X))<=>(creative(X)&~old(X))))&
(((~happy(alice)|kind(alice)))<=>(~kind(susan)))&
((?[X]:((funny(X)<~>generous(X))))=>(patient(susan)))&
((?[X]:((~creative(X)<~>~happy(X))))=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:((~rich(X)&humble(X))=>~creative(X)))&
(![X]:((funny(X)&~creative(X))<=>~calm(X)))&
((?[X]:(brave(X)))=>((funny(lucy)&~creative(lucy))))&
((brave(mary))=>(~generous(paul)))&
(((humble(john)<~>tall(john)))=>((~rich(susan)<~>~calm(susan))))&
(![X]:((funny(X)|~quiet(X))<=>~calm(X)))&
(![X]:((patient(X)<~>creative(X))=>(patient(X)<~>happy(X))))&
(((~quiet(fred)|patient(fred)))=>(?[X]:((brave(X)<~>~old(X)))))&
(![X]:(old(X)<=>(happy(X)<~>~wise(X))))&
(((~funny(alice)|calm(alice)))=>((rich(alice)<~>old(alice))))&
((~strong(alice))=>((~brave(lucy)|~generous(lucy))))&
((?[X]:(~wise(X)))<=>(?[X]:((quiet(X)<~>~wise(X)))))&
(?[X]:(humble(X)))&
(quiet(john))&
(?[X]:((rich(X)&~tall(X))))&
((kind(paul)&~curious(paul)))&
(?[X]:((~calm(X)<~>wise(X))))&
(humble(susan))&
(?[X]:((quiet(X)&~generous(X))))&
((brave(lucy)|~old(lucy))) | kind(paul) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3823694988990408143444499
% SZS output start Proof for 3823694988990408143444499
20. ~curious(paul) & kind(paul) [input p19]
25. ~kind(paul) [input hypothesis]
28. kind(paul) [pure predicate removal 20]
125. kind(paul) [cnf transformation 28]
132. ~kind(paul) [cnf transformation 25]
313. $false [subsumption resolution 132,125]
% SZS output end Proof for 3823694988990408143444499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and not quiet then mary is creative or brave and vice versa.
If susan is curious then paul is either not rich or calm and vice versa.
If someone is not calm then paul is both not rich and kind and vice versa.
Everyone who is either patient or wise is either not old or creative.
Everyone who is either not old or calm is both tall and not brave and vice versa.
If someone is both not brave and happy then lucy is both not tall and not calm.
If someone is not calm then someone is old and vice versa.
If someone is both kind and not happy then lucy is either not patient or curious.
If someone is not strong or calm then lucy is both not calm and not wise and vice versa.
Everyone who is generous is either generous or patient.
Everyone who is not happy or patient is either not strong or not humble.
Everyone who is brave is not kind or rich.
Everyone who is strong is not kind.
If someone is both not tall and not funny then lucy is either not wise or not brave.
Everyone who is both not rich and generous is not funny.
Someone is old or not calm.
Mary is quiet or generous.
Susan is calm or quiet.
Someone is both old and calm.
Mary is not wise or not curious.
Alice is wise or not rich.
Someone is not tall.
Someone is wise. | Lucy is not calm. | entailment | ((?[X]:((quiet(X)&~quiet(X))))<=>((creative(mary)|brave(mary))))&
((curious(susan))<=>((~rich(paul)<~>calm(paul))))&
((?[X]:(~calm(X)))<=>((~rich(paul)&kind(paul))))&
(![X]:((patient(X)<~>wise(X))=>(~old(X)<~>creative(X))))&
(![X]:((~old(X)<~>calm(X))<=>(tall(X)&~brave(X))))&
((?[X]:((~brave(X)&happy(X))))=>((~tall(lucy)&~calm(lucy))))&
((?[X]:(~calm(X)))<=>(?[X]:(old(X))))&
((?[X]:((kind(X)&~happy(X))))=>((~patient(lucy)<~>curious(lucy))))&
((?[X]:((~strong(X)|calm(X))))<=>((~calm(lucy)&~wise(lucy))))&
(![X]:(generous(X)=>(generous(X)<~>patient(X))))&
(![X]:((~happy(X)|patient(X))=>(~strong(X)<~>~humble(X))))&
(![X]:(brave(X)=>(~kind(X)|rich(X))))&
(![X]:(strong(X)=>~kind(X)))&
((?[X]:((~tall(X)&~funny(X))))=>((~wise(lucy)<~>~brave(lucy))))&
(![X]:((~rich(X)&generous(X))=>~funny(X)))&
(?[X]:((old(X)|~calm(X))))&
((quiet(mary)|generous(mary)))&
((calm(susan)|quiet(susan)))&
(?[X]:((old(X)&calm(X))))&
((~wise(mary)|~curious(mary)))&
((wise(alice)|~rich(alice)))&
(?[X]:(~tall(X)))&
(?[X]:(wise(X))) | ~calm(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 223882541628047958300027
% SZS output start Proof for 223882541628047958300027
9. ? [X0] : (calm(X0) | ~strong(X0)) <=> (~wise(lucy) & ~calm(lucy)) [input p8]
24. calm(lucy) [input hypothesis]
57. (? [X0] : (calm(X0) | ~strong(X0)) | (wise(lucy) | calm(lucy))) & ((~wise(lucy) & ~calm(lucy)) | ! [X0] : (~calm(X0) & strong(X0))) [nnf transformation 9]
58. (? [X0] : (calm(X0) | ~strong(X0)) | wise(lucy) | calm(lucy)) & ((~wise(lucy) & ~calm(lucy)) | ! [X0] : (~calm(X0) & strong(X0))) [flattening 57]
59. (? [X0] : (calm(X0) | ~strong(X0)) | wise(lucy) | calm(lucy)) & ((~wise(lucy) & ~calm(lucy)) | ! [X1] : (~calm(X1) & strong(X1))) [rectify 58]
60. ? [X0] : (calm(X0) | ~strong(X0)) => (calm(sK4) | ~strong(sK4)) [choice axiom]
61. ((calm(sK4) | ~strong(sK4)) | wise(lucy) | calm(lucy)) & ((~wise(lucy) & ~calm(lucy)) | ! [X1] : (~calm(X1) & strong(X1))) [skolemisation 59,60]
102. ~calm(lucy) | ~calm(X1) [cnf transformation 61]
126. calm(lucy) [cnf transformation 24]
178. 11 <=> calm(lucy) [avatar definition]
179. calm(lucy) <- (11) [avatar component clause 178]
227. 22 <=> ! [X1] : ~calm(X1) [avatar definition]
228. ~calm(X1) <- (22) [avatar component clause 227]
234. 22 | ~11 [avatar split clause 102,178,227]
290. 11 [avatar split clause 126,178]
291. $false <- (11, 22) [subsumption resolution 179,228]
292. ~11 | ~22 [avatar contradiction clause 291]
297. $false [avatar sat refutation 234,290,292]
% SZS output end Proof for 223882541628047958300027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich or not quiet then lucy is both not quiet and wise.
If mary is not kind or brave then mary is not humble and vice versa.
If fred is brave then someone is not happy.
If someone is not happy or old then mary is both creative and old and vice versa.
Everyone who is rich or not wise is kind and vice versa.
If someone is rich or quiet then john is both rich and wise.
If someone is both not happy and not quiet then someone is quiet or wise.
If someone is funny or happy then susan is both funny and not creative.
Everyone who is humble is wise or happy and vice versa.
If someone is both old and quiet then mary is either strong or humble and vice versa.
Everyone who is either not curious or happy is either not calm or tall and vice versa.
Everyone who is happy is quiet or humble and vice versa.
Everyone who is not brave or calm is both strong and wise.
If lucy is either wise or strong then paul is either not happy or not tall.
If someone is quiet then someone is both not old and not happy and vice versa.
If someone is either not rich or not wise then susan is not curious and vice versa.
Someone is not happy or not old.
Someone is either creative or not quiet.
Someone is either rich or not happy.
Someone is both wise and not calm.
John is humble.
Someone is not old.
Lucy is both curious and kind.
Someone is both strong and funny. | Lucy is quiet. | contradiction | ((?[X]:((rich(X)|~quiet(X))))=>((~quiet(lucy)&wise(lucy))))&
(((~kind(mary)|brave(mary)))<=>(~humble(mary)))&
((brave(fred))=>(?[X]:(~happy(X))))&
((?[X]:((~happy(X)|old(X))))<=>((creative(mary)&old(mary))))&
(![X]:((rich(X)|~wise(X))<=>kind(X)))&
((?[X]:((rich(X)|quiet(X))))=>((rich(john)&wise(john))))&
((?[X]:((~happy(X)&~quiet(X))))=>(?[X]:((quiet(X)|wise(X)))))&
((?[X]:((funny(X)|happy(X))))=>((funny(susan)&~creative(susan))))&
(![X]:(humble(X)<=>(wise(X)|happy(X))))&
((?[X]:((old(X)&quiet(X))))<=>((strong(mary)<~>humble(mary))))&
(![X]:((~curious(X)<~>happy(X))<=>(~calm(X)<~>tall(X))))&
(![X]:(happy(X)<=>(quiet(X)|humble(X))))&
(![X]:((~brave(X)|calm(X))=>(strong(X)&wise(X))))&
(((wise(lucy)<~>strong(lucy)))=>((~happy(paul)<~>~tall(paul))))&
((?[X]:(quiet(X)))<=>(?[X]:((~old(X)&~happy(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(~curious(susan)))&
(?[X]:((~happy(X)|~old(X))))&
(?[X]:((creative(X)<~>~quiet(X))))&
(?[X]:((rich(X)<~>~happy(X))))&
(?[X]:((wise(X)&~calm(X))))&
(humble(john))&
(?[X]:(~old(X)))&
((curious(lucy)&kind(lucy)))&
(?[X]:((strong(X)&funny(X)))) | quiet(lucy) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4946862060981668129779340
% SZS output start Proof for 4946862060981668129779340
1. ? [X0] : (~quiet(X0) | rich(X0)) => (wise(lucy) & ~quiet(lucy)) [input p0]
6. ? [X0] : (quiet(X0) | rich(X0)) => (wise(john) & rich(john)) [input p5]
25. quiet(lucy) [input hypothesis]
28. (wise(lucy) & ~quiet(lucy)) | ! [X0] : (quiet(X0) & ~rich(X0)) [ennf transformation 1]
30. (wise(john) & rich(john)) | ! [X0] : (~quiet(X0) & ~rich(X0)) [ennf transformation 6]
82. ~quiet(lucy) | ~rich(X0) [cnf transformation 28]
99. rich(john) | ~quiet(X0) [cnf transformation 30]
155. quiet(lucy) [cnf transformation 25]
165. 3 <=> ! [X0] : ~rich(X0) [avatar definition]
166. ~rich(X0) <- (3) [avatar component clause 165]
169. 4 <=> quiet(lucy) [avatar definition]
170. quiet(lucy) <- (4) [avatar component clause 169]
173. 3 | ~4 [avatar split clause 82,169,165]
226. 16 <=> ! [X0] : ~quiet(X0) [avatar definition]
227. ~quiet(X0) <- (16) [avatar component clause 226]
235. 18 <=> rich(john) [avatar definition]
237. rich(john) <- (18) [avatar component clause 235]
238. 16 | 18 [avatar split clause 99,235,226]
376. 4 [avatar split clause 155,169]
379. $false <- (4, 16) [subsumption resolution 170,227]
380. ~4 | ~16 [avatar contradiction clause 379]
383. $false <- (3, 18) [subsumption resolution 237,166]
384. ~3 | ~18 [avatar contradiction clause 383]
385. $false [avatar sat refutation 173,238,376,380,384]
% SZS output end Proof for 4946862060981668129779340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not quiet is both not patient and not tall.
If lucy is curious then someone is not old and vice versa.
Everyone who is both patient and old is either not wise or not old and vice versa.
If lucy is either not calm or funny then john is not curious or not patient.
Everyone who is both not generous and quiet is either not calm or not creative.
If someone is either old or patient then someone is both not calm and quiet and vice versa.
Everyone who is either old or not quiet is patient or not old and vice versa.
If lucy is not rich or not creative then lucy is both not curious and tall and vice versa.
If susan is not quiet or not funny then someone is not patient and vice versa.
Everyone who is either patient or rich is not strong or not happy.
Everyone who is either not kind or kind is generous or not curious and vice versa.
Everyone who is either not creative or not quiet is not funny.
If john is quiet then someone is humble.
Everyone who is either strong or curious is not humble.
If someone is either calm or quiet then lucy is not patient.
Everyone who is either funny or not kind is either not creative or not quiet and vice versa.
Alice is either not curious or calm.
Alice is both not calm and quiet.
Someone is both not generous and not funny.
Paul is tall.
Someone is not rich.
Someone is not calm or kind.
Someone is quiet or creative.
Someone is both not funny and generous. | Paul is not tall. | contradiction | (![X]:((~funny(X)&~quiet(X))=>(~patient(X)&~tall(X))))&
((curious(lucy))<=>(?[X]:(~old(X))))&
(![X]:((patient(X)&old(X))<=>(~wise(X)<~>~old(X))))&
(((~calm(lucy)<~>funny(lucy)))=>((~curious(john)|~patient(john))))&
(![X]:((~generous(X)&quiet(X))=>(~calm(X)<~>~creative(X))))&
((?[X]:((old(X)<~>patient(X))))<=>(?[X]:((~calm(X)&quiet(X)))))&
(![X]:((old(X)<~>~quiet(X))<=>(patient(X)|~old(X))))&
(((~rich(lucy)|~creative(lucy)))<=>((~curious(lucy)&tall(lucy))))&
(((~quiet(susan)|~funny(susan)))<=>(?[X]:(~patient(X))))&
(![X]:((patient(X)<~>rich(X))=>(~strong(X)|~happy(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(generous(X)|~curious(X))))&
(![X]:((~creative(X)<~>~quiet(X))=>~funny(X)))&
((quiet(john))=>(?[X]:(humble(X))))&
(![X]:((strong(X)<~>curious(X))=>~humble(X)))&
((?[X]:((calm(X)<~>quiet(X))))=>(~patient(lucy)))&
(![X]:((funny(X)<~>~kind(X))<=>(~creative(X)<~>~quiet(X))))&
((~curious(alice)<~>calm(alice)))&
((~calm(alice)&quiet(alice)))&
(?[X]:((~generous(X)&~funny(X))))&
(tall(paul))&
(?[X]:(~rich(X)))&
(?[X]:((~calm(X)|kind(X))))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:((~funny(X)&generous(X)))) | ~tall(paul) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1129338377239794272761300
% SZS output start Proof for 1129338377239794272761300
20. tall(paul) [input p19]
25. ~tall(paul) [input hypothesis]
140. tall(paul) [cnf transformation 20]
146. ~tall(paul) [cnf transformation 25]
304. $false [subsumption resolution 146,140]
% SZS output end Proof for 1129338377239794272761300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not calm then alice is either not wise or calm and vice versa.
If john is either kind or not happy then someone is either happy or not brave and vice versa.
Everyone who is not wise is both not quiet and brave.
Everyone who is not patient or not humble is brave and vice versa.
Everyone who is both kind and not calm is both not tall and happy.
Everyone who is both not curious and calm is both humble and strong.
If paul is not tall or not happy then paul is either strong or not calm and vice versa.
If alice is not curious or not strong then lucy is either not quiet or brave and vice versa.
Everyone who is not old is both generous and tall and vice versa.
Everyone who is not humble is both tall and calm.
Everyone who is either quiet or funny is happy or brave and vice versa.
Everyone who is both not tall and not humble is both not generous and not old and vice versa.
Everyone who is either creative or brave is both generous and not humble and vice versa.
If someone is both not happy and patient then someone is both not funny and quiet.
If mary is either strong or not patient then paul is both funny and creative.
Everyone who is humble or funny is either tall or not strong.
Someone is not funny or not kind.
Mary is quiet or generous.
Someone is either brave or tall.
Someone is both brave and not tall.
Someone is either generous or not tall.
Someone is calm or curious.
Someone is quiet.
Fred is rich or not patient. | Lucy is quiet. | neutral | ((?[X]:(~calm(X)))<=>((~wise(alice)<~>calm(alice))))&
(((kind(john)<~>~happy(john)))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:(~wise(X)=>(~quiet(X)&brave(X))))&
(![X]:((~patient(X)|~humble(X))<=>brave(X)))&
(![X]:((kind(X)&~calm(X))=>(~tall(X)&happy(X))))&
(![X]:((~curious(X)&calm(X))=>(humble(X)&strong(X))))&
(((~tall(paul)|~happy(paul)))<=>((strong(paul)<~>~calm(paul))))&
(((~curious(alice)|~strong(alice)))<=>((~quiet(lucy)<~>brave(lucy))))&
(![X]:(~old(X)<=>(generous(X)&tall(X))))&
(![X]:(~humble(X)=>(tall(X)&calm(X))))&
(![X]:((quiet(X)<~>funny(X))<=>(happy(X)|brave(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~generous(X)&~old(X))))&
(![X]:((creative(X)<~>brave(X))<=>(generous(X)&~humble(X))))&
((?[X]:((~happy(X)&patient(X))))=>(?[X]:((~funny(X)&quiet(X)))))&
(((strong(mary)<~>~patient(mary)))=>((funny(paul)&creative(paul))))&
(![X]:((humble(X)|funny(X))=>(tall(X)<~>~strong(X))))&
(?[X]:((~funny(X)|~kind(X))))&
((quiet(mary)|generous(mary)))&
(?[X]:((brave(X)<~>tall(X))))&
(?[X]:((brave(X)&~tall(X))))&
(?[X]:((generous(X)<~>~tall(X))))&
(?[X]:((calm(X)|curious(X))))&
(?[X]:(quiet(X)))&
((rich(fred)|~patient(fred))) | quiet(lucy) | [] | null | 0 |
Everyone who is either patient or not old is generous or not curious.
Everyone who is both humble and strong is not calm and vice versa.
Everyone who is not rich is either strong or not happy.
If someone is not brave or not strong then john is both rich and not old.
Everyone who is not kind or not strong is humble and vice versa.
If john is not patient then someone is either not creative or curious.
If someone is both not brave and tall then someone is strong and vice versa.
Everyone who is not curious or not quiet is both not curious and creative.
Everyone who is humble or strong is both quiet and calm.
If someone is not old or not kind then mary is either not creative or not tall.
Everyone who is funny is both not rich and not quiet.
If someone is not happy then mary is wise.
Everyone who is both brave and not kind is not curious or generous and vice versa.
If paul is not patient then mary is not strong.
Everyone who is either not creative or calm is not calm or not curious and vice versa.
Everyone who is both happy and kind is not tall.
Lucy is not brave or not curious.
Susan is either not calm or quiet.
Susan is either quiet or creative.
Someone is strong.
Someone is not patient.
Fred is both quiet and creative.
Mary is either not happy or funny. | Paul is funny. | contradiction | (![X]:((patient(X)<~>~old(X))=>(generous(X)|~curious(X))))&
(![X]:((humble(X)&strong(X))<=>~calm(X)))&
(![X]:(~rich(X)=>(strong(X)<~>~happy(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((rich(john)&~old(john))))&
(![X]:((~kind(X)|~strong(X))<=>humble(X)))&
((~patient(john))=>(?[X]:((~creative(X)<~>curious(X)))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:(strong(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~curious(X)&creative(X))))&
(![X]:((humble(X)|strong(X))=>(quiet(X)&calm(X))))&
((?[X]:((~old(X)|~kind(X))))=>((~creative(mary)<~>~tall(mary))))&
(![X]:(funny(X)=>(~rich(X)&~quiet(X))))&
((?[X]:(~happy(X)))=>(wise(mary)))&
(![X]:((brave(X)&~kind(X))<=>(~curious(X)|generous(X))))&
((~patient(paul))=>(~strong(mary)))&
(![X]:((~creative(X)<~>calm(X))<=>(~calm(X)|~curious(X))))&
(![X]:((happy(X)&kind(X))=>~tall(X)))&
((~brave(lucy)|~curious(lucy)))&
((~calm(susan)<~>quiet(susan)))&
((quiet(susan)<~>creative(susan)))&
(?[X]:(strong(X)))&
(?[X]:(~patient(X)))&
((quiet(fred)&creative(fred)))&
((~happy(mary)<~>funny(mary))) | funny(paul) | [
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4013278144208793850540226
% SZS output start Proof for 4013278144208793850540226
5. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> humble(X0)) [input p4]
9. ! [X0] : ((strong(X0) | humble(X0)) => (calm(X0) & quiet(X0))) [input p8]
11. ! [X0] : (funny(X0) => (~quiet(X0) & ~rich(X0))) [input p10]
24. funny(paul) [input hypothesis]
33. ! [X0] : ((calm(X0) & quiet(X0)) | (~strong(X0) & ~humble(X0))) [ennf transformation 9]
35. ! [X0] : ((~quiet(X0) & ~rich(X0)) | ~funny(X0)) [ennf transformation 11]
43. ! [X0] : (((~strong(X0) | ~kind(X0)) | ~humble(X0)) & (humble(X0) | (strong(X0) & kind(X0)))) [nnf transformation 5]
44. ! [X0] : ((~strong(X0) | ~kind(X0) | ~humble(X0)) & (humble(X0) | (strong(X0) & kind(X0)))) [flattening 43]
77. strong(X0) | humble(X0) [cnf transformation 44]
88. ~humble(X0) | quiet(X0) [cnf transformation 33]
89. ~strong(X0) | quiet(X0) [cnf transformation 33]
97. ~funny(X0) | ~quiet(X0) [cnf transformation 35]
122. funny(paul) [cnf transformation 24]
238. quiet(X0) | humble(X0) [resolution 89,77]
239. quiet(X0) [subsumption resolution 238,88]
241. ~quiet(paul) [resolution 97,122]
242. $false [subsumption resolution 241,239]
% SZS output end Proof for 4013278144208793850540226
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and creative then alice is brave or kind and vice versa.
