premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is generous or not quiet is both kind and generous and vice versa.
If mary is not creative then fred is both humble and strong and vice versa.
If someone is both not strong and curious then someone is either not generous or not strong.
If someone is not tall or not strong then fred is not generous.
Everyone who is generous or old is both brave and curious and vice versa.
Everyone who is not old is not strong or not creative and vice versa.
Everyone who is either humble or not humble is brave or old.
Everyone who is both not creative and not humble is both not humble and wise and vice versa.
Everyone who is creative or funny is not generous.
Everyone who is creative is not strong or kind and vice versa.
If mary is not patient then someone is both not funny and not old and vice versa.
If someone is not old or tall then fred is either happy or not humble.
If someone is both not creative and quiet then someone is both happy and generous.
If someone is not kind or not creative then someone is not calm and vice versa.
Everyone who is wise or curious is creative or patient and vice versa.
If mary is either brave or not old then someone is both not wise and kind and vice versa.
Someone is not rich or happy.
Alice is funny or kind.
Someone is either patient or funny.
John is both not humble and kind.
Someone is patient.
Someone is not happy. | John is not funny. | neutral | (![X]:((generous(X)|~quiet(X))<=>(kind(X)&generous(X))))&
((~creative(mary))<=>((humble(fred)&strong(fred))))&
((?[X]:((~strong(X)&curious(X))))=>(?[X]:((~generous(X)<~>~strong(X)))))&
((?[X]:((~tall(X)|~strong(X))))=>(~generous(fred)))&
(![X]:((generous(X)|old(X))<=>(brave(X)&curious(X))))&
(![X]:(~old(X)<=>(~strong(X)|~creative(X))))&
(![X]:((humble(X)<~>~humble(X))=>(brave(X)|old(X))))&
(![X]:((~creative(X)&~humble(X))<=>(~humble(X)&wise(X))))&
(![X]:((creative(X)|funny(X))=>~generous(X)))&
(![X]:(creative(X)<=>(~strong(X)|kind(X))))&
((~patient(mary))<=>(?[X]:((~funny(X)&~old(X)))))&
((?[X]:((~old(X)|tall(X))))=>((happy(fred)<~>~humble(fred))))&
((?[X]:((~creative(X)&quiet(X))))=>(?[X]:((happy(X)&generous(X)))))&
((?[X]:((~kind(X)|~creative(X))))<=>(?[X]:(~calm(X))))&
(![X]:((wise(X)|curious(X))<=>(creative(X)|patient(X))))&
(((brave(mary)<~>~old(mary)))<=>(?[X]:((~wise(X)&kind(X)))))&
(?[X]:((~rich(X)|happy(X))))&
((funny(alice)|kind(alice)))&
(?[X]:((patient(X)<~>funny(X))))&
((~humble(john)&kind(john)))&
(?[X]:(patient(X)))&
(?[X]:(~happy(X))) | ~funny(john) | [] | null | 0 |
Everyone who is both not patient and happy is funny and vice versa.
If someone is not strong or tall then paul is not humble or not happy.
If someone is either wise or creative then someone is both happy and wise and vice versa.
Everyone who is both tall and not funny is both wise and not strong.
Everyone who is both not curious and not tall is not patient or not creative.
Everyone who is not tall is kind or tall and vice versa.
Everyone who is both quiet and happy is both quiet and not humble.
Everyone who is either funny or not kind is either humble or not humble.
If someone is both creative and quiet then someone is calm and vice versa.
Everyone who is both brave and kind is either not wise or tall.
Everyone who is either not rich or not happy is calm.
Everyone who is not generous or funny is not funny or calm and vice versa.
If someone is both calm and not funny then fred is patient or not generous and vice versa.
Everyone who is either kind or not patient is either not patient or funny.
Everyone who is not quiet or not calm is both humble and not creative and vice versa.
Fred is either strong or not funny.
Someone is brave or old.
Someone is kind or not happy.
Fred is happy.
Someone is either not rich or not old.
Someone is not patient.
Someone is not calm or not creative. | Fred is calm. | entailment | (![X]:((~patient(X)&happy(X))<=>funny(X)))&
((?[X]:((~strong(X)|tall(X))))=>((~humble(paul)|~happy(paul))))&
((?[X]:((wise(X)<~>creative(X))))<=>(?[X]:((happy(X)&wise(X)))))&
(![X]:((tall(X)&~funny(X))=>(wise(X)&~strong(X))))&
(![X]:((~curious(X)&~tall(X))=>(~patient(X)|~creative(X))))&
(![X]:(~tall(X)<=>(kind(X)|tall(X))))&
(![X]:((quiet(X)&happy(X))=>(quiet(X)&~humble(X))))&
(![X]:((funny(X)<~>~kind(X))=>(humble(X)<~>~humble(X))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:(calm(X))))&
(![X]:((brave(X)&kind(X))=>(~wise(X)<~>tall(X))))&
(![X]:((~rich(X)<~>~happy(X))=>calm(X)))&
(![X]:((~generous(X)|funny(X))<=>(~funny(X)|calm(X))))&
((?[X]:((calm(X)&~funny(X))))<=>((patient(fred)|~generous(fred))))&
(![X]:((kind(X)<~>~patient(X))=>(~patient(X)<~>funny(X))))&
(![X]:((~quiet(X)|~calm(X))<=>(humble(X)&~creative(X))))&
((strong(fred)<~>~funny(fred)))&
(?[X]:((brave(X)|old(X))))&
(?[X]:((kind(X)|~happy(X))))&
(happy(fred))&
(?[X]:((~rich(X)<~>~old(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)|~creative(X)))) | calm(fred) | [
"p0",
"p5",
"p11",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1826134670672907689749790
% SZS output start Proof for 1826134670672907689749790
1. ! [X0] : ((happy(X0) & ~patient(X0)) <=> funny(X0)) [input p0]
6. ! [X0] : (~tall(X0) <=> (tall(X0) | kind(X0))) [input p5]
12. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (calm(X0) | ~funny(X0))) [input p11]
14. ! [X0] : ((kind(X0) <~> ~patient(X0)) => (~patient(X0) <~> funny(X0))) [input p13]
19. happy(fred) [input p18]
23. ~calm(fred) [input hypothesis]
37. ! [X0] : ((~patient(X0) <~> funny(X0)) | (kind(X0) <=> ~patient(X0))) [ennf transformation 14]
38. ! [X0] : (((happy(X0) & ~patient(X0)) | ~funny(X0)) & (funny(X0) | (~happy(X0) | patient(X0)))) [nnf transformation 1]
39. ! [X0] : (((happy(X0) & ~patient(X0)) | ~funny(X0)) & (funny(X0) | ~happy(X0) | patient(X0))) [flattening 38]
45. ! [X0] : ((~tall(X0) | (~tall(X0) & ~kind(X0))) & ((tall(X0) | kind(X0)) | tall(X0))) [nnf transformation 6]
46. ! [X0] : ((~tall(X0) | (~tall(X0) & ~kind(X0))) & (tall(X0) | kind(X0) | tall(X0))) [flattening 45]
55. ! [X0] : (((funny(X0) | ~generous(X0)) | (~calm(X0) & funny(X0))) & ((calm(X0) | ~funny(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 12]
56. ! [X0] : ((funny(X0) | ~generous(X0) | (~calm(X0) & funny(X0))) & (calm(X0) | ~funny(X0) | (~funny(X0) & generous(X0)))) [flattening 55]
62. ! [X0] : (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) [nnf transformation 37]
77. ~happy(X0) | funny(X0) | patient(X0) [cnf transformation 39]
78. ~funny(X0) | ~patient(X0) [cnf transformation 39]
90. tall(X0) | kind(X0) | tall(X0) [cnf transformation 46]
92. ~tall(X0) | ~tall(X0) [cnf transformation 46]
107. calm(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 56]
115. funny(X0) | ~patient(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 62]
128. happy(fred) [cnf transformation 19]
133. ~calm(fred) [cnf transformation 23]
134. funny(X0) | ~patient(X0) | ~kind(X0) [duplicate literal removal 115]
136. ~funny(X0) | calm(X0) [duplicate literal removal 107]
138. kind(X0) | tall(X0) [duplicate literal removal 90]
139. ~tall(X0) [duplicate literal removal 92]
141. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
142. ~tall(X0) <- (1) [avatar component clause 141]
187. 1 [avatar split clause 139,141]
235. ~kind(X0) | ~patient(X0) [subsumption resolution 134,78]
241. 23 <=> funny(fred) [avatar definition]
243. funny(fred) <- (23) [avatar component clause 241]
298. ~patient(X0) | tall(X0) [resolution 235,138]
299. ~patient(X0) <- (1) [subsumption resolution 298,142]
300. funny(fred) | patient(fred) [resolution 77,128]
304. funny(fred) <- (1) [subsumption resolution 300,299]
305. 23 | ~1 [avatar split clause 304,141,241]
307. calm(fred) <- (23) [resolution 243,136]
310. $false <- (23) [subsumption resolution 307,133]
311. ~23 [avatar contradiction clause 310]
312. $false [avatar sat refutation 187,305,311]
% SZS output end Proof for 1826134670672907689749790
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not creative is kind or creative and vice versa.
If alice is not calm or curious then someone is not curious or not old and vice versa.
Everyone who is humble is either not tall or not old.
If someone is not old then someone is either not brave or quiet and vice versa.
Everyone who is old is both wise and not rich and vice versa.
Everyone who is patient or old is both quiet and not kind.
Everyone who is not patient or not wise is either quiet or old and vice versa.
Everyone who is both not calm and calm is either calm or humble.
Everyone who is calm is either not old or rich.
Everyone who is not curious or rich is either not rich or tall.
Everyone who is not wise or not patient is either kind or humble and vice versa.
Everyone who is happy is either not curious or not old and vice versa.
Everyone who is both not humble and happy is humble or curious and vice versa.
Everyone who is not wise is not curious.
If fred is either calm or not quiet then lucy is both not patient and wise.
Everyone who is not wise is either not kind or not creative and vice versa.
Someone is either creative or strong.
Fred is either not strong or creative.
Alice is not calm.
Fred is not creative.
Susan is either creative or not brave.
Paul is not brave or humble. | Susan is brave. | contradiction | (![X]:((patient(X)|~creative(X))<=>(kind(X)|creative(X))))&
(((~calm(alice)|curious(alice)))<=>(?[X]:((~curious(X)|~old(X)))))&
(![X]:(humble(X)=>(~tall(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:(old(X)<=>(wise(X)&~rich(X))))&
(![X]:((patient(X)|old(X))=>(quiet(X)&~kind(X))))&
(![X]:((~patient(X)|~wise(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~calm(X)&calm(X))=>(calm(X)<~>humble(X))))&
(![X]:(calm(X)=>(~old(X)<~>rich(X))))&
(![X]:((~curious(X)|rich(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|~patient(X))<=>(kind(X)<~>humble(X))))&
(![X]:(happy(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~humble(X)&happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~wise(X)=>~curious(X)))&
(((calm(fred)<~>~quiet(fred)))=>((~patient(lucy)&wise(lucy))))&
(![X]:(~wise(X)<=>(~kind(X)<~>~creative(X))))&
(?[X]:((creative(X)<~>strong(X))))&
((~strong(fred)<~>creative(fred)))&
(~calm(alice))&
(~creative(fred))&
((creative(susan)<~>~brave(susan)))&
((~brave(paul)|humble(paul))) | brave(susan) | [
"p0",
"p5",
"p10",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 337460711946004327320012
% SZS output start Proof for 337460711946004327320012
1. ! [X0] : ((~creative(X0) | patient(X0)) <=> (creative(X0) | kind(X0))) [input p0]
6. ! [X0] : ((old(X0) | patient(X0)) => (~kind(X0) & quiet(X0))) [input p5]
11. ! [X0] : ((~patient(X0) | ~wise(X0)) <=> (kind(X0) <~> humble(X0))) [input p10]
13. ! [X0] : ((happy(X0) & ~humble(X0)) <=> (curious(X0) | humble(X0))) [input p12]
16. ! [X0] : (~wise(X0) <=> (~kind(X0) <~> ~creative(X0))) [input p15]
21. creative(susan) <~> ~brave(susan) [input p20]
23. brave(susan) [input hypothesis]
26. ! [X0] : ((~kind(X0) & quiet(X0)) | (~old(X0) & ~patient(X0))) [ennf transformation 6]
33. ! [X0] : (((~creative(X0) | patient(X0)) | (~creative(X0) & ~kind(X0))) & ((creative(X0) | kind(X0)) | (creative(X0) & ~patient(X0)))) [nnf transformation 1]
34. ! [X0] : ((~creative(X0) | patient(X0) | (~creative(X0) & ~kind(X0))) & (creative(X0) | kind(X0) | (creative(X0) & ~patient(X0)))) [flattening 33]
53. ! [X0] : (((~patient(X0) | ~wise(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & wise(X0)))) [nnf transformation 11]
54. ! [X0] : ((~patient(X0) | ~wise(X0) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & wise(X0)))) [flattening 53]
56. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (~happy(X0) | humble(X0)))) [nnf transformation 13]
57. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | ~happy(X0) | humble(X0))) [flattening 56]
59. ! [X0] : ((~wise(X0) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0)))) & (((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | wise(X0))) [nnf transformation 16]
64. (brave(susan) | ~creative(susan)) & (~brave(susan) | creative(susan)) [nnf transformation 21]
66. creative(X0) | kind(X0) | creative(X0) [cnf transformation 34]
68. ~creative(X0) | patient(X0) | ~creative(X0) [cnf transformation 34]
84. ~kind(X0) | ~patient(X0) [cnf transformation 26]
100. wise(X0) | kind(X0) | humble(X0) [cnf transformation 54]
111. ~humble(X0) | ~humble(X0) [cnf transformation 57]
122. ~wise(X0) | ~creative(X0) | kind(X0) [cnf transformation 59]
130. ~brave(susan) | creative(susan) [cnf transformation 64]
133. brave(susan) [cnf transformation 23]
135. ~humble(X0) [duplicate literal removal 111]
139. kind(X0) | creative(X0) [duplicate literal removal 66]
140. ~creative(X0) | patient(X0) [duplicate literal removal 68]
216. ~wise(X0) | kind(X0) [subsumption resolution 122,139]
240. 19 <=> creative(susan) [avatar definition]
241. creative(susan) <- (19) [avatar component clause 240]
244. 20 <=> brave(susan) [avatar definition]
248. 19 | ~20 [avatar split clause 130,244,240]
250. 20 [avatar split clause 133,244]
255. patient(susan) <- (19) [resolution 140,241]
264. kind(X1) | humble(X1) | kind(X1) [resolution 100,216]
266. kind(X1) | humble(X1) [duplicate literal removal 264]
268. kind(X1) [subsumption resolution 266,135]
274. ~patient(X0) [resolution 268,84]
276. $false <- (19) [resolution 274,255]
277. ~19 [avatar contradiction clause 276]
279. $false [avatar sat refutation 248,250,277]
% SZS output end Proof for 337460711946004327320012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not old is not brave or tall and vice versa.
If someone is old or not happy then someone is not generous.
If paul is both quiet and funny then susan is not funny or not brave and vice versa.
If alice is not curious or not tall then fred is both rich and brave.
If someone is either tall or not creative then someone is either not humble or not brave and vice versa.
If someone is curious then john is quiet or strong.
Everyone who is either not quiet or curious is either brave or happy and vice versa.
Everyone who is not calm or curious is not curious or not old.
If someone is not happy or not wise then someone is not patient or not strong and vice versa.
If someone is both not tall and funny then john is not wise.
Everyone who is not wise or not patient is rich or not rich.
Everyone who is both not quiet and creative is either funny or not funny.
Everyone who is both generous and curious is brave or not quiet and vice versa.
If someone is calm then fred is not kind and vice versa.
Everyone who is both strong and not funny is either patient or not happy.
If someone is not creative then susan is either generous or kind.
Mary is not curious.
John is either not generous or patient.
Someone is tall or not wise.
Alice is both not wise and humble.
Susan is either not kind or kind.
Someone is either not wise or not curious.
Susan is not kind or patient. | Paul is rich. | neutral | (![X]:((generous(X)<~>~old(X))<=>(~brave(X)|tall(X))))&
((?[X]:((old(X)|~happy(X))))=>(?[X]:(~generous(X))))&
(((quiet(paul)&funny(paul)))<=>((~funny(susan)|~brave(susan))))&
(((~curious(alice)|~tall(alice)))=>((rich(fred)&brave(fred))))&
((?[X]:((tall(X)<~>~creative(X))))<=>(?[X]:((~humble(X)<~>~brave(X)))))&
((?[X]:(curious(X)))=>((quiet(john)|strong(john))))&
(![X]:((~quiet(X)<~>curious(X))<=>(brave(X)<~>happy(X))))&
(![X]:((~calm(X)|curious(X))=>(~curious(X)|~old(X))))&
((?[X]:((~happy(X)|~wise(X))))<=>(?[X]:((~patient(X)|~strong(X)))))&
((?[X]:((~tall(X)&funny(X))))=>(~wise(john)))&
(![X]:((~wise(X)|~patient(X))=>(rich(X)|~rich(X))))&
(![X]:((~quiet(X)&creative(X))=>(funny(X)<~>~funny(X))))&
(![X]:((generous(X)&curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:(calm(X)))<=>(~kind(fred)))&
(![X]:((strong(X)&~funny(X))=>(patient(X)<~>~happy(X))))&
((?[X]:(~creative(X)))=>((generous(susan)<~>kind(susan))))&
(~curious(mary))&
((~generous(john)<~>patient(john)))&
(?[X]:((tall(X)|~wise(X))))&
((~wise(alice)&humble(alice)))&
((~kind(susan)<~>kind(susan)))&
(?[X]:((~wise(X)<~>~curious(X))))&
((~kind(susan)|patient(susan))) | rich(paul) | [] | null | 0 |
If someone is quiet then paul is either happy or tall and vice versa.
Everyone who is either old or not curious is patient and vice versa.
If lucy is not tall then fred is both not calm and rich and vice versa.
Everyone who is either brave or not calm is humble or wise and vice versa.
Everyone who is either not rich or happy is either not patient or not humble.
If paul is both not wise and creative then mary is both rich and curious.
Everyone who is both not strong and happy is not tall and vice versa.
If mary is both not kind and not generous then someone is not funny or wise and vice versa.
If someone is both strong and not patient then lucy is happy or calm and vice versa.
If someone is both not calm and rich then someone is both kind and not curious and vice versa.
If someone is not strong then someone is not generous or strong and vice versa.
Everyone who is either wise or brave is both not humble and wise and vice versa.
If susan is strong or creative then fred is both not creative and not funny.
Everyone who is not happy or not brave is not strong.
If lucy is either funny or not curious then john is not calm.
Everyone who is either generous or not kind is not humble or not calm.
Someone is patient or happy.
Someone is either tall or not wise.
Someone is both not strong and not patient.
Someone is both old and not rich.
John is rich.
Fred is either not brave or not curious. | Fred is not creative. | neutral | ((?[X]:(quiet(X)))<=>((happy(paul)<~>tall(paul))))&
(![X]:((old(X)<~>~curious(X))<=>patient(X)))&
((~tall(lucy))<=>((~calm(fred)&rich(fred))))&
(![X]:((brave(X)<~>~calm(X))<=>(humble(X)|wise(X))))&
(![X]:((~rich(X)<~>happy(X))=>(~patient(X)<~>~humble(X))))&
(((~wise(paul)&creative(paul)))=>((rich(mary)&curious(mary))))&
(![X]:((~strong(X)&happy(X))<=>~tall(X)))&
(((~kind(mary)&~generous(mary)))<=>(?[X]:((~funny(X)|wise(X)))))&
((?[X]:((strong(X)&~patient(X))))<=>((happy(lucy)|calm(lucy))))&
((?[X]:((~calm(X)&rich(X))))<=>(?[X]:((kind(X)&~curious(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((~generous(X)|strong(X)))))&
(![X]:((wise(X)<~>brave(X))<=>(~humble(X)&wise(X))))&
(((strong(susan)|creative(susan)))=>((~creative(fred)&~funny(fred))))&
(![X]:((~happy(X)|~brave(X))=>~strong(X)))&
(((funny(lucy)<~>~curious(lucy)))=>(~calm(john)))&
(![X]:((generous(X)<~>~kind(X))=>(~humble(X)|~calm(X))))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:((old(X)&~rich(X))))&
(rich(john))&
((~brave(fred)<~>~curious(fred))) | ~creative(fred) | [] | null | 0 |
Everyone who is either not patient or curious is generous.
If someone is not calm or brave then someone is either not humble or quiet.
Everyone who is not patient is curious and vice versa.
Everyone who is either generous or strong is brave.
If paul is both not calm and not humble then someone is not old or not humble.
Everyone who is either kind or not curious is both not calm and not patient and vice versa.
Everyone who is either brave or not humble is not old.
Everyone who is both not humble and rich is old.
Everyone who is rich is funny and vice versa.
Everyone who is both not kind and quiet is rich and vice versa.
Everyone who is not quiet is either not curious or not humble and vice versa.
Everyone who is both humble and calm is not calm and vice versa.
Everyone who is both not tall and rich is kind or brave.
If susan is either not humble or not strong then susan is not tall or kind and vice versa.
If paul is either kind or not strong then susan is not generous and vice versa.
Everyone who is both old and creative is both not kind and calm and vice versa.
Someone is curious.
Someone is not strong.
Alice is curious.
Alice is not generous or not kind.
Mary is kind or humble.
Someone is either not wise or old. | Mary is not rich. | entailment | (![X]:((~patient(X)<~>curious(X))=>generous(X)))&
((?[X]:((~calm(X)|brave(X))))=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:(~patient(X)<=>curious(X)))&
(![X]:((generous(X)<~>strong(X))=>brave(X)))&
(((~calm(paul)&~humble(paul)))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((kind(X)<~>~curious(X))<=>(~calm(X)&~patient(X))))&
(![X]:((brave(X)<~>~humble(X))=>~old(X)))&
(![X]:((~humble(X)&rich(X))=>old(X)))&
(![X]:(rich(X)<=>funny(X)))&
(![X]:((~kind(X)&quiet(X))<=>rich(X)))&
(![X]:(~quiet(X)<=>(~curious(X)<~>~humble(X))))&
(![X]:((humble(X)&calm(X))<=>~calm(X)))&
(![X]:((~tall(X)&rich(X))=>(kind(X)|brave(X))))&
(((~humble(susan)<~>~strong(susan)))<=>((~tall(susan)|kind(susan))))&
(((kind(paul)<~>~strong(paul)))<=>(~generous(susan)))&
(![X]:((old(X)&creative(X))<=>(~kind(X)&calm(X))))&
(?[X]:(curious(X)))&
(?[X]:(~strong(X)))&
(curious(alice))&
((~generous(alice)|~kind(alice)))&
((kind(mary)|humble(mary)))&
(?[X]:((~wise(X)<~>old(X)))) | ~rich(mary) | [
"p9",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7094706485606584453963256
% SZS output start Proof for 7094706485606584453963256
10. ! [X0] : ((quiet(X0) & ~kind(X0)) <=> rich(X0)) [input p9]
12. ! [X0] : ((calm(X0) & humble(X0)) <=> ~calm(X0)) [input p11]
21. humble(mary) | kind(mary) [input p20]
23. rich(mary) [input hypothesis]
48. ! [X0] : (((quiet(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | (~quiet(X0) | kind(X0)))) [nnf transformation 10]
49. ! [X0] : (((quiet(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | ~quiet(X0) | kind(X0))) [flattening 48]
51. ! [X0] : (((calm(X0) & humble(X0)) | calm(X0)) & (~calm(X0) | (~calm(X0) | ~humble(X0)))) [nnf transformation 12]
52. ! [X0] : (((calm(X0) & humble(X0)) | calm(X0)) & (~calm(X0) | ~calm(X0) | ~humble(X0))) [flattening 51]
88. ~rich(X0) | ~kind(X0) [cnf transformation 49]
94. ~calm(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 52]
96. calm(X0) | calm(X0) [cnf transformation 52]
116. humble(mary) | kind(mary) [cnf transformation 21]
119. rich(mary) [cnf transformation 23]
120. ~humble(X0) | ~calm(X0) [duplicate literal removal 94]
121. calm(X0) [duplicate literal removal 96]
135. 4 <=> ! [X1] : calm(X1) [avatar definition]
136. calm(X1) <- (4) [avatar component clause 135]
159. 4 [avatar split clause 121,135]
209. 18 <=> kind(mary) [avatar definition]
213. 19 <=> humble(mary) [avatar definition]
215. humble(mary) <- (19) [avatar component clause 213]
216. 18 | 19 [avatar split clause 116,213,209]
232. ~kind(mary) [resolution 88,119]
235. ~18 [avatar split clause 232,209]
240. ~calm(mary) <- (19) [resolution 120,215]
244. $false <- (4, 19) [subsumption resolution 240,136]
245. ~4 | ~19 [avatar contradiction clause 244]
246. $false [avatar sat refutation 159,216,235,245]
% SZS output end Proof for 7094706485606584453963256
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not funny or not rich then someone is not curious.
If mary is wise then john is not wise or not tall.
Everyone who is either not curious or patient is old or not kind.
Everyone who is not happy is both not strong and not patient.
Everyone who is both brave and happy is not creative and vice versa.
If john is both not strong and kind then someone is either calm or rich and vice versa.
Everyone who is both not happy and creative is both not calm and not generous and vice versa.
Everyone who is either kind or not tall is not old or not tall and vice versa.
Everyone who is both funny and wise is not calm and vice versa.
Everyone who is both funny and not wise is calm or old and vice versa.
Everyone who is not patient is not humble and vice versa.
Everyone who is happy or generous is not curious or not old and vice versa.
Everyone who is not quiet or patient is patient and vice versa.
If someone is both not brave and kind then paul is not kind or not quiet and vice versa.
Everyone who is kind or not calm is curious or not wise.
If alice is not patient or wise then fred is either not happy or not generous and vice versa.
Lucy is either patient or not quiet.
Lucy is not calm.
Alice is funny or kind.
Someone is not brave or tall.
Someone is not calm or not funny.
Lucy is not rich or not happy.
Alice is old or humble.
Susan is not creative. | John is not wise. | neutral | (((~funny(paul)<~>~rich(paul)))=>(?[X]:(~curious(X))))&
((wise(mary))=>((~wise(john)|~tall(john))))&
(![X]:((~curious(X)<~>patient(X))=>(old(X)|~kind(X))))&
(![X]:(~happy(X)=>(~strong(X)&~patient(X))))&
(![X]:((brave(X)&happy(X))<=>~creative(X)))&
(((~strong(john)&kind(john)))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~happy(X)&creative(X))<=>(~calm(X)&~generous(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(~old(X)|~tall(X))))&
(![X]:((funny(X)&wise(X))<=>~calm(X)))&
(![X]:((funny(X)&~wise(X))<=>(calm(X)|old(X))))&
(![X]:(~patient(X)<=>~humble(X)))&
(![X]:((happy(X)|generous(X))<=>(~curious(X)|~old(X))))&
(![X]:((~quiet(X)|patient(X))<=>patient(X)))&
((?[X]:((~brave(X)&kind(X))))<=>((~kind(paul)|~quiet(paul))))&
(![X]:((kind(X)|~calm(X))=>(curious(X)|~wise(X))))&
(((~patient(alice)|wise(alice)))<=>((~happy(fred)<~>~generous(fred))))&
((patient(lucy)<~>~quiet(lucy)))&
(~calm(lucy))&
((funny(alice)|kind(alice)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~calm(X)|~funny(X))))&
((~rich(lucy)|~happy(lucy)))&
((old(alice)|humble(alice)))&
(~creative(susan)) | ~wise(john) | [] | null | 0 |
Everyone who is tall is both generous and not happy and vice versa.
If alice is either kind or happy then someone is patient or not generous and vice versa.
If alice is brave or humble then someone is strong.
If someone is happy or curious then mary is both patient and humble.
Everyone who is either wise or not humble is either not generous or not wise and vice versa.
Everyone who is not calm is old and vice versa.
If fred is both not humble and not strong then paul is not kind.
Everyone who is quiet or rich is both not kind and not wise.
If someone is either not tall or not humble then someone is either not funny or not happy and vice versa.
Everyone who is either brave or kind is not generous or not wise and vice versa.
If fred is both patient and not quiet then lucy is humble or kind and vice versa.
Everyone who is either strong or not rich is not funny and vice versa.
Everyone who is brave or humble is not funny or not old.
Everyone who is both strong and not quiet is both brave and patient and vice versa.
Everyone who is both patient and humble is either quiet or happy and vice versa.
If john is either not humble or not tall then fred is both rich and kind and vice versa.
Someone is not strong.
Someone is not kind or quiet.
Lucy is not old.
Someone is both creative and quiet.
Paul is both not curious and quiet.
Someone is either not creative or not patient.
Mary is either not generous or brave.
Lucy is not funny. | Paul is patient. | contradiction | (![X]:(tall(X)<=>(generous(X)&~happy(X))))&
(((kind(alice)<~>happy(alice)))<=>(?[X]:((patient(X)|~generous(X)))))&
(((brave(alice)|humble(alice)))=>(?[X]:(strong(X))))&
((?[X]:((happy(X)|curious(X))))=>((patient(mary)&humble(mary))))&
(![X]:((wise(X)<~>~humble(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:(~calm(X)<=>old(X)))&
(((~humble(fred)&~strong(fred)))=>(~kind(paul)))&
(![X]:((quiet(X)|rich(X))=>(~kind(X)&~wise(X))))&
((?[X]:((~tall(X)<~>~humble(X))))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((brave(X)<~>kind(X))<=>(~generous(X)|~wise(X))))&
(((patient(fred)&~quiet(fred)))<=>((humble(lucy)|kind(lucy))))&
(![X]:((strong(X)<~>~rich(X))<=>~funny(X)))&
(![X]:((brave(X)|humble(X))=>(~funny(X)|~old(X))))&
(![X]:((strong(X)&~quiet(X))<=>(brave(X)&patient(X))))&
(![X]:((patient(X)&humble(X))<=>(quiet(X)<~>happy(X))))&
(((~humble(john)<~>~tall(john)))<=>((rich(fred)&kind(fred))))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)|quiet(X))))&
(~old(lucy))&
(?[X]:((creative(X)&quiet(X))))&
((~curious(paul)&quiet(paul)))&
(?[X]:((~creative(X)<~>~patient(X))))&
((~generous(mary)<~>brave(mary)))&
(~funny(lucy)) | patient(paul) | [
"p7",
"p9",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4437279178605299924943240
% SZS output start Proof for 4437279178605299924943240
8. ! [X0] : ((rich(X0) | quiet(X0)) => (~wise(X0) & ~kind(X0))) [input p7]
10. ! [X0] : ((brave(X0) <~> kind(X0)) <=> (~wise(X0) | ~generous(X0))) [input p9]
14. ! [X0] : ((~quiet(X0) & strong(X0)) <=> (patient(X0) & brave(X0))) [input p13]
21. quiet(paul) & ~curious(paul) [input p20]
25. patient(paul) [input hypothesis]
29. quiet(paul) [pure predicate removal 21]
35. ! [X0] : ((~wise(X0) & ~kind(X0)) | (~rich(X0) & ~quiet(X0))) [ennf transformation 8]
50. ! [X0] : ((((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (wise(X0) & generous(X0))) & ((~wise(X0) | ~generous(X0)) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0))))) [nnf transformation 10]
51. ! [X0] : ((((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (wise(X0) & generous(X0))) & (~wise(X0) | ~generous(X0) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0))))) [flattening 50]
55. ! [X0] : (((~quiet(X0) & strong(X0)) | (~patient(X0) | ~brave(X0))) & ((patient(X0) & brave(X0)) | (quiet(X0) | ~strong(X0)))) [nnf transformation 14]
56. ! [X0] : (((~quiet(X0) & strong(X0)) | ~patient(X0) | ~brave(X0)) & ((patient(X0) & brave(X0)) | quiet(X0) | ~strong(X0))) [flattening 55]
93. ~quiet(X0) | ~kind(X0) [cnf transformation 35]
95. ~quiet(X0) | ~wise(X0) [cnf transformation 35]
108. wise(X0) | brave(X0) | kind(X0) [cnf transformation 51]
123. ~quiet(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 56]
140. quiet(paul) [cnf transformation 29]
146. patient(paul) [cnf transformation 25]
217. 15 <=> kind(paul) [avatar definition]
321. ~kind(paul) [resolution 93,140]
323. ~wise(paul) [resolution 95,140]
360. brave(paul) | kind(paul) [resolution 108,323]
419. ~patient(paul) | ~brave(paul) [resolution 123,140]
421. ~brave(paul) [subsumption resolution 419,146]
424. kind(paul) [subsumption resolution 360,421]
425. 15 [avatar split clause 424,217]
426. ~15 [avatar split clause 321,217]
427. $false [avatar sat refutation 425,426]
% SZS output end Proof for 4437279178605299924943240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or not wise then mary is creative.
Everyone who is both funny and strong is curious or not rich and vice versa.
If alice is wise then someone is rich or not quiet.
Everyone who is either kind or not old is either curious or not wise and vice versa.
Everyone who is not calm or wise is either quiet or calm and vice versa.
Everyone who is both not humble and not kind is either not wise or strong and vice versa.
If someone is either not curious or quiet then someone is calm or not brave.
Everyone who is both not creative and not curious is happy or not old and vice versa.
Everyone who is not patient or not wise is not strong.
If someone is either not funny or not old then john is not old or tall.
Everyone who is either not generous or generous is both not tall and not brave and vice versa.
Everyone who is tall is rich or quiet and vice versa.
Everyone who is both kind and tall is not humble or patient.
If someone is both not quiet and not curious then paul is either tall or not brave and vice versa.
John is either not calm or not curious.
Lucy is not generous or rich.
John is not quiet. | Alice is quiet. | contradiction | ((?[X]:((strong(X)<~>~wise(X))))=>(creative(mary)))&
(![X]:((funny(X)&strong(X))<=>(curious(X)|~rich(X))))&
((wise(alice))=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((kind(X)<~>~old(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((~calm(X)|wise(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~humble(X)&~kind(X))<=>(~wise(X)<~>strong(X))))&
((?[X]:((~curious(X)<~>quiet(X))))=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~creative(X)&~curious(X))<=>(happy(X)|~old(X))))&
(![X]:((~patient(X)|~wise(X))=>~strong(X)))&
((?[X]:((~funny(X)<~>~old(X))))=>((~old(john)|tall(john))))&
(![X]:((~generous(X)<~>generous(X))<=>(~tall(X)&~brave(X))))&
(![X]:(tall(X)<=>(rich(X)|quiet(X))))&
(![X]:((kind(X)&tall(X))=>(~humble(X)|patient(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>((tall(paul)<~>~brave(paul))))&
((~calm(john)<~>~curious(john)))&
((~generous(lucy)|rich(lucy)))&
(~quiet(john)) | quiet(alice) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7091624171966356827407775
% SZS output start Proof for 7091624171966356827407775
11. ! [X0] : ((~generous(X0) <~> generous(X0)) <=> (~brave(X0) & ~tall(X0))) [input p10]
12. ! [X0] : (tall(X0) <=> (quiet(X0) | rich(X0))) [input p11]
18. quiet(alice) [input hypothesis]
45. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [nnf transformation 11]
46. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [flattening 45]
47. ! [X0] : ((tall(X0) | (~quiet(X0) & ~rich(X0))) & ((quiet(X0) | rich(X0)) | ~tall(X0))) [nnf transformation 12]
48. ! [X0] : ((tall(X0) | (~quiet(X0) & ~rich(X0))) & (quiet(X0) | rich(X0) | ~tall(X0))) [flattening 47]
92. ~tall(X0) | generous(X0) | generous(X0) [cnf transformation 46]
93. ~tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 46]
100. tall(X0) | ~quiet(X0) [cnf transformation 48]
111. quiet(alice) [cnf transformation 18]
112. ~tall(X0) | generous(X0) [duplicate literal removal 92]
113. ~tall(X0) | ~generous(X0) [duplicate literal removal 93]
176. ~tall(X0) [subsumption resolution 112,113]
177. ~quiet(X0) [subsumption resolution 100,176]
192. $false [subsumption resolution 111,177]
% SZS output end Proof for 7091624171966356827407775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or tall is quiet or funny. Everyone who is not old is quiet. If susan is not happy then john is rich. If someone is strong then someone is both not happy and creative and vice versa. Everyone who is not patient is both quiet and not tall and vice versa. Everyone who is either not patient or not generous is happy or not happy and vice versa. If susan is both curious and patient then someone is either calm or not rich. Everyone who is both not happy and curious is both not tall and rich. Everyone who is brave or not patient is not funny and vice versa. Everyone who is tall is both not generous and not quiet. Everyone who is not creative is either kind or creative. Everyone who is either not calm or not tall is either not strong or not tall and vice versa. Everyone who is not brave or not patient is humble and vice versa. Everyone who is not brave or patient is creative or humble. Everyone who is either tall or not funny is either brave or funny and vice versa. Everyone who is either kind or quiet is quiet and vice versa. Someone is either quiet or funny. Fred is brave. Someone is either not creative or not old. Alice is both old and not calm. Mary is not old or not quiet. Someone is either not old or not brave. | John is not rich. | neutral | (![X]:((generous(X)<~>tall(X))=>(quiet(X)|funny(X))))&
(![X]:(~old(X)=>quiet(X)))&
((~happy(susan))=>(rich(john)))&
((?[X]:(strong(X)))<=>(?[X]:((~happy(X)&creative(X)))))&
(![X]:(~patient(X)<=>(quiet(X)&~tall(X))))&
(![X]:((~patient(X)<~>~generous(X))<=>(happy(X)|~happy(X))))&
(((curious(susan)&patient(susan)))=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:((~happy(X)&curious(X))=>(~tall(X)&rich(X))))&
(![X]:((brave(X)|~patient(X))<=>~funny(X)))&
(![X]:(tall(X)=>(~generous(X)&~quiet(X))))&
(![X]:(~creative(X)=>(kind(X)<~>creative(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~strong(X)<~>~tall(X))))&
(![X]:((~brave(X)|~patient(X))<=>humble(X)))&
(![X]:((~brave(X)|patient(X))=>(creative(X)|humble(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)<~>funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>quiet(X)))&
(?[X]:((quiet(X)<~>funny(X))))&
(brave(fred))&
(?[X]:((~creative(X)<~>~old(X))))&
((old(alice)&~calm(alice)))&
((~old(mary)|~quiet(mary)))&
(?[X]:((~old(X)<~>~brave(X)))) | ~rich(john) | [] | null | 0 |
If fred is either not wise or not brave then someone is either not strong or not curious and vice versa.
Everyone who is tall or not old is not curious and vice versa.
If lucy is both rich and not kind then paul is not kind or rich and vice versa.
Everyone who is both tall and not humble is not old or wise.
Everyone who is either generous or not wise is either not brave or generous.
Everyone who is old is either not wise or wise and vice versa.
Everyone who is either not quiet or not kind is both not strong and not calm and vice versa.
Everyone who is both wise and calm is either calm or not creative.
Everyone who is calm is happy.
If mary is not funny or not kind then susan is either not kind or not rich.
Everyone who is either kind or not generous is either old or not old and vice versa.
If lucy is either funny or creative then john is tall or not funny.
If lucy is not funny or brave then mary is rich.
If susan is wise then someone is tall and vice versa.
If someone is not quiet or patient then someone is both quiet and patient and vice versa.
Everyone who is both generous and not generous is not curious and vice versa.
Susan is either brave or calm.
Mary is both not humble and not happy.
Someone is kind.
Alice is happy or strong.
Someone is both curious and patient.
John is either not patient or not creative. | Fred is old. | entailment | (((~wise(fred)<~>~brave(fred)))<=>(?[X]:((~strong(X)<~>~curious(X)))))&
(![X]:((tall(X)|~old(X))<=>~curious(X)))&
(((rich(lucy)&~kind(lucy)))<=>((~kind(paul)|rich(paul))))&
(![X]:((tall(X)&~humble(X))=>(~old(X)|wise(X))))&
(![X]:((generous(X)<~>~wise(X))=>(~brave(X)<~>generous(X))))&
(![X]:(old(X)<=>(~wise(X)<~>wise(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(~strong(X)&~calm(X))))&
(![X]:((wise(X)&calm(X))=>(calm(X)<~>~creative(X))))&
(![X]:(calm(X)=>happy(X)))&
(((~funny(mary)|~kind(mary)))=>((~kind(susan)<~>~rich(susan))))&
(![X]:((kind(X)<~>~generous(X))<=>(old(X)<~>~old(X))))&
(((funny(lucy)<~>creative(lucy)))=>((tall(john)|~funny(john))))&
(((~funny(lucy)|brave(lucy)))=>(rich(mary)))&
((wise(susan))<=>(?[X]:(tall(X))))&
((?[X]:((~quiet(X)|patient(X))))<=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:((generous(X)&~generous(X))<=>~curious(X)))&
((brave(susan)<~>calm(susan)))&
((~humble(mary)&~happy(mary)))&
(?[X]:(kind(X)))&
((happy(alice)|strong(alice)))&
(?[X]:((curious(X)&patient(X))))&
((~patient(john)<~>~creative(john))) | old(fred) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 304861900714545981794466
% SZS output start Proof for 304861900714545981794466
6. ! [X0] : (old(X0) <=> (~wise(X0) <~> wise(X0))) [input p5]
23. ~old(fred) [input hypothesis]
44. ! [X0] : ((old(X0) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~old(X0))) [nnf transformation 6]
91. old(X0) | wise(X0) | wise(X0) [cnf transformation 44]
92. old(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 44]
138. ~old(fred) [cnf transformation 23]
144. old(X0) | wise(X0) [duplicate literal removal 91]
145. old(X0) | ~wise(X0) [duplicate literal removal 92]
199. old(X0) [subsumption resolution 144,145]
323. $false [subsumption resolution 138,199]
% SZS output end Proof for 304861900714545981794466
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not rich then lucy is not wise or not funny.
If susan is both not creative and generous then someone is patient.
Everyone who is creative or rich is either creative or not funny and vice versa.
If john is calm then someone is patient and vice versa.
Everyone who is curious or not quiet is tall or not generous and vice versa.
Everyone who is both tall and not kind is not patient or humble and vice versa.
If alice is not happy then someone is both not rich and not patient and vice versa.
Everyone who is not humble is not patient.
Everyone who is either not quiet or calm is either not patient or not strong.
If mary is not curious or not brave then someone is either not rich or not quiet.
If someone is both brave and not quiet then someone is wise or not funny.
Everyone who is not quiet is both humble and not generous.
If fred is not kind or not tall then mary is patient or not rich and vice versa.
Everyone who is brave or not quiet is both not calm and curious and vice versa.
If fred is not calm or creative then susan is not creative or not kind and vice versa.
If mary is both not brave and not generous then mary is either not patient or quiet.
Paul is either wise or not tall.
Paul is not old or curious.
Someone is either brave or funny.
Someone is either not strong or not generous.
John is not calm or old.
Someone is both funny and not old.
Someone is not quiet or not wise. | Lucy is not rich. | neutral | ((?[X]:((~humble(X)&~rich(X))))=>((~wise(lucy)|~funny(lucy))))&
(((~creative(susan)&generous(susan)))=>(?[X]:(patient(X))))&
(![X]:((creative(X)|rich(X))<=>(creative(X)<~>~funny(X))))&
((calm(john))<=>(?[X]:(patient(X))))&
(![X]:((curious(X)|~quiet(X))<=>(tall(X)|~generous(X))))&
(![X]:((tall(X)&~kind(X))<=>(~patient(X)|humble(X))))&
((~happy(alice))<=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:(~humble(X)=>~patient(X)))&
(![X]:((~quiet(X)<~>calm(X))=>(~patient(X)<~>~strong(X))))&
(((~curious(mary)|~brave(mary)))=>(?[X]:((~rich(X)<~>~quiet(X)))))&
((?[X]:((brave(X)&~quiet(X))))=>(?[X]:((wise(X)|~funny(X)))))&
(![X]:(~quiet(X)=>(humble(X)&~generous(X))))&
(((~kind(fred)|~tall(fred)))<=>((patient(mary)|~rich(mary))))&
(![X]:((brave(X)|~quiet(X))<=>(~calm(X)&curious(X))))&
(((~calm(fred)|creative(fred)))<=>((~creative(susan)|~kind(susan))))&
(((~brave(mary)&~generous(mary)))=>((~patient(mary)<~>quiet(mary))))&
((wise(paul)<~>~tall(paul)))&
((~old(paul)|curious(paul)))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((~strong(X)<~>~generous(X))))&
((~calm(john)|old(john)))&
(?[X]:((funny(X)&~old(X))))&
(?[X]:((~quiet(X)|~wise(X)))) | ~rich(lucy) | [] | null | 0 |
Everyone who is not wise or brave is both not tall and not rich and vice versa.
Everyone who is either not old or not rich is calm or funny and vice versa.
Everyone who is either brave or humble is either patient or old and vice versa.
Everyone who is both creative and not tall is both not old and patient.
If someone is not generous then someone is both not generous and not rich and vice versa.
If someone is humble then alice is curious and vice versa.
If mary is not old then someone is humble and vice versa.
If someone is both funny and not generous then alice is either rich or funny.
Everyone who is not rich or curious is tall or not rich and vice versa.
Everyone who is either rich or old is not humble.
Everyone who is tall or not creative is quiet.
Everyone who is both generous and not patient is not calm or funny.
Everyone who is either humble or strong is both creative and funny.
Everyone who is not humble or not funny is both strong and not funny and vice versa.
Everyone who is old is not strong or tall and vice versa.
If someone is either old or curious then someone is kind or not rich and vice versa.
Someone is not wise.
Lucy is not tall or not strong.
Someone is either not kind or not generous.
Fred is both not rich and not brave.
Someone is both patient and not rich.
Someone is either generous or not funny. | Alice is not brave. | neutral | (![X]:((~wise(X)|brave(X))<=>(~tall(X)&~rich(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(calm(X)|funny(X))))&
(![X]:((brave(X)<~>humble(X))<=>(patient(X)<~>old(X))))&
(![X]:((creative(X)&~tall(X))=>(~old(X)&patient(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)&~rich(X)))))&
((?[X]:(humble(X)))<=>(curious(alice)))&
((~old(mary))<=>(?[X]:(humble(X))))&
((?[X]:((funny(X)&~generous(X))))=>((rich(alice)<~>funny(alice))))&
(![X]:((~rich(X)|curious(X))<=>(tall(X)|~rich(X))))&
(![X]:((rich(X)<~>old(X))=>~humble(X)))&
(![X]:((tall(X)|~creative(X))=>quiet(X)))&
(![X]:((generous(X)&~patient(X))=>(~calm(X)|funny(X))))&
(![X]:((humble(X)<~>strong(X))=>(creative(X)&funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(strong(X)&~funny(X))))&
(![X]:(old(X)<=>(~strong(X)|tall(X))))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:((kind(X)|~rich(X)))))&
(?[X]:(~wise(X)))&
((~tall(lucy)|~strong(lucy)))&
(?[X]:((~kind(X)<~>~generous(X))))&
((~rich(fred)&~brave(fred)))&
(?[X]:((patient(X)&~rich(X))))&
(?[X]:((generous(X)<~>~funny(X)))) | ~brave(alice) | [] | null | 0 |
Everyone who is either not calm or quiet is both old and kind.
Everyone who is either creative or not creative is both patient and not curious.
If paul is both rich and not brave then mary is both not old and generous and vice versa.
Everyone who is brave is humble or calm.
If fred is both quiet and patient then someone is both creative and calm and vice versa.
Everyone who is wise or not kind is either rich or not brave and vice versa.
Everyone who is either not brave or brave is happy or not brave and vice versa.
Everyone who is calm is not tall or not generous and vice versa.
Everyone who is either brave or not humble is not creative.
If paul is both not quiet and quiet then someone is not humble and vice versa.
If mary is patient then fred is not quiet or not calm.
If someone is creative then someone is not rich and vice versa.
Everyone who is not rich or old is not happy or curious and vice versa.
If fred is not kind or not calm then fred is either rich or not calm.
Everyone who is not calm or not kind is not kind and vice versa.
Everyone who is not curious is rich or calm.
Someone is either not humble or generous.
Lucy is either not curious or generous.
Fred is both not strong and not funny.
Someone is happy or creative.
Fred is not curious or curious.
John is both not strong and not kind.
Paul is not happy or not patient. | John is generous. | neutral | (![X]:((~calm(X)<~>quiet(X))=>(old(X)&kind(X))))&
(![X]:((creative(X)<~>~creative(X))=>(patient(X)&~curious(X))))&
(((rich(paul)&~brave(paul)))<=>((~old(mary)&generous(mary))))&
(![X]:(brave(X)=>(humble(X)|calm(X))))&
(((quiet(fred)&patient(fred)))<=>(?[X]:((creative(X)&calm(X)))))&
(![X]:((wise(X)|~kind(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(happy(X)|~brave(X))))&
(![X]:(calm(X)<=>(~tall(X)|~generous(X))))&
(![X]:((brave(X)<~>~humble(X))=>~creative(X)))&
(((~quiet(paul)&quiet(paul)))<=>(?[X]:(~humble(X))))&
((patient(mary))=>((~quiet(fred)|~calm(fred))))&
((?[X]:(creative(X)))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|old(X))<=>(~happy(X)|curious(X))))&
(((~kind(fred)|~calm(fred)))=>((rich(fred)<~>~calm(fred))))&
(![X]:((~calm(X)|~kind(X))<=>~kind(X)))&
(![X]:(~curious(X)=>(rich(X)|calm(X))))&
(?[X]:((~humble(X)<~>generous(X))))&
((~curious(lucy)<~>generous(lucy)))&
((~strong(fred)&~funny(fred)))&
(?[X]:((happy(X)|creative(X))))&
((~curious(fred)|curious(fred)))&
((~strong(john)&~kind(john)))&
((~happy(paul)|~patient(paul))) | generous(john) | [] | null | 0 |
If someone is either not funny or not generous then john is not tall or happy and vice versa.
If fred is either not tall or rich then someone is both not wise and not happy.
Everyone who is not wise or not brave is both not patient and not creative.
If alice is tall or generous then someone is both not tall and creative.
If someone is funny or not funny then someone is quiet.
If john is either tall or kind then someone is either funny or creative and vice versa.
If someone is not funny then someone is either creative or curious.
Everyone who is not curious is either not rich or humble and vice versa.
Everyone who is both calm and not quiet is both happy and not kind.
Everyone who is both humble and happy is not quiet or tall and vice versa.
If someone is both tall and not rich then someone is rich or quiet.
If alice is kind then someone is both not wise and not creative and vice versa.
Everyone who is calm is not kind or patient and vice versa.
Everyone who is wise or not old is not kind or creative and vice versa.
If alice is both calm and patient then someone is either brave or not calm.
If paul is creative or not brave then someone is either not curious or not quiet.
Someone is both happy and funny.
Fred is either not happy or calm.
Lucy is either not humble or generous.
Susan is either not funny or not curious.
Someone is curious or not old.
Mary is not happy.
Fred is both not brave and not happy.
Susan is both kind and not generous. | Alice is not kind. | contradiction | ((?[X]:((~funny(X)<~>~generous(X))))<=>((~tall(john)|happy(john))))&
(((~tall(fred)<~>rich(fred)))=>(?[X]:((~wise(X)&~happy(X)))))&
(![X]:((~wise(X)|~brave(X))=>(~patient(X)&~creative(X))))&
(((tall(alice)|generous(alice)))=>(?[X]:((~tall(X)&creative(X)))))&
((?[X]:((funny(X)|~funny(X))))=>(?[X]:(quiet(X))))&
(((tall(john)<~>kind(john)))<=>(?[X]:((funny(X)<~>creative(X)))))&
((?[X]:(~funny(X)))=>(?[X]:((creative(X)<~>curious(X)))))&
(![X]:(~curious(X)<=>(~rich(X)<~>humble(X))))&
(![X]:((calm(X)&~quiet(X))=>(happy(X)&~kind(X))))&
(![X]:((humble(X)&happy(X))<=>(~quiet(X)|tall(X))))&
((?[X]:((tall(X)&~rich(X))))=>(?[X]:((rich(X)|quiet(X)))))&
((kind(alice))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(calm(X)<=>(~kind(X)|patient(X))))&
(![X]:((wise(X)|~old(X))<=>(~kind(X)|creative(X))))&
(((calm(alice)&patient(alice)))=>(?[X]:((brave(X)<~>~calm(X)))))&
(((creative(paul)|~brave(paul)))=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(?[X]:((happy(X)&funny(X))))&
((~happy(fred)<~>calm(fred)))&
((~humble(lucy)<~>generous(lucy)))&
((~funny(susan)<~>~curious(susan)))&
(?[X]:((curious(X)|~old(X))))&
(~happy(mary))&
((~brave(fred)&~happy(fred)))&
((kind(susan)&~generous(susan))) | ~kind(alice) | [
"p2",
"p11",
"p12",
"p13",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8700786445726591995115104
% SZS output start Proof for 8700786445726591995115104
3. ! [X0] : ((~brave(X0) | ~wise(X0)) => (~creative(X0) & ~patient(X0))) [input p2]
12. kind(alice) <=> ? [X0] : (~creative(X0) & ~wise(X0)) [input p11]
13. ! [X0] : (calm(X0) <=> (patient(X0) | ~kind(X0))) [input p12]
14. ! [X0] : ((~old(X0) | wise(X0)) <=> (creative(X0) | ~kind(X0))) [input p13]
18. ~happy(fred) <~> calm(fred) [input p17]
23. ~happy(fred) & ~brave(fred) [input p22]
25. ~kind(alice) [input hypothesis]
30. ! [X0] : ((~creative(X0) & ~patient(X0)) | (brave(X0) & wise(X0))) [ennf transformation 3]
67. (kind(alice) | ! [X0] : (creative(X0) | wise(X0))) & (? [X0] : (~creative(X0) & ~wise(X0)) | ~kind(alice)) [nnf transformation 12]
68. (kind(alice) | ! [X0] : (creative(X0) | wise(X0))) & (? [X1] : (~creative(X1) & ~wise(X1)) | ~kind(alice)) [rectify 67]
69. ? [X1] : (~creative(X1) & ~wise(X1)) => (~creative(sK7) & ~wise(sK7)) [choice axiom]
70. (kind(alice) | ! [X0] : (creative(X0) | wise(X0))) & ((~creative(sK7) & ~wise(sK7)) | ~kind(alice)) [skolemisation 68,69]
71. ! [X0] : ((calm(X0) | (~patient(X0) & kind(X0))) & ((patient(X0) | ~kind(X0)) | ~calm(X0))) [nnf transformation 13]
72. ! [X0] : ((calm(X0) | (~patient(X0) & kind(X0))) & (patient(X0) | ~kind(X0) | ~calm(X0))) [flattening 71]
73. ! [X0] : (((~old(X0) | wise(X0)) | (~creative(X0) & kind(X0))) & ((creative(X0) | ~kind(X0)) | (old(X0) & ~wise(X0)))) [nnf transformation 14]
74. ! [X0] : ((~old(X0) | wise(X0) | (~creative(X0) & kind(X0))) & (creative(X0) | ~kind(X0) | (old(X0) & ~wise(X0)))) [flattening 73]
83. (~calm(fred) | happy(fred)) & (calm(fred) | ~happy(fred)) [nnf transformation 18]
100. ~creative(X0) | wise(X0) [cnf transformation 30]
101. ~creative(X0) | brave(X0) [cnf transformation 30]
132. kind(alice) | creative(X0) | wise(X0) [cnf transformation 70]
134. calm(X0) | kind(X0) [cnf transformation 72]
136. ~kind(X0) | creative(X0) | ~wise(X0) [cnf transformation 74]
149. ~calm(fred) | happy(fred) [cnf transformation 83]
156. ~brave(fred) [cnf transformation 23]
157. ~happy(fred) [cnf transformation 23]
160. ~kind(alice) [cnf transformation 25]
289. kind(alice) | wise(X0) [subsumption resolution 132,100]
291. 28 <=> ! [X0] : wise(X0) [avatar definition]
292. wise(X0) <- (28) [avatar component clause 291]
294. 29 <=> kind(alice) [avatar definition]
297. 28 | 29 [avatar split clause 289,294,291]
345. 39 <=> happy(fred) [avatar definition]
349. 40 <=> calm(fred) [avatar definition]
351. ~calm(fred) <- (~40) [avatar component clause 349]
352. 39 | ~40 [avatar split clause 149,349,345]
383. ~39 [avatar split clause 157,345]
384. ~29 [avatar split clause 160,294]
391. kind(fred) <- (~40) [resolution 134,351]
434. creative(fred) | ~wise(fred) <- (~40) [resolution 136,391]
435. creative(fred) <- (28, ~40) [subsumption resolution 434,292]
439. brave(fred) <- (28, ~40) [resolution 435,101]
441. $false <- (28, ~40) [subsumption resolution 439,156]
442. ~28 | 40 [avatar contradiction clause 441]
443. $false [avatar sat refutation 297,352,383,384,442]
% SZS output end Proof for 8700786445726591995115104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not old and vice versa.
If john is both calm and not calm then lucy is not wise.
If someone is both not patient and kind then mary is either not calm or not wise.
Everyone who is not funny or not generous is both happy and brave.
Everyone who is kind or not wise is either not tall or not generous.
Everyone who is not humble is either strong or creative.
Everyone who is kind or not wise is quiet or wise and vice versa.
Everyone who is either curious or strong is happy.
Everyone who is not curious is both not generous and not strong and vice versa.
If fred is quiet then fred is both happy and not creative and vice versa.
Everyone who is both rich and not old is both rich and strong.
Everyone who is old is quiet or happy and vice versa.
Everyone who is either not creative or curious is brave.
Everyone who is not wise or kind is both curious and generous and vice versa.
If someone is both rich and kind then someone is both tall and funny and vice versa.
Everyone who is tall is either not old or rich.
Alice is not funny or not old.
