premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not kind is not calm.
Everyone who is either not generous or strong is tall or funny and vice versa.
If lucy is not rich or patient then someone is brave.
Everyone who is both tall and not creative is either kind or old and vice versa.
If lucy is rich then someone is either not funny or old.
Everyone who is either wise or not tall is either happy or tall.
If someone is both funny and not quiet then mary is rich.
Everyone who is either not creative or brave is patient.
Everyone who is both not curious and humble is either not rich or quiet and vice versa.
Everyone who is either not kind or happy is not strong.
If someone is not strong then someone is tall and vice versa.
Everyone who is both not old and not curious is kind or not rich and vice versa.
Everyone who is not generous or wise is quiet and vice versa.
If someone is not old or patient then someone is both not creative and not rich.
Everyone who is both not old and not patient is wise.
Everyone who is not patient or not kind is both not happy and funny.
Fred is both not kind and wise.
Mary is either wise or not curious.
Someone is both not kind and not patient.
Someone is both tall and not rich.
Alice is not old or not curious.
Someone is either curious or strong. | Fred is not old. | neutral | (![X]:(~kind(X)=>~calm(X)))&
(![X]:((~generous(X)<~>strong(X))<=>(tall(X)|funny(X))))&
(((~rich(lucy)|patient(lucy)))=>(?[X]:(brave(X))))&
(![X]:((tall(X)&~creative(X))<=>(kind(X)<~>old(X))))&
((rich(lucy))=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((wise(X)<~>~tall(X))=>(happy(X)<~>tall(X))))&
((?[X]:((funny(X)&~quiet(X))))=>(rich(mary)))&
(![X]:((~creative(X)<~>brave(X))=>patient(X)))&
(![X]:((~curious(X)&humble(X))<=>(~rich(X)<~>quiet(X))))&
(![X]:((~kind(X)<~>happy(X))=>~strong(X)))&
((?[X]:(~strong(X)))<=>(?[X]:(tall(X))))&
(![X]:((~old(X)&~curious(X))<=>(kind(X)|~rich(X))))&
(![X]:((~generous(X)|wise(X))<=>quiet(X)))&
((?[X]:((~old(X)|patient(X))))=>(?[X]:((~creative(X)&~rich(X)))))&
(![X]:((~old(X)&~patient(X))=>wise(X)))&
(![X]:((~patient(X)|~kind(X))=>(~happy(X)&funny(X))))&
((~kind(fred)&wise(fred)))&
((wise(mary)<~>~curious(mary)))&
(?[X]:((~kind(X)&~patient(X))))&
(?[X]:((tall(X)&~rich(X))))&
((~old(alice)|~curious(alice)))&
(?[X]:((curious(X)<~>strong(X)))) | ~old(fred) | [] | null | 0 |
Everyone who is not humble or not generous is tall or generous.
If john is funny then someone is not tall or not strong.
If someone is not creative then fred is not curious and vice versa.
If fred is both not funny and not tall then paul is both not kind and kind and vice versa.
Everyone who is not humble or not patient is humble or rich.
Everyone who is both patient and not quiet is not creative or curious.
Everyone who is both generous and strong is both not humble and not strong.
If someone is funny then someone is both not old and not curious.
Everyone who is either not humble or humble is not happy and vice versa.
If john is either not tall or generous then someone is strong and vice versa.
If paul is both happy and brave then alice is either patient or happy and vice versa.
Everyone who is both not funny and generous is happy.
Everyone who is either not humble or not old is happy or not humble and vice versa.
Everyone who is not brave is either not strong or curious and vice versa.
Everyone who is not quiet or wise is not old.
If fred is not calm then mary is happy and vice versa.
Mary is not curious or not quiet.
Someone is rich.
Someone is either not creative or not generous.
John is not wise or not happy.
Someone is both not curious and humble.
Someone is either not rich or not calm.
Someone is both not funny and brave. | Fred is not old. | contradiction | (![X]:((~humble(X)|~generous(X))=>(tall(X)|generous(X))))&
((funny(john))=>(?[X]:((~tall(X)|~strong(X)))))&
((?[X]:(~creative(X)))<=>(~curious(fred)))&
(((~funny(fred)&~tall(fred)))<=>((~kind(paul)&kind(paul))))&
(![X]:((~humble(X)|~patient(X))=>(humble(X)|rich(X))))&
(![X]:((patient(X)&~quiet(X))=>(~creative(X)|curious(X))))&
(![X]:((generous(X)&strong(X))=>(~humble(X)&~strong(X))))&
((?[X]:(funny(X)))=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:((~humble(X)<~>humble(X))<=>~happy(X)))&
(((~tall(john)<~>generous(john)))<=>(?[X]:(strong(X))))&
(((happy(paul)&brave(paul)))<=>((patient(alice)<~>happy(alice))))&
(![X]:((~funny(X)&generous(X))=>happy(X)))&
(![X]:((~humble(X)<~>~old(X))<=>(happy(X)|~humble(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>curious(X))))&
(![X]:((~quiet(X)|wise(X))=>~old(X)))&
((~calm(fred))<=>(happy(mary)))&
((~curious(mary)|~quiet(mary)))&
(?[X]:(rich(X)))&
(?[X]:((~creative(X)<~>~generous(X))))&
((~wise(john)|~happy(john)))&
(?[X]:((~curious(X)&humble(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~funny(X)&brave(X)))) | ~old(fred) | [
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6373666878748843143470826
% SZS output start Proof for 6373666878748843143470826
9. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> ~happy(X0)) [input p8]
13. ! [X0] : ((~humble(X0) <~> ~old(X0)) <=> (~humble(X0) | happy(X0))) [input p12]
24. ~old(fred) [input hypothesis]
52. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | happy(X0)) & (~happy(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 9]
59. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (humble(X0) & ~happy(X0))) & ((~humble(X0) | happy(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [nnf transformation 13]
60. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (humble(X0) & ~happy(X0))) & (~humble(X0) | happy(X0) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [flattening 59]
91. ~happy(X0) | humble(X0) | humble(X0) [cnf transformation 52]
92. ~happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 52]
107. ~humble(X0) | happy(X0) | ~humble(X0) | old(X0) [cnf transformation 60]
111. old(X0) | humble(X0) | humble(X0) [cnf transformation 60]
129. ~old(fred) [cnf transformation 24]
130. ~humble(X0) | happy(X0) | old(X0) [duplicate literal removal 107]
131. old(X0) | humble(X0) [duplicate literal removal 111]
132. ~happy(X0) | humble(X0) [duplicate literal removal 91]
133. ~happy(X0) | ~humble(X0) [duplicate literal removal 92]
190. ~happy(X0) [subsumption resolution 132,133]
225. ~humble(X0) | old(X0) [subsumption resolution 130,190]
226. old(X0) [subsumption resolution 225,131]
250. $false [subsumption resolution 129,226]
% SZS output end Proof for 6373666878748843143470826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not creative is humble and vice versa.
Everyone who is either calm or not brave is not patient and vice versa.
Everyone who is both not brave and not strong is both not quiet and not wise.
Everyone who is not generous or rich is both tall and not brave.
Everyone who is not happy or funny is not patient or kind.
Everyone who is not strong is both patient and not tall and vice versa.
Everyone who is not calm or humble is both not humble and not happy and vice versa.
Everyone who is both not funny and not strong is not happy or quiet and vice versa.
If someone is not happy then someone is both not old and not creative.
If susan is both curious and not funny then someone is both kind and not curious and vice versa.
Everyone who is both not kind and not calm is both not creative and humble and vice versa.
Everyone who is both patient and not creative is not rich and vice versa.
Everyone who is either funny or generous is not old or strong.
If fred is creative then lucy is both humble and not patient.
If someone is either tall or old then someone is curious or not wise and vice versa.
If alice is either patient or tall then mary is calm or not humble and vice versa.
Fred is either not strong or old.
Someone is either creative or curious.
Someone is creative or not tall.
Someone is either not calm or not tall.
Someone is not brave.
Susan is not tall.
Someone is either funny or old.
Fred is either generous or rich. | Fred is strong. | contradiction | (![X]:((~strong(X)<~>~creative(X))<=>humble(X)))&
(![X]:((calm(X)<~>~brave(X))<=>~patient(X)))&
(![X]:((~brave(X)&~strong(X))=>(~quiet(X)&~wise(X))))&
(![X]:((~generous(X)|rich(X))=>(tall(X)&~brave(X))))&
(![X]:((~happy(X)|funny(X))=>(~patient(X)|kind(X))))&
(![X]:(~strong(X)<=>(patient(X)&~tall(X))))&
(![X]:((~calm(X)|humble(X))<=>(~humble(X)&~happy(X))))&
(![X]:((~funny(X)&~strong(X))<=>(~happy(X)|quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~old(X)&~creative(X)))))&
(((curious(susan)&~funny(susan)))<=>(?[X]:((kind(X)&~curious(X)))))&
(![X]:((~kind(X)&~calm(X))<=>(~creative(X)&humble(X))))&
(![X]:((patient(X)&~creative(X))<=>~rich(X)))&
(![X]:((funny(X)<~>generous(X))=>(~old(X)|strong(X))))&
((creative(fred))=>((humble(lucy)&~patient(lucy))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((curious(X)|~wise(X)))))&
(((patient(alice)<~>tall(alice)))<=>((calm(mary)|~humble(mary))))&
((~strong(fred)<~>old(fred)))&
(?[X]:((creative(X)<~>curious(X))))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:(~brave(X)))&
(~tall(susan))&
(?[X]:((funny(X)<~>old(X))))&
((generous(fred)<~>rich(fred))) | strong(fred) | [
"p0",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 584776724774520274436530
% SZS output start Proof for 584776724774520274436530
1. ! [X0] : ((~strong(X0) <~> ~creative(X0)) <=> humble(X0)) [input p0]
7. ! [X0] : ((humble(X0) | ~calm(X0)) <=> (~happy(X0) & ~humble(X0))) [input p6]
14. creative(fred) => (~patient(lucy) & humble(lucy)) [input p13]
25. strong(fred) [input hypothesis]
36. (~patient(lucy) & humble(lucy)) | ~creative(fred) [ennf transformation 14]
37. ! [X0] : ((((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | ~humble(X0)) & (humble(X0) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))))) [nnf transformation 1]
41. ! [X0] : (((humble(X0) | ~calm(X0)) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | (~humble(X0) & calm(X0)))) [nnf transformation 7]
42. ! [X0] : ((humble(X0) | ~calm(X0) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | (~humble(X0) & calm(X0)))) [flattening 41]
81. ~strong(X0) | humble(X0) | creative(X0) [cnf transformation 37]
100. ~humble(X0) | ~humble(X0) [cnf transformation 42]
124. humble(lucy) | ~creative(fred) [cnf transformation 36]
151. strong(fred) [cnf transformation 25]
152. ~humble(X0) [duplicate literal removal 100]
192. 9 <=> creative(fred) [avatar definition]
194. ~creative(fred) <- (~9) [avatar component clause 192]
200. ~creative(fred) [subsumption resolution 124,152]
201. ~9 [avatar split clause 200,192]
255. 22 <=> strong(fred) [avatar definition]
257. strong(fred) <- (22) [avatar component clause 255]
313. 22 [avatar split clause 151,255]
340. humble(fred) | creative(fred) <- (22) [resolution 81,257]
343. creative(fred) <- (22) [subsumption resolution 340,152]
344. $false <- (~9, 22) [subsumption resolution 343,194]
345. 9 | ~22 [avatar contradiction clause 344]
347. $false [avatar sat refutation 201,313,345]
% SZS output end Proof for 584776724774520274436530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is funny and vice versa.
Everyone who is not funny is either tall or kind and vice versa.
If someone is not humble then someone is brave and vice versa.
Everyone who is calm is both creative and not calm.
Everyone who is either not tall or calm is both tall and wise.
Everyone who is either strong or not patient is both creative and not brave and vice versa.
If paul is either curious or old then susan is happy and vice versa.
Everyone who is both tall and not happy is not old or not rich.
Everyone who is not funny or not generous is happy or not wise.
If lucy is not humble or wise then paul is either not rich or not generous and vice versa.
If someone is happy or humble then paul is both not wise and wise.
Everyone who is not creative is rich.
If someone is either creative or not generous then paul is not happy or wise and vice versa.
Everyone who is funny is both quiet and generous.
If paul is kind then someone is either not patient or not wise.
Everyone who is calm is either patient or humble.
Someone is either happy or not brave.
Susan is both quiet and not wise.
John is creative.
Mary is both not humble and not strong.
Someone is brave.
Paul is either not curious or not creative.
Someone is not kind or humble. | Paul is not old. | entailment | (![X]:(humble(X)<=>funny(X)))&
(![X]:(~funny(X)<=>(tall(X)<~>kind(X))))&
((?[X]:(~humble(X)))<=>(?[X]:(brave(X))))&
(![X]:(calm(X)=>(creative(X)&~calm(X))))&
(![X]:((~tall(X)<~>calm(X))=>(tall(X)&wise(X))))&
(![X]:((strong(X)<~>~patient(X))<=>(creative(X)&~brave(X))))&
(((curious(paul)<~>old(paul)))<=>(happy(susan)))&
(![X]:((tall(X)&~happy(X))=>(~old(X)|~rich(X))))&
(![X]:((~funny(X)|~generous(X))=>(happy(X)|~wise(X))))&
(((~humble(lucy)|wise(lucy)))<=>((~rich(paul)<~>~generous(paul))))&
((?[X]:((happy(X)|humble(X))))=>((~wise(paul)&wise(paul))))&
(![X]:(~creative(X)=>rich(X)))&
((?[X]:((creative(X)<~>~generous(X))))<=>((~happy(paul)|wise(paul))))&
(![X]:(funny(X)=>(quiet(X)&generous(X))))&
((kind(paul))=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:(calm(X)=>(patient(X)<~>humble(X))))&
(?[X]:((happy(X)<~>~brave(X))))&
((quiet(susan)&~wise(susan)))&
(creative(john))&
((~humble(mary)&~strong(mary)))&
(?[X]:(brave(X)))&
((~curious(paul)<~>~creative(paul)))&
(?[X]:((~kind(X)|humble(X)))) | ~old(paul) | [
"p3",
"p4",
"p6",
"p7",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7018968054568548576759913
% SZS output start Proof for 7018968054568548576759913
4. ! [X0] : (calm(X0) => (~calm(X0) & creative(X0))) [input p3]
5. ! [X0] : ((~tall(X0) <~> calm(X0)) => (wise(X0) & tall(X0))) [input p4]
7. (curious(paul) <~> old(paul)) <=> happy(susan) [input p6]
8. ! [X0] : ((~happy(X0) & tall(X0)) => (~rich(X0) | ~old(X0))) [input p7]
11. ? [X0] : (humble(X0) | happy(X0)) => (wise(paul) & ~wise(paul)) [input p10]
12. ! [X0] : (~creative(X0) => rich(X0)) [input p11]
22. ~curious(paul) <~> ~creative(paul) [input p21]
24. old(paul) [input hypothesis]
28. ! [X0] : ((~calm(X0) & creative(X0)) | ~calm(X0)) [ennf transformation 4]
29. ! [X0] : ((wise(X0) & tall(X0)) | (~tall(X0) <=> calm(X0))) [ennf transformation 5]
30. ! [X0] : ((~rich(X0) | ~old(X0)) | (happy(X0) | ~tall(X0))) [ennf transformation 8]
31. ! [X0] : (~rich(X0) | ~old(X0) | happy(X0) | ~tall(X0)) [flattening 30]
34. (wise(paul) & ~wise(paul)) | ! [X0] : (~humble(X0) & ~happy(X0)) [ennf transformation 11]
35. ! [X0] : (rich(X0) | creative(X0)) [ennf transformation 12]
46. ! [X0] : ((wise(X0) & tall(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0)))) [nnf transformation 29]
49. (((~old(paul) | ~curious(paul)) & (old(paul) | curious(paul))) | ~happy(susan)) & (happy(susan) | ((curious(paul) | ~old(paul)) & (old(paul) | ~curious(paul)))) [nnf transformation 7]
66. (creative(paul) | curious(paul)) & (~creative(paul) | ~curious(paul)) [nnf transformation 22]
78. ~calm(X0) | ~calm(X0) [cnf transformation 28]
79. tall(X0) | calm(X0) | tall(X0) [cnf transformation 46]
90. happy(susan) | curious(paul) | ~old(paul) [cnf transformation 49]
93. ~rich(X0) | ~old(X0) | happy(X0) | ~tall(X0) [cnf transformation 31]
102. ~wise(paul) | ~happy(X0) [cnf transformation 34]
104. wise(paul) | ~happy(X0) [cnf transformation 34]
106. rich(X0) | creative(X0) [cnf transformation 35]
125. ~creative(paul) | ~curious(paul) [cnf transformation 66]
128. old(paul) [cnf transformation 24]
129. tall(X0) | calm(X0) [duplicate literal removal 79]
130. ~calm(X0) [duplicate literal removal 78]
148. tall(X0) [subsumption resolution 129,130]
150. 5 <=> happy(susan) [avatar definition]
151. happy(susan) <- (5) [avatar component clause 150]
154. 6 <=> curious(paul) [avatar definition]
158. 7 <=> old(paul) [avatar definition]
159. old(paul) <- (7) [avatar component clause 158]
163. ~7 | 6 | 5 [avatar split clause 90,150,154,158]
165. ~rich(X0) | ~old(X0) | happy(X0) [subsumption resolution 93,148]
171. 9 <=> rich(paul) [avatar definition]
172. rich(paul) <- (9) [avatar component clause 171]
173. ~rich(paul) <- (~9) [avatar component clause 171]
192. 13 <=> wise(paul) [avatar definition]
197. 14 <=> ! [X0] : ~happy(X0) [avatar definition]
198. ~happy(X0) <- (14) [avatar component clause 197]
199. 14 | 13 [avatar split clause 104,192,197]
201. 14 | ~13 [avatar split clause 102,192,197]
251. 25 <=> creative(paul) [avatar definition]
252. ~creative(paul) <- (~25) [avatar component clause 251]
255. ~6 | ~25 [avatar split clause 125,251,154]
265. 7 [avatar split clause 128,158]
266. creative(paul) <- (~9) [resolution 106,173]
267. $false <- (~9, ~25) [subsumption resolution 266,252]
268. 9 | 25 [avatar contradiction clause 267]
323. $false <- (5, 14) [subsumption resolution 151,198]
324. ~5 | ~14 [avatar contradiction clause 323]
328. ~old(paul) | happy(paul) <- (9) [resolution 165,172]
330. happy(paul) <- (7, 9) [subsumption resolution 328,159]
331. $false <- (7, 9, 14) [subsumption resolution 330,198]
332. ~7 | ~9 | ~14 [avatar contradiction clause 331]
333. $false [avatar sat refutation 163,199,201,255,265,268,324,332]
% SZS output end Proof for 7018968054568548576759913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is not humble or not generous and vice versa.
Everyone who is either old or not funny is humble or not brave and vice versa.
If someone is either funny or calm then someone is both not brave and funny.
If someone is not kind or generous then fred is not patient.
If someone is both humble and tall then mary is either not quiet or wise.
If paul is both not curious and not patient then lucy is old or not humble and vice versa.
Everyone who is both not humble and humble is either strong or not quiet and vice versa.
Everyone who is either calm or not quiet is both wise and curious and vice versa.
Everyone who is not old or happy is both generous and not quiet and vice versa.
If mary is strong or curious then someone is not rich or kind.
If someone is both generous and strong then fred is calm or brave and vice versa.
If someone is either tall or not happy then someone is both strong and brave and vice versa.
If someone is not strong or tall then someone is old.
Everyone who is both not rich and not strong is either happy or wise.
Everyone who is strong or not wise is both not generous and tall and vice versa.
Everyone who is not calm is either not calm or not rich and vice versa.
Mary is either brave or not brave.
Someone is not creative.
Lucy is wise.
Someone is wise.
Someone is either funny or not humble.
Fred is not curious or not brave.
Someone is kind.
Someone is not funny or brave. | Fred is old. | entailment | (![X]:(~wise(X)<=>(~humble(X)|~generous(X))))&
(![X]:((old(X)<~>~funny(X))<=>(humble(X)|~brave(X))))&
((?[X]:((funny(X)<~>calm(X))))=>(?[X]:((~brave(X)&funny(X)))))&
((?[X]:((~kind(X)|generous(X))))=>(~patient(fred)))&
((?[X]:((humble(X)&tall(X))))=>((~quiet(mary)<~>wise(mary))))&
(((~curious(paul)&~patient(paul)))<=>((old(lucy)|~humble(lucy))))&
(![X]:((~humble(X)&humble(X))<=>(strong(X)<~>~quiet(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>(wise(X)&curious(X))))&
(![X]:((~old(X)|happy(X))<=>(generous(X)&~quiet(X))))&
(((strong(mary)|curious(mary)))=>(?[X]:((~rich(X)|kind(X)))))&
((?[X]:((generous(X)&strong(X))))<=>((calm(fred)|brave(fred))))&
((?[X]:((tall(X)<~>~happy(X))))<=>(?[X]:((strong(X)&brave(X)))))&
((?[X]:((~strong(X)|tall(X))))=>(?[X]:(old(X))))&
(![X]:((~rich(X)&~strong(X))=>(happy(X)<~>wise(X))))&
(![X]:((strong(X)|~wise(X))<=>(~generous(X)&tall(X))))&
(![X]:(~calm(X)<=>(~calm(X)<~>~rich(X))))&
((brave(mary)<~>~brave(mary)))&
(?[X]:(~creative(X)))&
(wise(lucy))&
(?[X]:(wise(X)))&
(?[X]:((funny(X)<~>~humble(X))))&
((~curious(fred)|~brave(fred)))&
(?[X]:(kind(X)))&
(?[X]:((~funny(X)|brave(X)))) | old(fred) | [
"p6",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9206341378515914227925558
% SZS output start Proof for 9206341378515914227925558
7. ! [X0] : ((humble(X0) & ~humble(X0)) <=> (strong(X0) <~> ~quiet(X0))) [input p6]
9. ! [X0] : ((happy(X0) | ~old(X0)) <=> (~quiet(X0) & generous(X0))) [input p8]
15. ! [X0] : ((~wise(X0) | strong(X0)) <=> (tall(X0) & ~generous(X0))) [input p14]
25. ~old(fred) [input hypothesis]
50. ! [X0] : (((humble(X0) & ~humble(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (~humble(X0) | humble(X0)))) [nnf transformation 7]
51. ! [X0] : (((humble(X0) & ~humble(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | ~humble(X0) | humble(X0))) [flattening 50]
54. ! [X0] : (((happy(X0) | ~old(X0)) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 9]
55. ! [X0] : ((happy(X0) | ~old(X0) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | (~happy(X0) & old(X0)))) [flattening 54]
70. ! [X0] : (((~wise(X0) | strong(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (wise(X0) & ~strong(X0)))) [nnf transformation 15]
71. ! [X0] : ((~wise(X0) | strong(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (wise(X0) & ~strong(X0)))) [flattening 70]
105. ~humble(X0) | strong(X0) | quiet(X0) [cnf transformation 51]
107. strong(X0) | humble(X0) | quiet(X0) [cnf transformation 51]
114. old(X0) | generous(X0) [cnf transformation 55]
116. ~quiet(X0) | old(X0) [cnf transformation 55]
134. ~generous(X0) | ~strong(X0) [cnf transformation 71]
151. ~old(fred) [cnf transformation 25]
214. strong(X0) | quiet(X0) [subsumption resolution 105,107]
237. 18 <=> ! [X1] : (~strong(X1) | ~generous(X1)) [avatar definition]
238. ~strong(X1) | ~generous(X1) <- (18) [avatar component clause 237]
283. 18 [avatar split clause 134,237]
316. generous(fred) [resolution 114,151]
329. ~generous(X0) | quiet(X0) <- (18) [resolution 238,214]
375. quiet(fred) <- (18) [resolution 329,316]
384. old(fred) <- (18) [resolution 375,116]
385. $false <- (18) [subsumption resolution 384,151]
386. ~18 [avatar contradiction clause 385]
387. $false [avatar sat refutation 283,386]
% SZS output end Proof for 9206341378515914227925558
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or funny is curious.
Everyone who is not calm or not rich is generous or rich and vice versa.
If someone is either creative or rich then lucy is patient and vice versa.
Everyone who is both tall and generous is both not wise and creative.
If someone is either not calm or not generous then susan is creative or generous.
Everyone who is not humble or not brave is funny or not calm and vice versa.
Everyone who is not patient is both not calm and humble.
Everyone who is both not kind and creative is either not brave or tall.
If someone is wise or rich then someone is not curious.
If susan is not generous or not strong then alice is not patient or not brave.
Everyone who is not humble is not calm or not funny.
If someone is not humble or not happy then someone is brave.
If someone is either happy or funny then someone is both not curious and not creative and vice versa.
Everyone who is funny is both tall and not tall.
Everyone who is either not quiet or old is both rich and not old.
If someone is both patient and old then lucy is either creative or patient.
Fred is quiet or not rich.
Lucy is both generous and strong.
Susan is happy.
Someone is both not funny and not brave.
Someone is not curious or old.
Fred is humble.
Someone is either not strong or creative.
Someone is both not humble and happy. | Lucy is quiet. | neutral | (![X]:((~humble(X)|funny(X))=>curious(X)))&
(![X]:((~calm(X)|~rich(X))<=>(generous(X)|rich(X))))&
((?[X]:((creative(X)<~>rich(X))))<=>(patient(lucy)))&
(![X]:((tall(X)&generous(X))=>(~wise(X)&creative(X))))&
((?[X]:((~calm(X)<~>~generous(X))))=>((creative(susan)|generous(susan))))&
(![X]:((~humble(X)|~brave(X))<=>(funny(X)|~calm(X))))&
(![X]:(~patient(X)=>(~calm(X)&humble(X))))&
(![X]:((~kind(X)&creative(X))=>(~brave(X)<~>tall(X))))&
((?[X]:((wise(X)|rich(X))))=>(?[X]:(~curious(X))))&
(((~generous(susan)|~strong(susan)))=>((~patient(alice)|~brave(alice))))&
(![X]:(~humble(X)=>(~calm(X)|~funny(X))))&
((?[X]:((~humble(X)|~happy(X))))=>(?[X]:(brave(X))))&
((?[X]:((happy(X)<~>funny(X))))<=>(?[X]:((~curious(X)&~creative(X)))))&
(![X]:(funny(X)=>(tall(X)&~tall(X))))&
(![X]:((~quiet(X)<~>old(X))=>(rich(X)&~old(X))))&
((?[X]:((patient(X)&old(X))))=>((creative(lucy)<~>patient(lucy))))&
((quiet(fred)|~rich(fred)))&
((generous(lucy)&strong(lucy)))&
(happy(susan))&
(?[X]:((~funny(X)&~brave(X))))&
(?[X]:((~curious(X)|old(X))))&
(humble(fred))&
(?[X]:((~strong(X)<~>creative(X))))&
(?[X]:((~humble(X)&happy(X)))) | quiet(lucy) | [] | null | 0 |
Everyone who is patient or kind is funny and vice versa. If susan is either curious or kind then paul is both not creative and not brave. If someone is both strong and rich then someone is both kind and not old. Everyone who is either curious or not old is either quiet or not humble. Everyone who is both not happy and rich is both not kind and not brave. Everyone who is not happy is old. Everyone who is creative is either not wise or wise. If mary is either tall or not brave then someone is either strong or not rich and vice versa. Everyone who is kind or happy is either not strong or patient. Everyone who is either quiet or not funny is not strong or not rich. Everyone who is both not wise and patient is brave or not calm and vice versa. Everyone who is not calm or not kind is not happy. Everyone who is both not curious and happy is not calm. If john is not creative or tall then susan is not curious or quiet. Everyone who is either brave or happy is not funny or not tall and vice versa. If someone is both not humble and not calm then john is both not curious and old. Mary is either tall or generous. Someone is either not happy or creative. Someone is either happy or not happy. Someone is both brave and not quiet. Fred is creative or not strong. Lucy is either not funny or generous. Someone is either not old or not calm. Someone is either patient or not generous. | Fred is not funny. | contradiction | (![X]:((patient(X)|kind(X))<=>funny(X)))&
(((curious(susan)<~>kind(susan)))=>((~creative(paul)&~brave(paul))))&
((?[X]:((strong(X)&rich(X))))=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((curious(X)<~>~old(X))=>(quiet(X)<~>~humble(X))))&
(![X]:((~happy(X)&rich(X))=>(~kind(X)&~brave(X))))&
(![X]:(~happy(X)=>old(X)))&
(![X]:(creative(X)=>(~wise(X)<~>wise(X))))&
(((tall(mary)<~>~brave(mary)))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(![X]:((kind(X)|happy(X))=>(~strong(X)<~>patient(X))))&
(![X]:((quiet(X)<~>~funny(X))=>(~strong(X)|~rich(X))))&
(![X]:((~wise(X)&patient(X))<=>(brave(X)|~calm(X))))&
(![X]:((~calm(X)|~kind(X))=>~happy(X)))&
(![X]:((~curious(X)&happy(X))=>~calm(X)))&
(((~creative(john)|tall(john)))=>((~curious(susan)|quiet(susan))))&
(![X]:((brave(X)<~>happy(X))<=>(~funny(X)|~tall(X))))&
((?[X]:((~humble(X)&~calm(X))))=>((~curious(john)&old(john))))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((brave(X)&~quiet(X))))&
((creative(fred)|~strong(fred)))&
((~funny(lucy)<~>generous(lucy)))&
(?[X]:((~old(X)<~>~calm(X))))&
(?[X]:((patient(X)<~>~generous(X)))) | ~funny(fred) | [
"p0",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3136337485957137877855884
% SZS output start Proof for 3136337485957137877855884
1. ! [X0] : ((kind(X0) | patient(X0)) <=> funny(X0)) [input p0]
11. ! [X0] : ((patient(X0) & ~wise(X0)) <=> (~calm(X0) | brave(X0))) [input p10]
12. ! [X0] : ((~kind(X0) | ~calm(X0)) => ~happy(X0)) [input p11]
15. ! [X0] : ((brave(X0) <~> happy(X0)) <=> (~tall(X0) | ~funny(X0))) [input p14]
25. ~funny(fred) [input hypothesis]
37. ! [X0] : (~happy(X0) | (kind(X0) & calm(X0))) [ennf transformation 12]
43. ! [X0] : (((kind(X0) | patient(X0)) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~patient(X0)))) [nnf transformation 1]
44. ! [X0] : ((kind(X0) | patient(X0) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~patient(X0)))) [flattening 43]
57. ! [X0] : (((patient(X0) & ~wise(X0)) | (calm(X0) & ~brave(X0))) & ((~calm(X0) | brave(X0)) | (~patient(X0) | wise(X0)))) [nnf transformation 11]
58. ! [X0] : (((patient(X0) & ~wise(X0)) | (calm(X0) & ~brave(X0))) & (~calm(X0) | brave(X0) | ~patient(X0) | wise(X0))) [flattening 57]
59. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (tall(X0) & funny(X0))) & ((~tall(X0) | ~funny(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [nnf transformation 15]
60. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (tall(X0) & funny(X0))) & (~tall(X0) | ~funny(X0) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [flattening 59]
77. ~patient(X0) | funny(X0) [cnf transformation 44]
78. ~kind(X0) | funny(X0) [cnf transformation 44]
112. ~brave(X0) | patient(X0) [cnf transformation 58]
115. ~happy(X0) | kind(X0) [cnf transformation 37]
121. happy(X0) | brave(X0) | funny(X0) [cnf transformation 60]
142. ~funny(fred) [cnf transformation 25]
307. brave(X3) | funny(X3) | kind(X3) [resolution 121,115]
320. brave(X3) | funny(X3) [subsumption resolution 307,78]
372. funny(X0) | patient(X0) [resolution 320,112]
374. funny(X0) [subsumption resolution 372,77]
395. $false [resolution 374,142]
% SZS output end Proof for 3136337485957137877855884
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or happy is not quiet and vice versa.
Everyone who is not quiet or not curious is not quiet.
If fred is old then alice is both not brave and funny.
Everyone who is not humble is both wise and not happy.
If someone is strong or not quiet then someone is both not funny and old and vice versa.
If john is not tall or calm then fred is either not funny or tall and vice versa.
Everyone who is either calm or not kind is calm and vice versa.
If someone is both strong and wise then fred is either wise or tall and vice versa.
Everyone who is either not quiet or not humble is humble or tall.
If john is not patient then mary is both brave and calm and vice versa.
If someone is either patient or wise then someone is both humble and wise.
Everyone who is wise or creative is both rich and strong.
If lucy is either patient or not quiet then mary is either not creative or not humble and vice versa.
Everyone who is both not wise and not humble is curious.
Everyone who is both curious and not strong is either humble or not brave and vice versa.
Everyone who is curious or not old is either not happy or tall and vice versa.
Someone is both kind and rich.
John is both not strong and humble.
Someone is either calm or not calm.
Lucy is not kind or not creative.
Fred is not humble or old.
Someone is either humble or not strong.
John is either not happy or not humble.
Susan is both rich and kind. | Alice is not brave. | entailment | (![X]:((humble(X)|happy(X))<=>~quiet(X)))&
(![X]:((~quiet(X)|~curious(X))=>~quiet(X)))&
((old(fred))=>((~brave(alice)&funny(alice))))&
(![X]:(~humble(X)=>(wise(X)&~happy(X))))&
((?[X]:((strong(X)|~quiet(X))))<=>(?[X]:((~funny(X)&old(X)))))&
(((~tall(john)|calm(john)))<=>((~funny(fred)<~>tall(fred))))&
(![X]:((calm(X)<~>~kind(X))<=>calm(X)))&
((?[X]:((strong(X)&wise(X))))<=>((wise(fred)<~>tall(fred))))&
(![X]:((~quiet(X)<~>~humble(X))=>(humble(X)|tall(X))))&
((~patient(john))<=>((brave(mary)&calm(mary))))&
((?[X]:((patient(X)<~>wise(X))))=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((wise(X)|creative(X))=>(rich(X)&strong(X))))&
(((patient(lucy)<~>~quiet(lucy)))<=>((~creative(mary)<~>~humble(mary))))&
(![X]:((~wise(X)&~humble(X))=>curious(X)))&
(![X]:((curious(X)&~strong(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((curious(X)|~old(X))<=>(~happy(X)<~>tall(X))))&
(?[X]:((kind(X)&rich(X))))&
((~strong(john)&humble(john)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~kind(lucy)|~creative(lucy)))&
((~humble(fred)|old(fred)))&
(?[X]:((humble(X)<~>~strong(X))))&
((~happy(john)<~>~humble(john)))&
((rich(susan)&kind(susan))) | ~brave(alice) | [
"p0",
"p2",
"p3",
"p7",
"p8",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3507802212953523055184613
% SZS output start Proof for 3507802212953523055184613
1. ! [X0] : ((happy(X0) | humble(X0)) <=> ~quiet(X0)) [input p0]
3. old(fred) => (funny(alice) & ~brave(alice)) [input p2]
4. ! [X0] : (~humble(X0) => (~happy(X0) & wise(X0))) [input p3]
8. ? [X0] : (wise(X0) & strong(X0)) <=> (wise(fred) <~> tall(fred)) [input p7]
9. ! [X0] : ((~quiet(X0) <~> ~humble(X0)) => (tall(X0) | humble(X0))) [input p8]
12. ! [X0] : ((creative(X0) | wise(X0)) => (strong(X0) & rich(X0))) [input p11]
21. old(fred) | ~humble(fred) [input p20]
25. brave(alice) [input hypothesis]
30. ! [X0] : ((creative(X0) | wise(X0)) => strong(X0)) [pure predicate removal 12]
32. (funny(alice) & ~brave(alice)) | ~old(fred) [ennf transformation 3]
33. ! [X0] : ((~happy(X0) & wise(X0)) | humble(X0)) [ennf transformation 4]
34. ! [X0] : ((tall(X0) | humble(X0)) | (~quiet(X0) <=> ~humble(X0))) [ennf transformation 9]
35. ! [X0] : (tall(X0) | humble(X0) | (~quiet(X0) <=> ~humble(X0))) [flattening 34]
37. ! [X0] : (strong(X0) | (~creative(X0) & ~wise(X0))) [ennf transformation 30]
40. ! [X0] : (((happy(X0) | humble(X0)) | quiet(X0)) & (~quiet(X0) | (~happy(X0) & ~humble(X0)))) [nnf transformation 1]
41. ! [X0] : ((happy(X0) | humble(X0) | quiet(X0)) & (~quiet(X0) | (~happy(X0) & ~humble(X0)))) [flattening 40]
50. (? [X0] : (wise(X0) & strong(X0)) | ((wise(fred) | ~tall(fred)) & (tall(fred) | ~wise(fred)))) & (((~tall(fred) | ~wise(fred)) & (tall(fred) | wise(fred))) | ! [X0] : (~wise(X0) | ~strong(X0))) [nnf transformation 8]
51. (? [X0] : (wise(X0) & strong(X0)) | ((wise(fred) | ~tall(fred)) & (tall(fred) | ~wise(fred)))) & (((~tall(fred) | ~wise(fred)) & (tall(fred) | wise(fred))) | ! [X1] : (~wise(X1) | ~strong(X1))) [rectify 50]
52. ? [X0] : (wise(X0) & strong(X0)) => (wise(sK2) & strong(sK2)) [choice axiom]
53. ((wise(sK2) & strong(sK2)) | ((wise(fred) | ~tall(fred)) & (tall(fred) | ~wise(fred)))) & (((~tall(fred) | ~wise(fred)) & (tall(fred) | wise(fred))) | ! [X1] : (~wise(X1) | ~strong(X1))) [skolemisation 51,52]
54. ! [X0] : (tall(X0) | humble(X0) | ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0)))) [nnf transformation 35]
75. ~quiet(X0) | ~humble(X0) [cnf transformation 41]
77. quiet(X0) | humble(X0) | happy(X0) [cnf transformation 41]
80. ~brave(alice) | ~old(fred) [cnf transformation 32]
82. wise(X0) | humble(X0) [cnf transformation 33]
83. ~happy(X0) | humble(X0) [cnf transformation 33]
100. ~tall(fred) | ~wise(fred) | ~wise(X1) | ~strong(X1) [cnf transformation 53]
106. tall(X0) | humble(X0) | ~quiet(X0) | humble(X0) [cnf transformation 54]
114. ~wise(X0) | strong(X0) [cnf transformation 37]
143. old(fred) | ~humble(fred) [cnf transformation 21]
149. brave(alice) [cnf transformation 25]
150. tall(X0) | humble(X0) | ~quiet(X0) [duplicate literal removal 106]
154. 1 <=> old(fred) [avatar definition]
163. 3 <=> brave(alice) [avatar definition]
166. ~1 | ~3 [avatar split clause 80,163,154]
198. 11 <=> tall(fred) [avatar definition]
200. ~tall(fred) <- (~11) [avatar component clause 198]
221. 15 <=> wise(fred) [avatar definition]
222. ~wise(fred) <- (~15) [avatar component clause 221]
223. wise(fred) <- (15) [avatar component clause 221]
237. 18 <=> ! [X1] : (~wise(X1) | ~strong(X1)) [avatar definition]
238. ~wise(X1) | ~strong(X1) <- (18) [avatar component clause 237]
239. 18 | ~15 | ~11 [avatar split clause 100,198,221,237]
241. ~quiet(X0) | tall(X0) [subsumption resolution 150,75]
301. 30 <=> humble(fred) [avatar definition]
303. ~humble(fred) <- (~30) [avatar component clause 301]
304. ~30 | 1 [avatar split clause 143,154,301]
316. 3 [avatar split clause 149,163]
328. humble(fred) <- (~15) [resolution 82,222]
329. $false <- (~15, ~30) [subsumption resolution 328,303]
330. 15 | 30 [avatar contradiction clause 329]
331. ~wise(X1) <- (18) [subsumption resolution 238,114]
332. $false <- (15, 18) [subsumption resolution 223,331]
333. ~15 | ~18 [avatar contradiction clause 332]
346. humble(X0) | happy(X0) | tall(X0) [resolution 77,241]
352. tall(X0) | humble(X0) [subsumption resolution 346,83]
445. humble(fred) <- (~11) [resolution 352,200]
449. $false <- (~11, ~30) [subsumption resolution 445,303]
450. 11 | 30 [avatar contradiction clause 449]
454. $false [avatar sat refutation 166,239,304,316,330,333,450]
% SZS output end Proof for 3507802212953523055184613
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either generous or patient then someone is calm and vice versa.
Everyone who is both humble and brave is either not patient or tall.
Everyone who is both humble and kind is either calm or old and vice versa.
If paul is both not humble and wise then mary is generous and vice versa.
If someone is both curious and old then alice is either funny or happy.
If someone is not kind then john is both wise and old.
If fred is both not kind and curious then someone is either not patient or not generous and vice versa.
If someone is not creative then someone is both humble and not strong.
Everyone who is either calm or not patient is either not creative or brave.
If susan is not old then paul is humble and vice versa.
Everyone who is kind is either brave or creative and vice versa.
Everyone who is funny is both not quiet and not patient.
Everyone who is either not happy or brave is either wise or funny and vice versa.
Everyone who is either creative or funny is either quiet or generous.
Everyone who is both generous and not calm is both not strong and creative and vice versa.
Everyone who is not brave or curious is either not strong or patient.
Paul is curious.
Someone is either not quiet or quiet.
Lucy is creative or quiet.
Mary is not generous.
Someone is old or not old.
Someone is not kind or not wise.
Paul is not tall.
Someone is generous or wise. | John is not old. | contradiction | (((generous(fred)<~>patient(fred)))<=>(?[X]:(calm(X))))&
(![X]:((humble(X)&brave(X))=>(~patient(X)<~>tall(X))))&
(![X]:((humble(X)&kind(X))<=>(calm(X)<~>old(X))))&
(((~humble(paul)&wise(paul)))<=>(generous(mary)))&
((?[X]:((curious(X)&old(X))))=>((funny(alice)<~>happy(alice))))&
((?[X]:(~kind(X)))=>((wise(john)&old(john))))&
(((~kind(fred)&curious(fred)))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
((?[X]:(~creative(X)))=>(?[X]:((humble(X)&~strong(X)))))&
(![X]:((calm(X)<~>~patient(X))=>(~creative(X)<~>brave(X))))&
((~old(susan))<=>(humble(paul)))&
(![X]:(kind(X)<=>(brave(X)<~>creative(X))))&
(![X]:(funny(X)=>(~quiet(X)&~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(wise(X)<~>funny(X))))&
(![X]:((creative(X)<~>funny(X))=>(quiet(X)<~>generous(X))))&
(![X]:((generous(X)&~calm(X))<=>(~strong(X)&creative(X))))&
(![X]:((~brave(X)|curious(X))=>(~strong(X)<~>patient(X))))&
(curious(paul))&
(?[X]:((~quiet(X)<~>quiet(X))))&
((creative(lucy)|quiet(lucy)))&
(~generous(mary))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~kind(X)|~wise(X))))&
(~tall(paul))&
(?[X]:((generous(X)|wise(X)))) | ~old(john) | [
"p0",
"p5",
"p6",
"p8",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5939074150431487208630121
% SZS output start Proof for 5939074150431487208630121
1. (generous(fred) <~> patient(fred)) <=> ? [X0] : calm(X0) [input p0]
6. ? [X0] : ~kind(X0) => (old(john) & wise(john)) [input p5]
7. (curious(fred) & ~kind(fred)) <=> ? [X0] : (~patient(X0) <~> ~generous(X0)) [input p6]
9. ! [X0] : ((calm(X0) <~> ~patient(X0)) => (~creative(X0) <~> brave(X0))) [input p8]
11. ! [X0] : (kind(X0) <=> (brave(X0) <~> creative(X0))) [input p10]
15. ! [X0] : ((~calm(X0) & generous(X0)) <=> (creative(X0) & ~strong(X0))) [input p14]
16. ! [X0] : ((curious(X0) | ~brave(X0)) => (~strong(X0) <~> patient(X0))) [input p15]
25. ~old(john) [input hypothesis]
30. (old(john) & wise(john)) | ! [X0] : kind(X0) [ennf transformation 6]
32. ! [X0] : ((~creative(X0) <~> brave(X0)) | (calm(X0) <=> ~patient(X0))) [ennf transformation 9]
35. ! [X0] : ((~strong(X0) <~> patient(X0)) | (~curious(X0) & brave(X0))) [ennf transformation 16]
36. (((~patient(fred) | ~generous(fred)) & (patient(fred) | generous(fred))) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ((generous(fred) | ~patient(fred)) & (patient(fred) | ~generous(fred)))) [nnf transformation 1]
37. (((~patient(fred) | ~generous(fred)) & (patient(fred) | generous(fred))) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ((generous(fred) | ~patient(fred)) & (patient(fred) | ~generous(fred)))) [rectify 36]
38. ? [X1] : calm(X1) => calm(sK0) [choice axiom]
39. (((~patient(fred) | ~generous(fred)) & (patient(fred) | generous(fred))) | ! [X0] : ~calm(X0)) & (calm(sK0) | ((generous(fred) | ~patient(fred)) & (patient(fred) | ~generous(fred)))) [skolemisation 37,38]
46. ((curious(fred) & ~kind(fred)) | ! [X0] : ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0)))) & (? [X0] : ((generous(X0) | patient(X0)) & (~generous(X0) | ~patient(X0))) | (~curious(fred) | kind(fred))) [nnf transformation 7]
47. ((curious(fred) & ~kind(fred)) | ! [X0] : ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0)))) & (? [X0] : ((generous(X0) | patient(X0)) & (~generous(X0) | ~patient(X0))) | ~curious(fred) | kind(fred)) [flattening 46]
48. ((curious(fred) & ~kind(fred)) | ! [X0] : ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0)))) & (? [X1] : ((generous(X1) | patient(X1)) & (~generous(X1) | ~patient(X1))) | ~curious(fred) | kind(fred)) [rectify 47]
49. ? [X1] : ((generous(X1) | patient(X1)) & (~generous(X1) | ~patient(X1))) => ((generous(sK1) | patient(sK1)) & (~generous(sK1) | ~patient(sK1))) [choice axiom]
50. ((curious(fred) & ~kind(fred)) | ! [X0] : ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0)))) & (((generous(sK1) | patient(sK1)) & (~generous(sK1) | ~patient(sK1))) | ~curious(fred) | kind(fred)) [skolemisation 48,49]
54. ! [X0] : (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0)))) [nnf transformation 32]
56. ! [X0] : ((kind(X0) | ((brave(X0) | ~creative(X0)) & (creative(X0) | ~brave(X0)))) & (((~creative(X0) | ~brave(X0)) & (creative(X0) | brave(X0))) | ~kind(X0))) [nnf transformation 11]
59. ! [X0] : (((~calm(X0) & generous(X0)) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | (calm(X0) | ~generous(X0)))) [nnf transformation 15]
60. ! [X0] : (((~calm(X0) & generous(X0)) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | calm(X0) | ~generous(X0))) [flattening 59]
61. ! [X0] : (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~curious(X0) & brave(X0))) [nnf transformation 35]
73. patient(fred) | generous(fred) | ~calm(X0) [cnf transformation 39]
74. ~patient(fred) | ~generous(fred) | ~calm(X0) [cnf transformation 39]
89. old(john) | kind(X0) [cnf transformation 30]
92. ~kind(fred) | ~generous(X0) | patient(X0) [cnf transformation 50]
93. ~kind(fred) | ~patient(X0) | generous(X0) [cnf transformation 50]
101. ~brave(X0) | creative(X0) | calm(X0) | patient(X0) [cnf transformation 54]
104. ~kind(X0) | brave(X0) | creative(X0) [cnf transformation 56]
105. ~creative(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 56]
122. ~strong(X0) | calm(X0) | ~generous(X0) [cnf transformation 60]
123. ~generous(X0) | calm(X0) | creative(X0) [cnf transformation 60]
124. ~creative(X0) | generous(X0) | strong(X0) [cnf transformation 60]
126. ~strong(X0) | patient(X0) | brave(X0) [cnf transformation 61]
128. ~patient(X0) | strong(X0) | brave(X0) [cnf transformation 61]
139. ~old(john) [cnf transformation 25]
141. 1 <=> ! [X0] : ~calm(X0) [avatar definition]
142. ~calm(X0) <- (1) [avatar component clause 141]
144. 2 <=> generous(fred) [avatar definition]
145. generous(fred) <- (2) [avatar component clause 144]
148. 3 <=> patient(fred) [avatar definition]
149. patient(fred) <- (3) [avatar component clause 148]
150. ~patient(fred) <- (~3) [avatar component clause 148]
151. 1 | ~2 | ~3 [avatar split clause 74,148,144,141]
152. 1 | 2 | 3 [avatar split clause 73,148,144,141]
188. 11 <=> ! [X0] : kind(X0) [avatar definition]
189. kind(X0) <- (11) [avatar component clause 188]
191. 12 <=> old(john) [avatar definition]
194. 11 | 12 [avatar split clause 89,191,188]
201. 14 <=> ! [X0] : (~patient(X0) | generous(X0)) [avatar definition]
202. ~patient(X0) | generous(X0) <- (14) [avatar component clause 201]
209. 16 <=> ! [X0] : (~generous(X0) | patient(X0)) [avatar definition]
210. ~generous(X0) | patient(X0) <- (16) [avatar component clause 209]
213. 17 <=> kind(fred) [avatar definition]
215. ~kind(fred) <- (~17) [avatar component clause 213]
216. 14 | ~17 [avatar split clause 93,213,201]
217. 16 | ~17 [avatar split clause 92,213,209]
250. 24 <=> creative(lucy) [avatar definition]
251. ~creative(lucy) <- (~24) [avatar component clause 250]
252. creative(lucy) <- (24) [avatar component clause 250]
277. ~12 [avatar split clause 139,191]
281. patient(fred) <- (2, 16) [resolution 210,145]
283. $false <- (2, ~3, 16) [subsumption resolution 281,150]
284. ~2 | 3 | ~16 [avatar contradiction clause 283]
285. $false <- (11, ~17) [subsumption resolution 215,189]
286. ~11 | 17 [avatar contradiction clause 285]
287. generous(fred) <- (3, 14) [resolution 149,202]
290. 2 | ~3 | ~14 [avatar split clause 287,201,148,144]
300. creative(X0) | brave(X0) <- (11) [resolution 104,189]
302. ~brave(lucy) | ~kind(lucy) <- (24) [resolution 105,252]
309. generous(lucy) | strong(lucy) <- (24) [resolution 124,252]
323. 30 <=> strong(lucy) [avatar definition]
325. strong(lucy) <- (30) [avatar component clause 323]
327. 31 <=> generous(lucy) [avatar definition]
328. ~generous(lucy) <- (~31) [avatar component clause 327]
329. generous(lucy) <- (31) [avatar component clause 327]
330. 30 | 31 | ~24 [avatar split clause 309,250,327,323]
333. ~brave(lucy) <- (11, 24) [subsumption resolution 302,189]
335. patient(lucy) <- (16, 31) [resolution 329,210]
391. strong(lucy) | brave(lucy) <- (16, 31) [resolution 335,128]
393. strong(lucy) <- (11, 16, 24, 31) [subsumption resolution 391,333]
394. 30 | ~11 | ~16 | ~24 | ~31 [avatar split clause 393,327,250,209,188,323]
396. patient(lucy) | brave(lucy) <- (30) [resolution 325,126]
397. calm(lucy) | ~generous(lucy) <- (30) [resolution 325,122]
398. ~generous(lucy) <- (1, 30) [subsumption resolution 397,142]
401. ~31 | ~1 | ~30 [avatar split clause 398,323,141,327]
402. patient(lucy) <- (11, 24, 30) [subsumption resolution 396,333]
416. generous(lucy) <- (11, 14, 24, 30) [resolution 402,202]
417. $false <- (11, 14, 24, 30, ~31) [subsumption resolution 416,328]
418. ~11 | ~14 | ~24 | ~30 | 31 [avatar contradiction clause 417]
434. brave(lucy) <- (11, ~24) [resolution 300,251]
441. creative(lucy) | calm(lucy) | patient(lucy) <- (11, ~24) [resolution 434,101]
445. calm(lucy) | patient(lucy) <- (11, ~24) [subsumption resolution 441,251]
446. patient(lucy) <- (1, 11, ~24) [subsumption resolution 445,142]
460. generous(lucy) <- (1, 11, 14, ~24) [resolution 446,202]
463. 31 | ~1 | ~11 | ~14 | 24 [avatar split clause 460,250,201,188,141,327]
465. calm(lucy) | creative(lucy) <- (31) [resolution 329,123]
467. creative(lucy) <- (1, 31) [subsumption resolution 465,142]
468. $false <- (1, ~24, 31) [subsumption resolution 467,251]
469. ~1 | 24 | ~31 [avatar contradiction clause 468]
470. $false [avatar sat refutation 151,152,194,216,217,277,284,286,290,330,394,401,418,463,469]
% SZS output end Proof for 5939074150431487208630121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not wise or calm is both not humble and generous.
Everyone who is funny or patient is either not strong or funny.
If someone is both not strong and strong then someone is not tall or not humble.
Everyone who is both wise and happy is both kind and not tall.
Everyone who is both creative and not kind is both not rich and generous and vice versa.
If someone is either not calm or tall then someone is quiet and vice versa.
Everyone who is both rich and not quiet is rich or not funny and vice versa.
If paul is not brave or strong then paul is not brave and vice versa.
If someone is not creative or not strong then someone is either humble or old.
Everyone who is both old and not old is brave and vice versa.
If someone is both funny and generous then lucy is not quiet and vice versa.
Everyone who is wise is patient or not funny and vice versa.
If paul is humble then someone is either not humble or funny and vice versa.
Everyone who is generous or quiet is not quiet or not humble.
If susan is either not tall or patient then lucy is not generous.
Everyone who is curious is either calm or happy and vice versa.
Lucy is either not strong or not tall.
Someone is either happy or rich.
Someone is both not calm and happy.
Someone is either humble or generous.
Someone is not wise.
Someone is old or calm.
Lucy is both strong and not curious.
Lucy is wise. | Lucy is not rich. | neutral | (![X]:((~wise(X)|calm(X))=>(~humble(X)&generous(X))))&
(![X]:((funny(X)|patient(X))=>(~strong(X)<~>funny(X))))&
((?[X]:((~strong(X)&strong(X))))=>(?[X]:((~tall(X)|~humble(X)))))&
(![X]:((wise(X)&happy(X))=>(kind(X)&~tall(X))))&
(![X]:((creative(X)&~kind(X))<=>(~rich(X)&generous(X))))&
((?[X]:((~calm(X)<~>tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:((rich(X)&~quiet(X))<=>(rich(X)|~funny(X))))&
(((~brave(paul)|strong(paul)))<=>(~brave(paul)))&
((?[X]:((~creative(X)|~strong(X))))=>(?[X]:((humble(X)<~>old(X)))))&
(![X]:((old(X)&~old(X))<=>brave(X)))&
((?[X]:((funny(X)&generous(X))))<=>(~quiet(lucy)))&
(![X]:(wise(X)<=>(patient(X)|~funny(X))))&
((humble(paul))<=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((generous(X)|quiet(X))=>(~quiet(X)|~humble(X))))&
(((~tall(susan)<~>patient(susan)))=>(~generous(lucy)))&
(![X]:(curious(X)<=>(calm(X)<~>happy(X))))&
((~strong(lucy)<~>~tall(lucy)))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:((~calm(X)&happy(X))))&
(?[X]:((humble(X)<~>generous(X))))&
(?[X]:(~wise(X)))&
(?[X]:((old(X)|calm(X))))&
((strong(lucy)&~curious(lucy)))&
(wise(lucy)) | ~rich(lucy) | [] | null | 0 |
If someone is not creative or tall then paul is both not brave and not wise and vice versa.
If someone is funny or not curious then susan is either strong or not generous and vice versa.
If someone is not tall then someone is not wise or quiet.
Everyone who is not happy is happy.
If someone is both quiet and not quiet then susan is both not curious and not generous.
If mary is either not wise or not calm then someone is generous.
Everyone who is both brave and not creative is kind and vice versa.
Everyone who is both not old and happy is not patient or not kind and vice versa.
If susan is curious then someone is either not tall or funny.
Everyone who is not rich or not happy is brave or generous.
If john is either curious or quiet then paul is creative or not strong.
If someone is both not tall and happy then someone is not generous and vice versa.
Everyone who is both not old and funny is not funny or rich and vice versa.
Everyone who is either strong or not old is both curious and not quiet.
Everyone who is both not patient and not creative is both not tall and not humble and vice versa.
If someone is not curious or not generous then someone is not strong and vice versa.
Someone is either tall or not calm.
Mary is not strong.
Someone is rich or not wise.
Someone is patient.
Mary is either creative or not patient.
John is not quiet.
Paul is calm.
Paul is not humble. | Mary is quiet. | contradiction | ((?[X]:((~creative(X)|tall(X))))<=>((~brave(paul)&~wise(paul))))&
((?[X]:((funny(X)|~curious(X))))<=>((strong(susan)<~>~generous(susan))))&
((?[X]:(~tall(X)))=>(?[X]:((~wise(X)|quiet(X)))))&
(![X]:(~happy(X)=>happy(X)))&
((?[X]:((quiet(X)&~quiet(X))))=>((~curious(susan)&~generous(susan))))&
(((~wise(mary)<~>~calm(mary)))=>(?[X]:(generous(X))))&
(![X]:((brave(X)&~creative(X))<=>kind(X)))&
(![X]:((~old(X)&happy(X))<=>(~patient(X)|~kind(X))))&
((curious(susan))=>(?[X]:((~tall(X)<~>funny(X)))))&
(![X]:((~rich(X)|~happy(X))=>(brave(X)|generous(X))))&
(((curious(john)<~>quiet(john)))=>((creative(paul)|~strong(paul))))&
((?[X]:((~tall(X)&happy(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~old(X)&funny(X))<=>(~funny(X)|rich(X))))&
(![X]:((strong(X)<~>~old(X))=>(curious(X)&~quiet(X))))&
(![X]:((~patient(X)&~creative(X))<=>(~tall(X)&~humble(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>(?[X]:(~strong(X))))&
(?[X]:((tall(X)<~>~calm(X))))&
(~strong(mary))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:(patient(X)))&
((creative(mary)<~>~patient(mary)))&
(~quiet(john))&
(calm(paul))&
(~humble(paul)) | quiet(mary) | [
"p6",
"p7",
"p13",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7068736549373008093870028
% SZS output start Proof for 7068736549373008093870028
7. ! [X0] : ((~creative(X0) & brave(X0)) <=> kind(X0)) [input p6]
8. ! [X0] : ((happy(X0) & ~old(X0)) <=> (~kind(X0) | ~patient(X0))) [input p7]
14. ! [X0] : ((strong(X0) <~> ~old(X0)) => (~quiet(X0) & curious(X0))) [input p13]
18. ~strong(mary) [input p17]
21. creative(mary) <~> ~patient(mary) [input p20]
25. quiet(mary) [input hypothesis]
38. ! [X0] : ((~quiet(X0) & curious(X0)) | (strong(X0) <=> ~old(X0))) [ennf transformation 14]
54. ! [X0] : (((~creative(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | (creative(X0) | ~brave(X0)))) [nnf transformation 7]
55. ! [X0] : (((~creative(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | creative(X0) | ~brave(X0))) [flattening 54]
56. ! [X0] : (((happy(X0) & ~old(X0)) | (kind(X0) & patient(X0))) & ((~kind(X0) | ~patient(X0)) | (~happy(X0) | old(X0)))) [nnf transformation 8]
57. ! [X0] : (((happy(X0) & ~old(X0)) | (kind(X0) & patient(X0))) & (~kind(X0) | ~patient(X0) | ~happy(X0) | old(X0))) [flattening 56]
69. ! [X0] : ((~quiet(X0) & curious(X0)) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) [nnf transformation 38]
84. (patient(mary) | ~creative(mary)) & (~patient(mary) | creative(mary)) [nnf transformation 21]
104. ~kind(X0) | ~creative(X0) [cnf transformation 55]
106. ~old(X0) | patient(X0) [cnf transformation 57]
107. ~old(X0) | kind(X0) [cnf transformation 57]
127. ~quiet(X0) | strong(X0) | old(X0) [cnf transformation 69]
137. ~strong(mary) [cnf transformation 18]
140. ~patient(mary) | creative(mary) [cnf transformation 84]
145. quiet(mary) [cnf transformation 25]
316. 37 <=> creative(mary) [avatar definition]
317. creative(mary) <- (37) [avatar component clause 316]
320. 38 <=> patient(mary) [avatar definition]
324. 37 | ~38 [avatar split clause 140,320,316]
335. strong(mary) | old(mary) [resolution 127,145]
336. old(mary) [subsumption resolution 335,137]
339. kind(mary) [resolution 336,107]
340. patient(mary) [resolution 336,106]
343. 38 [avatar split clause 340,320]
344. ~creative(mary) [resolution 339,104]
346. $false <- (37) [subsumption resolution 344,317]
347. ~37 [avatar contradiction clause 346]
348. $false [avatar sat refutation 324,343,347]
% SZS output end Proof for 7068736549373008093870028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is not brave and vice versa.