If someone is old or generous then fred is either not rich or not happy and vice versa.
Everyone who is either not generous or old is both not brave and not strong.
If susan is not old or not happy then someone is either old or not old.
Everyone who is both not old and not generous is not curious and vice versa.
If someone is both strong and not calm then someone is not quiet or not humble and vice versa.
Everyone who is either not quiet or not curious is either not funny or old and vice versa.
Everyone who is not curious or funny is either curious or strong.
If alice is wise or strong then someone is not creative or curious and vice versa.
If lucy is both not wise and not quiet then someone is both strong and not quiet and vice versa.
Everyone who is either strong or rich is either not strong or tall.
If someone is calm then lucy is curious and vice versa.
If mary is either old or not generous then someone is either not kind or generous and vice versa.
Everyone who is not strong or tall is tall and vice versa.
If paul is either patient or rich then someone is either not funny or not happy and vice versa.
If fred is either not wise or humble then someone is not generous or quiet.
Someone is either not wise or not funny.
Alice is both generous and wise.
Someone is both humble and happy.
Paul is both not old and not quiet.
Someone is old or generous.
Alice is not quiet or wise.
Someone is either not tall or old.
Alice is not creative. | Paul is curious. | entailment | ((?[X]:((~rich(X)&creative(X))))<=>((brave(alice)|kind(alice))))&
((?[X]:((old(X)|generous(X))))<=>((~rich(fred)<~>~happy(fred))))&
(![X]:((~generous(X)<~>old(X))=>(~brave(X)&~strong(X))))&
(((~old(susan)|~happy(susan)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:((~old(X)&~generous(X))<=>~curious(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~curious(X)|funny(X))=>(curious(X)<~>strong(X))))&
(((wise(alice)|strong(alice)))<=>(?[X]:((~creative(X)|curious(X)))))&
(((~wise(lucy)&~quiet(lucy)))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((strong(X)<~>rich(X))=>(~strong(X)<~>tall(X))))&
((?[X]:(calm(X)))<=>(curious(lucy)))&
(((old(mary)<~>~generous(mary)))<=>(?[X]:((~kind(X)<~>generous(X)))))&
(![X]:((~strong(X)|tall(X))<=>tall(X)))&
(((patient(paul)<~>rich(paul)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~wise(fred)<~>humble(fred)))=>(?[X]:((~generous(X)|quiet(X)))))&
(?[X]:((~wise(X)<~>~funny(X))))&
((generous(alice)&wise(alice)))&
(?[X]:((humble(X)&happy(X))))&
((~old(paul)&~quiet(paul)))&
(?[X]:((old(X)|generous(X))))&
((~quiet(alice)|wise(alice)))&
(?[X]:((~tall(X)<~>old(X))))&
(~creative(alice)) | curious(paul) | [
"p2",
"p4",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3730899105925202600412332
% SZS output start Proof for 3730899105925202600412332
3. ! [X0] : ((~generous(X0) <~> old(X0)) => (~strong(X0) & ~brave(X0))) [input p2]
5. ! [X0] : ((~generous(X0) & ~old(X0)) <=> ~curious(X0)) [input p4]
8. ! [X0] : ((funny(X0) | ~curious(X0)) => (curious(X0) <~> strong(X0))) [input p7]
20. ~quiet(paul) & ~old(paul) [input p19]
25. ~curious(paul) [input hypothesis]
27. ! [X0] : ((~strong(X0) & ~brave(X0)) | (~generous(X0) <=> old(X0))) [ennf transformation 3]
29. ! [X0] : ((curious(X0) <~> strong(X0)) | (~funny(X0) & curious(X0))) [ennf transformation 8]
41. ! [X0] : ((~strong(X0) & ~brave(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) [nnf transformation 27]
45. ! [X0] : (((~generous(X0) & ~old(X0)) | curious(X0)) & (~curious(X0) | (generous(X0) | old(X0)))) [nnf transformation 5]
46. ! [X0] : (((~generous(X0) & ~old(X0)) | curious(X0)) & (~curious(X0) | generous(X0) | old(X0))) [flattening 45]
53. ! [X0] : (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (~funny(X0) & curious(X0))) [nnf transformation 29]
105. ~strong(X0) | old(X0) | generous(X0) [cnf transformation 41]
113. ~generous(X0) | curious(X0) [cnf transformation 46]
127. strong(X0) | curious(X0) | curious(X0) [cnf transformation 53]
172. ~old(paul) [cnf transformation 20]
179. ~curious(paul) [cnf transformation 25]
182. curious(X0) | strong(X0) [duplicate literal removal 127]
450. strong(paul) [resolution 182,179]
463. old(paul) | generous(paul) [resolution 105,450]
467. generous(paul) [subsumption resolution 463,172]
589. curious(paul) [resolution 467,113]
590. $false [subsumption resolution 589,179]
% SZS output end Proof for 3730899105925202600412332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or funny is both old and not creative.
Everyone who is old or not curious is both not old and not strong.
Everyone who is not strong or not happy is both not happy and kind.
Everyone who is not kind or generous is calm and vice versa.
If john is both not quiet and tall then someone is tall or humble and vice versa.
Everyone who is curious or quiet is both funny and rich.
Everyone who is not patient is both not old and funny and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
Everyone who is quiet is kind.
Someone is brave or strong.
Alice is wise.
Someone is not strong or not rich.
Mary is rich. | Paul is not humble. | entailment | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|~curious(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((brave(X)|strong(X))))&
(wise(alice))&
(?[X]:((~strong(X)|~rich(X))))&
(rich(mary)) | ~humble(paul) | [
"p0",
"p1",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 80811817848244636619437
% SZS output start Proof for 80811817848244636619437
1. ! [X0] : ((~curious(X0) <~> funny(X0)) => (~creative(X0) & old(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | old(X0)) => (~strong(X0) & ~old(X0))) [input p1]
6. ! [X0] : ((quiet(X0) | curious(X0)) => (rich(X0) & funny(X0))) [input p5]
8. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (kind(X0) & ~humble(X0))) [input p7]
20. humble(paul) [input hypothesis]
22. ! [X0] : ((~creative(X0) & old(X0)) | (~curious(X0) <=> funny(X0))) [ennf transformation 1]
23. ! [X0] : ((~strong(X0) & ~old(X0)) | (curious(X0) & ~old(X0))) [ennf transformation 2]
25. ! [X0] : ((rich(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0))) [ennf transformation 6]
30. ! [X0] : ((~creative(X0) & old(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) [nnf transformation 22]
38. ! [X0] : (((calm(X0) | ~curious(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 8]
39. ! [X0] : ((calm(X0) | ~curious(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [flattening 38]
57. ~funny(X0) | ~curious(X0) | old(X0) [cnf transformation 30]
60. ~old(X0) | ~old(X0) [cnf transformation 23]
76. ~curious(X0) | funny(X0) [cnf transformation 25]
80. ~humble(X0) | curious(X0) [cnf transformation 39]
111. humble(paul) [cnf transformation 20]
112. ~old(X0) [duplicate literal removal 60]
186. 15 <=> curious(paul) [avatar definition]
188. curious(paul) <- (15) [avatar component clause 186]
220. curious(paul) [resolution 80,111]
221. 15 [avatar split clause 220,186]
223. funny(paul) <- (15) [resolution 188,76]
230. ~curious(paul) | old(paul) <- (15) [resolution 57,223]
232. old(paul) <- (15) [subsumption resolution 230,188]
233. $false <- (15) [subsumption resolution 232,112]
234. ~15 [avatar contradiction clause 233]
236. $false [avatar sat refutation 221,234]
% SZS output end Proof for 80811817848244636619437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not happy is either patient or happy and vice versa.
If someone is either tall or strong then someone is not curious and vice versa.
Everyone who is either generous or not curious is either not rich or kind.
Everyone who is both not patient and happy is tall or not wise.
Everyone who is humble is both not funny and not curious and vice versa.
Everyone who is not brave is both not funny and tall and vice versa.
If someone is both not generous and brave then paul is kind.
If lucy is not wise then someone is not quiet and vice versa.
Everyone who is not generous or wise is either curious or happy.
Everyone who is not rich or not funny is wise.
Everyone who is both not curious and patient is not calm and vice versa.
If paul is either not humble or old then someone is either tall or not humble and vice versa.
If alice is either not quiet or not creative then lucy is both not funny and not calm and vice versa.
If someone is either not creative or not happy then someone is brave or kind.
If lucy is not calm then someone is not brave and vice versa.
Everyone who is old is either generous or wise and vice versa.
Lucy is not funny.
Someone is calm.
Alice is not rich or wise.
Someone is rich.
Someone is not creative or not brave.
Alice is brave or humble.
John is either not quiet or kind.
Someone is either tall or not wise. | Lucy is patient. | entailment | (![X]:((quiet(X)|~happy(X))<=>(patient(X)<~>happy(X))))&
((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)<~>~curious(X))=>(~rich(X)<~>kind(X))))&
(![X]:((~patient(X)&happy(X))=>(tall(X)|~wise(X))))&
(![X]:(humble(X)<=>(~funny(X)&~curious(X))))&
(![X]:(~brave(X)<=>(~funny(X)&tall(X))))&
((?[X]:((~generous(X)&brave(X))))=>(kind(paul)))&
((~wise(lucy))<=>(?[X]:(~quiet(X))))&
(![X]:((~generous(X)|wise(X))=>(curious(X)<~>happy(X))))&
(![X]:((~rich(X)|~funny(X))=>wise(X)))&
(![X]:((~curious(X)&patient(X))<=>~calm(X)))&
(((~humble(paul)<~>old(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(((~quiet(alice)<~>~creative(alice)))<=>((~funny(lucy)&~calm(lucy))))&
((?[X]:((~creative(X)<~>~happy(X))))=>(?[X]:((brave(X)|kind(X)))))&
((~calm(lucy))<=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>(generous(X)<~>wise(X))))&
(~funny(lucy))&
(?[X]:(calm(X)))&
((~rich(alice)|wise(alice)))&
(?[X]:(rich(X)))&
(?[X]:((~creative(X)|~brave(X))))&
((brave(alice)|humble(alice)))&
((~quiet(john)<~>kind(john)))&
(?[X]:((tall(X)<~>~wise(X)))) | patient(lucy) | [
"p0",
"p3",
"p5",
"p9",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 193262779090917116433670
% SZS output start Proof for 193262779090917116433670
1. ! [X0] : ((~happy(X0) | quiet(X0)) <=> (patient(X0) <~> happy(X0))) [input p0]
4. ! [X0] : ((happy(X0) & ~patient(X0)) => (~wise(X0) | tall(X0))) [input p3]
6. ! [X0] : (~brave(X0) <=> (tall(X0) & ~funny(X0))) [input p5]
10. ! [X0] : ((~funny(X0) | ~rich(X0)) => wise(X0)) [input p9]
11. ! [X0] : ((patient(X0) & ~curious(X0)) <=> ~calm(X0)) [input p10]
15. ~calm(lucy) <=> ? [X0] : ~brave(X0) [input p14]
17. ~funny(lucy) [input p16]
25. ~patient(lucy) [input hypothesis]
29. ! [X0] : ((~wise(X0) | tall(X0)) | (~happy(X0) | patient(X0))) [ennf transformation 4]
30. ! [X0] : (~wise(X0) | tall(X0) | ~happy(X0) | patient(X0)) [flattening 29]
33. ! [X0] : (wise(X0) | (funny(X0) & rich(X0))) [ennf transformation 10]
35. ! [X0] : (((~happy(X0) | quiet(X0)) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0)))) & (((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | (happy(X0) & ~quiet(X0)))) [nnf transformation 1]
36. ! [X0] : ((~happy(X0) | quiet(X0) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0)))) & (((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | (happy(X0) & ~quiet(X0)))) [flattening 35]
45. ! [X0] : ((~brave(X0) | (~tall(X0) | funny(X0))) & ((tall(X0) & ~funny(X0)) | brave(X0))) [nnf transformation 6]
46. ! [X0] : ((~brave(X0) | ~tall(X0) | funny(X0)) & ((tall(X0) & ~funny(X0)) | brave(X0))) [flattening 45]
52. ! [X0] : (((patient(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | (~patient(X0) | curious(X0)))) [nnf transformation 11]
53. ! [X0] : (((patient(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | ~patient(X0) | curious(X0))) [flattening 52]
64. (~calm(lucy) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | calm(lucy)) [nnf transformation 15]
65. (~calm(lucy) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | calm(lucy)) [rectify 64]
66. ? [X1] : ~brave(X1) => ~brave(sK5) [choice axiom]
67. (~calm(lucy) | ! [X0] : brave(X0)) & (~brave(sK5) | calm(lucy)) [skolemisation 65,66]
80. happy(X0) | patient(X0) | happy(X0) [cnf transformation 36]
93. ~wise(X0) | tall(X0) | ~happy(X0) | patient(X0) [cnf transformation 30]
99. ~brave(X0) | ~tall(X0) | funny(X0) [cnf transformation 46]
108. funny(X0) | wise(X0) [cnf transformation 33]
111. calm(X0) | patient(X0) [cnf transformation 53]
129. ~calm(lucy) | brave(X0) [cnf transformation 67]
134. ~funny(lucy) [cnf transformation 17]
144. ~patient(lucy) [cnf transformation 25]
145. patient(X0) | happy(X0) [duplicate literal removal 80]
172. ~wise(X0) | tall(X0) | patient(X0) [subsumption resolution 93,145]
185. 10 <=> wise(lucy) [avatar definition]
186. wise(lucy) <- (10) [avatar component clause 185]
225. 18 <=> funny(lucy) [avatar definition]
226. ~funny(lucy) <- (~18) [avatar component clause 225]
229. 19 <=> calm(lucy) [avatar definition]
230. ~calm(lucy) <- (~19) [avatar component clause 229]
263. 26 <=> ! [X0] : brave(X0) [avatar definition]
264. brave(X0) <- (26) [avatar component clause 263]
265. 26 | ~19 [avatar split clause 129,229,263]
271. ~18 [avatar split clause 134,225]
315. wise(lucy) <- (~18) [resolution 108,226]
320. 10 | 18 [avatar split clause 315,225,185]
325. patient(lucy) <- (~19) [resolution 111,230]
326. $false <- (~19) [subsumption resolution 325,144]
327. 19 [avatar contradiction clause 326]
354. ~tall(X0) | funny(X0) <- (26) [resolution 99,264]
454. tall(lucy) | patient(lucy) <- (10) [resolution 172,186]
456. tall(lucy) <- (10) [subsumption resolution 454,144]
603. funny(lucy) <- (10, 26) [resolution 354,456]
604. $false <- (10, ~18, 26) [subsumption resolution 603,226]
605. ~10 | 18 | ~26 [avatar contradiction clause 604]
606. $false [avatar sat refutation 265,271,320,327,605]
% SZS output end Proof for 193262779090917116433670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not rich is not calm or calm and vice versa. Everyone who is either brave or funny is wise or not quiet and vice versa. Everyone who is both curious and quiet is both quiet and not funny and vice versa. If someone is either tall or calm then alice is not quiet or not patient. If someone is both tall and not happy then susan is calm. If someone is either not creative or strong then john is either wise or not curious. If someone is not wise then john is both not funny and brave and vice versa. If someone is not calm or happy then susan is not tall and vice versa. Everyone who is wise is either not funny or quiet and vice versa. If lucy is calm or creative then paul is not wise and vice versa. If paul is both not rich and old then someone is happy and vice versa. Everyone who is both funny and not rich is happy or rich and vice versa. Everyone who is both not strong and funny is not wise or generous and vice versa. If someone is not kind or not quiet then susan is either creative or not brave. If fred is both not funny and calm then someone is not quiet or not strong and vice versa. If john is calm or brave then someone is both not wise and kind. Alice is either quiet or funny. Paul is generous. Fred is not strong. Someone is both happy and not strong. Someone is either not funny or not strong. John is either happy or not humble. Someone is both not kind and humble. Someone is either not quiet or quiet. | Fred is generous. | contradiction | (![X]:((~strong(X)&~rich(X))<=>(~calm(X)|calm(X))))&
(![X]:((brave(X)<~>funny(X))<=>(wise(X)|~quiet(X))))&
(![X]:((curious(X)&quiet(X))<=>(quiet(X)&~funny(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~quiet(alice)|~patient(alice))))&
((?[X]:((tall(X)&~happy(X))))=>(calm(susan)))&
((?[X]:((~creative(X)<~>strong(X))))=>((wise(john)<~>~curious(john))))&
((?[X]:(~wise(X)))<=>((~funny(john)&brave(john))))&
((?[X]:((~calm(X)|happy(X))))<=>(~tall(susan)))&
(![X]:(wise(X)<=>(~funny(X)<~>quiet(X))))&
(((calm(lucy)|creative(lucy)))<=>(~wise(paul)))&
(((~rich(paul)&old(paul)))<=>(?[X]:(happy(X))))&
(![X]:((funny(X)&~rich(X))<=>(happy(X)|rich(X))))&
(![X]:((~strong(X)&funny(X))<=>(~wise(X)|generous(X))))&
((?[X]:((~kind(X)|~quiet(X))))=>((creative(susan)<~>~brave(susan))))&
(((~funny(fred)&calm(fred)))<=>(?[X]:((~quiet(X)|~strong(X)))))&
(((calm(john)|brave(john)))=>(?[X]:((~wise(X)&kind(X)))))&
((quiet(alice)<~>funny(alice)))&
(generous(paul))&
(~strong(fred))&
(?[X]:((happy(X)&~strong(X))))&
(?[X]:((~funny(X)<~>~strong(X))))&
((happy(john)<~>~humble(john)))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((~quiet(X)<~>quiet(X)))) | generous(fred) | [
"p0",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6629127461995167965974636
% SZS output start Proof for 6629127461995167965974636
1. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> (calm(X0) | ~calm(X0))) [input p0]
13. ! [X0] : ((funny(X0) & ~strong(X0)) <=> (generous(X0) | ~wise(X0))) [input p12]
15. (calm(fred) & ~funny(fred)) <=> ? [X0] : (~strong(X0) | ~quiet(X0)) [input p14]
25. generous(fred) [input hypothesis]
31. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~calm(X0) & calm(X0))) & ((calm(X0) | ~calm(X0)) | (rich(X0) | strong(X0)))) [nnf transformation 1]
32. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~calm(X0) & calm(X0))) & (calm(X0) | ~calm(X0) | rich(X0) | strong(X0))) [flattening 31]
57. ! [X0] : (((funny(X0) & ~strong(X0)) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | (~funny(X0) | strong(X0)))) [nnf transformation 13]
58. ! [X0] : (((funny(X0) & ~strong(X0)) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | ~funny(X0) | strong(X0))) [flattening 57]
60. ((calm(fred) & ~funny(fred)) | ! [X0] : (strong(X0) & quiet(X0))) & (? [X0] : (~strong(X0) | ~quiet(X0)) | (~calm(fred) | funny(fred))) [nnf transformation 15]
61. ((calm(fred) & ~funny(fred)) | ! [X0] : (strong(X0) & quiet(X0))) & (? [X0] : (~strong(X0) | ~quiet(X0)) | ~calm(fred) | funny(fred)) [flattening 60]
62. ((calm(fred) & ~funny(fred)) | ! [X0] : (strong(X0) & quiet(X0))) & (? [X1] : (~strong(X1) | ~quiet(X1)) | ~calm(fred) | funny(fred)) [rectify 61]
63. ? [X1] : (~strong(X1) | ~quiet(X1)) => (~strong(sK3) | ~quiet(sK3)) [choice axiom]
64. ((calm(fred) & ~funny(fred)) | ! [X0] : (strong(X0) & quiet(X0))) & ((~strong(sK3) | ~quiet(sK3)) | ~calm(fred) | funny(fred)) [skolemisation 62,63]
80. ~strong(X0) | calm(X0) [cnf transformation 32]
81. ~calm(X0) | ~strong(X0) [cnf transformation 32]
124. ~generous(X0) | funny(X0) [cnf transformation 58]
131. ~funny(fred) | strong(X0) [cnf transformation 64]
152. generous(fred) [cnf transformation 25]
156. ~strong(X0) [subsumption resolution 80,81]
266. ~funny(fred) [subsumption resolution 131,156]
315. funny(fred) [resolution 124,152]
316. $false [subsumption resolution 315,266]
% SZS output end Proof for 6629127461995167965974636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then someone is not happy. If john is calm then someone is either patient or brave and vice versa. If john is quiet then alice is either not generous or not old. If john is strong then someone is kind or not brave. Everyone who is calm or creative is both not curious and not brave and vice versa. Everyone who is either creative or quiet is both happy and tall and vice versa. Everyone who is either patient or not curious is either rich or brave. If mary is both not humble and not creative then mary is strong. Everyone who is either brave or not creative is brave or not wise and vice versa. Everyone who is either strong or not kind is either kind or wise. If someone is calm or funny then someone is not humble. If someone is happy then someone is not tall and vice versa. Everyone who is creative is either calm or humble and vice versa. If fred is generous or not funny then susan is both not brave and not strong. Everyone who is either not calm or humble is generous or not calm and vice versa. Everyone who is either not humble or brave is either creative or not happy. Mary is not old. Alice is not humble. Mary is not kind. Someone is creative or kind. Mary is not rich or not calm. | Alice is not happy. | neutral | ((patient(fred))=>(?[X]:(~happy(X))))&
((calm(john))<=>(?[X]:((patient(X)<~>brave(X)))))&
((quiet(john))=>((~generous(alice)<~>~old(alice))))&
((strong(john))=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:((calm(X)|creative(X))<=>(~curious(X)&~brave(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(happy(X)&tall(X))))&
(![X]:((patient(X)<~>~curious(X))=>(rich(X)<~>brave(X))))&
(((~humble(mary)&~creative(mary)))=>(strong(mary)))&
(![X]:((brave(X)<~>~creative(X))<=>(brave(X)|~wise(X))))&
(![X]:((strong(X)<~>~kind(X))=>(kind(X)<~>wise(X))))&
((?[X]:((calm(X)|funny(X))))=>(?[X]:(~humble(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~tall(X))))&
(![X]:(creative(X)<=>(calm(X)<~>humble(X))))&
(((generous(fred)|~funny(fred)))=>((~brave(susan)&~strong(susan))))&
(![X]:((~calm(X)<~>humble(X))<=>(generous(X)|~calm(X))))&
(![X]:((~humble(X)<~>brave(X))=>(creative(X)<~>~happy(X))))&
(~old(mary))&
(~humble(alice))&
(~kind(mary))&
(?[X]:((creative(X)|kind(X))))&
((~rich(mary)|~calm(mary))) | ~happy(alice) | [] | null | 0 |
If someone is either not creative or not generous then lucy is happy. If someone is old or not brave then fred is not quiet or old. Everyone who is either rich or kind is not patient or not curious and vice versa. If mary is not humble or not patient then someone is either curious or not strong and vice versa. If susan is curious or not patient then fred is not rich or not patient and vice versa. Everyone who is either curious or calm is both old and not calm and vice versa. Everyone who is funny or kind is not happy or not funny. Everyone who is curious is not old or strong. If lucy is not creative then susan is not brave or not strong and vice versa. Everyone who is happy or not old is quiet. If mary is either not curious or not old then alice is creative and vice versa. Everyone who is either patient or wise is both not patient and not curious and vice versa. Everyone who is happy is not wise or not humble. Everyone who is not kind is funny or brave. Everyone who is not generous or quiet is either generous or not funny. Everyone who is both not quiet and strong is strong or curious and vice versa. Someone is both not tall and not quiet. Mary is not generous or not calm. Fred is not funny. Someone is either not calm or old. John is not generous. Someone is not rich. Susan is humble. | Susan is wise. | neutral | ((?[X]:((~creative(X)<~>~generous(X))))=>(happy(lucy)))&
((?[X]:((old(X)|~brave(X))))=>((~quiet(fred)|old(fred))))&
(![X]:((rich(X)<~>kind(X))<=>(~patient(X)|~curious(X))))&
(((~humble(mary)|~patient(mary)))<=>(?[X]:((curious(X)<~>~strong(X)))))&
(((curious(susan)|~patient(susan)))<=>((~rich(fred)|~patient(fred))))&
(![X]:((curious(X)<~>calm(X))<=>(old(X)&~calm(X))))&
(![X]:((funny(X)|kind(X))=>(~happy(X)|~funny(X))))&
(![X]:(curious(X)=>(~old(X)|strong(X))))&
((~creative(lucy))<=>((~brave(susan)|~strong(susan))))&
(![X]:((happy(X)|~old(X))=>quiet(X)))&
(((~curious(mary)<~>~old(mary)))<=>(creative(alice)))&
(![X]:((patient(X)<~>wise(X))<=>(~patient(X)&~curious(X))))&
(![X]:(happy(X)=>(~wise(X)|~humble(X))))&
(![X]:(~kind(X)=>(funny(X)|brave(X))))&
(![X]:((~generous(X)|quiet(X))=>(generous(X)<~>~funny(X))))&
(![X]:((~quiet(X)&strong(X))<=>(strong(X)|curious(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
((~generous(mary)|~calm(mary)))&
(~funny(fred))&
(?[X]:((~calm(X)<~>old(X))))&
(~generous(john))&
(?[X]:(~rich(X)))&
(humble(susan)) | wise(susan) | [] | null | 0 |
If john is generous or old then someone is both humble and brave.