Someone is either generous or tall. | Alice is funny. | contradiction | (![X]:(quiet(X)<=>~old(X)))&
(((calm(john)&~calm(john)))=>(~wise(lucy)))&
((?[X]:((~patient(X)&kind(X))))=>((~calm(mary)<~>~wise(mary))))&
(![X]:((~funny(X)|~generous(X))=>(happy(X)&brave(X))))&
(![X]:((kind(X)|~wise(X))=>(~tall(X)<~>~generous(X))))&
(![X]:(~humble(X)=>(strong(X)<~>creative(X))))&
(![X]:((kind(X)|~wise(X))<=>(quiet(X)|wise(X))))&
(![X]:((curious(X)<~>strong(X))=>happy(X)))&
(![X]:(~curious(X)<=>(~generous(X)&~strong(X))))&
((quiet(fred))<=>((happy(fred)&~creative(fred))))&
(![X]:((rich(X)&~old(X))=>(rich(X)&strong(X))))&
(![X]:(old(X)<=>(quiet(X)|happy(X))))&
(![X]:((~creative(X)<~>curious(X))=>brave(X)))&
(![X]:((~wise(X)|kind(X))<=>(curious(X)&generous(X))))&
((?[X]:((rich(X)&kind(X))))<=>(?[X]:((tall(X)&funny(X)))))&
(![X]:(tall(X)=>(~old(X)<~>rich(X))))&
((~funny(alice)|~old(alice)))&
(?[X]:((generous(X)<~>tall(X)))) | funny(alice) | [
"p0",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1789398925321023674948155
% SZS output start Proof for 1789398925321023674948155
1. ! [X0] : (quiet(X0) <=> ~old(X0)) [input p0]
12. ! [X0] : (old(X0) <=> (happy(X0) | quiet(X0))) [input p11]
17. ~old(alice) | ~funny(alice) [input p16]
19. funny(alice) [input hypothesis]
33. ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0))) [nnf transformation 1]
42. ! [X0] : ((old(X0) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | ~old(X0))) [nnf transformation 12]
43. ! [X0] : ((old(X0) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~old(X0))) [flattening 42]
55. ~old(X0) | ~quiet(X0) [cnf transformation 33]
56. old(X0) | quiet(X0) [cnf transformation 33]
79. old(X0) | ~quiet(X0) [cnf transformation 43]
92. ~old(alice) | ~funny(alice) [cnf transformation 17]
95. funny(alice) [cnf transformation 19]
113. ~quiet(X0) [subsumption resolution 79,55]
142. 10 <=> funny(alice) [avatar definition]
146. 11 <=> old(alice) [avatar definition]
148. ~old(alice) <- (~11) [avatar component clause 146]
149. ~10 | ~11 [avatar split clause 92,146,142]
160. 10 [avatar split clause 95,142]
161. quiet(alice) <- (~11) [resolution 56,148]
163. $false <- (~11) [subsumption resolution 161,113]
164. 11 [avatar contradiction clause 163]
165. $false [avatar sat refutation 149,160,164]
% SZS output end Proof for 1789398925321023674948155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or tall is both brave and not kind and vice versa.
Everyone who is either funny or not old is old.
If fred is wise then someone is either generous or not strong and vice versa.
Everyone who is both not quiet and strong is both not humble and curious and vice versa.
If someone is not calm or not strong then someone is both tall and not generous and vice versa.
Everyone who is not strong is not wise or quiet and vice versa.
If someone is not curious or not old then alice is wise or old and vice versa.
Everyone who is generous or rich is either not patient or not brave.
If someone is humble then susan is both not quiet and brave and vice versa.
Everyone who is not patient or not creative is both humble and not generous and vice versa.
Everyone who is either not quiet or not patient is both brave and not calm.
If john is both not old and not rich then someone is not kind or happy.
Everyone who is either not rich or patient is both not creative and not happy and vice versa.
Everyone who is both funny and not kind is either humble or not old.
Everyone who is not happy or not kind is old and vice versa.
Lucy is patient.
Someone is either not quiet or old.
John is both not generous and not curious.
Someone is not tall or not kind.
Susan is both wise and brave.
Mary is either creative or kind.
Alice is both tall and quiet.
Paul is humble. | Paul is brave. | neutral | (![X]:((~old(X)<~>tall(X))<=>(brave(X)&~kind(X))))&
(![X]:((funny(X)<~>~old(X))=>old(X)))&
((wise(fred))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~quiet(X)&strong(X))<=>(~humble(X)&curious(X))))&
((?[X]:((~calm(X)|~strong(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(![X]:(~strong(X)<=>(~wise(X)|quiet(X))))&
((?[X]:((~curious(X)|~old(X))))<=>((wise(alice)|old(alice))))&
(![X]:((generous(X)|rich(X))=>(~patient(X)<~>~brave(X))))&
((?[X]:(humble(X)))<=>((~quiet(susan)&brave(susan))))&
(![X]:((~patient(X)|~creative(X))<=>(humble(X)&~generous(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(brave(X)&~calm(X))))&
(((~old(john)&~rich(john)))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((~rich(X)<~>patient(X))<=>(~creative(X)&~happy(X))))&
(![X]:((funny(X)&~kind(X))=>(humble(X)<~>~old(X))))&
(![X]:((~happy(X)|~kind(X))<=>old(X)))&
(patient(lucy))&
(?[X]:((~quiet(X)<~>old(X))))&
((~generous(john)&~curious(john)))&
(?[X]:((~tall(X)|~kind(X))))&
((wise(susan)&brave(susan)))&
((creative(mary)<~>kind(mary)))&
((tall(alice)&quiet(alice)))&
(humble(paul)) | brave(paul) | [] | null | 0 |
If someone is either kind or not calm then someone is both humble and not happy and vice versa.
If someone is both not tall and not happy then paul is both funny and not humble and vice versa.
Everyone who is not humble is either creative or not calm.
Everyone who is both patient and happy is both tall and happy.
Everyone who is generous is not generous or quiet and vice versa.
If someone is either strong or not generous then john is either not happy or quiet and vice versa.
If someone is not patient then someone is either wise or not happy and vice versa.
Everyone who is not generous is either not kind or not happy.
If alice is either brave or wise then someone is either not creative or not happy.
If someone is both old and not generous then paul is either not creative or not humble and vice versa.
If someone is humble or not kind then someone is not curious or not quiet and vice versa.
If john is not funny then someone is either not rich or not funny.
If john is rich then someone is either happy or old.
Everyone who is curious is generous and vice versa.
If mary is patient then someone is creative or curious and vice versa.
If someone is not kind or tall then john is not old and vice versa.
Someone is not rich or calm.
Mary is either rich or tall.
Someone is not wise.
Paul is not wise or not happy.
Fred is funny.
Paul is strong or quiet.
John is not wise or tall. | Paul is kind. | entailment | ((?[X]:((kind(X)<~>~calm(X))))<=>(?[X]:((humble(X)&~happy(X)))))&
((?[X]:((~tall(X)&~happy(X))))<=>((funny(paul)&~humble(paul))))&
(![X]:(~humble(X)=>(creative(X)<~>~calm(X))))&
(![X]:((patient(X)&happy(X))=>(tall(X)&happy(X))))&
(![X]:(generous(X)<=>(~generous(X)|quiet(X))))&
((?[X]:((strong(X)<~>~generous(X))))<=>((~happy(john)<~>quiet(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:(~generous(X)=>(~kind(X)<~>~happy(X))))&
(((brave(alice)<~>wise(alice)))=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((old(X)&~generous(X))))<=>((~creative(paul)<~>~humble(paul))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~curious(X)|~quiet(X)))))&
((~funny(john))=>(?[X]:((~rich(X)<~>~funny(X)))))&
((rich(john))=>(?[X]:((happy(X)<~>old(X)))))&
(![X]:(curious(X)<=>generous(X)))&
((patient(mary))<=>(?[X]:((creative(X)|curious(X)))))&
((?[X]:((~kind(X)|tall(X))))<=>(~old(john)))&
(?[X]:((~rich(X)|calm(X))))&
((rich(mary)<~>tall(mary)))&
(?[X]:(~wise(X)))&
((~wise(paul)|~happy(paul)))&
(funny(fred))&
((strong(paul)|quiet(paul)))&
((~wise(john)|tall(john))) | kind(paul) | [
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5870151978340153116551389
% SZS output start Proof for 5870151978340153116551389
5. ! [X0] : (generous(X0) <=> (quiet(X0) | ~generous(X0))) [input p4]
11. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X0] : (~quiet(X0) | ~curious(X0)) [input p10]
14. ! [X0] : (curious(X0) <=> generous(X0)) [input p13]
24. ~kind(paul) [input hypothesis]
27. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X1] : (~quiet(X1) | ~curious(X1)) [rectify 11]
46. ! [X0] : ((generous(X0) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | ~generous(X0))) [nnf transformation 5]
47. ! [X0] : ((generous(X0) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | ~generous(X0))) [flattening 46]
65. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (quiet(X1) & curious(X1))) & (? [X1] : (~quiet(X1) | ~curious(X1)) | ! [X0] : (kind(X0) & ~humble(X0))) [nnf transformation 27]
66. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (quiet(X1) & curious(X1))) & (? [X2] : (~quiet(X2) | ~curious(X2)) | ! [X3] : (kind(X3) & ~humble(X3))) [rectify 65]
67. ? [X0] : (~kind(X0) | humble(X0)) => (~kind(sK8) | humble(sK8)) [choice axiom]
68. ? [X2] : (~quiet(X2) | ~curious(X2)) => (~quiet(sK9) | ~curious(sK9)) [choice axiom]
69. ((~kind(sK8) | humble(sK8)) | ! [X1] : (quiet(X1) & curious(X1))) & ((~quiet(sK9) | ~curious(sK9)) | ! [X3] : (kind(X3) & ~humble(X3))) [skolemisation 66,68,67]
76. ! [X0] : ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0))) [nnf transformation 14]
104. quiet(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 47]
105. generous(X0) | generous(X0) [cnf transformation 47]
132. ~quiet(sK9) | ~curious(sK9) | kind(X3) [cnf transformation 69]
140. curious(X0) | ~generous(X0) [cnf transformation 76]
155. ~kind(paul) [cnf transformation 24]
156. quiet(X0) | ~generous(X0) [duplicate literal removal 104]
157. generous(X0) [duplicate literal removal 105]
212. quiet(X0) [subsumption resolution 156,157]
290. 28 <=> ! [X1] : curious(X1) [avatar definition]
291. curious(X1) <- (28) [avatar component clause 290]
301. ~curious(sK9) | kind(X3) [subsumption resolution 132,212]
303. 31 <=> ! [X3] : kind(X3) [avatar definition]
304. kind(X3) <- (31) [avatar component clause 303]
306. 32 <=> curious(sK9) [avatar definition]
308. ~curious(sK9) <- (~32) [avatar component clause 306]
309. 31 | ~32 [avatar split clause 301,306,303]
343. curious(X0) [subsumption resolution 140,157]
344. 28 [avatar split clause 343,290]
423. $false <- (28, ~32) [subsumption resolution 308,291]
424. ~28 | 32 [avatar contradiction clause 423]
427. $false <- (31) [resolution 304,155]
430. ~31 [avatar contradiction clause 427]
431. $false [avatar sat refutation 309,344,424,430]
% SZS output end Proof for 5870151978340153116551389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is tall. If someone is both tall and not humble then mary is calm. If someone is not rich or not humble then john is tall or patient and vice versa. Everyone who is both not wise and not quiet is not funny. Everyone who is old or not strong is both kind and generous. Everyone who is either not patient or wise is both strong and not wise and vice versa. If someone is both old and not calm then someone is not wise or not generous and vice versa. If someone is both not funny and not quiet then someone is either wise or quiet and vice versa. If someone is not creative or strong then someone is not kind and vice versa. If john is either quiet or humble then someone is both tall and not strong and vice versa. If fred is both funny and wise then alice is strong or patient. Everyone who is tall is generous or not brave and vice versa. If susan is both strong and not patient then fred is happy. Everyone who is wise or rich is either not patient or calm. Everyone who is not quiet or not rich is not old or quiet. Everyone who is not humble or creative is not happy and vice versa. Mary is not funny or strong. Someone is not rich. Paul is not calm. Susan is not tall or not wise. Alice is not strong. Paul is happy. Someone is creative or not strong. Someone is both not patient and old. | Susan is not wise. | neutral | (![X]:(~brave(X)=>tall(X)))&
((?[X]:((tall(X)&~humble(X))))=>(calm(mary)))&
((?[X]:((~rich(X)|~humble(X))))<=>((tall(john)|patient(john))))&
(![X]:((~wise(X)&~quiet(X))=>~funny(X)))&
(![X]:((old(X)|~strong(X))=>(kind(X)&generous(X))))&
(![X]:((~patient(X)<~>wise(X))<=>(strong(X)&~wise(X))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:((~wise(X)|~generous(X)))))&
((?[X]:((~funny(X)&~quiet(X))))<=>(?[X]:((wise(X)<~>quiet(X)))))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:(~kind(X))))&
(((quiet(john)<~>humble(john)))<=>(?[X]:((tall(X)&~strong(X)))))&
(((funny(fred)&wise(fred)))=>((strong(alice)|patient(alice))))&
(![X]:(tall(X)<=>(generous(X)|~brave(X))))&
(((strong(susan)&~patient(susan)))=>(happy(fred)))&
(![X]:((wise(X)|rich(X))=>(~patient(X)<~>calm(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~old(X)|quiet(X))))&
(![X]:((~humble(X)|creative(X))<=>~happy(X)))&
((~funny(mary)|strong(mary)))&
(?[X]:(~rich(X)))&
(~calm(paul))&
((~tall(susan)|~wise(susan)))&
(~strong(alice))&
(happy(paul))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:((~patient(X)&old(X)))) | ~wise(susan) | [] | null | 0 |
If someone is either not happy or not quiet then susan is both not old and kind and vice versa. If lucy is quiet or not tall then someone is not tall or not strong. Everyone who is not kind or not creative is not calm. If someone is calm or not funny then alice is not quiet or not kind and vice versa. Everyone who is both strong and rich is either brave or curious and vice versa. Everyone who is generous is either calm or not calm. If john is not generous then alice is kind or not old and vice versa. If someone is tall or not funny then someone is either not tall or not brave and vice versa. Everyone who is either not humble or humble is both happy and kind. If susan is either not patient or curious then someone is either kind or not rich. If someone is both not kind and not wise then john is both not quiet and not rich. If someone is either generous or not strong then paul is not kind and vice versa. Everyone who is both not curious and creative is not curious and vice versa. If someone is either not quiet or wise then alice is either happy or not curious. John is both calm and funny. Someone is both humble and quiet. Mary is both not quiet and not humble. Alice is both not curious and tall. Susan is not patient. Alice is either quiet or not rich. | Alice is wise. | entailment | ((?[X]:((~happy(X)<~>~quiet(X))))<=>((~old(susan)&kind(susan))))&
(((quiet(lucy)|~tall(lucy)))=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:((~kind(X)|~creative(X))=>~calm(X)))&
((?[X]:((calm(X)|~funny(X))))<=>((~quiet(alice)|~kind(alice))))&
(![X]:((strong(X)&rich(X))<=>(brave(X)<~>curious(X))))&
(![X]:(generous(X)=>(calm(X)<~>~calm(X))))&
((~generous(john))<=>((kind(alice)|~old(alice))))&
((?[X]:((tall(X)|~funny(X))))<=>(?[X]:((~tall(X)<~>~brave(X)))))&
(![X]:((~humble(X)<~>humble(X))=>(happy(X)&kind(X))))&
(((~patient(susan)<~>curious(susan)))=>(?[X]:((kind(X)<~>~rich(X)))))&
((?[X]:((~kind(X)&~wise(X))))=>((~quiet(john)&~rich(john))))&
((?[X]:((generous(X)<~>~strong(X))))<=>(~kind(paul)))&
(![X]:((~curious(X)&creative(X))<=>~curious(X)))&
((?[X]:((~quiet(X)<~>wise(X))))=>((happy(alice)<~>~curious(alice))))&
((calm(john)&funny(john)))&
(?[X]:((humble(X)&quiet(X))))&
((~quiet(mary)&~humble(mary)))&
((~curious(alice)&tall(alice)))&
(~patient(susan))&
((quiet(alice)<~>~rich(alice))) | wise(alice) | [
"p3",
"p8",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2690838303129315681577241
% SZS output start Proof for 2690838303129315681577241
4. ? [X0] : (~funny(X0) | calm(X0)) <=> (~kind(alice) | ~quiet(alice)) [input p3]
9. ! [X0] : ((~humble(X0) <~> humble(X0)) => (kind(X0) & happy(X0))) [input p8]
14. ? [X0] : (~quiet(X0) <~> wise(X0)) => (happy(alice) <~> ~curious(alice)) [input p13]
15. funny(john) & calm(john) [input p14]
18. tall(alice) & ~curious(alice) [input p17]
21. ~wise(alice) [input hypothesis]
26. ! [X0] : ((kind(X0) & happy(X0)) | (~humble(X0) <=> humble(X0))) [ennf transformation 9]
29. (happy(alice) <~> ~curious(alice)) | ! [X0] : (~quiet(X0) <=> wise(X0)) [ennf transformation 14]
37. (? [X0] : (~funny(X0) | calm(X0)) | (kind(alice) & quiet(alice))) & ((~kind(alice) | ~quiet(alice)) | ! [X0] : (funny(X0) & ~calm(X0))) [nnf transformation 4]
38. (? [X0] : (~funny(X0) | calm(X0)) | (kind(alice) & quiet(alice))) & (~kind(alice) | ~quiet(alice) | ! [X0] : (funny(X0) & ~calm(X0))) [flattening 37]
39. (? [X0] : (~funny(X0) | calm(X0)) | (kind(alice) & quiet(alice))) & (~kind(alice) | ~quiet(alice) | ! [X1] : (funny(X1) & ~calm(X1))) [rectify 38]
40. ? [X0] : (~funny(X0) | calm(X0)) => (~funny(sK2) | calm(sK2)) [choice axiom]
41. ((~funny(sK2) | calm(sK2)) | (kind(alice) & quiet(alice))) & (~kind(alice) | ~quiet(alice) | ! [X1] : (funny(X1) & ~calm(X1))) [skolemisation 39,40]
52. ! [X0] : ((kind(X0) & happy(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 26]
62. ((curious(alice) | ~happy(alice)) & (~curious(alice) | happy(alice))) | ! [X0] : ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))) [nnf transformation 29]
76. ~kind(alice) | ~quiet(alice) | ~calm(X1) [cnf transformation 41]
97. happy(X0) | humble(X0) | humble(X0) [cnf transformation 52]
98. happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 52]
99. kind(X0) | humble(X0) | humble(X0) [cnf transformation 52]
100. kind(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 52]
116. curious(alice) | ~happy(alice) | wise(X0) | quiet(X0) [cnf transformation 62]
118. calm(john) [cnf transformation 15]
124. ~curious(alice) [cnf transformation 18]
129. ~wise(alice) [cnf transformation 21]
130. happy(X0) | humble(X0) [duplicate literal removal 97]
131. ~humble(X0) | happy(X0) [duplicate literal removal 98]
132. kind(X0) | humble(X0) [duplicate literal removal 99]
133. ~humble(X0) | kind(X0) [duplicate literal removal 100]
181. 11 <=> kind(alice) [avatar definition]
182. ~kind(alice) <- (~11) [avatar component clause 181]
194. 14 <=> quiet(alice) [avatar definition]
203. 16 <=> ! [X1] : ~calm(X1) [avatar definition]
204. ~calm(X1) <- (16) [avatar component clause 203]
205. 16 | ~14 | ~11 [avatar split clause 76,181,194,203]
248. kind(X0) [subsumption resolution 132,133]
249. happy(X0) [subsumption resolution 130,131]
273. 30 <=> curious(alice) [avatar definition]
277. curious(alice) | wise(X0) | quiet(X0) [subsumption resolution 116,249]
279. 31 <=> ! [X0] : (wise(X0) | quiet(X0)) [avatar definition]
280. wise(X0) | quiet(X0) <- (31) [avatar component clause 279]
281. 31 | 30 [avatar split clause 277,273,279]
282. ~30 [avatar split clause 124,273]
290. $false <- (~11) [subsumption resolution 182,248]
291. 11 [avatar contradiction clause 290]
299. quiet(alice) <- (31) [resolution 280,129]
303. 14 | ~31 [avatar split clause 299,279,194]
308. $false <- (16) [resolution 204,118]
309. ~16 [avatar contradiction clause 308]
310. $false [avatar sat refutation 205,281,282,291,303,309]
% SZS output end Proof for 2690838303129315681577241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not old is happy. Everyone who is not tall is not patient. If lucy is not strong then mary is funny and vice versa. Everyone who is kind or not quiet is not brave or happy and vice versa. Everyone who is either not curious or happy is either humble or not happy. If someone is tall or curious then alice is either not quiet or calm. Everyone who is both patient and not happy is either kind or humble and vice versa. Everyone who is both not funny and not strong is not kind and vice versa. Everyone who is both not old and not kind is generous or not wise and vice versa. If someone is not calm or not kind then paul is both humble and generous. If someone is either funny or not tall then paul is strong. If someone is old then alice is either not funny or wise and vice versa. Everyone who is both not curious and not brave is calm or not quiet. If someone is calm then susan is happy or tall and vice versa. Everyone who is curious is both not strong and tall. Everyone who is rich is both wise and strong and vice versa. Someone is strong or not wise. John is either not humble or happy. Someone is quiet. Fred is not humble or not generous. Someone is not generous. Someone is not old. Someone is either generous or tall. | Mary is not wise. | contradiction | (![X]:((curious(X)&~old(X))=>happy(X)))&
(![X]:(~tall(X)=>~patient(X)))&
((~strong(lucy))<=>(funny(mary)))&
(![X]:((kind(X)|~quiet(X))<=>(~brave(X)|happy(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~happy(X))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((patient(X)&~happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~funny(X)&~strong(X))<=>~kind(X)))&
(![X]:((~old(X)&~kind(X))<=>(generous(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))=>((humble(paul)&generous(paul))))&
((?[X]:((funny(X)<~>~tall(X))))=>(strong(paul)))&
((?[X]:(old(X)))<=>((~funny(alice)<~>wise(alice))))&
(![X]:((~curious(X)&~brave(X))=>(calm(X)|~quiet(X))))&
((?[X]:(calm(X)))<=>((happy(susan)|tall(susan))))&
(![X]:(curious(X)=>(~strong(X)&tall(X))))&
(![X]:(rich(X)<=>(wise(X)&strong(X))))&
(?[X]:((strong(X)|~wise(X))))&
((~humble(john)<~>happy(john)))&
(?[X]:(quiet(X)))&
((~humble(fred)|~generous(fred)))&
(?[X]:(~generous(X)))&
(?[X]:(~old(X)))&
(?[X]:((generous(X)<~>tall(X)))) | ~wise(mary) | [
"p0",
"p4",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6969671257358975945904909
% SZS output start Proof for 6969671257358975945904909
1. ! [X0] : ((~old(X0) & curious(X0)) => happy(X0)) [input p0]
5. ! [X0] : ((~curious(X0) <~> happy(X0)) => (humble(X0) <~> ~happy(X0))) [input p4]
7. ! [X0] : ((~happy(X0) & patient(X0)) <=> (kind(X0) <~> humble(X0))) [input p6]
9. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~wise(X0) | generous(X0))) [input p8]
10. ? [X0] : (~kind(X0) | ~calm(X0)) => (generous(paul) & humble(paul)) [input p9]
24. ~wise(mary) [input hypothesis]
25. ! [X0] : (happy(X0) | (old(X0) | ~curious(X0))) [ennf transformation 1]
26. ! [X0] : (happy(X0) | old(X0) | ~curious(X0)) [flattening 25]
28. ! [X0] : ((humble(X0) <~> ~happy(X0)) | (~curious(X0) <=> happy(X0))) [ennf transformation 5]
30. (generous(paul) & humble(paul)) | ! [X0] : (kind(X0) & calm(X0)) [ennf transformation 10]
38. ! [X0] : (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) [nnf transformation 28]
40. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (happy(X0) | ~patient(X0)))) [nnf transformation 7]
41. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | happy(X0) | ~patient(X0))) [flattening 40]
44. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (kind(X0) | old(X0)))) [nnf transformation 9]
45. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | kind(X0) | old(X0))) [flattening 44]
68. ~curious(X0) | old(X0) | happy(X0) [cnf transformation 26]
78. happy(X0) | ~humble(X0) | happy(X0) | curious(X0) [cnf transformation 38]
89. ~humble(X0) | kind(X0) | ~happy(X0) [cnf transformation 41]
94. ~generous(X0) | ~old(X0) [cnf transformation 45]
96. ~generous(X0) | ~kind(X0) [cnf transformation 45]
97. ~kind(X0) | wise(X0) [cnf transformation 45]
99. humble(paul) | kind(X0) [cnf transformation 30]
101. generous(paul) | kind(X0) [cnf transformation 30]
123. ~wise(mary) [cnf transformation 24]
125. ~humble(X0) | happy(X0) | curious(X0) [duplicate literal removal 78]
155. 7 <=> ! [X0] : kind(X0) [avatar definition]
156. kind(X0) <- (7) [avatar component clause 155]
158. 8 <=> generous(paul) [avatar definition]
160. generous(paul) <- (8) [avatar component clause 158]
161. 7 | 8 [avatar split clause 101,158,155]
167. 10 <=> humble(paul) [avatar definition]
169. humble(paul) <- (10) [avatar component clause 167]
170. 7 | 10 [avatar split clause 99,167,155]
268. ~kind(paul) <- (8) [resolution 160,96]
269. ~old(paul) <- (8) [resolution 160,94]
340. kind(paul) | ~happy(paul) <- (10) [resolution 89,169]
341. ~happy(paul) <- (8, 10) [subsumption resolution 340,268]
353. happy(paul) | curious(paul) <- (10) [resolution 125,169]
354. curious(paul) <- (8, 10) [subsumption resolution 353,341]
355. old(paul) | happy(paul) <- (8, 10) [resolution 354,68]
357. happy(paul) <- (8, 10) [subsumption resolution 355,269]
358. $false <- (8, 10) [subsumption resolution 357,341]
359. ~8 | ~10 [avatar contradiction clause 358]
382. wise(X3) <- (7) [resolution 156,97]
403. $false <- (7) [resolution 382,123]
408. ~7 [avatar contradiction clause 403]
409. $false [avatar sat refutation 161,170,359,408]
% SZS output end Proof for 6969671257358975945904909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not quiet or not creative then someone is either wise or rich. Everyone who is either not quiet or brave is either rich or happy and vice versa. If alice is not wise or calm then john is quiet or generous. Everyone who is not brave or creative is not funny and vice versa. If lucy is not creative or humble then susan is both creative and not tall and vice versa. If john is generous or not generous then paul is humble or not funny and vice versa. If john is not generous or not curious then paul is both not patient and not rich and vice versa. Everyone who is both not strong and not calm is not rich or not curious and vice versa. Everyone who is brave is either not curious or funny. If someone is not curious or quiet then john is both not patient and not humble. Everyone who is not wise is both wise and not quiet and vice versa. If susan is creative or not wise then someone is both old and not humble and vice versa. If alice is creative or not wise then someone is both brave and not kind. If someone is both quiet and not old then paul is tall. Everyone who is either rich or strong is not funny and vice versa. Alice is strong or wise. Someone is curious. Someone is not wise or creative. Someone is generous. Paul is either funny or not strong. Fred is wise. | Paul is wise. | entailment | ((?[X]:((~quiet(X)<~>~creative(X))))=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~quiet(X)<~>brave(X))<=>(rich(X)<~>happy(X))))&
(((~wise(alice)|calm(alice)))=>((quiet(john)|generous(john))))&
(![X]:((~brave(X)|creative(X))<=>~funny(X)))&
(((~creative(lucy)|humble(lucy)))<=>((creative(susan)&~tall(susan))))&
(((generous(john)|~generous(john)))<=>((humble(paul)|~funny(paul))))&
(((~generous(john)|~curious(john)))<=>((~patient(paul)&~rich(paul))))&
(![X]:((~strong(X)&~calm(X))<=>(~rich(X)|~curious(X))))&
(![X]:(brave(X)=>(~curious(X)<~>funny(X))))&
((?[X]:((~curious(X)|quiet(X))))=>((~patient(john)&~humble(john))))&
(![X]:(~wise(X)<=>(wise(X)&~quiet(X))))&
(((creative(susan)|~wise(susan)))<=>(?[X]:((old(X)&~humble(X)))))&
(((creative(alice)|~wise(alice)))=>(?[X]:((brave(X)&~kind(X)))))&
((?[X]:((quiet(X)&~old(X))))=>(tall(paul)))&
(![X]:((rich(X)<~>strong(X))<=>~funny(X)))&
((strong(alice)|wise(alice)))&
(?[X]:(curious(X)))&
(?[X]:((~wise(X)|creative(X))))&
(?[X]:(generous(X)))&
((funny(paul)<~>~strong(paul)))&
(wise(fred)) | wise(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1758280434271786750408640
% SZS output start Proof for 1758280434271786750408640
11. ! [X0] : (~wise(X0) <=> (~quiet(X0) & wise(X0))) [input p10]
22. ~wise(paul) [input hypothesis]
48. ! [X0] : ((~wise(X0) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | wise(X0))) [nnf transformation 11]
49. ! [X0] : ((~wise(X0) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | wise(X0))) [flattening 48]
107. wise(X0) | wise(X0) [cnf transformation 49]
129. ~wise(paul) [cnf transformation 22]
130. wise(X0) [duplicate literal removal 107]
275. $false [subsumption resolution 129,130]
% SZS output end Proof for 1758280434271786750408640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or strong then john is either rich or strong and vice versa. Everyone who is generous is both kind and rich and vice versa. If someone is not creative then alice is not humble or not old. If someone is either happy or not quiet then someone is not happy and vice versa. Everyone who is either not tall or kind is wise. If john is wise then alice is not tall or not humble. Everyone who is not curious or not funny is both not brave and not humble and vice versa. Everyone who is both not patient and not funny is not old or not curious and vice versa. Everyone who is patient is both tall and quiet and vice versa. If susan is both not calm and not generous then susan is old or brave. If someone is either patient or quiet then someone is not rich or brave. Everyone who is not old or curious is calm or rich. If someone is not tall or generous then someone is not strong and vice versa. If lucy is wise then fred is humble or not old. If mary is either not kind or wise then someone is not creative or wise and vice versa. Everyone who is both not old and not curious is either not strong or not kind and vice versa. Alice is not old or not funny. Someone is calm or rich. Someone is not strong or calm. Fred is not generous or not brave. Mary is wise or not wise. Someone is not creative or not generous. Someone is both quiet and happy. | Susan is not calm. | neutral | ((?[X]:((curious(X)<~>strong(X))))<=>((rich(john)<~>strong(john))))&
(![X]:(generous(X)<=>(kind(X)&rich(X))))&
((?[X]:(~creative(X)))=>((~humble(alice)|~old(alice))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)<~>kind(X))=>wise(X)))&
((wise(john))=>((~tall(alice)|~humble(alice))))&
(![X]:((~curious(X)|~funny(X))<=>(~brave(X)&~humble(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~old(X)|~curious(X))))&
(![X]:(patient(X)<=>(tall(X)&quiet(X))))&
(((~calm(susan)&~generous(susan)))=>((old(susan)|brave(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:((~rich(X)|brave(X)))))&
(![X]:((~old(X)|curious(X))=>(calm(X)|rich(X))))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:(~strong(X))))&
((wise(lucy))=>((humble(fred)|~old(fred))))&
(((~kind(mary)<~>wise(mary)))<=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((~old(X)&~curious(X))<=>(~strong(X)<~>~kind(X))))&
((~old(alice)|~funny(alice)))&
(?[X]:((calm(X)|rich(X))))&
(?[X]:((~strong(X)|calm(X))))&
((~generous(fred)|~brave(fred)))&
((wise(mary)|~wise(mary)))&
(?[X]:((~creative(X)|~generous(X))))&
(?[X]:((quiet(X)&happy(X)))) | ~calm(susan) | [] | null | 0 |
Everyone who is not old is either old or wise and vice versa. Everyone who is either old or not creative is either not rich or kind. Everyone who is either not calm or happy is either not quiet or curious. If someone is not tall then alice is either strong or not old. Everyone who is either calm or not strong is both happy and patient. If someone is both kind and creative then lucy is both not patient and not rich and vice versa. If alice is either not humble or not wise then lucy is strong or not creative and vice versa. If alice is either wise or tall then someone is both brave and quiet and vice versa. Everyone who is not generous is either not quiet or not patient and vice versa. If fred is both patient and not wise then someone is both calm and generous. Everyone who is old or strong is tall. If john is either old or tall then someone is creative. Everyone who is not strong or not rich is calm or curious. Everyone who is either not tall or brave is humble or strong and vice versa. If susan is patient then someone is both curious and not humble. Everyone who is both not curious and not tall is both wise and calm. Alice is happy or not happy. Someone is creative or humble. Susan is quiet or not curious. Someone is not humble or generous. Mary is both not funny and not tall. Someone is humble or kind. Susan is not brave. Mary is not generous or old. | Lucy is wise. | entailment | (![X]:(~old(X)<=>(old(X)<~>wise(X))))&
(![X]:((old(X)<~>~creative(X))=>(~rich(X)<~>kind(X))))&
(![X]:((~calm(X)<~>happy(X))=>(~quiet(X)<~>curious(X))))&
((?[X]:(~tall(X)))=>((strong(alice)<~>~old(alice))))&
(![X]:((calm(X)<~>~strong(X))=>(happy(X)&patient(X))))&
((?[X]:((kind(X)&creative(X))))<=>((~patient(lucy)&~rich(lucy))))&
(((~humble(alice)<~>~wise(alice)))<=>((strong(lucy)|~creative(lucy))))&
(((wise(alice)<~>tall(alice)))<=>(?[X]:((brave(X)&quiet(X)))))&
(![X]:(~generous(X)<=>(~quiet(X)<~>~patient(X))))&
(((patient(fred)&~wise(fred)))=>(?[X]:((calm(X)&generous(X)))))&
(![X]:((old(X)|strong(X))=>tall(X)))&
(((old(john)<~>tall(john)))=>(?[X]:(creative(X))))&
(![X]:((~strong(X)|~rich(X))=>(calm(X)|curious(X))))&
(![X]:((~tall(X)<~>brave(X))<=>(humble(X)|strong(X))))&
((patient(susan))=>(?[X]:((curious(X)&~humble(X)))))&
(![X]:((~curious(X)&~tall(X))=>(wise(X)&calm(X))))&
((happy(alice)|~happy(alice)))&
(?[X]:((creative(X)|humble(X))))&
((quiet(susan)|~curious(susan)))&
(?[X]:((~humble(X)|generous(X))))&
((~funny(mary)&~tall(mary)))&
(?[X]:((humble(X)|kind(X))))&
(~brave(susan))&
((~generous(mary)|old(mary))) | wise(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 270786508076933406866119
% SZS output start Proof for 270786508076933406866119
1. ! [X0] : (~old(X0) <=> (old(X0) <~> wise(X0))) [input p0]
25. ~wise(lucy) [input hypothesis]
40. ! [X0] : ((~old(X0) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0)))) & (((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | old(X0))) [nnf transformation 1]
72. wise(X0) | old(X0) | old(X0) [cnf transformation 40]
74. ~old(X0) | wise(X0) | ~old(X0) [cnf transformation 40]
136. ~wise(lucy) [cnf transformation 25]
137. wise(X0) | old(X0) [duplicate literal removal 72]
138. ~old(X0) | wise(X0) [duplicate literal removal 74]
139. wise(X0) [subsumption resolution 137,138]
289. $false [subsumption resolution 136,139]
% SZS output end Proof for 270786508076933406866119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is tall or not old then lucy is both happy and not humble and vice versa. Everyone who is patient or curious is either kind or calm. Everyone who is both not wise and not brave is either not brave or not tall. If john is both humble and not patient then john is both patient and tall. If alice is not rich then someone is both not happy and not creative. If john is either humble or not rich then alice is humble or happy and vice versa. Everyone who is both not curious and generous is rich. Everyone who is patient or kind is patient or not brave. Everyone who is both old and tall is both old and not curious. If fred is creative or generous then alice is not happy. If someone is either humble or not brave then mary is both brave and patient. Everyone who is quiet is not happy. If paul is old then susan is rich or kind and vice versa. Everyone who is both not brave and not quiet is not brave or not generous. If someone is either generous or brave then lucy is either creative or not brave and vice versa. Everyone who is patient is both happy and funny and vice versa. Paul is tall or funny. Someone is both tall and not old. Susan is happy. Someone is either wise or not old. Lucy is both curious and not quiet. Someone is both not kind and not old. Someone is quiet. Mary is generous. | Fred is patient. | neutral | (((tall(alice)|~old(alice)))<=>((happy(lucy)&~humble(lucy))))&
(![X]:((patient(X)|curious(X))=>(kind(X)<~>calm(X))))&
(![X]:((~wise(X)&~brave(X))=>(~brave(X)<~>~tall(X))))&
(((humble(john)&~patient(john)))=>((patient(john)&tall(john))))&
((~rich(alice))=>(?[X]:((~happy(X)&~creative(X)))))&
(((humble(john)<~>~rich(john)))<=>((humble(alice)|happy(alice))))&
(![X]:((~curious(X)&generous(X))=>rich(X)))&
(![X]:((patient(X)|kind(X))=>(patient(X)|~brave(X))))&
(![X]:((old(X)&tall(X))=>(old(X)&~curious(X))))&
(((creative(fred)|generous(fred)))=>(~happy(alice)))&
((?[X]:((humble(X)<~>~brave(X))))=>((brave(mary)&patient(mary))))&
(![X]:(quiet(X)=>~happy(X)))&
((old(paul))<=>((rich(susan)|kind(susan))))&
(![X]:((~brave(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
((?[X]:((generous(X)<~>brave(X))))<=>((creative(lucy)<~>~brave(lucy))))&
(![X]:(patient(X)<=>(happy(X)&funny(X))))&
((tall(paul)|funny(paul)))&
(?[X]:((tall(X)&~old(X))))&
(happy(susan))&
(?[X]:((wise(X)<~>~old(X))))&
((curious(lucy)&~quiet(lucy)))&
(?[X]:((~kind(X)&~old(X))))&
(?[X]:(quiet(X)))&
(generous(mary)) | patient(fred) | [] | null | 0 |
Everyone who is not generous is either not wise or not patient.
Everyone who is either humble or not generous is not curious or funny and vice versa.
Everyone who is not curious is either not curious or not creative and vice versa.
If someone is not kind or not humble then susan is not creative.
Everyone who is calm or creative is not quiet and vice versa.
If fred is not generous or not calm then john is kind.
If mary is both not quiet and not creative then mary is both not funny and not wise and vice versa.
If someone is both not generous and rich then lucy is either strong or not wise.
If john is not calm or generous then fred is either not happy or generous.
Everyone who is tall is both happy and not happy.
Everyone who is not humble or quiet is not happy.
Everyone who is curious is both generous and not humble.
If paul is either creative or not curious then someone is both strong and generous and vice versa.
If fred is either not wise or strong then alice is either happy or curious and vice versa.
Everyone who is old is both curious and not creative and vice versa.
Everyone who is either not brave or not tall is kind and vice versa.
John is either not tall or patient.
Someone is both not curious and patient.
John is either not happy or old.
Lucy is either not humble or not curious. | Fred is curious. | contradiction | (![X]:(~generous(X)=>(~wise(X)<~>~patient(X))))&
(![X]:((humble(X)<~>~generous(X))<=>(~curious(X)|funny(X))))&
(![X]:(~curious(X)<=>(~curious(X)<~>~creative(X))))&
((?[X]:((~kind(X)|~humble(X))))=>(~creative(susan)))&
(![X]:((calm(X)|creative(X))<=>~quiet(X)))&
(((~generous(fred)|~calm(fred)))=>(kind(john)))&
(((~quiet(mary)&~creative(mary)))<=>((~funny(mary)&~wise(mary))))&
((?[X]:((~generous(X)&rich(X))))=>((strong(lucy)<~>~wise(lucy))))&
(((~calm(john)|generous(john)))=>((~happy(fred)<~>generous(fred))))&
(![X]:(tall(X)=>(happy(X)&~happy(X))))&
(![X]:((~humble(X)|quiet(X))=>~happy(X)))&
(![X]:(curious(X)=>(generous(X)&~humble(X))))&
(((creative(paul)<~>~curious(paul)))<=>(?[X]:((strong(X)&generous(X)))))&
(((~wise(fred)<~>strong(fred)))<=>((happy(alice)<~>curious(alice))))&
(![X]:(old(X)<=>(curious(X)&~creative(X))))&
(![X]:((~brave(X)<~>~tall(X))<=>kind(X)))&
((~tall(john)<~>patient(john)))&
(?[X]:((~curious(X)&patient(X))))&
((~happy(john)<~>old(john)))&
((~humble(lucy)<~>~curious(lucy))) | curious(fred) | [
"p2",
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1315960573668036824952660
% SZS output start Proof for 1315960573668036824952660
3. ! [X0] : (~curious(X0) <=> (~curious(X0) <~> ~creative(X0))) [input p2]
4. ? [X0] : (~humble(X0) | ~kind(X0)) => ~creative(susan) [input p3]
12. ! [X0] : (curious(X0) => (~humble(X0) & generous(X0))) [input p11]
21. curious(fred) [input hypothesis]
25. ~creative(susan) | ! [X0] : (humble(X0) & kind(X0)) [ennf transformation 4]
30. ! [X0] : ((~humble(X0) & generous(X0)) | ~curious(X0)) [ennf transformation 12]
35. ! [X0] : ((~curious(X0) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | curious(X0))) [nnf transformation 3]
63. creative(X0) | curious(X0) | curious(X0) [cnf transformation 35]
65. ~curious(X0) | ~curious(X0) | creative(X0) [cnf transformation 35]
67. ~creative(susan) | humble(X0) [cnf transformation 25]
86. ~humble(X0) | ~curious(X0) [cnf transformation 30]
114. curious(fred) [cnf transformation 21]
115. creative(X0) | curious(X0) [duplicate literal removal 63]
116. ~curious(X0) | creative(X0) [duplicate literal removal 65]
117. creative(X0) [subsumption resolution 115,116]
118. humble(X0) [subsumption resolution 67,117]
152. ~curious(X0) [subsumption resolution 86,118]
180. $false [subsumption resolution 114,152]
% SZS output end Proof for 1315960573668036824952660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not curious then someone is not calm or patient. Everyone who is not old or curious is both not calm and not strong. Everyone who is not happy is either not humble or not wise and vice versa. Everyone who is both not creative and not generous is both generous and not rich. If someone is both not brave and patient then someone is both quiet and not humble and vice versa. Everyone who is both not calm and not quiet is quiet or generous. If someone is tall then mary is either not tall or rich and vice versa. If john is not quiet then paul is tall and vice versa. Everyone who is either wise or tall is both patient and not quiet and vice versa. If someone is humble or kind then someone is old. If susan is not wise or not brave then lucy is both not rich and not creative. Everyone who is either not strong or calm is generous or not kind. If mary is generous or tall then someone is not old. If someone is patient then fred is generous. If someone is not wise then someone is either not tall or rich and vice versa. Everyone who is not wise or not humble is happy and vice versa. Mary is both creative and rich. Paul is both creative and not quiet. Someone is both not funny and not generous. Someone is not humble or not brave. Someone is either not patient or not wise. Alice is either not generous or calm. Fred is both funny and not strong. | Lucy is wise. | contradiction | ((?[X]:((brave(X)<~>~curious(X))))=>(?[X]:((~calm(X)|patient(X)))))&
(![X]:((~old(X)|curious(X))=>(~calm(X)&~strong(X))))&
(![X]:(~happy(X)<=>(~humble(X)<~>~wise(X))))&
(![X]:((~creative(X)&~generous(X))=>(generous(X)&~rich(X))))&
((?[X]:((~brave(X)&patient(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(![X]:((~calm(X)&~quiet(X))=>(quiet(X)|generous(X))))&
((?[X]:(tall(X)))<=>((~tall(mary)<~>rich(mary))))&
((~quiet(john))<=>(tall(paul)))&
(![X]:((wise(X)<~>tall(X))<=>(patient(X)&~quiet(X))))&
((?[X]:((humble(X)|kind(X))))=>(?[X]:(old(X))))&
(((~wise(susan)|~brave(susan)))=>((~rich(lucy)&~creative(lucy))))&
(![X]:((~strong(X)<~>calm(X))=>(generous(X)|~kind(X))))&
(((generous(mary)|tall(mary)))=>(?[X]:(~old(X))))&
((?[X]:(patient(X)))=>(generous(fred)))&
((?[X]:(~wise(X)))<=>(?[X]:((~tall(X)<~>rich(X)))))&
(![X]:((~wise(X)|~humble(X))<=>happy(X)))&
((creative(mary)&rich(mary)))&
((creative(paul)&~quiet(paul)))&
(?[X]:((~funny(X)&~generous(X))))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:((~patient(X)<~>~wise(X))))&
((~generous(alice)<~>calm(alice)))&
((funny(fred)&~strong(fred))) | wise(lucy) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2013075761543333435421077
% SZS output start Proof for 2013075761543333435421077
3. ! [X0] : (~happy(X0) <=> (~humble(X0) <~> ~wise(X0))) [input p2]
16. ! [X0] : ((~humble(X0) | ~wise(X0)) <=> happy(X0)) [input p15]
24. wise(lucy) [input hypothesis]
47. ! [X0] : ((~happy(X0) | ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0)))) & (((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | happy(X0))) [nnf transformation 3]
70. ! [X0] : (((~humble(X0) | ~wise(X0)) | ~happy(X0)) & (happy(X0) | (humble(X0) & wise(X0)))) [nnf transformation 16]
71. ! [X0] : ((~humble(X0) | ~wise(X0) | ~happy(X0)) & (happy(X0) | (humble(X0) & wise(X0)))) [flattening 70]
84. ~wise(X0) | ~humble(X0) | happy(X0) [cnf transformation 47]
86. ~wise(X0) | ~happy(X0) | humble(X0) [cnf transformation 47]
119. wise(X0) | happy(X0) [cnf transformation 71]
120. humble(X0) | happy(X0) [cnf transformation 71]
121. ~humble(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 71]
134. wise(lucy) [cnf transformation 24]
279. ~wise(X0) | ~happy(X0) [subsumption resolution 121,86]
319. ~happy(lucy) [resolution 279,134]
324. ~humble(X0) | happy(X0) | happy(X0) [resolution 84,119]
325. ~humble(X0) | happy(X0) [duplicate literal removal 324]
327. happy(X0) [subsumption resolution 325,120]
340. $false [resolution 327,319]
% SZS output end Proof for 2013075761543333435421077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is either not generous or quiet.
If someone is both not strong and not funny then someone is happy or not kind.
Everyone who is either curious or tall is either not creative or tall.
If mary is not funny or not brave then mary is wise or happy and vice versa.
Everyone who is either rich or not funny is wise or not patient.
Everyone who is both not tall and funny is either not happy or not creative and vice versa.
If someone is either quiet or not creative then mary is happy and vice versa.
Everyone who is not creative or not patient is either not brave or not patient and vice versa.
Everyone who is quiet or not strong is tall or not strong.
If john is strong then fred is both strong and tall and vice versa.
If someone is creative then mary is either not tall or not curious.
If someone is both not kind and funny then fred is either happy or not old.
Everyone who is both strong and kind is both not quiet and patient and vice versa.
If someone is either generous or not wise then someone is not happy.
If someone is either not patient or wise then someone is not quiet.
If alice is either curious or not curious then someone is both not strong and humble and vice versa.
Mary is tall.
Someone is kind or quiet.
Alice is not curious or not rich.
Someone is rich or not curious.
John is both not rich and not quiet.
Someone is either brave or curious.
Fred is not kind.
Someone is humble. | Mary is funny. | contradiction | (![X]:(~kind(X)=>(~generous(X)<~>quiet(X))))&
((?[X]:((~strong(X)&~funny(X))))=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((curious(X)<~>tall(X))=>(~creative(X)<~>tall(X))))&
(((~funny(mary)|~brave(mary)))<=>((wise(mary)|happy(mary))))&
(![X]:((rich(X)<~>~funny(X))=>(wise(X)|~patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~happy(X)<~>~creative(X))))&
((?[X]:((quiet(X)<~>~creative(X))))<=>(happy(mary)))&
(![X]:((~creative(X)|~patient(X))<=>(~brave(X)<~>~patient(X))))&
(![X]:((quiet(X)|~strong(X))=>(tall(X)|~strong(X))))&
((strong(john))<=>((strong(fred)&tall(fred))))&
((?[X]:(creative(X)))=>((~tall(mary)<~>~curious(mary))))&
((?[X]:((~kind(X)&funny(X))))=>((happy(fred)<~>~old(fred))))&
(![X]:((strong(X)&kind(X))<=>(~quiet(X)&patient(X))))&
((?[X]:((generous(X)<~>~wise(X))))=>(?[X]:(~happy(X))))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:(~quiet(X))))&
(((curious(alice)<~>~curious(alice)))<=>(?[X]:((~strong(X)&humble(X)))))&
(tall(mary))&
(?[X]:((kind(X)|quiet(X))))&
((~curious(alice)|~rich(alice)))&
(?[X]:((rich(X)|~curious(X))))&
((~rich(john)&~quiet(john)))&
(?[X]:((brave(X)<~>curious(X))))&
(~kind(fred))&
(?[X]:(humble(X))) | funny(mary) | [
"p2",
"p3",
"p5",
"p6",
"p7",
"p10",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7664687022533318061598203
% SZS output start Proof for 7664687022533318061598203
3. ! [X0] : ((curious(X0) <~> tall(X0)) => (~creative(X0) <~> tall(X0))) [input p2]
4. (~brave(mary) | ~funny(mary)) <=> (happy(mary) | wise(mary)) [input p3]
6. ! [X0] : ((funny(X0) & ~tall(X0)) <=> (~happy(X0) <~> ~creative(X0))) [input p5]
7. ? [X0] : (quiet(X0) <~> ~creative(X0)) <=> happy(mary) [input p6]
8. ! [X0] : ((~patient(X0) | ~creative(X0)) <=> (~brave(X0) <~> ~patient(X0))) [input p7]
11. ? [X0] : creative(X0) => (~tall(mary) <~> ~curious(mary)) [input p10]
17. tall(mary) [input p16]
21. ~quiet(john) & ~rich(john) [input p20]
25. funny(mary) [input hypothesis]
31. ! [X0] : ((~creative(X0) <~> tall(X0)) | (curious(X0) <=> tall(X0))) [ennf transformation 3]
36. (~tall(mary) <~> ~curious(mary)) | ! [X0] : ~creative(X0) [ennf transformation 11]
44. ! [X0] : (((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 31]
45. ((~brave(mary) | ~funny(mary)) | (~happy(mary) & ~wise(mary))) & ((happy(mary) | wise(mary)) | (brave(mary) & funny(mary))) [nnf transformation 4]
46. (~brave(mary) | ~funny(mary) | (~happy(mary) & ~wise(mary))) & (happy(mary) | wise(mary) | (brave(mary) & funny(mary))) [flattening 45]
48. ! [X0] : (((funny(X0) & ~tall(X0)) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0)))) & (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | (~funny(X0) | tall(X0)))) [nnf transformation 6]
49. ! [X0] : (((funny(X0) & ~tall(X0)) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0)))) & (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | ~funny(X0) | tall(X0))) [flattening 48]
50. (? [X0] : ((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | ~happy(mary)) & (happy(mary) | ! [X0] : ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0)))) [nnf transformation 7]
51. (? [X0] : ((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | ~happy(mary)) & (happy(mary) | ! [X1] : ((quiet(X1) | creative(X1)) & (~creative(X1) | ~quiet(X1)))) [rectify 50]
52. ? [X0] : ((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) => ((creative(sK1) | ~quiet(sK1)) & (~creative(sK1) | quiet(sK1))) [choice axiom]
53. (((creative(sK1) | ~quiet(sK1)) & (~creative(sK1) | quiet(sK1))) | ~happy(mary)) & (happy(mary) | ! [X1] : ((quiet(X1) | creative(X1)) & (~creative(X1) | ~quiet(X1)))) [skolemisation 51,52]
54. ! [X0] : (((~patient(X0) | ~creative(X0)) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) & (((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | (patient(X0) & creative(X0)))) [nnf transformation 8]
55. ! [X0] : ((~patient(X0) | ~creative(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) & (((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | (patient(X0) & creative(X0)))) [flattening 54]
58. ((curious(mary) | tall(mary)) & (~curious(mary) | ~tall(mary))) | ! [X0] : ~creative(X0) [nnf transformation 36]
89. ~tall(X0) | creative(X0) | curious(X0) | ~tall(X0) [cnf transformation 44]
93. ~brave(mary) | ~funny(mary) | ~happy(mary) [cnf transformation 46]
98. ~creative(X0) | ~tall(X0) | happy(X0) [cnf transformation 49]
99. ~tall(X0) | ~happy(X0) | creative(X0) [cnf transformation 49]
103. happy(mary) | quiet(X1) | creative(X1) [cnf transformation 53]
109. patient(X0) | brave(X0) | patient(X0) [cnf transformation 55]
110. ~patient(X0) | ~creative(X0) | ~patient(X0) | brave(X0) [cnf transformation 55]
117. ~curious(mary) | ~tall(mary) | ~creative(X0) [cnf transformation 58]
135. tall(mary) [cnf transformation 17]
140. ~quiet(john) [cnf transformation 21]
145. funny(mary) [cnf transformation 25]
150. patient(X0) | brave(X0) [duplicate literal removal 109]
151. ~patient(X0) | ~creative(X0) | brave(X0) [duplicate literal removal 110]
153. ~tall(X0) | creative(X0) | curious(X0) [duplicate literal removal 89]
167. 4 <=> happy(mary) [avatar definition]
168. happy(mary) <- (4) [avatar component clause 167]
169. ~happy(mary) <- (~4) [avatar component clause 167]
171. 5 <=> funny(mary) [avatar definition]
175. 6 <=> brave(mary) [avatar definition]
177. ~brave(mary) <- (~6) [avatar component clause 175]
178. ~4 | ~5 | ~6 [avatar split clause 93,175,171,167]
197. 10 <=> ! [X1] : (quiet(X1) | creative(X1)) [avatar definition]
198. creative(X1) | quiet(X1) <- (10) [avatar component clause 197]
199. 10 | 4 [avatar split clause 103,167,197]
220. 15 <=> ! [X0] : ~creative(X0) [avatar definition]
221. ~creative(X0) <- (15) [avatar component clause 220]
223. 16 <=> tall(mary) [avatar definition]
225. tall(mary) <- (16) [avatar component clause 223]
227. 17 <=> curious(mary) [avatar definition]
231. 15 | ~16 | ~17 [avatar split clause 117,227,223,220]
285. 16 [avatar split clause 135,223]
319. 5 [avatar split clause 145,171]
320. ~happy(mary) | creative(mary) <- (16) [resolution 99,225]
321. creative(mary) <- (4, 16) [subsumption resolution 320,168]
328. ~creative(X0) | brave(X0) | brave(X0) [resolution 151,150]
329. ~creative(X0) | brave(X0) [duplicate literal removal 328]
330. brave(mary) <- (4, 16) [resolution 329,321]
331. $false <- (4, ~6, 16) [subsumption resolution 330,177]
332. ~4 | 6 | ~16 [avatar contradiction clause 331]
334. 37 <=> creative(mary) [avatar definition]
336. creative(mary) <- (37) [avatar component clause 334]
376. creative(mary) | curious(mary) <- (16) [resolution 153,225]
383. ~tall(mary) | happy(mary) <- (37) [resolution 336,98]
388. happy(mary) <- (16, 37) [subsumption resolution 383,225]
389. $false <- (~4, 16, 37) [subsumption resolution 388,169]
390. 4 | ~16 | ~37 [avatar contradiction clause 389]
391. 17 | 37 | ~16 [avatar split clause 376,223,334,227]
392. quiet(X0) <- (10, 15) [resolution 221,198]
397. $false <- (10, 15) [resolution 392,140]
400. ~10 | ~15 [avatar contradiction clause 397]
401. $false [avatar sat refutation 178,199,231,285,319,332,390,391,400]
% SZS output end Proof for 7664687022533318061598203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or wise is both not strong and not happy and vice versa.
If someone is not quiet then someone is both humble and old and vice versa.
If someone is not old or strong then someone is either not rich or patient.
If someone is not generous or not kind then susan is either not strong or curious and vice versa.
If alice is funny or not generous then someone is not rich and vice versa.
If john is not calm or not patient then john is either patient or funny and vice versa.
Everyone who is old or not rich is not creative and vice versa.
Everyone who is not wise is brave or curious and vice versa.
Everyone who is either kind or not old is not generous or curious and vice versa.
If someone is both strong and not strong then someone is kind.
If mary is both not patient and not strong then someone is both wise and not wise.
Everyone who is both funny and wise is not funny or funny and vice versa.
Everyone who is both not old and not funny is quiet and vice versa.
If someone is funny then john is either not patient or generous.
If someone is funny or not creative then someone is not tall or not kind.
Someone is creative or not happy.
Alice is either funny or strong.
Someone is not patient.
Someone is either not generous or old.
Alice is both not quiet and not strong.
Mary is not quiet. | Alice is not happy. | neutral | (![X]:((rich(X)<~>wise(X))<=>(~strong(X)&~happy(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((humble(X)&old(X)))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((~rich(X)<~>patient(X)))))&
((?[X]:((~generous(X)|~kind(X))))<=>((~strong(susan)<~>curious(susan))))&
(((funny(alice)|~generous(alice)))<=>(?[X]:(~rich(X))))&
(((~calm(john)|~patient(john)))<=>((patient(john)<~>funny(john))))&
(![X]:((old(X)|~rich(X))<=>~creative(X)))&
(![X]:(~wise(X)<=>(brave(X)|curious(X))))&
(![X]:((kind(X)<~>~old(X))<=>(~generous(X)|curious(X))))&
((?[X]:((strong(X)&~strong(X))))=>(?[X]:(kind(X))))&
(((~patient(mary)&~strong(mary)))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((funny(X)&wise(X))<=>(~funny(X)|funny(X))))&
(![X]:((~old(X)&~funny(X))<=>quiet(X)))&
((?[X]:(funny(X)))=>((~patient(john)<~>generous(john))))&
((?[X]:((funny(X)|~creative(X))))=>(?[X]:((~tall(X)|~kind(X)))))&
(?[X]:((creative(X)|~happy(X))))&
((funny(alice)<~>strong(alice)))&
(?[X]:(~patient(X)))&
(?[X]:((~generous(X)<~>old(X))))&
((~quiet(alice)&~strong(alice)))&
(~quiet(mary)) | ~happy(alice) | [] | null | 0 |
Everyone who is both patient and not funny is not kind or creative.
If fred is both generous and rich then paul is either funny or wise and vice versa.
If alice is either old or not calm then john is curious.
Everyone who is both not wise and not funny is either funny or generous and vice versa.
If mary is funny then someone is either patient or not funny and vice versa.
If someone is kind or not wise then paul is brave or not tall.
Everyone who is both not wise and quiet is not calm.
If someone is not generous then someone is either rich or not patient and vice versa.
Everyone who is calm or not generous is rich.
Everyone who is both not happy and not brave is either not calm or tall.
If john is not generous or not happy then paul is tall or not wise.
If someone is either curious or not kind then susan is wise or creative and vice versa.
Everyone who is creative is not creative.
Everyone who is both not happy and tall is calm or not old and vice versa.
