premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is not kind then someone is either not tall or patient.
Everyone who is both not happy and not calm is old or kind.
If someone is both not wise and not generous then fred is wise or not kind.
Everyone who is not calm is not tall.
Everyone who is not tall is not tall or strong and vice versa.
Everyone who is not wise or tall is calm or not brave and vice versa.
Everyone who is not strong or curious is both creative and brave and vice versa.
Everyone who is patient is not strong or not brave.
Everyone who is humble is both wise and not humble and vice versa.
If someone is either not happy or not calm then john is either generous or not humble.
If alice is both kind and quiet then someone is creative or not patient.
Everyone who is funny is kind or not kind and vice versa.
If paul is either curious or not brave then someone is both not kind and not funny and vice versa.
Everyone who is either patient or brave is funny or calm and vice versa.
If lucy is either generous or not patient then someone is both humble and tall and vice versa.
Everyone who is patient or wise is quiet and vice versa.
Mary is strong.
Someone is both curious and kind.
Someone is either not happy or kind.
Someone is not funny or happy.
Someone is either not wise or not kind.
John is rich or not curious.
John is both not patient and not quiet.
Someone is both not curious and brave. | John is funny. | entailment | ((?[X]:(~kind(X)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(![X]:((~happy(X)&~calm(X))=>(old(X)|kind(X))))&
((?[X]:((~wise(X)&~generous(X))))=>((wise(fred)|~kind(fred))))&
(![X]:(~calm(X)=>~tall(X)))&
(![X]:(~tall(X)<=>(~tall(X)|strong(X))))&
(![X]:((~wise(X)|tall(X))<=>(calm(X)|~brave(X))))&
(![X]:((~strong(X)|curious(X))<=>(creative(X)&brave(X))))&
(![X]:(patient(X)=>(~strong(X)|~brave(X))))&
(![X]:(humble(X)<=>(wise(X)&~humble(X))))&
((?[X]:((~happy(X)<~>~calm(X))))=>((generous(john)<~>~humble(john))))&
(((kind(alice)&quiet(alice)))=>(?[X]:((creative(X)|~patient(X)))))&
(![X]:(funny(X)<=>(kind(X)|~kind(X))))&
(((curious(paul)<~>~brave(paul)))<=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((patient(X)<~>brave(X))<=>(funny(X)|calm(X))))&
(((generous(lucy)<~>~patient(lucy)))<=>(?[X]:((humble(X)&tall(X)))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(strong(mary))&
(?[X]:((curious(X)&kind(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
(?[X]:((~funny(X)|happy(X))))&
(?[X]:((~wise(X)<~>~kind(X))))&
((rich(john)|~curious(john)))&
((~patient(john)&~quiet(john)))&
(?[X]:((~curious(X)&brave(X)))) | funny(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8542904876853744975404516
% SZS output start Proof for 8542904876853744975404516
12. ! [X0] : (funny(X0) <=> (~kind(X0) | kind(X0))) [input p11]
25. ~funny(john) [input hypothesis]
55. ! [X0] : ((funny(X0) | (kind(X0) & ~kind(X0))) & ((~kind(X0) | kind(X0)) | ~funny(X0))) [nnf transformation 12]
56. ! [X0] : ((funny(X0) | (kind(X0) & ~kind(X0))) & (~kind(X0) | kind(X0) | ~funny(X0))) [flattening 55]
105. funny(X0) | ~kind(X0) [cnf transformation 56]
106. funny(X0) | kind(X0) [cnf transformation 56]
139. ~funny(john) [cnf transformation 25]
198. funny(X0) [subsumption resolution 105,106]
244. $false [subsumption resolution 139,198]
% SZS output end Proof for 8542904876853744975404516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and happy is not creative or not curious.
If someone is both generous and not quiet then someone is not tall and vice versa.
Everyone who is kind is creative and vice versa.
Everyone who is generous or not strong is both wise and not patient.
Everyone who is brave is rich.
Everyone who is tall is happy.
If someone is old or not creative then paul is either not strong or humble.
Everyone who is humble or not funny is either rich or not generous and vice versa.
Everyone who is both quiet and kind is not kind or generous and vice versa.
If lucy is not old or not humble then someone is not creative or not rich and vice versa.
Everyone who is both not creative and patient is brave and vice versa.
If lucy is either generous or strong then someone is not old.
If someone is curious then someone is either not generous or tall and vice versa.
If susan is not brave or not strong then john is creative or not wise.
If fred is both not quiet and not happy then fred is both quiet and not calm.
If susan is both not creative and not curious then someone is not calm or not happy and vice versa.
Lucy is not strong or not generous.
Someone is not funny.
Paul is not kind or curious.
Someone is strong.
Paul is not patient.
Someone is quiet.
Alice is not old.
Susan is funny. | Fred is not brave. | entailment | (![X]:((~wise(X)&happy(X))=>(~creative(X)|~curious(X))))&
((?[X]:((generous(X)&~quiet(X))))<=>(?[X]:(~tall(X))))&
(![X]:(kind(X)<=>creative(X)))&
(![X]:((generous(X)|~strong(X))=>(wise(X)&~patient(X))))&
(![X]:(brave(X)=>rich(X)))&
(![X]:(tall(X)=>happy(X)))&
((?[X]:((old(X)|~creative(X))))=>((~strong(paul)<~>humble(paul))))&
(![X]:((humble(X)|~funny(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((quiet(X)&kind(X))<=>(~kind(X)|generous(X))))&
(((~old(lucy)|~humble(lucy)))<=>(?[X]:((~creative(X)|~rich(X)))))&
(![X]:((~creative(X)&patient(X))<=>brave(X)))&
(((generous(lucy)<~>strong(lucy)))=>(?[X]:(~old(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~generous(X)<~>tall(X)))))&
(((~brave(susan)|~strong(susan)))=>((creative(john)|~wise(john))))&
(((~quiet(fred)&~happy(fred)))=>((quiet(fred)&~calm(fred))))&
(((~creative(susan)&~curious(susan)))<=>(?[X]:((~calm(X)|~happy(X)))))&
((~strong(lucy)|~generous(lucy)))&
(?[X]:(~funny(X)))&
((~kind(paul)|curious(paul)))&
(?[X]:(strong(X)))&
(~patient(paul))&
(?[X]:(quiet(X)))&
(~old(alice))&
(funny(susan)) | ~brave(fred) | [
"p2",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5940391121323679330907578
% SZS output start Proof for 5940391121323679330907578
3. ! [X0] : (kind(X0) <=> creative(X0)) [input p2]
9. ! [X0] : ((kind(X0) & quiet(X0)) <=> (generous(X0) | ~kind(X0))) [input p8]
11. ! [X0] : ((patient(X0) & ~creative(X0)) <=> brave(X0)) [input p10]
25. brave(fred) [input hypothesis]
44. ! [X0] : ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0))) [nnf transformation 3]
48. ! [X0] : (((kind(X0) & quiet(X0)) | (~generous(X0) & kind(X0))) & ((generous(X0) | ~kind(X0)) | (~kind(X0) | ~quiet(X0)))) [nnf transformation 9]
49. ! [X0] : (((kind(X0) & quiet(X0)) | (~generous(X0) & kind(X0))) & (generous(X0) | ~kind(X0) | ~kind(X0) | ~quiet(X0))) [flattening 48]
55. ! [X0] : (((patient(X0) & ~creative(X0)) | ~brave(X0)) & (brave(X0) | (~patient(X0) | creative(X0)))) [nnf transformation 11]
56. ! [X0] : (((patient(X0) & ~creative(X0)) | ~brave(X0)) & (brave(X0) | ~patient(X0) | creative(X0))) [flattening 55]
80. ~kind(X0) | creative(X0) [cnf transformation 44]
101. kind(X0) | kind(X0) [cnf transformation 49]
108. ~brave(X0) | ~creative(X0) [cnf transformation 56]
133. brave(fred) [cnf transformation 25]
136. kind(X0) [duplicate literal removal 101]
159. 6 <=> ! [X0] : creative(X0) [avatar definition]
160. creative(X0) <- (6) [avatar component clause 159]
301. creative(X0) [resolution 80,136]
302. 6 [avatar split clause 301,159]
313. ~creative(fred) [resolution 108,133]
314. $false <- (6) [subsumption resolution 313,160]
315. ~6 [avatar contradiction clause 314]
316. $false [avatar sat refutation 302,315]
% SZS output end Proof for 5940391121323679330907578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is either old or not rich and vice versa.
If mary is generous or strong then alice is both calm and kind and vice versa.
If paul is generous then someone is both not funny and quiet and vice versa.
If someone is not wise or not old then susan is generous and vice versa.
If mary is rich then someone is humble and vice versa.
If someone is not calm then paul is curious.
Everyone who is wise is not old and vice versa.
If someone is brave then mary is either calm or happy.
Everyone who is both not curious and old is funny.
If mary is either strong or quiet then someone is kind or old and vice versa.
If susan is either quiet or not kind then someone is both not wise and not patient.
If someone is not strong then alice is both kind and not rich and vice versa.
If paul is calm then someone is both not curious and kind and vice versa.
Everyone who is calm or strong is both not tall and not humble and vice versa.
If paul is rich then lucy is either not old or not rich.
Someone is old or wise.
Mary is strong or patient.
Lucy is not funny.
Someone is both not rich and brave.
Lucy is not humble or patient.
Someone is either not wise or strong.
Someone is not creative or funny. | Paul is not rich. | neutral | ((?[X]:(~creative(X)))<=>(?[X]:((old(X)<~>~rich(X)))))&
(((generous(mary)|strong(mary)))<=>((calm(alice)&kind(alice))))&
((generous(paul))<=>(?[X]:((~funny(X)&quiet(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>(generous(susan)))&
((rich(mary))<=>(?[X]:(humble(X))))&
((?[X]:(~calm(X)))=>(curious(paul)))&
(![X]:(wise(X)<=>~old(X)))&
((?[X]:(brave(X)))=>((calm(mary)<~>happy(mary))))&
(![X]:((~curious(X)&old(X))=>funny(X)))&
(((strong(mary)<~>quiet(mary)))<=>(?[X]:((kind(X)|old(X)))))&
(((quiet(susan)<~>~kind(susan)))=>(?[X]:((~wise(X)&~patient(X)))))&
((?[X]:(~strong(X)))<=>((kind(alice)&~rich(alice))))&
((calm(paul))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((calm(X)|strong(X))<=>(~tall(X)&~humble(X))))&
((rich(paul))=>((~old(lucy)<~>~rich(lucy))))&
(?[X]:((old(X)|wise(X))))&
((strong(mary)|patient(mary)))&
(~funny(lucy))&
(?[X]:((~rich(X)&brave(X))))&
((~humble(lucy)|patient(lucy)))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~creative(X)|funny(X)))) | ~rich(paul) | [] | null | 0 |
Everyone who is quiet is not rich or not old and vice versa. Everyone who is funny or strong is generous. Everyone who is not calm is creative or not old. If someone is not happy then someone is either not brave or not humble and vice versa. If john is either not curious or not patient then susan is not calm. Everyone who is funny or not kind is either not generous or not wise. If susan is not humble or kind then mary is either tall or not generous. Everyone who is wise or rich is tall and vice versa. If fred is either generous or curious then susan is not strong. Everyone who is not funny or humble is both not curious and humble. If lucy is not quiet or creative then someone is either not funny or not brave. If susan is either creative or funny then john is both not tall and calm. Everyone who is creative is brave or not brave. Everyone who is quiet or funny is either generous or calm. Everyone who is both not humble and rich is not quiet and vice versa. If someone is brave then alice is wise or humble. Someone is not wise or not funny. John is not quiet or rich. Someone is not tall. Alice is not strong or tall. John is either not humble or quiet. Someone is both old and not kind. Lucy is not quiet. | Alice is not curious. | neutral | (![X]:(quiet(X)<=>(~rich(X)|~old(X))))&
(![X]:((funny(X)|strong(X))=>generous(X)))&
(![X]:(~calm(X)=>(creative(X)|~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(((~curious(john)<~>~patient(john)))=>(~calm(susan)))&
(![X]:((funny(X)|~kind(X))=>(~generous(X)<~>~wise(X))))&
(((~humble(susan)|kind(susan)))=>((tall(mary)<~>~generous(mary))))&
(![X]:((wise(X)|rich(X))<=>tall(X)))&
(((generous(fred)<~>curious(fred)))=>(~strong(susan)))&
(![X]:((~funny(X)|humble(X))=>(~curious(X)&humble(X))))&
(((~quiet(lucy)|creative(lucy)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(((creative(susan)<~>funny(susan)))=>((~tall(john)&calm(john))))&
(![X]:(creative(X)=>(brave(X)|~brave(X))))&
(![X]:((quiet(X)|funny(X))=>(generous(X)<~>calm(X))))&
(![X]:((~humble(X)&rich(X))<=>~quiet(X)))&
((?[X]:(brave(X)))=>((wise(alice)|humble(alice))))&
(?[X]:((~wise(X)|~funny(X))))&
((~quiet(john)|rich(john)))&
(?[X]:(~tall(X)))&
((~strong(alice)|tall(alice)))&
((~humble(john)<~>quiet(john)))&
(?[X]:((old(X)&~kind(X))))&
(~quiet(lucy)) | ~curious(alice) | [] | null | 0 |
Everyone who is creative or not patient is both not generous and calm.
Everyone who is creative or not quiet is both happy and quiet and vice versa.
Everyone who is not generous is calm or not wise.
If susan is not wise then someone is not tall and vice versa.
If someone is either kind or humble then someone is not strong or humble and vice versa.
Everyone who is not creative is both generous and not creative and vice versa.
If someone is generous or not creative then someone is both not brave and quiet.
Everyone who is both generous and wise is either not generous or tall and vice versa.
Everyone who is both not funny and not creative is both generous and happy and vice versa.
If someone is not happy or not tall then someone is not humble or not calm.
Everyone who is both creative and not quiet is either not calm or not brave and vice versa.
If lucy is either patient or not strong then someone is not kind and vice versa.
Everyone who is both quiet and funny is both not patient and rich and vice versa.
Everyone who is kind or not curious is not brave or calm and vice versa.
If someone is quiet then paul is not generous.
Everyone who is both humble and wise is either not strong or curious.
Someone is either not old or not kind.
Someone is both quiet and patient.
Someone is curious.
John is either rich or wise.
Someone is not quiet or quiet.
Lucy is either brave or curious. | Susan is not tall. | contradiction | (![X]:((creative(X)|~patient(X))=>(~generous(X)&calm(X))))&
(![X]:((creative(X)|~quiet(X))<=>(happy(X)&quiet(X))))&
(![X]:(~generous(X)=>(calm(X)|~wise(X))))&
((~wise(susan))<=>(?[X]:(~tall(X))))&
((?[X]:((kind(X)<~>humble(X))))<=>(?[X]:((~strong(X)|humble(X)))))&
(![X]:(~creative(X)<=>(generous(X)&~creative(X))))&
((?[X]:((generous(X)|~creative(X))))=>(?[X]:((~brave(X)&quiet(X)))))&
(![X]:((generous(X)&wise(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((~funny(X)&~creative(X))<=>(generous(X)&happy(X))))&
((?[X]:((~happy(X)|~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((creative(X)&~quiet(X))<=>(~calm(X)<~>~brave(X))))&
(((patient(lucy)<~>~strong(lucy)))<=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)&funny(X))<=>(~patient(X)&rich(X))))&
(![X]:((kind(X)|~curious(X))<=>(~brave(X)|calm(X))))&
((?[X]:(quiet(X)))=>(~generous(paul)))&
(![X]:((humble(X)&wise(X))=>(~strong(X)<~>curious(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
(?[X]:((quiet(X)&patient(X))))&
(?[X]:(curious(X)))&
((rich(john)<~>wise(john)))&
(?[X]:((~quiet(X)|quiet(X))))&
((brave(lucy)<~>curious(lucy))) | ~tall(susan) | [
"p0",
"p1",
"p5",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1284561031399498828401440
% SZS output start Proof for 1284561031399498828401440
1. ! [X0] : ((~patient(X0) | creative(X0)) => (calm(X0) & ~generous(X0))) [input p0]
2. ! [X0] : ((~quiet(X0) | creative(X0)) <=> (quiet(X0) & happy(X0))) [input p1]
6. ! [X0] : (~creative(X0) <=> (~creative(X0) & generous(X0))) [input p5]
8. ! [X0] : ((wise(X0) & generous(X0)) <=> (~generous(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & ~funny(X0)) <=> (happy(X0) & generous(X0))) [input p8]
13. ! [X0] : ((funny(X0) & quiet(X0)) <=> (rich(X0) & ~patient(X0))) [input p12]
23. ~tall(susan) [input hypothesis]
27. ! [X0] : ((calm(X0) & ~generous(X0)) | (patient(X0) & ~creative(X0))) [ennf transformation 1]
35. ! [X0] : (((~quiet(X0) | creative(X0)) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | (quiet(X0) & ~creative(X0)))) [nnf transformation 2]
36. ! [X0] : ((~quiet(X0) | creative(X0) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | (quiet(X0) & ~creative(X0)))) [flattening 35]
46. ! [X0] : ((~creative(X0) | (creative(X0) | ~generous(X0))) & ((~creative(X0) & generous(X0)) | creative(X0))) [nnf transformation 6]
47. ! [X0] : ((~creative(X0) | creative(X0) | ~generous(X0)) & ((~creative(X0) & generous(X0)) | creative(X0))) [flattening 46]
51. ! [X0] : (((wise(X0) & generous(X0)) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | (~wise(X0) | ~generous(X0)))) [nnf transformation 8]
52. ! [X0] : (((wise(X0) & generous(X0)) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | ~wise(X0) | ~generous(X0))) [flattening 51]
53. ! [X0] : (((~creative(X0) & ~funny(X0)) | (~happy(X0) | ~generous(X0))) & ((happy(X0) & generous(X0)) | (creative(X0) | funny(X0)))) [nnf transformation 9]
54. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0) | ~generous(X0)) & ((happy(X0) & generous(X0)) | creative(X0) | funny(X0))) [flattening 53]
64. ! [X0] : (((funny(X0) & quiet(X0)) | (~rich(X0) | patient(X0))) & ((rich(X0) & ~patient(X0)) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 13]
65. ! [X0] : (((funny(X0) & quiet(X0)) | ~rich(X0) | patient(X0)) & ((rich(X0) & ~patient(X0)) | ~funny(X0) | ~quiet(X0))) [flattening 64]
80. ~generous(X0) | ~creative(X0) [cnf transformation 27]
81. ~generous(X0) | patient(X0) [cnf transformation 27]
84. ~creative(X0) | happy(X0) [cnf transformation 36]
87. quiet(X0) | quiet(X0) [cnf transformation 36]
88. ~quiet(X0) | creative(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 36]
98. generous(X0) | creative(X0) [cnf transformation 47]
107. generous(X0) | tall(X0) | generous(X0) [cnf transformation 52]
112. happy(X0) | creative(X0) | funny(X0) [cnf transformation 54]
127. ~patient(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 65]
148. ~tall(susan) [cnf transformation 23]
150. tall(X0) | generous(X0) [duplicate literal removal 107]
151. quiet(X0) [duplicate literal removal 87]
152. ~happy(X0) | creative(X0) | ~quiet(X0) [duplicate literal removal 88]
201. 12 <=> ! [X1] : creative(X1) [avatar definition]
202. creative(X1) <- (12) [avatar component clause 201]
213. funny(X0) | happy(X0) [subsumption resolution 112,84]
224. 17 <=> ! [X1] : happy(X1) [avatar definition]
225. happy(X1) <- (17) [avatar component clause 224]
249. ~funny(X0) | ~patient(X0) [subsumption resolution 127,151]
283. patient(X0) | creative(X0) [resolution 98,81]
287. generous(susan) [resolution 150,148]
290. ~creative(susan) [resolution 287,80]
298. ~patient(X0) | happy(X0) [resolution 249,213]
365. happy(X0) | creative(X0) [resolution 298,283]
372. happy(X0) [subsumption resolution 365,84]
373. 17 [avatar split clause 372,224]
374. creative(X0) | ~quiet(X0) <- (17) [resolution 225,152]
375. creative(X0) <- (17) [subsumption resolution 374,151]
376. 12 | ~17 [avatar split clause 375,224,201]
379. $false <- (12) [resolution 202,290]
382. ~12 [avatar contradiction clause 379]
383. $false [avatar sat refutation 373,376,382]
% SZS output end Proof for 1284561031399498828401440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is either wise or not calm. If john is strong then john is both not funny and happy. Everyone who is generous or not kind is either not wise or not patient. Everyone who is wise or humble is generous and vice versa. If someone is generous then john is both not brave and wise. Everyone who is either strong or brave is kind. Everyone who is both not calm and not patient is brave. Everyone who is not old or not rich is either not funny or curious and vice versa. Everyone who is both not kind and not brave is either not wise or generous and vice versa. If lucy is both not generous and not tall then lucy is either calm or not generous and vice versa. Everyone who is both kind and not patient is either not brave or patient and vice versa. If john is either brave or not old then someone is both not quiet and not brave and vice versa. Everyone who is calm is both not happy and not funny. Everyone who is tall or curious is not humble or curious and vice versa. Everyone who is wise or kind is both not brave and not calm. If alice is both quiet and wise then mary is either not rich or not calm. Someone is both rich and not calm. Mary is rich. Alice is either not tall or happy. Susan is both patient and not curious. Someone is not humble. | Lucy is not humble. | entailment | (![X]:(~tall(X)=>(wise(X)<~>~calm(X))))&
((strong(john))=>((~funny(john)&happy(john))))&
(![X]:((generous(X)|~kind(X))=>(~wise(X)<~>~patient(X))))&
(![X]:((wise(X)|humble(X))<=>generous(X)))&
((?[X]:(generous(X)))=>((~brave(john)&wise(john))))&
(![X]:((strong(X)<~>brave(X))=>kind(X)))&
(![X]:((~calm(X)&~patient(X))=>brave(X)))&
(![X]:((~old(X)|~rich(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((~kind(X)&~brave(X))<=>(~wise(X)<~>generous(X))))&
(((~generous(lucy)&~tall(lucy)))<=>((calm(lucy)<~>~generous(lucy))))&
(![X]:((kind(X)&~patient(X))<=>(~brave(X)<~>patient(X))))&
(((brave(john)<~>~old(john)))<=>(?[X]:((~quiet(X)&~brave(X)))))&
(![X]:(calm(X)=>(~happy(X)&~funny(X))))&
(![X]:((tall(X)|curious(X))<=>(~humble(X)|curious(X))))&
(![X]:((wise(X)|kind(X))=>(~brave(X)&~calm(X))))&
(((quiet(alice)&wise(alice)))=>((~rich(mary)<~>~calm(mary))))&
(?[X]:((rich(X)&~calm(X))))&
(rich(mary))&
((~tall(alice)<~>happy(alice)))&
((patient(susan)&~curious(susan)))&
(?[X]:(~humble(X))) | ~humble(lucy) | [
"p2",
"p3",
"p4",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2200301895148392882867866
% SZS output start Proof for 2200301895148392882867866
3. ! [X0] : ((~kind(X0) | generous(X0)) => (~wise(X0) <~> ~patient(X0))) [input p2]
4. ! [X0] : ((humble(X0) | wise(X0)) <=> generous(X0)) [input p3]
5. ? [X0] : generous(X0) => (wise(john) & ~brave(john)) [input p4]
7. ! [X0] : ((~patient(X0) & ~calm(X0)) => brave(X0)) [input p6]
15. ! [X0] : ((kind(X0) | wise(X0)) => (~calm(X0) & ~brave(X0))) [input p14]
22. humble(lucy) [input hypothesis]
25. ! [X0] : ((~wise(X0) <~> ~patient(X0)) | (kind(X0) & ~generous(X0))) [ennf transformation 3]
26. (wise(john) & ~brave(john)) | ! [X0] : ~generous(X0) [ennf transformation 5]
28. ! [X0] : (brave(X0) | (patient(X0) | calm(X0))) [ennf transformation 7]
29. ! [X0] : (brave(X0) | patient(X0) | calm(X0)) [flattening 28]
31. ! [X0] : ((~calm(X0) & ~brave(X0)) | (~kind(X0) & ~wise(X0))) [ennf transformation 15]
35. ! [X0] : (((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | (kind(X0) & ~generous(X0))) [nnf transformation 25]
36. ! [X0] : (((humble(X0) | wise(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) & ~wise(X0)))) [nnf transformation 4]
37. ! [X0] : ((humble(X0) | wise(X0) | ~generous(X0)) & (generous(X0) | (~humble(X0) & ~wise(X0)))) [flattening 36]
63. ~patient(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 35]
67. ~wise(X0) | generous(X0) [cnf transformation 37]
68. ~humble(X0) | generous(X0) [cnf transformation 37]
70. ~brave(john) | ~generous(X0) [cnf transformation 26]
71. wise(john) | ~generous(X0) [cnf transformation 26]
74. brave(X0) | patient(X0) | calm(X0) [cnf transformation 29]
113. ~calm(X0) | ~wise(X0) [cnf transformation 31]
125. humble(lucy) [cnf transformation 22]
145. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
146. ~generous(X0) <- (4) [avatar component clause 145]
148. 5 <=> wise(john) [avatar definition]
150. wise(john) <- (5) [avatar component clause 148]
151. 4 | 5 [avatar split clause 71,148,145]
153. 6 <=> brave(john) [avatar definition]
155. ~brave(john) <- (~6) [avatar component clause 153]
156. 4 | ~6 [avatar split clause 70,153,145]
228. generous(lucy) [resolution 68,125]
229. $false <- (4) [subsumption resolution 228,146]
230. ~4 [avatar contradiction clause 229]
232. generous(john) <- (5) [resolution 150,67]
239. 21 <=> calm(john) [avatar definition]
241. calm(john) <- (21) [avatar component clause 239]
268. patient(john) | calm(john) <- (~6) [resolution 74,155]
276. 24 <=> patient(john) [avatar definition]
278. patient(john) <- (24) [avatar component clause 276]
279. 21 | 24 | 6 [avatar split clause 268,153,276,239]
309. ~wise(john) <- (21) [resolution 241,113]
310. $false <- (5, 21) [subsumption resolution 309,150]
311. ~5 | ~21 [avatar contradiction clause 310]
316. ~wise(john) | ~generous(john) <- (24) [resolution 278,63]
318. ~generous(john) <- (5, 24) [subsumption resolution 316,150]
319. $false <- (5, 24) [subsumption resolution 318,232]
320. ~5 | ~24 [avatar contradiction clause 319]
321. $false [avatar sat refutation 151,156,230,279,311,320]
% SZS output end Proof for 2200301895148392882867866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not calm or old. If someone is both patient and kind then susan is both not quiet and not curious. If paul is both not creative and old then someone is not old or old and vice versa. Everyone who is generous is either not humble or not happy. If susan is either not tall or strong then someone is either quiet or not curious. If someone is either not creative or old then someone is both not wise and quiet and vice versa. If someone is both rich and happy then someone is strong and vice versa. Everyone who is either not rich or not creative is funny. If someone is not humble then susan is not patient and vice versa. Everyone who is not curious is funny and vice versa. Everyone who is not generous or wise is not wise or not patient and vice versa. If someone is not creative then someone is both quiet and patient. Everyone who is both happy and calm is either humble or calm. Everyone who is not humble or not generous is rich. If someone is either not funny or quiet then someone is creative or not wise. Everyone who is creative is not tall or not rich. Paul is brave. Someone is both not happy and not kind. Fred is either not creative or not strong. John is both not kind and rich. Someone is both rich and not strong. Alice is either creative or not kind. John is curious. Fred is either strong or not old. | Paul is brave. | entailment | (![X]:(tall(X)=>(~calm(X)|old(X))))&
((?[X]:((patient(X)&kind(X))))=>((~quiet(susan)&~curious(susan))))&
(((~creative(paul)&old(paul)))<=>(?[X]:((~old(X)|old(X)))))&
(![X]:(generous(X)=>(~humble(X)<~>~happy(X))))&
(((~tall(susan)<~>strong(susan)))=>(?[X]:((quiet(X)<~>~curious(X)))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((~wise(X)&quiet(X)))))&
((?[X]:((rich(X)&happy(X))))<=>(?[X]:(strong(X))))&
(![X]:((~rich(X)<~>~creative(X))=>funny(X)))&
((?[X]:(~humble(X)))<=>(~patient(susan)))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((~generous(X)|wise(X))<=>(~wise(X)|~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:((happy(X)&calm(X))=>(humble(X)<~>calm(X))))&
(![X]:((~humble(X)|~generous(X))=>rich(X)))&
((?[X]:((~funny(X)<~>quiet(X))))=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:(creative(X)=>(~tall(X)|~rich(X))))&
(brave(paul))&
(?[X]:((~happy(X)&~kind(X))))&
((~creative(fred)<~>~strong(fred)))&
((~kind(john)&rich(john)))&
(?[X]:((rich(X)&~strong(X))))&
((creative(alice)<~>~kind(alice)))&
(curious(john))&
((strong(fred)<~>~old(fred))) | brave(paul) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4929045047929584057388483
% SZS output start Proof for 4929045047929584057388483
17. brave(paul) [input p16]
25. ~brave(paul) [input hypothesis]
127. brave(paul) [cnf transformation 17]
141. ~brave(paul) [cnf transformation 25]
316. $false [subsumption resolution 141,127]
% SZS output end Proof for 4929045047929584057388483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not calm is creative or curious and vice versa.
Everyone who is both not wise and not generous is both not funny and creative and vice versa.
Everyone who is either humble or not funny is both not strong and curious.
Everyone who is either not generous or happy is either curious or not tall.
If fred is not old then lucy is not rich.
If fred is funny or tall then fred is either not tall or funny and vice versa.
Everyone who is not tall or not rich is either not patient or not curious and vice versa.
Everyone who is both patient and quiet is both brave and old.
If someone is not humble then john is either not brave or not patient and vice versa.
Everyone who is not humble or brave is both not wise and not strong and vice versa.
If fred is both strong and not patient then someone is not old or not happy.
Everyone who is wise is not patient or generous and vice versa.
If someone is both not creative and old then paul is either not generous or not kind.
If lucy is both calm and brave then someone is creative.
If someone is either not brave or not kind then someone is both not kind and curious and vice versa.
Everyone who is brave is happy or creative and vice versa.
Susan is both wise and tall.
Someone is either not calm or patient.
Someone is rich or not brave.
John is not kind or not rich.
Susan is both not creative and calm. | Fred is not strong. | entailment | (![X]:((~humble(X)<~>~calm(X))<=>(creative(X)|curious(X))))&
(![X]:((~wise(X)&~generous(X))<=>(~funny(X)&creative(X))))&
(![X]:((humble(X)<~>~funny(X))=>(~strong(X)&curious(X))))&
(![X]:((~generous(X)<~>happy(X))=>(curious(X)<~>~tall(X))))&
((~old(fred))=>(~rich(lucy)))&
(((funny(fred)|tall(fred)))<=>((~tall(fred)<~>funny(fred))))&
(![X]:((~tall(X)|~rich(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((patient(X)&quiet(X))=>(brave(X)&old(X))))&
((?[X]:(~humble(X)))<=>((~brave(john)<~>~patient(john))))&
(![X]:((~humble(X)|brave(X))<=>(~wise(X)&~strong(X))))&
(((strong(fred)&~patient(fred)))=>(?[X]:((~old(X)|~happy(X)))))&
(![X]:(wise(X)<=>(~patient(X)|generous(X))))&
((?[X]:((~creative(X)&old(X))))=>((~generous(paul)<~>~kind(paul))))&
(((calm(lucy)&brave(lucy)))=>(?[X]:(creative(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:(brave(X)<=>(happy(X)|creative(X))))&
((wise(susan)&tall(susan)))&
(?[X]:((~calm(X)<~>patient(X))))&
(?[X]:((rich(X)|~brave(X))))&
((~kind(john)|~rich(john)))&
((~creative(susan)&calm(susan))) | ~strong(fred) | [
"p2",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 430809431311920221485074
% SZS output start Proof for 430809431311920221485074
3. ! [X0] : ((humble(X0) <~> ~funny(X0)) => (curious(X0) & ~strong(X0))) [input p2]
6. (tall(fred) | funny(fred)) <=> (~tall(fred) <~> funny(fred)) [input p5]
10. ! [X0] : ((brave(X0) | ~humble(X0)) <=> (~strong(X0) & ~wise(X0))) [input p9]
22. strong(fred) [input hypothesis]
25. ! [X0] : ((curious(X0) & ~strong(X0)) | (humble(X0) <=> ~funny(X0))) [ennf transformation 3]
37. ! [X0] : ((curious(X0) & ~strong(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) [nnf transformation 25]
39. ((tall(fred) | funny(fred)) | ((~tall(fred) | ~funny(fred)) & (funny(fred) | tall(fred)))) & (((~funny(fred) | tall(fred)) & (funny(fred) | ~tall(fred))) | (~tall(fred) & ~funny(fred))) [nnf transformation 6]
40. (tall(fred) | funny(fred) | ((~tall(fred) | ~funny(fred)) & (funny(fred) | tall(fred)))) & (((~funny(fred) | tall(fred)) & (funny(fred) | ~tall(fred))) | (~tall(fred) & ~funny(fred))) [flattening 39]
47. ! [X0] : (((brave(X0) | ~humble(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [nnf transformation 10]
48. ! [X0] : ((brave(X0) | ~humble(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [flattening 47]
78. ~strong(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 37]
88. funny(fred) | ~tall(fred) | ~tall(fred) [cnf transformation 40]
91. tall(fred) | funny(fred) | funny(fred) | tall(fred) [cnf transformation 40]
105. ~strong(X0) | humble(X0) [cnf transformation 48]
132. strong(fred) [cnf transformation 22]
133. funny(fred) | ~tall(fred) [duplicate literal removal 88]
135. tall(fred) | funny(fred) [duplicate literal removal 91]
146. 3 <=> funny(fred) [avatar definition]
148. funny(fred) <- (3) [avatar component clause 146]
150. 4 <=> tall(fred) [avatar definition]
153. 3 | 4 [avatar split clause 135,150,146]
155. ~4 | 3 [avatar split clause 133,146,150]
176. 9 <=> strong(fred) [avatar definition]
177. strong(fred) <- (9) [avatar component clause 176]
277. 9 [avatar split clause 132,176]
279. humble(fred) <- (9) [resolution 105,177]
328. ~funny(fred) | ~humble(fred) <- (9) [resolution 78,177]
329. ~humble(fred) <- (3, 9) [subsumption resolution 328,148]
330. $false <- (3, 9) [subsumption resolution 329,279]
331. ~3 | ~9 [avatar contradiction clause 330]
332. $false [avatar sat refutation 153,155,277,331]
% SZS output end Proof for 430809431311920221485074
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not strong is not tall.
Everyone who is strong or not wise is both humble and not calm and vice versa.
Everyone who is either not curious or old is generous or not funny.
Everyone who is both wise and not calm is not patient or not brave and vice versa.
If someone is not wise or not creative then someone is both not creative and humble and vice versa.
If someone is not creative or quiet then someone is strong and vice versa.
Everyone who is both generous and wise is either humble or not humble and vice versa.
If someone is not wise then someone is either quiet or not curious and vice versa.
If someone is both not brave and not patient then someone is both rich and not wise and vice versa.
If john is not brave then paul is not kind and vice versa.
Everyone who is not funny or not happy is both not humble and not old.
Everyone who is either old or not generous is either not generous or not old.
If fred is either kind or not patient then susan is either not curious or tall.
If someone is not old then someone is either not happy or not kind.
Everyone who is either happy or not generous is not tall or old and vice versa.
Everyone who is both funny and generous is either happy or not patient and vice versa.
John is not brave or calm.
Susan is not creative.
Someone is not kind or not curious.
Someone is either not humble or not strong.
Fred is calm or humble.
Someone is rich.
Someone is either not creative or not funny.
Paul is strong. | Fred is patient. | entailment | (![X]:((funny(X)|~strong(X))=>~tall(X)))&
(![X]:((strong(X)|~wise(X))<=>(humble(X)&~calm(X))))&
(![X]:((~curious(X)<~>old(X))=>(generous(X)|~funny(X))))&
(![X]:((wise(X)&~calm(X))<=>(~patient(X)|~brave(X))))&
((?[X]:((~wise(X)|~creative(X))))<=>(?[X]:((~creative(X)&humble(X)))))&
((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:(strong(X))))&
(![X]:((generous(X)&wise(X))<=>(humble(X)<~>~humble(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((quiet(X)<~>~curious(X)))))&
((?[X]:((~brave(X)&~patient(X))))<=>(?[X]:((rich(X)&~wise(X)))))&
((~brave(john))<=>(~kind(paul)))&
(![X]:((~funny(X)|~happy(X))=>(~humble(X)&~old(X))))&
(![X]:((old(X)<~>~generous(X))=>(~generous(X)<~>~old(X))))&
(((kind(fred)<~>~patient(fred)))=>((~curious(susan)<~>tall(susan))))&
((?[X]:(~old(X)))=>(?[X]:((~happy(X)<~>~kind(X)))))&
(![X]:((happy(X)<~>~generous(X))<=>(~tall(X)|old(X))))&
(![X]:((funny(X)&generous(X))<=>(happy(X)<~>~patient(X))))&
((~brave(john)|calm(john)))&
(~creative(susan))&
(?[X]:((~kind(X)|~curious(X))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((calm(fred)|humble(fred)))&
(?[X]:(rich(X)))&
(?[X]:((~creative(X)<~>~funny(X))))&
(strong(paul)) | patient(fred) | [
"p0",
"p3",
"p6",
"p10",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 966856292054155500600906
% SZS output start Proof for 966856292054155500600906
1. ! [X0] : ((~strong(X0) | funny(X0)) => ~tall(X0)) [input p0]
4. ! [X0] : ((~calm(X0) & wise(X0)) <=> (~brave(X0) | ~patient(X0))) [input p3]
7. ! [X0] : ((wise(X0) & generous(X0)) <=> (humble(X0) <~> ~humble(X0))) [input p6]
11. ! [X0] : ((~happy(X0) | ~funny(X0)) => (~old(X0) & ~humble(X0))) [input p10]
15. ! [X0] : ((happy(X0) <~> ~generous(X0)) <=> (old(X0) | ~tall(X0))) [input p14]
16. ! [X0] : ((generous(X0) & funny(X0)) <=> (happy(X0) <~> ~patient(X0))) [input p15]
21. humble(fred) | calm(fred) [input p20]
25. ~patient(fred) [input hypothesis]
31. ! [X0] : (~tall(X0) | (strong(X0) & ~funny(X0))) [ennf transformation 1]
34. ! [X0] : ((~old(X0) & ~humble(X0)) | (happy(X0) & funny(X0))) [ennf transformation 11]
41. ! [X0] : (((~calm(X0) & wise(X0)) | (brave(X0) & patient(X0))) & ((~brave(X0) | ~patient(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 4]
42. ! [X0] : (((~calm(X0) & wise(X0)) | (brave(X0) & patient(X0))) & (~brave(X0) | ~patient(X0) | calm(X0) | ~wise(X0))) [flattening 41]
53. ! [X0] : (((wise(X0) & generous(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) & (((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | (~wise(X0) | ~generous(X0)))) [nnf transformation 7]
54. ! [X0] : (((wise(X0) & generous(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) & (((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | ~wise(X0) | ~generous(X0))) [flattening 53]
72. ! [X0] : ((((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | (~old(X0) & tall(X0))) & ((old(X0) | ~tall(X0)) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))))) [nnf transformation 15]
73. ! [X0] : ((((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | (~old(X0) & tall(X0))) & (old(X0) | ~tall(X0) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))))) [flattening 72]
74. ! [X0] : (((generous(X0) & funny(X0)) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0)))) & (((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (~generous(X0) | ~funny(X0)))) [nnf transformation 16]
75. ! [X0] : (((generous(X0) & funny(X0)) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0)))) & (((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | ~generous(X0) | ~funny(X0))) [flattening 74]
86. ~tall(X0) | ~funny(X0) [cnf transformation 31]
98. ~calm(X0) | patient(X0) [cnf transformation 42]
110. generous(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 54]
111. generous(X0) | humble(X0) | humble(X0) [cnf transformation 54]
124. ~humble(X0) | funny(X0) [cnf transformation 34]
140. ~generous(X0) | happy(X0) | tall(X0) [cnf transformation 73]
145. patient(X0) | ~happy(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 75]
155. humble(fred) | calm(fred) [cnf transformation 21]
160. ~patient(fred) [cnf transformation 25]
163. generous(X0) | ~humble(X0) [duplicate literal removal 110]
164. generous(X0) | humble(X0) [duplicate literal removal 111]
220. generous(X0) [subsumption resolution 163,164]
281. 26 <=> patient(fred) [avatar definition]
282. ~patient(fred) <- (~26) [avatar component clause 281]
312. happy(X0) | tall(X0) [subsumption resolution 140,220]
315. ~happy(X0) | patient(X0) | ~funny(X0) [subsumption resolution 145,220]
334. 35 <=> calm(fred) [avatar definition]
336. calm(fred) <- (35) [avatar component clause 334]
338. 36 <=> humble(fred) [avatar definition]
340. humble(fred) <- (36) [avatar component clause 338]
341. 35 | 36 [avatar split clause 155,338,334]
352. ~26 [avatar split clause 160,281]
372. patient(fred) <- (35) [resolution 98,336]
373. $false <- (~26, 35) [subsumption resolution 372,282]
374. 26 | ~35 [avatar contradiction clause 373]
377. funny(fred) <- (36) [resolution 124,340]
418. patient(X1) | ~funny(X1) | tall(X1) [resolution 315,312]
424. ~funny(X1) | patient(X1) [subsumption resolution 418,86]
510. patient(fred) <- (36) [resolution 424,377]
514. $false <- (~26, 36) [subsumption resolution 510,282]
515. 26 | ~36 [avatar contradiction clause 514]
516. $false [avatar sat refutation 341,352,374,515]
% SZS output end Proof for 966856292054155500600906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not quiet is either not brave or funny and vice versa.
Everyone who is either humble or not tall is both happy and not quiet and vice versa.
Everyone who is either generous or not rich is not strong and vice versa.
If lucy is humble then someone is both not patient and strong and vice versa.
If someone is either not patient or not generous then susan is humble and vice versa.
Everyone who is both generous and kind is humble and vice versa.
If someone is either not strong or not wise then alice is not tall or rich.
If alice is both tall and not old then someone is both humble and not creative and vice versa.
Everyone who is rich is both not happy and not creative.
Everyone who is both not generous and rich is both strong and not funny.
Everyone who is happy or not brave is not old.
If someone is both curious and generous then someone is calm.
Everyone who is either strong or not generous is not strong or not patient and vice versa.
Everyone who is both not strong and kind is either not calm or wise and vice versa.
If someone is both not humble and not old then paul is both not humble and quiet and vice versa.
Everyone who is brave or generous is generous or not quiet and vice versa.
Someone is both not tall and calm.
Lucy is both brave and creative.
Someone is both not wise and not old.
John is not old or tall.
Susan is not tall or not kind.
Alice is not old.
Mary is calm or not tall.
Someone is either strong or not kind. | Mary is not funny. | neutral | (![X]:((brave(X)<~>~quiet(X))<=>(~brave(X)<~>funny(X))))&
(![X]:((humble(X)<~>~tall(X))<=>(happy(X)&~quiet(X))))&
(![X]:((generous(X)<~>~rich(X))<=>~strong(X)))&
((humble(lucy))<=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>(humble(susan)))&
(![X]:((generous(X)&kind(X))<=>humble(X)))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~tall(alice)|rich(alice))))&
(((tall(alice)&~old(alice)))<=>(?[X]:((humble(X)&~creative(X)))))&
(![X]:(rich(X)=>(~happy(X)&~creative(X))))&
(![X]:((~generous(X)&rich(X))=>(strong(X)&~funny(X))))&
(![X]:((happy(X)|~brave(X))=>~old(X)))&
((?[X]:((curious(X)&generous(X))))=>(?[X]:(calm(X))))&
(![X]:((strong(X)<~>~generous(X))<=>(~strong(X)|~patient(X))))&
(![X]:((~strong(X)&kind(X))<=>(~calm(X)<~>wise(X))))&
((?[X]:((~humble(X)&~old(X))))<=>((~humble(paul)&quiet(paul))))&
(![X]:((brave(X)|generous(X))<=>(generous(X)|~quiet(X))))&
(?[X]:((~tall(X)&calm(X))))&
((brave(lucy)&creative(lucy)))&
(?[X]:((~wise(X)&~old(X))))&
((~old(john)|tall(john)))&
((~tall(susan)|~kind(susan)))&
(~old(alice))&
((calm(mary)|~tall(mary)))&
(?[X]:((strong(X)<~>~kind(X)))) | ~funny(mary) | [] | null | 0 |
Everyone who is not kind or not wise is either not creative or not old.
Everyone who is curious is both brave and happy and vice versa.
Everyone who is not kind or not rich is either kind or not humble.
If john is both not happy and strong then someone is happy or kind.
Everyone who is not brave is tall or not funny and vice versa.
Everyone who is generous is not kind or quiet and vice versa.
Everyone who is both not generous and creative is both patient and tall.
If someone is curious then fred is funny and vice versa.
Everyone who is not rich is both not humble and not curious and vice versa.
Everyone who is brave or generous is either strong or quiet and vice versa.
Everyone who is both tall and quiet is both not happy and rich.
Everyone who is both patient and not calm is happy or not happy and vice versa.
Everyone who is both rich and not strong is not wise.
Everyone who is not calm or patient is not happy or kind.
If paul is both not wise and not patient then someone is quiet.
Everyone who is both not wise and not curious is either creative or not happy.
Paul is happy or wise.
Someone is not wise.
Someone is both not curious and brave.
Someone is both kind and quiet.
Someone is both not generous and not funny.
Someone is rich.
Someone is not creative.
Susan is not funny or not brave. | Fred is not happy. | neutral | (![X]:((~kind(X)|~wise(X))=>(~creative(X)<~>~old(X))))&
(![X]:(curious(X)<=>(brave(X)&happy(X))))&
(![X]:((~kind(X)|~rich(X))=>(kind(X)<~>~humble(X))))&
(((~happy(john)&strong(john)))=>(?[X]:((happy(X)|kind(X)))))&
(![X]:(~brave(X)<=>(tall(X)|~funny(X))))&
(![X]:(generous(X)<=>(~kind(X)|quiet(X))))&
(![X]:((~generous(X)&creative(X))=>(patient(X)&tall(X))))&
((?[X]:(curious(X)))<=>(funny(fred)))&
(![X]:(~rich(X)<=>(~humble(X)&~curious(X))))&
(![X]:((brave(X)|generous(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((tall(X)&quiet(X))=>(~happy(X)&rich(X))))&
(![X]:((patient(X)&~calm(X))<=>(happy(X)|~happy(X))))&
(![X]:((rich(X)&~strong(X))=>~wise(X)))&
(![X]:((~calm(X)|patient(X))=>(~happy(X)|kind(X))))&
(((~wise(paul)&~patient(paul)))=>(?[X]:(quiet(X))))&
(![X]:((~wise(X)&~curious(X))=>(creative(X)<~>~happy(X))))&
((happy(paul)|wise(paul)))&
(?[X]:(~wise(X)))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((kind(X)&quiet(X))))&
(?[X]:((~generous(X)&~funny(X))))&
(?[X]:(rich(X)))&
(?[X]:(~creative(X)))&
((~funny(susan)|~brave(susan))) | ~happy(fred) | [] | null | 0 |
If someone is both happy and kind then someone is not curious and vice versa.
Everyone who is either not quiet or not curious is both not funny and not generous and vice versa.
If someone is both not creative and not generous then fred is both strong and not funny.
If someone is kind or calm then someone is both tall and kind.
Everyone who is creative or kind is not patient.
Everyone who is both patient and happy is humble or rich and vice versa.
Everyone who is both not wise and not happy is curious or not patient.
Everyone who is wise or not brave is both not rich and old and vice versa.
Everyone who is quiet is both tall and not curious and vice versa.
Everyone who is creative or not curious is not patient.
Everyone who is either brave or not strong is humble.
If someone is not rich then susan is quiet and vice versa.
Everyone who is both not old and wise is not calm.
If fred is either not patient or not old then fred is not funny and vice versa.
Everyone who is not funny is happy.
If someone is either strong or not wise then someone is quiet or not calm.
Someone is not calm or not strong.
Someone is either patient or wise.
Someone is creative or not old.
Fred is not tall.
Lucy is either not strong or wise.
Someone is either not tall or happy.
Susan is both not humble and tall.
John is both rich and not funny. | John is not generous. | entailment | ((?[X]:((happy(X)&kind(X))))<=>(?[X]:(~curious(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~funny(X)&~generous(X))))&
((?[X]:((~creative(X)&~generous(X))))=>((strong(fred)&~funny(fred))))&
((?[X]:((kind(X)|calm(X))))=>(?[X]:((tall(X)&kind(X)))))&
(![X]:((creative(X)|kind(X))=>~patient(X)))&
(![X]:((patient(X)&happy(X))<=>(humble(X)|rich(X))))&
(![X]:((~wise(X)&~happy(X))=>(curious(X)|~patient(X))))&
(![X]:((wise(X)|~brave(X))<=>(~rich(X)&old(X))))&
(![X]:(quiet(X)<=>(tall(X)&~curious(X))))&
(![X]:((creative(X)|~curious(X))=>~patient(X)))&
(![X]:((brave(X)<~>~strong(X))=>humble(X)))&
((?[X]:(~rich(X)))<=>(quiet(susan)))&
(![X]:((~old(X)&wise(X))=>~calm(X)))&
(((~patient(fred)<~>~old(fred)))<=>(~funny(fred)))&
(![X]:(~funny(X)=>happy(X)))&
((?[X]:((strong(X)<~>~wise(X))))=>(?[X]:((quiet(X)|~calm(X)))))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:((patient(X)<~>wise(X))))&
(?[X]:((creative(X)|~old(X))))&
(~tall(fred))&
((~strong(lucy)<~>wise(lucy)))&
(?[X]:((~tall(X)<~>happy(X))))&
((~humble(susan)&tall(susan)))&
((rich(john)&~funny(john))) | ~generous(john) | [
"p1",
"p5",
"p8",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8310999646659513591946310
% SZS output start Proof for 8310999646659513591946310
2. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) <=> (~generous(X0) & ~funny(X0))) [input p1]
6. ! [X0] : ((happy(X0) & patient(X0)) <=> (rich(X0) | humble(X0))) [input p5]
9. ! [X0] : (quiet(X0) <=> (~curious(X0) & tall(X0))) [input p8]
10. ! [X0] : ((~curious(X0) | creative(X0)) => ~patient(X0)) [input p9]
24. ~funny(john) & rich(john) [input p23]
25. generous(john) [input hypothesis]
38. ! [X0] : (~patient(X0) | (curious(X0) & ~creative(X0))) [ennf transformation 10]
46. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (generous(X0) | funny(X0))) & ((~generous(X0) & ~funny(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [nnf transformation 2]
47. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | generous(X0) | funny(X0)) & ((~generous(X0) & ~funny(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [flattening 46]
51. ! [X0] : (((happy(X0) & patient(X0)) | (~rich(X0) & ~humble(X0))) & ((rich(X0) | humble(X0)) | (~happy(X0) | ~patient(X0)))) [nnf transformation 6]
52. ! [X0] : (((happy(X0) & patient(X0)) | (~rich(X0) & ~humble(X0))) & (rich(X0) | humble(X0) | ~happy(X0) | ~patient(X0))) [flattening 51]
55. ! [X0] : ((quiet(X0) | (curious(X0) | ~tall(X0))) & ((~curious(X0) & tall(X0)) | ~quiet(X0))) [nnf transformation 9]
56. ! [X0] : ((quiet(X0) | curious(X0) | ~tall(X0)) & ((~curious(X0) & tall(X0)) | ~quiet(X0))) [flattening 55]
77. ~generous(X0) | ~curious(X0) | quiet(X0) [cnf transformation 47]
89. ~rich(X0) | patient(X0) [cnf transformation 52]
99. ~quiet(X0) | ~curious(X0) [cnf transformation 56]
102. ~patient(X0) | curious(X0) [cnf transformation 38]
122. rich(john) [cnf transformation 24]
124. generous(john) [cnf transformation 25]
240. patient(john) [resolution 89,122]
250. curious(john) [resolution 102,240]
262. ~curious(john) | quiet(john) [resolution 77,124]
264. quiet(john) [subsumption resolution 262,250]
266. ~curious(john) [resolution 264,99]
268. $false [subsumption resolution 266,250]
% SZS output end Proof for 8310999646659513591946310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not wise is brave or not happy and vice versa.
Everyone who is not quiet is either curious or generous.
If someone is not creative then paul is either not quiet or not tall and vice versa.
Everyone who is funny or not strong is both patient and brave.
If mary is not old then someone is kind or quiet and vice versa.
If paul is either creative or not rich then someone is old or not rich and vice versa.
If someone is not old then paul is funny and vice versa.
Everyone who is funny or tall is not funny or not quiet.
If someone is both not creative and not happy then someone is both not quiet and not wise.
Everyone who is both brave and not tall is both not old and creative.
Everyone who is happy or not kind is strong and vice versa.
Everyone who is both not strong and not rich is both quiet and not funny.
If someone is either not humble or not calm then paul is either creative or not rich and vice versa.
Everyone who is either not rich or not calm is both not curious and not happy.
If lucy is not patient or not rich then paul is both not strong and not old.
If someone is both tall and funny then someone is not calm and vice versa.
Fred is either creative or brave.
Paul is humble or strong.
Mary is patient or brave.
Someone is both creative and brave.
Lucy is not strong.
Lucy is both generous and not tall.
Someone is both not humble and quiet.