Everyone who is strong or calm is either not quiet or not calm and vice versa.
Everyone who is either strong or not strong is both generous and strong.
Everyone who is either creative or tall is humble.
Everyone who is either humble or curious is not rich or not tall.
Everyone who is old or not funny is funny or generous.
Everyone who is funny or brave is rich and vice versa.
If susan is brave then someone is rich or not kind.
Everyone who is not tall or humble is not rich or not funny and vice versa.
Everyone who is not brave or not wise is old and vice versa.
Everyone who is not humble is not quiet.
If fred is happy then someone is brave or happy and vice versa.
Everyone who is both not old and old is not calm or not curious.
If fred is both patient and not old then someone is both calm and not creative.
Everyone who is both not rich and not brave is not strong.
If someone is quiet then someone is not calm or rich.
Lucy is happy or humble.
Mary is not calm or humble.
Someone is either not calm or not tall.
Paul is both happy and not tall.
Someone is old or strong.
Someone is wise or not happy.
Someone is both strong and happy.
Fred is both quiet and not patient. | Mary is not calm. | neutral | (![X]:(~generous(X)<=>~brave(X)))&
(![X]:((strong(X)|calm(X))<=>(~quiet(X)<~>~calm(X))))&
(![X]:((strong(X)<~>~strong(X))=>(generous(X)&strong(X))))&
(![X]:((creative(X)<~>tall(X))=>humble(X)))&
(![X]:((humble(X)<~>curious(X))=>(~rich(X)|~tall(X))))&
(![X]:((old(X)|~funny(X))=>(funny(X)|generous(X))))&
(![X]:((funny(X)|brave(X))<=>rich(X)))&
((brave(susan))=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((~tall(X)|humble(X))<=>(~rich(X)|~funny(X))))&
(![X]:((~brave(X)|~wise(X))<=>old(X)))&
(![X]:(~humble(X)=>~quiet(X)))&
((happy(fred))<=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((~old(X)&old(X))=>(~calm(X)|~curious(X))))&
(((patient(fred)&~old(fred)))=>(?[X]:((calm(X)&~creative(X)))))&
(![X]:((~rich(X)&~brave(X))=>~strong(X)))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|rich(X)))))&
((happy(lucy)|humble(lucy)))&
((~calm(mary)|humble(mary)))&
(?[X]:((~calm(X)<~>~tall(X))))&
((happy(paul)&~tall(paul)))&
(?[X]:((old(X)|strong(X))))&
(?[X]:((wise(X)|~happy(X))))&
(?[X]:((strong(X)&happy(X))))&
((quiet(fred)&~patient(fred))) | ~calm(mary) | [] | null | 0 |
Everyone who is calm or creative is both not old and not curious.
If someone is old then mary is not creative or kind and vice versa.
Everyone who is not curious is not calm and vice versa.
If someone is happy or not kind then someone is not patient or not strong.
Everyone who is not funny or not old is both not quiet and generous and vice versa.
If paul is wise or not tall then john is curious or not tall and vice versa.
If alice is not brave then someone is not wise or not patient.
If paul is either not patient or not kind then susan is either old or not humble and vice versa.
Everyone who is either patient or not quiet is calm and vice versa.
Everyone who is both not humble and not wise is not calm or not rich and vice versa.
Everyone who is not brave is rich and vice versa.
If someone is not curious or not strong then someone is not creative or quiet and vice versa.
If someone is not happy or old then someone is not quiet or kind and vice versa.
If lucy is generous then someone is either not humble or funny.
Everyone who is not calm or calm is both old and funny.
If someone is not creative then paul is rich or not old.
Someone is funny or patient.
Someone is both not creative and not kind.
Paul is not wise.
Someone is both not happy and quiet.
Someone is generous or not happy.
Paul is both not calm and not humble. | Mary is not humble. | entailment | (![X]:((calm(X)|creative(X))=>(~old(X)&~curious(X))))&
((?[X]:(old(X)))<=>((~creative(mary)|kind(mary))))&
(![X]:(~curious(X)<=>~calm(X)))&
((?[X]:((happy(X)|~kind(X))))=>(?[X]:((~patient(X)|~strong(X)))))&
(![X]:((~funny(X)|~old(X))<=>(~quiet(X)&generous(X))))&
(((wise(paul)|~tall(paul)))<=>((curious(john)|~tall(john))))&
((~brave(alice))=>(?[X]:((~wise(X)|~patient(X)))))&
(((~patient(paul)<~>~kind(paul)))<=>((old(susan)<~>~humble(susan))))&
(![X]:((patient(X)<~>~quiet(X))<=>calm(X)))&
(![X]:((~humble(X)&~wise(X))<=>(~calm(X)|~rich(X))))&
(![X]:(~brave(X)<=>rich(X)))&
((?[X]:((~curious(X)|~strong(X))))<=>(?[X]:((~creative(X)|quiet(X)))))&
((?[X]:((~happy(X)|old(X))))<=>(?[X]:((~quiet(X)|kind(X)))))&
((generous(lucy))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~calm(X)|calm(X))=>(old(X)&funny(X))))&
((?[X]:(~creative(X)))=>((rich(paul)|~old(paul))))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(~wise(paul))&
(?[X]:((~happy(X)&quiet(X))))&
(?[X]:((generous(X)|~happy(X))))&
((~calm(paul)&~humble(paul))) | ~humble(mary) | [
"p0",
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6973048801028876435844474
% SZS output start Proof for 6973048801028876435844474
1. ! [X0] : ((creative(X0) | calm(X0)) => (~curious(X0) & ~old(X0))) [input p0]
3. ! [X0] : (~curious(X0) <=> ~calm(X0)) [input p2]
10. ! [X0] : ((~wise(X0) & ~humble(X0)) <=> (~rich(X0) | ~calm(X0))) [input p9]
23. humble(mary) [input hypothesis]
28. ! [X0] : ((~curious(X0) & ~old(X0)) | (~creative(X0) & ~calm(X0))) [ennf transformation 1]
41. ! [X0] : ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))) [nnf transformation 3]
53. ! [X0] : (((~wise(X0) & ~humble(X0)) | (rich(X0) & calm(X0))) & ((~rich(X0) | ~calm(X0)) | (wise(X0) | humble(X0)))) [nnf transformation 10]
54. ! [X0] : (((~wise(X0) & ~humble(X0)) | (rich(X0) & calm(X0))) & (~rich(X0) | ~calm(X0) | wise(X0) | humble(X0))) [flattening 53]
78. ~curious(X0) | ~calm(X0) [cnf transformation 28]
83. ~calm(X0) | curious(X0) [cnf transformation 41]
84. ~curious(X0) | calm(X0) [cnf transformation 41]
110. ~humble(X0) | calm(X0) [cnf transformation 54]
139. humble(mary) [cnf transformation 23]
158. ~curious(X0) [subsumption resolution 84,78]
159. ~calm(X0) [subsumption resolution 83,158]
233. ~humble(X0) [subsumption resolution 110,159]
307. $false [subsumption resolution 139,233]
% SZS output end Proof for 6973048801028876435844474
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or not creative then someone is not funny.
Everyone who is either not funny or quiet is happy.
Everyone who is not rich is not humble.
If john is either not strong or not humble then someone is either not brave or strong.
If someone is humble then someone is funny and vice versa.
If someone is not happy then someone is both not funny and not curious and vice versa.
Everyone who is old or strong is generous and vice versa.
If someone is not humble or not generous then mary is curious or not humble and vice versa.
Everyone who is either not creative or not old is either not rich or kind.
If paul is quiet or not old then susan is either not patient or kind.
Everyone who is not old or generous is either patient or old and vice versa.
If someone is brave then someone is either not funny or not rich.
If someone is not tall then mary is either not humble or not generous.
Everyone who is curious is not wise or not rich.
If someone is not humble or creative then someone is creative.
Everyone who is either not funny or generous is curious or not wise.
Someone is either not wise or not generous.
Paul is either kind or humble.
Mary is both brave and generous.
Someone is not patient or not wise.
Lucy is both not curious and humble.
John is not rich or not funny.
Someone is either not happy or not strong.
Someone is brave or old. | Mary is not happy. | neutral | ((?[X]:((~generous(X)<~>~creative(X))))=>(?[X]:(~funny(X))))&
(![X]:((~funny(X)<~>quiet(X))=>happy(X)))&
(![X]:(~rich(X)=>~humble(X)))&
(((~strong(john)<~>~humble(john)))=>(?[X]:((~brave(X)<~>strong(X)))))&
((?[X]:(humble(X)))<=>(?[X]:(funny(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~funny(X)&~curious(X)))))&
(![X]:((old(X)|strong(X))<=>generous(X)))&
((?[X]:((~humble(X)|~generous(X))))<=>((curious(mary)|~humble(mary))))&
(![X]:((~creative(X)<~>~old(X))=>(~rich(X)<~>kind(X))))&
(((quiet(paul)|~old(paul)))=>((~patient(susan)<~>kind(susan))))&
(![X]:((~old(X)|generous(X))<=>(patient(X)<~>old(X))))&
((?[X]:(brave(X)))=>(?[X]:((~funny(X)<~>~rich(X)))))&
((?[X]:(~tall(X)))=>((~humble(mary)<~>~generous(mary))))&
(![X]:(curious(X)=>(~wise(X)|~rich(X))))&
((?[X]:((~humble(X)|creative(X))))=>(?[X]:(creative(X))))&
(![X]:((~funny(X)<~>generous(X))=>(curious(X)|~wise(X))))&
(?[X]:((~wise(X)<~>~generous(X))))&
((kind(paul)<~>humble(paul)))&
((brave(mary)&generous(mary)))&
(?[X]:((~patient(X)|~wise(X))))&
((~curious(lucy)&humble(lucy)))&
((~rich(john)|~funny(john)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((brave(X)|old(X)))) | ~happy(mary) | [] | null | 0 |
Everyone who is creative is not tall and vice versa.
Everyone who is either curious or creative is funny.
Everyone who is creative or tall is both not kind and quiet and vice versa.
Everyone who is not humble or not creative is either not creative or funny and vice versa.
Everyone who is not happy is patient or not creative and vice versa.
Everyone who is not humble is tall or happy.
Everyone who is not humble is both not rich and patient and vice versa.
If someone is both patient and not tall then john is both not quiet and not curious.
Everyone who is both kind and not old is either not generous or not creative.
Everyone who is both not tall and not strong is both generous and brave and vice versa.
If lucy is both not humble and not calm then someone is either curious or humble and vice versa.
Everyone who is both tall and not old is both not tall and not generous.
If paul is either patient or not kind then someone is rich and vice versa.
Everyone who is both not rich and strong is either not calm or not curious and vice versa.
If someone is either not old or not humble then fred is both wise and funny.
Someone is happy or not rich.
Alice is either not curious or curious.
Alice is not patient or not wise.
Susan is either not old or old.
Someone is brave. | Fred is humble. | entailment | (![X]:(creative(X)<=>~tall(X)))&
(![X]:((curious(X)<~>creative(X))=>funny(X)))&
(![X]:((creative(X)|tall(X))<=>(~kind(X)&quiet(X))))&
(![X]:((~humble(X)|~creative(X))<=>(~creative(X)<~>funny(X))))&
(![X]:(~happy(X)<=>(patient(X)|~creative(X))))&
(![X]:(~humble(X)=>(tall(X)|happy(X))))&
(![X]:(~humble(X)<=>(~rich(X)&patient(X))))&
((?[X]:((patient(X)&~tall(X))))=>((~quiet(john)&~curious(john))))&
(![X]:((kind(X)&~old(X))=>(~generous(X)<~>~creative(X))))&
(![X]:((~tall(X)&~strong(X))<=>(generous(X)&brave(X))))&
(((~humble(lucy)&~calm(lucy)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((tall(X)&~old(X))=>(~tall(X)&~generous(X))))&
(((patient(paul)<~>~kind(paul)))<=>(?[X]:(rich(X))))&
(![X]:((~rich(X)&strong(X))<=>(~calm(X)<~>~curious(X))))&
((?[X]:((~old(X)<~>~humble(X))))=>((wise(fred)&funny(fred))))&
(?[X]:((happy(X)|~rich(X))))&
((~curious(alice)<~>curious(alice)))&
((~patient(alice)|~wise(alice)))&
((~old(susan)<~>old(susan)))&
(?[X]:(brave(X))) | humble(fred) | [
"p0",
"p2",
"p3",
"p6",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7302191820725478259530108
% SZS output start Proof for 7302191820725478259530108
1. ! [X0] : (creative(X0) <=> ~tall(X0)) [input p0]
3. ! [X0] : ((tall(X0) | creative(X0)) <=> (quiet(X0) & ~kind(X0))) [input p2]
4. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (~creative(X0) <~> funny(X0))) [input p3]
7. ! [X0] : (~humble(X0) <=> (patient(X0) & ~rich(X0))) [input p6]
8. ? [X0] : (~tall(X0) & patient(X0)) => (~curious(john) & ~quiet(john)) [input p7]
12. ! [X0] : ((~old(X0) & tall(X0)) => (~generous(X0) & ~tall(X0))) [input p11]
15. ? [X0] : (~old(X0) <~> ~humble(X0)) => (funny(fred) & wise(fred)) [input p14]
21. ~humble(fred) [input hypothesis]
27. (~curious(john) & ~quiet(john)) | ! [X0] : (tall(X0) | ~patient(X0)) [ennf transformation 8]
30. ! [X0] : ((~generous(X0) & ~tall(X0)) | (old(X0) | ~tall(X0))) [ennf transformation 12]
31. ! [X0] : ((~generous(X0) & ~tall(X0)) | old(X0) | ~tall(X0)) [flattening 30]
32. (funny(fred) & wise(fred)) | ! [X0] : (~old(X0) <=> ~humble(X0)) [ennf transformation 15]
33. ! [X0] : ((creative(X0) | tall(X0)) & (~tall(X0) | ~creative(X0))) [nnf transformation 1]
35. ! [X0] : (((tall(X0) | creative(X0)) | (~quiet(X0) | kind(X0))) & ((quiet(X0) & ~kind(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 3]
36. ! [X0] : ((tall(X0) | creative(X0) | ~quiet(X0) | kind(X0)) & ((quiet(X0) & ~kind(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 35]
37. ! [X0] : (((~creative(X0) | ~humble(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (creative(X0) & humble(X0)))) [nnf transformation 4]
38. ! [X0] : ((~creative(X0) | ~humble(X0) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (creative(X0) & humble(X0)))) [flattening 37]
39. ! [X0] : ((~humble(X0) | (~patient(X0) | rich(X0))) & ((patient(X0) & ~rich(X0)) | humble(X0))) [nnf transformation 7]
40. ! [X0] : ((~humble(X0) | ~patient(X0) | rich(X0)) & ((patient(X0) & ~rich(X0)) | humble(X0))) [flattening 39]
55. (funny(fred) & wise(fred)) | ! [X0] : ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))) [nnf transformation 32]
62. ~tall(X0) | ~creative(X0) [cnf transformation 33]
63. tall(X0) | creative(X0) [cnf transformation 33]
68. ~creative(X0) | quiet(X0) [cnf transformation 36]
69. ~tall(X0) | quiet(X0) [cnf transformation 36]
74. ~funny(X0) | creative(X0) | creative(X0) [cnf transformation 38]
81. patient(X0) | humble(X0) [cnf transformation 40]
83. ~quiet(john) | tall(X0) | ~patient(X0) [cnf transformation 27]
97. ~tall(X0) | old(X0) | ~tall(X0) [cnf transformation 31]
112. funny(fred) | ~old(X0) | humble(X0) [cnf transformation 55]
120. ~humble(fred) [cnf transformation 21]
121. ~tall(X0) | old(X0) [duplicate literal removal 97]
122. ~funny(X0) | creative(X0) [duplicate literal removal 74]
125. 1 <=> ! [X0] : (tall(X0) | ~patient(X0)) [avatar definition]
126. ~patient(X0) | tall(X0) <- (1) [avatar component clause 125]
133. 3 <=> quiet(john) [avatar definition]
135. ~quiet(john) <- (~3) [avatar component clause 133]
136. 1 | ~3 [avatar split clause 83,133,125]
186. 14 <=> ! [X0] : (~old(X0) | humble(X0)) [avatar definition]
187. ~old(X0) | humble(X0) <- (14) [avatar component clause 186]
189. 15 <=> funny(fred) [avatar definition]
191. funny(fred) <- (15) [avatar component clause 189]
192. 14 | 15 [avatar split clause 112,189,186]
222. quiet(X0) | creative(X0) [resolution 69,63]
223. quiet(X0) [subsumption resolution 222,68]
224. $false <- (~3) [resolution 223,135]
225. 3 [avatar contradiction clause 224]
229. old(X0) | creative(X0) [resolution 121,63]
231. humble(X0) | tall(X0) <- (1) [resolution 126,81]
324. humble(X0) | creative(X0) <- (14) [resolution 229,187]
328. tall(fred) <- (1) [resolution 231,120]
343. ~creative(fred) <- (1) [resolution 328,62]
348. creative(fred) <- (14) [resolution 324,120]
351. $false <- (1, 14) [subsumption resolution 348,343]
352. ~1 | ~14 [avatar contradiction clause 351]
353. creative(fred) <- (15) [resolution 191,122]
354. $false <- (1, 15) [subsumption resolution 353,343]
355. ~1 | ~15 [avatar contradiction clause 354]
356. $false [avatar sat refutation 136,192,225,352,355]
% SZS output end Proof for 7302191820725478259530108
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not old is not brave or not humble.
Everyone who is kind is both kind and not patient.
If someone is both humble and not rich then fred is not calm.
Everyone who is both not kind and happy is both not old and not humble.
If alice is not old then someone is humble.
Everyone who is either funny or generous is quiet.
Everyone who is not creative is either not tall or not old.
If alice is brave then someone is not rich or not quiet.
If paul is old then fred is either not curious or not calm.
If susan is not kind or not strong then fred is happy or brave and vice versa.
Everyone who is either generous or old is not creative or old.
If someone is both not old and wise then alice is not wise.
If alice is both not tall and calm then someone is both creative and old.
Everyone who is either brave or not funny is calm or not calm and vice versa.
Everyone who is both quiet and not calm is both not old and not curious and vice versa.
If paul is either generous or tall then someone is wise.
Paul is generous or funny.
Someone is calm.
Lucy is either not brave or rich.
Someone is not calm.
Someone is both not calm and quiet.
Lucy is both not creative and curious.
Someone is patient.
Someone is either not kind or quiet. | Fred is brave. | neutral | (![X]:((funny(X)|~old(X))=>(~brave(X)|~humble(X))))&
(![X]:(kind(X)=>(kind(X)&~patient(X))))&
((?[X]:((humble(X)&~rich(X))))=>(~calm(fred)))&
(![X]:((~kind(X)&happy(X))=>(~old(X)&~humble(X))))&
((~old(alice))=>(?[X]:(humble(X))))&
(![X]:((funny(X)<~>generous(X))=>quiet(X)))&
(![X]:(~creative(X)=>(~tall(X)<~>~old(X))))&
((brave(alice))=>(?[X]:((~rich(X)|~quiet(X)))))&
((old(paul))=>((~curious(fred)<~>~calm(fred))))&
(((~kind(susan)|~strong(susan)))<=>((happy(fred)|brave(fred))))&
(![X]:((generous(X)<~>old(X))=>(~creative(X)|old(X))))&
((?[X]:((~old(X)&wise(X))))=>(~wise(alice)))&
(((~tall(alice)&calm(alice)))=>(?[X]:((creative(X)&old(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(calm(X)|~calm(X))))&
(![X]:((quiet(X)&~calm(X))<=>(~old(X)&~curious(X))))&
(((generous(paul)<~>tall(paul)))=>(?[X]:(wise(X))))&
((generous(paul)|funny(paul)))&
(?[X]:(calm(X)))&
((~brave(lucy)<~>rich(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((~calm(X)&quiet(X))))&
((~creative(lucy)&curious(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((~kind(X)<~>quiet(X)))) | brave(fred) | [] | null | 0 |
If paul is quiet then mary is either not happy or wise and vice versa.
Everyone who is tall or humble is not tall.
Everyone who is both not strong and not humble is old or rich and vice versa.
Everyone who is not wise is strong and vice versa.
Everyone who is old or calm is not brave and vice versa.
If someone is both rich and kind then someone is both tall and not happy.
Everyone who is not tall is both not strong and not tall and vice versa.
Everyone who is either creative or strong is either happy or not creative and vice versa.
If alice is strong then lucy is quiet or not kind and vice versa.
Everyone who is not patient is either creative or not generous and vice versa.
Everyone who is either not rich or calm is either not brave or wise and vice versa.
Everyone who is creative is rich.
Everyone who is calm is rich and vice versa.
If fred is quiet then alice is brave or old.
Everyone who is both generous and happy is either brave or tall and vice versa.
Someone is both not funny and curious.
Paul is both not kind and not curious.
Someone is not humble or not curious.
Someone is quiet.
Someone is generous or not happy.
Paul is not curious. | Paul is quiet. | entailment | ((quiet(paul))<=>((~happy(mary)<~>wise(mary))))&
(![X]:((tall(X)|humble(X))=>~tall(X)))&
(![X]:((~strong(X)&~humble(X))<=>(old(X)|rich(X))))&
(![X]:(~wise(X)<=>strong(X)))&
(![X]:((old(X)|calm(X))<=>~brave(X)))&
((?[X]:((rich(X)&kind(X))))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:(~tall(X)<=>(~strong(X)&~tall(X))))&
(![X]:((creative(X)<~>strong(X))<=>(happy(X)<~>~creative(X))))&
((strong(alice))<=>((quiet(lucy)|~kind(lucy))))&
(![X]:(~patient(X)<=>(creative(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>calm(X))<=>(~brave(X)<~>wise(X))))&
(![X]:(creative(X)=>rich(X)))&
(![X]:(calm(X)<=>rich(X)))&
((quiet(fred))=>((brave(alice)|old(alice))))&
(![X]:((generous(X)&happy(X))<=>(brave(X)<~>tall(X))))&
(?[X]:((~funny(X)&curious(X))))&
((~kind(paul)&~curious(paul)))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)|~happy(X))))&
(~curious(paul)) | quiet(paul) | [
"p0",
"p1",
"p3",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5715487497906442391998590
% SZS output start Proof for 5715487497906442391998590
1. quiet(paul) <=> (~happy(mary) <~> wise(mary)) [input p0]
2. ! [X0] : ((humble(X0) | tall(X0)) => ~tall(X0)) [input p1]
4. ! [X0] : (~wise(X0) <=> strong(X0)) [input p3]
7. ! [X0] : (~tall(X0) <=> (~tall(X0) & ~strong(X0))) [input p6]
8. ! [X0] : ((creative(X0) <~> strong(X0)) <=> (happy(X0) <~> ~creative(X0))) [input p7]
22. ~quiet(paul) [input hypothesis]
25. ! [X0] : (~tall(X0) | (~humble(X0) & ~tall(X0))) [ennf transformation 2]
30. (quiet(paul) | ((~happy(mary) | ~wise(mary)) & (wise(mary) | happy(mary)))) & (((~wise(mary) | happy(mary)) & (wise(mary) | ~happy(mary))) | ~quiet(paul)) [nnf transformation 1]
33. ! [X0] : ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0))) [nnf transformation 4]
39. ! [X0] : ((~tall(X0) | (tall(X0) | strong(X0))) & ((~tall(X0) & ~strong(X0)) | tall(X0))) [nnf transformation 7]
40. ! [X0] : ((~tall(X0) | tall(X0) | strong(X0)) & ((~tall(X0) & ~strong(X0)) | tall(X0))) [flattening 39]
41. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) & (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [nnf transformation 8]
59. quiet(paul) | ~happy(mary) | ~wise(mary) [cnf transformation 30]
60. ~tall(X0) | ~tall(X0) [cnf transformation 25]
67. strong(X0) | wise(X0) [cnf transformation 33]
74. ~strong(X0) | tall(X0) [cnf transformation 40]
77. ~creative(X0) | happy(X0) | strong(X0) | ~creative(X0) [cnf transformation 41]
82. strong(X0) | creative(X0) | happy(X0) | creative(X0) [cnf transformation 41]
113. ~quiet(paul) [cnf transformation 22]
114. ~creative(X0) | happy(X0) | strong(X0) [duplicate literal removal 77]
116. strong(X0) | creative(X0) | happy(X0) [duplicate literal removal 82]
118. ~tall(X0) [duplicate literal removal 60]
120. 1 <=> wise(mary) [avatar definition]
122. ~wise(mary) <- (~1) [avatar component clause 120]
124. 2 <=> happy(mary) [avatar definition]
126. ~happy(mary) <- (~2) [avatar component clause 124]
128. 3 <=> quiet(paul) [avatar definition]
131. ~1 | ~2 | 3 [avatar split clause 59,128,124,120]
145. ~strong(X0) [subsumption resolution 74,118]
146. creative(X0) | happy(X0) [subsumption resolution 116,145]
147. ~creative(X0) | happy(X0) [subsumption resolution 114,145]
148. happy(X0) [subsumption resolution 147,146]
181. ~3 [avatar split clause 113,128]
182. wise(X0) [resolution 67,145]
183. $false <- (~1) [resolution 182,122]
184. 1 [avatar contradiction clause 183]
185. $false <- (~2) [subsumption resolution 126,148]
186. 2 [avatar contradiction clause 185]
187. $false [avatar sat refutation 131,181,184,186]
% SZS output end Proof for 5715487497906442391998590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not wise is happy and vice versa. If fred is funny then fred is both rich and not brave. Everyone who is curious is both not funny and not generous and vice versa. If mary is both brave and humble then john is either not generous or humble and vice versa. Everyone who is either not humble or old is both funny and not tall and vice versa. Everyone who is not funny or not calm is both wise and humble and vice versa. Everyone who is funny is either not calm or not kind. Everyone who is creative or patient is either not wise or happy and vice versa. If paul is either tall or not patient then someone is either patient or brave. If susan is either old or happy then mary is both not tall and not humble. Everyone who is both funny and not humble is both patient and not generous. If john is curious or not curious then susan is both humble and strong and vice versa. Everyone who is either strong or curious is funny or not generous and vice versa. If paul is rich or generous then john is strong or patient. If paul is both curious and not wise then fred is either patient or not curious and vice versa. If mary is either not generous or humble then someone is calm or happy. Alice is both humble and strong. Fred is kind. Fred is brave or not humble. Someone is both not happy and not curious. Someone is calm. Alice is either not patient or calm. Someone is both not generous and not happy. | Alice is not kind. | contradiction | (![X]:((~calm(X)<~>~wise(X))<=>happy(X)))&
((funny(fred))=>((rich(fred)&~brave(fred))))&
(![X]:(curious(X)<=>(~funny(X)&~generous(X))))&
(((brave(mary)&humble(mary)))<=>((~generous(john)<~>humble(john))))&
(![X]:((~humble(X)<~>old(X))<=>(funny(X)&~tall(X))))&
(![X]:((~funny(X)|~calm(X))<=>(wise(X)&humble(X))))&
(![X]:(funny(X)=>(~calm(X)<~>~kind(X))))&
(![X]:((creative(X)|patient(X))<=>(~wise(X)<~>happy(X))))&
(((tall(paul)<~>~patient(paul)))=>(?[X]:((patient(X)<~>brave(X)))))&
(((old(susan)<~>happy(susan)))=>((~tall(mary)&~humble(mary))))&
(![X]:((funny(X)&~humble(X))=>(patient(X)&~generous(X))))&
(((curious(john)|~curious(john)))<=>((humble(susan)&strong(susan))))&
(![X]:((strong(X)<~>curious(X))<=>(funny(X)|~generous(X))))&
(((rich(paul)|generous(paul)))=>((strong(john)|patient(john))))&
(((curious(paul)&~wise(paul)))<=>((patient(fred)<~>~curious(fred))))&
(((~generous(mary)<~>humble(mary)))=>(?[X]:((calm(X)|happy(X)))))&
((humble(alice)&strong(alice)))&
(kind(fred))&
((brave(fred)|~humble(fred)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:(calm(X)))&
((~patient(alice)<~>calm(alice)))&
(?[X]:((~generous(X)&~happy(X)))) | ~kind(alice) | [
"p0",
"p2",
"p5",
"p6",
"p7",
"p12",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4099901401090147630513266
% SZS output start Proof for 4099901401090147630513266
1. ! [X0] : ((~calm(X0) <~> ~wise(X0)) <=> happy(X0)) [input p0]
3. ! [X0] : (curious(X0) <=> (~generous(X0) & ~funny(X0))) [input p2]
6. ! [X0] : ((~calm(X0) | ~funny(X0)) <=> (humble(X0) & wise(X0))) [input p5]
7. ! [X0] : (funny(X0) => (~calm(X0) <~> ~kind(X0))) [input p6]
8. ! [X0] : ((patient(X0) | creative(X0)) <=> (~wise(X0) <~> happy(X0))) [input p7]
13. ! [X0] : ((strong(X0) <~> curious(X0)) <=> (~generous(X0) | funny(X0))) [input p12]
17. strong(alice) & humble(alice) [input p16]
22. ~patient(alice) <~> calm(alice) [input p21]
24. ~kind(alice) [input hypothesis]
26. ! [X0] : ((~calm(X0) <~> ~kind(X0)) | ~funny(X0)) [ennf transformation 7]
34. ! [X0] : ((((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | ~happy(X0)) & (happy(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))))) [nnf transformation 1]
35. ! [X0] : ((curious(X0) | (generous(X0) | funny(X0))) & ((~generous(X0) & ~funny(X0)) | ~curious(X0))) [nnf transformation 3]
36. ! [X0] : ((curious(X0) | generous(X0) | funny(X0)) & ((~generous(X0) & ~funny(X0)) | ~curious(X0))) [flattening 35]
41. ! [X0] : (((~calm(X0) | ~funny(X0)) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | (calm(X0) & funny(X0)))) [nnf transformation 6]
42. ! [X0] : ((~calm(X0) | ~funny(X0) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | (calm(X0) & funny(X0)))) [flattening 41]
43. ! [X0] : (((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | ~funny(X0)) [nnf transformation 26]
44. ! [X0] : (((patient(X0) | creative(X0)) | ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0)))) & (((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | (~patient(X0) & ~creative(X0)))) [nnf transformation 8]
45. ! [X0] : ((patient(X0) | creative(X0) | ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0)))) & (((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | (~patient(X0) & ~creative(X0)))) [flattening 44]
52. ! [X0] : ((((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (generous(X0) & ~funny(X0))) & ((~generous(X0) | funny(X0)) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0))))) [nnf transformation 13]
53. ! [X0] : ((((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (generous(X0) & ~funny(X0))) & (~generous(X0) | funny(X0) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0))))) [flattening 52]
63. (~calm(alice) | patient(alice)) & (calm(alice) | ~patient(alice)) [nnf transformation 22]
67. ~calm(X0) | happy(X0) | wise(X0) [cnf transformation 34]
73. ~generous(X0) | ~curious(X0) [cnf transformation 36]
74. generous(X0) | curious(X0) | funny(X0) [cnf transformation 36]
91. ~humble(X0) | ~funny(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 42]
93. ~funny(X0) | calm(X0) | kind(X0) [cnf transformation 43]
97. ~patient(X0) | wise(X0) | ~happy(X0) [cnf transformation 45]
115. ~generous(X0) | funny(X0) | curious(X0) | ~strong(X0) [cnf transformation 53]
120. ~curious(X0) | ~strong(X0) | generous(X0) [cnf transformation 53]
131. humble(alice) [cnf transformation 17]
132. strong(alice) [cnf transformation 17]
139. ~calm(alice) | patient(alice) [cnf transformation 63]
142. ~kind(alice) [cnf transformation 24]
233. ~strong(X0) | ~curious(X0) [subsumption resolution 120,73]
235. ~strong(X0) | funny(X0) | ~generous(X0) [subsumption resolution 115,233]
298. 30 <=> patient(alice) [avatar definition]
300. patient(alice) <- (30) [avatar component clause 298]
302. 31 <=> calm(alice) [avatar definition]
303. calm(alice) <- (31) [avatar component clause 302]
305. 30 | ~31 [avatar split clause 139,302,298]
319. ~curious(alice) [resolution 233,132]
434. funny(alice) | ~generous(alice) [resolution 235,132]
445. 47 <=> generous(alice) [avatar definition]
447. ~generous(alice) <- (~47) [avatar component clause 445]
449. 48 <=> funny(alice) [avatar definition]
451. funny(alice) <- (48) [avatar component clause 449]
452. ~47 | 48 [avatar split clause 434,449,445]
505. ~funny(alice) | ~calm(alice) | ~wise(alice) [resolution 91,131]
540. 58 <=> wise(alice) [avatar definition]
541. ~wise(alice) <- (~58) [avatar component clause 540]
544. 59 <=> happy(alice) [avatar definition]
545. ~happy(alice) <- (~59) [avatar component clause 544]
552. wise(alice) | ~happy(alice) <- (30) [resolution 300,97]
554. ~59 | 58 | ~30 [avatar split clause 552,298,540,544]
556. happy(alice) | wise(alice) <- (31) [resolution 303,67]
557. wise(alice) <- (31, ~59) [subsumption resolution 556,545]
558. $false <- (31, ~58, ~59) [subsumption resolution 557,541]
559. ~31 | 58 | 59 [avatar contradiction clause 558]
562. curious(alice) | funny(alice) <- (~47) [resolution 447,74]
563. funny(alice) <- (~47) [subsumption resolution 562,319]
566. 48 | 47 [avatar split clause 563,445,449]
567. calm(alice) | kind(alice) <- (48) [resolution 451,93]
572. calm(alice) <- (48) [subsumption resolution 567,142]
573. 31 | ~48 [avatar split clause 572,449,302]
574. ~calm(alice) | ~wise(alice) <- (48) [subsumption resolution 505,451]
575. ~58 | ~31 | ~48 [avatar split clause 574,449,302,540]
576. $false [avatar sat refutation 305,452,554,559,566,573,575]
% SZS output end Proof for 4099901401090147630513266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then someone is either not funny or not quiet and vice versa.
Everyone who is not quiet or not rich is either wise or not happy.
If paul is both tall and not old then someone is brave or creative.
Everyone who is both not strong and not creative is not strong or not tall and vice versa.
Everyone who is calm is not creative or old.
If someone is either not quiet or calm then fred is old or not brave.
Everyone who is either not tall or humble is either not funny or kind.
Everyone who is either not brave or not generous is either quiet or not funny.
If mary is either not kind or tall then john is both not generous and not brave and vice versa.
If paul is not strong or not brave then someone is not calm.
If mary is both funny and patient then someone is either not happy or wise.
Everyone who is either old or rich is either not brave or rich and vice versa.
If someone is either tall or not curious then someone is strong and vice versa.
If mary is not funny then someone is not quiet or creative and vice versa.
If lucy is either not kind or not strong then alice is not creative or rich.
Everyone who is brave is either patient or not generous.
Susan is not strong or humble.
Fred is not creative or brave.
John is creative.
Someone is either creative or not quiet.
Susan is tall.
Someone is either kind or not quiet.
Someone is not brave or not curious. | Mary is not rich. | neutral | ((?[X]:(curious(X)))<=>(?[X]:((~funny(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)|~rich(X))=>(wise(X)<~>~happy(X))))&
(((tall(paul)&~old(paul)))=>(?[X]:((brave(X)|creative(X)))))&
(![X]:((~strong(X)&~creative(X))<=>(~strong(X)|~tall(X))))&
(![X]:(calm(X)=>(~creative(X)|old(X))))&
((?[X]:((~quiet(X)<~>calm(X))))=>((old(fred)|~brave(fred))))&
(![X]:((~tall(X)<~>humble(X))=>(~funny(X)<~>kind(X))))&
(![X]:((~brave(X)<~>~generous(X))=>(quiet(X)<~>~funny(X))))&
(((~kind(mary)<~>tall(mary)))<=>((~generous(john)&~brave(john))))&
(((~strong(paul)|~brave(paul)))=>(?[X]:(~calm(X))))&
(((funny(mary)&patient(mary)))=>(?[X]:((~happy(X)<~>wise(X)))))&
(![X]:((old(X)<~>rich(X))<=>(~brave(X)<~>rich(X))))&
((?[X]:((tall(X)<~>~curious(X))))<=>(?[X]:(strong(X))))&
((~funny(mary))<=>(?[X]:((~quiet(X)|creative(X)))))&
(((~kind(lucy)<~>~strong(lucy)))=>((~creative(alice)|rich(alice))))&
(![X]:(brave(X)=>(patient(X)<~>~generous(X))))&
((~strong(susan)|humble(susan)))&
((~creative(fred)|brave(fred)))&
(creative(john))&
(?[X]:((creative(X)<~>~quiet(X))))&
(tall(susan))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:((~brave(X)|~curious(X)))) | ~rich(mary) | [] | null | 0 |
Everyone who is both humble and not calm is calm and vice versa.
Everyone who is either wise or patient is not creative or calm and vice versa.
Everyone who is kind or brave is either not calm or curious.
Everyone who is either not happy or curious is not brave and vice versa.
Everyone who is calm or humble is both not old and not generous and vice versa.
Everyone who is either creative or tall is not wise or patient.
Everyone who is either not happy or wise is either not rich or not old and vice versa.
Everyone who is tall or not curious is either happy or not tall and vice versa.
Everyone who is either not brave or rich is both not quiet and humble and vice versa.
If someone is rich then someone is not kind or not creative and vice versa.
If paul is both not curious and not rich then susan is not curious or not happy and vice versa.
Everyone who is not creative is either brave or not rich and vice versa.
If fred is not strong or calm then someone is either not tall or humble.
If alice is either rich or funny then lucy is both humble and not kind.
If fred is both not generous and not creative then john is not curious or brave.
Fred is brave.
Mary is not tall or curious.
Someone is both creative and funny.
Someone is not brave or kind.
Someone is not calm or not tall.
Mary is either not creative or tall.
Alice is not calm.
Someone is either generous or not old. | Alice is creative. | entailment | (![X]:((humble(X)&~calm(X))<=>calm(X)))&
(![X]:((wise(X)<~>patient(X))<=>(~creative(X)|calm(X))))&
(![X]:((kind(X)|brave(X))=>(~calm(X)<~>curious(X))))&
(![X]:((~happy(X)<~>curious(X))<=>~brave(X)))&
(![X]:((calm(X)|humble(X))<=>(~old(X)&~generous(X))))&
(![X]:((creative(X)<~>tall(X))=>(~wise(X)|patient(X))))&
(![X]:((~happy(X)<~>wise(X))<=>(~rich(X)<~>~old(X))))&
(![X]:((tall(X)|~curious(X))<=>(happy(X)<~>~tall(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~quiet(X)&humble(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~kind(X)|~creative(X)))))&
(((~curious(paul)&~rich(paul)))<=>((~curious(susan)|~happy(susan))))&
(![X]:(~creative(X)<=>(brave(X)<~>~rich(X))))&
(((~strong(fred)|calm(fred)))=>(?[X]:((~tall(X)<~>humble(X)))))&
(((rich(alice)<~>funny(alice)))=>((humble(lucy)&~kind(lucy))))&
(((~generous(fred)&~creative(fred)))=>((~curious(john)|brave(john))))&
(brave(fred))&
((~tall(mary)|curious(mary)))&
(?[X]:((creative(X)&funny(X))))&
(?[X]:((~brave(X)|kind(X))))&
(?[X]:((~calm(X)|~tall(X))))&
((~creative(mary)<~>tall(mary)))&
(~calm(alice))&
(?[X]:((generous(X)<~>~old(X)))) | creative(alice) | [
"p0",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6470201879868059011373292
% SZS output start Proof for 6470201879868059011373292
1. ! [X0] : ((~calm(X0) & humble(X0)) <=> calm(X0)) [input p0]
9. ! [X0] : ((~brave(X0) <~> rich(X0)) <=> (humble(X0) & ~quiet(X0))) [input p8]
12. ! [X0] : (~creative(X0) <=> (brave(X0) <~> ~rich(X0))) [input p11]
24. ~creative(alice) [input hypothesis]
34. ! [X0] : (((~calm(X0) & humble(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) | ~humble(X0)))) [nnf transformation 1]
35. ! [X0] : (((~calm(X0) & humble(X0)) | ~calm(X0)) & (calm(X0) | calm(X0) | ~humble(X0))) [flattening 34]
46. ! [X0] : ((((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | (~humble(X0) | quiet(X0))) & ((humble(X0) & ~quiet(X0)) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | ~humble(X0) | quiet(X0)) & ((humble(X0) & ~quiet(X0)) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0))))) [flattening 46]
55. ! [X0] : ((~creative(X0) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | creative(X0))) [nnf transformation 12]
70. calm(X0) | calm(X0) | ~humble(X0) [cnf transformation 35]
72. ~calm(X0) | ~calm(X0) [cnf transformation 35]
110. humble(X0) | rich(X0) | brave(X0) [cnf transformation 47]
111. humble(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 47]
122. ~rich(X0) | brave(X0) | creative(X0) [cnf transformation 55]
123. rich(X0) | ~brave(X0) | creative(X0) [cnf transformation 55]
144. ~creative(alice) [cnf transformation 24]
147. calm(X0) | ~humble(X0) [duplicate literal removal 70]
148. ~calm(X0) [duplicate literal removal 72]
149. ~humble(X0) [subsumption resolution 147,148]
160. ~brave(X0) | ~rich(X0) [subsumption resolution 111,149]
161. rich(X0) | brave(X0) [subsumption resolution 110,149]
163. 1 <=> ! [X1] : creative(X1) [avatar definition]
164. creative(X1) <- (1) [avatar component clause 163]
208. rich(X0) | creative(X0) [subsumption resolution 123,161]
209. ~rich(X0) | creative(X0) [subsumption resolution 122,160]
210. creative(X0) [subsumption resolution 209,208]
211. 1 [avatar split clause 210,163]
270. $false <- (1) [resolution 164,144]
271. ~1 [avatar contradiction clause 270]
272. $false [avatar sat refutation 211,271]
% SZS output end Proof for 6470201879868059011373292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or quiet is patient or humble. Everyone who is either not tall or not old is either not patient or not generous and vice versa. If mary is either not tall or not funny then someone is wise and vice versa. Everyone who is not rich is generous or not kind and vice versa. If john is not rich then alice is humble. Everyone who is not patient or quiet is both happy and rich and vice versa. Everyone who is both brave and kind is either not brave or not wise. Everyone who is calm or generous is either funny or not funny. Everyone who is either not strong or patient is not quiet. Everyone who is either not generous or not kind is wise. Everyone who is either brave or old is quiet or not old and vice versa. Everyone who is quiet is not kind or not curious. If mary is not creative or not calm then someone is both not happy and happy and vice versa. Everyone who is calm or curious is either calm or not happy. Everyone who is either humble or generous is kind and vice versa. If someone is not happy then mary is not wise or not curious and vice versa. Mary is not generous. Someone is not patient. Someone is either generous or not curious. Mary is either not happy or creative. Someone is either rich or not quiet. Someone is not tall. Fred is either not calm or not curious. Lucy is not calm. | Mary is not happy. | contradiction | (![X]:((tall(X)<~>quiet(X))=>(patient(X)|humble(X))))&
(![X]:((~tall(X)<~>~old(X))<=>(~patient(X)<~>~generous(X))))&
(((~tall(mary)<~>~funny(mary)))<=>(?[X]:(wise(X))))&
(![X]:(~rich(X)<=>(generous(X)|~kind(X))))&
((~rich(john))=>(humble(alice)))&
(![X]:((~patient(X)|quiet(X))<=>(happy(X)&rich(X))))&
(![X]:((brave(X)&kind(X))=>(~brave(X)<~>~wise(X))))&
(![X]:((calm(X)|generous(X))=>(funny(X)<~>~funny(X))))&
(![X]:((~strong(X)<~>patient(X))=>~quiet(X)))&
(![X]:((~generous(X)<~>~kind(X))=>wise(X)))&
(![X]:((brave(X)<~>old(X))<=>(quiet(X)|~old(X))))&
(![X]:(quiet(X)=>(~kind(X)|~curious(X))))&
(((~creative(mary)|~calm(mary)))<=>(?[X]:((~happy(X)&happy(X)))))&
(![X]:((calm(X)|curious(X))=>(calm(X)<~>~happy(X))))&
(![X]:((humble(X)<~>generous(X))<=>kind(X)))&
((?[X]:(~happy(X)))<=>((~wise(mary)|~curious(mary))))&
(~generous(mary))&
(?[X]:(~patient(X)))&
(?[X]:((generous(X)<~>~curious(X))))&
((~happy(mary)<~>creative(mary)))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:(~tall(X)))&
((~calm(fred)<~>~curious(fred)))&
(~calm(lucy)) | ~happy(mary) | [
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1732461162527947097257793
% SZS output start Proof for 1732461162527947097257793
13. (~calm(mary) | ~creative(mary)) <=> ? [X0] : (happy(X0) & ~happy(X0)) [input p12]
20. ~happy(mary) <~> creative(mary) [input p19]
25. ~happy(mary) [input hypothesis]
53. ((~calm(mary) | ~creative(mary)) | ! [X0] : (~happy(X0) | happy(X0))) & (? [X0] : (happy(X0) & ~happy(X0)) | (calm(mary) & creative(mary))) [nnf transformation 13]
54. (~calm(mary) | ~creative(mary) | ! [X0] : (~happy(X0) | happy(X0))) & (? [X0] : (happy(X0) & ~happy(X0)) | (calm(mary) & creative(mary))) [flattening 53]
55. (~calm(mary) | ~creative(mary) | ! [X0] : (~happy(X0) | happy(X0))) & (? [X1] : (happy(X1) & ~happy(X1)) | (calm(mary) & creative(mary))) [rectify 54]
56. ? [X1] : (happy(X1) & ~happy(X1)) => (happy(sK1) & ~happy(sK1)) [choice axiom]
57. (~calm(mary) | ~creative(mary) | ! [X0] : (~happy(X0) | happy(X0))) & ((happy(sK1) & ~happy(sK1)) | (calm(mary) & creative(mary))) [skolemisation 55,56]
70. (~creative(mary) | happy(mary)) & (creative(mary) | ~happy(mary)) [nnf transformation 20]
117. ~happy(sK1) | creative(mary) [cnf transformation 57]
119. happy(sK1) | creative(mary) [cnf transformation 57]
138. ~creative(mary) | happy(mary) [cnf transformation 70]
145. ~happy(mary) [cnf transformation 25]
184. 8 <=> happy(sK1) [avatar definition]
189. 9 <=> creative(mary) [avatar definition]
192. 9 | 8 [avatar split clause 119,184,189]
194. 9 | ~8 [avatar split clause 117,184,189]
224. 16 <=> happy(mary) [avatar definition]
227. 16 | ~9 [avatar split clause 138,189,224]
248. ~16 [avatar split clause 145,224]
249. $false [avatar sat refutation 192,194,227,248]
% SZS output end Proof for 1732461162527947097257793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then someone is brave or not funny and vice versa.
If someone is strong or brave then lucy is not humble or calm.
If john is not humble or not quiet then john is either kind or not strong and vice versa.
If alice is not strong then someone is both not kind and not old.
If someone is calm then fred is wise or not quiet.
Everyone who is both not old and not generous is both not curious and rich.
Everyone who is not kind is happy or kind.
Everyone who is tall or kind is both curious and not generous.
If someone is either rich or generous then susan is both strong and not creative and vice versa.
If alice is either funny or not calm then mary is brave and vice versa.
Everyone who is not wise is not happy or generous and vice versa.
Everyone who is both not strong and brave is creative and vice versa.
If fred is both not happy and not rich then someone is curious or not patient and vice versa.
Everyone who is patient or not patient is not calm or funny and vice versa.
If fred is not kind or patient then someone is either humble or calm.
If alice is rich or not rich then someone is not quiet or happy.
Someone is not kind.
Someone is both old and not brave.
John is curious.
Alice is either not kind or creative.
Someone is either generous or patient.
Someone is generous.
Someone is either not strong or calm.
Mary is either rich or not brave. | Fred is not happy. | entailment | ((?[X]:(old(X)))<=>(?[X]:((brave(X)|~funny(X)))))&
((?[X]:((strong(X)|brave(X))))=>((~humble(lucy)|calm(lucy))))&
(((~humble(john)|~quiet(john)))<=>((kind(john)<~>~strong(john))))&
((~strong(alice))=>(?[X]:((~kind(X)&~old(X)))))&
((?[X]:(calm(X)))=>((wise(fred)|~quiet(fred))))&
(![X]:((~old(X)&~generous(X))=>(~curious(X)&rich(X))))&
(![X]:(~kind(X)=>(happy(X)|kind(X))))&
(![X]:((tall(X)|kind(X))=>(curious(X)&~generous(X))))&
((?[X]:((rich(X)<~>generous(X))))<=>((strong(susan)&~creative(susan))))&
(((funny(alice)<~>~calm(alice)))<=>(brave(mary)))&
(![X]:(~wise(X)<=>(~happy(X)|generous(X))))&
(![X]:((~strong(X)&brave(X))<=>creative(X)))&
(((~happy(fred)&~rich(fred)))<=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:((patient(X)|~patient(X))<=>(~calm(X)|funny(X))))&
(((~kind(fred)|patient(fred)))=>(?[X]:((humble(X)<~>calm(X)))))&
(((rich(alice)|~rich(alice)))=>(?[X]:((~quiet(X)|happy(X)))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)&~brave(X))))&
(curious(john))&
((~kind(alice)<~>creative(alice)))&
(?[X]:((generous(X)<~>patient(X))))&
(?[X]:(generous(X)))&
(?[X]:((~strong(X)<~>calm(X))))&
((rich(mary)<~>~brave(mary))) | ~happy(fred) | [
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1617512135070430962565
% SZS output start Proof for 1617512135070430962565
13. (~rich(fred) & ~happy(fred)) <=> ? [X0] : (~patient(X0) | curious(X0)) [input p12]
19. curious(john) [input p18]
25. happy(fred) [input hypothesis]
59. ((~rich(fred) & ~happy(fred)) | ! [X0] : (patient(X0) & ~curious(X0))) & (? [X0] : (~patient(X0) | curious(X0)) | (rich(fred) | happy(fred))) [nnf transformation 13]
60. ((~rich(fred) & ~happy(fred)) | ! [X0] : (patient(X0) & ~curious(X0))) & (? [X0] : (~patient(X0) | curious(X0)) | rich(fred) | happy(fred)) [flattening 59]
61. ((~rich(fred) & ~happy(fred)) | ! [X0] : (patient(X0) & ~curious(X0))) & (? [X1] : (~patient(X1) | curious(X1)) | rich(fred) | happy(fred)) [rectify 60]
62. ? [X1] : (~patient(X1) | curious(X1)) => (~patient(sK4) | curious(sK4)) [choice axiom]
63. ((~rich(fred) & ~happy(fred)) | ! [X0] : (patient(X0) & ~curious(X0))) & ((~patient(sK4) | curious(sK4)) | rich(fred) | happy(fred)) [skolemisation 61,62]
120. ~happy(fred) | ~curious(X0) [cnf transformation 63]
137. curious(john) [cnf transformation 19]
147. happy(fred) [cnf transformation 25]
287. 31 <=> ! [X0] : ~curious(X0) [avatar definition]
288. ~curious(X0) <- (31) [avatar component clause 287]
291. 32 <=> happy(fred) [avatar definition]
295. 31 | ~32 [avatar split clause 120,291,287]
376. 32 [avatar split clause 147,291]
377. $false <- (31) [resolution 288,137]
378. ~31 [avatar contradiction clause 377]
379. $false [avatar sat refutation 295,376,378]
% SZS output end Proof for 1617512135070430962565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. If lucy is funny or not creative then someone is either not curious or not brave and vice versa. Everyone who is either creative or rich is not funny or old and vice versa. Everyone who is either not tall or not kind is both not strong and not patient and vice versa. If susan is both curious and generous then someone is curious and vice versa. Everyone who is both generous and not humble is not strong and vice versa. Everyone who is either creative or old is both tall and humble and vice versa. Everyone who is either strong or creative is both generous and curious. If someone is not tall then fred is not wise or not rich and vice versa. If someone is either not wise or not rich then someone is rich or not funny. John is happy. Someone is either rich or not kind. Someone is not quiet or not old. Mary is either not patient or not wise. Someone is not funny or kind. Alice is strong. | Mary is not quiet. | contradiction | (![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))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
((?[X]:(~tall(X)))<=>((~wise(fred)|~rich(fred))))&
((?[X]:((~wise(X)<~>~rich(X))))=>(?[X]:((rich(X)|~funny(X)))))&
(happy(john))&
(?[X]:((rich(X)<~>~kind(X))))&
(?[X]:((~quiet(X)|~old(X))))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X))))&
(strong(alice)) | ~quiet(mary) | [
"p0",
"p4",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8227297573143278709761154
% SZS output start Proof for 8227297573143278709761154
1. ! [X0] : (~generous(X0) <=> (generous(X0) | happy(X0))) [input p0]
5. ! [X0] : ((~patient(X0) | wise(X0)) => (humble(X0) & curious(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p5]
10. (generous(susan) & curious(susan)) <=> ? [X0] : curious(X0) [input p9]
22. ~quiet(mary) [input hypothesis]
26. ! [X0] : ((humble(X0) & curious(X0)) | (patient(X0) & ~wise(X0))) [ennf transformation 5]
27. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 6]
30. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | generous(X0))) [nnf transformation 1]
31. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | generous(X0))) [flattening 30]
49. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~generous(susan) | ~curious(susan))) [nnf transformation 10]
50. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ~generous(susan) | ~curious(susan)) [flattening 49]
51. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ~generous(susan) | ~curious(susan)) [rectify 50]
52. ? [X1] : curious(X1) => curious(sK2) [choice axiom]
53. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (curious(sK2) | ~generous(susan) | ~curious(susan)) [skolemisation 51,52]
78. ~generous(X0) | ~generous(X0) [cnf transformation 31]
94. curious(X0) | patient(X0) [cnf transformation 26]
98. ~patient(X0) | quiet(X0) [cnf transformation 27]
121. generous(susan) | ~curious(X0) [cnf transformation 53]
148. ~quiet(mary) [cnf transformation 22]
152. ~generous(X0) [duplicate literal removal 78]
198. ~curious(X0) [subsumption resolution 121,152]
256. 22 <=> patient(mary) [avatar definition]
257. ~patient(mary) <- (~22) [avatar component clause 256]
258. patient(mary) <- (22) [avatar component clause 256]
275. patient(X0) [resolution 94,198]
276. quiet(mary) <- (22) [resolution 98,258]
279. $false <- (22) [subsumption resolution 276,148]
280. ~22 [avatar contradiction clause 279]
281. $false <- (~22) [subsumption resolution 257,275]
282. 22 [avatar contradiction clause 281]
283. $false [avatar sat refutation 280,282]
% SZS output end Proof for 8227297573143278709761154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and strong is either funny or not calm.
If lucy is both quiet and not humble then someone is either not tall or generous.
Everyone who is either not quiet or not rich is either old or not old and vice versa.
Everyone who is either creative or not rich is both not kind and rich.
If someone is either not calm or calm then alice is either quiet or not calm.
Everyone who is both strong and not calm is quiet or calm and vice versa.
If paul is both funny and rich then alice is either not humble or kind and vice versa.
Everyone who is both not funny and not brave is not curious and vice versa.
If paul is both not calm and not creative then fred is not happy.
If someone is either strong or calm then someone is not rich or not kind and vice versa.
If fred is both strong and generous then alice is both strong and not humble.
Everyone who is happy or wise is not rich or humble.
Everyone who is not calm is not old and vice versa.
Everyone who is either not brave or kind is both kind and strong.
If someone is either generous or not humble then alice is both not wise and not tall.
Everyone who is either generous or kind is either not quiet or not funny.
Susan is patient.
Someone is not strong or not funny.
Mary is both not wise and not quiet.
Someone is funny.
Someone is happy.
Fred is not funny or not strong.
Someone is creative.
John is humble or not patient. | Lucy is calm. | contradiction | (![X]:((patient(X)&strong(X))=>(funny(X)<~>~calm(X))))&
(((quiet(lucy)&~humble(lucy)))=>(?[X]:((~tall(X)<~>generous(X)))))&
(![X]:((~quiet(X)<~>~rich(X))<=>(old(X)<~>~old(X))))&
(![X]:((creative(X)<~>~rich(X))=>(~kind(X)&rich(X))))&
((?[X]:((~calm(X)<~>calm(X))))=>((quiet(alice)<~>~calm(alice))))&
(![X]:((strong(X)&~calm(X))<=>(quiet(X)|calm(X))))&
(((funny(paul)&rich(paul)))<=>((~humble(alice)<~>kind(alice))))&
(![X]:((~funny(X)&~brave(X))<=>~curious(X)))&
(((~calm(paul)&~creative(paul)))=>(~happy(fred)))&
((?[X]:((strong(X)<~>calm(X))))<=>(?[X]:((~rich(X)|~kind(X)))))&
(((strong(fred)&generous(fred)))=>((strong(alice)&~humble(alice))))&
(![X]:((happy(X)|wise(X))=>(~rich(X)|humble(X))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:((~brave(X)<~>kind(X))=>(kind(X)&strong(X))))&
((?[X]:((generous(X)<~>~humble(X))))=>((~wise(alice)&~tall(alice))))&
(![X]:((generous(X)<~>kind(X))=>(~quiet(X)<~>~funny(X))))&
(patient(susan))&
(?[X]:((~strong(X)|~funny(X))))&
((~wise(mary)&~quiet(mary)))&
(?[X]:(funny(X)))&
(?[X]:(happy(X)))&
((~funny(fred)|~strong(fred)))&
(?[X]:(creative(X)))&
((humble(john)|~patient(john))) | calm(lucy) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6872023751393142005459796
% SZS output start Proof for 6872023751393142005459796
6. ! [X0] : ((~calm(X0) & strong(X0)) <=> (calm(X0) | quiet(X0))) [input p5]
25. calm(lucy) [input hypothesis]
52. ! [X0] : (((~calm(X0) & strong(X0)) | (~calm(X0) & ~quiet(X0))) & ((calm(X0) | quiet(X0)) | (calm(X0) | ~strong(X0)))) [nnf transformation 6]
53. ! [X0] : (((~calm(X0) & strong(X0)) | (~calm(X0) & ~quiet(X0))) & (calm(X0) | quiet(X0) | calm(X0) | ~strong(X0))) [flattening 52]
97. ~calm(X0) | ~calm(X0) [cnf transformation 53]
134. calm(lucy) [cnf transformation 25]
137. ~calm(X0) [duplicate literal removal 97]
168. 5 <=> ! [X0] : ~calm(X0) [avatar definition]
169. ~calm(X0) <- (5) [avatar component clause 168]
185. 5 [avatar split clause 137,168]
306. $false <- (5) [resolution 169,134]
307. ~5 [avatar contradiction clause 306]
308. $false [avatar sat refutation 185,307]
% SZS output end Proof for 6872023751393142005459796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or not tall then mary is either generous or curious and vice versa.
Everyone who is both not rich and happy is both funny and not kind and vice versa.
Everyone who is both calm and kind is both kind and not happy and vice versa.
Everyone who is both not old and not creative is not patient or not strong and vice versa.
Everyone who is either not generous or kind is both creative and not generous and vice versa.
Everyone who is not calm or wise is calm and vice versa.
Everyone who is patient is rich and vice versa.
Everyone who is happy or not happy is funny or quiet.
If someone is either strong or not calm then alice is either not kind or rich.
If mary is either not patient or wise then someone is either not wise or humble.
Everyone who is brave or not wise is both brave and creative.
Everyone who is not humble or kind is not old and vice versa.
If someone is both humble and not old then mary is humble or curious and vice versa.
Everyone who is not calm or brave is not strong or brave and vice versa.
If someone is both not brave and quiet then lucy is not kind.
Everyone who is either generous or funny is both humble and not generous and vice versa.
Lucy is either quiet or tall.
Someone is both generous and not old.
Someone is both not rich and not kind.
Someone is quiet.
Someone is either not happy or strong.
Someone is rich.
Paul is either not patient or kind.
