premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If alice is either not curious or not funny then susan is both not quiet and rich and vice versa. Everyone who is both funny and tall is either kind or not happy. Everyone who is both tall and not quiet is not strong. Everyone who is both rich and not old is tall or not quiet and vice versa. Everyone who is both funny and not generous is not brave. Everyone who is either not humble or not funny is either kind or not generous. If someone is both not rich and not wise then someone is either calm or curious. Everyone who is calm or not creative is humble or not humble. Everyone who is not rich or quiet is not patient and vice versa. Everyone who is both not generous and not old is not funny and vice versa. Everyone who is either happy or not kind is not wise or strong. If someone is either not calm or not rich then someone is kind or not kind and vice versa. Everyone who is either curious or not old is both creative and humble and vice versa. Everyone who is both not brave and generous is not rich and vice versa. If someone is either not quiet or creative then someone is patient and vice versa. Everyone who is not funny or strong is strong or not generous and vice versa. Lucy is either not quiet or not funny. Susan is both not rich and happy. Someone is not brave or not curious. John is not creative or generous. Fred is both not generous and brave. Susan is not strong or creative. Fred is both happy and not curious. | Fred is funny. | contradiction | (((~curious(alice)<~>~funny(alice)))<=>((~quiet(susan)&rich(susan))))&
(![X]:((funny(X)&tall(X))=>(kind(X)<~>~happy(X))))&
(![X]:((tall(X)&~quiet(X))=>~strong(X)))&
(![X]:((rich(X)&~old(X))<=>(tall(X)|~quiet(X))))&
(![X]:((funny(X)&~generous(X))=>~brave(X)))&
(![X]:((~humble(X)<~>~funny(X))=>(kind(X)<~>~generous(X))))&
((?[X]:((~rich(X)&~wise(X))))=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:((calm(X)|~creative(X))=>(humble(X)|~humble(X))))&
(![X]:((~rich(X)|quiet(X))<=>~patient(X)))&
(![X]:((~generous(X)&~old(X))<=>~funny(X)))&
(![X]:((happy(X)<~>~kind(X))=>(~wise(X)|strong(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((curious(X)<~>~old(X))<=>(creative(X)&humble(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))<=>(strong(X)|~generous(X))))&
((~quiet(lucy)<~>~funny(lucy)))&
((~rich(susan)&happy(susan)))&
(?[X]:((~brave(X)|~curious(X))))&
((~creative(john)|generous(john)))&
((~generous(fred)&brave(fred)))&
((~strong(susan)|creative(susan)))&
((happy(fred)&~curious(fred))) | funny(fred) | [
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5500615913988218196372739
% SZS output start Proof for 5500615913988218196372739
5. ! [X0] : ((~generous(X0) & funny(X0)) => ~brave(X0)) [input p4]
21. brave(fred) & ~generous(fred) [input p20]
24. funny(fred) [input hypothesis]
32. ! [X0] : (~brave(X0) | (generous(X0) | ~funny(X0))) [ennf transformation 5]
33. ! [X0] : (~brave(X0) | generous(X0) | ~funny(X0)) [flattening 32]
88. ~brave(X0) | generous(X0) | ~funny(X0) [cnf transformation 33]
134. ~generous(fred) [cnf transformation 21]
135. brave(fred) [cnf transformation 21]
139. funny(fred) [cnf transformation 24]
271. generous(fred) | ~funny(fred) [resolution 88,135]
272. ~funny(fred) [subsumption resolution 271,134]
273. $false [subsumption resolution 272,139]
% SZS output end Proof for 5500615913988218196372739
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not curious then someone is not brave and vice versa. Everyone who is not brave is quiet or brave. If lucy is either not rich or not patient then susan is either not humble or generous. If someone is either not strong or old then someone is either not old or old. If someone is not patient or not wise then someone is both strong and tall and vice versa. If someone is calm then someone is either generous or strong. Everyone who is either happy or kind is brave or not happy and vice versa. Everyone who is both not quiet and old is both quiet and old and vice versa. If paul is both rich and patient then john is both not tall and generous. If mary is both not patient and not humble then lucy is either not curious or not strong. If someone is wise or tall then fred is either not funny or not wise and vice versa. Everyone who is not wise is creative or not quiet and vice versa. If fred is old then someone is both not strong and not old. Everyone who is either creative or not wise is both strong and not quiet. Everyone who is not old or humble is both not creative and calm and vice versa. If lucy is quiet then alice is not happy. Someone is both strong and funny. Mary is happy. Someone is rich. John is either not kind or happy. Fred is not patient or not creative. Susan is both not happy and not wise. | Susan is quiet. | contradiction | ((~curious(paul))<=>(?[X]:(~brave(X))))&
(![X]:(~brave(X)=>(quiet(X)|brave(X))))&
(((~rich(lucy)<~>~patient(lucy)))=>((~humble(susan)<~>generous(susan))))&
((?[X]:((~strong(X)<~>old(X))))=>(?[X]:((~old(X)<~>old(X)))))&
((?[X]:((~patient(X)|~wise(X))))<=>(?[X]:((strong(X)&tall(X)))))&
((?[X]:(calm(X)))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:((happy(X)<~>kind(X))<=>(brave(X)|~happy(X))))&
(![X]:((~quiet(X)&old(X))<=>(quiet(X)&old(X))))&
(((rich(paul)&patient(paul)))=>((~tall(john)&generous(john))))&
(((~patient(mary)&~humble(mary)))=>((~curious(lucy)<~>~strong(lucy))))&
((?[X]:((wise(X)|tall(X))))<=>((~funny(fred)<~>~wise(fred))))&
(![X]:(~wise(X)<=>(creative(X)|~quiet(X))))&
((old(fred))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:((creative(X)<~>~wise(X))=>(strong(X)&~quiet(X))))&
(![X]:((~old(X)|humble(X))<=>(~creative(X)&calm(X))))&
((quiet(lucy))=>(~happy(alice)))&
(?[X]:((strong(X)&funny(X))))&
(happy(mary))&
(?[X]:(rich(X)))&
((~kind(john)<~>happy(john)))&
((~patient(fred)|~creative(fred)))&
((~happy(susan)&~wise(susan))) | quiet(susan) | [
"p7",
"p11",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7064836139546218519690801
% SZS output start Proof for 7064836139546218519690801
8. ! [X0] : ((old(X0) & ~quiet(X0)) <=> (old(X0) & quiet(X0))) [input p7]
12. ! [X0] : (~wise(X0) <=> (~quiet(X0) | creative(X0))) [input p11]
15. ! [X0] : ((humble(X0) | ~old(X0)) <=> (calm(X0) & ~creative(X0))) [input p14]
22. ~wise(susan) & ~happy(susan) [input p21]
23. quiet(susan) [input hypothesis]
59. ! [X0] : (((old(X0) & ~quiet(X0)) | (~old(X0) | ~quiet(X0))) & ((old(X0) & quiet(X0)) | (~old(X0) | quiet(X0)))) [nnf transformation 8]
60. ! [X0] : (((old(X0) & ~quiet(X0)) | ~old(X0) | ~quiet(X0)) & ((old(X0) & quiet(X0)) | ~old(X0) | quiet(X0))) [flattening 59]
66. ! [X0] : ((~wise(X0) | (quiet(X0) & ~creative(X0))) & ((~quiet(X0) | creative(X0)) | wise(X0))) [nnf transformation 12]
67. ! [X0] : ((~wise(X0) | (quiet(X0) & ~creative(X0))) & (~quiet(X0) | creative(X0) | wise(X0))) [flattening 66]
71. ! [X0] : (((humble(X0) | ~old(X0)) | (~calm(X0) | creative(X0))) & ((calm(X0) & ~creative(X0)) | (~humble(X0) & old(X0)))) [nnf transformation 15]
72. ! [X0] : ((humble(X0) | ~old(X0) | ~calm(X0) | creative(X0)) & ((calm(X0) & ~creative(X0)) | (~humble(X0) & old(X0)))) [flattening 71]
102. quiet(X0) | ~old(X0) | quiet(X0) [cnf transformation 60]
104. ~quiet(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 60]
116. ~quiet(X0) | creative(X0) | wise(X0) [cnf transformation 67]
125. ~creative(X0) | old(X0) [cnf transformation 72]
139. ~wise(susan) [cnf transformation 22]
140. quiet(susan) [cnf transformation 23]
141. quiet(X0) | ~old(X0) [duplicate literal removal 102]
142. ~old(X0) | ~quiet(X0) [duplicate literal removal 104]
223. ~old(X0) [subsumption resolution 141,142]
289. ~creative(X0) [subsumption resolution 125,223]
319. creative(susan) | wise(susan) [resolution 116,140]
324. wise(susan) [subsumption resolution 319,289]
325. $false [subsumption resolution 324,139]
% SZS output end Proof for 7064836139546218519690801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not rich then susan is both not brave and brave. Everyone who is not funny is generous or not brave and vice versa. If john is not quiet then susan is curious and vice versa. If someone is not old or rich then someone is either old or generous. Everyone who is happy or not strong is wise or not generous. Everyone who is either not kind or brave is rich or not patient. If paul is not happy or not funny then paul is both not kind and quiet and vice versa. If mary is either not strong or not patient then paul is both kind and wise and vice versa. Everyone who is either not funny or not old is either not rich or not patient and vice versa. Everyone who is either old or not brave is wise or tall and vice versa. Everyone who is not calm or happy is curious or not curious and vice versa. If someone is not curious then someone is happy or not wise. If someone is both not kind and old then john is not rich. Everyone who is either strong or humble is both wise and not funny. If someone is rich then mary is either brave or not rich. If fred is either calm or not curious then john is both not creative and old. Someone is either patient or not quiet. John is either not creative or not wise. Someone is old or creative. Someone is not tall. Paul is both humble and patient. Someone is both brave and not strong. John is either humble or brave. | Paul is strong. | entailment | ((?[X]:((~old(X)|~rich(X))))=>((~brave(susan)&brave(susan))))&
(![X]:(~funny(X)<=>(generous(X)|~brave(X))))&
((~quiet(john))<=>(curious(susan)))&
((?[X]:((~old(X)|rich(X))))=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:((happy(X)|~strong(X))=>(wise(X)|~generous(X))))&
(![X]:((~kind(X)<~>brave(X))=>(rich(X)|~patient(X))))&
(((~happy(paul)|~funny(paul)))<=>((~kind(paul)&quiet(paul))))&
(((~strong(mary)<~>~patient(mary)))<=>((kind(paul)&wise(paul))))&
(![X]:((~funny(X)<~>~old(X))<=>(~rich(X)<~>~patient(X))))&
(![X]:((old(X)<~>~brave(X))<=>(wise(X)|tall(X))))&
(![X]:((~calm(X)|happy(X))<=>(curious(X)|~curious(X))))&
((?[X]:(~curious(X)))=>(?[X]:((happy(X)|~wise(X)))))&
((?[X]:((~kind(X)&old(X))))=>(~rich(john)))&
(![X]:((strong(X)<~>humble(X))=>(wise(X)&~funny(X))))&
((?[X]:(rich(X)))=>((brave(mary)<~>~rich(mary))))&
(((calm(fred)<~>~curious(fred)))=>((~creative(john)&old(john))))&
(?[X]:((patient(X)<~>~quiet(X))))&
((~creative(john)<~>~wise(john)))&
(?[X]:((old(X)|creative(X))))&
(?[X]:(~tall(X)))&
((humble(paul)&patient(paul)))&
(?[X]:((brave(X)&~strong(X))))&
((humble(john)<~>brave(john))) | strong(paul) | [
"p0",
"p6",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7819322696327050711829405
% SZS output start Proof for 7819322696327050711829405
1. ? [X0] : (~rich(X0) | ~old(X0)) => (brave(susan) & ~brave(susan)) [input p0]
7. (~funny(paul) | ~happy(paul)) <=> (quiet(paul) & ~kind(paul)) [input p6]
13. ? [X0] : (old(X0) & ~kind(X0)) => ~rich(john) [input p12]
14. ! [X0] : ((strong(X0) <~> humble(X0)) => (~funny(X0) & wise(X0))) [input p13]
21. patient(paul) & humble(paul) [input p20]
24. ~strong(paul) [input hypothesis]
27. (brave(susan) & ~brave(susan)) | ! [X0] : (rich(X0) & old(X0)) [ennf transformation 1]
34. ~rich(john) | ! [X0] : (~old(X0) | kind(X0)) [ennf transformation 13]
35. ! [X0] : ((~funny(X0) & wise(X0)) | (strong(X0) <=> humble(X0))) [ennf transformation 14]
46. ((~funny(paul) | ~happy(paul)) | (~quiet(paul) | kind(paul))) & ((quiet(paul) & ~kind(paul)) | (funny(paul) & happy(paul))) [nnf transformation 7]
47. (~funny(paul) | ~happy(paul) | ~quiet(paul) | kind(paul)) & ((quiet(paul) & ~kind(paul)) | (funny(paul) & happy(paul))) [flattening 46]
58. ! [X0] : ((~funny(X0) & wise(X0)) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [nnf transformation 35]
72. ~brave(susan) | old(X0) [cnf transformation 27]
73. ~brave(susan) | rich(X0) [cnf transformation 27]
74. brave(susan) | old(X0) [cnf transformation 27]
75. brave(susan) | rich(X0) [cnf transformation 27]
90. ~kind(paul) | funny(paul) [cnf transformation 47]
119. ~rich(john) | ~old(X0) | kind(X0) [cnf transformation 34]
123. ~humble(X0) | strong(X0) | ~funny(X0) [cnf transformation 58]
136. humble(paul) [cnf transformation 21]
142. ~strong(paul) [cnf transformation 24]
144. 1 <=> ! [X0] : rich(X0) [avatar definition]
145. rich(X0) <- (1) [avatar component clause 144]
147. 2 <=> brave(susan) [avatar definition]
150. 1 | 2 [avatar split clause 75,147,144]
152. 3 <=> ! [X0] : old(X0) [avatar definition]
153. old(X0) <- (3) [avatar component clause 152]
154. 3 | 2 [avatar split clause 74,147,152]
155. 1 | ~2 [avatar split clause 73,147,144]
156. 3 | ~2 [avatar split clause 72,147,152]
183. 9 <=> kind(paul) [avatar definition]
184. ~kind(paul) <- (~9) [avatar component clause 183]
195. 12 <=> funny(paul) [avatar definition]
196. funny(paul) <- (12) [avatar component clause 195]
201. 12 | ~9 [avatar split clause 90,183,195]
235. 19 <=> ! [X0] : (~old(X0) | kind(X0)) [avatar definition]
236. ~old(X0) | kind(X0) <- (19) [avatar component clause 235]
238. 20 <=> rich(john) [avatar definition]
240. ~rich(john) <- (~20) [avatar component clause 238]
241. 19 | ~20 [avatar split clause 119,238,235]
311. $false <- (1, ~20) [resolution 240,145]
312. ~1 | 20 [avatar contradiction clause 311]
313. kind(X0) <- (3, 19) [subsumption resolution 236,153]
314. $false <- (3, ~9, 19) [resolution 313,184]
315. ~3 | 9 | ~19 [avatar contradiction clause 314]
378. strong(paul) | ~funny(paul) [resolution 123,136]
380. ~funny(paul) [subsumption resolution 378,142]
381. $false <- (12) [subsumption resolution 380,196]
382. ~12 [avatar contradiction clause 381]
383. $false [avatar sat refutation 150,154,155,156,201,241,312,315,382]
% SZS output end Proof for 7819322696327050711829405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not happy or brave.
If someone is both wise and generous then paul is both not creative and not funny and vice versa.
Everyone who is not generous or patient is old.
If susan is calm then mary is generous or brave.
Everyone who is not happy or kind is not brave.
Everyone who is not curious is not calm.
Everyone who is both not creative and calm is both not creative and not strong.
If someone is either not generous or rich then lucy is either not brave or not tall and vice versa.
Everyone who is not brave is either patient or not funny and vice versa.
Everyone who is not tall is either rich or patient and vice versa.
If someone is either not happy or not creative then someone is not funny and vice versa.
Everyone who is both not curious and kind is both tall and not generous.
Everyone who is happy or not generous is either not tall or not funny and vice versa.
If someone is both not strong and rich then paul is both old and patient.
If someone is kind or happy then alice is both happy and not happy and vice versa.
Everyone who is not brave or not rich is not brave or not tall and vice versa.
Fred is not curious.
Someone is not calm.
Someone is either not kind or not strong.
Susan is tall or patient.
Someone is not funny or creative.
Someone is not tall or old.
Someone is wise or brave.
Lucy is not curious. | Mary is generous. | neutral | (![X]:(brave(X)=>(~happy(X)|brave(X))))&
((?[X]:((wise(X)&generous(X))))<=>((~creative(paul)&~funny(paul))))&
(![X]:((~generous(X)|patient(X))=>old(X)))&
((calm(susan))=>((generous(mary)|brave(mary))))&
(![X]:((~happy(X)|kind(X))=>~brave(X)))&
(![X]:(~curious(X)=>~calm(X)))&
(![X]:((~creative(X)&calm(X))=>(~creative(X)&~strong(X))))&
((?[X]:((~generous(X)<~>rich(X))))<=>((~brave(lucy)<~>~tall(lucy))))&
(![X]:(~brave(X)<=>(patient(X)<~>~funny(X))))&
(![X]:(~tall(X)<=>(rich(X)<~>patient(X))))&
((?[X]:((~happy(X)<~>~creative(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)&kind(X))=>(tall(X)&~generous(X))))&
(![X]:((happy(X)|~generous(X))<=>(~tall(X)<~>~funny(X))))&
((?[X]:((~strong(X)&rich(X))))=>((old(paul)&patient(paul))))&
((?[X]:((kind(X)|happy(X))))<=>((happy(alice)&~happy(alice))))&
(![X]:((~brave(X)|~rich(X))<=>(~brave(X)|~tall(X))))&
(~curious(fred))&
(?[X]:(~calm(X)))&
(?[X]:((~kind(X)<~>~strong(X))))&
((tall(susan)|patient(susan)))&
(?[X]:((~funny(X)|creative(X))))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((wise(X)|brave(X))))&
(~curious(lucy)) | generous(mary) | [] | null | 0 |
Everyone who is calm or strong is curious and vice versa.
If paul is both strong and not calm then someone is either happy or not old and vice versa.
If susan is either not quiet or funny then someone is both funny and not brave.
Everyone who is both not quiet and rich is both wise and not quiet.
Everyone who is both creative and not curious is both brave and curious and vice versa.
If someone is creative then lucy is both not quiet and not creative.
Everyone who is curious is not patient and vice versa.
If someone is both wise and generous then someone is either strong or old and vice versa.
If alice is not old then fred is old or humble and vice versa.
If someone is both not tall and not generous then someone is old.
Everyone who is not curious is not old or not generous and vice versa.
Everyone who is either not brave or patient is both creative and not generous.
Everyone who is either not patient or not generous is either not patient or generous.
Everyone who is both kind and not rich is brave or tall.
Everyone who is not creative is either not curious or old.
Everyone who is not calm is either not rich or not funny.
Someone is not strong or rich.
Someone is not curious.
Paul is not curious.
Someone is both quiet and not kind.
Someone is either humble or kind.
Someone is both not kind and not strong.
Someone is either calm or not rich. | Fred is calm. | contradiction | (![X]:((calm(X)|strong(X))<=>curious(X)))&
(((strong(paul)&~calm(paul)))<=>(?[X]:((happy(X)<~>~old(X)))))&
(((~quiet(susan)<~>funny(susan)))=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((~quiet(X)&rich(X))=>(wise(X)&~quiet(X))))&
(![X]:((creative(X)&~curious(X))<=>(brave(X)&curious(X))))&
((?[X]:(creative(X)))=>((~quiet(lucy)&~creative(lucy))))&
(![X]:(curious(X)<=>~patient(X)))&
((?[X]:((wise(X)&generous(X))))<=>(?[X]:((strong(X)<~>old(X)))))&
((~old(alice))<=>((old(fred)|humble(fred))))&
((?[X]:((~tall(X)&~generous(X))))=>(?[X]:(old(X))))&
(![X]:(~curious(X)<=>(~old(X)|~generous(X))))&
(![X]:((~brave(X)<~>patient(X))=>(creative(X)&~generous(X))))&
(![X]:((~patient(X)<~>~generous(X))=>(~patient(X)<~>generous(X))))&
(![X]:((kind(X)&~rich(X))=>(brave(X)|tall(X))))&
(![X]:(~creative(X)=>(~curious(X)<~>old(X))))&
(![X]:(~calm(X)=>(~rich(X)<~>~funny(X))))&
(?[X]:((~strong(X)|rich(X))))&
(?[X]:(~curious(X)))&
(~curious(paul))&
(?[X]:((quiet(X)&~kind(X))))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((calm(X)<~>~rich(X)))) | calm(fred) | [
"p0",
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8556668763619056758926048
% SZS output start Proof for 8556668763619056758926048
1. ! [X0] : ((strong(X0) | calm(X0)) <=> curious(X0)) [input p0]
7. ! [X0] : (curious(X0) <=> ~patient(X0)) [input p6]
11. ! [X0] : (~curious(X0) <=> (~generous(X0) | ~old(X0))) [input p10]
13. ! [X0] : ((~patient(X0) <~> ~generous(X0)) => (~patient(X0) <~> generous(X0))) [input p12]
24. calm(fred) [input hypothesis]
34. ! [X0] : ((~patient(X0) <~> generous(X0)) | (~patient(X0) <=> ~generous(X0))) [ennf transformation 13]
37. ! [X0] : (((strong(X0) | calm(X0)) | ~curious(X0)) & (curious(X0) | (~strong(X0) & ~calm(X0)))) [nnf transformation 1]
38. ! [X0] : ((strong(X0) | calm(X0) | ~curious(X0)) & (curious(X0) | (~strong(X0) & ~calm(X0)))) [flattening 37]
49. ! [X0] : ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0))) [nnf transformation 7]
57. ! [X0] : ((~curious(X0) | (generous(X0) & old(X0))) & ((~generous(X0) | ~old(X0)) | curious(X0))) [nnf transformation 11]
58. ! [X0] : ((~curious(X0) | (generous(X0) & old(X0))) & (~generous(X0) | ~old(X0) | curious(X0))) [flattening 57]
60. ! [X0] : (((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0)))) [nnf transformation 34]
77. ~calm(X0) | curious(X0) [cnf transformation 38]
98. ~patient(X0) | ~curious(X0) [cnf transformation 49]
99. patient(X0) | curious(X0) [cnf transformation 49]
111. ~curious(X0) | generous(X0) [cnf transformation 58]
117. generous(X0) | ~patient(X0) | ~patient(X0) | generous(X0) [cnf transformation 60]
118. ~generous(X0) | patient(X0) | ~generous(X0) | patient(X0) [cnf transformation 60]
135. calm(fred) [cnf transformation 24]
136. ~patient(X0) | generous(X0) [duplicate literal removal 117]
137. ~generous(X0) | patient(X0) [duplicate literal removal 118]
277. curious(fred) [resolution 77,135]
285. generous(X0) | curious(X0) [resolution 136,99]
286. generous(X0) [subsumption resolution 285,111]
287. patient(X0) [resolution 137,286]
290. ~curious(X1) [resolution 287,98]
291. $false [resolution 290,277]
% SZS output end Proof for 8556668763619056758926048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not old is both creative and not patient and vice versa.
If someone is happy then fred is both happy and not old and vice versa.
If mary is tall then someone is both strong and not curious.
Everyone who is either not tall or not curious is either not brave or not funny.
Everyone who is either not patient or calm is brave or not rich and vice versa.
If someone is both curious and not tall then someone is rich or not kind and vice versa.
Everyone who is both wise and not old is either not happy or not calm and vice versa.
If alice is either not rich or calm then paul is funny and vice versa.
Everyone who is rich is not quiet and vice versa.
If alice is either not quiet or not tall then someone is either not funny or not happy and vice versa.
If someone is both not curious and old then john is not old or creative.
If susan is patient or brave then mary is not kind.
Everyone who is either brave or not funny is either tall or not tall and vice versa.
Everyone who is either funny or strong is either not kind or not creative.
Everyone who is not calm is not kind or not humble.
If someone is either not brave or creative then someone is either not quiet or not creative.
Someone is old.
Someone is not happy.
Someone is either not rich or not old.
Someone is not curious.
Fred is kind.
Mary is both curious and generous.
Someone is kind. | Susan is not quiet. | contradiction | (![X]:((patient(X)|~old(X))<=>(creative(X)&~patient(X))))&
((?[X]:(happy(X)))<=>((happy(fred)&~old(fred))))&
((tall(mary))=>(?[X]:((strong(X)&~curious(X)))))&
(![X]:((~tall(X)<~>~curious(X))=>(~brave(X)<~>~funny(X))))&
(![X]:((~patient(X)<~>calm(X))<=>(brave(X)|~rich(X))))&
((?[X]:((curious(X)&~tall(X))))<=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((wise(X)&~old(X))<=>(~happy(X)<~>~calm(X))))&
(((~rich(alice)<~>calm(alice)))<=>(funny(paul)))&
(![X]:(rich(X)<=>~quiet(X)))&
(((~quiet(alice)<~>~tall(alice)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
((?[X]:((~curious(X)&old(X))))=>((~old(john)|creative(john))))&
(((patient(susan)|brave(susan)))=>(~kind(mary)))&
(![X]:((brave(X)<~>~funny(X))<=>(tall(X)<~>~tall(X))))&
(![X]:((funny(X)<~>strong(X))=>(~kind(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(~kind(X)|~humble(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(?[X]:(old(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~rich(X)<~>~old(X))))&
(?[X]:(~curious(X)))&
(kind(fred))&
((curious(mary)&generous(mary)))&
(?[X]:(kind(X))) | ~quiet(susan) | [
"p3",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1823813057245712475265323
% SZS output start Proof for 1823813057245712475265323
4. ! [X0] : ((~tall(X0) <~> ~curious(X0)) => (~brave(X0) <~> ~funny(X0))) [input p3]
6. ? [X0] : (~tall(X0) & curious(X0)) <=> ? [X0] : (~kind(X0) | rich(X0)) [input p5]
9. ! [X0] : (rich(X0) <=> ~quiet(X0)) [input p8]
13. ! [X0] : ((brave(X0) <~> ~funny(X0)) <=> (tall(X0) <~> ~tall(X0))) [input p12]
24. ~quiet(susan) [input hypothesis]
25. ? [X0] : (~tall(X0) & curious(X0)) <=> ? [X1] : (~kind(X1) | rich(X1)) [rectify 6]
30. ! [X0] : ((~brave(X0) <~> ~funny(X0)) | (~tall(X0) <=> ~curious(X0))) [ennf transformation 4]
45. ! [X0] : (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0)))) [nnf transformation 30]
48. (? [X0] : (~tall(X0) & curious(X0)) | ! [X1] : (kind(X1) & ~rich(X1))) & (? [X1] : (~kind(X1) | rich(X1)) | ! [X0] : (tall(X0) | ~curious(X0))) [nnf transformation 25]
49. (? [X0] : (~tall(X0) & curious(X0)) | ! [X1] : (kind(X1) & ~rich(X1))) & (? [X2] : (~kind(X2) | rich(X2)) | ! [X3] : (tall(X3) | ~curious(X3))) [rectify 48]
50. ? [X0] : (~tall(X0) & curious(X0)) => (~tall(sK2) & curious(sK2)) [choice axiom]
51. ? [X2] : (~kind(X2) | rich(X2)) => (~kind(sK3) | rich(sK3)) [choice axiom]
52. ((~tall(sK2) & curious(sK2)) | ! [X1] : (kind(X1) & ~rich(X1))) & ((~kind(sK3) | rich(sK3)) | ! [X3] : (tall(X3) | ~curious(X3))) [skolemisation 49,51,50]
56. ! [X0] : ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))) [nnf transformation 9]
61. ! [X0] : ((((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))))) [nnf transformation 13]
88. ~funny(X0) | ~brave(X0) | ~curious(X0) | tall(X0) [cnf transformation 45]
90. ~curious(X0) | brave(X0) | funny(X0) | tall(X0) [cnf transformation 45]
99. curious(sK2) | ~rich(X1) [cnf transformation 52]
101. ~tall(sK2) | ~rich(X1) [cnf transformation 52]
114. quiet(X0) | rich(X0) [cnf transformation 56]
130. ~funny(X0) | brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 61]
131. ~funny(X0) | brave(X0) | tall(X0) | tall(X0) [cnf transformation 61]
132. funny(X0) | ~brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 61]
133. funny(X0) | ~brave(X0) | tall(X0) | tall(X0) [cnf transformation 61]
150. ~quiet(susan) [cnf transformation 24]
151. ~funny(X0) | brave(X0) | ~tall(X0) [duplicate literal removal 130]
152. ~funny(X0) | brave(X0) | tall(X0) [duplicate literal removal 131]
153. funny(X0) | ~brave(X0) | ~tall(X0) [duplicate literal removal 132]
154. ~brave(X0) | funny(X0) | tall(X0) [duplicate literal removal 133]
196. 9 <=> tall(sK2) [avatar definition]
198. ~tall(sK2) <- (~9) [avatar component clause 196]
201. 10 <=> ! [X1] : ~rich(X1) [avatar definition]
202. ~rich(X1) <- (10) [avatar component clause 201]
203. 10 | ~9 [avatar split clause 101,196,201]
205. 11 <=> curious(sK2) [avatar definition]
207. curious(sK2) <- (11) [avatar component clause 205]
209. 10 | 11 [avatar split clause 99,205,201]
287. ~brave(X0) | funny(X0) [subsumption resolution 153,154]
288. ~funny(X0) | brave(X0) [subsumption resolution 151,152]
325. rich(susan) [resolution 114,150]
369. brave(sK2) | funny(sK2) | tall(sK2) <- (11) [resolution 90,207]
374. brave(sK2) | funny(sK2) <- (~9, 11) [subsumption resolution 369,198]
375. funny(sK2) <- (~9, 11) [subsumption resolution 374,287]
424. ~brave(sK2) | ~curious(sK2) | tall(sK2) <- (~9, 11) [resolution 375,88]
426. brave(sK2) <- (~9, 11) [resolution 375,288]
428. ~brave(sK2) | tall(sK2) <- (~9, 11) [subsumption resolution 424,207]
429. ~brave(sK2) <- (~9, 11) [subsumption resolution 428,198]
433. $false <- (~9, 11) [subsumption resolution 426,429]
434. 9 | ~11 [avatar contradiction clause 433]
446. $false <- (10) [resolution 202,325]
449. ~10 [avatar contradiction clause 446]
451. $false [avatar sat refutation 203,209,434,449]
% SZS output end Proof for 1823813057245712475265323
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and funny then someone is both brave and not happy. Everyone who is not generous or not quiet is not creative or creative. Everyone who is both rich and not strong is funny and vice versa. Everyone who is both not funny and quiet is both not old and kind and vice versa. If mary is both wise and not humble then someone is old and vice versa. Everyone who is happy is both patient and not curious. If alice is not strong or humble then someone is not creative. Everyone who is both not old and not patient is both tall and kind. If paul is funny then alice is either funny or not generous. Everyone who is both not happy and calm is both not curious and old. If someone is either not curious or not rich then susan is not brave. If paul is either calm or patient then fred is both generous and funny. Everyone who is either creative or humble is not humble and vice versa. Everyone who is either brave or not creative is not funny and vice versa. Everyone who is either strong or curious is calm or wise. Everyone who is both calm and funny is not quiet or not calm and vice versa. Someone is not tall. Someone is curious or humble. Someone is either not creative or quiet. | Alice is humble. | contradiction | ((?[X]:((~curious(X)&funny(X))))=>(?[X]:((brave(X)&~happy(X)))))&
(![X]:((~generous(X)|~quiet(X))=>(~creative(X)|creative(X))))&
(![X]:((rich(X)&~strong(X))<=>funny(X)))&
(![X]:((~funny(X)&quiet(X))<=>(~old(X)&kind(X))))&
(((wise(mary)&~humble(mary)))<=>(?[X]:(old(X))))&
(![X]:(happy(X)=>(patient(X)&~curious(X))))&
(((~strong(alice)|humble(alice)))=>(?[X]:(~creative(X))))&
(![X]:((~old(X)&~patient(X))=>(tall(X)&kind(X))))&
((funny(paul))=>((funny(alice)<~>~generous(alice))))&
(![X]:((~happy(X)&calm(X))=>(~curious(X)&old(X))))&
((?[X]:((~curious(X)<~>~rich(X))))=>(~brave(susan)))&
(((calm(paul)<~>patient(paul)))=>((generous(fred)&funny(fred))))&
(![X]:((creative(X)<~>humble(X))<=>~humble(X)))&
(![X]:((brave(X)<~>~creative(X))<=>~funny(X)))&
(![X]:((strong(X)<~>curious(X))=>(calm(X)|wise(X))))&
(![X]:((calm(X)&funny(X))<=>(~quiet(X)|~calm(X))))&
(?[X]:(~tall(X)))&
(?[X]:((curious(X)|humble(X))))&
(?[X]:((~creative(X)<~>quiet(X)))) | humble(alice) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5513390463455793061955804
% SZS output start Proof for 5513390463455793061955804
7. (humble(alice) | ~strong(alice)) => ? [X0] : ~creative(X0) [input p6]
13. ! [X0] : ((creative(X0) <~> humble(X0)) <=> ~humble(X0)) [input p12]
20. humble(alice) [input hypothesis]
26. ? [X0] : ~creative(X0) | (~humble(alice) & strong(alice)) [ennf transformation 7]
48. ? [X0] : ~creative(X0) => ~creative(sK2) [choice axiom]
49. ~creative(sK2) | (~humble(alice) & strong(alice)) [skolemisation 26,48]
53. ! [X0] : ((((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | humble(X0)) & (~humble(X0) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0))))) [nnf transformation 13]
82. ~creative(sK2) | ~humble(alice) [cnf transformation 49]
96. ~humble(X0) | creative(X0) | ~humble(X0) [cnf transformation 53]
97. humble(X0) | creative(X0) | humble(X0) [cnf transformation 53]
114. humble(alice) [cnf transformation 20]
117. ~humble(X0) | creative(X0) [duplicate literal removal 96]
118. humble(X0) | creative(X0) [duplicate literal removal 97]
151. 8 <=> humble(alice) [avatar definition]
155. 9 <=> creative(sK2) [avatar definition]
157. ~creative(sK2) <- (~9) [avatar component clause 155]
158. ~8 | ~9 [avatar split clause 82,155,151]
211. creative(X0) [subsumption resolution 117,118]
226. 8 [avatar split clause 114,151]
229. $false <- (~9) [subsumption resolution 157,211]
230. 9 [avatar contradiction clause 229]
231. $false [avatar sat refutation 158,226,230]
% SZS output end Proof for 5513390463455793061955804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or quiet then someone is both not patient and wise and vice versa.
If mary is both humble and not brave then john is not creative.
Everyone who is old or strong is both funny and not quiet and vice versa.
If someone is both strong and not creative then alice is either not tall or patient and vice versa.
Everyone who is either not strong or old is strong or quiet.
Everyone who is either not generous or not old is both not calm and patient and vice versa.
Everyone who is old is both not brave and patient.
Everyone who is not rich or not old is quiet and vice versa.
If lucy is both not happy and not old then someone is rich or generous and vice versa.
If lucy is either funny or not funny then someone is either not wise or not patient and vice versa.
If someone is both not strong and not kind then someone is not creative and vice versa.
If john is not tall then fred is patient and vice versa.
Everyone who is patient or calm is either not funny or not kind and vice versa.
If someone is both strong and not generous then someone is either old or not kind.
Everyone who is either brave or not old is not calm and vice versa.
If someone is both not humble and funny then someone is both funny and happy and vice versa.
Mary is not calm.
Alice is either old or strong.
Paul is not calm.
Lucy is patient.
Someone is either generous or patient.
Someone is not brave or quiet.
Someone is either generous or rich.
Someone is not curious or not patient. | Alice is not rich. | contradiction | ((?[X]:((calm(X)<~>quiet(X))))<=>(?[X]:((~patient(X)&wise(X)))))&
(((humble(mary)&~brave(mary)))=>(~creative(john)))&
(![X]:((old(X)|strong(X))<=>(funny(X)&~quiet(X))))&
((?[X]:((strong(X)&~creative(X))))<=>((~tall(alice)<~>patient(alice))))&
(![X]:((~strong(X)<~>old(X))=>(strong(X)|quiet(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(~calm(X)&patient(X))))&
(![X]:(old(X)=>(~brave(X)&patient(X))))&
(![X]:((~rich(X)|~old(X))<=>quiet(X)))&
(((~happy(lucy)&~old(lucy)))<=>(?[X]:((rich(X)|generous(X)))))&
(((funny(lucy)<~>~funny(lucy)))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:(~creative(X))))&
((~tall(john))<=>(patient(fred)))&
(![X]:((patient(X)|calm(X))<=>(~funny(X)<~>~kind(X))))&
((?[X]:((strong(X)&~generous(X))))=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((brave(X)<~>~old(X))<=>~calm(X)))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:((funny(X)&happy(X)))))&
(~calm(mary))&
((old(alice)<~>strong(alice)))&
(~calm(paul))&
(patient(lucy))&
(?[X]:((generous(X)<~>patient(X))))&
(?[X]:((~brave(X)|quiet(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((~curious(X)|~patient(X)))) | ~rich(alice) | [
"p2",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 889272421679021241525633
% SZS output start Proof for 889272421679021241525633
3. ! [X0] : ((strong(X0) | old(X0)) <=> (~quiet(X0) & funny(X0))) [input p2]
8. ! [X0] : ((~old(X0) | ~rich(X0)) <=> quiet(X0)) [input p7]
18. old(alice) <~> strong(alice) [input p17]
25. ~rich(alice) [input hypothesis]
42. ! [X0] : (((strong(X0) | old(X0)) | (quiet(X0) | ~funny(X0))) & ((~quiet(X0) & funny(X0)) | (~strong(X0) & ~old(X0)))) [nnf transformation 3]
43. ! [X0] : ((strong(X0) | old(X0) | quiet(X0) | ~funny(X0)) & ((~quiet(X0) & funny(X0)) | (~strong(X0) & ~old(X0)))) [flattening 42]
51. ! [X0] : (((~old(X0) | ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) & rich(X0)))) [nnf transformation 8]
52. ! [X0] : ((~old(X0) | ~rich(X0) | ~quiet(X0)) & (quiet(X0) | (old(X0) & rich(X0)))) [flattening 51]
80. (~strong(alice) | ~old(alice)) & (strong(alice) | old(alice)) [nnf transformation 18]
98. ~old(X0) | ~quiet(X0) [cnf transformation 43]
99. ~strong(X0) | ~quiet(X0) [cnf transformation 43]
117. rich(X0) | quiet(X0) [cnf transformation 52]
155. strong(alice) | old(alice) [cnf transformation 80]
164. ~rich(alice) [cnf transformation 25]
355. 41 <=> old(alice) [avatar definition]
356. old(alice) <- (41) [avatar component clause 355]
359. 42 <=> strong(alice) [avatar definition]
360. strong(alice) <- (42) [avatar component clause 359]
363. 41 | 42 [avatar split clause 155,359,355]
405. ~quiet(alice) <- (42) [resolution 360,99]
407. quiet(alice) [resolution 117,164]
409. $false <- (42) [subsumption resolution 407,405]
410. ~42 [avatar contradiction clause 409]
413. ~quiet(alice) <- (41) [resolution 356,98]
415. $false <- (41) [subsumption resolution 413,407]
416. ~41 [avatar contradiction clause 415]
417. $false [avatar sat refutation 363,410,416]
% SZS output end Proof for 889272421679021241525633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both old and not wise then fred is not old or calm.
Everyone who is calm or not generous is either not humble or not patient.
If paul is either old or wise then someone is either not patient or not creative and vice versa.
If someone is tall or not calm then someone is either creative or not curious.
Everyone who is not wise is both kind and not tall.
If someone is either not generous or not curious then someone is either not funny or not wise and vice versa.
If fred is either not kind or not humble then someone is both curious and patient.
If someone is both not generous and not rich then someone is either not generous or not strong.
Everyone who is old or brave is both strong and not old and vice versa.
If mary is both funny and not brave then someone is tall.
Everyone who is both tall and not funny is rich or not rich and vice versa.
Everyone who is either not kind or creative is either not patient or not creative and vice versa.
Everyone who is both quiet and rich is both not creative and rich and vice versa.
Everyone who is either not happy or humble is not humble.
If alice is either not wise or calm then someone is both wise and patient and vice versa.
Everyone who is either calm or rich is either curious or not quiet.
Someone is humble or not generous.
Someone is wise.
Someone is kind.
Someone is not quiet or creative.
Someone is either patient or creative.
Mary is not curious.
Someone is not patient.
Someone is not funny. | Mary is old. | contradiction | (((old(fred)&~wise(fred)))=>((~old(fred)|calm(fred))))&
(![X]:((calm(X)|~generous(X))=>(~humble(X)<~>~patient(X))))&
(((old(paul)<~>wise(paul)))<=>(?[X]:((~patient(X)<~>~creative(X)))))&
((?[X]:((tall(X)|~calm(X))))=>(?[X]:((creative(X)<~>~curious(X)))))&
(![X]:(~wise(X)=>(kind(X)&~tall(X))))&
((?[X]:((~generous(X)<~>~curious(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(((~kind(fred)<~>~humble(fred)))=>(?[X]:((curious(X)&patient(X)))))&
((?[X]:((~generous(X)&~rich(X))))=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((old(X)|brave(X))<=>(strong(X)&~old(X))))&
(((funny(mary)&~brave(mary)))=>(?[X]:(tall(X))))&
(![X]:((tall(X)&~funny(X))<=>(rich(X)|~rich(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(~patient(X)<~>~creative(X))))&
(![X]:((quiet(X)&rich(X))<=>(~creative(X)&rich(X))))&
(![X]:((~happy(X)<~>humble(X))=>~humble(X)))&
(((~wise(alice)<~>calm(alice)))<=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((calm(X)<~>rich(X))=>(curious(X)<~>~quiet(X))))&
(?[X]:((humble(X)|~generous(X))))&
(?[X]:(wise(X)))&
(?[X]:(kind(X)))&
(?[X]:((~quiet(X)|creative(X))))&
(?[X]:((patient(X)<~>creative(X))))&
(~curious(mary))&
(?[X]:(~patient(X)))&
(?[X]:(~funny(X))) | old(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2832654326495535967605723
% SZS output start Proof for 2832654326495535967605723
9. ! [X0] : ((brave(X0) | old(X0)) <=> (~old(X0) & strong(X0))) [input p8]
25. old(mary) [input hypothesis]
61. ! [X0] : (((brave(X0) | old(X0)) | (old(X0) | ~strong(X0))) & ((~old(X0) & strong(X0)) | (~brave(X0) & ~old(X0)))) [nnf transformation 9]
62. ! [X0] : ((brave(X0) | old(X0) | old(X0) | ~strong(X0)) & ((~old(X0) & strong(X0)) | (~brave(X0) & ~old(X0)))) [flattening 61]
126. ~old(X0) | ~old(X0) [cnf transformation 62]
168. old(mary) [cnf transformation 25]
174. ~old(X0) [duplicate literal removal 126]
377. $false [subsumption resolution 168,174]
% SZS output end Proof for 2832654326495535967605723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and generous is creative or patient and vice versa.
If mary is not funny then someone is either funny or happy.
If someone is both old and calm then someone is both not quiet and not humble.
Everyone who is funny is not wise and vice versa.
If someone is tall then alice is either strong or humble.
Everyone who is both not quiet and patient is either happy or generous and vice versa.
If someone is both creative and quiet then someone is either not kind or not quiet.
If someone is patient then lucy is both tall and calm.
If fred is either calm or not brave then john is both strong and not happy.
If someone is not calm or kind then susan is both not happy and not generous.
Everyone who is either not tall or patient is not curious or not generous.
Everyone who is old or quiet is both tall and patient and vice versa.
Everyone who is quiet or rich is either brave or not funny.
Everyone who is funny or not generous is not quiet and vice versa.
Everyone who is patient or not wise is not strong or old and vice versa.
If mary is both not quiet and calm then john is not brave or funny.
Alice is not strong or not creative.
John is both not patient and not rich.
Lucy is both not tall and not old.
Someone is tall.
Paul is not calm.
Someone is either happy or creative.
Alice is either not creative or not old.
Fred is brave. | Alice is curious. | contradiction | (![X]:((~tall(X)&generous(X))<=>(creative(X)|patient(X))))&
((~funny(mary))=>(?[X]:((funny(X)<~>happy(X)))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:(tall(X)))=>((strong(alice)<~>humble(alice))))&
(![X]:((~quiet(X)&patient(X))<=>(happy(X)<~>generous(X))))&
((?[X]:((creative(X)&quiet(X))))=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((?[X]:(patient(X)))=>((tall(lucy)&calm(lucy))))&
(((calm(fred)<~>~brave(fred)))=>((strong(john)&~happy(john))))&
((?[X]:((~calm(X)|kind(X))))=>((~happy(susan)&~generous(susan))))&
(![X]:((~tall(X)<~>patient(X))=>(~curious(X)|~generous(X))))&
(![X]:((old(X)|quiet(X))<=>(tall(X)&patient(X))))&
(![X]:((quiet(X)|rich(X))=>(brave(X)<~>~funny(X))))&
(![X]:((funny(X)|~generous(X))<=>~quiet(X)))&
(![X]:((patient(X)|~wise(X))<=>(~strong(X)|old(X))))&
(((~quiet(mary)&calm(mary)))=>((~brave(john)|funny(john))))&
((~strong(alice)|~creative(alice)))&
((~patient(john)&~rich(john)))&
((~tall(lucy)&~old(lucy)))&
(?[X]:(tall(X)))&
(~calm(paul))&
(?[X]:((happy(X)<~>creative(X))))&
((~creative(alice)<~>~old(alice)))&
(brave(fred)) | curious(alice) | [
"p0",
"p7",
"p10",
"p11",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2597668566020411434154816
% SZS output start Proof for 2597668566020411434154816
1. ! [X0] : ((generous(X0) & ~tall(X0)) <=> (patient(X0) | creative(X0))) [input p0]
8. ? [X0] : patient(X0) => (calm(lucy) & tall(lucy)) [input p7]
11. ! [X0] : ((~tall(X0) <~> patient(X0)) => (~generous(X0) | ~curious(X0))) [input p10]
12. ! [X0] : ((quiet(X0) | old(X0)) <=> (patient(X0) & tall(X0))) [input p11]
19. ~old(lucy) & ~tall(lucy) [input p18]
23. ~creative(alice) <~> ~old(alice) [input p22]
25. curious(alice) [input hypothesis]
34. (calm(lucy) & tall(lucy)) | ! [X0] : ~patient(X0) [ennf transformation 8]
37. ! [X0] : ((~generous(X0) | ~curious(X0)) | (~tall(X0) <=> patient(X0))) [ennf transformation 11]
38. ! [X0] : (~generous(X0) | ~curious(X0) | (~tall(X0) <=> patient(X0))) [flattening 37]
42. ! [X0] : (((generous(X0) & ~tall(X0)) | (~patient(X0) & ~creative(X0))) & ((patient(X0) | creative(X0)) | (~generous(X0) | tall(X0)))) [nnf transformation 1]
43. ! [X0] : (((generous(X0) & ~tall(X0)) | (~patient(X0) & ~creative(X0))) & (patient(X0) | creative(X0) | ~generous(X0) | tall(X0))) [flattening 42]
59. ! [X0] : (~generous(X0) | ~curious(X0) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) [nnf transformation 38]
60. ! [X0] : (((quiet(X0) | old(X0)) | (~patient(X0) | ~tall(X0))) & ((patient(X0) & tall(X0)) | (~quiet(X0) & ~old(X0)))) [nnf transformation 12]
61. ! [X0] : ((quiet(X0) | old(X0) | ~patient(X0) | ~tall(X0)) & ((patient(X0) & tall(X0)) | (~quiet(X0) & ~old(X0)))) [flattening 60]
72. (old(alice) | creative(alice)) & (~old(alice) | ~creative(alice)) [nnf transformation 23]
74. ~creative(X0) | ~tall(X0) [cnf transformation 43]
76. ~creative(X0) | generous(X0) [cnf transformation 43]
94. tall(lucy) | ~patient(X0) [cnf transformation 34]
104. ~curious(X0) | ~generous(X0) | patient(X0) | tall(X0) [cnf transformation 59]
108. ~old(X0) | patient(X0) [cnf transformation 61]
123. ~tall(lucy) [cnf transformation 19]
130. old(alice) | creative(alice) [cnf transformation 72]
132. curious(alice) [cnf transformation 25]
189. 13 <=> ! [X0] : ~patient(X0) [avatar definition]
190. ~patient(X0) <- (13) [avatar component clause 189]
197. 15 <=> tall(lucy) [avatar definition]
200. 13 | 15 [avatar split clause 94,197,189]
257. 28 <=> creative(alice) [avatar definition]
258. creative(alice) <- (28) [avatar component clause 257]
261. ~15 [avatar split clause 123,197]
273. 31 <=> old(alice) [avatar definition]
275. old(alice) <- (31) [avatar component clause 273]
276. 28 | 31 [avatar split clause 130,273,257]
313. patient(alice) <- (31) [resolution 275,108]
315. $false <- (13, 31) [subsumption resolution 313,190]
316. ~13 | ~31 [avatar contradiction clause 315]
317. generous(alice) <- (28) [resolution 258,76]
318. ~tall(alice) <- (28) [resolution 258,74]
358. ~generous(alice) | patient(alice) | tall(alice) [resolution 104,132]
359. patient(alice) | tall(alice) <- (28) [subsumption resolution 358,317]
360. tall(alice) <- (13, 28) [subsumption resolution 359,190]
361. $false <- (13, 28) [subsumption resolution 360,318]
362. ~13 | ~28 [avatar contradiction clause 361]
363. $false [avatar sat refutation 200,261,276,316,362]
% SZS output end Proof for 2597668566020411434154816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not patient is either calm or curious and vice versa. Everyone who is quiet is calm and vice versa. Everyone who is either not tall or happy is quiet or calm. Everyone who is not creative or not calm is quiet or creative and vice versa. Everyone who is both not old and not patient is both not generous and humble. If someone is both old and not funny then susan is not tall or quiet. If someone is either not brave or generous then john is not old and vice versa. If someone is generous then mary is both not curious and patient. If fred is not curious then john is both not kind and kind and vice versa. Everyone who is not brave or not generous is kind and vice versa. If someone is both not curious and not wise then someone is either brave or tall and vice versa. Everyone who is either tall or creative is both not patient and curious and vice versa. Everyone who is kind or not curious is old and vice versa. Everyone who is not old is both not humble and happy and vice versa. If someone is both brave and strong then alice is either calm or kind. If mary is creative then susan is both humble and not wise. Someone is not generous. Susan is either not creative or rich. Someone is humble or not wise. Someone is generous or not quiet. Mary is either patient or not brave. Someone is either not rich or happy. Someone is generous or not rich. Alice is wise. | Mary is patient. | entailment | (![X]:((calm(X)&~patient(X))<=>(calm(X)<~>curious(X))))&
(![X]:(quiet(X)<=>calm(X)))&
(![X]:((~tall(X)<~>happy(X))=>(quiet(X)|calm(X))))&
(![X]:((~creative(X)|~calm(X))<=>(quiet(X)|creative(X))))&
(![X]:((~old(X)&~patient(X))=>(~generous(X)&humble(X))))&
((?[X]:((old(X)&~funny(X))))=>((~tall(susan)|quiet(susan))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(~old(john)))&
((?[X]:(generous(X)))=>((~curious(mary)&patient(mary))))&
((~curious(fred))<=>((~kind(john)&kind(john))))&
(![X]:((~brave(X)|~generous(X))<=>kind(X)))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((tall(X)<~>creative(X))<=>(~patient(X)&curious(X))))&
(![X]:((kind(X)|~curious(X))<=>old(X)))&
(![X]:(~old(X)<=>(~humble(X)&happy(X))))&
((?[X]:((brave(X)&strong(X))))=>((calm(alice)<~>kind(alice))))&
((creative(mary))=>((humble(susan)&~wise(susan))))&
(?[X]:(~generous(X)))&
((~creative(susan)<~>rich(susan)))&
(?[X]:((humble(X)|~wise(X))))&
(?[X]:((generous(X)|~quiet(X))))&
((patient(mary)<~>~brave(mary)))&
(?[X]:((~rich(X)<~>happy(X))))&
(?[X]:((generous(X)|~rich(X))))&
(wise(alice)) | patient(mary) | [
"p6",
"p7",
"p9",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1308585863591177720160438
% SZS output start Proof for 1308585863591177720160438
7. ? [X0] : (~brave(X0) <~> generous(X0)) <=> ~old(john) [input p6]
8. ? [X0] : generous(X0) => (patient(mary) & ~curious(mary)) [input p7]
10. ! [X0] : ((~generous(X0) | ~brave(X0)) <=> kind(X0)) [input p9]
13. ! [X0] : ((~curious(X0) | kind(X0)) <=> old(X0)) [input p12]
21. patient(mary) <~> ~brave(mary) [input p20]
25. ~patient(mary) [input hypothesis]
33. (patient(mary) & ~curious(mary)) | ! [X0] : ~generous(X0) [ennf transformation 8]
41. (? [X0] : ((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | old(john)) & (~old(john) | ! [X0] : ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0)))) [nnf transformation 7]
42. (? [X0] : ((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | old(john)) & (~old(john) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) [rectify 41]
43. ? [X0] : ((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) => ((~generous(sK0) | brave(sK0)) & (generous(sK0) | ~brave(sK0))) [choice axiom]
44. (((~generous(sK0) | brave(sK0)) & (generous(sK0) | ~brave(sK0))) | old(john)) & (~old(john) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) [skolemisation 42,43]
47. ! [X0] : (((~generous(X0) | ~brave(X0)) | ~kind(X0)) & (kind(X0) | (generous(X0) & brave(X0)))) [nnf transformation 10]
48. ! [X0] : ((~generous(X0) | ~brave(X0) | ~kind(X0)) & (kind(X0) | (generous(X0) & brave(X0)))) [flattening 47]
56. ! [X0] : (((~curious(X0) | kind(X0)) | ~old(X0)) & (old(X0) | (curious(X0) & ~kind(X0)))) [nnf transformation 13]
57. ! [X0] : ((~curious(X0) | kind(X0) | ~old(X0)) & (old(X0) | (curious(X0) & ~kind(X0)))) [flattening 56]
67. (brave(mary) | ~patient(mary)) & (~brave(mary) | patient(mary)) [nnf transformation 21]
89. ~old(john) | generous(X1) | brave(X1) [cnf transformation 44]
94. patient(mary) | ~generous(X0) [cnf transformation 33]
99. kind(X0) | generous(X0) [cnf transformation 48]
113. ~kind(X0) | old(X0) [cnf transformation 57]
126. ~brave(mary) | patient(mary) [cnf transformation 67]
132. ~patient(mary) [cnf transformation 25]
142. 1 <=> old(john) [avatar definition]
143. ~old(john) <- (~1) [avatar component clause 142]
160. 5 <=> ! [X1] : (generous(X1) | brave(X1)) [avatar definition]
161. generous(X1) | brave(X1) <- (5) [avatar component clause 160]
162. 5 | ~1 [avatar split clause 89,142,160]
164. 6 <=> ! [X0] : ~generous(X0) [avatar definition]
165. ~generous(X0) <- (6) [avatar component clause 164]
167. 7 <=> patient(mary) [avatar definition]
170. 6 | 7 [avatar split clause 94,167,164]
260. 27 <=> brave(mary) [avatar definition]
261. ~brave(mary) <- (~27) [avatar component clause 260]
264. 7 | ~27 [avatar split clause 126,260,167]
284. ~7 [avatar split clause 132,167]
285. old(X0) | generous(X0) [resolution 113,99]
287. old(X0) <- (6) [subsumption resolution 285,165]
289. $false <- (~1, 6) [resolution 287,143]
290. 1 | ~6 [avatar contradiction clause 289]
291. brave(X1) <- (5, 6) [subsumption resolution 161,165]
293. $false <- (5, 6, ~27) [resolution 291,261]
294. ~5 | ~6 | 27 [avatar contradiction clause 293]
296. $false [avatar sat refutation 162,170,264,284,290,294]
% SZS output end Proof for 1308585863591177720160438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or patient is wise or tall.
Everyone who is both not happy and brave is either not calm or not kind and vice versa.
Everyone who is either patient or calm is either not patient or not strong and vice versa.
Everyone who is both not quiet and not wise is calm.
Everyone who is not happy or not strong is rich or not rich.
Everyone who is not curious or humble is both not funny and not humble.