Someone is either tall or patient. | Mary is calm. | neutral | (![X]:((~curious(X)&~wise(X))<=>(brave(X)|~happy(X))))&
(![X]:(~quiet(X)=>(curious(X)<~>generous(X))))&
((?[X]:(~creative(X)))<=>((~quiet(paul)<~>~tall(paul))))&
(![X]:((funny(X)|~strong(X))=>(patient(X)&brave(X))))&
((~old(mary))<=>(?[X]:((kind(X)|quiet(X)))))&
(((creative(paul)<~>~rich(paul)))<=>(?[X]:((old(X)|~rich(X)))))&
((?[X]:(~old(X)))<=>(funny(paul)))&
(![X]:((funny(X)|tall(X))=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)&~happy(X))))=>(?[X]:((~quiet(X)&~wise(X)))))&
(![X]:((brave(X)&~tall(X))=>(~old(X)&creative(X))))&
(![X]:((happy(X)|~kind(X))<=>strong(X)))&
(![X]:((~strong(X)&~rich(X))=>(quiet(X)&~funny(X))))&
((?[X]:((~humble(X)<~>~calm(X))))<=>((creative(paul)<~>~rich(paul))))&
(![X]:((~rich(X)<~>~calm(X))=>(~curious(X)&~happy(X))))&
(((~patient(lucy)|~rich(lucy)))=>((~strong(paul)&~old(paul))))&
((?[X]:((tall(X)&funny(X))))<=>(?[X]:(~calm(X))))&
((creative(fred)<~>brave(fred)))&
((humble(paul)|strong(paul)))&
((patient(mary)|brave(mary)))&
(?[X]:((creative(X)&brave(X))))&
(~strong(lucy))&
((generous(lucy)&~tall(lucy)))&
(?[X]:((~humble(X)&quiet(X))))&
(?[X]:((tall(X)<~>patient(X)))) | calm(mary) | [] | null | 0 |
Everyone who is either creative or not rich is both not old and old. Everyone who is both not curious and not happy is generous or not wise. Everyone who is both not strong and not generous is calm and vice versa. Everyone who is not humble or patient is not wise or brave and vice versa. If someone is not quiet or not wise then mary is both not humble and humble. If someone is both not old and tall then someone is either brave or not tall and vice versa. If someone is either kind or not happy then someone is curious. If someone is curious or rich then alice is curious or not strong. Everyone who is patient or humble is not kind. Everyone who is not funny or wise is either not old or not generous. Everyone who is either strong or not calm is not humble and vice versa. If someone is either humble or kind then mary is both not quiet and not creative and vice versa. If john is either tall or kind then lucy is not wise or not generous and vice versa. Everyone who is either humble or calm is strong or not strong. Everyone who is creative or not rich is both generous and old. Someone is patient or not rich. Susan is not calm or not rich. Lucy is not funny or strong. Someone is not kind. | Susan is not generous. | contradiction | (![X]:((creative(X)<~>~rich(X))=>(~old(X)&old(X))))&
(![X]:((~curious(X)&~happy(X))=>(generous(X)|~wise(X))))&
(![X]:((~strong(X)&~generous(X))<=>calm(X)))&
(![X]:((~humble(X)|patient(X))<=>(~wise(X)|brave(X))))&
((?[X]:((~quiet(X)|~wise(X))))=>((~humble(mary)&humble(mary))))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:((brave(X)<~>~tall(X)))))&
((?[X]:((kind(X)<~>~happy(X))))=>(?[X]:(curious(X))))&
((?[X]:((curious(X)|rich(X))))=>((curious(alice)|~strong(alice))))&
(![X]:((patient(X)|humble(X))=>~kind(X)))&
(![X]:((~funny(X)|wise(X))=>(~old(X)<~>~generous(X))))&
(![X]:((strong(X)<~>~calm(X))<=>~humble(X)))&
((?[X]:((humble(X)<~>kind(X))))<=>((~quiet(mary)&~creative(mary))))&
(((tall(john)<~>kind(john)))<=>((~wise(lucy)|~generous(lucy))))&
(![X]:((humble(X)<~>calm(X))=>(strong(X)|~strong(X))))&
(![X]:((creative(X)|~rich(X))=>(generous(X)&old(X))))&
(?[X]:((patient(X)|~rich(X))))&
((~calm(susan)|~rich(susan)))&
((~funny(lucy)|strong(lucy)))&
(?[X]:(~kind(X))) | ~generous(susan) | [
"p2",
"p4",
"p8",
"p10",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 828883724516209132874996
% SZS output start Proof for 828883724516209132874996
3. ! [X0] : ((~generous(X0) & ~strong(X0)) <=> calm(X0)) [input p2]
5. ? [X0] : (~wise(X0) | ~quiet(X0)) => (humble(mary) & ~humble(mary)) [input p4]
9. ! [X0] : ((humble(X0) | patient(X0)) => ~kind(X0)) [input p8]
11. ! [X0] : ((strong(X0) <~> ~calm(X0)) <=> ~humble(X0)) [input p10]
12. ? [X0] : (humble(X0) <~> kind(X0)) <=> (~creative(mary) & ~quiet(mary)) [input p11]
15. ! [X0] : ((~rich(X0) | creative(X0)) => (old(X0) & generous(X0))) [input p14]
17. ~rich(susan) | ~calm(susan) [input p16]
20. ~generous(susan) [input hypothesis]
26. (humble(mary) & ~humble(mary)) | ! [X0] : (wise(X0) & quiet(X0)) [ennf transformation 5]
30. ! [X0] : (~kind(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 9]
34. ! [X0] : ((old(X0) & generous(X0)) | (rich(X0) & ~creative(X0))) [ennf transformation 15]
36. ! [X0] : (((~generous(X0) & ~strong(X0)) | ~calm(X0)) & (calm(X0) | (generous(X0) | strong(X0)))) [nnf transformation 3]
37. ! [X0] : (((~generous(X0) & ~strong(X0)) | ~calm(X0)) & (calm(X0) | generous(X0) | strong(X0))) [flattening 36]
50. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | humble(X0)) & (~humble(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [nnf transformation 11]
51. (? [X0] : ((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (creative(mary) | quiet(mary))) & ((~creative(mary) & ~quiet(mary)) | ! [X0] : ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) [nnf transformation 12]
52. (? [X0] : ((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | creative(mary) | quiet(mary)) & ((~creative(mary) & ~quiet(mary)) | ! [X0] : ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) [flattening 51]
53. (? [X0] : ((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | creative(mary) | quiet(mary)) & ((~creative(mary) & ~quiet(mary)) | ! [X1] : ((humble(X1) | ~kind(X1)) & (kind(X1) | ~humble(X1)))) [rectify 52]
54. ? [X0] : ((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) => ((~kind(sK3) | ~humble(sK3)) & (kind(sK3) | humble(sK3))) [choice axiom]
55. (((~kind(sK3) | ~humble(sK3)) & (kind(sK3) | humble(sK3))) | creative(mary) | quiet(mary)) & ((~creative(mary) & ~quiet(mary)) | ! [X1] : ((humble(X1) | ~kind(X1)) & (kind(X1) | ~humble(X1)))) [skolemisation 53,54]
68. calm(X0) | generous(X0) | strong(X0) [cnf transformation 37]
69. ~calm(X0) | ~strong(X0) [cnf transformation 37]
75. ~humble(mary) | quiet(X0) [cnf transformation 26]
77. humble(mary) | quiet(X0) [cnf transformation 26]
90. ~kind(X0) | ~humble(X0) [cnf transformation 30]
98. calm(X0) | ~strong(X0) | humble(X0) [cnf transformation 50]
99. ~quiet(mary) | kind(X1) | ~humble(X1) [cnf transformation 55]
114. generous(X0) | rich(X0) [cnf transformation 34]
118. ~rich(susan) | ~calm(susan) [cnf transformation 17]
121. ~generous(susan) [cnf transformation 20]
128. 2 <=> humble(mary) [avatar definition]
133. 3 <=> ! [X0] : quiet(X0) [avatar definition]
134. quiet(X0) <- (3) [avatar component clause 133]
135. 3 | 2 [avatar split clause 77,128,133]
137. 3 | ~2 [avatar split clause 75,128,133]
197. ~strong(X0) | humble(X0) [subsumption resolution 98,69]
200. 18 <=> quiet(mary) [avatar definition]
201. ~quiet(mary) <- (~18) [avatar component clause 200]
223. 23 <=> ! [X1] : ~humble(X1) [avatar definition]
224. ~humble(X1) <- (23) [avatar component clause 223]
228. ~quiet(mary) | ~humble(X1) [subsumption resolution 99,90]
229. 23 | ~18 [avatar split clause 228,200,223]
262. 30 <=> calm(susan) [avatar definition]
264. ~calm(susan) <- (~30) [avatar component clause 262]
266. 31 <=> rich(susan) [avatar definition]
269. ~30 | ~31 [avatar split clause 118,266,262]
279. $false <- (3, ~18) [resolution 201,134]
280. ~3 | 18 [avatar contradiction clause 279]
283. rich(susan) [resolution 114,121]
285. 31 [avatar split clause 283,266]
299. generous(susan) | strong(susan) <- (~30) [resolution 68,264]
303. strong(susan) <- (~30) [subsumption resolution 299,121]
305. humble(susan) <- (~30) [resolution 303,197]
306. $false <- (23, ~30) [subsumption resolution 305,224]
307. ~23 | 30 [avatar contradiction clause 306]
308. $false [avatar sat refutation 135,137,229,269,280,285,307]
% SZS output end Proof for 828883724516209132874996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or happy is either not humble or wise.
If someone is not funny then mary is not patient and vice versa.
Everyone who is both generous and wise is both tall and patient.
Everyone who is funny or not quiet is both not patient and not curious and vice versa.
If someone is both strong and humble then someone is both not wise and not calm.
If mary is generous then fred is both not calm and tall.
Everyone who is either curious or creative is both funny and generous and vice versa.
Everyone who is not tall or kind is patient and vice versa.
Everyone who is both old and tall is both creative and not strong.
Everyone who is not creative is funny.
Everyone who is kind is not curious.
If susan is old then someone is both brave and old.
Everyone who is brave or kind is either not kind or quiet.
Everyone who is both not quiet and not happy is creative or not brave.
Everyone who is either not tall or calm is both not happy and not rich and vice versa.
Everyone who is either not quiet or wise is both rich and calm and vice versa.
Alice is both generous and not curious.
Someone is not rich or not patient.
Fred is either funny or not humble.
Someone is both not wise and funny.
Lucy is not brave.
Someone is old or not humble.
Someone is either tall or not curious. | Susan is not kind. | entailment | (![X]:((kind(X)<~>happy(X))=>(~humble(X)<~>wise(X))))&
((?[X]:(~funny(X)))<=>(~patient(mary)))&
(![X]:((generous(X)&wise(X))=>(tall(X)&patient(X))))&
(![X]:((funny(X)|~quiet(X))<=>(~patient(X)&~curious(X))))&
((?[X]:((strong(X)&humble(X))))=>(?[X]:((~wise(X)&~calm(X)))))&
((generous(mary))=>((~calm(fred)&tall(fred))))&
(![X]:((curious(X)<~>creative(X))<=>(funny(X)&generous(X))))&
(![X]:((~tall(X)|kind(X))<=>patient(X)))&
(![X]:((old(X)&tall(X))=>(creative(X)&~strong(X))))&
(![X]:(~creative(X)=>funny(X)))&
(![X]:(kind(X)=>~curious(X)))&
((old(susan))=>(?[X]:((brave(X)&old(X)))))&
(![X]:((brave(X)|kind(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((~quiet(X)&~happy(X))=>(creative(X)|~brave(X))))&
(![X]:((~tall(X)<~>calm(X))<=>(~happy(X)&~rich(X))))&
(![X]:((~quiet(X)<~>wise(X))<=>(rich(X)&calm(X))))&
((generous(alice)&~curious(alice)))&
(?[X]:((~rich(X)|~patient(X))))&
((funny(fred)<~>~humble(fred)))&
(?[X]:((~wise(X)&funny(X))))&
(~brave(lucy))&
(?[X]:((old(X)|~humble(X))))&
(?[X]:((tall(X)<~>~curious(X)))) | ~kind(susan) | [
"p3",
"p6",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4856400810627793710537537
% SZS output start Proof for 4856400810627793710537537
4. ! [X0] : ((~quiet(X0) | funny(X0)) <=> (~curious(X0) & ~patient(X0))) [input p3]
7. ! [X0] : ((curious(X0) <~> creative(X0)) <=> (generous(X0) & funny(X0))) [input p6]
8. ! [X0] : ((kind(X0) | ~tall(X0)) <=> patient(X0)) [input p7]
10. ! [X0] : (~creative(X0) => funny(X0)) [input p9]
11. ! [X0] : (kind(X0) => ~curious(X0)) [input p10]
24. kind(susan) [input hypothesis]
34. ! [X0] : (funny(X0) | creative(X0)) [ennf transformation 10]
35. ! [X0] : (~curious(X0) | ~kind(X0)) [ennf transformation 11]
45. ! [X0] : (((~quiet(X0) | funny(X0)) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | (quiet(X0) & ~funny(X0)))) [nnf transformation 4]
46. ! [X0] : ((~quiet(X0) | funny(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | (quiet(X0) & ~funny(X0)))) [flattening 45]
47. ! [X0] : ((((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~generous(X0) | ~funny(X0))) & ((generous(X0) & funny(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | ~generous(X0) | ~funny(X0)) & ((generous(X0) & funny(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))))) [flattening 47]
49. ! [X0] : (((kind(X0) | ~tall(X0)) | ~patient(X0)) & (patient(X0) | (~kind(X0) & tall(X0)))) [nnf transformation 8]
50. ! [X0] : ((kind(X0) | ~tall(X0) | ~patient(X0)) & (patient(X0) | (~kind(X0) & tall(X0)))) [flattening 49]
76. ~patient(X0) | ~funny(X0) [cnf transformation 46]
84. ~creative(X0) | curious(X0) | funny(X0) [cnf transformation 48]
90. ~kind(X0) | patient(X0) [cnf transformation 50]
93. creative(X0) | funny(X0) [cnf transformation 34]
94. ~curious(X0) | ~kind(X0) [cnf transformation 35]
125. kind(susan) [cnf transformation 24]
209. patient(susan) [resolution 90,125]
213. ~funny(susan) [resolution 209,76]
226. curious(X0) | funny(X0) | funny(X0) [resolution 84,93]
227. curious(X0) | funny(X0) [duplicate literal removal 226]
231. ~kind(X1) | funny(X1) [resolution 227,94]
248. funny(susan) [resolution 231,125]
249. $false [subsumption resolution 248,213]
% SZS output end Proof for 4856400810627793710537537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either not generous or old.
If someone is not curious then mary is both tall and not curious.
Everyone who is brave is not calm.
Everyone who is either not calm or creative is not patient or tall and vice versa.
If someone is brave then paul is either not patient or funny.
Everyone who is funny is patient or not patient and vice versa.
Everyone who is either not happy or old is either patient or not humble and vice versa.
Everyone who is old is not happy or not calm.
If someone is happy or tall then mary is both not patient and not tall.
Everyone who is curious is both not creative and rich and vice versa.
If alice is not curious then alice is both strong and creative and vice versa.
If someone is tall then lucy is kind or not creative.
Everyone who is funny or creative is either not tall or happy.
If someone is both quiet and humble then mary is either not rich or not creative.
Everyone who is not creative or not brave is either not patient or not rich and vice versa.
If susan is kind then fred is either funny or not brave and vice versa.
Someone is both not creative and not tall.
Someone is not quiet.
Someone is either not generous or brave.
John is not strong or not rich. | Mary is not brave. | entailment | (![X]:(~humble(X)=>(~generous(X)<~>old(X))))&
((?[X]:(~curious(X)))=>((tall(mary)&~curious(mary))))&
(![X]:(brave(X)=>~calm(X)))&
(![X]:((~calm(X)<~>creative(X))<=>(~patient(X)|tall(X))))&
((?[X]:(brave(X)))=>((~patient(paul)<~>funny(paul))))&
(![X]:(funny(X)<=>(patient(X)|~patient(X))))&
(![X]:((~happy(X)<~>old(X))<=>(patient(X)<~>~humble(X))))&
(![X]:(old(X)=>(~happy(X)|~calm(X))))&
((?[X]:((happy(X)|tall(X))))=>((~patient(mary)&~tall(mary))))&
(![X]:(curious(X)<=>(~creative(X)&rich(X))))&
((~curious(alice))<=>((strong(alice)&creative(alice))))&
((?[X]:(tall(X)))=>((kind(lucy)|~creative(lucy))))&
(![X]:((funny(X)|creative(X))=>(~tall(X)<~>happy(X))))&
((?[X]:((quiet(X)&humble(X))))=>((~rich(mary)<~>~creative(mary))))&
(![X]:((~creative(X)|~brave(X))<=>(~patient(X)<~>~rich(X))))&
((kind(susan))<=>((funny(fred)<~>~brave(fred))))&
(?[X]:((~creative(X)&~tall(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)<~>brave(X))))&
((~strong(john)|~rich(john))) | ~brave(mary) | [
"p1",
"p4",
"p5",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4015206183984573764509557
% SZS output start Proof for 4015206183984573764509557
2. ? [X0] : ~curious(X0) => (~curious(mary) & tall(mary)) [input p1]
5. ? [X0] : brave(X0) => (~patient(paul) <~> funny(paul)) [input p4]
6. ! [X0] : (funny(X0) <=> (~patient(X0) | patient(X0))) [input p5]
9. ? [X0] : (tall(X0) | happy(X0)) => (~tall(mary) & ~patient(mary)) [input p8]
10. ! [X0] : (curious(X0) <=> (rich(X0) & ~creative(X0))) [input p9]
15. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (~patient(X0) <~> ~rich(X0))) [input p14]
21. brave(mary) [input hypothesis]
25. (~curious(mary) & tall(mary)) | ! [X0] : curious(X0) [ennf transformation 2]
27. (~patient(paul) <~> funny(paul)) | ! [X0] : ~brave(X0) [ennf transformation 5]
30. (~tall(mary) & ~patient(mary)) | ! [X0] : (~tall(X0) & ~happy(X0)) [ennf transformation 9]
37. ((~funny(paul) | patient(paul)) & (funny(paul) | ~patient(paul))) | ! [X0] : ~brave(X0) [nnf transformation 27]
38. ! [X0] : ((funny(X0) | (patient(X0) & ~patient(X0))) & ((~patient(X0) | patient(X0)) | ~funny(X0))) [nnf transformation 6]
39. ! [X0] : ((funny(X0) | (patient(X0) & ~patient(X0))) & (~patient(X0) | patient(X0) | ~funny(X0))) [flattening 38]
41. ! [X0] : ((curious(X0) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | ~curious(X0))) [nnf transformation 10]
42. ! [X0] : ((curious(X0) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | ~curious(X0))) [flattening 41]
46. ! [X0] : (((~brave(X0) | ~creative(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (brave(X0) & creative(X0)))) [nnf transformation 15]
47. ! [X0] : ((~brave(X0) | ~creative(X0) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (brave(X0) & creative(X0)))) [flattening 46]
56. tall(mary) | curious(X0) [cnf transformation 25]
66. ~funny(paul) | patient(paul) | ~brave(X0) [cnf transformation 37]
68. funny(X0) | ~patient(X0) [cnf transformation 39]
69. funny(X0) | patient(X0) [cnf transformation 39]
82. ~tall(mary) | ~tall(X0) [cnf transformation 30]
83. ~creative(X0) | ~curious(X0) [cnf transformation 42]
84. ~curious(X0) | rich(X0) [cnf transformation 42]
94. ~rich(X0) | ~patient(X0) | creative(X0) [cnf transformation 47]
109. brave(mary) [cnf transformation 21]
111. 1 <=> ! [X0] : curious(X0) [avatar definition]
112. curious(X0) <- (1) [avatar component clause 111]
119. 3 <=> tall(mary) [avatar definition]
121. tall(mary) <- (3) [avatar component clause 119]
122. 1 | 3 [avatar split clause 56,119,111]
124. 4 <=> ! [X0] : ~brave(X0) [avatar definition]
125. ~brave(X0) <- (4) [avatar component clause 124]
127. 5 <=> patient(paul) [avatar definition]
129. patient(paul) <- (5) [avatar component clause 127]
131. 6 <=> funny(paul) [avatar definition]
133. ~funny(paul) <- (~6) [avatar component clause 131]
134. 4 | 5 | ~6 [avatar split clause 66,131,127,124]
136. funny(X0) [subsumption resolution 68,69]
138. 7 <=> ! [X0] : ~tall(X0) [avatar definition]
139. ~tall(X0) <- (7) [avatar component clause 138]
140. 7 | ~3 [avatar split clause 82,119,138]
207. $false <- (~6) [subsumption resolution 133,136]
208. 6 [avatar contradiction clause 207]
209. $false <- (3, 7) [subsumption resolution 121,139]
210. ~3 | ~7 [avatar contradiction clause 209]
213. rich(X0) <- (1) [resolution 84,112]
218. ~patient(X0) | creative(X0) <- (1) [resolution 94,213]
219. creative(paul) <- (1, 5) [resolution 218,129]
224. ~curious(paul) <- (1, 5) [resolution 219,83]
225. $false <- (1, 5) [subsumption resolution 224,112]
226. ~1 | ~5 [avatar contradiction clause 225]
227. $false <- (4) [resolution 125,109]
228. ~4 [avatar contradiction clause 227]
229. $false [avatar sat refutation 122,134,140,208,210,226,228]
% SZS output end Proof for 4015206183984573764509557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or calm is either tall or not happy and vice versa. If lucy is either not wise or not generous then someone is tall or patient and vice versa. Everyone who is not funny is both humble and curious and vice versa. Everyone who is happy or generous is both patient and not tall. If lucy is both not generous and not tall then lucy is either old or not funny and vice versa. Everyone who is both not curious and generous is not curious and vice versa. If paul is both not patient and rich then someone is not quiet or not brave. Everyone who is both not wise and tall is not funny and vice versa. If someone is happy then susan is not happy or patient and vice versa. Everyone who is both not quiet and not strong is not happy or not wise and vice versa. If john is curious or tall then john is not curious or not calm. Everyone who is tall is not tall. Everyone who is not old or not tall is not tall or not kind. If someone is both not patient and not humble then someone is quiet or not brave and vice versa. If someone is not happy then someone is both kind and happy and vice versa. Everyone who is not wise or strong is both not kind and rich and vice versa. Paul is not patient or not generous. Mary is not humble or old. Someone is either not calm or not quiet. Someone is patient or not rich. Someone is kind or not old. John is humble or quiet. Someone is brave or old. Susan is not kind. | Susan is funny. | entailment | (![X]:((generous(X)<~>calm(X))<=>(tall(X)<~>~happy(X))))&
(((~wise(lucy)<~>~generous(lucy)))<=>(?[X]:((tall(X)|patient(X)))))&
(![X]:(~funny(X)<=>(humble(X)&curious(X))))&
(![X]:((happy(X)|generous(X))=>(patient(X)&~tall(X))))&
(((~generous(lucy)&~tall(lucy)))<=>((old(lucy)<~>~funny(lucy))))&
(![X]:((~curious(X)&generous(X))<=>~curious(X)))&
(((~patient(paul)&rich(paul)))=>(?[X]:((~quiet(X)|~brave(X)))))&
(![X]:((~wise(X)&tall(X))<=>~funny(X)))&
((?[X]:(happy(X)))<=>((~happy(susan)|patient(susan))))&
(![X]:((~quiet(X)&~strong(X))<=>(~happy(X)|~wise(X))))&
(((curious(john)|tall(john)))=>((~curious(john)|~calm(john))))&
(![X]:(tall(X)=>~tall(X)))&
(![X]:((~old(X)|~tall(X))=>(~tall(X)|~kind(X))))&
((?[X]:((~patient(X)&~humble(X))))<=>(?[X]:((quiet(X)|~brave(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((kind(X)&happy(X)))))&
(![X]:((~wise(X)|strong(X))<=>(~kind(X)&rich(X))))&
((~patient(paul)|~generous(paul)))&
((~humble(mary)|old(mary)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
(?[X]:((patient(X)|~rich(X))))&
(?[X]:((kind(X)|~old(X))))&
((humble(john)|quiet(john)))&
(?[X]:((brave(X)|old(X))))&
(~kind(susan)) | funny(susan) | [
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1030132664605539116159278
% SZS output start Proof for 1030132664605539116159278
8. ! [X0] : ((tall(X0) & ~wise(X0)) <=> ~funny(X0)) [input p7]
12. ! [X0] : (tall(X0) => ~tall(X0)) [input p11]
25. ~funny(susan) [input hypothesis]
33. ! [X0] : (~tall(X0) | ~tall(X0)) [ennf transformation 12]
49. ! [X0] : (((tall(X0) & ~wise(X0)) | funny(X0)) & (~funny(X0) | (~tall(X0) | wise(X0)))) [nnf transformation 8]
50. ! [X0] : (((tall(X0) & ~wise(X0)) | funny(X0)) & (~funny(X0) | ~tall(X0) | wise(X0))) [flattening 49]
112. funny(X0) | tall(X0) [cnf transformation 50]
123. ~tall(X0) | ~tall(X0) [cnf transformation 33]
148. ~funny(susan) [cnf transformation 25]
149. ~tall(X0) [duplicate literal removal 123]
164. 4 <=> ! [X0] : ~tall(X0) [avatar definition]
165. ~tall(X0) <- (4) [avatar component clause 164]
242. 4 [avatar split clause 149,164]
371. tall(susan) [resolution 112,148]
373. $false <- (4) [subsumption resolution 371,165]
374. ~4 [avatar contradiction clause 373]
377. $false [avatar sat refutation 242,374]
% SZS output end Proof for 1030132664605539116159278
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If fred is humble or curious then someone is both rich and not humble.
If someone is both not generous and not kind then lucy is not happy or not generous.
If someone is funny or not old then mary is both not strong and funny and vice versa.
If someone is either not quiet or not patient then lucy is old and vice versa.
Everyone who is rich or humble is not generous or generous and vice versa.
Everyone who is not rich is creative or strong.
If someone is either generous or rich then alice is either humble or not rich.
Everyone who is not generous or not humble is both kind and not generous and vice versa.
Everyone who is both not quiet and not humble is either brave or not curious and vice versa.
Everyone who is happy is either kind or not generous.
Everyone who is not kind or not curious is not old and vice versa.
If someone is not tall then lucy is not humble or not generous and vice versa.
Everyone who is not funny is either not tall or tall and vice versa.
Everyone who is tall or not strong is both quiet and funny and vice versa.
Everyone who is either not happy or creative is not quiet or not calm.
Everyone who is not generous or funny is both quiet and strong.
Someone is both strong and not wise.
Someone is either happy or old.
Paul is either tall or old.
Someone is both not creative and not wise.
Lucy is not tall. | Paul is not strong. | contradiction | (((humble(fred)|curious(fred)))=>(?[X]:((rich(X)&~humble(X)))))&
((?[X]:((~generous(X)&~kind(X))))=>((~happy(lucy)|~generous(lucy))))&
((?[X]:((funny(X)|~old(X))))<=>((~strong(mary)&funny(mary))))&
((?[X]:((~quiet(X)<~>~patient(X))))<=>(old(lucy)))&
(![X]:((rich(X)|humble(X))<=>(~generous(X)|generous(X))))&
(![X]:(~rich(X)=>(creative(X)|strong(X))))&
((?[X]:((generous(X)<~>rich(X))))=>((humble(alice)<~>~rich(alice))))&
(![X]:((~generous(X)|~humble(X))<=>(kind(X)&~generous(X))))&
(![X]:((~quiet(X)&~humble(X))<=>(brave(X)<~>~curious(X))))&
(![X]:(happy(X)=>(kind(X)<~>~generous(X))))&
(![X]:((~kind(X)|~curious(X))<=>~old(X)))&
((?[X]:(~tall(X)))<=>((~humble(lucy)|~generous(lucy))))&
(![X]:(~funny(X)<=>(~tall(X)<~>tall(X))))&
(![X]:((tall(X)|~strong(X))<=>(quiet(X)&funny(X))))&
(![X]:((~happy(X)<~>creative(X))=>(~quiet(X)|~calm(X))))&
(![X]:((~generous(X)|funny(X))=>(quiet(X)&strong(X))))&
(?[X]:((strong(X)&~wise(X))))&
(?[X]:((happy(X)<~>old(X))))&
((tall(paul)<~>old(paul)))&
(?[X]:((~creative(X)&~wise(X))))&
(~tall(lucy)) | ~strong(paul) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3609415589947325767470991
% SZS output start Proof for 3609415589947325767470991
14. ! [X0] : ((~strong(X0) | tall(X0)) <=> (funny(X0) & quiet(X0))) [input p13]
16. ! [X0] : ((funny(X0) | ~generous(X0)) => (strong(X0) & quiet(X0))) [input p15]
22. ~strong(paul) [input hypothesis]
33. ! [X0] : ((strong(X0) & quiet(X0)) | (~funny(X0) & generous(X0))) [ennf transformation 16]
61. ! [X0] : (((~strong(X0) | tall(X0)) | (~funny(X0) | ~quiet(X0))) & ((funny(X0) & quiet(X0)) | (strong(X0) & ~tall(X0)))) [nnf transformation 14]
62. ! [X0] : ((~strong(X0) | tall(X0) | ~funny(X0) | ~quiet(X0)) & ((funny(X0) & quiet(X0)) | (strong(X0) & ~tall(X0)))) [flattening 61]
120. funny(X0) | strong(X0) [cnf transformation 62]
125. strong(X0) | ~funny(X0) [cnf transformation 33]
133. ~strong(paul) [cnf transformation 22]
260. strong(X0) [subsumption resolution 125,120]
272. $false [subsumption resolution 133,260]
% SZS output end Proof for 3609415589947325767470991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or quiet then paul is humble or creative and vice versa.
If someone is not brave or humble then someone is either not creative or not quiet.
Everyone who is not happy is not tall and vice versa.
If lucy is either not funny or rich then john is either patient or not tall and vice versa.
Everyone who is not curious or not kind is either tall or quiet.
If alice is old or not strong then someone is not patient or old and vice versa.
Everyone who is wise or brave is either not happy or brave.
Everyone who is not patient or creative is both not rich and not strong.
If someone is rich or not humble then someone is both not kind and rich and vice versa.
If susan is both not strong and generous then lucy is both quiet and not calm and vice versa.
If mary is not old then someone is either not strong or wise.
If susan is either generous or not strong then lucy is not tall or brave.
If paul is not humble then lucy is not old or old and vice versa.
Everyone who is either not happy or wise is both not rich and not funny and vice versa.
Everyone who is humble or brave is both curious and wise.
Everyone who is wise or not kind is not humble or wise.
Paul is both not creative and not rich.
Paul is either not creative or curious.
Someone is either not calm or curious.
John is strong.
Mary is either not brave or not strong.
Someone is not generous or strong.
Someone is not kind or old.
Susan is either not kind or old. | John is creative. | contradiction | ((?[X]:((~calm(X)|quiet(X))))<=>((humble(paul)|creative(paul))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:(~happy(X)<=>~tall(X)))&
(((~funny(lucy)<~>rich(lucy)))<=>((patient(john)<~>~tall(john))))&
(![X]:((~curious(X)|~kind(X))=>(tall(X)<~>quiet(X))))&
(((old(alice)|~strong(alice)))<=>(?[X]:((~patient(X)|old(X)))))&
(![X]:((wise(X)|brave(X))=>(~happy(X)<~>brave(X))))&
(![X]:((~patient(X)|creative(X))=>(~rich(X)&~strong(X))))&
((?[X]:((rich(X)|~humble(X))))<=>(?[X]:((~kind(X)&rich(X)))))&
(((~strong(susan)&generous(susan)))<=>((quiet(lucy)&~calm(lucy))))&
((~old(mary))=>(?[X]:((~strong(X)<~>wise(X)))))&
(((generous(susan)<~>~strong(susan)))=>((~tall(lucy)|brave(lucy))))&
((~humble(paul))<=>((~old(lucy)|old(lucy))))&
(![X]:((~happy(X)<~>wise(X))<=>(~rich(X)&~funny(X))))&
(![X]:((humble(X)|brave(X))=>(curious(X)&wise(X))))&
(![X]:((wise(X)|~kind(X))=>(~humble(X)|wise(X))))&
((~creative(paul)&~rich(paul)))&
((~creative(paul)<~>curious(paul)))&
(?[X]:((~calm(X)<~>curious(X))))&
(strong(john))&
((~brave(mary)<~>~strong(mary)))&
(?[X]:((~generous(X)|strong(X))))&
(?[X]:((~kind(X)|old(X))))&
((~kind(susan)<~>old(susan))) | creative(john) | [
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9067467911130913369806196
% SZS output start Proof for 9067467911130913369806196
8. ! [X0] : ((creative(X0) | ~patient(X0)) => (~strong(X0) & ~rich(X0))) [input p7]
20. strong(john) [input p19]
25. creative(john) [input hypothesis]
31. ! [X0] : ((~strong(X0) & ~rich(X0)) | (~creative(X0) & patient(X0))) [ennf transformation 8]
114. ~strong(X0) | ~creative(X0) [cnf transformation 31]
149. strong(john) [cnf transformation 20]
156. creative(john) [cnf transformation 25]
396. ~creative(john) [resolution 114,149]
397. $false [subsumption resolution 396,156]
% SZS output end Proof for 9067467911130913369806196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or old is both wise and not strong.
If someone is not kind then paul is both not rich and tall and vice versa.
If someone is either patient or not generous then fred is kind or not brave and vice versa.
If someone is old then lucy is both brave and not tall and vice versa.
Everyone who is either not old or humble is patient and vice versa.
Everyone who is both not wise and not rich is either not tall or not creative.
If lucy is both not patient and not humble then susan is rich or old.
If someone is either not patient or not funny then someone is either not wise or not old and vice versa.
If paul is happy then someone is either generous or curious.
If someone is quiet or happy then mary is not old and vice versa.
If someone is generous or not happy then someone is both quiet and brave.
If someone is not wise or not funny then someone is either not happy or strong.
Everyone who is either not old or not kind is calm and vice versa.
Everyone who is not happy or rich is either quiet or creative.
Everyone who is either not strong or not calm is either not old or brave and vice versa.
Everyone who is not humble is either not patient or not tall and vice versa.
Lucy is not calm or not happy.
Mary is both not patient and not rich.
John is not kind.
Mary is either old or not happy.
Susan is either tall or not creative.
Someone is either creative or kind.
Someone is not creative. | Mary is old. | contradiction | (![X]:((funny(X)|old(X))=>(wise(X)&~strong(X))))&
((?[X]:(~kind(X)))<=>((~rich(paul)&tall(paul))))&
((?[X]:((patient(X)<~>~generous(X))))<=>((kind(fred)|~brave(fred))))&
((?[X]:(old(X)))<=>((brave(lucy)&~tall(lucy))))&
(![X]:((~old(X)<~>humble(X))<=>patient(X)))&
(![X]:((~wise(X)&~rich(X))=>(~tall(X)<~>~creative(X))))&
(((~patient(lucy)&~humble(lucy)))=>((rich(susan)|old(susan))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(?[X]:((~wise(X)<~>~old(X)))))&
((happy(paul))=>(?[X]:((generous(X)<~>curious(X)))))&
((?[X]:((quiet(X)|happy(X))))<=>(~old(mary)))&
((?[X]:((generous(X)|~happy(X))))=>(?[X]:((quiet(X)&brave(X)))))&
((?[X]:((~wise(X)|~funny(X))))=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:((~old(X)<~>~kind(X))<=>calm(X)))&
(![X]:((~happy(X)|rich(X))=>(quiet(X)<~>creative(X))))&
(![X]:((~strong(X)<~>~calm(X))<=>(~old(X)<~>brave(X))))&
(![X]:(~humble(X)<=>(~patient(X)<~>~tall(X))))&
((~calm(lucy)|~happy(lucy)))&
((~patient(mary)&~rich(mary)))&
(~kind(john))&
((old(mary)<~>~happy(mary)))&
((tall(susan)<~>~creative(susan)))&
(?[X]:((creative(X)<~>kind(X))))&
(?[X]:(~creative(X))) | old(mary) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5228286929906670397794693
% SZS output start Proof for 5228286929906670397794693
10. ? [X0] : (happy(X0) | quiet(X0)) <=> ~old(mary) [input p9]
11. ? [X0] : (~happy(X0) | generous(X0)) => ? [X0] : (brave(X0) & quiet(X0)) [input p10]
24. old(mary) [input hypothesis]
26. ? [X0] : (~happy(X0) | generous(X0)) => ? [X1] : (brave(X1) & quiet(X1)) [rectify 11]
34. ? [X1] : (brave(X1) & quiet(X1)) | ! [X0] : (happy(X0) & ~generous(X0)) [ennf transformation 26]
62. (? [X0] : (happy(X0) | quiet(X0)) | old(mary)) & (~old(mary) | ! [X0] : (~happy(X0) & ~quiet(X0))) [nnf transformation 10]
63. (? [X0] : (happy(X0) | quiet(X0)) | old(mary)) & (~old(mary) | ! [X1] : (~happy(X1) & ~quiet(X1))) [rectify 62]
64. ? [X0] : (happy(X0) | quiet(X0)) => (happy(sK6) | quiet(sK6)) [choice axiom]
65. ((happy(sK6) | quiet(sK6)) | old(mary)) & (~old(mary) | ! [X1] : (~happy(X1) & ~quiet(X1))) [skolemisation 63,64]
66. ? [X0] : (brave(X0) & quiet(X0)) | ! [X1] : (happy(X1) & ~generous(X1)) [rectify 34]
67. ? [X0] : (brave(X0) & quiet(X0)) => (brave(sK7) & quiet(sK7)) [choice axiom]
68. (brave(sK7) & quiet(sK7)) | ! [X1] : (happy(X1) & ~generous(X1)) [skolemisation 66,67]
117. ~old(mary) | ~quiet(X1) [cnf transformation 65]
118. ~old(mary) | ~happy(X1) [cnf transformation 65]
121. quiet(sK7) | happy(X1) [cnf transformation 68]
159. old(mary) [cnf transformation 24]
291. 29 <=> old(mary) [avatar definition]
304. 32 <=> ! [X1] : ~happy(X1) [avatar definition]
305. ~happy(X1) <- (32) [avatar component clause 304]
306. 32 | ~29 [avatar split clause 118,291,304]
308. 33 <=> ! [X1] : ~quiet(X1) [avatar definition]
309. ~quiet(X1) <- (33) [avatar component clause 308]
310. 33 | ~29 [avatar split clause 117,291,308]
312. 34 <=> ! [X1] : happy(X1) [avatar definition]
313. happy(X1) <- (34) [avatar component clause 312]
324. 37 <=> quiet(sK7) [avatar definition]
326. quiet(sK7) <- (37) [avatar component clause 324]
327. 34 | 37 [avatar split clause 121,324,312]
386. 29 [avatar split clause 159,291]
387. $false <- (32, 34) [subsumption resolution 305,313]
388. ~32 | ~34 [avatar contradiction clause 387]
391. $false <- (33, 37) [subsumption resolution 326,309]
392. ~33 | ~37 [avatar contradiction clause 391]
393. $false [avatar sat refutation 306,310,327,386,388,392]
% SZS output end Proof for 5228286929906670397794693
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not funny and generous then susan is both not humble and not rich and vice versa.
Everyone who is not strong or funny is either not curious or not wise.
If someone is both not generous and humble then someone is either funny or not old and vice versa.
Everyone who is tall or not wise is quiet or not humble and vice versa.
Everyone who is either curious or wise is not funny and vice versa.
Everyone who is both patient and not tall is either not tall or not calm.
If someone is both not funny and funny then john is quiet and vice versa.
Everyone who is both not quiet and humble is not brave.
If lucy is both not kind and rich then someone is not generous or not old.
If someone is kind then alice is both not old and wise.
If paul is not strong then someone is humble.
If someone is creative or not creative then someone is both humble and calm and vice versa.
If alice is funny then paul is either quiet or not humble and vice versa.
Everyone who is both not strong and creative is both not tall and tall and vice versa.
Everyone who is both not strong and quiet is both not funny and tall and vice versa.
If fred is not kind or funny then someone is both curious and not kind and vice versa.
Someone is kind or funny.
Someone is both patient and creative.
Alice is both happy and kind.
Someone is either not old or rich.
Someone is not curious.
Fred is not generous or calm.
Someone is both not brave and not generous.
Someone is generous. | Alice is not creative. | neutral | (((~funny(susan)&generous(susan)))<=>((~humble(susan)&~rich(susan))))&
(![X]:((~strong(X)|funny(X))=>(~curious(X)<~>~wise(X))))&
((?[X]:((~generous(X)&humble(X))))<=>(?[X]:((funny(X)<~>~old(X)))))&
(![X]:((tall(X)|~wise(X))<=>(quiet(X)|~humble(X))))&
(![X]:((curious(X)<~>wise(X))<=>~funny(X)))&
(![X]:((patient(X)&~tall(X))=>(~tall(X)<~>~calm(X))))&
((?[X]:((~funny(X)&funny(X))))<=>(quiet(john)))&
(![X]:((~quiet(X)&humble(X))=>~brave(X)))&
(((~kind(lucy)&rich(lucy)))=>(?[X]:((~generous(X)|~old(X)))))&
((?[X]:(kind(X)))=>((~old(alice)&wise(alice))))&
((~strong(paul))=>(?[X]:(humble(X))))&
((?[X]:((creative(X)|~creative(X))))<=>(?[X]:((humble(X)&calm(X)))))&
((funny(alice))<=>((quiet(paul)<~>~humble(paul))))&
(![X]:((~strong(X)&creative(X))<=>(~tall(X)&tall(X))))&
(![X]:((~strong(X)&quiet(X))<=>(~funny(X)&tall(X))))&
(((~kind(fred)|funny(fred)))<=>(?[X]:((curious(X)&~kind(X)))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((patient(X)&creative(X))))&
((happy(alice)&kind(alice)))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:(~curious(X)))&
((~generous(fred)|calm(fred)))&
(?[X]:((~brave(X)&~generous(X))))&
(?[X]:(generous(X))) | ~creative(alice) | [] | null | 0 |
If someone is not kind then lucy is either not humble or wise and vice versa.
If someone is funny then mary is both not tall and brave and vice versa.
If someone is both not creative and happy then lucy is either strong or not creative and vice versa.
Everyone who is either wise or not funny is happy.
If someone is either calm or patient then paul is not kind or humble.
Everyone who is not quiet is either not generous or not tall and vice versa.
Everyone who is rich or not generous is kind or wise.
If susan is either not humble or not funny then john is either not tall or humble and vice versa.
Everyone who is either not strong or humble is old or not calm.
Everyone who is either wise or not curious is both patient and not quiet.
Everyone who is not calm or calm is both tall and not calm.
If lucy is either quiet or not kind then someone is either happy or curious.
Everyone who is either humble or not rich is both old and not calm and vice versa.
If someone is creative then someone is both generous and brave and vice versa.
Everyone who is strong is both quiet and calm and vice versa.
Lucy is quiet.
Fred is either not patient or not old.
Mary is old or not patient. | Fred is not tall. | contradiction | ((?[X]:(~kind(X)))<=>((~humble(lucy)<~>wise(lucy))))&
((?[X]:(funny(X)))<=>((~tall(mary)&brave(mary))))&
((?[X]:((~creative(X)&happy(X))))<=>((strong(lucy)<~>~creative(lucy))))&
(![X]:((wise(X)<~>~funny(X))=>happy(X)))&
((?[X]:((calm(X)<~>patient(X))))=>((~kind(paul)|humble(paul))))&
(![X]:(~quiet(X)<=>(~generous(X)<~>~tall(X))))&
(![X]:((rich(X)|~generous(X))=>(kind(X)|wise(X))))&
(((~humble(susan)<~>~funny(susan)))<=>((~tall(john)<~>humble(john))))&
(![X]:((~strong(X)<~>humble(X))=>(old(X)|~calm(X))))&
(![X]:((wise(X)<~>~curious(X))=>(patient(X)&~quiet(X))))&
(![X]:((~calm(X)|calm(X))=>(tall(X)&~calm(X))))&
(((quiet(lucy)<~>~kind(lucy)))=>(?[X]:((happy(X)<~>curious(X)))))&
(![X]:((humble(X)<~>~rich(X))<=>(old(X)&~calm(X))))&
((?[X]:(creative(X)))<=>(?[X]:((generous(X)&brave(X)))))&
(![X]:(strong(X)<=>(quiet(X)&calm(X))))&
(quiet(lucy))&
((~patient(fred)<~>~old(fred)))&
((old(mary)|~patient(mary))) | ~tall(fred) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4816744523501855461307774
% SZS output start Proof for 4816744523501855461307774
11. ! [X0] : ((calm(X0) | ~calm(X0)) => (~calm(X0) & tall(X0))) [input p10]
19. ~tall(fred) [input hypothesis]
29. ! [X0] : ((~calm(X0) & tall(X0)) | (~calm(X0) & calm(X0))) [ennf transformation 11]
100. tall(X0) | calm(X0) [cnf transformation 29]
103. ~calm(X0) | ~calm(X0) [cnf transformation 29]
124. ~tall(fred) [cnf transformation 19]
125. ~calm(X0) [duplicate literal removal 103]
228. tall(X0) [subsumption resolution 100,125]
293. $false [subsumption resolution 124,228]
% SZS output end Proof for 4816744523501855461307774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is not strong.
Everyone who is not funny is either calm or not kind.
If someone is both not calm and rich then john is funny or calm and vice versa.
Everyone who is not brave is both quiet and not funny.
If someone is either not brave or not rich then alice is creative or not generous and vice versa.
Everyone who is not old is calm or quiet.
If someone is not kind or quiet then paul is both not patient and brave.
Everyone who is old or creative is happy.
Everyone who is both not tall and not brave is both old and not old.
Everyone who is both kind and not strong is both humble and not patient.
If susan is both not happy and not generous then someone is creative or not wise.
Everyone who is both generous and not quiet is either old or quiet.
Everyone who is quiet is not wise.
Everyone who is both not humble and kind is both not wise and strong and vice versa.
Everyone who is both not tall and calm is not happy or patient and vice versa.
If someone is not strong or humble then someone is either not happy or not humble.
Mary is both not strong and not curious.
Fred is not strong or not curious.
Someone is either funny or rich.
Alice is not old or curious.
Susan is not kind or funny.
Susan is either strong or patient.
Someone is both generous and tall.
Someone is either curious or strong. | Alice is humble. | neutral | ((?[X]:(~generous(X)))=>(?[X]:(~strong(X))))&
(![X]:(~funny(X)=>(calm(X)<~>~kind(X))))&
((?[X]:((~calm(X)&rich(X))))<=>((funny(john)|calm(john))))&
(![X]:(~brave(X)=>(quiet(X)&~funny(X))))&
((?[X]:((~brave(X)<~>~rich(X))))<=>((creative(alice)|~generous(alice))))&
(![X]:(~old(X)=>(calm(X)|quiet(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((~patient(paul)&brave(paul))))&
(![X]:((old(X)|creative(X))=>happy(X)))&
(![X]:((~tall(X)&~brave(X))=>(old(X)&~old(X))))&
(![X]:((kind(X)&~strong(X))=>(humble(X)&~patient(X))))&
(((~happy(susan)&~generous(susan)))=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:((generous(X)&~quiet(X))=>(old(X)<~>quiet(X))))&
(![X]:(quiet(X)=>~wise(X)))&
(![X]:((~humble(X)&kind(X))<=>(~wise(X)&strong(X))))&
(![X]:((~tall(X)&calm(X))<=>(~happy(X)|patient(X))))&
((?[X]:((~strong(X)|humble(X))))=>(?[X]:((~happy(X)<~>~humble(X)))))&
((~strong(mary)&~curious(mary)))&
((~strong(fred)|~curious(fred)))&
(?[X]:((funny(X)<~>rich(X))))&
((~old(alice)|curious(alice)))&
((~kind(susan)|funny(susan)))&
((strong(susan)<~>patient(susan)))&
(?[X]:((generous(X)&tall(X))))&
(?[X]:((curious(X)<~>strong(X)))) | humble(alice) | [] | null | 0 |
If alice is both happy and not rich then john is both not generous and not wise and vice versa.
If someone is strong then susan is kind or wise.
Everyone who is either not tall or kind is both not quiet and not patient and vice versa.
Everyone who is both not creative and quiet is not funny or not strong.
If alice is calm then someone is not patient or not calm and vice versa.
If someone is either not kind or not funny then susan is either kind or strong and vice versa.
If someone is either not humble or not rich then someone is both not wise and humble and vice versa.
If someone is not strong then someone is both brave and not kind and vice versa.
If lucy is creative then someone is either brave or not strong.
Everyone who is not tall or creative is tall and vice versa.
Everyone who is not rich or curious is patient and vice versa.
Everyone who is both not old and not happy is not quiet or curious and vice versa.
Everyone who is either not calm or not generous is wise.
Everyone who is humble or not calm is wise.
Everyone who is happy is not funny or not patient and vice versa.
If john is not creative then susan is not generous or not wise and vice versa.
Someone is not patient or creative.
Mary is strong.
Mary is both curious and not quiet.
Someone is not funny or humble.
Someone is not patient.
Fred is rich.
Someone is both not happy and funny.
Susan is generous or not rich. | Fred is not kind. | entailment | (((happy(alice)&~rich(alice)))<=>((~generous(john)&~wise(john))))&
((?[X]:(strong(X)))=>((kind(susan)|wise(susan))))&
(![X]:((~tall(X)<~>kind(X))<=>(~quiet(X)&~patient(X))))&
(![X]:((~creative(X)&quiet(X))=>(~funny(X)|~strong(X))))&
((calm(alice))<=>(?[X]:((~patient(X)|~calm(X)))))&
((?[X]:((~kind(X)<~>~funny(X))))<=>((kind(susan)<~>strong(susan))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>(?[X]:((~wise(X)&humble(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((brave(X)&~kind(X)))))&
((creative(lucy))=>(?[X]:((brave(X)<~>~strong(X)))))&
(![X]:((~tall(X)|creative(X))<=>tall(X)))&
(![X]:((~rich(X)|curious(X))<=>patient(X)))&
(![X]:((~old(X)&~happy(X))<=>(~quiet(X)|curious(X))))&
(![X]:((~calm(X)<~>~generous(X))=>wise(X)))&
(![X]:((humble(X)|~calm(X))=>wise(X)))&
(![X]:(happy(X)<=>(~funny(X)|~patient(X))))&
((~creative(john))<=>((~generous(susan)|~wise(susan))))&
(?[X]:((~patient(X)|creative(X))))&
(strong(mary))&
((curious(mary)&~quiet(mary)))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:(~patient(X)))&
(rich(fred))&
(?[X]:((~happy(X)&funny(X))))&
((generous(susan)|~rich(susan))) | ~kind(fred) | [
"p2",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6956892246949444426115350
% SZS output start Proof for 6956892246949444426115350
3. ! [X0] : ((~tall(X0) <~> kind(X0)) <=> (~patient(X0) & ~quiet(X0))) [input p2]
10. ! [X0] : ((creative(X0) | ~tall(X0)) <=> tall(X0)) [input p9]
12. ! [X0] : ((~happy(X0) & ~old(X0)) <=> (curious(X0) | ~quiet(X0))) [input p11]
15. ! [X0] : (happy(X0) <=> (~patient(X0) | ~funny(X0))) [input p14]
25. kind(fred) [input hypothesis]
37. ! [X0] : ((((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | (patient(X0) | quiet(X0))) & ((~patient(X0) & ~quiet(X0)) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0))))) [nnf transformation 3]
38. ! [X0] : ((((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | patient(X0) | quiet(X0)) & ((~patient(X0) & ~quiet(X0)) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0))))) [flattening 37]
60. ! [X0] : (((creative(X0) | ~tall(X0)) | ~tall(X0)) & (tall(X0) | (~creative(X0) & tall(X0)))) [nnf transformation 10]
61. ! [X0] : ((creative(X0) | ~tall(X0) | ~tall(X0)) & (tall(X0) | (~creative(X0) & tall(X0)))) [flattening 60]
64. ! [X0] : (((~happy(X0) & ~old(X0)) | (~curious(X0) & quiet(X0))) & ((curious(X0) | ~quiet(X0)) | (happy(X0) | old(X0)))) [nnf transformation 12]
65. ! [X0] : (((~happy(X0) & ~old(X0)) | (~curious(X0) & quiet(X0))) & (curious(X0) | ~quiet(X0) | happy(X0) | old(X0))) [flattening 64]
67. ! [X0] : ((happy(X0) | (patient(X0) & funny(X0))) & ((~patient(X0) | ~funny(X0)) | ~happy(X0))) [nnf transformation 15]
68. ! [X0] : ((happy(X0) | (patient(X0) & funny(X0))) & (~patient(X0) | ~funny(X0) | ~happy(X0))) [flattening 67]
85. ~quiet(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 38]
87. ~patient(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 38]
113. tall(X0) | tall(X0) [cnf transformation 61]
122. ~happy(X0) | quiet(X0) [cnf transformation 65]
130. patient(X0) | happy(X0) [cnf transformation 68]
144. kind(fred) [cnf transformation 25]
145. tall(X0) [duplicate literal removal 113]
367. ~tall(X0) | ~kind(X0) | happy(X0) [resolution 87,130]
370. ~kind(X0) | happy(X0) [subsumption resolution 367,145]
431. happy(fred) [resolution 370,144]
460. quiet(fred) [resolution 431,122]
477. ~tall(fred) | ~kind(fred) [resolution 460,85]
479. ~kind(fred) [subsumption resolution 477,145]
480. $false [subsumption resolution 479,144]
% SZS output end Proof for 6956892246949444426115350
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or curious is patient.
Everyone who is both not kind and happy is generous or happy and vice versa.
If someone is calm or curious then fred is both creative and funny.
Everyone who is not happy is patient or not happy.
If fred is both tall and not happy then fred is not strong and vice versa.
If lucy is both not brave and not wise then someone is not rich or curious and vice versa.
Everyone who is either tall or calm is both not quiet and not calm.
If lucy is both not strong and curious then someone is not kind or brave and vice versa.
Everyone who is both brave and not humble is not patient.
Everyone who is calm is not kind or old.
Everyone who is funny is either not old or not patient and vice versa.
Everyone who is not generous is both old and creative.
Everyone who is both patient and not patient is either wise or not rich.
Everyone who is both not tall and not patient is either strong or not tall.
Everyone who is both not generous and kind is quiet or rich and vice versa.
If lucy is creative then someone is both not generous and brave and vice versa.
Someone is brave.
Paul is either not quiet or humble.
Someone is either not calm or patient.
Someone is either generous or not funny.
Alice is either calm or not humble.
Someone is both tall and patient.
Someone is not strong.