Lucy is both rich and not tall. | Lucy is not funny. | entailment | ((?[X]:((~brave(X)|~tall(X))))<=>((generous(mary)<~>curious(mary))))&
(![X]:((~rich(X)&happy(X))<=>(funny(X)&~kind(X))))&
(![X]:((calm(X)&kind(X))<=>(kind(X)&~happy(X))))&
(![X]:((~old(X)&~creative(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(creative(X)&~generous(X))))&
(![X]:((~calm(X)|wise(X))<=>calm(X)))&
(![X]:(patient(X)<=>rich(X)))&
(![X]:((happy(X)|~happy(X))=>(funny(X)|quiet(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>((~kind(alice)<~>rich(alice))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((brave(X)|~wise(X))=>(brave(X)&creative(X))))&
(![X]:((~humble(X)|kind(X))<=>~old(X)))&
((?[X]:((humble(X)&~old(X))))<=>((humble(mary)|curious(mary))))&
(![X]:((~calm(X)|brave(X))<=>(~strong(X)|brave(X))))&
((?[X]:((~brave(X)&quiet(X))))=>(~kind(lucy)))&
(![X]:((generous(X)<~>funny(X))<=>(humble(X)&~generous(X))))&
((quiet(lucy)<~>tall(lucy)))&
(?[X]:((generous(X)&~old(X))))&
(?[X]:((~rich(X)&~kind(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:(rich(X)))&
((~patient(paul)<~>kind(paul)))&
((rich(lucy)&~tall(lucy))) | ~funny(lucy) | [
"p1",
"p4",
"p10",
"p14",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8380754861651701755600384
% SZS output start Proof for 8380754861651701755600384
2. ! [X0] : ((happy(X0) & ~rich(X0)) <=> (~kind(X0) & funny(X0))) [input p1]
5. ! [X0] : ((~generous(X0) <~> kind(X0)) <=> (~generous(X0) & creative(X0))) [input p4]
11. ! [X0] : ((~wise(X0) | brave(X0)) => (creative(X0) & brave(X0))) [input p10]
15. ? [X0] : (quiet(X0) & ~brave(X0)) => ~kind(lucy) [input p14]
17. quiet(lucy) <~> tall(lucy) [input p16]
24. ~tall(lucy) & rich(lucy) [input p23]
25. funny(lucy) [input hypothesis]
30. ! [X0] : ((creative(X0) & brave(X0)) | (wise(X0) & ~brave(X0))) [ennf transformation 11]
31. ~kind(lucy) | ! [X0] : (~quiet(X0) | brave(X0)) [ennf transformation 15]
36. ! [X0] : (((happy(X0) & ~rich(X0)) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | (~happy(X0) | rich(X0)))) [nnf transformation 2]
37. ! [X0] : (((happy(X0) & ~rich(X0)) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | ~happy(X0) | rich(X0))) [flattening 36]
42. ! [X0] : ((((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (generous(X0) | ~creative(X0))) & ((~generous(X0) & creative(X0)) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))))) [nnf transformation 5]
43. ! [X0] : ((((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | generous(X0) | ~creative(X0)) & ((~generous(X0) & creative(X0)) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))))) [flattening 42]
62. (~tall(lucy) | ~quiet(lucy)) & (tall(lucy) | quiet(lucy)) [nnf transformation 17]
83. ~funny(X0) | kind(X0) | ~rich(X0) [cnf transformation 37]
97. ~generous(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 43]
99. ~kind(X0) | generous(X0) | generous(X0) | ~creative(X0) [cnf transformation 43]
117. ~brave(X0) | creative(X0) [cnf transformation 30]
131. ~kind(lucy) | ~quiet(X0) | brave(X0) [cnf transformation 31]
138. tall(lucy) | quiet(lucy) [cnf transformation 62]
150. rich(lucy) [cnf transformation 24]
151. ~tall(lucy) [cnf transformation 24]
152. funny(lucy) [cnf transformation 25]
157. ~kind(X0) | ~generous(X0) [duplicate literal removal 97]
158. ~creative(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 99]
245. 18 <=> ! [X0] : (~quiet(X0) | brave(X0)) [avatar definition]
246. ~quiet(X0) | brave(X0) <- (18) [avatar component clause 245]
248. 19 <=> kind(lucy) [avatar definition]
249. kind(lucy) <- (19) [avatar component clause 248]
251. 18 | ~19 [avatar split clause 131,248,245]
253. 20 <=> quiet(lucy) [avatar definition]
254. quiet(lucy) <- (20) [avatar component clause 253]
257. 21 <=> tall(lucy) [avatar definition]
261. 20 | 21 [avatar split clause 138,257,253]
282. ~21 [avatar split clause 151,257]
317. kind(lucy) | ~rich(lucy) [resolution 83,152]
341. kind(lucy) [subsumption resolution 317,150]
342. 19 [avatar split clause 341,248]
344. ~generous(lucy) <- (19) [resolution 249,157]
346. brave(lucy) <- (18, 20) [resolution 246,254]
371. creative(lucy) <- (18, 20) [resolution 346,117]
587. generous(lucy) | ~kind(lucy) <- (18, 20) [resolution 371,158]
590. ~kind(lucy) <- (18, 19, 20) [subsumption resolution 587,344]
591. $false <- (18, 19, 20) [subsumption resolution 590,249]
592. ~18 | ~19 | ~20 [avatar contradiction clause 591]
593. $false [avatar sat refutation 251,261,282,342,592]
% SZS output end Proof for 8380754861651701755600384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or quiet is curious or not wise.
Everyone who is not happy is not old or not creative.
If lucy is calm or wise then paul is either not wise or not brave and vice versa.
If lucy is either humble or happy then susan is not rich or creative.
If susan is not calm or not generous then someone is both generous and quiet and vice versa.
Everyone who is not rich is not generous or creative and vice versa.
If susan is humble or creative then someone is creative and vice versa.
Everyone who is both brave and generous is not calm and vice versa.
Everyone who is not patient is both funny and strong.
If fred is generous then john is funny and vice versa.
Everyone who is not strong is creative or not generous and vice versa.
If someone is either kind or not old then mary is both tall and not calm.
Everyone who is both strong and not old is not happy or not generous and vice versa.
Everyone who is calm is not quiet.
Everyone who is both happy and not creative is not quiet or generous and vice versa.
Everyone who is not calm is not funny or old and vice versa.
Alice is either not quiet or not happy.
Someone is not wise.
Alice is either tall or quiet.
Paul is either not happy or funny.
Lucy is both not funny and wise. | Paul is not wise. | entailment | (![X]:((~old(X)<~>quiet(X))=>(curious(X)|~wise(X))))&
(![X]:(~happy(X)=>(~old(X)|~creative(X))))&
(((calm(lucy)|wise(lucy)))<=>((~wise(paul)<~>~brave(paul))))&
(((humble(lucy)<~>happy(lucy)))=>((~rich(susan)|creative(susan))))&
(((~calm(susan)|~generous(susan)))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:(~rich(X)<=>(~generous(X)|creative(X))))&
(((humble(susan)|creative(susan)))<=>(?[X]:(creative(X))))&
(![X]:((brave(X)&generous(X))<=>~calm(X)))&
(![X]:(~patient(X)=>(funny(X)&strong(X))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(![X]:((happy(X)&~creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:(~calm(X)<=>(~funny(X)|old(X))))&
((~quiet(alice)<~>~happy(alice)))&
(?[X]:(~wise(X)))&
((tall(alice)<~>quiet(alice)))&
((~happy(paul)<~>funny(paul)))&
((~funny(lucy)&wise(lucy))) | ~wise(paul) | [
"p2",
"p7",
"p10",
"p12",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2324222165195519579474611
% SZS output start Proof for 2324222165195519579474611
3. (wise(lucy) | calm(lucy)) <=> (~wise(paul) <~> ~brave(paul)) [input p2]
8. ! [X0] : ((generous(X0) & brave(X0)) <=> ~calm(X0)) [input p7]
11. ! [X0] : (~strong(X0) <=> (~generous(X0) | creative(X0))) [input p10]
13. ! [X0] : ((~old(X0) & strong(X0)) <=> (~generous(X0) | ~happy(X0))) [input p12]
15. ! [X0] : ((~creative(X0) & happy(X0)) <=> (generous(X0) | ~quiet(X0))) [input p14]
16. ! [X0] : (~calm(X0) <=> (old(X0) | ~funny(X0))) [input p15]
21. wise(lucy) & ~funny(lucy) [input p20]
22. wise(paul) [input hypothesis]
34. ((wise(lucy) | calm(lucy)) | ((~wise(paul) | brave(paul)) & (~brave(paul) | wise(paul)))) & (((brave(paul) | wise(paul)) & (~brave(paul) | ~wise(paul))) | (~wise(lucy) & ~calm(lucy))) [nnf transformation 3]
35. (wise(lucy) | calm(lucy) | ((~wise(paul) | brave(paul)) & (~brave(paul) | wise(paul)))) & (((brave(paul) | wise(paul)) & (~brave(paul) | ~wise(paul))) | (~wise(lucy) & ~calm(lucy))) [flattening 34]
47. ! [X0] : (((generous(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | (~generous(X0) | ~brave(X0)))) [nnf transformation 8]
48. ! [X0] : (((generous(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | ~generous(X0) | ~brave(X0))) [flattening 47]
50. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | strong(X0))) [nnf transformation 11]
51. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | strong(X0))) [flattening 50]
53. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (old(X0) | ~strong(X0)))) [nnf transformation 13]
54. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0))) [flattening 53]
55. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 15]
56. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | creative(X0) | ~happy(X0))) [flattening 55]
57. ! [X0] : ((~calm(X0) | (~old(X0) & funny(X0))) & ((old(X0) | ~funny(X0)) | calm(X0))) [nnf transformation 16]
58. ! [X0] : ((~calm(X0) | (~old(X0) & funny(X0))) & (old(X0) | ~funny(X0) | calm(X0))) [flattening 57]
66. ~brave(paul) | ~wise(paul) | ~wise(lucy) [cnf transformation 35]
83. brave(X0) | calm(X0) [cnf transformation 48]
87. ~generous(X0) | creative(X0) | strong(X0) [cnf transformation 51]
89. ~strong(X0) | generous(X0) [cnf transformation 51]
94. ~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0) [cnf transformation 54]
96. strong(X0) | generous(X0) [cnf transformation 54]
102. happy(X0) | ~generous(X0) [cnf transformation 56]
104. ~creative(X0) | ~generous(X0) [cnf transformation 56]
107. ~calm(X0) | ~old(X0) [cnf transformation 58]
116. wise(lucy) [cnf transformation 21]
117. wise(paul) [cnf transformation 22]
119. 1 <=> brave(paul) [avatar definition]
120. ~brave(paul) <- (~1) [avatar component clause 119]
123. 2 <=> wise(paul) [avatar definition]
131. 4 <=> wise(lucy) [avatar definition]
138. ~4 | ~2 | ~1 [avatar split clause 66,119,123,131]
183. 14 <=> ! [X0] : ~creative(X0) [avatar definition]
184. ~creative(X0) <- (14) [avatar component clause 183]
224. generous(X0) [subsumption resolution 96,89]
225. ~strong(X0) | old(X0) | ~happy(X0) [subsumption resolution 94,224]
226. ~creative(X0) [subsumption resolution 104,224]
227. 14 [avatar split clause 226,183]
228. happy(X0) [subsumption resolution 102,224]
232. 4 [avatar split clause 116,131]
233. 2 [avatar split clause 117,123]
237. calm(paul) <- (~1) [resolution 83,120]
245. ~old(paul) <- (~1) [resolution 107,237]
258. creative(X1) | strong(X1) [resolution 87,224]
260. strong(X1) <- (14) [subsumption resolution 258,184]
279. old(X0) | ~happy(X0) <- (14) [resolution 225,260]
281. old(X0) <- (14) [subsumption resolution 279,228]
285. $false <- (~1, 14) [resolution 281,245]
290. 1 | ~14 [avatar contradiction clause 285]
291. $false [avatar sat refutation 138,227,232,233,290]
% SZS output end Proof for 2324222165195519579474611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is quiet or not old then someone is both not patient and not quiet. If paul is not curious or not old then alice is not calm or rich and vice versa. Everyone who is either not tall or not generous is happy or not old and vice versa. If fred is not quiet then susan is both tall and not strong. If someone is both not brave and funny then someone is either patient or generous and vice versa. If someone is either patient or not wise then john is not calm and vice versa. Everyone who is quiet or not humble is both not kind and not quiet and vice versa. Everyone who is both generous and not brave is either not creative or not tall and vice versa. If mary is either not calm or quiet then someone is not brave or strong and vice versa. If someone is quiet or not funny then someone is curious or not quiet. Everyone who is not curious is quiet or not old and vice versa. If someone is not rich or happy then someone is tall or creative. Everyone who is both not happy and generous is both humble and not quiet and vice versa. Everyone who is either not brave or not curious is both not generous and patient. If someone is not generous or curious then paul is rich or not brave and vice versa. Everyone who is humble is both not strong and kind and vice versa. Lucy is funny or kind. Mary is both calm and not creative. Someone is both patient and old. Someone is wise. Someone is generous or not wise. Someone is rich or patient. Someone is both not funny and wise. John is either not funny or wise. | Mary is old. | entailment | (((quiet(john)|~old(john)))=>(?[X]:((~patient(X)&~quiet(X)))))&
(((~curious(paul)|~old(paul)))<=>((~calm(alice)|rich(alice))))&
(![X]:((~tall(X)<~>~generous(X))<=>(happy(X)|~old(X))))&
((~quiet(fred))=>((tall(susan)&~strong(susan))))&
((?[X]:((~brave(X)&funny(X))))<=>(?[X]:((patient(X)<~>generous(X)))))&
((?[X]:((patient(X)<~>~wise(X))))<=>(~calm(john)))&
(![X]:((quiet(X)|~humble(X))<=>(~kind(X)&~quiet(X))))&
(![X]:((generous(X)&~brave(X))<=>(~creative(X)<~>~tall(X))))&
(((~calm(mary)<~>quiet(mary)))<=>(?[X]:((~brave(X)|strong(X)))))&
((?[X]:((quiet(X)|~funny(X))))=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:(~curious(X)<=>(quiet(X)|~old(X))))&
((?[X]:((~rich(X)|happy(X))))=>(?[X]:((tall(X)|creative(X)))))&
(![X]:((~happy(X)&generous(X))<=>(humble(X)&~quiet(X))))&
(![X]:((~brave(X)<~>~curious(X))=>(~generous(X)&patient(X))))&
((?[X]:((~generous(X)|curious(X))))<=>((rich(paul)|~brave(paul))))&
(![X]:(humble(X)<=>(~strong(X)&kind(X))))&
((funny(lucy)|kind(lucy)))&
((calm(mary)&~creative(mary)))&
(?[X]:((patient(X)&old(X))))&
(?[X]:(wise(X)))&
(?[X]:((generous(X)|~wise(X))))&
(?[X]:((rich(X)|patient(X))))&
(?[X]:((~funny(X)&wise(X))))&
((~funny(john)<~>wise(john))) | old(mary) | [
"p2",
"p6",
"p7",
"p8",
"p10",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1144482218451658556626715
% SZS output start Proof for 1144482218451658556626715
3. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (~old(X0) | happy(X0))) [input p2]
7. ! [X0] : ((~humble(X0) | quiet(X0)) <=> (~quiet(X0) & ~kind(X0))) [input p6]
8. ! [X0] : ((~brave(X0) & generous(X0)) <=> (~creative(X0) <~> ~tall(X0))) [input p7]
9. (~calm(mary) <~> quiet(mary)) <=> ? [X0] : (strong(X0) | ~brave(X0)) [input p8]
11. ! [X0] : (~curious(X0) <=> (~old(X0) | quiet(X0))) [input p10]
14. ! [X0] : ((~brave(X0) <~> ~curious(X0)) => (patient(X0) & ~generous(X0))) [input p13]
18. ~creative(mary) & calm(mary) [input p17]
25. ~old(mary) [input hypothesis]
33. ! [X0] : ((patient(X0) & ~generous(X0)) | (~brave(X0) <=> ~curious(X0))) [ennf transformation 14]
38. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (old(X0) & ~happy(X0))) & ((~old(X0) | happy(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 3]
39. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (old(X0) & ~happy(X0))) & (~old(X0) | happy(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 38]
49. ! [X0] : (((~humble(X0) | quiet(X0)) | (quiet(X0) | kind(X0))) & ((~quiet(X0) & ~kind(X0)) | (humble(X0) & ~quiet(X0)))) [nnf transformation 7]
50. ! [X0] : ((~humble(X0) | quiet(X0) | quiet(X0) | kind(X0)) & ((~quiet(X0) & ~kind(X0)) | (humble(X0) & ~quiet(X0)))) [flattening 49]
51. ! [X0] : (((~brave(X0) & generous(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (brave(X0) | ~generous(X0)))) [nnf transformation 8]
52. ! [X0] : (((~brave(X0) & generous(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | brave(X0) | ~generous(X0))) [flattening 51]
53. (((~quiet(mary) | calm(mary)) & (quiet(mary) | ~calm(mary))) | ! [X0] : (~strong(X0) & brave(X0))) & (? [X0] : (strong(X0) | ~brave(X0)) | ((~calm(mary) | ~quiet(mary)) & (quiet(mary) | calm(mary)))) [nnf transformation 9]
54. (((~quiet(mary) | calm(mary)) & (quiet(mary) | ~calm(mary))) | ! [X0] : (~strong(X0) & brave(X0))) & (? [X1] : (strong(X1) | ~brave(X1)) | ((~calm(mary) | ~quiet(mary)) & (quiet(mary) | calm(mary)))) [rectify 53]
55. ? [X1] : (strong(X1) | ~brave(X1)) => (strong(sK4) | ~brave(sK4)) [choice axiom]
56. (((~quiet(mary) | calm(mary)) & (quiet(mary) | ~calm(mary))) | ! [X0] : (~strong(X0) & brave(X0))) & ((strong(sK4) | ~brave(sK4)) | ((~calm(mary) | ~quiet(mary)) & (quiet(mary) | calm(mary)))) [skolemisation 54,55]
60. ! [X0] : ((~curious(X0) | (old(X0) & ~quiet(X0))) & ((~old(X0) | quiet(X0)) | curious(X0))) [nnf transformation 11]
61. ! [X0] : ((~curious(X0) | (old(X0) & ~quiet(X0))) & (~old(X0) | quiet(X0) | curious(X0))) [flattening 60]
67. ! [X0] : ((patient(X0) & ~generous(X0)) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) [nnf transformation 33]
99. generous(X0) | tall(X0) | old(X0) [cnf transformation 39]
114. ~quiet(X0) | ~quiet(X0) [cnf transformation 50]
121. ~brave(X0) | ~tall(X0) | creative(X0) [cnf transformation 52]
125. quiet(mary) | ~calm(mary) | brave(X0) [cnf transformation 56]
131. ~old(X0) | quiet(X0) | curious(X0) [cnf transformation 61]
133. ~curious(X0) | old(X0) [cnf transformation 61]
141. ~brave(X0) | ~generous(X0) | curious(X0) [cnf transformation 67]
152. calm(mary) [cnf transformation 18]
153. ~creative(mary) [cnf transformation 18]
163. ~old(mary) [cnf transformation 25]
164. ~quiet(X0) [duplicate literal removal 114]
278. 25 <=> calm(mary) [avatar definition]
282. ~calm(mary) | brave(X0) [subsumption resolution 125,164]
284. 26 <=> ! [X0] : brave(X0) [avatar definition]
285. brave(X0) <- (26) [avatar component clause 284]
286. 26 | ~25 [avatar split clause 282,278,284]
297. ~old(X0) | curious(X0) [subsumption resolution 131,164]
351. 25 [avatar split clause 152,278]
436. ~tall(X0) | creative(X0) <- (26) [resolution 121,285]
472. ~generous(X0) | curious(X0) <- (26) [resolution 141,285]
523. curious(X0) | tall(X0) | old(X0) <- (26) [resolution 472,99]
525. tall(X0) | curious(X0) <- (26) [subsumption resolution 523,297]
575. creative(X0) | curious(X0) <- (26) [resolution 525,436]
587. curious(mary) <- (26) [resolution 575,153]
604. old(mary) <- (26) [resolution 587,133]
605. $false <- (26) [subsumption resolution 604,163]
606. ~26 [avatar contradiction clause 605]
607. $false [avatar sat refutation 286,351,606]
% SZS output end Proof for 1144482218451658556626715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either kind or not happy then someone is not strong or not curious and vice versa.
Everyone who is both not calm and strong is not funny or not happy and vice versa.
If alice is not kind then someone is either not brave or not creative.
Everyone who is either not quiet or tall is both not tall and not kind and vice versa.
Everyone who is both not quiet and not rich is rich.
Everyone who is not happy is both quiet and not happy and vice versa.
If someone is kind or old then someone is either not patient or generous.
Everyone who is not happy is both not kind and not old.
If mary is both not kind and not tall then fred is either not creative or kind.
Everyone who is either humble or not brave is both curious and not generous.
Everyone who is not humble or humble is either wise or curious and vice versa.
Everyone who is either kind or wise is both not strong and calm.
Everyone who is not kind is either curious or strong and vice versa.
Everyone who is both patient and rich is generous and vice versa.
Everyone who is humble is both happy and not generous.
If alice is not curious or brave then john is either not quiet or curious.
Susan is patient.
John is not strong or not quiet.
Someone is not strong or not wise.
Someone is both not creative and quiet.
Lucy is both happy and not calm. | Alice is rich. | neutral | (((kind(alice)<~>~happy(alice)))<=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((~calm(X)&strong(X))<=>(~funny(X)|~happy(X))))&
((~kind(alice))=>(?[X]:((~brave(X)<~>~creative(X)))))&
(![X]:((~quiet(X)<~>tall(X))<=>(~tall(X)&~kind(X))))&
(![X]:((~quiet(X)&~rich(X))=>rich(X)))&
(![X]:(~happy(X)<=>(quiet(X)&~happy(X))))&
((?[X]:((kind(X)|old(X))))=>(?[X]:((~patient(X)<~>generous(X)))))&
(![X]:(~happy(X)=>(~kind(X)&~old(X))))&
(((~kind(mary)&~tall(mary)))=>((~creative(fred)<~>kind(fred))))&
(![X]:((humble(X)<~>~brave(X))=>(curious(X)&~generous(X))))&
(![X]:((~humble(X)|humble(X))<=>(wise(X)<~>curious(X))))&
(![X]:((kind(X)<~>wise(X))=>(~strong(X)&calm(X))))&
(![X]:(~kind(X)<=>(curious(X)<~>strong(X))))&
(![X]:((patient(X)&rich(X))<=>generous(X)))&
(![X]:(humble(X)=>(happy(X)&~generous(X))))&
(((~curious(alice)|brave(alice)))=>((~quiet(john)<~>curious(john))))&
(patient(susan))&
((~strong(john)|~quiet(john)))&
(?[X]:((~strong(X)|~wise(X))))&
(?[X]:((~creative(X)&quiet(X))))&
((happy(lucy)&~calm(lucy))) | rich(alice) | [] | null | 0 |
If john is not curious then fred is both not strong and creative and vice versa. If mary is not happy then fred is calm and vice versa. If mary is either calm or not patient then john is both generous and not brave and vice versa. If someone is both not rich and brave then someone is humble or not curious. Everyone who is both not generous and happy is either not tall or not creative and vice versa. Everyone who is either not kind or not happy is brave or not happy. Everyone who is either not brave or tall is both humble and curious and vice versa. If john is not rich or generous then someone is curious or wise and vice versa. Everyone who is both not rich and not wise is either not calm or not brave. If someone is wise then alice is either not creative or old. If mary is both happy and rich then someone is not kind. Everyone who is either humble or happy is both strong and not brave and vice versa. If john is not curious or not funny then someone is curious and vice versa. Everyone who is not old or not creative is either not quiet or not patient. Everyone who is not generous or creative is either rich or old. Everyone who is both quiet and strong is happy and vice versa. Someone is both strong and not calm. Someone is humble. Someone is brave. Someone is generous or funny. Someone is both rich and happy. John is strong. Paul is strong. Alice is either not brave or not rich. | John is not funny. | neutral | ((~curious(john))<=>((~strong(fred)&creative(fred))))&
((~happy(mary))<=>(calm(fred)))&
(((calm(mary)<~>~patient(mary)))<=>((generous(john)&~brave(john))))&
((?[X]:((~rich(X)&brave(X))))=>(?[X]:((humble(X)|~curious(X)))))&
(![X]:((~generous(X)&happy(X))<=>(~tall(X)<~>~creative(X))))&
(![X]:((~kind(X)<~>~happy(X))=>(brave(X)|~happy(X))))&
(![X]:((~brave(X)<~>tall(X))<=>(humble(X)&curious(X))))&
(((~rich(john)|generous(john)))<=>(?[X]:((curious(X)|wise(X)))))&
(![X]:((~rich(X)&~wise(X))=>(~calm(X)<~>~brave(X))))&
((?[X]:(wise(X)))=>((~creative(alice)<~>old(alice))))&
(((happy(mary)&rich(mary)))=>(?[X]:(~kind(X))))&
(![X]:((humble(X)<~>happy(X))<=>(strong(X)&~brave(X))))&
(((~curious(john)|~funny(john)))<=>(?[X]:(curious(X))))&
(![X]:((~old(X)|~creative(X))=>(~quiet(X)<~>~patient(X))))&
(![X]:((~generous(X)|creative(X))=>(rich(X)<~>old(X))))&
(![X]:((quiet(X)&strong(X))<=>happy(X)))&
(?[X]:((strong(X)&~calm(X))))&
(?[X]:(humble(X)))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)|funny(X))))&
(?[X]:((rich(X)&happy(X))))&
(strong(john))&
(strong(paul))&
((~brave(alice)<~>~rich(alice))) | ~funny(john) | [] | null | 0 |
Everyone who is generous or humble is wise and vice versa. Everyone who is either brave or generous is both calm and not quiet and vice versa. Everyone who is generous or rich is both generous and not strong and vice versa. If someone is not rich then someone is old and vice versa. Everyone who is calm is both not generous and not creative and vice versa. Everyone who is both not rich and not kind is kind and vice versa. Everyone who is wise is either curious or happy and vice versa. Everyone who is not creative is curious and vice versa. If someone is not quiet then someone is not quiet or creative and vice versa. If someone is not happy then paul is not kind or strong. Everyone who is either tall or creative is either not brave or happy and vice versa. If fred is creative then lucy is creative or not humble and vice versa. Everyone who is either curious or rich is funny. John is not funny or patient. Someone is either not kind or not rich. Someone is not calm. Lucy is tall or not patient. John is both not kind and not strong. Someone is not funny. Susan is not happy or not tall. | Fred is not humble. | neutral | (![X]:((generous(X)|humble(X))<=>wise(X)))&
(![X]:((brave(X)<~>generous(X))<=>(calm(X)&~quiet(X))))&
(![X]:((generous(X)|rich(X))<=>(generous(X)&~strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:(old(X))))&
(![X]:(calm(X)<=>(~generous(X)&~creative(X))))&
(![X]:((~rich(X)&~kind(X))<=>kind(X)))&
(![X]:(wise(X)<=>(curious(X)<~>happy(X))))&
(![X]:(~creative(X)<=>curious(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:((~quiet(X)|creative(X)))))&
((?[X]:(~happy(X)))=>((~kind(paul)|strong(paul))))&
(![X]:((tall(X)<~>creative(X))<=>(~brave(X)<~>happy(X))))&
((creative(fred))<=>((creative(lucy)|~humble(lucy))))&
(![X]:((curious(X)<~>rich(X))=>funny(X)))&
((~funny(john)|patient(john)))&
(?[X]:((~kind(X)<~>~rich(X))))&
(?[X]:(~calm(X)))&
((tall(lucy)|~patient(lucy)))&
((~kind(john)&~strong(john)))&
(?[X]:(~funny(X)))&
((~happy(susan)|~tall(susan))) | ~humble(fred) | [] | null | 0 |
Everyone who is either not curious or generous is humble and vice versa.
Everyone who is old is either happy or not creative.
Everyone who is both old and not happy is generous or not rich and vice versa.
If someone is not patient then someone is not humble or funny and vice versa.
Everyone who is generous is curious.
If someone is happy or not brave then someone is either not quiet or curious.
If someone is not humble or not wise then mary is both funny and not curious and vice versa.
Everyone who is either not rich or funny is both happy and not brave.
Everyone who is not kind is not humble or not quiet and vice versa.
Everyone who is either rich or tall is happy or not strong and vice versa.
Everyone who is both not kind and not happy is humble or not humble and vice versa.
Everyone who is both humble and not rich is funny and vice versa.
Everyone who is both strong and not generous is not tall.
Everyone who is funny or not humble is not calm or generous and vice versa.
If someone is generous then john is tall and vice versa.
If alice is both not humble and not tall then fred is not rich or not humble.
Someone is brave or not brave.
Someone is either generous or not wise.
John is creative.
Fred is either not generous or quiet.
John is tall or not humble. | Mary is not funny. | contradiction | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((old(X)&~happy(X))<=>(generous(X)|~rich(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:(generous(X)=>curious(X)))&
((?[X]:((happy(X)|~brave(X))))=>(?[X]:((~quiet(X)<~>curious(X)))))&
((?[X]:((~humble(X)|~wise(X))))<=>((funny(mary)&~curious(mary))))&
(![X]:((~rich(X)<~>funny(X))=>(happy(X)&~brave(X))))&
(![X]:(~kind(X)<=>(~humble(X)|~quiet(X))))&
(![X]:((rich(X)<~>tall(X))<=>(happy(X)|~strong(X))))&
(![X]:((~kind(X)&~happy(X))<=>(humble(X)|~humble(X))))&
(![X]:((humble(X)&~rich(X))<=>funny(X)))&
(![X]:((strong(X)&~generous(X))=>~tall(X)))&
(![X]:((funny(X)|~humble(X))<=>(~calm(X)|generous(X))))&
((?[X]:(generous(X)))<=>(tall(john)))&
(((~humble(alice)&~tall(alice)))=>((~rich(fred)|~humble(fred))))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((generous(X)<~>~wise(X))))&
(creative(john))&
((~generous(fred)<~>quiet(fred)))&
((tall(john)|~humble(john))) | ~funny(mary) | [
"p1",
"p2",
"p6",
"p9",
"p10",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8471428173122592117445269
% SZS output start Proof for 8471428173122592117445269
2. ! [X0] : (old(X0) => (happy(X0) <~> ~creative(X0))) [input p1]
3. ! [X0] : ((~happy(X0) & old(X0)) <=> (~rich(X0) | generous(X0))) [input p2]
7. ? [X0] : (~wise(X0) | ~humble(X0)) <=> (~curious(mary) & funny(mary)) [input p6]
10. ! [X0] : ((rich(X0) <~> tall(X0)) <=> (~strong(X0) | happy(X0))) [input p9]
11. ! [X0] : ((~happy(X0) & ~kind(X0)) <=> (~humble(X0) | humble(X0))) [input p10]
13. ! [X0] : ((~generous(X0) & strong(X0)) => ~tall(X0)) [input p12]
19. creative(john) [input p18]
21. ~humble(john) | tall(john) [input p20]
22. ~funny(mary) [input hypothesis]
25. ! [X0] : ((happy(X0) <~> ~creative(X0)) | ~old(X0)) [ennf transformation 2]
29. ! [X0] : (~tall(X0) | (generous(X0) | ~strong(X0))) [ennf transformation 13]
30. ! [X0] : (~tall(X0) | generous(X0) | ~strong(X0)) [flattening 29]
34. ! [X0] : (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~old(X0)) [nnf transformation 25]
35. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & ((~rich(X0) | generous(X0)) | (happy(X0) | ~old(X0)))) [nnf transformation 3]
36. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & (~rich(X0) | generous(X0) | happy(X0) | ~old(X0))) [flattening 35]
46. (? [X0] : (~wise(X0) | ~humble(X0)) | (curious(mary) | ~funny(mary))) & ((~curious(mary) & funny(mary)) | ! [X0] : (wise(X0) & humble(X0))) [nnf transformation 7]
47. (? [X0] : (~wise(X0) | ~humble(X0)) | curious(mary) | ~funny(mary)) & ((~curious(mary) & funny(mary)) | ! [X0] : (wise(X0) & humble(X0))) [flattening 46]
48. (? [X0] : (~wise(X0) | ~humble(X0)) | curious(mary) | ~funny(mary)) & ((~curious(mary) & funny(mary)) | ! [X1] : (wise(X1) & humble(X1))) [rectify 47]
49. ? [X0] : (~wise(X0) | ~humble(X0)) => (~wise(sK3) | ~humble(sK3)) [choice axiom]
50. ((~wise(sK3) | ~humble(sK3)) | curious(mary) | ~funny(mary)) & ((~curious(mary) & funny(mary)) | ! [X1] : (wise(X1) & humble(X1))) [skolemisation 48,49]
54. ! [X0] : ((((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0))))) [nnf transformation 10]
55. ! [X0] : ((((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0))))) [flattening 54]
56. ! [X0] : (((~happy(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | (happy(X0) | kind(X0)))) [nnf transformation 11]
57. ! [X0] : (((~happy(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | happy(X0) | kind(X0))) [flattening 56]
76. ~creative(X0) | happy(X0) | ~old(X0) [cnf transformation 34]
79. ~generous(X0) | old(X0) [cnf transformation 36]
80. rich(X0) | old(X0) [cnf transformation 36]
91. funny(mary) | humble(X1) [cnf transformation 50]
108. ~tall(X0) | ~rich(X0) | strong(X0) [cnf transformation 55]
112. ~happy(X0) | ~humble(X0) [cnf transformation 57]
113. ~happy(X0) | humble(X0) [cnf transformation 57]
117. ~strong(X0) | generous(X0) | ~tall(X0) [cnf transformation 30]
128. creative(john) [cnf transformation 19]
131. ~humble(john) | tall(john) [cnf transformation 21]
132. ~funny(mary) [cnf transformation 22]
142. 3 <=> ! [X1] : humble(X1) [avatar definition]
143. humble(X1) <- (3) [avatar component clause 142]
170. 10 <=> ! [X1] : ~happy(X1) [avatar definition]
171. ~happy(X1) <- (10) [avatar component clause 170]
176. 11 <=> funny(mary) [avatar definition]
198. 3 | 11 [avatar split clause 91,176,142]
202. ~happy(X0) [subsumption resolution 112,113]
203. 10 [avatar split clause 202,170]
206. 16 <=> tall(john) [avatar definition]
207. tall(john) <- (16) [avatar component clause 206]
256. 27 <=> humble(john) [avatar definition]
258. ~humble(john) <- (~27) [avatar component clause 256]
259. 16 | ~27 [avatar split clause 131,256,206]
260. ~11 [avatar split clause 132,176]
287. happy(john) | ~old(john) [resolution 76,128]
288. ~old(john) <- (10) [subsumption resolution 287,171]
291. ~rich(john) | strong(john) <- (16) [resolution 108,207]
293. 28 <=> strong(john) [avatar definition]
295. strong(john) <- (28) [avatar component clause 293]
297. 29 <=> rich(john) [avatar definition]
299. ~rich(john) <- (~29) [avatar component clause 297]
300. 28 | ~29 | ~16 [avatar split clause 291,206,297,293]
302. old(john) <- (~29) [resolution 299,80]
303. $false <- (10, ~29) [subsumption resolution 302,288]
304. ~10 | 29 [avatar contradiction clause 303]
305. $false <- (3, ~27) [subsumption resolution 258,143]
306. ~3 | 27 [avatar contradiction clause 305]
313. generous(john) | ~tall(john) <- (28) [resolution 295,117]
314. generous(john) <- (16, 28) [subsumption resolution 313,207]
320. old(john) <- (16, 28) [resolution 314,79]
321. $false <- (10, 16, 28) [subsumption resolution 320,288]
322. ~10 | ~16 | ~28 [avatar contradiction clause 321]
323. $false [avatar sat refutation 198,203,259,260,300,304,306,322]
% SZS output end Proof for 8471428173122592117445269
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or calm is both calm and not old and vice versa. If someone is both brave and not quiet then alice is not generous or patient and vice versa. Everyone who is both strong and rich is both happy and not kind. If someone is both kind and quiet then john is happy or not funny. Everyone who is either humble or not strong is either not happy or happy. Everyone who is brave or curious is wise. If someone is both kind and not funny then someone is either not quiet or patient and vice versa. If paul is not funny then someone is quiet. Everyone who is rich or wise is quiet and vice versa. If someone is either old or not strong then fred is not wise. Everyone who is not generous or calm is either not curious or not brave and vice versa. If someone is either patient or generous then someone is not funny or not strong. Everyone who is not patient or brave is not curious. Everyone who is either generous or calm is both not wise and not rich. Everyone who is patient or quiet is not kind and vice versa. If fred is both not happy and kind then someone is not creative and vice versa. Someone is either creative or not tall. Mary is not old. Someone is not generous or not humble. Someone is both happy and wise. Someone is either funny or curious. | Alice is old. | contradiction | (![X]:((~calm(X)|calm(X))<=>(calm(X)&~old(X))))&
((?[X]:((brave(X)&~quiet(X))))<=>((~generous(alice)|patient(alice))))&
(![X]:((strong(X)&rich(X))=>(happy(X)&~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>((happy(john)|~funny(john))))&
(![X]:((humble(X)<~>~strong(X))=>(~happy(X)<~>happy(X))))&
(![X]:((brave(X)|curious(X))=>wise(X)))&
((?[X]:((kind(X)&~funny(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
((~funny(paul))=>(?[X]:(quiet(X))))&
(![X]:((rich(X)|wise(X))<=>quiet(X)))&
((?[X]:((old(X)<~>~strong(X))))=>(~wise(fred)))&
(![X]:((~generous(X)|calm(X))<=>(~curious(X)<~>~brave(X))))&
((?[X]:((patient(X)<~>generous(X))))=>(?[X]:((~funny(X)|~strong(X)))))&
(![X]:((~patient(X)|brave(X))=>~curious(X)))&
(![X]:((generous(X)<~>calm(X))=>(~wise(X)&~rich(X))))&
(![X]:((patient(X)|quiet(X))<=>~kind(X)))&
(((~happy(fred)&kind(fred)))<=>(?[X]:(~creative(X))))&
(?[X]:((creative(X)<~>~tall(X))))&
(~old(mary))&
(?[X]:((~generous(X)|~humble(X))))&
(?[X]:((happy(X)&wise(X))))&
(?[X]:((funny(X)<~>curious(X)))) | old(alice) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7885634704362074201961963
% SZS output start Proof for 7885634704362074201961963
1. ! [X0] : ((calm(X0) | ~calm(X0)) <=> (~old(X0) & calm(X0))) [input p0]
22. old(alice) [input hypothesis]
36. ! [X0] : (((calm(X0) | ~calm(X0)) | (old(X0) | ~calm(X0))) & ((~old(X0) & calm(X0)) | (~calm(X0) & calm(X0)))) [nnf transformation 1]
37. ! [X0] : ((calm(X0) | ~calm(X0) | old(X0) | ~calm(X0)) & ((~old(X0) & calm(X0)) | (~calm(X0) & calm(X0)))) [flattening 36]
80. ~old(X0) | calm(X0) [cnf transformation 37]
81. ~old(X0) | ~calm(X0) [cnf transformation 37]
137. old(alice) [cnf transformation 22]
140. ~old(X0) [subsumption resolution 80,81]
294. $false [subsumption resolution 137,140]
% SZS output end Proof for 7885634704362074201961963
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or old is either not creative or not wise. If someone is patient or not kind then lucy is not patient and vice versa. If someone is either old or quiet then susan is not brave or not kind and vice versa. Everyone who is both patient and not funny is either not funny or not calm and vice versa. If paul is not calm then paul is curious or patient and vice versa. Everyone who is kind is curious or not old. If someone is either kind or curious then john is both not tall and calm. Everyone who is not rich or not quiet is creative or not wise. Everyone who is either curious or not humble is both generous and happy and vice versa. Everyone who is not patient or patient is both calm and not generous. If someone is strong or not kind then someone is not humble or strong and vice versa. Everyone who is both not old and funny is both not creative and humble and vice versa. Everyone who is both not curious and wise is either not humble or not brave. Everyone who is either not humble or not curious is wise. Everyone who is old or happy is not old. Everyone who is not humble is old or not old. John is both kind and happy. Someone is both wise and curious. Someone is either strong or patient. Someone is either not wise or patient. Someone is happy or creative. Someone is both not generous and not tall. Susan is not generous or not old. | Lucy is funny. | entailment | (![X]:((~rich(X)<~>old(X))=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~kind(X))))<=>(~patient(lucy)))&
((?[X]:((old(X)<~>quiet(X))))<=>((~brave(susan)|~kind(susan))))&
(![X]:((patient(X)&~funny(X))<=>(~funny(X)<~>~calm(X))))&
((~calm(paul))<=>((curious(paul)|patient(paul))))&
(![X]:(kind(X)=>(curious(X)|~old(X))))&
((?[X]:((kind(X)<~>curious(X))))=>((~tall(john)&calm(john))))&
(![X]:((~rich(X)|~quiet(X))=>(creative(X)|~wise(X))))&
(![X]:((curious(X)<~>~humble(X))<=>(generous(X)&happy(X))))&
(![X]:((~patient(X)|patient(X))=>(calm(X)&~generous(X))))&
((?[X]:((strong(X)|~kind(X))))<=>(?[X]:((~humble(X)|strong(X)))))&
(![X]:((~old(X)&funny(X))<=>(~creative(X)&humble(X))))&
(![X]:((~curious(X)&wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~curious(X))=>wise(X)))&
(![X]:((old(X)|happy(X))=>~old(X)))&
(![X]:(~humble(X)=>(old(X)|~old(X))))&
((kind(john)&happy(john)))&
(?[X]:((wise(X)&curious(X))))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((~wise(X)<~>patient(X))))&
(?[X]:((happy(X)|creative(X))))&
(?[X]:((~generous(X)&~tall(X))))&
((~generous(susan)|~old(susan))) | funny(lucy) | [
"p1",
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1084217974883825814972557
% SZS output start Proof for 1084217974883825814972557
2. ? [X0] : (~kind(X0) | patient(X0)) <=> ~patient(lucy) [input p1]
4. ! [X0] : ((~funny(X0) & patient(X0)) <=> (~funny(X0) <~> ~calm(X0))) [input p3]
10. ! [X0] : ((patient(X0) | ~patient(X0)) => (~generous(X0) & calm(X0))) [input p9]
24. ~funny(lucy) [input hypothesis]
34. ! [X0] : ((~generous(X0) & calm(X0)) | (~patient(X0) & patient(X0))) [ennf transformation 10]
42. (? [X0] : (~kind(X0) | patient(X0)) | patient(lucy)) & (~patient(lucy) | ! [X0] : (kind(X0) & ~patient(X0))) [nnf transformation 2]
43. (? [X0] : (~kind(X0) | patient(X0)) | patient(lucy)) & (~patient(lucy) | ! [X1] : (kind(X1) & ~patient(X1))) [rectify 42]
44. ? [X0] : (~kind(X0) | patient(X0)) => (~kind(sK0) | patient(sK0)) [choice axiom]
45. ((~kind(sK0) | patient(sK0)) | patient(lucy)) & (~patient(lucy) | ! [X1] : (kind(X1) & ~patient(X1))) [skolemisation 43,44]
51. ! [X0] : (((~funny(X0) & patient(X0)) | ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0)))) & (((calm(X0) | funny(X0)) & (~calm(X0) | ~funny(X0))) | (funny(X0) | ~patient(X0)))) [nnf transformation 4]
52. ! [X0] : (((~funny(X0) & patient(X0)) | ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0)))) & (((calm(X0) | funny(X0)) & (~calm(X0) | ~funny(X0))) | funny(X0) | ~patient(X0))) [flattening 51]
83. ~patient(lucy) | ~patient(X1) [cnf transformation 45]
93. calm(X0) | funny(X0) | funny(X0) | ~patient(X0) [cnf transformation 52]
94. ~calm(X0) | patient(X0) | funny(X0) [cnf transformation 52]
97. ~funny(X0) | ~funny(X0) | calm(X0) [cnf transformation 52]
112. calm(X0) | patient(X0) [cnf transformation 34]
142. ~funny(lucy) [cnf transformation 24]
144. calm(X0) | funny(X0) | ~patient(X0) [duplicate literal removal 93]
145. ~funny(X0) | calm(X0) [duplicate literal removal 97]
147. 1 <=> patient(lucy) [avatar definition]
149. patient(lucy) <- (1) [avatar component clause 147]
164. 5 <=> ! [X1] : ~patient(X1) [avatar definition]
165. ~patient(X1) <- (5) [avatar component clause 164]
166. 5 | ~1 [avatar split clause 83,147,164]
195. ~patient(X0) | calm(X0) [subsumption resolution 144,145]
221. calm(X0) [subsumption resolution 112,195]
283. funny(X0) | patient(X0) [resolution 94,221]
284. patient(lucy) [resolution 283,142]
288. 1 [avatar split clause 284,147]
289. $false <- (1, 5) [subsumption resolution 149,165]
290. ~1 | ~5 [avatar contradiction clause 289]
291. $false [avatar sat refutation 166,288,290]
% SZS output end Proof for 1084217974883825814972557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or kind is either old or not generous.
Everyone who is either kind or not happy is both not happy and humble and vice versa.
Everyone who is both not happy and not wise is not old and vice versa.
Everyone who is old or not strong is either patient or not creative.
If mary is humble then lucy is not curious and vice versa.
Everyone who is not calm is not wise and vice versa.
If someone is both strong and creative then john is old or tall and vice versa.
Everyone who is not old or happy is either not happy or not kind and vice versa.
Everyone who is rich or not generous is not brave.
If someone is either not curious or not funny then lucy is not calm or not old.
If fred is not humble then someone is either curious or not generous and vice versa.
Everyone who is not humble is both not quiet and not happy and vice versa.
Everyone who is rich or not curious is wise or not creative.
If john is either not old or curious then mary is not happy or not patient.
Everyone who is both happy and kind is not old.
Everyone who is both not creative and humble is patient or tall and vice versa.
Someone is both calm and not funny.
John is not happy or not brave.
Fred is either strong or rich.
Someone is not quiet or funny.
Someone is funny or humble. | John is brave. | neutral | (![X]:((calm(X)|kind(X))=>(old(X)<~>~generous(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~happy(X)&humble(X))))&
(![X]:((~happy(X)&~wise(X))<=>~old(X)))&
(![X]:((old(X)|~strong(X))=>(patient(X)<~>~creative(X))))&
((humble(mary))<=>(~curious(lucy)))&
(![X]:(~calm(X)<=>~wise(X)))&
((?[X]:((strong(X)&creative(X))))<=>((old(john)|tall(john))))&
(![X]:((~old(X)|happy(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((rich(X)|~generous(X))=>~brave(X)))&
((?[X]:((~curious(X)<~>~funny(X))))=>((~calm(lucy)|~old(lucy))))&
((~humble(fred))<=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:(~humble(X)<=>(~quiet(X)&~happy(X))))&
(![X]:((rich(X)|~curious(X))=>(wise(X)|~creative(X))))&
(((~old(john)<~>curious(john)))=>((~happy(mary)|~patient(mary))))&
(![X]:((happy(X)&kind(X))=>~old(X)))&
(![X]:((~creative(X)&humble(X))<=>(patient(X)|tall(X))))&
(?[X]:((calm(X)&~funny(X))))&
((~happy(john)|~brave(john)))&
((strong(fred)<~>rich(fred)))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((funny(X)|humble(X)))) | brave(john) | [] | null | 0 |
Everyone who is happy or not calm is both kind and not happy and vice versa.
Everyone who is either not curious or not generous is not humble and vice versa.
Everyone who is not creative is either strong or patient and vice versa.
Everyone who is both not wise and not brave is brave and vice versa.
Everyone who is both kind and not old is both not kind and humble.
If lucy is both not patient and creative then someone is tall or brave and vice versa.
Everyone who is not brave or not kind is curious or not rich and vice versa.
Everyone who is not calm or creative is not wise or brave and vice versa.
If someone is either rich or brave then lucy is both humble and calm and vice versa.
Everyone who is both not quiet and not wise is not old or strong and vice versa.
Everyone who is both not kind and not curious is brave.
If alice is not patient then someone is humble and vice versa.
If someone is either creative or not calm then someone is quiet or not rich.
If someone is not quiet or strong then mary is both not quiet and creative.
Everyone who is quiet or not quiet is calm or not creative and vice versa.
Someone is either wise or brave.
Someone is both not brave and not tall.
Fred is funny.
Someone is quiet or not old.
John is both not generous and funny.
John is either calm or rich.
Mary is not creative or kind. | John is not patient. | contradiction | (![X]:((happy(X)|~calm(X))<=>(kind(X)&~happy(X))))&
(![X]:((~curious(X)<~>~generous(X))<=>~humble(X)))&
(![X]:(~creative(X)<=>(strong(X)<~>patient(X))))&
(![X]:((~wise(X)&~brave(X))<=>brave(X)))&
(![X]:((kind(X)&~old(X))=>(~kind(X)&humble(X))))&
(((~patient(lucy)&creative(lucy)))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~brave(X)|~kind(X))<=>(curious(X)|~rich(X))))&
(![X]:((~calm(X)|creative(X))<=>(~wise(X)|brave(X))))&
((?[X]:((rich(X)<~>brave(X))))<=>((humble(lucy)&calm(lucy))))&
(![X]:((~quiet(X)&~wise(X))<=>(~old(X)|strong(X))))&
(![X]:((~kind(X)&~curious(X))=>brave(X)))&
((~patient(alice))<=>(?[X]:(humble(X))))&
((?[X]:((creative(X)<~>~calm(X))))=>(?[X]:((quiet(X)|~rich(X)))))&
((?[X]:((~quiet(X)|strong(X))))=>((~quiet(mary)&creative(mary))))&
(![X]:((quiet(X)|~quiet(X))<=>(calm(X)|~creative(X))))&
(?[X]:((wise(X)<~>brave(X))))&
(?[X]:((~brave(X)&~tall(X))))&
(funny(fred))&
(?[X]:((quiet(X)|~old(X))))&
((~generous(john)&funny(john)))&
((calm(john)<~>rich(john)))&
((~creative(mary)|kind(mary))) | ~patient(john) | [
"p2",
"p3",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2541969677900507815806150
% SZS output start Proof for 2541969677900507815806150
3. ! [X0] : (~creative(X0) <=> (strong(X0) <~> patient(X0))) [input p2]
4. ! [X0] : ((~brave(X0) & ~wise(X0)) <=> brave(X0)) [input p3]
8. ! [X0] : ((creative(X0) | ~calm(X0)) <=> (brave(X0) | ~wise(X0))) [input p7]
10. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (strong(X0) | ~old(X0))) [input p9]
23. ~patient(john) [input hypothesis]
36. ! [X0] : ((~creative(X0) | ((strong(X0) | ~patient(X0)) & (patient(X0) | ~strong(X0)))) & (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | creative(X0))) [nnf transformation 3]
37. ! [X0] : (((~brave(X0) & ~wise(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) | wise(X0)))) [nnf transformation 4]
38. ! [X0] : (((~brave(X0) & ~wise(X0)) | ~brave(X0)) & (brave(X0) | brave(X0) | wise(X0))) [flattening 37]
46. ! [X0] : (((creative(X0) | ~calm(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (~creative(X0) & calm(X0)))) [nnf transformation 8]
47. ! [X0] : ((creative(X0) | ~calm(X0) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | (~creative(X0) & calm(X0)))) [flattening 46]
53. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~strong(X0) & old(X0))) & ((strong(X0) | ~old(X0)) | (wise(X0) | quiet(X0)))) [nnf transformation 10]
54. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~strong(X0) & old(X0))) & (strong(X0) | ~old(X0) | wise(X0) | quiet(X0))) [flattening 53]
82. patient(X0) | strong(X0) | creative(X0) [cnf transformation 36]
86. brave(X0) | brave(X0) | wise(X0) [cnf transformation 38]
88. ~brave(X0) | ~brave(X0) [cnf transformation 38]
101. brave(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 47]
114. ~wise(X0) | ~strong(X0) [cnf transformation 54]
137. ~patient(john) [cnf transformation 23]
139. brave(X0) | wise(X0) [duplicate literal removal 86]
140. ~brave(X0) [duplicate literal removal 88]
143. wise(X0) [subsumption resolution 139,140]
164. ~wise(X0) | ~creative(X0) [subsumption resolution 101,140]
165. ~creative(X0) [subsumption resolution 164,143]
184. ~strong(X0) [subsumption resolution 114,143]
244. strong(john) | creative(john) [resolution 82,137]
247. creative(john) [subsumption resolution 244,184]
248. $false [subsumption resolution 247,165]
% SZS output end Proof for 2541969677900507815806150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not old is creative or not rich and vice versa. Everyone who is tall is patient or not humble. If someone is strong then someone is either creative or not strong and vice versa. Everyone who is either old or patient is wise. Everyone who is either not quiet or not calm is both not funny and not curious. Everyone who is either not humble or funny is both not old and curious. If alice is either strong or quiet then someone is happy or not happy and vice versa. Everyone who is kind or not kind is both not quiet and patient and vice versa. Everyone who is strong is not kind. If john is either brave or not rich then someone is not wise or curious and vice versa. If alice is either not happy or not funny then paul is both not quiet and happy and vice versa. If lucy is funny or humble then lucy is both quiet and not creative and vice versa. Everyone who is either kind or strong is not rich. Everyone who is not wise or kind is either not tall or not creative and vice versa. If someone is either patient or curious then someone is not generous or not wise and vice versa. If mary is both not brave and humble then someone is funny. Susan is both humble and curious. Someone is not patient or not wise. Someone is brave. Mary is both brave and not wise. Someone is quiet or not generous. Someone is calm or not funny. Alice is not wise or humble. | Lucy is not creative. | entailment | (![X]:((curious(X)<~>~old(X))<=>(creative(X)|~rich(X))))&
(![X]:(tall(X)=>(patient(X)|~humble(X))))&
((?[X]:(strong(X)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((old(X)<~>patient(X))=>wise(X)))&
(![X]:((~quiet(X)<~>~calm(X))=>(~funny(X)&~curious(X))))&
(![X]:((~humble(X)<~>funny(X))=>(~old(X)&curious(X))))&
(((strong(alice)<~>quiet(alice)))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((kind(X)|~kind(X))<=>(~quiet(X)&patient(X))))&
(![X]:(strong(X)=>~kind(X)))&
(((brave(john)<~>~rich(john)))<=>(?[X]:((~wise(X)|curious(X)))))&
(((~happy(alice)<~>~funny(alice)))<=>((~quiet(paul)&happy(paul))))&
(((funny(lucy)|humble(lucy)))<=>((quiet(lucy)&~creative(lucy))))&
(![X]:((kind(X)<~>strong(X))=>~rich(X)))&
(![X]:((~wise(X)|kind(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:((patient(X)<~>curious(X))))<=>(?[X]:((~generous(X)|~wise(X)))))&
(((~brave(mary)&humble(mary)))=>(?[X]:(funny(X))))&
((humble(susan)&curious(susan)))&
(?[X]:((~patient(X)|~wise(X))))&
(?[X]:(brave(X)))&
((brave(mary)&~wise(mary)))&
(?[X]:((quiet(X)|~generous(X))))&
(?[X]:((calm(X)|~funny(X))))&
((~wise(alice)|humble(alice))) | ~creative(lucy) | [
"p0",
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1434103572907347140664501
% SZS output start Proof for 1434103572907347140664501
1. ! [X0] : ((curious(X0) <~> ~old(X0)) <=> (~rich(X0) | creative(X0))) [input p0]
6. ! [X0] : ((~humble(X0) <~> funny(X0)) => (curious(X0) & ~old(X0))) [input p5]
8. ! [X0] : ((~kind(X0) | kind(X0)) <=> (patient(X0) & ~quiet(X0))) [input p7]
12. (humble(lucy) | funny(lucy)) <=> (~creative(lucy) & quiet(lucy)) [input p11]
24. creative(lucy) [input hypothesis]
31. ! [X0] : ((curious(X0) & ~old(X0)) | (~humble(X0) <=> funny(X0))) [ennf transformation 6]
36. ! [X0] : ((((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (rich(X0) & ~creative(X0))) & ((~rich(X0) | creative(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))))) [nnf transformation 1]
37. ! [X0] : ((((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (rich(X0) & ~creative(X0))) & (~rich(X0) | creative(X0) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))))) [flattening 36]
45. ! [X0] : ((curious(X0) & ~old(X0)) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [nnf transformation 31]
50. ! [X0] : (((~kind(X0) | kind(X0)) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | (kind(X0) & ~kind(X0)))) [nnf transformation 8]
51. ! [X0] : ((~kind(X0) | kind(X0) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | (kind(X0) & ~kind(X0)))) [flattening 50]
58. ((humble(lucy) | funny(lucy)) | (creative(lucy) | ~quiet(lucy))) & ((~creative(lucy) & quiet(lucy)) | (~humble(lucy) & ~funny(lucy))) [nnf transformation 12]
59. (humble(lucy) | funny(lucy) | creative(lucy) | ~quiet(lucy)) & ((~creative(lucy) & quiet(lucy)) | (~humble(lucy) & ~funny(lucy))) [flattening 58]
82. ~creative(X0) | ~curious(X0) | old(X0) [cnf transformation 37]
95. ~old(X0) | funny(X0) | humble(X0) [cnf transformation 45]
97. funny(X0) | curious(X0) | humble(X0) [cnf transformation 45]
105. ~quiet(X0) | ~kind(X0) [cnf transformation 51]
106. ~quiet(X0) | kind(X0) [cnf transformation 51]
123. quiet(lucy) | ~funny(lucy) [cnf transformation 59]
124. quiet(lucy) | ~humble(lucy) [cnf transformation 59]
152. creative(lucy) [cnf transformation 24]
197. ~quiet(X0) [subsumption resolution 105,106]
245. 20 <=> humble(lucy) [avatar definition]
247. ~humble(lucy) <- (~20) [avatar component clause 245]
249. 21 <=> creative(lucy) [avatar definition]
250. creative(lucy) <- (21) [avatar component clause 249]
254. 22 <=> funny(lucy) [avatar definition]
256. ~funny(lucy) <- (~22) [avatar component clause 254]
258. ~humble(lucy) [subsumption resolution 124,197]
259. ~20 [avatar split clause 258,245]
260. ~funny(lucy) [subsumption resolution 123,197]
261. ~22 [avatar split clause 260,254]
322. 21 [avatar split clause 152,249]
329. 35 <=> old(lucy) [avatar definition]
330. old(lucy) <- (35) [avatar component clause 329]
333. 36 <=> curious(lucy) [avatar definition]
337. ~curious(lucy) | old(lucy) <- (21) [resolution 82,250]
425. curious(lucy) | humble(lucy) <- (~22) [resolution 97,256]
440. 35 | ~36 | ~21 [avatar split clause 337,249,333,329]
441. curious(lucy) <- (~20, ~22) [subsumption resolution 425,247]
442. 36 | 20 | 22 [avatar split clause 441,254,245,333]
443. funny(lucy) | humble(lucy) <- (35) [resolution 330,95]
446. humble(lucy) <- (~22, 35) [subsumption resolution 443,256]
447. $false <- (~20, ~22, 35) [subsumption resolution 446,247]
448. 20 | 22 | ~35 [avatar contradiction clause 447]
449. $false [avatar sat refutation 259,261,322,440,442,448]
% SZS output end Proof for 1434103572907347140664501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both generous and not tall then someone is either not rich or not kind.
If fred is not patient then fred is not kind or patient and vice versa.
Everyone who is both calm and humble is not humble or not wise and vice versa.
Everyone who is either old or not old is both funny and wise.
Everyone who is wise or not kind is not strong.
Everyone who is tall is strong or old and vice versa.
If fred is either creative or not patient then someone is strong or creative and vice versa.
Everyone who is either curious or not quiet is not kind or not happy and vice versa.
Everyone who is either not funny or not happy is both not creative and generous and vice versa.
Everyone who is not curious or not quiet is both not old and not kind.
If lucy is either not patient or brave then susan is tall or not rich and vice versa.
Everyone who is not funny is humble.
If fred is either not curious or not quiet then someone is either wise or not old.
Everyone who is not kind is either not calm or quiet.
Everyone who is generous or not funny is either not brave or not funny.
Everyone who is not tall or humble is not brave or humble.
Paul is not happy or not old.
Someone is either not generous or humble.
Someone is not happy or humble.
Someone is not kind.
Susan is either not creative or kind.