If someone is not rich then someone is both not tall and not patient and vice versa.
If someone is not calm or happy then mary is not humble or not kind.
If someone is either funny or not humble then someone is both tall and not generous.
If john is either funny or wise then mary is not curious or curious.
Everyone who is generous or curious is rich or wise and vice versa.
If someone is both funny and not tall then lucy is both wise and not strong and vice versa.
If someone is both rich and not creative then someone is either funny or humble.
Everyone who is happy is either not humble or not brave and vice versa.
Everyone who is either not humble or not funny is both not kind and rich and vice versa.
Everyone who is both strong and tall is generous and vice versa.
Someone is not happy or calm.
Someone is both not patient and creative.
Mary is curious.
Alice is not strong.
Mary is both rich and not calm.
Someone is not brave or tall.
Paul is both not brave and not generous. | Alice is calm. | contradiction | (![X]:((curious(X)|patient(X))=>(wise(X)|tall(X))))&
(![X]:((~happy(X)&brave(X))<=>(~calm(X)<~>~kind(X))))&
(![X]:((patient(X)<~>calm(X))<=>(~patient(X)<~>~strong(X))))&
(![X]:((~quiet(X)&~wise(X))=>calm(X)))&
(![X]:((~happy(X)|~strong(X))=>(rich(X)|~rich(X))))&
(![X]:((~curious(X)|humble(X))=>(~funny(X)&~humble(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~tall(X)&~patient(X)))))&
((?[X]:((~calm(X)|happy(X))))=>((~humble(mary)|~kind(mary))))&
((?[X]:((funny(X)<~>~humble(X))))=>(?[X]:((tall(X)&~generous(X)))))&
(((funny(john)<~>wise(john)))=>((~curious(mary)|curious(mary))))&
(![X]:((generous(X)|curious(X))<=>(rich(X)|wise(X))))&
((?[X]:((funny(X)&~tall(X))))<=>((wise(lucy)&~strong(lucy))))&
((?[X]:((rich(X)&~creative(X))))=>(?[X]:((funny(X)<~>humble(X)))))&
(![X]:(happy(X)<=>(~humble(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>(~kind(X)&rich(X))))&
(![X]:((strong(X)&tall(X))<=>generous(X)))&
(?[X]:((~happy(X)|calm(X))))&
(?[X]:((~patient(X)&creative(X))))&
(curious(mary))&
(~strong(alice))&
((rich(mary)&~calm(mary)))&
(?[X]:((~brave(X)|tall(X))))&
((~brave(paul)&~generous(paul))) | calm(alice) | [
"p2",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 255328180868609800952330
% SZS output start Proof for 255328180868609800952330
3. ! [X0] : ((patient(X0) <~> calm(X0)) <=> (~patient(X0) <~> ~strong(X0))) [input p2]
20. ~strong(alice) [input p19]
24. calm(alice) [input hypothesis]
43. ! [X0] : ((((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0))))) [nnf transformation 3]
83. strong(X0) | patient(X0) | patient(X0) | ~calm(X0) [cnf transformation 43]
87. ~calm(X0) | ~patient(X0) | ~patient(X0) | strong(X0) [cnf transformation 43]
129. ~strong(alice) [cnf transformation 20]
135. calm(alice) [cnf transformation 24]
138. strong(X0) | patient(X0) | ~calm(X0) [duplicate literal removal 83]
140. ~calm(X0) | ~patient(X0) | strong(X0) [duplicate literal removal 87]
141. ~calm(X0) | strong(X0) [subsumption resolution 138,140]
227. strong(alice) [resolution 141,135]
228. $false [subsumption resolution 227,129]
% SZS output end Proof for 255328180868609800952330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or curious is not creative. Everyone who is both funny and kind is either not wise or not quiet. Everyone who is funny is not brave. If paul is not funny then mary is not kind or quiet. If someone is generous or happy then mary is both not wise and quiet and vice versa. Everyone who is patient is quiet and vice versa. Everyone who is tall or rich is either not funny or humble. Everyone who is humble is wise or happy. If someone is either generous or not calm then paul is both patient and not strong. Everyone who is old is either strong or not humble and vice versa. Everyone who is tall is both not brave and not curious. Everyone who is not old or creative is either tall or not humble. Everyone who is either not rich or tall is both generous and calm and vice versa. Everyone who is not wise is both calm and not tall. Everyone who is funny or creative is not tall and vice versa. Everyone who is happy is curious or kind. Paul is tall. Fred is both not funny and tall. Mary is calm. Someone is not creative or humble. Alice is patient or not humble. Fred is either brave or not funny. Someone is not rich. Mary is either not funny or brave. | Alice is happy. | neutral | (![X]:((~rich(X)|curious(X))=>~creative(X)))&
(![X]:((funny(X)&kind(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:(funny(X)=>~brave(X)))&
((~funny(paul))=>((~kind(mary)|quiet(mary))))&
((?[X]:((generous(X)|happy(X))))<=>((~wise(mary)&quiet(mary))))&
(![X]:(patient(X)<=>quiet(X)))&
(![X]:((tall(X)|rich(X))=>(~funny(X)<~>humble(X))))&
(![X]:(humble(X)=>(wise(X)|happy(X))))&
((?[X]:((generous(X)<~>~calm(X))))=>((patient(paul)&~strong(paul))))&
(![X]:(old(X)<=>(strong(X)<~>~humble(X))))&
(![X]:(tall(X)=>(~brave(X)&~curious(X))))&
(![X]:((~old(X)|creative(X))=>(tall(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(generous(X)&calm(X))))&
(![X]:(~wise(X)=>(calm(X)&~tall(X))))&
(![X]:((funny(X)|creative(X))<=>~tall(X)))&
(![X]:(happy(X)=>(curious(X)|kind(X))))&
(tall(paul))&
((~funny(fred)&tall(fred)))&
(calm(mary))&
(?[X]:((~creative(X)|humble(X))))&
((patient(alice)|~humble(alice)))&
((brave(fred)<~>~funny(fred)))&
(?[X]:(~rich(X)))&
((~funny(mary)<~>brave(mary))) | happy(alice) | [] | null | 0 |
Everyone who is either not old or not creative is not quiet or funny and vice versa. If mary is both not generous and curious then paul is kind and vice versa. If someone is funny or not patient then alice is creative. If someone is both not calm and not happy then mary is either rich or creative and vice versa. If john is patient or not happy then someone is quiet and vice versa. Everyone who is both curious and not tall is quiet or not generous and vice versa. Everyone who is both not kind and not generous is curious or tall. Everyone who is not kind is not generous or not brave. Everyone who is not old or not rich is humble or not funny and vice versa. If john is either not tall or rich then someone is not happy. Everyone who is both not kind and brave is kind or not humble. If alice is both old and wise then someone is not curious or not humble. If someone is wise then someone is quiet or not calm. Everyone who is either calm or happy is not calm. Everyone who is both not funny and not kind is not tall or not creative and vice versa. If john is strong then john is not happy and vice versa. Someone is happy. Fred is brave. Fred is funny. Someone is strong. Someone is both patient and kind. Someone is strong or not creative. John is quiet. Someone is either patient or wise. | Alice is creative. | entailment | (![X]:((~old(X)<~>~creative(X))<=>(~quiet(X)|funny(X))))&
(((~generous(mary)&curious(mary)))<=>(kind(paul)))&
((?[X]:((funny(X)|~patient(X))))=>(creative(alice)))&
((?[X]:((~calm(X)&~happy(X))))<=>((rich(mary)<~>creative(mary))))&
(((patient(john)|~happy(john)))<=>(?[X]:(quiet(X))))&
(![X]:((curious(X)&~tall(X))<=>(quiet(X)|~generous(X))))&
(![X]:((~kind(X)&~generous(X))=>(curious(X)|tall(X))))&
(![X]:(~kind(X)=>(~generous(X)|~brave(X))))&
(![X]:((~old(X)|~rich(X))<=>(humble(X)|~funny(X))))&
(((~tall(john)<~>rich(john)))=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)&brave(X))=>(kind(X)|~humble(X))))&
(((old(alice)&wise(alice)))=>(?[X]:((~curious(X)|~humble(X)))))&
((?[X]:(wise(X)))=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((calm(X)<~>happy(X))=>~calm(X)))&
(![X]:((~funny(X)&~kind(X))<=>(~tall(X)|~creative(X))))&
((strong(john))<=>(~happy(john)))&
(?[X]:(happy(X)))&
(brave(fred))&
(funny(fred))&
(?[X]:(strong(X)))&
(?[X]:((patient(X)&kind(X))))&
(?[X]:((strong(X)|~creative(X))))&
(quiet(john))&
(?[X]:((patient(X)<~>wise(X)))) | creative(alice) | [
"p2",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1004557891661958402842731
% SZS output start Proof for 1004557891661958402842731
3. ? [X0] : (~patient(X0) | funny(X0)) => creative(alice) [input p2]
19. funny(fred) [input p18]
25. ~creative(alice) [input hypothesis]
27. creative(alice) | ! [X0] : (patient(X0) & ~funny(X0)) [ennf transformation 3]
88. creative(alice) | ~funny(X0) [cnf transformation 27]
126. funny(fred) [cnf transformation 19]
134. ~creative(alice) [cnf transformation 25]
156. 5 <=> creative(alice) [avatar definition]
161. 6 <=> ! [X0] : ~funny(X0) [avatar definition]
162. ~funny(X0) <- (6) [avatar component clause 161]
163. 6 | 5 [avatar split clause 88,156,161]
275. ~5 [avatar split clause 134,156]
276. $false <- (6) [resolution 162,126]
277. ~6 [avatar contradiction clause 276]
278. $false [avatar sat refutation 163,275,277]
% SZS output end Proof for 1004557891661958402842731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not calm then mary is either not creative or not happy and vice versa.
Everyone who is tall or curious is both strong and not creative.
If fred is creative or quiet then john is either not strong or curious.
If mary is calm then lucy is not quiet and vice versa.
Everyone who is both quiet and not happy is not happy and vice versa.
Everyone who is creative is not wise or tall and vice versa.
If john is not patient then susan is either not curious or creative and vice versa.
If someone is both not funny and not generous then paul is strong or brave and vice versa.
If someone is humble then someone is both kind and not funny and vice versa.
Everyone who is not happy or strong is either not strong or not patient.
Everyone who is not funny is either not patient or strong.
Everyone who is not humble is calm or wise.
Everyone who is brave is not creative.
Everyone who is not happy is not strong or not calm and vice versa.
Everyone who is both brave and not patient is wise or brave.
If someone is not humble then someone is rich or generous.
Mary is either calm or not patient.
Someone is not patient.
Someone is either not calm or not old.
Someone is both funny and not wise. | John is not patient. | neutral | ((?[X]:((strong(X)|~calm(X))))<=>((~creative(mary)<~>~happy(mary))))&
(![X]:((tall(X)|curious(X))=>(strong(X)&~creative(X))))&
(((creative(fred)|quiet(fred)))=>((~strong(john)<~>curious(john))))&
((calm(mary))<=>(~quiet(lucy)))&
(![X]:((quiet(X)&~happy(X))<=>~happy(X)))&
(![X]:(creative(X)<=>(~wise(X)|tall(X))))&
((~patient(john))<=>((~curious(susan)<~>creative(susan))))&
((?[X]:((~funny(X)&~generous(X))))<=>((strong(paul)|brave(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((~happy(X)|strong(X))=>(~strong(X)<~>~patient(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>strong(X))))&
(![X]:(~humble(X)=>(calm(X)|wise(X))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~calm(X))))&
(![X]:((brave(X)&~patient(X))=>(wise(X)|brave(X))))&
((?[X]:(~humble(X)))=>(?[X]:((rich(X)|generous(X)))))&
((calm(mary)<~>~patient(mary)))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)<~>~old(X))))&
(?[X]:((funny(X)&~wise(X)))) | ~patient(john) | [] | null | 0 |
Everyone who is not humble or brave is both not brave and not tall and vice versa. If someone is not patient or happy then someone is both not kind and not curious. If someone is both not calm and not kind then paul is humble or not curious and vice versa. If fred is both wise and not generous then fred is both old and happy. If susan is not strong then someone is not creative or not curious and vice versa. Everyone who is both not humble and not funny is not strong or not humble. If someone is old or not kind then alice is both wise and not generous. Everyone who is both not curious and wise is both curious and not humble and vice versa. If susan is patient then paul is creative. If someone is both tall and creative then someone is either not calm or not patient and vice versa. If susan is either not calm or not wise then susan is both not brave and humble. Everyone who is both not calm and kind is both not funny and not calm. Everyone who is either old or not rich is not quiet or quiet. Everyone who is either not quiet or not creative is not quiet or brave and vice versa. If someone is either tall or calm then mary is funny or brave. If someone is both generous and happy then alice is both not humble and happy. Lucy is not wise. Someone is not old. Mary is not strong or patient. Someone is not humble or patient. Lucy is quiet. Someone is funny or kind. Fred is both creative and not happy. | Susan is strong. | neutral | (![X]:((~humble(X)|brave(X))<=>(~brave(X)&~tall(X))))&
((?[X]:((~patient(X)|happy(X))))=>(?[X]:((~kind(X)&~curious(X)))))&
((?[X]:((~calm(X)&~kind(X))))<=>((humble(paul)|~curious(paul))))&
(((wise(fred)&~generous(fred)))=>((old(fred)&happy(fred))))&
((~strong(susan))<=>(?[X]:((~creative(X)|~curious(X)))))&
(![X]:((~humble(X)&~funny(X))=>(~strong(X)|~humble(X))))&
((?[X]:((old(X)|~kind(X))))=>((wise(alice)&~generous(alice))))&
(![X]:((~curious(X)&wise(X))<=>(curious(X)&~humble(X))))&
((patient(susan))=>(creative(paul)))&
((?[X]:((tall(X)&creative(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(((~calm(susan)<~>~wise(susan)))=>((~brave(susan)&humble(susan))))&
(![X]:((~calm(X)&kind(X))=>(~funny(X)&~calm(X))))&
(![X]:((old(X)<~>~rich(X))=>(~quiet(X)|quiet(X))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(~quiet(X)|brave(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((funny(mary)|brave(mary))))&
((?[X]:((generous(X)&happy(X))))=>((~humble(alice)&happy(alice))))&
(~wise(lucy))&
(?[X]:(~old(X)))&
((~strong(mary)|patient(mary)))&
(?[X]:((~humble(X)|patient(X))))&
(quiet(lucy))&
(?[X]:((funny(X)|kind(X))))&
((creative(fred)&~happy(fred))) | strong(susan) | [] | null | 0 |
Everyone who is either generous or not curious is humble or curious. Everyone who is strong or patient is not calm or calm and vice versa. If susan is not happy then someone is both not quiet and not funny. Everyone who is not funny is either not strong or wise and vice versa. Everyone who is both wise and funny is quiet or not generous. Everyone who is generous is both not patient and generous and vice versa. Everyone who is not funny is quiet or tall and vice versa. If lucy is both creative and not rich then paul is either not brave or not generous and vice versa. If someone is both not happy and not creative then mary is both not patient and not strong. Everyone who is curious or old is either not strong or quiet. If lucy is not old or not rich then fred is either creative or not kind and vice versa. Everyone who is either funny or not calm is generous and vice versa. If lucy is happy then someone is both not happy and not generous and vice versa. If someone is not funny or wise then alice is either not funny or not strong and vice versa. Everyone who is generous is either not rich or not curious and vice versa. If someone is either not strong or not wise then fred is both not happy and strong. Someone is humble. Someone is both not creative and funny. Susan is not patient. Paul is creative or curious. Mary is not kind or brave. Alice is both not creative and not humble. Paul is not kind. Paul is both not creative and not old. | Alice is not strong. | neutral | (![X]:((generous(X)<~>~curious(X))=>(humble(X)|curious(X))))&
(![X]:((strong(X)|patient(X))<=>(~calm(X)|calm(X))))&
((~happy(susan))=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:(~funny(X)<=>(~strong(X)<~>wise(X))))&
(![X]:((wise(X)&funny(X))=>(quiet(X)|~generous(X))))&
(![X]:(generous(X)<=>(~patient(X)&generous(X))))&
(![X]:(~funny(X)<=>(quiet(X)|tall(X))))&
(((creative(lucy)&~rich(lucy)))<=>((~brave(paul)<~>~generous(paul))))&
((?[X]:((~happy(X)&~creative(X))))=>((~patient(mary)&~strong(mary))))&
(![X]:((curious(X)|old(X))=>(~strong(X)<~>quiet(X))))&
(((~old(lucy)|~rich(lucy)))<=>((creative(fred)<~>~kind(fred))))&
(![X]:((funny(X)<~>~calm(X))<=>generous(X)))&
((happy(lucy))<=>(?[X]:((~happy(X)&~generous(X)))))&
((?[X]:((~funny(X)|wise(X))))<=>((~funny(alice)<~>~strong(alice))))&
(![X]:(generous(X)<=>(~rich(X)<~>~curious(X))))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~happy(fred)&strong(fred))))&
(?[X]:(humble(X)))&
(?[X]:((~creative(X)&funny(X))))&
(~patient(susan))&
((creative(paul)|curious(paul)))&
((~kind(mary)|brave(mary)))&
((~creative(alice)&~humble(alice)))&
(~kind(paul))&
((~creative(paul)&~old(paul))) | ~strong(alice) | [] | null | 0 |
If someone is either not rich or patient then fred is happy or curious and vice versa.
Everyone who is brave is happy or strong.
If someone is curious or not tall then mary is kind or not patient.
If mary is creative or not quiet then lucy is humble or generous.
Everyone who is either strong or wise is wise or not calm.
Everyone who is not funny or brave is both brave and not calm.
If fred is both not old and tall then someone is creative or funny and vice versa.
Everyone who is either rich or not wise is either not tall or wise and vice versa.
Everyone who is not curious or not funny is kind or not curious.
Everyone who is both happy and not tall is humble or not wise and vice versa.
Everyone who is both curious and quiet is brave.
Everyone who is either calm or curious is generous or not rich and vice versa.
If someone is both not creative and curious then mary is not strong or creative.
If fred is wise or not calm then fred is both not rich and strong and vice versa.
If someone is generous or not old then alice is not rich or funny.
Everyone who is not brave is either not tall or strong and vice versa.
Someone is both generous and rich.
Someone is kind or creative.
Someone is curious.
Lucy is old or patient.
Someone is not calm or tall. | Fred is not brave. | contradiction | ((?[X]:((~rich(X)<~>patient(X))))<=>((happy(fred)|curious(fred))))&
(![X]:(brave(X)=>(happy(X)|strong(X))))&
((?[X]:((curious(X)|~tall(X))))=>((kind(mary)|~patient(mary))))&
(((creative(mary)|~quiet(mary)))=>((humble(lucy)|generous(lucy))))&
(![X]:((strong(X)<~>wise(X))=>(wise(X)|~calm(X))))&
(![X]:((~funny(X)|brave(X))=>(brave(X)&~calm(X))))&
(((~old(fred)&tall(fred)))<=>(?[X]:((creative(X)|funny(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~curious(X)|~funny(X))=>(kind(X)|~curious(X))))&
(![X]:((happy(X)&~tall(X))<=>(humble(X)|~wise(X))))&
(![X]:((curious(X)&quiet(X))=>brave(X)))&
(![X]:((calm(X)<~>curious(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~creative(X)&curious(X))))=>((~strong(mary)|creative(mary))))&
(((wise(fred)|~calm(fred)))<=>((~rich(fred)&strong(fred))))&
((?[X]:((generous(X)|~old(X))))=>((~rich(alice)|funny(alice))))&
(![X]:(~brave(X)<=>(~tall(X)<~>strong(X))))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:(curious(X)))&
((old(lucy)|patient(lucy)))&
(?[X]:((~calm(X)|tall(X)))) | ~brave(fred) | [
"p5",
"p6",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3826579350960304467774936
% SZS output start Proof for 3826579350960304467774936
6. ! [X0] : ((brave(X0) | ~funny(X0)) => (~calm(X0) & brave(X0))) [input p5]
7. (tall(fred) & ~old(fred)) <=> ? [X0] : (funny(X0) | creative(X0)) [input p6]
8. ! [X0] : ((rich(X0) <~> ~wise(X0)) <=> (~tall(X0) <~> wise(X0))) [input p7]
10. ! [X0] : ((~tall(X0) & happy(X0)) <=> (~wise(X0) | humble(X0))) [input p9]
14. (~calm(fred) | wise(fred)) <=> (strong(fred) & ~rich(fred)) [input p13]
22. ~brave(fred) [input hypothesis]
32. ! [X0] : ((~calm(X0) & brave(X0)) | (~brave(X0) & funny(X0))) [ennf transformation 6]
45. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | (~tall(fred) | old(fred))) [nnf transformation 7]
46. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | ~tall(fred) | old(fred)) [flattening 45]
47. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X1] : (funny(X1) | creative(X1)) | ~tall(fred) | old(fred)) [rectify 46]
48. ? [X1] : (funny(X1) | creative(X1)) => (funny(sK1) | creative(sK1)) [choice axiom]
49. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & ((funny(sK1) | creative(sK1)) | ~tall(fred) | old(fred)) [skolemisation 47,48]
50. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [nnf transformation 8]
51. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 10]
52. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | tall(X0) | ~happy(X0))) [flattening 51]
55. ((~calm(fred) | wise(fred)) | (~strong(fred) | rich(fred))) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [nnf transformation 14]
56. (~calm(fred) | wise(fred) | ~strong(fred) | rich(fred)) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [flattening 55]
75. funny(X0) | brave(X0) [cnf transformation 32]
83. tall(fred) | ~funny(X0) [cnf transformation 49]
85. wise(X0) | ~tall(X0) | rich(X0) | wise(X0) [cnf transformation 50]
89. ~wise(X0) | rich(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 50]
96. ~tall(X0) | wise(X0) [cnf transformation 52]
105. ~rich(fred) | ~wise(fred) [cnf transformation 56]
121. ~brave(fred) [cnf transformation 22]
122. wise(X0) | ~tall(X0) | rich(X0) [duplicate literal removal 85]
124. ~wise(X0) | rich(X0) | ~tall(X0) [duplicate literal removal 89]
174. 11 <=> ! [X0] : ~funny(X0) [avatar definition]
175. ~funny(X0) <- (11) [avatar component clause 174]
177. 12 <=> tall(fred) [avatar definition]
179. tall(fred) <- (12) [avatar component clause 177]
180. 11 | 12 [avatar split clause 83,177,174]
201. ~tall(X0) | rich(X0) [subsumption resolution 122,124]
220. 21 <=> wise(fred) [avatar definition]
225. 22 <=> rich(fred) [avatar definition]
227. ~rich(fred) <- (~22) [avatar component clause 225]
229. ~21 | ~22 [avatar split clause 105,225,220]
264. brave(X0) <- (11) [resolution 75,175]
265. $false <- (11) [resolution 264,121]
266. ~11 [avatar contradiction clause 265]
272. wise(fred) <- (12) [resolution 96,179]
275. 21 | ~12 [avatar split clause 272,177,220]
277. rich(fred) <- (12) [resolution 201,179]
278. $false <- (12, ~22) [subsumption resolution 277,227]
279. ~12 | 22 [avatar contradiction clause 278]
280. $false [avatar sat refutation 180,229,266,275,279]
% SZS output end Proof for 3826579350960304467774936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or quiet is both not kind and quiet and vice versa. Everyone who is not strong or patient is old. Everyone who is either not calm or not creative is wise and vice versa. Everyone who is not old is both not funny and not creative. If fred is both rich and not tall then fred is both not patient and happy. Everyone who is either not happy or brave is both not kind and not funny. If lucy is both not quiet and creative then fred is both not funny and not generous. Everyone who is not creative or funny is generous or creative. Everyone who is patient or creative is both not generous and quiet. Everyone who is both not rich and old is both not creative and happy and vice versa. Everyone who is not generous is both not patient and not creative. Everyone who is calm is kind or not funny and vice versa. If lucy is either brave or creative then someone is either patient or not calm. Everyone who is either wise or not tall is not wise. If lucy is either not old or wise then someone is not old and vice versa. If someone is both creative and generous then someone is quiet and vice versa. John is both rich and brave. Someone is either not creative or rich. Lucy is not generous or calm. Someone is not strong. Someone is kind. Someone is brave or wise. Lucy is either wise or not funny. | Lucy is old. | entailment | (![X]:((~humble(X)<~>quiet(X))<=>(~kind(X)&quiet(X))))&
(![X]:((~strong(X)|patient(X))=>old(X)))&
(![X]:((~calm(X)<~>~creative(X))<=>wise(X)))&
(![X]:(~old(X)=>(~funny(X)&~creative(X))))&
(((rich(fred)&~tall(fred)))=>((~patient(fred)&happy(fred))))&
(![X]:((~happy(X)<~>brave(X))=>(~kind(X)&~funny(X))))&
(((~quiet(lucy)&creative(lucy)))=>((~funny(fred)&~generous(fred))))&
(![X]:((~creative(X)|funny(X))=>(generous(X)|creative(X))))&
(![X]:((patient(X)|creative(X))=>(~generous(X)&quiet(X))))&
(![X]:((~rich(X)&old(X))<=>(~creative(X)&happy(X))))&
(![X]:(~generous(X)=>(~patient(X)&~creative(X))))&
(![X]:(calm(X)<=>(kind(X)|~funny(X))))&
(((brave(lucy)<~>creative(lucy)))=>(?[X]:((patient(X)<~>~calm(X)))))&
(![X]:((wise(X)<~>~tall(X))=>~wise(X)))&
(((~old(lucy)<~>wise(lucy)))<=>(?[X]:(~old(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:(quiet(X))))&
((rich(john)&brave(john)))&
(?[X]:((~creative(X)<~>rich(X))))&
((~generous(lucy)|calm(lucy)))&
(?[X]:(~strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((brave(X)|wise(X))))&
((wise(lucy)<~>~funny(lucy))) | old(lucy) | [
"p2",
"p7",
"p8",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7971261048925752665371423
% SZS output start Proof for 7971261048925752665371423
3. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> wise(X0)) [input p2]
8. ! [X0] : ((funny(X0) | ~creative(X0)) => (creative(X0) | generous(X0))) [input p7]
9. ! [X0] : ((creative(X0) | patient(X0)) => (quiet(X0) & ~generous(X0))) [input p8]
11. ! [X0] : (~generous(X0) => (~creative(X0) & ~patient(X0))) [input p10]
15. (~old(lucy) <~> wise(lucy)) <=> ? [X0] : ~old(X0) [input p14]
19. calm(lucy) | ~generous(lucy) [input p18]
24. ~old(lucy) [input hypothesis]
33. ! [X0] : ((creative(X0) | generous(X0)) | (~funny(X0) & creative(X0))) [ennf transformation 8]
34. ! [X0] : (creative(X0) | generous(X0) | (~funny(X0) & creative(X0))) [flattening 33]
35. ! [X0] : ((quiet(X0) & ~generous(X0)) | (~creative(X0) & ~patient(X0))) [ennf transformation 9]
36. ! [X0] : ((~creative(X0) & ~patient(X0)) | generous(X0)) [ennf transformation 11]
41. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | ~wise(X0)) & (wise(X0) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 3]
51. (((~wise(lucy) | old(lucy)) & (wise(lucy) | ~old(lucy))) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ((~old(lucy) | ~wise(lucy)) & (wise(lucy) | old(lucy)))) [nnf transformation 15]
52. (((~wise(lucy) | old(lucy)) & (wise(lucy) | ~old(lucy))) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ((~old(lucy) | ~wise(lucy)) & (wise(lucy) | old(lucy)))) [rectify 51]
53. ? [X1] : ~old(X1) => ~old(sK1) [choice axiom]
54. (((~wise(lucy) | old(lucy)) & (wise(lucy) | ~old(lucy))) | ! [X0] : old(X0)) & (~old(sK1) | ((~old(lucy) | ~wise(lucy)) & (wise(lucy) | old(lucy)))) [skolemisation 52,53]
79. ~calm(X0) | wise(X0) | creative(X0) [cnf transformation 41]
92. creative(X0) | generous(X0) | creative(X0) [cnf transformation 34]
95. ~generous(X0) | ~creative(X0) [cnf transformation 35]
103. ~creative(X0) | generous(X0) [cnf transformation 36]
116. ~wise(lucy) | old(lucy) | old(X0) [cnf transformation 54]
124. calm(lucy) | ~generous(lucy) [cnf transformation 19]
130. ~old(lucy) [cnf transformation 24]
132. generous(X0) | creative(X0) [duplicate literal removal 92]
173. generous(X0) [subsumption resolution 103,132]
191. 12 <=> ! [X0] : old(X0) [avatar definition]
192. old(X0) <- (12) [avatar component clause 191]
194. 13 <=> old(lucy) [avatar definition]
195. ~old(lucy) <- (~13) [avatar component clause 194]
198. 14 <=> wise(lucy) [avatar definition]
201. 12 | 13 | ~14 [avatar split clause 116,198,194,191]
226. calm(lucy) [subsumption resolution 124,173]
242. ~13 [avatar split clause 130,194]
246. ~creative(X0) [resolution 95,173]
254. wise(lucy) | creative(lucy) [resolution 79,226]
268. wise(lucy) [subsumption resolution 254,246]
269. 14 [avatar split clause 268,198]
272. $false <- (12, ~13) [resolution 192,195]
275. ~12 | 13 [avatar contradiction clause 272]
276. $false [avatar sat refutation 201,242,269,275]
% SZS output end Proof for 7971261048925752665371423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or rich is either happy or humble.
Everyone who is either generous or not brave is either not calm or not rich and vice versa.
If someone is brave then someone is either generous or not humble.
Everyone who is funny is funny or not calm and vice versa.
Everyone who is not kind is not brave and vice versa.
Everyone who is quiet or not kind is generous and vice versa.
If someone is either not generous or happy then someone is either calm or not calm and vice versa.
If lucy is either generous or not old then paul is not tall.
If fred is either creative or not rich then someone is not strong and vice versa.
Everyone who is curious is either not strong or not calm and vice versa.
If someone is either not kind or not generous then someone is not tall or not brave and vice versa.
Everyone who is old is either not creative or not calm.
Everyone who is both not creative and not wise is both calm and not tall and vice versa.
If john is either not generous or generous then someone is either not old or not calm.
Everyone who is either brave or not funny is either calm or not brave and vice versa.
Everyone who is brave is not patient or not calm.
Someone is both curious and not tall.
Lucy is generous or not funny.
Someone is not quiet or not rich.
Someone is strong.
Someone is not old or tall.
Someone is not rich.
Someone is not kind or brave.
Paul is both old and not wise. | Paul is not creative. | entailment | (![X]:((quiet(X)<~>rich(X))=>(happy(X)<~>humble(X))))&
(![X]:((generous(X)<~>~brave(X))<=>(~calm(X)<~>~rich(X))))&
((?[X]:(brave(X)))=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:(funny(X)<=>(funny(X)|~calm(X))))&
(![X]:(~kind(X)<=>~brave(X)))&
(![X]:((quiet(X)|~kind(X))<=>generous(X)))&
((?[X]:((~generous(X)<~>happy(X))))<=>(?[X]:((calm(X)<~>~calm(X)))))&
(((generous(lucy)<~>~old(lucy)))=>(~tall(paul)))&
(((creative(fred)<~>~rich(fred)))<=>(?[X]:(~strong(X))))&
(![X]:(curious(X)<=>(~strong(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(old(X)=>(~creative(X)<~>~calm(X))))&
(![X]:((~creative(X)&~wise(X))<=>(calm(X)&~tall(X))))&
(((~generous(john)<~>generous(john)))=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(calm(X)<~>~brave(X))))&
(![X]:(brave(X)=>(~patient(X)|~calm(X))))&
(?[X]:((curious(X)&~tall(X))))&
((generous(lucy)|~funny(lucy)))&
(?[X]:((~quiet(X)|~rich(X))))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~kind(X)|brave(X))))&
((old(paul)&~wise(paul))) | ~creative(paul) | [
"p3",
"p11",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2080700483949571109233495
% SZS output start Proof for 2080700483949571109233495
4. ! [X0] : (funny(X0) <=> (~calm(X0) | funny(X0))) [input p3]
12. ! [X0] : (old(X0) => (~creative(X0) <~> ~calm(X0))) [input p11]
15. ! [X0] : ((brave(X0) <~> ~funny(X0)) <=> (calm(X0) <~> ~brave(X0))) [input p14]
24. ~wise(paul) & old(paul) [input p23]
25. creative(paul) [input hypothesis]
35. ! [X0] : ((~creative(X0) <~> ~calm(X0)) | ~old(X0)) [ennf transformation 12]
43. ! [X0] : ((funny(X0) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | ~funny(X0))) [nnf transformation 4]
44. ! [X0] : ((funny(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | ~funny(X0))) [flattening 43]
64. ! [X0] : (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ~old(X0)) [nnf transformation 35]
70. ! [X0] : ((((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))))) [nnf transformation 15]
99. funny(X0) | calm(X0) [cnf transformation 44]
127. ~creative(X0) | ~calm(X0) | ~old(X0) [cnf transformation 64]
137. ~brave(X0) | calm(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 70]
140. brave(X0) | ~calm(X0) | brave(X0) | funny(X0) [cnf transformation 70]
142. ~funny(X0) | brave(X0) | calm(X0) | brave(X0) [cnf transformation 70]
143. funny(X0) | ~brave(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 70]
153. old(paul) [cnf transformation 24]
155. creative(paul) [cnf transformation 25]
156. ~brave(X0) | calm(X0) | ~funny(X0) [duplicate literal removal 137]
157. brave(X0) | ~calm(X0) | funny(X0) [duplicate literal removal 140]
158. ~funny(X0) | brave(X0) | calm(X0) [duplicate literal removal 142]
159. funny(X0) | ~brave(X0) | ~calm(X0) [duplicate literal removal 143]
182. 4 <=> ! [X1] : calm(X1) [avatar definition]
183. calm(X1) <- (4) [avatar component clause 182]
282. ~brave(X0) | funny(X0) [subsumption resolution 159,99]
283. calm(X0) | brave(X0) [subsumption resolution 158,99]
284. brave(X0) | funny(X0) [subsumption resolution 157,99]
285. funny(X0) [subsumption resolution 284,282]
286. ~brave(X0) | calm(X0) [subsumption resolution 156,285]
287. calm(X0) [subsumption resolution 286,283]
288. 4 [avatar split clause 287,182]
324. ~calm(paul) | ~old(paul) [resolution 127,155]
325. ~old(paul) <- (4) [subsumption resolution 324,183]
326. $false <- (4) [subsumption resolution 325,153]
327. ~4 [avatar contradiction clause 326]
328. $false [avatar sat refutation 288,327]
% SZS output end Proof for 2080700483949571109233495
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and generous is happy or strong and vice versa. Everyone who is not wise is either not old or happy. If mary is tall or not curious then susan is both not rich and not curious and vice versa. If someone is not quiet then fred is either not brave or tall. Everyone who is quiet or not calm is not creative. If fred is not tall then paul is not old. Everyone who is quiet or generous is either not kind or not calm. If alice is not happy or tall then john is not quiet or rich. If someone is both not strong and not brave then someone is not happy or not calm. Everyone who is not rich is humble and vice versa. If susan is either strong or not funny then lucy is wise and vice versa. Everyone who is not kind or kind is curious and vice versa. Everyone who is either brave or not funny is either strong or not tall. Everyone who is both rich and not humble is both quiet and not creative and vice versa. If someone is both not brave and happy then lucy is quiet or creative. Everyone who is not kind is both strong and not curious and vice versa. Mary is both not brave and calm. Lucy is not wise. Someone is generous. Susan is either not curious or not tall. Paul is both not strong and not quiet. Someone is not strong. Fred is not patient. | Susan is brave. | neutral | (![X]:((~brave(X)&generous(X))<=>(happy(X)|strong(X))))&
(![X]:(~wise(X)=>(~old(X)<~>happy(X))))&
(((tall(mary)|~curious(mary)))<=>((~rich(susan)&~curious(susan))))&
((?[X]:(~quiet(X)))=>((~brave(fred)<~>tall(fred))))&
(![X]:((quiet(X)|~calm(X))=>~creative(X)))&
((~tall(fred))=>(~old(paul)))&
(![X]:((quiet(X)|generous(X))=>(~kind(X)<~>~calm(X))))&
(((~happy(alice)|tall(alice)))=>((~quiet(john)|rich(john))))&
((?[X]:((~strong(X)&~brave(X))))=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:(~rich(X)<=>humble(X)))&
(((strong(susan)<~>~funny(susan)))<=>(wise(lucy)))&
(![X]:((~kind(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)<~>~funny(X))=>(strong(X)<~>~tall(X))))&
(![X]:((rich(X)&~humble(X))<=>(quiet(X)&~creative(X))))&
((?[X]:((~brave(X)&happy(X))))=>((quiet(lucy)|creative(lucy))))&
(![X]:(~kind(X)<=>(strong(X)&~curious(X))))&
((~brave(mary)&calm(mary)))&
(~wise(lucy))&
(?[X]:(generous(X)))&
((~curious(susan)<~>~tall(susan)))&
((~strong(paul)&~quiet(paul)))&
(?[X]:(~strong(X)))&
(~patient(fred)) | brave(susan) | [] | null | 0 |
Everyone who is either not brave or not funny is not rich and vice versa. Everyone who is not rich is not quiet or not tall and vice versa. Everyone who is humble is kind or rich. If someone is both humble and not quiet then mary is funny or not generous. Everyone who is either humble or quiet is not rich and vice versa. If someone is funny then mary is both not curious and curious. Everyone who is happy or not rich is not patient. If someone is brave then fred is both not brave and not humble. If fred is tall or rich then mary is either not patient or creative and vice versa. Everyone who is not curious or not quiet is humble. Everyone who is not wise is either not creative or generous and vice versa. Everyone who is either old or not happy is either not generous or happy and vice versa. If someone is both not curious and happy then someone is either not brave or curious. Everyone who is curious is not funny or brave and vice versa. If alice is either not rich or wise then someone is rich. If mary is tall then alice is old. Susan is either generous or calm. Susan is rich or wise. Someone is not strong or quiet. John is either not tall or quiet. Someone is either kind or not rich. Someone is not strong. Someone is old or creative. | Mary is not brave. | entailment | (![X]:((~brave(X)<~>~funny(X))<=>~rich(X)))&
(![X]:(~rich(X)<=>(~quiet(X)|~tall(X))))&
(![X]:(humble(X)=>(kind(X)|rich(X))))&
((?[X]:((humble(X)&~quiet(X))))=>((funny(mary)|~generous(mary))))&
(![X]:((humble(X)<~>quiet(X))<=>~rich(X)))&
((?[X]:(funny(X)))=>((~curious(mary)&curious(mary))))&
(![X]:((happy(X)|~rich(X))=>~patient(X)))&
((?[X]:(brave(X)))=>((~brave(fred)&~humble(fred))))&
(((tall(fred)|rich(fred)))<=>((~patient(mary)<~>creative(mary))))&
(![X]:((~curious(X)|~quiet(X))=>humble(X)))&
(![X]:(~wise(X)<=>(~creative(X)<~>generous(X))))&
(![X]:((old(X)<~>~happy(X))<=>(~generous(X)<~>happy(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~brave(X)<~>curious(X)))))&
(![X]:(curious(X)<=>(~funny(X)|brave(X))))&
(((~rich(alice)<~>wise(alice)))=>(?[X]:(rich(X))))&
((tall(mary))=>(old(alice)))&
((generous(susan)<~>calm(susan)))&
((rich(susan)|wise(susan)))&
(?[X]:((~strong(X)|quiet(X))))&
((~tall(john)<~>quiet(john)))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:(~strong(X)))&
(?[X]:((old(X)|creative(X)))) | ~brave(mary) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4580500511817093179142224
% SZS output start Proof for 4580500511817093179142224
1. ! [X0] : ((~brave(X0) <~> ~funny(X0)) <=> ~rich(X0)) [input p0]
2. ! [X0] : (~rich(X0) <=> (~tall(X0) | ~quiet(X0))) [input p1]
5. ! [X0] : ((humble(X0) <~> quiet(X0)) <=> ~rich(X0)) [input p4]
6. ? [X0] : funny(X0) => (curious(mary) & ~curious(mary)) [input p5]
8. ? [X0] : brave(X0) => (~humble(fred) & ~brave(fred)) [input p7]
14. ! [X0] : (curious(X0) <=> (brave(X0) | ~funny(X0))) [input p13]
24. brave(mary) [input hypothesis]
32. (curious(mary) & ~curious(mary)) | ! [X0] : ~funny(X0) [ennf transformation 6]
34. (~humble(fred) & ~brave(fred)) | ! [X0] : ~brave(X0) [ennf transformation 8]
39. ! [X0] : ((((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | rich(X0)) & (~rich(X0) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0))))) [nnf transformation 1]
40. ! [X0] : ((~rich(X0) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | rich(X0))) [nnf transformation 2]
41. ! [X0] : ((~rich(X0) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | rich(X0))) [flattening 40]
42. ! [X0] : ((((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | rich(X0)) & (~rich(X0) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0))))) [nnf transformation 5]
51. ! [X0] : ((curious(X0) | (~brave(X0) & funny(X0))) & ((brave(X0) | ~funny(X0)) | ~curious(X0))) [nnf transformation 14]
52. ! [X0] : ((curious(X0) | (~brave(X0) & funny(X0))) & (brave(X0) | ~funny(X0) | ~curious(X0))) [flattening 51]
66. rich(X0) | brave(X0) | funny(X0) [cnf transformation 39]
68. ~rich(X0) | quiet(X0) [cnf transformation 41]
73. ~rich(X0) | humble(X0) | ~quiet(X0) [cnf transformation 42]
74. quiet(X0) | humble(X0) | rich(X0) [cnf transformation 42]
76. ~curious(mary) | ~funny(X0) [cnf transformation 32]
80. ~brave(fred) | ~brave(X0) [cnf transformation 34]
81. ~humble(fred) | ~brave(X0) [cnf transformation 34]
106. ~brave(X0) | curious(X0) [cnf transformation 52]
118. brave(mary) [cnf transformation 24]
135. humble(X0) | quiet(X0) [subsumption resolution 74,68]
136. ~rich(X0) | humble(X0) [subsumption resolution 73,135]
138. 4 <=> ! [X0] : ~funny(X0) [avatar definition]
139. ~funny(X0) <- (4) [avatar component clause 138]
141. 5 <=> curious(mary) [avatar definition]
145. 4 | ~5 [avatar split clause 76,141,138]
147. 6 <=> ! [X0] : ~brave(X0) [avatar definition]
148. ~brave(X0) <- (6) [avatar component clause 147]
150. 7 <=> humble(fred) [avatar definition]
152. ~humble(fred) <- (~7) [avatar component clause 150]
153. 6 | ~7 [avatar split clause 81,150,147]
155. 8 <=> brave(fred) [avatar definition]
158. 6 | ~8 [avatar split clause 80,155,147]
176. 12 <=> rich(fred) [avatar definition]
177. rich(fred) <- (12) [avatar component clause 176]
178. ~rich(fred) <- (~12) [avatar component clause 176]
275. curious(mary) [resolution 106,118]
277. 5 [avatar split clause 275,141]
292. brave(fred) | funny(fred) <- (~12) [resolution 66,178]
305. brave(fred) <- (4, ~12) [subsumption resolution 292,139]
306. 8 | ~4 | 12 [avatar split clause 305,176,138,155]
307. $false <- (6) [resolution 148,118]
310. ~6 [avatar contradiction clause 307]
313. humble(fred) <- (12) [resolution 177,136]
316. $false <- (~7, 12) [subsumption resolution 313,152]
317. 7 | ~12 [avatar contradiction clause 316]
318. $false [avatar sat refutation 145,153,158,277,306,310,317]
% SZS output end Proof for 4580500511817093179142224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is patient or not rich then someone is kind or not funny and vice versa.
Everyone who is both not brave and not creative is both not quiet and curious.
Everyone who is patient or quiet is either generous or wise and vice versa.
Everyone who is both not strong and not funny is not brave.
Everyone who is both rich and strong is not old or not tall.
Everyone who is either not quiet or not strong is not strong and vice versa.
Everyone who is strong or not old is rich or not old.
Everyone who is either not calm or old is not happy.
If fred is both generous and not curious then someone is humble.
If john is either brave or generous then susan is both tall and not rich and vice versa.
Everyone who is either not rich or not happy is curious or not rich and vice versa.
Everyone who is either not strong or generous is wise.
Everyone who is both humble and wise is either not rich or not old.
Everyone who is either not generous or quiet is either rich or curious and vice versa.
If john is either wise or kind then someone is rich or not kind and vice versa.
Everyone who is either not wise or curious is not brave and vice versa.
Someone is both brave and not kind.
Someone is either creative or kind.
Susan is not kind or brave.
Fred is not funny or not tall.
Someone is either not curious or strong.
John is both not old and humble. | Fred is patient. | neutral | (((patient(susan)|~rich(susan)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((~brave(X)&~creative(X))=>(~quiet(X)&curious(X))))&
(![X]:((patient(X)|quiet(X))<=>(generous(X)<~>wise(X))))&
(![X]:((~strong(X)&~funny(X))=>~brave(X)))&
(![X]:((rich(X)&strong(X))=>(~old(X)|~tall(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>~strong(X)))&
(![X]:((strong(X)|~old(X))=>(rich(X)|~old(X))))&
(![X]:((~calm(X)<~>old(X))=>~happy(X)))&
(((generous(fred)&~curious(fred)))=>(?[X]:(humble(X))))&
(((brave(john)<~>generous(john)))<=>((tall(susan)&~rich(susan))))&
(![X]:((~rich(X)<~>~happy(X))<=>(curious(X)|~rich(X))))&
(![X]:((~strong(X)<~>generous(X))=>wise(X)))&
(![X]:((humble(X)&wise(X))=>(~rich(X)<~>~old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(rich(X)<~>curious(X))))&
(((wise(john)<~>kind(john)))<=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>~brave(X)))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:((creative(X)<~>kind(X))))&
((~kind(susan)|brave(susan)))&
((~funny(fred)|~tall(fred)))&
(?[X]:((~curious(X)<~>strong(X))))&
((~old(john)&humble(john))) | patient(fred) | [] | null | 0 |
Everyone who is both not kind and kind is either old or not funny and vice versa.
Everyone who is curious or not humble is not funny or tall.
If someone is not quiet then mary is not creative.
If susan is either not tall or not old then someone is either calm or not calm and vice versa.
If fred is wise then fred is either not kind or not strong.
Everyone who is either not tall or happy is humble or not wise.
If someone is either not patient or wise then someone is quiet or not funny and vice versa.
Everyone who is both not rich and not wise is happy and vice versa.
Everyone who is both not rich and not wise is either calm or brave and vice versa.
Everyone who is happy or calm is old and vice versa.
If someone is either curious or humble then paul is patient or not humble.
If someone is not brave then paul is both not humble and not curious and vice versa.
Everyone who is not funny is not calm or patient.
Everyone who is both not brave and wise is funny or not wise and vice versa.
Everyone who is not quiet or generous is either curious or creative and vice versa.
Everyone who is either patient or not wise is both quiet and not generous and vice versa.
Someone is either not kind or not happy.
John is generous.
Fred is calm.
Susan is either wise or not rich.
Someone is either not rich or not calm.
Mary is both not calm and quiet. | John is not old. | entailment | (![X]:((~kind(X)&kind(X))<=>(old(X)<~>~funny(X))))&
(![X]:((curious(X)|~humble(X))=>(~funny(X)|tall(X))))&
((?[X]:(~quiet(X)))=>(~creative(mary)))&
(((~tall(susan)<~>~old(susan)))<=>(?[X]:((calm(X)<~>~calm(X)))))&
((wise(fred))=>((~kind(fred)<~>~strong(fred))))&
(![X]:((~tall(X)<~>happy(X))=>(humble(X)|~wise(X))))&
((?[X]:((~patient(X)<~>wise(X))))<=>(?[X]:((quiet(X)|~funny(X)))))&
(![X]:((~rich(X)&~wise(X))<=>happy(X)))&
(![X]:((~rich(X)&~wise(X))<=>(calm(X)<~>brave(X))))&
(![X]:((happy(X)|calm(X))<=>old(X)))&
((?[X]:((curious(X)<~>humble(X))))=>((patient(paul)|~humble(paul))))&
((?[X]:(~brave(X)))<=>((~humble(paul)&~curious(paul))))&
(![X]:(~funny(X)=>(~calm(X)|patient(X))))&
(![X]:((~brave(X)&wise(X))<=>(funny(X)|~wise(X))))&
(![X]:((~quiet(X)|generous(X))<=>(curious(X)<~>creative(X))))&
(![X]:((patient(X)<~>~wise(X))<=>(quiet(X)&~generous(X))))&
(?[X]:((~kind(X)<~>~happy(X))))&
(generous(john))&
(calm(fred))&
((wise(susan)<~>~rich(susan)))&
(?[X]:((~rich(X)<~>~calm(X))))&
((~calm(mary)&quiet(mary))) | ~old(john) | [
"p0",
"p7",
"p9",
"p12",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 153077966143682370490538
% SZS output start Proof for 153077966143682370490538
1. ! [X0] : ((kind(X0) & ~kind(X0)) <=> (old(X0) <~> ~funny(X0))) [input p0]
8. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> happy(X0)) [input p7]
10. ! [X0] : ((calm(X0) | happy(X0)) <=> old(X0)) [input p9]
13. ! [X0] : (~funny(X0) => (patient(X0) | ~calm(X0))) [input p12]
14. ! [X0] : ((wise(X0) & ~brave(X0)) <=> (~wise(X0) | funny(X0))) [input p13]
16. ! [X0] : ((patient(X0) <~> ~wise(X0)) <=> (~generous(X0) & quiet(X0))) [input p15]
18. generous(john) [input p17]
23. old(john) [input hypothesis]
33. ! [X0] : ((patient(X0) | ~calm(X0)) | funny(X0)) [ennf transformation 13]
34. ! [X0] : (patient(X0) | ~calm(X0) | funny(X0)) [flattening 33]
35. ! [X0] : (((kind(X0) & ~kind(X0)) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0)))) & (((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | (~kind(X0) | kind(X0)))) [nnf transformation 1]
36. ! [X0] : (((kind(X0) & ~kind(X0)) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0)))) & (((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | ~kind(X0) | kind(X0))) [flattening 35]
48. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~happy(X0)) & (happy(X0) | (wise(X0) | rich(X0)))) [nnf transformation 8]
49. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~happy(X0)) & (happy(X0) | wise(X0) | rich(X0))) [flattening 48]
52. ! [X0] : (((calm(X0) | happy(X0)) | ~old(X0)) & (old(X0) | (~calm(X0) & ~happy(X0)))) [nnf transformation 10]
53. ! [X0] : ((calm(X0) | happy(X0) | ~old(X0)) & (old(X0) | (~calm(X0) & ~happy(X0)))) [flattening 52]
60. ! [X0] : (((wise(X0) & ~brave(X0)) | (wise(X0) & ~funny(X0))) & ((~wise(X0) | funny(X0)) | (~wise(X0) | brave(X0)))) [nnf transformation 14]
61. ! [X0] : (((wise(X0) & ~brave(X0)) | (wise(X0) & ~funny(X0))) & (~wise(X0) | funny(X0) | ~wise(X0) | brave(X0))) [flattening 60]
64. ! [X0] : ((((wise(X0) | ~patient(X0)) & (~wise(X0) | patient(X0))) | (generous(X0) | ~quiet(X0))) & ((~generous(X0) & quiet(X0)) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0))))) [nnf transformation 16]
65. ! [X0] : ((((wise(X0) | ~patient(X0)) & (~wise(X0) | patient(X0))) | generous(X0) | ~quiet(X0)) & ((~generous(X0) & quiet(X0)) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0))))) [flattening 64]
75. ~kind(X0) | ~funny(X0) | ~old(X0) [cnf transformation 36]
77. ~funny(X0) | kind(X0) | ~old(X0) [cnf transformation 36]
102. ~happy(X0) | ~wise(X0) [cnf transformation 49]
111. ~old(X0) | happy(X0) | calm(X0) [cnf transformation 53]
117. ~calm(X0) | patient(X0) | funny(X0) [cnf transformation 34]
122. wise(X0) | wise(X0) [cnf transformation 61]
131. ~generous(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 65]
137. generous(john) [cnf transformation 18]
145. old(john) [cnf transformation 23]
147. wise(X0) [duplicate literal removal 122]
153. ~funny(X0) | ~old(X0) [subsumption resolution 75,77]
260. ~generous(X0) | ~patient(X0) [subsumption resolution 131,147]
294. ~patient(john) [resolution 260,137]
364. happy(john) | calm(john) [resolution 111,145]
376. 37 <=> calm(john) [avatar definition]
378. calm(john) <- (37) [avatar component clause 376]
380. 38 <=> happy(john) [avatar definition]
382. happy(john) <- (38) [avatar component clause 380]
383. 37 | 38 [avatar split clause 364,380,376]
449. patient(john) | funny(john) <- (37) [resolution 378,117]
451. funny(john) <- (37) [subsumption resolution 449,294]
579. ~old(john) <- (37) [resolution 451,153]
581. $false <- (37) [subsumption resolution 579,145]
582. ~37 [avatar contradiction clause 581]
586. ~wise(john) <- (38) [resolution 382,102]
589. $false <- (38) [subsumption resolution 586,147]
590. ~38 [avatar contradiction clause 589]
591. $false [avatar sat refutation 383,582,590]
% SZS output end Proof for 153077966143682370490538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is either strong or creative. If mary is tall then susan is not humble or not kind. If someone is calm then someone is not brave. Everyone who is not happy is not creative. Everyone who is not strong or not kind is patient. Everyone who is either rich or calm is either not happy or generous. Everyone who is not rich or creative is either humble or patient. If someone is old then someone is not strong or not humble. If someone is creative or not quiet then someone is tall. Everyone who is generous or creative is humble. Everyone who is not patient or not creative is both calm and not quiet and vice versa. If susan is both not rich and not patient then someone is not creative or kind and vice versa. Everyone who is both calm and rich is not generous. Everyone who is either not generous or not tall is not calm. If someone is generous then someone is funny. Someone is both rich and not quiet. Susan is not generous. Someone is not rich. Someone is either not old or not kind. Mary is not strong. | Susan is kind. | entailment | (![X]:(~patient(X)=>(strong(X)<~>creative(X))))&
((tall(mary))=>((~humble(susan)|~kind(susan))))&
((?[X]:(calm(X)))=>(?[X]:(~brave(X))))&
(![X]:(~happy(X)=>~creative(X)))&
(![X]:((~strong(X)|~kind(X))=>patient(X)))&
(![X]:((rich(X)<~>calm(X))=>(~happy(X)<~>generous(X))))&
(![X]:((~rich(X)|creative(X))=>(humble(X)<~>patient(X))))&
((?[X]:(old(X)))=>(?[X]:((~strong(X)|~humble(X)))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:(tall(X))))&
(![X]:((generous(X)|creative(X))=>humble(X)))&
(![X]:((~patient(X)|~creative(X))<=>(calm(X)&~quiet(X))))&
(((~rich(susan)&~patient(susan)))<=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((calm(X)&rich(X))=>~generous(X)))&
(![X]:((~generous(X)<~>~tall(X))=>~calm(X)))&
((?[X]:(generous(X)))=>(?[X]:(funny(X))))&
(?[X]:((rich(X)&~quiet(X))))&
(~generous(susan))&
(?[X]:(~rich(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~strong(mary)) | kind(susan) | [
"p4",
"p6",
"p9",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 441009324980631912119740
% SZS output start Proof for 441009324980631912119740
5. ! [X0] : ((~kind(X0) | ~strong(X0)) => patient(X0)) [input p4]
7. ! [X0] : ((creative(X0) | ~rich(X0)) => (humble(X0) <~> patient(X0))) [input p6]
10. ! [X0] : ((creative(X0) | generous(X0)) => humble(X0)) [input p9]
12. (~patient(susan) & ~rich(susan)) <=> ? [X0] : (kind(X0) | ~creative(X0)) [input p11]
18. ? [X0] : ~rich(X0) [input p17]
21. ~kind(susan) [input hypothesis]
32. ! [X0] : (patient(X0) | (kind(X0) & strong(X0))) [ennf transformation 5]
34. ! [X0] : ((humble(X0) <~> patient(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 7]
37. ! [X0] : (humble(X0) | (~creative(X0) & ~generous(X0))) [ennf transformation 10]
43. ! [X0] : (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~creative(X0) & rich(X0))) [nnf transformation 34]
52. ((~patient(susan) & ~rich(susan)) | ! [X0] : (~kind(X0) & creative(X0))) & (? [X0] : (kind(X0) | ~creative(X0)) | (patient(susan) | rich(susan))) [nnf transformation 12]
53. ((~patient(susan) & ~rich(susan)) | ! [X0] : (~kind(X0) & creative(X0))) & (? [X0] : (kind(X0) | ~creative(X0)) | patient(susan) | rich(susan)) [flattening 52]
54. ((~patient(susan) & ~rich(susan)) | ! [X0] : (~kind(X0) & creative(X0))) & (? [X1] : (kind(X1) | ~creative(X1)) | patient(susan) | rich(susan)) [rectify 53]
55. ? [X1] : (kind(X1) | ~creative(X1)) => (kind(sK2) | ~creative(sK2)) [choice axiom]
56. ((~patient(susan) & ~rich(susan)) | ! [X0] : (~kind(X0) & creative(X0))) & ((kind(sK2) | ~creative(sK2)) | patient(susan) | rich(susan)) [skolemisation 54,55]
60. ? [X0] : ~rich(X0) => ~rich(sK4) [choice axiom]
61. ~rich(sK4) [skolemisation 18,60]
70. kind(X0) | patient(X0) [cnf transformation 32]
77. ~humble(X0) | ~patient(X0) | rich(X0) [cnf transformation 43]
83. ~creative(X0) | humble(X0) [cnf transformation 37]
92. ~patient(susan) | creative(X0) [cnf transformation 56]
93. ~patient(susan) | ~kind(X0) [cnf transformation 56]
100. ~rich(sK4) [cnf transformation 61]
104. ~kind(susan) [cnf transformation 21]
114. 3 <=> kind(susan) [avatar definition]
116. ~kind(susan) <- (~3) [avatar component clause 114]
143. 10 <=> ! [X0] : ~kind(X0) [avatar definition]
144. ~kind(X0) <- (10) [avatar component clause 143]
146. 11 <=> patient(susan) [avatar definition]
149. 10 | ~11 [avatar split clause 93,146,143]
151. 12 <=> ! [X0] : creative(X0) [avatar definition]
152. creative(X0) <- (12) [avatar component clause 151]
153. 12 | ~11 [avatar split clause 92,146,151]
179. ~3 [avatar split clause 104,114]
182. patient(susan) <- (~3) [resolution 70,116]
186. 11 | 3 [avatar split clause 182,114,146]
187. patient(X0) <- (10) [resolution 144,70]
191. humble(X0) <- (12) [resolution 83,152]
202. ~patient(X0) | rich(X0) <- (12) [resolution 77,191]
203. rich(X0) <- (10, 12) [subsumption resolution 202,187]
204. $false <- (10, 12) [resolution 203,100]
207. ~10 | ~12 [avatar contradiction clause 204]
208. $false [avatar sat refutation 149,153,179,186,207]
% SZS output end Proof for 441009324980631912119740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and generous is funny or quiet.