Paul is old or not patient. | Lucy is not strong. | entailment | (![X]:((tall(X)|curious(X))=>patient(X)))&
(![X]:((~kind(X)&happy(X))<=>(generous(X)|happy(X))))&
((?[X]:((calm(X)|curious(X))))=>((creative(fred)&funny(fred))))&
(![X]:(~happy(X)=>(patient(X)|~happy(X))))&
(((tall(fred)&~happy(fred)))<=>(~strong(fred)))&
(((~brave(lucy)&~wise(lucy)))<=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((tall(X)<~>calm(X))=>(~quiet(X)&~calm(X))))&
(((~strong(lucy)&curious(lucy)))<=>(?[X]:((~kind(X)|brave(X)))))&
(![X]:((brave(X)&~humble(X))=>~patient(X)))&
(![X]:(calm(X)=>(~kind(X)|old(X))))&
(![X]:(funny(X)<=>(~old(X)<~>~patient(X))))&
(![X]:(~generous(X)=>(old(X)&creative(X))))&
(![X]:((patient(X)&~patient(X))=>(wise(X)<~>~rich(X))))&
(![X]:((~tall(X)&~patient(X))=>(strong(X)<~>~tall(X))))&
(![X]:((~generous(X)&kind(X))<=>(quiet(X)|rich(X))))&
((creative(lucy))<=>(?[X]:((~generous(X)&brave(X)))))&
(?[X]:(brave(X)))&
((~quiet(paul)<~>humble(paul)))&
(?[X]:((~calm(X)<~>patient(X))))&
(?[X]:((generous(X)<~>~funny(X))))&
((calm(alice)<~>~humble(alice)))&
(?[X]:((tall(X)&patient(X))))&
(?[X]:(~strong(X)))&
((old(paul)|~patient(paul))) | ~strong(lucy) | [
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3227903063777174563245574
% SZS output start Proof for 3227903063777174563245574
8. (curious(lucy) & ~strong(lucy)) <=> ? [X0] : (brave(X0) | ~kind(X0)) [input p7]
17. ? [X0] : brave(X0) [input p16]
25. strong(lucy) [input hypothesis]
50. ((curious(lucy) & ~strong(lucy)) | ! [X0] : (~brave(X0) & kind(X0))) & (? [X0] : (brave(X0) | ~kind(X0)) | (~curious(lucy) | strong(lucy))) [nnf transformation 8]
51. ((curious(lucy) & ~strong(lucy)) | ! [X0] : (~brave(X0) & kind(X0))) & (? [X0] : (brave(X0) | ~kind(X0)) | ~curious(lucy) | strong(lucy)) [flattening 50]
52. ((curious(lucy) & ~strong(lucy)) | ! [X0] : (~brave(X0) & kind(X0))) & (? [X1] : (brave(X1) | ~kind(X1)) | ~curious(lucy) | strong(lucy)) [rectify 51]
53. ? [X1] : (brave(X1) | ~kind(X1)) => (brave(sK1) | ~kind(sK1)) [choice axiom]
54. ((curious(lucy) & ~strong(lucy)) | ! [X0] : (~brave(X0) & kind(X0))) & ((brave(sK1) | ~kind(sK1)) | ~curious(lucy) | strong(lucy)) [skolemisation 52,53]
64. ? [X0] : brave(X0) => brave(sK3) [choice axiom]
65. brave(sK3) [skolemisation 17,64]
104. ~strong(lucy) | ~brave(X0) [cnf transformation 54]
127. brave(sK3) [cnf transformation 65]
140. strong(lucy) [cnf transformation 25]
201. 13 <=> ! [X0] : ~brave(X0) [avatar definition]
202. ~brave(X0) <- (13) [avatar component clause 201]
213. 16 <=> strong(lucy) [avatar definition]
216. 13 | ~16 [avatar split clause 104,213,201]
296. 16 [avatar split clause 140,213]
297. $false <- (13) [resolution 202,127]
298. ~13 [avatar contradiction clause 297]
299. $false [avatar sat refutation 216,296,298]
% SZS output end Proof for 3227903063777174563245574
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and quiet is either wise or old and vice versa. If someone is quiet then alice is both creative and not old and vice versa. Everyone who is either brave or not patient is old or wise. Everyone who is patient is not strong or not brave and vice versa. Everyone who is both wise and happy is not old or kind and vice versa. Everyone who is either not old or not curious is not wise or not funny and vice versa. If someone is either not strong or not funny then alice is not kind or humble and vice versa. Everyone who is either not funny or not generous is both funny and brave. If lucy is not curious or old then someone is brave or not brave and vice versa. Everyone who is either not happy or tall is both kind and not funny and vice versa. If mary is not calm then someone is either not patient or curious and vice versa. Everyone who is rich or funny is not quiet or old and vice versa. Everyone who is either wise or quiet is both humble and rich and vice versa. If alice is calm or rich then fred is not humble or curious and vice versa. Everyone who is generous or not happy is both tall and wise and vice versa. Everyone who is both not rich and creative is creative or funny. Someone is both not patient and happy. Susan is happy. Someone is not calm or not curious. | Susan is not generous. | entailment | (![X]:((kind(X)&quiet(X))<=>(wise(X)<~>old(X))))&
((?[X]:(quiet(X)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(humble(X)&rich(X))))&
(((calm(alice)|rich(alice)))<=>((~humble(fred)|curious(fred))))&
(![X]:((generous(X)|~happy(X))<=>(tall(X)&wise(X))))&
(![X]:((~rich(X)&creative(X))=>(creative(X)|funny(X))))&
(?[X]:((~patient(X)&happy(X))))&
(happy(susan))&
(?[X]:((~calm(X)|~curious(X)))) | ~generous(susan) | [
"p7",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7446651269649029368458122
% SZS output start Proof for 7446651269649029368458122
8. ! [X0] : ((~funny(X0) <~> ~generous(X0)) => (brave(X0) & funny(X0))) [input p7]
10. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (~funny(X0) & kind(X0))) [input p9]
15. ! [X0] : ((~happy(X0) | generous(X0)) <=> (wise(X0) & tall(X0))) [input p14]
18. happy(susan) [input p17]
20. generous(susan) [input hypothesis]
23. ! [X0] : ((brave(X0) & funny(X0)) | (~funny(X0) <=> ~generous(X0))) [ennf transformation 8]
45. ! [X0] : ((brave(X0) & funny(X0)) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) [nnf transformation 23]
51. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 10]
52. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 51]
63. ! [X0] : (((~happy(X0) | generous(X0)) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | (happy(X0) & ~generous(X0)))) [nnf transformation 15]
64. ! [X0] : ((~happy(X0) | generous(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | (happy(X0) & ~generous(X0)))) [flattening 63]
100. funny(X0) | ~generous(X0) | funny(X0) [cnf transformation 45]
111. ~tall(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 52]
132. ~generous(X0) | tall(X0) [cnf transformation 64]
140. happy(susan) [cnf transformation 18]
142. generous(susan) [cnf transformation 20]
143. ~generous(X0) | funny(X0) [duplicate literal removal 100]
264. tall(susan) [resolution 132,142]
266. funny(susan) [resolution 143,142]
316. ~happy(susan) | ~funny(susan) [resolution 111,264]
318. ~funny(susan) [subsumption resolution 316,140]
319. $false [subsumption resolution 318,266]
% SZS output end Proof for 7446651269649029368458122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or curious is both patient and quiet and vice versa.
If mary is either old or not brave then fred is either not happy or calm and vice versa.
Everyone who is either not calm or patient is humble and vice versa.
Everyone who is generous is not rich and vice versa.
If someone is both not creative and curious then mary is not rich.
If someone is either not wise or funny then john is not old and vice versa.
Everyone who is both not strong and not wise is both generous and not brave and vice versa.
Everyone who is either patient or calm is either wise or not strong.
Everyone who is wise or generous is both not old and strong and vice versa.
Everyone who is both kind and tall is both kind and not tall.
Everyone who is curious is not patient.
Everyone who is both creative and not kind is not patient.
If someone is both rich and tall then mary is both not tall and tall and vice versa.
Everyone who is either not quiet or strong is either not curious or not tall.
Everyone who is not old or not wise is both humble and not rich.
If lucy is not tall then fred is either brave or strong and vice versa.
Someone is not old or not brave.
John is either brave or calm.
Someone is rich or tall.
Mary is either kind or not happy.
Alice is old or not wise.
Someone is not kind or not funny. | Alice is not curious. | entailment | (![X]:((~wise(X)|curious(X))<=>(patient(X)&quiet(X))))&
(((old(mary)<~>~brave(mary)))<=>((~happy(fred)<~>calm(fred))))&
(![X]:((~calm(X)<~>patient(X))<=>humble(X)))&
(![X]:(generous(X)<=>~rich(X)))&
((?[X]:((~creative(X)&curious(X))))=>(~rich(mary)))&
((?[X]:((~wise(X)<~>funny(X))))<=>(~old(john)))&
(![X]:((~strong(X)&~wise(X))<=>(generous(X)&~brave(X))))&
(![X]:((patient(X)<~>calm(X))=>(wise(X)<~>~strong(X))))&
(![X]:((wise(X)|generous(X))<=>(~old(X)&strong(X))))&
(![X]:((kind(X)&tall(X))=>(kind(X)&~tall(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((creative(X)&~kind(X))=>~patient(X)))&
((?[X]:((rich(X)&tall(X))))<=>((~tall(mary)&tall(mary))))&
(![X]:((~quiet(X)<~>strong(X))=>(~curious(X)<~>~tall(X))))&
(![X]:((~old(X)|~wise(X))=>(humble(X)&~rich(X))))&
((~tall(lucy))<=>((brave(fred)<~>strong(fred))))&
(?[X]:((~old(X)|~brave(X))))&
((brave(john)<~>calm(john)))&
(?[X]:((rich(X)|tall(X))))&
((kind(mary)<~>~happy(mary)))&
((old(alice)|~wise(alice)))&
(?[X]:((~kind(X)|~funny(X)))) | ~curious(alice) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4424039270103003656524118
% SZS output start Proof for 4424039270103003656524118
1. ! [X0] : ((curious(X0) | ~wise(X0)) <=> (quiet(X0) & patient(X0))) [input p0]
11. ! [X0] : (curious(X0) => ~patient(X0)) [input p10]
23. curious(alice) [input hypothesis]
30. ! [X0] : (~patient(X0) | ~curious(X0)) [ennf transformation 11]
35. ! [X0] : (((curious(X0) | ~wise(X0)) | (~quiet(X0) | ~patient(X0))) & ((quiet(X0) & patient(X0)) | (~curious(X0) & wise(X0)))) [nnf transformation 1]
36. ! [X0] : ((curious(X0) | ~wise(X0) | ~quiet(X0) | ~patient(X0)) & ((quiet(X0) & patient(X0)) | (~curious(X0) & wise(X0)))) [flattening 35]
65. patient(X0) | ~curious(X0) [cnf transformation 36]
101. ~patient(X0) | ~curious(X0) [cnf transformation 30]
127. curious(alice) [cnf transformation 23]
186. ~curious(X0) [subsumption resolution 101,65]
262. $false [subsumption resolution 127,186]
% SZS output end Proof for 4424039270103003656524118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then paul is both brave and not quiet.
If john is creative or not rich then fred is either not quiet or quiet and vice versa.
If someone is both not creative and happy then fred is either generous or not curious and vice versa.
Everyone who is either patient or not old is either not kind or not brave and vice versa.
If someone is generous then mary is funny and vice versa.
If someone is not kind then someone is both not brave and calm and vice versa.
If someone is both not brave and not happy then mary is either not rich or not curious and vice versa.
Everyone who is not tall or happy is both tall and not quiet and vice versa.
Everyone who is either wise or not tall is both not patient and strong and vice versa.
Everyone who is funny or patient is both not rich and rich.
Everyone who is either curious or not strong is not humble or generous.
If someone is not happy or not creative then alice is not tall or quiet and vice versa.
Everyone who is both patient and brave is either kind or not brave and vice versa.
If paul is both not tall and calm then john is both curious and not kind and vice versa.
If someone is not creative or not rich then someone is strong or not wise.
Mary is not rich or not strong.
Someone is old or not quiet.
John is both not old and tall.
Mary is not creative.
Someone is either not brave or not patient.
Someone is not brave or quiet.
Someone is not patient.
Someone is either not patient or not quiet. | Alice is not tall. | contradiction | ((?[X]:(funny(X)))=>((brave(paul)&~quiet(paul))))&
(((creative(john)|~rich(john)))<=>((~quiet(fred)<~>quiet(fred))))&
((?[X]:((~creative(X)&happy(X))))<=>((generous(fred)<~>~curious(fred))))&
(![X]:((patient(X)<~>~old(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:(generous(X)))<=>(funny(mary)))&
((?[X]:(~kind(X)))<=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((~brave(X)&~happy(X))))<=>((~rich(mary)<~>~curious(mary))))&
(![X]:((~tall(X)|happy(X))<=>(tall(X)&~quiet(X))))&
(![X]:((wise(X)<~>~tall(X))<=>(~patient(X)&strong(X))))&
(![X]:((funny(X)|patient(X))=>(~rich(X)&rich(X))))&
(![X]:((curious(X)<~>~strong(X))=>(~humble(X)|generous(X))))&
((?[X]:((~happy(X)|~creative(X))))<=>((~tall(alice)|quiet(alice))))&
(![X]:((patient(X)&brave(X))<=>(kind(X)<~>~brave(X))))&
(((~tall(paul)&calm(paul)))<=>((curious(john)&~kind(john))))&
((?[X]:((~creative(X)|~rich(X))))=>(?[X]:((strong(X)|~wise(X)))))&
((~rich(mary)|~strong(mary)))&
(?[X]:((old(X)|~quiet(X))))&
((~old(john)&tall(john)))&
(~creative(mary))&
(?[X]:((~brave(X)<~>~patient(X))))&
(?[X]:((~brave(X)|quiet(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~patient(X)<~>~quiet(X)))) | ~tall(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8072111969288916655710411
% SZS output start Proof for 8072111969288916655710411
8. ! [X0] : ((happy(X0) | ~tall(X0)) <=> (~quiet(X0) & tall(X0))) [input p7]
24. ~tall(alice) [input hypothesis]
51. ! [X0] : (((happy(X0) | ~tall(X0)) | (quiet(X0) | ~tall(X0))) & ((~quiet(X0) & tall(X0)) | (~happy(X0) & tall(X0)))) [nnf transformation 8]
52. ! [X0] : ((happy(X0) | ~tall(X0) | quiet(X0) | ~tall(X0)) & ((~quiet(X0) & tall(X0)) | (~happy(X0) & tall(X0)))) [flattening 51]
112. tall(X0) | tall(X0) [cnf transformation 52]
154. ~tall(alice) [cnf transformation 24]
157. tall(X0) [duplicate literal removal 112]
342. $false [subsumption resolution 154,157]
% SZS output end Proof for 8072111969288916655710411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and not curious then someone is both not rich and brave.
Everyone who is not curious or creative is either not generous or not happy.
If paul is brave then someone is not strong.
Everyone who is either not brave or rich is not happy or happy.
Everyone who is kind or not brave is not creative and vice versa.
Everyone who is not kind or curious is not humble.
Everyone who is both not curious and funny is either not happy or brave and vice versa.
Everyone who is either curious or creative is either brave or kind.
If someone is either not happy or not calm then paul is both funny and kind and vice versa.
Everyone who is both generous and happy is both old and not rich and vice versa.
Everyone who is curious or tall is not brave.
Everyone who is either wise or not rich is both creative and quiet and vice versa.
Everyone who is either humble or old is either kind or tall.
Everyone who is patient or not kind is both wise and not happy.
If someone is not strong then someone is both strong and brave.
Everyone who is not tall or not curious is both not patient and not strong and vice versa.
Someone is both not funny and curious.
Someone is brave or not funny.
Someone is funny.
Someone is either brave or not creative.
Someone is either not strong or strong. | Paul is not old. | entailment | ((?[X]:((~happy(X)&~curious(X))))=>(?[X]:((~rich(X)&brave(X)))))&
(![X]:((~curious(X)|creative(X))=>(~generous(X)<~>~happy(X))))&
((brave(paul))=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~happy(X)|happy(X))))&
(![X]:((kind(X)|~brave(X))<=>~creative(X)))&
(![X]:((~kind(X)|curious(X))=>~humble(X)))&
(![X]:((~curious(X)&funny(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((curious(X)<~>creative(X))=>(brave(X)<~>kind(X))))&
((?[X]:((~happy(X)<~>~calm(X))))<=>((funny(paul)&kind(paul))))&
(![X]:((generous(X)&happy(X))<=>(old(X)&~rich(X))))&
(![X]:((curious(X)|tall(X))=>~brave(X)))&
(![X]:((wise(X)<~>~rich(X))<=>(creative(X)&quiet(X))))&
(![X]:((humble(X)<~>old(X))=>(kind(X)<~>tall(X))))&
(![X]:((patient(X)|~kind(X))=>(wise(X)&~happy(X))))&
((?[X]:(~strong(X)))=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((~tall(X)|~curious(X))<=>(~patient(X)&~strong(X))))&
(?[X]:((~funny(X)&curious(X))))&
(?[X]:((brave(X)|~funny(X))))&
(?[X]:(funny(X)))&
(?[X]:((brave(X)<~>~creative(X))))&
(?[X]:((~strong(X)<~>strong(X)))) | ~old(paul) | [
"p5",
"p6",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 983112647123978827637321
% SZS output start Proof for 983112647123978827637321
6. ! [X0] : ((curious(X0) | ~kind(X0)) => ~humble(X0)) [input p5]
7. ! [X0] : ((funny(X0) & ~curious(X0)) <=> (~happy(X0) <~> brave(X0))) [input p6]
11. ! [X0] : ((tall(X0) | curious(X0)) => ~brave(X0)) [input p10]
13. ! [X0] : ((humble(X0) <~> old(X0)) => (kind(X0) <~> tall(X0))) [input p12]
14. ! [X0] : ((~kind(X0) | patient(X0)) => (~happy(X0) & wise(X0))) [input p13]
15. ? [X0] : ~strong(X0) => ? [X0] : (brave(X0) & strong(X0)) [input p14]
16. ! [X0] : ((~curious(X0) | ~tall(X0)) <=> (~strong(X0) & ~patient(X0))) [input p15]
22. old(paul) [input hypothesis]
24. ? [X0] : ~strong(X0) => ? [X1] : (brave(X1) & strong(X1)) [rectify 15]
30. ! [X0] : (~humble(X0) | (~curious(X0) & kind(X0))) [ennf transformation 6]
32. ! [X0] : (~brave(X0) | (~tall(X0) & ~curious(X0))) [ennf transformation 11]
33. ! [X0] : ((kind(X0) <~> tall(X0)) | (humble(X0) <=> old(X0))) [ennf transformation 13]
34. ! [X0] : ((~happy(X0) & wise(X0)) | (kind(X0) & ~patient(X0))) [ennf transformation 14]
35. ? [X1] : (brave(X1) & strong(X1)) | ! [X0] : strong(X0) [ennf transformation 24]
45. ! [X0] : (((funny(X0) & ~curious(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) | curious(X0)))) [nnf transformation 7]
46. ! [X0] : (((funny(X0) & ~curious(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ~funny(X0) | curious(X0))) [flattening 45]
57. ! [X0] : (((~tall(X0) | ~kind(X0)) & (tall(X0) | kind(X0))) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0)))) [nnf transformation 33]
58. ? [X0] : (brave(X0) & strong(X0)) | ! [X1] : strong(X1) [rectify 35]
59. ? [X0] : (brave(X0) & strong(X0)) => (brave(sK3) & strong(sK3)) [choice axiom]
60. (brave(sK3) & strong(sK3)) | ! [X1] : strong(X1) [skolemisation 58,59]
61. ! [X0] : (((~curious(X0) | ~tall(X0)) | (strong(X0) | patient(X0))) & ((~strong(X0) & ~patient(X0)) | (curious(X0) & tall(X0)))) [nnf transformation 16]
62. ! [X0] : ((~curious(X0) | ~tall(X0) | strong(X0) | patient(X0)) & ((~strong(X0) & ~patient(X0)) | (curious(X0) & tall(X0)))) [flattening 61]
88. ~humble(X0) | ~curious(X0) [cnf transformation 30]
91. ~curious(X0) | brave(X0) | happy(X0) [cnf transformation 46]
109. ~brave(X0) | ~curious(X0) [cnf transformation 32]
110. ~tall(X0) | ~brave(X0) [cnf transformation 32]
120. ~tall(X0) | ~kind(X0) | humble(X0) | ~old(X0) [cnf transformation 57]
124. ~happy(X0) | kind(X0) [cnf transformation 34]
125. strong(sK3) | strong(X1) [cnf transformation 60]
126. brave(sK3) | strong(X1) [cnf transformation 60]
129. ~strong(X0) | tall(X0) [cnf transformation 62]
130. ~strong(X0) | curious(X0) [cnf transformation 62]
140. old(paul) [cnf transformation 22]
196. 12 <=> ! [X1] : strong(X1) [avatar definition]
197. strong(X1) <- (12) [avatar component clause 196]
199. 13 <=> brave(sK3) [avatar definition]
201. brave(sK3) <- (13) [avatar component clause 199]
202. 12 | 13 [avatar split clause 126,199,196]
204. 14 <=> strong(sK3) [avatar definition]
206. strong(sK3) <- (14) [avatar component clause 204]
207. 12 | 14 [avatar split clause 125,204,196]
239. ~curious(sK3) <- (13) [resolution 201,109]
240. curious(sK3) <- (14) [resolution 206,130]
242. $false <- (13, 14) [subsumption resolution 240,239]
243. ~13 | ~14 [avatar contradiction clause 242]
244. curious(X0) <- (12) [resolution 197,130]
245. tall(X1) <- (12) [resolution 197,129]
252. ~brave(X0) <- (12) [resolution 245,110]
255. brave(X0) | happy(X0) <- (12) [resolution 91,244]
260. happy(X0) <- (12) [subsumption resolution 255,252]
265. kind(X0) <- (12) [resolution 260,124]
327. ~kind(X0) | humble(X0) | ~old(X0) <- (12) [resolution 120,245]
331. ~old(X0) | humble(X0) <- (12) [subsumption resolution 327,265]
334. humble(paul) <- (12) [resolution 331,140]
336. ~curious(paul) <- (12) [resolution 334,88]
338. $false <- (12) [subsumption resolution 336,244]
339. ~12 [avatar contradiction clause 338]
340. $false [avatar sat refutation 202,207,243,339]
% SZS output end Proof for 983112647123978827637321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or tall then someone is not curious or brave and vice versa. Everyone who is creative or not tall is both quiet and old. If someone is both curious and not old then fred is both quiet and not funny and vice versa. Everyone who is either not curious or not wise is quiet or not brave. If alice is either tall or quiet then someone is kind. Everyone who is not humble is either funny or not generous and vice versa. If someone is both humble and not brave then someone is either patient or not rich. Everyone who is not wise is happy or old and vice versa. If paul is humble then someone is either not patient or not happy. Everyone who is both happy and generous is both not creative and brave and vice versa. Everyone who is both brave and strong is wise. If alice is rich then someone is not calm or kind and vice versa. If someone is creative then susan is generous or kind. Everyone who is kind or not wise is both not quiet and not kind and vice versa. Everyone who is tall or not wise is not humble. Everyone who is not patient is not rich or not happy. Alice is either brave or quiet. Someone is not quiet or not patient. Someone is both not strong and not humble. Paul is either brave or not happy. Alice is not kind. Someone is funny or not creative. | Fred is not humble. | entailment | (((~kind(paul)|tall(paul)))<=>(?[X]:((~curious(X)|brave(X)))))&
(![X]:((creative(X)|~tall(X))=>(quiet(X)&old(X))))&
((?[X]:((curious(X)&~old(X))))<=>((quiet(fred)&~funny(fred))))&
(![X]:((~curious(X)<~>~wise(X))=>(quiet(X)|~brave(X))))&
(((tall(alice)<~>quiet(alice)))=>(?[X]:(kind(X))))&
(![X]:(~humble(X)<=>(funny(X)<~>~generous(X))))&
((?[X]:((humble(X)&~brave(X))))=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:(~wise(X)<=>(happy(X)|old(X))))&
((humble(paul))=>(?[X]:((~patient(X)<~>~happy(X)))))&
(![X]:((happy(X)&generous(X))<=>(~creative(X)&brave(X))))&
(![X]:((brave(X)&strong(X))=>wise(X)))&
((rich(alice))<=>(?[X]:((~calm(X)|kind(X)))))&
((?[X]:(creative(X)))=>((generous(susan)|kind(susan))))&
(![X]:((kind(X)|~wise(X))<=>(~quiet(X)&~kind(X))))&
(![X]:((tall(X)|~wise(X))=>~humble(X)))&
(![X]:(~patient(X)=>(~rich(X)|~happy(X))))&
((brave(alice)<~>quiet(alice)))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((~strong(X)&~humble(X))))&
((brave(paul)<~>~happy(paul)))&
(~kind(alice))&
(?[X]:((funny(X)|~creative(X)))) | ~humble(fred) | [
"p1",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6368243334625326253260782
% SZS output start Proof for 6368243334625326253260782
2. ! [X0] : ((~tall(X0) | creative(X0)) => (old(X0) & quiet(X0))) [input p1]
8. ! [X0] : (~wise(X0) <=> (old(X0) | happy(X0))) [input p7]
14. ! [X0] : ((~wise(X0) | kind(X0)) <=> (~kind(X0) & ~quiet(X0))) [input p13]
15. ! [X0] : ((~wise(X0) | tall(X0)) => ~humble(X0)) [input p14]
23. humble(fred) [input hypothesis]
27. ! [X0] : ((old(X0) & quiet(X0)) | (tall(X0) & ~creative(X0))) [ennf transformation 2]
35. ! [X0] : (~humble(X0) | (wise(X0) & ~tall(X0))) [ennf transformation 15]
57. ! [X0] : ((~wise(X0) | (~old(X0) & ~happy(X0))) & ((old(X0) | happy(X0)) | wise(X0))) [nnf transformation 8]
58. ! [X0] : ((~wise(X0) | (~old(X0) & ~happy(X0))) & (old(X0) | happy(X0) | wise(X0))) [flattening 57]
68. ! [X0] : (((~wise(X0) | kind(X0)) | (kind(X0) | quiet(X0))) & ((~kind(X0) & ~quiet(X0)) | (wise(X0) & ~kind(X0)))) [nnf transformation 14]
69. ! [X0] : ((~wise(X0) | kind(X0) | kind(X0) | quiet(X0)) & ((~kind(X0) & ~quiet(X0)) | (wise(X0) & ~kind(X0)))) [flattening 68]
83. quiet(X0) | tall(X0) [cnf transformation 27]
85. old(X0) | tall(X0) [cnf transformation 27]
102. ~wise(X0) | ~old(X0) [cnf transformation 58]
114. ~quiet(X0) | wise(X0) [cnf transformation 69]
118. ~humble(X0) | ~tall(X0) [cnf transformation 35]
129. humble(fred) [cnf transformation 23]
159. 7 <=> quiet(fred) [avatar definition]
160. quiet(fred) <- (7) [avatar component clause 159]
161. ~quiet(fred) <- (~7) [avatar component clause 159]
296. wise(fred) <- (7) [resolution 114,160]
299. ~old(fred) <- (7) [resolution 296,102]
300. ~tall(fred) [resolution 118,129]
303. tall(fred) <- (7) [resolution 299,85]
304. $false <- (7) [subsumption resolution 303,300]
305. ~7 [avatar contradiction clause 304]
306. tall(fred) <- (~7) [resolution 161,83]
307. $false <- (~7) [subsumption resolution 306,300]
308. 7 [avatar contradiction clause 307]
309. $false [avatar sat refutation 305,308]
% SZS output end Proof for 6368243334625326253260782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not rich is not humble or quiet and vice versa. If mary is both humble and funny then mary is rich or not happy and vice versa. If fred is both old and strong then lucy is funny and vice versa. If alice is not generous or humble then mary is not strong or rich and vice versa. Everyone who is strong or quiet is happy or not tall and vice versa. Everyone who is both not rich and old is either not rich or patient and vice versa. Everyone who is both tall and not happy is rich or patient and vice versa. Everyone who is either old or not creative is either curious or calm and vice versa. If someone is either not happy or calm then someone is not calm or kind and vice versa. Everyone who is either not happy or wise is tall or not curious and vice versa. If someone is not kind then fred is either not old or quiet and vice versa. Everyone who is either rich or not happy is either generous or strong and vice versa. If someone is both not quiet and not humble then john is both humble and not strong. Everyone who is both calm and rich is calm or curious and vice versa. If fred is both generous and patient then lucy is either kind or calm. Everyone who is not happy is patient and vice versa. Mary is humble or not humble. Alice is either not curious or not tall. Someone is both kind and not calm. Someone is either not wise or strong. Paul is both humble and tall. John is not old or not funny. Fred is either not strong or funny. | Fred is not curious. | entailment | (![X]:((rich(X)&~rich(X))<=>(~humble(X)|quiet(X))))&
(((humble(mary)&funny(mary)))<=>((rich(mary)|~happy(mary))))&
(((old(fred)&strong(fred)))<=>(funny(lucy)))&
(((~generous(alice)|humble(alice)))<=>((~strong(mary)|rich(mary))))&
(![X]:((strong(X)|quiet(X))<=>(happy(X)|~tall(X))))&
(![X]:((~rich(X)&old(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((tall(X)&~happy(X))<=>(rich(X)|patient(X))))&
(![X]:((old(X)<~>~creative(X))<=>(curious(X)<~>calm(X))))&
((?[X]:((~happy(X)<~>calm(X))))<=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((~happy(X)<~>wise(X))<=>(tall(X)|~curious(X))))&
((?[X]:(~kind(X)))<=>((~old(fred)<~>quiet(fred))))&
(![X]:((rich(X)<~>~happy(X))<=>(generous(X)<~>strong(X))))&
((?[X]:((~quiet(X)&~humble(X))))=>((humble(john)&~strong(john))))&
(![X]:((calm(X)&rich(X))<=>(calm(X)|curious(X))))&
(((generous(fred)&patient(fred)))=>((kind(lucy)<~>calm(lucy))))&
(![X]:(~happy(X)<=>patient(X)))&
((humble(mary)|~humble(mary)))&
((~curious(alice)<~>~tall(alice)))&
(?[X]:((kind(X)&~calm(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
((humble(paul)&tall(paul)))&
((~old(john)|~funny(john)))&
((~strong(fred)<~>funny(fred))) | ~curious(fred) | [
"p5",
"p6",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7271220769409870867276601
% SZS output start Proof for 7271220769409870867276601
6. ! [X0] : ((old(X0) & ~rich(X0)) <=> (~rich(X0) <~> patient(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & tall(X0)) <=> (patient(X0) | rich(X0))) [input p6]
14. ! [X0] : ((rich(X0) & calm(X0)) <=> (curious(X0) | calm(X0))) [input p13]
16. ! [X0] : (~happy(X0) <=> patient(X0)) [input p15]
24. curious(fred) [input hypothesis]
39. ! [X0] : (((old(X0) & ~rich(X0)) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0)))) & (((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (~old(X0) | rich(X0)))) [nnf transformation 6]
40. ! [X0] : (((old(X0) & ~rich(X0)) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0)))) & (((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ~old(X0) | rich(X0))) [flattening 39]
41. ! [X0] : (((~happy(X0) & tall(X0)) | (~patient(X0) & ~rich(X0))) & ((patient(X0) | rich(X0)) | (happy(X0) | ~tall(X0)))) [nnf transformation 7]
42. ! [X0] : (((~happy(X0) & tall(X0)) | (~patient(X0) & ~rich(X0))) & (patient(X0) | rich(X0) | happy(X0) | ~tall(X0))) [flattening 41]
56. ! [X0] : (((rich(X0) & calm(X0)) | (~curious(X0) & ~calm(X0))) & ((curious(X0) | calm(X0)) | (~rich(X0) | ~calm(X0)))) [nnf transformation 14]
57. ! [X0] : (((rich(X0) & calm(X0)) | (~curious(X0) & ~calm(X0))) & (curious(X0) | calm(X0) | ~rich(X0) | ~calm(X0))) [flattening 56]
59. ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))) [nnf transformation 16]
91. ~rich(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 40]
97. ~happy(X0) | ~rich(X0) [cnf transformation 42]
135. ~curious(X0) | calm(X0) [cnf transformation 57]
136. ~calm(X0) | rich(X0) [cnf transformation 57]
140. patient(X0) | happy(X0) [cnf transformation 59]
154. curious(fred) [cnf transformation 24]
156. ~patient(X0) | ~rich(X0) [duplicate literal removal 91]
307. calm(fred) [resolution 135,154]
309. rich(fred) [resolution 136,307]
321. ~rich(X0) | happy(X0) [resolution 156,140]
322. ~rich(X0) [subsumption resolution 321,97]
323. $false [resolution 322,309]
% SZS output end Proof for 7271220769409870867276601
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and not humble then mary is both happy and not quiet. If someone is not humble then paul is both not patient and not creative and vice versa. If someone is either not tall or generous then mary is both not brave and not happy and vice versa. If someone is creative or not quiet then someone is both strong and not strong. If mary is calm or not happy then paul is both not tall and old. If mary is either not strong or kind then someone is either not quiet or not happy and vice versa. If someone is both tall and calm then someone is either not generous or not curious and vice versa. If someone is both calm and not rich then john is strong and vice versa. Everyone who is either old or patient is either not patient or not calm. If someone is not calm or happy then someone is creative or strong. Everyone who is generous or wise is curious or not happy and vice versa. Everyone who is not calm or strong is generous. Everyone who is creative is not strong or not brave. Everyone who is not strong is wise or not curious. If someone is patient or not creative then paul is funny. Someone is kind or happy. Mary is tall. Someone is not humble. Paul is either wise or not tall. Fred is curious or old. Lucy is curious. | Fred is not creative. | entailment | ((?[X]:((~patient(X)&~humble(X))))=>((happy(mary)&~quiet(mary))))&
((?[X]:(~humble(X)))<=>((~patient(paul)&~creative(paul))))&
((?[X]:((~tall(X)<~>generous(X))))<=>((~brave(mary)&~happy(mary))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(((calm(mary)|~happy(mary)))=>((~tall(paul)&old(paul))))&
(((~strong(mary)<~>kind(mary)))<=>(?[X]:((~quiet(X)<~>~happy(X)))))&
((?[X]:((tall(X)&calm(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((calm(X)&~rich(X))))<=>(strong(john)))&
(![X]:((old(X)<~>patient(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:((~calm(X)|happy(X))))=>(?[X]:((creative(X)|strong(X)))))&
(![X]:((generous(X)|wise(X))<=>(curious(X)|~happy(X))))&
(![X]:((~calm(X)|strong(X))=>generous(X)))&
(![X]:(creative(X)=>(~strong(X)|~brave(X))))&
(![X]:(~strong(X)=>(wise(X)|~curious(X))))&
((?[X]:((patient(X)|~creative(X))))=>(funny(paul)))&
(?[X]:((kind(X)|happy(X))))&
(tall(mary))&
(?[X]:(~humble(X)))&
((wise(paul)<~>~tall(paul)))&
((curious(fred)|old(fred)))&
(curious(lucy)) | ~creative(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7828375201487351997267568
% SZS output start Proof for 7828375201487351997267568
4. ? [X0] : (~quiet(X0) | creative(X0)) => ? [X0] : (~strong(X0) & strong(X0)) [input p3]
22. creative(fred) [input hypothesis]
23. ? [X0] : (~quiet(X0) | creative(X0)) => ? [X1] : (~strong(X1) & strong(X1)) [rectify 4]
28. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (quiet(X0) & ~creative(X0)) [ennf transformation 23]
47. ? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (quiet(X1) & ~creative(X1)) [rectify 28]
48. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK2) & strong(sK2)) [choice axiom]
49. (~strong(sK2) & strong(sK2)) | ! [X1] : (quiet(X1) & ~creative(X1)) [skolemisation 47,48]
85. strong(sK2) | ~creative(X1) [cnf transformation 49]
87. ~strong(sK2) | ~creative(X1) [cnf transformation 49]
131. creative(fred) [cnf transformation 22]
193. 14 <=> strong(sK2) [avatar definition]
198. 15 <=> ! [X1] : ~creative(X1) [avatar definition]
199. ~creative(X1) <- (15) [avatar component clause 198]
200. 15 | ~14 [avatar split clause 87,193,198]
202. 15 | 14 [avatar split clause 85,193,198]
340. $false <- (15) [resolution 199,131]
341. ~15 [avatar contradiction clause 340]
342. $false [avatar sat refutation 200,202,341]
% SZS output end Proof for 7828375201487351997267568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not patient is both creative and not old.
Everyone who is both strong and wise is either not creative or not kind and vice versa.
If someone is both curious and strong then susan is not curious and vice versa.
Everyone who is both old and generous is either funny or rich.
Everyone who is either not kind or tall is not creative.
If someone is not curious then someone is both kind and not rich and vice versa.
Everyone who is wise or not creative is not patient and vice versa.
Everyone who is either quiet or brave is not calm.
Everyone who is both not funny and not generous is either not creative or tall and vice versa.
Everyone who is creative or not happy is not funny or happy.
If someone is wise or funny then susan is either curious or not generous.
Everyone who is humble is either humble or not strong.
If someone is both not kind and not funny then someone is not old or generous.
If someone is generous or not generous then someone is not old or old.
Everyone who is both old and not old is either tall or happy and vice versa.
John is rich.
Mary is happy.
Mary is either quiet or not funny.
Susan is not creative or brave.
Fred is either not creative or happy.
Alice is calm or not creative.
Paul is both not funny and not patient.
Someone is quiet or humble. | Fred is not patient. | entailment | (![X]:((~funny(X)|~patient(X))=>(creative(X)&~old(X))))&
(![X]:((strong(X)&wise(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:((curious(X)&strong(X))))<=>(~curious(susan)))&
(![X]:((old(X)&generous(X))=>(funny(X)<~>rich(X))))&
(![X]:((~kind(X)<~>tall(X))=>~creative(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((kind(X)&~rich(X)))))&
(![X]:((wise(X)|~creative(X))<=>~patient(X)))&
(![X]:((quiet(X)<~>brave(X))=>~calm(X)))&
(![X]:((~funny(X)&~generous(X))<=>(~creative(X)<~>tall(X))))&
(![X]:((creative(X)|~happy(X))=>(~funny(X)|happy(X))))&
((?[X]:((wise(X)|funny(X))))=>((curious(susan)<~>~generous(susan))))&
(![X]:(humble(X)=>(humble(X)<~>~strong(X))))&
((?[X]:((~kind(X)&~funny(X))))=>(?[X]:((~old(X)|generous(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(?[X]:((~old(X)|old(X)))))&
(![X]:((old(X)&~old(X))<=>(tall(X)<~>happy(X))))&
(rich(john))&
(happy(mary))&
((quiet(mary)<~>~funny(mary)))&
((~creative(susan)|brave(susan)))&
((~creative(fred)<~>happy(fred)))&
((calm(alice)|~creative(alice)))&
((~funny(paul)&~patient(paul)))&
(?[X]:((quiet(X)|humble(X)))) | ~patient(fred) | [
"p0",
"p1",
"p4",
"p6",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7012322526621950268881001
% SZS output start Proof for 7012322526621950268881001
1. ! [X0] : ((~patient(X0) | ~funny(X0)) => (~old(X0) & creative(X0))) [input p0]
2. ! [X0] : ((wise(X0) & strong(X0)) <=> (~creative(X0) <~> ~kind(X0))) [input p1]
5. ! [X0] : ((~kind(X0) <~> tall(X0)) => ~creative(X0)) [input p4]
7. ! [X0] : ((~creative(X0) | wise(X0)) <=> ~patient(X0)) [input p6]
15. ! [X0] : ((~old(X0) & old(X0)) <=> (tall(X0) <~> happy(X0))) [input p14]
20. ~creative(fred) <~> happy(fred) [input p19]
24. patient(fred) [input hypothesis]
28. ! [X0] : ((~old(X0) & creative(X0)) | (patient(X0) & funny(X0))) [ennf transformation 1]
31. ! [X0] : (~creative(X0) | (~kind(X0) <=> tall(X0))) [ennf transformation 5]
39. ! [X0] : (((wise(X0) & strong(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0)))) & (((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (~wise(X0) | ~strong(X0)))) [nnf transformation 2]
40. ! [X0] : (((wise(X0) & strong(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0)))) & (((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | ~wise(X0) | ~strong(X0))) [flattening 39]
46. ! [X0] : (~creative(X0) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0)))) [nnf transformation 31]
52. ! [X0] : (((~creative(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (creative(X0) & ~wise(X0)))) [nnf transformation 7]
53. ! [X0] : ((~creative(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (creative(X0) & ~wise(X0)))) [flattening 52]
65. ! [X0] : (((~old(X0) & old(X0)) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) & (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | (old(X0) | ~old(X0)))) [nnf transformation 15]
66. ! [X0] : (((~old(X0) & old(X0)) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) & (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | old(X0) | ~old(X0))) [flattening 65]
68. (~happy(fred) | creative(fred)) & (happy(fred) | ~creative(fred)) [nnf transformation 20]
72. creative(X0) | patient(X0) [cnf transformation 28]
80. ~creative(X0) | wise(X0) | kind(X0) [cnf transformation 40]
87. ~tall(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 46]
91. ~wise(X0) | ~patient(X0) [cnf transformation 53]
92. ~patient(X0) | creative(X0) [cnf transformation 53]
116. old(X0) | tall(X0) | ~happy(X0) [cnf transformation 66]
118. ~happy(X0) | tall(X0) | ~old(X0) [cnf transformation 66]
124. happy(fred) | ~creative(fred) [cnf transformation 68]
130. patient(fred) [cnf transformation 24]
174. creative(X0) [subsumption resolution 92,72]
204. ~happy(X0) | tall(X0) [subsumption resolution 116,118]
217. happy(fred) [subsumption resolution 124,174]
234. tall(fred) [resolution 204,217]
248. kind(X2) | wise(X2) [resolution 80,174]
256. ~kind(fred) | ~creative(fred) [resolution 87,234]
258. ~kind(fred) [subsumption resolution 256,174]
312. wise(fred) [resolution 248,258]
324. ~patient(fred) [resolution 312,91]
325. $false [subsumption resolution 324,130]
% SZS output end Proof for 7012322526621950268881001
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not happy is not generous and vice versa. If alice is either creative or not patient then someone is old and vice versa. Everyone who is patient or not patient is not funny and vice versa. Everyone who is either rich or not strong is either brave or tall and vice versa. Everyone who is not humble or not tall is either calm or not creative and vice versa. Everyone who is either kind or old is not generous or not patient. If someone is both funny and kind then someone is both not strong and generous. If someone is both happy and not old then susan is either not tall or not patient and vice versa. If someone is kind or not kind then someone is either funny or not calm. Everyone who is both calm and not old is either wise or not funny. If john is both old and humble then fred is generous or wise and vice versa. Everyone who is both old and not kind is both wise and not brave. If someone is happy or patient then paul is not curious or not humble. If someone is not funny then someone is either calm or curious and vice versa. Everyone who is not kind or not patient is not curious and vice versa. If john is funny then someone is quiet and vice versa. Someone is both not creative and not happy. Someone is both not kind and calm. Fred is not happy or generous. Fred is either not curious or not quiet. Someone is old. Someone is creative. Susan is not creative or kind. Alice is either old or tall. | Fred is not funny. | entailment | (![X]:((~patient(X)&~happy(X))<=>~generous(X)))&
(((creative(alice)<~>~patient(alice)))<=>(?[X]:(old(X))))&
(![X]:((patient(X)|~patient(X))<=>~funny(X)))&
(![X]:((rich(X)<~>~strong(X))<=>(brave(X)<~>tall(X))))&
(![X]:((~humble(X)|~tall(X))<=>(calm(X)<~>~creative(X))))&
(![X]:((kind(X)<~>old(X))=>(~generous(X)|~patient(X))))&
((?[X]:((funny(X)&kind(X))))=>(?[X]:((~strong(X)&generous(X)))))&
((?[X]:((happy(X)&~old(X))))<=>((~tall(susan)<~>~patient(susan))))&
((?[X]:((kind(X)|~kind(X))))=>(?[X]:((funny(X)<~>~calm(X)))))&
(![X]:((calm(X)&~old(X))=>(wise(X)<~>~funny(X))))&
(((old(john)&humble(john)))<=>((generous(fred)|wise(fred))))&
(![X]:((old(X)&~kind(X))=>(wise(X)&~brave(X))))&
((?[X]:((happy(X)|patient(X))))=>((~curious(paul)|~humble(paul))))&
((?[X]:(~funny(X)))<=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:((~kind(X)|~patient(X))<=>~curious(X)))&
((funny(john))<=>(?[X]:(quiet(X))))&
(?[X]:((~creative(X)&~happy(X))))&
(?[X]:((~kind(X)&calm(X))))&
((~happy(fred)|generous(fred)))&
((~curious(fred)<~>~quiet(fred)))&
(?[X]:(old(X)))&
(?[X]:(creative(X)))&
((~creative(susan)|kind(susan)))&
((old(alice)<~>tall(alice))) | ~funny(fred) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 3957972350169887183747593
% SZS output start Proof for 3957972350169887183747593
3. ! [X0] : ((~patient(X0) | patient(X0)) <=> ~funny(X0)) [input p2]
25. funny(fred) [input hypothesis]
45. ! [X0] : (((~patient(X0) | patient(X0)) | funny(X0)) & (~funny(X0) | (patient(X0) & ~patient(X0)))) [nnf transformation 3]
46. ! [X0] : ((~patient(X0) | patient(X0) | funny(X0)) & (~funny(X0) | (patient(X0) & ~patient(X0)))) [flattening 45]
93. ~funny(X0) | ~patient(X0) [cnf transformation 46]
94. ~funny(X0) | patient(X0) [cnf transformation 46]
156. funny(fred) [cnf transformation 25]
176. ~funny(X0) [subsumption resolution 93,94]
289. $false [subsumption resolution 156,176]
% SZS output end Proof for 3957972350169887183747593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and patient is not happy or not tall and vice versa.
If alice is both not humble and wise then alice is either patient or quiet and vice versa.
If paul is old then someone is both patient and not humble and vice versa.
Everyone who is not wise or rich is happy or wise.
If someone is not tall then someone is brave.
If fred is both not kind and not strong then someone is not rich or patient.
Everyone who is both not wise and not happy is happy or not calm.
Everyone who is both not strong and not funny is creative or not humble.
Everyone who is either not kind or not old is both old and not quiet and vice versa.
If someone is both funny and not wise then john is wise or funny.
If john is creative or not happy then paul is curious or not strong and vice versa.
If someone is both not curious and strong then someone is either patient or kind.
Everyone who is rich is not strong.
Everyone who is either not tall or not kind is not curious.
If paul is generous then someone is rich and vice versa.
Everyone who is funny or quiet is either not old or not quiet.
Alice is both not humble and not generous.
Alice is happy.
Paul is calm or quiet.
Someone is not happy or humble.
Lucy is not curious.
Lucy is not old.
Someone is not tall or tall. | Paul is calm. | neutral | (![X]:((~happy(X)&patient(X))<=>(~happy(X)|~tall(X))))&
(((~humble(alice)&wise(alice)))<=>((patient(alice)<~>quiet(alice))))&
((old(paul))<=>(?[X]:((patient(X)&~humble(X)))))&
(![X]:((~wise(X)|rich(X))=>(happy(X)|wise(X))))&
((?[X]:(~tall(X)))=>(?[X]:(brave(X))))&
(((~kind(fred)&~strong(fred)))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((~wise(X)&~happy(X))=>(happy(X)|~calm(X))))&
(![X]:((~strong(X)&~funny(X))=>(creative(X)|~humble(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(old(X)&~quiet(X))))&
((?[X]:((funny(X)&~wise(X))))=>((wise(john)|funny(john))))&
(((creative(john)|~happy(john)))<=>((curious(paul)|~strong(paul))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((patient(X)<~>kind(X)))))&
(![X]:(rich(X)=>~strong(X)))&
(![X]:((~tall(X)<~>~kind(X))=>~curious(X)))&
((generous(paul))<=>(?[X]:(rich(X))))&
(![X]:((funny(X)|quiet(X))=>(~old(X)<~>~quiet(X))))&
((~humble(alice)&~generous(alice)))&
(happy(alice))&
((calm(paul)|quiet(paul)))&
(?[X]:((~happy(X)|humble(X))))&
(~curious(lucy))&
(~old(lucy))&
(?[X]:((~tall(X)|tall(X)))) | calm(paul) | [] | null | 0 |
Everyone who is either wise or curious is both quiet and not quiet. Everyone who is either happy or not curious is either kind or old and vice versa. If someone is not creative or strong then someone is both patient and tall and vice versa. If paul is both funny and not rich then someone is not curious and vice versa. Everyone who is brave or not curious is both patient and curious and vice versa. If susan is not strong or not rich then someone is not humble and vice versa. Everyone who is not brave or strong is not patient or not strong and vice versa. Everyone who is both not humble and generous is rich and vice versa. If someone is either not happy or tall then someone is not patient or not curious and vice versa. Everyone who is either not calm or calm is curious or creative and vice versa. Everyone who is both not rich and not calm is creative or calm. Everyone who is both not humble and not strong is either not wise or not calm. Everyone who is either creative or quiet is either not rich or humble and vice versa. Everyone who is either curious or not funny is curious or not wise and vice versa. Mary is both not humble and old. Alice is not strong. Mary is funny. Someone is happy or patient. Someone is both kind and tall. Someone is both calm and not strong. Susan is not humble or old. | Mary is curious. | entailment | (![X]:((wise(X)<~>curious(X))=>(quiet(X)&~quiet(X))))&
(![X]:((happy(X)<~>~curious(X))<=>(kind(X)<~>old(X))))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:((patient(X)&tall(X)))))&
(((funny(paul)&~rich(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((brave(X)|~curious(X))<=>(patient(X)&curious(X))))&
(((~strong(susan)|~rich(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)|strong(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~humble(X)&generous(X))<=>rich(X)))&
((?[X]:((~happy(X)<~>tall(X))))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(curious(X)|creative(X))))&
(![X]:((~rich(X)&~calm(X))=>(creative(X)|calm(X))))&
(![X]:((~humble(X)&~strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(curious(X)|~wise(X))))&
((~humble(mary)&old(mary)))&
(~strong(alice))&
(funny(mary))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:((kind(X)&tall(X))))&
(?[X]:((calm(X)&~strong(X))))&
((~humble(susan)|old(susan))) | curious(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6513034616726223962211218
% SZS output start Proof for 6513034616726223962211218
5. ! [X0] : ((~curious(X0) | brave(X0)) <=> (curious(X0) & patient(X0))) [input p4]
22. ~curious(mary) [input hypothesis]
42. ! [X0] : (((~curious(X0) | brave(X0)) | (~curious(X0) | ~patient(X0))) & ((curious(X0) & patient(X0)) | (curious(X0) & ~brave(X0)))) [nnf transformation 5]
43. ! [X0] : ((~curious(X0) | brave(X0) | ~curious(X0) | ~patient(X0)) & ((curious(X0) & patient(X0)) | (curious(X0) & ~brave(X0)))) [flattening 42]
93. curious(X0) | curious(X0) [cnf transformation 43]
144. ~curious(mary) [cnf transformation 22]
152. curious(X0) [duplicate literal removal 93]
187. 8 <=> ! [X0] : curious(X0) [avatar definition]
188. curious(X0) <- (8) [avatar component clause 187]
204. 8 [avatar split clause 152,187]
280. $false <- (8) [resolution 188,144]
281. ~8 [avatar contradiction clause 280]
282. $false [avatar sat refutation 204,281]
% SZS output end Proof for 6513034616726223962211218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and creative is both kind and old.
If someone is either humble or not strong then someone is old.
Everyone who is either not calm or wise is both not generous and patient and vice versa.
Everyone who is either not creative or old is both strong and not wise and vice versa.
Everyone who is not old is kind or generous and vice versa.
If alice is calm or wise then someone is both quiet and not creative and vice versa.
If someone is patient then mary is both creative and strong.
If mary is both old and tall then paul is either not rich or not tall and vice versa.
Everyone who is not wise is either old or not funny and vice versa.
If alice is both not quiet and not brave then alice is rich or brave.
If paul is both quiet and not generous then mary is both not strong and not wise.
Everyone who is funny is both not quiet and not curious.
Everyone who is either funny or curious is brave and vice versa.
Everyone who is not old or not tall is not rich or not humble.
Everyone who is either not wise or humble is either not humble or not brave and vice versa.
If someone is both rich and not creative then someone is happy or not patient and vice versa.
Fred is either creative or wise.
Lucy is both curious and patient.
John is humble or not creative.
Fred is either not rich or not patient.
Someone is brave.
Alice is not happy.
Someone is not curious or not brave.
Someone is not humble or creative. | Lucy is not brave. | contradiction | (![X]:((kind(X)&creative(X))=>(kind(X)&old(X))))&
((?[X]:((humble(X)<~>~strong(X))))=>(?[X]:(old(X))))&
(![X]:((~calm(X)<~>wise(X))<=>(~generous(X)&patient(X))))&
(![X]:((~creative(X)<~>old(X))<=>(strong(X)&~wise(X))))&
(![X]:(~old(X)<=>(kind(X)|generous(X))))&
(((calm(alice)|wise(alice)))<=>(?[X]:((quiet(X)&~creative(X)))))&
((?[X]:(patient(X)))=>((creative(mary)&strong(mary))))&
(((old(mary)&tall(mary)))<=>((~rich(paul)<~>~tall(paul))))&
(![X]:(~wise(X)<=>(old(X)<~>~funny(X))))&
(((~quiet(alice)&~brave(alice)))=>((rich(alice)|brave(alice))))&
(((quiet(paul)&~generous(paul)))=>((~strong(mary)&~wise(mary))))&
(![X]:(funny(X)=>(~quiet(X)&~curious(X))))&
(![X]:((funny(X)<~>curious(X))<=>brave(X)))&
(![X]:((~old(X)|~tall(X))=>(~rich(X)|~humble(X))))&
(![X]:((~wise(X)<~>humble(X))<=>(~humble(X)<~>~brave(X))))&
((?[X]:((rich(X)&~creative(X))))<=>(?[X]:((happy(X)|~patient(X)))))&
((creative(fred)<~>wise(fred)))&
((curious(lucy)&patient(lucy)))&
((humble(john)|~creative(john)))&
((~rich(fred)<~>~patient(fred)))&
(?[X]:(brave(X)))&
(~happy(alice))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:((~humble(X)|creative(X)))) | ~brave(lucy) | [
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8700355605688621255263925
% SZS output start Proof for 8700355605688621255263925
12. ! [X0] : (funny(X0) => (~curious(X0) & ~quiet(X0))) [input p11]
13. ! [X0] : ((funny(X0) <~> curious(X0)) <=> brave(X0)) [input p12]
18. patient(lucy) & curious(lucy) [input p17]
25. ~brave(lucy) [input hypothesis]
36. ! [X0] : ((~curious(X0) & ~quiet(X0)) | ~funny(X0)) [ennf transformation 12]
57. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | ~brave(X0)) & (brave(X0) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 13]
112. ~curious(X0) | ~funny(X0) [cnf transformation 36]
114. brave(X0) | funny(X0) | ~curious(X0) [cnf transformation 57]
134. curious(lucy) [cnf transformation 18]
143. ~brave(lucy) [cnf transformation 25]
247. ~curious(X0) | brave(X0) [subsumption resolution 114,112]
327. brave(lucy) [resolution 247,134]
328. $false [subsumption resolution 327,143]
% SZS output end Proof for 8700355605688621255263925
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or calm is either quiet or not humble.