Paul is calm or kind.
Someone is happy. | Lucy is not quiet. | neutral | (((generous(paul)&~tall(paul)))=>(?[X]:((~rich(X)<~>~kind(X)))))&
((~patient(fred))<=>((~kind(fred)|patient(fred))))&
(![X]:((calm(X)&humble(X))<=>(~humble(X)|~wise(X))))&
(![X]:((old(X)<~>~old(X))=>(funny(X)&wise(X))))&
(![X]:((wise(X)|~kind(X))=>~strong(X)))&
(![X]:(tall(X)<=>(strong(X)|old(X))))&
(((creative(fred)<~>~patient(fred)))<=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~creative(X)&generous(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~old(X)&~kind(X))))&
(((~patient(lucy)<~>brave(lucy)))<=>((tall(susan)|~rich(susan))))&
(![X]:(~funny(X)=>humble(X)))&
(((~curious(fred)<~>~quiet(fred)))=>(?[X]:((wise(X)<~>~old(X)))))&
(![X]:(~kind(X)=>(~calm(X)<~>quiet(X))))&
(![X]:((generous(X)|~funny(X))=>(~brave(X)<~>~funny(X))))&
(![X]:((~tall(X)|humble(X))=>(~brave(X)|humble(X))))&
((~happy(paul)|~old(paul)))&
(?[X]:((~generous(X)<~>humble(X))))&
(?[X]:((~happy(X)|humble(X))))&
(?[X]:(~kind(X)))&
((~creative(susan)<~>kind(susan)))&
((calm(paul)|kind(paul)))&
(?[X]:(happy(X))) | ~quiet(lucy) | [] | null | 0 |
If john is brave then someone is quiet. If alice is not generous then susan is both not tall and not strong and vice versa. If alice is old then john is curious and vice versa. Everyone who is old is not creative and vice versa. Everyone who is tall is both humble and strong. If someone is quiet or generous then someone is either wise or kind and vice versa. Everyone who is not happy is creative. Everyone who is creative or happy is either not creative or happy. Everyone who is not rich or not brave is either tall or not patient. Everyone who is creative or calm is either not rich or old and vice versa. If alice is both not generous and kind then alice is both not brave and humble and vice versa. Everyone who is old is either not creative or rich and vice versa. If susan is brave then susan is either not kind or not strong and vice versa. If someone is either not wise or wise then alice is both not kind and not old and vice versa. If someone is not funny or happy then lucy is kind and vice versa. Everyone who is both generous and not humble is either not curious or patient. Someone is either strong or tall. Fred is both not generous and curious. Paul is not strong. John is both calm and not kind. Alice is either not calm or curious. Susan is either not calm or not wise. | Susan is old. | contradiction | ((brave(john))=>(?[X]:(quiet(X))))&
((~generous(alice))<=>((~tall(susan)&~strong(susan))))&
((old(alice))<=>(curious(john)))&
(![X]:(old(X)<=>~creative(X)))&
(![X]:(tall(X)=>(humble(X)&strong(X))))&
((?[X]:((quiet(X)|generous(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
(![X]:(~happy(X)=>creative(X)))&
(![X]:((creative(X)|happy(X))=>(~creative(X)<~>happy(X))))&
(![X]:((~rich(X)|~brave(X))=>(tall(X)<~>~patient(X))))&
(![X]:((creative(X)|calm(X))<=>(~rich(X)<~>old(X))))&
(((~generous(alice)&kind(alice)))<=>((~brave(alice)&humble(alice))))&
(![X]:(old(X)<=>(~creative(X)<~>rich(X))))&
((brave(susan))<=>((~kind(susan)<~>~strong(susan))))&
((?[X]:((~wise(X)<~>wise(X))))<=>((~kind(alice)&~old(alice))))&
((?[X]:((~funny(X)|happy(X))))<=>(kind(lucy)))&
(![X]:((generous(X)&~humble(X))=>(~curious(X)<~>patient(X))))&
(?[X]:((strong(X)<~>tall(X))))&
((~generous(fred)&curious(fred)))&
(~strong(paul))&
((calm(john)&~kind(john)))&
((~calm(alice)<~>curious(alice)))&
((~calm(susan)<~>~wise(susan))) | old(susan) | [
"p3",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3862048166301737247295542
% SZS output start Proof for 3862048166301737247295542
4. ! [X0] : (old(X0) <=> ~creative(X0)) [input p3]
7. ! [X0] : (~happy(X0) => creative(X0)) [input p6]
8. ! [X0] : ((happy(X0) | creative(X0)) => (~creative(X0) <~> happy(X0))) [input p7]
23. old(susan) [input hypothesis]
27. ! [X0] : (creative(X0) | happy(X0)) [ennf transformation 7]
28. ! [X0] : ((~creative(X0) <~> happy(X0)) | (~happy(X0) & ~creative(X0))) [ennf transformation 8]
37. ! [X0] : ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))) [nnf transformation 4]
43. ! [X0] : (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~happy(X0) & ~creative(X0))) [nnf transformation 28]
72. ~creative(X0) | ~old(X0) [cnf transformation 37]
82. creative(X0) | happy(X0) [cnf transformation 27]
86. ~happy(X0) | creative(X0) | ~happy(X0) [cnf transformation 43]
131. old(susan) [cnf transformation 23]
137. ~happy(X0) | creative(X0) [duplicate literal removal 86]
206. creative(X0) [subsumption resolution 137,82]
270. ~old(X0) [resolution 72,206]
272. $false [resolution 270,131]
% SZS output end Proof for 3862048166301737247295542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble is both not happy and funny and vice versa. If someone is wise or patient then mary is patient or not old and vice versa. Everyone who is not brave or not rich is either not calm or not wise and vice versa. Everyone who is not patient or not old is both not brave and not quiet and vice versa. Everyone who is either brave or not kind is patient. Everyone who is not patient is both not wise and not generous and vice versa. Everyone who is not humble or generous is either happy or old. If someone is not generous or not wise then mary is not calm or kind and vice versa. If paul is both quiet and curious then alice is both curious and not humble. Everyone who is not rich or not strong is either not creative or not rich. Everyone who is both patient and not brave is kind or not humble and vice versa. If someone is both tall and funny then lucy is curious. Everyone who is both not old and funny is both not old and kind and vice versa. Everyone who is both not calm and patient is not funny. Everyone who is either not curious or funny is not funny or strong. Everyone who is wise is either not humble or calm and vice versa. Someone is either rich or not kind. Alice is not kind. John is not quiet. Paul is not funny or patient. Someone is either quiet or calm. John is both not quiet and not wise. Alice is either not old or generous. Someone is not kind. | Lucy is not patient. | contradiction | (![X]:((~curious(X)<~>~humble(X))<=>(~happy(X)&funny(X))))&
((?[X]:((wise(X)|patient(X))))<=>((patient(mary)|~old(mary))))&
(![X]:((~brave(X)|~rich(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((~patient(X)|~old(X))<=>(~brave(X)&~quiet(X))))&
(![X]:((brave(X)<~>~kind(X))=>patient(X)))&
(![X]:(~patient(X)<=>(~wise(X)&~generous(X))))&
(![X]:((~humble(X)|generous(X))=>(happy(X)<~>old(X))))&
((?[X]:((~generous(X)|~wise(X))))<=>((~calm(mary)|kind(mary))))&
(((quiet(paul)&curious(paul)))=>((curious(alice)&~humble(alice))))&
(![X]:((~rich(X)|~strong(X))=>(~creative(X)<~>~rich(X))))&
(![X]:((patient(X)&~brave(X))<=>(kind(X)|~humble(X))))&
((?[X]:((tall(X)&funny(X))))=>(curious(lucy)))&
(![X]:((~old(X)&funny(X))<=>(~old(X)&kind(X))))&
(![X]:((~calm(X)&patient(X))=>~funny(X)))&
(![X]:((~curious(X)<~>funny(X))=>(~funny(X)|strong(X))))&
(![X]:(wise(X)<=>(~humble(X)<~>calm(X))))&
(?[X]:((rich(X)<~>~kind(X))))&
(~kind(alice))&
(~quiet(john))&
((~funny(paul)|patient(paul)))&
(?[X]:((quiet(X)<~>calm(X))))&
((~quiet(john)&~wise(john)))&
((~old(alice)<~>generous(alice)))&
(?[X]:(~kind(X))) | ~patient(lucy) | [
"p3",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6325458909584170376754578
% SZS output start Proof for 6325458909584170376754578
4. ! [X0] : ((~old(X0) | ~patient(X0)) <=> (~quiet(X0) & ~brave(X0))) [input p3]
5. ! [X0] : ((brave(X0) <~> ~kind(X0)) => patient(X0)) [input p4]
11. ! [X0] : ((~brave(X0) & patient(X0)) <=> (~humble(X0) | kind(X0))) [input p10]
25. ~patient(lucy) [input hypothesis]
29. ! [X0] : (patient(X0) | (brave(X0) <=> ~kind(X0))) [ennf transformation 5]
45. ! [X0] : (((~old(X0) | ~patient(X0)) | (quiet(X0) | brave(X0))) & ((~quiet(X0) & ~brave(X0)) | (old(X0) & patient(X0)))) [nnf transformation 4]
46. ! [X0] : ((~old(X0) | ~patient(X0) | quiet(X0) | brave(X0)) & ((~quiet(X0) & ~brave(X0)) | (old(X0) & patient(X0)))) [flattening 45]
47. ! [X0] : (patient(X0) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0)))) [nnf transformation 29]
57. ! [X0] : (((~brave(X0) & patient(X0)) | (humble(X0) & ~kind(X0))) & ((~humble(X0) | kind(X0)) | (brave(X0) | ~patient(X0)))) [nnf transformation 11]
58. ! [X0] : (((~brave(X0) & patient(X0)) | (humble(X0) & ~kind(X0))) & (~humble(X0) | kind(X0) | brave(X0) | ~patient(X0))) [flattening 57]
87. ~brave(X0) | patient(X0) [cnf transformation 46]
93. patient(X0) | brave(X0) | kind(X0) [cnf transformation 47]
110. patient(X0) | ~kind(X0) [cnf transformation 58]
135. ~patient(lucy) [cnf transformation 25]
163. patient(X0) | kind(X0) [subsumption resolution 93,87]
208. patient(X0) [subsumption resolution 110,163]
241. $false [subsumption resolution 135,208]
% SZS output end Proof for 6325458909584170376754578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not kind and patient then someone is either humble or funny and vice versa.
If someone is quiet then lucy is both not curious and old.
Everyone who is either kind or not brave is both happy and not strong.
If someone is not curious then lucy is tall and vice versa.
Everyone who is both not patient and happy is not funny or happy.
Everyone who is old or happy is both kind and not creative.
Everyone who is either not curious or not old is either strong or calm and vice versa.
If susan is patient then lucy is old.
If someone is not happy then someone is either calm or wise and vice versa.
Everyone who is either calm or not happy is either kind or not strong and vice versa.
If mary is not happy or rich then someone is either calm or kind and vice versa.
Everyone who is not creative is curious or not kind.
Everyone who is not funny is both old and not strong.
If someone is both not funny and not curious then someone is not patient.
Everyone who is curious is not calm and vice versa.
Everyone who is old is either not creative or not kind.
Mary is both not kind and not quiet.
Someone is happy.
John is both not humble and not brave.
Someone is creative.
Someone is strong or not kind.
Someone is old.
Paul is both not calm and not quiet.
Someone is kind or creative. | Mary is not calm. | contradiction | (((~kind(paul)&patient(paul)))<=>(?[X]:((humble(X)<~>funny(X)))))&
((?[X]:(quiet(X)))=>((~curious(lucy)&old(lucy))))&
(![X]:((kind(X)<~>~brave(X))=>(happy(X)&~strong(X))))&
((?[X]:(~curious(X)))<=>(tall(lucy)))&
(![X]:((~patient(X)&happy(X))=>(~funny(X)|happy(X))))&
(![X]:((old(X)|happy(X))=>(kind(X)&~creative(X))))&
(![X]:((~curious(X)<~>~old(X))<=>(strong(X)<~>calm(X))))&
((patient(susan))=>(old(lucy)))&
((?[X]:(~happy(X)))<=>(?[X]:((calm(X)<~>wise(X)))))&
(![X]:((calm(X)<~>~happy(X))<=>(kind(X)<~>~strong(X))))&
(((~happy(mary)|rich(mary)))<=>(?[X]:((calm(X)<~>kind(X)))))&
(![X]:(~creative(X)=>(curious(X)|~kind(X))))&
(![X]:(~funny(X)=>(old(X)&~strong(X))))&
((?[X]:((~funny(X)&~curious(X))))=>(?[X]:(~patient(X))))&
(![X]:(curious(X)<=>~calm(X)))&
(![X]:(old(X)=>(~creative(X)<~>~kind(X))))&
((~kind(mary)&~quiet(mary)))&
(?[X]:(happy(X)))&
((~humble(john)&~brave(john)))&
(?[X]:(creative(X)))&
(?[X]:((strong(X)|~kind(X))))&
(?[X]:(old(X)))&
((~calm(paul)&~quiet(paul)))&
(?[X]:((kind(X)|creative(X)))) | ~calm(mary) | [
"p5",
"p6",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8717637136760097669931288
% SZS output start Proof for 8717637136760097669931288
6. ! [X0] : ((happy(X0) | old(X0)) => (~creative(X0) & kind(X0))) [input p5]
7. ! [X0] : ((~curious(X0) <~> ~old(X0)) <=> (strong(X0) <~> calm(X0))) [input p6]
10. ! [X0] : ((calm(X0) <~> ~happy(X0)) <=> (kind(X0) <~> ~strong(X0))) [input p9]
15. ! [X0] : (curious(X0) <=> ~calm(X0)) [input p14]
17. ~quiet(mary) & ~kind(mary) [input p16]
25. ~calm(mary) [input hypothesis]
29. ~kind(mary) [pure predicate removal 17]
34. ! [X0] : ((~creative(X0) & kind(X0)) | (~happy(X0) & ~old(X0))) [ennf transformation 6]
51. ! [X0] : ((((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) & (((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))))) [nnf transformation 7]
57. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0)))) & (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [nnf transformation 10]
66. ! [X0] : ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))) [nnf transformation 15]
91. ~old(X0) | kind(X0) [cnf transformation 34]
92. ~happy(X0) | kind(X0) [cnf transformation 34]
96. ~curious(X0) | strong(X0) | calm(X0) | old(X0) [cnf transformation 51]
109. ~strong(X0) | kind(X0) | calm(X0) | happy(X0) [cnf transformation 57]
112. ~happy(X0) | calm(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 57]
127. calm(X0) | curious(X0) [cnf transformation 66]
130. ~kind(mary) [cnf transformation 29]
139. ~calm(mary) [cnf transformation 25]
216. ~strong(X0) | calm(X0) | ~happy(X0) [subsumption resolution 112,92]
218. ~strong(X0) | kind(X0) | calm(X0) [subsumption resolution 109,216]
291. curious(mary) [resolution 127,139]
382. strong(mary) | calm(mary) | old(mary) [resolution 96,291]
393. strong(mary) | old(mary) [subsumption resolution 382,139]
395. 40 <=> old(mary) [avatar definition]
397. old(mary) <- (40) [avatar component clause 395]
399. 41 <=> strong(mary) [avatar definition]
401. strong(mary) <- (41) [avatar component clause 399]
402. 40 | 41 [avatar split clause 393,399,395]
510. kind(mary) <- (40) [resolution 397,91]
511. $false <- (40) [subsumption resolution 510,130]
512. ~40 [avatar contradiction clause 511]
537. kind(mary) | calm(mary) <- (41) [resolution 401,218]
538. calm(mary) <- (41) [subsumption resolution 537,130]
539. $false <- (41) [subsumption resolution 538,139]
540. ~41 [avatar contradiction clause 539]
541. $false [avatar sat refutation 402,512,540]
% SZS output end Proof for 8717637136760097669931288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or quiet is not old and vice versa.
If someone is both not humble and creative then fred is both not calm and not rich.
If paul is either generous or patient then alice is strong.
Everyone who is either not creative or not generous is not quiet.
Everyone who is both not old and old is not quiet.
If someone is both calm and not brave then someone is either not quiet or happy.
If someone is both curious and not generous then someone is quiet and vice versa.
Everyone who is either funny or brave is funny or not brave and vice versa.
Everyone who is both not generous and curious is both not creative and not generous and vice versa.
Everyone who is both not quiet and tall is either curious or generous.
If paul is both not happy and not rich then paul is quiet.
If susan is rich then lucy is either not quiet or kind and vice versa.
Everyone who is creative is calm and vice versa.
If someone is happy or not curious then mary is either patient or kind and vice versa.
Everyone who is not funny is either rich or old.
Alice is both not rich and not tall.
John is either not tall or happy.
John is not kind.
Someone is not curious.
Paul is happy or not wise. | Fred is not funny. | contradiction | (![X]:((~kind(X)|quiet(X))<=>~old(X)))&
((?[X]:((~humble(X)&creative(X))))=>((~calm(fred)&~rich(fred))))&
(((generous(paul)<~>patient(paul)))=>(strong(alice)))&
(![X]:((~creative(X)<~>~generous(X))=>~quiet(X)))&
(![X]:((~old(X)&old(X))=>~quiet(X)))&
((?[X]:((calm(X)&~brave(X))))=>(?[X]:((~quiet(X)<~>happy(X)))))&
((?[X]:((curious(X)&~generous(X))))<=>(?[X]:(quiet(X))))&
(![X]:((funny(X)<~>brave(X))<=>(funny(X)|~brave(X))))&
(![X]:((~generous(X)&curious(X))<=>(~creative(X)&~generous(X))))&
(![X]:((~quiet(X)&tall(X))=>(curious(X)<~>generous(X))))&
(((~happy(paul)&~rich(paul)))=>(quiet(paul)))&
((rich(susan))<=>((~quiet(lucy)<~>kind(lucy))))&
(![X]:(creative(X)<=>calm(X)))&
((?[X]:((happy(X)|~curious(X))))<=>((patient(mary)<~>kind(mary))))&
(![X]:(~funny(X)=>(rich(X)<~>old(X))))&
((~rich(alice)&~tall(alice)))&
((~tall(john)<~>happy(john)))&
(~kind(john))&
(?[X]:(~curious(X)))&
((happy(paul)|~wise(paul))) | ~funny(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 9018816071641380605593211
% SZS output start Proof for 9018816071641380605593211
8. ! [X0] : ((funny(X0) <~> brave(X0)) <=> (~brave(X0) | funny(X0))) [input p7]
21. ~funny(fred) [input hypothesis]
48. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (brave(X0) & ~funny(X0))) & ((~brave(X0) | funny(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 8]
49. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (brave(X0) & ~funny(X0))) & (~brave(X0) | funny(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [flattening 48]
75. ~brave(X0) | funny(X0) | funny(X0) | ~brave(X0) [cnf transformation 49]
77. brave(X0) | funny(X0) | brave(X0) [cnf transformation 49]
107. ~funny(fred) [cnf transformation 21]
108. ~brave(X0) | funny(X0) [duplicate literal removal 75]
109. brave(X0) | funny(X0) [duplicate literal removal 77]
145. funny(X0) [subsumption resolution 108,109]
213. $false [subsumption resolution 107,145]
% SZS output end Proof for 9018816071641380605593211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not rich then someone is wise and vice versa. Everyone who is both not quiet and not old is happy. Everyone who is not humble or brave is humble and vice versa. If alice is either funny or creative then someone is strong or not patient and vice versa. If fred is not wise or rich then someone is generous. If alice is funny then someone is both brave and not patient. If someone is either old or not quiet then fred is not rich or happy. If someone is not humble then mary is generous. If alice is both not quiet and not creative then someone is both kind and happy and vice versa. If paul is brave or not quiet then someone is either not funny or old. If someone is both not humble and not tall then john is not humble or not tall. If someone is both not old and patient then someone is both patient and old. Everyone who is either not strong or not patient is either not patient or not generous and vice versa. If paul is either calm or brave then paul is either quiet or not brave and vice versa. If mary is kind or quiet then someone is both not patient and not generous. Everyone who is both not happy and quiet is both creative and humble and vice versa. Someone is curious or patient. Someone is generous. Someone is both generous and happy. Someone is not rich or not wise. Paul is not rich or not quiet. Alice is rich or not kind. John is both curious and calm. Someone is not quiet or funny. | Alice is brave. | entailment | ((?[X]:((generous(X)<~>~rich(X))))<=>(?[X]:(wise(X))))&
(![X]:((~quiet(X)&~old(X))=>happy(X)))&
(![X]:((~humble(X)|brave(X))<=>humble(X)))&
(((funny(alice)<~>creative(alice)))<=>(?[X]:((strong(X)|~patient(X)))))&
(((~wise(fred)|rich(fred)))=>(?[X]:(generous(X))))&
((funny(alice))=>(?[X]:((brave(X)&~patient(X)))))&
((?[X]:((old(X)<~>~quiet(X))))=>((~rich(fred)|happy(fred))))&
((?[X]:(~humble(X)))=>(generous(mary)))&
(((~quiet(alice)&~creative(alice)))<=>(?[X]:((kind(X)&happy(X)))))&
(((brave(paul)|~quiet(paul)))=>(?[X]:((~funny(X)<~>old(X)))))&
((?[X]:((~humble(X)&~tall(X))))=>((~humble(john)|~tall(john))))&
((?[X]:((~old(X)&patient(X))))=>(?[X]:((patient(X)&old(X)))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~patient(X)<~>~generous(X))))&
(((calm(paul)<~>brave(paul)))<=>((quiet(paul)<~>~brave(paul))))&
(((kind(mary)|quiet(mary)))=>(?[X]:((~patient(X)&~generous(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(creative(X)&humble(X))))&
(?[X]:((curious(X)|patient(X))))&
(?[X]:(generous(X)))&
(?[X]:((generous(X)&happy(X))))&
(?[X]:((~rich(X)|~wise(X))))&
((~rich(paul)|~quiet(paul)))&
((rich(alice)|~kind(alice)))&
((curious(john)&calm(john)))&
(?[X]:((~quiet(X)|funny(X)))) | brave(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8176519961589114645120906
% SZS output start Proof for 8176519961589114645120906
3. ! [X0] : ((brave(X0) | ~humble(X0)) <=> humble(X0)) [input p2]
25. ~brave(alice) [input hypothesis]
47. ! [X0] : (((brave(X0) | ~humble(X0)) | ~humble(X0)) & (humble(X0) | (~brave(X0) & humble(X0)))) [nnf transformation 3]
48. ! [X0] : ((brave(X0) | ~humble(X0) | ~humble(X0)) & (humble(X0) | (~brave(X0) & humble(X0)))) [flattening 47]
88. humble(X0) | humble(X0) [cnf transformation 48]
90. brave(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 48]
147. ~brave(alice) [cnf transformation 25]
156. humble(X0) [duplicate literal removal 88]
157. ~humble(X0) | brave(X0) [duplicate literal removal 90]
363. brave(X0) [resolution 157,156]
364. $false [resolution 363,147]
% SZS output end Proof for 8176519961589114645120906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not funny and vice versa. If fred is both not curious and kind then alice is both not kind and not happy. If someone is funny then lucy is brave and vice versa. Everyone who is rich is both not rich and not creative and vice versa. If someone is old or not kind then someone is not strong and vice versa. Everyone who is both wise and not happy is both rich and kind. Everyone who is either not creative or quiet is calm and vice versa. If mary is not wise then mary is both not strong and not quiet. Everyone who is either not funny or not brave is funny. If someone is creative then someone is not strong or wise and vice versa. If someone is not humble or not rich then someone is not wise and vice versa. If fred is both not funny and not calm then alice is kind or old. If mary is not curious or not happy then susan is not patient or not happy and vice versa. If mary is both quiet and tall then someone is not generous and vice versa. Everyone who is both not rich and not kind is old and vice versa. Everyone who is both creative and old is both kind and tall and vice versa. Someone is either not happy or patient. Susan is both not rich and not curious. Someone is not humble. Paul is either not wise or happy. Alice is not humble or not quiet. Someone is not quiet or curious. Susan is funny or rich. | Mary is curious. | neutral | (![X]:(~calm(X)<=>~funny(X)))&
(((~curious(fred)&kind(fred)))=>((~kind(alice)&~happy(alice))))&
((?[X]:(funny(X)))<=>(brave(lucy)))&
(![X]:(rich(X)<=>(~rich(X)&~creative(X))))&
((?[X]:((old(X)|~kind(X))))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)&~happy(X))=>(rich(X)&kind(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>calm(X)))&
((~wise(mary))=>((~strong(mary)&~quiet(mary))))&
(![X]:((~funny(X)<~>~brave(X))=>funny(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~strong(X)|wise(X)))))&
((?[X]:((~humble(X)|~rich(X))))<=>(?[X]:(~wise(X))))&
(((~funny(fred)&~calm(fred)))=>((kind(alice)|old(alice))))&
(((~curious(mary)|~happy(mary)))<=>((~patient(susan)|~happy(susan))))&
(((quiet(mary)&tall(mary)))<=>(?[X]:(~generous(X))))&
(![X]:((~rich(X)&~kind(X))<=>old(X)))&
(![X]:((creative(X)&old(X))<=>(kind(X)&tall(X))))&
(?[X]:((~happy(X)<~>patient(X))))&
((~rich(susan)&~curious(susan)))&
(?[X]:(~humble(X)))&
((~wise(paul)<~>happy(paul)))&
((~humble(alice)|~quiet(alice)))&
(?[X]:((~quiet(X)|curious(X))))&
((funny(susan)|rich(susan))) | curious(mary) | [] | null | 0 |
If someone is creative then john is not rich or old and vice versa.
Everyone who is not curious is either not quiet or not patient and vice versa.
Everyone who is funny is not patient or kind and vice versa.
Everyone who is either not quiet or humble is humble and vice versa.
Everyone who is both not curious and not wise is both not quiet and funny.
If someone is generous then mary is not patient and vice versa.
Everyone who is either wise or humble is either not creative or not quiet.
Everyone who is either quiet or curious is quiet and vice versa.
Everyone who is not calm or creative is generous and vice versa.
Everyone who is either not patient or creative is wise or not kind and vice versa.
Everyone who is generous or funny is not old or quiet and vice versa.
Everyone who is old or strong is generous or funny.
If someone is rich or humble then lucy is not humble or happy.
Everyone who is funny or curious is brave or not rich and vice versa.
Everyone who is either creative or curious is calm and vice versa.
If paul is both curious and not happy then paul is humble or not generous and vice versa.
Susan is either not strong or not happy.
Alice is not wise or generous.
Someone is either not old or not happy.
Fred is both not rich and tall.
Alice is either not kind or creative. | Paul is not happy. | neutral | ((?[X]:(creative(X)))<=>((~rich(john)|old(john))))&
(![X]:(~curious(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:(funny(X)<=>(~patient(X)|kind(X))))&
(![X]:((~quiet(X)<~>humble(X))<=>humble(X)))&
(![X]:((~curious(X)&~wise(X))=>(~quiet(X)&funny(X))))&
((?[X]:(generous(X)))<=>(~patient(mary)))&
(![X]:((wise(X)<~>humble(X))=>(~creative(X)<~>~quiet(X))))&
(![X]:((quiet(X)<~>curious(X))<=>quiet(X)))&
(![X]:((~calm(X)|creative(X))<=>generous(X)))&
(![X]:((~patient(X)<~>creative(X))<=>(wise(X)|~kind(X))))&
(![X]:((generous(X)|funny(X))<=>(~old(X)|quiet(X))))&
(![X]:((old(X)|strong(X))=>(generous(X)|funny(X))))&
((?[X]:((rich(X)|humble(X))))=>((~humble(lucy)|happy(lucy))))&
(![X]:((funny(X)|curious(X))<=>(brave(X)|~rich(X))))&
(![X]:((creative(X)<~>curious(X))<=>calm(X)))&
(((curious(paul)&~happy(paul)))<=>((humble(paul)|~generous(paul))))&
((~strong(susan)<~>~happy(susan)))&
((~wise(alice)|generous(alice)))&
(?[X]:((~old(X)<~>~happy(X))))&
((~rich(fred)&tall(fred)))&
((~kind(alice)<~>creative(alice))) | ~happy(paul) | [] | null | 0 |
Everyone who is either not funny or wise is either not creative or not kind and vice versa.
Everyone who is rich is curious and vice versa.
Everyone who is brave or not calm is old or not old.
Everyone who is not calm is humble or not happy.
If someone is both not strong and tall then mary is wise or tall.
If someone is either creative or not calm then fred is either not funny or not rich and vice versa.
Everyone who is not calm is both not tall and kind.
If someone is both not tall and creative then someone is brave or happy.
If fred is not happy or not humble then someone is both not wise and not funny and vice versa.
If john is either not quiet or calm then someone is both calm and not strong.
If susan is not patient then someone is both brave and not rich.
If alice is humble or old then john is brave.
If paul is either not happy or not brave then john is calm and vice versa.
If fred is brave or not curious then paul is brave or rich.
If alice is both happy and quiet then someone is either strong or not generous and vice versa.
If susan is both generous and strong then someone is funny.
Susan is strong.
Someone is not wise.
Alice is either calm or creative.
Susan is both not calm and rich.
Someone is curious.
Someone is not rich or happy.
Susan is funny or old.
Susan is both quiet and curious. | Susan is not kind. | contradiction | (![X]:((~funny(X)<~>wise(X))<=>(~creative(X)<~>~kind(X))))&
(![X]:(rich(X)<=>curious(X)))&
(![X]:((brave(X)|~calm(X))=>(old(X)|~old(X))))&
(![X]:(~calm(X)=>(humble(X)|~happy(X))))&
((?[X]:((~strong(X)&tall(X))))=>((wise(mary)|tall(mary))))&
((?[X]:((creative(X)<~>~calm(X))))<=>((~funny(fred)<~>~rich(fred))))&
(![X]:(~calm(X)=>(~tall(X)&kind(X))))&
((?[X]:((~tall(X)&creative(X))))=>(?[X]:((brave(X)|happy(X)))))&
(((~happy(fred)|~humble(fred)))<=>(?[X]:((~wise(X)&~funny(X)))))&
(((~quiet(john)<~>calm(john)))=>(?[X]:((calm(X)&~strong(X)))))&
((~patient(susan))=>(?[X]:((brave(X)&~rich(X)))))&
(((humble(alice)|old(alice)))=>(brave(john)))&
(((~happy(paul)<~>~brave(paul)))<=>(calm(john)))&
(((brave(fred)|~curious(fred)))=>((brave(paul)|rich(paul))))&
(((happy(alice)&quiet(alice)))<=>(?[X]:((strong(X)<~>~generous(X)))))&
(((generous(susan)&strong(susan)))=>(?[X]:(funny(X))))&
(strong(susan))&
(?[X]:(~wise(X)))&
((calm(alice)<~>creative(alice)))&
((~calm(susan)&rich(susan)))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)|happy(X))))&
((funny(susan)|old(susan)))&
((quiet(susan)&curious(susan))) | ~kind(susan) | [
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5061442448469014896671979
% SZS output start Proof for 5061442448469014896671979
7. ! [X0] : (~calm(X0) => (kind(X0) & ~tall(X0))) [input p6]
20. rich(susan) & ~calm(susan) [input p19]
25. ~kind(susan) [input hypothesis]
34. ! [X0] : ((kind(X0) & ~tall(X0)) | calm(X0)) [ennf transformation 7]
97. calm(X0) | kind(X0) [cnf transformation 34]
127. ~calm(susan) [cnf transformation 20]
134. ~kind(susan) [cnf transformation 25]
349. kind(susan) [resolution 97,127]
351. $false [subsumption resolution 349,134]
% SZS output end Proof for 5061442448469014896671979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or strong is both not creative and patient and vice versa.
If someone is both not strong and strong then someone is humble and vice versa.
If someone is not tall or curious then someone is both not generous and kind and vice versa.
If someone is calm or curious then susan is both not old and not kind and vice versa.
If someone is not brave then someone is both not creative and curious.
If susan is funny or strong then mary is not calm.
If lucy is either not humble or not wise then someone is both kind and tall.
If someone is creative then someone is kind or creative and vice versa.
If someone is not quiet then susan is not tall or generous and vice versa.
If someone is not wise or rich then susan is happy or patient.
Everyone who is either wise or not humble is old and vice versa.
If someone is not creative then someone is rich.
If alice is creative then someone is either rich or not wise.
Everyone who is quiet is not humble or tall and vice versa.
If someone is not quiet or not wise then someone is not brave or not tall and vice versa.
Alice is not patient.
Someone is creative or not patient.
Someone is not wise or wise.
Alice is either happy or humble.
Someone is either creative or not calm. | Susan is not tall. | contradiction | (![X]:((wise(X)<~>strong(X))<=>(~creative(X)&patient(X))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
((?[X]:((calm(X)|curious(X))))<=>((~old(susan)&~kind(susan))))&
((?[X]:(~brave(X)))=>(?[X]:((~creative(X)&curious(X)))))&
(((funny(susan)|strong(susan)))=>(~calm(mary)))&
(((~humble(lucy)<~>~wise(lucy)))=>(?[X]:((kind(X)&tall(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((kind(X)|creative(X)))))&
((?[X]:(~quiet(X)))<=>((~tall(susan)|generous(susan))))&
((?[X]:((~wise(X)|rich(X))))=>((happy(susan)|patient(susan))))&
(![X]:((wise(X)<~>~humble(X))<=>old(X)))&
((?[X]:(~creative(X)))=>(?[X]:(rich(X))))&
((creative(alice))=>(?[X]:((rich(X)<~>~wise(X)))))&
(![X]:(quiet(X)<=>(~humble(X)|tall(X))))&
((?[X]:((~quiet(X)|~wise(X))))<=>(?[X]:((~brave(X)|~tall(X)))))&
(~patient(alice))&
(?[X]:((creative(X)|~patient(X))))&
(?[X]:((~wise(X)|wise(X))))&
((happy(alice)<~>humble(alice)))&
(?[X]:((creative(X)<~>~calm(X)))) | ~tall(susan) | [
"p1",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8726629708124163383702754
% SZS output start Proof for 8726629708124163383702754
2. ? [X0] : (strong(X0) & ~strong(X0)) <=> ? [X0] : humble(X0) [input p1]
9. ? [X0] : ~quiet(X0) <=> (generous(susan) | ~tall(susan)) [input p8]
14. ! [X0] : (quiet(X0) <=> (tall(X0) | ~humble(X0))) [input p13]
21. ~tall(susan) [input hypothesis]
22. ? [X0] : (strong(X0) & ~strong(X0)) <=> ? [X1] : humble(X1) [rectify 2]
38. (? [X0] : (strong(X0) & ~strong(X0)) | ! [X1] : ~humble(X1)) & (? [X1] : humble(X1) | ! [X0] : (~strong(X0) | strong(X0))) [nnf transformation 22]
39. (? [X0] : (strong(X0) & ~strong(X0)) | ! [X1] : ~humble(X1)) & (? [X2] : humble(X2) | ! [X3] : (~strong(X3) | strong(X3))) [rectify 38]
40. ? [X0] : (strong(X0) & ~strong(X0)) => (strong(sK0) & ~strong(sK0)) [choice axiom]
41. ? [X2] : humble(X2) => humble(sK1) [choice axiom]
42. ((strong(sK0) & ~strong(sK0)) | ! [X1] : ~humble(X1)) & (humble(sK1) | ! [X3] : (~strong(X3) | strong(X3))) [skolemisation 39,41,40]
64. (? [X0] : ~quiet(X0) | (~generous(susan) & tall(susan))) & ((generous(susan) | ~tall(susan)) | ! [X0] : quiet(X0)) [nnf transformation 9]
65. (? [X0] : ~quiet(X0) | (~generous(susan) & tall(susan))) & (generous(susan) | ~tall(susan) | ! [X0] : quiet(X0)) [flattening 64]
66. (? [X0] : ~quiet(X0) | (~generous(susan) & tall(susan))) & (generous(susan) | ~tall(susan) | ! [X1] : quiet(X1)) [rectify 65]
67. ? [X0] : ~quiet(X0) => ~quiet(sK9) [choice axiom]
68. (~quiet(sK9) | (~generous(susan) & tall(susan))) & (generous(susan) | ~tall(susan) | ! [X1] : quiet(X1)) [skolemisation 66,67]
76. ! [X0] : ((quiet(X0) | (~tall(X0) & humble(X0))) & ((tall(X0) | ~humble(X0)) | ~quiet(X0))) [nnf transformation 14]
77. ! [X0] : ((quiet(X0) | (~tall(X0) & humble(X0))) & (tall(X0) | ~humble(X0) | ~quiet(X0))) [flattening 76]
98. ~strong(sK0) | ~humble(X1) [cnf transformation 42]
99. strong(sK0) | ~humble(X1) [cnf transformation 42]
121. ~quiet(sK9) | tall(susan) [cnf transformation 68]
133. quiet(X0) | humble(X0) [cnf transformation 77]
146. ~tall(susan) [cnf transformation 21]
148. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
149. ~humble(X1) <- (1) [avatar component clause 148]
151. 2 <=> strong(sK0) [avatar definition]
154. 1 | 2 [avatar split clause 99,151,148]
155. 1 | ~2 [avatar split clause 98,151,148]
278. 30 <=> quiet(sK9) [avatar definition]
280. ~quiet(sK9) <- (~30) [avatar component clause 278]
283. 31 <=> tall(susan) [avatar definition]
286. 31 | ~30 [avatar split clause 121,278,283]
378. ~31 [avatar split clause 146,283]
395. humble(sK9) <- (~30) [resolution 133,280]
396. $false <- (1, ~30) [subsumption resolution 395,149]
397. ~1 | 30 [avatar contradiction clause 396]
398. $false [avatar sat refutation 154,155,286,378,397]
% SZS output end Proof for 8726629708124163383702754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not patient is calm or not rich and vice versa.
If someone is either not creative or not tall then someone is either not rich or not curious and vice versa.
If someone is both strong and wise then mary is both not humble and not generous and vice versa.
If someone is either creative or not creative then mary is generous and vice versa.
If lucy is either generous or rich then alice is both not generous and curious.
If paul is both humble and not calm then someone is either not patient or not humble.
If alice is both not creative and not patient then someone is either brave or wise and vice versa.
Everyone who is either wise or not rich is patient.
Everyone who is both not tall and wise is either curious or creative.
Everyone who is both wise and humble is both not tall and rich and vice versa.
If john is both kind and not rich then john is not creative.
If someone is either kind or generous then someone is not brave.
Everyone who is not old or creative is old or not wise and vice versa.
Everyone who is not wise is both not calm and not tall and vice versa.
Everyone who is not quiet is both not funny and kind.
Everyone who is both patient and creative is both not creative and old and vice versa.
Someone is both curious and creative.
Someone is not generous.
Alice is both not patient and old.
Someone is funny.
Someone is either not quiet or old.
Paul is both generous and calm. | Lucy is not rich. | entailment | (![X]:((old(X)|~patient(X))<=>(calm(X)|~rich(X))))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:((strong(X)&wise(X))))<=>((~humble(mary)&~generous(mary))))&
((?[X]:((creative(X)<~>~creative(X))))<=>(generous(mary)))&
(((generous(lucy)<~>rich(lucy)))=>((~generous(alice)&curious(alice))))&
(((humble(paul)&~calm(paul)))=>(?[X]:((~patient(X)<~>~humble(X)))))&
(((~creative(alice)&~patient(alice)))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((wise(X)<~>~rich(X))=>patient(X)))&
(![X]:((~tall(X)&wise(X))=>(curious(X)<~>creative(X))))&
(![X]:((wise(X)&humble(X))<=>(~tall(X)&rich(X))))&
(((kind(john)&~rich(john)))=>(~creative(john)))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|creative(X))<=>(old(X)|~wise(X))))&
(![X]:(~wise(X)<=>(~calm(X)&~tall(X))))&
(![X]:(~quiet(X)=>(~funny(X)&kind(X))))&
(![X]:((patient(X)&creative(X))<=>(~creative(X)&old(X))))&
(?[X]:((curious(X)&creative(X))))&
(?[X]:(~generous(X)))&
((~patient(alice)&old(alice)))&
(?[X]:(funny(X)))&
(?[X]:((~quiet(X)<~>old(X))))&
((generous(paul)&calm(paul))) | ~rich(lucy) | [
"p0",
"p7",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5892026368058112169560596
% SZS output start Proof for 5892026368058112169560596
1. ! [X0] : ((~patient(X0) | old(X0)) <=> (~rich(X0) | calm(X0))) [input p0]
8. ! [X0] : ((wise(X0) <~> ~rich(X0)) => patient(X0)) [input p7]
10. ! [X0] : ((humble(X0) & wise(X0)) <=> (rich(X0) & ~tall(X0))) [input p9]
13. ! [X0] : ((creative(X0) | ~old(X0)) <=> (~wise(X0) | old(X0))) [input p12]
14. ! [X0] : (~wise(X0) <=> (~tall(X0) & ~calm(X0))) [input p13]
16. ! [X0] : ((creative(X0) & patient(X0)) <=> (old(X0) & ~creative(X0))) [input p15]
23. rich(lucy) [input hypothesis]
29. ! [X0] : (patient(X0) | (wise(X0) <=> ~rich(X0))) [ennf transformation 8]
36. ! [X0] : (((~patient(X0) | old(X0)) | (rich(X0) & ~calm(X0))) & ((~rich(X0) | calm(X0)) | (patient(X0) & ~old(X0)))) [nnf transformation 1]
37. ! [X0] : ((~patient(X0) | old(X0) | (rich(X0) & ~calm(X0))) & (~rich(X0) | calm(X0) | (patient(X0) & ~old(X0)))) [flattening 36]
61. ! [X0] : (patient(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0)))) [nnf transformation 29]
63. ! [X0] : (((humble(X0) & wise(X0)) | (~rich(X0) | tall(X0))) & ((rich(X0) & ~tall(X0)) | (~humble(X0) | ~wise(X0)))) [nnf transformation 10]
64. ! [X0] : (((humble(X0) & wise(X0)) | ~rich(X0) | tall(X0)) & ((rich(X0) & ~tall(X0)) | ~humble(X0) | ~wise(X0))) [flattening 63]
69. ! [X0] : (((creative(X0) | ~old(X0)) | (wise(X0) & ~old(X0))) & ((~wise(X0) | old(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 13]
70. ! [X0] : ((creative(X0) | ~old(X0) | (wise(X0) & ~old(X0))) & (~wise(X0) | old(X0) | (~creative(X0) & old(X0)))) [flattening 69]
71. ! [X0] : ((~wise(X0) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | wise(X0))) [nnf transformation 14]
72. ! [X0] : ((~wise(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | wise(X0))) [flattening 71]
73. ! [X0] : (((creative(X0) & patient(X0)) | (~old(X0) | creative(X0))) & ((old(X0) & ~creative(X0)) | (~creative(X0) | ~patient(X0)))) [nnf transformation 16]
74. ! [X0] : (((creative(X0) & patient(X0)) | ~old(X0) | creative(X0)) & ((old(X0) & ~creative(X0)) | ~creative(X0) | ~patient(X0))) [flattening 73]
84. ~rich(X0) | calm(X0) | ~old(X0) [cnf transformation 37]
116. ~wise(X0) | ~rich(X0) | patient(X0) [cnf transformation 61]
122. ~rich(X0) | wise(X0) | tall(X0) [cnf transformation 64]
127. ~wise(X0) | old(X0) | old(X0) [cnf transformation 70]
129. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 70]
131. ~calm(X0) | wise(X0) [cnf transformation 72]
132. ~tall(X0) | wise(X0) [cnf transformation 72]
136. ~creative(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 74]
150. rich(lucy) [cnf transformation 23]
151. ~creative(X0) | ~patient(X0) [duplicate literal removal 136]
153. ~wise(X0) | old(X0) [duplicate literal removal 127]
154. ~old(X0) | creative(X0) [duplicate literal removal 129]
225. 16 <=> rich(lucy) [avatar definition]
226. rich(lucy) <- (16) [avatar component clause 225]
327. 16 [avatar split clause 150,225]
342. calm(lucy) | ~old(lucy) <- (16) [resolution 84,226]
353. 40 <=> old(lucy) [avatar definition]
354. old(lucy) <- (40) [avatar component clause 353]
355. ~old(lucy) <- (~40) [avatar component clause 353]
357. 41 <=> calm(lucy) [avatar definition]
359. calm(lucy) <- (41) [avatar component clause 357]
360. ~40 | 41 | ~16 [avatar split clause 342,225,357,353]
369. 43 <=> patient(lucy) [avatar definition]
371. patient(lucy) <- (43) [avatar component clause 369]
375. wise(lucy) <- (41) [resolution 359,131]
380. ~rich(lucy) | patient(lucy) <- (41) [resolution 375,116]
384. patient(lucy) <- (16, 41) [subsumption resolution 380,226]
391. 43 | ~16 | ~41 [avatar split clause 384,357,225,369]
398. creative(lucy) <- (40) [resolution 354,154]
400. wise(lucy) | tall(lucy) <- (16) [resolution 122,226]
401. ~patient(lucy) <- (40) [resolution 398,151]
402. $false <- (40, 43) [subsumption resolution 401,371]
403. ~40 | ~43 [avatar contradiction clause 402]
404. wise(lucy) <- (16) [subsumption resolution 400,132]
423. old(lucy) <- (16) [resolution 404,153]
425. $false <- (16, ~40) [subsumption resolution 423,355]
426. ~16 | 40 [avatar contradiction clause 425]
427. $false [avatar sat refutation 327,360,391,403,426]
% SZS output end Proof for 5892026368058112169560596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not generous is either not quiet or happy and vice versa. If someone is either humble or not generous then susan is both not old and not humble. If susan is either not patient or not happy then someone is generous or not strong and vice versa. If alice is either not brave or not wise then someone is either not old or patient and vice versa. Everyone who is both not wise and not patient is both strong and generous and vice versa. If someone is not rich or not funny then john is either not old or creative. If someone is both calm and patient then someone is strong. If someone is both not funny and not strong then someone is either creative or generous and vice versa. Everyone who is either happy or brave is both rich and not curious and vice versa. If someone is not patient or happy then someone is either calm or not creative. Everyone who is both not humble and rich is either not tall or not curious. If lucy is funny or not funny then someone is either not happy or calm and vice versa. If susan is either generous or not humble then someone is either kind or brave. Everyone who is either not rich or funny is either not generous or old. If paul is brave or generous then lucy is either not funny or wise. If paul is both funny and tall then paul is either brave or happy and vice versa. Susan is either tall or strong. Someone is calm. Fred is both quiet and calm. Someone is either rich or not rich. Fred is both not patient and not funny. Paul is not kind. Someone is strong or not humble. Someone is both calm and not happy. | Lucy is creative. | neutral | (![X]:((~old(X)<~>~generous(X))<=>(~quiet(X)<~>happy(X))))&
((?[X]:((humble(X)<~>~generous(X))))=>((~old(susan)&~humble(susan))))&
(((~patient(susan)<~>~happy(susan)))<=>(?[X]:((generous(X)|~strong(X)))))&
(((~brave(alice)<~>~wise(alice)))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~wise(X)&~patient(X))<=>(strong(X)&generous(X))))&
((?[X]:((~rich(X)|~funny(X))))=>((~old(john)<~>creative(john))))&
((?[X]:((calm(X)&patient(X))))=>(?[X]:(strong(X))))&
((?[X]:((~funny(X)&~strong(X))))<=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(rich(X)&~curious(X))))&
((?[X]:((~patient(X)|happy(X))))=>(?[X]:((calm(X)<~>~creative(X)))))&
(![X]:((~humble(X)&rich(X))=>(~tall(X)<~>~curious(X))))&
(((funny(lucy)|~funny(lucy)))<=>(?[X]:((~happy(X)<~>calm(X)))))&
(((generous(susan)<~>~humble(susan)))=>(?[X]:((kind(X)<~>brave(X)))))&
(![X]:((~rich(X)<~>funny(X))=>(~generous(X)<~>old(X))))&
(((brave(paul)|generous(paul)))=>((~funny(lucy)<~>wise(lucy))))&
(((funny(paul)&tall(paul)))<=>((brave(paul)<~>happy(paul))))&
((tall(susan)<~>strong(susan)))&
(?[X]:(calm(X)))&
((quiet(fred)&calm(fred)))&
(?[X]:((rich(X)<~>~rich(X))))&
((~patient(fred)&~funny(fred)))&
(~kind(paul))&
(?[X]:((strong(X)|~humble(X))))&
(?[X]:((calm(X)&~happy(X)))) | creative(lucy) | [] | null | 0 |
Everyone who is either not rich or generous is not kind or not quiet.
Everyone who is funny or not generous is brave or curious and vice versa.
If alice is both not curious and not brave then someone is either calm or not strong and vice versa.
If someone is both funny and wise then someone is either patient or not old.
Everyone who is either old or not strong is kind and vice versa.
Everyone who is not old is both kind and not creative and vice versa.
If someone is both old and patient then mary is either kind or rich and vice versa.
Everyone who is either strong or quiet is not generous and vice versa.
Everyone who is brave is quiet or not happy.
Everyone who is both not kind and not funny is not creative or not humble and vice versa.
Everyone who is not creative or not brave is strong and vice versa.
Everyone who is either rich or creative is either not curious or not tall and vice versa.
If someone is old or quiet then someone is either not calm or not kind and vice versa.
If mary is both not wise and not generous then someone is both brave and humble.
If paul is either brave or not wise then paul is not funny or curious and vice versa.
If fred is old or calm then paul is curious and vice versa.
Mary is either not happy or funny.
Fred is either kind or not quiet.
Fred is not kind.
Alice is either not patient or not rich.
Someone is creative or not strong.
Someone is not funny.
Someone is both tall and happy.
Someone is either not brave or patient. | Mary is old. | entailment | (![X]:((~rich(X)<~>generous(X))=>(~kind(X)|~quiet(X))))&
(![X]:((funny(X)|~generous(X))<=>(brave(X)|curious(X))))&
(((~curious(alice)&~brave(alice)))<=>(?[X]:((calm(X)<~>~strong(X)))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:((old(X)<~>~strong(X))<=>kind(X)))&
(![X]:(~old(X)<=>(kind(X)&~creative(X))))&
((?[X]:((old(X)&patient(X))))<=>((kind(mary)<~>rich(mary))))&
(![X]:((strong(X)<~>quiet(X))<=>~generous(X)))&
(![X]:(brave(X)=>(quiet(X)|~happy(X))))&
(![X]:((~kind(X)&~funny(X))<=>(~creative(X)|~humble(X))))&
(![X]:((~creative(X)|~brave(X))<=>strong(X)))&
(![X]:((rich(X)<~>creative(X))<=>(~curious(X)<~>~tall(X))))&
((?[X]:((old(X)|quiet(X))))<=>(?[X]:((~calm(X)<~>~kind(X)))))&
(((~wise(mary)&~generous(mary)))=>(?[X]:((brave(X)&humble(X)))))&
(((brave(paul)<~>~wise(paul)))<=>((~funny(paul)|curious(paul))))&
(((old(fred)|calm(fred)))<=>(curious(paul)))&
((~happy(mary)<~>funny(mary)))&
((kind(fred)<~>~quiet(fred)))&
(~kind(fred))&
((~patient(alice)<~>~rich(alice)))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:(~funny(X)))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:((~brave(X)<~>patient(X)))) | old(mary) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8991485883691995888567920
% SZS output start Proof for 8991485883691995888567920
6. ! [X0] : (~old(X0) <=> (~creative(X0) & kind(X0))) [input p5]
10. ! [X0] : ((~funny(X0) & ~kind(X0)) <=> (~humble(X0) | ~creative(X0))) [input p9]
25. ~old(mary) [input hypothesis]
48. ! [X0] : ((~old(X0) | (creative(X0) | ~kind(X0))) & ((~creative(X0) & kind(X0)) | old(X0))) [nnf transformation 6]
49. ! [X0] : ((~old(X0) | creative(X0) | ~kind(X0)) & ((~creative(X0) & kind(X0)) | old(X0))) [flattening 48]
55. ! [X0] : (((~funny(X0) & ~kind(X0)) | (humble(X0) & creative(X0))) & ((~humble(X0) | ~creative(X0)) | (funny(X0) | kind(X0)))) [nnf transformation 10]
56. ! [X0] : (((~funny(X0) & ~kind(X0)) | (humble(X0) & creative(X0))) & (~humble(X0) | ~creative(X0) | funny(X0) | kind(X0))) [flattening 55]
101. old(X0) | kind(X0) [cnf transformation 49]
102. ~creative(X0) | old(X0) [cnf transformation 49]
116. ~kind(X0) | creative(X0) [cnf transformation 56]
161. ~old(mary) [cnf transformation 25]
208. 11 <=> kind(mary) [avatar definition]
210. kind(mary) <- (11) [avatar component clause 208]
355. kind(mary) [resolution 101,161]
362. 11 [avatar split clause 355,208]
364. creative(mary) <- (11) [resolution 116,210]
366. old(mary) <- (11) [resolution 364,102]
367. $false <- (11) [subsumption resolution 366,161]
368. ~11 [avatar contradiction clause 367]
369. $false [avatar sat refutation 362,368]
% SZS output end Proof for 8991485883691995888567920
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not patient or curious then lucy is calm. Everyone who is brave or wise is not tall or patient and vice versa. Everyone who is not wise or not generous is both not wise and not funny. If someone is not kind then someone is both quiet and not quiet and vice versa. Everyone who is both not wise and not calm is both not tall and not happy and vice versa. If someone is quiet then fred is either strong or brave. If someone is both not humble and not tall then someone is patient or kind. If someone is not wise or humble then susan is not curious or old. Everyone who is either not calm or kind is either not humble or not quiet and vice versa. Everyone who is rich or strong is both not calm and calm and vice versa. Everyone who is either patient or happy is either quiet or kind. If someone is not kind or not happy then susan is either not humble or not rich. If fred is both happy and rich then someone is both wise and calm. Everyone who is both not kind and happy is rich. If alice is either patient or not quiet then someone is tall and vice versa. Everyone who is either not funny or rich is quiet. Someone is not strong or not funny. Lucy is both calm and not quiet. Someone is not calm or generous. Mary is not old. Someone is both not tall and not happy. Someone is both kind and not humble. Someone is either humble or not generous. Someone is not quiet. | Mary is happy. | neutral | (((~patient(lucy)|curious(lucy)))=>(calm(lucy)))&
(![X]:((brave(X)|wise(X))<=>(~tall(X)|patient(X))))&
(![X]:((~wise(X)|~generous(X))=>(~wise(X)&~funny(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((~wise(X)&~calm(X))<=>(~tall(X)&~happy(X))))&
((?[X]:(quiet(X)))=>((strong(fred)<~>brave(fred))))&
((?[X]:((~humble(X)&~tall(X))))=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:((~wise(X)|humble(X))))=>((~curious(susan)|old(susan))))&
(![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((rich(X)|strong(X))<=>(~calm(X)&calm(X))))&
(![X]:((patient(X)<~>happy(X))=>(quiet(X)<~>kind(X))))&
((?[X]:((~kind(X)|~happy(X))))=>((~humble(susan)<~>~rich(susan))))&
(((happy(fred)&rich(fred)))=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((~kind(X)&happy(X))=>rich(X)))&
(((patient(alice)<~>~quiet(alice)))<=>(?[X]:(tall(X))))&
(![X]:((~funny(X)<~>rich(X))=>quiet(X)))&
(?[X]:((~strong(X)|~funny(X))))&
((calm(lucy)&~quiet(lucy)))&
(?[X]:((~calm(X)|generous(X))))&
(~old(mary))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((kind(X)&~humble(X))))&
(?[X]:((humble(X)<~>~generous(X))))&
(?[X]:(~quiet(X))) | happy(mary) | [] | null | 0 |
If someone is not happy then paul is not old. Everyone who is both not tall and quiet is wise or humble and vice versa. Everyone who is not humble or not quiet is both tall and funny. Everyone who is either not strong or tall is both brave and not brave and vice versa. If mary is both not patient and not quiet then paul is not creative or not quiet and vice versa. If someone is either not patient or not happy then someone is not curious and vice versa. Everyone who is curious is either brave or not rich and vice versa. Everyone who is quiet is not kind and vice versa. Everyone who is either not rich or generous is wise or quiet and vice versa. Everyone who is both not brave and strong is either not curious or not quiet. Everyone who is both kind and not patient is brave or happy and vice versa. If alice is not strong or patient then someone is either not quiet or not patient and vice versa. If fred is not strong or kind then paul is either old or not patient. Everyone who is not quiet is not tall or old. Everyone who is both wise and tall is both quiet and generous and vice versa. If someone is not wise then lucy is either happy or not humble and vice versa. Someone is not curious or calm. Lucy is not happy. Someone is quiet or humble. Someone is both quiet and not brave. Alice is either not creative or generous. | Paul is not brave. | entailment | ((?[X]:(~happy(X)))=>(~old(paul)))&
(![X]:((~tall(X)&quiet(X))<=>(wise(X)|humble(X))))&
(![X]:((~humble(X)|~quiet(X))=>(tall(X)&funny(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(brave(X)&~brave(X))))&
(((~patient(mary)&~quiet(mary)))<=>((~creative(paul)|~quiet(paul))))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(?[X]:(~curious(X))))&
(![X]:(curious(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>~kind(X)))&
(![X]:((~rich(X)<~>generous(X))<=>(wise(X)|quiet(X))))&
(![X]:((~brave(X)&strong(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:((kind(X)&~patient(X))<=>(brave(X)|happy(X))))&
(((~strong(alice)|patient(alice)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(((~strong(fred)|kind(fred)))=>((old(paul)<~>~patient(paul))))&
(![X]:(~quiet(X)=>(~tall(X)|old(X))))&
(![X]:((wise(X)&tall(X))<=>(quiet(X)&generous(X))))&
((?[X]:(~wise(X)))<=>((happy(lucy)<~>~humble(lucy))))&
(?[X]:((~curious(X)|calm(X))))&
(~happy(lucy))&
(?[X]:((quiet(X)|humble(X))))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(alice)<~>generous(alice))) | ~brave(paul) | [
"p0",
"p2",
"p7",
"p10",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3925667880314928381551985
% SZS output start Proof for 3925667880314928381551985
1. ? [X0] : ~happy(X0) => ~old(paul) [input p0]
3. ! [X0] : ((~quiet(X0) | ~humble(X0)) => (funny(X0) & tall(X0))) [input p2]
8. ! [X0] : (quiet(X0) <=> ~kind(X0)) [input p7]
11. ! [X0] : ((~patient(X0) & kind(X0)) <=> (happy(X0) | brave(X0))) [input p10]
14. ! [X0] : (~quiet(X0) => (old(X0) | ~tall(X0))) [input p13]
18. ~happy(lucy) [input p17]
22. brave(paul) [input hypothesis]
25. ! [X0] : ((~quiet(X0) | ~humble(X0)) => tall(X0)) [pure predicate removal 3]
26. ~old(paul) | ! [X0] : happy(X0) [ennf transformation 1]
27. ! [X0] : (tall(X0) | (quiet(X0) & humble(X0))) [ennf transformation 25]
31. ! [X0] : ((old(X0) | ~tall(X0)) | quiet(X0)) [ennf transformation 14]
32. ! [X0] : (old(X0) | ~tall(X0) | quiet(X0)) [flattening 31]
45. ! [X0] : ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))) [nnf transformation 8]
49. ! [X0] : (((~patient(X0) & kind(X0)) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | (patient(X0) | ~kind(X0)))) [nnf transformation 11]
50. ! [X0] : (((~patient(X0) & kind(X0)) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | patient(X0) | ~kind(X0))) [flattening 49]
68. ~old(paul) | happy(X0) [cnf transformation 26]
75. quiet(X0) | tall(X0) [cnf transformation 27]
95. ~kind(X0) | ~quiet(X0) [cnf transformation 45]
106. ~brave(X0) | kind(X0) [cnf transformation 50]
120. old(X0) | ~tall(X0) | quiet(X0) [cnf transformation 32]
129. ~happy(lucy) [cnf transformation 18]
135. brave(paul) [cnf transformation 22]
137. 1 <=> ! [X0] : happy(X0) [avatar definition]
138. happy(X0) <- (1) [avatar component clause 137]
140. 2 <=> old(paul) [avatar definition]
143. 1 | ~2 [avatar split clause 68,140,137]
147. 3 <=> quiet(paul) [avatar definition]
148. ~quiet(paul) <- (~3) [avatar component clause 147]
238. quiet(X0) | old(X0) [subsumption resolution 120,75]
245. 23 <=> happy(lucy) [avatar definition]
246. ~happy(lucy) <- (~23) [avatar component clause 245]
259. ~23 [avatar split clause 129,245]
279. kind(paul) [resolution 106,135]
280. ~quiet(paul) [resolution 279,95]
292. old(paul) <- (~3) [resolution 238,148]
297. 2 | 3 [avatar split clause 292,147,140]
299. $false <- (1, ~23) [resolution 138,246]
301. ~1 | 23 [avatar contradiction clause 299]
303. ~3 [avatar split clause 280,147]
304. $false [avatar sat refutation 143,259,297,301,303]
% SZS output end Proof for 3925667880314928381551985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not curious then john is curious or brave and vice versa.
