premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If fred is either happy or old then paul is curious.
Everyone who is either creative or not strong is either not quiet or curious and vice versa.
If fred is both not tall and strong then fred is both curious and humble.
Everyone who is not quiet or quiet is both old and happy and vice versa.
Everyone who is patient is not curious and vice versa.
Everyone who is kind is either tall or brave and vice versa.
If someone is either not strong or strong then john is either quiet or not happy and vice versa.
If john is tall or patient then someone is patient or not wise.
If someone is not curious then susan is both humble and generous.
Everyone who is either kind or not quiet is both patient and not patient and vice versa.
Everyone who is both not old and tall is both not tall and not funny.
Everyone who is both strong and not strong is not quiet.
Everyone who is quiet or not happy is old or funny.
Everyone who is both not tall and not generous is both kind and not curious.
If alice is both not funny and not tall then mary is both not humble and curious and vice versa.
If someone is not humble then mary is both humble and not quiet and vice versa.
Fred is not strong.
Mary is both wise and not rich.
Someone is humble or not curious.
Someone is not funny or creative.
Fred is either rich or not calm.
Someone is both kind and strong.
Paul is either not humble or not creative.
Lucy is both brave and tall. | Mary is humble. | entailment | (((happy(fred)<~>old(fred)))=>(curious(paul)))&
(![X]:((creative(X)<~>~strong(X))<=>(~quiet(X)<~>curious(X))))&
(((~tall(fred)&strong(fred)))=>((curious(fred)&humble(fred))))&
(![X]:((~quiet(X)|quiet(X))<=>(old(X)&happy(X))))&
(![X]:(patient(X)<=>~curious(X)))&
(![X]:(kind(X)<=>(tall(X)<~>brave(X))))&
((?[X]:((~strong(X)<~>strong(X))))<=>((quiet(john)<~>~happy(john))))&
(((tall(john)|patient(john)))=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:(~curious(X)))=>((humble(susan)&generous(susan))))&
(![X]:((kind(X)<~>~quiet(X))<=>(patient(X)&~patient(X))))&
(![X]:((~old(X)&tall(X))=>(~tall(X)&~funny(X))))&
(![X]:((strong(X)&~strong(X))=>~quiet(X)))&
(![X]:((quiet(X)|~happy(X))=>(old(X)|funny(X))))&
(![X]:((~tall(X)&~generous(X))=>(kind(X)&~curious(X))))&
(((~funny(alice)&~tall(alice)))<=>((~humble(mary)&curious(mary))))&
((?[X]:(~humble(X)))<=>((humble(mary)&~quiet(mary))))&
(~strong(fred))&
((wise(mary)&~rich(mary)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((~funny(X)|creative(X))))&
((rich(fred)<~>~calm(fred)))&
(?[X]:((kind(X)&strong(X))))&
((~humble(paul)<~>~creative(paul)))&
((brave(lucy)&tall(lucy))) | humble(mary) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3136812421026956994943395
% SZS output start Proof for 3136812421026956994943395
16. ? [X0] : ~humble(X0) <=> (~quiet(mary) & humble(mary)) [input p15]
25. ~humble(mary) [input hypothesis]
55. (? [X0] : ~humble(X0) | (quiet(mary) | ~humble(mary))) & ((~quiet(mary) & humble(mary)) | ! [X0] : humble(X0)) [nnf transformation 16]
56. (? [X0] : ~humble(X0) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X0] : humble(X0)) [flattening 55]
57. (? [X0] : ~humble(X0) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X1] : humble(X1)) [rectify 56]
58. ? [X0] : ~humble(X0) => ~humble(sK2) [choice axiom]
59. (~humble(sK2) | quiet(mary) | ~humble(mary)) & ((~quiet(mary) & humble(mary)) | ! [X1] : humble(X1)) [skolemisation 57,58]
117. humble(mary) | humble(X1) [cnf transformation 59]
133. ~humble(mary) [cnf transformation 25]
216. 17 <=> humble(mary) [avatar definition]
217. ~humble(mary) <- (~17) [avatar component clause 216]
245. 23 <=> ! [X1] : humble(X1) [avatar definition]
246. humble(X1) <- (23) [avatar component clause 245]
248. 23 | 17 [avatar split clause 117,216,245]
288. ~17 [avatar split clause 133,216]
289. $false <- (~17, 23) [subsumption resolution 217,246]
290. 17 | ~23 [avatar contradiction clause 289]
295. $false [avatar sat refutation 248,288,290]
% SZS output end Proof for 3136812421026956994943395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or generous then someone is either calm or not strong.
Everyone who is either not wise or not funny is both strong and rich.
If mary is both tall and humble then someone is both not kind and creative and vice versa.
Everyone who is either not curious or curious is either not funny or calm.
Everyone who is either not humble or calm is not rich and vice versa.
Everyone who is not patient or not humble is either patient or not generous and vice versa.
If someone is strong or not tall then john is patient or old.
If someone is either not humble or strong then susan is either strong or calm.
If fred is not quiet or happy then john is old or not curious and vice versa.
Everyone who is either calm or not happy is both not creative and wise.
If someone is both kind and brave then susan is not funny.
If fred is both not curious and kind then alice is both not kind and not happy.
If someone is funny then lucy is brave and vice versa.
Everyone who is rich is both not rich and not creative and vice versa.
If someone is old or not kind then someone is not strong and vice versa.
Everyone who is both wise and not happy is both rich and kind.
Paul is either not patient or not quiet.
Someone is either humble or not wise.
Mary is both not strong and not quiet.
John is either not old or tall.
Alice is either not brave or creative.
Someone is not wise.
Paul is either not calm or curious.
Someone is both kind and not wise. | Susan is funny. | contradiction | ((?[X]:((~patient(X)|generous(X))))=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:((~wise(X)<~>~funny(X))=>(strong(X)&rich(X))))&
(((tall(mary)&humble(mary)))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((~curious(X)<~>curious(X))=>(~funny(X)<~>calm(X))))&
(![X]:((~humble(X)<~>calm(X))<=>~rich(X)))&
(![X]:((~patient(X)|~humble(X))<=>(patient(X)<~>~generous(X))))&
((?[X]:((strong(X)|~tall(X))))=>((patient(john)|old(john))))&
((?[X]:((~humble(X)<~>strong(X))))=>((strong(susan)<~>calm(susan))))&
(((~quiet(fred)|happy(fred)))<=>((old(john)|~curious(john))))&
(![X]:((calm(X)<~>~happy(X))=>(~creative(X)&wise(X))))&
((?[X]:((kind(X)&brave(X))))=>(~funny(susan)))&
(((~curious(fred)&kind(fred)))=>((~kind(alice)&~happy(alice))))&
((?[X]:(funny(X)))<=>(brave(lucy)))&
(![X]:(rich(X)<=>(~rich(X)&~creative(X))))&
((?[X]:((old(X)|~kind(X))))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)&~happy(X))=>(rich(X)&kind(X))))&
((~patient(paul)<~>~quiet(paul)))&
(?[X]:((humble(X)<~>~wise(X))))&
((~strong(mary)&~quiet(mary)))&
((~old(john)<~>tall(john)))&
((~brave(alice)<~>creative(alice)))&
(?[X]:(~wise(X)))&
((~calm(paul)<~>curious(paul)))&
(?[X]:((kind(X)&~wise(X)))) | funny(susan) | [
"p1",
"p3",
"p4",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2930720735834102895962974
% SZS output start Proof for 2930720735834102895962974
2. ! [X0] : ((~wise(X0) <~> ~funny(X0)) => (rich(X0) & strong(X0))) [input p1]
4. ! [X0] : ((~curious(X0) <~> curious(X0)) => (~funny(X0) <~> calm(X0))) [input p3]
5. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> ~rich(X0)) [input p4]
8. ? [X0] : (~humble(X0) <~> strong(X0)) => (strong(susan) <~> calm(susan)) [input p7]
10. ! [X0] : ((calm(X0) <~> ~happy(X0)) => (wise(X0) & ~creative(X0))) [input p9]
14. ! [X0] : (rich(X0) <=> (~creative(X0) & ~rich(X0))) [input p13]
16. ! [X0] : ((~happy(X0) & wise(X0)) => (kind(X0) & rich(X0))) [input p15]
25. funny(susan) [input hypothesis]
29. ! [X0] : ((rich(X0) & strong(X0)) | (~wise(X0) <=> ~funny(X0))) [ennf transformation 2]
30. ! [X0] : ((~funny(X0) <~> calm(X0)) | (~curious(X0) <=> curious(X0))) [ennf transformation 4]
33. (strong(susan) <~> calm(susan)) | ! [X0] : (~humble(X0) <=> strong(X0)) [ennf transformation 8]
34. ! [X0] : ((wise(X0) & ~creative(X0)) | (calm(X0) <=> ~happy(X0))) [ennf transformation 10]
38. ! [X0] : ((kind(X0) & rich(X0)) | (happy(X0) | ~wise(X0))) [ennf transformation 16]
39. ! [X0] : ((kind(X0) & rich(X0)) | happy(X0) | ~wise(X0)) [flattening 38]
44. ! [X0] : ((rich(X0) & strong(X0)) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0)))) [nnf transformation 29]
50. ! [X0] : (((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 30]
51. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | rich(X0)) & (~rich(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 5]
54. ((~calm(susan) | ~strong(susan)) & (calm(susan) | strong(susan))) | ! [X0] : ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0))) [nnf transformation 33]
57. ! [X0] : ((wise(X0) & ~creative(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0)))) [nnf transformation 34]
62. ! [X0] : ((rich(X0) | (creative(X0) | rich(X0))) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [nnf transformation 14]
63. ! [X0] : ((rich(X0) | creative(X0) | rich(X0)) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [flattening 62]
84. ~funny(X0) | strong(X0) | wise(X0) [cnf transformation 44]
92. calm(X0) | ~funny(X0) | curious(X0) | curious(X0) [cnf transformation 50]
93. calm(X0) | ~funny(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 50]
99. ~calm(X0) | humble(X0) | rich(X0) [cnf transformation 51]
111. ~calm(susan) | ~strong(susan) | ~humble(X0) | ~strong(X0) [cnf transformation 54]
116. ~happy(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 57]
125. ~rich(X0) | ~rich(X0) [cnf transformation 63]
127. rich(X0) | creative(X0) | rich(X0) [cnf transformation 63]
131. rich(X0) | happy(X0) | ~wise(X0) [cnf transformation 39]
148. funny(susan) [cnf transformation 25]
149. ~rich(X0) [duplicate literal removal 125]
150. creative(X0) | rich(X0) [duplicate literal removal 127]
153. calm(X0) | ~funny(X0) | curious(X0) [duplicate literal removal 92]
154. calm(X0) | ~funny(X0) | ~curious(X0) [duplicate literal removal 93]
199. ~funny(X0) | calm(X0) [subsumption resolution 153,154]
217. 14 <=> ! [X0] : (~humble(X0) | ~strong(X0)) [avatar definition]
218. ~humble(X0) | ~strong(X0) <- (14) [avatar component clause 217]
220. 15 <=> strong(susan) [avatar definition]
221. strong(susan) <- (15) [avatar component clause 220]
222. ~strong(susan) <- (~15) [avatar component clause 220]
224. 16 <=> calm(susan) [avatar definition]
225. calm(susan) <- (16) [avatar component clause 224]
227. 14 | ~15 | ~16 [avatar split clause 111,224,220,217]
254. 22 <=> funny(susan) [avatar definition]
255. funny(susan) <- (22) [avatar component clause 254]
313. ~wise(X0) | happy(X0) [subsumption resolution 131,149]
360. 22 [avatar split clause 148,254]
372. calm(susan) <- (22) [resolution 199,255]
376. 16 | ~22 [avatar split clause 372,254,224]
382. strong(susan) | wise(susan) <- (22) [resolution 84,255]
384. wise(susan) <- (~15, 22) [subsumption resolution 382,222]
399. happy(susan) <- (~15, 22) [resolution 384,313]
412. humble(susan) | rich(susan) <- (16) [resolution 99,225]
415. humble(susan) <- (16) [subsumption resolution 412,149]
445. ~creative(susan) | ~calm(susan) <- (~15, 22) [resolution 116,399]
447. ~creative(susan) <- (~15, 16, 22) [subsumption resolution 445,225]
460. rich(susan) <- (~15, 16, 22) [resolution 447,150]
461. $false <- (~15, 16, 22) [subsumption resolution 460,149]
462. 15 | ~16 | ~22 [avatar contradiction clause 461]
471. ~strong(susan) <- (14, 16) [resolution 218,415]
473. $false <- (14, 15, 16) [subsumption resolution 471,221]
474. ~14 | ~15 | ~16 [avatar contradiction clause 473]
476. $false [avatar sat refutation 227,360,376,462,474]
% SZS output end Proof for 2930720735834102895962974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If fred is wise or calm then lucy is both not patient and old.
Everyone who is kind or not wise is old or happy.
Everyone who is either not funny or quiet is humble.
Everyone who is creative or not strong is both not funny and not strong and vice versa.
Everyone who is both not generous and not rich is humble or funny and vice versa.
If paul is not tall then john is either curious or not generous and vice versa.
Everyone who is calm is not kind or quiet.
Everyone who is old or not strong is both not curious and funny.
If someone is either tall or not old then alice is not rich or old.
Everyone who is both tall and not humble is brave or not creative and vice versa.
Everyone who is either wise or kind is not funny or rich.
If someone is happy or old then john is funny or tall.
If someone is happy or strong then john is funny or humble.
If someone is both happy and curious then paul is curious and vice versa.
Everyone who is either brave or not strong is strong or not humble.
Everyone who is either happy or not quiet is either happy or humble.
Alice is brave.
Someone is either strong or not happy.
Lucy is curious or not wise.
Mary is either not quiet or creative.
Fred is both curious and not quiet.
Susan is patient or not generous.
Someone is tall. | Paul is not generous. | neutral | (((wise(fred)|calm(fred)))=>((~patient(lucy)&old(lucy))))&
(![X]:((kind(X)|~wise(X))=>(old(X)|happy(X))))&
(![X]:((~funny(X)<~>quiet(X))=>humble(X)))&
(![X]:((creative(X)|~strong(X))<=>(~funny(X)&~strong(X))))&
(![X]:((~generous(X)&~rich(X))<=>(humble(X)|funny(X))))&
((~tall(paul))<=>((curious(john)<~>~generous(john))))&
(![X]:(calm(X)=>(~kind(X)|quiet(X))))&
(![X]:((old(X)|~strong(X))=>(~curious(X)&funny(X))))&
((?[X]:((tall(X)<~>~old(X))))=>((~rich(alice)|old(alice))))&
(![X]:((tall(X)&~humble(X))<=>(brave(X)|~creative(X))))&
(![X]:((wise(X)<~>kind(X))=>(~funny(X)|rich(X))))&
((?[X]:((happy(X)|old(X))))=>((funny(john)|tall(john))))&
((?[X]:((happy(X)|strong(X))))=>((funny(john)|humble(john))))&
((?[X]:((happy(X)&curious(X))))<=>(curious(paul)))&
(![X]:((brave(X)<~>~strong(X))=>(strong(X)|~humble(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(happy(X)<~>humble(X))))&
(brave(alice))&
(?[X]:((strong(X)<~>~happy(X))))&
((curious(lucy)|~wise(lucy)))&
((~quiet(mary)<~>creative(mary)))&
((curious(fred)&~quiet(fred)))&
((patient(susan)|~generous(susan)))&
(?[X]:(tall(X))) | ~generous(paul) | [] | null | 0 |
Everyone who is generous is not rich.
If someone is either not creative or calm then someone is both rich and wise.
If fred is either tall or not humble then someone is both not funny and not creative.
If someone is curious then mary is not generous and vice versa.
Everyone who is not quiet is not tall or brave and vice versa.
Everyone who is not strong is either not kind or old.
Everyone who is either not strong or not creative is either rich or not strong and vice versa.
Everyone who is both not calm and not creative is humble or funny and vice versa.
Everyone who is not quiet or not patient is happy and vice versa.
Everyone who is old or not old is either not humble or creative.
Everyone who is tall or not wise is not curious or happy.
Everyone who is not brave or not kind is not strong.
Everyone who is not creative is both not funny and strong.
Everyone who is both not funny and not patient is not curious and vice versa.
If john is either not kind or not tall then john is patient or not creative.
Someone is kind.
Fred is happy or not old.
Mary is either patient or wise.
Paul is not curious.
Someone is either generous or not wise.
Someone is tall or creative.
Mary is rich or kind. | Fred is brave. | entailment | (![X]:(generous(X)=>~rich(X)))&
((?[X]:((~creative(X)<~>calm(X))))=>(?[X]:((rich(X)&wise(X)))))&
(((tall(fred)<~>~humble(fred)))=>(?[X]:((~funny(X)&~creative(X)))))&
((?[X]:(curious(X)))<=>(~generous(mary)))&
(![X]:(~quiet(X)<=>(~tall(X)|brave(X))))&
(![X]:(~strong(X)=>(~kind(X)<~>old(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>(rich(X)<~>~strong(X))))&
(![X]:((~calm(X)&~creative(X))<=>(humble(X)|funny(X))))&
(![X]:((~quiet(X)|~patient(X))<=>happy(X)))&
(![X]:((old(X)|~old(X))=>(~humble(X)<~>creative(X))))&
(![X]:((tall(X)|~wise(X))=>(~curious(X)|happy(X))))&
(![X]:((~brave(X)|~kind(X))=>~strong(X)))&
(![X]:(~creative(X)=>(~funny(X)&strong(X))))&
(![X]:((~funny(X)&~patient(X))<=>~curious(X)))&
(((~kind(john)<~>~tall(john)))=>((patient(john)|~creative(john))))&
(?[X]:(kind(X)))&
((happy(fred)|~old(fred)))&
((patient(mary)<~>wise(mary)))&
(~curious(paul))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:((tall(X)|creative(X))))&
((rich(mary)|kind(mary))) | brave(fred) | [
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6393395888714790955619629
% SZS output start Proof for 6393395888714790955619629
8. ! [X0] : ((~creative(X0) & ~calm(X0)) <=> (funny(X0) | humble(X0))) [input p7]
10. ! [X0] : ((~old(X0) | old(X0)) => (~humble(X0) <~> creative(X0))) [input p9]
12. ! [X0] : ((~kind(X0) | ~brave(X0)) => ~strong(X0)) [input p11]
13. ! [X0] : (~creative(X0) => (strong(X0) & ~funny(X0))) [input p12]
23. ~brave(fred) [input hypothesis]
35. ! [X0] : ((~humble(X0) <~> creative(X0)) | (old(X0) & ~old(X0))) [ennf transformation 10]
38. ! [X0] : (~strong(X0) | (kind(X0) & brave(X0))) [ennf transformation 12]
39. ! [X0] : ((strong(X0) & ~funny(X0)) | creative(X0)) [ennf transformation 13]
55. ! [X0] : (((~creative(X0) & ~calm(X0)) | (~funny(X0) & ~humble(X0))) & ((funny(X0) | humble(X0)) | (creative(X0) | calm(X0)))) [nnf transformation 8]
56. ! [X0] : (((~creative(X0) & ~calm(X0)) | (~funny(X0) & ~humble(X0))) & (funny(X0) | humble(X0) | creative(X0) | calm(X0))) [flattening 55]
57. ! [X0] : (((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | (old(X0) & ~old(X0))) [nnf transformation 35]
94. ~humble(X0) | ~creative(X0) [cnf transformation 56]
99. ~creative(X0) | humble(X0) | ~old(X0) [cnf transformation 57]
100. ~creative(X0) | humble(X0) | old(X0) [cnf transformation 57]
103. ~strong(X0) | brave(X0) [cnf transformation 38]
106. strong(X0) | creative(X0) [cnf transformation 39]
121. ~brave(fred) [cnf transformation 23]
179. ~creative(X0) | old(X0) [subsumption resolution 100,94]
180. ~creative(X0) | ~old(X0) [subsumption resolution 99,94]
181. ~creative(X0) [subsumption resolution 180,179]
185. strong(X0) [subsumption resolution 106,181]
229. brave(X0) [resolution 103,185]
230. $false [resolution 229,121]
% SZS output end Proof for 6393395888714790955619629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then fred is old.
Everyone who is both not curious and not brave is both old and not rich.
If mary is both not funny and not kind then someone is funny.
If alice is either old or not old then someone is kind or not wise.
Everyone who is either not rich or wise is not patient or not calm.
Everyone who is both not creative and not generous is not humble and vice versa.
Everyone who is both humble and happy is either not creative or not quiet and vice versa.
Everyone who is either not quiet or not calm is either funny or generous.
If someone is either kind or not strong then someone is either not curious or humble and vice versa.
Everyone who is not old is generous or calm and vice versa.
Everyone who is either not curious or funny is either not brave or curious and vice versa.
If someone is not rich then someone is either not creative or not calm.
Everyone who is rich is calm or not wise and vice versa.
If fred is not quiet then fred is either brave or calm and vice versa.
If someone is both strong and not old then paul is either brave or not strong.
Everyone who is both not generous and not kind is either not happy or not creative.
Someone is not calm or not strong.
Fred is both not wise and creative.
Someone is both generous and calm.
Paul is both not brave and happy.
Lucy is not patient.
John is both creative and not curious.
Mary is both patient and kind.
Someone is not strong. | John is not humble. | contradiction | ((?[X]:(funny(X)))=>(old(fred)))&
(![X]:((~curious(X)&~brave(X))=>(old(X)&~rich(X))))&
(((~funny(mary)&~kind(mary)))=>(?[X]:(funny(X))))&
(((old(alice)<~>~old(alice)))=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((~rich(X)<~>wise(X))=>(~patient(X)|~calm(X))))&
(![X]:((~creative(X)&~generous(X))<=>~humble(X)))&
(![X]:((humble(X)&happy(X))<=>(~creative(X)<~>~quiet(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>(funny(X)<~>generous(X))))&
((?[X]:((kind(X)<~>~strong(X))))<=>(?[X]:((~curious(X)<~>humble(X)))))&
(![X]:(~old(X)<=>(generous(X)|calm(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(~brave(X)<~>curious(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:(rich(X)<=>(calm(X)|~wise(X))))&
((~quiet(fred))<=>((brave(fred)<~>calm(fred))))&
((?[X]:((strong(X)&~old(X))))=>((brave(paul)<~>~strong(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)<~>~creative(X))))&
(?[X]:((~calm(X)|~strong(X))))&
((~wise(fred)&creative(fred)))&
(?[X]:((generous(X)&calm(X))))&
((~brave(paul)&happy(paul)))&
(~patient(lucy))&
((creative(john)&~curious(john)))&
((patient(mary)&kind(mary)))&
(?[X]:(~strong(X))) | ~humble(john) | [
"p5",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 869961114771483717272040
% SZS output start Proof for 869961114771483717272040
6. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> ~humble(X0)) [input p5]
22. ~curious(john) & creative(john) [input p21]
25. ~humble(john) [input hypothesis]
47. ! [X0] : (((~generous(X0) & ~creative(X0)) | humble(X0)) & (~humble(X0) | (generous(X0) | creative(X0)))) [nnf transformation 6]
48. ! [X0] : (((~generous(X0) & ~creative(X0)) | humble(X0)) & (~humble(X0) | generous(X0) | creative(X0))) [flattening 47]
84. ~creative(X0) | humble(X0) [cnf transformation 48]
136. creative(john) [cnf transformation 22]
141. ~humble(john) [cnf transformation 25]
277. humble(john) [resolution 84,136]
278. $false [subsumption resolution 277,141]
% SZS output end Proof for 869961114771483717272040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not funny is generous and vice versa.
If lucy is not happy then fred is both tall and old.
Everyone who is either not patient or not humble is not kind or patient.
Everyone who is both not old and brave is patient.
Everyone who is not curious or not calm is not creative.
Everyone who is tall or not brave is wise or generous.
Everyone who is not quiet is both quiet and generous and vice versa.
Everyone who is kind or happy is quiet.
If someone is either creative or not brave then someone is either not curious or generous and vice versa.
If alice is either not calm or not strong then fred is happy and vice versa.
Everyone who is both not brave and not curious is both not curious and not calm and vice versa.
If paul is either old or not patient then someone is creative or calm and vice versa.
Everyone who is either calm or kind is either quiet or not humble.
If someone is not creative then alice is both not old and not wise.
Everyone who is not kind or not patient is not calm and vice versa.
Everyone who is brave is either tall or not funny.
Someone is not tall.
Someone is either calm or happy.
Someone is both not kind and not tall.
Fred is tall.
John is old.
Someone is either not patient or not tall.
Mary is both not creative and not generous. | Alice is patient. | entailment | (![X]:((~curious(X)&~funny(X))<=>generous(X)))&
((~happy(lucy))=>((tall(fred)&old(fred))))&
(![X]:((~patient(X)<~>~humble(X))=>(~kind(X)|patient(X))))&
(![X]:((~old(X)&brave(X))=>patient(X)))&
(![X]:((~curious(X)|~calm(X))=>~creative(X)))&
(![X]:((tall(X)|~brave(X))=>(wise(X)|generous(X))))&
(![X]:(~quiet(X)<=>(quiet(X)&generous(X))))&
(![X]:((kind(X)|happy(X))=>quiet(X)))&
((?[X]:((creative(X)<~>~brave(X))))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(((~calm(alice)<~>~strong(alice)))<=>(happy(fred)))&
(![X]:((~brave(X)&~curious(X))<=>(~curious(X)&~calm(X))))&
(((old(paul)<~>~patient(paul)))<=>(?[X]:((creative(X)|calm(X)))))&
(![X]:((calm(X)<~>kind(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:(~creative(X)))=>((~old(alice)&~wise(alice))))&
(![X]:((~kind(X)|~patient(X))<=>~calm(X)))&
(![X]:(brave(X)=>(tall(X)<~>~funny(X))))&
(?[X]:(~tall(X)))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((~kind(X)&~tall(X))))&
(tall(fred))&
(old(john))&
(?[X]:((~patient(X)<~>~tall(X))))&
((~creative(mary)&~generous(mary))) | patient(alice) | [
"p3",
"p5",
"p6",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 800348763765285170640605
% SZS output start Proof for 800348763765285170640605
4. ! [X0] : ((brave(X0) & ~old(X0)) => patient(X0)) [input p3]
6. ! [X0] : ((~brave(X0) | tall(X0)) => (generous(X0) | wise(X0))) [input p5]
7. ! [X0] : (~quiet(X0) <=> (generous(X0) & quiet(X0))) [input p6]
14. ? [X0] : ~creative(X0) => (~wise(alice) & ~old(alice)) [input p13]
23. ~generous(mary) & ~creative(mary) [input p22]
24. ~patient(alice) [input hypothesis]
29. ! [X0] : (patient(X0) | (~brave(X0) | old(X0))) [ennf transformation 4]
30. ! [X0] : (patient(X0) | ~brave(X0) | old(X0)) [flattening 29]
32. ! [X0] : ((generous(X0) | wise(X0)) | (brave(X0) & ~tall(X0))) [ennf transformation 6]
33. ! [X0] : (generous(X0) | wise(X0) | (brave(X0) & ~tall(X0))) [flattening 32]
36. (~wise(alice) & ~old(alice)) | ! [X0] : creative(X0) [ennf transformation 14]
41. ! [X0] : ((~quiet(X0) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | quiet(X0))) [nnf transformation 7]
42. ! [X0] : ((~quiet(X0) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | quiet(X0))) [flattening 41]
76. ~brave(X0) | patient(X0) | old(X0) [cnf transformation 30]
80. wise(X0) | generous(X0) | brave(X0) [cnf transformation 33]
81. quiet(X0) | quiet(X0) [cnf transformation 42]
83. ~quiet(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 42]
112. ~old(alice) | creative(X0) [cnf transformation 36]
113. ~wise(alice) | creative(X0) [cnf transformation 36]
128. ~creative(mary) [cnf transformation 23]
130. ~patient(alice) [cnf transformation 24]
131. quiet(X0) [duplicate literal removal 81]
132. ~quiet(X0) | ~generous(X0) [duplicate literal removal 83]
228. 19 <=> ! [X0] : creative(X0) [avatar definition]
229. creative(X0) <- (19) [avatar component clause 228]
231. 20 <=> wise(alice) [avatar definition]
233. ~wise(alice) <- (~20) [avatar component clause 231]
234. 19 | ~20 [avatar split clause 113,231,228]
236. 21 <=> old(alice) [avatar definition]
239. 19 | ~21 [avatar split clause 112,236,228]
264. ~generous(X1) [resolution 132,131]
282. generous(alice) | brave(alice) <- (~20) [resolution 80,233]
283. brave(alice) <- (~20) [subsumption resolution 282,264]
284. patient(alice) | old(alice) <- (~20) [resolution 283,76]
285. old(alice) <- (~20) [subsumption resolution 284,130]
288. 21 | 20 [avatar split clause 285,231,236]
299. $false <- (19) [resolution 229,128]
302. ~19 [avatar contradiction clause 299]
303. $false [avatar sat refutation 234,239,288,302]
% SZS output end Proof for 800348763765285170640605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and not curious then someone is not humble or not quiet and vice versa.
Everyone who is funny is either strong or not brave.
Everyone who is wise or not creative is strong.
Everyone who is happy is both not funny and not curious and vice versa.
If someone is either kind or not rich then someone is both not quiet and tall and vice versa.
If someone is not tall or not quiet then someone is quiet.
If someone is both not generous and funny then someone is either strong or creative.
Everyone who is both quiet and not curious is not old and vice versa.
Everyone who is happy is either humble or not generous and vice versa.
Everyone who is not creative or generous is both not quiet and not calm.
Everyone who is not creative or creative is not wise or tall.
Everyone who is funny is not calm or humble and vice versa.
Everyone who is kind or not rich is either quiet or happy.
Everyone who is not tall or creative is humble.
If someone is creative or old then lucy is both curious and wise and vice versa.
Susan is either wise or not tall.
Lucy is not generous or funny.
Someone is quiet or humble.
Fred is not rich.
Someone is either not wise or not humble.
Someone is either strong or not old.
Susan is not humble. | Lucy is quiet. | neutral | ((?[X]:((~calm(X)&~curious(X))))<=>(?[X]:((~humble(X)|~quiet(X)))))&
(![X]:(funny(X)=>(strong(X)<~>~brave(X))))&
(![X]:((wise(X)|~creative(X))=>strong(X)))&
(![X]:(happy(X)<=>(~funny(X)&~curious(X))))&
((?[X]:((kind(X)<~>~rich(X))))<=>(?[X]:((~quiet(X)&tall(X)))))&
((?[X]:((~tall(X)|~quiet(X))))=>(?[X]:(quiet(X))))&
((?[X]:((~generous(X)&funny(X))))=>(?[X]:((strong(X)<~>creative(X)))))&
(![X]:((quiet(X)&~curious(X))<=>~old(X)))&
(![X]:(happy(X)<=>(humble(X)<~>~generous(X))))&
(![X]:((~creative(X)|generous(X))=>(~quiet(X)&~calm(X))))&
(![X]:((~creative(X)|creative(X))=>(~wise(X)|tall(X))))&
(![X]:(funny(X)<=>(~calm(X)|humble(X))))&
(![X]:((kind(X)|~rich(X))=>(quiet(X)<~>happy(X))))&
(![X]:((~tall(X)|creative(X))=>humble(X)))&
((?[X]:((creative(X)|old(X))))<=>((curious(lucy)&wise(lucy))))&
((wise(susan)<~>~tall(susan)))&
((~generous(lucy)|funny(lucy)))&
(?[X]:((quiet(X)|humble(X))))&
(~rich(fred))&
(?[X]:((~wise(X)<~>~humble(X))))&
(?[X]:((strong(X)<~>~old(X))))&
(~humble(susan)) | quiet(lucy) | [] | null | 0 |
Everyone who is not happy is both not rich and generous.
Everyone who is not quiet is both wise and not calm and vice versa.
Everyone who is not rich is either not old or rich and vice versa.
If someone is old then someone is calm and vice versa.
If someone is both tall and curious then paul is both rich and not generous.
Everyone who is both generous and patient is either not tall or old and vice versa.
Everyone who is not rich or curious is strong or not patient.
If someone is tall then fred is either not humble or happy and vice versa.
Everyone who is strong is not strong or brave and vice versa.
If someone is not kind then someone is not happy or not patient.
Everyone who is not kind or quiet is not old.
Everyone who is not curious or not patient is either not happy or not curious.
Everyone who is either happy or tall is either rich or not calm and vice versa.
If fred is not rich then susan is not strong or not old and vice versa.
Everyone who is not strong or not rich is either not curious or funny.
Someone is either not happy or not humble.
Someone is either wise or calm.
Fred is not strong or not curious.
John is both not curious and not patient.
Someone is either not rich or brave.
Lucy is not tall or not curious.
John is not kind or calm.
Someone is both not wise and not tall. | John is not happy. | contradiction | (![X]:(~happy(X)=>(~rich(X)&generous(X))))&
(![X]:(~quiet(X)<=>(wise(X)&~calm(X))))&
(![X]:(~rich(X)<=>(~old(X)<~>rich(X))))&
((?[X]:(old(X)))<=>(?[X]:(calm(X))))&
((?[X]:((tall(X)&curious(X))))=>((rich(paul)&~generous(paul))))&
(![X]:((generous(X)&patient(X))<=>(~tall(X)<~>old(X))))&
(![X]:((~rich(X)|curious(X))=>(strong(X)|~patient(X))))&
((?[X]:(tall(X)))<=>((~humble(fred)<~>happy(fred))))&
(![X]:(strong(X)<=>(~strong(X)|brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((~kind(X)|quiet(X))=>~old(X)))&
(![X]:((~curious(X)|~patient(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((happy(X)<~>tall(X))<=>(rich(X)<~>~calm(X))))&
((~rich(fred))<=>((~strong(susan)|~old(susan))))&
(![X]:((~strong(X)|~rich(X))=>(~curious(X)<~>funny(X))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(?[X]:((wise(X)<~>calm(X))))&
((~strong(fred)|~curious(fred)))&
((~curious(john)&~patient(john)))&
(?[X]:((~rich(X)<~>brave(X))))&
((~tall(lucy)|~curious(lucy)))&
((~kind(john)|calm(john)))&
(?[X]:((~wise(X)&~tall(X)))) | ~happy(john) | [
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6651654825356346587881840
% SZS output start Proof for 6651654825356346587881840
12. ! [X0] : ((~patient(X0) | ~curious(X0)) => (~happy(X0) <~> ~curious(X0))) [input p11]
19. ~patient(john) & ~curious(john) [input p18]
24. ~happy(john) [input hypothesis]
35. ! [X0] : ((~happy(X0) <~> ~curious(X0)) | (patient(X0) & curious(X0))) [ennf transformation 12]
54. ! [X0] : (((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (patient(X0) & curious(X0))) [nnf transformation 35]
102. curious(X0) | happy(X0) | curious(X0) [cnf transformation 54]
124. ~curious(john) [cnf transformation 19]
132. ~happy(john) [cnf transformation 24]
133. curious(X0) | happy(X0) [duplicate literal removal 102]
222. happy(john) [resolution 133,124]
224. $false [subsumption resolution 222,132]
% SZS output end Proof for 6651654825356346587881840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not kind or not curious then someone is either not strong or not generous and vice versa. Everyone who is either not humble or not old is not happy. Everyone who is either quiet or creative is either not funny or not creative and vice versa. Everyone who is not quiet is both calm and not calm. If alice is either humble or kind then someone is either not quiet or not kind and vice versa. If john is both not creative and brave then paul is either not tall or not humble and vice versa. Everyone who is not happy or not strong is both wise and not funny. Everyone who is wise or not rich is either quiet or not old. If paul is brave then someone is either not old or quiet. Everyone who is rich or not old is both happy and tall. If paul is calm then someone is patient or creative and vice versa. Everyone who is either wise or strong is either humble or old and vice versa. Everyone who is not brave is both quiet and curious. If lucy is humble or strong then someone is funny. Everyone who is not happy is either kind or not brave. Everyone who is both not brave and patient is either not kind or not calm and vice versa. Susan is either curious or not funny. Someone is brave. Fred is brave. Lucy is curious. Fred is both rich and not calm. Alice is not brave. John is strong. | Paul is tall. | neutral | (((~kind(alice)|~curious(alice)))<=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((~humble(X)<~>~old(X))=>~happy(X)))&
(![X]:((quiet(X)<~>creative(X))<=>(~funny(X)<~>~creative(X))))&
(![X]:(~quiet(X)=>(calm(X)&~calm(X))))&
(((humble(alice)<~>kind(alice)))<=>(?[X]:((~quiet(X)<~>~kind(X)))))&
(((~creative(john)&brave(john)))<=>((~tall(paul)<~>~humble(paul))))&
(![X]:((~happy(X)|~strong(X))=>(wise(X)&~funny(X))))&
(![X]:((wise(X)|~rich(X))=>(quiet(X)<~>~old(X))))&
((brave(paul))=>(?[X]:((~old(X)<~>quiet(X)))))&
(![X]:((rich(X)|~old(X))=>(happy(X)&tall(X))))&
((calm(paul))<=>(?[X]:((patient(X)|creative(X)))))&
(![X]:((wise(X)<~>strong(X))<=>(humble(X)<~>old(X))))&
(![X]:(~brave(X)=>(quiet(X)&curious(X))))&
(((humble(lucy)|strong(lucy)))=>(?[X]:(funny(X))))&
(![X]:(~happy(X)=>(kind(X)<~>~brave(X))))&
(![X]:((~brave(X)&patient(X))<=>(~kind(X)<~>~calm(X))))&
((curious(susan)<~>~funny(susan)))&
(?[X]:(brave(X)))&
(brave(fred))&
(curious(lucy))&
((rich(fred)&~calm(fred)))&
(~brave(alice))&
(strong(john)) | tall(paul) | [] | null | 0 |
If someone is both old and calm then alice is kind or generous and vice versa.
Everyone who is both generous and not wise is either old or strong.
Everyone who is both not calm and humble is either wise or quiet.
Everyone who is quiet is both brave and humble and vice versa.
If paul is not curious then mary is not wise or not kind.
If someone is both generous and not wise then someone is either not funny or old and vice versa.
If alice is creative then alice is not kind.
Everyone who is both strong and kind is either not patient or tall and vice versa.
If someone is happy or not kind then mary is both quiet and not old and vice versa.
Everyone who is either not happy or not curious is creative and vice versa.
If fred is either not generous or patient then alice is both not humble and funny and vice versa.
Everyone who is rich or funny is strong or not quiet.
If someone is generous or rich then someone is not patient or happy and vice versa.
Everyone who is either not wise or happy is not rich.
Everyone who is patient or tall is not happy.
Everyone who is either not generous or tall is both not rich and calm.
Someone is both tall and rich.
John is humble.
Someone is either patient or not generous.
Fred is either calm or not patient.
Someone is tall or quiet.
Fred is wise or generous.
Someone is both not creative and not funny.
Someone is not happy. | Mary is kind. | neutral | ((?[X]:((old(X)&calm(X))))<=>((kind(alice)|generous(alice))))&
(![X]:((generous(X)&~wise(X))=>(old(X)<~>strong(X))))&
(![X]:((~calm(X)&humble(X))=>(wise(X)<~>quiet(X))))&
(![X]:(quiet(X)<=>(brave(X)&humble(X))))&
((~curious(paul))=>((~wise(mary)|~kind(mary))))&
((?[X]:((generous(X)&~wise(X))))<=>(?[X]:((~funny(X)<~>old(X)))))&
((creative(alice))=>(~kind(alice)))&
(![X]:((strong(X)&kind(X))<=>(~patient(X)<~>tall(X))))&
((?[X]:((happy(X)|~kind(X))))<=>((quiet(mary)&~old(mary))))&
(![X]:((~happy(X)<~>~curious(X))<=>creative(X)))&
(((~generous(fred)<~>patient(fred)))<=>((~humble(alice)&funny(alice))))&
(![X]:((rich(X)|funny(X))=>(strong(X)|~quiet(X))))&
((?[X]:((generous(X)|rich(X))))<=>(?[X]:((~patient(X)|happy(X)))))&
(![X]:((~wise(X)<~>happy(X))=>~rich(X)))&
(![X]:((patient(X)|tall(X))=>~happy(X)))&
(![X]:((~generous(X)<~>tall(X))=>(~rich(X)&calm(X))))&
(?[X]:((tall(X)&rich(X))))&
(humble(john))&
(?[X]:((patient(X)<~>~generous(X))))&
((calm(fred)<~>~patient(fred)))&
(?[X]:((tall(X)|quiet(X))))&
((wise(fred)|generous(fred)))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:(~happy(X))) | kind(mary) | [] | null | 0 |
Everyone who is kind or brave is not humble and vice versa. If someone is both curious and not rich then mary is calm and vice versa. If fred is both not old and not calm then paul is either wise or not rich. If someone is humble or not creative then lucy is either curious or calm. If someone is kind or patient then fred is either wise or not kind. If mary is brave then someone is both not quiet and not old. If someone is either not rich or creative then someone is creative. Everyone who is brave is not kind. If john is not wise or not calm then susan is either creative or not creative and vice versa. Everyone who is both not generous and not rich is rich or wise. If john is either not happy or wise then susan is not calm or patient and vice versa. Everyone who is both not curious and strong is both old and not wise. Everyone who is both not tall and brave is not brave or not happy and vice versa. If someone is brave then paul is kind or happy. If susan is not old or patient then someone is either not generous or kind and vice versa. Someone is generous or not kind. Someone is both not funny and not kind. Someone is not tall. Someone is generous. Alice is either not wise or not creative. | Alice is brave. | entailment | (![X]:((kind(X)|brave(X))<=>~humble(X)))&
((?[X]:((curious(X)&~rich(X))))<=>(calm(mary)))&
(((~old(fred)&~calm(fred)))=>((wise(paul)<~>~rich(paul))))&
((?[X]:((humble(X)|~creative(X))))=>((curious(lucy)<~>calm(lucy))))&
((?[X]:((kind(X)|patient(X))))=>((wise(fred)<~>~kind(fred))))&
((brave(mary))=>(?[X]:((~quiet(X)&~old(X)))))&
((?[X]:((~rich(X)<~>creative(X))))=>(?[X]:(creative(X))))&
(![X]:(brave(X)=>~kind(X)))&
(((~wise(john)|~calm(john)))<=>((creative(susan)<~>~creative(susan))))&
(![X]:((~generous(X)&~rich(X))=>(rich(X)|wise(X))))&
(((~happy(john)<~>wise(john)))<=>((~calm(susan)|patient(susan))))&
(![X]:((~curious(X)&strong(X))=>(old(X)&~wise(X))))&
(![X]:((~tall(X)&brave(X))<=>(~brave(X)|~happy(X))))&
((?[X]:(brave(X)))=>((kind(paul)|happy(paul))))&
(((~old(susan)|patient(susan)))<=>(?[X]:((~generous(X)<~>kind(X)))))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((~funny(X)&~kind(X))))&
(?[X]:(~tall(X)))&
(?[X]:(generous(X)))&
((~wise(alice)<~>~creative(alice))) | brave(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4159034489474853098348559
% SZS output start Proof for 4159034489474853098348559
13. ! [X0] : ((brave(X0) & ~tall(X0)) <=> (~happy(X0) | ~brave(X0))) [input p12]
21. ~brave(alice) [input hypothesis]
57. ! [X0] : (((brave(X0) & ~tall(X0)) | (happy(X0) & brave(X0))) & ((~happy(X0) | ~brave(X0)) | (~brave(X0) | tall(X0)))) [nnf transformation 13]
58. ! [X0] : (((brave(X0) & ~tall(X0)) | (happy(X0) & brave(X0))) & (~happy(X0) | ~brave(X0) | ~brave(X0) | tall(X0))) [flattening 57]
107. brave(X0) | brave(X0) [cnf transformation 58]
122. ~brave(alice) [cnf transformation 21]
124. brave(X0) [duplicate literal removal 107]
307. $false [subsumption resolution 122,124]
% SZS output end Proof for 4159034489474853098348559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or wise is both not curious and creative and vice versa. Everyone who is either strong or generous is rich or curious. If someone is either creative or humble then alice is not curious or not wise and vice versa. Everyone who is both not brave and not kind is brave and vice versa. If someone is either not funny or not calm then susan is not curious. Everyone who is both not humble and not generous is not humble or not calm. If john is not brave or generous then someone is not creative or calm and vice versa. If someone is not strong or humble then someone is either not generous or not wise and vice versa. Everyone who is quiet is both strong and humble and vice versa. Everyone who is not calm or not kind is not old. Everyone who is either not humble or quiet is either not patient or happy and vice versa. Everyone who is not patient is wise or not brave. If someone is either not calm or not curious then someone is either not creative or brave. If john is old or not old then susan is not quiet and vice versa. If susan is brave or not old then someone is both not strong and not quiet and vice versa. If john is both not wise and not old then paul is not brave and vice versa. Susan is not old or not wise. Someone is either kind or strong. Someone is tall. Someone is either not strong or not wise. Someone is curious or not tall. Someone is quiet. Susan is either funny or curious. Someone is not generous or not strong. | John is not happy. | neutral | (![X]:((~funny(X)<~>wise(X))<=>(~curious(X)&creative(X))))&
(![X]:((strong(X)<~>generous(X))=>(rich(X)|curious(X))))&
((?[X]:((creative(X)<~>humble(X))))<=>((~curious(alice)|~wise(alice))))&
(![X]:((~brave(X)&~kind(X))<=>brave(X)))&
((?[X]:((~funny(X)<~>~calm(X))))=>(~curious(susan)))&
(![X]:((~humble(X)&~generous(X))=>(~humble(X)|~calm(X))))&
(((~brave(john)|generous(john)))<=>(?[X]:((~creative(X)|calm(X)))))&
((?[X]:((~strong(X)|humble(X))))<=>(?[X]:((~generous(X)<~>~wise(X)))))&
(![X]:(quiet(X)<=>(strong(X)&humble(X))))&
(![X]:((~calm(X)|~kind(X))=>~old(X)))&
(![X]:((~humble(X)<~>quiet(X))<=>(~patient(X)<~>happy(X))))&
(![X]:(~patient(X)=>(wise(X)|~brave(X))))&
((?[X]:((~calm(X)<~>~curious(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
(((old(john)|~old(john)))<=>(~quiet(susan)))&
(((brave(susan)|~old(susan)))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(((~wise(john)&~old(john)))<=>(~brave(paul)))&
((~old(susan)|~wise(susan)))&
(?[X]:((kind(X)<~>strong(X))))&
(?[X]:(tall(X)))&
(?[X]:((~strong(X)<~>~wise(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:(quiet(X)))&
((funny(susan)<~>curious(susan)))&
(?[X]:((~generous(X)|~strong(X)))) | ~happy(john) | [] | null | 0 |
If someone is both curious and patient then someone is not quiet.
If susan is either calm or curious then someone is either tall or funny and vice versa.
If someone is either old or happy then lucy is not old and vice versa.
If john is happy then someone is both not calm and not patient and vice versa.
If lucy is not brave or not quiet then susan is not quiet or strong.
Everyone who is not funny is both strong and not happy and vice versa.
Everyone who is either rich or calm is either not happy or patient and vice versa.
If someone is both not patient and not strong then someone is both funny and not wise.
Everyone who is either wise or quiet is curious.
Everyone who is both not old and strong is wise or not brave.
Everyone who is both not kind and not calm is humble and vice versa.
If john is either not patient or curious then someone is both not happy and not kind.
Everyone who is humble is not quiet or not funny and vice versa.
Everyone who is not kind is both brave and funny.
Everyone who is both not brave and not quiet is not kind or tall.
Everyone who is not humble or not happy is both tall and quiet and vice versa.
Someone is both rich and not strong.
Susan is both not wise and curious.
Someone is not old or old.
John is both not generous and not strong.
Someone is either not old or not patient.
Someone is generous or not happy.
Mary is either rich or tall.