If someone is brave or not calm then lucy is both not curious and not funny.
Everyone who is both curious and patient is strong or not creative and vice versa.
Everyone who is not strong is not kind or rich and vice versa.
If someone is not rich then someone is both not kind and not creative and vice versa.
If alice is old or not humble then susan is either not tall or not brave and vice versa.
If someone is not generous then someone is both kind and not old and vice versa.
Everyone who is either not rich or patient is both not happy and not calm and vice versa.
If fred is strong or quiet then someone is not kind or tall.
If someone is both tall and not generous then susan is either not calm or tall and vice versa.
If fred is not old then someone is both old and not brave and vice versa.
Everyone who is both patient and not tall is both creative and not funny and vice versa.
If lucy is humble then mary is both humble and brave.
If someone is not rich then someone is calm or not wise and vice versa.
Everyone who is not curious or not rich is either wise or brave.
Everyone who is not humble is not kind or strong.
Fred is creative.
Fred is wise or generous.
John is humble or brave.
Someone is not strong or not patient.
Susan is both not kind and rich.
Someone is either strong or not patient.
Fred is either curious or kind.
Susan is strong or not kind. | Fred is happy. | neutral | (![X]:((~quiet(X)<~>calm(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((brave(X)|~calm(X))))=>((~curious(lucy)&~funny(lucy))))&
(![X]:((curious(X)&patient(X))<=>(strong(X)|~creative(X))))&
(![X]:(~strong(X)<=>(~kind(X)|rich(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~kind(X)&~creative(X)))))&
(((old(alice)|~humble(alice)))<=>((~tall(susan)<~>~brave(susan))))&
((?[X]:(~generous(X)))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((~rich(X)<~>patient(X))<=>(~happy(X)&~calm(X))))&
(((strong(fred)|quiet(fred)))=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((tall(X)&~generous(X))))<=>((~calm(susan)<~>tall(susan))))&
((~old(fred))<=>(?[X]:((old(X)&~brave(X)))))&
(![X]:((patient(X)&~tall(X))<=>(creative(X)&~funny(X))))&
((humble(lucy))=>((humble(mary)&brave(mary))))&
((?[X]:(~rich(X)))<=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:((~curious(X)|~rich(X))=>(wise(X)<~>brave(X))))&
(![X]:(~humble(X)=>(~kind(X)|strong(X))))&
(creative(fred))&
((wise(fred)|generous(fred)))&
((humble(john)|brave(john)))&
(?[X]:((~strong(X)|~patient(X))))&
((~kind(susan)&rich(susan)))&
(?[X]:((strong(X)<~>~patient(X))))&
((curious(fred)<~>kind(fred)))&
((strong(susan)|~kind(susan))) | happy(fred) | [] | null | 0 |
Everyone who is not wise is kind or not calm.
Everyone who is not kind or not funny is both funny and not old.
If someone is both generous and not rich then someone is not generous or not happy and vice versa.
Everyone who is rich is not patient.
Everyone who is both not kind and curious is either quiet or not old and vice versa.
If paul is both creative and not strong then alice is creative and vice versa.
Everyone who is old is either not brave or not quiet.
If john is both kind and patient then someone is not generous.
If paul is either calm or wise then someone is funny.
Everyone who is calm is both creative and wise.
Everyone who is either not wise or calm is either humble or not creative and vice versa.
Everyone who is both not old and wise is either not quiet or not patient and vice versa.
If someone is not happy or wise then paul is either not funny or kind.
Everyone who is not kind is not rich or not happy and vice versa.
Everyone who is both not tall and creative is not brave and vice versa.
Everyone who is tall is not old or creative and vice versa.
John is either old or strong.
Someone is both not humble and not rich.
Someone is quiet or not creative.
Lucy is not humble.
Someone is rich or not old.
Mary is kind or not brave.
Alice is not patient or not kind. | Mary is not patient. | entailment | (![X]:(~wise(X)=>(kind(X)|~calm(X))))&
(![X]:((~kind(X)|~funny(X))=>(funny(X)&~old(X))))&
((?[X]:((generous(X)&~rich(X))))<=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:(rich(X)=>~patient(X)))&
(![X]:((~kind(X)&curious(X))<=>(quiet(X)<~>~old(X))))&
(((creative(paul)&~strong(paul)))<=>(creative(alice)))&
(![X]:(old(X)=>(~brave(X)<~>~quiet(X))))&
(((kind(john)&patient(john)))=>(?[X]:(~generous(X))))&
(((calm(paul)<~>wise(paul)))=>(?[X]:(funny(X))))&
(![X]:(calm(X)=>(creative(X)&wise(X))))&
(![X]:((~wise(X)<~>calm(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((~old(X)&wise(X))<=>(~quiet(X)<~>~patient(X))))&
((?[X]:((~happy(X)|wise(X))))=>((~funny(paul)<~>kind(paul))))&
(![X]:(~kind(X)<=>(~rich(X)|~happy(X))))&
(![X]:((~tall(X)&creative(X))<=>~brave(X)))&
(![X]:(tall(X)<=>(~old(X)|creative(X))))&
((old(john)<~>strong(john)))&
(?[X]:((~humble(X)&~rich(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(~humble(lucy))&
(?[X]:((rich(X)|~old(X))))&
((kind(mary)|~brave(mary)))&
((~patient(alice)|~kind(alice))) | ~patient(mary) | [
"p1",
"p3",
"p4",
"p6",
"p13",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2822096107284941953276425
% SZS output start Proof for 2822096107284941953276425
2. ! [X0] : ((~funny(X0) | ~kind(X0)) => (~old(X0) & funny(X0))) [input p1]
4. ! [X0] : (rich(X0) => ~patient(X0)) [input p3]
5. ! [X0] : ((curious(X0) & ~kind(X0)) <=> (quiet(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : (old(X0) => (~brave(X0) <~> ~quiet(X0))) [input p6]
14. ! [X0] : (~kind(X0) <=> (~happy(X0) | ~rich(X0))) [input p13]
15. ! [X0] : ((creative(X0) & ~tall(X0)) <=> ~brave(X0)) [input p14]
16. ! [X0] : (tall(X0) <=> (creative(X0) | ~old(X0))) [input p15]
22. ~brave(mary) | kind(mary) [input p21]
24. patient(mary) [input hypothesis]
28. ! [X0] : ((~old(X0) & funny(X0)) | (funny(X0) & kind(X0))) [ennf transformation 2]
29. ! [X0] : (~patient(X0) | ~rich(X0)) [ennf transformation 4]
30. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) | ~old(X0)) [ennf transformation 7]
41. ! [X0] : (((curious(X0) & ~kind(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | (~curious(X0) | kind(X0)))) [nnf transformation 5]
42. ! [X0] : (((curious(X0) & ~kind(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ~curious(X0) | kind(X0))) [flattening 41]
45. ! [X0] : (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | ~old(X0)) [nnf transformation 30]
55. ! [X0] : ((~kind(X0) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | kind(X0))) [nnf transformation 14]
56. ! [X0] : ((~kind(X0) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | kind(X0))) [flattening 55]
57. ! [X0] : (((creative(X0) & ~tall(X0)) | brave(X0)) & (~brave(X0) | (~creative(X0) | tall(X0)))) [nnf transformation 15]
58. ! [X0] : (((creative(X0) & ~tall(X0)) | brave(X0)) & (~brave(X0) | ~creative(X0) | tall(X0))) [flattening 57]
59. ! [X0] : ((tall(X0) | (~creative(X0) & old(X0))) & ((creative(X0) | ~old(X0)) | ~tall(X0))) [nnf transformation 16]
60. ! [X0] : ((tall(X0) | (~creative(X0) & old(X0))) & (creative(X0) | ~old(X0) | ~tall(X0))) [flattening 59]
71. ~old(X0) | kind(X0) [cnf transformation 28]
78. ~patient(X0) | ~rich(X0) [cnf transformation 29]
81. ~kind(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 42]
89. quiet(X0) | brave(X0) | ~old(X0) [cnf transformation 45]
114. ~kind(X0) | rich(X0) [cnf transformation 56]
117. ~tall(X0) | brave(X0) [cnf transformation 58]
120. tall(X0) | old(X0) [cnf transformation 60]
129. ~brave(mary) | kind(mary) [cnf transformation 22]
131. patient(mary) [cnf transformation 24]
163. ~old(X0) | ~quiet(X0) [subsumption resolution 81,71]
180. brave(X0) | ~old(X0) [subsumption resolution 89,163]
241. 22 <=> kind(mary) [avatar definition]
243. kind(mary) <- (22) [avatar component clause 241]
245. 23 <=> brave(mary) [avatar definition]
247. ~brave(mary) <- (~23) [avatar component clause 245]
248. 22 | ~23 [avatar split clause 129,245,241]
261. ~rich(mary) [resolution 78,131]
267. old(X0) | brave(X0) [resolution 120,117]
268. brave(X0) [subsumption resolution 267,180]
270. $false <- (~23) [resolution 268,247]
271. 23 [avatar contradiction clause 270]
273. rich(mary) <- (22) [resolution 243,114]
274. $false <- (22) [subsumption resolution 273,261]
275. ~22 [avatar contradiction clause 274]
276. $false [avatar sat refutation 248,271,275]
% SZS output end Proof for 2822096107284941953276425
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both brave and strong then someone is not brave or patient. If someone is not brave then someone is not tall or calm. Everyone who is either not humble or calm is not happy or not kind and vice versa. If someone is wise then susan is both rich and quiet. Everyone who is not rich or not quiet is not calm or not brave and vice versa. Everyone who is not calm is not old or not happy and vice versa. Everyone who is both strong and humble is old or not brave and vice versa. If someone is both not quiet and not curious then someone is not curious. If mary is tall or calm then fred is either tall or not quiet and vice versa. If someone is kind then someone is both not humble and not brave and vice versa. Everyone who is not generous is either strong or not kind. If fred is either kind or rich then lucy is not happy and vice versa. Everyone who is kind is either not strong or generous and vice versa. Everyone who is not patient is not curious or quiet and vice versa. If fred is both wise and funny then fred is both not curious and not kind and vice versa. If mary is not brave or not quiet then lucy is wise or curious and vice versa. Someone is either not wise or calm. John is both not old and rich. Alice is not funny or not generous. Mary is either funny or calm. Paul is either old or not funny. Someone is either creative or not wise. | Susan is old. | contradiction | ((?[X]:((brave(X)&strong(X))))=>(?[X]:((~brave(X)|patient(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:((~humble(X)<~>calm(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(wise(X)))=>((rich(susan)&quiet(susan))))&
(![X]:((~rich(X)|~quiet(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~calm(X)<=>(~old(X)|~happy(X))))&
(![X]:((strong(X)&humble(X))<=>(old(X)|~brave(X))))&
((?[X]:((~quiet(X)&~curious(X))))=>(?[X]:(~curious(X))))&
(((tall(mary)|calm(mary)))<=>((tall(fred)<~>~quiet(fred))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:(~generous(X)=>(strong(X)<~>~kind(X))))&
(((kind(fred)<~>rich(fred)))<=>(~happy(lucy)))&
(![X]:(kind(X)<=>(~strong(X)<~>generous(X))))&
(![X]:(~patient(X)<=>(~curious(X)|quiet(X))))&
(((wise(fred)&funny(fred)))<=>((~curious(fred)&~kind(fred))))&
(((~brave(mary)|~quiet(mary)))<=>((wise(lucy)|curious(lucy))))&
(?[X]:((~wise(X)<~>calm(X))))&
((~old(john)&rich(john)))&
((~funny(alice)|~generous(alice)))&
((funny(mary)<~>calm(mary)))&
((old(paul)<~>~funny(paul)))&
(?[X]:((creative(X)<~>~wise(X)))) | old(susan) | [
"p6",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2044233517773877925860825
% SZS output start Proof for 2044233517773877925860825
7. ! [X0] : ((humble(X0) & strong(X0)) <=> (~brave(X0) | old(X0))) [input p6]
10. ? [X0] : kind(X0) <=> ? [X0] : (~brave(X0) & ~humble(X0)) [input p9]
11. ! [X0] : (~generous(X0) => (strong(X0) <~> ~kind(X0))) [input p10]
13. ! [X0] : (kind(X0) <=> (~strong(X0) <~> generous(X0))) [input p12]
23. old(susan) [input hypothesis]
27. ? [X0] : kind(X0) <=> ? [X1] : (~brave(X1) & ~humble(X1)) [rectify 10]
33. ! [X0] : ((strong(X0) <~> ~kind(X0)) | generous(X0)) [ennf transformation 11]
47. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 7]
48. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~humble(X0) | ~strong(X0))) [flattening 47]
54. (? [X0] : kind(X0) | ! [X1] : (brave(X1) | humble(X1))) & (? [X1] : (~brave(X1) & ~humble(X1)) | ! [X0] : ~kind(X0)) [nnf transformation 27]
55. (? [X0] : kind(X0) | ! [X1] : (brave(X1) | humble(X1))) & (? [X2] : (~brave(X2) & ~humble(X2)) | ! [X3] : ~kind(X3)) [rectify 54]
56. ? [X0] : kind(X0) => kind(sK3) [choice axiom]
57. ? [X2] : (~brave(X2) & ~humble(X2)) => (~brave(sK4) & ~humble(sK4)) [choice axiom]
58. (kind(sK3) | ! [X1] : (brave(X1) | humble(X1))) & ((~brave(sK4) & ~humble(sK4)) | ! [X3] : ~kind(X3)) [skolemisation 55,57,56]
59. ! [X0] : (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | generous(X0)) [nnf transformation 33]
61. ! [X0] : ((kind(X0) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ~kind(X0))) [nnf transformation 13]
92. ~old(X0) | strong(X0) [cnf transformation 48]
95. humble(X0) | brave(X0) [cnf transformation 48]
103. ~humble(sK4) | ~kind(X3) [cnf transformation 58]
104. ~brave(sK4) | ~kind(X3) [cnf transformation 58]
107. kind(X0) | ~strong(X0) | generous(X0) [cnf transformation 59]
115. kind(X0) | ~strong(X0) | ~generous(X0) [cnf transformation 61]
137. old(susan) [cnf transformation 23]
206. 16 <=> ! [X3] : ~kind(X3) [avatar definition]
207. ~kind(X3) <- (16) [avatar component clause 206]
209. 17 <=> brave(sK4) [avatar definition]
212. 16 | ~17 [avatar split clause 104,209,206]
214. 18 <=> humble(sK4) [avatar definition]
216. ~humble(sK4) <- (~18) [avatar component clause 214]
217. 16 | ~18 [avatar split clause 103,214,206]
234. ~strong(X0) | kind(X0) [subsumption resolution 115,107]
321. strong(susan) [resolution 92,137]
325. brave(sK4) <- (~18) [resolution 95,216]
328. 17 | 18 [avatar split clause 325,214,209]
332. kind(susan) [resolution 234,321]
336. $false <- (16) [subsumption resolution 332,207]
337. ~16 [avatar contradiction clause 336]
340. $false [avatar sat refutation 212,217,328,337]
% SZS output end Proof for 2044233517773877925860825
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old then someone is creative or not funny and vice versa. If someone is calm then someone is calm or not funny and vice versa. Everyone who is patient is tall or not old and vice versa. Everyone who is generous is both rich and not quiet and vice versa. Everyone who is not funny is either not old or patient and vice versa. If someone is not tall then someone is not brave or not generous and vice versa. Everyone who is either curious or not quiet is both not patient and not rich. If fred is either generous or not patient then fred is not brave. Everyone who is old is both creative and not funny and vice versa. Everyone who is both not quiet and not curious is wise or not funny and vice versa. Everyone who is both calm and not curious is not funny and vice versa. If mary is not strong or strong then someone is creative. If someone is humble then susan is not curious and vice versa. If someone is not happy then someone is not calm or rich and vice versa. Everyone who is creative is not strong or tall. Everyone who is tall or not quiet is both not tall and brave. Mary is both rich and not brave. Someone is not kind. John is both not tall and not calm. Someone is not brave. Someone is calm or tall. Fred is not curious. Paul is either tall or generous. Someone is both strong and not happy. | Fred is generous. | contradiction | ((~old(alice))<=>(?[X]:((creative(X)|~funny(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:(patient(X)<=>(tall(X)|~old(X))))&
(![X]:(generous(X)<=>(rich(X)&~quiet(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((curious(X)<~>~quiet(X))=>(~patient(X)&~rich(X))))&
(((generous(fred)<~>~patient(fred)))=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(wise(X)|~funny(X))))&
(![X]:((calm(X)&~curious(X))<=>~funny(X)))&
(((~strong(mary)|strong(mary)))=>(?[X]:(creative(X))))&
((?[X]:(humble(X)))<=>(~curious(susan)))&
((?[X]:(~happy(X)))<=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:(creative(X)=>(~strong(X)|tall(X))))&
(![X]:((tall(X)|~quiet(X))=>(~tall(X)&brave(X))))&
((rich(mary)&~brave(mary)))&
(?[X]:(~kind(X)))&
((~tall(john)&~calm(john)))&
(?[X]:(~brave(X)))&
(?[X]:((calm(X)|tall(X))))&
(~curious(fred))&
((tall(paul)<~>generous(paul)))&
(?[X]:((strong(X)&~happy(X)))) | generous(fred) | [
"p2",
"p3",
"p4",
"p7",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3960942764809653142354275
% SZS output start Proof for 3960942764809653142354275
3. ! [X0] : (patient(X0) <=> (~old(X0) | tall(X0))) [input p2]
4. ! [X0] : (generous(X0) <=> (~quiet(X0) & rich(X0))) [input p3]
5. ! [X0] : (~funny(X0) <=> (~old(X0) <~> patient(X0))) [input p4]
8. (generous(fred) <~> ~patient(fred)) => ~brave(fred) [input p7]
9. ! [X0] : (old(X0) <=> (~funny(X0) & creative(X0))) [input p8]
16. ! [X0] : ((~quiet(X0) | tall(X0)) => (brave(X0) & ~tall(X0))) [input p15]
25. generous(fred) [input hypothesis]
31. ~brave(fred) | (generous(fred) <=> ~patient(fred)) [ennf transformation 8]
35. ! [X0] : ((brave(X0) & ~tall(X0)) | (quiet(X0) & ~tall(X0))) [ennf transformation 16]
45. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | ~patient(X0))) [nnf transformation 3]
46. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ~patient(X0))) [flattening 45]
47. ! [X0] : ((generous(X0) | (quiet(X0) | ~rich(X0))) & ((~quiet(X0) & rich(X0)) | ~generous(X0))) [nnf transformation 4]
48. ! [X0] : ((generous(X0) | quiet(X0) | ~rich(X0)) & ((~quiet(X0) & rich(X0)) | ~generous(X0))) [flattening 47]
49. ! [X0] : ((~funny(X0) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) & (((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | funny(X0))) [nnf transformation 5]
56. ~brave(fred) | ((generous(fred) | patient(fred)) & (~patient(fred) | ~generous(fred))) [nnf transformation 31]
57. ! [X0] : ((old(X0) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | ~old(X0))) [nnf transformation 9]
58. ! [X0] : ((old(X0) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | ~old(X0))) [flattening 57]
87. ~patient(X0) | tall(X0) | ~old(X0) [cnf transformation 46]
89. patient(X0) | old(X0) [cnf transformation 46]
91. ~quiet(X0) | ~generous(X0) [cnf transformation 48]
93. patient(X0) | ~old(X0) | funny(X0) [cnf transformation 49]
94. ~patient(X0) | old(X0) | funny(X0) [cnf transformation 49]
104. ~brave(fred) | ~patient(fred) | ~generous(fred) [cnf transformation 56]
107. ~funny(X0) | ~old(X0) [cnf transformation 58]
125. ~tall(X0) | ~tall(X0) [cnf transformation 35]
128. brave(X0) | quiet(X0) [cnf transformation 35]
140. generous(fred) [cnf transformation 25]
141. ~tall(X0) [duplicate literal removal 125]
181. funny(X0) | old(X0) [subsumption resolution 94,89]
182. patient(X0) | funny(X0) [subsumption resolution 93,181]
208. 16 <=> patient(fred) [avatar definition]
209. ~patient(fred) <- (~16) [avatar component clause 208]
212. 17 <=> generous(fred) [avatar definition]
214. generous(fred) <- (17) [avatar component clause 212]
216. 18 <=> brave(fred) [avatar definition]
218. ~brave(fred) <- (~18) [avatar component clause 216]
220. ~17 | ~16 | ~18 [avatar split clause 104,216,208,212]
270. 17 [avatar split clause 140,212]
279. quiet(fred) <- (~18) [resolution 128,218]
288. ~generous(fred) <- (~18) [resolution 279,91]
289. $false <- (17, ~18) [subsumption resolution 288,214]
290. ~17 | 18 [avatar contradiction clause 289]
292. old(fred) <- (~16) [resolution 209,89]
293. tall(X0) | ~old(X0) | funny(X0) [resolution 87,182]
295. ~old(X0) | funny(X0) [subsumption resolution 293,141]
296. ~old(X0) [subsumption resolution 295,107]
316. $false <- (~16) [resolution 296,292]
317. 16 [avatar contradiction clause 316]
319. $false [avatar sat refutation 220,270,290,317]
% SZS output end Proof for 3960942764809653142354275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and calm is not generous or not strong and vice versa.
Everyone who is happy is both not tall and old and vice versa.
If someone is both not humble and tall then alice is either tall or not happy.
Everyone who is both not wise and not rich is not calm.
If fred is either not kind or old then someone is both not quiet and creative and vice versa.
Everyone who is tall or old is not patient or brave.
Everyone who is either funny or not happy is either not tall or patient and vice versa.
Everyone who is not curious is either tall or happy.
If alice is both not happy and old then john is both rich and brave and vice versa.
If someone is either not strong or not patient then someone is not strong and vice versa.
If john is either not tall or not creative then john is humble or not calm and vice versa.
Everyone who is not wise or calm is funny.
Everyone who is either quiet or not strong is not patient or not old and vice versa.
Everyone who is both not generous and strong is not humble or not calm and vice versa.
Everyone who is both not brave and calm is either wise or tall.
Lucy is not creative.
Someone is either not quiet or not kind.
Someone is either brave or curious.
Susan is kind.
Someone is either not kind or generous. | Lucy is not curious. | contradiction | (![X]:((strong(X)&calm(X))<=>(~generous(X)|~strong(X))))&
(![X]:(happy(X)<=>(~tall(X)&old(X))))&
((?[X]:((~humble(X)&tall(X))))=>((tall(alice)<~>~happy(alice))))&
(![X]:((~wise(X)&~rich(X))=>~calm(X)))&
(((~kind(fred)<~>old(fred)))<=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:((tall(X)|old(X))=>(~patient(X)|brave(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~tall(X)<~>patient(X))))&
(![X]:(~curious(X)=>(tall(X)<~>happy(X))))&
(((~happy(alice)&old(alice)))<=>((rich(john)&brave(john))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>(?[X]:(~strong(X))))&
(((~tall(john)<~>~creative(john)))<=>((humble(john)|~calm(john))))&
(![X]:((~wise(X)|calm(X))=>funny(X)))&
(![X]:((quiet(X)<~>~strong(X))<=>(~patient(X)|~old(X))))&
(![X]:((~generous(X)&strong(X))<=>(~humble(X)|~calm(X))))&
(![X]:((~brave(X)&calm(X))=>(wise(X)<~>tall(X))))&
(~creative(lucy))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((brave(X)<~>curious(X))))&
(kind(susan))&
(?[X]:((~kind(X)<~>generous(X)))) | ~curious(lucy) | [
"p0",
"p1",
"p6",
"p7",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9194901025245938887500752
% SZS output start Proof for 9194901025245938887500752
1. ! [X0] : ((calm(X0) & strong(X0)) <=> (~strong(X0) | ~generous(X0))) [input p0]
2. ! [X0] : (happy(X0) <=> (old(X0) & ~tall(X0))) [input p1]
7. ! [X0] : ((funny(X0) <~> ~happy(X0)) <=> (~tall(X0) <~> patient(X0))) [input p6]
8. ! [X0] : (~curious(X0) => (tall(X0) <~> happy(X0))) [input p7]
10. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> ? [X0] : ~strong(X0) [input p9]
12. ! [X0] : ((calm(X0) | ~wise(X0)) => funny(X0)) [input p11]
14. ! [X0] : ((strong(X0) & ~generous(X0)) <=> (~calm(X0) | ~humble(X0))) [input p13]
21. ~curious(lucy) [input hypothesis]
22. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> ? [X1] : ~strong(X1) [rectify 10]
28. ! [X0] : ((tall(X0) <~> happy(X0)) | curious(X0)) [ennf transformation 8]
29. ! [X0] : (funny(X0) | (~calm(X0) & wise(X0))) [ennf transformation 12]
32. ! [X0] : (((calm(X0) & strong(X0)) | (strong(X0) & generous(X0))) & ((~strong(X0) | ~generous(X0)) | (~calm(X0) | ~strong(X0)))) [nnf transformation 1]
33. ! [X0] : (((calm(X0) & strong(X0)) | (strong(X0) & generous(X0))) & (~strong(X0) | ~generous(X0) | ~calm(X0) | ~strong(X0))) [flattening 32]
34. ! [X0] : ((happy(X0) | (~old(X0) | tall(X0))) & ((old(X0) & ~tall(X0)) | ~happy(X0))) [nnf transformation 2]
35. ! [X0] : ((happy(X0) | ~old(X0) | tall(X0)) & ((old(X0) & ~tall(X0)) | ~happy(X0))) [flattening 34]
41. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) & (((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [nnf transformation 7]
42. ! [X0] : (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | curious(X0)) [nnf transformation 28]
45. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 22]
46. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : ((~strong(X3) | patient(X3)) & (~patient(X3) | strong(X3)))) [rectify 45]
47. ? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) => ((patient(sK1) | strong(sK1)) & (~patient(sK1) | ~strong(sK1))) [choice axiom]
48. ? [X2] : ~strong(X2) => ~strong(sK2) [choice axiom]
49. (((patient(sK1) | strong(sK1)) & (~patient(sK1) | ~strong(sK1))) | ! [X1] : strong(X1)) & (~strong(sK2) | ! [X3] : ((~strong(X3) | patient(X3)) & (~patient(X3) | strong(X3)))) [skolemisation 46,48,47]
54. ! [X0] : (((strong(X0) & ~generous(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (~strong(X0) | generous(X0)))) [nnf transformation 14]
55. ! [X0] : (((strong(X0) & ~generous(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | ~strong(X0) | generous(X0))) [flattening 54]
68. strong(X0) | strong(X0) [cnf transformation 33]
69. generous(X0) | calm(X0) [cnf transformation 33]
71. ~tall(X0) | ~happy(X0) [cnf transformation 35]
87. ~patient(X0) | tall(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 41]
92. happy(X0) | ~funny(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 41]
93. curious(X0) | tall(X0) | happy(X0) [cnf transformation 42]
100. ~strong(sK2) | ~strong(X3) | patient(X3) [cnf transformation 49]
110. ~calm(X0) | funny(X0) [cnf transformation 29]
119. ~generous(X0) | calm(X0) [cnf transformation 55]
132. ~curious(lucy) [cnf transformation 21]
134. strong(X0) [duplicate literal removal 68]
176. ~funny(X0) | ~tall(X0) | ~patient(X0) [subsumption resolution 92,71]
178. ~funny(X0) | ~happy(X0) | ~patient(X0) [subsumption resolution 87,176]
196. ~strong(X3) | patient(X3) [subsumption resolution 100,134]
197. patient(X3) [subsumption resolution 196,134]
223. calm(X0) [subsumption resolution 119,69]
260. funny(X1) [resolution 110,223]
269. tall(lucy) | happy(lucy) [resolution 93,132]
272. 22 <=> happy(lucy) [avatar definition]
274. happy(lucy) <- (22) [avatar component clause 272]
276. 23 <=> tall(lucy) [avatar definition]
278. tall(lucy) <- (23) [avatar component clause 276]
279. 22 | 23 [avatar split clause 269,276,272]
290. ~tall(X0) | ~patient(X0) [resolution 176,260]
292. ~tall(X0) [subsumption resolution 290,197]
295. ~happy(X0) | ~patient(X0) [resolution 178,260]
297. ~happy(X0) [subsumption resolution 295,197]
298. $false <- (22) [resolution 297,274]
299. ~22 [avatar contradiction clause 298]
300. $false <- (23) [subsumption resolution 278,292]
301. ~23 [avatar contradiction clause 300]
302. $false [avatar sat refutation 279,299,301]
% SZS output end Proof for 9194901025245938887500752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or not humble then someone is both not quiet and kind and vice versa. If paul is either not strong or not wise then fred is either not creative or old and vice versa. Everyone who is not generous or not happy is either not humble or kind. Everyone who is either happy or not creative is not quiet and vice versa. Everyone who is either kind or not wise is both not curious and not funny. Everyone who is generous or not curious is either not creative or not funny and vice versa. If someone is not patient or patient then someone is either not curious or tall and vice versa. If someone is both happy and generous then paul is both not patient and not tall and vice versa. If someone is either strong or not wise then someone is not creative or not calm. Everyone who is humble is both not wise and not brave. Everyone who is wise is either rich or not happy. Everyone who is calm is either not tall or happy and vice versa. Everyone who is quiet or calm is both not rich and quiet and vice versa. Everyone who is either not creative or not wise is not patient and vice versa. Everyone who is either not creative or not brave is either not humble or not old. Susan is not wise. Someone is not generous or funny. Someone is kind or generous. Fred is either not humble or happy. Someone is not patient or not wise. Fred is either not humble or not quiet. Someone is curious or not funny. Paul is both tall and humble. | Fred is not calm. | neutral | ((?[X]:((~kind(X)|~humble(X))))<=>(?[X]:((~quiet(X)&kind(X)))))&
(((~strong(paul)<~>~wise(paul)))<=>((~creative(fred)<~>old(fred))))&
(![X]:((~generous(X)|~happy(X))=>(~humble(X)<~>kind(X))))&
(![X]:((happy(X)<~>~creative(X))<=>~quiet(X)))&
(![X]:((kind(X)<~>~wise(X))=>(~curious(X)&~funny(X))))&
(![X]:((generous(X)|~curious(X))<=>(~creative(X)<~>~funny(X))))&
((?[X]:((~patient(X)|patient(X))))<=>(?[X]:((~curious(X)<~>tall(X)))))&
((?[X]:((happy(X)&generous(X))))<=>((~patient(paul)&~tall(paul))))&
((?[X]:((strong(X)<~>~wise(X))))=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:(humble(X)=>(~wise(X)&~brave(X))))&
(![X]:(wise(X)=>(rich(X)<~>~happy(X))))&
(![X]:(calm(X)<=>(~tall(X)<~>happy(X))))&
(![X]:((quiet(X)|calm(X))<=>(~rich(X)&quiet(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>~patient(X)))&
(![X]:((~creative(X)<~>~brave(X))=>(~humble(X)<~>~old(X))))&
(~wise(susan))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:((kind(X)|generous(X))))&
((~humble(fred)<~>happy(fred)))&
(?[X]:((~patient(X)|~wise(X))))&
((~humble(fred)<~>~quiet(fred)))&
(?[X]:((curious(X)|~funny(X))))&
((tall(paul)&humble(paul))) | ~calm(fred) | [] | null | 0 |
Everyone who is humble or not old is not calm or happy.
Everyone who is both curious and not brave is either not funny or not strong and vice versa.
Everyone who is not calm or not generous is either not strong or not patient.
If someone is either not old or not curious then someone is both not kind and not curious.
Everyone who is either not happy or creative is either not kind or not generous.
Everyone who is both tall and not calm is tall or rich.
Everyone who is either wise or creative is either not kind or not generous and vice versa.
Everyone who is generous is both brave and old and vice versa.
If someone is either tall or not curious then someone is either strong or humble.
Everyone who is either not kind or not funny is funny and vice versa.
Everyone who is not quiet or not brave is both not wise and creative.
Everyone who is not quiet is not generous or not brave and vice versa.
Everyone who is both strong and humble is not strong or humble and vice versa.
If someone is funny then alice is either strong or creative and vice versa.
Everyone who is creative is either not patient or not kind.
Alice is old.
Alice is calm.
Someone is not quiet or not kind.
Fred is happy or not old.
Someone is both patient and brave.
Mary is happy or not funny. | Fred is not generous. | contradiction | (![X]:((humble(X)|~old(X))=>(~calm(X)|happy(X))))&
(![X]:((curious(X)&~brave(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:((~calm(X)|~generous(X))=>(~strong(X)<~>~patient(X))))&
((?[X]:((~old(X)<~>~curious(X))))=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((tall(X)&~calm(X))=>(tall(X)|rich(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~kind(X)<~>~generous(X))))&
(![X]:(generous(X)<=>(brave(X)&old(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((~kind(X)<~>~funny(X))<=>funny(X)))&
(![X]:((~quiet(X)|~brave(X))=>(~wise(X)&creative(X))))&
(![X]:(~quiet(X)<=>(~generous(X)|~brave(X))))&
(![X]:((strong(X)&humble(X))<=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((strong(alice)<~>creative(alice))))&
(![X]:(creative(X)=>(~patient(X)<~>~kind(X))))&
(old(alice))&
(calm(alice))&
(?[X]:((~quiet(X)|~kind(X))))&
((happy(fred)|~old(fred)))&
(?[X]:((patient(X)&brave(X))))&
((happy(mary)|~funny(mary))) | ~generous(fred) | [
"p2",
"p9",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5884846295283124346158970
% SZS output start Proof for 5884846295283124346158970
3. ! [X0] : ((~generous(X0) | ~calm(X0)) => (~strong(X0) <~> ~patient(X0))) [input p2]
10. ! [X0] : ((~kind(X0) <~> ~funny(X0)) <=> funny(X0)) [input p9]
11. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (creative(X0) & ~wise(X0))) [input p10]
12. ! [X0] : (~quiet(X0) <=> (~brave(X0) | ~generous(X0))) [input p11]
13. ! [X0] : ((humble(X0) & strong(X0)) <=> (humble(X0) | ~strong(X0))) [input p12]
15. ! [X0] : (creative(X0) => (~patient(X0) <~> ~kind(X0))) [input p14]
22. ~generous(fred) [input hypothesis]
28. ! [X0] : ((~strong(X0) <~> ~patient(X0)) | (generous(X0) & calm(X0))) [ennf transformation 3]
32. ! [X0] : ((creative(X0) & ~wise(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 11]
33. ! [X0] : ((~patient(X0) <~> ~kind(X0)) | ~creative(X0)) [ennf transformation 15]
36. ! [X0] : (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (generous(X0) & calm(X0))) [nnf transformation 28]
49. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~funny(X0)) & (funny(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [nnf transformation 10]
50. ! [X0] : ((~quiet(X0) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | quiet(X0))) [nnf transformation 12]
51. ! [X0] : ((~quiet(X0) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | quiet(X0))) [flattening 50]
52. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & ((humble(X0) | ~strong(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 13]
53. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & (humble(X0) | ~strong(X0) | ~humble(X0) | ~strong(X0))) [flattening 52]
58. ! [X0] : (((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ~creative(X0)) [nnf transformation 33]
72. ~patient(X0) | ~strong(X0) | generous(X0) [cnf transformation 36]
99. funny(X0) | ~kind(X0) | funny(X0) [cnf transformation 49]
100. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 49]
104. quiet(X0) | creative(X0) [cnf transformation 32]
107. ~quiet(X0) | generous(X0) [cnf transformation 51]
111. strong(X0) | ~humble(X0) [cnf transformation 53]
112. strong(X0) | humble(X0) [cnf transformation 53]
119. kind(X0) | patient(X0) | ~creative(X0) [cnf transformation 58]
127. ~generous(fred) [cnf transformation 22]
130. funny(X0) | ~kind(X0) [duplicate literal removal 99]
131. ~kind(X0) | ~funny(X0) [duplicate literal removal 100]
168. ~kind(X0) [subsumption resolution 130,131]
170. strong(X0) [subsumption resolution 111,112]
186. ~creative(X0) | patient(X0) [subsumption resolution 119,168]
206. creative(X0) | generous(X0) [resolution 107,104]
210. patient(X0) | generous(X0) [resolution 206,186]
295. generous(X0) | ~strong(X0) | generous(X0) [resolution 210,72]
297. generous(X0) | ~strong(X0) [duplicate literal removal 295]
298. generous(X0) [subsumption resolution 297,170]
304. $false [resolution 298,127]
% SZS output end Proof for 5884846295283124346158970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not funny then someone is either not rich or rich. Everyone who is either not strong or not quiet is both rich and kind. If susan is either patient or not humble then susan is either patient or calm and vice versa. Everyone who is either not brave or not calm is not brave and vice versa. Everyone who is not curious is not calm and vice versa. If paul is kind then john is both funny and curious. If someone is either curious or patient then someone is either happy or not rich and vice versa. Everyone who is either not funny or calm is not patient. If someone is not curious or patient then alice is funny or not calm and vice versa. Everyone who is not patient or not rich is either tall or patient. Everyone who is either patient or humble is either not kind or not quiet. If someone is tall or not rich then someone is either funny or not curious and vice versa. Everyone who is both not kind and tall is both creative and not brave. Everyone who is both wise and creative is both not patient and not funny. If someone is not wise then someone is not tall. Susan is kind. Someone is both old and not tall. Someone is rich or curious. Someone is both not creative and patient. Lucy is patient. Someone is either brave or tall. Alice is quiet. | Alice is not funny. | contradiction | ((?[X]:((~happy(X)|~funny(X))))=>(?[X]:((~rich(X)<~>rich(X)))))&
(![X]:((~strong(X)<~>~quiet(X))=>(rich(X)&kind(X))))&
(((patient(susan)<~>~humble(susan)))<=>((patient(susan)<~>calm(susan))))&
(![X]:((~brave(X)<~>~calm(X))<=>~brave(X)))&
(![X]:(~curious(X)<=>~calm(X)))&
((kind(paul))=>((funny(john)&curious(john))))&
((?[X]:((curious(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>~rich(X)))))&
(![X]:((~funny(X)<~>calm(X))=>~patient(X)))&
((?[X]:((~curious(X)|patient(X))))<=>((funny(alice)|~calm(alice))))&
(![X]:((~patient(X)|~rich(X))=>(tall(X)<~>patient(X))))&
(![X]:((patient(X)<~>humble(X))=>(~kind(X)<~>~quiet(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((funny(X)<~>~curious(X)))))&
(![X]:((~kind(X)&tall(X))=>(creative(X)&~brave(X))))&
(![X]:((wise(X)&creative(X))=>(~patient(X)&~funny(X))))&
((?[X]:(~wise(X)))=>(?[X]:(~tall(X))))&
(kind(susan))&
(?[X]:((old(X)&~tall(X))))&
(?[X]:((rich(X)|curious(X))))&
(?[X]:((~creative(X)&patient(X))))&
(patient(lucy))&
(?[X]:((brave(X)<~>tall(X))))&
(quiet(alice)) | ~funny(alice) | [
"p3",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8053701177335181666444031
% SZS output start Proof for 8053701177335181666444031
4. ! [X0] : ((~brave(X0) <~> ~calm(X0)) <=> ~brave(X0)) [input p3]
9. ? [X0] : (patient(X0) | ~curious(X0)) <=> (~calm(alice) | funny(alice)) [input p8]
19. ? [X0] : (patient(X0) & ~creative(X0)) [input p18]
23. ~funny(alice) [input hypothesis]
46. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | brave(X0)) & (~brave(X0) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [nnf transformation 4]
54. (? [X0] : (patient(X0) | ~curious(X0)) | (calm(alice) & ~funny(alice))) & ((~calm(alice) | funny(alice)) | ! [X0] : (~patient(X0) & curious(X0))) [nnf transformation 9]
55. (? [X0] : (patient(X0) | ~curious(X0)) | (calm(alice) & ~funny(alice))) & (~calm(alice) | funny(alice) | ! [X0] : (~patient(X0) & curious(X0))) [flattening 54]
56. (? [X0] : (patient(X0) | ~curious(X0)) | (calm(alice) & ~funny(alice))) & (~calm(alice) | funny(alice) | ! [X1] : (~patient(X1) & curious(X1))) [rectify 55]
57. ? [X0] : (patient(X0) | ~curious(X0)) => (patient(sK3) | ~curious(sK3)) [choice axiom]
58. ((patient(sK3) | ~curious(sK3)) | (calm(alice) & ~funny(alice))) & (~calm(alice) | funny(alice) | ! [X1] : (~patient(X1) & curious(X1))) [skolemisation 56,57]
73. ? [X0] : (patient(X0) & ~creative(X0)) => (patient(sK9) & ~creative(sK9)) [choice axiom]
74. patient(sK9) & ~creative(sK9) [skolemisation 19,73]
95. ~brave(X0) | ~brave(X0) | calm(X0) [cnf transformation 46]
97. calm(X0) | brave(X0) | brave(X0) [cnf transformation 46]
113. ~calm(alice) | funny(alice) | ~patient(X1) [cnf transformation 58]
139. patient(sK9) [cnf transformation 74]
144. ~funny(alice) [cnf transformation 23]
146. ~brave(X0) | calm(X0) [duplicate literal removal 95]
147. calm(X0) | brave(X0) [duplicate literal removal 97]
168. calm(X0) [subsumption resolution 146,147]
211. 12 <=> funny(alice) [avatar definition]
219. funny(alice) | ~patient(X1) [subsumption resolution 113,168]
221. 14 <=> ! [X1] : ~patient(X1) [avatar definition]
222. ~patient(X1) <- (14) [avatar component clause 221]
223. 14 | 12 [avatar split clause 219,211,221]
269. ~12 [avatar split clause 144,211]
272. $false <- (14) [resolution 222,139]
275. ~14 [avatar contradiction clause 272]
276. $false [avatar sat refutation 223,269,275]
% SZS output end Proof for 8053701177335181666444031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not happy or not humble then someone is both not creative and not wise and vice versa.
Everyone who is not quiet is not patient or rich and vice versa.
If someone is curious then someone is either generous or not brave.
If paul is quiet then someone is either not strong or not calm.
Everyone who is curious is both not tall and wise and vice versa.
If alice is either not strong or not creative then someone is not creative or not tall.
If someone is both not generous and humble then someone is wise or tall.
If someone is both strong and quiet then john is not wise or not generous.
If someone is both not happy and not calm then susan is either strong or wise and vice versa.
If someone is both quiet and not brave then paul is generous or strong.
If susan is quiet then susan is tall or funny.
If someone is either not curious or happy then someone is both not creative and not humble and vice versa.
Everyone who is rich or not tall is generous or not happy.
If john is either not rich or not generous then someone is either generous or not funny.
Everyone who is not creative is not funny.
Everyone who is both old and quiet is old and vice versa.
Fred is both creative and not patient.
Paul is either not kind or funny.
Someone is not happy.
Someone is not rich.
Someone is both generous and not humble.
Someone is both not patient and not generous.
Mary is both not humble and not happy.
Someone is both brave and not strong. | Mary is not humble. | entailment | (((~happy(mary)<~>~humble(mary)))<=>(?[X]:((~creative(X)&~wise(X)))))&
(![X]:(~quiet(X)<=>(~patient(X)|rich(X))))&
((?[X]:(curious(X)))=>(?[X]:((generous(X)<~>~brave(X)))))&
((quiet(paul))=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:(curious(X)<=>(~tall(X)&wise(X))))&
(((~strong(alice)<~>~creative(alice)))=>(?[X]:((~creative(X)|~tall(X)))))&
((?[X]:((~generous(X)&humble(X))))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((strong(X)&quiet(X))))=>((~wise(john)|~generous(john))))&
((?[X]:((~happy(X)&~calm(X))))<=>((strong(susan)<~>wise(susan))))&
((?[X]:((quiet(X)&~brave(X))))=>((generous(paul)|strong(paul))))&
((quiet(susan))=>((tall(susan)|funny(susan))))&
((?[X]:((~curious(X)<~>happy(X))))<=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((rich(X)|~tall(X))=>(generous(X)|~happy(X))))&
(((~rich(john)<~>~generous(john)))=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:(~creative(X)=>~funny(X)))&
(![X]:((old(X)&quiet(X))<=>old(X)))&
((creative(fred)&~patient(fred)))&
((~kind(paul)<~>funny(paul)))&
(?[X]:(~happy(X)))&
(?[X]:(~rich(X)))&
(?[X]:((generous(X)&~humble(X))))&
(?[X]:((~patient(X)&~generous(X))))&
((~humble(mary)&~happy(mary)))&
(?[X]:((brave(X)&~strong(X)))) | ~humble(mary) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8134786678546264331600804
% SZS output start Proof for 8134786678546264331600804
23. ~happy(mary) & ~humble(mary) [input p22]
25. humble(mary) [input hypothesis]
143. ~humble(mary) [cnf transformation 23]
147. humble(mary) [cnf transformation 25]
156. 3 <=> humble(mary) [avatar definition]
350. ~3 [avatar split clause 143,156]
351. 3 [avatar split clause 147,156]
352. $false [avatar sat refutation 350,351]
% SZS output end Proof for 8134786678546264331600804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not curious then alice is either quiet or strong and vice versa.
If fred is calm then lucy is either not curious or calm and vice versa.
Everyone who is old or tall is both tall and quiet and vice versa.
If lucy is happy then susan is both not strong and curious.
Everyone who is brave is happy and vice versa.
If someone is either quiet or not creative then alice is rich or not old.
Everyone who is both not humble and generous is either not creative or calm.
Everyone who is not humble is either not quiet or wise and vice versa.
Everyone who is generous is both not generous and funny and vice versa.
Everyone who is humble or calm is wise or not humble.
If someone is curious or not strong then someone is both humble and strong.
If susan is not patient or humble then mary is not creative or creative.
Everyone who is both wise and not old is not tall or kind and vice versa.
Everyone who is old or not humble is rich or not creative and vice versa.
Everyone who is either not curious or funny is not patient or curious and vice versa.
Everyone who is either rich or funny is both not strong and tall.
Someone is not quiet or funny.
Someone is not curious.
Someone is creative.
John is either quiet or calm.
Someone is not curious or not old.
Alice is both not tall and not kind. | Mary is tall. | neutral | (((~humble(lucy)<~>~curious(lucy)))<=>((quiet(alice)<~>strong(alice))))&
((calm(fred))<=>((~curious(lucy)<~>calm(lucy))))&
(![X]:((old(X)|tall(X))<=>(tall(X)&quiet(X))))&
((happy(lucy))=>((~strong(susan)&curious(susan))))&
(![X]:(brave(X)<=>happy(X)))&
((?[X]:((quiet(X)<~>~creative(X))))=>((rich(alice)|~old(alice))))&
(![X]:((~humble(X)&generous(X))=>(~creative(X)<~>calm(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>wise(X))))&
(![X]:(generous(X)<=>(~generous(X)&funny(X))))&
(![X]:((humble(X)|calm(X))=>(wise(X)|~humble(X))))&
((?[X]:((curious(X)|~strong(X))))=>(?[X]:((humble(X)&strong(X)))))&
(((~patient(susan)|humble(susan)))=>((~creative(mary)|creative(mary))))&
(![X]:((wise(X)&~old(X))<=>(~tall(X)|kind(X))))&
(![X]:((old(X)|~humble(X))<=>(rich(X)|~creative(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(~patient(X)|curious(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&tall(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:(creative(X)))&
((quiet(john)<~>calm(john)))&
(?[X]:((~curious(X)|~old(X))))&
((~tall(alice)&~kind(alice))) | tall(mary) | [] | null | 0 |
Everyone who is either not calm or strong is not tall or not humble. If lucy is both not happy and not quiet then someone is not kind and vice versa. If susan is not curious or rich then someone is not old and vice versa. Everyone who is calm or humble is both happy and tall and vice versa. Everyone who is humble or not calm is both not kind and not humble and vice versa. If someone is both wise and funny then someone is both not generous and humble. If john is not wise then someone is either not curious or strong and vice versa. Everyone who is not humble or not calm is both quiet and happy and vice versa. If someone is either humble or not creative then paul is not generous and vice versa. If paul is humble then fred is either not brave or not strong and vice versa. If susan is both kind and humble then alice is patient and vice versa. If someone is either generous or not old then someone is not funny or not creative and vice versa. If alice is either strong or not creative then someone is either patient or not strong and vice versa. If someone is not rich or curious then someone is quiet or not strong. Everyone who is not old is not generous or brave and vice versa. If john is both not humble and not calm then someone is patient or tall. Someone is not patient. John is both patient and rich. Paul is old or quiet. Mary is either quiet or not old. John is either not humble or not creative. Someone is not happy or quiet. | Lucy is not calm. | contradiction | (![X]:((~calm(X)<~>strong(X))=>(~tall(X)|~humble(X))))&
(((~happy(lucy)&~quiet(lucy)))<=>(?[X]:(~kind(X))))&
(((~curious(susan)|rich(susan)))<=>(?[X]:(~old(X))))&
(![X]:((calm(X)|humble(X))<=>(happy(X)&tall(X))))&
(![X]:((humble(X)|~calm(X))<=>(~kind(X)&~humble(X))))&
((?[X]:((wise(X)&funny(X))))=>(?[X]:((~generous(X)&humble(X)))))&
((~wise(john))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((~humble(X)|~calm(X))<=>(quiet(X)&happy(X))))&
((?[X]:((humble(X)<~>~creative(X))))<=>(~generous(paul)))&
((humble(paul))<=>((~brave(fred)<~>~strong(fred))))&
(((kind(susan)&humble(susan)))<=>(patient(alice)))&
((?[X]:((generous(X)<~>~old(X))))<=>(?[X]:((~funny(X)|~creative(X)))))&
(((strong(alice)<~>~creative(alice)))<=>(?[X]:((patient(X)<~>~strong(X)))))&
((?[X]:((~rich(X)|curious(X))))=>(?[X]:((quiet(X)|~strong(X)))))&
(![X]:(~old(X)<=>(~generous(X)|brave(X))))&
(((~humble(john)&~calm(john)))=>(?[X]:((patient(X)|tall(X)))))&
(?[X]:(~patient(X)))&
((patient(john)&rich(john)))&
((old(paul)|quiet(paul)))&
((quiet(mary)<~>~old(mary)))&
((~humble(john)<~>~creative(john)))&
(?[X]:((~happy(X)|quiet(X)))) | ~calm(lucy) | [
"p1",
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5102058080530940560765892
% SZS output start Proof for 5102058080530940560765892
2. (~quiet(lucy) & ~happy(lucy)) <=> ? [X0] : ~kind(X0) [input p1]
4. ! [X0] : ((humble(X0) | calm(X0)) <=> (tall(X0) & happy(X0))) [input p3]
5. ! [X0] : ((~calm(X0) | humble(X0)) <=> (~humble(X0) & ~kind(X0))) [input p4]
8. ! [X0] : ((~calm(X0) | ~humble(X0)) <=> (happy(X0) & quiet(X0))) [input p7]
23. ~calm(lucy) [input hypothesis]
34. ((~quiet(lucy) & ~happy(lucy)) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | (quiet(lucy) | happy(lucy))) [nnf transformation 2]
35. ((~quiet(lucy) & ~happy(lucy)) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | quiet(lucy) | happy(lucy)) [flattening 34]
36. ((~quiet(lucy) & ~happy(lucy)) | ! [X0] : kind(X0)) & (? [X1] : ~kind(X1) | quiet(lucy) | happy(lucy)) [rectify 35]
37. ? [X1] : ~kind(X1) => ~kind(sK0) [choice axiom]
38. ((~quiet(lucy) & ~happy(lucy)) | ! [X0] : kind(X0)) & (~kind(sK0) | quiet(lucy) | happy(lucy)) [skolemisation 36,37]
44. ! [X0] : (((humble(X0) | calm(X0)) | (~tall(X0) | ~happy(X0))) & ((tall(X0) & happy(X0)) | (~humble(X0) & ~calm(X0)))) [nnf transformation 4]
45. ! [X0] : ((humble(X0) | calm(X0) | ~tall(X0) | ~happy(X0)) & ((tall(X0) & happy(X0)) | (~humble(X0) & ~calm(X0)))) [flattening 44]
46. ! [X0] : (((~calm(X0) | humble(X0)) | (humble(X0) | kind(X0))) & ((~humble(X0) & ~kind(X0)) | (calm(X0) & ~humble(X0)))) [nnf transformation 5]
47. ! [X0] : ((~calm(X0) | humble(X0) | humble(X0) | kind(X0)) & ((~humble(X0) & ~kind(X0)) | (calm(X0) & ~humble(X0)))) [flattening 46]
55. ! [X0] : (((~calm(X0) | ~humble(X0)) | (~happy(X0) | ~quiet(X0))) & ((happy(X0) & quiet(X0)) | (calm(X0) & humble(X0)))) [nnf transformation 8]
56. ! [X0] : ((~calm(X0) | ~humble(X0) | ~happy(X0) | ~quiet(X0)) & ((happy(X0) & quiet(X0)) | (calm(X0) & humble(X0)))) [flattening 55]
89. ~happy(lucy) | kind(X0) [cnf transformation 38]
94. ~calm(X0) | happy(X0) [cnf transformation 45]
100. ~kind(X0) | calm(X0) [cnf transformation 47]
113. happy(X0) | calm(X0) [cnf transformation 56]
155. ~calm(lucy) [cnf transformation 23]
159. 1 <=> ! [X0] : kind(X0) [avatar definition]
160. kind(X0) <- (1) [avatar component clause 159]
167. 3 <=> happy(lucy) [avatar definition]
169. ~happy(lucy) <- (~3) [avatar component clause 167]
170. 1 | ~3 [avatar split clause 89,167,159]
217. happy(X0) [subsumption resolution 113,94]
324. $false <- (~3) [subsumption resolution 169,217]
325. 3 [avatar contradiction clause 324]
332. calm(X0) <- (1) [resolution 100,160]
333. $false <- (1) [resolution 332,155]
336. ~1 [avatar contradiction clause 333]
337. $false [avatar sat refutation 170,325,336]
% SZS output end Proof for 5102058080530940560765892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not wise then someone is either creative or funny and vice versa. Everyone who is both not quiet and not wise is not humble and vice versa. Everyone who is either not strong or not funny is calm or not quiet and vice versa. Everyone who is either funny or not wise is not patient and vice versa. Everyone who is either not generous or not calm is both humble and not happy and vice versa. Everyone who is either tall or kind is not old or not kind. If someone is either not generous or patient then someone is not generous and vice versa. Everyone who is both rich and curious is not quiet or not rich. Everyone who is not rich is wise. Everyone who is wise is not curious or calm. Everyone who is both not generous and not humble is patient or not happy and vice versa. Everyone who is either rich or not old is not creative or not curious. If someone is not kind or patient then paul is not kind or not rich. If someone is both calm and not happy then alice is not strong or not rich and vice versa. Everyone who is not quiet is either not wise or patient. Everyone who is not rich is funny and vice versa. Someone is brave or generous. Someone is not brave or not kind. Someone is either calm or not rich. John is not brave or brave. Alice is both not curious and not quiet. Someone is both rich and happy. Alice is not calm or brave. | Alice is not funny. | entailment | ((?[X]:((funny(X)&~wise(X))))<=>(?[X]:((creative(X)<~>funny(X)))))&
(![X]:((~quiet(X)&~wise(X))<=>~humble(X)))&
(![X]:((~strong(X)<~>~funny(X))<=>(calm(X)|~quiet(X))))&
(![X]:((funny(X)<~>~wise(X))<=>~patient(X)))&
(![X]:((~generous(X)<~>~calm(X))<=>(humble(X)&~happy(X))))&
(![X]:((tall(X)<~>kind(X))=>(~old(X)|~kind(X))))&
((?[X]:((~generous(X)<~>patient(X))))<=>(?[X]:(~generous(X))))&
(![X]:((rich(X)&curious(X))=>(~quiet(X)|~rich(X))))&
(![X]:(~rich(X)=>wise(X)))&
(![X]:(wise(X)=>(~curious(X)|calm(X))))&
(![X]:((~generous(X)&~humble(X))<=>(patient(X)|~happy(X))))&
(![X]:((rich(X)<~>~old(X))=>(~creative(X)|~curious(X))))&
((?[X]:((~kind(X)|patient(X))))=>((~kind(paul)|~rich(paul))))&
((?[X]:((calm(X)&~happy(X))))<=>((~strong(alice)|~rich(alice))))&
(![X]:(~quiet(X)=>(~wise(X)<~>patient(X))))&
(![X]:(~rich(X)<=>funny(X)))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:((~brave(X)|~kind(X))))&
(?[X]:((calm(X)<~>~rich(X))))&
((~brave(john)|brave(john)))&
((~curious(alice)&~quiet(alice)))&
(?[X]:((rich(X)&happy(X))))&
((~calm(alice)|brave(alice))) | ~funny(alice) | [
"p4",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5342186431056762087261210
% SZS output start Proof for 5342186431056762087261210
5. ! [X0] : ((~generous(X0) <~> ~calm(X0)) <=> (~happy(X0) & humble(X0))) [input p4]
11. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (~happy(X0) | patient(X0))) [input p10]
14. ? [X0] : (~happy(X0) & calm(X0)) <=> (~rich(alice) | ~strong(alice)) [input p13]
16. ! [X0] : (~rich(X0) <=> funny(X0)) [input p15]
24. funny(alice) [input hypothesis]
46. ! [X0] : ((((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (happy(X0) | ~humble(X0))) & ((~happy(X0) & humble(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))))) [nnf transformation 5]
47. ! [X0] : ((((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | happy(X0) | ~humble(X0)) & ((~happy(X0) & humble(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))))) [flattening 46]
53. ! [X0] : (((~humble(X0) & ~generous(X0)) | (happy(X0) & ~patient(X0))) & ((~happy(X0) | patient(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 11]
54. ! [X0] : (((~humble(X0) & ~generous(X0)) | (happy(X0) & ~patient(X0))) & (~happy(X0) | patient(X0) | humble(X0) | generous(X0))) [flattening 53]
55. (? [X0] : (~happy(X0) & calm(X0)) | (rich(alice) & strong(alice))) & ((~rich(alice) | ~strong(alice)) | ! [X0] : (happy(X0) | ~calm(X0))) [nnf transformation 14]
56. (? [X0] : (~happy(X0) & calm(X0)) | (rich(alice) & strong(alice))) & (~rich(alice) | ~strong(alice) | ! [X0] : (happy(X0) | ~calm(X0))) [flattening 55]
57. (? [X0] : (~happy(X0) & calm(X0)) | (rich(alice) & strong(alice))) & (~rich(alice) | ~strong(alice) | ! [X1] : (happy(X1) | ~calm(X1))) [rectify 56]
58. ? [X0] : (~happy(X0) & calm(X0)) => (~happy(sK4) & calm(sK4)) [choice axiom]
59. ((~happy(sK4) & calm(sK4)) | (rich(alice) & strong(alice))) & (~rich(alice) | ~strong(alice) | ! [X1] : (happy(X1) | ~calm(X1))) [skolemisation 57,58]
61. ! [X0] : ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0))) [nnf transformation 16]
90. ~calm(X0) | humble(X0) | generous(X0) [cnf transformation 47]
103. ~generous(X0) | happy(X0) [cnf transformation 54]
105. ~humble(X0) | happy(X0) [cnf transformation 54]
110. calm(sK4) | rich(alice) [cnf transformation 59]
112. ~happy(sK4) | rich(alice) [cnf transformation 59]
116. ~rich(X0) | ~funny(X0) [cnf transformation 61]
126. funny(alice) [cnf transformation 24]
201. 18 <=> rich(alice) [avatar definition]
203. rich(alice) <- (18) [avatar component clause 201]
205. 19 <=> happy(sK4) [avatar definition]
207. ~happy(sK4) <- (~19) [avatar component clause 205]
208. 18 | ~19 [avatar split clause 112,205,201]
215. 21 <=> calm(sK4) [avatar definition]
217. calm(sK4) <- (21) [avatar component clause 215]
218. 18 | 21 [avatar split clause 110,215,201]
309. humble(sK4) | generous(sK4) <- (21) [resolution 90,217]
311. 33 <=> generous(sK4) [avatar definition]
313. generous(sK4) <- (33) [avatar component clause 311]
315. 34 <=> humble(sK4) [avatar definition]
317. humble(sK4) <- (34) [avatar component clause 315]
318. 33 | 34 | ~21 [avatar split clause 309,215,315,311]
321. happy(sK4) <- (33) [resolution 313,103]
322. $false <- (~19, 33) [subsumption resolution 321,207]
323. 19 | ~33 [avatar contradiction clause 322]
344. happy(sK4) <- (34) [resolution 317,105]
354. $false <- (~19, 34) [subsumption resolution 344,207]
355. 19 | ~34 [avatar contradiction clause 354]
366. ~funny(alice) <- (18) [resolution 203,116]
367. $false <- (18) [subsumption resolution 366,126]
368. ~18 [avatar contradiction clause 367]
369. $false [avatar sat refutation 208,218,318,323,355,368]
% SZS output end Proof for 5342186431056762087261210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not kind is calm or brave.