Everyone who is not tall is patient or wise.
Everyone who is both not tall and calm is not curious or not generous and vice versa.
Everyone who is both strong and not calm is either humble or brave and vice versa.
Everyone who is not tall or strong is not curious or not brave and vice versa.
If fred is not kind then someone is humble and vice versa.
If someone is wise or happy then fred is funny.
Everyone who is either not happy or not funny is both not generous and curious.
Everyone who is not happy is either not tall or not rich.
Everyone who is creative or kind is both not kind and rich and vice versa.
If someone is both calm and not strong then alice is both not curious and kind.
If someone is not tall then paul is both wise and rich.
If someone is either not quiet or old then someone is creative or quiet and vice versa.
Everyone who is either not brave or not curious is both curious and creative and vice versa.
If someone is both happy and quiet then someone is either quiet or not kind and vice versa.
If john is either old or not old then someone is both not creative and calm and vice versa.
Someone is both not brave and not old.
Someone is not creative or patient.
Fred is either generous or curious.
Someone is either not old or not patient.
Fred is not rich or tall.
Mary is not tall. | Alice is not rich. | neutral | (![X]:((~old(X)&generous(X))=>(funny(X)|quiet(X))))&
(![X]:(~tall(X)=>(patient(X)|wise(X))))&
(![X]:((~tall(X)&calm(X))<=>(~curious(X)|~generous(X))))&
(![X]:((strong(X)&~calm(X))<=>(humble(X)<~>brave(X))))&
(![X]:((~tall(X)|strong(X))<=>(~curious(X)|~brave(X))))&
((~kind(fred))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)|happy(X))))=>(funny(fred)))&
(![X]:((~happy(X)<~>~funny(X))=>(~generous(X)&curious(X))))&
(![X]:(~happy(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((creative(X)|kind(X))<=>(~kind(X)&rich(X))))&
((?[X]:((calm(X)&~strong(X))))=>((~curious(alice)&kind(alice))))&
((?[X]:(~tall(X)))=>((wise(paul)&rich(paul))))&
((?[X]:((~quiet(X)<~>old(X))))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>(curious(X)&creative(X))))&
((?[X]:((happy(X)&quiet(X))))<=>(?[X]:((quiet(X)<~>~kind(X)))))&
(((old(john)<~>~old(john)))<=>(?[X]:((~creative(X)&calm(X)))))&
(?[X]:((~brave(X)&~old(X))))&
(?[X]:((~creative(X)|patient(X))))&
((generous(fred)<~>curious(fred)))&
(?[X]:((~old(X)<~>~patient(X))))&
((~rich(fred)|tall(fred)))&
(~tall(mary)) | ~rich(alice) | [] | null | 0 |
If someone is not kind or old then lucy is generous.
Everyone who is both not patient and quiet is curious or not patient.
If someone is both rich and not happy then alice is kind or not rich.
If someone is not curious or strong then fred is curious or not funny and vice versa.
If someone is quiet or not calm then fred is both curious and not quiet and vice versa.
If alice is either not calm or not quiet then fred is not quiet or happy.
Everyone who is both curious and not strong is both not wise and not happy.
If lucy is both calm and quiet then lucy is either not tall or not old.
If someone is both not calm and not wise then someone is both not patient and wise and vice versa.
Everyone who is both not curious and not humble is patient or not quiet and vice versa.
If alice is both not kind and not calm then susan is old or not kind.
If someone is both not rich and not strong then someone is both strong and happy and vice versa.
If lucy is either quiet or calm then alice is either not patient or not wise.
Everyone who is wise is not curious or not funny.
Everyone who is not patient or generous is either rich or not tall and vice versa.
Everyone who is either funny or not humble is either brave or not wise and vice versa.
Someone is either humble or old.
John is either not quiet or creative.
Susan is not curious.
Someone is curious or brave.
Someone is either not patient or quiet.
Susan is brave or not old.
Someone is humble or not tall.
Someone is not patient. | Alice is not quiet. | entailment | ((?[X]:((~kind(X)|old(X))))=>(generous(lucy)))&
(![X]:((~patient(X)&quiet(X))=>(curious(X)|~patient(X))))&
((?[X]:((rich(X)&~happy(X))))=>((kind(alice)|~rich(alice))))&
((?[X]:((~curious(X)|strong(X))))<=>((curious(fred)|~funny(fred))))&
((?[X]:((quiet(X)|~calm(X))))<=>((curious(fred)&~quiet(fred))))&
(((~calm(alice)<~>~quiet(alice)))=>((~quiet(fred)|happy(fred))))&
(![X]:((curious(X)&~strong(X))=>(~wise(X)&~happy(X))))&
(((calm(lucy)&quiet(lucy)))=>((~tall(lucy)<~>~old(lucy))))&
((?[X]:((~calm(X)&~wise(X))))<=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:((~curious(X)&~humble(X))<=>(patient(X)|~quiet(X))))&
(((~kind(alice)&~calm(alice)))=>((old(susan)|~kind(susan))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((strong(X)&happy(X)))))&
(((quiet(lucy)<~>calm(lucy)))=>((~patient(alice)<~>~wise(alice))))&
(![X]:(wise(X)=>(~curious(X)|~funny(X))))&
(![X]:((~patient(X)|generous(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((funny(X)<~>~humble(X))<=>(brave(X)<~>~wise(X))))&
(?[X]:((humble(X)<~>old(X))))&
((~quiet(john)<~>creative(john)))&
(~curious(susan))&
(?[X]:((curious(X)|brave(X))))&
(?[X]:((~patient(X)<~>quiet(X))))&
((brave(susan)|~old(susan)))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:(~patient(X))) | ~quiet(alice) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 591800190107147905842751
% SZS output start Proof for 591800190107147905842751
5. ? [X0] : (~calm(X0) | quiet(X0)) <=> (~quiet(fred) & curious(fred)) [input p4]
10. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (~quiet(X0) | patient(X0))) [input p9]
25. quiet(alice) [input hypothesis]
49. (? [X0] : (~calm(X0) | quiet(X0)) | (quiet(fred) | ~curious(fred))) & ((~quiet(fred) & curious(fred)) | ! [X0] : (calm(X0) & ~quiet(X0))) [nnf transformation 5]
50. (? [X0] : (~calm(X0) | quiet(X0)) | quiet(fred) | ~curious(fred)) & ((~quiet(fred) & curious(fred)) | ! [X0] : (calm(X0) & ~quiet(X0))) [flattening 49]
51. (? [X0] : (~calm(X0) | quiet(X0)) | quiet(fred) | ~curious(fred)) & ((~quiet(fred) & curious(fred)) | ! [X1] : (calm(X1) & ~quiet(X1))) [rectify 50]
52. ? [X0] : (~calm(X0) | quiet(X0)) => (~calm(sK1) | quiet(sK1)) [choice axiom]
53. ((~calm(sK1) | quiet(sK1)) | quiet(fred) | ~curious(fred)) & ((~quiet(fred) & curious(fred)) | ! [X1] : (calm(X1) & ~quiet(X1))) [skolemisation 51,52]
61. ! [X0] : (((~humble(X0) & ~curious(X0)) | (quiet(X0) & ~patient(X0))) & ((~quiet(X0) | patient(X0)) | (humble(X0) | curious(X0)))) [nnf transformation 10]
62. ! [X0] : (((~humble(X0) & ~curious(X0)) | (quiet(X0) & ~patient(X0))) & (~quiet(X0) | patient(X0) | humble(X0) | curious(X0))) [flattening 61]
93. curious(fred) | ~quiet(X1) [cnf transformation 53]
95. ~quiet(fred) | ~quiet(X1) [cnf transformation 53]
110. ~curious(X0) | quiet(X0) [cnf transformation 62]
148. quiet(alice) [cnf transformation 25]
187. 10 <=> curious(fred) [avatar definition]
188. curious(fred) <- (10) [avatar component clause 187]
200. 13 <=> quiet(fred) [avatar definition]
201. ~quiet(fred) <- (~13) [avatar component clause 200]
217. 17 <=> ! [X1] : ~quiet(X1) [avatar definition]
218. ~quiet(X1) <- (17) [avatar component clause 217]
219. 17 | ~13 [avatar split clause 95,200,217]
221. 17 | 10 [avatar split clause 93,187,217]
223. 18 <=> quiet(alice) [avatar definition]
225. quiet(alice) <- (18) [avatar component clause 223]
380. 18 [avatar split clause 148,223]
383. quiet(fred) <- (10) [resolution 110,188]
385. $false <- (10, ~13) [subsumption resolution 383,201]
386. ~10 | 13 [avatar contradiction clause 385]
397. $false <- (17, 18) [resolution 218,225]
398. ~17 | ~18 [avatar contradiction clause 397]
399. $false [avatar sat refutation 219,221,380,386,398]
% SZS output end Proof for 591800190107147905842751
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or not old then someone is either not wise or not humble.
Everyone who is not funny or wise is both wise and not patient.
Everyone who is not humble is wise and vice versa.
If alice is both not calm and wise then lucy is both not kind and not brave.
Everyone who is either patient or rich is humble.
Everyone who is either wise or not creative is either happy or not tall.
Everyone who is both not curious and calm is either not rich or calm.
Everyone who is kind is not creative or creative.
If lucy is both kind and not quiet then john is either not kind or generous.
Everyone who is not calm is either not kind or not rich and vice versa.
Everyone who is humble is either humble or not humble and vice versa.
Everyone who is either brave or not generous is not tall or funny.
If alice is tall then paul is kind or old and vice versa.
If paul is both not generous and old then susan is calm.
If alice is either kind or generous then someone is both tall and not brave and vice versa.
Everyone who is tall is not creative and vice versa.
Susan is funny.
John is either not happy or wise.
Susan is not calm or not quiet.
Fred is not curious or patient.
Someone is either curious or not funny.
Someone is both curious and not old.
Alice is not tall. | John is not tall. | entailment | ((?[X]:((generous(X)|~old(X))))=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((~funny(X)|wise(X))=>(wise(X)&~patient(X))))&
(![X]:(~humble(X)<=>wise(X)))&
(((~calm(alice)&wise(alice)))=>((~kind(lucy)&~brave(lucy))))&
(![X]:((patient(X)<~>rich(X))=>humble(X)))&
(![X]:((wise(X)<~>~creative(X))=>(happy(X)<~>~tall(X))))&
(![X]:((~curious(X)&calm(X))=>(~rich(X)<~>calm(X))))&
(![X]:(kind(X)=>(~creative(X)|creative(X))))&
(((kind(lucy)&~quiet(lucy)))=>((~kind(john)<~>generous(john))))&
(![X]:(~calm(X)<=>(~kind(X)<~>~rich(X))))&
(![X]:(humble(X)<=>(humble(X)<~>~humble(X))))&
(![X]:((brave(X)<~>~generous(X))=>(~tall(X)|funny(X))))&
((tall(alice))<=>((kind(paul)|old(paul))))&
(((~generous(paul)&old(paul)))=>(calm(susan)))&
(((kind(alice)<~>generous(alice)))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:(tall(X)<=>~creative(X)))&
(funny(susan))&
((~happy(john)<~>wise(john)))&
((~calm(susan)|~quiet(susan)))&
((~curious(fred)|patient(fred)))&
(?[X]:((curious(X)<~>~funny(X))))&
(?[X]:((curious(X)&~old(X))))&
(~tall(alice)) | ~tall(john) | [
"p2",
"p5",
"p10",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8430338819702161187619318
% SZS output start Proof for 8430338819702161187619318
3. ! [X0] : (~humble(X0) <=> wise(X0)) [input p2]
6. ! [X0] : ((wise(X0) <~> ~creative(X0)) => (happy(X0) <~> ~tall(X0))) [input p5]
11. ! [X0] : (humble(X0) <=> (humble(X0) <~> ~humble(X0))) [input p10]
16. ! [X0] : (tall(X0) <=> ~creative(X0)) [input p15]
18. ~happy(john) <~> wise(john) [input p17]
24. tall(john) [input hypothesis]
31. ! [X0] : ((happy(X0) <~> ~tall(X0)) | (wise(X0) <=> ~creative(X0))) [ennf transformation 6]
46. ! [X0] : ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))) [nnf transformation 3]
48. ! [X0] : (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | ((wise(X0) | creative(X0)) & (~creative(X0) | ~wise(X0)))) [nnf transformation 31]
52. ! [X0] : ((humble(X0) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) & (((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 11]
60. ! [X0] : ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))) [nnf transformation 16]
61. (~wise(john) | happy(john)) & (wise(john) | ~happy(john)) [nnf transformation 18]
76. ~humble(X0) | ~wise(X0) [cnf transformation 46]
82. ~tall(X0) | happy(X0) | wise(X0) | creative(X0) [cnf transformation 48]
97. humble(X0) | humble(X0) | humble(X0) [cnf transformation 52]
110. ~tall(X0) | ~creative(X0) [cnf transformation 60]
113. wise(john) | ~happy(john) [cnf transformation 61]
122. tall(john) [cnf transformation 24]
126. humble(X0) [duplicate literal removal 97]
228. 22 <=> happy(john) [avatar definition]
229. ~happy(john) <- (~22) [avatar component clause 228]
232. 23 <=> wise(john) [avatar definition]
233. wise(john) <- (23) [avatar component clause 232]
234. ~wise(john) <- (~23) [avatar component clause 232]
236. ~22 | 23 [avatar split clause 113,232,228]
268. ~wise(X1) [resolution 76,126]
269. ~creative(john) [resolution 110,122]
284. happy(john) | wise(john) | creative(john) [resolution 82,122]
287. wise(john) | creative(john) <- (~22) [subsumption resolution 284,229]
288. creative(john) <- (~22, ~23) [subsumption resolution 287,234]
289. $false <- (~22, ~23) [subsumption resolution 288,269]
290. 22 | 23 [avatar contradiction clause 289]
292. $false <- (23) [subsumption resolution 233,268]
293. ~23 [avatar contradiction clause 292]
294. $false [avatar sat refutation 236,290,293]
% SZS output end Proof for 8430338819702161187619318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or wise is not funny or tall and vice versa.
Everyone who is not calm or not kind is humble or not old and vice versa.
If someone is humble then alice is creative or not wise.
If someone is both funny and not calm then lucy is either wise or patient and vice versa.
Everyone who is either creative or not calm is either creative or not funny and vice versa.
If someone is not tall or not creative then someone is both generous and quiet and vice versa.
Everyone who is both happy and not generous is not calm or funny and vice versa.
Everyone who is either not old or not funny is not humble and vice versa.
If someone is calm then someone is not brave and vice versa.
Everyone who is either not kind or not generous is either humble or creative.
Everyone who is both wise and not curious is either not humble or not patient.
Everyone who is not funny or curious is either not strong or creative and vice versa.
If fred is old or not strong then someone is either not calm or not tall.
If someone is either not strong or not humble then alice is either old or funny and vice versa.
If paul is wise or not happy then someone is patient and vice versa.
Everyone who is either patient or not calm is not strong and vice versa.
Someone is either not quiet or not old.
John is either not wise or humble.
Alice is calm or not humble.
Alice is not funny or not quiet.
Someone is tall or strong. | Fred is curious. | entailment | (![X]:((creative(X)<~>wise(X))<=>(~funny(X)|tall(X))))&
(![X]:((~calm(X)|~kind(X))<=>(humble(X)|~old(X))))&
((?[X]:(humble(X)))=>((creative(alice)|~wise(alice))))&
((?[X]:((funny(X)&~calm(X))))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((creative(X)<~>~calm(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:((happy(X)&~generous(X))<=>(~calm(X)|funny(X))))&
(![X]:((~old(X)<~>~funny(X))<=>~humble(X)))&
((?[X]:(calm(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(humble(X)<~>creative(X))))&
(![X]:((wise(X)&~curious(X))=>(~humble(X)<~>~patient(X))))&
(![X]:((~funny(X)|curious(X))<=>(~strong(X)<~>creative(X))))&
(((old(fred)|~strong(fred)))=>(?[X]:((~calm(X)<~>~tall(X)))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>((old(alice)<~>funny(alice))))&
(((wise(paul)|~happy(paul)))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)<~>~calm(X))<=>~strong(X)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~wise(john)<~>humble(john)))&
((calm(alice)|~humble(alice)))&
((~funny(alice)|~quiet(alice)))&
(?[X]:((tall(X)|strong(X)))) | curious(fred) | [
"p0",
"p4",
"p5",
"p6",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6389377337939801096952546
% SZS output start Proof for 6389377337939801096952546
1. ! [X0] : ((creative(X0) <~> wise(X0)) <=> (tall(X0) | ~funny(X0))) [input p0]
5. ! [X0] : ((creative(X0) <~> ~calm(X0)) <=> (creative(X0) <~> ~funny(X0))) [input p4]
6. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X0] : (quiet(X0) & generous(X0)) [input p5]
7. ! [X0] : ((~generous(X0) & happy(X0)) <=> (funny(X0) | ~calm(X0))) [input p6]
12. ! [X0] : ((curious(X0) | ~funny(X0)) <=> (~strong(X0) <~> creative(X0))) [input p11]
15. (~happy(paul) | wise(paul)) <=> ? [X0] : patient(X0) [input p14]
16. ! [X0] : ((patient(X0) <~> ~calm(X0)) <=> ~strong(X0)) [input p15]
22. ~curious(fred) [input hypothesis]
23. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X1] : (quiet(X1) & generous(X1)) [rectify 6]
31. ! [X0] : ((((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))))) [nnf transformation 1]
32. ! [X0] : ((((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))))) [flattening 31]
39. ! [X0] : ((((calm(X0) | ~creative(X0)) & (~calm(X0) | creative(X0))) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0)))) & (((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0))))) [nnf transformation 5]
40. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & (? [X1] : (quiet(X1) & generous(X1)) | ! [X0] : (creative(X0) & tall(X0))) [nnf transformation 23]
41. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & (? [X2] : (quiet(X2) & generous(X2)) | ! [X3] : (creative(X3) & tall(X3))) [rectify 40]
42. ? [X0] : (~creative(X0) | ~tall(X0)) => (~creative(sK1) | ~tall(sK1)) [choice axiom]
43. ? [X2] : (quiet(X2) & generous(X2)) => (quiet(sK2) & generous(sK2)) [choice axiom]
44. ((~creative(sK1) | ~tall(sK1)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & ((quiet(sK2) & generous(sK2)) | ! [X3] : (creative(X3) & tall(X3))) [skolemisation 41,43,42]
45. ! [X0] : (((~generous(X0) & happy(X0)) | (~funny(X0) & calm(X0))) & ((funny(X0) | ~calm(X0)) | (generous(X0) | ~happy(X0)))) [nnf transformation 7]
46. ! [X0] : (((~generous(X0) & happy(X0)) | (~funny(X0) & calm(X0))) & (funny(X0) | ~calm(X0) | generous(X0) | ~happy(X0))) [flattening 45]
55. ! [X0] : (((curious(X0) | ~funny(X0)) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0)))) & (((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | (~curious(X0) & funny(X0)))) [nnf transformation 12]
56. ! [X0] : ((curious(X0) | ~funny(X0) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0)))) & (((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | (~curious(X0) & funny(X0)))) [flattening 55]
64. ((~happy(paul) | wise(paul)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (happy(paul) & ~wise(paul))) [nnf transformation 15]
65. (~happy(paul) | wise(paul) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (happy(paul) & ~wise(paul))) [flattening 64]
66. (~happy(paul) | wise(paul) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | (happy(paul) & ~wise(paul))) [rectify 65]
67. ? [X1] : patient(X1) => patient(sK7) [choice axiom]
68. (~happy(paul) | wise(paul) | ! [X0] : ~patient(X0)) & (patient(sK7) | (happy(paul) & ~wise(paul))) [skolemisation 66,67]
69. ! [X0] : ((((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | strong(X0)) & (~strong(X0) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0))))) [nnf transformation 16]
81. ~tall(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 32]
95. funny(X0) | ~creative(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 39]
98. ~calm(X0) | creative(X0) | creative(X0) | funny(X0) [cnf transformation 39]
99. calm(X0) | ~creative(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 39]
101. generous(sK2) | tall(X3) [cnf transformation 44]
102. generous(sK2) | creative(X3) [cnf transformation 44]
107. happy(X0) | calm(X0) [cnf transformation 46]
108. ~funny(X0) | happy(X0) [cnf transformation 46]
109. ~generous(X0) | calm(X0) [cnf transformation 46]
110. ~generous(X0) | ~funny(X0) [cnf transformation 46]
125. ~creative(X0) | strong(X0) | funny(X0) [cnf transformation 56]
128. ~strong(X0) | ~funny(X0) | curious(X0) | ~creative(X0) [cnf transformation 56]
143. ~happy(paul) | wise(paul) | ~patient(X0) [cnf transformation 68]
145. ~strong(X0) | patient(X0) | calm(X0) [cnf transformation 69]
146. ~calm(X0) | patient(X0) | strong(X0) [cnf transformation 69]
155. ~curious(fred) [cnf transformation 22]
157. funny(X0) | ~creative(X0) | ~calm(X0) [duplicate literal removal 95]
158. ~calm(X0) | creative(X0) | funny(X0) [duplicate literal removal 98]
159. ~funny(X0) | ~creative(X0) | calm(X0) [duplicate literal removal 99]
197. ~calm(X0) | funny(X0) [subsumption resolution 157,158]
213. 12 <=> ! [X3] : creative(X3) [avatar definition]
214. creative(X3) <- (12) [avatar component clause 213]
221. 14 <=> ! [X3] : tall(X3) [avatar definition]
222. tall(X3) <- (14) [avatar component clause 221]
225. 15 <=> generous(sK2) [avatar definition]
227. generous(sK2) <- (15) [avatar component clause 225]
228. 12 | 15 [avatar split clause 102,225,213]
229. 14 | 15 [avatar split clause 101,225,221]
247. 20 <=> strong(fred) [avatar definition]
248. ~strong(fred) <- (~20) [avatar component clause 247]
249. strong(fred) <- (20) [avatar component clause 247]
297. 30 <=> ! [X0] : ~patient(X0) [avatar definition]
298. ~patient(X0) <- (30) [avatar component clause 297]
300. 31 <=> wise(paul) [avatar definition]
302. wise(paul) <- (31) [avatar component clause 300]
304. 32 <=> happy(paul) [avatar definition]
306. ~happy(paul) <- (~32) [avatar component clause 304]
307. 30 | 31 | ~32 [avatar split clause 143,304,300,297]
377. ~wise(X0) | ~creative(X0) <- (14) [resolution 81,222]
397. 44 <=> funny(fred) [avatar definition]
398. ~funny(fred) <- (~44) [avatar component clause 397]
399. funny(fred) <- (44) [avatar component clause 397]
421. 48 <=> calm(fred) [avatar definition]
422. calm(fred) <- (48) [avatar component clause 421]
423. ~calm(fred) <- (~48) [avatar component clause 421]
428. strong(X0) | funny(X0) <- (12) [resolution 125,214]
522. funny(fred) <- (12, ~20) [resolution 428,248]
526. $false <- (12, ~20, ~44) [subsumption resolution 522,398]
527. ~12 | 20 | 44 [avatar contradiction clause 526]
605. ~funny(sK2) <- (15) [resolution 227,110]
606. calm(sK2) <- (15) [resolution 227,109]
685. ~creative(fred) | calm(fred) <- (44) [resolution 399,159]
688. calm(fred) <- (12, 44) [subsumption resolution 685,214]
689. $false <- (12, 44, ~48) [subsumption resolution 688,423]
690. ~12 | ~44 | 48 [avatar contradiction clause 689]
701. ~funny(fred) | curious(fred) | ~creative(fred) <- (20) [resolution 249,128]
702. patient(fred) | calm(fred) <- (20) [resolution 249,145]
748. funny(sK2) <- (15) [resolution 606,197]
750. $false <- (15) [subsumption resolution 748,605]
751. ~15 [avatar contradiction clause 750]
783. funny(fred) <- (48) [resolution 422,197]
784. $false <- (~44, 48) [subsumption resolution 783,398]
785. 44 | ~48 [avatar contradiction clause 784]
816. 79 <=> patient(fred) [avatar definition]
817. patient(fred) <- (79) [avatar component clause 816]
818. ~patient(fred) <- (~79) [avatar component clause 816]
848. 48 | 79 | ~20 [avatar split clause 702,247,816,421]
850. calm(paul) <- (~32) [resolution 306,107]
902. funny(paul) <- (~32) [resolution 850,197]
1008. happy(paul) <- (~32) [resolution 902,108]
1009. $false <- (~32) [subsumption resolution 1008,306]
1010. 32 [avatar contradiction clause 1009]
1011. ~creative(paul) <- (14, 31) [resolution 302,377]
1014. $false <- (12, 14, 31) [subsumption resolution 1011,214]
1015. ~12 | ~14 | ~31 [avatar contradiction clause 1014]
1018. ~funny(fred) | ~creative(fred) <- (20) [subsumption resolution 701,155]
1019. ~funny(fred) <- (12, 20) [subsumption resolution 1018,214]
1020. ~44 | ~12 | ~20 [avatar split clause 1019,247,213,397]
1072. patient(fred) | strong(fred) <- (48) [resolution 422,146]
1074. strong(fred) <- (48, ~79) [subsumption resolution 1072,818]
1075. $false <- (~20, 48, ~79) [subsumption resolution 1074,248]
1076. 20 | ~48 | 79 [avatar contradiction clause 1075]
1080. $false <- (30, 79) [subsumption resolution 817,298]
1081. ~30 | ~79 [avatar contradiction clause 1080]
1082. $false [avatar sat refutation 228,229,307,527,690,751,785,848,1010,1015,1020,1076,1081]
% SZS output end Proof for 6389377337939801096952546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both funny and happy then john is curious or generous and vice versa.
Everyone who is not generous is both not tall and not old.
Everyone who is either happy or brave is generous or old and vice versa.
If someone is not wise or tall then fred is not funny or not tall and vice versa.
If someone is both not patient and creative then susan is brave.
If lucy is strong or not kind then someone is not calm or rich.
Everyone who is not quiet is both not patient and brave and vice versa.
Everyone who is strong or funny is either not wise or patient and vice versa.
If mary is either not funny or calm then someone is not wise.
If someone is either wise or brave then someone is not humble and vice versa.
Everyone who is either not tall or not wise is not funny or happy.
Everyone who is strong is either not old or not calm and vice versa.
Everyone who is not strong is either not quiet or strong and vice versa.
Everyone who is both calm and funny is wise.
If someone is old then someone is both rich and strong and vice versa.
If lucy is not rich or rich then lucy is both not strong and wise and vice versa.
Susan is both not generous and not funny.
Someone is either not patient or kind.
Susan is not wise or calm.
Someone is either not brave or wise.
Someone is old.
John is not curious.
Someone is not generous or tall. | John is not quiet. | entailment | (((funny(mary)&happy(mary)))<=>((curious(john)|generous(john))))&
(![X]:(~generous(X)=>(~tall(X)&~old(X))))&
(![X]:((happy(X)<~>brave(X))<=>(generous(X)|old(X))))&
((?[X]:((~wise(X)|tall(X))))<=>((~funny(fred)|~tall(fred))))&
((?[X]:((~patient(X)&creative(X))))=>(brave(susan)))&
(((strong(lucy)|~kind(lucy)))=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:(~quiet(X)<=>(~patient(X)&brave(X))))&
(![X]:((strong(X)|funny(X))<=>(~wise(X)<~>patient(X))))&
(((~funny(mary)<~>calm(mary)))=>(?[X]:(~wise(X))))&
((?[X]:((wise(X)<~>brave(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)<~>~wise(X))=>(~funny(X)|happy(X))))&
(![X]:(strong(X)<=>(~old(X)<~>~calm(X))))&
(![X]:(~strong(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((calm(X)&funny(X))=>wise(X)))&
((?[X]:(old(X)))<=>(?[X]:((rich(X)&strong(X)))))&
(((~rich(lucy)|rich(lucy)))<=>((~strong(lucy)&wise(lucy))))&
((~generous(susan)&~funny(susan)))&
(?[X]:((~patient(X)<~>kind(X))))&
((~wise(susan)|calm(susan)))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:(old(X)))&
(~curious(john))&
(?[X]:((~generous(X)|tall(X)))) | ~quiet(john) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6216287325269065957632789
% SZS output start Proof for 6216287325269065957632789
13. ! [X0] : (~strong(X0) <=> (~quiet(X0) <~> strong(X0))) [input p12]
24. quiet(john) [input hypothesis]
60. ! [X0] : ((~strong(X0) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | strong(X0))) [nnf transformation 13]
118. strong(X0) | ~quiet(X0) | strong(X0) [cnf transformation 60]
121. ~strong(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 60]
141. quiet(john) [cnf transformation 24]
142. strong(X0) | ~quiet(X0) [duplicate literal removal 118]
143. ~strong(X0) | ~quiet(X0) [duplicate literal removal 121]
246. ~quiet(X0) [subsumption resolution 142,143]
319. $false [subsumption resolution 141,246]
% SZS output end Proof for 6216287325269065957632789
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or funny is both old and not creative.
Everyone who is both old and patient is both not old and not strong.
Everyone who is not strong or not happy is both not happy and kind.
Everyone who is not kind or generous is calm and vice versa.
If john is both not quiet and tall then someone is tall or humble and vice versa.
Everyone who is curious or quiet is both funny and rich.
Everyone who is not patient is both not old and funny and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
If paul is not creative or not strong then someone is strong and vice versa.
Everyone who is quiet is kind.
Someone is brave or strong.
Alice is wise.
Someone is not strong or not rich.
Someone is happy or not kind.
Mary is rich. | Susan is tall. | entailment | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)&patient(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((brave(X)|strong(X))))&
(wise(alice))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((happy(X)|~kind(X))))&
(rich(mary)) | tall(susan) | [
"p1",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8058015188684979407665389
% SZS output start Proof for 8058015188684979407665389
2. ! [X0] : ((patient(X0) & old(X0)) => (~strong(X0) & ~old(X0))) [input p1]
7. ! [X0] : (~patient(X0) <=> (funny(X0) & ~old(X0))) [input p6]
13. (~humble(fred) & old(fred)) <=> ? [X0] : (old(X0) <~> ~tall(X0)) [input p12]
22. ~tall(susan) [input hypothesis]
23. ! [X0] : (~patient(X0) => (funny(X0) & ~old(X0))) [unused predicate definition removal 7]
26. ! [X0] : ((~strong(X0) & ~old(X0)) | (~patient(X0) | ~old(X0))) [ennf transformation 2]
27. ! [X0] : ((~strong(X0) & ~old(X0)) | ~patient(X0) | ~old(X0)) [flattening 26]
30. ! [X0] : ((funny(X0) & ~old(X0)) | patient(X0)) [ennf transformation 23]
50. ((~humble(fred) & old(fred)) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X0] : ((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (humble(fred) | ~old(fred))) [nnf transformation 13]
51. ((~humble(fred) & old(fred)) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X0] : ((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | humble(fred) | ~old(fred)) [flattening 50]
52. ((~humble(fred) & old(fred)) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X1] : ((tall(X1) | ~old(X1)) & (~tall(X1) | old(X1))) | humble(fred) | ~old(fred)) [rectify 51]
53. ? [X1] : ((tall(X1) | ~old(X1)) & (~tall(X1) | old(X1))) => ((tall(sK1) | ~old(sK1)) & (~tall(sK1) | old(sK1))) [choice axiom]
54. ((~humble(fred) & old(fred)) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(sK1) | ~old(sK1)) & (~tall(sK1) | old(sK1))) | humble(fred) | ~old(fred)) [skolemisation 52,53]
72. ~old(X0) | ~patient(X0) | ~old(X0) [cnf transformation 27]
90. ~old(X0) | patient(X0) [cnf transformation 30]
113. old(fred) | old(X0) | tall(X0) [cnf transformation 54]
127. ~tall(susan) [cnf transformation 22]
128. ~old(X0) | ~patient(X0) [duplicate literal removal 72]
156. ~old(X0) [subsumption resolution 90,128]
209. 16 <=> ! [X0] : tall(X0) [avatar definition]
210. tall(X0) <- (16) [avatar component clause 209]
216. old(X0) | tall(X0) [subsumption resolution 113,156]
217. tall(X0) [subsumption resolution 216,156]
218. 16 [avatar split clause 217,209]
252. $false <- (16) [resolution 210,127]
253. ~16 [avatar contradiction clause 252]
254. $false [avatar sat refutation 218,253]
% SZS output end Proof for 8058015188684979407665389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is either not old or not generous.
If someone is both kind and brave then fred is either wise or patient.
If susan is either humble or strong then john is both quiet and not happy and vice versa.
If john is old then john is both not strong and not creative and vice versa.
Everyone who is tall is not curious and vice versa.
Everyone who is not curious is either not calm or not old.
Everyone who is humble is either creative or not old and vice versa.
Everyone who is both tall and not quiet is either strong or patient.
If lucy is humble or kind then someone is not creative or patient and vice versa.
If fred is either brave or not tall then john is either curious or not tall and vice versa.
Everyone who is not kind or not old is both not wise and not generous.
Everyone who is either calm or not kind is not tall or not kind and vice versa.
Everyone who is both not generous and not quiet is either not patient or calm.
Everyone who is both not curious and funny is not curious or not humble.
Everyone who is not funny is both brave and not calm.
Everyone who is both not old and creative is not generous or not rich.
Lucy is wise.
Someone is generous.
Paul is not kind.
Mary is either calm or tall.
Someone is not kind.
Lucy is either generous or not happy.
John is brave.
Susan is both not brave and funny. | Mary is old. | entailment | (![X]:(calm(X)=>(~old(X)<~>~generous(X))))&
((?[X]:((kind(X)&brave(X))))=>((wise(fred)<~>patient(fred))))&
(((humble(susan)<~>strong(susan)))<=>((quiet(john)&~happy(john))))&
((old(john))<=>((~strong(john)&~creative(john))))&
(![X]:(tall(X)<=>~curious(X)))&
(![X]:(~curious(X)=>(~calm(X)<~>~old(X))))&
(![X]:(humble(X)<=>(creative(X)<~>~old(X))))&
(![X]:((tall(X)&~quiet(X))=>(strong(X)<~>patient(X))))&
(((humble(lucy)|kind(lucy)))<=>(?[X]:((~creative(X)|patient(X)))))&
(((brave(fred)<~>~tall(fred)))<=>((curious(john)<~>~tall(john))))&
(![X]:((~kind(X)|~old(X))=>(~wise(X)&~generous(X))))&
(![X]:((calm(X)<~>~kind(X))<=>(~tall(X)|~kind(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~patient(X)<~>calm(X))))&
(![X]:((~curious(X)&funny(X))=>(~curious(X)|~humble(X))))&
(![X]:(~funny(X)=>(brave(X)&~calm(X))))&
(![X]:((~old(X)&creative(X))=>(~generous(X)|~rich(X))))&
(wise(lucy))&
(?[X]:(generous(X)))&
(~kind(paul))&
((calm(mary)<~>tall(mary)))&
(?[X]:(~kind(X)))&
((generous(lucy)<~>~happy(lucy)))&
(brave(john))&
((~brave(susan)&funny(susan))) | old(mary) | [
"p0",
"p4",
"p5",
"p10",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5979117594441345048116311
% SZS output start Proof for 5979117594441345048116311
1. ! [X0] : (calm(X0) => (~old(X0) <~> ~generous(X0))) [input p0]
5. ! [X0] : (tall(X0) <=> ~curious(X0)) [input p4]
6. ! [X0] : (~curious(X0) => (~calm(X0) <~> ~old(X0))) [input p5]
11. ! [X0] : ((~old(X0) | ~kind(X0)) => (~generous(X0) & ~wise(X0))) [input p10]
12. ! [X0] : ((calm(X0) <~> ~kind(X0)) <=> (~kind(X0) | ~tall(X0))) [input p11]
20. calm(mary) <~> tall(mary) [input p19]
25. ~old(mary) [input hypothesis]
27. ! [X0] : ((~old(X0) <~> ~generous(X0)) | ~calm(X0)) [ennf transformation 1]
29. ! [X0] : ((~calm(X0) <~> ~old(X0)) | curious(X0)) [ennf transformation 6]
32. ! [X0] : ((~generous(X0) & ~wise(X0)) | (old(X0) & kind(X0))) [ennf transformation 11]
38. ! [X0] : (((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | ~calm(X0)) [nnf transformation 27]
44. ! [X0] : ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))) [nnf transformation 5]
45. ! [X0] : (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | curious(X0)) [nnf transformation 29]
54. ! [X0] : ((((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (kind(X0) & tall(X0))) & ((~kind(X0) | ~tall(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0))))) [nnf transformation 12]
55. ! [X0] : ((((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (kind(X0) & tall(X0))) & (~kind(X0) | ~tall(X0) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0))))) [flattening 54]
59. (~tall(mary) | ~calm(mary)) & (tall(mary) | calm(mary)) [nnf transformation 20]
64. ~calm(X0) | old(X0) | generous(X0) [cnf transformation 38]
76. ~curious(X0) | ~tall(X0) [cnf transformation 44]
79. curious(X0) | calm(X0) | old(X0) [cnf transformation 45]
101. ~generous(X0) | old(X0) [cnf transformation 32]
102. ~kind(X0) | ~tall(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 55]
107. kind(X0) | ~calm(X0) | kind(X0) [cnf transformation 55]
116. tall(mary) | calm(mary) [cnf transformation 59]
124. ~old(mary) [cnf transformation 25]
125. ~kind(X0) | ~tall(X0) | ~calm(X0) [duplicate literal removal 102]
126. ~calm(X0) | kind(X0) [duplicate literal removal 107]
223. ~tall(X0) | ~calm(X0) [subsumption resolution 125,126]
225. 20 <=> calm(mary) [avatar definition]
227. calm(mary) <- (20) [avatar component clause 225]
229. 21 <=> tall(mary) [avatar definition]
231. tall(mary) <- (21) [avatar component clause 229]
232. 20 | 21 [avatar split clause 116,229,225]
258. old(mary) | generous(mary) <- (20) [resolution 64,227]
259. generous(mary) <- (20) [subsumption resolution 258,124]
273. calm(X0) | old(X0) | ~tall(X0) [resolution 79,76]
277. ~tall(X0) | old(X0) [subsumption resolution 273,223]
283. old(mary) <- (20) [resolution 259,101]
285. $false <- (20) [subsumption resolution 283,124]
286. ~20 [avatar contradiction clause 285]
451. old(mary) <- (21) [resolution 277,231]
453. $false <- (21) [subsumption resolution 451,124]
454. ~21 [avatar contradiction clause 453]
455. $false [avatar sat refutation 232,286,454]
% SZS output end Proof for 5979117594441345048116311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is wise or not creative then someone is both not old and rich and vice versa.
If fred is happy or not old then someone is not happy or rich.
Everyone who is either not old or wise is generous or strong.
If susan is rich or happy then paul is creative.
Everyone who is happy is rich.
If someone is not rich or happy then lucy is both not funny and not wise and vice versa.
Everyone who is happy is either strong or not old and vice versa.
If paul is brave or creative then paul is not brave or kind and vice versa.
If someone is either old or generous then susan is either calm or patient and vice versa.
Everyone who is not rich or not old is old or kind.
Everyone who is not generous is happy or generous and vice versa.
If someone is either not wise or not generous then someone is either not strong or not quiet.
Everyone who is humble or tall is tall or funny and vice versa.
Everyone who is either not brave or rich is not rich or patient and vice versa.
Everyone who is wise or not patient is both curious and humble.
Everyone who is generous or not quiet is both not patient and wise.
Paul is either wise or not old.
Susan is not rich or patient.
Someone is calm.
Fred is either not strong or brave.
Paul is old.
Susan is patient.
Someone is funny.
Alice is either not generous or quiet. | Lucy is not generous. | entailment | (((wise(lucy)|~creative(lucy)))<=>(?[X]:((~old(X)&rich(X)))))&
(((happy(fred)|~old(fred)))=>(?[X]:((~happy(X)|rich(X)))))&
(![X]:((~old(X)<~>wise(X))=>(generous(X)|strong(X))))&
(((rich(susan)|happy(susan)))=>(creative(paul)))&
(![X]:(happy(X)=>rich(X)))&
((?[X]:((~rich(X)|happy(X))))<=>((~funny(lucy)&~wise(lucy))))&
(![X]:(happy(X)<=>(strong(X)<~>~old(X))))&
(((brave(paul)|creative(paul)))<=>((~brave(paul)|kind(paul))))&
((?[X]:((old(X)<~>generous(X))))<=>((calm(susan)<~>patient(susan))))&
(![X]:((~rich(X)|~old(X))=>(old(X)|kind(X))))&
(![X]:(~generous(X)<=>(happy(X)|generous(X))))&
((?[X]:((~wise(X)<~>~generous(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((humble(X)|tall(X))<=>(tall(X)|funny(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|patient(X))))&
(![X]:((wise(X)|~patient(X))=>(curious(X)&humble(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
((wise(paul)<~>~old(paul)))&
((~rich(susan)|patient(susan)))&
(?[X]:(calm(X)))&
((~strong(fred)<~>brave(fred)))&
(old(paul))&
(patient(susan))&
(?[X]:(funny(X)))&
((~generous(alice)<~>quiet(alice))) | ~generous(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4620986610871586483549201
% SZS output start Proof for 4620986610871586483549201
11. ! [X0] : (~generous(X0) <=> (generous(X0) | happy(X0))) [input p10]
25. generous(lucy) [input hypothesis]
58. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | generous(X0))) [nnf transformation 11]
59. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | generous(X0))) [flattening 58]
112. ~generous(X0) | ~generous(X0) [cnf transformation 59]
144. generous(lucy) [cnf transformation 25]
148. ~generous(X0) [duplicate literal removal 112]
314. $false [subsumption resolution 144,148]
% SZS output end Proof for 4620986610871586483549201
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or old is funny or generous and vice versa. Everyone who is either not strong or humble is not tall and vice versa. Everyone who is happy or not creative is both not brave and tall. If someone is tall then mary is either calm or strong. Everyone who is curious is happy and vice versa. Everyone who is both brave and not kind is quiet and vice versa. Everyone who is kind or old is brave or not quiet and vice versa. Everyone who is not kind or calm is not brave or not funny. Everyone who is wise is not humble. Everyone who is humble or wise is both not generous and not creative. Everyone who is humble is rich or brave and vice versa. If someone is brave then lucy is not patient or not generous and vice versa. If someone is not quiet or calm then someone is not happy and vice versa. If alice is either wise or not generous then someone is both not brave and old and vice versa. Everyone who is kind is old and vice versa. If someone is both wise and not patient then someone is either wise or not wise and vice versa. Someone is not quiet or not curious. John is tall or creative. Alice is not curious. Someone is either rich or not tall. Susan is either old or not generous. Someone is both wise and patient. John is not tall or not calm. | Mary is not strong. | neutral | (![X]:((humble(X)<~>old(X))<=>(funny(X)|generous(X))))&
(![X]:((~strong(X)<~>humble(X))<=>~tall(X)))&
(![X]:((happy(X)|~creative(X))=>(~brave(X)&tall(X))))&
((?[X]:(tall(X)))=>((calm(mary)<~>strong(mary))))&
(![X]:(curious(X)<=>happy(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((kind(X)|old(X))<=>(brave(X)|~quiet(X))))&
(![X]:((~kind(X)|calm(X))=>(~brave(X)|~funny(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))=>(~generous(X)&~creative(X))))&
(![X]:(humble(X)<=>(rich(X)|brave(X))))&
((?[X]:(brave(X)))<=>((~patient(lucy)|~generous(lucy))))&
((?[X]:((~quiet(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((~brave(X)&old(X)))))&
(![X]:(kind(X)<=>old(X)))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(?[X]:((~quiet(X)|~curious(X))))&
((tall(john)|creative(john)))&
(~curious(alice))&
(?[X]:((rich(X)<~>~tall(X))))&
((old(susan)<~>~generous(susan)))&
(?[X]:((wise(X)&patient(X))))&
((~tall(john)|~calm(john))) | ~strong(mary) | [] | null | 0 |
If someone is kind or humble then fred is generous. If someone is strong or old then lucy is both not patient and not tall. If fred is humble then alice is patient or not humble. Everyone who is not generous or brave is not strong and vice versa. If someone is not funny or not generous then someone is either happy or not rich. Everyone who is not humble or not kind is either brave or curious and vice versa. If susan is not old then john is tall and vice versa. Everyone who is not curious or tall is both funny and rich. If someone is humble then lucy is not generous and vice versa. If paul is not generous or not old then mary is not happy and vice versa. Everyone who is quiet is curious or wise. Everyone who is either not strong or not patient is kind or funny. Everyone who is both not creative and not generous is either not quiet or not creative. If fred is both tall and not strong then mary is quiet or not kind and vice versa. Everyone who is either curious or rich is either not rich or not happy. If someone is strong or not wise then alice is wise or not kind. Someone is not curious. Someone is not brave. John is creative or not quiet. Fred is patient. Susan is either not creative or creative. Paul is both not strong and not generous. Someone is not creative or not calm. | John is brave. | neutral | ((?[X]:((kind(X)|humble(X))))=>(generous(fred)))&
((?[X]:((strong(X)|old(X))))=>((~patient(lucy)&~tall(lucy))))&
((humble(fred))=>((patient(alice)|~humble(alice))))&
(![X]:((~generous(X)|brave(X))<=>~strong(X)))&
((?[X]:((~funny(X)|~generous(X))))=>(?[X]:((happy(X)<~>~rich(X)))))&
(![X]:((~humble(X)|~kind(X))<=>(brave(X)<~>curious(X))))&
((~old(susan))<=>(tall(john)))&
(![X]:((~curious(X)|tall(X))=>(funny(X)&rich(X))))&
((?[X]:(humble(X)))<=>(~generous(lucy)))&
(((~generous(paul)|~old(paul)))<=>(~happy(mary)))&
(![X]:(quiet(X)=>(curious(X)|wise(X))))&
(![X]:((~strong(X)<~>~patient(X))=>(kind(X)|funny(X))))&
(![X]:((~creative(X)&~generous(X))=>(~quiet(X)<~>~creative(X))))&
(((tall(fred)&~strong(fred)))<=>((quiet(mary)|~kind(mary))))&
(![X]:((curious(X)<~>rich(X))=>(~rich(X)<~>~happy(X))))&
((?[X]:((strong(X)|~wise(X))))=>((wise(alice)|~kind(alice))))&
(?[X]:(~curious(X)))&
(?[X]:(~brave(X)))&
((creative(john)|~quiet(john)))&
(patient(fred))&
((~creative(susan)<~>creative(susan)))&
((~strong(paul)&~generous(paul)))&
(?[X]:((~creative(X)|~calm(X)))) | brave(john) | [] | null | 0 |
Everyone who is either tall or not patient is either not curious or strong and vice versa. Everyone who is not calm is either not tall or not old. Everyone who is not kind is both quiet and brave and vice versa. If someone is not happy or generous then someone is funny or humble and vice versa. If someone is both curious and not humble then someone is not patient or brave. Everyone who is both funny and happy is humble. Everyone who is strong is either generous or not strong and vice versa. Everyone who is funny is both humble and kind. Everyone who is not funny or humble is not funny or calm and vice versa. If someone is not wise then lucy is rich or not old. If john is both creative and not patient then someone is not brave and vice versa. If john is brave then john is curious or not brave and vice versa. Everyone who is not patient or not curious is either strong or not humble. If someone is either not humble or brave then alice is calm. Everyone who is wise or old is not curious and vice versa. Someone is both not tall and curious. Someone is either not old or not rich. Someone is old. Someone is either not tall or not quiet. Paul is not kind. Susan is both rich and wise. Lucy is either not quiet or not brave. | Lucy is happy. | neutral | (![X]:((tall(X)<~>~patient(X))<=>(~curious(X)<~>strong(X))))&
(![X]:(~calm(X)=>(~tall(X)<~>~old(X))))&
(![X]:(~kind(X)<=>(quiet(X)&brave(X))))&
((?[X]:((~happy(X)|generous(X))))<=>(?[X]:((funny(X)|humble(X)))))&
((?[X]:((curious(X)&~humble(X))))=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:((funny(X)&happy(X))=>humble(X)))&
(![X]:(strong(X)<=>(generous(X)<~>~strong(X))))&
(![X]:(funny(X)=>(humble(X)&kind(X))))&
(![X]:((~funny(X)|humble(X))<=>(~funny(X)|calm(X))))&
((?[X]:(~wise(X)))=>((rich(lucy)|~old(lucy))))&
(((creative(john)&~patient(john)))<=>(?[X]:(~brave(X))))&
((brave(john))<=>((curious(john)|~brave(john))))&
(![X]:((~patient(X)|~curious(X))=>(strong(X)<~>~humble(X))))&
((?[X]:((~humble(X)<~>brave(X))))=>(calm(alice)))&
(![X]:((wise(X)|old(X))<=>~curious(X)))&
(?[X]:((~tall(X)&curious(X))))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(~kind(paul))&
((rich(susan)&wise(susan)))&
((~quiet(lucy)<~>~brave(lucy))) | happy(lucy) | [] | null | 0 |
If paul is not funny or patient then paul is not old or curious. Everyone who is generous or rich is both humble and not brave and vice versa. If fred is both not happy and not old then fred is either generous or not curious and vice versa. Everyone who is not rich or not generous is either brave or not kind and vice versa. If alice is not humble then someone is either not patient or funny and vice versa. If mary is not patient then susan is generous and vice versa. Everyone who is either rich or not wise is not generous or calm. Everyone who is not strong or strong is not creative or not happy. If fred is old then someone is both not funny and not generous and vice versa. Everyone who is both not humble and not generous is both curious and not humble and vice versa. Everyone who is not brave or humble is wise or not calm and vice versa. Everyone who is either brave or not tall is not kind. Everyone who is either calm or not patient is either brave or not old. Everyone who is not kind or old is patient or brave and vice versa. Everyone who is either not rich or rich is brave and vice versa. If someone is either wise or funny then someone is quiet and vice versa. Mary is either not creative or not rich. Someone is strong. Someone is either funny or not patient. Someone is either not generous or tall. Someone is creative. | Alice is not wise. | entailment | (((~funny(paul)|patient(paul)))=>((~old(paul)|curious(paul))))&
(![X]:((generous(X)|rich(X))<=>(humble(X)&~brave(X))))&
(((~happy(fred)&~old(fred)))<=>((generous(fred)<~>~curious(fred))))&
(![X]:((~rich(X)|~generous(X))<=>(brave(X)<~>~kind(X))))&
((~humble(alice))<=>(?[X]:((~patient(X)<~>funny(X)))))&
((~patient(mary))<=>(generous(susan)))&
(![X]:((rich(X)<~>~wise(X))=>(~generous(X)|calm(X))))&
(![X]:((~strong(X)|strong(X))=>(~creative(X)|~happy(X))))&
((old(fred))<=>(?[X]:((~funny(X)&~generous(X)))))&
(![X]:((~humble(X)&~generous(X))<=>(curious(X)&~humble(X))))&
(![X]:((~brave(X)|humble(X))<=>(wise(X)|~calm(X))))&
(![X]:((brave(X)<~>~tall(X))=>~kind(X)))&
(![X]:((calm(X)<~>~patient(X))=>(brave(X)<~>~old(X))))&
(![X]:((~kind(X)|old(X))<=>(patient(X)|brave(X))))&
(![X]:((~rich(X)<~>rich(X))<=>brave(X)))&
((?[X]:((wise(X)<~>funny(X))))<=>(?[X]:(quiet(X))))&
((~creative(mary)<~>~rich(mary)))&
(?[X]:(strong(X)))&
(?[X]:((funny(X)<~>~patient(X))))&
(?[X]:((~generous(X)<~>tall(X))))&
(?[X]:(creative(X))) | ~wise(alice) | [
"p1",
"p4",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4391075615041309137358448
% SZS output start Proof for 4391075615041309137358448
2. ! [X0] : ((rich(X0) | generous(X0)) <=> (~brave(X0) & humble(X0))) [input p1]
5. ~humble(alice) <=> ? [X0] : (~patient(X0) <~> funny(X0)) [input p4]
11. ! [X0] : ((humble(X0) | ~brave(X0)) <=> (~calm(X0) | wise(X0))) [input p10]
15. ! [X0] : ((~rich(X0) <~> rich(X0)) <=> brave(X0)) [input p14]
19. ? [X0] : (funny(X0) <~> ~patient(X0)) [input p18]
22. wise(alice) [input hypothesis]
32. ! [X0] : (((rich(X0) | generous(X0)) | (brave(X0) | ~humble(X0))) & ((~brave(X0) & humble(X0)) | (~rich(X0) & ~generous(X0)))) [nnf transformation 2]
33. ! [X0] : ((rich(X0) | generous(X0) | brave(X0) | ~humble(X0)) & ((~brave(X0) & humble(X0)) | (~rich(X0) & ~generous(X0)))) [flattening 32]
38. (~humble(alice) | ! [X0] : ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (? [X0] : ((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | humble(alice)) [nnf transformation 5]
39. (~humble(alice) | ! [X0] : ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (? [X1] : ((~funny(X1) | patient(X1)) & (funny(X1) | ~patient(X1))) | humble(alice)) [rectify 38]
40. ? [X1] : ((~funny(X1) | patient(X1)) & (funny(X1) | ~patient(X1))) => ((~funny(sK0) | patient(sK0)) & (funny(sK0) | ~patient(sK0))) [choice axiom]
41. (~humble(alice) | ! [X0] : ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (((~funny(sK0) | patient(sK0)) & (funny(sK0) | ~patient(sK0))) | humble(alice)) [skolemisation 39,40]
50. ! [X0] : (((humble(X0) | ~brave(X0)) | (calm(X0) & ~wise(X0))) & ((~calm(X0) | wise(X0)) | (~humble(X0) & brave(X0)))) [nnf transformation 11]
51. ! [X0] : ((humble(X0) | ~brave(X0) | (calm(X0) & ~wise(X0))) & (~calm(X0) | wise(X0) | (~humble(X0) & brave(X0)))) [flattening 50]
56. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | ~brave(X0)) & (brave(X0) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [nnf transformation 15]
65. ? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) [nnf transformation 19]
66. ? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) => ((patient(sK5) | ~funny(sK5)) & (~patient(sK5) | funny(sK5))) [choice axiom]
67. (patient(sK5) | ~funny(sK5)) & (~patient(sK5) | funny(sK5)) [skolemisation 65,66]
78. ~brave(X0) | ~rich(X0) [cnf transformation 33]
94. ~humble(alice) | funny(X0) | patient(X0) [cnf transformation 41]
95. ~humble(alice) | ~patient(X0) | ~funny(X0) [cnf transformation 41]
111. ~wise(X0) | ~brave(X0) | humble(X0) [cnf transformation 51]
123. brave(X0) | rich(X0) | rich(X0) [cnf transformation 56]
124. brave(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 56]
134. ~patient(sK5) | funny(sK5) [cnf transformation 67]
135. patient(sK5) | ~funny(sK5) [cnf transformation 67]
139. wise(alice) [cnf transformation 22]
140. brave(X0) | rich(X0) [duplicate literal removal 123]
141. brave(X0) | ~rich(X0) [duplicate literal removal 124]
185. 9 <=> ! [X0] : (~patient(X0) | ~funny(X0)) [avatar definition]
186. ~patient(X0) | ~funny(X0) <- (9) [avatar component clause 185]
188. 10 <=> humble(alice) [avatar definition]
191. 9 | ~10 [avatar split clause 95,188,185]
193. 11 <=> ! [X0] : (funny(X0) | patient(X0)) [avatar definition]
194. patient(X0) | funny(X0) <- (11) [avatar component clause 193]
195. 11 | ~10 [avatar split clause 94,188,193]
235. ~rich(X0) [subsumption resolution 141,78]
236. brave(X0) [subsumption resolution 140,235]
264. 25 <=> funny(sK5) [avatar definition]
265. funny(sK5) <- (25) [avatar component clause 264]
266. ~funny(sK5) <- (~25) [avatar component clause 264]
268. 26 <=> patient(sK5) [avatar definition]
269. ~patient(sK5) <- (~26) [avatar component clause 268]
270. patient(sK5) <- (26) [avatar component clause 268]
271. ~25 | 26 [avatar split clause 135,268,264]
272. 25 | ~26 [avatar split clause 134,268,264]
303. ~brave(alice) | humble(alice) [resolution 111,139]
305. humble(alice) [subsumption resolution 303,236]
309. 10 [avatar split clause 305,188]
312. funny(sK5) <- (11, ~26) [resolution 194,269]
316. $false <- (11, ~25, ~26) [subsumption resolution 312,266]
317. ~11 | 25 | 26 [avatar contradiction clause 316]
319. ~funny(sK5) <- (9, 26) [resolution 270,186]
320. $false <- (9, 25, 26) [subsumption resolution 319,265]
321. ~9 | ~25 | ~26 [avatar contradiction clause 320]
322. $false [avatar sat refutation 191,195,271,272,309,317,321]
% SZS output end Proof for 4391075615041309137358448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both funny and not rich then lucy is old and vice versa. If someone is both not tall and not wise then someone is either not humble or calm. If someone is not kind then someone is both not quiet and not patient and vice versa. Everyone who is either not tall or not rich is creative and vice versa. If lucy is either funny or not tall then someone is either generous or curious and vice versa. Everyone who is wise or funny is not creative or not humble. If someone is both happy and funny then lucy is humble and vice versa. If fred is not calm then fred is both not wise and not tall. If alice is either tall or not generous then alice is generous. If fred is both not happy and creative then someone is wise and vice versa. Everyone who is not calm or not funny is both not strong and not happy and vice versa. If susan is quiet or generous then fred is either not humble or quiet. If paul is both kind and creative then paul is not patient and vice versa. If someone is both not strong and creative then alice is generous and vice versa. Everyone who is not happy is either humble or not generous. If someone is either not wise or not brave then alice is strong. Susan is both not old and calm. Someone is strong or not strong. Someone is both tall and generous. Someone is both not brave and old. Someone is either brave or not curious. Mary is either patient or curious. Fred is both not tall and strong. Someone is not curious or happy. | Fred is not calm. | contradiction | (((funny(susan)&~rich(susan)))<=>(old(lucy)))&
((?[X]:((~tall(X)&~wise(X))))=>(?[X]:((~humble(X)<~>calm(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:((~tall(X)<~>~rich(X))<=>creative(X)))&
(((funny(lucy)<~>~tall(lucy)))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((wise(X)|funny(X))=>(~creative(X)|~humble(X))))&
((?[X]:((happy(X)&funny(X))))<=>(humble(lucy)))&
((~calm(fred))=>((~wise(fred)&~tall(fred))))&
(((tall(alice)<~>~generous(alice)))=>(generous(alice)))&
(((~happy(fred)&creative(fred)))<=>(?[X]:(wise(X))))&
(![X]:((~calm(X)|~funny(X))<=>(~strong(X)&~happy(X))))&
(((quiet(susan)|generous(susan)))=>((~humble(fred)<~>quiet(fred))))&
(((kind(paul)&creative(paul)))<=>(~patient(paul)))&
((?[X]:((~strong(X)&creative(X))))<=>(generous(alice)))&
(![X]:(~happy(X)=>(humble(X)<~>~generous(X))))&
((?[X]:((~wise(X)<~>~brave(X))))=>(strong(alice)))&
((~old(susan)&calm(susan)))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:((tall(X)&generous(X))))&
(?[X]:((~brave(X)&old(X))))&
(?[X]:((brave(X)<~>~curious(X))))&
((patient(mary)<~>curious(mary)))&
((~tall(fred)&strong(fred)))&
(?[X]:((~curious(X)|happy(X)))) | ~calm(fred) | [
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5243480857207033239725994
% SZS output start Proof for 5243480857207033239725994
11. ! [X0] : ((~funny(X0) | ~calm(X0)) <=> (~happy(X0) & ~strong(X0))) [input p10]
23. strong(fred) & ~tall(fred) [input p22]
25. ~calm(fred) [input hypothesis]
62. ! [X0] : (((~funny(X0) | ~calm(X0)) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & calm(X0)))) [nnf transformation 11]
63. ! [X0] : ((~funny(X0) | ~calm(X0) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & calm(X0)))) [flattening 62]
117. ~strong(X0) | calm(X0) [cnf transformation 63]
148. strong(fred) [cnf transformation 23]
150. ~calm(fred) [cnf transformation 25]
250. 22 <=> calm(fred) [avatar definition]
251. ~calm(fred) <- (~22) [avatar component clause 250]
381. ~22 [avatar split clause 150,250]
382. calm(fred) [resolution 117,148]
384. $false <- (~22) [subsumption resolution 382,251]
385. 22 [avatar contradiction clause 384]
386. $false [avatar sat refutation 381,385]
% SZS output end Proof for 5243480857207033239725994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and quiet is both not generous and patient and vice versa.