Someone is funny. | John is quiet. | neutral | ((?[X]:((curious(X)&patient(X))))=>(?[X]:(~quiet(X))))&
(((calm(susan)<~>curious(susan)))<=>(?[X]:((tall(X)<~>funny(X)))))&
((?[X]:((old(X)<~>happy(X))))<=>(~old(lucy)))&
((happy(john))<=>(?[X]:((~calm(X)&~patient(X)))))&
(((~brave(lucy)|~quiet(lucy)))=>((~quiet(susan)|strong(susan))))&
(![X]:(~funny(X)<=>(strong(X)&~happy(X))))&
(![X]:((rich(X)<~>calm(X))<=>(~happy(X)<~>patient(X))))&
((?[X]:((~patient(X)&~strong(X))))=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((wise(X)<~>quiet(X))=>curious(X)))&
(![X]:((~old(X)&strong(X))=>(wise(X)|~brave(X))))&
(![X]:((~kind(X)&~calm(X))<=>humble(X)))&
(((~patient(john)<~>curious(john)))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:(humble(X)<=>(~quiet(X)|~funny(X))))&
(![X]:(~kind(X)=>(brave(X)&funny(X))))&
(![X]:((~brave(X)&~quiet(X))=>(~kind(X)|tall(X))))&
(![X]:((~humble(X)|~happy(X))<=>(tall(X)&quiet(X))))&
(?[X]:((rich(X)&~strong(X))))&
((~wise(susan)&curious(susan)))&
(?[X]:((~old(X)|old(X))))&
((~generous(john)&~strong(john)))&
(?[X]:((~old(X)<~>~patient(X))))&
(?[X]:((generous(X)|~happy(X))))&
((rich(mary)<~>tall(mary)))&
(?[X]:(funny(X))) | quiet(john) | [] | null | 0 |
Everyone who is patient or wise is humble or not tall. Everyone who is happy or not patient is not happy or not tall and vice versa. Everyone who is quiet is quiet or not quiet. If susan is rich then lucy is either not kind or not funny and vice versa. Everyone who is wise or quiet is either not funny or not quiet and vice versa. Everyone who is both not generous and not strong is tall. Everyone who is both brave and creative is both rich and not happy. If someone is both tall and not happy then someone is not humble or not wise. Everyone who is not humble or not brave is not old or rich and vice versa. Everyone who is not rich is not humble and vice versa. Everyone who is patient is both not old and creative. If someone is creative or patient then susan is not patient or generous. Everyone who is calm is wise and vice versa. Everyone who is tall or not funny is either funny or tall. If lucy is both curious and strong then someone is either patient or not tall and vice versa. Everyone who is both quiet and not creative is both not curious and not calm. Fred is either kind or not creative. Someone is rich or not wise. Someone is either not old or not kind. Paul is quiet. Mary is both curious and not old. Someone is both tall and quiet. Someone is either not creative or humble. | Paul is humble. | neutral | (![X]:((patient(X)|wise(X))=>(humble(X)|~tall(X))))&
(![X]:((happy(X)|~patient(X))<=>(~happy(X)|~tall(X))))&
(![X]:(quiet(X)=>(quiet(X)|~quiet(X))))&
((rich(susan))<=>((~kind(lucy)<~>~funny(lucy))))&
(![X]:((wise(X)|quiet(X))<=>(~funny(X)<~>~quiet(X))))&
(![X]:((~generous(X)&~strong(X))=>tall(X)))&
(![X]:((brave(X)&creative(X))=>(rich(X)&~happy(X))))&
((?[X]:((tall(X)&~happy(X))))=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((~humble(X)|~brave(X))<=>(~old(X)|rich(X))))&
(![X]:(~rich(X)<=>~humble(X)))&
(![X]:(patient(X)=>(~old(X)&creative(X))))&
((?[X]:((creative(X)|patient(X))))=>((~patient(susan)|generous(susan))))&
(![X]:(calm(X)<=>wise(X)))&
(![X]:((tall(X)|~funny(X))=>(funny(X)<~>tall(X))))&
(((curious(lucy)&strong(lucy)))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((quiet(X)&~creative(X))=>(~curious(X)&~calm(X))))&
((kind(fred)<~>~creative(fred)))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
(quiet(paul))&
((curious(mary)&~old(mary)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:((~creative(X)<~>humble(X)))) | humble(paul) | [] | null | 0 |
Everyone who is funny or kind is both not strong and not old and vice versa. If someone is either not generous or not humble then paul is both creative and not generous. Everyone who is both kind and rich is either patient or not humble and vice versa. If someone is not generous then someone is not strong and vice versa. Everyone who is generous is not happy or strong and vice versa. Everyone who is not calm or not tall is not calm or not quiet. Everyone who is both not tall and not old is patient or not happy. Everyone who is not funny is both not wise and not kind and vice versa. Everyone who is not generous or curious is rich or old. Everyone who is both not curious and not brave is not rich or not funny. Everyone who is not generous is either generous or not rich and vice versa. Everyone who is either rich or calm is either strong or not kind. Everyone who is happy is either not calm or not creative. If john is not tall then someone is either not kind or happy. Everyone who is not wise is patient or not patient and vice versa. If alice is either calm or curious then mary is either not curious or not funny. Alice is kind or not old. Someone is quiet or curious. Mary is not brave or not strong. Alice is happy. Someone is not rich or not curious. Mary is both not kind and strong. Someone is both not quiet and old. | Alice is not kind. | entailment | (![X]:((funny(X)|kind(X))<=>(~strong(X)&~old(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>((creative(paul)&~generous(paul))))&
(![X]:((kind(X)&rich(X))<=>(patient(X)<~>~humble(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~strong(X))))&
(![X]:(generous(X)<=>(~happy(X)|strong(X))))&
(![X]:((~calm(X)|~tall(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~tall(X)&~old(X))=>(patient(X)|~happy(X))))&
(![X]:(~funny(X)<=>(~wise(X)&~kind(X))))&
(![X]:((~generous(X)|curious(X))=>(rich(X)|old(X))))&
(![X]:((~curious(X)&~brave(X))=>(~rich(X)|~funny(X))))&
(![X]:(~generous(X)<=>(generous(X)<~>~rich(X))))&
(![X]:((rich(X)<~>calm(X))=>(strong(X)<~>~kind(X))))&
(![X]:(happy(X)=>(~calm(X)<~>~creative(X))))&
((~tall(john))=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:(~wise(X)<=>(patient(X)|~patient(X))))&
(((calm(alice)<~>curious(alice)))=>((~curious(mary)<~>~funny(mary))))&
((kind(alice)|~old(alice)))&
(?[X]:((quiet(X)|curious(X))))&
((~brave(mary)|~strong(mary)))&
(happy(alice))&
(?[X]:((~rich(X)|~curious(X))))&
((~kind(mary)&strong(mary)))&
(?[X]:((~quiet(X)&old(X)))) | ~kind(alice) | [
"p0",
"p4",
"p7",
"p8",
"p10",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5643003374402277057292199
% SZS output start Proof for 5643003374402277057292199
1. ! [X0] : ((kind(X0) | funny(X0)) <=> (~old(X0) & ~strong(X0))) [input p0]
5. ! [X0] : (generous(X0) <=> (strong(X0) | ~happy(X0))) [input p4]
8. ! [X0] : (~funny(X0) <=> (~kind(X0) & ~wise(X0))) [input p7]
9. ! [X0] : ((curious(X0) | ~generous(X0)) => (old(X0) | rich(X0))) [input p8]
11. ! [X0] : (~generous(X0) <=> (generous(X0) <~> ~rich(X0))) [input p10]
17. ~old(alice) | kind(alice) [input p16]
20. happy(alice) [input p19]
24. kind(alice) [input hypothesis]
32. ! [X0] : ((old(X0) | rich(X0)) | (~curious(X0) & generous(X0))) [ennf transformation 9]
33. ! [X0] : (old(X0) | rich(X0) | (~curious(X0) & generous(X0))) [flattening 32]
39. ! [X0] : (((kind(X0) | funny(X0)) | (old(X0) | strong(X0))) & ((~old(X0) & ~strong(X0)) | (~kind(X0) & ~funny(X0)))) [nnf transformation 1]
40. ! [X0] : ((kind(X0) | funny(X0) | old(X0) | strong(X0)) & ((~old(X0) & ~strong(X0)) | (~kind(X0) & ~funny(X0)))) [flattening 39]
49. ! [X0] : ((generous(X0) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | ~generous(X0))) [nnf transformation 5]
50. ! [X0] : ((generous(X0) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | ~generous(X0))) [flattening 49]
51. ! [X0] : ((~funny(X0) | (kind(X0) | wise(X0))) & ((~kind(X0) & ~wise(X0)) | funny(X0))) [nnf transformation 8]
52. ! [X0] : ((~funny(X0) | kind(X0) | wise(X0)) & ((~kind(X0) & ~wise(X0)) | funny(X0))) [flattening 51]
53. ! [X0] : ((~generous(X0) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) & (((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | generous(X0))) [nnf transformation 11]
65. ~strong(X0) | ~funny(X0) [cnf transformation 40]
68. ~old(X0) | ~kind(X0) [cnf transformation 40]
82. ~happy(X0) | strong(X0) | ~generous(X0) [cnf transformation 50]
87. ~kind(X0) | funny(X0) [cnf transformation 52]
89. rich(X0) | old(X0) | generous(X0) [cnf transformation 33]
92. ~rich(X0) | generous(X0) | generous(X0) [cnf transformation 53]
94. ~generous(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 53]
109. ~old(alice) | kind(alice) [cnf transformation 17]
112. happy(alice) [cnf transformation 20]
118. kind(alice) [cnf transformation 24]
119. ~rich(X0) | generous(X0) [duplicate literal removal 92]
120. ~rich(X0) | ~generous(X0) [duplicate literal removal 94]
155. ~rich(X0) [subsumption resolution 119,120]
181. ~old(alice) [subsumption resolution 109,68]
206. funny(alice) [resolution 87,118]
213. strong(alice) | ~generous(alice) [resolution 82,112]
216. 17 <=> generous(alice) [avatar definition]
218. ~generous(alice) <- (~17) [avatar component clause 216]
220. 18 <=> strong(alice) [avatar definition]
222. strong(alice) <- (18) [avatar component clause 220]
223. ~17 | 18 [avatar split clause 213,220,216]
226. generous(X1) | old(X1) [resolution 89,155]
229. old(alice) <- (~17) [resolution 226,218]
230. $false <- (~17) [subsumption resolution 229,181]
231. 17 [avatar contradiction clause 230]
234. ~funny(alice) <- (18) [resolution 222,65]
237. $false <- (18) [subsumption resolution 234,206]
238. ~18 [avatar contradiction clause 237]
239. $false [avatar sat refutation 223,231,238]
% SZS output end Proof for 5643003374402277057292199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not curious then someone is either not tall or old.
If someone is not kind or kind then mary is not generous or rich and vice versa.
Everyone who is generous is not funny and vice versa.
If paul is not old or generous then someone is wise and vice versa.
If paul is creative then john is not generous or not kind.
If mary is either tall or not patient then fred is brave.
If someone is rich then someone is quiet.
Everyone who is either not old or not brave is tall or not strong and vice versa.
If someone is both funny and patient then paul is curious.
If someone is both not strong and not old then mary is both not happy and not quiet and vice versa.
If susan is old or rich then someone is both rich and not curious.
Everyone who is both wise and calm is either not humble or not happy and vice versa.
If someone is either not kind or funny then alice is both happy and wise.
Everyone who is not curious is both creative and rich and vice versa.
If someone is both strong and wise then susan is either wise or funny and vice versa.
Everyone who is not strong or strong is both funny and patient.
Someone is brave.
Someone is tall.
Someone is happy.
Lucy is funny.
Lucy is humble.
John is not curious.
Susan is rich. | Lucy is patient. | entailment | (((~creative(paul)|~curious(paul)))=>(?[X]:((~tall(X)<~>old(X)))))&
((?[X]:((~kind(X)|kind(X))))<=>((~generous(mary)|rich(mary))))&
(![X]:(generous(X)<=>~funny(X)))&
(((~old(paul)|generous(paul)))<=>(?[X]:(wise(X))))&
((creative(paul))=>((~generous(john)|~kind(john))))&
(((tall(mary)<~>~patient(mary)))=>(brave(fred)))&
((?[X]:(rich(X)))=>(?[X]:(quiet(X))))&
(![X]:((~old(X)<~>~brave(X))<=>(tall(X)|~strong(X))))&
((?[X]:((funny(X)&patient(X))))=>(curious(paul)))&
((?[X]:((~strong(X)&~old(X))))<=>((~happy(mary)&~quiet(mary))))&
(((old(susan)|rich(susan)))=>(?[X]:((rich(X)&~curious(X)))))&
(![X]:((wise(X)&calm(X))<=>(~humble(X)<~>~happy(X))))&
((?[X]:((~kind(X)<~>funny(X))))=>((happy(alice)&wise(alice))))&
(![X]:(~curious(X)<=>(creative(X)&rich(X))))&
((?[X]:((strong(X)&wise(X))))<=>((wise(susan)<~>funny(susan))))&
(![X]:((~strong(X)|strong(X))=>(funny(X)&patient(X))))&
(?[X]:(brave(X)))&
(?[X]:(tall(X)))&
(?[X]:(happy(X)))&
(funny(lucy))&
(humble(lucy))&
(~curious(john))&
(rich(susan)) | patient(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3621994599688557624691792
% SZS output start Proof for 3621994599688557624691792
16. ! [X0] : ((strong(X0) | ~strong(X0)) => (patient(X0) & funny(X0))) [input p15]
24. ~patient(lucy) [input hypothesis]
34. ! [X0] : ((patient(X0) & funny(X0)) | (~strong(X0) & strong(X0))) [ennf transformation 16]
130. patient(X0) | strong(X0) [cnf transformation 34]
131. patient(X0) | ~strong(X0) [cnf transformation 34]
139. ~patient(lucy) [cnf transformation 24]
315. patient(X0) [subsumption resolution 130,131]
318. $false [subsumption resolution 139,315]
% SZS output end Proof for 3621994599688557624691792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not tall then alice is both not patient and brave and vice versa.
Everyone who is not calm is kind or not happy and vice versa.
Everyone who is not tall is not wise or not strong.
Everyone who is not patient or funny is generous.
Everyone who is not kind is both not rich and curious.
Everyone who is not humble is not funny or creative.
Everyone who is happy or creative is not creative.
If someone is curious or tall then someone is either not strong or not quiet and vice versa.
Everyone who is not kind is either not generous or quiet.
If someone is both not strong and not funny then someone is happy or not kind.
Everyone who is either curious or tall is either not creative or tall.
If mary is not funny or not brave then mary is wise or happy and vice versa.
Everyone who is either rich or not funny is wise or not patient.
Everyone who is both not tall and funny is either not happy or not creative and vice versa.
If someone is either quiet or not creative then mary is happy and vice versa.
Everyone who is not creative or not patient is either not brave or not patient and vice versa.
Someone is strong.
John is strong.
Alice is either creative or curious.
Someone is not patient or strong.
Alice is either generous or creative.
Mary is either not tall or not curious.
Lucy is not generous. | Mary is curious. | entailment | ((~tall(fred))<=>((~patient(alice)&brave(alice))))&
(![X]:(~calm(X)<=>(kind(X)|~happy(X))))&
(![X]:(~tall(X)=>(~wise(X)|~strong(X))))&
(![X]:((~patient(X)|funny(X))=>generous(X)))&
(![X]:(~kind(X)=>(~rich(X)&curious(X))))&
(![X]:(~humble(X)=>(~funny(X)|creative(X))))&
(![X]:((happy(X)|creative(X))=>~creative(X)))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:(~kind(X)=>(~generous(X)<~>quiet(X))))&
((?[X]:((~strong(X)&~funny(X))))=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((curious(X)<~>tall(X))=>(~creative(X)<~>tall(X))))&
(((~funny(mary)|~brave(mary)))<=>((wise(mary)|happy(mary))))&
(![X]:((rich(X)<~>~funny(X))=>(wise(X)|~patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~happy(X)<~>~creative(X))))&
((?[X]:((quiet(X)<~>~creative(X))))<=>(happy(mary)))&
(![X]:((~creative(X)|~patient(X))<=>(~brave(X)<~>~patient(X))))&
(?[X]:(strong(X)))&
(strong(john))&
((creative(alice)<~>curious(alice)))&
(?[X]:((~patient(X)|strong(X))))&
((generous(alice)<~>creative(alice)))&
((~tall(mary)<~>~curious(mary)))&
(~generous(lucy)) | curious(mary) | [
"p6",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7673661351162802935219376
% SZS output start Proof for 7673661351162802935219376
7. ! [X0] : ((creative(X0) | happy(X0)) => ~creative(X0)) [input p6]
11. ! [X0] : ((curious(X0) <~> tall(X0)) => (~creative(X0) <~> tall(X0))) [input p10]
22. ~tall(mary) <~> ~curious(mary) [input p21]
24. ~curious(mary) [input hypothesis]
32. ! [X0] : (~creative(X0) | (~creative(X0) & ~happy(X0))) [ennf transformation 7]
35. ! [X0] : ((~creative(X0) <~> tall(X0)) | (curious(X0) <=> tall(X0))) [ennf transformation 11]
49. ! [X0] : (((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 35]
67. (curious(mary) | tall(mary)) & (~curious(mary) | ~tall(mary)) [nnf transformation 22]
77. ~creative(X0) | ~creative(X0) [cnf transformation 32]
90. ~tall(X0) | creative(X0) | curious(X0) | ~tall(X0) [cnf transformation 49]
121. curious(mary) | tall(mary) [cnf transformation 67]
123. ~curious(mary) [cnf transformation 24]
127. ~tall(X0) | creative(X0) | curious(X0) [duplicate literal removal 90]
128. ~creative(X0) [duplicate literal removal 77]
190. ~tall(X0) | curious(X0) [subsumption resolution 127,128]
237. curious(mary) [subsumption resolution 121,190]
239. $false [subsumption resolution 123,237]
% SZS output end Proof for 7673661351162802935219376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not funny then someone is not rich or not strong and vice versa. Everyone who is quiet or generous is both not wise and generous. Everyone who is funny or not quiet is either wise or not old and vice versa. If someone is generous or not tall then lucy is not quiet. Everyone who is not brave is both not funny and not generous and vice versa. Everyone who is creative is both not curious and curious and vice versa. If someone is tall then fred is both old and not happy. If someone is generous or funny then someone is either funny or not funny and vice versa. If someone is either rich or curious then someone is not curious and vice versa. If paul is patient then someone is not creative. Everyone who is not humble or not generous is not brave and vice versa. Everyone who is both not humble and not creative is happy or rich and vice versa. If paul is either not generous or patient then susan is humble or not tall and vice versa. Everyone who is kind or not brave is both funny and not strong. Everyone who is not tall or not old is not curious and vice versa. If someone is rich then someone is both not calm and not rich and vice versa. Someone is either not funny or patient. John is happy or not wise. Someone is not funny or not humble. Someone is not curious. John is not quiet. Mary is both not kind and not old. Alice is not old or quiet. | Alice is humble. | entailment | ((~funny(mary))<=>(?[X]:((~rich(X)|~strong(X)))))&
(![X]:((quiet(X)|generous(X))=>(~wise(X)&generous(X))))&
(![X]:((funny(X)|~quiet(X))<=>(wise(X)<~>~old(X))))&
((?[X]:((generous(X)|~tall(X))))=>(~quiet(lucy)))&
(![X]:(~brave(X)<=>(~funny(X)&~generous(X))))&
(![X]:(creative(X)<=>(~curious(X)&curious(X))))&
((?[X]:(tall(X)))=>((old(fred)&~happy(fred))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
((?[X]:((rich(X)<~>curious(X))))<=>(?[X]:(~curious(X))))&
((patient(paul))=>(?[X]:(~creative(X))))&
(![X]:((~humble(X)|~generous(X))<=>~brave(X)))&
(![X]:((~humble(X)&~creative(X))<=>(happy(X)|rich(X))))&
(((~generous(paul)<~>patient(paul)))<=>((humble(susan)|~tall(susan))))&
(![X]:((kind(X)|~brave(X))=>(funny(X)&~strong(X))))&
(![X]:((~tall(X)|~old(X))<=>~curious(X)))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)&~rich(X)))))&
(?[X]:((~funny(X)<~>patient(X))))&
((happy(john)|~wise(john)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:(~curious(X)))&
(~quiet(john))&
((~kind(mary)&~old(mary)))&
((~old(alice)|quiet(alice))) | humble(alice) | [
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6116398582452212828838008
% SZS output start Proof for 6116398582452212828838008
5. ! [X0] : (~brave(X0) <=> (~generous(X0) & ~funny(X0))) [input p4]
11. ! [X0] : ((~generous(X0) | ~humble(X0)) <=> ~brave(X0)) [input p10]
14. ! [X0] : ((~brave(X0) | kind(X0)) => (~strong(X0) & funny(X0))) [input p13]
24. ~humble(alice) [input hypothesis]
28. ! [X0] : (~brave(X0) => (~strong(X0) & funny(X0))) [pure predicate removal 14]
34. ! [X0] : ((~strong(X0) & funny(X0)) | brave(X0)) [ennf transformation 28]
41. ! [X0] : ((~brave(X0) | (generous(X0) | funny(X0))) & ((~generous(X0) & ~funny(X0)) | brave(X0))) [nnf transformation 5]
42. ! [X0] : ((~brave(X0) | generous(X0) | funny(X0)) & ((~generous(X0) & ~funny(X0)) | brave(X0))) [flattening 41]
57. ! [X0] : (((~generous(X0) | ~humble(X0)) | brave(X0)) & (~brave(X0) | (generous(X0) & humble(X0)))) [nnf transformation 11]
58. ! [X0] : ((~generous(X0) | ~humble(X0) | brave(X0)) & (~brave(X0) | (generous(X0) & humble(X0)))) [flattening 57]
92. ~funny(X0) | brave(X0) [cnf transformation 42]
111. ~brave(X0) | humble(X0) [cnf transformation 58]
125. funny(X0) | brave(X0) [cnf transformation 34]
141. ~humble(alice) [cnf transformation 24]
257. brave(X0) [subsumption resolution 125,92]
319. humble(X0) [resolution 111,257]
320. $false [resolution 319,141]
% SZS output end Proof for 6116398582452212828838008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not rich then lucy is both not patient and not quiet and vice versa.
Everyone who is either not happy or not funny is both not calm and generous.
If someone is both rich and creative then lucy is either not strong or not calm.
Everyone who is curious or calm is either not kind or happy and vice versa.
If someone is not old then fred is either old or not humble and vice versa.
If fred is either happy or not brave then paul is not humble or creative and vice versa.
Everyone who is calm is curious or strong and vice versa.
If alice is both not humble and strong then john is curious or not strong and vice versa.
If someone is not patient then fred is both not old and generous and vice versa.
Everyone who is creative is both generous and quiet.
Everyone who is either not calm or not strong is either not old or not strong and vice versa.
Everyone who is either not brave or not humble is strong and vice versa.
If someone is not wise then someone is both not calm and not happy and vice versa.
Everyone who is not rich or not curious is not generous or not funny.
Everyone who is both brave and not humble is either rich or brave and vice versa.
If fred is both not brave and humble then someone is tall or not funny and vice versa.
Fred is not kind or not wise.
Mary is not quiet.
Lucy is not funny.
Someone is not tall.
Someone is not strong or tall.
Alice is patient or not creative.
Mary is both not curious and funny. | Fred is not brave. | entailment | (((tall(lucy)<~>~rich(lucy)))<=>((~patient(lucy)&~quiet(lucy))))&
(![X]:((~happy(X)<~>~funny(X))=>(~calm(X)&generous(X))))&
((?[X]:((rich(X)&creative(X))))=>((~strong(lucy)<~>~calm(lucy))))&
(![X]:((curious(X)|calm(X))<=>(~kind(X)<~>happy(X))))&
((?[X]:(~old(X)))<=>((old(fred)<~>~humble(fred))))&
(((happy(fred)<~>~brave(fred)))<=>((~humble(paul)|creative(paul))))&
(![X]:(calm(X)<=>(curious(X)|strong(X))))&
(((~humble(alice)&strong(alice)))<=>((curious(john)|~strong(john))))&
((?[X]:(~patient(X)))<=>((~old(fred)&generous(fred))))&
(![X]:(creative(X)=>(generous(X)&quiet(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(~old(X)<~>~strong(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>strong(X)))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)&~happy(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~generous(X)|~funny(X))))&
(![X]:((brave(X)&~humble(X))<=>(rich(X)<~>brave(X))))&
(((~brave(fred)&humble(fred)))<=>(?[X]:((tall(X)|~funny(X)))))&
((~kind(fred)|~wise(fred)))&
(~quiet(mary))&
(~funny(lucy))&
(?[X]:(~tall(X)))&
(?[X]:((~strong(X)|tall(X))))&
((patient(alice)|~creative(alice)))&
((~curious(mary)&funny(mary))) | ~brave(fred) | [
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5359555785145348559473350
% SZS output start Proof for 5359555785145348559473350
16. (humble(fred) & ~brave(fred)) <=> ? [X0] : (~funny(X0) | tall(X0)) [input p15]
19. ~funny(lucy) [input p18]
24. brave(fred) [input hypothesis]
61. ((humble(fred) & ~brave(fred)) | ! [X0] : (funny(X0) & ~tall(X0))) & (? [X0] : (~funny(X0) | tall(X0)) | (~humble(fred) | brave(fred))) [nnf transformation 16]
62. ((humble(fred) & ~brave(fred)) | ! [X0] : (funny(X0) & ~tall(X0))) & (? [X0] : (~funny(X0) | tall(X0)) | ~humble(fred) | brave(fred)) [flattening 61]
63. ((humble(fred) & ~brave(fred)) | ! [X0] : (funny(X0) & ~tall(X0))) & (? [X1] : (~funny(X1) | tall(X1)) | ~humble(fred) | brave(fred)) [rectify 62]
64. ? [X1] : (~funny(X1) | tall(X1)) => (~funny(sK4) | tall(sK4)) [choice axiom]
65. ((humble(fred) & ~brave(fred)) | ! [X0] : (funny(X0) & ~tall(X0))) & ((~funny(sK4) | tall(sK4)) | ~humble(fred) | brave(fred)) [skolemisation 63,64]
136. ~brave(fred) | funny(X0) [cnf transformation 65]
141. ~funny(lucy) [cnf transformation 19]
147. brave(fred) [cnf transformation 24]
217. 14 <=> brave(fred) [avatar definition]
291. 28 <=> ! [X0] : funny(X0) [avatar definition]
292. funny(X0) <- (28) [avatar component clause 291]
298. 28 | ~14 [avatar split clause 136,217,291]
336. 14 [avatar split clause 147,217]
337. $false <- (28) [resolution 292,141]
338. ~28 [avatar contradiction clause 337]
339. $false [avatar sat refutation 298,336,338]
% SZS output end Proof for 5359555785145348559473350
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and strong is kind or not humble and vice versa.
Everyone who is not strong is old or not curious.
If susan is both wise and quiet then mary is quiet or strong and vice versa.
Everyone who is strong or rich is either not wise or not kind and vice versa.
If lucy is either not wise or old then john is both not brave and generous.
Everyone who is not calm or creative is kind and vice versa.
Everyone who is not curious or wise is both not generous and not creative.
If john is not old then john is creative or humble and vice versa.
If someone is creative then someone is either quiet or not happy and vice versa.
Everyone who is not brave or not rich is either creative or not calm and vice versa.
Everyone who is funny or not quiet is quiet or generous and vice versa.
If someone is curious or not funny then mary is either not wise or not humble.
Everyone who is both not generous and kind is not patient or not wise and vice versa.
If someone is either generous or strong then mary is not happy or not creative and vice versa.
If someone is not calm then john is either wise or tall and vice versa.
If john is not strong then mary is patient or not old and vice versa.
Someone is calm.
Someone is both not old and not wise.
Paul is not strong.
Mary is both rich and not happy.
Someone is humble.
Mary is both old and not curious.
Lucy is funny or not humble.
Someone is funny or not generous. | John is wise. | entailment | (![X]:((~tall(X)&strong(X))<=>(kind(X)|~humble(X))))&
(![X]:(~strong(X)=>(old(X)|~curious(X))))&
(((wise(susan)&quiet(susan)))<=>((quiet(mary)|strong(mary))))&
(![X]:((strong(X)|rich(X))<=>(~wise(X)<~>~kind(X))))&
(((~wise(lucy)<~>old(lucy)))=>((~brave(john)&generous(john))))&
(![X]:((~calm(X)|creative(X))<=>kind(X)))&
(![X]:((~curious(X)|wise(X))=>(~generous(X)&~creative(X))))&
((~old(john))<=>((creative(john)|humble(john))))&
((?[X]:(creative(X)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~rich(X))<=>(creative(X)<~>~calm(X))))&
(![X]:((funny(X)|~quiet(X))<=>(quiet(X)|generous(X))))&
((?[X]:((curious(X)|~funny(X))))=>((~wise(mary)<~>~humble(mary))))&
(![X]:((~generous(X)&kind(X))<=>(~patient(X)|~wise(X))))&
((?[X]:((generous(X)<~>strong(X))))<=>((~happy(mary)|~creative(mary))))&
((?[X]:(~calm(X)))<=>((wise(john)<~>tall(john))))&
((~strong(john))<=>((patient(mary)|~old(mary))))&
(?[X]:(calm(X)))&
(?[X]:((~old(X)&~wise(X))))&
(~strong(paul))&
((rich(mary)&~happy(mary)))&
(?[X]:(humble(X)))&
((old(mary)&~curious(mary)))&
((funny(lucy)|~humble(lucy)))&
(?[X]:((funny(X)|~generous(X)))) | wise(john) | [
"p0",
"p5",
"p6",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5582049154816437550162466
% SZS output start Proof for 5582049154816437550162466
1. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (~humble(X0) | kind(X0))) [input p0]
6. ! [X0] : ((creative(X0) | ~calm(X0)) <=> kind(X0)) [input p5]
7. ! [X0] : ((wise(X0) | ~curious(X0)) => (~creative(X0) & ~generous(X0))) [input p6]
13. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (~wise(X0) | ~patient(X0))) [input p12]
15. ? [X0] : ~calm(X0) <=> (wise(john) <~> tall(john)) [input p14]
16. ~strong(john) <=> (~old(mary) | patient(mary)) [input p15]
22. ~curious(mary) & old(mary) [input p21]
25. ~wise(john) [input hypothesis]
30. ! [X0] : ((~creative(X0) & ~generous(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 7]
32. ! [X0] : (((strong(X0) & ~tall(X0)) | (humble(X0) & ~kind(X0))) & ((~humble(X0) | kind(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 1]
33. ! [X0] : (((strong(X0) & ~tall(X0)) | (humble(X0) & ~kind(X0))) & (~humble(X0) | kind(X0) | ~strong(X0) | tall(X0))) [flattening 32]
39. ! [X0] : (((creative(X0) | ~calm(X0)) | ~kind(X0)) & (kind(X0) | (~creative(X0) & calm(X0)))) [nnf transformation 6]
40. ! [X0] : ((creative(X0) | ~calm(X0) | ~kind(X0)) & (kind(X0) | (~creative(X0) & calm(X0)))) [flattening 39]
53. ! [X0] : (((kind(X0) & ~generous(X0)) | (wise(X0) & patient(X0))) & ((~wise(X0) | ~patient(X0)) | (~kind(X0) | generous(X0)))) [nnf transformation 13]
54. ! [X0] : (((kind(X0) & ~generous(X0)) | (wise(X0) & patient(X0))) & (~wise(X0) | ~patient(X0) | ~kind(X0) | generous(X0))) [flattening 53]
60. (? [X0] : ~calm(X0) | ((wise(john) | ~tall(john)) & (tall(john) | ~wise(john)))) & (((~tall(john) | ~wise(john)) & (tall(john) | wise(john))) | ! [X0] : calm(X0)) [nnf transformation 15]
61. (? [X0] : ~calm(X0) | ((wise(john) | ~tall(john)) & (tall(john) | ~wise(john)))) & (((~tall(john) | ~wise(john)) & (tall(john) | wise(john))) | ! [X1] : calm(X1)) [rectify 60]
62. ? [X0] : ~calm(X0) => ~calm(sK3) [choice axiom]
63. (~calm(sK3) | ((wise(john) | ~tall(john)) & (tall(john) | ~wise(john)))) & (((~tall(john) | ~wise(john)) & (tall(john) | wise(john))) | ! [X1] : calm(X1)) [skolemisation 61,62]
64. (~strong(john) | (old(mary) & ~patient(mary))) & ((~old(mary) | patient(mary)) | strong(john)) [nnf transformation 16]
65. (~strong(john) | (old(mary) & ~patient(mary))) & (~old(mary) | patient(mary) | strong(john)) [flattening 64]
75. ~kind(X0) | ~tall(X0) [cnf transformation 33]
77. ~kind(X0) | strong(X0) [cnf transformation 33]
97. ~calm(X0) | creative(X0) | ~kind(X0) [cnf transformation 40]
100. ~creative(X0) | curious(X0) [cnf transformation 30]
126. patient(X0) | kind(X0) [cnf transformation 54]
127. wise(X0) | kind(X0) [cnf transformation 54]
134. tall(john) | wise(john) | calm(X1) [cnf transformation 63]
139. ~strong(john) | ~patient(mary) [cnf transformation 65]
149. ~curious(mary) [cnf transformation 22]
152. ~wise(john) [cnf transformation 25]
259. 22 <=> creative(mary) [avatar definition]
261. creative(mary) <- (22) [avatar component clause 259]
279. 26 <=> tall(john) [avatar definition]
283. 27 <=> wise(john) [avatar definition]
284. ~wise(john) <- (~27) [avatar component clause 283]
293. 29 <=> ! [X1] : calm(X1) [avatar definition]
294. calm(X1) <- (29) [avatar component clause 293]
296. 29 | 27 | 26 [avatar split clause 134,279,283,293]
302. 31 <=> strong(john) [avatar definition]
307. 32 <=> patient(mary) [avatar definition]
309. ~patient(mary) <- (~32) [avatar component clause 307]
310. ~32 | ~31 [avatar split clause 139,302,307]
323. ~27 [avatar split clause 152,283]
344. kind(john) <- (~27) [resolution 127,284]
359. strong(john) <- (~27) [resolution 344,77]
360. ~tall(john) <- (~27) [resolution 344,75]
365. ~26 | 27 [avatar split clause 360,283,279]
366. 31 | 27 [avatar split clause 359,283,302]
369. kind(mary) <- (~32) [resolution 309,126]
411. ~kind(X0) | creative(X0) <- (29) [resolution 97,294]
499. creative(mary) <- (29, ~32) [resolution 411,369]
504. 22 | ~29 | 32 [avatar split clause 499,307,293,259]
522. curious(mary) <- (22) [resolution 261,100]
526. $false <- (22) [subsumption resolution 522,149]
527. ~22 [avatar contradiction clause 526]
528. $false [avatar sat refutation 296,310,323,365,366,504,527]
% SZS output end Proof for 5582049154816437550162466
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or creative is brave or humble.
Everyone who is strong is generous or not patient and vice versa.
Everyone who is both not funny and quiet is not old or not calm and vice versa.
Everyone who is not happy is either happy or not patient and vice versa.
If someone is patient or not funny then someone is not quiet.
Everyone who is both not patient and patient is both old and brave and vice versa.
If mary is both patient and generous then lucy is not rich.
Everyone who is both not strong and not old is both funny and not generous.
Everyone who is either generous or not old is either patient or not tall.
If fred is old or not kind then john is both not happy and not creative and vice versa.
Everyone who is not happy is either strong or not rich.
If fred is both not humble and generous then someone is not kind and vice versa.
If fred is both strong and not patient then lucy is both quiet and not humble.
If someone is creative or humble then fred is happy or wise.
If someone is not humble or humble then someone is either brave or not tall.
If someone is either strong or not happy then susan is either tall or patient and vice versa.
Someone is funny.
Someone is brave.
Someone is both old and not creative.
Someone is not kind.
Someone is both not creative and not calm.
Alice is old.
Someone is either not funny or not strong.
Someone is tall. | Lucy is not quiet. | contradiction | (![X]:((~curious(X)<~>creative(X))=>(brave(X)|humble(X))))&
(![X]:(strong(X)<=>(generous(X)|~patient(X))))&
(![X]:((~funny(X)&quiet(X))<=>(~old(X)|~calm(X))))&
(![X]:(~happy(X)<=>(happy(X)<~>~patient(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~patient(X)&patient(X))<=>(old(X)&brave(X))))&
(((patient(mary)&generous(mary)))=>(~rich(lucy)))&
(![X]:((~strong(X)&~old(X))=>(funny(X)&~generous(X))))&
(![X]:((generous(X)<~>~old(X))=>(patient(X)<~>~tall(X))))&
(((old(fred)|~kind(fred)))<=>((~happy(john)&~creative(john))))&
(![X]:(~happy(X)=>(strong(X)<~>~rich(X))))&
(((~humble(fred)&generous(fred)))<=>(?[X]:(~kind(X))))&
(((strong(fred)&~patient(fred)))=>((quiet(lucy)&~humble(lucy))))&
((?[X]:((creative(X)|humble(X))))=>((happy(fred)|wise(fred))))&
((?[X]:((~humble(X)|humble(X))))=>(?[X]:((brave(X)<~>~tall(X)))))&
((?[X]:((strong(X)<~>~happy(X))))<=>((tall(susan)<~>patient(susan))))&
(?[X]:(funny(X)))&
(?[X]:(brave(X)))&
(?[X]:((old(X)&~creative(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~creative(X)&~calm(X))))&
(old(alice))&
(?[X]:((~funny(X)<~>~strong(X))))&
(?[X]:(tall(X))) | ~quiet(lucy) | [
"p1",
"p3",
"p11",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3973017128241041261754184
% SZS output start Proof for 3973017128241041261754184
2. ! [X0] : (strong(X0) <=> (~patient(X0) | generous(X0))) [input p1]
4. ! [X0] : (~happy(X0) <=> (happy(X0) <~> ~patient(X0))) [input p3]
12. (generous(fred) & ~humble(fred)) <=> ? [X0] : ~kind(X0) [input p11]
13. (~patient(fred) & strong(fred)) => (~humble(lucy) & quiet(lucy)) [input p12]
20. ? [X0] : ~kind(X0) [input p19]
25. ~quiet(lucy) [input hypothesis]
38. (~humble(lucy) & quiet(lucy)) | (patient(fred) | ~strong(fred)) [ennf transformation 13]
39. (~humble(lucy) & quiet(lucy)) | patient(fred) | ~strong(fred) [flattening 38]
42. ! [X0] : ((strong(X0) | (patient(X0) & ~generous(X0))) & ((~patient(X0) | generous(X0)) | ~strong(X0))) [nnf transformation 2]
43. ! [X0] : ((strong(X0) | (patient(X0) & ~generous(X0))) & (~patient(X0) | generous(X0) | ~strong(X0))) [flattening 42]
46. ! [X0] : ((~happy(X0) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0)))) & (((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | happy(X0))) [nnf transformation 4]
56. ((generous(fred) & ~humble(fred)) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | (~generous(fred) | humble(fred))) [nnf transformation 12]
57. ((generous(fred) & ~humble(fred)) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | ~generous(fred) | humble(fred)) [flattening 56]
58. ((generous(fred) & ~humble(fred)) | ! [X0] : kind(X0)) & (? [X1] : ~kind(X1) | ~generous(fred) | humble(fred)) [rectify 57]
59. ? [X1] : ~kind(X1) => ~kind(sK1) [choice axiom]
60. ((generous(fred) & ~humble(fred)) | ! [X0] : kind(X0)) & (~kind(sK1) | ~generous(fred) | humble(fred)) [skolemisation 58,59]
75. ? [X0] : ~kind(X0) => ~kind(sK7) [choice axiom]
76. ~kind(sK7) [skolemisation 20,75]
87. ~generous(X0) | strong(X0) [cnf transformation 43]
94. ~patient(X0) | happy(X0) | happy(X0) [cnf transformation 46]
96. ~happy(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 46]
120. generous(fred) | kind(X0) [cnf transformation 60]
121. quiet(lucy) | patient(fred) | ~strong(fred) [cnf transformation 39]
139. ~kind(sK7) [cnf transformation 76]
146. ~quiet(lucy) [cnf transformation 25]
147. ~patient(X0) | happy(X0) [duplicate literal removal 94]
148. ~happy(X0) | ~patient(X0) [duplicate literal removal 96]
149. ~patient(X0) [subsumption resolution 147,148]
184. 7 <=> ! [X0] : kind(X0) [avatar definition]
185. kind(X0) <- (7) [avatar component clause 184]
187. 8 <=> generous(fred) [avatar definition]
189. generous(fred) <- (8) [avatar component clause 187]
190. 7 | 8 [avatar split clause 120,187,184]
203. 11 <=> strong(fred) [avatar definition]
205. ~strong(fred) <- (~11) [avatar component clause 203]
211. quiet(lucy) | ~strong(fred) [subsumption resolution 121,149]
213. 13 <=> quiet(lucy) [avatar definition]
216. ~11 | 13 [avatar split clause 211,213,203]
271. ~13 [avatar split clause 146,213]
274. $false <- (7) [resolution 185,139]
275. ~7 [avatar contradiction clause 274]
276. strong(fred) <- (8) [resolution 87,189]
277. $false <- (8, ~11) [subsumption resolution 276,205]
278. ~8 | 11 [avatar contradiction clause 277]
279. $false [avatar sat refutation 190,216,271,275,278]
% SZS output end Proof for 3973017128241041261754184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or strong is strong and vice versa. Everyone who is not kind is generous. Everyone who is happy is not curious or calm and vice versa. Everyone who is not generous or not rich is either rich or not tall and vice versa. If someone is either not humble or not rich then someone is not calm or rich. Everyone who is both curious and not tall is not tall or curious and vice versa. If susan is not funny then lucy is either not creative or not quiet and vice versa. If someone is curious or not humble then paul is not calm. If paul is curious then susan is not tall or not patient and vice versa. If someone is not strong then susan is both strong and wise and vice versa. If john is not rich then someone is both tall and humble and vice versa. Everyone who is not rich or not funny is happy or patient and vice versa. If john is not calm or rich then lucy is strong. Everyone who is not calm is not funny. Everyone who is both wise and brave is strong or not curious. Everyone who is wise or not calm is not patient and vice versa. Fred is either funny or rich. Someone is either not calm or not humble. Someone is either not curious or humble. Someone is either patient or not strong. Mary is both not kind and not brave. Paul is both happy and tall. Alice is both generous and old. | Mary is not funny. | neutral | (![X]:((~curious(X)|strong(X))<=>strong(X)))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:(happy(X)<=>(~curious(X)|calm(X))))&
(![X]:((~generous(X)|~rich(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:((curious(X)&~tall(X))<=>(~tall(X)|curious(X))))&
((~funny(susan))<=>((~creative(lucy)<~>~quiet(lucy))))&
((?[X]:((curious(X)|~humble(X))))=>(~calm(paul)))&
((curious(paul))<=>((~tall(susan)|~patient(susan))))&
((?[X]:(~strong(X)))<=>((strong(susan)&wise(susan))))&
((~rich(john))<=>(?[X]:((tall(X)&humble(X)))))&
(![X]:((~rich(X)|~funny(X))<=>(happy(X)|patient(X))))&
(((~calm(john)|rich(john)))=>(strong(lucy)))&
(![X]:(~calm(X)=>~funny(X)))&
(![X]:((wise(X)&brave(X))=>(strong(X)|~curious(X))))&
(![X]:((wise(X)|~calm(X))<=>~patient(X)))&
((funny(fred)<~>rich(fred)))&
(?[X]:((~calm(X)<~>~humble(X))))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:((patient(X)<~>~strong(X))))&
((~kind(mary)&~brave(mary)))&
((happy(paul)&tall(paul)))&
((generous(alice)&old(alice))) | ~funny(mary) | [] | null | 0 |
If susan is kind or strong then someone is both kind and not brave.
Everyone who is not brave is not humble and vice versa.
Everyone who is both not creative and not humble is brave and vice versa.
If someone is either not curious or strong then susan is both strong and kind and vice versa.
If fred is humble or not brave then mary is funny.
If susan is either not creative or quiet then paul is not patient or rich.
If fred is either tall or creative then someone is not brave or not strong and vice versa.
If susan is creative then john is either not tall or quiet.
If someone is both humble and not rich then someone is not strong and vice versa.
Everyone who is old is not wise and vice versa.
If alice is curious then susan is both not creative and creative.
Everyone who is either curious or not creative is both not tall and calm.
Everyone who is calm is funny or humble and vice versa.
Everyone who is kind is either humble or tall.
Everyone who is not patient is not strong or calm.
Someone is either not old or happy.
Paul is funny or not old.
Susan is both rich and not tall.
Alice is quiet or humble.
Someone is not quiet or not generous.
Someone is either not creative or not generous.
Someone is both not wise and strong.
John is both not wise and calm. | Susan is strong. | entailment | (((kind(susan)|strong(susan)))=>(?[X]:((kind(X)&~brave(X)))))&
(![X]:(~brave(X)<=>~humble(X)))&
(![X]:((~creative(X)&~humble(X))<=>brave(X)))&
((?[X]:((~curious(X)<~>strong(X))))<=>((strong(susan)&kind(susan))))&
(((humble(fred)|~brave(fred)))=>(funny(mary)))&
(((~creative(susan)<~>quiet(susan)))=>((~patient(paul)|rich(paul))))&
(((tall(fred)<~>creative(fred)))<=>(?[X]:((~brave(X)|~strong(X)))))&
((creative(susan))=>((~tall(john)<~>quiet(john))))&
((?[X]:((humble(X)&~rich(X))))<=>(?[X]:(~strong(X))))&
(![X]:(old(X)<=>~wise(X)))&
((curious(alice))=>((~creative(susan)&creative(susan))))&
(![X]:((curious(X)<~>~creative(X))=>(~tall(X)&calm(X))))&
(![X]:(calm(X)<=>(funny(X)|humble(X))))&
(![X]:(kind(X)=>(humble(X)<~>tall(X))))&
(![X]:(~patient(X)=>(~strong(X)|calm(X))))&
(?[X]:((~old(X)<~>happy(X))))&
((funny(paul)|~old(paul)))&
((rich(susan)&~tall(susan)))&
((quiet(alice)|humble(alice)))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:((~creative(X)<~>~generous(X))))&
(?[X]:((~wise(X)&strong(X))))&
((~wise(john)&calm(john))) | strong(susan) | [
"p1",
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8098469833008802921580195
% SZS output start Proof for 8098469833008802921580195
2. ! [X0] : (~brave(X0) <=> ~humble(X0)) [input p1]
3. ! [X0] : ((~humble(X0) & ~creative(X0)) <=> brave(X0)) [input p2]
9. ? [X0] : (~rich(X0) & humble(X0)) <=> ? [X0] : ~strong(X0) [input p8]
24. ~strong(susan) [input hypothesis]
25. ? [X0] : (~rich(X0) & humble(X0)) <=> ? [X1] : ~strong(X1) [rectify 9]
41. ! [X0] : ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))) [nnf transformation 2]
42. ! [X0] : (((~humble(X0) & ~creative(X0)) | ~brave(X0)) & (brave(X0) | (humble(X0) | creative(X0)))) [nnf transformation 3]
43. ! [X0] : (((~humble(X0) & ~creative(X0)) | ~brave(X0)) & (brave(X0) | humble(X0) | creative(X0))) [flattening 42]
54. (? [X0] : (~rich(X0) & humble(X0)) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : (rich(X0) | ~humble(X0))) [nnf transformation 25]
55. (? [X0] : (~rich(X0) & humble(X0)) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : (rich(X3) | ~humble(X3))) [rectify 54]
56. ? [X0] : (~rich(X0) & humble(X0)) => (~rich(sK3) & humble(sK3)) [choice axiom]
57. ? [X2] : ~strong(X2) => ~strong(sK4) [choice axiom]
58. ((~rich(sK3) & humble(sK3)) | ! [X1] : strong(X1)) & (~strong(sK4) | ! [X3] : (rich(X3) | ~humble(X3))) [skolemisation 55,57,56]
76. ~humble(X0) | brave(X0) [cnf transformation 41]
80. ~humble(X0) | ~brave(X0) [cnf transformation 43]
96. humble(sK3) | strong(X1) [cnf transformation 58]
117. ~strong(susan) [cnf transformation 24]
119. 1 <=> strong(susan) [avatar definition]
121. ~strong(susan) <- (~1) [avatar component clause 119]
138. ~humble(X0) [subsumption resolution 80,76]
161. 9 <=> ! [X0] : strong(X0) [avatar definition]
162. strong(X0) <- (9) [avatar component clause 161]
207. strong(X1) [subsumption resolution 96,138]
208. 9 [avatar split clause 207,161]
246. ~1 [avatar split clause 117,119]
248. $false <- (~1, 9) [subsumption resolution 121,162]
249. 1 | ~9 [avatar contradiction clause 248]
250. $false [avatar sat refutation 208,246,249]
% SZS output end Proof for 8098469833008802921580195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or old then someone is either not happy or happy and vice versa.
Everyone who is both generous and rich is not calm and vice versa.
If someone is both not generous and brave then someone is both not creative and not generous.
Everyone who is both not tall and not calm is not patient and vice versa.
Everyone who is either not wise or not generous is wise or not calm and vice versa.
Everyone who is patient or funny is calm.
Everyone who is humble or not humble is strong.
Everyone who is tall or not tall is not patient and vice versa.
If someone is not strong or not generous then someone is either patient or humble and vice versa.
Everyone who is either not rich or kind is funny and vice versa.
If someone is either not curious or strong then someone is quiet or not funny.
If someone is not calm or not curious then susan is either happy or curious and vice versa.
Everyone who is both generous and old is not quiet and vice versa.
Everyone who is either not rich or not generous is kind.
If paul is wise or generous then lucy is both quiet and not patient and vice versa.
Mary is old or not rich.
Someone is not generous or brave.
Lucy is either quiet or not curious. | Lucy is not quiet. | contradiction | ((?[X]:((~kind(X)|old(X))))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((generous(X)&rich(X))<=>~calm(X)))&
((?[X]:((~generous(X)&brave(X))))=>(?[X]:((~creative(X)&~generous(X)))))&
(![X]:((~tall(X)&~calm(X))<=>~patient(X)))&
(![X]:((~wise(X)<~>~generous(X))<=>(wise(X)|~calm(X))))&
(![X]:((patient(X)|funny(X))=>calm(X)))&
(![X]:((humble(X)|~humble(X))=>strong(X)))&
(![X]:((tall(X)|~tall(X))<=>~patient(X)))&
((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~rich(X)<~>kind(X))<=>funny(X)))&
((?[X]:((~curious(X)<~>strong(X))))=>(?[X]:((quiet(X)|~funny(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>((happy(susan)<~>curious(susan))))&
(![X]:((generous(X)&old(X))<=>~quiet(X)))&
(![X]:((~rich(X)<~>~generous(X))=>kind(X)))&
(((wise(paul)|generous(paul)))<=>((quiet(lucy)&~patient(lucy))))&
((old(mary)|~rich(mary)))&
(?[X]:((~generous(X)|brave(X))))&
((quiet(lucy)<~>~curious(lucy))) | ~quiet(lucy) | [
"p1",
"p3",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2947104678987397026170588
% SZS output start Proof for 2947104678987397026170588
2. ! [X0] : ((rich(X0) & generous(X0)) <=> ~calm(X0)) [input p1]
4. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> ~patient(X0)) [input p3]
8. ! [X0] : ((~tall(X0) | tall(X0)) <=> ~patient(X0)) [input p7]
15. (generous(paul) | wise(paul)) <=> (~patient(lucy) & quiet(lucy)) [input p14]
19. ~quiet(lucy) [input hypothesis]
37. ! [X0] : (((rich(X0) & generous(X0)) | calm(X0)) & (~calm(X0) | (~rich(X0) | ~generous(X0)))) [nnf transformation 2]
38. ! [X0] : (((rich(X0) & generous(X0)) | calm(X0)) & (~calm(X0) | ~rich(X0) | ~generous(X0))) [flattening 37]
42. ! [X0] : (((~calm(X0) & ~tall(X0)) | patient(X0)) & (~patient(X0) | (calm(X0) | tall(X0)))) [nnf transformation 4]
43. ! [X0] : (((~calm(X0) & ~tall(X0)) | patient(X0)) & (~patient(X0) | calm(X0) | tall(X0))) [flattening 42]
46. ! [X0] : (((~tall(X0) | tall(X0)) | patient(X0)) & (~patient(X0) | (tall(X0) & ~tall(X0)))) [nnf transformation 8]
47. ! [X0] : ((~tall(X0) | tall(X0) | patient(X0)) & (~patient(X0) | (tall(X0) & ~tall(X0)))) [flattening 46]
65. ((generous(paul) | wise(paul)) | (patient(lucy) | ~quiet(lucy))) & ((~patient(lucy) & quiet(lucy)) | (~generous(paul) & ~wise(paul))) [nnf transformation 15]
66. (generous(paul) | wise(paul) | patient(lucy) | ~quiet(lucy)) & ((~patient(lucy) & quiet(lucy)) | (~generous(paul) & ~wise(paul))) [flattening 65]
77. calm(X0) | generous(X0) [cnf transformation 38]
82. ~calm(X0) | patient(X0) [cnf transformation 43]
93. ~patient(X0) | ~tall(X0) [cnf transformation 47]
94. ~patient(X0) | tall(X0) [cnf transformation 47]
118. quiet(lucy) | ~generous(paul) [cnf transformation 66]
126. ~quiet(lucy) [cnf transformation 19]
158. ~patient(X0) [subsumption resolution 93,94]
171. 9 <=> ! [X3] : generous(X3) [avatar definition]
172. generous(X3) <- (9) [avatar component clause 171]
221. 20 <=> quiet(lucy) [avatar definition]
229. 22 <=> generous(paul) [avatar definition]
230. ~generous(paul) <- (~22) [avatar component clause 229]
233. ~22 | 20 [avatar split clause 118,221,229]
259. ~20 [avatar split clause 126,221]
264. $false <- (9, ~22) [resolution 230,172]
265. ~9 | 22 [avatar contradiction clause 264]
269. patient(X1) | generous(X1) [resolution 82,77]
271. generous(X1) [subsumption resolution 269,158]
272. 9 [avatar split clause 271,171]
273. $false [avatar sat refutation 233,259,265,272]
% SZS output end Proof for 2947104678987397026170588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is both not humble and generous and vice versa. Everyone who is funny is curious or funny. If someone is curious then mary is tall. If john is either brave or not calm then someone is either funny or quiet and vice versa. Everyone who is both not old and tall is either not calm or calm and vice versa. If someone is not humble then someone is either not patient or not quiet and vice versa. Everyone who is both not rich and not humble is not rich. Everyone who is either happy or not calm is both curious and not creative. If someone is both not wise and not strong then paul is either not rich or tall. If someone is not old or not brave then john is calm and vice versa. Everyone who is either calm or not rich is either wise or not strong. If paul is not rich then someone is wise or not tall and vice versa. Everyone who is not creative is rich or not strong and vice versa. Everyone who is both not creative and old is not creative or happy and vice versa. Everyone who is both happy and not calm is not generous or brave. Everyone who is both not patient and calm is either curious or not old and vice versa. Mary is not kind. Someone is happy or not old. Paul is either generous or kind. Someone is either kind or creative. Someone is both generous and not patient. Someone is not rich or not tall. | Paul is generous. | entailment | (![X]:(tall(X)<=>(~humble(X)&generous(X))))&
(![X]:(funny(X)=>(curious(X)|funny(X))))&
((?[X]:(curious(X)))=>(tall(mary)))&
(((brave(john)<~>~calm(john)))<=>(?[X]:((funny(X)<~>quiet(X)))))&
(![X]:((~old(X)&tall(X))<=>(~calm(X)<~>calm(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:((~rich(X)&~humble(X))=>~rich(X)))&
(![X]:((happy(X)<~>~calm(X))=>(curious(X)&~creative(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~rich(paul)<~>tall(paul))))&
((?[X]:((~old(X)|~brave(X))))<=>(calm(john)))&
(![X]:((calm(X)<~>~rich(X))=>(wise(X)<~>~strong(X))))&
((~rich(paul))<=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(~creative(X)<=>(rich(X)|~strong(X))))&
(![X]:((~creative(X)&old(X))<=>(~creative(X)|happy(X))))&
(![X]:((happy(X)&~calm(X))=>(~generous(X)|brave(X))))&
(![X]:((~patient(X)&calm(X))<=>(curious(X)<~>~old(X))))&
(~kind(mary))&
(?[X]:((happy(X)|~old(X))))&
((generous(paul)<~>kind(paul)))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((~rich(X)|~tall(X)))) | generous(paul) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7431480249408560773824926
% SZS output start Proof for 7431480249408560773824926
1. ! [X0] : (tall(X0) <=> (generous(X0) & ~humble(X0))) [input p0]
5. ! [X0] : ((tall(X0) & ~old(X0)) <=> (~calm(X0) <~> calm(X0))) [input p4]
23. ~generous(paul) [input hypothesis]
35. ! [X0] : ((tall(X0) | (~generous(X0) | humble(X0))) & ((generous(X0) & ~humble(X0)) | ~tall(X0))) [nnf transformation 1]
36. ! [X0] : ((tall(X0) | ~generous(X0) | humble(X0)) & ((generous(X0) & ~humble(X0)) | ~tall(X0))) [flattening 35]
41. ! [X0] : (((tall(X0) & ~old(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~tall(X0) | old(X0)))) [nnf transformation 5]
42. ! [X0] : (((tall(X0) & ~old(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~tall(X0) | old(X0))) [flattening 41]
76. ~tall(X0) | generous(X0) [cnf transformation 36]
92. tall(X0) | calm(X0) | calm(X0) [cnf transformation 42]
93. tall(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 42]
139. ~generous(paul) [cnf transformation 23]
142. tall(X0) | calm(X0) [duplicate literal removal 92]
143. tall(X0) | ~calm(X0) [duplicate literal removal 93]
182. tall(X0) [subsumption resolution 142,143]
240. 20 <=> generous(paul) [avatar definition]
242. ~generous(paul) <- (~20) [avatar component clause 240]
251. ~20 [avatar split clause 139,240]
260. generous(X0) [resolution 76,182]
261. $false <- (~20) [resolution 260,242]
262. 20 [avatar contradiction clause 261]
263. $false [avatar sat refutation 251,262]
% SZS output end Proof for 7431480249408560773824926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or tall is not old or calm.