Everyone who is either creative or happy is not creative.
Everyone who is either curious or patient is not kind or not wise and vice versa.
Everyone who is not curious is calm and vice versa.
Everyone who is not wise or quiet is both patient and strong.
If susan is both curious and brave then someone is not creative or wise.
Everyone who is tall or not rich is humble and vice versa.
Everyone who is either not creative or not tall is either old or generous and vice versa.
If fred is both not old and humble then someone is not humble or humble and vice versa.
Everyone who is not brave is either not funny or not curious and vice versa.
Everyone who is both happy and not tall is either not wise or not rich.
Everyone who is both not quiet and not happy is not strong and vice versa.
If lucy is either strong or creative then paul is both brave and generous.
Everyone who is generous or humble is either not creative or not old.
Everyone who is both happy and old is both not curious and generous.
If lucy is old or generous then someone is rich or not curious and vice versa.
Someone is both not calm and kind.
Someone is either brave or rich.
John is either happy or not wise.
Someone is not humble.
Someone is not funny or calm.
Someone is not rich or not wise.
Susan is both kind and wise.
Someone is both not humble and not generous. | Fred is creative. | entailment | ((?[X]:((~happy(X)|~curious(X))))<=>((curious(john)|brave(john))))&
(![X]:((creative(X)<~>happy(X))=>~creative(X)))&
(![X]:((curious(X)<~>patient(X))<=>(~kind(X)|~wise(X))))&
(![X]:(~curious(X)<=>calm(X)))&
(![X]:((~wise(X)|quiet(X))=>(patient(X)&strong(X))))&
(((curious(susan)&brave(susan)))=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((tall(X)|~rich(X))<=>humble(X)))&
(![X]:((~creative(X)<~>~tall(X))<=>(old(X)<~>generous(X))))&
(((~old(fred)&humble(fred)))<=>(?[X]:((~humble(X)|humble(X)))))&
(![X]:(~brave(X)<=>(~funny(X)<~>~curious(X))))&
(![X]:((happy(X)&~tall(X))=>(~wise(X)<~>~rich(X))))&
(![X]:((~quiet(X)&~happy(X))<=>~strong(X)))&
(((strong(lucy)<~>creative(lucy)))=>((brave(paul)&generous(paul))))&
(![X]:((generous(X)|humble(X))=>(~creative(X)<~>~old(X))))&
(![X]:((happy(X)&old(X))=>(~curious(X)&generous(X))))&
(((old(lucy)|generous(lucy)))<=>(?[X]:((rich(X)|~curious(X)))))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:((brave(X)<~>rich(X))))&
((happy(john)<~>~wise(john)))&
(?[X]:(~humble(X)))&
(?[X]:((~funny(X)|calm(X))))&
(?[X]:((~rich(X)|~wise(X))))&
((kind(susan)&wise(susan)))&
(?[X]:((~humble(X)&~generous(X)))) | creative(fred) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5054769432049255111285131
% SZS output start Proof for 5054769432049255111285131
9. (humble(fred) & ~old(fred)) <=> ? [X0] : (humble(X0) | ~humble(X0)) [input p8]
14. ! [X0] : ((humble(X0) | generous(X0)) => (~creative(X0) <~> ~old(X0))) [input p13]
25. ~creative(fred) [input hypothesis]
33. ! [X0] : ((~creative(X0) <~> ~old(X0)) | (~humble(X0) & ~generous(X0))) [ennf transformation 14]
50. ((humble(fred) & ~old(fred)) | ! [X0] : (~humble(X0) & humble(X0))) & (? [X0] : (humble(X0) | ~humble(X0)) | (~humble(fred) | old(fred))) [nnf transformation 9]
51. ((humble(fred) & ~old(fred)) | ! [X0] : (~humble(X0) & humble(X0))) & (? [X0] : (humble(X0) | ~humble(X0)) | ~humble(fred) | old(fred)) [flattening 50]
52. ((humble(fred) & ~old(fred)) | ! [X0] : (~humble(X0) & humble(X0))) & (? [X1] : (humble(X1) | ~humble(X1)) | ~humble(fred) | old(fred)) [rectify 51]
53. ? [X1] : (humble(X1) | ~humble(X1)) => (humble(sK2) | ~humble(sK2)) [choice axiom]
54. ((humble(fred) & ~old(fred)) | ! [X0] : (~humble(X0) & humble(X0))) & ((humble(sK2) | ~humble(sK2)) | ~humble(fred) | old(fred)) [skolemisation 52,53]
60. ! [X0] : (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (~humble(X0) & ~generous(X0))) [nnf transformation 33]
111. ~old(fred) | humble(X0) [cnf transformation 54]
112. ~old(fred) | ~humble(X0) [cnf transformation 54]
113. humble(fred) | humble(X0) [cnf transformation 54]
114. humble(fred) | ~humble(X0) [cnf transformation 54]
131. ~humble(X0) | creative(X0) | old(X0) [cnf transformation 60]
151. ~creative(fred) [cnf transformation 25]
197. 11 <=> ! [X0] : ~humble(X0) [avatar definition]
198. ~humble(X0) <- (11) [avatar component clause 197]
200. 12 <=> humble(fred) [avatar definition]
202. humble(fred) <- (12) [avatar component clause 200]
203. 11 | 12 [avatar split clause 114,200,197]
205. 13 <=> ! [X0] : humble(X0) [avatar definition]
206. humble(X0) <- (13) [avatar component clause 205]
207. 13 | 12 [avatar split clause 113,200,205]
209. 14 <=> old(fred) [avatar definition]
212. 11 | ~14 [avatar split clause 112,209,197]
213. 13 | ~14 [avatar split clause 111,209,205]
348. creative(fred) | old(fred) <- (12) [resolution 131,202]
350. old(fred) <- (12) [subsumption resolution 348,151]
353. 14 | ~12 [avatar split clause 350,200,209]
354. $false <- (11, 13) [subsumption resolution 198,206]
355. ~11 | ~13 [avatar contradiction clause 354]
356. $false [avatar sat refutation 203,207,212,213,353,355]
% SZS output end Proof for 5054769432049255111285131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or generous is either humble or not humble.
If someone is not happy then fred is funny and vice versa.
Everyone who is both funny and tall is quiet or not curious and vice versa.
Everyone who is both not funny and funny is not quiet.
Everyone who is not brave is strong or creative.
Everyone who is either quiet or strong is both not quiet and tall and vice versa.
Everyone who is either brave or humble is either not wise or tall and vice versa.
If lucy is either rich or old then lucy is both wise and not brave and vice versa.
Everyone who is generous is not generous or rich.
Everyone who is either strong or not brave is old and vice versa.
If someone is either not curious or not happy then someone is not old or not funny and vice versa.
If susan is either wise or not brave then susan is either rich or calm and vice versa.
Everyone who is both not patient and calm is both not tall and not curious.
Everyone who is not rich is not strong and vice versa.
Everyone who is quiet or not tall is either not calm or not tall.
If susan is both not generous and curious then alice is curious or not patient.
Alice is both humble and tall.
Susan is both not curious and not patient.
Someone is not happy.
Someone is rich or not humble.
Someone is both tall and not brave.
Someone is both not funny and old.
Mary is either not humble or rich. | Alice is not calm. | neutral | (![X]:((~humble(X)|generous(X))=>(humble(X)<~>~humble(X))))&
((?[X]:(~happy(X)))<=>(funny(fred)))&
(![X]:((funny(X)&tall(X))<=>(quiet(X)|~curious(X))))&
(![X]:((~funny(X)&funny(X))=>~quiet(X)))&
(![X]:(~brave(X)=>(strong(X)|creative(X))))&
(![X]:((quiet(X)<~>strong(X))<=>(~quiet(X)&tall(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~wise(X)<~>tall(X))))&
(((rich(lucy)<~>old(lucy)))<=>((wise(lucy)&~brave(lucy))))&
(![X]:(generous(X)=>(~generous(X)|rich(X))))&
(![X]:((strong(X)<~>~brave(X))<=>old(X)))&
((?[X]:((~curious(X)<~>~happy(X))))<=>(?[X]:((~old(X)|~funny(X)))))&
(((wise(susan)<~>~brave(susan)))<=>((rich(susan)<~>calm(susan))))&
(![X]:((~patient(X)&calm(X))=>(~tall(X)&~curious(X))))&
(![X]:(~rich(X)<=>~strong(X)))&
(![X]:((quiet(X)|~tall(X))=>(~calm(X)<~>~tall(X))))&
(((~generous(susan)&curious(susan)))=>((curious(alice)|~patient(alice))))&
((humble(alice)&tall(alice)))&
((~curious(susan)&~patient(susan)))&
(?[X]:(~happy(X)))&
(?[X]:((rich(X)|~humble(X))))&
(?[X]:((tall(X)&~brave(X))))&
(?[X]:((~funny(X)&old(X))))&
((~humble(mary)<~>rich(mary))) | ~calm(alice) | [] | null | 0 |
Everyone who is not tall is calm or not brave and vice versa.
Everyone who is tall is both humble and not funny and vice versa.
If someone is not calm then john is not curious.
If someone is curious then someone is both not old and kind.
Everyone who is brave or generous is both not quiet and not wise and vice versa.
If alice is either kind or generous then someone is both not curious and funny and vice versa.
If someone is generous then someone is patient.
Everyone who is not happy or kind is happy or not tall and vice versa.
Everyone who is strong is both curious and not strong and vice versa.
If john is both not quiet and happy then someone is not tall.
Everyone who is either not happy or quiet is not brave.
Everyone who is either brave or not creative is happy.
If someone is both not old and not quiet then someone is calm or not funny.
If someone is calm or not calm then alice is not happy and vice versa.
Everyone who is not funny is both not happy and not brave and vice versa.
Everyone who is creative is not generous and vice versa.
Lucy is not strong.
Paul is both quiet and not happy.
Someone is both not quiet and wise.
Someone is not funny.
Lucy is either wise or not kind.
Someone is either curious or old.
Mary is calm.
Someone is both kind and not old. | John is not quiet. | neutral | (![X]:(~tall(X)<=>(calm(X)|~brave(X))))&
(![X]:(tall(X)<=>(humble(X)&~funny(X))))&
((?[X]:(~calm(X)))=>(~curious(john)))&
((?[X]:(curious(X)))=>(?[X]:((~old(X)&kind(X)))))&
(![X]:((brave(X)|generous(X))<=>(~quiet(X)&~wise(X))))&
(((kind(alice)<~>generous(alice)))<=>(?[X]:((~curious(X)&funny(X)))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
(![X]:((~happy(X)|kind(X))<=>(happy(X)|~tall(X))))&
(![X]:(strong(X)<=>(curious(X)&~strong(X))))&
(((~quiet(john)&happy(john)))=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)<~>quiet(X))=>~brave(X)))&
(![X]:((brave(X)<~>~creative(X))=>happy(X)))&
((?[X]:((~old(X)&~quiet(X))))=>(?[X]:((calm(X)|~funny(X)))))&
((?[X]:((calm(X)|~calm(X))))<=>(~happy(alice)))&
(![X]:(~funny(X)<=>(~happy(X)&~brave(X))))&
(![X]:(creative(X)<=>~generous(X)))&
(~strong(lucy))&
((quiet(paul)&~happy(paul)))&
(?[X]:((~quiet(X)&wise(X))))&
(?[X]:(~funny(X)))&
((wise(lucy)<~>~kind(lucy)))&
(?[X]:((curious(X)<~>old(X))))&
(calm(mary))&
(?[X]:((kind(X)&~old(X)))) | ~quiet(john) | [] | null | 0 |
If fred is humble or curious then someone is both rich and not humble.
If someone is both not generous and not kind then lucy is not happy or not generous.
If someone is funny or not old then mary is both not strong and funny and vice versa.
If someone is either not quiet or not patient then lucy is old and vice versa.
Everyone who is rich or humble is not generous or generous and vice versa.
Everyone who is not rich is creative or strong.
If someone is either generous or rich then alice is either humble or not rich.
Everyone who is not generous or not humble is both kind and not generous and vice versa.
Everyone who is both not quiet and not humble is either brave or not curious and vice versa.
Everyone who is happy is either kind or not generous.
Everyone who is not kind or not curious is not old and vice versa.
If someone is not tall then lucy is not humble or not generous and vice versa.
Everyone who is not funny is either not tall or tall and vice versa.
Everyone who is tall or not strong is both quiet and funny and vice versa.
Everyone who is either not happy or creative is not quiet or not calm.
Everyone who is not generous or funny is both quiet and strong.
Someone is both strong and not wise.
Someone is either happy or old.
Paul is either tall or old.
Someone is both not creative and not wise.
Lucy is not tall. | Paul is not strong. | contradiction | (((humble(fred)|curious(fred)))=>(?[X]:((rich(X)&~humble(X)))))&
((?[X]:((~generous(X)&~kind(X))))=>((~happy(lucy)|~generous(lucy))))&
((?[X]:((funny(X)|~old(X))))<=>((~strong(mary)&funny(mary))))&
((?[X]:((~quiet(X)<~>~patient(X))))<=>(old(lucy)))&
(![X]:((rich(X)|humble(X))<=>(~generous(X)|generous(X))))&
(![X]:(~rich(X)=>(creative(X)|strong(X))))&
((?[X]:((generous(X)<~>rich(X))))=>((humble(alice)<~>~rich(alice))))&
(![X]:((~generous(X)|~humble(X))<=>(kind(X)&~generous(X))))&
(![X]:((~quiet(X)&~humble(X))<=>(brave(X)<~>~curious(X))))&
(![X]:(happy(X)=>(kind(X)<~>~generous(X))))&
(![X]:((~kind(X)|~curious(X))<=>~old(X)))&
((?[X]:(~tall(X)))<=>((~humble(lucy)|~generous(lucy))))&
(![X]:(~funny(X)<=>(~tall(X)<~>tall(X))))&
(![X]:((tall(X)|~strong(X))<=>(quiet(X)&funny(X))))&
(![X]:((~happy(X)<~>creative(X))=>(~quiet(X)|~calm(X))))&
(![X]:((~generous(X)|funny(X))=>(quiet(X)&strong(X))))&
(?[X]:((strong(X)&~wise(X))))&
(?[X]:((happy(X)<~>old(X))))&
((tall(paul)<~>old(paul)))&
(?[X]:((~creative(X)&~wise(X))))&
(~tall(lucy)) | ~strong(paul) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3609415589947325767726788
% SZS output start Proof for 3609415589947325767726788
14. ! [X0] : ((~strong(X0) | tall(X0)) <=> (funny(X0) & quiet(X0))) [input p13]
16. ! [X0] : ((funny(X0) | ~generous(X0)) => (strong(X0) & quiet(X0))) [input p15]
22. ~strong(paul) [input hypothesis]
33. ! [X0] : ((strong(X0) & quiet(X0)) | (~funny(X0) & generous(X0))) [ennf transformation 16]
61. ! [X0] : (((~strong(X0) | tall(X0)) | (~funny(X0) | ~quiet(X0))) & ((funny(X0) & quiet(X0)) | (strong(X0) & ~tall(X0)))) [nnf transformation 14]
62. ! [X0] : ((~strong(X0) | tall(X0) | ~funny(X0) | ~quiet(X0)) & ((funny(X0) & quiet(X0)) | (strong(X0) & ~tall(X0)))) [flattening 61]
120. funny(X0) | strong(X0) [cnf transformation 62]
125. strong(X0) | ~funny(X0) [cnf transformation 33]
133. ~strong(paul) [cnf transformation 22]
260. strong(X0) [subsumption resolution 125,120]
272. $false [subsumption resolution 133,260]
% SZS output end Proof for 3609415589947325767726788
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and humble is both quiet and not curious and vice versa. If someone is not creative or old then someone is either not patient or wise. Everyone who is both not generous and not old is either quiet or humble. If fred is tall or patient then someone is both not strong and not wise. Everyone who is both patient and not kind is creative. Everyone who is creative or not patient is both not brave and quiet and vice versa. Everyone who is both calm and not creative is both not humble and strong and vice versa. If someone is not funny or calm then fred is both creative and not brave and vice versa. If paul is not generous or brave then someone is not kind or not funny and vice versa. Everyone who is tall is not quiet or not tall. If someone is not curious or wise then someone is curious or not happy and vice versa. If paul is either calm or strong then someone is either happy or brave and vice versa. If paul is not creative then someone is not kind or not calm and vice versa. Everyone who is either strong or kind is funny or not old. If someone is both humble and brave then someone is both brave and strong and vice versa. Everyone who is both brave and humble is rich or not generous. Someone is either not kind or happy. Someone is curious or not patient. Lucy is calm or curious. Someone is kind or not patient. Paul is either tall or calm. Someone is either happy or brave. Lucy is not quiet. Mary is kind or not funny. | Mary is not kind. | contradiction | (![X]:((~creative(X)&humble(X))<=>(quiet(X)&~curious(X))))&
((?[X]:((~creative(X)|old(X))))=>(?[X]:((~patient(X)<~>wise(X)))))&
(![X]:((~generous(X)&~old(X))=>(quiet(X)<~>humble(X))))&
(((tall(fred)|patient(fred)))=>(?[X]:((~strong(X)&~wise(X)))))&
(![X]:((patient(X)&~kind(X))=>creative(X)))&
(![X]:((creative(X)|~patient(X))<=>(~brave(X)&quiet(X))))&
(![X]:((calm(X)&~creative(X))<=>(~humble(X)&strong(X))))&
((?[X]:((~funny(X)|calm(X))))<=>((creative(fred)&~brave(fred))))&
(((~generous(paul)|brave(paul)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(tall(X)=>(~quiet(X)|~tall(X))))&
((?[X]:((~curious(X)|wise(X))))<=>(?[X]:((curious(X)|~happy(X)))))&
(((calm(paul)<~>strong(paul)))<=>(?[X]:((happy(X)<~>brave(X)))))&
((~creative(paul))<=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:((strong(X)<~>kind(X))=>(funny(X)|~old(X))))&
((?[X]:((humble(X)&brave(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(![X]:((brave(X)&humble(X))=>(rich(X)|~generous(X))))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:((curious(X)|~patient(X))))&
((calm(lucy)|curious(lucy)))&
(?[X]:((kind(X)|~patient(X))))&
((tall(paul)<~>calm(paul)))&
(?[X]:((happy(X)<~>brave(X))))&
(~quiet(lucy))&
((kind(mary)|~funny(mary))) | ~kind(mary) | [
"p0",
"p6",
"p9",
"p11",
"p12",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3233523049529655290620093
% SZS output start Proof for 3233523049529655290620093
1. ! [X0] : ((humble(X0) & ~creative(X0)) <=> (~curious(X0) & quiet(X0))) [input p0]
7. ! [X0] : ((~creative(X0) & calm(X0)) <=> (strong(X0) & ~humble(X0))) [input p6]
10. ! [X0] : (tall(X0) => (~tall(X0) | ~quiet(X0))) [input p9]
12. (calm(paul) <~> strong(paul)) <=> ? [X0] : (happy(X0) <~> brave(X0)) [input p11]
13. ~creative(paul) <=> ? [X0] : (~calm(X0) | ~kind(X0)) [input p12]
21. tall(paul) <~> calm(paul) [input p20]
22. ? [X0] : (happy(X0) <~> brave(X0)) [input p21]
25. ~kind(mary) [input hypothesis]
36. ! [X0] : ((~tall(X0) | ~quiet(X0)) | ~tall(X0)) [ennf transformation 10]
37. ! [X0] : (~tall(X0) | ~quiet(X0) | ~tall(X0)) [flattening 36]
40. ! [X0] : (((humble(X0) & ~creative(X0)) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | (~humble(X0) | creative(X0)))) [nnf transformation 1]
41. ! [X0] : (((humble(X0) & ~creative(X0)) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | ~humble(X0) | creative(X0))) [flattening 40]
51. ! [X0] : (((~creative(X0) & calm(X0)) | (~strong(X0) | humble(X0))) & ((strong(X0) & ~humble(X0)) | (creative(X0) | ~calm(X0)))) [nnf transformation 7]
52. ! [X0] : (((~creative(X0) & calm(X0)) | ~strong(X0) | humble(X0)) & ((strong(X0) & ~humble(X0)) | creative(X0) | ~calm(X0))) [flattening 51]
68. (((~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul))) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ((calm(paul) | ~strong(paul)) & (strong(paul) | ~calm(paul)))) [nnf transformation 12]
69. (((~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul))) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (? [X1] : ((~brave(X1) | ~happy(X1)) & (brave(X1) | happy(X1))) | ((calm(paul) | ~strong(paul)) & (strong(paul) | ~calm(paul)))) [rectify 68]
70. ? [X1] : ((~brave(X1) | ~happy(X1)) & (brave(X1) | happy(X1))) => ((~brave(sK6) | ~happy(sK6)) & (brave(sK6) | happy(sK6))) [choice axiom]
71. (((~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul))) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(sK6) | ~happy(sK6)) & (brave(sK6) | happy(sK6))) | ((calm(paul) | ~strong(paul)) & (strong(paul) | ~calm(paul)))) [skolemisation 69,70]
72. (~creative(paul) | ! [X0] : (calm(X0) & kind(X0))) & (? [X0] : (~calm(X0) | ~kind(X0)) | creative(paul)) [nnf transformation 13]
73. (~creative(paul) | ! [X0] : (calm(X0) & kind(X0))) & (? [X1] : (~calm(X1) | ~kind(X1)) | creative(paul)) [rectify 72]
74. ? [X1] : (~calm(X1) | ~kind(X1)) => (~calm(sK7) | ~kind(sK7)) [choice axiom]
75. (~creative(paul) | ! [X0] : (calm(X0) & kind(X0))) & ((~calm(sK7) | ~kind(sK7)) | creative(paul)) [skolemisation 73,74]
89. (~calm(paul) | ~tall(paul)) & (calm(paul) | tall(paul)) [nnf transformation 21]
90. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) [nnf transformation 22]
91. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) => ((~brave(sK13) | ~happy(sK13)) & (brave(sK13) | happy(sK13))) [choice axiom]
92. (~brave(sK13) | ~happy(sK13)) & (brave(sK13) | happy(sK13)) [skolemisation 90,91]
93. ~humble(X0) | quiet(X0) | creative(X0) [cnf transformation 41]
113. ~calm(X0) | creative(X0) | ~humble(X0) [cnf transformation 52]
114. ~calm(X0) | creative(X0) | strong(X0) [cnf transformation 52]
115. ~strong(X0) | calm(X0) | humble(X0) [cnf transformation 52]
126. ~tall(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 37]
135. strong(paul) | calm(paul) | brave(X0) | ~happy(X0) [cnf transformation 71]
136. strong(paul) | calm(paul) | happy(X0) | ~brave(X0) [cnf transformation 71]
137. ~strong(paul) | ~calm(paul) | brave(X0) | ~happy(X0) [cnf transformation 71]
138. ~strong(paul) | ~calm(paul) | happy(X0) | ~brave(X0) [cnf transformation 71]
140. ~creative(paul) | kind(X0) [cnf transformation 75]
153. calm(paul) | tall(paul) [cnf transformation 89]
155. brave(sK13) | happy(sK13) [cnf transformation 92]
156. ~brave(sK13) | ~happy(sK13) [cnf transformation 92]
159. ~kind(mary) [cnf transformation 25]
160. ~tall(X0) | ~quiet(X0) [duplicate literal removal 126]
237. 17 <=> ! [X0] : kind(X0) [avatar definition]
238. kind(X0) <- (17) [avatar component clause 237]
283. 28 <=> ! [X0] : (happy(X0) | ~brave(X0)) [avatar definition]
284. ~brave(X0) | happy(X0) <- (28) [avatar component clause 283]
286. 29 <=> calm(paul) [avatar definition]
287. calm(paul) <- (29) [avatar component clause 286]
290. 30 <=> strong(paul) [avatar definition]
291. strong(paul) <- (30) [avatar component clause 290]
292. ~strong(paul) <- (~30) [avatar component clause 290]
293. 28 | ~29 | ~30 [avatar split clause 138,290,286,283]
295. 31 <=> ! [X0] : (brave(X0) | ~happy(X0)) [avatar definition]
296. ~happy(X0) | brave(X0) <- (31) [avatar component clause 295]
297. 31 | ~29 | ~30 [avatar split clause 137,290,286,295]
298. 28 | 29 | 30 [avatar split clause 136,290,286,283]
299. 31 | 29 | 30 [avatar split clause 135,290,286,295]
316. 35 <=> creative(paul) [avatar definition]
318. ~creative(paul) <- (~35) [avatar component clause 316]
320. 17 | ~35 [avatar split clause 140,316,237]
394. 52 <=> tall(paul) [avatar definition]
395. tall(paul) <- (52) [avatar component clause 394]
398. 52 | 29 [avatar split clause 153,286,394]
400. 53 <=> happy(sK13) [avatar definition]
401. happy(sK13) <- (53) [avatar component clause 400]
402. ~happy(sK13) <- (~53) [avatar component clause 400]
404. 54 <=> brave(sK13) [avatar definition]
405. brave(sK13) <- (54) [avatar component clause 404]
406. ~brave(sK13) <- (~54) [avatar component clause 404]
407. ~53 | ~54 [avatar split clause 156,404,400]
408. 53 | 54 [avatar split clause 155,404,400]
410. 55 <=> kind(mary) [avatar definition]
411. ~kind(mary) <- (~55) [avatar component clause 410]
418. ~55 [avatar split clause 159,410]
423. brave(sK13) <- (31, 53) [resolution 296,401]
424. $false <- (31, 53, ~54) [subsumption resolution 423,406]
425. ~31 | ~53 | 54 [avatar contradiction clause 424]
481. creative(paul) | ~humble(paul) <- (29) [resolution 113,287]
493. creative(paul) | strong(paul) <- (29) [resolution 114,287]
503. creative(paul) <- (29, ~30) [subsumption resolution 493,292]
504. 35 | ~29 | 30 [avatar split clause 503,290,286,316]
506. 68 <=> humble(paul) [avatar definition]
507. humble(paul) <- (68) [avatar component clause 506]
509. ~68 | 35 | ~29 [avatar split clause 481,286,316,506]
512. $false <- (17, ~55) [resolution 238,411]
513. ~17 | 55 [avatar contradiction clause 512]
519. ~quiet(paul) <- (52) [resolution 395,160]
520. calm(paul) | humble(paul) <- (30) [resolution 115,291]
524. quiet(paul) | creative(paul) <- (68) [resolution 507,93]
525. creative(paul) <- (52, 68) [subsumption resolution 524,519]
526. $false <- (~35, 52, 68) [subsumption resolution 525,318]
527. 35 | ~52 | ~68 [avatar contradiction clause 526]
528. 68 | 29 | ~30 [avatar split clause 520,290,286,506]
533. happy(sK13) <- (28, 54) [resolution 405,284]
536. $false <- (28, ~53, 54) [subsumption resolution 533,402]
537. ~28 | 53 | ~54 [avatar contradiction clause 536]
538. $false [avatar sat refutation 293,297,298,299,320,398,407,408,418,425,504,509,513,527,528,537]
% SZS output end Proof for 3233523049529655290620093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and quiet then someone is humble and vice versa. Everyone who is either calm or funny is either wise or not kind and vice versa. Everyone who is quiet or not wise is not happy or old. If mary is either humble or not old then paul is either old or not calm and vice versa. Everyone who is not happy is not rich or not quiet and vice versa. Everyone who is both not old and not generous is not wise and vice versa. Everyone who is not wise or humble is both not strong and rich and vice versa. Everyone who is not happy or creative is both not creative and not brave. Everyone who is both quiet and not tall is both not funny and not creative and vice versa. If someone is not quiet then someone is both not patient and strong and vice versa. If someone is not rich then fred is not strong. Everyone who is either not calm or not quiet is either not funny or patient and vice versa. If fred is brave or generous then someone is not kind. If someone is both not humble and strong then paul is wise or kind. Lucy is not wise or not quiet. Someone is either happy or patient. Someone is not humble or generous. Fred is either not quiet or calm. Someone is both not old and quiet. | Lucy is brave. | contradiction | ((?[X]:((old(X)&quiet(X))))<=>(?[X]:(humble(X))))&
(![X]:((calm(X)<~>funny(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((quiet(X)|~wise(X))=>(~happy(X)|old(X))))&
(((humble(mary)<~>~old(mary)))<=>((old(paul)<~>~calm(paul))))&
(![X]:(~happy(X)<=>(~rich(X)|~quiet(X))))&
(![X]:((~old(X)&~generous(X))<=>~wise(X)))&
(![X]:((~wise(X)|humble(X))<=>(~strong(X)&rich(X))))&
(![X]:((~happy(X)|creative(X))=>(~creative(X)&~brave(X))))&
(![X]:((quiet(X)&~tall(X))<=>(~funny(X)&~creative(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:(~rich(X)))=>(~strong(fred)))&
(![X]:((~calm(X)<~>~quiet(X))<=>(~funny(X)<~>patient(X))))&
(((brave(fred)|generous(fred)))=>(?[X]:(~kind(X))))&
((?[X]:((~humble(X)&strong(X))))=>((wise(paul)|kind(paul))))&
((~wise(lucy)|~quiet(lucy)))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((~humble(X)|generous(X))))&
((~quiet(fred)<~>calm(fred)))&
(?[X]:((~old(X)&quiet(X)))) | brave(lucy) | [
"p2",
"p4",
"p5",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 169759103977177627272021
% SZS output start Proof for 169759103977177627272021
3. ! [X0] : ((~wise(X0) | quiet(X0)) => (old(X0) | ~happy(X0))) [input p2]
5. ! [X0] : (~happy(X0) <=> (~quiet(X0) | ~rich(X0))) [input p4]
6. ! [X0] : ((~generous(X0) & ~old(X0)) <=> ~wise(X0)) [input p5]
8. ! [X0] : ((creative(X0) | ~happy(X0)) => (~brave(X0) & ~creative(X0))) [input p7]
15. ~quiet(lucy) | ~wise(lucy) [input p14]
20. brave(lucy) [input hypothesis]
23. ! [X0] : ((old(X0) | ~happy(X0)) | (wise(X0) & ~quiet(X0))) [ennf transformation 3]
24. ! [X0] : (old(X0) | ~happy(X0) | (wise(X0) & ~quiet(X0))) [flattening 23]
25. ! [X0] : ((~brave(X0) & ~creative(X0)) | (~creative(X0) & happy(X0))) [ennf transformation 8]
37. ! [X0] : ((~happy(X0) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | happy(X0))) [nnf transformation 5]
38. ! [X0] : ((~happy(X0) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | happy(X0))) [flattening 37]
39. ! [X0] : (((~generous(X0) & ~old(X0)) | wise(X0)) & (~wise(X0) | (generous(X0) | old(X0)))) [nnf transformation 6]
40. ! [X0] : (((~generous(X0) & ~old(X0)) | wise(X0)) & (~wise(X0) | generous(X0) | old(X0))) [flattening 39]
72. ~happy(X0) | old(X0) | ~quiet(X0) [cnf transformation 24]
84. ~happy(X0) | quiet(X0) [cnf transformation 38]
86. ~old(X0) | wise(X0) [cnf transformation 40]
95. ~brave(X0) | happy(X0) [cnf transformation 25]
116. ~quiet(lucy) | ~wise(lucy) [cnf transformation 15]
124. brave(lucy) [cnf transformation 20]
234. 23 <=> wise(lucy) [avatar definition]
236. ~wise(lucy) <- (~23) [avatar component clause 234]
238. 24 <=> quiet(lucy) [avatar definition]
239. quiet(lucy) <- (24) [avatar component clause 238]
241. ~23 | ~24 [avatar split clause 116,238,234]
283. happy(lucy) [resolution 95,124]
284. quiet(lucy) [resolution 283,84]
288. 24 [avatar split clause 284,238]
297. old(lucy) | ~quiet(lucy) [resolution 72,283]
304. old(lucy) <- (24) [subsumption resolution 297,239]
342. wise(lucy) <- (24) [resolution 304,86]
343. $false <- (~23, 24) [subsumption resolution 342,236]
344. 23 | ~24 [avatar contradiction clause 343]
345. $false [avatar sat refutation 241,288,344]
% SZS output end Proof for 169759103977177627272021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not curious then john is both not old and not happy and vice versa.
Everyone who is both quiet and curious is not kind and vice versa.
If susan is both old and tall then fred is not old or not tall and vice versa.
Everyone who is wise is either patient or funny.
Everyone who is either humble or not strong is rich.
Everyone who is happy or wise is both rich and not generous.
Everyone who is either not quiet or kind is both old and funny.
Everyone who is kind is either not strong or not wise.
If someone is both not tall and not generous then susan is both not tall and not curious.
If someone is either creative or not kind then fred is both not brave and not curious and vice versa.
If someone is patient then susan is not calm or wise and vice versa.
Everyone who is strong is not quiet or not creative and vice versa.
If mary is both not curious and rich then someone is old and vice versa.
Everyone who is wise is both strong and not old and vice versa.
If someone is not curious or rich then alice is not wise or not funny and vice versa.
Fred is not old or not calm.
Someone is both rich and wise.
Lucy is either not calm or old.
Someone is not rich.
Lucy is both brave and tall.
Someone is not happy. | Fred is strong. | entailment | ((?[X]:((funny(X)&~curious(X))))<=>((~old(john)&~happy(john))))&
(![X]:((quiet(X)&curious(X))<=>~kind(X)))&
(((old(susan)&tall(susan)))<=>((~old(fred)|~tall(fred))))&
(![X]:(wise(X)=>(patient(X)<~>funny(X))))&
(![X]:((humble(X)<~>~strong(X))=>rich(X)))&
(![X]:((happy(X)|wise(X))=>(rich(X)&~generous(X))))&
(![X]:((~quiet(X)<~>kind(X))=>(old(X)&funny(X))))&
(![X]:(kind(X)=>(~strong(X)<~>~wise(X))))&
((?[X]:((~tall(X)&~generous(X))))=>((~tall(susan)&~curious(susan))))&
((?[X]:((creative(X)<~>~kind(X))))<=>((~brave(fred)&~curious(fred))))&
((?[X]:(patient(X)))<=>((~calm(susan)|wise(susan))))&
(![X]:(strong(X)<=>(~quiet(X)|~creative(X))))&
(((~curious(mary)&rich(mary)))<=>(?[X]:(old(X))))&
(![X]:(wise(X)<=>(strong(X)&~old(X))))&
((?[X]:((~curious(X)|rich(X))))<=>((~wise(alice)|~funny(alice))))&
((~old(fred)|~calm(fred)))&
(?[X]:((rich(X)&wise(X))))&
((~calm(lucy)<~>old(lucy)))&
(?[X]:(~rich(X)))&
((brave(lucy)&tall(lucy)))&
(?[X]:(~happy(X))) | strong(fred) | [
"p1",
"p7",
"p9",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6267159459252819046941610
% SZS output start Proof for 6267159459252819046941610
2. ! [X0] : ((curious(X0) & quiet(X0)) <=> ~kind(X0)) [input p1]
8. ! [X0] : (kind(X0) => (~strong(X0) <~> ~wise(X0))) [input p7]
10. ? [X0] : (creative(X0) <~> ~kind(X0)) <=> (~curious(fred) & ~brave(fred)) [input p9]
12. ! [X0] : (strong(X0) <=> (~creative(X0) | ~quiet(X0))) [input p11]
14. ! [X0] : (wise(X0) <=> (~old(X0) & strong(X0))) [input p13]
17. ? [X0] : (wise(X0) & rich(X0)) [input p16]
22. ~strong(fred) [input hypothesis]
27. ! [X0] : ((~strong(X0) <~> ~wise(X0)) | ~kind(X0)) [ennf transformation 8]
34. ! [X0] : (((curious(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 2]
35. ! [X0] : (((curious(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | ~curious(X0) | ~quiet(X0))) [flattening 34]
41. ! [X0] : (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | ~kind(X0)) [nnf transformation 27]
42. (? [X0] : ((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (curious(fred) | brave(fred))) & ((~curious(fred) & ~brave(fred)) | ! [X0] : ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) [nnf transformation 10]
43. (? [X0] : ((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | curious(fred) | brave(fred)) & ((~curious(fred) & ~brave(fred)) | ! [X0] : ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) [flattening 42]
44. (? [X0] : ((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | curious(fred) | brave(fred)) & ((~curious(fred) & ~brave(fred)) | ! [X1] : ((creative(X1) | kind(X1)) & (~kind(X1) | ~creative(X1)))) [rectify 43]
45. ? [X0] : ((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) => ((kind(sK1) | ~creative(sK1)) & (~kind(sK1) | creative(sK1))) [choice axiom]
46. (((kind(sK1) | ~creative(sK1)) & (~kind(sK1) | creative(sK1))) | curious(fred) | brave(fred)) & ((~curious(fred) & ~brave(fred)) | ! [X1] : ((creative(X1) | kind(X1)) & (~kind(X1) | ~creative(X1)))) [skolemisation 44,45]
52. ! [X0] : ((strong(X0) | (creative(X0) & quiet(X0))) & ((~creative(X0) | ~quiet(X0)) | ~strong(X0))) [nnf transformation 12]
53. ! [X0] : ((strong(X0) | (creative(X0) & quiet(X0))) & (~creative(X0) | ~quiet(X0) | ~strong(X0))) [flattening 52]
59. ! [X0] : ((wise(X0) | (old(X0) | ~strong(X0))) & ((~old(X0) & strong(X0)) | ~wise(X0))) [nnf transformation 14]
60. ! [X0] : ((wise(X0) | old(X0) | ~strong(X0)) & ((~old(X0) & strong(X0)) | ~wise(X0))) [flattening 59]
66. ? [X0] : (wise(X0) & rich(X0)) => (wise(sK5) & rich(sK5)) [choice axiom]
67. wise(sK5) & rich(sK5) [skolemisation 17,66]
78. kind(X0) | quiet(X0) [cnf transformation 35]
79. kind(X0) | curious(X0) [cnf transformation 35]
97. ~strong(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 41]
98. ~kind(X0) | strong(X0) | wise(X0) [cnf transformation 41]
104. ~curious(fred) | creative(X1) | kind(X1) [cnf transformation 46]
110. ~creative(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 53]
116. ~wise(X0) | strong(X0) [cnf transformation 60]
125. wise(sK5) [cnf transformation 67]
132. ~strong(fred) [cnf transformation 22]
191. 13 <=> curious(fred) [avatar definition]
205. 16 <=> ! [X1] : (creative(X1) | kind(X1)) [avatar definition]
206. creative(X1) | kind(X1) <- (16) [avatar component clause 205]
207. 16 | ~13 [avatar split clause 104,191,205]
300. strong(sK5) [resolution 116,125]
358. ~wise(sK5) | ~kind(sK5) [resolution 97,300]
360. ~kind(sK5) [subsumption resolution 358,125]
363. strong(X0) | wise(X0) | curious(X0) [resolution 98,79]
365. strong(X0) | curious(X0) [subsumption resolution 363,116]
381. curious(fred) [resolution 365,132]
388. 13 [avatar split clause 381,191]
390. kind(X0) | ~quiet(X0) | ~strong(X0) <- (16) [resolution 206,110]
393. ~strong(X0) | kind(X0) <- (16) [subsumption resolution 390,78]
403. kind(sK5) <- (16) [resolution 393,300]
404. $false <- (16) [subsumption resolution 403,360]
405. ~16 [avatar contradiction clause 404]
406. $false [avatar sat refutation 207,388,405]
% SZS output end Proof for 6267159459252819046941610
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not happy then mary is not humble or old and vice versa.
If someone is wise then john is both brave and humble.
Everyone who is humble is either not old or not curious.
Everyone who is both funny and not kind is both quiet and creative and vice versa.
Everyone who is not wise is strong or not kind.
If mary is either creative or not curious then someone is strong or not quiet and vice versa.
If paul is not tall then someone is either brave or kind.
If paul is either not patient or not rich then mary is both quiet and not generous.
If susan is patient then susan is either happy or not generous.
Everyone who is humble is calm or happy.
Everyone who is old or not brave is strong.
Everyone who is either creative or not patient is rich or strong.
If someone is not wise then mary is not humble or not curious and vice versa.
Everyone who is either kind or happy is not quiet or patient and vice versa.
Everyone who is both not patient and funny is either kind or not kind and vice versa.
Everyone who is both not funny and brave is quiet and vice versa.
Someone is both generous and rich.
Fred is both humble and tall.
Someone is both wise and generous.
Paul is funny or calm.
Fred is both not creative and not old.
Someone is either quiet or not calm.
Someone is either not wise or not curious. | Susan is not happy. | entailment | ((?[X]:((brave(X)&~happy(X))))<=>((~humble(mary)|old(mary))))&
((?[X]:(wise(X)))=>((brave(john)&humble(john))))&
(![X]:(humble(X)=>(~old(X)<~>~curious(X))))&
(![X]:((funny(X)&~kind(X))<=>(quiet(X)&creative(X))))&
(![X]:(~wise(X)=>(strong(X)|~kind(X))))&
(((creative(mary)<~>~curious(mary)))<=>(?[X]:((strong(X)|~quiet(X)))))&
((~tall(paul))=>(?[X]:((brave(X)<~>kind(X)))))&
(((~patient(paul)<~>~rich(paul)))=>((quiet(mary)&~generous(mary))))&
((patient(susan))=>((happy(susan)<~>~generous(susan))))&
(![X]:(humble(X)=>(calm(X)|happy(X))))&
(![X]:((old(X)|~brave(X))=>strong(X)))&
(![X]:((creative(X)<~>~patient(X))=>(rich(X)|strong(X))))&
((?[X]:(~wise(X)))<=>((~humble(mary)|~curious(mary))))&
(![X]:((kind(X)<~>happy(X))<=>(~quiet(X)|patient(X))))&
(![X]:((~patient(X)&funny(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((~funny(X)&brave(X))<=>quiet(X)))&
(?[X]:((generous(X)&rich(X))))&
((humble(fred)&tall(fred)))&
(?[X]:((wise(X)&generous(X))))&
((funny(paul)|calm(paul)))&
((~creative(fred)&~old(fred)))&
(?[X]:((quiet(X)<~>~calm(X))))&
(?[X]:((~wise(X)<~>~curious(X)))) | ~happy(susan) | [
"p3",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 217296076748580375236659
% SZS output start Proof for 217296076748580375236659
4. ! [X0] : ((~kind(X0) & funny(X0)) <=> (creative(X0) & quiet(X0))) [input p3]
14. ! [X0] : ((kind(X0) <~> happy(X0)) <=> (patient(X0) | ~quiet(X0))) [input p13]
15. ! [X0] : ((funny(X0) & ~patient(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p14]
16. ! [X0] : ((brave(X0) & ~funny(X0)) <=> quiet(X0)) [input p15]
24. happy(susan) [input hypothesis]
44. ! [X0] : (((~kind(X0) & funny(X0)) | (~creative(X0) | ~quiet(X0))) & ((creative(X0) & quiet(X0)) | (kind(X0) | ~funny(X0)))) [nnf transformation 4]
45. ! [X0] : (((~kind(X0) & funny(X0)) | ~creative(X0) | ~quiet(X0)) & ((creative(X0) & quiet(X0)) | kind(X0) | ~funny(X0))) [flattening 44]
58. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (~patient(X0) & quiet(X0))) & ((patient(X0) | ~quiet(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [nnf transformation 14]
59. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (~patient(X0) & quiet(X0))) & (patient(X0) | ~quiet(X0) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [flattening 58]
60. ! [X0] : (((funny(X0) & ~patient(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | (~funny(X0) | patient(X0)))) [nnf transformation 15]
61. ! [X0] : (((funny(X0) & ~patient(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~funny(X0) | patient(X0))) [flattening 60]
62. ! [X0] : (((brave(X0) & ~funny(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) | funny(X0)))) [nnf transformation 16]
63. ! [X0] : (((brave(X0) & ~funny(X0)) | ~quiet(X0)) & (quiet(X0) | ~brave(X0) | funny(X0))) [flattening 62]
83. ~funny(X0) | kind(X0) | quiet(X0) [cnf transformation 45]
112. ~kind(X0) | ~happy(X0) | quiet(X0) [cnf transformation 59]
118. funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 61]
119. funny(X0) | kind(X0) | kind(X0) [cnf transformation 61]
121. ~funny(X0) | ~quiet(X0) [cnf transformation 63]
135. happy(susan) [cnf transformation 24]
138. funny(X0) | ~kind(X0) [duplicate literal removal 118]
139. kind(X0) | funny(X0) [duplicate literal removal 119]
230. 20 <=> happy(susan) [avatar definition]
231. happy(susan) <- (20) [avatar component clause 230]
249. funny(X0) [subsumption resolution 138,139]
251. ~quiet(X0) [subsumption resolution 121,249]
263. 20 [avatar split clause 135,230]
278. kind(X0) | quiet(X0) [resolution 83,249]
279. kind(X0) [subsumption resolution 278,251]
309. ~happy(X0) | quiet(X0) [resolution 112,279]
311. ~happy(X0) [subsumption resolution 309,251]
312. $false <- (20) [resolution 311,231]
317. ~20 [avatar contradiction clause 312]
318. $false [avatar sat refutation 263,317]
% SZS output end Proof for 217296076748580375236659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then someone is either not quiet or quiet. If susan is not kind or not funny then someone is not rich or creative and vice versa. Everyone who is not strong is both humble and calm. Everyone who is wise or humble is both quiet and not funny and vice versa. Everyone who is not generous is not old. If paul is creative then lucy is both rich and not wise and vice versa. Everyone who is either tall or wise is either not strong or not calm. Everyone who is strong or creative is both not curious and generous. If someone is both wise and kind then alice is both humble and tall and vice versa. If someone is either not wise or not happy then paul is not humble or kind and vice versa. If someone is not happy or not rich then someone is both patient and generous and vice versa. Everyone who is patient is rich or not wise and vice versa. If fred is both funny and not patient then lucy is tall and vice versa. Everyone who is strong or not humble is not quiet or not generous and vice versa. Everyone who is not tall is both happy and not wise. Someone is either not strong or not quiet. Fred is both not calm and brave. Someone is both rich and not tall. Someone is either not humble or not generous. Someone is both wise and rich. | Alice is calm. | neutral | ((?[X]:(~rich(X)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(((~kind(susan)|~funny(susan)))<=>(?[X]:((~rich(X)|creative(X)))))&
(![X]:(~strong(X)=>(humble(X)&calm(X))))&
(![X]:((wise(X)|humble(X))<=>(quiet(X)&~funny(X))))&
(![X]:(~generous(X)=>~old(X)))&
((creative(paul))<=>((rich(lucy)&~wise(lucy))))&
(![X]:((tall(X)<~>wise(X))=>(~strong(X)<~>~calm(X))))&
(![X]:((strong(X)|creative(X))=>(~curious(X)&generous(X))))&
((?[X]:((wise(X)&kind(X))))<=>((humble(alice)&tall(alice))))&
((?[X]:((~wise(X)<~>~happy(X))))<=>((~humble(paul)|kind(paul))))&
((?[X]:((~happy(X)|~rich(X))))<=>(?[X]:((patient(X)&generous(X)))))&
(![X]:(patient(X)<=>(rich(X)|~wise(X))))&
(((funny(fred)&~patient(fred)))<=>(tall(lucy)))&
(![X]:((strong(X)|~humble(X))<=>(~quiet(X)|~generous(X))))&
(![X]:(~tall(X)=>(happy(X)&~wise(X))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~calm(fred)&brave(fred)))&
(?[X]:((rich(X)&~tall(X))))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:((wise(X)&rich(X)))) | calm(alice) | [] | null | 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. | Fred is not old. | contradiction | (![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)))) | ~old(fred) | [
"p0",
"p1",
"p3",
"p4",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4089446414076339351462135
% SZS output start Proof for 4089446414076339351462135
1. ! [X0] : (generous(X0) <=> (~kind(X0) | ~quiet(X0))) [input p0]
2. ! [X0] : ((~happy(X0) | kind(X0)) <=> ~quiet(X0)) [input p1]
4. ! [X0] : (kind(X0) <=> ~curious(X0)) [input p3]
5. ! [X0] : ((curious(X0) | ~tall(X0)) => (~funny(X0) & ~calm(X0))) [input p4]
9. calm(paul) <=> ? [X0] : (calm(X0) <~> ~old(X0)) [input p8]
13. ! [X0] : ((calm(X0) & generous(X0)) => quiet(X0)) [input p12]
24. ~old(fred) [input hypothesis]
32. ! [X0] : ((~funny(X0) & ~calm(X0)) | (~curious(X0) & tall(X0))) [ennf transformation 5]
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]
46. ! [X0] : ((kind(X0) | curious(X0)) & (~curious(X0) | ~kind(X0))) [nnf transformation 4]
52. (calm(paul) | ! [X0] : ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (? [X0] : ((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | ~calm(paul)) [nnf transformation 9]
53. (calm(paul) | ! [X0] : ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (? [X1] : ((old(X1) | ~calm(X1)) & (~old(X1) | calm(X1))) | ~calm(paul)) [rectify 52]
54. ? [X1] : ((old(X1) | ~calm(X1)) & (~old(X1) | calm(X1))) => ((old(sK1) | ~calm(sK1)) & (~old(sK1) | calm(sK1))) [choice axiom]
55. (calm(paul) | ! [X0] : ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(sK1) | ~calm(sK1)) & (~old(sK1) | calm(sK1))) | ~calm(paul)) [skolemisation 53,54]
77. quiet(X0) | generous(X0) [cnf transformation 42]
79. ~kind(X0) | ~quiet(X0) [cnf transformation 44]
85. curious(X0) | kind(X0) [cnf transformation 46]
87. ~calm(X0) | ~curious(X0) [cnf transformation 32]
100. calm(paul) | calm(X0) | old(X0) [cnf transformation 55]
111. quiet(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 37]
130. ~old(fred) [cnf transformation 24]
153. 6 <=> quiet(paul) [avatar definition]
154. quiet(paul) <- (6) [avatar component clause 153]
177. 11 <=> ! [X0] : (calm(X0) | old(X0)) [avatar definition]
178. old(X0) | calm(X0) <- (11) [avatar component clause 177]
180. 12 <=> calm(paul) [avatar definition]
182. calm(paul) <- (12) [avatar component clause 180]
183. 11 | 12 [avatar split clause 100,180,177]
250. ~calm(X0) | quiet(X0) [subsumption resolution 111,77]
282. ~curious(paul) <- (12) [resolution 87,182]
284. kind(paul) <- (12) [resolution 282,85]
291. quiet(paul) <- (12) [resolution 250,182]
294. 6 | ~12 [avatar split clause 291,180,153]
296. ~quiet(paul) <- (12) [resolution 284,79]
297. $false <- (6, 12) [subsumption resolution 296,154]
298. ~6 | ~12 [avatar contradiction clause 297]
299. calm(fred) <- (11) [resolution 178,130]
310. quiet(fred) <- (11) [resolution 299,250]
311. ~curious(fred) <- (11) [resolution 299,87]
426. kind(fred) <- (11) [resolution 311,85]
458. ~quiet(fred) <- (11) [resolution 426,79]
462. $false <- (11) [subsumption resolution 458,310]
463. ~11 [avatar contradiction clause 462]
464. $false [avatar sat refutation 183,294,298,463]
% SZS output end Proof for 4089446414076339351462135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not happy or funny then mary is not brave.
Everyone who is not strong or not rich is both wise and not funny and vice versa.
If someone is old or not patient then paul is kind.
Everyone who is both brave and quiet is not funny and vice versa.
If someone is either not creative or humble then alice is both not kind and not strong and vice versa.
If susan is generous or not humble then fred is either curious or not strong.
Everyone who is both not funny and not curious is both strong and not creative and vice versa.
If paul is not old or creative then lucy is not funny and vice versa.
If susan is not happy or calm then someone is not brave.
If someone is both calm and rich then fred is rich or kind and vice versa.
Everyone who is not tall is both calm and brave.
Everyone who is humble or not humble is both generous and not humble.
Everyone who is either not happy or not rich is either not curious or strong.
If susan is not rich or tall then alice is both brave and not patient and vice versa.
If someone is not kind then fred is not rich.
If someone is not old then someone is generous or not kind.
John is both quiet and rich.
Someone is strong or not tall.
Someone is both not old and rich.
Alice is either not generous or tall.
Someone is tall.
Someone is not brave. | Lucy is not generous. | contradiction | (((~happy(alice)|funny(alice)))=>(~brave(mary)))&
(![X]:((~strong(X)|~rich(X))<=>(wise(X)&~funny(X))))&
((?[X]:((old(X)|~patient(X))))=>(kind(paul)))&
(![X]:((brave(X)&quiet(X))<=>~funny(X)))&
((?[X]:((~creative(X)<~>humble(X))))<=>((~kind(alice)&~strong(alice))))&
(((generous(susan)|~humble(susan)))=>((curious(fred)<~>~strong(fred))))&
(![X]:((~funny(X)&~curious(X))<=>(strong(X)&~creative(X))))&
(((~old(paul)|creative(paul)))<=>(~funny(lucy)))&
(((~happy(susan)|calm(susan)))=>(?[X]:(~brave(X))))&
((?[X]:((calm(X)&rich(X))))<=>((rich(fred)|kind(fred))))&
(![X]:(~tall(X)=>(calm(X)&brave(X))))&
(![X]:((humble(X)|~humble(X))=>(generous(X)&~humble(X))))&
(![X]:((~happy(X)<~>~rich(X))=>(~curious(X)<~>strong(X))))&
(((~rich(susan)|tall(susan)))<=>((brave(alice)&~patient(alice))))&
((?[X]:(~kind(X)))=>(~rich(fred)))&
((?[X]:(~old(X)))=>(?[X]:((generous(X)|~kind(X)))))&
((quiet(john)&rich(john)))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~old(X)&rich(X))))&
((~generous(alice)<~>tall(alice)))&
(?[X]:(tall(X)))&
(?[X]:(~brave(X))) | ~generous(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7582378395276551520379337
% SZS output start Proof for 7582378395276551520379337
12. ! [X0] : ((~humble(X0) | humble(X0)) => (~humble(X0) & generous(X0))) [input p11]
23. ~generous(lucy) [input hypothesis]
30. ! [X0] : ((~humble(X0) & generous(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 12]
109. generous(X0) | humble(X0) [cnf transformation 30]
110. ~humble(X0) | ~humble(X0) [cnf transformation 30]
132. ~generous(lucy) [cnf transformation 23]
133. ~humble(X0) [duplicate literal removal 110]
263. generous(X0) [subsumption resolution 109,133]
303. $false [subsumption resolution 132,263]
% SZS output end Proof for 7582378395276551520379337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is rich or patient and vice versa.
Everyone who is both creative and old is both strong and happy.
If someone is not creative or strong then someone is either not funny or tall and vice versa.
Everyone who is not strong or not old is strong or not old.
Everyone who is both quiet and tall is either happy or not rich and vice versa.
Everyone who is not tall or funny is either not happy or not wise.
If someone is kind then someone is brave.
If someone is brave then someone is either not strong or not kind.
Everyone who is not patient or not wise is not generous.
If paul is both not strong and not curious then john is not rich or rich and vice versa.
Everyone who is either generous or brave is either calm or not generous and vice versa.
If susan is generous then someone is both old and not wise and vice versa.
Everyone who is both not funny and kind is both funny and not rich.
Everyone who is both strong and rich is either quiet or rich.
Everyone who is not funny is both humble and curious and vice versa.
Everyone who is either quiet or not tall is not old or not patient.
Someone is kind or creative.
Paul is either not old or not patient.
Susan is both wise and patient.
Someone is both not tall and not happy.
Someone is either rich or not tall.
Someone is not rich or not strong.
Someone is rich or funny.