Everyone who is either rich or not generous is both happy and not curious and vice versa.
Everyone who is curious is either not brave or curious.
Paul is both kind and not funny.
Susan is both not happy and not wise.
Someone is both not funny and humble.
Paul is either funny or calm.
Someone is funny or not rich.
Lucy is either not kind or quiet.
Someone is not patient or not tall. | Fred is not happy. | contradiction | (![X]:((patient(X)&~funny(X))=>(~kind(X)|creative(X))))&
(((generous(fred)&rich(fred)))<=>((funny(paul)<~>wise(paul))))&
(((old(alice)<~>~calm(alice)))=>(curious(john)))&
(![X]:((~wise(X)&~funny(X))<=>(funny(X)<~>generous(X))))&
((funny(mary))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:((kind(X)|~wise(X))))=>((brave(paul)|~tall(paul))))&
(![X]:((~wise(X)&quiet(X))=>~calm(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((rich(X)<~>~patient(X)))))&
(![X]:((calm(X)|~generous(X))=>rich(X)))&
(![X]:((~happy(X)&~brave(X))=>(~calm(X)<~>tall(X))))&
(((~generous(john)|~happy(john)))=>((tall(paul)|~wise(paul))))&
((?[X]:((curious(X)<~>~kind(X))))<=>((wise(susan)|creative(susan))))&
(![X]:(creative(X)=>~creative(X)))&
(![X]:((~happy(X)&tall(X))<=>(calm(X)|~old(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(happy(X)&~curious(X))))&
(![X]:(curious(X)=>(~brave(X)<~>curious(X))))&
((kind(paul)&~funny(paul)))&
((~happy(susan)&~wise(susan)))&
(?[X]:((~funny(X)&humble(X))))&
((funny(paul)<~>calm(paul)))&
(?[X]:((funny(X)|~rich(X))))&
((~kind(lucy)<~>quiet(lucy)))&
(?[X]:((~patient(X)|~tall(X)))) | ~happy(fred) | [
"p1",
"p3",
"p8",
"p13",
"p14",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1519872462678137493527623
% SZS output start Proof for 1519872462678137493527623
2. (rich(fred) & generous(fred)) <=> (funny(paul) <~> wise(paul)) [input p1]
4. ! [X0] : ((~funny(X0) & ~wise(X0)) <=> (funny(X0) <~> generous(X0))) [input p3]
9. ! [X0] : ((~generous(X0) | calm(X0)) => rich(X0)) [input p8]
14. ! [X0] : ((tall(X0) & ~happy(X0)) <=> (~old(X0) | calm(X0))) [input p13]
15. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (~curious(X0) & happy(X0))) [input p14]
17. ~funny(paul) & kind(paul) [input p16]
20. funny(paul) <~> calm(paul) [input p19]
24. ~happy(fred) [input hypothesis]
34. ! [X0] : (rich(X0) | (generous(X0) & ~calm(X0))) [ennf transformation 9]
41. ((rich(fred) & generous(fred)) | ((funny(paul) | ~wise(paul)) & (wise(paul) | ~funny(paul)))) & (((~wise(paul) | ~funny(paul)) & (wise(paul) | funny(paul))) | (~rich(fred) | ~generous(fred))) [nnf transformation 2]
42. ((rich(fred) & generous(fred)) | ((funny(paul) | ~wise(paul)) & (wise(paul) | ~funny(paul)))) & (((~wise(paul) | ~funny(paul)) & (wise(paul) | funny(paul))) | ~rich(fred) | ~generous(fred)) [flattening 41]
44. ! [X0] : (((~funny(X0) & ~wise(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (funny(X0) | wise(X0)))) [nnf transformation 4]
45. ! [X0] : (((~funny(X0) & ~wise(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | funny(X0) | wise(X0))) [flattening 44]
61. ! [X0] : (((tall(X0) & ~happy(X0)) | (old(X0) & ~calm(X0))) & ((~old(X0) | calm(X0)) | (~tall(X0) | happy(X0)))) [nnf transformation 14]
62. ! [X0] : (((tall(X0) & ~happy(X0)) | (old(X0) & ~calm(X0))) & (~old(X0) | calm(X0) | ~tall(X0) | happy(X0))) [flattening 61]
63. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (curious(X0) | ~happy(X0))) & ((~curious(X0) & happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 15]
64. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | curious(X0) | ~happy(X0)) & ((~curious(X0) & happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [flattening 63]
68. (~calm(paul) | ~funny(paul)) & (calm(paul) | funny(paul)) [nnf transformation 20]
78. generous(fred) | funny(paul) | ~wise(paul) [cnf transformation 42]
80. rich(fred) | funny(paul) | ~wise(paul) [cnf transformation 42]
83. generous(X0) | funny(X0) | funny(X0) | wise(X0) [cnf transformation 45]
87. ~funny(X0) | generous(X0) | ~funny(X0) [cnf transformation 45]
100. ~calm(X0) | rich(X0) [cnf transformation 34]
114. ~happy(X0) | ~calm(X0) [cnf transformation 62]
118. ~rich(X0) | ~generous(X0) | happy(X0) [cnf transformation 64]
127. ~funny(paul) [cnf transformation 17]
131. calm(paul) | funny(paul) [cnf transformation 68]
137. ~happy(fred) [cnf transformation 24]
140. generous(X0) | funny(X0) | wise(X0) [duplicate literal removal 83]
141. ~funny(X0) | generous(X0) [duplicate literal removal 87]
143. 1 <=> wise(paul) [avatar definition]
145. ~wise(paul) <- (~1) [avatar component clause 143]
147. 2 <=> funny(paul) [avatar definition]
151. 3 <=> rich(fred) [avatar definition]
153. rich(fred) <- (3) [avatar component clause 151]
154. ~1 | 2 | 3 [avatar split clause 80,151,147,143]
157. 4 <=> generous(fred) [avatar definition]
159. generous(fred) <- (4) [avatar component clause 157]
160. ~1 | 2 | 4 [avatar split clause 78,157,147,143]
178. wise(X0) | generous(X0) [subsumption resolution 140,141]
282. ~2 [avatar split clause 127,147]
285. 31 <=> calm(paul) [avatar definition]
286. calm(paul) <- (31) [avatar component clause 285]
289. 2 | 31 [avatar split clause 131,285,147]
321. rich(paul) <- (31) [resolution 100,286]
330. generous(paul) <- (~1) [resolution 178,145]
342. ~generous(paul) | happy(paul) <- (31) [resolution 118,321]
352. happy(paul) <- (~1, 31) [subsumption resolution 342,330]
375. ~calm(paul) <- (~1, 31) [resolution 352,114]
376. $false <- (~1, 31) [subsumption resolution 375,286]
377. 1 | ~31 [avatar contradiction clause 376]
388. ~generous(fred) | happy(fred) <- (3) [resolution 153,118]
389. happy(fred) <- (3, 4) [subsumption resolution 388,159]
390. $false <- (3, 4) [subsumption resolution 389,137]
391. ~3 | ~4 [avatar contradiction clause 390]
392. $false [avatar sat refutation 154,160,282,289,377,391]
% SZS output end Proof for 1519872462678137493527623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is either not strong or not old and vice versa. If someone is patient then someone is both not humble and not patient. If someone is either strong or curious then someone is either happy or not wise and vice versa. Everyone who is either not patient or not funny is either not curious or not tall and vice versa. Everyone who is either curious or wise is calm and vice versa. Everyone who is both not curious and not rich is generous or not patient and vice versa. Everyone who is either not creative or not old is either humble or not strong. If someone is humble then someone is either creative or not brave. If fred is either not creative or not curious then someone is either not strong or creative and vice versa. If mary is not generous then someone is both not brave and calm. If someone is curious or quiet then someone is curious and vice versa. If lucy is either brave or quiet then someone is both funny and rich and vice versa. Everyone who is either not wise or curious is not wise or not strong and vice versa. Everyone who is calm or rich is not creative or not rich and vice versa. Everyone who is happy or creative is curious or not creative. Everyone who is not old or calm is not humble or not wise. Someone is either creative or not quiet. Someone is either creative or wise. John is both calm and quiet. Fred is rich. Someone is either not creative or old. Alice is either not calm or creative. Someone is either not funny or humble. | Alice is rich. | entailment | (![X]:(~rich(X)<=>(~strong(X)<~>~old(X))))&
((?[X]:(patient(X)))=>(?[X]:((~humble(X)&~patient(X)))))&
((?[X]:((strong(X)<~>curious(X))))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((~patient(X)<~>~funny(X))<=>(~curious(X)<~>~tall(X))))&
(![X]:((curious(X)<~>wise(X))<=>calm(X)))&
(![X]:((~curious(X)&~rich(X))<=>(generous(X)|~patient(X))))&
(![X]:((~creative(X)<~>~old(X))=>(humble(X)<~>~strong(X))))&
((?[X]:(humble(X)))=>(?[X]:((creative(X)<~>~brave(X)))))&
(((~creative(fred)<~>~curious(fred)))<=>(?[X]:((~strong(X)<~>creative(X)))))&
((~generous(mary))=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((curious(X)|quiet(X))))<=>(?[X]:(curious(X))))&
(((brave(lucy)<~>quiet(lucy)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~wise(X)|~strong(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)|~rich(X))))&
(![X]:((happy(X)|creative(X))=>(curious(X)|~creative(X))))&
(![X]:((~old(X)|calm(X))=>(~humble(X)|~wise(X))))&
(?[X]:((creative(X)<~>~quiet(X))))&
(?[X]:((creative(X)<~>wise(X))))&
((calm(john)&quiet(john)))&
(rich(fred))&
(?[X]:((~creative(X)<~>old(X))))&
((~calm(alice)<~>creative(alice)))&
(?[X]:((~funny(X)<~>humble(X)))) | rich(alice) | [
"p4",
"p12",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3932697432707222326290669
% SZS output start Proof for 3932697432707222326290669
5. ! [X0] : ((curious(X0) <~> wise(X0)) <=> calm(X0)) [input p4]
13. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (~strong(X0) | ~wise(X0))) [input p12]
14. ! [X0] : ((rich(X0) | calm(X0)) <=> (~rich(X0) | ~creative(X0))) [input p13]
15. ! [X0] : ((creative(X0) | happy(X0)) => (~creative(X0) | curious(X0))) [input p14]
22. ~calm(alice) <~> creative(alice) [input p21]
24. ~rich(alice) [input hypothesis]
33. ! [X0] : ((~creative(X0) | curious(X0)) | (~creative(X0) & ~happy(X0))) [ennf transformation 15]
34. ! [X0] : (~creative(X0) | curious(X0) | (~creative(X0) & ~happy(X0))) [flattening 33]
47. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | ~calm(X0)) & (calm(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [nnf transformation 5]
70. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (strong(X0) & wise(X0))) & ((~strong(X0) | ~wise(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 13]
71. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (strong(X0) & wise(X0))) & (~strong(X0) | ~wise(X0) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [flattening 70]
72. ! [X0] : (((rich(X0) | calm(X0)) | (rich(X0) & creative(X0))) & ((~rich(X0) | ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 14]
73. ! [X0] : ((rich(X0) | calm(X0) | (rich(X0) & creative(X0))) & (~rich(X0) | ~creative(X0) | (~rich(X0) & ~calm(X0)))) [flattening 72]
83. (~creative(alice) | calm(alice)) & (creative(alice) | ~calm(alice)) [nnf transformation 22]
112. ~calm(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 47]
147. ~curious(X0) | wise(X0) | wise(X0) [cnf transformation 71]
152. rich(X0) | calm(X0) | rich(X0) [cnf transformation 73]
154. ~creative(X0) | curious(X0) | ~creative(X0) [cnf transformation 34]
166. creative(alice) | ~calm(alice) [cnf transformation 83]
170. ~rich(alice) [cnf transformation 24]
171. ~creative(X0) | curious(X0) [duplicate literal removal 154]
173. calm(X0) | rich(X0) [duplicate literal removal 152]
175. ~curious(X0) | wise(X0) [duplicate literal removal 147]
360. 40 <=> calm(alice) [avatar definition]
361. ~calm(alice) <- (~40) [avatar component clause 360]
362. calm(alice) <- (40) [avatar component clause 360]
364. 41 <=> creative(alice) [avatar definition]
365. creative(alice) <- (41) [avatar component clause 364]
368. ~40 | 41 [avatar split clause 166,364,360]
395. rich(alice) <- (~40) [resolution 173,361]
396. $false <- (~40) [subsumption resolution 395,170]
397. 40 [avatar contradiction clause 396]
399. curious(alice) <- (41) [resolution 365,171]
406. wise(alice) <- (41) [resolution 399,175]
462. ~curious(alice) | ~wise(alice) <- (40) [resolution 112,362]
466. ~wise(alice) <- (40, 41) [subsumption resolution 462,399]
467. $false <- (40, 41) [subsumption resolution 466,406]
468. ~40 | ~41 [avatar contradiction clause 467]
471. $false [avatar sat refutation 368,397,468]
% SZS output end Proof for 3932697432707222326290669
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not funny is not happy. Everyone who is either brave or rich is brave or not patient and vice versa. If someone is not happy then someone is not quiet or humble. Everyone who is not generous or humble is both not generous and old. Everyone who is humble or not funny is not wise or not funny. Everyone who is either happy or not funny is either not kind or not rich and vice versa. Everyone who is both not rich and humble is not brave or not curious and vice versa. If alice is either generous or not tall then lucy is either creative or not old. Everyone who is both calm and not curious is either strong or happy and vice versa. Everyone who is either humble or not kind is both not happy and strong. If someone is wise or old then someone is both not old and patient. Everyone who is both not generous and not tall is both not rich and quiet. If someone is calm or not quiet then someone is not calm and vice versa. Everyone who is happy or quiet is not happy and vice versa. Everyone who is happy or old is not brave or not creative. If someone is both not happy and creative then someone is wise or not happy. Someone is not quiet or funny. Someone is old. Someone is either not generous or not patient. Alice is not kind. John is not calm or not strong. Someone is not generous. Fred is not rich. Mary is either not old or not funny. | Alice is wise. | contradiction | (![X]:((funny(X)&~funny(X))=>~happy(X)))&
(![X]:((brave(X)<~>rich(X))<=>(brave(X)|~patient(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((~generous(X)|humble(X))=>(~generous(X)&old(X))))&
(![X]:((humble(X)|~funny(X))=>(~wise(X)|~funny(X))))&
(![X]:((happy(X)<~>~funny(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((~rich(X)&humble(X))<=>(~brave(X)|~curious(X))))&
(((generous(alice)<~>~tall(alice)))=>((creative(lucy)<~>~old(lucy))))&
(![X]:((calm(X)&~curious(X))<=>(strong(X)<~>happy(X))))&
(![X]:((humble(X)<~>~kind(X))=>(~happy(X)&strong(X))))&
((?[X]:((wise(X)|old(X))))=>(?[X]:((~old(X)&patient(X)))))&
(![X]:((~generous(X)&~tall(X))=>(~rich(X)&quiet(X))))&
((?[X]:((calm(X)|~quiet(X))))<=>(?[X]:(~calm(X))))&
(![X]:((happy(X)|quiet(X))<=>~happy(X)))&
(![X]:((happy(X)|old(X))=>(~brave(X)|~creative(X))))&
((?[X]:((~happy(X)&creative(X))))=>(?[X]:((wise(X)|~happy(X)))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:(old(X)))&
(?[X]:((~generous(X)<~>~patient(X))))&
(~kind(alice))&
((~calm(john)|~strong(john)))&
(?[X]:(~generous(X)))&
(~rich(fred))&
((~old(mary)<~>~funny(mary))) | wise(alice) | [
"p1",
"p4",
"p5",
"p6",
"p8",
"p9",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5320405072331567362598924
% SZS output start Proof for 5320405072331567362598924
2. ! [X0] : ((brave(X0) <~> rich(X0)) <=> (~patient(X0) | brave(X0))) [input p1]
5. ! [X0] : ((~funny(X0) | humble(X0)) => (~funny(X0) | ~wise(X0))) [input p4]
6. ! [X0] : ((happy(X0) <~> ~funny(X0)) <=> (~kind(X0) <~> ~rich(X0))) [input p5]
7. ! [X0] : ((humble(X0) & ~rich(X0)) <=> (~curious(X0) | ~brave(X0))) [input p6]
9. ! [X0] : ((~curious(X0) & calm(X0)) <=> (strong(X0) <~> happy(X0))) [input p8]
10. ! [X0] : ((humble(X0) <~> ~kind(X0)) => (strong(X0) & ~happy(X0))) [input p9]
14. ! [X0] : ((quiet(X0) | happy(X0)) <=> ~happy(X0)) [input p13]
20. ~kind(alice) [input p19]
25. wise(alice) [input hypothesis]
34. ! [X0] : ((~funny(X0) | ~wise(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 5]
35. ! [X0] : (~funny(X0) | ~wise(X0) | (funny(X0) & ~humble(X0))) [flattening 34]
37. ! [X0] : ((strong(X0) & ~happy(X0)) | (humble(X0) <=> ~kind(X0))) [ennf transformation 10]
44. ! [X0] : ((((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | (patient(X0) & ~brave(X0))) & ((~patient(X0) | brave(X0)) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0))))) [nnf transformation 2]
45. ! [X0] : ((((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | (patient(X0) & ~brave(X0))) & (~patient(X0) | brave(X0) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0))))) [flattening 44]
49. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [nnf transformation 6]
50. ! [X0] : (((humble(X0) & ~rich(X0)) | (curious(X0) & brave(X0))) & ((~curious(X0) | ~brave(X0)) | (~humble(X0) | rich(X0)))) [nnf transformation 7]
51. ! [X0] : (((humble(X0) & ~rich(X0)) | (curious(X0) & brave(X0))) & (~curious(X0) | ~brave(X0) | ~humble(X0) | rich(X0))) [flattening 50]
53. ! [X0] : (((~curious(X0) & calm(X0)) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) & (((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | (curious(X0) | ~calm(X0)))) [nnf transformation 9]
54. ! [X0] : (((~curious(X0) & calm(X0)) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) & (((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | curious(X0) | ~calm(X0))) [flattening 53]
55. ! [X0] : ((strong(X0) & ~happy(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) [nnf transformation 37]
64. ! [X0] : (((quiet(X0) | happy(X0)) | happy(X0)) & (~happy(X0) | (~quiet(X0) & ~happy(X0)))) [nnf transformation 14]
65. ! [X0] : ((quiet(X0) | happy(X0) | happy(X0)) & (~happy(X0) | (~quiet(X0) & ~happy(X0)))) [flattening 64]
84. ~rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 45]
91. ~wise(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 35]
96. kind(X0) | rich(X0) | happy(X0) | funny(X0) [cnf transformation 49]
102. ~rich(X0) | brave(X0) [cnf transformation 51]
105. curious(X0) | humble(X0) [cnf transformation 51]
114. ~strong(X0) | happy(X0) | ~curious(X0) [cnf transformation 54]
119. strong(X0) | humble(X0) | kind(X0) [cnf transformation 55]
129. ~happy(X0) | ~happy(X0) [cnf transformation 65]
139. ~kind(alice) [cnf transformation 20]
145. wise(alice) [cnf transformation 25]
146. ~happy(X0) [duplicate literal removal 129]
149. ~rich(X0) | ~brave(X0) [duplicate literal removal 84]
163. ~rich(X0) [subsumption resolution 102,149]
297. ~funny(alice) | ~humble(alice) [resolution 91,145]
299. 26 <=> humble(alice) [avatar definition]
303. 27 <=> funny(alice) [avatar definition]
305. ~funny(alice) <- (~27) [avatar component clause 303]
306. ~26 | ~27 [avatar split clause 297,303,299]
309. humble(X0) | kind(X0) | happy(X0) | ~curious(X0) [resolution 119,114]
311. humble(X0) | kind(X0) | ~curious(X0) [subsumption resolution 309,146]
312. kind(X0) | humble(X0) [subsumption resolution 311,105]
313. humble(alice) [resolution 312,139]
318. 26 [avatar split clause 313,299]
333. rich(alice) | happy(alice) | funny(alice) [resolution 96,139]
339. happy(alice) | funny(alice) [subsumption resolution 333,163]
340. funny(alice) [subsumption resolution 339,146]
341. $false <- (~27) [subsumption resolution 340,305]
342. 27 [avatar contradiction clause 341]
345. $false [avatar sat refutation 306,318,342]
% SZS output end Proof for 5320405072331567362598924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and not curious is not rich or not patient and vice versa.
Everyone who is either funny or tall is not calm or humble.
If someone is not rich then someone is wise or not rich.
If someone is happy or strong then mary is not tall or not generous.
Everyone who is either wise or not calm is not rich.
Everyone who is both patient and not patient is brave or funny and vice versa.
If someone is not wise then john is either not strong or humble.
Everyone who is either not humble or creative is both not happy and wise and vice versa.
Everyone who is either calm or generous is either not strong or strong and vice versa.
Everyone who is both strong and not kind is both not strong and generous.
If alice is not generous or not quiet then someone is both tall and not quiet.
Everyone who is not tall is old.
Everyone who is quiet or strong is either wise or not patient.
If mary is both tall and old then paul is not rich and vice versa.
Everyone who is rich is not rich.
Everyone who is happy or strong is both humble and kind and vice versa.
Someone is wise.
Lucy is both not creative and calm.
Someone is not tall.
Someone is not brave or not funny. | Alice is not calm. | neutral | (![X]:((~kind(X)&~curious(X))<=>(~rich(X)|~patient(X))))&
(![X]:((funny(X)<~>tall(X))=>(~calm(X)|humble(X))))&
((?[X]:(~rich(X)))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:((happy(X)|strong(X))))=>((~tall(mary)|~generous(mary))))&
(![X]:((wise(X)<~>~calm(X))=>~rich(X)))&
(![X]:((patient(X)&~patient(X))<=>(brave(X)|funny(X))))&
((?[X]:(~wise(X)))=>((~strong(john)<~>humble(john))))&
(![X]:((~humble(X)<~>creative(X))<=>(~happy(X)&wise(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((strong(X)&~kind(X))=>(~strong(X)&generous(X))))&
(((~generous(alice)|~quiet(alice)))=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:(~tall(X)=>old(X)))&
(![X]:((quiet(X)|strong(X))=>(wise(X)<~>~patient(X))))&
(((tall(mary)&old(mary)))<=>(~rich(paul)))&
(![X]:(rich(X)=>~rich(X)))&
(![X]:((happy(X)|strong(X))<=>(humble(X)&kind(X))))&
(?[X]:(wise(X)))&
((~creative(lucy)&calm(lucy)))&
(?[X]:(~tall(X)))&
(?[X]:((~brave(X)|~funny(X)))) | ~calm(alice) | [] | null | 0 |
Everyone who is not calm or brave is calm and vice versa.
If someone is both not curious and humble then lucy is not wise or rich.
Everyone who is quiet or not calm is not rich.
If fred is rich then someone is old or not kind and vice versa.
Everyone who is both creative and not kind is funny and vice versa.
If fred is both kind and not humble then someone is not creative or not funny.
Everyone who is not kind or generous is both not strong and not kind and vice versa.
If lucy is not strong or not tall then someone is happy and vice versa.
Everyone who is not wise or not brave is not strong or rich and vice versa.
If someone is patient or rich then someone is not creative or rich and vice versa.
If someone is patient or not strong then john is old and vice versa.
Everyone who is kind or not funny is not strong or not happy.
If someone is tall then someone is not kind or happy and vice versa.
If someone is both not curious and wise then lucy is both not calm and wise.
Everyone who is either curious or not brave is either not rich or not funny.
If mary is both quiet and old then alice is not curious or brave and vice versa.
Someone is old.
Fred is quiet or not funny.
Someone is both creative and not quiet.
Fred is either not kind or not creative.
Someone is happy or not rich.
Someone is humble. | Fred is generous. | contradiction | (![X]:((~calm(X)|brave(X))<=>calm(X)))&
((?[X]:((~curious(X)&humble(X))))=>((~wise(lucy)|rich(lucy))))&
(![X]:((quiet(X)|~calm(X))=>~rich(X)))&
((rich(fred))<=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((creative(X)&~kind(X))<=>funny(X)))&
(((kind(fred)&~humble(fred)))=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((~kind(X)|generous(X))<=>(~strong(X)&~kind(X))))&
(((~strong(lucy)|~tall(lucy)))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~strong(X)|rich(X))))&
((?[X]:((patient(X)|rich(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
((?[X]:((patient(X)|~strong(X))))<=>(old(john)))&
(![X]:((kind(X)|~funny(X))=>(~strong(X)|~happy(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~kind(X)|happy(X)))))&
((?[X]:((~curious(X)&wise(X))))=>((~calm(lucy)&wise(lucy))))&
(![X]:((curious(X)<~>~brave(X))=>(~rich(X)<~>~funny(X))))&
(((quiet(mary)&old(mary)))<=>((~curious(alice)|brave(alice))))&
(?[X]:(old(X)))&
((quiet(fred)|~funny(fred)))&
(?[X]:((creative(X)&~quiet(X))))&
((~kind(fred)<~>~creative(fred)))&
(?[X]:((happy(X)|~rich(X))))&
(?[X]:(humble(X))) | generous(fred) | [
"p2",
"p3",
"p4",
"p6",
"p16",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9143020024299798904527877
% SZS output start Proof for 9143020024299798904527877
3. ! [X0] : ((~calm(X0) | quiet(X0)) => ~rich(X0)) [input p2]
4. rich(fred) <=> ? [X0] : (~kind(X0) | old(X0)) [input p3]
5. ! [X0] : ((~kind(X0) & creative(X0)) <=> funny(X0)) [input p4]
7. ! [X0] : ((generous(X0) | ~kind(X0)) <=> (~kind(X0) & ~strong(X0))) [input p6]
17. ? [X0] : old(X0) [input p16]
18. ~funny(fred) | quiet(fred) [input p17]
20. ~kind(fred) <~> ~creative(fred) [input p19]
23. generous(fred) [input hypothesis]
28. ! [X0] : (~rich(X0) | (calm(X0) & ~quiet(X0))) [ennf transformation 3]
37. (rich(fred) | ! [X0] : (kind(X0) & ~old(X0))) & (? [X0] : (~kind(X0) | old(X0)) | ~rich(fred)) [nnf transformation 4]
38. (rich(fred) | ! [X0] : (kind(X0) & ~old(X0))) & (? [X1] : (~kind(X1) | old(X1)) | ~rich(fred)) [rectify 37]
39. ? [X1] : (~kind(X1) | old(X1)) => (~kind(sK0) | old(sK0)) [choice axiom]
40. (rich(fred) | ! [X0] : (kind(X0) & ~old(X0))) & ((~kind(sK0) | old(sK0)) | ~rich(fred)) [skolemisation 38,39]
41. ! [X0] : (((~kind(X0) & creative(X0)) | ~funny(X0)) & (funny(X0) | (kind(X0) | ~creative(X0)))) [nnf transformation 5]
42. ! [X0] : (((~kind(X0) & creative(X0)) | ~funny(X0)) & (funny(X0) | kind(X0) | ~creative(X0))) [flattening 41]
45. ! [X0] : (((generous(X0) | ~kind(X0)) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | (~generous(X0) & kind(X0)))) [nnf transformation 7]
46. ! [X0] : ((generous(X0) | ~kind(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | (~generous(X0) & kind(X0)))) [flattening 45]
71. ? [X0] : old(X0) => old(sK8) [choice axiom]
72. old(sK8) [skolemisation 17,71]
75. (creative(fred) | kind(fred)) & (~creative(fred) | ~kind(fred)) [nnf transformation 20]
84. ~quiet(X0) | ~rich(X0) [cnf transformation 28]
87. rich(fred) | ~old(X0) [cnf transformation 40]
89. ~creative(X0) | kind(X0) | funny(X0) [cnf transformation 42]
96. ~generous(X0) | ~kind(X0) [cnf transformation 46]
128. old(sK8) [cnf transformation 72]
129. ~funny(fred) | quiet(fred) [cnf transformation 18]
133. creative(fred) | kind(fred) [cnf transformation 75]
136. generous(fred) [cnf transformation 23]
155. 5 <=> rich(fred) [avatar definition]
157. rich(fred) <- (5) [avatar component clause 155]
160. 6 <=> ! [X0] : ~old(X0) [avatar definition]
161. ~old(X0) <- (6) [avatar component clause 160]
162. 6 | 5 [avatar split clause 87,155,160]
174. 9 <=> kind(fred) [avatar definition]
176. ~kind(fred) <- (~9) [avatar component clause 174]
298. 36 <=> quiet(fred) [avatar definition]
300. quiet(fred) <- (36) [avatar component clause 298]
302. 37 <=> funny(fred) [avatar definition]
305. 36 | ~37 [avatar split clause 129,302,298]
307. 38 <=> creative(fred) [avatar definition]
309. creative(fred) <- (38) [avatar component clause 307]
310. 9 | 38 [avatar split clause 133,307,174]
323. $false <- (6) [resolution 161,128]
324. ~6 [avatar contradiction clause 323]
329. ~kind(fred) [resolution 96,136]
332. ~9 [avatar split clause 329,174]
339. kind(fred) | funny(fred) <- (38) [resolution 89,309]
349. funny(fred) <- (~9, 38) [subsumption resolution 339,176]
352. 37 | 9 | ~38 [avatar split clause 349,307,174,302]
353. ~rich(fred) <- (36) [resolution 300,84]
354. $false <- (5, 36) [subsumption resolution 353,157]
355. ~5 | ~36 [avatar contradiction clause 354]
356. $false [avatar sat refutation 162,305,310,324,332,352,355]
% SZS output end Proof for 9143020024299798904527877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is both not strong and not happy. Everyone who is both brave and not rich is either wise or patient. Everyone who is both not quiet and strong is patient or not happy and vice versa. Everyone who is both brave and funny is strong. Everyone who is not patient or quiet is happy or patient. If someone is either not strong or brave then fred is patient or kind. If someone is not rich then someone is either curious or patient and vice versa. If someone is both not kind and curious then someone is both not happy and wise. Everyone who is not patient or not quiet is tall or not quiet and vice versa. If paul is either happy or not quiet then someone is not calm or not tall and vice versa. If someone is both tall and not kind then mary is both curious and not curious and vice versa. If someone is not wise or happy then lucy is not generous or not rich and vice versa. If lucy is calm then mary is both creative and wise. Everyone who is both generous and kind is patient. If fred is not quiet or not strong then someone is both brave and not generous. Someone is not calm or rich. Someone is either not tall or rich. Someone is both calm and humble. Susan is not creative or rich. Someone is not humble. Someone is both not humble and creative. Lucy is humble or not creative. Someone is either not strong or rich. | Mary is not kind. | neutral | (![X]:(happy(X)=>(~strong(X)&~happy(X))))&
(![X]:((brave(X)&~rich(X))=>(wise(X)<~>patient(X))))&
(![X]:((~quiet(X)&strong(X))<=>(patient(X)|~happy(X))))&
(![X]:((brave(X)&funny(X))=>strong(X)))&
(![X]:((~patient(X)|quiet(X))=>(happy(X)|patient(X))))&
((?[X]:((~strong(X)<~>brave(X))))=>((patient(fred)|kind(fred))))&
((?[X]:(~rich(X)))<=>(?[X]:((curious(X)<~>patient(X)))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(tall(X)|~quiet(X))))&
(((happy(paul)<~>~quiet(paul)))<=>(?[X]:((~calm(X)|~tall(X)))))&
((?[X]:((tall(X)&~kind(X))))<=>((curious(mary)&~curious(mary))))&
((?[X]:((~wise(X)|happy(X))))<=>((~generous(lucy)|~rich(lucy))))&
((calm(lucy))=>((creative(mary)&wise(mary))))&
(![X]:((generous(X)&kind(X))=>patient(X)))&
(((~quiet(fred)|~strong(fred)))=>(?[X]:((brave(X)&~generous(X)))))&
(?[X]:((~calm(X)|rich(X))))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((calm(X)&humble(X))))&
((~creative(susan)|rich(susan)))&
(?[X]:(~humble(X)))&
(?[X]:((~humble(X)&creative(X))))&
((humble(lucy)|~creative(lucy)))&
(?[X]:((~strong(X)<~>rich(X)))) | ~kind(mary) | [] | null | 0 |
Everyone who is old is both not curious and not old.
Everyone who is not happy is kind or not wise and vice versa.
If fred is either not tall or not funny then paul is either rich or humble and vice versa.
Everyone who is either generous or not creative is either not patient or creative and vice versa.
If someone is creative or not funny then someone is both not generous and humble.
If mary is either calm or old then someone is either patient or happy and vice versa.
If someone is both calm and not humble then someone is not rich or wise and vice versa.
If someone is generous or happy then someone is either not tall or creative and vice versa.
Everyone who is either generous or not kind is either not happy or happy and vice versa.
Everyone who is not kind is not happy and vice versa.
If mary is both funny and not generous then john is curious and vice versa.
Everyone who is not generous or not calm is not rich or not curious and vice versa.
Everyone who is either not humble or not strong is not generous or not kind.
Everyone who is not humble is either not creative or not funny.
If someone is either strong or humble then lucy is not curious or not rich and vice versa.
Everyone who is kind is generous and vice versa.
Someone is either not strong or not humble.
Someone is either not curious or funny.
John is not creative or not happy.
Paul is brave.
Mary is either kind or humble.
John is not generous. | Fred is rich. | neutral | (![X]:(old(X)=>(~curious(X)&~old(X))))&
(![X]:(~happy(X)<=>(kind(X)|~wise(X))))&
(((~tall(fred)<~>~funny(fred)))<=>((rich(paul)<~>humble(paul))))&
(![X]:((generous(X)<~>~creative(X))<=>(~patient(X)<~>creative(X))))&
((?[X]:((creative(X)|~funny(X))))=>(?[X]:((~generous(X)&humble(X)))))&
(((calm(mary)<~>old(mary)))<=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((generous(X)|happy(X))))<=>(?[X]:((~tall(X)<~>creative(X)))))&
(![X]:((generous(X)<~>~kind(X))<=>(~happy(X)<~>happy(X))))&
(![X]:(~kind(X)<=>~happy(X)))&
(((funny(mary)&~generous(mary)))<=>(curious(john)))&
(![X]:((~generous(X)|~calm(X))<=>(~rich(X)|~curious(X))))&
(![X]:((~humble(X)<~>~strong(X))=>(~generous(X)|~kind(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>~funny(X))))&
((?[X]:((strong(X)<~>humble(X))))<=>((~curious(lucy)|~rich(lucy))))&
(![X]:(kind(X)<=>generous(X)))&
(?[X]:((~strong(X)<~>~humble(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
((~creative(john)|~happy(john)))&
(brave(paul))&
((kind(mary)<~>humble(mary)))&
(~generous(john)) | rich(fred) | [] | null | 0 |
If someone is brave or not generous then fred is strong or not old. Everyone who is strong is both not creative and quiet and vice versa. Everyone who is either generous or rich is both quiet and not creative and vice versa. Everyone who is generous or not happy is not generous and vice versa. Everyone who is generous or strong is both not patient and quiet. Everyone who is both calm and not generous is funny or not curious and vice versa. Everyone who is not wise is either old or not creative. If someone is either not generous or strong then someone is both not creative and brave. If someone is not old or generous then someone is not brave or wise and vice versa. If someone is either rich or kind then paul is not calm or funny and vice versa. Everyone who is curious or strong is happy or quiet and vice versa. Everyone who is kind or not kind is not tall or not happy. Everyone who is both rich and not wise is both quiet and not strong and vice versa. Everyone who is both patient and funny is not creative or not strong and vice versa. Everyone who is not patient is not brave. Paul is either rich or not tall. Mary is calm. Someone is not creative. John is not creative or not kind. Someone is both kind and not tall. Susan is not tall or not calm. | John is patient. | entailment | ((?[X]:((brave(X)|~generous(X))))=>((strong(fred)|~old(fred))))&
(![X]:(strong(X)<=>(~creative(X)&quiet(X))))&
(![X]:((generous(X)<~>rich(X))<=>(quiet(X)&~creative(X))))&
(![X]:((generous(X)|~happy(X))<=>~generous(X)))&
(![X]:((generous(X)|strong(X))=>(~patient(X)&quiet(X))))&
(![X]:((calm(X)&~generous(X))<=>(funny(X)|~curious(X))))&
(![X]:(~wise(X)=>(old(X)<~>~creative(X))))&
((?[X]:((~generous(X)<~>strong(X))))=>(?[X]:((~creative(X)&brave(X)))))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((rich(X)<~>kind(X))))<=>((~calm(paul)|funny(paul))))&
(![X]:((curious(X)|strong(X))<=>(happy(X)|quiet(X))))&
(![X]:((kind(X)|~kind(X))=>(~tall(X)|~happy(X))))&
(![X]:((rich(X)&~wise(X))<=>(quiet(X)&~strong(X))))&
(![X]:((patient(X)&funny(X))<=>(~creative(X)|~strong(X))))&
(![X]:(~patient(X)=>~brave(X)))&
((rich(paul)<~>~tall(paul)))&
(calm(mary))&
(?[X]:(~creative(X)))&
((~creative(john)|~kind(john)))&
(?[X]:((kind(X)&~tall(X))))&
((~tall(susan)|~calm(susan))) | patient(john) | [
"p1",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3901677598444472386734
% SZS output start Proof for 3901677598444472386734
2. ! [X0] : (strong(X0) <=> (quiet(X0) & ~creative(X0))) [input p1]
5. ! [X0] : ((strong(X0) | generous(X0)) => (quiet(X0) & ~patient(X0))) [input p4]
14. ! [X0] : ((funny(X0) & patient(X0)) <=> (~strong(X0) | ~creative(X0))) [input p13]
22. ~patient(john) [input hypothesis]
27. ! [X0] : ((quiet(X0) & ~patient(X0)) | (~strong(X0) & ~generous(X0))) [ennf transformation 5]
33. ! [X0] : ((strong(X0) | (~quiet(X0) | creative(X0))) & ((quiet(X0) & ~creative(X0)) | ~strong(X0))) [nnf transformation 2]
34. ! [X0] : ((strong(X0) | ~quiet(X0) | creative(X0)) & ((quiet(X0) & ~creative(X0)) | ~strong(X0))) [flattening 33]
60. ! [X0] : (((funny(X0) & patient(X0)) | (strong(X0) & creative(X0))) & ((~strong(X0) | ~creative(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 14]
61. ! [X0] : (((funny(X0) & patient(X0)) | (strong(X0) & creative(X0))) & (~strong(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0))) [flattening 60]
69. ~creative(X0) | ~strong(X0) [cnf transformation 34]
82. ~patient(X0) | ~strong(X0) [cnf transformation 27]
117. patient(X0) | creative(X0) [cnf transformation 61]
118. patient(X0) | strong(X0) [cnf transformation 61]
130. ~patient(john) [cnf transformation 22]
250. creative(X0) | ~strong(X0) [resolution 117,82]
253. strong(john) [resolution 118,130]
260. ~strong(X0) [subsumption resolution 250,69]
264. $false [resolution 260,253]
% SZS output end Proof for 3901677598444472386734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either generous or rich then someone is calm or kind.
If someone is either not tall or not brave then someone is not old or calm.
If someone is both not happy and humble then someone is funny and vice versa.
Everyone who is kind or not quiet is calm and vice versa.
If someone is both calm and patient then paul is not rich.
Everyone who is both not tall and not quiet is tall or not curious.
If fred is both not creative and happy then someone is both rich and curious and vice versa.
If someone is creative then fred is quiet or not old and vice versa.
If alice is not patient then someone is not strong or strong.
If susan is old then fred is either not patient or not tall.
If paul is both not tall and not wise then someone is both wise and calm and vice versa.
Everyone who is either not strong or brave is funny or not brave and vice versa.
If susan is curious or kind then alice is either funny or happy and vice versa.
Everyone who is both not kind and brave is either quiet or brave and vice versa.
Everyone who is old or generous is both not brave and not calm.
If someone is not quiet then someone is not calm and vice versa.
Lucy is not wise.
John is either wise or not brave.
Someone is funny or wise.
Someone is both brave and calm.
Mary is curious.
Someone is both not funny and creative.
Lucy is either not tall or patient.
Paul is both brave and not tall. | Lucy is old. | contradiction | (((generous(fred)<~>rich(fred)))=>(?[X]:((calm(X)|kind(X)))))&
((?[X]:((~tall(X)<~>~brave(X))))=>(?[X]:((~old(X)|calm(X)))))&
((?[X]:((~happy(X)&humble(X))))<=>(?[X]:(funny(X))))&
(![X]:((kind(X)|~quiet(X))<=>calm(X)))&
((?[X]:((calm(X)&patient(X))))=>(~rich(paul)))&
(![X]:((~tall(X)&~quiet(X))=>(tall(X)|~curious(X))))&
(((~creative(fred)&happy(fred)))<=>(?[X]:((rich(X)&curious(X)))))&
((?[X]:(creative(X)))<=>((quiet(fred)|~old(fred))))&
((~patient(alice))=>(?[X]:((~strong(X)|strong(X)))))&
((old(susan))=>((~patient(fred)<~>~tall(fred))))&
(((~tall(paul)&~wise(paul)))<=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((~strong(X)<~>brave(X))<=>(funny(X)|~brave(X))))&
(((curious(susan)|kind(susan)))<=>((funny(alice)<~>happy(alice))))&
(![X]:((~kind(X)&brave(X))<=>(quiet(X)<~>brave(X))))&
(![X]:((old(X)|generous(X))=>(~brave(X)&~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(~calm(X))))&
(~wise(lucy))&
((wise(john)<~>~brave(john)))&
(?[X]:((funny(X)|wise(X))))&
(?[X]:((brave(X)&calm(X))))&
(curious(mary))&
(?[X]:((~funny(X)&creative(X))))&
((~tall(lucy)<~>patient(lucy)))&
((brave(paul)&~tall(paul))) | old(lucy) | [
"p3",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6042787635299374240650518
% SZS output start Proof for 6042787635299374240650518
4. ! [X0] : ((~quiet(X0) | kind(X0)) <=> calm(X0)) [input p3]
14. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (quiet(X0) <~> brave(X0))) [input p13]
15. ! [X0] : ((generous(X0) | old(X0)) => (~calm(X0) & ~brave(X0))) [input p14]
25. old(lucy) [input hypothesis]
36. ! [X0] : ((~calm(X0) & ~brave(X0)) | (~generous(X0) & ~old(X0))) [ennf transformation 15]
49. ! [X0] : (((~quiet(X0) | kind(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) & ~kind(X0)))) [nnf transformation 4]
50. ! [X0] : ((~quiet(X0) | kind(X0) | ~calm(X0)) & (calm(X0) | (quiet(X0) & ~kind(X0)))) [flattening 49]
73. ! [X0] : (((brave(X0) & ~kind(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (~brave(X0) | kind(X0)))) [nnf transformation 14]
74. ! [X0] : (((brave(X0) & ~kind(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ~brave(X0) | kind(X0))) [flattening 73]
95. ~kind(X0) | calm(X0) [cnf transformation 50]
96. quiet(X0) | calm(X0) [cnf transformation 50]
127. ~brave(X0) | ~quiet(X0) | ~brave(X0) | kind(X0) [cnf transformation 74]
130. brave(X0) | brave(X0) | ~quiet(X0) [cnf transformation 74]
134. ~old(X0) | ~calm(X0) [cnf transformation 36]
151. old(lucy) [cnf transformation 25]
152. ~brave(X0) | ~quiet(X0) | kind(X0) [duplicate literal removal 127]
153. ~quiet(X0) | brave(X0) [duplicate literal removal 130]
321. ~quiet(X0) | kind(X0) [subsumption resolution 152,153]
323. 37 <=> ! [X1] : calm(X1) [avatar definition]
324. calm(X1) <- (37) [avatar component clause 323]
374. ~calm(lucy) [resolution 134,151]
383. kind(X0) | calm(X0) [resolution 321,96]
384. calm(X0) [subsumption resolution 383,95]
385. 37 [avatar split clause 384,323]
388. $false <- (37) [resolution 324,374]
391. ~37 [avatar contradiction clause 388]
393. $false [avatar sat refutation 385,391]
% SZS output end Proof for 6042787635299374240650518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either not patient or strong and vice versa.
If paul is both kind and not tall then lucy is both not strong and rich and vice versa.
Everyone who is either old or not wise is either patient or rich and vice versa.
If someone is not funny or kind then john is both not quiet and calm and vice versa.
If paul is both not quiet and old then someone is not creative.
Everyone who is not wise or patient is both not brave and tall and vice versa.
If someone is not generous or not strong then john is either strong or tall.
If paul is not kind then someone is not happy or patient.
If someone is both quiet and not brave then someone is either calm or not calm and vice versa.
If someone is both not tall and not happy then someone is both strong and not brave.
Everyone who is both not tall and humble is not generous or not kind and vice versa.
If mary is not brave or tall then lucy is both not kind and not quiet and vice versa.
Everyone who is either wise or not strong is not calm or calm and vice versa.
If someone is both kind and not generous then someone is not tall or patient.
Everyone who is not brave is both strong and quiet and vice versa.
Everyone who is not creative is brave and vice versa.
Someone is either not brave or not calm.
Someone is not calm.
Mary is not brave or not tall.
Paul is either quiet or not happy.
John is not old.
Fred is not patient.
Mary is not kind or not happy.
Someone is not patient or not funny. | John is humble. | neutral | (![X]:(~wise(X)<=>(~patient(X)<~>strong(X))))&
(((kind(paul)&~tall(paul)))<=>((~strong(lucy)&rich(lucy))))&
(![X]:((old(X)<~>~wise(X))<=>(patient(X)<~>rich(X))))&
((?[X]:((~funny(X)|kind(X))))<=>((~quiet(john)&calm(john))))&
(((~quiet(paul)&old(paul)))=>(?[X]:(~creative(X))))&
(![X]:((~wise(X)|patient(X))<=>(~brave(X)&tall(X))))&
((?[X]:((~generous(X)|~strong(X))))=>((strong(john)<~>tall(john))))&
((~kind(paul))=>(?[X]:((~happy(X)|patient(X)))))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((calm(X)<~>~calm(X)))))&
((?[X]:((~tall(X)&~happy(X))))=>(?[X]:((strong(X)&~brave(X)))))&
(![X]:((~tall(X)&humble(X))<=>(~generous(X)|~kind(X))))&
(((~brave(mary)|tall(mary)))<=>((~kind(lucy)&~quiet(lucy))))&
(![X]:((wise(X)<~>~strong(X))<=>(~calm(X)|calm(X))))&
((?[X]:((kind(X)&~generous(X))))=>(?[X]:((~tall(X)|patient(X)))))&
(![X]:(~brave(X)<=>(strong(X)&quiet(X))))&
(![X]:(~creative(X)<=>brave(X)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:(~calm(X)))&
((~brave(mary)|~tall(mary)))&
((quiet(paul)<~>~happy(paul)))&
(~old(john))&
(~patient(fred))&
((~kind(mary)|~happy(mary)))&
(?[X]:((~patient(X)|~funny(X)))) | humble(john) | [] | null | 0 |
If susan is not tall then susan is both generous and funny.
Everyone who is either patient or not generous is not tall or not happy and vice versa.
If susan is either quiet or not strong then mary is either curious or not wise and vice versa.
Everyone who is either not tall or not creative is either creative or quiet and vice versa.
If someone is either not old or not calm then someone is not funny and vice versa.
Everyone who is not old or calm is humble.
Everyone who is not humble or tall is either rich or not creative and vice versa.
Everyone who is not humble or not funny is either wise or not funny.
Everyone who is curious or humble is both creative and quiet.
Everyone who is both not strong and happy is either not strong or not calm and vice versa.
If john is either not brave or not happy then someone is rich or funny and vice versa.
Everyone who is not rich is either not brave or wise and vice versa.
Everyone who is not happy is not old or not generous.
If someone is either not humble or not tall then someone is not calm or strong and vice versa.
If john is generous then someone is happy or not creative.
If someone is rich or not old then lucy is both not patient and not strong.
Someone is either not curious or curious.
Someone is calm.
Someone is not strong.
Lucy is old or not rich.
Someone is either not old or happy.
Someone is not old or old.
Someone is kind.
Someone is both strong and quiet. | Lucy is old. | entailment | ((~tall(susan))=>((generous(susan)&funny(susan))))&
(![X]:((patient(X)<~>~generous(X))<=>(~tall(X)|~happy(X))))&
(((quiet(susan)<~>~strong(susan)))<=>((curious(mary)<~>~wise(mary))))&
(![X]:((~tall(X)<~>~creative(X))<=>(creative(X)<~>quiet(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)|calm(X))=>humble(X)))&
(![X]:((~humble(X)|tall(X))<=>(rich(X)<~>~creative(X))))&
(![X]:((~humble(X)|~funny(X))=>(wise(X)<~>~funny(X))))&
(![X]:((curious(X)|humble(X))=>(creative(X)&quiet(X))))&
(![X]:((~strong(X)&happy(X))<=>(~strong(X)<~>~calm(X))))&
(((~brave(john)<~>~happy(john)))<=>(?[X]:((rich(X)|funny(X)))))&
(![X]:(~rich(X)<=>(~brave(X)<~>wise(X))))&
(![X]:(~happy(X)=>(~old(X)|~generous(X))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(?[X]:((~calm(X)|strong(X)))))&
((generous(john))=>(?[X]:((happy(X)|~creative(X)))))&
((?[X]:((rich(X)|~old(X))))=>((~patient(lucy)&~strong(lucy))))&
(?[X]:((~curious(X)<~>curious(X))))&
(?[X]:(calm(X)))&
(?[X]:(~strong(X)))&
((old(lucy)|~rich(lucy)))&
(?[X]:((~old(X)<~>happy(X))))&
(?[X]:((~old(X)|old(X))))&
(?[X]:(kind(X)))&
(?[X]:((strong(X)&quiet(X)))) | old(lucy) | [
"p3",
"p5",
"p6",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3629500970291725475139456
% SZS output start Proof for 3629500970291725475139456
4. ! [X0] : ((~tall(X0) <~> ~creative(X0)) <=> (creative(X0) <~> quiet(X0))) [input p3]
6. ! [X0] : ((calm(X0) | ~old(X0)) => humble(X0)) [input p5]
7. ! [X0] : ((tall(X0) | ~humble(X0)) <=> (rich(X0) <~> ~creative(X0))) [input p6]
9. ! [X0] : ((humble(X0) | curious(X0)) => (quiet(X0) & creative(X0))) [input p8]
20. ~rich(lucy) | old(lucy) [input p19]
25. ~old(lucy) [input hypothesis]
30. ! [X0] : (humble(X0) | (~calm(X0) & old(X0))) [ennf transformation 6]
32. ! [X0] : ((quiet(X0) & creative(X0)) | (~humble(X0) & ~curious(X0))) [ennf transformation 9]
40. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) & (((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [nnf transformation 4]
46. ! [X0] : (((tall(X0) | ~humble(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (~tall(X0) & humble(X0)))) [nnf transformation 7]
47. ! [X0] : ((tall(X0) | ~humble(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (~tall(X0) & humble(X0)))) [flattening 46]
95. ~quiet(X0) | ~creative(X0) | ~creative(X0) | tall(X0) [cnf transformation 40]
100. creative(X0) | tall(X0) | creative(X0) | ~quiet(X0) [cnf transformation 40]
105. humble(X0) | old(X0) [cnf transformation 30]
108. ~creative(X0) | rich(X0) | ~tall(X0) [cnf transformation 47]
118. ~humble(X0) | creative(X0) [cnf transformation 32]
120. ~humble(X0) | quiet(X0) [cnf transformation 32]
153. ~rich(lucy) | old(lucy) [cnf transformation 20]
159. ~old(lucy) [cnf transformation 25]
164. ~quiet(X0) | ~creative(X0) | tall(X0) [duplicate literal removal 95]
166. ~quiet(X0) | tall(X0) | creative(X0) [duplicate literal removal 100]
205. ~quiet(X0) | tall(X0) [subsumption resolution 164,166]
324. 34 <=> old(lucy) [avatar definition]
325. ~old(lucy) <- (~34) [avatar component clause 324]
328. 35 <=> rich(lucy) [avatar definition]
330. ~rich(lucy) <- (~35) [avatar component clause 328]
331. 34 | ~35 [avatar split clause 153,328,324]
342. ~34 [avatar split clause 159,324]
349. old(X0) | creative(X0) [resolution 118,105]
352. old(X0) | quiet(X0) [resolution 120,105]
548. creative(lucy) <- (~34) [resolution 349,325]
552. rich(lucy) | ~tall(lucy) <- (~34) [resolution 548,108]
554. ~tall(lucy) <- (~34, ~35) [subsumption resolution 552,330]
556. quiet(lucy) <- (~34) [resolution 352,325]
577. tall(lucy) <- (~34) [resolution 556,205]
578. $false <- (~34, ~35) [subsumption resolution 577,554]
579. 34 | 35 [avatar contradiction clause 578]
580. $false [avatar sat refutation 331,342,579]
% SZS output end Proof for 3629500970291725475139456
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not wise then paul is either patient or generous and vice versa. If mary is old then lucy is not happy or brave. Everyone who is tall or not old is not generous. Everyone who is both not curious and not wise is quiet or generous and vice versa. If fred is both patient and curious then someone is not funny. Everyone who is either brave or not kind is both not tall and generous. Everyone who is quiet or not generous is both rich and not kind. Everyone who is not funny is wise. If john is not brave or not generous then susan is both not creative and not funny and vice versa. Everyone who is both tall and not happy is rich and vice versa. If someone is not funny then fred is both not wise and not old. Everyone who is both curious and happy is both not tall and calm. If someone is not old then someone is either calm or happy and vice versa. If mary is not brave or not patient then alice is both tall and kind. Everyone who is not tall or happy is either tall or not wise. Everyone who is funny is both not calm and generous and vice versa. Lucy is either humble or rich. Someone is both not happy and not humble. Someone is generous. Someone is either wise or not creative. Someone is not brave or not rich. Someone is not tall or not happy. | Mary is calm. | contradiction | ((?[X]:((~happy(X)|~wise(X))))<=>((patient(paul)<~>generous(paul))))&
((old(mary))=>((~happy(lucy)|brave(lucy))))&
(![X]:((tall(X)|~old(X))=>~generous(X)))&
(![X]:((~curious(X)&~wise(X))<=>(quiet(X)|generous(X))))&
(((patient(fred)&curious(fred)))=>(?[X]:(~funny(X))))&
(![X]:((brave(X)<~>~kind(X))=>(~tall(X)&generous(X))))&
(![X]:((quiet(X)|~generous(X))=>(rich(X)&~kind(X))))&
(![X]:(~funny(X)=>wise(X)))&
(((~brave(john)|~generous(john)))<=>((~creative(susan)&~funny(susan))))&
(![X]:((tall(X)&~happy(X))<=>rich(X)))&
((?[X]:(~funny(X)))=>((~wise(fred)&~old(fred))))&
(![X]:((curious(X)&happy(X))=>(~tall(X)&calm(X))))&
((?[X]:(~old(X)))<=>(?[X]:((calm(X)<~>happy(X)))))&
(((~brave(mary)|~patient(mary)))=>((tall(alice)&kind(alice))))&
(![X]:((~tall(X)|happy(X))=>(tall(X)<~>~wise(X))))&
(![X]:(funny(X)<=>(~calm(X)&generous(X))))&
((humble(lucy)<~>rich(lucy)))&
(?[X]:((~happy(X)&~humble(X))))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~tall(X)|~happy(X)))) | calm(mary) | [
"p2",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8953944484340594466784328
% SZS output start Proof for 8953944484340594466784328
3. ! [X0] : ((~old(X0) | tall(X0)) => ~generous(X0)) [input p2]
8. ! [X0] : (~funny(X0) => wise(X0)) [input p7]
11. ? [X0] : ~funny(X0) => (~old(fred) & ~wise(fred)) [input p10]
16. ! [X0] : (funny(X0) <=> (generous(X0) & ~calm(X0))) [input p15]
23. calm(mary) [input hypothesis]
27. ! [X0] : (~generous(X0) | (old(X0) & ~tall(X0))) [ennf transformation 3]
32. ! [X0] : (wise(X0) | funny(X0)) [ennf transformation 8]
33. (~old(fred) & ~wise(fred)) | ! [X0] : funny(X0) [ennf transformation 11]
57. ! [X0] : ((funny(X0) | (~generous(X0) | calm(X0))) & ((generous(X0) & ~calm(X0)) | ~funny(X0))) [nnf transformation 16]
58. ! [X0] : ((funny(X0) | ~generous(X0) | calm(X0)) & ((generous(X0) & ~calm(X0)) | ~funny(X0))) [flattening 57]
79. ~generous(X0) | old(X0) [cnf transformation 27]
94. funny(X0) | wise(X0) [cnf transformation 32]
103. ~wise(fred) | funny(X0) [cnf transformation 33]
104. ~old(fred) | funny(X0) [cnf transformation 33]
119. ~calm(X0) | ~funny(X0) [cnf transformation 58]
120. ~funny(X0) | generous(X0) [cnf transformation 58]
131. calm(mary) [cnf transformation 23]
209. 17 <=> ! [X0] : funny(X0) [avatar definition]
210. funny(X0) <- (17) [avatar component clause 209]
212. 18 <=> old(fred) [avatar definition]
214. ~old(fred) <- (~18) [avatar component clause 212]
215. 17 | ~18 [avatar split clause 104,212,209]
217. 19 <=> wise(fred) [avatar definition]
219. ~wise(fred) <- (~19) [avatar component clause 217]
220. 17 | ~19 [avatar split clause 103,217,209]
324. ~funny(mary) [resolution 119,131]
325. $false <- (17) [subsumption resolution 324,210]
326. ~17 [avatar contradiction clause 325]
328. generous(X0) | wise(X0) [resolution 120,94]
463. old(X2) | wise(X2) [resolution 328,79]
567. wise(fred) <- (~18) [resolution 463,214]
569. $false <- (~18, ~19) [subsumption resolution 567,219]
570. 18 | 19 [avatar contradiction clause 569]
571. $false [avatar sat refutation 215,220,326,570]
% SZS output end Proof for 8953944484340594466784328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not old or old then someone is not kind or not calm. Everyone who is either brave or not strong is curious and vice versa. If paul is wise then someone is strong or old and vice versa. Everyone who is brave or happy is not kind and vice versa. Everyone who is rich or not calm is not generous. If lucy is not humble or not wise then fred is happy or not wise and vice versa. Everyone who is patient is either not generous or patient and vice versa. Everyone who is not funny is both not wise and rich and vice versa. If john is strong then someone is not calm and vice versa. If someone is both wise and old then someone is either not rich or humble and vice versa. Everyone who is both not funny and not wise is both not old and calm and vice versa. Everyone who is not creative or kind is either not creative or wise and vice versa. Everyone who is not quiet or strong is not kind and vice versa. Everyone who is either not brave or not humble is not brave. If paul is either creative or strong then lucy is both wise and not brave. If someone is not patient or calm then someone is funny and vice versa. Alice is not old or not tall. Mary is not curious or happy. Someone is both not kind and not brave. Someone is patient or quiet. Someone is not quiet or generous. Fred is either not curious or kind. Someone is both old and not brave. Alice is either not old or kind. | Lucy is happy. | contradiction | (((~old(alice)<~>old(alice)))=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>curious(X)))&
((wise(paul))<=>(?[X]:((strong(X)|old(X)))))&
(![X]:((brave(X)|happy(X))<=>~kind(X)))&
(![X]:((rich(X)|~calm(X))=>~generous(X)))&
(((~humble(lucy)|~wise(lucy)))<=>((happy(fred)|~wise(fred))))&
(![X]:(patient(X)<=>(~generous(X)<~>patient(X))))&
(![X]:(~funny(X)<=>(~wise(X)&rich(X))))&
((strong(john))<=>(?[X]:(~calm(X))))&
((?[X]:((wise(X)&old(X))))<=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~funny(X)&~wise(X))<=>(~old(X)&calm(X))))&
(![X]:((~creative(X)|kind(X))<=>(~creative(X)<~>wise(X))))&
(![X]:((~quiet(X)|strong(X))<=>~kind(X)))&
(![X]:((~brave(X)<~>~humble(X))=>~brave(X)))&
(((creative(paul)<~>strong(paul)))=>((wise(lucy)&~brave(lucy))))&
((?[X]:((~patient(X)|calm(X))))<=>(?[X]:(funny(X))))&
((~old(alice)|~tall(alice)))&
((~curious(mary)|happy(mary)))&
(?[X]:((~kind(X)&~brave(X))))&
(?[X]:((patient(X)|quiet(X))))&
(?[X]:((~quiet(X)|generous(X))))&
((~curious(fred)<~>kind(fred)))&
(?[X]:((old(X)&~brave(X))))&
((~old(alice)<~>kind(alice))) | happy(lucy) | [
"p2",
"p3",
"p11",
"p12",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1011893880110766304203359
% SZS output start Proof for 1011893880110766304203359
3. wise(paul) <=> ? [X0] : (old(X0) | strong(X0)) [input p2]
4. ! [X0] : ((happy(X0) | brave(X0)) <=> ~kind(X0)) [input p3]
12. ! [X0] : ((kind(X0) | ~creative(X0)) <=> (~creative(X0) <~> wise(X0))) [input p11]
13. ! [X0] : ((strong(X0) | ~quiet(X0)) <=> ~kind(X0)) [input p12]
15. (creative(paul) <~> strong(paul)) => (~brave(lucy) & wise(lucy)) [input p14]
23. ? [X0] : (~brave(X0) & old(X0)) [input p22]
25. happy(lucy) [input hypothesis]
32. (~brave(lucy) & wise(lucy)) | (creative(paul) <=> strong(paul)) [ennf transformation 15]
37. (wise(paul) | ! [X0] : (~old(X0) & ~strong(X0))) & (? [X0] : (old(X0) | strong(X0)) | ~wise(paul)) [nnf transformation 3]
38. (wise(paul) | ! [X0] : (~old(X0) & ~strong(X0))) & (? [X1] : (old(X1) | strong(X1)) | ~wise(paul)) [rectify 37]
39. ? [X1] : (old(X1) | strong(X1)) => (old(sK1) | strong(sK1)) [choice axiom]
40. (wise(paul) | ! [X0] : (~old(X0) & ~strong(X0))) & ((old(sK1) | strong(sK1)) | ~wise(paul)) [skolemisation 38,39]
41. ! [X0] : (((happy(X0) | brave(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) & ~brave(X0)))) [nnf transformation 4]
42. ! [X0] : ((happy(X0) | brave(X0) | kind(X0)) & (~kind(X0) | (~happy(X0) & ~brave(X0)))) [flattening 41]
59. ! [X0] : (((kind(X0) | ~creative(X0)) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (~kind(X0) & creative(X0)))) [nnf transformation 12]
60. ! [X0] : ((kind(X0) | ~creative(X0) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (~kind(X0) & creative(X0)))) [flattening 59]
61. ! [X0] : (((strong(X0) | ~quiet(X0)) | kind(X0)) & (~kind(X0) | (~strong(X0) & quiet(X0)))) [nnf transformation 13]
62. ! [X0] : ((strong(X0) | ~quiet(X0) | kind(X0)) & (~kind(X0) | (~strong(X0) & quiet(X0)))) [flattening 61]
64. (~brave(lucy) & wise(lucy)) | ((creative(paul) | ~strong(paul)) & (strong(paul) | ~creative(paul))) [nnf transformation 32]
77. ? [X0] : (~brave(X0) & old(X0)) => (~brave(sK10) & old(sK10)) [choice axiom]
78. ~brave(sK10) & old(sK10) [skolemisation 23,77]
88. wise(paul) | ~old(X0) [cnf transformation 40]
90. ~happy(X0) | ~kind(X0) [cnf transformation 42]
119. ~wise(X0) | creative(X0) | creative(X0) [cnf transformation 60]
122. kind(X0) | ~creative(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 60]
124. ~strong(X0) | ~kind(X0) [cnf transformation 62]
128. wise(lucy) | strong(paul) | ~creative(paul) [cnf transformation 64]
142. old(sK10) [cnf transformation 78]
146. happy(lucy) [cnf transformation 25]
148. ~wise(X0) | creative(X0) [duplicate literal removal 119]
149. ~creative(X0) | kind(X0) | ~wise(X0) [duplicate literal removal 122]
169. 4 <=> ! [X0] : ~old(X0) [avatar definition]
170. ~old(X0) <- (4) [avatar component clause 169]
172. 5 <=> wise(paul) [avatar definition]
174. wise(paul) <- (5) [avatar component clause 172]
175. 4 | 5 [avatar split clause 88,172,169]
198. 11 <=> wise(lucy) [avatar definition]
199. wise(lucy) <- (11) [avatar component clause 198]
257. 23 <=> strong(paul) [avatar definition]
258. strong(paul) <- (23) [avatar component clause 257]
261. 24 <=> creative(paul) [avatar definition]
263. creative(paul) <- (24) [avatar component clause 261]
271. ~24 | 23 | 11 [avatar split clause 128,198,257,261]
330. $false <- (4) [resolution 170,142]
331. ~4 [avatar contradiction clause 330]
336. ~kind(lucy) [resolution 90,146]
342. creative(paul) <- (5) [resolution 148,174]
345. 24 | ~5 [avatar split clause 342,172,261]
346. creative(lucy) <- (11) [resolution 199,148]
440. kind(paul) | ~wise(paul) <- (24) [resolution 149,263]
441. kind(lucy) | ~wise(lucy) <- (11) [resolution 149,346]
443. kind(paul) <- (5, 24) [subsumption resolution 440,174]
444. ~wise(lucy) <- (11) [subsumption resolution 441,336]
445. $false <- (11) [subsumption resolution 444,199]
446. ~11 [avatar contradiction clause 445]
449. ~kind(paul) <- (23) [resolution 258,124]
459. $false <- (5, 23, 24) [subsumption resolution 449,443]
460. ~5 | ~23 | ~24 [avatar contradiction clause 459]
461. $false [avatar sat refutation 175,271,331,345,446,460]
% SZS output end Proof for 1011893880110766304203359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and rich is not rich or old.