If lucy is not kind then someone is either calm or generous and vice versa.
If susan is both calm and not funny then susan is both kind and not strong and vice versa.
Everyone who is wise or brave is funny or not calm and vice versa.
Everyone who is kind is not humble and vice versa.
Everyone who is not humble or happy is either not funny or rich and vice versa.
Everyone who is either kind or not curious is either not tall or patient.
Everyone who is either old or funny is brave.
Everyone who is either not generous or creative is not brave and vice versa.
Everyone who is either funny or not strong is both not happy and patient.
If someone is wise or kind then someone is either not tall or not strong.
Everyone who is either not strong or not quiet is either not creative or patient.
Everyone who is both patient and curious is not creative or wise.
Everyone who is either not happy or happy is either not old or not humble and vice versa.
Everyone who is tall or humble is both not humble and old and vice versa.
Everyone who is both not creative and patient is either humble or brave and vice versa.
Someone is either not funny or brave.
Someone is either not calm or not funny.
Someone is either patient or happy.
Someone is both strong and not creative.
Alice is generous or rich.
Susan is creative or not generous.
Someone is not patient.
Mary is tall. | Lucy is not rich. | contradiction | (![X]:((~happy(X)|~kind(X))=>(calm(X)|brave(X))))&
((~kind(lucy))<=>(?[X]:((calm(X)<~>generous(X)))))&
(((calm(susan)&~funny(susan)))<=>((kind(susan)&~strong(susan))))&
(![X]:((wise(X)|brave(X))<=>(funny(X)|~calm(X))))&
(![X]:(kind(X)<=>~humble(X)))&
(![X]:((~humble(X)|happy(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((kind(X)<~>~curious(X))=>(~tall(X)<~>patient(X))))&
(![X]:((old(X)<~>funny(X))=>brave(X)))&
(![X]:((~generous(X)<~>creative(X))<=>~brave(X)))&
(![X]:((funny(X)<~>~strong(X))=>(~happy(X)&patient(X))))&
((?[X]:((wise(X)|kind(X))))=>(?[X]:((~tall(X)<~>~strong(X)))))&
(![X]:((~strong(X)<~>~quiet(X))=>(~creative(X)<~>patient(X))))&
(![X]:((patient(X)&curious(X))=>(~creative(X)|wise(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~old(X)<~>~humble(X))))&
(![X]:((tall(X)|humble(X))<=>(~humble(X)&old(X))))&
(![X]:((~creative(X)&patient(X))<=>(humble(X)<~>brave(X))))&
(?[X]:((~funny(X)<~>brave(X))))&
(?[X]:((~calm(X)<~>~funny(X))))&
(?[X]:((patient(X)<~>happy(X))))&
(?[X]:((strong(X)&~creative(X))))&
((generous(alice)|rich(alice)))&
((creative(susan)|~generous(susan)))&
(?[X]:(~patient(X)))&
(tall(mary)) | ~rich(lucy) | [
"p1",
"p3",
"p4",
"p5",
"p7",
"p8",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2431625643160777019297920
% SZS output start Proof for 2431625643160777019297920
2. ~kind(lucy) <=> ? [X0] : (calm(X0) <~> generous(X0)) [input p1]
4. ! [X0] : ((brave(X0) | wise(X0)) <=> (~calm(X0) | funny(X0))) [input p3]
5. ! [X0] : (kind(X0) <=> ~humble(X0)) [input p4]
6. ! [X0] : ((happy(X0) | ~humble(X0)) <=> (~funny(X0) <~> rich(X0))) [input p5]
8. ! [X0] : ((old(X0) <~> funny(X0)) => brave(X0)) [input p7]
9. ! [X0] : ((~generous(X0) <~> creative(X0)) <=> ~brave(X0)) [input p8]
14. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> (~old(X0) <~> ~humble(X0))) [input p13]
15. ! [X0] : ((humble(X0) | tall(X0)) <=> (old(X0) & ~humble(X0))) [input p14]
16. ! [X0] : ((patient(X0) & ~creative(X0)) <=> (humble(X0) <~> brave(X0))) [input p15]
25. ~rich(lucy) [input hypothesis]
30. ! [X0] : (brave(X0) | (old(X0) <=> funny(X0))) [ennf transformation 8]
36. (~kind(lucy) | ! [X0] : ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (? [X0] : ((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | kind(lucy)) [nnf transformation 2]
37. (~kind(lucy) | ! [X0] : ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (? [X1] : ((~generous(X1) | ~calm(X1)) & (generous(X1) | calm(X1))) | kind(lucy)) [rectify 36]
38. ? [X1] : ((~generous(X1) | ~calm(X1)) & (generous(X1) | calm(X1))) => ((~generous(sK0) | ~calm(sK0)) & (generous(sK0) | calm(sK0))) [choice axiom]
39. (~kind(lucy) | ! [X0] : ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(sK0) | ~calm(sK0)) & (generous(sK0) | calm(sK0))) | kind(lucy)) [skolemisation 37,38]
42. ! [X0] : (((brave(X0) | wise(X0)) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | (~brave(X0) & ~wise(X0)))) [nnf transformation 4]
43. ! [X0] : ((brave(X0) | wise(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | (~brave(X0) & ~wise(X0)))) [flattening 42]
44. ! [X0] : ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0))) [nnf transformation 5]
45. ! [X0] : (((happy(X0) | ~humble(X0)) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | (~happy(X0) & humble(X0)))) [nnf transformation 6]
46. ! [X0] : ((happy(X0) | ~humble(X0) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | (~happy(X0) & humble(X0)))) [flattening 45]
48. ! [X0] : (brave(X0) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) [nnf transformation 30]
49. ! [X0] : ((((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | brave(X0)) & (~brave(X0) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0)))) & (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 14]
57. ! [X0] : (((humble(X0) | tall(X0)) | (~old(X0) | humble(X0))) & ((old(X0) & ~humble(X0)) | (~humble(X0) & ~tall(X0)))) [nnf transformation 15]
58. ! [X0] : ((humble(X0) | tall(X0) | ~old(X0) | humble(X0)) & ((old(X0) & ~humble(X0)) | (~humble(X0) & ~tall(X0)))) [flattening 57]
59. ! [X0] : (((patient(X0) & ~creative(X0)) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) & (((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (~patient(X0) | creative(X0)))) [nnf transformation 16]
60. ! [X0] : (((patient(X0) & ~creative(X0)) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) & (((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | ~patient(X0) | creative(X0))) [flattening 59]
79. ~kind(lucy) | calm(X0) | ~generous(X0) [cnf transformation 39]
85. ~brave(X0) | funny(X0) | ~calm(X0) [cnf transformation 43]
89. humble(X0) | kind(X0) [cnf transformation 44]
90. ~funny(X0) | rich(X0) | humble(X0) [cnf transformation 46]
100. ~old(X0) | funny(X0) | brave(X0) [cnf transformation 48]
102. ~brave(X0) | creative(X0) | generous(X0) [cnf transformation 49]
121. humble(X0) | old(X0) | happy(X0) | happy(X0) [cnf transformation 56]
122. humble(X0) | old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 56]
128. ~humble(X0) | ~humble(X0) [cnf transformation 58]
135. ~creative(X0) | humble(X0) | ~brave(X0) [cnf transformation 60]
150. ~rich(lucy) [cnf transformation 25]
151. ~humble(X0) [duplicate literal removal 128]
155. humble(X0) | old(X0) | happy(X0) [duplicate literal removal 121]
156. ~happy(X0) | old(X0) | humble(X0) [duplicate literal removal 122]
158. 1 <=> ! [X0] : (calm(X0) | ~generous(X0)) [avatar definition]
159. ~generous(X0) | calm(X0) <- (1) [avatar component clause 158]
161. 2 <=> kind(lucy) [avatar definition]
163. ~kind(lucy) <- (~2) [avatar component clause 161]
164. 1 | ~2 [avatar split clause 79,161,158]
217. old(X0) | humble(X0) [subsumption resolution 155,156]
222. ~creative(X0) | ~brave(X0) [subsumption resolution 135,151]
273. kind(X1) [resolution 89,151]
274. $false <- (~2) [resolution 273,163]
277. 2 [avatar contradiction clause 274]
315. funny(X0) | brave(X0) | humble(X0) [resolution 100,217]
317. funny(X0) | brave(X0) [subsumption resolution 315,151]
320. brave(X1) | rich(X1) | humble(X1) [resolution 317,90]
323. rich(X1) | brave(X1) [subsumption resolution 320,151]
804. brave(lucy) [resolution 323,150]
859. creative(lucy) | generous(lucy) [resolution 804,102]
860. funny(lucy) | ~calm(lucy) [resolution 804,85]
863. 75 <=> generous(lucy) [avatar definition]
865. generous(lucy) <- (75) [avatar component clause 863]
867. 76 <=> creative(lucy) [avatar definition]
869. creative(lucy) <- (76) [avatar component clause 867]
870. 75 | 76 [avatar split clause 859,867,863]
872. 77 <=> calm(lucy) [avatar definition]
876. 78 <=> funny(lucy) [avatar definition]
878. funny(lucy) <- (78) [avatar component clause 876]
879. ~77 | 78 [avatar split clause 860,876,872]
902. ~brave(lucy) <- (76) [resolution 869,222]
915. $false <- (76) [subsumption resolution 902,804]
916. ~76 [avatar contradiction clause 915]
927. calm(lucy) <- (1, 75) [resolution 865,159]
930. 77 | ~1 | ~75 [avatar split clause 927,863,158,872]
935. rich(lucy) | humble(lucy) <- (78) [resolution 878,90]
938. humble(lucy) <- (78) [subsumption resolution 935,150]
939. $false <- (78) [subsumption resolution 938,151]
940. ~78 [avatar contradiction clause 939]
941. $false [avatar sat refutation 164,277,870,879,916,930,940]
% SZS output end Proof for 2431625643160777019297920
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich or not happy then mary is rich or old and vice versa.
Everyone who is both not happy and curious is both happy and not strong and vice versa.
If someone is both not quiet and humble then susan is not wise and vice versa.
Everyone who is both not quiet and rich is not creative.
If someone is either wise or calm then lucy is either not calm or generous.
If someone is old or not patient then someone is not creative.
If someone is not happy or not kind then susan is tall or creative.
Everyone who is both funny and curious is either not rich or not kind.
If someone is funny or curious then someone is either happy or not brave and vice versa.
Everyone who is not happy or quiet is both old and not brave and vice versa.
Everyone who is both curious and not strong is not kind or not happy and vice versa.
Everyone who is patient is not generous and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not quiet or creative is not kind or not generous.
If alice is funny or not curious then someone is humble or tall and vice versa.
Everyone who is wise or quiet is either not kind or not funny and vice versa.
Susan is not brave.
Alice is calm.
Someone is rich or kind.
Mary is not creative or not humble.
Someone is not humble or wise.
Someone is both brave and curious.
Someone is either humble or not patient. | Lucy is old. | neutral | ((?[X]:((rich(X)|~happy(X))))<=>((rich(mary)|old(mary))))&
(![X]:((~happy(X)&curious(X))<=>(happy(X)&~strong(X))))&
((?[X]:((~quiet(X)&humble(X))))<=>(~wise(susan)))&
(![X]:((~quiet(X)&rich(X))=>~creative(X)))&
((?[X]:((wise(X)<~>calm(X))))=>((~calm(lucy)<~>generous(lucy))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((tall(susan)|creative(susan))))&
(![X]:((funny(X)&curious(X))=>(~rich(X)<~>~kind(X))))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(old(X)&~brave(X))))&
(![X]:((curious(X)&~strong(X))<=>(~kind(X)|~happy(X))))&
(![X]:(patient(X)<=>~generous(X)))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:((~quiet(X)|creative(X))=>(~kind(X)|~generous(X))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)<~>~funny(X))))&
(~brave(susan))&
(calm(alice))&
(?[X]:((rich(X)|kind(X))))&
((~creative(mary)|~humble(mary)))&
(?[X]:((~humble(X)|wise(X))))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | old(lucy) | [] | null | 0 |
If someone is not patient or not tall then alice is either not patient or not wise. Everyone who is either wise or creative is either not rich or not funny and vice versa. Everyone who is not curious is both calm and not wise. Everyone who is not funny is patient or not wise and vice versa. If someone is happy or brave then john is either not calm or rich. Everyone who is funny is either wise or not patient and vice versa. Everyone who is not generous is humble or quiet. Everyone who is both not patient and not generous is either funny or not humble and vice versa. If fred is either not rich or not humble then lucy is not generous. If someone is not old or not creative then someone is not wise and vice versa. Everyone who is either brave or not brave is either quiet or rich and vice versa. Everyone who is both curious and humble is both not old and not rich and vice versa. If john is rich or not happy then paul is generous or quiet and vice versa. Everyone who is both calm and not patient is either brave or not calm. Everyone who is not strong or patient is both happy and not curious. Mary is not curious or funny. Someone is humble. Someone is happy. Someone is not calm or not tall. | Alice is not rich. | neutral | ((?[X]:((~patient(X)|~tall(X))))=>((~patient(alice)<~>~wise(alice))))&
(![X]:((wise(X)<~>creative(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:(~curious(X)=>(calm(X)&~wise(X))))&
(![X]:(~funny(X)<=>(patient(X)|~wise(X))))&
((?[X]:((happy(X)|brave(X))))=>((~calm(john)<~>rich(john))))&
(![X]:(funny(X)<=>(wise(X)<~>~patient(X))))&
(![X]:(~generous(X)=>(humble(X)|quiet(X))))&
(![X]:((~patient(X)&~generous(X))<=>(funny(X)<~>~humble(X))))&
(((~rich(fred)<~>~humble(fred)))=>(~generous(lucy)))&
((?[X]:((~old(X)|~creative(X))))<=>(?[X]:(~wise(X))))&
(![X]:((brave(X)<~>~brave(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((curious(X)&humble(X))<=>(~old(X)&~rich(X))))&
(((rich(john)|~happy(john)))<=>((generous(paul)|quiet(paul))))&
(![X]:((calm(X)&~patient(X))=>(brave(X)<~>~calm(X))))&
(![X]:((~strong(X)|patient(X))=>(happy(X)&~curious(X))))&
((~curious(mary)|funny(mary)))&
(?[X]:(humble(X)))&
(?[X]:(happy(X)))&
(?[X]:((~calm(X)|~tall(X)))) | ~rich(alice) | [] | null | 0 |
If susan is either not quiet or not tall then someone is rich or funny and vice versa.
Everyone who is both patient and not humble is either not creative or curious.
If paul is both generous and not tall then someone is either not rich or not kind.
If fred is both not strong and humble then someone is either not happy or strong and vice versa.
If lucy is both not happy and curious then mary is not generous and vice versa.
If someone is not strong or not rich then someone is either not patient or not kind and vice versa.
Everyone who is not wise or patient is either not curious or quiet.
Everyone who is brave or old is not brave or funny and vice versa.
Everyone who is both old and wise is not brave and vice versa.
If someone is either wise or patient then someone is either not creative or happy and vice versa.
If mary is both strong and not strong then someone is strong or creative.
Everyone who is either curious or not quiet is not kind or not happy and vice versa.
Everyone who is either not funny or not happy is both not creative and generous and vice versa.
Everyone who is not curious or not quiet is both not old and not kind.
If lucy is either not patient or brave then susan is tall or not rich and vice versa.
Everyone who is not funny is humble.
Someone is either not brave or not quiet.
Paul is either happy or not humble.
Alice is either creative or not generous.
Alice is not funny or quiet.
Susan is not humble.
Paul is not calm.
Someone is generous. | Lucy is humble. | neutral | (((~quiet(susan)<~>~tall(susan)))<=>(?[X]:((rich(X)|funny(X)))))&
(![X]:((patient(X)&~humble(X))=>(~creative(X)<~>curious(X))))&
(((generous(paul)&~tall(paul)))=>(?[X]:((~rich(X)<~>~kind(X)))))&
(((~strong(fred)&humble(fred)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(((~happy(lucy)&curious(lucy)))<=>(~generous(mary)))&
((?[X]:((~strong(X)|~rich(X))))<=>(?[X]:((~patient(X)<~>~kind(X)))))&
(![X]:((~wise(X)|patient(X))=>(~curious(X)<~>quiet(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)|funny(X))))&
(![X]:((old(X)&wise(X))<=>~brave(X)))&
((?[X]:((wise(X)<~>patient(X))))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(((strong(mary)&~strong(mary)))=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~creative(X)&generous(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~old(X)&~kind(X))))&
(((~patient(lucy)<~>brave(lucy)))<=>((tall(susan)|~rich(susan))))&
(![X]:(~funny(X)=>humble(X)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((happy(paul)<~>~humble(paul)))&
((creative(alice)<~>~generous(alice)))&
((~funny(alice)|quiet(alice)))&
(~humble(susan))&
(~calm(paul))&
(?[X]:(generous(X))) | humble(lucy) | [] | null | 0 |
Everyone who is not old is either strong or quiet and vice versa.
Everyone who is either not rich or funny is either happy or not quiet and vice versa.
Everyone who is both not strong and old is either tall or happy.
Everyone who is either tall or not patient is either wise or not brave and vice versa.
Everyone who is either not creative or creative is either not kind or calm and vice versa.
If someone is tall then lucy is strong and vice versa.
Everyone who is both not humble and rich is either not rich or creative and vice versa.
Everyone who is either brave or old is not humble.
Everyone who is either happy or old is quiet.
If someone is both not funny and happy then someone is both quiet and not happy.
Everyone who is funny or patient is either not old or funny.
If someone is both not patient and not funny then fred is either not calm or brave and vice versa.
If john is both not rich and not tall then someone is either not quiet or wise.
If someone is both happy and not kind then someone is strong and vice versa.
Everyone who is either humble or strong is not patient and vice versa.
If alice is both strong and not old then someone is both not happy and not wise.
John is not strong.
John is either not brave or tall.
Susan is humble.
Mary is either old or not patient.
Alice is both not funny and patient.
Susan is happy or not wise.
Alice is either humble or kind.
Someone is both wise and happy. | John is humble. | neutral | (![X]:(~old(X)<=>(strong(X)<~>quiet(X))))&
(![X]:((~rich(X)<~>funny(X))<=>(happy(X)<~>~quiet(X))))&
(![X]:((~strong(X)&old(X))=>(tall(X)<~>happy(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(~kind(X)<~>calm(X))))&
((?[X]:(tall(X)))<=>(strong(lucy)))&
(![X]:((~humble(X)&rich(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((brave(X)<~>old(X))=>~humble(X)))&
(![X]:((happy(X)<~>old(X))=>quiet(X)))&
((?[X]:((~funny(X)&happy(X))))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((funny(X)|patient(X))=>(~old(X)<~>funny(X))))&
((?[X]:((~patient(X)&~funny(X))))<=>((~calm(fred)<~>brave(fred))))&
(((~rich(john)&~tall(john)))=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((happy(X)&~kind(X))))<=>(?[X]:(strong(X))))&
(![X]:((humble(X)<~>strong(X))<=>~patient(X)))&
(((strong(alice)&~old(alice)))=>(?[X]:((~happy(X)&~wise(X)))))&
(~strong(john))&
((~brave(john)<~>tall(john)))&
(humble(susan))&
((old(mary)<~>~patient(mary)))&
((~funny(alice)&patient(alice)))&
((happy(susan)|~wise(susan)))&
((humble(alice)<~>kind(alice)))&
(?[X]:((wise(X)&happy(X)))) | humble(john) | [] | null | 0 |
Everyone who is either not generous or not kind is humble and vice versa.
If alice is not generous then lucy is old and vice versa.
If someone is not humble then fred is either not kind or not rich.
If john is kind then someone is tall or curious and vice versa.
Everyone who is curious or not humble is both wise and curious.
If mary is both not old and brave then john is both not funny and not happy.
Everyone who is either rich or funny is humble or not quiet.
If susan is not old or brave then someone is either strong or not calm and vice versa.
Everyone who is either not funny or not calm is either not rich or not quiet and vice versa.
If alice is not strong then mary is both not calm and not patient.
If susan is calm or not rich then lucy is both old and not curious.
If someone is not patient then paul is both calm and strong and vice versa.
Everyone who is not brave or not tall is both not strong and patient.
If paul is either not humble or funny then paul is either humble or generous.
Everyone who is either not calm or kind is both happy and not calm and vice versa.
Everyone who is generous is both not patient and not curious.
Someone is not old or quiet.
Lucy is creative.
Lucy is not funny.
John is not calm.
Someone is both patient and humble.
Someone is either happy or not rich.
Alice is either strong or not brave. | Fred is rich. | neutral | (![X]:((~generous(X)<~>~kind(X))<=>humble(X)))&
((~generous(alice))<=>(old(lucy)))&
((?[X]:(~humble(X)))=>((~kind(fred)<~>~rich(fred))))&
((kind(john))<=>(?[X]:((tall(X)|curious(X)))))&
(![X]:((curious(X)|~humble(X))=>(wise(X)&curious(X))))&
(((~old(mary)&brave(mary)))=>((~funny(john)&~happy(john))))&
(![X]:((rich(X)<~>funny(X))=>(humble(X)|~quiet(X))))&
(((~old(susan)|brave(susan)))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:((~funny(X)<~>~calm(X))<=>(~rich(X)<~>~quiet(X))))&
((~strong(alice))=>((~calm(mary)&~patient(mary))))&
(((calm(susan)|~rich(susan)))=>((old(lucy)&~curious(lucy))))&
((?[X]:(~patient(X)))<=>((calm(paul)&strong(paul))))&
(![X]:((~brave(X)|~tall(X))=>(~strong(X)&patient(X))))&
(((~humble(paul)<~>funny(paul)))=>((humble(paul)<~>generous(paul))))&
(![X]:((~calm(X)<~>kind(X))<=>(happy(X)&~calm(X))))&
(![X]:(generous(X)=>(~patient(X)&~curious(X))))&
(?[X]:((~old(X)|quiet(X))))&
(creative(lucy))&
(~funny(lucy))&
(~calm(john))&
(?[X]:((patient(X)&humble(X))))&
(?[X]:((happy(X)<~>~rich(X))))&
((strong(alice)<~>~brave(alice))) | rich(fred) | [] | null | 0 |
If someone is calm or not brave then someone is not brave or not curious.
If lucy is not calm or tall then someone is both not old and kind.
If mary is kind or tall then fred is both tall and wise and vice versa.
If john is generous then someone is either kind or tall and vice versa.
If someone is generous then fred is calm.
Everyone who is both wise and happy is either not old or not rich.
If someone is both creative and not calm then someone is either not rich or rich.
Everyone who is calm is both not curious and not wise and vice versa.
If someone is not happy then someone is both not patient and not calm and vice versa.
Everyone who is not funny is both humble and funny and vice versa.
If fred is either old or not calm then fred is curious or funny.
Everyone who is generous is wise.
If lucy is either not kind or not generous then john is not happy or not funny and vice versa.
Everyone who is either not creative or old is either not humble or patient and vice versa.
Everyone who is curious or calm is brave.
If mary is either not calm or not rich then someone is either old or not quiet.
Someone is either not happy or not generous.
Fred is both not humble and happy.
Lucy is both not patient and calm.
Alice is both tall and creative.
Susan is not humble or not strong.
Mary is not tall or generous.
Someone is both not generous and curious. | Mary is tall. | contradiction | ((?[X]:((calm(X)|~brave(X))))=>(?[X]:((~brave(X)|~curious(X)))))&
(((~calm(lucy)|tall(lucy)))=>(?[X]:((~old(X)&kind(X)))))&
(((kind(mary)|tall(mary)))<=>((tall(fred)&wise(fred))))&
((generous(john))<=>(?[X]:((kind(X)<~>tall(X)))))&
((?[X]:(generous(X)))=>(calm(fred)))&
(![X]:((wise(X)&happy(X))=>(~old(X)<~>~rich(X))))&
((?[X]:((creative(X)&~calm(X))))=>(?[X]:((~rich(X)<~>rich(X)))))&
(![X]:(calm(X)<=>(~curious(X)&~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~patient(X)&~calm(X)))))&
(![X]:(~funny(X)<=>(humble(X)&funny(X))))&
(((old(fred)<~>~calm(fred)))=>((curious(fred)|funny(fred))))&
(![X]:(generous(X)=>wise(X)))&
(((~kind(lucy)<~>~generous(lucy)))<=>((~happy(john)|~funny(john))))&
(![X]:((~creative(X)<~>old(X))<=>(~humble(X)<~>patient(X))))&
(![X]:((curious(X)|calm(X))=>brave(X)))&
(((~calm(mary)<~>~rich(mary)))=>(?[X]:((old(X)<~>~quiet(X)))))&
(?[X]:((~happy(X)<~>~generous(X))))&
((~humble(fred)&happy(fred)))&
((~patient(lucy)&calm(lucy)))&
((tall(alice)&creative(alice)))&
((~humble(susan)|~strong(susan)))&
((~tall(mary)|generous(mary)))&
(?[X]:((~generous(X)&curious(X)))) | tall(mary) | [
"p2",
"p4",
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2186466676994672231573457
% SZS output start Proof for 2186466676994672231573457
3. (tall(mary) | kind(mary)) <=> (wise(fred) & tall(fred)) [input p2]
5. ? [X0] : generous(X0) => calm(fred) [input p4]
8. ! [X0] : (calm(X0) <=> (~wise(X0) & ~curious(X0))) [input p7]
22. generous(mary) | ~tall(mary) [input p21]
24. tall(mary) [input hypothesis]
31. calm(fred) | ! [X0] : ~generous(X0) [ennf transformation 5]
45. ((tall(mary) | kind(mary)) | (~wise(fred) | ~tall(fred))) & ((wise(fred) & tall(fred)) | (~tall(mary) & ~kind(mary))) [nnf transformation 3]
46. (tall(mary) | kind(mary) | ~wise(fred) | ~tall(fred)) & ((wise(fred) & tall(fred)) | (~tall(mary) & ~kind(mary))) [flattening 45]
56. ! [X0] : ((calm(X0) | (wise(X0) | curious(X0))) & ((~wise(X0) & ~curious(X0)) | ~calm(X0))) [nnf transformation 8]
57. ! [X0] : ((calm(X0) | wise(X0) | curious(X0)) & ((~wise(X0) & ~curious(X0)) | ~calm(X0))) [flattening 56]
86. wise(fred) | ~tall(mary) [cnf transformation 46]
92. calm(fred) | ~generous(X0) [cnf transformation 31]
98. ~wise(X0) | ~calm(X0) [cnf transformation 57]
137. generous(mary) | ~tall(mary) [cnf transformation 22]
140. tall(mary) [cnf transformation 24]
184. 10 <=> wise(fred) [avatar definition]
185. wise(fred) <- (10) [avatar component clause 184]
192. 12 <=> tall(mary) [avatar definition]
196. ~12 | 10 [avatar split clause 86,184,192]
223. 18 <=> ! [X0] : ~generous(X0) [avatar definition]
224. ~generous(X0) <- (18) [avatar component clause 223]
226. 19 <=> calm(fred) [avatar definition]
228. calm(fred) <- (19) [avatar component clause 226]
229. 18 | 19 [avatar split clause 92,226,223]
301. 34 <=> generous(mary) [avatar definition]
303. generous(mary) <- (34) [avatar component clause 301]
304. ~12 | 34 [avatar split clause 137,301,192]
305. 12 [avatar split clause 140,192]
306. $false <- (18, 34) [resolution 303,224]
307. ~18 | ~34 [avatar contradiction clause 306]
309. ~calm(fred) <- (10) [resolution 98,185]
310. $false <- (10, 19) [subsumption resolution 309,228]
311. ~10 | ~19 [avatar contradiction clause 310]
312. $false [avatar sat refutation 196,229,304,305,307,311]
% SZS output end Proof for 2186466676994672231573457
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall then lucy is creative or strong and vice versa. Everyone who is generous or not strong is either curious or not wise and vice versa. Everyone who is not humble is either curious or not patient and vice versa. If someone is calm then john is not strong. If mary is both not wise and not tall then fred is either not funny or not rich. Everyone who is either not patient or calm is both rich and not happy and vice versa. Everyone who is generous or not patient is both humble and brave. If someone is kind then fred is both not brave and not calm and vice versa. If susan is creative then john is both not strong and patient and vice versa. Everyone who is both not happy and tall is both not tall and not creative. Everyone who is either not creative or happy is not rich or not tall. If someone is both quiet and not tall then fred is wise or creative. If alice is either not funny or not happy then paul is not funny or strong. If susan is creative or generous then someone is both not wise and brave and vice versa. Everyone who is either tall or not tall is either tall or generous and vice versa. Everyone who is not tall is either not old or humble and vice versa. Someone is both kind and happy. Someone is happy. Someone is brave. Someone is happy or not strong. Mary is not calm. Someone is either humble or patient. Mary is old or not tall. Susan is both not rich and not humble. | Susan is not patient. | contradiction | ((?[X]:(tall(X)))<=>((creative(lucy)|strong(lucy))))&
(![X]:((generous(X)|~strong(X))<=>(curious(X)<~>~wise(X))))&
(![X]:(~humble(X)<=>(curious(X)<~>~patient(X))))&
((?[X]:(calm(X)))=>(~strong(john)))&
(((~wise(mary)&~tall(mary)))=>((~funny(fred)<~>~rich(fred))))&
(![X]:((~patient(X)<~>calm(X))<=>(rich(X)&~happy(X))))&
(![X]:((generous(X)|~patient(X))=>(humble(X)&brave(X))))&
((?[X]:(kind(X)))<=>((~brave(fred)&~calm(fred))))&
((creative(susan))<=>((~strong(john)&patient(john))))&
(![X]:((~happy(X)&tall(X))=>(~tall(X)&~creative(X))))&
(![X]:((~creative(X)<~>happy(X))=>(~rich(X)|~tall(X))))&
((?[X]:((quiet(X)&~tall(X))))=>((wise(fred)|creative(fred))))&
(((~funny(alice)<~>~happy(alice)))=>((~funny(paul)|strong(paul))))&
(((creative(susan)|generous(susan)))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((tall(X)<~>~tall(X))<=>(tall(X)<~>generous(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>humble(X))))&
(?[X]:((kind(X)&happy(X))))&
(?[X]:(happy(X)))&
(?[X]:(brave(X)))&
(?[X]:((happy(X)|~strong(X))))&
(~calm(mary))&
(?[X]:((humble(X)<~>patient(X))))&
((old(mary)|~tall(mary)))&
((~rich(susan)&~humble(susan))) | ~patient(susan) | [
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5734895336627173321988073
% SZS output start Proof for 5734895336627173321988073
7. ! [X0] : ((~patient(X0) | generous(X0)) => (brave(X0) & humble(X0))) [input p6]
24. ~humble(susan) & ~rich(susan) [input p23]
25. ~patient(susan) [input hypothesis]
30. ! [X0] : ((brave(X0) & humble(X0)) | (patient(X0) & ~generous(X0))) [ennf transformation 7]
98. patient(X0) | humble(X0) [cnf transformation 30]
140. ~humble(susan) [cnf transformation 24]
141. ~patient(susan) [cnf transformation 25]
286. humble(susan) [resolution 98,141]
288. $false [subsumption resolution 286,140]
% SZS output end Proof for 5734895336627173321988073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is creative then someone is wise and vice versa. Everyone who is either not rich or curious is either patient or generous and vice versa. If lucy is either old or quiet then susan is both not strong and not quiet and vice versa. Everyone who is not happy or not patient is not happy. Everyone who is old is both not patient and not curious and vice versa. If paul is either not kind or wise then john is both not kind and funny. Everyone who is tall is not strong and vice versa. If john is both not kind and not wise then fred is not curious or quiet. Everyone who is humble is either not rich or not calm and vice versa. Everyone who is strong or kind is either not generous or strong. Everyone who is both not funny and funny is both happy and old. Everyone who is both happy and humble is either not quiet or humble. If paul is not brave then someone is either not creative or not curious and vice versa. Everyone who is either generous or kind is both not tall and not funny. If someone is not calm or quiet then paul is either happy or not funny and vice versa. Everyone who is both brave and old is both not quiet and funny and vice versa. Someone is happy or creative. John is not quiet. John is either happy or not calm. Someone is both not old and not strong. Paul is either not creative or funny. Fred is either not patient or humble. Someone is not strong. | Paul is kind. | neutral | ((creative(john))<=>(?[X]:(wise(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(patient(X)<~>generous(X))))&
(((old(lucy)<~>quiet(lucy)))<=>((~strong(susan)&~quiet(susan))))&
(![X]:((~happy(X)|~patient(X))=>~happy(X)))&
(![X]:(old(X)<=>(~patient(X)&~curious(X))))&
(((~kind(paul)<~>wise(paul)))=>((~kind(john)&funny(john))))&
(![X]:(tall(X)<=>~strong(X)))&
(((~kind(john)&~wise(john)))=>((~curious(fred)|quiet(fred))))&
(![X]:(humble(X)<=>(~rich(X)<~>~calm(X))))&
(![X]:((strong(X)|kind(X))=>(~generous(X)<~>strong(X))))&
(![X]:((~funny(X)&funny(X))=>(happy(X)&old(X))))&
(![X]:((happy(X)&humble(X))=>(~quiet(X)<~>humble(X))))&
((~brave(paul))<=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:((generous(X)<~>kind(X))=>(~tall(X)&~funny(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>((happy(paul)<~>~funny(paul))))&
(![X]:((brave(X)&old(X))<=>(~quiet(X)&funny(X))))&
(?[X]:((happy(X)|creative(X))))&
(~quiet(john))&
((happy(john)<~>~calm(john)))&
(?[X]:((~old(X)&~strong(X))))&
((~creative(paul)<~>funny(paul)))&
((~patient(fred)<~>humble(fred)))&
(?[X]:(~strong(X))) | kind(paul) | [] | null | 0 |
If someone is not kind then someone is not happy or calm.
Everyone who is either not generous or not tall is either quiet or not patient.
Everyone who is both not calm and not rich is quiet.
If paul is tall then someone is either not creative or not happy and vice versa.
Everyone who is not funny is either not funny or not quiet and vice versa.
If lucy is quiet or wise then someone is either not patient or not old and vice versa.
If someone is wise then someone is calm or not wise and vice versa.
If someone is funny or not wise then someone is both generous and creative.
Everyone who is either not strong or calm is both not old and not kind.
If lucy is rich then someone is both not creative and not strong.
If lucy is not happy or brave then someone is not old or not tall and vice versa.
If someone is tall then someone is generous and vice versa.
Everyone who is calm is either not tall or not creative.
If someone is not tall then someone is both not old and not generous.
Everyone who is not tall is funny or not curious.
If alice is patient then someone is both patient and calm.
Someone is both not kind and rich.
Someone is not rich or not tall.
Mary is kind or not tall.
Someone is not happy or not generous.
Someone is either not old or not wise.
Someone is both strong and not kind.
John is both not rich and creative.
Lucy is either happy or not strong. | Alice is not tall. | neutral | ((?[X]:(~kind(X)))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((~generous(X)<~>~tall(X))=>(quiet(X)<~>~patient(X))))&
(![X]:((~calm(X)&~rich(X))=>quiet(X)))&
((tall(paul))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
(![X]:(~funny(X)<=>(~funny(X)<~>~quiet(X))))&
(((quiet(lucy)|wise(lucy)))<=>(?[X]:((~patient(X)<~>~old(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((calm(X)|~wise(X)))))&
((?[X]:((funny(X)|~wise(X))))=>(?[X]:((generous(X)&creative(X)))))&
(![X]:((~strong(X)<~>calm(X))=>(~old(X)&~kind(X))))&
((rich(lucy))=>(?[X]:((~creative(X)&~strong(X)))))&
(((~happy(lucy)|brave(lucy)))<=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:(tall(X)))<=>(?[X]:(generous(X))))&
(![X]:(calm(X)=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:(~tall(X)=>(funny(X)|~curious(X))))&
((patient(alice))=>(?[X]:((patient(X)&calm(X)))))&
(?[X]:((~kind(X)&rich(X))))&
(?[X]:((~rich(X)|~tall(X))))&
((kind(mary)|~tall(mary)))&
(?[X]:((~happy(X)|~generous(X))))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((strong(X)&~kind(X))))&
((~rich(john)&creative(john)))&
((happy(lucy)<~>~strong(lucy))) | ~tall(alice) | [] | null | 0 |
If someone is calm or not generous then alice is not funny or strong and vice versa. If alice is funny or not humble then fred is funny or curious. Everyone who is either strong or not generous is humble. Everyone who is not rich is either not curious or humble. Everyone who is not strong or creative is either not calm or not rich. If someone is not happy then lucy is not creative. Everyone who is not creative is both curious and wise and vice versa. If someone is both not curious and not rich then john is both tall and brave and vice versa. Everyone who is kind or not funny is both curious and rich and vice versa. Everyone who is both not creative and not brave is both generous and not tall and vice versa. If someone is generous or tall then john is either not tall or brave and vice versa. Everyone who is not generous is wise or curious and vice versa. Everyone who is humble is not old or not generous. If alice is not happy or strong then someone is not creative and vice versa. Everyone who is not humble or not calm is either not wise or kind. Everyone who is both not curious and not patient is not happy or patient and vice versa. Someone is both kind and not old. Someone is not strong. Someone is both not humble and not generous. Fred is both not patient and brave. Lucy is both calm and creative. John is both calm and kind. Paul is both kind and funny. Someone is both not calm and funny. | Alice is brave. | neutral | ((?[X]:((calm(X)|~generous(X))))<=>((~funny(alice)|strong(alice))))&
(((funny(alice)|~humble(alice)))=>((funny(fred)|curious(fred))))&
(![X]:((strong(X)<~>~generous(X))=>humble(X)))&
(![X]:(~rich(X)=>(~curious(X)<~>humble(X))))&
(![X]:((~strong(X)|creative(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:(~happy(X)))=>(~creative(lucy)))&
(![X]:(~creative(X)<=>(curious(X)&wise(X))))&
((?[X]:((~curious(X)&~rich(X))))<=>((tall(john)&brave(john))))&
(![X]:((kind(X)|~funny(X))<=>(curious(X)&rich(X))))&
(![X]:((~creative(X)&~brave(X))<=>(generous(X)&~tall(X))))&
((?[X]:((generous(X)|tall(X))))<=>((~tall(john)<~>brave(john))))&
(![X]:(~generous(X)<=>(wise(X)|curious(X))))&
(![X]:(humble(X)=>(~old(X)|~generous(X))))&
(((~happy(alice)|strong(alice)))<=>(?[X]:(~creative(X))))&
(![X]:((~humble(X)|~calm(X))=>(~wise(X)<~>kind(X))))&
(![X]:((~curious(X)&~patient(X))<=>(~happy(X)|patient(X))))&
(?[X]:((kind(X)&~old(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~humble(X)&~generous(X))))&
((~patient(fred)&brave(fred)))&
((calm(lucy)&creative(lucy)))&
((calm(john)&kind(john)))&
((kind(paul)&funny(paul)))&
(?[X]:((~calm(X)&funny(X)))) | brave(alice) | [] | null | 0 |
Everyone who is rich is both not creative and curious and vice versa.
Everyone who is kind is not kind or quiet and vice versa.
Everyone who is both not tall and humble is both generous and not curious.
Everyone who is both not humble and curious is both not brave and old.
If susan is either funny or not happy then someone is not patient.
If john is patient or generous then someone is either old or not rich and vice versa.
Everyone who is brave or strong is not curious or not old.
Everyone who is either brave or kind is not rich or humble.
If someone is either curious or rich then alice is kind or humble.
If alice is quiet or not quiet then lucy is kind.
If fred is both funny and kind then someone is not creative or tall and vice versa.
If someone is both curious and not old then someone is not kind and vice versa.
If someone is either not wise or generous then someone is either humble or not curious and vice versa.
Everyone who is strong or not calm is both not rich and not patient and vice versa.
Everyone who is either not generous or not tall is either not humble or not calm and vice versa.
If alice is both not funny and not happy then fred is both not old and old and vice versa.
Paul is either strong or humble.
Someone is either kind or strong.
Someone is not creative or rich.
Mary is not quiet or not old.
Someone is not tall or creative.
Paul is either creative or rich.
Susan is both kind and happy.
Paul is both creative and strong. | Mary is not rich. | entailment | (![X]:(rich(X)<=>(~creative(X)&curious(X))))&
(![X]:(kind(X)<=>(~kind(X)|quiet(X))))&
(![X]:((~tall(X)&humble(X))=>(generous(X)&~curious(X))))&
(![X]:((~humble(X)&curious(X))=>(~brave(X)&old(X))))&
(((funny(susan)<~>~happy(susan)))=>(?[X]:(~patient(X))))&
(((patient(john)|generous(john)))<=>(?[X]:((old(X)<~>~rich(X)))))&
(![X]:((brave(X)|strong(X))=>(~curious(X)|~old(X))))&
(![X]:((brave(X)<~>kind(X))=>(~rich(X)|humble(X))))&
((?[X]:((curious(X)<~>rich(X))))=>((kind(alice)|humble(alice))))&
(((quiet(alice)|~quiet(alice)))=>(kind(lucy)))&
(((funny(fred)&kind(fred)))<=>(?[X]:((~creative(X)|tall(X)))))&
((?[X]:((curious(X)&~old(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((~wise(X)<~>generous(X))))<=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:((strong(X)|~calm(X))<=>(~rich(X)&~patient(X))))&
(![X]:((~generous(X)<~>~tall(X))<=>(~humble(X)<~>~calm(X))))&
(((~funny(alice)&~happy(alice)))<=>((~old(fred)&old(fred))))&
((strong(paul)<~>humble(paul)))&
(?[X]:((kind(X)<~>strong(X))))&
(?[X]:((~creative(X)|rich(X))))&
((~quiet(mary)|~old(mary)))&
(?[X]:((~tall(X)|creative(X))))&
((creative(paul)<~>rich(paul)))&
((kind(susan)&happy(susan)))&
((creative(paul)&strong(paul))) | ~rich(mary) | [
"p0",
"p1",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 460182541975040053482796
% SZS output start Proof for 460182541975040053482796
1. ! [X0] : (rich(X0) <=> (curious(X0) & ~creative(X0))) [input p0]
2. ! [X0] : (kind(X0) <=> (quiet(X0) | ~kind(X0))) [input p1]
12. ? [X0] : (~old(X0) & curious(X0)) <=> ? [X0] : ~kind(X0) [input p11]
20. ~old(mary) | ~quiet(mary) [input p19]
25. rich(mary) [input hypothesis]
26. ? [X0] : (~old(X0) & curious(X0)) <=> ? [X1] : ~kind(X1) [rectify 12]
40. ! [X0] : ((rich(X0) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | ~rich(X0))) [nnf transformation 1]
41. ! [X0] : ((rich(X0) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | ~rich(X0))) [flattening 40]
42. ! [X0] : ((kind(X0) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | ~kind(X0))) [nnf transformation 2]
43. ! [X0] : ((kind(X0) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | ~kind(X0))) [flattening 42]
59. (? [X0] : (~old(X0) & curious(X0)) | ! [X1] : kind(X1)) & (? [X1] : ~kind(X1) | ! [X0] : (old(X0) | ~curious(X0))) [nnf transformation 26]
60. (? [X0] : (~old(X0) & curious(X0)) | ! [X1] : kind(X1)) & (? [X2] : ~kind(X2) | ! [X3] : (old(X3) | ~curious(X3))) [rectify 59]
61. ? [X0] : (~old(X0) & curious(X0)) => (~old(sK3) & curious(sK3)) [choice axiom]
62. ? [X2] : ~kind(X2) => ~kind(sK4) [choice axiom]
63. ((~old(sK3) & curious(sK3)) | ! [X1] : kind(X1)) & (~kind(sK4) | ! [X3] : (old(X3) | ~curious(X3))) [skolemisation 60,62,61]
84. ~rich(X0) | curious(X0) [cnf transformation 41]
86. quiet(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 43]
87. kind(X0) | kind(X0) [cnf transformation 43]
114. ~kind(sK4) | old(X3) | ~curious(X3) [cnf transformation 63]
147. ~old(mary) | ~quiet(mary) [cnf transformation 20]
155. rich(mary) [cnf transformation 25]
156. quiet(X0) | ~kind(X0) [duplicate literal removal 86]
157. kind(X0) [duplicate literal removal 87]
158. quiet(X0) [subsumption resolution 156,157]
224. ~curious(X3) | old(X3) [subsumption resolution 114,157]
290. ~old(mary) [subsumption resolution 147,158]
314. curious(mary) [resolution 84,155]
320. old(mary) [resolution 224,314]
321. $false [subsumption resolution 320,290]
% SZS output end Proof for 460182541975040053482796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not old or humble and vice versa.
Everyone who is both generous and rich is not kind and vice versa.
Everyone who is either not kind or creative is not old or humble.
If susan is not curious then someone is either quiet or not creative.
If mary is either not calm or tall then alice is not kind or brave.
Everyone who is not humble or kind is quiet.
Everyone who is quiet or not generous is rich.
If someone is not strong or generous then someone is kind and vice versa.
If someone is either not patient or patient then mary is both generous and not kind.
If lucy is not generous then john is either wise or not curious and vice versa.
Everyone who is both quiet and not rich is either funny or not wise and vice versa.
Everyone who is both not curious and creative is strong.
Everyone who is either not strong or not humble is not funny.
If someone is not old or creative then paul is funny or not wise.
If mary is either not patient or curious then mary is either not patient or not old and vice versa.
Everyone who is not happy or funny is not creative or not wise and vice versa.
Alice is either rich or happy.
Alice is wise or brave.
Someone is both tall and not curious.
John is not tall.
Alice is both wise and not humble.
Someone is not happy.
Mary is kind or not creative. | John is not happy. | neutral | (![X]:(~quiet(X)<=>(~old(X)|humble(X))))&
(![X]:((generous(X)&rich(X))<=>~kind(X)))&
(![X]:((~kind(X)<~>creative(X))=>(~old(X)|humble(X))))&
((~curious(susan))=>(?[X]:((quiet(X)<~>~creative(X)))))&
(((~calm(mary)<~>tall(mary)))=>((~kind(alice)|brave(alice))))&
(![X]:((~humble(X)|kind(X))=>quiet(X)))&
(![X]:((quiet(X)|~generous(X))=>rich(X)))&
((?[X]:((~strong(X)|generous(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)<~>patient(X))))=>((generous(mary)&~kind(mary))))&
((~generous(lucy))<=>((wise(john)<~>~curious(john))))&
(![X]:((quiet(X)&~rich(X))<=>(funny(X)<~>~wise(X))))&
(![X]:((~curious(X)&creative(X))=>strong(X)))&
(![X]:((~strong(X)<~>~humble(X))=>~funny(X)))&
((?[X]:((~old(X)|creative(X))))=>((funny(paul)|~wise(paul))))&
(((~patient(mary)<~>curious(mary)))<=>((~patient(mary)<~>~old(mary))))&
(![X]:((~happy(X)|funny(X))<=>(~creative(X)|~wise(X))))&
((rich(alice)<~>happy(alice)))&
((wise(alice)|brave(alice)))&
(?[X]:((tall(X)&~curious(X))))&
(~tall(john))&
((wise(alice)&~humble(alice)))&
(?[X]:(~happy(X)))&
((kind(mary)|~creative(mary))) | ~happy(john) | [] | null | 0 |
Everyone who is either not funny or funny is both not kind and not wise.
Everyone who is either quiet or creative is rich or not happy.
If someone is either creative or not wise then paul is both kind and creative and vice versa.
Everyone who is kind or not tall is both not strong and not wise.
If someone is either calm or not strong then someone is not rich or not brave.
Everyone who is both not patient and not tall is not rich and vice versa.
If lucy is both old and not funny then susan is either not humble or not strong.