Everyone who is wise is either not kind or quiet.
If alice is both kind and wise then someone is not rich or old and vice versa.
Everyone who is not generous or tall is not wise or curious.
If someone is both not kind and wise then someone is wise or not generous and vice versa.
Everyone who is not kind is both not generous and strong.
If fred is both funny and not brave then someone is either not happy or creative.
Everyone who is both quiet and not curious is either humble or calm and vice versa.
If mary is not curious then alice is old or quiet and vice versa.
Everyone who is both kind and creative is kind and vice versa.
If fred is either not old or not happy then someone is either not calm or kind.
Everyone who is both quiet and strong is not happy or quiet and vice versa.
Everyone who is either not old or not funny is either strong or humble and vice versa.
If paul is both not humble and not old then lucy is patient or not tall and vice versa.
Everyone who is either kind or creative is either old or not tall and vice versa.
Everyone who is not creative is either not creative or creative and vice versa.
Alice is happy.
Someone is either not curious or brave.
Someone is either not generous or not calm.
Mary is wise.
Someone is not brave or wise.
Someone is brave or not quiet.
Alice is generous or patient. | Paul is not old. | entailment | (![X]:((~strong(X)|tall(X))=>(~old(X)|calm(X))))&
(![X]:(wise(X)=>(~kind(X)<~>quiet(X))))&
(((kind(alice)&wise(alice)))<=>(?[X]:((~rich(X)|old(X)))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)|curious(X))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~generous(X)&strong(X))))&
(((funny(fred)&~brave(fred)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(humble(X)<~>calm(X))))&
((~curious(mary))<=>((old(alice)|quiet(alice))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>creative(X))))&
(happy(alice))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(wise(mary))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice))) | ~old(paul) | [
"p2",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4133412792416292326866896
% SZS output start Proof for 4133412792416292326866896
3. (wise(alice) & kind(alice)) <=> ? [X0] : (old(X0) | ~rich(X0)) [input p2]
10. ! [X0] : ((creative(X0) & kind(X0)) <=> kind(X0)) [input p9]
16. ! [X0] : (~creative(X0) <=> (~creative(X0) <~> creative(X0))) [input p15]
24. old(paul) [input hypothesis]
36. ((wise(alice) & kind(alice)) | ! [X0] : (~old(X0) & rich(X0))) & (? [X0] : (old(X0) | ~rich(X0)) | (~wise(alice) | ~kind(alice))) [nnf transformation 3]
37. ((wise(alice) & kind(alice)) | ! [X0] : (~old(X0) & rich(X0))) & (? [X0] : (old(X0) | ~rich(X0)) | ~wise(alice) | ~kind(alice)) [flattening 36]
38. ((wise(alice) & kind(alice)) | ! [X0] : (~old(X0) & rich(X0))) & (? [X1] : (old(X1) | ~rich(X1)) | ~wise(alice) | ~kind(alice)) [rectify 37]
39. ? [X1] : (old(X1) | ~rich(X1)) => (old(sK0) | ~rich(sK0)) [choice axiom]
40. ((wise(alice) & kind(alice)) | ! [X0] : (~old(X0) & rich(X0))) & ((old(sK0) | ~rich(sK0)) | ~wise(alice) | ~kind(alice)) [skolemisation 38,39]
53. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | (~creative(X0) | ~kind(X0)))) [nnf transformation 10]
54. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | ~creative(X0) | ~kind(X0))) [flattening 53]
64. ! [X0] : ((~creative(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | creative(X0))) [nnf transformation 16]
81. kind(alice) | ~old(X0) [cnf transformation 40]
106. ~kind(X0) | creative(X0) [cnf transformation 54]
140. ~creative(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 64]
150. old(paul) [cnf transformation 24]
154. ~creative(X0) [duplicate literal removal 140]
156. 1 <=> ! [X0] : ~old(X0) [avatar definition]
157. ~old(X0) <- (1) [avatar component clause 156]
168. 4 <=> kind(alice) [avatar definition]
170. kind(alice) <- (4) [avatar component clause 168]
171. 1 | 4 [avatar split clause 81,168,156]
270. 26 <=> old(paul) [avatar definition]
271. old(paul) <- (26) [avatar component clause 270]
337. 26 [avatar split clause 150,270]
342. creative(alice) <- (4) [resolution 106,170]
345. $false <- (4) [subsumption resolution 342,154]
346. ~4 [avatar contradiction clause 345]
351. $false <- (1, 26) [resolution 157,271]
352. ~1 | ~26 [avatar contradiction clause 351]
353. $false [avatar sat refutation 171,337,346,352]
% SZS output end Proof for 4133412792416292326866896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or patient is not happy.
Everyone who is humble or funny is either brave or generous.
If someone is both humble and kind then paul is tall.
If someone is either quiet or not quiet then fred is both not patient and old.
Everyone who is rich is either humble or rich and vice versa.
Everyone who is both not patient and not generous is strong or brave and vice versa.
If someone is not funny or not strong then lucy is both strong and not funny.
Everyone who is either not rich or not tall is either generous or funny and vice versa.
If paul is both not calm and not old then lucy is not funny or not calm.
Everyone who is strong or not kind is either wise or not funny and vice versa.
If someone is brave then lucy is not old or quiet.
If lucy is either kind or not curious then lucy is either wise or not strong.
Everyone who is not old is not patient or creative.
Everyone who is rich is either kind or funny and vice versa.
If someone is not curious or brave then alice is not funny.
Everyone who is creative or not kind is either humble or not tall.
Someone is not generous.
Someone is not calm or not funny.
Alice is both not patient and not quiet.
Fred is either not generous or not strong.
Someone is calm or not old.
Lucy is either not brave or wise.
Someone is strong or not tall.
Susan is either funny or creative. | Fred is patient. | contradiction | (![X]:((humble(X)<~>patient(X))=>~happy(X)))&
(![X]:((humble(X)|funny(X))=>(brave(X)<~>generous(X))))&
((?[X]:((humble(X)&kind(X))))=>(tall(paul)))&
((?[X]:((quiet(X)<~>~quiet(X))))=>((~patient(fred)&old(fred))))&
(![X]:(rich(X)<=>(humble(X)<~>rich(X))))&
(![X]:((~patient(X)&~generous(X))<=>(strong(X)|brave(X))))&
((?[X]:((~funny(X)|~strong(X))))=>((strong(lucy)&~funny(lucy))))&
(![X]:((~rich(X)<~>~tall(X))<=>(generous(X)<~>funny(X))))&
(((~calm(paul)&~old(paul)))=>((~funny(lucy)|~calm(lucy))))&
(![X]:((strong(X)|~kind(X))<=>(wise(X)<~>~funny(X))))&
((?[X]:(brave(X)))=>((~old(lucy)|quiet(lucy))))&
(((kind(lucy)<~>~curious(lucy)))=>((wise(lucy)<~>~strong(lucy))))&
(![X]:(~old(X)=>(~patient(X)|creative(X))))&
(![X]:(rich(X)<=>(kind(X)<~>funny(X))))&
((?[X]:((~curious(X)|brave(X))))=>(~funny(alice)))&
(![X]:((creative(X)|~kind(X))=>(humble(X)<~>~tall(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~calm(X)|~funny(X))))&
((~patient(alice)&~quiet(alice)))&
((~generous(fred)<~>~strong(fred)))&
(?[X]:((calm(X)|~old(X))))&
((~brave(lucy)<~>wise(lucy)))&
(?[X]:((strong(X)|~tall(X))))&
((funny(susan)<~>creative(susan))) | patient(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 116480852808331076667065
% SZS output start Proof for 116480852808331076667065
4. ? [X0] : (quiet(X0) <~> ~quiet(X0)) => (old(fred) & ~patient(fred)) [input p3]
25. patient(fred) [input hypothesis]
29. (old(fred) & ~patient(fred)) | ! [X0] : (quiet(X0) <=> ~quiet(X0)) [ennf transformation 4]
41. (old(fred) & ~patient(fred)) | ! [X0] : ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0))) [nnf transformation 29]
67. ~patient(fred) | ~quiet(X0) | ~quiet(X0) [cnf transformation 41]
68. ~patient(fred) | quiet(X0) | quiet(X0) [cnf transformation 41]
127. patient(fred) [cnf transformation 25]
130. ~patient(fred) | ~quiet(X0) [duplicate literal removal 67]
131. ~patient(fred) | quiet(X0) [duplicate literal removal 68]
143. 3 <=> ! [X0] : quiet(X0) [avatar definition]
144. quiet(X0) <- (3) [avatar component clause 143]
151. 5 <=> ! [X0] : ~quiet(X0) [avatar definition]
152. ~quiet(X0) <- (5) [avatar component clause 151]
155. 6 <=> patient(fred) [avatar definition]
158. 3 | ~6 [avatar split clause 131,155,143]
159. 5 | ~6 [avatar split clause 130,155,151]
283. 6 [avatar split clause 127,155]
286. $false <- (3, 5) [subsumption resolution 144,152]
287. ~3 | ~5 [avatar contradiction clause 286]
288. $false [avatar sat refutation 158,159,283,287]
% SZS output end Proof for 116480852808331076667065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not tall then john is not brave or patient and vice versa.
If john is either curious or not tall then someone is either not strong or generous.
Everyone who is either quiet or not rich is creative and vice versa.
Everyone who is both humble and rich is not patient or humble and vice versa.
Everyone who is either kind or happy is both funny and brave and vice versa.
Everyone who is both not brave and not creative is either calm or not old.
Everyone who is both brave and not funny is either not quiet or not rich.
If someone is happy then someone is not curious or not happy and vice versa.
Everyone who is old or not brave is either not funny or not kind.
If alice is both not humble and not funny then someone is both not patient and wise.
Everyone who is not humble is either not happy or not humble and vice versa.
If alice is either not funny or patient then mary is not patient.
Everyone who is either humble or not old is either strong or not old and vice versa.
If paul is not rich or creative then someone is either kind or not creative and vice versa.
Everyone who is not patient is not generous or not creative and vice versa.
Everyone who is both humble and quiet is either not humble or not brave and vice versa.
Someone is both funny and wise.
Someone is both not creative and not funny.
Someone is calm or not creative.
Susan is both funny and wise.
Someone is both funny and strong.
Someone is not brave.
Paul is not generous.
Susan is not generous or strong. | Susan is kind. | contradiction | ((~tall(mary))<=>((~brave(john)|patient(john))))&
(((curious(john)<~>~tall(john)))=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>creative(X)))&
(![X]:((humble(X)&rich(X))<=>(~patient(X)|humble(X))))&
(![X]:((kind(X)<~>happy(X))<=>(funny(X)&brave(X))))&
(![X]:((~brave(X)&~creative(X))=>(calm(X)<~>~old(X))))&
(![X]:((brave(X)&~funny(X))=>(~quiet(X)<~>~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)|~happy(X)))))&
(![X]:((old(X)|~brave(X))=>(~funny(X)<~>~kind(X))))&
(((~humble(alice)&~funny(alice)))=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:(~humble(X)<=>(~happy(X)<~>~humble(X))))&
(((~funny(alice)<~>patient(alice)))=>(~patient(mary)))&
(![X]:((humble(X)<~>~old(X))<=>(strong(X)<~>~old(X))))&
(((~rich(paul)|creative(paul)))<=>(?[X]:((kind(X)<~>~creative(X)))))&
(![X]:(~patient(X)<=>(~generous(X)|~creative(X))))&
(![X]:((humble(X)&quiet(X))<=>(~humble(X)<~>~brave(X))))&
(?[X]:((funny(X)&wise(X))))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((calm(X)|~creative(X))))&
((funny(susan)&wise(susan)))&
(?[X]:((funny(X)&strong(X))))&
(?[X]:(~brave(X)))&
(~generous(paul))&
((~generous(susan)|strong(susan))) | kind(susan) | [
"p4",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 240087395836993308857698
% SZS output start Proof for 240087395836993308857698
5. ! [X0] : ((kind(X0) <~> happy(X0)) <=> (brave(X0) & funny(X0))) [input p4]
9. ! [X0] : ((~brave(X0) | old(X0)) => (~funny(X0) <~> ~kind(X0))) [input p8]
11. ! [X0] : (~humble(X0) <=> (~happy(X0) <~> ~humble(X0))) [input p10]
20. wise(susan) & funny(susan) [input p19]
25. kind(susan) [input hypothesis]
29. funny(susan) [pure predicate removal 20]
35. ! [X0] : ((~funny(X0) <~> ~kind(X0)) | (brave(X0) & ~old(X0))) [ennf transformation 9]
47. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (~brave(X0) | ~funny(X0))) & ((brave(X0) & funny(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [nnf transformation 5]
48. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ~brave(X0) | ~funny(X0)) & ((brave(X0) & funny(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [flattening 47]
56. ! [X0] : (((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (brave(X0) & ~old(X0))) [nnf transformation 35]
59. ! [X0] : ((~humble(X0) | ((~happy(X0) | humble(X0)) & (~humble(X0) | happy(X0)))) & (((humble(X0) | happy(X0)) & (~humble(X0) | ~happy(X0))) | humble(X0))) [nnf transformation 11]
102. ~funny(X0) | ~kind(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 48]
111. ~funny(X0) | ~kind(X0) | brave(X0) [cnf transformation 56]
116. humble(X0) | happy(X0) | humble(X0) [cnf transformation 59]
117. ~humble(X0) | ~humble(X0) | happy(X0) [cnf transformation 59]
148. funny(susan) [cnf transformation 29]
154. kind(susan) [cnf transformation 25]
161. humble(X0) | happy(X0) [duplicate literal removal 116]
162. ~humble(X0) | happy(X0) [duplicate literal removal 117]
199. 8 <=> ! [X1] : happy(X1) [avatar definition]
200. happy(X1) <- (8) [avatar component clause 199]
235. happy(X0) [subsumption resolution 161,162]
236. 8 [avatar split clause 235,199]
400. ~kind(susan) | brave(susan) [resolution 111,148]
403. brave(susan) [subsumption resolution 400,154]
457. ~kind(susan) | ~brave(susan) | ~happy(susan) [resolution 102,148]
460. ~brave(susan) | ~happy(susan) [subsumption resolution 457,154]
461. ~happy(susan) [subsumption resolution 460,403]
462. $false <- (8) [subsumption resolution 461,200]
463. ~8 [avatar contradiction clause 462]
468. $false [avatar sat refutation 236,463]
% SZS output end Proof for 240087395836993308857698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not quiet or quiet then mary is either not tall or strong.
Everyone who is either funny or humble is not creative.
Everyone who is curious is humble or not old.
If paul is both generous and not generous then alice is not humble.
Everyone who is both old and curious is old or not old and vice versa.
If someone is curious or not humble then someone is humble and vice versa.
Everyone who is not funny or kind is generous or strong.
If susan is either old or quiet then someone is rich.
Everyone who is both not old and humble is calm and vice versa.
Everyone who is either wise or not curious is both tall and not curious and vice versa.
If susan is either not rich or strong then someone is both calm and not humble and vice versa.
If someone is curious then mary is kind.
Everyone who is either tall or not patient is either patient or creative.
Everyone who is not humble is both happy and not strong.
If someone is not curious then susan is not creative.
Everyone who is both not calm and not funny is tall.
Someone is not creative.
Someone is humble or not rich.
Someone is happy or not wise.
Someone is not brave or not generous.
Mary is not creative or strong.
Someone is either rich or not tall. | Mary is humble. | entailment | (((~quiet(mary)|quiet(mary)))=>((~tall(mary)<~>strong(mary))))&
(![X]:((funny(X)<~>humble(X))=>~creative(X)))&
(![X]:(curious(X)=>(humble(X)|~old(X))))&
(((generous(paul)&~generous(paul)))=>(~humble(alice)))&
(![X]:((old(X)&curious(X))<=>(old(X)|~old(X))))&
((?[X]:((curious(X)|~humble(X))))<=>(?[X]:(humble(X))))&
(![X]:((~funny(X)|kind(X))=>(generous(X)|strong(X))))&
(((old(susan)<~>quiet(susan)))=>(?[X]:(rich(X))))&
(![X]:((~old(X)&humble(X))<=>calm(X)))&
(![X]:((wise(X)<~>~curious(X))<=>(tall(X)&~curious(X))))&
(((~rich(susan)<~>strong(susan)))<=>(?[X]:((calm(X)&~humble(X)))))&
((?[X]:(curious(X)))=>(kind(mary)))&
(![X]:((tall(X)<~>~patient(X))=>(patient(X)<~>creative(X))))&
(![X]:(~humble(X)=>(happy(X)&~strong(X))))&
((?[X]:(~curious(X)))=>(~creative(susan)))&
(![X]:((~calm(X)&~funny(X))=>tall(X)))&
(?[X]:(~creative(X)))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:((happy(X)|~wise(X))))&
(?[X]:((~brave(X)|~generous(X))))&
((~creative(mary)|strong(mary)))&
(?[X]:((rich(X)<~>~tall(X)))) | humble(mary) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6408630720290914878134803
% SZS output start Proof for 6408630720290914878134803
3. ! [X0] : (curious(X0) => (~old(X0) | humble(X0))) [input p2]
5. ! [X0] : ((curious(X0) & old(X0)) <=> (~old(X0) | old(X0))) [input p4]
23. ~humble(mary) [input hypothesis]
30. ! [X0] : ((~old(X0) | humble(X0)) | ~curious(X0)) [ennf transformation 3]
31. ! [X0] : (~old(X0) | humble(X0) | ~curious(X0)) [flattening 30]
45. ! [X0] : (((curious(X0) & old(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 5]
46. ! [X0] : (((curious(X0) & old(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~curious(X0) | ~old(X0))) [flattening 45]
77. ~old(X0) | humble(X0) | ~curious(X0) [cnf transformation 31]
81. old(X0) | old(X0) [cnf transformation 46]
82. curious(X0) | ~old(X0) [cnf transformation 46]
83. old(X0) | curious(X0) [cnf transformation 46]
119. ~humble(mary) [cnf transformation 23]
125. old(X0) [duplicate literal removal 81]
142. curious(X0) [subsumption resolution 82,83]
144. 4 <=> ! [X3] : humble(X3) [avatar definition]
145. humble(X3) <- (4) [avatar component clause 144]
211. humble(X1) | ~curious(X1) [resolution 77,125]
212. humble(X1) [subsumption resolution 211,142]
213. 4 [avatar split clause 212,144]
214. $false <- (4) [resolution 145,119]
215. ~4 [avatar contradiction clause 214]
216. $false [avatar sat refutation 213,215]
% SZS output end Proof for 6408630720290914878134803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or happy is both curious and funny and vice versa.
Everyone who is not calm or rich is not rich or not humble.
Everyone who is not rich or not old is happy.
Everyone who is happy or not humble is not old or not tall.
Everyone who is both not curious and not brave is either rich or not quiet.
If susan is both brave and not curious then someone is either curious or happy and vice versa.
Everyone who is calm or happy is generous.
Everyone who is calm is generous or not calm.
If fred is both not quiet and generous then someone is strong and vice versa.
If paul is curious then someone is not kind or not quiet and vice versa.
If alice is either strong or happy then lucy is both wise and not creative and vice versa.
If someone is not calm then someone is either not old or brave.
If someone is both brave and quiet then paul is both happy and wise and vice versa.
Everyone who is both not brave and tall is not patient and vice versa.
If alice is rich then someone is either kind or not strong.
If fred is either not curious or not rich then someone is both kind and not happy and vice versa.
Paul is either not generous or not tall.
Someone is both patient and not funny.
Someone is kind or not rich.
Someone is either quiet or kind.
Fred is not calm or brave.
Someone is strong.
Susan is either not brave or happy.
Someone is either not funny or not quiet. | Fred is not calm. | neutral | (![X]:((~quiet(X)<~>happy(X))<=>(curious(X)&funny(X))))&
(![X]:((~calm(X)|rich(X))=>(~rich(X)|~humble(X))))&
(![X]:((~rich(X)|~old(X))=>happy(X)))&
(![X]:((happy(X)|~humble(X))=>(~old(X)|~tall(X))))&
(![X]:((~curious(X)&~brave(X))=>(rich(X)<~>~quiet(X))))&
(((brave(susan)&~curious(susan)))<=>(?[X]:((curious(X)<~>happy(X)))))&
(![X]:((calm(X)|happy(X))=>generous(X)))&
(![X]:(calm(X)=>(generous(X)|~calm(X))))&
(((~quiet(fred)&generous(fred)))<=>(?[X]:(strong(X))))&
((curious(paul))<=>(?[X]:((~kind(X)|~quiet(X)))))&
(((strong(alice)<~>happy(alice)))<=>((wise(lucy)&~creative(lucy))))&
((?[X]:(~calm(X)))=>(?[X]:((~old(X)<~>brave(X)))))&
((?[X]:((brave(X)&quiet(X))))<=>((happy(paul)&wise(paul))))&
(![X]:((~brave(X)&tall(X))<=>~patient(X)))&
((rich(alice))=>(?[X]:((kind(X)<~>~strong(X)))))&
(((~curious(fred)<~>~rich(fred)))<=>(?[X]:((kind(X)&~happy(X)))))&
((~generous(paul)<~>~tall(paul)))&
(?[X]:((patient(X)&~funny(X))))&
(?[X]:((kind(X)|~rich(X))))&
(?[X]:((quiet(X)<~>kind(X))))&
((~calm(fred)|brave(fred)))&
(?[X]:(strong(X)))&
((~brave(susan)<~>happy(susan)))&
(?[X]:((~funny(X)<~>~quiet(X)))) | ~calm(fred) | [] | null | 0 |
If someone is kind then lucy is either not strong or creative. If someone is either not strong or not brave then john is not wise or not creative and vice versa. If someone is generous or happy then someone is both not strong and curious. Everyone who is curious is not wise and vice versa. Everyone who is not wise is both not quiet and not curious. Everyone who is kind or not creative is humble or not calm and vice versa. Everyone who is quiet or rich is either not generous or not old. If someone is both not creative and humble then someone is not happy. If someone is not patient then someone is both not patient and not brave and vice versa. If someone is generous or not quiet then someone is both not kind and rich. Everyone who is not brave is strong. If paul is either humble or quiet then alice is old or wise and vice versa. Everyone who is both old and kind is quiet or not generous and vice versa. Everyone who is not curious is tall and vice versa. Everyone who is either not humble or strong is kind or not curious and vice versa. Someone is calm. Paul is either not generous or calm. Someone is either not funny or calm. Someone is patient. Lucy is brave. Someone is either patient or not happy. | Paul is brave. | entailment | ((?[X]:(kind(X)))=>((~strong(lucy)<~>creative(lucy))))&
((?[X]:((~strong(X)<~>~brave(X))))<=>((~wise(john)|~creative(john))))&
((?[X]:((generous(X)|happy(X))))=>(?[X]:((~strong(X)&curious(X)))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:(~wise(X)=>(~quiet(X)&~curious(X))))&
(![X]:((kind(X)|~creative(X))<=>(humble(X)|~calm(X))))&
(![X]:((quiet(X)|rich(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((~creative(X)&humble(X))))=>(?[X]:(~happy(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~patient(X)&~brave(X)))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:(~brave(X)=>strong(X)))&
(((humble(paul)<~>quiet(paul)))<=>((old(alice)|wise(alice))))&
(![X]:((old(X)&kind(X))<=>(quiet(X)|~generous(X))))&
(![X]:(~curious(X)<=>tall(X)))&
(![X]:((~humble(X)<~>strong(X))<=>(kind(X)|~curious(X))))&
(?[X]:(calm(X)))&
((~generous(paul)<~>calm(paul)))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:(patient(X)))&
(brave(lucy))&
(?[X]:((patient(X)<~>~happy(X)))) | brave(paul) | [
"p2",
"p3",
"p4",
"p9",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4042556579583084749631329
% SZS output start Proof for 4042556579583084749631329
3. ? [X0] : (happy(X0) | generous(X0)) => ? [X0] : (curious(X0) & ~strong(X0)) [input p2]
4. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p3]
5. ! [X0] : (~wise(X0) => (~curious(X0) & ~quiet(X0))) [input p4]
10. ? [X0] : (~quiet(X0) | generous(X0)) => ? [X0] : (rich(X0) & ~kind(X0)) [input p9]
11. ! [X0] : (~brave(X0) => strong(X0)) [input p10]
12. (humble(paul) <~> quiet(paul)) <=> (wise(alice) | old(alice)) [input p11]
13. ! [X0] : ((kind(X0) & old(X0)) <=> (~generous(X0) | quiet(X0))) [input p12]
15. ! [X0] : ((~humble(X0) <~> strong(X0)) <=> (~curious(X0) | kind(X0))) [input p14]
22. ~brave(paul) [input hypothesis]
23. ? [X0] : (happy(X0) | generous(X0)) => ? [X1] : (curious(X1) & ~strong(X1)) [rectify 3]
26. ? [X0] : (~quiet(X0) | generous(X0)) => ? [X1] : (rich(X1) & ~kind(X1)) [rectify 10]
28. ? [X1] : (curious(X1) & ~strong(X1)) | ! [X0] : (~happy(X0) & ~generous(X0)) [ennf transformation 23]
29. ! [X0] : ((~curious(X0) & ~quiet(X0)) | wise(X0)) [ennf transformation 5]
32. ? [X1] : (rich(X1) & ~kind(X1)) | ! [X0] : (quiet(X0) & ~generous(X0)) [ennf transformation 26]
33. ! [X0] : (strong(X0) | brave(X0)) [ennf transformation 11]
40. ? [X0] : (curious(X0) & ~strong(X0)) | ! [X1] : (~happy(X1) & ~generous(X1)) [rectify 28]
41. ? [X0] : (curious(X0) & ~strong(X0)) => (curious(sK1) & ~strong(sK1)) [choice axiom]
42. (curious(sK1) & ~strong(sK1)) | ! [X1] : (~happy(X1) & ~generous(X1)) [skolemisation 40,41]
43. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 4]
55. ? [X0] : (rich(X0) & ~kind(X0)) | ! [X1] : (quiet(X1) & ~generous(X1)) [rectify 32]
56. ? [X0] : (rich(X0) & ~kind(X0)) => (rich(sK5) & ~kind(sK5)) [choice axiom]
57. (rich(sK5) & ~kind(sK5)) | ! [X1] : (quiet(X1) & ~generous(X1)) [skolemisation 55,56]
58. (((~quiet(paul) | ~humble(paul)) & (quiet(paul) | humble(paul))) | (~wise(alice) & ~old(alice))) & ((wise(alice) | old(alice)) | ((humble(paul) | ~quiet(paul)) & (quiet(paul) | ~humble(paul)))) [nnf transformation 12]
59. (((~quiet(paul) | ~humble(paul)) & (quiet(paul) | humble(paul))) | (~wise(alice) & ~old(alice))) & (wise(alice) | old(alice) | ((humble(paul) | ~quiet(paul)) & (quiet(paul) | ~humble(paul)))) [flattening 58]
60. ! [X0] : (((kind(X0) & old(X0)) | (generous(X0) & ~quiet(X0))) & ((~generous(X0) | quiet(X0)) | (~kind(X0) | ~old(X0)))) [nnf transformation 13]
61. ! [X0] : (((kind(X0) & old(X0)) | (generous(X0) & ~quiet(X0))) & (~generous(X0) | quiet(X0) | ~kind(X0) | ~old(X0))) [flattening 60]
63. ! [X0] : ((((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | (curious(X0) & ~kind(X0))) & ((~curious(X0) | kind(X0)) | ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | (curious(X0) & ~kind(X0))) & (~curious(X0) | kind(X0) | ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0))))) [flattening 63]
86. curious(sK1) | ~generous(X1) [cnf transformation 42]
88. ~curious(X0) | ~wise(X0) [cnf transformation 43]
89. curious(X0) | wise(X0) [cnf transformation 43]
91. ~curious(X0) | wise(X0) [cnf transformation 29]
105. ~kind(sK5) | quiet(X1) [cnf transformation 57]
108. brave(X0) | strong(X0) [cnf transformation 33]
114. ~quiet(paul) | ~humble(paul) | ~wise(alice) [cnf transformation 59]
119. generous(X0) | kind(X0) [cnf transformation 61]
126. ~strong(X0) | humble(X0) | ~kind(X0) [cnf transformation 64]
137. ~brave(paul) [cnf transformation 22]
183. 11 <=> curious(sK1) [avatar definition]
185. curious(sK1) <- (11) [avatar component clause 183]
188. 12 <=> ! [X1] : ~generous(X1) [avatar definition]
189. ~generous(X1) <- (12) [avatar component clause 188]
190. 12 | 11 [avatar split clause 86,183,188]
197. wise(X0) [subsumption resolution 91,89]
228. 21 <=> ! [X1] : quiet(X1) [avatar definition]
229. quiet(X1) <- (21) [avatar component clause 228]
237. 23 <=> kind(sK5) [avatar definition]
239. ~kind(sK5) <- (~23) [avatar component clause 237]
240. 21 | ~23 [avatar split clause 105,237,228]
242. ~quiet(paul) | ~humble(paul) [subsumption resolution 114,197]
244. 24 <=> humble(paul) [avatar definition]
246. ~humble(paul) <- (~24) [avatar component clause 244]
248. 25 <=> quiet(paul) [avatar definition]
250. ~quiet(paul) <- (~25) [avatar component clause 248]
251. ~24 | ~25 [avatar split clause 242,248,244]
291. $false <- (21, ~25) [resolution 250,229]
292. ~21 | 25 [avatar contradiction clause 291]
294. strong(paul) [resolution 108,137]
297. kind(X0) <- (12) [resolution 119,189]
299. $false <- (12, ~23) [resolution 297,239]
300. ~12 | 23 [avatar contradiction clause 299]
301. ~wise(sK1) <- (11) [resolution 185,88]
302. $false <- (11) [subsumption resolution 301,197]
303. ~11 [avatar contradiction clause 302]
305. kind(X0) <- (12) [resolution 189,119]
325. humble(paul) | ~kind(paul) [resolution 126,294]
329. ~kind(paul) <- (~24) [subsumption resolution 325,246]
334. $false <- (12, ~24) [subsumption resolution 329,305]
335. ~12 | 24 [avatar contradiction clause 334]
338. $false [avatar sat refutation 190,240,251,292,300,303,335]
% SZS output end Proof for 4042556579583084749631329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not humble is happy and vice versa. If someone is rich then someone is not calm and vice versa. If john is either funny or calm then john is not strong or patient and vice versa. If alice is wise or old then someone is either generous or not creative. Everyone who is wise is either not kind or not funny and vice versa. Everyone who is both generous and happy is rich or not wise and vice versa. Everyone who is patient is either not wise or generous and vice versa. Everyone who is happy is not generous or not happy. If someone is both humble and old then someone is either curious or not old. Everyone who is not calm is both calm and not calm and vice versa. Everyone who is not brave or not patient is not wise. Everyone who is either not quiet or humble is either not humble or wise. Everyone who is both not funny and not old is wise or old. Everyone who is not kind or not curious is not happy and vice versa. If someone is either not humble or not generous then fred is either tall or calm and vice versa. Everyone who is not calm or not rich is tall or humble and vice versa. Mary is either not happy or tall. Alice is not happy. Someone is either not curious or funny. Someone is either curious or not patient. Someone is funny or curious. John is strong or not creative. | Fred is not happy. | entailment | (![X]:(~humble(X)<=>happy(X)))&
((?[X]:(rich(X)))<=>(?[X]:(~calm(X))))&
(((funny(john)<~>calm(john)))<=>((~strong(john)|patient(john))))&
(((wise(alice)|old(alice)))=>(?[X]:((generous(X)<~>~creative(X)))))&
(![X]:(wise(X)<=>(~kind(X)<~>~funny(X))))&
(![X]:((generous(X)&happy(X))<=>(rich(X)|~wise(X))))&
(![X]:(patient(X)<=>(~wise(X)<~>generous(X))))&
(![X]:(happy(X)=>(~generous(X)|~happy(X))))&
((?[X]:((humble(X)&old(X))))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:(~calm(X)<=>(calm(X)&~calm(X))))&
(![X]:((~brave(X)|~patient(X))=>~wise(X)))&
(![X]:((~quiet(X)<~>humble(X))=>(~humble(X)<~>wise(X))))&
(![X]:((~funny(X)&~old(X))=>(wise(X)|old(X))))&
(![X]:((~kind(X)|~curious(X))<=>~happy(X)))&
((?[X]:((~humble(X)<~>~generous(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:((~calm(X)|~rich(X))<=>(tall(X)|humble(X))))&
((~happy(mary)<~>tall(mary)))&
(~happy(alice))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:((funny(X)|curious(X))))&
((strong(john)|~creative(john))) | ~happy(fred) | [
"p0",
"p5",
"p6",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8942814639794678023316744
% SZS output start Proof for 8942814639794678023316744
1. ! [X0] : (~humble(X0) <=> happy(X0)) [input p0]
6. ! [X0] : ((happy(X0) & generous(X0)) <=> (~wise(X0) | rich(X0))) [input p5]
7. ! [X0] : (patient(X0) <=> (~wise(X0) <~> generous(X0))) [input p6]
8. ! [X0] : (happy(X0) => (~happy(X0) | ~generous(X0))) [input p7]
11. ! [X0] : ((~patient(X0) | ~brave(X0)) => ~wise(X0)) [input p10]
15. ? [X0] : (~humble(X0) <~> ~generous(X0)) <=> (tall(fred) <~> calm(fred)) [input p14]
23. happy(fred) [input hypothesis]
26. ! [X0] : (~patient(X0) => ~wise(X0)) [pure predicate removal 11]
28. ! [X0] : ((~happy(X0) | ~generous(X0)) | ~happy(X0)) [ennf transformation 8]
29. ! [X0] : (~happy(X0) | ~generous(X0) | ~happy(X0)) [flattening 28]
31. ! [X0] : (~wise(X0) | patient(X0)) [ennf transformation 26]
35. ! [X0] : ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))) [nnf transformation 1]
47. ! [X0] : (((happy(X0) & generous(X0)) | (wise(X0) & ~rich(X0))) & ((~wise(X0) | rich(X0)) | (~happy(X0) | ~generous(X0)))) [nnf transformation 6]
48. ! [X0] : (((happy(X0) & generous(X0)) | (wise(X0) & ~rich(X0))) & (~wise(X0) | rich(X0) | ~happy(X0) | ~generous(X0))) [flattening 47]
49. ! [X0] : ((patient(X0) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | ~patient(X0))) [nnf transformation 7]
59. (? [X0] : ((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ((tall(fred) | ~calm(fred)) & (calm(fred) | ~tall(fred)))) & (((~calm(fred) | ~tall(fred)) & (calm(fred) | tall(fred))) | ! [X0] : ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) [nnf transformation 15]
60. (? [X0] : ((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ((tall(fred) | ~calm(fred)) & (calm(fred) | ~tall(fred)))) & (((~calm(fred) | ~tall(fred)) & (calm(fred) | tall(fred))) | ! [X1] : ((~humble(X1) | generous(X1)) & (~generous(X1) | humble(X1)))) [rectify 59]
61. ? [X0] : ((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) => ((generous(sK4) | humble(sK4)) & (~generous(sK4) | ~humble(sK4))) [choice axiom]
62. (((generous(sK4) | humble(sK4)) & (~generous(sK4) | ~humble(sK4))) | ((tall(fred) | ~calm(fred)) & (calm(fred) | ~tall(fred)))) & (((~calm(fred) | ~tall(fred)) & (calm(fred) | tall(fred))) | ! [X1] : ((~humble(X1) | generous(X1)) & (~generous(X1) | humble(X1)))) [skolemisation 60,61]
74. happy(X0) | humble(X0) [cnf transformation 35]
75. ~happy(X0) | ~humble(X0) [cnf transformation 35]
94. generous(X0) | wise(X0) [cnf transformation 48]
96. wise(X0) | happy(X0) [cnf transformation 48]
97. generous(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 49]
98. ~generous(X0) | wise(X0) | ~patient(X0) [cnf transformation 49]
101. ~happy(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 29]
107. ~wise(X0) | patient(X0) [cnf transformation 31]
116. calm(fred) | tall(fred) | ~generous(X1) | humble(X1) [cnf transformation 62]
118. ~calm(fred) | ~tall(fred) | ~generous(X1) | humble(X1) [cnf transformation 62]
120. ~generous(sK4) | ~humble(sK4) | calm(fred) | ~tall(fred) [cnf transformation 62]
121. ~generous(sK4) | ~humble(sK4) | tall(fred) | ~calm(fred) [cnf transformation 62]
137. happy(fred) [cnf transformation 23]
143. ~generous(X0) | ~happy(X0) [duplicate literal removal 101]
202. ~patient(X0) | wise(X0) [subsumption resolution 98,94]
203. ~patient(X0) | generous(X0) [subsumption resolution 97,202]
219. 16 <=> calm(fred) [avatar definition]
223. 17 <=> tall(fred) [avatar definition]
227. 18 <=> humble(sK4) [avatar definition]
231. 19 <=> generous(sK4) [avatar definition]
232. ~generous(sK4) <- (~19) [avatar component clause 231]
233. generous(sK4) <- (19) [avatar component clause 231]
236. ~16 | 17 | ~18 | ~19 [avatar split clause 121,231,227,223,219]
237. ~17 | 16 | ~18 | ~19 [avatar split clause 120,231,227,219,223]
243. 21 <=> ! [X1] : (~generous(X1) | humble(X1)) [avatar definition]
244. ~generous(X1) | humble(X1) <- (21) [avatar component clause 243]
245. 21 | ~17 | ~16 [avatar split clause 118,219,223,243]
247. 21 | 17 | 16 [avatar split clause 116,219,223,243]
298. ~humble(fred) [resolution 75,137]
301. wise(sK4) <- (~19) [resolution 94,232]
303. patient(sK4) <- (~19) [resolution 107,301]
309. ~happy(X0) | wise(X0) [resolution 143,94]
310. wise(X0) [subsumption resolution 309,96]
311. patient(X0) [resolution 310,107]
325. generous(sK4) <- (~19) [resolution 303,203]
327. $false <- (~19) [subsumption resolution 325,232]
328. 19 [avatar contradiction clause 327]
329. ~happy(sK4) <- (19) [resolution 233,143]
331. humble(sK4) <- (19) [resolution 329,74]
334. 18 | ~19 [avatar split clause 331,231,227]
340. generous(X0) [resolution 311,203]
371. humble(X1) <- (21) [resolution 340,244]
374. $false <- (21) [resolution 371,298]
376. ~21 [avatar contradiction clause 374]
377. $false [avatar sat refutation 236,237,245,247,328,334,376]
% SZS output end Proof for 8942814639794678023316744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is creative then mary is either brave or not calm and vice versa.
Everyone who is both happy and not wise is both patient and happy and vice versa.
Everyone who is both not tall and happy is both brave and generous and vice versa.
If someone is both curious and patient then paul is either generous or not patient.
If someone is both generous and not generous then someone is creative or generous and vice versa.
Everyone who is not generous is either funny or calm and vice versa.
If someone is funny or wise then alice is not patient and vice versa.
If someone is both wise and not kind then someone is wise and vice versa.
If mary is not wise or curious then someone is not rich and vice versa.
Everyone who is not humble is quiet or rich.
Everyone who is not curious or rich is brave and vice versa.
If john is not humble then someone is old.
Everyone who is either kind or not quiet is either not rich or not generous.
If someone is rich then alice is patient or not old and vice versa.
If someone is kind or strong then mary is both not humble and patient and vice versa.
Everyone who is not kind or quiet is not curious or patient and vice versa.
Someone is not rich or not strong.
Someone is either not rich or not calm.
Mary is either not generous or not curious.
Alice is either not generous or curious.
Someone is either not happy or creative.
John is both rich and not strong.
Someone is not tall.
Fred is either not quiet or not kind. | Paul is creative. | contradiction | ((creative(susan))<=>((brave(mary)<~>~calm(mary))))&
(![X]:((happy(X)&~wise(X))<=>(patient(X)&happy(X))))&
(![X]:((~tall(X)&happy(X))<=>(brave(X)&generous(X))))&
((?[X]:((curious(X)&patient(X))))=>((generous(paul)<~>~patient(paul))))&
((?[X]:((generous(X)&~generous(X))))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:(~generous(X)<=>(funny(X)<~>calm(X))))&
((?[X]:((funny(X)|wise(X))))<=>(~patient(alice)))&
((?[X]:((wise(X)&~kind(X))))<=>(?[X]:(wise(X))))&
(((~wise(mary)|curious(mary)))<=>(?[X]:(~rich(X))))&
(![X]:(~humble(X)=>(quiet(X)|rich(X))))&
(![X]:((~curious(X)|rich(X))<=>brave(X)))&
((~humble(john))=>(?[X]:(old(X))))&
(![X]:((kind(X)<~>~quiet(X))=>(~rich(X)<~>~generous(X))))&
((?[X]:(rich(X)))<=>((patient(alice)|~old(alice))))&
((?[X]:((kind(X)|strong(X))))<=>((~humble(mary)&patient(mary))))&
(![X]:((~kind(X)|quiet(X))<=>(~curious(X)|patient(X))))&
(?[X]:((~rich(X)|~strong(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
((~generous(mary)<~>~curious(mary)))&
((~generous(alice)<~>curious(alice)))&
(?[X]:((~happy(X)<~>creative(X))))&
((rich(john)&~strong(john)))&
(?[X]:(~tall(X)))&
((~quiet(fred)<~>~kind(fred))) | creative(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7043279306480965762576585
% SZS output start Proof for 7043279306480965762576585
5. ? [X0] : (~generous(X0) & generous(X0)) <=> ? [X0] : (generous(X0) | creative(X0)) [input p4]
25. creative(paul) [input hypothesis]
26. ? [X0] : (~generous(X0) & generous(X0)) <=> ? [X1] : (generous(X1) | creative(X1)) [rectify 5]
39. (? [X0] : (~generous(X0) & generous(X0)) | ! [X1] : (~generous(X1) & ~creative(X1))) & (? [X1] : (generous(X1) | creative(X1)) | ! [X0] : (generous(X0) | ~generous(X0))) [nnf transformation 26]
40. (? [X0] : (~generous(X0) & generous(X0)) | ! [X1] : (~generous(X1) & ~creative(X1))) & (? [X2] : (generous(X2) | creative(X2)) | ! [X3] : (generous(X3) | ~generous(X3))) [rectify 39]
41. ? [X0] : (~generous(X0) & generous(X0)) => (~generous(sK0) & generous(sK0)) [choice axiom]
42. ? [X2] : (generous(X2) | creative(X2)) => (generous(sK1) | creative(sK1)) [choice axiom]
43. ((~generous(sK0) & generous(sK0)) | ! [X1] : (~generous(X1) & ~creative(X1))) & ((generous(sK1) | creative(sK1)) | ! [X3] : (generous(X3) | ~generous(X3))) [skolemisation 40,42,41]
104. generous(sK0) | ~creative(X1) [cnf transformation 43]
106. ~generous(sK0) | ~creative(X1) [cnf transformation 43]
156. creative(paul) [cnf transformation 25]
190. 8 <=> generous(sK0) [avatar definition]
195. 9 <=> ! [X1] : ~creative(X1) [avatar definition]
196. ~creative(X1) <- (9) [avatar component clause 195]
197. 9 | ~8 [avatar split clause 106,190,195]
199. 9 | 8 [avatar split clause 104,190,195]
364. $false <- (9) [resolution 196,156]
365. ~9 [avatar contradiction clause 364]
366. $false [avatar sat refutation 197,199,365]
% SZS output end Proof for 7043279306480965762576585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not calm then someone is funny or not strong and vice versa.
Everyone who is both rich and wise is not humble and vice versa.
Everyone who is curious is both patient and creative and vice versa.
If john is tall or not curious then someone is both not patient and quiet.
If someone is either not patient or calm then alice is either not funny or not happy and vice versa.
Everyone who is rich or humble is old and vice versa.
Everyone who is either not old or calm is both not brave and not tall.
If someone is either happy or calm then someone is either not generous or tall and vice versa.
If lucy is not happy then someone is either kind or curious.
Everyone who is wise or generous is both not happy and creative.
Everyone who is rich or not patient is wise.
Everyone who is happy or not humble is not patient and vice versa.
Everyone who is either not rich or funny is quiet.
If mary is not curious then someone is kind or curious and vice versa.
If someone is strong then someone is either patient or not kind and vice versa.
Everyone who is tall is patient or quiet.
Someone is either patient or not patient.
Someone is not funny.
Someone is generous or not curious.
Someone is either not curious or patient.
John is either not tall or creative.
Someone is not strong or not curious. | Alice is quiet. | neutral | ((~calm(fred))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:((rich(X)&wise(X))<=>~humble(X)))&
(![X]:(curious(X)<=>(patient(X)&creative(X))))&
(((tall(john)|~curious(john)))=>(?[X]:((~patient(X)&quiet(X)))))&
((?[X]:((~patient(X)<~>calm(X))))<=>((~funny(alice)<~>~happy(alice))))&
(![X]:((rich(X)|humble(X))<=>old(X)))&
(![X]:((~old(X)<~>calm(X))=>(~brave(X)&~tall(X))))&
((?[X]:((happy(X)<~>calm(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
((~happy(lucy))=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:((wise(X)|generous(X))=>(~happy(X)&creative(X))))&
(![X]:((rich(X)|~patient(X))=>wise(X)))&
(![X]:((happy(X)|~humble(X))<=>~patient(X)))&
(![X]:((~rich(X)<~>funny(X))=>quiet(X)))&
((~curious(mary))<=>(?[X]:((kind(X)|curious(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((patient(X)<~>~kind(X)))))&
(![X]:(tall(X)=>(patient(X)|quiet(X))))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:((generous(X)|~curious(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
((~tall(john)<~>creative(john)))&
(?[X]:((~strong(X)|~curious(X)))) | quiet(alice) | [] | null | 0 |
Everyone who is both not creative and brave is both not humble and not brave and vice versa.
Everyone who is not curious is either kind or not generous and vice versa.
Everyone who is either rich or kind is either creative or calm.
If someone is strong or brave then john is quiet and vice versa.
Everyone who is both not kind and kind is either not strong or generous and vice versa.
If someone is both happy and not creative then someone is either tall or not happy.
Everyone who is either not calm or not funny is both tall and kind.
Everyone who is either strong or curious is not curious or not happy and vice versa.
Everyone who is both not calm and not funny is both not rich and not brave and vice versa.
Everyone who is not wise or not quiet is not curious.
If someone is not humble or wise then susan is not rich or quiet.
Everyone who is not curious or not strong is both not patient and rich.
Everyone who is both not tall and humble is either not happy or happy and vice versa.
If paul is both not creative and not old then mary is not strong or not creative and vice versa.
If fred is either humble or not calm then alice is either not quiet or not humble.
Everyone who is either not patient or not calm is not tall or creative.
Alice is either not creative or not rich.
Susan is quiet.
Someone is creative.
Susan is strong or not strong.
Mary is either not old or not generous.
Fred is humble.
Someone is both calm and not generous. | Paul is not tall. | entailment | (![X]:((~creative(X)&brave(X))<=>(~humble(X)&~brave(X))))&
(![X]:(~curious(X)<=>(kind(X)<~>~generous(X))))&
(![X]:((rich(X)<~>kind(X))=>(creative(X)<~>calm(X))))&
((?[X]:((strong(X)|brave(X))))<=>(quiet(john)))&
(![X]:((~kind(X)&kind(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:((happy(X)&~creative(X))))=>(?[X]:((tall(X)<~>~happy(X)))))&
(![X]:((~calm(X)<~>~funny(X))=>(tall(X)&kind(X))))&
(![X]:((strong(X)<~>curious(X))<=>(~curious(X)|~happy(X))))&
(![X]:((~calm(X)&~funny(X))<=>(~rich(X)&~brave(X))))&
(![X]:((~wise(X)|~quiet(X))=>~curious(X)))&
((?[X]:((~humble(X)|wise(X))))=>((~rich(susan)|quiet(susan))))&
(![X]:((~curious(X)|~strong(X))=>(~patient(X)&rich(X))))&
(![X]:((~tall(X)&humble(X))<=>(~happy(X)<~>happy(X))))&
(((~creative(paul)&~old(paul)))<=>((~strong(mary)|~creative(mary))))&
(((humble(fred)<~>~calm(fred)))=>((~quiet(alice)<~>~humble(alice))))&
(![X]:((~patient(X)<~>~calm(X))=>(~tall(X)|creative(X))))&
((~creative(alice)<~>~rich(alice)))&
(quiet(susan))&
(?[X]:(creative(X)))&
((strong(susan)|~strong(susan)))&
((~old(mary)<~>~generous(mary)))&
(humble(fred))&
(?[X]:((calm(X)&~generous(X)))) | ~tall(paul) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1026043820206285006958757
% SZS output start Proof for 1026043820206285006958757
13. ! [X0] : ((humble(X0) & ~tall(X0)) <=> (~happy(X0) <~> happy(X0))) [input p12]
24. tall(paul) [input hypothesis]
55. ! [X0] : (((humble(X0) & ~tall(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (~humble(X0) | tall(X0)))) [nnf transformation 13]
56. ! [X0] : (((humble(X0) & ~tall(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~humble(X0) | tall(X0))) [flattening 55]
114. ~tall(X0) | happy(X0) | happy(X0) [cnf transformation 56]
115. ~tall(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 56]
139. tall(paul) [cnf transformation 24]
140. ~tall(X0) | happy(X0) [duplicate literal removal 114]
141. ~tall(X0) | ~happy(X0) [duplicate literal removal 115]
203. ~tall(X0) [subsumption resolution 140,141]
267. $false [subsumption resolution 139,203]
% SZS output end Proof for 1026043820206285006958757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not kind is either kind or funny and vice versa.
If fred is not creative then john is either brave or not creative.
Everyone who is generous is either not kind or tall.
If fred is humble then lucy is both kind and not old and vice versa.
Everyone who is both old and not quiet is either quiet or not happy and vice versa.
Everyone who is either not patient or strong is not wise and vice versa.
Everyone who is not kind is either rich or old.
Everyone who is funny is not wise or patient and vice versa.
If someone is not calm or not rich then someone is both funny and kind and vice versa.
If john is not tall or old then someone is both old and not patient and vice versa.
If alice is either happy or not rich then someone is both not tall and not curious.
Everyone who is calm is either not old or not calm and vice versa.
Everyone who is both happy and brave is not wise or wise and vice versa.
If lucy is generous then susan is either curious or kind.
Everyone who is both not generous and not creative is both quiet and humble.