John is either not old or not curious. | John is brave. | neutral | (![X]:(~old(X)<=>(rich(X)|patient(X))))&
(![X]:((creative(X)&old(X))=>(strong(X)&happy(X))))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:((~funny(X)<~>tall(X)))))&
(![X]:((~strong(X)|~old(X))=>(strong(X)|~old(X))))&
(![X]:((quiet(X)&tall(X))<=>(happy(X)<~>~rich(X))))&
(![X]:((~tall(X)|funny(X))=>(~happy(X)<~>~wise(X))))&
((?[X]:(kind(X)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~wise(X))=>~generous(X)))&
(((~strong(paul)&~curious(paul)))<=>((~rich(john)|rich(john))))&
(![X]:((generous(X)<~>brave(X))<=>(calm(X)<~>~generous(X))))&
((generous(susan))<=>(?[X]:((old(X)&~wise(X)))))&
(![X]:((~funny(X)&kind(X))=>(funny(X)&~rich(X))))&
(![X]:((strong(X)&rich(X))=>(quiet(X)<~>rich(X))))&
(![X]:(~funny(X)<=>(humble(X)&curious(X))))&
(![X]:((quiet(X)<~>~tall(X))=>(~old(X)|~patient(X))))&
(?[X]:((kind(X)|creative(X))))&
((~old(paul)<~>~patient(paul)))&
((wise(susan)&patient(susan)))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((rich(X)<~>~tall(X))))&
(?[X]:((~rich(X)|~strong(X))))&
(?[X]:((rich(X)|funny(X))))&
((~old(john)<~>~curious(john))) | brave(john) | [] | null | 0 |
If someone is old then john is not brave or creative. Everyone who is old is both calm and not creative. Everyone who is not curious is not patient and vice versa. Everyone who is not kind is either strong or not strong. If someone is creative then alice is brave. If susan is both not generous and not funny then someone is curious and vice versa. If someone is brave or not generous then someone is not brave or not rich. Everyone who is not kind is both happy and strong. If someone is both not patient and not tall then someone is either kind or not brave and vice versa. Everyone who is both rich and tall is strong or humble and vice versa. Everyone who is rich or not humble is either creative or old. If someone is not old then someone is both not curious and kind and vice versa. Everyone who is both patient and funny is either patient or not humble. Everyone who is both not rich and wise is either not wise or generous. If someone is happy then mary is humble and vice versa. Everyone who is both rich and old is either not humble or humble and vice versa. Mary is either not tall or not strong. Fred is either patient or not curious. Susan is both wise and not funny. John is old. Someone is humble. Mary is funny or humble. Fred is either kind or not funny. | Fred is tall. | entailment | ((?[X]:(old(X)))=>((~brave(john)|creative(john))))&
(![X]:(old(X)=>(calm(X)&~creative(X))))&
(![X]:(~curious(X)<=>~patient(X)))&
(![X]:(~kind(X)=>(strong(X)<~>~strong(X))))&
((?[X]:(creative(X)))=>(brave(alice)))&
(((~generous(susan)&~funny(susan)))<=>(?[X]:(curious(X))))&
((?[X]:((brave(X)|~generous(X))))=>(?[X]:((~brave(X)|~rich(X)))))&
(![X]:(~kind(X)=>(happy(X)&strong(X))))&
((?[X]:((~patient(X)&~tall(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((rich(X)&tall(X))<=>(strong(X)|humble(X))))&
(![X]:((rich(X)|~humble(X))=>(creative(X)<~>old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((patient(X)&funny(X))=>(patient(X)<~>~humble(X))))&
(![X]:((~rich(X)&wise(X))=>(~wise(X)<~>generous(X))))&
((?[X]:(happy(X)))<=>(humble(mary)))&
(![X]:((rich(X)&old(X))<=>(~humble(X)<~>humble(X))))&
((~tall(mary)<~>~strong(mary)))&
((patient(fred)<~>~curious(fred)))&
((wise(susan)&~funny(susan)))&
(old(john))&
(?[X]:(humble(X)))&
((funny(mary)|humble(mary)))&
((kind(fred)<~>~funny(fred))) | tall(fred) | [
"p2",
"p7",
"p9",
"p11",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6430199633559783990486279
% SZS output start Proof for 6430199633559783990486279
3. ! [X0] : (~curious(X0) <=> ~patient(X0)) [input p2]
8. ! [X0] : (~kind(X0) => (strong(X0) & happy(X0))) [input p7]
10. ! [X0] : ((tall(X0) & rich(X0)) <=> (humble(X0) | strong(X0))) [input p9]
12. ? [X0] : ~old(X0) <=> ? [X0] : (kind(X0) & ~curious(X0)) [input p11]
13. ! [X0] : ((funny(X0) & patient(X0)) => (patient(X0) <~> ~humble(X0))) [input p12]
16. ! [X0] : ((old(X0) & rich(X0)) <=> (~humble(X0) <~> humble(X0))) [input p15]
23. kind(fred) <~> ~funny(fred) [input p22]
24. ~tall(fred) [input hypothesis]
27. ? [X0] : ~old(X0) <=> ? [X1] : (kind(X1) & ~curious(X1)) [rectify 12]
35. ! [X0] : ((strong(X0) & happy(X0)) | kind(X0)) [ennf transformation 8]
37. ! [X0] : ((patient(X0) <~> ~humble(X0)) | (~funny(X0) | ~patient(X0))) [ennf transformation 13]
38. ! [X0] : ((patient(X0) <~> ~humble(X0)) | ~funny(X0) | ~patient(X0)) [flattening 37]
41. ! [X0] : ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0))) [nnf transformation 3]
56. ! [X0] : (((tall(X0) & rich(X0)) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | (~tall(X0) | ~rich(X0)))) [nnf transformation 10]
57. ! [X0] : (((tall(X0) & rich(X0)) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ~tall(X0) | ~rich(X0))) [flattening 56]
59. (? [X0] : ~old(X0) | ! [X1] : (~kind(X1) | curious(X1))) & (? [X1] : (kind(X1) & ~curious(X1)) | ! [X0] : old(X0)) [nnf transformation 27]
60. (? [X0] : ~old(X0) | ! [X1] : (~kind(X1) | curious(X1))) & (? [X2] : (kind(X2) & ~curious(X2)) | ! [X3] : old(X3)) [rectify 59]
61. ? [X0] : ~old(X0) => ~old(sK4) [choice axiom]
62. ? [X2] : (kind(X2) & ~curious(X2)) => (kind(sK5) & ~curious(sK5)) [choice axiom]
63. (~old(sK4) | ! [X1] : (~kind(X1) | curious(X1))) & ((kind(sK5) & ~curious(sK5)) | ! [X3] : old(X3)) [skolemisation 60,62,61]
64. ! [X0] : (((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | ~funny(X0) | ~patient(X0)) [nnf transformation 38]
70. ! [X0] : (((old(X0) & rich(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~old(X0) | ~rich(X0)))) [nnf transformation 16]
71. ! [X0] : (((old(X0) & rich(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~old(X0) | ~rich(X0))) [flattening 70]
76. (funny(fred) | ~kind(fred)) & (~funny(fred) | kind(fred)) [nnf transformation 23]
80. ~curious(X0) | patient(X0) [cnf transformation 41]
90. strong(X0) | kind(X0) [cnf transformation 35]
100. ~strong(X0) | tall(X0) [cnf transformation 57]
101. ~humble(X0) | tall(X0) [cnf transformation 57]
108. ~old(sK4) | ~kind(X1) | curious(X1) [cnf transformation 63]
110. humble(X0) | ~patient(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 64]
119. old(X0) | humble(X0) | humble(X0) [cnf transformation 71]
120. old(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 71]
131. funny(fred) | ~kind(fred) [cnf transformation 76]
132. ~tall(fred) [cnf transformation 24]
135. old(X0) | humble(X0) [duplicate literal removal 119]
136. ~humble(X0) | old(X0) [duplicate literal removal 120]
138. ~funny(X0) | ~patient(X0) | humble(X0) [duplicate literal removal 110]
225. 21 <=> ! [X1] : (~kind(X1) | curious(X1)) [avatar definition]
226. ~kind(X1) | curious(X1) <- (21) [avatar component clause 225]
228. 22 <=> old(sK4) [avatar definition]
230. ~old(sK4) <- (~22) [avatar component clause 228]
231. 21 | ~22 [avatar split clause 108,228,225]
233. 23 <=> ! [X3] : old(X3) [avatar definition]
234. old(X3) <- (23) [avatar component clause 233]
258. old(X0) [subsumption resolution 135,136]
259. 23 [avatar split clause 258,233]
270. 30 <=> kind(fred) [avatar definition]
271. kind(fred) <- (30) [avatar component clause 270]
274. 31 <=> funny(fred) [avatar definition]
276. funny(fred) <- (31) [avatar component clause 274]
277. ~30 | 31 [avatar split clause 131,274,270]
279. $false <- (~22, 23) [subsumption resolution 230,234]
280. 22 | ~23 [avatar contradiction clause 279]
290. tall(X0) | kind(X0) [resolution 100,90]
304. kind(fred) [resolution 290,132]
308. 30 [avatar split clause 304,270]
309. curious(fred) <- (21, 30) [resolution 271,226]
310. ~patient(fred) | humble(fred) <- (31) [resolution 138,276]
312. 32 <=> humble(fred) [avatar definition]
314. humble(fred) <- (32) [avatar component clause 312]
316. 33 <=> patient(fred) [avatar definition]
319. 32 | ~33 | ~31 [avatar split clause 310,274,316,312]
320. patient(fred) <- (21, 30) [resolution 309,80]
323. 33 | ~21 | ~30 [avatar split clause 320,270,225,316]
328. tall(fred) <- (32) [resolution 314,101]
330. $false <- (32) [subsumption resolution 328,132]
331. ~32 [avatar contradiction clause 330]
332. $false [avatar sat refutation 231,259,277,280,308,319,323,331]
% SZS output end Proof for 6430199633559783990486279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or rich is not kind and vice versa.
Everyone who is either old or strong is both not strong and curious.
If someone is either creative or humble then someone is not patient and vice versa.
If someone is not brave then someone is either not calm or generous and vice versa.
Everyone who is not rich is not happy and vice versa.
If someone is both not generous and kind then alice is not calm.
Everyone who is not generous is both not kind and brave and vice versa.
If susan is not quiet or rich then mary is either patient or not wise and vice versa.
Everyone who is both not funny and not wise is both not generous and generous.
Everyone who is either old or not curious is either not strong or curious and vice versa.
Everyone who is kind or rich is both happy and rich.
If paul is either not old or not creative then someone is funny or not rich.
If john is both humble and not quiet then someone is not humble or wise.
Everyone who is not rich or generous is not wise or not humble and vice versa.
Everyone who is rich is not brave or brave and vice versa.
If someone is not quiet then someone is rich.
Fred is either not generous or calm.
Fred is either not wise or not strong.
Someone is not curious.
Paul is both generous and not brave.
Mary is not calm or wise.
Paul is not patient or kind.
Susan is wise or kind. | Fred is not strong. | neutral | (![X]:((funny(X)|rich(X))<=>~kind(X)))&
(![X]:((old(X)<~>strong(X))=>(~strong(X)&curious(X))))&
((?[X]:((creative(X)<~>humble(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((~calm(X)<~>generous(X)))))&
(![X]:(~rich(X)<=>~happy(X)))&
((?[X]:((~generous(X)&kind(X))))=>(~calm(alice)))&
(![X]:(~generous(X)<=>(~kind(X)&brave(X))))&
(((~quiet(susan)|rich(susan)))<=>((patient(mary)<~>~wise(mary))))&
(![X]:((~funny(X)&~wise(X))=>(~generous(X)&generous(X))))&
(![X]:((old(X)<~>~curious(X))<=>(~strong(X)<~>curious(X))))&
(![X]:((kind(X)|rich(X))=>(happy(X)&rich(X))))&
(((~old(paul)<~>~creative(paul)))=>(?[X]:((funny(X)|~rich(X)))))&
(((humble(john)&~quiet(john)))=>(?[X]:((~humble(X)|wise(X)))))&
(![X]:((~rich(X)|generous(X))<=>(~wise(X)|~humble(X))))&
(![X]:(rich(X)<=>(~brave(X)|brave(X))))&
((?[X]:(~quiet(X)))=>(?[X]:(rich(X))))&
((~generous(fred)<~>calm(fred)))&
((~wise(fred)<~>~strong(fred)))&
(?[X]:(~curious(X)))&
((generous(paul)&~brave(paul)))&
((~calm(mary)|wise(mary)))&
((~patient(paul)|kind(paul)))&
((wise(susan)|kind(susan))) | ~strong(fred) | [] | null | 0 |
Everyone who is not kind is both wise and not happy. If alice is brave or not strong then john is either not tall or curious and vice versa. If someone is either humble or wise then someone is strong or not kind and vice versa. Everyone who is either not funny or not creative is both not patient and calm. If paul is not funny or rich then lucy is quiet or not kind. If someone is either not humble or not generous then someone is both rich and not creative and vice versa. Everyone who is not rich is both not calm and not generous and vice versa. Everyone who is not generous is both old and funny. Everyone who is either kind or calm is either not happy or strong. If someone is either not quiet or patient then someone is both old and not creative and vice versa. Everyone who is both rich and not brave is either not rich or not funny and vice versa. If someone is old or not quiet then someone is both not brave and funny and vice versa. If someone is either calm or quiet then someone is either kind or not old and vice versa. Everyone who is not quiet or not calm is both not quiet and not strong and vice versa. Everyone who is both not rich and generous is curious. If someone is both not kind and tall then susan is creative and vice versa. Paul is both not curious and strong. Fred is not tall or calm. Someone is either old or not wise. Someone is both not wise and strong. Someone is either funny or not rich. Paul is brave. | Fred is calm. | entailment | (![X]:(~kind(X)=>(wise(X)&~happy(X))))&
(((brave(alice)|~strong(alice)))<=>((~tall(john)<~>curious(john))))&
((?[X]:((humble(X)<~>wise(X))))<=>(?[X]:((strong(X)|~kind(X)))))&
(![X]:((~funny(X)<~>~creative(X))=>(~patient(X)&calm(X))))&
(((~funny(paul)|rich(paul)))=>((quiet(lucy)|~kind(lucy))))&
((?[X]:((~humble(X)<~>~generous(X))))<=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:(~rich(X)<=>(~calm(X)&~generous(X))))&
(![X]:(~generous(X)=>(old(X)&funny(X))))&
(![X]:((kind(X)<~>calm(X))=>(~happy(X)<~>strong(X))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((rich(X)&~brave(X))<=>(~rich(X)<~>~funny(X))))&
((?[X]:((old(X)|~quiet(X))))<=>(?[X]:((~brave(X)&funny(X)))))&
((?[X]:((calm(X)<~>quiet(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
(![X]:((~quiet(X)|~calm(X))<=>(~quiet(X)&~strong(X))))&
(![X]:((~rich(X)&generous(X))=>curious(X)))&
((?[X]:((~kind(X)&tall(X))))<=>(creative(susan)))&
((~curious(paul)&strong(paul)))&
((~tall(fred)|calm(fred)))&
(?[X]:((old(X)<~>~wise(X))))&
(?[X]:((~wise(X)&strong(X))))&
(?[X]:((funny(X)<~>~rich(X))))&
(brave(paul)) | calm(fred) | [
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8735546145695120882446569
% SZS output start Proof for 8735546145695120882446569
11. ! [X0] : ((~brave(X0) & rich(X0)) <=> (~rich(X0) <~> ~funny(X0))) [input p10]
12. ? [X0] : (~quiet(X0) | old(X0)) <=> ? [X0] : (funny(X0) & ~brave(X0)) [input p11]
14. ! [X0] : ((~calm(X0) | ~quiet(X0)) <=> (~strong(X0) & ~quiet(X0))) [input p13]
23. ~calm(fred) [input hypothesis]
27. ? [X0] : (~quiet(X0) | old(X0)) <=> ? [X1] : (funny(X1) & ~brave(X1)) [rectify 12]
58. ! [X0] : (((~brave(X0) & rich(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (brave(X0) | ~rich(X0)))) [nnf transformation 11]
59. ! [X0] : (((~brave(X0) & rich(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | brave(X0) | ~rich(X0))) [flattening 58]
60. (? [X0] : (~quiet(X0) | old(X0)) | ! [X1] : (~funny(X1) | brave(X1))) & (? [X1] : (funny(X1) & ~brave(X1)) | ! [X0] : (quiet(X0) & ~old(X0))) [nnf transformation 27]
61. (? [X0] : (~quiet(X0) | old(X0)) | ! [X1] : (~funny(X1) | brave(X1))) & (? [X2] : (funny(X2) & ~brave(X2)) | ! [X3] : (quiet(X3) & ~old(X3))) [rectify 60]
62. ? [X0] : (~quiet(X0) | old(X0)) => (~quiet(sK6) | old(sK6)) [choice axiom]
63. ? [X2] : (funny(X2) & ~brave(X2)) => (funny(sK7) & ~brave(sK7)) [choice axiom]
64. ((~quiet(sK6) | old(sK6)) | ! [X1] : (~funny(X1) | brave(X1))) & ((funny(sK7) & ~brave(sK7)) | ! [X3] : (quiet(X3) & ~old(X3))) [skolemisation 61,63,62]
70. ! [X0] : (((~calm(X0) | ~quiet(X0)) | (strong(X0) | quiet(X0))) & ((~strong(X0) & ~quiet(X0)) | (calm(X0) & quiet(X0)))) [nnf transformation 14]
71. ! [X0] : ((~calm(X0) | ~quiet(X0) | strong(X0) | quiet(X0)) & ((~strong(X0) & ~quiet(X0)) | (calm(X0) & quiet(X0)))) [flattening 70]
125. ~funny(X0) | ~rich(X0) | brave(X0) | ~rich(X0) [cnf transformation 59]
127. rich(X0) | ~funny(X0) | rich(X0) [cnf transformation 59]
132. ~brave(sK7) | quiet(X3) [cnf transformation 64]
134. funny(sK7) | quiet(X3) [cnf transformation 64]
145. ~quiet(X0) | calm(X0) [cnf transformation 71]
163. ~calm(fred) [cnf transformation 23]
164. ~funny(X0) | ~rich(X0) | brave(X0) [duplicate literal removal 125]
165. ~funny(X0) | rich(X0) [duplicate literal removal 127]
304. ~funny(X0) | brave(X0) [subsumption resolution 164,165]
306. 31 <=> ! [X3] : quiet(X3) [avatar definition]
307. quiet(X3) <- (31) [avatar component clause 306]
309. 32 <=> funny(sK7) [avatar definition]
311. funny(sK7) <- (32) [avatar component clause 309]
312. 31 | 32 [avatar split clause 134,309,306]
318. 34 <=> brave(sK7) [avatar definition]
320. ~brave(sK7) <- (~34) [avatar component clause 318]
321. 31 | ~34 [avatar split clause 132,318,306]
342. 39 <=> ! [X3] : (calm(X3) | ~quiet(X3)) [avatar definition]
343. ~quiet(X3) | calm(X3) <- (39) [avatar component clause 342]
359. 39 [avatar split clause 145,342]
383. 48 <=> calm(fred) [avatar definition]
384. ~calm(fred) <- (~48) [avatar component clause 383]
406. ~48 [avatar split clause 163,383]
443. brave(sK7) <- (32) [resolution 304,311]
445. $false <- (32, ~34) [subsumption resolution 443,320]
446. ~32 | 34 [avatar contradiction clause 445]
451. calm(X0) <- (31, 39) [resolution 343,307]
458. $false <- (31, 39, ~48) [resolution 451,384]
462. ~31 | ~39 | 48 [avatar contradiction clause 458]
463. $false [avatar sat refutation 312,321,359,406,446,462]
% SZS output end Proof for 8735546145695120882446569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is both not wise and not funny.
Everyone who is both not creative and wise is not brave.
Everyone who is not rich is either not tall or not calm and vice versa.
Everyone who is either happy or not tall is either curious or happy and vice versa.
Everyone who is both not humble and not wise is either not funny or not wise and vice versa.
Everyone who is not humble is both not patient and kind and vice versa.
Everyone who is both not curious and calm is not tall or quiet and vice versa.
If alice is either wise or not quiet then paul is both strong and funny and vice versa.
Everyone who is both not quiet and not creative is either not funny or not strong and vice versa.
If fred is strong or wise then someone is either not humble or kind and vice versa.
Everyone who is not wise or happy is both not generous and not wise.
Everyone who is not tall or not quiet is strong and vice versa.
Everyone who is brave or creative is both not strong and not generous and vice versa.
If fred is both curious and not humble then lucy is not funny or not curious.
If fred is patient then someone is either patient or not rich.
If someone is humble or not brave then someone is not old and vice versa.
Someone is either not patient or patient.
Paul is either strong or not curious.
Someone is not quiet or creative.
Someone is rich or not kind.
Someone is happy or not tall.
Someone is either kind or rich.
Someone is not happy or old. | Alice is not rich. | contradiction | (![X]:(~tall(X)=>(~wise(X)&~funny(X))))&
(![X]:((~creative(X)&wise(X))=>~brave(X)))&
(![X]:(~rich(X)<=>(~tall(X)<~>~calm(X))))&
(![X]:((happy(X)<~>~tall(X))<=>(curious(X)<~>happy(X))))&
(![X]:((~humble(X)&~wise(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:(~humble(X)<=>(~patient(X)&kind(X))))&
(![X]:((~curious(X)&calm(X))<=>(~tall(X)|quiet(X))))&
(((wise(alice)<~>~quiet(alice)))<=>((strong(paul)&funny(paul))))&
(![X]:((~quiet(X)&~creative(X))<=>(~funny(X)<~>~strong(X))))&
(((strong(fred)|wise(fred)))<=>(?[X]:((~humble(X)<~>kind(X)))))&
(![X]:((~wise(X)|happy(X))=>(~generous(X)&~wise(X))))&
(![X]:((~tall(X)|~quiet(X))<=>strong(X)))&
(![X]:((brave(X)|creative(X))<=>(~strong(X)&~generous(X))))&
(((curious(fred)&~humble(fred)))=>((~funny(lucy)|~curious(lucy))))&
((patient(fred))=>(?[X]:((patient(X)<~>~rich(X)))))&
((?[X]:((humble(X)|~brave(X))))<=>(?[X]:(~old(X))))&
(?[X]:((~patient(X)<~>patient(X))))&
((strong(paul)<~>~curious(paul)))&
(?[X]:((~quiet(X)|creative(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((happy(X)|~tall(X))))&
(?[X]:((kind(X)<~>rich(X))))&
(?[X]:((~happy(X)|old(X)))) | ~rich(alice) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8927520762774715831167978
% SZS output start Proof for 8927520762774715831167978
3. ! [X0] : (~rich(X0) <=> (~tall(X0) <~> ~calm(X0))) [input p2]
4. ! [X0] : ((happy(X0) <~> ~tall(X0)) <=> (curious(X0) <~> happy(X0))) [input p3]
5. ! [X0] : ((~wise(X0) & ~humble(X0)) <=> (~funny(X0) <~> ~wise(X0))) [input p4]
7. ! [X0] : ((calm(X0) & ~curious(X0)) <=> (quiet(X0) | ~tall(X0))) [input p6]
8. (wise(alice) <~> ~quiet(alice)) <=> (funny(paul) & strong(paul)) [input p7]
9. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> (~funny(X0) <~> ~strong(X0))) [input p8]
12. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> strong(X0)) [input p11]
13. ! [X0] : ((creative(X0) | brave(X0)) <=> (~generous(X0) & ~strong(X0))) [input p12]
18. strong(paul) <~> ~curious(paul) [input p17]
24. ~rich(alice) [input hypothesis]
33. ! [X0] : ((~rich(X0) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) & (((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | rich(X0))) [nnf transformation 3]
34. ! [X0] : ((((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0)))) & (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0))))) [nnf transformation 4]
35. ! [X0] : (((~wise(X0) & ~humble(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | (wise(X0) | humble(X0)))) [nnf transformation 5]
36. ! [X0] : (((~wise(X0) & ~humble(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | wise(X0) | humble(X0))) [flattening 35]
39. ! [X0] : (((calm(X0) & ~curious(X0)) | (~quiet(X0) & tall(X0))) & ((quiet(X0) | ~tall(X0)) | (~calm(X0) | curious(X0)))) [nnf transformation 7]
40. ! [X0] : (((calm(X0) & ~curious(X0)) | (~quiet(X0) & tall(X0))) & (quiet(X0) | ~tall(X0) | ~calm(X0) | curious(X0))) [flattening 39]
41. (((quiet(alice) | ~wise(alice)) & (~quiet(alice) | wise(alice))) | (~funny(paul) | ~strong(paul))) & ((funny(paul) & strong(paul)) | ((wise(alice) | quiet(alice)) & (~quiet(alice) | ~wise(alice)))) [nnf transformation 8]
42. (((quiet(alice) | ~wise(alice)) & (~quiet(alice) | wise(alice))) | ~funny(paul) | ~strong(paul)) & ((funny(paul) & strong(paul)) | ((wise(alice) | quiet(alice)) & (~quiet(alice) | ~wise(alice)))) [flattening 41]
43. ! [X0] : (((~creative(X0) & ~quiet(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (creative(X0) | quiet(X0)))) [nnf transformation 9]
44. ! [X0] : (((~creative(X0) & ~quiet(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | creative(X0) | quiet(X0))) [flattening 43]
50. ! [X0] : (((~quiet(X0) | ~tall(X0)) | ~strong(X0)) & (strong(X0) | (quiet(X0) & tall(X0)))) [nnf transformation 12]
51. ! [X0] : ((~quiet(X0) | ~tall(X0) | ~strong(X0)) & (strong(X0) | (quiet(X0) & tall(X0)))) [flattening 50]
52. ! [X0] : (((creative(X0) | brave(X0)) | (generous(X0) | strong(X0))) & ((~generous(X0) & ~strong(X0)) | (~creative(X0) & ~brave(X0)))) [nnf transformation 13]
53. ! [X0] : ((creative(X0) | brave(X0) | generous(X0) | strong(X0)) & ((~generous(X0) & ~strong(X0)) | (~creative(X0) & ~brave(X0)))) [flattening 52]
65. (curious(paul) | ~strong(paul)) & (~curious(paul) | strong(paul)) [nnf transformation 18]
80. ~calm(X0) | ~tall(X0) | rich(X0) [cnf transformation 33]
85. happy(X0) | curious(X0) | happy(X0) | tall(X0) [cnf transformation 34]
86. ~happy(X0) | ~curious(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 34]
88. ~tall(X0) | happy(X0) | happy(X0) | ~curious(X0) [cnf transformation 34]
91. tall(X0) | ~happy(X0) | curious(X0) | ~happy(X0) [cnf transformation 34]
96. ~wise(X0) | ~wise(X0) | funny(X0) [cnf transformation 36]
102. ~curious(X0) | tall(X0) [cnf transformation 40]
105. ~quiet(X0) | calm(X0) [cnf transformation 40]
107. strong(paul) | wise(alice) | quiet(alice) [cnf transformation 42]
112. ~strong(X0) | ~funny(X0) | creative(X0) | quiet(X0) [cnf transformation 44]
129. strong(X0) | quiet(X0) [cnf transformation 51]
132. ~strong(X0) | ~creative(X0) [cnf transformation 53]
145. curious(paul) | ~strong(paul) [cnf transformation 65]
152. ~rich(alice) [cnf transformation 24]
154. ~wise(X0) | funny(X0) [duplicate literal removal 96]
155. happy(X0) | curious(X0) | tall(X0) [duplicate literal removal 85]
156. ~happy(X0) | ~curious(X0) | ~tall(X0) [duplicate literal removal 86]
157. ~curious(X0) | happy(X0) | ~tall(X0) [duplicate literal removal 88]
158. ~happy(X0) | tall(X0) | curious(X0) [duplicate literal removal 91]
159. ~curious(X0) | ~tall(X0) [subsumption resolution 156,157]
160. curious(X0) | tall(X0) [subsumption resolution 155,158]
162. ~curious(X0) [subsumption resolution 102,159]
165. 1 <=> strong(paul) [avatar definition]
173. 3 <=> wise(alice) [avatar definition]
174. wise(alice) <- (3) [avatar component clause 173]
177. 4 <=> quiet(alice) [avatar definition]
178. ~quiet(alice) <- (~4) [avatar component clause 177]
179. quiet(alice) <- (4) [avatar component clause 177]
184. 4 | 3 | 1 [avatar split clause 107,165,173,177]
252. ~strong(paul) [subsumption resolution 145,162]
253. ~1 [avatar split clause 252,165]
308. ~creative(X0) | quiet(X0) [resolution 132,129]
314. funny(alice) <- (3) [resolution 154,174]
317. tall(X1) [resolution 160,162]
370. ~funny(X0) | creative(X0) | quiet(X0) | quiet(X0) [resolution 112,129]
372. ~funny(X0) | creative(X0) | quiet(X0) [duplicate literal removal 370]
373. ~funny(X0) | quiet(X0) [subsumption resolution 372,308]
374. quiet(alice) <- (3) [resolution 373,314]
376. $false <- (3, ~4) [subsumption resolution 374,178]
377. ~3 | 4 [avatar contradiction clause 376]
379. calm(alice) <- (4) [resolution 179,105]
403. ~tall(alice) | rich(alice) <- (4) [resolution 379,80]
404. rich(alice) <- (4) [subsumption resolution 403,317]
405. $false <- (4) [subsumption resolution 404,152]
406. ~4 [avatar contradiction clause 405]
407. $false [avatar sat refutation 184,253,377,406]
% SZS output end Proof for 8927520762774715831167978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and happy is strong. If someone is both not patient and rich then lucy is funny or not brave and vice versa. If john is quiet then susan is both not brave and not tall. Everyone who is quiet or not patient is both not rich and quiet and vice versa. Everyone who is both quiet and happy is not kind and vice versa. Everyone who is both happy and kind is kind or not tall and vice versa. Everyone who is patient or not old is rich and vice versa. Everyone who is not creative is not calm or brave. If someone is either happy or not funny then someone is both brave and not brave and vice versa. Everyone who is not kind is not patient. If john is either generous or old then someone is not funny. Everyone who is both not curious and curious is both wise and funny. Everyone who is both calm and happy is both not curious and not humble and vice versa. Everyone who is not humble is both not funny and quiet. Everyone who is both brave and not generous is either not tall or quiet and vice versa. Everyone who is old is either not quiet or not patient and vice versa. Lucy is both strong and generous. John is not quiet or old. Susan is both humble and rich. Paul is creative or not strong. Alice is strong or not quiet. Mary is either not calm or curious. | John is humble. | entailment | (![X]:((~happy(X)&happy(X))=>strong(X)))&
((?[X]:((~patient(X)&rich(X))))<=>((funny(lucy)|~brave(lucy))))&
((quiet(john))=>((~brave(susan)&~tall(susan))))&
(![X]:((quiet(X)|~patient(X))<=>(~rich(X)&quiet(X))))&
(![X]:((quiet(X)&happy(X))<=>~kind(X)))&
(![X]:((happy(X)&kind(X))<=>(kind(X)|~tall(X))))&
(![X]:((patient(X)|~old(X))<=>rich(X)))&
(![X]:(~creative(X)=>(~calm(X)|brave(X))))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:(~kind(X)=>~patient(X)))&
(((generous(john)<~>old(john)))=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)&curious(X))=>(wise(X)&funny(X))))&
(![X]:((calm(X)&happy(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~humble(X)=>(~funny(X)&quiet(X))))&
(![X]:((brave(X)&~generous(X))<=>(~tall(X)<~>quiet(X))))&
(![X]:(old(X)<=>(~quiet(X)<~>~patient(X))))&
((strong(lucy)&generous(lucy)))&
((~quiet(john)|old(john)))&
((humble(susan)&rich(susan)))&
((creative(paul)|~strong(paul)))&
((strong(alice)|~quiet(alice)))&
((~calm(mary)<~>curious(mary))) | humble(john) | [
"p2",
"p3",
"p4",
"p5",
"p9",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5634047741760980396169939
% SZS output start Proof for 5634047741760980396169939
3. quiet(john) => (~tall(susan) & ~brave(susan)) [input p2]
4. ! [X0] : ((~patient(X0) | quiet(X0)) <=> (quiet(X0) & ~rich(X0))) [input p3]
5. ! [X0] : ((happy(X0) & quiet(X0)) <=> ~kind(X0)) [input p4]
6. ! [X0] : ((kind(X0) & happy(X0)) <=> (~tall(X0) | kind(X0))) [input p5]
10. ! [X0] : (~kind(X0) => ~patient(X0)) [input p9]
14. ! [X0] : (~humble(X0) => (quiet(X0) & ~funny(X0))) [input p13]
15. ! [X0] : ((~generous(X0) & brave(X0)) <=> (~tall(X0) <~> quiet(X0))) [input p14]
19. rich(susan) & humble(susan) [input p18]
23. ~humble(john) [input hypothesis]
31. (~tall(susan) & ~brave(susan)) | ~quiet(john) [ennf transformation 3]
32. ! [X0] : (~patient(X0) | kind(X0)) [ennf transformation 10]
36. ! [X0] : ((quiet(X0) & ~funny(X0)) | humble(X0)) [ennf transformation 14]
42. ! [X0] : (((~patient(X0) | quiet(X0)) | (~quiet(X0) | rich(X0))) & ((quiet(X0) & ~rich(X0)) | (patient(X0) & ~quiet(X0)))) [nnf transformation 4]
43. ! [X0] : ((~patient(X0) | quiet(X0) | ~quiet(X0) | rich(X0)) & ((quiet(X0) & ~rich(X0)) | (patient(X0) & ~quiet(X0)))) [flattening 42]
44. ! [X0] : (((happy(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) | ~quiet(X0)))) [nnf transformation 5]
45. ! [X0] : (((happy(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | ~happy(X0) | ~quiet(X0))) [flattening 44]
46. ! [X0] : (((kind(X0) & happy(X0)) | (tall(X0) & ~kind(X0))) & ((~tall(X0) | kind(X0)) | (~kind(X0) | ~happy(X0)))) [nnf transformation 6]
47. ! [X0] : (((kind(X0) & happy(X0)) | (tall(X0) & ~kind(X0))) & (~tall(X0) | kind(X0) | ~kind(X0) | ~happy(X0))) [flattening 46]
60. ! [X0] : (((~generous(X0) & brave(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0)))) & (((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (generous(X0) | ~brave(X0)))) [nnf transformation 15]
61. ! [X0] : (((~generous(X0) & brave(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0)))) & (((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | generous(X0) | ~brave(X0))) [flattening 60]
69. ~brave(susan) | ~quiet(john) [cnf transformation 31]
70. ~tall(susan) | ~quiet(john) [cnf transformation 31]
72. ~rich(X0) | patient(X0) [cnf transformation 43]
76. ~kind(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 45]
78. kind(X0) | happy(X0) [cnf transformation 45]
80. happy(X0) | ~kind(X0) [cnf transformation 47]
93. ~patient(X0) | kind(X0) [cnf transformation 32]
102. humble(X0) | quiet(X0) [cnf transformation 36]
105. tall(X0) | quiet(X0) | brave(X0) [cnf transformation 61]
116. rich(susan) [cnf transformation 19]
119. ~humble(john) [cnf transformation 23]
141. 5 <=> ! [X1] : (~rich(X1) | patient(X1)) [avatar definition]
142. ~rich(X1) | patient(X1) <- (5) [avatar component clause 141]
145. 6 <=> quiet(john) [avatar definition]
149. 7 <=> tall(susan) [avatar definition]
151. ~tall(susan) <- (~7) [avatar component clause 149]
152. ~6 | ~7 [avatar split clause 70,149,145]
154. 8 <=> brave(susan) [avatar definition]
156. ~brave(susan) <- (~8) [avatar component clause 154]
157. ~6 | ~8 [avatar split clause 69,154,145]
158. 5 [avatar split clause 72,141]
159. happy(X0) [subsumption resolution 80,78]
197. quiet(john) [resolution 102,119]
200. 6 [avatar split clause 197,145]
203. patient(susan) <- (5) [resolution 142,116]
207. kind(susan) <- (5) [resolution 203,93]
214. ~happy(susan) | ~quiet(susan) <- (5) [resolution 76,207]
216. ~quiet(susan) <- (5) [subsumption resolution 214,159]
235. quiet(susan) | brave(susan) <- (~7) [resolution 105,151]
236. brave(susan) <- (5, ~7) [subsumption resolution 235,216]
237. $false <- (5, ~7, ~8) [subsumption resolution 236,156]
238. ~5 | 7 | 8 [avatar contradiction clause 237]
239. $false [avatar sat refutation 152,157,158,200,238]
% SZS output end Proof for 5634047741760980396169939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either curious or old then someone is curious or kind and vice versa.
Everyone who is not humble or creative is either not calm or humble.
Everyone who is both calm and funny is both humble and kind.
Everyone who is funny or not rich is not humble.
If someone is not creative or generous then someone is curious or rich and vice versa.
Everyone who is both creative and old is creative and vice versa.
Everyone who is not calm or not humble is either calm or not wise and vice versa.
If mary is strong or not curious then fred is both rich and happy.
Everyone who is not brave or not wise is calm and vice versa.
Everyone who is either not funny or generous is not tall or curious.
If someone is either not curious or wise then lucy is not quiet and vice versa.
Everyone who is both happy and not strong is both brave and not kind.
If susan is either generous or quiet then someone is old or not generous.
Everyone who is not brave or not happy is both not quiet and generous.
Everyone who is either not wise or not humble is happy.
Everyone who is calm is quiet or not calm.
Fred is quiet.
Susan is calm or not old.
Someone is patient.
Lucy is not generous or not curious.
John is either generous or old.
Paul is generous or not calm.
Mary is either not funny or not calm. | Fred is funny. | contradiction | (((curious(john)<~>old(john)))<=>(?[X]:((curious(X)|kind(X)))))&
(![X]:((~humble(X)|creative(X))=>(~calm(X)<~>humble(X))))&
(![X]:((calm(X)&funny(X))=>(humble(X)&kind(X))))&
(![X]:((funny(X)|~rich(X))=>~humble(X)))&
((?[X]:((~creative(X)|generous(X))))<=>(?[X]:((curious(X)|rich(X)))))&
(![X]:((creative(X)&old(X))<=>creative(X)))&
(![X]:((~calm(X)|~humble(X))<=>(calm(X)<~>~wise(X))))&
(((strong(mary)|~curious(mary)))=>((rich(fred)&happy(fred))))&
(![X]:((~brave(X)|~wise(X))<=>calm(X)))&
(![X]:((~funny(X)<~>generous(X))=>(~tall(X)|curious(X))))&
((?[X]:((~curious(X)<~>wise(X))))<=>(~quiet(lucy)))&
(![X]:((happy(X)&~strong(X))=>(brave(X)&~kind(X))))&
(((generous(susan)<~>quiet(susan)))=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~brave(X)|~happy(X))=>(~quiet(X)&generous(X))))&
(![X]:((~wise(X)<~>~humble(X))=>happy(X)))&
(![X]:(calm(X)=>(quiet(X)|~calm(X))))&
(quiet(fred))&
((calm(susan)|~old(susan)))&
(?[X]:(patient(X)))&
((~generous(lucy)|~curious(lucy)))&
((generous(john)<~>old(john)))&
((generous(paul)|~calm(paul)))&
((~funny(mary)<~>~calm(mary))) | funny(fred) | [
"p1",
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7528513303125771739471567
% SZS output start Proof for 7528513303125771739471567
2. ! [X0] : ((creative(X0) | ~humble(X0)) => (~calm(X0) <~> humble(X0))) [input p1]
4. ! [X0] : ((~rich(X0) | funny(X0)) => ~humble(X0)) [input p3]
7. ! [X0] : ((~humble(X0) | ~calm(X0)) <=> (calm(X0) <~> ~wise(X0))) [input p6]
9. ! [X0] : ((~wise(X0) | ~brave(X0)) <=> calm(X0)) [input p8]
24. funny(fred) [input hypothesis]
28. ! [X0] : ((~calm(X0) <~> humble(X0)) | (~creative(X0) & humble(X0))) [ennf transformation 2]
31. ! [X0] : (~humble(X0) | (rich(X0) & ~funny(X0))) [ennf transformation 4]
44. ! [X0] : (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | (~creative(X0) & humble(X0))) [nnf transformation 28]
52. ! [X0] : (((~humble(X0) | ~calm(X0)) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (humble(X0) & calm(X0)))) [nnf transformation 7]
53. ! [X0] : ((~humble(X0) | ~calm(X0) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (humble(X0) & calm(X0)))) [flattening 52]
54. ! [X0] : (((~wise(X0) | ~brave(X0)) | ~calm(X0)) & (calm(X0) | (wise(X0) & brave(X0)))) [nnf transformation 9]
55. ! [X0] : ((~wise(X0) | ~brave(X0) | ~calm(X0)) & (calm(X0) | (wise(X0) & brave(X0)))) [flattening 54]
72. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 44]
78. ~funny(X0) | ~humble(X0) [cnf transformation 31]
87. ~wise(X0) | calm(X0) | calm(X0) [cnf transformation 53]
91. ~humble(X0) | ~calm(X0) | ~wise(X0) | ~calm(X0) [cnf transformation 53]
98. calm(X0) | wise(X0) [cnf transformation 55]
123. funny(fred) [cnf transformation 24]
125. ~wise(X0) | calm(X0) [duplicate literal removal 87]
126. ~humble(X0) | ~calm(X0) | ~wise(X0) [duplicate literal removal 91]
127. ~calm(X0) | humble(X0) [duplicate literal removal 72]
185. ~calm(X0) | ~wise(X0) [subsumption resolution 126,127]
187. ~wise(X0) [subsumption resolution 125,185]
208. calm(X0) [subsumption resolution 98,187]
267. ~humble(fred) [resolution 78,123]
270. humble(X0) [resolution 127,208]
271. $false [resolution 270,267]
% SZS output end Proof for 7528513303125771739471567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and not wise then someone is either not brave or curious and vice versa. Everyone who is not humble or tall is happy and vice versa. Everyone who is both not quiet and not brave is either brave or not wise and vice versa. Everyone who is not brave is not old and vice versa. Everyone who is both patient and not curious is both not quiet and curious. If someone is both calm and not creative then susan is either brave or funny and vice versa. If someone is both not patient and not curious then someone is both not creative and generous. Everyone who is not rich or happy is either curious or quiet. Everyone who is either generous or humble is both kind and happy. Everyone who is brave or not calm is not wise and vice versa. Everyone who is not kind is either not kind or not humble and vice versa. Everyone who is either calm or not calm is curious or generous. Everyone who is patient or not funny is patient or not brave. If someone is either wise or creative then someone is either generous or old and vice versa. Everyone who is not curious or not wise is both old and not rich and vice versa. If mary is both generous and not tall then someone is both not calm and funny. John is either kind or humble. Paul is not kind. Someone is either not generous or not tall. John is happy. Someone is not tall or funny. Mary is not generous or not humble. Paul is tall or not rich. | John is rich. | contradiction | ((?[X]:((quiet(X)&~wise(X))))<=>(?[X]:((~brave(X)<~>curious(X)))))&
(![X]:((~humble(X)|tall(X))<=>happy(X)))&
(![X]:((~quiet(X)&~brave(X))<=>(brave(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>~old(X)))&
(![X]:((patient(X)&~curious(X))=>(~quiet(X)&curious(X))))&
((?[X]:((calm(X)&~creative(X))))<=>((brave(susan)<~>funny(susan))))&
((?[X]:((~patient(X)&~curious(X))))=>(?[X]:((~creative(X)&generous(X)))))&
(![X]:((~rich(X)|happy(X))=>(curious(X)<~>quiet(X))))&
(![X]:((generous(X)<~>humble(X))=>(kind(X)&happy(X))))&
(![X]:((brave(X)|~calm(X))<=>~wise(X)))&
(![X]:(~kind(X)<=>(~kind(X)<~>~humble(X))))&
(![X]:((calm(X)<~>~calm(X))=>(curious(X)|generous(X))))&
(![X]:((patient(X)|~funny(X))=>(patient(X)|~brave(X))))&
((?[X]:((wise(X)<~>creative(X))))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((~curious(X)|~wise(X))<=>(old(X)&~rich(X))))&
(((generous(mary)&~tall(mary)))=>(?[X]:((~calm(X)&funny(X)))))&
((kind(john)<~>humble(john)))&
(~kind(paul))&
(?[X]:((~generous(X)<~>~tall(X))))&
(happy(john))&
(?[X]:((~tall(X)|funny(X))))&
((~generous(mary)|~humble(mary)))&
((tall(paul)|~rich(paul))) | rich(john) | [
"p2",
"p7",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4728555253923085689118463
% SZS output start Proof for 4728555253923085689118463
3. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (brave(X0) <~> ~wise(X0))) [input p2]
8. ! [X0] : ((happy(X0) | ~rich(X0)) => (curious(X0) <~> quiet(X0))) [input p7]
15. ! [X0] : ((~wise(X0) | ~curious(X0)) <=> (~rich(X0) & old(X0))) [input p14]
20. happy(john) [input p19]
24. rich(john) [input hypothesis]
31. ! [X0] : ((curious(X0) <~> quiet(X0)) | (~happy(X0) & rich(X0))) [ennf transformation 8]
46. ! [X0] : (((~brave(X0) & ~quiet(X0)) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0)))) & (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (brave(X0) | quiet(X0)))) [nnf transformation 3]
47. ! [X0] : (((~brave(X0) & ~quiet(X0)) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0)))) & (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | brave(X0) | quiet(X0))) [flattening 46]
56. ! [X0] : (((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (~happy(X0) & rich(X0))) [nnf transformation 31]
67. ! [X0] : (((~wise(X0) | ~curious(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (wise(X0) & curious(X0)))) [nnf transformation 15]
68. ! [X0] : ((~wise(X0) | ~curious(X0) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | (wise(X0) & curious(X0)))) [flattening 67]
86. ~wise(X0) | brave(X0) | brave(X0) | quiet(X0) [cnf transformation 47]
90. ~brave(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 47]
107. ~happy(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 56]
133. ~rich(X0) | curious(X0) [cnf transformation 68]
134. ~rich(X0) | wise(X0) [cnf transformation 68]
143. happy(john) [cnf transformation 20]
147. rich(john) [cnf transformation 24]
153. ~wise(X0) | brave(X0) | quiet(X0) [duplicate literal removal 86]
154. ~brave(X0) | ~wise(X0) [duplicate literal removal 90]
186. ~wise(X0) | quiet(X0) [subsumption resolution 153,154]
324. curious(john) [resolution 133,147]
326. wise(john) [resolution 134,147]
331. quiet(john) [resolution 186,326]
359. ~curious(john) | ~quiet(john) [resolution 107,143]
375. ~curious(john) [subsumption resolution 359,331]
378. $false [subsumption resolution 324,375]
% SZS output end Proof for 4728555253923085689118463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either humble or not generous.
If susan is not old or tall then lucy is not funny.
If someone is not old then mary is not happy or brave.
Everyone who is either humble or old is both not brave and not curious and vice versa.
Everyone who is not generous is not funny and vice versa.
If mary is either rich or kind then someone is not quiet.
If fred is not humble or not generous then alice is not curious and vice versa.
Everyone who is not creative is either not humble or not funny.
Everyone who is either wise or funny is not brave.
Everyone who is both not creative and strong is not tall.
Everyone who is both curious and not wise is both humble and not strong and vice versa.
Everyone who is either generous or not humble is not strong or generous and vice versa.
If someone is not funny or not humble then someone is either calm or not wise and vice versa.
Everyone who is not calm or not creative is either not brave or not old.
Everyone who is not wise or not curious is not curious and vice versa.
If lucy is both not patient and quiet then someone is humble.
Someone is either brave or creative.
Someone is not patient.
Someone is both tall and calm.
Lucy is calm.
Alice is either not curious or happy.
Someone is either not brave or old.
Lucy is either not curious or creative.
Someone is either not creative or strong. | Lucy is not creative. | contradiction | (![X]:((~creative(X)<~>wise(X))=>(humble(X)<~>~generous(X))))&
(((~old(susan)|tall(susan)))=>(~funny(lucy)))&
((?[X]:(~old(X)))=>((~happy(mary)|brave(mary))))&
(![X]:((humble(X)<~>old(X))<=>(~brave(X)&~curious(X))))&
(![X]:(~generous(X)<=>~funny(X)))&
(((rich(mary)<~>kind(mary)))=>(?[X]:(~quiet(X))))&
(((~humble(fred)|~generous(fred)))<=>(~curious(alice)))&
(![X]:(~creative(X)=>(~humble(X)<~>~funny(X))))&
(![X]:((wise(X)<~>funny(X))=>~brave(X)))&
(![X]:((~creative(X)&strong(X))=>~tall(X)))&
(![X]:((curious(X)&~wise(X))<=>(humble(X)&~strong(X))))&
(![X]:((generous(X)<~>~humble(X))<=>(~strong(X)|generous(X))))&
((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:((~calm(X)|~creative(X))=>(~brave(X)<~>~old(X))))&
(![X]:((~wise(X)|~curious(X))<=>~curious(X)))&
(((~patient(lucy)&quiet(lucy)))=>(?[X]:(humble(X))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)&calm(X))))&
(calm(lucy))&
((~curious(alice)<~>happy(alice)))&
(?[X]:((~brave(X)<~>old(X))))&
((~curious(lucy)<~>creative(lucy)))&
(?[X]:((~creative(X)<~>strong(X)))) | ~creative(lucy) | [
"p3",
"p4",
"p7",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2197617885923504488272028
% SZS output start Proof for 2197617885923504488272028
4. ! [X0] : ((humble(X0) <~> old(X0)) <=> (~curious(X0) & ~brave(X0))) [input p3]
5. ! [X0] : (~generous(X0) <=> ~funny(X0)) [input p4]
8. ! [X0] : (~creative(X0) => (~humble(X0) <~> ~funny(X0))) [input p7]
12. ! [X0] : ((generous(X0) <~> ~humble(X0)) <=> (generous(X0) | ~strong(X0))) [input p11]
14. ! [X0] : ((~creative(X0) | ~calm(X0)) => (~brave(X0) <~> ~old(X0))) [input p13]
23. ~curious(lucy) <~> creative(lucy) [input p22]
25. ~creative(lucy) [input hypothesis]
34. ! [X0] : ((~humble(X0) <~> ~funny(X0)) | creative(X0)) [ennf transformation 8]
38. ! [X0] : ((~brave(X0) <~> ~old(X0)) | (creative(X0) & calm(X0))) [ennf transformation 14]
40. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (curious(X0) | brave(X0))) & ((~curious(X0) & ~brave(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | curious(X0) | brave(X0)) & ((~curious(X0) & ~brave(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 40]
42. ! [X0] : ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))) [nnf transformation 5]
45. ! [X0] : (((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | creative(X0)) [nnf transformation 34]
49. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (~generous(X0) & strong(X0))) & ((generous(X0) | ~strong(X0)) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [nnf transformation 12]
50. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (~generous(X0) & strong(X0))) & (generous(X0) | ~strong(X0) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [flattening 49]
56. ! [X0] : (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (creative(X0) & calm(X0))) [nnf transformation 38]
68. (~creative(lucy) | curious(lucy)) & (creative(lucy) | ~curious(lucy)) [nnf transformation 23]
79. ~brave(X0) | old(X0) | ~humble(X0) [cnf transformation 41]
84. ~old(X0) | ~humble(X0) | curious(X0) | brave(X0) [cnf transformation 41]
85. ~funny(X0) | generous(X0) [cnf transformation 42]
91. funny(X0) | humble(X0) | creative(X0) [cnf transformation 45]
104. humble(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
112. ~brave(X0) | ~old(X0) | creative(X0) [cnf transformation 56]
114. brave(X0) | old(X0) | creative(X0) [cnf transformation 56]
127. creative(lucy) | ~curious(lucy) [cnf transformation 68]
131. ~creative(lucy) [cnf transformation 25]
133. ~generous(X0) | humble(X0) [duplicate literal removal 104]
237. 23 <=> curious(lucy) [avatar definition]
238. ~curious(lucy) <- (~23) [avatar component clause 237]
241. 24 <=> creative(lucy) [avatar definition]
243. ~creative(lucy) <- (~24) [avatar component clause 241]
245. ~23 | 24 [avatar split clause 127,241,237]
256. ~24 [avatar split clause 131,241]
272. humble(X1) | creative(X1) | generous(X1) [resolution 91,85]
275. humble(X1) | creative(X1) [subsumption resolution 272,133]
323. old(X5) | creative(X5) | old(X5) | ~humble(X5) [resolution 114,79]
325. old(X5) | creative(X5) | ~humble(X5) [duplicate literal removal 323]
328. old(X5) | creative(X5) [subsumption resolution 325,275]
403. 41 <=> brave(lucy) [avatar definition]
405. brave(lucy) <- (41) [avatar component clause 403]
407. 42 <=> old(lucy) [avatar definition]
408. ~old(lucy) <- (~42) [avatar component clause 407]
451. ~humble(X0) | curious(X0) | brave(X0) | creative(X0) [resolution 84,328]
453. curious(X0) | brave(X0) | creative(X0) [subsumption resolution 451,275]
468. ~old(lucy) | creative(lucy) <- (41) [resolution 405,112]
474. ~old(lucy) <- (~24, 41) [subsumption resolution 468,243]
475. ~42 | 24 | ~41 [avatar split clause 474,403,241,407]
591. brave(lucy) | creative(lucy) <- (~23) [resolution 453,238]
595. brave(lucy) <- (~23, ~24) [subsumption resolution 591,243]
596. 41 | 23 | 24 [avatar split clause 595,241,237,403]
614. creative(lucy) <- (~42) [resolution 408,328]
615. $false <- (~24, ~42) [subsumption resolution 614,243]
616. 24 | 42 [avatar contradiction clause 615]
617. $false [avatar sat refutation 245,256,475,596,616]
% SZS output end Proof for 2197617885923504488272028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is both not kind and funny.
If someone is not creative then someone is not rich and vice versa.
Everyone who is not quiet is not tall and vice versa.
If someone is both not quiet and not rich then fred is both humble and not patient and vice versa.
Everyone who is not generous or strong is brave.
Everyone who is either old or kind is old.
Everyone who is not wise or not generous is happy.
If susan is either funny or happy then susan is not quiet and vice versa.
Everyone who is either curious or not tall is both humble and not kind and vice versa.
Everyone who is either humble or old is not quiet and vice versa.
Everyone who is either not old or tall is not tall and vice versa.
Everyone who is both happy and not happy is patient or happy and vice versa.
If susan is not happy then fred is curious or calm.
Everyone who is not quiet is both curious and not brave and vice versa.
If alice is either old or not creative then someone is either strong or not curious.
Everyone who is either wise or creative is both creative and not quiet.
John is not creative or not brave.
Someone is not strong.
Someone is rich.
Someone is either not kind or humble.
Someone is calm or not creative.
Fred is either not strong or calm.
Alice is both quiet and not happy. | Susan is humble. | contradiction | (![X]:(~brave(X)=>(~kind(X)&funny(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~rich(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
((?[X]:((~quiet(X)&~rich(X))))<=>((humble(fred)&~patient(fred))))&
(![X]:((~generous(X)|strong(X))=>brave(X)))&
(![X]:((old(X)<~>kind(X))=>old(X)))&
(![X]:((~wise(X)|~generous(X))=>happy(X)))&
(((funny(susan)<~>happy(susan)))<=>(~quiet(susan)))&
(![X]:((curious(X)<~>~tall(X))<=>(humble(X)&~kind(X))))&
(![X]:((humble(X)<~>old(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>tall(X))<=>~tall(X)))&
(![X]:((happy(X)&~happy(X))<=>(patient(X)|happy(X))))&
((~happy(susan))=>((curious(fred)|calm(fred))))&
(![X]:(~quiet(X)<=>(curious(X)&~brave(X))))&
(((old(alice)<~>~creative(alice)))=>(?[X]:((strong(X)<~>~curious(X)))))&
(![X]:((wise(X)<~>creative(X))=>(creative(X)&~quiet(X))))&
((~creative(john)|~brave(john)))&
(?[X]:(~strong(X)))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)<~>humble(X))))&
(?[X]:((calm(X)|~creative(X))))&
((~strong(fred)<~>calm(fred)))&
((quiet(alice)&~happy(alice))) | humble(susan) | [
"p2",
"p5",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4796503249823556424420213
% SZS output start Proof for 4796503249823556424420213
3. ! [X0] : (~quiet(X0) <=> ~tall(X0)) [input p2]
6. ! [X0] : ((old(X0) <~> kind(X0)) => old(X0)) [input p5]
9. ! [X0] : ((curious(X0) <~> ~tall(X0)) <=> (~kind(X0) & humble(X0))) [input p8]
10. ! [X0] : ((humble(X0) <~> old(X0)) <=> ~quiet(X0)) [input p9]
11. ! [X0] : ((~old(X0) <~> tall(X0)) <=> ~tall(X0)) [input p10]
14. ! [X0] : (~quiet(X0) <=> (~brave(X0) & curious(X0))) [input p13]
24. humble(susan) [input hypothesis]
30. ! [X0] : (old(X0) | (old(X0) <=> kind(X0))) [ennf transformation 6]
41. ! [X0] : ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))) [nnf transformation 3]
47. ! [X0] : (old(X0) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0)))) [nnf transformation 30]
49. ! [X0] : ((((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (kind(X0) | ~humble(X0))) & ((~kind(X0) & humble(X0)) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0))))) [nnf transformation 9]
50. ! [X0] : ((((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | kind(X0) | ~humble(X0)) & ((~kind(X0) & humble(X0)) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0))))) [flattening 49]
51. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | quiet(X0)) & (~quiet(X0) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 10]
52. ! [X0] : ((((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | tall(X0)) & (~tall(X0) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))))) [nnf transformation 11]
55. ! [X0] : ((~quiet(X0) | (brave(X0) | ~curious(X0))) & ((~brave(X0) & curious(X0)) | quiet(X0))) [nnf transformation 14]
56. ! [X0] : ((~quiet(X0) | brave(X0) | ~curious(X0)) & ((~brave(X0) & curious(X0)) | quiet(X0))) [flattening 55]
75. ~tall(X0) | quiet(X0) [cnf transformation 41]
76. ~quiet(X0) | tall(X0) [cnf transformation 41]
83. old(X0) | old(X0) | ~kind(X0) [cnf transformation 47]
94. ~curious(X0) | tall(X0) | kind(X0) | ~humble(X0) [cnf transformation 50]
95. ~humble(X0) | old(X0) | ~quiet(X0) [cnf transformation 51]
97. old(X0) | humble(X0) | quiet(X0) [cnf transformation 51]
100. ~tall(X0) | ~old(X0) | ~tall(X0) [cnf transformation 52]
101. tall(X0) | ~old(X0) | tall(X0) [cnf transformation 52]
109. curious(X0) | quiet(X0) [cnf transformation 56]
130. humble(susan) [cnf transformation 24]
134. ~tall(X0) | ~old(X0) [duplicate literal removal 100]
135. ~old(X0) | tall(X0) [duplicate literal removal 101]
136. ~kind(X0) | old(X0) [duplicate literal removal 83]
177. 10 <=> quiet(susan) [avatar definition]
178. ~quiet(susan) <- (~10) [avatar component clause 177]
192. ~old(X0) [subsumption resolution 134,135]
285. old(susan) | ~quiet(susan) [resolution 95,130]
286. ~quiet(susan) [subsumption resolution 285,192]
289. ~10 [avatar split clause 286,177]
292. humble(X2) | quiet(X2) [resolution 97,192]
322. 25 <=> tall(susan) [avatar definition]
323. tall(susan) <- (25) [avatar component clause 322]
324. ~tall(susan) <- (~25) [avatar component clause 322]
326. 26 <=> kind(susan) [avatar definition]
328. kind(susan) <- (26) [avatar component clause 326]
335. tall(X1) | kind(X1) | ~humble(X1) | quiet(X1) [resolution 94,109]
337. tall(X1) | kind(X1) | quiet(X1) [subsumption resolution 335,292]
338. tall(X1) | kind(X1) [subsumption resolution 337,76]
345. kind(susan) <- (~25) [resolution 338,324]
346. 26 | 25 [avatar split clause 345,322,326]
348. old(susan) <- (26) [resolution 328,136]
352. $false <- (26) [subsumption resolution 348,192]
353. ~26 [avatar contradiction clause 352]
354. quiet(susan) <- (25) [resolution 323,75]
355. $false <- (~10, 25) [subsumption resolution 354,178]
356. 10 | ~25 [avatar contradiction clause 355]
357. $false [avatar sat refutation 289,346,353,356]
% SZS output end Proof for 4796503249823556424420213
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not patient or not happy and vice versa.
Everyone who is not rich or old is tall or not happy.
If fred is both not old and funny then someone is not kind or patient and vice versa.
If someone is kind or creative then someone is either not patient or patient and vice versa.
Everyone who is funny or humble is not calm.
Everyone who is either not quiet or wise is not brave or not calm and vice versa.
Everyone who is wise is not kind.
If someone is creative or calm then paul is both not rich and tall and vice versa.
If mary is wise then someone is either not brave or humble and vice versa.
If mary is wise then someone is either happy or not quiet.
If alice is generous or strong then mary is both quiet and not kind.
Everyone who is not calm or not wise is both not funny and not rich and vice versa.
Everyone who is not strong or not creative is not happy or not humble.
If susan is either creative or not curious then alice is not patient and vice versa.
If someone is both not rich and quiet then susan is either not creative or old.
Everyone who is not rich is not wise.
Someone is either not happy or creative.
Someone is both creative and not calm.
John is either not kind or tall.
Someone is both not happy and not strong.
Someone is both not strong and not wise. | Mary is not quiet. | neutral | (![X]:(brave(X)<=>(~patient(X)|~happy(X))))&
(![X]:((~rich(X)|old(X))=>(tall(X)|~happy(X))))&
(((~old(fred)&funny(fred)))<=>(?[X]:((~kind(X)|patient(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:((funny(X)|humble(X))=>~calm(X)))&
(![X]:((~quiet(X)<~>wise(X))<=>(~brave(X)|~calm(X))))&
(![X]:(wise(X)=>~kind(X)))&
((?[X]:((creative(X)|calm(X))))<=>((~rich(paul)&tall(paul))))&
((wise(mary))<=>(?[X]:((~brave(X)<~>humble(X)))))&
((wise(mary))=>(?[X]:((happy(X)<~>~quiet(X)))))&
(((generous(alice)|strong(alice)))=>((quiet(mary)&~kind(mary))))&
(![X]:((~calm(X)|~wise(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~strong(X)|~creative(X))=>(~happy(X)|~humble(X))))&
(((creative(susan)<~>~curious(susan)))<=>(~patient(alice)))&
((?[X]:((~rich(X)&quiet(X))))=>((~creative(susan)<~>old(susan))))&
(![X]:(~rich(X)=>~wise(X)))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((creative(X)&~calm(X))))&
((~kind(john)<~>tall(john)))&
(?[X]:((~happy(X)&~strong(X))))&
(?[X]:((~strong(X)&~wise(X)))) | ~quiet(mary) | [] | null | 0 |
Everyone who is not humble or humble is either not happy or not tall.
Everyone who is patient is both quiet and not old and vice versa.
Everyone who is either creative or wise is either not generous or rich and vice versa.
If someone is creative or not quiet then alice is either not tall or patient and vice versa.
Everyone who is either quiet or wise is not funny and vice versa.
If someone is not kind then mary is both old and kind and vice versa.
Everyone who is both rich and not humble is not kind and vice versa.
Everyone who is both not brave and not curious is not strong or humble and vice versa.
If john is not happy or not curious then mary is not humble.
If fred is either rich or not kind then someone is both patient and old and vice versa.
Everyone who is not strong is either humble or not old.
If mary is both not generous and patient then paul is both calm and not brave.
Everyone who is both not curious and not kind is both not quiet and not patient and vice versa.
Everyone who is generous or not generous is not humble.
If someone is both not calm and funny then john is calm.
Everyone who is not humble is quiet or calm.
Someone is both not calm and not rich.
Someone is both generous and not curious.
Someone is either not calm or creative.
Someone is patient or strong.
Someone is not rich.
Alice is not curious or calm.
John is quiet or wise.