If lucy is wise then alice is both not strong and not happy.
Everyone who is not strong is generous and vice versa.
If lucy is old or creative then someone is both not creative and quiet and vice versa.
If alice is both old and brave then john is either tall or humble.
If fred is not patient or not strong then lucy is not patient and vice versa.
Everyone who is both not rich and not calm is both creative and patient and vice versa.
If someone is kind or old then someone is quiet or strong.
If lucy is not tall then someone is both quiet and old and vice versa.
Everyone who is both wise and humble is generous and vice versa.
Everyone who is either quiet or tall is both rich and kind and vice versa.
If someone is both not kind and rich then john is both tall and strong and vice versa.
Everyone who is not curious is either not curious or not generous and vice versa.
Everyone who is tall or not quiet is brave.
If someone is not calm or not patient then susan is generous or not old and vice versa.
Everyone who is quiet is patient or not kind and vice versa.
Someone is either strong or curious.
Alice is either tall or not calm.
Paul is quiet or not tall.
Someone is both not calm and brave.
Mary is both not old and happy.
Someone is either not patient or not calm.
Paul is either not old or rich.
Lucy is either old or not wise. | Alice is generous. | entailment | (![X]:((calm(X)&rich(X))=>(~rich(X)|old(X))))&
((wise(lucy))=>((~strong(alice)&~happy(alice))))&
(![X]:(~strong(X)<=>generous(X)))&
(((old(lucy)|creative(lucy)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(((old(alice)&brave(alice)))=>((tall(john)<~>humble(john))))&
(((~patient(fred)|~strong(fred)))<=>(~patient(lucy)))&
(![X]:((~rich(X)&~calm(X))<=>(creative(X)&patient(X))))&
((?[X]:((kind(X)|old(X))))=>(?[X]:((quiet(X)|strong(X)))))&
((~tall(lucy))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((wise(X)&humble(X))<=>generous(X)))&
(![X]:((quiet(X)<~>tall(X))<=>(rich(X)&kind(X))))&
((?[X]:((~kind(X)&rich(X))))<=>((tall(john)&strong(john))))&
(![X]:(~curious(X)<=>(~curious(X)<~>~generous(X))))&
(![X]:((tall(X)|~quiet(X))=>brave(X)))&
((?[X]:((~calm(X)|~patient(X))))<=>((generous(susan)|~old(susan))))&
(![X]:(quiet(X)<=>(patient(X)|~kind(X))))&
(?[X]:((strong(X)<~>curious(X))))&
((tall(alice)<~>~calm(alice)))&
((quiet(paul)|~tall(paul)))&
(?[X]:((~calm(X)&brave(X))))&
((~old(mary)&happy(mary)))&
(?[X]:((~patient(X)<~>~calm(X))))&
((~old(paul)<~>rich(paul)))&
((old(lucy)<~>~wise(lucy))) | generous(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6365404392902652406950140
% SZS output start Proof for 6365404392902652406950140
13. ! [X0] : (~curious(X0) <=> (~curious(X0) <~> ~generous(X0))) [input p12]
25. ~generous(alice) [input hypothesis]
61. ! [X0] : ((~curious(X0) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0)))) & (((generous(X0) | curious(X0)) & (~generous(X0) | ~curious(X0))) | curious(X0))) [nnf transformation 13]
118. generous(X0) | curious(X0) | curious(X0) [cnf transformation 61]
120. ~curious(X0) | ~curious(X0) | generous(X0) [cnf transformation 61]
145. ~generous(alice) [cnf transformation 25]
146. generous(X0) | curious(X0) [duplicate literal removal 118]
147. ~curious(X0) | generous(X0) [duplicate literal removal 120]
273. generous(X0) [subsumption resolution 146,147]
340. $false [subsumption resolution 145,273]
% SZS output end Proof for 6365404392902652406950140
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both creative and generous then susan is funny or creative and vice versa.
If paul is not funny then someone is both brave and not old and vice versa.
Everyone who is not strong or patient is either not generous or old.
If someone is humble or generous then someone is either not happy or calm and vice versa.
Everyone who is either not kind or rich is not strong or not rich.
Everyone who is curious or not curious is both not rich and humble.
Everyone who is not humble or creative is patient or creative.
If someone is either not creative or not wise then mary is either not rich or wise and vice versa.
Everyone who is either kind or not generous is both not brave and wise and vice versa.
Everyone who is either not rich or kind is either creative or not patient.
Everyone who is not humble or humble is generous or not strong and vice versa.
If alice is not creative or calm then someone is either strong or humble and vice versa.
Everyone who is both funny and calm is quiet.
Everyone who is patient is not tall or not wise.
If someone is not quiet or curious then mary is tall and vice versa.
If john is both not curious and not humble then paul is both patient and old and vice versa.
Someone is not tall.
Susan is not old.
John is not wise.
Someone is patient or brave.
Fred is not generous.
Someone is both not calm and curious.
Mary is either old or not curious. | Fred is not tall. | neutral | (((creative(paul)&generous(paul)))<=>((funny(susan)|creative(susan))))&
((~funny(paul))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((~strong(X)|patient(X))=>(~generous(X)<~>old(X))))&
((?[X]:((humble(X)|generous(X))))<=>(?[X]:((~happy(X)<~>calm(X)))))&
(![X]:((~kind(X)<~>rich(X))=>(~strong(X)|~rich(X))))&
(![X]:((curious(X)|~curious(X))=>(~rich(X)&humble(X))))&
(![X]:((~humble(X)|creative(X))=>(patient(X)|creative(X))))&
((?[X]:((~creative(X)<~>~wise(X))))<=>((~rich(mary)<~>wise(mary))))&
(![X]:((kind(X)<~>~generous(X))<=>(~brave(X)&wise(X))))&
(![X]:((~rich(X)<~>kind(X))=>(creative(X)<~>~patient(X))))&
(![X]:((~humble(X)|humble(X))<=>(generous(X)|~strong(X))))&
(((~creative(alice)|calm(alice)))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((funny(X)&calm(X))=>quiet(X)))&
(![X]:(patient(X)=>(~tall(X)|~wise(X))))&
((?[X]:((~quiet(X)|curious(X))))<=>(tall(mary)))&
(((~curious(john)&~humble(john)))<=>((patient(paul)&old(paul))))&
(?[X]:(~tall(X)))&
(~old(susan))&
(~wise(john))&
(?[X]:((patient(X)|brave(X))))&
(~generous(fred))&
(?[X]:((~calm(X)&curious(X))))&
((old(mary)<~>~curious(mary))) | ~tall(fred) | [] | null | 0 |
Everyone who is either brave or generous is either curious or quiet.
Everyone who is not funny or not curious is both not patient and creative and vice versa.
If alice is either brave or not quiet then fred is not tall.
If john is either not wise or calm then someone is humble.
If mary is both brave and not happy then someone is strong or calm.
If mary is tall or not funny then someone is both not kind and creative.
Everyone who is not rich or rich is not funny and vice versa.
If someone is both not patient and happy then fred is both humble and kind and vice versa.
If fred is not old then alice is both not curious and calm and vice versa.
If someone is both not calm and not generous then someone is either not humble or not quiet and vice versa.
Everyone who is both not strong and not tall is funny or not curious.
Everyone who is humble is generous.
If someone is happy or quiet then someone is not quiet.
Everyone who is not generous or happy is happy or quiet.
If lucy is not curious or not funny then someone is old.
If someone is not funny then someone is creative or generous and vice versa.
Someone is not patient.
Someone is both not curious and not kind.
Mary is not patient.
Someone is rich.
Someone is not creative or not kind.
Someone is strong.
Someone is either not brave or kind.
Alice is either generous or patient. | Alice is funny. | contradiction | (![X]:((brave(X)<~>generous(X))=>(curious(X)<~>quiet(X))))&
(![X]:((~funny(X)|~curious(X))<=>(~patient(X)&creative(X))))&
(((brave(alice)<~>~quiet(alice)))=>(~tall(fred)))&
(((~wise(john)<~>calm(john)))=>(?[X]:(humble(X))))&
(((brave(mary)&~happy(mary)))=>(?[X]:((strong(X)|calm(X)))))&
(((tall(mary)|~funny(mary)))=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((~rich(X)|rich(X))<=>~funny(X)))&
((?[X]:((~patient(X)&happy(X))))<=>((humble(fred)&kind(fred))))&
((~old(fred))<=>((~curious(alice)&calm(alice))))&
((?[X]:((~calm(X)&~generous(X))))<=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(![X]:((~strong(X)&~tall(X))=>(funny(X)|~curious(X))))&
(![X]:(humble(X)=>generous(X)))&
((?[X]:((happy(X)|quiet(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~generous(X)|happy(X))=>(happy(X)|quiet(X))))&
(((~curious(lucy)|~funny(lucy)))=>(?[X]:(old(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((creative(X)|generous(X)))))&
(?[X]:(~patient(X)))&
(?[X]:((~curious(X)&~kind(X))))&
(~patient(mary))&
(?[X]:(rich(X)))&
(?[X]:((~creative(X)|~kind(X))))&
(?[X]:(strong(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((generous(alice)<~>patient(alice))) | funny(alice) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6660205544275664998551033
% SZS output start Proof for 6660205544275664998551033
7. ! [X0] : ((rich(X0) | ~rich(X0)) <=> ~funny(X0)) [input p6]
25. funny(alice) [input hypothesis]
50. ! [X0] : (((rich(X0) | ~rich(X0)) | funny(X0)) & (~funny(X0) | (~rich(X0) & rich(X0)))) [nnf transformation 7]
51. ! [X0] : ((rich(X0) | ~rich(X0) | funny(X0)) & (~funny(X0) | (~rich(X0) & rich(X0)))) [flattening 50]
99. ~funny(X0) | rich(X0) [cnf transformation 51]
100. ~funny(X0) | ~rich(X0) [cnf transformation 51]
135. funny(alice) [cnf transformation 25]
164. ~funny(X0) [subsumption resolution 99,100]
286. $false [subsumption resolution 135,164]
% SZS output end Proof for 6660205544275664998551033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not funny then mary is both not patient and not calm. Everyone who is either kind or not quiet is either not brave or not kind and vice versa. If someone is both not humble and patient then someone is both not patient and not strong. Everyone who is not brave is not calm and vice versa. Everyone who is both not funny and not quiet is not calm. Everyone who is either wise or patient is both funny and not curious. Everyone who is not wise or not calm is not wise and vice versa. Everyone who is either not humble or old is either not curious or not generous and vice versa. If mary is either rich or not wise then paul is either strong or not generous and vice versa. If paul is both not generous and not brave then someone is not patient or not curious and vice versa. Everyone who is both not patient and calm is not calm or not old and vice versa. If paul is patient then john is not wise or not rich. Everyone who is either not kind or not quiet is either old or not tall. Everyone who is not happy is not strong and vice versa. Everyone who is not rich is old or not curious and vice versa. John is humble or calm. Lucy is either strong or calm. Someone is both patient and not generous. Someone is happy or curious. | Paul is not calm. | contradiction | ((~funny(paul))=>((~patient(mary)&~calm(mary))))&
(![X]:((kind(X)<~>~quiet(X))<=>(~brave(X)<~>~kind(X))))&
((?[X]:((~humble(X)&patient(X))))=>(?[X]:((~patient(X)&~strong(X)))))&
(![X]:(~brave(X)<=>~calm(X)))&
(![X]:((~funny(X)&~quiet(X))=>~calm(X)))&
(![X]:((wise(X)<~>patient(X))=>(funny(X)&~curious(X))))&
(![X]:((~wise(X)|~calm(X))<=>~wise(X)))&
(![X]:((~humble(X)<~>old(X))<=>(~curious(X)<~>~generous(X))))&
(((rich(mary)<~>~wise(mary)))<=>((strong(paul)<~>~generous(paul))))&
(((~generous(paul)&~brave(paul)))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((~patient(X)&calm(X))<=>(~calm(X)|~old(X))))&
((patient(paul))=>((~wise(john)|~rich(john))))&
(![X]:((~kind(X)<~>~quiet(X))=>(old(X)<~>~tall(X))))&
(![X]:(~happy(X)<=>~strong(X)))&
(![X]:(~rich(X)<=>(old(X)|~curious(X))))&
((humble(john)|calm(john)))&
((strong(lucy)<~>calm(lucy)))&
(?[X]:((patient(X)&~generous(X))))&
(?[X]:((happy(X)|curious(X)))) | ~calm(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1340302631767228670735437
% SZS output start Proof for 1340302631767228670735437
11. ! [X0] : ((calm(X0) & ~patient(X0)) <=> (~old(X0) | ~calm(X0))) [input p10]
20. ~calm(paul) [input hypothesis]
47. ! [X0] : (((calm(X0) & ~patient(X0)) | (old(X0) & calm(X0))) & ((~old(X0) | ~calm(X0)) | (~calm(X0) | patient(X0)))) [nnf transformation 11]
48. ! [X0] : (((calm(X0) & ~patient(X0)) | (old(X0) & calm(X0))) & (~old(X0) | ~calm(X0) | ~calm(X0) | patient(X0))) [flattening 47]
98. calm(X0) | calm(X0) [cnf transformation 48]
115. ~calm(paul) [cnf transformation 20]
117. calm(X0) [duplicate literal removal 98]
208. $false [subsumption resolution 115,117]
% SZS output end Proof for 1340302631767228670735437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and patient is happy or not brave. Everyone who is old or not strong is either not wise or curious and vice versa. Everyone who is old is both not kind and curious and vice versa. Everyone who is either curious or not rich is both curious and not tall and vice versa. Everyone who is brave is both humble and not creative. If someone is both wise and not generous then someone is both creative and rich and vice versa. Everyone who is not calm or not happy is both kind and patient and vice versa. If paul is either not calm or wise then someone is creative or wise and vice versa. If alice is happy or not patient then someone is humble. If susan is not creative or wise then someone is either brave or tall. Everyone who is not calm or not funny is humble or not tall. Everyone who is both not calm and strong is not patient and vice versa. Everyone who is both not brave and kind is not strong and vice versa. If someone is both patient and not generous then alice is patient. Everyone who is not wise or not quiet is both patient and happy and vice versa. Everyone who is either not creative or not rich is both not creative and not old and vice versa. Someone is not generous. Someone is creative. Someone is not generous or not rich. Someone is old. Someone is either kind or not calm. Susan is not rich or brave. Someone is both not quiet and happy. Someone is both happy and patient. | Alice is humble. | neutral | (![X]:((~creative(X)&patient(X))=>(happy(X)|~brave(X))))&
(![X]:((old(X)|~strong(X))<=>(~wise(X)<~>curious(X))))&
(![X]:(old(X)<=>(~kind(X)&curious(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(curious(X)&~tall(X))))&
(![X]:(brave(X)=>(humble(X)&~creative(X))))&
((?[X]:((wise(X)&~generous(X))))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((~calm(X)|~happy(X))<=>(kind(X)&patient(X))))&
(((~calm(paul)<~>wise(paul)))<=>(?[X]:((creative(X)|wise(X)))))&
(((happy(alice)|~patient(alice)))=>(?[X]:(humble(X))))&
(((~creative(susan)|wise(susan)))=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~calm(X)|~funny(X))=>(humble(X)|~tall(X))))&
(![X]:((~calm(X)&strong(X))<=>~patient(X)))&
(![X]:((~brave(X)&kind(X))<=>~strong(X)))&
((?[X]:((patient(X)&~generous(X))))=>(patient(alice)))&
(![X]:((~wise(X)|~quiet(X))<=>(patient(X)&happy(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~creative(X)&~old(X))))&
(?[X]:(~generous(X)))&
(?[X]:(creative(X)))&
(?[X]:((~generous(X)|~rich(X))))&
(?[X]:(old(X)))&
(?[X]:((kind(X)<~>~calm(X))))&
((~rich(susan)|brave(susan)))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:((happy(X)&patient(X)))) | humble(alice) | [] | null | 0 |
Everyone who is not humble is quiet or curious and vice versa.
If lucy is either tall or not kind then lucy is either not old or not kind and vice versa.
Everyone who is not rich or not brave is either brave or not tall.
Everyone who is both tall and not funny is either creative or not wise.
Everyone who is either not rich or generous is rich.
If paul is both not kind and funny then someone is creative or not patient.
Everyone who is not generous or not wise is both brave and not curious and vice versa.
Everyone who is both curious and kind is quiet or not patient and vice versa.
If alice is not curious or not kind then someone is both creative and humble.
Everyone who is either patient or happy is both not happy and not curious.
Everyone who is not generous is both not kind and generous and vice versa.
Everyone who is creative is either not old or curious and vice versa.
If someone is either not happy or rich then someone is calm.
Everyone who is not kind is not curious and vice versa.
Everyone who is either not patient or not brave is happy or not kind.
If lucy is either not happy or not brave then alice is not quiet or funny.
Lucy is both generous and happy.
Someone is both curious and not rich.
Someone is either not calm or not strong.
Someone is either creative or strong.
Someone is either not brave or generous.
Someone is either not creative or humble. | Paul is not old. | neutral | (![X]:(~humble(X)<=>(quiet(X)|curious(X))))&
(((tall(lucy)<~>~kind(lucy)))<=>((~old(lucy)<~>~kind(lucy))))&
(![X]:((~rich(X)|~brave(X))=>(brave(X)<~>~tall(X))))&
(![X]:((tall(X)&~funny(X))=>(creative(X)<~>~wise(X))))&
(![X]:((~rich(X)<~>generous(X))=>rich(X)))&
(((~kind(paul)&funny(paul)))=>(?[X]:((creative(X)|~patient(X)))))&
(![X]:((~generous(X)|~wise(X))<=>(brave(X)&~curious(X))))&
(![X]:((curious(X)&kind(X))<=>(quiet(X)|~patient(X))))&
(((~curious(alice)|~kind(alice)))=>(?[X]:((creative(X)&humble(X)))))&
(![X]:((patient(X)<~>happy(X))=>(~happy(X)&~curious(X))))&
(![X]:(~generous(X)<=>(~kind(X)&generous(X))))&
(![X]:(creative(X)<=>(~old(X)<~>curious(X))))&
((?[X]:((~happy(X)<~>rich(X))))=>(?[X]:(calm(X))))&
(![X]:(~kind(X)<=>~curious(X)))&
(![X]:((~patient(X)<~>~brave(X))=>(happy(X)|~kind(X))))&
(((~happy(lucy)<~>~brave(lucy)))=>((~quiet(alice)|funny(alice))))&
((generous(lucy)&happy(lucy)))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((~calm(X)<~>~strong(X))))&
(?[X]:((creative(X)<~>strong(X))))&
(?[X]:((~brave(X)<~>generous(X))))&
(?[X]:((~creative(X)<~>humble(X)))) | ~old(paul) | [] | null | 0 |
Everyone who is both happy and not humble is either not creative or not humble and vice versa.
Everyone who is happy is either funny or wise and vice versa.
Everyone who is not old is generous.
If paul is both not happy and not calm then someone is both tall and not happy.
Everyone who is old or not funny is either rich or happy and vice versa.
If fred is tall or old then someone is either quiet or not quiet.
Everyone who is either not wise or happy is not brave and vice versa.
If susan is not quiet then someone is either old or strong.
If someone is either tall or generous then alice is both not humble and not tall.
Everyone who is generous or not tall is kind and vice versa.
Everyone who is either not patient or not funny is both not tall and patient and vice versa.
If someone is either rich or patient then someone is either happy or not funny and vice versa.
Everyone who is not creative or old is both wise and funny.
If someone is funny or tall then lucy is both not tall and old.
Everyone who is both not calm and kind is tall.
Everyone who is both rich and not wise is not creative.
Someone is happy or not old.
John is humble.
Fred is generous or not quiet.
Someone is either generous or not kind. | Alice is happy. | entailment | (![X]:((happy(X)&~humble(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:(happy(X)<=>(funny(X)<~>wise(X))))&
(![X]:(~old(X)=>generous(X)))&
(((~happy(paul)&~calm(paul)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((old(X)|~funny(X))<=>(rich(X)<~>happy(X))))&
(((tall(fred)|old(fred)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>happy(X))<=>~brave(X)))&
((~quiet(susan))=>(?[X]:((old(X)<~>strong(X)))))&
((?[X]:((tall(X)<~>generous(X))))=>((~humble(alice)&~tall(alice))))&
(![X]:((generous(X)|~tall(X))<=>kind(X)))&
(![X]:((~patient(X)<~>~funny(X))<=>(~tall(X)&patient(X))))&
((?[X]:((rich(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>~funny(X)))))&
(![X]:((~creative(X)|old(X))=>(wise(X)&funny(X))))&
((?[X]:((funny(X)|tall(X))))=>((~tall(lucy)&old(lucy))))&
(![X]:((~calm(X)&kind(X))=>tall(X)))&
(![X]:((rich(X)&~wise(X))=>~creative(X)))&
(?[X]:((happy(X)|~old(X))))&
(humble(john))&
((generous(fred)|~quiet(fred)))&
(?[X]:((generous(X)<~>~kind(X)))) | happy(alice) | [
"p1",
"p4",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6616590659469084880789448
% SZS output start Proof for 6616590659469084880789448
2. ! [X0] : (happy(X0) <=> (funny(X0) <~> wise(X0))) [input p1]
5. ! [X0] : ((~funny(X0) | old(X0)) <=> (rich(X0) <~> happy(X0))) [input p4]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (patient(X0) & ~tall(X0))) [input p10]
13. ! [X0] : ((old(X0) | ~creative(X0)) => (funny(X0) & wise(X0))) [input p12]
14. ? [X0] : (tall(X0) | funny(X0)) => (old(lucy) & ~tall(lucy)) [input p13]
16. ! [X0] : ((~wise(X0) & rich(X0)) => ~creative(X0)) [input p15]
21. ~happy(alice) [input hypothesis]
29. ! [X0] : ((funny(X0) & wise(X0)) | (~old(X0) & creative(X0))) [ennf transformation 13]
30. (old(lucy) & ~tall(lucy)) | ! [X0] : (~tall(X0) & ~funny(X0)) [ennf transformation 14]
31. ! [X0] : (~creative(X0) | (wise(X0) | ~rich(X0))) [ennf transformation 16]
32. ! [X0] : (~creative(X0) | wise(X0) | ~rich(X0)) [flattening 31]
35. ! [X0] : ((happy(X0) | ((funny(X0) | ~wise(X0)) & (wise(X0) | ~funny(X0)))) & (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | ~happy(X0))) [nnf transformation 2]
36. ! [X0] : (((~funny(X0) | old(X0)) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (funny(X0) & ~old(X0)))) [nnf transformation 5]
37. ! [X0] : ((~funny(X0) | old(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (funny(X0) & ~old(X0)))) [flattening 36]
47. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (~patient(X0) | tall(X0))) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
48. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ~patient(X0) | tall(X0)) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [flattening 47]
65. ~happy(X0) | funny(X0) | wise(X0) [cnf transformation 35]
68. ~wise(X0) | funny(X0) | happy(X0) [cnf transformation 35]
71. rich(X0) | happy(X0) | funny(X0) [cnf transformation 37]
91. patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 48]
93. ~funny(X0) | ~patient(X0) | ~patient(X0) | tall(X0) [cnf transformation 48]
103. wise(X0) | creative(X0) [cnf transformation 29]
106. ~old(X0) | funny(X0) [cnf transformation 29]
107. ~tall(lucy) | ~funny(X0) [cnf transformation 30]
109. old(lucy) | ~funny(X0) [cnf transformation 30]
111. ~creative(X0) | wise(X0) | ~rich(X0) [cnf transformation 32]
117. ~happy(alice) [cnf transformation 21]
118. ~funny(X0) | patient(X0) [duplicate literal removal 91]
119. ~patient(X0) | ~funny(X0) | tall(X0) [duplicate literal removal 93]
195. 17 <=> old(lucy) [avatar definition]
197. old(lucy) <- (17) [avatar component clause 195]
200. 18 <=> ! [X0] : ~funny(X0) [avatar definition]
201. ~funny(X0) <- (18) [avatar component clause 200]
202. 18 | 17 [avatar split clause 109,195,200]
204. 19 <=> tall(lucy) [avatar definition]
206. ~tall(lucy) <- (~19) [avatar component clause 204]
208. 18 | ~19 [avatar split clause 107,204,200]
209. ~rich(X0) | wise(X0) [subsumption resolution 111,103]
243. funny(lucy) <- (17) [resolution 106,197]
247. patient(lucy) <- (17) [resolution 243,118]
282. happy(X0) | funny(X0) | wise(X0) [resolution 71,209]
284. wise(X0) | funny(X0) [subsumption resolution 282,65]
309. ~funny(lucy) | tall(lucy) <- (17) [resolution 119,247]
312. tall(lucy) <- (17) [subsumption resolution 309,243]
313. $false <- (17, ~19) [subsumption resolution 312,206]
314. ~17 | 19 [avatar contradiction clause 313]
334. funny(X0) | funny(X0) | happy(X0) [resolution 284,68]
336. funny(X0) | happy(X0) [duplicate literal removal 334]
337. happy(X0) <- (18) [subsumption resolution 336,201]
340. $false <- (18) [resolution 337,117]
343. ~18 [avatar contradiction clause 340]
344. $false [avatar sat refutation 202,208,314,343]
% SZS output end Proof for 6616590659469084880789448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not funny and not brave is not rich or not tall and vice versa.
If mary is not generous or strong then someone is either not creative or not brave and vice versa.
Everyone who is either generous or not curious is either not generous or strong.
Everyone who is either not wise or strong is not tall and vice versa.
If fred is either not humble or not rich then fred is not old or tall and vice versa.
If john is both not creative and not curious then someone is not calm or patient.
Everyone who is both not curious and not patient is old and vice versa.
Everyone who is humble or not funny is both wise and funny.
If someone is not calm then someone is not tall and vice versa.
If someone is not curious or not happy then someone is either not tall or not kind and vice versa.
Everyone who is curious is not strong and vice versa.
If fred is not kind then susan is not wise.
If susan is both not old and not generous then paul is patient or not patient and vice versa.
If someone is either wise or not generous then someone is both not rich and creative and vice versa.
Everyone who is generous is both not calm and not brave and vice versa.
If someone is both creative and not creative then paul is not creative or calm.
Someone is not funny or quiet.
Someone is either not wise or not happy. | Susan is not patient. | neutral | (![X]:((~funny(X)&~brave(X))<=>(~rich(X)|~tall(X))))&
(((~generous(mary)|strong(mary)))<=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((generous(X)<~>~curious(X))=>(~generous(X)<~>strong(X))))&
(![X]:((~wise(X)<~>strong(X))<=>~tall(X)))&
(((~humble(fred)<~>~rich(fred)))<=>((~old(fred)|tall(fred))))&
(((~creative(john)&~curious(john)))=>(?[X]:((~calm(X)|patient(X)))))&
(![X]:((~curious(X)&~patient(X))<=>old(X)))&
(![X]:((humble(X)|~funny(X))=>(wise(X)&funny(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~tall(X))))&
((?[X]:((~curious(X)|~happy(X))))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
(![X]:(curious(X)<=>~strong(X)))&
((~kind(fred))=>(~wise(susan)))&
(((~old(susan)&~generous(susan)))<=>((patient(paul)|~patient(paul))))&
((?[X]:((wise(X)<~>~generous(X))))<=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:(generous(X)<=>(~calm(X)&~brave(X))))&
((?[X]:((creative(X)&~creative(X))))=>((~creative(paul)|calm(paul))))&
(?[X]:((~funny(X)|quiet(X))))&
(?[X]:((~wise(X)<~>~happy(X)))) | ~patient(susan) | [] | null | 0 |
Everyone who is either rich or curious is old and vice versa.
If susan is brave or creative then john is not funny.
If someone is not old then alice is both not happy and not patient and vice versa.
Everyone who is not tall is either not generous or not patient and vice versa.
If fred is both tall and old then someone is both patient and wise and vice versa.
If someone is both not old and old then lucy is both not rich and not creative and vice versa.
If susan is both not tall and brave then lucy is not happy or not brave and vice versa.
Everyone who is both brave and old is happy or creative and vice versa.
If someone is not wise or not tall then lucy is not quiet or not tall and vice versa.
Everyone who is both creative and patient is either not wise or not tall and vice versa.
If paul is both quiet and not generous then someone is either not rich or not humble and vice versa.
Everyone who is either not happy or not quiet is not curious and vice versa.
Everyone who is either humble or kind is either quiet or not happy.
If someone is curious then susan is not old or not kind and vice versa.
Everyone who is both creative and rich is either generous or old.
If lucy is both not wise and not brave then alice is not calm.
Susan is both not curious and humble.
Alice is funny or not curious.
Someone is creative or old.
Fred is either funny or not rich.
Someone is both humble and funny.
Someone is not generous.
Fred is creative.
Mary is not creative. | Lucy is not creative. | neutral | (![X]:((rich(X)<~>curious(X))<=>old(X)))&
(((brave(susan)|creative(susan)))=>(~funny(john)))&
((?[X]:(~old(X)))<=>((~happy(alice)&~patient(alice))))&
(![X]:(~tall(X)<=>(~generous(X)<~>~patient(X))))&
(((tall(fred)&old(fred)))<=>(?[X]:((patient(X)&wise(X)))))&
((?[X]:((~old(X)&old(X))))<=>((~rich(lucy)&~creative(lucy))))&
(((~tall(susan)&brave(susan)))<=>((~happy(lucy)|~brave(lucy))))&
(![X]:((brave(X)&old(X))<=>(happy(X)|creative(X))))&
((?[X]:((~wise(X)|~tall(X))))<=>((~quiet(lucy)|~tall(lucy))))&
(![X]:((creative(X)&patient(X))<=>(~wise(X)<~>~tall(X))))&
(((quiet(paul)&~generous(paul)))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~happy(X)<~>~quiet(X))<=>~curious(X)))&
(![X]:((humble(X)<~>kind(X))=>(quiet(X)<~>~happy(X))))&
((?[X]:(curious(X)))<=>((~old(susan)|~kind(susan))))&
(![X]:((creative(X)&rich(X))=>(generous(X)<~>old(X))))&
(((~wise(lucy)&~brave(lucy)))=>(~calm(alice)))&
((~curious(susan)&humble(susan)))&
((funny(alice)|~curious(alice)))&
(?[X]:((creative(X)|old(X))))&
((funny(fred)<~>~rich(fred)))&
(?[X]:((humble(X)&funny(X))))&
(?[X]:(~generous(X)))&
(creative(fred))&
(~creative(mary)) | ~creative(lucy) | [] | null | 0 |
If someone is happy then someone is both not happy and not patient and vice versa.
Everyone who is not old or not patient is not strong.
If susan is either not kind or quiet then alice is both not wise and patient.
If someone is wise then susan is either wise or happy and vice versa.
Everyone who is not old or not creative is not happy or not brave.
If someone is creative then lucy is not generous or not creative and vice versa.
If someone is quiet then someone is humble or not humble and vice versa.
Everyone who is both creative and generous is either quiet or kind and vice versa.
Everyone who is both not rich and not patient is either not brave or quiet and vice versa.
Everyone who is not humble is not funny.
If someone is either not happy or patient then john is both tall and generous and vice versa.
Everyone who is both tall and not happy is either brave or not funny and vice versa.
Everyone who is either not patient or creative is both happy and not humble.
If someone is both patient and kind then susan is both curious and not patient and vice versa.
If someone is humble then alice is patient or quiet.
Everyone who is not tall or not generous is not generous or funny and vice versa.
Susan is wise or brave.
Someone is either kind or not kind.
Someone is both tall and calm.
Someone is either strong or not calm.
John is strong or not generous.
Fred is both not tall and not patient.
Someone is generous or funny.
Someone is wise or brave. | John is not funny. | entailment | ((?[X]:(happy(X)))<=>(?[X]:((~happy(X)&~patient(X)))))&
(![X]:((~old(X)|~patient(X))=>~strong(X)))&
(((~kind(susan)<~>quiet(susan)))=>((~wise(alice)&patient(alice))))&
((?[X]:(wise(X)))<=>((wise(susan)<~>happy(susan))))&
(![X]:((~old(X)|~creative(X))=>(~happy(X)|~brave(X))))&
((?[X]:(creative(X)))<=>((~generous(lucy)|~creative(lucy))))&
((?[X]:(quiet(X)))<=>(?[X]:((humble(X)|~humble(X)))))&
(![X]:((creative(X)&generous(X))<=>(quiet(X)<~>kind(X))))&
(![X]:((~rich(X)&~patient(X))<=>(~brave(X)<~>quiet(X))))&
(![X]:(~humble(X)=>~funny(X)))&
((?[X]:((~happy(X)<~>patient(X))))<=>((tall(john)&generous(john))))&
(![X]:((tall(X)&~happy(X))<=>(brave(X)<~>~funny(X))))&
(![X]:((~patient(X)<~>creative(X))=>(happy(X)&~humble(X))))&
((?[X]:((patient(X)&kind(X))))<=>((curious(susan)&~patient(susan))))&
((?[X]:(humble(X)))=>((patient(alice)|quiet(alice))))&
(![X]:((~tall(X)|~generous(X))<=>(~generous(X)|funny(X))))&
((wise(susan)|brave(susan)))&
(?[X]:((kind(X)<~>~kind(X))))&
(?[X]:((tall(X)&calm(X))))&
(?[X]:((strong(X)<~>~calm(X))))&
((strong(john)|~generous(john)))&
((~tall(fred)&~patient(fred)))&
(?[X]:((generous(X)|funny(X))))&
(?[X]:((wise(X)|brave(X)))) | ~funny(john) | [
"p0",
"p5",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 806896672236124424976471
% SZS output start Proof for 806896672236124424976471
1. ? [X0] : happy(X0) <=> ? [X0] : (~patient(X0) & ~happy(X0)) [input p0]
6. ? [X0] : creative(X0) <=> (~creative(lucy) | ~generous(lucy)) [input p5]
11. ? [X0] : (~happy(X0) <~> patient(X0)) <=> (generous(john) & tall(john)) [input p10]
13. ! [X0] : ((~patient(X0) <~> creative(X0)) => (~humble(X0) & happy(X0))) [input p12]
16. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (funny(X0) | ~generous(X0))) [input p15]
25. funny(john) [input hypothesis]
26. ? [X0] : happy(X0) <=> ? [X1] : (~patient(X1) & ~happy(X1)) [rectify 1]
35. ! [X0] : ((~humble(X0) & happy(X0)) | (~patient(X0) <=> creative(X0))) [ennf transformation 13]
38. (? [X0] : happy(X0) | ! [X1] : (patient(X1) | happy(X1))) & (? [X1] : (~patient(X1) & ~happy(X1)) | ! [X0] : ~happy(X0)) [nnf transformation 26]
39. (? [X0] : happy(X0) | ! [X1] : (patient(X1) | happy(X1))) & (? [X2] : (~patient(X2) & ~happy(X2)) | ! [X3] : ~happy(X3)) [rectify 38]
40. ? [X0] : happy(X0) => happy(sK0) [choice axiom]
41. ? [X2] : (~patient(X2) & ~happy(X2)) => (~patient(sK1) & ~happy(sK1)) [choice axiom]
42. (happy(sK0) | ! [X1] : (patient(X1) | happy(X1))) & ((~patient(sK1) & ~happy(sK1)) | ! [X3] : ~happy(X3)) [skolemisation 39,41,40]
48. (? [X0] : creative(X0) | (creative(lucy) & generous(lucy))) & ((~creative(lucy) | ~generous(lucy)) | ! [X0] : ~creative(X0)) [nnf transformation 6]
49. (? [X0] : creative(X0) | (creative(lucy) & generous(lucy))) & (~creative(lucy) | ~generous(lucy) | ! [X0] : ~creative(X0)) [flattening 48]
50. (? [X0] : creative(X0) | (creative(lucy) & generous(lucy))) & (~creative(lucy) | ~generous(lucy) | ! [X1] : ~creative(X1)) [rectify 49]
51. ? [X0] : creative(X0) => creative(sK3) [choice axiom]
52. (creative(sK3) | (creative(lucy) & generous(lucy))) & (~creative(lucy) | ~generous(lucy) | ! [X1] : ~creative(X1)) [skolemisation 50,51]
62. (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | (~generous(john) | ~tall(john))) & ((generous(john) & tall(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) [nnf transformation 11]
63. (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ~generous(john) | ~tall(john)) & ((generous(john) & tall(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) [flattening 62]
64. (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ~generous(john) | ~tall(john)) & ((generous(john) & tall(john)) | ! [X1] : ((~happy(X1) | ~patient(X1)) & (patient(X1) | happy(X1)))) [rectify 63]
65. ? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) => ((~patient(sK6) | happy(sK6)) & (patient(sK6) | ~happy(sK6))) [choice axiom]
66. (((~patient(sK6) | happy(sK6)) & (patient(sK6) | ~happy(sK6))) | ~generous(john) | ~tall(john)) & ((generous(john) & tall(john)) | ! [X1] : ((~happy(X1) | ~patient(X1)) & (patient(X1) | happy(X1)))) [skolemisation 64,65]
69. ! [X0] : ((~humble(X0) & happy(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) [nnf transformation 35]
75. ! [X0] : (((~generous(X0) | ~tall(X0)) | (~funny(X0) & generous(X0))) & ((funny(X0) | ~generous(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 16]
76. ! [X0] : ((~generous(X0) | ~tall(X0) | (~funny(X0) & generous(X0))) & (funny(X0) | ~generous(X0) | (generous(X0) & tall(X0)))) [flattening 75]
89. ~happy(sK1) | ~happy(X3) [cnf transformation 42]
90. ~patient(sK1) | ~happy(X3) [cnf transformation 42]
102. ~creative(lucy) | ~generous(lucy) | ~creative(X1) [cnf transformation 52]
103. creative(sK3) | generous(lucy) [cnf transformation 52]
104. creative(sK3) | creative(lucy) [cnf transformation 52]
121. tall(john) | patient(X1) | happy(X1) [cnf transformation 66]
123. generous(john) | patient(X1) | happy(X1) [cnf transformation 66]
134. ~creative(X0) | ~patient(X0) | happy(X0) [cnf transformation 69]
145. ~tall(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 76]
158. funny(john) [cnf transformation 25]
160. 1 <=> ! [X1] : (patient(X1) | happy(X1)) [avatar definition]
161. patient(X1) | happy(X1) <- (1) [avatar component clause 160]
168. 3 <=> ! [X3] : ~happy(X3) [avatar definition]
169. ~happy(X3) <- (3) [avatar component clause 168]
171. 4 <=> patient(sK1) [avatar definition]
173. ~patient(sK1) <- (~4) [avatar component clause 171]
174. 3 | ~4 [avatar split clause 90,171,168]
176. 5 <=> happy(sK1) [avatar definition]
178. ~happy(sK1) <- (~5) [avatar component clause 176]
179. 3 | ~5 [avatar split clause 89,176,168]
220. 14 <=> creative(lucy) [avatar definition]
222. creative(lucy) <- (14) [avatar component clause 220]
224. 15 <=> creative(sK3) [avatar definition]
226. creative(sK3) <- (15) [avatar component clause 224]
227. 14 | 15 [avatar split clause 104,224,220]
229. 16 <=> generous(lucy) [avatar definition]
232. 16 | 15 [avatar split clause 103,224,229]
234. 17 <=> ! [X1] : ~creative(X1) [avatar definition]
235. ~creative(X1) <- (17) [avatar component clause 234]
236. 17 | ~16 | ~14 [avatar split clause 102,220,229,234]
250. 21 <=> tall(john) [avatar definition]
251. tall(john) <- (21) [avatar component clause 250]
254. 22 <=> generous(john) [avatar definition]
271. 1 | 22 [avatar split clause 123,254,160]
273. 1 | 21 [avatar split clause 121,250,160]
459. ~patient(sK3) | happy(sK3) <- (15) [resolution 134,226]
464. 58 <=> happy(sK3) [avatar definition]
466. happy(sK3) <- (58) [avatar component clause 464]
468. 59 <=> patient(sK3) [avatar definition]
470. ~patient(sK3) <- (~59) [avatar component clause 468]
471. 58 | ~59 | ~15 [avatar split clause 459,224,468,464]
487. ~generous(john) | ~funny(john) <- (21) [resolution 145,251]
504. ~generous(john) <- (21) [subsumption resolution 487,158]
505. ~22 | ~21 [avatar split clause 504,250,254]
509. happy(sK1) <- (1, ~4) [resolution 161,173]
510. happy(sK3) <- (1, ~59) [resolution 161,470]
514. $false <- (1, ~4, ~5) [subsumption resolution 509,178]
515. ~1 | 4 | 5 [avatar contradiction clause 514]
516. 58 | ~1 | 59 [avatar split clause 510,468,160,464]
582. $false <- (3, 58) [resolution 466,169]
584. ~3 | ~58 [avatar contradiction clause 582]
594. $false <- (14, 17) [subsumption resolution 222,235]
595. ~14 | ~17 [avatar contradiction clause 594]
596. $false [avatar sat refutation 174,179,227,232,236,271,273,471,505,515,516,584,595]
% SZS output end Proof for 806896672236124424976471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or calm is creative or happy.
Everyone who is either old or not generous is not tall or not rich.
If paul is both brave and not generous then john is not curious and vice versa.
If someone is not funny then mary is not generous or not curious.
If someone is brave or not quiet then fred is both not patient and not happy and vice versa.
Everyone who is rich or not old is both not wise and not strong.
Everyone who is either not patient or kind is not creative or not generous and vice versa.
Everyone who is either not kind or kind is both not rich and not wise.
Everyone who is both not humble and kind is quiet or not patient.
If alice is both not brave and creative then alice is not calm and vice versa.
Everyone who is either patient or not kind is either calm or not wise.
If someone is strong then susan is generous or creative and vice versa.
Everyone who is either not happy or happy is not strong or patient and vice versa.
If mary is rich or not wise then someone is both not humble and curious and vice versa.
Everyone who is both funny and patient is not rich and vice versa.
Everyone who is wise or not patient is either kind or not strong and vice versa.
Fred is either generous or brave.
Someone is either not wise or not patient.
Someone is either not curious or not funny.
John is calm or strong. | John is generous. | entailment | (![X]:((old(X)<~>calm(X))=>(creative(X)|happy(X))))&
(![X]:((old(X)<~>~generous(X))=>(~tall(X)|~rich(X))))&
(((brave(paul)&~generous(paul)))<=>(~curious(john)))&
((?[X]:(~funny(X)))=>((~generous(mary)|~curious(mary))))&
((?[X]:((brave(X)|~quiet(X))))<=>((~patient(fred)&~happy(fred))))&
(![X]:((rich(X)|~old(X))=>(~wise(X)&~strong(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~creative(X)|~generous(X))))&
(![X]:((~kind(X)<~>kind(X))=>(~rich(X)&~wise(X))))&
(![X]:((~humble(X)&kind(X))=>(quiet(X)|~patient(X))))&
(((~brave(alice)&creative(alice)))<=>(~calm(alice)))&
(![X]:((patient(X)<~>~kind(X))=>(calm(X)<~>~wise(X))))&
((?[X]:(strong(X)))<=>((generous(susan)|creative(susan))))&
(![X]:((~happy(X)<~>happy(X))<=>(~strong(X)|patient(X))))&
(((rich(mary)|~wise(mary)))<=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((funny(X)&patient(X))<=>~rich(X)))&
(![X]:((wise(X)|~patient(X))<=>(kind(X)<~>~strong(X))))&
((generous(fred)<~>brave(fred)))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
((calm(john)|strong(john))) | generous(john) | [
"p6",
"p7",
"p10",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 365277182428038905534739
% SZS output start Proof for 365277182428038905534739
7. ! [X0] : ((~patient(X0) <~> kind(X0)) <=> (~generous(X0) | ~creative(X0))) [input p6]
8. ! [X0] : ((~kind(X0) <~> kind(X0)) => (~wise(X0) & ~rich(X0))) [input p7]
11. ! [X0] : ((patient(X0) <~> ~kind(X0)) => (calm(X0) <~> ~wise(X0))) [input p10]
15. ! [X0] : ((patient(X0) & funny(X0)) <=> ~rich(X0)) [input p14]
16. ! [X0] : ((~patient(X0) | wise(X0)) <=> (kind(X0) <~> ~strong(X0))) [input p15]
20. strong(john) | calm(john) [input p19]
21. ~generous(john) [input hypothesis]
28. ! [X0] : ((~wise(X0) & ~rich(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 8]
31. ! [X0] : ((calm(X0) <~> ~wise(X0)) | (patient(X0) <=> ~kind(X0))) [ennf transformation 11]
40. ! [X0] : ((((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | (generous(X0) & creative(X0))) & ((~generous(X0) | ~creative(X0)) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0))))) [nnf transformation 7]
41. ! [X0] : ((((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | (generous(X0) & creative(X0))) & (~generous(X0) | ~creative(X0) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0))))) [flattening 40]
42. ! [X0] : ((~wise(X0) & ~rich(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 28]
45. ! [X0] : (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) [nnf transformation 31]
58. ! [X0] : (((patient(X0) & funny(X0)) | rich(X0)) & (~rich(X0) | (~patient(X0) | ~funny(X0)))) [nnf transformation 15]
59. ! [X0] : (((patient(X0) & funny(X0)) | rich(X0)) & (~rich(X0) | ~patient(X0) | ~funny(X0))) [flattening 58]
60. ! [X0] : (((~patient(X0) | wise(X0)) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0)))) & (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (patient(X0) & ~wise(X0)))) [nnf transformation 16]
61. ! [X0] : ((~patient(X0) | wise(X0) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0)))) & (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (patient(X0) & ~wise(X0)))) [flattening 60]
87. ~patient(X0) | kind(X0) | generous(X0) [cnf transformation 41]
90. ~rich(X0) | kind(X0) | kind(X0) [cnf transformation 42]
91. ~rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
92. ~wise(X0) | kind(X0) | kind(X0) [cnf transformation 42]
93. ~wise(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
100. wise(X0) | ~calm(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 45]
118. patient(X0) | rich(X0) [cnf transformation 59]
123. ~patient(X0) | wise(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 61]
124. ~patient(X0) | wise(X0) | kind(X0) | strong(X0) [cnf transformation 61]
131. strong(john) | calm(john) [cnf transformation 20]
132. ~generous(john) [cnf transformation 21]
135. ~rich(X0) | kind(X0) [duplicate literal removal 90]
136. ~kind(X0) | ~rich(X0) [duplicate literal removal 91]
137. ~wise(X0) | kind(X0) [duplicate literal removal 92]
138. ~kind(X0) | ~wise(X0) [duplicate literal removal 93]
193. ~wise(X0) [subsumption resolution 137,138]
194. ~rich(X0) [subsumption resolution 135,136]
211. ~kind(X0) | ~calm(X0) | ~patient(X0) [subsumption resolution 100,193]
233. patient(X0) [subsumption resolution 118,194]
236. wise(X0) | kind(X0) | strong(X0) [subsumption resolution 124,233]
237. kind(X0) | strong(X0) [subsumption resolution 236,193]
238. wise(X0) | ~strong(X0) | ~kind(X0) [subsumption resolution 123,233]
239. ~kind(X0) | ~strong(X0) [subsumption resolution 238,193]
261. 24 <=> calm(john) [avatar definition]
263. calm(john) <- (24) [avatar component clause 261]
265. 25 <=> strong(john) [avatar definition]
267. strong(john) <- (25) [avatar component clause 265]
268. 24 | 25 [avatar split clause 131,265,261]
287. kind(X0) | generous(X0) [resolution 87,233]
288. ~strong(X0) | generous(X0) [resolution 287,239]
306. ~calm(X2) | ~patient(X2) | strong(X2) [resolution 211,237]
309. ~calm(X2) | strong(X2) [subsumption resolution 306,233]
311. strong(john) <- (24) [resolution 309,263]
312. 25 | ~24 [avatar split clause 311,261,265]
313. generous(john) <- (25) [resolution 267,288]
319. $false <- (25) [subsumption resolution 313,132]
320. ~25 [avatar contradiction clause 319]
321. $false [avatar sat refutation 268,312,320]
% SZS output end Proof for 365277182428038905534739
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient then someone is not creative.
Everyone who is either not old or tall is both not quiet and not humble and vice versa.
If susan is either not strong or not calm then susan is either strong or brave and vice versa.
If someone is both patient and not quiet then someone is either not quiet or brave and vice versa.
Everyone who is not old is either not rich or not creative.
If john is either not wise or patient then john is both not calm and generous and vice versa.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
Alice is either quiet or not happy.
Susan is either strong or not generous.
Someone is happy.
Lucy is generous or not brave.