Mary is either kind or rich.
Paul is either not tall or not strong.
Someone is not kind or not strong.
Someone is kind or strong.
John is either not calm or old. | Fred is not funny. | contradiction | (![X]:((rich(X)&~kind(X))<=>(kind(X)<~>funny(X))))&
((~creative(fred))=>((brave(john)<~>~creative(john))))&
(![X]:(generous(X)=>(~kind(X)<~>tall(X))))&
((humble(fred))<=>((kind(lucy)&~old(lucy))))&
(![X]:((old(X)&~quiet(X))<=>(quiet(X)<~>~happy(X))))&
(![X]:((~patient(X)<~>strong(X))<=>~wise(X)))&
(![X]:(~kind(X)=>(rich(X)<~>old(X))))&
(![X]:(funny(X)<=>(~wise(X)|patient(X))))&
((?[X]:((~calm(X)|~rich(X))))<=>(?[X]:((funny(X)&kind(X)))))&
(((~tall(john)|old(john)))<=>(?[X]:((old(X)&~patient(X)))))&
(((happy(alice)<~>~rich(alice)))=>(?[X]:((~tall(X)&~curious(X)))))&
(![X]:(calm(X)<=>(~old(X)<~>~calm(X))))&
(![X]:((happy(X)&brave(X))<=>(~wise(X)|wise(X))))&
((generous(lucy))=>((curious(susan)<~>kind(susan))))&
(![X]:((~generous(X)&~creative(X))=>(quiet(X)&humble(X))))&
((kind(mary)<~>rich(mary)))&
((~tall(paul)<~>~strong(paul)))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((kind(X)|strong(X))))&
((~calm(john)<~>old(john))) | ~funny(fred) | [
"p0",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4638183502135990346509121
% SZS output start Proof for 4638183502135990346509121
1. ! [X0] : ((~kind(X0) & rich(X0)) <=> (kind(X0) <~> funny(X0))) [input p0]
7. ! [X0] : (~kind(X0) => (rich(X0) <~> old(X0))) [input p6]
12. ! [X0] : (calm(X0) <=> (~old(X0) <~> ~calm(X0))) [input p11]
21. ~funny(fred) [input hypothesis]
25. ! [X0] : ((rich(X0) <~> old(X0)) | kind(X0)) [ennf transformation 7]
30. ! [X0] : (((~kind(X0) & rich(X0)) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | (kind(X0) | ~rich(X0)))) [nnf transformation 1]
31. ! [X0] : (((~kind(X0) & rich(X0)) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | kind(X0) | ~rich(X0))) [flattening 30]
39. ! [X0] : (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | kind(X0)) [nnf transformation 25]
55. ! [X0] : ((calm(X0) | ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0)))) & (((calm(X0) | old(X0)) & (~calm(X0) | ~old(X0))) | ~calm(X0))) [nnf transformation 12]
66. funny(X0) | kind(X0) | kind(X0) | ~rich(X0) [cnf transformation 31]
70. ~kind(X0) | funny(X0) | ~kind(X0) [cnf transformation 31]
89. old(X0) | rich(X0) | kind(X0) [cnf transformation 39]
108. ~calm(X0) | ~old(X0) | ~calm(X0) [cnf transformation 55]
111. calm(X0) | ~old(X0) | calm(X0) [cnf transformation 55]
129. ~funny(fred) [cnf transformation 21]
130. ~calm(X0) | ~old(X0) [duplicate literal removal 108]
131. ~old(X0) | calm(X0) [duplicate literal removal 111]
134. funny(X0) | kind(X0) | ~rich(X0) [duplicate literal removal 66]
135. ~kind(X0) | funny(X0) [duplicate literal removal 70]
136. ~rich(X0) | funny(X0) [subsumption resolution 134,135]
242. ~old(X0) [subsumption resolution 130,131]
353. kind(X1) | rich(X1) [resolution 89,242]
358. rich(X0) | funny(X0) [resolution 353,135]
359. funny(X0) [subsumption resolution 358,136]
365. $false [resolution 359,129]
% SZS output end Proof for 4638183502135990346509121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then someone is either humble or not tall and vice versa.
If alice is rich or wise then john is funny.
Everyone who is either not tall or quiet is creative and vice versa.
If someone is not creative then paul is not tall.
Everyone who is not wise or strong is either not generous or patient and vice versa.
Everyone who is not old is curious or not humble and vice versa.
If mary is either quiet or old then someone is both brave and generous.
If alice is both not generous and not rich then someone is either strong or not brave and vice versa.
Everyone who is either not happy or brave is curious or creative and vice versa.
If someone is both not wise and rich then someone is humble and vice versa.
Everyone who is either patient or kind is calm and vice versa.
Everyone who is both not creative and wise is not brave or rich and vice versa.
Everyone who is not funny or wise is both quiet and not kind and vice versa.
Everyone who is either not curious or happy is either humble or not generous.
If someone is not wise or brave then lucy is not humble and vice versa.
If someone is both strong and quiet then susan is calm and vice versa.
Someone is tall or not brave.
John is either calm or not strong.
Lucy is both not funny and wise.
Someone is not kind or not calm.
Someone is not humble or old.
Someone is not creative or tall.
Fred is not quiet or creative.
Alice is wise or not kind. | Mary is not curious. | neutral | ((brave(paul))<=>(?[X]:((humble(X)<~>~tall(X)))))&
(((rich(alice)|wise(alice)))=>(funny(john)))&
(![X]:((~tall(X)<~>quiet(X))<=>creative(X)))&
((?[X]:(~creative(X)))=>(~tall(paul)))&
(![X]:((~wise(X)|strong(X))<=>(~generous(X)<~>patient(X))))&
(![X]:(~old(X)<=>(curious(X)|~humble(X))))&
(((quiet(mary)<~>old(mary)))=>(?[X]:((brave(X)&generous(X)))))&
(((~generous(alice)&~rich(alice)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(curious(X)|creative(X))))&
((?[X]:((~wise(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((patient(X)<~>kind(X))<=>calm(X)))&
(![X]:((~creative(X)&wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~funny(X)|wise(X))<=>(quiet(X)&~kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~generous(X))))&
((?[X]:((~wise(X)|brave(X))))<=>(~humble(lucy)))&
((?[X]:((strong(X)&quiet(X))))<=>(calm(susan)))&
(?[X]:((tall(X)|~brave(X))))&
((calm(john)<~>~strong(john)))&
((~funny(lucy)&wise(lucy)))&
(?[X]:((~kind(X)|~calm(X))))&
(?[X]:((~humble(X)|old(X))))&
(?[X]:((~creative(X)|tall(X))))&
((~quiet(fred)|creative(fred)))&
((wise(alice)|~kind(alice))) | ~curious(mary) | [] | null | 0 |
If someone is both not wise and not generous then alice is both kind and not happy. Everyone who is creative or happy is both not calm and happy. If john is both kind and not kind then someone is not rich and vice versa. If someone is generous then lucy is not wise or calm and vice versa. If someone is either not calm or humble then lucy is either rich or strong. If lucy is not kind or wise then fred is patient or not strong and vice versa. Everyone who is not curious or not patient is either tall or not humble and vice versa. Everyone who is either not creative or tall is either not brave or old and vice versa. If someone is not humble then paul is generous or old. Everyone who is both tall and generous is both happy and old. Everyone who is humble or tall is either happy or not generous and vice versa. If someone is either not brave or humble then mary is curious. If paul is not curious then alice is not rich and vice versa. If alice is both old and not patient then lucy is not kind. If john is both not calm and not generous then someone is wise and vice versa. Everyone who is rich or creative is happy. Someone is either kind or not generous. Mary is either not curious or not creative. Fred is not strong or strong. Someone is both generous and rich. Someone is either tall or kind. Mary is either not strong or not calm. Fred is both tall and not patient. Someone is quiet. | Fred is not rich. | contradiction | ((?[X]:((~wise(X)&~generous(X))))=>((kind(alice)&~happy(alice))))&
(![X]:((creative(X)|happy(X))=>(~calm(X)&happy(X))))&
(((kind(john)&~kind(john)))<=>(?[X]:(~rich(X))))&
((?[X]:(generous(X)))<=>((~wise(lucy)|calm(lucy))))&
((?[X]:((~calm(X)<~>humble(X))))=>((rich(lucy)<~>strong(lucy))))&
(((~kind(lucy)|wise(lucy)))<=>((patient(fred)|~strong(fred))))&
(![X]:((~curious(X)|~patient(X))<=>(tall(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>tall(X))<=>(~brave(X)<~>old(X))))&
((?[X]:(~humble(X)))=>((generous(paul)|old(paul))))&
(![X]:((tall(X)&generous(X))=>(happy(X)&old(X))))&
(![X]:((humble(X)|tall(X))<=>(happy(X)<~>~generous(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>(curious(mary)))&
((~curious(paul))<=>(~rich(alice)))&
(((old(alice)&~patient(alice)))=>(~kind(lucy)))&
(((~calm(john)&~generous(john)))<=>(?[X]:(wise(X))))&
(![X]:((rich(X)|creative(X))=>happy(X)))&
(?[X]:((kind(X)<~>~generous(X))))&
((~curious(mary)<~>~creative(mary)))&
((~strong(fred)|strong(fred)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((tall(X)<~>kind(X))))&
((~strong(mary)<~>~calm(mary)))&
((tall(fred)&~patient(fred)))&
(?[X]:(quiet(X))) | ~rich(fred) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8603034758319215974836417
% SZS output start Proof for 8603034758319215974836417
3. (~kind(john) & kind(john)) <=> ? [X0] : ~rich(X0) [input p2]
25. ~rich(fred) [input hypothesis]
38. ((~kind(john) & kind(john)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | (kind(john) | ~kind(john))) [nnf transformation 3]
39. ((~kind(john) & kind(john)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | kind(john) | ~kind(john)) [flattening 38]
40. ((~kind(john) & kind(john)) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | kind(john) | ~kind(john)) [rectify 39]
41. ? [X1] : ~rich(X1) => ~rich(sK0) [choice axiom]
42. ((~kind(john) & kind(john)) | ! [X0] : rich(X0)) & (~rich(sK0) | kind(john) | ~kind(john)) [skolemisation 40,41]
80. kind(john) | rich(X0) [cnf transformation 42]
81. ~kind(john) | rich(X0) [cnf transformation 42]
139. ~rich(fred) [cnf transformation 25]
154. 4 <=> ! [X0] : rich(X0) [avatar definition]
155. rich(X0) <- (4) [avatar component clause 154]
157. 5 <=> kind(john) [avatar definition]
160. 4 | ~5 [avatar split clause 81,157,154]
161. 4 | 5 [avatar split clause 80,157,154]
312. $false <- (4) [resolution 155,139]
313. ~4 [avatar contradiction clause 312]
314. $false [avatar sat refutation 160,161,313]
% SZS output end Proof for 8603034758319215974836417
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not generous then lucy is not happy or rich.
Everyone who is not quiet or rich is patient.
Everyone who is both not old and happy is both not wise and patient and vice versa.
If john is either not happy or creative then someone is not brave or not tall.
Everyone who is either not funny or not creative is either not brave or wise and vice versa.
If someone is rich or wise then someone is either not brave or not wise and vice versa.
If john is not curious then someone is wise.
If mary is both humble and kind then someone is quiet and vice versa.
Everyone who is both not quiet and not old is either old or not wise and vice versa.
Everyone who is strong or rich is kind.
Everyone who is rich or not curious is both not wise and calm.
Everyone who is both curious and kind is either not rich or brave and vice versa.
Everyone who is patient is not brave and vice versa.
If mary is kind or humble then someone is either happy or wise.
If lucy is not generous or strong then someone is both creative and curious.
If alice is both not funny and not curious then susan is generous or not quiet.
Someone is not rich.
Someone is strong.
Mary is not humble.
John is either not happy or calm.
Someone is funny.
Lucy is brave or tall.
Paul is either humble or not strong. | Susan is not curious. | contradiction | ((~generous(paul))=>((~happy(lucy)|rich(lucy))))&
(![X]:((~quiet(X)|rich(X))=>patient(X)))&
(![X]:((~old(X)&happy(X))<=>(~wise(X)&patient(X))))&
(((~happy(john)<~>creative(john)))=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~brave(X)<~>wise(X))))&
((?[X]:((rich(X)|wise(X))))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((~curious(john))=>(?[X]:(wise(X))))&
(((humble(mary)&kind(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~old(X))<=>(old(X)<~>~wise(X))))&
(![X]:((strong(X)|rich(X))=>kind(X)))&
(![X]:((rich(X)|~curious(X))=>(~wise(X)&calm(X))))&
(![X]:((curious(X)&kind(X))<=>(~rich(X)<~>brave(X))))&
(![X]:(patient(X)<=>~brave(X)))&
(((kind(mary)|humble(mary)))=>(?[X]:((happy(X)<~>wise(X)))))&
(((~generous(lucy)|strong(lucy)))=>(?[X]:((creative(X)&curious(X)))))&
(((~funny(alice)&~curious(alice)))=>((generous(susan)|~quiet(susan))))&
(?[X]:(~rich(X)))&
(?[X]:(strong(X)))&
(~humble(mary))&
((~happy(john)<~>calm(john)))&
(?[X]:(funny(X)))&
((brave(lucy)|tall(lucy)))&
((humble(paul)<~>~strong(paul))) | ~curious(susan) | [
"p1",
"p5",
"p7",
"p8",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 929106447421028745115563
% SZS output start Proof for 929106447421028745115563
2. ! [X0] : ((rich(X0) | ~quiet(X0)) => patient(X0)) [input p1]
6. ? [X0] : (wise(X0) | rich(X0)) <=> ? [X0] : (~brave(X0) <~> ~wise(X0)) [input p5]
8. (kind(mary) & humble(mary)) <=> ? [X0] : quiet(X0) [input p7]
9. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> (old(X0) <~> ~wise(X0))) [input p8]
12. ! [X0] : ((kind(X0) & curious(X0)) <=> (~rich(X0) <~> brave(X0))) [input p11]
13. ! [X0] : (patient(X0) <=> ~brave(X0)) [input p12]
19. ~humble(mary) [input p18]
24. ~curious(susan) [input hypothesis]
25. ? [X0] : (wise(X0) | rich(X0)) <=> ? [X1] : (~brave(X1) <~> ~wise(X1)) [rectify 6]
29. ! [X0] : (patient(X0) | (~rich(X0) & quiet(X0))) [ennf transformation 2]
42. (? [X0] : (wise(X0) | rich(X0)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (? [X1] : ((wise(X1) | brave(X1)) & (~wise(X1) | ~brave(X1))) | ! [X0] : (~wise(X0) & ~rich(X0))) [nnf transformation 25]
43. (? [X0] : (wise(X0) | rich(X0)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (? [X2] : ((wise(X2) | brave(X2)) & (~wise(X2) | ~brave(X2))) | ! [X3] : (~wise(X3) & ~rich(X3))) [rectify 42]
44. ? [X0] : (wise(X0) | rich(X0)) => (wise(sK1) | rich(sK1)) [choice axiom]
45. ? [X2] : ((wise(X2) | brave(X2)) & (~wise(X2) | ~brave(X2))) => ((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) [choice axiom]
46. ((wise(sK1) | rich(sK1)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) | ! [X3] : (~wise(X3) & ~rich(X3))) [skolemisation 43,45,44]
49. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | (~kind(mary) | ~humble(mary))) [nnf transformation 8]
50. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ~kind(mary) | ~humble(mary)) [flattening 49]
51. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ~kind(mary) | ~humble(mary)) [rectify 50]
52. ? [X1] : quiet(X1) => quiet(sK4) [choice axiom]
53. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (quiet(sK4) | ~kind(mary) | ~humble(mary)) [skolemisation 51,52]
54. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (old(X0) | quiet(X0)))) [nnf transformation 9]
55. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | old(X0) | quiet(X0))) [flattening 54]
56. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~kind(X0) | ~curious(X0)))) [nnf transformation 12]
57. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~kind(X0) | ~curious(X0))) [flattening 56]
58. ! [X0] : ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))) [nnf transformation 13]
72. patient(X0) | quiet(X0) [cnf transformation 29]
90. wise(sK2) | brave(sK2) | ~rich(X3) [cnf transformation 46]
91. wise(sK2) | brave(sK2) | ~wise(X3) [cnf transformation 46]
93. wise(sK1) | rich(sK1) | ~brave(X1) | wise(X1) [cnf transformation 46]
96. humble(mary) | ~quiet(X0) [cnf transformation 53]
98. ~wise(X0) | old(X0) | old(X0) | quiet(X0) [cnf transformation 55]
102. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 55]
112. curious(X0) | brave(X0) | rich(X0) [cnf transformation 57]
116. ~brave(X0) | ~patient(X0) [cnf transformation 58]
126. ~humble(mary) [cnf transformation 19]
133. ~curious(susan) [cnf transformation 24]
134. ~wise(X0) | old(X0) | quiet(X0) [duplicate literal removal 98]
135. ~wise(X0) | ~old(X0) [duplicate literal removal 102]
155. 5 <=> ! [X1] : (~brave(X1) | wise(X1)) [avatar definition]
156. ~brave(X1) | wise(X1) <- (5) [avatar component clause 155]
158. 6 <=> rich(sK1) [avatar definition]
160. rich(sK1) <- (6) [avatar component clause 158]
162. 7 <=> wise(sK1) [avatar definition]
164. wise(sK1) <- (7) [avatar component clause 162]
165. 5 | 6 | 7 [avatar split clause 93,162,158,155]
171. 9 <=> ! [X3] : ~wise(X3) [avatar definition]
172. ~wise(X3) <- (9) [avatar component clause 171]
174. 10 <=> brave(sK2) [avatar definition]
176. brave(sK2) <- (10) [avatar component clause 174]
178. 11 <=> wise(sK2) [avatar definition]
180. wise(sK2) <- (11) [avatar component clause 178]
181. 9 | 10 | 11 [avatar split clause 91,178,174,171]
183. 12 <=> ! [X3] : ~rich(X3) [avatar definition]
184. ~rich(X3) <- (12) [avatar component clause 183]
185. 12 | 10 | 11 [avatar split clause 90,178,174,183]
198. 15 <=> ! [X0] : ~quiet(X0) [avatar definition]
199. ~quiet(X0) <- (15) [avatar component clause 198]
206. 17 <=> humble(mary) [avatar definition]
209. 15 | 17 [avatar split clause 96,206,198]
215. ~wise(X0) | quiet(X0) [subsumption resolution 134,135]
244. ~17 [avatar split clause 126,206]
275. ~patient(sK2) <- (10) [resolution 116,176]
278. quiet(sK2) <- (10) [resolution 275,72]
279. $false <- (10, 15) [subsumption resolution 278,199]
280. ~10 | ~15 [avatar contradiction clause 279]
289. quiet(sK2) <- (11) [resolution 215,180]
290. $false <- (11, 15) [subsumption resolution 289,199]
291. ~11 | ~15 [avatar contradiction clause 290]
292. $false <- (6, 12) [resolution 184,160]
293. ~6 | ~12 [avatar contradiction clause 292]
294. $false <- (7, 9) [subsumption resolution 164,172]
295. ~7 | ~9 [avatar contradiction clause 294]
296. ~brave(X1) <- (5, 9) [subsumption resolution 156,172]
310. brave(susan) | rich(susan) [resolution 112,133]
311. rich(susan) <- (5, 9) [subsumption resolution 310,296]
312. $false <- (5, 9, 12) [subsumption resolution 311,184]
313. ~5 | ~9 | ~12 [avatar contradiction clause 312]
314. $false [avatar sat refutation 165,181,185,209,244,280,291,293,295,313]
% SZS output end Proof for 929106447421028745115563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is both brave and not rich.
Everyone who is not rich or strong is not humble and vice versa.
Everyone who is patient is both not kind and generous.
Everyone who is both strong and not calm is either not wise or not humble.
Everyone who is either not brave or not wise is both not patient and not humble.
Everyone who is happy or quiet is not rich or not wise.
Everyone who is not patient or generous is both not quiet and curious.
If susan is either tall or strong then fred is either not rich or not kind.
Everyone who is not calm or not patient is generous or curious and vice versa.
If alice is either creative or generous then someone is not old.
Everyone who is strong or not kind is both not happy and not wise and vice versa.
Everyone who is not calm or not wise is both tall and not curious.
Everyone who is quiet is not generous or patient.
If someone is either humble or tall then someone is old.
If paul is not old or calm then someone is not wise or creative and vice versa.
Someone is old.
Mary is either wise or strong.
Someone is rich.
Someone is either not tall or patient.
Someone is humble.
Fred is creative or not wise. | Paul is strong. | contradiction | (![X]:(strong(X)=>(brave(X)&~rich(X))))&
(![X]:((~rich(X)|strong(X))<=>~humble(X)))&
(![X]:(patient(X)=>(~kind(X)&generous(X))))&
(![X]:((strong(X)&~calm(X))=>(~wise(X)<~>~humble(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~patient(X)&~humble(X))))&
(![X]:((happy(X)|quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((~patient(X)|generous(X))=>(~quiet(X)&curious(X))))&
(((tall(susan)<~>strong(susan)))=>((~rich(fred)<~>~kind(fred))))&
(![X]:((~calm(X)|~patient(X))<=>(generous(X)|curious(X))))&
(((creative(alice)<~>generous(alice)))=>(?[X]:(~old(X))))&
(![X]:((strong(X)|~kind(X))<=>(~happy(X)&~wise(X))))&
(![X]:((~calm(X)|~wise(X))=>(tall(X)&~curious(X))))&
(![X]:(quiet(X)=>(~generous(X)|patient(X))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:(old(X))))&
(((~old(paul)|calm(paul)))<=>(?[X]:((~wise(X)|creative(X)))))&
(?[X]:(old(X)))&
((wise(mary)<~>strong(mary)))&
(?[X]:(rich(X)))&
(?[X]:((~tall(X)<~>patient(X))))&
(?[X]:(humble(X)))&
((creative(fred)|~wise(fred))) | strong(paul) | [
"p2",
"p6",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4570733188120965703878255
% SZS output start Proof for 4570733188120965703878255
3. ! [X0] : (patient(X0) => (generous(X0) & ~kind(X0))) [input p2]
7. ! [X0] : ((generous(X0) | ~patient(X0)) => (curious(X0) & ~quiet(X0))) [input p6]
9. ! [X0] : ((~patient(X0) | ~calm(X0)) <=> (curious(X0) | generous(X0))) [input p8]
11. ! [X0] : ((~kind(X0) | strong(X0)) <=> (~wise(X0) & ~happy(X0))) [input p10]
12. ! [X0] : ((~wise(X0) | ~calm(X0)) => (~curious(X0) & tall(X0))) [input p11]
22. strong(paul) [input hypothesis]
25. ! [X0] : ((generous(X0) | ~patient(X0)) => curious(X0)) [pure predicate removal 7]
28. ! [X0] : ((generous(X0) & ~kind(X0)) | ~patient(X0)) [ennf transformation 3]
34. ! [X0] : (curious(X0) | (~generous(X0) & patient(X0))) [ennf transformation 25]
37. ! [X0] : ((~curious(X0) & tall(X0)) | (wise(X0) & calm(X0))) [ennf transformation 12]
44. ! [X0] : (((~patient(X0) | ~calm(X0)) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | (patient(X0) & calm(X0)))) [nnf transformation 9]
45. ! [X0] : ((~patient(X0) | ~calm(X0) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | (patient(X0) & calm(X0)))) [flattening 44]
49. ! [X0] : (((~kind(X0) | strong(X0)) | (wise(X0) | happy(X0))) & ((~wise(X0) & ~happy(X0)) | (kind(X0) & ~strong(X0)))) [nnf transformation 11]
50. ! [X0] : ((~kind(X0) | strong(X0) | wise(X0) | happy(X0)) & ((~wise(X0) & ~happy(X0)) | (kind(X0) & ~strong(X0)))) [flattening 49]
76. ~patient(X0) | generous(X0) [cnf transformation 28]
84. curious(X0) | patient(X0) [cnf transformation 34]
85. ~generous(X0) | curious(X0) [cnf transformation 34]
90. curious(X0) | generous(X0) | calm(X0) [cnf transformation 45]
92. ~patient(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 45]
98. ~wise(X0) | ~strong(X0) [cnf transformation 50]
103. ~curious(X0) | calm(X0) [cnf transformation 37]
104. ~curious(X0) | wise(X0) [cnf transformation 37]
119. strong(paul) [cnf transformation 22]
142. ~calm(X0) | ~patient(X0) [subsumption resolution 92,76]
143. curious(X0) | calm(X0) [subsumption resolution 90,85]
158. calm(X0) [subsumption resolution 103,143]
225. wise(X0) | patient(X0) [resolution 104,84]
232. ~patient(X0) [resolution 142,158]
302. patient(X3) | ~strong(X3) [resolution 225,98]
309. ~strong(X3) [subsumption resolution 302,232]
321. $false [resolution 309,119]
% SZS output end Proof for 4570733188120965703878255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not patient and quiet then john is both wise and not quiet. Everyone who is not happy or not generous is either not kind or not wise and vice versa. Everyone who is not generous is funny or creative. Everyone who is either not tall or not kind is both not calm and happy. Everyone who is kind is curious or not funny and vice versa. Everyone who is either strong or not strong is funny and vice versa. Everyone who is not generous or tall is strong. If someone is both rich and calm then someone is either funny or generous and vice versa. If someone is either old or curious then mary is either wise or rich. Everyone who is humble is both kind and strong and vice versa. Everyone who is both not curious and not kind is either calm or not generous and vice versa. Everyone who is both generous and strong is not calm. If someone is either humble or not happy then someone is not creative or not tall and vice versa. If mary is strong or not curious then someone is not rich and vice versa. Everyone who is brave is old and vice versa. If someone is not wise or not strong then paul is both humble and creative and vice versa. Paul is calm. Fred is either not generous or not curious. John is not humble or humble. Someone is not humble. John is both not curious and not happy. Someone is funny. Lucy is either not wise or not generous. | John is humble. | contradiction | (((~patient(lucy)&quiet(lucy)))=>((wise(john)&~quiet(john))))&
(![X]:((~happy(X)|~generous(X))<=>(~kind(X)<~>~wise(X))))&
(![X]:(~generous(X)=>(funny(X)|creative(X))))&
(![X]:((~tall(X)<~>~kind(X))=>(~calm(X)&happy(X))))&
(![X]:(kind(X)<=>(curious(X)|~funny(X))))&
(![X]:((strong(X)<~>~strong(X))<=>funny(X)))&
(![X]:((~generous(X)|tall(X))=>strong(X)))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
((?[X]:((old(X)<~>curious(X))))=>((wise(mary)<~>rich(mary))))&
(![X]:(humble(X)<=>(kind(X)&strong(X))))&
(![X]:((~curious(X)&~kind(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((generous(X)&strong(X))=>~calm(X)))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:((~creative(X)|~tall(X)))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:(~rich(X))))&
(![X]:(brave(X)<=>old(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>((humble(paul)&creative(paul))))&
(calm(paul))&
((~generous(fred)<~>~curious(fred)))&
((~humble(john)|humble(john)))&
(?[X]:(~humble(X)))&
((~curious(john)&~happy(john)))&
(?[X]:(funny(X)))&
((~wise(lucy)<~>~generous(lucy))) | humble(john) | [
"p4",
"p5",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8487237414310218895282629
% SZS output start Proof for 8487237414310218895282629
5. ! [X0] : (kind(X0) <=> (~funny(X0) | curious(X0))) [input p4]
6. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> funny(X0)) [input p5]
10. ! [X0] : (humble(X0) <=> (strong(X0) & kind(X0))) [input p9]
21. ~happy(john) & ~curious(john) [input p20]
24. humble(john) [input hypothesis]
38. ! [X0] : ((kind(X0) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | ~kind(X0))) [nnf transformation 5]
39. ! [X0] : ((kind(X0) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | ~kind(X0))) [flattening 38]
40. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~funny(X0)) & (funny(X0) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 6]
47. ! [X0] : ((humble(X0) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ~humble(X0))) [nnf transformation 10]
48. ! [X0] : ((humble(X0) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ~humble(X0))) [flattening 47]
83. ~funny(X0) | curious(X0) | ~kind(X0) [cnf transformation 39]
86. funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 40]
87. funny(X0) | strong(X0) | strong(X0) [cnf transformation 40]
102. ~humble(X0) | kind(X0) [cnf transformation 48]
131. ~curious(john) [cnf transformation 21]
136. humble(john) [cnf transformation 24]
137. funny(X0) | ~strong(X0) [duplicate literal removal 86]
138. strong(X0) | funny(X0) [duplicate literal removal 87]
139. funny(X0) [subsumption resolution 137,138]
284. kind(john) [resolution 102,136]
365. ~kind(X1) | curious(X1) [resolution 83,139]
508. curious(john) [resolution 365,284]
512. $false [subsumption resolution 508,131]
% SZS output end Proof for 8487237414310218895282629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and quiet is not kind or calm. Everyone who is either not curious or brave is happy or old and vice versa. If someone is not strong or not funny then susan is both wise and happy. Everyone who is strong or humble is generous or calm. If someone is happy or not generous then someone is brave. Everyone who is not curious is funny. If john is not tall then alice is not wise and vice versa. If someone is either not creative or not strong then someone is either not creative or not rich and vice versa. Everyone who is old or wise is both funny and not curious and vice versa. If someone is quiet then someone is strong or not wise. If someone is brave or not kind then john is either not generous or not quiet and vice versa. If someone is generous or old then paul is both not old and not tall and vice versa. Everyone who is both not old and curious is kind. Everyone who is not humble is not funny. If someone is calm then someone is both calm and rich. Everyone who is rich or not creative is either not calm or strong. Someone is either not brave or not wise. John is not kind. Mary is not strong or wise. Mary is both not happy and not generous. Someone is both not rich and not funny. Lucy is funny. Fred is both calm and patient. Someone is both not quiet and not calm. | John is humble. | entailment | (![X]:((~old(X)&quiet(X))=>(~kind(X)|calm(X))))&
(![X]:((~curious(X)<~>brave(X))<=>(happy(X)|old(X))))&
((?[X]:((~strong(X)|~funny(X))))=>((wise(susan)&happy(susan))))&
(![X]:((strong(X)|humble(X))=>(generous(X)|calm(X))))&
((?[X]:((happy(X)|~generous(X))))=>(?[X]:(brave(X))))&
(![X]:(~curious(X)=>funny(X)))&
((~tall(john))<=>(~wise(alice)))&
((?[X]:((~creative(X)<~>~strong(X))))<=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((old(X)|wise(X))<=>(funny(X)&~curious(X))))&
((?[X]:(quiet(X)))=>(?[X]:((strong(X)|~wise(X)))))&
((?[X]:((brave(X)|~kind(X))))<=>((~generous(john)<~>~quiet(john))))&
((?[X]:((generous(X)|old(X))))<=>((~old(paul)&~tall(paul))))&
(![X]:((~old(X)&curious(X))=>kind(X)))&
(![X]:(~humble(X)=>~funny(X)))&
((?[X]:(calm(X)))=>(?[X]:((calm(X)&rich(X)))))&
(![X]:((rich(X)|~creative(X))=>(~calm(X)<~>strong(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
(~kind(john))&
((~strong(mary)|wise(mary)))&
((~happy(mary)&~generous(mary)))&
(?[X]:((~rich(X)&~funny(X))))&
(funny(lucy))&
((calm(fred)&patient(fred)))&
(?[X]:((~quiet(X)&~calm(X)))) | humble(john) | [
"p5",
"p8",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2028611882704997583609298
% SZS output start Proof for 2028611882704997583609298
6. ! [X0] : (~curious(X0) => funny(X0)) [input p5]
9. ! [X0] : ((wise(X0) | old(X0)) <=> (~curious(X0) & funny(X0))) [input p8]
13. ! [X0] : ((curious(X0) & ~old(X0)) => kind(X0)) [input p12]
14. ! [X0] : (~humble(X0) => ~funny(X0)) [input p13]
18. ~kind(john) [input p17]
25. ~humble(john) [input hypothesis]
37. ! [X0] : (funny(X0) | curious(X0)) [ennf transformation 6]
39. ! [X0] : (kind(X0) | (~curious(X0) | old(X0))) [ennf transformation 13]
40. ! [X0] : (kind(X0) | ~curious(X0) | old(X0)) [flattening 39]
41. ! [X0] : (~funny(X0) | humble(X0)) [ennf transformation 14]
55. ! [X0] : (((wise(X0) | old(X0)) | (curious(X0) | ~funny(X0))) & ((~curious(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 9]
56. ! [X0] : ((wise(X0) | old(X0) | curious(X0) | ~funny(X0)) & ((~curious(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [flattening 55]
95. funny(X0) | curious(X0) [cnf transformation 37]
108. ~curious(X0) | ~old(X0) [cnf transformation 56]
123. kind(X0) | ~curious(X0) | old(X0) [cnf transformation 40]
124. ~funny(X0) | humble(X0) [cnf transformation 41]
133. ~kind(john) [cnf transformation 18]
143. ~humble(john) [cnf transformation 25]
288. ~curious(X0) | kind(X0) [subsumption resolution 123,108]
328. humble(X0) | curious(X0) [resolution 124,95]
333. curious(john) [resolution 328,143]
527. kind(john) [resolution 333,288]
538. $false [subsumption resolution 527,133]
% SZS output end Proof for 2028611882704997583609298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or not rich then someone is either not calm or not patient and vice versa.
Everyone who is either not quiet or quiet is either funny or humble and vice versa.
Everyone who is both not tall and brave is both happy and not old.
Everyone who is wise or not kind is either not creative or quiet and vice versa.
If someone is rich or creative then alice is either strong or tall.
Everyone who is either not tall or rich is either not old or not calm.
Everyone who is both not generous and not brave is not creative or creative.
If lucy is both quiet and not old then fred is not curious.
Everyone who is either happy or old is old.
Everyone who is not happy or not strong is both not kind and kind and vice versa.
If someone is calm then someone is both happy and not calm and vice versa.
If alice is either not rich or not strong then susan is both calm and not wise.
If susan is either generous or old then paul is creative and vice versa.
Everyone who is either patient or not funny is either humble or happy.
If susan is not generous or not humble then fred is not quiet.
Everyone who is either patient or humble is either not strong or funny and vice versa.
Fred is both not curious and not rich.
Susan is either happy or not strong.
Paul is curious.
Fred is not old or not generous.
Mary is calm or patient.
Fred is either not quiet or not happy.
Fred is not calm. | Alice is not patient. | contradiction | ((?[X]:((strong(X)<~>~rich(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(funny(X)<~>humble(X))))&
(![X]:((~tall(X)&brave(X))=>(happy(X)&~old(X))))&
(![X]:((wise(X)|~kind(X))<=>(~creative(X)<~>quiet(X))))&
((?[X]:((rich(X)|creative(X))))=>((strong(alice)<~>tall(alice))))&
(![X]:((~tall(X)<~>rich(X))=>(~old(X)<~>~calm(X))))&
(![X]:((~generous(X)&~brave(X))=>(~creative(X)|creative(X))))&
(((quiet(lucy)&~old(lucy)))=>(~curious(fred)))&
(![X]:((happy(X)<~>old(X))=>old(X)))&
(![X]:((~happy(X)|~strong(X))<=>(~kind(X)&kind(X))))&
((?[X]:(calm(X)))<=>(?[X]:((happy(X)&~calm(X)))))&
(((~rich(alice)<~>~strong(alice)))=>((calm(susan)&~wise(susan))))&
(((generous(susan)<~>old(susan)))<=>(creative(paul)))&
(![X]:((patient(X)<~>~funny(X))=>(humble(X)<~>happy(X))))&
(((~generous(susan)|~humble(susan)))=>(~quiet(fred)))&
(![X]:((patient(X)<~>humble(X))<=>(~strong(X)<~>funny(X))))&
((~curious(fred)&~rich(fred)))&
((happy(susan)<~>~strong(susan)))&
(curious(paul))&
((~old(fred)|~generous(fred)))&
((calm(mary)|patient(mary)))&
((~quiet(fred)<~>~happy(fred)))&
(~calm(fred)) | ~patient(alice) | [
"p1",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 216783633067224252062938
% SZS output start Proof for 216783633067224252062938
2. ! [X0] : ((~quiet(X0) <~> quiet(X0)) <=> (funny(X0) <~> humble(X0))) [input p1]
10. ! [X0] : ((~strong(X0) | ~happy(X0)) <=> (kind(X0) & ~kind(X0))) [input p9]
14. ! [X0] : ((patient(X0) <~> ~funny(X0)) => (humble(X0) <~> happy(X0))) [input p13]
16. ! [X0] : ((patient(X0) <~> humble(X0)) <=> (~strong(X0) <~> funny(X0))) [input p15]
24. ~patient(alice) [input hypothesis]
37. ! [X0] : ((humble(X0) <~> happy(X0)) | (patient(X0) <=> ~funny(X0))) [ennf transformation 14]
44. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0)))) & (((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [nnf transformation 2]
50. ! [X0] : (((~strong(X0) | ~happy(X0)) | (~kind(X0) | kind(X0))) & ((kind(X0) & ~kind(X0)) | (strong(X0) & happy(X0)))) [nnf transformation 10]
51. ! [X0] : ((~strong(X0) | ~happy(X0) | ~kind(X0) | kind(X0)) & ((kind(X0) & ~kind(X0)) | (strong(X0) & happy(X0)))) [flattening 50]
59. ! [X0] : (((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) [nnf transformation 37]
60. ! [X0] : ((((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) & (((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))))) [nnf transformation 16]
71. humble(X0) | funny(X0) | quiet(X0) | quiet(X0) [cnf transformation 44]
72. humble(X0) | funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 44]
73. ~humble(X0) | ~funny(X0) | quiet(X0) | quiet(X0) [cnf transformation 44]
74. ~humble(X0) | ~funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 44]
99. ~kind(X0) | happy(X0) [cnf transformation 51]
100. ~kind(X0) | strong(X0) [cnf transformation 51]
101. kind(X0) | happy(X0) [cnf transformation 51]
102. kind(X0) | strong(X0) [cnf transformation 51]
118. ~happy(X0) | ~humble(X0) | patient(X0) | funny(X0) [cnf transformation 59]
126. humble(X0) | patient(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 60]
139. ~patient(alice) [cnf transformation 24]
141. humble(X0) | funny(X0) | quiet(X0) [duplicate literal removal 71]
142. humble(X0) | funny(X0) | ~quiet(X0) [duplicate literal removal 72]
143. ~humble(X0) | ~funny(X0) | quiet(X0) [duplicate literal removal 73]
144. ~humble(X0) | ~funny(X0) | ~quiet(X0) [duplicate literal removal 74]
181. ~humble(X0) | ~funny(X0) [subsumption resolution 143,144]
182. humble(X0) | funny(X0) [subsumption resolution 141,142]
214. strong(X0) [subsumption resolution 100,102]
215. happy(X0) [subsumption resolution 99,101]
265. ~humble(X0) | patient(X0) | funny(X0) [subsumption resolution 118,215]
266. ~humble(X0) | patient(X0) [subsumption resolution 265,181]
277. humble(X0) | patient(X0) | ~funny(X0) [subsumption resolution 126,214]
278. humble(X0) | patient(X0) [subsumption resolution 277,182]
279. patient(X0) [subsumption resolution 278,266]
292. $false [subsumption resolution 139,279]
% SZS output end Proof for 216783633067224252062938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is strong and vice versa. Everyone who is either happy or not funny is tall or not quiet. If john is either kind or rich then someone is either not rich or kind. Everyone who is either not old or not strong is not happy or not brave and vice versa. Everyone who is either not creative or not kind is generous or calm and vice versa. If alice is either rich or happy then mary is both happy and not wise and vice versa. Everyone who is either calm or strong is humble or not old and vice versa. Everyone who is either brave or calm is either not humble or not strong and vice versa. Everyone who is not funny is both not calm and curious. If someone is quiet then someone is either humble or not strong and vice versa. If someone is brave or happy then someone is both funny and not curious and vice versa. If someone is either not patient or quiet then someone is not brave or not wise. If someone is both not creative and not tall then paul is tall or not patient and vice versa. Everyone who is not brave is both not patient and not rich. If susan is not kind or not calm then someone is both not patient and not happy and vice versa. If susan is either kind or strong then fred is either not calm or not humble and vice versa. Someone is quiet. Someone is either rich or creative. Lucy is either tall or generous. Alice is either not tall or quiet. John is brave. Someone is not creative or humble. Susan is either not old or rich. Lucy is either not rich or funny. | Lucy is happy. | entailment | (![X]:(old(X)<=>strong(X)))&
(![X]:((happy(X)<~>~funny(X))=>(tall(X)|~quiet(X))))&
(((kind(john)<~>rich(john)))=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:((~old(X)<~>~strong(X))<=>(~happy(X)|~brave(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>(generous(X)|calm(X))))&
(((rich(alice)<~>happy(alice)))<=>((happy(mary)&~wise(mary))))&
(![X]:((calm(X)<~>strong(X))<=>(humble(X)|~old(X))))&
(![X]:((brave(X)<~>calm(X))<=>(~humble(X)<~>~strong(X))))&
(![X]:(~funny(X)=>(~calm(X)&curious(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((humble(X)<~>~strong(X)))))&
((?[X]:((brave(X)|happy(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))=>(?[X]:((~brave(X)|~wise(X)))))&
((?[X]:((~creative(X)&~tall(X))))<=>((tall(paul)|~patient(paul))))&
(![X]:(~brave(X)=>(~patient(X)&~rich(X))))&
(((~kind(susan)|~calm(susan)))<=>(?[X]:((~patient(X)&~happy(X)))))&
(((kind(susan)<~>strong(susan)))<=>((~calm(fred)<~>~humble(fred))))&
(?[X]:(quiet(X)))&
(?[X]:((rich(X)<~>creative(X))))&
((tall(lucy)<~>generous(lucy)))&
((~tall(alice)<~>quiet(alice)))&
(brave(john))&
(?[X]:((~creative(X)|humble(X))))&
((~old(susan)<~>rich(susan)))&
((~rich(lucy)<~>funny(lucy))) | happy(lucy) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2161167001404830283521805
% SZS output start Proof for 2161167001404830283521805
1. ! [X0] : (old(X0) <=> strong(X0)) [input p0]
4. ! [X0] : ((~old(X0) <~> ~strong(X0)) <=> (~brave(X0) | ~happy(X0))) [input p3]
25. ~happy(lucy) [input hypothesis]
35. ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))) [nnf transformation 1]
40. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (brave(X0) & happy(X0))) & ((~brave(X0) | ~happy(X0)) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [nnf transformation 4]
41. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (brave(X0) & happy(X0))) & (~brave(X0) | ~happy(X0) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [flattening 40]
85. ~old(X0) | strong(X0) [cnf transformation 35]
86. ~strong(X0) | old(X0) [cnf transformation 35]
95. ~strong(X0) | ~old(X0) | happy(X0) [cnf transformation 41]
97. strong(X0) | old(X0) | happy(X0) [cnf transformation 41]
171. ~happy(lucy) [cnf transformation 25]
193. happy(X0) | old(X0) [subsumption resolution 97,86]
195. ~strong(X0) | happy(X0) [subsumption resolution 95,193]
433. old(lucy) [resolution 193,171]
436. strong(lucy) [resolution 433,85]
467. happy(lucy) [resolution 436,195]
470. $false [subsumption resolution 467,171]
% SZS output end Proof for 2161167001404830283521805
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and creative is either not humble or not old and vice versa.
If someone is either tall or not strong then lucy is not creative and vice versa.
Everyone who is happy or patient is not humble.
If fred is either curious or calm then someone is both strong and creative and vice versa.
Everyone who is either tall or brave is tall or patient and vice versa.
Everyone who is not old or brave is happy and vice versa.
Everyone who is brave or not wise is humble.
Everyone who is either not old or kind is both generous and not kind.
Everyone who is creative is both humble and patient.
Everyone who is funny or happy is both creative and not strong.
Everyone who is not quiet or not funny is old and vice versa.
If someone is either patient or old then john is both humble and not quiet and vice versa.
If fred is not humble or not rich then someone is both funny and not creative.
Everyone who is humble is strong and vice versa.
If someone is patient or calm then alice is both rich and not brave.
Alice is either not rich or curious.
Lucy is both not curious and not tall.
Paul is not happy or not brave.
John is not brave or strong.
Fred is not curious or tall. | Alice is old. | entailment | (![X]:((brave(X)&creative(X))<=>(~humble(X)<~>~old(X))))&
((?[X]:((tall(X)<~>~strong(X))))<=>(~creative(lucy)))&
(![X]:((happy(X)|patient(X))=>~humble(X)))&
(((curious(fred)<~>calm(fred)))<=>(?[X]:((strong(X)&creative(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(tall(X)|patient(X))))&
(![X]:((~old(X)|brave(X))<=>happy(X)))&
(![X]:((brave(X)|~wise(X))=>humble(X)))&
(![X]:((~old(X)<~>kind(X))=>(generous(X)&~kind(X))))&
(![X]:(creative(X)=>(humble(X)&patient(X))))&
(![X]:((funny(X)|happy(X))=>(creative(X)&~strong(X))))&
(![X]:((~quiet(X)|~funny(X))<=>old(X)))&
((?[X]:((patient(X)<~>old(X))))<=>((humble(john)&~quiet(john))))&
(((~humble(fred)|~rich(fred)))=>(?[X]:((funny(X)&~creative(X)))))&
(![X]:(humble(X)<=>strong(X)))&
((?[X]:((patient(X)|calm(X))))=>((rich(alice)&~brave(alice))))&
((~rich(alice)<~>curious(alice)))&
((~curious(lucy)&~tall(lucy)))&
((~happy(paul)|~brave(paul)))&
((~brave(john)|strong(john)))&
((~curious(fred)|tall(fred))) | old(alice) | [
"p0",
"p2",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8099816821451249428529608
% SZS output start Proof for 8099816821451249428529608
1. ! [X0] : ((creative(X0) & brave(X0)) <=> (~humble(X0) <~> ~old(X0))) [input p0]
3. ! [X0] : ((patient(X0) | happy(X0)) => ~humble(X0)) [input p2]
6. ! [X0] : ((brave(X0) | ~old(X0)) <=> happy(X0)) [input p5]
9. ! [X0] : (creative(X0) => (patient(X0) & humble(X0))) [input p8]
10. ! [X0] : ((happy(X0) | funny(X0)) => (~strong(X0) & creative(X0))) [input p9]
21. ~old(alice) [input hypothesis]
22. ! [X0] : ((brave(X0) | ~old(X0)) => happy(X0)) [unused predicate definition removal 6]
25. ! [X0] : (~humble(X0) | (~patient(X0) & ~happy(X0))) [ennf transformation 3]
26. ! [X0] : (happy(X0) | (~brave(X0) & old(X0))) [ennf transformation 22]
29. ! [X0] : ((patient(X0) & humble(X0)) | ~creative(X0)) [ennf transformation 9]
30. ! [X0] : ((~strong(X0) & creative(X0)) | (~happy(X0) & ~funny(X0))) [ennf transformation 10]
33. ! [X0] : (((creative(X0) & brave(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0)))) & (((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (~creative(X0) | ~brave(X0)))) [nnf transformation 1]
34. ! [X0] : (((creative(X0) & brave(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0)))) & (((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ~creative(X0) | ~brave(X0))) [flattening 33]
61. ~old(X0) | creative(X0) | humble(X0) [cnf transformation 34]
68. ~patient(X0) | ~humble(X0) [cnf transformation 25]
81. happy(X0) | old(X0) [cnf transformation 26]
86. ~creative(X0) | humble(X0) [cnf transformation 29]
87. ~creative(X0) | patient(X0) [cnf transformation 29]
89. ~happy(X0) | creative(X0) [cnf transformation 30]
118. ~old(alice) [cnf transformation 21]
260. old(X0) | creative(X0) [resolution 89,81]
340. creative(alice) [resolution 260,118]
342. creative(X1) | creative(X1) | humble(X1) [resolution 260,61]
344. creative(X1) | humble(X1) [duplicate literal removal 342]
345. humble(X1) [subsumption resolution 344,86]
350. patient(alice) [resolution 340,87]
365. ~humble(alice) [resolution 350,68]
367. $false [subsumption resolution 365,345]
% SZS output end Proof for 8099816821451249428529608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both strong and wise then susan is not funny and vice versa. Everyone who is either not kind or curious is calm or happy and vice versa. Everyone who is both rich and wise is kind. If alice is both creative and strong then someone is not strong. If someone is either not rich or kind then someone is old or not wise. Everyone who is not funny is not humble and vice versa. If john is both wise and creative then someone is not generous. If someone is rich or not old then someone is creative and vice versa. Everyone who is both not brave and not calm is either kind or not funny. If lucy is both not old and generous then john is both calm and humble and vice versa. Everyone who is quiet is both not rich and creative. Everyone who is humble or not strong is both generous and patient. If someone is funny or not calm then someone is either not quiet or humble. If alice is both not curious and not funny then someone is not quiet. Everyone who is kind or not brave is old or not tall and vice versa. Everyone who is not tall or not funny is both generous and not brave. John is brave. Someone is humble or not humble. Alice is both tall and not humble. Fred is creative or calm. Paul is funny. Fred is not humble or not kind. | Lucy is not generous. | contradiction | (((strong(susan)&wise(susan)))<=>(~funny(susan)))&
(![X]:((~kind(X)<~>curious(X))<=>(calm(X)|happy(X))))&
(![X]:((rich(X)&wise(X))=>kind(X)))&
(((creative(alice)&strong(alice)))=>(?[X]:(~strong(X))))&
((?[X]:((~rich(X)<~>kind(X))))=>(?[X]:((old(X)|~wise(X)))))&
(![X]:(~funny(X)<=>~humble(X)))&
(((wise(john)&creative(john)))=>(?[X]:(~generous(X))))&
((?[X]:((rich(X)|~old(X))))<=>(?[X]:(creative(X))))&
(![X]:((~brave(X)&~calm(X))=>(kind(X)<~>~funny(X))))&
(((~old(lucy)&generous(lucy)))<=>((calm(john)&humble(john))))&
(![X]:(quiet(X)=>(~rich(X)&creative(X))))&
(![X]:((humble(X)|~strong(X))=>(generous(X)&patient(X))))&
((?[X]:((funny(X)|~calm(X))))=>(?[X]:((~quiet(X)<~>humble(X)))))&
(((~curious(alice)&~funny(alice)))=>(?[X]:(~quiet(X))))&
(![X]:((kind(X)|~brave(X))<=>(old(X)|~tall(X))))&
(![X]:((~tall(X)|~funny(X))=>(generous(X)&~brave(X))))&
(brave(john))&
(?[X]:((humble(X)|~humble(X))))&
((tall(alice)&~humble(alice)))&
((creative(fred)|calm(fred)))&
(funny(paul))&
((~humble(fred)|~kind(fred))) | ~generous(lucy) | [
"p5",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6690842220643339214596298
% SZS output start Proof for 6690842220643339214596298
6. ! [X0] : (~funny(X0) <=> ~humble(X0)) [input p5]
12. ! [X0] : ((~strong(X0) | humble(X0)) => (patient(X0) & generous(X0))) [input p11]
16. ! [X0] : ((~funny(X0) | ~tall(X0)) => (~brave(X0) & generous(X0))) [input p15]
23. ~generous(lucy) [input hypothesis]
27. ! [X0] : ((~strong(X0) | humble(X0)) => generous(X0)) [pure predicate removal 12]
38. ! [X0] : (generous(X0) | (strong(X0) & ~humble(X0))) [ennf transformation 27]
42. ! [X0] : ((~brave(X0) & generous(X0)) | (funny(X0) & tall(X0))) [ennf transformation 16]
53. ! [X0] : ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0))) [nnf transformation 6]
88. ~funny(X0) | humble(X0) [cnf transformation 53]
101. ~humble(X0) | generous(X0) [cnf transformation 38]
113. generous(X0) | funny(X0) [cnf transformation 42]
123. ~generous(lucy) [cnf transformation 23]
214. 22 <=> generous(lucy) [avatar definition]
215. ~generous(lucy) <- (~22) [avatar component clause 214]
274. ~22 [avatar split clause 123,214]
279. funny(lucy) <- (~22) [resolution 113,215]
280. humble(lucy) <- (~22) [resolution 279,88]
287. generous(lucy) <- (~22) [resolution 280,101]
289. $false <- (~22) [subsumption resolution 287,215]
290. 22 [avatar contradiction clause 289]
291. $false [avatar sat refutation 274,290]
% SZS output end Proof for 6690842220643339214596298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not kind is not wise or calm and vice versa. Everyone who is both not wise and not happy is either wise or not rich. Everyone who is both not creative and not curious is humble or not creative and vice versa. If someone is both curious and happy then paul is either creative or not tall. Everyone who is either not old or patient is funny. If mary is either not funny or not happy then someone is either not funny or curious and vice versa. If mary is not old then someone is humble and vice versa. If someone is both funny and not generous then alice is either rich or funny. Everyone who is not rich or curious is tall or not rich and vice versa. Everyone who is either rich or old is not humble. Everyone who is tall or not creative is quiet. Everyone who is both generous and not patient is not calm or funny. Everyone who is either humble or strong is both creative and funny. Everyone who is not humble or not funny is both strong and not funny and vice versa. Everyone who is old is not strong or tall and vice versa. Lucy is not tall or not strong. Someone is either not kind or not generous. Someone is either generous or not funny. | Lucy is tall. | contradiction | (![X]:((creative(X)&~kind(X))<=>(~wise(X)|calm(X))))&
(![X]:((~wise(X)&~happy(X))=>(wise(X)<~>~rich(X))))&
(![X]:((~creative(X)&~curious(X))<=>(humble(X)|~creative(X))))&
((?[X]:((curious(X)&happy(X))))=>((creative(paul)<~>~tall(paul))))&
(![X]:((~old(X)<~>patient(X))=>funny(X)))&
(((~funny(mary)<~>~happy(mary)))<=>(?[X]:((~funny(X)<~>curious(X)))))&
((~old(mary))<=>(?[X]:(humble(X))))&
((?[X]:((funny(X)&~generous(X))))=>((rich(alice)<~>funny(alice))))&
(![X]:((~rich(X)|curious(X))<=>(tall(X)|~rich(X))))&
(![X]:((rich(X)<~>old(X))=>~humble(X)))&
(![X]:((tall(X)|~creative(X))=>quiet(X)))&
(![X]:((generous(X)&~patient(X))=>(~calm(X)|funny(X))))&
(![X]:((humble(X)<~>strong(X))=>(creative(X)&funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(strong(X)&~funny(X))))&
(![X]:(old(X)<=>(~strong(X)|tall(X))))&
((~tall(lucy)|~strong(lucy)))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((generous(X)<~>~funny(X)))) | tall(lucy) | [
"p2",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3910802106816662038471144
% SZS output start Proof for 3910802106816662038471144
3. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (~creative(X0) | humble(X0))) [input p2]
13. ! [X0] : ((humble(X0) <~> strong(X0)) => (funny(X0) & creative(X0))) [input p12]
14. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~funny(X0) & strong(X0))) [input p13]
16. ~strong(lucy) | ~tall(lucy) [input p15]
19. tall(lucy) [input hypothesis]
29. ! [X0] : ((funny(X0) & creative(X0)) | (humble(X0) <=> strong(X0))) [ennf transformation 13]
33. ! [X0] : (((~curious(X0) & ~creative(X0)) | (creative(X0) & ~humble(X0))) & ((~creative(X0) | humble(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 3]
34. ! [X0] : (((~curious(X0) & ~creative(X0)) | (creative(X0) & ~humble(X0))) & (~creative(X0) | humble(X0) | curious(X0) | creative(X0))) [flattening 33]
49. ! [X0] : ((funny(X0) & creative(X0)) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0)))) [nnf transformation 29]
50. ! [X0] : (((~funny(X0) | ~humble(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 14]
51. ! [X0] : ((~funny(X0) | ~humble(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [flattening 50]
68. ~creative(X0) | ~humble(X0) [cnf transformation 34]
95. creative(X0) | strong(X0) | ~humble(X0) [cnf transformation 49]
99. strong(X0) | humble(X0) [cnf transformation 51]
107. ~strong(lucy) | ~tall(lucy) [cnf transformation 16]
112. tall(lucy) [cnf transformation 19]
183. strong(X0) | ~humble(X0) [subsumption resolution 95,68]
184. strong(X0) [subsumption resolution 99,183]
186. ~tall(lucy) [subsumption resolution 107,184]
207. $false [subsumption resolution 112,186]
% SZS output end Proof for 3910802106816662038471144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not calm is not wise or creative.