If lucy is not creative or creative then paul is not patient and vice versa.
Everyone who is not creative is either not quiet or funny.
If mary is old then someone is both creative and quiet.
Everyone who is both not happy and calm is generous.
If alice is either not funny or not brave then someone is either brave or happy and vice versa.
Everyone who is both not happy and funny is not calm and vice versa.
Everyone who is both tall and not patient is generous.
Everyone who is either calm or not tall is either not curious or old.
If someone is either kind or not tall then someone is either not rich or tall and vice versa.
If fred is both not wise and not kind then mary is quiet and vice versa.
Everyone who is either not brave or wise is kind.
Everyone who is both not happy and curious is both not rich and not strong and vice versa.
Everyone who is not quiet is happy.
If someone is funny or not humble then someone is either brave or humble and vice versa.
If someone is not creative or not tall then someone is either not wise or strong and vice versa.
Someone is wise or rich.
Paul is both funny and not tall.
Mary is both humble and not strong.
Susan is not tall.
Someone is both brave and not calm.
Susan is either creative or not brave.
Lucy is both kind and happy.
Fred is both not humble and patient. | Fred is not patient. | contradiction | (((generous(john)|old(john)))=>(?[X]:((humble(X)&brave(X)))))&
(((~creative(lucy)|creative(lucy)))<=>(~patient(paul)))&
(![X]:(~creative(X)=>(~quiet(X)<~>funny(X))))&
((old(mary))=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~happy(X)&calm(X))=>generous(X)))&
(((~funny(alice)<~>~brave(alice)))<=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((~happy(X)&funny(X))<=>~calm(X)))&
(![X]:((tall(X)&~patient(X))=>generous(X)))&
(![X]:((calm(X)<~>~tall(X))=>(~curious(X)<~>old(X))))&
((?[X]:((kind(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>tall(X)))))&
(((~wise(fred)&~kind(fred)))<=>(quiet(mary)))&
(![X]:((~brave(X)<~>wise(X))=>kind(X)))&
(![X]:((~happy(X)&curious(X))<=>(~rich(X)&~strong(X))))&
(![X]:(~quiet(X)=>happy(X)))&
((?[X]:((funny(X)|~humble(X))))<=>(?[X]:((brave(X)<~>humble(X)))))&
((?[X]:((~creative(X)|~tall(X))))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(?[X]:((wise(X)|rich(X))))&
((funny(paul)&~tall(paul)))&
((humble(mary)&~strong(mary)))&
(~tall(susan))&
(?[X]:((brave(X)&~calm(X))))&
((creative(susan)<~>~brave(susan)))&
((kind(lucy)&happy(lucy)))&
((~humble(fred)&patient(fred))) | ~patient(fred) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3605797301831091766157028
% SZS output start Proof for 3605797301831091766157028
24. patient(fred) & ~humble(fred) [input p23]
25. ~patient(fred) [input hypothesis]
149. patient(fred) [cnf transformation 24]
150. ~patient(fred) [cnf transformation 25]
363. $false [subsumption resolution 150,149]
% SZS output end Proof for 3605797301831091766157028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not tall is funny or calm and vice versa.
Everyone who is tall or not quiet is humble and vice versa.
Everyone who is not calm or rich is both not happy and patient.
Everyone who is either generous or not creative is curious and vice versa.
Everyone who is not quiet is both not happy and not strong.
Everyone who is both not calm and old is both not wise and creative.
Everyone who is brave or wise is either not tall or rich.
If fred is either not humble or not curious then fred is not rich and vice versa.
If someone is both not patient and not strong then someone is kind and vice versa.
If someone is not humble then fred is patient or generous.
Everyone who is not kind or wise is not patient and vice versa.
If someone is not humble or brave then john is not quiet or kind and vice versa.
Everyone who is both curious and not tall is both not kind and not funny and vice versa.
If someone is either not wise or wise then someone is either funny or not strong.
If someone is both quiet and not funny then someone is both humble and not patient and vice versa.
If someone is either not brave or not quiet then susan is either not generous or tall.
John is not happy or humble.
Someone is tall.
Someone is not strong.
Mary is both not rich and old.
Someone is old.
Fred is not tall.
Lucy is not kind or not creative. | Fred is patient. | neutral | (![X]:((~old(X)&~tall(X))<=>(funny(X)|calm(X))))&
(![X]:((tall(X)|~quiet(X))<=>humble(X)))&
(![X]:((~calm(X)|rich(X))=>(~happy(X)&patient(X))))&
(![X]:((generous(X)<~>~creative(X))<=>curious(X)))&
(![X]:(~quiet(X)=>(~happy(X)&~strong(X))))&
(![X]:((~calm(X)&old(X))=>(~wise(X)&creative(X))))&
(![X]:((brave(X)|wise(X))=>(~tall(X)<~>rich(X))))&
(((~humble(fred)<~>~curious(fred)))<=>(~rich(fred)))&
((?[X]:((~patient(X)&~strong(X))))<=>(?[X]:(kind(X))))&
((?[X]:(~humble(X)))=>((patient(fred)|generous(fred))))&
(![X]:((~kind(X)|wise(X))<=>~patient(X)))&
((?[X]:((~humble(X)|brave(X))))<=>((~quiet(john)|kind(john))))&
(![X]:((curious(X)&~tall(X))<=>(~kind(X)&~funny(X))))&
((?[X]:((~wise(X)<~>wise(X))))=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((quiet(X)&~funny(X))))<=>(?[X]:((humble(X)&~patient(X)))))&
((?[X]:((~brave(X)<~>~quiet(X))))=>((~generous(susan)<~>tall(susan))))&
((~happy(john)|humble(john)))&
(?[X]:(tall(X)))&
(?[X]:(~strong(X)))&
((~rich(mary)&old(mary)))&
(?[X]:(old(X)))&
(~tall(fred))&
((~kind(lucy)|~creative(lucy))) | patient(fred) | [] | null | 0 |
If someone is not curious or happy then someone is calm or wise. Everyone who is curious or tall is funny and vice versa. If fred is not happy or kind then someone is both patient and not old and vice versa. Everyone who is both rich and not curious is either happy or kind and vice versa. Everyone who is both not patient and strong is both not rich and generous. Everyone who is both not brave and funny is patient or not creative and vice versa. If fred is either creative or not happy then lucy is either creative or not tall and vice versa. Everyone who is both not quiet and not creative is not happy. Everyone who is either not quiet or quiet is tall. If fred is curious then mary is either tall or humble and vice versa. Everyone who is both not patient and not tall is either calm or old and vice versa. If someone is not generous then alice is both quiet and happy. Everyone who is both funny and humble is both calm and not quiet and vice versa. Everyone who is either old or kind is happy and vice versa. Susan is either not patient or strong. Paul is both creative and not kind. Someone is not kind or old. Someone is not rich or wise. John is strong. Lucy is old. Someone is either quiet or creative. | Paul is not creative. | contradiction | ((?[X]:((~curious(X)|happy(X))))=>(?[X]:((calm(X)|wise(X)))))&
(![X]:((curious(X)|tall(X))<=>funny(X)))&
(((~happy(fred)|kind(fred)))<=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((rich(X)&~curious(X))<=>(happy(X)<~>kind(X))))&
(![X]:((~patient(X)&strong(X))=>(~rich(X)&generous(X))))&
(![X]:((~brave(X)&funny(X))<=>(patient(X)|~creative(X))))&
(((creative(fred)<~>~happy(fred)))<=>((creative(lucy)<~>~tall(lucy))))&
(![X]:((~quiet(X)&~creative(X))=>~happy(X)))&
(![X]:((~quiet(X)<~>quiet(X))=>tall(X)))&
((curious(fred))<=>((tall(mary)<~>humble(mary))))&
(![X]:((~patient(X)&~tall(X))<=>(calm(X)<~>old(X))))&
((?[X]:(~generous(X)))=>((quiet(alice)&happy(alice))))&
(![X]:((funny(X)&humble(X))<=>(calm(X)&~quiet(X))))&
(![X]:((old(X)<~>kind(X))<=>happy(X)))&
((~patient(susan)<~>strong(susan)))&
((creative(paul)&~kind(paul)))&
(?[X]:((~kind(X)|old(X))))&
(?[X]:((~rich(X)|wise(X))))&
(strong(john))&
(old(lucy))&
(?[X]:((quiet(X)<~>creative(X)))) | ~creative(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8292957583170461664974738
% SZS output start Proof for 8292957583170461664974738
16. ~kind(paul) & creative(paul) [input p15]
22. ~creative(paul) [input hypothesis]
109. creative(paul) [cnf transformation 16]
116. ~creative(paul) [cnf transformation 22]
207. $false [subsumption resolution 116,109]
% SZS output end Proof for 8292957583170461664974738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and not generous is either brave or not tall.
Everyone who is both strong and funny is patient or quiet.
If someone is both tall and not wise then alice is not old or not calm and vice versa.
If mary is quiet then lucy is not kind.
If someone is not tall then someone is either not rich or not wise and vice versa.
If alice is creative then lucy is brave or not patient.
Everyone who is both old and not quiet is either brave or not old.
Everyone who is not kind is not curious.
Everyone who is either not curious or brave is creative.
If someone is both not rich and not generous then someone is not calm.
If john is both creative and curious then lucy is both kind and wise and vice versa.
Everyone who is both old and not strong is brave or funny and vice versa.
Everyone who is happy or creative is not generous and vice versa.
Everyone who is generous is not humble and vice versa.
Everyone who is brave or not calm is strong and vice versa.
Everyone who is both happy and patient is either strong or patient and vice versa.
Someone is either curious or humble.
Fred is either not funny or not brave.
Someone is either not old or not generous.
Someone is generous.
Mary is either patient or not rich.
Fred is calm or not happy.
Someone is either not happy or generous.
Lucy is either rich or not rich. | Alice is not brave. | entailment | (![X]:((~happy(X)&~generous(X))=>(brave(X)<~>~tall(X))))&
(![X]:((strong(X)&funny(X))=>(patient(X)|quiet(X))))&
((?[X]:((tall(X)&~wise(X))))<=>((~old(alice)|~calm(alice))))&
((quiet(mary))=>(~kind(lucy)))&
((?[X]:(~tall(X)))<=>(?[X]:((~rich(X)<~>~wise(X)))))&
((creative(alice))=>((brave(lucy)|~patient(lucy))))&
(![X]:((old(X)&~quiet(X))=>(brave(X)<~>~old(X))))&
(![X]:(~kind(X)=>~curious(X)))&
(![X]:((~curious(X)<~>brave(X))=>creative(X)))&
((?[X]:((~rich(X)&~generous(X))))=>(?[X]:(~calm(X))))&
(((creative(john)&curious(john)))<=>((kind(lucy)&wise(lucy))))&
(![X]:((old(X)&~strong(X))<=>(brave(X)|funny(X))))&
(![X]:((happy(X)|creative(X))<=>~generous(X)))&
(![X]:(generous(X)<=>~humble(X)))&
(![X]:((brave(X)|~calm(X))<=>strong(X)))&
(![X]:((happy(X)&patient(X))<=>(strong(X)<~>patient(X))))&
(?[X]:((curious(X)<~>humble(X))))&
((~funny(fred)<~>~brave(fred)))&
(?[X]:((~old(X)<~>~generous(X))))&
(?[X]:(generous(X)))&
((patient(mary)<~>~rich(mary)))&
((calm(fred)|~happy(fred)))&
(?[X]:((~happy(X)<~>generous(X))))&
((rich(lucy)<~>~rich(lucy))) | ~brave(alice) | [
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6551332697795034897117950
% SZS output start Proof for 6551332697795034897117950
12. ! [X0] : ((~strong(X0) & old(X0)) <=> (funny(X0) | brave(X0))) [input p11]
15. ! [X0] : ((~calm(X0) | brave(X0)) <=> strong(X0)) [input p14]
25. brave(alice) [input hypothesis]
58. ! [X0] : (((~strong(X0) & old(X0)) | (~funny(X0) & ~brave(X0))) & ((funny(X0) | brave(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 12]
59. ! [X0] : (((~strong(X0) & old(X0)) | (~funny(X0) & ~brave(X0))) & (funny(X0) | brave(X0) | strong(X0) | ~old(X0))) [flattening 58]
63. ! [X0] : (((~calm(X0) | brave(X0)) | ~strong(X0)) & (strong(X0) | (calm(X0) & ~brave(X0)))) [nnf transformation 15]
64. ! [X0] : ((~calm(X0) | brave(X0) | ~strong(X0)) & (strong(X0) | (calm(X0) & ~brave(X0)))) [flattening 63]
108. ~strong(X0) | ~brave(X0) [cnf transformation 59]
115. strong(X0) | ~brave(X0) [cnf transformation 64]
138. brave(alice) [cnf transformation 25]
238. ~brave(X0) [subsumption resolution 115,108]
282. $false [subsumption resolution 138,238]
% SZS output end Proof for 6551332697795034897117950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not curious or strong then someone is both calm and not kind and vice versa.
If fred is not wise or not patient then someone is both not funny and not happy and vice versa.
If someone is both not wise and calm then someone is both not calm and tall and vice versa.
Everyone who is old or not old is both patient and old and vice versa.
If susan is either wise or curious then someone is either not funny or not old and vice versa.
Everyone who is both humble and not humble is not kind or patient.
If someone is happy then lucy is both tall and not kind.
Everyone who is not tall is either strong or patient.
If someone is not tall then mary is both not generous and creative and vice versa.
Everyone who is both brave and not strong is either curious or tall and vice versa.
If someone is not humble or not creative then fred is either patient or generous and vice versa.
Everyone who is both not kind and not strong is either generous or not funny and vice versa.
If someone is not tall or old then susan is both not happy and curious.
If fred is either not brave or not creative then someone is curious and vice versa.
Everyone who is both quiet and old is kind.
If fred is either not calm or not tall then fred is kind or happy.
Susan is either not strong or not tall.
Someone is both not tall and quiet.
Paul is not kind or generous.
Someone is both not wise and not happy.
Lucy is not calm.
Someone is both curious and not kind.
Alice is calm. | Mary is curious. | neutral | (((~curious(mary)<~>strong(mary)))<=>(?[X]:((calm(X)&~kind(X)))))&
(((~wise(fred)|~patient(fred)))<=>(?[X]:((~funny(X)&~happy(X)))))&
((?[X]:((~wise(X)&calm(X))))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((old(X)|~old(X))<=>(patient(X)&old(X))))&
(((wise(susan)<~>curious(susan)))<=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((humble(X)&~humble(X))=>(~kind(X)|patient(X))))&
((?[X]:(happy(X)))=>((tall(lucy)&~kind(lucy))))&
(![X]:(~tall(X)=>(strong(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>((~generous(mary)&creative(mary))))&
(![X]:((brave(X)&~strong(X))<=>(curious(X)<~>tall(X))))&
((?[X]:((~humble(X)|~creative(X))))<=>((patient(fred)<~>generous(fred))))&
(![X]:((~kind(X)&~strong(X))<=>(generous(X)<~>~funny(X))))&
((?[X]:((~tall(X)|old(X))))=>((~happy(susan)&curious(susan))))&
(((~brave(fred)<~>~creative(fred)))<=>(?[X]:(curious(X))))&
(![X]:((quiet(X)&old(X))=>kind(X)))&
(((~calm(fred)<~>~tall(fred)))=>((kind(fred)|happy(fred))))&
((~strong(susan)<~>~tall(susan)))&
(?[X]:((~tall(X)&quiet(X))))&
((~kind(paul)|generous(paul)))&
(?[X]:((~wise(X)&~happy(X))))&
(~calm(lucy))&
(?[X]:((curious(X)&~kind(X))))&
(calm(alice)) | curious(mary) | [] | null | 0 |
Everyone who is both not strong and not wise is either not rich or brave and vice versa.
Everyone who is strong or not old is not generous and vice versa.
If mary is funny or old then someone is generous.
Everyone who is either patient or not old is not quiet or brave and vice versa.
If someone is both rich and quiet then someone is both tall and calm.
Everyone who is both not quiet and happy is old or not old and vice versa.
Everyone who is either funny or creative is not quiet or curious.
Everyone who is both not calm and happy is creative or not happy and vice versa.
If someone is not creative then mary is not funny or creative.
If someone is either tall or not curious then someone is either not curious or strong and vice versa.
Everyone who is curious or generous is either not old or not quiet.
Everyone who is calm is not quiet or old and vice versa.
Everyone who is both wise and not wise is not happy.
Everyone who is either patient or wise is old.
Everyone who is quiet or not patient is either not wise or not tall and vice versa.
Everyone who is both not brave and not curious is strong or old and vice versa.
Alice is not humble.
Someone is either rich or not strong.
Someone is tall or not happy.