Everyone who is either brave or calm is patient or funny and vice versa.
If someone is not brave then lucy is not brave and vice versa.
Everyone who is wise or not patient is wise or not generous and vice versa.
Everyone who is both brave and not rich is both curious and not old and vice versa.
Everyone who is either wise or kind is both not brave and kind and vice versa.
Everyone who is not patient or patient is quiet.
If john is either not generous or not brave then someone is either not quiet or quiet and vice versa.
If susan is both calm and not old then someone is both wise and not old.
Everyone who is both quiet and not creative is curious or calm and vice versa.
Someone is both tall and funny.
John is not kind.
Someone is rich or wise.
Someone is rich.
Fred is patient.
Paul is not curious. | John is rich. | entailment | (![X]:((~funny(X)<~>funny(X))=>(~kind(X)&~wise(X))))&
(![X]:((quiet(X)<~>creative(X))=>(rich(X)|~happy(X))))&
((?[X]:((creative(X)<~>~wise(X))))<=>((kind(paul)&creative(paul))))&
(![X]:((kind(X)|~tall(X))=>(~strong(X)&~wise(X))))&
((?[X]:((calm(X)<~>~strong(X))))=>(?[X]:((~rich(X)|~brave(X)))))&
(![X]:((~patient(X)&~tall(X))<=>~rich(X)))&
(((old(lucy)&~funny(lucy)))=>((~humble(susan)<~>~strong(susan))))&
(![X]:((brave(X)<~>calm(X))<=>(patient(X)|funny(X))))&
((?[X]:(~brave(X)))<=>(~brave(lucy)))&
(![X]:((wise(X)|~patient(X))<=>(wise(X)|~generous(X))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)&~old(X))))&
(![X]:((wise(X)<~>kind(X))<=>(~brave(X)&kind(X))))&
(![X]:((~patient(X)|patient(X))=>quiet(X)))&
(((~generous(john)<~>~brave(john)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(((calm(susan)&~old(susan)))=>(?[X]:((wise(X)&~old(X)))))&
(![X]:((quiet(X)&~creative(X))<=>(curious(X)|calm(X))))&
(?[X]:((tall(X)&funny(X))))&
(~kind(john))&
(?[X]:((rich(X)|wise(X))))&
(?[X]:(rich(X)))&
(patient(fred))&
(~curious(paul)) | rich(john) | [
"p0",
"p2",
"p5",
"p9",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 19980254175804118613621
% SZS output start Proof for 19980254175804118613621
1. ! [X0] : ((~funny(X0) <~> funny(X0)) => (~wise(X0) & ~kind(X0))) [input p0]
3. ? [X0] : (creative(X0) <~> ~wise(X0)) <=> (creative(paul) & kind(paul)) [input p2]
6. ! [X0] : ((~tall(X0) & ~patient(X0)) <=> ~rich(X0)) [input p5]
10. ! [X0] : ((~patient(X0) | wise(X0)) <=> (~generous(X0) | wise(X0))) [input p9]
11. ! [X0] : ((~rich(X0) & brave(X0)) <=> (~old(X0) & curious(X0))) [input p10]
13. ! [X0] : ((patient(X0) | ~patient(X0)) => quiet(X0)) [input p12]
14. (~generous(john) <~> ~brave(john)) <=> ? [X0] : (~quiet(X0) <~> quiet(X0)) [input p13]
16. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (calm(X0) | curious(X0))) [input p15]
23. ~rich(john) [input hypothesis]
26. ! [X0] : ((~wise(X0) & ~kind(X0)) | (~funny(X0) <=> funny(X0))) [ennf transformation 1]
31. ! [X0] : (quiet(X0) | (~patient(X0) & patient(X0))) [ennf transformation 13]
34. ! [X0] : ((~wise(X0) & ~kind(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) [nnf transformation 26]
35. (? [X0] : ((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (~creative(paul) | ~kind(paul))) & ((creative(paul) & kind(paul)) | ! [X0] : ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) [nnf transformation 3]
36. (? [X0] : ((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | ~creative(paul) | ~kind(paul)) & ((creative(paul) & kind(paul)) | ! [X0] : ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) [flattening 35]
37. (? [X0] : ((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | ~creative(paul) | ~kind(paul)) & ((creative(paul) & kind(paul)) | ! [X1] : ((creative(X1) | wise(X1)) & (~wise(X1) | ~creative(X1)))) [rectify 36]
38. ? [X0] : ((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) => ((wise(sK0) | ~creative(sK0)) & (~wise(sK0) | creative(sK0))) [choice axiom]
39. (((wise(sK0) | ~creative(sK0)) & (~wise(sK0) | creative(sK0))) | ~creative(paul) | ~kind(paul)) & ((creative(paul) & kind(paul)) | ! [X1] : ((creative(X1) | wise(X1)) & (~wise(X1) | ~creative(X1)))) [skolemisation 37,38]
44. ! [X0] : (((~tall(X0) & ~patient(X0)) | rich(X0)) & (~rich(X0) | (tall(X0) | patient(X0)))) [nnf transformation 6]
45. ! [X0] : (((~tall(X0) & ~patient(X0)) | rich(X0)) & (~rich(X0) | tall(X0) | patient(X0))) [flattening 44]
53. ! [X0] : (((~patient(X0) | wise(X0)) | (generous(X0) & ~wise(X0))) & ((~generous(X0) | wise(X0)) | (patient(X0) & ~wise(X0)))) [nnf transformation 10]
54. ! [X0] : ((~patient(X0) | wise(X0) | (generous(X0) & ~wise(X0))) & (~generous(X0) | wise(X0) | (patient(X0) & ~wise(X0)))) [flattening 53]
55. ! [X0] : (((~rich(X0) & brave(X0)) | (old(X0) | ~curious(X0))) & ((~old(X0) & curious(X0)) | (rich(X0) | ~brave(X0)))) [nnf transformation 11]
56. ! [X0] : (((~rich(X0) & brave(X0)) | old(X0) | ~curious(X0)) & ((~old(X0) & curious(X0)) | rich(X0) | ~brave(X0))) [flattening 55]
59. (((brave(john) | generous(john)) & (~brave(john) | ~generous(john))) | ! [X0] : ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) & (? [X0] : ((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | ((~generous(john) | brave(john)) & (~brave(john) | generous(john)))) [nnf transformation 14]
60. (((brave(john) | generous(john)) & (~brave(john) | ~generous(john))) | ! [X0] : ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) & (? [X1] : ((~quiet(X1) | quiet(X1)) & (quiet(X1) | ~quiet(X1))) | ((~generous(john) | brave(john)) & (~brave(john) | generous(john)))) [rectify 59]
61. ? [X1] : ((~quiet(X1) | quiet(X1)) & (quiet(X1) | ~quiet(X1))) => ((~quiet(sK3) | quiet(sK3)) & (quiet(sK3) | ~quiet(sK3))) [choice axiom]
62. (((brave(john) | generous(john)) & (~brave(john) | ~generous(john))) | ! [X0] : ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) & (((~quiet(sK3) | quiet(sK3)) & (quiet(sK3) | ~quiet(sK3))) | ((~generous(john) | brave(john)) & (~brave(john) | generous(john)))) [skolemisation 60,61]
65. ! [X0] : (((~creative(X0) & quiet(X0)) | (~calm(X0) & ~curious(X0))) & ((calm(X0) | curious(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 16]
66. ! [X0] : (((~creative(X0) & quiet(X0)) | (~calm(X0) & ~curious(X0))) & (calm(X0) | curious(X0) | creative(X0) | ~quiet(X0))) [flattening 65]
73. ~kind(X0) | funny(X0) | funny(X0) [cnf transformation 34]
74. ~kind(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 34]
75. ~wise(X0) | funny(X0) | funny(X0) [cnf transformation 34]
76. ~wise(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 34]
78. kind(paul) | creative(X1) | wise(X1) [cnf transformation 39]
90. ~patient(X0) | rich(X0) [cnf transformation 45]
103. ~generous(X0) | wise(X0) | patient(X0) [cnf transformation 54]
106. ~brave(X0) | rich(X0) | curious(X0) [cnf transformation 56]
116. quiet(X0) | patient(X0) [cnf transformation 31]
117. ~patient(X0) | quiet(X0) [cnf transformation 31]
125. brave(john) | generous(john) | ~quiet(X0) | ~quiet(X0) [cnf transformation 62]
131. ~curious(X0) | ~creative(X0) [cnf transformation 66]
140. ~rich(john) [cnf transformation 23]
144. brave(john) | generous(john) | ~quiet(X0) [duplicate literal removal 125]
147. ~kind(X0) | funny(X0) [duplicate literal removal 73]
148. ~kind(X0) | ~funny(X0) [duplicate literal removal 74]
149. ~wise(X0) | funny(X0) [duplicate literal removal 75]
150. ~wise(X0) | ~funny(X0) [duplicate literal removal 76]
151. ~wise(X0) [subsumption resolution 149,150]
152. ~kind(X0) [subsumption resolution 147,148]
155. 1 <=> ! [X1] : creative(X1) [avatar definition]
156. creative(X1) <- (1) [avatar component clause 155]
162. creative(X1) | wise(X1) [subsumption resolution 78,152]
163. creative(X1) [subsumption resolution 162,151]
164. 1 [avatar split clause 163,155]
213. ~generous(X0) | patient(X0) [subsumption resolution 103,151]
214. quiet(X0) [subsumption resolution 116,117]
215. brave(john) | generous(john) [subsumption resolution 144,214]
217. 14 <=> generous(john) [avatar definition]
219. generous(john) <- (14) [avatar component clause 217]
221. 15 <=> brave(john) [avatar definition]
223. brave(john) <- (15) [avatar component clause 221]
224. 14 | 15 [avatar split clause 215,221,217]
248. patient(john) <- (14) [resolution 213,219]
274. rich(john) <- (14) [resolution 248,90]
275. $false <- (14) [subsumption resolution 274,140]
276. ~14 [avatar contradiction clause 275]
339. rich(john) | curious(john) <- (15) [resolution 106,223]
340. curious(john) <- (15) [subsumption resolution 339,140]
370. ~creative(john) <- (15) [resolution 340,131]
371. $false <- (1, 15) [subsumption resolution 370,156]
372. ~1 | ~15 [avatar contradiction clause 371]
373. $false [avatar sat refutation 164,224,276,372]
% SZS output end Proof for 19980254175804118613621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not funny and not happy then someone is either not happy or brave.
Everyone who is not kind is both not humble and not old.
If someone is both funny and not strong then someone is quiet or curious.
Everyone who is wise or kind is both not generous and old.
Everyone who is wise is not wise or patient.
If someone is not generous then susan is either not generous or old and vice versa.
If someone is both not strong and not curious then mary is generous or not calm and vice versa.
Everyone who is not generous or humble is both quiet and not kind.
If someone is both strong and curious then alice is not humble or humble.
If someone is quiet then someone is funny and vice versa.
Everyone who is either creative or not kind is either happy or not humble.
Everyone who is not tall or old is either quiet or kind.
Everyone who is either not happy or tall is both old and creative and vice versa.
If susan is both wise and brave then lucy is old or happy and vice versa.
Everyone who is brave or quiet is not creative and vice versa.
If paul is kind or not wise then fred is brave and vice versa.
Alice is either happy or not quiet.
Susan is either not old or not rich.
Fred is both generous and rich.
Someone is either generous or not strong.
Fred is either wise or funny.
Someone is either curious or not happy. | Susan is tall. | entailment | (((~funny(alice)&~happy(alice)))=>(?[X]:((~happy(X)<~>brave(X)))))&
(![X]:(~kind(X)=>(~humble(X)&~old(X))))&
((?[X]:((funny(X)&~strong(X))))=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((wise(X)|kind(X))=>(~generous(X)&old(X))))&
(![X]:(wise(X)=>(~wise(X)|patient(X))))&
((?[X]:(~generous(X)))<=>((~generous(susan)<~>old(susan))))&
((?[X]:((~strong(X)&~curious(X))))<=>((generous(mary)|~calm(mary))))&
(![X]:((~generous(X)|humble(X))=>(quiet(X)&~kind(X))))&
((?[X]:((strong(X)&curious(X))))=>((~humble(alice)|humble(alice))))&
((?[X]:(quiet(X)))<=>(?[X]:(funny(X))))&
(![X]:((creative(X)<~>~kind(X))=>(happy(X)<~>~humble(X))))&
(![X]:((~tall(X)|old(X))=>(quiet(X)<~>kind(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(old(X)&creative(X))))&
(((wise(susan)&brave(susan)))<=>((old(lucy)|happy(lucy))))&
(![X]:((brave(X)|quiet(X))<=>~creative(X)))&
(((kind(paul)|~wise(paul)))<=>(brave(fred)))&
((happy(alice)<~>~quiet(alice)))&
((~old(susan)<~>~rich(susan)))&
((generous(fred)&rich(fred)))&
(?[X]:((generous(X)<~>~strong(X))))&
((wise(fred)<~>funny(fred)))&
(?[X]:((curious(X)<~>~happy(X)))) | tall(susan) | [
"p1",
"p3",
"p7",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2483384723454211235440227
% SZS output start Proof for 2483384723454211235440227
2. ! [X0] : (~kind(X0) => (~old(X0) & ~humble(X0))) [input p1]
4. ! [X0] : ((kind(X0) | wise(X0)) => (old(X0) & ~generous(X0))) [input p3]
8. ! [X0] : ((humble(X0) | ~generous(X0)) => (~kind(X0) & quiet(X0))) [input p7]
11. ! [X0] : ((creative(X0) <~> ~kind(X0)) => (happy(X0) <~> ~humble(X0))) [input p10]
12. ! [X0] : ((old(X0) | ~tall(X0)) => (quiet(X0) <~> kind(X0))) [input p11]
13. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (creative(X0) & old(X0))) [input p12]
15. ! [X0] : ((quiet(X0) | brave(X0)) <=> ~creative(X0)) [input p14]
23. ~tall(susan) [input hypothesis]
29. ! [X0] : ((~old(X0) & ~humble(X0)) | kind(X0)) [ennf transformation 2]
31. ! [X0] : ((old(X0) & ~generous(X0)) | (~kind(X0) & ~wise(X0))) [ennf transformation 4]
32. ! [X0] : ((~kind(X0) & quiet(X0)) | (~humble(X0) & generous(X0))) [ennf transformation 8]
35. ! [X0] : ((happy(X0) <~> ~humble(X0)) | (creative(X0) <=> ~kind(X0))) [ennf transformation 11]
36. ! [X0] : ((quiet(X0) <~> kind(X0)) | (~old(X0) & tall(X0))) [ennf transformation 12]
57. ! [X0] : (((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) [nnf transformation 35]
58. ! [X0] : (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | (~old(X0) & tall(X0))) [nnf transformation 36]
59. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~creative(X0) | ~old(X0))) & ((creative(X0) & old(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 13]
60. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | ~creative(X0) | ~old(X0)) & ((creative(X0) & old(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 59]
63. ! [X0] : (((quiet(X0) | brave(X0)) | creative(X0)) & (~creative(X0) | (~quiet(X0) & ~brave(X0)))) [nnf transformation 15]
64. ! [X0] : ((quiet(X0) | brave(X0) | creative(X0)) & (~creative(X0) | (~quiet(X0) & ~brave(X0)))) [flattening 63]
78. ~humble(X0) | kind(X0) [cnf transformation 29]
82. ~generous(X0) | ~kind(X0) [cnf transformation 31]
96. ~kind(X0) | generous(X0) [cnf transformation 32]
97. ~kind(X0) | ~humble(X0) [cnf transformation 32]
104. humble(X0) | ~happy(X0) | creative(X0) | kind(X0) [cnf transformation 57]
105. kind(X0) | quiet(X0) | tall(X0) [cnf transformation 58]
111. creative(X0) | tall(X0) | happy(X0) [cnf transformation 60]
121. ~creative(X0) | ~quiet(X0) [cnf transformation 64]
138. ~tall(susan) [cnf transformation 23]
212. ~humble(X0) [subsumption resolution 97,78]
213. ~kind(X0) [subsumption resolution 96,82]
230. ~happy(X0) | creative(X0) | kind(X0) [subsumption resolution 104,212]
231. ~happy(X0) | creative(X0) [subsumption resolution 230,213]
232. tall(X0) | quiet(X0) [subsumption resolution 105,213]
234. tall(X0) | creative(X0) [subsumption resolution 111,231]
328. quiet(susan) [resolution 232,138]
329. creative(susan) [resolution 234,138]
330. ~quiet(susan) [resolution 329,121]
335. $false [subsumption resolution 328,330]
% SZS output end Proof for 2483384723454211235440227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not calm is either not happy or not funny. If mary is not strong then someone is old or quiet and vice versa. If susan is not kind or kind then john is not humble and vice versa. Everyone who is both curious and quiet is not patient or not curious. Everyone who is either not old or quiet is either calm or not kind and vice versa. Everyone who is either not quiet or curious is not wise and vice versa. Everyone who is calm is either wise or quiet. Everyone who is both not tall and wise is humble or not brave. If someone is rich or old then someone is curious and vice versa. If mary is both not curious and creative then paul is either calm or not quiet. Everyone who is both not brave and not funny is not happy or happy. If paul is happy or not funny then mary is not wise or generous. If someone is both wise and humble then someone is either quiet or funny. If john is both calm and humble then paul is not generous. Everyone who is not creative or quiet is funny or patient and vice versa. Everyone who is not curious or old is both wise and calm. Paul is either not rich or old. Alice is not old or calm. Someone is either happy or generous. Fred is generous. Fred is strong or not curious. Someone is not calm. Someone is either not happy or patient. | Mary is not strong. | neutral | (![X]:((calm(X)&~calm(X))=>(~happy(X)<~>~funny(X))))&
((~strong(mary))<=>(?[X]:((old(X)|quiet(X)))))&
(((~kind(susan)|kind(susan)))<=>(~humble(john)))&
(![X]:((curious(X)&quiet(X))=>(~patient(X)|~curious(X))))&
(![X]:((~old(X)<~>quiet(X))<=>(calm(X)<~>~kind(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>~wise(X)))&
(![X]:(calm(X)=>(wise(X)<~>quiet(X))))&
(![X]:((~tall(X)&wise(X))=>(humble(X)|~brave(X))))&
((?[X]:((rich(X)|old(X))))<=>(?[X]:(curious(X))))&
(((~curious(mary)&creative(mary)))=>((calm(paul)<~>~quiet(paul))))&
(![X]:((~brave(X)&~funny(X))=>(~happy(X)|happy(X))))&
(((happy(paul)|~funny(paul)))=>((~wise(mary)|generous(mary))))&
((?[X]:((wise(X)&humble(X))))=>(?[X]:((quiet(X)<~>funny(X)))))&
(((calm(john)&humble(john)))=>(~generous(paul)))&
(![X]:((~creative(X)|quiet(X))<=>(funny(X)|patient(X))))&
(![X]:((~curious(X)|old(X))=>(wise(X)&calm(X))))&
((~rich(paul)<~>old(paul)))&
((~old(alice)|calm(alice)))&
(?[X]:((happy(X)<~>generous(X))))&
(generous(fred))&
((strong(fred)|~curious(fred)))&
(?[X]:(~calm(X)))&
(?[X]:((~happy(X)<~>patient(X)))) | ~strong(mary) | [] | null | 0 |
If mary is either brave or funny then someone is funny and vice versa.
If someone is quiet or not happy then someone is curious and vice versa.
Everyone who is both quiet and not old is either humble or not quiet and vice versa.
If someone is both rich and not curious then paul is both not wise and quiet.
Everyone who is both not old and not rich is happy or not curious and vice versa.
Everyone who is brave or calm is both not old and humble.
Everyone who is either creative or strong is not happy or not brave.
Everyone who is not humble or quiet is not tall.
Everyone who is not old or not creative is not strong and vice versa.
If mary is either not creative or strong then mary is either patient or wise and vice versa.
If mary is both not happy and rich then fred is generous and vice versa.
Everyone who is both not tall and funny is not quiet.
Everyone who is either not funny or not patient is either not happy or creative and vice versa.
Everyone who is both humble and strong is not happy.
Everyone who is both not funny and not generous is not calm or not happy and vice versa.
If alice is rich then lucy is both curious and not kind and vice versa.
Paul is both not rich and brave.
Paul is either not humble or not quiet.
Someone is either not wise or tall.
Fred is both old and not generous.
Susan is not calm or not brave.
Someone is both patient and not funny. | Mary is rich. | contradiction | (((brave(mary)<~>funny(mary)))<=>(?[X]:(funny(X))))&
((?[X]:((quiet(X)|~happy(X))))<=>(?[X]:(curious(X))))&
(![X]:((quiet(X)&~old(X))<=>(humble(X)<~>~quiet(X))))&
((?[X]:((rich(X)&~curious(X))))=>((~wise(paul)&quiet(paul))))&
(![X]:((~old(X)&~rich(X))<=>(happy(X)|~curious(X))))&
(![X]:((brave(X)|calm(X))=>(~old(X)&humble(X))))&
(![X]:((creative(X)<~>strong(X))=>(~happy(X)|~brave(X))))&
(![X]:((~humble(X)|quiet(X))=>~tall(X)))&
(![X]:((~old(X)|~creative(X))<=>~strong(X)))&
(((~creative(mary)<~>strong(mary)))<=>((patient(mary)<~>wise(mary))))&
(((~happy(mary)&rich(mary)))<=>(generous(fred)))&
(![X]:((~tall(X)&funny(X))=>~quiet(X)))&
(![X]:((~funny(X)<~>~patient(X))<=>(~happy(X)<~>creative(X))))&
(![X]:((humble(X)&strong(X))=>~happy(X)))&
(![X]:((~funny(X)&~generous(X))<=>(~calm(X)|~happy(X))))&
((rich(alice))<=>((curious(lucy)&~kind(lucy))))&
((~rich(paul)&brave(paul)))&
((~humble(paul)<~>~quiet(paul)))&
(?[X]:((~wise(X)<~>tall(X))))&
((old(fred)&~generous(fred)))&
((~calm(susan)|~brave(susan)))&
(?[X]:((patient(X)&~funny(X)))) | rich(mary) | [
"p4",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3133818088522881281334139
% SZS output start Proof for 3133818088522881281334139
5. ! [X0] : ((~rich(X0) & ~old(X0)) <=> (~curious(X0) | happy(X0))) [input p4]
11. (rich(mary) & ~happy(mary)) <=> generous(fred) [input p10]
20. ~generous(fred) & old(fred) [input p19]
23. rich(mary) [input hypothesis]
45. ! [X0] : (((~rich(X0) & ~old(X0)) | (curious(X0) & ~happy(X0))) & ((~curious(X0) | happy(X0)) | (rich(X0) | old(X0)))) [nnf transformation 5]
46. ! [X0] : (((~rich(X0) & ~old(X0)) | (curious(X0) & ~happy(X0))) & (~curious(X0) | happy(X0) | rich(X0) | old(X0))) [flattening 45]
51. ((rich(mary) & ~happy(mary)) | ~generous(fred)) & (generous(fred) | (~rich(mary) | happy(mary))) [nnf transformation 11]
52. ((rich(mary) & ~happy(mary)) | ~generous(fred)) & (generous(fred) | ~rich(mary) | happy(mary)) [flattening 51]
82. ~rich(X0) | ~happy(X0) [cnf transformation 46]
103. generous(fred) | ~rich(mary) | happy(mary) [cnf transformation 52]
131. ~generous(fred) [cnf transformation 20]
135. rich(mary) [cnf transformation 23]
223. 18 <=> generous(fred) [avatar definition]
227. 19 <=> rich(mary) [avatar definition]
236. generous(fred) | ~rich(mary) [subsumption resolution 103,82]
237. ~19 | 18 [avatar split clause 236,223,227]
269. ~18 [avatar split clause 131,223]
279. 19 [avatar split clause 135,227]
280. $false [avatar sat refutation 237,269,279]
% SZS output end Proof for 3133818088522881281334139
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not old or humble then susan is both humble and kind. If someone is not happy then mary is both not strong and strong and vice versa. Everyone who is both not humble and curious is both not happy and wise and vice versa. Everyone who is not kind is both not kind and calm and vice versa. Everyone who is not generous or curious is funny. If someone is generous then lucy is either not curious or not humble and vice versa. Everyone who is either not wise or not curious is not rich and vice versa. Everyone who is not humble is curious and vice versa. Everyone who is patient is not curious or strong. Everyone who is not strong or curious is rich. If someone is strong then alice is both not wise and generous. Everyone who is either not generous or wise is not calm and vice versa. If someone is either not funny or creative then mary is not creative and vice versa. If paul is either not wise or not old then someone is either funny or not strong and vice versa. If paul is patient then john is either quiet or strong. Everyone who is creative is funny or kind. John is not strong or not old. Someone is either not brave or brave. John is happy or tall. Alice is not brave or calm. John is wise. Someone is not quiet. Someone is not kind. | Alice is not happy. | contradiction | ((?[X]:((~old(X)|humble(X))))=>((humble(susan)&kind(susan))))&
((?[X]:(~happy(X)))<=>((~strong(mary)&strong(mary))))&
(![X]:((~humble(X)&curious(X))<=>(~happy(X)&wise(X))))&
(![X]:(~kind(X)<=>(~kind(X)&calm(X))))&
(![X]:((~generous(X)|curious(X))=>funny(X)))&
((?[X]:(generous(X)))<=>((~curious(lucy)<~>~humble(lucy))))&
(![X]:((~wise(X)<~>~curious(X))<=>~rich(X)))&
(![X]:(~humble(X)<=>curious(X)))&
(![X]:(patient(X)=>(~curious(X)|strong(X))))&
(![X]:((~strong(X)|curious(X))=>rich(X)))&
((?[X]:(strong(X)))=>((~wise(alice)&generous(alice))))&
(![X]:((~generous(X)<~>wise(X))<=>~calm(X)))&
((?[X]:((~funny(X)<~>creative(X))))<=>(~creative(mary)))&
(((~wise(paul)<~>~old(paul)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((patient(paul))=>((quiet(john)<~>strong(john))))&
(![X]:(creative(X)=>(funny(X)|kind(X))))&
((~strong(john)|~old(john)))&
(?[X]:((~brave(X)<~>brave(X))))&
((happy(john)|tall(john)))&
((~brave(alice)|calm(alice)))&
(wise(john))&
(?[X]:(~quiet(X)))&
(?[X]:(~kind(X))) | ~happy(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 2659837658056421556912228
% SZS output start Proof for 2659837658056421556912228
2. ? [X0] : ~happy(X0) <=> (strong(mary) & ~strong(mary)) [input p1]
24. ~happy(alice) [input hypothesis]
37. (? [X0] : ~happy(X0) | (~strong(mary) | strong(mary))) & ((strong(mary) & ~strong(mary)) | ! [X0] : happy(X0)) [nnf transformation 2]
38. (? [X0] : ~happy(X0) | ~strong(mary) | strong(mary)) & ((strong(mary) & ~strong(mary)) | ! [X0] : happy(X0)) [flattening 37]
39. (? [X0] : ~happy(X0) | ~strong(mary) | strong(mary)) & ((strong(mary) & ~strong(mary)) | ! [X1] : happy(X1)) [rectify 38]
40. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
41. (~happy(sK0) | ~strong(mary) | strong(mary)) & ((strong(mary) & ~strong(mary)) | ! [X1] : happy(X1)) [skolemisation 39,40]
70. ~strong(mary) | happy(X1) [cnf transformation 41]
71. strong(mary) | happy(X1) [cnf transformation 41]
117. ~happy(alice) [cnf transformation 24]
137. 5 <=> ! [X1] : happy(X1) [avatar definition]
138. happy(X1) <- (5) [avatar component clause 137]
140. 6 <=> strong(mary) [avatar definition]
143. 5 | 6 [avatar split clause 71,140,137]
144. 5 | ~6 [avatar split clause 70,140,137]
247. $false <- (5) [resolution 138,117]
248. ~5 [avatar contradiction clause 247]
249. $false [avatar sat refutation 143,144,248]
% SZS output end Proof for 2659837658056421556912228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is rich or old and vice versa. Everyone who is either strong or rich is both generous and quiet and vice versa. If john is either not happy or calm then someone is not brave or not creative. Everyone who is old is not happy or brave. If someone is both rich and curious then john is quiet or happy. If john is both not patient and happy then susan is either not creative or not calm. Everyone who is either not strong or not brave is not happy. Everyone who is both not generous and not strong is rich and vice versa. If someone is both not quiet and rich then fred is not brave or not quiet and vice versa. If fred is both not funny and creative then fred is funny and vice versa. Everyone who is tall is either patient or rich and vice versa. Everyone who is either not rich or creative is not tall or humble. Everyone who is kind is either funny or not curious. Everyone who is both rich and not quiet is kind and vice versa. If mary is not calm then alice is either not strong or old and vice versa. Susan is not creative. Alice is not calm. Alice is either not strong or not wise. Lucy is both not old and funny. Someone is creative or not curious. Someone is rich or not creative. | John is old. | neutral | (![X]:(~funny(X)<=>(rich(X)|old(X))))&
(![X]:((strong(X)<~>rich(X))<=>(generous(X)&quiet(X))))&
(((~happy(john)<~>calm(john)))=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:(old(X)=>(~happy(X)|brave(X))))&
((?[X]:((rich(X)&curious(X))))=>((quiet(john)|happy(john))))&
(((~patient(john)&happy(john)))=>((~creative(susan)<~>~calm(susan))))&
(![X]:((~strong(X)<~>~brave(X))=>~happy(X)))&
(![X]:((~generous(X)&~strong(X))<=>rich(X)))&
((?[X]:((~quiet(X)&rich(X))))<=>((~brave(fred)|~quiet(fred))))&
(((~funny(fred)&creative(fred)))<=>(funny(fred)))&
(![X]:(tall(X)<=>(patient(X)<~>rich(X))))&
(![X]:((~rich(X)<~>creative(X))=>(~tall(X)|humble(X))))&
(![X]:(kind(X)=>(funny(X)<~>~curious(X))))&
(![X]:((rich(X)&~quiet(X))<=>kind(X)))&
((~calm(mary))<=>((~strong(alice)<~>old(alice))))&
(~creative(susan))&
(~calm(alice))&
((~strong(alice)<~>~wise(alice)))&
((~old(lucy)&funny(lucy)))&
(?[X]:((creative(X)|~curious(X))))&
(?[X]:((rich(X)|~creative(X)))) | old(john) | [] | null | 0 |
Everyone who is generous or humble is not humble or not creative.
If susan is funny or not kind then someone is either not patient or wise.
If fred is both not strong and quiet then paul is not brave or funny and vice versa.
If fred is quiet or generous then someone is both not patient and kind and vice versa.
Everyone who is both not calm and brave is both not patient and not curious.
Everyone who is either not rich or not patient is either not tall or calm and vice versa.
If lucy is not kind or happy then someone is either not generous or humble and vice versa.
Everyone who is not generous or not funny is not funny or funny and vice versa.
If lucy is not curious or not patient then paul is calm.
If someone is not generous then paul is either strong or wise and vice versa.
Everyone who is either not calm or not creative is brave or funny and vice versa.
If someone is either happy or not curious then someone is both not brave and strong.
Everyone who is both not creative and quiet is not tall and vice versa.
If lucy is not patient then susan is both quiet and creative.
Everyone who is not humble or calm is not tall and vice versa.
Everyone who is not curious is quiet or generous and vice versa.
Someone is either calm or not strong.
Lucy is either not curious or not quiet.
Lucy is not quiet or strong.
Someone is both curious and not brave.
Someone is old.
Someone is kind or not happy.
Fred is not calm.
Lucy is either creative or not curious. | Paul is funny. | neutral | (![X]:((generous(X)|humble(X))=>(~humble(X)|~creative(X))))&
(((funny(susan)|~kind(susan)))=>(?[X]:((~patient(X)<~>wise(X)))))&
(((~strong(fred)&quiet(fred)))<=>((~brave(paul)|funny(paul))))&
(((quiet(fred)|generous(fred)))<=>(?[X]:((~patient(X)&kind(X)))))&
(![X]:((~calm(X)&brave(X))=>(~patient(X)&~curious(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>(~tall(X)<~>calm(X))))&
(((~kind(lucy)|happy(lucy)))<=>(?[X]:((~generous(X)<~>humble(X)))))&
(![X]:((~generous(X)|~funny(X))<=>(~funny(X)|funny(X))))&
(((~curious(lucy)|~patient(lucy)))=>(calm(paul)))&
((?[X]:(~generous(X)))<=>((strong(paul)<~>wise(paul))))&
(![X]:((~calm(X)<~>~creative(X))<=>(brave(X)|funny(X))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:((~creative(X)&quiet(X))<=>~tall(X)))&
((~patient(lucy))=>((quiet(susan)&creative(susan))))&
(![X]:((~humble(X)|calm(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>(quiet(X)|generous(X))))&
(?[X]:((calm(X)<~>~strong(X))))&
((~curious(lucy)<~>~quiet(lucy)))&
((~quiet(lucy)|strong(lucy)))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:(old(X)))&
(?[X]:((kind(X)|~happy(X))))&
(~calm(fred))&
((creative(lucy)<~>~curious(lucy))) | funny(paul) | [] | null | 0 |
Everyone who is old is both not generous and not calm.
Everyone who is not brave or not patient is not creative and vice versa.
Everyone who is generous is curious or patient and vice versa.
Everyone who is not old is both not curious and not rich.
Everyone who is not tall or tall is either not tall or generous.
Everyone who is both strong and not wise is both not creative and brave and vice versa.
If someone is humble then fred is happy or not kind.
If john is curious then someone is patient or not calm and vice versa.
If mary is curious then someone is both funny and generous.
Everyone who is old is either wise or not patient and vice versa.
If fred is strong or not calm then paul is not humble and vice versa.
If john is either not kind or not generous then alice is either not quiet or creative.
If someone is funny then someone is not quiet and vice versa.
Everyone who is either quiet or not creative is not rich and vice versa.
Everyone who is not tall is funny and vice versa.
Everyone who is not humble or humble is both not patient and not rich.
John is either not rich or not strong.
Paul is calm.
Someone is both not old and humble.
Someone is curious or not generous.
Fred is either not generous or rich. | John is quiet. | contradiction | (![X]:(old(X)=>(~generous(X)&~calm(X))))&
(![X]:((~brave(X)|~patient(X))<=>~creative(X)))&
(![X]:(generous(X)<=>(curious(X)|patient(X))))&
(![X]:(~old(X)=>(~curious(X)&~rich(X))))&
(![X]:((~tall(X)|tall(X))=>(~tall(X)<~>generous(X))))&
(![X]:((strong(X)&~wise(X))<=>(~creative(X)&brave(X))))&
((?[X]:(humble(X)))=>((happy(fred)|~kind(fred))))&
((curious(john))<=>(?[X]:((patient(X)|~calm(X)))))&
((curious(mary))=>(?[X]:((funny(X)&generous(X)))))&
(![X]:(old(X)<=>(wise(X)<~>~patient(X))))&
(((strong(fred)|~calm(fred)))<=>(~humble(paul)))&
(((~kind(john)<~>~generous(john)))=>((~quiet(alice)<~>creative(alice))))&
((?[X]:(funny(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~humble(X)|humble(X))=>(~patient(X)&~rich(X))))&
((~rich(john)<~>~strong(john)))&
(calm(paul))&
(?[X]:((~old(X)&humble(X))))&
(?[X]:((curious(X)|~generous(X))))&
((~generous(fred)<~>rich(fred))) | quiet(john) | [
"p1",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 706325680263252620500978
% SZS output start Proof for 706325680263252620500978
2. ! [X0] : ((~patient(X0) | ~brave(X0)) <=> ~creative(X0)) [input p1]
14. ! [X0] : ((quiet(X0) <~> ~creative(X0)) <=> ~rich(X0)) [input p13]
16. ! [X0] : ((humble(X0) | ~humble(X0)) => (~rich(X0) & ~patient(X0))) [input p15]
22. quiet(john) [input hypothesis]
30. ! [X0] : ((~rich(X0) & ~patient(X0)) | (~humble(X0) & humble(X0))) [ennf transformation 16]
31. ! [X0] : (((~patient(X0) | ~brave(X0)) | creative(X0)) & (~creative(X0) | (patient(X0) & brave(X0)))) [nnf transformation 2]
32. ! [X0] : ((~patient(X0) | ~brave(X0) | creative(X0)) & (~creative(X0) | (patient(X0) & brave(X0)))) [flattening 31]
53. ! [X0] : ((((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | rich(X0)) & (~rich(X0) | ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0))))) [nnf transformation 14]
64. ~creative(X0) | patient(X0) [cnf transformation 32]
100. ~quiet(X0) | creative(X0) | rich(X0) [cnf transformation 53]
103. ~patient(X0) | humble(X0) [cnf transformation 30]
104. ~humble(X0) | ~patient(X0) [cnf transformation 30]
105. ~rich(X0) | humble(X0) [cnf transformation 30]
106. ~humble(X0) | ~rich(X0) [cnf transformation 30]
115. quiet(john) [cnf transformation 22]
127. 3 <=> ! [X0] : ~patient(X0) [avatar definition]
128. ~patient(X0) <- (3) [avatar component clause 127]
204. ~rich(X0) [subsumption resolution 105,106]
205. ~patient(X0) [subsumption resolution 103,104]
206. 3 [avatar split clause 205,127]
248. 22 <=> creative(john) [avatar definition]
249. creative(john) <- (22) [avatar component clause 248]
275. creative(john) | rich(john) [resolution 100,115]
279. creative(john) [subsumption resolution 275,204]
280. 22 [avatar split clause 279,248]
282. patient(john) <- (22) [resolution 249,64]
284. $false <- (3, 22) [subsumption resolution 282,128]
285. ~3 | ~22 [avatar contradiction clause 284]
288. $false [avatar sat refutation 206,280,285]
% SZS output end Proof for 706325680263252620500978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is not strong and vice versa.
Everyone who is either not tall or strong is either quiet or not brave and vice versa.
If someone is quiet or brave then someone is both strong and funny.
If susan is both not patient and old then someone is both calm and humble and vice versa.
Everyone who is both rich and not funny is happy and vice versa.
Everyone who is either not old or strong is brave.
Everyone who is either not kind or calm is both creative and tall.
Everyone who is generous or not creative is not happy or kind.
If john is calm or old then someone is both not generous and strong and vice versa.
Everyone who is either calm or not patient is not calm or not tall.
If someone is not curious then someone is both funny and happy and vice versa.
If someone is wise then paul is not generous and vice versa.
Everyone who is both not happy and not old is patient or not curious.
Everyone who is happy or not strong is humble or not rich and vice versa.
If fred is either not brave or not tall then lucy is humble.
If fred is not quiet or not patient then susan is both quiet and funny and vice versa.
Someone is either quiet or not happy.
Alice is not wise or kind.
Alice is either rich or not patient.
Someone is either quiet or not wise.
Someone is either tall or not patient.
Someone is not tall.
Mary is both not wise and curious. | Mary is humble. | neutral | (![X]:(happy(X)<=>~strong(X)))&
(![X]:((~tall(X)<~>strong(X))<=>(quiet(X)<~>~brave(X))))&
((?[X]:((quiet(X)|brave(X))))=>(?[X]:((strong(X)&funny(X)))))&
(((~patient(susan)&old(susan)))<=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((rich(X)&~funny(X))<=>happy(X)))&
(![X]:((~old(X)<~>strong(X))=>brave(X)))&
(![X]:((~kind(X)<~>calm(X))=>(creative(X)&tall(X))))&
(![X]:((generous(X)|~creative(X))=>(~happy(X)|kind(X))))&
(((calm(john)|old(john)))<=>(?[X]:((~generous(X)&strong(X)))))&
(![X]:((calm(X)<~>~patient(X))=>(~calm(X)|~tall(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((funny(X)&happy(X)))))&
((?[X]:(wise(X)))<=>(~generous(paul)))&
(![X]:((~happy(X)&~old(X))=>(patient(X)|~curious(X))))&
(![X]:((happy(X)|~strong(X))<=>(humble(X)|~rich(X))))&
(((~brave(fred)<~>~tall(fred)))=>(humble(lucy)))&
(((~quiet(fred)|~patient(fred)))<=>((quiet(susan)&funny(susan))))&
(?[X]:((quiet(X)<~>~happy(X))))&
((~wise(alice)|kind(alice)))&
((rich(alice)<~>~patient(alice)))&
(?[X]:((quiet(X)<~>~wise(X))))&
(?[X]:((tall(X)<~>~patient(X))))&
(?[X]:(~tall(X)))&
((~wise(mary)&curious(mary))) | humble(mary) | [] | null | 0 |
If alice is both not patient and not calm then fred is not old or patient.
Everyone who is brave or kind is both tall and brave and vice versa.
If someone is calm then someone is not quiet and vice versa.
Everyone who is both not rich and not funny is both tall and calm and vice versa.
Everyone who is not humble or funny is either rich or tall.
Everyone who is strong or not calm is both funny and not creative and vice versa.
Everyone who is both not creative and not happy is both kind and not old and vice versa.
Everyone who is not curious is either not generous or not brave.
Everyone who is not old or not wise is quiet or wise and vice versa.
If someone is not kind or not rich then someone is brave or funny and vice versa.
Everyone who is not funny or not wise is generous or not funny and vice versa.
Everyone who is humble or creative is not rich and vice versa.
If susan is humble then someone is not brave.
If fred is not generous then mary is either kind or not patient and vice versa.
If someone is both not humble and not strong then someone is either patient or not strong.
Everyone who is both not happy and not quiet is both strong and not creative.
Susan is strong.
Someone is either not brave or brave.
Someone is generous or curious.
Someone is both not rich and curious.
John is both not creative and not old.
Someone is curious or not calm.
Someone is not funny.
John is both wise and tall. | Alice is not creative. | neutral | (((~patient(alice)&~calm(alice)))=>((~old(fred)|patient(fred))))&
(![X]:((brave(X)|kind(X))<=>(tall(X)&brave(X))))&
((?[X]:(calm(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((~rich(X)&~funny(X))<=>(tall(X)&calm(X))))&
(![X]:((~humble(X)|funny(X))=>(rich(X)<~>tall(X))))&
(![X]:((strong(X)|~calm(X))<=>(funny(X)&~creative(X))))&
(![X]:((~creative(X)&~happy(X))<=>(kind(X)&~old(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~brave(X))))&
(![X]:((~old(X)|~wise(X))<=>(quiet(X)|wise(X))))&
((?[X]:((~kind(X)|~rich(X))))<=>(?[X]:((brave(X)|funny(X)))))&
(![X]:((~funny(X)|~wise(X))<=>(generous(X)|~funny(X))))&
(![X]:((humble(X)|creative(X))<=>~rich(X)))&
((humble(susan))=>(?[X]:(~brave(X))))&
((~generous(fred))<=>((kind(mary)<~>~patient(mary))))&
((?[X]:((~humble(X)&~strong(X))))=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:((~happy(X)&~quiet(X))=>(strong(X)&~creative(X))))&
(strong(susan))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:((~rich(X)&curious(X))))&
((~creative(john)&~old(john)))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:(~funny(X)))&
((wise(john)&tall(john))) | ~creative(alice) | [] | null | 0 |
If fred is happy or curious then someone is not patient or brave.
If someone is either humble or not calm then someone is both not quiet and not curious.
If someone is either old or not rich then paul is either rich or not tall and vice versa.
Everyone who is not curious or funny is curious and vice versa.
If fred is both not happy and not tall then lucy is creative.
If someone is either not funny or not old then mary is either not tall or not kind.
If lucy is either not brave or generous then someone is either not old or not generous and vice versa.
Everyone who is either rich or not creative is not patient or not creative and vice versa.
If someone is humble or not brave then fred is both creative and not creative.
If paul is rich or generous then paul is either not curious or not calm and vice versa.
If fred is not rich then fred is either not creative or not strong.
Everyone who is tall is both humble and not humble and vice versa.
Everyone who is generous is patient or creative.
If susan is both not funny and rich then someone is either not funny or curious.
If someone is both patient and not curious then susan is both not old and quiet.
Susan is generous or not humble.
Someone is either wise or rich.
Someone is either strong or rich.
Lucy is not strong or not generous. | Fred is not tall. | entailment | (((happy(fred)|curious(fred)))=>(?[X]:((~patient(X)|brave(X)))))&
((?[X]:((humble(X)<~>~calm(X))))=>(?[X]:((~quiet(X)&~curious(X)))))&
((?[X]:((old(X)<~>~rich(X))))<=>((rich(paul)<~>~tall(paul))))&
(![X]:((~curious(X)|funny(X))<=>curious(X)))&
(((~happy(fred)&~tall(fred)))=>(creative(lucy)))&
((?[X]:((~funny(X)<~>~old(X))))=>((~tall(mary)<~>~kind(mary))))&
(((~brave(lucy)<~>generous(lucy)))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((rich(X)<~>~creative(X))<=>(~patient(X)|~creative(X))))&
((?[X]:((humble(X)|~brave(X))))=>((creative(fred)&~creative(fred))))&
(((rich(paul)|generous(paul)))<=>((~curious(paul)<~>~calm(paul))))&
((~rich(fred))=>((~creative(fred)<~>~strong(fred))))&
(![X]:(tall(X)<=>(humble(X)&~humble(X))))&
(![X]:(generous(X)=>(patient(X)|creative(X))))&
(((~funny(susan)&rich(susan)))=>(?[X]:((~funny(X)<~>curious(X)))))&
((?[X]:((patient(X)&~curious(X))))=>((~old(susan)&quiet(susan))))&
((generous(susan)|~humble(susan)))&
(?[X]:((wise(X)<~>rich(X))))&
(?[X]:((strong(X)<~>rich(X))))&
((~strong(lucy)|~generous(lucy))) | ~tall(fred) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8901764334918413753903826
% SZS output start Proof for 8901764334918413753903826
12. ! [X0] : (tall(X0) <=> (~humble(X0) & humble(X0))) [input p11]
20. tall(fred) [input hypothesis]
56. ! [X0] : ((tall(X0) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | ~tall(X0))) [nnf transformation 12]
57. ! [X0] : ((tall(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ~tall(X0))) [flattening 56]
115. humble(X0) | ~tall(X0) [cnf transformation 57]
116. ~humble(X0) | ~tall(X0) [cnf transformation 57]
129. tall(fred) [cnf transformation 20]
297. ~tall(X0) [subsumption resolution 115,116]
332. $false [subsumption resolution 129,297]
% SZS output end Proof for 8901764334918413753903826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then lucy is both happy and not kind.
Everyone who is patient is not kind or wise and vice versa.
Everyone who is not brave is curious or kind.
Everyone who is both humble and not humble is both not quiet and not creative.
Everyone who is either not calm or brave is quiet and vice versa.
Everyone who is funny or not brave is both not happy and not calm.
Everyone who is not old or not tall is not creative.
Everyone who is not wise is both not tall and not brave.
Everyone who is rich is either old or wise and vice versa.
Everyone who is both not funny and patient is not rich.
Everyone who is not wise or not creative is not tall or calm.
If someone is not happy then someone is either not creative or calm and vice versa.
If mary is either strong or calm then mary is strong.
Everyone who is not creative or wise is not quiet or not creative and vice versa.
If someone is quiet then paul is happy or not quiet.
Everyone who is either not creative or not quiet is either calm or old.
Someone is not kind.
Someone is not creative.
Susan is either not wise or not funny.
John is wise.
Someone is patient.
Alice is not old or funny.
Someone is both old and funny.
Someone is not rich or not generous. | Lucy is brave. | entailment | ((?[X]:(~tall(X)))=>((happy(lucy)&~kind(lucy))))&
(![X]:(patient(X)<=>(~kind(X)|wise(X))))&
(![X]:(~brave(X)=>(curious(X)|kind(X))))&
(![X]:((humble(X)&~humble(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~calm(X)<~>brave(X))<=>quiet(X)))&
(![X]:((funny(X)|~brave(X))=>(~happy(X)&~calm(X))))&
(![X]:((~old(X)|~tall(X))=>~creative(X)))&
(![X]:(~wise(X)=>(~tall(X)&~brave(X))))&
(![X]:(rich(X)<=>(old(X)<~>wise(X))))&
(![X]:((~funny(X)&patient(X))=>~rich(X)))&
(![X]:((~wise(X)|~creative(X))=>(~tall(X)|calm(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(((strong(mary)<~>calm(mary)))=>(strong(mary)))&
(![X]:((~creative(X)|wise(X))<=>(~quiet(X)|~creative(X))))&
((?[X]:(quiet(X)))=>((happy(paul)|~quiet(paul))))&
(![X]:((~creative(X)<~>~quiet(X))=>(calm(X)<~>old(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~creative(X)))&
((~wise(susan)<~>~funny(susan)))&
(wise(john))&
(?[X]:(patient(X)))&
((~old(alice)|funny(alice)))&
(?[X]:((old(X)&funny(X))))&
(?[X]:((~rich(X)|~generous(X)))) | brave(lucy) | [
"p0",
"p4",
"p5",
"p7",
"p10",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1818830330653790130602734
% SZS output start Proof for 1818830330653790130602734
1. ? [X0] : ~tall(X0) => (~kind(lucy) & happy(lucy)) [input p0]
5. ! [X0] : ((~calm(X0) <~> brave(X0)) <=> quiet(X0)) [input p4]
6. ! [X0] : ((~brave(X0) | funny(X0)) => (~calm(X0) & ~happy(X0))) [input p5]
8. ! [X0] : (~wise(X0) => (~brave(X0) & ~tall(X0))) [input p7]
11. ! [X0] : ((~creative(X0) | ~wise(X0)) => (calm(X0) | ~tall(X0))) [input p10]
12. ? [X0] : ~happy(X0) <=> ? [X0] : (~creative(X0) <~> calm(X0)) [input p11]
14. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (~creative(X0) | ~quiet(X0))) [input p13]
23. ? [X0] : (funny(X0) & old(X0)) [input p22]
25. ~brave(lucy) [input hypothesis]
26. ? [X0] : ~happy(X0) <=> ? [X1] : (~creative(X1) <~> calm(X1)) [rectify 12]
30. (~kind(lucy) & happy(lucy)) | ! [X0] : tall(X0) [ennf transformation 1]
33. ! [X0] : ((~calm(X0) & ~happy(X0)) | (brave(X0) & ~funny(X0))) [ennf transformation 6]
35. ! [X0] : ((~brave(X0) & ~tall(X0)) | wise(X0)) [ennf transformation 8]
39. ! [X0] : ((calm(X0) | ~tall(X0)) | (creative(X0) & wise(X0))) [ennf transformation 11]
40. ! [X0] : (calm(X0) | ~tall(X0) | (creative(X0) & wise(X0))) [flattening 39]
47. ! [X0] : ((((~brave(X0) | calm(X0)) & (brave(X0) | ~calm(X0))) | ~quiet(X0)) & (quiet(X0) | ((~calm(X0) | ~brave(X0)) & (brave(X0) | calm(X0))))) [nnf transformation 5]
49. (? [X0] : ~happy(X0) | ! [X1] : ((~creative(X1) | ~calm(X1)) & (calm(X1) | creative(X1)))) & (? [X1] : ((~calm(X1) | creative(X1)) & (calm(X1) | ~creative(X1))) | ! [X0] : happy(X0)) [nnf transformation 26]
50. (? [X0] : ~happy(X0) | ! [X1] : ((~creative(X1) | ~calm(X1)) & (calm(X1) | creative(X1)))) & (? [X2] : ((~calm(X2) | creative(X2)) & (calm(X2) | ~creative(X2))) | ! [X3] : happy(X3)) [rectify 49]
51. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
52. ? [X2] : ((~calm(X2) | creative(X2)) & (calm(X2) | ~creative(X2))) => ((~calm(sK1) | creative(sK1)) & (calm(sK1) | ~creative(sK1))) [choice axiom]
53. (~happy(sK0) | ! [X1] : ((~creative(X1) | ~calm(X1)) & (calm(X1) | creative(X1)))) & (((~calm(sK1) | creative(sK1)) & (calm(sK1) | ~creative(sK1))) | ! [X3] : happy(X3)) [skolemisation 50,52,51]
55. ! [X0] : (((wise(X0) | ~creative(X0)) | (creative(X0) & quiet(X0))) & ((~creative(X0) | ~quiet(X0)) | (~wise(X0) & creative(X0)))) [nnf transformation 14]
56. ! [X0] : ((wise(X0) | ~creative(X0) | (creative(X0) & quiet(X0))) & (~creative(X0) | ~quiet(X0) | (~wise(X0) & creative(X0)))) [flattening 55]
65. ? [X0] : (funny(X0) & old(X0)) => (funny(sK5) & old(sK5)) [choice axiom]
66. funny(sK5) & old(sK5) [skolemisation 23,65]
67. happy(lucy) | tall(X0) [cnf transformation 30]
74. calm(X0) | brave(X0) | quiet(X0) [cnf transformation 47]
75. ~calm(X0) | quiet(X0) | ~brave(X0) [cnf transformation 47]
76. ~calm(X0) | brave(X0) | ~quiet(X0) [cnf transformation 47]
78. ~funny(X0) | ~happy(X0) [cnf transformation 33]
79. ~happy(X0) | brave(X0) [cnf transformation 33]
81. ~calm(X0) | brave(X0) [cnf transformation 33]
84. ~tall(X0) | wise(X0) [cnf transformation 35]
90. ~tall(X0) | calm(X0) | creative(X0) [cnf transformation 40]
91. calm(sK1) | ~creative(sK1) | happy(X3) [cnf transformation 53]
92. ~calm(sK1) | creative(sK1) | happy(X3) [cnf transformation 53]
98. ~creative(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 56]
114. funny(sK5) [cnf transformation 66]
115. ~brave(lucy) [cnf transformation 25]
118. 1 <=> ! [X0] : tall(X0) [avatar definition]
119. tall(X0) <- (1) [avatar component clause 118]
126. 3 <=> happy(lucy) [avatar definition]
128. happy(lucy) <- (3) [avatar component clause 126]
129. 1 | 3 [avatar split clause 67,126,118]
139. 6 <=> ! [X1] : (calm(X1) | creative(X1)) [avatar definition]
140. calm(X1) | creative(X1) <- (6) [avatar component clause 139]
143. 7 <=> ! [X3] : happy(X3) [avatar definition]
144. happy(X3) <- (7) [avatar component clause 143]
146. 8 <=> creative(sK1) [avatar definition]
148. creative(sK1) <- (8) [avatar component clause 146]
150. 9 <=> calm(sK1) [avatar definition]
151. calm(sK1) <- (9) [avatar component clause 150]
152. ~calm(sK1) <- (~9) [avatar component clause 150]
153. 7 | 8 | ~9 [avatar split clause 92,150,146,143]
154. 7 | ~8 | 9 [avatar split clause 91,150,146,143]
199. ~happy(sK5) [resolution 78,114]
200. brave(lucy) <- (3) [resolution 79,128]
201. $false <- (3) [subsumption resolution 200,115]
202. ~3 [avatar contradiction clause 201]
204. wise(X0) <- (1) [resolution 84,119]
211. brave(X0) | quiet(X0) | brave(X0) [resolution 74,81]
215. quiet(X0) | brave(X0) [duplicate literal removal 211]
249. calm(X0) | creative(X0) <- (1) [resolution 90,119]
250. 6 | ~1 [avatar split clause 249,118,139]
259. creative(sK1) <- (6, ~9) [resolution 140,152]
265. 8 | ~6 | 9 [avatar split clause 259,150,139,146]
269. $false <- (7) [resolution 144,199]
270. ~7 [avatar contradiction clause 269]
275. brave(sK1) | ~quiet(sK1) <- (9) [resolution 151,76]
276. quiet(sK1) | ~brave(sK1) <- (9) [resolution 151,75]
278. brave(sK1) <- (9) [subsumption resolution 275,215]
279. quiet(sK1) <- (9) [subsumption resolution 276,278]
280. ~quiet(sK1) | ~wise(sK1) <- (8) [resolution 98,148]
281. ~wise(sK1) <- (8, 9) [subsumption resolution 280,279]
282. $false <- (1, 8, 9) [subsumption resolution 281,204]
283. ~1 | ~8 | ~9 [avatar contradiction clause 282]
284. $false [avatar sat refutation 129,153,154,202,250,265,270,283]
% SZS output end Proof for 1818830330653790130602734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not quiet is not happy and vice versa.