Susan is not creative. | John is not humble. | contradiction | ((?[X]:(patient(X)))=>(?[X]:(~creative(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~quiet(X)&~humble(X))))&
(((~strong(susan)<~>~calm(susan)))<=>((strong(susan)<~>brave(susan))))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
(![X]:(~old(X)=>(~rich(X)<~>~creative(X))))&
(((~wise(john)<~>patient(john)))<=>((~calm(john)&generous(john))))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((quiet(alice)<~>~happy(alice)))&
((strong(susan)<~>~generous(susan)))&
(?[X]:(happy(X)))&
((generous(lucy)|~brave(lucy)))&
(~creative(susan)) | ~humble(john) | [
"p1",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7794122492662900403575772
% SZS output start Proof for 7794122492662900403575772
2. ! [X0] : ((~old(X0) <~> tall(X0)) <=> (~humble(X0) & ~quiet(X0))) [input p1]
10. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p9]
13. ! [X0] : ((~patient(X0) & ~quiet(X0)) => (old(X0) & ~tall(X0))) [input p12]
21. ~humble(john) [input hypothesis]
30. ! [X0] : ((old(X0) & ~tall(X0)) | (patient(X0) | quiet(X0))) [ennf transformation 13]
31. ! [X0] : ((old(X0) & ~tall(X0)) | patient(X0) | quiet(X0)) [flattening 30]
36. ! [X0] : ((((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | (humble(X0) | quiet(X0))) & ((~humble(X0) & ~quiet(X0)) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))))) [nnf transformation 2]
37. ! [X0] : ((((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | humble(X0) | quiet(X0)) & ((~humble(X0) & ~quiet(X0)) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))))) [flattening 36]
58. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 10]
59. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 58]
75. ~old(X0) | tall(X0) | humble(X0) | quiet(X0) [cnf transformation 37]
110. ~patient(X0) | ~patient(X0) [cnf transformation 59]
112. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 59]
116. ~tall(X0) | patient(X0) | quiet(X0) [cnf transformation 31]
117. old(X0) | patient(X0) | quiet(X0) [cnf transformation 31]
133. ~humble(john) [cnf transformation 21]
134. ~patient(X0) [duplicate literal removal 110]
135. ~quiet(X0) | patient(X0) [duplicate literal removal 112]
141. 1 <=> ! [X1] : ~patient(X1) [avatar definition]
142. ~patient(X1) <- (1) [avatar component clause 141]
259. 1 [avatar split clause 134,141]
283. old(X0) | patient(X0) [subsumption resolution 117,135]
284. ~tall(X0) | patient(X0) [subsumption resolution 116,135]
360. tall(X0) | humble(X0) | quiet(X0) | patient(X0) [resolution 75,283]
374. humble(X0) | tall(X0) | quiet(X0) <- (1) [subsumption resolution 360,142]
390. tall(john) | quiet(john) <- (1) [resolution 374,133]
396. 42 <=> quiet(john) [avatar definition]
398. quiet(john) <- (42) [avatar component clause 396]
400. 43 <=> tall(john) [avatar definition]
402. tall(john) <- (43) [avatar component clause 400]
403. 42 | 43 | ~1 [avatar split clause 390,141,400,396]
451. patient(john) <- (42) [resolution 398,135]
459. $false <- (1, 42) [subsumption resolution 451,142]
460. ~1 | ~42 [avatar contradiction clause 459]
469. patient(john) <- (43) [resolution 402,284]
474. $false <- (1, 43) [subsumption resolution 469,142]
475. ~1 | ~43 [avatar contradiction clause 474]
476. $false [avatar sat refutation 259,403,460,475]
% SZS output end Proof for 7794122492662900403575772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not calm is not quiet or not humble. If someone is either not rich or strong then susan is not generous and vice versa. Everyone who is both not curious and strong is both not creative and not quiet. Everyone who is both happy and not happy is not rich or curious and vice versa. If john is happy or not old then someone is tall. If someone is either quiet or rich then fred is either not humble or not kind. If alice is humble then someone is either funny or not brave and vice versa. Everyone who is quiet or not patient is not wise or not old and vice versa. If lucy is either brave or funny then someone is not wise or patient. If someone is either tall or not patient then someone is rich. If mary is both curious and creative then lucy is creative and vice versa. Everyone who is both kind and not humble is strong or patient and vice versa. If someone is either calm or brave then alice is both not kind and humble and vice versa. If lucy is both not wise and not kind then someone is both strong and patient. If paul is either not quiet or patient then someone is either not tall or not old. If alice is not old or not rich then someone is both not patient and not brave. Someone is not quiet or brave. Someone is not tall. Someone is either not rich or brave. Someone is both wise and creative. Someone is not brave. Mary is not strong. Someone is not curious or not quiet. Alice is either not curious or not rich. | Susan is not rich. | contradiction | (![X]:((humble(X)&~calm(X))=>(~quiet(X)|~humble(X))))&
((?[X]:((~rich(X)<~>strong(X))))<=>(~generous(susan)))&
(![X]:((~curious(X)&strong(X))=>(~creative(X)&~quiet(X))))&
(![X]:((happy(X)&~happy(X))<=>(~rich(X)|curious(X))))&
(((happy(john)|~old(john)))=>(?[X]:(tall(X))))&
((?[X]:((quiet(X)<~>rich(X))))=>((~humble(fred)<~>~kind(fred))))&
((humble(alice))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:((quiet(X)|~patient(X))<=>(~wise(X)|~old(X))))&
(((brave(lucy)<~>funny(lucy)))=>(?[X]:((~wise(X)|patient(X)))))&
((?[X]:((tall(X)<~>~patient(X))))=>(?[X]:(rich(X))))&
(((curious(mary)&creative(mary)))<=>(creative(lucy)))&
(![X]:((kind(X)&~humble(X))<=>(strong(X)|patient(X))))&
((?[X]:((calm(X)<~>brave(X))))<=>((~kind(alice)&humble(alice))))&
(((~wise(lucy)&~kind(lucy)))=>(?[X]:((strong(X)&patient(X)))))&
(((~quiet(paul)<~>patient(paul)))=>(?[X]:((~tall(X)<~>~old(X)))))&
(((~old(alice)|~rich(alice)))=>(?[X]:((~patient(X)&~brave(X)))))&
(?[X]:((~quiet(X)|brave(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:((wise(X)&creative(X))))&
(?[X]:(~brave(X)))&
(~strong(mary))&
(?[X]:((~curious(X)|~quiet(X))))&
((~curious(alice)<~>~rich(alice))) | ~rich(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8665385206198221610777657
% SZS output start Proof for 8665385206198221610777657
4. ! [X0] : ((~happy(X0) & happy(X0)) <=> (curious(X0) | ~rich(X0))) [input p3]
25. ~rich(susan) [input hypothesis]
43. ! [X0] : (((~happy(X0) & happy(X0)) | (~curious(X0) & rich(X0))) & ((curious(X0) | ~rich(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 4]
44. ! [X0] : (((~happy(X0) & happy(X0)) | (~curious(X0) & rich(X0))) & (curious(X0) | ~rich(X0) | happy(X0) | ~happy(X0))) [flattening 43]
99. happy(X0) | rich(X0) [cnf transformation 44]
101. ~happy(X0) | rich(X0) [cnf transformation 44]
156. ~rich(susan) [cnf transformation 25]
181. rich(X0) [subsumption resolution 99,101]
348. $false [subsumption resolution 156,181]
% SZS output end Proof for 8665385206198221610777657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or curious is humble. Everyone who is either humble or creative is creative and vice versa. Everyone who is not old is rich. If someone is either curious or tall then john is either rich or kind. Everyone who is not quiet or not tall is both old and wise and vice versa. Everyone who is both not brave and old is not humble and vice versa. Everyone who is both old and brave is funny or not strong. If someone is brave then susan is either strong or wise and vice versa. If mary is not brave or not happy then susan is curious. Everyone who is not kind is not creative or not patient and vice versa. If someone is both not calm and not brave then someone is kind and vice versa. If someone is either strong or not old then susan is funny or not calm and vice versa. Everyone who is either not tall or old is both funny and calm. If someone is wise then lucy is not funny or rich and vice versa. Everyone who is kind is not funny and vice versa. Everyone who is either not kind or not creative is happy or old. Mary is both kind and rich. Paul is not strong or not tall. Susan is both not generous and not strong. Someone is either not brave or not tall. Mary is happy or old. Lucy is not brave. Someone is creative or brave. John is either calm or generous. | Susan is not tall. | contradiction | (![X]:((old(X)<~>curious(X))=>humble(X)))&
(![X]:((humble(X)<~>creative(X))<=>creative(X)))&
(![X]:(~old(X)=>rich(X)))&
((?[X]:((curious(X)<~>tall(X))))=>((rich(john)<~>kind(john))))&
(![X]:((~quiet(X)|~tall(X))<=>(old(X)&wise(X))))&
(![X]:((~brave(X)&old(X))<=>~humble(X)))&
(![X]:((old(X)&brave(X))=>(funny(X)|~strong(X))))&
((?[X]:(brave(X)))<=>((strong(susan)<~>wise(susan))))&
(((~brave(mary)|~happy(mary)))=>(curious(susan)))&
(![X]:(~kind(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((~calm(X)&~brave(X))))<=>(?[X]:(kind(X))))&
((?[X]:((strong(X)<~>~old(X))))<=>((funny(susan)|~calm(susan))))&
(![X]:((~tall(X)<~>old(X))=>(funny(X)&calm(X))))&
((?[X]:(wise(X)))<=>((~funny(lucy)|rich(lucy))))&
(![X]:(kind(X)<=>~funny(X)))&
(![X]:((~kind(X)<~>~creative(X))=>(happy(X)|old(X))))&
((kind(mary)&rich(mary)))&
((~strong(paul)|~tall(paul)))&
((~generous(susan)&~strong(susan)))&
(?[X]:((~brave(X)<~>~tall(X))))&
((happy(mary)|old(mary)))&
(~brave(lucy))&
(?[X]:((creative(X)|brave(X))))&
((calm(john)<~>generous(john))) | ~tall(susan) | [
"p1",
"p4",
"p5",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3060714274092357584517984
% SZS output start Proof for 3060714274092357584517984
2. ! [X0] : ((humble(X0) <~> creative(X0)) <=> creative(X0)) [input p1]
5. ! [X0] : ((~tall(X0) | ~quiet(X0)) <=> (wise(X0) & old(X0))) [input p4]
6. ! [X0] : ((old(X0) & ~brave(X0)) <=> ~humble(X0)) [input p5]
8. ? [X0] : brave(X0) <=> (strong(susan) <~> wise(susan)) [input p7]
19. ~strong(susan) & ~generous(susan) [input p18]
25. ~tall(susan) [input hypothesis]
38. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | ~creative(X0)) & (creative(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [nnf transformation 2]
40. ! [X0] : (((~tall(X0) | ~quiet(X0)) | (~wise(X0) | ~old(X0))) & ((wise(X0) & old(X0)) | (tall(X0) & quiet(X0)))) [nnf transformation 5]
41. ! [X0] : ((~tall(X0) | ~quiet(X0) | ~wise(X0) | ~old(X0)) & ((wise(X0) & old(X0)) | (tall(X0) & quiet(X0)))) [flattening 40]
42. ! [X0] : (((old(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | (~old(X0) | brave(X0)))) [nnf transformation 6]
43. ! [X0] : (((old(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | ~old(X0) | brave(X0))) [flattening 42]
44. (? [X0] : brave(X0) | ((strong(susan) | ~wise(susan)) & (wise(susan) | ~strong(susan)))) & (((~wise(susan) | ~strong(susan)) & (wise(susan) | strong(susan))) | ! [X0] : ~brave(X0)) [nnf transformation 8]
45. (? [X0] : brave(X0) | ((strong(susan) | ~wise(susan)) & (wise(susan) | ~strong(susan)))) & (((~wise(susan) | ~strong(susan)) & (wise(susan) | strong(susan))) | ! [X1] : ~brave(X1)) [rectify 44]
46. ? [X0] : brave(X0) => brave(sK0) [choice axiom]
47. (brave(sK0) | ((strong(susan) | ~wise(susan)) & (wise(susan) | ~strong(susan)))) & (((~wise(susan) | ~strong(susan)) & (wise(susan) | strong(susan))) | ! [X1] : ~brave(X1)) [skolemisation 45,46]
75. creative(X0) | creative(X0) | ~humble(X0) [cnf transformation 38]
78. ~creative(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 38]
87. wise(X0) | tall(X0) [cnf transformation 41]
90. ~brave(X0) | humble(X0) [cnf transformation 43]
96. brave(sK0) | strong(susan) | ~wise(susan) [cnf transformation 47]
123. ~strong(susan) [cnf transformation 19]
130. ~tall(susan) [cnf transformation 25]
131. creative(X0) | ~humble(X0) [duplicate literal removal 75]
132. ~creative(X0) | ~humble(X0) [duplicate literal removal 78]
133. ~humble(X0) [subsumption resolution 131,132]
153. ~brave(X0) [subsumption resolution 90,133]
154. strong(susan) | ~wise(susan) [subsumption resolution 96,153]
156. 5 <=> wise(susan) [avatar definition]
158. ~wise(susan) <- (~5) [avatar component clause 156]
160. 6 <=> strong(susan) [avatar definition]
163. ~5 | 6 [avatar split clause 154,160,156]
234. ~6 [avatar split clause 123,160]
253. tall(susan) <- (~5) [resolution 87,158]
254. $false <- (~5) [subsumption resolution 253,130]
255. 5 [avatar contradiction clause 254]
256. $false [avatar sat refutation 163,234,255]
% SZS output end Proof for 3060714274092357584517984
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not tall or not old then alice is both not curious and tall.
Everyone who is not wise is quiet or humble and vice versa.
Everyone who is both not wise and not creative is both not happy and not old.
Everyone who is not quiet is both rich and quiet and vice versa.
Everyone who is brave or rich is humble.
Everyone who is quiet or rich is not funny and vice versa.
Everyone who is not brave is both creative and kind.
If lucy is not humble or not rich then someone is generous or patient and vice versa.
Everyone who is calm or generous is either quiet or patient and vice versa.
Everyone who is both old and patient is not old and vice versa.
Everyone who is not brave is humble or strong.
If paul is strong then alice is both not generous and not old and vice versa.
If alice is happy or brave then someone is both not brave and kind.
Everyone who is either not curious or rich is both not tall and not happy and vice versa.
Alice is not curious or not strong.
Someone is either not generous or strong.
Someone is either old or kind.
Someone is happy.
John is not generous or not curious. | Lucy is not happy. | neutral | (((~tall(lucy)<~>~old(lucy)))=>((~curious(alice)&tall(alice))))&
(![X]:(~wise(X)<=>(quiet(X)|humble(X))))&
(![X]:((~wise(X)&~creative(X))=>(~happy(X)&~old(X))))&
(![X]:(~quiet(X)<=>(rich(X)&quiet(X))))&
(![X]:((brave(X)|rich(X))=>humble(X)))&
(![X]:((quiet(X)|rich(X))<=>~funny(X)))&
(![X]:(~brave(X)=>(creative(X)&kind(X))))&
(((~humble(lucy)|~rich(lucy)))<=>(?[X]:((generous(X)|patient(X)))))&
(![X]:((calm(X)|generous(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((old(X)&patient(X))<=>~old(X)))&
(![X]:(~brave(X)=>(humble(X)|strong(X))))&
((strong(paul))<=>((~generous(alice)&~old(alice))))&
(((happy(alice)|brave(alice)))=>(?[X]:((~brave(X)&kind(X)))))&
(![X]:((~curious(X)<~>rich(X))<=>(~tall(X)&~happy(X))))&
((~curious(alice)|~strong(alice)))&
(?[X]:((~generous(X)<~>strong(X))))&
(?[X]:((old(X)<~>kind(X))))&
(?[X]:(happy(X)))&
((~generous(john)|~curious(john))) | ~happy(lucy) | [] | null | 0 |
If alice is either not happy or kind then alice is both not happy and strong. Everyone who is both not generous and not quiet is both tall and not generous and vice versa. If paul is both not calm and funny then someone is not creative and vice versa. Everyone who is not wise or not funny is either tall or not happy. If susan is not kind or calm then someone is strong or tall. Everyone who is both not funny and curious is calm. If mary is both not patient and not rich then someone is not brave and vice versa. Everyone who is quiet or generous is not strong. If paul is strong or calm then someone is either not happy or not creative. If mary is strong then someone is both not generous and generous. Everyone who is both not strong and patient is not happy. Everyone who is either kind or curious is not rich or not curious and vice versa. If susan is not old or generous then susan is both not quiet and happy. If lucy is not patient then paul is not humble or generous and vice versa. Everyone who is either not quiet or creative is old and vice versa. Everyone who is both tall and patient is brave or not generous and vice versa. Lucy is both not funny and humble. Paul is both not funny and humble. Someone is curious or not quiet. John is either happy or humble. Alice is generous or tall. Someone is not patient or old. Alice is either old or brave. | Mary is patient. | neutral | (((~happy(alice)<~>kind(alice)))=>((~happy(alice)&strong(alice))))&
(![X]:((~generous(X)&~quiet(X))<=>(tall(X)&~generous(X))))&
(((~calm(paul)&funny(paul)))<=>(?[X]:(~creative(X))))&
(![X]:((~wise(X)|~funny(X))=>(tall(X)<~>~happy(X))))&
(((~kind(susan)|calm(susan)))=>(?[X]:((strong(X)|tall(X)))))&
(![X]:((~funny(X)&curious(X))=>calm(X)))&
(((~patient(mary)&~rich(mary)))<=>(?[X]:(~brave(X))))&
(![X]:((quiet(X)|generous(X))=>~strong(X)))&
(((strong(paul)|calm(paul)))=>(?[X]:((~happy(X)<~>~creative(X)))))&
((strong(mary))=>(?[X]:((~generous(X)&generous(X)))))&
(![X]:((~strong(X)&patient(X))=>~happy(X)))&
(![X]:((kind(X)<~>curious(X))<=>(~rich(X)|~curious(X))))&
(((~old(susan)|generous(susan)))=>((~quiet(susan)&happy(susan))))&
((~patient(lucy))<=>((~humble(paul)|generous(paul))))&
(![X]:((~quiet(X)<~>creative(X))<=>old(X)))&
(![X]:((tall(X)&patient(X))<=>(brave(X)|~generous(X))))&
((~funny(lucy)&humble(lucy)))&
((~funny(paul)&humble(paul)))&
(?[X]:((curious(X)|~quiet(X))))&
((happy(john)<~>humble(john)))&
((generous(alice)|tall(alice)))&
(?[X]:((~patient(X)|old(X))))&
((old(alice)<~>brave(alice))) | patient(mary) | [] | null | 0 |
Everyone who is rich or not humble is both old and not old.
If john is either kind or not humble then someone is rich or not rich and vice versa.
If someone is both rich and brave then mary is not curious or not rich.
Everyone who is not curious or curious is either curious or not kind.
Everyone who is both rich and not quiet is both not funny and not creative.
Everyone who is both curious and funny is not tall and vice versa.
Everyone who is not wise is not rich or humble.
Everyone who is not generous is both not tall and not quiet and vice versa.
Everyone who is not patient or not creative is not curious and vice versa.
Everyone who is humble or not brave is kind and vice versa.
If someone is strong then someone is both wise and not wise.
Everyone who is both not creative and funny is strong and vice versa.
If fred is calm then lucy is either not generous or generous.
If someone is not tall or not funny then someone is not strong or brave and vice versa.
Paul is either not happy or kind.
Someone is both not funny and not calm.
Someone is either not humble or not strong.
Lucy is generous.
Fred is not humble or old.
Lucy is kind. | John is not patient. | contradiction | (![X]:((rich(X)|~humble(X))=>(old(X)&~old(X))))&
(((kind(john)<~>~humble(john)))<=>(?[X]:((rich(X)|~rich(X)))))&
((?[X]:((rich(X)&brave(X))))=>((~curious(mary)|~rich(mary))))&
(![X]:((~curious(X)|curious(X))=>(curious(X)<~>~kind(X))))&
(![X]:((rich(X)&~quiet(X))=>(~funny(X)&~creative(X))))&
(![X]:((curious(X)&funny(X))<=>~tall(X)))&
(![X]:(~wise(X)=>(~rich(X)|humble(X))))&
(![X]:(~generous(X)<=>(~tall(X)&~quiet(X))))&
(![X]:((~patient(X)|~creative(X))<=>~curious(X)))&
(![X]:((humble(X)|~brave(X))<=>kind(X)))&
((?[X]:(strong(X)))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~creative(X)&funny(X))<=>strong(X)))&
((calm(fred))=>((~generous(lucy)<~>generous(lucy))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~strong(X)|brave(X)))))&
((~happy(paul)<~>kind(paul)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((~humble(X)<~>~strong(X))))&
(generous(lucy))&
((~humble(fred)|old(fred)))&
(kind(lucy)) | ~patient(john) | [
"p0",
"p1",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8923212367419627374861617
% SZS output start Proof for 8923212367419627374861617
1. ! [X0] : ((~humble(X0) | rich(X0)) => (~old(X0) & old(X0))) [input p0]
2. (kind(john) <~> ~humble(john)) <=> ? [X0] : (~rich(X0) | rich(X0)) [input p1]
4. ! [X0] : ((curious(X0) | ~curious(X0)) => (curious(X0) <~> ~kind(X0))) [input p3]
9. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> ~curious(X0)) [input p8]
21. ~patient(john) [input hypothesis]
30. ! [X0] : ((~old(X0) & old(X0)) | (humble(X0) & ~rich(X0))) [ennf transformation 1]
33. ! [X0] : ((curious(X0) <~> ~kind(X0)) | (~curious(X0) & curious(X0))) [ennf transformation 4]
37. (((humble(john) | ~kind(john)) & (~humble(john) | kind(john))) | ! [X0] : (rich(X0) & ~rich(X0))) & (? [X0] : (~rich(X0) | rich(X0)) | ((kind(john) | humble(john)) & (~humble(john) | ~kind(john)))) [nnf transformation 2]
38. (((humble(john) | ~kind(john)) & (~humble(john) | kind(john))) | ! [X0] : (rich(X0) & ~rich(X0))) & (? [X1] : (~rich(X1) | rich(X1)) | ((kind(john) | humble(john)) & (~humble(john) | ~kind(john)))) [rectify 37]
39. ? [X1] : (~rich(X1) | rich(X1)) => (~rich(sK0) | rich(sK0)) [choice axiom]
40. (((humble(john) | ~kind(john)) & (~humble(john) | kind(john))) | ! [X0] : (rich(X0) & ~rich(X0))) & ((~rich(sK0) | rich(sK0)) | ((kind(john) | humble(john)) & (~humble(john) | ~kind(john)))) [skolemisation 38,39]
41. ! [X0] : (((kind(X0) | ~curious(X0)) & (~kind(X0) | curious(X0))) | (~curious(X0) & curious(X0))) [nnf transformation 33]
44. ! [X0] : (((~creative(X0) | ~patient(X0)) | curious(X0)) & (~curious(X0) | (creative(X0) & patient(X0)))) [nnf transformation 9]
45. ! [X0] : ((~creative(X0) | ~patient(X0) | curious(X0)) & (~curious(X0) | (creative(X0) & patient(X0)))) [flattening 44]
64. old(X0) | ~rich(X0) [cnf transformation 30]
65. old(X0) | humble(X0) [cnf transformation 30]
66. ~old(X0) | ~rich(X0) [cnf transformation 30]
67. ~old(X0) | humble(X0) [cnf transformation 30]
71. ~humble(john) | kind(john) | rich(X0) [cnf transformation 40]
75. ~kind(X0) | curious(X0) | curious(X0) [cnf transformation 41]
83. ~curious(X0) | patient(X0) [cnf transformation 45]
105. ~patient(john) [cnf transformation 21]
106. ~kind(X0) | curious(X0) [duplicate literal removal 75]
108. humble(X0) [subsumption resolution 65,67]
109. ~rich(X0) [subsumption resolution 64,66]
110. kind(john) | rich(X0) [subsumption resolution 71,108]
111. kind(john) [subsumption resolution 110,109]
164. curious(john) [resolution 106,111]
167. patient(john) [resolution 164,83]
168. $false [subsumption resolution 167,105]
% SZS output end Proof for 8923212367419627374861617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or old is not curious or tall.
If mary is not happy then lucy is both rich and not funny.
If paul is patient then alice is not patient.
If john is both strong and not patient then someone is curious or brave and vice versa.
Everyone who is not strong or creative is both not curious and rich and vice versa.
If mary is either funny or not curious then someone is happy or not creative and vice versa.
Everyone who is both kind and not funny is not kind.
Everyone who is not curious or not calm is humble.
If someone is either generous or brave then alice is both not generous and brave and vice versa.
Everyone who is not funny or happy is both not creative and brave and vice versa.
If someone is either rich or wise then susan is either not humble or not old and vice versa.
If someone is either not wise or calm then lucy is either not curious or not happy and vice versa.
If susan is both not humble and not rich then someone is either not brave or not happy.
Everyone who is not happy is either quiet or calm.
Everyone who is creative is both calm and not happy and vice versa.
Everyone who is not kind or calm is brave and vice versa.
Someone is creative.
Someone is not happy or happy.
Someone is either wise or not patient.
Lucy is calm or not rich.
John is either not rich or not calm.
Susan is either not quiet or curious.
Lucy is both creative and not happy.
Someone is quiet or funny. | Lucy is not wise. | entailment | (![X]:((~creative(X)|old(X))=>(~curious(X)|tall(X))))&
((~happy(mary))=>((rich(lucy)&~funny(lucy))))&
((patient(paul))=>(~patient(alice)))&
(((strong(john)&~patient(john)))<=>(?[X]:((curious(X)|brave(X)))))&
(![X]:((~strong(X)|creative(X))<=>(~curious(X)&rich(X))))&
(((funny(mary)<~>~curious(mary)))<=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:((kind(X)&~funny(X))=>~kind(X)))&
(![X]:((~curious(X)|~calm(X))=>humble(X)))&
((?[X]:((generous(X)<~>brave(X))))<=>((~generous(alice)&brave(alice))))&
(![X]:((~funny(X)|happy(X))<=>(~creative(X)&brave(X))))&
((?[X]:((rich(X)<~>wise(X))))<=>((~humble(susan)<~>~old(susan))))&
((?[X]:((~wise(X)<~>calm(X))))<=>((~curious(lucy)<~>~happy(lucy))))&
(((~humble(susan)&~rich(susan)))=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:(~happy(X)=>(quiet(X)<~>calm(X))))&
(![X]:(creative(X)<=>(calm(X)&~happy(X))))&
(![X]:((~kind(X)|calm(X))<=>brave(X)))&
(?[X]:(creative(X)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((wise(X)<~>~patient(X))))&
((calm(lucy)|~rich(lucy)))&
((~rich(john)<~>~calm(john)))&
((~quiet(susan)<~>curious(susan)))&
((creative(lucy)&~happy(lucy)))&
(?[X]:((quiet(X)|funny(X)))) | ~wise(lucy) | [
"p4",
"p11",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9119659959053558489328877
% SZS output start Proof for 9119659959053558489328877
5. ! [X0] : ((creative(X0) | ~strong(X0)) <=> (rich(X0) & ~curious(X0))) [input p4]
12. ? [X0] : (~wise(X0) <~> calm(X0)) <=> (~curious(lucy) <~> ~happy(lucy)) [input p11]
15. ! [X0] : (creative(X0) <=> (~happy(X0) & calm(X0))) [input p14]
23. ~happy(lucy) & creative(lucy) [input p22]
25. wise(lucy) [input hypothesis]
40. ! [X0] : (((creative(X0) | ~strong(X0)) | (~rich(X0) | curious(X0))) & ((rich(X0) & ~curious(X0)) | (~creative(X0) & strong(X0)))) [nnf transformation 5]
41. ! [X0] : ((creative(X0) | ~strong(X0) | ~rich(X0) | curious(X0)) & ((rich(X0) & ~curious(X0)) | (~creative(X0) & strong(X0)))) [flattening 40]
57. (? [X0] : ((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ((~curious(lucy) | happy(lucy)) & (~happy(lucy) | curious(lucy)))) & (((happy(lucy) | curious(lucy)) & (~happy(lucy) | ~curious(lucy))) | ! [X0] : ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) [nnf transformation 12]
58. (? [X0] : ((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ((~curious(lucy) | happy(lucy)) & (~happy(lucy) | curious(lucy)))) & (((happy(lucy) | curious(lucy)) & (~happy(lucy) | ~curious(lucy))) | ! [X1] : ((~wise(X1) | ~calm(X1)) & (calm(X1) | wise(X1)))) [rectify 57]
59. ? [X0] : ((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) => ((~calm(sK4) | wise(sK4)) & (calm(sK4) | ~wise(sK4))) [choice axiom]
60. (((~calm(sK4) | wise(sK4)) & (calm(sK4) | ~wise(sK4))) | ((~curious(lucy) | happy(lucy)) & (~happy(lucy) | curious(lucy)))) & (((happy(lucy) | curious(lucy)) & (~happy(lucy) | ~curious(lucy))) | ! [X1] : ((~wise(X1) | ~calm(X1)) & (calm(X1) | wise(X1)))) [skolemisation 58,59]
65. ! [X0] : ((creative(X0) | (happy(X0) | ~calm(X0))) & ((~happy(X0) & calm(X0)) | ~creative(X0))) [nnf transformation 15]
66. ! [X0] : ((creative(X0) | happy(X0) | ~calm(X0)) & ((~happy(X0) & calm(X0)) | ~creative(X0))) [flattening 65]
89. ~curious(X0) | ~creative(X0) [cnf transformation 41]
124. happy(lucy) | curious(lucy) | ~wise(X1) | ~calm(X1) [cnf transformation 60]
133. ~creative(X0) | calm(X0) [cnf transformation 66]
148. creative(lucy) [cnf transformation 23]
149. ~happy(lucy) [cnf transformation 23]
151. wise(lucy) [cnf transformation 25]
290. 30 <=> happy(lucy) [avatar definition]
294. 31 <=> curious(lucy) [avatar definition]
295. curious(lucy) <- (31) [avatar component clause 294]
310. 34 <=> ! [X1] : (~wise(X1) | ~calm(X1)) [avatar definition]
311. ~wise(X1) | ~calm(X1) <- (34) [avatar component clause 310]
312. 34 | 31 | 30 [avatar split clause 124,290,294,310]
346. 41 <=> calm(lucy) [avatar definition]
370. ~30 [avatar split clause 149,290]
387. ~creative(lucy) <- (31) [resolution 89,295]
388. $false <- (31) [subsumption resolution 387,148]
389. ~31 [avatar contradiction clause 388]
401. calm(lucy) [resolution 133,148]
405. ~calm(lucy) <- (34) [resolution 311,151]
409. ~41 | ~34 [avatar split clause 405,310,346]
410. 41 [avatar split clause 401,346]
411. $false [avatar sat refutation 312,370,389,409,410]
% SZS output end Proof for 9119659959053558489328877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not strong then someone is wise or quiet.
Everyone who is both not happy and not tall is either tall or happy.
If someone is not patient then fred is either not creative or generous.
Everyone who is either not strong or quiet is both not humble and not happy and vice versa.
If mary is either humble or wise then someone is either rich or happy and vice versa.
If paul is either not quiet or strong then someone is calm or not rich and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is not old or not rich is creative and vice versa.
If mary is either not calm or strong then someone is not calm or not brave and vice versa.
If someone is either not wise or not humble then someone is wise.
Everyone who is not humble is not creative or old and vice versa.
Everyone who is not rich is humble and vice versa.
Everyone who is not happy or not calm is either not tall or not brave.
If susan is both not humble and generous then someone is both rich and not humble.
Everyone who is not tall or funny is not funny.
Everyone who is strong is not funny or not brave.
John is both not quiet and not wise.
Someone is brave.
Alice is both not wise and not generous.
Susan is not patient or strong.
Someone is not quiet or generous. | John is calm. | contradiction | ((~strong(mary))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((~happy(X)&~tall(X))=>(tall(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>((~creative(fred)<~>generous(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~humble(X)&~happy(X))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((rich(X)<~>happy(X)))))&
(((~quiet(paul)<~>strong(paul)))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~old(X)|~rich(X))<=>creative(X)))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:((~calm(X)|~brave(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)<=>(~creative(X)|old(X))))&
(![X]:(~rich(X)<=>humble(X)))&
(![X]:((~happy(X)|~calm(X))=>(~tall(X)<~>~brave(X))))&
(((~humble(susan)&generous(susan)))=>(?[X]:((rich(X)&~humble(X)))))&
(![X]:((~tall(X)|funny(X))=>~funny(X)))&
(![X]:(strong(X)=>(~funny(X)|~brave(X))))&
((~quiet(john)&~wise(john)))&
(?[X]:(brave(X)))&
((~wise(alice)&~generous(alice)))&
((~patient(susan)|strong(susan)))&
(?[X]:((~quiet(X)|generous(X)))) | calm(john) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8870311603938804495634685
% SZS output start Proof for 8870311603938804495634685
4. ! [X0] : ((~strong(X0) <~> quiet(X0)) <=> (~happy(X0) & ~humble(X0))) [input p3]
5. (humble(mary) <~> wise(mary)) <=> ? [X0] : (rich(X0) <~> happy(X0)) [input p4]
6. (~quiet(paul) <~> strong(paul)) <=> ? [X0] : (~rich(X0) | calm(X0)) [input p5]
7. ! [X0] : (~old(X0) <=> wise(X0)) [input p6]
8. ! [X0] : ((~rich(X0) | ~old(X0)) <=> creative(X0)) [input p7]
11. ! [X0] : (~humble(X0) <=> (old(X0) | ~creative(X0))) [input p10]
12. ! [X0] : (~rich(X0) <=> humble(X0)) [input p11]
22. calm(john) [input hypothesis]
38. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [nnf transformation 4]
39. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [flattening 38]
40. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [nnf transformation 5]
41. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [rectify 40]
42. ? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) => ((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) [choice axiom]
43. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [skolemisation 41,42]
44. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X0] : (~rich(X0) | calm(X0)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [nnf transformation 6]
45. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X1] : (~rich(X1) | calm(X1)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [rectify 44]
46. ? [X1] : (~rich(X1) | calm(X1)) => (~rich(sK2) | calm(sK2)) [choice axiom]
47. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & ((~rich(sK2) | calm(sK2)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [skolemisation 45,46]
48. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 7]
49. ! [X0] : (((~rich(X0) | ~old(X0)) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [nnf transformation 8]
50. ! [X0] : ((~rich(X0) | ~old(X0) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [flattening 49]
59. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & ((old(X0) | ~creative(X0)) | humble(X0))) [nnf transformation 11]
60. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & (old(X0) | ~creative(X0) | humble(X0))) [flattening 59]
61. ! [X0] : ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))) [nnf transformation 12]
74. ~humble(X0) | quiet(X0) | strong(X0) [cnf transformation 39]
75. ~humble(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 39]
76. ~happy(X0) | quiet(X0) | strong(X0) [cnf transformation 39]
77. ~happy(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 39]
84. wise(mary) | humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 43]
86. ~wise(mary) | ~humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 43]
90. strong(paul) | ~quiet(paul) | ~calm(X0) [cnf transformation 47]
92. ~strong(paul) | quiet(paul) | ~calm(X0) [cnf transformation 47]
94. old(X0) | wise(X0) [cnf transformation 48]
95. ~old(X0) | ~wise(X0) [cnf transformation 48]
96. old(X0) | creative(X0) [cnf transformation 50]
107. old(X0) | ~creative(X0) | humble(X0) [cnf transformation 60]
109. ~old(X0) | ~humble(X0) [cnf transformation 60]
110. rich(X0) | humble(X0) [cnf transformation 61]
125. calm(john) [cnf transformation 22]
157. 8 <=> humble(mary) [avatar definition]
158. humble(mary) <- (8) [avatar component clause 157]
159. ~humble(mary) <- (~8) [avatar component clause 157]
161. 9 <=> wise(mary) [avatar definition]
162. wise(mary) <- (9) [avatar component clause 161]
163. ~wise(mary) <- (~9) [avatar component clause 161]
166. 10 <=> ! [X0] : (happy(X0) | ~rich(X0)) [avatar definition]
167. ~rich(X0) | happy(X0) <- (10) [avatar component clause 166]
168. 10 | ~8 | ~9 [avatar split clause 86,161,157,166]
170. 10 | 8 | 9 [avatar split clause 84,161,157,166]
187. 14 <=> quiet(paul) [avatar definition]
188. ~quiet(paul) <- (~14) [avatar component clause 187]
189. quiet(paul) <- (14) [avatar component clause 187]
191. 15 <=> strong(paul) [avatar definition]
192. strong(paul) <- (15) [avatar component clause 191]
193. ~strong(paul) <- (~15) [avatar component clause 191]
196. 16 <=> ! [X0] : ~calm(X0) [avatar definition]
197. ~calm(X0) <- (16) [avatar component clause 196]
198. 16 | 14 | ~15 [avatar split clause 92,191,187,196]
200. 16 | ~14 | 15 [avatar split clause 90,191,187,196]
236. 24 <=> ! [X1] : (~wise(X1) | humble(X1)) [avatar definition]
237. ~wise(X1) | humble(X1) <- (24) [avatar component clause 236]
244. 26 <=> ! [X1] : (~humble(X1) | wise(X1)) [avatar definition]
245. ~humble(X1) | wise(X1) <- (26) [avatar component clause 244]
247. old(X0) | humble(X0) [subsumption resolution 107,96]
289. ~humble(X1) | wise(X1) [resolution 109,94]
290. 26 [avatar split clause 289,244]
295. humble(X0) | happy(X0) <- (10) [resolution 167,110]
299. humble(X1) | ~wise(X1) [resolution 247,95]
300. 24 [avatar split clause 299,236]
396. happy(X0) | ~strong(X0) | ~quiet(X0) <- (10) [resolution 295,75]
397. happy(X1) | quiet(X1) | strong(X1) <- (10) [resolution 295,74]
400. ~quiet(X0) | ~strong(X0) <- (10) [subsumption resolution 396,77]
401. quiet(X1) | strong(X1) <- (10) [subsumption resolution 397,76]
428. strong(paul) <- (10, ~14) [resolution 401,188]
434. $false <- (10, ~14, ~15) [subsumption resolution 428,193]
435. ~10 | 14 | 15 [avatar contradiction clause 434]
441. ~strong(paul) <- (10, 14) [resolution 189,400]
443. $false <- (10, 14, 15) [subsumption resolution 441,192]
444. ~10 | ~14 | ~15 [avatar contradiction clause 443]
450. $false <- (16) [resolution 197,125]
451. ~16 [avatar contradiction clause 450]
482. wise(mary) <- (8, 26) [resolution 158,245]
485. $false <- (8, ~9, 26) [subsumption resolution 482,163]
486. ~8 | 9 | ~26 [avatar contradiction clause 485]
488. humble(mary) <- (9, 24) [resolution 162,237]
489. $false <- (~8, 9, 24) [subsumption resolution 488,159]
490. 8 | ~9 | ~24 [avatar contradiction clause 489]
491. $false [avatar sat refutation 168,170,198,200,290,300,435,444,451,486,490]
% SZS output end Proof for 8870311603938804495634685
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If alice is tall or creative then someone is either not generous or not curious and vice versa. If john is both not patient and strong then paul is not funny or humble. Everyone who is funny or quiet is either not humble or not rich. If lucy is either funny or not humble then alice is either humble or not kind. If mary is both wise and not humble then someone is not rich and vice versa. If someone is not old then paul is strong. Everyone who is either rich or generous is either not tall or wise. If someone is not rich then someone is not creative or happy and vice versa. If susan is not wise then paul is rich and vice versa. If alice is both calm and not wise then someone is not wise or not humble. Everyone who is patient or creative is brave. Everyone who is not curious is both tall and wise. Everyone who is either not quiet or tall is not quiet or not old. Everyone who is both creative and wise is either creative or not generous and vice versa. Everyone who is generous or curious is both humble and not tall. Everyone who is not tall or humble is funny or humble and vice versa. Paul is not funny or not strong. Someone is not patient. John is rich or creative. John is quiet or old. Someone is either not rich or not calm. | Alice is quiet. | contradiction | (((tall(alice)|creative(alice)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(((~patient(john)&strong(john)))=>((~funny(paul)|humble(paul))))&
(![X]:((funny(X)|quiet(X))=>(~humble(X)<~>~rich(X))))&
(((funny(lucy)<~>~humble(lucy)))=>((humble(alice)<~>~kind(alice))))&
(((wise(mary)&~humble(mary)))<=>(?[X]:(~rich(X))))&
((?[X]:(~old(X)))=>(strong(paul)))&
(![X]:((rich(X)<~>generous(X))=>(~tall(X)<~>wise(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)|happy(X)))))&
((~wise(susan))<=>(rich(paul)))&
(((calm(alice)&~wise(alice)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((patient(X)|creative(X))=>brave(X)))&
(![X]:(~curious(X)=>(tall(X)&wise(X))))&
(![X]:((~quiet(X)<~>tall(X))=>(~quiet(X)|~old(X))))&
(![X]:((creative(X)&wise(X))<=>(creative(X)<~>~generous(X))))&
(![X]:((generous(X)|curious(X))=>(humble(X)&~tall(X))))&
(![X]:((~tall(X)|humble(X))<=>(funny(X)|humble(X))))&
((~funny(paul)|~strong(paul)))&
(?[X]:(~patient(X)))&
((rich(john)|creative(john)))&
((quiet(john)|old(john)))&
(?[X]:((~rich(X)<~>~calm(X)))) | quiet(alice) | [
"p2",
"p4",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 893907541228677825276010
% SZS output start Proof for 893907541228677825276010
3. ! [X0] : ((quiet(X0) | funny(X0)) => (~humble(X0) <~> ~rich(X0))) [input p2]
5. (~humble(mary) & wise(mary)) <=> ? [X0] : ~rich(X0) [input p4]
12. ! [X0] : (~curious(X0) => (wise(X0) & tall(X0))) [input p11]
14. ! [X0] : ((wise(X0) & creative(X0)) <=> (creative(X0) <~> ~generous(X0))) [input p13]
15. ! [X0] : ((curious(X0) | generous(X0)) => (~tall(X0) & humble(X0))) [input p14]
22. quiet(alice) [input hypothesis]
27. ! [X0] : ((~humble(X0) <~> ~rich(X0)) | (~quiet(X0) & ~funny(X0))) [ennf transformation 3]
33. ! [X0] : ((wise(X0) & tall(X0)) | curious(X0)) [ennf transformation 12]
36. ! [X0] : ((~tall(X0) & humble(X0)) | (~curious(X0) & ~generous(X0))) [ennf transformation 15]
42. ! [X0] : (((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | (~quiet(X0) & ~funny(X0))) [nnf transformation 27]
44. ((~humble(mary) & wise(mary)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | (humble(mary) | ~wise(mary))) [nnf transformation 5]
45. ((~humble(mary) & wise(mary)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | humble(mary) | ~wise(mary)) [flattening 44]
46. ((~humble(mary) & wise(mary)) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | humble(mary) | ~wise(mary)) [rectify 45]
47. ? [X1] : ~rich(X1) => ~rich(sK1) [choice axiom]
48. ((~humble(mary) & wise(mary)) | ! [X0] : rich(X0)) & (~rich(sK1) | humble(mary) | ~wise(mary)) [skolemisation 46,47]
59. ! [X0] : (((wise(X0) & creative(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | (~wise(X0) | ~creative(X0)))) [nnf transformation 14]
60. ! [X0] : (((wise(X0) & creative(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | ~wise(X0) | ~creative(X0))) [flattening 59]
76. ~rich(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 42]
84. wise(mary) | rich(X0) [cnf transformation 48]
85. ~humble(mary) | rich(X0) [cnf transformation 48]
97. curious(X0) | tall(X0) [cnf transformation 33]
98. wise(X0) | curious(X0) [cnf transformation 33]
102. generous(X0) | ~creative(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 60]
104. creative(X0) | creative(X0) | generous(X0) [cnf transformation 60]
107. ~generous(X0) | humble(X0) [cnf transformation 36]
108. ~curious(X0) | humble(X0) [cnf transformation 36]
109. ~generous(X0) | ~tall(X0) [cnf transformation 36]
110. ~curious(X0) | ~tall(X0) [cnf transformation 36]
121. quiet(alice) [cnf transformation 22]
122. generous(X0) | ~creative(X0) | ~wise(X0) [duplicate literal removal 102]
123. generous(X0) | creative(X0) [duplicate literal removal 104]
129. 2 <=> tall(alice) [avatar definition]
131. tall(alice) <- (2) [avatar component clause 129]
179. 13 <=> humble(alice) [avatar definition]
181. ~humble(alice) <- (~13) [avatar component clause 179]
191. 15 <=> ! [X0] : rich(X0) [avatar definition]
192. rich(X0) <- (15) [avatar component clause 191]
194. 16 <=> humble(mary) [avatar definition]
197. 15 | ~16 [avatar split clause 85,194,191]
199. 17 <=> wise(mary) [avatar definition]
201. wise(mary) <- (17) [avatar component clause 199]
202. 15 | 17 [avatar split clause 84,199,191]
264. ~wise(X0) | generous(X0) [subsumption resolution 122,123]
300. humble(X0) | tall(X0) [resolution 108,97]
318. generous(mary) <- (17) [resolution 264,201]
319. curious(X0) | generous(X0) [resolution 264,98]
324. humble(mary) <- (17) [resolution 318,107]
327. 16 | ~17 [avatar split clause 324,199,194]
341. ~quiet(X0) | ~humble(X0) <- (15) [resolution 76,192]
395. ~humble(alice) <- (15) [resolution 341,121]
401. ~13 | ~15 [avatar split clause 395,191,179]
445. tall(alice) <- (~13) [resolution 181,300]
452. 2 | 13 [avatar split clause 445,179,129]
454. generous(X0) | ~tall(X0) [resolution 319,110]
456. ~tall(X0) [subsumption resolution 454,109]
485. $false <- (2) [resolution 456,131]
486. ~2 [avatar contradiction clause 485]
487. $false [avatar sat refutation 197,202,327,401,452,486]
% SZS output end Proof for 893907541228677825276010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both calm and not tall then fred is quiet.
If someone is either not kind or not curious then john is both old and not tall and vice versa.
Everyone who is both not funny and not creative is not kind.
Everyone who is either not old or not brave is either happy or not kind.
If someone is either not creative or happy then someone is both not wise and not quiet and vice versa.
Everyone who is calm or not brave is not calm and vice versa.
Everyone who is both not tall and generous is not wise and vice versa.
If someone is either rich or not patient then john is both kind and not generous.
Everyone who is both not brave and kind is either calm or happy and vice versa.
Everyone who is not calm is either calm or wise.
Everyone who is both not patient and not curious is humble and vice versa.
Everyone who is either generous or not creative is not happy or brave and vice versa.
If lucy is not quiet or not happy then mary is both quiet and calm.
If someone is not old then lucy is either rich or not quiet and vice versa.
If someone is not humble then paul is wise.
Someone is not humble.
Fred is either not kind or not funny.
Someone is not quiet or tall.
Paul is rich or happy.
Susan is wise or not old.
Susan is not calm or not wise.
Someone is either wise or not kind. | Alice is calm. | contradiction | (((calm(alice)&~tall(alice)))=>(quiet(fred)))&
((?[X]:((~kind(X)<~>~curious(X))))<=>((old(john)&~tall(john))))&
(![X]:((~funny(X)&~creative(X))=>~kind(X)))&
(![X]:((~old(X)<~>~brave(X))=>(happy(X)<~>~kind(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:((calm(X)|~brave(X))<=>~calm(X)))&
(![X]:((~tall(X)&generous(X))<=>~wise(X)))&
((?[X]:((rich(X)<~>~patient(X))))=>((kind(john)&~generous(john))))&
(![X]:((~brave(X)&kind(X))<=>(calm(X)<~>happy(X))))&
(![X]:(~calm(X)=>(calm(X)<~>wise(X))))&
(![X]:((~patient(X)&~curious(X))<=>humble(X)))&
(![X]:((generous(X)<~>~creative(X))<=>(~happy(X)|brave(X))))&
(((~quiet(lucy)|~happy(lucy)))=>((quiet(mary)&calm(mary))))&
((?[X]:(~old(X)))<=>((rich(lucy)<~>~quiet(lucy))))&
((?[X]:(~humble(X)))=>(wise(paul)))&
(?[X]:(~humble(X)))&
((~kind(fred)<~>~funny(fred)))&
(?[X]:((~quiet(X)|tall(X))))&
((rich(paul)|happy(paul)))&
((wise(susan)|~old(susan)))&
((~calm(susan)|~wise(susan)))&
(?[X]:((wise(X)<~>~kind(X)))) | calm(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2934867670832890638687828
% SZS output start Proof for 2934867670832890638687828
6. ! [X0] : ((~brave(X0) | calm(X0)) <=> ~calm(X0)) [input p5]
23. calm(alice) [input hypothesis]
45. ! [X0] : (((~brave(X0) | calm(X0)) | calm(X0)) & (~calm(X0) | (brave(X0) & ~calm(X0)))) [nnf transformation 6]
46. ! [X0] : ((~brave(X0) | calm(X0) | calm(X0)) & (~calm(X0) | (brave(X0) & ~calm(X0)))) [flattening 45]
87. ~calm(X0) | ~calm(X0) [cnf transformation 46]
132. calm(alice) [cnf transformation 23]
134. ~calm(X0) [duplicate literal removal 87]
275. $false [subsumption resolution 132,134]
% SZS output end Proof for 2934867670832890638687828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is either not tall or not funny and vice versa.
Everyone who is either calm or generous is not funny or not calm and vice versa.
Everyone who is either not generous or tall is either funny or not creative and vice versa.
If susan is either creative or curious then someone is both not patient and quiet.
If fred is creative or not curious then someone is happy or not old and vice versa.
If someone is either rich or not quiet then mary is either calm or not curious and vice versa.
If someone is not kind or not brave then someone is humble or strong and vice versa.
Everyone who is either not old or not tall is generous or curious and vice versa.
If someone is tall or strong then someone is either rich or curious and vice versa.
Everyone who is both not old and tall is both not tall and not happy and vice versa.
Everyone who is both humble and calm is not brave.
Everyone who is patient or not patient is either not happy or not kind and vice versa.
Everyone who is either not rich or funny is not funny or not rich and vice versa.
Everyone who is either creative or not strong is calm.
If alice is not happy or generous then someone is patient or not humble.
Someone is both not humble and not strong.
Susan is brave.
Paul is either humble or not generous.
John is not humble or not happy. | Paul is curious. | neutral | (![X]:(calm(X)<=>(~tall(X)<~>~funny(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~funny(X)|~calm(X))))&
(![X]:((~generous(X)<~>tall(X))<=>(funny(X)<~>~creative(X))))&
(((creative(susan)<~>curious(susan)))=>(?[X]:((~patient(X)&quiet(X)))))&
(((creative(fred)|~curious(fred)))<=>(?[X]:((happy(X)|~old(X)))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>((calm(mary)<~>~curious(mary))))&
((?[X]:((~kind(X)|~brave(X))))<=>(?[X]:((humble(X)|strong(X)))))&
(![X]:((~old(X)<~>~tall(X))<=>(generous(X)|curious(X))))&
((?[X]:((tall(X)|strong(X))))<=>(?[X]:((rich(X)<~>curious(X)))))&
(![X]:((~old(X)&tall(X))<=>(~tall(X)&~happy(X))))&
(![X]:((humble(X)&calm(X))=>~brave(X)))&
(![X]:((patient(X)|~patient(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((~rich(X)<~>funny(X))<=>(~funny(X)|~rich(X))))&
(![X]:((creative(X)<~>~strong(X))=>calm(X)))&
(((~happy(alice)|generous(alice)))=>(?[X]:((patient(X)|~humble(X)))))&
(?[X]:((~humble(X)&~strong(X))))&
(brave(susan))&
((humble(paul)<~>~generous(paul)))&
((~humble(john)|~happy(john))) | curious(paul) | [] | null | 0 |
If someone is both not calm and not wise then lucy is not quiet. Everyone who is both quiet and not happy is not calm and vice versa. Everyone who is not humble is not curious or calm and vice versa. Everyone who is not funny is both funny and not old. Everyone who is both not curious and not generous is either old or not rich and vice versa. If someone is either not humble or brave then someone is both curious and not creative and vice versa. Everyone who is not brave is either humble or not old. Everyone who is quiet or patient is either wise or not curious. If paul is not funny then alice is either not happy or happy. Everyone who is either humble or not wise is not rich or not humble and vice versa. If paul is not calm then paul is both not funny and not kind. If lucy is not funny or funny then fred is either wise or patient. Everyone who is either not creative or rich is either wise or kind and vice versa. Everyone who is brave is both quiet and rich and vice versa. Everyone who is either not patient or curious is both not kind and funny and vice versa. Everyone who is either quiet or curious is both not strong and not kind and vice versa. Someone is not quiet or not funny. Paul is either not calm or not old. Someone is quiet or wise. Someone is not happy. Lucy is rich. Someone is both strong and calm. Fred is calm. Someone is not patient. | Lucy is not calm. | contradiction | ((?[X]:((~calm(X)&~wise(X))))=>(~quiet(lucy)))&
(![X]:((quiet(X)&~happy(X))<=>~calm(X)))&
(![X]:(~humble(X)<=>(~curious(X)|calm(X))))&
(![X]:(~funny(X)=>(funny(X)&~old(X))))&
(![X]:((~curious(X)&~generous(X))<=>(old(X)<~>~rich(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((curious(X)&~creative(X)))))&
(![X]:(~brave(X)=>(humble(X)<~>~old(X))))&
(![X]:((quiet(X)|patient(X))=>(wise(X)<~>~curious(X))))&
((~funny(paul))=>((~happy(alice)<~>happy(alice))))&
(![X]:((humble(X)<~>~wise(X))<=>(~rich(X)|~humble(X))))&
((~calm(paul))=>((~funny(paul)&~kind(paul))))&
(((~funny(lucy)|funny(lucy)))=>((wise(fred)<~>patient(fred))))&
(![X]:((~creative(X)<~>rich(X))<=>(wise(X)<~>kind(X))))&
(![X]:(brave(X)<=>(quiet(X)&rich(X))))&
(![X]:((~patient(X)<~>curious(X))<=>(~kind(X)&funny(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(~strong(X)&~kind(X))))&
(?[X]:((~quiet(X)|~funny(X))))&
((~calm(paul)<~>~old(paul)))&
(?[X]:((quiet(X)|wise(X))))&
(?[X]:(~happy(X)))&
(rich(lucy))&
(?[X]:((strong(X)&calm(X))))&
(calm(fred))&
(?[X]:(~patient(X))) | ~calm(lucy) | [
"p0",
"p1",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 68318822148384023166271
% SZS output start Proof for 68318822148384023166271
1. ? [X0] : (~wise(X0) & ~calm(X0)) => ~quiet(lucy) [input p0]
2. ! [X0] : ((~happy(X0) & quiet(X0)) <=> ~calm(X0)) [input p1]
10. ! [X0] : ((humble(X0) <~> ~wise(X0)) <=> (~humble(X0) | ~rich(X0))) [input p9]
21. rich(lucy) [input p20]
25. ~calm(lucy) [input hypothesis]
27. ~quiet(lucy) | ! [X0] : (wise(X0) | calm(X0)) [ennf transformation 1]
34. ! [X0] : (((~happy(X0) & quiet(X0)) | calm(X0)) & (~calm(X0) | (happy(X0) | ~quiet(X0)))) [nnf transformation 2]
35. ! [X0] : (((~happy(X0) & quiet(X0)) | calm(X0)) & (~calm(X0) | happy(X0) | ~quiet(X0))) [flattening 34]
48. ! [X0] : ((((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | (humble(X0) & rich(X0))) & ((~humble(X0) | ~rich(X0)) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0))))) [nnf transformation 10]
49. ! [X0] : ((((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | (humble(X0) & rich(X0))) & (~humble(X0) | ~rich(X0) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0))))) [flattening 48]
69. ~quiet(lucy) | wise(X0) | calm(X0) [cnf transformation 27]
71. quiet(X0) | calm(X0) [cnf transformation 35]
98. ~humble(X0) | ~rich(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 49]
101. ~wise(X0) | humble(X0) | humble(X0) [cnf transformation 49]
138. rich(lucy) [cnf transformation 21]
143. ~calm(lucy) [cnf transformation 25]
144. ~humble(X0) | ~rich(X0) | ~wise(X0) [duplicate literal removal 98]
145. ~wise(X0) | humble(X0) [duplicate literal removal 101]
148. 1 <=> ! [X0] : (wise(X0) | calm(X0)) [avatar definition]
149. wise(X0) | calm(X0) <- (1) [avatar component clause 148]
151. 2 <=> quiet(lucy) [avatar definition]
153. ~quiet(lucy) <- (~2) [avatar component clause 151]
154. 1 | ~2 [avatar split clause 69,151,148]
186. ~rich(X0) | ~wise(X0) [subsumption resolution 144,145]
232. calm(lucy) <- (~2) [resolution 71,153]
234. $false <- (~2) [subsumption resolution 232,143]
235. 2 [avatar contradiction clause 234]
249. ~wise(lucy) [resolution 186,138]
250. calm(lucy) <- (1) [resolution 249,149]
251. $false <- (1) [subsumption resolution 250,143]
252. ~1 [avatar contradiction clause 251]
253. $false [avatar sat refutation 154,235,252]
% SZS output end Proof for 68318822148384023166271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or creative is old. Everyone who is either wise or generous is both not wise and wise and vice versa. If fred is either not wise or generous then alice is either not quiet or calm and vice versa. Everyone who is either not kind or calm is both calm and happy and vice versa. Everyone who is either not kind or patient is both not happy and generous. If someone is not old then lucy is not generous or kind and vice versa. Everyone who is either tall or old is either not generous or old. Everyone who is both not calm and not strong is not generous or strong. Everyone who is both generous and happy is both not strong and curious. Everyone who is funny or wise is both strong and not calm and vice versa. If someone is either strong or rich then someone is either not calm or creative and vice versa. Everyone who is both not funny and humble is funny or rich and vice versa. Everyone who is not curious or not tall is funny or not quiet and vice versa. Everyone who is wise is both not old and not kind and vice versa. If someone is either not humble or not wise then alice is not rich. If someone is rich or not old then someone is both not happy and not tall. Alice is patient or not kind. Susan is not generous. Paul is both not funny and not strong. Fred is not kind or strong. Fred is both calm and brave. Mary is generous or tall. Someone is either wise or curious. | Fred is not funny. | entailment | (![X]:((~rich(X)|creative(X))=>old(X)))&
(![X]:((wise(X)<~>generous(X))<=>(~wise(X)&wise(X))))&
(((~wise(fred)<~>generous(fred)))<=>((~quiet(alice)<~>calm(alice))))&
(![X]:((~kind(X)<~>calm(X))<=>(calm(X)&happy(X))))&
(![X]:((~kind(X)<~>patient(X))=>(~happy(X)&generous(X))))&
((?[X]:(~old(X)))<=>((~generous(lucy)|kind(lucy))))&
(![X]:((tall(X)<~>old(X))=>(~generous(X)<~>old(X))))&
(![X]:((~calm(X)&~strong(X))=>(~generous(X)|strong(X))))&
(![X]:((generous(X)&happy(X))=>(~strong(X)&curious(X))))&
(![X]:((funny(X)|wise(X))<=>(strong(X)&~calm(X))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~funny(X)&humble(X))<=>(funny(X)|rich(X))))&
(![X]:((~curious(X)|~tall(X))<=>(funny(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~old(X)&~kind(X))))&
((?[X]:((~humble(X)<~>~wise(X))))=>(~rich(alice)))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((~happy(X)&~tall(X)))))&
((patient(alice)|~kind(alice)))&
(~generous(susan))&
((~funny(paul)&~strong(paul)))&
((~kind(fred)|strong(fred)))&
((calm(fred)&brave(fred)))&
((generous(mary)|tall(mary)))&
(?[X]:((wise(X)<~>curious(X)))) | ~funny(fred) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3224065940623781884378328
% SZS output start Proof for 3224065940623781884378328
12. ! [X0] : ((humble(X0) & ~funny(X0)) <=> (rich(X0) | funny(X0))) [input p11]
24. funny(fred) [input hypothesis]
56. ! [X0] : (((humble(X0) & ~funny(X0)) | (~rich(X0) & ~funny(X0))) & ((rich(X0) | funny(X0)) | (~humble(X0) | funny(X0)))) [nnf transformation 12]
57. ! [X0] : (((humble(X0) & ~funny(X0)) | (~rich(X0) & ~funny(X0))) & (rich(X0) | funny(X0) | ~humble(X0) | funny(X0))) [flattening 56]
119. ~funny(X0) | ~funny(X0) [cnf transformation 57]
145. funny(fred) [cnf transformation 24]
147. ~funny(X0) [duplicate literal removal 119]
302. $false [subsumption resolution 145,147]
% SZS output end Proof for 3224065940623781884378328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not kind and quiet then someone is not tall or rich. Everyone who is both not humble and not curious is not rich and vice versa. If someone is both not funny and not rich then someone is either not generous or not old. If someone is not generous or happy then someone is not creative and vice versa. Everyone who is rich is both old and happy. Everyone who is both not kind and kind is either old or tall and vice versa. Everyone who is both not old and not generous is either generous or old. Everyone who is either patient or old is either happy or not curious and vice versa. Everyone who is not kind is both not strong and calm. Everyone who is not old or generous is not wise or not old and vice versa. Everyone who is either not happy or brave is either not calm or rich and vice versa. Everyone who is generous or rich is either old or rich. If someone is either funny or humble then someone is creative. If someone is either not quiet or not kind then someone is either humble or not humble. If someone is not curious or funny then someone is calm. If mary is quiet then lucy is both creative and humble and vice versa. Fred is either brave or quiet. Mary is strong. Lucy is either funny or generous. Someone is tall. Someone is not funny or not kind. Someone is either happy or not curious. Fred is both not brave and quiet. | Mary is tall. | entailment | (((~kind(mary)&quiet(mary)))=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((~humble(X)&~curious(X))<=>~rich(X)))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~generous(X)<~>~old(X)))))&
((?[X]:((~generous(X)|happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:(rich(X)=>(old(X)&happy(X))))&
(![X]:((~kind(X)&kind(X))<=>(old(X)<~>tall(X))))&
(![X]:((~old(X)&~generous(X))=>(generous(X)<~>old(X))))&
(![X]:((patient(X)<~>old(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(~kind(X)=>(~strong(X)&calm(X))))&
(![X]:((~old(X)|generous(X))<=>(~wise(X)|~old(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((generous(X)|rich(X))=>(old(X)<~>rich(X))))&
((?[X]:((funny(X)<~>humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~curious(X)|funny(X))))=>(?[X]:(calm(X))))&
((quiet(mary))<=>((creative(lucy)&humble(lucy))))&
((brave(fred)<~>quiet(fred)))&
(strong(mary))&
((funny(lucy)<~>generous(lucy)))&
(?[X]:(tall(X)))&
(?[X]:((~funny(X)|~kind(X))))&
(?[X]:((happy(X)<~>~curious(X))))&
((~brave(fred)&quiet(fred))) | tall(mary) | [
"p4",
"p5",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4972230108777182237135931
% SZS output start Proof for 4972230108777182237135931
5. ! [X0] : (rich(X0) => (happy(X0) & old(X0))) [input p4]
6. ! [X0] : ((kind(X0) & ~kind(X0)) <=> (old(X0) <~> tall(X0))) [input p5]
7. ! [X0] : ((~generous(X0) & ~old(X0)) => (generous(X0) <~> old(X0))) [input p6]
12. ! [X0] : ((rich(X0) | generous(X0)) => (old(X0) <~> rich(X0))) [input p11]
24. ~tall(mary) [input hypothesis]
33. ! [X0] : ((happy(X0) & old(X0)) | ~rich(X0)) [ennf transformation 5]
34. ! [X0] : ((generous(X0) <~> old(X0)) | (generous(X0) | old(X0))) [ennf transformation 7]
35. ! [X0] : ((generous(X0) <~> old(X0)) | generous(X0) | old(X0)) [flattening 34]
37. ! [X0] : ((old(X0) <~> rich(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 12]
54. ! [X0] : (((kind(X0) & ~kind(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~kind(X0) | kind(X0)))) [nnf transformation 6]
55. ! [X0] : (((kind(X0) & ~kind(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | ~kind(X0) | kind(X0))) [flattening 54]
56. ! [X0] : (((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | generous(X0) | old(X0)) [nnf transformation 35]
61. ! [X0] : (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (~rich(X0) & ~generous(X0))) [nnf transformation 37]
93. ~rich(X0) | old(X0) [cnf transformation 33]
97. ~kind(X0) | tall(X0) | ~old(X0) [cnf transformation 55]
99. kind(X0) | tall(X0) | ~old(X0) [cnf transformation 55]
101. old(X0) | generous(X0) | generous(X0) | old(X0) [cnf transformation 56]
125. rich(X0) | old(X0) | ~generous(X0) [cnf transformation 61]
128. ~rich(X0) | ~old(X0) | ~rich(X0) [cnf transformation 61]
151. ~tall(mary) [cnf transformation 24]
152. ~rich(X0) | ~old(X0) [duplicate literal removal 128]
153. old(X0) | generous(X0) [duplicate literal removal 101]
209. ~old(X0) | tall(X0) [subsumption resolution 97,99]
215. ~rich(X0) [subsumption resolution 152,93]
216. old(X0) | ~generous(X0) [subsumption resolution 125,215]
217. old(X0) [subsumption resolution 216,153]
303. tall(X1) [resolution 209,217]
304. $false [resolution 303,151]
% SZS output end Proof for 4972230108777182237135931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich and not generous is either quiet or not tall and vice versa.