Someone is brave or humble. | Mary is not humble. | entailment | (![X]:((~humble(X)|humble(X))=>(~happy(X)<~>~tall(X))))&
(![X]:(patient(X)<=>(quiet(X)&~old(X))))&
(![X]:((creative(X)<~>wise(X))<=>(~generous(X)<~>rich(X))))&
((?[X]:((creative(X)|~quiet(X))))<=>((~tall(alice)<~>patient(alice))))&
(![X]:((quiet(X)<~>wise(X))<=>~funny(X)))&
((?[X]:(~kind(X)))<=>((old(mary)&kind(mary))))&
(![X]:((rich(X)&~humble(X))<=>~kind(X)))&
(![X]:((~brave(X)&~curious(X))<=>(~strong(X)|humble(X))))&
(((~happy(john)|~curious(john)))=>(~humble(mary)))&
(((rich(fred)<~>~kind(fred)))<=>(?[X]:((patient(X)&old(X)))))&
(![X]:(~strong(X)=>(humble(X)<~>~old(X))))&
(((~generous(mary)&patient(mary)))=>((calm(paul)&~brave(paul))))&
(![X]:((~curious(X)&~kind(X))<=>(~quiet(X)&~patient(X))))&
(![X]:((generous(X)|~generous(X))=>~humble(X)))&
((?[X]:((~calm(X)&funny(X))))=>(calm(john)))&
(![X]:(~humble(X)=>(quiet(X)|calm(X))))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((generous(X)&~curious(X))))&
(?[X]:((~calm(X)<~>creative(X))))&
(?[X]:((patient(X)|strong(X))))&
(?[X]:(~rich(X)))&
((~curious(alice)|calm(alice)))&
((quiet(john)|wise(john)))&
(?[X]:((brave(X)|humble(X)))) | ~humble(mary) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 480115706864566210597798
% SZS output start Proof for 480115706864566210597798
14. ! [X0] : ((~generous(X0) | generous(X0)) => ~humble(X0)) [input p13]
25. humble(mary) [input hypothesis]
33. ! [X0] : (~humble(X0) | (generous(X0) & ~generous(X0))) [ennf transformation 14]
125. ~humble(X0) | ~generous(X0) [cnf transformation 33]
126. ~humble(X0) | generous(X0) [cnf transformation 33]
140. humble(mary) [cnf transformation 25]
241. ~humble(X0) [subsumption resolution 125,126]
289. $false [subsumption resolution 140,241]
% SZS output end Proof for 480115706864566210597798
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is not curious.
Everyone who is both brave and not funny is strong or not old and vice versa.
If someone is either generous or not kind then someone is not wise or curious and vice versa.
Everyone who is both tall and not funny is not calm and vice versa.
Everyone who is kind is either strong or not kind.
Everyone who is either old or strong is funny and vice versa.
If alice is funny then someone is not calm or not old.
If someone is both not generous and not old then someone is both happy and generous.
Everyone who is rich or brave is not rich.
Everyone who is either kind or not creative is both not generous and rich and vice versa.
If someone is both not tall and humble then someone is generous and vice versa.
If someone is not curious then john is both generous and old and vice versa.
If mary is both creative and not wise then lucy is not happy.
Everyone who is humble is either not old or not generous and vice versa.
Everyone who is creative or strong is tall.
Alice is patient.
Someone is creative.
Paul is either kind or funny.
Someone is either curious or calm.
Alice is old or not quiet. | Paul is not creative. | contradiction | (![X]:((kind(X)&~creative(X))=>~curious(X)))&
(![X]:((brave(X)&~funny(X))<=>(strong(X)|~old(X))))&
((?[X]:((generous(X)<~>~kind(X))))<=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((tall(X)&~funny(X))<=>~calm(X)))&
(![X]:(kind(X)=>(strong(X)<~>~kind(X))))&
(![X]:((old(X)<~>strong(X))<=>funny(X)))&
((funny(alice))=>(?[X]:((~calm(X)|~old(X)))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:((happy(X)&generous(X)))))&
(![X]:((rich(X)|brave(X))=>~rich(X)))&
(![X]:((kind(X)<~>~creative(X))<=>(~generous(X)&rich(X))))&
((?[X]:((~tall(X)&humble(X))))<=>(?[X]:(generous(X))))&
((?[X]:(~curious(X)))<=>((generous(john)&old(john))))&
(((creative(mary)&~wise(mary)))=>(~happy(lucy)))&
(![X]:(humble(X)<=>(~old(X)<~>~generous(X))))&
(![X]:((creative(X)|strong(X))=>tall(X)))&
(patient(alice))&
(?[X]:(creative(X)))&
((kind(paul)<~>funny(paul)))&
(?[X]:((curious(X)<~>calm(X))))&
((old(alice)|~quiet(alice))) | ~creative(paul) | [
"p0",
"p4",
"p8",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2139057476833985141764924
% SZS output start Proof for 2139057476833985141764924
1. ! [X0] : ((~creative(X0) & kind(X0)) => ~curious(X0)) [input p0]
5. ! [X0] : (kind(X0) => (strong(X0) <~> ~kind(X0))) [input p4]
9. ! [X0] : ((brave(X0) | rich(X0)) => ~rich(X0)) [input p8]
10. ! [X0] : ((kind(X0) <~> ~creative(X0)) <=> (rich(X0) & ~generous(X0))) [input p9]
11. ? [X0] : (humble(X0) & ~tall(X0)) <=> ? [X0] : generous(X0) [input p10]
12. ? [X0] : ~curious(X0) <=> (old(john) & generous(john)) [input p11]
15. ! [X0] : ((strong(X0) | creative(X0)) => tall(X0)) [input p14]
21. ~creative(paul) [input hypothesis]
24. ? [X0] : (humble(X0) & ~tall(X0)) <=> ? [X1] : generous(X1) [rectify 11]
27. ! [X0] : (~curious(X0) | (creative(X0) | ~kind(X0))) [ennf transformation 1]
28. ! [X0] : (~curious(X0) | creative(X0) | ~kind(X0)) [flattening 27]
29. ! [X0] : ((strong(X0) <~> ~kind(X0)) | ~kind(X0)) [ennf transformation 5]
32. ! [X0] : (~rich(X0) | (~brave(X0) & ~rich(X0))) [ennf transformation 9]
35. ! [X0] : (tall(X0) | (~strong(X0) & ~creative(X0))) [ennf transformation 15]
45. ! [X0] : (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ~kind(X0)) [nnf transformation 29]
52. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | (~rich(X0) | generous(X0))) & ((rich(X0) & ~generous(X0)) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [nnf transformation 10]
53. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | ~rich(X0) | generous(X0)) & ((rich(X0) & ~generous(X0)) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [flattening 52]
54. (? [X0] : (humble(X0) & ~tall(X0)) | ! [X1] : ~generous(X1)) & (? [X1] : generous(X1) | ! [X0] : (~humble(X0) | tall(X0))) [nnf transformation 24]
55. (? [X0] : (humble(X0) & ~tall(X0)) | ! [X1] : ~generous(X1)) & (? [X2] : generous(X2) | ! [X3] : (~humble(X3) | tall(X3))) [rectify 54]
56. ? [X0] : (humble(X0) & ~tall(X0)) => (humble(sK4) & ~tall(sK4)) [choice axiom]
57. ? [X2] : generous(X2) => generous(sK5) [choice axiom]
58. ((humble(sK4) & ~tall(sK4)) | ! [X1] : ~generous(X1)) & (generous(sK5) | ! [X3] : (~humble(X3) | tall(X3))) [skolemisation 55,57,56]
59. (? [X0] : ~curious(X0) | (~old(john) | ~generous(john))) & ((old(john) & generous(john)) | ! [X0] : curious(X0)) [nnf transformation 12]
60. (? [X0] : ~curious(X0) | ~old(john) | ~generous(john)) & ((old(john) & generous(john)) | ! [X0] : curious(X0)) [flattening 59]
61. (? [X0] : ~curious(X0) | ~old(john) | ~generous(john)) & ((old(john) & generous(john)) | ! [X1] : curious(X1)) [rectify 60]
62. ? [X0] : ~curious(X0) => ~curious(sK6) [choice axiom]
63. (~curious(sK6) | ~old(john) | ~generous(john)) & ((old(john) & generous(john)) | ! [X1] : curious(X1)) [skolemisation 61,62]
71. ~curious(X0) | creative(X0) | ~kind(X0) [cnf transformation 28]
86. ~kind(X0) | strong(X0) | ~kind(X0) [cnf transformation 45]
95. ~rich(X0) | ~rich(X0) [cnf transformation 32]
99. rich(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 53]
100. rich(X0) | kind(X0) | creative(X0) [cnf transformation 53]
104. ~tall(sK4) | ~generous(X1) [cnf transformation 58]
106. generous(john) | curious(X1) [cnf transformation 63]
114. ~creative(X0) | tall(X0) [cnf transformation 35]
115. ~strong(X0) | tall(X0) [cnf transformation 35]
121. ~creative(paul) [cnf transformation 21]
122. ~rich(X0) [duplicate literal removal 95]
123. ~kind(X0) | strong(X0) [duplicate literal removal 86]
185. creative(X0) | kind(X0) [subsumption resolution 100,122]
186. ~creative(X0) | ~kind(X0) [subsumption resolution 99,122]
188. 15 <=> ! [X1] : ~generous(X1) [avatar definition]
189. ~generous(X1) <- (15) [avatar component clause 188]
196. 17 <=> tall(sK4) [avatar definition]
198. ~tall(sK4) <- (~17) [avatar component clause 196]
199. 15 | ~17 [avatar split clause 104,196,188]
209. 20 <=> generous(john) [avatar definition]
210. generous(john) <- (20) [avatar component clause 209]
222. 23 <=> ! [X1] : curious(X1) [avatar definition]
223. curious(X1) <- (23) [avatar component clause 222]
225. 23 | 20 [avatar split clause 106,209,222]
260. $false <- (15, 20) [resolution 210,189]
261. ~15 | ~20 [avatar contradiction clause 260]
270. kind(paul) [resolution 185,121]
271. tall(X0) | kind(X0) [resolution 185,114]
305. creative(X0) | ~kind(X0) <- (23) [resolution 223,71]
307. ~kind(X0) <- (23) [subsumption resolution 305,186]
320. $false <- (23) [subsumption resolution 270,307]
321. ~23 [avatar contradiction clause 320]
405. kind(sK4) <- (~17) [resolution 271,198]
437. strong(sK4) <- (~17) [resolution 405,123]
445. tall(sK4) <- (~17) [resolution 437,115]
450. $false <- (~17) [subsumption resolution 445,198]
451. 17 [avatar contradiction clause 450]
452. $false [avatar sat refutation 199,225,261,321,451]
% SZS output end Proof for 2139057476833985141764924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or generous then someone is not humble or rich.
Everyone who is either not quiet or not calm is curious or not creative and vice versa.
If alice is not rich then someone is both not happy and not tall and vice versa.
If alice is not strong then someone is either generous or tall.
If mary is not old then someone is either brave or not funny.
Everyone who is humble or not funny is calm.
Everyone who is either not happy or not calm is either funny or quiet.
Everyone who is both funny and humble is creative.
If someone is not generous then someone is rich or not rich.
If someone is either creative or quiet then someone is wise.
Everyone who is both not brave and humble is not funny and vice versa.
Everyone who is both calm and not wise is both curious and funny.
If mary is either not old or calm then someone is generous and vice versa.
If someone is old or humble then someone is not generous and vice versa.
Everyone who is either not quiet or not curious is both generous and not humble.
Everyone who is both calm and not brave is both curious and kind.
Someone is both not patient and not wise.
Someone is brave.
Lucy is brave.
Someone is either not brave or not curious.
Susan is strong or not strong.
Fred is not patient or not strong.
Susan is both rich and patient.
Someone is not generous or not humble. | Alice is humble. | contradiction | ((?[X]:((~wise(X)<~>generous(X))))=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(curious(X)|~creative(X))))&
((~rich(alice))<=>(?[X]:((~happy(X)&~tall(X)))))&
((~strong(alice))=>(?[X]:((generous(X)<~>tall(X)))))&
((~old(mary))=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((humble(X)|~funny(X))=>calm(X)))&
(![X]:((~happy(X)<~>~calm(X))=>(funny(X)<~>quiet(X))))&
(![X]:((funny(X)&humble(X))=>creative(X)))&
((?[X]:(~generous(X)))=>(?[X]:((rich(X)|~rich(X)))))&
((?[X]:((creative(X)<~>quiet(X))))=>(?[X]:(wise(X))))&
(![X]:((~brave(X)&humble(X))<=>~funny(X)))&
(![X]:((calm(X)&~wise(X))=>(curious(X)&funny(X))))&
(((~old(mary)<~>calm(mary)))<=>(?[X]:(generous(X))))&
((?[X]:((old(X)|humble(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>(generous(X)&~humble(X))))&
(![X]:((calm(X)&~brave(X))=>(curious(X)&kind(X))))&
(?[X]:((~patient(X)&~wise(X))))&
(?[X]:(brave(X)))&
(brave(lucy))&
(?[X]:((~brave(X)<~>~curious(X))))&
((strong(susan)|~strong(susan)))&
((~patient(fred)|~strong(fred)))&
((rich(susan)&patient(susan)))&
(?[X]:((~generous(X)|~humble(X)))) | humble(alice) | [
"p1",
"p5",
"p7",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 802297145922954382784985
% SZS output start Proof for 802297145922954382784985
2. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~creative(X0) | curious(X0))) [input p1]
6. ! [X0] : ((~funny(X0) | humble(X0)) => calm(X0)) [input p5]
8. ! [X0] : ((humble(X0) & funny(X0)) => creative(X0)) [input p7]
11. ! [X0] : ((humble(X0) & ~brave(X0)) <=> ~funny(X0)) [input p10]
15. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) => (~humble(X0) & generous(X0))) [input p14]
16. ! [X0] : ((~brave(X0) & calm(X0)) => (kind(X0) & curious(X0))) [input p15]
25. humble(alice) [input hypothesis]
30. ! [X0] : ((~brave(X0) & calm(X0)) => curious(X0)) [pure predicate removal 16]
34. ! [X0] : (calm(X0) | (funny(X0) & ~humble(X0))) [ennf transformation 6]
36. ! [X0] : (creative(X0) | (~humble(X0) | ~funny(X0))) [ennf transformation 8]
37. ! [X0] : (creative(X0) | ~humble(X0) | ~funny(X0)) [flattening 36]
42. ! [X0] : ((~humble(X0) & generous(X0)) | (~quiet(X0) <=> ~curious(X0))) [ennf transformation 15]
43. ! [X0] : (curious(X0) | (brave(X0) | ~calm(X0))) [ennf transformation 30]
44. ! [X0] : (curious(X0) | brave(X0) | ~calm(X0)) [flattening 43]
49. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 2]
50. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [flattening 49]
69. ! [X0] : (((humble(X0) & ~brave(X0)) | funny(X0)) & (~funny(X0) | (~humble(X0) | brave(X0)))) [nnf transformation 11]
70. ! [X0] : (((humble(X0) & ~brave(X0)) | funny(X0)) & (~funny(X0) | ~humble(X0) | brave(X0))) [flattening 69]
80. ! [X0] : ((~humble(X0) & generous(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) [nnf transformation 42]
92. ~creative(X0) | curious(X0) | ~calm(X0) | quiet(X0) [cnf transformation 50]
94. ~curious(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 50]
105. ~humble(X0) | calm(X0) [cnf transformation 34]
111. ~funny(X0) | ~humble(X0) | creative(X0) [cnf transformation 37]
116. ~brave(X0) | funny(X0) [cnf transformation 70]
129. ~curious(X0) | ~humble(X0) | quiet(X0) [cnf transformation 80]
130. ~quiet(X0) | ~humble(X0) | curious(X0) [cnf transformation 80]
131. ~calm(X0) | brave(X0) | curious(X0) [cnf transformation 44]
143. humble(alice) [cnf transformation 25]
292. calm(alice) [resolution 105,143]
303. 33 <=> creative(alice) [avatar definition]
305. creative(alice) <- (33) [avatar component clause 303]
307. 34 <=> quiet(alice) [avatar definition]
308. quiet(alice) <- (34) [avatar component clause 307]
309. ~quiet(alice) <- (~34) [avatar component clause 307]
362. 43 <=> curious(alice) [avatar definition]
363. ~curious(alice) <- (~43) [avatar component clause 362]
364. curious(alice) <- (43) [avatar component clause 362]
374. ~humble(alice) | quiet(alice) <- (43) [resolution 129,364]
375. quiet(alice) <- (43) [subsumption resolution 374,143]
376. $false <- (~34, 43) [subsumption resolution 375,309]
377. 34 | ~43 [avatar contradiction clause 376]
378. brave(alice) | curious(alice) [resolution 131,292]
380. brave(alice) <- (~43) [subsumption resolution 378,363]
382. funny(alice) <- (~43) [resolution 380,116]
423. ~humble(alice) | creative(alice) <- (~43) [resolution 382,111]
424. creative(alice) <- (~43) [subsumption resolution 423,143]
425. 33 | 43 [avatar split clause 424,362,303]
487. curious(alice) | ~calm(alice) | quiet(alice) <- (33) [resolution 305,92]
488. ~calm(alice) | quiet(alice) <- (33, ~43) [subsumption resolution 487,363]
489. quiet(alice) <- (33, ~43) [subsumption resolution 488,292]
492. 34 | ~33 | 43 [avatar split clause 489,362,303,307]
500. ~humble(alice) | curious(alice) <- (34) [resolution 308,130]
502. curious(alice) <- (34) [subsumption resolution 500,143]
511. 43 | ~34 [avatar split clause 502,307,362]
521. ~quiet(alice) | ~calm(alice) <- (43) [resolution 364,94]
522. ~calm(alice) <- (34, 43) [subsumption resolution 521,308]
523. $false <- (34, 43) [subsumption resolution 522,292]
524. ~34 | ~43 [avatar contradiction clause 523]
525. $false [avatar sat refutation 377,425,492,511,524]
% SZS output end Proof for 802297145922954382784985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not kind or tall then someone is both not rich and kind and vice versa. If someone is both rich and happy then fred is not kind and vice versa. If lucy is not curious or brave then someone is generous or brave and vice versa. Everyone who is not rich or funny is wise or not wise. Everyone who is either not tall or wise is kind. Everyone who is funny is kind. If someone is both not wise and wise then someone is both brave and not wise and vice versa. Everyone who is either wise or curious is either not quiet or humble and vice versa. If lucy is not brave or kind then susan is both quiet and not brave. Everyone who is not patient or happy is either not brave or not quiet and vice versa. Everyone who is not rich is either wise or curious. Everyone who is either not strong or quiet is not curious and vice versa. If mary is funny then mary is either generous or not rich and vice versa. If someone is tall or not creative then someone is either not creative or brave. If alice is brave then someone is not kind. Everyone who is humble or patient is either funny or happy. Someone is not happy or curious. Someone is not strong. Mary is generous or old. Someone is not quiet or generous. Someone is either quiet or kind. John is rich. Fred is both patient and strong. | Lucy is kind. | neutral | ((?[X]:((~kind(X)<~>tall(X))))<=>(?[X]:((~rich(X)&kind(X)))))&
((?[X]:((rich(X)&happy(X))))<=>(~kind(fred)))&
(((~curious(lucy)|brave(lucy)))<=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~rich(X)|funny(X))=>(wise(X)|~wise(X))))&
(![X]:((~tall(X)<~>wise(X))=>kind(X)))&
(![X]:(funny(X)=>kind(X)))&
((?[X]:((~wise(X)&wise(X))))<=>(?[X]:((brave(X)&~wise(X)))))&
(![X]:((wise(X)<~>curious(X))<=>(~quiet(X)<~>humble(X))))&
(((~brave(lucy)|kind(lucy)))=>((quiet(susan)&~brave(susan))))&
(![X]:((~patient(X)|happy(X))<=>(~brave(X)<~>~quiet(X))))&
(![X]:(~rich(X)=>(wise(X)<~>curious(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>~curious(X)))&
((funny(mary))<=>((generous(mary)<~>~rich(mary))))&
((?[X]:((tall(X)|~creative(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
((brave(alice))=>(?[X]:(~kind(X))))&
(![X]:((humble(X)|patient(X))=>(funny(X)<~>happy(X))))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:(~strong(X)))&
((generous(mary)|old(mary)))&
(?[X]:((~quiet(X)|generous(X))))&
(?[X]:((quiet(X)<~>kind(X))))&
(rich(john))&
((patient(fred)&strong(fred))) | kind(lucy) | [] | null | 0 |
If someone is either not strong or not funny then lucy is not old or kind and vice versa.
If someone is humble then mary is either not happy or happy.
Everyone who is both not tall and rich is both not rich and wise.
Everyone who is either not tall or quiet is not patient.
Everyone who is quiet or not curious is either not patient or curious.
If someone is both calm and not happy then someone is both calm and not wise.
If someone is curious or patient then mary is both not funny and funny and vice versa.
If paul is both old and tall then susan is generous or strong.
Everyone who is both generous and not old is either curious or not old and vice versa.
Everyone who is either not curious or not calm is not brave or not curious and vice versa.
Everyone who is both tall and rich is both not humble and quiet.
Everyone who is both rich and not curious is generous.
Everyone who is not brave is not brave or not strong.
Everyone who is both humble and not old is either not calm or not creative.
If someone is either not funny or not creative then fred is not curious.
If someone is not creative then lucy is funny or wise and vice versa.
Alice is either not kind or not calm.
Someone is either rich or humble.
Paul is both not strong and calm.
Mary is either quiet or not strong.
Someone is either not generous or patient.
Someone is strong or generous.
Alice is both happy and not funny.
Someone is not humble or funny. | Mary is not calm. | contradiction | ((?[X]:((~strong(X)<~>~funny(X))))<=>((~old(lucy)|kind(lucy))))&
((?[X]:(humble(X)))=>((~happy(mary)<~>happy(mary))))&
(![X]:((~tall(X)&rich(X))=>(~rich(X)&wise(X))))&
(![X]:((~tall(X)<~>quiet(X))=>~patient(X)))&
(![X]:((quiet(X)|~curious(X))=>(~patient(X)<~>curious(X))))&
((?[X]:((calm(X)&~happy(X))))=>(?[X]:((calm(X)&~wise(X)))))&
((?[X]:((curious(X)|patient(X))))<=>((~funny(mary)&funny(mary))))&
(((old(paul)&tall(paul)))=>((generous(susan)|strong(susan))))&
(![X]:((generous(X)&~old(X))<=>(curious(X)<~>~old(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>(~brave(X)|~curious(X))))&
(![X]:((tall(X)&rich(X))=>(~humble(X)&quiet(X))))&
(![X]:((rich(X)&~curious(X))=>generous(X)))&
(![X]:(~brave(X)=>(~brave(X)|~strong(X))))&
(![X]:((humble(X)&~old(X))=>(~calm(X)<~>~creative(X))))&
((?[X]:((~funny(X)<~>~creative(X))))=>(~curious(fred)))&
((?[X]:(~creative(X)))<=>((funny(lucy)|wise(lucy))))&
((~kind(alice)<~>~calm(alice)))&
(?[X]:((rich(X)<~>humble(X))))&
((~strong(paul)&calm(paul)))&
((quiet(mary)<~>~strong(mary)))&
(?[X]:((~generous(X)<~>patient(X))))&
(?[X]:((strong(X)|generous(X))))&
((happy(alice)&~funny(alice)))&
(?[X]:((~humble(X)|funny(X)))) | ~calm(mary) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8697697987358195050401327
% SZS output start Proof for 8697697987358195050401327
7. ? [X0] : (patient(X0) | curious(X0)) <=> (funny(mary) & ~funny(mary)) [input p6]
10. ! [X0] : ((~curious(X0) <~> ~calm(X0)) <=> (~curious(X0) | ~brave(X0))) [input p9]
25. ~calm(mary) [input hypothesis]
55. (? [X0] : (patient(X0) | curious(X0)) | (~funny(mary) | funny(mary))) & ((funny(mary) & ~funny(mary)) | ! [X0] : (~patient(X0) & ~curious(X0))) [nnf transformation 7]
56. (? [X0] : (patient(X0) | curious(X0)) | ~funny(mary) | funny(mary)) & ((funny(mary) & ~funny(mary)) | ! [X0] : (~patient(X0) & ~curious(X0))) [flattening 55]
57. (? [X0] : (patient(X0) | curious(X0)) | ~funny(mary) | funny(mary)) & ((funny(mary) & ~funny(mary)) | ! [X1] : (~patient(X1) & ~curious(X1))) [rectify 56]
58. ? [X0] : (patient(X0) | curious(X0)) => (patient(sK2) | curious(sK2)) [choice axiom]
59. ((patient(sK2) | curious(sK2)) | ~funny(mary) | funny(mary)) & ((funny(mary) & ~funny(mary)) | ! [X1] : (~patient(X1) & ~curious(X1))) [skolemisation 57,58]
62. ! [X0] : ((((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | (curious(X0) & brave(X0))) & ((~curious(X0) | ~brave(X0)) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))))) [nnf transformation 10]
63. ! [X0] : ((((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | (curious(X0) & brave(X0))) & (~curious(X0) | ~brave(X0) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))))) [flattening 62]
101. ~funny(mary) | ~curious(X1) [cnf transformation 59]
103. funny(mary) | ~curious(X1) [cnf transformation 59]
118. calm(X0) | curious(X0) | curious(X0) [cnf transformation 63]
144. ~calm(mary) [cnf transformation 25]
146. calm(X0) | curious(X0) [duplicate literal removal 118]
196. 11 <=> funny(mary) [avatar definition]
201. 12 <=> ! [X1] : ~curious(X1) [avatar definition]
202. ~curious(X1) <- (12) [avatar component clause 201]
203. 12 | 11 [avatar split clause 103,196,201]
205. 12 | ~11 [avatar split clause 101,196,201]
314. curious(mary) [resolution 146,144]
316. $false <- (12) [subsumption resolution 314,202]
317. ~12 [avatar contradiction clause 316]
320. $false [avatar sat refutation 203,205,317]
% SZS output end Proof for 8697697987358195050401327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is not wise or happy then lucy is either not humble or not wise and vice versa.
Everyone who is not rich is funny or tall and vice versa.
If susan is creative then alice is kind and vice versa.
If alice is curious then john is either humble or not funny and vice versa.
If someone is either brave or not humble then paul is either quiet or creative.
If someone is either generous or not patient then alice is either not old or old and vice versa.
If someone is not creative or not strong then paul is either not patient or happy.
Everyone who is not creative is either humble or not creative.
Everyone who is both not calm and calm is not rich or not patient.
Everyone who is old or happy is not curious.
If paul is brave or not creative then john is funny.
Everyone who is not funny is both not wise and humble.
Everyone who is funny or rich is either not rich or not kind.
If paul is either not humble or not quiet then john is not happy or not tall.
If john is either strong or not quiet then john is either quiet or not creative.
Everyone who is both strong and not humble is tall or creative and vice versa.
Mary is not generous or curious.
Paul is funny.
Someone is either kind or not tall.
Someone is both strong and not humble.
Paul is either not creative or not old.
Someone is old or brave.
Someone is either rich or not curious.
Paul is either wise or not funny. | Lucy is not humble. | entailment | (((~wise(john)|happy(john)))<=>((~humble(lucy)<~>~wise(lucy))))&
(![X]:(~rich(X)<=>(funny(X)|tall(X))))&
((creative(susan))<=>(kind(alice)))&
((curious(alice))<=>((humble(john)<~>~funny(john))))&
((?[X]:((brave(X)<~>~humble(X))))=>((quiet(paul)<~>creative(paul))))&
((?[X]:((generous(X)<~>~patient(X))))<=>((~old(alice)<~>old(alice))))&
((?[X]:((~creative(X)|~strong(X))))=>((~patient(paul)<~>happy(paul))))&
(![X]:(~creative(X)=>(humble(X)<~>~creative(X))))&
(![X]:((~calm(X)&calm(X))=>(~rich(X)|~patient(X))))&
(![X]:((old(X)|happy(X))=>~curious(X)))&
(((brave(paul)|~creative(paul)))=>(funny(john)))&
(![X]:(~funny(X)=>(~wise(X)&humble(X))))&
(![X]:((funny(X)|rich(X))=>(~rich(X)<~>~kind(X))))&
(((~humble(paul)<~>~quiet(paul)))=>((~happy(john)|~tall(john))))&
(((strong(john)<~>~quiet(john)))=>((quiet(john)<~>~creative(john))))&
(![X]:((strong(X)&~humble(X))<=>(tall(X)|creative(X))))&
((~generous(mary)|curious(mary)))&
(funny(paul))&
(?[X]:((kind(X)<~>~tall(X))))&
(?[X]:((strong(X)&~humble(X))))&
((~creative(paul)<~>~old(paul)))&
(?[X]:((old(X)|brave(X))))&
(?[X]:((rich(X)<~>~curious(X))))&
((wise(paul)<~>~funny(paul))) | ~humble(lucy) | [
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6562040715300514996293196
% SZS output start Proof for 6562040715300514996293196
8. ! [X0] : (~creative(X0) => (humble(X0) <~> ~creative(X0))) [input p7]
16. ! [X0] : ((~humble(X0) & strong(X0)) <=> (creative(X0) | tall(X0))) [input p15]
25. humble(lucy) [input hypothesis]
28. ! [X0] : ((humble(X0) <~> ~creative(X0)) | creative(X0)) [ennf transformation 8]
50. ! [X0] : (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | creative(X0)) [nnf transformation 28]
54. ! [X0] : (((~humble(X0) & strong(X0)) | (~creative(X0) & ~tall(X0))) & ((creative(X0) | tall(X0)) | (humble(X0) | ~strong(X0)))) [nnf transformation 16]
55. ! [X0] : (((~humble(X0) & strong(X0)) | (~creative(X0) & ~tall(X0))) & (creative(X0) | tall(X0) | humble(X0) | ~strong(X0))) [flattening 54]
100. creative(X0) | ~humble(X0) | creative(X0) [cnf transformation 50]
122. ~humble(X0) | ~creative(X0) [cnf transformation 55]
136. humble(lucy) [cnf transformation 25]
140. creative(X0) | ~humble(X0) [duplicate literal removal 100]
276. ~humble(X0) [subsumption resolution 122,140]
323. $false [subsumption resolution 136,276]
% SZS output end Proof for 6562040715300514996293196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is creative or kind then lucy is happy.
Everyone who is both curious and patient is not rich or not old.
If someone is both not brave and creative then someone is old or not patient and vice versa.
Everyone who is both humble and not brave is humble.
If someone is either calm or not humble then alice is both humble and not humble and vice versa.
If someone is either not generous or curious then someone is generous.
If paul is not generous then someone is generous or not generous.
If lucy is calm or not funny then john is either not calm or rich.
Everyone who is generous is not generous.
If someone is both old and kind then fred is not happy or not curious and vice versa.
Everyone who is both not old and funny is either brave or happy.
If someone is patient or not funny then someone is either not kind or patient.
Everyone who is both old and humble is not quiet and vice versa.
Everyone who is both happy and rich is either strong or kind and vice versa.
Everyone who is both brave and not patient is wise.
If someone is either rich or wise then someone is both quiet and old.
Someone is not brave or creative.
Someone is either not wise or not kind.
Lucy is either calm or not funny.
Fred is either tall or not old.
Someone is both kind and not happy.
Alice is not strong.
Someone is not brave or quiet. | Fred is generous. | contradiction | (((creative(mary)|kind(mary)))=>(happy(lucy)))&
(![X]:((curious(X)&patient(X))=>(~rich(X)|~old(X))))&
((?[X]:((~brave(X)&creative(X))))<=>(?[X]:((old(X)|~patient(X)))))&
(![X]:((humble(X)&~brave(X))=>humble(X)))&
((?[X]:((calm(X)<~>~humble(X))))<=>((humble(alice)&~humble(alice))))&
((?[X]:((~generous(X)<~>curious(X))))=>(?[X]:(generous(X))))&
((~generous(paul))=>(?[X]:((generous(X)|~generous(X)))))&
(((calm(lucy)|~funny(lucy)))=>((~calm(john)<~>rich(john))))&
(![X]:(generous(X)=>~generous(X)))&
((?[X]:((old(X)&kind(X))))<=>((~happy(fred)|~curious(fred))))&
(![X]:((~old(X)&funny(X))=>(brave(X)<~>happy(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~kind(X)<~>patient(X)))))&
(![X]:((old(X)&humble(X))<=>~quiet(X)))&
(![X]:((happy(X)&rich(X))<=>(strong(X)<~>kind(X))))&
(![X]:((brave(X)&~patient(X))=>wise(X)))&
((?[X]:((rich(X)<~>wise(X))))=>(?[X]:((quiet(X)&old(X)))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((~wise(X)<~>~kind(X))))&
((calm(lucy)<~>~funny(lucy)))&
((tall(fred)<~>~old(fred)))&
(?[X]:((kind(X)&~happy(X))))&
(~strong(alice))&
(?[X]:((~brave(X)|quiet(X)))) | generous(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6053100881346994504937316
% SZS output start Proof for 6053100881346994504937316
9. ! [X0] : (generous(X0) => ~generous(X0)) [input p8]
24. generous(fred) [input hypothesis]
38. ! [X0] : (~generous(X0) | ~generous(X0)) [ennf transformation 9]
113. ~generous(X0) | ~generous(X0) [cnf transformation 38]
148. generous(fred) [cnf transformation 24]
149. ~generous(X0) [duplicate literal removal 113]
340. $false [subsumption resolution 148,149]
% SZS output end Proof for 6053100881346994504937316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or strong then someone is either not curious or creative.
If john is generous then lucy is happy and vice versa.
Everyone who is not happy is patient.
If susan is both tall and brave then someone is not rich or not patient.
If fred is both not creative and not happy then someone is not happy and vice versa.
Everyone who is not old or not curious is either curious or wise and vice versa.
Everyone who is not quiet or not kind is both creative and not old and vice versa.
If someone is either not curious or not brave then someone is not happy or calm.
Everyone who is both generous and curious is humble or not quiet and vice versa.
If someone is not funny then someone is tall and vice versa.
If someone is both generous and quiet then someone is not curious or calm and vice versa.
Everyone who is both not generous and not funny is old or not happy and vice versa.
Everyone who is curious or not patient is generous and vice versa.
If someone is creative then someone is not funny and vice versa.
If someone is not brave then fred is either wise or not calm.
If someone is either happy or wise then paul is both not brave and humble and vice versa.
Someone is rich.
Someone is both not quiet and rich.
Someone is either tall or not brave.
Fred is both generous and wise.
Someone is either kind or not old.
Someone is quiet.
Someone is both not humble and not quiet.
Lucy is either old or tall. | Paul is not wise. | entailment | ((?[X]:((calm(X)|strong(X))))=>(?[X]:((~curious(X)<~>creative(X)))))&
((generous(john))<=>(happy(lucy)))&
(![X]:(~happy(X)=>patient(X)))&
(((tall(susan)&brave(susan)))=>(?[X]:((~rich(X)|~patient(X)))))&
(((~creative(fred)&~happy(fred)))<=>(?[X]:(~happy(X))))&
(![X]:((~old(X)|~curious(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~quiet(X)|~kind(X))<=>(creative(X)&~old(X))))&
((?[X]:((~curious(X)<~>~brave(X))))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((generous(X)&curious(X))<=>(humble(X)|~quiet(X))))&
((?[X]:(~funny(X)))<=>(?[X]:(tall(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:((~generous(X)&~funny(X))<=>(old(X)|~happy(X))))&
(![X]:((curious(X)|~patient(X))<=>generous(X)))&
((?[X]:(creative(X)))<=>(?[X]:(~funny(X))))&
((?[X]:(~brave(X)))=>((wise(fred)<~>~calm(fred))))&
((?[X]:((happy(X)<~>wise(X))))<=>((~brave(paul)&humble(paul))))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)&rich(X))))&
(?[X]:((tall(X)<~>~brave(X))))&
((generous(fred)&wise(fred)))&
(?[X]:((kind(X)<~>~old(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~humble(X)&~quiet(X))))&
((old(lucy)<~>tall(lucy))) | ~wise(paul) | [
"p4",
"p5",
"p6",
"p8",
"p11",
"p15",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6133583553327165956976651
% SZS output start Proof for 6133583553327165956976651
5. (~happy(fred) & ~creative(fred)) <=> ? [X0] : ~happy(X0) [input p4]
6. ! [X0] : ((~curious(X0) | ~old(X0)) <=> (curious(X0) <~> wise(X0))) [input p5]
7. ! [X0] : ((~kind(X0) | ~quiet(X0)) <=> (~old(X0) & creative(X0))) [input p6]
9. ! [X0] : ((curious(X0) & generous(X0)) <=> (~quiet(X0) | humble(X0))) [input p8]
12. ! [X0] : ((~funny(X0) & ~generous(X0)) <=> (~happy(X0) | old(X0))) [input p11]
16. ? [X0] : (happy(X0) <~> wise(X0)) <=> (humble(paul) & ~brave(paul)) [input p15]
18. ? [X0] : (rich(X0) & ~quiet(X0)) [input p17]
20. wise(fred) & generous(fred) [input p19]
25. wise(paul) [input hypothesis]
45. ((~happy(fred) & ~creative(fred)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (happy(fred) | creative(fred))) [nnf transformation 5]
46. ((~happy(fred) & ~creative(fred)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | happy(fred) | creative(fred)) [flattening 45]
47. ((~happy(fred) & ~creative(fred)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | happy(fred) | creative(fred)) [rectify 46]
48. ? [X1] : ~happy(X1) => ~happy(sK2) [choice axiom]
49. ((~happy(fred) & ~creative(fred)) | ! [X0] : happy(X0)) & (~happy(sK2) | happy(fred) | creative(fred)) [skolemisation 47,48]
50. ! [X0] : (((~curious(X0) | ~old(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (curious(X0) & old(X0)))) [nnf transformation 6]
51. ! [X0] : ((~curious(X0) | ~old(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (curious(X0) & old(X0)))) [flattening 50]
52. ! [X0] : (((~kind(X0) | ~quiet(X0)) | (old(X0) | ~creative(X0))) & ((~old(X0) & creative(X0)) | (kind(X0) & quiet(X0)))) [nnf transformation 7]
53. ! [X0] : ((~kind(X0) | ~quiet(X0) | old(X0) | ~creative(X0)) & ((~old(X0) & creative(X0)) | (kind(X0) & quiet(X0)))) [flattening 52]
58. ! [X0] : (((curious(X0) & generous(X0)) | (quiet(X0) & ~humble(X0))) & ((~quiet(X0) | humble(X0)) | (~curious(X0) | ~generous(X0)))) [nnf transformation 9]
59. ! [X0] : (((curious(X0) & generous(X0)) | (quiet(X0) & ~humble(X0))) & (~quiet(X0) | humble(X0) | ~curious(X0) | ~generous(X0))) [flattening 58]
70. ! [X0] : (((~funny(X0) & ~generous(X0)) | (happy(X0) & ~old(X0))) & ((~happy(X0) | old(X0)) | (funny(X0) | generous(X0)))) [nnf transformation 12]
71. ! [X0] : (((~funny(X0) & ~generous(X0)) | (happy(X0) & ~old(X0))) & (~happy(X0) | old(X0) | funny(X0) | generous(X0))) [flattening 70]
80. (? [X0] : ((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | (~humble(paul) | brave(paul))) & ((humble(paul) & ~brave(paul)) | ! [X0] : ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0)))) [nnf transformation 16]
81. (? [X0] : ((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | ~humble(paul) | brave(paul)) & ((humble(paul) & ~brave(paul)) | ! [X0] : ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0)))) [flattening 80]
82. (? [X0] : ((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | ~humble(paul) | brave(paul)) & ((humble(paul) & ~brave(paul)) | ! [X1] : ((happy(X1) | ~wise(X1)) & (wise(X1) | ~happy(X1)))) [rectify 81]
83. ? [X0] : ((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) => ((~wise(sK10) | ~happy(sK10)) & (wise(sK10) | happy(sK10))) [choice axiom]
84. (((~wise(sK10) | ~happy(sK10)) & (wise(sK10) | happy(sK10))) | ~humble(paul) | brave(paul)) & ((humble(paul) & ~brave(paul)) | ! [X1] : ((happy(X1) | ~wise(X1)) & (wise(X1) | ~happy(X1)))) [skolemisation 82,83]
87. ? [X0] : (rich(X0) & ~quiet(X0)) => (rich(sK12) & ~quiet(sK12)) [choice axiom]
88. rich(sK12) & ~quiet(sK12) [skolemisation 18,87]
108. ~happy(fred) | happy(X0) [cnf transformation 49]
111. ~wise(X0) | ~curious(X0) | old(X0) [cnf transformation 51]
117. ~old(X0) | quiet(X0) [cnf transformation 53]
123. ~humble(X0) | generous(X0) [cnf transformation 59]
125. ~humble(X0) | curious(X0) [cnf transformation 59]
126. quiet(X0) | curious(X0) [cnf transformation 59]
135. ~old(X0) | ~generous(X0) [cnf transformation 71]
136. ~generous(X0) | happy(X0) [cnf transformation 71]
148. humble(paul) | wise(X1) | ~happy(X1) [cnf transformation 84]
153. ~quiet(sK12) [cnf transformation 88]
157. generous(fred) [cnf transformation 20]
166. wise(paul) [cnf transformation 25]
210. 10 <=> ! [X0] : happy(X0) [avatar definition]
211. happy(X0) <- (10) [avatar component clause 210]
213. 11 <=> happy(fred) [avatar definition]
216. 10 | ~11 [avatar split clause 108,213,210]
317. 35 <=> humble(paul) [avatar definition]
318. humble(paul) <- (35) [avatar component clause 317]
335. 39 <=> ! [X1] : (wise(X1) | ~happy(X1)) [avatar definition]
336. wise(X1) | ~happy(X1) <- (39) [avatar component clause 335]
337. 39 | 35 [avatar split clause 148,317,335]
383. generous(paul) <- (35) [resolution 123,318]
386. curious(paul) <- (35) [resolution 125,318]
387. curious(sK12) [resolution 126,153]
390. happy(fred) [resolution 136,157]
397. 11 [avatar split clause 390,213]
410. ~curious(paul) | old(paul) [resolution 111,166]
413. old(paul) <- (35) [subsumption resolution 410,386]
423. ~generous(paul) <- (35) [resolution 413,135]
426. $false <- (35) [subsumption resolution 423,383]
427. ~35 [avatar contradiction clause 426]
437. wise(X1) <- (10, 39) [subsumption resolution 336,211]
439. ~curious(X0) | old(X0) <- (10, 39) [resolution 437,111]
478. old(sK12) <- (10, 39) [resolution 439,387]
486. quiet(sK12) <- (10, 39) [resolution 478,117]
489. $false <- (10, 39) [subsumption resolution 486,153]
490. ~10 | ~39 [avatar contradiction clause 489]
491. $false [avatar sat refutation 216,337,397,427,490]
% SZS output end Proof for 6133583553327165956976651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is humble then fred is either not rich or curious and vice versa. Everyone who is both humble and not quiet is not curious or creative and vice versa. Everyone who is both not calm and old is not brave or kind and vice versa. Everyone who is both funny and old is both not calm and not kind and vice versa. Everyone who is not strong or happy is brave or not tall. Everyone who is old or kind is not quiet or not curious and vice versa. Everyone who is either tall or not quiet is both tall and kind. If paul is not wise then susan is either calm or generous. Everyone who is either brave or not tall is both happy and creative. Everyone who is either curious or generous is both not funny and not tall. Everyone who is both strong and not humble is old. If fred is creative or rich then someone is both not tall and curious and vice versa. If lucy is either kind or quiet then alice is not brave and vice versa. Everyone who is not tall is not brave. If alice is not curious or calm then someone is either kind or funny. If alice is either not humble or not generous then alice is not kind and vice versa. Fred is both not generous and not wise. Someone is either kind or tall. John is both tall and happy. Someone is not strong. Lucy is either not old or funny. Mary is not tall or not calm. Someone is not strong or happy. Lucy is either tall or happy. | Lucy is not kind. | entailment | ((humble(lucy))<=>((~rich(fred)<~>curious(fred))))&
(![X]:((humble(X)&~quiet(X))<=>(~curious(X)|creative(X))))&
(![X]:((~calm(X)&old(X))<=>(~brave(X)|kind(X))))&
(![X]:((funny(X)&old(X))<=>(~calm(X)&~kind(X))))&
(![X]:((~strong(X)|happy(X))=>(brave(X)|~tall(X))))&
(![X]:((old(X)|kind(X))<=>(~quiet(X)|~curious(X))))&
(![X]:((tall(X)<~>~quiet(X))=>(tall(X)&kind(X))))&
((~wise(paul))=>((calm(susan)<~>generous(susan))))&
(![X]:((brave(X)<~>~tall(X))=>(happy(X)&creative(X))))&
(![X]:((curious(X)<~>generous(X))=>(~funny(X)&~tall(X))))&
(![X]:((strong(X)&~humble(X))=>old(X)))&
(((creative(fred)|rich(fred)))<=>(?[X]:((~tall(X)&curious(X)))))&
(((kind(lucy)<~>quiet(lucy)))<=>(~brave(alice)))&
(![X]:(~tall(X)=>~brave(X)))&
(((~curious(alice)|calm(alice)))=>(?[X]:((kind(X)<~>funny(X)))))&
(((~humble(alice)<~>~generous(alice)))<=>(~kind(alice)))&
((~generous(fred)&~wise(fred)))&
(?[X]:((kind(X)<~>tall(X))))&
((tall(john)&happy(john)))&
(?[X]:(~strong(X)))&
((~old(lucy)<~>funny(lucy)))&
((~tall(mary)|~calm(mary)))&
(?[X]:((~strong(X)|happy(X))))&
((tall(lucy)<~>happy(lucy))) | ~kind(lucy) | [
"p2",
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 372151206105251316349281
% SZS output start Proof for 372151206105251316349281
3. ! [X0] : ((old(X0) & ~calm(X0)) <=> (kind(X0) | ~brave(X0))) [input p2]
4. ! [X0] : ((old(X0) & funny(X0)) <=> (~kind(X0) & ~calm(X0))) [input p3]
21. ~old(lucy) <~> funny(lucy) [input p20]
25. kind(lucy) [input hypothesis]
39. ! [X0] : (((old(X0) & ~calm(X0)) | (~kind(X0) & brave(X0))) & ((kind(X0) | ~brave(X0)) | (~old(X0) | calm(X0)))) [nnf transformation 3]
40. ! [X0] : (((old(X0) & ~calm(X0)) | (~kind(X0) & brave(X0))) & (kind(X0) | ~brave(X0) | ~old(X0) | calm(X0))) [flattening 39]
41. ! [X0] : (((old(X0) & funny(X0)) | (kind(X0) | calm(X0))) & ((~kind(X0) & ~calm(X0)) | (~old(X0) | ~funny(X0)))) [nnf transformation 4]
42. ! [X0] : (((old(X0) & funny(X0)) | kind(X0) | calm(X0)) & ((~kind(X0) & ~calm(X0)) | ~old(X0) | ~funny(X0))) [flattening 41]
64. (~funny(lucy) | old(lucy)) & (funny(lucy) | ~old(lucy)) [nnf transformation 21]
81. ~kind(X0) | old(X0) [cnf transformation 40]
83. ~kind(X0) | ~old(X0) | ~funny(X0) [cnf transformation 42]
132. funny(lucy) | ~old(lucy) [cnf transformation 64]
138. kind(lucy) [cnf transformation 25]
157. ~funny(X0) | ~kind(X0) [subsumption resolution 83,81]
202. 12 <=> kind(lucy) [avatar definition]
204. kind(lucy) <- (12) [avatar component clause 202]
259. 23 <=> old(lucy) [avatar definition]
263. 24 <=> funny(lucy) [avatar definition]
264. funny(lucy) <- (24) [avatar component clause 263]
267. ~23 | 24 [avatar split clause 132,263,259]
296. 12 [avatar split clause 138,202]
304. old(lucy) <- (12) [resolution 81,204]
310. 23 | ~12 [avatar split clause 304,202,259]
314. ~kind(lucy) <- (24) [resolution 157,264]
315. $false <- (12, 24) [subsumption resolution 314,204]
316. ~12 | ~24 [avatar contradiction clause 315]
317. $false [avatar sat refutation 267,296,310,316]
% SZS output end Proof for 372151206105251316349281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or quiet is patient or curious.
Everyone who is either not tall or quiet is either not patient or strong.
If paul is both happy and not old then someone is funny or patient.
If susan is either patient or rich then someone is either not tall or not curious and vice versa.
If john is old then paul is old and vice versa.
Everyone who is either not wise or patient is either not rich or not funny and vice versa.
If john is wise then mary is curious and vice versa.
Everyone who is patient or funny is both not brave and not patient.
If john is either funny or not brave then someone is both kind and funny and vice versa.
If someone is not happy then paul is not patient and vice versa.
If susan is either rich or curious then lucy is not funny and vice versa.
If someone is both not curious and humble then someone is either not wise or brave.
Everyone who is not patient or not quiet is both not strong and old.
If someone is funny or creative then susan is happy or not tall.
If mary is not old or not brave then someone is either strong or wise and vice versa.
If susan is not humble or strong then someone is funny or not old.
Alice is kind.
Mary is both not creative and humble.
Mary is not wise.
John is either funny or wise.
Someone is rich or not funny.
Someone is either happy or wise.
Someone is old.
Susan is not patient. | John is not old. | contradiction | (![X]:((happy(X)<~>quiet(X))=>(patient(X)|curious(X))))&
(![X]:((~tall(X)<~>quiet(X))=>(~patient(X)<~>strong(X))))&
(((happy(paul)&~old(paul)))=>(?[X]:((funny(X)|patient(X)))))&
(((patient(susan)<~>rich(susan)))<=>(?[X]:((~tall(X)<~>~curious(X)))))&
((old(john))<=>(old(paul)))&
(![X]:((~wise(X)<~>patient(X))<=>(~rich(X)<~>~funny(X))))&
((wise(john))<=>(curious(mary)))&
(![X]:((patient(X)|funny(X))=>(~brave(X)&~patient(X))))&
(((funny(john)<~>~brave(john)))<=>(?[X]:((kind(X)&funny(X)))))&
((?[X]:(~happy(X)))<=>(~patient(paul)))&
(((rich(susan)<~>curious(susan)))<=>(~funny(lucy)))&
((?[X]:((~curious(X)&humble(X))))=>(?[X]:((~wise(X)<~>brave(X)))))&
(![X]:((~patient(X)|~quiet(X))=>(~strong(X)&old(X))))&
((?[X]:((funny(X)|creative(X))))=>((happy(susan)|~tall(susan))))&
(((~old(mary)|~brave(mary)))<=>(?[X]:((strong(X)<~>wise(X)))))&
(((~humble(susan)|strong(susan)))=>(?[X]:((funny(X)|~old(X)))))&
(kind(alice))&
((~creative(mary)&humble(mary)))&
(~wise(mary))&
((funny(john)<~>wise(john)))&
(?[X]:((rich(X)|~funny(X))))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:(old(X)))&
(~patient(susan)) | ~old(john) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6982786727832306141904517
% SZS output start Proof for 6982786727832306141904517
8. ! [X0] : ((funny(X0) | patient(X0)) => (~patient(X0) & ~brave(X0))) [input p7]
13. ! [X0] : ((~quiet(X0) | ~patient(X0)) => (old(X0) & ~strong(X0))) [input p12]
25. ~old(john) [input hypothesis]
34. ! [X0] : ((~patient(X0) & ~brave(X0)) | (~funny(X0) & ~patient(X0))) [ennf transformation 8]
36. ! [X0] : ((old(X0) & ~strong(X0)) | (quiet(X0) & patient(X0))) [ennf transformation 13]
108. ~patient(X0) | ~patient(X0) [cnf transformation 34]
126. old(X0) | patient(X0) [cnf transformation 36]
147. ~old(john) [cnf transformation 25]
148. ~patient(X0) [duplicate literal removal 108]
263. old(X0) [subsumption resolution 126,148]
324. $false [subsumption resolution 147,263]
% SZS output end Proof for 6982786727832306141904517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not funny or quiet then alice is quiet or generous.
Everyone who is humble or tall is not patient and vice versa.
If someone is not kind or not tall then someone is humble or not rich and vice versa.
Everyone who is both strong and wise is not humble or kind.
Everyone who is not strong or old is either wise or not strong and vice versa.
Everyone who is both rich and not quiet is not brave or not strong and vice versa.
Everyone who is either not tall or tall is either not old or not tall and vice versa.
Everyone who is either rich or brave is both creative and kind.
Everyone who is both curious and rich is not old.
If someone is either quiet or not happy then someone is not humble or not creative.
If someone is not old or not happy then john is both strong and not wise.
If someone is not patient then fred is either kind or happy.
If someone is either not wise or funny then someone is wise or rich.
Everyone who is generous is both kind and old and vice versa.
Everyone who is either not kind or brave is patient or generous and vice versa.
Someone is either generous or not calm.
Someone is rich or creative.
Paul is not humble.
Mary is not wise or not patient.
Someone is quiet or curious. | Alice is tall. | neutral | (((~funny(john)<~>quiet(john)))=>((quiet(alice)|generous(alice))))&
(![X]:((humble(X)|tall(X))<=>~patient(X)))&
((?[X]:((~kind(X)|~tall(X))))<=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:((strong(X)&wise(X))=>(~humble(X)|kind(X))))&
(![X]:((~strong(X)|old(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((rich(X)&~quiet(X))<=>(~brave(X)|~strong(X))))&
(![X]:((~tall(X)<~>tall(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((rich(X)<~>brave(X))=>(creative(X)&kind(X))))&
(![X]:((curious(X)&rich(X))=>~old(X)))&
((?[X]:((quiet(X)<~>~happy(X))))=>(?[X]:((~humble(X)|~creative(X)))))&
((?[X]:((~old(X)|~happy(X))))=>((strong(john)&~wise(john))))&
((?[X]:(~patient(X)))=>((kind(fred)<~>happy(fred))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((wise(X)|rich(X)))))&
(![X]:(generous(X)<=>(kind(X)&old(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(patient(X)|generous(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((rich(X)|creative(X))))&
(~humble(paul))&
((~wise(mary)|~patient(mary)))&
(?[X]:((quiet(X)|curious(X)))) | tall(alice) | [] | null | 0 |
If someone is either kind or not strong then someone is not funny or not kind.
If susan is either kind or creative then fred is either brave or not creative.
Everyone who is old or not wise is both not strong and not tall.
Everyone who is both not humble and creative is funny or curious.
If john is either not strong or not old then someone is wise.
Everyone who is happy is either not strong or not funny and vice versa.
Everyone who is curious or not old is curious.
Everyone who is not happy or happy is strong.
If someone is not strong or not quiet then someone is both not funny and patient.
Everyone who is not tall or kind is curious and vice versa.
Everyone who is both brave and not quiet is both quiet and not rich and vice versa.
Everyone who is happy is not happy or not kind and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
Someone is either not tall or not creative.
Someone is both humble and creative.
Someone is not calm or strong.
Someone is either not funny or old.
Alice is brave or patient.
Someone is either tall or creative. | Alice is brave. | neutral | ((?[X]:((kind(X)<~>~strong(X))))=>(?[X]:((~funny(X)|~kind(X)))))&
(((kind(susan)<~>creative(susan)))=>((brave(fred)<~>~creative(fred))))&
(![X]:((old(X)|~wise(X))=>(~strong(X)&~tall(X))))&
(![X]:((~humble(X)&creative(X))=>(funny(X)|curious(X))))&
(((~strong(john)<~>~old(john)))=>(?[X]:(wise(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~funny(X)<~>old(X))))&
((brave(alice)|patient(alice)))&
(?[X]:((tall(X)<~>creative(X)))) | brave(alice) | [] | null | 0 |
If alice is not tall then paul is not generous or creative. If someone is either humble or not strong then alice is tall or not rich. If lucy is both wise and rich then john is both curious and not brave. If someone is both brave and not happy then mary is both not wise and not strong. Everyone who is not rich or tall is happy and vice versa. Everyone who is either not old or not patient is both curious and not patient. Everyone who is not strong or patient is not tall or not generous. If susan is both generous and not strong then mary is both quiet and creative and vice versa. Everyone who is not humble is either humble or curious. Everyone who is not quiet or patient is patient or curious. Everyone who is either calm or not brave is both wise and old. If lucy is both strong and not kind then someone is humble or not tall and vice versa. Everyone who is both not rich and not brave is kind and vice versa. Everyone who is wise or not quiet is not generous or tall. Everyone who is not old is not rich or old and vice versa. Everyone who is quiet is not curious. Mary is both not creative and tall. Someone is not calm or wise. Susan is not creative. Someone is either happy or generous. Someone is not kind. Someone is calm. Alice is either not patient or wise. | Alice is not old. | entailment | ((~tall(alice))=>((~generous(paul)|creative(paul))))&
((?[X]:((humble(X)<~>~strong(X))))=>((tall(alice)|~rich(alice))))&
(((wise(lucy)&rich(lucy)))=>((curious(john)&~brave(john))))&
((?[X]:((brave(X)&~happy(X))))=>((~wise(mary)&~strong(mary))))&
(![X]:((~rich(X)|tall(X))<=>happy(X)))&
(![X]:((~old(X)<~>~patient(X))=>(curious(X)&~patient(X))))&
(![X]:((~strong(X)|patient(X))=>(~tall(X)|~generous(X))))&
(((generous(susan)&~strong(susan)))<=>((quiet(mary)&creative(mary))))&
(![X]:(~humble(X)=>(humble(X)<~>curious(X))))&
(![X]:((~quiet(X)|patient(X))=>(patient(X)|curious(X))))&
(![X]:((calm(X)<~>~brave(X))=>(wise(X)&old(X))))&
(((strong(lucy)&~kind(lucy)))<=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~rich(X)&~brave(X))<=>kind(X)))&
(![X]:((wise(X)|~quiet(X))=>(~generous(X)|tall(X))))&
(![X]:(~old(X)<=>(~rich(X)|old(X))))&
(![X]:(quiet(X)=>~curious(X)))&
((~creative(mary)&tall(mary)))&
(?[X]:((~calm(X)|wise(X))))&
(~creative(susan))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:(~kind(X)))&
(?[X]:(calm(X)))&
((~patient(alice)<~>wise(alice))) | ~old(alice) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6318758705018459980151049
% SZS output start Proof for 6318758705018459980151049
15. ! [X0] : (~old(X0) <=> (old(X0) | ~rich(X0))) [input p14]
24. old(alice) [input hypothesis]
57. ! [X0] : ((~old(X0) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | old(X0))) [nnf transformation 15]
58. ! [X0] : ((~old(X0) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | old(X0))) [flattening 57]
109. ~old(X0) | ~old(X0) [cnf transformation 58]
121. old(alice) [cnf transformation 24]
123. ~old(X0) [duplicate literal removal 109]
260. $false [subsumption resolution 121,123]
% SZS output end Proof for 6318758705018459980151049
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or patient is either generous or brave and vice versa. Everyone who is either patient or not strong is either not brave or funny. Everyone who is not patient or not tall is both not patient and not humble and vice versa. If john is both not old and tall then paul is funny or old and vice versa. Everyone who is not tall is either generous or not brave and vice versa. If alice is not kind then alice is either not rich or not creative. If someone is both curious and not happy then someone is not generous or patient and vice versa. Everyone who is patient or not creative is brave or not quiet. If someone is both calm and not humble then someone is tall or quiet. Everyone who is both quiet and not calm is not rich. Everyone who is either not patient or funny is not happy and vice versa. Everyone who is tall or curious is not rich or not strong. Everyone who is old is not tall or kind and vice versa. Everyone who is not rich is generous or not kind. Everyone who is both not quiet and humble is strong or funny. If lucy is both funny and generous then mary is not strong. Someone is either not quiet or funny. John is not humble or not calm. Alice is not generous. Paul is not curious. Fred is both not wise and brave. Someone is funny. Someone is curious or not creative. John is funny or not creative. | Fred is not wise. | entailment | (![X]:((~strong(X)<~>patient(X))<=>(generous(X)<~>brave(X))))&
(![X]:((patient(X)<~>~strong(X))=>(~brave(X)<~>funny(X))))&
(![X]:((~patient(X)|~tall(X))<=>(~patient(X)&~humble(X))))&
(((~old(john)&tall(john)))<=>((funny(paul)|old(paul))))&
(![X]:(~tall(X)<=>(generous(X)<~>~brave(X))))&
((~kind(alice))=>((~rich(alice)<~>~creative(alice))))&
((?[X]:((curious(X)&~happy(X))))<=>(?[X]:((~generous(X)|patient(X)))))&
(![X]:((patient(X)|~creative(X))=>(brave(X)|~quiet(X))))&
((?[X]:((calm(X)&~humble(X))))=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:((quiet(X)&~calm(X))=>~rich(X)))&
(![X]:((~patient(X)<~>funny(X))<=>~happy(X)))&
(![X]:((tall(X)|curious(X))=>(~rich(X)|~strong(X))))&
(![X]:(old(X)<=>(~tall(X)|kind(X))))&
(![X]:(~rich(X)=>(generous(X)|~kind(X))))&
(![X]:((~quiet(X)&humble(X))=>(strong(X)|funny(X))))&
(((funny(lucy)&generous(lucy)))=>(~strong(mary)))&
(?[X]:((~quiet(X)<~>funny(X))))&
((~humble(john)|~calm(john)))&
(~generous(alice))&
(~curious(paul))&
((~wise(fred)&brave(fred)))&
(?[X]:(funny(X)))&
(?[X]:((curious(X)|~creative(X))))&
((funny(john)|~creative(john))) | ~wise(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3553956452806355735962478
% SZS output start Proof for 3553956452806355735962478
21. brave(fred) & ~wise(fred) [input p20]
25. wise(fred) [input hypothesis]
123. ~wise(fred) [cnf transformation 21]
128. wise(fred) [cnf transformation 25]
256. $false [subsumption resolution 128,123]
% SZS output end Proof for 3553956452806355735962478
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both creative and not old then susan is patient.