If john is curious or not generous then alice is either quiet or calm and vice versa.
If someone is either wise or brave then lucy is both not generous and not creative.
If alice is either old or not strong then someone is not generous.
If someone is not humble then someone is not creative or tall.
Everyone who is both quiet and patient is not generous.
Everyone who is either not strong or strong is both generous and creative.
If someone is both funny and not quiet then someone is both generous and kind.
If lucy is either not wise or calm then john is patient.
If john is not wise then lucy is brave.
Everyone who is generous or strong is brave and vice versa.
Everyone who is not humble is both quiet and not humble.
Everyone who is either quiet or wise is both rich and not wise and vice versa.
If someone is both creative and rich then someone is both tall and not funny.
Everyone who is not old is either not happy or generous.
If someone is not creative then mary is funny or tall.
Someone is not humble.
Fred is both rich and not old.
Paul is not rich or calm.
John is either not patient or not kind.
Someone is rich.
Someone is creative.
Someone is both funny and brave. | Mary is not humble. | entailment | (![X]:((humble(X)&quiet(X))<=>(~generous(X)&patient(X))))&
(((curious(john)|~generous(john)))<=>((quiet(alice)<~>calm(alice))))&
((?[X]:((wise(X)<~>brave(X))))=>((~generous(lucy)&~creative(lucy))))&
(((old(alice)<~>~strong(alice)))=>(?[X]:(~generous(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~creative(X)|tall(X)))))&
(![X]:((quiet(X)&patient(X))=>~generous(X)))&
(![X]:((~strong(X)<~>strong(X))=>(generous(X)&creative(X))))&
((?[X]:((funny(X)&~quiet(X))))=>(?[X]:((generous(X)&kind(X)))))&
(((~wise(lucy)<~>calm(lucy)))=>(patient(john)))&
((~wise(john))=>(brave(lucy)))&
(![X]:((generous(X)|strong(X))<=>brave(X)))&
(![X]:(~humble(X)=>(quiet(X)&~humble(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(rich(X)&~wise(X))))&
((?[X]:((creative(X)&rich(X))))=>(?[X]:((tall(X)&~funny(X)))))&
(![X]:(~old(X)=>(~happy(X)<~>generous(X))))&
((?[X]:(~creative(X)))=>((funny(mary)|tall(mary))))&
(?[X]:(~humble(X)))&
((rich(fred)&~old(fred)))&
((~rich(paul)|calm(paul)))&
((~patient(john)<~>~kind(john)))&
(?[X]:(rich(X)))&
(?[X]:(creative(X)))&
(?[X]:((funny(X)&brave(X)))) | ~humble(mary) | [
"p0",
"p2",
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8640681972127343955604231
% SZS output start Proof for 8640681972127343955604231
1. ! [X0] : ((quiet(X0) & humble(X0)) <=> (patient(X0) & ~generous(X0))) [input p0]
3. ? [X0] : (wise(X0) <~> brave(X0)) => (~creative(lucy) & ~generous(lucy)) [input p2]
7. ! [X0] : ((~strong(X0) <~> strong(X0)) => (creative(X0) & generous(X0))) [input p6]
11. ! [X0] : ((strong(X0) | generous(X0)) <=> brave(X0)) [input p10]
13. ! [X0] : ((quiet(X0) <~> wise(X0)) <=> (~wise(X0) & rich(X0))) [input p12]
24. humble(mary) [input hypothesis]
31. (~creative(lucy) & ~generous(lucy)) | ! [X0] : (wise(X0) <=> brave(X0)) [ennf transformation 3]
35. ! [X0] : ((creative(X0) & generous(X0)) | (~strong(X0) <=> strong(X0))) [ennf transformation 7]
42. ! [X0] : (((quiet(X0) & humble(X0)) | (~patient(X0) | generous(X0))) & ((patient(X0) & ~generous(X0)) | (~quiet(X0) | ~humble(X0)))) [nnf transformation 1]
43. ! [X0] : (((quiet(X0) & humble(X0)) | ~patient(X0) | generous(X0)) & ((patient(X0) & ~generous(X0)) | ~quiet(X0) | ~humble(X0))) [flattening 42]
46. (~creative(lucy) & ~generous(lucy)) | ! [X0] : ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))) [nnf transformation 31]
50. ! [X0] : ((creative(X0) & generous(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 35]
55. ! [X0] : (((strong(X0) | generous(X0)) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [nnf transformation 11]
56. ! [X0] : ((strong(X0) | generous(X0) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [flattening 55]
57. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [nnf transformation 13]
58. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [flattening 57]
72. ~generous(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 43]
83. ~generous(lucy) | wise(X0) | ~brave(X0) [cnf transformation 46]
89. generous(X0) | strong(X0) | strong(X0) [cnf transformation 50]
90. generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 50]
98. brave(X0) | ~generous(X0) [cnf transformation 56]
106. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 58]
122. humble(mary) [cnf transformation 24]
123. ~wise(X0) | quiet(X0) [duplicate literal removal 106]
125. generous(X0) | strong(X0) [duplicate literal removal 89]
126. ~strong(X0) | generous(X0) [duplicate literal removal 90]
152. 5 <=> ! [X0] : (wise(X0) | ~brave(X0)) [avatar definition]
153. wise(X0) | ~brave(X0) <- (5) [avatar component clause 152]
164. 8 <=> generous(lucy) [avatar definition]
166. ~generous(lucy) <- (~8) [avatar component clause 164]
167. 5 | ~8 [avatar split clause 83,164,152]
184. generous(X0) [subsumption resolution 125,126]
216. brave(X0) [subsumption resolution 98,184]
244. $false <- (~8) [subsumption resolution 166,184]
245. 8 [avatar contradiction clause 244]
250. wise(X0) <- (5) [subsumption resolution 153,216]
254. quiet(X0) <- (5) [resolution 123,250]
260. ~quiet(X0) | ~humble(X0) [resolution 72,184]
261. ~humble(X0) <- (5) [subsumption resolution 260,254]
262. $false <- (5) [resolution 261,122]
263. ~5 [avatar contradiction clause 262]
264. $false [avatar sat refutation 167,245,263]
% SZS output end Proof for 8640681972127343955604231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not brave is old and vice versa.
Everyone who is both not humble and not funny is either old or quiet.
If john is either not generous or not quiet then someone is either wise or patient.
Everyone who is generous is either old or generous and vice versa.
If someone is both old and not patient then someone is either patient or not quiet and vice versa.
If someone is patient then paul is old or kind and vice versa.
Everyone who is both patient and not calm is not wise or calm.
Everyone who is both not kind and not brave is not old or not kind and vice versa.
Everyone who is quiet or not strong is strong or funny.
Everyone who is not generous or humble is generous.
Everyone who is both not generous and humble is either happy or not wise and vice versa.
Everyone who is not rich or curious is both not quiet and not wise and vice versa.
If alice is quiet then someone is quiet.
Lucy is not tall or calm.
Someone is not kind or not strong.
John is not curious.
Alice is funny or creative. | Paul is kind. | contradiction | (![X]:((~wise(X)<~>~brave(X))<=>old(X)))&
(![X]:((~humble(X)&~funny(X))=>(old(X)<~>quiet(X))))&
(((~generous(john)<~>~quiet(john)))=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:(generous(X)<=>(old(X)<~>generous(X))))&
((?[X]:((old(X)&~patient(X))))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
((?[X]:(patient(X)))<=>((old(paul)|kind(paul))))&
(![X]:((patient(X)&~calm(X))=>(~wise(X)|calm(X))))&
(![X]:((~kind(X)&~brave(X))<=>(~old(X)|~kind(X))))&
(![X]:((quiet(X)|~strong(X))=>(strong(X)|funny(X))))&
(![X]:((~generous(X)|humble(X))=>generous(X)))&
(![X]:((~generous(X)&humble(X))<=>(happy(X)<~>~wise(X))))&
(![X]:((~rich(X)|curious(X))<=>(~quiet(X)&~wise(X))))&
((quiet(alice))=>(?[X]:(quiet(X))))&
((~tall(lucy)|calm(lucy)))&
(?[X]:((~kind(X)|~strong(X))))&
(~curious(john))&
((funny(alice)|creative(alice))) | kind(paul) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8459532786894560716452852
% SZS output start Proof for 8459532786894560716452852
4. ! [X0] : (generous(X0) <=> (old(X0) <~> generous(X0))) [input p3]
8. ! [X0] : ((~brave(X0) & ~kind(X0)) <=> (~kind(X0) | ~old(X0))) [input p7]
18. kind(paul) [input hypothesis]
33. ! [X0] : ((generous(X0) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) & (((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~generous(X0))) [nnf transformation 4]
44. ! [X0] : (((~brave(X0) & ~kind(X0)) | (kind(X0) & old(X0))) & ((~kind(X0) | ~old(X0)) | (brave(X0) | kind(X0)))) [nnf transformation 8]
45. ! [X0] : (((~brave(X0) & ~kind(X0)) | (kind(X0) & old(X0))) & (~kind(X0) | ~old(X0) | brave(X0) | kind(X0))) [flattening 44]
61. ~generous(X0) | ~old(X0) | ~generous(X0) [cnf transformation 33]
62. generous(X0) | generous(X0) | ~old(X0) [cnf transformation 33]
74. ~kind(X0) | old(X0) [cnf transformation 45]
93. kind(paul) [cnf transformation 18]
95. ~generous(X0) | ~old(X0) [duplicate literal removal 61]
96. generous(X0) | ~old(X0) [duplicate literal removal 62]
117. ~old(X0) [subsumption resolution 95,96]
149. ~kind(X0) [subsumption resolution 74,117]
161. $false [subsumption resolution 93,149]
% SZS output end Proof for 8459532786894560716452852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not kind is not creative and vice versa.
Everyone who is both humble and not calm is both happy and not brave.
Everyone who is both not creative and generous is both old and not creative and vice versa.
If someone is not kind then paul is either quiet or curious.
Everyone who is not strong or calm is both humble and not wise and vice versa.
If alice is not rich or strong then someone is not happy or patient and vice versa.
Everyone who is both not generous and old is either generous or strong and vice versa.
Everyone who is not wise is both kind and not kind.
Everyone who is happy or not curious is humble.
Everyone who is either not happy or brave is both not strong and not rich.
Everyone who is not calm or not quiet is either funny or wise.
Everyone who is not strong is either rich or strong and vice versa.
Everyone who is either rich or strong is either creative or not brave and vice versa.
If alice is either wise or tall then paul is not curious.
If someone is both not creative and not wise then susan is patient.
If someone is calm then someone is curious or not old.
Alice is patient.
John is either not patient or not kind.
Paul is both tall and not quiet.
Alice is either not kind or humble.
John is happy or humble.
Someone is either not patient or generous.
Lucy is not funny. | Alice is rich. | entailment | (![X]:((humble(X)&~kind(X))<=>~creative(X)))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&~brave(X))))&
(![X]:((~creative(X)&generous(X))<=>(old(X)&~creative(X))))&
((?[X]:(~kind(X)))=>((quiet(paul)<~>curious(paul))))&
(![X]:((~strong(X)|calm(X))<=>(humble(X)&~wise(X))))&
(((~rich(alice)|strong(alice)))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)<~>strong(X))))&
(![X]:(~wise(X)=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|~curious(X))=>humble(X)))&
(![X]:((~happy(X)<~>brave(X))=>(~strong(X)&~rich(X))))&
(![X]:((~calm(X)|~quiet(X))=>(funny(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>strong(X))))&
(![X]:((rich(X)<~>strong(X))<=>(creative(X)<~>~brave(X))))&
(((wise(alice)<~>tall(alice)))=>(~curious(paul)))&
((?[X]:((~creative(X)&~wise(X))))=>(patient(susan)))&
((?[X]:(calm(X)))=>(?[X]:((curious(X)|~old(X)))))&
(patient(alice))&
((~patient(john)<~>~kind(john)))&
((tall(paul)&~quiet(paul)))&
((~kind(alice)<~>humble(alice)))&
((happy(john)|humble(john)))&
(?[X]:((~patient(X)<~>generous(X))))&
(~funny(lucy)) | rich(alice) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3075205911563723137961982
% SZS output start Proof for 3075205911563723137961982
12. ! [X0] : (~strong(X0) <=> (rich(X0) <~> strong(X0))) [input p11]
24. ~rich(alice) [input hypothesis]
52. ! [X0] : ((~strong(X0) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) & (((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | strong(X0))) [nnf transformation 12]
101. strong(X0) | rich(X0) | strong(X0) [cnf transformation 52]
104. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 52]
128. ~rich(alice) [cnf transformation 24]
129. strong(X0) | rich(X0) [duplicate literal removal 101]
130. ~strong(X0) | rich(X0) [duplicate literal removal 104]
176. rich(X0) [subsumption resolution 129,130]
231. $false [subsumption resolution 128,176]
% SZS output end Proof for 3075205911563723137961982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is both kind and not patient and vice versa.
If paul is either wise or curious then mary is brave or not calm.
Everyone who is either old or funny is not happy or not generous and vice versa.
Everyone who is kind or not calm is either wise or not humble and vice versa.
Everyone who is both brave and humble is not patient or curious.
Everyone who is both not patient and creative is either humble or rich.
Everyone who is not wise or kind is happy or brave.
Everyone who is not curious is kind.
Everyone who is brave or not rich is both not patient and funny.
Everyone who is kind is either not strong or tall and vice versa.
Everyone who is either not humble or not rich is both not funny and old and vice versa.
Everyone who is not quiet or kind is both old and humble and vice versa.
If someone is either wise or not strong then someone is happy and vice versa.
Everyone who is not creative or kind is either not brave or not calm.
Everyone who is both not brave and quiet is not quiet or curious.
Everyone who is not curious or calm is not brave.
Someone is funny or not strong.
Someone is patient or brave.
Fred is both funny and humble.
Someone is both quiet and strong.
Fred is kind or not kind.
John is kind.
Someone is happy or not brave.
Mary is quiet. | John is not happy. | contradiction | (![X]:(brave(X)<=>(kind(X)&~patient(X))))&
(((wise(paul)<~>curious(paul)))=>((brave(mary)|~calm(mary))))&
(![X]:((old(X)<~>funny(X))<=>(~happy(X)|~generous(X))))&
(![X]:((kind(X)|~calm(X))<=>(wise(X)<~>~humble(X))))&
(![X]:((brave(X)&humble(X))=>(~patient(X)|curious(X))))&
(![X]:((~patient(X)&creative(X))=>(humble(X)<~>rich(X))))&
(![X]:((~wise(X)|kind(X))=>(happy(X)|brave(X))))&
(![X]:(~curious(X)=>kind(X)))&
(![X]:((brave(X)|~rich(X))=>(~patient(X)&funny(X))))&
(![X]:(kind(X)<=>(~strong(X)<~>tall(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~funny(X)&old(X))))&
(![X]:((~quiet(X)|kind(X))<=>(old(X)&humble(X))))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:(happy(X))))&
(![X]:((~creative(X)|kind(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((~brave(X)&quiet(X))=>(~quiet(X)|curious(X))))&
(![X]:((~curious(X)|calm(X))=>~brave(X)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((patient(X)|brave(X))))&
((funny(fred)&humble(fred)))&
(?[X]:((quiet(X)&strong(X))))&
((kind(fred)|~kind(fred)))&
(kind(john))&
(?[X]:((happy(X)|~brave(X))))&
(quiet(mary)) | ~happy(john) | [
"p2",
"p6",
"p8",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1774990343150961770753773
% SZS output start Proof for 1774990343150961770753773
3. ! [X0] : ((old(X0) <~> funny(X0)) <=> (~generous(X0) | ~happy(X0))) [input p2]
7. ! [X0] : ((kind(X0) | ~wise(X0)) => (brave(X0) | happy(X0))) [input p6]
9. ! [X0] : ((~rich(X0) | brave(X0)) => (funny(X0) & ~patient(X0))) [input p8]
12. ! [X0] : ((kind(X0) | ~quiet(X0)) <=> (humble(X0) & old(X0))) [input p11]
22. kind(john) [input p21]
25. ~happy(john) [input hypothesis]
33. ! [X0] : ((brave(X0) | happy(X0)) | (~kind(X0) & wise(X0))) [ennf transformation 7]
34. ! [X0] : (brave(X0) | happy(X0) | (~kind(X0) & wise(X0))) [flattening 33]
36. ! [X0] : ((funny(X0) & ~patient(X0)) | (rich(X0) & ~brave(X0))) [ennf transformation 9]
44. ! [X0] : ((((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))))) [nnf transformation 3]
45. ! [X0] : ((((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))))) [flattening 44]
52. ! [X0] : (((kind(X0) | ~quiet(X0)) | (~humble(X0) | ~old(X0))) & ((humble(X0) & old(X0)) | (~kind(X0) & quiet(X0)))) [nnf transformation 12]
53. ! [X0] : ((kind(X0) | ~quiet(X0) | ~humble(X0) | ~old(X0)) & ((humble(X0) & old(X0)) | (~kind(X0) & quiet(X0)))) [flattening 52]
77. ~funny(X0) | ~old(X0) | happy(X0) [cnf transformation 45]
89. ~kind(X0) | happy(X0) | brave(X0) [cnf transformation 34]
93. ~brave(X0) | funny(X0) [cnf transformation 36]
106. ~kind(X0) | old(X0) [cnf transformation 53]
128. kind(john) [cnf transformation 22]
131. ~happy(john) [cnf transformation 25]
209. old(john) [resolution 106,128]
215. 17 <=> brave(john) [avatar definition]
216. ~brave(john) <- (~17) [avatar component clause 215]
217. brave(john) <- (17) [avatar component clause 215]
224. funny(john) <- (17) [resolution 217,93]
228. ~old(john) | happy(john) <- (17) [resolution 77,224]
238. happy(john) <- (17) [subsumption resolution 228,209]
239. $false <- (17) [subsumption resolution 238,131]
240. ~17 [avatar contradiction clause 239]
268. happy(john) | brave(john) [resolution 89,128]
269. brave(john) [subsumption resolution 268,131]
270. $false <- (~17) [subsumption resolution 269,216]
271. 17 [avatar contradiction clause 270]
272. $false [avatar sat refutation 240,271]
% SZS output end Proof for 1774990343150961770753773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and not funny then mary is curious.
If someone is not funny or not curious then alice is either not curious or not brave.
If someone is patient or creative then mary is either curious or not calm.
Everyone who is calm or old is either not strong or generous.
If john is either humble or strong then someone is funny.
Everyone who is not tall or wise is not wise.
If fred is wise or not strong then paul is strong.
If someone is creative or rich then someone is either calm or not happy and vice versa.
Everyone who is either not tall or not patient is both creative and brave.
If fred is funny or curious then alice is not strong or kind and vice versa.
If someone is humble then someone is either not tall or strong and vice versa.
If someone is brave or tall then alice is both not rich and calm.
If someone is both wise and not patient then someone is not rich or not calm and vice versa.
Everyone who is either not generous or not wise is funny.
Someone is rich or not wise.
John is both not quiet and generous.
Someone is not tall or not quiet.
Alice is either not curious or not old.
Someone is not funny.
Fred is either not curious or not quiet.
Mary is not calm or rich. | John is wise. | contradiction | ((?[X]:((brave(X)&~funny(X))))=>(curious(mary)))&
((?[X]:((~funny(X)|~curious(X))))=>((~curious(alice)<~>~brave(alice))))&
((?[X]:((patient(X)|creative(X))))=>((curious(mary)<~>~calm(mary))))&
(![X]:((calm(X)|old(X))=>(~strong(X)<~>generous(X))))&
(((humble(john)<~>strong(john)))=>(?[X]:(funny(X))))&
(![X]:((~tall(X)|wise(X))=>~wise(X)))&
(((wise(fred)|~strong(fred)))=>(strong(paul)))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((calm(X)<~>~happy(X)))))&
(![X]:((~tall(X)<~>~patient(X))=>(creative(X)&brave(X))))&
(((funny(fred)|curious(fred)))<=>((~strong(alice)|kind(alice))))&
((?[X]:(humble(X)))<=>(?[X]:((~tall(X)<~>strong(X)))))&
((?[X]:((brave(X)|tall(X))))=>((~rich(alice)&calm(alice))))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((~rich(X)|~calm(X)))))&
(![X]:((~generous(X)<~>~wise(X))=>funny(X)))&
(?[X]:((rich(X)|~wise(X))))&
((~quiet(john)&generous(john)))&
(?[X]:((~tall(X)|~quiet(X))))&
((~curious(alice)<~>~old(alice)))&
(?[X]:(~funny(X)))&
((~curious(fred)<~>~quiet(fred)))&
((~calm(mary)|rich(mary))) | wise(john) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 897159169389398346921945
% SZS output start Proof for 897159169389398346921945
6. ! [X0] : ((wise(X0) | ~tall(X0)) => ~wise(X0)) [input p5]
22. wise(john) [input hypothesis]
31. ! [X0] : (~wise(X0) | (~wise(X0) & tall(X0))) [ennf transformation 6]
85. ~wise(X0) | ~wise(X0) [cnf transformation 31]
127. wise(john) [cnf transformation 22]
128. ~wise(X0) [duplicate literal removal 85]
329. $false [subsumption resolution 127,128]
% SZS output end Proof for 897159169389398346921945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not calm is happy.
Everyone who is both patient and curious is old or patient.
If someone is not curious or not patient then john is either not brave or creative.
If someone is both happy and not old then someone is not curious or creative and vice versa.
Everyone who is not quiet or not patient is both brave and not generous and vice versa.
Everyone who is old is either old or not happy and vice versa.
If someone is not humble or old then mary is both curious and brave and vice versa.
If susan is either not rich or not wise then someone is not rich and vice versa.
Everyone who is tall or funny is old or quiet.
If lucy is not kind then someone is not creative or curious and vice versa.
Everyone who is either not strong or not rich is either not brave or not patient and vice versa.
If someone is either not funny or kind then someone is kind and vice versa.
If alice is not patient or old then alice is both curious and creative.
Everyone who is not patient is both tall and patient.
Everyone who is not kind or kind is either not strong or patient and vice versa.
Everyone who is not creative or strong is either not strong or not humble and vice versa.
Alice is either not humble or not curious.
Lucy is both generous and patient.
John is not calm.
Someone is either not curious or calm.
Alice is not patient or tall.
Lucy is brave or not old. | Lucy is kind. | contradiction | (![X]:((old(X)&~calm(X))=>happy(X)))&
(![X]:((patient(X)&curious(X))=>(old(X)|patient(X))))&
((?[X]:((~curious(X)|~patient(X))))=>((~brave(john)<~>creative(john))))&
((?[X]:((happy(X)&~old(X))))<=>(?[X]:((~curious(X)|creative(X)))))&
(![X]:((~quiet(X)|~patient(X))<=>(brave(X)&~generous(X))))&
(![X]:(old(X)<=>(old(X)<~>~happy(X))))&
((?[X]:((~humble(X)|old(X))))<=>((curious(mary)&brave(mary))))&
(((~rich(susan)<~>~wise(susan)))<=>(?[X]:(~rich(X))))&
(![X]:((tall(X)|funny(X))=>(old(X)|quiet(X))))&
((~kind(lucy))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~brave(X)<~>~patient(X))))&
((?[X]:((~funny(X)<~>kind(X))))<=>(?[X]:(kind(X))))&
(((~patient(alice)|old(alice)))=>((curious(alice)&creative(alice))))&
(![X]:(~patient(X)=>(tall(X)&patient(X))))&
(![X]:((~kind(X)|kind(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((~creative(X)|strong(X))<=>(~strong(X)<~>~humble(X))))&
((~humble(alice)<~>~curious(alice)))&
((generous(lucy)&patient(lucy)))&
(~calm(john))&
(?[X]:((~curious(X)<~>calm(X))))&
((~patient(alice)|tall(alice)))&
((brave(lucy)|~old(lucy))) | kind(lucy) | [
"p6",
"p9",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7213943525340643620623295
% SZS output start Proof for 7213943525340643620623295
7. ? [X0] : (old(X0) | ~humble(X0)) <=> (brave(mary) & curious(mary)) [input p6]
10. ~kind(lucy) <=> ? [X0] : (curious(X0) | ~creative(X0)) [input p9]
15. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (~strong(X0) <~> patient(X0))) [input p14]
16. ! [X0] : ((strong(X0) | ~creative(X0)) <=> (~strong(X0) <~> ~humble(X0))) [input p15]
18. patient(lucy) & generous(lucy) [input p17]
23. kind(lucy) [input hypothesis]
44. (? [X0] : (old(X0) | ~humble(X0)) | (~brave(mary) | ~curious(mary))) & ((brave(mary) & curious(mary)) | ! [X0] : (~old(X0) & humble(X0))) [nnf transformation 7]
45. (? [X0] : (old(X0) | ~humble(X0)) | ~brave(mary) | ~curious(mary)) & ((brave(mary) & curious(mary)) | ! [X0] : (~old(X0) & humble(X0))) [flattening 44]
46. (? [X0] : (old(X0) | ~humble(X0)) | ~brave(mary) | ~curious(mary)) & ((brave(mary) & curious(mary)) | ! [X1] : (~old(X1) & humble(X1))) [rectify 45]
47. ? [X0] : (old(X0) | ~humble(X0)) => (old(sK2) | ~humble(sK2)) [choice axiom]
48. ((old(sK2) | ~humble(sK2)) | ~brave(mary) | ~curious(mary)) & ((brave(mary) & curious(mary)) | ! [X1] : (~old(X1) & humble(X1))) [skolemisation 46,47]
53. (~kind(lucy) | ! [X0] : (~curious(X0) & creative(X0))) & (? [X0] : (curious(X0) | ~creative(X0)) | kind(lucy)) [nnf transformation 10]
54. (~kind(lucy) | ! [X0] : (~curious(X0) & creative(X0))) & (? [X1] : (curious(X1) | ~creative(X1)) | kind(lucy)) [rectify 53]
55. ? [X1] : (curious(X1) | ~creative(X1)) => (curious(sK4) | ~creative(sK4)) [choice axiom]
56. (~kind(lucy) | ! [X0] : (~curious(X0) & creative(X0))) & ((curious(sK4) | ~creative(sK4)) | kind(lucy)) [skolemisation 54,55]
63. ! [X0] : (((kind(X0) | ~kind(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~kind(X0) & kind(X0)))) [nnf transformation 15]
64. ! [X0] : ((kind(X0) | ~kind(X0) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~kind(X0) & kind(X0)))) [flattening 63]
65. ! [X0] : (((strong(X0) | ~creative(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~strong(X0) & creative(X0)))) [nnf transformation 16]
66. ! [X0] : ((strong(X0) | ~creative(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~strong(X0) & creative(X0)))) [flattening 65]
91. curious(mary) | humble(X1) [cnf transformation 48]
104. ~kind(lucy) | ~curious(X0) [cnf transformation 56]
125. ~patient(X0) | strong(X0) | kind(X0) [cnf transformation 64]
126. ~patient(X0) | strong(X0) | ~kind(X0) [cnf transformation 64]
130. ~humble(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 66]
138. patient(lucy) [cnf transformation 18]
144. kind(lucy) [cnf transformation 23]
145. ~strong(X0) | ~humble(X0) [duplicate literal removal 130]
197. 11 <=> curious(mary) [avatar definition]
198. curious(mary) <- (11) [avatar component clause 197]
218. 16 <=> ! [X1] : humble(X1) [avatar definition]
219. humble(X1) <- (16) [avatar component clause 218]
222. 16 | 11 [avatar split clause 91,197,218]
243. 21 <=> ! [X0] : ~curious(X0) [avatar definition]
244. ~curious(X0) <- (21) [avatar component clause 243]
246. 22 <=> kind(lucy) [avatar definition]
249. 21 | ~22 [avatar split clause 104,246,243]
313. ~patient(X0) | strong(X0) [subsumption resolution 125,126]
341. 22 [avatar split clause 144,246]
342. $false <- (11, 21) [subsumption resolution 198,244]
343. ~11 | ~21 [avatar contradiction clause 342]
358. strong(lucy) [resolution 313,138]
361. ~humble(lucy) [resolution 358,145]
362. $false <- (16) [subsumption resolution 361,219]
363. ~16 [avatar contradiction clause 362]
364. $false [avatar sat refutation 222,249,341,343,363]
% SZS output end Proof for 7213943525340643620623295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both calm and old and vice versa.
Everyone who is both not happy and creative is not strong.
Everyone who is either not quiet or not curious is both not strong and not patient and vice versa.
If someone is either not rich or kind then someone is both tall and not curious.
If john is both not creative and wise then someone is either not wise or patient.
Everyone who is wise is both patient and curious.
Everyone who is not quiet is generous or happy and vice versa.
Everyone who is either wise or calm is patient.
Everyone who is not funny or quiet is both not wise and tall and vice versa.
Everyone who is both creative and humble is not wise.
Everyone who is brave is not quiet or not happy.
If paul is not kind or not rich then someone is funny or quiet.
If paul is both not humble and quiet then mary is not generous.
Everyone who is both creative and not curious is not kind or not wise and vice versa.
Everyone who is either not curious or patient is either not calm or not happy and vice versa.
If susan is not kind or generous then someone is both not happy and not brave and vice versa.
Someone is both generous and not rich.
Someone is both patient and not strong.
Someone is either not generous or generous.
Alice is either not rich or not wise.
Someone is kind or not patient.
Someone is funny.
Someone is both funny and calm. | Paul is calm. | entailment | (![X]:(~curious(X)<=>(calm(X)&old(X))))&
(![X]:((~happy(X)&creative(X))=>~strong(X)))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~strong(X)&~patient(X))))&
((?[X]:((~rich(X)<~>kind(X))))=>(?[X]:((tall(X)&~curious(X)))))&
(((~creative(john)&wise(john)))=>(?[X]:((~wise(X)<~>patient(X)))))&
(![X]:(wise(X)=>(patient(X)&curious(X))))&
(![X]:(~quiet(X)<=>(generous(X)|happy(X))))&
(![X]:((wise(X)<~>calm(X))=>patient(X)))&
(![X]:((~funny(X)|quiet(X))<=>(~wise(X)&tall(X))))&
(![X]:((creative(X)&humble(X))=>~wise(X)))&
(![X]:(brave(X)=>(~quiet(X)|~happy(X))))&
(((~kind(paul)|~rich(paul)))=>(?[X]:((funny(X)|quiet(X)))))&
(((~humble(paul)&quiet(paul)))=>(~generous(mary)))&
(![X]:((creative(X)&~curious(X))<=>(~kind(X)|~wise(X))))&
(![X]:((~curious(X)<~>patient(X))<=>(~calm(X)<~>~happy(X))))&
(((~kind(susan)|generous(susan)))<=>(?[X]:((~happy(X)&~brave(X)))))&
(?[X]:((generous(X)&~rich(X))))&
(?[X]:((patient(X)&~strong(X))))&
(?[X]:((~generous(X)<~>generous(X))))&
((~rich(alice)<~>~wise(alice)))&
(?[X]:((kind(X)|~patient(X))))&
(?[X]:(funny(X)))&
(?[X]:((funny(X)&calm(X)))) | calm(paul) | [
"p0",
"p2",
"p5",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6094199181396173842979105
% SZS output start Proof for 6094199181396173842979105
1. ! [X0] : (~curious(X0) <=> (old(X0) & calm(X0))) [input p0]
3. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) <=> (~patient(X0) & ~strong(X0))) [input p2]
6. ! [X0] : (wise(X0) => (curious(X0) & patient(X0))) [input p5]
9. ! [X0] : ((quiet(X0) | ~funny(X0)) <=> (tall(X0) & ~wise(X0))) [input p8]
14. ! [X0] : ((~curious(X0) & creative(X0)) <=> (~wise(X0) | ~kind(X0))) [input p13]
24. ~calm(paul) [input hypothesis]
31. ! [X0] : ((curious(X0) & patient(X0)) | ~wise(X0)) [ennf transformation 6]
40. ! [X0] : ((~curious(X0) | (~old(X0) | ~calm(X0))) & ((old(X0) & calm(X0)) | curious(X0))) [nnf transformation 1]
41. ! [X0] : ((~curious(X0) | ~old(X0) | ~calm(X0)) & ((old(X0) & calm(X0)) | curious(X0))) [flattening 40]
42. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [nnf transformation 3]
43. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [flattening 42]
54. ! [X0] : (((quiet(X0) | ~funny(X0)) | (~tall(X0) | wise(X0))) & ((tall(X0) & ~wise(X0)) | (~quiet(X0) & funny(X0)))) [nnf transformation 9]
55. ! [X0] : ((quiet(X0) | ~funny(X0) | ~tall(X0) | wise(X0)) & ((tall(X0) & ~wise(X0)) | (~quiet(X0) & funny(X0)))) [flattening 54]
58. ! [X0] : (((~curious(X0) & creative(X0)) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | (curious(X0) | ~creative(X0)))) [nnf transformation 14]
59. ! [X0] : (((~curious(X0) & creative(X0)) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | curious(X0) | ~creative(X0))) [flattening 58]
80. calm(X0) | curious(X0) [cnf transformation 41]
86. ~patient(X0) | ~curious(X0) | quiet(X0) [cnf transformation 43]
96. ~wise(X0) | patient(X0) [cnf transformation 31]
104. ~wise(X0) | ~quiet(X0) [cnf transformation 55]
117. ~curious(X0) | wise(X0) [cnf transformation 59]
143. ~calm(paul) [cnf transformation 24]
204. 14 <=> quiet(paul) [avatar definition]
206. ~quiet(paul) <- (~14) [avatar component clause 204]
261. curious(paul) [resolution 80,143]
273. wise(paul) [resolution 117,261]
281. ~quiet(paul) [resolution 273,104]
284. patient(paul) [resolution 273,96]
285. ~14 [avatar split clause 281,204]
292. ~curious(paul) | quiet(paul) [resolution 86,284]
311. quiet(paul) [subsumption resolution 292,261]
312. $false <- (~14) [subsumption resolution 311,206]
313. 14 [avatar contradiction clause 312]
314. $false [avatar sat refutation 285,313]
% SZS output end Proof for 6094199181396173842979105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then paul is both brave and not quiet.
If john is creative or not rich then fred is either not quiet or quiet and vice versa.
If someone is both not creative and happy then fred is either generous or not curious and vice versa.
Everyone who is either patient or not old is either not kind or not brave and vice versa.
If someone is generous then mary is funny and vice versa.
If someone is not kind then someone is both not brave and calm and vice versa.
If someone is both not brave and not happy then mary is either not rich or not curious and vice versa.
Everyone who is not tall or happy is both tall and not quiet and vice versa.
Everyone who is either wise or not tall is both not patient and strong and vice versa.
Everyone who is funny or patient is both not rich and rich.
Everyone who is either curious or not strong is not humble or generous.
If someone is not happy or not creative then alice is not tall or quiet and vice versa.
Everyone who is both patient and brave is either kind or not brave and vice versa.
If paul is both not tall and calm then john is both curious and not kind and vice versa.
If someone is not creative or not rich then someone is strong or not wise.
Mary is not rich or not strong.
Someone is old or not quiet.
John is both not old and tall.
Mary is not creative.
Someone is either not brave or not patient.
Someone is not brave or quiet.
Someone is not patient.
Someone is either not patient or not quiet. | Paul is curious. | neutral | ((?[X]:(funny(X)))=>((brave(paul)&~quiet(paul))))&
(((creative(john)|~rich(john)))<=>((~quiet(fred)<~>quiet(fred))))&
((?[X]:((~creative(X)&happy(X))))<=>((generous(fred)<~>~curious(fred))))&
(![X]:((patient(X)<~>~old(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:(generous(X)))<=>(funny(mary)))&
((?[X]:(~kind(X)))<=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((~brave(X)&~happy(X))))<=>((~rich(mary)<~>~curious(mary))))&
(![X]:((~tall(X)|happy(X))<=>(tall(X)&~quiet(X))))&
(![X]:((wise(X)<~>~tall(X))<=>(~patient(X)&strong(X))))&
(![X]:((funny(X)|patient(X))=>(~rich(X)&rich(X))))&
(![X]:((curious(X)<~>~strong(X))=>(~humble(X)|generous(X))))&
((?[X]:((~happy(X)|~creative(X))))<=>((~tall(alice)|quiet(alice))))&
(![X]:((patient(X)&brave(X))<=>(kind(X)<~>~brave(X))))&
(((~tall(paul)&calm(paul)))<=>((curious(john)&~kind(john))))&
((?[X]:((~creative(X)|~rich(X))))=>(?[X]:((strong(X)|~wise(X)))))&
((~rich(mary)|~strong(mary)))&
(?[X]:((old(X)|~quiet(X))))&
((~old(john)&tall(john)))&
(~creative(mary))&
(?[X]:((~brave(X)<~>~patient(X))))&
(?[X]:((~brave(X)|quiet(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~patient(X)<~>~quiet(X)))) | curious(paul) | [] | null | 0 |
If someone is tall or brave then someone is strong and vice versa. Everyone who is funny or wise is quiet and vice versa. If alice is not curious or kind then susan is both not wise and quiet and vice versa. If mary is not strong then someone is not old and vice versa. Everyone who is not old is quiet and vice versa. If alice is either generous or not strong then lucy is both not calm and patient and vice versa. Everyone who is not patient is generous. If someone is not wise then mary is either wise or not kind. If fred is creative then someone is not quiet or not creative. If john is both quiet and not creative then susan is generous or not humble and vice versa. Everyone who is both strong and tall is not kind or not humble and vice versa. Everyone who is either not kind or not tall is both not wise and not quiet. If someone is both not funny and patient then someone is both calm and humble. Everyone who is both funny and generous is both strong and curious. If john is kind then mary is both not patient and not kind. Everyone who is not generous or curious is not strong or calm and vice versa. John is not calm. Fred is happy. John is not generous. Someone is not wise. Someone is either generous or kind. John is not quiet or humble. | Susan is quiet. | contradiction | ((?[X]:((tall(X)|brave(X))))<=>(?[X]:(strong(X))))&
(![X]:((funny(X)|wise(X))<=>quiet(X)))&
(((~curious(alice)|kind(alice)))<=>((~wise(susan)&quiet(susan))))&
((~strong(mary))<=>(?[X]:(~old(X))))&
(![X]:(~old(X)<=>quiet(X)))&
(((generous(alice)<~>~strong(alice)))<=>((~calm(lucy)&patient(lucy))))&
(![X]:(~patient(X)=>generous(X)))&
((?[X]:(~wise(X)))=>((wise(mary)<~>~kind(mary))))&
((creative(fred))=>(?[X]:((~quiet(X)|~creative(X)))))&
(((quiet(john)&~creative(john)))<=>((generous(susan)|~humble(susan))))&
(![X]:((strong(X)&tall(X))<=>(~kind(X)|~humble(X))))&
(![X]:((~kind(X)<~>~tall(X))=>(~wise(X)&~quiet(X))))&
((?[X]:((~funny(X)&patient(X))))=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((funny(X)&generous(X))=>(strong(X)&curious(X))))&
((kind(john))=>((~patient(mary)&~kind(mary))))&
(![X]:((~generous(X)|curious(X))<=>(~strong(X)|calm(X))))&
(~calm(john))&
(happy(fred))&
(~generous(john))&
(?[X]:(~wise(X)))&
(?[X]:((generous(X)<~>kind(X))))&
((~quiet(john)|humble(john))) | quiet(susan) | [
"p3",
"p4",
"p10",
"p14",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 698634452256691277909114
% SZS output start Proof for 698634452256691277909114
4. ~strong(mary) <=> ? [X0] : ~old(X0) [input p3]
5. ! [X0] : (~old(X0) <=> quiet(X0)) [input p4]
11. ! [X0] : ((tall(X0) & strong(X0)) <=> (~humble(X0) | ~kind(X0))) [input p10]
15. kind(john) => (~kind(mary) & ~patient(mary)) [input p14]
16. ! [X0] : ((curious(X0) | ~generous(X0)) <=> (calm(X0) | ~strong(X0))) [input p15]
17. ~calm(john) [input p16]
19. ~generous(john) [input p18]
23. quiet(susan) [input hypothesis]
34. (~kind(mary) & ~patient(mary)) | ~kind(john) [ennf transformation 15]
44. (~strong(mary) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | strong(mary)) [nnf transformation 4]
45. (~strong(mary) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | strong(mary)) [rectify 44]
46. ? [X1] : ~old(X1) => ~old(sK2) [choice axiom]
47. (~strong(mary) | ! [X0] : old(X0)) & (~old(sK2) | strong(mary)) [skolemisation 45,46]
48. ! [X0] : ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0))) [nnf transformation 5]
56. ! [X0] : (((tall(X0) & strong(X0)) | (humble(X0) & kind(X0))) & ((~humble(X0) | ~kind(X0)) | (~tall(X0) | ~strong(X0)))) [nnf transformation 11]
57. ! [X0] : (((tall(X0) & strong(X0)) | (humble(X0) & kind(X0))) & (~humble(X0) | ~kind(X0) | ~tall(X0) | ~strong(X0))) [flattening 56]
62. ! [X0] : (((curious(X0) | ~generous(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (~curious(X0) & generous(X0)))) [nnf transformation 16]
63. ! [X0] : ((curious(X0) | ~generous(X0) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | (~curious(X0) & generous(X0)))) [flattening 62]
81. ~strong(mary) | old(X0) [cnf transformation 47]
83. ~old(X0) | ~quiet(X0) [cnf transformation 48]
100. kind(X0) | strong(X0) [cnf transformation 57]
113. ~kind(mary) | ~kind(john) [cnf transformation 34]
114. ~strong(X0) | calm(X0) | generous(X0) [cnf transformation 63]
118. ~calm(john) [cnf transformation 17]
119. ~generous(john) [cnf transformation 19]
124. quiet(susan) [cnf transformation 23]
154. 8 <=> quiet(susan) [avatar definition]
155. quiet(susan) <- (8) [avatar component clause 154]
171. 11 <=> ! [X0] : old(X0) [avatar definition]
172. old(X0) <- (11) [avatar component clause 171]
174. 12 <=> strong(mary) [avatar definition]
177. 11 | ~12 [avatar split clause 81,174,171]
213. 20 <=> kind(mary) [avatar definition]
214. ~kind(mary) <- (~20) [avatar component clause 213]
270. 31 <=> kind(john) [avatar definition]
272. ~kind(john) <- (~31) [avatar component clause 270]
273. ~31 | ~20 [avatar split clause 113,213,270]
294. 8 [avatar split clause 124,154]
297. strong(mary) <- (~20) [resolution 100,214]
298. strong(john) <- (~31) [resolution 100,272]
302. 12 | 20 [avatar split clause 297,213,174]
304. ~quiet(X0) <- (11) [resolution 172,83]
309. $false <- (8, 11) [resolution 304,155]
310. ~8 | ~11 [avatar contradiction clause 309]
356. calm(john) | generous(john) <- (~31) [resolution 114,298]
359. generous(john) <- (~31) [subsumption resolution 356,118]
360. $false <- (~31) [subsumption resolution 359,119]
361. 31 [avatar contradiction clause 360]
371. $false [avatar sat refutation 177,273,294,302,310,361]
% SZS output end Proof for 698634452256691277909114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and not brave then someone is either generous or tall and vice versa.
Everyone who is calm or not happy is both quiet and not quiet.
If alice is both tall and not wise then john is not creative.
If someone is both not humble and not generous then lucy is either not generous or not happy.
If someone is quiet then someone is strong.
If someone is either curious or quiet then someone is either wise or not humble and vice versa.
If alice is either humble or funny then someone is either not old or not strong and vice versa.
Everyone who is not generous or patient is wise or not patient and vice versa.
If someone is either not quiet or humble then someone is not quiet and vice versa.
If someone is tall or calm then someone is both old and curious and vice versa.
Everyone who is not tall or quiet is either not strong or tall and vice versa.
If alice is either quiet or old then someone is not generous or not calm and vice versa.
Everyone who is either not generous or rich is both not kind and kind.
Everyone who is both old and kind is either not brave or brave.
Everyone who is either tall or not wise is quiet or old.
Everyone who is not humble or not kind is not patient and vice versa.
Someone is generous.
Someone is either strong or happy.
Someone is happy or kind.
Someone is creative or not brave.
Someone is rich.
Someone is not tall.
Someone is both not brave and not strong.
Someone is not strong. | Alice is funny. | neutral | ((?[X]:((happy(X)&~brave(X))))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((calm(X)|~happy(X))=>(quiet(X)&~quiet(X))))&
(((tall(alice)&~wise(alice)))=>(~creative(john)))&
((?[X]:((~humble(X)&~generous(X))))=>((~generous(lucy)<~>~happy(lucy))))&
((?[X]:(quiet(X)))=>(?[X]:(strong(X))))&
((?[X]:((curious(X)<~>quiet(X))))<=>(?[X]:((wise(X)<~>~humble(X)))))&
(((humble(alice)<~>funny(alice)))<=>(?[X]:((~old(X)<~>~strong(X)))))&
(![X]:((~generous(X)|patient(X))<=>(wise(X)|~patient(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((tall(X)|calm(X))))<=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~tall(X)|quiet(X))<=>(~strong(X)<~>tall(X))))&
(((quiet(alice)<~>old(alice)))<=>(?[X]:((~generous(X)|~calm(X)))))&
(![X]:((~generous(X)<~>rich(X))=>(~kind(X)&kind(X))))&
(![X]:((old(X)&kind(X))=>(~brave(X)<~>brave(X))))&
(![X]:((tall(X)<~>~wise(X))=>(quiet(X)|old(X))))&
(![X]:((~humble(X)|~kind(X))<=>~patient(X)))&
(?[X]:(generous(X)))&
(?[X]:((strong(X)<~>happy(X))))&
(?[X]:((happy(X)|kind(X))))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:(rich(X)))&
(?[X]:(~tall(X)))&
(?[X]:((~brave(X)&~strong(X))))&
(?[X]:(~strong(X))) | funny(alice) | [] | null | 0 |
If susan is either not wise or not patient then someone is not humble or not curious and vice versa. If alice is not quiet then john is calm or not creative. If someone is calm then susan is either calm or strong. If someone is both generous and tall then mary is not brave and vice versa. If paul is generous or not rich then someone is either patient or funny and vice versa. Everyone who is not tall or not rich is happy. Everyone who is both patient and humble is both old and not strong. If mary is strong then someone is not old and vice versa. Everyone who is both not creative and generous is both old and wise and vice versa. Everyone who is not happy or humble is either old or curious and vice versa. If mary is humble or not curious then someone is both old and not tall and vice versa. Everyone who is both not creative and not tall is both not strong and old and vice versa. Everyone who is creative is both tall and funny. Everyone who is not brave or not happy is curious. Everyone who is both creative and not wise is both not kind and not generous and vice versa. If someone is strong then someone is both not rich and not creative and vice versa. Mary is both quiet and not patient. Lucy is curious or not old. Someone is either humble or not humble. Fred is either kind or not strong. Alice is not brave. Mary is either not tall or kind. Mary is either tall or not rich. John is either strong or humble. | Fred is not creative. | neutral | (((~wise(susan)<~>~patient(susan)))<=>(?[X]:((~humble(X)|~curious(X)))))&
((~quiet(alice))=>((calm(john)|~creative(john))))&
((?[X]:(calm(X)))=>((calm(susan)<~>strong(susan))))&
((?[X]:((generous(X)&tall(X))))<=>(~brave(mary)))&
(((generous(paul)|~rich(paul)))<=>(?[X]:((patient(X)<~>funny(X)))))&
(![X]:((~tall(X)|~rich(X))=>happy(X)))&
(![X]:((patient(X)&humble(X))=>(old(X)&~strong(X))))&
((strong(mary))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)&generous(X))<=>(old(X)&wise(X))))&
(![X]:((~happy(X)|humble(X))<=>(old(X)<~>curious(X))))&
(((humble(mary)|~curious(mary)))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((~creative(X)&~tall(X))<=>(~strong(X)&old(X))))&
(![X]:(creative(X)=>(tall(X)&funny(X))))&
(![X]:((~brave(X)|~happy(X))=>curious(X)))&
(![X]:((creative(X)&~wise(X))<=>(~kind(X)&~generous(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~rich(X)&~creative(X)))))&
((quiet(mary)&~patient(mary)))&
((curious(lucy)|~old(lucy)))&
(?[X]:((humble(X)<~>~humble(X))))&
((kind(fred)<~>~strong(fred)))&
(~brave(alice))&
((~tall(mary)<~>kind(mary)))&
((tall(mary)<~>~rich(mary)))&
((strong(john)<~>humble(john))) | ~creative(fred) | [] | null | 0 |
If someone is either tall or calm then susan is either happy or not kind.
If fred is either not quiet or strong then someone is not wise or not funny.
Everyone who is both not funny and quiet is not quiet and vice versa.
If alice is old then someone is not wise or not kind and vice versa.
Everyone who is not happy is not rich.
If someone is not patient then someone is not funny or generous.
Everyone who is not generous is generous or happy and vice versa.
Everyone who is both rich and not humble is both funny and quiet.
If someone is both funny and not calm then someone is both not patient and old.
If someone is not tall or generous then alice is not humble or kind and vice versa.
If paul is humble then someone is happy or not humble.
If paul is not rich then someone is not tall or calm and vice versa.
If someone is both tall and creative then someone is either not rich or not funny.
Everyone who is both old and happy is both rich and brave and vice versa.
If mary is both calm and not happy then someone is either not humble or generous and vice versa.
Someone is old.
Lucy is not calm or not wise.
Paul is both happy and not creative.
John is both humble and not strong.
Paul is not patient or happy.
Mary is either generous or creative.