If someone is both not funny and curious then someone is both quiet and not humble and vice versa.
If fred is either strong or not creative then someone is patient or creative.
If susan is both not brave and wise then someone is calm.
Everyone who is both wise and generous is both not quiet and curious and vice versa.
If fred is not quiet or not kind then someone is both happy and creative and vice versa.
If susan is both strong and not patient then someone is either curious or quiet.
Everyone who is creative is funny.
Everyone who is not brave is either brave or not happy and vice versa.
Everyone who is not old is either generous or not patient.
If lucy is both patient and not happy then paul is either quiet or not humble.
Everyone who is rich is patient and vice versa.
Everyone who is both not wise and not generous is both happy and generous.
If someone is strong or not quiet then someone is curious or not tall.
If paul is either brave or not calm then mary is not kind or not humble and vice versa.
Everyone who is both not rich and brave is both brave and not calm and vice versa.
Susan is both not curious and old.
Someone is curious.
Fred is either not calm or not rich.
Someone is generous.
Someone is both quiet and not happy.
Someone is either curious or humble. | Fred is not strong. | neutral | (![X]:((~rich(X)&~generous(X))<=>(quiet(X)<~>~tall(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((strong(fred)<~>~creative(fred)))=>(?[X]:((patient(X)|creative(X)))))&
(((~brave(susan)&wise(susan)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)&curious(X))))&
(((~quiet(fred)|~kind(fred)))<=>(?[X]:((happy(X)&creative(X)))))&
(((strong(susan)&~patient(susan)))=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:(creative(X)=>funny(X)))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~old(X)=>(generous(X)<~>~patient(X))))&
(((patient(lucy)&~happy(lucy)))=>((quiet(paul)<~>~humble(paul))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))=>(happy(X)&generous(X))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(((brave(paul)<~>~calm(paul)))<=>((~kind(mary)|~humble(mary))))&
(![X]:((~rich(X)&brave(X))<=>(brave(X)&~calm(X))))&
((~curious(susan)&old(susan)))&
(?[X]:(curious(X)))&
((~calm(fred)<~>~rich(fred)))&
(?[X]:(generous(X)))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:((curious(X)<~>humble(X)))) | ~strong(fred) | [] | null | 0 |
Everyone who is patient is both not quiet and not tall.
Everyone who is funny is rich and vice versa.
Everyone who is both not tall and not wise is strong or brave and vice versa.
Everyone who is either strong or calm is both humble and not generous and vice versa.
If someone is both creative and not funny then susan is either creative or not creative and vice versa.
If alice is either calm or not generous then someone is funny or not tall and vice versa.
Everyone who is not kind is either not strong or wise.
If someone is wise or funny then someone is creative or kind.
If alice is not patient then alice is both not strong and creative.
If fred is both not wise and not brave then someone is either happy or not curious and vice versa.
Everyone who is either not strong or not brave is not tall.
If fred is either generous or not creative then someone is both humble and not kind.
Everyone who is not curious or not rich is old or not funny.
Everyone who is either not quiet or quiet is both not calm and tall.
If mary is calm then someone is either strong or humble and vice versa.
Everyone who is not wise is both not wise and not humble.
John is either strong or not wise.
Someone is either not curious or tall.
Fred is both not brave and not wise.
Fred is either not tall or not calm.
John is either creative or not curious.
Someone is both quiet and not brave.
Someone is not creative or curious. | John is wise. | contradiction | (![X]:(patient(X)=>(~quiet(X)&~tall(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:((~tall(X)&~wise(X))<=>(strong(X)|brave(X))))&
(![X]:((strong(X)<~>calm(X))<=>(humble(X)&~generous(X))))&
((?[X]:((creative(X)&~funny(X))))<=>((creative(susan)<~>~creative(susan))))&
(((calm(alice)<~>~generous(alice)))<=>(?[X]:((funny(X)|~tall(X)))))&
(![X]:(~kind(X)=>(~strong(X)<~>wise(X))))&
((?[X]:((wise(X)|funny(X))))=>(?[X]:((creative(X)|kind(X)))))&
((~patient(alice))=>((~strong(alice)&creative(alice))))&
(((~wise(fred)&~brave(fred)))<=>(?[X]:((happy(X)<~>~curious(X)))))&
(![X]:((~strong(X)<~>~brave(X))=>~tall(X)))&
(((generous(fred)<~>~creative(fred)))=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:((~curious(X)|~rich(X))=>(old(X)|~funny(X))))&
(![X]:((~quiet(X)<~>quiet(X))=>(~calm(X)&tall(X))))&
((calm(mary))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:(~wise(X)=>(~wise(X)&~humble(X))))&
((strong(john)<~>~wise(john)))&
(?[X]:((~curious(X)<~>tall(X))))&
((~brave(fred)&~wise(fred)))&
((~tall(fred)<~>~calm(fred)))&
((creative(john)<~>~curious(john)))&
(?[X]:((quiet(X)&~brave(X))))&
(?[X]:((~creative(X)|curious(X)))) | wise(john) | [
"p2",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6964914896347398585582364
% SZS output start Proof for 6964914896347398585582364
3. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (brave(X0) | strong(X0))) [input p2]
17. strong(john) <~> ~wise(john) [input p16]
24. wise(john) [input hypothesis]
36. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~brave(X0) & ~strong(X0))) & ((brave(X0) | strong(X0)) | (wise(X0) | tall(X0)))) [nnf transformation 3]
37. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~brave(X0) & ~strong(X0))) & (brave(X0) | strong(X0) | wise(X0) | tall(X0))) [flattening 36]
66. (wise(john) | ~strong(john)) & (~wise(john) | strong(john)) [nnf transformation 17]
83. ~wise(X0) | ~strong(X0) [cnf transformation 37]
131. ~wise(john) | strong(john) [cnf transformation 66]
132. wise(john) | ~strong(john) [cnf transformation 66]
144. wise(john) [cnf transformation 24]
279. ~strong(john) [subsumption resolution 132,83]
280. ~wise(john) [subsumption resolution 131,279]
313. $false [subsumption resolution 144,280]
% SZS output end Proof for 6964914896347398585582364
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not happy or curious then mary is brave and vice versa. If mary is both happy and not tall then someone is not funny. If lucy is creative or humble then alice is not calm or not creative and vice versa. Everyone who is not creative or funny is not rich or not generous and vice versa. Everyone who is both not curious and not funny is both curious and kind and vice versa. Everyone who is both wise and not funny is curious or happy and vice versa. Everyone who is either kind or not generous is patient or not generous. Everyone who is not curious or kind is not creative and vice versa. Everyone who is not funny is either strong or not old. If fred is either not creative or tall then alice is both funny and happy and vice versa. If fred is either not patient or curious then paul is either quiet or happy and vice versa. Everyone who is both not quiet and rich is either not kind or brave. If paul is both tall and not creative then lucy is not wise and vice versa. Everyone who is both not tall and not creative is not brave. Everyone who is wise or kind is both wise and happy. Everyone who is both creative and quiet is either not kind or not brave and vice versa. Someone is not generous. Someone is happy or not humble. Lucy is not creative. Alice is both not quiet and not curious. Paul is funny or not generous. Alice is not happy or tall. Someone is either curious or old. Someone is funny. | Mary is not rich. | contradiction | (((~happy(mary)<~>curious(mary)))<=>(brave(mary)))&
(((happy(mary)&~tall(mary)))=>(?[X]:(~funny(X))))&
(((creative(lucy)|humble(lucy)))<=>((~calm(alice)|~creative(alice))))&
(![X]:((~creative(X)|funny(X))<=>(~rich(X)|~generous(X))))&
(![X]:((~curious(X)&~funny(X))<=>(curious(X)&kind(X))))&
(![X]:((wise(X)&~funny(X))<=>(curious(X)|happy(X))))&
(![X]:((kind(X)<~>~generous(X))=>(patient(X)|~generous(X))))&
(![X]:((~curious(X)|kind(X))<=>~creative(X)))&
(![X]:(~funny(X)=>(strong(X)<~>~old(X))))&
(((~creative(fred)<~>tall(fred)))<=>((funny(alice)&happy(alice))))&
(((~patient(fred)<~>curious(fred)))<=>((quiet(paul)<~>happy(paul))))&
(![X]:((~quiet(X)&rich(X))=>(~kind(X)<~>brave(X))))&
(((tall(paul)&~creative(paul)))<=>(~wise(lucy)))&
(![X]:((~tall(X)&~creative(X))=>~brave(X)))&
(![X]:((wise(X)|kind(X))=>(wise(X)&happy(X))))&
(![X]:((creative(X)&quiet(X))<=>(~kind(X)<~>~brave(X))))&
(?[X]:(~generous(X)))&
(?[X]:((happy(X)|~humble(X))))&
(~creative(lucy))&
((~quiet(alice)&~curious(alice)))&
((funny(paul)|~generous(paul)))&
((~happy(alice)|tall(alice)))&
(?[X]:((curious(X)<~>old(X))))&
(?[X]:(funny(X))) | ~rich(mary) | [
"p0",
"p3",
"p4",
"p5",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5679715523357881841948960
% SZS output start Proof for 5679715523357881841948960
1. (~happy(mary) <~> curious(mary)) <=> brave(mary) [input p0]
4. ! [X0] : ((funny(X0) | ~creative(X0)) <=> (~generous(X0) | ~rich(X0))) [input p3]
5. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (kind(X0) & curious(X0))) [input p4]
6. ! [X0] : ((~funny(X0) & wise(X0)) <=> (happy(X0) | curious(X0))) [input p5]
8. ! [X0] : ((kind(X0) | ~curious(X0)) <=> ~creative(X0)) [input p7]
15. ! [X0] : ((kind(X0) | wise(X0)) => (happy(X0) & wise(X0))) [input p14]
16. ! [X0] : ((quiet(X0) & creative(X0)) <=> (~kind(X0) <~> ~brave(X0))) [input p15]
25. ~rich(mary) [input hypothesis]
35. ! [X0] : ((happy(X0) & wise(X0)) | (~kind(X0) & ~wise(X0))) [ennf transformation 15]
36. (((~curious(mary) | happy(mary)) & (curious(mary) | ~happy(mary))) | ~brave(mary)) & (brave(mary) | ((~happy(mary) | ~curious(mary)) & (curious(mary) | happy(mary)))) [nnf transformation 1]
41. ! [X0] : (((funny(X0) | ~creative(X0)) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | (~funny(X0) & creative(X0)))) [nnf transformation 4]
42. ! [X0] : ((funny(X0) | ~creative(X0) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | (~funny(X0) & creative(X0)))) [flattening 41]
43. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~kind(X0) | ~curious(X0))) & ((kind(X0) & curious(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 5]
44. ! [X0] : (((~funny(X0) & ~curious(X0)) | ~kind(X0) | ~curious(X0)) & ((kind(X0) & curious(X0)) | funny(X0) | curious(X0))) [flattening 43]
45. ! [X0] : (((~funny(X0) & wise(X0)) | (~happy(X0) & ~curious(X0))) & ((happy(X0) | curious(X0)) | (funny(X0) | ~wise(X0)))) [nnf transformation 6]
46. ! [X0] : (((~funny(X0) & wise(X0)) | (~happy(X0) & ~curious(X0))) & (happy(X0) | curious(X0) | funny(X0) | ~wise(X0))) [flattening 45]
48. ! [X0] : (((kind(X0) | ~curious(X0)) | creative(X0)) & (~creative(X0) | (~kind(X0) & curious(X0)))) [nnf transformation 8]
49. ! [X0] : ((kind(X0) | ~curious(X0) | creative(X0)) & (~creative(X0) | (~kind(X0) & curious(X0)))) [flattening 48]
57. ! [X0] : (((quiet(X0) & creative(X0)) | ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (((brave(X0) | kind(X0)) & (~brave(X0) | ~kind(X0))) | (~quiet(X0) | ~creative(X0)))) [nnf transformation 16]
58. ! [X0] : (((quiet(X0) & creative(X0)) | ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (((brave(X0) | kind(X0)) & (~brave(X0) | ~kind(X0))) | ~quiet(X0) | ~creative(X0))) [flattening 57]
68. brave(mary) | curious(mary) | happy(mary) [cnf transformation 36]
79. ~creative(X0) | funny(X0) | rich(X0) [cnf transformation 42]
81. curious(X0) | funny(X0) | curious(X0) [cnf transformation 44]
83. ~curious(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 44]
88. ~funny(X0) | ~curious(X0) [cnf transformation 46]
89. ~funny(X0) | ~happy(X0) [cnf transformation 46]
92. ~creative(X0) | curious(X0) [cnf transformation 49]
94. kind(X0) | ~curious(X0) | creative(X0) [cnf transformation 49]
120. ~kind(X0) | happy(X0) [cnf transformation 35]
123. ~brave(X0) | creative(X0) | kind(X0) [cnf transformation 58]
137. ~rich(mary) [cnf transformation 25]
139. funny(X0) | curious(X0) [duplicate literal removal 81]
140. ~kind(X0) | ~curious(X0) [duplicate literal removal 83]
142. 1 <=> brave(mary) [avatar definition]
143. brave(mary) <- (1) [avatar component clause 142]
146. 2 <=> happy(mary) [avatar definition]
147. ~happy(mary) <- (~2) [avatar component clause 146]
148. happy(mary) <- (2) [avatar component clause 146]
150. 3 <=> curious(mary) [avatar definition]
151. curious(mary) <- (3) [avatar component clause 150]
152. ~curious(mary) <- (~3) [avatar component clause 150]
156. 2 | 3 | 1 [avatar split clause 68,142,150,146]
186. ~curious(X0) | creative(X0) [subsumption resolution 94,140]
294. ~happy(X0) | curious(X0) [resolution 139,89]
303. curious(mary) <- (2) [resolution 294,148]
310. 3 | ~2 [avatar split clause 303,146,150]
311. creative(mary) <- (3) [resolution 151,186]
325. funny(mary) | rich(mary) <- (3) [resolution 311,79]
327. funny(mary) <- (3) [subsumption resolution 325,137]
345. ~curious(mary) <- (3) [resolution 327,88]
348. $false <- (3) [subsumption resolution 345,151]
349. ~3 [avatar contradiction clause 348]
370. 32 <=> creative(mary) [avatar definition]
371. ~creative(mary) <- (~32) [avatar component clause 370]
372. creative(mary) <- (32) [avatar component clause 370]
376. curious(mary) <- (32) [resolution 372,92]
388. $false <- (~3, 32) [subsumption resolution 376,152]
389. 3 | ~32 [avatar contradiction clause 388]
390. creative(mary) | kind(mary) <- (1) [resolution 123,143]
391. kind(mary) <- (1, ~32) [subsumption resolution 390,371]
395. happy(mary) <- (1, ~32) [resolution 391,120]
398. $false <- (1, ~2, ~32) [subsumption resolution 395,147]
399. ~1 | 2 | 32 [avatar contradiction clause 398]
400. $false [avatar sat refutation 156,310,349,389,399]
% SZS output end Proof for 5679715523357881841948960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is tall or patient.
If someone is kind then lucy is strong or not tall.
Everyone who is either strong or tall is both wise and not rich.
If someone is not kind or strong then alice is either not strong or strong and vice versa.
Everyone who is not funny or not calm is both creative and calm and vice versa.
Everyone who is either not strong or strong is either not generous or funny.
If alice is not old or generous then someone is either not wise or wise and vice versa.
If fred is both not calm and old then john is either generous or not rich and vice versa.
Everyone who is not old is not quiet and vice versa.
If someone is old then someone is not strong or happy and vice versa.
If paul is strong then susan is not curious or quiet and vice versa.
If someone is quiet then mary is not calm and vice versa.
Everyone who is rich is strong and vice versa.
If someone is both rich and tall then someone is either strong or funny and vice versa.
If someone is not calm or kind then someone is not patient and vice versa.
Everyone who is either not brave or not rich is both calm and not strong.
Lucy is generous or not creative.
Someone is either rich or patient.
Someone is not creative.
Lucy is both calm and humble. | Alice is not brave. | contradiction | (![X]:(quiet(X)=>(tall(X)|patient(X))))&
((?[X]:(kind(X)))=>((strong(lucy)|~tall(lucy))))&
(![X]:((strong(X)<~>tall(X))=>(wise(X)&~rich(X))))&
((?[X]:((~kind(X)|strong(X))))<=>((~strong(alice)<~>strong(alice))))&
(![X]:((~funny(X)|~calm(X))<=>(creative(X)&calm(X))))&
(![X]:((~strong(X)<~>strong(X))=>(~generous(X)<~>funny(X))))&
(((~old(alice)|generous(alice)))<=>(?[X]:((~wise(X)<~>wise(X)))))&
(((~calm(fred)&old(fred)))<=>((generous(john)<~>~rich(john))))&
(![X]:(~old(X)<=>~quiet(X)))&
((?[X]:(old(X)))<=>(?[X]:((~strong(X)|happy(X)))))&
((strong(paul))<=>((~curious(susan)|quiet(susan))))&
((?[X]:(quiet(X)))<=>(~calm(mary)))&
(![X]:(rich(X)<=>strong(X)))&
((?[X]:((rich(X)&tall(X))))<=>(?[X]:((strong(X)<~>funny(X)))))&
((?[X]:((~calm(X)|kind(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(calm(X)&~strong(X))))&
((generous(lucy)|~creative(lucy)))&
(?[X]:((rich(X)<~>patient(X))))&
(?[X]:(~creative(X)))&
((calm(lucy)&humble(lucy))) | ~brave(alice) | [
"p4",
"p8",
"p9",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7184512923582501095915855
% SZS output start Proof for 7184512923582501095915855
5. ! [X0] : ((~calm(X0) | ~funny(X0)) <=> (calm(X0) & creative(X0))) [input p4]
9. ! [X0] : (~old(X0) <=> ~quiet(X0)) [input p8]
10. ? [X0] : old(X0) <=> ? [X0] : (happy(X0) | ~strong(X0)) [input p9]
12. ? [X0] : quiet(X0) <=> ~calm(mary) [input p11]
13. ! [X0] : (rich(X0) <=> strong(X0)) [input p12]
16. ! [X0] : ((~brave(X0) <~> ~rich(X0)) => (~strong(X0) & calm(X0))) [input p15]
21. ~brave(alice) [input hypothesis]
22. ? [X0] : old(X0) <=> ? [X1] : (happy(X1) | ~strong(X1)) [rectify 10]
32. ! [X0] : ((~strong(X0) & calm(X0)) | (~brave(X0) <=> ~rich(X0))) [ennf transformation 16]
38. ! [X0] : (((~calm(X0) | ~funny(X0)) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | (calm(X0) & funny(X0)))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | ~funny(X0) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | (calm(X0) & funny(X0)))) [flattening 38]
48. ! [X0] : ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))) [nnf transformation 9]
49. (? [X0] : old(X0) | ! [X1] : (~happy(X1) & strong(X1))) & (? [X1] : (happy(X1) | ~strong(X1)) | ! [X0] : ~old(X0)) [nnf transformation 22]
50. (? [X0] : old(X0) | ! [X1] : (~happy(X1) & strong(X1))) & (? [X2] : (happy(X2) | ~strong(X2)) | ! [X3] : ~old(X3)) [rectify 49]
51. ? [X0] : old(X0) => old(sK2) [choice axiom]
52. ? [X2] : (happy(X2) | ~strong(X2)) => (happy(sK3) | ~strong(sK3)) [choice axiom]
53. (old(sK2) | ! [X1] : (~happy(X1) & strong(X1))) & ((happy(sK3) | ~strong(sK3)) | ! [X3] : ~old(X3)) [skolemisation 50,52,51]
56. (? [X0] : quiet(X0) | calm(mary)) & (~calm(mary) | ! [X0] : ~quiet(X0)) [nnf transformation 12]
57. (? [X0] : quiet(X0) | calm(mary)) & (~calm(mary) | ! [X1] : ~quiet(X1)) [rectify 56]
58. ? [X0] : quiet(X0) => quiet(sK4) [choice axiom]
59. (quiet(sK4) | calm(mary)) & (~calm(mary) | ! [X1] : ~quiet(X1)) [skolemisation 57,58]
60. ! [X0] : ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))) [nnf transformation 13]
71. ! [X0] : ((~strong(X0) & calm(X0)) | ((~brave(X0) | rich(X0)) & (~rich(X0) | brave(X0)))) [nnf transformation 32]
92. calm(X0) | calm(X0) [cnf transformation 39]
111. ~old(X0) | quiet(X0) [cnf transformation 48]
113. old(sK2) | strong(X1) [cnf transformation 53]
118. ~calm(mary) | ~quiet(X1) [cnf transformation 59]
120. ~rich(X0) | strong(X0) [cnf transformation 60]
121. ~strong(X0) | rich(X0) [cnf transformation 60]
133. ~strong(X0) | ~rich(X0) | brave(X0) [cnf transformation 71]
140. ~brave(alice) [cnf transformation 21]
147. calm(X0) [duplicate literal removal 92]
217. 15 <=> old(sK2) [avatar definition]
219. old(sK2) <- (15) [avatar component clause 217]
222. 16 <=> ! [X1] : strong(X1) [avatar definition]
223. strong(X1) <- (16) [avatar component clause 222]
224. 16 | 15 [avatar split clause 113,217,222]
252. ~quiet(X1) [subsumption resolution 118,147]
298. ~rich(X0) | brave(X0) [subsumption resolution 133,120]
322. quiet(sK2) <- (15) [resolution 111,219]
323. $false <- (15) [subsumption resolution 322,252]
324. ~15 [avatar contradiction clause 323]
330. rich(X0) <- (16) [resolution 121,223]
350. brave(X0) <- (16) [resolution 298,330]
392. $false <- (16) [resolution 350,140]
393. ~16 [avatar contradiction clause 392]
394. $false [avatar sat refutation 224,324,393]
% SZS output end Proof for 7184512923582501095915855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is wise or old and vice versa. Everyone who is wise or strong is either not happy or not tall. Everyone who is not old or not strong is wise or not rich. Everyone who is both rich and kind is not calm. Everyone who is both happy and funny is not rich or not funny and vice versa. If lucy is both not humble and curious then paul is creative. Everyone who is either funny or brave is not rich or happy and vice versa. Everyone who is both kind and not old is not happy and vice versa. If lucy is humble or not wise then someone is not tall or kind and vice versa. Everyone who is either not creative or not tall is tall or not tall and vice versa. If someone is not generous then someone is humble and vice versa. If someone is either humble or generous then someone is either calm or not strong and vice versa. If mary is not happy then someone is not happy or not funny and vice versa. Everyone who is tall or quiet is either funny or generous. If alice is not calm then alice is either not generous or not wise and vice versa. Everyone who is brave or creative is both kind and brave. Someone is quiet. Someone is tall or not kind. Mary is either strong or happy. Lucy is both kind and quiet. Fred is not brave. Paul is quiet or not happy. Someone is either happy or humble. Paul is not curious. | Mary is not generous. | entailment | (![X]:(funny(X)<=>(wise(X)|old(X))))&
(![X]:((wise(X)|strong(X))=>(~happy(X)<~>~tall(X))))&
(![X]:((~old(X)|~strong(X))=>(wise(X)|~rich(X))))&
(![X]:((rich(X)&kind(X))=>~calm(X)))&
(![X]:((happy(X)&funny(X))<=>(~rich(X)|~funny(X))))&
(((~humble(lucy)&curious(lucy)))=>(creative(paul)))&
(![X]:((funny(X)<~>brave(X))<=>(~rich(X)|happy(X))))&
(![X]:((kind(X)&~old(X))<=>~happy(X)))&
(((humble(lucy)|~wise(lucy)))<=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:((~creative(X)<~>~tall(X))<=>(tall(X)|~tall(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(humble(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>(?[X]:((calm(X)<~>~strong(X)))))&
((~happy(mary))<=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((tall(X)|quiet(X))=>(funny(X)<~>generous(X))))&
((~calm(alice))<=>((~generous(alice)<~>~wise(alice))))&
(![X]:((brave(X)|creative(X))=>(kind(X)&brave(X))))&
(?[X]:(quiet(X)))&
(?[X]:((tall(X)|~kind(X))))&
((strong(mary)<~>happy(mary)))&
((kind(lucy)&quiet(lucy)))&
(~brave(fred))&
((quiet(paul)|~happy(paul)))&
(?[X]:((happy(X)<~>humble(X))))&
(~curious(paul)) | ~generous(mary) | [
"p1",
"p4",
"p6",
"p9",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3148492043628091659211113
% SZS output start Proof for 3148492043628091659211113
2. ! [X0] : ((strong(X0) | wise(X0)) => (~happy(X0) <~> ~tall(X0))) [input p1]
5. ! [X0] : ((funny(X0) & happy(X0)) <=> (~funny(X0) | ~rich(X0))) [input p4]
7. ! [X0] : ((funny(X0) <~> brave(X0)) <=> (happy(X0) | ~rich(X0))) [input p6]
10. ! [X0] : ((~creative(X0) <~> ~tall(X0)) <=> (~tall(X0) | tall(X0))) [input p9]
14. ! [X0] : ((quiet(X0) | tall(X0)) => (funny(X0) <~> generous(X0))) [input p13]
16. ! [X0] : ((creative(X0) | brave(X0)) => (brave(X0) & kind(X0))) [input p15]
19. strong(mary) <~> happy(mary) [input p18]
25. generous(mary) [input hypothesis]
30. ! [X0] : ((~happy(X0) <~> ~tall(X0)) | (~strong(X0) & ~wise(X0))) [ennf transformation 2]
35. ! [X0] : ((funny(X0) <~> generous(X0)) | (~quiet(X0) & ~tall(X0))) [ennf transformation 14]
36. ! [X0] : ((brave(X0) & kind(X0)) | (~creative(X0) & ~brave(X0))) [ennf transformation 16]
39. ! [X0] : (((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (~strong(X0) & ~wise(X0))) [nnf transformation 30]
40. ! [X0] : (((funny(X0) & happy(X0)) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | (~funny(X0) | ~happy(X0)))) [nnf transformation 5]
41. ! [X0] : (((funny(X0) & happy(X0)) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | ~funny(X0) | ~happy(X0))) [flattening 40]
42. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 7]
43. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [flattening 42]
51. ! [X0] : ((((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (tall(X0) & ~tall(X0))) & ((~tall(X0) | tall(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0))))) [nnf transformation 10]
52. ! [X0] : ((((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (tall(X0) & ~tall(X0))) & (~tall(X0) | tall(X0) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0))))) [flattening 51]
67. ! [X0] : (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~quiet(X0) & ~tall(X0))) [nnf transformation 35]
73. (~happy(mary) | ~strong(mary)) & (happy(mary) | strong(mary)) [nnf transformation 19]
83. ~strong(X0) | happy(X0) | tall(X0) [cnf transformation 39]
91. funny(X0) | funny(X0) [cnf transformation 41]
97. ~brave(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 43]
110. tall(X0) | creative(X0) | tall(X0) [cnf transformation 52]
126. ~generous(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 67]
135. ~creative(X0) | brave(X0) [cnf transformation 36]
138. happy(mary) | strong(mary) [cnf transformation 73]
146. generous(mary) [cnf transformation 25]
150. creative(X0) | tall(X0) [duplicate literal removal 110]
152. funny(X0) [duplicate literal removal 91]
154. ~brave(X0) | ~happy(X0) [subsumption resolution 97,152]
240. 20 <=> happy(mary) [avatar definition]
241. happy(mary) <- (20) [avatar component clause 240]
242. ~happy(mary) <- (~20) [avatar component clause 240]
251. ~generous(X0) | ~tall(X0) [subsumption resolution 126,152]
278. 27 <=> strong(mary) [avatar definition]
279. strong(mary) <- (27) [avatar component clause 278]
282. 27 | 20 [avatar split clause 138,240,278]
311. brave(X1) | tall(X1) [resolution 150,135]
317. ~tall(mary) [resolution 251,146]
321. ~happy(X1) | tall(X1) [resolution 311,154]
338. happy(mary) | tall(mary) <- (27) [resolution 83,279]
339. tall(mary) <- (~20, 27) [subsumption resolution 338,242]
340. $false <- (~20, 27) [subsumption resolution 339,317]
341. 20 | ~27 [avatar contradiction clause 340]
378. tall(mary) <- (20) [resolution 321,241]
382. $false <- (20) [subsumption resolution 378,317]
383. ~20 [avatar contradiction clause 382]
384. $false [avatar sat refutation 282,341,383]
% SZS output end Proof for 3148492043628091659211113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or not brave is quiet and vice versa. If john is both curious and not tall then someone is both not rich and not wise. Everyone who is wise is not old. Everyone who is either kind or not quiet is either calm or funny and vice versa. Everyone who is not strong is both quiet and calm and vice versa. Everyone who is not happy or not curious is either not strong or not happy. If lucy is either not funny or patient then paul is strong and vice versa. Everyone who is either not generous or not wise is patient and vice versa. Everyone who is not happy is either patient or not strong and vice versa. If someone is not old or tall then alice is not humble and vice versa. Everyone who is both not humble and brave is either rich or not tall and vice versa. Everyone who is both not strong and old is calm or quiet and vice versa. If someone is either not patient or old then someone is not brave. If someone is tall or rich then someone is calm and vice versa. Everyone who is both not calm and funny is patient or brave and vice versa. Everyone who is both rich and not humble is both old and not strong. Alice is not calm. Susan is either humble or not tall. Fred is not generous or not old. Someone is not wise. Alice is both not curious and not tall. John is strong. | Fred is happy. | contradiction | (![X]:((old(X)<~>~brave(X))<=>quiet(X)))&
(((curious(john)&~tall(john)))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:(wise(X)=>~old(X)))&
(![X]:((kind(X)<~>~quiet(X))<=>(calm(X)<~>funny(X))))&
(![X]:(~strong(X)<=>(quiet(X)&calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~strong(X)<~>~happy(X))))&
(((~funny(lucy)<~>patient(lucy)))<=>(strong(paul)))&
(![X]:((~generous(X)<~>~wise(X))<=>patient(X)))&
(![X]:(~happy(X)<=>(patient(X)<~>~strong(X))))&
((?[X]:((~old(X)|tall(X))))<=>(~humble(alice)))&
(![X]:((~humble(X)&brave(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((~strong(X)&old(X))<=>(calm(X)|quiet(X))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:(~brave(X))))&
((?[X]:((tall(X)|rich(X))))<=>(?[X]:(calm(X))))&
(![X]:((~calm(X)&funny(X))<=>(patient(X)|brave(X))))&
(![X]:((rich(X)&~humble(X))=>(old(X)&~strong(X))))&
(~calm(alice))&
((humble(susan)<~>~tall(susan)))&
((~generous(fred)|~old(fred)))&
(?[X]:(~wise(X)))&
((~curious(alice)&~tall(alice)))&
(strong(john)) | happy(fred) | [
"p0",
"p4",
"p5",
"p8",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4315962791720421831785231
% SZS output start Proof for 4315962791720421831785231
1. ! [X0] : ((old(X0) <~> ~brave(X0)) <=> quiet(X0)) [input p0]
5. ! [X0] : (~strong(X0) <=> (calm(X0) & quiet(X0))) [input p4]
6. ! [X0] : ((~curious(X0) | ~happy(X0)) => (~strong(X0) <~> ~happy(X0))) [input p5]
9. ! [X0] : (~happy(X0) <=> (patient(X0) <~> ~strong(X0))) [input p8]
11. ! [X0] : ((brave(X0) & ~humble(X0)) <=> (rich(X0) <~> ~tall(X0))) [input p10]
12. ! [X0] : ((old(X0) & ~strong(X0)) <=> (quiet(X0) | calm(X0))) [input p11]
13. ? [X0] : (~patient(X0) <~> old(X0)) => ? [X0] : ~brave(X0) [input p12]
14. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X0] : calm(X0) [input p13]
15. ! [X0] : ((funny(X0) & ~calm(X0)) <=> (brave(X0) | patient(X0))) [input p14]
23. happy(fred) [input hypothesis]
24. ? [X0] : (~patient(X0) <~> old(X0)) => ? [X1] : ~brave(X1) [rectify 13]
25. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X1] : calm(X1) [rectify 14]
29. ! [X0] : ((~strong(X0) <~> ~happy(X0)) | (curious(X0) & happy(X0))) [ennf transformation 6]
30. ? [X1] : ~brave(X1) | ! [X0] : (~patient(X0) <=> old(X0)) [ennf transformation 24]
33. ! [X0] : ((((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | ~quiet(X0)) & (quiet(X0) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0))))) [nnf transformation 1]
37. ! [X0] : ((~strong(X0) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | strong(X0))) [nnf transformation 5]
38. ! [X0] : ((~strong(X0) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | strong(X0))) [flattening 37]
39. ! [X0] : (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | (curious(X0) & happy(X0))) [nnf transformation 29]
42. ! [X0] : ((~happy(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) & (((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | happy(X0))) [nnf transformation 9]
47. ! [X0] : (((brave(X0) & ~humble(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | (~brave(X0) | humble(X0)))) [nnf transformation 11]
48. ! [X0] : (((brave(X0) & ~humble(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | ~brave(X0) | humble(X0))) [flattening 47]
49. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (~old(X0) | strong(X0)))) [nnf transformation 12]
50. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | ~old(X0) | strong(X0))) [flattening 49]
51. ? [X1] : ~brave(X1) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0))) [nnf transformation 30]
52. ? [X0] : ~brave(X0) | ! [X1] : ((~patient(X1) | ~old(X1)) & (old(X1) | patient(X1))) [rectify 51]
53. ? [X0] : ~brave(X0) => ~brave(sK2) [choice axiom]
54. ~brave(sK2) | ! [X1] : ((~patient(X1) | ~old(X1)) & (old(X1) | patient(X1))) [skolemisation 52,53]
55. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : (~rich(X0) & ~tall(X0))) [nnf transformation 25]
56. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : (~rich(X3) & ~tall(X3))) [rectify 55]
57. ? [X0] : (rich(X0) | tall(X0)) => (rich(sK3) | tall(sK3)) [choice axiom]
58. ? [X2] : calm(X2) => calm(sK4) [choice axiom]
59. ((rich(sK3) | tall(sK3)) | ! [X1] : ~calm(X1)) & (calm(sK4) | ! [X3] : (~rich(X3) & ~tall(X3))) [skolemisation 56,58,57]
60. ! [X0] : (((funny(X0) & ~calm(X0)) | (~brave(X0) & ~patient(X0))) & ((brave(X0) | patient(X0)) | (~funny(X0) | calm(X0)))) [nnf transformation 15]
61. ! [X0] : (((funny(X0) & ~calm(X0)) | (~brave(X0) & ~patient(X0))) & (brave(X0) | patient(X0) | ~funny(X0) | calm(X0))) [flattening 60]
65. ~brave(X0) | quiet(X0) | ~old(X0) [cnf transformation 33]
81. strong(X0) | calm(X0) [cnf transformation 38]
85. happy(X0) | strong(X0) | happy(X0) [cnf transformation 39]
97. ~patient(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 42]
98. ~happy(X0) | patient(X0) | strong(X0) [cnf transformation 42]
107. rich(X0) | brave(X0) | tall(X0) [cnf transformation 48]
109. ~strong(X0) | ~calm(X0) [cnf transformation 50]
110. ~strong(X0) | ~quiet(X0) [cnf transformation 50]
113. ~brave(sK2) | old(X1) | patient(X1) [cnf transformation 54]
115. calm(sK4) | ~tall(X3) [cnf transformation 59]
116. calm(sK4) | ~rich(X3) [cnf transformation 59]
119. ~patient(X0) | ~calm(X0) [cnf transformation 61]
133. happy(fred) [cnf transformation 23]
134. happy(X0) | strong(X0) [duplicate literal removal 85]
169. patient(X0) | strong(X0) [subsumption resolution 98,134]
185. 11 <=> ! [X1] : ~tall(X1) [avatar definition]
186. ~tall(X1) <- (11) [avatar component clause 185]
196. 14 <=> brave(sK2) [avatar definition]
198. ~brave(sK2) <- (~14) [avatar component clause 196]
201. 15 <=> ! [X1] : (old(X1) | patient(X1)) [avatar definition]
202. patient(X1) | old(X1) <- (15) [avatar component clause 201]
203. 15 | ~14 [avatar split clause 113,196,201]
205. 16 <=> ! [X1] : ~calm(X1) [avatar definition]
206. ~calm(X1) <- (16) [avatar component clause 205]
217. 19 <=> ! [X3] : ~rich(X3) [avatar definition]
218. ~rich(X3) <- (19) [avatar component clause 217]
220. 20 <=> calm(sK4) [avatar definition]
222. calm(sK4) <- (20) [avatar component clause 220]
223. 19 | 20 [avatar split clause 116,220,217]
224. 11 | 20 [avatar split clause 115,220,185]
240. 24 <=> old(fred) [avatar definition]
241. old(fred) <- (24) [avatar component clause 240]
255. strong(X1) | ~calm(X1) [resolution 169,119]
290. ~calm(X1) [subsumption resolution 255,109]
291. 16 [avatar split clause 290,205]
315. 30 <=> strong(fred) [avatar definition]
316. strong(fred) <- (30) [avatar component clause 315]
317. ~strong(fred) <- (~30) [avatar component clause 315]
320. calm(fred) <- (~30) [resolution 317,81]
322. $false <- (16, ~30) [subsumption resolution 320,206]
323. ~16 | 30 [avatar contradiction clause 322]
327. ~quiet(fred) <- (30) [resolution 316,110]
343. brave(X1) | tall(X1) <- (19) [resolution 107,218]
345. brave(X1) <- (11, 19) [subsumption resolution 343,186]
346. $false <- (11, ~14, 19) [resolution 345,198]
349. ~11 | 14 | ~19 [avatar contradiction clause 346]
354. $false <- (16, 20) [subsumption resolution 222,206]
355. ~16 | ~20 [avatar contradiction clause 354]
390. brave(X0) | tall(X0) <- (19) [resolution 218,107]
391. brave(X0) <- (11, 19) [subsumption resolution 390,186]
393. ~happy(X1) | ~strong(X1) | old(X1) <- (15) [resolution 202,97]
438. ~old(X0) | quiet(X0) <- (11, 19) [resolution 391,65]
496. ~strong(fred) | old(fred) <- (15) [resolution 393,133]
500. old(fred) <- (15, 30) [subsumption resolution 496,316]
501. 24 | ~15 | ~30 [avatar split clause 500,315,201,240]
502. quiet(fred) <- (11, 19, 24) [resolution 241,438]
505. $false <- (11, 19, 24, 30) [subsumption resolution 502,327]
506. ~11 | ~19 | ~24 | ~30 [avatar contradiction clause 505]
507. $false [avatar sat refutation 203,223,224,291,323,349,355,501,506]
% SZS output end Proof for 4315962791720421831785231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either tall or patient then alice is kind or not strong.
Everyone who is not old is either tall or not rich and vice versa.
Everyone who is not funny or happy is both happy and not quiet and vice versa.
Everyone who is either not curious or not wise is both calm and kind and vice versa.
If fred is both generous and humble then someone is not old or tall.
Everyone who is wise is both curious and wise.
Everyone who is both not funny and not generous is not happy.
If john is curious or not funny then someone is not strong or calm and vice versa.
Everyone who is either not strong or patient is either not rich or wise.
If mary is not generous then susan is not kind or not old and vice versa.
If someone is happy or creative then fred is either patient or curious and vice versa.
Everyone who is both not happy and rich is either not quiet or not funny.
Everyone who is not curious is either quiet or not wise and vice versa.
If someone is either calm or not patient then john is rich or not wise.
Everyone who is curious is both not happy and not quiet.
Everyone who is not happy is happy.
John is not kind.
Someone is not creative.
Lucy is calm.
Lucy is not funny or not kind.
Lucy is happy.
Someone is not humble.
Someone is happy or quiet. | Susan is wise. | contradiction | (((tall(paul)<~>patient(paul)))=>((kind(alice)|~strong(alice))))&
(![X]:(~old(X)<=>(tall(X)<~>~rich(X))))&
(![X]:((~funny(X)|happy(X))<=>(happy(X)&~quiet(X))))&
(![X]:((~curious(X)<~>~wise(X))<=>(calm(X)&kind(X))))&
(((generous(fred)&humble(fred)))=>(?[X]:((~old(X)|tall(X)))))&
(![X]:(wise(X)=>(curious(X)&wise(X))))&
(![X]:((~funny(X)&~generous(X))=>~happy(X)))&
(((curious(john)|~funny(john)))<=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~strong(X)<~>patient(X))=>(~rich(X)<~>wise(X))))&
((~generous(mary))<=>((~kind(susan)|~old(susan))))&
((?[X]:((happy(X)|creative(X))))<=>((patient(fred)<~>curious(fred))))&
(![X]:((~happy(X)&rich(X))=>(~quiet(X)<~>~funny(X))))&
(![X]:(~curious(X)<=>(quiet(X)<~>~wise(X))))&
((?[X]:((calm(X)<~>~patient(X))))=>((rich(john)|~wise(john))))&
(![X]:(curious(X)=>(~happy(X)&~quiet(X))))&
(![X]:(~happy(X)=>happy(X)))&
(~kind(john))&
(?[X]:(~creative(X)))&
(calm(lucy))&
((~funny(lucy)|~kind(lucy)))&
(happy(lucy))&
(?[X]:(~humble(X)))&
(?[X]:((happy(X)|quiet(X)))) | wise(susan) | [
"p5",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 89667696468459720793512
% SZS output start Proof for 89667696468459720793512
6. ! [X0] : (wise(X0) => (wise(X0) & curious(X0))) [input p5]
15. ! [X0] : (curious(X0) => (~quiet(X0) & ~happy(X0))) [input p14]
16. ! [X0] : (~happy(X0) => happy(X0)) [input p15]
24. wise(susan) [input hypothesis]
29. ! [X0] : ((wise(X0) & curious(X0)) | ~wise(X0)) [ennf transformation 6]
37. ! [X0] : ((~quiet(X0) & ~happy(X0)) | ~curious(X0)) [ennf transformation 15]
38. ! [X0] : (happy(X0) | happy(X0)) [ennf transformation 16]
81. ~wise(X0) | curious(X0) [cnf transformation 29]
109. ~curious(X0) | ~happy(X0) [cnf transformation 37]
111. happy(X0) | happy(X0) [cnf transformation 38]
118. wise(susan) [cnf transformation 24]
119. happy(X0) [duplicate literal removal 111]
238. curious(susan) [resolution 81,118]
245. ~happy(susan) [resolution 238,109]
246. $false [subsumption resolution 245,119]
% SZS output end Proof for 89667696468459720793512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is old or not tall then paul is wise or curious. Everyone who is not humble is either not tall or humble and vice versa. Everyone who is both not strong and not generous is calm or strong. If someone is happy then mary is either tall or kind. Everyone who is either tall or not happy is not happy or not curious and vice versa. If someone is quiet then fred is happy or quiet and vice versa. Everyone who is funny or strong is tall or not wise. If someone is generous then someone is either not old or not funny and vice versa. Everyone who is both not funny and quiet is not rich or not tall and vice versa. If fred is not creative then someone is creative or quiet. Everyone who is not creative is not tall and vice versa. If someone is both not old and happy then someone is funny. If someone is not happy then someone is generous. Everyone who is either old or not wise is not humble. Everyone who is not brave or not kind is not calm and vice versa. Someone is either not calm or not generous. Mary is either not humble or happy. Someone is not rich. Susan is both humble and calm. Paul is not quiet or not tall. Someone is either old or wise. John is old. Someone is both old and not generous. | Mary is not creative. | entailment | (((old(lucy)|~tall(lucy)))=>((wise(paul)|curious(paul))))&
(![X]:(~humble(X)<=>(~tall(X)<~>humble(X))))&
(![X]:((~strong(X)&~generous(X))=>(calm(X)|strong(X))))&
((?[X]:(happy(X)))=>((tall(mary)<~>kind(mary))))&
(![X]:((tall(X)<~>~happy(X))<=>(~happy(X)|~curious(X))))&
((?[X]:(quiet(X)))<=>((happy(fred)|quiet(fred))))&
(![X]:((funny(X)|strong(X))=>(tall(X)|~wise(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~old(X)<~>~funny(X)))))&
(![X]:((~funny(X)&quiet(X))<=>(~rich(X)|~tall(X))))&
((~creative(fred))=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:(~creative(X)<=>~tall(X)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:(funny(X))))&
((?[X]:(~happy(X)))=>(?[X]:(generous(X))))&
(![X]:((old(X)<~>~wise(X))=>~humble(X)))&
(![X]:((~brave(X)|~kind(X))<=>~calm(X)))&
(?[X]:((~calm(X)<~>~generous(X))))&
((~humble(mary)<~>happy(mary)))&
(?[X]:(~rich(X)))&
((humble(susan)&calm(susan)))&
((~quiet(paul)|~tall(paul)))&
(?[X]:((old(X)<~>wise(X))))&
(old(john))&
(?[X]:((old(X)&~generous(X)))) | ~creative(mary) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4337648547573920482434674
% SZS output start Proof for 4337648547573920482434674
2. ! [X0] : (~humble(X0) <=> (~tall(X0) <~> humble(X0))) [input p1]
11. ! [X0] : (~creative(X0) <=> ~tall(X0)) [input p10]
24. creative(mary) [input hypothesis]
28. ! [X0] : (~tall(X0) => ~creative(X0)) [unused predicate definition removal 11]
37. ! [X0] : (~creative(X0) | tall(X0)) [ennf transformation 28]
41. ! [X0] : ((~humble(X0) | ((~tall(X0) | ~humble(X0)) & (humble(X0) | tall(X0)))) & (((~humble(X0) | tall(X0)) & (humble(X0) | ~tall(X0))) | humble(X0))) [nnf transformation 2]
81. humble(X0) | ~tall(X0) | humble(X0) [cnf transformation 41]
84. ~humble(X0) | ~tall(X0) | ~humble(X0) [cnf transformation 41]
109. ~creative(X0) | tall(X0) [cnf transformation 37]
130. creative(mary) [cnf transformation 24]
134. humble(X0) | ~tall(X0) [duplicate literal removal 81]
135. ~humble(X0) | ~tall(X0) [duplicate literal removal 84]
154. ~tall(X0) [subsumption resolution 134,135]
212. ~creative(X0) [subsumption resolution 109,154]
252. $false [subsumption resolution 130,212]
% SZS output end Proof for 4337648547573920482434674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and funny is creative or wise.
If susan is both not funny and not kind then someone is either wise or not calm.
If someone is either not calm or humble then someone is both not strong and funny.
If susan is not calm or not funny then someone is old.
Everyone who is not patient is generous or strong and vice versa.
If someone is happy then someone is both not curious and calm and vice versa.
Everyone who is creative or not tall is both brave and not wise and vice versa.
Everyone who is both happy and not rich is happy.
Everyone who is either curious or not kind is either quiet or old and vice versa.
If someone is either happy or quiet then someone is both curious and funny and vice versa.
Everyone who is either not humble or not generous is wise and vice versa.
Everyone who is not quiet is curious and vice versa.
Everyone who is both not strong and creative is not tall.
Everyone who is either not kind or not quiet is creative or wise.
If someone is both calm and not happy then lucy is either not generous or happy and vice versa.
Everyone who is either not strong or not wise is wise and vice versa.
Paul is both not curious and wise.
Lucy is creative or not funny.
Alice is either not creative or happy.
Alice is generous or curious.
Alice is either not humble or rich.
Fred is not kind.