If someone is either brave or curious then alice is brave or funny.
If paul is either quiet or not creative then mary is humble.
Everyone who is not curious or kind is not patient or not rich and vice versa.
Everyone who is both not humble and happy is both not kind and not curious.
If someone is happy or not humble then lucy is either calm or not patient.
If lucy is either happy or rich then someone is either calm or curious and vice versa.
Everyone who is not humble is both calm and curious.
Everyone who is either not happy or not rich is both not rich and calm.
If paul is both humble and rich then john is either not funny or not old.
If fred is either not calm or quiet then someone is both creative and not happy and vice versa.
Everyone who is either not rich or not quiet is both not rich and not strong.
If someone is not happy then alice is both quiet and not quiet and vice versa.
Everyone who is not quiet or not patient is generous.
Everyone who is old is either not rich or rich.
If fred is funny then someone is either funny or not brave and vice versa.
John is not quiet.
Someone is both not quiet and happy.
Someone is strong or not funny.
Someone is either not kind or quiet.
Someone is calm or not kind.
Someone is both not curious and not old.
Alice is not generous or rich.
Fred is either patient or not kind. | Paul is humble. | entailment | (![X]:((rich(X)<~>~calm(X))=>(~wise(X)|creative(X))))&
((?[X]:((brave(X)<~>curious(X))))=>((brave(alice)|funny(alice))))&
(((quiet(paul)<~>~creative(paul)))=>(humble(mary)))&
(![X]:((~curious(X)|kind(X))<=>(~patient(X)|~rich(X))))&
(![X]:((~humble(X)&happy(X))=>(~kind(X)&~curious(X))))&
((?[X]:((happy(X)|~humble(X))))=>((calm(lucy)<~>~patient(lucy))))&
(((happy(lucy)<~>rich(lucy)))<=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:(~humble(X)=>(calm(X)&curious(X))))&
(![X]:((~happy(X)<~>~rich(X))=>(~rich(X)&calm(X))))&
(((humble(paul)&rich(paul)))=>((~funny(john)<~>~old(john))))&
(((~calm(fred)<~>quiet(fred)))<=>(?[X]:((creative(X)&~happy(X)))))&
(![X]:((~rich(X)<~>~quiet(X))=>(~rich(X)&~strong(X))))&
((?[X]:(~happy(X)))<=>((quiet(alice)&~quiet(alice))))&
(![X]:((~quiet(X)|~patient(X))=>generous(X)))&
(![X]:(old(X)=>(~rich(X)<~>rich(X))))&
((funny(fred))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(~quiet(john))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:((strong(X)|~funny(X))))&
(?[X]:((~kind(X)<~>quiet(X))))&
(?[X]:((calm(X)|~kind(X))))&
(?[X]:((~curious(X)&~old(X))))&
((~generous(alice)|rich(alice)))&
((patient(fred)<~>~kind(fred))) | humble(paul) | [
"p4",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5298502752525040974297227
% SZS output start Proof for 5298502752525040974297227
5. ! [X0] : ((happy(X0) & ~humble(X0)) => (~curious(X0) & ~kind(X0))) [input p4]
8. ! [X0] : (~humble(X0) => (curious(X0) & calm(X0))) [input p7]
13. ? [X0] : ~happy(X0) <=> (~quiet(alice) & quiet(alice)) [input p12]
25. ~humble(paul) [input hypothesis]
30. ! [X0] : ((~curious(X0) & ~kind(X0)) | (~happy(X0) | humble(X0))) [ennf transformation 5]
31. ! [X0] : ((~curious(X0) & ~kind(X0)) | ~happy(X0) | humble(X0)) [flattening 30]
33. ! [X0] : ((curious(X0) & calm(X0)) | humble(X0)) [ennf transformation 8]
56. (? [X0] : ~happy(X0) | (quiet(alice) | ~quiet(alice))) & ((~quiet(alice) & quiet(alice)) | ! [X0] : happy(X0)) [nnf transformation 13]
57. (? [X0] : ~happy(X0) | quiet(alice) | ~quiet(alice)) & ((~quiet(alice) & quiet(alice)) | ! [X0] : happy(X0)) [flattening 56]
58. (? [X0] : ~happy(X0) | quiet(alice) | ~quiet(alice)) & ((~quiet(alice) & quiet(alice)) | ! [X1] : happy(X1)) [rectify 57]
59. ? [X0] : ~happy(X0) => ~happy(sK2) [choice axiom]
60. (~happy(sK2) | quiet(alice) | ~quiet(alice)) & ((~quiet(alice) & quiet(alice)) | ! [X1] : happy(X1)) [skolemisation 58,59]
87. ~happy(X0) | ~curious(X0) | humble(X0) [cnf transformation 31]
101. humble(X0) | curious(X0) [cnf transformation 33]
118. quiet(alice) | happy(X1) [cnf transformation 60]
119. ~quiet(alice) | happy(X1) [cnf transformation 60]
141. ~humble(paul) [cnf transformation 25]
175. 8 <=> ! [X0] : humble(X0) [avatar definition]
176. humble(X0) <- (8) [avatar component clause 175]
223. 18 <=> humble(paul) [avatar definition]
225. ~humble(paul) <- (~18) [avatar component clause 223]
266. 27 <=> ! [X1] : happy(X1) [avatar definition]
267. happy(X1) <- (27) [avatar component clause 266]
269. 28 <=> quiet(alice) [avatar definition]
272. 27 | ~28 [avatar split clause 119,269,266]
273. 27 | 28 [avatar split clause 118,269,266]
343. ~18 [avatar split clause 141,223]
398. ~curious(X0) | humble(X0) <- (27) [resolution 87,267]
401. humble(X0) <- (27) [subsumption resolution 398,101]
402. 8 | ~27 [avatar split clause 401,266,175]
403. $false <- (8, ~18) [resolution 176,225]
404. ~8 | 18 [avatar contradiction clause 403]
405. $false [avatar sat refutation 272,273,343,402,404]
% SZS output end Proof for 5298502752525040974297227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not calm is either patient or calm.
Everyone who is curious or not patient is either not generous or not calm and vice versa.
Everyone who is both curious and patient is not creative.
Everyone who is not kind is funny.
If john is either not creative or not wise then someone is either not calm or tall.
Everyone who is creative is both old and creative and vice versa.
Everyone who is either funny or not rich is either creative or not curious and vice versa.
Everyone who is generous or creative is both rich and not kind and vice versa.
Everyone who is both generous and not creative is wise or not creative and vice versa.
Everyone who is both kind and not wise is both not generous and strong.
Everyone who is not calm is not old or not humble and vice versa.
Everyone who is both funny and not strong is creative and vice versa.
Everyone who is not funny is wise.
If someone is both happy and humble then someone is both strong and funny.
Everyone who is both humble and generous is not quiet and vice versa.
If susan is either not happy or not tall then lucy is either not strong or not patient and vice versa.
Fred is not quiet or patient.
Paul is not brave or not funny.
Someone is either wise or humble.
Alice is curious.
Susan is brave or kind.
Someone is either not rich or not kind.
Paul is not quiet.
John is not old. | John is not strong. | contradiction | (![X]:((~strong(X)&~calm(X))=>(patient(X)<~>calm(X))))&
(![X]:((curious(X)|~patient(X))<=>(~generous(X)<~>~calm(X))))&
(![X]:((curious(X)&patient(X))=>~creative(X)))&
(![X]:(~kind(X)=>funny(X)))&
(((~creative(john)<~>~wise(john)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:(creative(X)<=>(old(X)&creative(X))))&
(![X]:((funny(X)<~>~rich(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((generous(X)|creative(X))<=>(rich(X)&~kind(X))))&
(![X]:((generous(X)&~creative(X))<=>(wise(X)|~creative(X))))&
(![X]:((kind(X)&~wise(X))=>(~generous(X)&strong(X))))&
(![X]:(~calm(X)<=>(~old(X)|~humble(X))))&
(![X]:((funny(X)&~strong(X))<=>creative(X)))&
(![X]:(~funny(X)=>wise(X)))&
((?[X]:((happy(X)&humble(X))))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((humble(X)&generous(X))<=>~quiet(X)))&
(((~happy(susan)<~>~tall(susan)))<=>((~strong(lucy)<~>~patient(lucy))))&
((~quiet(fred)|patient(fred)))&
((~brave(paul)|~funny(paul)))&
(?[X]:((wise(X)<~>humble(X))))&
(curious(alice))&
((brave(susan)|kind(susan)))&
(?[X]:((~rich(X)<~>~kind(X))))&
(~quiet(paul))&
(~old(john)) | ~strong(john) | [
"p3",
"p5",
"p7",
"p8",
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 161411233115518833693879
% SZS output start Proof for 161411233115518833693879
4. ! [X0] : (~kind(X0) => funny(X0)) [input p3]
6. ! [X0] : (creative(X0) <=> (creative(X0) & old(X0))) [input p5]
8. ! [X0] : ((creative(X0) | generous(X0)) <=> (~kind(X0) & rich(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & generous(X0)) <=> (~creative(X0) | wise(X0))) [input p8]
12. ! [X0] : ((~strong(X0) & funny(X0)) <=> creative(X0)) [input p11]
24. ~old(john) [input p23]
25. ~strong(john) [input hypothesis]
32. ! [X0] : (funny(X0) | kind(X0)) [ennf transformation 4]
45. ! [X0] : ((creative(X0) | (~creative(X0) | ~old(X0))) & ((creative(X0) & old(X0)) | ~creative(X0))) [nnf transformation 6]
46. ! [X0] : ((creative(X0) | ~creative(X0) | ~old(X0)) & ((creative(X0) & old(X0)) | ~creative(X0))) [flattening 45]
48. ! [X0] : (((creative(X0) | generous(X0)) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | (~creative(X0) & ~generous(X0)))) [nnf transformation 8]
49. ! [X0] : ((creative(X0) | generous(X0) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | (~creative(X0) & ~generous(X0)))) [flattening 48]
50. ! [X0] : (((~creative(X0) & generous(X0)) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | (creative(X0) | ~generous(X0)))) [nnf transformation 9]
51. ! [X0] : (((~creative(X0) & generous(X0)) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | creative(X0) | ~generous(X0))) [flattening 50]
54. ! [X0] : (((~strong(X0) & funny(X0)) | ~creative(X0)) & (creative(X0) | (strong(X0) | ~funny(X0)))) [nnf transformation 12]
55. ! [X0] : (((~strong(X0) & funny(X0)) | ~creative(X0)) & (creative(X0) | strong(X0) | ~funny(X0))) [flattening 54]
75. funny(X0) | kind(X0) [cnf transformation 32]
80. ~creative(X0) | old(X0) [cnf transformation 46]
93. ~kind(X0) | ~generous(X0) [cnf transformation 49]
98. creative(X0) | generous(X0) [cnf transformation 51]
106. ~funny(X0) | strong(X0) | creative(X0) [cnf transformation 55]
131. ~old(john) [cnf transformation 24]
132. ~strong(john) [cnf transformation 25]
139. 2 <=> creative(john) [avatar definition]
140. creative(john) <- (2) [avatar component clause 139]
141. ~creative(john) <- (~2) [avatar component clause 139]
329. kind(X0) | creative(X0) | strong(X0) [resolution 106,75]
449. creative(X2) | strong(X2) | ~generous(X2) [resolution 329,93]
452. creative(X2) | strong(X2) [subsumption resolution 449,98]
518. strong(john) <- (~2) [resolution 452,141]
520. $false <- (~2) [subsumption resolution 518,132]
521. 2 [avatar contradiction clause 520]
526. old(john) <- (2) [resolution 140,80]
535. $false <- (2) [subsumption resolution 526,131]
536. ~2 [avatar contradiction clause 535]
537. $false [avatar sat refutation 521,536]
% SZS output end Proof for 161411233115518833693879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not strong or not brave and vice versa.
Everyone who is either not patient or not curious is wise or rich and vice versa.
If someone is either curious or not patient then someone is not curious or not kind.
If mary is not old then mary is generous.
If someone is not calm then alice is both wise and calm.
Everyone who is not kind is both not tall and not rich and vice versa.
If lucy is funny or brave then lucy is not quiet or patient and vice versa.
Everyone who is either funny or not kind is not curious and vice versa.
Everyone who is not wise or creative is either tall or quiet and vice versa.
If lucy is both tall and happy then someone is both not brave and patient.
If someone is either not patient or not strong then someone is curious or not strong.
If fred is either brave or not happy then paul is quiet.
Everyone who is either not humble or not brave is tall and vice versa.
Everyone who is creative or tall is funny or not tall.
If someone is funny or happy then someone is not funny or not generous and vice versa.
If susan is not kind or generous then someone is either curious or generous and vice versa.
Someone is not strong or strong.
Someone is funny.
John is not funny or calm.
Someone is not tall or not happy.
Susan is both patient and quiet.
Someone is both old and calm.
Someone is both not calm and wise.
Someone is either kind or not patient. | Lucy is tall. | neutral | (![X]:(~patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((~patient(X)<~>~curious(X))<=>(wise(X)|rich(X))))&
((?[X]:((curious(X)<~>~patient(X))))=>(?[X]:((~curious(X)|~kind(X)))))&
((~old(mary))=>(generous(mary)))&
((?[X]:(~calm(X)))=>((wise(alice)&calm(alice))))&
(![X]:(~kind(X)<=>(~tall(X)&~rich(X))))&
(((funny(lucy)|brave(lucy)))<=>((~quiet(lucy)|patient(lucy))))&
(![X]:((funny(X)<~>~kind(X))<=>~curious(X)))&
(![X]:((~wise(X)|creative(X))<=>(tall(X)<~>quiet(X))))&
(((tall(lucy)&happy(lucy)))=>(?[X]:((~brave(X)&patient(X)))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:((curious(X)|~strong(X)))))&
(((brave(fred)<~>~happy(fred)))=>(quiet(paul)))&
(![X]:((~humble(X)<~>~brave(X))<=>tall(X)))&
(![X]:((creative(X)|tall(X))=>(funny(X)|~tall(X))))&
((?[X]:((funny(X)|happy(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
(((~kind(susan)|generous(susan)))<=>(?[X]:((curious(X)<~>generous(X)))))&
(?[X]:((~strong(X)|strong(X))))&
(?[X]:(funny(X)))&
((~funny(john)|calm(john)))&
(?[X]:((~tall(X)|~happy(X))))&
((patient(susan)&quiet(susan)))&
(?[X]:((old(X)&calm(X))))&
(?[X]:((~calm(X)&wise(X))))&
(?[X]:((kind(X)<~>~patient(X)))) | tall(lucy) | [] | null | 0 |
Everyone who is strong or not rich is both not rich and not strong and vice versa.
Everyone who is both not rich and not calm is both not tall and not old and vice versa.
Everyone who is not old or not patient is tall and vice versa.
Everyone who is generous or not creative is either not brave or not curious.
If alice is either tall or patient then alice is creative and vice versa.
Everyone who is either not humble or curious is both not funny and tall.
Everyone who is both happy and patient is either not funny or wise.
Everyone who is not funny or brave is both not patient and patient and vice versa.
If susan is quiet then fred is both generous and not old and vice versa.
Everyone who is either humble or not creative is not patient or humble.
Everyone who is both kind and not old is not calm or not curious.
If mary is humble then susan is not rich.
If someone is strong then fred is either curious or tall and vice versa.
Everyone who is humble is both strong and not patient.
Everyone who is either strong or old is both calm and curious and vice versa.
Everyone who is not quiet or not happy is both humble and not happy and vice versa.
Paul is both patient and old.
Mary is not strong.
Lucy is humble or not brave.
Mary is curious.
Someone is creative or not generous.
John is not patient.
Alice is not patient or quiet. | John is tall. | entailment | (![X]:((strong(X)|~rich(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~rich(X)&~calm(X))<=>(~tall(X)&~old(X))))&
(![X]:((~old(X)|~patient(X))<=>tall(X)))&
(![X]:((generous(X)|~creative(X))=>(~brave(X)<~>~curious(X))))&
(((tall(alice)<~>patient(alice)))<=>(creative(alice)))&
(![X]:((~humble(X)<~>curious(X))=>(~funny(X)&tall(X))))&
(![X]:((happy(X)&patient(X))=>(~funny(X)<~>wise(X))))&
(![X]:((~funny(X)|brave(X))<=>(~patient(X)&patient(X))))&
((quiet(susan))<=>((generous(fred)&~old(fred))))&
(![X]:((humble(X)<~>~creative(X))=>(~patient(X)|humble(X))))&
(![X]:((kind(X)&~old(X))=>(~calm(X)|~curious(X))))&
((humble(mary))=>(~rich(susan)))&
((?[X]:(strong(X)))<=>((curious(fred)<~>tall(fred))))&
(![X]:(humble(X)=>(strong(X)&~patient(X))))&
(![X]:((strong(X)<~>old(X))<=>(calm(X)&curious(X))))&
(![X]:((~quiet(X)|~happy(X))<=>(humble(X)&~happy(X))))&
((patient(paul)&old(paul)))&
(~strong(mary))&
((humble(lucy)|~brave(lucy)))&
(curious(mary))&
(?[X]:((creative(X)|~generous(X))))&
(~patient(john))&
((~patient(alice)|quiet(alice))) | tall(john) | [
"p2",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5265462334655399815266500
% SZS output start Proof for 5265462334655399815266500
3. ! [X0] : ((~patient(X0) | ~old(X0)) <=> tall(X0)) [input p2]
22. ~patient(john) [input p21]
24. ~tall(john) [input hypothesis]
38. ! [X0] : (((~patient(X0) | ~old(X0)) | ~tall(X0)) & (tall(X0) | (patient(X0) & old(X0)))) [nnf transformation 3]
39. ! [X0] : ((~patient(X0) | ~old(X0) | ~tall(X0)) & (tall(X0) | (patient(X0) & old(X0)))) [flattening 38]
69. patient(X0) | tall(X0) [cnf transformation 39]
119. ~patient(john) [cnf transformation 22]
121. ~tall(john) [cnf transformation 24]
201. tall(john) [resolution 69,119]
202. $false [subsumption resolution 201,121]
% SZS output end Proof for 5265462334655399815266500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not quiet is generous or not funny and vice versa.
If susan is both not curious and humble then mary is either not curious or happy.
Everyone who is wise or not generous is both brave and not wise and vice versa.
Everyone who is either rich or not strong is both not generous and not wise and vice versa.
Everyone who is both funny and kind is not calm and vice versa.
Everyone who is strong is either calm or generous and vice versa.
If someone is curious then john is patient.
If alice is not happy or not tall then paul is tall or strong and vice versa.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Fred is not strong or not creative.
Someone is generous or not kind. | Fred is not curious. | entailment | (![X]:((calm(X)|~quiet(X))<=>(generous(X)|~funny(X))))&
(((~curious(susan)&humble(susan)))=>((~curious(mary)<~>happy(mary))))&
(![X]:((wise(X)|~generous(X))<=>(brave(X)&~wise(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~wise(X))))&
(![X]:((funny(X)&kind(X))<=>~calm(X)))&
(![X]:(strong(X)<=>(calm(X)<~>generous(X))))&
((?[X]:(curious(X)))=>(patient(john)))&
(((~happy(alice)|~tall(alice)))<=>((tall(paul)|strong(paul))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | ~curious(fred) | [
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3631686777125296758540133
% SZS output start Proof for 3631686777125296758540133
3. ! [X0] : ((~generous(X0) | wise(X0)) <=> (~wise(X0) & brave(X0))) [input p2]
4. ! [X0] : ((rich(X0) <~> ~strong(X0)) <=> (~wise(X0) & ~generous(X0))) [input p3]
5. ! [X0] : ((kind(X0) & funny(X0)) <=> ~calm(X0)) [input p4]
6. ! [X0] : (strong(X0) <=> (calm(X0) <~> generous(X0))) [input p5]
7. ? [X0] : curious(X0) => patient(john) [input p6]
9. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~rich(X0)) [input p8]
10. ! [X0] : ((~rich(X0) | rich(X0)) <=> ~funny(X0)) [input p9]
11. ! [X0] : (quiet(X0) <=> (generous(X0) & humble(X0))) [input p10]
22. curious(fred) [input hypothesis]
25. patient(john) | ! [X0] : ~curious(X0) [ennf transformation 7]
26. ! [X0] : (~rich(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 9]
33. ! [X0] : (((~generous(X0) | wise(X0)) | (wise(X0) | ~brave(X0))) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [nnf transformation 3]
34. ! [X0] : ((~generous(X0) | wise(X0) | wise(X0) | ~brave(X0)) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [flattening 33]
35. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (wise(X0) | generous(X0))) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [nnf transformation 4]
36. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | wise(X0) | generous(X0)) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [flattening 35]
37. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | (~kind(X0) | ~funny(X0)))) [nnf transformation 5]
38. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | ~kind(X0) | ~funny(X0))) [flattening 37]
39. ! [X0] : ((strong(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ~strong(X0))) [nnf transformation 6]
42. ! [X0] : (((~rich(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 10]
43. ! [X0] : ((~rich(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [flattening 42]
44. ! [X0] : ((quiet(X0) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 11]
45. ! [X0] : ((quiet(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [flattening 44]
66. ~wise(X0) | ~wise(X0) [cnf transformation 34]
70. ~generous(X0) | rich(X0) | strong(X0) [cnf transformation 36]
73. ~strong(X0) | rich(X0) | wise(X0) | generous(X0) [cnf transformation 36]
76. funny(X0) | calm(X0) [cnf transformation 38]
79. ~strong(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 39]
80. ~calm(X0) | generous(X0) | strong(X0) [cnf transformation 39]
82. patient(john) | ~curious(X0) [cnf transformation 25]
87. ~rich(X0) | quiet(X0) [cnf transformation 26]
88. ~patient(X0) | ~rich(X0) [cnf transformation 26]
89. ~funny(X0) | ~rich(X0) [cnf transformation 43]
90. ~funny(X0) | rich(X0) [cnf transformation 43]
93. ~quiet(X0) | generous(X0) [cnf transformation 45]
114. curious(fred) [cnf transformation 22]
115. ~wise(X0) [duplicate literal removal 66]
136. ~strong(X0) | rich(X0) | generous(X0) [subsumption resolution 73,115]
138. 5 <=> ! [X0] : ~curious(X0) [avatar definition]
139. ~curious(X0) <- (5) [avatar component clause 138]
141. 6 <=> patient(john) [avatar definition]
143. patient(john) <- (6) [avatar component clause 141]
144. 5 | 6 [avatar split clause 82,141,138]
165. ~funny(X0) [subsumption resolution 89,90]
214. $false <- (5) [resolution 139,114]
215. ~5 [avatar contradiction clause 214]
216. calm(X0) [resolution 76,165]
219. ~rich(john) <- (6) [resolution 88,143]
239. strong(X0) | generous(X0) [resolution 80,216]
268. rich(X0) | generous(X0) | generous(X0) [resolution 136,239]
269. rich(X0) | generous(X0) [duplicate literal removal 268]
288. generous(X2) | quiet(X2) [resolution 269,87]
291. generous(X2) [subsumption resolution 288,93]
296. strong(X1) | rich(X1) [resolution 291,70]
308. rich(X1) | ~calm(X1) | ~generous(X1) [resolution 296,79]
313. rich(X1) | ~generous(X1) [subsumption resolution 308,216]
314. rich(X1) [subsumption resolution 313,291]
319. $false <- (6) [resolution 314,219]
320. ~6 [avatar contradiction clause 319]
321. $false [avatar sat refutation 144,215,320]
% SZS output end Proof for 3631686777125296758540133
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not calm is both not wise and calm. If fred is not calm then alice is not humble or old and vice versa. Everyone who is patient is either not funny or brave. Everyone who is both not funny and not rich is wise and vice versa. Everyone who is both quiet and not happy is not creative and vice versa. Everyone who is either not quiet or creative is both not creative and wise and vice versa. If someone is generous or curious then someone is not patient and vice versa. If someone is either kind or funny then someone is not funny. Everyone who is both wise and not brave is either kind or not brave. Everyone who is not generous or funny is not rich. If mary is creative or not generous then john is humble or not calm and vice versa. If john is both generous and calm then mary is curious and vice versa. If someone is both not strong and curious then someone is both not kind and calm and vice versa. Everyone who is both not kind and strong is either not quiet or not generous and vice versa. If someone is both happy and creative then someone is wise or creative. Everyone who is either old or not tall is not quiet or not brave. Paul is curious. Someone is either not calm or generous. Someone is not curious. John is either tall or quiet. Paul is not calm. Alice is either rich or not old. Mary is either not funny or strong. Fred is both tall and funny. | Fred is not rich. | entailment | (![X]:((funny(X)&~calm(X))=>(~wise(X)&calm(X))))&
((~calm(fred))<=>((~humble(alice)|old(alice))))&
(![X]:(patient(X)=>(~funny(X)<~>brave(X))))&
(![X]:((~funny(X)&~rich(X))<=>wise(X)))&
(![X]:((quiet(X)&~happy(X))<=>~creative(X)))&
(![X]:((~quiet(X)<~>creative(X))<=>(~creative(X)&wise(X))))&
((?[X]:((generous(X)|curious(X))))<=>(?[X]:(~patient(X))))&
((?[X]:((kind(X)<~>funny(X))))=>(?[X]:(~funny(X))))&
(![X]:((wise(X)&~brave(X))=>(kind(X)<~>~brave(X))))&
(![X]:((~generous(X)|funny(X))=>~rich(X)))&
(((creative(mary)|~generous(mary)))<=>((humble(john)|~calm(john))))&
(((generous(john)&calm(john)))<=>(curious(mary)))&
((?[X]:((~strong(X)&curious(X))))<=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:((~kind(X)&strong(X))<=>(~quiet(X)<~>~generous(X))))&
((?[X]:((happy(X)&creative(X))))=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((old(X)<~>~tall(X))=>(~quiet(X)|~brave(X))))&
(curious(paul))&
(?[X]:((~calm(X)<~>generous(X))))&
(?[X]:(~curious(X)))&
((tall(john)<~>quiet(john)))&
(~calm(paul))&
((rich(alice)<~>~old(alice)))&
((~funny(mary)<~>strong(mary)))&
((tall(fred)&funny(fred))) | ~rich(fred) | [
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 64101021907369166232724
% SZS output start Proof for 64101021907369166232724
10. ! [X0] : ((funny(X0) | ~generous(X0)) => ~rich(X0)) [input p9]
24. funny(fred) & tall(fred) [input p23]
25. rich(fred) [input hypothesis]
36. ! [X0] : (~rich(X0) | (~funny(X0) & generous(X0))) [ennf transformation 10]
109. ~rich(X0) | ~funny(X0) [cnf transformation 36]
142. funny(fred) [cnf transformation 24]
143. rich(fred) [cnf transformation 25]
307. ~funny(fred) [resolution 109,143]
308. $false [subsumption resolution 307,142]
% SZS output end Proof for 64101021907369166232724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or humble then someone is both not funny and rich and vice versa.
If someone is both not tall and kind then someone is generous or not strong and vice versa.
Everyone who is not kind is both not creative and curious and vice versa.
If someone is quiet or not rich then someone is both brave and not creative.
If someone is not curious or creative then mary is funny or curious.
Everyone who is either not curious or not old is kind or patient and vice versa.
Everyone who is either not humble or not rich is both kind and tall and vice versa.
Everyone who is both not generous and not quiet is not tall.
Everyone who is not quiet is either not humble or patient.
Everyone who is patient is not strong or strong and vice versa.
Everyone who is either not wise or not old is generous.
If john is both not brave and not strong then someone is patient or generous and vice versa.
Everyone who is not rich or not calm is either not brave or not tall and vice versa.
If lucy is both not curious and quiet then someone is both tall and not quiet and vice versa.
If susan is happy then someone is kind.
If someone is quiet or not creative then susan is funny or not funny and vice versa.
Someone is either not wise or rich.
Someone is not curious or curious.
Someone is either strong or not brave.
Someone is either not calm or not old.
Someone is brave.
Someone is either creative or wise.
Someone is not generous or not brave. | John is curious. | neutral | ((?[X]:((~calm(X)|humble(X))))<=>(?[X]:((~funny(X)&rich(X)))))&
((?[X]:((~tall(X)&kind(X))))<=>(?[X]:((generous(X)|~strong(X)))))&
(![X]:(~kind(X)<=>(~creative(X)&curious(X))))&
((?[X]:((quiet(X)|~rich(X))))=>(?[X]:((brave(X)&~creative(X)))))&
((?[X]:((~curious(X)|creative(X))))=>((funny(mary)|curious(mary))))&
(![X]:((~curious(X)<~>~old(X))<=>(kind(X)|patient(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(kind(X)&tall(X))))&
(![X]:((~generous(X)&~quiet(X))=>~tall(X)))&
(![X]:(~quiet(X)=>(~humble(X)<~>patient(X))))&
(![X]:(patient(X)<=>(~strong(X)|strong(X))))&
(![X]:((~wise(X)<~>~old(X))=>generous(X)))&
(((~brave(john)&~strong(john)))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~brave(X)<~>~tall(X))))&
(((~curious(lucy)&quiet(lucy)))<=>(?[X]:((tall(X)&~quiet(X)))))&
((happy(susan))=>(?[X]:(kind(X))))&
((?[X]:((quiet(X)|~creative(X))))<=>((funny(susan)|~funny(susan))))&
(?[X]:((~wise(X)<~>rich(X))))&
(?[X]:((~curious(X)|curious(X))))&
(?[X]:((strong(X)<~>~brave(X))))&
(?[X]:((~calm(X)<~>~old(X))))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)<~>wise(X))))&
(?[X]:((~generous(X)|~brave(X)))) | curious(john) | [] | null | 0 |
Everyone who is strong is kind. Everyone who is both not funny and funny is not creative or generous and vice versa. Everyone who is both strong and brave is not strong. If someone is both patient and curious then someone is kind or not quiet and vice versa. If fred is either calm or not kind then susan is not happy or brave and vice versa. Everyone who is not tall is not brave or not quiet and vice versa. If someone is strong then john is old and vice versa. If fred is not rich then someone is happy or not happy. Everyone who is kind or not curious is not patient. If susan is either not humble or happy then someone is not patient and vice versa. Everyone who is both not happy and not humble is both old and not calm. If someone is not happy then someone is either not brave or humble. If someone is curious then someone is not generous or not tall and vice versa. Everyone who is kind is strong. Everyone who is either not humble or rich is not rich or not happy and vice versa. Everyone who is not humble or calm is both kind and not kind. Someone is brave or not strong. Paul is either tall or not old. Someone is either not generous or funny. Someone is generous or not old. Fred is not happy. Someone is funny or happy. | John is curious. | entailment | (![X]:(strong(X)=>kind(X)))&
(![X]:((~funny(X)&funny(X))<=>(~creative(X)|generous(X))))&
(![X]:((strong(X)&brave(X))=>~strong(X)))&
((?[X]:((patient(X)&curious(X))))<=>(?[X]:((kind(X)|~quiet(X)))))&
(((calm(fred)<~>~kind(fred)))<=>((~happy(susan)|brave(susan))))&
(![X]:(~tall(X)<=>(~brave(X)|~quiet(X))))&
((?[X]:(strong(X)))<=>(old(john)))&
((~rich(fred))=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((kind(X)|~curious(X))=>~patient(X)))&
(((~humble(susan)<~>happy(susan)))<=>(?[X]:(~patient(X))))&
(![X]:((~happy(X)&~humble(X))=>(old(X)&~calm(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~brave(X)<~>humble(X)))))&
((?[X]:(curious(X)))<=>(?[X]:((~generous(X)|~tall(X)))))&
(![X]:(kind(X)=>strong(X)))&
(![X]:((~humble(X)<~>rich(X))<=>(~rich(X)|~happy(X))))&
(![X]:((~humble(X)|calm(X))=>(kind(X)&~kind(X))))&
(?[X]:((brave(X)|~strong(X))))&
((tall(paul)<~>~old(paul)))&
(?[X]:((~generous(X)<~>funny(X))))&
(?[X]:((generous(X)|~old(X))))&
(~happy(fred))&
(?[X]:((funny(X)|happy(X)))) | curious(john) | [
"p8",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 740106044308229406249177
% SZS output start Proof for 740106044308229406249177
9. ! [X0] : ((~curious(X0) | kind(X0)) => ~patient(X0)) [input p8]
10. (~humble(susan) <~> happy(susan)) <=> ? [X0] : ~patient(X0) [input p9]
15. ! [X0] : ((~humble(X0) <~> rich(X0)) <=> (~happy(X0) | ~rich(X0))) [input p14]
16. ! [X0] : ((calm(X0) | ~humble(X0)) => (~kind(X0) & kind(X0))) [input p15]
23. ~curious(john) [input hypothesis]
31. ! [X0] : (~patient(X0) | (curious(X0) & ~kind(X0))) [ennf transformation 9]
36. ! [X0] : ((~kind(X0) & kind(X0)) | (~calm(X0) & humble(X0))) [ennf transformation 16]
54. (((~happy(susan) | humble(susan)) & (happy(susan) | ~humble(susan))) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ((~humble(susan) | ~happy(susan)) & (happy(susan) | humble(susan)))) [nnf transformation 10]
55. (((~happy(susan) | humble(susan)) & (happy(susan) | ~humble(susan))) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ((~humble(susan) | ~happy(susan)) & (happy(susan) | humble(susan)))) [rectify 54]
56. ? [X1] : ~patient(X1) => ~patient(sK4) [choice axiom]
57. (((~happy(susan) | humble(susan)) & (happy(susan) | ~humble(susan))) | ! [X0] : patient(X0)) & (~patient(sK4) | ((~humble(susan) | ~happy(susan)) & (happy(susan) | humble(susan)))) [skolemisation 55,56]
67. ! [X0] : ((((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0))))) [nnf transformation 15]
68. ! [X0] : ((((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0))))) [flattening 67]
104. ~patient(X0) | curious(X0) [cnf transformation 31]
107. happy(susan) | ~humble(susan) | patient(X0) [cnf transformation 57]
118. ~happy(X0) | ~rich(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 68]
119. rich(X0) | ~humble(X0) | rich(X0) [cnf transformation 68]
123. kind(X0) | humble(X0) [cnf transformation 36]
125. ~kind(X0) | humble(X0) [cnf transformation 36]
135. ~curious(john) [cnf transformation 23]
136. ~happy(X0) | ~rich(X0) | ~humble(X0) [duplicate literal removal 118]
137. ~humble(X0) | rich(X0) [duplicate literal removal 119]
185. 11 <=> happy(susan) [avatar definition]
187. happy(susan) <- (11) [avatar component clause 185]
207. 15 <=> ! [X0] : patient(X0) [avatar definition]
208. patient(X0) <- (15) [avatar component clause 207]
210. 16 <=> humble(susan) [avatar definition]
211. ~humble(susan) <- (~16) [avatar component clause 210]
214. 15 | ~16 | 11 [avatar split clause 107,185,210,207]
244. ~humble(X0) | ~happy(X0) [subsumption resolution 136,137]
246. humble(X0) [subsumption resolution 123,125]
271. $false <- (~16) [subsumption resolution 211,246]
272. 16 [avatar contradiction clause 271]
283. ~happy(X0) [resolution 244,246]
286. $false <- (11) [resolution 283,187]
287. ~11 [avatar contradiction clause 286]
289. curious(X0) <- (15) [resolution 208,104]
295. $false <- (15) [resolution 289,135]
296. ~15 [avatar contradiction clause 295]
297. $false [avatar sat refutation 214,272,287,296]
% SZS output end Proof for 740106044308229406249177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both happy and not happy and vice versa. Everyone who is either funny or not generous is both not brave and brave and vice versa. If lucy is both kind and calm then someone is not old or not curious. If lucy is patient or calm then someone is either not wise or rich. Everyone who is not patient is quiet. If fred is either not funny or generous then paul is both tall and brave. If lucy is quiet or not old then someone is humble or not calm and vice versa. If someone is old or rich then someone is either old or curious. Everyone who is not tall is wise or quiet. Everyone who is both not creative and not quiet is not strong or old and vice versa. If someone is both not old and kind then someone is both not funny and funny. If someone is either calm or kind then someone is curious and vice versa. Everyone who is either brave or not strong is tall. Everyone who is brave or wise is both strong and not strong and vice versa. If mary is both not creative and not funny then someone is kind or funny. Everyone who is either curious or strong is both strong and creative and vice versa. Someone is both not curious and happy. Someone is either curious or quiet. Someone is either calm or not generous. Someone is either happy or generous. Susan is both generous and not funny. Fred is not wise. Someone is creative or not kind. Alice is either curious or tall. | Fred is brave. | contradiction | (![X]:(~creative(X)<=>(happy(X)&~happy(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~brave(X)&brave(X))))&
(((kind(lucy)&calm(lucy)))=>(?[X]:((~old(X)|~curious(X)))))&
(((patient(lucy)|calm(lucy)))=>(?[X]:((~wise(X)<~>rich(X)))))&
(![X]:(~patient(X)=>quiet(X)))&
(((~funny(fred)<~>generous(fred)))=>((tall(paul)&brave(paul))))&
(((quiet(lucy)|~old(lucy)))<=>(?[X]:((humble(X)|~calm(X)))))&
((?[X]:((old(X)|rich(X))))=>(?[X]:((old(X)<~>curious(X)))))&
(![X]:(~tall(X)=>(wise(X)|quiet(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(~strong(X)|old(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((calm(X)<~>kind(X))))<=>(?[X]:(curious(X))))&
(![X]:((brave(X)<~>~strong(X))=>tall(X)))&
(![X]:((brave(X)|wise(X))<=>(strong(X)&~strong(X))))&
(((~creative(mary)&~funny(mary)))=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((curious(X)<~>strong(X))<=>(strong(X)&creative(X))))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((calm(X)<~>~generous(X))))&
(?[X]:((happy(X)<~>generous(X))))&
((generous(susan)&~funny(susan)))&
(~wise(fred))&
(?[X]:((creative(X)|~kind(X))))&
((curious(alice)<~>tall(alice))) | brave(fred) | [
"p0",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1038377888568496608631946
% SZS output start Proof for 1038377888568496608631946
1. ! [X0] : (~creative(X0) <=> (~happy(X0) & happy(X0))) [input p0]
10. ! [X0] : ((~quiet(X0) & ~creative(X0)) <=> (old(X0) | ~strong(X0))) [input p9]
14. ! [X0] : ((wise(X0) | brave(X0)) <=> (~strong(X0) & strong(X0))) [input p13]
25. brave(fred) [input hypothesis]
41. ! [X0] : ((~creative(X0) | (happy(X0) | ~happy(X0))) & ((~happy(X0) & happy(X0)) | creative(X0))) [nnf transformation 1]
42. ! [X0] : ((~creative(X0) | happy(X0) | ~happy(X0)) & ((~happy(X0) & happy(X0)) | creative(X0))) [flattening 41]
60. ! [X0] : (((~quiet(X0) & ~creative(X0)) | (~old(X0) & strong(X0))) & ((old(X0) | ~strong(X0)) | (quiet(X0) | creative(X0)))) [nnf transformation 10]
61. ! [X0] : (((~quiet(X0) & ~creative(X0)) | (~old(X0) & strong(X0))) & (old(X0) | ~strong(X0) | quiet(X0) | creative(X0))) [flattening 60]
71. ! [X0] : (((wise(X0) | brave(X0)) | (strong(X0) | ~strong(X0))) & ((~strong(X0) & strong(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 14]
72. ! [X0] : ((wise(X0) | brave(X0) | strong(X0) | ~strong(X0)) & ((~strong(X0) & strong(X0)) | (~wise(X0) & ~brave(X0)))) [flattening 71]
91. happy(X0) | creative(X0) [cnf transformation 42]
92. ~happy(X0) | creative(X0) [cnf transformation 42]
120. ~creative(X0) | strong(X0) [cnf transformation 61]
134. ~strong(X0) | ~brave(X0) [cnf transformation 72]
158. brave(fred) [cnf transformation 25]
161. creative(X0) [subsumption resolution 91,92]
243. strong(X0) [subsumption resolution 120,161]
280. ~brave(X0) [subsumption resolution 134,243]
324. $false [subsumption resolution 158,280]
% SZS output end Proof for 1038377888568496608631946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or brave is not tall or happy. If someone is not creative or not rich then someone is either not generous or kind and vice versa. Everyone who is both curious and not old is old and vice versa. Everyone who is not old or brave is either generous or not creative and vice versa. Everyone who is both generous and not brave is either funny or kind and vice versa. Everyone who is either curious or rich is strong. Everyone who is not funny or funny is curious or not humble. Everyone who is kind is both not humble and funny. If someone is both quiet and curious then someone is either happy or brave and vice versa. Everyone who is rich or not strong is strong or not humble. If someone is brave or curious then paul is either not curious or not generous. Everyone who is either humble or not funny is not wise. If alice is not funny then alice is either happy or not quiet. If susan is not generous or patient then someone is both kind and not funny. If someone is either rich or kind then someone is not wise. Everyone who is both not tall and tall is tall and vice versa. Someone is either not calm or not tall. Someone is either creative or not old. Mary is not tall. John is wise. Someone is calm. Someone is not tall. Lucy is both not strong and not brave. Lucy is patient. | Lucy is humble. | contradiction | (![X]:((~wise(X)<~>brave(X))=>(~tall(X)|happy(X))))&
((?[X]:((~creative(X)|~rich(X))))<=>(?[X]:((~generous(X)<~>kind(X)))))&
(![X]:((curious(X)&~old(X))<=>old(X)))&
(![X]:((~old(X)|brave(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((generous(X)&~brave(X))<=>(funny(X)<~>kind(X))))&
(![X]:((curious(X)<~>rich(X))=>strong(X)))&
(![X]:((~funny(X)|funny(X))=>(curious(X)|~humble(X))))&
(![X]:(kind(X)=>(~humble(X)&funny(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((rich(X)|~strong(X))=>(strong(X)|~humble(X))))&
((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((humble(X)<~>~funny(X))=>~wise(X)))&
((~funny(alice))=>((happy(alice)<~>~quiet(alice))))&
(((~generous(susan)|patient(susan)))=>(?[X]:((kind(X)&~funny(X)))))&
((?[X]:((rich(X)<~>kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>tall(X)))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(~tall(mary))&
(wise(john))&
(?[X]:(calm(X)))&
(?[X]:(~tall(X)))&
((~strong(lucy)&~brave(lucy)))&
(patient(lucy)) | humble(lucy) | [
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5941122005983658984547778
% SZS output start Proof for 5941122005983658984547778
3. ! [X0] : ((~old(X0) & curious(X0)) <=> old(X0)) [input p2]
7. ! [X0] : ((funny(X0) | ~funny(X0)) => (~humble(X0) | curious(X0))) [input p6]
25. humble(lucy) [input hypothesis]
32. ! [X0] : ((~humble(X0) | curious(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 7]
33. ! [X0] : (~humble(X0) | curious(X0) | (~funny(X0) & funny(X0))) [flattening 32]
48. ! [X0] : (((~old(X0) & curious(X0)) | ~old(X0)) & (old(X0) | (old(X0) | ~curious(X0)))) [nnf transformation 3]
49. ! [X0] : (((~old(X0) & curious(X0)) | ~old(X0)) & (old(X0) | old(X0) | ~curious(X0))) [flattening 48]
89. old(X0) | old(X0) | ~curious(X0) [cnf transformation 49]
91. ~old(X0) | ~old(X0) [cnf transformation 49]
106. ~humble(X0) | curious(X0) | funny(X0) [cnf transformation 33]
107. ~humble(X0) | curious(X0) | ~funny(X0) [cnf transformation 33]
146. humble(lucy) [cnf transformation 25]
150. old(X0) | ~curious(X0) [duplicate literal removal 89]
151. ~old(X0) [duplicate literal removal 91]
186. ~curious(X0) [subsumption resolution 150,151]
190. ~humble(X0) | ~funny(X0) [subsumption resolution 107,186]
191. ~humble(X0) | funny(X0) [subsumption resolution 106,186]
192. ~humble(X0) [subsumption resolution 191,190]
253. $false [subsumption resolution 146,192]
% SZS output end Proof for 5941122005983658984547778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or old is strong. Everyone who is either not creative or not happy is humble or not creative and vice versa. Everyone who is rich is either not creative or creative. If lucy is both not quiet and funny then someone is either creative or strong and vice versa. Everyone who is happy or not calm is either old or not patient. If someone is not rich then someone is not happy or generous and vice versa. Everyone who is not calm is not old or humble and vice versa. Everyone who is either not rich or quiet is not creative. If lucy is not patient then lucy is patient. Everyone who is not creative is both not creative and not brave. If fred is both rich and not creative then lucy is not quiet and vice versa. Everyone who is generous is either happy or humble and vice versa. Everyone who is 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. Paul is both not kind and brave. Susan is both not happy and funny. Someone is not wise. Alice is not tall or rich. Paul is not old. Someone is both not old and not patient. Someone is strong. Someone is both rich and funny. | Susan is creative. | entailment | (![X]:((~rich(X)<~>old(X))=>strong(X)))&
(![X]:((~creative(X)<~>~happy(X))<=>(humble(X)|~creative(X))))&
(![X]:(rich(X)=>(~creative(X)<~>creative(X))))&
(((~quiet(lucy)&funny(lucy)))<=>(?[X]:((creative(X)<~>strong(X)))))&
(![X]:((happy(X)|~calm(X))=>(old(X)<~>~patient(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:(~calm(X)<=>(~old(X)|humble(X))))&
(![X]:((~rich(X)<~>quiet(X))=>~creative(X)))&
((~patient(lucy))=>(patient(lucy)))&
(![X]:(~creative(X)=>(~creative(X)&~brave(X))))&
(((rich(fred)&~creative(fred)))<=>(~quiet(lucy)))&
(![X]:(generous(X)<=>(happy(X)<~>humble(X))))&
(![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)))&
((~kind(paul)&brave(paul)))&
((~happy(susan)&funny(susan)))&
(?[X]:(~wise(X)))&
((~tall(alice)|rich(alice)))&
(~old(paul))&
(?[X]:((~old(X)&~patient(X))))&
(?[X]:(strong(X)))&
(?[X]:((rich(X)&funny(X)))) | creative(susan) | [
"p1",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1021105078672910000589487
% SZS output start Proof for 1021105078672910000589487
2. ! [X0] : ((~creative(X0) <~> ~happy(X0)) <=> (~creative(X0) | humble(X0))) [input p1]
18. funny(susan) & ~happy(susan) [input p17]
25. ~creative(susan) [input hypothesis]
40. ! [X0] : ((((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | (creative(X0) & ~humble(X0))) & ((~creative(X0) | humble(X0)) | ((~creative(X0) | happy(X0)) & (~happy(X0) | creative(X0))))) [nnf transformation 2]
41. ! [X0] : ((((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | (creative(X0) & ~humble(X0))) & (~creative(X0) | humble(X0) | ((~creative(X0) | happy(X0)) & (~happy(X0) | creative(X0))))) [flattening 40]
80. happy(X0) | creative(X0) | creative(X0) [cnf transformation 41]
124. ~happy(susan) [cnf transformation 18]
133. ~creative(susan) [cnf transformation 25]
136. happy(X0) | creative(X0) [duplicate literal removal 80]
254. creative(susan) [resolution 136,124]
256. $false [subsumption resolution 254,133]
% SZS output end Proof for 1021105078672910000589487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both creative and not creative then someone is not generous or curious.
If susan is either not calm or rich then someone is not calm or quiet and vice versa.
If someone is not quiet or not patient then alice is generous or not brave.
Everyone who is not generous or brave is not calm or curious and vice versa.
If lucy is either old or brave then alice is humble and vice versa.
Everyone who is either not happy or not creative is not curious or not old.
Everyone who is both not calm and not wise is not humble or humble.
If susan is both not patient and not funny then mary is not creative or generous.
If someone is not rich or not brave then john is not funny.
Everyone who is both generous and not funny is not creative.
If susan is not wise or not creative then mary is calm.
If someone is either quiet or generous then someone is rich and vice versa.
Everyone who is calm or not happy is old and vice versa.
If mary is both not old and calm then someone is brave and vice versa.
Everyone who is either generous or not humble is not rich or not patient and vice versa.