Paul is either not tall or not kind.
Someone is rich.
Mary is not kind or not generous.
Someone is either patient or kind.
Lucy is brave or kind. | Lucy is not curious. | entailment | (![X]:((~strong(X)&~wise(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((strong(X)|~old(X))<=>~generous(X)))&
(((funny(mary)|old(mary)))=>(?[X]:(generous(X))))&
(![X]:((patient(X)<~>~old(X))<=>(~quiet(X)|brave(X))))&
((?[X]:((rich(X)&quiet(X))))=>(?[X]:((tall(X)&calm(X)))))&
(![X]:((~quiet(X)&happy(X))<=>(old(X)|~old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~quiet(X)|curious(X))))&
(![X]:((~calm(X)&happy(X))<=>(creative(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~funny(mary)|creative(mary))))&
((?[X]:((tall(X)<~>~curious(X))))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((curious(X)|generous(X))=>(~old(X)<~>~quiet(X))))&
(![X]:(calm(X)<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)&~wise(X))=>~happy(X)))&
(![X]:((patient(X)<~>wise(X))=>old(X)))&
(![X]:((quiet(X)|~patient(X))<=>(~wise(X)<~>~tall(X))))&
(![X]:((~brave(X)&~curious(X))<=>(strong(X)|old(X))))&
(~humble(alice))&
(?[X]:((rich(X)<~>~strong(X))))&
(?[X]:((tall(X)|~happy(X))))&
((~tall(paul)<~>~kind(paul)))&
(?[X]:(rich(X)))&
((~kind(mary)|~generous(mary)))&
(?[X]:((patient(X)<~>kind(X))))&
((brave(lucy)|kind(lucy))) | ~curious(lucy) | [
"p5",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2856080552100076884486425
% SZS output start Proof for 2856080552100076884486425
6. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (~old(X0) | old(X0))) [input p5]
11. ! [X0] : ((generous(X0) | curious(X0)) => (~old(X0) <~> ~quiet(X0))) [input p10]
16. ! [X0] : ((~curious(X0) & ~brave(X0)) <=> (old(X0) | strong(X0))) [input p15]
25. curious(lucy) [input hypothesis]
35. ! [X0] : ((~old(X0) <~> ~quiet(X0)) | (~generous(X0) & ~curious(X0))) [ennf transformation 11]
50. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~happy(X0) | quiet(X0)))) [nnf transformation 6]
51. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~happy(X0) | quiet(X0))) [flattening 50]
60. ! [X0] : (((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (~generous(X0) & ~curious(X0))) [nnf transformation 35]
66. ! [X0] : (((~curious(X0) & ~brave(X0)) | (~old(X0) & ~strong(X0))) & ((old(X0) | strong(X0)) | (curious(X0) | brave(X0)))) [nnf transformation 16]
67. ! [X0] : (((~curious(X0) & ~brave(X0)) | (~old(X0) & ~strong(X0))) & (old(X0) | strong(X0) | curious(X0) | brave(X0))) [flattening 66]
99. ~quiet(X0) | ~old(X0) [cnf transformation 51]
100. ~quiet(X0) | old(X0) [cnf transformation 51]
121. quiet(X0) | old(X0) | ~curious(X0) [cnf transformation 60]
139. ~curious(X0) | ~old(X0) [cnf transformation 67]
150. curious(lucy) [cnf transformation 25]
181. ~quiet(X0) [subsumption resolution 99,100]
227. old(X0) | ~curious(X0) [subsumption resolution 121,181]
231. ~curious(X0) [subsumption resolution 139,227]
282. $false [subsumption resolution 150,231]
% SZS output end Proof for 2856080552100076884486425
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or wise is both not rich and strong and vice versa. Everyone who is either not old or creative is both not kind and not curious and vice versa. If john is either not quiet or not happy then fred is both not strong and not wise. Everyone who is both curious and not humble is either brave or happy. Everyone who is kind is either kind or not happy and vice versa. If someone is both funny and happy then john is creative. Everyone who is patient or calm is either quiet or not rich. Everyone who is both not tall and not rich is either happy or not calm and vice versa. Everyone who is old is brave. If lucy is not creative or wise then paul is calm or not rich. Everyone who is not calm or not curious is old or not happy and vice versa. If someone is humble then john is both happy and not humble and vice versa. If someone is not tall then john is not funny and vice versa. If lucy is curious or kind then mary is not brave and vice versa. Someone is happy or rich. Someone is generous. Susan is kind or not kind. Someone is either calm or not kind. Someone is both not kind and not generous. Someone is not quiet or not patient. Someone is rich or calm. Alice is both quiet and not creative. | Alice is generous. | neutral | (![X]:((~curious(X)<~>wise(X))<=>(~rich(X)&strong(X))))&
(![X]:((~old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(((~quiet(john)<~>~happy(john)))=>((~strong(fred)&~wise(fred))))&
(![X]:((curious(X)&~humble(X))=>(brave(X)<~>happy(X))))&
(![X]:(kind(X)<=>(kind(X)<~>~happy(X))))&
((?[X]:((funny(X)&happy(X))))=>(creative(john)))&
(![X]:((patient(X)|calm(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~tall(X)&~rich(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(old(X)=>brave(X)))&
(((~creative(lucy)|wise(lucy)))=>((calm(paul)|~rich(paul))))&
(![X]:((~calm(X)|~curious(X))<=>(old(X)|~happy(X))))&
((?[X]:(humble(X)))<=>((happy(john)&~humble(john))))&
((?[X]:(~tall(X)))<=>(~funny(john)))&
(((curious(lucy)|kind(lucy)))<=>(~brave(mary)))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(generous(X)))&
((kind(susan)|~kind(susan)))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((rich(X)|calm(X))))&
((quiet(alice)&~creative(alice))) | generous(alice) | [] | null | 0 |
Everyone who is either funny or not curious is either old or tall. Everyone who is not patient is happy and vice versa. If lucy is both wise and not wise then someone is not curious or rich. If someone is either not old or not curious then paul is either not happy or kind and vice versa. Everyone who is patient or strong is not curious or not humble. Everyone who is calm or not old is not creative and vice versa. If alice is not strong then someone is not kind. Everyone who is not brave or not humble is brave and vice versa. Everyone who is not rich is both not funny and quiet. If mary is either happy or calm then paul is both calm and not brave and vice versa. Everyone who is either wise or not quiet is either not brave or not quiet and vice versa. If john is funny then paul is not tall. Everyone who is calm is not old or calm. Everyone who is either creative or rich is both not quiet and curious. Everyone who is humble or not happy is creative or not calm. Everyone who is not rich is generous or not humble and vice versa. Mary is curious or strong. Alice is tall or not calm. Someone is not kind or brave. Mary is either not quiet or not rich. Someone is either strong or patient. Someone is both not calm and generous. Someone is not patient. | John is rich. | contradiction | (![X]:((funny(X)<~>~curious(X))=>(old(X)<~>tall(X))))&
(![X]:(~patient(X)<=>happy(X)))&
(((wise(lucy)&~wise(lucy)))=>(?[X]:((~curious(X)|rich(X)))))&
((?[X]:((~old(X)<~>~curious(X))))<=>((~happy(paul)<~>kind(paul))))&
(![X]:((patient(X)|strong(X))=>(~curious(X)|~humble(X))))&
(![X]:((calm(X)|~old(X))<=>~creative(X)))&
((~strong(alice))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)|~humble(X))<=>brave(X)))&
(![X]:(~rich(X)=>(~funny(X)&quiet(X))))&
(((happy(mary)<~>calm(mary)))<=>((calm(paul)&~brave(paul))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~brave(X)<~>~quiet(X))))&
((funny(john))=>(~tall(paul)))&
(![X]:(calm(X)=>(~old(X)|calm(X))))&
(![X]:((creative(X)<~>rich(X))=>(~quiet(X)&curious(X))))&
(![X]:((humble(X)|~happy(X))=>(creative(X)|~calm(X))))&
(![X]:(~rich(X)<=>(generous(X)|~humble(X))))&
((curious(mary)|strong(mary)))&
((tall(alice)|~calm(alice)))&
(?[X]:((~kind(X)|brave(X))))&
((~quiet(mary)<~>~rich(mary)))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((~calm(X)&generous(X))))&
(?[X]:(~patient(X))) | rich(john) | [
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8815878191829126115562976
% SZS output start Proof for 8815878191829126115562976
8. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> brave(X0)) [input p7]
16. ! [X0] : (~rich(X0) <=> (~humble(X0) | generous(X0))) [input p15]
24. rich(john) [input hypothesis]
50. ! [X0] : (((~humble(X0) | ~brave(X0)) | ~brave(X0)) & (brave(X0) | (humble(X0) & brave(X0)))) [nnf transformation 8]
51. ! [X0] : ((~humble(X0) | ~brave(X0) | ~brave(X0)) & (brave(X0) | (humble(X0) & brave(X0)))) [flattening 50]
56. ! [X0] : ((~rich(X0) | (humble(X0) & ~generous(X0))) & ((~humble(X0) | generous(X0)) | rich(X0))) [nnf transformation 16]
57. ! [X0] : ((~rich(X0) | (humble(X0) & ~generous(X0))) & (~humble(X0) | generous(X0) | rich(X0))) [flattening 56]
89. brave(X0) | brave(X0) [cnf transformation 51]
91. ~humble(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 51]
118. ~rich(X0) | humble(X0) [cnf transformation 57]
129. rich(john) [cnf transformation 24]
134. brave(X0) [duplicate literal removal 89]
135. ~brave(X0) | ~humble(X0) [duplicate literal removal 91]
251. humble(john) [resolution 118,129]
253. ~humble(X1) [resolution 135,134]
254. $false [resolution 253,251]
% SZS output end Proof for 8815878191829126115562976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is quiet and vice versa.
If lucy is not generous or not funny then someone is not patient or generous and vice versa.
Everyone who is both patient and brave is not tall or generous and vice versa.
Everyone who is not curious or patient is not wise or brave and vice versa.
Everyone who is both quiet and funny is both patient and wise and vice versa.
Everyone who is creative or wise is brave.
If alice is either tall or not generous then fred is not old or not kind.
Everyone who is both brave and quiet is either not wise or wise and vice versa.
Everyone who is humble or not kind is either wise or not rich.
If alice is either quiet or wise then lucy is both patient and not wise.
Everyone who is not calm or wise is not patient or tall.
If someone is either rich or not funny then mary is happy or not quiet and vice versa.
If fred is not strong or patient then someone is kind or not funny and vice versa.
If someone is creative then someone is either not wise or not humble and vice versa.
Everyone who is both patient and brave is not wise and vice versa.
Someone is either calm or not old.
Mary is both quiet and creative.
Someone is not funny.
Someone is both patient and curious.
Someone is funny or old.
Susan is both tall and not happy. | Mary is not curious. | neutral | (![X]:(calm(X)<=>quiet(X)))&
(((~generous(lucy)|~funny(lucy)))<=>(?[X]:((~patient(X)|generous(X)))))&
(![X]:((patient(X)&brave(X))<=>(~tall(X)|generous(X))))&
(![X]:((~curious(X)|patient(X))<=>(~wise(X)|brave(X))))&
(![X]:((quiet(X)&funny(X))<=>(patient(X)&wise(X))))&
(![X]:((creative(X)|wise(X))=>brave(X)))&
(((tall(alice)<~>~generous(alice)))=>((~old(fred)|~kind(fred))))&
(![X]:((brave(X)&quiet(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((humble(X)|~kind(X))=>(wise(X)<~>~rich(X))))&
(((quiet(alice)<~>wise(alice)))=>((patient(lucy)&~wise(lucy))))&
(![X]:((~calm(X)|wise(X))=>(~patient(X)|tall(X))))&
((?[X]:((rich(X)<~>~funny(X))))<=>((happy(mary)|~quiet(mary))))&
(((~strong(fred)|patient(fred)))<=>(?[X]:((kind(X)|~funny(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((patient(X)&brave(X))<=>~wise(X)))&
(?[X]:((calm(X)<~>~old(X))))&
((quiet(mary)&creative(mary)))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)&curious(X))))&
(?[X]:((funny(X)|old(X))))&
((tall(susan)&~happy(susan))) | ~curious(mary) | [] | null | 0 |
Everyone who is either funny or not humble is curious or not wise and vice versa.
Everyone who is curious or wise is both not patient and patient and vice versa.
Everyone who is both rich and patient is strong or old and vice versa.
Everyone who is old is both not curious and generous and vice versa.
If lucy is both patient and generous then paul is either not humble or creative.
If someone is either not old or not strong then someone is not brave and vice versa.
If someone is not rich then susan is generous and vice versa.
Everyone who is generous is funny.
Everyone who is wise is both not kind and brave.
If susan is either patient or not rich then mary is patient or not curious and vice versa.
If someone is not strong or happy then alice is both old and not creative and vice versa.
If someone is not generous or not rich then someone is creative.
Everyone who is either not generous or happy is both not calm and patient and vice versa.
Everyone who is not rich or funny is not kind or not quiet and vice versa.
Everyone who is kind is either rich or quiet and vice versa.
Someone is strong.
Someone is either rich or not strong.
John is either not happy or funny.
Fred is not tall.
John is not quiet or not brave.
Someone is not wise or curious.
Someone is both humble and not wise.
Someone is both not wise and humble. | Alice is not generous. | contradiction | (![X]:((funny(X)<~>~humble(X))<=>(curious(X)|~wise(X))))&
(![X]:((curious(X)|wise(X))<=>(~patient(X)&patient(X))))&
(![X]:((rich(X)&patient(X))<=>(strong(X)|old(X))))&
(![X]:(old(X)<=>(~curious(X)&generous(X))))&
(((patient(lucy)&generous(lucy)))=>((~humble(paul)<~>creative(paul))))&
((?[X]:((~old(X)<~>~strong(X))))<=>(?[X]:(~brave(X))))&
((?[X]:(~rich(X)))<=>(generous(susan)))&
(![X]:(generous(X)=>funny(X)))&
(![X]:(wise(X)=>(~kind(X)&brave(X))))&
(((patient(susan)<~>~rich(susan)))<=>((patient(mary)|~curious(mary))))&
((?[X]:((~strong(X)|happy(X))))<=>((old(alice)&~creative(alice))))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:(creative(X))))&
(![X]:((~generous(X)<~>happy(X))<=>(~calm(X)&patient(X))))&
(![X]:((~rich(X)|funny(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(kind(X)<=>(rich(X)<~>quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:((rich(X)<~>~strong(X))))&
((~happy(john)<~>funny(john)))&
(~tall(fred))&
((~quiet(john)|~brave(john)))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:((humble(X)&~wise(X))))&
(?[X]:((~wise(X)&humble(X)))) | ~generous(alice) | [
"p2",
"p3",
"p10",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6761635064423936120282082
% SZS output start Proof for 6761635064423936120282082
3. ! [X0] : ((patient(X0) & rich(X0)) <=> (old(X0) | strong(X0))) [input p2]
4. ! [X0] : (old(X0) <=> (generous(X0) & ~curious(X0))) [input p3]
11. ? [X0] : (happy(X0) | ~strong(X0)) <=> (~creative(alice) & old(alice)) [input p10]
14. ! [X0] : ((funny(X0) | ~rich(X0)) <=> (~quiet(X0) | ~kind(X0))) [input p13]
15. ! [X0] : (kind(X0) <=> (rich(X0) <~> quiet(X0))) [input p14]
18. ~happy(john) <~> funny(john) [input p17]
24. ~generous(alice) [input hypothesis]
37. ! [X0] : (((patient(X0) & rich(X0)) | (~old(X0) & ~strong(X0))) & ((old(X0) | strong(X0)) | (~patient(X0) | ~rich(X0)))) [nnf transformation 3]
38. ! [X0] : (((patient(X0) & rich(X0)) | (~old(X0) & ~strong(X0))) & (old(X0) | strong(X0) | ~patient(X0) | ~rich(X0))) [flattening 37]
39. ! [X0] : ((old(X0) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | ~old(X0))) [nnf transformation 4]
40. ! [X0] : ((old(X0) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | ~old(X0))) [flattening 39]
53. (? [X0] : (happy(X0) | ~strong(X0)) | (creative(alice) | ~old(alice))) & ((~creative(alice) & old(alice)) | ! [X0] : (~happy(X0) & strong(X0))) [nnf transformation 11]
54. (? [X0] : (happy(X0) | ~strong(X0)) | creative(alice) | ~old(alice)) & ((~creative(alice) & old(alice)) | ! [X0] : (~happy(X0) & strong(X0))) [flattening 53]
55. (? [X0] : (happy(X0) | ~strong(X0)) | creative(alice) | ~old(alice)) & ((~creative(alice) & old(alice)) | ! [X1] : (~happy(X1) & strong(X1))) [rectify 54]
56. ? [X0] : (happy(X0) | ~strong(X0)) => (happy(sK3) | ~strong(sK3)) [choice axiom]
57. ((happy(sK3) | ~strong(sK3)) | creative(alice) | ~old(alice)) & ((~creative(alice) & old(alice)) | ! [X1] : (~happy(X1) & strong(X1))) [skolemisation 55,56]
63. ! [X0] : (((funny(X0) | ~rich(X0)) | (quiet(X0) & kind(X0))) & ((~quiet(X0) | ~kind(X0)) | (~funny(X0) & rich(X0)))) [nnf transformation 14]
64. ! [X0] : ((funny(X0) | ~rich(X0) | (quiet(X0) & kind(X0))) & (~quiet(X0) | ~kind(X0) | (~funny(X0) & rich(X0)))) [flattening 63]
65. ! [X0] : ((kind(X0) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | ~kind(X0))) [nnf transformation 15]
71. (~funny(john) | happy(john)) & (funny(john) | ~happy(john)) [nnf transformation 18]
90. ~strong(X0) | rich(X0) [cnf transformation 38]
95. ~old(X0) | generous(X0) [cnf transformation 40]
114. old(alice) | strong(X1) [cnf transformation 57]
115. old(alice) | ~happy(X1) [cnf transformation 57]
127. ~quiet(X0) | ~kind(X0) | rich(X0) [cnf transformation 64]
129. ~rich(X0) | funny(X0) | kind(X0) [cnf transformation 64]
130. ~rich(X0) | funny(X0) | quiet(X0) [cnf transformation 64]
132. ~quiet(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 65]
139. ~funny(john) | happy(john) [cnf transformation 71]
146. ~generous(alice) [cnf transformation 24]
203. 13 <=> ! [X1] : rich(X1) [avatar definition]
204. rich(X1) <- (13) [avatar component clause 203]
225. 17 <=> old(alice) [avatar definition]
226. old(alice) <- (17) [avatar component clause 225]
242. 21 <=> ! [X1] : ~happy(X1) [avatar definition]
243. ~happy(X1) <- (21) [avatar component clause 242]
246. 22 <=> ! [X1] : strong(X1) [avatar definition]
247. strong(X1) <- (22) [avatar component clause 246]
249. 21 | 17 [avatar split clause 115,225,242]
250. 22 | 17 [avatar split clause 114,225,246]
261. ~quiet(X0) | ~kind(X0) [subsumption resolution 132,127]
273. 27 <=> happy(john) [avatar definition]
275. happy(john) <- (27) [avatar component clause 273]
277. 28 <=> funny(john) [avatar definition]
279. ~funny(john) <- (~28) [avatar component clause 277]
280. 27 | ~28 [avatar split clause 139,277,273]
300. generous(alice) <- (17) [resolution 95,226]
301. $false <- (17) [subsumption resolution 300,146]
302. ~17 [avatar contradiction clause 301]
306. rich(X1) <- (22) [resolution 247,90]
309. 13 | ~22 [avatar split clause 306,246,203]
329. kind(X0) | funny(X0) <- (13) [resolution 129,204]
341. quiet(X0) | funny(X0) <- (13) [resolution 130,204]
355. funny(X2) | ~kind(X2) <- (13) [resolution 341,261]
357. funny(X2) <- (13) [subsumption resolution 355,329]
360. $false <- (13, ~28) [resolution 357,279]
362. ~13 | 28 [avatar contradiction clause 360]
364. $false <- (21, 27) [subsumption resolution 275,243]
365. ~21 | ~27 [avatar contradiction clause 364]
366. $false [avatar sat refutation 249,250,280,302,309,362,365]
% SZS output end Proof for 6761635064423936120282082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious or not old then someone is both not rich and humble.
Everyone who is both not happy and rich is creative and vice versa.
Everyone who is kind or patient is both tall and old and vice versa.
Everyone who is either not generous or rich is rich and vice versa.
Everyone who is not quiet is not curious.
If someone is old or brave then paul is not creative and vice versa.
If someone is both kind and not funny then alice is either creative or kind and vice versa.
If someone is both not patient and not wise then someone is both not creative and calm.
Everyone who is kind is not happy or happy and vice versa.
If someone is not funny or not quiet then lucy is either brave or not generous.
Everyone who is old is both old and not patient and vice versa.
Everyone who is both happy and kind is either rich or old and vice versa.
Everyone who is not curious or wise is both not old and tall and vice versa.
Everyone who is either not strong or not quiet is not strong.
If paul is not patient or not calm then paul is both brave and not wise.
John is both tall and not funny.
Alice is tall or not calm.
Someone is both brave and rich.
Someone is either calm or not kind.
Someone is not calm or rich.