Someone is not tall. | Alice is not curious. | neutral | (![X]:((creative(X)&funny(X))=>(creative(X)|wise(X))))&
(((~funny(susan)&~kind(susan)))=>(?[X]:((wise(X)<~>~calm(X)))))&
((?[X]:((~calm(X)<~>humble(X))))=>(?[X]:((~strong(X)&funny(X)))))&
(((~calm(susan)|~funny(susan)))=>(?[X]:(old(X))))&
(![X]:(~patient(X)<=>(generous(X)|strong(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)&calm(X)))))&
(![X]:((creative(X)|~tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((happy(X)&~rich(X))=>happy(X)))&
(![X]:((curious(X)<~>~kind(X))<=>(quiet(X)<~>old(X))))&
((?[X]:((happy(X)<~>quiet(X))))<=>(?[X]:((curious(X)&funny(X)))))&
(![X]:((~humble(X)<~>~generous(X))<=>wise(X)))&
(![X]:(~quiet(X)<=>curious(X)))&
(![X]:((~strong(X)&creative(X))=>~tall(X)))&
(![X]:((~kind(X)<~>~quiet(X))=>(creative(X)|wise(X))))&
((?[X]:((calm(X)&~happy(X))))<=>((~generous(lucy)<~>happy(lucy))))&
(![X]:((~strong(X)<~>~wise(X))<=>wise(X)))&
((~curious(paul)&wise(paul)))&
((creative(lucy)|~funny(lucy)))&
((~creative(alice)<~>happy(alice)))&
((generous(alice)|curious(alice)))&
((~humble(alice)<~>rich(alice)))&
(~kind(fred))&
(?[X]:(~tall(X))) | ~curious(alice) | [] | null | 0 |
Everyone who is both not creative and curious is not humble. Everyone who is either not creative or generous is either not patient or old. Everyone who is either not generous or quiet is not patient and vice versa. Everyone who is both not tall and not happy is either quiet or humble and vice versa. Everyone who is curious is either old or not patient and vice versa. Everyone who is funny is not funny or not creative and vice versa. If alice is either not curious or humble then lucy is either creative or not wise. If someone is either not brave or not curious then mary is curious or calm and vice versa. Everyone who is both happy and not happy is calm or quiet and vice versa. If someone is rich or patient then someone is kind. Everyone who is tall is creative or rich. If someone is not creative or tall then someone is funny or happy and vice versa. Everyone who is either not old or not brave is both not calm and not tall. Everyone who is either calm or creative is generous or rich and vice versa. Fred is either not patient or not strong. Someone is both funny and not generous. Someone is either humble or not patient. | Mary is not curious. | contradiction | (![X]:((~creative(X)&curious(X))=>~humble(X)))&
(![X]:((~creative(X)<~>generous(X))=>(~patient(X)<~>old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>~patient(X)))&
(![X]:((~tall(X)&~happy(X))<=>(quiet(X)<~>humble(X))))&
(![X]:(curious(X)<=>(old(X)<~>~patient(X))))&
(![X]:(funny(X)<=>(~funny(X)|~creative(X))))&
(((~curious(alice)<~>humble(alice)))=>((creative(lucy)<~>~wise(lucy))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>((curious(mary)|calm(mary))))&
(![X]:((happy(X)&~happy(X))<=>(calm(X)|quiet(X))))&
((?[X]:((rich(X)|patient(X))))=>(?[X]:(kind(X))))&
(![X]:(tall(X)=>(creative(X)|rich(X))))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(~calm(X)&~tall(X))))&
(![X]:((calm(X)<~>creative(X))<=>(generous(X)|rich(X))))&
((~patient(fred)<~>~strong(fred)))&
(?[X]:((funny(X)&~generous(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | ~curious(mary) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4265154254386179965356505
% SZS output start Proof for 4265154254386179965356505
2. ! [X0] : ((~creative(X0) <~> generous(X0)) => (~patient(X0) <~> old(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> quiet(X0)) <=> ~patient(X0)) [input p2]
5. ! [X0] : (curious(X0) <=> (old(X0) <~> ~patient(X0))) [input p4]
6. ! [X0] : (funny(X0) <=> (~creative(X0) | ~funny(X0))) [input p5]
9. ! [X0] : ((~happy(X0) & happy(X0)) <=> (quiet(X0) | calm(X0))) [input p8]
14. ! [X0] : ((calm(X0) <~> creative(X0)) <=> (rich(X0) | generous(X0))) [input p13]
18. ~curious(mary) [input hypothesis]
24. ! [X0] : ((~patient(X0) <~> old(X0)) | (~creative(X0) <=> generous(X0))) [ennf transformation 2]
29. ! [X0] : (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) [nnf transformation 24]
30. ! [X0] : ((((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | patient(X0)) & (~patient(X0) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0))))) [nnf transformation 3]
33. ! [X0] : ((curious(X0) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) & (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | ~curious(X0))) [nnf transformation 5]
34. ! [X0] : ((funny(X0) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 6]
35. ! [X0] : ((funny(X0) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~funny(X0))) [flattening 34]
42. ! [X0] : (((~happy(X0) & happy(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 9]
43. ! [X0] : (((~happy(X0) & happy(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | happy(X0) | ~happy(X0))) [flattening 42]
50. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & ~generous(X0))) & ((rich(X0) | generous(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [nnf transformation 14]
51. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & ~generous(X0))) & (rich(X0) | generous(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [flattening 50]
61. ~old(X0) | patient(X0) | generous(X0) | creative(X0) [cnf transformation 29]
63. ~patient(X0) | quiet(X0) | generous(X0) [cnf transformation 30]
76. old(X0) | curious(X0) | patient(X0) [cnf transformation 33]
77. ~creative(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 35]
78. funny(X0) | funny(X0) [cnf transformation 35]
91. happy(X0) | ~calm(X0) [cnf transformation 43]
92. happy(X0) | ~quiet(X0) [cnf transformation 43]
93. ~calm(X0) | ~happy(X0) [cnf transformation 43]
94. ~happy(X0) | ~quiet(X0) [cnf transformation 43]
106. creative(X0) | calm(X0) | ~generous(X0) [cnf transformation 51]
116. ~curious(mary) [cnf transformation 18]
117. ~creative(X0) | ~funny(X0) [duplicate literal removal 77]
118. funny(X0) [duplicate literal removal 78]
119. ~creative(X0) [subsumption resolution 117,118]
150. 7 <=> curious(mary) [avatar definition]
152. ~curious(mary) <- (~7) [avatar component clause 150]
164. ~quiet(X0) [subsumption resolution 92,94]
165. ~calm(X0) [subsumption resolution 91,93]
169. calm(X0) | ~generous(X0) [subsumption resolution 106,119]
170. ~generous(X0) [subsumption resolution 169,165]
191. ~7 [avatar split clause 116,150]
217. patient(X0) | generous(X0) | creative(X0) | curious(X0) | patient(X0) [resolution 61,76]
218. patient(X0) | generous(X0) | creative(X0) | curious(X0) [duplicate literal removal 217]
219. patient(X0) | creative(X0) | curious(X0) [subsumption resolution 218,170]
220. patient(X0) | curious(X0) [subsumption resolution 219,119]
225. curious(X3) | quiet(X3) | generous(X3) [resolution 220,63]
229. curious(X3) | generous(X3) [subsumption resolution 225,164]
230. curious(X3) [subsumption resolution 229,170]
239. $false <- (~7) [resolution 230,152]
241. 7 [avatar contradiction clause 239]
242. $false [avatar sat refutation 191,241]
% SZS output end Proof for 4265154254386179965356505
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not creative or not quiet then someone is either not brave or not tall. Everyone who is both not strong and patient is tall. If alice is both funny and tall then someone is either not creative or rich. If fred is not funny then someone is either curious or happy. If lucy is both not generous and generous then lucy is both brave and not creative. If someone is both brave and calm then susan is either not kind or not funny and vice versa. Everyone who is both kind and brave is either tall or old. If someone is funny then someone is either calm or not patient and vice versa. Everyone who is not wise is tall. Everyone who is not curious or not happy is not old. If paul is not patient or not quiet then mary is quiet or not tall and vice versa. Everyone who is both funny and not calm is both old and kind. If alice is either tall or not patient then someone is either calm or curious. Everyone who is not quiet is not quiet or old and vice versa. Everyone who is either not creative or tall is not quiet or wise. Everyone who is creative is both brave and strong. Paul is both curious and not tall. Susan is not happy. Someone is brave. Someone is both calm and not quiet. Mary is either calm or not curious. Paul is strong. Someone is not wise or wise. John is brave or generous. | Alice is funny. | neutral | (((~creative(paul)|~quiet(paul)))=>(?[X]:((~brave(X)<~>~tall(X)))))&
(![X]:((~strong(X)&patient(X))=>tall(X)))&
(((funny(alice)&tall(alice)))=>(?[X]:((~creative(X)<~>rich(X)))))&
((~funny(fred))=>(?[X]:((curious(X)<~>happy(X)))))&
(((~generous(lucy)&generous(lucy)))=>((brave(lucy)&~creative(lucy))))&
((?[X]:((brave(X)&calm(X))))<=>((~kind(susan)<~>~funny(susan))))&
(![X]:((kind(X)&brave(X))=>(tall(X)<~>old(X))))&
((?[X]:(funny(X)))<=>(?[X]:((calm(X)<~>~patient(X)))))&
(![X]:(~wise(X)=>tall(X)))&
(![X]:((~curious(X)|~happy(X))=>~old(X)))&
(((~patient(paul)|~quiet(paul)))<=>((quiet(mary)|~tall(mary))))&
(![X]:((funny(X)&~calm(X))=>(old(X)&kind(X))))&
(((tall(alice)<~>~patient(alice)))=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:(~quiet(X)<=>(~quiet(X)|old(X))))&
(![X]:((~creative(X)<~>tall(X))=>(~quiet(X)|wise(X))))&
(![X]:(creative(X)=>(brave(X)&strong(X))))&
((curious(paul)&~tall(paul)))&
(~happy(susan))&
(?[X]:(brave(X)))&
(?[X]:((calm(X)&~quiet(X))))&
((calm(mary)<~>~curious(mary)))&
(strong(paul))&
(?[X]:((~wise(X)|wise(X))))&
((brave(john)|generous(john))) | funny(alice) | [] | null | 0 |
If someone is both patient and happy then john is both brave and generous and vice versa. Everyone who is both not patient and humble is both not strong and not kind and vice versa. Everyone who is both not old and not rich is not rich. If someone is not curious or not generous then someone is either calm or strong. Everyone who is brave or not tall is both not creative and not strong. Everyone who is brave is either humble or not funny and vice versa. Everyone who is rich is creative and vice versa. If mary is happy or creative then someone is not funny and vice versa. Everyone who is either not old or not kind is kind. If susan is not strong then alice is both kind and not humble and vice versa. Everyone who is either kind or creative is rich or brave and vice versa. If alice is not humble then someone is both generous and not quiet and vice versa. Everyone who is both not generous and patient is not patient and vice versa. Everyone who is kind or rich is old. Everyone who is either calm or not patient is either not curious or not kind and vice versa. If someone is both not quiet and rich then fred is not kind and vice versa. John is both patient and generous. Alice is strong. Someone is quiet or curious. Lucy is not brave or kind. Fred is generous or kind. John is not happy. | Susan is strong. | entailment | ((?[X]:((patient(X)&happy(X))))<=>((brave(john)&generous(john))))&
(![X]:((~patient(X)&humble(X))<=>(~strong(X)&~kind(X))))&
(![X]:((~old(X)&~rich(X))=>~rich(X)))&
((?[X]:((~curious(X)|~generous(X))))=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((brave(X)|~tall(X))=>(~creative(X)&~strong(X))))&
(![X]:(brave(X)<=>(humble(X)<~>~funny(X))))&
(![X]:(rich(X)<=>creative(X)))&
(((happy(mary)|creative(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)<~>~kind(X))=>kind(X)))&
((~strong(susan))<=>((kind(alice)&~humble(alice))))&
(![X]:((kind(X)<~>creative(X))<=>(rich(X)|brave(X))))&
((~humble(alice))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~generous(X)&patient(X))<=>~patient(X)))&
(![X]:((kind(X)|rich(X))=>old(X)))&
(![X]:((calm(X)<~>~patient(X))<=>(~curious(X)<~>~kind(X))))&
((?[X]:((~quiet(X)&rich(X))))<=>(~kind(fred)))&
((patient(john)&generous(john)))&
(strong(alice))&
(?[X]:((quiet(X)|curious(X))))&
((~brave(lucy)|kind(lucy)))&
((generous(fred)|kind(fred)))&
(~happy(john)) | strong(susan) | [
"p4",
"p6",
"p9",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6998652760877690072875509
% SZS output start Proof for 6998652760877690072875509
5. ! [X0] : ((~tall(X0) | brave(X0)) => (~strong(X0) & ~creative(X0))) [input p4]
7. ! [X0] : (rich(X0) <=> creative(X0)) [input p6]
10. ~strong(susan) <=> (~humble(alice) & kind(alice)) [input p9]
11. ! [X0] : ((kind(X0) <~> creative(X0)) <=> (brave(X0) | rich(X0))) [input p10]
18. strong(alice) [input p17]
23. ~strong(susan) [input hypothesis]
25. ! [X0] : (brave(X0) => (~strong(X0) & ~creative(X0))) [pure predicate removal 5]
29. ! [X0] : ((~strong(X0) & ~creative(X0)) | ~brave(X0)) [ennf transformation 25]
44. ! [X0] : ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0))) [nnf transformation 7]
51. (~strong(susan) | (humble(alice) | ~kind(alice))) & ((~humble(alice) & kind(alice)) | strong(susan)) [nnf transformation 10]
52. (~strong(susan) | humble(alice) | ~kind(alice)) & ((~humble(alice) & kind(alice)) | strong(susan)) [flattening 51]
53. ! [X0] : ((((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0))))) [nnf transformation 11]
54. ! [X0] : ((((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0))))) [flattening 53]
82. ~strong(X0) | ~brave(X0) [cnf transformation 29]
87. ~rich(X0) | creative(X0) [cnf transformation 44]
88. ~creative(X0) | rich(X0) [cnf transformation 44]
94. kind(alice) | strong(susan) [cnf transformation 52]
97. brave(X0) | rich(X0) | creative(X0) | ~kind(X0) [cnf transformation 54]
101. ~creative(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 54]
124. strong(alice) [cnf transformation 18]
129. ~strong(susan) [cnf transformation 23]
193. 14 <=> kind(alice) [avatar definition]
194. kind(alice) <- (14) [avatar component clause 193]
201. 16 <=> strong(susan) [avatar definition]
206. 16 | 14 [avatar split clause 94,193,201]
207. ~creative(X0) | ~kind(X0) [subsumption resolution 101,88]
209. brave(X0) | creative(X0) | ~kind(X0) [subsumption resolution 97,87]
210. ~kind(X0) | brave(X0) [subsumption resolution 209,207]
264. ~16 [avatar split clause 129,201]
271. ~brave(alice) [resolution 82,124]
283. brave(alice) <- (14) [resolution 210,194]
285. $false <- (14) [subsumption resolution 283,271]
286. ~14 [avatar contradiction clause 285]
287. $false [avatar sat refutation 206,264,286]
% SZS output end Proof for 6998652760877690072875509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise or not rich is both not brave and not kind and vice versa. Everyone who is not strong is calm or funny and vice versa. Everyone who is quiet or strong is both not humble and not old and vice versa. Everyone who is both not patient and not kind is both strong and not tall and vice versa. Everyone who is either generous or not old is not strong or rich. If someone is either humble or patient then john is not curious or not tall. If alice is both quiet and strong then someone is not brave. If mary is both not old and brave then someone is either not kind or humble. Everyone who is both creative and generous is either generous or not wise and vice versa. Everyone who is either happy or humble is both funny and not strong. Everyone who is strong is humble or funny and vice versa. Everyone who is either not tall or not rich is not kind or brave and vice versa. Everyone who is both rich and creative is either not quiet or generous and vice versa. Everyone who is both humble and not generous is not happy. Everyone who is either not tall or calm is both not calm and not old and vice versa. Alice is either quiet or tall. Mary is either not funny or not generous. Alice is either brave or strong. Someone is either strong or brave. Mary is wise or brave. | John is brave. | neutral | (![X]:((~wise(X)|~rich(X))<=>(~brave(X)&~kind(X))))&
(![X]:(~strong(X)<=>(calm(X)|funny(X))))&
(![X]:((quiet(X)|strong(X))<=>(~humble(X)&~old(X))))&
(![X]:((~patient(X)&~kind(X))<=>(strong(X)&~tall(X))))&
(![X]:((generous(X)<~>~old(X))=>(~strong(X)|rich(X))))&
((?[X]:((humble(X)<~>patient(X))))=>((~curious(john)|~tall(john))))&
(((quiet(alice)&strong(alice)))=>(?[X]:(~brave(X))))&
(((~old(mary)&brave(mary)))=>(?[X]:((~kind(X)<~>humble(X)))))&
(![X]:((creative(X)&generous(X))<=>(generous(X)<~>~wise(X))))&
(![X]:((happy(X)<~>humble(X))=>(funny(X)&~strong(X))))&
(![X]:(strong(X)<=>(humble(X)|funny(X))))&
(![X]:((~tall(X)<~>~rich(X))<=>(~kind(X)|brave(X))))&
(![X]:((rich(X)&creative(X))<=>(~quiet(X)<~>generous(X))))&
(![X]:((humble(X)&~generous(X))=>~happy(X)))&
(![X]:((~tall(X)<~>calm(X))<=>(~calm(X)&~old(X))))&
((quiet(alice)<~>tall(alice)))&
((~funny(mary)<~>~generous(mary)))&
((brave(alice)<~>strong(alice)))&
(?[X]:((strong(X)<~>brave(X))))&
((wise(mary)|brave(mary))) | brave(john) | [] | null | 0 |
Everyone who is both not generous and quiet is strong or not rich. Everyone who is not rich is either creative or strong and vice versa. Everyone who is either curious or not old is either not curious or rich and vice versa. Everyone who is kind or generous is both quiet and old. If lucy is not quiet then paul is not humble. If someone is quiet then mary is not wise or old and vice versa. Everyone who is funny or not curious is both not strong and not generous. If someone is calm or tall then someone is patient and vice versa. If fred is creative or not happy then someone is not brave and vice versa. If someone is not strong or patient then someone is not curious or humble. Everyone who is both rich and humble is both not happy and not creative and vice versa. Everyone who is not wise or happy is either not curious or not old and vice versa. If someone is not quiet or quiet then someone is both funny and not creative. If alice is both not old and rich then alice is old or not strong and vice versa. If someone is either not wise or not generous then someone is not happy and vice versa. Someone is not strong. Someone is either not kind or old. John is not patient. Someone is both quiet and not generous. Someone is both not happy and tall. Paul is not kind or humble. John is not tall or not funny. Fred is not old. | Fred is not generous. | entailment | (![X]:((~generous(X)&quiet(X))=>(strong(X)|~rich(X))))&
(![X]:(~rich(X)<=>(creative(X)<~>strong(X))))&
(![X]:((curious(X)<~>~old(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((kind(X)|generous(X))=>(quiet(X)&old(X))))&
((~quiet(lucy))=>(~humble(paul)))&
((?[X]:(quiet(X)))<=>((~wise(mary)|old(mary))))&
(![X]:((funny(X)|~curious(X))=>(~strong(X)&~generous(X))))&
((?[X]:((calm(X)|tall(X))))<=>(?[X]:(patient(X))))&
(((creative(fred)|~happy(fred)))<=>(?[X]:(~brave(X))))&
((?[X]:((~strong(X)|patient(X))))=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:((rich(X)&humble(X))<=>(~happy(X)&~creative(X))))&
(![X]:((~wise(X)|happy(X))<=>(~curious(X)<~>~old(X))))&
((?[X]:((~quiet(X)|quiet(X))))=>(?[X]:((funny(X)&~creative(X)))))&
(((~old(alice)&rich(alice)))<=>((old(alice)|~strong(alice))))&
((?[X]:((~wise(X)<~>~generous(X))))<=>(?[X]:(~happy(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)<~>old(X))))&
(~patient(john))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((~happy(X)&tall(X))))&
((~kind(paul)|humble(paul)))&
((~tall(john)|~funny(john)))&
(~old(fred)) | ~generous(fred) | [
"p3",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6129198964478390192122724
% SZS output start Proof for 6129198964478390192122724
4. ! [X0] : ((generous(X0) | kind(X0)) => (old(X0) & quiet(X0))) [input p3]
23. ~old(fred) [input p22]
24. generous(fred) [input hypothesis]
31. ! [X0] : ((old(X0) & quiet(X0)) | (~generous(X0) & ~kind(X0))) [ennf transformation 4]
95. ~generous(X0) | old(X0) [cnf transformation 31]
145. ~old(fred) [cnf transformation 23]
146. generous(fred) [cnf transformation 24]
326. old(fred) [resolution 95,146]
327. $false [subsumption resolution 326,145]
% SZS output end Proof for 6129198964478390192122724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is old then john is not quiet or quiet. If lucy is not funny or funny then someone is both funny and happy and vice versa. Everyone who is either not brave or tall is old or not brave. Everyone who is both quiet and not generous is not brave or curious and vice versa. If someone is either not funny or curious then john is either not patient or not quiet. Everyone who is either not patient or wise is patient and vice versa. If someone is either not rich or not patient then susan is both tall and not brave. Everyone who is brave or not generous is not tall and vice versa. Everyone who is funny or not brave is either brave or strong. If fred is either quiet or not strong then mary is generous. If someone is not wise or generous then susan is either not patient or not humble. If someone is not brave then fred is either patient or quiet and vice versa. Everyone who is rich or not generous is either humble or not old and vice versa. If fred is not quiet then someone is both quiet and calm. If someone is happy then someone is wise or tall and vice versa. If fred is either creative or not funny then lucy is both curious and kind and vice versa. Mary is calm. Lucy is not funny. Alice is either not generous or happy. Someone is either happy or not curious. Mary is creative. Lucy is funny or not creative. Someone is patient. | Alice is wise. | entailment | ((old(lucy))=>((~quiet(john)|quiet(john))))&
(((~funny(lucy)|funny(lucy)))<=>(?[X]:((funny(X)&happy(X)))))&
(![X]:((~brave(X)<~>tall(X))=>(old(X)|~brave(X))))&
(![X]:((quiet(X)&~generous(X))<=>(~brave(X)|curious(X))))&
((?[X]:((~funny(X)<~>curious(X))))=>((~patient(john)<~>~quiet(john))))&
(![X]:((~patient(X)<~>wise(X))<=>patient(X)))&
((?[X]:((~rich(X)<~>~patient(X))))=>((tall(susan)&~brave(susan))))&
(![X]:((brave(X)|~generous(X))<=>~tall(X)))&
(![X]:((funny(X)|~brave(X))=>(brave(X)<~>strong(X))))&
(((quiet(fred)<~>~strong(fred)))=>(generous(mary)))&
((?[X]:((~wise(X)|generous(X))))=>((~patient(susan)<~>~humble(susan))))&
((?[X]:(~brave(X)))<=>((patient(fred)<~>quiet(fred))))&
(![X]:((rich(X)|~generous(X))<=>(humble(X)<~>~old(X))))&
((~quiet(fred))=>(?[X]:((quiet(X)&calm(X)))))&
((?[X]:(happy(X)))<=>(?[X]:((wise(X)|tall(X)))))&
(((creative(fred)<~>~funny(fred)))<=>((curious(lucy)&kind(lucy))))&
(calm(mary))&
(~funny(lucy))&
((~generous(alice)<~>happy(alice)))&
(?[X]:((happy(X)<~>~curious(X))))&
(creative(mary))&
((funny(lucy)|~creative(lucy)))&
(?[X]:(patient(X))) | wise(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 793628474011222056423428
% SZS output start Proof for 793628474011222056423428
6. ! [X0] : ((~patient(X0) <~> wise(X0)) <=> patient(X0)) [input p5]
24. ~wise(alice) [input hypothesis]
47. ! [X0] : ((((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0))))) [nnf transformation 6]
92. patient(X0) | wise(X0) | patient(X0) [cnf transformation 47]
94. wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 47]
141. ~wise(alice) [cnf transformation 24]
143. patient(X0) | wise(X0) [duplicate literal removal 92]
144. wise(X0) | ~patient(X0) [duplicate literal removal 94]
180. wise(X0) [subsumption resolution 143,144]
304. $false [subsumption resolution 141,180]
% SZS output end Proof for 793628474011222056423428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then mary is brave or not rich and vice versa. If someone is both not brave and humble then someone is not strong or not humble. Everyone who is either patient or creative is both old and quiet. Everyone who is both not happy and generous is not calm and vice versa. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. If lucy is brave or old then lucy is either rich or humble. Everyone who is strong is humble and vice versa. If mary is both not calm and rich then someone is not old and vice versa. Everyone who is calm is either old or kind. Fred is both tall and not strong. Someone is not strong or happy. Someone is not wise or strong. Someone is curious. Someone is either generous or calm. Someone is either not happy or strong. | Mary is not brave. | entailment | ((?[X]:(generous(X)))<=>((brave(mary)|~rich(mary))))&
((?[X]:((~brave(X)&humble(X))))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((patient(X)<~>creative(X))=>(old(X)&quiet(X))))&
(![X]:((~happy(X)&generous(X))<=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
(((brave(lucy)|old(lucy)))=>((rich(lucy)<~>humble(lucy))))&
(![X]:(strong(X)<=>humble(X)))&
(((~calm(mary)&rich(mary)))<=>(?[X]:(~old(X))))&
(![X]:(calm(X)=>(old(X)<~>kind(X))))&
((tall(fred)&~strong(fred)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~wise(X)|strong(X))))&
(?[X]:(curious(X)))&
(?[X]:((generous(X)<~>calm(X))))&
(?[X]:((~happy(X)<~>strong(X)))) | ~brave(mary) | [
"p0",
"p3",
"p5",
"p7",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2668308486738160458712942
% SZS output start Proof for 2668308486738160458712942
1. ? [X0] : generous(X0) <=> (~rich(mary) | brave(mary)) [input p0]
4. ! [X0] : ((generous(X0) & ~happy(X0)) <=> ~calm(X0)) [input p3]
6. ! [X0] : ((old(X0) | kind(X0)) <=> quiet(X0)) [input p5]
8. ! [X0] : ((generous(X0) | funny(X0)) => ~quiet(X0)) [input p7]
10. ! [X0] : ((~patient(X0) | wise(X0)) => ~generous(X0)) [input p9]
12. ! [X0] : ((~wise(X0) & rich(X0)) <=> (~calm(X0) <~> ~old(X0))) [input p11]
15. (rich(mary) & ~calm(mary)) <=> ? [X0] : ~old(X0) [input p14]
23. brave(mary) [input hypothesis]
28. ! [X0] : (~quiet(X0) | (~generous(X0) & ~funny(X0))) [ennf transformation 8]
30. ! [X0] : (~generous(X0) | (patient(X0) & ~wise(X0))) [ennf transformation 10]
33. (? [X0] : generous(X0) | (rich(mary) & ~brave(mary))) & ((~rich(mary) | brave(mary)) | ! [X0] : ~generous(X0)) [nnf transformation 1]
34. (? [X0] : generous(X0) | (rich(mary) & ~brave(mary))) & (~rich(mary) | brave(mary) | ! [X0] : ~generous(X0)) [flattening 33]
35. (? [X0] : generous(X0) | (rich(mary) & ~brave(mary))) & (~rich(mary) | brave(mary) | ! [X1] : ~generous(X1)) [rectify 34]
36. ? [X0] : generous(X0) => generous(sK0) [choice axiom]
37. (generous(sK0) | (rich(mary) & ~brave(mary))) & (~rich(mary) | brave(mary) | ! [X1] : ~generous(X1)) [skolemisation 35,36]
42. ! [X0] : (((generous(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | (~generous(X0) | happy(X0)))) [nnf transformation 4]
43. ! [X0] : (((generous(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | ~generous(X0) | happy(X0))) [flattening 42]
46. ! [X0] : (((old(X0) | kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & ~kind(X0)))) [nnf transformation 6]
47. ! [X0] : ((old(X0) | kind(X0) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & ~kind(X0)))) [flattening 46]
53. ! [X0] : (((~wise(X0) & rich(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | (wise(X0) | ~rich(X0)))) [nnf transformation 12]
54. ! [X0] : (((~wise(X0) & rich(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | wise(X0) | ~rich(X0))) [flattening 53]
57. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | (~rich(mary) | calm(mary))) [nnf transformation 15]
58. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~rich(mary) | calm(mary)) [flattening 57]
59. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~rich(mary) | calm(mary)) [rectify 58]
60. ? [X1] : ~old(X1) => ~old(sK2) [choice axiom]
61. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (~old(sK2) | ~rich(mary) | calm(mary)) [skolemisation 59,60]
74. generous(sK0) | ~brave(mary) [cnf transformation 37]
83. calm(X0) | generous(X0) [cnf transformation 43]
88. ~old(X0) | quiet(X0) [cnf transformation 47]
97. ~quiet(X0) | ~generous(X0) [cnf transformation 28]
100. ~wise(X0) | ~generous(X0) [cnf transformation 30]
106. ~rich(X0) | calm(X0) | wise(X0) | old(X0) [cnf transformation 54]
118. ~calm(mary) | old(X0) [cnf transformation 61]
119. rich(mary) | old(X0) [cnf transformation 61]
130. brave(mary) [cnf transformation 23]
132. 1 <=> rich(mary) [avatar definition]
134. rich(mary) <- (1) [avatar component clause 132]
136. 2 <=> generous(sK0) [avatar definition]
138. generous(sK0) <- (2) [avatar component clause 136]
141. 3 <=> brave(mary) [avatar definition]
144. ~3 | 2 [avatar split clause 74,136,141]
146. 4 <=> ! [X1] : ~generous(X1) [avatar definition]
147. ~generous(X1) <- (4) [avatar component clause 146]
204. 17 <=> ! [X0] : old(X0) [avatar definition]
205. old(X0) <- (17) [avatar component clause 204]
206. 17 | 1 [avatar split clause 119,132,204]
208. 18 <=> calm(mary) [avatar definition]
210. ~calm(mary) <- (~18) [avatar component clause 208]
211. 17 | ~18 [avatar split clause 118,208,204]
254. 3 [avatar split clause 130,141]
258. quiet(X0) <- (17) [resolution 88,205]
259. ~generous(X0) <- (17) [resolution 97,258]
260. 4 | ~17 [avatar split clause 259,204,146]
279. 30 <=> old(mary) [avatar definition]
280. ~old(mary) <- (~30) [avatar component clause 279]
281. old(mary) <- (30) [avatar component clause 279]
287. $false <- (2, 4) [resolution 147,138]
288. ~2 | ~4 [avatar contradiction clause 287]
289. generous(mary) <- (~18) [resolution 210,83]
320. 35 <=> quiet(mary) [avatar definition]
322. quiet(mary) <- (35) [avatar component clause 320]
326. quiet(mary) <- (30) [resolution 281,88]
328. 35 | ~30 [avatar split clause 326,279,320]
406. calm(mary) | wise(mary) | old(mary) <- (1) [resolution 106,134]
408. wise(mary) | old(mary) <- (1, ~18) [subsumption resolution 406,210]
409. wise(mary) <- (1, ~18, ~30) [subsumption resolution 408,280]
412. ~generous(mary) <- (1, ~18, ~30) [resolution 409,100]
413. $false <- (1, ~18, ~30) [subsumption resolution 412,289]
414. ~1 | 18 | 30 [avatar contradiction clause 413]
474. ~generous(mary) <- (35) [resolution 322,97]
475. $false <- (~18, 35) [subsumption resolution 474,289]
476. 18 | ~35 [avatar contradiction clause 475]
477. $false [avatar sat refutation 144,206,211,254,260,288,328,414,476]
% SZS output end Proof for 2668308486738160458712942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both curious and patient then someone is both quiet and generous. Everyone who is brave is not creative or kind and vice versa. If susan is either old or happy then lucy is not curious or curious and vice versa. Everyone who is old or not funny is both not creative and not humble and vice versa. Everyone who is either not creative or not old is happy. Everyone who is both not strong and not patient is not funny and vice versa. Everyone who is either not generous or not happy is not quiet or curious. Everyone who is strong is not strong or not quiet and vice versa. Everyone who is not creative or not quiet is either humble or not funny. Everyone who is not humble or happy is creative. If alice is not creative or not generous then someone is not old and vice versa. Everyone who is brave is humble or brave and vice versa. Everyone who is both not tall and not happy is either not rich or not curious and vice versa. Everyone who is not happy is both not humble and quiet and vice versa. If john is not tall then someone is not brave or not kind and vice versa. Everyone who is old is not happy and vice versa. Susan is not quiet or quiet. Lucy is either happy or not brave. John is either not happy or happy. Paul is not quiet or creative. Someone is not old or kind. Fred is both rich and humble. | Fred is old. | contradiction | (((curious(paul)&patient(paul)))=>(?[X]:((quiet(X)&generous(X)))))&
(![X]:(brave(X)<=>(~creative(X)|kind(X))))&
(((old(susan)<~>happy(susan)))<=>((~curious(lucy)|curious(lucy))))&
(![X]:((old(X)|~funny(X))<=>(~creative(X)&~humble(X))))&
(![X]:((~creative(X)<~>~old(X))=>happy(X)))&
(![X]:((~strong(X)&~patient(X))<=>~funny(X)))&
(![X]:((~generous(X)<~>~happy(X))=>(~quiet(X)|curious(X))))&
(![X]:(strong(X)<=>(~strong(X)|~quiet(X))))&
(![X]:((~creative(X)|~quiet(X))=>(humble(X)<~>~funny(X))))&
(![X]:((~humble(X)|happy(X))=>creative(X)))&
(((~creative(alice)|~generous(alice)))<=>(?[X]:(~old(X))))&
(![X]:(brave(X)<=>(humble(X)|brave(X))))&
(![X]:((~tall(X)&~happy(X))<=>(~rich(X)<~>~curious(X))))&
(![X]:(~happy(X)<=>(~humble(X)&quiet(X))))&
((~tall(john))<=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:(old(X)<=>~happy(X)))&
((~quiet(susan)|quiet(susan)))&
((happy(lucy)<~>~brave(lucy)))&
((~happy(john)<~>happy(john)))&
((~quiet(paul)|creative(paul)))&
(?[X]:((~old(X)|kind(X))))&
((rich(fred)&humble(fred))) | old(fred) | [
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6955005780368365903507515
% SZS output start Proof for 6955005780368365903507515
8. ! [X0] : (strong(X0) <=> (~quiet(X0) | ~strong(X0))) [input p7]
14. ! [X0] : (~happy(X0) <=> (quiet(X0) & ~humble(X0))) [input p13]
16. ! [X0] : (old(X0) <=> ~happy(X0)) [input p15]
23. old(fred) [input hypothesis]
43. ! [X0] : ((strong(X0) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | ~strong(X0))) [nnf transformation 8]
44. ! [X0] : ((strong(X0) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | ~strong(X0))) [flattening 43]
55. ! [X0] : ((~happy(X0) | (~quiet(X0) | humble(X0))) & ((quiet(X0) & ~humble(X0)) | happy(X0))) [nnf transformation 14]
56. ! [X0] : ((~happy(X0) | ~quiet(X0) | humble(X0)) & ((quiet(X0) & ~humble(X0)) | happy(X0))) [flattening 55]
61. ! [X0] : ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0))) [nnf transformation 16]
89. ~quiet(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 44]
90. strong(X0) | strong(X0) [cnf transformation 44]
111. quiet(X0) | happy(X0) [cnf transformation 56]
116. ~happy(X0) | ~old(X0) [cnf transformation 61]
127. old(fred) [cnf transformation 23]
128. ~quiet(X0) | ~strong(X0) [duplicate literal removal 89]
129. strong(X0) [duplicate literal removal 90]
166. ~quiet(X0) [subsumption resolution 128,129]
186. happy(X0) [subsumption resolution 111,166]
205. ~old(X0) [subsumption resolution 116,186]
207. $false [subsumption resolution 127,205]
% SZS output end Proof for 6955005780368365903507515
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or happy is not patient or not funny. Everyone who is old or not creative is patient or creative. If someone is wise then someone is both not humble and brave. If susan is old or creative then someone is not generous or happy and vice versa. Everyone who is both not patient and kind is either curious or brave. Everyone who is not kind or not generous is not humble and vice versa. Everyone who is both quiet and not patient is either not happy or tall and vice versa. If alice is not curious then lucy is either wise or patient. Everyone who is either funny or tall is curious or tall and vice versa. If lucy is not wise or not old then someone is not strong or funny. Everyone who is either not happy or brave is not old or quiet and vice versa. If someone is wise or patient then alice is funny or not old and vice versa. Everyone who is both not humble and tall is not humble or patient. Everyone who is either rich or not happy is humble and vice versa. Everyone who is either kind or not curious is not strong. If someone is both creative and not rich then fred is not old. Someone is kind or not patient. Lucy is either not curious or not brave. Alice is rich. Someone is either old or happy. John is not creative or brave. Someone is both not tall and quiet. Someone is both happy and brave. Someone is not humble or not old. | Fred is not funny. | neutral | (![X]:((brave(X)<~>happy(X))=>(~patient(X)|~funny(X))))&
(![X]:((old(X)|~creative(X))=>(patient(X)|creative(X))))&
((?[X]:(wise(X)))=>(?[X]:((~humble(X)&brave(X)))))&
(((old(susan)|creative(susan)))<=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~patient(X)&kind(X))=>(curious(X)<~>brave(X))))&
(![X]:((~kind(X)|~generous(X))<=>~humble(X)))&
(![X]:((quiet(X)&~patient(X))<=>(~happy(X)<~>tall(X))))&
((~curious(alice))=>((wise(lucy)<~>patient(lucy))))&
(![X]:((funny(X)<~>tall(X))<=>(curious(X)|tall(X))))&
(((~wise(lucy)|~old(lucy)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|quiet(X))))&
((?[X]:((wise(X)|patient(X))))<=>((funny(alice)|~old(alice))))&
(![X]:((~humble(X)&tall(X))=>(~humble(X)|patient(X))))&
(![X]:((rich(X)<~>~happy(X))<=>humble(X)))&
(![X]:((kind(X)<~>~curious(X))=>~strong(X)))&
((?[X]:((creative(X)&~rich(X))))=>(~old(fred)))&
(?[X]:((kind(X)|~patient(X))))&
((~curious(lucy)<~>~brave(lucy)))&
(rich(alice))&
(?[X]:((old(X)<~>happy(X))))&
((~creative(john)|brave(john)))&
(?[X]:((~tall(X)&quiet(X))))&
(?[X]:((happy(X)&brave(X))))&
(?[X]:((~humble(X)|~old(X)))) | ~funny(fred) | [] | null | 0 |
If someone is not curious then someone is humble and vice versa.
Everyone who is both old and not tall is either not curious or not funny and vice versa.
If someone is both not curious and not generous then someone is not wise.
Everyone who is not generous is both not calm and not quiet and vice versa.
If someone is not happy or patient then someone is not brave or quiet and vice versa.
If paul is both brave and generous then someone is patient or strong.
Everyone who is both strong and not kind is either not funny or not patient.
Everyone who is not kind is both quiet and not quiet.
If someone is not funny or not curious then paul is not wise.
Everyone who is not generous or not tall is either curious or not calm.
If someone is both brave and not strong then lucy is not creative and vice versa.
Everyone who is not tall or tall is not strong.
Everyone who is both wise and not happy is not quiet or wise and vice versa.
If someone is either not wise or kind then susan is brave and vice versa.
Everyone who is not funny is either not generous or not tall and vice versa.
Everyone who is patient or creative is not brave or not funny and vice versa.
Someone is curious or not curious.
Lucy is patient.
John is curious or not brave.
Someone is either not quiet or not old.
Fred is either not tall or not wise.
Someone is brave.
Someone is funny or happy.
John is either brave or not happy. | John is old. | neutral | ((?[X]:(~curious(X)))<=>(?[X]:(humble(X))))&
(![X]:((old(X)&~tall(X))<=>(~curious(X)<~>~funny(X))))&
((?[X]:((~curious(X)&~generous(X))))=>(?[X]:(~wise(X))))&
(![X]:(~generous(X)<=>(~calm(X)&~quiet(X))))&
((?[X]:((~happy(X)|patient(X))))<=>(?[X]:((~brave(X)|quiet(X)))))&
(((brave(paul)&generous(paul)))=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((strong(X)&~kind(X))=>(~funny(X)<~>~patient(X))))&
(![X]:(~kind(X)=>(quiet(X)&~quiet(X))))&
((?[X]:((~funny(X)|~curious(X))))=>(~wise(paul)))&
(![X]:((~generous(X)|~tall(X))=>(curious(X)<~>~calm(X))))&
((?[X]:((brave(X)&~strong(X))))<=>(~creative(lucy)))&
(![X]:((~tall(X)|tall(X))=>~strong(X)))&
(![X]:((wise(X)&~happy(X))<=>(~quiet(X)|wise(X))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(brave(susan)))&
(![X]:(~funny(X)<=>(~generous(X)<~>~tall(X))))&
(![X]:((patient(X)|creative(X))<=>(~brave(X)|~funny(X))))&
(?[X]:((curious(X)|~curious(X))))&
(patient(lucy))&
((curious(john)|~brave(john)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~tall(fred)<~>~wise(fred)))&
(?[X]:(brave(X)))&
(?[X]:((funny(X)|happy(X))))&
((brave(john)<~>~happy(john))) | old(john) | [] | null | 0 |
Everyone who is either kind or not old is rich and vice versa.
If paul is both not generous and wise then susan is either not curious or not kind.
If paul is patient then someone is both tall and not kind.
Everyone who is both happy and not wise is wise.
Everyone who is both not calm and generous is not calm.
If someone is not strong or not wise then john is not old.
Everyone who is both not funny and patient is not rich and vice versa.
If someone is both happy and not generous then lucy is both strong and not kind and vice versa.
If fred is not wise then fred is funny and vice versa.
If someone is not quiet or not calm then mary is both not patient and not funny and vice versa.
Everyone who is both creative and not calm is either patient or not kind.
Everyone who is old or rich is not rich.
If mary is not humble or not brave then someone is not patient or not creative.
If paul is quiet then someone is not happy or not wise and vice versa.
If mary is wise or not brave then lucy is either not creative or humble.
If john is either not humble or not rich then someone is old or happy.
Someone is kind.
Someone is not tall or not quiet.
Paul is not wise.
Someone is not curious or wise.
Someone is humble.
Someone is both kind and not old. | Susan is not calm. | contradiction | (![X]:((kind(X)<~>~old(X))<=>rich(X)))&
(((~generous(paul)&wise(paul)))=>((~curious(susan)<~>~kind(susan))))&
((patient(paul))=>(?[X]:((tall(X)&~kind(X)))))&
(![X]:((happy(X)&~wise(X))=>wise(X)))&
(![X]:((~calm(X)&generous(X))=>~calm(X)))&
((?[X]:((~strong(X)|~wise(X))))=>(~old(john)))&
(![X]:((~funny(X)&patient(X))<=>~rich(X)))&
((?[X]:((happy(X)&~generous(X))))<=>((strong(lucy)&~kind(lucy))))&
((~wise(fred))<=>(funny(fred)))&
((?[X]:((~quiet(X)|~calm(X))))<=>((~patient(mary)&~funny(mary))))&
(![X]:((creative(X)&~calm(X))=>(patient(X)<~>~kind(X))))&
(![X]:((old(X)|rich(X))=>~rich(X)))&
(((~humble(mary)|~brave(mary)))=>(?[X]:((~patient(X)|~creative(X)))))&
((quiet(paul))<=>(?[X]:((~happy(X)|~wise(X)))))&
(((wise(mary)|~brave(mary)))=>((~creative(lucy)<~>humble(lucy))))&
(((~humble(john)<~>~rich(john)))=>(?[X]:((old(X)|happy(X)))))&
(?[X]:(kind(X)))&
(?[X]:((~tall(X)|~quiet(X))))&
(~wise(paul))&
(?[X]:((~curious(X)|wise(X))))&
(?[X]:(humble(X)))&
(?[X]:((kind(X)&~old(X)))) | ~calm(susan) | [
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 281368023794450749787765
% SZS output start Proof for 281368023794450749787765
7. ! [X0] : ((patient(X0) & ~funny(X0)) <=> ~rich(X0)) [input p6]
10. ? [X0] : (~calm(X0) | ~quiet(X0)) <=> (~funny(mary) & ~patient(mary)) [input p9]
12. ! [X0] : ((rich(X0) | old(X0)) => ~rich(X0)) [input p11]
23. ~calm(susan) [input hypothesis]
36. ! [X0] : (~rich(X0) | (~rich(X0) & ~old(X0))) [ennf transformation 12]
44. ! [X0] : (((patient(X0) & ~funny(X0)) | rich(X0)) & (~rich(X0) | (~patient(X0) | funny(X0)))) [nnf transformation 7]
45. ! [X0] : (((patient(X0) & ~funny(X0)) | rich(X0)) & (~rich(X0) | ~patient(X0) | funny(X0))) [flattening 44]
52. (? [X0] : (~calm(X0) | ~quiet(X0)) | (funny(mary) | patient(mary))) & ((~funny(mary) & ~patient(mary)) | ! [X0] : (calm(X0) & quiet(X0))) [nnf transformation 10]
53. (? [X0] : (~calm(X0) | ~quiet(X0)) | funny(mary) | patient(mary)) & ((~funny(mary) & ~patient(mary)) | ! [X0] : (calm(X0) & quiet(X0))) [flattening 52]
54. (? [X0] : (~calm(X0) | ~quiet(X0)) | funny(mary) | patient(mary)) & ((~funny(mary) & ~patient(mary)) | ! [X1] : (calm(X1) & quiet(X1))) [rectify 53]
55. ? [X0] : (~calm(X0) | ~quiet(X0)) => (~calm(sK2) | ~quiet(sK2)) [choice axiom]
56. ((~calm(sK2) | ~quiet(sK2)) | funny(mary) | patient(mary)) & ((~funny(mary) & ~patient(mary)) | ! [X1] : (calm(X1) & quiet(X1))) [skolemisation 54,55]
92. patient(X0) | rich(X0) [cnf transformation 45]
100. ~patient(mary) | calm(X1) [cnf transformation 56]
107. ~rich(X0) | ~rich(X0) [cnf transformation 36]
123. ~calm(susan) [cnf transformation 23]
124. ~rich(X0) [duplicate literal removal 107]
204. 18 <=> patient(mary) [avatar definition]
205. ~patient(mary) <- (~18) [avatar component clause 204]
221. 22 <=> ! [X1] : calm(X1) [avatar definition]
222. calm(X1) <- (22) [avatar component clause 221]
228. 22 | ~18 [avatar split clause 100,204,221]
309. rich(mary) <- (~18) [resolution 92,205]
312. $false <- (~18) [subsumption resolution 309,124]
313. 18 [avatar contradiction clause 312]
314. $false <- (22) [resolution 222,123]
317. ~22 [avatar contradiction clause 314]
318. $false [avatar sat refutation 228,313,317]
% SZS output end Proof for 281368023794450749787765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not strong then someone is both not brave and old and vice versa.
Everyone who is both kind and not quiet is either not tall or quiet and vice versa.
If paul is either not wise or not tall then lucy is either not calm or kind and vice versa.
If someone is not patient then someone is wise.
If fred is quiet or not curious then someone is old.
Everyone who is either creative or not tall is generous.
Everyone who is kind is not kind or tall.
Everyone who is either not curious or not calm is not happy.
If lucy is not strong then susan is not old or humble and vice versa.
Everyone who is either not generous or wise is both patient and kind.
Everyone who is either not brave or generous is both tall and funny.
Everyone who is rich is not creative and vice versa.
Everyone who is tall or not rich is either not funny or not rich.
Everyone who is either humble or calm is both not calm and strong and vice versa.
Everyone who is not happy or rich is not patient and vice versa.
If someone is either kind or not humble then susan is not happy or patient and vice versa.
Someone is not rich.
Paul is both patient and brave.
Someone is either calm or rich.
John is both funny and rich.
Alice is not wise.
Mary is either curious or not wise.
Paul is patient or not rich. | John is not quiet. | contradiction | ((?[X]:((~rich(X)|~strong(X))))<=>(?[X]:((~brave(X)&old(X)))))&
(![X]:((kind(X)&~quiet(X))<=>(~tall(X)<~>quiet(X))))&
(((~wise(paul)<~>~tall(paul)))<=>((~calm(lucy)<~>kind(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:(wise(X))))&
(((quiet(fred)|~curious(fred)))=>(?[X]:(old(X))))&
(![X]:((creative(X)<~>~tall(X))=>generous(X)))&
(![X]:(kind(X)=>(~kind(X)|tall(X))))&
(![X]:((~curious(X)<~>~calm(X))=>~happy(X)))&
((~strong(lucy))<=>((~old(susan)|humble(susan))))&
(![X]:((~generous(X)<~>wise(X))=>(patient(X)&kind(X))))&
(![X]:((~brave(X)<~>generous(X))=>(tall(X)&funny(X))))&
(![X]:(rich(X)<=>~creative(X)))&
(![X]:((tall(X)|~rich(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((humble(X)<~>calm(X))<=>(~calm(X)&strong(X))))&
(![X]:((~happy(X)|rich(X))<=>~patient(X)))&
((?[X]:((kind(X)<~>~humble(X))))<=>((~happy(susan)|patient(susan))))&
(?[X]:(~rich(X)))&
((patient(paul)&brave(paul)))&
(?[X]:((calm(X)<~>rich(X))))&
((funny(john)&rich(john)))&
(~wise(alice))&
((curious(mary)<~>~wise(mary)))&
((patient(paul)|~rich(paul))) | ~quiet(john) | [
"p1",
"p6",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6541594194117128216730409
% SZS output start Proof for 6541594194117128216730409
2. ! [X0] : ((~quiet(X0) & kind(X0)) <=> (~tall(X0) <~> quiet(X0))) [input p1]
7. ! [X0] : (kind(X0) => (tall(X0) | ~kind(X0))) [input p6]
13. ! [X0] : ((~rich(X0) | tall(X0)) => (~funny(X0) <~> ~rich(X0))) [input p12]
20. rich(john) & funny(john) [input p19]
24. ~quiet(john) [input hypothesis]
30. ! [X0] : ((tall(X0) | ~kind(X0)) | ~kind(X0)) [ennf transformation 7]
31. ! [X0] : (tall(X0) | ~kind(X0) | ~kind(X0)) [flattening 30]
35. ! [X0] : ((~funny(X0) <~> ~rich(X0)) | (rich(X0) & ~tall(X0))) [ennf transformation 13]
41. ! [X0] : (((~quiet(X0) & kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0)))) & (((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (quiet(X0) | ~kind(X0)))) [nnf transformation 2]
42. ! [X0] : (((~quiet(X0) & kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0)))) & (((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | quiet(X0) | ~kind(X0))) [flattening 41]
56. ! [X0] : (((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | (rich(X0) & ~tall(X0))) [nnf transformation 35]
77. quiet(X0) | ~tall(X0) | quiet(X0) | ~kind(X0) [cnf transformation 42]
79. tall(X0) | quiet(X0) | kind(X0) [cnf transformation 42]
82. ~quiet(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 42]
96. tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 31]
112. ~funny(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 56]
136. funny(john) [cnf transformation 20]
137. rich(john) [cnf transformation 20]
142. ~quiet(john) [cnf transformation 24]
146. tall(X0) | ~kind(X0) [duplicate literal removal 96]
147. quiet(X0) | ~tall(X0) | ~kind(X0) [duplicate literal removal 77]
148. ~tall(X0) | ~quiet(X0) [duplicate literal removal 82]
179. ~tall(X0) | ~kind(X0) [subsumption resolution 147,148]
226. ~kind(X0) [subsumption resolution 146,179]
325. ~rich(john) | ~tall(john) [resolution 112,136]
328. ~tall(john) [subsumption resolution 325,137]
330. quiet(john) | kind(john) [resolution 328,79]
331. kind(john) [subsumption resolution 330,142]
332. $false [subsumption resolution 331,226]
% SZS output end Proof for 6541594194117128216730409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or tall is both kind and tall.
Everyone who is quiet or not generous is not patient and vice versa.
If susan is both not generous and generous then someone is not patient and vice versa.
Everyone who is not old is brave or strong.
If lucy is strong or funny then paul is both not strong and rich.
If lucy is both kind and happy then someone is both not strong and curious.
Everyone who is brave is generous and vice versa.
Everyone who is quiet or not patient is calm and vice versa.
Everyone who is not kind or not wise is either funny or not wise and vice versa.
If someone is not old then someone is either brave or not rich.
If someone is not patient or not wise then someone is both creative and quiet.
Everyone who is both strong and not curious is either not strong or not creative.
If someone is both patient and kind then john is both kind and not happy.
If fred is both brave and not quiet then alice is wise and vice versa.
Everyone who is not kind is not wise or tall.
Fred is tall or not rich.
Someone is either curious or creative.
Mary is tall.
Lucy is not tall or not old.
Mary is not humble.
Lucy is both curious and not creative. | John is not kind. | contradiction | (![X]:((~funny(X)<~>tall(X))=>(kind(X)&tall(X))))&
(![X]:((quiet(X)|~generous(X))<=>~patient(X)))&
(((~generous(susan)&generous(susan)))<=>(?[X]:(~patient(X))))&
(![X]:(~old(X)=>(brave(X)|strong(X))))&
(((strong(lucy)|funny(lucy)))=>((~strong(paul)&rich(paul))))&
(((kind(lucy)&happy(lucy)))=>(?[X]:((~strong(X)&curious(X)))))&
(![X]:(brave(X)<=>generous(X)))&
(![X]:((quiet(X)|~patient(X))<=>calm(X)))&
(![X]:((~kind(X)|~wise(X))<=>(funny(X)<~>~wise(X))))&
((?[X]:(~old(X)))=>(?[X]:((brave(X)<~>~rich(X)))))&
((?[X]:((~patient(X)|~wise(X))))=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((strong(X)&~curious(X))=>(~strong(X)<~>~creative(X))))&
((?[X]:((patient(X)&kind(X))))=>((kind(john)&~happy(john))))&
(((brave(fred)&~quiet(fred)))<=>(wise(alice)))&
(![X]:(~kind(X)=>(~wise(X)|tall(X))))&
((tall(fred)|~rich(fred)))&
(?[X]:((curious(X)<~>creative(X))))&
(tall(mary))&
((~tall(lucy)|~old(lucy)))&
(~humble(mary))&
((curious(lucy)&~creative(lucy))) | ~kind(john) | [
"p0",
"p1",
"p2",
"p8",
"p10",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5046318589088196243130680
% SZS output start Proof for 5046318589088196243130680
1. ! [X0] : ((~funny(X0) <~> tall(X0)) => (tall(X0) & kind(X0))) [input p0]
2. ! [X0] : ((~generous(X0) | quiet(X0)) <=> ~patient(X0)) [input p1]
3. (generous(susan) & ~generous(susan)) <=> ? [X0] : ~patient(X0) [input p2]
9. ! [X0] : ((~wise(X0) | ~kind(X0)) <=> (funny(X0) <~> ~wise(X0))) [input p8]
11. ? [X0] : (~wise(X0) | ~patient(X0)) => ? [X0] : (quiet(X0) & creative(X0)) [input p10]
13. ? [X0] : (kind(X0) & patient(X0)) => (~happy(john) & kind(john)) [input p12]
18. tall(mary) [input p17]
22. ~kind(john) [input hypothesis]
24. ? [X0] : (~wise(X0) | ~patient(X0)) => ? [X1] : (quiet(X1) & creative(X1)) [rectify 11]
27. ? [X0] : (kind(X0) & patient(X0)) => kind(john) [pure predicate removal 13]
28. ! [X0] : ((tall(X0) & kind(X0)) | (~funny(X0) <=> tall(X0))) [ennf transformation 1]
33. ? [X1] : (quiet(X1) & creative(X1)) | ! [X0] : (wise(X0) & patient(X0)) [ennf transformation 24]
36. kind(john) | ! [X0] : (~kind(X0) | ~patient(X0)) [ennf transformation 27]
39. ! [X0] : ((tall(X0) & kind(X0)) | ((~funny(X0) | ~tall(X0)) & (tall(X0) | funny(X0)))) [nnf transformation 28]
40. ! [X0] : (((~generous(X0) | quiet(X0)) | patient(X0)) & (~patient(X0) | (generous(X0) & ~quiet(X0)))) [nnf transformation 2]
41. ! [X0] : ((~generous(X0) | quiet(X0) | patient(X0)) & (~patient(X0) | (generous(X0) & ~quiet(X0)))) [flattening 40]
42. ((generous(susan) & ~generous(susan)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (~generous(susan) | generous(susan))) [nnf transformation 3]
43. ((generous(susan) & ~generous(susan)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ~generous(susan) | generous(susan)) [flattening 42]
44. ((generous(susan) & ~generous(susan)) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ~generous(susan) | generous(susan)) [rectify 43]
45. ? [X1] : ~patient(X1) => ~patient(sK0) [choice axiom]
46. ((generous(susan) & ~generous(susan)) | ! [X0] : patient(X0)) & (~patient(sK0) | ~generous(susan) | generous(susan)) [skolemisation 44,45]
48. ! [X0] : (((~wise(X0) | ~kind(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0)))) & (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (wise(X0) & kind(X0)))) [nnf transformation 9]
49. ! [X0] : ((~wise(X0) | ~kind(X0) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0)))) & (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (wise(X0) & kind(X0)))) [flattening 48]
54. ? [X0] : (quiet(X0) & creative(X0)) | ! [X1] : (wise(X1) & patient(X1)) [rectify 33]
55. ? [X0] : (quiet(X0) & creative(X0)) => (quiet(sK2) & creative(sK2)) [choice axiom]
56. (quiet(sK2) & creative(sK2)) | ! [X1] : (wise(X1) & patient(X1)) [skolemisation 54,55]
64. ~tall(X0) | ~funny(X0) | kind(X0) [cnf transformation 39]
67. ~patient(X0) | ~quiet(X0) [cnf transformation 41]
71. ~generous(susan) | patient(X0) [cnf transformation 46]
72. generous(susan) | patient(X0) [cnf transformation 46]
80. ~wise(X0) | funny(X0) | kind(X0) [cnf transformation 49]
91. quiet(sK2) | wise(X1) [cnf transformation 56]
94. kind(john) | ~kind(X0) | ~patient(X0) [cnf transformation 36]
102. tall(mary) [cnf transformation 18]
106. ~kind(john) [cnf transformation 22]
112. 1 <=> ! [X0] : patient(X0) [avatar definition]
113. patient(X0) <- (1) [avatar component clause 112]
115. 2 <=> generous(susan) [avatar definition]
118. 1 | 2 [avatar split clause 72,115,112]
119. 1 | ~2 [avatar split clause 71,115,112]
154. 10 <=> ! [X1] : wise(X1) [avatar definition]
155. wise(X1) <- (10) [avatar component clause 154]
157. 11 <=> quiet(sK2) [avatar definition]
159. quiet(sK2) <- (11) [avatar component clause 157]
160. 10 | 11 [avatar split clause 91,157,154]
169. 13 <=> ! [X0] : (~kind(X0) | ~patient(X0)) [avatar definition]
170. ~patient(X0) | ~kind(X0) <- (13) [avatar component clause 169]
172. 14 <=> kind(john) [avatar definition]
175. 13 | 14 [avatar split clause 94,172,169]
219. ~14 [avatar split clause 106,172]
222. ~quiet(X0) <- (1) [resolution 67,113]
231. ~kind(X0) <- (1, 13) [resolution 170,113]
232. ~funny(mary) | kind(mary) [resolution 64,102]
234. ~funny(mary) <- (1, 13) [subsumption resolution 232,231]
237. funny(X0) | kind(X0) <- (10) [resolution 80,155]
238. funny(X0) <- (1, 10, 13) [subsumption resolution 237,231]
243. $false <- (1, 10, 13) [resolution 238,234]
244. ~1 | ~10 | ~13 [avatar contradiction clause 243]
246. $false <- (1, 11) [subsumption resolution 159,222]
247. ~1 | ~11 [avatar contradiction clause 246]
248. $false [avatar sat refutation 118,119,160,175,219,244,247]
% SZS output end Proof for 5046318589088196243130680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not wise is not curious or not old. Everyone who is rich is both not wise and not strong and vice versa. If someone is either generous or not wise then someone is tall and vice versa. If susan is not patient then lucy is either not strong or not happy. Everyone who is both rich and not funny is rich or not rich and vice versa. If someone is either quiet or not strong then someone is either not wise or curious and vice versa. Everyone who is either curious or not funny is curious or not curious. If fred is happy or not rich then susan is not strong or not curious and vice versa. If someone is wise then someone is wise or not strong. If someone is either not wise or not creative then someone is humble and vice versa. Everyone who is tall or creative is strong. If fred is either curious or not brave then someone is not kind and vice versa. Everyone who is both kind and funny is generous. Everyone who is both not wise and curious is curious or strong. Everyone who is not rich is both not patient and not kind. Everyone who is both not patient and not creative is both not strong and not humble and vice versa. Someone is calm or not old. Susan is funny or quiet. Someone is curious or not curious. Someone is curious or not old. Someone is either not patient or calm. Someone is either humble or not happy. | Lucy is not calm. | neutral | (![X]:((funny(X)&~wise(X))=>(~curious(X)|~old(X))))&
(![X]:(rich(X)<=>(~wise(X)&~strong(X))))&
((?[X]:((generous(X)<~>~wise(X))))<=>(?[X]:(tall(X))))&
((~patient(susan))=>((~strong(lucy)<~>~happy(lucy))))&
(![X]:((rich(X)&~funny(X))<=>(rich(X)|~rich(X))))&
((?[X]:((quiet(X)<~>~strong(X))))<=>(?[X]:((~wise(X)<~>curious(X)))))&
(![X]:((curious(X)<~>~funny(X))=>(curious(X)|~curious(X))))&
(((happy(fred)|~rich(fred)))<=>((~strong(susan)|~curious(susan))))&
((?[X]:(wise(X)))=>(?[X]:((wise(X)|~strong(X)))))&
((?[X]:((~wise(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)|creative(X))=>strong(X)))&
(((curious(fred)<~>~brave(fred)))<=>(?[X]:(~kind(X))))&
(![X]:((kind(X)&funny(X))=>generous(X)))&
(![X]:((~wise(X)&curious(X))=>(curious(X)|strong(X))))&
(![X]:(~rich(X)=>(~patient(X)&~kind(X))))&
(![X]:((~patient(X)&~creative(X))<=>(~strong(X)&~humble(X))))&
(?[X]:((calm(X)|~old(X))))&
((funny(susan)|quiet(susan)))&
(?[X]:((curious(X)|~curious(X))))&
(?[X]:((curious(X)|~old(X))))&
(?[X]:((~patient(X)<~>calm(X))))&
(?[X]:((humble(X)<~>~happy(X)))) | ~calm(lucy) | [] | null | 0 |
Everyone who is both not calm and not strong is either brave or tall and vice versa.
Everyone who is old is both humble and not kind and vice versa.
Everyone who is old is calm or not wise and vice versa.
If lucy is tall or rich then someone is not creative.
If susan is either generous or not humble then someone is either not generous or funny and vice versa.
Everyone who is not curious or tall is either quiet or not humble.
If someone is either curious or quiet then someone is either generous or old.
If someone is generous then someone is both quiet and happy and vice versa.
If someone is both not humble and humble then someone is not old.
Everyone who is both happy and creative is both not kind and curious and vice versa.
Everyone who is either not funny or curious is both quiet and rich.
If someone is both not kind and kind then john is not tall.
Everyone who is not quiet is either happy or not funny and vice versa.
Everyone who is not humble is not funny and vice versa.
Everyone who is not patient or wise is not humble and vice versa.
Everyone who is not patient is quiet.
John is not old.
Someone is creative.
Someone is both not old and not generous.
Susan is both not calm and tall.
Someone is brave or old.
Someone is either not kind or rich.
Lucy is either kind or not humble.
Someone is either not wise or not brave. | John is humble. | contradiction | (![X]:((~calm(X)&~strong(X))<=>(brave(X)<~>tall(X))))&
(![X]:(old(X)<=>(humble(X)&~kind(X))))&
(![X]:(old(X)<=>(calm(X)|~wise(X))))&
(((tall(lucy)|rich(lucy)))=>(?[X]:(~creative(X))))&
(((generous(susan)<~>~humble(susan)))<=>(?[X]:((~generous(X)<~>funny(X)))))&
(![X]:((~curious(X)|tall(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:((generous(X)<~>old(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((quiet(X)&happy(X)))))&
((?[X]:((~humble(X)&humble(X))))=>(?[X]:(~old(X))))&
(![X]:((happy(X)&creative(X))<=>(~kind(X)&curious(X))))&
(![X]:((~funny(X)<~>curious(X))=>(quiet(X)&rich(X))))&
((?[X]:((~kind(X)&kind(X))))=>(~tall(john)))&
(![X]:(~quiet(X)<=>(happy(X)<~>~funny(X))))&
(![X]:(~humble(X)<=>~funny(X)))&
(![X]:((~patient(X)|wise(X))<=>~humble(X)))&
(![X]:(~patient(X)=>quiet(X)))&
(~old(john))&
(?[X]:(creative(X)))&
(?[X]:((~old(X)&~generous(X))))&
((~calm(susan)&tall(susan)))&
(?[X]:((brave(X)|old(X))))&
(?[X]:((~kind(X)<~>rich(X))))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((~wise(X)<~>~brave(X)))) | humble(john) | [
"p2",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1813446136172563851156532
% SZS output start Proof for 1813446136172563851156532
3. ! [X0] : (old(X0) <=> (~wise(X0) | calm(X0))) [input p2]
15. ! [X0] : ((wise(X0) | ~patient(X0)) <=> ~humble(X0)) [input p14]
17. ~old(john) [input p16]
25. humble(john) [input hypothesis]
40. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & ((~wise(X0) | calm(X0)) | ~old(X0))) [nnf transformation 3]
41. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & (~wise(X0) | calm(X0) | ~old(X0))) [flattening 40]
66. ! [X0] : (((wise(X0) | ~patient(X0)) | humble(X0)) & (~humble(X0) | (~wise(X0) & patient(X0)))) [nnf transformation 15]
67. ! [X0] : ((wise(X0) | ~patient(X0) | humble(X0)) & (~humble(X0) | (~wise(X0) & patient(X0)))) [flattening 66]
92. wise(X0) | old(X0) [cnf transformation 41]
131. ~wise(X0) | ~humble(X0) [cnf transformation 67]
134. ~old(john) [cnf transformation 17]
147. humble(john) [cnf transformation 25]
279. ~humble(X0) | old(X0) [resolution 131,92]
292. old(john) [resolution 279,147]
294. $false [subsumption resolution 292,134]
% SZS output end Proof for 1813446136172563851156532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not generous and not old then alice is both rich and not kind.