Paul is either patient or kind. | Paul is old. | contradiction | ((?[X]:((tall(X)<~>calm(X))))=>((happy(susan)<~>~kind(susan))))&
(((~quiet(fred)<~>strong(fred)))=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:((~funny(X)&quiet(X))<=>~quiet(X)))&
((old(alice))<=>(?[X]:((~wise(X)|~kind(X)))))&
(![X]:(~happy(X)=>~rich(X)))&
((?[X]:(~patient(X)))=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:(~generous(X)<=>(generous(X)|happy(X))))&
(![X]:((rich(X)&~humble(X))=>(funny(X)&quiet(X))))&
((?[X]:((funny(X)&~calm(X))))=>(?[X]:((~patient(X)&old(X)))))&
((?[X]:((~tall(X)|generous(X))))<=>((~humble(alice)|kind(alice))))&
((humble(paul))=>(?[X]:((happy(X)|~humble(X)))))&
((~rich(paul))<=>(?[X]:((~tall(X)|calm(X)))))&
((?[X]:((tall(X)&creative(X))))=>(?[X]:((~rich(X)<~>~funny(X)))))&
(![X]:((old(X)&happy(X))<=>(rich(X)&brave(X))))&
(((calm(mary)&~happy(mary)))<=>(?[X]:((~humble(X)<~>generous(X)))))&
(?[X]:(old(X)))&
((~calm(lucy)|~wise(lucy)))&
((happy(paul)&~creative(paul)))&
((humble(john)&~strong(john)))&
((~patient(paul)|happy(paul)))&
((generous(mary)<~>creative(mary)))&
((patient(paul)<~>kind(paul))) | old(paul) | [
"p2",
"p5",
"p6",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5501121644530028550407686
% SZS output start Proof for 5501121644530028550407686
3. ! [X0] : ((quiet(X0) & ~funny(X0)) <=> ~quiet(X0)) [input p2]
6. ? [X0] : ~patient(X0) => ? [X0] : (generous(X0) | ~funny(X0)) [input p5]
7. ! [X0] : (~generous(X0) <=> (happy(X0) | generous(X0))) [input p6]
9. ? [X0] : (~calm(X0) & funny(X0)) => ? [X0] : (old(X0) & ~patient(X0)) [input p8]
12. ~rich(paul) <=> ? [X0] : (calm(X0) | ~tall(X0)) [input p11]
14. ! [X0] : ((happy(X0) & old(X0)) <=> (brave(X0) & rich(X0))) [input p13]
23. old(paul) [input hypothesis]
24. ? [X0] : ~patient(X0) => ? [X1] : (generous(X1) | ~funny(X1)) [rectify 6]
25. ? [X0] : (~calm(X0) & funny(X0)) => ? [X1] : (old(X1) & ~patient(X1)) [rectify 9]
30. ? [X1] : (generous(X1) | ~funny(X1)) | ! [X0] : patient(X0) [ennf transformation 24]
33. ? [X1] : (old(X1) & ~patient(X1)) | ! [X0] : (calm(X0) | ~funny(X0)) [ennf transformation 25]
40. ! [X0] : (((quiet(X0) & ~funny(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) | funny(X0)))) [nnf transformation 3]
41. ! [X0] : (((quiet(X0) & ~funny(X0)) | quiet(X0)) & (~quiet(X0) | ~quiet(X0) | funny(X0))) [flattening 40]
46. ? [X0] : (generous(X0) | ~funny(X0)) | ! [X1] : patient(X1) [rectify 30]
47. ? [X0] : (generous(X0) | ~funny(X0)) => (generous(sK2) | ~funny(sK2)) [choice axiom]
48. (generous(sK2) | ~funny(sK2)) | ! [X1] : patient(X1) [skolemisation 46,47]
49. ! [X0] : ((~generous(X0) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | generous(X0))) [nnf transformation 7]
50. ! [X0] : ((~generous(X0) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | generous(X0))) [flattening 49]
51. ? [X0] : (old(X0) & ~patient(X0)) | ! [X1] : (calm(X1) | ~funny(X1)) [rectify 33]
52. ? [X0] : (old(X0) & ~patient(X0)) => (old(sK3) & ~patient(sK3)) [choice axiom]
53. (old(sK3) & ~patient(sK3)) | ! [X1] : (calm(X1) | ~funny(X1)) [skolemisation 51,52]
61. (~rich(paul) | ! [X0] : (~calm(X0) & tall(X0))) & (? [X0] : (calm(X0) | ~tall(X0)) | rich(paul)) [nnf transformation 12]
62. (~rich(paul) | ! [X0] : (~calm(X0) & tall(X0))) & (? [X1] : (calm(X1) | ~tall(X1)) | rich(paul)) [rectify 61]
63. ? [X1] : (calm(X1) | ~tall(X1)) => (calm(sK6) | ~tall(sK6)) [choice axiom]
64. (~rich(paul) | ! [X0] : (~calm(X0) & tall(X0))) & ((calm(sK6) | ~tall(sK6)) | rich(paul)) [skolemisation 62,63]
69. ! [X0] : (((happy(X0) & old(X0)) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | (~happy(X0) | ~old(X0)))) [nnf transformation 14]
70. ! [X0] : (((happy(X0) & old(X0)) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ~happy(X0) | ~old(X0))) [flattening 69]
86. ~quiet(X0) | ~quiet(X0) | funny(X0) [cnf transformation 41]
88. quiet(X0) | quiet(X0) [cnf transformation 41]
93. generous(sK2) | ~funny(sK2) | patient(X1) [cnf transformation 48]
94. happy(X0) | generous(X0) | generous(X0) [cnf transformation 50]
95. ~generous(X0) | ~generous(X0) [cnf transformation 50]
99. ~patient(sK3) | calm(X1) | ~funny(X1) [cnf transformation 53]
108. ~rich(paul) | ~calm(X0) [cnf transformation 64]
111. rich(X0) | ~happy(X0) | ~old(X0) [cnf transformation 70]
132. old(paul) [cnf transformation 23]
133. happy(X0) | generous(X0) [duplicate literal removal 94]
134. ~generous(X0) [duplicate literal removal 95]
135. ~quiet(X0) | funny(X0) [duplicate literal removal 86]
136. quiet(X0) [duplicate literal removal 88]
173. funny(X0) [subsumption resolution 135,136]
195. generous(sK2) | patient(X1) [subsumption resolution 93,173]
197. 14 <=> ! [X1] : patient(X1) [avatar definition]
198. patient(X1) <- (14) [avatar component clause 197]
200. 15 <=> generous(sK2) [avatar definition]
202. generous(sK2) <- (15) [avatar component clause 200]
203. 14 | 15 [avatar split clause 195,200,197]
204. happy(X0) [subsumption resolution 133,134]
207. 16 <=> ! [X1] : calm(X1) [avatar definition]
208. calm(X1) <- (16) [avatar component clause 207]
214. ~patient(sK3) | calm(X1) [subsumption resolution 99,173]
216. 18 <=> patient(sK3) [avatar definition]
218. ~patient(sK3) <- (~18) [avatar component clause 216]
219. 16 | ~18 [avatar split clause 214,216,207]
241. 23 <=> ! [X0] : ~calm(X0) [avatar definition]
242. ~calm(X0) <- (23) [avatar component clause 241]
244. 24 <=> rich(paul) [avatar definition]
247. 23 | ~24 [avatar split clause 108,244,241]
268. ~old(X0) | rich(X0) [subsumption resolution 111,204]
297. $false <- (14, ~18) [subsumption resolution 218,198]
298. ~14 | 18 [avatar contradiction clause 297]
299. $false <- (15) [subsumption resolution 202,134]
300. ~15 [avatar contradiction clause 299]
306. rich(paul) [resolution 268,132]
311. 24 [avatar split clause 306,244]
312. $false <- (16, 23) [subsumption resolution 242,208]
313. ~16 | ~23 [avatar contradiction clause 312]
314. $false [avatar sat refutation 203,219,247,298,300,311,313]
% SZS output end Proof for 5501121644530028550407686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and funny is either not rich or patient and vice versa.
Everyone who is either humble or not kind is calm or not generous.
Everyone who is not old is both not wise and not rich and vice versa.
Everyone who is not funny or not curious is not generous or not brave.
If someone is not tall then paul is not calm or not patient and vice versa.
Everyone who is both not wise and not kind is either not happy or not brave and vice versa.
Everyone who is not happy is humble or not creative.
If someone is either happy or not old then someone is not rich and vice versa.
Everyone who is both not brave and kind is either not funny or not kind.
If someone is both quiet and happy then someone is both calm and not strong.
If someone is tall or strong then someone is calm and vice versa.
Everyone who is not humble is both not tall and not brave and vice versa.
If paul is both not kind and not quiet then someone is either not strong or not calm and vice versa.
Everyone who is both not happy and not curious is kind and vice versa.
Everyone who is generous or not rich is either not generous or not kind.
Everyone who is calm is both generous and humble and vice versa.
Fred is both not patient and creative.
Susan is not wise or kind.
Someone is not funny.
Someone is either wise or not strong.
Susan is either not funny or humble.
Someone is either not rich or not creative.
Someone is either not kind or wise.
Someone is not happy. | Fred is not generous. | neutral | (![X]:((rich(X)&funny(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((humble(X)<~>~kind(X))=>(calm(X)|~generous(X))))&
(![X]:(~old(X)<=>(~wise(X)&~rich(X))))&
(![X]:((~funny(X)|~curious(X))=>(~generous(X)|~brave(X))))&
((?[X]:(~tall(X)))<=>((~calm(paul)|~patient(paul))))&
(![X]:((~wise(X)&~kind(X))<=>(~happy(X)<~>~brave(X))))&
(![X]:(~happy(X)=>(humble(X)|~creative(X))))&
((?[X]:((happy(X)<~>~old(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)&kind(X))=>(~funny(X)<~>~kind(X))))&
((?[X]:((quiet(X)&happy(X))))=>(?[X]:((calm(X)&~strong(X)))))&
((?[X]:((tall(X)|strong(X))))<=>(?[X]:(calm(X))))&
(![X]:(~humble(X)<=>(~tall(X)&~brave(X))))&
(((~kind(paul)&~quiet(paul)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((~happy(X)&~curious(X))<=>kind(X)))&
(![X]:((generous(X)|~rich(X))=>(~generous(X)<~>~kind(X))))&
(![X]:(calm(X)<=>(generous(X)&humble(X))))&
((~patient(fred)&creative(fred)))&
((~wise(susan)|kind(susan)))&
(?[X]:(~funny(X)))&
(?[X]:((wise(X)<~>~strong(X))))&
((~funny(susan)<~>humble(susan)))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:((~kind(X)<~>wise(X))))&
(?[X]:(~happy(X))) | ~generous(fred) | [] | null | 0 |
If john is either not curious or not tall then john is both not tall and curious and vice versa. Everyone who is curious or not creative is either not brave or humble and vice versa. Everyone who is patient is both tall and not quiet. Everyone who is both creative and not tall is either not quiet or brave. If paul is wise then someone is not calm and vice versa. Everyone who is both patient and humble is either not generous or curious and vice versa. Everyone who is generous is tall. If john is both not curious and not rich then someone is not generous or kind and vice versa. Everyone who is both calm and not strong is not quiet. If fred is not generous then someone is both not rich and strong. If fred is both not rich and not strong then someone is either kind or rich and vice versa. Everyone who is both not humble and curious is not old or not funny. Everyone who is not quiet is either funny or kind and vice versa. Everyone who is both not humble and curious is either kind or not funny. Everyone who is old or not brave is either generous or not tall. Mary is not humble. Paul is either not quiet or curious. Someone is funny or not generous. Someone is both not humble and generous. Susan is not old. Someone is both happy and generous. Someone is either calm or happy. Someone is creative or old. | Paul is kind. | contradiction | (((~curious(john)<~>~tall(john)))<=>((~tall(john)&curious(john))))&
(![X]:((curious(X)|~creative(X))<=>(~brave(X)<~>humble(X))))&
(![X]:(patient(X)=>(tall(X)&~quiet(X))))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)<~>brave(X))))&
((wise(paul))<=>(?[X]:(~calm(X))))&
(![X]:((patient(X)&humble(X))<=>(~generous(X)<~>curious(X))))&
(![X]:(generous(X)=>tall(X)))&
(((~curious(john)&~rich(john)))<=>(?[X]:((~generous(X)|kind(X)))))&
(![X]:((calm(X)&~strong(X))=>~quiet(X)))&
((~generous(fred))=>(?[X]:((~rich(X)&strong(X)))))&
(((~rich(fred)&~strong(fred)))<=>(?[X]:((kind(X)<~>rich(X)))))&
(![X]:((~humble(X)&curious(X))=>(~old(X)|~funny(X))))&
(![X]:(~quiet(X)<=>(funny(X)<~>kind(X))))&
(![X]:((~humble(X)&curious(X))=>(kind(X)<~>~funny(X))))&
(![X]:((old(X)|~brave(X))=>(generous(X)<~>~tall(X))))&
(~humble(mary))&
((~quiet(paul)<~>curious(paul)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((~humble(X)&generous(X))))&
(~old(susan))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((creative(X)|old(X)))) | kind(paul) | [
"p0",
"p2",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2579059034060531263484008
% SZS output start Proof for 2579059034060531263484008
1. (~curious(john) <~> ~tall(john)) <=> (curious(john) & ~tall(john)) [input p0]
3. ! [X0] : (patient(X0) => (~quiet(X0) & tall(X0))) [input p2]
6. ! [X0] : ((humble(X0) & patient(X0)) <=> (~generous(X0) <~> curious(X0))) [input p5]
7. ! [X0] : (generous(X0) => tall(X0)) [input p6]
8. (~rich(john) & ~curious(john)) <=> ? [X0] : (kind(X0) | ~generous(X0)) [input p7]
24. kind(paul) [input hypothesis]
25. ! [X0] : ((~quiet(X0) & tall(X0)) | ~patient(X0)) [ennf transformation 3]
28. ! [X0] : (tall(X0) | ~generous(X0)) [ennf transformation 7]
37. (((tall(john) | curious(john)) & (~tall(john) | ~curious(john))) | (~curious(john) | tall(john))) & ((curious(john) & ~tall(john)) | ((~curious(john) | tall(john)) & (~tall(john) | curious(john)))) [nnf transformation 1]
38. (((tall(john) | curious(john)) & (~tall(john) | ~curious(john))) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ((~curious(john) | tall(john)) & (~tall(john) | curious(john)))) [flattening 37]
46. ! [X0] : (((humble(X0) & patient(X0)) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) & (((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | (~humble(X0) | ~patient(X0)))) [nnf transformation 6]
47. ! [X0] : (((humble(X0) & patient(X0)) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) & (((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | ~humble(X0) | ~patient(X0))) [flattening 46]
48. ((~rich(john) & ~curious(john)) | ! [X0] : (~kind(X0) & generous(X0))) & (? [X0] : (kind(X0) | ~generous(X0)) | (rich(john) | curious(john))) [nnf transformation 8]
49. ((~rich(john) & ~curious(john)) | ! [X0] : (~kind(X0) & generous(X0))) & (? [X0] : (kind(X0) | ~generous(X0)) | rich(john) | curious(john)) [flattening 48]
50. ((~rich(john) & ~curious(john)) | ! [X0] : (~kind(X0) & generous(X0))) & (? [X1] : (kind(X1) | ~generous(X1)) | rich(john) | curious(john)) [rectify 49]
51. ? [X1] : (kind(X1) | ~generous(X1)) => (kind(sK1) | ~generous(sK1)) [choice axiom]
52. ((~rich(john) & ~curious(john)) | ! [X0] : (~kind(X0) & generous(X0))) & ((kind(sK1) | ~generous(sK1)) | rich(john) | curious(john)) [skolemisation 50,51]
75. ~tall(john) | ~tall(john) | curious(john) [cnf transformation 38]
87. ~patient(X0) | tall(X0) [cnf transformation 25]
95. generous(X0) | curious(X0) | patient(X0) [cnf transformation 47]
99. ~generous(X0) | tall(X0) [cnf transformation 28]
102. ~curious(john) | ~kind(X0) [cnf transformation 52]
137. kind(paul) [cnf transformation 24]
138. ~tall(john) | curious(john) [duplicate literal removal 75]
143. 1 <=> tall(john) [avatar definition]
145. ~tall(john) <- (~1) [avatar component clause 143]
147. 2 <=> curious(john) [avatar definition]
148. ~curious(john) <- (~2) [avatar component clause 147]
151. 2 | ~1 [avatar split clause 138,143,147]
166. 6 <=> ! [X0] : ~kind(X0) [avatar definition]
167. ~kind(X0) <- (6) [avatar component clause 166]
177. 6 | ~2 [avatar split clause 102,147,166]
275. curious(X0) | patient(X0) | tall(X0) [resolution 95,99]
294. tall(X0) | curious(X0) [subsumption resolution 275,87]
295. $false <- (6) [resolution 167,137]
296. ~6 [avatar contradiction clause 295]
399. curious(john) <- (~1) [resolution 294,145]
401. $false <- (~1, ~2) [subsumption resolution 399,148]
402. 1 | 2 [avatar contradiction clause 401]
403. $false [avatar sat refutation 151,177,296,402]
% SZS output end Proof for 2579059034060531263484008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or strong is patient or not generous.
Everyone who is both humble and wise is either not funny or not calm.
Everyone who is not kind or old is either not calm or patient.
If someone is either not strong or wise then someone is rich and vice versa.
Everyone who is quiet is calm or not humble and vice versa.
Everyone who is not funny is not brave or not old and vice versa.
Everyone who is either not brave or brave is not wise and vice versa.
If fred is humble then someone is both strong and old and vice versa.
Everyone who is not curious is creative or not curious.
Everyone who is either funny or not old is either not brave or humble and vice versa.
Everyone who is both not old and not calm is either not curious or not strong.
If someone is both not old and happy then alice is not funny or not tall and vice versa.
If someone is either not humble or not wise then someone is funny and vice versa.
If someone is both not humble and not quiet then someone is either not creative or funny and vice versa.
If alice is both not creative and not strong then mary is old or strong.
Everyone who is not old is not wise and vice versa.
Someone is both not curious and kind.
Someone is not strong.
Someone is both not humble and not kind.
Someone is wise or not curious.
Someone is happy or patient.
John is curious or rich.
Alice is not strong or not kind. | John is not quiet. | contradiction | (![X]:((old(X)<~>strong(X))=>(patient(X)|~generous(X))))&
(![X]:((humble(X)&wise(X))=>(~funny(X)<~>~calm(X))))&
(![X]:((~kind(X)|old(X))=>(~calm(X)<~>patient(X))))&
((?[X]:((~strong(X)<~>wise(X))))<=>(?[X]:(rich(X))))&
(![X]:(quiet(X)<=>(calm(X)|~humble(X))))&
(![X]:(~funny(X)<=>(~brave(X)|~old(X))))&
(![X]:((~brave(X)<~>brave(X))<=>~wise(X)))&
((humble(fred))<=>(?[X]:((strong(X)&old(X)))))&
(![X]:(~curious(X)=>(creative(X)|~curious(X))))&
(![X]:((funny(X)<~>~old(X))<=>(~brave(X)<~>humble(X))))&
(![X]:((~old(X)&~calm(X))=>(~curious(X)<~>~strong(X))))&
((?[X]:((~old(X)&happy(X))))<=>((~funny(alice)|~tall(alice))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~humble(X)&~quiet(X))))<=>(?[X]:((~creative(X)<~>funny(X)))))&
(((~creative(alice)&~strong(alice)))=>((old(mary)|strong(mary))))&
(![X]:(~old(X)<=>~wise(X)))&
(?[X]:((~curious(X)&kind(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~humble(X)&~kind(X))))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((happy(X)|patient(X))))&
((curious(john)|rich(john)))&
((~strong(alice)|~kind(alice))) | ~quiet(john) | [
"p4",
"p5",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3481628623037772460672019
% SZS output start Proof for 3481628623037772460672019
5. ! [X0] : (quiet(X0) <=> (~humble(X0) | calm(X0))) [input p4]
6. ! [X0] : (~funny(X0) <=> (~old(X0) | ~brave(X0))) [input p5]
7. ! [X0] : ((~brave(X0) <~> brave(X0)) <=> ~wise(X0)) [input p6]
13. ? [X0] : (~humble(X0) <~> ~wise(X0)) <=> ? [X0] : funny(X0) [input p12]
16. ! [X0] : (~old(X0) <=> ~wise(X0)) [input p15]
24. ~quiet(john) [input hypothesis]
26. ? [X0] : (~humble(X0) <~> ~wise(X0)) <=> ? [X1] : funny(X1) [rectify 13]
45. ! [X0] : ((quiet(X0) | (humble(X0) & ~calm(X0))) & ((~humble(X0) | calm(X0)) | ~quiet(X0))) [nnf transformation 5]
46. ! [X0] : ((quiet(X0) | (humble(X0) & ~calm(X0))) & (~humble(X0) | calm(X0) | ~quiet(X0))) [flattening 45]
47. ! [X0] : ((~funny(X0) | (old(X0) & brave(X0))) & ((~old(X0) | ~brave(X0)) | funny(X0))) [nnf transformation 6]
48. ! [X0] : ((~funny(X0) | (old(X0) & brave(X0))) & (~old(X0) | ~brave(X0) | funny(X0))) [flattening 47]
49. ! [X0] : ((((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | wise(X0)) & (~wise(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0))))) [nnf transformation 7]
61. (? [X0] : ((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | ! [X1] : ~funny(X1)) & (? [X1] : funny(X1) | ! [X0] : ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0)))) [nnf transformation 26]
62. (? [X0] : ((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | ! [X1] : ~funny(X1)) & (? [X2] : funny(X2) | ! [X3] : ((~humble(X3) | wise(X3)) & (~wise(X3) | humble(X3)))) [rectify 61]
63. ? [X0] : ((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) => ((wise(sK4) | humble(sK4)) & (~wise(sK4) | ~humble(sK4))) [choice axiom]
64. ? [X2] : funny(X2) => funny(sK5) [choice axiom]
65. (((wise(sK4) | humble(sK4)) & (~wise(sK4) | ~humble(sK4))) | ! [X1] : ~funny(X1)) & (funny(sK5) | ! [X3] : ((~humble(X3) | wise(X3)) & (~wise(X3) | humble(X3)))) [skolemisation 62,64,63]
71. ! [X0] : ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0))) [nnf transformation 16]
94. quiet(X0) | humble(X0) [cnf transformation 46]
97. ~funny(X0) | old(X0) [cnf transformation 48]
98. ~wise(X0) | brave(X0) | brave(X0) [cnf transformation 49]
99. ~wise(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 49]
122. funny(sK5) | ~humble(X3) | wise(X3) [cnf transformation 65]
133. ~old(X0) | wise(X0) [cnf transformation 71]
143. ~quiet(john) [cnf transformation 24]
144. ~wise(X0) | brave(X0) [duplicate literal removal 98]
145. ~wise(X0) | ~brave(X0) [duplicate literal removal 99]
171. ~wise(X0) [subsumption resolution 144,145]
228. funny(sK5) | ~humble(X3) [subsumption resolution 122,171]
230. 18 <=> ! [X3] : ~humble(X3) [avatar definition]
231. ~humble(X3) <- (18) [avatar component clause 230]
233. 19 <=> funny(sK5) [avatar definition]
235. funny(sK5) <- (19) [avatar component clause 233]
236. 18 | 19 [avatar split clause 228,233,230]
272. ~old(X0) [subsumption resolution 133,171]
297. humble(john) [resolution 94,143]
299. $false <- (18) [subsumption resolution 297,231]
300. ~18 [avatar contradiction clause 299]
307. old(sK5) <- (19) [resolution 97,235]
308. $false <- (19) [subsumption resolution 307,272]
309. ~19 [avatar contradiction clause 308]
310. $false [avatar sat refutation 236,300,309]
% SZS output end Proof for 3481628623037772460672019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and old is both not patient and patient.
If someone is not calm or old then someone is either brave or quiet and vice versa.
If someone is both not brave and funny then mary is either wise or kind and vice versa.
If fred is not creative then paul is either not tall or not calm and vice versa.
If someone is creative or not humble then fred is both kind and rich and vice versa.
If someone is old or generous then someone is not happy or generous.
Everyone who is both not curious and curious is not quiet or creative.
If someone is both patient and not kind then someone is either not tall or not funny.
If someone is patient or not generous then susan is either not rich or not strong and vice versa.
Everyone who is quiet is both not old and rich.
If lucy is both not calm and generous then someone is both happy and not humble.
Everyone who is not quiet is both tall and not humble.
Everyone who is both not humble and happy is both patient and humble.
If fred is both not old and not patient then someone is not funny and vice versa.
If someone is not calm or not happy then fred is not patient or funny and vice versa.
If alice is both strong and not strong then someone is both calm and not generous.
Someone is both calm and creative.
Someone is both rich and not calm.
Someone is both generous and tall.
Susan is either rich or not tall.
Someone is not old or rich.
Paul is either not creative or not humble.
Someone is not rich or calm. | Fred is not old. | entailment | (![X]:((kind(X)&old(X))=>(~patient(X)&patient(X))))&
((?[X]:((~calm(X)|old(X))))<=>(?[X]:((brave(X)<~>quiet(X)))))&
((?[X]:((~brave(X)&funny(X))))<=>((wise(mary)<~>kind(mary))))&
((~creative(fred))<=>((~tall(paul)<~>~calm(paul))))&
((?[X]:((creative(X)|~humble(X))))<=>((kind(fred)&rich(fred))))&
((?[X]:((old(X)|generous(X))))=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:((~curious(X)&curious(X))=>(~quiet(X)|creative(X))))&
((?[X]:((patient(X)&~kind(X))))=>(?[X]:((~tall(X)<~>~funny(X)))))&
((?[X]:((patient(X)|~generous(X))))<=>((~rich(susan)<~>~strong(susan))))&
(![X]:(quiet(X)=>(~old(X)&rich(X))))&
(((~calm(lucy)&generous(lucy)))=>(?[X]:((happy(X)&~humble(X)))))&
(![X]:(~quiet(X)=>(tall(X)&~humble(X))))&
(![X]:((~humble(X)&happy(X))=>(patient(X)&humble(X))))&
(((~old(fred)&~patient(fred)))<=>(?[X]:(~funny(X))))&
((?[X]:((~calm(X)|~happy(X))))<=>((~patient(fred)|funny(fred))))&
(((strong(alice)&~strong(alice)))=>(?[X]:((calm(X)&~generous(X)))))&
(?[X]:((calm(X)&creative(X))))&
(?[X]:((rich(X)&~calm(X))))&
(?[X]:((generous(X)&tall(X))))&
((rich(susan)<~>~tall(susan)))&
(?[X]:((~old(X)|rich(X))))&
((~creative(paul)<~>~humble(paul)))&
(?[X]:((~rich(X)|calm(X)))) | ~old(fred) | [
"p0",
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6669870302561974908973942
% SZS output start Proof for 6669870302561974908973942
1. ! [X0] : ((old(X0) & kind(X0)) => (patient(X0) & ~patient(X0))) [input p0]
5. ? [X0] : (~humble(X0) | creative(X0)) <=> (rich(fred) & kind(fred)) [input p4]
17. ? [X0] : (creative(X0) & calm(X0)) [input p16]
24. old(fred) [input hypothesis]
28. ! [X0] : ((patient(X0) & ~patient(X0)) | (~old(X0) | ~kind(X0))) [ennf transformation 1]
29. ! [X0] : ((patient(X0) & ~patient(X0)) | ~old(X0) | ~kind(X0)) [flattening 28]
52. (? [X0] : (~humble(X0) | creative(X0)) | (~rich(fred) | ~kind(fred))) & ((rich(fred) & kind(fred)) | ! [X0] : (humble(X0) & ~creative(X0))) [nnf transformation 5]
53. (? [X0] : (~humble(X0) | creative(X0)) | ~rich(fred) | ~kind(fred)) & ((rich(fred) & kind(fred)) | ! [X0] : (humble(X0) & ~creative(X0))) [flattening 52]
54. (? [X0] : (~humble(X0) | creative(X0)) | ~rich(fred) | ~kind(fred)) & ((rich(fred) & kind(fred)) | ! [X1] : (humble(X1) & ~creative(X1))) [rectify 53]
55. ? [X0] : (~humble(X0) | creative(X0)) => (~humble(sK3) | creative(sK3)) [choice axiom]
56. ((~humble(sK3) | creative(sK3)) | ~rich(fred) | ~kind(fred)) & ((rich(fred) & kind(fred)) | ! [X1] : (humble(X1) & ~creative(X1))) [skolemisation 54,55]
82. ? [X0] : (creative(X0) & calm(X0)) => (creative(sK11) & calm(sK11)) [choice axiom]
83. creative(sK11) & calm(sK11) [skolemisation 17,82]
94. ~patient(X0) | ~old(X0) | ~kind(X0) [cnf transformation 29]
95. patient(X0) | ~old(X0) | ~kind(X0) [cnf transformation 29]
112. kind(fred) | ~creative(X1) [cnf transformation 56]
146. creative(sK11) [cnf transformation 83]
157. old(fred) [cnf transformation 24]
159. ~old(X0) | ~kind(X0) [subsumption resolution 94,95]
236. 17 <=> kind(fred) [avatar definition]
257. 22 <=> ! [X1] : ~creative(X1) [avatar definition]
258. ~creative(X1) <- (22) [avatar component clause 257]
261. 22 | 17 [avatar split clause 112,236,257]
343. 41 <=> old(fred) [avatar definition]
344. old(fred) <- (41) [avatar component clause 343]
405. 41 [avatar split clause 157,343]
414. ~kind(fred) <- (41) [resolution 159,344]
417. ~17 | ~41 [avatar split clause 414,343,236]
423. $false <- (22) [resolution 258,146]
424. ~22 [avatar contradiction clause 423]
425. $false [avatar sat refutation 261,405,417,424]
% SZS output end Proof for 6669870302561974908973942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not generous. If alice is either not rich or brave then someone is either not old or not funny and vice versa. Everyone who is not strong or strong is strong. Everyone who is quiet is patient and vice versa. If paul is either not rich or kind then someone is either creative or not brave and vice versa. Everyone who is old or brave is either humble or patient and vice versa. Everyone who is both wise and kind is either not rich or not tall and vice versa. Everyone who is either not quiet or not funny is both creative and wise. Everyone who is both not old and not humble is either calm or quiet. Everyone who is tall or happy is quiet or not generous. Everyone who is either quiet or not funny is patient or creative and vice versa. Everyone who is not curious is either humble or not calm and vice versa. If mary is both not calm and not wise then fred is not patient or curious and vice versa. If mary is both patient and curious then susan is not rich. Everyone who is humble or tall is not strong or not rich and vice versa. Everyone who is both not quiet and not wise is both not wise and not happy. Someone is either wise or humble. Lucy is not old or brave. Someone is either not creative or kind. Lucy is tall or not strong. Someone is both not kind and humble. Someone is not strong or not brave. Someone is old. | Mary is not calm. | neutral | (![X]:(~quiet(X)=>~generous(X)))&
(((~rich(alice)<~>brave(alice)))<=>(?[X]:((~old(X)<~>~funny(X)))))&
(![X]:((~strong(X)|strong(X))=>strong(X)))&
(![X]:(quiet(X)<=>patient(X)))&
(((~rich(paul)<~>kind(paul)))<=>(?[X]:((creative(X)<~>~brave(X)))))&
(![X]:((old(X)|brave(X))<=>(humble(X)<~>patient(X))))&
(![X]:((wise(X)&kind(X))<=>(~rich(X)<~>~tall(X))))&
(![X]:((~quiet(X)<~>~funny(X))=>(creative(X)&wise(X))))&
(![X]:((~old(X)&~humble(X))=>(calm(X)<~>quiet(X))))&
(![X]:((tall(X)|happy(X))=>(quiet(X)|~generous(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>(patient(X)|creative(X))))&
(![X]:(~curious(X)<=>(humble(X)<~>~calm(X))))&
(((~calm(mary)&~wise(mary)))<=>((~patient(fred)|curious(fred))))&
(((patient(mary)&curious(mary)))=>(~rich(susan)))&
(![X]:((humble(X)|tall(X))<=>(~strong(X)|~rich(X))))&
(![X]:((~quiet(X)&~wise(X))=>(~wise(X)&~happy(X))))&
(?[X]:((wise(X)<~>humble(X))))&
((~old(lucy)|brave(lucy)))&
(?[X]:((~creative(X)<~>kind(X))))&
((tall(lucy)|~strong(lucy)))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((~strong(X)|~brave(X))))&
(?[X]:(old(X))) | ~calm(mary) | [] | null | 0 |
Everyone who is either not humble or old is either creative or curious and vice versa. If john is not patient or not wise then alice is not tall. Everyone who is either happy or rich is both not curious and generous. Everyone who is either kind or not kind is not tall and vice versa. Everyone who is not calm is either calm or not rich. Everyone who is either curious or strong is either not brave or not rich. Everyone who is tall is either strong or not generous. Everyone who is either not brave or wise is not old or not brave and vice versa. Everyone who is both not happy and funny is either not humble or patient. If alice is old then someone is not kind. Everyone who is either quiet or not funny is old or not old and vice versa. If mary is both not wise and happy then alice is either humble or not happy. If john is either strong or not humble then john is both brave and not wise. Everyone who is not funny or not wise is both strong and not wise. Everyone who is both not curious and tall is both brave and not wise and vice versa. Everyone who is both not tall and tall is not wise or not calm and vice versa. Fred is creative. Alice is creative. John is both strong and not tall. Paul is either not old or not humble. | John is not brave. | contradiction | (![X]:((~humble(X)<~>old(X))<=>(creative(X)<~>curious(X))))&
(((~patient(john)|~wise(john)))=>(~tall(alice)))&
(![X]:((happy(X)<~>rich(X))=>(~curious(X)&generous(X))))&
(![X]:((kind(X)<~>~kind(X))<=>~tall(X)))&
(![X]:(~calm(X)=>(calm(X)<~>~rich(X))))&
(![X]:((curious(X)<~>strong(X))=>(~brave(X)<~>~rich(X))))&
(![X]:(tall(X)=>(strong(X)<~>~generous(X))))&
(![X]:((~brave(X)<~>wise(X))<=>(~old(X)|~brave(X))))&
(![X]:((~happy(X)&funny(X))=>(~humble(X)<~>patient(X))))&
((old(alice))=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>(old(X)|~old(X))))&
(((~wise(mary)&happy(mary)))=>((humble(alice)<~>~happy(alice))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(creative(fred))&
(creative(alice))&
((strong(john)&~tall(john)))&
((~old(paul)<~>~humble(paul))) | ~brave(john) | [
"p3",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2147491019328901780609616
% SZS output start Proof for 2147491019328901780609616
4. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> ~tall(X0)) [input p3]
8. ! [X0] : ((~brave(X0) <~> wise(X0)) <=> (~brave(X0) | ~old(X0))) [input p7]
16. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | ~wise(X0))) [input p15]
21. ~brave(john) [input hypothesis]
36. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | tall(X0)) & (~tall(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 4]
40. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (brave(X0) & old(X0))) & ((~brave(X0) | ~old(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [nnf transformation 8]
41. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (brave(X0) & old(X0))) & (~brave(X0) | ~old(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [flattening 40]
51. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 16]
52. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0) | tall(X0))) [flattening 51]
68. ~tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 36]
69. ~tall(X0) | kind(X0) | kind(X0) [cnf transformation 36]
85. ~wise(X0) | brave(X0) | brave(X0) [cnf transformation 41]
112. tall(X0) | wise(X0) [cnf transformation 52]
120. ~brave(john) [cnf transformation 21]
122. ~wise(X0) | brave(X0) [duplicate literal removal 85]
124. ~tall(X0) | ~kind(X0) [duplicate literal removal 68]
125. ~tall(X0) | kind(X0) [duplicate literal removal 69]
140. ~tall(X0) [subsumption resolution 124,125]
182. 12 <=> brave(john) [avatar definition]
183. ~brave(john) <- (~12) [avatar component clause 182]
189. wise(X0) [subsumption resolution 112,140]
201. ~12 [avatar split clause 120,182]
203. brave(X0) [resolution 122,189]
204. $false <- (~12) [resolution 203,183]
205. 12 [avatar contradiction clause 204]
206. $false [avatar sat refutation 201,205]
% SZS output end Proof for 2147491019328901780609616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both funny and generous and vice versa. Everyone who is not brave is not wise or generous and vice versa. Everyone who is curious is either not patient or tall. Everyone who is not strong is either rich or not old and vice versa. If john is both not curious and not humble then someone is not humble and vice versa. Everyone who is not patient or not creative is either not calm or not happy. If someone is patient then someone is either not happy or not calm and vice versa. Everyone who is not calm or kind is either not calm or not wise and vice versa. Everyone who is both strong and not generous is both rich and generous. Everyone who is not rich or not generous is both not calm and generous. Everyone who is not humble is both kind and tall. If someone is both kind and not old then someone is rich or tall. Everyone who is not brave or generous is both not wise and not funny and vice versa. Everyone who is not funny is not strong or not humble and vice versa. Everyone who is calm is old and vice versa. If someone is not quiet then someone is happy. Someone is humble. Lucy is not humble. Someone is either not strong or brave. Someone is both not wise and humble. Someone is not creative or strong. | John is rich. | entailment | (![X]:(happy(X)<=>(funny(X)&generous(X))))&
(![X]:(~brave(X)<=>(~wise(X)|generous(X))))&
(![X]:(curious(X)=>(~patient(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>~old(X))))&
(((~curious(john)&~humble(john)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)|~creative(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((~calm(X)|kind(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~generous(X))=>(rich(X)&generous(X))))&
(![X]:((~rich(X)|~generous(X))=>(~calm(X)&generous(X))))&
(![X]:(~humble(X)=>(kind(X)&tall(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:(~funny(X)<=>(~strong(X)|~humble(X))))&
(![X]:(calm(X)<=>old(X)))&
((?[X]:(~quiet(X)))=>(?[X]:(happy(X))))&
(?[X]:(humble(X)))&
(~humble(lucy))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((~creative(X)|strong(X)))) | rich(john) | [
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 9011784655843324295269498
% SZS output start Proof for 9011784655843324295269498
8. ! [X0] : ((kind(X0) | ~calm(X0)) <=> (~calm(X0) <~> ~wise(X0))) [input p7]
10. ! [X0] : ((~generous(X0) | ~rich(X0)) => (generous(X0) & ~calm(X0))) [input p9]
13. ! [X0] : ((generous(X0) | ~brave(X0)) <=> (~funny(X0) & ~wise(X0))) [input p12]
22. ~rich(john) [input hypothesis]
31. ! [X0] : ((generous(X0) & ~calm(X0)) | (generous(X0) & rich(X0))) [ennf transformation 10]
51. ! [X0] : (((kind(X0) | ~calm(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (~kind(X0) & calm(X0)))) [nnf transformation 8]
52. ! [X0] : ((kind(X0) | ~calm(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (~kind(X0) & calm(X0)))) [flattening 51]
56. ! [X0] : (((generous(X0) | ~brave(X0)) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [nnf transformation 13]
57. ! [X0] : ((generous(X0) | ~brave(X0) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [flattening 56]
95. wise(X0) | calm(X0) | calm(X0) [cnf transformation 52]
101. ~calm(X0) | rich(X0) [cnf transformation 31]
104. generous(X0) | generous(X0) [cnf transformation 31]
109. ~wise(X0) | ~generous(X0) [cnf transformation 57]
125. ~rich(john) [cnf transformation 22]
126. generous(X0) [duplicate literal removal 104]
128. calm(X0) | wise(X0) [duplicate literal removal 95]
186. ~wise(X0) [subsumption resolution 109,126]
217. wise(X1) | rich(X1) [resolution 128,101]
221. rich(X1) [subsumption resolution 217,186]
228. $false [resolution 221,125]
% SZS output end Proof for 9011784655843324295269498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not creative and vice versa.
Everyone who is both not happy and quiet is not rich or old and vice versa.
Everyone who is either happy or quiet is both not old and generous and vice versa.
Everyone who is generous is both creative and quiet and vice versa.
Everyone who is either humble or quiet is funny.
Everyone who is both old and happy is humble or not strong and vice versa.
Everyone who is rich is either not humble or not tall.
If susan is strong then someone is calm.
If mary is calm or not generous then someone is both not rich and tall.
If john is both curious and not generous then someone is not happy or kind.
If fred is rich then someone is both not generous and not happy.
Everyone who is not strong is both not patient and not generous and vice versa.
If someone is not wise then alice is not happy and vice versa.
Everyone who is brave is not happy.
Everyone who is happy is either wise or rich.
Paul is both not kind and tall.
Someone is either not generous or quiet.
Someone is either old or not humble.
John is either not creative or happy.
Susan is either not rich or not kind. | Mary is not quiet. | contradiction | (![X]:(tall(X)<=>~creative(X)))&
(![X]:((~happy(X)&quiet(X))<=>(~rich(X)|old(X))))&
(![X]:((happy(X)<~>quiet(X))<=>(~old(X)&generous(X))))&
(![X]:(generous(X)<=>(creative(X)&quiet(X))))&
(![X]:((humble(X)<~>quiet(X))=>funny(X)))&
(![X]:((old(X)&happy(X))<=>(humble(X)|~strong(X))))&
(![X]:(rich(X)=>(~humble(X)<~>~tall(X))))&
((strong(susan))=>(?[X]:(calm(X))))&
(((calm(mary)|~generous(mary)))=>(?[X]:((~rich(X)&tall(X)))))&
(((curious(john)&~generous(john)))=>(?[X]:((~happy(X)|kind(X)))))&
((rich(fred))=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:(~strong(X)<=>(~patient(X)&~generous(X))))&
((?[X]:(~wise(X)))<=>(~happy(alice)))&
(![X]:(brave(X)=>~happy(X)))&
(![X]:(happy(X)=>(wise(X)<~>rich(X))))&
((~kind(paul)&tall(paul)))&
(?[X]:((~generous(X)<~>quiet(X))))&
(?[X]:((old(X)<~>~humble(X))))&
((~creative(john)<~>happy(john)))&
((~rich(susan)<~>~kind(susan))) | ~quiet(mary) | [
"p0",
"p1",
"p2",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1020493799662962315918015
% SZS output start Proof for 1020493799662962315918015
1. ! [X0] : (tall(X0) <=> ~creative(X0)) [input p0]
2. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (old(X0) | ~rich(X0))) [input p1]
3. ! [X0] : ((happy(X0) <~> quiet(X0)) <=> (generous(X0) & ~old(X0))) [input p2]
4. ! [X0] : (generous(X0) <=> (quiet(X0) & creative(X0))) [input p3]
9. (~generous(mary) | calm(mary)) => ? [X0] : (tall(X0) & ~rich(X0)) [input p8]
21. ~quiet(mary) [input hypothesis]
27. ? [X0] : (tall(X0) & ~rich(X0)) | (generous(mary) & ~calm(mary)) [ennf transformation 9]
30. ! [X0] : ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))) [nnf transformation 1]
31. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | (~quiet(X0) | happy(X0)))) [nnf transformation 2]
32. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | ~quiet(X0) | happy(X0))) [flattening 31]
33. ! [X0] : ((((~quiet(X0) | ~happy(X0)) & (quiet(X0) | happy(X0))) | (~generous(X0) | old(X0))) & ((generous(X0) & ~old(X0)) | ((happy(X0) | ~quiet(X0)) & (quiet(X0) | ~happy(X0))))) [nnf transformation 3]
34. ! [X0] : ((((~quiet(X0) | ~happy(X0)) & (quiet(X0) | happy(X0))) | ~generous(X0) | old(X0)) & ((generous(X0) & ~old(X0)) | ((happy(X0) | ~quiet(X0)) & (quiet(X0) | ~happy(X0))))) [flattening 33]
35. ! [X0] : ((generous(X0) | (~quiet(X0) | ~creative(X0))) & ((quiet(X0) & creative(X0)) | ~generous(X0))) [nnf transformation 4]
36. ! [X0] : ((generous(X0) | ~quiet(X0) | ~creative(X0)) & ((quiet(X0) & creative(X0)) | ~generous(X0))) [flattening 35]
42. ? [X0] : (tall(X0) & ~rich(X0)) => (tall(sK1) & ~rich(sK1)) [choice axiom]
43. (tall(sK1) & ~rich(sK1)) | (generous(mary) & ~calm(mary)) [skolemisation 27,42]
61. ~creative(X0) | ~tall(X0) [cnf transformation 30]
64. ~happy(X0) | rich(X0) [cnf transformation 32]
66. rich(X0) | quiet(X0) [cnf transformation 32]
71. ~quiet(X0) | happy(X0) | generous(X0) [cnf transformation 34]
74. ~generous(X0) | creative(X0) [cnf transformation 36]
75. ~generous(X0) | quiet(X0) [cnf transformation 36]
86. ~rich(sK1) | generous(mary) [cnf transformation 43]
88. tall(sK1) | generous(mary) [cnf transformation 43]
108. ~quiet(mary) [cnf transformation 21]
118. 1 <=> generous(mary) [avatar definition]
120. generous(mary) <- (1) [avatar component clause 118]
122. 2 <=> tall(sK1) [avatar definition]
124. tall(sK1) <- (2) [avatar component clause 122]
125. 1 | 2 [avatar split clause 88,122,118]
132. 4 <=> rich(sK1) [avatar definition]
134. ~rich(sK1) <- (~4) [avatar component clause 132]
135. 1 | ~4 [avatar split clause 86,132,118]
207. 17 <=> generous(sK1) [avatar definition]
209. generous(sK1) <- (17) [avatar component clause 207]
211. 18 <=> happy(sK1) [avatar definition]
213. happy(sK1) <- (18) [avatar component clause 211]
224. quiet(mary) <- (1) [resolution 120,75]
226. $false <- (1) [subsumption resolution 224,108]
227. ~1 [avatar contradiction clause 226]
228. quiet(sK1) <- (~4) [resolution 134,66]
233. happy(sK1) | generous(sK1) <- (~4) [resolution 228,71]
258. creative(sK1) <- (17) [resolution 209,74]
261. ~tall(sK1) <- (17) [resolution 258,61]
262. $false <- (2, 17) [subsumption resolution 261,124]
263. ~2 | ~17 [avatar contradiction clause 262]
264. 17 | 18 | 4 [avatar split clause 233,132,211,207]
271. rich(sK1) <- (18) [resolution 213,64]
272. $false <- (~4, 18) [subsumption resolution 271,134]
273. 4 | ~18 [avatar contradiction clause 272]
274. $false [avatar sat refutation 125,135,227,263,264,273]
% SZS output end Proof for 1020493799662962315918015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or funny is not strong or tall and vice versa. If someone is either strong or not brave then paul is not generous or not kind and vice versa. Everyone who is not patient or not creative is both generous and not generous. Everyone who is either not creative or not generous is not rich and vice versa. Everyone who is curious or creative is both not curious and wise and vice versa. If someone is quiet then someone is not patient or wise. Everyone who is both not strong and strong is tall and vice versa. If someone is both curious and wise then someone is not wise. Everyone who is quiet is strong. Everyone who is humble or not humble is creative. Everyone who is either not curious or not funny is both not quiet and old. Everyone who is either tall or creative is both calm and wise. Everyone who is generous or not quiet is not quiet or kind. Everyone who is both not old and calm is both not curious and not funny and vice versa. Everyone who is tall is strong or old and vice versa. Everyone who is both generous and kind is either not creative or not wise and vice versa. Fred is not tall. Someone is not funny or quiet. Susan is either not tall or strong. Fred is not happy. | Paul is not funny. | entailment | (![X]:((~happy(X)<~>funny(X))<=>(~strong(X)|tall(X))))&
((?[X]:((strong(X)<~>~brave(X))))<=>((~generous(paul)|~kind(paul))))&
(![X]:((~patient(X)|~creative(X))=>(generous(X)&~generous(X))))&
(![X]:((~creative(X)<~>~generous(X))<=>~rich(X)))&
(![X]:((curious(X)|creative(X))<=>(~curious(X)&wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((~strong(X)&strong(X))<=>tall(X)))&
((?[X]:((curious(X)&wise(X))))=>(?[X]:(~wise(X))))&
(![X]:(quiet(X)=>strong(X)))&
(![X]:((humble(X)|~humble(X))=>creative(X)))&
(![X]:((~curious(X)<~>~funny(X))=>(~quiet(X)&old(X))))&
(![X]:((tall(X)<~>creative(X))=>(calm(X)&wise(X))))&
(![X]:((generous(X)|~quiet(X))=>(~quiet(X)|kind(X))))&
(![X]:((~old(X)&calm(X))<=>(~curious(X)&~funny(X))))&
(![X]:(tall(X)<=>(strong(X)|old(X))))&
(![X]:((generous(X)&kind(X))<=>(~creative(X)<~>~wise(X))))&
(~tall(fred))&
(?[X]:((~funny(X)|quiet(X))))&
((~tall(susan)<~>strong(susan)))&
(~happy(fred)) | ~funny(paul) | [
"p2",
"p4",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3495459431838255854220257
% SZS output start Proof for 3495459431838255854220257
3. ! [X0] : ((~creative(X0) | ~patient(X0)) => (~generous(X0) & generous(X0))) [input p2]
5. ! [X0] : ((creative(X0) | curious(X0)) <=> (wise(X0) & ~curious(X0))) [input p4]
7. ! [X0] : ((strong(X0) & ~strong(X0)) <=> tall(X0)) [input p6]
11. ! [X0] : ((~curious(X0) <~> ~funny(X0)) => (old(X0) & ~quiet(X0))) [input p10]
15. ! [X0] : (tall(X0) <=> (old(X0) | strong(X0))) [input p14]
21. funny(paul) [input hypothesis]
24. ! [X0] : ((~generous(X0) & generous(X0)) | (creative(X0) & patient(X0))) [ennf transformation 3]
29. ! [X0] : ((old(X0) & ~quiet(X0)) | (~curious(X0) <=> ~funny(X0))) [ennf transformation 11]
40. ! [X0] : (((creative(X0) | curious(X0)) | (~wise(X0) | curious(X0))) & ((wise(X0) & ~curious(X0)) | (~creative(X0) & ~curious(X0)))) [nnf transformation 5]
41. ! [X0] : ((creative(X0) | curious(X0) | ~wise(X0) | curious(X0)) & ((wise(X0) & ~curious(X0)) | (~creative(X0) & ~curious(X0)))) [flattening 40]
45. ! [X0] : (((strong(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | (~strong(X0) | strong(X0)))) [nnf transformation 7]
46. ! [X0] : (((strong(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | ~strong(X0) | strong(X0))) [flattening 45]
50. ! [X0] : ((old(X0) & ~quiet(X0)) | ((~curious(X0) | funny(X0)) & (~funny(X0) | curious(X0)))) [nnf transformation 29]
54. ! [X0] : ((tall(X0) | (~old(X0) & ~strong(X0))) & ((old(X0) | strong(X0)) | ~tall(X0))) [nnf transformation 15]
55. ! [X0] : ((tall(X0) | (~old(X0) & ~strong(X0))) & (old(X0) | strong(X0) | ~tall(X0))) [flattening 54]
74. generous(X0) | creative(X0) [cnf transformation 24]
76. ~generous(X0) | creative(X0) [cnf transformation 24]
78. ~curious(X0) | ~creative(X0) [cnf transformation 41]
84. ~strong(X0) | ~tall(X0) [cnf transformation 46]
85. ~tall(X0) | strong(X0) [cnf transformation 46]
92. old(X0) | ~funny(X0) | curious(X0) [cnf transformation 50]
106. tall(X0) | ~old(X0) [cnf transformation 55]
118. funny(paul) [cnf transformation 21]
149. creative(X0) [subsumption resolution 74,76]
152. ~curious(X0) [subsumption resolution 78,149]
153. ~tall(X0) [subsumption resolution 84,85]
154. ~funny(X0) | old(X0) [subsumption resolution 92,152]
159. ~old(X0) [subsumption resolution 106,153]
164. old(paul) [resolution 154,118]
165. $false [subsumption resolution 164,159]
% SZS output end Proof for 3495459431838255854220257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not rich is calm or creative and vice versa. If someone is either quiet or not old then paul is both calm and wise and vice versa. Everyone who is tall or calm is either strong or not humble and vice versa. Everyone who is both tall and brave is tall. If someone is not funny then someone is either not wise or calm and vice versa. Everyone who is curious or not wise is strong or generous. If susan is funny then paul is not humble or not creative. Everyone who is both tall and not humble is either strong or humble. If john is both tall and not happy then john is not happy. If someone is both brave and not brave then fred is kind. Everyone who is either not patient or not humble is creative or not happy and vice versa. If paul is either tall or not rich then someone is not humble. If someone is funny then someone is old or quiet. Everyone who is both not brave and not old is both not old and creative and vice versa. Everyone who is both not old and not happy is humble and vice versa. Everyone who is both not calm and creative is either creative or wise and vice versa. Someone is tall or generous. Alice is rich. Paul is either not curious or not quiet. Someone is either not humble or not wise. Paul is both curious and not old. Someone is not kind. Someone is brave. | Susan is funny. | contradiction | (![X]:((strong(X)&~rich(X))<=>(calm(X)|creative(X))))&
((?[X]:((quiet(X)<~>~old(X))))<=>((calm(paul)&wise(paul))))&
(![X]:((tall(X)|calm(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((tall(X)&brave(X))=>tall(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:((curious(X)|~wise(X))=>(strong(X)|generous(X))))&
((funny(susan))=>((~humble(paul)|~creative(paul))))&
(![X]:((tall(X)&~humble(X))=>(strong(X)<~>humble(X))))&
(((tall(john)&~happy(john)))=>(~happy(john)))&
((?[X]:((brave(X)&~brave(X))))=>(kind(fred)))&
(![X]:((~patient(X)<~>~humble(X))<=>(creative(X)|~happy(X))))&
(((tall(paul)<~>~rich(paul)))=>(?[X]:(~humble(X))))&
((?[X]:(funny(X)))=>(?[X]:((old(X)|quiet(X)))))&
(![X]:((~brave(X)&~old(X))<=>(~old(X)&creative(X))))&
(![X]:((~old(X)&~happy(X))<=>humble(X)))&
(![X]:((~calm(X)&creative(X))<=>(creative(X)<~>wise(X))))&
(?[X]:((tall(X)|generous(X))))&
(rich(alice))&
((~curious(paul)<~>~quiet(paul)))&
(?[X]:((~humble(X)<~>~wise(X))))&
((curious(paul)&~old(paul)))&
(?[X]:(~kind(X)))&
(?[X]:(brave(X))) | funny(susan) | [
"p0",
"p1",
"p2",
"p6",
"p15",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1828308848236733918674508
% SZS output start Proof for 1828308848236733918674508
1. ! [X0] : ((~rich(X0) & strong(X0)) <=> (creative(X0) | calm(X0))) [input p0]
2. ? [X0] : (quiet(X0) <~> ~old(X0)) <=> (wise(paul) & calm(paul)) [input p1]
3. ! [X0] : ((calm(X0) | tall(X0)) <=> (strong(X0) <~> ~humble(X0))) [input p2]
7. funny(susan) => (~creative(paul) | ~humble(paul)) [input p6]
16. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (creative(X0) <~> wise(X0))) [input p15]
19. ~curious(paul) <~> ~quiet(paul) [input p18]
21. ~old(paul) & curious(paul) [input p20]
24. funny(susan) [input hypothesis]
31. (~creative(paul) | ~humble(paul)) | ~funny(susan) [ennf transformation 7]
32. ~creative(paul) | ~humble(paul) | ~funny(susan) [flattening 31]
40. ! [X0] : (((~rich(X0) & strong(X0)) | (~creative(X0) & ~calm(X0))) & ((creative(X0) | calm(X0)) | (rich(X0) | ~strong(X0)))) [nnf transformation 1]
41. ! [X0] : (((~rich(X0) & strong(X0)) | (~creative(X0) & ~calm(X0))) & (creative(X0) | calm(X0) | rich(X0) | ~strong(X0))) [flattening 40]
42. (? [X0] : ((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | (~wise(paul) | ~calm(paul))) & ((wise(paul) & calm(paul)) | ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) [nnf transformation 2]
43. (? [X0] : ((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ~wise(paul) | ~calm(paul)) & ((wise(paul) & calm(paul)) | ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) [flattening 42]
44. (? [X0] : ((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ~wise(paul) | ~calm(paul)) & ((wise(paul) & calm(paul)) | ! [X1] : ((quiet(X1) | old(X1)) & (~old(X1) | ~quiet(X1)))) [rectify 43]
45. ? [X0] : ((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) => ((old(sK0) | ~quiet(sK0)) & (~old(sK0) | quiet(sK0))) [choice axiom]
46. (((old(sK0) | ~quiet(sK0)) & (~old(sK0) | quiet(sK0))) | ~wise(paul) | ~calm(paul)) & ((wise(paul) & calm(paul)) | ! [X1] : ((quiet(X1) | old(X1)) & (~old(X1) | ~quiet(X1)))) [skolemisation 44,45]
47. ! [X0] : (((calm(X0) | tall(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~calm(X0) & ~tall(X0)))) [nnf transformation 3]
48. ! [X0] : ((calm(X0) | tall(X0) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~calm(X0) & ~tall(X0)))) [flattening 47]
67. ! [X0] : (((creative(X0) & ~calm(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~creative(X0) | calm(X0)))) [nnf transformation 16]
68. ! [X0] : (((creative(X0) & ~calm(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | ~creative(X0) | calm(X0))) [flattening 67]
69. (quiet(paul) | curious(paul)) & (~quiet(paul) | ~curious(paul)) [nnf transformation 19]
78. ~calm(X0) | strong(X0) [cnf transformation 41]
83. calm(paul) | quiet(X1) | old(X1) [cnf transformation 46]
85. wise(paul) | quiet(X1) | old(X1) [cnf transformation 46]
91. humble(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 48]
99. ~creative(paul) | ~humble(paul) | ~funny(susan) [cnf transformation 32]
125. creative(X0) | creative(X0) | ~wise(X0) [cnf transformation 68]
127. ~quiet(paul) | ~curious(paul) [cnf transformation 69]
131. curious(paul) [cnf transformation 21]
132. ~old(paul) [cnf transformation 21]
135. funny(susan) [cnf transformation 24]
137. ~wise(X0) | creative(X0) [duplicate literal removal 125]
140. 1 <=> calm(paul) [avatar definition]
141. calm(paul) <- (1) [avatar component clause 140]
144. 2 <=> wise(paul) [avatar definition]
145. wise(paul) <- (2) [avatar component clause 144]
158. 5 <=> ! [X1] : (quiet(X1) | old(X1)) [avatar definition]
159. old(X1) | quiet(X1) <- (5) [avatar component clause 158]
160. 5 | 2 [avatar split clause 85,144,158]
165. 5 | 1 [avatar split clause 83,140,158]
168. ~calm(X0) | humble(X0) [subsumption resolution 91,78]
195. 13 <=> funny(susan) [avatar definition]
199. 14 <=> humble(paul) [avatar definition]
201. ~humble(paul) <- (~14) [avatar component clause 199]
203. 15 <=> creative(paul) [avatar definition]
206. ~13 | ~14 | ~15 [avatar split clause 99,203,199,195]
236. 22 <=> curious(paul) [avatar definition]
240. 23 <=> quiet(paul) [avatar definition]
241. ~quiet(paul) <- (~23) [avatar component clause 240]
244. ~22 | ~23 [avatar split clause 127,240,236]
255. 22 [avatar split clause 131,236]
256. 13 [avatar split clause 135,195]
260. quiet(paul) <- (5) [resolution 159,132]
262. $false <- (5, ~23) [subsumption resolution 260,241]
263. ~5 | 23 [avatar contradiction clause 262]
267. creative(paul) <- (2) [resolution 145,137]
270. 15 | ~2 [avatar split clause 267,144,203]
275. humble(paul) <- (1) [resolution 168,141]
276. $false <- (1, ~14) [subsumption resolution 275,201]
277. ~1 | 14 [avatar contradiction clause 276]
278. $false [avatar sat refutation 160,165,206,244,255,256,263,270,277]
% SZS output end Proof for 1828308848236733918674508
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both wise and not generous then someone is rich or not rich.