Alice is either not rich or brave. | John is not patient. | entailment | (((~curious(alice)|~old(alice)))=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((~happy(X)&rich(X))<=>creative(X)))&
(![X]:((kind(X)|patient(X))<=>(tall(X)&old(X))))&
(![X]:((~generous(X)<~>rich(X))<=>rich(X)))&
(![X]:(~quiet(X)=>~curious(X)))&
((?[X]:((old(X)|brave(X))))<=>(~creative(paul)))&
((?[X]:((kind(X)&~funny(X))))<=>((creative(alice)<~>kind(alice))))&
((?[X]:((~patient(X)&~wise(X))))=>(?[X]:((~creative(X)&calm(X)))))&
(![X]:(kind(X)<=>(~happy(X)|happy(X))))&
((?[X]:((~funny(X)|~quiet(X))))=>((brave(lucy)<~>~generous(lucy))))&
(![X]:(old(X)<=>(old(X)&~patient(X))))&
(![X]:((happy(X)&kind(X))<=>(rich(X)<~>old(X))))&
(![X]:((~curious(X)|wise(X))<=>(~old(X)&tall(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>~strong(X)))&
(((~patient(paul)|~calm(paul)))=>((brave(paul)&~wise(paul))))&
((tall(john)&~funny(john)))&
((tall(alice)|~calm(alice)))&
(?[X]:((brave(X)&rich(X))))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((~calm(X)|rich(X))))&
((~rich(alice)<~>brave(alice))) | ~patient(john) | [
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4122243370381510975103340
% SZS output start Proof for 4122243370381510975103340
3. ! [X0] : ((patient(X0) | kind(X0)) <=> (old(X0) & tall(X0))) [input p2]
11. ! [X0] : (old(X0) <=> (~patient(X0) & old(X0))) [input p10]
22. patient(john) [input hypothesis]
35. ! [X0] : (((patient(X0) | kind(X0)) | (~old(X0) | ~tall(X0))) & ((old(X0) & tall(X0)) | (~patient(X0) & ~kind(X0)))) [nnf transformation 3]
36. ! [X0] : ((patient(X0) | kind(X0) | ~old(X0) | ~tall(X0)) & ((old(X0) & tall(X0)) | (~patient(X0) & ~kind(X0)))) [flattening 35]
52. ! [X0] : ((old(X0) | (patient(X0) | ~old(X0))) & ((~patient(X0) & old(X0)) | ~old(X0))) [nnf transformation 11]
53. ! [X0] : ((old(X0) | patient(X0) | ~old(X0)) & ((~patient(X0) & old(X0)) | ~old(X0))) [flattening 52]
75. old(X0) | ~patient(X0) [cnf transformation 36]
101. ~patient(X0) | ~old(X0) [cnf transformation 53]
130. patient(john) [cnf transformation 22]
223. ~patient(X0) [subsumption resolution 101,75]
272. $false [subsumption resolution 130,223]
% SZS output end Proof for 4122243370381510975103340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is not rich or not humble.
Everyone who is either not calm or not happy is strong or not patient and vice versa.
Everyone who is both not brave and old is either humble or old and vice versa.
Everyone who is not humble is both not kind and tall and vice versa.
If someone is not calm or calm then someone is either not curious or not generous.
Everyone who is brave or creative is either kind or quiet.
If paul is either not happy or not creative then mary is rich or not curious and vice versa.
Everyone who is wise is not tall or not happy and vice versa.
If someone is either not funny or tall then paul is both funny and not brave and vice versa.
Everyone who is not tall is not quiet or generous.
Everyone who is old or wise is either quiet or not wise and vice versa.
Everyone who is not funny is either patient or quiet.
Everyone who is both not funny and curious is quiet.
If someone is patient then someone is either not tall or not creative and vice versa.
If someone is both not happy and not tall then fred is both not generous and calm and vice versa.
Everyone who is both happy and not funny is both brave and patient and vice versa.
Paul is humble or not brave.
Paul is not wise.
Someone is either curious or not quiet.
Susan is both not humble and not rich.
Someone is both not old and not funny.
Someone is wise or not wise.
Someone is strong or not curious.
Mary is either not quiet or not tall. | Mary is humble. | neutral | (![X]:(humble(X)=>(~rich(X)|~humble(X))))&
(![X]:((~calm(X)<~>~happy(X))<=>(strong(X)|~patient(X))))&
(![X]:((~brave(X)&old(X))<=>(humble(X)<~>old(X))))&
(![X]:(~humble(X)<=>(~kind(X)&tall(X))))&
((?[X]:((~calm(X)|calm(X))))=>(?[X]:((~curious(X)<~>~generous(X)))))&
(![X]:((brave(X)|creative(X))=>(kind(X)<~>quiet(X))))&
(((~happy(paul)<~>~creative(paul)))<=>((rich(mary)|~curious(mary))))&
(![X]:(wise(X)<=>(~tall(X)|~happy(X))))&
((?[X]:((~funny(X)<~>tall(X))))<=>((funny(paul)&~brave(paul))))&
(![X]:(~tall(X)=>(~quiet(X)|generous(X))))&
(![X]:((old(X)|wise(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:(~funny(X)=>(patient(X)<~>quiet(X))))&
(![X]:((~funny(X)&curious(X))=>quiet(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~tall(X)<~>~creative(X)))))&
((?[X]:((~happy(X)&~tall(X))))<=>((~generous(fred)&calm(fred))))&
(![X]:((happy(X)&~funny(X))<=>(brave(X)&patient(X))))&
((humble(paul)|~brave(paul)))&
(~wise(paul))&
(?[X]:((curious(X)<~>~quiet(X))))&
((~humble(susan)&~rich(susan)))&
(?[X]:((~old(X)&~funny(X))))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:((strong(X)|~curious(X))))&
((~quiet(mary)<~>~tall(mary))) | humble(mary) | [] | null | 0 |
If fred is not wise or not calm then alice is both not curious and not funny and vice versa.
Everyone who is both not curious and wise is kind.
If someone is both brave and not calm then someone is both not funny and old.
If lucy is wise then paul is rich and vice versa.
If fred is either not humble or wise then someone is kind and vice versa.
If susan is either not patient or not strong then fred is tall.
Everyone who is not rich is both humble and not generous and vice versa.
Everyone who is either generous or strong is either humble or curious and vice versa.
Everyone who is curious or not quiet is both not wise and curious and vice versa.
If fred is either not curious or wise then someone is not funny and vice versa.
Everyone who is not humble is quiet or not calm and vice versa.
Everyone who is both tall and not generous is either curious or not patient.
Everyone who is both wise and not quiet is not kind or not patient and vice versa.
If someone is both not creative and not rich then lucy is both not tall and not creative and vice versa.
Everyone who is both not curious and calm is not humble or brave and vice versa.
Everyone who is both not happy and not brave is both not calm and not quiet and vice versa.
Someone is wise or not generous.
Mary is either not humble or wise.
Someone is either not happy or not strong.
Someone is not old.
Someone is not quiet or curious.
Someone is either funny or not generous.
Someone is calm or creative. | Alice is not happy. | neutral | (((~wise(fred)|~calm(fred)))<=>((~curious(alice)&~funny(alice))))&
(![X]:((~curious(X)&wise(X))=>kind(X)))&
((?[X]:((brave(X)&~calm(X))))=>(?[X]:((~funny(X)&old(X)))))&
((wise(lucy))<=>(rich(paul)))&
(((~humble(fred)<~>wise(fred)))<=>(?[X]:(kind(X))))&
(((~patient(susan)<~>~strong(susan)))=>(tall(fred)))&
(![X]:(~rich(X)<=>(humble(X)&~generous(X))))&
(![X]:((generous(X)<~>strong(X))<=>(humble(X)<~>curious(X))))&
(![X]:((curious(X)|~quiet(X))<=>(~wise(X)&curious(X))))&
(((~curious(fred)<~>wise(fred)))<=>(?[X]:(~funny(X))))&
(![X]:(~humble(X)<=>(quiet(X)|~calm(X))))&
(![X]:((tall(X)&~generous(X))=>(curious(X)<~>~patient(X))))&
(![X]:((wise(X)&~quiet(X))<=>(~kind(X)|~patient(X))))&
((?[X]:((~creative(X)&~rich(X))))<=>((~tall(lucy)&~creative(lucy))))&
(![X]:((~curious(X)&calm(X))<=>(~humble(X)|brave(X))))&
(![X]:((~happy(X)&~brave(X))<=>(~calm(X)&~quiet(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~humble(mary)<~>wise(mary)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:(~old(X)))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:((funny(X)<~>~generous(X))))&
(?[X]:((calm(X)|creative(X)))) | ~happy(alice) | [] | null | 0 |
Everyone who is either not brave or brave is rich.
If mary is patient or strong then paul is wise or not strong.
Everyone who is both creative and not brave is both humble and not rich and vice versa.
If someone is tall then someone is calm.
If alice is happy then someone is either patient or not old.
Everyone who is not tall is both not humble and tall.
Everyone who is not happy or brave is not humble and vice versa.
Everyone who is either quiet or not patient is strong and vice versa.
If someone is quiet then someone is kind.
Everyone who is both not creative and quiet is not humble or not strong and vice versa.
If paul is both happy and rich then someone is both not calm and curious and vice versa.
If lucy is both patient and not strong then susan is not quiet and vice versa.
If someone is either humble or not brave then mary is not quiet or quiet and vice versa.
Everyone who is happy or not humble is either not tall or quiet.
Everyone who is creative is either not happy or funny.
Fred is generous or not generous.
Paul is quiet.
Fred is both old and not humble.
John is either wise or not funny.
Alice is humble or rich.
Someone is humble.
Susan is both curious and humble. | Alice is not rich. | contradiction | (![X]:((~brave(X)<~>brave(X))=>rich(X)))&
(((patient(mary)|strong(mary)))=>((wise(paul)|~strong(paul))))&
(![X]:((creative(X)&~brave(X))<=>(humble(X)&~rich(X))))&
((?[X]:(tall(X)))=>(?[X]:(calm(X))))&
((happy(alice))=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:(~tall(X)=>(~humble(X)&tall(X))))&
(![X]:((~happy(X)|brave(X))<=>~humble(X)))&
(![X]:((quiet(X)<~>~patient(X))<=>strong(X)))&
((?[X]:(quiet(X)))=>(?[X]:(kind(X))))&
(![X]:((~creative(X)&quiet(X))<=>(~humble(X)|~strong(X))))&
(((happy(paul)&rich(paul)))<=>(?[X]:((~calm(X)&curious(X)))))&
(((patient(lucy)&~strong(lucy)))<=>(~quiet(susan)))&
((?[X]:((humble(X)<~>~brave(X))))<=>((~quiet(mary)|quiet(mary))))&
(![X]:((happy(X)|~humble(X))=>(~tall(X)<~>quiet(X))))&
(![X]:(creative(X)=>(~happy(X)<~>funny(X))))&
((generous(fred)|~generous(fred)))&
(quiet(paul))&
((old(fred)&~humble(fred)))&
((wise(john)<~>~funny(john)))&
((humble(alice)|rich(alice)))&
(?[X]:(humble(X)))&
((curious(susan)&humble(susan))) | ~rich(alice) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5522306346208687604481938
% SZS output start Proof for 5522306346208687604481938
1. ! [X0] : ((~brave(X0) <~> brave(X0)) => rich(X0)) [input p0]
23. ~rich(alice) [input hypothesis]
27. ! [X0] : (rich(X0) | (~brave(X0) <=> brave(X0))) [ennf transformation 1]
35. ! [X0] : (rich(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 27]
66. rich(X0) | brave(X0) | brave(X0) [cnf transformation 35]
67. rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 35]
120. ~rich(alice) [cnf transformation 23]
122. rich(X0) | brave(X0) [duplicate literal removal 66]
123. rich(X0) | ~brave(X0) [duplicate literal removal 67]
124. rich(X0) [subsumption resolution 122,123]
232. $false [subsumption resolution 120,124]
% SZS output end Proof for 5522306346208687604481938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not curious is not curious.
Everyone who is either calm or generous is tall.
Everyone who is not brave is both kind and not strong and vice versa.
Everyone who is either quiet or not calm is not creative.
If paul is both generous and creative then someone is not funny or happy and vice versa.
Everyone who is patient or not wise is not curious.
If someone is either old or not wise then someone is both not calm and not strong and vice versa.
Everyone who is patient or strong is both kind and happy and vice versa.
Everyone who is both not calm and rich is both quiet and humble and vice versa.
If someone is kind or not old then mary is not rich.
Everyone who is both strong and patient is not rich or wise.
Everyone who is either not kind or not generous is either wise or not funny.
Everyone who is both not brave and curious is strong or brave and vice versa.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
Someone is creative or patient.
Someone is not wise or not calm.
Lucy is either tall or not funny.
Someone is either tall or not humble.
Someone is both not curious and quiet.
Fred is not curious or brave.
Mary is both not patient and not creative. | Lucy is not quiet. | neutral | (![X]:((old(X)|~curious(X))=>~curious(X)))&
(![X]:((calm(X)<~>generous(X))=>tall(X)))&
(![X]:(~brave(X)<=>(kind(X)&~strong(X))))&
(![X]:((quiet(X)<~>~calm(X))=>~creative(X)))&
(((generous(paul)&creative(paul)))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((patient(X)|~wise(X))=>~curious(X)))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~calm(X)&~strong(X)))))&
(![X]:((patient(X)|strong(X))<=>(kind(X)&happy(X))))&
(![X]:((~calm(X)&rich(X))<=>(quiet(X)&humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(~rich(mary)))&
(![X]:((strong(X)&patient(X))=>(~rich(X)|wise(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)|brave(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((~wise(X)|~calm(X))))&
((tall(lucy)<~>~funny(lucy)))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((~curious(X)&quiet(X))))&
((~curious(fred)|brave(fred)))&
((~patient(mary)&~creative(mary))) | ~quiet(lucy) | [] | null | 0 |
If someone is either tall or wise then someone is patient or not funny and vice versa.
Everyone who is either not happy or tall is not calm or not generous and vice versa.
If someone is wise then someone is not generous or not old.
Everyone who is old is both not patient and not funny.
Everyone who is both not wise and not tall is both generous and kind.
If someone is rich or kind then someone is either tall or not old.
Everyone who is either not tall or old is either not kind or calm.
Everyone who is curious or not patient is either not rich or not strong.
If john is humble then someone is both generous and not rich.
Everyone who is humble or wise is both not creative and not brave.
Everyone who is brave is either old or not strong.
Everyone who is both funny and calm is either curious or patient and vice versa.
Everyone who is creative or not strong is both not old and not generous and vice versa.
Everyone who is calm or not old is either old or tall and vice versa.
Everyone who is not tall is both not humble and happy and vice versa.
Everyone who is happy or not calm is funny or tall.
Someone is both not calm and generous.
Someone is not tall or not humble.
Lucy is patient.
Someone is either not calm or humble.
Someone is wise. | John is not brave. | entailment | ((?[X]:((tall(X)<~>wise(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(~calm(X)|~generous(X))))&
((?[X]:(wise(X)))=>(?[X]:((~generous(X)|~old(X)))))&
(![X]:(old(X)=>(~patient(X)&~funny(X))))&
(![X]:((~wise(X)&~tall(X))=>(generous(X)&kind(X))))&
((?[X]:((rich(X)|kind(X))))=>(?[X]:((tall(X)<~>~old(X)))))&
(![X]:((~tall(X)<~>old(X))=>(~kind(X)<~>calm(X))))&
(![X]:((curious(X)|~patient(X))=>(~rich(X)<~>~strong(X))))&
((humble(john))=>(?[X]:((generous(X)&~rich(X)))))&
(![X]:((humble(X)|wise(X))=>(~creative(X)&~brave(X))))&
(![X]:(brave(X)=>(old(X)<~>~strong(X))))&
(![X]:((funny(X)&calm(X))<=>(curious(X)<~>patient(X))))&
(![X]:((creative(X)|~strong(X))<=>(~old(X)&~generous(X))))&
(![X]:((calm(X)|~old(X))<=>(old(X)<~>tall(X))))&
(![X]:(~tall(X)<=>(~humble(X)&happy(X))))&
(![X]:((happy(X)|~calm(X))=>(funny(X)|tall(X))))&
(?[X]:((~calm(X)&generous(X))))&
(?[X]:((~tall(X)|~humble(X))))&
(patient(lucy))&
(?[X]:((~calm(X)<~>humble(X))))&
(?[X]:(wise(X))) | ~brave(john) | [
"p1",
"p3",
"p9",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 511045004093652806704220
% SZS output start Proof for 511045004093652806704220
2. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (~generous(X0) | ~calm(X0))) [input p1]
4. ! [X0] : (old(X0) => (~funny(X0) & ~patient(X0))) [input p3]
10. ! [X0] : ((wise(X0) | humble(X0)) => (~brave(X0) & ~creative(X0))) [input p9]
11. ! [X0] : (brave(X0) => (old(X0) <~> ~strong(X0))) [input p10]
13. ! [X0] : ((~strong(X0) | creative(X0)) <=> (~generous(X0) & ~old(X0))) [input p12]
14. ! [X0] : ((~old(X0) | calm(X0)) <=> (old(X0) <~> tall(X0))) [input p13]
15. ! [X0] : (~tall(X0) <=> (happy(X0) & ~humble(X0))) [input p14]
16. ! [X0] : ((~calm(X0) | happy(X0)) => (tall(X0) | funny(X0))) [input p15]
22. brave(john) [input hypothesis]
27. ! [X0] : ((~funny(X0) & ~patient(X0)) | ~old(X0)) [ennf transformation 4]
34. ! [X0] : ((~brave(X0) & ~creative(X0)) | (~wise(X0) & ~humble(X0))) [ennf transformation 10]
35. ! [X0] : ((old(X0) <~> ~strong(X0)) | ~brave(X0)) [ennf transformation 11]
36. ! [X0] : ((tall(X0) | funny(X0)) | (calm(X0) & ~happy(X0))) [ennf transformation 16]
37. ! [X0] : (tall(X0) | funny(X0) | (calm(X0) & ~happy(X0))) [flattening 36]
43. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (generous(X0) & calm(X0))) & ((~generous(X0) | ~calm(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 2]
44. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (generous(X0) & calm(X0))) & (~generous(X0) | ~calm(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 43]
56. ! [X0] : (((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | ~brave(X0)) [nnf transformation 35]
59. ! [X0] : (((~strong(X0) | creative(X0)) | (generous(X0) | old(X0))) & ((~generous(X0) & ~old(X0)) | (strong(X0) & ~creative(X0)))) [nnf transformation 13]
60. ! [X0] : ((~strong(X0) | creative(X0) | generous(X0) | old(X0)) & ((~generous(X0) & ~old(X0)) | (strong(X0) & ~creative(X0)))) [flattening 59]
61. ! [X0] : (((~old(X0) | calm(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (old(X0) & ~calm(X0)))) [nnf transformation 14]
62. ! [X0] : ((~old(X0) | calm(X0) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (old(X0) & ~calm(X0)))) [flattening 61]
63. ! [X0] : ((~tall(X0) | (~happy(X0) | humble(X0))) & ((happy(X0) & ~humble(X0)) | tall(X0))) [nnf transformation 15]
64. ! [X0] : ((~tall(X0) | ~happy(X0) | humble(X0)) & ((happy(X0) & ~humble(X0)) | tall(X0))) [flattening 63]
84. ~tall(X0) | happy(X0) | calm(X0) [cnf transformation 44]
85. ~tall(X0) | happy(X0) | generous(X0) [cnf transformation 44]
88. ~old(X0) | ~funny(X0) [cnf transformation 27]
107. ~brave(X0) | ~humble(X0) [cnf transformation 34]
109. ~brave(X0) | old(X0) | ~strong(X0) [cnf transformation 56]
120. ~generous(X0) | strong(X0) [cnf transformation 60]
123. tall(X0) | old(X0) | old(X0) [cnf transformation 62]
124. ~old(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 62]
129. happy(X0) | tall(X0) [cnf transformation 64]
130. ~happy(X0) | ~tall(X0) | humble(X0) [cnf transformation 64]
131. tall(X0) | funny(X0) | ~happy(X0) [cnf transformation 37]
140. brave(john) [cnf transformation 22]
141. old(X0) | tall(X0) [duplicate literal removal 123]
208. 16 <=> humble(john) [avatar definition]
210. ~humble(john) <- (~16) [avatar component clause 208]
221. funny(X0) | tall(X0) [subsumption resolution 131,129]
233. ~humble(john) [resolution 107,140]
239. tall(X1) | ~funny(X1) [resolution 141,88]
243. tall(X1) [subsumption resolution 239,221]
254. calm(X0) | happy(X0) [resolution 84,243]
275. generous(X0) | happy(X0) [resolution 85,243]
311. old(john) | ~strong(john) [resolution 109,140]
313. 30 <=> strong(john) [avatar definition]
315. ~strong(john) <- (~30) [avatar component clause 313]
317. 31 <=> old(john) [avatar definition]
319. old(john) <- (31) [avatar component clause 317]
320. ~30 | 31 [avatar split clause 311,317,313]
418. strong(X2) | happy(X2) [resolution 275,120]
455. 45 <=> calm(john) [avatar definition]
457. ~calm(john) <- (~45) [avatar component clause 455]
472. happy(john) <- (~30) [resolution 418,315]
535. ~tall(john) | humble(john) <- (~30) [resolution 472,130]
538. humble(john) <- (~30) [subsumption resolution 535,243]
541. 16 | 30 [avatar split clause 538,313,208]
542. ~16 [avatar split clause 233,208]
567. ~tall(john) | ~calm(john) <- (31) [resolution 319,124]
577. ~calm(john) <- (31) [subsumption resolution 567,243]
578. ~45 | ~31 [avatar split clause 577,317,455]
591. happy(john) <- (~45) [resolution 457,254]
607. ~tall(john) | humble(john) <- (~45) [resolution 591,130]
610. humble(john) <- (~45) [subsumption resolution 607,243]
611. $false <- (~16, ~45) [subsumption resolution 610,210]
612. 16 | 45 [avatar contradiction clause 611]
613. $false [avatar sat refutation 320,541,542,578,612]
% SZS output end Proof for 511045004093652806704220
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or happy is either not brave or funny. If someone is not kind or not old then someone is strong or not generous. Everyone who is funny or generous is either calm or creative. If someone is either not brave or old then susan is either calm or not creative. If someone is either calm or kind then fred is either quiet or not strong and vice versa. Everyone who is both not humble and quiet is strong. If someone is not creative or funny then lucy is both not old and tall. If fred is either creative or not tall then paul is not curious or not tall. Everyone who is either not old or not wise is happy or brave. Everyone who is either humble or old is patient or wise and vice versa. Everyone who is either strong or not patient is not calm and vice versa. If susan is either strong or not old then someone is not strong or not wise and vice versa. If someone is both not quiet and not brave then someone is not tall. Everyone who is not tall is both not strong and not patient and vice versa. If lucy is not humble then someone is either not kind or kind. Everyone who is old is not creative or curious and vice versa. Someone is calm or generous. Alice is not humble or calm. Alice is not quiet. Someone is creative or calm. Someone is both not kind and tall. Paul is not happy. Someone is both kind and funny. | Paul is tall. | neutral | (![X]:((~humble(X)<~>happy(X))=>(~brave(X)<~>funny(X))))&
((?[X]:((~kind(X)|~old(X))))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((funny(X)|generous(X))=>(calm(X)<~>creative(X))))&
((?[X]:((~brave(X)<~>old(X))))=>((calm(susan)<~>~creative(susan))))&
((?[X]:((calm(X)<~>kind(X))))<=>((quiet(fred)<~>~strong(fred))))&
(![X]:((~humble(X)&quiet(X))=>strong(X)))&
((?[X]:((~creative(X)|funny(X))))=>((~old(lucy)&tall(lucy))))&
(((creative(fred)<~>~tall(fred)))=>((~curious(paul)|~tall(paul))))&
(![X]:((~old(X)<~>~wise(X))=>(happy(X)|brave(X))))&
(![X]:((humble(X)<~>old(X))<=>(patient(X)|wise(X))))&
(![X]:((strong(X)<~>~patient(X))<=>~calm(X)))&
(((strong(susan)<~>~old(susan)))<=>(?[X]:((~strong(X)|~wise(X)))))&
((?[X]:((~quiet(X)&~brave(X))))=>(?[X]:(~tall(X))))&
(![X]:(~tall(X)<=>(~strong(X)&~patient(X))))&
((~humble(lucy))=>(?[X]:((~kind(X)<~>kind(X)))))&
(![X]:(old(X)<=>(~creative(X)|curious(X))))&
(?[X]:((calm(X)|generous(X))))&
((~humble(alice)|calm(alice)))&
(~quiet(alice))&
(?[X]:((creative(X)|calm(X))))&
(?[X]:((~kind(X)&tall(X))))&
(~happy(paul))&
(?[X]:((kind(X)&funny(X)))) | tall(paul) | [] | null | 0 |
Everyone who is both not curious and kind is happy and vice versa.