If someone is both calm and old then paul is either not kind or generous and vice versa.
John is either wise or not generous.
Mary is strong.
Someone is not strong.
Someone is either patient or humble.
Someone is not quiet or not funny.
Someone is either patient or old. | Lucy is patient. | neutral | (((creative(paul)&~creative(paul)))=>(?[X]:((~generous(X)|curious(X)))))&
(((~calm(susan)<~>rich(susan)))<=>(?[X]:((~calm(X)|quiet(X)))))&
((?[X]:((~quiet(X)|~patient(X))))=>((generous(alice)|~brave(alice))))&
(![X]:((~generous(X)|brave(X))<=>(~calm(X)|curious(X))))&
(((old(lucy)<~>brave(lucy)))<=>(humble(alice)))&
(![X]:((~happy(X)<~>~creative(X))=>(~curious(X)|~old(X))))&
(![X]:((~calm(X)&~wise(X))=>(~humble(X)|humble(X))))&
(((~patient(susan)&~funny(susan)))=>((~creative(mary)|generous(mary))))&
((?[X]:((~rich(X)|~brave(X))))=>(~funny(john)))&
(![X]:((generous(X)&~funny(X))=>~creative(X)))&
(((~wise(susan)|~creative(susan)))=>(calm(mary)))&
((?[X]:((quiet(X)<~>generous(X))))<=>(?[X]:(rich(X))))&
(![X]:((calm(X)|~happy(X))<=>old(X)))&
(((~old(mary)&calm(mary)))<=>(?[X]:(brave(X))))&
(![X]:((generous(X)<~>~humble(X))<=>(~rich(X)|~patient(X))))&
((?[X]:((calm(X)&old(X))))<=>((~kind(paul)<~>generous(paul))))&
((wise(john)<~>~generous(john)))&
(strong(mary))&
(?[X]:(~strong(X)))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((~quiet(X)|~funny(X))))&
(?[X]:((patient(X)<~>old(X)))) | patient(lucy) | [] | null | 0 |
Everyone who is either not quiet or not creative is not old and vice versa. Everyone who is both not rich and calm is either not wise or wise and vice versa. Everyone who is wise is funny and vice versa. Everyone who is not curious is both not old and patient and vice versa. If susan is both not wise and not generous then someone is not humble or strong and vice versa. If someone is either not rich or generous then fred is happy and vice versa. If someone is not happy then lucy is either tall or not generous and vice versa. Everyone who is kind or wise is generous and vice versa. If someone is not strong then lucy is either not old or not curious and vice versa. Everyone who is both curious and kind is curious or patient and vice versa. If alice is wise then someone is not rich or not humble and vice versa. If lucy is both not calm and rich then someone is either kind or rich. Everyone who is strong is either not curious or old. Everyone who is creative is either not curious or not old and vice versa. Everyone who is tall or brave is either tall or rich and vice versa. Someone is either not kind or not rich. Susan is either generous or not brave. John is either not kind or brave. Mary is not patient or not happy. | Mary is funny. | neutral | (![X]:((~quiet(X)<~>~creative(X))<=>~old(X)))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)<~>wise(X))))&
(![X]:(wise(X)<=>funny(X)))&
(![X]:(~curious(X)<=>(~old(X)&patient(X))))&
(((~wise(susan)&~generous(susan)))<=>(?[X]:((~humble(X)|strong(X)))))&
((?[X]:((~rich(X)<~>generous(X))))<=>(happy(fred)))&
((?[X]:(~happy(X)))<=>((tall(lucy)<~>~generous(lucy))))&
(![X]:((kind(X)|wise(X))<=>generous(X)))&
((?[X]:(~strong(X)))<=>((~old(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&kind(X))<=>(curious(X)|patient(X))))&
((wise(alice))<=>(?[X]:((~rich(X)|~humble(X)))))&
(((~calm(lucy)&rich(lucy)))=>(?[X]:((kind(X)<~>rich(X)))))&
(![X]:(strong(X)=>(~curious(X)<~>old(X))))&
(![X]:(creative(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((tall(X)|brave(X))<=>(tall(X)<~>rich(X))))&
(?[X]:((~kind(X)<~>~rich(X))))&
((generous(susan)<~>~brave(susan)))&
((~kind(john)<~>brave(john)))&
((~patient(mary)|~happy(mary))) | funny(mary) | [] | null | 0 |
Everyone who is calm or rich is not brave.
Everyone who is both not strong and not generous is either brave or happy.
Everyone who is funny or tall is either rich or wise and vice versa.
Everyone who is happy or not generous is funny and vice versa.
Everyone who is both not funny and happy is not tall or funny and vice versa.
Everyone who is curious is not kind or not funny.
If someone is not quiet then someone is old or not quiet and vice versa.
If someone is not curious or curious then alice is not wise and vice versa.
If mary is either not rich or calm then alice is curious.
If fred is either creative or funny then someone is not wise and vice versa.
Everyone who is not strong is either patient or not kind.
If someone is rich then someone is either not wise or strong and vice versa.
Everyone who is either not calm or not rich is both not strong and old and vice versa.
If someone is not funny then someone is either old or creative and vice versa.
Everyone who is not creative or tall is not curious or tall.
Someone is either quiet or not quiet.
Someone is curious or not quiet.
Someone is either not patient or creative.
Someone is funny or wise.
John is either not rich or kind.
Mary is either wise or happy.
Someone is not old or not wise. | Alice is not calm. | neutral | (![X]:((calm(X)|rich(X))=>~brave(X)))&
(![X]:((~strong(X)&~generous(X))=>(brave(X)<~>happy(X))))&
(![X]:((funny(X)|tall(X))<=>(rich(X)<~>wise(X))))&
(![X]:((happy(X)|~generous(X))<=>funny(X)))&
(![X]:((~funny(X)&happy(X))<=>(~tall(X)|funny(X))))&
(![X]:(curious(X)=>(~kind(X)|~funny(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((old(X)|~quiet(X)))))&
((?[X]:((~curious(X)|curious(X))))<=>(~wise(alice)))&
(((~rich(mary)<~>calm(mary)))=>(curious(alice)))&
(((creative(fred)<~>funny(fred)))<=>(?[X]:(~wise(X))))&
(![X]:(~strong(X)=>(patient(X)<~>~kind(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:((~calm(X)<~>~rich(X))<=>(~strong(X)&old(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((~creative(X)|tall(X))=>(~curious(X)|tall(X))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
(?[X]:((curious(X)|~quiet(X))))&
(?[X]:((~patient(X)<~>creative(X))))&
(?[X]:((funny(X)|wise(X))))&
((~rich(john)<~>kind(john)))&
((wise(mary)<~>happy(mary)))&
(?[X]:((~old(X)|~wise(X)))) | ~calm(alice) | [] | null | 0 |
Everyone who is not curious or not humble is both not humble and not creative and vice versa. Everyone who is either strong or brave is creative and vice versa. If susan is not quiet or brave then fred is either not happy or not generous. Everyone who is either generous or not calm is not strong and vice versa. Everyone who is curious or not curious is either calm or not quiet and vice versa. If paul is either happy or old then someone is either not funny or happy and vice versa. If mary is happy or wise then someone is happy. Everyone who is either generous or not humble is either not brave or funny. Everyone who is either patient or not old is not strong and vice versa. If fred is not generous or not rich then someone is either brave or quiet. Everyone who is both not happy and not funny is not curious or calm. If fred is generous then someone is both strong and not funny. If alice is both not humble and humble then someone is not happy or not brave. If lucy is rich then someone is both not creative and not happy and vice versa. If someone is either not tall or not brave then susan is both kind and not calm and vice versa. Everyone who is funny is either strong or not old. Someone is both brave and not old. Someone is both humble and not old. John is either not patient or not tall. Lucy is either not happy or patient. Mary is brave or quiet. Lucy is either not creative or curious. Susan is both not wise and kind. | Susan is not generous. | neutral | (![X]:((~curious(X)|~humble(X))<=>(~humble(X)&~creative(X))))&
(![X]:((strong(X)<~>brave(X))<=>creative(X)))&
(((~quiet(susan)|brave(susan)))=>((~happy(fred)<~>~generous(fred))))&
(![X]:((generous(X)<~>~calm(X))<=>~strong(X)))&
(![X]:((curious(X)|~curious(X))<=>(calm(X)<~>~quiet(X))))&
(((happy(paul)<~>old(paul)))<=>(?[X]:((~funny(X)<~>happy(X)))))&
(((happy(mary)|wise(mary)))=>(?[X]:(happy(X))))&
(![X]:((generous(X)<~>~humble(X))=>(~brave(X)<~>funny(X))))&
(![X]:((patient(X)<~>~old(X))<=>~strong(X)))&
(((~generous(fred)|~rich(fred)))=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((~happy(X)&~funny(X))=>(~curious(X)|calm(X))))&
((generous(fred))=>(?[X]:((strong(X)&~funny(X)))))&
(((~humble(alice)&humble(alice)))=>(?[X]:((~happy(X)|~brave(X)))))&
((rich(lucy))<=>(?[X]:((~creative(X)&~happy(X)))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>((kind(susan)&~calm(susan))))&
(![X]:(funny(X)=>(strong(X)<~>~old(X))))&
(?[X]:((brave(X)&~old(X))))&
(?[X]:((humble(X)&~old(X))))&
((~patient(john)<~>~tall(john)))&
((~happy(lucy)<~>patient(lucy)))&
((brave(mary)|quiet(mary)))&
((~creative(lucy)<~>curious(lucy)))&
((~wise(susan)&kind(susan))) | ~generous(susan) | [] | null | 0 |
If someone is both not old and not humble then someone is kind or creative.
Everyone who is both kind and not generous is either generous or not generous and vice versa.
Everyone who is wise is either not generous or old and vice versa.
Everyone who is brave or not curious is generous.
Everyone who is not patient or creative is either happy or wise.
Everyone who is curious is either not kind or not quiet and vice versa.
If someone is not quiet or not strong then someone is both not creative and strong.
Everyone who is either quiet or calm is patient or not creative and vice versa.
Everyone who is both generous and creative is strong or not humble.
Everyone who is not curious is either not old or funny.
If alice is funny then mary is both not brave and not creative and vice versa.
If someone is both funny and not happy then fred is not calm or old.
If someone is both rich and humble then someone is both wise and not brave and vice versa.
If someone is creative or not rich then john is funny and vice versa.
If someone is both calm and not creative then someone is creative or not kind.
Someone is brave or not creative.
Paul is either not generous or not curious.
Paul is both not happy and not calm.
Paul is not funny or curious.
Someone is both not strong and not old.
Fred is not rich.
Paul is either generous or rich. | Paul is creative. | entailment | ((?[X]:((~old(X)&~humble(X))))=>(?[X]:((kind(X)|creative(X)))))&
(![X]:((kind(X)&~generous(X))<=>(generous(X)<~>~generous(X))))&
(![X]:(wise(X)<=>(~generous(X)<~>old(X))))&
(![X]:((brave(X)|~curious(X))=>generous(X)))&
(![X]:((~patient(X)|creative(X))=>(happy(X)<~>wise(X))))&
(![X]:(curious(X)<=>(~kind(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)|~strong(X))))=>(?[X]:((~creative(X)&strong(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(patient(X)|~creative(X))))&
(![X]:((generous(X)&creative(X))=>(strong(X)|~humble(X))))&
(![X]:(~curious(X)=>(~old(X)<~>funny(X))))&
((funny(alice))<=>((~brave(mary)&~creative(mary))))&
((?[X]:((funny(X)&~happy(X))))=>((~calm(fred)|old(fred))))&
((?[X]:((rich(X)&humble(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
((?[X]:((creative(X)|~rich(X))))<=>(funny(john)))&
((?[X]:((calm(X)&~creative(X))))=>(?[X]:((creative(X)|~kind(X)))))&
(?[X]:((brave(X)|~creative(X))))&
((~generous(paul)<~>~curious(paul)))&
((~happy(paul)&~calm(paul)))&
((~funny(paul)|curious(paul)))&
(?[X]:((~strong(X)&~old(X))))&
(~rich(fred))&
((generous(paul)<~>rich(paul))) | creative(paul) | [
"p1",
"p3",
"p5",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2026908335676321659228220
% SZS output start Proof for 2026908335676321659228220
2. ! [X0] : ((~generous(X0) & kind(X0)) <=> (generous(X0) <~> ~generous(X0))) [input p1]
4. ! [X0] : ((~curious(X0) | brave(X0)) => generous(X0)) [input p3]
6. ! [X0] : (curious(X0) <=> (~kind(X0) <~> ~quiet(X0))) [input p5]
8. ! [X0] : ((quiet(X0) <~> calm(X0)) <=> (~creative(X0) | patient(X0))) [input p7]
18. ~calm(paul) & ~happy(paul) [input p17]
23. ~creative(paul) [input hypothesis]
29. ! [X0] : (generous(X0) | (curious(X0) & ~brave(X0))) [ennf transformation 4]
41. ! [X0] : (((~generous(X0) & kind(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | (generous(X0) | ~kind(X0)))) [nnf transformation 2]
42. ! [X0] : (((~generous(X0) & kind(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | generous(X0) | ~kind(X0))) [flattening 41]
45. ! [X0] : ((curious(X0) | ((~kind(X0) | quiet(X0)) & (~quiet(X0) | kind(X0)))) & (((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) | ~curious(X0))) [nnf transformation 6]
49. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [nnf transformation 8]
50. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [flattening 49]
76. kind(X0) | generous(X0) | generous(X0) [cnf transformation 42]
77. ~generous(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 42]
84. generous(X0) | curious(X0) [cnf transformation 29]
89. ~quiet(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 45]
100. calm(X0) | quiet(X0) | creative(X0) [cnf transformation 50]
122. ~calm(paul) [cnf transformation 18]
129. ~creative(paul) [cnf transformation 23]
133. kind(X0) | generous(X0) [duplicate literal removal 76]
134. ~generous(X0) [duplicate literal removal 77]
148. kind(X0) [subsumption resolution 133,134]
151. curious(X0) [subsumption resolution 84,134]
153. ~quiet(X0) | ~curious(X0) [subsumption resolution 89,148]
154. ~quiet(X0) [subsumption resolution 153,151]
172. calm(X0) | creative(X0) [subsumption resolution 100,154]
260. creative(paul) [resolution 172,122]
262. $false [subsumption resolution 260,129]
% SZS output end Proof for 2026908335676321659228220
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and brave then lucy is wise or not creative and vice versa.
If someone is tall or rich then susan is not old or not curious.
Everyone who is not calm or not brave is both happy and not wise and vice versa.
Everyone who is either happy or not creative is either not calm or not curious and vice versa.
If fred is not funny or not kind then someone is funny.
Everyone who is not kind or not quiet is both not humble and happy and vice versa.
Everyone who is both happy and not kind is not old.
If someone is either not rich or creative then alice is creative and vice versa.
Everyone who is creative or curious is not kind or not creative.
Everyone who is not brave is not curious or not humble and vice versa.
If someone is either happy or not rich then someone is either not humble or not rich and vice versa.
If john is both funny and tall then susan is either not humble or funny.
Everyone who is not calm or not curious is kind.
If someone is both not quiet and patient then fred is patient and vice versa.
If john is both quiet and old then susan is not humble and vice versa.
Everyone who is not generous is not brave and vice versa.
Lucy is either not kind or not rich.
Someone is generous.
Someone is not old.
Someone is not wise.
Someone is both tall and strong. | Lucy is happy. | entailment | ((?[X]:((patient(X)&brave(X))))<=>((wise(lucy)|~creative(lucy))))&
((?[X]:((tall(X)|rich(X))))=>((~old(susan)|~curious(susan))))&
(![X]:((~calm(X)|~brave(X))<=>(happy(X)&~wise(X))))&
(![X]:((happy(X)<~>~creative(X))<=>(~calm(X)<~>~curious(X))))&
(((~funny(fred)|~kind(fred)))=>(?[X]:(funny(X))))&
(![X]:((~kind(X)|~quiet(X))<=>(~humble(X)&happy(X))))&
(![X]:((happy(X)&~kind(X))=>~old(X)))&
((?[X]:((~rich(X)<~>creative(X))))<=>(creative(alice)))&
(![X]:((creative(X)|curious(X))=>(~kind(X)|~creative(X))))&
(![X]:(~brave(X)<=>(~curious(X)|~humble(X))))&
((?[X]:((happy(X)<~>~rich(X))))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
(((funny(john)&tall(john)))=>((~humble(susan)<~>funny(susan))))&
(![X]:((~calm(X)|~curious(X))=>kind(X)))&
((?[X]:((~quiet(X)&patient(X))))<=>(patient(fred)))&
(((quiet(john)&old(john)))<=>(~humble(susan)))&
(![X]:(~generous(X)<=>~brave(X)))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~old(X)))&
(?[X]:(~wise(X)))&
(?[X]:((tall(X)&strong(X)))) | happy(lucy) | [
"p2",
"p3",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 637786532728707104161690
% SZS output start Proof for 637786532728707104161690
3. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (~wise(X0) & happy(X0))) [input p2]
4. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> (~calm(X0) <~> ~curious(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> (happy(X0) & ~humble(X0))) [input p5]
9. ! [X0] : ((curious(X0) | creative(X0)) => (~creative(X0) | ~kind(X0))) [input p8]
10. ! [X0] : (~brave(X0) <=> (~humble(X0) | ~curious(X0))) [input p9]
22. ~happy(lucy) [input hypothesis]
31. ! [X0] : ((~creative(X0) | ~kind(X0)) | (~curious(X0) & ~creative(X0))) [ennf transformation 9]
32. ! [X0] : (~creative(X0) | ~kind(X0) | (~curious(X0) & ~creative(X0))) [flattening 31]
42. ! [X0] : (((~brave(X0) | ~calm(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 3]
43. ! [X0] : ((~brave(X0) | ~calm(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (brave(X0) & calm(X0)))) [flattening 42]
44. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0)))) & (((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 4]
47. ! [X0] : (((~quiet(X0) | ~kind(X0)) | (~happy(X0) | humble(X0))) & ((happy(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [nnf transformation 6]
48. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~happy(X0) | humble(X0)) & ((happy(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [flattening 47]
53. ! [X0] : ((~brave(X0) | (humble(X0) & curious(X0))) & ((~humble(X0) | ~curious(X0)) | brave(X0))) [nnf transformation 10]
54. ! [X0] : ((~brave(X0) | (humble(X0) & curious(X0))) & (~humble(X0) | ~curious(X0) | brave(X0))) [flattening 53]
83. happy(X0) | calm(X0) [cnf transformation 43]
84. happy(X0) | brave(X0) [cnf transformation 43]
89. ~curious(X0) | ~calm(X0) | happy(X0) | creative(X0) [cnf transformation 44]
98. ~humble(X0) | kind(X0) [cnf transformation 48]
109. ~kind(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 32]
111. ~brave(X0) | curious(X0) [cnf transformation 54]
112. ~brave(X0) | humble(X0) [cnf transformation 54]
138. ~happy(lucy) [cnf transformation 22]
141. 1 <=> creative(lucy) [avatar definition]
142. ~creative(lucy) <- (~1) [avatar component clause 141]
183. ~curious(X0) | happy(X0) | creative(X0) [subsumption resolution 89,83]
305. 36 <=> kind(lucy) [avatar definition]
307. kind(lucy) <- (36) [avatar component clause 305]
316. brave(lucy) [resolution 84,138]
325. curious(lucy) [resolution 111,316]
328. humble(lucy) [resolution 112,316]
348. kind(lucy) [resolution 328,98]
395. 36 [avatar split clause 348,305]
399. ~creative(lucy) | ~curious(lucy) <- (36) [resolution 307,109]
407. ~creative(lucy) <- (36) [subsumption resolution 399,325]
408. ~1 | ~36 [avatar split clause 407,305,141]
423. happy(lucy) | creative(lucy) [resolution 183,325]
426. creative(lucy) [subsumption resolution 423,138]
427. $false <- (~1) [subsumption resolution 426,142]
428. 1 [avatar contradiction clause 427]
430. $false [avatar sat refutation 395,408,428]
% SZS output end Proof for 637786532728707104161690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is 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. | Paul is brave. | entailment | ((?[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)))) | brave(paul) | [
"p6",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5651984616859046594472180
% SZS output start Proof for 5651984616859046594472180
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. ~brave(paul) [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]
93. strong(X0) | brave(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. ~brave(paul) [cnf transformation 23]
151. 4 <=> ! [X1] : brave(X1) [avatar definition]
152. brave(X1) <- (4) [avatar component clause 151]
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]
323. brave(sK4) <- (~18) [resolution 95,216]
326. 17 | 18 [avatar split clause 323,214,209]
329. kind(X0) | brave(X0) [resolution 234,93]
331. brave(X0) <- (16) [subsumption resolution 329,207]
332. 4 | ~16 [avatar split clause 331,206,151]
336. $false <- (4) [resolution 152,137]
339. ~4 [avatar contradiction clause 336]
341. $false [avatar sat refutation 212,217,326,332,339]
% SZS output end Proof for 5651984616859046594472180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both quiet and not strong then lucy is both old and curious.
Everyone who is both curious and tall is either curious or not curious and vice versa.
If someone is brave or happy then paul is both rich and not calm.
If someone is not patient then paul is not tall and vice versa.
If someone is either not funny or strong then john is either quiet or not strong and vice versa.
Everyone who is calm or not brave is both happy and patient and vice versa.
If alice is happy or not kind then lucy is wise or curious.
Everyone who is both wise and not calm is not creative or not funny.
If someone is either not humble or not kind then someone is both old and not happy.
If mary is wise or brave then someone is both not humble and not happy.
Everyone who is both curious and happy is not humble or not rich and vice versa.
If someone is both not brave and not curious then someone is both tall and not kind and vice versa.
If someone is not old then someone is both not generous and humble and vice versa.
Everyone who is both kind and tall is old or not strong and vice versa.
Everyone who is tall is either not strong or not patient and vice versa.
Everyone who is not rich is both not old and patient and vice versa.
John is patient or creative.
Someone is not happy or not funny.
Someone is both humble and tall.
Lucy is either not rich or happy.
Someone is both quiet and not brave. | Paul is patient. | entailment | (((quiet(lucy)&~strong(lucy)))=>((old(lucy)&curious(lucy))))&
(![X]:((curious(X)&tall(X))<=>(curious(X)<~>~curious(X))))&
((?[X]:((brave(X)|happy(X))))=>((rich(paul)&~calm(paul))))&
((?[X]:(~patient(X)))<=>(~tall(paul)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((quiet(john)<~>~strong(john))))&
(![X]:((calm(X)|~brave(X))<=>(happy(X)&patient(X))))&
(((happy(alice)|~kind(alice)))=>((wise(lucy)|curious(lucy))))&
(![X]:((wise(X)&~calm(X))=>(~creative(X)|~funny(X))))&
((?[X]:((~humble(X)<~>~kind(X))))=>(?[X]:((old(X)&~happy(X)))))&
(((wise(mary)|brave(mary)))=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((curious(X)&happy(X))<=>(~humble(X)|~rich(X))))&
((?[X]:((~brave(X)&~curious(X))))<=>(?[X]:((tall(X)&~kind(X)))))&
((?[X]:(~old(X)))<=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((kind(X)&tall(X))<=>(old(X)|~strong(X))))&
(![X]:(tall(X)<=>(~strong(X)<~>~patient(X))))&
(![X]:(~rich(X)<=>(~old(X)&patient(X))))&
((patient(john)|creative(john)))&
(?[X]:((~happy(X)|~funny(X))))&
(?[X]:((humble(X)&tall(X))))&
((~rich(lucy)<~>happy(lucy)))&
(?[X]:((quiet(X)&~brave(X)))) | patient(paul) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8971206507298958008169138
% SZS output start Proof for 8971206507298958008169138
2. ! [X0] : ((tall(X0) & curious(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p1]
4. ? [X0] : ~patient(X0) <=> ~tall(paul) [input p3]
22. ~patient(paul) [input hypothesis]
35. ! [X0] : (((tall(X0) & curious(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (~tall(X0) | ~curious(X0)))) [nnf transformation 2]
36. ! [X0] : (((tall(X0) & curious(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ~tall(X0) | ~curious(X0))) [flattening 35]
37. (? [X0] : ~patient(X0) | tall(paul)) & (~tall(paul) | ! [X0] : patient(X0)) [nnf transformation 4]
38. (? [X0] : ~patient(X0) | tall(paul)) & (~tall(paul) | ! [X1] : patient(X1)) [rectify 37]
39. ? [X0] : ~patient(X0) => ~patient(sK0) [choice axiom]
40. (~patient(sK0) | tall(paul)) & (~tall(paul) | ! [X1] : patient(X1)) [skolemisation 38,39]
83. tall(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 36]
84. tall(X0) | curious(X0) | curious(X0) [cnf transformation 36]
89. ~tall(paul) | patient(X1) [cnf transformation 40]
147. ~patient(paul) [cnf transformation 22]
152. tall(X0) | ~curious(X0) [duplicate literal removal 83]
153. tall(X0) | curious(X0) [duplicate literal removal 84]
172. tall(X0) [subsumption resolution 152,153]
191. patient(X1) [subsumption resolution 89,172]
301. $false [subsumption resolution 147,191]
% SZS output end Proof for 8971206507298958008169138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and funny is not tall and vice versa. Everyone who is not tall is quiet or not humble. If mary is not tall then someone is not rich or not brave and vice versa. If john is either calm or not strong then someone is not wise or quiet. If someone is not curious or not wise then someone is curious or not creative. Everyone who is quiet is either creative or quiet. Everyone who is either rich or not humble is not patient and vice versa. Everyone who is either strong or not brave is creative and vice versa. Everyone who is either strong or humble is either generous or calm and vice versa. Everyone who is either not happy or not curious is either brave or strong. If someone is curious then paul is not happy or generous. Everyone who is either creative or not kind is humble and vice versa. Everyone who is not curious or not kind is both not tall and rich. If paul is either strong or generous then someone is patient and vice versa. If someone is both not old and happy then alice is either humble or quiet and vice versa. If someone is either not creative or not strong then someone is not quiet or creative. Someone is creative. Someone is either not curious or generous. Alice is either not patient or calm. Lucy is calm. Mary is either not calm or strong. Lucy is happy or funny. Someone is either not rich or creative. Someone is both not calm and patient. | Mary is not rich. | contradiction | (![X]:((~funny(X)&funny(X))<=>~tall(X)))&
(![X]:(~tall(X)=>(quiet(X)|~humble(X))))&
((~tall(mary))<=>(?[X]:((~rich(X)|~brave(X)))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((~wise(X)|quiet(X)))))&
((?[X]:((~curious(X)|~wise(X))))=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(quiet(X)=>(creative(X)<~>quiet(X))))&
(![X]:((rich(X)<~>~humble(X))<=>~patient(X)))&
(![X]:((strong(X)<~>~brave(X))<=>creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~happy(X)<~>~curious(X))=>(brave(X)<~>strong(X))))&
((?[X]:(curious(X)))=>((~happy(paul)|generous(paul))))&
(![X]:((creative(X)<~>~kind(X))<=>humble(X)))&
(![X]:((~curious(X)|~kind(X))=>(~tall(X)&rich(X))))&
(((strong(paul)<~>generous(paul)))<=>(?[X]:(patient(X))))&
((?[X]:((~old(X)&happy(X))))<=>((humble(alice)<~>quiet(alice))))&
((?[X]:((~creative(X)<~>~strong(X))))=>(?[X]:((~quiet(X)|creative(X)))))&
(?[X]:(creative(X)))&
(?[X]:((~curious(X)<~>generous(X))))&
((~patient(alice)<~>calm(alice)))&
(calm(lucy))&
((~calm(mary)<~>strong(mary)))&
((happy(lucy)|funny(lucy)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((~calm(X)&patient(X)))) | ~rich(mary) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 104991994315781022927380
% SZS output start Proof for 104991994315781022927380
1. ! [X0] : ((funny(X0) & ~funny(X0)) <=> ~tall(X0)) [input p0]
3. ~tall(mary) <=> ? [X0] : (~brave(X0) | ~rich(X0)) [input p2]
25. ~rich(mary) [input hypothesis]
38. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) | funny(X0)))) [nnf transformation 1]
39. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | ~funny(X0) | funny(X0))) [flattening 38]
40. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X0] : (~brave(X0) | ~rich(X0)) | tall(mary)) [nnf transformation 3]
41. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X1] : (~brave(X1) | ~rich(X1)) | tall(mary)) [rectify 40]
42. ? [X1] : (~brave(X1) | ~rich(X1)) => (~brave(sK0) | ~rich(sK0)) [choice axiom]
43. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & ((~brave(sK0) | ~rich(sK0)) | tall(mary)) [skolemisation 41,42]
81. ~funny(X0) | tall(X0) [cnf transformation 39]
82. funny(X0) | tall(X0) [cnf transformation 39]
85. ~tall(mary) | rich(X0) [cnf transformation 43]
147. ~rich(mary) [cnf transformation 25]
149. tall(X0) [subsumption resolution 81,82]
151. rich(X0) [subsumption resolution 85,149]
287. $false [subsumption resolution 147,151]
% SZS output end Proof for 104991994315781022927380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not calm then alice is kind or not rich and vice versa.
If someone is rich then fred is humble.
Everyone who is either rich or not quiet is funny.
If lucy is not brave or not patient then someone is both strong and kind.
Everyone who is both not wise and kind is either not brave or patient.
Everyone who is not funny is both not generous and not brave.
Everyone who is either patient or tall is not wise or not brave and vice versa.
If someone is funny or patient then someone is happy.
Everyone who is not quiet or not strong is not strong and vice versa.
If lucy is both not tall and patient then someone is humble or funny.
Everyone who is humble or not rich is both generous and quiet and vice versa.
If someone is happy or patient then someone is not curious or curious and vice versa.
Everyone who is not happy is not patient and vice versa.
Everyone who is not strong or not brave is not humble or tall.
If mary is happy then john is not rich.
Everyone who is not strong is either curious or not creative and vice versa.
John is not creative.
Paul is either generous or calm.
Someone is calm or not humble.
Someone is not strong or not wise.
Fred is both not rich and not humble.
Someone is not curious or rich.
Lucy is kind. | Lucy is brave. | neutral | ((?[X]:((~patient(X)&~calm(X))))<=>((kind(alice)|~rich(alice))))&
((?[X]:(rich(X)))=>(humble(fred)))&
(![X]:((rich(X)<~>~quiet(X))=>funny(X)))&
(((~brave(lucy)|~patient(lucy)))=>(?[X]:((strong(X)&kind(X)))))&
(![X]:((~wise(X)&kind(X))=>(~brave(X)<~>patient(X))))&
(![X]:(~funny(X)=>(~generous(X)&~brave(X))))&
(![X]:((patient(X)<~>tall(X))<=>(~wise(X)|~brave(X))))&
((?[X]:((funny(X)|patient(X))))=>(?[X]:(happy(X))))&
(![X]:((~quiet(X)|~strong(X))<=>~strong(X)))&
(((~tall(lucy)&patient(lucy)))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:((humble(X)|~rich(X))<=>(generous(X)&quiet(X))))&
((?[X]:((happy(X)|patient(X))))<=>(?[X]:((~curious(X)|curious(X)))))&
(![X]:(~happy(X)<=>~patient(X)))&
(![X]:((~strong(X)|~brave(X))=>(~humble(X)|tall(X))))&
((happy(mary))=>(~rich(john)))&
(![X]:(~strong(X)<=>(curious(X)<~>~creative(X))))&
(~creative(john))&
((generous(paul)<~>calm(paul)))&
(?[X]:((calm(X)|~humble(X))))&
(?[X]:((~strong(X)|~wise(X))))&
((~rich(fred)&~humble(fred)))&
(?[X]:((~curious(X)|rich(X))))&
(kind(lucy)) | brave(lucy) | [] | null | 0 |
If john is both not tall and happy then someone is both quiet and not creative.
Everyone who is both not patient and funny is either not funny or not wise.
If someone is not kind or not patient then someone is either kind or not brave and vice versa.
Everyone who is kind is not old.
Everyone who is not strong is wise or tall.
If someone is both strong and kind then lucy is not curious and vice versa.
If someone is tall then susan is generous or quiet and vice versa.
If fred is both funny and not happy then mary is quiet or not brave and vice versa.
If fred is both humble and not generous then paul is either not rich or not old.
Everyone who is either funny or not quiet is brave and vice versa.
Everyone who is not rich or not wise is both not patient and humble and vice versa.
If paul is both tall and not tall then someone is both calm and funny and vice versa.
Everyone who is either not brave or calm is either not strong or not quiet and vice versa.
If lucy is strong then someone is creative and vice versa.
Everyone who is both creative and not quiet is tall.
If susan is brave then fred is either not creative or brave.
Paul is not rich.
Mary is both generous and not calm.
Someone is happy.
Someone is patient or humble.
Someone is both not calm and rich.
Someone is both not funny and tall.
John is either humble or kind.
Alice is both not generous and not kind. | Paul is not humble. | contradiction | (((~tall(john)&happy(john)))=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~patient(X)&funny(X))=>(~funny(X)<~>~wise(X))))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:(kind(X)=>~old(X)))&
(![X]:(~strong(X)=>(wise(X)|tall(X))))&
((?[X]:((strong(X)&kind(X))))<=>(~curious(lucy)))&
((?[X]:(tall(X)))<=>((generous(susan)|quiet(susan))))&
(((funny(fred)&~happy(fred)))<=>((quiet(mary)|~brave(mary))))&
(((humble(fred)&~generous(fred)))=>((~rich(paul)<~>~old(paul))))&
(![X]:((funny(X)<~>~quiet(X))<=>brave(X)))&
(![X]:((~rich(X)|~wise(X))<=>(~patient(X)&humble(X))))&
(((tall(paul)&~tall(paul)))<=>(?[X]:((calm(X)&funny(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(~strong(X)<~>~quiet(X))))&
((strong(lucy))<=>(?[X]:(creative(X))))&
(![X]:((creative(X)&~quiet(X))=>tall(X)))&
((brave(susan))=>((~creative(fred)<~>brave(fred))))&
(~rich(paul))&
((generous(mary)&~calm(mary)))&
(?[X]:(happy(X)))&
(?[X]:((patient(X)|humble(X))))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((~funny(X)&tall(X))))&
((humble(john)<~>kind(john)))&
((~generous(alice)&~kind(alice))) | ~humble(paul) | [
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5962240704093243957550071
% SZS output start Proof for 5962240704093243957550071
11. ! [X0] : ((~wise(X0) | ~rich(X0)) <=> (humble(X0) & ~patient(X0))) [input p10]
17. ~rich(paul) [input p16]
25. ~humble(paul) [input hypothesis]
60. ! [X0] : (((~wise(X0) | ~rich(X0)) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | (wise(X0) & rich(X0)))) [nnf transformation 11]
61. ! [X0] : ((~wise(X0) | ~rich(X0) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | (wise(X0) & rich(X0)))) [flattening 60]
113. rich(X0) | humble(X0) [cnf transformation 61]
133. ~rich(paul) [cnf transformation 17]
146. ~humble(paul) [cnf transformation 25]
266. 27 <=> rich(paul) [avatar definition]
267. ~rich(paul) <- (~27) [avatar component clause 266]
311. ~27 [avatar split clause 133,266]
333. humble(paul) <- (~27) [resolution 113,267]
334. $false <- (~27) [subsumption resolution 333,146]
335. 27 [avatar contradiction clause 334]
336. $false [avatar sat refutation 311,335]
% SZS output end Proof for 5962240704093243957550071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or brave is both funny and strong.
If john is not rich then lucy is either not patient or wise.
Everyone who is not brave or quiet is humble.
If someone is both not calm and funny then someone is curious.
If someone is rich then lucy is not kind or not funny and vice versa.
Everyone who is either not brave or creative is not quiet or quiet and vice versa.
Everyone who is not happy is either generous or not generous.
If john is quiet then someone is either old or kind.
If alice is not kind then alice is either not happy or not generous.
Everyone who is funny is either not calm or not old and vice versa.
If mary is not calm or not brave then someone is both kind and creative and vice versa.
If someone is not generous or creative then john is happy or kind.
Everyone who is either not kind or not tall is either not kind or not generous.
Everyone who is either not rich or wise is calm.
If paul is either generous or kind then alice is either not calm or not tall.
Everyone who is both kind and wise is either generous or not funny and vice versa.
Someone is either not wise or humble.
Someone is funny.
Mary is both strong and brave.
Fred is either not calm or not brave.
Someone is either calm or rich.
Someone is rich.
Someone is not humble or not strong.
Mary is both not calm and not patient. | Mary is not funny. | contradiction | (![X]:((strong(X)|brave(X))=>(funny(X)&strong(X))))&
((~rich(john))=>((~patient(lucy)<~>wise(lucy))))&
(![X]:((~brave(X)|quiet(X))=>humble(X)))&
((?[X]:((~calm(X)&funny(X))))=>(?[X]:(curious(X))))&
((?[X]:(rich(X)))<=>((~kind(lucy)|~funny(lucy))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(![X]:((~kind(X)<~>~tall(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>wise(X))=>calm(X)))&
(((generous(paul)<~>kind(paul)))=>((~calm(alice)<~>~tall(alice))))&
(![X]:((kind(X)&wise(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:(funny(X)))&
((strong(mary)&brave(mary)))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((~humble(X)|~strong(X))))&
((~calm(mary)&~patient(mary))) | ~funny(mary) | [
"p0",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6937134265633328871797907
% SZS output start Proof for 6937134265633328871797907
1. ! [X0] : ((brave(X0) | strong(X0)) => (strong(X0) & funny(X0))) [input p0]
19. brave(mary) & strong(mary) [input p18]
25. ~funny(mary) [input hypothesis]
28. ! [X0] : ((strong(X0) & funny(X0)) | (~brave(X0) & ~strong(X0))) [ennf transformation 1]
76. ~strong(X0) | funny(X0) [cnf transformation 28]
129. strong(mary) [cnf transformation 19]
139. ~funny(mary) [cnf transformation 25]
305. funny(mary) [resolution 76,129]
306. $false [subsumption resolution 305,139]
% SZS output end Proof for 6937134265633328871797907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is strong then someone is rich or kind and vice versa.
If someone is both old and brave then someone is patient or old and vice versa.
If alice is both not kind and strong then someone is quiet or happy.
Everyone who is either creative or strong is both humble and strong.
Everyone who is both not old and strong is either not kind or not tall.
If someone is creative then fred is not strong or not happy.
If alice is brave then lucy is happy or not humble and vice versa.
If someone is generous then mary is funny and vice versa.
If fred is not tall or not strong then fred is both not rich and patient.
If someone is either tall or quiet then fred is both not tall and not old.
Everyone who is humble or creative is not curious or brave and vice versa.
If lucy is not patient or happy then john is either rich or generous.
If someone is both strong and calm then mary is both not wise and not humble and vice versa.
Everyone who is calm or quiet is happy or not quiet.
If mary is either wise or not funny then someone is not quiet or not wise.
If someone is both generous and not quiet then someone is not quiet and vice versa.
Someone is not quiet.
Lucy is not tall or curious.
Someone is either not generous or not tall.
Mary is either not brave or not rich.
Someone is not happy.
Lucy is either not kind or tall.
Someone is either patient or not old.
Someone is tall or not generous. | Lucy is happy. | neutral | ((strong(lucy))<=>(?[X]:((rich(X)|kind(X)))))&
((?[X]:((old(X)&brave(X))))<=>(?[X]:((patient(X)|old(X)))))&
(((~kind(alice)&strong(alice)))=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:((creative(X)<~>strong(X))=>(humble(X)&strong(X))))&
(![X]:((~old(X)&strong(X))=>(~kind(X)<~>~tall(X))))&
((?[X]:(creative(X)))=>((~strong(fred)|~happy(fred))))&
((brave(alice))<=>((happy(lucy)|~humble(lucy))))&
((?[X]:(generous(X)))<=>(funny(mary)))&
(((~tall(fred)|~strong(fred)))=>((~rich(fred)&patient(fred))))&
((?[X]:((tall(X)<~>quiet(X))))=>((~tall(fred)&~old(fred))))&
(![X]:((humble(X)|creative(X))<=>(~curious(X)|brave(X))))&
(((~patient(lucy)|happy(lucy)))=>((rich(john)<~>generous(john))))&
((?[X]:((strong(X)&calm(X))))<=>((~wise(mary)&~humble(mary))))&
(![X]:((calm(X)|quiet(X))=>(happy(X)|~quiet(X))))&
(((wise(mary)<~>~funny(mary)))=>(?[X]:((~quiet(X)|~wise(X)))))&
((?[X]:((generous(X)&~quiet(X))))<=>(?[X]:(~quiet(X))))&
(?[X]:(~quiet(X)))&
((~tall(lucy)|curious(lucy)))&
(?[X]:((~generous(X)<~>~tall(X))))&
((~brave(mary)<~>~rich(mary)))&
(?[X]:(~happy(X)))&
((~kind(lucy)<~>tall(lucy)))&
(?[X]:((patient(X)<~>~old(X))))&
(?[X]:((tall(X)|~generous(X)))) | happy(lucy) | [] | null | 0 |
Everyone who is both happy and not rich is calm or not old. Everyone who is either not generous or wise is quiet. If mary is not calm or not rich then lucy is both tall and funny. Everyone who is both not happy and not quiet is generous. If someone is either not rich or not kind then someone is not tall or happy. Everyone who is either not creative or not rich is funny. Everyone who is both brave and not humble is either not strong or not old and vice versa. If paul is not humble then someone is humble. If fred is both wise and not calm then fred is both calm and not quiet and vice versa. Everyone who is both old and not funny is both old and not happy. Everyone who is both not brave and funny is quiet and vice versa. Everyone who is rich or not patient is not patient or creative and vice versa. If alice is either not patient or humble then alice is not creative or not generous. Everyone who is either calm or creative is both not patient and not curious and vice versa. If lucy is not kind or not patient then alice is not rich and vice versa. Everyone who is either not rich or happy is not wise or quiet and vice versa. Paul is not creative or not humble. Mary is both not happy and brave. Someone is funny. John is creative or not tall. Alice is not kind or tall. Someone is funny or not calm. Someone is either not calm or not strong. | Mary is generous. | entailment | (![X]:((happy(X)&~rich(X))=>(calm(X)|~old(X))))&
(![X]:((~generous(X)<~>wise(X))=>quiet(X)))&
(((~calm(mary)|~rich(mary)))=>((tall(lucy)&funny(lucy))))&
(![X]:((~happy(X)&~quiet(X))=>generous(X)))&
((?[X]:((~rich(X)<~>~kind(X))))=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:((~creative(X)<~>~rich(X))=>funny(X)))&
(![X]:((brave(X)&~humble(X))<=>(~strong(X)<~>~old(X))))&
((~humble(paul))=>(?[X]:(humble(X))))&
(((wise(fred)&~calm(fred)))<=>((calm(fred)&~quiet(fred))))&
(![X]:((old(X)&~funny(X))=>(old(X)&~happy(X))))&
(![X]:((~brave(X)&funny(X))<=>quiet(X)))&
(![X]:((rich(X)|~patient(X))<=>(~patient(X)|creative(X))))&
(((~patient(alice)<~>humble(alice)))=>((~creative(alice)|~generous(alice))))&
(![X]:((calm(X)<~>creative(X))<=>(~patient(X)&~curious(X))))&
(((~kind(lucy)|~patient(lucy)))<=>(~rich(alice)))&
(![X]:((~rich(X)<~>happy(X))<=>(~wise(X)|quiet(X))))&
((~creative(paul)|~humble(paul)))&
((~happy(mary)&brave(mary)))&
(?[X]:(funny(X)))&
((creative(john)|~tall(john)))&
((~kind(alice)|tall(alice)))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:((~calm(X)<~>~strong(X)))) | generous(mary) | [
"p3",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5079832164214084670492000
% SZS output start Proof for 5079832164214084670492000
4. ! [X0] : ((~quiet(X0) & ~happy(X0)) => generous(X0)) [input p3]
11. ! [X0] : ((funny(X0) & ~brave(X0)) <=> quiet(X0)) [input p10]
18. brave(mary) & ~happy(mary) [input p17]
24. ~generous(mary) [input hypothesis]
30. ! [X0] : (generous(X0) | (quiet(X0) | happy(X0))) [ennf transformation 4]
31. ! [X0] : (generous(X0) | quiet(X0) | happy(X0)) [flattening 30]
51. ! [X0] : (((funny(X0) & ~brave(X0)) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) | brave(X0)))) [nnf transformation 11]
52. ! [X0] : (((funny(X0) & ~brave(X0)) | ~quiet(X0)) & (quiet(X0) | ~funny(X0) | brave(X0))) [flattening 51]
76. quiet(X0) | generous(X0) | happy(X0) [cnf transformation 31]
95. ~brave(X0) | ~quiet(X0) [cnf transformation 52]
119. ~happy(mary) [cnf transformation 18]
120. brave(mary) [cnf transformation 18]
127. ~generous(mary) [cnf transformation 24]
266. ~quiet(mary) [resolution 95,120]
271. generous(mary) | happy(mary) [resolution 76,266]
273. happy(mary) [subsumption resolution 271,127]
274. $false [subsumption resolution 273,119]
% SZS output end Proof for 5079832164214084670492000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or not rich then someone is not creative or not funny and vice versa.
Everyone who is both humble and creative is generous and vice versa.
Everyone who is both quiet and funny is both not happy and tall.
Everyone who is both not tall and not strong is not creative.
Everyone who is not strong or rich is either generous or quiet.
Everyone who is not patient or not old is both calm and not happy.
If someone is not curious or not old then susan is old or not quiet.
If alice is both generous and not brave then susan is humble.
Everyone who is patient is brave or not patient and vice versa.
If someone is both not patient and not brave then someone is either old or not patient and vice versa.
If someone is both not kind and not quiet then someone is not creative.
If someone is both not creative and not funny then fred is not happy or not old.
If someone is either wise or tall then fred is not kind.
Everyone who is both not rich and creative is not wise or not kind.
Everyone who is either not calm or old is not wise and vice versa.
If someone is humble then someone is not wise or patient and vice versa.
Someone is not old.
Fred is rich.
Someone is not humble.
Someone is tall or not kind.
Someone is old or quiet. | Lucy is not tall. | neutral | (((~creative(lucy)|~rich(lucy)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((humble(X)&creative(X))<=>generous(X)))&
(![X]:((quiet(X)&funny(X))=>(~happy(X)&tall(X))))&
(![X]:((~tall(X)&~strong(X))=>~creative(X)))&
(![X]:((~strong(X)|rich(X))=>(generous(X)<~>quiet(X))))&
(![X]:((~patient(X)|~old(X))=>(calm(X)&~happy(X))))&
((?[X]:((~curious(X)|~old(X))))=>((old(susan)|~quiet(susan))))&
(((generous(alice)&~brave(alice)))=>(humble(susan)))&
(![X]:(patient(X)<=>(brave(X)|~patient(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((old(X)<~>~patient(X)))))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~creative(X)&~funny(X))))=>((~happy(fred)|~old(fred))))&
((?[X]:((wise(X)<~>tall(X))))=>(~kind(fred)))&
(![X]:((~rich(X)&creative(X))=>(~wise(X)|~kind(X))))&
(![X]:((~calm(X)<~>old(X))<=>~wise(X)))&
((?[X]:(humble(X)))<=>(?[X]:((~wise(X)|patient(X)))))&
(?[X]:(~old(X)))&
(rich(fred))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((old(X)|quiet(X)))) | ~tall(lucy) | [] | null | 0 |
Everyone who is either not rich or not brave is both calm and not generous.
Everyone who is both brave and happy is not rich or not funny.
Everyone who is generous is both wise and generous.
Everyone who is not rich is either not happy or not calm.
If alice is not strong or not kind then someone is either creative or not old.
If alice is both old and strong then paul is either not humble or quiet.
Everyone who is wise or not patient is both happy and curious.
If someone is happy or old then mary is both tall and not wise.
Everyone who is rich or not creative is either not wise or rich and vice versa.
Everyone who is either not kind or not quiet is both not happy and calm.
Everyone who is both calm and patient is both not curious and quiet.
If susan is either not humble or wise then someone is either rich or patient and vice versa.
If someone is wise or not quiet then mary is both strong and quiet and vice versa.
If alice is either not rich or creative then someone is both not wise and quiet and vice versa.
If john is quiet then lucy is kind or not humble and vice versa.
Everyone who is either funny or quiet is brave and vice versa.
Someone is strong or tall.
Mary is either generous or old.
Paul is not wise.
Someone is either wise or not brave.
Someone is tall.
Paul is old or curious.
Susan is both not generous and not calm.
Someone is generous. | Mary is not strong. | contradiction | (![X]:((~rich(X)<~>~brave(X))=>(calm(X)&~generous(X))))&
(![X]:((brave(X)&happy(X))=>(~rich(X)|~funny(X))))&
(![X]:(generous(X)=>(wise(X)&generous(X))))&
(![X]:(~rich(X)=>(~happy(X)<~>~calm(X))))&
(((~strong(alice)|~kind(alice)))=>(?[X]:((creative(X)<~>~old(X)))))&
(((old(alice)&strong(alice)))=>((~humble(paul)<~>quiet(paul))))&
(![X]:((wise(X)|~patient(X))=>(happy(X)&curious(X))))&
((?[X]:((happy(X)|old(X))))=>((tall(mary)&~wise(mary))))&
(![X]:((rich(X)|~creative(X))<=>(~wise(X)<~>rich(X))))&
(![X]:((~kind(X)<~>~quiet(X))=>(~happy(X)&calm(X))))&
(![X]:((calm(X)&patient(X))=>(~curious(X)&quiet(X))))&
(((~humble(susan)<~>wise(susan)))<=>(?[X]:((rich(X)<~>patient(X)))))&
((?[X]:((wise(X)|~quiet(X))))<=>((strong(mary)&quiet(mary))))&
(((~rich(alice)<~>creative(alice)))<=>(?[X]:((~wise(X)&quiet(X)))))&
((quiet(john))<=>((kind(lucy)|~humble(lucy))))&
(![X]:((funny(X)<~>quiet(X))<=>brave(X)))&
(?[X]:((strong(X)|tall(X))))&
((generous(mary)<~>old(mary)))&
(~wise(paul))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:(tall(X)))&
((old(paul)|curious(paul)))&
((~generous(susan)&~calm(susan)))&
(?[X]:(generous(X))) | ~strong(mary) | [
"p2",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8679482593991249827295308
% SZS output start Proof for 8679482593991249827295308
3. ! [X0] : (generous(X0) => (generous(X0) & wise(X0))) [input p2]
13. ? [X0] : (~quiet(X0) | wise(X0)) <=> (quiet(mary) & strong(mary)) [input p12]
24. ? [X0] : generous(X0) [input p23]
25. ~strong(mary) [input hypothesis]
32. ! [X0] : ((generous(X0) & wise(X0)) | ~generous(X0)) [ennf transformation 3]
55. (? [X0] : (~quiet(X0) | wise(X0)) | (~quiet(mary) | ~strong(mary))) & ((quiet(mary) & strong(mary)) | ! [X0] : (quiet(X0) & ~wise(X0))) [nnf transformation 13]
56. (? [X0] : (~quiet(X0) | wise(X0)) | ~quiet(mary) | ~strong(mary)) & ((quiet(mary) & strong(mary)) | ! [X0] : (quiet(X0) & ~wise(X0))) [flattening 55]
57. (? [X0] : (~quiet(X0) | wise(X0)) | ~quiet(mary) | ~strong(mary)) & ((quiet(mary) & strong(mary)) | ! [X1] : (quiet(X1) & ~wise(X1))) [rectify 56]
58. ? [X0] : (~quiet(X0) | wise(X0)) => (~quiet(sK2) | wise(sK2)) [choice axiom]
59. ((~quiet(sK2) | wise(sK2)) | ~quiet(mary) | ~strong(mary)) & ((quiet(mary) & strong(mary)) | ! [X1] : (quiet(X1) & ~wise(X1))) [skolemisation 57,58]
71. ? [X0] : generous(X0) => generous(sK5) [choice axiom]
72. generous(sK5) [skolemisation 24,71]
78. ~generous(X0) | wise(X0) [cnf transformation 32]
114. strong(mary) | ~wise(X1) [cnf transformation 59]
140. generous(sK5) [cnf transformation 72]
141. ~strong(mary) [cnf transformation 25]
221. 17 <=> strong(mary) [avatar definition]
242. 22 <=> ! [X1] : ~wise(X1) [avatar definition]
243. ~wise(X1) <- (22) [avatar component clause 242]
246. 22 | 17 [avatar split clause 114,221,242]
316. ~17 [avatar split clause 141,221]
319. wise(sK5) [resolution 78,140]
321. $false <- (22) [subsumption resolution 319,243]
322. ~22 [avatar contradiction clause 321]
325. $false [avatar sat refutation 246,316,322]
% SZS output end Proof for 8679482593991249827295308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not humble is either funny or not rich and vice versa.