Everyone who is not tall or curious is both not generous and patient.
Everyone who is not quiet is calm and vice versa.
Everyone who is either not strong or not generous is not quiet and vice versa.
Everyone who is wise is either patient or funny and vice versa.
If mary is both old and patient then someone is happy or quiet.
Everyone who is old is either not humble or not generous.
Everyone who is not tall is not brave or kind and vice versa.
Everyone who is either not kind or happy is generous.
If someone is both brave and not old then someone is either not patient or calm.
If lucy is old or not creative then alice is tall and vice versa.
Everyone who is either calm or quiet is either not brave or rich and vice versa.
Everyone who is not generous or not brave is not rich and vice versa.
Everyone who is both not brave and old is both funny and happy and vice versa.
If paul is both not rich and not creative then lucy is both not generous and not creative.
If susan is both strong and quiet then someone is kind or not humble.
Lucy is both calm and not generous.
Alice is both rich and not funny.
Someone is wise or humble.
Someone is not funny or happy.
Paul is both not calm and generous.
Fred is either funny or not calm.
John is either not wise or not creative.
Someone is not rich. | Lucy is not tall. | entailment | (((creative(fred)&~old(fred)))=>(patient(susan)))&
(![X]:((~tall(X)|curious(X))=>(~generous(X)&patient(X))))&
(![X]:(~quiet(X)<=>calm(X)))&
(![X]:((~strong(X)<~>~generous(X))<=>~quiet(X)))&
(![X]:(wise(X)<=>(patient(X)<~>funny(X))))&
(((old(mary)&patient(mary)))=>(?[X]:((happy(X)|quiet(X)))))&
(![X]:(old(X)=>(~humble(X)<~>~generous(X))))&
(![X]:(~tall(X)<=>(~brave(X)|kind(X))))&
(![X]:((~kind(X)<~>happy(X))=>generous(X)))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((~patient(X)<~>calm(X)))))&
(((old(lucy)|~creative(lucy)))<=>(tall(alice)))&
(![X]:((calm(X)<~>quiet(X))<=>(~brave(X)<~>rich(X))))&
(![X]:((~generous(X)|~brave(X))<=>~rich(X)))&
(![X]:((~brave(X)&old(X))<=>(funny(X)&happy(X))))&
(((~rich(paul)&~creative(paul)))=>((~generous(lucy)&~creative(lucy))))&
(((strong(susan)&quiet(susan)))=>(?[X]:((kind(X)|~humble(X)))))&
((calm(lucy)&~generous(lucy)))&
((rich(alice)&~funny(alice)))&
(?[X]:((wise(X)|humble(X))))&
(?[X]:((~funny(X)|happy(X))))&
((~calm(paul)&generous(paul)))&
((funny(fred)<~>~calm(fred)))&
((~wise(john)<~>~creative(john)))&
(?[X]:(~rich(X))) | ~tall(lucy) | [
"p2",
"p7",
"p11",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1145408060789161396356941
% SZS output start Proof for 1145408060789161396356941
3. ! [X0] : (~quiet(X0) <=> calm(X0)) [input p2]
8. ! [X0] : (~tall(X0) <=> (kind(X0) | ~brave(X0))) [input p7]
12. ! [X0] : ((calm(X0) <~> quiet(X0)) <=> (~brave(X0) <~> rich(X0))) [input p11]
13. ! [X0] : ((~brave(X0) | ~generous(X0)) <=> ~rich(X0)) [input p12]
17. ~generous(lucy) & calm(lucy) [input p16]
25. tall(lucy) [input hypothesis]
40. ! [X0] : ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))) [nnf transformation 3]
46. ! [X0] : ((~tall(X0) | (~kind(X0) & brave(X0))) & ((kind(X0) | ~brave(X0)) | tall(X0))) [nnf transformation 8]
47. ! [X0] : ((~tall(X0) | (~kind(X0) & brave(X0))) & (kind(X0) | ~brave(X0) | tall(X0))) [flattening 46]
55. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [nnf transformation 12]
56. ! [X0] : (((~brave(X0) | ~generous(X0)) | rich(X0)) & (~rich(X0) | (brave(X0) & generous(X0)))) [nnf transformation 13]
57. ! [X0] : ((~brave(X0) | ~generous(X0) | rich(X0)) & (~rich(X0) | (brave(X0) & generous(X0)))) [flattening 56]
73. calm(X0) | quiet(X0) [cnf transformation 40]
74. ~calm(X0) | ~quiet(X0) [cnf transformation 40]
87. ~tall(X0) | brave(X0) [cnf transformation 47]
96. rich(X0) | ~brave(X0) | quiet(X0) | ~calm(X0) [cnf transformation 55]
97. rich(X0) | ~brave(X0) | calm(X0) | ~quiet(X0) [cnf transformation 55]
104. ~rich(X0) | generous(X0) [cnf transformation 57]
115. ~generous(lucy) [cnf transformation 17]
127. tall(lucy) [cnf transformation 25]
189. rich(X0) | ~brave(X0) | calm(X0) [subsumption resolution 97,73]
190. rich(X0) | ~brave(X0) | ~calm(X0) [subsumption resolution 96,74]
191. ~brave(X0) | rich(X0) [subsumption resolution 190,189]
202. 16 <=> generous(lucy) [avatar definition]
204. ~generous(lucy) <- (~16) [avatar component clause 202]
223. ~16 [avatar split clause 115,202]
269. brave(lucy) [resolution 87,127]
274. rich(lucy) [resolution 191,269]
304. generous(lucy) [resolution 274,104]
305. $false <- (~16) [subsumption resolution 304,204]
306. 16 [avatar contradiction clause 305]
307. $false [avatar sat refutation 223,306]
% SZS output end Proof for 1145408060789161396356941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble or not patient then someone is both calm and patient and vice versa.
If someone is wise then someone is old or not strong and vice versa.
Everyone who is both not happy and brave is either not generous or not patient and vice versa.
Everyone who is brave or tall is both tall and creative and vice versa.
If susan is both not creative and not strong then someone is not brave or not tall.
If someone is not kind or wise then john is either not curious or brave and vice versa.
If someone is either patient or not patient then john is both not calm and not quiet and vice versa.
Everyone who is either kind or not curious is generous and vice versa.
Everyone who is either happy or not funny is both curious and happy and vice versa.
If susan is both not rich and quiet then lucy is funny or not humble and vice versa.
If someone is both not wise and curious then someone is either quiet or not tall.
Everyone who is both not happy and not brave is not curious or generous and vice versa.
If someone is not humble then someone is not happy or patient.
Everyone who is curious is both old and creative and vice versa.
If someone is not calm or calm then someone is quiet and vice versa.
If someone is both strong and creative then paul is either strong or rich.
Someone is both not curious and not rich.
Someone is not patient.
John is funny or not rich.
John is not generous.
John is both humble and not happy.
Susan is either not generous or not tall.
Paul is strong or tall. | Susan is not rich. | entailment | ((?[X]:((humble(X)|~patient(X))))<=>(?[X]:((calm(X)&patient(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~happy(X)&brave(X))<=>(~generous(X)<~>~patient(X))))&
(![X]:((brave(X)|tall(X))<=>(tall(X)&creative(X))))&
(((~creative(susan)&~strong(susan)))=>(?[X]:((~brave(X)|~tall(X)))))&
((?[X]:((~kind(X)|wise(X))))<=>((~curious(john)<~>brave(john))))&
((?[X]:((patient(X)<~>~patient(X))))<=>((~calm(john)&~quiet(john))))&
(![X]:((kind(X)<~>~curious(X))<=>generous(X)))&
(![X]:((happy(X)<~>~funny(X))<=>(curious(X)&happy(X))))&
(((~rich(susan)&quiet(susan)))<=>((funny(lucy)|~humble(lucy))))&
((?[X]:((~wise(X)&curious(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((~happy(X)&~brave(X))<=>(~curious(X)|generous(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:(curious(X)<=>(old(X)&creative(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((strong(X)&creative(X))))=>((strong(paul)<~>rich(paul))))&
(?[X]:((~curious(X)&~rich(X))))&
(?[X]:(~patient(X)))&
((funny(john)|~rich(john)))&
(~generous(john))&
((humble(john)&~happy(john)))&
((~generous(susan)<~>~tall(susan)))&
((strong(paul)|tall(paul))) | ~rich(susan) | [
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8074235316532389134643702
% SZS output start Proof for 8074235316532389134643702
9. ! [X0] : ((happy(X0) <~> ~funny(X0)) <=> (happy(X0) & curious(X0))) [input p8]
10. (quiet(susan) & ~rich(susan)) <=> (~humble(lucy) | funny(lucy)) [input p9]
12. ! [X0] : ((~brave(X0) & ~happy(X0)) <=> (generous(X0) | ~curious(X0))) [input p11]
24. rich(susan) [input hypothesis]
61. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [nnf transformation 9]
62. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [flattening 61]
63. ((quiet(susan) & ~rich(susan)) | (humble(lucy) & ~funny(lucy))) & ((~humble(lucy) | funny(lucy)) | (~quiet(susan) | rich(susan))) [nnf transformation 10]
64. ((quiet(susan) & ~rich(susan)) | (humble(lucy) & ~funny(lucy))) & (~humble(lucy) | funny(lucy) | ~quiet(susan) | rich(susan)) [flattening 63]
69. ! [X0] : (((~brave(X0) & ~happy(X0)) | (~generous(X0) & curious(X0))) & ((generous(X0) | ~curious(X0)) | (brave(X0) | happy(X0)))) [nnf transformation 12]
70. ! [X0] : (((~brave(X0) & ~happy(X0)) | (~generous(X0) & curious(X0))) & (generous(X0) | ~curious(X0) | brave(X0) | happy(X0))) [flattening 69]
126. happy(X0) | happy(X0) | funny(X0) [cnf transformation 62]
128. funny(X0) | ~happy(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 62]
130. ~rich(susan) | ~funny(lucy) [cnf transformation 64]
137. ~happy(X0) | curious(X0) [cnf transformation 70]
160. rich(susan) [cnf transformation 24]
161. funny(X0) | happy(X0) [duplicate literal removal 126]
162. ~curious(X0) | ~happy(X0) | funny(X0) [duplicate literal removal 128]
285. 27 <=> funny(lucy) [avatar definition]
287. ~funny(lucy) <- (~27) [avatar component clause 285]
290. 28 <=> rich(susan) [avatar definition]
294. ~27 | ~28 [avatar split clause 130,290,285]
370. 28 [avatar split clause 160,290]
377. happy(lucy) <- (~27) [resolution 161,287]
378. curious(lucy) <- (~27) [resolution 377,137]
460. ~happy(lucy) | funny(lucy) <- (~27) [resolution 162,378]
462. funny(lucy) <- (~27) [subsumption resolution 460,377]
463. $false <- (~27) [subsumption resolution 462,287]
464. 27 [avatar contradiction clause 463]
466. $false [avatar sat refutation 294,370,464]
% SZS output end Proof for 8074235316532389134643702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not rich is either not happy or quiet.
Everyone who is not patient is not wise or calm and vice versa.
If someone is brave then someone is both not brave and not humble.
Everyone who is either not rich or patient is happy.
Everyone who is either kind or not strong is tall and vice versa.
Everyone who is kind or rich is not strong or calm.
If fred is creative then someone is not funny and vice versa.
Everyone who is both not brave and patient is brave and vice versa.
If someone is both patient and brave then fred is not quiet.
Everyone who is funny or not calm is patient and vice versa.
Everyone who is either not humble or not funny is not tall.
Everyone who is generous or old is both not curious and tall.
If someone is both not creative and not humble then susan is either not kind or generous and vice versa.
Everyone who is either creative or not wise is not calm or not brave and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Someone is generous.
Mary is not kind or curious.
Lucy is either not old or wise.
Mary is either not strong or brave.
Someone is old or not wise.
Someone is not old.
Someone is either not funny or old.
Susan is either not curious or not brave. | Fred is patient. | contradiction | (![X]:((~funny(X)&~rich(X))=>(~happy(X)<~>quiet(X))))&
(![X]:(~patient(X)<=>(~wise(X)|calm(X))))&
((?[X]:(brave(X)))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((~rich(X)<~>patient(X))=>happy(X)))&
(![X]:((kind(X)<~>~strong(X))<=>tall(X)))&
(![X]:((kind(X)|rich(X))=>(~strong(X)|calm(X))))&
((creative(fred))<=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&patient(X))<=>brave(X)))&
((?[X]:((patient(X)&brave(X))))=>(~quiet(fred)))&
(![X]:((funny(X)|~calm(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(?[X]:(generous(X)))&
((~kind(mary)|curious(mary)))&
((~old(lucy)<~>wise(lucy)))&
((~strong(mary)<~>brave(mary)))&
(?[X]:((old(X)|~wise(X))))&
(?[X]:(~old(X)))&
(?[X]:((~funny(X)<~>old(X))))&
((~curious(susan)<~>~brave(susan))) | patient(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6668788488695900951939485
% SZS output start Proof for 6668788488695900951939485
8. ! [X0] : ((patient(X0) & ~brave(X0)) <=> brave(X0)) [input p7]
25. patient(fred) [input hypothesis]
50. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 8]
51. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | ~patient(X0) | brave(X0))) [flattening 50]
92. brave(X0) | ~patient(X0) | brave(X0) [cnf transformation 51]
93. ~brave(X0) | ~brave(X0) [cnf transformation 51]
134. patient(fred) [cnf transformation 25]
135. ~patient(X0) | brave(X0) [duplicate literal removal 92]
136. ~brave(X0) [duplicate literal removal 93]
138. 1 <=> ! [X1] : ~brave(X1) [avatar definition]
139. ~brave(X1) <- (1) [avatar component clause 138]
163. 1 [avatar split clause 136,138]
288. brave(fred) [resolution 135,134]
289. $false <- (1) [subsumption resolution 288,139]
290. ~1 [avatar contradiction clause 289]
291. $false [avatar sat refutation 163,290]
% SZS output end Proof for 6668788488695900951939485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then mary is not rich and vice versa.
If someone is both not patient and not humble then someone is both quiet and kind.
If someone is both not creative and not patient then someone is both not calm and not strong.
If fred is either happy or not old then someone is old.
Everyone who is both not wise and not creative is not strong or patient.
Everyone who is wise is happy and vice versa.
Everyone who is both not quiet and old is curious or creative and vice versa.
Everyone who is not generous is not rich and vice versa.
If someone is either not humble or generous then john is both not curious and not patient and vice versa.
If fred is both old and not funny then john is either humble or not calm and vice versa.
Everyone who is both not generous and calm is rich and vice versa.
If someone is both not wise and not strong then fred is both not creative and funny and vice versa.
If someone is tall or not patient then susan is not patient or not old and vice versa.
If fred is patient then someone is both happy and tall and vice versa.
If someone is either wise or generous then paul is not creative and vice versa.
If lucy is calm then lucy is both calm and not rich.
Someone is not creative.
Someone is rich or not strong.
Someone is both not strong and not tall.
Fred is either not brave or rich.
Someone is not creative or not brave.
Alice is both not wise and tall.
Fred is either not quiet or not curious.
Someone is not tall or old. | John is not calm. | entailment | ((?[X]:(~patient(X)))<=>(~rich(mary)))&
((?[X]:((~patient(X)&~humble(X))))=>(?[X]:((quiet(X)&kind(X)))))&
((?[X]:((~creative(X)&~patient(X))))=>(?[X]:((~calm(X)&~strong(X)))))&
(((happy(fred)<~>~old(fred)))=>(?[X]:(old(X))))&
(![X]:((~wise(X)&~creative(X))=>(~strong(X)|patient(X))))&
(![X]:(wise(X)<=>happy(X)))&
(![X]:((~quiet(X)&old(X))<=>(curious(X)|creative(X))))&
(![X]:(~generous(X)<=>~rich(X)))&
((?[X]:((~humble(X)<~>generous(X))))<=>((~curious(john)&~patient(john))))&
(((old(fred)&~funny(fred)))<=>((humble(john)<~>~calm(john))))&
(![X]:((~generous(X)&calm(X))<=>rich(X)))&
((?[X]:((~wise(X)&~strong(X))))<=>((~creative(fred)&funny(fred))))&
((?[X]:((tall(X)|~patient(X))))<=>((~patient(susan)|~old(susan))))&
((patient(fred))<=>(?[X]:((happy(X)&tall(X)))))&
((?[X]:((wise(X)<~>generous(X))))<=>(~creative(paul)))&
((calm(lucy))=>((calm(lucy)&~rich(lucy))))&
(?[X]:(~creative(X)))&
(?[X]:((rich(X)|~strong(X))))&
(?[X]:((~strong(X)&~tall(X))))&
((~brave(fred)<~>rich(fred)))&
(?[X]:((~creative(X)|~brave(X))))&
((~wise(alice)&tall(alice)))&
((~quiet(fred)<~>~curious(fred)))&
(?[X]:((~tall(X)|old(X)))) | ~calm(john) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1233991065421338810300545
% SZS output start Proof for 1233991065421338810300545
8. ! [X0] : (~generous(X0) <=> ~rich(X0)) [input p7]
11. ! [X0] : ((calm(X0) & ~generous(X0)) <=> rich(X0)) [input p10]
25. calm(john) [input hypothesis]
51. ! [X0] : ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))) [nnf transformation 8]
59. ! [X0] : (((calm(X0) & ~generous(X0)) | ~rich(X0)) & (rich(X0) | (~calm(X0) | generous(X0)))) [nnf transformation 11]
60. ! [X0] : (((calm(X0) & ~generous(X0)) | ~rich(X0)) & (rich(X0) | ~calm(X0) | generous(X0))) [flattening 59]
106. ~rich(X0) | generous(X0) [cnf transformation 51]
107. ~generous(X0) | rich(X0) [cnf transformation 51]
120. rich(X0) | ~calm(X0) | generous(X0) [cnf transformation 60]
121. ~generous(X0) | ~rich(X0) [cnf transformation 60]
152. calm(john) [cnf transformation 25]
230. 18 <=> calm(john) [avatar definition]
232. calm(john) <- (18) [avatar component clause 230]
247. ~rich(X0) [subsumption resolution 121,106]
248. ~calm(X0) | generous(X0) [subsumption resolution 120,247]
360. 18 [avatar split clause 152,230]
367. generous(john) <- (18) [resolution 248,232]
369. rich(john) <- (18) [resolution 367,107]
370. $false <- (18) [subsumption resolution 369,247]
371. ~18 [avatar contradiction clause 370]
372. $false [avatar sat refutation 360,371]
% SZS output end Proof for 1233991065421338810300545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or rich then someone is not calm or not patient. If john is brave or generous then someone is either not quiet or not patient and vice versa. If lucy is calm or not rich then fred is both kind and curious and vice versa. If mary is quiet then paul is either brave or not strong and vice versa. If someone is not patient or funny then someone is not quiet or old. Everyone who is either kind or tall is not creative or not happy. If susan is either not kind or strong then someone is either generous or not generous and vice versa. If someone is creative then mary is patient or happy and vice versa. Everyone who is not curious is not quiet. Everyone who is wise or humble is both funny and not creative and vice versa. Everyone who is both not brave and not kind is both happy and not patient and vice versa. If alice is creative or not curious then paul is either not rich or rich. If lucy is both tall and not brave then someone is generous. If alice is both not creative and calm then someone is funny. Everyone who is generous or curious is both not generous and humble and vice versa. Everyone who is either not happy or happy is not strong. Alice is either not wise or patient. John is both brave and funny. Fred is either not tall or not wise. Mary is both not rich and not wise. Paul is tall or not old. Someone is not happy. Alice is either not wise or not tall. | John is strong. | contradiction | ((?[X]:((~wise(X)|rich(X))))=>(?[X]:((~calm(X)|~patient(X)))))&
(((brave(john)|generous(john)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(((calm(lucy)|~rich(lucy)))<=>((kind(fred)&curious(fred))))&
((quiet(mary))<=>((brave(paul)<~>~strong(paul))))&
((?[X]:((~patient(X)|funny(X))))=>(?[X]:((~quiet(X)|old(X)))))&
(![X]:((kind(X)<~>tall(X))=>(~creative(X)|~happy(X))))&
(((~kind(susan)<~>strong(susan)))<=>(?[X]:((generous(X)<~>~generous(X)))))&
((?[X]:(creative(X)))<=>((patient(mary)|happy(mary))))&
(![X]:(~curious(X)=>~quiet(X)))&
(![X]:((wise(X)|humble(X))<=>(funny(X)&~creative(X))))&
(![X]:((~brave(X)&~kind(X))<=>(happy(X)&~patient(X))))&
(((creative(alice)|~curious(alice)))=>((~rich(paul)<~>rich(paul))))&
(((tall(lucy)&~brave(lucy)))=>(?[X]:(generous(X))))&
(((~creative(alice)&calm(alice)))=>(?[X]:(funny(X))))&
(![X]:((generous(X)|curious(X))<=>(~generous(X)&humble(X))))&
(![X]:((~happy(X)<~>happy(X))=>~strong(X)))&
((~wise(alice)<~>patient(alice)))&
((brave(john)&funny(john)))&
((~tall(fred)<~>~wise(fred)))&
((~rich(mary)&~wise(mary)))&
((tall(paul)|~old(paul)))&
(?[X]:(~happy(X)))&
((~wise(alice)<~>~tall(alice))) | strong(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5003608937427026668155494
% SZS output start Proof for 5003608937427026668155494
16. ! [X0] : ((~happy(X0) <~> happy(X0)) => ~strong(X0)) [input p15]
24. strong(john) [input hypothesis]
37. ! [X0] : (~strong(X0) | (~happy(X0) <=> happy(X0))) [ennf transformation 16]
73. ! [X0] : (~strong(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 37]
132. ~strong(X0) | happy(X0) | happy(X0) [cnf transformation 73]
133. ~strong(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 73]
146. strong(john) [cnf transformation 24]
147. ~strong(X0) | happy(X0) [duplicate literal removal 132]
148. ~strong(X0) | ~happy(X0) [duplicate literal removal 133]
315. ~strong(X0) [subsumption resolution 147,148]
352. $false [subsumption resolution 146,315]
% SZS output end Proof for 5003608937427026668155494
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is not creative or not calm.
If someone is both rich and not rich then someone is wise or not old.
Everyone who is not generous or not creative is both creative and patient.
Everyone who is not kind is both not wise and not happy and vice versa.
Everyone who is both wise and not happy is patient or not brave and vice versa.
If alice is brave then lucy is not humble or not patient.
If susan is both not rich and strong then someone is both not brave and not funny.
If someone is not old then john is either brave or happy.
Everyone who is wise is either curious or old.
Everyone who is not patient or wise is both humble and strong and vice versa.
Everyone who is not calm is either not brave or not creative and vice versa.
If someone is happy then john is either not rich or strong and vice versa.
Everyone who is curious or not quiet is not kind and vice versa.
If john is both not patient and not calm then someone is both wise and not creative and vice versa.
If susan is both humble and not kind then alice is old.
If mary is not curious then alice is both tall and not humble.
Lucy is both not brave and not happy.
Mary is either not calm or not wise.
Paul is both quiet and wise.
Lucy is not rich or quiet.
Alice is either not curious or brave.
Someone is quiet or generous.
Someone is not curious.
Paul is not kind or not funny. | Mary is not kind. | entailment | (![X]:(~curious(X)=>(~creative(X)|~calm(X))))&
((?[X]:((rich(X)&~rich(X))))=>(?[X]:((wise(X)|~old(X)))))&
(![X]:((~generous(X)|~creative(X))=>(creative(X)&patient(X))))&
(![X]:(~kind(X)<=>(~wise(X)&~happy(X))))&
(![X]:((wise(X)&~happy(X))<=>(patient(X)|~brave(X))))&
((brave(alice))=>((~humble(lucy)|~patient(lucy))))&
(((~rich(susan)&strong(susan)))=>(?[X]:((~brave(X)&~funny(X)))))&
((?[X]:(~old(X)))=>((brave(john)<~>happy(john))))&
(![X]:(wise(X)=>(curious(X)<~>old(X))))&
(![X]:((~patient(X)|wise(X))<=>(humble(X)&strong(X))))&
(![X]:(~calm(X)<=>(~brave(X)<~>~creative(X))))&
((?[X]:(happy(X)))<=>((~rich(john)<~>strong(john))))&
(![X]:((curious(X)|~quiet(X))<=>~kind(X)))&
(((~patient(john)&~calm(john)))<=>(?[X]:((wise(X)&~creative(X)))))&
(((humble(susan)&~kind(susan)))=>(old(alice)))&
((~curious(mary))=>((tall(alice)&~humble(alice))))&
((~brave(lucy)&~happy(lucy)))&
((~calm(mary)<~>~wise(mary)))&
((quiet(paul)&wise(paul)))&
((~rich(lucy)|quiet(lucy)))&
((~curious(alice)<~>brave(alice)))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:(~curious(X)))&
((~kind(paul)|~funny(paul))) | ~kind(mary) | [
"p4",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 823651090633432936812602
% SZS output start Proof for 823651090633432936812602
5. ! [X0] : ((~happy(X0) & wise(X0)) <=> (~brave(X0) | patient(X0))) [input p4]
10. ! [X0] : ((wise(X0) | ~patient(X0)) <=> (strong(X0) & humble(X0))) [input p9]
13. ! [X0] : ((~quiet(X0) | curious(X0)) <=> ~kind(X0)) [input p12]
16. ~curious(mary) => (~humble(alice) & tall(alice)) [input p15]
25. kind(mary) [input hypothesis]
27. ~curious(mary) => ~humble(alice) [pure predicate removal 16]
44. ~humble(alice) | curious(mary) [ennf transformation 27]
50. ! [X0] : (((~happy(X0) & wise(X0)) | (brave(X0) & ~patient(X0))) & ((~brave(X0) | patient(X0)) | (happy(X0) | ~wise(X0)))) [nnf transformation 5]
51. ! [X0] : (((~happy(X0) & wise(X0)) | (brave(X0) & ~patient(X0))) & (~brave(X0) | patient(X0) | happy(X0) | ~wise(X0))) [flattening 50]
56. ! [X0] : (((wise(X0) | ~patient(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~wise(X0) & patient(X0)))) [nnf transformation 10]
57. ! [X0] : ((wise(X0) | ~patient(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~wise(X0) & patient(X0)))) [flattening 56]
63. ! [X0] : (((~quiet(X0) | curious(X0)) | kind(X0)) & (~kind(X0) | (quiet(X0) & ~curious(X0)))) [nnf transformation 13]
64. ! [X0] : ((~quiet(X0) | curious(X0) | kind(X0)) & (~kind(X0) | (quiet(X0) & ~curious(X0)))) [flattening 63]
82. ~patient(X0) | wise(X0) [cnf transformation 51]
92. humble(X0) | patient(X0) [cnf transformation 57]
93. ~wise(X0) | humble(X0) [cnf transformation 57]
105. ~kind(X0) | ~curious(X0) [cnf transformation 64]
113. ~humble(alice) | curious(mary) [cnf transformation 44]
124. kind(mary) [cnf transformation 25]
217. 20 <=> curious(mary) [avatar definition]
221. 21 <=> humble(alice) [avatar definition]
223. ~humble(alice) <- (~21) [avatar component clause 221]
224. 20 | ~21 [avatar split clause 113,221,217]
264. patient(alice) <- (~21) [resolution 92,223]
287. wise(alice) <- (~21) [resolution 264,82]
288. ~curious(mary) [resolution 105,124]
290. ~20 [avatar split clause 288,217]
354. humble(alice) <- (~21) [resolution 287,93]
358. $false <- (~21) [subsumption resolution 354,223]
359. 21 [avatar contradiction clause 358]
360. $false [avatar sat refutation 224,290,359]
% SZS output end Proof for 823651090633432936812602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both funny and not rich is either not wise or curious and vice versa.
If someone is not quiet or creative then someone is both generous and not rich.
Everyone who is not kind is either not brave or humble.
Everyone who is kind is not funny.
If someone is either not wise or wise then mary is both not happy and not kind.
Everyone who is either curious or not patient is either not wise or not generous and vice versa.
If someone is not old then lucy is either not wise or humble and vice versa.
Everyone who is not calm is both brave and not patient and vice versa.
Everyone who is either not funny or kind is rich or not rich and vice versa.
Everyone who is either not kind or creative is not tall or not creative and vice versa.
Everyone who is either not creative or calm is both not happy and happy and vice versa.
If john is not wise or not calm then fred is both not creative and not rich and vice versa.
Everyone who is old or not tall is not generous or not brave.
Everyone who is either not tall or not patient is either strong or not strong and vice versa.
If someone is either not kind or not rich then mary is either not generous or tall.
Everyone who is either strong or not curious is both not happy and creative and vice versa.
Someone is not tall.
Fred is curious or happy.
Alice is not calm.
Lucy is both quiet and strong.
Paul is humble or curious. | John is not rich. | entailment | (![X]:((funny(X)&~rich(X))<=>(~wise(X)<~>curious(X))))&
((?[X]:((~quiet(X)|creative(X))))=>(?[X]:((generous(X)&~rich(X)))))&
(![X]:(~kind(X)=>(~brave(X)<~>humble(X))))&
(![X]:(kind(X)=>~funny(X)))&
((?[X]:((~wise(X)<~>wise(X))))=>((~happy(mary)&~kind(mary))))&
(![X]:((curious(X)<~>~patient(X))<=>(~wise(X)<~>~generous(X))))&
((?[X]:(~old(X)))<=>((~wise(lucy)<~>humble(lucy))))&
(![X]:(~calm(X)<=>(brave(X)&~patient(X))))&
(![X]:((~funny(X)<~>kind(X))<=>(rich(X)|~rich(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(~tall(X)|~creative(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(~happy(X)&happy(X))))&
(((~wise(john)|~calm(john)))<=>((~creative(fred)&~rich(fred))))&
(![X]:((old(X)|~tall(X))=>(~generous(X)|~brave(X))))&
(![X]:((~tall(X)<~>~patient(X))<=>(strong(X)<~>~strong(X))))&
((?[X]:((~kind(X)<~>~rich(X))))=>((~generous(mary)<~>tall(mary))))&
(![X]:((strong(X)<~>~curious(X))<=>(~happy(X)&creative(X))))&
(?[X]:(~tall(X)))&
((curious(fred)|happy(fred)))&
(~calm(alice))&
((quiet(lucy)&strong(lucy)))&
((humble(paul)|curious(paul))) | ~rich(john) | [
"p0",
"p3",
"p5",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5957241756256933917856952
% SZS output start Proof for 5957241756256933917856952
1. ! [X0] : ((~rich(X0) & funny(X0)) <=> (~wise(X0) <~> curious(X0))) [input p0]
4. ! [X0] : (kind(X0) => ~funny(X0)) [input p3]
6. ! [X0] : ((curious(X0) <~> ~patient(X0)) <=> (~wise(X0) <~> ~generous(X0))) [input p5]
9. ! [X0] : ((~funny(X0) <~> kind(X0)) <=> (~rich(X0) | rich(X0))) [input p8]
14. ! [X0] : ((~tall(X0) <~> ~patient(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p13]
15. ? [X0] : (~kind(X0) <~> ~rich(X0)) => (~generous(mary) <~> tall(mary)) [input p14]
22. rich(john) [input hypothesis]
28. ! [X0] : (~funny(X0) | ~kind(X0)) [ennf transformation 4]
32. (~generous(mary) <~> tall(mary)) | ! [X0] : (~kind(X0) <=> ~rich(X0)) [ennf transformation 15]
33. ! [X0] : (((~rich(X0) & funny(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0)))) & (((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (rich(X0) | ~funny(X0)))) [nnf transformation 1]
34. ! [X0] : (((~rich(X0) & funny(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0)))) & (((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | rich(X0) | ~funny(X0))) [flattening 33]
40. ! [X0] : ((((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) & (((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0))))) [nnf transformation 6]
47. ! [X0] : ((((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (rich(X0) & ~rich(X0))) & ((~rich(X0) | rich(X0)) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))))) [nnf transformation 9]
48. ! [X0] : ((((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (rich(X0) & ~rich(X0))) & (~rich(X0) | rich(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))))) [flattening 47]
55. ! [X0] : ((((patient(X0) | tall(X0)) & (~patient(X0) | ~tall(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0))))) [nnf transformation 14]
56. ((~tall(mary) | generous(mary)) & (tall(mary) | ~generous(mary))) | ! [X0] : ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0))) [nnf transformation 32]
63. curious(X0) | funny(X0) | wise(X0) [cnf transformation 34]
64. ~curious(X0) | ~wise(X0) | funny(X0) [cnf transformation 34]
71. ~kind(X0) | ~funny(X0) [cnf transformation 28]
77. ~generous(X0) | ~wise(X0) | curious(X0) | patient(X0) [cnf transformation 40]
78. ~patient(X0) | wise(X0) | generous(X0) | ~curious(X0) [cnf transformation 40]
81. ~patient(X0) | curious(X0) | ~wise(X0) | generous(X0) [cnf transformation 40]
82. ~generous(X0) | ~curious(X0) | patient(X0) | wise(X0) [cnf transformation 40]
93. kind(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 48]
94. kind(X0) | ~funny(X0) | rich(X0) [cnf transformation 48]
95. ~kind(X0) | funny(X0) | ~rich(X0) [cnf transformation 48]
96. ~kind(X0) | funny(X0) | rich(X0) [cnf transformation 48]
120. ~patient(X0) | ~tall(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 55]
121. ~patient(X0) | ~tall(X0) | strong(X0) | strong(X0) [cnf transformation 55]
122. patient(X0) | tall(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 55]
123. patient(X0) | tall(X0) | strong(X0) | strong(X0) [cnf transformation 55]
124. tall(mary) | ~generous(mary) | ~rich(X0) | kind(X0) [cnf transformation 56]
126. ~tall(mary) | generous(mary) | ~rich(X0) | kind(X0) [cnf transformation 56]
139. rich(john) [cnf transformation 22]
140. ~patient(X0) | ~tall(X0) | ~strong(X0) [duplicate literal removal 120]
141. ~tall(X0) | ~patient(X0) | strong(X0) [duplicate literal removal 121]
142. patient(X0) | tall(X0) | ~strong(X0) [duplicate literal removal 122]
143. strong(X0) | tall(X0) | patient(X0) [duplicate literal removal 123]
200. ~kind(X0) | rich(X0) [subsumption resolution 96,71]
201. ~kind(X0) | funny(X0) [subsumption resolution 95,200]
202. ~kind(X0) [subsumption resolution 201,71]
203. ~funny(X0) | rich(X0) [subsumption resolution 94,202]
204. ~funny(X0) | ~rich(X0) [subsumption resolution 93,202]
205. ~funny(X0) [subsumption resolution 204,203]
230. tall(X0) | patient(X0) [subsumption resolution 142,143]
231. ~tall(X0) | ~patient(X0) [subsumption resolution 140,141]
232. ~tall(mary) | generous(mary) | ~rich(X0) [subsumption resolution 126,202]
234. 16 <=> ! [X0] : ~rich(X0) [avatar definition]
235. ~rich(X0) <- (16) [avatar component clause 234]
237. 17 <=> generous(mary) [avatar definition]
238. ~generous(mary) <- (~17) [avatar component clause 237]
239. generous(mary) <- (17) [avatar component clause 237]
241. 18 <=> tall(mary) [avatar definition]
242. tall(mary) <- (18) [avatar component clause 241]
243. ~tall(mary) <- (~18) [avatar component clause 241]
244. 16 | 17 | ~18 [avatar split clause 232,241,237,234]
245. tall(mary) | ~generous(mary) | ~rich(X0) [subsumption resolution 124,202]
246. 16 | ~17 | 18 [avatar split clause 245,241,237,234]
272. patient(mary) <- (~18) [resolution 230,243]
401. wise(mary) | generous(mary) | ~curious(mary) <- (~18) [resolution 78,272]
405. wise(mary) | ~curious(mary) <- (~17, ~18) [subsumption resolution 401,238]
407. 35 <=> curious(mary) [avatar definition]
408. curious(mary) <- (35) [avatar component clause 407]
409. ~curious(mary) <- (~35) [avatar component clause 407]
411. 36 <=> wise(mary) [avatar definition]
412. ~wise(mary) <- (~36) [avatar component clause 411]
414. ~35 | 36 | 17 | 18 [avatar split clause 405,241,237,411,407]
443. curious(mary) | ~wise(mary) | generous(mary) <- (~18) [resolution 81,272]
449. funny(mary) | wise(mary) <- (~35) [resolution 409,63]
450. wise(mary) <- (~35) [subsumption resolution 449,205]
451. $false <- (~35, ~36) [subsumption resolution 450,412]
452. 35 | 36 [avatar contradiction clause 451]
453. curious(mary) | ~wise(mary) <- (~17, ~18) [subsumption resolution 443,238]
454. ~36 | 35 | 17 | 18 [avatar split clause 453,241,237,407,411]
516. ~wise(mary) | funny(mary) <- (35) [resolution 408,64]
523. 44 <=> patient(mary) [avatar definition]
527. ~wise(mary) <- (35) [subsumption resolution 516,205]
528. ~36 | ~35 [avatar split clause 527,407,411]
534. $false <- (16) [resolution 235,139]
535. ~16 [avatar contradiction clause 534]
536. ~curious(mary) | patient(mary) | wise(mary) <- (17) [resolution 239,82]
537. ~wise(mary) | curious(mary) | patient(mary) <- (17) [resolution 239,77]
542. ~patient(mary) <- (18) [resolution 242,231]
546. 36 | 44 | ~35 | ~17 [avatar split clause 536,237,407,523,411]
547. 44 | 35 | ~36 | ~17 [avatar split clause 537,237,411,407,523]
548. ~44 | ~18 [avatar split clause 542,241,523]
554. $false [avatar sat refutation 244,246,414,452,454,528,535,546,547,548]
% SZS output end Proof for 5957241756256933917856952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not calm or not humble then someone is not happy or not old.
Everyone who is not funny or curious is not strong and vice versa.
Everyone who is not funny is both not tall and not patient.
Everyone who is both not tall and generous is not humble or brave and vice versa.
If someone is both not old and kind then someone is old or not brave.
Everyone who is happy or not strong is not calm and vice versa.
Everyone who is old is wise and vice versa.
Everyone who is both wise and not curious is either patient or not happy and vice versa.
If someone is not tall or not wise then someone is both patient and not wise.
Everyone who is either humble or not old is both brave and funny and vice versa.
Everyone who is funny is both not kind and humble.
If someone is either not wise or not brave then paul is not humble and vice versa.
Everyone who is not quiet is either not tall or not quiet and vice versa.
If susan is either old or strong then susan is happy.
Everyone who is either creative or not generous is not generous or not wise.
If someone is not old then someone is both not strong and quiet.
Alice is quiet or funny.
Alice is funny or not kind.
Someone is both not calm and creative.
Someone is either brave or not happy.
Lucy is patient or not rich.
Someone is tall. | Alice is not curious. | neutral | (((~calm(lucy)|~humble(lucy)))=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:((~funny(X)|curious(X))<=>~strong(X)))&
(![X]:(~funny(X)=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&generous(X))<=>(~humble(X)|brave(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>~calm(X)))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((wise(X)&~curious(X))<=>(patient(X)<~>~happy(X))))&
((?[X]:((~tall(X)|~wise(X))))=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((humble(X)<~>~old(X))<=>(brave(X)&funny(X))))&
(![X]:(funny(X)=>(~kind(X)&humble(X))))&
((?[X]:((~wise(X)<~>~brave(X))))<=>(~humble(paul)))&
(![X]:(~quiet(X)<=>(~tall(X)<~>~quiet(X))))&
(((old(susan)<~>strong(susan)))=>(happy(susan)))&
(![X]:((creative(X)<~>~generous(X))=>(~generous(X)|~wise(X))))&
((?[X]:(~old(X)))=>(?[X]:((~strong(X)&quiet(X)))))&
((quiet(alice)|funny(alice)))&
((funny(alice)|~kind(alice)))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((brave(X)<~>~happy(X))))&
((patient(lucy)|~rich(lucy)))&
(?[X]:(tall(X))) | ~curious(alice) | [] | null | 0 |
Everyone who is both not humble and patient is rich and vice versa. If susan is either not happy or patient then paul is both not rich and strong and vice versa. Everyone who is either old or brave is not tall and vice versa. Everyone who is either happy or wise is not quiet or funny and vice versa. Everyone who is generous is both creative and not funny. Everyone who is not generous or patient is not old and vice versa. Everyone who is both not strong and not humble is not generous or wise and vice versa. If someone is both not brave and not strong then someone is not patient. If someone is not brave or old then someone is either not strong or not creative and vice versa. If someone is both patient and not happy then lucy is humble or not kind and vice versa. Everyone who is not generous or not kind is generous and vice versa. Everyone who is either not brave or not curious is both strong and wise. If someone is both not brave and old then someone is both not tall and not happy. If someone is both patient and quiet then john is both humble and patient. If someone is quiet then john is either happy or quiet and vice versa. If someone is humble then someone is both calm and happy. John is not wise or not strong. Someone is wise. Susan is either not curious or creative. Mary is either happy or not strong. Alice is not strong or funny. Paul is both not rich and generous. Someone is not funny. Paul is quiet. | Paul is kind. | contradiction | (![X]:((~humble(X)&patient(X))<=>rich(X)))&
(((~happy(susan)<~>patient(susan)))<=>((~rich(paul)&strong(paul))))&
(![X]:((old(X)<~>brave(X))<=>~tall(X)))&
(![X]:((happy(X)<~>wise(X))<=>(~quiet(X)|funny(X))))&
(![X]:(generous(X)=>(creative(X)&~funny(X))))&
(![X]:((~generous(X)|patient(X))<=>~old(X)))&
(![X]:((~strong(X)&~humble(X))<=>(~generous(X)|wise(X))))&
((?[X]:((~brave(X)&~strong(X))))=>(?[X]:(~patient(X))))&
((?[X]:((~brave(X)|old(X))))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
((?[X]:((patient(X)&~happy(X))))<=>((humble(lucy)|~kind(lucy))))&
(![X]:((~generous(X)|~kind(X))<=>generous(X)))&
(![X]:((~brave(X)<~>~curious(X))=>(strong(X)&wise(X))))&
((?[X]:((~brave(X)&old(X))))=>(?[X]:((~tall(X)&~happy(X)))))&
((?[X]:((patient(X)&quiet(X))))=>((humble(john)&patient(john))))&
((?[X]:(quiet(X)))<=>((happy(john)<~>quiet(john))))&
((?[X]:(humble(X)))=>(?[X]:((calm(X)&happy(X)))))&
((~wise(john)|~strong(john)))&
(?[X]:(wise(X)))&
((~curious(susan)<~>creative(susan)))&
((happy(mary)<~>~strong(mary)))&
((~strong(alice)|funny(alice)))&
((~rich(paul)&generous(paul)))&
(?[X]:(~funny(X)))&
(quiet(paul)) | kind(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8081332868522282745706155
% SZS output start Proof for 8081332868522282745706155
11. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> generous(X0)) [input p10]
25. kind(paul) [input hypothesis]
63. ! [X0] : (((~kind(X0) | ~generous(X0)) | ~generous(X0)) & (generous(X0) | (kind(X0) & generous(X0)))) [nnf transformation 11]
64. ! [X0] : ((~kind(X0) | ~generous(X0) | ~generous(X0)) & (generous(X0) | (kind(X0) & generous(X0)))) [flattening 63]
121. generous(X0) | generous(X0) [cnf transformation 64]
123. ~kind(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 64]
148. kind(paul) [cnf transformation 25]
149. generous(X0) [duplicate literal removal 121]
150. ~kind(X0) | ~generous(X0) [duplicate literal removal 123]
329. ~generous(paul) [resolution 150,148]
331. $false [subsumption resolution 329,149]
% SZS output end Proof for 8081332868522282745706155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not calm is not happy. Everyone who is happy is humble and vice versa. Everyone who is either not curious or not funny is strong and vice versa. Everyone who is either not kind or not rich is either not happy or brave and vice versa. Everyone who is both not calm and not humble is not rich or wise and vice versa. If alice is not calm then someone is not strong or not brave and vice versa. Everyone who is happy is not curious or not happy and vice versa. If lucy is not tall then mary is not kind or not funny and vice versa. Everyone who is either creative or not old is kind and vice versa. If someone is either generous or not calm then paul is either tall or not kind and vice versa. Everyone who is either not happy or not strong is both not creative and strong. If mary is not kind then fred is not old and vice versa. If fred is both not happy and quiet then lucy is either not strong or not quiet. Everyone who is humble is both funny and rich and vice versa. If paul is wise then mary is either tall or quiet. If someone is wise then someone is not happy. Someone is funny or not tall. Susan is both not generous and not kind. Someone is quiet. Someone is quiet or rich. Lucy is brave or wise. Someone is either strong or not rich. | Paul is not funny. | contradiction | (![X]:((humble(X)<~>~calm(X))=>~happy(X)))&
(![X]:(happy(X)<=>humble(X)))&
(![X]:((~curious(X)<~>~funny(X))<=>strong(X)))&
(![X]:((~kind(X)<~>~rich(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~calm(X)&~humble(X))<=>(~rich(X)|wise(X))))&
((~calm(alice))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:(happy(X)<=>(~curious(X)|~happy(X))))&
((~tall(lucy))<=>((~kind(mary)|~funny(mary))))&
(![X]:((creative(X)<~>~old(X))<=>kind(X)))&
((?[X]:((generous(X)<~>~calm(X))))<=>((tall(paul)<~>~kind(paul))))&
(![X]:((~happy(X)<~>~strong(X))=>(~creative(X)&strong(X))))&
((~kind(mary))<=>(~old(fred)))&
(((~happy(fred)&quiet(fred)))=>((~strong(lucy)<~>~quiet(lucy))))&
(![X]:(humble(X)<=>(funny(X)&rich(X))))&
((wise(paul))=>((tall(mary)<~>quiet(mary))))&
((?[X]:(wise(X)))=>(?[X]:(~happy(X))))&
(?[X]:((funny(X)|~tall(X))))&
((~generous(susan)&~kind(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((quiet(X)|rich(X))))&
((brave(lucy)|wise(lucy)))&
(?[X]:((strong(X)<~>~rich(X)))) | ~funny(paul) | [
"p1",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5938093519024585955265391
% SZS output start Proof for 5938093519024585955265391
2. ! [X0] : (happy(X0) <=> humble(X0)) [input p1]
7. ! [X0] : (happy(X0) <=> (~happy(X0) | ~curious(X0))) [input p6]
14. ! [X0] : (humble(X0) <=> (rich(X0) & funny(X0))) [input p13]
23. ~funny(paul) [input hypothesis]
32. ! [X0] : ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0))) [nnf transformation 2]
41. ! [X0] : ((happy(X0) | (happy(X0) & curious(X0))) & ((~happy(X0) | ~curious(X0)) | ~happy(X0))) [nnf transformation 7]
42. ! [X0] : ((happy(X0) | (happy(X0) & curious(X0))) & (~happy(X0) | ~curious(X0) | ~happy(X0))) [flattening 41]
53. ! [X0] : ((humble(X0) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | ~humble(X0))) [nnf transformation 14]
54. ! [X0] : ((humble(X0) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | ~humble(X0))) [flattening 53]
70. ~happy(X0) | humble(X0) [cnf transformation 32]
94. happy(X0) | happy(X0) [cnf transformation 42]
118. ~humble(X0) | funny(X0) [cnf transformation 54]
132. ~funny(paul) [cnf transformation 23]
135. happy(X0) [duplicate literal removal 94]
260. humble(X0) [resolution 70,135]
263. funny(X0) [resolution 118,260]
264. $false [resolution 263,132]
% SZS output end Proof for 5938093519024585955265391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or wise is both not happy and creative and vice versa.
Everyone who is both not humble and funny is both not strong and kind.
If alice is calm then someone is both calm and generous.
If alice is humble or happy then someone is both humble and not old.
Everyone who is both not wise and not humble is either rich or strong.
Everyone who is both not happy and wise is both not strong and old and vice versa.
If alice is either not wise or patient then alice is funny and vice versa.
Everyone who is either not tall or calm is both old and rich.
If alice is both funny and happy then paul is both rich and creative and vice versa.
If mary is not kind then mary is funny or not patient and vice versa.
If john is either wise or tall then paul is not humble and vice versa.
Everyone who is creative is not strong or happy.
Everyone who is either not generous or brave is both brave and not brave.
Everyone who is both patient and not brave is not calm or wise and vice versa.
If lucy is strong then john is both not patient and not old.
If someone is both not strong and rich then john is both not humble and not strong.
Someone is not creative or curious.
Mary is both not curious and not quiet.
Someone is kind or generous.
Susan is generous or humble.
Mary is not patient.
John is not quiet.
Someone is quiet or old.
Susan is both curious and funny. | Lucy is not happy. | neutral | (![X]:((creative(X)<~>wise(X))<=>(~happy(X)&creative(X))))&
(![X]:((~humble(X)&funny(X))=>(~strong(X)&kind(X))))&
((calm(alice))=>(?[X]:((calm(X)&generous(X)))))&
(((humble(alice)|happy(alice)))=>(?[X]:((humble(X)&~old(X)))))&
(![X]:((~wise(X)&~humble(X))=>(rich(X)<~>strong(X))))&
(![X]:((~happy(X)&wise(X))<=>(~strong(X)&old(X))))&
(((~wise(alice)<~>patient(alice)))<=>(funny(alice)))&
(![X]:((~tall(X)<~>calm(X))=>(old(X)&rich(X))))&
(((funny(alice)&happy(alice)))<=>((rich(paul)&creative(paul))))&
((~kind(mary))<=>((funny(mary)|~patient(mary))))&
(((wise(john)<~>tall(john)))<=>(~humble(paul)))&
(![X]:(creative(X)=>(~strong(X)|happy(X))))&
(![X]:((~generous(X)<~>brave(X))=>(brave(X)&~brave(X))))&
(![X]:((patient(X)&~brave(X))<=>(~calm(X)|wise(X))))&
((strong(lucy))=>((~patient(john)&~old(john))))&
((?[X]:((~strong(X)&rich(X))))=>((~humble(john)&~strong(john))))&
(?[X]:((~creative(X)|curious(X))))&
((~curious(mary)&~quiet(mary)))&
(?[X]:((kind(X)|generous(X))))&
((generous(susan)|humble(susan)))&
(~patient(mary))&
(~quiet(john))&
(?[X]:((quiet(X)|old(X))))&
((curious(susan)&funny(susan))) | ~happy(lucy) | [] | null | 0 |
If someone is creative then john is quiet or old.
Everyone who is not creative or strong is either not quiet or humble and vice versa.
Everyone who is not brave is creative and vice versa.
Everyone who is not funny or humble is both calm and rich.
If john is either not quiet or not generous then john is creative.
If someone is both not brave and patient then fred is both kind and not humble and vice versa.
If someone is either not funny or not rich then fred is both humble and rich.
Everyone who is not wise is not creative.
If mary is not generous then susan is either not funny or wise.
Everyone who is both not patient and not quiet is brave or not wise and vice versa.
If someone is not curious or brave then someone is not tall and vice versa.
Everyone who is both rich and not humble is both not curious and quiet.
Everyone who is both quiet and not strong is both not humble and not wise.
If someone is not humble then someone is both quiet and not patient and vice versa.
If lucy is quiet then someone is either not kind or not curious and vice versa.
If someone is either wise or rich then mary is generous.
Mary is not creative.
Mary is either not creative or not happy.
Someone is not humble.
Lucy is not old.
Fred is not quiet or not curious.
Someone is both brave and tall. | Mary is rich. | contradiction | ((?[X]:(creative(X)))=>((quiet(john)|old(john))))&
(![X]:((~creative(X)|strong(X))<=>(~quiet(X)<~>humble(X))))&
(![X]:(~brave(X)<=>creative(X)))&
(![X]:((~funny(X)|humble(X))=>(calm(X)&rich(X))))&
(((~quiet(john)<~>~generous(john)))=>(creative(john)))&
((?[X]:((~brave(X)&patient(X))))<=>((kind(fred)&~humble(fred))))&
((?[X]:((~funny(X)<~>~rich(X))))=>((humble(fred)&rich(fred))))&
(![X]:(~wise(X)=>~creative(X)))&
((~generous(mary))=>((~funny(susan)<~>wise(susan))))&
(![X]:((~patient(X)&~quiet(X))<=>(brave(X)|~wise(X))))&
((?[X]:((~curious(X)|brave(X))))<=>(?[X]:(~tall(X))))&
(![X]:((rich(X)&~humble(X))=>(~curious(X)&quiet(X))))&
(![X]:((quiet(X)&~strong(X))=>(~humble(X)&~wise(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((quiet(X)&~patient(X)))))&
((quiet(lucy))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
((?[X]:((wise(X)<~>rich(X))))=>(generous(mary)))&
(~creative(mary))&
((~creative(mary)<~>~happy(mary)))&
(?[X]:(~humble(X)))&
(~old(lucy))&
((~quiet(fred)|~curious(fred)))&
(?[X]:((brave(X)&tall(X)))) | rich(mary) | [
"p1",
"p2",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5314470477894245243992589
% SZS output start Proof for 5314470477894245243992589
2. ! [X0] : ((strong(X0) | ~creative(X0)) <=> (~quiet(X0) <~> humble(X0))) [input p1]
3. ! [X0] : (~brave(X0) <=> creative(X0)) [input p2]
10. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (~wise(X0) | brave(X0))) [input p9]
12. ! [X0] : ((~humble(X0) & rich(X0)) => (quiet(X0) & ~curious(X0))) [input p11]
17. ~creative(mary) [input p16]
23. rich(mary) [input hypothesis]
34. ! [X0] : ((quiet(X0) & ~curious(X0)) | (humble(X0) | ~rich(X0))) [ennf transformation 12]
35. ! [X0] : ((quiet(X0) & ~curious(X0)) | humble(X0) | ~rich(X0)) [flattening 34]
39. ! [X0] : (((strong(X0) | ~creative(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0)))) & (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & creative(X0)))) [nnf transformation 2]
40. ! [X0] : ((strong(X0) | ~creative(X0) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0)))) & (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & creative(X0)))) [flattening 39]
41. ! [X0] : ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))) [nnf transformation 3]
50. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (wise(X0) & ~brave(X0))) & ((~wise(X0) | brave(X0)) | (quiet(X0) | patient(X0)))) [nnf transformation 10]
51. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (wise(X0) & ~brave(X0))) & (~wise(X0) | brave(X0) | quiet(X0) | patient(X0))) [flattening 50]
75. ~humble(X0) | quiet(X0) | creative(X0) [cnf transformation 40]
79. brave(X0) | creative(X0) [cnf transformation 41]
99. ~brave(X0) | ~quiet(X0) [cnf transformation 51]
105. ~rich(X0) | humble(X0) | quiet(X0) [cnf transformation 35]
117. ~creative(mary) [cnf transformation 17]
125. rich(mary) [cnf transformation 23]
305. ~quiet(X0) | creative(X0) [resolution 99,79]
325. humble(mary) | quiet(mary) [resolution 105,125]
330. 37 <=> quiet(mary) [avatar definition]
331. ~quiet(mary) <- (~37) [avatar component clause 330]
332. quiet(mary) <- (37) [avatar component clause 330]
334. 38 <=> humble(mary) [avatar definition]
336. humble(mary) <- (38) [avatar component clause 334]
337. 37 | 38 [avatar split clause 325,334,330]
350. creative(mary) <- (37) [resolution 332,305]
355. $false <- (37) [subsumption resolution 350,117]
356. ~37 [avatar contradiction clause 355]
363. quiet(mary) | creative(mary) <- (38) [resolution 336,75]
366. creative(mary) <- (~37, 38) [subsumption resolution 363,331]
367. $false <- (~37, 38) [subsumption resolution 366,117]
368. 37 | ~38 [avatar contradiction clause 367]
369. $false [avatar sat refutation 337,356,368]
% SZS output end Proof for 5314470477894245243992589
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then john is both happy and quiet. Everyone who is either quiet or funny is strong or creative. If john is both humble and curious then lucy is either not curious or not wise. If someone is either not wise or strong then someone is either generous or not quiet. Everyone who is either old or brave is either not funny or not brave. Everyone who is both not strong and strong is rich. If someone is not brave or brave then susan is both not humble and not brave and vice versa. Everyone who is both tall and humble is both brave and not patient and vice versa. Everyone who is both not brave and happy is wise or not creative. Everyone who is not wise is either not funny or quiet and vice versa. Everyone who is calm or wise is not tall and vice versa. Everyone who is both tall and not funny is not tall and vice versa. Everyone who is not patient or not brave is either funny or not funny and vice versa. If alice is either not brave or not funny then someone is both old and strong. Everyone who is both humble and not rich is either strong or not kind. If alice is both strong and not generous then alice is not brave or not strong. Someone is either not humble or old. Someone is both brave and not calm. Mary is either creative or not strong. Someone is strong or not happy. Susan is not old or not humble. Someone is both kind and brave. Someone is either not patient or curious. | Mary is not wise. | entailment | ((?[X]:(~wise(X)))=>((happy(john)&quiet(john))))&
(![X]:((quiet(X)<~>funny(X))=>(strong(X)|creative(X))))&
(((humble(john)&curious(john)))=>((~curious(lucy)<~>~wise(lucy))))&
((?[X]:((~wise(X)<~>strong(X))))=>(?[X]:((generous(X)<~>~quiet(X)))))&
(![X]:((old(X)<~>brave(X))=>(~funny(X)<~>~brave(X))))&
(![X]:((~strong(X)&strong(X))=>rich(X)))&
((?[X]:((~brave(X)|brave(X))))<=>((~humble(susan)&~brave(susan))))&
(![X]:((tall(X)&humble(X))<=>(brave(X)&~patient(X))))&
(![X]:((~brave(X)&happy(X))=>(wise(X)|~creative(X))))&
(![X]:(~wise(X)<=>(~funny(X)<~>quiet(X))))&
(![X]:((calm(X)|wise(X))<=>~tall(X)))&
(![X]:((tall(X)&~funny(X))<=>~tall(X)))&
(![X]:((~patient(X)|~brave(X))<=>(funny(X)<~>~funny(X))))&
(((~brave(alice)<~>~funny(alice)))=>(?[X]:((old(X)&strong(X)))))&
(![X]:((humble(X)&~rich(X))=>(strong(X)<~>~kind(X))))&
(((strong(alice)&~generous(alice)))=>((~brave(alice)|~strong(alice))))&
(?[X]:((~humble(X)<~>old(X))))&
(?[X]:((brave(X)&~calm(X))))&
((creative(mary)<~>~strong(mary)))&
(?[X]:((strong(X)|~happy(X))))&
((~old(susan)|~humble(susan)))&
(?[X]:((kind(X)&brave(X))))&
(?[X]:((~patient(X)<~>curious(X)))) | ~wise(mary) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8232861468366239996104204
% SZS output start Proof for 8232861468366239996104204
11. ! [X0] : ((wise(X0) | calm(X0)) <=> ~tall(X0)) [input p10]
12. ! [X0] : ((~funny(X0) & tall(X0)) <=> ~tall(X0)) [input p11]
24. wise(mary) [input hypothesis]
56. ! [X0] : (((wise(X0) | calm(X0)) | tall(X0)) & (~tall(X0) | (~wise(X0) & ~calm(X0)))) [nnf transformation 11]
57. ! [X0] : ((wise(X0) | calm(X0) | tall(X0)) & (~tall(X0) | (~wise(X0) & ~calm(X0)))) [flattening 56]
58. ! [X0] : (((~funny(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | (funny(X0) | ~tall(X0)))) [nnf transformation 12]
59. ! [X0] : (((~funny(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | funny(X0) | ~tall(X0))) [flattening 58]
107. ~tall(X0) | ~wise(X0) [cnf transformation 57]
110. tall(X0) | tall(X0) [cnf transformation 59]
134. wise(mary) [cnf transformation 24]
139. tall(X0) [duplicate literal removal 110]
280. ~wise(X0) [resolution 107,139]
281. $false [resolution 280,134]
% SZS output end Proof for 8232861468366239996104204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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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