If fred is both calm and not happy then alice is either funny or not tall.
If someone is wise or calm then mary is both not kind and not happy and vice versa.
If john is either happy or brave then someone is not tall or generous and vice versa.
If alice is not humble then someone is either not tall or wise and vice versa.
If someone is both old and not strong then someone is either not kind or wise and vice versa.
If someone is either not funny or tall then john is either not wise or not kind and vice versa.
If paul is not rich then susan is either not curious or wise.
If someone is not brave then someone is both curious and not old.
If mary is either not funny or patient then someone is not curious.
If someone is not creative then john is not tall or humble.
If mary is both not calm and happy then alice is not generous.
If paul is generous then someone is either humble or patient and vice versa.
If alice is both humble and not curious then lucy is both patient and old and vice versa.
Everyone who is calm or not kind is kind or not funny and vice versa.
If someone is brave then someone is both not tall and not calm and vice versa.
Paul is either strong or old.
Lucy is both not curious and wise.
Someone is both not tall and not humble.
Someone is creative.
Someone is old or patient.
Someone is not creative.
Someone is strong.
Someone is either calm or not generous. | Mary is quiet. | contradiction | (![X]:((~patient(X)&~quiet(X))<=>~happy(X)))&
(((calm(fred)&~happy(fred)))=>((funny(alice)<~>~tall(alice))))&
((?[X]:((wise(X)|calm(X))))<=>((~kind(mary)&~happy(mary))))&
(((happy(john)<~>brave(john)))<=>(?[X]:((~tall(X)|generous(X)))))&
((~humble(alice))<=>(?[X]:((~tall(X)<~>wise(X)))))&
((?[X]:((old(X)&~strong(X))))<=>(?[X]:((~kind(X)<~>wise(X)))))&
((?[X]:((~funny(X)<~>tall(X))))<=>((~wise(john)<~>~kind(john))))&
((~rich(paul))=>((~curious(susan)<~>wise(susan))))&
((?[X]:(~brave(X)))=>(?[X]:((curious(X)&~old(X)))))&
(((~funny(mary)<~>patient(mary)))=>(?[X]:(~curious(X))))&
((?[X]:(~creative(X)))=>((~tall(john)|humble(john))))&
(((~calm(mary)&happy(mary)))=>(~generous(alice)))&
((generous(paul))<=>(?[X]:((humble(X)<~>patient(X)))))&
(((humble(alice)&~curious(alice)))<=>((patient(lucy)&old(lucy))))&
(![X]:((calm(X)|~kind(X))<=>(kind(X)|~funny(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~tall(X)&~calm(X)))))&
((strong(paul)<~>old(paul)))&
((~curious(lucy)&wise(lucy)))&
(?[X]:((~tall(X)&~humble(X))))&
(?[X]:(creative(X)))&
(?[X]:((old(X)|patient(X))))&
(?[X]:(~creative(X)))&
(?[X]:(strong(X)))&
(?[X]:((calm(X)<~>~generous(X)))) | quiet(mary) | [
"p0",
"p2",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4607116027552289759588587
% SZS output start Proof for 4607116027552289759588587
1. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> ~happy(X0)) [input p0]
3. ? [X0] : (calm(X0) | wise(X0)) <=> (~happy(mary) & ~kind(mary)) [input p2]
18. wise(lucy) & ~curious(lucy) [input p17]
25. quiet(mary) [input hypothesis]
38. ! [X0] : (((~quiet(X0) & ~patient(X0)) | happy(X0)) & (~happy(X0) | (quiet(X0) | patient(X0)))) [nnf transformation 1]
39. ! [X0] : (((~quiet(X0) & ~patient(X0)) | happy(X0)) & (~happy(X0) | quiet(X0) | patient(X0))) [flattening 38]
41. (? [X0] : (calm(X0) | wise(X0)) | (happy(mary) | kind(mary))) & ((~happy(mary) & ~kind(mary)) | ! [X0] : (~calm(X0) & ~wise(X0))) [nnf transformation 3]
42. (? [X0] : (calm(X0) | wise(X0)) | happy(mary) | kind(mary)) & ((~happy(mary) & ~kind(mary)) | ! [X0] : (~calm(X0) & ~wise(X0))) [flattening 41]
43. (? [X0] : (calm(X0) | wise(X0)) | happy(mary) | kind(mary)) & ((~happy(mary) & ~kind(mary)) | ! [X1] : (~calm(X1) & ~wise(X1))) [rectify 42]
44. ? [X0] : (calm(X0) | wise(X0)) => (calm(sK0) | wise(sK0)) [choice axiom]
45. ((calm(sK0) | wise(sK0)) | happy(mary) | kind(mary)) & ((~happy(mary) & ~kind(mary)) | ! [X1] : (~calm(X1) & ~wise(X1))) [skolemisation 43,44]
98. ~quiet(X0) | happy(X0) [cnf transformation 39]
103. ~happy(mary) | ~wise(X1) [cnf transformation 45]
154. wise(lucy) [cnf transformation 18]
163. quiet(mary) [cnf transformation 25]
189. 6 <=> happy(mary) [avatar definition]
206. 10 <=> ! [X1] : ~wise(X1) [avatar definition]
207. ~wise(X1) <- (10) [avatar component clause 206]
208. 10 | ~6 [avatar split clause 103,189,206]
460. happy(mary) [resolution 98,163]
463. 6 [avatar split clause 460,189]
464. $false <- (10) [resolution 207,154]
467. ~10 [avatar contradiction clause 464]
468. $false [avatar sat refutation 208,463,467]
% SZS output end Proof for 4607116027552289759588587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not old or calm then someone is either not tall or not humble and vice versa. Everyone who is both brave and strong is both not brave and not curious and vice versa. Everyone who is kind or not old is not happy and vice versa. Everyone who is humble or not generous is both not old and not generous. Everyone who is calm or tall is not rich or not kind. Everyone who is rich or happy is both not creative and not happy. Everyone who is happy is both not rich and curious. If mary is both not generous and creative then someone is either not curious or not generous and vice versa. Everyone who is not curious is happy or rich. Everyone who is both not brave and not wise is both happy and humble and vice versa. Everyone who is either not calm or not brave is both funny and happy. If fred is brave then fred is both quiet and not tall. If someone is curious then lucy is creative or not creative. Everyone who is happy is either happy or not kind and vice versa. Everyone who is both strong and patient is either not patient or wise. If john is either not rich or not humble then alice is not calm and vice versa. Someone is patient. Someone is either not rich or not quiet. Paul is not rich or happy. Someone is both creative and tall. Lucy is not old or not funny. Someone is both strong and quiet. Mary is calm or happy. Someone is both not humble and tall. | Mary is not rich. | entailment | (((~old(lucy)|calm(lucy)))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((brave(X)&strong(X))<=>(~brave(X)&~curious(X))))&
(![X]:((kind(X)|~old(X))<=>~happy(X)))&
(![X]:((humble(X)|~generous(X))=>(~old(X)&~generous(X))))&
(![X]:((calm(X)|tall(X))=>(~rich(X)|~kind(X))))&
(![X]:((rich(X)|happy(X))=>(~creative(X)&~happy(X))))&
(![X]:(happy(X)=>(~rich(X)&curious(X))))&
(((~generous(mary)&creative(mary)))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
(![X]:(~curious(X)=>(happy(X)|rich(X))))&
(![X]:((~brave(X)&~wise(X))<=>(happy(X)&humble(X))))&
(![X]:((~calm(X)<~>~brave(X))=>(funny(X)&happy(X))))&
((brave(fred))=>((quiet(fred)&~tall(fred))))&
((?[X]:(curious(X)))=>((creative(lucy)|~creative(lucy))))&
(![X]:(happy(X)<=>(happy(X)<~>~kind(X))))&
(![X]:((strong(X)&patient(X))=>(~patient(X)<~>wise(X))))&
(((~rich(john)<~>~humble(john)))<=>(~calm(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~rich(X)<~>~quiet(X))))&
((~rich(paul)|happy(paul)))&
(?[X]:((creative(X)&tall(X))))&
((~old(lucy)|~funny(lucy)))&
(?[X]:((strong(X)&quiet(X))))&
((calm(mary)|happy(mary)))&
(?[X]:((~humble(X)&tall(X)))) | ~rich(mary) | [
"p4",
"p5",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3086416341549447388722502
% SZS output start Proof for 3086416341549447388722502
5. ! [X0] : ((tall(X0) | calm(X0)) => (~kind(X0) | ~rich(X0))) [input p4]
6. ! [X0] : ((happy(X0) | rich(X0)) => (~happy(X0) & ~creative(X0))) [input p5]
14. ! [X0] : (happy(X0) <=> (happy(X0) <~> ~kind(X0))) [input p13]
23. happy(mary) | calm(mary) [input p22]
25. rich(mary) [input hypothesis]
27. ! [X0] : ((~kind(X0) | ~rich(X0)) | (~tall(X0) & ~calm(X0))) [ennf transformation 5]
28. ! [X0] : (~kind(X0) | ~rich(X0) | (~tall(X0) & ~calm(X0))) [flattening 27]
29. ! [X0] : ((~happy(X0) & ~creative(X0)) | (~happy(X0) & ~rich(X0))) [ennf transformation 6]
56. ! [X0] : ((happy(X0) | ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0)))) & (((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | ~happy(X0))) [nnf transformation 14]
87. ~rich(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 28]
92. ~happy(X0) | ~happy(X0) [cnf transformation 29]
116. happy(X0) | happy(X0) | kind(X0) [cnf transformation 56]
132. happy(mary) | calm(mary) [cnf transformation 23]
135. rich(mary) [cnf transformation 25]
138. happy(X0) | kind(X0) [duplicate literal removal 116]
139. ~happy(X0) [duplicate literal removal 92]
216. kind(X0) [subsumption resolution 138,139]
249. calm(mary) [subsumption resolution 132,139]
277. ~kind(mary) | ~calm(mary) [resolution 87,135]
280. ~calm(mary) [subsumption resolution 277,216]
281. $false [subsumption resolution 280,249]
% SZS output end Proof for 3086416341549447388722502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not strong then susan is not brave and vice versa. If john is either tall or humble then someone is kind or humble and vice versa. Everyone who is both calm and not creative is either tall or not humble and vice versa. Everyone who is funny is brave. If lucy is both wise and not kind then someone is either not calm or calm. Everyone who is either not happy or not curious is quiet and vice versa. Everyone who is not curious or not rich is generous and vice versa. Everyone who is both rich and not calm is happy or not curious. Everyone who is either not brave or not old is not happy or not strong and vice versa. Everyone who is either not creative or curious is not funny or not generous and vice versa. Everyone who is both not old and brave is not calm or not quiet and vice versa. Everyone who is not patient is humble and vice versa. If lucy is not strong or funny then someone is both not strong and not humble. If someone is generous then someone is either not brave or not old. Everyone who is both not strong and happy is both not happy and not old and vice versa. If lucy is generous then fred is not kind. Mary is calm. Alice is rich. Someone is either not funny or generous. Someone is humble. Someone is either old or tall. Alice is either not quiet or strong. Mary is creative or not old. | Mary is not creative. | neutral | ((?[X]:((curious(X)&~strong(X))))<=>(~brave(susan)))&
(((tall(john)<~>humble(john)))<=>(?[X]:((kind(X)|humble(X)))))&
(![X]:((calm(X)&~creative(X))<=>(tall(X)<~>~humble(X))))&
(![X]:(funny(X)=>brave(X)))&
(((wise(lucy)&~kind(lucy)))=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((~happy(X)<~>~curious(X))<=>quiet(X)))&
(![X]:((~curious(X)|~rich(X))<=>generous(X)))&
(![X]:((rich(X)&~calm(X))=>(happy(X)|~curious(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~happy(X)|~strong(X))))&
(![X]:((~creative(X)<~>curious(X))<=>(~funny(X)|~generous(X))))&
(![X]:((~old(X)&brave(X))<=>(~calm(X)|~quiet(X))))&
(![X]:(~patient(X)<=>humble(X)))&
(((~strong(lucy)|funny(lucy)))=>(?[X]:((~strong(X)&~humble(X)))))&
((?[X]:(generous(X)))=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((~strong(X)&happy(X))<=>(~happy(X)&~old(X))))&
((generous(lucy))=>(~kind(fred)))&
(calm(mary))&
(rich(alice))&
(?[X]:((~funny(X)<~>generous(X))))&
(?[X]:(humble(X)))&
(?[X]:((old(X)<~>tall(X))))&
((~quiet(alice)<~>strong(alice)))&
((creative(mary)|~old(mary))) | ~creative(mary) | [] | null | 0 |
If someone is not happy then fred is tall.
Everyone who is not quiet or kind is creative and vice versa.
If john is both wise and humble then susan is both wise and not quiet.
Everyone who is not patient or funny is funny or tall.
Everyone who is both calm and not creative is either curious or not quiet.
Everyone who is happy is not quiet or tall.
If someone is old or calm then lucy is both brave and not calm.
If someone is calm or quiet then mary is old or strong and vice versa.
Everyone who is both old and not happy is both quiet and not brave.
If someone is strong or not strong then alice is creative and vice versa.
If paul is both old and not patient then someone is either generous or creative.
Everyone who is not brave is both not calm and generous and vice versa.
Everyone who is either strong or patient is both not calm and not funny.
Everyone who is either funny or patient is happy and vice versa.
If fred is either curious or not kind then john is both quiet and not old.
If mary is both not tall and humble then someone is not strong.
Someone is both old and not patient.
Someone is brave.
Someone is not happy.
Lucy is both not calm and strong.
Someone is quiet or humble.
Mary is both curious and not quiet.
Someone is both quiet and not brave.
Alice is either not creative or generous. | Fred is kind. | neutral | ((?[X]:(~happy(X)))=>(tall(fred)))&
(![X]:((~quiet(X)|kind(X))<=>creative(X)))&
(((wise(john)&humble(john)))=>((wise(susan)&~quiet(susan))))&
(![X]:((~patient(X)|funny(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&~creative(X))=>(curious(X)<~>~quiet(X))))&
(![X]:(happy(X)=>(~quiet(X)|tall(X))))&
((?[X]:((old(X)|calm(X))))=>((brave(lucy)&~calm(lucy))))&
((?[X]:((calm(X)|quiet(X))))<=>((old(mary)|strong(mary))))&
(![X]:((old(X)&~happy(X))=>(quiet(X)&~brave(X))))&
((?[X]:((strong(X)|~strong(X))))<=>(creative(alice)))&
(((old(paul)&~patient(paul)))=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(~brave(X)<=>(~calm(X)&generous(X))))&
(![X]:((strong(X)<~>patient(X))=>(~calm(X)&~funny(X))))&
(![X]:((funny(X)<~>patient(X))<=>happy(X)))&
(((curious(fred)<~>~kind(fred)))=>((quiet(john)&~old(john))))&
(((~tall(mary)&humble(mary)))=>(?[X]:(~strong(X))))&
(?[X]:((old(X)&~patient(X))))&
(?[X]:(brave(X)))&
(?[X]:(~happy(X)))&
((~calm(lucy)&strong(lucy)))&
(?[X]:((quiet(X)|humble(X))))&
((curious(mary)&~quiet(mary)))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(alice)<~>generous(alice))) | kind(fred) | [] | null | 0 |
Everyone who is calm or not brave is funny or patient.
Everyone who is not strong or not patient is both strong and calm.
If fred is either tall or happy then someone is either not strong or not calm and vice versa.
Everyone who is humble or not wise is both not generous and funny.
If paul is not quiet or not kind then someone is either tall or wise and vice versa.
Everyone who is either not rich or not generous is both not generous and not kind.
Everyone who is either strong or kind is both not strong and not kind and vice versa.
If john is both not quiet and not rich then someone is tall and vice versa.
If paul is not rich then someone is not patient.
Everyone who is patient is not patient or not quiet.
Everyone who is either not generous or quiet is not curious or not tall and vice versa.
If alice is either not funny or happy then someone is both not kind and old.
Everyone who is either not old or not strong is either humble or not funny and vice versa.
If mary is either not brave or kind then susan is not creative or curious.
Lucy is not happy or curious.
Someone is both old and not happy.
Someone is either happy or tall.
Lucy is not funny or not brave.
Someone is not calm.
Someone is funny or brave.
Susan is generous. | Susan is not humble. | entailment | (![X]:((calm(X)|~brave(X))=>(funny(X)|patient(X))))&
(![X]:((~strong(X)|~patient(X))=>(strong(X)&calm(X))))&
(((tall(fred)<~>happy(fred)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((humble(X)|~wise(X))=>(~generous(X)&funny(X))))&
(((~quiet(paul)|~kind(paul)))<=>(?[X]:((tall(X)<~>wise(X)))))&
(![X]:((~rich(X)<~>~generous(X))=>(~generous(X)&~kind(X))))&
(![X]:((strong(X)<~>kind(X))<=>(~strong(X)&~kind(X))))&
(((~quiet(john)&~rich(john)))<=>(?[X]:(tall(X))))&
((~rich(paul))=>(?[X]:(~patient(X))))&
(![X]:(patient(X)=>(~patient(X)|~quiet(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(~curious(X)|~tall(X))))&
(((~funny(alice)<~>happy(alice)))=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((~old(X)<~>~strong(X))<=>(humble(X)<~>~funny(X))))&
(((~brave(mary)<~>kind(mary)))=>((~creative(susan)|curious(susan))))&
((~happy(lucy)|curious(lucy)))&
(?[X]:((old(X)&~happy(X))))&
(?[X]:((happy(X)<~>tall(X))))&
((~funny(lucy)|~brave(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((funny(X)|brave(X))))&
(generous(susan)) | ~humble(susan) | [
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8095840063642325562506996
% SZS output start Proof for 8095840063642325562506996
4. ! [X0] : ((~wise(X0) | humble(X0)) => (funny(X0) & ~generous(X0))) [input p3]
21. generous(susan) [input p20]
22. humble(susan) [input hypothesis]
27. ! [X0] : ((funny(X0) & ~generous(X0)) | (wise(X0) & ~humble(X0))) [ennf transformation 4]
81. ~generous(X0) | ~humble(X0) [cnf transformation 27]
132. generous(susan) [cnf transformation 21]
133. humble(susan) [cnf transformation 22]
283. ~humble(susan) [resolution 81,132]
284. $false [subsumption resolution 283,133]
% SZS output end Proof for 8095840063642325562506996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not humble is both rich and old.
Everyone who is not old is either not generous or brave and vice versa.
If someone is not quiet then someone is not old.
If lucy is not wise or not funny then lucy is humble.
Everyone who is not curious or kind is either not funny or not happy.
If someone is not kind or not brave then someone is not happy or not quiet and vice versa.
If someone is brave or tall then someone is either not patient or not happy and vice versa.
If fred is brave then alice is not happy or wise and vice versa.
Everyone who is either not patient or not strong is either curious or not happy.
If mary is calm then mary is rich.
Everyone who is either creative or not happy is tall or not generous and vice versa.
Everyone who is either generous or humble is not generous or not patient and vice versa.
If someone is not generous then alice is not calm and vice versa.
Everyone who is either brave or not rich is happy and vice versa.
If someone is both patient and not brave then someone is both wise and not creative and vice versa.
Everyone who is curious is not rich and vice versa.
Someone is both not curious and not patient.
Paul is rich or not patient.
Someone is either curious or not funny.
John is both humble and not rich.
Mary is wise or not generous.
Someone is both kind and not creative.
Lucy is not brave.
Someone is either not kind or quiet. | Paul is not patient. | neutral | (![X]:((~funny(X)<~>~humble(X))=>(rich(X)&old(X))))&
(![X]:(~old(X)<=>(~generous(X)<~>brave(X))))&
((?[X]:(~quiet(X)))=>(?[X]:(~old(X))))&
(((~wise(lucy)|~funny(lucy)))=>(humble(lucy)))&
(![X]:((~curious(X)|kind(X))=>(~funny(X)<~>~happy(X))))&
((?[X]:((~kind(X)|~brave(X))))<=>(?[X]:((~happy(X)|~quiet(X)))))&
((?[X]:((brave(X)|tall(X))))<=>(?[X]:((~patient(X)<~>~happy(X)))))&
((brave(fred))<=>((~happy(alice)|wise(alice))))&
(![X]:((~patient(X)<~>~strong(X))=>(curious(X)<~>~happy(X))))&
((calm(mary))=>(rich(mary)))&
(![X]:((creative(X)<~>~happy(X))<=>(tall(X)|~generous(X))))&
(![X]:((generous(X)<~>humble(X))<=>(~generous(X)|~patient(X))))&
((?[X]:(~generous(X)))<=>(~calm(alice)))&
(![X]:((brave(X)<~>~rich(X))<=>happy(X)))&
((?[X]:((patient(X)&~brave(X))))<=>(?[X]:((wise(X)&~creative(X)))))&
(![X]:(curious(X)<=>~rich(X)))&
(?[X]:((~curious(X)&~patient(X))))&
((rich(paul)|~patient(paul)))&
(?[X]:((curious(X)<~>~funny(X))))&
((humble(john)&~rich(john)))&
((wise(mary)|~generous(mary)))&
(?[X]:((kind(X)&~creative(X))))&
(~brave(lucy))&
(?[X]:((~kind(X)<~>quiet(X)))) | ~patient(paul) | [] | null | 0 |
Everyone who is both funny and not old is not kind and vice versa.
If fred is both not quiet and old then someone is either generous or not happy.
Everyone who is funny is both creative and not humble.
Everyone who is both not curious and not kind is either not funny or not humble.
If fred is both not brave and creative then someone is either funny or not humble and vice versa.
Everyone who is either not curious or brave is generous.
If mary is both not tall and funny then paul is happy and vice versa.
Everyone who is old or quiet is both quiet and not tall and vice versa.
If mary is either not generous or creative then lucy is humble or not funny.
Everyone who is not curious is either humble or not curious and vice versa.
If someone is creative or kind then someone is both not calm and not funny and vice versa.
If alice is not rich or curious then someone is either not tall or not humble and vice versa.
Everyone who is not old is old or wise.
If someone is both not calm and kind then fred is generous or not creative.
Everyone who is both not humble and generous is either not funny or not quiet.
Everyone who is not calm is happy or not quiet.
Lucy is not generous.
Susan is both not tall and creative.
Fred is either calm or not kind.
Paul is either tall or not creative.
Someone is both not creative and not quiet.
Someone is either not wise or not curious.
Someone is not strong or rich.
John is creative or kind. | Paul is humble. | contradiction | (![X]:((funny(X)&~old(X))<=>~kind(X)))&
(((~quiet(fred)&old(fred)))=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:(funny(X)=>(creative(X)&~humble(X))))&
(![X]:((~curious(X)&~kind(X))=>(~funny(X)<~>~humble(X))))&
(((~brave(fred)&creative(fred)))<=>(?[X]:((funny(X)<~>~humble(X)))))&
(![X]:((~curious(X)<~>brave(X))=>generous(X)))&
(((~tall(mary)&funny(mary)))<=>(happy(paul)))&
(![X]:((old(X)|quiet(X))<=>(quiet(X)&~tall(X))))&
(((~generous(mary)<~>creative(mary)))=>((humble(lucy)|~funny(lucy))))&
(![X]:(~curious(X)<=>(humble(X)<~>~curious(X))))&
((?[X]:((creative(X)|kind(X))))<=>(?[X]:((~calm(X)&~funny(X)))))&
(((~rich(alice)|curious(alice)))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:(~old(X)=>(old(X)|wise(X))))&
((?[X]:((~calm(X)&kind(X))))=>((generous(fred)|~creative(fred))))&
(![X]:((~humble(X)&generous(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:(~calm(X)=>(happy(X)|~quiet(X))))&
(~generous(lucy))&
((~tall(susan)&creative(susan)))&
((calm(fred)<~>~kind(fred)))&
((tall(paul)<~>~creative(paul)))&
(?[X]:((~creative(X)&~quiet(X))))&
(?[X]:((~wise(X)<~>~curious(X))))&
(?[X]:((~strong(X)|rich(X))))&
((creative(john)|kind(john))) | humble(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4155128085408425659264499
% SZS output start Proof for 4155128085408425659264499
10. ! [X0] : (~curious(X0) <=> (humble(X0) <~> ~curious(X0))) [input p9]
25. humble(paul) [input hypothesis]
61. ! [X0] : ((~curious(X0) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0)))) & (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | curious(X0))) [nnf transformation 10]
108. curious(X0) | ~humble(X0) | curious(X0) [cnf transformation 61]
109. ~curious(X0) | ~curious(X0) | ~humble(X0) [cnf transformation 61]
139. humble(paul) [cnf transformation 25]
141. curious(X0) | ~humble(X0) [duplicate literal removal 108]
142. ~curious(X0) | ~humble(X0) [duplicate literal removal 109]
217. ~humble(X0) [subsumption resolution 141,142]
318. $false [subsumption resolution 139,217]
% SZS output end Proof for 4155128085408425659264499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or wise is rich and vice versa.
If someone is brave or creative then paul is not tall and vice versa.
If paul is either not kind or generous then mary is both not brave and not generous.
If someone is happy or not brave then fred is both funny and calm and vice versa.
Everyone who is either not creative or not rich is either not patient or strong.
Everyone who is both strong and not creative is not patient or quiet and vice versa.
If someone is not patient or curious then someone is generous or not curious.
Everyone who is happy is not humble and vice versa.
Everyone who is both funny and old is not tall.
Everyone who is both kind and not patient is both wise and tall and vice versa.
Everyone who is humble is either wise or not humble and vice versa.
Everyone who is wise is either not brave or humble.
Everyone who is not happy or not quiet is brave and vice versa.
Everyone who is calm is either calm or not strong and vice versa.
If susan is not curious then paul is kind or quiet and vice versa.
If mary is wise or happy then fred is generous or not tall.
Susan is both wise and not creative.
Lucy is not creative.
Alice is both not patient and not funny.
Someone is not calm or brave.
Alice is funny or not quiet.
Someone is not patient.
Someone is both curious and tall. | Lucy is not quiet. | neutral | (![X]:((brave(X)<~>wise(X))<=>rich(X)))&
((?[X]:((brave(X)|creative(X))))<=>(~tall(paul)))&
(((~kind(paul)<~>generous(paul)))=>((~brave(mary)&~generous(mary))))&
((?[X]:((happy(X)|~brave(X))))<=>((funny(fred)&calm(fred))))&
(![X]:((~creative(X)<~>~rich(X))=>(~patient(X)<~>strong(X))))&
(![X]:((strong(X)&~creative(X))<=>(~patient(X)|quiet(X))))&
((?[X]:((~patient(X)|curious(X))))=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:(happy(X)<=>~humble(X)))&
(![X]:((funny(X)&old(X))=>~tall(X)))&
(![X]:((kind(X)&~patient(X))<=>(wise(X)&tall(X))))&
(![X]:(humble(X)<=>(wise(X)<~>~humble(X))))&
(![X]:(wise(X)=>(~brave(X)<~>humble(X))))&
(![X]:((~happy(X)|~quiet(X))<=>brave(X)))&
(![X]:(calm(X)<=>(calm(X)<~>~strong(X))))&
((~curious(susan))<=>((kind(paul)|quiet(paul))))&
(((wise(mary)|happy(mary)))=>((generous(fred)|~tall(fred))))&
((wise(susan)&~creative(susan)))&
(~creative(lucy))&
((~patient(alice)&~funny(alice)))&
(?[X]:((~calm(X)|brave(X))))&
((funny(alice)|~quiet(alice)))&
(?[X]:(~patient(X)))&
(?[X]:((curious(X)&tall(X)))) | ~quiet(lucy) | [] | null | 0 |
If someone is not happy or not funny then someone is both not kind and wise.
Everyone who is not curious is tall or strong and vice versa.
Everyone who is not funny or not generous is not strong and vice versa.
Everyone who is not quiet is either not humble or curious.
Everyone who is both humble and happy is either not tall or funny and vice versa.
If someone is not funny then fred is either not tall or not old.
If john is curious then john is not curious or calm.
If someone is either quiet or kind then lucy is both not generous and not wise.
Everyone who is humble is not happy or old.
Everyone who is tall or old is not tall or strong and vice versa.
If someone is quiet or not old then someone is both not wise and wise.
If someone is both patient and not quiet then fred is calm.
Everyone who is either not tall or not calm is both creative and not wise and vice versa.
If someone is not creative or not generous then someone is both wise and not kind.
If fred is both happy and old then john is funny and vice versa.
Everyone who is both not happy and funny is not funny and vice versa.
Mary is both not curious and patient.
Alice is happy or funny.
Mary is not creative.
Someone is not calm or strong.
Alice is not old or funny.
Alice is both not quiet and creative.
Someone is not calm.
Someone is happy. | Alice is not strong. | contradiction | ((?[X]:((~happy(X)|~funny(X))))=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:(~curious(X)<=>(tall(X)|strong(X))))&
(![X]:((~funny(X)|~generous(X))<=>~strong(X)))&
(![X]:(~quiet(X)=>(~humble(X)<~>curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(~funny(X)))=>((~tall(fred)<~>~old(fred))))&
((curious(john))=>((~curious(john)|calm(john))))&
((?[X]:((quiet(X)<~>kind(X))))=>((~generous(lucy)&~wise(lucy))))&
(![X]:(humble(X)=>(~happy(X)|old(X))))&
(![X]:((tall(X)|old(X))<=>(~tall(X)|strong(X))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(![X]:((~happy(X)&funny(X))<=>~funny(X)))&
((~curious(mary)&patient(mary)))&
((happy(alice)|funny(alice)))&
(~creative(mary))&
(?[X]:((~calm(X)|strong(X))))&
((~old(alice)|funny(alice)))&
((~quiet(alice)&creative(alice)))&
(?[X]:(~calm(X)))&
(?[X]:(happy(X))) | ~strong(alice) | [
"p1",
"p3",
"p4",
"p9",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 886677304501728955123082
% SZS output start Proof for 886677304501728955123082
2. ! [X0] : (~curious(X0) <=> (strong(X0) | tall(X0))) [input p1]
4. ! [X0] : (~quiet(X0) => (~humble(X0) <~> curious(X0))) [input p3]
5. ! [X0] : ((happy(X0) & humble(X0)) <=> (~tall(X0) <~> funny(X0))) [input p4]
10. ! [X0] : ((old(X0) | tall(X0)) <=> (strong(X0) | ~tall(X0))) [input p9]
16. ! [X0] : ((funny(X0) & ~happy(X0)) <=> ~funny(X0)) [input p15]
18. funny(alice) | happy(alice) [input p17]
22. creative(alice) & ~quiet(alice) [input p21]
25. ~strong(alice) [input hypothesis]
30. ! [X0] : ((~humble(X0) <~> curious(X0)) | quiet(X0)) [ennf transformation 4]
43. ! [X0] : ((~curious(X0) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | curious(X0))) [nnf transformation 2]
44. ! [X0] : ((~curious(X0) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | curious(X0))) [flattening 43]
47. ! [X0] : (((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | quiet(X0)) [nnf transformation 30]
48. ! [X0] : (((happy(X0) & humble(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (~happy(X0) | ~humble(X0)))) [nnf transformation 5]
49. ! [X0] : (((happy(X0) & humble(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ~happy(X0) | ~humble(X0))) [flattening 48]
52. ! [X0] : (((old(X0) | tall(X0)) | (~strong(X0) & tall(X0))) & ((strong(X0) | ~tall(X0)) | (~old(X0) & ~tall(X0)))) [nnf transformation 10]
53. ! [X0] : ((old(X0) | tall(X0) | (~strong(X0) & tall(X0))) & (strong(X0) | ~tall(X0) | (~old(X0) & ~tall(X0)))) [flattening 52]
64. ! [X0] : (((funny(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) | happy(X0)))) [nnf transformation 16]
65. ! [X0] : (((funny(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | ~funny(X0) | happy(X0))) [flattening 64]
76. strong(X0) | tall(X0) | curious(X0) [cnf transformation 44]
83. ~curious(X0) | humble(X0) | quiet(X0) [cnf transformation 47]
85. ~humble(X0) | tall(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 49]
98. strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 53]
120. ~funny(X0) | ~funny(X0) | happy(X0) [cnf transformation 65]
121. ~happy(X0) | funny(X0) [cnf transformation 65]
125. funny(alice) | happy(alice) [cnf transformation 18]
129. ~quiet(alice) [cnf transformation 22]
133. ~strong(alice) [cnf transformation 25]
134. ~funny(X0) | happy(X0) [duplicate literal removal 120]
136. ~tall(X0) | strong(X0) [duplicate literal removal 98]
246. funny(alice) [subsumption resolution 125,121]
266. happy(alice) [resolution 134,246]
270. tall(alice) | curious(alice) [resolution 76,133]
275. 26 <=> curious(alice) [avatar definition]
277. curious(alice) <- (26) [avatar component clause 275]
279. 27 <=> tall(alice) [avatar definition]
281. tall(alice) <- (27) [avatar component clause 279]
282. 26 | 27 [avatar split clause 270,279,275]
295. humble(alice) | quiet(alice) <- (26) [resolution 83,277]
296. humble(alice) <- (26) [subsumption resolution 295,129]
345. tall(alice) | ~happy(alice) | ~funny(alice) <- (26) [resolution 85,296]
351. tall(alice) | ~happy(alice) <- (26) [subsumption resolution 345,246]
353. 30 <=> happy(alice) [avatar definition]
356. ~30 | 27 | ~26 [avatar split clause 351,275,279,353]
357. 30 [avatar split clause 266,353]
377. strong(alice) <- (27) [resolution 281,136]
381. $false <- (27) [subsumption resolution 377,133]
382. ~27 [avatar contradiction clause 381]
385. $false [avatar sat refutation 282,356,357,382]
% SZS output end Proof for 886677304501728955123082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not generous is not generous and vice versa.
Everyone who is either curious or not old is not rich or not generous and vice versa.
Everyone who is either quiet or generous is both tall and old and vice versa.
If someone is not kind or not generous then fred is either kind or brave.
If susan is not funny then mary is both old and not tall and vice versa.
Everyone who is both not generous and not tall is not kind or quiet and vice versa.
If mary is not patient then someone is either brave or strong and vice versa.
If paul is strong or brave then mary is both not creative and humble and vice versa.
If someone is not brave or curious then alice is both not creative and rich and vice versa.
If susan is either not happy or not calm then someone is both not funny and creative.
Everyone who is not kind or happy is kind or not happy.
If paul is kind or not patient then paul is brave or not wise and vice versa.
Everyone who is both humble and not humble is both funny and not humble and vice versa.
If someone is not patient or not quiet then someone is funny or wise.
Everyone who is not strong is humble or not patient.
Everyone who is not strong is not wise.
Someone is patient.
Someone is not calm.
Fred is both generous and not humble.
Someone is both brave and rich.
Someone is both not generous and kind.
Someone is either not quiet or strong.
Someone is not funny or quiet. | Mary is not tall. | neutral | (![X]:((~wise(X)&~generous(X))<=>~generous(X)))&
(![X]:((curious(X)<~>~old(X))<=>(~rich(X)|~generous(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(tall(X)&old(X))))&
((?[X]:((~kind(X)|~generous(X))))=>((kind(fred)<~>brave(fred))))&
((~funny(susan))<=>((old(mary)&~tall(mary))))&
(![X]:((~generous(X)&~tall(X))<=>(~kind(X)|quiet(X))))&
((~patient(mary))<=>(?[X]:((brave(X)<~>strong(X)))))&
(((strong(paul)|brave(paul)))<=>((~creative(mary)&humble(mary))))&
((?[X]:((~brave(X)|curious(X))))<=>((~creative(alice)&rich(alice))))&
(((~happy(susan)<~>~calm(susan)))=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((~kind(X)|happy(X))=>(kind(X)|~happy(X))))&
(((kind(paul)|~patient(paul)))<=>((brave(paul)|~wise(paul))))&
(![X]:((humble(X)&~humble(X))<=>(funny(X)&~humble(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>(?[X]:((funny(X)|wise(X)))))&
(![X]:(~strong(X)=>(humble(X)|~patient(X))))&
(![X]:(~strong(X)=>~wise(X)))&
(?[X]:(patient(X)))&
(?[X]:(~calm(X)))&
((generous(fred)&~humble(fred)))&
(?[X]:((brave(X)&rich(X))))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:((~quiet(X)<~>strong(X))))&
(?[X]:((~funny(X)|quiet(X)))) | ~tall(mary) | [] | null | 0 |
Everyone who is not kind is wise and vice versa.
If someone is quiet then someone is both not quiet and tall and vice versa.
If fred is not funny then someone is either not quiet or calm and vice versa.
If someone is both rich and not curious then someone is either not strong or creative and vice versa.
If alice is either not calm or not funny then susan is not humble.
Everyone who is both not wise and not creative is calm or not kind.
If mary is funny or not humble then someone is happy and vice versa.
Everyone who is tall is not curious or not patient.
Everyone who is either not wise or calm is humble or not funny.
If someone is not generous then someone is both not generous and quiet.
If alice is not tall then someone is not creative or not quiet and vice versa.
If susan is either rich or patient then lucy is either curious or not humble.
Everyone who is either not quiet or not creative is both strong and brave and vice versa.
Everyone who is both happy and strong is brave or quiet and vice versa.
Everyone who is both old and brave is not brave and vice versa.
If fred is rich then alice is wise or not curious and vice versa.
Someone is either brave or creative.
Someone is both not funny and kind.
Alice is kind.
Someone is both not humble and patient.
Someone is either not humble or humble.
Alice is strong or not creative.
Fred is wise or curious.
Someone is both not generous and not rich. | Susan is strong. | entailment | (![X]:(~kind(X)<=>wise(X)))&
((?[X]:(quiet(X)))<=>(?[X]:((~quiet(X)&tall(X)))))&
((~funny(fred))<=>(?[X]:((~quiet(X)<~>calm(X)))))&
((?[X]:((rich(X)&~curious(X))))<=>(?[X]:((~strong(X)<~>creative(X)))))&
(((~calm(alice)<~>~funny(alice)))=>(~humble(susan)))&
(![X]:((~wise(X)&~creative(X))=>(calm(X)|~kind(X))))&
(((funny(mary)|~humble(mary)))<=>(?[X]:(happy(X))))&
(![X]:(tall(X)=>(~curious(X)|~patient(X))))&
(![X]:((~wise(X)<~>calm(X))=>(humble(X)|~funny(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~generous(X)&quiet(X)))))&
((~tall(alice))<=>(?[X]:((~creative(X)|~quiet(X)))))&
(((rich(susan)<~>patient(susan)))=>((curious(lucy)<~>~humble(lucy))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(strong(X)&brave(X))))&
(![X]:((happy(X)&strong(X))<=>(brave(X)|quiet(X))))&
(![X]:((old(X)&brave(X))<=>~brave(X)))&
((rich(fred))<=>((wise(alice)|~curious(alice))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:((~funny(X)&kind(X))))&
(kind(alice))&
(?[X]:((~humble(X)&patient(X))))&
(?[X]:((~humble(X)<~>humble(X))))&
((strong(alice)|~creative(alice)))&
((wise(fred)|curious(fred)))&
(?[X]:((~generous(X)&~rich(X)))) | strong(susan) | [
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 494503997989938067790934
% SZS output start Proof for 494503997989938067790934
14. ! [X0] : ((strong(X0) & happy(X0)) <=> (quiet(X0) | brave(X0))) [input p13]
15. ! [X0] : ((brave(X0) & old(X0)) <=> ~brave(X0)) [input p14]
25. ~strong(susan) [input hypothesis]
70. ! [X0] : (((strong(X0) & happy(X0)) | (~quiet(X0) & ~brave(X0))) & ((quiet(X0) | brave(X0)) | (~strong(X0) | ~happy(X0)))) [nnf transformation 14]
71. ! [X0] : (((strong(X0) & happy(X0)) | (~quiet(X0) & ~brave(X0))) & (quiet(X0) | brave(X0) | ~strong(X0) | ~happy(X0))) [flattening 70]
72. ! [X0] : (((brave(X0) & old(X0)) | brave(X0)) & (~brave(X0) | (~brave(X0) | ~old(X0)))) [nnf transformation 15]
73. ! [X0] : (((brave(X0) & old(X0)) | brave(X0)) & (~brave(X0) | ~brave(X0) | ~old(X0))) [flattening 72]
130. ~brave(X0) | strong(X0) [cnf transformation 71]
134. brave(X0) | brave(X0) [cnf transformation 73]
151. ~strong(susan) [cnf transformation 25]
153. brave(X0) [duplicate literal removal 134]
364. strong(X0) [resolution 130,153]
366. $false [resolution 364,151]
% SZS output end Proof for 494503997989938067790934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not quiet then alice is both not kind and not generous and vice versa.
If someone is both kind and patient then someone is not funny or wise and vice versa.
Everyone who is not strong is both not old and patient and vice versa.
Everyone who is not strong is calm and vice versa.
If alice is both not brave and not tall then someone is creative or brave.
Everyone who is either humble or generous is old.
If john is both old and not calm then mary is both not funny and not old and vice versa.
If alice is rich or not rich then alice is both humble and not quiet.
Everyone who is either brave or not strong is both calm and brave and vice versa.
Everyone who is either patient or quiet is not humble or not tall and vice versa.
Everyone who is either not creative or not happy is either quiet or not creative.
Everyone who is humble or patient is either rich or not brave.
If alice is not old then fred is not kind or tall.
If john is not patient or brave then mary is not funny and vice versa.
Everyone who is not funny is creative or not kind and vice versa.
If someone is quiet then someone is not calm or old.
Fred is both rich and not kind.
Mary is both curious and happy.
Susan is not curious.
Paul is either not quiet or not tall.
John is both quiet and kind.
Mary is curious or brave. | Fred is not patient. | entailment | ((~quiet(john))<=>((~kind(alice)&~generous(alice))))&
((?[X]:((kind(X)&patient(X))))<=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:(~strong(X)<=>(~old(X)&patient(X))))&
(![X]:(~strong(X)<=>calm(X)))&
(((~brave(alice)&~tall(alice)))=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((humble(X)<~>generous(X))=>old(X)))&
(((old(john)&~calm(john)))<=>((~funny(mary)&~old(mary))))&
(((rich(alice)|~rich(alice)))=>((humble(alice)&~quiet(alice))))&
(![X]:((brave(X)<~>~strong(X))<=>(calm(X)&brave(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~humble(X)|~tall(X))))&
(![X]:((~creative(X)<~>~happy(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((humble(X)|patient(X))=>(rich(X)<~>~brave(X))))&
((~old(alice))=>((~kind(fred)|tall(fred))))&
(((~patient(john)|brave(john)))<=>(~funny(mary)))&
(![X]:(~funny(X)<=>(creative(X)|~kind(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|old(X)))))&
((rich(fred)&~kind(fred)))&
((curious(mary)&happy(mary)))&
(~curious(susan))&
((~quiet(paul)<~>~tall(paul)))&
((quiet(john)&kind(john)))&
((curious(mary)|brave(mary))) | ~patient(fred) | [
"p3",
"p8",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1270067983629987225382559
% SZS output start Proof for 1270067983629987225382559
4. ! [X0] : (~strong(X0) <=> calm(X0)) [input p3]
9. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (brave(X0) & calm(X0))) [input p8]
12. ! [X0] : ((patient(X0) | humble(X0)) => (rich(X0) <~> ~brave(X0))) [input p11]
17. ~kind(fred) & rich(fred) [input p16]
23. patient(fred) [input hypothesis]
31. ! [X0] : ((rich(X0) <~> ~brave(X0)) | (~patient(X0) & ~humble(X0))) [ennf transformation 12]
44. ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0))) [nnf transformation 4]
50. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 9]
51. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 50]
55. ! [X0] : (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | (~patient(X0) & ~humble(X0))) [nnf transformation 31]
75. calm(X0) | strong(X0) [cnf transformation 44]
76. ~calm(X0) | ~strong(X0) [cnf transformation 44]
88. calm(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 51]
93. strong(X0) | ~brave(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 51]
107. brave(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 55]
116. rich(fred) [cnf transformation 17]
126. patient(fred) [cnf transformation 23]
130. strong(X0) | ~brave(X0) | ~calm(X0) [duplicate literal removal 93]
229. ~brave(X0) | ~calm(X0) [subsumption resolution 130,76]
230. calm(X0) | ~brave(X0) [subsumption resolution 88,75]
231. ~brave(X0) [subsumption resolution 230,229]
232. ~rich(X0) | ~patient(X0) [subsumption resolution 107,231]
287. ~patient(fred) [resolution 232,116]
288. $false [subsumption resolution 287,126]
% SZS output end Proof for 1270067983629987225382559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not curious is both generous and not creative. Everyone who is not old is either not kind or rich. If fred is either not strong or not generous then someone is brave and vice versa. Everyone who is either strong or not creative is either not brave or patient. Everyone who is either not curious or strong is not generous. Everyone who is both strong and not quiet is not kind or generous and vice versa. Everyone who is brave or not generous is both calm and patient and vice versa. Everyone who is either not generous or happy is generous or calm and vice versa. Everyone who is patient or happy is funny or calm. If john is creative or old then fred is both not curious and not calm and vice versa. If mary is not calm or not wise then mary is not quiet. If john is humble then paul is both calm and not funny. Everyone who is not funny or not wise is humble or quiet and vice versa. If john is either not humble or not funny then someone is both tall and strong. Everyone who is wise or old is both not curious and humble and vice versa. Everyone who is not patient or creative is either curious or not curious. Someone is either humble or not curious. Someone is either not humble or not quiet. Susan is quiet. Fred is both funny and not calm. Someone is not calm or tall. Someone is not wise or not strong. Mary is not rich or not strong. Paul is either tall or not patient. | Fred is old. | entailment | (![X]:((happy(X)|~curious(X))=>(generous(X)&~creative(X))))&
(![X]:(~old(X)=>(~kind(X)<~>rich(X))))&
(((~strong(fred)<~>~generous(fred)))<=>(?[X]:(brave(X))))&
(![X]:((strong(X)<~>~creative(X))=>(~brave(X)<~>patient(X))))&
(![X]:((~curious(X)<~>strong(X))=>~generous(X)))&
(![X]:((strong(X)&~quiet(X))<=>(~kind(X)|generous(X))))&
(![X]:((brave(X)|~generous(X))<=>(calm(X)&patient(X))))&
(![X]:((~generous(X)<~>happy(X))<=>(generous(X)|calm(X))))&
(![X]:((patient(X)|happy(X))=>(funny(X)|calm(X))))&
(((creative(john)|old(john)))<=>((~curious(fred)&~calm(fred))))&
(((~calm(mary)|~wise(mary)))=>(~quiet(mary)))&
((humble(john))=>((calm(paul)&~funny(paul))))&
(![X]:((~funny(X)|~wise(X))<=>(humble(X)|quiet(X))))&
(((~humble(john)<~>~funny(john)))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((wise(X)|old(X))<=>(~curious(X)&humble(X))))&
(![X]:((~patient(X)|creative(X))=>(curious(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~curious(X))))&
(?[X]:((~humble(X)<~>~quiet(X))))&
(quiet(susan))&
((funny(fred)&~calm(fred)))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:((~wise(X)|~strong(X))))&
((~rich(mary)|~strong(mary)))&
((tall(paul)<~>~patient(paul))) | old(fred) | [
"p4",
"p5",
"p6",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 669237493087563703909702
% SZS output start Proof for 669237493087563703909702
5. ! [X0] : ((~curious(X0) <~> strong(X0)) => ~generous(X0)) [input p4]
6. ! [X0] : ((~quiet(X0) & strong(X0)) <=> (generous(X0) | ~kind(X0))) [input p5]
7. ! [X0] : ((~generous(X0) | brave(X0)) <=> (patient(X0) & calm(X0))) [input p6]
13. ! [X0] : ((~wise(X0) | ~funny(X0)) <=> (quiet(X0) | humble(X0))) [input p12]
15. ! [X0] : ((old(X0) | wise(X0)) <=> (humble(X0) & ~curious(X0))) [input p14]
20. ~calm(fred) & funny(fred) [input p19]
25. ~old(fred) [input hypothesis]
29. ! [X0] : (~generous(X0) | (~curious(X0) <=> strong(X0))) [ennf transformation 5]
42. ! [X0] : (~generous(X0) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) [nnf transformation 29]
43. ! [X0] : (((~quiet(X0) & strong(X0)) | (~generous(X0) & kind(X0))) & ((generous(X0) | ~kind(X0)) | (quiet(X0) | ~strong(X0)))) [nnf transformation 6]
44. ! [X0] : (((~quiet(X0) & strong(X0)) | (~generous(X0) & kind(X0))) & (generous(X0) | ~kind(X0) | quiet(X0) | ~strong(X0))) [flattening 43]
45. ! [X0] : (((~generous(X0) | brave(X0)) | (~patient(X0) | ~calm(X0))) & ((patient(X0) & calm(X0)) | (generous(X0) & ~brave(X0)))) [nnf transformation 7]
46. ! [X0] : ((~generous(X0) | brave(X0) | ~patient(X0) | ~calm(X0)) & ((patient(X0) & calm(X0)) | (generous(X0) & ~brave(X0)))) [flattening 45]
51. ! [X0] : (((~wise(X0) | ~funny(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (wise(X0) & funny(X0)))) [nnf transformation 13]
52. ! [X0] : ((~wise(X0) | ~funny(X0) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | (wise(X0) & funny(X0)))) [flattening 51]
56. ! [X0] : (((old(X0) | wise(X0)) | (~humble(X0) | curious(X0))) & ((humble(X0) & ~curious(X0)) | (~old(X0) & ~wise(X0)))) [nnf transformation 15]
57. ! [X0] : ((old(X0) | wise(X0) | ~humble(X0) | curious(X0)) & ((humble(X0) & ~curious(X0)) | (~old(X0) & ~wise(X0)))) [flattening 56]
85. ~strong(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 42]
88. ~generous(X0) | strong(X0) [cnf transformation 44]
90. ~quiet(X0) | ~generous(X0) [cnf transformation 44]
92. calm(X0) | generous(X0) [cnf transformation 46]
114. humble(X0) | quiet(X0) | wise(X0) [cnf transformation 52]
115. ~humble(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 52]
116. ~wise(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 52]
121. ~wise(X0) | ~curious(X0) [cnf transformation 57]
123. ~wise(X0) | humble(X0) [cnf transformation 57]
124. ~old(X0) | humble(X0) [cnf transformation 57]
125. ~humble(X0) | wise(X0) | old(X0) | curious(X0) [cnf transformation 57]
135. funny(fred) [cnf transformation 20]
136. ~calm(fred) [cnf transformation 20]
142. ~old(fred) [cnf transformation 25]
149. 2 <=> strong(fred) [avatar definition]
151. strong(fred) <- (2) [avatar component clause 149]
153. 3 <=> generous(fred) [avatar definition]
155. generous(fred) <- (3) [avatar component clause 153]
166. 5 <=> curious(fred) [avatar definition]
167. ~curious(fred) <- (~5) [avatar component clause 166]
170. 6 <=> calm(fred) [avatar definition]
171. ~calm(fred) <- (~6) [avatar component clause 170]
250. ~6 [avatar split clause 136,170]
295. generous(fred) <- (~6) [resolution 92,171]
299. 3 | 6 [avatar split clause 295,170,153]
303. strong(fred) <- (3) [resolution 155,88]
306. 2 | ~3 [avatar split clause 303,153,149]
340. ~curious(fred) | ~generous(fred) <- (2) [resolution 85,151]
358. ~curious(fred) <- (2, 3) [subsumption resolution 340,155]
359. ~5 | ~2 | ~3 [avatar split clause 358,153,149,166]
436. wise(X0) | old(X0) | curious(X0) | quiet(X0) | wise(X0) [resolution 125,114]
441. wise(X0) | old(X0) | curious(X0) | quiet(X0) [duplicate literal removal 436]
495. old(X1) | curious(X1) | quiet(X1) | humble(X1) [resolution 441,123]
499. humble(X1) | quiet(X1) | curious(X1) [subsumption resolution 495,124]
517. quiet(X1) | curious(X1) | ~funny(X1) | ~wise(X1) [resolution 499,115]
519. curious(X1) | ~funny(X1) | ~wise(X1) [subsumption resolution 517,116]
520. ~wise(X1) | ~funny(X1) [subsumption resolution 519,121]
529. ~funny(X0) | old(X0) | curious(X0) | quiet(X0) [resolution 520,441]
531. old(fred) | curious(fred) | quiet(fred) [resolution 529,135]
534. curious(fred) | quiet(fred) [subsumption resolution 531,142]
535. quiet(fred) <- (~5) [subsumption resolution 534,167]
559. ~generous(fred) <- (~5) [resolution 535,90]
561. $false <- (3, ~5) [subsumption resolution 559,155]
562. ~3 | 5 [avatar contradiction clause 561]
563. $false [avatar sat refutation 250,299,306,359,562]
% SZS output end Proof for 669237493087563703909702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not patient or not happy and vice versa.
Everyone who is not rich or old is tall or not happy.