Everyone who is wise is either not wise or not strong and vice versa.
Everyone who is either not tall or not rich is both not generous and not patient and vice versa.
If fred is either not funny or humble then someone is both not patient and quiet and vice versa.
If mary is not patient then paul is both not old and old.
Everyone who is both quiet and not humble is both not generous and old.
Everyone who is both creative and not brave is humble or not wise.
If someone is patient then someone is not brave or calm and vice versa.
Everyone who is strong or old is either strong or not curious and vice versa.
If john is not brave or creative then paul is old.
Everyone who is wise or patient is quiet or curious and vice versa.
If mary is either generous or calm then susan is quiet or calm and vice versa.
Everyone who is either tall or old is both kind and wise.
If someone is either quiet or funny then lucy is not strong and vice versa.
Everyone who is quiet is curious or rich and vice versa.
Everyone who is either tall or rich is both not strong and not generous and vice versa.
Someone is not calm or quiet.
Someone is either curious or humble.
John is either not humble or old.
Fred is either happy or not kind.
Someone is not generous.
Someone is both not funny and not calm.
Someone is both calm and not curious.
Fred is not quiet. | Mary is not quiet. | contradiction | (![X]:((~curious(X)<~>~humble(X))<=>(funny(X)<~>~rich(X))))&
(![X]:(wise(X)<=>(~wise(X)<~>~strong(X))))&
(![X]:((~tall(X)<~>~rich(X))<=>(~generous(X)&~patient(X))))&
(((~funny(fred)<~>humble(fred)))<=>(?[X]:((~patient(X)&quiet(X)))))&
((~patient(mary))=>((~old(paul)&old(paul))))&
(![X]:((quiet(X)&~humble(X))=>(~generous(X)&old(X))))&
(![X]:((creative(X)&~brave(X))=>(humble(X)|~wise(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)|calm(X)))))&
(![X]:((strong(X)|old(X))<=>(strong(X)<~>~curious(X))))&
(((~brave(john)|creative(john)))=>(old(paul)))&
(![X]:((wise(X)|patient(X))<=>(quiet(X)|curious(X))))&
(((generous(mary)<~>calm(mary)))<=>((quiet(susan)|calm(susan))))&
(![X]:((tall(X)<~>old(X))=>(kind(X)&wise(X))))&
((?[X]:((quiet(X)<~>funny(X))))<=>(~strong(lucy)))&
(![X]:(quiet(X)<=>(curious(X)|rich(X))))&
(![X]:((tall(X)<~>rich(X))<=>(~strong(X)&~generous(X))))&
(?[X]:((~calm(X)|quiet(X))))&
(?[X]:((curious(X)<~>humble(X))))&
((~humble(john)<~>old(john)))&
((happy(fred)<~>~kind(fred)))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((calm(X)&~curious(X))))&
(~quiet(fred)) | ~quiet(mary) | [
"p4",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 745739889043280750070950
% SZS output start Proof for 745739889043280750070950
5. ~patient(mary) => (old(paul) & ~old(paul)) [input p4]
11. ! [X0] : ((patient(X0) | wise(X0)) <=> (curious(X0) | quiet(X0))) [input p10]
15. ! [X0] : (quiet(X0) <=> (rich(X0) | curious(X0))) [input p14]
25. ~quiet(mary) [input hypothesis]
29. (old(paul) & ~old(paul)) | patient(mary) [ennf transformation 5]
49. ! [X0] : (((patient(X0) | wise(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (~patient(X0) & ~wise(X0)))) [nnf transformation 11]
50. ! [X0] : ((patient(X0) | wise(X0) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | (~patient(X0) & ~wise(X0)))) [flattening 49]
58. ! [X0] : ((quiet(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | ~quiet(X0))) [nnf transformation 15]
59. ! [X0] : ((quiet(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~quiet(X0))) [flattening 58]
99. ~old(paul) | patient(mary) [cnf transformation 29]
100. old(paul) | patient(mary) [cnf transformation 29]
114. ~patient(X0) | quiet(X0) | curious(X0) [cnf transformation 50]
132. ~curious(X0) | quiet(X0) [cnf transformation 59]
153. ~quiet(mary) [cnf transformation 25]
185. 6 <=> patient(mary) [avatar definition]
187. patient(mary) <- (6) [avatar component clause 185]
189. 7 <=> old(paul) [avatar definition]
192. 6 | 7 [avatar split clause 100,189,185]
193. 6 | ~7 [avatar split clause 99,189,185]
374. quiet(mary) | curious(mary) <- (6) [resolution 114,187]
376. curious(mary) <- (6) [subsumption resolution 374,153]
435. quiet(mary) <- (6) [resolution 376,132]
436. $false <- (6) [subsumption resolution 435,153]
437. ~6 [avatar contradiction clause 436]
438. $false [avatar sat refutation 192,193,437]
% SZS output end Proof for 745739889043280750070950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not strong then someone is either curious or quiet and vice versa. If lucy is either not creative or not tall then lucy is not wise and vice versa. Everyone who is old or patient is both patient and quiet and vice versa. Everyone who is both humble and not tall is not humble and vice versa. Everyone who is not old is not strong. If someone is both wise and not curious then someone is either not calm or wise. If someone is not wise then someone is both not funny and not rich. If someone is kind then someone is both generous and not generous and vice versa. Everyone who is either brave or rich is not brave. If lucy is patient then someone is either patient or not old. If someone is either not funny or curious then someone is either not old or generous. Everyone who is not old is not patient and vice versa. If mary is both tall and not wise then mary is not strong. Everyone who is not humble or not tall is either not strong or patient. If someone is not kind then someone is curious. Everyone who is not happy is not brave and vice versa. Paul is either brave or patient. Mary is either rich or old. Alice is either not quiet or not wise. Mary is both quiet and humble. Fred is either curious or old. | Paul is not brave. | neutral | ((~strong(alice))<=>(?[X]:((curious(X)<~>quiet(X)))))&
(((~creative(lucy)<~>~tall(lucy)))<=>(~wise(lucy)))&
(![X]:((old(X)|patient(X))<=>(patient(X)&quiet(X))))&
(![X]:((humble(X)&~tall(X))<=>~humble(X)))&
(![X]:(~old(X)=>~strong(X)))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~calm(X)<~>wise(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((~funny(X)&~rich(X)))))&
((?[X]:(kind(X)))<=>(?[X]:((generous(X)&~generous(X)))))&
(![X]:((brave(X)<~>rich(X))=>~brave(X)))&
((patient(lucy))=>(?[X]:((patient(X)<~>~old(X)))))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~old(X)<~>generous(X)))))&
(![X]:(~old(X)<=>~patient(X)))&
(((tall(mary)&~wise(mary)))=>(~strong(mary)))&
(![X]:((~humble(X)|~tall(X))=>(~strong(X)<~>patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:(curious(X))))&
(![X]:(~happy(X)<=>~brave(X)))&
((brave(paul)<~>patient(paul)))&
((rich(mary)<~>old(mary)))&
((~quiet(alice)<~>~wise(alice)))&
((quiet(mary)&humble(mary)))&
((curious(fred)<~>old(fred))) | ~brave(paul) | [] | null | 0 |
If alice is old then lucy is either not creative or not curious and vice versa.
Everyone who is both happy and not quiet is either not creative or tall and vice versa.
If paul is creative then someone is both generous and rich and vice versa.
If paul is not funny then someone is kind and vice versa.
Everyone who is funny is brave.
If mary is both creative and wise then john is either not generous or not calm.
Everyone who is not rich or not calm is either not wise or rich.
If fred is not tall or calm then alice is not quiet or not patient and vice versa.
Everyone who is brave is both curious and tall and vice versa.
Everyone who is not creative is quiet or not tall.
Everyone who is wise or patient is either humble or not brave.
If fred is not humble then someone is both creative and not curious and vice versa.
Everyone who is either not strong or calm is not kind and vice versa.
If paul is not old or brave then someone is strong.
If someone is both not brave and curious then mary is strong and vice versa.
If someone is both tall and brave then someone is either generous or quiet and vice versa.
Alice is both not strong and humble.
Alice is both not strong and wise.
Someone is either quiet or not curious.
Someone is either not generous or not happy.
Someone is either not funny or not happy.
Lucy is not patient.
Lucy is not quiet or not curious.
John is both not wise and calm. | Mary is creative. | neutral | ((old(alice))<=>((~creative(lucy)<~>~curious(lucy))))&
(![X]:((happy(X)&~quiet(X))<=>(~creative(X)<~>tall(X))))&
((creative(paul))<=>(?[X]:((generous(X)&rich(X)))))&
((~funny(paul))<=>(?[X]:(kind(X))))&
(![X]:(funny(X)=>brave(X)))&
(((creative(mary)&wise(mary)))=>((~generous(john)<~>~calm(john))))&
(![X]:((~rich(X)|~calm(X))=>(~wise(X)<~>rich(X))))&
(((~tall(fred)|calm(fred)))<=>((~quiet(alice)|~patient(alice))))&
(![X]:(brave(X)<=>(curious(X)&tall(X))))&
(![X]:(~creative(X)=>(quiet(X)|~tall(X))))&
(![X]:((wise(X)|patient(X))=>(humble(X)<~>~brave(X))))&
((~humble(fred))<=>(?[X]:((creative(X)&~curious(X)))))&
(![X]:((~strong(X)<~>calm(X))<=>~kind(X)))&
(((~old(paul)|brave(paul)))=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(strong(mary)))&
((?[X]:((tall(X)&brave(X))))<=>(?[X]:((generous(X)<~>quiet(X)))))&
((~strong(alice)&humble(alice)))&
((~strong(alice)&wise(alice)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((~funny(X)<~>~happy(X))))&
(~patient(lucy))&
((~quiet(lucy)|~curious(lucy)))&
((~wise(john)&calm(john))) | creative(mary) | [] | null | 0 |
If susan is both not calm and humble then lucy is both calm and not strong and vice versa. If paul is not brave then someone is not happy and vice versa. Everyone who is calm or not tall is either not quiet or not calm and vice versa. Everyone who is both not brave and old is either kind or not funny and vice versa. Everyone who is either calm or not patient is both calm and not patient and vice versa. If someone is rich then paul is either not creative or not calm and vice versa. If someone is either not humble or calm then someone is wise or quiet. Everyone who is both quiet and brave is not curious or creative and vice versa. Everyone who is not humble is not brave. If someone is not calm or strong then someone is not strong. Everyone who is both not wise and not strong is either kind or not patient. Everyone who is not strong is happy or not patient. Everyone who is either not curious or not tall is both not generous and quiet and vice versa. Everyone who is not humble is both not calm and happy. If someone is not quiet then someone is either old or not creative. Everyone who is not creative or rich is either curious or kind. Someone is not humble. Someone is kind. Paul is kind. Someone is rich. Someone is both humble and patient. Lucy is not rich. Someone is both not tall and not funny. Lucy is either happy or not strong. | Susan is not brave. | entailment | (((~calm(susan)&humble(susan)))<=>((calm(lucy)&~strong(lucy))))&
((~brave(paul))<=>(?[X]:(~happy(X))))&
(![X]:((calm(X)|~tall(X))<=>(~quiet(X)<~>~calm(X))))&
(![X]:((~brave(X)&old(X))<=>(kind(X)<~>~funny(X))))&
(![X]:((calm(X)<~>~patient(X))<=>(calm(X)&~patient(X))))&
((?[X]:(rich(X)))<=>((~creative(paul)<~>~calm(paul))))&
((?[X]:((~humble(X)<~>calm(X))))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((quiet(X)&brave(X))<=>(~curious(X)|creative(X))))&
(![X]:(~humble(X)=>~brave(X)))&
((?[X]:((~calm(X)|strong(X))))=>(?[X]:(~strong(X))))&
(![X]:((~wise(X)&~strong(X))=>(kind(X)<~>~patient(X))))&
(![X]:(~strong(X)=>(happy(X)|~patient(X))))&
(![X]:((~curious(X)<~>~tall(X))<=>(~generous(X)&quiet(X))))&
(![X]:(~humble(X)=>(~calm(X)&happy(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((old(X)<~>~creative(X)))))&
(![X]:((~creative(X)|rich(X))=>(curious(X)<~>kind(X))))&
(?[X]:(~humble(X)))&
(?[X]:(kind(X)))&
(kind(paul))&
(?[X]:(rich(X)))&
(?[X]:((humble(X)&patient(X))))&
(~rich(lucy))&
(?[X]:((~tall(X)&~funny(X))))&
((happy(lucy)<~>~strong(lucy))) | ~brave(susan) | [
"p0",
"p4",
"p8",
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 769322116978051042953974
% SZS output start Proof for 769322116978051042953974
1. (humble(susan) & ~calm(susan)) <=> (~strong(lucy) & calm(lucy)) [input p0]
5. ! [X0] : ((calm(X0) <~> ~patient(X0)) <=> (~patient(X0) & calm(X0))) [input p4]
9. ! [X0] : (~humble(X0) => ~brave(X0)) [input p8]
12. ! [X0] : (~strong(X0) => (~patient(X0) | happy(X0))) [input p11]
24. happy(lucy) <~> ~strong(lucy) [input p23]
25. brave(susan) [input hypothesis]
31. ! [X0] : (~brave(X0) | humble(X0)) [ennf transformation 9]
33. ! [X0] : ((~patient(X0) | happy(X0)) | strong(X0)) [ennf transformation 12]
34. ! [X0] : (~patient(X0) | happy(X0) | strong(X0)) [flattening 33]
38. ((humble(susan) & ~calm(susan)) | (strong(lucy) | ~calm(lucy))) & ((~strong(lucy) & calm(lucy)) | (~humble(susan) | calm(susan))) [nnf transformation 1]
39. ((humble(susan) & ~calm(susan)) | strong(lucy) | ~calm(lucy)) & ((~strong(lucy) & calm(lucy)) | ~humble(susan) | calm(susan)) [flattening 38]
48. ! [X0] : ((((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | (patient(X0) | ~calm(X0))) & ((~patient(X0) & calm(X0)) | ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0))))) [nnf transformation 5]
49. ! [X0] : ((((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | patient(X0) | ~calm(X0)) & ((~patient(X0) & calm(X0)) | ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0))))) [flattening 48]
76. (strong(lucy) | ~happy(lucy)) & (~strong(lucy) | happy(lucy)) [nnf transformation 24]
78. ~strong(lucy) | ~humble(susan) | calm(susan) [cnf transformation 39]
96. calm(X0) | calm(X0) | patient(X0) [cnf transformation 49]
97. ~patient(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 49]
100. patient(X0) | ~calm(X0) | patient(X0) | ~calm(X0) [cnf transformation 49]
110. ~brave(X0) | humble(X0) [cnf transformation 31]
113. ~patient(X0) | happy(X0) | strong(X0) [cnf transformation 34]
138. strong(lucy) | ~happy(lucy) [cnf transformation 76]
139. brave(susan) [cnf transformation 25]
140. calm(X0) | patient(X0) [duplicate literal removal 96]
141. ~patient(X0) | ~calm(X0) [duplicate literal removal 97]
142. patient(X0) | ~calm(X0) [duplicate literal removal 100]
150. 2 <=> strong(lucy) [avatar definition]
154. 3 <=> humble(susan) [avatar definition]
159. 4 <=> calm(susan) [avatar definition]
160. calm(susan) <- (4) [avatar component clause 159]
163. 4 | ~3 | ~2 [avatar split clause 78,150,154,159]
178. ~calm(X0) [subsumption resolution 141,142]
179. patient(X0) [subsumption resolution 140,178]
205. happy(X0) | strong(X0) [subsumption resolution 113,179]
221. strong(lucy) [subsumption resolution 138,205]
222. 2 [avatar split clause 221,150]
237. humble(susan) [resolution 110,139]
241. 3 [avatar split clause 237,154]
242. $false <- (4) [subsumption resolution 160,178]
243. ~4 [avatar contradiction clause 242]
244. $false [avatar sat refutation 163,222,241,243]
% SZS output end Proof for 769322116978051042953974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or calm is either not quiet or generous.
If john is rich or old then someone is not tall or not kind.
If alice is kind or rich then someone is either humble or old.
If someone is generous or creative then someone is humble and vice versa.
Everyone who is patient is not tall or not brave.
Everyone who is tall is either kind or not rich.
Everyone who is not humble or not kind is both kind and not calm and vice versa.
If fred is both not patient and not rich then someone is both not brave and not old.
If lucy is generous or happy then someone is rich or not creative and vice versa.
If alice is happy then fred is both tall and creative and vice versa.
If someone is either not old or creative then someone is calm or patient and vice versa.
If susan is both not happy and not funny then fred is both old and not rich and vice versa.
Everyone who is both patient and not wise is brave.
If someone is either not patient or funny then mary is not tall or old and vice versa.
Everyone who is either old or not generous is not humble and vice versa.
Everyone who is both not tall and curious is not funny.
Someone is both not patient and not generous.
Susan is either not generous or not creative.
Fred is patient.
Someone is both not quiet and funny.
Someone is either happy or not funny.
Someone is either old or not quiet.
Someone is wise.
Someone is quiet or not quiet. | Fred is not patient. | contradiction | (![X]:((~happy(X)|calm(X))=>(~quiet(X)<~>generous(X))))&
(((rich(john)|old(john)))=>(?[X]:((~tall(X)|~kind(X)))))&
(((kind(alice)|rich(alice)))=>(?[X]:((humble(X)<~>old(X)))))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:(humble(X))))&
(![X]:(patient(X)=>(~tall(X)|~brave(X))))&
(![X]:(tall(X)=>(kind(X)<~>~rich(X))))&
(![X]:((~humble(X)|~kind(X))<=>(kind(X)&~calm(X))))&
(((~patient(fred)&~rich(fred)))=>(?[X]:((~brave(X)&~old(X)))))&
(((generous(lucy)|happy(lucy)))<=>(?[X]:((rich(X)|~creative(X)))))&
((happy(alice))<=>((tall(fred)&creative(fred))))&
((?[X]:((~old(X)<~>creative(X))))<=>(?[X]:((calm(X)|patient(X)))))&
(((~happy(susan)&~funny(susan)))<=>((old(fred)&~rich(fred))))&
(![X]:((patient(X)&~wise(X))=>brave(X)))&
((?[X]:((~patient(X)<~>funny(X))))<=>((~tall(mary)|old(mary))))&
(![X]:((old(X)<~>~generous(X))<=>~humble(X)))&
(![X]:((~tall(X)&curious(X))=>~funny(X)))&
(?[X]:((~patient(X)&~generous(X))))&
((~generous(susan)<~>~creative(susan)))&
(patient(fred))&
(?[X]:((~quiet(X)&funny(X))))&
(?[X]:((happy(X)<~>~funny(X))))&
(?[X]:((old(X)<~>~quiet(X))))&
(?[X]:(wise(X)))&
(?[X]:((quiet(X)|~quiet(X)))) | ~patient(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3594814611880520284796420
% SZS output start Proof for 3594814611880520284796420
19. patient(fred) [input p18]
25. ~patient(fred) [input hypothesis]
140. patient(fred) [cnf transformation 19]
148. ~patient(fred) [cnf transformation 25]
214. 15 <=> patient(fred) [avatar definition]
355. 15 [avatar split clause 140,214]
376. ~15 [avatar split clause 148,214]
377. $false [avatar sat refutation 355,376]
% SZS output end Proof for 3594814611880520284796420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not curious and not quiet then mary is both not happy and not creative.
If someone is not wise then someone is funny or not humble.
If susan is either not rich or humble then fred is wise or not funny and vice versa.
Everyone who is both not kind and rich is not tall.
If paul is both funny and not happy then alice is both not strong and not creative and vice versa.
If someone is wise or not old then lucy is not happy or not funny and vice versa.
If someone is not patient then susan is both curious and kind and vice versa.
Everyone who is rich is not happy and vice versa.
Everyone who is not happy or brave is both not creative and not strong and vice versa.
If susan is both not patient and humble then someone is both not creative and not patient and vice versa.
If someone is both quiet and not happy then someone is not quiet or brave.
Everyone who is both strong and calm is not rich and vice versa.
Everyone who is either strong or not tall is tall and vice versa.
If john is either generous or funny then someone is not rich or not quiet.
Everyone who is calm or not patient is not quiet or not old and vice versa.
If alice is not quiet then someone is not quiet and vice versa.
Someone is both happy and not old.
Someone is generous or not brave.
Someone is generous or tall.
Lucy is both humble and old.
Someone is not calm or funny.
John is either not rich or generous.
Someone is both not kind and not tall. | Mary is not strong. | contradiction | (((~curious(fred)&~quiet(fred)))=>((~happy(mary)&~creative(mary))))&
((?[X]:(~wise(X)))=>(?[X]:((funny(X)|~humble(X)))))&
(((~rich(susan)<~>humble(susan)))<=>((wise(fred)|~funny(fred))))&
(![X]:((~kind(X)&rich(X))=>~tall(X)))&
(((funny(paul)&~happy(paul)))<=>((~strong(alice)&~creative(alice))))&
((?[X]:((wise(X)|~old(X))))<=>((~happy(lucy)|~funny(lucy))))&
((?[X]:(~patient(X)))<=>((curious(susan)&kind(susan))))&
(![X]:(rich(X)<=>~happy(X)))&
(![X]:((~happy(X)|brave(X))<=>(~creative(X)&~strong(X))))&
(((~patient(susan)&humble(susan)))<=>(?[X]:((~creative(X)&~patient(X)))))&
((?[X]:((quiet(X)&~happy(X))))=>(?[X]:((~quiet(X)|brave(X)))))&
(![X]:((strong(X)&calm(X))<=>~rich(X)))&
(![X]:((strong(X)<~>~tall(X))<=>tall(X)))&
(((generous(john)<~>funny(john)))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((calm(X)|~patient(X))<=>(~quiet(X)|~old(X))))&
((~quiet(alice))<=>(?[X]:(~quiet(X))))&
(?[X]:((happy(X)&~old(X))))&
(?[X]:((generous(X)|~brave(X))))&
(?[X]:((generous(X)|tall(X))))&
((humble(lucy)&old(lucy)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(john)<~>generous(john)))&
(?[X]:((~kind(X)&~tall(X)))) | ~strong(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7175043094848902605917242
% SZS output start Proof for 7175043094848902605917242
13. ! [X0] : ((strong(X0) <~> ~tall(X0)) <=> tall(X0)) [input p12]
24. ~strong(mary) [input hypothesis]
64. ! [X0] : ((((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | ~tall(X0)) & (tall(X0) | ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))))) [nnf transformation 13]
122. tall(X0) | strong(X0) | tall(X0) [cnf transformation 64]
123. ~tall(X0) | strong(X0) | ~tall(X0) [cnf transformation 64]
144. ~strong(mary) [cnf transformation 24]
145. tall(X0) | strong(X0) [duplicate literal removal 122]
146. ~tall(X0) | strong(X0) [duplicate literal removal 123]
294. strong(X0) [subsumption resolution 145,146]
359. $false [subsumption resolution 144,294]
% SZS output end Proof for 7175043094848902605917242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both generous and patient then alice is quiet or not calm and vice versa.
Everyone who is both not kind and brave is either humble or quiet and vice versa.
If someone is strong then lucy is both old and calm.
Everyone who is funny is both brave and tall and vice versa.
Everyone who is not patient is both old and funny.
If fred is not happy or wise then someone is both patient and not creative.
If someone is either kind or tall then mary is not happy or humble and vice versa.
Everyone who is either old or not patient is not patient.
If someone is happy or not kind then fred is not brave or not quiet and vice versa.
Everyone who is not curious is both wise and not calm.
Everyone who is both tall and funny is not strong and vice versa.
Everyone who is either brave or not quiet is not old.
Everyone who is both brave and not kind is quiet and vice versa.
Everyone who is not old or creative is strong and vice versa.
If fred is quiet then paul is either not happy or humble.
Everyone who is rich or calm is both brave and old and vice versa.
Susan is not rich or not kind.
Someone is either not creative or funny.
Someone is happy or funny.
Paul is both patient and not happy.
Someone is either not kind or not generous.
Someone is either old or calm. | Paul is humble. | contradiction | (((generous(mary)&patient(mary)))<=>((quiet(alice)|~calm(alice))))&
(![X]:((~kind(X)&brave(X))<=>(humble(X)<~>quiet(X))))&
((?[X]:(strong(X)))=>((old(lucy)&calm(lucy))))&
(![X]:(funny(X)<=>(brave(X)&tall(X))))&
(![X]:(~patient(X)=>(old(X)&funny(X))))&
(((~happy(fred)|wise(fred)))=>(?[X]:((patient(X)&~creative(X)))))&
((?[X]:((kind(X)<~>tall(X))))<=>((~happy(mary)|humble(mary))))&
(![X]:((old(X)<~>~patient(X))=>~patient(X)))&
((?[X]:((happy(X)|~kind(X))))<=>((~brave(fred)|~quiet(fred))))&
(![X]:(~curious(X)=>(wise(X)&~calm(X))))&
(![X]:((tall(X)&funny(X))<=>~strong(X)))&
(![X]:((brave(X)<~>~quiet(X))=>~old(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((~old(X)|creative(X))<=>strong(X)))&
((quiet(fred))=>((~happy(paul)<~>humble(paul))))&
(![X]:((rich(X)|calm(X))<=>(brave(X)&old(X))))&
((~rich(susan)|~kind(susan)))&
(?[X]:((~creative(X)<~>funny(X))))&
(?[X]:((happy(X)|funny(X))))&
((patient(paul)&~happy(paul)))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((old(X)<~>calm(X)))) | humble(paul) | [
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3091404093030631519246520
% SZS output start Proof for 3091404093030631519246520
2. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (humble(X0) <~> quiet(X0))) [input p1]
13. ! [X0] : ((~kind(X0) & brave(X0)) <=> quiet(X0)) [input p12]
23. humble(paul) [input hypothesis]
34. ! [X0] : (((brave(X0) & ~kind(X0)) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | (~brave(X0) | kind(X0)))) [nnf transformation 2]
35. ! [X0] : (((brave(X0) & ~kind(X0)) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ~brave(X0) | kind(X0))) [flattening 34]
54. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | (kind(X0) | ~brave(X0)))) [nnf transformation 13]
55. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | kind(X0) | ~brave(X0))) [flattening 54]
78. ~humble(X0) | ~quiet(X0) | ~brave(X0) | kind(X0) [cnf transformation 35]
79. ~humble(X0) | quiet(X0) | ~kind(X0) [cnf transformation 35]
81. ~humble(X0) | quiet(X0) | brave(X0) [cnf transformation 35]
109. ~brave(X0) | kind(X0) | quiet(X0) [cnf transformation 55]
110. ~quiet(X0) | brave(X0) [cnf transformation 55]
111. ~kind(X0) | ~quiet(X0) [cnf transformation 55]
132. humble(paul) [cnf transformation 23]
242. 24 <=> humble(paul) [avatar definition]
243. humble(paul) <- (24) [avatar component clause 242]
288. 24 [avatar split clause 132,242]
308. quiet(paul) | ~kind(paul) <- (24) [resolution 79,243]
309. ~kind(paul) <- (24) [subsumption resolution 308,111]
312. quiet(paul) | brave(paul) <- (24) [resolution 81,243]
313. brave(paul) <- (24) [subsumption resolution 312,110]
331. kind(paul) | quiet(paul) <- (24) [resolution 109,313]
333. quiet(paul) <- (24) [subsumption resolution 331,309]
361. ~quiet(paul) | ~brave(paul) | kind(paul) <- (24) [resolution 78,243]
362. ~brave(paul) | kind(paul) <- (24) [subsumption resolution 361,333]
363. kind(paul) <- (24) [subsumption resolution 362,313]
364. $false <- (24) [subsumption resolution 363,309]
365. ~24 [avatar contradiction clause 364]
366. $false [avatar sat refutation 288,365]
% SZS output end Proof for 3091404093030631519246520
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or happy is both quiet and not brave.
Everyone who is either not curious or strong is either not patient or happy.
If someone is both generous and not tall then alice is patient or not humble.
Everyone who is either happy or not old is both generous and creative and vice versa.
If john is both old and tall then someone is not calm or not quiet and vice versa.
If alice is not humble then someone is not calm and vice versa.
Everyone who is both not strong and funny is both not old and not funny and vice versa.
Everyone who is both generous and not strong is both not wise and not old.
If fred is either not creative or not wise then someone is both rich and old.
Everyone who is either not brave or not curious is not brave and vice versa.
Everyone who is not generous or patient is either happy or generous and vice versa.
Everyone who is both not humble and not generous is not kind or not creative and vice versa.
If someone is wise then john is not calm or not creative.
Paul is strong or not wise.
Someone is either not happy or quiet.
Someone is either not funny or strong.
Someone is either not tall or not happy. | John is not quiet. | contradiction | (![X]:((~brave(X)|happy(X))=>(quiet(X)&~brave(X))))&
(![X]:((~curious(X)<~>strong(X))=>(~patient(X)<~>happy(X))))&
((?[X]:((generous(X)&~tall(X))))=>((patient(alice)|~humble(alice))))&
(![X]:((happy(X)<~>~old(X))<=>(generous(X)&creative(X))))&
(((old(john)&tall(john)))<=>(?[X]:((~calm(X)|~quiet(X)))))&
((~humble(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~strong(X)&funny(X))<=>(~old(X)&~funny(X))))&
(![X]:((generous(X)&~strong(X))=>(~wise(X)&~old(X))))&
(((~creative(fred)<~>~wise(fred)))=>(?[X]:((rich(X)&old(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((~generous(X)|patient(X))<=>(happy(X)<~>generous(X))))&
(![X]:((~humble(X)&~generous(X))<=>(~kind(X)|~creative(X))))&
((?[X]:(wise(X)))=>((~calm(john)|~creative(john))))&
((strong(paul)|~wise(paul)))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((~funny(X)<~>strong(X))))&
(?[X]:((~tall(X)<~>~happy(X)))) | ~quiet(john) | [
"p0",
"p1",
"p3",
"p6",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 836984588735811364418157
% SZS output start Proof for 836984588735811364418157
1. ! [X0] : ((happy(X0) | ~brave(X0)) => (~brave(X0) & quiet(X0))) [input p0]
2. ! [X0] : ((~curious(X0) <~> strong(X0)) => (~patient(X0) <~> happy(X0))) [input p1]
4. ! [X0] : ((happy(X0) <~> ~old(X0)) <=> (creative(X0) & generous(X0))) [input p3]
7. ! [X0] : ((funny(X0) & ~strong(X0)) <=> (~funny(X0) & ~old(X0))) [input p6]
8. ! [X0] : ((~strong(X0) & generous(X0)) => (~old(X0) & ~wise(X0))) [input p7]
10. ! [X0] : ((~brave(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p9]
11. ! [X0] : ((patient(X0) | ~generous(X0)) <=> (happy(X0) <~> generous(X0))) [input p10]
18. ~quiet(john) [input hypothesis]
20. ! [X0] : ((~brave(X0) & quiet(X0)) | (~happy(X0) & brave(X0))) [ennf transformation 1]
21. ! [X0] : ((~patient(X0) <~> happy(X0)) | (~curious(X0) <=> strong(X0))) [ennf transformation 2]
24. ! [X0] : ((~old(X0) & ~wise(X0)) | (strong(X0) | ~generous(X0))) [ennf transformation 8]
25. ! [X0] : ((~old(X0) & ~wise(X0)) | strong(X0) | ~generous(X0)) [flattening 24]
29. ! [X0] : (((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) [nnf transformation 21]
30. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~creative(X0) | ~generous(X0))) & ((creative(X0) & generous(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [nnf transformation 4]
31. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | ~creative(X0) | ~generous(X0)) & ((creative(X0) & generous(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [flattening 30]
41. ! [X0] : (((funny(X0) & ~strong(X0)) | (funny(X0) | old(X0))) & ((~funny(X0) & ~old(X0)) | (~funny(X0) | strong(X0)))) [nnf transformation 7]
42. ! [X0] : (((funny(X0) & ~strong(X0)) | funny(X0) | old(X0)) & ((~funny(X0) & ~old(X0)) | ~funny(X0) | strong(X0))) [flattening 41]
46. ! [X0] : ((((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | brave(X0)) & (~brave(X0) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))))) [nnf transformation 10]
47. ! [X0] : (((patient(X0) | ~generous(X0)) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | (~patient(X0) & generous(X0)))) [nnf transformation 11]
48. ! [X0] : ((patient(X0) | ~generous(X0) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | (~patient(X0) & generous(X0)))) [flattening 47]
61. ~happy(X0) | quiet(X0) [cnf transformation 20]
65. ~patient(X0) | happy(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 29]
69. ~old(X0) | generous(X0) | ~happy(X0) [cnf transformation 31]
83. ~funny(X0) | ~funny(X0) | strong(X0) [cnf transformation 42]
85. funny(X0) | funny(X0) | old(X0) [cnf transformation 42]
87. ~old(X0) | strong(X0) | ~generous(X0) [cnf transformation 25]
91. ~brave(X0) | ~brave(X0) | curious(X0) [cnf transformation 46]
93. curious(X0) | brave(X0) | brave(X0) [cnf transformation 46]
94. generous(X0) | happy(X0) | generous(X0) [cnf transformation 48]
99. patient(X0) | ~generous(X0) | happy(X0) | ~generous(X0) [cnf transformation 48]
113. ~quiet(john) [cnf transformation 18]
114. generous(X0) | happy(X0) [duplicate literal removal 94]
115. ~generous(X0) | patient(X0) | happy(X0) [duplicate literal removal 99]
116. ~brave(X0) | curious(X0) [duplicate literal removal 91]
117. curious(X0) | brave(X0) [duplicate literal removal 93]
118. ~funny(X0) | strong(X0) [duplicate literal removal 83]
119. funny(X0) | old(X0) [duplicate literal removal 85]
133. 4 <=> ! [X0] : quiet(X0) [avatar definition]
134. quiet(X0) <- (4) [avatar component clause 133]
179. curious(X0) [subsumption resolution 116,117]
229. $false <- (4) [resolution 134,113]
230. ~4 [avatar contradiction clause 229]
238. old(X0) | strong(X0) [resolution 119,118]
268. patient(X0) | happy(X0) | happy(X0) [resolution 115,114]
270. patient(X0) | happy(X0) [duplicate literal removal 268]
271. strong(X0) | strong(X0) | ~generous(X0) [resolution 238,87]
273. strong(X2) | generous(X2) | ~happy(X2) [resolution 238,69]
274. strong(X0) | ~generous(X0) [duplicate literal removal 271]
276. strong(X2) | generous(X2) [subsumption resolution 273,114]
277. strong(X2) [subsumption resolution 276,274]
281. happy(X0) | happy(X0) | ~curious(X0) | ~strong(X0) [resolution 270,65]
287. happy(X0) | ~curious(X0) | ~strong(X0) [duplicate literal removal 281]
288. happy(X0) | ~strong(X0) [subsumption resolution 287,179]
289. happy(X0) [subsumption resolution 288,277]
294. quiet(X2) [resolution 289,61]
296. 4 [avatar split clause 294,133]
297. $false [avatar sat refutation 230,296]
% SZS output end Proof for 836984588735811364418157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and funny then alice is old or wise and vice versa.
Everyone who is either patient or not generous is either wise or patient.
Everyone who is either happy or funny is not funny and vice versa.
Everyone who is both not creative and old is quiet.
Everyone who is quiet or creative is funny and vice versa.
Everyone who is not happy is either not rich or not happy.
If alice is quiet then lucy is either brave or not funny.
If fred is not happy or old then fred is not old.
Everyone who is either happy or not wise is not funny or not happy and vice versa.
Everyone who is either happy or not curious is either not brave or happy.
Everyone who is both not rich and not generous is either not old or not tall and vice versa.
Everyone who is funny or old is kind or rich.
If someone is both not happy and not generous then susan is creative or patient and vice versa.
Everyone who is not generous is strong and vice versa.
If paul is either happy or calm then fred is either brave or not happy.
Everyone who is not quiet is both funny and not creative.
Someone is both old and not rich.
Lucy is creative.
Paul is both not rich and not humble.
Someone is both not humble and not patient.
Alice is not creative.
Someone is not humble.
Someone is not strong or quiet. | Fred is not wise. | entailment | ((?[X]:((patient(X)&funny(X))))<=>((old(alice)|wise(alice))))&
(![X]:((patient(X)<~>~generous(X))=>(wise(X)<~>patient(X))))&
(![X]:((happy(X)<~>funny(X))<=>~funny(X)))&
(![X]:((~creative(X)&old(X))=>quiet(X)))&
(![X]:((quiet(X)|creative(X))<=>funny(X)))&
(![X]:(~happy(X)=>(~rich(X)<~>~happy(X))))&
((quiet(alice))=>((brave(lucy)<~>~funny(lucy))))&
(((~happy(fred)|old(fred)))=>(~old(fred)))&
(![X]:((happy(X)<~>~wise(X))<=>(~funny(X)|~happy(X))))&
(![X]:((happy(X)<~>~curious(X))=>(~brave(X)<~>happy(X))))&
(![X]:((~rich(X)&~generous(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((funny(X)|old(X))=>(kind(X)|rich(X))))&
((?[X]:((~happy(X)&~generous(X))))<=>((creative(susan)|patient(susan))))&
(![X]:(~generous(X)<=>strong(X)))&
(((happy(paul)<~>calm(paul)))=>((brave(fred)<~>~happy(fred))))&
(![X]:(~quiet(X)=>(funny(X)&~creative(X))))&
(?[X]:((old(X)&~rich(X))))&
(creative(lucy))&
((~rich(paul)&~humble(paul)))&
(?[X]:((~humble(X)&~patient(X))))&
(~creative(alice))&
(?[X]:(~humble(X)))&
(?[X]:((~strong(X)|quiet(X)))) | ~wise(fred) | [
"p2",
"p4",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 338982786155096082456116
% SZS output start Proof for 338982786155096082456116
3. ! [X0] : ((happy(X0) <~> funny(X0)) <=> ~funny(X0)) [input p2]
5. ! [X0] : ((creative(X0) | quiet(X0)) <=> funny(X0)) [input p4]
9. ! [X0] : ((happy(X0) <~> ~wise(X0)) <=> (~happy(X0) | ~funny(X0))) [input p8]
16. ! [X0] : (~quiet(X0) => (~creative(X0) & funny(X0))) [input p15]
24. wise(fred) [input hypothesis]
37. ! [X0] : ((~creative(X0) & funny(X0)) | quiet(X0)) [ennf transformation 16]
44. ! [X0] : ((((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) | funny(X0)) & (~funny(X0) | ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0))))) [nnf transformation 3]
45. ! [X0] : (((creative(X0) | quiet(X0)) | ~funny(X0)) & (funny(X0) | (~creative(X0) & ~quiet(X0)))) [nnf transformation 5]
46. ! [X0] : ((creative(X0) | quiet(X0) | ~funny(X0)) & (funny(X0) | (~creative(X0) & ~quiet(X0)))) [flattening 45]
49. ! [X0] : ((((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | (happy(X0) & funny(X0))) & ((~happy(X0) | ~funny(X0)) | ((happy(X0) | wise(X0)) & (~wise(X0) | ~happy(X0))))) [nnf transformation 9]
50. ! [X0] : ((((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | (happy(X0) & funny(X0))) & (~happy(X0) | ~funny(X0) | ((happy(X0) | wise(X0)) & (~wise(X0) | ~happy(X0))))) [flattening 49]
77. ~funny(X0) | happy(X0) | ~funny(X0) [cnf transformation 44]
78. funny(X0) | happy(X0) | funny(X0) [cnf transformation 44]
81. ~quiet(X0) | funny(X0) [cnf transformation 46]
90. ~happy(X0) | ~funny(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 50]
117. funny(X0) | quiet(X0) [cnf transformation 37]
126. wise(fred) [cnf transformation 24]
129. ~happy(X0) | ~funny(X0) | ~wise(X0) [duplicate literal removal 90]
133. ~funny(X0) | happy(X0) [duplicate literal removal 77]
134. happy(X0) | funny(X0) [duplicate literal removal 78]
161. happy(X0) [subsumption resolution 133,134]
177. ~wise(X0) | ~funny(X0) [subsumption resolution 129,161]
208. funny(X0) [subsumption resolution 117,81]
224. ~funny(fred) [resolution 177,126]
226. $false [subsumption resolution 224,208]
% SZS output end Proof for 338982786155096082456116
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not kind and not strong then john is generous or not calm and vice versa.
Everyone who is either not humble or strong is happy.
If someone is funny or curious then someone is not humble or not generous and vice versa.
Everyone who is either not wise or not brave is not quiet.
Everyone who is both happy and old is not happy or quiet.
If someone is both not kind and not tall then someone is either curious or not creative.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is either humble or old then paul is either patient or happy.
If someone is calm or generous then someone is not old.
Everyone who is quiet or funny is either not patient or not calm.
If someone is kind then paul is curious and vice versa.
If someone is both not curious and brave then someone is not old or not funny.
Everyone who is old or not humble is not humble or not patient and vice versa.
Everyone who is both humble and not calm is both happy and kind.
Everyone who is tall is either kind or not brave and vice versa.
Everyone who is either not old or not generous is not generous and vice versa.
Someone is either wise or rich.
Someone is either not happy or brave.
Someone is both not quiet and not humble.
Someone is kind.
Someone is both not funny and not quiet.
Alice is either generous or not generous.
Mary is rich or curious.
Someone is either curious or humble. | John is humble. | contradiction | (((~kind(lucy)&~strong(lucy)))<=>((generous(john)|~calm(john))))&
(![X]:((~humble(X)<~>strong(X))=>happy(X)))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>~quiet(X)))&
(![X]:((happy(X)&old(X))=>(~happy(X)|quiet(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>((patient(paul)<~>happy(paul))))&
((?[X]:((calm(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|funny(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:(kind(X)))<=>(curious(paul)))&
((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((old(X)|~humble(X))<=>(~humble(X)|~patient(X))))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&kind(X))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
(![X]:((~old(X)<~>~generous(X))<=>~generous(X)))&
(?[X]:((wise(X)<~>rich(X))))&
(?[X]:((~happy(X)<~>brave(X))))&
(?[X]:((~quiet(X)&~humble(X))))&
(?[X]:(kind(X)))&
(?[X]:((~funny(X)&~quiet(X))))&
((generous(alice)<~>~generous(alice)))&
((rich(mary)|curious(mary)))&
(?[X]:((curious(X)<~>humble(X)))) | humble(john) | [
"p4",
"p8",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1994333629634012558469335
% SZS output start Proof for 1994333629634012558469335
5. ! [X0] : ((old(X0) & happy(X0)) => (quiet(X0) | ~happy(X0))) [input p4]
9. ? [X0] : (generous(X0) | calm(X0)) => ? [X0] : ~old(X0) [input p8]
10. ! [X0] : ((funny(X0) | quiet(X0)) => (~patient(X0) <~> ~calm(X0))) [input p9]
13. ! [X0] : ((~humble(X0) | old(X0)) <=> (~patient(X0) | ~humble(X0))) [input p12]
14. ! [X0] : ((~calm(X0) & humble(X0)) => (kind(X0) & happy(X0))) [input p13]
16. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> ~generous(X0)) [input p15]
25. humble(john) [input hypothesis]
28. ? [X0] : (generous(X0) | calm(X0)) => ? [X1] : ~old(X1) [rectify 9]
33. ! [X0] : ((quiet(X0) | ~happy(X0)) | (~old(X0) | ~happy(X0))) [ennf transformation 5]
34. ! [X0] : (quiet(X0) | ~happy(X0) | ~old(X0) | ~happy(X0)) [flattening 33]
37. ? [X1] : ~old(X1) | ! [X0] : (~generous(X0) & ~calm(X0)) [ennf transformation 28]
38. ! [X0] : ((~patient(X0) <~> ~calm(X0)) | (~funny(X0) & ~quiet(X0))) [ennf transformation 10]
40. ! [X0] : ((kind(X0) & happy(X0)) | (calm(X0) | ~humble(X0))) [ennf transformation 14]
41. ! [X0] : ((kind(X0) & happy(X0)) | calm(X0) | ~humble(X0)) [flattening 40]
59. ? [X0] : ~old(X0) | ! [X1] : (~generous(X1) & ~calm(X1)) [rectify 37]
60. ? [X0] : ~old(X0) => ~old(sK3) [choice axiom]
61. ~old(sK3) | ! [X1] : (~generous(X1) & ~calm(X1)) [skolemisation 59,60]
62. ! [X0] : (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~funny(X0) & ~quiet(X0))) [nnf transformation 38]
70. ! [X0] : (((~humble(X0) | old(X0)) | (patient(X0) & humble(X0))) & ((~patient(X0) | ~humble(X0)) | (humble(X0) & ~old(X0)))) [nnf transformation 13]
71. ! [X0] : ((~humble(X0) | old(X0) | (patient(X0) & humble(X0))) & (~patient(X0) | ~humble(X0) | (humble(X0) & ~old(X0)))) [flattening 70]
73. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | generous(X0)) & (~generous(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 16]
103. quiet(X0) | ~happy(X0) | ~old(X0) | ~happy(X0) [cnf transformation 34]
115. ~old(sK3) | ~calm(X1) [cnf transformation 61]
116. ~old(sK3) | ~generous(X1) [cnf transformation 61]
119. ~quiet(X0) | patient(X0) | calm(X0) [cnf transformation 62]
124. ~patient(X0) | ~humble(X0) | ~old(X0) [cnf transformation 71]
128. ~humble(X0) | calm(X0) | happy(X0) [cnf transformation 41]
132. ~generous(X0) | ~generous(X0) | old(X0) [cnf transformation 73]
135. generous(X0) | old(X0) | generous(X0) [cnf transformation 73]
150. humble(john) [cnf transformation 25]
151. ~generous(X0) | old(X0) [duplicate literal removal 132]
152. old(X0) | generous(X0) [duplicate literal removal 135]
153. ~old(X0) | ~happy(X0) | quiet(X0) [duplicate literal removal 103]
155. 1 <=> calm(john) [avatar definition]
156. ~calm(john) <- (~1) [avatar component clause 155]
157. calm(john) <- (1) [avatar component clause 155]
239. 20 <=> ! [X1] : ~generous(X1) [avatar definition]
240. ~generous(X1) <- (20) [avatar component clause 239]
242. 21 <=> old(sK3) [avatar definition]
244. ~old(sK3) <- (~21) [avatar component clause 242]
245. 20 | ~21 [avatar split clause 116,242,239]
247. 22 <=> ! [X1] : ~calm(X1) [avatar definition]
248. ~calm(X1) <- (22) [avatar component clause 247]
249. 22 | ~21 [avatar split clause 115,242,247]
275. old(X0) [subsumption resolution 151,152]
307. $false <- (~21) [subsumption resolution 244,275]
308. 21 [avatar contradiction clause 307]
362. 42 <=> happy(john) [avatar definition]
364. happy(john) <- (42) [avatar component clause 362]
394. calm(john) | happy(john) [resolution 128,150]
396. happy(john) <- (~1) [subsumption resolution 394,156]
397. 42 | 1 [avatar split clause 396,155,362]
403. ~happy(X0) | quiet(X0) | generous(X0) [resolution 153,152]
405. ~happy(X0) | quiet(X0) <- (20) [subsumption resolution 403,240]
408. quiet(john) <- (20, 42) [resolution 405,364]
414. patient(john) | calm(john) <- (20, 42) [resolution 408,119]
417. patient(john) <- (~1, 20, 42) [subsumption resolution 414,156]
449. ~humble(john) | ~old(john) <- (~1, 20, 42) [resolution 417,124]
452. ~old(john) <- (~1, 20, 42) [subsumption resolution 449,150]
453. $false <- (~1, 20, 42) [subsumption resolution 452,275]
454. 1 | ~20 | ~42 [avatar contradiction clause 453]
457. $false <- (1, 22) [subsumption resolution 157,248]
458. ~1 | ~22 [avatar contradiction clause 457]
459. $false [avatar sat refutation 245,249,308,397,454,458]
% SZS output end Proof for 1994333629634012558469335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not calm is not patient and vice versa. If susan is happy then someone is both not tall and not humble and vice versa. Everyone who is either not calm or not rich is both not quiet and old. If someone is not curious then john is both not tall and not generous and vice versa. If fred is generous then someone is happy. If someone is either not patient or happy then someone is quiet and vice versa. Everyone who is either not creative or not funny is not happy. Everyone who is tall is either patient or not rich and vice versa. Everyone who is either wise or not brave is either not generous or patient and vice versa. If susan is both not patient and strong then someone is either quiet or happy. If paul is both old and happy then someone is both old and quiet and vice versa. If someone is patient then someone is either not humble or kind. If john is either brave or curious then someone is funny. Everyone who is both not generous and not happy is both humble and rich and vice versa. Everyone who is either not creative or creative is not creative and vice versa. Everyone who is either not wise or not rich is both calm and happy. Someone is not creative. Someone is kind. Someone is both not humble and not old. Someone is brave or not calm. Someone is either funny or wise. Paul is brave or not curious. Someone is either funny or not old. Paul is either generous or not strong. | Susan is not creative. | entailment | (![X]:((~rich(X)<~>~calm(X))<=>~patient(X)))&
((happy(susan))<=>(?[X]:((~tall(X)&~humble(X)))))&
(![X]:((~calm(X)<~>~rich(X))=>(~quiet(X)&old(X))))&
((?[X]:(~curious(X)))<=>((~tall(john)&~generous(john))))&
((generous(fred))=>(?[X]:(happy(X))))&
((?[X]:((~patient(X)<~>happy(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~creative(X)<~>~funny(X))=>~happy(X)))&
(![X]:(tall(X)<=>(patient(X)<~>~rich(X))))&
(![X]:((wise(X)<~>~brave(X))<=>(~generous(X)<~>patient(X))))&
(((~patient(susan)&strong(susan)))=>(?[X]:((quiet(X)<~>happy(X)))))&
(((old(paul)&happy(paul)))<=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~humble(X)<~>kind(X)))))&
(((brave(john)<~>curious(john)))=>(?[X]:(funny(X))))&
(![X]:((~generous(X)&~happy(X))<=>(humble(X)&rich(X))))&
(![X]:((~creative(X)<~>creative(X))<=>~creative(X)))&
(![X]:((~wise(X)<~>~rich(X))=>(calm(X)&happy(X))))&
(?[X]:(~creative(X)))&
(?[X]:(kind(X)))&
(?[X]:((~humble(X)&~old(X))))&
(?[X]:((brave(X)|~calm(X))))&
(?[X]:((funny(X)<~>wise(X))))&
((brave(paul)|~curious(paul)))&
(?[X]:((funny(X)<~>~old(X))))&
((generous(paul)<~>~strong(paul))) | ~creative(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8422490883831351921858762
% SZS output start Proof for 8422490883831351921858762
15. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> ~creative(X0)) [input p14]
25. creative(susan) [input hypothesis]
74. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | creative(X0)) & (~creative(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 15]
139. ~creative(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 74]
158. creative(susan) [cnf transformation 25]
160. ~creative(X0) [duplicate literal removal 139]
349. $false [subsumption resolution 158,160]
% SZS output end Proof for 8422490883831351921858762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and funny is curious or not humble and vice versa.
If alice is both tall and not patient then someone is happy and vice versa.
Everyone who is either kind or patient is humble and vice versa.
Everyone who is not patient or not wise is both not kind and brave.
If someone is generous or wise then someone is not tall or generous.
Everyone who is either curious or wise is not rich and vice versa.
If someone is both patient and tall then susan is funny.
Everyone who is creative or kind is both strong and not generous.
Everyone who is calm is not patient.
Everyone who is both not rich and creative is either creative or not creative and vice versa.
If lucy is tall or not calm then susan is either not quiet or quiet.
If someone is both not strong and curious then someone is either not generous or generous.