Everyone who is wise is not creative and vice versa.
If someone is both not humble and tall then someone is strong or not wise and vice versa.
If susan is creative then lucy is patient or not calm and vice versa.
Everyone who is either not patient or creative is humble and vice versa.
Everyone who is not calm is both humble and not curious.
Everyone who is not quiet is happy or old and vice versa.
If alice is old then someone is either creative or not tall.
Everyone who is brave or generous is both not generous and not quiet.
Everyone who is either brave or kind is either not kind or not curious and vice versa.
Everyone who is either not brave or not tall is both quiet and not happy and vice versa.
If someone is both kind and patient then susan is either tall or patient.
If john is either not creative or not kind then someone is either creative or not calm and vice versa.
If paul is both wise and calm then someone is tall or not wise.
Everyone who is not calm is either not happy or wise and vice versa.
If susan is quiet then someone is not humble or quiet.
Someone is humble.
Someone is not calm or not patient.
Someone is curious.
Someone is old or not happy.
Someone is both not patient and not strong.
Someone is both not tall and not rich.
Alice is not happy.
Paul is both not brave and funny. | Susan is quiet. | neutral | ((?[X]:((wise(X)&~generous(X))))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:(wise(X)<=>~creative(X)))&
((?[X]:((~humble(X)&tall(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
((creative(susan))<=>((patient(lucy)|~calm(lucy))))&
(![X]:((~patient(X)<~>creative(X))<=>humble(X)))&
(![X]:(~calm(X)=>(humble(X)&~curious(X))))&
(![X]:(~quiet(X)<=>(happy(X)|old(X))))&
((old(alice))=>(?[X]:((creative(X)<~>~tall(X)))))&
(![X]:((brave(X)|generous(X))=>(~generous(X)&~quiet(X))))&
(![X]:((brave(X)<~>kind(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:((~brave(X)<~>~tall(X))<=>(quiet(X)&~happy(X))))&
((?[X]:((kind(X)&patient(X))))=>((tall(susan)<~>patient(susan))))&
(((~creative(john)<~>~kind(john)))<=>(?[X]:((creative(X)<~>~calm(X)))))&
(((wise(paul)&calm(paul)))=>(?[X]:((tall(X)|~wise(X)))))&
(![X]:(~calm(X)<=>(~happy(X)<~>wise(X))))&
((quiet(susan))=>(?[X]:((~humble(X)|quiet(X)))))&
(?[X]:(humble(X)))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:(curious(X)))&
(?[X]:((old(X)|~happy(X))))&
(?[X]:((~patient(X)&~strong(X))))&
(?[X]:((~tall(X)&~rich(X))))&
(~happy(alice))&
((~brave(paul)&funny(paul))) | quiet(susan) | [] | null | 0 |
Everyone who is kind or generous is either not brave or not happy and vice versa.
If someone is funny then lucy is generous.
Everyone who is not generous or creative is not funny and vice versa.
If susan is either brave or not strong then john is both patient and tall and vice versa.
If someone is generous or brave then someone is not brave.
Everyone who is both old and not strong is not funny or strong and vice versa.
Everyone who is both not old and wise is strong.
Everyone who is both tall and humble is either not curious or not brave and vice versa.
Everyone who is not happy or tall is not humble or not wise and vice versa.
Everyone who is both not tall and not calm is old and vice versa.
If paul is either not curious or not humble then john is not brave or quiet.
Everyone who is both not rich and not kind is both funny and kind and vice versa.
Everyone who is generous is either not strong or happy and vice versa.
Everyone who is patient is both curious and funny.
Everyone who is both not calm and old is quiet and vice versa.
Someone is either not patient or not happy.
Someone is tall.
Fred is either not humble or patient.
Someone is not brave or humble.
Someone is happy or not humble.
Lucy is not wise or not rich.
Someone is either quiet or generous.
Someone is patient. | Lucy is not funny. | neutral | (![X]:((kind(X)|generous(X))<=>(~brave(X)<~>~happy(X))))&
((?[X]:(funny(X)))=>(generous(lucy)))&
(![X]:((~generous(X)|creative(X))<=>~funny(X)))&
(((brave(susan)<~>~strong(susan)))<=>((patient(john)&tall(john))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:(~brave(X))))&
(![X]:((old(X)&~strong(X))<=>(~funny(X)|strong(X))))&
(![X]:((~old(X)&wise(X))=>strong(X)))&
(![X]:((tall(X)&humble(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((~happy(X)|tall(X))<=>(~humble(X)|~wise(X))))&
(![X]:((~tall(X)&~calm(X))<=>old(X)))&
(((~curious(paul)<~>~humble(paul)))=>((~brave(john)|quiet(john))))&
(![X]:((~rich(X)&~kind(X))<=>(funny(X)&kind(X))))&
(![X]:(generous(X)<=>(~strong(X)<~>happy(X))))&
(![X]:(patient(X)=>(curious(X)&funny(X))))&
(![X]:((~calm(X)&old(X))<=>quiet(X)))&
(?[X]:((~patient(X)<~>~happy(X))))&
(?[X]:(tall(X)))&
((~humble(fred)<~>patient(fred)))&
(?[X]:((~brave(X)|humble(X))))&
(?[X]:((happy(X)|~humble(X))))&
((~wise(lucy)|~rich(lucy)))&
(?[X]:((quiet(X)<~>generous(X))))&
(?[X]:(patient(X))) | ~funny(lucy) | [] | null | 0 |
If someone is not generous or not curious then fred is not wise and vice versa. Everyone who is either not calm or not happy is not calm and vice versa. If someone is not curious then someone is kind or not happy. Everyone who is either not kind or not rich is tall and vice versa. Everyone who is not generous or not rich is curious. If john is either humble or kind then john is either not kind or not brave. Everyone who is not patient is old or calm. Everyone who is not generous or not brave is both old and kind. Everyone who is not brave is not curious and vice versa. If lucy is not creative or happy then someone is not calm. If someone is not funny then someone is not quiet or calm and vice versa. If mary is rich then paul is calm and vice versa. Everyone who is either not old or rich is not humble or not wise and vice versa. Everyone who is either brave or not rich is calm and vice versa. Everyone who is both not wise and not quiet is not curious or not funny and vice versa. If alice is either not tall or not calm then someone is either not patient or creative and vice versa. Mary is both not creative and not strong. Alice is either humble or rich. Someone is brave. Fred is not kind. Someone is patient or not creative. Paul is not rich or not patient. Someone is either not humble or old. Someone is both happy and creative. | Alice is kind. | neutral | ((?[X]:((~generous(X)|~curious(X))))<=>(~wise(fred)))&
(![X]:((~calm(X)<~>~happy(X))<=>~calm(X)))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((~kind(X)<~>~rich(X))<=>tall(X)))&
(![X]:((~generous(X)|~rich(X))=>curious(X)))&
(((humble(john)<~>kind(john)))=>((~kind(john)<~>~brave(john))))&
(![X]:(~patient(X)=>(old(X)|calm(X))))&
(![X]:((~generous(X)|~brave(X))=>(old(X)&kind(X))))&
(![X]:(~brave(X)<=>~curious(X)))&
(((~creative(lucy)|happy(lucy)))=>(?[X]:(~calm(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~quiet(X)|calm(X)))))&
((rich(mary))<=>(calm(paul)))&
(![X]:((~old(X)<~>rich(X))<=>(~humble(X)|~wise(X))))&
(![X]:((brave(X)<~>~rich(X))<=>calm(X)))&
(![X]:((~wise(X)&~quiet(X))<=>(~curious(X)|~funny(X))))&
(((~tall(alice)<~>~calm(alice)))<=>(?[X]:((~patient(X)<~>creative(X)))))&
((~creative(mary)&~strong(mary)))&
((humble(alice)<~>rich(alice)))&
(?[X]:(brave(X)))&
(~kind(fred))&
(?[X]:((patient(X)|~creative(X))))&
((~rich(paul)|~patient(paul)))&
(?[X]:((~humble(X)<~>old(X))))&
(?[X]:((happy(X)&creative(X)))) | kind(alice) | [] | null | 0 |
Everyone who is tall or wise is not curious.
If someone is funny or not wise then someone is either not wise or quiet.
If someone is either not calm or curious then someone is either happy or old.
If mary is humble then lucy is curious or creative and vice versa.
Everyone who is wise is either curious or happy.
If someone is either not brave or not calm then someone is both old and rich.
Everyone who is either strong or not kind is both not funny and not calm.
If someone is not strong or not quiet then susan is not happy and vice versa.
If someone is both not curious and not kind then alice is quiet or generous and vice versa.
Everyone who is quiet is not kind.
Everyone who is happy is both happy and not patient.
If someone is either not happy or tall then john is both funny and kind.
Everyone who is not happy is either not wise or generous and vice versa.
If someone is not curious or not tall then fred is not generous.
If john is both not rich and generous then someone is not generous or brave.
If someone is curious or strong then susan is either not rich or not humble and vice versa.
Alice is both generous and curious.
Mary is both humble and quiet.
Mary is either not happy or creative.
Alice is either not strong or generous.
Someone is not brave or wise.
Lucy is either not brave or not funny.
Fred is not patient. | Alice is happy. | entailment | (![X]:((tall(X)|wise(X))=>~curious(X)))&
((?[X]:((funny(X)|~wise(X))))=>(?[X]:((~wise(X)<~>quiet(X)))))&
((?[X]:((~calm(X)<~>curious(X))))=>(?[X]:((happy(X)<~>old(X)))))&
((humble(mary))<=>((curious(lucy)|creative(lucy))))&
(![X]:(wise(X)=>(curious(X)<~>happy(X))))&
((?[X]:((~brave(X)<~>~calm(X))))=>(?[X]:((old(X)&rich(X)))))&
(![X]:((strong(X)<~>~kind(X))=>(~funny(X)&~calm(X))))&
((?[X]:((~strong(X)|~quiet(X))))<=>(~happy(susan)))&
((?[X]:((~curious(X)&~kind(X))))<=>((quiet(alice)|generous(alice))))&
(![X]:(quiet(X)=>~kind(X)))&
(![X]:(happy(X)=>(happy(X)&~patient(X))))&
((?[X]:((~happy(X)<~>tall(X))))=>((funny(john)&kind(john))))&
(![X]:(~happy(X)<=>(~wise(X)<~>generous(X))))&
((?[X]:((~curious(X)|~tall(X))))=>(~generous(fred)))&
(((~rich(john)&generous(john)))=>(?[X]:((~generous(X)|brave(X)))))&
((?[X]:((curious(X)|strong(X))))<=>((~rich(susan)<~>~humble(susan))))&
((generous(alice)&curious(alice)))&
((humble(mary)&quiet(mary)))&
((~happy(mary)<~>creative(mary)))&
((~strong(alice)<~>generous(alice)))&
(?[X]:((~brave(X)|wise(X))))&
((~brave(lucy)<~>~funny(lucy)))&
(~patient(fred)) | happy(alice) | [
"p0",
"p4",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3208658418191886623676538
% SZS output start Proof for 3208658418191886623676538
1. ! [X0] : ((wise(X0) | tall(X0)) => ~curious(X0)) [input p0]
5. ! [X0] : (wise(X0) => (curious(X0) <~> happy(X0))) [input p4]
13. ! [X0] : (~happy(X0) <=> (~wise(X0) <~> generous(X0))) [input p12]
17. curious(alice) & generous(alice) [input p16]
24. ~happy(alice) [input hypothesis]
30. ! [X0] : (~curious(X0) | (~wise(X0) & ~tall(X0))) [ennf transformation 1]
33. ! [X0] : ((curious(X0) <~> happy(X0)) | ~wise(X0)) [ennf transformation 5]
52. ! [X0] : (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | ~wise(X0)) [nnf transformation 33]
68. ! [X0] : ((~happy(X0) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | happy(X0))) [nnf transformation 13]
81. ~curious(X0) | ~wise(X0) [cnf transformation 30]
93. happy(X0) | curious(X0) | ~wise(X0) [cnf transformation 52]
118. ~generous(X0) | wise(X0) | happy(X0) [cnf transformation 68]
130. generous(alice) [cnf transformation 17]
141. ~happy(alice) [cnf transformation 24]
193. ~wise(X0) | happy(X0) [subsumption resolution 93,81]
234. 21 <=> generous(alice) [avatar definition]
235. generous(alice) <- (21) [avatar component clause 234]
276. ~generous(X0) | happy(X0) [subsumption resolution 118,193]
334. 21 [avatar split clause 130,234]
386. happy(alice) <- (21) [resolution 276,235]
387. $false <- (21) [subsumption resolution 386,141]
388. ~21 [avatar contradiction clause 387]
389. $false [avatar sat refutation 334,388]
% SZS output end Proof for 3208658418191886623676538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and patient then someone is both not rich and not funny. Everyone who is old or not kind is either kind or tall and vice versa. If fred is either not calm or generous then someone is not old and vice versa. If someone is both not creative and kind then someone is either tall or old and vice versa. If lucy is not tall or old then lucy is both calm and wise. Everyone who is either not kind or humble is both calm and humble. Everyone who is not humble or not curious is both not happy and not strong and vice versa. If lucy is both happy and not strong then john is both rich and funny. Everyone who is both not strong and not patient is not creative. Everyone who is not tall is both not wise and humble. Everyone who is funny is not quiet and vice versa. Everyone who is either quiet or not generous is either quiet or patient. Everyone who is both not brave and not rich is not happy or tall and vice versa. Everyone who is rich or not happy is either not rich or tall. Everyone who is not kind or old is either not rich or not calm. If someone is either not happy or not kind then someone is not brave or not quiet. Mary is calm or not patient. Someone is calm. Someone is either not patient or not quiet. Someone is either not creative or wise. Mary is not strong. Mary is quiet. Someone is both old and wise. Someone is not calm or curious. | Lucy is not strong. | contradiction | ((?[X]:((brave(X)&patient(X))))=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((old(X)|~kind(X))<=>(kind(X)<~>tall(X))))&
(((~calm(fred)<~>generous(fred)))<=>(?[X]:(~old(X))))&
((?[X]:((~creative(X)&kind(X))))<=>(?[X]:((tall(X)<~>old(X)))))&
(((~tall(lucy)|old(lucy)))=>((calm(lucy)&wise(lucy))))&
(![X]:((~kind(X)<~>humble(X))=>(calm(X)&humble(X))))&
(![X]:((~humble(X)|~curious(X))<=>(~happy(X)&~strong(X))))&
(((happy(lucy)&~strong(lucy)))=>((rich(john)&funny(john))))&
(![X]:((~strong(X)&~patient(X))=>~creative(X)))&
(![X]:(~tall(X)=>(~wise(X)&humble(X))))&
(![X]:(funny(X)<=>~quiet(X)))&
(![X]:((quiet(X)<~>~generous(X))=>(quiet(X)<~>patient(X))))&
(![X]:((~brave(X)&~rich(X))<=>(~happy(X)|tall(X))))&
(![X]:((rich(X)|~happy(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~kind(X)|old(X))=>(~rich(X)<~>~calm(X))))&
((?[X]:((~happy(X)<~>~kind(X))))=>(?[X]:((~brave(X)|~quiet(X)))))&
((calm(mary)|~patient(mary)))&
(?[X]:(calm(X)))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((~creative(X)<~>wise(X))))&
(~strong(mary))&
(quiet(mary))&
(?[X]:((old(X)&wise(X))))&
(?[X]:((~calm(X)|curious(X)))) | ~strong(lucy) | [
"p4",
"p7",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8438109119607217520512670
% SZS output start Proof for 8438109119607217520512670
5. (old(lucy) | ~tall(lucy)) => (wise(lucy) & calm(lucy)) [input p4]
8. (~strong(lucy) & happy(lucy)) => (funny(john) & rich(john)) [input p7]
10. ! [X0] : (~tall(X0) => (humble(X0) & ~wise(X0))) [input p9]
13. ! [X0] : ((~rich(X0) & ~brave(X0)) <=> (tall(X0) | ~happy(X0))) [input p12]
14. ! [X0] : ((~happy(X0) | rich(X0)) => (~rich(X0) <~> tall(X0))) [input p13]
25. ~strong(lucy) [input hypothesis]
30. (wise(lucy) & calm(lucy)) | (~old(lucy) & tall(lucy)) [ennf transformation 5]
32. (funny(john) & rich(john)) | (strong(lucy) | ~happy(lucy)) [ennf transformation 8]
33. (funny(john) & rich(john)) | strong(lucy) | ~happy(lucy) [flattening 32]
36. ! [X0] : ((humble(X0) & ~wise(X0)) | tall(X0)) [ennf transformation 10]
38. ! [X0] : ((~rich(X0) <~> tall(X0)) | (happy(X0) & ~rich(X0))) [ennf transformation 14]
60. ! [X0] : (((~rich(X0) & ~brave(X0)) | (~tall(X0) & happy(X0))) & ((tall(X0) | ~happy(X0)) | (rich(X0) | brave(X0)))) [nnf transformation 13]
61. ! [X0] : (((~rich(X0) & ~brave(X0)) | (~tall(X0) & happy(X0))) & (tall(X0) | ~happy(X0) | rich(X0) | brave(X0))) [flattening 60]
62. ! [X0] : (((~tall(X0) | rich(X0)) & (tall(X0) | ~rich(X0))) | (happy(X0) & ~rich(X0))) [nnf transformation 38]
100. wise(lucy) | tall(lucy) [cnf transformation 30]
111. rich(john) | strong(lucy) | ~happy(lucy) [cnf transformation 33]
114. ~wise(X0) | tall(X0) [cnf transformation 36]
125. ~rich(X0) | happy(X0) [cnf transformation 61]
126. ~tall(X0) | ~rich(X0) [cnf transformation 61]
127. tall(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 62]
130. ~tall(X0) | rich(X0) | happy(X0) [cnf transformation 62]
148. ~strong(lucy) [cnf transformation 25]
149. tall(X0) | ~rich(X0) [duplicate literal removal 127]
223. 16 <=> wise(lucy) [avatar definition]
225. wise(lucy) <- (16) [avatar component clause 223]
228. 17 <=> tall(lucy) [avatar definition]
230. tall(lucy) <- (17) [avatar component clause 228]
231. 17 | 16 [avatar split clause 100,223,228]
239. 19 <=> happy(lucy) [avatar definition]
241. ~happy(lucy) <- (~19) [avatar component clause 239]
243. 20 <=> strong(lucy) [avatar definition]
252. 22 <=> rich(john) [avatar definition]
254. rich(john) <- (22) [avatar component clause 252]
255. ~19 | 20 | 22 [avatar split clause 111,252,243,239]
256. ~tall(X0) | happy(X0) [subsumption resolution 130,125]
257. ~rich(X0) [subsumption resolution 149,126]
314. ~20 [avatar split clause 148,243]
337. happy(lucy) <- (17) [resolution 256,230]
340. $false <- (17, ~19) [subsumption resolution 337,241]
341. ~17 | 19 [avatar contradiction clause 340]
342. tall(lucy) <- (16) [resolution 225,114]
345. 17 | ~16 [avatar split clause 342,223,228]
346. $false <- (22) [subsumption resolution 254,257]
347. ~22 [avatar contradiction clause 346]
348. $false [avatar sat refutation 231,255,314,341,345,347]
% SZS output end Proof for 8438109119607217520512670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or strong then someone is either not calm or not wise and vice versa. If paul is either creative or not generous then someone is not strong. If someone is happy or not wise then someone is not strong and vice versa. Everyone who is strong or not generous is both not wise and not patient. If someone is not creative or not funny then paul is tall and vice versa. If susan is either old or not quiet then someone is old and vice versa. Everyone who is either not kind or curious is wise or calm. Everyone who is strong or funny is brave. Everyone who is not patient is either humble or not wise. Everyone who is both not creative and creative is patient or not curious and vice versa. Everyone who is either happy or not wise is funny or creative and vice versa. If susan is happy then mary is both not wise and funny and vice versa. Everyone who is not calm or rich is either kind or happy and vice versa. Everyone who is not tall is not rich and vice versa. If someone is both not humble and not kind then fred is not humble and vice versa. Everyone who is either not happy or not funny is both humble and patient. Someone is both old and tall. Someone is quiet. Someone is old or not funny. Someone is not happy. Someone is either not happy or not creative. Someone is creative. Someone is both curious and not calm. | Paul is tall. | entailment | ((?[X]:((happy(X)|strong(X))))<=>(?[X]:((~calm(X)<~>~wise(X)))))&
(((creative(paul)<~>~generous(paul)))=>(?[X]:(~strong(X))))&
((?[X]:((happy(X)|~wise(X))))<=>(?[X]:(~strong(X))))&
(![X]:((strong(X)|~generous(X))=>(~wise(X)&~patient(X))))&
((?[X]:((~creative(X)|~funny(X))))<=>(tall(paul)))&
(((old(susan)<~>~quiet(susan)))<=>(?[X]:(old(X))))&
(![X]:((~kind(X)<~>curious(X))=>(wise(X)|calm(X))))&
(![X]:((strong(X)|funny(X))=>brave(X)))&
(![X]:(~patient(X)=>(humble(X)<~>~wise(X))))&
(![X]:((~creative(X)&creative(X))<=>(patient(X)|~curious(X))))&
(![X]:((happy(X)<~>~wise(X))<=>(funny(X)|creative(X))))&
((happy(susan))<=>((~wise(mary)&funny(mary))))&
(![X]:((~calm(X)|rich(X))<=>(kind(X)<~>happy(X))))&
(![X]:(~tall(X)<=>~rich(X)))&
((?[X]:((~humble(X)&~kind(X))))<=>(~humble(fred)))&
(![X]:((~happy(X)<~>~funny(X))=>(humble(X)&patient(X))))&
(?[X]:((old(X)&tall(X))))&
(?[X]:(quiet(X)))&
(?[X]:((old(X)|~funny(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)<~>~creative(X))))&
(?[X]:(creative(X)))&
(?[X]:((curious(X)&~calm(X)))) | tall(paul) | [
"p4",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 460841512253787003390734
% SZS output start Proof for 460841512253787003390734
5. ? [X0] : (~funny(X0) | ~creative(X0)) <=> tall(paul) [input p4]
10. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (~curious(X0) | patient(X0))) [input p9]
16. ! [X0] : ((~happy(X0) <~> ~funny(X0)) => (patient(X0) & humble(X0))) [input p15]
20. ? [X0] : ~happy(X0) [input p19]
24. ~tall(paul) [input hypothesis]
33. ! [X0] : ((patient(X0) & humble(X0)) | (~happy(X0) <=> ~funny(X0))) [ennf transformation 16]
47. (? [X0] : (~funny(X0) | ~creative(X0)) | ~tall(paul)) & (tall(paul) | ! [X0] : (funny(X0) & creative(X0))) [nnf transformation 5]
48. (? [X0] : (~funny(X0) | ~creative(X0)) | ~tall(paul)) & (tall(paul) | ! [X1] : (funny(X1) & creative(X1))) [rectify 47]
49. ? [X0] : (~funny(X0) | ~creative(X0)) => (~funny(sK5) | ~creative(sK5)) [choice axiom]
50. ((~funny(sK5) | ~creative(sK5)) | ~tall(paul)) & (tall(paul) | ! [X1] : (funny(X1) & creative(X1))) [skolemisation 48,49]
57. ! [X0] : (((creative(X0) & ~creative(X0)) | (curious(X0) & ~patient(X0))) & ((~curious(X0) | patient(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 10]
58. ! [X0] : (((creative(X0) & ~creative(X0)) | (curious(X0) & ~patient(X0))) & (~curious(X0) | patient(X0) | ~creative(X0) | creative(X0))) [flattening 57]
70. ! [X0] : ((patient(X0) & humble(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) [nnf transformation 33]
77. ? [X0] : ~happy(X0) => ~happy(sK11) [choice axiom]
78. ~happy(sK11) [skolemisation 20,77]
102. tall(paul) | funny(X1) [cnf transformation 50]
113. ~creative(X0) | ~patient(X0) [cnf transformation 58]
115. ~patient(X0) | creative(X0) [cnf transformation 58]
139. patient(X0) | ~funny(X0) | happy(X0) [cnf transformation 70]
145. ~happy(sK11) [cnf transformation 78]
151. ~tall(paul) [cnf transformation 24]
222. 17 <=> tall(paul) [avatar definition]
235. 20 <=> ! [X1] : funny(X1) [avatar definition]
236. funny(X1) <- (20) [avatar component clause 235]
237. 20 | 17 [avatar split clause 102,222,235]
262. ~patient(X0) [subsumption resolution 113,115]
297. ~funny(X0) | happy(X0) [subsumption resolution 139,262]
317. ~17 [avatar split clause 151,222]
331. happy(X0) <- (20) [resolution 297,236]
336. $false <- (20) [resolution 331,145]
339. ~20 [avatar contradiction clause 336]
341. $false [avatar sat refutation 237,317,339]
% SZS output end Proof for 460841512253787003390734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not humble is not kind or not patient and vice versa. Everyone who is both not wise and brave is either not wise or wise and vice versa. Everyone who is happy or quiet is not funny and vice versa. If john is both not creative and not brave then someone is humble and vice versa. Everyone who is both not creative and not strong is both not generous and brave. Everyone who is either kind or wise is both not wise and patient. If john is funny then paul is quiet. If mary is calm or not brave then lucy is strong or not rich. Everyone who is either strong or generous is both not old and not wise and vice versa. If someone is not old or not creative then someone is both not curious and calm and vice versa. Everyone who is strong is not wise. Everyone who is not happy or rich is both rich and generous. If john is calm then paul is generous. Everyone who is curious is both old and not funny. If someone is not creative then someone is either calm or patient. Everyone who is either kind or calm is either not creative or happy. Someone is either strong or not wise. Someone is either rich or not generous. Paul is either not wise or not old. John is either humble or curious. Paul is both tall and brave. Mary is happy or not strong. Susan is either not happy or humble. Mary is both not rich and not old. | John is kind. | contradiction | (![X]:((curious(X)&~humble(X))<=>(~kind(X)|~patient(X))))&
(![X]:((~wise(X)&brave(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((happy(X)|quiet(X))<=>~funny(X)))&
(((~creative(john)&~brave(john)))<=>(?[X]:(humble(X))))&
(![X]:((~creative(X)&~strong(X))=>(~generous(X)&brave(X))))&
(![X]:((kind(X)<~>wise(X))=>(~wise(X)&patient(X))))&
((funny(john))=>(quiet(paul)))&
(((calm(mary)|~brave(mary)))=>((strong(lucy)|~rich(lucy))))&
(![X]:((strong(X)<~>generous(X))<=>(~old(X)&~wise(X))))&
((?[X]:((~old(X)|~creative(X))))<=>(?[X]:((~curious(X)&calm(X)))))&
(![X]:(strong(X)=>~wise(X)))&
(![X]:((~happy(X)|rich(X))=>(rich(X)&generous(X))))&
((calm(john))=>(generous(paul)))&
(![X]:(curious(X)=>(old(X)&~funny(X))))&
((?[X]:(~creative(X)))=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:((kind(X)<~>calm(X))=>(~creative(X)<~>happy(X))))&
(?[X]:((strong(X)<~>~wise(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
((~wise(paul)<~>~old(paul)))&
((humble(john)<~>curious(john)))&
((tall(paul)&brave(paul)))&
((happy(mary)|~strong(mary)))&
((~happy(susan)<~>humble(susan)))&
((~rich(mary)&~old(mary))) | kind(john) | [
"p0",
"p1",
"p3",
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9025790644306450133683823
% SZS output start Proof for 9025790644306450133683823
1. ! [X0] : ((~humble(X0) & curious(X0)) <=> (~patient(X0) | ~kind(X0))) [input p0]
2. ! [X0] : ((brave(X0) & ~wise(X0)) <=> (~wise(X0) <~> wise(X0))) [input p1]
4. (~brave(john) & ~creative(john)) <=> ? [X0] : humble(X0) [input p3]
6. ! [X0] : ((kind(X0) <~> wise(X0)) => (patient(X0) & ~wise(X0))) [input p5]
20. humble(john) <~> curious(john) [input p19]
25. kind(john) [input hypothesis]
35. ! [X0] : ((patient(X0) & ~wise(X0)) | (kind(X0) <=> wise(X0))) [ennf transformation 6]
44. ! [X0] : (((~humble(X0) & curious(X0)) | (patient(X0) & kind(X0))) & ((~patient(X0) | ~kind(X0)) | (humble(X0) | ~curious(X0)))) [nnf transformation 1]
45. ! [X0] : (((~humble(X0) & curious(X0)) | (patient(X0) & kind(X0))) & (~patient(X0) | ~kind(X0) | humble(X0) | ~curious(X0))) [flattening 44]
46. ! [X0] : (((brave(X0) & ~wise(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~brave(X0) | wise(X0)))) [nnf transformation 2]
47. ! [X0] : (((brave(X0) & ~wise(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~brave(X0) | wise(X0))) [flattening 46]
48. ((~brave(john) & ~creative(john)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (brave(john) | creative(john))) [nnf transformation 4]
49. ((~brave(john) & ~creative(john)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | brave(john) | creative(john)) [flattening 48]
50. ((~brave(john) & ~creative(john)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | brave(john) | creative(john)) [rectify 49]
51. ? [X1] : humble(X1) => humble(sK0) [choice axiom]
52. ((~brave(john) & ~creative(john)) | ! [X0] : ~humble(X0)) & (humble(sK0) | brave(john) | creative(john)) [skolemisation 50,51]
53. ! [X0] : ((patient(X0) & ~wise(X0)) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0)))) [nnf transformation 35]
73. (~curious(john) | ~humble(john)) & (curious(john) | humble(john)) [nnf transformation 20]
75. ~patient(X0) | ~kind(X0) | humble(X0) | ~curious(X0) [cnf transformation 45]
83. ~wise(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 47]
84. brave(X0) | wise(X0) | wise(X0) [cnf transformation 47]
85. brave(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 47]
88. ~brave(john) | ~humble(X0) [cnf transformation 52]
93. patient(X0) | wise(X0) | ~kind(X0) [cnf transformation 53]
127. curious(john) | humble(john) [cnf transformation 73]
135. kind(john) [cnf transformation 25]
140. ~wise(X0) [duplicate literal removal 83]
141. brave(X0) | wise(X0) [duplicate literal removal 84]
142. ~wise(X0) | brave(X0) [duplicate literal removal 85]
143. brave(X0) [subsumption resolution 141,142]
144. ~humble(X0) [subsumption resolution 88,143]
145. ~kind(X0) | patient(X0) [subsumption resolution 93,140]
221. curious(john) [subsumption resolution 127,144]
239. patient(john) [resolution 145,135]
291. ~kind(john) | humble(john) | ~curious(john) [resolution 75,239]
292. humble(john) | ~curious(john) [subsumption resolution 291,135]
293. ~curious(john) [subsumption resolution 292,144]
294. $false [subsumption resolution 293,221]
% SZS output end Proof for 9025790644306450133683823
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or old is either not wise or wise.
Everyone who is both kind and not quiet is old or not quiet.
Everyone who is not creative or not kind is generous or creative.
If fred is either not curious or not calm then paul is not old or quiet.
If someone is either wise or humble then mary is tall or not happy.
Everyone who is either not quiet or creative is either funny or old and vice versa.
If someone is either not patient or quiet then alice is either not kind or not patient and vice versa.
Everyone who is old or patient is calm or not happy.
Everyone who is both patient and not wise is calm or humble and vice versa.
If paul is not brave or not tall then lucy is calm or old and vice versa.
If someone is either not generous or rich then someone is not strong and vice versa.
Everyone who is not quiet is happy.
Everyone who is not generous or tall is creative.
Everyone who is both not creative and not wise is both not happy and not curious.
If alice is either not rich or calm then someone is tall.
Everyone who is not curious is both not tall and rich.
Someone is not calm.
Someone is calm.
Someone is not rich.
Someone is strong or kind.
Lucy is tall or humble.
Mary is generous or not old.
Susan is both not kind and rich. | Fred is calm. | neutral | (![X]:((rich(X)<~>old(X))=>(~wise(X)<~>wise(X))))&
(![X]:((kind(X)&~quiet(X))=>(old(X)|~quiet(X))))&
(![X]:((~creative(X)|~kind(X))=>(generous(X)|creative(X))))&
(((~curious(fred)<~>~calm(fred)))=>((~old(paul)|quiet(paul))))&
((?[X]:((wise(X)<~>humble(X))))=>((tall(mary)|~happy(mary))))&
(![X]:((~quiet(X)<~>creative(X))<=>(funny(X)<~>old(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>((~kind(alice)<~>~patient(alice))))&
(![X]:((old(X)|patient(X))=>(calm(X)|~happy(X))))&
(![X]:((patient(X)&~wise(X))<=>(calm(X)|humble(X))))&
(((~brave(paul)|~tall(paul)))<=>((calm(lucy)|old(lucy))))&
((?[X]:((~generous(X)<~>rich(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~quiet(X)=>happy(X)))&
(![X]:((~generous(X)|tall(X))=>creative(X)))&
(![X]:((~creative(X)&~wise(X))=>(~happy(X)&~curious(X))))&
(((~rich(alice)<~>calm(alice)))=>(?[X]:(tall(X))))&
(![X]:(~curious(X)=>(~tall(X)&rich(X))))&
(?[X]:(~calm(X)))&
(?[X]:(calm(X)))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)|kind(X))))&
((tall(lucy)|humble(lucy)))&
((generous(mary)|~old(mary)))&
((~kind(susan)&rich(susan))) | calm(fred) | [] | null | 0 |
Everyone who is both not rich and not generous is both not kind and wise and vice versa. If someone is happy then paul is both happy and not patient. If someone is both not patient and not curious then lucy is both not brave and quiet and vice versa. Everyone who is either wise or brave is not humble or brave and vice versa. Everyone who is both curious and humble is both not happy and brave. Everyone who is both not humble and not happy is not brave and vice versa. Everyone who is calm or not old is calm or not rich and vice versa. Everyone who is either funny or wise is either not strong or not calm and vice versa. Everyone who is not old is not happy or funny. If someone is either not old or not patient then someone is not wise. Everyone who is curious is not kind and vice versa. Everyone who is wise is both not rich and patient. Everyone who is rich or not happy is both not quiet and not curious. If someone is not kind then john is not old and vice versa. Everyone who is humble or calm is not funny or happy and vice versa. Everyone who is brave or kind is rich and vice versa. Paul is not quiet or brave. Fred is both not curious and generous. Someone is wise or not strong. Mary is either not old or not happy. Someone is humble. | Paul is happy. | contradiction | (![X]:((~rich(X)&~generous(X))<=>(~kind(X)&wise(X))))&
((?[X]:(happy(X)))=>((happy(paul)&~patient(paul))))&
((?[X]:((~patient(X)&~curious(X))))<=>((~brave(lucy)&quiet(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~humble(X)|brave(X))))&
(![X]:((curious(X)&humble(X))=>(~happy(X)&brave(X))))&
(![X]:((~humble(X)&~happy(X))<=>~brave(X)))&
(![X]:((calm(X)|~old(X))<=>(calm(X)|~rich(X))))&
(![X]:((funny(X)<~>wise(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:(~old(X)=>(~happy(X)|funny(X))))&
((?[X]:((~old(X)<~>~patient(X))))=>(?[X]:(~wise(X))))&
(![X]:(curious(X)<=>~kind(X)))&
(![X]:(wise(X)=>(~rich(X)&patient(X))))&
(![X]:((rich(X)|~happy(X))=>(~quiet(X)&~curious(X))))&
((?[X]:(~kind(X)))<=>(~old(john)))&
(![X]:((humble(X)|calm(X))<=>(~funny(X)|happy(X))))&
(![X]:((brave(X)|kind(X))<=>rich(X)))&
((~quiet(paul)|brave(paul)))&
((~curious(fred)&generous(fred)))&
(?[X]:((wise(X)|~strong(X))))&
((~old(mary)<~>~happy(mary)))&
(?[X]:(humble(X))) | happy(paul) | [
"p1",
"p2",
"p5",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8009365498622778903660597
% SZS output start Proof for 8009365498622778903660597
2. ? [X0] : happy(X0) => (~patient(paul) & happy(paul)) [input p1]
3. ? [X0] : (~curious(X0) & ~patient(X0)) <=> (quiet(lucy) & ~brave(lucy)) [input p2]
6. ! [X0] : ((~happy(X0) & ~humble(X0)) <=> ~brave(X0)) [input p5]
13. ! [X0] : ((~happy(X0) | rich(X0)) => (~curious(X0) & ~quiet(X0))) [input p12]
16. ! [X0] : ((kind(X0) | brave(X0)) <=> rich(X0)) [input p15]
22. happy(paul) [input hypothesis]
24. (~patient(paul) & happy(paul)) | ! [X0] : ~happy(X0) [ennf transformation 2]
31. ! [X0] : ((~curious(X0) & ~quiet(X0)) | (happy(X0) & ~rich(X0))) [ennf transformation 13]
34. (? [X0] : (~curious(X0) & ~patient(X0)) | (~quiet(lucy) | brave(lucy))) & ((quiet(lucy) & ~brave(lucy)) | ! [X0] : (curious(X0) | patient(X0))) [nnf transformation 3]
35. (? [X0] : (~curious(X0) & ~patient(X0)) | ~quiet(lucy) | brave(lucy)) & ((quiet(lucy) & ~brave(lucy)) | ! [X0] : (curious(X0) | patient(X0))) [flattening 34]
36. (? [X0] : (~curious(X0) & ~patient(X0)) | ~quiet(lucy) | brave(lucy)) & ((quiet(lucy) & ~brave(lucy)) | ! [X1] : (curious(X1) | patient(X1))) [rectify 35]
37. ? [X0] : (~curious(X0) & ~patient(X0)) => (~curious(sK0) & ~patient(sK0)) [choice axiom]
38. ((~curious(sK0) & ~patient(sK0)) | ~quiet(lucy) | brave(lucy)) & ((quiet(lucy) & ~brave(lucy)) | ! [X1] : (curious(X1) | patient(X1))) [skolemisation 36,37]
41. ! [X0] : (((~happy(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | (happy(X0) | humble(X0)))) [nnf transformation 6]
42. ! [X0] : (((~happy(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | happy(X0) | humble(X0))) [flattening 41]
57. ! [X0] : (((kind(X0) | brave(X0)) | ~rich(X0)) & (rich(X0) | (~kind(X0) & ~brave(X0)))) [nnf transformation 16]
58. ! [X0] : ((kind(X0) | brave(X0) | ~rich(X0)) & (rich(X0) | (~kind(X0) & ~brave(X0)))) [flattening 57]
69. ~patient(paul) | ~happy(X0) [cnf transformation 24]
70. ~brave(lucy) | curious(X1) | patient(X1) [cnf transformation 38]
71. quiet(lucy) | curious(X1) | patient(X1) [cnf transformation 38]
84. ~happy(X0) | brave(X0) [cnf transformation 42]
105. ~quiet(X0) | happy(X0) [cnf transformation 31]
106. ~curious(X0) | ~rich(X0) [cnf transformation 31]
114. ~brave(X0) | rich(X0) [cnf transformation 58]
124. happy(paul) [cnf transformation 22]
128. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
129. ~happy(X0) <- (1) [avatar component clause 128]
131. 2 <=> patient(paul) [avatar definition]
133. ~patient(paul) <- (~2) [avatar component clause 131]
134. 1 | ~2 [avatar split clause 69,131,128]
136. 3 <=> happy(paul) [avatar definition]
138. happy(paul) <- (3) [avatar component clause 136]
141. 4 <=> brave(lucy) [avatar definition]
142. ~brave(lucy) <- (~4) [avatar component clause 141]
145. 5 <=> quiet(lucy) [avatar definition]
146. quiet(lucy) <- (5) [avatar component clause 145]
159. 8 <=> ! [X1] : (curious(X1) | patient(X1)) [avatar definition]
160. curious(X1) | patient(X1) <- (8) [avatar component clause 159]
161. 8 | 5 [avatar split clause 71,145,159]
162. 8 | ~4 [avatar split clause 70,141,159]
194. 16 <=> brave(paul) [avatar definition]
196. brave(paul) <- (16) [avatar component clause 194]
217. 3 [avatar split clause 124,136]
219. brave(paul) <- (3) [resolution 84,138]
220. 16 | ~3 [avatar split clause 219,136,194]
225. happy(lucy) <- (5) [resolution 105,146]
227. brave(lucy) <- (5) [resolution 225,84]
228. $false <- (~4, 5) [subsumption resolution 227,142]
229. 4 | ~5 [avatar contradiction clause 228]
231. rich(paul) <- (16) [resolution 114,196]
240. ~rich(X1) | patient(X1) <- (8) [resolution 160,106]
375. $false <- (1, 3) [resolution 129,138]
376. ~1 | ~3 [avatar contradiction clause 375]
462. patient(paul) <- (8, 16) [resolution 240,231]
467. $false <- (~2, 8, 16) [subsumption resolution 462,133]
468. 2 | ~8 | ~16 [avatar contradiction clause 467]
469. $false [avatar sat refutation 134,161,162,217,220,229,376,468]
% SZS output end Proof for 8009365498622778903660597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not old or patient then fred is curious and vice versa. Everyone who is quiet is either not generous or generous and vice versa. Everyone who is both old and kind is humble. Everyone who is both strong and funny is humble and vice versa. Everyone who is either happy or not quiet is either happy or calm and vice versa. Everyone who is both not humble and brave is either curious or not calm and vice versa. Everyone who is not calm or quiet is both not old and rich and vice versa. If someone is either not old or quiet then someone is either not wise or not generous. If alice is humble or calm then someone is both quiet and not funny and vice versa. Everyone who is strong is both not wise and tall. Everyone who is both not wise and not brave is either funny or not old and vice versa. Everyone who is rich is both not generous and not strong and vice versa. Everyone who is either curious or not calm is either humble or not old. If fred is generous then paul is not tall or patient. Everyone who is both creative and not humble is both not rich and brave. Everyone who is both calm and brave is creative and vice versa. Paul is either happy or tall. Susan is not generous or tall. Paul is not curious or not old. Fred is tall or quiet. Alice is not brave or not tall. Mary is both not generous and rich. | Fred is not quiet. | contradiction | (((~old(mary)|patient(mary)))<=>(curious(fred)))&
(![X]:(quiet(X)<=>(~generous(X)<~>generous(X))))&
(![X]:((old(X)&kind(X))=>humble(X)))&
(![X]:((strong(X)&funny(X))<=>humble(X)))&
(![X]:((happy(X)<~>~quiet(X))<=>(happy(X)<~>calm(X))))&
(![X]:((~humble(X)&brave(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((~calm(X)|quiet(X))<=>(~old(X)&rich(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(((humble(alice)|calm(alice)))<=>(?[X]:((quiet(X)&~funny(X)))))&
(![X]:(strong(X)=>(~wise(X)&tall(X))))&
(![X]:((~wise(X)&~brave(X))<=>(funny(X)<~>~old(X))))&
(![X]:(rich(X)<=>(~generous(X)&~strong(X))))&
(![X]:((curious(X)<~>~calm(X))=>(humble(X)<~>~old(X))))&
((generous(fred))=>((~tall(paul)|patient(paul))))&
(![X]:((creative(X)&~humble(X))=>(~rich(X)&brave(X))))&
(![X]:((calm(X)&brave(X))<=>creative(X)))&
((happy(paul)<~>tall(paul)))&
((~generous(susan)|tall(susan)))&
((~curious(paul)|~old(paul)))&
((tall(fred)|quiet(fred)))&
((~brave(alice)|~tall(alice)))&
((~generous(mary)&rich(mary))) | ~quiet(fred) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 3209472982995120409506983
% SZS output start Proof for 3209472982995120409506983
2. ! [X0] : (quiet(X0) <=> (~generous(X0) <~> generous(X0))) [input p1]
23. ~quiet(fred) [input hypothesis]
38. ! [X0] : ((quiet(X0) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | ~quiet(X0))) [nnf transformation 2]
66. quiet(X0) | generous(X0) | generous(X0) [cnf transformation 38]
67. quiet(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 38]
126. ~quiet(fred) [cnf transformation 23]
131. quiet(X0) | generous(X0) [duplicate literal removal 66]
132. quiet(X0) | ~generous(X0) [duplicate literal removal 67]
148. quiet(X0) [subsumption resolution 131,132]
197. $false [subsumption resolution 126,148]
% SZS output end Proof for 3209472982995120409506983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not kind then fred is old and vice versa.
If alice is kind or not strong then paul is both old and not creative and vice versa.
If someone is wise then someone is both not kind and not quiet and vice versa.
If someone is not patient then alice is not generous and vice versa.
Everyone who is not patient or rich is both not rich and not old.
Everyone who is patient is either patient or kind.
Everyone who is either creative or wise is not tall.
Everyone who is both generous and strong is not quiet.
If john is both not funny and happy then fred is both not wise and not creative and vice versa.
Everyone who is not funny is calm or patient and vice versa.
If fred is either rich or not brave then alice is not patient.
Everyone who is not creative or not patient is both brave and quiet.
If someone is not generous then someone is kind or not brave and vice versa.
Everyone who is not rich is not happy or not generous.
Everyone who is either generous or not curious is not kind and vice versa.
If someone is either not patient or not generous then alice is funny.
Fred is not tall.
Someone is either not happy or rich.
Alice is tall or not funny.
Someone is both not old and not humble.
Someone is either creative or not wise.
Someone is curious or not old.
Someone is not creative or happy.
Someone is rich or not patient. | Fred is creative. | neutral | ((?[X]:((~humble(X)&~kind(X))))<=>(old(fred)))&
(((kind(alice)|~strong(alice)))<=>((old(paul)&~creative(paul))))&
((?[X]:(wise(X)))<=>(?[X]:((~kind(X)&~quiet(X)))))&
((?[X]:(~patient(X)))<=>(~generous(alice)))&
(![X]:((~patient(X)|rich(X))=>(~rich(X)&~old(X))))&
(![X]:(patient(X)=>(patient(X)<~>kind(X))))&
(![X]:((creative(X)<~>wise(X))=>~tall(X)))&
(![X]:((generous(X)&strong(X))=>~quiet(X)))&
(((~funny(john)&happy(john)))<=>((~wise(fred)&~creative(fred))))&
(![X]:(~funny(X)<=>(calm(X)|patient(X))))&
(((rich(fred)<~>~brave(fred)))=>(~patient(alice)))&
(![X]:((~creative(X)|~patient(X))=>(brave(X)&quiet(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:(~rich(X)=>(~happy(X)|~generous(X))))&
(![X]:((generous(X)<~>~curious(X))<=>~kind(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(funny(alice)))&
(~tall(fred))&
(?[X]:((~happy(X)<~>rich(X))))&
((tall(alice)|~funny(alice)))&
(?[X]:((~old(X)&~humble(X))))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((curious(X)|~old(X))))&
(?[X]:((~creative(X)|happy(X))))&
(?[X]:((rich(X)|~patient(X)))) | creative(fred) | [] | null | 0 |
If john is either curious or not strong then lucy is brave.
If paul is rich then someone is both not creative and kind.
Everyone who is creative or not patient is not humble or not patient.
Everyone who is both not quiet and not kind is not curious and vice versa.
Everyone who is both generous and wise is not generous.
If someone is not rich then lucy is not humble or not wise and vice versa.
Everyone who is both generous and humble is not strong or not kind.
Everyone who is either not humble or patient is either not humble or not calm.
Everyone who is not curious or not creative is either generous or strong and vice versa.
If john is either not old or wise then paul is both funny and not brave and vice versa.
If someone is both not wise and not generous then someone is either not strong or calm.
Everyone who is not kind or not old is either not tall or brave.
If someone is either brave or happy then paul is not kind or tall.
Everyone who is either creative or not curious is tall or not rich.
Everyone who is both not funny and not generous is either not curious or not happy.
Everyone who is both not happy and not calm is not quiet.
John is both brave and not generous.
Someone is either patient or not kind.
Someone is funny or not quiet.
Someone is strong or brave.
Someone is either strong or not curious.
Someone is either not brave or calm.
Someone is funny or strong.
Someone is either not happy or not rich. | Lucy is not generous. | neutral | (((curious(john)<~>~strong(john)))=>(brave(lucy)))&
((rich(paul))=>(?[X]:((~creative(X)&kind(X)))))&
(![X]:((creative(X)|~patient(X))=>(~humble(X)|~patient(X))))&
(![X]:((~quiet(X)&~kind(X))<=>~curious(X)))&
(![X]:((generous(X)&wise(X))=>~generous(X)))&
((?[X]:(~rich(X)))<=>((~humble(lucy)|~wise(lucy))))&
(![X]:((generous(X)&humble(X))=>(~strong(X)|~kind(X))))&
(![X]:((~humble(X)<~>patient(X))=>(~humble(X)<~>~calm(X))))&
(![X]:((~curious(X)|~creative(X))<=>(generous(X)<~>strong(X))))&
(((~old(john)<~>wise(john)))<=>((funny(paul)&~brave(paul))))&
((?[X]:((~wise(X)&~generous(X))))=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:((~kind(X)|~old(X))=>(~tall(X)<~>brave(X))))&
((?[X]:((brave(X)<~>happy(X))))=>((~kind(paul)|tall(paul))))&
(![X]:((creative(X)<~>~curious(X))=>(tall(X)|~rich(X))))&
(![X]:((~funny(X)&~generous(X))=>(~curious(X)<~>~happy(X))))&
(![X]:((~happy(X)&~calm(X))=>~quiet(X)))&
((brave(john)&~generous(john)))&
(?[X]:((patient(X)<~>~kind(X))))&
(?[X]:((funny(X)|~quiet(X))))&
(?[X]:((strong(X)|brave(X))))&
(?[X]:((strong(X)<~>~curious(X))))&
(?[X]:((~brave(X)<~>calm(X))))&
(?[X]:((funny(X)|strong(X))))&
(?[X]:((~happy(X)<~>~rich(X)))) | ~generous(lucy) | [] | null | 0 |
Everyone who is rich or not quiet is brave or not old and vice versa.
If someone is old then someone is both brave and not brave and vice versa.
Everyone who is tall or not rich is patient.
Everyone who is either rich or brave is both not generous and not creative and vice versa.
If susan is not quiet or not funny then someone is both generous and not quiet and vice versa.
Everyone who is not generous or generous is either not brave or not humble and vice versa.
Everyone who is not happy or not humble is quiet.
Everyone who is both not funny and not brave is wise and vice versa.
If someone is both not patient and not happy then someone is both not creative and not wise.
Everyone who is either not rich or not calm is both not generous and not rich.
Everyone who is either not funny or not tall is not curious and vice versa.
If paul is either not curious or tall then mary is both old and strong and vice versa.
If someone is creative or not happy then someone is strong or not old.
Everyone who is not old or not generous is both not creative and not brave.
Everyone who is both curious and quiet is not tall.
If someone is brave or not happy then someone is not strong or kind and vice versa.
Someone is either not creative or not humble.
John is creative or generous.
John is either quiet or generous.
Someone is creative or not tall.
Alice is quiet.
Someone is either calm or tall.
Fred is not creative. | Mary is not generous. | neutral | (![X]:((rich(X)|~quiet(X))<=>(brave(X)|~old(X))))&
((?[X]:(old(X)))<=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:((tall(X)|~rich(X))=>patient(X)))&
(![X]:((rich(X)<~>brave(X))<=>(~generous(X)&~creative(X))))&
(((~quiet(susan)|~funny(susan)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~generous(X)|generous(X))<=>(~brave(X)<~>~humble(X))))&
(![X]:((~happy(X)|~humble(X))=>quiet(X)))&
(![X]:((~funny(X)&~brave(X))<=>wise(X)))&
((?[X]:((~patient(X)&~happy(X))))=>(?[X]:((~creative(X)&~wise(X)))))&
(![X]:((~rich(X)<~>~calm(X))=>(~generous(X)&~rich(X))))&
(![X]:((~funny(X)<~>~tall(X))<=>~curious(X)))&
(((~curious(paul)<~>tall(paul)))<=>((old(mary)&strong(mary))))&
((?[X]:((creative(X)|~happy(X))))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((~old(X)|~generous(X))=>(~creative(X)&~brave(X))))&
(![X]:((curious(X)&quiet(X))=>~tall(X)))&
((?[X]:((brave(X)|~happy(X))))<=>(?[X]:((~strong(X)|kind(X)))))&
(?[X]:((~creative(X)<~>~humble(X))))&
((creative(john)|generous(john)))&
((quiet(john)<~>generous(john)))&
(?[X]:((creative(X)|~tall(X))))&
(quiet(alice))&
(?[X]:((calm(X)<~>tall(X))))&
(~creative(fred)) | ~generous(mary) | [] | null | 0 |
If fred is both not old and humble then mary is either happy or not patient and vice versa.
If someone is not quiet or strong then someone is old or not generous and vice versa.
If someone is both not humble and not quiet then someone is brave or patient.
If someone is not brave then someone is either humble or rich.
If susan is either not creative or not old then someone is both rich and not patient and vice versa.
Everyone who is humble or not happy is happy or old and vice versa.
Everyone who is old is both not rich and creative and vice versa.
If someone is not humble or not wise then someone is both not curious and patient and vice versa.
If paul is both not wise and not funny then paul is wise or brave.
Everyone who is not rich or patient is creative or not calm and vice versa.
Everyone who is not rich is both humble and patient.
If paul is both generous and not generous then someone is not rich or kind and vice versa.
Everyone who is either not strong or not calm is patient.
Everyone who is either strong or brave is either not creative or humble.
If mary is rich then alice is not patient or not happy and vice versa.
Someone is either not strong or not tall.
Mary is generous or not funny.
Someone is not patient or not tall.
Someone is either happy or old.