If lucy is both brave and humble then someone is patient or wise.
Everyone who is creative is generous or not calm and vice versa.
If susan is both not calm and happy then someone is both rich and not old and vice versa.
If someone is not brave or not patient then fred is old and vice versa.
If lucy is not creative then fred is not wise and vice versa.
Everyone who is brave or not tall is calm or not rich and vice versa.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Susan is not happy.
Fred is not patient.
Mary is brave or curious.
Someone is patient.
Susan is calm or not rich.
Someone is happy or strong. | Lucy is not quiet. | neutral | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:(creative(X)<=>(generous(X)|~calm(X))))&
(((~calm(susan)&happy(susan)))<=>(?[X]:((rich(X)&~old(X)))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(~happy(susan))&
(~patient(fred))&
((brave(mary)|curious(mary)))&
(?[X]:(patient(X)))&
((calm(susan)|~rich(susan)))&
(?[X]:((happy(X)|strong(X)))) | ~quiet(lucy) | [] | null | 0 |
If susan is not rich then susan is humble or not calm. Everyone who is not calm is either quiet or humble and vice versa. If fred is not creative or not generous then someone is not calm or not tall. Everyone who is funny is not kind or patient and vice versa. If someone is either brave or funny then someone is both not generous and brave. Everyone who is not generous or wise is either not humble or not quiet. Everyone who is both wise and not wise is both not rich and not tall and vice versa. If someone is not creative or not brave then susan is both not calm and not creative and vice versa. Everyone who is either generous or not humble is brave or not old and vice versa. Everyone who is funny or not generous is both patient and old. Everyone who is either not funny or wise is brave and vice versa. Everyone who is wise or not kind is not patient and vice versa. Everyone who is creative is patient. If someone is not generous or rich then someone is not patient or not funny. Everyone who is either quiet or not happy is generous or not generous and vice versa. John is either quiet or strong. Paul is curious or happy. Someone is either quiet or curious. John is either patient or not quiet. Lucy is not curious. Alice is either not creative or tall. Someone is not calm or not funny. | Alice is calm. | contradiction | ((~rich(susan))=>((humble(susan)|~calm(susan))))&
(![X]:(~calm(X)<=>(quiet(X)<~>humble(X))))&
(((~creative(fred)|~generous(fred)))=>(?[X]:((~calm(X)|~tall(X)))))&
(![X]:(funny(X)<=>(~kind(X)|patient(X))))&
((?[X]:((brave(X)<~>funny(X))))=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((~generous(X)|wise(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((wise(X)&~wise(X))<=>(~rich(X)&~tall(X))))&
((?[X]:((~creative(X)|~brave(X))))<=>((~calm(susan)&~creative(susan))))&
(![X]:((generous(X)<~>~humble(X))<=>(brave(X)|~old(X))))&
(![X]:((funny(X)|~generous(X))=>(patient(X)&old(X))))&
(![X]:((~funny(X)<~>wise(X))<=>brave(X)))&
(![X]:((wise(X)|~kind(X))<=>~patient(X)))&
(![X]:(creative(X)=>patient(X)))&
((?[X]:((~generous(X)|rich(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((quiet(X)<~>~happy(X))<=>(generous(X)|~generous(X))))&
((quiet(john)<~>strong(john)))&
((curious(paul)|happy(paul)))&
(?[X]:((quiet(X)<~>curious(X))))&
((patient(john)<~>~quiet(john)))&
(~curious(lucy))&
((~creative(alice)<~>tall(alice)))&
(?[X]:((~calm(X)|~funny(X)))) | calm(alice) | [
"p1",
"p3",
"p4",
"p5",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 114786982537413483099543
% SZS output start Proof for 114786982537413483099543
2. ! [X0] : (~calm(X0) <=> (quiet(X0) <~> humble(X0))) [input p1]
4. ! [X0] : (funny(X0) <=> (patient(X0) | ~kind(X0))) [input p3]
5. ? [X0] : (brave(X0) <~> funny(X0)) => ? [X0] : (brave(X0) & ~generous(X0)) [input p4]
6. ! [X0] : ((wise(X0) | ~generous(X0)) => (~humble(X0) <~> ~quiet(X0))) [input p5]
10. ! [X0] : ((~generous(X0) | funny(X0)) => (old(X0) & patient(X0))) [input p9]
11. ! [X0] : ((~funny(X0) <~> wise(X0)) <=> brave(X0)) [input p10]
12. ! [X0] : ((~kind(X0) | wise(X0)) <=> ~patient(X0)) [input p11]
23. calm(alice) [input hypothesis]
24. ? [X0] : (brave(X0) <~> funny(X0)) => ? [X1] : (brave(X1) & ~generous(X1)) [rectify 5]
29. ? [X1] : (brave(X1) & ~generous(X1)) | ! [X0] : (brave(X0) <=> funny(X0)) [ennf transformation 24]
30. ! [X0] : ((~humble(X0) <~> ~quiet(X0)) | (~wise(X0) & generous(X0))) [ennf transformation 6]
31. ! [X0] : ((old(X0) & patient(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 10]
34. ! [X0] : ((~calm(X0) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0)))) & (((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | calm(X0))) [nnf transformation 2]
37. ! [X0] : ((funny(X0) | (~patient(X0) & kind(X0))) & ((patient(X0) | ~kind(X0)) | ~funny(X0))) [nnf transformation 4]
38. ! [X0] : ((funny(X0) | (~patient(X0) & kind(X0))) & (patient(X0) | ~kind(X0) | ~funny(X0))) [flattening 37]
39. ? [X1] : (brave(X1) & ~generous(X1)) | ! [X0] : ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))) [nnf transformation 29]
40. ? [X0] : (brave(X0) & ~generous(X0)) | ! [X1] : ((brave(X1) | ~funny(X1)) & (funny(X1) | ~brave(X1))) [rectify 39]
41. ? [X0] : (brave(X0) & ~generous(X0)) => (brave(sK1) & ~generous(sK1)) [choice axiom]
42. (brave(sK1) & ~generous(sK1)) | ! [X1] : ((brave(X1) | ~funny(X1)) & (funny(X1) | ~brave(X1))) [skolemisation 40,41]
43. ! [X0] : (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | (~wise(X0) & generous(X0))) [nnf transformation 30]
53. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | ~brave(X0)) & (brave(X0) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [nnf transformation 11]
54. ! [X0] : (((~kind(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (kind(X0) & ~wise(X0)))) [nnf transformation 12]
55. ! [X0] : ((~kind(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (kind(X0) & ~wise(X0)))) [flattening 54]
72. ~quiet(X0) | humble(X0) | ~calm(X0) [cnf transformation 34]
73. ~calm(X0) | quiet(X0) | ~humble(X0) [cnf transformation 34]
77. kind(X0) | funny(X0) [cnf transformation 38]
78. ~patient(X0) | funny(X0) [cnf transformation 38]
82. brave(sK1) | brave(X1) | ~funny(X1) [cnf transformation 42]
84. ~wise(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 43]
86. ~wise(X0) | humble(X0) | quiet(X0) [cnf transformation 43]
102. ~funny(X0) | patient(X0) [cnf transformation 31]
108. ~brave(X0) | ~funny(X0) | wise(X0) [cnf transformation 53]
109. ~wise(X0) | funny(X0) | ~brave(X0) [cnf transformation 53]
110. ~wise(X0) | ~patient(X0) [cnf transformation 55]
112. ~kind(X0) | wise(X0) | patient(X0) [cnf transformation 55]
133. calm(alice) [cnf transformation 23]
166. 8 <=> ! [X1] : (brave(X1) | ~funny(X1)) [avatar definition]
167. ~funny(X1) | brave(X1) <- (8) [avatar component clause 166]
169. 9 <=> brave(sK1) [avatar definition]
171. brave(sK1) <- (9) [avatar component clause 169]
172. 8 | 9 [avatar split clause 82,169,166]
174. 10 <=> ! [X1] : (funny(X1) | ~brave(X1)) [avatar definition]
175. ~brave(X1) | funny(X1) <- (10) [avatar component clause 174]
323. quiet(alice) | ~humble(alice) [resolution 73,133]
325. 35 <=> humble(alice) [avatar definition]
326. humble(alice) <- (35) [avatar component clause 325]
329. 36 <=> quiet(alice) [avatar definition]
331. quiet(alice) <- (36) [avatar component clause 329]
332. ~35 | 36 [avatar split clause 323,329,325]
353. funny(sK1) <- (9, 10) [resolution 175,171]
356. patient(sK1) <- (9, 10) [resolution 353,102]
416. ~funny(sK1) | wise(sK1) <- (9) [resolution 108,171]
418. wise(sK1) <- (9, 10) [subsumption resolution 416,353]
427. wise(X0) | patient(X0) | funny(X0) [resolution 112,77]
430. wise(X0) | funny(X0) [subsumption resolution 427,78]
448. ~patient(sK1) <- (9, 10) [resolution 418,110]
452. $false <- (9, 10) [subsumption resolution 448,356]
453. ~9 | ~10 [avatar contradiction clause 452]
483. funny(X0) | funny(X0) | ~brave(X0) [resolution 430,109]
486. funny(X3) | humble(X3) | quiet(X3) [resolution 430,86]
487. ~quiet(X4) | ~humble(X4) | funny(X4) [resolution 430,84]
489. funny(X0) | ~brave(X0) [duplicate literal removal 483]
610. 10 [avatar split clause 489,174]
660. brave(X0) | quiet(X0) | humble(X0) <- (8) [resolution 486,167]
725. quiet(X1) | humble(X1) | ~funny(X1) | wise(X1) <- (8) [resolution 660,108]
732. quiet(X1) | humble(X1) | wise(X1) <- (8) [subsumption resolution 725,430]
733. quiet(X1) | humble(X1) <- (8) [subsumption resolution 732,86]
737. humble(X3) | humble(X3) | ~calm(X3) <- (8) [resolution 733,72]
742. ~calm(X3) | humble(X3) <- (8) [duplicate literal removal 737]
756. humble(alice) <- (8) [resolution 742,133]
759. 35 | ~8 [avatar split clause 756,166,325]
762. ~humble(alice) | funny(alice) <- (36) [resolution 331,487]
768. funny(alice) <- (35, 36) [subsumption resolution 762,326]
771. brave(alice) <- (8, 35, 36) [resolution 768,167]
773. patient(alice) <- (35, 36) [resolution 768,102]
775. ~funny(alice) | wise(alice) <- (8, 35, 36) [resolution 771,108]
778. wise(alice) <- (8, 35, 36) [subsumption resolution 775,768]
788. ~patient(alice) <- (8, 35, 36) [resolution 778,110]
792. $false <- (8, 35, 36) [subsumption resolution 788,773]
793. ~8 | ~35 | ~36 [avatar contradiction clause 792]
794. $false [avatar sat refutation 172,332,453,610,759,793]
% SZS output end Proof for 114786982537413483099543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or wise is both calm and quiet.
Everyone who is not happy or not generous is not kind and vice versa.
If fred is patient then someone is not wise or creative and vice versa.
If someone is not brave then mary is both kind and not rich and vice versa.
Everyone who is not quiet is both humble and old and vice versa.
Everyone who is not humble or not creative is not creative.
Everyone who is generous or not calm is generous.
Everyone who is both not strong and not brave is not old and vice versa.
Everyone who is either not wise or not strong is both not happy and not strong and vice versa.
Everyone who is not rich is either strong or not patient.
Everyone who is either kind or not rich is not funny and vice versa.
If someone is either not curious or not tall then john is not creative or humble.
Everyone who is both kind and rich is either not curious or old.
If john is not tall or not curious then fred is brave and vice versa.
Everyone who is calm or funny is not generous and vice versa.
Everyone who is either old or not happy is not kind or brave and vice versa.
Fred is either not kind or not calm.
Mary is not rich.
John is rich or calm.
Someone is generous.
Susan is not patient or creative.
Fred is either not humble or strong.
Someone is not wise or not tall. | Fred is not quiet. | contradiction | (![X]:((quiet(X)|wise(X))=>(calm(X)&quiet(X))))&
(![X]:((~happy(X)|~generous(X))<=>~kind(X)))&
((patient(fred))<=>(?[X]:((~wise(X)|creative(X)))))&
((?[X]:(~brave(X)))<=>((kind(mary)&~rich(mary))))&
(![X]:(~quiet(X)<=>(humble(X)&old(X))))&
(![X]:((~humble(X)|~creative(X))=>~creative(X)))&
(![X]:((generous(X)|~calm(X))=>generous(X)))&
(![X]:((~strong(X)&~brave(X))<=>~old(X)))&
(![X]:((~wise(X)<~>~strong(X))<=>(~happy(X)&~strong(X))))&
(![X]:(~rich(X)=>(strong(X)<~>~patient(X))))&
(![X]:((kind(X)<~>~rich(X))<=>~funny(X)))&
((?[X]:((~curious(X)<~>~tall(X))))=>((~creative(john)|humble(john))))&
(![X]:((kind(X)&rich(X))=>(~curious(X)<~>old(X))))&
(((~tall(john)|~curious(john)))<=>(brave(fred)))&
(![X]:((calm(X)|funny(X))<=>~generous(X)))&
(![X]:((old(X)<~>~happy(X))<=>(~kind(X)|brave(X))))&
((~kind(fred)<~>~calm(fred)))&
(~rich(mary))&
((rich(john)|calm(john)))&
(?[X]:(generous(X)))&
((~patient(susan)|creative(susan)))&
((~humble(fred)<~>strong(fred)))&
(?[X]:((~wise(X)|~tall(X)))) | ~quiet(fred) | [
"p0",
"p4",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9178100285326010569680160
% SZS output start Proof for 9178100285326010569680160
1. ! [X0] : ((wise(X0) | quiet(X0)) => (quiet(X0) & calm(X0))) [input p0]
5. ! [X0] : (~quiet(X0) <=> (old(X0) & humble(X0))) [input p4]
9. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~strong(X0) & ~happy(X0))) [input p8]
22. ~humble(fred) <~> strong(fred) [input p21]
24. ~quiet(fred) [input hypothesis]
25. ! [X0] : ((quiet(X0) & calm(X0)) | (~wise(X0) & ~quiet(X0))) [ennf transformation 1]
44. ! [X0] : ((~quiet(X0) | (~old(X0) | ~humble(X0))) & ((old(X0) & humble(X0)) | quiet(X0))) [nnf transformation 5]
45. ! [X0] : ((~quiet(X0) | ~old(X0) | ~humble(X0)) & ((old(X0) & humble(X0)) | quiet(X0))) [flattening 44]
48. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (strong(X0) | happy(X0))) & ((~strong(X0) & ~happy(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 9]
49. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | strong(X0) | happy(X0)) & ((~strong(X0) & ~happy(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [flattening 48]
63. (~strong(fred) | humble(fred)) & (strong(fred) | ~humble(fred)) [nnf transformation 22]
69. ~wise(X0) | quiet(X0) [cnf transformation 25]
79. humble(X0) | quiet(X0) [cnf transformation 45]
91. ~strong(X0) | ~strong(X0) | wise(X0) [cnf transformation 49]
123. strong(fred) | ~humble(fred) [cnf transformation 63]
126. ~quiet(fred) [cnf transformation 24]
127. ~strong(X0) | wise(X0) [duplicate literal removal 91]
216. 19 <=> humble(fred) [avatar definition]
217. ~humble(fred) <- (~19) [avatar component clause 216]
220. 20 <=> strong(fred) [avatar definition]
221. strong(fred) <- (20) [avatar component clause 220]
224. ~19 | 20 [avatar split clause 123,220,216]
238. quiet(fred) <- (~19) [resolution 79,217]
239. $false <- (~19) [subsumption resolution 238,126]
240. 19 [avatar contradiction clause 239]
247. wise(fred) <- (20) [resolution 127,221]
248. quiet(fred) <- (20) [resolution 247,69]
250. $false <- (20) [subsumption resolution 248,126]
251. ~20 [avatar contradiction clause 250]
254. $false [avatar sat refutation 224,240,251]
% SZS output end Proof for 9178100285326010569680160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not creative is not quiet or quiet.
Everyone who is not patient is both not kind and not patient.
Everyone who is not curious or creative is kind or strong and vice versa.
Everyone who is both not calm and not tall is both calm and not quiet and vice versa.
Everyone who is either happy or generous is not calm and vice versa.
Everyone who is tall is not strong.
If someone is either wise or humble then john is not brave.
If someone is either quiet or funny then paul is not curious or brave and vice versa.
Everyone who is kind or brave is happy or not calm.
Everyone who is not wise is either not tall or not patient.
If someone is brave or quiet then fred is either brave or rich.
Everyone who is strong or not quiet is either rich or not strong.
Everyone who is both humble and rich is both not brave and not kind and vice versa.
Everyone who is curious or quiet is both funny and curious and vice versa.
Everyone who is either brave or not rich is either not curious or not calm.
Everyone who is not humble or not creative is not curious and vice versa.
Someone is not old.
Fred is not humble.
Someone is either strong or not quiet.
Paul is either not wise or not creative.
Someone is not patient.
Someone is not generous or not tall.