If fred is both not old and funny then someone is not kind or patient and vice versa.
If someone is kind or creative then someone is either not patient or patient and vice versa.
Everyone who is funny or humble is not calm.
Everyone who is either not quiet or wise is not brave or not calm and vice versa.
Everyone who is wise is not kind.
If someone is creative or calm then paul is both not rich and tall and vice versa.
If mary is wise then someone is either not brave or humble and vice versa.
If mary is wise then someone is either happy or not quiet.
If alice is generous or strong then mary is both quiet and not kind.
Everyone who is not calm or not wise is both not funny and not rich and vice versa.
Everyone who is not strong or not creative is not happy or not humble.
If susan is either creative or not curious then alice is not patient and vice versa.
If someone is both not rich and quiet then susan is either not creative or old.
Everyone who is not rich is not wise.
Someone is either not happy or creative.
Someone is both creative and not calm.
John is either not kind or tall.
Someone is both not happy and not strong.
Someone is both not strong and not wise. | Paul is calm. | neutral | (![X]:(brave(X)<=>(~patient(X)|~happy(X))))&
(![X]:((~rich(X)|old(X))=>(tall(X)|~happy(X))))&
(((~old(fred)&funny(fred)))<=>(?[X]:((~kind(X)|patient(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:((funny(X)|humble(X))=>~calm(X)))&
(![X]:((~quiet(X)<~>wise(X))<=>(~brave(X)|~calm(X))))&
(![X]:(wise(X)=>~kind(X)))&
((?[X]:((creative(X)|calm(X))))<=>((~rich(paul)&tall(paul))))&
((wise(mary))<=>(?[X]:((~brave(X)<~>humble(X)))))&
((wise(mary))=>(?[X]:((happy(X)<~>~quiet(X)))))&
(((generous(alice)|strong(alice)))=>((quiet(mary)&~kind(mary))))&
(![X]:((~calm(X)|~wise(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~strong(X)|~creative(X))=>(~happy(X)|~humble(X))))&
(((creative(susan)<~>~curious(susan)))<=>(~patient(alice)))&
((?[X]:((~rich(X)&quiet(X))))=>((~creative(susan)<~>old(susan))))&
(![X]:(~rich(X)=>~wise(X)))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((creative(X)&~calm(X))))&
((~kind(john)<~>tall(john)))&
(?[X]:((~happy(X)&~strong(X))))&
(?[X]:((~strong(X)&~wise(X)))) | calm(paul) | [] | null | 0 |
If susan is either not kind or strong then paul is either not tall or quiet and vice versa.
Everyone who is not creative is both quiet and rich and vice versa.
Everyone who is not strong is either rich or strong and vice versa.
If someone is both brave and generous then mary is wise or rich.
Everyone who is either wise or not old is both strong and not kind and vice versa.
If mary is rich or not tall then alice is not quiet.
If someone is tall or not curious then someone is tall or humble and vice versa.
If mary is either not patient or tall then someone is not curious.
Everyone who is not tall or quiet is either not funny or not old and vice versa.
Everyone who is not generous or not calm is either wise or strong.
Everyone who is curious is not happy.
If alice is curious or not strong then fred is both not humble and not rich.
If someone is not happy or not kind then mary is not funny or rich.
If someone is either not calm or not curious then someone is rich or generous.
Everyone who is humble or not calm is both old and not rich and vice versa.
Everyone who is not strong or not kind is tall and vice versa.
Someone is both not humble and not kind.
Someone is curious.
Someone is not brave or kind.
Lucy is either patient or not brave.
Someone is either humble or not quiet.
Someone is both not kind and happy.
Mary is both not old and not kind. | Alice is curious. | contradiction | (((~kind(susan)<~>strong(susan)))<=>((~tall(paul)<~>quiet(paul))))&
(![X]:(~creative(X)<=>(quiet(X)&rich(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>strong(X))))&
((?[X]:((brave(X)&generous(X))))=>((wise(mary)|rich(mary))))&
(![X]:((wise(X)<~>~old(X))<=>(strong(X)&~kind(X))))&
(((rich(mary)|~tall(mary)))=>(~quiet(alice)))&
((?[X]:((tall(X)|~curious(X))))<=>(?[X]:((tall(X)|humble(X)))))&
(((~patient(mary)<~>tall(mary)))=>(?[X]:(~curious(X))))&
(![X]:((~tall(X)|quiet(X))<=>(~funny(X)<~>~old(X))))&
(![X]:((~generous(X)|~calm(X))=>(wise(X)<~>strong(X))))&
(![X]:(curious(X)=>~happy(X)))&
(((curious(alice)|~strong(alice)))=>((~humble(fred)&~rich(fred))))&
((?[X]:((~happy(X)|~kind(X))))=>((~funny(mary)|rich(mary))))&
((?[X]:((~calm(X)<~>~curious(X))))=>(?[X]:((rich(X)|generous(X)))))&
(![X]:((humble(X)|~calm(X))<=>(old(X)&~rich(X))))&
(![X]:((~strong(X)|~kind(X))<=>tall(X)))&
(?[X]:((~humble(X)&~kind(X))))&
(?[X]:(curious(X)))&
(?[X]:((~brave(X)|kind(X))))&
((patient(lucy)<~>~brave(lucy)))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:((~kind(X)&happy(X))))&
((~old(mary)&~kind(mary))) | curious(alice) | [
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6760612152694712908559136
% SZS output start Proof for 6760612152694712908559136
3. ! [X0] : (~strong(X0) <=> (rich(X0) <~> strong(X0))) [input p2]
12. (~strong(alice) | curious(alice)) => (~rich(fred) & ~humble(fred)) [input p11]
24. curious(alice) [input hypothesis]
33. (~rich(fred) & ~humble(fred)) | (strong(alice) & ~curious(alice)) [ennf transformation 12]
38. ! [X0] : ((~strong(X0) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) & (((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | strong(X0))) [nnf transformation 3]
80. strong(X0) | rich(X0) | strong(X0) [cnf transformation 38]
83. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 38]
112. ~rich(fred) | ~curious(alice) [cnf transformation 33]
138. curious(alice) [cnf transformation 24]
139. strong(X0) | rich(X0) [duplicate literal removal 80]
140. ~strong(X0) | rich(X0) [duplicate literal removal 83]
165. rich(X0) [subsumption resolution 139,140]
217. ~curious(alice) [subsumption resolution 112,165]
250. $false [subsumption resolution 138,217]
% SZS output end Proof for 6760612152694712908559136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is wise or creative then lucy is both calm and not brave. Everyone who is not strong or not curious is either not tall or not brave. If susan is both happy and calm then paul is creative. If someone is patient or not curious then someone is not old or patient. Everyone who is both quiet and rich is not creative and vice versa. If susan is brave then john is not kind or wise. Everyone who is both humble and not calm is calm and vice versa. Everyone who is either not wise or not old is not old or not funny and vice versa. If someone is either old or not funny then someone is either not calm or happy and vice versa. Everyone who is brave is not rich or not curious and vice versa. Everyone who is either happy or humble is either strong or tall and vice versa. Everyone who is both curious and not humble is either funny or patient and vice versa. Everyone who is not patient or not happy is not old and vice versa. If paul is creative or not patient then mary is humble and vice versa. Someone is both curious and not strong. Someone is both not brave and not happy. Fred is both not curious and generous. Someone is both not calm and wise. Someone is either funny or not strong. Someone is either not patient or not wise. Someone is generous or funny. | Lucy is kind. | neutral | (((wise(alice)|creative(alice)))=>((calm(lucy)&~brave(lucy))))&
(![X]:((~strong(X)|~curious(X))=>(~tall(X)<~>~brave(X))))&
(((happy(susan)&calm(susan)))=>(creative(paul)))&
((?[X]:((patient(X)|~curious(X))))=>(?[X]:((~old(X)|patient(X)))))&
(![X]:((quiet(X)&rich(X))<=>~creative(X)))&
((brave(susan))=>((~kind(john)|wise(john))))&
(![X]:((humble(X)&~calm(X))<=>calm(X)))&
(![X]:((~wise(X)<~>~old(X))<=>(~old(X)|~funny(X))))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~calm(X)<~>happy(X)))))&
(![X]:(brave(X)<=>(~rich(X)|~curious(X))))&
(![X]:((happy(X)<~>humble(X))<=>(strong(X)<~>tall(X))))&
(![X]:((curious(X)&~humble(X))<=>(funny(X)<~>patient(X))))&
(![X]:((~patient(X)|~happy(X))<=>~old(X)))&
(((creative(paul)|~patient(paul)))<=>(humble(mary)))&
(?[X]:((curious(X)&~strong(X))))&
(?[X]:((~brave(X)&~happy(X))))&
((~curious(fred)&generous(fred)))&
(?[X]:((~calm(X)&wise(X))))&
(?[X]:((funny(X)<~>~strong(X))))&
(?[X]:((~patient(X)<~>~wise(X))))&
(?[X]:((generous(X)|funny(X)))) | kind(lucy) | [] | null | 0 |
Everyone who is both rich and creative is both old and curious and vice versa.
Everyone who is not happy is not wise and vice versa.
Everyone who is either patient or humble is both not brave and not strong and vice versa.
Everyone who is wise or kind is either not kind or not curious and vice versa.
If someone is both not quiet and funny then someone is both not old and old and vice versa.
Everyone who is not strong is both quiet and not generous.
Everyone who is strong is humble.
If susan is both not funny and patient then someone is calm and vice versa.
If someone is both not humble and happy then someone is strong and vice versa.
Everyone who is both not quiet and humble is not patient and vice versa.
Everyone who is not quiet is both old and happy and vice versa.
If mary is both not wise and brave then someone is humble and vice versa.
Everyone who is tall is both patient and not generous.
Everyone who is both not generous and funny is curious and vice versa.
If mary is quiet then susan is either happy or not brave.
Everyone who is either kind or not generous is both quiet and calm and vice versa.
John is both not old and wise.
Paul is tall.
Paul is both not humble and not happy.
Someone is not humble.
Someone is either tall or not curious.
Someone is not funny or calm.
Alice is humble.
Someone is not wise or not quiet. | Paul is quiet. | entailment | (![X]:((rich(X)&creative(X))<=>(old(X)&curious(X))))&
(![X]:(~happy(X)<=>~wise(X)))&
(![X]:((patient(X)<~>humble(X))<=>(~brave(X)&~strong(X))))&
(![X]:((wise(X)|kind(X))<=>(~kind(X)<~>~curious(X))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:((~old(X)&old(X)))))&
(![X]:(~strong(X)=>(quiet(X)&~generous(X))))&
(![X]:(strong(X)=>humble(X)))&
(((~funny(susan)&patient(susan)))<=>(?[X]:(calm(X))))&
((?[X]:((~humble(X)&happy(X))))<=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)&humble(X))<=>~patient(X)))&
(![X]:(~quiet(X)<=>(old(X)&happy(X))))&
(((~wise(mary)&brave(mary)))<=>(?[X]:(humble(X))))&
(![X]:(tall(X)=>(patient(X)&~generous(X))))&
(![X]:((~generous(X)&funny(X))<=>curious(X)))&
((quiet(mary))=>((happy(susan)<~>~brave(susan))))&
(![X]:((kind(X)<~>~generous(X))<=>(quiet(X)&calm(X))))&
((~old(john)&wise(john)))&
(tall(paul))&
((~humble(paul)&~happy(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)<~>~curious(X))))&
(?[X]:((~funny(X)|calm(X))))&
(humble(alice))&
(?[X]:((~wise(X)|~quiet(X)))) | quiet(paul) | [
"p5",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 253918338106528444213601
% SZS output start Proof for 253918338106528444213601
6. ! [X0] : (~strong(X0) => (~generous(X0) & quiet(X0))) [input p5]
7. ! [X0] : (strong(X0) => humble(X0)) [input p6]
19. ~happy(paul) & ~humble(paul) [input p18]
25. ~quiet(paul) [input hypothesis]
28. ! [X0] : ((~generous(X0) & quiet(X0)) | strong(X0)) [ennf transformation 6]
29. ! [X0] : (humble(X0) | ~strong(X0)) [ennf transformation 7]
99. quiet(X0) | strong(X0) [cnf transformation 28]
101. ~strong(X0) | humble(X0) [cnf transformation 29]
133. ~humble(paul) [cnf transformation 19]
141. ~quiet(paul) [cnf transformation 25]
257. strong(paul) [resolution 99,141]
264. humble(paul) [resolution 101,257]
266. $false [subsumption resolution 264,133]
% SZS output end Proof for 253918338106528444213601
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not rich and rich then lucy is either rich or humble.
If someone is humble or brave then someone is kind.
If someone is both generous and not creative then paul is either quiet or not brave.
If someone is both not rich and rich then mary is rich and vice versa.
If susan is wise or not old then someone is either creative or not generous and vice versa.
Everyone who is not wise is not humble and vice versa.
If fred is not creative then mary is either generous or quiet and vice versa.
Everyone who is not curious is calm and vice versa.
If lucy is either not tall or not kind then someone is strong or kind.
If someone is tall or curious then paul is both not quiet and humble.
If someone is either not happy or happy then someone is not calm or not humble.
Everyone who is calm is not curious or not generous.
If someone is funny or curious then someone is both not rich and rich and vice versa.
If someone is kind then fred is both quiet and not humble and vice versa.
Everyone who is not wise is patient or not patient and vice versa.
If someone is strong then someone is both not funny and not old.
Alice is humble or not generous.
Fred is either not generous or generous.
John is both not curious and kind.
Susan is not brave.
Someone is both not curious and happy.
Someone is both not tall and not funny.
Paul is either not quiet or not generous. | Susan is tall. | contradiction | (((~rich(lucy)&rich(lucy)))=>((rich(lucy)<~>humble(lucy))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(kind(X))))&
((?[X]:((generous(X)&~creative(X))))=>((quiet(paul)<~>~brave(paul))))&
((?[X]:((~rich(X)&rich(X))))<=>(rich(mary)))&
(((wise(susan)|~old(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~wise(X)<=>~humble(X)))&
((~creative(fred))<=>((generous(mary)<~>quiet(mary))))&
(![X]:(~curious(X)<=>calm(X)))&
(((~tall(lucy)<~>~kind(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(paul)&humble(paul))))&
((?[X]:((~happy(X)<~>happy(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:(calm(X)=>(~curious(X)|~generous(X))))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~rich(X)&rich(X)))))&
((?[X]:(kind(X)))<=>((quiet(fred)&~humble(fred))))&
(![X]:(~wise(X)<=>(patient(X)|~patient(X))))&
((?[X]:(strong(X)))=>(?[X]:((~funny(X)&~old(X)))))&
((humble(alice)|~generous(alice)))&
((~generous(fred)<~>generous(fred)))&
((~curious(john)&kind(john)))&
(~brave(susan))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((~tall(X)&~funny(X))))&
((~quiet(paul)<~>~generous(paul))) | tall(susan) | [
"p5",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5383826150775252980522479
% SZS output start Proof for 5383826150775252980522479
6. ! [X0] : (~wise(X0) <=> ~humble(X0)) [input p5]
10. ? [X0] : (curious(X0) | tall(X0)) => (humble(paul) & ~quiet(paul)) [input p9]
15. ! [X0] : (~wise(X0) <=> (~patient(X0) | patient(X0))) [input p14]
24. tall(susan) [input hypothesis]
34. (humble(paul) & ~quiet(paul)) | ! [X0] : (~curious(X0) & ~tall(X0)) [ennf transformation 10]
53. ! [X0] : ((~wise(X0) | humble(X0)) & (~humble(X0) | wise(X0))) [nnf transformation 6]
73. ! [X0] : ((~wise(X0) | (patient(X0) & ~patient(X0))) & ((~patient(X0) | patient(X0)) | wise(X0))) [nnf transformation 15]
74. ! [X0] : ((~wise(X0) | (patient(X0) & ~patient(X0))) & (~patient(X0) | patient(X0) | wise(X0))) [flattening 73]
99. ~humble(X0) | wise(X0) [cnf transformation 53]
111. humble(paul) | ~tall(X0) [cnf transformation 34]
125. ~wise(X0) | ~patient(X0) [cnf transformation 74]
126. ~wise(X0) | patient(X0) [cnf transformation 74]
141. tall(susan) [cnf transformation 24]
247. 23 <=> humble(paul) [avatar definition]
249. humble(paul) <- (23) [avatar component clause 247]
252. 24 <=> ! [X0] : ~tall(X0) [avatar definition]
253. ~tall(X0) <- (24) [avatar component clause 252]
254. 24 | 23 [avatar split clause 111,247,252]
302. ~wise(X0) [subsumption resolution 125,126]
331. $false <- (24) [resolution 253,141]
332. ~24 [avatar contradiction clause 331]
333. wise(paul) <- (23) [resolution 99,249]
334. $false <- (23) [subsumption resolution 333,302]
335. ~23 [avatar contradiction clause 334]
336. $false [avatar sat refutation 254,332,335]
% SZS output end Proof for 5383826150775252980522479
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or calm is either not generous or not patient and vice versa. Everyone who is both not tall and humble is not tall and vice versa. Everyone who is strong is not kind. If paul is strong or old then someone is either not brave or old and vice versa. If fred is funny then someone is either not generous or not wise and vice versa. Everyone who is both generous and strong is rich or humble and vice versa. Everyone who is patient or not curious is either wise or patient and vice versa. Everyone who is both not funny and kind is both not funny and not generous. Everyone who is not humble is humble. If lucy is brave or funny then someone is not quiet. Everyone who is both old and generous is either tall or not brave. Everyone who is not generous is not wise. If susan is either brave or rich then mary is tall or creative. Everyone who is not strong or strong is either not creative or not calm. Everyone who is creative or patient is either not funny or not kind. Everyone who is either humble or quiet is not calm. Alice is not calm or not strong. Mary is both not patient and happy. John is not calm. Someone is both not happy and not quiet. Lucy is not creative. | Susan is happy. | neutral | (![X]:((~funny(X)|calm(X))<=>(~generous(X)<~>~patient(X))))&
(![X]:((~tall(X)&humble(X))<=>~tall(X)))&
(![X]:(strong(X)=>~kind(X)))&
(((strong(paul)|old(paul)))<=>(?[X]:((~brave(X)<~>old(X)))))&
((funny(fred))<=>(?[X]:((~generous(X)<~>~wise(X)))))&
(![X]:((generous(X)&strong(X))<=>(rich(X)|humble(X))))&
(![X]:((patient(X)|~curious(X))<=>(wise(X)<~>patient(X))))&
(![X]:((~funny(X)&kind(X))=>(~funny(X)&~generous(X))))&
(![X]:(~humble(X)=>humble(X)))&
(((brave(lucy)|funny(lucy)))=>(?[X]:(~quiet(X))))&
(![X]:((old(X)&generous(X))=>(tall(X)<~>~brave(X))))&
(![X]:(~generous(X)=>~wise(X)))&
(((brave(susan)<~>rich(susan)))=>((tall(mary)|creative(mary))))&
(![X]:((~strong(X)|strong(X))=>(~creative(X)<~>~calm(X))))&
(![X]:((creative(X)|patient(X))=>(~funny(X)<~>~kind(X))))&
(![X]:((humble(X)<~>quiet(X))=>~calm(X)))&
((~calm(alice)|~strong(alice)))&
((~patient(mary)&happy(mary)))&
(~calm(john))&
(?[X]:((~happy(X)&~quiet(X))))&
(~creative(lucy)) | happy(susan) | [] | null | 0 |
If someone is either not happy or not funny then fred is both not humble and not happy.
If susan is not generous then someone is both creative and kind.
Everyone who is both calm and not old is both funny and patient and vice versa.
Everyone who is wise is not rich or not generous.
Everyone who is both creative and not strong is either happy or brave and vice versa.
If alice is both not humble and not brave then someone is either not curious or brave and vice versa.
Everyone who is curious or not old is both not generous and old.
Everyone who is not rich or curious is both not wise and generous.
Everyone who is both not rich and not calm is not kind.
Everyone who is kind or not rich is either not generous or not curious and vice versa.
Everyone who is not wise or not curious is not creative or rich and vice versa.
If fred is brave or funny then someone is happy or not generous and vice versa.
If someone is not happy then someone is patient.
Everyone who is not patient or not wise is not strong or wise and vice versa.
Everyone who is either strong or brave is humble.
Everyone who is funny is not old.
Lucy is tall or not brave.
Alice is either kind or curious.
Someone is not quiet.
Paul is not tall or calm.
Someone is either not humble or not quiet.
Paul is creative or not kind. | Alice is not strong. | entailment | ((?[X]:((~happy(X)<~>~funny(X))))=>((~humble(fred)&~happy(fred))))&
((~generous(susan))=>(?[X]:((creative(X)&kind(X)))))&
(![X]:((calm(X)&~old(X))<=>(funny(X)&patient(X))))&
(![X]:(wise(X)=>(~rich(X)|~generous(X))))&
(![X]:((creative(X)&~strong(X))<=>(happy(X)<~>brave(X))))&
(((~humble(alice)&~brave(alice)))<=>(?[X]:((~curious(X)<~>brave(X)))))&
(![X]:((curious(X)|~old(X))=>(~generous(X)&old(X))))&
(![X]:((~rich(X)|curious(X))=>(~wise(X)&generous(X))))&
(![X]:((~rich(X)&~calm(X))=>~kind(X)))&
(![X]:((kind(X)|~rich(X))<=>(~generous(X)<~>~curious(X))))&
(![X]:((~wise(X)|~curious(X))<=>(~creative(X)|rich(X))))&
(((brave(fred)|funny(fred)))<=>(?[X]:((happy(X)|~generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:(patient(X))))&
(![X]:((~patient(X)|~wise(X))<=>(~strong(X)|wise(X))))&
(![X]:((strong(X)<~>brave(X))=>humble(X)))&
(![X]:(funny(X)=>~old(X)))&
((tall(lucy)|~brave(lucy)))&
((kind(alice)<~>curious(alice)))&
(?[X]:(~quiet(X)))&
((~tall(paul)|calm(paul)))&
(?[X]:((~humble(X)<~>~quiet(X))))&
((creative(paul)|~kind(paul))) | ~strong(alice) | [
"p3",
"p6",
"p7",
"p9",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 377898123406896307118603
% SZS output start Proof for 377898123406896307118603
4. ! [X0] : (wise(X0) => (~generous(X0) | ~rich(X0))) [input p3]
7. ! [X0] : ((~old(X0) | curious(X0)) => (old(X0) & ~generous(X0))) [input p6]
8. ! [X0] : ((curious(X0) | ~rich(X0)) => (generous(X0) & ~wise(X0))) [input p7]
10. ! [X0] : ((~rich(X0) | kind(X0)) <=> (~generous(X0) <~> ~curious(X0))) [input p9]
14. ! [X0] : ((~wise(X0) | ~patient(X0)) <=> (wise(X0) | ~strong(X0))) [input p13]
18. kind(alice) <~> curious(alice) [input p17]
23. strong(alice) [input hypothesis]
27. ! [X0] : ((~generous(X0) | ~rich(X0)) | ~wise(X0)) [ennf transformation 4]
28. ! [X0] : (~generous(X0) | ~rich(X0) | ~wise(X0)) [flattening 27]
29. ! [X0] : ((old(X0) & ~generous(X0)) | (old(X0) & ~curious(X0))) [ennf transformation 7]
30. ! [X0] : ((generous(X0) & ~wise(X0)) | (~curious(X0) & rich(X0))) [ennf transformation 8]
48. ! [X0] : (((~rich(X0) | kind(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (rich(X0) & ~kind(X0)))) [nnf transformation 10]
49. ! [X0] : ((~rich(X0) | kind(X0) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (rich(X0) & ~kind(X0)))) [flattening 48]
60. ! [X0] : (((~wise(X0) | ~patient(X0)) | (~wise(X0) & strong(X0))) & ((wise(X0) | ~strong(X0)) | (wise(X0) & patient(X0)))) [nnf transformation 14]
61. ! [X0] : ((~wise(X0) | ~patient(X0) | (~wise(X0) & strong(X0))) & (wise(X0) | ~strong(X0) | (wise(X0) & patient(X0)))) [flattening 60]
63. (~curious(alice) | ~kind(alice)) & (curious(alice) | kind(alice)) [nnf transformation 18]
79. ~rich(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 28]
92. ~curious(X0) | ~generous(X0) [cnf transformation 29]
96. ~wise(X0) | rich(X0) [cnf transformation 30]
99. generous(X0) | ~curious(X0) [cnf transformation 30]
103. curious(X0) | generous(X0) | ~kind(X0) [cnf transformation 49]
117. wise(X0) | ~strong(X0) | wise(X0) [cnf transformation 61]
124. curious(alice) | kind(alice) [cnf transformation 63]
131. strong(alice) [cnf transformation 23]
132. ~strong(X0) | wise(X0) [duplicate literal removal 117]
195. ~curious(X0) [subsumption resolution 99,92]
197. ~kind(X0) | generous(X0) [subsumption resolution 103,195]
243. kind(alice) [subsumption resolution 124,195]
274. wise(alice) [resolution 132,131]
275. rich(alice) [resolution 274,96]
277. generous(alice) [resolution 197,243]
281. ~generous(alice) | ~wise(alice) [resolution 79,275]
282. ~wise(alice) [subsumption resolution 281,277]
283. $false [subsumption resolution 282,274]
% SZS output end Proof for 377898123406896307118603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not old is strong and vice versa.
Everyone who is not quiet or generous is either kind or curious and vice versa.
If someone is curious then mary is both not humble and not wise.
Everyone who is either strong or not curious is both not humble and wise and vice versa.
Everyone who is both curious and patient is strong or happy and vice versa.
If susan is either not quiet or not funny then someone is both kind and quiet.
If john is not rich then fred is not old.
Everyone who is not curious is both not quiet and wise and vice versa.
If mary is both not funny and not happy then paul is not curious or brave.
Everyone who is not happy or tall is either not generous or not funny and vice versa.
If susan is not curious then mary is both not quiet and not creative and vice versa.
Everyone who is humble is both quiet and generous and vice versa.
Everyone who is both not wise and not quiet is either brave or patient and vice versa.
Everyone who is wise is not humble or wise and vice versa.
Everyone who is both not old and tall is both happy and generous and vice versa.
Someone is funny.
Someone is either not patient or not calm.
Susan is both creative and rich.
Someone is either not tall or not happy.
Susan is tall.
Someone is both creative and not calm. | Paul is not strong. | entailment | (![X]:((strong(X)<~>~old(X))<=>strong(X)))&
(![X]:((~quiet(X)|generous(X))<=>(kind(X)<~>curious(X))))&
((?[X]:(curious(X)))=>((~humble(mary)&~wise(mary))))&
(![X]:((strong(X)<~>~curious(X))<=>(~humble(X)&wise(X))))&
(![X]:((curious(X)&patient(X))<=>(strong(X)|happy(X))))&
(((~quiet(susan)<~>~funny(susan)))=>(?[X]:((kind(X)&quiet(X)))))&
((~rich(john))=>(~old(fred)))&
(![X]:(~curious(X)<=>(~quiet(X)&wise(X))))&
(((~funny(mary)&~happy(mary)))=>((~curious(paul)|brave(paul))))&
(![X]:((~happy(X)|tall(X))<=>(~generous(X)<~>~funny(X))))&
((~curious(susan))<=>((~quiet(mary)&~creative(mary))))&
(![X]:(humble(X)<=>(quiet(X)&generous(X))))&
(![X]:((~wise(X)&~quiet(X))<=>(brave(X)<~>patient(X))))&
(![X]:(wise(X)<=>(~humble(X)|wise(X))))&
(![X]:((~old(X)&tall(X))<=>(happy(X)&generous(X))))&
(?[X]:(funny(X)))&
(?[X]:((~patient(X)<~>~calm(X))))&
((creative(susan)&rich(susan)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(tall(susan))&
(?[X]:((creative(X)&~calm(X)))) | ~strong(paul) | [
"p2",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 856924821296429183205184
% SZS output start Proof for 856924821296429183205184
3. ? [X0] : curious(X0) => (~wise(mary) & ~humble(mary)) [input p2]
5. ! [X0] : ((patient(X0) & curious(X0)) <=> (happy(X0) | strong(X0))) [input p4]
14. ! [X0] : (wise(X0) <=> (wise(X0) | ~humble(X0))) [input p13]
22. strong(paul) [input hypothesis]
25. (~wise(mary) & ~humble(mary)) | ! [X0] : ~curious(X0) [ennf transformation 3]
34. ! [X0] : (((patient(X0) & curious(X0)) | (~happy(X0) & ~strong(X0))) & ((happy(X0) | strong(X0)) | (~patient(X0) | ~curious(X0)))) [nnf transformation 5]
35. ! [X0] : (((patient(X0) & curious(X0)) | (~happy(X0) & ~strong(X0))) & (happy(X0) | strong(X0) | ~patient(X0) | ~curious(X0))) [flattening 34]
49. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & ((wise(X0) | ~humble(X0)) | ~wise(X0))) [nnf transformation 14]
50. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & (wise(X0) | ~humble(X0) | ~wise(X0))) [flattening 49]
73. ~humble(mary) | ~curious(X0) [cnf transformation 25]
74. ~wise(mary) | ~curious(X0) [cnf transformation 25]
82. ~strong(X0) | curious(X0) [cnf transformation 35]
113. wise(X0) | humble(X0) [cnf transformation 50]
128. strong(paul) [cnf transformation 22]
133. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
134. ~curious(X0) <- (1) [avatar component clause 133]
136. 2 <=> wise(mary) [avatar definition]
138. ~wise(mary) <- (~2) [avatar component clause 136]
139. 1 | ~2 [avatar split clause 74,136,133]
141. 3 <=> humble(mary) [avatar definition]
143. ~humble(mary) <- (~3) [avatar component clause 141]
144. 1 | ~3 [avatar split clause 73,141,133]
174. 10 <=> curious(paul) [avatar definition]
175. curious(paul) <- (10) [avatar component clause 174]
218. curious(paul) [resolution 82,128]
221. 10 [avatar split clause 218,174]
224. humble(mary) <- (~2) [resolution 113,138]
225. $false <- (~2, ~3) [subsumption resolution 224,143]
226. 2 | 3 [avatar contradiction clause 225]
227. $false <- (1, 10) [resolution 134,175]
228. ~1 | ~10 [avatar contradiction clause 227]
229. $false [avatar sat refutation 139,144,221,226,228]
% SZS output end Proof for 856924821296429183205184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not patient and brave then someone is either strong or not kind.
Everyone who is both not brave and creative is either quiet or not quiet.
Everyone who is either not kind or not old is not happy.
Everyone who is creative is either not kind or tall.
If mary is kind then lucy is both curious and generous.
Everyone who is curious or brave is not calm or brave.
Everyone who is not rich or funny is wise or not wise.
Everyone who is either not tall or wise is kind.
Everyone who is funny is kind.
If someone is both not wise and wise then someone is both brave and not wise and vice versa.
Everyone who is either wise or curious is either not quiet or humble and vice versa.
If lucy is not brave or kind then susan is both quiet and not brave.
Everyone who is not patient or happy is either not brave or not quiet and vice versa.
Everyone who is not rich is either wise or curious.
Everyone who is either not strong or quiet is not curious and vice versa.
Someone is both funny and calm.
Someone is either curious or not rich.
Someone is either tall or not creative.
Someone is either not creative or brave.
Alice is brave.
Someone is not kind.
Fred is both calm and patient.
Someone is patient. | Alice is wise. | entailment | (((~patient(lucy)&brave(lucy)))=>(?[X]:((strong(X)<~>~kind(X)))))&
(![X]:((~brave(X)&creative(X))=>(quiet(X)<~>~quiet(X))))&
(![X]:((~kind(X)<~>~old(X))=>~happy(X)))&
(![X]:(creative(X)=>(~kind(X)<~>tall(X))))&
((kind(mary))=>((curious(lucy)&generous(lucy))))&
(![X]:((curious(X)|brave(X))=>(~calm(X)|brave(X))))&
(![X]:((~rich(X)|funny(X))=>(wise(X)|~wise(X))))&
(![X]:((~tall(X)<~>wise(X))=>kind(X)))&
(![X]:(funny(X)=>kind(X)))&
((?[X]:((~wise(X)&wise(X))))<=>(?[X]:((brave(X)&~wise(X)))))&
(![X]:((wise(X)<~>curious(X))<=>(~quiet(X)<~>humble(X))))&
(((~brave(lucy)|kind(lucy)))=>((quiet(susan)&~brave(susan))))&
(![X]:((~patient(X)|happy(X))<=>(~brave(X)<~>~quiet(X))))&
(![X]:(~rich(X)=>(wise(X)<~>curious(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>~curious(X)))&
(?[X]:((funny(X)&calm(X))))&
(?[X]:((curious(X)<~>~rich(X))))&
(?[X]:((tall(X)<~>~creative(X))))&
(?[X]:((~creative(X)<~>brave(X))))&
(brave(alice))&
(?[X]:(~kind(X)))&
((calm(fred)&patient(fred)))&
(?[X]:(patient(X))) | wise(alice) | [
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1516699871746794145105927
% SZS output start Proof for 1516699871746794145105927
10. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X0] : (~wise(X0) & brave(X0)) [input p9]
20. brave(alice) [input p19]
24. ~wise(alice) [input hypothesis]
25. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X1] : (~wise(X1) & brave(X1)) [rectify 10]
49. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (wise(X1) | ~brave(X1))) & (? [X1] : (~wise(X1) & brave(X1)) | ! [X0] : (~wise(X0) | wise(X0))) [nnf transformation 25]
50. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (wise(X1) | ~brave(X1))) & (? [X2] : (~wise(X2) & brave(X2)) | ! [X3] : (~wise(X3) | wise(X3))) [rectify 49]
51. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK1) & ~wise(sK1)) [choice axiom]
52. ? [X2] : (~wise(X2) & brave(X2)) => (~wise(sK2) & brave(sK2)) [choice axiom]
53. ((wise(sK1) & ~wise(sK1)) | ! [X1] : (wise(X1) | ~brave(X1))) & ((~wise(sK2) & brave(sK2)) | ! [X3] : (~wise(X3) | wise(X3))) [skolemisation 50,52,51]
92. ~wise(sK1) | wise(X1) | ~brave(X1) [cnf transformation 53]
93. wise(sK1) | wise(X1) | ~brave(X1) [cnf transformation 53]
126. brave(alice) [cnf transformation 20]
131. ~wise(alice) [cnf transformation 24]
160. 7 <=> ! [X1] : (wise(X1) | ~brave(X1)) [avatar definition]
161. ~brave(X1) | wise(X1) <- (7) [avatar component clause 160]
163. 8 <=> wise(sK1) [avatar definition]
166. 7 | 8 [avatar split clause 93,163,160]
167. 7 | ~8 [avatar split clause 92,163,160]
215. wise(alice) <- (7) [resolution 161,126]
217. $false <- (7) [subsumption resolution 215,131]
218. ~7 [avatar contradiction clause 217]
219. $false [avatar sat refutation 166,167,218]
% SZS output end Proof for 1516699871746794145105927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is calm or old.
Everyone who is tall or not brave is both not quiet and not happy and vice versa.
Everyone who is either not curious or not wise is wise and vice versa.
Everyone who is either humble or calm is both patient and not creative.
If susan is not generous or funny then someone is not curious and vice versa.
Everyone who is patient or not happy is either quiet or not kind and vice versa.
If someone is either quiet or not strong then someone is both not generous and kind.
If paul is not strong or not calm then fred is kind and vice versa.
Everyone who is not generous is humble and vice versa.
If alice is quiet then someone is both not wise and brave and vice versa.
Everyone who is either brave or calm is not tall or not happy and vice versa.
Everyone who is not happy or kind is not calm or humble and vice versa.
If someone is rich or old then susan is patient.
If someone is humble then someone is both kind and calm.
If someone is both not creative and not generous then susan is both not patient and brave and vice versa.
If mary is both quiet and calm then someone is rich or happy and vice versa.
Someone is not creative.
Someone is patient.
Someone is not old or brave.
Alice is not old or not tall. | Mary is not calm. | entailment | (![X]:(~brave(X)=>(calm(X)|old(X))))&
(![X]:((tall(X)|~brave(X))<=>(~quiet(X)&~happy(X))))&
(![X]:((~curious(X)<~>~wise(X))<=>wise(X)))&
(![X]:((humble(X)<~>calm(X))=>(patient(X)&~creative(X))))&
(((~generous(susan)|funny(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((patient(X)|~happy(X))<=>(quiet(X)<~>~kind(X))))&
((?[X]:((quiet(X)<~>~strong(X))))=>(?[X]:((~generous(X)&kind(X)))))&
(((~strong(paul)|~calm(paul)))<=>(kind(fred)))&
(![X]:(~generous(X)<=>humble(X)))&
((quiet(alice))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~happy(X)|kind(X))<=>(~calm(X)|humble(X))))&
((?[X]:((rich(X)|old(X))))=>(patient(susan)))&
((?[X]:(humble(X)))=>(?[X]:((kind(X)&calm(X)))))&
((?[X]:((~creative(X)&~generous(X))))<=>((~patient(susan)&brave(susan))))&
(((quiet(mary)&calm(mary)))<=>(?[X]:((rich(X)|happy(X)))))&
(?[X]:(~creative(X)))&
(?[X]:(patient(X)))&
(?[X]:((~old(X)|brave(X))))&
((~old(alice)|~tall(alice))) | ~calm(mary) | [
"p1",
"p5",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 599690904827335781510507
% SZS output start Proof for 599690904827335781510507
2. ! [X0] : ((~brave(X0) | tall(X0)) <=> (~happy(X0) & ~quiet(X0))) [input p1]
6. ! [X0] : ((~happy(X0) | patient(X0)) <=> (quiet(X0) <~> ~kind(X0))) [input p5]
11. ! [X0] : ((brave(X0) <~> calm(X0)) <=> (~happy(X0) | ~tall(X0))) [input p10]
12. ! [X0] : ((kind(X0) | ~happy(X0)) <=> (humble(X0) | ~calm(X0))) [input p11]
14. ? [X0] : humble(X0) => ? [X0] : (calm(X0) & kind(X0)) [input p13]
16. (calm(mary) & quiet(mary)) <=> ? [X0] : (happy(X0) | rich(X0)) [input p15]
21. calm(mary) [input hypothesis]
23. ? [X0] : humble(X0) => ? [X1] : (calm(X1) & kind(X1)) [rectify 14]
29. ? [X1] : (calm(X1) & kind(X1)) | ! [X0] : ~humble(X0) [ennf transformation 23]
30. ! [X0] : (((~brave(X0) | tall(X0)) | (happy(X0) | quiet(X0))) & ((~happy(X0) & ~quiet(X0)) | (brave(X0) & ~tall(X0)))) [nnf transformation 2]
31. ! [X0] : ((~brave(X0) | tall(X0) | happy(X0) | quiet(X0)) & ((~happy(X0) & ~quiet(X0)) | (brave(X0) & ~tall(X0)))) [flattening 30]
39. ! [X0] : (((~happy(X0) | patient(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (happy(X0) & ~patient(X0)))) [nnf transformation 6]
40. ! [X0] : ((~happy(X0) | patient(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (happy(X0) & ~patient(X0)))) [flattening 39]
52. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [nnf transformation 11]
53. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [flattening 52]
54. ! [X0] : (((kind(X0) | ~happy(X0)) | (~humble(X0) & calm(X0))) & ((humble(X0) | ~calm(X0)) | (~kind(X0) & happy(X0)))) [nnf transformation 12]
55. ! [X0] : ((kind(X0) | ~happy(X0) | (~humble(X0) & calm(X0))) & (humble(X0) | ~calm(X0) | (~kind(X0) & happy(X0)))) [flattening 54]
56. ? [X0] : (calm(X0) & kind(X0)) | ! [X1] : ~humble(X1) [rectify 29]
57. ? [X0] : (calm(X0) & kind(X0)) => (calm(sK3) & kind(sK3)) [choice axiom]
58. (calm(sK3) & kind(sK3)) | ! [X1] : ~humble(X1) [skolemisation 56,57]
64. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & (? [X0] : (happy(X0) | rich(X0)) | (~calm(mary) | ~quiet(mary))) [nnf transformation 16]
65. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & (? [X0] : (happy(X0) | rich(X0)) | ~calm(mary) | ~quiet(mary)) [flattening 64]
66. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & (? [X1] : (happy(X1) | rich(X1)) | ~calm(mary) | ~quiet(mary)) [rectify 65]
67. ? [X1] : (happy(X1) | rich(X1)) => (happy(sK5) | rich(sK5)) [choice axiom]
68. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & ((happy(sK5) | rich(sK5)) | ~calm(mary) | ~quiet(mary)) [skolemisation 66,67]
76. ~quiet(X0) | ~tall(X0) [cnf transformation 31]
77. ~quiet(X0) | brave(X0) [cnf transformation 31]
93. ~kind(X0) | quiet(X0) | happy(X0) [cnf transformation 40]
114. ~calm(X0) | ~brave(X0) | tall(X0) [cnf transformation 53]
116. ~calm(X0) | humble(X0) | happy(X0) [cnf transformation 55]
122. kind(sK3) | ~humble(X1) [cnf transformation 58]
123. calm(sK3) | ~humble(X1) [cnf transformation 58]
130. quiet(mary) | ~happy(X0) [cnf transformation 68]
137. calm(mary) [cnf transformation 21]
216. 17 <=> ! [X1] : ~humble(X1) [avatar definition]
217. ~humble(X1) <- (17) [avatar component clause 216]
219. 18 <=> calm(sK3) [avatar definition]
221. calm(sK3) <- (18) [avatar component clause 219]
222. 17 | 18 [avatar split clause 123,219,216]
224. 19 <=> kind(sK3) [avatar definition]
226. kind(sK3) <- (19) [avatar component clause 224]
227. 17 | 19 [avatar split clause 122,224,216]
248. 24 <=> ! [X0] : ~happy(X0) [avatar definition]
249. ~happy(X0) <- (24) [avatar component clause 248]
251. 25 <=> calm(mary) [avatar definition]
253. calm(mary) <- (25) [avatar component clause 251]
257. 26 <=> quiet(mary) [avatar definition]
259. quiet(mary) <- (26) [avatar component clause 257]
260. 24 | 26 [avatar split clause 130,257,248]
289. 25 [avatar split clause 137,251]
380. quiet(sK3) | happy(sK3) <- (19) [resolution 93,226]
401. ~brave(mary) | tall(mary) <- (25) [resolution 114,253]
402. ~brave(sK3) | tall(sK3) <- (18) [resolution 114,221]
405. 45 <=> tall(mary) [avatar definition]
409. 46 <=> brave(mary) [avatar definition]
411. ~brave(mary) <- (~46) [avatar component clause 409]
412. 45 | ~46 | ~25 [avatar split clause 401,251,409,405]
417. 47 <=> tall(sK3) [avatar definition]
421. 48 <=> brave(sK3) [avatar definition]
423. ~brave(sK3) <- (~48) [avatar component clause 421]
424. 47 | ~48 | ~18 [avatar split clause 402,219,421,417]
425. quiet(sK3) <- (19, 24) [subsumption resolution 380,249]
430. humble(mary) | happy(mary) <- (25) [resolution 116,253]
451. brave(sK3) <- (19, 24) [resolution 425,77]
452. ~tall(sK3) <- (19, 24) [resolution 425,76]
453. $false <- (19, 24, ~48) [subsumption resolution 451,423]
454. ~19 | ~24 | 48 [avatar contradiction clause 453]
455. ~47 | ~19 | ~24 [avatar split clause 452,248,224,417]
487. brave(mary) <- (26) [resolution 259,77]
488. ~tall(mary) <- (26) [resolution 259,76]
491. $false <- (26, ~46) [subsumption resolution 487,411]
492. ~26 | 46 [avatar contradiction clause 491]
493. ~45 | ~26 [avatar split clause 488,257,405]
502. happy(mary) <- (17, 25) [subsumption resolution 430,217]
508. $false <- (17, 24, 25) [subsumption resolution 502,249]
509. ~17 | ~24 | ~25 [avatar contradiction clause 508]
512. $false [avatar sat refutation 222,227,260,289,412,424,454,455,492,493,509]
% SZS output end Proof for 599690904827335781510507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and curious is curious.
If john is both not strong and not funny then someone is both not curious and not happy and vice versa.
If someone is not patient then someone is either not creative or creative.
If john is rich then someone is strong or not happy.
Everyone who is generous is not humble or happy and vice versa.
Everyone who is not generous or not patient is either not curious or not wise.
Everyone who is not funny is kind.
If someone is both humble and not funny then someone is not quiet and vice versa.
Everyone who is strong is not old and vice versa.
Everyone who is old is not quiet and vice versa.
If john is creative then mary is not humble or not kind and vice versa.
Everyone who is either quiet or not brave is not strong or humble and vice versa.
If someone is either rich or brave then mary is brave and vice versa.
Everyone who is either not patient or rich is not happy or not patient and vice versa.
If someone is not creative or creative then john is not patient or not happy.
Everyone who is not brave or not creative is either not tall or happy.
Someone is either curious or not kind.
Someone is either kind or calm.
Someone is either not curious or strong.
Someone is both strong and kind.
Someone is either old or not funny.
Mary is both not calm and not patient.
Someone is either not kind or not old.
Someone is brave or not happy. | John is not humble. | neutral | (![X]:((~creative(X)&curious(X))=>curious(X)))&
(((~strong(john)&~funny(john)))<=>(?[X]:((~curious(X)&~happy(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~creative(X)<~>creative(X)))))&
((rich(john))=>(?[X]:((strong(X)|~happy(X)))))&
(![X]:(generous(X)<=>(~humble(X)|happy(X))))&
(![X]:((~generous(X)|~patient(X))=>(~curious(X)<~>~wise(X))))&
(![X]:(~funny(X)=>kind(X)))&
((?[X]:((humble(X)&~funny(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(strong(X)<=>~old(X)))&
(![X]:(old(X)<=>~quiet(X)))&
((creative(john))<=>((~humble(mary)|~kind(mary))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)|humble(X))))&
((?[X]:((rich(X)<~>brave(X))))<=>(brave(mary)))&
(![X]:((~patient(X)<~>rich(X))<=>(~happy(X)|~patient(X))))&
((?[X]:((~creative(X)|creative(X))))=>((~patient(john)|~happy(john))))&
(![X]:((~brave(X)|~creative(X))=>(~tall(X)<~>happy(X))))&
(?[X]:((curious(X)<~>~kind(X))))&
(?[X]:((kind(X)<~>calm(X))))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:((strong(X)&kind(X))))&
(?[X]:((old(X)<~>~funny(X))))&
((~calm(mary)&~patient(mary)))&
(?[X]:((~kind(X)<~>~old(X))))&
(?[X]:((brave(X)|~happy(X)))) | ~humble(john) | [] | null | 0 |
Everyone who is either kind or funny is both not quiet and quiet. Everyone who is both not humble and tall is quiet or wise. If mary is creative or not kind then someone is kind or not happy and vice versa. If someone is kind then mary is both not brave and not generous. Everyone who is generous or tall is either wise or not quiet and vice versa. Everyone who is both quiet and patient is either calm or not generous. If someone is tall or not rich then someone is both not old and generous. Everyone who is funny or kind is either not rich or generous. If someone is either not old or not wise then someone is not old and vice versa. Everyone who is old is not wise or not kind and vice versa. If lucy is not patient or generous then lucy is either strong or old and vice versa. Everyone who is either funny or not funny is either rich or not generous and vice versa. If someone is either creative or brave then fred is either curious or patient and vice versa. Everyone who is both not calm and not funny is generous and vice versa. Everyone who is either not tall or not creative is either not old or not happy and vice versa. John is brave. Alice is either not patient or not happy. Fred is not kind. Someone is either quiet or not humble. | Lucy is curious. | neutral | (![X]:((kind(X)<~>funny(X))=>(~quiet(X)&quiet(X))))&
(![X]:((~humble(X)&tall(X))=>(quiet(X)|wise(X))))&
(((creative(mary)|~kind(mary)))<=>(?[X]:((kind(X)|~happy(X)))))&
((?[X]:(kind(X)))=>((~brave(mary)&~generous(mary))))&
(![X]:((generous(X)|tall(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((quiet(X)&patient(X))=>(calm(X)<~>~generous(X))))&
((?[X]:((tall(X)|~rich(X))))=>(?[X]:((~old(X)&generous(X)))))&
(![X]:((funny(X)|kind(X))=>(~rich(X)<~>generous(X))))&
((?[X]:((~old(X)<~>~wise(X))))<=>(?[X]:(~old(X))))&
(![X]:(old(X)<=>(~wise(X)|~kind(X))))&
(((~patient(lucy)|generous(lucy)))<=>((strong(lucy)<~>old(lucy))))&
(![X]:((funny(X)<~>~funny(X))<=>(rich(X)<~>~generous(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>((curious(fred)<~>patient(fred))))&
(![X]:((~calm(X)&~funny(X))<=>generous(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>(~old(X)<~>~happy(X))))&
(brave(john))&
((~patient(alice)<~>~happy(alice)))&
(~kind(fred))&
(?[X]:((quiet(X)<~>~humble(X)))) | curious(lucy) | [] | null | 0 |
Everyone who is both curious and not old is patient or funny.
Everyone who is not humble is generous or wise.
If john is both brave and not tall then someone is patient or generous and vice versa.
Everyone who is both not wise and not funny is brave or not rich and vice versa.
If alice is either not curious or not rich then john is funny.
Everyone who is either creative or wise is both not curious and not funny and vice versa.
If susan is not old then fred is patient or not generous.
Everyone who is not curious is both not strong and rich and vice versa.
If someone is humble or not curious then john is either not creative or not old and vice versa.
Everyone who is not quiet or not tall is generous or not tall and vice versa.
If someone is old then fred is either not wise or generous and vice versa.
If john is both not rich and wise then fred is not happy or not humble and vice versa.
If susan is either not creative or kind then alice is not calm or generous and vice versa.
Everyone who is both generous and strong is generous or quiet.
If someone is wise or patient then someone is either not patient or quiet.
If someone is not old then someone is not quiet.
Someone is both not rich and not tall.
Paul is not brave or not funny.
Lucy is not tall.
John is brave.
Someone is not generous or kind.
Someone is either creative or not curious.
Someone is not kind or wise.
Someone is brave. | Alice is not rich. | contradiction | (![X]:((curious(X)&~old(X))=>(patient(X)|funny(X))))&
(![X]:(~humble(X)=>(generous(X)|wise(X))))&
(((brave(john)&~tall(john)))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~wise(X)&~funny(X))<=>(brave(X)|~rich(X))))&
(((~curious(alice)<~>~rich(alice)))=>(funny(john)))&
(![X]:((creative(X)<~>wise(X))<=>(~curious(X)&~funny(X))))&
((~old(susan))=>((patient(fred)|~generous(fred))))&
(![X]:(~curious(X)<=>(~strong(X)&rich(X))))&
((?[X]:((humble(X)|~curious(X))))<=>((~creative(john)<~>~old(john))))&
(![X]:((~quiet(X)|~tall(X))<=>(generous(X)|~tall(X))))&
((?[X]:(old(X)))<=>((~wise(fred)<~>generous(fred))))&
(((~rich(john)&wise(john)))<=>((~happy(fred)|~humble(fred))))&
(((~creative(susan)<~>kind(susan)))<=>((~calm(alice)|generous(alice))))&
(![X]:((generous(X)&strong(X))=>(generous(X)|quiet(X))))&
((?[X]:((wise(X)|patient(X))))=>(?[X]:((~patient(X)<~>quiet(X)))))&
((?[X]:(~old(X)))=>(?[X]:(~quiet(X))))&
(?[X]:((~rich(X)&~tall(X))))&
((~brave(paul)|~funny(paul)))&
(~tall(lucy))&
(brave(john))&
(?[X]:((~generous(X)|kind(X))))&
(?[X]:((creative(X)<~>~curious(X))))&
(?[X]:((~kind(X)|wise(X))))&
(?[X]:(brave(X))) | ~rich(alice) | [
"p3",
"p4",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1608270273370648085695077
% SZS output start Proof for 1608270273370648085695077
4. ! [X0] : ((~funny(X0) & ~wise(X0)) <=> (~rich(X0) | brave(X0))) [input p3]
5. (~curious(alice) <~> ~rich(alice)) => funny(john) [input p4]
8. ! [X0] : (~curious(X0) <=> (rich(X0) & ~strong(X0))) [input p7]
20. brave(john) [input p19]
25. ~rich(alice) [input hypothesis]
32. funny(john) | (~curious(alice) <=> ~rich(alice)) [ennf transformation 5]
44. ! [X0] : (((~funny(X0) & ~wise(X0)) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | (funny(X0) | wise(X0)))) [nnf transformation 4]
45. ! [X0] : (((~funny(X0) & ~wise(X0)) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | funny(X0) | wise(X0))) [flattening 44]
46. funny(john) | ((~curious(alice) | rich(alice)) & (~rich(alice) | curious(alice))) [nnf transformation 32]
49. ! [X0] : ((~curious(X0) | (~rich(X0) | strong(X0))) & ((rich(X0) & ~strong(X0)) | curious(X0))) [nnf transformation 8]
50. ! [X0] : ((~curious(X0) | ~rich(X0) | strong(X0)) & ((rich(X0) & ~strong(X0)) | curious(X0))) [flattening 49]
93. ~brave(X0) | ~funny(X0) [cnf transformation 45]
96. funny(john) | ~curious(alice) | rich(alice) [cnf transformation 46]
105. rich(X0) | curious(X0) [cnf transformation 50]
142. brave(john) [cnf transformation 20]
148. ~rich(alice) [cnf transformation 25]
162. 4 <=> brave(john) [avatar definition]
164. brave(john) <- (4) [avatar component clause 162]
177. 7 <=> rich(alice) [avatar definition]
178. ~rich(alice) <- (~7) [avatar component clause 177]
181. 8 <=> curious(alice) [avatar definition]
183. ~curious(alice) <- (~8) [avatar component clause 181]
185. 9 <=> funny(john) [avatar definition]
188. 7 | ~8 | 9 [avatar split clause 96,185,181,177]
311. 4 [avatar split clause 142,162]
340. ~7 [avatar split clause 148,177]
347. ~funny(john) <- (4) [resolution 93,164]
348. ~9 | ~4 [avatar split clause 347,162,185]
350. curious(alice) <- (~7) [resolution 105,178]
352. $false <- (~7, ~8) [subsumption resolution 350,183]
353. 7 | 8 [avatar contradiction clause 352]
354. $false [avatar sat refutation 188,311,340,348,353]
% SZS output end Proof for 1608270273370648085695077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.