Susan is either not tall or not happy. | Mary is rich. | entailment | (((~old(fred)&humble(fred)))<=>((happy(mary)<~>~patient(mary))))&
((?[X]:((~quiet(X)|strong(X))))<=>(?[X]:((old(X)|~generous(X)))))&
((?[X]:((~humble(X)&~quiet(X))))=>(?[X]:((brave(X)|patient(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((humble(X)<~>rich(X)))))&
(((~creative(susan)<~>~old(susan)))<=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:((humble(X)|~happy(X))<=>(happy(X)|old(X))))&
(![X]:(old(X)<=>(~rich(X)&creative(X))))&
((?[X]:((~humble(X)|~wise(X))))<=>(?[X]:((~curious(X)&patient(X)))))&
(((~wise(paul)&~funny(paul)))=>((wise(paul)|brave(paul))))&
(![X]:((~rich(X)|patient(X))<=>(creative(X)|~calm(X))))&
(![X]:(~rich(X)=>(humble(X)&patient(X))))&
(((generous(paul)&~generous(paul)))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~strong(X)<~>~calm(X))=>patient(X)))&
(![X]:((strong(X)<~>brave(X))=>(~creative(X)<~>humble(X))))&
((rich(mary))<=>((~patient(alice)|~happy(alice))))&
(?[X]:((~strong(X)<~>~tall(X))))&
((generous(mary)|~funny(mary)))&
(?[X]:((~patient(X)|~tall(X))))&
(?[X]:((happy(X)<~>old(X))))&
((~tall(susan)<~>~happy(susan))) | rich(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5774400812866255245386021
% SZS output start Proof for 5774400812866255245386021
12. (~generous(paul) & generous(paul)) <=> ? [X0] : (kind(X0) | ~rich(X0)) [input p11]
21. ~rich(mary) [input hypothesis]
62. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & (? [X0] : (kind(X0) | ~rich(X0)) | (generous(paul) | ~generous(paul))) [nnf transformation 12]
63. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & (? [X0] : (kind(X0) | ~rich(X0)) | generous(paul) | ~generous(paul)) [flattening 62]
64. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & (? [X1] : (kind(X1) | ~rich(X1)) | generous(paul) | ~generous(paul)) [rectify 63]
65. ? [X1] : (kind(X1) | ~rich(X1)) => (kind(sK7) | ~rich(sK7)) [choice axiom]
66. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & ((kind(sK7) | ~rich(sK7)) | generous(paul) | ~generous(paul)) [skolemisation 64,65]
119. generous(paul) | rich(X0) [cnf transformation 66]
121. ~generous(paul) | rich(X0) [cnf transformation 66]
140. ~rich(mary) [cnf transformation 21]
295. 35 <=> generous(paul) [avatar definition]
300. 36 <=> ! [X0] : rich(X0) [avatar definition]
301. rich(X0) <- (36) [avatar component clause 300]
302. 36 | ~35 [avatar split clause 121,295,300]
304. 36 | 35 [avatar split clause 119,295,300]
310. 38 <=> rich(mary) [avatar definition]
311. ~rich(mary) <- (~38) [avatar component clause 310]
367. ~38 [avatar split clause 140,310]
369. $false <- (36, ~38) [resolution 311,301]
370. ~36 | 38 [avatar contradiction clause 369]
371. $false [avatar sat refutation 302,304,367,370]
% SZS output end Proof for 5774400812866255245386021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not patient and vice versa. Everyone who is not old or not creative is both generous and not strong. Everyone who is both wise and strong is not funny and vice versa. Everyone who is not happy or creative is both curious and quiet and vice versa. Everyone who is either not happy or not calm is brave. If lucy is either not funny or not curious then susan is both funny and strong. Everyone who is either not strong or not tall is both patient and not strong. Everyone who is both funny and calm is happy. Everyone who is not funny is not tall and vice versa. Everyone who is either quiet or not old is either funny or not calm. If someone is both not tall and not curious then someone is kind and vice versa. Everyone who is either generous or not happy is not curious and vice versa. If mary is either strong or not calm then someone is either brave or not kind and vice versa. If someone is not calm or not humble then someone is both creative and not humble and vice versa. John is not creative or old. Someone is not kind. Someone is not funny or humble. | John is not creative. | contradiction | (![X]:(~strong(X)<=>~patient(X)))&
(![X]:((~old(X)|~creative(X))=>(generous(X)&~strong(X))))&
(![X]:((wise(X)&strong(X))<=>~funny(X)))&
(![X]:((~happy(X)|creative(X))<=>(curious(X)&quiet(X))))&
(![X]:((~happy(X)<~>~calm(X))=>brave(X)))&
(((~funny(lucy)<~>~curious(lucy)))=>((funny(susan)&strong(susan))))&
(![X]:((~strong(X)<~>~tall(X))=>(patient(X)&~strong(X))))&
(![X]:((funny(X)&calm(X))=>happy(X)))&
(![X]:(~funny(X)<=>~tall(X)))&
(![X]:((quiet(X)<~>~old(X))=>(funny(X)<~>~calm(X))))&
((?[X]:((~tall(X)&~curious(X))))<=>(?[X]:(kind(X))))&
(![X]:((generous(X)<~>~happy(X))<=>~curious(X)))&
(((strong(mary)<~>~calm(mary)))<=>(?[X]:((brave(X)<~>~kind(X)))))&
((?[X]:((~calm(X)|~humble(X))))<=>(?[X]:((creative(X)&~humble(X)))))&
((~creative(john)|old(john)))&
(?[X]:(~kind(X)))&
(?[X]:((~funny(X)|humble(X)))) | ~creative(john) | [
"p0",
"p1",
"p2",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4172222712363249987911818
% SZS output start Proof for 4172222712363249987911818
1. ! [X0] : (~strong(X0) <=> ~patient(X0)) [input p0]
2. ! [X0] : ((~creative(X0) | ~old(X0)) => (~strong(X0) & generous(X0))) [input p1]
3. ! [X0] : ((strong(X0) & wise(X0)) <=> ~funny(X0)) [input p2]
7. ! [X0] : ((~strong(X0) <~> ~tall(X0)) => (~strong(X0) & patient(X0))) [input p6]
9. ! [X0] : (~funny(X0) <=> ~tall(X0)) [input p8]
18. ~creative(john) [input hypothesis]
21. ! [X0] : ((~strong(X0) & generous(X0)) | (creative(X0) & old(X0))) [ennf transformation 2]
24. ! [X0] : ((~strong(X0) & patient(X0)) | (~strong(X0) <=> ~tall(X0))) [ennf transformation 7]
28. ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0))) [nnf transformation 1]
29. ! [X0] : (((strong(X0) & wise(X0)) | funny(X0)) & (~funny(X0) | (~strong(X0) | ~wise(X0)))) [nnf transformation 3]
30. ! [X0] : (((strong(X0) & wise(X0)) | funny(X0)) & (~funny(X0) | ~strong(X0) | ~wise(X0))) [flattening 29]
35. ! [X0] : ((~strong(X0) & patient(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0)))) [nnf transformation 24]
36. ! [X0] : ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0))) [nnf transformation 9]
57. ~patient(X0) | strong(X0) [cnf transformation 28]
58. ~strong(X0) | patient(X0) [cnf transformation 28]
62. ~strong(X0) | creative(X0) [cnf transformation 21]
65. funny(X0) | strong(X0) [cnf transformation 30]
77. patient(X0) | ~tall(X0) | strong(X0) [cnf transformation 35]
80. ~strong(X0) | ~strong(X0) | tall(X0) [cnf transformation 35]
83. ~funny(X0) | tall(X0) [cnf transformation 36]
111. ~creative(john) [cnf transformation 18]
112. ~strong(X0) | tall(X0) [duplicate literal removal 80]
133. ~tall(X0) | patient(X0) [subsumption resolution 77,58]
218. 23 <=> creative(john) [avatar definition]
220. ~creative(john) <- (~23) [avatar component clause 218]
235. ~23 [avatar split clause 111,218]
264. tall(X0) | strong(X0) [resolution 83,65]
267. tall(X0) [subsumption resolution 264,112]
275. patient(X0) [resolution 133,267]
299. strong(X0) [resolution 275,57]
318. creative(X1) [resolution 299,62]
332. $false <- (~23) [resolution 318,220]
335. 23 [avatar contradiction clause 332]
336. $false [avatar sat refutation 235,335]
% SZS output end Proof for 4172222712363249987911818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not funny is not humble or rich.
Everyone who is not calm is either quiet or not brave and vice versa.
Everyone who is not tall is both not creative and not humble.
If someone is not kind then someone is both not rich and old and vice versa.
If someone is both not brave and kind then someone is either not rich or not brave.
If alice is either quiet or rich then someone is generous and vice versa.
If someone is not brave or patient then alice is either kind or brave.
Everyone who is either not generous or not curious is both quiet and brave.
If someone is not tall then paul is both brave and patient and vice versa.
Everyone who is either not tall or not funny is both strong and patient and vice versa.
If someone is not rich then someone is not quiet or not generous.
If fred is calm then susan is both wise and not brave.
Everyone who is not wise is both not funny and old.
If someone is either not calm or funny then john is not kind or rich.
Everyone who is both not wise and not generous is not strong or curious and vice versa.
Everyone who is tall or funny is either humble or curious.
Someone is quiet or not brave.
Alice is not brave.
Lucy is not quiet.
Someone is not strong.
Someone is not tall or not wise.
Someone is either not happy or not kind.
Someone is both not old and patient. | Paul is funny. | contradiction | (![X]:((~creative(X)<~>~funny(X))=>(~humble(X)|rich(X))))&
(![X]:(~calm(X)<=>(quiet(X)<~>~brave(X))))&
(![X]:(~tall(X)=>(~creative(X)&~humble(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~rich(X)&old(X)))))&
((?[X]:((~brave(X)&kind(X))))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(((quiet(alice)<~>rich(alice)))<=>(?[X]:(generous(X))))&
((?[X]:((~brave(X)|patient(X))))=>((kind(alice)<~>brave(alice))))&
(![X]:((~generous(X)<~>~curious(X))=>(quiet(X)&brave(X))))&
((?[X]:(~tall(X)))<=>((brave(paul)&patient(paul))))&
(![X]:((~tall(X)<~>~funny(X))<=>(strong(X)&patient(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~quiet(X)|~generous(X)))))&
((calm(fred))=>((wise(susan)&~brave(susan))))&
(![X]:(~wise(X)=>(~funny(X)&old(X))))&
((?[X]:((~calm(X)<~>funny(X))))=>((~kind(john)|rich(john))))&
(![X]:((~wise(X)&~generous(X))<=>(~strong(X)|curious(X))))&
(![X]:((tall(X)|funny(X))=>(humble(X)<~>curious(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(~brave(alice))&
(~quiet(lucy))&
(?[X]:(~strong(X)))&
(?[X]:((~tall(X)|~wise(X))))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((~old(X)&patient(X)))) | funny(paul) | [
"p2",
"p8",
"p9",
"p12",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5854092358757271745583318
% SZS output start Proof for 5854092358757271745583318
3. ! [X0] : (~tall(X0) => (~humble(X0) & ~creative(X0))) [input p2]
9. ? [X0] : ~tall(X0) <=> (patient(paul) & brave(paul)) [input p8]
10. ! [X0] : ((~tall(X0) <~> ~funny(X0)) <=> (patient(X0) & strong(X0))) [input p9]
13. ! [X0] : (~wise(X0) => (old(X0) & ~funny(X0))) [input p12]
15. ! [X0] : ((~generous(X0) & ~wise(X0)) <=> (curious(X0) | ~strong(X0))) [input p14]
16. ! [X0] : ((funny(X0) | tall(X0)) => (humble(X0) <~> curious(X0))) [input p15]
20. ? [X0] : ~strong(X0) [input p19]
24. funny(paul) [input hypothesis]
30. ! [X0] : ((~humble(X0) & ~creative(X0)) | tall(X0)) [ennf transformation 3]
36. ! [X0] : ((old(X0) & ~funny(X0)) | wise(X0)) [ennf transformation 13]
39. ! [X0] : ((humble(X0) <~> curious(X0)) | (~funny(X0) & ~tall(X0))) [ennf transformation 16]
57. (? [X0] : ~tall(X0) | (~patient(paul) | ~brave(paul))) & ((patient(paul) & brave(paul)) | ! [X0] : tall(X0)) [nnf transformation 9]
58. (? [X0] : ~tall(X0) | ~patient(paul) | ~brave(paul)) & ((patient(paul) & brave(paul)) | ! [X0] : tall(X0)) [flattening 57]
59. (? [X0] : ~tall(X0) | ~patient(paul) | ~brave(paul)) & ((patient(paul) & brave(paul)) | ! [X1] : tall(X1)) [rectify 58]
60. ? [X0] : ~tall(X0) => ~tall(sK4) [choice axiom]
61. (~tall(sK4) | ~patient(paul) | ~brave(paul)) & ((patient(paul) & brave(paul)) | ! [X1] : tall(X1)) [skolemisation 59,60]
62. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [nnf transformation 10]
63. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [flattening 62]
68. ! [X0] : (((~generous(X0) & ~wise(X0)) | (~curious(X0) & strong(X0))) & ((curious(X0) | ~strong(X0)) | (generous(X0) | wise(X0)))) [nnf transformation 15]
69. ! [X0] : (((~generous(X0) & ~wise(X0)) | (~curious(X0) & strong(X0))) & (curious(X0) | ~strong(X0) | generous(X0) | wise(X0))) [flattening 68]
70. ! [X0] : (((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | (~funny(X0) & ~tall(X0))) [nnf transformation 39]
73. ? [X0] : ~strong(X0) => ~strong(sK7) [choice axiom]
74. ~strong(sK7) [skolemisation 20,73]
89. ~humble(X0) | tall(X0) [cnf transformation 30]
108. patient(paul) | tall(X1) [cnf transformation 61]
111. ~tall(X0) | strong(X0) | funny(X0) [cnf transformation 63]
114. ~strong(X0) | ~tall(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 63]
119. ~funny(X0) | wise(X0) [cnf transformation 36]
124. ~wise(X0) | strong(X0) [cnf transformation 69]
125. ~wise(X0) | ~curious(X0) [cnf transformation 69]
129. ~funny(X0) | humble(X0) | curious(X0) [cnf transformation 70]
135. ~strong(sK7) [cnf transformation 74]
141. funny(paul) [cnf transformation 24]
218. 18 <=> patient(paul) [avatar definition]
219. patient(paul) <- (18) [avatar component clause 218]
227. 20 <=> ! [X1] : tall(X1) [avatar definition]
228. tall(X1) <- (20) [avatar component clause 227]
229. 20 | 18 [avatar split clause 108,218,227]
309. wise(paul) [resolution 119,141]
311. strong(paul) [resolution 124,309]
313. ~curious(paul) [resolution 125,309]
347. strong(X0) | funny(X0) <- (20) [resolution 111,228]
348. funny(sK7) <- (20) [resolution 347,135]
352. wise(sK7) <- (20) [resolution 348,119]
355. strong(sK7) <- (20) [resolution 352,124]
356. $false <- (20) [subsumption resolution 355,135]
357. ~20 [avatar contradiction clause 356]
363. humble(paul) | curious(paul) [resolution 129,141]
364. humble(paul) [subsumption resolution 363,313]
365. tall(paul) [resolution 364,89]
382. ~tall(paul) | ~patient(paul) | ~funny(paul) [resolution 114,311]
384. ~patient(paul) | ~funny(paul) [subsumption resolution 382,365]
385. ~funny(paul) <- (18) [subsumption resolution 384,219]
386. $false <- (18) [subsumption resolution 385,141]
387. ~18 [avatar contradiction clause 386]
388. $false [avatar sat refutation 229,357,387]
% SZS output end Proof for 5854092358757271745583318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and creative then someone is old or kind and vice versa.
If someone is either not patient or strong then someone is not humble.
Everyone who is not funny or happy is either not kind or strong.
Everyone who is both happy and tall is either not kind or old and vice versa.
Everyone who is not brave is not calm.
Everyone who is tall is rich or wise and vice versa.
If someone is humble or quiet then fred is not wise.
Everyone who is both calm and not happy is brave or strong and vice versa.
Everyone who is both not creative and funny is not calm or happy.
If someone is both tall and not funny then someone is humble or rich and vice versa.
Everyone who is rich is calm or brave.
If someone is both creative and strong then mary is both not kind and happy and vice versa.
If susan is not brave or kind then fred is either not old or not funny.
If lucy is both not patient and happy then paul is not generous or not calm.
If someone is creative then paul is both brave and rich and vice versa.
If someone is not humble then paul is both quiet and wise.
Someone is not brave.
Someone is not kind or not funny.
Someone is not humble or generous.
Someone is old.
Lucy is funny.
Someone is not rich or not old.
Someone is either humble or not calm. | Paul is rich. | entailment | ((?[X]:((~kind(X)&creative(X))))<=>(?[X]:((old(X)|kind(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:(~humble(X))))&
(![X]:((~funny(X)|happy(X))=>(~kind(X)<~>strong(X))))&
(![X]:((happy(X)&tall(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~brave(X)=>~calm(X)))&
(![X]:(tall(X)<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)|quiet(X))))=>(~wise(fred)))&
(![X]:((calm(X)&~happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~creative(X)&funny(X))=>(~calm(X)|happy(X))))&
((?[X]:((tall(X)&~funny(X))))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(rich(X)=>(calm(X)|brave(X))))&
((?[X]:((creative(X)&strong(X))))<=>((~kind(mary)&happy(mary))))&
(((~brave(susan)|kind(susan)))=>((~old(fred)<~>~funny(fred))))&
(((~patient(lucy)&happy(lucy)))=>((~generous(paul)|~calm(paul))))&
((?[X]:(creative(X)))<=>((brave(paul)&rich(paul))))&
((?[X]:(~humble(X)))=>((quiet(paul)&wise(paul))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)|~funny(X))))&
(?[X]:((~humble(X)|generous(X))))&
(?[X]:(old(X)))&
(funny(lucy))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((humble(X)<~>~calm(X)))) | rich(paul) | [
"p0",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9148932456338158379222750
% SZS output start Proof for 9148932456338158379222750
1. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X0] : (kind(X0) | old(X0)) [input p0]
15. ? [X0] : creative(X0) <=> (rich(paul) & brave(paul)) [input p14]
20. ? [X0] : old(X0) [input p19]
24. ~rich(paul) [input hypothesis]
25. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X1] : (kind(X1) | old(X1)) [rectify 1]
40. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~kind(X1) & ~old(X1))) & (? [X1] : (kind(X1) | old(X1)) | ! [X0] : (~creative(X0) | kind(X0))) [nnf transformation 25]
41. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~kind(X1) & ~old(X1))) & (? [X2] : (kind(X2) | old(X2)) | ! [X3] : (~creative(X3) | kind(X3))) [rectify 40]
42. ? [X0] : (creative(X0) & ~kind(X0)) => (creative(sK0) & ~kind(sK0)) [choice axiom]
43. ? [X2] : (kind(X2) | old(X2)) => (kind(sK1) | old(sK1)) [choice axiom]
44. ((creative(sK0) & ~kind(sK0)) | ! [X1] : (~kind(X1) & ~old(X1))) & ((kind(sK1) | old(sK1)) | ! [X3] : (~creative(X3) | kind(X3))) [skolemisation 41,43,42]
67. (? [X0] : creative(X0) | (~rich(paul) | ~brave(paul))) & ((rich(paul) & brave(paul)) | ! [X0] : ~creative(X0)) [nnf transformation 15]
68. (? [X0] : creative(X0) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X0] : ~creative(X0)) [flattening 67]
69. (? [X0] : creative(X0) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X1] : ~creative(X1)) [rectify 68]
70. ? [X0] : creative(X0) => creative(sK6) [choice axiom]
71. (creative(sK6) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X1] : ~creative(X1)) [skolemisation 69,70]
78. ? [X0] : old(X0) => old(sK10) [choice axiom]
79. old(sK10) [skolemisation 20,78]
88. creative(sK0) | ~old(X1) [cnf transformation 44]
130. rich(paul) | ~creative(X1) [cnf transformation 71]
137. old(sK10) [cnf transformation 79]
142. ~rich(paul) [cnf transformation 24]
147. 2 <=> creative(sK0) [avatar definition]
149. creative(sK0) <- (2) [avatar component clause 147]
152. 3 <=> ! [X1] : ~old(X1) [avatar definition]
153. ~old(X1) <- (3) [avatar component clause 152]
154. 3 | 2 [avatar split clause 88,147,152]
290. 34 <=> rich(paul) [avatar definition]
299. 36 <=> ! [X1] : ~creative(X1) [avatar definition]
300. ~creative(X1) <- (36) [avatar component clause 299]
301. 36 | 34 [avatar split clause 130,290,299]
353. ~34 [avatar split clause 142,290]
360. $false <- (2, 36) [subsumption resolution 149,300]
361. ~2 | ~36 [avatar contradiction clause 360]
362. $false <- (3) [resolution 153,137]
363. ~3 [avatar contradiction clause 362]
364. $false [avatar sat refutation 154,301,353,361,363]
% SZS output end Proof for 9148932456338158379222750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or wise is not wise or not calm and vice versa.
Everyone who is wise is calm or not strong.
Everyone who is not quiet is either strong or rich.
If someone is both quiet and not humble then someone is quiet.
Everyone who is either quiet or not funny is not humble and vice versa.
If someone is kind then someone is either happy or not kind and vice versa.
Everyone who is either humble or tall is brave or kind and vice versa.
Everyone who is not strong or quiet is funny and vice versa.
Everyone who is either not calm or not kind is not tall or funny and vice versa.
Everyone who is both not quiet and brave is both not curious and funny and vice versa.
Everyone who is both not humble and not generous is strong.
Everyone who is not kind is rich or generous and vice versa.
If mary is either humble or wise then paul is both not creative and wise and vice versa.
Everyone who is tall is both patient and not brave and vice versa.
Someone is either not wise or quiet.
Someone is generous or strong.
Fred is generous or strong.
John is both not calm and happy. | John is strong. | entailment | (![X]:((~rich(X)<~>wise(X))<=>(~wise(X)|~calm(X))))&
(![X]:(wise(X)=>(calm(X)|~strong(X))))&
(![X]:(~quiet(X)=>(strong(X)<~>rich(X))))&
((?[X]:((quiet(X)&~humble(X))))=>(?[X]:(quiet(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>~humble(X)))&
((?[X]:(kind(X)))<=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((humble(X)<~>tall(X))<=>(brave(X)|kind(X))))&
(![X]:((~strong(X)|quiet(X))<=>funny(X)))&
(![X]:((~calm(X)<~>~kind(X))<=>(~tall(X)|funny(X))))&
(![X]:((~quiet(X)&brave(X))<=>(~curious(X)&funny(X))))&
(![X]:((~humble(X)&~generous(X))=>strong(X)))&
(![X]:(~kind(X)<=>(rich(X)|generous(X))))&
(((humble(mary)<~>wise(mary)))<=>((~creative(paul)&wise(paul))))&
(![X]:(tall(X)<=>(patient(X)&~brave(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((generous(X)|strong(X))))&
((generous(fred)|strong(fred)))&
((~calm(john)&happy(john))) | strong(john) | [
"p0",
"p2",
"p4",
"p7",
"p8",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8681180706866446705462701
% SZS output start Proof for 8681180706866446705462701
1. ! [X0] : ((~rich(X0) <~> wise(X0)) <=> (~calm(X0) | ~wise(X0))) [input p0]
3. ! [X0] : (~quiet(X0) => (strong(X0) <~> rich(X0))) [input p2]
5. ! [X0] : ((quiet(X0) <~> ~funny(X0)) <=> ~humble(X0)) [input p4]
8. ! [X0] : ((quiet(X0) | ~strong(X0)) <=> funny(X0)) [input p7]
9. ! [X0] : ((~calm(X0) <~> ~kind(X0)) <=> (funny(X0) | ~tall(X0))) [input p8]
11. ! [X0] : ((~generous(X0) & ~humble(X0)) => strong(X0)) [input p10]
12. ! [X0] : (~kind(X0) <=> (generous(X0) | rich(X0))) [input p11]
18. happy(john) & ~calm(john) [input p17]
19. ~strong(john) [input hypothesis]
24. ! [X0] : ((strong(X0) <~> rich(X0)) | quiet(X0)) [ennf transformation 3]
26. ! [X0] : (strong(X0) | (generous(X0) | humble(X0))) [ennf transformation 11]
27. ! [X0] : (strong(X0) | generous(X0) | humble(X0)) [flattening 26]
28. ! [X0] : ((((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0))))) [nnf transformation 1]
29. ! [X0] : ((((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0))))) [flattening 28]
30. ! [X0] : (((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | quiet(X0)) [nnf transformation 24]
34. ! [X0] : ((((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | humble(X0)) & (~humble(X0) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0))))) [nnf transformation 5]
42. ! [X0] : (((quiet(X0) | ~strong(X0)) | ~funny(X0)) & (funny(X0) | (~quiet(X0) & strong(X0)))) [nnf transformation 8]
43. ! [X0] : ((quiet(X0) | ~strong(X0) | ~funny(X0)) & (funny(X0) | (~quiet(X0) & strong(X0)))) [flattening 42]
44. ! [X0] : ((((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | (~funny(X0) & tall(X0))) & ((funny(X0) | ~tall(X0)) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0))))) [nnf transformation 9]
45. ! [X0] : ((((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | (~funny(X0) & tall(X0))) & (funny(X0) | ~tall(X0) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0))))) [flattening 44]
48. ! [X0] : ((~kind(X0) | (~generous(X0) & ~rich(X0))) & ((generous(X0) | rich(X0)) | kind(X0))) [nnf transformation 12]
49. ! [X0] : ((~kind(X0) | (~generous(X0) & ~rich(X0))) & (generous(X0) | rich(X0) | kind(X0))) [flattening 48]
60. ~calm(X0) | ~wise(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 29]
61. wise(X0) | ~rich(X0) | wise(X0) [cnf transformation 29]
66. quiet(X0) | strong(X0) | rich(X0) [cnf transformation 30]
69. ~funny(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 34]
83. funny(X0) | strong(X0) [cnf transformation 43]
91. ~funny(X0) | calm(X0) | kind(X0) [cnf transformation 45]
96. generous(X0) | strong(X0) | humble(X0) [cnf transformation 27]
98. ~kind(X0) | ~rich(X0) [cnf transformation 49]
99. ~generous(X0) | ~kind(X0) [cnf transformation 49]
113. ~calm(john) [cnf transformation 18]
115. ~strong(john) [cnf transformation 19]
116. ~calm(X0) | ~wise(X0) | ~rich(X0) [duplicate literal removal 60]
117. ~rich(X0) | wise(X0) [duplicate literal removal 61]
118. ~calm(X0) | ~rich(X0) [subsumption resolution 116,117]
235. ~humble(X0) | ~quiet(X0) | strong(X0) [resolution 69,83]
289. kind(X0) | calm(X0) | strong(X0) [resolution 91,83]
313. ~kind(X0) | humble(X0) | strong(X0) [resolution 96,99]
392. calm(X3) | strong(X3) | ~rich(X3) [resolution 289,98]
397. ~rich(X3) | strong(X3) [subsumption resolution 392,118]
443. humble(X0) | strong(X0) | calm(X0) | strong(X0) [resolution 313,289]
444. humble(X0) | strong(X0) | calm(X0) [duplicate literal removal 443]
455. strong(X0) | calm(X0) | ~quiet(X0) | strong(X0) [resolution 444,235]
461. ~quiet(X0) | calm(X0) | strong(X0) [duplicate literal removal 455]
611. calm(X0) | strong(X0) | strong(X0) | rich(X0) [resolution 461,66]
613. calm(X0) | strong(X0) | rich(X0) [duplicate literal removal 611]
614. strong(X0) | calm(X0) [subsumption resolution 613,397]
697. calm(john) [resolution 614,115]
702. $false [subsumption resolution 697,113]
% SZS output end Proof for 8681180706866446705462701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not calm is both not creative and calm and vice versa.
Everyone who is both generous and not wise is either quiet or curious and vice versa.
If someone is either not old or not creative then fred is generous or patient and vice versa.
Everyone who is not humble or not wise is not humble or not kind and vice versa.
Everyone who is not wise is not brave and vice versa.
Everyone who is not brave or kind is not humble and vice versa.
Everyone who is curious or rich is old or not old.
Everyone who is not wise or not happy is not tall.
Everyone who is strong is not creative and vice versa.
Everyone who is curious is either wise or not tall and vice versa.
If someone is both old and not rich then susan is either funny or quiet.
Everyone who is creative or generous is either patient or not creative and vice versa.
If mary is patient or not old then fred is not happy or not funny.
If someone is either tall or not creative then fred is not strong or brave and vice versa.
Everyone who is both not humble and wise is not calm and vice versa.
Everyone who is generous or not old is not old or creative.
Someone is not curious or not kind.
Mary is funny or generous.
Someone is either quiet or funny.
Someone is curious or not old.
Someone is either humble or funny.
Alice is both rich and not strong.
Someone is both not calm and not old.
Susan is both curious and not quiet. | Susan is not strong. | entailment | (![X]:((tall(X)&~calm(X))<=>(~creative(X)&calm(X))))&
(![X]:((generous(X)&~wise(X))<=>(quiet(X)<~>curious(X))))&
((?[X]:((~old(X)<~>~creative(X))))<=>((generous(fred)|patient(fred))))&
(![X]:((~humble(X)|~wise(X))<=>(~humble(X)|~kind(X))))&
(![X]:(~wise(X)<=>~brave(X)))&
(![X]:((~brave(X)|kind(X))<=>~humble(X)))&
(![X]:((curious(X)|rich(X))=>(old(X)|~old(X))))&
(![X]:((~wise(X)|~happy(X))=>~tall(X)))&
(![X]:(strong(X)<=>~creative(X)))&
(![X]:(curious(X)<=>(wise(X)<~>~tall(X))))&
((?[X]:((old(X)&~rich(X))))=>((funny(susan)<~>quiet(susan))))&
(![X]:((creative(X)|generous(X))<=>(patient(X)<~>~creative(X))))&
(((patient(mary)|~old(mary)))=>((~happy(fred)|~funny(fred))))&
((?[X]:((tall(X)<~>~creative(X))))<=>((~strong(fred)|brave(fred))))&
(![X]:((~humble(X)&wise(X))<=>~calm(X)))&
(![X]:((generous(X)|~old(X))=>(~old(X)|creative(X))))&
(?[X]:((~curious(X)|~kind(X))))&
((funny(mary)|generous(mary)))&
(?[X]:((quiet(X)<~>funny(X))))&
(?[X]:((curious(X)|~old(X))))&
(?[X]:((humble(X)<~>funny(X))))&
((rich(alice)&~strong(alice)))&
(?[X]:((~calm(X)&~old(X))))&
((curious(susan)&~quiet(susan))) | ~strong(susan) | [
"p0",
"p1",
"p8",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4481486190027570568297457
% SZS output start Proof for 4481486190027570568297457
1. ! [X0] : ((~calm(X0) & tall(X0)) <=> (calm(X0) & ~creative(X0))) [input p0]
2. ! [X0] : ((~wise(X0) & generous(X0)) <=> (quiet(X0) <~> curious(X0))) [input p1]
9. ! [X0] : (strong(X0) <=> ~creative(X0)) [input p8]
15. ! [X0] : ((wise(X0) & ~humble(X0)) <=> ~calm(X0)) [input p14]
24. ~quiet(susan) & curious(susan) [input p23]
25. strong(susan) [input hypothesis]
34. ! [X0] : (((~calm(X0) & tall(X0)) | (~calm(X0) | creative(X0))) & ((calm(X0) & ~creative(X0)) | (calm(X0) | ~tall(X0)))) [nnf transformation 1]
35. ! [X0] : (((~calm(X0) & tall(X0)) | ~calm(X0) | creative(X0)) & ((calm(X0) & ~creative(X0)) | calm(X0) | ~tall(X0))) [flattening 34]
36. ! [X0] : (((~wise(X0) & generous(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (wise(X0) | ~generous(X0)))) [nnf transformation 2]
37. ! [X0] : (((~wise(X0) & generous(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | wise(X0) | ~generous(X0))) [flattening 36]
48. ! [X0] : ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0))) [nnf transformation 9]
58. ! [X0] : (((wise(X0) & ~humble(X0)) | calm(X0)) & (~calm(X0) | (~wise(X0) | humble(X0)))) [nnf transformation 15]
59. ! [X0] : (((wise(X0) & ~humble(X0)) | calm(X0)) & (~calm(X0) | ~wise(X0) | humble(X0))) [flattening 58]
75. ~calm(X0) | ~calm(X0) | creative(X0) [cnf transformation 35]
81. ~curious(X0) | quiet(X0) | ~wise(X0) [cnf transformation 37]
101. ~strong(X0) | ~creative(X0) [cnf transformation 48]
125. wise(X0) | calm(X0) [cnf transformation 59]
139. curious(susan) [cnf transformation 24]
140. ~quiet(susan) [cnf transformation 24]
141. strong(susan) [cnf transformation 25]
145. ~calm(X0) | creative(X0) [duplicate literal removal 75]
184. 9 <=> quiet(susan) [avatar definition]
186. ~quiet(susan) <- (~9) [avatar component clause 184]
282. ~9 [avatar split clause 140,184]
286. ~creative(susan) [resolution 101,141]
316. quiet(susan) | ~wise(susan) [resolution 81,139]
318. ~wise(susan) <- (~9) [subsumption resolution 316,186]
319. calm(susan) <- (~9) [resolution 318,125]
388. creative(susan) <- (~9) [resolution 319,145]
389. $false <- (~9) [subsumption resolution 388,286]
390. 9 [avatar contradiction clause 389]
391. $false [avatar sat refutation 282,390]
% SZS output end Proof for 4481486190027570568297457
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is not brave or kind.
If fred is tall then someone is not curious and vice versa.
Everyone who is both not brave and happy is funny or calm.
If susan is both not funny and brave then someone is curious and vice versa.
If mary is either not humble or not creative then someone is either generous or quiet and vice versa.
Everyone who is either humble or calm is either happy or old.
Everyone who is curious or patient is either strong or kind.
If fred is both curious and happy then susan is funny and vice versa.
Everyone who is curious or creative is both not kind and generous.
Everyone who is happy or not kind is not curious.
Everyone who is not brave is both not happy and not brave.
Everyone who is both happy and not tall is generous and vice versa.
If someone is not calm or not humble then mary is not strong or calm and vice versa.
If someone is not creative then someone is not strong or not creative and vice versa.
Everyone who is not humble is both not kind and not brave.
If john is either old or tall then someone is not happy.
John is not quiet.
Paul is either curious or not happy.
Fred is humble or not kind.
Someone is either quiet or not curious.
Alice is either not old or not generous.
Someone is not old.
Someone is either not kind or creative.
Someone is either not humble or old. | Paul is not curious. | entailment | ((?[X]:(~wise(X)))=>(?[X]:((~brave(X)|kind(X)))))&
((tall(fred))<=>(?[X]:(~curious(X))))&
(![X]:((~brave(X)&happy(X))=>(funny(X)|calm(X))))&
(((~funny(susan)&brave(susan)))<=>(?[X]:(curious(X))))&
(((~humble(mary)<~>~creative(mary)))<=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:((humble(X)<~>calm(X))=>(happy(X)<~>old(X))))&
(![X]:((curious(X)|patient(X))=>(strong(X)<~>kind(X))))&
(((curious(fred)&happy(fred)))<=>(funny(susan)))&
(![X]:((curious(X)|creative(X))=>(~kind(X)&generous(X))))&
(![X]:((happy(X)|~kind(X))=>~curious(X)))&
(![X]:(~brave(X)=>(~happy(X)&~brave(X))))&
(![X]:((happy(X)&~tall(X))<=>generous(X)))&
((?[X]:((~calm(X)|~humble(X))))<=>((~strong(mary)|calm(mary))))&
((?[X]:(~creative(X)))<=>(?[X]:((~strong(X)|~creative(X)))))&
(![X]:(~humble(X)=>(~kind(X)&~brave(X))))&
(((old(john)<~>tall(john)))=>(?[X]:(~happy(X))))&
(~quiet(john))&
((curious(paul)<~>~happy(paul)))&
((humble(fred)|~kind(fred)))&
(?[X]:((quiet(X)<~>~curious(X))))&
((~old(alice)<~>~generous(alice)))&
(?[X]:(~old(X)))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((~humble(X)<~>old(X)))) | ~curious(paul) | [
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 9144730538948176062506230
% SZS output start Proof for 9144730538948176062506230
10. ! [X0] : ((~kind(X0) | happy(X0)) => ~curious(X0)) [input p9]
18. curious(paul) <~> ~happy(paul) [input p17]
25. curious(paul) [input hypothesis]
35. ! [X0] : (~curious(X0) | (kind(X0) & ~happy(X0))) [ennf transformation 10]
71. (happy(paul) | ~curious(paul)) & (~happy(paul) | curious(paul)) [nnf transformation 18]
111. ~curious(X0) | ~happy(X0) [cnf transformation 35]
131. happy(paul) | ~curious(paul) [cnf transformation 71]
142. curious(paul) [cnf transformation 25]
278. ~curious(paul) [subsumption resolution 131,111]
312. $false [subsumption resolution 142,278]
% SZS output end Proof for 9144730538948176062506230
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not patient is either creative or old.
Everyone who is both tall and not wise is both not funny and wise and vice versa.
Everyone who is either wise or not brave is both not kind and not old and vice versa.
If john is not calm or not generous then someone is either strong or brave.
If lucy is not brave or not happy then fred is not happy.
If susan is both rich and not old then susan is either not rich or not wise and vice versa.
Everyone who is both not creative and not happy is tall or not strong and vice versa.
If someone is creative then paul is funny and vice versa.
If lucy is not patient or not funny then lucy is either happy or tall and vice versa.
If someone is not calm then someone is both not old and not humble.
If someone is generous or patient then lucy is either not patient or funny and vice versa.
Everyone who is kind or patient is both not kind and creative and vice versa.
Everyone who is humble is either not kind or patient.
Everyone who is not quiet or not generous is creative and vice versa.
If someone is either rich or not calm then someone is both brave and patient and vice versa.
If lucy is either creative or not generous then susan is both not brave and creative and vice versa.
Someone is not brave or not humble.
John is brave or wise.
Someone is not old or strong.
Someone is either not creative or creative.
Lucy is creative.
Someone is either creative or kind.
John is patient or not patient. | Lucy is not brave. | neutral | (![X]:((~kind(X)&~patient(X))=>(creative(X)<~>old(X))))&
(![X]:((tall(X)&~wise(X))<=>(~funny(X)&wise(X))))&
(![X]:((wise(X)<~>~brave(X))<=>(~kind(X)&~old(X))))&
(((~calm(john)|~generous(john)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~brave(lucy)|~happy(lucy)))=>(~happy(fred)))&
(((rich(susan)&~old(susan)))<=>((~rich(susan)<~>~wise(susan))))&
(![X]:((~creative(X)&~happy(X))<=>(tall(X)|~strong(X))))&
((?[X]:(creative(X)))<=>(funny(paul)))&
(((~patient(lucy)|~funny(lucy)))<=>((happy(lucy)<~>tall(lucy))))&
((?[X]:(~calm(X)))=>(?[X]:((~old(X)&~humble(X)))))&
((?[X]:((generous(X)|patient(X))))<=>((~patient(lucy)<~>funny(lucy))))&
(![X]:((kind(X)|patient(X))<=>(~kind(X)&creative(X))))&
(![X]:(humble(X)=>(~kind(X)<~>patient(X))))&
(![X]:((~quiet(X)|~generous(X))<=>creative(X)))&
((?[X]:((rich(X)<~>~calm(X))))<=>(?[X]:((brave(X)&patient(X)))))&
(((creative(lucy)<~>~generous(lucy)))<=>((~brave(susan)&creative(susan))))&
(?[X]:((~brave(X)|~humble(X))))&
((brave(john)|wise(john)))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:((~creative(X)<~>creative(X))))&
(creative(lucy))&
(?[X]:((creative(X)<~>kind(X))))&
((patient(john)|~patient(john))) | ~brave(lucy) | [] | null | 0 |
Everyone who is both calm and not funny is humble or not generous and vice versa. Everyone who is either funny or happy is not patient. If susan is not happy then someone is not brave or wise. If someone is both humble and creative then lucy is old or brave and vice versa. If someone is either brave or not humble then lucy is either tall or creative and vice versa. If someone is not old then fred is not humble and vice versa. Everyone who is either kind or old is both happy and rich. If mary is either strong or wise then alice is both generous and creative and vice versa. Everyone who is either strong or kind is brave. If fred is both not brave and not humble then fred is not generous and vice versa. If someone is either strong or not creative then someone is either not wise or happy and vice versa. If john is not rich then someone is brave. If mary is either humble or not funny then susan is either creative or not kind. Everyone who is both curious and kind is either not quiet or not humble and vice versa. Everyone who is both not brave and funny is not funny or wise and vice versa. If alice is either brave or calm then someone is both tall and kind and vice versa. Someone is not strong or not old. John is wise. Paul is either not old or not rich. Lucy is old or quiet. Someone is happy. | Fred is old. | neutral | (![X]:((calm(X)&~funny(X))<=>(humble(X)|~generous(X))))&
(![X]:((funny(X)<~>happy(X))=>~patient(X)))&
((~happy(susan))=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((humble(X)&creative(X))))<=>((old(lucy)|brave(lucy))))&
((?[X]:((brave(X)<~>~humble(X))))<=>((tall(lucy)<~>creative(lucy))))&
((?[X]:(~old(X)))<=>(~humble(fred)))&
(![X]:((kind(X)<~>old(X))=>(happy(X)&rich(X))))&
(((strong(mary)<~>wise(mary)))<=>((generous(alice)&creative(alice))))&
(![X]:((strong(X)<~>kind(X))=>brave(X)))&
(((~brave(fred)&~humble(fred)))<=>(~generous(fred)))&
((?[X]:((strong(X)<~>~creative(X))))<=>(?[X]:((~wise(X)<~>happy(X)))))&
((~rich(john))=>(?[X]:(brave(X))))&
(((humble(mary)<~>~funny(mary)))=>((creative(susan)<~>~kind(susan))))&
(![X]:((curious(X)&kind(X))<=>(~quiet(X)<~>~humble(X))))&
(![X]:((~brave(X)&funny(X))<=>(~funny(X)|wise(X))))&
(((brave(alice)<~>calm(alice)))<=>(?[X]:((tall(X)&kind(X)))))&
(?[X]:((~strong(X)|~old(X))))&
(wise(john))&
((~old(paul)<~>~rich(paul)))&
((old(lucy)|quiet(lucy)))&
(?[X]:(happy(X))) | old(fred) | [] | null | 0 |
Everyone who is generous is both not calm and not rich. If john is either not creative or calm then someone is not strong. Everyone who is both not old and not creative is both brave and not strong. If someone is either happy or generous then lucy is either funny or not creative. If someone is both not tall and calm then mary is curious. If lucy is not creative then john is quiet and vice versa. Everyone who is not creative or funny is not curious or rich and vice versa. Everyone who is funny is either not calm or tall and vice versa. Everyone who is not old or not funny is both funny and wise. Everyone who is not happy is not quiet or not brave. If lucy is wise or not curious then john is calm or happy and vice versa. Everyone who is not patient or wise is both generous and curious and vice versa. If someone is brave or not rich then mary is not generous and vice versa. If alice is both not brave and not happy then someone is rich or not kind. Everyone who is not calm is not humble or strong. Everyone who is either patient or generous is either not strong or patient and vice versa. Someone is either strong or not rich. Fred is quiet or not creative. Fred is both happy and not humble. Someone is both tall and not happy. Mary is happy. Someone is both not rich and tall. Someone is not strong or old. Mary is either strong or rich. | Mary is curious. | contradiction | (![X]:(generous(X)=>(~calm(X)&~rich(X))))&
(((~creative(john)<~>calm(john)))=>(?[X]:(~strong(X))))&
(![X]:((~old(X)&~creative(X))=>(brave(X)&~strong(X))))&
((?[X]:((happy(X)<~>generous(X))))=>((funny(lucy)<~>~creative(lucy))))&
((?[X]:((~tall(X)&calm(X))))=>(curious(mary)))&
((~creative(lucy))<=>(quiet(john)))&
(![X]:((~creative(X)|funny(X))<=>(~curious(X)|rich(X))))&
(![X]:(funny(X)<=>(~calm(X)<~>tall(X))))&
(![X]:((~old(X)|~funny(X))=>(funny(X)&wise(X))))&
(![X]:(~happy(X)=>(~quiet(X)|~brave(X))))&
(((wise(lucy)|~curious(lucy)))<=>((calm(john)|happy(john))))&
(![X]:((~patient(X)|wise(X))<=>(generous(X)&curious(X))))&
((?[X]:((brave(X)|~rich(X))))<=>(~generous(mary)))&
(((~brave(alice)&~happy(alice)))=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:(~calm(X)=>(~humble(X)|strong(X))))&
(![X]:((patient(X)<~>generous(X))<=>(~strong(X)<~>patient(X))))&
(?[X]:((strong(X)<~>~rich(X))))&
((quiet(fred)|~creative(fred)))&
((happy(fred)&~humble(fred)))&
(?[X]:((tall(X)&~happy(X))))&
(happy(mary))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((~strong(X)|old(X))))&
((strong(mary)<~>rich(mary))) | curious(mary) | [
"p6",
"p8",
"p11",
"p12",
"p15",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5287255189727831915683122
% SZS output start Proof for 5287255189727831915683122
7. ! [X0] : ((funny(X0) | ~creative(X0)) <=> (rich(X0) | ~curious(X0))) [input p6]
9. ! [X0] : ((~funny(X0) | ~old(X0)) => (wise(X0) & funny(X0))) [input p8]
12. ! [X0] : ((wise(X0) | ~patient(X0)) <=> (curious(X0) & generous(X0))) [input p11]
13. ? [X0] : (~rich(X0) | brave(X0)) <=> ~generous(mary) [input p12]
16. ! [X0] : ((patient(X0) <~> generous(X0)) <=> (~strong(X0) <~> patient(X0))) [input p15]
22. ? [X0] : (tall(X0) & ~rich(X0)) [input p21]
24. strong(mary) <~> rich(mary) [input p23]
25. curious(mary) [input hypothesis]
30. ! [X0] : (~funny(X0) => (wise(X0) & funny(X0))) [pure predicate removal 9]
36. ! [X0] : ((wise(X0) & funny(X0)) | funny(X0)) [ennf transformation 30]
44. ! [X0] : (((funny(X0) | ~creative(X0)) | (~rich(X0) & curious(X0))) & ((rich(X0) | ~curious(X0)) | (~funny(X0) & creative(X0)))) [nnf transformation 7]
45. ! [X0] : ((funny(X0) | ~creative(X0) | (~rich(X0) & curious(X0))) & (rich(X0) | ~curious(X0) | (~funny(X0) & creative(X0)))) [flattening 44]
49. ! [X0] : (((wise(X0) | ~patient(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (~wise(X0) & patient(X0)))) [nnf transformation 12]
50. ! [X0] : ((wise(X0) | ~patient(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | (~wise(X0) & patient(X0)))) [flattening 49]
51. (? [X0] : (~rich(X0) | brave(X0)) | generous(mary)) & (~generous(mary) | ! [X0] : (rich(X0) & ~brave(X0))) [nnf transformation 13]
52. (? [X0] : (~rich(X0) | brave(X0)) | generous(mary)) & (~generous(mary) | ! [X1] : (rich(X1) & ~brave(X1))) [rectify 51]
53. ? [X0] : (~rich(X0) | brave(X0)) => (~rich(sK1) | brave(sK1)) [choice axiom]
54. ((~rich(sK1) | brave(sK1)) | generous(mary)) & (~generous(mary) | ! [X1] : (rich(X1) & ~brave(X1))) [skolemisation 52,53]
55. ! [X0] : ((((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0))))) [nnf transformation 16]
61. ? [X0] : (tall(X0) & ~rich(X0)) => (tall(sK4) & ~rich(sK4)) [choice axiom]
62. tall(sK4) & ~rich(sK4) [skolemisation 22,61]
63. (~rich(mary) | ~strong(mary)) & (rich(mary) | strong(mary)) [nnf transformation 24]
76. ~curious(X0) | rich(X0) | ~funny(X0) [cnf transformation 45]
83. funny(X0) | funny(X0) [cnf transformation 36]
90. patient(X0) | generous(X0) [cnf transformation 50]
96. ~generous(mary) | rich(X1) [cnf transformation 54]
100. ~patient(X0) | strong(X0) | generous(X0) | ~patient(X0) [cnf transformation 55]
113. ~rich(sK4) [cnf transformation 62]
116. ~rich(mary) | ~strong(mary) [cnf transformation 63]
117. curious(mary) [cnf transformation 25]
119. ~patient(X0) | strong(X0) | generous(X0) [duplicate literal removal 100]
122. funny(X0) [duplicate literal removal 83]
159. 9 <=> curious(mary) [avatar definition]
161. curious(mary) <- (9) [avatar component clause 159]
186. 14 <=> generous(mary) [avatar definition]
199. 17 <=> ! [X1] : rich(X1) [avatar definition]
200. rich(X1) <- (17) [avatar component clause 199]
201. 17 | ~14 [avatar split clause 96,186,199]
206. strong(X0) | generous(X0) [subsumption resolution 119,90]
228. 23 <=> strong(mary) [avatar definition]
230. ~strong(mary) <- (~23) [avatar component clause 228]
232. 24 <=> rich(mary) [avatar definition]
235. ~23 | ~24 [avatar split clause 116,232,228]
237. 9 [avatar split clause 117,159]
246. rich(mary) | ~funny(mary) <- (9) [resolution 76,161]
250. rich(mary) <- (9) [subsumption resolution 246,122]
251. 24 | ~9 [avatar split clause 250,159,232]
257. generous(mary) <- (~23) [resolution 230,206]
260. 14 | 23 [avatar split clause 257,228,186]
264. $false <- (17) [resolution 200,113]
265. ~17 [avatar contradiction clause 264]
268. $false [avatar sat refutation 201,235,237,251,260,265]
% SZS output end Proof for 5287255189727831915683122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Paul is not kind. | contradiction | (![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))) | ~kind(paul) | [
"p0",
"p2",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8411620244843849027507549
% SZS output start Proof for 8411620244843849027507549
1. ! [X0] : (strong(X0) <=> (~quiet(X0) & curious(X0))) [input p0]
3. ! [X0] : ((~rich(X0) | ~funny(X0)) <=> (~curious(X0) & humble(X0))) [input p2]
7. ! [X0] : (~strong(X0) <=> (kind(X0) & creative(X0))) [input p6]
14. ~funny(paul) <=> ? [X0] : (~kind(X0) <~> ~funny(X0)) [input p13]
22. ~kind(paul) [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]
39. ! [X0] : (((~rich(X0) | ~funny(X0)) | (curious(X0) | ~humble(X0))) & ((~curious(X0) & humble(X0)) | (rich(X0) & funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((~rich(X0) | ~funny(X0) | curious(X0) | ~humble(X0)) & ((~curious(X0) & humble(X0)) | (rich(X0) & funny(X0)))) [flattening 39]
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]
61. (~funny(paul) | ! [X0] : ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (? [X0] : ((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | funny(paul)) [nnf transformation 14]
62. (~funny(paul) | ! [X0] : ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (? [X1] : ((funny(X1) | kind(X1)) & (~funny(X1) | ~kind(X1))) | funny(paul)) [rectify 61]
63. ? [X1] : ((funny(X1) | kind(X1)) & (~funny(X1) | ~kind(X1))) => ((funny(sK4) | kind(sK4)) & (~funny(sK4) | ~kind(sK4))) [choice axiom]
64. (~funny(paul) | ! [X0] : ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(sK4) | kind(sK4)) & (~funny(sK4) | ~kind(sK4))) | funny(paul)) [skolemisation 62,63]
77. ~strong(X0) | curious(X0) [cnf transformation 33]
85. ~curious(X0) | funny(X0) [cnf transformation 40]
103. kind(X0) | strong(X0) [cnf transformation 50]
127. ~funny(paul) | ~funny(X0) | kind(X0) [cnf transformation 64]
138. ~kind(paul) [cnf transformation 22]
241. 23 <=> funny(paul) [avatar definition]
242. funny(paul) <- (23) [avatar component clause 241]
243. ~funny(paul) <- (~23) [avatar component clause 241]
246. 24 <=> ! [X0] : (~funny(X0) | kind(X0)) [avatar definition]
247. ~funny(X0) | kind(X0) <- (24) [avatar component clause 246]
248. 24 | ~23 [avatar split clause 127,241,246]
303. strong(paul) [resolution 103,138]
304. curious(paul) [resolution 303,77]
309. kind(paul) <- (23, 24) [resolution 247,242]
312. $false <- (23, 24) [subsumption resolution 309,138]
313. ~23 | ~24 [avatar contradiction clause 312]
359. funny(paul) [resolution 304,85]
360. $false <- (~23) [subsumption resolution 359,243]
361. 23 [avatar contradiction clause 360]
362. $false [avatar sat refutation 248,313,361]
% SZS output end Proof for 8411620244843849027507549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise or not rich is both quiet and generous and vice versa.
If someone is not tall or generous then paul is either not happy or humble.
If someone is either not creative or kind then paul is not funny or not wise and vice versa.
Everyone who is either not quiet or not wise is either wise or creative.
Everyone who is kind or wise is rich or brave and vice versa.
Everyone who is not happy or wise is not creative.
Everyone who is patient is both not strong and kind.
Everyone who is quiet is either not funny or not quiet.
Everyone who is both not old and not generous is either not strong or not quiet and vice versa.
Everyone who is not brave is not curious or not humble and vice versa.
Everyone who is not curious is not quiet or not rich.
If someone is either not curious or not rich then mary is brave or not quiet.
If susan is not quiet then someone is both not generous and not rich and vice versa.
Everyone who is either not happy or not kind is both not creative and not happy.
Everyone who is wise is quiet and vice versa.
Everyone who is not happy or not funny is both creative and quiet.
Someone is either not creative or quiet.
Someone is not strong or not kind.
Someone is creative or not old.
Someone is brave or calm.
Paul is not curious or happy.
John is both not creative and curious. | Mary is not rich. | entailment | (![X]:((~wise(X)<~>~rich(X))<=>(quiet(X)&generous(X))))&
((?[X]:((~tall(X)|generous(X))))=>((~happy(paul)<~>humble(paul))))&
((?[X]:((~creative(X)<~>kind(X))))<=>((~funny(paul)|~wise(paul))))&
(![X]:((~quiet(X)<~>~wise(X))=>(wise(X)<~>creative(X))))&
(![X]:((kind(X)|wise(X))<=>(rich(X)|brave(X))))&
(![X]:((~happy(X)|wise(X))=>~creative(X)))&
(![X]:(patient(X)=>(~strong(X)&kind(X))))&
(![X]:(quiet(X)=>(~funny(X)<~>~quiet(X))))&
(![X]:((~old(X)&~generous(X))<=>(~strong(X)<~>~quiet(X))))&
(![X]:(~brave(X)<=>(~curious(X)|~humble(X))))&
(![X]:(~curious(X)=>(~quiet(X)|~rich(X))))&
((?[X]:((~curious(X)<~>~rich(X))))=>((brave(mary)|~quiet(mary))))&
((~quiet(susan))<=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((~happy(X)<~>~kind(X))=>(~creative(X)&~happy(X))))&
(![X]:(wise(X)<=>quiet(X)))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
(?[X]:((~creative(X)<~>quiet(X))))&
(?[X]:((~strong(X)|~kind(X))))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((brave(X)|calm(X))))&
((~curious(paul)|happy(paul)))&
((~creative(john)&curious(john))) | ~rich(mary) | [
"p0",
"p5",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6791329123934794586986285
% SZS output start Proof for 6791329123934794586986285
1. ! [X0] : ((~wise(X0) <~> ~rich(X0)) <=> (generous(X0) & quiet(X0))) [input p0]
6. ! [X0] : ((wise(X0) | ~happy(X0)) => ~creative(X0)) [input p5]
8. ! [X0] : (quiet(X0) => (~funny(X0) <~> ~quiet(X0))) [input p7]
15. ! [X0] : (wise(X0) <=> quiet(X0)) [input p14]
16. ! [X0] : ((~funny(X0) | ~happy(X0)) => (quiet(X0) & creative(X0))) [input p15]
23. rich(mary) [input hypothesis]
29. ! [X0] : (~creative(X0) | (~wise(X0) & happy(X0))) [ennf transformation 6]
30. ! [X0] : ((~funny(X0) <~> ~quiet(X0)) | ~quiet(X0)) [ennf transformation 8]
36. ! [X0] : ((quiet(X0) & creative(X0)) | (funny(X0) & happy(X0))) [ennf transformation 16]
37. ! [X0] : ((((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0))))) [nnf transformation 1]
38. ! [X0] : ((((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0))))) [flattening 37]
48. ! [X0] : (((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | ~quiet(X0)) [nnf transformation 30]
59. ! [X0] : ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0))) [nnf transformation 15]
67. ~rich(X0) | quiet(X0) | wise(X0) [cnf transformation 38]
90. ~creative(X0) | ~wise(X0) [cnf transformation 29]
91. ~quiet(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 48]
112. ~wise(X0) | quiet(X0) [cnf transformation 59]
113. ~quiet(X0) | wise(X0) [cnf transformation 59]
115. funny(X0) | creative(X0) [cnf transformation 36]
125. rich(mary) [cnf transformation 23]
127. ~funny(X0) | ~quiet(X0) [duplicate literal removal 91]
179. 12 <=> quiet(mary) [avatar definition]
180. quiet(mary) <- (12) [avatar component clause 179]
243. ~quiet(X1) | creative(X1) [resolution 127,115]
244. quiet(mary) | wise(mary) [resolution 67,125]
249. quiet(mary) [subsumption resolution 244,112]
250. 12 [avatar split clause 249,179]
253. wise(mary) <- (12) [resolution 180,113]
260. creative(mary) <- (12) [resolution 243,180]
262. ~wise(mary) <- (12) [resolution 260,90]
264. $false <- (12) [subsumption resolution 262,253]
265. ~12 [avatar contradiction clause 264]
266. $false [avatar sat refutation 250,265]
% SZS output end Proof for 6791329123934794586986285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is either not tall or not brave and vice versa.