Susan is both brave and not creative. | Fred is not strong. | entailment | (![X]:((brave(X)<~>~creative(X))=>(~quiet(X)|quiet(X))))&
(![X]:(~patient(X)=>(~kind(X)&~patient(X))))&
(![X]:((~curious(X)|creative(X))<=>(kind(X)|strong(X))))&
(![X]:((~calm(X)&~tall(X))<=>(calm(X)&~quiet(X))))&
(![X]:((happy(X)<~>generous(X))<=>~calm(X)))&
(![X]:(tall(X)=>~strong(X)))&
((?[X]:((wise(X)<~>humble(X))))=>(~brave(john)))&
((?[X]:((quiet(X)<~>funny(X))))<=>((~curious(paul)|brave(paul))))&
(![X]:((kind(X)|brave(X))=>(happy(X)|~calm(X))))&
(![X]:(~wise(X)=>(~tall(X)<~>~patient(X))))&
((?[X]:((brave(X)|quiet(X))))=>((brave(fred)<~>rich(fred))))&
(![X]:((strong(X)|~quiet(X))=>(rich(X)<~>~strong(X))))&
(![X]:((humble(X)&rich(X))<=>(~brave(X)&~kind(X))))&
(![X]:((curious(X)|quiet(X))<=>(funny(X)&curious(X))))&
(![X]:((brave(X)<~>~rich(X))=>(~curious(X)<~>~calm(X))))&
(![X]:((~humble(X)|~creative(X))<=>~curious(X)))&
(?[X]:(~old(X)))&
(~humble(fred))&
(?[X]:((strong(X)<~>~quiet(X))))&
((~wise(paul)<~>~creative(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((~generous(X)|~tall(X))))&
((brave(susan)&~creative(susan))) | ~strong(fred) | [
"p3",
"p5",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6648604689020878491674938
% SZS output start Proof for 6648604689020878491674938
4. ! [X0] : ((~tall(X0) & ~calm(X0)) <=> (~quiet(X0) & calm(X0))) [input p3]
6. ! [X0] : (tall(X0) => ~strong(X0)) [input p5]
14. ! [X0] : ((quiet(X0) | curious(X0)) <=> (curious(X0) & funny(X0))) [input p13]
16. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> ~curious(X0)) [input p15]
18. ~humble(fred) [input p17]
24. strong(fred) [input hypothesis]
29. ! [X0] : (~strong(X0) | ~tall(X0)) [ennf transformation 6]
40. ! [X0] : (((~tall(X0) & ~calm(X0)) | (quiet(X0) | ~calm(X0))) & ((~quiet(X0) & calm(X0)) | (tall(X0) | calm(X0)))) [nnf transformation 4]
41. ! [X0] : (((~tall(X0) & ~calm(X0)) | quiet(X0) | ~calm(X0)) & ((~quiet(X0) & calm(X0)) | tall(X0) | calm(X0))) [flattening 40]
54. ! [X0] : (((quiet(X0) | curious(X0)) | (~curious(X0) | ~funny(X0))) & ((curious(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0)))) [nnf transformation 14]
55. ! [X0] : ((quiet(X0) | curious(X0) | ~curious(X0) | ~funny(X0)) & ((curious(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0)))) [flattening 54]
57. ! [X0] : (((~creative(X0) | ~humble(X0)) | curious(X0)) & (~curious(X0) | (creative(X0) & humble(X0)))) [nnf transformation 16]
58. ! [X0] : ((~creative(X0) | ~humble(X0) | curious(X0)) & (~curious(X0) | (creative(X0) & humble(X0)))) [flattening 57]
75. calm(X0) | tall(X0) | calm(X0) [cnf transformation 41]
77. ~calm(X0) | quiet(X0) | ~calm(X0) [cnf transformation 41]
83. ~tall(X0) | ~strong(X0) [cnf transformation 29]
111. ~quiet(X0) | curious(X0) [cnf transformation 55]
117. ~curious(X0) | humble(X0) [cnf transformation 58]
120. ~humble(fred) [cnf transformation 18]
129. strong(fred) [cnf transformation 24]
131. tall(X0) | calm(X0) [duplicate literal removal 75]
132. ~calm(X0) | quiet(X0) [duplicate literal removal 77]
231. ~strong(X0) | calm(X0) [resolution 131,83]
291. calm(fred) [resolution 231,129]
299. quiet(fred) [resolution 291,132]
313. curious(fred) [resolution 299,111]
335. humble(fred) [resolution 313,117]
338. $false [subsumption resolution 335,120]
% SZS output end Proof for 6648604689020878491674938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or strong is both curious and not calm. Everyone who is either not wise or not tall is creative. If paul is wise then alice is either not generous or not wise. If someone is not rich or not humble then alice is not strong. If paul is both creative and curious then someone is not rich. Everyone who is both not happy and happy is not strong and vice versa. If john is both rich and not generous then lucy is either patient or not brave. If someone is either happy or not wise then lucy is funny and vice versa. Everyone who is either not humble or funny is both not quiet and patient. Everyone who is wise is humble or old and vice versa. Everyone who is not tall or not quiet is tall or rich and vice versa. If someone is both old and strong then lucy is quiet. If lucy is either funny or not quiet then fred is quiet and vice versa. If mary is generous then someone is either not calm or old and vice versa. Everyone who is not tall is both strong and old. Everyone who is curious is either not calm or generous and vice versa. Alice is both quiet and not tall. Mary is both brave and quiet. Someone is wise or strong. Someone is both kind and wise. Alice is not brave or curious. Someone is tall. Someone is either kind or quiet. | Alice is strong. | entailment | (![X]:((creative(X)<~>strong(X))=>(curious(X)&~calm(X))))&
(![X]:((~wise(X)<~>~tall(X))=>creative(X)))&
((wise(paul))=>((~generous(alice)<~>~wise(alice))))&
((?[X]:((~rich(X)|~humble(X))))=>(~strong(alice)))&
(((creative(paul)&curious(paul)))=>(?[X]:(~rich(X))))&
(![X]:((~happy(X)&happy(X))<=>~strong(X)))&
(((rich(john)&~generous(john)))=>((patient(lucy)<~>~brave(lucy))))&
((?[X]:((happy(X)<~>~wise(X))))<=>(funny(lucy)))&
(![X]:((~humble(X)<~>funny(X))=>(~quiet(X)&patient(X))))&
(![X]:(wise(X)<=>(humble(X)|old(X))))&
(![X]:((~tall(X)|~quiet(X))<=>(tall(X)|rich(X))))&
((?[X]:((old(X)&strong(X))))=>(quiet(lucy)))&
(((funny(lucy)<~>~quiet(lucy)))<=>(quiet(fred)))&
((generous(mary))<=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:(~tall(X)=>(strong(X)&old(X))))&
(![X]:(curious(X)<=>(~calm(X)<~>generous(X))))&
((quiet(alice)&~tall(alice)))&
((brave(mary)&quiet(mary)))&
(?[X]:((wise(X)|strong(X))))&
(?[X]:((kind(X)&wise(X))))&
((~brave(alice)|curious(alice)))&
(?[X]:(tall(X)))&
(?[X]:((kind(X)<~>quiet(X)))) | strong(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1020221434661743484787006
% SZS output start Proof for 1020221434661743484787006
6. ! [X0] : ((happy(X0) & ~happy(X0)) <=> ~strong(X0)) [input p5]
24. ~strong(alice) [input hypothesis]
41. ! [X0] : (((happy(X0) & ~happy(X0)) | strong(X0)) & (~strong(X0) | (~happy(X0) | happy(X0)))) [nnf transformation 6]
42. ! [X0] : (((happy(X0) & ~happy(X0)) | strong(X0)) & (~strong(X0) | ~happy(X0) | happy(X0))) [flattening 41]
80. ~happy(X0) | strong(X0) [cnf transformation 42]
81. happy(X0) | strong(X0) [cnf transformation 42]
125. ~strong(alice) [cnf transformation 24]
167. strong(X0) [subsumption resolution 80,81]
266. $false [subsumption resolution 125,167]
% SZS output end Proof for 1020221434661743484787006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either brave or calm.
If john is curious or strong then susan is not humble and vice versa.
If alice is either humble or wise then someone is not funny or curious.
Everyone who is not patient or strong is either not strong or not patient and vice versa.
If someone is either not tall or not rich then lucy is either not rich or generous.
Everyone who is either calm or wise is brave.
Everyone who is either creative or not old is not quiet.
Everyone who is both calm and not old is either not wise or tall and vice versa.
If someone is not humble then someone is both not wise and not quiet and vice versa.
Everyone who is not wise or calm is not tall.
Everyone who is not rich is both quiet and humble and vice versa.
Everyone who is either strong or not brave is not curious.
If someone is not tall then someone is not curious and vice versa.
If alice is old or quiet then paul is either not curious or not calm and vice versa.
If someone is not humble or not curious then mary is not wise or tall and vice versa.
Everyone who is either not rich or not humble is wise or rich and vice versa.
Lucy is not generous.
Someone is rich or calm.
Someone is not creative.
Someone is not curious or creative.
Susan is either not generous or old.
Lucy is not creative.
Someone is either not happy or rich.
Someone is not patient. | Lucy is not wise. | contradiction | (![X]:(happy(X)=>(brave(X)<~>calm(X))))&
(((curious(john)|strong(john)))<=>(~humble(susan)))&
(((humble(alice)<~>wise(alice)))=>(?[X]:((~funny(X)|curious(X)))))&
(![X]:((~patient(X)|strong(X))<=>(~strong(X)<~>~patient(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>((~rich(lucy)<~>generous(lucy))))&
(![X]:((calm(X)<~>wise(X))=>brave(X)))&
(![X]:((creative(X)<~>~old(X))=>~quiet(X)))&
(![X]:((calm(X)&~old(X))<=>(~wise(X)<~>tall(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:((~wise(X)|calm(X))=>~tall(X)))&
(![X]:(~rich(X)<=>(quiet(X)&humble(X))))&
(![X]:((strong(X)<~>~brave(X))=>~curious(X)))&
((?[X]:(~tall(X)))<=>(?[X]:(~curious(X))))&
(((old(alice)|quiet(alice)))<=>((~curious(paul)<~>~calm(paul))))&
((?[X]:((~humble(X)|~curious(X))))<=>((~wise(mary)|tall(mary))))&
(![X]:((~rich(X)<~>~humble(X))<=>(wise(X)|rich(X))))&
(~generous(lucy))&
(?[X]:((rich(X)|calm(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~curious(X)|creative(X))))&
((~generous(susan)<~>old(susan)))&
(~creative(lucy))&
(?[X]:((~happy(X)<~>rich(X))))&
(?[X]:(~patient(X))) | ~wise(lucy) | [
"p4",
"p9",
"p10",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8401853977204546596358632
% SZS output start Proof for 8401853977204546596358632
5. ? [X0] : (~tall(X0) <~> ~rich(X0)) => (~rich(lucy) <~> generous(lucy)) [input p4]
10. ! [X0] : ((calm(X0) | ~wise(X0)) => ~tall(X0)) [input p9]
11. ! [X0] : (~rich(X0) <=> (humble(X0) & quiet(X0))) [input p10]
16. ! [X0] : ((~rich(X0) <~> ~humble(X0)) <=> (rich(X0) | wise(X0))) [input p15]
17. ~generous(lucy) [input p16]
25. ~wise(lucy) [input hypothesis]
30. (~rich(lucy) <~> generous(lucy)) | ! [X0] : (~tall(X0) <=> ~rich(X0)) [ennf transformation 5]
33. ! [X0] : (~tall(X0) | (~calm(X0) & wise(X0))) [ennf transformation 10]
40. ((~generous(lucy) | rich(lucy)) & (generous(lucy) | ~rich(lucy))) | ! [X0] : ((~tall(X0) | rich(X0)) & (~rich(X0) | tall(X0))) [nnf transformation 30]
50. ! [X0] : ((~rich(X0) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | rich(X0))) [nnf transformation 11]
51. ! [X0] : ((~rich(X0) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | rich(X0))) [flattening 50]
65. ! [X0] : ((((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | (~rich(X0) & ~wise(X0))) & ((rich(X0) | wise(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))))) [nnf transformation 16]
66. ! [X0] : ((((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | (~rich(X0) & ~wise(X0))) & (rich(X0) | wise(X0) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))))) [flattening 65]
90. generous(lucy) | ~rich(lucy) | ~rich(X0) | tall(X0) [cnf transformation 40]
107. ~tall(X0) | wise(X0) [cnf transformation 33]
110. rich(X0) | humble(X0) [cnf transformation 51]
126. rich(X0) | wise(X0) | ~humble(X0) | rich(X0) [cnf transformation 66]
129. ~humble(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 66]
132. ~generous(lucy) [cnf transformation 17]
142. ~wise(lucy) [cnf transformation 25]
143. rich(X0) | wise(X0) | ~humble(X0) [duplicate literal removal 126]
144. ~rich(X0) | ~humble(X0) [duplicate literal removal 129]
169. 5 <=> rich(lucy) [avatar definition]
170. ~rich(lucy) <- (~5) [avatar component clause 169]
171. rich(lucy) <- (5) [avatar component clause 169]
173. 6 <=> generous(lucy) [avatar definition]
178. 7 <=> ! [X0] : (~rich(X0) | tall(X0)) [avatar definition]
179. ~rich(X0) | tall(X0) <- (7) [avatar component clause 178]
182. 7 | ~5 | 6 [avatar split clause 90,173,169,178]
263. ~humble(X0) | wise(X0) [subsumption resolution 143,144]
264. ~6 [avatar split clause 132,173]
305. humble(lucy) <- (~5) [resolution 110,170]
312. wise(lucy) <- (~5) [resolution 263,305]
314. $false <- (~5) [subsumption resolution 312,142]
315. 5 [avatar contradiction clause 314]
319. tall(lucy) <- (5, 7) [resolution 179,171]
324. wise(lucy) <- (5, 7) [resolution 319,107]
325. $false <- (5, 7) [subsumption resolution 324,142]
326. ~5 | ~7 [avatar contradiction clause 325]
327. $false [avatar sat refutation 182,264,315,326]
% SZS output end Proof for 8401853977204546596358632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old and not calm is either not tall or not happy and vice versa.
Everyone who is not kind or not funny is either wise or not funny and vice versa.
Everyone who is either quiet or not kind is quiet or kind.
If alice is not patient then mary is either creative or not brave.
Everyone who is both tall and strong is both brave and generous and vice versa.
Everyone who is funny or not wise is both tall and rich and vice versa.
Everyone who is happy or not patient is patient.
Everyone who is tall is both strong and humble and vice versa.
If someone is either happy or brave then someone is not patient and vice versa.
If someone is not kind then someone is brave or not creative.
If lucy is brave or old then someone is either not strong or patient and vice versa.
If alice is both not brave and humble then alice is either quiet or calm.
If someone is either happy or not creative then someone is either not humble or patient.
If paul is curious then susan is either not humble or old and vice versa.
Everyone who is both rich and not creative is either not happy or curious.
Everyone who is rich is not curious or creative.
Someone is not rich or calm.
Lucy is funny.
Someone is either not old or brave.
Alice is either tall or kind.
Mary is brave or not quiet.
Someone is tall. | Lucy is creative. | entailment | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(quiet(X)|kind(X))))&
((~patient(alice))=>((creative(mary)<~>~brave(mary))))&
(![X]:((tall(X)&strong(X))<=>(brave(X)&generous(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)&rich(X))))&
(![X]:((happy(X)|~patient(X))=>patient(X)))&
(![X]:(tall(X)<=>(strong(X)&humble(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)|~creative(X)))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~brave(alice)&humble(alice)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
((curious(paul))<=>((~humble(susan)<~>old(susan))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)<~>curious(X))))&
(![X]:(rich(X)=>(~curious(X)|creative(X))))&
(?[X]:((~rich(X)|calm(X))))&
(funny(lucy))&
(?[X]:((~old(X)<~>brave(X))))&
((tall(alice)<~>kind(alice)))&
((brave(mary)|~quiet(mary)))&
(?[X]:(tall(X))) | creative(lucy) | [
"p4",
"p5",
"p6",
"p7",
"p8",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2041238034797329651289940
% SZS output start Proof for 2041238034797329651289940
5. ! [X0] : ((strong(X0) & tall(X0)) <=> (generous(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | funny(X0)) <=> (rich(X0) & tall(X0))) [input p5]
7. ! [X0] : ((~patient(X0) | happy(X0)) => patient(X0)) [input p6]
8. ! [X0] : (tall(X0) <=> (humble(X0) & strong(X0))) [input p7]
9. ? [X0] : (happy(X0) <~> brave(X0)) <=> ? [X0] : ~patient(X0) [input p8]
15. ! [X0] : ((~creative(X0) & rich(X0)) => (~happy(X0) <~> curious(X0))) [input p14]
16. ! [X0] : (rich(X0) => (creative(X0) | ~curious(X0))) [input p15]
18. funny(lucy) [input p17]
23. ~creative(lucy) [input hypothesis]
24. ? [X0] : (happy(X0) <~> brave(X0)) <=> ? [X1] : ~patient(X1) [rectify 9]
30. ! [X0] : (patient(X0) | (patient(X0) & ~happy(X0))) [ennf transformation 7]
35. ! [X0] : ((~happy(X0) <~> curious(X0)) | (creative(X0) | ~rich(X0))) [ennf transformation 15]
36. ! [X0] : ((~happy(X0) <~> curious(X0)) | creative(X0) | ~rich(X0)) [flattening 35]
37. ! [X0] : ((creative(X0) | ~curious(X0)) | ~rich(X0)) [ennf transformation 16]
38. ! [X0] : (creative(X0) | ~curious(X0) | ~rich(X0)) [flattening 37]
45. ! [X0] : (((strong(X0) & tall(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 5]
46. ! [X0] : (((strong(X0) & tall(X0)) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | ~strong(X0) | ~tall(X0))) [flattening 45]
47. ! [X0] : (((~wise(X0) | funny(X0)) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [nnf transformation 6]
48. ! [X0] : ((~wise(X0) | funny(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [flattening 47]
49. ! [X0] : ((tall(X0) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | ~tall(X0))) [nnf transformation 8]
50. ! [X0] : ((tall(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | ~tall(X0))) [flattening 49]
51. (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) [nnf transformation 24]
52. (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : ((happy(X3) | ~brave(X3)) & (brave(X3) | ~happy(X3)))) [rectify 51]
53. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) => ((~brave(sK0) | ~happy(sK0)) & (brave(sK0) | happy(sK0))) [choice axiom]
54. ? [X2] : ~patient(X2) => ~patient(sK1) [choice axiom]
55. (((~brave(sK0) | ~happy(sK0)) & (brave(sK0) | happy(sK0))) | ! [X1] : patient(X1)) & (~patient(sK1) | ! [X3] : ((happy(X3) | ~brave(X3)) & (brave(X3) | ~happy(X3)))) [skolemisation 52,54,53]
70. ! [X0] : (((~curious(X0) | happy(X0)) & (curious(X0) | ~happy(X0))) | creative(X0) | ~rich(X0)) [nnf transformation 36]
95. ~strong(X0) | brave(X0) | ~tall(X0) [cnf transformation 46]
99. ~funny(X0) | tall(X0) [cnf transformation 48]
101. ~funny(X0) | rich(X0) [cnf transformation 48]
105. patient(X0) | patient(X0) [cnf transformation 30]
106. ~tall(X0) | strong(X0) [cnf transformation 50]
110. ~patient(sK1) | happy(X3) | ~brave(X3) [cnf transformation 55]
130. ~rich(X0) | ~happy(X0) | creative(X0) | curious(X0) [cnf transformation 70]
132. ~curious(X0) | creative(X0) | ~rich(X0) [cnf transformation 38]
134. funny(lucy) [cnf transformation 18]
141. ~creative(lucy) [cnf transformation 23]
142. patient(X0) [duplicate literal removal 105]
160. ~brave(X3) | happy(X3) [subsumption resolution 110,142]
179. 8 <=> brave(lucy) [avatar definition]
181. brave(lucy) <- (8) [avatar component clause 179]
277. tall(lucy) [resolution 99,134]
278. rich(lucy) [resolution 101,134]
282. strong(lucy) [resolution 106,277]
329. brave(lucy) | ~tall(lucy) [resolution 95,282]
337. brave(lucy) [subsumption resolution 329,277]
338. 8 [avatar split clause 337,179]
339. happy(lucy) <- (8) [resolution 181,160]
392. ~happy(lucy) | creative(lucy) | curious(lucy) [resolution 130,278]
394. creative(lucy) | curious(lucy) <- (8) [subsumption resolution 392,339]
395. curious(lucy) <- (8) [subsumption resolution 394,141]
441. creative(lucy) | ~rich(lucy) <- (8) [resolution 395,132]
442. ~rich(lucy) <- (8) [subsumption resolution 441,141]
443. $false <- (8) [subsumption resolution 442,278]
444. ~8 [avatar contradiction clause 443]
445. $false [avatar sat refutation 338,444]
% SZS output end Proof for 2041238034797329651289940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not old and humble then susan is both tall and generous.
Everyone who is quiet is both humble and not old.
Everyone who is either kind or patient is both kind and not curious and vice versa.
If lucy is either not strong or not tall then john is not funny and vice versa.
Everyone who is both creative and kind is not old or not strong and vice versa.
Everyone who is funny is either not wise or not strong and vice versa.
Everyone who is either not curious or not brave is either kind or rich.
If someone is strong or not strong then lucy is strong or rich.
If paul is not quiet then someone is not old and vice versa.
Everyone who is not humble is tall.
If fred is both not curious and not wise then susan is both not old and humble and vice versa.
Everyone who is quiet or wise is both calm and quiet.
Everyone who is not happy or not generous is not kind and vice versa.
If fred is patient then someone is not wise or creative and vice versa.
If someone is not brave then mary is both kind and not rich and vice versa.
Everyone who is not quiet is both humble and old and vice versa.