Everyone who is either not funny or wise is both not curious and tall and vice versa.
If someone is not happy then susan is brave.
Everyone who is not strong is both funny and rich.
Fred is either curious or not funny.
Lucy is wise or tall.
Fred is both not quiet and not old.
John is either not patient or rich.
Someone is not tall or not strong.
Mary is not humble. | John is curious. | neutral | (![X]:((~generous(X)&funny(X))<=>(curious(X)|~humble(X))))&
(((tall(alice)&~patient(alice)))<=>(?[X]:(happy(X))))&
(![X]:((kind(X)<~>patient(X))<=>humble(X)))&
(![X]:((~patient(X)|~wise(X))=>(~kind(X)&brave(X))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((curious(X)<~>wise(X))<=>~rich(X)))&
((?[X]:((patient(X)&tall(X))))=>(funny(susan)))&
(![X]:((creative(X)|kind(X))=>(strong(X)&~generous(X))))&
(![X]:(calm(X)=>~patient(X)))&
(![X]:((~rich(X)&creative(X))<=>(creative(X)<~>~creative(X))))&
(((tall(lucy)|~calm(lucy)))=>((~quiet(susan)<~>quiet(susan))))&
((?[X]:((~strong(X)&curious(X))))=>(?[X]:((~generous(X)<~>generous(X)))))&
(![X]:((~funny(X)<~>wise(X))<=>(~curious(X)&tall(X))))&
((?[X]:(~happy(X)))=>(brave(susan)))&
(![X]:(~strong(X)=>(funny(X)&rich(X))))&
((curious(fred)<~>~funny(fred)))&
((wise(lucy)|tall(lucy)))&
((~quiet(fred)&~old(fred)))&
((~patient(john)<~>rich(john)))&
(?[X]:((~tall(X)|~strong(X))))&
(~humble(mary)) | curious(john) | [] | null | 0 |
If someone is both curious and patient then someone is not quiet.
If susan is either calm or curious then someone is either tall or funny and vice versa.
If someone is either old or happy then lucy is not old and vice versa.
If john is happy then someone is both not calm and not patient and vice versa.
If lucy is not brave or not quiet then susan is not quiet or strong.
Everyone who is not funny is both strong and not happy and vice versa.
Everyone who is either rich or calm is either not happy or patient and vice versa.
If someone is both not patient and not strong then someone is both funny and not wise.
Everyone who is either wise or quiet is curious.
Everyone who is both not old and strong is wise or not brave.
Everyone who is both not kind and not calm is humble and vice versa.
If john is either not patient or curious then someone is both not happy and not kind.
Everyone who is humble is not quiet or not funny and vice versa.
Everyone who is not kind is both brave and funny.
Everyone who is both not brave and not quiet is not kind or tall.
Everyone who is not humble or not happy is both tall and quiet and vice versa.
Someone is both rich and not strong.
Susan is both not wise and curious.
Someone is not old or old.
John is both not generous and not strong.
Someone is either not old or not patient.
Someone is generous or not happy.
Mary is either rich or tall.
Someone is funny. | Lucy is rich. | neutral | ((?[X]:((curious(X)&patient(X))))=>(?[X]:(~quiet(X))))&
(((calm(susan)<~>curious(susan)))<=>(?[X]:((tall(X)<~>funny(X)))))&
((?[X]:((old(X)<~>happy(X))))<=>(~old(lucy)))&
((happy(john))<=>(?[X]:((~calm(X)&~patient(X)))))&
(((~brave(lucy)|~quiet(lucy)))=>((~quiet(susan)|strong(susan))))&
(![X]:(~funny(X)<=>(strong(X)&~happy(X))))&
(![X]:((rich(X)<~>calm(X))<=>(~happy(X)<~>patient(X))))&
((?[X]:((~patient(X)&~strong(X))))=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((wise(X)<~>quiet(X))=>curious(X)))&
(![X]:((~old(X)&strong(X))=>(wise(X)|~brave(X))))&
(![X]:((~kind(X)&~calm(X))<=>humble(X)))&
(((~patient(john)<~>curious(john)))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:(humble(X)<=>(~quiet(X)|~funny(X))))&
(![X]:(~kind(X)=>(brave(X)&funny(X))))&
(![X]:((~brave(X)&~quiet(X))=>(~kind(X)|tall(X))))&
(![X]:((~humble(X)|~happy(X))<=>(tall(X)&quiet(X))))&
(?[X]:((rich(X)&~strong(X))))&
((~wise(susan)&curious(susan)))&
(?[X]:((~old(X)|old(X))))&
((~generous(john)&~strong(john)))&
(?[X]:((~old(X)<~>~patient(X))))&
(?[X]:((generous(X)|~happy(X))))&
((rich(mary)<~>tall(mary)))&
(?[X]:(funny(X))) | rich(lucy) | [] | null | 0 |
Everyone who is kind or not humble is both old and not tall.
Everyone who is strong or old is both not wise and rich and vice versa.
Everyone who is calm or old is both not patient and old and vice versa.
If someone is either not creative or quiet then fred is kind or not happy and vice versa.
If lucy is either not tall or generous then john is either generous or happy.
Everyone who is brave is not kind.
Everyone who is either not patient or patient is either not old or old and vice versa.
Everyone who is both old and funny is both not calm and old.
Everyone who is not wise is not tall.
Everyone who is not brave or strong is generous or not curious and vice versa.
Everyone who is either wise or not funny is both not humble and not patient and vice versa.
Everyone who is both not creative and creative is both not funny and wise and vice versa.
If someone is tall or not curious then fred is wise and vice versa.
If john is not patient then someone is both wise and happy.
If someone is either not humble or not old then someone is both not tall and not creative.
Someone is strong.
Someone is both not happy and calm.
Someone is creative or kind.
Paul is either not humble or not quiet.
Someone is either not creative or not happy.
Alice is either patient or rich.
Someone is creative. | Paul is not curious. | contradiction | (![X]:((kind(X)|~humble(X))=>(old(X)&~tall(X))))&
(![X]:((strong(X)|old(X))<=>(~wise(X)&rich(X))))&
(![X]:((calm(X)|old(X))<=>(~patient(X)&old(X))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((kind(fred)|~happy(fred))))&
(((~tall(lucy)<~>generous(lucy)))=>((generous(john)<~>happy(john))))&
(![X]:(brave(X)=>~kind(X)))&
(![X]:((~patient(X)<~>patient(X))<=>(~old(X)<~>old(X))))&
(![X]:((old(X)&funny(X))=>(~calm(X)&old(X))))&
(![X]:(~wise(X)=>~tall(X)))&
(![X]:((~brave(X)|strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((wise(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~creative(X)&creative(X))<=>(~funny(X)&wise(X))))&
((?[X]:((tall(X)|~curious(X))))<=>(wise(fred)))&
((~patient(john))=>(?[X]:((wise(X)&happy(X)))))&
((?[X]:((~humble(X)<~>~old(X))))=>(?[X]:((~tall(X)&~creative(X)))))&
(?[X]:(strong(X)))&
(?[X]:((~happy(X)&calm(X))))&
(?[X]:((creative(X)|kind(X))))&
((~humble(paul)<~>~quiet(paul)))&
(?[X]:((~creative(X)<~>~happy(X))))&
((patient(alice)<~>rich(alice)))&
(?[X]:(creative(X))) | ~curious(paul) | [
"p0",
"p1",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 838746296662473873432078
% SZS output start Proof for 838746296662473873432078
1. ! [X0] : ((~humble(X0) | kind(X0)) => (~tall(X0) & old(X0))) [input p0]
2. ! [X0] : ((old(X0) | strong(X0)) <=> (rich(X0) & ~wise(X0))) [input p1]
11. ! [X0] : ((wise(X0) <~> ~funny(X0)) <=> (~patient(X0) & ~humble(X0))) [input p10]
12. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (wise(X0) & ~funny(X0))) [input p11]
13. ? [X0] : (~curious(X0) | tall(X0)) <=> wise(fred) [input p12]
23. ~curious(paul) [input hypothesis]
25. ! [X0] : ((~tall(X0) & old(X0)) | (humble(X0) & ~kind(X0))) [ennf transformation 1]
33. ! [X0] : (((old(X0) | strong(X0)) | (~rich(X0) | wise(X0))) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 2]
34. ! [X0] : ((old(X0) | strong(X0) | ~rich(X0) | wise(X0)) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [flattening 33]
46. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (patient(X0) | humble(X0))) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [nnf transformation 11]
47. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | patient(X0) | humble(X0)) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [flattening 46]
48. ! [X0] : (((creative(X0) & ~creative(X0)) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 12]
49. ! [X0] : (((creative(X0) & ~creative(X0)) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ~creative(X0) | creative(X0))) [flattening 48]
50. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X0] : (curious(X0) & ~tall(X0))) [nnf transformation 13]
51. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [rectify 50]
52. ? [X0] : (~curious(X0) | tall(X0)) => (~curious(sK1) | tall(sK1)) [choice axiom]
53. ((~curious(sK1) | tall(sK1)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [skolemisation 51,52]
74. old(X0) | humble(X0) [cnf transformation 25]
78. ~wise(X0) | ~old(X0) [cnf transformation 34]
113. ~funny(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 47]
121. ~creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 49]
122. creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 49]
124. wise(fred) | curious(X1) [cnf transformation 53]
143. ~curious(paul) [cnf transformation 23]
201. ~wise(X0) | funny(X0) [subsumption resolution 121,122]
203. 11 <=> wise(fred) [avatar definition]
204. wise(fred) <- (11) [avatar component clause 203]
216. 14 <=> ! [X1] : curious(X1) [avatar definition]
217. curious(X1) <- (14) [avatar component clause 216]
218. 14 | 11 [avatar split clause 124,203,216]
299. ~old(fred) <- (11) [resolution 78,204]
300. humble(fred) <- (11) [resolution 299,74]
311. funny(fred) <- (11) [resolution 201,204]
314. ~humble(fred) | ~wise(fred) <- (11) [resolution 113,311]
315. ~wise(fred) <- (11) [subsumption resolution 314,300]
316. $false <- (11) [subsumption resolution 315,204]
317. ~11 [avatar contradiction clause 316]
318. $false <- (14) [resolution 217,143]
323. ~14 [avatar contradiction clause 318]
324. $false [avatar sat refutation 218,317,323]
% SZS output end Proof for 838746296662473873432078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If john is tall or not creative then someone is not old.
Everyone who is either quiet or not brave is not brave and vice versa.
Everyone who is not old is not generous and vice versa.
Everyone who is either old or patient is rich or not funny and vice versa.
Everyone who is either generous or not wise is not calm and vice versa.
Everyone who is not tall is both not generous and humble and vice versa.
Everyone who is either not quiet or not creative is either curious or not wise and vice versa.
Everyone who is not wise is rich and vice versa.
Everyone who is either patient or not curious is either creative or generous.
Everyone who is not brave or brave is kind and vice versa.
If john is tall or not strong then someone is not humble and vice versa.
Everyone who is both creative and not kind is not old.
Everyone who is not curious is not creative or not wise.
Everyone who is either rich or not tall is both wise and not wise.
Everyone who is not patient is both not curious and creative and vice versa.
Susan is patient or generous.
Susan is not calm.
John is not quiet or not strong.
Mary is not happy or not quiet.
John is both happy and brave. | Mary is happy. | neutral | (((tall(john)|~creative(john)))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)<~>~brave(X))<=>~brave(X)))&
(![X]:(~old(X)<=>~generous(X)))&
(![X]:((old(X)<~>patient(X))<=>(rich(X)|~funny(X))))&
(![X]:((generous(X)<~>~wise(X))<=>~calm(X)))&
(![X]:(~tall(X)<=>(~generous(X)&humble(X))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(curious(X)<~>~wise(X))))&
(![X]:(~wise(X)<=>rich(X)))&
(![X]:((patient(X)<~>~curious(X))=>(creative(X)<~>generous(X))))&
(![X]:((~brave(X)|brave(X))<=>kind(X)))&
(((tall(john)|~strong(john)))<=>(?[X]:(~humble(X))))&
(![X]:((creative(X)&~kind(X))=>~old(X)))&
(![X]:(~curious(X)=>(~creative(X)|~wise(X))))&
(![X]:((rich(X)<~>~tall(X))=>(wise(X)&~wise(X))))&
(![X]:(~patient(X)<=>(~curious(X)&creative(X))))&
((patient(susan)|generous(susan)))&
(~calm(susan))&
((~quiet(john)|~strong(john)))&
((~happy(mary)|~quiet(mary)))&
((happy(john)&brave(john))) | happy(mary) | [] | null | 0 |
Everyone who is either brave or not brave is calm and vice versa.
If someone is strong or brave then lucy is both funny and not generous and vice versa.
If mary is either not generous or funny then someone is rich or wise.
If lucy is either humble or old then someone is not wise or not strong.
Everyone who is not brave is both patient and not tall and vice versa.
Everyone who is either not kind or not old is either calm or not humble and vice versa.
If someone is both quiet and not patient then someone is brave or not strong.
If fred is either not generous or not funny then lucy is not patient and vice versa.
Everyone who is not curious is not patient.
If someone is not humble then john is both creative and quiet and vice versa.
If someone is generous or rich then someone is both funny and not wise and vice versa.
Everyone who is both not humble and rich is curious or not curious and vice versa.
Everyone who is either not generous or calm is funny or not humble.
Everyone who is kind or brave is not kind.
Everyone who is patient is strong or wise.
Someone is patient.
Someone is both not strong and quiet.
Mary is happy or not quiet.
Paul is either old or not happy.
Someone is both not creative and calm.
Lucy is either not calm or funny.
Someone is either funny or calm.
Lucy is either not quiet or not funny. | Fred is calm. | entailment | (![X]:((brave(X)<~>~brave(X))<=>calm(X)))&
((?[X]:((strong(X)|brave(X))))<=>((funny(lucy)&~generous(lucy))))&
(((~generous(mary)<~>funny(mary)))=>(?[X]:((rich(X)|wise(X)))))&
(((humble(lucy)<~>old(lucy)))=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:(~brave(X)<=>(patient(X)&~tall(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(calm(X)<~>~humble(X))))&
((?[X]:((quiet(X)&~patient(X))))=>(?[X]:((brave(X)|~strong(X)))))&
(((~generous(fred)<~>~funny(fred)))<=>(~patient(lucy)))&
(![X]:(~curious(X)=>~patient(X)))&
((?[X]:(~humble(X)))<=>((creative(john)&quiet(john))))&
((?[X]:((generous(X)|rich(X))))<=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((~humble(X)&rich(X))<=>(curious(X)|~curious(X))))&
(![X]:((~generous(X)<~>calm(X))=>(funny(X)|~humble(X))))&
(![X]:((kind(X)|brave(X))=>~kind(X)))&
(![X]:(patient(X)=>(strong(X)|wise(X))))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)&quiet(X))))&
((happy(mary)|~quiet(mary)))&
((old(paul)<~>~happy(paul)))&
(?[X]:((~creative(X)&calm(X))))&
((~calm(lucy)<~>funny(lucy)))&
(?[X]:((funny(X)<~>calm(X))))&
((~quiet(lucy)<~>~funny(lucy))) | calm(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 716284897559331991301452
% SZS output start Proof for 716284897559331991301452
1. ! [X0] : ((brave(X0) <~> ~brave(X0)) <=> calm(X0)) [input p0]
24. ~calm(fred) [input hypothesis]
36. ! [X0] : ((((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | ~calm(X0)) & (calm(X0) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0))))) [nnf transformation 1]
80. calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 36]
81. calm(X0) | brave(X0) | brave(X0) [cnf transformation 36]
142. ~calm(fred) [cnf transformation 24]
144. calm(X0) | ~brave(X0) [duplicate literal removal 80]
145. calm(X0) | brave(X0) [duplicate literal removal 81]
146. calm(X0) [subsumption resolution 144,145]
320. $false [subsumption resolution 142,146]
% SZS output end Proof for 716284897559331991301452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or kind then paul is either generous or curious.
Everyone who is not curious is not old and vice versa.
If susan is old or not curious then fred is either not generous or happy and vice versa.
Everyone who is either not humble or patient is not tall and vice versa.
Everyone who is patient is not curious or not calm and vice versa.
Everyone who is not rich is both old and creative.
Everyone who is calm is either brave or rich.
If alice is not kind then someone is either not wise or old and vice versa.
Everyone who is both calm and not calm is not kind or quiet and vice versa.
Everyone who is either patient or not wise is not calm or not tall.
Everyone who is not creative or happy is either creative or generous.
Everyone who is either kind or creative is not funny or strong.
Everyone who is both not rich and old is either kind or not brave.
If mary is generous or curious then someone is tall or calm.
Everyone who is not tall or not funny is tall or happy.
Everyone who is old is creative or not happy and vice versa.
Someone is both not old and happy.
Someone is both not curious and not strong.
Paul is not wise.
Someone is humble or not patient.
Someone is not generous.
Mary is brave or not kind. | Susan is patient. | neutral | ((?[X]:((~kind(X)|kind(X))))=>((generous(paul)<~>curious(paul))))&
(![X]:(~curious(X)<=>~old(X)))&
(((old(susan)|~curious(susan)))<=>((~generous(fred)<~>happy(fred))))&
(![X]:((~humble(X)<~>patient(X))<=>~tall(X)))&
(![X]:(patient(X)<=>(~curious(X)|~calm(X))))&
(![X]:(~rich(X)=>(old(X)&creative(X))))&
(![X]:(calm(X)=>(brave(X)<~>rich(X))))&
((~kind(alice))<=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:((calm(X)&~calm(X))<=>(~kind(X)|quiet(X))))&
(![X]:((patient(X)<~>~wise(X))=>(~calm(X)|~tall(X))))&
(![X]:((~creative(X)|happy(X))=>(creative(X)<~>generous(X))))&
(![X]:((kind(X)<~>creative(X))=>(~funny(X)|strong(X))))&
(![X]:((~rich(X)&old(X))=>(kind(X)<~>~brave(X))))&
(((generous(mary)|curious(mary)))=>(?[X]:((tall(X)|calm(X)))))&
(![X]:((~tall(X)|~funny(X))=>(tall(X)|happy(X))))&
(![X]:(old(X)<=>(creative(X)|~happy(X))))&
(?[X]:((~old(X)&happy(X))))&
(?[X]:((~curious(X)&~strong(X))))&
(~wise(paul))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:(~generous(X)))&
((brave(mary)|~kind(mary))) | patient(susan) | [] | null | 0 |
If someone is either calm or not quiet then john is both not funny and creative and vice versa.
If lucy is both not humble and calm then fred is not quiet or humble.
If susan is not old then someone is both generous and not wise and vice versa.
If someone is either not curious or patient then someone is humble or strong.
Everyone who is both not wise and not rich is quiet or not tall and vice versa.
If lucy is generous or not calm then someone is either rich or quiet and vice versa.
If susan is not rich then lucy is not patient.
If someone is tall then paul is tall or brave and vice versa.
Everyone who is generous is not funny or kind.
Everyone who is both generous and calm is either strong or not curious and vice versa.
If alice is both humble and not tall then lucy is funny.
Everyone who is generous or not generous is both not curious and old.
Everyone who is either happy or patient is either curious or happy.
Everyone who is either not wise or not creative is either not generous or not tall and vice versa.
Everyone who is calm or not humble is both not happy and creative and vice versa.
If someone is not old or not quiet then fred is both happy and not rich.
Mary is both happy and not funny.
Someone is generous or tall.
Susan is not funny or quiet.
John is creative or tall.
Susan is both kind and wise.
Lucy is calm.
Susan is either not creative or humble.
Fred is either creative or kind. | Susan is quiet. | contradiction | ((?[X]:((calm(X)<~>~quiet(X))))<=>((~funny(john)&creative(john))))&
(((~humble(lucy)&calm(lucy)))=>((~quiet(fred)|humble(fred))))&
((~old(susan))<=>(?[X]:((generous(X)&~wise(X)))))&
((?[X]:((~curious(X)<~>patient(X))))=>(?[X]:((humble(X)|strong(X)))))&
(![X]:((~wise(X)&~rich(X))<=>(quiet(X)|~tall(X))))&
(((generous(lucy)|~calm(lucy)))<=>(?[X]:((rich(X)<~>quiet(X)))))&
((~rich(susan))=>(~patient(lucy)))&
((?[X]:(tall(X)))<=>((tall(paul)|brave(paul))))&
(![X]:(generous(X)=>(~funny(X)|kind(X))))&
(![X]:((generous(X)&calm(X))<=>(strong(X)<~>~curious(X))))&
(((humble(alice)&~tall(alice)))=>(funny(lucy)))&
(![X]:((generous(X)|~generous(X))=>(~curious(X)&old(X))))&
(![X]:((happy(X)<~>patient(X))=>(curious(X)<~>happy(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(~generous(X)<~>~tall(X))))&
(![X]:((calm(X)|~humble(X))<=>(~happy(X)&creative(X))))&
((?[X]:((~old(X)|~quiet(X))))=>((happy(fred)&~rich(fred))))&
((happy(mary)&~funny(mary)))&
(?[X]:((generous(X)|tall(X))))&
((~funny(susan)|quiet(susan)))&
((creative(john)|tall(john)))&
((kind(susan)&wise(susan)))&
(calm(lucy))&
((~creative(susan)<~>humble(susan)))&
((creative(fred)<~>kind(fred))) | quiet(susan) | [
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8673351469643141593993646
% SZS output start Proof for 8673351469643141593993646
5. ! [X0] : ((~rich(X0) & ~wise(X0)) <=> (~tall(X0) | quiet(X0))) [input p4]
21. wise(susan) & kind(susan) [input p20]
25. quiet(susan) [input hypothesis]
51. ! [X0] : (((~rich(X0) & ~wise(X0)) | (tall(X0) & ~quiet(X0))) & ((~tall(X0) | quiet(X0)) | (rich(X0) | wise(X0)))) [nnf transformation 5]
52. ! [X0] : (((~rich(X0) & ~wise(X0)) | (tall(X0) & ~quiet(X0))) & (~tall(X0) | quiet(X0) | rich(X0) | wise(X0))) [flattening 51]
86. ~wise(X0) | ~quiet(X0) [cnf transformation 52]
139. wise(susan) [cnf transformation 21]
145. quiet(susan) [cnf transformation 25]
325. 39 <=> quiet(susan) [avatar definition]
327. quiet(susan) <- (39) [avatar component clause 325]
347. 39 [avatar split clause 145,325]
358. ~quiet(susan) [resolution 86,139]
359. $false <- (39) [subsumption resolution 358,327]
360. ~39 [avatar contradiction clause 359]
361. $false [avatar sat refutation 347,360]
% SZS output end Proof for 8673351469643141593993646
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or old is both calm and not brave and vice versa. Everyone who is both humble and calm is both wise and rich. Everyone who is not rich or not patient is creative. Everyone who is humble or not humble is both not strong and not tall. Everyone who is brave or not old is tall. If someone is either not funny or not creative then paul is strong or old. If someone is not wise then someone is either calm or not curious and vice versa. If someone is either not patient or not curious then fred is not patient. If lucy is both kind and not generous then fred is either old or patient and vice versa. Everyone who is both funny and happy is not patient or funny. If alice is both tall and not rich then someone is brave or happy and vice versa. If someone is either not strong or not curious then fred is not generous or strong and vice versa. If someone is both rich and kind then someone is either not strong or happy. If someone is either humble or not kind then someone is either not brave or not strong and vice versa. Everyone who is tall is tall or not curious. Paul is either strong or quiet. John is curious. Paul is not tall. Someone is not tall. Someone is both creative and not wise. Someone is either wise or brave. Paul is not happy or not strong. Paul is both creative and quiet. | Lucy is not strong. | entailment | (![X]:((happy(X)<~>old(X))<=>(calm(X)&~brave(X))))&
(![X]:((humble(X)&calm(X))=>(wise(X)&rich(X))))&
(![X]:((~rich(X)|~patient(X))=>creative(X)))&
(![X]:((humble(X)|~humble(X))=>(~strong(X)&~tall(X))))&
(![X]:((brave(X)|~old(X))=>tall(X)))&
((?[X]:((~funny(X)<~>~creative(X))))=>((strong(paul)|old(paul))))&
((?[X]:(~wise(X)))<=>(?[X]:((calm(X)<~>~curious(X)))))&
((?[X]:((~patient(X)<~>~curious(X))))=>(~patient(fred)))&
(((kind(lucy)&~generous(lucy)))<=>((old(fred)<~>patient(fred))))&
(![X]:((funny(X)&happy(X))=>(~patient(X)|funny(X))))&
(((tall(alice)&~rich(alice)))<=>(?[X]:((brave(X)|happy(X)))))&
((?[X]:((~strong(X)<~>~curious(X))))<=>((~generous(fred)|strong(fred))))&
((?[X]:((rich(X)&kind(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:(tall(X)=>(tall(X)|~curious(X))))&
((strong(paul)<~>quiet(paul)))&
(curious(john))&
(~tall(paul))&
(?[X]:(~tall(X)))&
(?[X]:((creative(X)&~wise(X))))&
(?[X]:((wise(X)<~>brave(X))))&
((~happy(paul)|~strong(paul)))&
((creative(paul)&quiet(paul))) | ~strong(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6569874463157413802522073
% SZS output start Proof for 6569874463157413802522073
4. ! [X0] : ((~humble(X0) | humble(X0)) => (~tall(X0) & ~strong(X0))) [input p3]
24. strong(lucy) [input hypothesis]
31. ! [X0] : ((~tall(X0) & ~strong(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 4]
89. ~strong(X0) | ~humble(X0) [cnf transformation 31]
90. ~strong(X0) | humble(X0) [cnf transformation 31]
144. strong(lucy) [cnf transformation 24]
146. ~strong(X0) [subsumption resolution 89,90]
241. $false [subsumption resolution 144,146]
% SZS output end Proof for 6569874463157413802522073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not wise then fred is both not funny and curious. Everyone who is both kind and not old is both not kind and not wise. Everyone who is either tall or kind is not creative or patient. Everyone who is brave or generous is both not rich and not humble. Everyone who is not patient or patient is both humble and patient. Everyone who is both not curious and not strong is kind or not funny. 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. Someone is not wise or not kind. Mary is either wise or not wise. Susan is either wise or patient. Someone is creative or not happy. Lucy is not happy or not quiet. | Paul is not brave. | entailment | ((?[X]:((~quiet(X)&~wise(X))))=>((~funny(fred)&curious(fred))))&
(![X]:((kind(X)&~old(X))=>(~kind(X)&~wise(X))))&
(![X]:((tall(X)<~>kind(X))=>(~creative(X)|patient(X))))&
(![X]:((brave(X)|generous(X))=>(~rich(X)&~humble(X))))&
(![X]:((~patient(X)|patient(X))=>(humble(X)&patient(X))))&
(![X]:((~curious(X)&~strong(X))=>(kind(X)|~funny(X))))&
(![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]:((~wise(X)|~kind(X))))&
((wise(mary)<~>~wise(mary)))&
((wise(susan)<~>patient(susan)))&
(?[X]:((creative(X)|~happy(X))))&
((~happy(lucy)|~quiet(lucy))) | ~brave(paul) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 714652118110894707612482
% SZS output start Proof for 714652118110894707612482
4. ! [X0] : ((generous(X0) | brave(X0)) => (~humble(X0) & ~rich(X0))) [input p3]
5. ! [X0] : ((patient(X0) | ~patient(X0)) => (patient(X0) & humble(X0))) [input p4]
22. brave(paul) [input hypothesis]
31. ! [X0] : ((~humble(X0) & ~rich(X0)) | (~generous(X0) & ~brave(X0))) [ennf transformation 4]
32. ! [X0] : ((patient(X0) & humble(X0)) | (~patient(X0) & patient(X0))) [ennf transformation 5]
77. ~humble(X0) | ~brave(X0) [cnf transformation 31]
80. humble(X0) | ~patient(X0) [cnf transformation 32]
81. patient(X0) | patient(X0) [cnf transformation 32]
120. brave(paul) [cnf transformation 22]
122. patient(X0) [duplicate literal removal 81]
137. humble(X0) [subsumption resolution 80,122]
260. ~brave(X0) [resolution 77,137]
261. $false [resolution 260,120]
% SZS output end Proof for 714652118110894707612482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or kind is both quiet and not patient.
If john is not happy then someone is tall or not tall.
Everyone who is not happy is humble or not strong and vice versa.
If susan is either creative or curious then lucy is not calm and vice versa.
If someone is creative then someone is strong or tall and vice versa.
If mary is either not creative or generous then john is both not wise and not generous.
If someone is not wise then alice is both not generous and not tall and vice versa.
If someone is calm then someone is patient or not patient and vice versa.
Everyone who is either humble or patient is not rich or strong.
If someone is either not tall or not rich then someone is humble.
Everyone who is either old or not tall is both not tall and wise and vice versa.
Everyone who is both curious and not calm is either generous or quiet and vice versa.
Everyone who is either humble or not tall is either brave or not brave and vice versa.
If someone is humble then alice is both not wise and not kind.
Everyone who is not funny is not brave and vice versa.
Everyone who is quiet is kind.
Someone is happy or strong.
Paul is either not quiet or patient.
Someone is either not funny or generous.
John is not old.
Someone is either not creative or not calm.
John is patient.
Someone is tall or not funny. | Lucy is curious. | neutral | (![X]:((calm(X)|kind(X))=>(quiet(X)&~patient(X))))&
((~happy(john))=>(?[X]:((tall(X)|~tall(X)))))&
(![X]:(~happy(X)<=>(humble(X)|~strong(X))))&
(((creative(susan)<~>curious(susan)))<=>(~calm(lucy)))&
((?[X]:(creative(X)))<=>(?[X]:((strong(X)|tall(X)))))&
(((~creative(mary)<~>generous(mary)))=>((~wise(john)&~generous(john))))&
((?[X]:(~wise(X)))<=>((~generous(alice)&~tall(alice))))&
((?[X]:(calm(X)))<=>(?[X]:((patient(X)|~patient(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~rich(X)|strong(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>(?[X]:(humble(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~tall(X)&wise(X))))&
(![X]:((curious(X)&~calm(X))<=>(generous(X)<~>quiet(X))))&
(![X]:((humble(X)<~>~tall(X))<=>(brave(X)<~>~brave(X))))&
((?[X]:(humble(X)))=>((~wise(alice)&~kind(alice))))&
(![X]:(~funny(X)<=>~brave(X)))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((happy(X)|strong(X))))&
((~quiet(paul)<~>patient(paul)))&
(?[X]:((~funny(X)<~>generous(X))))&
(~old(john))&
(?[X]:((~creative(X)<~>~calm(X))))&
(patient(john))&
(?[X]:((tall(X)|~funny(X)))) | curious(lucy) | [] | null | 0 |
Everyone who is not humble is both not creative and patient and vice versa.
Everyone who is not brave or not old is patient and vice versa.
Everyone who is either curious or not wise is old and vice versa.
Everyone who is brave is both not tall and not old and vice versa.
If paul is either generous or not humble then lucy is not patient or wise and vice versa.
If someone is not rich then paul is either not calm or not strong and vice versa.
Everyone who is happy is not old and vice versa.
If alice is both not rich and not tall then someone is not creative or not wise.
Everyone who is either not creative or not old is both rich and brave and vice versa.
If someone is not rich then someone is either not humble or rich.
If susan is not calm or wise then fred is either not strong or brave.
If someone is curious or creative then susan is old or not old.
If alice is either not patient or not old then susan is either not brave or not creative and vice versa.
Everyone who is not old or creative is generous and vice versa.
Everyone who is either strong or not patient is both not kind and not humble.
Everyone who is funny or humble is strong.
John is not calm or calm.
Mary is tall.
Susan is either happy or tall.
Someone is either calm or kind.
Someone is not calm or not wise.
Alice is not calm. | Lucy is generous. | entailment | (![X]:(~humble(X)<=>(~creative(X)&patient(X))))&
(![X]:((~brave(X)|~old(X))<=>patient(X)))&
(![X]:((curious(X)<~>~wise(X))<=>old(X)))&
(![X]:(brave(X)<=>(~tall(X)&~old(X))))&
(((generous(paul)<~>~humble(paul)))<=>((~patient(lucy)|wise(lucy))))&
((?[X]:(~rich(X)))<=>((~calm(paul)<~>~strong(paul))))&
(![X]:(happy(X)<=>~old(X)))&
(((~rich(alice)&~tall(alice)))=>(?[X]:((~creative(X)|~wise(X)))))&
(![X]:((~creative(X)<~>~old(X))<=>(rich(X)&brave(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~humble(X)<~>rich(X)))))&
(((~calm(susan)|wise(susan)))=>((~strong(fred)<~>brave(fred))))&
((?[X]:((curious(X)|creative(X))))=>((old(susan)|~old(susan))))&
(((~patient(alice)<~>~old(alice)))<=>((~brave(susan)<~>~creative(susan))))&
(![X]:((~old(X)|creative(X))<=>generous(X)))&
(![X]:((strong(X)<~>~patient(X))=>(~kind(X)&~humble(X))))&
(![X]:((funny(X)|humble(X))=>strong(X)))&
((~calm(john)|calm(john)))&
(tall(mary))&
((happy(susan)<~>tall(susan)))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((~calm(X)|~wise(X))))&
(~calm(alice)) | generous(lucy) | [
"p3",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 44908026503591330891310
% SZS output start Proof for 44908026503591330891310
4. ! [X0] : (brave(X0) <=> (~old(X0) & ~tall(X0))) [input p3]
9. ! [X0] : ((~creative(X0) <~> ~old(X0)) <=> (brave(X0) & rich(X0))) [input p8]
14. ! [X0] : ((creative(X0) | ~old(X0)) <=> generous(X0)) [input p13]
23. ~generous(lucy) [input hypothesis]
39. ! [X0] : ((brave(X0) | (old(X0) | tall(X0))) & ((~old(X0) & ~tall(X0)) | ~brave(X0))) [nnf transformation 4]
40. ! [X0] : ((brave(X0) | old(X0) | tall(X0)) & ((~old(X0) & ~tall(X0)) | ~brave(X0))) [flattening 39]
50. ! [X0] : ((((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0))))) [nnf transformation 9]
51. ! [X0] : ((((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0))))) [flattening 50]
58. ! [X0] : (((creative(X0) | ~old(X0)) | ~generous(X0)) & (generous(X0) | (~creative(X0) & old(X0)))) [nnf transformation 14]
59. ! [X0] : ((creative(X0) | ~old(X0) | ~generous(X0)) & (generous(X0) | (~creative(X0) & old(X0)))) [flattening 58]
78. ~old(X0) | ~brave(X0) [cnf transformation 40]
95. brave(X0) | ~old(X0) | creative(X0) [cnf transformation 51]
115. generous(X0) | old(X0) [cnf transformation 59]
116. ~creative(X0) | generous(X0) [cnf transformation 59]
131. ~generous(lucy) [cnf transformation 23]
191. ~old(X0) | creative(X0) [subsumption resolution 95,78]
293. old(lucy) [resolution 115,131]
300. creative(lucy) [resolution 191,293]
314. generous(lucy) [resolution 300,116]
316. $false [subsumption resolution 314,131]
% SZS output end Proof for 44908026503591330891310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not rich is both quiet and not tall.
If someone is humble or not funny then paul is either rich or curious and vice versa.
Everyone who is both not quiet and not calm is both calm and not wise and vice versa.
If someone is generous then someone is both not brave and not quiet and vice versa.
If lucy is either strong or funny then lucy is not tall.
Everyone who is tall or wise is both not tall and not calm and vice versa.
Everyone who is either tall or old is either wise or not kind.
If john is either funny or wise then someone is not quiet or humble.
Everyone who is not generous or not strong is tall or not calm.
If paul is both not wise and brave then lucy is either not happy or happy.
Everyone who is not creative is either not calm or not tall.
Everyone who is rich is tall or old and vice versa.
If someone is tall or not rich then someone is either quiet or creative and vice versa.
Everyone who is kind or not generous is either strong or not quiet and vice versa.
If someone is either calm or not wise then someone is not tall.
Everyone who is both not calm and brave is kind and vice versa.
Susan is patient or not happy.
Someone is either not generous or not old.
Someone is not generous.
Susan is either humble or calm.
Someone is not patient or funny. | Susan is old. | entailment | (![X]:((generous(X)<~>~rich(X))=>(quiet(X)&~tall(X))))&
((?[X]:((humble(X)|~funny(X))))<=>((rich(paul)<~>curious(paul))))&
(![X]:((~quiet(X)&~calm(X))<=>(calm(X)&~wise(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
(((strong(lucy)<~>funny(lucy)))=>(~tall(lucy)))&
(![X]:((tall(X)|wise(X))<=>(~tall(X)&~calm(X))))&
(![X]:((tall(X)<~>old(X))=>(wise(X)<~>~kind(X))))&
(((funny(john)<~>wise(john)))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((~generous(X)|~strong(X))=>(tall(X)|~calm(X))))&
(((~wise(paul)&brave(paul)))=>((~happy(lucy)<~>happy(lucy))))&
(![X]:(~creative(X)=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)&brave(X))<=>kind(X)))&
((patient(susan)|~happy(susan)))&
(?[X]:((~generous(X)<~>~old(X))))&
(?[X]:(~generous(X)))&
((humble(susan)<~>calm(susan)))&
(?[X]:((~patient(X)|funny(X)))) | old(susan) | [
"p2",
"p5",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6696020795246465273973568
% SZS output start Proof for 6696020795246465273973568
3. ! [X0] : ((~calm(X0) & ~quiet(X0)) <=> (~wise(X0) & calm(X0))) [input p2]
6. ! [X0] : ((wise(X0) | tall(X0)) <=> (~calm(X0) & ~tall(X0))) [input p5]
11. ! [X0] : (~creative(X0) => (~calm(X0) <~> ~tall(X0))) [input p10]
12. ! [X0] : (rich(X0) <=> (old(X0) | tall(X0))) [input p11]
13. ? [X0] : (~rich(X0) | tall(X0)) <=> ? [X0] : (quiet(X0) <~> creative(X0)) [input p12]
22. ~old(susan) [input hypothesis]
24. ? [X0] : (~rich(X0) | tall(X0)) <=> ? [X1] : (quiet(X1) <~> creative(X1)) [rectify 13]
34. ! [X0] : ((~calm(X0) <~> ~tall(X0)) | creative(X0)) [ennf transformation 11]
41. ! [X0] : (((~calm(X0) & ~quiet(X0)) | (wise(X0) | ~calm(X0))) & ((~wise(X0) & calm(X0)) | (calm(X0) | quiet(X0)))) [nnf transformation 3]
42. ! [X0] : (((~calm(X0) & ~quiet(X0)) | wise(X0) | ~calm(X0)) & ((~wise(X0) & calm(X0)) | calm(X0) | quiet(X0))) [flattening 41]
49. ! [X0] : (((wise(X0) | tall(X0)) | (calm(X0) | tall(X0))) & ((~calm(X0) & ~tall(X0)) | (~wise(X0) & ~tall(X0)))) [nnf transformation 6]
50. ! [X0] : ((wise(X0) | tall(X0) | calm(X0) | tall(X0)) & ((~calm(X0) & ~tall(X0)) | (~wise(X0) & ~tall(X0)))) [flattening 49]
56. ! [X0] : (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | creative(X0)) [nnf transformation 34]
57. ! [X0] : ((rich(X0) | (~old(X0) & ~tall(X0))) & ((old(X0) | tall(X0)) | ~rich(X0))) [nnf transformation 12]
58. ! [X0] : ((rich(X0) | (~old(X0) & ~tall(X0))) & (old(X0) | tall(X0) | ~rich(X0))) [flattening 57]
59. (? [X0] : (~rich(X0) | tall(X0)) | ! [X1] : ((quiet(X1) | ~creative(X1)) & (creative(X1) | ~quiet(X1)))) & (? [X1] : ((~creative(X1) | ~quiet(X1)) & (creative(X1) | quiet(X1))) | ! [X0] : (rich(X0) & ~tall(X0))) [nnf transformation 24]
60. (? [X0] : (~rich(X0) | tall(X0)) | ! [X1] : ((quiet(X1) | ~creative(X1)) & (creative(X1) | ~quiet(X1)))) & (? [X2] : ((~creative(X2) | ~quiet(X2)) & (creative(X2) | quiet(X2))) | ! [X3] : (rich(X3) & ~tall(X3))) [rectify 59]
61. ? [X0] : (~rich(X0) | tall(X0)) => (~rich(sK4) | tall(sK4)) [choice axiom]
62. ? [X2] : ((~creative(X2) | ~quiet(X2)) & (creative(X2) | quiet(X2))) => ((~creative(sK5) | ~quiet(sK5)) & (creative(sK5) | quiet(sK5))) [choice axiom]
63. ((~rich(sK4) | tall(sK4)) | ! [X1] : ((quiet(X1) | ~creative(X1)) & (creative(X1) | ~quiet(X1)))) & (((~creative(sK5) | ~quiet(sK5)) & (creative(sK5) | quiet(sK5))) | ! [X3] : (rich(X3) & ~tall(X3))) [skolemisation 60,62,61]
90. calm(X0) | calm(X0) | quiet(X0) [cnf transformation 42]
93. ~calm(X0) | wise(X0) | ~calm(X0) [cnf transformation 42]
99. ~tall(X0) | ~tall(X0) [cnf transformation 50]
102. ~calm(X0) | ~wise(X0) [cnf transformation 50]
115. tall(X0) | calm(X0) | creative(X0) [cnf transformation 56]
116. old(X0) | tall(X0) | ~rich(X0) [cnf transformation 58]
122. ~creative(sK5) | ~quiet(sK5) | rich(X3) [cnf transformation 63]
143. ~old(susan) [cnf transformation 22]
144. ~tall(X0) [duplicate literal removal 99]
146. calm(X0) | quiet(X0) [duplicate literal removal 90]
147. ~calm(X0) | wise(X0) [duplicate literal removal 93]
212. ~calm(X0) [subsumption resolution 102,147]
232. calm(X0) | creative(X0) [subsumption resolution 115,144]
233. creative(X0) [subsumption resolution 232,212]
234. ~rich(X0) | old(X0) [subsumption resolution 116,144]
238. 19 <=> ! [X1] : quiet(X1) [avatar definition]
239. quiet(X1) <- (19) [avatar component clause 238]
245. ~quiet(sK5) | rich(X3) [subsumption resolution 122,233]
247. 21 <=> ! [X3] : rich(X3) [avatar definition]
248. rich(X3) <- (21) [avatar component clause 247]
250. 22 <=> quiet(sK5) [avatar definition]
252. ~quiet(sK5) <- (~22) [avatar component clause 250]
253. 21 | ~22 [avatar split clause 245,250,247]
284. quiet(X0) [resolution 146,212]
285. 19 [avatar split clause 284,238]
288. $false <- (19, ~22) [resolution 239,252]
289. ~19 | 22 [avatar contradiction clause 288]
305. old(X0) <- (21) [resolution 234,248]
308. $false <- (21) [resolution 305,143]
310. ~21 [avatar contradiction clause 308]
311. $false [avatar sat refutation 253,285,289,310]
% SZS output end Proof for 6696020795246465273973568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not quiet or kind then someone is rich and vice versa.
If paul is both not humble and not rich then someone is both not tall and old and vice versa.
If someone is old then someone is quiet or not old.
If someone is not wise or not humble then fred is either tall or brave.
Everyone who is not old is both not calm and not strong.
If fred is either not brave or not tall then fred is both kind and not happy.
If someone is not kind or tall then someone is either not creative or not brave and vice versa.
Everyone who is not patient or not old is both not kind and not funny and vice versa.
Everyone who is both not quiet and not curious is either creative or calm and vice versa.
If lucy is not kind then someone is both quiet and funny.
If lucy is both rich and not rich then someone is both wise and not happy.
If someone is not tall then someone is both curious and not tall.
Everyone who is either tall or curious is either funny or not creative.
Everyone who is creative or not brave is either old or kind and vice versa.
Everyone who is either not funny or funny is not humble or curious and vice versa.
If lucy is not happy or creative then someone is either happy or generous and vice versa.
Susan is either patient or humble.
Lucy is both rich and generous.
Someone is not humble or patient.
Alice is wise or happy.
John is not happy.
Alice is kind or not wise.
Fred is not calm. | Fred is not tall. | neutral | (((~quiet(lucy)<~>kind(lucy)))<=>(?[X]:(rich(X))))&
(((~humble(paul)&~rich(paul)))<=>(?[X]:((~tall(X)&old(X)))))&
((?[X]:(old(X)))=>(?[X]:((quiet(X)|~old(X)))))&
((?[X]:((~wise(X)|~humble(X))))=>((tall(fred)<~>brave(fred))))&
(![X]:(~old(X)=>(~calm(X)&~strong(X))))&
(((~brave(fred)<~>~tall(fred)))=>((kind(fred)&~happy(fred))))&
((?[X]:((~kind(X)|tall(X))))<=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((~patient(X)|~old(X))<=>(~kind(X)&~funny(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(creative(X)<~>calm(X))))&
((~kind(lucy))=>(?[X]:((quiet(X)&funny(X)))))&
(((rich(lucy)&~rich(lucy)))=>(?[X]:((wise(X)&~happy(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((curious(X)&~tall(X)))))&
(![X]:((tall(X)<~>curious(X))=>(funny(X)<~>~creative(X))))&
(![X]:((creative(X)|~brave(X))<=>(old(X)<~>kind(X))))&
(![X]:((~funny(X)<~>funny(X))<=>(~humble(X)|curious(X))))&
(((~happy(lucy)|creative(lucy)))<=>(?[X]:((happy(X)<~>generous(X)))))&
((patient(susan)<~>humble(susan)))&
((rich(lucy)&generous(lucy)))&
(?[X]:((~humble(X)|patient(X))))&
((wise(alice)|happy(alice)))&
(~happy(john))&
((kind(alice)|~wise(alice)))&
(~calm(fred)) | ~tall(fred) | [] | null | 0 |
Everyone who is either not generous or not humble is not brave or kind.
If someone is curious or not patient then mary is either not happy or not humble.
Everyone who is either not humble or not generous is either not strong or not humble and vice versa.
If someone is humble then susan is either not rich or patient.
Everyone who is both not tall and not funny is brave or patient.
Everyone who is either not happy or happy is not generous or tall and vice versa.
Everyone who is both creative and kind is not quiet or quiet.
Everyone who is tall or old is not wise or funny and vice versa.
If mary is not happy then someone is either calm or patient and vice versa.
Everyone who is not strong is strong.
Everyone who is both rich and not funny is not wise or not calm and vice versa.
Everyone who is either wise or calm is generous or humble.
Everyone who is old or not humble is happy or tall.
Everyone who is patient is either old or not wise and vice versa.
If alice is both old and tall then fred is not calm or not humble and vice versa.
If susan is either creative or not old then mary is not curious.
Someone is generous.
Someone is not humble or kind.
Lucy is old or strong.
Paul is either funny or creative.
John is generous or creative.
Someone is not strong or generous.
Someone is calm or not creative.
Lucy is not strong or not rich. | Lucy is generous. | entailment | (![X]:((~generous(X)<~>~humble(X))=>(~brave(X)|kind(X))))&
((?[X]:((curious(X)|~patient(X))))=>((~happy(mary)<~>~humble(mary))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~strong(X)<~>~humble(X))))&
((?[X]:(humble(X)))=>((~rich(susan)<~>patient(susan))))&
(![X]:((~tall(X)&~funny(X))=>(brave(X)|patient(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~generous(X)|tall(X))))&
(![X]:((creative(X)&kind(X))=>(~quiet(X)|quiet(X))))&
(![X]:((tall(X)|old(X))<=>(~wise(X)|funny(X))))&
((~happy(mary))<=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:(~strong(X)=>strong(X)))&
(![X]:((rich(X)&~funny(X))<=>(~wise(X)|~calm(X))))&
(![X]:((wise(X)<~>calm(X))=>(generous(X)|humble(X))))&
(![X]:((old(X)|~humble(X))=>(happy(X)|tall(X))))&
(![X]:(patient(X)<=>(old(X)<~>~wise(X))))&
(((old(alice)&tall(alice)))<=>((~calm(fred)|~humble(fred))))&
(((creative(susan)<~>~old(susan)))=>(~curious(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~humble(X)|kind(X))))&
((old(lucy)|strong(lucy)))&
((funny(paul)<~>creative(paul)))&
((generous(john)|creative(john)))&
(?[X]:((~strong(X)|generous(X))))&
(?[X]:((calm(X)|~creative(X))))&
((~strong(lucy)|~rich(lucy))) | generous(lucy) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2400310042634037927982397
% SZS output start Proof for 2400310042634037927982397
3. ! [X0] : ((~humble(X0) <~> ~generous(X0)) <=> (~strong(X0) <~> ~humble(X0))) [input p2]
10. ! [X0] : (~strong(X0) => strong(X0)) [input p9]
25. ~generous(lucy) [input hypothesis]
36. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 10]
43. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [nnf transformation 3]
73. ~humble(X0) | ~strong(X0) | ~humble(X0) | generous(X0) [cnf transformation 43]
79. generous(X0) | humble(X0) | ~strong(X0) | humble(X0) [cnf transformation 43]
98. strong(X0) | strong(X0) [cnf transformation 36]
126. ~generous(lucy) [cnf transformation 25]
127. strong(X0) [duplicate literal removal 98]
130. ~humble(X0) | ~strong(X0) | generous(X0) [duplicate literal removal 73]
133. generous(X0) | humble(X0) | ~strong(X0) [duplicate literal removal 79]
148. ~strong(X0) | generous(X0) [subsumption resolution 130,133]
244. generous(X0) [resolution 148,127]
245. $false [resolution 244,126]
% SZS output end Proof for 2400310042634037927982397
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not tall or wise then someone is not kind.
Everyone who is rich is either not curious or funny.
Everyone who is both tall and not humble is either not curious or not funny and vice versa.
Everyone who is not creative or not tall is either not kind or not quiet and vice versa.
If susan is not patient then john is not rich or not kind and vice versa.
Everyone who is either creative or not old is either not brave or old and vice versa.
Everyone who is funny is either wise or not calm and vice versa.
Everyone who is not calm is happy or funny and vice versa.
If susan is not quiet or not calm then someone is not old or not strong and vice versa.
Everyone who is creative or not humble is not tall or not happy.
Everyone who is either not patient or patient is tall and vice versa.
Everyone who is either not rich or not funny is either kind or not humble.
If lucy is curious or not wise then someone is both calm and not happy.
If someone is either not patient or not curious then someone is not tall and vice versa.
Everyone who is not tall or creative is calm and vice versa.
If lucy is creative then paul is both patient and funny and vice versa.
Someone is not strong or not rich.
Someone is quiet or funny.
Alice is both strong and not kind.
Paul is calm.
Someone is kind.
Alice is tall.
John is either happy or not wise.
Someone is rich. | Susan is strong. | neutral | (((~tall(paul)<~>wise(paul)))=>(?[X]:(~kind(X))))&
(![X]:(rich(X)=>(~curious(X)<~>funny(X))))&
(![X]:((tall(X)&~humble(X))<=>(~curious(X)<~>~funny(X))))&
(![X]:((~creative(X)|~tall(X))<=>(~kind(X)<~>~quiet(X))))&
((~patient(susan))<=>((~rich(john)|~kind(john))))&
(![X]:((creative(X)<~>~old(X))<=>(~brave(X)<~>old(X))))&
(![X]:(funny(X)<=>(wise(X)<~>~calm(X))))&
(![X]:(~calm(X)<=>(happy(X)|funny(X))))&
(((~quiet(susan)|~calm(susan)))<=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((creative(X)|~humble(X))=>(~tall(X)|~happy(X))))&
(![X]:((~patient(X)<~>patient(X))<=>tall(X)))&
(![X]:((~rich(X)<~>~funny(X))=>(kind(X)<~>~humble(X))))&
(((curious(lucy)|~wise(lucy)))=>(?[X]:((calm(X)&~happy(X)))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)|creative(X))<=>calm(X)))&
((creative(lucy))<=>((patient(paul)&funny(paul))))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((quiet(X)|funny(X))))&
((strong(alice)&~kind(alice)))&
(calm(paul))&
(?[X]:(kind(X)))&
(tall(alice))&
((happy(john)<~>~wise(john)))&
(?[X]:(rich(X))) | strong(susan) | [] | null | 0 |
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