Everyone who is generous or kind is tall and vice versa.
Everyone who is either not calm or creative is either not happy or strong and vice versa.
If alice is kind or rich then someone is not calm or patient and vice versa.
Everyone who is either not kind or generous is not strong.
If mary is wise or not rich then someone is either not funny or not humble.
If susan is not strong or not tall then mary is either not tall or strong and vice versa.
If someone is calm then someone is both not rich and not strong.
Everyone who is both not rich and wise is both not creative and not strong.
If someone is either quiet or calm then mary is rich or not generous.
Everyone who is not strong or not curious is either quiet or strong.
Everyone who is old is kind.
Everyone who is either strong or not curious is not rich or happy.
If someone is both wise and not creative then lucy is both tall and humble.
If fred is either brave or wise then someone is humble and vice versa.
Everyone who is brave is not creative or not curious.
Paul is both not strong and not kind.
Alice is both wise and generous.
Someone is not brave or generous.
Paul is both not strong and funny.
Lucy is both funny and quiet.
Someone is both not tall and wise.
Someone is either not humble or generous.
Someone is generous or calm. | Paul is old. | contradiction | (![X]:(strong(X)<=>(~tall(X)<~>~brave(X))))&
(![X]:((generous(X)|kind(X))<=>tall(X)))&
(![X]:((~calm(X)<~>creative(X))<=>(~happy(X)<~>strong(X))))&
(((kind(alice)|rich(alice)))<=>(?[X]:((~calm(X)|patient(X)))))&
(![X]:((~kind(X)<~>generous(X))=>~strong(X)))&
(((wise(mary)|~rich(mary)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((~strong(susan)|~tall(susan)))<=>((~tall(mary)<~>strong(mary))))&
((?[X]:(calm(X)))=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((~rich(X)&wise(X))=>(~creative(X)&~strong(X))))&
((?[X]:((quiet(X)<~>calm(X))))=>((rich(mary)|~generous(mary))))&
(![X]:((~strong(X)|~curious(X))=>(quiet(X)<~>strong(X))))&
(![X]:(old(X)=>kind(X)))&
(![X]:((strong(X)<~>~curious(X))=>(~rich(X)|happy(X))))&
((?[X]:((wise(X)&~creative(X))))=>((tall(lucy)&humble(lucy))))&
(((brave(fred)<~>wise(fred)))<=>(?[X]:(humble(X))))&
(![X]:(brave(X)=>(~creative(X)|~curious(X))))&
((~strong(paul)&~kind(paul)))&
((wise(alice)&generous(alice)))&
(?[X]:((~brave(X)|generous(X))))&
((~strong(paul)&funny(paul)))&
((funny(lucy)&quiet(lucy)))&
(?[X]:((~tall(X)&wise(X))))&
(?[X]:((~humble(X)<~>generous(X))))&
(?[X]:((generous(X)|calm(X)))) | old(paul) | [
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 213756164230377452831929
% SZS output start Proof for 213756164230377452831929
12. ! [X0] : (old(X0) => kind(X0)) [input p11]
17. ~kind(paul) & ~strong(paul) [input p16]
25. old(paul) [input hypothesis]
35. ! [X0] : (kind(X0) | ~old(X0)) [ennf transformation 12]
116. ~old(X0) | kind(X0) [cnf transformation 35]
127. ~kind(paul) [cnf transformation 17]
140. old(paul) [cnf transformation 25]
298. kind(paul) [resolution 116,140]
299. $false [subsumption resolution 298,127]
% SZS output end Proof for 213756164230377452831929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or brave is not brave.
Everyone who is not wise or not happy is not kind or not funny.
Everyone who is either generous or not wise is either humble or not tall and vice versa.
If susan is both not strong and not brave then lucy is both not kind and brave and vice versa.
If mary is not rich or kind then someone is not funny or wise.
If someone is not humble or patient then lucy is tall or happy.
Everyone who is both creative and not old is creative and vice versa.
Everyone who is both funny and not generous is calm and vice versa.
If alice is funny then someone is rich and vice versa.
Everyone who is generous or happy is both generous and kind.
Everyone who is either not kind or generous is both quiet and not strong and vice versa.
Everyone who is not humble or funny is either creative or funny.
If susan is not rich or not creative then john is either not calm or not brave and vice versa.
Everyone who is both not kind and not rich is happy or not patient and vice versa.
Someone is both tall and patient.
Alice is patient or not creative.
Alice is either not patient or tall.
Someone is not funny or not tall.
Someone is both creative and not brave.
Susan is not quiet. | Susan is strong. | entailment | (![X]:((~tall(X)|brave(X))=>~brave(X)))&
(![X]:((~wise(X)|~happy(X))=>(~kind(X)|~funny(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(humble(X)<~>~tall(X))))&
(((~strong(susan)&~brave(susan)))<=>((~kind(lucy)&brave(lucy))))&
(((~rich(mary)|kind(mary)))=>(?[X]:((~funny(X)|wise(X)))))&
((?[X]:((~humble(X)|patient(X))))=>((tall(lucy)|happy(lucy))))&
(![X]:((creative(X)&~old(X))<=>creative(X)))&
(![X]:((funny(X)&~generous(X))<=>calm(X)))&
((funny(alice))<=>(?[X]:(rich(X))))&
(![X]:((generous(X)|happy(X))=>(generous(X)&kind(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(quiet(X)&~strong(X))))&
(![X]:((~humble(X)|funny(X))=>(creative(X)<~>funny(X))))&
(((~rich(susan)|~creative(susan)))<=>((~calm(john)<~>~brave(john))))&
(![X]:((~kind(X)&~rich(X))<=>(happy(X)|~patient(X))))&
(?[X]:((tall(X)&patient(X))))&
((patient(alice)|~creative(alice)))&
((~patient(alice)<~>tall(alice)))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((creative(X)&~brave(X))))&
(~quiet(susan)) | strong(susan) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 65083569207554348181686
% SZS output start Proof for 65083569207554348181686
1. ! [X0] : ((brave(X0) | ~tall(X0)) => ~brave(X0)) [input p0]
4. (~brave(susan) & ~strong(susan)) <=> (brave(lucy) & ~kind(lucy)) [input p3]
21. ~strong(susan) [input hypothesis]
22. ! [X0] : (~brave(X0) | (~brave(X0) & tall(X0))) [ennf transformation 1]
31. ((~brave(susan) & ~strong(susan)) | (~brave(lucy) | kind(lucy))) & ((brave(lucy) & ~kind(lucy)) | (brave(susan) | strong(susan))) [nnf transformation 4]
32. ((~brave(susan) & ~strong(susan)) | ~brave(lucy) | kind(lucy)) & ((brave(lucy) & ~kind(lucy)) | brave(susan) | strong(susan)) [flattening 31]
58. ~brave(X0) | ~brave(X0) [cnf transformation 22]
70. brave(lucy) | brave(susan) | strong(susan) [cnf transformation 32]
119. ~strong(susan) [cnf transformation 21]
121. ~brave(X0) [duplicate literal removal 58]
122. brave(susan) | strong(susan) [subsumption resolution 70,121]
123. strong(susan) [subsumption resolution 122,121]
219. $false [subsumption resolution 119,123]
% SZS output end Proof for 65083569207554348181686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either happy or not tall then john is either not creative or not old and vice versa. Everyone who is not patient is both not quiet and strong and vice versa. If someone is not old then john is either not brave or calm. If someone is both not brave and not happy then someone is either not creative or curious and vice versa. If paul is not old or not patient then alice is either not wise or funny. If someone is tall then john is both not curious and calm. If john is kind or patient then mary is either old or funny. Everyone who is either not calm or not funny is not brave and vice versa. Everyone who is either not old or not funny is old and vice versa. Everyone who is not generous or creative is both wise and curious and vice versa. Everyone who is both kind and funny is not curious or not calm. If alice is either tall or not old then someone is both not tall and patient and vice versa. If mary is generous then alice is not calm or generous and vice versa. If someone is not curious then someone is not tall. Everyone who is wise or not curious is both not tall and not old and vice versa. If lucy is not quiet or humble then someone is not funny. Paul is old or not creative. Alice is either kind or strong. Someone is either quiet or not creative. John is both rich and old. Someone is quiet or not wise. | Mary is not tall. | entailment | (((happy(fred)<~>~tall(fred)))<=>((~creative(john)<~>~old(john))))&
(![X]:(~patient(X)<=>(~quiet(X)&strong(X))))&
((?[X]:(~old(X)))=>((~brave(john)<~>calm(john))))&
((?[X]:((~brave(X)&~happy(X))))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(((~old(paul)|~patient(paul)))=>((~wise(alice)<~>funny(alice))))&
((?[X]:(tall(X)))=>((~curious(john)&calm(john))))&
(((kind(john)|patient(john)))=>((old(mary)<~>funny(mary))))&
(![X]:((~calm(X)<~>~funny(X))<=>~brave(X)))&
(![X]:((~old(X)<~>~funny(X))<=>old(X)))&
(![X]:((~generous(X)|creative(X))<=>(wise(X)&curious(X))))&
(![X]:((kind(X)&funny(X))=>(~curious(X)|~calm(X))))&
(((tall(alice)<~>~old(alice)))<=>(?[X]:((~tall(X)&patient(X)))))&
((generous(mary))<=>((~calm(alice)|generous(alice))))&
((?[X]:(~curious(X)))=>(?[X]:(~tall(X))))&
(![X]:((wise(X)|~curious(X))<=>(~tall(X)&~old(X))))&
(((~quiet(lucy)|humble(lucy)))=>(?[X]:(~funny(X))))&
((old(paul)|~creative(paul)))&
((kind(alice)<~>strong(alice)))&
(?[X]:((quiet(X)<~>~creative(X))))&
((rich(john)&old(john)))&
(?[X]:((quiet(X)|~wise(X)))) | ~tall(mary) | [
"p5",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2680321251777523796328478
% SZS output start Proof for 2680321251777523796328478
6. ? [X0] : tall(X0) => (calm(john) & ~curious(john)) [input p5]
15. ! [X0] : ((~curious(X0) | wise(X0)) <=> (~old(X0) & ~tall(X0))) [input p14]
20. old(john) & rich(john) [input p19]
22. tall(mary) [input hypothesis]
25. old(john) [pure predicate removal 20]
29. (calm(john) & ~curious(john)) | ! [X0] : ~tall(X0) [ennf transformation 6]
59. ! [X0] : (((~curious(X0) | wise(X0)) | (old(X0) | tall(X0))) & ((~old(X0) & ~tall(X0)) | (curious(X0) & ~wise(X0)))) [nnf transformation 15]
60. ! [X0] : ((~curious(X0) | wise(X0) | old(X0) | tall(X0)) & ((~old(X0) & ~tall(X0)) | (curious(X0) & ~wise(X0)))) [flattening 59]
92. ~curious(john) | ~tall(X0) [cnf transformation 29]
125. ~old(X0) | curious(X0) [cnf transformation 60]
133. old(john) [cnf transformation 25]
135. tall(mary) [cnf transformation 22]
139. 1 <=> old(john) [avatar definition]
141. old(john) <- (1) [avatar component clause 139]
227. 19 <=> ! [X0] : ~tall(X0) [avatar definition]
228. ~tall(X0) <- (19) [avatar component clause 227]
231. 20 <=> curious(john) [avatar definition]
234. 19 | ~20 [avatar split clause 92,231,227]
329. 1 [avatar split clause 133,139]
344. curious(john) <- (1) [resolution 125,141]
347. 20 | ~1 [avatar split clause 344,139,231]
348. $false <- (19) [resolution 228,135]
351. ~19 [avatar contradiction clause 348]
352. $false [avatar sat refutation 234,329,347,351]
% SZS output end Proof for 2680321251777523796328478
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not brave then someone is not kind or tall and vice versa.
If someone is both generous and funny then alice is creative or not patient and vice versa.
Everyone who is either not kind or not quiet is either not calm or not wise.
Everyone who is either funny or old is brave or not rich and vice versa.
Everyone who is both quiet and kind is brave and vice versa.
Everyone who is either not humble or not creative is both not kind and kind.
If john is either not happy or generous then someone is either not rich or creative and vice versa.
Everyone who is either generous or creative is creative or not creative.
Everyone who is not humble or patient is not rich.
Everyone who is both tall and not humble is either humble or kind and vice versa.
If someone is both quiet and not creative then someone is either curious or not brave and vice versa.
Everyone who is not brave or kind is not tall or happy and vice versa.
If someone is not rich or not kind then susan is either not tall or not brave.
Everyone who is not brave or not humble is both generous and not humble and vice versa.
If alice is not funny or strong then someone is both not calm and not rich.
If someone is both calm and not creative then someone is old or not humble and vice versa.
Someone is not curious or not creative.
Alice is not wise or not humble.
Someone is either humble or patient.
John is not humble.
Mary is both not strong and wise.
Someone is not happy.
Alice is both not calm and not old. | Alice is not curious. | neutral | ((~brave(paul))<=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((generous(X)&funny(X))))<=>((creative(alice)|~patient(alice))))&
(![X]:((~kind(X)<~>~quiet(X))=>(~calm(X)<~>~wise(X))))&
(![X]:((funny(X)<~>old(X))<=>(brave(X)|~rich(X))))&
(![X]:((quiet(X)&kind(X))<=>brave(X)))&
(![X]:((~humble(X)<~>~creative(X))=>(~kind(X)&kind(X))))&
(((~happy(john)<~>generous(john)))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((generous(X)<~>creative(X))=>(creative(X)|~creative(X))))&
(![X]:((~humble(X)|patient(X))=>~rich(X)))&
(![X]:((tall(X)&~humble(X))<=>(humble(X)<~>kind(X))))&
((?[X]:((quiet(X)&~creative(X))))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:((~brave(X)|kind(X))<=>(~tall(X)|happy(X))))&
((?[X]:((~rich(X)|~kind(X))))=>((~tall(susan)<~>~brave(susan))))&
(![X]:((~brave(X)|~humble(X))<=>(generous(X)&~humble(X))))&
(((~funny(alice)|strong(alice)))=>(?[X]:((~calm(X)&~rich(X)))))&
((?[X]:((calm(X)&~creative(X))))<=>(?[X]:((old(X)|~humble(X)))))&
(?[X]:((~curious(X)|~creative(X))))&
((~wise(alice)|~humble(alice)))&
(?[X]:((humble(X)<~>patient(X))))&
(~humble(john))&
((~strong(mary)&wise(mary)))&
(?[X]:(~happy(X)))&
((~calm(alice)&~old(alice))) | ~curious(alice) | [] | null | 0 |
Everyone who is not kind is either funny or not funny and vice versa.
Everyone who is either creative or not quiet is both humble and wise.
Everyone who is not rich or not generous is either not funny or happy.
Everyone who is not creative or funny is both happy and not patient and vice versa.
If fred is not funny or not quiet then someone is not patient and vice versa.
Everyone who is both not kind and not brave is both generous and not generous and vice versa.
If someone is generous or not kind then lucy is either quiet or not quiet and vice versa.
Everyone who is not calm or old is both not funny and not curious and vice versa.
If someone is either curious or wise then someone is not strong and vice versa.
Everyone who is not happy is both not kind and not curious and vice versa.
If alice is not patient then someone is both brave and funny and vice versa.
Everyone who is either not rich or brave is either happy or wise.
Everyone who is both calm and patient is both not old and kind.
If mary is either not quiet or not strong then mary is both not strong and rich.
If lucy is not funny or curious then someone is not creative and vice versa.
Paul is generous.
Someone is not old or rich.
Alice is either not happy or not wise.
Someone is not tall.
Lucy is either kind or not wise.
Someone is both not patient and not creative.
Someone is either wise or not funny.
Fred is not curious or wise. | Mary is not curious. | neutral | (![X]:(~kind(X)<=>(funny(X)<~>~funny(X))))&
(![X]:((creative(X)<~>~quiet(X))=>(humble(X)&wise(X))))&
(![X]:((~rich(X)|~generous(X))=>(~funny(X)<~>happy(X))))&
(![X]:((~creative(X)|funny(X))<=>(happy(X)&~patient(X))))&
(((~funny(fred)|~quiet(fred)))<=>(?[X]:(~patient(X))))&
(![X]:((~kind(X)&~brave(X))<=>(generous(X)&~generous(X))))&
((?[X]:((generous(X)|~kind(X))))<=>((quiet(lucy)<~>~quiet(lucy))))&
(![X]:((~calm(X)|old(X))<=>(~funny(X)&~curious(X))))&
((?[X]:((curious(X)<~>wise(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~happy(X)<=>(~kind(X)&~curious(X))))&
((~patient(alice))<=>(?[X]:((brave(X)&funny(X)))))&
(![X]:((~rich(X)<~>brave(X))=>(happy(X)<~>wise(X))))&
(![X]:((calm(X)&patient(X))=>(~old(X)&kind(X))))&
(((~quiet(mary)<~>~strong(mary)))=>((~strong(mary)&rich(mary))))&
(((~funny(lucy)|curious(lucy)))<=>(?[X]:(~creative(X))))&
(generous(paul))&
(?[X]:((~old(X)|rich(X))))&
((~happy(alice)<~>~wise(alice)))&
(?[X]:(~tall(X)))&
((kind(lucy)<~>~wise(lucy)))&
(?[X]:((~patient(X)&~creative(X))))&
(?[X]:((wise(X)<~>~funny(X))))&
((~curious(fred)|wise(fred))) | ~curious(mary) | [] | null | 0 |
If someone is funny or strong then someone is not humble or humble and vice versa.
If someone is wise or humble then someone is both not strong and patient and vice versa.
Everyone who is both quiet and calm is either curious or patient and vice versa.
Everyone who is either patient or wise is not funny.
Everyone who is quiet is both curious and not curious.
Everyone who is both not brave and not generous is either strong or happy and vice versa.
Everyone who is both not patient and kind is either not generous or patient.
Everyone who is strong or not wise is either not humble or creative.
Everyone who is not strong is quiet and vice versa.
If someone is either quiet or humble then susan is not quiet or tall.
If someone is brave then someone is not quiet or not calm and vice versa.
Everyone who is not humble or not creative is rich.
If someone is both not funny and quiet then someone is not quiet or humble.
If someone is either not kind or not humble then someone is not wise or not brave and vice versa.
Everyone who is not rich is strong.
If someone is not curious then alice is either not patient or calm and vice versa.
Someone is both generous and not patient.
Someone is happy.
Someone is wise or strong.
Susan is either strong or curious.
Someone is either funny or wise.
Mary is kind or not happy.
Lucy is calm. | Mary is not quiet. | entailment | ((?[X]:((funny(X)|strong(X))))<=>(?[X]:((~humble(X)|humble(X)))))&
((?[X]:((wise(X)|humble(X))))<=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((quiet(X)&calm(X))<=>(curious(X)<~>patient(X))))&
(![X]:((patient(X)<~>wise(X))=>~funny(X)))&
(![X]:(quiet(X)=>(curious(X)&~curious(X))))&
(![X]:((~brave(X)&~generous(X))<=>(strong(X)<~>happy(X))))&
(![X]:((~patient(X)&kind(X))=>(~generous(X)<~>patient(X))))&
(![X]:((strong(X)|~wise(X))=>(~humble(X)<~>creative(X))))&
(![X]:(~strong(X)<=>quiet(X)))&
((?[X]:((quiet(X)<~>humble(X))))=>((~quiet(susan)|tall(susan))))&
((?[X]:(brave(X)))<=>(?[X]:((~quiet(X)|~calm(X)))))&
(![X]:((~humble(X)|~creative(X))=>rich(X)))&
((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
((?[X]:((~kind(X)<~>~humble(X))))<=>(?[X]:((~wise(X)|~brave(X)))))&
(![X]:(~rich(X)=>strong(X)))&
((?[X]:(~curious(X)))<=>((~patient(alice)<~>calm(alice))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:(happy(X)))&
(?[X]:((wise(X)|strong(X))))&
((strong(susan)<~>curious(susan)))&
(?[X]:((funny(X)<~>wise(X))))&
((kind(mary)|~happy(mary)))&
(calm(lucy)) | ~quiet(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7447412850906298966569717
% SZS output start Proof for 7447412850906298966569717
5. ! [X0] : (quiet(X0) => (~curious(X0) & curious(X0))) [input p4]
24. quiet(mary) [input hypothesis]
34. ! [X0] : ((~curious(X0) & curious(X0)) | ~quiet(X0)) [ennf transformation 5]
101. curious(X0) | ~quiet(X0) [cnf transformation 34]
102. ~curious(X0) | ~quiet(X0) [cnf transformation 34]
141. quiet(mary) [cnf transformation 24]
186. ~quiet(X0) [subsumption resolution 101,102]
271. $false [subsumption resolution 141,186]
% SZS output end Proof for 7447412850906298966569717
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or funny is both not funny and rich.
Everyone who is either funny or creative is not rich and vice versa.
If mary is strong then someone is both not calm and creative.
If fred is rich or not funny then someone is either not kind or not tall.
If someone is either tall or not kind then someone is generous.
If susan is not generous then susan is either not strong or not patient and vice versa.
If fred is not curious then lucy is both not funny and kind.
Everyone who is both happy and strong is kind or not wise.
Everyone who is both not strong and creative is funny or calm and vice versa.
Everyone who is rich is either not patient or not wise and vice versa.
If someone is either not calm or not humble then someone is both funny and rich.
Everyone who is both happy and not old is not generous.
If fred is both happy and not kind then susan is either generous or wise.
Everyone who is either funny or not strong is not rich or not happy and vice versa.
Everyone who is not funny or tall is both creative and not curious and vice versa.
If john is tall then fred is wise or not strong and vice versa.
Paul is either not happy or not humble.
Paul is not tall or strong.
Someone is either not tall or strong.
Someone is not calm or not generous.
Fred is kind. | Susan is kind. | neutral | (![X]:((~calm(X)|funny(X))=>(~funny(X)&rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>~rich(X)))&
((strong(mary))=>(?[X]:((~calm(X)&creative(X)))))&
(((rich(fred)|~funny(fred)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
((?[X]:((tall(X)<~>~kind(X))))=>(?[X]:(generous(X))))&
((~generous(susan))<=>((~strong(susan)<~>~patient(susan))))&
((~curious(fred))=>((~funny(lucy)&kind(lucy))))&
(![X]:((happy(X)&strong(X))=>(kind(X)|~wise(X))))&
(![X]:((~strong(X)&creative(X))<=>(funny(X)|calm(X))))&
(![X]:(rich(X)<=>(~patient(X)<~>~wise(X))))&
((?[X]:((~calm(X)<~>~humble(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((happy(X)&~old(X))=>~generous(X)))&
(((happy(fred)&~kind(fred)))=>((generous(susan)<~>wise(susan))))&
(![X]:((funny(X)<~>~strong(X))<=>(~rich(X)|~happy(X))))&
(![X]:((~funny(X)|tall(X))<=>(creative(X)&~curious(X))))&
((tall(john))<=>((wise(fred)|~strong(fred))))&
((~happy(paul)<~>~humble(paul)))&
((~tall(paul)|strong(paul)))&
(?[X]:((~tall(X)<~>strong(X))))&
(?[X]:((~calm(X)|~generous(X))))&
(kind(fred)) | kind(susan) | [] | null | 0 |
If someone is not brave then mary is both happy and creative and vice versa. Everyone who is either not old or not funny is either not strong or not wise and vice versa. Everyone who is either calm or not strong is both old and creative. Everyone who is not strong or quiet is both quiet and old. If someone is not rich then lucy is both tall and not kind. Everyone who is not rich or not quiet is both not tall and kind and vice versa. Everyone who is both not wise and not curious is not happy and vice versa. Everyone who is either creative or kind is patient or creative. Everyone who is curious is not humble. Everyone who is not patient or not strong is old or not patient and vice versa. Everyone who is either not calm or calm is either not creative or generous. Everyone who is calm or not calm is calm or brave. Everyone who is patient is tall. Everyone who is both not calm and not strong is patient. Everyone who is not strong or not happy is not wise. If someone is both old and generous then someone is happy or tall and vice versa. John is brave or old. Paul is calm or tall. Fred is both not tall and not creative. Someone is both not creative and not calm. Someone is not rich or not creative. Someone is either not curious or not creative. Lucy is either wise or calm. Someone is tall or curious. | Fred is not patient. | entailment | ((?[X]:(~brave(X)))<=>((happy(mary)&creative(mary))))&
(![X]:((~old(X)<~>~funny(X))<=>(~strong(X)<~>~wise(X))))&
(![X]:((calm(X)<~>~strong(X))=>(old(X)&creative(X))))&
(![X]:((~strong(X)|quiet(X))=>(quiet(X)&old(X))))&
((?[X]:(~rich(X)))=>((tall(lucy)&~kind(lucy))))&
(![X]:((~rich(X)|~quiet(X))<=>(~tall(X)&kind(X))))&
(![X]:((~wise(X)&~curious(X))<=>~happy(X)))&
(![X]:((creative(X)<~>kind(X))=>(patient(X)|creative(X))))&
(![X]:(curious(X)=>~humble(X)))&
(![X]:((~patient(X)|~strong(X))<=>(old(X)|~patient(X))))&
(![X]:((~calm(X)<~>calm(X))=>(~creative(X)<~>generous(X))))&
(![X]:((calm(X)|~calm(X))=>(calm(X)|brave(X))))&
(![X]:(patient(X)=>tall(X)))&
(![X]:((~calm(X)&~strong(X))=>patient(X)))&
(![X]:((~strong(X)|~happy(X))=>~wise(X)))&
((?[X]:((old(X)&generous(X))))<=>(?[X]:((happy(X)|tall(X)))))&
((brave(john)|old(john)))&
((calm(paul)|tall(paul)))&
((~tall(fred)&~creative(fred)))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((~curious(X)<~>~creative(X))))&
((wise(lucy)<~>calm(lucy)))&
(?[X]:((tall(X)|curious(X)))) | ~patient(fred) | [
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1705425560670051619593480
% SZS output start Proof for 1705425560670051619593480
13. ! [X0] : (patient(X0) => tall(X0)) [input p12]
19. ~creative(fred) & ~tall(fred) [input p18]
25. patient(fred) [input hypothesis]
36. ! [X0] : (tall(X0) | ~patient(X0)) [ennf transformation 13]
111. ~patient(X0) | tall(X0) [cnf transformation 36]
122. ~tall(fred) [cnf transformation 19]
132. patient(fred) [cnf transformation 25]
268. tall(fred) [resolution 111,132]
269. $false [subsumption resolution 268,122]
% SZS output end Proof for 1705425560670051619593480
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is generous.
Everyone who is not creative or not calm is not strong or not creative.
Everyone who is both not rich and not happy is not strong or not quiet.
Everyone who is humble is not wise and vice versa.
Everyone who is not tall or not patient is tall.
If someone is not creative then john is either not strong or not quiet.
Everyone who is not humble or wise is both kind and calm and vice versa.
Everyone who is either generous or not kind is kind.
Everyone who is either not generous or quiet is calm.
Everyone who is not rich is either brave or not wise.
If lucy is both not kind and quiet then paul is not wise.
If fred is creative then someone is kind.
Everyone who is not brave or not curious is not wise or patient and vice versa.
Everyone who is tall is kind and vice versa.
If someone is wise or brave then alice is either kind or generous and vice versa.
If someone is both not curious and funny then someone is both not wise and not kind.
Lucy is not old.
Paul is either quiet or not humble.
Fred is either humble or not generous.
John is happy.
Someone is either wise or brave.
Someone is not strong or not kind.
Fred is both curious and funny. | Alice is old. | neutral | (![X]:(wise(X)=>generous(X)))&
(![X]:((~creative(X)|~calm(X))=>(~strong(X)|~creative(X))))&
(![X]:((~rich(X)&~happy(X))=>(~strong(X)|~quiet(X))))&
(![X]:(humble(X)<=>~wise(X)))&
(![X]:((~tall(X)|~patient(X))=>tall(X)))&
((?[X]:(~creative(X)))=>((~strong(john)<~>~quiet(john))))&
(![X]:((~humble(X)|wise(X))<=>(kind(X)&calm(X))))&
(![X]:((generous(X)<~>~kind(X))=>kind(X)))&
(![X]:((~generous(X)<~>quiet(X))=>calm(X)))&
(![X]:(~rich(X)=>(brave(X)<~>~wise(X))))&
(((~kind(lucy)&quiet(lucy)))=>(~wise(paul)))&
((creative(fred))=>(?[X]:(kind(X))))&
(![X]:((~brave(X)|~curious(X))<=>(~wise(X)|patient(X))))&
(![X]:(tall(X)<=>kind(X)))&
((?[X]:((wise(X)|brave(X))))<=>((kind(alice)<~>generous(alice))))&
((?[X]:((~curious(X)&funny(X))))=>(?[X]:((~wise(X)&~kind(X)))))&
(~old(lucy))&
((quiet(paul)<~>~humble(paul)))&
((humble(fred)<~>~generous(fred)))&
(happy(john))&
(?[X]:((wise(X)<~>brave(X))))&
(?[X]:((~strong(X)|~kind(X))))&
((curious(fred)&funny(fred))) | old(alice) | [] | null | 0 |
Everyone who is both creative and not rich is tall. Everyone who is both old and brave is both old and not wise and vice versa. Everyone who is wise or not quiet is not funny or not creative and vice versa. Everyone who is either not happy or kind is old or not strong and vice versa. If susan is both creative and rich then someone is either not creative or tall. If someone is either wise or not strong then mary is tall or patient. Everyone who is kind or old is both not humble and not happy and vice versa. Everyone who is either curious or not happy is generous and vice versa. Everyone who is not tall is not quiet and vice versa. Everyone who is either not humble or strong is either not generous or wise. Everyone who is either brave or funny is happy and vice versa. If someone is not brave then someone is not humble or not old. If someone is not old then someone is funny or not tall and vice versa. If susan is both strong and not wise then alice is either tall or not humble. If john is either not brave or not calm then mary is either funny or not quiet and vice versa. If someone is wise or generous then someone is not generous or tall and vice versa. John is not generous or not kind. Someone is both rich and not strong. Someone is both quiet and patient. Fred is both brave and not happy. Alice is both calm and funny. Someone is either not happy or not rich. Lucy is not rich. Someone is both not brave and not rich. | John is not old. | neutral | (![X]:((creative(X)&~rich(X))=>tall(X)))&
(![X]:((old(X)&brave(X))<=>(old(X)&~wise(X))))&
(![X]:((wise(X)|~quiet(X))<=>(~funny(X)|~creative(X))))&
(![X]:((~happy(X)<~>kind(X))<=>(old(X)|~strong(X))))&
(((creative(susan)&rich(susan)))=>(?[X]:((~creative(X)<~>tall(X)))))&
((?[X]:((wise(X)<~>~strong(X))))=>((tall(mary)|patient(mary))))&
(![X]:((kind(X)|old(X))<=>(~humble(X)&~happy(X))))&
(![X]:((curious(X)<~>~happy(X))<=>generous(X)))&
(![X]:(~tall(X)<=>~quiet(X)))&
(![X]:((~humble(X)<~>strong(X))=>(~generous(X)<~>wise(X))))&
(![X]:((brave(X)<~>funny(X))<=>happy(X)))&
((?[X]:(~brave(X)))=>(?[X]:((~humble(X)|~old(X)))))&
((?[X]:(~old(X)))<=>(?[X]:((funny(X)|~tall(X)))))&
(((strong(susan)&~wise(susan)))=>((tall(alice)<~>~humble(alice))))&
(((~brave(john)<~>~calm(john)))<=>((funny(mary)<~>~quiet(mary))))&
((?[X]:((wise(X)|generous(X))))<=>(?[X]:((~generous(X)|tall(X)))))&
((~generous(john)|~kind(john)))&
(?[X]:((rich(X)&~strong(X))))&
(?[X]:((quiet(X)&patient(X))))&
((brave(fred)&~happy(fred)))&
((calm(alice)&funny(alice)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(~rich(lucy))&
(?[X]:((~brave(X)&~rich(X)))) | ~old(john) | [] | null | 0 |
Everyone who is wise is both generous and quiet and vice versa.
If someone is patient or not brave then lucy is both patient and not brave.
Everyone who is generous is not tall and vice versa.
If someone is both wise and creative then someone is either patient or not old.
Everyone who is either not old or generous is both rich and brave and vice versa.
If lucy is old then john is not quiet or quiet.
If lucy is not funny or funny then someone is both funny and happy and vice versa.
Everyone who is either not brave or tall is old or not brave.
Everyone who is both quiet and not generous is not brave or curious and vice versa.
If someone is either not funny or curious then john is either not patient or not quiet.
Everyone who is either not patient or wise is patient and vice versa.
If someone is either not rich or not patient then susan is both tall and not brave.
Everyone who is brave or not generous is not tall and vice versa.
Everyone who is funny or not brave is either brave or strong.
If fred is either quiet or not strong then mary is generous.
If someone is not wise or generous then susan is either not patient or not humble.
Someone is not calm.
Someone is quiet.
Someone is not patient.
Fred is both happy and creative.
Someone is either not generous or wise. | Fred is not rich. | entailment | (![X]:(wise(X)<=>(generous(X)&quiet(X))))&
((?[X]:((patient(X)|~brave(X))))=>((patient(lucy)&~brave(lucy))))&
(![X]:(generous(X)<=>~tall(X)))&
((?[X]:((wise(X)&creative(X))))=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:((~old(X)<~>generous(X))<=>(rich(X)&brave(X))))&
((old(lucy))=>((~quiet(john)|quiet(john))))&
(((~funny(lucy)|funny(lucy)))<=>(?[X]:((funny(X)&happy(X)))))&
(![X]:((~brave(X)<~>tall(X))=>(old(X)|~brave(X))))&
(![X]:((quiet(X)&~generous(X))<=>(~brave(X)|curious(X))))&
((?[X]:((~funny(X)<~>curious(X))))=>((~patient(john)<~>~quiet(john))))&
(![X]:((~patient(X)<~>wise(X))<=>patient(X)))&
((?[X]:((~rich(X)<~>~patient(X))))=>((tall(susan)&~brave(susan))))&
(![X]:((brave(X)|~generous(X))<=>~tall(X)))&
(![X]:((funny(X)|~brave(X))=>(brave(X)<~>strong(X))))&
(((quiet(fred)<~>~strong(fred)))=>(generous(mary)))&
((?[X]:((~wise(X)|generous(X))))=>((~patient(susan)<~>~humble(susan))))&
(?[X]:(~calm(X)))&
(?[X]:(quiet(X)))&
(?[X]:(~patient(X)))&
((happy(fred)&creative(fred)))&
(?[X]:((~generous(X)<~>wise(X)))) | ~rich(fred) | [
"p1",
"p2",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2123730892709851984805885
% SZS output start Proof for 2123730892709851984805885
2. ? [X0] : (~brave(X0) | patient(X0)) => (~brave(lucy) & patient(lucy)) [input p1]
3. ! [X0] : (generous(X0) <=> ~tall(X0)) [input p2]
9. ! [X0] : ((~generous(X0) & quiet(X0)) <=> (curious(X0) | ~brave(X0))) [input p8]
12. ? [X0] : (~rich(X0) <~> ~patient(X0)) => (~brave(susan) & tall(susan)) [input p11]
13. ! [X0] : ((~generous(X0) | brave(X0)) <=> ~tall(X0)) [input p12]
22. rich(fred) [input hypothesis]
25. (~brave(lucy) & patient(lucy)) | ! [X0] : (brave(X0) & ~patient(X0)) [ennf transformation 2]
32. (~brave(susan) & tall(susan)) | ! [X0] : (~rich(X0) <=> ~patient(X0)) [ennf transformation 12]
38. ! [X0] : ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0))) [nnf transformation 3]
51. ! [X0] : (((~generous(X0) & quiet(X0)) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | (generous(X0) | ~quiet(X0)))) [nnf transformation 9]
52. ! [X0] : (((~generous(X0) & quiet(X0)) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | generous(X0) | ~quiet(X0))) [flattening 51]
55. (~brave(susan) & tall(susan)) | ! [X0] : ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))) [nnf transformation 32]
56. ! [X0] : (((~generous(X0) | brave(X0)) | tall(X0)) & (~tall(X0) | (generous(X0) & ~brave(X0)))) [nnf transformation 13]
57. ! [X0] : ((~generous(X0) | brave(X0) | tall(X0)) & (~tall(X0) | (generous(X0) & ~brave(X0)))) [flattening 56]
73. ~brave(lucy) | ~patient(X0) [cnf transformation 25]
76. tall(X0) | generous(X0) [cnf transformation 38]
96. ~generous(X0) | brave(X0) [cnf transformation 52]
109. ~brave(susan) | ~rich(X0) | patient(X0) [cnf transformation 55]
111. ~tall(X0) | generous(X0) [cnf transformation 57]
129. rich(fred) [cnf transformation 22]
135. 1 <=> ! [X0] : brave(X0) [avatar definition]
136. brave(X0) <- (1) [avatar component clause 135]
138. 2 <=> brave(lucy) [avatar definition]
140. ~brave(lucy) <- (~2) [avatar component clause 138]
143. 3 <=> ! [X0] : ~patient(X0) [avatar definition]
144. ~patient(X0) <- (3) [avatar component clause 143]
145. 3 | ~2 [avatar split clause 73,138,143]
201. 15 <=> ! [X0] : (~rich(X0) | patient(X0)) [avatar definition]
202. ~rich(X0) | patient(X0) <- (15) [avatar component clause 201]
204. 16 <=> brave(susan) [avatar definition]
206. ~brave(susan) <- (~16) [avatar component clause 204]
207. 15 | ~16 [avatar split clause 109,204,201]
218. generous(X0) [subsumption resolution 111,76]
237. brave(X0) [resolution 96,218]
238. 1 [avatar split clause 237,135]
239. $false <- (1, ~2) [resolution 136,140]
240. ~1 | 2 [avatar contradiction clause 239]
252. patient(fred) <- (15) [resolution 202,129]
253. $false <- (3, 15) [subsumption resolution 252,144]
254. ~3 | ~15 [avatar contradiction clause 253]
255. $false <- (1, ~16) [subsumption resolution 206,136]
256. ~1 | 16 [avatar contradiction clause 255]
257. $false [avatar sat refutation 145,207,238,240,254,256]
% SZS output end Proof for 2123730892709851984805885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not funny then paul is not kind and vice versa. If lucy is either not creative or tall then someone is either not old or generous. If someone is either not strong or not calm then someone is curious or calm and vice versa. Everyone who is either not patient or kind is both kind and not kind and vice versa. If someone is not tall or not curious then susan is not funny or humble and vice versa. Everyone who is not humble is either not quiet or tall and vice versa. Everyone who is not generous or funny is not creative or not funny and vice versa. Everyone who is both funny and humble is both funny and creative and vice versa. Everyone who is both patient and quiet is not curious or not quiet. If someone is both calm and tall then someone is both tall and funny and vice versa. If fred is funny then mary is not calm or not wise and vice versa. Everyone who is not creative is both not funny and rich. If someone is not kind then fred is not humble or not tall and vice versa. Everyone who is both humble and curious is both wise and not humble and vice versa. Everyone who is not kind or happy is both happy and not generous. If someone is wise then someone is curious. Paul is humble or not funny. Someone is not strong or not generous. Alice is not strong or old. Susan is not tall. Someone is both creative and rich. Someone is either not creative or tall. | Mary is humble. | entailment | ((?[X]:((brave(X)<~>~funny(X))))<=>(~kind(paul)))&
(((~creative(lucy)<~>tall(lucy)))=>(?[X]:((~old(X)<~>generous(X)))))&
((?[X]:((~strong(X)<~>~calm(X))))<=>(?[X]:((curious(X)|calm(X)))))&
(![X]:((~patient(X)<~>kind(X))<=>(kind(X)&~kind(X))))&
((?[X]:((~tall(X)|~curious(X))))<=>((~funny(susan)|humble(susan))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>tall(X))))&
(![X]:((~generous(X)|funny(X))<=>(~creative(X)|~funny(X))))&
(![X]:((funny(X)&humble(X))<=>(funny(X)&creative(X))))&
(![X]:((patient(X)&quiet(X))=>(~curious(X)|~quiet(X))))&
((?[X]:((calm(X)&tall(X))))<=>(?[X]:((tall(X)&funny(X)))))&
((funny(fred))<=>((~calm(mary)|~wise(mary))))&
(![X]:(~creative(X)=>(~funny(X)&rich(X))))&
((?[X]:(~kind(X)))<=>((~humble(fred)|~tall(fred))))&
(![X]:((humble(X)&curious(X))<=>(wise(X)&~humble(X))))&
(![X]:((~kind(X)|happy(X))=>(happy(X)&~generous(X))))&
((?[X]:(wise(X)))=>(?[X]:(curious(X))))&
((humble(paul)|~funny(paul)))&
(?[X]:((~strong(X)|~generous(X))))&
((~strong(alice)|old(alice)))&
(~tall(susan))&
(?[X]:((creative(X)&rich(X))))&
(?[X]:((~creative(X)<~>tall(X)))) | humble(mary) | [
"p6",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5645465688566478693584084
% SZS output start Proof for 5645465688566478693584084
7. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (~funny(X0) | ~creative(X0))) [input p6]
11. funny(fred) <=> (~wise(mary) | ~calm(mary)) [input p10]
12. ! [X0] : (~creative(X0) => (rich(X0) & ~funny(X0))) [input p11]
14. ! [X0] : ((curious(X0) & humble(X0)) <=> (~humble(X0) & wise(X0))) [input p13]
23. ~humble(mary) [input hypothesis]
28. ! [X0] : (~creative(X0) => ~funny(X0)) [pure predicate removal 12]
32. ! [X0] : (~funny(X0) | creative(X0)) [ennf transformation 28]
55. ! [X0] : (((funny(X0) | ~generous(X0)) | (funny(X0) & creative(X0))) & ((~funny(X0) | ~creative(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 7]
56. ! [X0] : ((funny(X0) | ~generous(X0) | (funny(X0) & creative(X0))) & (~funny(X0) | ~creative(X0) | (~funny(X0) & generous(X0)))) [flattening 55]
64. (funny(fred) | (wise(mary) & calm(mary))) & ((~wise(mary) | ~calm(mary)) | ~funny(fred)) [nnf transformation 11]
65. (funny(fred) | (wise(mary) & calm(mary))) & (~wise(mary) | ~calm(mary) | ~funny(fred)) [flattening 64]
71. ! [X0] : (((curious(X0) & humble(X0)) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | (~curious(X0) | ~humble(X0)))) [nnf transformation 14]
72. ! [X0] : (((curious(X0) & humble(X0)) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | ~curious(X0) | ~humble(X0))) [flattening 71]
112. ~funny(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 56]
126. funny(fred) | wise(mary) [cnf transformation 65]
127. ~funny(X0) | creative(X0) [cnf transformation 32]
133. humble(X0) | humble(X0) | ~wise(X0) [cnf transformation 72]
147. ~humble(mary) [cnf transformation 23]
149. ~wise(X0) | humble(X0) [duplicate literal removal 133]
151. ~funny(X0) | ~creative(X0) [duplicate literal removal 112]
287. 30 <=> wise(mary) [avatar definition]
289. wise(mary) <- (30) [avatar component clause 287]
291. 31 <=> funny(fred) [avatar definition]
293. funny(fred) <- (31) [avatar component clause 291]
294. 30 | 31 [avatar split clause 126,291,287]
301. ~funny(X0) [subsumption resolution 127,151]
356. $false <- (31) [subsumption resolution 293,301]
357. ~31 [avatar contradiction clause 356]
361. humble(mary) <- (30) [resolution 149,289]
362. $false <- (30) [subsumption resolution 361,147]
363. ~30 [avatar contradiction clause 362]
364. $false [avatar sat refutation 294,357,363]
% SZS output end Proof for 5645465688566478693584084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not old is both not patient and not funny.
Everyone who is both not generous and not humble is happy or quiet and vice versa.
Everyone who is quiet is both not brave and old and vice versa.
If john is patient or not quiet then someone is both patient and not generous and vice versa.
Everyone who is both not quiet and not happy is either generous or creative and vice versa.
Everyone who is strong is both not rich and not generous and vice versa.
If someone is either curious or kind then mary is brave or not brave.
Everyone who is both old and not patient is both happy and humble and vice versa.
If paul is not humble then someone is either patient or not brave and vice versa.
Everyone who is not humble or creative is either brave or not wise and vice versa.
Everyone who is not happy is curious.
If susan is both creative and not quiet then alice is either not kind or not generous and vice versa.
If susan is not generous then paul is not funny.
If alice is not humble or not quiet then someone is tall or not calm and vice versa.
If someone is creative then lucy is either not strong or happy and vice versa.
If paul is not old or not calm then someone is wise.
Mary is patient.
Susan is either creative or curious.
Someone is rich or not creative.
Fred is both rich and not humble.
Someone is either not strong or rich.
Fred is kind.
Someone is curious or not funny. | Susan is humble. | neutral | (![X]:((happy(X)|~old(X))=>(~patient(X)&~funny(X))))&
(![X]:((~generous(X)&~humble(X))<=>(happy(X)|quiet(X))))&
(![X]:(quiet(X)<=>(~brave(X)&old(X))))&
(((patient(john)|~quiet(john)))<=>(?[X]:((patient(X)&~generous(X)))))&
(![X]:((~quiet(X)&~happy(X))<=>(generous(X)<~>creative(X))))&
(![X]:(strong(X)<=>(~rich(X)&~generous(X))))&
((?[X]:((curious(X)<~>kind(X))))=>((brave(mary)|~brave(mary))))&
(![X]:((old(X)&~patient(X))<=>(happy(X)&humble(X))))&
((~humble(paul))<=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((~humble(X)|creative(X))<=>(brave(X)<~>~wise(X))))&
(![X]:(~happy(X)=>curious(X)))&
(((creative(susan)&~quiet(susan)))<=>((~kind(alice)<~>~generous(alice))))&
((~generous(susan))=>(~funny(paul)))&
(((~humble(alice)|~quiet(alice)))<=>(?[X]:((tall(X)|~calm(X)))))&
((?[X]:(creative(X)))<=>((~strong(lucy)<~>happy(lucy))))&
(((~old(paul)|~calm(paul)))=>(?[X]:(wise(X))))&
(patient(mary))&
((creative(susan)<~>curious(susan)))&
(?[X]:((rich(X)|~creative(X))))&
((rich(fred)&~humble(fred)))&
(?[X]:((~strong(X)<~>rich(X))))&
(kind(fred))&
(?[X]:((curious(X)|~funny(X)))) | humble(susan) | [] | null | 0 |
Everyone who is both not generous and wise is either not curious or not calm and vice versa.
If someone is not generous or not quiet then mary is both creative and brave.
If someone is generous then alice is tall or not tall.
If john is not rich then someone is patient.
Everyone who is either not old or rich is both not strong and not calm and vice versa.
If someone is either not funny or not creative then john is either brave or not tall.
If someone is either patient or happy then someone is humble and vice versa.
If john is not happy or not kind then someone is either tall or kind and vice versa.
Everyone who is strong is both not kind and old and vice versa.
Everyone who is creative or not strong is not calm or not happy.
If someone is either not kind or patient then susan is both not happy and wise.
Everyone who is old is both not strong and strong.
Everyone who is happy is either not humble or not happy.
If lucy is not funny or not brave then lucy is either funny or not curious and vice versa.
Everyone who is both curious and brave is both not patient and old and vice versa.
If someone is either curious or funny then mary is both not funny and not old.
Someone is not strong.
John is both not calm and not wise.
Mary is not happy.
Someone is both wise and not kind.
Mary is both not brave and wise.
Someone is either curious or kind.
Someone is not kind or patient. | Alice is strong. | contradiction | (![X]:((~generous(X)&wise(X))<=>(~curious(X)<~>~calm(X))))&
((?[X]:((~generous(X)|~quiet(X))))=>((creative(mary)&brave(mary))))&
((?[X]:(generous(X)))=>((tall(alice)|~tall(alice))))&
((~rich(john))=>(?[X]:(patient(X))))&
(![X]:((~old(X)<~>rich(X))<=>(~strong(X)&~calm(X))))&
((?[X]:((~funny(X)<~>~creative(X))))=>((brave(john)<~>~tall(john))))&
((?[X]:((patient(X)<~>happy(X))))<=>(?[X]:(humble(X))))&
(((~happy(john)|~kind(john)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(strong(X)<=>(~kind(X)&old(X))))&
(![X]:((creative(X)|~strong(X))=>(~calm(X)|~happy(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>((~happy(susan)&wise(susan))))&
(![X]:(old(X)=>(~strong(X)&strong(X))))&
(![X]:(happy(X)=>(~humble(X)<~>~happy(X))))&
(((~funny(lucy)|~brave(lucy)))<=>((funny(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&brave(X))<=>(~patient(X)&old(X))))&
((?[X]:((curious(X)<~>funny(X))))=>((~funny(mary)&~old(mary))))&
(?[X]:(~strong(X)))&
((~calm(john)&~wise(john)))&
(~happy(mary))&
(?[X]:((wise(X)&~kind(X))))&
((~brave(mary)&wise(mary)))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:((~kind(X)|patient(X)))) | strong(alice) | [
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1886774213241834458999778
% SZS output start Proof for 1886774213241834458999778
9. ! [X0] : (strong(X0) <=> (old(X0) & ~kind(X0))) [input p8]
12. ! [X0] : (old(X0) => (strong(X0) & ~strong(X0))) [input p11]
24. strong(alice) [input hypothesis]
35. ! [X0] : ((strong(X0) & ~strong(X0)) | ~old(X0)) [ennf transformation 12]
55. ! [X0] : ((strong(X0) | (~old(X0) | kind(X0))) & ((old(X0) & ~kind(X0)) | ~strong(X0))) [nnf transformation 9]
56. ! [X0] : ((strong(X0) | ~old(X0) | kind(X0)) & ((old(X0) & ~kind(X0)) | ~strong(X0))) [flattening 55]
104. old(X0) | ~strong(X0) [cnf transformation 56]
112. ~strong(X0) | ~old(X0) [cnf transformation 35]
141. strong(alice) [cnf transformation 24]
256. ~strong(X0) [subsumption resolution 112,104]
311. $false [subsumption resolution 141,256]
% SZS output end Proof for 1886774213241834458999778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is not quiet or not kind and vice versa.
Everyone who is kind or not happy is not quiet and vice versa.
If john is both not rich and not generous then john is either not creative or curious.
Everyone who is kind is not curious and vice versa.
Everyone who is not tall or curious is both not calm and not funny.
If someone is not creative then paul is both not quiet and not strong.
If someone is both tall and rich then john is both creative and not funny and vice versa.
Everyone who is both happy and not curious is both creative and funny.
If paul is calm then someone is either calm or not old and vice versa.
If someone is either not generous or old then someone is either not brave or not rich and vice versa.
If someone is not kind then someone is not happy and vice versa.
If fred is kind or not quiet then john is not strong or not brave.
Everyone who is both generous and calm is quiet.
Everyone who is not creative or happy is both not humble and tall and vice versa.
If paul is both calm and not calm then paul is either not old or rich.
Everyone who is not creative is not humble.
Someone is both old and happy.
Lucy is both humble and funny.
Alice is either kind or patient.
Someone is rich.
Someone is not wise.
Paul is both happy and not humble.
Someone is creative or not kind. | Lucy is not calm. | entailment | (![X]:(generous(X)<=>(~quiet(X)|~kind(X))))&
(![X]:((kind(X)|~happy(X))<=>~quiet(X)))&
(((~rich(john)&~generous(john)))=>((~creative(john)<~>curious(john))))&
(![X]:(kind(X)<=>~curious(X)))&
(![X]:((~tall(X)|curious(X))=>(~calm(X)&~funny(X))))&
((?[X]:(~creative(X)))=>((~quiet(paul)&~strong(paul))))&
((?[X]:((tall(X)&rich(X))))<=>((creative(john)&~funny(john))))&
(![X]:((happy(X)&~curious(X))=>(creative(X)&funny(X))))&
((calm(paul))<=>(?[X]:((calm(X)<~>~old(X)))))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((~brave(X)<~>~rich(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:(~happy(X))))&
(((kind(fred)|~quiet(fred)))=>((~strong(john)|~brave(john))))&
(![X]:((generous(X)&calm(X))=>quiet(X)))&
(![X]:((~creative(X)|happy(X))<=>(~humble(X)&tall(X))))&
(((calm(paul)&~calm(paul)))=>((~old(paul)<~>rich(paul))))&
(![X]:(~creative(X)=>~humble(X)))&
(?[X]:((old(X)&happy(X))))&
((humble(lucy)&funny(lucy)))&
((kind(alice)<~>patient(alice)))&
(?[X]:(rich(X)))&
(?[X]:(~wise(X)))&
((happy(paul)&~humble(paul)))&
(?[X]:((creative(X)|~kind(X)))) | ~calm(lucy) | [
"p0",
"p1",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8909657251254610627756977
% SZS output start Proof for 8909657251254610627756977
1. ! [X0] : (generous(X0) <=> (~kind(X0) | ~quiet(X0))) [input p0]
2. ! [X0] : ((~happy(X0) | kind(X0)) <=> ~quiet(X0)) [input p1]
13. ! [X0] : ((calm(X0) & generous(X0)) => quiet(X0)) [input p12]
14. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (tall(X0) & ~humble(X0))) [input p13]
18. funny(lucy) & humble(lucy) [input p17]
24. calm(lucy) [input hypothesis]
36. ! [X0] : (quiet(X0) | (~calm(X0) | ~generous(X0))) [ennf transformation 13]
37. ! [X0] : (quiet(X0) | ~calm(X0) | ~generous(X0)) [flattening 36]
41. ! [X0] : ((generous(X0) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | ~generous(X0))) [nnf transformation 1]
42. ! [X0] : ((generous(X0) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | ~generous(X0))) [flattening 41]
43. ! [X0] : (((~happy(X0) | kind(X0)) | quiet(X0)) & (~quiet(X0) | (happy(X0) & ~kind(X0)))) [nnf transformation 2]
44. ! [X0] : ((~happy(X0) | kind(X0) | quiet(X0)) & (~quiet(X0) | (happy(X0) & ~kind(X0)))) [flattening 43]
66. ! [X0] : (((happy(X0) | ~creative(X0)) | (~tall(X0) | humble(X0))) & ((tall(X0) & ~humble(X0)) | (~happy(X0) & creative(X0)))) [nnf transformation 14]
67. ! [X0] : ((happy(X0) | ~creative(X0) | ~tall(X0) | humble(X0)) & ((tall(X0) & ~humble(X0)) | (~happy(X0) & creative(X0)))) [flattening 66]
77. quiet(X0) | generous(X0) [cnf transformation 42]
80. ~quiet(X0) | happy(X0) [cnf transformation 44]
111. quiet(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 37]
113. ~humble(X0) | ~happy(X0) [cnf transformation 67]
122. humble(lucy) [cnf transformation 18]
130. calm(lucy) [cnf transformation 24]
250. ~calm(X0) | quiet(X0) [subsumption resolution 111,77]
290. ~happy(lucy) [resolution 113,122]
293. quiet(lucy) [resolution 250,130]
299. happy(lucy) [resolution 293,80]
300. $false [subsumption resolution 299,290]
% SZS output end Proof for 8909657251254610627756977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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