Lucy is funny.
Someone is both not generous and not happy.
Fred is either not curious or old.
Someone is both not wise and not funny.
Someone is calm or not kind.
Someone is either not rich or happy. | Alice is quiet. | neutral | (((~old(alice)&humble(alice)))=>((tall(susan)&generous(susan))))&
(![X]:(quiet(X)=>(humble(X)&~old(X))))&
(![X]:((kind(X)<~>patient(X))<=>(kind(X)&~curious(X))))&
(((~strong(lucy)<~>~tall(lucy)))<=>(~funny(john)))&
(![X]:((creative(X)&kind(X))<=>(~old(X)|~strong(X))))&
(![X]:(funny(X)<=>(~wise(X)<~>~strong(X))))&
(![X]:((~curious(X)<~>~brave(X))=>(kind(X)<~>rich(X))))&
((?[X]:((strong(X)|~strong(X))))=>((strong(lucy)|rich(lucy))))&
((~quiet(paul))<=>(?[X]:(~old(X))))&
(![X]:(~humble(X)=>tall(X)))&
(((~curious(fred)&~wise(fred)))<=>((~old(susan)&humble(susan))))&
(![X]:((quiet(X)|wise(X))=>(calm(X)&quiet(X))))&
(![X]:((~happy(X)|~generous(X))<=>~kind(X)))&
((patient(fred))<=>(?[X]:((~wise(X)|creative(X)))))&
((?[X]:(~brave(X)))<=>((kind(mary)&~rich(mary))))&
(![X]:(~quiet(X)<=>(humble(X)&old(X))))&
(funny(lucy))&
(?[X]:((~generous(X)&~happy(X))))&
((~curious(fred)<~>old(fred)))&
(?[X]:((~wise(X)&~funny(X))))&
(?[X]:((calm(X)|~kind(X))))&
(?[X]:((~rich(X)<~>happy(X)))) | quiet(alice) | [] | null | 0 |
Everyone who is either not calm or kind is either not humble or not quiet and vice versa.
Everyone who is rich or strong is both not calm and calm and vice versa.
Everyone who is calm or not brave is either patient or old.
If fred is strong or old then someone is not kind.
Everyone who is both not brave and not humble is both not calm and strong.
Everyone who is either not curious or funny is both curious and creative and vice versa.
Everyone who is both not kind and not curious is both not strong and humble and vice versa.
Everyone who is patient is both brave and not quiet and vice versa.
If mary is brave or quiet then mary is either rich or not patient and vice versa.
Everyone who is both generous and not patient is both not kind and humble.
If someone is either strong or tall then alice is humble.
Everyone who is both not calm and not curious is old or rich and vice versa.
If someone is funny or not brave then someone is not curious or not kind and vice versa.
If someone is not wise or not old then lucy is curious or not calm and vice versa.
If alice is both not humble and funny then someone is not curious and vice versa.
Fred is brave or not humble.
Paul is not curious.
Paul is humble.
Someone is either calm or brave.
Someone is either happy or funny.
Someone is not quiet or strong.
Lucy is not calm or brave. | Mary is not calm. | entailment | (![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((rich(X)|strong(X))<=>(~calm(X)&calm(X))))&
(![X]:((calm(X)|~brave(X))=>(patient(X)<~>old(X))))&
(((strong(fred)|old(fred)))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)&~humble(X))=>(~calm(X)&strong(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(curious(X)&creative(X))))&
(![X]:((~kind(X)&~curious(X))<=>(~strong(X)&humble(X))))&
(![X]:(patient(X)<=>(brave(X)&~quiet(X))))&
(((brave(mary)|quiet(mary)))<=>((rich(mary)<~>~patient(mary))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((brave(fred)|~humble(fred)))&
(~curious(paul))&
(humble(paul))&
(?[X]:((calm(X)<~>brave(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy))) | ~calm(mary) | [
"p1",
"p2",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4517908777463201936709815
% SZS output start Proof for 4517908777463201936709815
2. ! [X0] : ((strong(X0) | rich(X0)) <=> (calm(X0) & ~calm(X0))) [input p1]
3. ! [X0] : ((~brave(X0) | calm(X0)) => (patient(X0) <~> old(X0))) [input p2]
8. ! [X0] : (patient(X0) <=> (~quiet(X0) & brave(X0))) [input p7]
9. (quiet(mary) | brave(mary)) <=> (rich(mary) <~> ~patient(mary)) [input p8]
12. ! [X0] : ((~curious(X0) & ~calm(X0)) <=> (rich(X0) | old(X0))) [input p11]
23. calm(mary) [input hypothesis]
26. ! [X0] : ((patient(X0) <~> old(X0)) | (brave(X0) & ~calm(X0))) [ennf transformation 3]
32. ! [X0] : (((strong(X0) | rich(X0)) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | (~strong(X0) & ~rich(X0)))) [nnf transformation 2]
33. ! [X0] : ((strong(X0) | rich(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | (~strong(X0) & ~rich(X0)))) [flattening 32]
34. ! [X0] : (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (brave(X0) & ~calm(X0))) [nnf transformation 26]
41. ! [X0] : ((patient(X0) | (quiet(X0) | ~brave(X0))) & ((~quiet(X0) & brave(X0)) | ~patient(X0))) [nnf transformation 8]
42. ! [X0] : ((patient(X0) | quiet(X0) | ~brave(X0)) & ((~quiet(X0) & brave(X0)) | ~patient(X0))) [flattening 41]
43. ((quiet(mary) | brave(mary)) | ((rich(mary) | patient(mary)) & (~patient(mary) | ~rich(mary)))) & (((patient(mary) | ~rich(mary)) & (~patient(mary) | rich(mary))) | (~quiet(mary) & ~brave(mary))) [nnf transformation 9]
44. (quiet(mary) | brave(mary) | ((rich(mary) | patient(mary)) & (~patient(mary) | ~rich(mary)))) & (((patient(mary) | ~rich(mary)) & (~patient(mary) | rich(mary))) | (~quiet(mary) & ~brave(mary))) [flattening 43]
46. ! [X0] : (((~curious(X0) & ~calm(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (curious(X0) | calm(X0)))) [nnf transformation 12]
47. ! [X0] : (((~curious(X0) & ~calm(X0)) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | curious(X0) | calm(X0))) [flattening 46]
79. ~calm(X0) | ~rich(X0) [cnf transformation 33]
81. ~rich(X0) | calm(X0) [cnf transformation 33]
84. ~calm(X0) | patient(X0) | old(X0) [cnf transformation 34]
102. ~patient(X0) | brave(X0) [cnf transformation 42]
105. ~patient(mary) | rich(mary) | ~brave(mary) [cnf transformation 44]
114. ~old(X0) | ~calm(X0) [cnf transformation 47]
138. calm(mary) [cnf transformation 23]
142. ~rich(X0) [subsumption resolution 79,81]
158. 3 <=> patient(mary) [avatar definition]
159. ~patient(mary) <- (~3) [avatar component clause 158]
166. ~patient(mary) | ~brave(mary) [subsumption resolution 105,142]
167. ~patient(mary) [subsumption resolution 166,102]
168. ~3 [avatar split clause 167,158]
285. patient(mary) | old(mary) [resolution 84,138]
287. old(mary) <- (~3) [subsumption resolution 285,159]
297. ~calm(mary) <- (~3) [resolution 287,114]
298. $false <- (~3) [subsumption resolution 297,138]
299. 3 [avatar contradiction clause 298]
300. $false [avatar sat refutation 168,299]
% SZS output end Proof for 4517908777463201936709815
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave or strong then susan is both not generous and wise and vice versa.
Everyone who is either not humble or strong is happy.
If someone is funny or curious then someone is not humble or not generous and vice versa.
Everyone who is either not wise or not brave is not quiet.
Everyone who is both happy and old is not happy or quiet.
If someone is both not kind and not tall then someone is either curious or not creative.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is either humble or old then paul is either patient or happy.
If someone is calm or generous then someone is not old.
Everyone who is quiet or funny is either not patient or not calm.
If someone is kind then paul is curious and vice versa.
If someone is both not curious and brave then someone is not old or not funny.
Everyone who is old or not humble is not humble or not patient and vice versa.
Everyone who is both humble and not calm is both happy and kind.
Everyone who is tall is either kind or not brave and vice versa.
Everyone who is either not old or not generous is not generous and vice versa.
John is either old or not rich.
Mary is both quiet and not strong.
Someone is old.
Fred is not happy.
Alice is not patient or not curious.
Fred is either not funny or not brave.
Paul is not brave or not humble. | Mary is humble. | contradiction | (((~brave(lucy)|strong(lucy)))<=>((~generous(susan)&wise(susan))))&
(![X]:((~humble(X)<~>strong(X))=>happy(X)))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>~quiet(X)))&
(![X]:((happy(X)&old(X))=>(~happy(X)|quiet(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>((patient(paul)<~>happy(paul))))&
((?[X]:((calm(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|funny(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:(kind(X)))<=>(curious(paul)))&
((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((old(X)|~humble(X))<=>(~humble(X)|~patient(X))))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&kind(X))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
(![X]:((~old(X)<~>~generous(X))<=>~generous(X)))&
((old(john)<~>~rich(john)))&
((quiet(mary)&~strong(mary)))&
(?[X]:(old(X)))&
(~happy(fred))&
((~patient(alice)|~curious(alice)))&
((~funny(fred)<~>~brave(fred)))&
((~brave(paul)|~humble(paul))) | humble(mary) | [
"p8",
"p9",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4244018041191153339682221
% SZS output start Proof for 4244018041191153339682221
9. ? [X0] : (generous(X0) | calm(X0)) => ? [X0] : ~old(X0) [input p8]
10. ! [X0] : ((funny(X0) | quiet(X0)) => (~patient(X0) <~> ~calm(X0))) [input p9]
13. ! [X0] : ((~humble(X0) | old(X0)) <=> (~patient(X0) | ~humble(X0))) [input p12]
16. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> ~generous(X0)) [input p15]
18. ~strong(mary) & quiet(mary) [input p17]
24. humble(mary) [input hypothesis]
27. ? [X0] : (generous(X0) | calm(X0)) => ? [X1] : ~old(X1) [rectify 9]
36. ? [X1] : ~old(X1) | ! [X0] : (~generous(X0) & ~calm(X0)) [ennf transformation 27]
37. ! [X0] : ((~patient(X0) <~> ~calm(X0)) | (~funny(X0) & ~quiet(X0))) [ennf transformation 10]
58. ? [X0] : ~old(X0) | ! [X1] : (~generous(X1) & ~calm(X1)) [rectify 36]
59. ? [X0] : ~old(X0) => ~old(sK3) [choice axiom]
60. ~old(sK3) | ! [X1] : (~generous(X1) & ~calm(X1)) [skolemisation 58,59]
61. ! [X0] : (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~funny(X0) & ~quiet(X0))) [nnf transformation 37]
69. ! [X0] : (((~humble(X0) | old(X0)) | (patient(X0) & humble(X0))) & ((~patient(X0) | ~humble(X0)) | (humble(X0) & ~old(X0)))) [nnf transformation 13]
70. ! [X0] : ((~humble(X0) | old(X0) | (patient(X0) & humble(X0))) & (~patient(X0) | ~humble(X0) | (humble(X0) & ~old(X0)))) [flattening 69]
72. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | generous(X0)) & (~generous(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 16]
102. ~old(sK3) | ~calm(X1) [cnf transformation 60]
106. ~quiet(X0) | patient(X0) | calm(X0) [cnf transformation 61]
111. ~patient(X0) | ~humble(X0) | ~old(X0) [cnf transformation 70]
119. ~generous(X0) | ~generous(X0) | old(X0) [cnf transformation 72]
122. generous(X0) | old(X0) | generous(X0) [cnf transformation 72]
125. quiet(mary) [cnf transformation 18]
133. humble(mary) [cnf transformation 24]
134. ~generous(X0) | old(X0) [duplicate literal removal 119]
135. old(X0) | generous(X0) [duplicate literal removal 122]
225. 21 <=> old(sK3) [avatar definition]
227. ~old(sK3) <- (~21) [avatar component clause 225]
230. 22 <=> ! [X1] : ~calm(X1) [avatar definition]
231. ~calm(X1) <- (22) [avatar component clause 230]
232. 22 | ~21 [avatar split clause 102,225,230]
258. old(X0) [subsumption resolution 134,135]
288. $false <- (~21) [subsumption resolution 227,258]
289. 21 [avatar contradiction clause 288]
333. patient(mary) | calm(mary) [resolution 106,125]
334. patient(mary) <- (22) [subsumption resolution 333,231]
340. ~humble(mary) | ~old(mary) <- (22) [resolution 111,334]
342. ~old(mary) <- (22) [subsumption resolution 340,133]
343. $false <- (22) [subsumption resolution 342,258]
344. ~22 [avatar contradiction clause 343]
346. $false [avatar sat refutation 232,289,344]
% SZS output end Proof for 4244018041191153339682221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not patient and happy then john is either brave or humble and vice versa. If someone is either not tall or not strong then someone is either happy or patient. Everyone who is both happy and not tall is not humble. If someone is happy then someone is both not patient and not wise and vice versa. Everyone who is not generous is both not tall and strong. Everyone who is either happy or not quiet is not tall and vice versa. Everyone who is both not old and strong is wise. Everyone who is quiet is both not quiet and not creative and vice versa. If someone is rich then paul is both curious and calm. Everyone who is both humble and curious is both not generous and not creative. If john is either creative or not old then someone is not rich. Everyone who is not rich or quiet is both curious and not wise and vice versa. If john is old then lucy is both not tall and strong. Everyone who is calm is patient and vice versa. Everyone who is not patient is kind. Someone is either humble or funny. Susan is both happy and not funny. Paul is not funny. Someone is both humble and happy. Alice is generous or not curious. Someone is not rich or wise. Someone is tall or not wise. Mary is either strong or not curious. | Alice is not creative. | contradiction | (((~patient(paul)&happy(paul)))<=>((brave(john)<~>humble(john))))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((happy(X)<~>patient(X)))))&
(![X]:((happy(X)&~tall(X))=>~humble(X)))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:(~generous(X)=>(~tall(X)&strong(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>~tall(X)))&
(![X]:((~old(X)&strong(X))=>wise(X)))&
(![X]:(quiet(X)<=>(~quiet(X)&~creative(X))))&
((?[X]:(rich(X)))=>((curious(paul)&calm(paul))))&
(![X]:((humble(X)&curious(X))=>(~generous(X)&~creative(X))))&
(((creative(john)<~>~old(john)))=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|quiet(X))<=>(curious(X)&~wise(X))))&
((old(john))=>((~tall(lucy)&strong(lucy))))&
(![X]:(calm(X)<=>patient(X)))&
(![X]:(~patient(X)=>kind(X)))&
(?[X]:((humble(X)<~>funny(X))))&
((happy(susan)&~funny(susan)))&
(~funny(paul))&
(?[X]:((humble(X)&happy(X))))&
((generous(alice)|~curious(alice)))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:((tall(X)|~wise(X))))&
((strong(mary)<~>~curious(mary))) | ~creative(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 682268353716022035481219
% SZS output start Proof for 682268353716022035481219
8. ! [X0] : (quiet(X0) <=> (~creative(X0) & ~quiet(X0))) [input p7]
24. ~creative(alice) [input hypothesis]
53. ! [X0] : ((quiet(X0) | (creative(X0) | quiet(X0))) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [nnf transformation 8]
54. ! [X0] : ((quiet(X0) | creative(X0) | quiet(X0)) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [flattening 53]
91. ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
93. quiet(X0) | creative(X0) | quiet(X0) [cnf transformation 54]
120. ~creative(alice) [cnf transformation 24]
121. ~quiet(X0) [duplicate literal removal 91]
122. creative(X0) | quiet(X0) [duplicate literal removal 93]
277. quiet(alice) [resolution 122,120]
279. $false [subsumption resolution 277,121]
% SZS output end Proof for 682268353716022035481219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not humble then someone is either not strong or funny and vice versa.
Everyone who is either not kind or not wise is not rich and vice versa.
If mary is funny or not calm then someone is kind and vice versa.
Everyone who is both not brave and not curious is tall and vice versa.
Everyone who is not creative is either generous or not funny and vice versa.
Everyone who is either not patient or not brave is both brave and not curious.
If paul is humble then fred is both not curious and quiet and vice versa.
If john is both not strong and not patient then someone is tall or not patient and vice versa.
Everyone who is not rich or curious is either old or rich and vice versa.
If susan is not calm then john is brave.
Everyone who is not quiet or creative is either not tall or not creative and vice versa.
If someone is not funny then alice is calm and vice versa.
Everyone who is both creative and old is both not calm and not curious.
If john is either not old or not tall then someone is not curious or old.
Everyone who is both not brave and curious is not tall and vice versa.
If fred is creative then mary is generous and vice versa.
Someone is not happy or tall.
Alice is calm or not calm.
Someone is either patient or curious.
Someone is either generous or kind.
Lucy is not calm.
Someone is both not wise and not patient. | Fred is not wise. | neutral | ((?[X]:((humble(X)&~humble(X))))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((~kind(X)<~>~wise(X))<=>~rich(X)))&
(((funny(mary)|~calm(mary)))<=>(?[X]:(kind(X))))&
(![X]:((~brave(X)&~curious(X))<=>tall(X)))&
(![X]:(~creative(X)<=>(generous(X)<~>~funny(X))))&
(![X]:((~patient(X)<~>~brave(X))=>(brave(X)&~curious(X))))&
((humble(paul))<=>((~curious(fred)&quiet(fred))))&
(((~strong(john)&~patient(john)))<=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:((~rich(X)|curious(X))<=>(old(X)<~>rich(X))))&
((~calm(susan))=>(brave(john)))&
(![X]:((~quiet(X)|creative(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:(~funny(X)))<=>(calm(alice)))&
(![X]:((creative(X)&old(X))=>(~calm(X)&~curious(X))))&
(((~old(john)<~>~tall(john)))=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((~brave(X)&curious(X))<=>~tall(X)))&
((creative(fred))<=>(generous(mary)))&
(?[X]:((~happy(X)|tall(X))))&
((calm(alice)|~calm(alice)))&
(?[X]:((patient(X)<~>curious(X))))&
(?[X]:((generous(X)<~>kind(X))))&
(~calm(lucy))&
(?[X]:((~wise(X)&~patient(X)))) | ~wise(fred) | [] | null | 0 |
Everyone who is either not creative or patient is both humble and not funny and vice versa. Everyone who is either not wise or creative is both not creative and old. If alice is either not rich or kind then someone is either calm or funny and vice versa. If paul is both not tall and not quiet then john is both not brave and not patient and vice versa. If fred is brave or not wise then fred is both not creative and kind. Everyone who is both happy and patient is either not strong or creative and vice versa. Everyone who is creative or happy is not kind or not funny and vice versa. If john is not curious then someone is not kind. Everyone who is calm or not patient is either not patient or not curious. Everyone who is old or not brave is calm. Everyone who is not quiet or kind is both patient and happy. If fred is not calm or curious then paul is either not happy or quiet and vice versa. Everyone who is both not generous and not rich is not tall and vice versa. Everyone who is either rich or not humble is not quiet and vice versa. Everyone who is either not kind or curious is curious or not curious and vice versa. Everyone who is not brave or curious is not creative or generous and vice versa. Paul is calm. Susan is brave. Alice is both not rich and not generous. Lucy is both not curious and patient. Mary is both not curious and not generous. Fred is not brave or not quiet. Mary is not kind. Someone is quiet or not humble. | Alice is not happy. | neutral | (![X]:((~creative(X)<~>patient(X))<=>(humble(X)&~funny(X))))&
(![X]:((~wise(X)<~>creative(X))=>(~creative(X)&old(X))))&
(((~rich(alice)<~>kind(alice)))<=>(?[X]:((calm(X)<~>funny(X)))))&
(((~tall(paul)&~quiet(paul)))<=>((~brave(john)&~patient(john))))&
(((brave(fred)|~wise(fred)))=>((~creative(fred)&kind(fred))))&
(![X]:((happy(X)&patient(X))<=>(~strong(X)<~>creative(X))))&
(![X]:((creative(X)|happy(X))<=>(~kind(X)|~funny(X))))&
((~curious(john))=>(?[X]:(~kind(X))))&
(![X]:((calm(X)|~patient(X))=>(~patient(X)<~>~curious(X))))&
(![X]:((old(X)|~brave(X))=>calm(X)))&
(![X]:((~quiet(X)|kind(X))=>(patient(X)&happy(X))))&
(((~calm(fred)|curious(fred)))<=>((~happy(paul)<~>quiet(paul))))&
(![X]:((~generous(X)&~rich(X))<=>~tall(X)))&
(![X]:((rich(X)<~>~humble(X))<=>~quiet(X)))&
(![X]:((~kind(X)<~>curious(X))<=>(curious(X)|~curious(X))))&
(![X]:((~brave(X)|curious(X))<=>(~creative(X)|generous(X))))&
(calm(paul))&
(brave(susan))&
((~rich(alice)&~generous(alice)))&
((~curious(lucy)&patient(lucy)))&
((~curious(mary)&~generous(mary)))&
((~brave(fred)|~quiet(fred)))&
(~kind(mary))&
(?[X]:((quiet(X)|~humble(X)))) | ~happy(alice) | [] | null | 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.