If someone is both patient and quiet then john is either tall or not patient and vice versa.
Everyone who is not quiet is not calm or strong and vice versa.
Everyone who is either rich or calm is not generous or curious.
Everyone who is old or wise is both quiet and not wise and vice versa.
If someone is both old and not funny then fred is both not generous and not wise and vice versa.
If someone is humble or quiet then someone is creative or funny and vice versa.
If alice is both not generous and not tall then someone is both not patient and strong.
Everyone who is wise or not wise is both not generous and not humble and vice versa.
If john is both not calm and strong then someone is both tall and humble.
If alice is either not curious or not humble then someone is either strong or not wise.
If mary is both not brave and strong then someone is old or not happy and vice versa.
Everyone who is either curious or tall is either funny or not generous and vice versa.
Everyone who is both quiet and not creative is wise or tall and vice versa.
If paul is both not creative and wise then john is either humble or not kind and vice versa.
Everyone who is not quiet is strong or not calm.
Someone is either happy or not wise.
John is strong.
Someone is old.
Someone is wise or not patient.
Someone is either not kind or not curious.
Mary is creative or generous.
Someone is not patient or humble.
Someone is both not old and not funny. | John is not humble. | entailment | ((?[X]:((~generous(X)&~old(X))))=>((rich(alice)&~kind(alice))))&
((?[X]:((patient(X)&quiet(X))))<=>((tall(john)<~>~patient(john))))&
(![X]:(~quiet(X)<=>(~calm(X)|strong(X))))&
(![X]:((rich(X)<~>calm(X))=>(~generous(X)|curious(X))))&
(![X]:((old(X)|wise(X))<=>(quiet(X)&~wise(X))))&
((?[X]:((old(X)&~funny(X))))<=>((~generous(fred)&~wise(fred))))&
((?[X]:((humble(X)|quiet(X))))<=>(?[X]:((creative(X)|funny(X)))))&
(((~generous(alice)&~tall(alice)))=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((wise(X)|~wise(X))<=>(~generous(X)&~humble(X))))&
(((~calm(john)&strong(john)))=>(?[X]:((tall(X)&humble(X)))))&
(((~curious(alice)<~>~humble(alice)))=>(?[X]:((strong(X)<~>~wise(X)))))&
(((~brave(mary)&strong(mary)))<=>(?[X]:((old(X)|~happy(X)))))&
(![X]:((curious(X)<~>tall(X))<=>(funny(X)<~>~generous(X))))&
(![X]:((quiet(X)&~creative(X))<=>(wise(X)|tall(X))))&
(((~creative(paul)&wise(paul)))<=>((humble(john)<~>~kind(john))))&
(![X]:(~quiet(X)=>(strong(X)|~calm(X))))&
(?[X]:((happy(X)<~>~wise(X))))&
(strong(john))&
(?[X]:(old(X)))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:((~kind(X)<~>~curious(X))))&
((creative(mary)|generous(mary)))&
(?[X]:((~patient(X)|humble(X))))&
(?[X]:((~old(X)&~funny(X)))) | ~humble(john) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4919097442809575587668545
% SZS output start Proof for 4919097442809575587668545
5. ! [X0] : ((wise(X0) | old(X0)) <=> (~wise(X0) & quiet(X0))) [input p4]
9. ! [X0] : ((~wise(X0) | wise(X0)) <=> (~humble(X0) & ~generous(X0))) [input p8]
25. humble(john) [input hypothesis]
44. ! [X0] : (((wise(X0) | old(X0)) | (wise(X0) | ~quiet(X0))) & ((~wise(X0) & quiet(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 5]
45. ! [X0] : ((wise(X0) | old(X0) | wise(X0) | ~quiet(X0)) & ((~wise(X0) & quiet(X0)) | (~wise(X0) & ~old(X0)))) [flattening 44]
58. ! [X0] : (((~wise(X0) | wise(X0)) | (humble(X0) | generous(X0))) & ((~humble(X0) & ~generous(X0)) | (wise(X0) & ~wise(X0)))) [nnf transformation 9]
59. ! [X0] : ((~wise(X0) | wise(X0) | humble(X0) | generous(X0)) & ((~humble(X0) & ~generous(X0)) | (wise(X0) & ~wise(X0)))) [flattening 58]
105. ~wise(X0) | ~wise(X0) [cnf transformation 45]
120. ~humble(X0) | wise(X0) [cnf transformation 59]
164. humble(john) [cnf transformation 25]
165. ~wise(X0) [duplicate literal removal 105]
254. 20 <=> ! [X3] : ~humble(X3) [avatar definition]
255. ~humble(X3) <- (20) [avatar component clause 254]
275. ~humble(X0) [subsumption resolution 120,165]
276. 20 [avatar split clause 275,254]
350. 39 <=> humble(john) [avatar definition]
352. humble(john) <- (39) [avatar component clause 350]
385. 39 [avatar split clause 164,350]
392. $false <- (20, 39) [resolution 352,255]
393. ~20 | ~39 [avatar contradiction clause 392]
394. $false [avatar sat refutation 276,385,393]
% SZS output end Proof for 4919097442809575587668545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and wise is not funny or not generous and vice versa. If someone is either rich or humble then john is either not wise or not strong and vice versa. Everyone who is either not creative or strong is generous. If paul is both not patient and not curious then lucy is not happy. If fred is both kind and not funny then someone is not humble and vice versa. If someone is either generous or happy then alice is both quiet and humble and vice versa. If someone is either not strong or not humble then someone is both not old and generous. If paul is not brave then someone is calm and vice versa. If someone is calm or generous then susan is either funny or not calm and vice versa. If someone is not old or not brave then someone is not generous and vice versa. Everyone who is happy is either strong or not kind and vice versa. Everyone who is wise or strong is either tall or humble. If someone is not strong or not calm then paul is either brave or not funny and vice versa. Everyone who is not patient or not humble is both not happy and rich. If susan is curious or not tall then someone is patient or not calm. Someone is either not rich or tall. Someone is either calm or patient. Someone is either not rich or not calm. Paul is either not old or happy. Someone is brave or calm. Someone is generous or not curious. | Alice is not strong. | contradiction | (![X]:((generous(X)&wise(X))<=>(~funny(X)|~generous(X))))&
((?[X]:((rich(X)<~>humble(X))))<=>((~wise(john)<~>~strong(john))))&
(![X]:((~creative(X)<~>strong(X))=>generous(X)))&
(((~patient(paul)&~curious(paul)))=>(~happy(lucy)))&
(((kind(fred)&~funny(fred)))<=>(?[X]:(~humble(X))))&
((?[X]:((generous(X)<~>happy(X))))<=>((quiet(alice)&humble(alice))))&
((?[X]:((~strong(X)<~>~humble(X))))=>(?[X]:((~old(X)&generous(X)))))&
((~brave(paul))<=>(?[X]:(calm(X))))&
((?[X]:((calm(X)|generous(X))))<=>((funny(susan)<~>~calm(susan))))&
((?[X]:((~old(X)|~brave(X))))<=>(?[X]:(~generous(X))))&
(![X]:(happy(X)<=>(strong(X)<~>~kind(X))))&
(![X]:((wise(X)|strong(X))=>(tall(X)<~>humble(X))))&
((?[X]:((~strong(X)|~calm(X))))<=>((brave(paul)<~>~funny(paul))))&
(![X]:((~patient(X)|~humble(X))=>(~happy(X)&rich(X))))&
(((curious(susan)|~tall(susan)))=>(?[X]:((patient(X)|~calm(X)))))&
(?[X]:((~rich(X)<~>tall(X))))&
(?[X]:((calm(X)<~>patient(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
((~old(paul)<~>happy(paul)))&
(?[X]:((brave(X)|calm(X))))&
(?[X]:((generous(X)|~curious(X)))) | ~strong(alice) | [
"p0",
"p5",
"p6",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 142100349864996433747617
% SZS output start Proof for 142100349864996433747617
1. ! [X0] : ((wise(X0) & generous(X0)) <=> (~generous(X0) | ~funny(X0))) [input p0]
6. ? [X0] : (generous(X0) <~> happy(X0)) <=> (humble(alice) & quiet(alice)) [input p5]
7. ? [X0] : (~strong(X0) <~> ~humble(X0)) => ? [X0] : (generous(X0) & ~old(X0)) [input p6]
10. ? [X0] : (~brave(X0) | ~old(X0)) <=> ? [X0] : ~generous(X0) [input p9]
14. ! [X0] : ((~humble(X0) | ~patient(X0)) => (rich(X0) & ~happy(X0))) [input p13]
22. ~strong(alice) [input hypothesis]
23. ? [X0] : (~strong(X0) <~> ~humble(X0)) => ? [X1] : (generous(X1) & ~old(X1)) [rectify 7]
24. ? [X0] : (~brave(X0) | ~old(X0)) <=> ? [X1] : ~generous(X1) [rectify 10]
28. ? [X1] : (generous(X1) & ~old(X1)) | ! [X0] : (~strong(X0) <=> ~humble(X0)) [ennf transformation 23]
30. ! [X0] : ((rich(X0) & ~happy(X0)) | (humble(X0) & patient(X0))) [ennf transformation 14]
32. ! [X0] : (((wise(X0) & generous(X0)) | (generous(X0) & funny(X0))) & ((~generous(X0) | ~funny(X0)) | (~wise(X0) | ~generous(X0)))) [nnf transformation 1]
33. ! [X0] : (((wise(X0) & generous(X0)) | (generous(X0) & funny(X0))) & (~generous(X0) | ~funny(X0) | ~wise(X0) | ~generous(X0))) [flattening 32]
44. (? [X0] : ((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | (~humble(alice) | ~quiet(alice))) & ((humble(alice) & quiet(alice)) | ! [X0] : ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0)))) [nnf transformation 6]
45. (? [X0] : ((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | ~humble(alice) | ~quiet(alice)) & ((humble(alice) & quiet(alice)) | ! [X0] : ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0)))) [flattening 44]
46. (? [X0] : ((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | ~humble(alice) | ~quiet(alice)) & ((humble(alice) & quiet(alice)) | ! [X1] : ((generous(X1) | ~happy(X1)) & (happy(X1) | ~generous(X1)))) [rectify 45]
47. ? [X0] : ((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) => ((~happy(sK2) | ~generous(sK2)) & (happy(sK2) | generous(sK2))) [choice axiom]
48. (((~happy(sK2) | ~generous(sK2)) & (happy(sK2) | generous(sK2))) | ~humble(alice) | ~quiet(alice)) & ((humble(alice) & quiet(alice)) | ! [X1] : ((generous(X1) | ~happy(X1)) & (happy(X1) | ~generous(X1)))) [skolemisation 46,47]
49. ? [X1] : (generous(X1) & ~old(X1)) | ! [X0] : ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))) [nnf transformation 28]
50. ? [X0] : (generous(X0) & ~old(X0)) | ! [X1] : ((~strong(X1) | humble(X1)) & (~humble(X1) | strong(X1))) [rectify 49]
51. ? [X0] : (generous(X0) & ~old(X0)) => (generous(sK3) & ~old(sK3)) [choice axiom]
52. (generous(sK3) & ~old(sK3)) | ! [X1] : ((~strong(X1) | humble(X1)) & (~humble(X1) | strong(X1))) [skolemisation 50,51]
61. (? [X0] : (~brave(X0) | ~old(X0)) | ! [X1] : generous(X1)) & (? [X1] : ~generous(X1) | ! [X0] : (brave(X0) & old(X0))) [nnf transformation 24]
62. (? [X0] : (~brave(X0) | ~old(X0)) | ! [X1] : generous(X1)) & (? [X2] : ~generous(X2) | ! [X3] : (brave(X3) & old(X3))) [rectify 61]
63. ? [X0] : (~brave(X0) | ~old(X0)) => (~brave(sK6) | ~old(sK6)) [choice axiom]
64. ? [X2] : ~generous(X2) => ~generous(sK7) [choice axiom]
65. ((~brave(sK6) | ~old(sK6)) | ! [X1] : generous(X1)) & (~generous(sK7) | ! [X3] : (brave(X3) & old(X3))) [skolemisation 62,64,63]
90. generous(X0) | generous(X0) [cnf transformation 33]
109. humble(alice) | happy(X1) | ~generous(X1) [cnf transformation 48]
113. ~old(sK3) | ~humble(X1) | strong(X1) [cnf transformation 52]
125. ~generous(sK7) | old(X3) [cnf transformation 65]
143. ~happy(X0) | humble(X0) [cnf transformation 30]
158. ~strong(alice) [cnf transformation 22]
160. generous(X0) [duplicate literal removal 90]
206. 10 <=> ! [X0] : humble(X0) [avatar definition]
207. humble(X0) <- (10) [avatar component clause 206]
229. 15 <=> humble(alice) [avatar definition]
230. humble(alice) <- (15) [avatar component clause 229]
231. ~humble(alice) <- (~15) [avatar component clause 229]
237. humble(alice) | happy(X1) [subsumption resolution 109,160]
239. 17 <=> ! [X1] : happy(X1) [avatar definition]
240. happy(X1) <- (17) [avatar component clause 239]
241. 17 | 15 [avatar split clause 237,229,239]
248. 19 <=> old(sK3) [avatar definition]
250. ~old(sK3) <- (~19) [avatar component clause 248]
253. 20 <=> ! [X1] : (~humble(X1) | strong(X1)) [avatar definition]
254. ~humble(X1) | strong(X1) <- (20) [avatar component clause 253]
255. 20 | ~19 [avatar split clause 113,248,253]
284. old(X3) [subsumption resolution 125,160]
358. $false <- (~19) [subsumption resolution 250,284]
359. 19 [avatar contradiction clause 358]
387. strong(alice) <- (15, 20) [resolution 254,230]
389. $false <- (15, 20) [subsumption resolution 387,158]
390. ~15 | ~20 [avatar contradiction clause 389]
394. humble(X0) <- (17) [resolution 240,143]
398. 10 | ~17 [avatar split clause 394,239,206]
401. $false <- (10, ~15) [resolution 207,231]
402. ~10 | 15 [avatar contradiction clause 401]
404. $false [avatar sat refutation 241,255,359,390,398,402]
% SZS output end Proof for 142100349864996433747617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is not rich and vice versa. Everyone who is both old and happy is either wise or not creative. Everyone who is not tall or strong is either tall or wise and vice versa. If john is both not patient and not brave then alice is either not tall or not brave. Everyone who is both not generous and kind is either not happy or rich and vice versa. If susan is strong then alice is both not quiet and not old. Everyone who is both not happy and not strong is not old or tall and vice versa. If someone is either not old or not rich then someone is both strong and wise and vice versa. If susan is not brave then paul is not humble or creative. If lucy is not calm then alice is not creative or not generous and vice versa. If susan is both curious and brave then someone is either not kind or generous and vice versa. If someone is patient or funny then someone is both not wise and not patient. Everyone who is both humble and funny is old or funny and vice versa. Everyone who is either not kind or generous is not wise or quiet and vice versa. If susan is both not wise and wise then someone is either not rich or funny. If lucy is curious or strong then paul is both not kind and kind. Someone is either not humble or not calm. Someone is not tall or not humble. Paul is not quiet. Fred is not patient. | Lucy is quiet. | contradiction | (![X]:(~generous(X)<=>~rich(X)))&
(![X]:((old(X)&happy(X))=>(wise(X)<~>~creative(X))))&
(![X]:((~tall(X)|strong(X))<=>(tall(X)<~>wise(X))))&
(((~patient(john)&~brave(john)))=>((~tall(alice)<~>~brave(alice))))&
(![X]:((~generous(X)&kind(X))<=>(~happy(X)<~>rich(X))))&
((strong(susan))=>((~quiet(alice)&~old(alice))))&
(![X]:((~happy(X)&~strong(X))<=>(~old(X)|tall(X))))&
((?[X]:((~old(X)<~>~rich(X))))<=>(?[X]:((strong(X)&wise(X)))))&
((~brave(susan))=>((~humble(paul)|creative(paul))))&
((~calm(lucy))<=>((~creative(alice)|~generous(alice))))&
(((curious(susan)&brave(susan)))<=>(?[X]:((~kind(X)<~>generous(X)))))&
((?[X]:((patient(X)|funny(X))))=>(?[X]:((~wise(X)&~patient(X)))))&
(![X]:((humble(X)&funny(X))<=>(old(X)|funny(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(~wise(X)|quiet(X))))&
(((~wise(susan)&wise(susan)))=>(?[X]:((~rich(X)<~>funny(X)))))&
(((curious(lucy)|strong(lucy)))=>((~kind(paul)&kind(paul))))&
(?[X]:((~humble(X)<~>~calm(X))))&
(?[X]:((~tall(X)|~humble(X))))&
(~quiet(paul))&
(~patient(fred)) | quiet(lucy) | [
"p0",
"p2",
"p4",
"p6",
"p7",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4109525165400853909331688
% SZS output start Proof for 4109525165400853909331688
1. ! [X0] : (~generous(X0) <=> ~rich(X0)) [input p0]
3. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (tall(X0) <~> wise(X0))) [input p2]
5. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (~happy(X0) <~> rich(X0))) [input p4]
7. ! [X0] : ((~strong(X0) & ~happy(X0)) <=> (tall(X0) | ~old(X0))) [input p6]
8. ? [X0] : (~old(X0) <~> ~rich(X0)) <=> ? [X0] : (wise(X0) & strong(X0)) [input p7]
11. (brave(susan) & curious(susan)) <=> ? [X0] : (~kind(X0) <~> generous(X0)) [input p10]
12. ? [X0] : (funny(X0) | patient(X0)) => ? [X0] : (~patient(X0) & ~wise(X0)) [input p11]
13. ! [X0] : ((funny(X0) & humble(X0)) <=> (funny(X0) | old(X0))) [input p12]
14. ! [X0] : ((~kind(X0) <~> generous(X0)) <=> (quiet(X0) | ~wise(X0))) [input p13]
21. quiet(lucy) [input hypothesis]
22. ? [X0] : (~old(X0) <~> ~rich(X0)) <=> ? [X1] : (wise(X1) & strong(X1)) [rectify 8]
23. ? [X0] : (funny(X0) | patient(X0)) => ? [X1] : (~patient(X1) & ~wise(X1)) [rectify 12]
31. ? [X1] : (~patient(X1) & ~wise(X1)) | ! [X0] : (~funny(X0) & ~patient(X0)) [ennf transformation 23]
35. ! [X0] : ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))) [nnf transformation 1]
37. ! [X0] : (((strong(X0) | ~tall(X0)) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~strong(X0) & tall(X0)))) [nnf transformation 3]
38. ! [X0] : ((strong(X0) | ~tall(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~strong(X0) & tall(X0)))) [flattening 37]
40. ! [X0] : (((kind(X0) & ~generous(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~kind(X0) | generous(X0)))) [nnf transformation 5]
41. ! [X0] : (((kind(X0) & ~generous(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | ~kind(X0) | generous(X0))) [flattening 40]
42. ! [X0] : (((~strong(X0) & ~happy(X0)) | (~tall(X0) & old(X0))) & ((tall(X0) | ~old(X0)) | (strong(X0) | happy(X0)))) [nnf transformation 7]
43. ! [X0] : (((~strong(X0) & ~happy(X0)) | (~tall(X0) & old(X0))) & (tall(X0) | ~old(X0) | strong(X0) | happy(X0))) [flattening 42]
44. (? [X0] : ((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ! [X1] : (~wise(X1) | ~strong(X1))) & (? [X1] : (wise(X1) & strong(X1)) | ! [X0] : ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0)))) [nnf transformation 22]
45. (? [X0] : ((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ! [X1] : (~wise(X1) | ~strong(X1))) & (? [X2] : (wise(X2) & strong(X2)) | ! [X3] : ((~old(X3) | rich(X3)) & (~rich(X3) | old(X3)))) [rectify 44]
46. ? [X0] : ((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) => ((rich(sK0) | old(sK0)) & (~rich(sK0) | ~old(sK0))) [choice axiom]
47. ? [X2] : (wise(X2) & strong(X2)) => (wise(sK1) & strong(sK1)) [choice axiom]
48. (((rich(sK0) | old(sK0)) & (~rich(sK0) | ~old(sK0))) | ! [X1] : (~wise(X1) | ~strong(X1))) & ((wise(sK1) & strong(sK1)) | ! [X3] : ((~old(X3) | rich(X3)) & (~rich(X3) | old(X3)))) [skolemisation 45,47,46]
51. ((brave(susan) & curious(susan)) | ! [X0] : ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (? [X0] : ((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (~brave(susan) | ~curious(susan))) [nnf transformation 11]
52. ((brave(susan) & curious(susan)) | ! [X0] : ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (? [X0] : ((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | ~brave(susan) | ~curious(susan)) [flattening 51]
53. ((brave(susan) & curious(susan)) | ! [X0] : ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (? [X1] : ((~generous(X1) | kind(X1)) & (generous(X1) | ~kind(X1))) | ~brave(susan) | ~curious(susan)) [rectify 52]
54. ? [X1] : ((~generous(X1) | kind(X1)) & (generous(X1) | ~kind(X1))) => ((~generous(sK2) | kind(sK2)) & (generous(sK2) | ~kind(sK2))) [choice axiom]
55. ((brave(susan) & curious(susan)) | ! [X0] : ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(sK2) | kind(sK2)) & (generous(sK2) | ~kind(sK2))) | ~brave(susan) | ~curious(susan)) [skolemisation 53,54]
56. ? [X0] : (~patient(X0) & ~wise(X0)) | ! [X1] : (~funny(X1) & ~patient(X1)) [rectify 31]
57. ? [X0] : (~patient(X0) & ~wise(X0)) => (~patient(sK3) & ~wise(sK3)) [choice axiom]
58. (~patient(sK3) & ~wise(sK3)) | ! [X1] : (~funny(X1) & ~patient(X1)) [skolemisation 56,57]
59. ! [X0] : (((funny(X0) & humble(X0)) | (~funny(X0) & ~old(X0))) & ((funny(X0) | old(X0)) | (~funny(X0) | ~humble(X0)))) [nnf transformation 13]
60. ! [X0] : (((funny(X0) & humble(X0)) | (~funny(X0) & ~old(X0))) & (funny(X0) | old(X0) | ~funny(X0) | ~humble(X0))) [flattening 59]
61. ! [X0] : ((((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (~quiet(X0) & wise(X0))) & ((quiet(X0) | ~wise(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (~quiet(X0) & wise(X0))) & (quiet(X0) | ~wise(X0) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))))) [flattening 61]
72. ~generous(X0) | rich(X0) [cnf transformation 35]
75. wise(X0) | tall(X0) | tall(X0) [cnf transformation 38]
79. strong(X0) | ~tall(X0) | wise(X0) | ~tall(X0) [cnf transformation 38]
87. kind(X0) | rich(X0) | happy(X0) [cnf transformation 41]
92. ~happy(X0) | old(X0) [cnf transformation 43]
94. ~strong(X0) | old(X0) [cnf transformation 43]
95. ~strong(X0) | ~tall(X0) [cnf transformation 43]
96. strong(sK1) | ~rich(X3) | old(X3) [cnf transformation 48]
97. strong(sK1) | ~old(X3) | rich(X3) [cnf transformation 48]
106. generous(sK2) | ~kind(sK2) | ~brave(susan) | ~curious(susan) [cnf transformation 55]
108. curious(susan) | generous(X0) | kind(X0) [cnf transformation 55]
109. curious(susan) | ~kind(X0) | ~generous(X0) [cnf transformation 55]
110. brave(susan) | generous(X0) | kind(X0) [cnf transformation 55]
111. brave(susan) | ~kind(X0) | ~generous(X0) [cnf transformation 55]
113. ~wise(sK3) | ~funny(X1) [cnf transformation 58]
119. ~old(X0) | funny(X0) [cnf transformation 60]
124. ~quiet(X0) | ~kind(X0) | generous(X0) [cnf transformation 62]
126. ~quiet(X0) | kind(X0) | ~generous(X0) [cnf transformation 62]
138. quiet(lucy) [cnf transformation 21]
139. tall(X0) | wise(X0) [duplicate literal removal 75]
140. ~tall(X0) | strong(X0) | wise(X0) [duplicate literal removal 79]
189. 11 <=> ! [X3] : (~old(X3) | rich(X3)) [avatar definition]
190. ~old(X3) | rich(X3) <- (11) [avatar component clause 189]
197. 13 <=> ! [X3] : (~rich(X3) | old(X3)) [avatar definition]
198. ~rich(X3) | old(X3) <- (13) [avatar component clause 197]
201. 14 <=> strong(sK1) [avatar definition]
203. strong(sK1) <- (14) [avatar component clause 201]
204. 11 | 14 [avatar split clause 97,201,189]
205. 13 | 14 [avatar split clause 96,201,197]
207. 15 <=> brave(susan) [avatar definition]
235. 21 <=> ! [X0] : (~kind(X0) | ~generous(X0)) [avatar definition]
236. ~kind(X0) | ~generous(X0) <- (21) [avatar component clause 235]
237. 21 | 15 [avatar split clause 111,207,235]
239. 22 <=> ! [X0] : (generous(X0) | kind(X0)) [avatar definition]
240. kind(X0) | generous(X0) <- (22) [avatar component clause 239]
241. 22 | 15 [avatar split clause 110,207,239]
243. 23 <=> curious(susan) [avatar definition]
246. 21 | 23 [avatar split clause 109,243,235]
247. 22 | 23 [avatar split clause 108,243,239]
249. 24 <=> kind(sK2) [avatar definition]
250. ~kind(sK2) <- (~24) [avatar component clause 249]
253. 25 <=> generous(sK2) [avatar definition]
254. generous(sK2) <- (25) [avatar component clause 253]
257. ~23 | ~15 | ~24 | 25 [avatar split clause 106,253,249,207,243]
259. 26 <=> ! [X1] : ~funny(X1) [avatar definition]
260. ~funny(X1) <- (26) [avatar component clause 259]
271. 29 <=> wise(sK3) [avatar definition]
273. ~wise(sK3) <- (~29) [avatar component clause 271]
274. 26 | ~29 [avatar split clause 113,271,259]
320. ~kind(lucy) | generous(lucy) [resolution 124,138]
333. generous(lucy) <- (22) [subsumption resolution 320,240]
337. 39 <=> happy(sK2) [avatar definition]
339. happy(sK2) <- (39) [avatar component clause 337]
341. 40 <=> rich(sK2) [avatar definition]
342. ~rich(sK2) <- (~40) [avatar component clause 341]
343. rich(sK2) <- (40) [avatar component clause 341]
348. rich(sK2) <- (25) [resolution 254,72]
349. 40 | ~25 [avatar split clause 348,253,341]
368. 42 <=> kind(lucy) [avatar definition]
370. kind(lucy) <- (42) [avatar component clause 368]
372. kind(lucy) | ~generous(lucy) [resolution 126,138]
373. kind(lucy) <- (22) [subsumption resolution 372,333]
374. 42 | ~22 [avatar split clause 373,239,368]
377. strong(X0) | wise(X0) | wise(X0) [resolution 140,139]
378. strong(X0) | wise(X0) [duplicate literal removal 377]
384. ~generous(lucy) <- (21, 42) [resolution 370,236]
386. $false <- (21, 22, 42) [subsumption resolution 384,333]
387. ~21 | ~22 | ~42 [avatar contradiction clause 386]
405. rich(sK2) | happy(sK2) <- (~24) [resolution 250,87]
410. 39 | 40 | 24 [avatar split clause 405,249,341,337]
414. old(sK2) <- (39) [resolution 339,92]
479. wise(X3) | ~tall(X3) [resolution 378,95]
482. wise(X3) [subsumption resolution 479,139]
487. rich(sK2) <- (11, 39) [resolution 414,190]
490. $false <- (11, 39, ~40) [subsumption resolution 487,342]
491. ~11 | ~39 | 40 [avatar contradiction clause 490]
498. old(sK1) <- (14) [resolution 203,94]
523. funny(sK1) <- (14) [resolution 498,119]
555. $false <- (~29) [resolution 482,273]
558. 29 [avatar contradiction clause 555]
566. $false <- (14, 26) [resolution 523,260]
568. ~14 | ~26 [avatar contradiction clause 566]
583. old(sK2) <- (13, 40) [resolution 198,343]
588. funny(sK2) <- (13, 40) [resolution 583,119]
592. $false <- (13, 26, 40) [subsumption resolution 588,260]
593. ~13 | ~26 | ~40 [avatar contradiction clause 592]
594. $false [avatar sat refutation 204,205,237,241,246,247,257,274,349,374,387,410,491,558,568,593]
% SZS output end Proof for 4109525165400853909331688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or wise then someone is both calm and not wise.
If mary is either not brave or not humble then john is not generous.
Everyone who is not kind is not brave or old.
Everyone who is not happy is both not wise and not humble.
If susan is either not quiet or not humble then paul is either quiet or not brave and vice versa.
Everyone who is calm is wise.
If paul is wise then someone is generous or not humble.
If john is happy then lucy is either curious or not calm and vice versa.
If mary is strong then someone is not creative.
Everyone who is not strong is wise.
Everyone who is either not wise or not kind is both quiet and not wise.
Everyone who is either brave or not wise is not humble or old and vice versa.
If someone is wise or not strong then alice is both humble and calm and vice versa.
Everyone who is either happy or not happy is both curious and patient and vice versa.
If alice is both wise and humble then someone is funny and vice versa.
Everyone who is either wise or humble is both wise and strong.
Someone is either brave or not strong.
Someone is not calm.
Susan is either strong or old.
Someone is either old or curious.
Someone is not old or strong.
Susan is both rich and tall.
Susan is happy.
Lucy is either not tall or not brave. | Alice is not strong. | entailment | (((~strong(alice)<~>wise(alice)))=>(?[X]:((calm(X)&~wise(X)))))&
(((~brave(mary)<~>~humble(mary)))=>(~generous(john)))&
(![X]:(~kind(X)=>(~brave(X)|old(X))))&
(![X]:(~happy(X)=>(~wise(X)&~humble(X))))&
(((~quiet(susan)<~>~humble(susan)))<=>((quiet(paul)<~>~brave(paul))))&
(![X]:(calm(X)=>wise(X)))&
((wise(paul))=>(?[X]:((generous(X)|~humble(X)))))&
((happy(john))<=>((curious(lucy)<~>~calm(lucy))))&
((strong(mary))=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>wise(X)))&
(![X]:((~wise(X)<~>~kind(X))=>(quiet(X)&~wise(X))))&
(![X]:((brave(X)<~>~wise(X))<=>(~humble(X)|old(X))))&
((?[X]:((wise(X)|~strong(X))))<=>((humble(alice)&calm(alice))))&
(![X]:((happy(X)<~>~happy(X))<=>(curious(X)&patient(X))))&
(((wise(alice)&humble(alice)))<=>(?[X]:(funny(X))))&
(![X]:((wise(X)<~>humble(X))=>(wise(X)&strong(X))))&
(?[X]:((brave(X)<~>~strong(X))))&
(?[X]:(~calm(X)))&
((strong(susan)<~>old(susan)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:((~old(X)|strong(X))))&
((rich(susan)&tall(susan)))&
(happy(susan))&
((~tall(lucy)<~>~brave(lucy))) | ~strong(alice) | [
"p0",
"p5",
"p11",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6984575027987315475640444
% SZS output start Proof for 6984575027987315475640444
1. (~strong(alice) <~> wise(alice)) => ? [X0] : (~wise(X0) & calm(X0)) [input p0]
6. ! [X0] : (calm(X0) => wise(X0)) [input p5]
12. ! [X0] : ((brave(X0) <~> ~wise(X0)) <=> (old(X0) | ~humble(X0))) [input p11]
13. ? [X0] : (~strong(X0) | wise(X0)) <=> (calm(alice) & humble(alice)) [input p12]
16. ! [X0] : ((wise(X0) <~> humble(X0)) => (strong(X0) & wise(X0))) [input p15]
17. ? [X0] : (brave(X0) <~> ~strong(X0)) [input p16]
25. strong(alice) [input hypothesis]
28. ? [X0] : (~wise(X0) & calm(X0)) | (~strong(alice) <=> wise(alice)) [ennf transformation 1]
33. ! [X0] : (wise(X0) | ~calm(X0)) [ennf transformation 6]
37. ! [X0] : ((strong(X0) & wise(X0)) | (wise(X0) <=> humble(X0))) [ennf transformation 16]
38. ? [X0] : (~wise(X0) & calm(X0)) | ((~strong(alice) | ~wise(alice)) & (wise(alice) | strong(alice))) [nnf transformation 28]
39. ? [X0] : (~wise(X0) & calm(X0)) => (~wise(sK0) & calm(sK0)) [choice axiom]
40. (~wise(sK0) & calm(sK0)) | ((~strong(alice) | ~wise(alice)) & (wise(alice) | strong(alice))) [skolemisation 38,39]
47. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (~old(X0) & humble(X0))) & ((old(X0) | ~humble(X0)) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [nnf transformation 12]
48. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (~old(X0) & humble(X0))) & (old(X0) | ~humble(X0) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [flattening 47]
49. (? [X0] : (~strong(X0) | wise(X0)) | (~calm(alice) | ~humble(alice))) & ((calm(alice) & humble(alice)) | ! [X0] : (strong(X0) & ~wise(X0))) [nnf transformation 13]
50. (? [X0] : (~strong(X0) | wise(X0)) | ~calm(alice) | ~humble(alice)) & ((calm(alice) & humble(alice)) | ! [X0] : (strong(X0) & ~wise(X0))) [flattening 49]
51. (? [X0] : (~strong(X0) | wise(X0)) | ~calm(alice) | ~humble(alice)) & ((calm(alice) & humble(alice)) | ! [X1] : (strong(X1) & ~wise(X1))) [rectify 50]
52. ? [X0] : (~strong(X0) | wise(X0)) => (~strong(sK2) | wise(sK2)) [choice axiom]
53. ((~strong(sK2) | wise(sK2)) | ~calm(alice) | ~humble(alice)) & ((calm(alice) & humble(alice)) | ! [X1] : (strong(X1) & ~wise(X1))) [skolemisation 51,52]
61. ! [X0] : ((strong(X0) & wise(X0)) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) [nnf transformation 37]
62. ? [X0] : ((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) [nnf transformation 17]
63. ? [X0] : ((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) => ((strong(sK4) | ~brave(sK4)) & (~strong(sK4) | brave(sK4))) [choice axiom]
64. (strong(sK4) | ~brave(sK4)) & (~strong(sK4) | brave(sK4)) [skolemisation 62,63]
75. calm(sK0) | ~strong(alice) | ~wise(alice) [cnf transformation 40]
77. ~wise(sK0) | ~strong(alice) | ~wise(alice) [cnf transformation 40]
91. ~calm(X0) | wise(X0) [cnf transformation 33]
106. ~brave(X0) | wise(X0) | humble(X0) [cnf transformation 48]
108. humble(alice) | ~wise(X1) [cnf transformation 53]
109. humble(alice) | strong(X1) [cnf transformation 53]
123. wise(X0) | wise(X0) | ~humble(X0) [cnf transformation 61]
126. ~strong(sK4) | brave(sK4) [cnf transformation 64]
138. strong(alice) [cnf transformation 25]
139. ~humble(X0) | wise(X0) [duplicate literal removal 123]
146. 1 <=> wise(alice) [avatar definition]
148. ~wise(alice) <- (~1) [avatar component clause 146]
150. 2 <=> strong(alice) [avatar definition]
154. 3 <=> wise(sK0) [avatar definition]
156. ~wise(sK0) <- (~3) [avatar component clause 154]
157. ~1 | ~2 | ~3 [avatar split clause 77,154,150,146]
160. 4 <=> calm(sK0) [avatar definition]
162. calm(sK0) <- (4) [avatar component clause 160]
163. ~1 | ~2 | 4 [avatar split clause 75,160,150,146]
234. 18 <=> humble(alice) [avatar definition]
235. humble(alice) <- (18) [avatar component clause 234]
247. 21 <=> ! [X1] : strong(X1) [avatar definition]
248. strong(X1) <- (21) [avatar component clause 247]
251. 22 <=> ! [X1] : ~wise(X1) [avatar definition]
252. ~wise(X1) <- (22) [avatar component clause 251]
254. 21 | 18 [avatar split clause 109,234,247]
255. 22 | 18 [avatar split clause 108,234,251]
270. 25 <=> brave(sK4) [avatar definition]
271. brave(sK4) <- (25) [avatar component clause 270]
274. 26 <=> strong(sK4) [avatar definition]
275. ~strong(sK4) <- (~26) [avatar component clause 274]
278. 25 | ~26 [avatar split clause 126,274,270]
309. 2 [avatar split clause 138,150]
317. $false <- (21, ~26) [resolution 248,275]
318. ~21 | 26 [avatar contradiction clause 317]
324. wise(alice) <- (18) [resolution 139,235]
325. $false <- (~1, 18) [subsumption resolution 324,148]
326. 1 | ~18 [avatar contradiction clause 325]
358. wise(sK0) <- (4) [resolution 162,91]
359. $false <- (~3, 4) [subsumption resolution 358,156]
360. 3 | ~4 [avatar contradiction clause 359]
367. wise(sK4) | humble(sK4) <- (25) [resolution 106,271]
368. humble(sK4) <- (22, 25) [subsumption resolution 367,252]
369. wise(sK4) <- (22, 25) [resolution 368,139]
371. $false <- (22, 25) [subsumption resolution 369,252]
372. ~22 | ~25 [avatar contradiction clause 371]
373. $false [avatar sat refutation 157,163,254,255,278,309,318,326,360,372]
% SZS output end Proof for 6984575027987315475640444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and patient then paul is both not calm and humble and vice versa.
Everyone who is patient is old.
Everyone who is both tall and not strong is brave.
Everyone who is both not rich and not calm is old or quiet.
If lucy is either creative or tall then someone is not creative or not brave.
Everyone who is not tall or rich is humble or old and vice versa.
Everyone who is not patient is either not happy or not generous.
If alice is wise or rich then someone is happy or not brave.
If lucy is either creative or not happy then someone is old and vice versa.
If paul is wise or happy then paul is both tall and not old.
Everyone who is either not tall or strong is rich or happy and vice versa.
Everyone who is old or creative is both not strong and not calm and vice versa.
Everyone who is both happy and generous is not quiet or not old.
Everyone who is either not old or not tall is funny or tall and vice versa.
Everyone who is both funny and not patient is not calm or humble.
Everyone who is rich is either humble or not brave and vice versa.
Lucy is rich.
Mary is both funny and generous.
Paul is quiet or tall.
Fred is brave or not happy.
Paul is not rich or tall.
Fred is not tall or quiet.
Someone is not happy.
Paul is either not old or wise. | Lucy is strong. | neutral | ((?[X]:((~humble(X)&patient(X))))<=>((~calm(paul)&humble(paul))))&
(![X]:(patient(X)=>old(X)))&
(![X]:((tall(X)&~strong(X))=>brave(X)))&
(![X]:((~rich(X)&~calm(X))=>(old(X)|quiet(X))))&
(((creative(lucy)<~>tall(lucy)))=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:((~tall(X)|rich(X))<=>(humble(X)|old(X))))&
(![X]:(~patient(X)=>(~happy(X)<~>~generous(X))))&
(((wise(alice)|rich(alice)))=>(?[X]:((happy(X)|~brave(X)))))&
(((creative(lucy)<~>~happy(lucy)))<=>(?[X]:(old(X))))&
(((wise(paul)|happy(paul)))=>((tall(paul)&~old(paul))))&
(![X]:((~tall(X)<~>strong(X))<=>(rich(X)|happy(X))))&
(![X]:((old(X)|creative(X))<=>(~strong(X)&~calm(X))))&
(![X]:((happy(X)&generous(X))=>(~quiet(X)|~old(X))))&
(![X]:((~old(X)<~>~tall(X))<=>(funny(X)|tall(X))))&
(![X]:((funny(X)&~patient(X))=>(~calm(X)|humble(X))))&
(![X]:(rich(X)<=>(humble(X)<~>~brave(X))))&
(rich(lucy))&
((funny(mary)&generous(mary)))&
((quiet(paul)|tall(paul)))&
((brave(fred)|~happy(fred)))&
((~rich(paul)|tall(paul)))&
((~tall(fred)|quiet(fred)))&
(?[X]:(~happy(X)))&
((~old(paul)<~>wise(paul))) | strong(lucy) | [] | null | 0 |
Everyone who is kind is not generous and vice versa. If paul is both old and quiet then someone is rich. Everyone who is both not tall and not kind is not funny. Everyone who is curious is wise or happy. Everyone who is either not strong or tall is not rich or not happy and vice versa. Everyone who is either calm or curious is both old and not curious and vice versa. If fred is rich or wise then mary is not generous. Everyone who is both not strong and not happy is funny or generous and vice versa. If someone is old then someone is both patient and rich and vice versa. If someone is either not strong or not generous then someone is both not creative and creative. If someone is not tall then fred is both patient and not quiet and vice versa. If someone is not wise or not tall then lucy is not curious or old and vice versa. Everyone who is either not funny or not quiet is both rich and not creative. Everyone who is both wise and curious is both strong and not kind and vice versa. Everyone who is either quiet or not kind is kind. If paul is creative then someone is both calm and creative. Someone is strong or not tall. John is either creative or rich. Susan is not funny or calm. Someone is both not tall and old. Someone is calm. Someone is either curious or not curious. Mary is not old. Someone is not tall. | Fred is patient. | entailment | (![X]:(kind(X)<=>~generous(X)))&
(((old(paul)&quiet(paul)))=>(?[X]:(rich(X))))&
(![X]:((~tall(X)&~kind(X))=>~funny(X)))&
(![X]:(curious(X)=>(wise(X)|happy(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~rich(X)|~happy(X))))&
(![X]:((calm(X)<~>curious(X))<=>(old(X)&~curious(X))))&
(((rich(fred)|wise(fred)))=>(~generous(mary)))&
(![X]:((~strong(X)&~happy(X))<=>(funny(X)|generous(X))))&
((?[X]:(old(X)))<=>(?[X]:((patient(X)&rich(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))=>(?[X]:((~creative(X)&creative(X)))))&
((?[X]:(~tall(X)))<=>((patient(fred)&~quiet(fred))))&
((?[X]:((~wise(X)|~tall(X))))<=>((~curious(lucy)|old(lucy))))&
(![X]:((~funny(X)<~>~quiet(X))=>(rich(X)&~creative(X))))&
(![X]:((wise(X)&curious(X))<=>(strong(X)&~kind(X))))&
(![X]:((quiet(X)<~>~kind(X))=>kind(X)))&
((creative(paul))=>(?[X]:((calm(X)&creative(X)))))&
(?[X]:((strong(X)|~tall(X))))&
((creative(john)<~>rich(john)))&
((~funny(susan)|calm(susan)))&
(?[X]:((~tall(X)&old(X))))&
(?[X]:(calm(X)))&
(?[X]:((curious(X)<~>~curious(X))))&
(~old(mary))&
(?[X]:(~tall(X))) | patient(fred) | [
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 360790638972203576943376
% SZS output start Proof for 360790638972203576943376
11. ? [X0] : ~tall(X0) <=> (~quiet(fred) & patient(fred)) [input p10]
20. ? [X0] : (old(X0) & ~tall(X0)) [input p19]
25. ~patient(fred) [input hypothesis]
57. (? [X0] : ~tall(X0) | (quiet(fred) | ~patient(fred))) & ((~quiet(fred) & patient(fred)) | ! [X0] : tall(X0)) [nnf transformation 11]
58. (? [X0] : ~tall(X0) | quiet(fred) | ~patient(fred)) & ((~quiet(fred) & patient(fred)) | ! [X0] : tall(X0)) [flattening 57]
59. (? [X0] : ~tall(X0) | quiet(fred) | ~patient(fred)) & ((~quiet(fred) & patient(fred)) | ! [X1] : tall(X1)) [rectify 58]
60. ? [X0] : ~tall(X0) => ~tall(sK4) [choice axiom]
61. (~tall(sK4) | quiet(fred) | ~patient(fred)) & ((~quiet(fred) & patient(fred)) | ! [X1] : tall(X1)) [skolemisation 59,60]
76. ? [X0] : (old(X0) & ~tall(X0)) => (old(sK8) & ~tall(sK8)) [choice axiom]
77. old(sK8) & ~tall(sK8) [skolemisation 20,76]
116. patient(fred) | tall(X1) [cnf transformation 61]
139. ~tall(sK8) [cnf transformation 77]
146. ~patient(fred) [cnf transformation 25]
217. 15 <=> patient(fred) [avatar definition]
230. 18 <=> ! [X1] : tall(X1) [avatar definition]
231. tall(X1) <- (18) [avatar component clause 230]
233. 18 | 15 [avatar split clause 116,217,230]
299. ~15 [avatar split clause 146,217]
302. $false <- (18) [resolution 231,139]
305. ~18 [avatar contradiction clause 302]
306. $false [avatar sat refutation 233,299,305]
% SZS output end Proof for 360790638972203576943376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not strong and not brave then mary is strong or humble.
Everyone who is either humble or funny is either not calm or happy.
If john is funny then john is either generous or not calm and vice versa.
If someone is not rich or quiet then someone is not happy or not wise and vice versa.
If lucy is both not humble and not calm then paul is both not strong and not patient.
Everyone who is either brave or strong is either not funny or patient.
If alice is brave or not rich then someone is not rich or happy.
If someone is not humble then fred is happy or creative.
Everyone who is calm is brave or not patient.
Everyone who is not quiet or funny is calm or not tall and vice versa.
Everyone who is quiet or curious is either not strong or strong and vice versa.
Everyone who is happy is not old.
Everyone who is either not wise or not curious is both not rich and not curious.
Everyone who is either tall or not calm is either not old or not calm.
Everyone who is not old is brave.
If fred is both happy and creative then alice is not brave or funny and vice versa.
Someone is either not creative or not strong.
Someone is not happy or not funny.
Paul is not rich or not patient.
Susan is kind.
Fred is either not calm or not patient.
Mary is old.
John is both rich and strong.
John is tall or not calm. | John is tall. | neutral | (((~strong(lucy)&~brave(lucy)))=>((strong(mary)|humble(mary))))&
(![X]:((humble(X)<~>funny(X))=>(~calm(X)<~>happy(X))))&
((funny(john))<=>((generous(john)<~>~calm(john))))&
((?[X]:((~rich(X)|quiet(X))))<=>(?[X]:((~happy(X)|~wise(X)))))&
(((~humble(lucy)&~calm(lucy)))=>((~strong(paul)&~patient(paul))))&
(![X]:((brave(X)<~>strong(X))=>(~funny(X)<~>patient(X))))&
(((brave(alice)|~rich(alice)))=>(?[X]:((~rich(X)|happy(X)))))&
((?[X]:(~humble(X)))=>((happy(fred)|creative(fred))))&
(![X]:(calm(X)=>(brave(X)|~patient(X))))&
(![X]:((~quiet(X)|funny(X))<=>(calm(X)|~tall(X))))&
(![X]:((quiet(X)|curious(X))<=>(~strong(X)<~>strong(X))))&
(![X]:(happy(X)=>~old(X)))&
(![X]:((~wise(X)<~>~curious(X))=>(~rich(X)&~curious(X))))&
(![X]:((tall(X)<~>~calm(X))=>(~old(X)<~>~calm(X))))&
(![X]:(~old(X)=>brave(X)))&
(((happy(fred)&creative(fred)))<=>((~brave(alice)|funny(alice))))&
(?[X]:((~creative(X)<~>~strong(X))))&
(?[X]:((~happy(X)|~funny(X))))&
((~rich(paul)|~patient(paul)))&
(kind(susan))&
((~calm(fred)<~>~patient(fred)))&
(old(mary))&
((rich(john)&strong(john)))&
((tall(john)|~calm(john))) | tall(john) | [] | null | 0 |
Everyone who is humble or happy is either not old or kind and vice versa. If someone is either curious or quiet then someone is quiet or generous and vice versa. Everyone who is either not kind or not calm is patient and vice versa. If alice is not happy or brave then someone is creative. If someone is both generous and quiet then someone is either not kind or calm and vice versa. Everyone who is not brave or old is both not funny and quiet. Everyone who is both patient and kind is generous and vice versa. Everyone who is either curious or patient is curious or not quiet and vice versa. Everyone who is wise is either calm or funny and vice versa. If someone is either brave or not old then lucy is strong. If john is both not strong and not curious then someone is both not generous and not tall. Everyone who is both quiet and curious is wise or happy and vice versa. If alice is either brave or not humble then someone is brave or not strong and vice versa. Lucy is either tall or not creative. Susan is patient or not tall. Someone is brave. Someone is not happy or not curious. Alice is either funny or wise. Someone is either not quiet or not funny. | Susan is not old. | entailment | (![X]:((humble(X)|happy(X))<=>(~old(X)<~>kind(X))))&
((?[X]:((curious(X)<~>quiet(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((~kind(X)<~>~calm(X))<=>patient(X)))&
(((~happy(alice)|brave(alice)))=>(?[X]:(creative(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:((~brave(X)|old(X))=>(~funny(X)&quiet(X))))&
(![X]:((patient(X)&kind(X))<=>generous(X)))&
(![X]:((curious(X)<~>patient(X))<=>(curious(X)|~quiet(X))))&
(![X]:(wise(X)<=>(calm(X)<~>funny(X))))&
((?[X]:((brave(X)<~>~old(X))))=>(strong(lucy)))&
(((~strong(john)&~curious(john)))=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|happy(X))))&
(((brave(alice)<~>~humble(alice)))<=>(?[X]:((brave(X)|~strong(X)))))&
((tall(lucy)<~>~creative(lucy)))&
((patient(susan)|~tall(susan)))&
(?[X]:(brave(X)))&
(?[X]:((~happy(X)|~curious(X))))&
((funny(alice)<~>wise(alice)))&
(?[X]:((~quiet(X)<~>~funny(X)))) | ~old(susan) | [
"p2",
"p4",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 536074540652964878673527
% SZS output start Proof for 536074540652964878673527
3. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> patient(X0)) [input p2]
5. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X0] : (~kind(X0) <~> calm(X0)) [input p4]
6. ! [X0] : ((old(X0) | ~brave(X0)) => (quiet(X0) & ~funny(X0))) [input p5]
7. ! [X0] : ((kind(X0) & patient(X0)) <=> generous(X0)) [input p6]
8. ! [X0] : ((curious(X0) <~> patient(X0)) <=> (~quiet(X0) | curious(X0))) [input p7]
20. old(susan) [input hypothesis]
22. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X1] : (~kind(X1) <~> calm(X1)) [rectify 5]
24. ! [X0] : ((quiet(X0) & ~funny(X0)) | (~old(X0) & brave(X0))) [ennf transformation 6]
35. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | ~patient(X0)) & (patient(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 3]
38. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (? [X1] : ((~calm(X1) | kind(X1)) & (calm(X1) | ~kind(X1))) | ! [X0] : (~quiet(X0) | ~generous(X0))) [nnf transformation 22]
39. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (? [X2] : ((~calm(X2) | kind(X2)) & (calm(X2) | ~kind(X2))) | ! [X3] : (~quiet(X3) | ~generous(X3))) [rectify 38]
40. ? [X0] : (quiet(X0) & generous(X0)) => (quiet(sK3) & generous(sK3)) [choice axiom]
41. ? [X2] : ((~calm(X2) | kind(X2)) & (calm(X2) | ~kind(X2))) => ((~calm(sK4) | kind(sK4)) & (calm(sK4) | ~kind(sK4))) [choice axiom]
42. ((quiet(sK3) & generous(sK3)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (((~calm(sK4) | kind(sK4)) & (calm(sK4) | ~kind(sK4))) | ! [X3] : (~quiet(X3) | ~generous(X3))) [skolemisation 39,41,40]
43. ! [X0] : (((kind(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | (~kind(X0) | ~patient(X0)))) [nnf transformation 7]
44. ! [X0] : (((kind(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | ~kind(X0) | ~patient(X0))) [flattening 43]
45. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [flattening 45]
78. ~calm(X0) | patient(X0) | kind(X0) [cnf transformation 35]
79. ~kind(X0) | patient(X0) | calm(X0) [cnf transformation 35]
86. generous(sK3) | calm(X1) | kind(X1) [cnf transformation 42]
87. generous(sK3) | ~kind(X1) | ~calm(X1) [cnf transformation 42]
88. quiet(sK3) | calm(X1) | kind(X1) [cnf transformation 42]
89. quiet(sK3) | ~kind(X1) | ~calm(X1) [cnf transformation 42]
93. ~old(X0) | quiet(X0) [cnf transformation 24]
95. ~generous(X0) | patient(X0) [cnf transformation 44]
98. ~quiet(X0) | curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 46]
101. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 46]
131. old(susan) [cnf transformation 20]
132. ~quiet(X0) | curious(X0) | ~patient(X0) [duplicate literal removal 98]
133. ~patient(X0) | ~curious(X0) [duplicate literal removal 101]
183. 12 <=> ! [X1] : (~kind(X1) | ~calm(X1)) [avatar definition]
184. ~calm(X1) | ~kind(X1) <- (12) [avatar component clause 183]
186. 13 <=> quiet(sK3) [avatar definition]
188. quiet(sK3) <- (13) [avatar component clause 186]
189. 12 | 13 [avatar split clause 89,186,183]
191. 14 <=> ! [X1] : (calm(X1) | kind(X1)) [avatar definition]
192. calm(X1) | kind(X1) <- (14) [avatar component clause 191]
193. 14 | 13 [avatar split clause 88,186,191]
195. 15 <=> generous(sK3) [avatar definition]
197. generous(sK3) <- (15) [avatar component clause 195]
198. 12 | 15 [avatar split clause 87,195,183]
199. 14 | 15 [avatar split clause 86,195,191]
213. ~patient(X0) | ~quiet(X0) [subsumption resolution 132,133]
279. 33 <=> patient(susan) [avatar definition]
281. patient(susan) <- (33) [avatar component clause 279]
313. quiet(susan) [resolution 93,131]
319. patient(sK3) <- (15) [resolution 197,95]
326. 40 <=> kind(susan) [avatar definition]
328. kind(susan) <- (40) [avatar component clause 326]
330. ~quiet(sK3) <- (15) [resolution 319,213]
332. $false <- (13, 15) [subsumption resolution 330,188]
333. ~13 | ~15 [avatar contradiction clause 332]
358. patient(X0) | kind(X0) | kind(X0) <- (14) [resolution 78,192]
359. patient(X0) | kind(X0) <- (14) [duplicate literal removal 358]
379. ~quiet(X3) | kind(X3) <- (14) [resolution 359,213]
386. kind(susan) <- (14) [resolution 379,313]
390. 40 | ~14 [avatar split clause 386,191,326]
391. patient(susan) | calm(susan) <- (40) [resolution 328,79]
395. 45 <=> calm(susan) [avatar definition]
397. calm(susan) <- (45) [avatar component clause 395]
398. 45 | 33 | ~40 [avatar split clause 391,326,279,395]
400. ~kind(susan) <- (12, 45) [resolution 397,184]
401. $false <- (12, 40, 45) [subsumption resolution 400,328]
402. ~12 | ~40 | ~45 [avatar contradiction clause 401]
407. ~quiet(susan) <- (33) [resolution 281,213]
410. $false <- (33) [subsumption resolution 407,313]
411. ~33 [avatar contradiction clause 410]
412. $false [avatar sat refutation 189,193,198,199,333,390,398,402,411]
% SZS output end Proof for 536074540652964878673527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not strong is not strong and vice versa.
Everyone who is wise or brave is not funny or brave and vice versa.
If john is not happy or not kind then someone is either not tall or humble.
If alice is not brave or tall then someone is calm.
Everyone who is creative is not brave.
Everyone who is either strong or tall is funny or not old and vice versa.
Everyone who is both not rich and rich is not quiet or brave.
Everyone who is both not curious and not funny is generous or curious and vice versa.
If someone is either not calm or not wise then mary is either not old or not brave.
Everyone who is either not patient or generous is both not wise and patient and vice versa.
Everyone who is humble is both not humble and rich and vice versa.
If someone is both creative and brave then fred is either rich or brave.
If john is both quiet and humble then alice is both not old and old and vice versa.
Everyone who is both not happy and old is not patient or not quiet.
If susan is both not happy and calm then someone is either not tall or not quiet and vice versa.
If someone is either rich or not humble then someone is generous and vice versa.
Lucy is either brave or curious.
Alice is not humble.
Paul is both not tall and not patient.
Susan is old or wise.
Susan is either tall or creative.
Susan is either funny or not strong.
Paul is either rich or not creative. | Mary is not old. | neutral | (![X]:((happy(X)<~>~strong(X))<=>~strong(X)))&
(![X]:((wise(X)|brave(X))<=>(~funny(X)|brave(X))))&
(((~happy(john)|~kind(john)))=>(?[X]:((~tall(X)<~>humble(X)))))&
(((~brave(alice)|tall(alice)))=>(?[X]:(calm(X))))&
(![X]:(creative(X)=>~brave(X)))&
(![X]:((strong(X)<~>tall(X))<=>(funny(X)|~old(X))))&
(![X]:((~rich(X)&rich(X))=>(~quiet(X)|brave(X))))&
(![X]:((~curious(X)&~funny(X))<=>(generous(X)|curious(X))))&
((?[X]:((~calm(X)<~>~wise(X))))=>((~old(mary)<~>~brave(mary))))&
(![X]:((~patient(X)<~>generous(X))<=>(~wise(X)&patient(X))))&
(![X]:(humble(X)<=>(~humble(X)&rich(X))))&
((?[X]:((creative(X)&brave(X))))=>((rich(fred)<~>brave(fred))))&
(((quiet(john)&humble(john)))<=>((~old(alice)&old(alice))))&
(![X]:((~happy(X)&old(X))=>(~patient(X)|~quiet(X))))&
(((~happy(susan)&calm(susan)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
((?[X]:((rich(X)<~>~humble(X))))<=>(?[X]:(generous(X))))&
((brave(lucy)<~>curious(lucy)))&
(~humble(alice))&
((~tall(paul)&~patient(paul)))&
((old(susan)|wise(susan)))&
((tall(susan)<~>creative(susan)))&
((funny(susan)<~>~strong(susan)))&
((rich(paul)<~>~creative(paul))) | ~old(mary) | [] | null | 0 |
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